Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.1816890625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 8x^{6} - 15x^{5} + 41x^{4} + 15x^{3} + 62x^{2} + 133x + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(0.594055 - 1.82831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.901 |
Dual form | 930.2.n.b.481.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.785038 | − | 2.41610i | −0.296716 | − | 0.913199i | −0.982639 | − | 0.185525i | \(-0.940601\pi\) |
0.685923 | − | 0.727674i | \(-0.259399\pi\) | |||||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −0.809017 | − | 0.587785i | −0.255834 | − | 0.185874i | ||||
\(11\) | −0.903072 | − | 2.77937i | −0.272286 | − | 0.838012i | −0.989925 | − | 0.141595i | \(-0.954777\pi\) |
0.717638 | − | 0.696416i | \(-0.245223\pi\) | |||||||
\(12\) | 0.809017 | + | 0.587785i | 0.233543 | + | 0.169679i | ||||
\(13\) | 4.17329 | − | 3.03207i | 1.15746 | − | 0.840946i | 0.168007 | − | 0.985786i | \(-0.446267\pi\) |
0.989455 | + | 0.144840i | \(0.0462668\pi\) | |||||||
\(14\) | 0.785038 | − | 2.41610i | 0.209810 | − | 0.645730i | ||||
\(15\) | −0.809017 | + | 0.587785i | −0.208887 | + | 0.151765i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 0.132854 | − | 0.408882i | 0.0322218 | − | 0.0991684i | −0.933652 | − | 0.358181i | \(-0.883397\pi\) |
0.965874 | + | 0.259013i | \(0.0833971\pi\) | |||||||
\(18\) | 0.809017 | − | 0.587785i | 0.190687 | − | 0.138542i | ||||
\(19\) | −1.30150 | − | 0.945592i | −0.298584 | − | 0.216934i | 0.428399 | − | 0.903590i | \(-0.359078\pi\) |
−0.726982 | + | 0.686656i | \(0.759078\pi\) | |||||||
\(20\) | −0.309017 | − | 0.951057i | −0.0690983 | − | 0.212663i | ||||
\(21\) | −2.05526 | − | 1.49323i | −0.448494 | − | 0.325850i | ||||
\(22\) | 0.903072 | − | 2.77937i | 0.192536 | − | 0.592564i | ||||
\(23\) | 0.461201 | − | 1.41943i | 0.0961671 | − | 0.295972i | −0.891389 | − | 0.453239i | \(-0.850268\pi\) |
0.987556 | + | 0.157267i | \(0.0502684\pi\) | |||||||
\(24\) | 0.309017 | + | 0.951057i | 0.0630778 | + | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.15847 | 1.01166 | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 2.05526 | − | 1.49323i | 0.388407 | − | 0.282194i | ||||
\(29\) | 1.21496 | + | 0.882722i | 0.225613 | + | 0.163917i | 0.694850 | − | 0.719155i | \(-0.255471\pi\) |
−0.469237 | + | 0.883072i | \(0.655471\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −0.753761 | − | 5.51651i | −0.135379 | − | 0.990794i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.36427 | − | 1.71775i | −0.411567 | − | 0.299021i | ||||
\(34\) | 0.347816 | − | 0.252703i | 0.0596499 | − | 0.0433382i | ||||
\(35\) | 0.785038 | + | 2.41610i | 0.132696 | + | 0.408395i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.99425 | 1.14985 | 0.574924 | − | 0.818207i | \(-0.305032\pi\) | ||||
0.574924 | + | 0.818207i | \(0.305032\pi\) | |||||||
\(38\) | −0.497127 | − | 1.53000i | −0.0806447 | − | 0.248199i | ||||
\(39\) | 1.59406 | − | 4.90600i | 0.255253 | − | 0.785588i | ||||
\(40\) | 0.309017 | − | 0.951057i | 0.0488599 | − | 0.150375i | ||||
\(41\) | 2.47766 | + | 1.80012i | 0.386945 | + | 0.281132i | 0.764203 | − | 0.644976i | \(-0.223133\pi\) |
−0.377257 | + | 0.926108i | \(0.623133\pi\) | |||||||
\(42\) | −0.785038 | − | 2.41610i | −0.121134 | − | 0.372812i | ||||
\(43\) | 5.25540 | + | 3.81827i | 0.801441 | + | 0.582281i | 0.911336 | − | 0.411662i | \(-0.135052\pi\) |
−0.109896 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(44\) | 2.36427 | − | 1.71775i | 0.356428 | − | 0.258960i | ||||
\(45\) | −0.309017 | + | 0.951057i | −0.0460655 | + | 0.141775i | ||||
\(46\) | 1.20744 | − | 0.877257i | 0.178027 | − | 0.129344i | ||||
\(47\) | −9.24500 | + | 6.71689i | −1.34852 | + | 0.979759i | −0.349439 | + | 0.936959i | \(0.613628\pi\) |
−0.999084 | + | 0.0427997i | \(0.986372\pi\) | |||||||
\(48\) | −0.309017 | + | 0.951057i | −0.0446028 | + | 0.137273i | ||||
\(49\) | 0.441871 | − | 0.321038i | 0.0631244 | − | 0.0458626i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | −0.132854 | − | 0.408882i | −0.0186033 | − | 0.0572549i | ||||
\(52\) | 4.17329 | + | 3.03207i | 0.578731 | + | 0.420473i | ||||
\(53\) | 1.63108 | − | 5.01994i | 0.224046 | − | 0.689542i | −0.774341 | − | 0.632768i | \(-0.781919\pi\) |
0.998387 | − | 0.0567739i | \(-0.0180814\pi\) | |||||||
\(54\) | 0.309017 | − | 0.951057i | 0.0420519 | − | 0.129422i | ||||
\(55\) | 0.903072 | + | 2.77937i | 0.121770 | + | 0.374770i | ||||
\(56\) | 2.54044 | 0.339480 | ||||||||
\(57\) | −1.60874 | −0.213082 | ||||||||
\(58\) | 0.464074 | + | 1.42827i | 0.0609359 | + | 0.187541i | ||||
\(59\) | 5.59569 | − | 4.06551i | 0.728497 | − | 0.529284i | −0.160591 | − | 0.987021i | \(-0.551340\pi\) |
0.889088 | + | 0.457737i | \(0.151340\pi\) | |||||||
\(60\) | −0.809017 | − | 0.587785i | −0.104444 | − | 0.0758827i | ||||
\(61\) | −4.69891 | −0.601633 | −0.300817 | − | 0.953682i | \(-0.597259\pi\) | ||||
−0.300817 | + | 0.953682i | \(0.597259\pi\) | |||||||
\(62\) | 2.63272 | − | 4.90600i | 0.334355 | − | 0.623062i | ||||
\(63\) | −2.54044 | −0.320065 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −4.17329 | + | 3.03207i | −0.517633 | + | 0.376082i | ||||
\(66\) | −0.903072 | − | 2.77937i | −0.111160 | − | 0.342117i | ||||
\(67\) | −11.6213 | −1.41977 | −0.709884 | − | 0.704318i | \(-0.751253\pi\) | ||||
−0.709884 | + | 0.704318i | \(0.751253\pi\) | |||||||
\(68\) | 0.429924 | 0.0521359 | ||||||||
\(69\) | −0.461201 | − | 1.41943i | −0.0555221 | − | 0.170879i | ||||
\(70\) | −0.785038 | + | 2.41610i | −0.0938300 | + | 0.288779i | ||||
\(71\) | −4.12711 | + | 12.7019i | −0.489798 | + | 1.50744i | 0.335113 | + | 0.942178i | \(0.391226\pi\) |
−0.824910 | + | 0.565264i | \(0.808774\pi\) | |||||||
\(72\) | 0.809017 | + | 0.587785i | 0.0953436 | + | 0.0692712i | ||||
\(73\) | 2.96926 | + | 9.13845i | 0.347526 | + | 1.06957i | 0.960218 | + | 0.279253i | \(0.0900868\pi\) |
−0.612692 | + | 0.790322i | \(0.709913\pi\) | |||||||
\(74\) | 5.65847 | + | 4.11112i | 0.657784 | + | 0.477908i | ||||
\(75\) | 0.809017 | − | 0.587785i | 0.0934172 | − | 0.0678716i | ||||
\(76\) | 0.497127 | − | 1.53000i | 0.0570244 | − | 0.175503i | ||||
\(77\) | −6.00629 | + | 4.36382i | −0.684480 | + | 0.497304i | ||||
\(78\) | 4.17329 | − | 3.03207i | 0.472532 | − | 0.343315i | ||||
\(79\) | 2.00738 | − | 6.17809i | 0.225848 | − | 0.695090i | −0.772356 | − | 0.635190i | \(-0.780922\pi\) |
0.998204 | − | 0.0598998i | \(-0.0190781\pi\) | |||||||
\(80\) | 0.809017 | − | 0.587785i | 0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0.946381 | + | 2.91266i | 0.104510 | + | 0.321650i | ||||
\(83\) | 1.41953 | + | 1.03135i | 0.155814 | + | 0.113205i | 0.662960 | − | 0.748655i | \(-0.269300\pi\) |
−0.507147 | + | 0.861860i | \(0.669300\pi\) | |||||||
\(84\) | 0.785038 | − | 2.41610i | 0.0856547 | − | 0.263618i | ||||
\(85\) | −0.132854 | + | 0.408882i | −0.0144100 | + | 0.0443495i | ||||
\(86\) | 2.00738 | + | 6.17809i | 0.216462 | + | 0.666201i | ||||
\(87\) | 1.50178 | 0.161007 | ||||||||
\(88\) | 2.92240 | 0.311529 | ||||||||
\(89\) | −2.26633 | − | 6.97506i | −0.240231 | − | 0.739354i | −0.996384 | − | 0.0849602i | \(-0.972924\pi\) |
0.756154 | − | 0.654394i | \(-0.227076\pi\) | |||||||
\(90\) | −0.809017 | + | 0.587785i | −0.0852779 | + | 0.0619580i | ||||
\(91\) | −10.6020 | − | 7.70279i | −1.11139 | − | 0.807472i | ||||
\(92\) | 1.49248 | 0.155602 | ||||||||
\(93\) | −3.85233 | − | 4.01990i | −0.399468 | − | 0.416844i | ||||
\(94\) | −11.4275 | −1.17865 | ||||||||
\(95\) | 1.30150 | + | 0.945592i | 0.133531 | + | 0.0970157i | ||||
\(96\) | −0.809017 | + | 0.587785i | −0.0825700 | + | 0.0599906i | ||||
\(97\) | −0.229782 | − | 0.707195i | −0.0233308 | − | 0.0718048i | 0.938713 | − | 0.344699i | \(-0.112019\pi\) |
−0.962044 | + | 0.272894i | \(0.912019\pi\) | |||||||
\(98\) | 0.546182 | 0.0551727 | ||||||||
\(99\) | −2.92240 | −0.293713 | ||||||||
\(100\) | 0.309017 | + | 0.951057i | 0.0309017 | + | 0.0951057i | ||||
\(101\) | −1.41502 | + | 4.35498i | −0.140800 | + | 0.433337i | −0.996447 | − | 0.0842226i | \(-0.973159\pi\) |
0.855647 | + | 0.517559i | \(0.173159\pi\) | |||||||
\(102\) | 0.132854 | − | 0.408882i | 0.0131545 | − | 0.0404853i | ||||
\(103\) | 1.23142 | + | 0.894679i | 0.121335 | + | 0.0881553i | 0.646798 | − | 0.762661i | \(-0.276108\pi\) |
−0.525463 | + | 0.850817i | \(0.676108\pi\) | |||||||
\(104\) | 1.59406 | + | 4.90600i | 0.156310 | + | 0.481073i | ||||
\(105\) | 2.05526 | + | 1.49323i | 0.200572 | + | 0.145724i | ||||
\(106\) | 4.27022 | − | 3.10250i | 0.414760 | − | 0.301341i | ||||
\(107\) | −2.53866 | + | 7.81320i | −0.245422 | + | 0.755330i | 0.750145 | + | 0.661273i | \(0.229984\pi\) |
−0.995567 | + | 0.0940569i | \(0.970016\pi\) | |||||||
\(108\) | 0.809017 | − | 0.587785i | 0.0778477 | − | 0.0565597i | ||||
\(109\) | 10.4736 | − | 7.60948i | 1.00318 | − | 0.728856i | 0.0404156 | − | 0.999183i | \(-0.487132\pi\) |
0.962769 | + | 0.270327i | \(0.0871318\pi\) | |||||||
\(110\) | −0.903072 | + | 2.77937i | −0.0861045 | + | 0.265003i | ||||
\(111\) | 5.65847 | − | 4.11112i | 0.537078 | − | 0.390210i | ||||
\(112\) | 2.05526 | + | 1.49323i | 0.194203 | + | 0.141097i | ||||
\(113\) | 1.00629 | + | 3.09703i | 0.0946634 | + | 0.291344i | 0.987166 | − | 0.159699i | \(-0.0510522\pi\) |
−0.892502 | + | 0.451043i | \(0.851052\pi\) | |||||||
\(114\) | −1.30150 | − | 0.945592i | −0.121896 | − | 0.0885628i | ||||
\(115\) | −0.461201 | + | 1.41943i | −0.0430072 | + | 0.132363i | ||||
\(116\) | −0.464074 | + | 1.42827i | −0.0430882 | + | 0.132612i | ||||
\(117\) | −1.59406 | − | 4.90600i | −0.147370 | − | 0.453560i | ||||
\(118\) | 6.91666 | 0.636730 | ||||||||
\(119\) | −1.09219 | −0.100121 | ||||||||
\(120\) | −0.309017 | − | 0.951057i | −0.0282093 | − | 0.0868192i | ||||
\(121\) | 1.98983 | − | 1.44570i | 0.180894 | − | 0.131427i | ||||
