Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(64,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.84454428669\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.169 |
Dual form | 231.2.j.d.190.1 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | + | 0.363271i | 0.353553 | + | 0.256872i | 0.750358 | − | 0.661031i | \(-0.229881\pi\) |
−0.396805 | + | 0.917903i | \(0.629881\pi\) | |||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | −0.500000 | − | 1.53884i | −0.250000 | − | 0.769421i | ||||
\(5\) | 0.309017 | − | 0.224514i | 0.138197 | − | 0.100406i | −0.516539 | − | 0.856264i | \(-0.672780\pi\) |
0.654736 | + | 0.755858i | \(0.272780\pi\) | |||||||
\(6\) | 0.500000 | − | 0.363271i | 0.204124 | − | 0.148305i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0.690983 | − | 2.12663i | 0.244299 | − | 0.751876i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0.236068 | 0.0746512 | ||||||||
\(11\) | 0.309017 | − | 3.30220i | 0.0931721 | − | 0.995650i | ||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | 0.809017 | + | 0.587785i | 0.224381 | + | 0.163022i | 0.694297 | − | 0.719689i | \(-0.255716\pi\) |
−0.469916 | + | 0.882711i | \(0.655716\pi\) | |||||||
\(14\) | −0.190983 | + | 0.587785i | −0.0510424 | + | 0.157092i | ||||
\(15\) | −0.118034 | − | 0.363271i | −0.0304762 | − | 0.0937962i | ||||
\(16\) | −1.50000 | + | 1.08981i | −0.375000 | + | 0.272453i | ||||
\(17\) | 3.42705 | − | 2.48990i | 0.831182 | − | 0.603889i | −0.0887115 | − | 0.996057i | \(-0.528275\pi\) |
0.919893 | + | 0.392168i | \(0.128275\pi\) | |||||||
\(18\) | −0.190983 | − | 0.587785i | −0.0450151 | − | 0.138542i | ||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −0.500000 | − | 0.363271i | −0.111803 | − | 0.0812299i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.35410 | − | 1.53884i | 0.288696 | − | 0.328082i | ||||
\(23\) | −3.23607 | −0.674767 | −0.337383 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(24\) | −1.80902 | − | 1.31433i | −0.369264 | − | 0.268286i | ||||
\(25\) | −1.50000 | + | 4.61653i | −0.300000 | + | 0.923305i | ||||
\(26\) | 0.190983 | + | 0.587785i | 0.0374548 | + | 0.115274i | ||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | 1.30902 | − | 0.951057i | 0.247381 | − | 0.179733i | ||||
\(29\) | 2.07295 | + | 6.37988i | 0.384937 | + | 1.18471i | 0.936526 | + | 0.350598i | \(0.114022\pi\) |
−0.551589 | + | 0.834116i | \(0.685978\pi\) | |||||||
\(30\) | 0.0729490 | − | 0.224514i | 0.0133186 | − | 0.0409905i | ||||
\(31\) | 8.28115 | + | 6.01661i | 1.48734 | + | 1.08062i | 0.975098 | + | 0.221773i | \(0.0711844\pi\) |
0.512241 | + | 0.858842i | \(0.328816\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −3.04508 | − | 1.31433i | −0.530081 | − | 0.228795i | ||||
\(34\) | 2.61803 | 0.448989 | ||||||||
\(35\) | 0.309017 | + | 0.224514i | 0.0522334 | + | 0.0379498i | ||||
\(36\) | −0.500000 | + | 1.53884i | −0.0833333 | + | 0.256474i | ||||
\(37\) | 2.14590 | + | 6.60440i | 0.352783 | + | 1.08576i | 0.957284 | + | 0.289151i | \(0.0933729\pi\) |
−0.604500 | + | 0.796605i | \(0.706627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.809017 | − | 0.587785i | 0.129546 | − | 0.0941210i | ||||
\(40\) | −0.263932 | − | 0.812299i | −0.0417313 | − | 0.128436i | ||||
\(41\) | 1.57295 | − | 4.84104i | 0.245653 | − | 0.756043i | −0.749875 | − | 0.661580i | \(-0.769886\pi\) |
0.995528 | − | 0.0944637i | \(-0.0301136\pi\) | |||||||
\(42\) | 0.500000 | + | 0.363271i | 0.0771517 | + | 0.0560540i | ||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | −5.23607 | + | 1.17557i | −0.789367 | + | 0.177224i | ||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | −1.61803 | − | 1.17557i | −0.238566 | − | 0.173328i | ||||
\(47\) | −2.26393 | + | 6.96767i | −0.330228 | + | 1.01634i | 0.638797 | + | 0.769376i | \(0.279433\pi\) |
−0.969025 | + | 0.246963i | \(0.920567\pi\) | |||||||
\(48\) | 0.572949 | + | 1.76336i | 0.0826981 | + | 0.254518i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | −2.42705 | + | 1.76336i | −0.343237 | + | 0.249376i | ||||
\(51\) | −1.30902 | − | 4.02874i | −0.183299 | − | 0.564136i | ||||
\(52\) | 0.500000 | − | 1.53884i | 0.0693375 | − | 0.213399i | ||||
\(53\) | −6.16312 | − | 4.47777i | −0.846569 | − | 0.615069i | 0.0776285 | − | 0.996982i | \(-0.475265\pi\) |
−0.924198 | + | 0.381914i | \(0.875265\pi\) | |||||||
\(54\) | −0.618034 | −0.0841038 | ||||||||
\(55\) | −0.645898 | − | 1.08981i | −0.0870929 | − | 0.146950i | ||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.28115 | + | 3.94298i | −0.168224 | + | 0.517739i | ||||
\(59\) | −1.28115 | − | 3.94298i | −0.166792 | − | 0.513333i | 0.832372 | − | 0.554217i | \(-0.186982\pi\) |
−0.999164 | + | 0.0408847i | \(0.986982\pi\) | |||||||
\(60\) | −0.500000 | + | 0.363271i | −0.0645497 | + | 0.0468981i | ||||
\(61\) | 4.66312 | − | 3.38795i | 0.597051 | − | 0.433783i | −0.247780 | − | 0.968816i | \(-0.579701\pi\) |
0.844831 | + | 0.535033i | \(0.179701\pi\) | |||||||
\(62\) | 1.95492 | + | 6.01661i | 0.248274 | + | 0.764110i | ||||
\(63\) | 0.309017 | − | 0.951057i | 0.0389325 | − | 0.119822i | ||||
\(64\) | 0.190983 | + | 0.138757i | 0.0238729 | + | 0.0173447i | ||||
\(65\) | 0.381966 | 0.0473771 | ||||||||
\(66\) | −1.04508 | − | 1.76336i | −0.128641 | − | 0.217054i | ||||
\(67\) | −9.23607 | −1.12837 | −0.564183 | − | 0.825650i | \(-0.690809\pi\) | ||||
−0.564183 | + | 0.825650i | \(0.690809\pi\) | |||||||
\(68\) | −5.54508 | − | 4.02874i | −0.672440 | − | 0.488556i | ||||
\(69\) | −1.00000 | + | 3.07768i | −0.120386 | + | 0.370510i | ||||
\(70\) | 0.0729490 | + | 0.224514i | 0.00871908 | + | 0.0268346i | ||||
\(71\) | 6.04508 | − | 4.39201i | 0.717420 | − | 0.521236i | −0.168139 | − | 0.985763i | \(-0.553776\pi\) |
0.885559 | + | 0.464527i | \(0.153776\pi\) | |||||||
\(72\) | −1.80902 | + | 1.31433i | −0.213195 | + | 0.154895i | ||||
\(73\) | 3.57295 | + | 10.9964i | 0.418182 | + | 1.28703i | 0.909374 | + | 0.415980i | \(0.136562\pi\) |
−0.491192 | + | 0.871052i | \(0.663438\pi\) | |||||||
\(74\) | −1.32624 | + | 4.08174i | −0.154172 | + | 0.474493i | ||||
\(75\) | 3.92705 | + | 2.85317i | 0.453457 | + | 0.329456i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23607 | − | 0.726543i | 0.368784 | − | 0.0827972i | ||||
\(78\) | 0.618034 | 0.0699786 | ||||||||
\(79\) | −8.78115 | − | 6.37988i | −0.987957 | − | 0.717793i | −0.0284842 | − | 0.999594i | \(-0.509068\pi\) |
−0.959473 | + | 0.281802i | \(0.909068\pi\) | |||||||
\(80\) | −0.218847 | + | 0.673542i | −0.0244678 | + | 0.0753043i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 2.54508 | − | 1.84911i | 0.281058 | − | 0.204200i | ||||
\(83\) | 4.85410 | − | 3.52671i | 0.532807 | − | 0.387107i | −0.288600 | − | 0.957450i | \(-0.593190\pi\) |
0.821407 | + | 0.570343i | \(0.193190\pi\) | |||||||
\(84\) | −0.500000 | − | 1.53884i | −0.0545545 | − | 0.167901i | ||||
\(85\) | 0.500000 | − | 1.53884i | 0.0542326 | − | 0.166911i | ||||
\(86\) | −0.500000 | − | 0.363271i | −0.0539164 | − | 0.0391725i | ||||
\(87\) | 6.70820 | 0.719195 | ||||||||
\(88\) | −6.80902 | − | 2.93893i | −0.725844 | − | 0.313291i | ||||
\(89\) | −6.38197 | −0.676487 | −0.338244 | − | 0.941059i | \(-0.609833\pi\) | ||||
−0.338244 | + | 0.941059i | \(0.609833\pi\) | |||||||
\(90\) | −0.190983 | − | 0.138757i | −0.0201314 | − | 0.0146263i | ||||
\(91\) | −0.309017 | + | 0.951057i | −0.0323938 | + | 0.0996978i | ||||
\(92\) | 1.61803 | + | 4.97980i | 0.168692 | + | 0.519180i | ||||
\(93\) | 8.28115 | − | 6.01661i | 0.858716 | − | 0.623893i | ||||
\(94\) | −3.66312 | + | 2.66141i | −0.377822 | + | 0.274504i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.73607 | + | 5.34307i | −0.177187 | + | 0.545325i | ||||
\(97\) | 13.7533 | + | 9.99235i | 1.39643 | + | 1.01457i | 0.995124 | + | 0.0986273i | \(0.0314452\pi\) |
0.401310 | + | 0.915942i | \(0.368555\pi\) | |||||||
\(98\) | −0.618034 | −0.0624309 | ||||||||
\(99\) | −2.19098 | + | 2.48990i | −0.220202 | + | 0.250244i | ||||
\(100\) | 7.85410 | 0.785410 | ||||||||
\(101\) | 3.38197 | + | 2.45714i | 0.336518 | + | 0.244495i | 0.743191 | − | 0.669079i | \(-0.233311\pi\) |
−0.406673 | + | 0.913574i | \(0.633311\pi\) | |||||||
\(102\) | 0.809017 | − | 2.48990i | 0.0801046 | − | 0.246537i | ||||
\(103\) | −3.92705 | − | 12.0862i | −0.386944 | − | 1.19089i | −0.935060 | − | 0.354489i | \(-0.884655\pi\) |
0.548116 | − | 0.836402i | \(-0.315345\pi\) | |||||||
\(104\) | 1.80902 | − | 1.31433i | 0.177389 | − | 0.128880i | ||||
\(105\) | 0.309017 | − | 0.224514i | 0.0301570 | − | 0.0219103i | ||||
\(106\) | −1.45492 | − | 4.47777i | −0.141314 | − | 0.434919i | ||||
\(107\) | 4.87132 | − | 14.9924i | 0.470929 | − | 1.44937i | −0.380442 | − | 0.924805i | \(-0.624228\pi\) |
0.851371 | − | 0.524564i | \(-0.175772\pi\) | |||||||
\(108\) | 1.30902 | + | 0.951057i | 0.125960 | + | 0.0915155i | ||||
\(109\) | −7.56231 | −0.724338 | −0.362169 | − | 0.932113i | \(-0.617964\pi\) | ||||
−0.362169 | + | 0.932113i | \(0.617964\pi\) | |||||||
\(110\) | 0.0729490 | − | 0.779543i | 0.00695542 | − | 0.0743265i | ||||
\(111\) | 6.94427 | 0.659121 | ||||||||
\(112\) | −1.50000 | − | 1.08981i | −0.141737 | − | 0.102978i | ||||
\(113\) | −3.60081 | + | 11.0822i | −0.338736 | + | 1.04252i | 0.626116 | + | 0.779730i | \(0.284643\pi\) |
−0.964852 | + | 0.262793i | \(0.915357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | + | 0.726543i | −0.0932505 | + | 0.0677504i | ||||
\(116\) | 8.78115 | − | 6.37988i | 0.815310 | − | 0.592357i | ||||
\(117\) | −0.309017 | − | 0.951057i | −0.0285686 | − | 0.0879252i | ||||
\(118\) | 0.791796 | − | 2.43690i | 0.0728907 | − | 0.224335i | ||||
\(119\) | 3.42705 | + | 2.48990i | 0.314157 | + | 0.228249i | ||||
\(120\) | −0.854102 | −0.0779685 | ||||||||
\(121\) | −10.8090 | − | 2.04087i | −0.982638 | − | 0.185534i | ||||
