Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
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 | 421.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.421 |
Dual form | 770.2.n.c.631.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | −0.500000 | − | 1.53884i | −0.288675 | − | 0.888451i | −0.985273 | − | 0.170989i | \(-0.945304\pi\) |
0.696598 | − | 0.717462i | \(-0.254696\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | −1.30902 | − | 0.951057i | −0.534404 | − | 0.388267i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | 0.309017 | − | 0.224514i | 0.103006 | − | 0.0748380i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.30902 | + | 0.224514i | 0.997706 | + | 0.0676935i | ||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | 0.618034 | − | 0.449028i | 0.171412 | − | 0.124538i | −0.498772 | − | 0.866733i | \(-0.666215\pi\) |
0.670184 | + | 0.742195i | \(0.266215\pi\) | |||||||
\(14\) | −0.309017 | − | 0.951057i | −0.0825883 | − | 0.254181i | ||||
\(15\) | 0.500000 | − | 1.53884i | 0.129099 | − | 0.397327i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −0.500000 | − | 0.363271i | −0.121268 | − | 0.0881062i | 0.525498 | − | 0.850795i | \(-0.323879\pi\) |
−0.646766 | + | 0.762688i | \(0.723879\pi\) | |||||||
\(18\) | 0.118034 | − | 0.363271i | 0.0278209 | − | 0.0856239i | ||||
\(19\) | −0.809017 | − | 2.48990i | −0.185601 | − | 0.571222i | 0.814357 | − | 0.580364i | \(-0.197090\pi\) |
−0.999958 | + | 0.00914245i | \(0.997090\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | −1.61803 | −0.353084 | ||||||||
\(22\) | 2.80902 | − | 1.76336i | 0.598884 | − | 0.375949i | ||||
\(23\) | 0.472136 | 0.0984472 | 0.0492236 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492236 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(24\) | −1.30902 | + | 0.951057i | −0.267202 | + | 0.194134i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0.236068 | − | 0.726543i | 0.0462967 | − | 0.142487i | ||||
\(27\) | −4.42705 | − | 3.21644i | −0.851986 | − | 0.619004i | ||||
\(28\) | −0.809017 | − | 0.587785i | −0.152890 | − | 0.111081i | ||||
\(29\) | 1.23607 | − | 3.80423i | 0.229532 | − | 0.706427i | −0.768268 | − | 0.640129i | \(-0.778881\pi\) |
0.997800 | − | 0.0662984i | \(-0.0211189\pi\) | |||||||
\(30\) | −0.500000 | − | 1.53884i | −0.0912871 | − | 0.280953i | ||||
\(31\) | −3.61803 | + | 2.62866i | −0.649818 | + | 0.472120i | −0.863209 | − | 0.504846i | \(-0.831549\pi\) |
0.213391 | + | 0.976967i | \(0.431549\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.30902 | − | 5.20431i | −0.227871 | − | 0.905954i | ||||
\(34\) | −0.618034 | −0.105992 | ||||||||
\(35\) | 0.809017 | − | 0.587785i | 0.136749 | − | 0.0993538i | ||||
\(36\) | −0.118034 | − | 0.363271i | −0.0196723 | − | 0.0605452i | ||||
\(37\) | −1.14590 | + | 3.52671i | −0.188384 | + | 0.579788i | −0.999990 | − | 0.00441771i | \(-0.998594\pi\) |
0.811606 | + | 0.584206i | \(0.198594\pi\) | |||||||
\(38\) | −2.11803 | − | 1.53884i | −0.343590 | − | 0.249633i | ||||
\(39\) | −1.00000 | − | 0.726543i | −0.160128 | − | 0.116340i | ||||
\(40\) | 0.309017 | − | 0.951057i | 0.0488599 | − | 0.150375i | ||||
\(41\) | 1.97214 | + | 6.06961i | 0.307996 | + | 0.947914i | 0.978542 | + | 0.206046i | \(0.0660597\pi\) |
−0.670546 | + | 0.741868i | \(0.733940\pi\) | |||||||
\(42\) | −1.30902 | + | 0.951057i | −0.201986 | + | 0.146751i | ||||
\(43\) | −2.38197 | −0.363246 | −0.181623 | − | 0.983368i | \(-0.558135\pi\) | ||||
−0.181623 | + | 0.983368i | \(0.558135\pi\) | |||||||
\(44\) | 1.23607 | − | 3.07768i | 0.186344 | − | 0.463978i | ||||
\(45\) | 0.381966 | 0.0569401 | ||||||||
\(46\) | 0.381966 | − | 0.277515i | 0.0563178 | − | 0.0409173i | ||||
\(47\) | −3.47214 | − | 10.6861i | −0.506463 | − | 1.55873i | −0.798297 | − | 0.602264i | \(-0.794265\pi\) |
0.291834 | − | 0.956469i | \(-0.405735\pi\) | |||||||
\(48\) | −0.500000 | + | 1.53884i | −0.0721688 | + | 0.222113i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | −0.309017 | + | 0.951057i | −0.0432710 | + | 0.133175i | ||||
\(52\) | −0.236068 | − | 0.726543i | −0.0327367 | − | 0.100753i | ||||
\(53\) | −2.00000 | + | 1.45309i | −0.274721 | + | 0.199597i | −0.716612 | − | 0.697472i | \(-0.754308\pi\) |
0.441891 | + | 0.897069i | \(0.354308\pi\) | |||||||
\(54\) | −5.47214 | −0.744663 | ||||||||
\(55\) | 2.54508 | + | 2.12663i | 0.343179 | + | 0.286754i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.42705 | + | 2.48990i | −0.453924 | + | 0.329795i | ||||
\(58\) | −1.23607 | − | 3.80423i | −0.162304 | − | 0.499519i | ||||
\(59\) | −0.427051 | + | 1.31433i | −0.0555973 | + | 0.171111i | −0.974999 | − | 0.222209i | \(-0.928673\pi\) |
0.919402 | + | 0.393320i | \(0.128673\pi\) | |||||||
\(60\) | −1.30902 | − | 0.951057i | −0.168993 | − | 0.122781i | ||||
\(61\) | 6.47214 | + | 4.70228i | 0.828672 | + | 0.602066i | 0.919183 | − | 0.393830i | \(-0.128850\pi\) |
−0.0905112 | + | 0.995895i | \(0.528850\pi\) | |||||||
\(62\) | −1.38197 | + | 4.25325i | −0.175510 | + | 0.540164i | ||||
\(63\) | −0.118034 | − | 0.363271i | −0.0148709 | − | 0.0457679i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0.763932 | 0.0947541 | ||||||||
\(66\) | −4.11803 | − | 3.44095i | −0.506895 | − | 0.423552i | ||||
\(67\) | 5.09017 | 0.621863 | 0.310932 | − | 0.950432i | \(-0.399359\pi\) | ||||
0.310932 | + | 0.950432i | \(0.399359\pi\) | |||||||
\(68\) | −0.500000 | + | 0.363271i | −0.0606339 | + | 0.0440531i | ||||
\(69\) | −0.236068 | − | 0.726543i | −0.0284192 | − | 0.0874654i | ||||
\(70\) | 0.309017 | − | 0.951057i | 0.0369346 | − | 0.113673i | ||||
\(71\) | 5.23607 | + | 3.80423i | 0.621407 | + | 0.451479i | 0.853413 | − | 0.521236i | \(-0.174529\pi\) |
−0.232006 | + | 0.972714i | \(0.574529\pi\) | |||||||
\(72\) | −0.309017 | − | 0.224514i | −0.0364180 | − | 0.0264592i | ||||
\(73\) | −3.50000 | + | 10.7719i | −0.409644 | + | 1.26075i | 0.507311 | + | 0.861763i | \(0.330640\pi\) |
−0.916955 | + | 0.398991i | \(0.869360\pi\) | |||||||
\(74\) | 1.14590 | + | 3.52671i | 0.133208 | + | 0.409972i | ||||
\(75\) | 1.30902 | − | 0.951057i | 0.151152 | − | 0.109819i | ||||
\(76\) | −2.61803 | −0.300309 | ||||||||
\(77\) | 1.23607 | − | 3.07768i | 0.140863 | − | 0.350735i | ||||
\(78\) | −1.23607 | −0.139957 | ||||||||
\(79\) | 9.47214 | − | 6.88191i | 1.06570 | − | 0.774275i | 0.0905644 | − | 0.995891i | \(-0.471133\pi\) |
0.975134 | + | 0.221615i | \(0.0711329\pi\) | |||||||
\(80\) | −0.309017 | − | 0.951057i | −0.0345492 | − | 0.106331i | ||||
\(81\) | −2.38197 | + | 7.33094i | −0.264663 | + | 0.814549i | ||||
\(82\) | 5.16312 | + | 3.75123i | 0.570171 | + | 0.414254i | ||||
\(83\) | 0.0729490 | + | 0.0530006i | 0.00800719 | + | 0.00581757i | 0.591782 | − | 0.806098i | \(-0.298425\pi\) |
−0.583774 | + | 0.811916i | \(0.698425\pi\) | |||||||
\(84\) | −0.500000 | + | 1.53884i | −0.0545545 | + | 0.167901i | ||||
\(85\) | −0.190983 | − | 0.587785i | −0.0207150 | − | 0.0637543i | ||||
\(86\) | −1.92705 | + | 1.40008i | −0.207799 | + | 0.150975i | ||||
\(87\) | −6.47214 | −0.693886 | ||||||||
\(88\) | −0.809017 | − | 3.21644i | −0.0862415 | − | 0.342874i | ||||
\(89\) | 3.14590 | 0.333465 | 0.166732 | − | 0.986002i | \(-0.446678\pi\) | ||||
0.166732 | + | 0.986002i | \(0.446678\pi\) | |||||||
\(90\) | 0.309017 | − | 0.224514i | 0.0325733 | − | 0.0236659i | ||||
\(91\) | −0.236068 | − | 0.726543i | −0.0247466 | − | 0.0761624i | ||||
\(92\) | 0.145898 | − | 0.449028i | 0.0152109 | − | 0.0468144i | ||||
\(93\) | 5.85410 | + | 4.25325i | 0.607042 | + | 0.441042i | ||||
\(94\) | −9.09017 | − | 6.60440i | −0.937579 | − | 0.681191i | ||||
\(95\) | 0.809017 | − | 2.48990i | 0.0830034 | − | 0.255458i | ||||
\(96\) | 0.500000 | + | 1.53884i | 0.0510310 | + | 0.157057i | ||||
\(97\) | −11.1631 | + | 8.11048i | −1.13344 | + | 0.823495i | −0.986192 | − | 0.165605i | \(-0.947042\pi\) |
−0.147251 | + | 0.989099i | \(0.547042\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.07295 | − | 0.673542i | 0.107835 | − | 0.0676935i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.3262 | + | 7.50245i | −1.02750 | + | 0.746522i | −0.967807 | − | 0.251695i | \(-0.919012\pi\) |
−0.0596925 | + | 0.998217i | \(0.519012\pi\) | |||||||
\(102\) | 0.309017 | + | 0.951057i | 0.0305972 | + | 0.0941686i | ||||
\(103\) | 4.23607 | − | 13.0373i | 0.417392 | − | 1.28460i | −0.492701 | − | 0.870198i | \(-0.663991\pi\) |
0.910094 | − | 0.414403i | \(-0.136009\pi\) | |||||||
\(104\) | −0.618034 | − | 0.449028i | −0.0606032 | − | 0.0440308i | ||||
\(105\) | −1.30902 | − | 0.951057i | −0.127747 | − | 0.0928136i | ||||
\(106\) | −0.763932 | + | 2.35114i | −0.0741996 | + | 0.228363i | ||||
\(107\) | 2.50000 | + | 7.69421i | 0.241684 | + | 0.743827i | 0.996164 | + | 0.0875042i | \(0.0278891\pi\) |