\(122\) | −3.80150 | − | 2.76195i | −0.344171 | − | 0.250055i | ||||
\(123\) | 3.06255 | 0.276141 | ||||||||
\(124\) | 5.01358 | − | 2.42156i | 0.450233 | − | 0.217463i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.05526 | − | 1.49323i | −0.183097 | − | 0.133028i | ||||
\(127\) | −2.33764 | + | 1.69840i | −0.207432 | + | 0.150708i | −0.686651 | − | 0.726987i | \(-0.740920\pi\) |
0.479219 | + | 0.877695i | \(0.340920\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 6.49603 | 0.571944 | ||||||||
\(130\) | −5.15847 | −0.452428 | ||||||||
\(131\) | 5.24897 | + | 16.1547i | 0.458605 | + | 1.41144i | 0.866850 | + | 0.498569i | \(0.166141\pi\) |
−0.408245 | + | 0.912872i | \(0.633859\pi\) | |||||||
\(132\) | 0.903072 | − | 2.77937i | 0.0786023 | − | 0.241913i | ||||
\(133\) | −1.26292 | + | 3.88687i | −0.109509 | + | 0.337034i | ||||
\(134\) | −9.40184 | − | 6.83083i | −0.812195 | − | 0.590094i | ||||
\(135\) | 0.309017 | + | 0.951057i | 0.0265959 | + | 0.0818539i | ||||
\(136\) | 0.347816 | + | 0.252703i | 0.0298250 | + | 0.0216691i | ||||
\(137\) | −1.40307 | + | 1.01939i | −0.119873 | + | 0.0870925i | −0.646106 | − | 0.763247i | \(-0.723604\pi\) |
0.526234 | + | 0.850340i | \(0.323604\pi\) | |||||||
\(138\) | 0.461201 | − | 1.41943i | 0.0392601 | − | 0.120830i | ||||
\(139\) | −16.3904 | + | 11.9083i | −1.39022 | + | 1.01005i | −0.394377 | + | 0.918949i | \(0.629039\pi\) |
−0.995841 | + | 0.0911038i | \(0.970961\pi\) | |||||||
\(140\) | −2.05526 | + | 1.49323i | −0.173701 | + | 0.126201i | ||||
\(141\) | −3.53128 | + | 10.8682i | −0.297387 | + | 0.915264i | ||||
\(142\) | −10.8049 | + | 7.85023i | −0.906728 | + | 0.658776i | ||||
\(143\) | −12.1960 | − | 8.86094i | −1.01988 | − | 0.740989i | ||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | −1.21496 | − | 0.882722i | −0.100897 | − | 0.0733060i | ||||
\(146\) | −2.96926 | + | 9.13845i | −0.245738 | + | 0.756304i | ||||
\(147\) | 0.168780 | − | 0.519450i | 0.0139207 | − | 0.0428435i | ||||
\(148\) | 2.16134 | + | 6.65193i | 0.177661 | + | 0.546785i | ||||
\(149\) | −2.53142 | −0.207382 | −0.103691 | − | 0.994610i | \(-0.533065\pi\) | ||||
−0.103691 | + | 0.994610i | \(0.533065\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 3.01482 | + | 9.27866i | 0.245343 | + | 0.755087i | 0.995580 | + | 0.0939182i | \(0.0299392\pi\) |
−0.750237 | + | 0.661169i | \(0.770061\pi\) | |||||||
\(152\) | 1.30150 | − | 0.945592i | 0.105565 | − | 0.0766976i | ||||
\(153\) | −0.347816 | − | 0.252703i | −0.0281192 | − | 0.0204298i | ||||
\(154\) | −7.42418 | −0.598257 | ||||||||
\(155\) | 0.753761 | + | 5.51651i | 0.0605435 | + | 0.443096i | ||||
\(156\) | 5.15847 | 0.413008 | ||||||||
\(157\) | −0.0851188 | − | 0.0618425i | −0.00679322 | − | 0.00493557i | 0.584383 | − | 0.811478i | \(-0.301336\pi\) |
−0.591177 | + | 0.806542i | \(0.701336\pi\) | |||||||
\(158\) | 5.25540 | − | 3.81827i | 0.418097 | − | 0.303765i | ||||
\(159\) | −1.63108 | − | 5.01994i | −0.129353 | − | 0.398107i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.79155 | −0.298816 | ||||||||
\(162\) | −0.309017 | − | 0.951057i | −0.0242787 | − | 0.0747221i | ||||
\(163\) | 6.48797 | − | 19.9679i | 0.508177 | − | 1.56401i | −0.287187 | − | 0.957875i | \(-0.592720\pi\) |
0.795363 | − | 0.606133i | \(-0.207280\pi\) | |||||||
\(164\) | −0.946381 | + | 2.91266i | −0.0739000 | + | 0.227441i | ||||
\(165\) | 2.36427 | + | 1.71775i | 0.184058 | + | 0.133726i | ||||
\(166\) | 0.542212 | + | 1.66876i | 0.0420838 | + | 0.129521i | ||||
\(167\) | 1.25089 | + | 0.908823i | 0.0967966 | + | 0.0703268i | 0.635131 | − | 0.772405i | \(-0.280946\pi\) |
−0.538334 | + | 0.842731i | \(0.680946\pi\) | |||||||
\(168\) | 2.05526 | − | 1.49323i | 0.158566 | − | 0.115205i | ||||
\(169\) | 4.20567 | − | 12.9437i | 0.323513 | − | 0.995670i | ||||
\(170\) | −0.347816 | + | 0.252703i | −0.0266762 | + | 0.0193814i | ||||
\(171\) | −1.30150 | + | 0.945592i | −0.0995279 | + | 0.0723112i | ||||
\(172\) | −2.00738 | + | 6.17809i | −0.153062 | + | 0.471075i | ||||
\(173\) | −12.3841 | + | 8.99761i | −0.941549 | + | 0.684075i | −0.948793 | − | 0.315898i | \(-0.897694\pi\) |
0.00724400 | + | 0.999974i | \(0.497694\pi\) | |||||||
\(174\) | 1.21496 | + | 0.882722i | 0.0921060 | + | 0.0669189i | ||||
\(175\) | −0.785038 | − | 2.41610i | −0.0593433 | − | 0.182640i | ||||
\(176\) | 2.36427 | + | 1.71775i | 0.178214 | + | 0.129480i | ||||
\(177\) | 2.13736 | − | 6.57813i | 0.160654 | − | 0.494443i | ||||
\(178\) | 2.26633 | − | 6.97506i | 0.169869 | − | 0.522803i | ||||
\(179\) | 2.80226 | + | 8.62447i | 0.209451 | + | 0.644623i | 0.999501 | + | 0.0315811i | \(0.0100543\pi\) |
−0.790051 | + | 0.613042i | \(0.789946\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 16.6432 | 1.23708 | 0.618539 | − | 0.785754i | \(-0.287725\pi\) | ||||
0.618539 | + | 0.785754i | \(0.287725\pi\) | |||||||
\(182\) | −4.04960 | − | 12.4634i | −0.300176 | − | 0.923847i | ||||
\(183\) | −3.80150 | + | 2.76195i | −0.281015 | + | 0.204169i | ||||
\(184\) | 1.20744 | + | 0.877257i | 0.0890137 | + | 0.0646722i | ||||
\(185\) | −6.99425 | −0.514228 | ||||||||
\(186\) | −0.753761 | − | 5.51651i | −0.0552684 | − | 0.404490i | ||||
\(187\) | −1.25641 | −0.0918778 | ||||||||
\(188\) | −9.24500 | − | 6.71689i | −0.674261 | − | 0.489879i | ||||
\(189\) | −2.05526 | + | 1.49323i | −0.149498 | + | 0.108617i | ||||
\(190\) | 0.497127 | + | 1.53000i | 0.0360654 | + | 0.110998i | ||||
\(191\) | 10.3702 | 0.750361 | 0.375181 | − | 0.926952i | \(-0.377581\pi\) | ||||
0.375181 | + | 0.926952i | \(0.377581\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 1.77943 | + | 5.47652i | 0.128086 | + | 0.394209i | 0.994451 | − | 0.105203i | \(-0.0335494\pi\) |
−0.866365 | + | 0.499412i | \(0.833549\pi\) | |||||||
\(194\) | 0.229782 | − | 0.707195i | 0.0164974 | − | 0.0507737i | ||||
\(195\) | −1.59406 | + | 4.90600i | −0.114153 | + | 0.351326i | ||||
\(196\) | 0.441871 | + | 0.321038i | 0.0315622 | + | 0.0229313i | ||||
\(197\) | 4.68865 | + | 14.4302i | 0.334053 | + | 1.02811i | 0.967187 | + | 0.254066i | \(0.0817681\pi\) |
−0.633134 | + | 0.774042i | \(0.718232\pi\) | |||||||
\(198\) | −2.36427 | − | 1.71775i | −0.168022 | − | 0.122075i | ||||
\(199\) | 18.1066 | − | 13.1552i | 1.28354 | − | 0.932550i | 0.283891 | − | 0.958857i | \(-0.408375\pi\) |
0.999654 | + | 0.0263067i | \(0.00837465\pi\) | |||||||
\(200\) | −0.309017 | + | 0.951057i | −0.0218508 | + | 0.0672499i | ||||
\(201\) | −9.40184 | + | 6.83083i | −0.663154 | + | 0.481810i | ||||
\(202\) | −3.70457 | + | 2.69153i | −0.260652 | + | 0.189375i | ||||
\(203\) | 1.17895 | − | 3.62844i | 0.0827461 | − | 0.254666i | ||||
\(204\) | 0.347816 | − | 0.252703i | 0.0243520 | − | 0.0176927i | ||||
\(205\) | −2.47766 | − | 1.80012i | −0.173047 | − | 0.125726i | ||||
\(206\) | 0.470360 | + | 1.44762i | 0.0327716 | + | 0.100860i | ||||
\(207\) | −1.20744 | − | 0.877257i | −0.0839229 | − | 0.0609736i | ||||
\(208\) | −1.59406 | + | 4.90600i | −0.110528 | + | 0.340170i | ||||
\(209\) | −1.45281 | + | 4.47128i | −0.100493 | + | 0.309285i | ||||
\(210\) | 0.785038 | + | 2.41610i | 0.0541728 | + | 0.166727i | ||||
\(211\) | −1.48318 | −0.102106 | −0.0510532 | − | 0.998696i | \(-0.516258\pi\) | ||||
−0.0510532 | + | 0.998696i | \(0.516258\pi\) | |||||||
\(212\) | 5.27828 | 0.362514 | ||||||||
\(213\) | 4.12711 | + | 12.7019i | 0.282785 | + | 0.870322i | ||||
\(214\) | −6.64630 | + | 4.82882i | −0.454332 | + | 0.330091i | ||||
\(215\) | −5.25540 | − | 3.81827i | −0.358415 | − | 0.260404i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −12.7367 | + | 6.15183i | −0.864623 | + | 0.417613i | ||||
\(218\) | 12.9460 | 0.876815 | ||||||||
\(219\) | 7.77363 | + | 5.64787i | 0.525293 | + | 0.381648i | ||||
\(220\) | −2.36427 | + | 1.71775i | −0.159399 | + | 0.115810i | ||||
\(221\) | −0.685322 | − | 2.10921i | −0.0460998 | − | 0.141881i | ||||
\(222\) | 6.99425 | 0.469424 | ||||||||
\(223\) | 0.334454 | 0.0223967 | 0.0111983 | − | 0.999937i | \(-0.496435\pi\) | ||||
0.0111983 | + | 0.999937i | \(0.496435\pi\) | |||||||
\(224\) | 0.785038 | + | 2.41610i | 0.0524526 | + | 0.161432i | ||||
\(225\) | 0.309017 | − | 0.951057i | 0.0206011 | − | 0.0634038i | ||||
\(226\) | −1.00629 | + | 3.09703i | −0.0669372 | + | 0.206011i | ||||
\(227\) | −8.69749 | − | 6.31910i | −0.577273 | − | 0.419413i | 0.260467 | − | 0.965483i | \(-0.416123\pi\) |
−0.837740 | + | 0.546069i | \(0.816123\pi\) | |||||||
\(228\) | −0.497127 | − | 1.53000i | −0.0329230 | − | 0.101327i | ||||
\(229\) | 12.4932 | + | 9.07687i | 0.825577 | + | 0.599817i | 0.918304 | − | 0.395875i | \(-0.129559\pi\) |
−0.0927278 | + | 0.995691i | \(0.529559\pi\) | |||||||
\(230\) | −1.20744 | + | 0.877257i | −0.0796163 | + | 0.0578446i | ||||
\(231\) | −2.29420 | + | 7.06081i | −0.150947 | + | 0.464567i | ||||
\(232\) | −1.21496 | + | 0.882722i | −0.0797662 | + | 0.0579535i | ||||
\(233\) | −3.99677 | + | 2.90382i | −0.261837 | + | 0.190236i | −0.710956 | − | 0.703236i | \(-0.751738\pi\) |
0.449120 | + | 0.893472i | \(0.351738\pi\) | |||||||
\(234\) | 1.59406 | − | 4.90600i | 0.104207 | − | 0.320715i | ||||
\(235\) | 9.24500 | − | 6.71689i | 0.603078 | − | 0.438162i | ||||
\(236\) | 5.59569 | + | 4.06551i | 0.364249 | + | 0.264642i | ||||
\(237\) | −2.00738 | − | 6.17809i | −0.130394 | − | 0.401310i | ||||
\(238\) | −0.883604 | − | 0.641976i | −0.0572755 | − | 0.0416131i | ||||
\(239\) | 5.76371 | − | 17.7389i | 0.372823 | − | 1.14743i | −0.572112 | − | 0.820175i | \(-0.693876\pi\) |
0.944935 | − | 0.327257i | \(-0.106124\pi\) | |||||||
\(240\) | 0.309017 | − | 0.951057i | 0.0199470 | − | 0.0613904i | ||||
\(241\) | −1.86647 | − | 5.74440i | −0.120230 | − | 0.370029i | 0.872772 | − | 0.488128i | \(-0.162320\pi\) |
−0.993002 | + | 0.118099i | \(0.962320\pi\) | |||||||
\(242\) | 2.45956 | 0.158107 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.45204 | − | 4.46893i | −0.0929575 | − | 0.286094i | ||||