\(122\) | 3.56231 | 0.322516 | ||||||||
\(123\) | −4.11803 | − | 2.99193i | −0.371311 | − | 0.269773i | ||||
\(124\) | 5.11803 | − | 15.7517i | 0.459613 | − | 1.41454i | ||||
\(125\) | 1.16312 | + | 3.57971i | 0.104033 | + | 0.320179i | ||||
\(126\) | 0.500000 | − | 0.363271i | 0.0445435 | − | 0.0323628i | ||||
\(127\) | 5.92705 | − | 4.30625i | 0.525941 | − | 0.382118i | −0.292896 | − | 0.956144i | \(-0.594619\pi\) |
0.818837 | + | 0.574026i | \(0.194619\pi\) | |||||||
\(128\) | 3.51722 | + | 10.8249i | 0.310881 | + | 0.956794i | ||||
\(129\) | −0.309017 | + | 0.951057i | −0.0272074 | + | 0.0837359i | ||||
\(130\) | 0.190983 | + | 0.138757i | 0.0167503 | + | 0.0121698i | ||||
\(131\) | −3.32624 | −0.290615 | −0.145307 | − | 0.989387i | \(-0.546417\pi\) | ||||
−0.145307 | + | 0.989387i | \(0.546417\pi\) | |||||||
\(132\) | −0.500000 | + | 5.34307i | −0.0435194 | + | 0.465054i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.61803 | − | 3.35520i | −0.398937 | − | 0.289845i | ||||
\(135\) | −0.118034 | + | 0.363271i | −0.0101587 | + | 0.0312654i | ||||
\(136\) | −2.92705 | − | 9.00854i | −0.250993 | − | 0.772476i | ||||
\(137\) | 2.47214 | − | 1.79611i | 0.211209 | − | 0.153452i | −0.477152 | − | 0.878821i | \(-0.658331\pi\) |
0.688360 | + | 0.725369i | \(0.258331\pi\) | |||||||
\(138\) | −1.61803 | + | 1.17557i | −0.137736 | + | 0.100071i | ||||
\(139\) | −5.42705 | − | 16.7027i | −0.460316 | − | 1.41671i | −0.864778 | − | 0.502154i | \(-0.832541\pi\) |
0.404462 | − | 0.914555i | \(-0.367459\pi\) | |||||||
\(140\) | 0.190983 | − | 0.587785i | 0.0161410 | − | 0.0496769i | ||||
\(141\) | 5.92705 | + | 4.30625i | 0.499148 | + | 0.362652i | ||||
\(142\) | 4.61803 | 0.387537 | ||||||||
\(143\) | 2.19098 | − | 2.48990i | 0.183219 | − | 0.208216i | ||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 2.07295 | + | 1.50609i | 0.172149 | + | 0.125074i | ||||
\(146\) | −2.20820 | + | 6.79615i | −0.182752 | + | 0.562454i | ||||
\(147\) | 0.309017 | + | 0.951057i | 0.0254873 | + | 0.0784418i | ||||
\(148\) | 9.09017 | − | 6.60440i | 0.747207 | − | 0.542878i | ||||
\(149\) | 10.5902 | − | 7.69421i | 0.867581 | − | 0.630334i | −0.0623561 | − | 0.998054i | \(-0.519861\pi\) |
0.929937 | + | 0.367720i | \(0.119861\pi\) | |||||||
\(150\) | 0.927051 | + | 2.85317i | 0.0756934 | + | 0.232960i | ||||
\(151\) | −6.51722 | + | 20.0579i | −0.530364 | + | 1.63229i | 0.223095 | + | 0.974797i | \(0.428384\pi\) |
−0.753458 | + | 0.657495i | \(0.771616\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.23607 | −0.342466 | ||||||||
\(154\) | 1.88197 | + | 0.812299i | 0.151653 | + | 0.0654569i | ||||
\(155\) | 3.90983 | 0.314045 | ||||||||
\(156\) | −1.30902 | − | 0.951057i | −0.104805 | − | 0.0761455i | ||||
\(157\) | −0.517221 | + | 1.59184i | −0.0412787 | + | 0.127043i | −0.969572 | − | 0.244806i | \(-0.921276\pi\) |
0.928293 | + | 0.371848i | \(0.121276\pi\) | |||||||
\(158\) | −2.07295 | − | 6.37988i | −0.164915 | − | 0.507556i | ||||
\(159\) | −6.16312 | + | 4.47777i | −0.488767 | + | 0.355110i | ||||
\(160\) | −1.73607 | + | 1.26133i | −0.137248 | + | 0.0997167i | ||||
\(161\) | −1.00000 | − | 3.07768i | −0.0788110 | − | 0.242555i | ||||
\(162\) | −0.190983 | + | 0.587785i | −0.0150050 | + | 0.0461808i | ||||
\(163\) | −4.88197 | − | 3.54696i | −0.382385 | − | 0.277819i | 0.379943 | − | 0.925010i | \(-0.375944\pi\) |
−0.762328 | + | 0.647191i | \(0.775944\pi\) | |||||||
\(164\) | −8.23607 | −0.643129 | ||||||||
\(165\) | −1.23607 | + | 0.277515i | −0.0962278 | + | 0.0216045i | ||||
\(166\) | 3.70820 | 0.287812 | ||||||||
\(167\) | −7.59017 | − | 5.51458i | −0.587345 | − | 0.426731i | 0.254020 | − | 0.967199i | \(-0.418247\pi\) |
−0.841365 | + | 0.540468i | \(0.818247\pi\) | |||||||
\(168\) | 0.690983 | − | 2.12663i | 0.0533105 | − | 0.164073i | ||||
\(169\) | −3.70820 | − | 11.4127i | −0.285246 | − | 0.877898i | ||||
\(170\) | 0.809017 | − | 0.587785i | 0.0620488 | − | 0.0450811i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | + | 1.53884i | 0.0381246 | + | 0.117336i | ||||
\(173\) | −4.51722 | + | 13.9026i | −0.343438 | + | 1.05699i | 0.618977 | + | 0.785409i | \(0.287547\pi\) |
−0.962415 | + | 0.271584i | \(0.912453\pi\) | |||||||
\(174\) | 3.35410 | + | 2.43690i | 0.254274 | + | 0.184741i | ||||
\(175\) | −4.85410 | −0.366936 | ||||||||
\(176\) | 3.13525 | + | 5.29007i | 0.236329 | + | 0.398754i | ||||
\(177\) | −4.14590 | −0.311625 | ||||||||
\(178\) | −3.19098 | − | 2.31838i | −0.239174 | − | 0.173770i | ||||
\(179\) | −0.690983 | + | 2.12663i | −0.0516465 | + | 0.158952i | −0.973553 | − | 0.228460i | \(-0.926631\pi\) |
0.921907 | + | 0.387412i | \(0.126631\pi\) | |||||||
\(180\) | 0.190983 | + | 0.587785i | 0.0142350 | + | 0.0438109i | ||||
\(181\) | 0.190983 | − | 0.138757i | 0.0141957 | − | 0.0103137i | −0.580665 | − | 0.814143i | \(-0.697207\pi\) |
0.594860 | + | 0.803829i | \(0.297207\pi\) | |||||||
\(182\) | −0.500000 | + | 0.363271i | −0.0370625 | + | 0.0269275i | ||||
\(183\) | −1.78115 | − | 5.48183i | −0.131667 | − | 0.405228i | ||||
\(184\) | −2.23607 | + | 6.88191i | −0.164845 | + | 0.507341i | ||||
\(185\) | 2.14590 | + | 1.55909i | 0.157770 | + | 0.114626i | ||||
\(186\) | 6.32624 | 0.463862 | ||||||||
\(187\) | −7.16312 | − | 12.0862i | −0.523819 | − | 0.883832i | ||||
\(188\) | 11.8541 | 0.864549 | ||||||||
\(189\) | −0.809017 | − | 0.587785i | −0.0588473 | − | 0.0427551i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.01722 | + | 9.28605i | 0.218318 | + | 0.671915i | 0.998901 | + | 0.0468628i | \(0.0149224\pi\) |
−0.780583 | + | 0.625052i | \(0.785078\pi\) | |||||||
\(192\) | 0.190983 | − | 0.138757i | 0.0137830 | − | 0.0100139i | ||||
\(193\) | −4.09017 | + | 2.97168i | −0.294417 | + | 0.213906i | −0.725181 | − | 0.688558i | \(-0.758244\pi\) |
0.430764 | + | 0.902464i | \(0.358244\pi\) | |||||||
\(194\) | 3.24671 | + | 9.99235i | 0.233100 | + | 0.717409i | ||||
\(195\) | 0.118034 | − | 0.363271i | 0.00845259 | − | 0.0260144i | ||||
\(196\) | 1.30902 | + | 0.951057i | 0.0935012 | + | 0.0679326i | ||||
\(197\) | −9.23607 | −0.658043 | −0.329021 | − | 0.944323i | \(-0.606719\pi\) | ||||
−0.329021 | + | 0.944323i | \(0.606719\pi\) | |||||||
\(198\) | −2.00000 | + | 0.449028i | −0.142134 | + | 0.0319110i | ||||
\(199\) | −7.56231 | −0.536078 | −0.268039 | − | 0.963408i | \(-0.586376\pi\) | ||||
−0.268039 | + | 0.963408i | \(0.586376\pi\) | |||||||
\(200\) | 8.78115 | + | 6.37988i | 0.620921 | + | 0.451126i | ||||
\(201\) | −2.85410 | + | 8.78402i | −0.201313 | + | 0.619577i | ||||
\(202\) | 0.798374 | + | 2.45714i | 0.0561734 | + | 0.172884i | ||||
\(203\) | −5.42705 | + | 3.94298i | −0.380904 | + | 0.276743i | ||||
\(204\) | −5.54508 | + | 4.02874i | −0.388234 | + | 0.282068i | ||||
\(205\) | −0.600813 | − | 1.84911i | −0.0419626 | − | 0.129148i | ||||
\(206\) | 2.42705 | − | 7.46969i | 0.169101 | − | 0.520438i | ||||
\(207\) | 2.61803 | + | 1.90211i | 0.181966 | + | 0.132206i | ||||
\(208\) | −1.85410 | −0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.236068 | 0.0162902 | ||||||||
\(211\) | −4.28115 | − | 3.11044i | −0.294727 | − | 0.214131i | 0.430589 | − | 0.902548i | \(-0.358306\pi\) |
−0.725315 | + | 0.688417i | \(0.758306\pi\) | |||||||
\(212\) | −3.80902 | + | 11.7229i | −0.261604 | + | 0.805135i | ||||
\(213\) | −2.30902 | − | 7.10642i | −0.158211 | − | 0.486924i | ||||
\(214\) | 7.88197 | − | 5.72658i | 0.538800 | − | 0.391461i | ||||
\(215\) | −0.309017 | + | 0.224514i | −0.0210748 | + | 0.0153117i | ||||
\(216\) | 0.690983 | + | 2.12663i | 0.0470154 | + | 0.144699i | ||||
\(217\) | −3.16312 | + | 9.73508i | −0.214727 | + | 0.660860i | ||||
\(218\) | −3.78115 | − | 2.74717i | −0.256092 | − | 0.186062i | ||||
\(219\) | 11.5623 | 0.781308 | ||||||||
\(220\) | −1.35410 | + | 1.53884i | −0.0912935 | + | 0.103749i | ||||
\(221\) | 4.23607 | 0.284949 | ||||||||
\(222\) | 3.47214 | + | 2.52265i | 0.233035 | + | 0.169309i | ||||
\(223\) | −3.92705 | + | 12.0862i | −0.262975 | + | 0.809353i | 0.729178 | + | 0.684324i | \(0.239903\pi\) |
−0.992153 | + | 0.125029i | \(0.960097\pi\) | |||||||
\(224\) | −1.73607 | − | 5.34307i | −0.115996 | − | 0.356999i | ||||
\(225\) | 3.92705 | − | 2.85317i | 0.261803 | − | 0.190211i | ||||
\(226\) | −5.82624 | + | 4.23301i | −0.387556 | + | 0.281576i | ||||
\(227\) | 5.86475 | + | 18.0498i | 0.389257 | + | 1.19801i | 0.933345 | + | 0.358981i | \(0.116876\pi\) |
−0.544088 | + | 0.839028i | \(0.683124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.47214 | + | 6.88191i | 0.625936 | + | 0.454769i | 0.854990 | − | 0.518644i | \(-0.173563\pi\) |
−0.229054 | + | 0.973414i | \(0.573563\pi\) | |||||||
\(230\) | −0.763932 | −0.0503722 | ||||||||
\(231\) | 0.309017 | − | 3.30220i | 0.0203318 | − | 0.217269i | ||||
\(232\) | 15.0000 | 0.984798 | ||||||||
\(233\) | −5.04508 | − | 3.66547i | −0.330515 | − | 0.240133i | 0.410134 | − | 0.912025i | \(-0.365482\pi\) |
−0.740649 | + | 0.671892i | \(0.765482\pi\) | |||||||
\(234\) | 0.190983 | − | 0.587785i | 0.0124849 | − | 0.0384247i | ||||
\(235\) | 0.864745 | + | 2.66141i | 0.0564097 | + | 0.173611i | ||||
\(236\) | −5.42705 | + | 3.94298i | −0.353271 | + | 0.256666i | ||||
\(237\) | −8.78115 | + | 6.37988i | −0.570397 | + | 0.414418i | ||||
\(238\) | 0.809017 | + | 2.48990i | 0.0524408 | + | 0.161396i | ||||
\(239\) | 5.91641 | − | 18.2088i | 0.382701 | − | 1.17783i | −0.555434 | − | 0.831561i | \(-0.687448\pi\) |
0.938135 | − | 0.346271i | \(-0.112552\pi\) | |||||||
\(240\) | 0.572949 | + | 0.416272i | 0.0369837 | + | 0.0268702i | ||||
\(241\) | −24.7082 | −1.59160 | −0.795798 | − | 0.605563i | \(-0.792948\pi\) | ||||
−0.795798 | + | 0.605563i | \(0.792948\pi\) | |||||||
\(242\) | −4.66312 | − | 4.94704i | −0.299757 | − | 0.318008i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.54508 | − | 5.48183i | −0.483025 | − | 0.350938i | ||||