−0.754480 | + | 0.656323i | \(0.772111\pi\) | |||||||
\(108\) | −4.42705 | + | 3.21644i | −0.425993 | + | 0.309502i | ||||
\(109\) | 10.1803 | 0.975100 | 0.487550 | − | 0.873095i | \(-0.337891\pi\) | ||||
0.487550 | + | 0.873095i | \(0.337891\pi\) | |||||||
\(110\) | 3.30902 | + | 0.224514i | 0.315502 | + | 0.0214066i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | −0.809017 | + | 0.587785i | −0.0764449 | + | 0.0555405i | ||||
\(113\) | −3.33688 | − | 10.2699i | −0.313907 | − | 0.966108i | −0.976202 | − | 0.216864i | \(-0.930417\pi\) |
0.662294 | − | 0.749244i | \(-0.269583\pi\) | |||||||
\(114\) | −1.30902 | + | 4.02874i | −0.122601 | + | 0.377326i | ||||
\(115\) | 0.381966 | + | 0.277515i | 0.0356185 | + | 0.0258784i | ||||
\(116\) | −3.23607 | − | 2.35114i | −0.300461 | − | 0.218298i | ||||
\(117\) | 0.0901699 | − | 0.277515i | 0.00833621 | − | 0.0256562i | ||||
\(118\) | 0.427051 | + | 1.31433i | 0.0393132 | + | 0.120994i | ||||
\(119\) | −0.500000 | + | 0.363271i | −0.0458349 | + | 0.0333010i | ||||
\(120\) | −1.61803 | −0.147706 | ||||||||
\(121\) | 10.8992 | + | 1.48584i | 0.990835 | + | 0.135076i | ||||
\(122\) | 8.00000 | 0.724286 | ||||||||
\(123\) | 8.35410 | − | 6.06961i | 0.753264 | − | 0.547278i | ||||
\(124\) | 1.38197 | + | 4.25325i | 0.124104 | + | 0.381953i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | −0.309017 | − | 0.224514i | −0.0275294 | − | 0.0200013i | ||||
\(127\) | 6.61803 | + | 4.80828i | 0.587256 | + | 0.426666i | 0.841333 | − | 0.540518i | \(-0.181772\pi\) |
−0.254077 | + | 0.967184i | \(0.581772\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | 1.19098 | + | 3.66547i | 0.104860 | + | 0.322727i | ||||
\(130\) | 0.618034 | − | 0.449028i | 0.0542052 | − | 0.0393824i | ||||
\(131\) | 8.14590 | 0.711710 | 0.355855 | − | 0.934541i | \(-0.384190\pi\) | ||||
0.355855 | + | 0.934541i | \(0.384190\pi\) | |||||||
\(132\) | −5.35410 | − | 0.363271i | −0.466015 | − | 0.0316187i | ||||
\(133\) | −2.61803 | −0.227012 | ||||||||
\(134\) | 4.11803 | − | 2.99193i | 0.355744 | − | 0.258463i | ||||
\(135\) | −1.69098 | − | 5.20431i | −0.145537 | − | 0.447916i | ||||
\(136\) | −0.190983 | + | 0.587785i | −0.0163767 | + | 0.0504022i | ||||
\(137\) | 10.3992 | + | 7.55545i | 0.888462 | + | 0.645506i | 0.935477 | − | 0.353388i | \(-0.114971\pi\) |
−0.0470142 | + | 0.998894i | \(0.514971\pi\) | |||||||
\(138\) | −0.618034 | − | 0.449028i | −0.0526105 | − | 0.0382238i | ||||
\(139\) | −0.472136 | + | 1.45309i | −0.0400460 | + | 0.123249i | −0.969081 | − | 0.246743i | \(-0.920640\pi\) |
0.929035 | + | 0.369992i | \(0.120640\pi\) | |||||||
\(140\) | −0.309017 | − | 0.951057i | −0.0261167 | − | 0.0803789i | ||||
\(141\) | −14.7082 | + | 10.6861i | −1.23865 | + | 0.899935i | ||||
\(142\) | 6.47214 | 0.543130 | ||||||||
\(143\) | 2.14590 | − | 1.34708i | 0.179449 | − | 0.112649i | ||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | 3.23607 | − | 2.35114i | 0.268741 | − | 0.195252i | ||||
\(146\) | 3.50000 | + | 10.7719i | 0.289662 | + | 0.891488i | ||||
\(147\) | −0.500000 | + | 1.53884i | −0.0412393 | + | 0.126922i | ||||
\(148\) | 3.00000 | + | 2.17963i | 0.246598 | + | 0.179164i | ||||
\(149\) | 6.23607 | + | 4.53077i | 0.510879 | + | 0.371175i | 0.813157 | − | 0.582045i | \(-0.197747\pi\) |
−0.302278 | + | 0.953220i | \(0.597747\pi\) | |||||||
\(150\) | 0.500000 | − | 1.53884i | 0.0408248 | − | 0.125646i | ||||
\(151\) | 6.23607 | + | 19.1926i | 0.507484 | + | 1.56188i | 0.796554 | + | 0.604567i | \(0.206654\pi\) |
−0.289070 | + | 0.957308i | \(0.593346\pi\) | |||||||
\(152\) | −2.11803 | + | 1.53884i | −0.171795 | + | 0.124817i | ||||
\(153\) | −0.236068 | −0.0190850 | ||||||||
\(154\) | −0.809017 | − | 3.21644i | −0.0651924 | − | 0.259188i | ||||
\(155\) | −4.47214 | −0.359211 | ||||||||
\(156\) | −1.00000 | + | 0.726543i | −0.0800641 | + | 0.0581700i | ||||
\(157\) | −1.90983 | − | 5.87785i | −0.152421 | − | 0.469104i | 0.845469 | − | 0.534024i | \(-0.179321\pi\) |
−0.997890 | + | 0.0649201i | \(0.979321\pi\) | |||||||
\(158\) | 3.61803 | − | 11.1352i | 0.287835 | − | 0.885866i | ||||
\(159\) | 3.23607 | + | 2.35114i | 0.256637 | + | 0.186458i | ||||
\(160\) | −0.809017 | − | 0.587785i | −0.0639584 | − | 0.0464685i | ||||
\(161\) | 0.145898 | − | 0.449028i | 0.0114984 | − | 0.0353884i | ||||
\(162\) | 2.38197 | + | 7.33094i | 0.187145 | + | 0.575973i | ||||
\(163\) | 18.2984 | − | 13.2945i | 1.43324 | − | 1.04131i | 0.443837 | − | 0.896107i | \(-0.353617\pi\) |
0.989402 | − | 0.145202i | \(-0.0463832\pi\) | |||||||
\(164\) | 6.38197 | 0.498348 | ||||||||
\(165\) | 2.00000 | − | 4.97980i | 0.155700 | − | 0.387677i | ||||
\(166\) | 0.0901699 | 0.00699854 | ||||||||
\(167\) | −8.09017 | + | 5.87785i | −0.626036 | + | 0.454842i | −0.855025 | − | 0.518587i | \(-0.826458\pi\) |
0.228989 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(168\) | 0.500000 | + | 1.53884i | 0.0385758 | + | 0.118724i | ||||
\(169\) | −3.83688 | + | 11.8087i | −0.295145 | + | 0.908362i | ||||
\(170\) | −0.500000 | − | 0.363271i | −0.0383482 | − | 0.0278616i | ||||
\(171\) | −0.809017 | − | 0.587785i | −0.0618671 | − | 0.0449491i | ||||
\(172\) | −0.736068 | + | 2.26538i | −0.0561247 | + | 0.172734i | ||||
\(173\) | 1.47214 | + | 4.53077i | 0.111924 | + | 0.344468i | 0.991293 | − | 0.131673i | \(-0.0420350\pi\) |
−0.879369 | + | 0.476141i | \(0.842035\pi\) | |||||||
\(174\) | −5.23607 | + | 3.80423i | −0.396945 | + | 0.288398i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −2.54508 | − | 2.12663i | −0.191843 | − | 0.160301i | ||||
\(177\) | 2.23607 | 0.168073 | ||||||||
\(178\) | 2.54508 | − | 1.84911i | 0.190762 | − | 0.138597i | ||||
\(179\) | −2.51722 | − | 7.74721i | −0.188146 | − | 0.579054i | 0.811842 | − | 0.583877i | \(-0.198465\pi\) |
−0.999988 | + | 0.00482295i | \(0.998465\pi\) | |||||||
\(180\) | 0.118034 | − | 0.363271i | 0.00879773 | − | 0.0270766i | ||||
\(181\) | 18.7082 | + | 13.5923i | 1.39057 | + | 1.01031i | 0.995803 | + | 0.0915270i | \(0.0291748\pi\) |
0.394767 | + | 0.918781i | \(0.370825\pi\) | |||||||
\(182\) | −0.618034 | − | 0.449028i | −0.0458117 | − | 0.0332842i | ||||
\(183\) | 4.00000 | − | 12.3107i | 0.295689 | − | 0.910036i | ||||
\(184\) | −0.145898 | − | 0.449028i | −0.0107557 | − | 0.0331028i | ||||
\(185\) | −3.00000 | + | 2.17963i | −0.220564 | + | 0.160249i | ||||
\(186\) | 7.23607 | 0.530574 | ||||||||
\(187\) | −1.57295 | − | 1.31433i | −0.115025 | − | 0.0961132i | ||||
\(188\) | −11.2361 | −0.819474 | ||||||||
\(189\) | −4.42705 | + | 3.21644i | −0.322021 | + | 0.233962i | ||||
\(190\) | −0.809017 | − | 2.48990i | −0.0586923 | − | 0.180636i | ||||
\(191\) | −0.618034 | + | 1.90211i | −0.0447194 | + | 0.137632i | −0.970923 | − | 0.239391i | \(-0.923052\pi\) |
0.926204 | + | 0.377023i | \(0.123052\pi\) | |||||||
\(192\) | 1.30902 | + | 0.951057i | 0.0944702 | + | 0.0686366i | ||||
\(193\) | 2.85410 | + | 2.07363i | 0.205443 | + | 0.149263i | 0.685749 | − | 0.727838i | \(-0.259475\pi\) |
−0.480307 | + | 0.877101i | \(0.659475\pi\) | |||||||
\(194\) | −4.26393 | + | 13.1230i | −0.306132 | + | 0.942179i | ||||
\(195\) | −0.381966 | − | 1.17557i | −0.0273532 | − | 0.0841844i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | −5.41641 | −0.385903 | −0.192952 | − | 0.981208i | \(-0.561806\pi\) | ||||
−0.192952 | + | 0.981208i | \(0.561806\pi\) | |||||||
\(198\) | 0.472136 | − | 1.17557i | 0.0335532 | − | 0.0835442i | ||||
\(199\) | 3.23607 | 0.229399 | 0.114699 | − | 0.993400i | \(-0.463410\pi\) | ||||
0.114699 | + | 0.993400i | \(0.463410\pi\) | |||||||
\(200\) | 0.809017 | − | 0.587785i | 0.0572061 | − | 0.0415627i | ||||
\(201\) | −2.54508 | − | 7.83297i | −0.179516 | − | 0.552495i | ||||
\(202\) | −3.94427 | + | 12.1392i | −0.277518 | + | 0.854113i | ||||
\(203\) | −3.23607 | − | 2.35114i | −0.227127 | − | 0.165018i | ||||
\(204\) | 0.809017 | + | 0.587785i | 0.0566425 | + | 0.0411532i | ||||
\(205\) | −1.97214 | + | 6.06961i | −0.137740 | + | 0.423920i | ||||
\(206\) | −4.23607 | − | 13.0373i | −0.295141 | − | 0.908350i | ||||
\(207\) | 0.145898 | − | 0.106001i | 0.0101406 | − | 0.00736759i | ||||
\(208\) | −0.763932 | −0.0529692 | ||||||||
\(209\) | −2.11803 | − | 8.42075i | −0.146507 | − | 0.582476i | ||||
\(210\) | −1.61803 | −0.111655 | ||||||||
\(211\) | −22.7254 | + | 16.5110i | −1.56448 | + | 1.13666i | −0.632273 | + | 0.774746i | \(0.717878\pi\) |
−0.932210 | + | 0.361917i | \(0.882122\pi\) | |||||||
\(212\) | 0.763932 | + | 2.35114i | 0.0524671 | + | 0.161477i | ||||
\(213\) | 3.23607 | − | 9.95959i | 0.221732 | − | 0.682420i | ||||
\(214\) | 6.54508 | + | 4.75528i | 0.447413 | + | 0.325064i | ||||
\(215\) | −1.92705 | − | 1.40008i | −0.131424 | − | 0.0954850i | ||||
\(216\) | −1.69098 | + | 5.20431i | −0.115057 | + | 0.354108i | ||||