\(245\) | −0.441871 | + | 0.321038i | −0.0282301 | + | 0.0205104i | ||||
\(246\) | 2.47766 | + | 1.80012i | 0.157970 | + | 0.114772i | ||||
\(247\) | −8.29862 | −0.528029 | ||||||||
\(248\) | 5.47943 | + | 0.987825i | 0.347944 | + | 0.0627270i | ||||
\(249\) | 1.75464 | 0.111195 | ||||||||
\(250\) | −0.809017 | − | 0.587785i | −0.0511667 | − | 0.0371748i | ||||
\(251\) | −20.1786 | + | 14.6606i | −1.27366 | + | 0.925368i | −0.999342 | − | 0.0362712i | \(-0.988452\pi\) |
−0.274318 | + | 0.961639i | \(0.588452\pi\) | |||||||
\(252\) | −0.785038 | − | 2.41610i | −0.0494527 | − | 0.152200i | ||||
\(253\) | −4.36162 | −0.274213 | ||||||||
\(254\) | −2.88949 | −0.181303 | ||||||||
\(255\) | 0.132854 | + | 0.408882i | 0.00831963 | + | 0.0256052i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −7.68245 | + | 23.6441i | −0.479218 | + | 1.47488i | 0.360965 | + | 0.932579i | \(0.382447\pi\) |
−0.840183 | + | 0.542302i | \(0.817553\pi\) | |||||||
\(258\) | 5.25540 | + | 3.81827i | 0.327187 | + | 0.237715i | ||||
\(259\) | −5.49076 | − | 16.8988i | −0.341179 | − | 1.05004i | ||||
\(260\) | −4.17329 | − | 3.03207i | −0.258816 | − | 0.188041i | ||||
\(261\) | 1.21496 | − | 0.882722i | 0.0752043 | − | 0.0546391i | ||||
\(262\) | −5.24897 | + | 16.1547i | −0.324283 | + | 0.998040i | ||||
\(263\) | 5.22426 | − | 3.79565i | 0.322142 | − | 0.234050i | −0.414947 | − | 0.909846i | \(-0.636200\pi\) |
0.737089 | + | 0.675796i | \(0.236200\pi\) | |||||||
\(264\) | 2.36427 | − | 1.71775i | 0.145511 | − | 0.105720i | ||||
\(265\) | −1.63108 | + | 5.01994i | −0.100196 | + | 0.308373i | ||||
\(266\) | −3.30637 | + | 2.40222i | −0.202726 | + | 0.147289i | ||||
\(267\) | −5.93334 | − | 4.31082i | −0.363114 | − | 0.263818i | ||||
\(268\) | −3.59118 | − | 11.0525i | −0.219366 | − | 0.675140i | ||||
\(269\) | 24.1921 | + | 17.5766i | 1.47502 | + | 1.07167i | 0.979119 | + | 0.203287i | \(0.0651626\pi\) |
0.495902 | + | 0.868378i | \(0.334837\pi\) | |||||||
\(270\) | −0.309017 | + | 0.951057i | −0.0188062 | + | 0.0578795i | ||||
\(271\) | 7.51435 | − | 23.1268i | 0.456464 | − | 1.40485i | −0.412943 | − | 0.910757i | \(-0.635499\pi\) |
0.869408 | − | 0.494096i | \(-0.164501\pi\) | |||||||
\(272\) | 0.132854 | + | 0.408882i | 0.00805544 | + | 0.0247921i | ||||
\(273\) | −13.1048 | −0.793137 | ||||||||
\(274\) | −1.73429 | −0.104772 | ||||||||
\(275\) | −0.903072 | − | 2.77937i | −0.0544573 | − | 0.167602i | ||||
\(276\) | 1.20744 | − | 0.877257i | 0.0726794 | − | 0.0528047i | ||||
\(277\) | −11.0544 | − | 8.03148i | −0.664193 | − | 0.482565i | 0.203883 | − | 0.978995i | \(-0.434644\pi\) |
−0.868076 | + | 0.496430i | \(0.834644\pi\) | |||||||
\(278\) | −20.2597 | −1.21510 | ||||||||
\(279\) | −5.47943 | − | 0.987825i | −0.328045 | − | 0.0591396i | ||||
\(280\) | −2.54044 | −0.151820 | ||||||||
\(281\) | −11.1363 | − | 8.09097i | −0.664334 | − | 0.482667i | 0.203790 | − | 0.979015i | \(-0.434674\pi\) |
−0.868124 | + | 0.496348i | \(0.834674\pi\) | |||||||
\(282\) | −9.24500 | + | 6.71689i | −0.550532 | + | 0.399985i | ||||
\(283\) | −0.556491 | − | 1.71270i | −0.0330800 | − | 0.101810i | 0.933153 | − | 0.359479i | \(-0.117046\pi\) |
−0.966233 | + | 0.257669i | \(0.917046\pi\) | |||||||
\(284\) | −13.3556 | −0.792509 | ||||||||
\(285\) | 1.60874 | 0.0952934 | ||||||||
\(286\) | −4.65847 | − | 14.3373i | −0.275461 | − | 0.847782i | ||||
\(287\) | 2.40422 | − | 7.39943i | 0.141917 | − | 0.436775i | ||||
\(288\) | −0.309017 | + | 0.951057i | −0.0182090 | + | 0.0560415i | ||||
\(289\) | 13.6038 | + | 9.88371i | 0.800221 | + | 0.581394i | ||||
\(290\) | −0.464074 | − | 1.42827i | −0.0272514 | − | 0.0838711i | ||||
\(291\) | −0.601576 | − | 0.437071i | −0.0352650 | − | 0.0256215i | ||||
\(292\) | −7.77363 | + | 5.64787i | −0.454917 | + | 0.330517i | ||||
\(293\) | 3.04960 | − | 9.38569i | 0.178159 | − | 0.548318i | −0.821604 | − | 0.570058i | \(-0.806921\pi\) |
0.999764 | + | 0.0217402i | \(0.00692068\pi\) | |||||||
\(294\) | 0.441871 | − | 0.321038i | 0.0257704 | − | 0.0187233i | ||||
\(295\) | −5.59569 | + | 4.06551i | −0.325794 | + | 0.236703i | ||||
\(296\) | −2.16134 | + | 6.65193i | −0.125626 | + | 0.386636i | ||||
\(297\) | −2.36427 | + | 1.71775i | −0.137189 | + | 0.0996737i | ||||
\(298\) | −2.04796 | − | 1.48793i | −0.118635 | − | 0.0861934i | ||||
\(299\) | −2.37909 | − | 7.32210i | −0.137587 | − | 0.423448i | ||||
\(300\) | 0.809017 | + | 0.587785i | 0.0467086 | + | 0.0339358i | ||||
\(301\) | 5.09963 | − | 15.6950i | 0.293938 | − | 0.904648i | ||||
\(302\) | −3.01482 | + | 9.27866i | −0.173483 | + | 0.533927i | ||||
\(303\) | 1.41502 | + | 4.35498i | 0.0812907 | + | 0.250187i | ||||
\(304\) | 1.60874 | 0.0922674 | ||||||||
\(305\) | 4.69891 | 0.269059 | ||||||||
\(306\) | −0.132854 | − | 0.408882i | −0.00759475 | − | 0.0233742i | ||||
\(307\) | −13.9467 | + | 10.1329i | −0.795980 | + | 0.578313i | −0.909732 | − | 0.415196i | \(-0.863713\pi\) |
0.113752 | + | 0.993509i | \(0.463713\pi\) | |||||||
\(308\) | −6.00629 | − | 4.36382i | −0.342240 | − | 0.248652i | ||||
\(309\) | 1.52212 | 0.0865903 | ||||||||
\(310\) | −2.63272 | + | 4.90600i | −0.149528 | + | 0.278642i | ||||
\(311\) | −6.77978 | −0.384446 | −0.192223 | − | 0.981351i | \(-0.561570\pi\) | ||||
−0.192223 | + | 0.981351i | \(0.561570\pi\) | |||||||
\(312\) | 4.17329 | + | 3.03207i | 0.236266 | + | 0.171657i | ||||
\(313\) | −14.2440 | + | 10.3489i | −0.805118 | + | 0.584952i | −0.912411 | − | 0.409275i | \(-0.865782\pi\) |
0.107293 | + | 0.994227i | \(0.465782\pi\) | |||||||
\(314\) | −0.0325125 | − | 0.100063i | −0.00183479 | − | 0.00564689i | ||||
\(315\) | 2.54044 | 0.143137 | ||||||||
\(316\) | 6.49603 | 0.365430 | ||||||||
\(317\) | 7.60649 | + | 23.4104i | 0.427223 | + | 1.31486i | 0.900850 | + | 0.434131i | \(0.142945\pi\) |
−0.473626 | + | 0.880726i | \(0.657055\pi\) | |||||||
\(318\) | 1.63108 | − | 5.01994i | 0.0914663 | − | 0.281504i | ||||
\(319\) | 1.35621 | − | 4.17399i | 0.0759333 | − | 0.233699i | ||||
\(320\) | 0.809017 | + | 0.587785i | 0.0452254 | + | 0.0328582i | ||||
\(321\) | 2.53866 | + | 7.81320i | 0.141694 | + | 0.436090i | ||||
\(322\) | −3.06743 | − | 2.22862i | −0.170941 | − | 0.124196i | ||||
\(323\) | −0.559544 | + | 0.406533i | −0.0311339 | + | 0.0226201i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | 4.17329 | − | 3.03207i | 0.231492 | − | 0.168189i | ||||
\(326\) | 16.9857 | − | 12.3408i | 0.940752 | − | 0.683496i | ||||
\(327\) | 4.00054 | − | 12.3124i | 0.221230 | − | 0.680877i | ||||
\(328\) | −2.47766 | + | 1.80012i | −0.136806 | + | 0.0993952i | ||||
\(329\) | 23.4863 | + | 17.0638i | 1.29484 | + | 0.940759i | ||||
\(330\) | 0.903072 | + | 2.77937i | 0.0497125 | + | 0.152999i | ||||
\(331\) | −21.1946 | − | 15.3988i | −1.16496 | − | 0.846392i | −0.174562 | − | 0.984646i | \(-0.555851\pi\) |
−0.990397 | + | 0.138254i | \(0.955851\pi\) | |||||||
\(332\) | −0.542212 | + | 1.66876i | −0.0297578 | + | 0.0915849i | ||||
\(333\) | 2.16134 | − | 6.65193i | 0.118441 | − | 0.364524i | ||||
\(334\) | 0.477797 | + | 1.47051i | 0.0261439 | + | 0.0804626i | ||||
\(335\) | 11.6213 | 0.634940 | ||||||||
\(336\) | 2.54044 | 0.138592 | ||||||||
\(337\) | 9.53122 | + | 29.3341i | 0.519199 | + | 1.59793i | 0.775510 | + | 0.631336i | \(0.217493\pi\) |
−0.256311 | + | 0.966594i | \(0.582507\pi\) | |||||||
\(338\) | 11.0106 | − | 7.99965i | 0.598896 | − | 0.435124i | ||||
\(339\) | 2.63449 | + | 1.91407i | 0.143086 | + | 0.103958i | ||||
\(340\) | −0.429924 | −0.0233159 | ||||||||
\(341\) | −14.6517 | + | 7.07678i | −0.793435 | + | 0.383229i | ||||
\(342\) | −1.60874 | −0.0869905 | ||||||||
\(343\) | −15.5093 | − | 11.2682i | −0.837426 | − | 0.608425i | ||||
\(344\) | −5.25540 | + | 3.81827i | −0.283352 | + | 0.205867i | ||||
\(345\) | 0.461201 | + | 1.41943i | 0.0248302 | + | 0.0764196i | ||||
\(346\) | −15.3076 | −0.822944 | ||||||||
\(347\) | 11.3481 | 0.609198 | 0.304599 | − | 0.952481i | \(-0.401477\pi\) | ||||
0.304599 | + | 0.952481i | \(0.401477\pi\) | |||||||
\(348\) | 0.464074 | + | 1.42827i | 0.0248770 | + | 0.0765635i | ||||
\(349\) | 8.93531 | − | 27.5001i | 0.478296 | − | 1.47204i | −0.363164 | − | 0.931725i | \(-0.618304\pi\) |
0.841460 | − | 0.540319i | \(-0.181696\pi\) | |||||||
\(350\) | 0.785038 | − | 2.41610i | 0.0419620 | − | 0.129146i | ||||
\(351\) | −4.17329 | − | 3.03207i | −0.222754 | − | 0.161840i | ||||
\(352\) | 0.903072 | + | 2.77937i | 0.0481339 | + | 0.148141i | ||||
\(353\) | −10.6662 | − | 7.74943i | −0.567703 | − | 0.412460i | 0.266567 | − | 0.963816i | \(-0.414111\pi\) |
−0.834270 | + | 0.551356i | \(0.814111\pi\) | |||||||
\(354\) | 5.59569 | − | 4.06551i | 0.297408 | − | 0.216079i | ||||
\(355\) | 4.12711 | − | 12.7019i | 0.219044 | − | 0.674149i | ||||
\(356\) | 5.93334 | − | 4.31082i | 0.314466 | − | 0.228473i | ||||
\(357\) | −0.883604 | + | 0.641976i | −0.0467653 | + | 0.0339770i | ||||
\(358\) | −2.80226 | + | 8.62447i | −0.148104 | + | 0.455817i | ||||
\(359\) | 18.9643 | − | 13.7783i | 1.00090 | − | 0.727193i | 0.0386151 | − | 0.999254i | \(-0.487705\pi\) |
0.962280 | + | 0.272061i | \(0.0877054\pi\) | |||||||
\(360\) | −0.809017 | − | 0.587785i | −0.0426389 | − | 0.0309790i | ||||
\(361\) | −5.07158 | − | 15.6087i | −0.266925 | − | 0.821511i | ||||
\(362\) | 13.4646 | + | 9.78262i | 0.707684 | + | 0.514163i | ||||
\(363\) | 0.760047 | − | 2.33918i | 0.0398921 | − | 0.122775i | ||||
\(364\) | 4.04960 | − | 12.4634i | 0.212256 | − | 0.653258i | ||||
\(365\) | −2.96926 | − | 9.13845i | −0.155418 | − | 0.478328i | ||||
\(366\) | −4.69891 | −0.245616 | ||||||||
\(367\) | −6.64148 | −0.346683 | −0.173341 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173341 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(368\) | 0.461201 | + | 1.41943i | 0.0240418 | + | 0.0739930i | ||||
\(369\) | 2.47766 | − | 1.80012i | 0.128982 | − | 0.0937107i | ||||