\(245\) | −0.118034 | + | 0.363271i | −0.00754091 | + | 0.0232085i | ||||
\(246\) | −0.972136 | − | 2.99193i | −0.0619811 | − | 0.190758i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 18.5172 | − | 13.4535i | 1.17584 | − | 0.854301i | ||||
\(249\) | −1.85410 | − | 5.70634i | −0.117499 | − | 0.361625i | ||||
\(250\) | −0.718847 | + | 2.21238i | −0.0454639 | + | 0.139923i | ||||
\(251\) | −21.5172 | − | 15.6332i | −1.35815 | − | 0.986757i | −0.998560 | − | 0.0536489i | \(-0.982915\pi\) |
−0.359595 | − | 0.933108i | \(-0.617085\pi\) | |||||||
\(252\) | −1.61803 | −0.101927 | ||||||||
\(253\) | −1.00000 | + | 10.6861i | −0.0628695 | + | 0.671832i | ||||
\(254\) | 4.52786 | 0.284103 | ||||||||
\(255\) | −1.30902 | − | 0.951057i | −0.0819738 | − | 0.0595575i | ||||
\(256\) | −2.02786 | + | 6.24112i | −0.126742 | + | 0.390070i | ||||
\(257\) | 8.32624 | + | 25.6255i | 0.519376 | + | 1.59848i | 0.775175 | + | 0.631746i | \(0.217662\pi\) |
−0.255799 | + | 0.966730i | \(0.582338\pi\) | |||||||
\(258\) | −0.500000 | + | 0.363271i | −0.0311286 | + | 0.0226163i | ||||
\(259\) | −5.61803 | + | 4.08174i | −0.349088 | + | 0.253627i | ||||
\(260\) | −0.190983 | − | 0.587785i | −0.0118443 | − | 0.0364529i | ||||
\(261\) | 2.07295 | − | 6.37988i | 0.128312 | − | 0.394905i | ||||
\(262\) | −1.66312 | − | 1.20833i | −0.102748 | − | 0.0746507i | ||||
\(263\) | 0.708204 | 0.0436697 | 0.0218349 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218349 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(264\) | −4.89919 | + | 5.56758i | −0.301524 | + | 0.342661i | ||||
\(265\) | −2.90983 | −0.178749 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.97214 | + | 6.06961i | −0.120693 | + | 0.371454i | ||||
\(268\) | 4.61803 | + | 14.2128i | 0.282091 | + | 0.868188i | ||||
\(269\) | −19.3713 | + | 14.0741i | −1.18109 | + | 0.858112i | −0.992294 | − | 0.123904i | \(-0.960459\pi\) |
−0.188796 | + | 0.982016i | \(0.560459\pi\) | |||||||
\(270\) | −0.190983 | + | 0.138757i | −0.0116229 | + | 0.00844450i | ||||
\(271\) | −1.98278 | − | 6.10237i | −0.120445 | − | 0.370692i | 0.872599 | − | 0.488438i | \(-0.162433\pi\) |
−0.993044 | + | 0.117746i | \(0.962433\pi\) | |||||||
\(272\) | −2.42705 | + | 7.46969i | −0.147162 | + | 0.452917i | ||||
\(273\) | 0.809017 | + | 0.587785i | 0.0489639 | + | 0.0355744i | ||||
\(274\) | 1.88854 | 0.114091 | ||||||||
\(275\) | 14.7812 | + | 6.37988i | 0.891337 | + | 0.384721i | ||||
\(276\) | 5.23607 | 0.315174 | ||||||||
\(277\) | 20.5623 | + | 14.9394i | 1.23547 | + | 0.897621i | 0.997288 | − | 0.0735998i | \(-0.0234487\pi\) |
0.238181 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(278\) | 3.35410 | − | 10.3229i | 0.201166 | − | 0.619124i | ||||
\(279\) | −3.16312 | − | 9.73508i | −0.189371 | − | 0.582824i | ||||
\(280\) | 0.690983 | − | 0.502029i | 0.0412941 | − | 0.0300019i | ||||
\(281\) | −12.6353 | + | 9.18005i | −0.753756 | + | 0.547636i | −0.896989 | − | 0.442053i | \(-0.854250\pi\) |
0.143233 | + | 0.989689i | \(0.454250\pi\) | |||||||
\(282\) | 1.39919 | + | 4.30625i | 0.0833204 | + | 0.256434i | ||||
\(283\) | 2.25329 | − | 6.93491i | 0.133944 | − | 0.412238i | −0.861480 | − | 0.507791i | \(-0.830462\pi\) |
0.995424 | + | 0.0955536i | \(0.0304621\pi\) | |||||||
\(284\) | −9.78115 | − | 7.10642i | −0.580405 | − | 0.421689i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | − | 0.449028i | 0.118262 | − | 0.0265516i | ||||
\(287\) | 5.09017 | 0.300463 | ||||||||
\(288\) | 4.54508 | + | 3.30220i | 0.267822 | + | 0.194584i | ||||
\(289\) | 0.291796 | − | 0.898056i | 0.0171645 | − | 0.0528268i | ||||
\(290\) | 0.489357 | + | 1.50609i | 0.0287360 | + | 0.0884404i | ||||
\(291\) | 13.7533 | − | 9.99235i | 0.806232 | − | 0.585762i | ||||
\(292\) | 15.1353 | − | 10.9964i | 0.885724 | − | 0.643516i | ||||
\(293\) | −4.09017 | − | 12.5882i | −0.238950 | − | 0.735413i | −0.996573 | − | 0.0827204i | \(-0.973639\pi\) |
0.757623 | − | 0.652693i | \(-0.226361\pi\) | |||||||
\(294\) | −0.190983 | + | 0.587785i | −0.0111384 | + | 0.0342803i | ||||
\(295\) | −1.28115 | − | 0.930812i | −0.0745916 | − | 0.0541940i | ||||
\(296\) | 15.5279 | 0.902539 | ||||||||
\(297\) | 1.69098 | + | 2.85317i | 0.0981208 | + | 0.165558i | ||||
\(298\) | 8.09017 | 0.468651 | ||||||||
\(299\) | −2.61803 | − | 1.90211i | −0.151405 | − | 0.110002i | ||||
\(300\) | 2.42705 | − | 7.46969i | 0.140126 | − | 0.431263i | ||||
\(301\) | −0.309017 | − | 0.951057i | −0.0178114 | − | 0.0548180i | ||||
\(302\) | −10.5451 | + | 7.66145i | −0.606801 | + | 0.440867i | ||||
\(303\) | 3.38197 | − | 2.45714i | 0.194289 | − | 0.141159i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.680340 | − | 2.09387i | 0.0389561 | − | 0.119895i | ||||
\(306\) | −2.11803 | − | 1.53884i | −0.121080 | − | 0.0879697i | ||||
\(307\) | 19.1803 | 1.09468 | 0.547340 | − | 0.836910i | \(-0.315640\pi\) | ||||
0.547340 | + | 0.836910i | \(0.315640\pi\) | |||||||
\(308\) | −2.73607 | − | 4.61653i | −0.155902 | − | 0.263051i | ||||
\(309\) | −12.7082 | −0.722944 | ||||||||
\(310\) | 1.95492 | + | 1.42033i | 0.111032 | + | 0.0806693i | ||||
\(311\) | 5.19098 | − | 15.9762i | 0.294354 | − | 0.905927i | −0.689084 | − | 0.724681i | \(-0.741987\pi\) |
0.983438 | − | 0.181246i | \(-0.0580130\pi\) | |||||||
\(312\) | −0.690983 | − | 2.12663i | −0.0391192 | − | 0.120397i | ||||
\(313\) | 12.7812 | − | 9.28605i | 0.722433 | − | 0.524879i | −0.164727 | − | 0.986339i | \(-0.552674\pi\) |
0.887161 | + | 0.461461i | \(0.152674\pi\) | |||||||
\(314\) | −0.836881 | + | 0.608030i | −0.0472279 | + | 0.0343131i | ||||
\(315\) | −0.118034 | − | 0.363271i | −0.00665046 | − | 0.0204680i | ||||
\(316\) | −5.42705 | + | 16.7027i | −0.305295 | + | 0.939603i | ||||
\(317\) | −20.5172 | − | 14.9066i | −1.15236 | − | 0.837240i | −0.163569 | − | 0.986532i | \(-0.552301\pi\) |
−0.988793 | + | 0.149292i | \(0.952301\pi\) | |||||||
\(318\) | −4.70820 | −0.264023 | ||||||||
\(319\) | 21.7082 | − | 4.87380i | 1.21543 | − | 0.272880i | ||||
\(320\) | 0.0901699 | 0.00504065 | ||||||||
\(321\) | −12.7533 | − | 9.26581i | −0.711819 | − | 0.517167i | ||||
\(322\) | 0.618034 | − | 1.90211i | 0.0344417 | − | 0.106001i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.30902 | − | 0.951057i | 0.0727232 | − | 0.0528365i | ||||
\(325\) | −3.92705 | + | 2.85317i | −0.217834 | + | 0.158265i | ||||
\(326\) | −1.15248 | − | 3.54696i | −0.0638297 | − | 0.196448i | ||||
\(327\) | −2.33688 | + | 7.19218i | −0.129230 | + | 0.397728i | ||||
\(328\) | −9.20820 | − | 6.69015i | −0.508438 | − | 0.369402i | ||||
\(329\) | −7.32624 | −0.403909 | ||||||||
\(330\) | −0.718847 | − | 0.310271i | −0.0395712 | − | 0.0170798i | ||||
\(331\) | −14.7082 | −0.808436 | −0.404218 | − | 0.914663i | \(-0.632456\pi\) | ||||
−0.404218 | + | 0.914663i | \(0.632456\pi\) | |||||||
\(332\) | −7.85410 | − | 5.70634i | −0.431050 | − | 0.313176i | ||||
\(333\) | 2.14590 | − | 6.60440i | 0.117594 | − | 0.361919i | ||||
\(334\) | −1.79180 | − | 5.51458i | −0.0980427 | − | 0.301744i | ||||
\(335\) | −2.85410 | + | 2.07363i | −0.155936 | + | 0.113294i | ||||
\(336\) | −1.50000 | + | 1.08981i | −0.0818317 | + | 0.0594542i | ||||
\(337\) | 0.399187 | + | 1.22857i | 0.0217451 | + | 0.0669245i | 0.961340 | − | 0.275363i | \(-0.0887982\pi\) |
−0.939595 | + | 0.342288i | \(0.888798\pi\) | |||||||
\(338\) | 2.29180 | − | 7.05342i | 0.124657 | − | 0.383656i | ||||
\(339\) | 9.42705 | + | 6.84915i | 0.512007 | + | 0.371995i | ||||
\(340\) | −2.61803 | −0.141983 | ||||||||
\(341\) | 22.4271 | − | 25.4868i | 1.21449 | − | 1.38019i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | −0.690983 | + | 2.12663i | −0.0372553 | + | 0.114660i | ||||
\(345\) | 0.381966 | + | 1.17557i | 0.0205644 | + | 0.0632906i | ||||
\(346\) | −7.30902 | + | 5.31031i | −0.392935 | + | 0.285484i | ||||
\(347\) | 20.5623 | − | 14.9394i | 1.10384 | − | 0.801988i | 0.122159 | − | 0.992510i | \(-0.461018\pi\) |
0.981683 | + | 0.190522i | \(0.0610181\pi\) | |||||||
\(348\) | −3.35410 | − | 10.3229i | −0.179799 | − | 0.553364i | ||||
\(349\) | 10.7918 | − | 33.2137i | 0.577672 | − | 1.77789i | −0.0492248 | − | 0.998788i | \(-0.515675\pi\) |
0.626896 | − | 0.779103i | \(-0.284325\pi\) | |||||||
\(350\) | −2.42705 | − | 1.76336i | −0.129731 | − | 0.0942553i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.73607 | + | 18.5519i | −0.0925327 | + | 0.988817i | ||||
\(353\) | −25.4721 | −1.35574 | −0.677872 | − | 0.735179i | \(-0.737098\pi\) | ||||
−0.677872 | + | 0.735179i | \(0.737098\pi\) | |||||||
\(354\) | −2.07295 | − | 1.50609i | −0.110176 | − | 0.0800475i | ||||
\(355\) | 0.881966 | − | 2.71441i | 0.0468099 | − | 0.144066i | ||||
\(356\) | 3.19098 | + | 9.82084i | 0.169122 | + | 0.520503i | ||||
\(357\) | 3.42705 | − | 2.48990i | 0.181379 | − | 0.131779i | ||||
\(358\) | −1.11803 | + | 0.812299i | −0.0590899 | + | 0.0429313i | ||||
\(359\) | −10.2639 | − | 31.5891i | −0.541710 | − | 1.66721i | −0.728687 | − | 0.684847i | \(-0.759869\pi\) |
0.186978 | − | 0.982364i | \(-0.440131\pi\) | |||||||
\(360\) | −0.263932 | + | 0.812299i | −0.0139104 | + | 0.0428119i | ||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | 0.145898 | 0.00766823 | ||||||||
\(363\) | −5.28115 | + | 9.64932i | −0.277189 | + | 0.506458i | ||||
\(364\) | 1.61803 | 0.0848080 | ||||||||
\(365\) | 3.57295 | + | 2.59590i | 0.187017 | + | 0.135876i | ||||
\(366\) | 1.10081 | − | 3.38795i | 0.0575404 | − | 0.177091i | ||||
\(367\) | 3.48936 | + | 10.7391i | 0.182143 | + | 0.560578i | 0.999887 | − | 0.0150030i | \(-0.00477579\pi\) |
−0.817745 | + | 0.575581i | \(0.804776\pi\) | |||||||
\(368\) | 4.85410 | − | 3.52671i | 0.253038 | − | 0.183843i | ||||
\(369\) | −4.11803 | + | 2.99193i | −0.214376 | + | 0.155753i | ||||
\(370\) | 0.506578 | + | 1.55909i | 0.0263357 | + | 0.0810530i | ||||