\(217\) | 1.38197 | + | 4.25325i | 0.0938140 | + | 0.288730i | ||||
\(218\) | 8.23607 | − | 5.98385i | 0.557817 | − | 0.405278i | ||||
\(219\) | 18.3262 | 1.23837 | ||||||||
\(220\) | 2.80902 | − | 1.76336i | 0.189384 | − | 0.118885i | ||||
\(221\) | −0.472136 | −0.0317593 | ||||||||
\(222\) | 4.85410 | − | 3.52671i | 0.325786 | − | 0.236697i | ||||
\(223\) | −7.09017 | − | 21.8213i | −0.474793 | − | 1.46126i | −0.846237 | − | 0.532807i | \(-0.821137\pi\) |
0.371444 | − | 0.928455i | \(-0.378863\pi\) | |||||||
\(224\) | −0.309017 | + | 0.951057i | −0.0206471 | + | 0.0635451i | ||||
\(225\) | 0.309017 | + | 0.224514i | 0.0206011 | + | 0.0149676i | ||||
\(226\) | −8.73607 | − | 6.34712i | −0.581115 | − | 0.422204i | ||||
\(227\) | −3.57295 | + | 10.9964i | −0.237145 | + | 0.729857i | 0.759685 | + | 0.650292i | \(0.225353\pi\) |
−0.996830 | + | 0.0795655i | \(0.974647\pi\) | |||||||
\(228\) | 1.30902 | + | 4.02874i | 0.0866918 | + | 0.266810i | ||||
\(229\) | −6.23607 | + | 4.53077i | −0.412091 | + | 0.299402i | −0.774448 | − | 0.632638i | \(-0.781972\pi\) |
0.362357 | + | 0.932039i | \(0.381972\pi\) | |||||||
\(230\) | 0.472136 | 0.0311317 | ||||||||
\(231\) | −5.35410 | − | 0.363271i | −0.352274 | − | 0.0239015i | ||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | −15.6353 | + | 11.3597i | −1.02430 | + | 0.744197i | −0.967160 | − | 0.254169i | \(-0.918198\pi\) |
−0.0571398 | + | 0.998366i | \(0.518198\pi\) | |||||||
\(234\) | −0.0901699 | − | 0.277515i | −0.00589459 | − | 0.0181417i | ||||
\(235\) | 3.47214 | − | 10.6861i | 0.226497 | − | 0.697087i | ||||
\(236\) | 1.11803 | + | 0.812299i | 0.0727778 | + | 0.0528762i | ||||
\(237\) | −15.3262 | − | 11.1352i | −0.995546 | − | 0.723307i | ||||
\(238\) | −0.190983 | + | 0.587785i | −0.0123796 | + | 0.0381005i | ||||
\(239\) | 1.32624 | + | 4.08174i | 0.0857872 | + | 0.264026i | 0.984743 | − | 0.174013i | \(-0.0556734\pi\) |
−0.898956 | + | 0.438038i | \(0.855673\pi\) | |||||||
\(240\) | −1.30902 | + | 0.951057i | −0.0844967 | + | 0.0613904i | ||||
\(241\) | −13.8541 | −0.892421 | −0.446211 | − | 0.894928i | \(-0.647227\pi\) | ||||
−0.446211 | + | 0.894928i | \(0.647227\pi\) | |||||||
\(242\) | 9.69098 | − | 5.20431i | 0.622960 | − | 0.334546i | ||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 6.47214 | − | 4.70228i | 0.414336 | − | 0.301033i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.0197424 | − | 0.0607608i | ||||
\(246\) | 3.19098 | − | 9.82084i | 0.203450 | − | 0.626154i | ||||
\(247\) | −1.61803 | − | 1.17557i | −0.102953 | − | 0.0747998i | ||||
\(248\) | 3.61803 | + | 2.62866i | 0.229745 | + | 0.166920i | ||||
\(249\) | 0.0450850 | − | 0.138757i | 0.00285714 | − | 0.00879339i | ||||
\(250\) | 0.309017 | + | 0.951057i | 0.0195440 | + | 0.0601501i | ||||
\(251\) | −14.4721 | + | 10.5146i | −0.913473 | + | 0.663677i | −0.941891 | − | 0.335919i | \(-0.890953\pi\) |
0.0284177 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(252\) | −0.381966 | −0.0240616 | ||||||||
\(253\) | 1.56231 | + | 0.106001i | 0.0982213 | + | 0.00666423i | ||||
\(254\) | 8.18034 | 0.513280 | ||||||||
\(255\) | −0.809017 | + | 0.587785i | −0.0506626 | + | 0.0368085i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −1.68034 | + | 5.17155i | −0.104817 | + | 0.322593i | −0.989687 | − | 0.143244i | \(-0.954247\pi\) |
0.884871 | + | 0.465837i | \(0.154247\pi\) | |||||||
\(258\) | 3.11803 | + | 2.26538i | 0.194120 | + | 0.141037i | ||||
\(259\) | 3.00000 | + | 2.17963i | 0.186411 | + | 0.135435i | ||||
\(260\) | 0.236068 | − | 0.726543i | 0.0146403 | − | 0.0450583i | ||||
\(261\) | −0.472136 | − | 1.45309i | −0.0292245 | − | 0.0899437i | ||||
\(262\) | 6.59017 | − | 4.78804i | 0.407142 | − | 0.295806i | ||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | −4.54508 | + | 2.85317i | −0.279731 | + | 0.175600i | ||||
\(265\) | −2.47214 | −0.151862 | ||||||||
\(266\) | −2.11803 | + | 1.53884i | −0.129865 | + | 0.0943524i | ||||
\(267\) | −1.57295 | − | 4.84104i | −0.0962629 | − | 0.296267i | ||||
\(268\) | 1.57295 | − | 4.84104i | 0.0960832 | − | 0.295714i | ||||
\(269\) | −11.3262 | − | 8.22899i | −0.690573 | − | 0.501731i | 0.186275 | − | 0.982498i | \(-0.440358\pi\) |
−0.876848 | + | 0.480767i | \(0.840358\pi\) | |||||||
\(270\) | −4.42705 | − | 3.21644i | −0.269422 | − | 0.195746i | ||||
\(271\) | 1.94427 | − | 5.98385i | 0.118106 | − | 0.363493i | −0.874476 | − | 0.485069i | \(-0.838795\pi\) |
0.992582 | + | 0.121575i | \(0.0387946\pi\) | |||||||
\(272\) | 0.190983 | + | 0.587785i | 0.0115800 | + | 0.0356397i | ||||
\(273\) | −1.00000 | + | 0.726543i | −0.0605228 | + | 0.0439724i | ||||
\(274\) | 12.8541 | 0.776545 | ||||||||
\(275\) | 0.809017 | + | 3.21644i | 0.0487856 | + | 0.193959i | ||||
\(276\) | −0.763932 | −0.0459833 | ||||||||
\(277\) | 13.8541 | − | 10.0656i | 0.832412 | − | 0.604783i | −0.0878285 | − | 0.996136i | \(-0.527993\pi\) |
0.920241 | + | 0.391353i | \(0.127993\pi\) | |||||||
\(278\) | 0.472136 | + | 1.45309i | 0.0283168 | + | 0.0871503i | ||||
\(279\) | −0.527864 | + | 1.62460i | −0.0316024 | + | 0.0972622i | ||||
\(280\) | −0.809017 | − | 0.587785i | −0.0483480 | − | 0.0351269i | ||||
\(281\) | −14.3992 | − | 10.4616i | −0.858983 | − | 0.624088i | 0.0686248 | − | 0.997643i | \(-0.478139\pi\) |
−0.927608 | + | 0.373555i | \(0.878139\pi\) | |||||||
\(282\) | −5.61803 | + | 17.2905i | −0.334549 | + | 1.02964i | ||||
\(283\) | 3.05573 | + | 9.40456i | 0.181644 | + | 0.559043i | 0.999874 | − | 0.0158474i | \(-0.00504458\pi\) |
−0.818230 | + | 0.574891i | \(0.805045\pi\) | |||||||
\(284\) | 5.23607 | − | 3.80423i | 0.310703 | − | 0.225739i | ||||
\(285\) | −4.23607 | −0.250923 | ||||||||
\(286\) | 0.944272 | − | 2.35114i | 0.0558360 | − | 0.139026i | ||||
\(287\) | 6.38197 | 0.376716 | ||||||||
\(288\) | −0.309017 | + | 0.224514i | −0.0182090 | + | 0.0132296i | ||||
\(289\) | −5.13525 | − | 15.8047i | −0.302074 | − | 0.929688i | ||||
\(290\) | 1.23607 | − | 3.80423i | 0.0725844 | − | 0.223392i | ||||
\(291\) | 18.0623 | + | 13.1230i | 1.05883 | + | 0.769286i | ||||
\(292\) | 9.16312 | + | 6.65740i | 0.536231 | + | 0.389595i | ||||
\(293\) | 4.85410 | − | 14.9394i | 0.283580 | − | 0.872768i | −0.703241 | − | 0.710951i | \(-0.748265\pi\) |
0.986821 | − | 0.161817i | \(-0.0517354\pi\) | |||||||
\(294\) | 0.500000 | + | 1.53884i | 0.0291606 | + | 0.0897471i | ||||
\(295\) | −1.11803 | + | 0.812299i | −0.0650945 | + | 0.0472939i | ||||
\(296\) | 3.70820 | 0.215535 | ||||||||
\(297\) | −13.9271 | − | 11.6372i | −0.808129 | − | 0.675258i | ||||
\(298\) | 7.70820 | 0.446524 | ||||||||
\(299\) | 0.291796 | − | 0.212002i | 0.0168750 | − | 0.0122604i | ||||
\(300\) | −0.500000 | − | 1.53884i | −0.0288675 | − | 0.0888451i | ||||
\(301\) | −0.736068 | + | 2.26538i | −0.0424263 | + | 0.130575i | ||||
\(302\) | 16.3262 | + | 11.8617i | 0.939469 | + | 0.682564i | ||||
\(303\) | 16.7082 | + | 12.1392i | 0.959861 | + | 0.697380i | ||||
\(304\) | −0.809017 | + | 2.48990i | −0.0464003 | + | 0.142805i | ||||
\(305\) | 2.47214 | + | 7.60845i | 0.141554 | + | 0.435659i | ||||
\(306\) | −0.190983 | + | 0.138757i | −0.0109178 | + | 0.00793223i | ||||
\(307\) | −3.50658 | −0.200131 | −0.100065 | − | 0.994981i | \(-0.531905\pi\) | ||||
−0.100065 | + | 0.994981i | \(0.531905\pi\) | |||||||
\(308\) | −2.54508 | − | 2.12663i | −0.145020 | − | 0.121176i | ||||
\(309\) | −22.1803 | −1.26180 | ||||||||
\(310\) | −3.61803 | + | 2.62866i | −0.205491 | + | 0.149298i | ||||
\(311\) | −0.381966 | − | 1.17557i | −0.0216593 | − | 0.0666605i | 0.939643 | − | 0.342157i | \(-0.111158\pi\) |
−0.961302 | + | 0.275497i | \(0.911158\pi\) | |||||||
\(312\) | −0.381966 | + | 1.17557i | −0.0216246 | + | 0.0665536i | ||||
\(313\) | 9.97214 | + | 7.24518i | 0.563658 | + | 0.409522i | 0.832796 | − | 0.553580i | \(-0.186739\pi\) |
−0.269138 | + | 0.963102i | \(0.586739\pi\) | |||||||
\(314\) | −5.00000 | − | 3.63271i | −0.282166 | − | 0.205006i | ||||
\(315\) | 0.118034 | − | 0.363271i | 0.00665046 | − | 0.0204680i | ||||
\(316\) | −3.61803 | − | 11.1352i | −0.203530 | − | 0.626402i | ||||
\(317\) | −14.4721 | + | 10.5146i | −0.812836 | + | 0.590560i | −0.914651 | − | 0.404243i | \(-0.867535\pi\) |
0.101815 | + | 0.994803i | \(0.467535\pi\) | |||||||
\(318\) | 4.00000 | 0.224309 | ||||||||
\(319\) | 4.94427 | − | 12.3107i | 0.276826 | − | 0.689269i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 10.5902 | − | 7.69421i | 0.591086 | − | 0.429449i | ||||
\(322\) | −0.145898 | − | 0.449028i | −0.00813058 | − | 0.0250234i | ||||
\(323\) | −0.500000 | + | 1.53884i | −0.0278207 | + | 0.0856234i | ||||
\(324\) | 6.23607 | + | 4.53077i | 0.346448 | + | 0.251709i | ||||
\(325\) | 0.618034 | + | 0.449028i | 0.0342824 | + | 0.0249076i | ||||