\(370\) | −5.65847 | − | 4.11112i | −0.294170 | − | 0.213727i | ||||
\(371\) | −13.4091 | −0.696168 | ||||||||
\(372\) | 2.63272 | − | 4.90600i | 0.136500 | − | 0.254364i | ||||
\(373\) | 8.05298 | 0.416968 | 0.208484 | − | 0.978026i | \(-0.433147\pi\) | ||||
0.208484 | + | 0.978026i | \(0.433147\pi\) | |||||||
\(374\) | −1.01646 | − | 0.738500i | −0.0525598 | − | 0.0381869i | ||||
\(375\) | −0.809017 | + | 0.587785i | −0.0417775 | + | 0.0303531i | ||||
\(376\) | −3.53128 | − | 10.8682i | −0.182112 | − | 0.560482i | ||||
\(377\) | 7.74686 | 0.398984 | ||||||||
\(378\) | −2.54044 | −0.130666 | ||||||||
\(379\) | 7.75751 | + | 23.8752i | 0.398476 | + | 1.22638i | 0.926221 | + | 0.376981i | \(0.123038\pi\) |
−0.527745 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(380\) | −0.497127 | + | 1.53000i | −0.0255021 | + | 0.0784873i | ||||
\(381\) | −0.892901 | + | 2.74807i | −0.0457447 | + | 0.140788i | ||||
\(382\) | 8.38967 | + | 6.09545i | 0.429253 | + | 0.311870i | ||||
\(383\) | 3.35588 | + | 10.3283i | 0.171477 | + | 0.527753i | 0.999455 | − | 0.0330080i | \(-0.0105087\pi\) |
−0.827978 | + | 0.560761i | \(0.810509\pi\) | |||||||
\(384\) | −0.809017 | − | 0.587785i | −0.0412850 | − | 0.0299953i | ||||
\(385\) | 6.00629 | − | 4.36382i | 0.306109 | − | 0.222401i | ||||
\(386\) | −1.77943 | + | 5.47652i | −0.0905706 | + | 0.278748i | ||||
\(387\) | 5.25540 | − | 3.81827i | 0.267147 | − | 0.194094i | ||||
\(388\) | 0.601576 | − | 0.437071i | 0.0305404 | − | 0.0221889i | ||||
\(389\) | 3.06783 | − | 9.44181i | 0.155545 | − | 0.478719i | −0.842671 | − | 0.538429i | \(-0.819018\pi\) |
0.998216 | + | 0.0597108i | \(0.0190179\pi\) | |||||||
\(390\) | −4.17329 | + | 3.03207i | −0.211323 | + | 0.153535i | ||||
\(391\) | −0.519108 | − | 0.377154i | −0.0262524 | − | 0.0190735i | ||||
\(392\) | 0.168780 | + | 0.519450i | 0.00852466 | + | 0.0262362i | ||||
\(393\) | 13.7420 | + | 9.98414i | 0.693192 | + | 0.503633i | ||||
\(394\) | −4.68865 | + | 14.4302i | −0.236211 | + | 0.726982i | ||||
\(395\) | −2.00738 | + | 6.17809i | −0.101002 | + | 0.310854i | ||||
\(396\) | −0.903072 | − | 2.77937i | −0.0453811 | − | 0.139669i | ||||
\(397\) | 28.4142 | 1.42607 | 0.713033 | − | 0.701131i | \(-0.247321\pi\) | ||||
0.713033 | + | 0.701131i | \(0.247321\pi\) | |||||||
\(398\) | 22.3810 | 1.12186 | ||||||||
\(399\) | 1.26292 | + | 3.88687i | 0.0632251 | + | 0.194587i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | 28.9425 | + | 21.0279i | 1.44532 | + | 1.05008i | 0.986897 | + | 0.161349i | \(0.0515843\pi\) |
0.458420 | + | 0.888736i | \(0.348416\pi\) | |||||||
\(402\) | −11.6213 | −0.579618 | ||||||||
\(403\) | −19.8721 | − | 20.7365i | −0.989900 | − | 1.03296i | ||||
\(404\) | −4.57910 | −0.227819 | ||||||||
\(405\) | 0.809017 | + | 0.587785i | 0.0402004 | + | 0.0292073i | ||||
\(406\) | 3.08653 | − | 2.24250i | 0.153182 | − | 0.111293i | ||||
\(407\) | −6.31632 | − | 19.4396i | −0.313088 | − | 0.963586i | ||||
\(408\) | 0.429924 | 0.0212844 | ||||||||
\(409\) | 0.787996 | 0.0389639 | 0.0194820 | − | 0.999810i | \(-0.493798\pi\) | ||||
0.0194820 | + | 0.999810i | \(0.493798\pi\) | |||||||
\(410\) | −0.946381 | − | 2.91266i | −0.0467384 | − | 0.143846i | ||||
\(411\) | −0.535926 | + | 1.64941i | −0.0264353 | + | 0.0813594i | ||||
\(412\) | −0.470360 | + | 1.44762i | −0.0231730 | + | 0.0713191i | ||||
\(413\) | −14.2155 | − | 10.3282i | −0.699499 | − | 0.508216i | ||||
\(414\) | −0.461201 | − | 1.41943i | −0.0226668 | − | 0.0697613i | ||||
\(415\) | −1.41953 | − | 1.03135i | −0.0696820 | − | 0.0506269i | ||||
\(416\) | −4.17329 | + | 3.03207i | −0.204612 | + | 0.148660i | ||||
\(417\) | −6.26059 | + | 19.2681i | −0.306582 | + | 0.943563i | ||||
\(418\) | −3.80349 | + | 2.76340i | −0.186035 | + | 0.135162i | ||||
\(419\) | 27.9669 | − | 20.3191i | 1.36627 | − | 0.992654i | 0.368253 | − | 0.929725i | \(-0.379956\pi\) |
0.998018 | − | 0.0629288i | \(-0.0200441\pi\) | |||||||
\(420\) | −0.785038 | + | 2.41610i | −0.0383059 | + | 0.117894i | ||||
\(421\) | 1.66900 | − | 1.21260i | 0.0813422 | − | 0.0590986i | −0.546371 | − | 0.837543i | \(-0.683991\pi\) |
0.627713 | + | 0.778445i | \(0.283991\pi\) | |||||||
\(422\) | −1.19992 | − | 0.871792i | −0.0584112 | − | 0.0424382i | ||||
\(423\) | 3.53128 | + | 10.8682i | 0.171697 | + | 0.528428i | ||||
\(424\) | 4.27022 | + | 3.10250i | 0.207380 | + | 0.150670i | ||||
\(425\) | 0.132854 | − | 0.408882i | 0.00644436 | − | 0.0198337i | ||||
\(426\) | −4.12711 | + | 12.7019i | −0.199959 | + | 0.615411i | ||||
\(427\) | 3.68882 | + | 11.3530i | 0.178515 | + | 0.549411i | ||||
\(428\) | −8.21528 | −0.397101 | ||||||||
\(429\) | −15.0751 | −0.727834 | ||||||||
\(430\) | −2.00738 | − | 6.17809i | −0.0968046 | − | 0.297934i | ||||
\(431\) | 28.2555 | − | 20.5288i | 1.36102 | − | 0.988837i | 0.362639 | − | 0.931930i | \(-0.381876\pi\) |
0.998379 | − | 0.0569075i | \(-0.0181240\pi\) | |||||||
\(432\) | 0.809017 | + | 0.587785i | 0.0389238 | + | 0.0282798i | ||||
\(433\) | 12.1410 | 0.583457 | 0.291729 | − | 0.956501i | \(-0.405770\pi\) | ||||
0.291729 | + | 0.956501i | \(0.405770\pi\) | |||||||
\(434\) | −13.9202 | − | 2.50951i | −0.668189 | − | 0.120460i | ||||
\(435\) | −1.50178 | −0.0720046 | ||||||||
\(436\) | 10.4736 | + | 7.60948i | 0.501592 | + | 0.364428i | ||||
\(437\) | −1.94245 | + | 1.41128i | −0.0929202 | + | 0.0675105i | ||||
\(438\) | 2.96926 | + | 9.13845i | 0.141877 | + | 0.436652i | ||||
\(439\) | −0.543817 | −0.0259550 | −0.0129775 | − | 0.999916i | \(-0.504131\pi\) | ||||
−0.0129775 | + | 0.999916i | \(0.504131\pi\) | |||||||
\(440\) | −2.92240 | −0.139320 | ||||||||
\(441\) | −0.168780 | − | 0.519450i | −0.00803712 | − | 0.0247357i | ||||
\(442\) | 0.685322 | − | 2.10921i | 0.0325975 | − | 0.100325i | ||||
\(443\) | −2.35635 | + | 7.25210i | −0.111954 | + | 0.344558i | −0.991299 | − | 0.131626i | \(-0.957980\pi\) |
0.879346 | + | 0.476184i | \(0.157980\pi\) | |||||||
\(444\) | 5.65847 | + | 4.11112i | 0.268539 | + | 0.195105i | ||||
\(445\) | 2.26633 | + | 6.97506i | 0.107434 | + | 0.330649i | ||||
\(446\) | 0.270579 | + | 0.196587i | 0.0128123 | + | 0.00930867i | ||||
\(447\) | −2.04796 | + | 1.48793i | −0.0968651 | + | 0.0703766i | ||||
\(448\) | −0.785038 | + | 2.41610i | −0.0370896 | + | 0.114150i | ||||
\(449\) | 2.04322 | − | 1.48449i | 0.0964257 | − | 0.0700574i | −0.538528 | − | 0.842608i | \(-0.681019\pi\) |
0.634953 | + | 0.772550i | \(0.281019\pi\) | |||||||
\(450\) | 0.809017 | − | 0.587785i | 0.0381374 | − | 0.0277085i | ||||
\(451\) | 2.76571 | − | 8.51197i | 0.130232 | − | 0.400813i | ||||
\(452\) | −2.63449 | + | 1.91407i | −0.123916 | + | 0.0900303i | ||||
\(453\) | 7.89290 | + | 5.73453i | 0.370841 | + | 0.269432i | ||||
\(454\) | −3.32215 | − | 10.2245i | −0.155916 | − | 0.479860i | ||||
\(455\) | 10.6020 | + | 7.70279i | 0.497028 | + | 0.361112i | ||||
\(456\) | 0.497127 | − | 1.53000i | 0.0232801 | − | 0.0716488i | ||||
\(457\) | −6.65906 | + | 20.4945i | −0.311498 | + | 0.958692i | 0.665674 | + | 0.746242i | \(0.268144\pi\) |
−0.977172 | + | 0.212449i | \(0.931856\pi\) | |||||||
\(458\) | 4.77199 | + | 14.6867i | 0.222981 | + | 0.686264i | ||||
\(459\) | −0.429924 | −0.0200671 | ||||||||
\(460\) | −1.49248 | −0.0695872 | ||||||||
\(461\) | −10.5479 | − | 32.4631i | −0.491264 | − | 1.51196i | −0.822699 | − | 0.568477i | \(-0.807533\pi\) |
0.331435 | − | 0.943478i | \(-0.392467\pi\) | |||||||
\(462\) | −6.00629 | + | 4.36382i | −0.279438 | + | 0.203023i | ||||
\(463\) | 24.5136 | + | 17.8102i | 1.13924 | + | 0.827710i | 0.987014 | − | 0.160635i | \(-0.0513542\pi\) |
0.152231 | + | 0.988345i | \(0.451354\pi\) | |||||||
\(464\) | −1.50178 | −0.0697182 | ||||||||
\(465\) | 3.85233 | + | 4.01990i | 0.178647 | + | 0.186418i | ||||
\(466\) | −4.94027 | −0.228854 | ||||||||
\(467\) | −21.2779 | − | 15.4593i | −0.984625 | − | 0.715372i | −0.0258873 | − | 0.999665i | \(-0.508241\pi\) |
−0.958737 | + | 0.284293i | \(0.908241\pi\) | |||||||
\(468\) | 4.17329 | − | 3.03207i | 0.192910 | − | 0.140158i | ||||
\(469\) | 9.12317 | + | 28.0782i | 0.421269 | + | 1.29653i | ||||
\(470\) | 11.4275 | 0.527109 | ||||||||
\(471\) | −0.105213 | −0.00484794 | ||||||||
\(472\) | 2.13736 | + | 6.57813i | 0.0983802 | + | 0.302783i | ||||
\(473\) | 5.86638 | − | 18.0549i | 0.269737 | − | 0.830164i | ||||
\(474\) | 2.00738 | − | 6.17809i | 0.0922022 | − | 0.283769i | ||||
\(475\) | −1.30150 | − | 0.945592i | −0.0597167 | − | 0.0433867i | ||||
\(476\) | −0.337507 | − | 1.03874i | −0.0154696 | − | 0.0476105i | ||||
\(477\) | −4.27022 | − | 3.10250i | −0.195520 | − | 0.142053i | ||||
\(478\) | 15.0896 | − | 10.9632i | 0.690182 | − | 0.501446i | ||||
\(479\) | 4.26768 | − | 13.1346i | 0.194995 | − | 0.600134i | −0.804981 | − | 0.593300i | \(-0.797825\pi\) |
0.999977 | − | 0.00683362i | \(-0.00217523\pi\) | |||||||
\(480\) | 0.809017 | − | 0.587785i | 0.0369264 | − | 0.0268286i | ||||
\(481\) | 29.1891 | − | 21.2071i | 1.33091 | − | 0.966960i | ||||
\(482\) | 1.86647 | − | 5.74440i | 0.0850153 | − | 0.261650i | ||||
\(483\) | −3.06743 | + | 2.22862i | −0.139573 | + | 0.101406i | ||||
\(484\) | 1.98983 | + | 1.44570i | 0.0904468 | + | 0.0657134i | ||||
\(485\) | 0.229782 | + | 0.707195i | 0.0104339 | + | 0.0321121i | ||||
\(486\) | −0.809017 | − | 0.587785i | −0.0366978 | − | 0.0266625i | ||||
\(487\) | 1.01755 | − | 3.13171i | 0.0461098 | − | 0.141911i | −0.925351 | − | 0.379111i | \(-0.876230\pi\) |
0.971461 | + | 0.237200i | \(0.0762297\pi\) | |||||||
\(488\) | 1.45204 | − | 4.46893i | 0.0657309 | − | 0.202299i | ||||
\(489\) | −6.48797 | − | 19.9679i | −0.293396 | − | 0.902980i | ||||
\(490\) | −0.546182 | −0.0246740 | ||||||||
\(491\) | 26.7565 | 1.20750 | 0.603752 | − | 0.797172i | \(-0.293672\pi\) | ||||
0.603752 | + | 0.797172i | \(0.293672\pi\) | |||||||
\(492\) | 0.946381 | + | 2.91266i | 0.0426662 | + | 0.131313i | ||||