\(371\) | 2.35410 | − | 7.24518i | 0.122219 | − | 0.376151i | ||||
\(372\) | −13.3992 | − | 9.73508i | −0.694715 | − | 0.504740i | ||||
\(373\) | 30.1803 | 1.56268 | 0.781339 | − | 0.624106i | \(-0.214537\pi\) | ||||
0.781339 | + | 0.624106i | \(0.214537\pi\) | |||||||
\(374\) | 0.809017 | − | 8.64527i | 0.0418333 | − | 0.447036i | ||||
\(375\) | 3.76393 | 0.194369 | ||||||||
\(376\) | 13.2533 | + | 9.62908i | 0.683486 | + | 0.496582i | ||||
\(377\) | −2.07295 | + | 6.37988i | −0.106762 | + | 0.328581i | ||||
\(378\) | −0.190983 | − | 0.587785i | −0.00982311 | − | 0.0302324i | ||||
\(379\) | 8.78115 | − | 6.37988i | 0.451058 | − | 0.327712i | −0.338956 | − | 0.940802i | \(-0.610074\pi\) |
0.790013 | + | 0.613090i | \(0.210074\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.26393 | − | 6.96767i | −0.115985 | − | 0.356964i | ||||
\(382\) | −1.86475 | + | 5.73910i | −0.0954087 | + | 0.293638i | ||||
\(383\) | 6.39919 | + | 4.64928i | 0.326983 | + | 0.237567i | 0.739149 | − | 0.673541i | \(-0.235228\pi\) |
−0.412166 | + | 0.911109i | \(0.635228\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 0.836881 | − | 0.951057i | 0.0426514 | − | 0.0484703i | ||||
\(386\) | −3.12461 | −0.159039 | ||||||||
\(387\) | 0.809017 | + | 0.587785i | 0.0411246 | + | 0.0298788i | ||||
\(388\) | 8.50000 | − | 26.1603i | 0.431522 | − | 1.32809i | ||||
\(389\) | 6.38197 | + | 19.6417i | 0.323579 | + | 0.995872i | 0.972078 | + | 0.234657i | \(0.0753968\pi\) |
−0.648500 | + | 0.761215i | \(0.724603\pi\) | |||||||
\(390\) | 0.190983 | − | 0.138757i | 0.00967080 | − | 0.00702625i | ||||
\(391\) | −11.0902 | + | 8.05748i | −0.560854 | + | 0.407484i | ||||
\(392\) | 0.690983 | + | 2.12663i | 0.0348999 | + | 0.107411i | ||||
\(393\) | −1.02786 | + | 3.16344i | −0.0518489 | + | 0.159574i | ||||
\(394\) | −4.61803 | − | 3.35520i | −0.232653 | − | 0.169032i | ||||
\(395\) | −4.14590 | −0.208603 | ||||||||
\(396\) | 4.92705 | + | 2.12663i | 0.247594 | + | 0.106867i | ||||
\(397\) | 25.6869 | 1.28919 | 0.644595 | − | 0.764524i | \(-0.277026\pi\) | ||||
0.644595 | + | 0.764524i | \(0.277026\pi\) | |||||||
\(398\) | −3.78115 | − | 2.74717i | −0.189532 | − | 0.137703i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.78115 | − | 8.55951i | −0.139058 | − | 0.427975i | ||||
\(401\) | −9.44427 | + | 6.86167i | −0.471624 | + | 0.342655i | −0.798074 | − | 0.602559i | \(-0.794148\pi\) |
0.326450 | + | 0.945215i | \(0.394148\pi\) | |||||||
\(402\) | −4.61803 | + | 3.35520i | −0.230327 | + | 0.167342i | ||||
\(403\) | 3.16312 | + | 9.73508i | 0.157566 | + | 0.484939i | ||||
\(404\) | 2.09017 | − | 6.43288i | 0.103990 | − | 0.320048i | ||||
\(405\) | 0.309017 | + | 0.224514i | 0.0153552 | + | 0.0111562i | ||||
\(406\) | −4.14590 | −0.205757 | ||||||||
\(407\) | 22.4721 | − | 5.04531i | 1.11390 | − | 0.250087i | ||||
\(408\) | −9.47214 | −0.468941 | ||||||||
\(409\) | 21.3435 | + | 15.5069i | 1.05537 | + | 0.766768i | 0.973226 | − | 0.229852i | \(-0.0738243\pi\) |
0.0821406 | + | 0.996621i | \(0.473824\pi\) | |||||||
\(410\) | 0.371323 | − | 1.14281i | 0.0183383 | − | 0.0564396i | ||||
\(411\) | −0.944272 | − | 2.90617i | −0.0465775 | − | 0.143351i | ||||
\(412\) | −16.6353 | + | 12.0862i | −0.819560 | + | 0.595445i | ||||
\(413\) | 3.35410 | − | 2.43690i | 0.165045 | − | 0.119912i | ||||
\(414\) | 0.618034 | + | 1.90211i | 0.0303747 | + | 0.0934838i | ||||
\(415\) | 0.708204 | − | 2.17963i | 0.0347644 | − | 0.106994i | ||||
\(416\) | −4.54508 | − | 3.30220i | −0.222841 | − | 0.161904i | ||||
\(417\) | −17.5623 | −0.860030 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.3262 | −0.748736 | −0.374368 | − | 0.927280i | \(-0.622140\pi\) | ||||
−0.374368 | + | 0.927280i | \(0.622140\pi\) | |||||||
\(420\) | −0.500000 | − | 0.363271i | −0.0243975 | − | 0.0177258i | ||||
\(421\) | 0.843459 | − | 2.59590i | 0.0411077 | − | 0.126516i | −0.928397 | − | 0.371591i | \(-0.878812\pi\) |
0.969504 | + | 0.245074i | \(0.0788124\pi\) | |||||||
\(422\) | −1.01064 | − | 3.11044i | −0.0491973 | − | 0.151414i | ||||
\(423\) | 5.92705 | − | 4.30625i | 0.288183 | − | 0.209377i | ||||
\(424\) | −13.7812 | + | 10.0126i | −0.669272 | + | 0.486255i | ||||
\(425\) | 6.35410 | + | 19.5559i | 0.308219 | + | 0.948601i | ||||
\(426\) | 1.42705 | − | 4.39201i | 0.0691408 | − | 0.212794i | ||||
\(427\) | 4.66312 | + | 3.38795i | 0.225664 | + | 0.163955i | ||||
\(428\) | −25.5066 | −1.23291 | ||||||||
\(429\) | −1.69098 | − | 2.85317i | −0.0816414 | − | 0.137752i | ||||
\(430\) | −0.236068 | −0.0113842 | ||||||||
\(431\) | 30.5795 | + | 22.2173i | 1.47296 | + | 1.07017i | 0.979741 | + | 0.200268i | \(0.0641813\pi\) |
0.493223 | + | 0.869903i | \(0.335819\pi\) | |||||||
\(432\) | 0.572949 | − | 1.76336i | 0.0275660 | − | 0.0848395i | ||||
\(433\) | −0.798374 | − | 2.45714i | −0.0383674 | − | 0.118083i | 0.930038 | − | 0.367462i | \(-0.119773\pi\) |
−0.968406 | + | 0.249380i | \(0.919773\pi\) | |||||||
\(434\) | −5.11803 | + | 3.71847i | −0.245673 | + | 0.178492i | ||||
\(435\) | 2.07295 | − | 1.50609i | 0.0993903 | − | 0.0722113i | ||||
\(436\) | 3.78115 | + | 11.6372i | 0.181084 | + | 0.557320i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 5.78115 | + | 4.20025i | 0.276234 | + | 0.200696i | ||||
\(439\) | 0.527864 | 0.0251936 | 0.0125968 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125968 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(440\) | −2.76393 | + | 0.620541i | −0.131765 | + | 0.0295832i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.11803 | + | 1.53884i | 0.100745 | + | 0.0731952i | ||||
\(443\) | −11.3262 | + | 34.8586i | −0.538126 | + | 1.65618i | 0.198671 | + | 0.980066i | \(0.436338\pi\) |
−0.736796 | + | 0.676115i | \(0.763662\pi\) | |||||||
\(444\) | −3.47214 | − | 10.6861i | −0.164780 | − | 0.507142i | ||||
\(445\) | −1.97214 | + | 1.43284i | −0.0934882 | + | 0.0679232i | ||||
\(446\) | −6.35410 | + | 4.61653i | −0.300875 | + | 0.218599i | ||||
\(447\) | −4.04508 | − | 12.4495i | −0.191326 | − | 0.588841i | ||||
\(448\) | −0.0729490 | + | 0.224514i | −0.00344652 | + | 0.0106073i | ||||
\(449\) | −12.6631 | − | 9.20029i | −0.597610 | − | 0.434189i | 0.247420 | − | 0.968908i | \(-0.420417\pi\) |
−0.845030 | + | 0.534720i | \(0.820417\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | −15.5000 | − | 6.69015i | −0.729866 | − | 0.315027i | ||||
\(452\) | 18.8541 | 0.886822 | ||||||||
\(453\) | 17.0623 | + | 12.3965i | 0.801657 | + | 0.582438i | ||||
\(454\) | −3.62461 | + | 11.1554i | −0.170111 | + | 0.523549i | ||||
\(455\) | 0.118034 | + | 0.363271i | 0.00553352 | + | 0.0170304i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.92705 | + | 7.21242i | −0.464368 | + | 0.337383i | −0.795242 | − | 0.606292i | \(-0.792656\pi\) |
0.330874 | + | 0.943675i | \(0.392656\pi\) | |||||||
\(458\) | 2.23607 | + | 6.88191i | 0.104485 | + | 0.321571i | ||||
\(459\) | −1.30902 | + | 4.02874i | −0.0610997 | + | 0.188045i | ||||
\(460\) | 1.61803 | + | 1.17557i | 0.0754412 | + | 0.0548113i | ||||
\(461\) | 23.1803 | 1.07962 | 0.539808 | − | 0.841788i | \(-0.318497\pi\) | ||||
0.539808 | + | 0.841788i | \(0.318497\pi\) | |||||||
\(462\) | 1.35410 | − | 1.53884i | 0.0629985 | − | 0.0715934i | ||||
\(463\) | −35.9230 | −1.66948 | −0.834741 | − | 0.550642i | \(-0.814383\pi\) | ||||
−0.834741 | + | 0.550642i | \(0.814383\pi\) | |||||||
\(464\) | −10.0623 | − | 7.31069i | −0.467131 | − | 0.339390i | ||||
\(465\) | 1.20820 | − | 3.71847i | 0.0560291 | − | 0.172440i | ||||
\(466\) | −1.19098 | − | 3.66547i | −0.0551712 | − | 0.169800i | ||||
\(467\) | −25.8435 | + | 18.7764i | −1.19589 | + | 0.868867i | −0.993874 | − | 0.110515i | \(-0.964750\pi\) |
−0.202018 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(468\) | −1.30902 | + | 0.951057i | −0.0605093 | + | 0.0439626i | ||||
\(469\) | −2.85410 | − | 8.78402i | −0.131790 | − | 0.405608i | ||||
\(470\) | −0.534442 | + | 1.64484i | −0.0246520 | + | 0.0758709i | ||||
\(471\) | 1.35410 | + | 0.983813i | 0.0623937 | + | 0.0453317i | ||||
\(472\) | −9.27051 | −0.426710 | ||||||||
\(473\) | −0.309017 | + | 3.30220i | −0.0142086 | + | 0.151835i | ||||
\(474\) | −6.70820 | −0.308118 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.11803 | − | 6.51864i | 0.0970799 | − | 0.298781i | ||||
\(477\) | 2.35410 | + | 7.24518i | 0.107787 | + | 0.331734i | ||||
\(478\) | 9.57295 | − | 6.95515i | 0.437856 | − | 0.318121i | ||||
\(479\) | −17.3992 | + | 12.6412i | −0.794989 | + | 0.577593i | −0.909440 | − | 0.415836i | \(-0.863489\pi\) |
0.114451 | + | 0.993429i | \(0.463489\pi\) | |||||||
\(480\) | 0.663119 | + | 2.04087i | 0.0302671 | + | 0.0931526i | ||||
\(481\) | −2.14590 | + | 6.60440i | −0.0978445 | + | 0.301134i | ||||
\(482\) | −12.3541 | − | 8.97578i | −0.562714 | − | 0.408836i | ||||
\(483\) | −3.23607 | −0.147246 | ||||||||
\(484\) | 2.26393 | + | 17.6538i | 0.102906 | + | 0.802446i | ||||
\(485\) | 6.49342 | 0.294851 | ||||||||
\(486\) | 0.500000 | + | 0.363271i | 0.0226805 | + | 0.0164783i | ||||
\(487\) | 5.13525 | − | 15.8047i | 0.232701 | − | 0.716179i | −0.764717 | − | 0.644366i | \(-0.777121\pi\) |
0.997418 | − | 0.0718131i | \(-0.0228785\pi\) | |||||||
\(488\) | −3.98278 | − | 12.2577i | −0.180292 | − | 0.554882i | ||||
\(489\) | −4.88197 | + | 3.54696i | −0.220770 | + | 0.160399i | ||||
\(490\) | −0.190983 | + | 0.138757i | −0.00862773 | + | 0.00626841i | ||||
\(491\) | 1.14590 | + | 3.52671i | 0.0517137 | + | 0.159158i | 0.973578 | − | 0.228354i | \(-0.0733344\pi\) |
−0.921864 | + | 0.387512i | \(0.873334\pi\) | |||||||
\(492\) | −2.54508 | + | 7.83297i | −0.114741 | + | 0.353137i | ||||
\(493\) | 22.9894 | + | 16.7027i | 1.03539 | + | 0.752254i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.118034 | + | 1.26133i | −0.00530523 | + | 0.0566924i | ||||
\(496\) | −18.9787 | −0.852169 | ||||||||