\(326\) | 6.98936 | − | 21.5110i | 0.387105 | − | 1.19139i | ||||
\(327\) | −5.09017 | − | 15.6659i | −0.281487 | − | 0.866328i | ||||
\(328\) | 5.16312 | − | 3.75123i | 0.285086 | − | 0.207127i | ||||
\(329\) | −11.2361 | −0.619464 | ||||||||
\(330\) | −1.30902 | − | 5.20431i | −0.0720590 | − | 0.286488i | ||||
\(331\) | −3.32624 | −0.182827 | −0.0914133 | − | 0.995813i | \(-0.529138\pi\) | ||||
−0.0914133 | + | 0.995813i | \(0.529138\pi\) | |||||||
\(332\) | 0.0729490 | − | 0.0530006i | 0.00400360 | − | 0.00290878i | ||||
\(333\) | 0.437694 | + | 1.34708i | 0.0239855 | + | 0.0738197i | ||||
\(334\) | −3.09017 | + | 9.51057i | −0.169087 | + | 0.520395i | ||||
\(335\) | 4.11803 | + | 2.99193i | 0.224992 | + | 0.163466i | ||||
\(336\) | 1.30902 | + | 0.951057i | 0.0714127 | + | 0.0518844i | ||||
\(337\) | −0.392609 | + | 1.20833i | −0.0213868 | + | 0.0658217i | −0.961180 | − | 0.275921i | \(-0.911017\pi\) |
0.939794 | + | 0.341743i | \(0.111017\pi\) | |||||||
\(338\) | 3.83688 | + | 11.8087i | 0.208699 | + | 0.642309i | ||||
\(339\) | −14.1353 | + | 10.2699i | −0.767722 | + | 0.557782i | ||||
\(340\) | −0.618034 | −0.0335176 | ||||||||
\(341\) | −12.5623 | + | 7.88597i | −0.680287 | + | 0.427049i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | 0.736068 | + | 2.26538i | 0.0396861 | + | 0.122141i | ||||
\(345\) | 0.236068 | − | 0.726543i | 0.0127095 | − | 0.0391157i | ||||
\(346\) | 3.85410 | + | 2.80017i | 0.207198 | + | 0.150538i | ||||
\(347\) | −1.64590 | − | 1.19581i | −0.0883564 | − | 0.0641947i | 0.542730 | − | 0.839907i | \(-0.317391\pi\) |
−0.631086 | + | 0.775713i | \(0.717391\pi\) | |||||||
\(348\) | −2.00000 | + | 6.15537i | −0.107211 | + | 0.329962i | ||||
\(349\) | 0.472136 | + | 1.45309i | 0.0252729 | + | 0.0777819i | 0.962897 | − | 0.269868i | \(-0.0869799\pi\) |
−0.937625 | + | 0.347649i | \(0.886980\pi\) | |||||||
\(350\) | 0.809017 | − | 0.587785i | 0.0432438 | − | 0.0314184i | ||||
\(351\) | −4.18034 | −0.223130 | ||||||||
\(352\) | −3.30902 | − | 0.224514i | −0.176371 | − | 0.0119666i | ||||
\(353\) | −12.0344 | −0.640529 | −0.320264 | − | 0.947328i | \(-0.603772\pi\) | ||||
−0.320264 | + | 0.947328i | \(0.603772\pi\) | |||||||
\(354\) | 1.80902 | − | 1.31433i | 0.0961482 | − | 0.0698557i | ||||
\(355\) | 2.00000 | + | 6.15537i | 0.106149 | + | 0.326693i | ||||
\(356\) | 0.972136 | − | 2.99193i | 0.0515231 | − | 0.158572i | ||||
\(357\) | 0.809017 | + | 0.587785i | 0.0428177 | + | 0.0311089i | ||||
\(358\) | −6.59017 | − | 4.78804i | −0.348301 | − | 0.253056i | ||||
\(359\) | 3.79837 | − | 11.6902i | 0.200471 | − | 0.616985i | −0.799399 | − | 0.600801i | \(-0.794848\pi\) |
0.999869 | − | 0.0161837i | \(-0.00515164\pi\) | |||||||
\(360\) | −0.118034 | − | 0.363271i | −0.00622094 | − | 0.0191461i | ||||
\(361\) | 9.82624 | − | 7.13918i | 0.517170 | − | 0.375746i | ||||
\(362\) | 23.1246 | 1.21540 | ||||||||
\(363\) | −3.16312 | − | 17.5150i | −0.166021 | − | 0.919301i | ||||
\(364\) | −0.763932 | −0.0400409 | ||||||||
\(365\) | −9.16312 | + | 6.65740i | −0.479620 | + | 0.348464i | ||||
\(366\) | −4.00000 | − | 12.3107i | −0.209083 | − | 0.643492i | ||||
\(367\) | 8.94427 | − | 27.5276i | 0.466887 | − | 1.43693i | −0.389706 | − | 0.920939i | \(-0.627423\pi\) |
0.856594 | − | 0.515992i | \(-0.172577\pi\) | |||||||
\(368\) | −0.381966 | − | 0.277515i | −0.0199114 | − | 0.0144664i | ||||
\(369\) | 1.97214 | + | 1.43284i | 0.102665 | + | 0.0745907i | ||||
\(370\) | −1.14590 | + | 3.52671i | −0.0595724 | + | 0.183345i | ||||
\(371\) | 0.763932 | + | 2.35114i | 0.0396614 | + | 0.122065i | ||||
\(372\) | 5.85410 | − | 4.25325i | 0.303521 | − | 0.220521i | ||||
\(373\) | 12.9443 | 0.670229 | 0.335114 | − | 0.942177i | \(-0.391225\pi\) | ||||
0.335114 | + | 0.942177i | \(0.391225\pi\) | |||||||
\(374\) | −2.04508 | − | 0.138757i | −0.105749 | − | 0.00717497i | ||||
\(375\) | 1.61803 | 0.0835549 | ||||||||
\(376\) | −9.09017 | + | 6.60440i | −0.468790 | + | 0.340596i | ||||
\(377\) | −0.944272 | − | 2.90617i | −0.0486325 | − | 0.149675i | ||||
\(378\) | −1.69098 | + | 5.20431i | −0.0869748 | + | 0.267681i | ||||
\(379\) | 13.6353 | + | 9.90659i | 0.700396 | + | 0.508867i | 0.880061 | − | 0.474860i | \(-0.157501\pi\) |
−0.179665 | + | 0.983728i | \(0.557501\pi\) | |||||||
\(380\) | −2.11803 | − | 1.53884i | −0.108653 | − | 0.0789409i | ||||
\(381\) | 4.09017 | − | 12.5882i | 0.209546 | − | 0.644916i | ||||
\(382\) | 0.618034 | + | 1.90211i | 0.0316214 | + | 0.0973206i | ||||
\(383\) | −3.47214 | + | 2.52265i | −0.177418 | + | 0.128902i | −0.672950 | − | 0.739688i | \(-0.734973\pi\) |
0.495532 | + | 0.868590i | \(0.334973\pi\) | |||||||
\(384\) | 1.61803 | 0.0825700 | ||||||||
\(385\) | 2.80902 | − | 1.76336i | 0.143161 | − | 0.0898689i | ||||
\(386\) | 3.52786 | 0.179564 | ||||||||
\(387\) | −0.736068 | + | 0.534785i | −0.0374164 | + | 0.0271846i | ||||
\(388\) | 4.26393 | + | 13.1230i | 0.216468 | + | 0.666221i | ||||
\(389\) | 2.47214 | − | 7.60845i | 0.125342 | − | 0.385764i | −0.868621 | − | 0.495477i | \(-0.834993\pi\) |
0.993963 | + | 0.109713i | \(0.0349933\pi\) | |||||||
\(390\) | −1.00000 | − | 0.726543i | −0.0506370 | − | 0.0367899i | ||||
\(391\) | −0.236068 | − | 0.171513i | −0.0119385 | − | 0.00867381i | ||||
\(392\) | −0.309017 | + | 0.951057i | −0.0156077 | + | 0.0480356i | ||||
\(393\) | −4.07295 | − | 12.5352i | −0.205453 | − | 0.632320i | ||||
\(394\) | −4.38197 | + | 3.18368i | −0.220760 | + | 0.160392i | ||||
\(395\) | 11.7082 | 0.589104 | ||||||||
\(396\) | −0.309017 | − | 1.22857i | −0.0155287 | − | 0.0617380i | ||||
\(397\) | 32.5410 | 1.63319 | 0.816593 | − | 0.577213i | \(-0.195860\pi\) | ||||
0.816593 | + | 0.577213i | \(0.195860\pi\) | |||||||
\(398\) | 2.61803 | − | 1.90211i | 0.131230 | − | 0.0953443i | ||||
\(399\) | 1.30902 | + | 4.02874i | 0.0655328 | + | 0.201689i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −22.2533 | − | 16.1680i | −1.11128 | − | 0.807389i | −0.128412 | − | 0.991721i | \(-0.540988\pi\) |
−0.982864 | + | 0.184331i | \(0.940988\pi\) | |||||||
\(402\) | −6.66312 | − | 4.84104i | −0.332326 | − | 0.241449i | ||||
\(403\) | −1.05573 | + | 3.24920i | −0.0525896 | + | 0.161854i | ||||
\(404\) | 3.94427 | + | 12.1392i | 0.196235 | + | 0.603949i | ||||
\(405\) | −6.23607 | + | 4.53077i | −0.309873 | + | 0.225136i | ||||
\(406\) | −4.00000 | −0.198517 | ||||||||
\(407\) | −4.58359 | + | 11.4127i | −0.227200 | + | 0.565705i | ||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −25.3262 | + | 18.4006i | −1.25230 | + | 0.909851i | −0.998353 | − | 0.0573671i | \(-0.981729\pi\) |
−0.253949 | + | 0.967218i | \(0.581729\pi\) | |||||||
\(410\) | 1.97214 | + | 6.06961i | 0.0973969 | + | 0.299757i | ||||
\(411\) | 6.42705 | − | 19.7804i | 0.317023 | − | 0.975697i | ||||
\(412\) | −11.0902 | − | 8.05748i | −0.546373 | − | 0.396964i | ||||
\(413\) | 1.11803 | + | 0.812299i | 0.0550149 | + | 0.0399706i | ||||
\(414\) | 0.0557281 | − | 0.171513i | 0.00273889 | − | 0.00842942i | ||||
\(415\) | 0.0278640 | + | 0.0857567i | 0.00136779 | + | 0.00420963i | ||||
\(416\) | −0.618034 | + | 0.449028i | −0.0303016 | + | 0.0220154i | ||||
\(417\) | 2.47214 | 0.121061 | ||||||||
\(418\) | −6.66312 | − | 5.56758i | −0.325904 | − | 0.272319i | ||||
\(419\) | −14.7426 | −0.720225 | −0.360113 | − | 0.932909i | \(-0.617262\pi\) | ||||
−0.360113 | + | 0.932909i | \(0.617262\pi\) | |||||||
\(420\) | −1.30902 | + | 0.951057i | −0.0638735 | + | 0.0464068i | ||||
\(421\) | 2.61803 | + | 8.05748i | 0.127595 | + | 0.392698i | 0.994365 | − | 0.106011i | \(-0.0338078\pi\) |
−0.866770 | + | 0.498708i | \(0.833808\pi\) | |||||||
\(422\) | −8.68034 | + | 26.7153i | −0.422552 | + | 1.30048i | ||||
\(423\) | −3.47214 | − | 2.52265i | −0.168821 | − | 0.122656i | ||||
\(424\) | 2.00000 | + | 1.45309i | 0.0971286 | + | 0.0705680i | ||||
\(425\) | 0.190983 | − | 0.587785i | 0.00926404 | − | 0.0285118i | ||||
\(426\) | −3.23607 | − | 9.95959i | −0.156788 | − | 0.482544i | ||||
\(427\) | 6.47214 | − | 4.70228i | 0.313209 | − | 0.227559i | ||||
\(428\) | 8.09017 | 0.391053 | ||||||||
\(429\) | −3.14590 | − | 2.62866i | −0.151885 | − | 0.126913i | ||||
\(430\) | −2.38197 | −0.114869 | ||||||||
\(431\) | −15.9443 | + | 11.5842i | −0.768009 | + | 0.557991i | −0.901356 | − | 0.433078i | \(-0.857427\pi\) |
0.133348 | + | 0.991069i | \(0.457427\pi\) | |||||||
\(432\) | 1.69098 | + | 5.20431i | 0.0813575 | + | 0.250393i | ||||
\(433\) | 0.371323 | − | 1.14281i | 0.0178446 | − | 0.0549202i | −0.941738 | − | 0.336348i | \(-0.890808\pi\) |
0.959582 | + | 0.281428i | \(0.0908081\pi\) | |||||||
\(434\) | 3.61803 | + | 2.62866i | 0.173671 | + | 0.126180i | ||||
\(435\) | −5.23607 | − | 3.80423i | −0.251050 | − | 0.182399i | ||||
\(436\) | 3.14590 | − | 9.68208i | 0.150661 | − | 0.463687i | ||||