\(493\) | 0.522341 | − | 0.379503i | 0.0235251 | − | 0.0170920i | ||||
\(494\) | −6.71373 | − | 4.87781i | −0.302065 | − | 0.219463i | ||||
\(495\) | 2.92240 | 0.131352 | ||||||||
\(496\) | 3.85233 | + | 4.01990i | 0.172975 | + | 0.180499i | ||||
\(497\) | 33.9291 | 1.52193 | ||||||||
\(498\) | 1.41953 | + | 1.03135i | 0.0636106 | + | 0.0462158i | ||||
\(499\) | −31.2871 | + | 22.7314i | −1.40060 | + | 1.01760i | −0.405997 | + | 0.913874i | \(0.633076\pi\) |
−0.994606 | + | 0.103723i | \(0.966924\pi\) | |||||||
\(500\) | −0.309017 | − | 0.951057i | −0.0138197 | − | 0.0425325i | ||||
\(501\) | 1.54618 | 0.0690783 | ||||||||
\(502\) | −24.9421 | −1.11322 | ||||||||
\(503\) | −6.22917 | − | 19.1714i | −0.277745 | − | 0.854811i | −0.988480 | − | 0.151351i | \(-0.951637\pi\) |
0.710735 | − | 0.703460i | \(-0.248363\pi\) | |||||||
\(504\) | 0.785038 | − | 2.41610i | 0.0349684 | − | 0.107622i | ||||
\(505\) | 1.41502 | − | 4.35498i | 0.0629675 | − | 0.193794i | ||||
\(506\) | −3.52863 | − | 2.56370i | −0.156867 | − | 0.113970i | ||||
\(507\) | −4.20567 | − | 12.9437i | −0.186780 | − | 0.574850i | ||||
\(508\) | −2.33764 | − | 1.69840i | −0.103716 | − | 0.0753542i | ||||
\(509\) | 17.6176 | − | 12.7999i | 0.780885 | − | 0.567346i | −0.124360 | − | 0.992237i | \(-0.539688\pi\) |
0.905244 | + | 0.424891i | \(0.139688\pi\) | |||||||
\(510\) | −0.132854 | + | 0.408882i | −0.00588286 | + | 0.0181056i | ||||
\(511\) | 19.7484 | − | 14.3481i | 0.873619 | − | 0.634721i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | −0.497127 | + | 1.53000i | −0.0219487 | + | 0.0675511i | ||||
\(514\) | −20.1129 | + | 14.6129i | −0.887143 | + | 0.644547i | ||||
\(515\) | −1.23142 | − | 0.894679i | −0.0542628 | − | 0.0394243i | ||||
\(516\) | 2.00738 | + | 6.17809i | 0.0883701 | + | 0.271975i | ||||
\(517\) | 27.0176 | + | 19.6295i | 1.18823 | + | 0.863302i | ||||
\(518\) | 5.49076 | − | 16.8988i | 0.241250 | − | 0.742491i | ||||
\(519\) | −4.73032 | + | 14.5584i | −0.207638 | + | 0.639044i | ||||
\(520\) | −1.59406 | − | 4.90600i | −0.0699039 | − | 0.215142i | ||||
\(521\) | −8.99273 | −0.393979 | −0.196989 | − | 0.980406i | \(-0.563116\pi\) | ||||
−0.196989 | + | 0.980406i | \(0.563116\pi\) | |||||||
\(522\) | 1.50178 | 0.0657309 | ||||||||
\(523\) | 3.49084 | + | 10.7437i | 0.152644 | + | 0.469789i | 0.997915 | − | 0.0645489i | \(-0.0205609\pi\) |
−0.845271 | + | 0.534338i | \(0.820561\pi\) | |||||||
\(524\) | −13.7420 | + | 9.98414i | −0.600322 | + | 0.436159i | ||||
\(525\) | −2.05526 | − | 1.49323i | −0.0896987 | − | 0.0651699i | ||||
\(526\) | 6.45754 | 0.281562 | ||||||||
\(527\) | −2.35574 | − | 0.424690i | −0.102618 | − | 0.0184998i | ||||
\(528\) | 2.92240 | 0.127181 | ||||||||
\(529\) | 16.8053 | + | 12.2098i | 0.730666 | + | 0.530860i | ||||
\(530\) | −4.27022 | + | 3.10250i | −0.185486 | + | 0.134764i | ||||
\(531\) | −2.13736 | − | 6.57813i | −0.0927537 | − | 0.285467i | ||||
\(532\) | −4.08689 | −0.177189 | ||||||||
\(533\) | 15.7981 | 0.684292 | ||||||||
\(534\) | −2.26633 | − | 6.97506i | −0.0980738 | − | 0.301840i | ||||
\(535\) | 2.53866 | − | 7.81320i | 0.109756 | − | 0.337794i | ||||
\(536\) | 3.59118 | − | 11.0525i | 0.155115 | − | 0.477396i | ||||
\(537\) | 7.33641 | + | 5.33021i | 0.316589 | + | 0.230016i | ||||
\(538\) | 9.24058 | + | 28.4396i | 0.398390 | + | 1.22612i | ||||
\(539\) | −1.29132 | − | 0.938202i | −0.0556213 | − | 0.0404112i | ||||
\(540\) | −0.809017 | + | 0.587785i | −0.0348145 | + | 0.0252942i | ||||
\(541\) | −3.48666 | + | 10.7308i | −0.149903 | + | 0.461355i | −0.997609 | − | 0.0691119i | \(-0.977983\pi\) |
0.847706 | + | 0.530467i | \(0.177983\pi\) | |||||||
\(542\) | 19.6728 | − | 14.2931i | 0.845020 | − | 0.613943i | ||||
\(543\) | 13.4646 | − | 9.78262i | 0.577822 | − | 0.419812i | ||||
\(544\) | −0.132854 | + | 0.408882i | −0.00569606 | + | 0.0175307i | ||||
\(545\) | −10.4736 | + | 7.60948i | −0.448638 | + | 0.325954i | ||||
\(546\) | −10.6020 | − | 7.70279i | −0.453723 | − | 0.329649i | ||||
\(547\) | −1.19702 | − | 3.68405i | −0.0511809 | − | 0.157519i | 0.922199 | − | 0.386715i | \(-0.126390\pi\) |
−0.973380 | + | 0.229196i | \(0.926390\pi\) | |||||||
\(548\) | −1.40307 | − | 1.01939i | −0.0599363 | − | 0.0435462i | ||||
\(549\) | −1.45204 | + | 4.46893i | −0.0619716 | + | 0.190729i | ||||
\(550\) | 0.903072 | − | 2.77937i | 0.0385071 | − | 0.118513i | ||||
\(551\) | −0.746573 | − | 2.29772i | −0.0318051 | − | 0.0978860i | ||||
\(552\) | 1.49248 | 0.0635241 | ||||||||
\(553\) | −16.5028 | −0.701768 | ||||||||
\(554\) | −4.22240 | − | 12.9952i | −0.179393 | − | 0.552113i | ||||
\(555\) | −5.65847 | + | 4.11112i | −0.240189 | + | 0.174507i | ||||
\(556\) | −16.3904 | − | 11.9083i | −0.695109 | − | 0.505026i | ||||
\(557\) | −30.2336 | −1.28104 | −0.640519 | − | 0.767942i | \(-0.721281\pi\) | ||||
−0.640519 | + | 0.767942i | \(0.721281\pi\) | |||||||
\(558\) | −3.85233 | − | 4.01990i | −0.163082 | − | 0.170176i | ||||
\(559\) | 33.5096 | 1.41730 | ||||||||
\(560\) | −2.05526 | − | 1.49323i | −0.0868504 | − | 0.0631005i | ||||
\(561\) | −1.01646 | + | 0.738500i | −0.0429149 | + | 0.0311795i | ||||
\(562\) | −4.25368 | − | 13.0915i | −0.179430 | − | 0.552230i | ||||
\(563\) | 15.8132 | 0.666449 | 0.333224 | − | 0.942848i | \(-0.391863\pi\) | ||||
0.333224 | + | 0.942848i | \(0.391863\pi\) | |||||||
\(564\) | −11.4275 | −0.481183 | ||||||||
\(565\) | −1.00629 | − | 3.09703i | −0.0423348 | − | 0.130293i | ||||
\(566\) | 0.556491 | − | 1.71270i | 0.0233911 | − | 0.0719903i | ||||
\(567\) | −0.785038 | + | 2.41610i | −0.0329685 | + | 0.101467i | ||||
\(568\) | −10.8049 | − | 7.85023i | −0.453364 | − | 0.329388i | ||||
\(569\) | −6.83805 | − | 21.0453i | −0.286666 | − | 0.882267i | −0.985894 | − | 0.167369i | \(-0.946473\pi\) |
0.699229 | − | 0.714898i | \(-0.253527\pi\) | |||||||
\(570\) | 1.30150 | + | 0.945592i | 0.0545137 | + | 0.0396065i | ||||
\(571\) | 10.0918 | − | 7.33213i | 0.422329 | − | 0.306840i | −0.356245 | − | 0.934392i | \(-0.615943\pi\) |
0.778574 | + | 0.627553i | \(0.215943\pi\) | |||||||
\(572\) | 4.65847 | − | 14.3373i | 0.194780 | − | 0.599473i | ||||
\(573\) | 8.38967 | − | 6.09545i | 0.350483 | − | 0.254641i | ||||
\(574\) | 6.29433 | − | 4.57310i | 0.262720 | − | 0.190878i | ||||
\(575\) | 0.461201 | − | 1.41943i | 0.0192334 | − | 0.0591944i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 29.9933 | + | 21.7914i | 1.24864 | + | 0.907188i | 0.998142 | − | 0.0609303i | \(-0.0194067\pi\) |
0.250495 | + | 0.968118i | \(0.419407\pi\) | |||||||
\(578\) | 5.19617 | + | 15.9922i | 0.216132 | + | 0.665187i | ||||
\(579\) | 4.65861 | + | 3.38468i | 0.193605 | + | 0.140662i | ||||
\(580\) | 0.464074 | − | 1.42827i | 0.0192696 | − | 0.0593058i | ||||
\(581\) | 1.37746 | − | 4.23937i | 0.0571465 | − | 0.175879i | ||||
\(582\) | −0.229782 | − | 0.707195i | −0.00952476 | − | 0.0293142i | ||||
\(583\) | −15.4253 | −0.638849 | ||||||||
\(584\) | −9.60874 | −0.397612 | ||||||||
\(585\) | 1.59406 | + | 4.90600i | 0.0659061 | + | 0.202838i | ||||
\(586\) | 7.98395 | − | 5.80068i | 0.329814 | − | 0.239624i | ||||
\(587\) | −32.7964 | − | 23.8280i | −1.35365 | − | 0.983486i | −0.998820 | − | 0.0485566i | \(-0.984538\pi\) |
−0.354833 | − | 0.934930i | \(-0.615462\pi\) | |||||||
\(588\) | 0.546182 | 0.0225242 | ||||||||
\(589\) | −4.23535 | + | 7.89246i | −0.174514 | + | 0.325203i | ||||
\(590\) | −6.91666 | −0.284754 | ||||||||
\(591\) | 12.2750 | + | 8.91834i | 0.504928 | + | 0.366852i | ||||
\(592\) | −5.65847 | + | 4.11112i | −0.232562 | + | 0.168966i | ||||
\(593\) | −7.29414 | − | 22.4491i | −0.299535 | − | 0.921873i | −0.981660 | − | 0.190638i | \(-0.938944\pi\) |
0.682126 | − | 0.731235i | \(-0.261056\pi\) | |||||||
\(594\) | −2.92240 | −0.119908 | ||||||||
\(595\) | 1.09219 | 0.0447756 | ||||||||
\(596\) | −0.782250 | − | 2.40752i | −0.0320422 | − | 0.0986158i | ||||
\(597\) | 6.91612 | − | 21.2856i | 0.283058 | − | 0.871162i | ||||
\(598\) | 2.37909 | − | 7.32210i | 0.0972884 | − | 0.299423i | ||||
\(599\) | −7.90161 | − | 5.74086i | −0.322851 | − | 0.234565i | 0.414540 | − | 0.910031i | \(-0.363943\pi\) |
−0.737391 | + | 0.675466i | \(0.763943\pi\) | |||||||
\(600\) | 0.309017 | + | 0.951057i | 0.0126156 | + | 0.0388267i | ||||
\(601\) | −5.41387 | − | 3.93341i | −0.220836 | − | 0.160447i | 0.471867 | − | 0.881670i | \(-0.343580\pi\) |
−0.692703 | + | 0.721223i | \(0.743580\pi\) | |||||||
\(602\) | 13.3510 | − | 9.70007i | 0.544146 | − | 0.395345i | ||||
\(603\) | −3.59118 | + | 11.0525i | −0.146244 | + | 0.450093i | ||||
\(604\) | −7.89290 | + | 5.73453i | −0.321158 | + | 0.233335i | ||||
\(605\) | −1.98983 | + | 1.44570i | −0.0808980 | + | 0.0587759i | ||||
\(606\) | −1.41502 | + | 4.35498i | −0.0574812 | + | 0.176909i | ||||
\(607\) | 26.1753 | − | 19.0175i | 1.06242 | − | 0.771896i | 0.0878886 | − | 0.996130i | \(-0.471988\pi\) |
0.974535 | + | 0.224234i | \(0.0719880\pi\) | |||||||
\(608\) | 1.30150 | + | 0.945592i | 0.0527826 | + | 0.0383488i | ||||
\(609\) | −1.17895 | − | 3.62844i | −0.0477735 | − | 0.147032i | ||||
\(610\) | 3.80150 | + | 2.76195i | 0.153918 | + | 0.111828i | ||||
\(611\) | −18.2160 | + | 56.0631i | −0.736940 | + | 2.26807i | ||||
\(612\) | 0.132854 | − | 0.408882i | 0.00537030 | − | 0.0165281i | ||||
\(613\) | 7.70500 | + | 23.7135i | 0.311202 | + | 0.957781i | 0.977290 | + | 0.211908i | \(0.0679676\pi\) |
−0.666088 | + | 0.745873i | \(0.732032\pi\) | |||||||
\(614\) | −17.2391 | −0.695712 | ||||||||
\(615\) | −3.06255 | −0.123494 | ||||||||
\(616\) | −2.29420 | − | 7.06081i | −0.0924358 | − | 0.284488i | ||||
\(617\) | −17.2373 | + | 12.5237i | −0.693949 | + | 0.504184i | −0.877956 | − | 0.478741i | \(-0.841093\pi\) |
0.184007 | + | 0.982925i | \(0.441093\pi\) | |||||||
\(618\) | 1.23142 | + | 0.894679i | 0.0495350 | + | 0.0359893i | ||||
\(619\) | −29.1394 | −1.17121 | −0.585605 | − | 0.810596i | \(-0.699143\pi\) | ||||