\(497\) | 6.04508 | + | 4.39201i | 0.271159 | + | 0.197009i | ||||
\(498\) | 1.14590 | − | 3.52671i | 0.0513489 | − | 0.158036i | ||||
\(499\) | −1.54508 | − | 4.75528i | −0.0691675 | − | 0.212876i | 0.910498 | − | 0.413514i | \(-0.135699\pi\) |
−0.979665 | + | 0.200638i | \(0.935699\pi\) | |||||||
\(500\) | 4.92705 | − | 3.57971i | 0.220344 | − | 0.160090i | ||||
\(501\) | −7.59017 | + | 5.51458i | −0.339104 | + | 0.246373i | ||||
\(502\) | −5.07953 | − | 15.6332i | −0.226710 | − | 0.697743i | ||||
\(503\) | −9.98278 | + | 30.7238i | −0.445110 | + | 1.36991i | 0.437253 | + | 0.899339i | \(0.355951\pi\) |
−0.882363 | + | 0.470569i | \(0.844049\pi\) | |||||||
\(504\) | −1.80902 | − | 1.31433i | −0.0805800 | − | 0.0585448i | ||||
\(505\) | 1.59675 | 0.0710543 | ||||||||
\(506\) | −4.38197 | + | 4.97980i | −0.194802 | + | 0.221379i | ||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | −9.59017 | − | 6.96767i | −0.425495 | − | 0.309140i | ||||
\(509\) | 12.9271 | − | 39.7854i | 0.572981 | − | 1.76346i | −0.0699705 | − | 0.997549i | \(-0.522291\pi\) |
0.642952 | − | 0.765907i | \(-0.277709\pi\) | |||||||
\(510\) | −0.309017 | − | 0.951057i | −0.0136835 | − | 0.0421135i | ||||
\(511\) | −9.35410 | + | 6.79615i | −0.413801 | + | 0.300644i | ||||
\(512\) | 15.1353 | − | 10.9964i | 0.668890 | − | 0.485977i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.14590 | + | 15.8374i | −0.226976 | + | 0.698560i | ||||
\(515\) | −3.92705 | − | 2.85317i | −0.173047 | − | 0.125726i | ||||
\(516\) | 1.61803 | 0.0712300 | ||||||||
\(517\) | 22.3090 | + | 9.62908i | 0.981149 | + | 0.423486i | ||||
\(518\) | −4.29180 | −0.188571 | ||||||||
\(519\) | 11.8262 | + | 8.59226i | 0.519114 | + | 0.377159i | ||||
\(520\) | 0.263932 | − | 0.812299i | 0.0115742 | − | 0.0356217i | ||||
\(521\) | −5.92705 | − | 18.2416i | −0.259669 | − | 0.799178i | −0.992874 | − | 0.119171i | \(-0.961976\pi\) |
0.733205 | − | 0.680008i | \(-0.238024\pi\) | |||||||
\(522\) | 3.35410 | − | 2.43690i | 0.146805 | − | 0.106660i | ||||
\(523\) | −16.4271 | + | 11.9350i | −0.718305 | + | 0.521879i | −0.885842 | − | 0.463987i | \(-0.846419\pi\) |
0.167537 | + | 0.985866i | \(0.446419\pi\) | |||||||
\(524\) | 1.66312 | + | 5.11855i | 0.0726537 | + | 0.223605i | ||||
\(525\) | −1.50000 | + | 4.61653i | −0.0654654 | + | 0.201482i | ||||
\(526\) | 0.354102 | + | 0.257270i | 0.0154396 | + | 0.0112175i | ||||
\(527\) | 43.3607 | 1.88882 | ||||||||
\(528\) | 6.00000 | − | 1.34708i | 0.261116 | − | 0.0586243i | ||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | −1.45492 | − | 1.05706i | −0.0631975 | − | 0.0459156i | ||||
\(531\) | −1.28115 | + | 3.94298i | −0.0555973 | + | 0.171111i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.11803 | − | 2.99193i | 0.178372 | − | 0.129595i | ||||
\(534\) | −3.19098 | + | 2.31838i | −0.138087 | + | 0.100326i | ||||
\(535\) | −1.86068 | − | 5.72658i | −0.0804442 | − | 0.247582i | ||||
\(536\) | −6.38197 | + | 19.6417i | −0.275659 | + | 0.848391i | ||||
\(537\) | 1.80902 | + | 1.31433i | 0.0780648 | + | 0.0567174i | ||||
\(538\) | −14.7984 | −0.638003 | ||||||||
\(539\) | 1.69098 | + | 2.85317i | 0.0728358 | + | 0.122895i | ||||
\(540\) | 0.618034 | 0.0265959 | ||||||||
\(541\) | −16.2533 | − | 11.8087i | −0.698783 | − | 0.507696i | 0.180752 | − | 0.983529i | \(-0.442147\pi\) |
−0.879536 | + | 0.475833i | \(0.842147\pi\) | |||||||
\(542\) | 1.22542 | − | 3.77147i | 0.0526365 | − | 0.161999i | ||||
\(543\) | −0.0729490 | − | 0.224514i | −0.00313054 | − | 0.00963482i | ||||
\(544\) | −19.2533 | + | 13.9883i | −0.825478 | + | 0.599745i | ||||
\(545\) | −2.33688 | + | 1.69784i | −0.100101 | + | 0.0727276i | ||||
\(546\) | 0.190983 | + | 0.587785i | 0.00817332 | + | 0.0251549i | ||||
\(547\) | 6.98278 | − | 21.4908i | 0.298562 | − | 0.918880i | −0.683440 | − | 0.730007i | \(-0.739517\pi\) |
0.982002 | − | 0.188872i | \(-0.0604833\pi\) | |||||||
\(548\) | −4.00000 | − | 2.90617i | −0.170872 | − | 0.124145i | ||||
\(549\) | −5.76393 | −0.245999 | ||||||||
\(550\) | 5.07295 | + | 8.55951i | 0.216311 | + | 0.364979i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 5.85410 | + | 4.25325i | 0.249167 | + | 0.181031i | ||||
\(553\) | 3.35410 | − | 10.3229i | 0.142631 | − | 0.438973i | ||||
\(554\) | 4.85410 | + | 14.9394i | 0.206231 | + | 0.634714i | ||||
\(555\) | 2.14590 | − | 1.55909i | 0.0910883 | − | 0.0661795i | ||||
\(556\) | −22.9894 | + | 16.7027i | −0.974966 | + | 0.708354i | ||||
\(557\) | 0.236068 | + | 0.726543i | 0.0100025 | + | 0.0307846i | 0.955933 | − | 0.293584i | \(-0.0948481\pi\) |
−0.945931 | + | 0.324369i | \(0.894848\pi\) | |||||||
\(558\) | 1.95492 | − | 6.01661i | 0.0827582 | − | 0.254703i | ||||
\(559\) | −0.809017 | − | 0.587785i | −0.0342178 | − | 0.0248607i | ||||
\(560\) | −0.708204 | −0.0299271 | ||||||||
\(561\) | −13.7082 | + | 3.07768i | −0.578761 | + | 0.129940i | ||||
\(562\) | −9.65248 | −0.407165 | ||||||||
\(563\) | 36.4615 | + | 26.4908i | 1.53667 | + | 1.11646i | 0.952382 | + | 0.304908i | \(0.0986257\pi\) |
0.584287 | + | 0.811547i | \(0.301374\pi\) | |||||||
\(564\) | 3.66312 | − | 11.2739i | 0.154245 | − | 0.474718i | ||||
\(565\) | 1.37539 | + | 4.23301i | 0.0578630 | + | 0.178084i | ||||
\(566\) | 3.64590 | − | 2.64890i | 0.153249 | − | 0.111342i | ||||
\(567\) | −0.809017 | + | 0.587785i | −0.0339755 | + | 0.0246847i | ||||
\(568\) | −5.16312 | − | 15.8904i | −0.216640 | − | 0.666748i | ||||
\(569\) | 12.0729 | − | 37.1567i | 0.506124 | − | 1.55769i | −0.292748 | − | 0.956190i | \(-0.594570\pi\) |
0.798872 | − | 0.601501i | \(-0.205430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | −4.92705 | − | 2.12663i | −0.206010 | − | 0.0889187i | ||||
\(573\) | 9.76393 | 0.407894 | ||||||||
\(574\) | 2.54508 | + | 1.84911i | 0.106230 | + | 0.0771805i | ||||
\(575\) | 4.85410 | − | 14.9394i | 0.202430 | − | 0.623016i | ||||
\(576\) | −0.0729490 | − | 0.224514i | −0.00303954 | − | 0.00935475i | ||||
\(577\) | 7.63525 | − | 5.54734i | 0.317860 | − | 0.230939i | −0.417402 | − | 0.908722i | \(-0.637059\pi\) |
0.735262 | + | 0.677783i | \(0.237059\pi\) | |||||||
\(578\) | 0.472136 | − | 0.343027i | 0.0196383 | − | 0.0142680i | ||||
\(579\) | 1.56231 | + | 4.80828i | 0.0649272 | + | 0.199825i | ||||
\(580\) | 1.28115 | − | 3.94298i | 0.0531970 | − | 0.163723i | ||||
\(581\) | 4.85410 | + | 3.52671i | 0.201382 | + | 0.146313i | ||||
\(582\) | 10.5066 | 0.435512 | ||||||||
\(583\) | −16.6910 | + | 18.9681i | −0.691270 | + | 0.785580i | ||||
\(584\) | 25.8541 | 1.06985 | ||||||||
\(585\) | −0.309017 | − | 0.224514i | −0.0127763 | − | 0.00928251i | ||||
\(586\) | 2.52786 | − | 7.77997i | 0.104425 | − | 0.321387i | ||||
\(587\) | 11.0902 | + | 34.1320i | 0.457740 | + | 1.40878i | 0.867888 | + | 0.496761i | \(0.165477\pi\) |
−0.410147 | + | 0.912019i | \(0.634523\pi\) | |||||||
\(588\) | 1.30902 | − | 0.951057i | 0.0539830 | − | 0.0392209i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.302439 | − | 0.930812i | −0.0124512 | − | 0.0383209i | ||||
\(591\) | −2.85410 | + | 8.78402i | −0.117402 | + | 0.361326i | ||||
\(592\) | −10.4164 | − | 7.56796i | −0.428112 | − | 0.311041i | ||||
\(593\) | −23.8885 | −0.980985 | −0.490492 | − | 0.871445i | \(-0.663183\pi\) | ||||
−0.490492 | + | 0.871445i | \(0.663183\pi\) | |||||||
\(594\) | −0.190983 | + | 2.04087i | −0.00783613 | + | 0.0837379i | ||||
\(595\) | 1.61803 | 0.0663329 | ||||||||
\(596\) | −17.1353 | − | 12.4495i | −0.701887 | − | 0.509951i | ||||
\(597\) | −2.33688 | + | 7.19218i | −0.0956422 | + | 0.294356i | ||||
\(598\) | −0.618034 | − | 1.90211i | −0.0252733 | − | 0.0777832i | ||||
\(599\) | −25.4894 | + | 18.5191i | −1.04147 | + | 0.756670i | −0.970571 | − | 0.240814i | \(-0.922586\pi\) |
−0.0708955 | + | 0.997484i | \(0.522586\pi\) | |||||||
\(600\) | 8.78115 | − | 6.37988i | 0.358489 | − | 0.260458i | ||||
\(601\) | −4.58359 | − | 14.1068i | −0.186969 | − | 0.575430i | 0.813008 | − | 0.582252i | \(-0.197828\pi\) |
−0.999977 | + | 0.00682211i | \(0.997828\pi\) | |||||||
\(602\) | 0.190983 | − | 0.587785i | 0.00778389 | − | 0.0239563i | ||||
\(603\) | 7.47214 | + | 5.42882i | 0.304289 | + | 0.221079i | ||||
\(604\) | 34.1246 | 1.38851 | ||||||||
\(605\) | −3.79837 | + | 1.79611i | −0.154426 | + | 0.0730223i | ||||
\(606\) | 2.58359 | 0.104951 | ||||||||
\(607\) | 13.0623 | + | 9.49032i | 0.530183 | + | 0.385200i | 0.820426 | − | 0.571753i | \(-0.193736\pi\) |
−0.290243 | + | 0.956953i | \(0.593736\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.07295 | + | 6.37988i | 0.0840001 | + | 0.258526i | ||||
\(610\) | 1.10081 | − | 0.799788i | 0.0445706 | − | 0.0323824i | ||||
\(611\) | −5.92705 | + | 4.30625i | −0.239783 | + | 0.174212i | ||||
\(612\) | 2.11803 | + | 6.51864i | 0.0856164 | + | 0.263500i | ||||
\(613\) | 10.6459 | − | 32.7647i | 0.429984 | − | 1.32335i | −0.468157 | − | 0.883645i | \(-0.655082\pi\) |
0.898141 | − | 0.439709i | \(-0.144918\pi\) | |||||||
\(614\) | 9.59017 | + | 6.96767i | 0.387028 | + | 0.281192i | ||||
\(615\) | −1.94427 | −0.0784006 | ||||||||
\(616\) | 0.690983 | − | 7.38394i | 0.0278405 | − | 0.297507i | ||||
\(617\) | −10.0902 | −0.406215 | −0.203107 | − | 0.979156i | \(-0.565104\pi\) | ||||
−0.203107 | + | 0.979156i | \(0.565104\pi\) | |||||||
\(618\) | −6.35410 | − | 4.61653i | −0.255599 | − | 0.185704i | ||||
\(619\) | 10.8541 | − | 33.4055i | 0.436263 | − | 1.34268i | −0.455523 | − | 0.890224i | \(-0.650548\pi\) |
0.891787 | − | 0.452456i | \(-0.149452\pi\) | |||||||
\(620\) | −1.95492 | − | 6.01661i | −0.0785113 | − | 0.241633i | ||||
\(621\) | 2.61803 | − | 1.90211i | 0.105058 | − | 0.0763292i | ||||
\(622\) | 8.39919 | − | 6.10237i | 0.336777 | − | 0.244683i | ||||
\(623\) | −1.97214 | − | 6.06961i | −0.0790120 | − | 0.243174i | ||||
\(624\) | −0.572949 | + | 1.76336i | −0.0229363 | + | 0.0705907i | ||||