\(437\) | −0.381966 | − | 1.17557i | −0.0182719 | − | 0.0562352i | ||||
\(438\) | 14.8262 | − | 10.7719i | 0.708425 | − | 0.514701i | ||||
\(439\) | 24.3607 | 1.16267 | 0.581336 | − | 0.813664i | \(-0.302530\pi\) | ||||
0.581336 | + | 0.813664i | \(0.302530\pi\) | |||||||
\(440\) | 1.23607 | − | 3.07768i | 0.0589272 | − | 0.146723i | ||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | −0.381966 | + | 0.277515i | −0.0181683 | + | 0.0132000i | ||||
\(443\) | −8.15248 | − | 25.0907i | −0.387336 | − | 1.19210i | −0.934772 | − | 0.355249i | \(-0.884396\pi\) |
0.547436 | − | 0.836848i | \(-0.315604\pi\) | |||||||
\(444\) | 1.85410 | − | 5.70634i | 0.0879918 | − | 0.270811i | ||||
\(445\) | 2.54508 | + | 1.84911i | 0.120649 | + | 0.0876563i | ||||
\(446\) | −18.5623 | − | 13.4863i | −0.878951 | − | 0.638595i | ||||
\(447\) | 3.85410 | − | 11.8617i | 0.182293 | − | 0.561039i | ||||
\(448\) | 0.309017 | + | 0.951057i | 0.0145997 | + | 0.0449332i | ||||
\(449\) | −22.4443 | + | 16.3067i | −1.05921 | + | 0.769562i | −0.973942 | − | 0.226796i | \(-0.927175\pi\) |
−0.0852685 | + | 0.996358i | \(0.527175\pi\) | |||||||
\(450\) | 0.381966 | 0.0180061 | ||||||||
\(451\) | 5.16312 | + | 20.5272i | 0.243122 | + | 0.966589i | ||||
\(452\) | −10.7984 | −0.507913 | ||||||||
\(453\) | 26.4164 | − | 19.1926i | 1.24115 | − | 0.901749i | ||||
\(454\) | 3.57295 | + | 10.9964i | 0.167687 | + | 0.516087i | ||||
\(455\) | 0.236068 | − | 0.726543i | 0.0110670 | − | 0.0340608i | ||||
\(456\) | 3.42705 | + | 2.48990i | 0.160486 | + | 0.116600i | ||||
\(457\) | 4.39919 | + | 3.19620i | 0.205785 | + | 0.149512i | 0.685905 | − | 0.727691i | \(-0.259407\pi\) |
−0.480119 | + | 0.877203i | \(0.659407\pi\) | |||||||
\(458\) | −2.38197 | + | 7.33094i | −0.111302 | + | 0.342552i | ||||
\(459\) | 1.04508 | + | 3.21644i | 0.0487804 | + | 0.150131i | ||||
\(460\) | 0.381966 | − | 0.277515i | 0.0178093 | − | 0.0129392i | ||||
\(461\) | 39.1246 | 1.82221 | 0.911107 | − | 0.412169i | \(-0.135229\pi\) | ||||
0.911107 | + | 0.412169i | \(0.135229\pi\) | |||||||
\(462\) | −4.54508 | + | 2.85317i | −0.211456 | + | 0.132741i | ||||
\(463\) | −30.6525 | −1.42454 | −0.712271 | − | 0.701905i | \(-0.752333\pi\) | ||||
−0.712271 | + | 0.701905i | \(0.752333\pi\) | |||||||
\(464\) | −3.23607 | + | 2.35114i | −0.150231 | + | 0.109149i | ||||
\(465\) | 2.23607 | + | 6.88191i | 0.103695 | + | 0.319141i | ||||
\(466\) | −5.97214 | + | 18.3803i | −0.276654 | + | 0.851453i | ||||
\(467\) | 0.763932 | + | 0.555029i | 0.0353506 | + | 0.0256837i | 0.605320 | − | 0.795982i | \(-0.293045\pi\) |
−0.569970 | + | 0.821666i | \(0.693045\pi\) | |||||||
\(468\) | −0.236068 | − | 0.171513i | −0.0109122 | − | 0.00792821i | ||||
\(469\) | 1.57295 | − | 4.84104i | 0.0726320 | − | 0.223538i | ||||
\(470\) | −3.47214 | − | 10.6861i | −0.160158 | − | 0.492915i | ||||
\(471\) | −8.09017 | + | 5.87785i | −0.372775 | + | 0.270837i | ||||
\(472\) | 1.38197 | 0.0636101 | ||||||||
\(473\) | −7.88197 | − | 0.534785i | −0.362413 | − | 0.0245894i | ||||
\(474\) | −18.9443 | −0.870139 | ||||||||
\(475\) | 2.11803 | − | 1.53884i | 0.0971821 | − | 0.0706069i | ||||
\(476\) | 0.190983 | + | 0.587785i | 0.00875369 | + | 0.0269411i | ||||
\(477\) | −0.291796 | + | 0.898056i | −0.0133604 | + | 0.0411192i | ||||
\(478\) | 3.47214 | + | 2.52265i | 0.158812 | + | 0.115384i | ||||
\(479\) | −18.7082 | − | 13.5923i | −0.854800 | − | 0.621048i | 0.0716656 | − | 0.997429i | \(-0.477169\pi\) |
−0.926465 | + | 0.376380i | \(0.877169\pi\) | |||||||
\(480\) | −0.500000 | + | 1.53884i | −0.0228218 | + | 0.0702382i | ||||
\(481\) | 0.875388 | + | 2.69417i | 0.0399143 | + | 0.122843i | ||||
\(482\) | −11.2082 | + | 8.14324i | −0.510520 | + | 0.370914i | ||||
\(483\) | −0.763932 | −0.0347601 | ||||||||
\(484\) | 4.78115 | − | 9.90659i | 0.217325 | − | 0.450300i | ||||
\(485\) | −13.7984 | −0.626552 | ||||||||
\(486\) | −3.19098 | + | 2.31838i | −0.144746 | + | 0.105164i | ||||
\(487\) | −10.4377 | − | 32.1239i | −0.472977 | − | 1.45567i | −0.848667 | − | 0.528928i | \(-0.822594\pi\) |
0.375690 | − | 0.926746i | \(-0.377406\pi\) | |||||||
\(488\) | 2.47214 | − | 7.60845i | 0.111908 | − | 0.344418i | ||||
\(489\) | −29.6074 | − | 21.5110i | −1.33889 | − | 0.972762i | ||||
\(490\) | −0.809017 | − | 0.587785i | −0.0365477 | − | 0.0265534i | ||||
\(491\) | 8.31966 | − | 25.6053i | 0.375461 | − | 1.15555i | −0.567706 | − | 0.823231i | \(-0.692169\pi\) |
0.943167 | − | 0.332319i | \(-0.107831\pi\) | |||||||
\(492\) | −3.19098 | − | 9.82084i | −0.143861 | − | 0.442757i | ||||
\(493\) | −2.00000 | + | 1.45309i | −0.0900755 | + | 0.0654437i | ||||
\(494\) | −2.00000 | −0.0899843 | ||||||||
\(495\) | 1.26393 | + | 0.0857567i | 0.0568095 | + | 0.00385448i | ||||
\(496\) | 4.47214 | 0.200805 | ||||||||
\(497\) | 5.23607 | − | 3.80423i | 0.234870 | − | 0.170643i | ||||
\(498\) | −0.0450850 | − | 0.138757i | −0.00202031 | − | 0.00621786i | ||||
\(499\) | −0.500000 | + | 1.53884i | −0.0223831 | + | 0.0688880i | −0.961624 | − | 0.274370i | \(-0.911531\pi\) |
0.939241 | + | 0.343258i | \(0.111531\pi\) | |||||||
\(500\) | 0.809017 | + | 0.587785i | 0.0361803 | + | 0.0262866i | ||||
\(501\) | 13.0902 | + | 9.51057i | 0.584826 | + | 0.424901i | ||||
\(502\) | −5.52786 | + | 17.0130i | −0.246721 | + | 0.759328i | ||||
\(503\) | −3.79837 | − | 11.6902i | −0.169361 | − | 0.521240i | 0.829970 | − | 0.557808i | \(-0.188357\pi\) |
−0.999331 | + | 0.0365680i | \(0.988357\pi\) | |||||||
\(504\) | −0.309017 | + | 0.224514i | −0.0137647 | + | 0.0100006i | ||||
\(505\) | −12.7639 | −0.567988 | ||||||||
\(506\) | 1.32624 | − | 0.832544i | 0.0589585 | − | 0.0370111i | ||||
\(507\) | 20.0902 | 0.892236 | ||||||||
\(508\) | 6.61803 | − | 4.80828i | 0.293628 | − | 0.213333i | ||||
\(509\) | 1.79837 | + | 5.53483i | 0.0797115 | + | 0.245327i | 0.982969 | − | 0.183773i | \(-0.0588310\pi\) |
−0.903257 | + | 0.429099i | \(0.858831\pi\) | |||||||
\(510\) | −0.309017 | + | 0.951057i | −0.0136835 | + | 0.0421135i | ||||
\(511\) | 9.16312 | + | 6.65740i | 0.405353 | + | 0.294506i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −4.42705 | + | 13.6251i | −0.195459 | + | 0.601561i | ||||
\(514\) | 1.68034 | + | 5.17155i | 0.0741166 | + | 0.228107i | ||||
\(515\) | 11.0902 | − | 8.05748i | 0.488691 | − | 0.355055i | ||||
\(516\) | 3.85410 | 0.169667 | ||||||||
\(517\) | −9.09017 | − | 36.1401i | −0.399785 | − | 1.58944i | ||||
\(518\) | 3.70820 | 0.162929 | ||||||||
\(519\) | 6.23607 | − | 4.53077i | 0.273733 | − | 0.198879i | ||||
\(520\) | −0.236068 | − | 0.726543i | −0.0103523 | − | 0.0318610i | ||||
\(521\) | 11.6074 | − | 35.7239i | 0.508529 | − | 1.56509i | −0.286227 | − | 0.958162i | \(-0.592401\pi\) |
0.794756 | − | 0.606929i | \(-0.207599\pi\) | |||||||
\(522\) | −1.23607 | − | 0.898056i | −0.0541012 | − | 0.0393068i | ||||
\(523\) | 29.0623 | + | 21.1150i | 1.27081 | + | 0.923295i | 0.999234 | − | 0.0391237i | \(-0.0124566\pi\) |
0.271572 | + | 0.962418i | \(0.412457\pi\) | |||||||
\(524\) | 2.51722 | − | 7.74721i | 0.109965 | − | 0.338438i | ||||
\(525\) | −0.500000 | − | 1.53884i | −0.0218218 | − | 0.0671606i | ||||
\(526\) | −9.70820 | + | 7.05342i | −0.423298 | + | 0.307544i | ||||
\(527\) | 2.76393 | 0.120399 | ||||||||
\(528\) | −2.00000 | + | 4.97980i | −0.0870388 | + | 0.216718i | ||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | −2.00000 | + | 1.45309i | −0.0868744 | + | 0.0631180i | ||||
\(531\) | 0.163119 | + | 0.502029i | 0.00707876 | + | 0.0217862i | ||||
\(532\) | −0.809017 | + | 2.48990i | −0.0350753 | + | 0.107951i | ||||
\(533\) | 3.94427 | + | 2.86568i | 0.170845 | + | 0.124126i | ||||
\(534\) | −4.11803 | − | 2.99193i | −0.178205 | − | 0.129473i | ||||
\(535\) | −2.50000 | + | 7.69421i | −0.108084 | + | 0.332650i | ||||
\(536\) | −1.57295 | − | 4.84104i | −0.0679410 | − | 0.209101i | ||||
\(537\) | −10.6631 | + | 7.74721i | −0.460148 | + | 0.334317i | ||||
\(538\) | −14.0000 | −0.603583 | ||||||||
\(539\) | −2.54508 | − | 2.12663i | −0.109625 | − | 0.0916003i | ||||
\(540\) | −5.47214 | −0.235483 | ||||||||
\(541\) | −14.4164 | + | 10.4741i | −0.619810 | + | 0.450318i | −0.852855 | − | 0.522148i | \(-0.825131\pi\) |
0.233045 | + | 0.972466i | \(0.425131\pi\) | |||||||
\(542\) | −1.94427 | − | 5.98385i | −0.0835136 | − | 0.257029i | ||||
\(543\) | 11.5623 | − | 35.5851i | 0.496186 | − | 1.52710i | ||||
\(544\) | 0.500000 | + | 0.363271i | 0.0214373 | + | 0.0155751i | ||||
\(545\) | 8.23607 | + | 5.98385i | 0.352794 | + | 0.256320i | ||||
\(546\) | −0.381966 | + | 1.17557i | −0.0163466 | + | 0.0503098i | ||||
\(547\) | 8.31559 | + | 25.5928i | 0.355549 | + | 1.09427i | 0.955690 | + | 0.294374i | \(0.0951110\pi\) |
−0.600141 | + | 0.799894i | \(0.704889\pi\) | |||||||