−0.585605 | + | 0.810596i | \(0.699143\pi\) | |||||||
\(620\) | −5.01358 | + | 2.42156i | −0.201350 | + | 0.0972523i | ||||
\(621\) | −1.49248 | −0.0598911 | ||||||||
\(622\) | −5.48496 | − | 3.98505i | −0.219927 | − | 0.159786i | ||||
\(623\) | −15.0733 | + | 10.9514i | −0.603898 | + | 0.438757i | ||||
\(624\) | 1.59406 | + | 4.90600i | 0.0638133 | + | 0.196397i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.6065 | −0.703699 | ||||||||
\(627\) | 1.45281 | + | 4.47128i | 0.0580195 | + | 0.178566i | ||||
\(628\) | 0.0325125 | − | 0.100063i | 0.00129739 | − | 0.00399296i | ||||
\(629\) | 0.929213 | − | 2.85982i | 0.0370502 | − | 0.114029i | ||||
\(630\) | 2.05526 | + | 1.49323i | 0.0818834 | + | 0.0594918i | ||||
\(631\) | 6.54188 | + | 20.1338i | 0.260428 | + | 0.801515i | 0.992711 | + | 0.120515i | \(0.0384546\pi\) |
−0.732283 | + | 0.681000i | \(0.761545\pi\) | |||||||
\(632\) | 5.25540 | + | 3.81827i | 0.209049 | + | 0.151883i | ||||
\(633\) | −1.19992 | + | 0.871792i | −0.0476925 | + | 0.0346506i | ||||
\(634\) | −7.60649 | + | 23.4104i | −0.302092 | + | 0.929744i | ||||
\(635\) | 2.33764 | − | 1.69840i | 0.0927666 | − | 0.0673989i | ||||
\(636\) | 4.27022 | − | 3.10250i | 0.169325 | − | 0.123022i | ||||
\(637\) | 0.870645 | − | 2.67957i | 0.0344962 | − | 0.106168i | ||||
\(638\) | 3.55061 | − | 2.57967i | 0.140570 | − | 0.102130i | ||||
\(639\) | 10.8049 | + | 7.85023i | 0.427436 | + | 0.310550i | ||||
\(640\) | 0.309017 | + | 0.951057i | 0.0122150 | + | 0.0375938i | ||||
\(641\) | −1.75039 | − | 1.27173i | −0.0691362 | − | 0.0502304i | 0.552680 | − | 0.833393i | \(-0.313605\pi\) |
−0.621817 | + | 0.783163i | \(0.713605\pi\) | |||||||
\(642\) | −2.53866 | + | 7.81320i | −0.100193 | + | 0.308362i | ||||
\(643\) | −5.15724 | + | 15.8723i | −0.203382 | + | 0.625944i | 0.796394 | + | 0.604778i | \(0.206738\pi\) |
−0.999776 | + | 0.0211664i | \(0.993262\pi\) | |||||||
\(644\) | −1.17165 | − | 3.60598i | −0.0461696 | − | 0.142095i | ||||
\(645\) | −6.49603 | −0.255781 | ||||||||
\(646\) | −0.691634 | −0.0272120 | ||||||||
\(647\) | −13.1967 | − | 40.6151i | −0.518814 | − | 1.59675i | −0.776233 | − | 0.630446i | \(-0.782872\pi\) |
0.257419 | − | 0.966300i | \(-0.417128\pi\) | |||||||
\(648\) | 0.809017 | − | 0.587785i | 0.0317812 | − | 0.0230904i | ||||
\(649\) | −16.3529 | − | 11.8811i | −0.641906 | − | 0.466372i | ||||
\(650\) | 5.15847 | 0.202332 | ||||||||
\(651\) | −6.68825 | + | 12.4634i | −0.262133 | + | 0.488478i | ||||
\(652\) | 20.9955 | 0.822247 | ||||||||
\(653\) | −5.57030 | − | 4.04706i | −0.217983 | − | 0.158374i | 0.473435 | − | 0.880829i | \(-0.343014\pi\) |
−0.691418 | + | 0.722455i | \(0.743014\pi\) | |||||||
\(654\) | 10.4736 | − | 7.60948i | 0.409548 | − | 0.297554i | ||||
\(655\) | −5.24897 | − | 16.1547i | −0.205094 | − | 0.631216i | ||||
\(656\) | −3.06255 | −0.119573 | ||||||||
\(657\) | 9.60874 | 0.374873 | ||||||||
\(658\) | 8.97099 | + | 27.6099i | 0.349725 | + | 1.07634i | ||||
\(659\) | −2.39487 | + | 7.37066i | −0.0932910 | + | 0.287120i | −0.986805 | − | 0.161916i | \(-0.948233\pi\) |
0.893514 | + | 0.449036i | \(0.148233\pi\) | |||||||
\(660\) | −0.903072 | + | 2.77937i | −0.0351520 | + | 0.108187i | ||||
\(661\) | −17.9870 | − | 13.0683i | −0.699613 | − | 0.508299i | 0.180193 | − | 0.983631i | \(-0.442328\pi\) |
−0.879806 | + | 0.475333i | \(0.842328\pi\) | |||||||
\(662\) | −8.09561 | − | 24.9157i | −0.314645 | − | 0.968377i | ||||
\(663\) | −1.79420 | − | 1.30356i | −0.0696808 | − | 0.0506261i | ||||
\(664\) | −1.41953 | + | 1.03135i | −0.0550884 | + | 0.0400241i | ||||
\(665\) | 1.26292 | − | 3.88687i | 0.0489739 | − | 0.150726i | ||||
\(666\) | 5.65847 | − | 4.11112i | 0.219261 | − | 0.159303i | ||||
\(667\) | 1.81330 | − | 1.31744i | 0.0702114 | − | 0.0510116i | ||||
\(668\) | −0.477797 | + | 1.47051i | −0.0184865 | + | 0.0568956i | ||||
\(669\) | 0.270579 | − | 0.196587i | 0.0104612 | − | 0.00760050i | ||||
\(670\) | 9.40184 | + | 6.83083i | 0.363225 | + | 0.263898i | ||||
\(671\) | 4.24345 | + | 13.0600i | 0.163817 | + | 0.504176i | ||||
\(672\) | 2.05526 | + | 1.49323i | 0.0792832 | + | 0.0576026i | ||||
\(673\) | −4.88132 | + | 15.0232i | −0.188161 | + | 0.579101i | −0.999988 | − | 0.00479699i | \(-0.998473\pi\) |
0.811827 | + | 0.583898i | \(0.198473\pi\) | |||||||
\(674\) | −9.53122 | + | 29.3341i | −0.367129 | + | 1.12991i | ||||
\(675\) | −0.309017 | − | 0.951057i | −0.0118941 | − | 0.0366062i | ||||
\(676\) | 13.6098 | 0.523455 | ||||||||
\(677\) | −12.1049 | −0.465231 | −0.232615 | − | 0.972569i | \(-0.574728\pi\) | ||||
−0.232615 | + | 0.972569i | \(0.574728\pi\) | |||||||
\(678\) | 1.00629 | + | 3.09703i | 0.0386462 | + | 0.118941i | ||||
\(679\) | −1.52827 | + | 1.11035i | −0.0586495 | + | 0.0426114i | ||||
\(680\) | −0.347816 | − | 0.252703i | −0.0133381 | − | 0.00969071i | ||||
\(681\) | −10.7507 | −0.411967 | ||||||||
\(682\) | −16.0131 | − | 2.88682i | −0.613174 | − | 0.110542i | ||||
\(683\) | 15.7509 | 0.602690 | 0.301345 | − | 0.953515i | \(-0.402564\pi\) | ||||
0.301345 | + | 0.953515i | \(0.402564\pi\) | |||||||
\(684\) | −1.30150 | − | 0.945592i | −0.0497639 | − | 0.0361556i | ||||
\(685\) | 1.40307 | − | 1.01939i | 0.0536086 | − | 0.0389489i | ||||
\(686\) | −5.92404 | − | 18.2323i | −0.226181 | − | 0.696113i | ||||
\(687\) | 15.4425 | 0.589168 | ||||||||
\(688\) | −6.49603 | −0.247659 | ||||||||
\(689\) | −8.41387 | − | 25.8952i | −0.320543 | − | 0.986530i | ||||
\(690\) | −0.461201 | + | 1.41943i | −0.0175576 | + | 0.0540368i | ||||
\(691\) | −0.826100 | + | 2.54247i | −0.0314263 | + | 0.0967203i | −0.965539 | − | 0.260257i | \(-0.916193\pi\) |
0.934113 | + | 0.356977i | \(0.116193\pi\) | |||||||
\(692\) | −12.3841 | − | 8.99761i | −0.470775 | − | 0.342038i | ||||
\(693\) | 2.29420 | + | 7.06081i | 0.0871493 | + | 0.268218i | ||||
\(694\) | 9.18081 | + | 6.67025i | 0.348499 | + | 0.253199i | ||||
\(695\) | 16.3904 | − | 11.9083i | 0.621724 | − | 0.451709i | ||||
\(696\) | −0.464074 | + | 1.42827i | −0.0175907 | + | 0.0541386i | ||||
\(697\) | 1.06520 | − | 0.773917i | 0.0403475 | − | 0.0293142i | ||||
\(698\) | 23.3929 | − | 16.9960i | 0.885436 | − | 0.643307i | ||||
\(699\) | −1.52663 | + | 4.69848i | −0.0577424 | + | 0.177713i | ||||
\(700\) | 2.05526 | − | 1.49323i | 0.0776814 | − | 0.0564388i | ||||
\(701\) | 16.8116 | + | 12.2143i | 0.634964 | + | 0.461328i | 0.858116 | − | 0.513455i | \(-0.171635\pi\) |
−0.223153 | + | 0.974784i | \(0.571635\pi\) | |||||||
\(702\) | −1.59406 | − | 4.90600i | −0.0601637 | − | 0.185165i | ||||
\(703\) | −9.10299 | − | 6.61371i | −0.343326 | − | 0.249441i | ||||
\(704\) | −0.903072 | + | 2.77937i | −0.0340358 | + | 0.104751i | ||||
\(705\) | 3.53128 | − | 10.8682i | 0.132996 | − | 0.409318i | ||||
\(706\) | −4.07412 | − | 12.5388i | −0.153331 | − | 0.471905i | ||||
\(707\) | 11.6329 | 0.437500 | ||||||||
\(708\) | 6.91666 | 0.259944 | ||||||||
\(709\) | 11.1946 | + | 34.4534i | 0.420422 | + | 1.29393i | 0.907311 | + | 0.420461i | \(0.138132\pi\) |
−0.486889 | + | 0.873464i | \(0.661868\pi\) | |||||||
\(710\) | 10.8049 | − | 7.85023i | 0.405501 | − | 0.294614i | ||||
\(711\) | −5.25540 | − | 3.81827i | −0.197093 | − | 0.143196i | ||||
\(712\) | 7.33401 | 0.274854 | ||||||||
\(713\) | −8.17794 | − | 1.47431i | −0.306266 | − | 0.0552133i | ||||
\(714\) | −1.09219 | −0.0408743 | ||||||||
\(715\) | 12.1960 | + | 8.86094i | 0.456106 | + | 0.331380i | ||||
\(716\) | −7.33641 | + | 5.33021i | −0.274174 | + | 0.199199i | ||||
\(717\) | −5.76371 | − | 17.7389i | −0.215250 | − | 0.662470i | ||||
\(718\) | 23.4411 | 0.874814 | ||||||||
\(719\) | −18.9254 | −0.705798 | −0.352899 | − | 0.935661i | \(-0.614804\pi\) | ||||
−0.352899 | + | 0.935661i | \(0.614804\pi\) | |||||||
\(720\) | −0.309017 | − | 0.951057i | −0.0115164 | − | 0.0354438i | ||||
\(721\) | 1.19492 | − | 3.67759i | 0.0445012 | − | 0.136961i | ||||
\(722\) | 5.07158 | − | 15.6087i | 0.188745 | − | 0.580896i | ||||
\(723\) | −4.88648 | − | 3.55023i | −0.181730 | − | 0.132035i | ||||
\(724\) | 5.14303 | + | 15.8286i | 0.191139 | + | 0.588265i | ||||
\(725\) | 1.21496 | + | 0.882722i | 0.0451226 | + | 0.0327835i | ||||
\(726\) | 1.98983 | − | 1.44570i | 0.0738495 | − | 0.0536548i | ||||
\(727\) | 13.2709 | − | 40.8437i | 0.492192 | − | 1.51481i | −0.329097 | − | 0.944296i | \(-0.606744\pi\) |
0.821288 | − | 0.570513i | \(-0.193256\pi\) | |||||||
\(728\) | 10.6020 | − | 7.70279i | 0.392935 | − | 0.285484i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 2.96926 | − | 9.13845i | 0.109897 | − | 0.338229i | ||||
\(731\) | 2.25942 | − | 1.64157i | 0.0835677 | − | 0.0607155i | ||||
\(732\) | −3.80150 | − | 2.76195i | −0.140507 | − | 0.102085i | ||||
\(733\) | −1.63851 | − | 5.04283i | −0.0605199 | − | 0.186261i | 0.916226 | − | 0.400662i | \(-0.131220\pi\) |
−0.976746 | + | 0.214401i | \(0.931220\pi\) | |||||||
\(734\) | −5.37307 | − | 3.90377i | −0.198324 | − | 0.144091i | ||||
\(735\) | −0.168780 | + | 0.519450i | −0.00622553 | + | 0.0191602i | ||||
\(736\) | −0.461201 | + | 1.41943i | −0.0170001 | + | 0.0523209i | ||||
\(737\) | 10.4949 | + | 32.2999i | 0.386584 | + | 1.18978i | ||||
\(738\) | 3.06255 | 0.112734 | ||||||||
\(739\) | −11.8474 | −0.435815 | −0.217908 | − | 0.975969i | \(-0.569923\pi\) | ||||
−0.217908 | + | 0.975969i | \(0.569923\pi\) | |||||||
\(740\) | −2.16134 | − | 6.65193i | −0.0794526 | − | 0.244530i | ||||
\(741\) | −6.71373 | + | 4.87781i | −0.246635 | + | 0.179191i | ||||
\(742\) | −10.8482 | − | 7.88169i | −0.398251 | − | 0.289346i | ||||
\(743\) | −44.5864 | −1.63572 | −0.817858 | − | 0.575421i | \(-0.804838\pi\) | ||||
−0.817858 | + | 0.575421i | \(0.804838\pi\) | |||||||
\(744\) | 5.01358 | − | 2.42156i | 0.183807 | − | 0.0887788i | ||||
\(745\) | 2.53142 | 0.0927439 | ||||||||
\(746\) | 6.51500 | + | 4.73342i | 0.238531 | + | 0.173303i | ||||
\(747\) | 1.41953 | − | 1.03135i | 0.0519379 | − | 0.0377351i | ||||