\(625\) | −18.4721 | − | 13.4208i | −0.738885 | − | 0.536832i | ||||
\(626\) | 9.76393 | 0.390245 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.70820 | 0.108069 | ||||||||
\(629\) | 23.7984 | + | 17.2905i | 0.948903 | + | 0.689419i | ||||
\(630\) | 0.0729490 | − | 0.224514i | 0.00290636 | − | 0.00894485i | ||||
\(631\) | −2.83688 | − | 8.73102i | −0.112934 | − | 0.347577i | 0.878576 | − | 0.477602i | \(-0.158494\pi\) |
−0.991511 | + | 0.130026i | \(0.958494\pi\) | |||||||
\(632\) | −19.6353 | + | 14.2658i | −0.781049 | + | 0.567465i | ||||
\(633\) | −4.28115 | + | 3.11044i | −0.170161 | + | 0.123629i | ||||
\(634\) | −4.84346 | − | 14.9066i | −0.192358 | − | 0.592018i | ||||
\(635\) | 0.864745 | − | 2.66141i | 0.0343164 | − | 0.105615i | ||||
\(636\) | 9.97214 | + | 7.24518i | 0.395421 | + | 0.287290i | ||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 12.6246 | + | 5.44907i | 0.499813 | + | 0.215731i | ||||
\(639\) | −7.47214 | −0.295593 | ||||||||
\(640\) | 3.51722 | + | 2.55541i | 0.139030 | + | 0.101011i | ||||
\(641\) | 8.64590 | − | 26.6093i | 0.341492 | − | 1.05101i | −0.621942 | − | 0.783063i | \(-0.713656\pi\) |
0.963435 | − | 0.267943i | \(-0.0863438\pi\) | |||||||
\(642\) | −3.01064 | − | 9.26581i | −0.118821 | − | 0.365692i | ||||
\(643\) | 12.9443 | − | 9.40456i | 0.510472 | − | 0.370880i | −0.302530 | − | 0.953140i | \(-0.597831\pi\) |
0.813003 | + | 0.582260i | \(0.197831\pi\) | |||||||
\(644\) | −4.23607 | + | 3.07768i | −0.166924 | + | 0.121278i | ||||
\(645\) | 0.118034 | + | 0.363271i | 0.00464758 | + | 0.0143038i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.89919 | − | 1.37984i | −0.0746647 | − | 0.0542471i | 0.549827 | − | 0.835279i | \(-0.314694\pi\) |
−0.624491 | + | 0.781032i | \(0.714694\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −13.4164 | + | 3.01217i | −0.526640 | + | 0.118238i | ||||
\(650\) | −3.00000 | −0.117670 | ||||||||
\(651\) | 8.28115 | + | 6.01661i | 0.324564 | + | 0.235810i | ||||
\(652\) | −3.01722 | + | 9.28605i | −0.118163 | + | 0.363670i | ||||
\(653\) | 0.218847 | + | 0.673542i | 0.00856415 | + | 0.0263577i | 0.955247 | − | 0.295808i | \(-0.0955890\pi\) |
−0.946683 | + | 0.322166i | \(0.895589\pi\) | |||||||
\(654\) | −3.78115 | + | 2.74717i | −0.147855 | + | 0.107423i | ||||
\(655\) | −1.02786 | + | 0.746787i | −0.0401620 | + | 0.0291794i | ||||
\(656\) | 2.91641 | + | 8.97578i | 0.113867 | + | 0.350445i | ||||
\(657\) | 3.57295 | − | 10.9964i | 0.139394 | − | 0.429011i | ||||
\(658\) | −3.66312 | − | 2.66141i | −0.142803 | − | 0.103753i | ||||
\(659\) | 41.8328 | 1.62958 | 0.814788 | − | 0.579760i | \(-0.196854\pi\) | ||||
0.814788 | + | 0.579760i | \(0.196854\pi\) | |||||||
\(660\) | 1.04508 | + | 1.76336i | 0.0406799 | + | 0.0686385i | ||||
\(661\) | −3.00000 | −0.116686 | −0.0583432 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583432 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(662\) | −7.35410 | − | 5.34307i | −0.285825 | − | 0.207664i | ||||
\(663\) | 1.30902 | − | 4.02874i | 0.0508380 | − | 0.156463i | ||||
\(664\) | −4.14590 | − | 12.7598i | −0.160892 | − | 0.495175i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.47214 | − | 2.52265i | 0.134543 | − | 0.0977509i | ||||
\(667\) | −6.70820 | − | 20.6457i | −0.259743 | − | 0.799406i | ||||
\(668\) | −4.69098 | + | 14.4374i | −0.181500 | + | 0.558598i | ||||
\(669\) | 10.2812 | + | 7.46969i | 0.397492 | + | 0.288795i | ||||
\(670\) | −2.18034 | −0.0842339 | ||||||||
\(671\) | −9.74671 | − | 16.4455i | −0.376268 | − | 0.634871i | ||||
\(672\) | −5.61803 | −0.216720 | ||||||||
\(673\) | 6.13525 | + | 4.45752i | 0.236497 | + | 0.171825i | 0.699721 | − | 0.714416i | \(-0.253308\pi\) |
−0.463224 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(674\) | −0.246711 | + | 0.759299i | −0.00950296 | + | 0.0292471i | ||||
\(675\) | −1.50000 | − | 4.61653i | −0.0577350 | − | 0.177690i | ||||
\(676\) | −15.7082 | + | 11.4127i | −0.604162 | + | 0.438949i | ||||
\(677\) | −18.9721 | + | 13.7841i | −0.729158 | + | 0.529765i | −0.889297 | − | 0.457330i | \(-0.848806\pi\) |
0.160139 | + | 0.987095i | \(0.448806\pi\) | |||||||
\(678\) | 2.22542 | + | 6.84915i | 0.0854669 | + | 0.263040i | ||||
\(679\) | −5.25329 | + | 16.1680i | −0.201603 | + | 0.620469i | ||||
\(680\) | −2.92705 | − | 2.12663i | −0.112247 | − | 0.0815524i | ||||
\(681\) | 18.9787 | 0.727266 | ||||||||
\(682\) | 20.4721 | − | 4.59628i | 0.783919 | − | 0.176001i | ||||
\(683\) | −32.3050 | −1.23611 | −0.618057 | − | 0.786133i | \(-0.712080\pi\) | ||||
−0.618057 | + | 0.786133i | \(0.712080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.360680 | − | 1.11006i | 0.0137809 | − | 0.0424131i | ||||
\(686\) | −0.190983 | − | 0.587785i | −0.00729177 | − | 0.0224417i | ||||
\(687\) | 9.47214 | − | 6.88191i | 0.361385 | − | 0.262561i | ||||
\(688\) | 1.50000 | − | 1.08981i | 0.0571870 | − | 0.0415488i | ||||
\(689\) | −2.35410 | − | 7.24518i | −0.0896841 | − | 0.276019i | ||||
\(690\) | −0.236068 | + | 0.726543i | −0.00898695 | + | 0.0276590i | ||||
\(691\) | −11.7812 | − | 8.55951i | −0.448176 | − | 0.325619i | 0.340699 | − | 0.940172i | \(-0.389336\pi\) |
−0.788875 | + | 0.614553i | \(0.789336\pi\) | |||||||
\(692\) | 23.6525 | 0.899132 | ||||||||
\(693\) | −3.04508 | − | 1.31433i | −0.115673 | − | 0.0499272i | ||||
\(694\) | 15.7082 | 0.596275 | ||||||||
\(695\) | −5.42705 | − | 3.94298i | −0.205860 | − | 0.149566i | ||||
\(696\) | 4.63525 | − | 14.2658i | 0.175699 | − | 0.540746i | ||||
\(697\) | −6.66312 | − | 20.5070i | −0.252384 | − | 0.776757i | ||||
\(698\) | 17.4615 | − | 12.6865i | 0.660927 | − | 0.480192i | ||||
\(699\) | −5.04508 | + | 3.66547i | −0.190823 | + | 0.138641i | ||||
\(700\) | 2.42705 | + | 7.46969i | 0.0917339 | + | 0.282328i | ||||
\(701\) | 8.34346 | − | 25.6785i | 0.315128 | − | 0.969865i | −0.660574 | − | 0.750761i | \(-0.729687\pi\) |
0.975702 | − | 0.219103i | \(-0.0703132\pi\) | |||||||
\(702\) | −0.500000 | − | 0.363271i | −0.0188713 | − | 0.0137108i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.517221 | − | 0.587785i | 0.0194935 | − | 0.0221530i | ||||
\(705\) | 2.79837 | 0.105393 | ||||||||
\(706\) | −12.7361 | − | 9.25330i | −0.479328 | − | 0.348252i | ||||
\(707\) | −1.29180 | + | 3.97574i | −0.0485830 | + | 0.149523i | ||||
\(708\) | 2.07295 | + | 6.37988i | 0.0779062 | + | 0.239771i | ||||
\(709\) | 40.9787 | − | 29.7728i | 1.53899 | − | 1.11814i | 0.588022 | − | 0.808845i | \(-0.299907\pi\) |
0.950966 | − | 0.309295i | \(-0.100093\pi\) | |||||||
\(710\) | 1.42705 | − | 1.03681i | 0.0535563 | − | 0.0389109i | ||||
\(711\) | 3.35410 | + | 10.3229i | 0.125789 | + | 0.387138i | ||||
\(712\) | −4.40983 | + | 13.5721i | −0.165265 | + | 0.508635i | ||||
\(713\) | −26.7984 | − | 19.4702i | −1.00361 | − | 0.729163i | ||||
\(714\) | 2.61803 | 0.0979775 | ||||||||
\(715\) | 0.118034 | − | 1.26133i | 0.00441422 | − | 0.0471710i | ||||
\(716\) | 3.61803 | 0.135212 | ||||||||
\(717\) | −15.4894 | − | 11.2537i | −0.578461 | − | 0.420276i | ||||
\(718\) | 6.34346 | − | 19.5232i | 0.236736 | − | 0.728598i | ||||
\(719\) | −2.66312 | − | 8.19624i | −0.0993176 | − | 0.305668i | 0.889037 | − | 0.457835i | \(-0.151375\pi\) |
−0.988355 | + | 0.152167i | \(0.951375\pi\) | |||||||
\(720\) | 0.572949 | − | 0.416272i | 0.0213525 | − | 0.0155135i | ||||
\(721\) | 10.2812 | − | 7.46969i | 0.382890 | − | 0.278186i | ||||
\(722\) | 3.62868 | + | 11.1679i | 0.135045 | + | 0.415627i | ||||
\(723\) | −7.63525 | + | 23.4989i | −0.283958 | + | 0.873933i | ||||
\(724\) | −0.309017 | − | 0.224514i | −0.0114845 | − | 0.00834400i | ||||
\(725\) | −32.5623 | −1.20933 | ||||||||
\(726\) | −6.14590 | + | 2.90617i | −0.228096 | + | 0.107858i | ||||
\(727\) | 22.1459 | 0.821346 | 0.410673 | − | 0.911783i | \(-0.365294\pi\) | ||||
0.410673 | + | 0.911783i | \(0.365294\pi\) | |||||||
\(728\) | 1.80902 | + | 1.31433i | 0.0670466 | + | 0.0487122i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0.843459 | + | 2.59590i | 0.0312178 | + | 0.0960785i | ||||
\(731\) | −3.42705 | + | 2.48990i | −0.126754 | + | 0.0920922i | ||||
\(732\) | −7.54508 | + | 5.48183i | −0.278874 | + | 0.202614i | ||||
\(733\) | 1.27458 | + | 3.92274i | 0.0470775 | + | 0.144890i | 0.971832 | − | 0.235674i | \(-0.0757299\pi\) |
−0.924755 | + | 0.380564i | \(0.875730\pi\) | |||||||
\(734\) | −2.15654 | + | 6.63715i | −0.0795994 | + | 0.244982i | ||||
\(735\) | 0.309017 | + | 0.224514i | 0.0113983 | + | 0.00828132i | ||||
\(736\) | 18.1803 | 0.670136 | ||||||||
\(737\) | −2.85410 | + | 30.4993i | −0.105132 | + | 1.12346i | ||||
\(738\) | −3.14590 | −0.115802 | ||||||||
\(739\) | −34.5344 | − | 25.0907i | −1.27037 | − | 0.922978i | −0.271153 | − | 0.962536i | \(-0.587405\pi\) |
−0.999217 | + | 0.0395585i | \(0.987405\pi\) | |||||||
\(740\) | 1.32624 | − | 4.08174i | 0.0487535 | − | 0.150048i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.80902 | − | 2.76741i | 0.139833 | − | 0.101595i | ||||
\(743\) | −20.9615 | + | 15.2294i | −0.769003 | + | 0.558713i | −0.901658 | − | 0.432449i | \(-0.857650\pi\) |
0.132656 | + | 0.991162i | \(0.457650\pi\) | |||||||
\(744\) | −7.07295 | − | 21.7683i | −0.259307 | − | 0.798065i | ||||
\(745\) | 1.54508 | − | 4.75528i | 0.0566075 | − | 0.174220i | ||||
\(746\) | 15.0902 | + | 10.9637i | 0.552490 | + | 0.401408i | ||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | −15.0172 | + | 17.0660i | −0.549084 | + | 0.623995i | ||||
\(749\) | 15.7639 | 0.576002 | ||||||||
\(750\) | 1.88197 | + | 1.36733i | 0.0687197 | + | 0.0499278i | ||||
\(751\) | −8.91641 | + | 27.4419i | −0.325364 | + | 1.00137i | 0.645912 | + | 0.763412i | \(0.276477\pi\) |
−0.971276 | + | 0.237956i | \(0.923523\pi\) | |||||||
\(752\) | −4.19756 | − | 12.9188i | −0.153069 | − | 0.471099i | ||||