\(548\) | 10.3992 | − | 7.55545i | 0.444231 | − | 0.322753i | ||||
\(549\) | 3.05573 | 0.130415 | ||||||||
\(550\) | 2.54508 | + | 2.12663i | 0.108523 | + | 0.0906797i | ||||
\(551\) | −10.4721 | −0.446128 | ||||||||
\(552\) | −0.618034 | + | 0.449028i | −0.0263053 | + | 0.0191119i | ||||
\(553\) | −3.61803 | − | 11.1352i | −0.153854 | − | 0.473515i | ||||
\(554\) | 5.29180 | − | 16.2865i | 0.224827 | − | 0.691946i | ||||
\(555\) | 4.85410 | + | 3.52671i | 0.206045 | + | 0.149701i | ||||
\(556\) | 1.23607 | + | 0.898056i | 0.0524210 | + | 0.0380861i | ||||
\(557\) | 1.34752 | − | 4.14725i | 0.0570964 | − | 0.175725i | −0.918441 | − | 0.395558i | \(-0.870551\pi\) |
0.975537 | + | 0.219833i | \(0.0705513\pi\) | |||||||
\(558\) | 0.527864 | + | 1.62460i | 0.0223463 | + | 0.0687747i | ||||
\(559\) | −1.47214 | + | 1.06957i | −0.0622647 | + | 0.0452380i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −1.23607 | + | 3.07768i | −0.0521868 | + | 0.129940i | ||||
\(562\) | −17.7984 | −0.750779 | ||||||||
\(563\) | −35.3435 | + | 25.6785i | −1.48955 | + | 1.08222i | −0.515229 | + | 0.857052i | \(0.672293\pi\) |
−0.974320 | + | 0.225169i | \(0.927707\pi\) | |||||||
\(564\) | 5.61803 | + | 17.2905i | 0.236562 | + | 0.728063i | ||||
\(565\) | 3.33688 | − | 10.2699i | 0.140384 | − | 0.432056i | ||||
\(566\) | 8.00000 | + | 5.81234i | 0.336265 | + | 0.244311i | ||||
\(567\) | 6.23607 | + | 4.53077i | 0.261890 | + | 0.190274i | ||||
\(568\) | 2.00000 | − | 6.15537i | 0.0839181 | − | 0.258273i | ||||
\(569\) | −6.01064 | − | 18.4989i | −0.251979 | − | 0.775512i | −0.994410 | − | 0.105589i | \(-0.966327\pi\) |
0.742431 | − | 0.669923i | \(-0.233673\pi\) | |||||||
\(570\) | −3.42705 | + | 2.48990i | −0.143543 | + | 0.104290i | ||||
\(571\) | 26.8328 | 1.12292 | 0.561459 | − | 0.827504i | \(-0.310240\pi\) | ||||
0.561459 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(572\) | −0.618034 | − | 2.45714i | −0.0258413 | − | 0.102738i | ||||
\(573\) | 3.23607 | 0.135189 | ||||||||
\(574\) | 5.16312 | − | 3.75123i | 0.215504 | − | 0.156573i | ||||
\(575\) | 0.145898 | + | 0.449028i | 0.00608437 | + | 0.0187258i | ||||
\(576\) | −0.118034 | + | 0.363271i | −0.00491808 | + | 0.0151363i | ||||
\(577\) | −19.6803 | − | 14.2986i | −0.819303 | − | 0.595259i | 0.0972096 | − | 0.995264i | \(-0.469008\pi\) |
−0.916513 | + | 0.400005i | \(0.869008\pi\) | |||||||
\(578\) | −13.4443 | − | 9.76784i | −0.559208 | − | 0.406288i | ||||
\(579\) | 1.76393 | − | 5.42882i | 0.0733065 | − | 0.225614i | ||||
\(580\) | −1.23607 | − | 3.80423i | −0.0513249 | − | 0.157962i | ||||
\(581\) | 0.0729490 | − | 0.0530006i | 0.00302644 | − | 0.00219883i | ||||
\(582\) | 22.3262 | 0.925452 | ||||||||
\(583\) | −6.94427 | + | 4.35926i | −0.287602 | + | 0.180542i | ||||
\(584\) | 11.3262 | 0.468683 | ||||||||
\(585\) | 0.236068 | − | 0.171513i | 0.00976021 | − | 0.00709121i | ||||
\(586\) | −4.85410 | − | 14.9394i | −0.200521 | − | 0.617141i | ||||
\(587\) | −3.28115 | + | 10.0984i | −0.135428 | + | 0.416804i | −0.995656 | − | 0.0931050i | \(-0.970321\pi\) |
0.860229 | + | 0.509909i | \(0.170321\pi\) | |||||||
\(588\) | 1.30902 | + | 0.951057i | 0.0539830 | + | 0.0392209i | ||||
\(589\) | 9.47214 | + | 6.88191i | 0.390293 | + | 0.283564i | ||||
\(590\) | −0.427051 | + | 1.31433i | −0.0175814 | + | 0.0541100i | ||||
\(591\) | 2.70820 | + | 8.33499i | 0.111401 | + | 0.342856i | ||||
\(592\) | 3.00000 | − | 2.17963i | 0.123299 | − | 0.0895821i | ||||
\(593\) | −12.6180 | −0.518161 | −0.259080 | − | 0.965856i | \(-0.583419\pi\) | ||||
−0.259080 | + | 0.965856i | \(0.583419\pi\) | |||||||
\(594\) | −18.1074 | − | 1.22857i | −0.742955 | − | 0.0504089i | ||||
\(595\) | −0.618034 | −0.0253369 | ||||||||
\(596\) | 6.23607 | − | 4.53077i | 0.255439 | − | 0.185588i | ||||
\(597\) | −1.61803 | − | 4.97980i | −0.0662217 | − | 0.203810i | ||||
\(598\) | 0.111456 | − | 0.343027i | 0.00455778 | − | 0.0140274i | ||||
\(599\) | −19.4164 | − | 14.1068i | −0.793333 | − | 0.576390i | 0.115618 | − | 0.993294i | \(-0.463115\pi\) |
−0.908951 | + | 0.416904i | \(0.863115\pi\) | |||||||
\(600\) | −1.30902 | − | 0.951057i | −0.0534404 | − | 0.0388267i | ||||
\(601\) | 2.02786 | − | 6.24112i | 0.0827183 | − | 0.254581i | −0.901141 | − | 0.433527i | \(-0.857269\pi\) |
0.983859 | + | 0.178946i | \(0.0572688\pi\) | |||||||
\(602\) | 0.736068 | + | 2.26538i | 0.0299999 | + | 0.0923302i | ||||
\(603\) | 1.57295 | − | 1.14281i | 0.0640554 | − | 0.0465390i | ||||
\(604\) | 20.1803 | 0.821126 | ||||||||
\(605\) | 7.94427 | + | 7.60845i | 0.322981 | + | 0.309328i | ||||
\(606\) | 20.6525 | 0.838949 | ||||||||
\(607\) | 27.5066 | − | 19.9847i | 1.11646 | − | 0.811154i | 0.132789 | − | 0.991144i | \(-0.457607\pi\) |
0.983668 | + | 0.179990i | \(0.0576067\pi\) | |||||||
\(608\) | 0.809017 | + | 2.48990i | 0.0328100 | + | 0.100979i | ||||
\(609\) | −2.00000 | + | 6.15537i | −0.0810441 | + | 0.249428i | ||||
\(610\) | 6.47214 | + | 4.70228i | 0.262049 | + | 0.190390i | ||||
\(611\) | −6.94427 | − | 5.04531i | −0.280935 | − | 0.204111i | ||||
\(612\) | −0.0729490 | + | 0.224514i | −0.00294879 | + | 0.00907544i | ||||
\(613\) | 14.8541 | + | 45.7162i | 0.599952 | + | 1.84646i | 0.528348 | + | 0.849028i | \(0.322812\pi\) |
0.0716033 | + | 0.997433i | \(0.477188\pi\) | |||||||
\(614\) | −2.83688 | + | 2.06111i | −0.114487 | + | 0.0831798i | ||||
\(615\) | 10.3262 | 0.416394 | ||||||||
\(616\) | −3.30902 | − | 0.224514i | −0.133324 | − | 0.00904593i | ||||
\(617\) | 13.2016 | 0.531477 | 0.265739 | − | 0.964045i | \(-0.414384\pi\) | ||||
0.265739 | + | 0.964045i | \(0.414384\pi\) | |||||||
\(618\) | −17.9443 | + | 13.0373i | −0.721824 | + | 0.524436i | ||||
\(619\) | 6.31559 | + | 19.4374i | 0.253845 | + | 0.781255i | 0.994055 | + | 0.108879i | \(0.0347262\pi\) |
−0.740210 | + | 0.672376i | \(0.765274\pi\) | |||||||
\(620\) | −1.38197 | + | 4.25325i | −0.0555011 | + | 0.170815i | ||||
\(621\) | −2.09017 | − | 1.51860i | −0.0838756 | − | 0.0609392i | ||||
\(622\) | −1.00000 | − | 0.726543i | −0.0400963 | − | 0.0291317i | ||||
\(623\) | 0.972136 | − | 2.99193i | 0.0389478 | − | 0.119869i | ||||
\(624\) | 0.381966 | + | 1.17557i | 0.0152909 | + | 0.0470605i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 12.3262 | 0.492656 | ||||||||
\(627\) | −11.8992 | + | 7.46969i | −0.475208 | + | 0.298311i | ||||
\(628\) | −6.18034 | −0.246622 | ||||||||
\(629\) | 1.85410 | − | 1.34708i | 0.0739279 | − | 0.0537118i | ||||
\(630\) | −0.118034 | − | 0.363271i | −0.00470259 | − | 0.0144731i | ||||
\(631\) | −6.41641 | + | 19.7477i | −0.255433 | + | 0.786142i | 0.738311 | + | 0.674461i | \(0.235624\pi\) |
−0.993744 | + | 0.111682i | \(0.964376\pi\) | |||||||
\(632\) | −9.47214 | − | 6.88191i | −0.376781 | − | 0.273748i | ||||
\(633\) | 36.7705 | + | 26.7153i | 1.46150 | + | 1.06184i | ||||
\(634\) | −5.52786 | + | 17.0130i | −0.219540 | + | 0.675673i | ||||
\(635\) | 2.52786 | + | 7.77997i | 0.100315 | + | 0.308739i | ||||
\(636\) | 3.23607 | − | 2.35114i | 0.128318 | − | 0.0932288i | ||||
\(637\) | −0.763932 | −0.0302681 | ||||||||
\(638\) | −3.23607 | − | 12.8658i | −0.128117 | − | 0.509360i | ||||
\(639\) | 2.47214 | 0.0977962 | ||||||||
\(640\) | −0.809017 | + | 0.587785i | −0.0319792 | + | 0.0232343i | ||||
\(641\) | 7.62461 | + | 23.4661i | 0.301154 | + | 0.926857i | 0.981084 | + | 0.193580i | \(0.0620100\pi\) |
−0.679930 | + | 0.733277i | \(0.737990\pi\) | |||||||
\(642\) | 4.04508 | − | 12.4495i | 0.159647 | − | 0.491342i | ||||
\(643\) | −5.30902 | − | 3.85723i | −0.209367 | − | 0.152114i | 0.478160 | − | 0.878273i | \(-0.341304\pi\) |
−0.687527 | + | 0.726158i | \(0.741304\pi\) | |||||||
\(644\) | −0.381966 | − | 0.277515i | −0.0150516 | − | 0.0109356i | ||||
\(645\) | −1.19098 | + | 3.66547i | −0.0468949 | + | 0.144328i | ||||
\(646\) | 0.500000 | + | 1.53884i | 0.0196722 | + | 0.0605449i | ||||
\(647\) | 6.38197 | − | 4.63677i | 0.250901 | − | 0.182290i | −0.455225 | − | 0.890376i | \(-0.650441\pi\) |
0.706126 | + | 0.708086i | \(0.250441\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | −1.70820 | + | 4.25325i | −0.0670529 | + | 0.166955i | ||||
\(650\) | 0.763932 | 0.0299639 | ||||||||
\(651\) | 5.85410 | − | 4.25325i | 0.229440 | − | 0.166698i | ||||
\(652\) | −6.98936 | − | 21.5110i | −0.273724 | − | 0.842437i | ||||
\(653\) | −1.85410 | + | 5.70634i | −0.0725566 | + | 0.223306i | −0.980758 | − | 0.195227i | \(-0.937456\pi\) |
0.908201 | + | 0.418533i | \(0.137456\pi\) | |||||||
\(654\) | −13.3262 | − | 9.68208i | −0.521097 | − | 0.378599i | ||||
\(655\) | 6.59017 | + | 4.78804i | 0.257499 | + | 0.187084i | ||||
\(656\) | 1.97214 | − | 6.06961i | 0.0769990 | − | 0.236978i | ||||
\(657\) | 1.33688 | + | 4.11450i | 0.0521567 | + | 0.160522i | ||||