\(748\) | −0.388252 | − | 1.19492i | −0.0141959 | − | 0.0436905i | ||||
\(749\) | 20.8704 | 0.762588 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −7.17256 | − | 22.0749i | −0.261730 | − | 0.805523i | −0.992429 | − | 0.122823i | \(-0.960805\pi\) |
0.730698 | − | 0.682701i | \(-0.239195\pi\) | |||||||
\(752\) | 3.53128 | − | 10.8682i | 0.128772 | − | 0.396321i | ||||
\(753\) | −7.70753 | + | 23.7213i | −0.280878 | + | 0.864453i | ||||
\(754\) | 6.26735 | + | 4.55349i | 0.228243 | + | 0.165828i | ||||
\(755\) | −3.01482 | − | 9.27866i | −0.109721 | − | 0.337685i | ||||
\(756\) | −2.05526 | − | 1.49323i | −0.0747489 | − | 0.0543083i | ||||
\(757\) | −31.5722 | + | 22.9386i | −1.14751 | + | 0.833716i | −0.988148 | − | 0.153503i | \(-0.950944\pi\) |
−0.159364 | + | 0.987220i | \(0.550944\pi\) | |||||||
\(758\) | −7.75751 | + | 23.8752i | −0.281765 | + | 0.867185i | ||||
\(759\) | −3.52863 | + | 2.56370i | −0.128081 | + | 0.0930563i | ||||
\(760\) | −1.30150 | + | 0.945592i | −0.0472102 | + | 0.0343002i | ||||
\(761\) | 13.3303 | − | 41.0264i | 0.483222 | − | 1.48720i | −0.351317 | − | 0.936257i | \(-0.614266\pi\) |
0.834539 | − | 0.550948i | \(-0.185734\pi\) | |||||||
\(762\) | −2.33764 | + | 1.69840i | −0.0846839 | + | 0.0615265i | ||||
\(763\) | −26.6074 | − | 19.3314i | −0.963252 | − | 0.699844i | ||||
\(764\) | 3.20457 | + | 9.86265i | 0.115937 | + | 0.356818i | ||||
\(765\) | 0.347816 | + | 0.252703i | 0.0125753 | + | 0.00913649i | ||||
\(766\) | −3.35588 | + | 10.3283i | −0.121253 | + | 0.373178i | ||||
\(767\) | 11.0255 | − | 33.9331i | 0.398109 | − | 1.22525i | ||||
\(768\) | −0.309017 | − | 0.951057i | −0.0111507 | − | 0.0343183i | ||||
\(769\) | −39.8430 | −1.43677 | −0.718387 | − | 0.695644i | \(-0.755119\pi\) | ||||
−0.718387 | + | 0.695644i | \(0.755119\pi\) | |||||||
\(770\) | 7.42418 | 0.267549 | ||||||||
\(771\) | 7.68245 | + | 23.6441i | 0.276677 | + | 0.851523i | ||||
\(772\) | −4.65861 | + | 3.38468i | −0.167667 | + | 0.121817i | ||||
\(773\) | −4.44351 | − | 3.22840i | −0.159822 | − | 0.116117i | 0.505000 | − | 0.863119i | \(-0.331493\pi\) |
−0.664822 | + | 0.747002i | \(0.731493\pi\) | |||||||
\(774\) | 6.49603 | 0.233495 | ||||||||
\(775\) | −0.753761 | − | 5.51651i | −0.0270759 | − | 0.198159i | ||||
\(776\) | 0.743589 | 0.0266933 | ||||||||
\(777\) | −14.3750 | − | 10.4440i | −0.515700 | − | 0.374678i | ||||
\(778\) | 8.03168 | − | 5.83536i | 0.287950 | − | 0.209208i | ||||
\(779\) | −1.52248 | − | 4.68571i | −0.0545485 | − | 0.167883i | ||||
\(780\) | −5.15847 | −0.184703 | ||||||||
\(781\) | 39.0304 | 1.39662 | ||||||||
\(782\) | −0.198281 | − | 0.610248i | −0.00709053 | − | 0.0218224i | ||||
\(783\) | 0.464074 | − | 1.42827i | 0.0165847 | − | 0.0510423i | ||||
\(784\) | −0.168780 | + | 0.519450i | −0.00602784 | + | 0.0185518i | ||||
\(785\) | 0.0851188 | + | 0.0618425i | 0.00303802 | + | 0.00220725i | ||||
\(786\) | 5.24897 | + | 16.1547i | 0.187225 | + | 0.576218i | ||||
\(787\) | 14.9213 | + | 10.8410i | 0.531887 | + | 0.386439i | 0.821063 | − | 0.570837i | \(-0.193381\pi\) |
−0.289176 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(788\) | −12.2750 | + | 8.91834i | −0.437280 | + | 0.317703i | ||||
\(789\) | 1.99549 | − | 6.14148i | 0.0710413 | − | 0.218643i | ||||
\(790\) | −5.25540 | + | 3.81827i | −0.186979 | + | 0.135848i | ||||
\(791\) | 6.69276 | − | 4.86257i | 0.237967 | − | 0.172893i | ||||
\(792\) | 0.903072 | − | 2.77937i | 0.0320893 | − | 0.0987606i | ||||
\(793\) | −19.6099 | + | 14.2474i | −0.696368 | + | 0.505941i | ||||
\(794\) | 22.9875 | + | 16.7014i | 0.815797 | + | 0.592711i | ||||
\(795\) | 1.63108 | + | 5.01994i | 0.0578484 | + | 0.178039i | ||||
\(796\) | 18.1066 | + | 13.1552i | 0.641772 | + | 0.466275i | ||||
\(797\) | −1.58634 | + | 4.88224i | −0.0561910 | + | 0.172938i | −0.975213 | − | 0.221268i | \(-0.928980\pi\) |
0.919022 | + | 0.394206i | \(0.128980\pi\) | |||||||
\(798\) | −1.26292 | + | 3.88687i | −0.0447069 | + | 0.137594i | ||||
\(799\) | 1.51818 | + | 4.67248i | 0.0537094 | + | 0.165300i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −7.33401 | −0.259134 | ||||||||
\(802\) | 11.0550 | + | 34.0239i | 0.390367 | + | 1.20143i | ||||
\(803\) | 22.7177 | − | 16.5054i | 0.801690 | − | 0.582462i | ||||
\(804\) | −9.40184 | − | 6.83083i | −0.331577 | − | 0.240905i | ||||
\(805\) | 3.79155 | 0.133634 | ||||||||
\(806\) | −3.88825 | − | 28.4567i | −0.136958 | − | 1.00235i | ||||
\(807\) | 29.9031 | 1.05264 | ||||||||
\(808\) | −3.70457 | − | 2.69153i | −0.130326 | − | 0.0946876i | ||||
\(809\) | −15.1272 | + | 10.9905i | −0.531844 | + | 0.386407i | −0.821047 | − | 0.570861i | \(-0.806610\pi\) |
0.289203 | + | 0.957268i | \(0.406610\pi\) | |||||||
\(810\) | 0.309017 | + | 0.951057i | 0.0108578 | + | 0.0334167i | ||||
\(811\) | −46.0138 | −1.61576 | −0.807882 | − | 0.589344i | \(-0.799386\pi\) | ||||
−0.807882 | + | 0.589344i | \(0.799386\pi\) | |||||||
\(812\) | 3.81517 | 0.133886 | ||||||||
\(813\) | −7.51435 | − | 23.1268i | −0.263540 | − | 0.811092i | ||||
\(814\) | 6.31632 | − | 19.4396i | 0.221387 | − | 0.681358i | ||||
\(815\) | −6.48797 | + | 19.9679i | −0.227264 | + | 0.699445i | ||||
\(816\) | 0.347816 | + | 0.252703i | 0.0121760 | + | 0.00884637i | ||||
\(817\) | −3.22935 | − | 9.93892i | −0.112981 | − | 0.347719i | ||||
\(818\) | 0.637502 | + | 0.463172i | 0.0222897 | + | 0.0161944i | ||||
\(819\) | −10.6020 | + | 7.70279i | −0.370463 | + | 0.269157i | ||||
\(820\) | 0.946381 | − | 2.91266i | 0.0330491 | − | 0.101715i | ||||
\(821\) | 6.34038 | − | 4.60656i | 0.221281 | − | 0.160770i | −0.471622 | − | 0.881801i | \(-0.656331\pi\) |
0.692903 | + | 0.721031i | \(0.256331\pi\) | |||||||
\(822\) | −1.40307 | + | 1.01939i | −0.0489378 | + | 0.0355554i | ||||
\(823\) | 1.54176 | − | 4.74504i | 0.0537423 | − | 0.165402i | −0.920583 | − | 0.390547i | \(-0.872286\pi\) |
0.974325 | + | 0.225146i | \(0.0722858\pi\) | |||||||
\(824\) | −1.23142 | + | 0.894679i | −0.0428985 | + | 0.0311676i | ||||
\(825\) | −2.36427 | − | 1.71775i | −0.0823134 | − | 0.0598042i | ||||
\(826\) | −5.42984 | − | 16.7113i | −0.188928 | − | 0.581461i | ||||
\(827\) | −2.71838 | − | 1.97502i | −0.0945272 | − | 0.0686780i | 0.539518 | − | 0.841974i | \(-0.318607\pi\) |
−0.634045 | + | 0.773296i | \(0.718607\pi\) | |||||||
\(828\) | 0.461201 | − | 1.41943i | 0.0160279 | − | 0.0493287i | ||||
\(829\) | −9.72945 | + | 29.9442i | −0.337918 | + | 1.04000i | 0.627349 | + | 0.778738i | \(0.284140\pi\) |
−0.965267 | + | 0.261266i | \(0.915860\pi\) | |||||||
\(830\) | −0.542212 | − | 1.66876i | −0.0188205 | − | 0.0579234i | ||||
\(831\) | −13.6640 | −0.473998 | ||||||||
\(832\) | −5.15847 | −0.178838 | ||||||||
\(833\) | −0.0725624 | − | 0.223324i | −0.00251414 | − | 0.00773772i | ||||
\(834\) | −16.3904 | + | 11.9083i | −0.567554 | + | 0.412352i | ||||
\(835\) | −1.25089 | − | 0.908823i | −0.0432888 | − | 0.0314511i | ||||
\(836\) | −4.70138 | −0.162601 | ||||||||
\(837\) | −5.01358 | + | 2.42156i | −0.173295 | + | 0.0837015i | ||||
\(838\) | 34.5690 | 1.19416 | ||||||||
\(839\) | −6.38124 | − | 4.63625i | −0.220305 | − | 0.160061i | 0.472159 | − | 0.881513i | \(-0.343475\pi\) |
−0.692464 | + | 0.721452i | \(0.743475\pi\) | |||||||
\(840\) | −2.05526 | + | 1.49323i | −0.0709131 | + | 0.0515214i | ||||
\(841\) | −8.26456 | − | 25.4357i | −0.284985 | − | 0.877093i | ||||
\(842\) | 2.06300 | 0.0710957 | ||||||||
\(843\) | −13.7652 | −0.474098 | ||||||||
\(844\) | −0.458328 | − | 1.41059i | −0.0157763 | − | 0.0485545i | ||||
\(845\) | −4.20567 | + | 12.9437i | −0.144679 | + | 0.445277i | ||||
\(846\) | −3.53128 | + | 10.8682i | −0.121408 | + | 0.373655i | ||||
\(847\) | −5.05503 | − | 3.67270i | −0.173693 | − | 0.126195i | ||||
\(848\) | 1.63108 | + | 5.01994i | 0.0560115 | + | 0.172386i | ||||
\(849\) | −1.45691 | − | 1.05851i | −0.0500011 | − | 0.0363280i | ||||
\(850\) | 0.347816 | − | 0.252703i | 0.0119300 | − | 0.00866764i | ||||
\(851\) | 3.22576 | − | 9.92786i | 0.110578 | − | 0.340323i | ||||
\(852\) | −10.8049 | + | 7.85023i | −0.370170 | + | 0.268944i | ||||
\(853\) | −27.7507 | + | 20.1621i | −0.950167 | + | 0.690337i | −0.950846 | − | 0.309663i | \(-0.899784\pi\) |
0.000679349 | 1.00000i | \(0.499784\pi\) | ||||||||
\(854\) | −3.68882 | + | 11.3530i | −0.126229 | + | 0.388492i | ||||
\(855\) | 1.30150 | − | 0.945592i | 0.0445102 | − | 0.0323386i | ||||
\(856\) | −6.64630 | − | 4.82882i | −0.227166 | − | 0.165046i | ||||
\(857\) | −5.26858 | − | 16.2150i | −0.179971 | − | 0.553895i | 0.819854 | − | 0.572572i | \(-0.194054\pi\) |
−0.999826 | + | 0.0186776i | \(0.994054\pi\) | |||||||
\(858\) | −12.1960 | − | 8.86094i | −0.416366 | − | 0.302507i | ||||
\(859\) | −1.27397 | + | 3.92086i | −0.0434671 | + | 0.133778i | −0.970435 | − | 0.241363i | \(-0.922406\pi\) |
0.926968 | + | 0.375141i | \(0.122406\pi\) | |||||||
\(860\) | 2.00738 | − | 6.17809i | 0.0684512 | − | 0.210671i | ||||
\(861\) | −2.40422 | − | 7.39943i | −0.0819357 | − | 0.252172i | ||||
\(862\) | 34.9257 | 1.18957 | ||||||||
\(863\) | −37.8863 | −1.28967 | −0.644833 | − | 0.764323i | \(-0.723073\pi\) | ||||
−0.644833 | + | 0.764323i | \(0.723073\pi\) | |||||||
\(864\) | 0.309017 | + | 0.951057i | 0.0105130 | + | 0.0323556i | ||||
\(865\) | 12.3841 | − | 8.99761i | 0.421074 | − | 0.305928i | ||||
\(866\) | 9.82224 | + | 7.13628i | 0.333773 | + | 0.242501i | ||||
\(867\) | 16.8152 | 0.571073 | ||||||||
\(868\) | −9.78659 | − | 10.2123i | −0.332179 | − | 0.346628i | ||||
\(869\) | −18.9840 | −0.643989 | ||||||||
\(870\) | −1.21496 | − | 0.882722i | −0.0411911 | − | 0.0299271i | ||||
\(871\) | −48.4991 | + | 35.2367i | −1.64333 | + | 1.19395i | ||||
\(872\) | 4.00054 | + | 12.3124i | 0.135475 | + | 0.416950i | ||||
\(873\) | −0.743589 | −0.0251667 | ||||||||
\(874\) | −2.40101 | −0.0812152 | ||||||||
\(875\) | 0.785038 | + | 2.41610i | 0.0265391 | + | 0.0816790i | ||||