\(753\) | −21.5172 | + | 15.6332i | −0.784131 | + | 0.569705i | ||||
\(754\) | −3.35410 | + | 2.43690i | −0.122149 | + | 0.0887466i | ||||
\(755\) | 2.48936 | + | 7.66145i | 0.0905970 | + | 0.278829i | ||||
\(756\) | −0.500000 | + | 1.53884i | −0.0181848 | + | 0.0559671i | ||||
\(757\) | −36.5967 | − | 26.5891i | −1.33013 | − | 0.966397i | −0.999746 | − | 0.0225510i | \(-0.992821\pi\) |
−0.330386 | − | 0.943846i | \(-0.607179\pi\) | |||||||
\(758\) | 6.70820 | 0.243653 | ||||||||
\(759\) | 9.85410 | + | 4.25325i | 0.357681 | + | 0.154383i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.0729490 | − | 0.0530006i | −0.00264440 | − | 0.00192127i | 0.586462 | − | 0.809977i | \(-0.300520\pi\) |
−0.589107 | + | 0.808055i | \(0.700520\pi\) | |||||||
\(762\) | 1.39919 | − | 4.30625i | 0.0506872 | − | 0.155999i | ||||
\(763\) | −2.33688 | − | 7.19218i | −0.0846008 | − | 0.260374i | ||||
\(764\) | 12.7812 | − | 9.28605i | 0.462406 | − | 0.335958i | ||||
\(765\) | −1.30902 | + | 0.951057i | −0.0473276 | + | 0.0343855i | ||||
\(766\) | 1.51064 | + | 4.64928i | 0.0545818 | + | 0.167985i | ||||
\(767\) | 1.28115 | − | 3.94298i | 0.0462598 | − | 0.142373i | ||||
\(768\) | 5.30902 | + | 3.85723i | 0.191573 | + | 0.139186i | ||||
\(769\) | 44.4721 | 1.60371 | 0.801853 | − | 0.597521i | \(-0.203848\pi\) | ||||
0.801853 | + | 0.597521i | \(0.203848\pi\) | |||||||
\(770\) | 0.763932 | − | 0.171513i | 0.0275302 | − | 0.00618091i | ||||
\(771\) | 26.9443 | 0.970374 | ||||||||
\(772\) | 6.61803 | + | 4.80828i | 0.238188 | + | 0.173054i | ||||
\(773\) | 3.27051 | − | 10.0656i | 0.117632 | − | 0.362034i | −0.874855 | − | 0.484385i | \(-0.839043\pi\) |
0.992487 | + | 0.122351i | \(0.0390433\pi\) | |||||||
\(774\) | 0.190983 | + | 0.587785i | 0.00686474 | + | 0.0211275i | ||||
\(775\) | −40.1976 | + | 29.2052i | −1.44394 | + | 1.04908i | ||||
\(776\) | 30.7533 | − | 22.3436i | 1.10398 | − | 0.802088i | ||||
\(777\) | 2.14590 | + | 6.60440i | 0.0769837 | + | 0.236931i | ||||
\(778\) | −3.94427 | + | 12.1392i | −0.141409 | + | 0.435212i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.618034 | −0.0221292 | ||||||||
\(781\) | −12.6353 | − | 21.3193i | −0.452125 | − | 0.762863i | ||||
\(782\) | −8.47214 | −0.302963 | ||||||||
\(783\) | −5.42705 | − | 3.94298i | −0.193947 | − | 0.140911i | ||||
\(784\) | 0.572949 | − | 1.76336i | 0.0204625 | − | 0.0629770i | ||||
\(785\) | 0.197561 | + | 0.608030i | 0.00705125 | + | 0.0217015i | ||||
\(786\) | −1.66312 | + | 1.20833i | −0.0593215 | + | 0.0430996i | ||||
\(787\) | 26.5795 | − | 19.3112i | 0.947458 | − | 0.688368i | −0.00274643 | − | 0.999996i | \(-0.500874\pi\) |
0.950204 | + | 0.311628i | \(0.100874\pi\) | |||||||
\(788\) | 4.61803 | + | 14.2128i | 0.164511 | + | 0.506312i | ||||
\(789\) | 0.218847 | − | 0.673542i | 0.00779116 | − | 0.0239787i | ||||
\(790\) | −2.07295 | − | 1.50609i | −0.0737522 | − | 0.0535841i | ||||
\(791\) | −11.6525 | −0.414314 | ||||||||
\(792\) | 3.78115 | + | 6.37988i | 0.134357 | + | 0.226699i | ||||
\(793\) | 5.76393 | 0.204683 | ||||||||
\(794\) | 12.8435 | + | 9.33132i | 0.455797 | + | 0.331156i | ||||
\(795\) | −0.899187 | + | 2.76741i | −0.0318909 | + | 0.0981500i | ||||
\(796\) | 3.78115 | + | 11.6372i | 0.134019 | + | 0.412469i | ||||
\(797\) | 26.2533 | − | 19.0741i | 0.929939 | − | 0.675640i | −0.0160387 | − | 0.999871i | \(-0.505106\pi\) |
0.945978 | + | 0.324231i | \(0.105106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.59017 | + | 29.5155i | 0.339276 | + | 1.04418i | ||||
\(800\) | 8.42705 | − | 25.9358i | 0.297941 | − | 0.916969i | ||||
\(801\) | 5.16312 | + | 3.75123i | 0.182430 | + | 0.132543i | ||||
\(802\) | −7.21478 | −0.254763 | ||||||||
\(803\) | 37.4164 | − | 8.40051i | 1.32040 | − | 0.296447i | ||||
\(804\) | 14.9443 | 0.527044 | ||||||||
\(805\) | −1.00000 | − | 0.726543i | −0.0352454 | − | 0.0256073i | ||||
\(806\) | −1.95492 | + | 6.01661i | −0.0688589 | + | 0.211926i | ||||
\(807\) | 7.39919 | + | 22.7724i | 0.260464 | + | 0.801625i | ||||
\(808\) | 7.56231 | − | 5.49434i | 0.266041 | − | 0.193290i | ||||
\(809\) | −25.0623 | + | 18.2088i | −0.881144 | + | 0.640188i | −0.933554 | − | 0.358437i | \(-0.883310\pi\) |
0.0524101 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(810\) | 0.0729490 | + | 0.224514i | 0.00256317 | + | 0.00788862i | ||||
\(811\) | −7.14590 | + | 21.9928i | −0.250926 | + | 0.772272i | 0.743679 | + | 0.668537i | \(0.233079\pi\) |
−0.994605 | + | 0.103735i | \(0.966921\pi\) | |||||||
\(812\) | 8.78115 | + | 6.37988i | 0.308158 | + | 0.223890i | ||||
\(813\) | −6.41641 | −0.225033 | ||||||||
\(814\) | 13.0689 | + | 5.64083i | 0.458064 | + | 0.197711i | ||||
\(815\) | −2.30495 | −0.0807389 | ||||||||
\(816\) | 6.35410 | + | 4.61653i | 0.222438 | + | 0.161611i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 5.03851 | + | 15.5069i | 0.176167 | + | 0.542187i | ||||
\(819\) | 0.809017 | − | 0.587785i | 0.0282693 | − | 0.0205389i | ||||
\(820\) | −2.54508 | + | 1.84911i | −0.0888782 | + | 0.0645738i | ||||
\(821\) | 1.79837 | + | 5.53483i | 0.0627637 | + | 0.193167i | 0.977521 | − | 0.210836i | \(-0.0676186\pi\) |
−0.914758 | + | 0.404003i | \(0.867619\pi\) | |||||||
\(822\) | 0.583592 | − | 1.79611i | 0.0203551 | − | 0.0626466i | ||||
\(823\) | 21.2361 | + | 15.4289i | 0.740243 | + | 0.537818i | 0.892787 | − | 0.450479i | \(-0.148747\pi\) |
−0.152544 | + | 0.988297i | \(0.548747\pi\) | |||||||
\(824\) | −28.4164 | −0.989932 | ||||||||
\(825\) | 10.6353 | − | 12.0862i | 0.370272 | − | 0.420788i | ||||
\(826\) | 2.56231 | 0.0891540 | ||||||||
\(827\) | −4.13525 | − | 3.00444i | −0.143797 | − | 0.104475i | 0.513561 | − | 0.858053i | \(-0.328326\pi\) |
−0.657358 | + | 0.753579i | \(0.728326\pi\) | |||||||
\(828\) | 1.61803 | − | 4.97980i | 0.0562306 | − | 0.173060i | ||||
\(829\) | 11.6459 | + | 35.8424i | 0.404479 | + | 1.24486i | 0.921330 | + | 0.388782i | \(0.127104\pi\) |
−0.516851 | + | 0.856075i | \(0.672896\pi\) | |||||||
\(830\) | 1.14590 | − | 0.832544i | 0.0397747 | − | 0.0288980i | ||||
\(831\) | 20.5623 | − | 14.9394i | 0.713298 | − | 0.518242i | ||||
\(832\) | 0.0729490 | + | 0.224514i | 0.00252905 | + | 0.00778362i | ||||
\(833\) | −1.30902 | + | 4.02874i | −0.0453548 | + | 0.139588i | ||||
\(834\) | −8.78115 | − | 6.37988i | −0.304066 | − | 0.220917i | ||||
\(835\) | −3.58359 | −0.124015 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.2361 | −0.353810 | ||||||||
\(838\) | −7.66312 | − | 5.56758i | −0.264718 | − | 0.192329i | ||||
\(839\) | 8.98278 | − | 27.6462i | 0.310120 | − | 0.954451i | −0.667597 | − | 0.744523i | \(-0.732677\pi\) |
0.977717 | − | 0.209928i | \(-0.0673230\pi\) | |||||||
\(840\) | −0.263932 | − | 0.812299i | −0.00910652 | − | 0.0280270i | ||||
\(841\) | −12.9443 | + | 9.40456i | −0.446354 | + | 0.324295i | ||||
\(842\) | 1.36475 | − | 0.991545i | 0.0470322 | − | 0.0341709i | ||||
\(843\) | 4.82624 | + | 14.8536i | 0.166224 | + | 0.511586i | ||||
\(844\) | −2.64590 | + | 8.14324i | −0.0910756 | + | 0.280302i | ||||
\(845\) | −3.70820 | − | 2.69417i | −0.127566 | − | 0.0926822i | ||||
\(846\) | 4.52786 | 0.155671 | ||||||||
\(847\) | −1.39919 | − | 10.9106i | −0.0480766 | − | 0.374894i | ||||
\(848\) | 14.1246 | 0.485041 | ||||||||
\(849\) | −5.89919 | − | 4.28601i | −0.202460 | − | 0.147095i | ||||
\(850\) | −3.92705 | + | 12.0862i | −0.134697 | + | 0.414554i | ||||
\(851\) | −6.94427 | − | 21.3723i | −0.238047 | − | 0.732632i | ||||
\(852\) | −9.78115 | + | 7.10642i | −0.335097 | + | 0.243462i | ||||
\(853\) | −7.44427 | + | 5.40858i | −0.254887 | + | 0.185186i | −0.707890 | − | 0.706323i | \(-0.750353\pi\) |
0.453003 | + | 0.891509i | \(0.350353\pi\) | |||||||
\(854\) | 1.10081 | + | 3.38795i | 0.0376690 | + | 0.115933i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.5172 | − | 20.7190i | −0.974699 | − | 0.708160i | ||||
\(857\) | −54.2361 | −1.85267 | −0.926334 | − | 0.376702i | \(-0.877058\pi\) | ||||
−0.926334 | + | 0.376702i | \(0.877058\pi\) | |||||||
\(858\) | 0.190983 | − | 2.04087i | 0.00652005 | − | 0.0696742i | ||||
\(859\) | −41.8328 | −1.42732 | −0.713659 | − | 0.700494i | \(-0.752963\pi\) | ||||
−0.713659 | + | 0.700494i | \(0.752963\pi\) | |||||||
\(860\) | 0.500000 | + | 0.363271i | 0.0170499 | + | 0.0123874i | ||||
\(861\) | 1.57295 | − | 4.84104i | 0.0536060 | − | 0.164982i | ||||
\(862\) | 7.21885 | + | 22.2173i | 0.245875 | + | 0.756725i | ||||
\(863\) | −25.3713 | + | 18.4333i | −0.863650 | + | 0.627478i | −0.928875 | − | 0.370392i | \(-0.879223\pi\) |
0.0652256 | + | 0.997871i | \(0.479223\pi\) | |||||||
\(864\) | 4.54508 | − | 3.30220i | 0.154627 | − | 0.112343i | ||||
\(865\) | 1.72542 | + | 5.31031i | 0.0586662 | + | 0.180556i | ||||
\(866\) | 0.493422 | − | 1.51860i | 0.0167672 | − | 0.0516040i | ||||
\(867\) | −0.763932 | − | 0.555029i | −0.0259445 | − | 0.0188498i | ||||
\(868\) | 16.5623 | 0.562161 | ||||||||
\(869\) | −23.7812 | + | 27.0256i | −0.806720 | + | 0.916781i | ||||
\(870\) | 1.58359 | 0.0536888 | ||||||||
\(871\) | −7.47214 | − | 5.42882i | −0.253184 | − | 0.183949i | ||||
\(872\) | −5.22542 | + | 16.0822i | −0.176955 | + | 0.544612i | ||||
\(873\) | −5.25329 | − | 16.1680i | −0.177797 | − | 0.547203i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.04508 | + | 2.21238i | −0.102943 | + | 0.0747922i | ||||
\(876\) | −5.78115 | − | 17.7926i | −0.195327 | − | 0.601155i | ||||
\(877\) | 12.8992 | − | 39.6996i | 0.435575 | − | 1.34056i | −0.456922 | − | 0.889507i | \(-0.651048\pi\) |
0.892497 | − | 0.451054i | \(-0.148952\pi\) | |||||||
\(878\) | 0.263932 | + | 0.191758i | 0.00890727 | + | 0.00647151i | ||||
\(879\) | −13.2361 | −0.446441 | ||||||||
\(880\) | 2.15654 | + | 0.930812i | 0.0726970 | + | 0.0313777i | ||||
\(881\) | −11.9443 | −0.402413 | −0.201206 | − | 0.979549i | \(-0.564486\pi\) | ||||
−0.201206 | + | 0.979549i | \(0.564486\pi\) | |||||||