\(658\) | −9.09017 | + | 6.60440i | −0.354372 | + | 0.257466i | ||||
\(659\) | 21.0902 | 0.821556 | 0.410778 | − | 0.911735i | \(-0.365257\pi\) | ||||
0.410778 | + | 0.911735i | \(0.365257\pi\) | |||||||
\(660\) | −4.11803 | − | 3.44095i | −0.160294 | − | 0.133939i | ||||
\(661\) | 37.7771 | 1.46936 | 0.734679 | − | 0.678415i | \(-0.237333\pi\) | ||||
0.734679 | + | 0.678415i | \(0.237333\pi\) | |||||||
\(662\) | −2.69098 | + | 1.95511i | −0.104588 | + | 0.0759876i | ||||
\(663\) | 0.236068 | + | 0.726543i | 0.00916812 | + | 0.0282166i | ||||
\(664\) | 0.0278640 | − | 0.0857567i | 0.00108133 | − | 0.00332801i | ||||
\(665\) | −2.11803 | − | 1.53884i | −0.0821338 | − | 0.0596737i | ||||
\(666\) | 1.14590 | + | 0.832544i | 0.0444026 | + | 0.0322604i | ||||
\(667\) | 0.583592 | − | 1.79611i | 0.0225968 | − | 0.0695457i | ||||
\(668\) | 3.09017 | + | 9.51057i | 0.119562 | + | 0.367975i | ||||
\(669\) | −30.0344 | + | 21.8213i | −1.16120 | + | 0.843660i | ||||
\(670\) | 5.09017 | 0.196650 | ||||||||
\(671\) | 20.3607 | + | 17.0130i | 0.786015 | + | 0.656780i | ||||
\(672\) | 1.61803 | 0.0624170 | ||||||||
\(673\) | −11.2082 | + | 8.14324i | −0.432045 | + | 0.313899i | −0.782466 | − | 0.622693i | \(-0.786038\pi\) |
0.350421 | + | 0.936592i | \(0.386038\pi\) | |||||||
\(674\) | 0.392609 | + | 1.20833i | 0.0151227 | + | 0.0465430i | ||||
\(675\) | 1.69098 | − | 5.20431i | 0.0650860 | − | 0.200314i | ||||
\(676\) | 10.0451 | + | 7.29818i | 0.386349 | + | 0.280699i | ||||
\(677\) | 8.85410 | + | 6.43288i | 0.340291 | + | 0.247236i | 0.744785 | − | 0.667305i | \(-0.232552\pi\) |
−0.404494 | + | 0.914541i | \(0.632552\pi\) | |||||||
\(678\) | −5.39919 | + | 16.6170i | −0.207355 | + | 0.638172i | ||||
\(679\) | 4.26393 | + | 13.1230i | 0.163635 | + | 0.503616i | ||||
\(680\) | −0.500000 | + | 0.363271i | −0.0191741 | + | 0.0139308i | ||||
\(681\) | 18.7082 | 0.716900 | ||||||||
\(682\) | −5.52786 | + | 13.7638i | −0.211673 | + | 0.527044i | ||||
\(683\) | −45.3050 | −1.73355 | −0.866773 | − | 0.498703i | \(-0.833810\pi\) | ||||
−0.866773 | + | 0.498703i | \(0.833810\pi\) | |||||||
\(684\) | −0.809017 | + | 0.587785i | −0.0309335 | + | 0.0224745i | ||||
\(685\) | 3.97214 | + | 12.2250i | 0.151768 | + | 0.467092i | ||||
\(686\) | −0.309017 | + | 0.951057i | −0.0117983 | + | 0.0363115i | ||||
\(687\) | 10.0902 | + | 7.33094i | 0.384964 | + | 0.279693i | ||||
\(688\) | 1.92705 | + | 1.40008i | 0.0734681 | + | 0.0533777i | ||||
\(689\) | −0.583592 | + | 1.79611i | −0.0222331 | + | 0.0684264i | ||||
\(690\) | −0.236068 | − | 0.726543i | −0.00898695 | − | 0.0276590i | ||||
\(691\) | 2.59017 | − | 1.88187i | 0.0985347 | − | 0.0715897i | −0.537427 | − | 0.843310i | \(-0.680604\pi\) |
0.635962 | + | 0.771721i | \(0.280604\pi\) | |||||||
\(692\) | 4.76393 | 0.181098 | ||||||||
\(693\) | −0.309017 | − | 1.22857i | −0.0117386 | − | 0.0466696i | ||||
\(694\) | −2.03444 | −0.0772264 | ||||||||
\(695\) | −1.23607 | + | 0.898056i | −0.0468867 | + | 0.0340652i | ||||
\(696\) | 2.00000 | + | 6.15537i | 0.0758098 | + | 0.233319i | ||||
\(697\) | 1.21885 | − | 3.75123i | 0.0461671 | − | 0.142088i | ||||
\(698\) | 1.23607 | + | 0.898056i | 0.0467859 | + | 0.0339919i | ||||
\(699\) | 25.2984 | + | 18.3803i | 0.956872 | + | 0.695208i | ||||
\(700\) | 0.309017 | − | 0.951057i | 0.0116797 | − | 0.0359466i | ||||
\(701\) | −1.29180 | − | 3.97574i | −0.0487905 | − | 0.150162i | 0.923693 | − | 0.383133i | \(-0.125155\pi\) |
−0.972484 | + | 0.232972i | \(0.925155\pi\) | |||||||
\(702\) | −3.38197 | + | 2.45714i | −0.127644 | + | 0.0927389i | ||||
\(703\) | 9.70820 | 0.366152 | ||||||||
\(704\) | −2.80902 | + | 1.76336i | −0.105869 | + | 0.0664590i | ||||
\(705\) | −18.1803 | −0.684711 | ||||||||
\(706\) | −9.73607 | + | 7.07367i | −0.366422 | + | 0.266221i | ||||
\(707\) | 3.94427 | + | 12.1392i | 0.148340 | + | 0.456542i | ||||
\(708\) | 0.690983 | − | 2.12663i | 0.0259687 | − | 0.0799235i | ||||
\(709\) | −26.5066 | − | 19.2582i | −0.995475 | − | 0.723255i | −0.0343621 | − | 0.999409i | \(-0.510940\pi\) |
−0.961113 | + | 0.276154i | \(0.910940\pi\) | |||||||
\(710\) | 5.23607 | + | 3.80423i | 0.196506 | + | 0.142770i | ||||
\(711\) | 1.38197 | − | 4.25325i | 0.0518278 | − | 0.159509i | ||||
\(712\) | −0.972136 | − | 2.99193i | −0.0364323 | − | 0.112127i | ||||
\(713\) | −1.70820 | + | 1.24108i | −0.0639727 | + | 0.0464789i | ||||
\(714\) | 1.00000 | 0.0374241 | ||||||||
\(715\) | 2.52786 | + | 0.171513i | 0.0945368 | + | 0.00641424i | ||||
\(716\) | −8.14590 | −0.304427 | ||||||||
\(717\) | 5.61803 | − | 4.08174i | 0.209809 | − | 0.152435i | ||||
\(718\) | −3.79837 | − | 11.6902i | −0.141754 | − | 0.436274i | ||||
\(719\) | 1.74265 | − | 5.36331i | 0.0649897 | − | 0.200018i | −0.913289 | − | 0.407313i | \(-0.866466\pi\) |
0.978279 | + | 0.207295i | \(0.0664659\pi\) | |||||||
\(720\) | −0.309017 | − | 0.224514i | −0.0115164 | − | 0.00836714i | ||||
\(721\) | −11.0902 | − | 8.05748i | −0.413020 | − | 0.300076i | ||||
\(722\) | 3.75329 | − | 11.5514i | 0.139683 | − | 0.429900i | ||||
\(723\) | 6.92705 | + | 21.3193i | 0.257620 | + | 0.792872i | ||||
\(724\) | 18.7082 | − | 13.5923i | 0.695285 | − | 0.505154i | ||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | −12.8541 | − | 12.3107i | −0.477060 | − | 0.456894i | ||||
\(727\) | −25.3050 | −0.938509 | −0.469254 | − | 0.883063i | \(-0.655477\pi\) | ||||
−0.469254 | + | 0.883063i | \(0.655477\pi\) | |||||||
\(728\) | −0.618034 | + | 0.449028i | −0.0229059 | + | 0.0166421i | ||||
\(729\) | 9.11803 | + | 28.0624i | 0.337705 | + | 1.03935i | ||||
\(730\) | −3.50000 | + | 10.7719i | −0.129541 | + | 0.398686i | ||||
\(731\) | 1.19098 | + | 0.865300i | 0.0440501 | + | 0.0320043i | ||||
\(732\) | −10.4721 | − | 7.60845i | −0.387061 | − | 0.281216i | ||||
\(733\) | −5.94427 | + | 18.2946i | −0.219557 | + | 0.675726i | 0.779242 | + | 0.626723i | \(0.215604\pi\) |
−0.998799 | + | 0.0490028i | \(0.984396\pi\) | |||||||
\(734\) | −8.94427 | − | 27.5276i | −0.330139 | − | 1.01606i | ||||
\(735\) | −1.30902 | + | 0.951057i | −0.0482838 | + | 0.0350802i | ||||
\(736\) | −0.472136 | −0.0174032 | ||||||||
\(737\) | 16.8435 | + | 1.14281i | 0.620437 | + | 0.0420961i | ||||
\(738\) | 2.43769 | 0.0897328 | ||||||||
\(739\) | 21.8262 | − | 15.8577i | 0.802891 | − | 0.583335i | −0.108870 | − | 0.994056i | \(-0.534723\pi\) |
0.911761 | + | 0.410721i | \(0.134723\pi\) | |||||||
\(740\) | 1.14590 | + | 3.52671i | 0.0421240 | + | 0.129644i | ||||
\(741\) | −1.00000 | + | 3.07768i | −0.0367359 | + | 0.113062i | ||||
\(742\) | 2.00000 | + | 1.45309i | 0.0734223 | + | 0.0533444i | ||||
\(743\) | 17.7984 | + | 12.9313i | 0.652959 | + | 0.474402i | 0.864278 | − | 0.503015i | \(-0.167776\pi\) |
−0.211319 | + | 0.977417i | \(0.567776\pi\) | |||||||
\(744\) | 2.23607 | − | 6.88191i | 0.0819782 | − | 0.252303i | ||||
\(745\) | 2.38197 | + | 7.33094i | 0.0872685 | + | 0.268585i | ||||
\(746\) | 10.4721 | − | 7.60845i | 0.383412 | − | 0.278565i | ||||
\(747\) | 0.0344419 | 0.00126016 | ||||||||
\(748\) | −1.73607 | + | 1.08981i | −0.0634769 | + | 0.0398475i | ||||
\(749\) | 8.09017 | 0.295608 | ||||||||
\(750\) | 1.30902 | − | 0.951057i | 0.0477985 | − | 0.0347277i | ||||
\(751\) | −15.2705 | − | 46.9978i | −0.557229 | − | 1.71497i | −0.689984 | − | 0.723825i | \(-0.742382\pi\) |
0.132755 | − | 0.991149i | \(-0.457618\pi\) | |||||||
\(752\) | −3.47214 | + | 10.6861i | −0.126616 | + | 0.389683i | ||||
\(753\) | 23.4164 | + | 17.0130i | 0.853341 | + | 0.619989i | ||||
\(754\) | −2.47214 | − | 1.79611i | −0.0900299 | − | 0.0654105i | ||||
\(755\) | −6.23607 | + | 19.1926i | −0.226954 | + | 0.698492i | ||||
\(756\) | 1.69098 | + | 5.20431i | 0.0615005 | + | 0.189279i | ||||
\(757\) | −21.0902 | + | 15.3229i | −0.766535 | + | 0.556920i | −0.900908 | − | 0.434010i | \(-0.857098\pi\) |
0.134373 | + | 0.990931i | \(0.457098\pi\) | |||||||
\(758\) | 16.8541 | 0.612169 | ||||||||
\(759\) | −0.618034 | − | 2.45714i | −0.0224332 | − | 0.0891886i | ||||
\(760\) | −2.61803 | −0.0949661 | ||||||||
\(761\) | −5.44427 | + | 3.95550i | −0.197355 | + | 0.143387i | −0.682074 | − | 0.731283i | \(-0.738922\pi\) |
0.484719 | + | 0.874670i | \(0.338922\pi\) | |||||||
\(762\) | −4.09017 | − | 12.5882i | −0.148171 | − | 0.456024i | ||||
\(763\) | 3.14590 | − | 9.68208i | 0.113889 | − | 0.350515i | ||||
\(764\) | 1.61803 | + | 1.17557i | 0.0585384 | + | 0.0425306i | ||||
\(765\) | −0.190983 | − | 0.138757i | −0.00690501 | − | 0.00501678i | ||||
\(766\) | −1.32624 | + | 4.08174i | −0.0479189 | + | 0.147479i | ||||
\(767\) | 0.326238 | + | 1.00406i | 0.0117798 | + | 0.0362544i | ||||
\(768\) | 1.30902 | − | 0.951057i | 0.0472351 | − | 0.0343183i | ||||
\(769\) | 25.4164 | 0.916539 | 0.458270 | − | 0.888813i | \(-0.348469\pi\) | ||||