\(876\) | −2.96926 | + | 9.13845i | −0.100322 | + | 0.308760i | ||||
\(877\) | −12.7722 | + | 39.3088i | −0.431287 | + | 1.32736i | 0.465558 | + | 0.885017i | \(0.345854\pi\) |
−0.896844 | + | 0.442346i | \(0.854146\pi\) | |||||||
\(878\) | −0.439957 | − | 0.319648i | −0.0148478 | − | 0.0107876i | ||||
\(879\) | −3.04960 | − | 9.38569i | −0.102860 | − | 0.316571i | ||||
\(880\) | −2.36427 | − | 1.71775i | −0.0796996 | − | 0.0579052i | ||||
\(881\) | −23.7829 | + | 17.2793i | −0.801266 | + | 0.582154i | −0.911285 | − | 0.411776i | \(-0.864909\pi\) |
0.110019 | + | 0.993929i | \(0.464909\pi\) | |||||||
\(882\) | 0.168780 | − | 0.519450i | 0.00568311 | − | 0.0174908i | ||||
\(883\) | −25.1422 | + | 18.2669i | −0.846103 | + | 0.614730i | −0.924069 | − | 0.382226i | \(-0.875158\pi\) |
0.0779657 | + | 0.996956i | \(0.475158\pi\) | |||||||
\(884\) | 1.79420 | − | 1.30356i | 0.0603454 | − | 0.0438435i | ||||
\(885\) | −2.13736 | + | 6.57813i | −0.0718467 | + | 0.221121i | ||||
\(886\) | −6.16900 | + | 4.48204i | −0.207252 | + | 0.150577i | ||||
\(887\) | 43.7246 | + | 31.7678i | 1.46813 | + | 1.06666i | 0.981151 | + | 0.193243i | \(0.0619005\pi\) |
0.486977 | + | 0.873415i | \(0.338099\pi\) | |||||||
\(888\) | 2.16134 | + | 6.65193i | 0.0725299 | + | 0.223224i | ||||
\(889\) | 5.93864 | + | 4.31467i | 0.199175 | + | 0.144709i | ||||
\(890\) | −2.26633 | + | 6.97506i | −0.0759677 | + | 0.233804i | ||||
\(891\) | −0.903072 | + | 2.77937i | −0.0302541 | + | 0.0931124i | ||||
\(892\) | 0.103352 | + | 0.318085i | 0.00346048 | + | 0.0106503i | ||||
\(893\) | 18.3838 | 0.615189 | ||||||||
\(894\) | −2.53142 | −0.0846632 | ||||||||
\(895\) | −2.80226 | − | 8.62447i | −0.0936692 | − | 0.288284i | ||||
\(896\) | −2.05526 | + | 1.49323i | −0.0686613 | + | 0.0498854i | ||||
\(897\) | −6.22855 | − | 4.52530i | −0.207965 | − | 0.151096i | ||||
\(898\) | 2.52556 | 0.0842792 | ||||||||
\(899\) | 3.95375 | − | 7.36771i | 0.131865 | − | 0.245727i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −1.83587 | − | 1.33384i | −0.0611617 | − | 0.0444365i | ||||
\(902\) | 7.24072 | − | 5.26069i | 0.241089 | − | 0.175162i | ||||
\(903\) | −5.09963 | − | 15.6950i | −0.169705 | − | 0.522299i | ||||
\(904\) | −3.25641 | −0.108307 | ||||||||
\(905\) | −16.6432 | −0.553238 | ||||||||
\(906\) | 3.01482 | + | 9.27866i | 0.100161 | + | 0.308263i | ||||
\(907\) | −14.9240 | + | 45.9314i | −0.495544 | + | 1.52513i | 0.320563 | + | 0.947227i | \(0.396128\pi\) |
−0.816107 | + | 0.577901i | \(0.803872\pi\) | |||||||
\(908\) | 3.32215 | − | 10.2245i | 0.110249 | − | 0.339312i | ||||
\(909\) | 3.70457 | + | 2.69153i | 0.122873 | + | 0.0892723i | ||||
\(910\) | 4.04960 | + | 12.4634i | 0.134243 | + | 0.413157i | ||||
\(911\) | 38.8304 | + | 28.2120i | 1.28651 | + | 0.934704i | 0.999729 | − | 0.0232923i | \(-0.00741485\pi\) |
0.286781 | + | 0.957996i | \(0.407415\pi\) | |||||||
\(912\) | 1.30150 | − | 0.945592i | 0.0430968 | − | 0.0313117i | ||||
\(913\) | 1.58456 | − | 4.87678i | 0.0524413 | − | 0.161398i | ||||
\(914\) | −17.4337 | + | 12.6663i | −0.576654 | + | 0.418964i | ||||
\(915\) | 3.80150 | − | 2.76195i | 0.125674 | − | 0.0913072i | ||||
\(916\) | −4.77199 | + | 14.6867i | −0.157671 | + | 0.485262i | ||||
\(917\) | 34.9107 | − | 25.3641i | 1.15285 | − | 0.837596i | ||||
\(918\) | −0.347816 | − | 0.252703i | −0.0114796 | − | 0.00834044i | ||||
\(919\) | 3.53570 | + | 10.8818i | 0.116632 | + | 0.358957i | 0.992284 | − | 0.123986i | \(-0.0395679\pi\) |
−0.875652 | + | 0.482943i | \(0.839568\pi\) | |||||||
\(920\) | −1.20744 | − | 0.877257i | −0.0398081 | − | 0.0289223i | ||||
\(921\) | −5.32716 | + | 16.3953i | −0.175536 | + | 0.540244i | ||||
\(922\) | 10.5479 | − | 32.4631i | 0.347376 | − | 1.06911i | ||||
\(923\) | 21.2896 | + | 65.5225i | 0.700755 | + | 2.15670i | ||||
\(924\) | −7.42418 | −0.244238 | ||||||||
\(925\) | 6.99425 | 0.229970 | ||||||||
\(926\) | 9.36337 | + | 28.8175i | 0.307700 | + | 0.947002i | ||||
\(927\) | 1.23142 | − | 0.894679i | 0.0404451 | − | 0.0293851i | ||||
\(928\) | −1.21496 | − | 0.882722i | −0.0398831 | − | 0.0289768i | ||||
\(929\) | −55.7354 | −1.82862 | −0.914309 | − | 0.405017i | \(-0.867266\pi\) | ||||
−0.914309 | + | 0.405017i | \(0.867266\pi\) | |||||||
\(930\) | 0.753761 | + | 5.51651i | 0.0247168 | + | 0.180893i | ||||
\(931\) | −0.878664 | −0.0287970 | ||||||||
\(932\) | −3.99677 | − | 2.90382i | −0.130918 | − | 0.0951178i | ||||
\(933\) | −5.48496 | + | 3.98505i | −0.179569 | + | 0.130465i | ||||
\(934\) | −8.12744 | − | 25.0137i | −0.265938 | − | 0.818473i | ||||
\(935\) | 1.25641 | 0.0410890 | ||||||||
\(936\) | 5.15847 | 0.168610 | ||||||||
\(937\) | 14.2282 | + | 43.7898i | 0.464814 | + | 1.43055i | 0.859217 | + | 0.511612i | \(0.170951\pi\) |
−0.394403 | + | 0.918938i | \(0.629049\pi\) | |||||||
\(938\) | −9.12317 | + | 28.0782i | −0.297882 | + | 0.916787i | ||||
\(939\) | −5.44072 | + | 16.7448i | −0.177551 | + | 0.546446i | ||||
\(940\) | 9.24500 | + | 6.71689i | 0.301539 | + | 0.219081i | ||||
\(941\) | 8.27541 | + | 25.4691i | 0.269771 | + | 0.830268i | 0.990556 | + | 0.137110i | \(0.0437814\pi\) |
−0.720785 | + | 0.693158i | \(0.756219\pi\) | |||||||
\(942\) | −0.0851188 | − | 0.0618425i | −0.00277332 | − | 0.00201494i | ||||
\(943\) | 3.69785 | − | 2.68665i | 0.120419 | − | 0.0874893i | ||||
\(944\) | −2.13736 | + | 6.57813i | −0.0695653 | + | 0.214100i | ||||
\(945\) | 2.05526 | − | 1.49323i | 0.0668575 | − | 0.0485748i | ||||
\(946\) | 15.3584 | − | 11.1585i | 0.499344 | − | 0.362795i | ||||
\(947\) | −2.84446 | + | 8.75435i | −0.0924326 | + | 0.284478i | −0.986576 | − | 0.163302i | \(-0.947785\pi\) |
0.894144 | + | 0.447780i | \(0.147785\pi\) | |||||||
\(948\) | 5.25540 | − | 3.81827i | 0.170687 | − | 0.124012i | ||||
\(949\) | 40.1000 | + | 29.1344i | 1.30170 | + | 0.945742i | ||||
\(950\) | −0.497127 | − | 1.53000i | −0.0161289 | − | 0.0496398i | ||||
\(951\) | 19.9140 | + | 14.4684i | 0.645757 | + | 0.469170i | ||||
\(952\) | 0.337507 | − | 1.03874i | 0.0109387 | − | 0.0336657i | ||||
\(953\) | 10.9724 | − | 33.7696i | 0.355431 | − | 1.09391i | −0.600327 | − | 0.799754i | \(-0.704963\pi\) |
0.955759 | − | 0.294151i | \(-0.0950369\pi\) | |||||||
\(954\) | −1.63108 | − | 5.01994i | −0.0528081 | − | 0.162527i | ||||
\(955\) | −10.3702 | −0.335572 | ||||||||
\(956\) | 18.6518 | 0.603241 | ||||||||
\(957\) | −1.35621 | − | 4.17399i | −0.0438401 | − | 0.134926i | ||||
\(958\) | 11.1729 | − | 8.11761i | 0.360981 | − | 0.262268i | ||||
\(959\) | 3.56442 | + | 2.58970i | 0.115101 | + | 0.0836258i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −29.8637 | + | 8.31625i | −0.963345 | + | 0.268266i | ||||
\(962\) | 36.0797 | 1.16325 | ||||||||
\(963\) | 6.64630 | + | 4.82882i | 0.214174 | + | 0.155607i | ||||
\(964\) | 4.88648 | − | 3.55023i | 0.157383 | − | 0.114345i | ||||
\(965\) | −1.77943 | − | 5.47652i | −0.0572819 | − | 0.176295i | ||||
\(966\) | −3.79155 | −0.121991 | ||||||||
\(967\) | −6.21928 | −0.199998 | −0.0999992 | − | 0.994988i | \(-0.531884\pi\) | ||||
−0.0999992 | + | 0.994988i | \(0.531884\pi\) | |||||||
\(968\) | 0.760047 | + | 2.33918i | 0.0244288 | + | 0.0751842i | ||||
\(969\) | −0.213727 | + | 0.657783i | −0.00686589 | + | 0.0211311i | ||||
\(970\) | −0.229782 | + | 0.707195i | −0.00737785 | + | 0.0227067i | ||||
\(971\) | −24.9388 | − | 18.1191i | −0.800325 | − | 0.581470i | 0.110684 | − | 0.993856i | \(-0.464696\pi\) |
−0.911010 | + | 0.412385i | \(0.864696\pi\) | |||||||
\(972\) | −0.309017 | − | 0.951057i | −0.00991172 | − | 0.0305052i | ||||
\(973\) | 41.6388 | + | 30.2524i | 1.33488 | + | 0.969847i | ||||
\(974\) | 2.66399 | − | 1.93550i | 0.0853599 | − | 0.0620176i | ||||
\(975\) | 1.59406 | − | 4.90600i | 0.0510506 | − | 0.157118i | ||||
\(976\) | 3.80150 | − | 2.76195i | 0.121683 | − | 0.0884078i | ||||
\(977\) | 5.83652 | − | 4.24048i | 0.186727 | − | 0.135665i | −0.490495 | − | 0.871444i | \(-0.663184\pi\) |
0.677221 | + | 0.735779i | \(0.263184\pi\) | |||||||
\(978\) | 6.48797 | − | 19.9679i | 0.207462 | − | 0.638503i | ||||
\(979\) | −17.3396 | + | 12.5980i | −0.554176 | + | 0.402632i | ||||
\(980\) | −0.441871 | − | 0.321038i | −0.0141150 | − | 0.0102552i | ||||
\(981\) | −4.00054 | − | 12.3124i | −0.127727 | − | 0.393105i | ||||
\(982\) | 21.6465 | + | 15.7271i | 0.690767 | + | 0.501872i | ||||
\(983\) | −5.17456 | + | 15.9257i | −0.165043 | + | 0.507949i | −0.999039 | − | 0.0438201i | \(-0.986047\pi\) |
0.833997 | + | 0.551769i | \(0.186047\pi\) | |||||||
\(984\) | −0.946381 | + | 2.91266i | −0.0301695 | + | 0.0928523i | ||||
\(985\) | −4.68865 | − | 14.4302i | −0.149393 | − | 0.459784i | ||||
\(986\) | 0.645649 | 0.0205617 | ||||||||
\(987\) | 29.0307 | 0.924058 | ||||||||
\(988\) | −2.56442 | − | 7.89246i | −0.0815849 | − | 0.251093i | ||||
\(989\) | 7.84357 | − | 5.69869i | 0.249411 | − | 0.181208i | ||||
\(990\) | 2.36427 | + | 1.71775i | 0.0751415 | + | 0.0545935i | ||||
\(991\) | 9.33531 | 0.296546 | 0.148273 | − | 0.988946i | \(-0.452629\pi\) | ||||
0.148273 | + | 0.988946i | \(0.452629\pi\) | |||||||
\(992\) | 0.753761 | + | 5.51651i | 0.0239319 | + | 0.175149i | ||||
\(993\) | −26.1979 | −0.831366 | ||||||||
\(994\) | 27.4492 | + | 19.9430i | 0.870635 | + | 0.632554i | ||||
\(995\) | −18.1066 | + | 13.1552i | −0.574019 | + | 0.417049i | ||||
\(996\) | 0.542212 | + | 1.66876i | 0.0171806 | + | 0.0528766i | ||||
\(997\) | −54.0993 | −1.71334 | −0.856671 | − | 0.515862i | \(-0.827472\pi\) | ||||
−0.856671 | + | 0.515862i | \(0.827472\pi\) | |||||||
\(998\) | −38.6730 | −1.22417 | ||||||||
\(999\) | −2.16134 | − | 6.65193i | −0.0683819 | − | 0.210458i |
(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 | 930.2.n.b.901.1 | yes | 8 | |
31.16 | even | 5 | inner | 930.2.n.b.481.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.b.481.1 | ✓ | 8 | 31.16 | even | 5 | inner | |
930.2.n.b.901.1 | yes | 8 | 1.1 | even | 1 | trivial |