\(882\) | 0.500000 | + | 0.363271i | 0.0168359 | + | 0.0122320i | ||||
\(883\) | −10.2082 | + | 31.4176i | −0.343533 | + | 1.05729i | 0.618831 | + | 0.785524i | \(0.287607\pi\) |
−0.962364 | + | 0.271763i | \(0.912393\pi\) | |||||||
\(884\) | −2.11803 | − | 6.51864i | −0.0712372 | − | 0.219246i | ||||
\(885\) | −1.28115 | + | 0.930812i | −0.0430655 | + | 0.0312889i | ||||
\(886\) | −18.3262 | + | 13.3148i | −0.615682 | + | 0.447319i | ||||
\(887\) | −6.63525 | − | 20.4212i | −0.222790 | − | 0.685677i | −0.998508 | − | 0.0545980i | \(-0.982612\pi\) |
0.775718 | − | 0.631079i | \(-0.217388\pi\) | |||||||
\(888\) | 4.79837 | − | 14.7679i | 0.161023 | − | 0.495577i | ||||
\(889\) | 5.92705 | + | 4.30625i | 0.198787 | + | 0.144427i | ||||
\(890\) | −1.50658 | −0.0505006 | ||||||||
\(891\) | 3.23607 | − | 0.726543i | 0.108412 | − | 0.0243401i | ||||
\(892\) | 20.5623 | 0.688477 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 2.50000 | − | 7.69421i | 0.0836125 | − | 0.257333i | ||||
\(895\) | 0.263932 | + | 0.812299i | 0.00882227 | + | 0.0271522i | ||||
\(896\) | −9.20820 | + | 6.69015i | −0.307625 | + | 0.223502i | ||||
\(897\) | −2.61803 | + | 1.90211i | −0.0874136 | + | 0.0635097i | ||||
\(898\) | −2.98936 | − | 9.20029i | −0.0997561 | − | 0.307018i | ||||
\(899\) | −21.2188 | + | 65.3049i | −0.707688 | + | 2.17804i | ||||
\(900\) | −6.35410 | − | 4.61653i | −0.211803 | − | 0.153884i | ||||
\(901\) | −32.2705 | −1.07509 | ||||||||
\(902\) | −5.31966 | − | 8.97578i | −0.177125 | − | 0.298861i | ||||
\(903\) | −1.00000 | −0.0332779 | ||||||||
\(904\) | 21.0795 | + | 15.3152i | 0.701095 | + | 0.509375i | ||||
\(905\) | 0.0278640 | − | 0.0857567i | 0.000926232 | − | 0.00285065i | ||||
\(906\) | 4.02786 | + | 12.3965i | 0.133817 | + | 0.411846i | ||||
\(907\) | −15.3541 | + | 11.1554i | −0.509825 | + | 0.370409i | −0.812757 | − | 0.582603i | \(-0.802034\pi\) |
0.302932 | + | 0.953012i | \(0.402034\pi\) | |||||||
\(908\) | 24.8435 | − | 18.0498i | 0.824459 | − | 0.599005i | ||||
\(909\) | −1.29180 | − | 3.97574i | −0.0428462 | − | 0.131867i | ||||
\(910\) | −0.0729490 | + | 0.224514i | −0.00241824 | + | 0.00744257i | ||||
\(911\) | 26.4336 | + | 19.2052i | 0.875785 | + | 0.636295i | 0.932133 | − | 0.362116i | \(-0.117946\pi\) |
−0.0563478 | + | 0.998411i | \(0.517946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1459 | − | 17.1190i | −0.335780 | − | 0.566557i | ||||
\(914\) | −7.58359 | −0.250843 | ||||||||
\(915\) | −1.78115 | − | 1.29408i | −0.0588831 | − | 0.0427811i | ||||
\(916\) | 5.85410 | − | 18.0171i | 0.193425 | − | 0.595301i | ||||
\(917\) | −1.02786 | − | 3.16344i | −0.0339431 | − | 0.104466i | ||||
\(918\) | −2.11803 | + | 1.53884i | −0.0699055 | + | 0.0507893i | ||||
\(919\) | 13.4164 | − | 9.74759i | 0.442566 | − | 0.321543i | −0.344087 | − | 0.938938i | \(-0.611812\pi\) |
0.786654 | + | 0.617394i | \(0.211812\pi\) | |||||||
\(920\) | 0.854102 | + | 2.62866i | 0.0281589 | + | 0.0866642i | ||||
\(921\) | 5.92705 | − | 18.2416i | 0.195303 | − | 0.601081i | ||||
\(922\) | 11.5902 | + | 8.42075i | 0.381702 | + | 0.277323i | ||||
\(923\) | 7.47214 | 0.245948 | ||||||||
\(924\) | −5.23607 | + | 1.17557i | −0.172254 | + | 0.0386734i | ||||
\(925\) | −33.7082 | −1.10832 | ||||||||
\(926\) | −17.9615 | − | 13.0498i | −0.590251 | − | 0.428843i | ||||
\(927\) | −3.92705 | + | 12.0862i | −0.128981 | + | 0.396964i | ||||
\(928\) | −11.6459 | − | 35.8424i | −0.382295 | − | 1.17658i | ||||
\(929\) | 12.7639 | − | 9.27354i | 0.418771 | − | 0.304255i | −0.358372 | − | 0.933579i | \(-0.616668\pi\) |
0.777143 | + | 0.629324i | \(0.216668\pi\) | |||||||
\(930\) | 1.95492 | − | 1.42033i | 0.0641042 | − | 0.0465744i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.11803 | + | 9.59632i | −0.102135 | + | 0.314338i | ||||
\(933\) | −13.5902 | − | 9.87384i | −0.444922 | − | 0.323255i | ||||
\(934\) | −19.7426 | −0.645999 | ||||||||
\(935\) | −4.92705 | − | 2.12663i | −0.161132 | − | 0.0695481i | ||||
\(936\) | −2.23607 | −0.0730882 | ||||||||
\(937\) | 5.66312 | + | 4.11450i | 0.185006 | + | 0.134415i | 0.676433 | − | 0.736504i | \(-0.263525\pi\) |
−0.491427 | + | 0.870919i | \(0.663525\pi\) | |||||||
\(938\) | 1.76393 | − | 5.42882i | 0.0575944 | − | 0.177257i | ||||
\(939\) | −4.88197 | − | 15.0251i | −0.159317 | − | 0.490327i | ||||
\(940\) | 3.66312 | − | 2.66141i | 0.119478 | − | 0.0868057i | ||||
\(941\) | 43.8328 | − | 31.8464i | 1.42891 | − | 1.03816i | 0.438690 | − | 0.898638i | \(-0.355442\pi\) |
0.990219 | − | 0.139525i | \(-0.0445575\pi\) | |||||||
\(942\) | 0.319660 | + | 0.983813i | 0.0104151 | + | 0.0320543i | ||||
\(943\) | −5.09017 | + | 15.6659i | −0.165759 | + | 0.510153i | ||||
\(944\) | 6.21885 | + | 4.51826i | 0.202406 | + | 0.147057i | ||||
\(945\) | −0.381966 | −0.0124254 | ||||||||
\(946\) | −1.35410 | + | 1.53884i | −0.0440257 | + | 0.0500321i | ||||
\(947\) | −0.618034 | −0.0200834 | −0.0100417 | − | 0.999950i | \(-0.503196\pi\) | ||||
−0.0100417 | + | 0.999950i | \(0.503196\pi\) | |||||||
\(948\) | 14.2082 | + | 10.3229i | 0.461461 | + | 0.335271i | ||||
\(949\) | −3.57295 | + | 10.9964i | −0.115983 | + | 0.356958i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.5172 | + | 14.9066i | −0.665316 | + | 0.483381i | ||||
\(952\) | 7.66312 | − | 5.56758i | 0.248363 | − | 0.180446i | ||||
\(953\) | 5.93363 | + | 18.2618i | 0.192209 | + | 0.591559i | 0.999998 | + | 0.00208665i | \(0.000664201\pi\) |
−0.807789 | + | 0.589472i | \(0.799336\pi\) | |||||||
\(954\) | −1.45492 | + | 4.47777i | −0.0471046 | + | 0.144973i | ||||
\(955\) | 3.01722 | + | 2.19214i | 0.0976350 | + | 0.0709360i | ||||
\(956\) | −30.9787 | −1.00192 | ||||||||
\(957\) | 2.07295 | − | 22.1518i | 0.0670089 | − | 0.716066i | ||||
\(958\) | −13.2918 | −0.429438 | ||||||||
\(959\) | 2.47214 | + | 1.79611i | 0.0798294 | + | 0.0579995i | ||||
\(960\) | 0.0278640 | − | 0.0857567i | 0.000899308 | − | 0.00276779i | ||||
\(961\) | 22.7984 | + | 70.1662i | 0.735431 | + | 2.26343i | ||||
\(962\) | −3.47214 | + | 2.52265i | −0.111946 | + | 0.0813336i | ||||
\(963\) | −12.7533 | + | 9.26581i | −0.410969 | + | 0.298586i | ||||
\(964\) | 12.3541 | + | 38.0220i | 0.397899 | + | 1.22461i | ||||
\(965\) | −0.596748 | + | 1.83660i | −0.0192100 | + | 0.0591223i | ||||
\(966\) | −1.61803 | − | 1.17557i | −0.0520594 | − | 0.0378234i | ||||
\(967\) | 36.2918 | 1.16707 | 0.583533 | − | 0.812090i | \(-0.301670\pi\) | ||||
0.583533 | + | 0.812090i | \(0.301670\pi\) | |||||||
\(968\) | −11.8090 | + | 21.5765i | −0.379556 | + | 0.693496i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.24671 | + | 2.35887i | 0.104246 | + | 0.0757389i | ||||
\(971\) | −7.63525 | + | 23.4989i | −0.245027 | + | 0.754116i | 0.750605 | + | 0.660751i | \(0.229762\pi\) |
−0.995632 | + | 0.0933644i | \(0.970238\pi\) | |||||||
\(972\) | −0.500000 | − | 1.53884i | −0.0160375 | − | 0.0493584i | ||||
\(973\) | 14.2082 | − | 10.3229i | 0.455494 | − | 0.330936i | ||||
\(974\) | 8.30902 | − | 6.03685i | 0.266238 | − | 0.193433i | ||||
\(975\) | 1.50000 | + | 4.61653i | 0.0480384 | + | 0.147847i | ||||
\(976\) | −3.30244 | + | 10.1639i | −0.105709 | + | 0.325337i | ||||
\(977\) | −26.6976 | − | 19.3969i | −0.854131 | − | 0.620562i | 0.0721512 | − | 0.997394i | \(-0.477014\pi\) |
−0.926282 | + | 0.376831i | \(0.877014\pi\) | |||||||
\(978\) | −3.72949 | −0.119256 | ||||||||
\(979\) | −1.97214 | + | 21.0745i | −0.0630297 | + | 0.673544i | ||||
\(980\) | 0.618034 | 0.0197424 | ||||||||
\(981\) | 6.11803 | + | 4.44501i | 0.195334 | + | 0.141918i | ||||
\(982\) | −0.708204 | + | 2.17963i | −0.0225997 | + | 0.0695547i | ||||
\(983\) | −9.25329 | − | 28.4787i | −0.295134 | − | 0.908329i | −0.983176 | − | 0.182659i | \(-0.941530\pi\) |
0.688042 | − | 0.725671i | \(-0.258470\pi\) | |||||||
\(984\) | −9.20820 | + | 6.69015i | −0.293547 | + | 0.213274i | ||||
\(985\) | −2.85410 | + | 2.07363i | −0.0909393 | + | 0.0660712i | ||||
\(986\) | 5.42705 | + | 16.7027i | 0.172833 | + | 0.531924i | ||||
\(987\) | −2.26393 | + | 6.96767i | −0.0720618 | + | 0.221783i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.23607 | 0.102901 | ||||||||
\(990\) | −0.517221 | + | 0.587785i | −0.0164384 | + | 0.0186810i | ||||
\(991\) | 33.6312 | 1.06833 | 0.534165 | − | 0.845380i | \(-0.320626\pi\) | ||||
0.534165 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(992\) | −46.5238 | − | 33.8015i | −1.47713 | − | 1.07320i | ||||
\(993\) | −4.54508 | + | 13.9883i | −0.144234 | + | 0.443906i | ||||
\(994\) | 1.42705 | + | 4.39201i | 0.0452633 | + | 0.139306i | ||||
\(995\) | −2.33688 | + | 1.69784i | −0.0740841 | + | 0.0538253i | ||||
\(996\) | −7.85410 | + | 5.70634i | −0.248867 | + | 0.180812i | ||||
\(997\) | 0.437694 | + | 1.34708i | 0.0138619 | + | 0.0426626i | 0.957748 | − | 0.287608i | \(-0.0928600\pi\) |
−0.943886 | + | 0.330271i | \(0.892860\pi\) | |||||||
\(998\) | 0.954915 | − | 2.93893i | 0.0302273 | − | 0.0930301i | ||||
\(999\) | −5.61803 | − | 4.08174i | −0.177747 | − | 0.129141i |
(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 | 231.2.j.d.169.1 | ✓ | 4 | |
3.2 | odd | 2 | 693.2.m.b.631.1 | 4 | |||
11.3 | even | 5 | inner | 231.2.j.d.190.1 | yes | 4 | |
11.5 | even | 5 | 2541.2.a.bb.1.1 | 2 | |||
11.6 | odd | 10 | 2541.2.a.s.1.2 | 2 | |||
33.5 | odd | 10 | 7623.2.a.ba.1.2 | 2 | |||
33.14 | odd | 10 | 693.2.m.b.190.1 | 4 | |||
33.17 | even | 10 | 7623.2.a.bp.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.d.169.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
231.2.j.d.190.1 | yes | 4 | 11.3 | even | 5 | inner | |
693.2.m.b.190.1 | 4 | 33.14 | odd | 10 | |||
693.2.m.b.631.1 | 4 | 3.2 | odd | 2 | |||
2541.2.a.s.1.2 | 2 | 11.6 | odd | 10 | |||
2541.2.a.bb.1.1 | 2 | 11.5 | even | 5 | |||
7623.2.a.ba.1.2 | 2 | 33.5 | odd | 10 | |||
7623.2.a.bp.1.1 | 2 | 33.17 | even | 10 |