0.458270 | + | 0.888813i | \(0.348469\pi\) | |||||||
\(770\) | 1.23607 | − | 3.07768i | 0.0445448 | − | 0.110912i | ||||
\(771\) | 8.79837 | 0.316866 | ||||||||
\(772\) | 2.85410 | − | 2.07363i | 0.102721 | − | 0.0746314i | ||||
\(773\) | 11.2361 | + | 34.5811i | 0.404133 | + | 1.24379i | 0.921617 | + | 0.388101i | \(0.126869\pi\) |
−0.517484 | + | 0.855693i | \(0.673131\pi\) | |||||||
\(774\) | −0.281153 | + | 0.865300i | −0.0101058 | + | 0.0311026i | ||||
\(775\) | −3.61803 | − | 2.62866i | −0.129964 | − | 0.0944241i | ||||
\(776\) | 11.1631 | + | 8.11048i | 0.400733 | + | 0.291149i | ||||
\(777\) | 1.85410 | − | 5.70634i | 0.0665155 | − | 0.204714i | ||||
\(778\) | −2.47214 | − | 7.60845i | −0.0886304 | − | 0.272776i | ||||
\(779\) | 13.5172 | − | 9.82084i | 0.484305 | − | 0.351868i | ||||
\(780\) | −1.23607 | −0.0442583 | ||||||||
\(781\) | 16.4721 | + | 13.7638i | 0.589419 | + | 0.492508i | ||||
\(782\) | −0.291796 | −0.0104346 | ||||||||
\(783\) | −17.7082 | + | 12.8658i | −0.632840 | + | 0.459785i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | 1.90983 | − | 5.87785i | 0.0681648 | − | 0.209790i | ||||
\(786\) | −10.6631 | − | 7.74721i | −0.380341 | − | 0.276334i | ||||
\(787\) | −11.3541 | − | 8.24924i | −0.404730 | − | 0.294054i | 0.366735 | − | 0.930326i | \(-0.380476\pi\) |
−0.771465 | + | 0.636272i | \(0.780476\pi\) | |||||||
\(788\) | −1.67376 | + | 5.15131i | −0.0596253 | + | 0.183508i | ||||
\(789\) | 6.00000 | + | 18.4661i | 0.213606 | + | 0.657411i | ||||
\(790\) | 9.47214 | − | 6.88191i | 0.337003 | − | 0.244847i | ||||
\(791\) | −10.7984 | −0.383946 | ||||||||
\(792\) | −0.972136 | − | 0.812299i | −0.0345433 | − | 0.0288638i | ||||
\(793\) | 6.11146 | 0.217024 | ||||||||
\(794\) | 26.3262 | − | 19.1271i | 0.934283 | − | 0.678796i | ||||
\(795\) | 1.23607 | + | 3.80423i | 0.0438388 | + | 0.134922i | ||||
\(796\) | 1.00000 | − | 3.07768i | 0.0354441 | − | 0.109086i | ||||
\(797\) | −27.8885 | − | 20.2622i | −0.987863 | − | 0.717724i | −0.0284109 | − | 0.999596i | \(-0.509045\pi\) |
−0.959452 | + | 0.281872i | \(0.909045\pi\) | |||||||
\(798\) | 3.42705 | + | 2.48990i | 0.121316 | + | 0.0881414i | ||||
\(799\) | −2.14590 | + | 6.60440i | −0.0759164 | + | 0.233647i | ||||
\(800\) | −0.309017 | − | 0.951057i | −0.0109254 | − | 0.0336249i | ||||
\(801\) | 0.972136 | − | 0.706298i | 0.0343487 | − | 0.0249558i | ||||
\(802\) | −27.5066 | −0.971291 | ||||||||
\(803\) | −14.0000 | + | 34.8586i | −0.494049 | + | 1.23013i | ||||
\(804\) | −8.23607 | −0.290464 | ||||||||
\(805\) | 0.381966 | − | 0.277515i | 0.0134625 | − | 0.00978110i | ||||
\(806\) | 1.05573 | + | 3.24920i | 0.0371864 | + | 0.114448i | ||||
\(807\) | −7.00000 | + | 21.5438i | −0.246412 | + | 0.758377i | ||||
\(808\) | 10.3262 | + | 7.50245i | 0.363276 | + | 0.263935i | ||||
\(809\) | −21.3885 | − | 15.5397i | −0.751981 | − | 0.546346i | 0.144459 | − | 0.989511i | \(-0.453856\pi\) |
−0.896440 | + | 0.443164i | \(0.853856\pi\) | |||||||
\(810\) | −2.38197 | + | 7.33094i | −0.0836938 | + | 0.257583i | ||||
\(811\) | 15.3885 | + | 47.3611i | 0.540365 | + | 1.66307i | 0.731763 | + | 0.681559i | \(0.238698\pi\) |
−0.191398 | + | 0.981513i | \(0.561302\pi\) | |||||||
\(812\) | −3.23607 | + | 2.35114i | −0.113564 | + | 0.0825089i | ||||
\(813\) | −10.1803 | −0.357040 | ||||||||
\(814\) | 3.00000 | + | 11.9272i | 0.105150 | + | 0.418049i | ||||
\(815\) | 22.6180 | 0.792275 | ||||||||
\(816\) | 0.809017 | − | 0.587785i | 0.0283213 | − | 0.0205766i | ||||
\(817\) | 1.92705 | + | 5.93085i | 0.0674190 | + | 0.207494i | ||||
\(818\) | −9.67376 | + | 29.7728i | −0.338235 | + | 1.04098i | ||||
\(819\) | −0.236068 | − | 0.171513i | −0.00824888 | − | 0.00599316i | ||||
\(820\) | 5.16312 | + | 3.75123i | 0.180304 | + | 0.130998i | ||||
\(821\) | 15.2918 | − | 47.0633i | 0.533687 | − | 1.64252i | −0.212781 | − | 0.977100i | \(-0.568252\pi\) |
0.746468 | − | 0.665421i | \(-0.231748\pi\) | |||||||
\(822\) | −6.42705 | − | 19.7804i | −0.224169 | − | 0.689922i | ||||
\(823\) | −41.6525 | + | 30.2623i | −1.45191 | + | 1.05488i | −0.466535 | + | 0.884503i | \(0.654498\pi\) |
−0.985379 | + | 0.170374i | \(0.945502\pi\) | |||||||
\(824\) | −13.7082 | −0.477548 | ||||||||
\(825\) | 4.54508 | − | 2.85317i | 0.158240 | − | 0.0993346i | ||||
\(826\) | 1.38197 | 0.0480847 | ||||||||
\(827\) | −20.8262 | + | 15.1311i | −0.724199 | + | 0.526162i | −0.887723 | − | 0.460378i | \(-0.847714\pi\) |
0.163524 | + | 0.986539i | \(0.447714\pi\) | |||||||
\(828\) | −0.0557281 | − | 0.171513i | −0.00193669 | − | 0.00596050i | ||||
\(829\) | 0.909830 | − | 2.80017i | 0.0315997 | − | 0.0972539i | −0.934013 | − | 0.357240i | \(-0.883718\pi\) |
0.965612 | + | 0.259986i | \(0.0837179\pi\) | |||||||
\(830\) | 0.0729490 | + | 0.0530006i | 0.00253210 | + | 0.00183968i | ||||
\(831\) | −22.4164 | − | 16.2865i | −0.777617 | − | 0.564972i | ||||
\(832\) | −0.236068 | + | 0.726543i | −0.00818418 | + | 0.0251883i | ||||
\(833\) | 0.190983 | + | 0.587785i | 0.00661717 | + | 0.0203656i | ||||
\(834\) | 2.00000 | − | 1.45309i | 0.0692543 | − | 0.0503162i | ||||
\(835\) | −10.0000 | −0.346064 | ||||||||
\(836\) | −8.66312 | − | 0.587785i | −0.299620 | − | 0.0203290i | ||||
\(837\) | 24.4721 | 0.845881 | ||||||||
\(838\) | −11.9271 | + | 8.66551i | −0.412013 | + | 0.299345i | ||||
\(839\) | −3.29180 | − | 10.1311i | −0.113645 | − | 0.349765i | 0.878017 | − | 0.478630i | \(-0.158866\pi\) |
−0.991662 | + | 0.128865i | \(0.958866\pi\) | |||||||
\(840\) | −0.500000 | + | 1.53884i | −0.0172516 | + | 0.0530951i | ||||
\(841\) | 10.5172 | + | 7.64121i | 0.362663 | + | 0.263490i | ||||
\(842\) | 6.85410 | + | 4.97980i | 0.236208 | + | 0.171615i | ||||
\(843\) | −8.89919 | + | 27.3889i | −0.306504 | + | 0.943323i | ||||
\(844\) | 8.68034 | + | 26.7153i | 0.298790 | + | 0.919580i | ||||
\(845\) | −10.0451 | + | 7.29818i | −0.345561 | + | 0.251065i | ||||
\(846\) | −4.29180 | −0.147555 | ||||||||
\(847\) | 4.78115 | − | 9.90659i | 0.164282 | − | 0.340395i | ||||
\(848\) | 2.47214 | 0.0848935 | ||||||||
\(849\) | 12.9443 | − | 9.40456i | 0.444246 | − | 0.322764i | ||||
\(850\) | −0.190983 | − | 0.587785i | −0.00655066 | − | 0.0201609i | ||||
\(851\) | −0.541020 | + | 1.66509i | −0.0185459 | + | 0.0570785i | ||||
\(852\) | −8.47214 | − | 6.15537i | −0.290251 | − | 0.210879i | ||||
\(853\) | 29.3607 | + | 21.3318i | 1.00529 | + | 0.730386i | 0.963216 | − | 0.268728i | \(-0.0866033\pi\) |
0.0420745 | + | 0.999114i | \(0.486603\pi\) | |||||||
\(854\) | 2.47214 | − | 7.60845i | 0.0845948 | − | 0.260356i | ||||
\(855\) | −0.309017 | − | 0.951057i | −0.0105682 | − | 0.0325254i | ||||
\(856\) | 6.54508 | − | 4.75528i | 0.223706 | − | 0.162532i | ||||
\(857\) | 47.6869 | 1.62895 | 0.814477 | − | 0.580196i | \(-0.197024\pi\) | ||||
0.814477 | + | 0.580196i | \(0.197024\pi\) | |||||||
\(858\) | −4.09017 | − | 0.277515i | −0.139636 | − | 0.00947419i | ||||
\(859\) | 43.8541 | 1.49628 | 0.748141 | − | 0.663539i | \(-0.230947\pi\) | ||||
0.748141 | + | 0.663539i | \(0.230947\pi\) | |||||||
\(860\) | −1.92705 | + | 1.40008i | −0.0657119 | + | 0.0477425i | ||||
\(861\) | −3.19098 | − | 9.82084i | −0.108748 | − | 0.334693i | ||||
\(862\) | −6.09017 | + | 18.7436i | −0.207432 | + | 0.638410i | ||||
\(863\) | −32.5623 | − | 23.6579i | −1.10843 | − | 0.805324i | −0.126018 | − | 0.992028i | \(-0.540220\pi\) |
−0.982416 | + | 0.186704i | \(0.940220\pi\) | |||||||
\(864\) | 4.42705 | + | 3.21644i | 0.150611 | + | 0.109426i | ||||
\(865\) | −1.47214 | + | 4.53077i | −0.0500541 | + | 0.154051i | ||||
\(866\) | −0.371323 | − | 1.14281i | −0.0126181 | − | 0.0388344i | ||||
\(867\) | −21.7533 | + | 15.8047i | −0.738780 | + | 0.536755i | ||||
\(868\) | 4.47214 | 0.151794 | ||||||||
\(869\) | 32.8885 | − | 20.6457i | 1.11567 | − | 0.700358i | ||||
\(870\) | −6.47214 | −0.219426 | ||||||||
\(871\) | 3.14590 | − | 2.28563i | 0.106595 | − | 0.0774456i | ||||
\(872\) | −3.14590 | − | 9.68208i | −0.106534 | − | 0.327877i | ||||
\(873\) | −1.62868 | + | 5.01255i | −0.0551224 | + | 0.169649i | ||||
\(874\) | −1.00000 | − | 0.726543i | −0.0338255 | − | 0.0245757i | ||||
\(875\) | 0.809017 | + | 0.587785i | 0.0273498 | + | 0.0198708i | ||||
\(876\) | 5.66312 | − | 17.4293i | 0.191339 | − | 0.588881i | ||||
\(877\) | −6.52786 | − | 20.0907i | −0.220430 | − | 0.678415i | −0.998723 | − | 0.0505135i | \(-0.983914\pi\) |
0.778293 | − | 0.627901i | \(-0.216086\pi\) | |||||||
\(878\) | 19.7082 | − | 14.3188i | 0.665120 | − | 0.483238i | ||||
\(879\) | −25.4164 | −0.857274 | ||||||||
\(880\) | −0.809017 | − | 3.21644i | −0.0272720 | − | 0.108426i | ||||
\(881\) | 34.3394 | 1.15692 | 0.578462 | − | 0.815709i | \(-0.303653\pi\) | ||||
0.578462 | + | 0.815709i | \(0.303653\pi\) | |||||||
\(882\) | −0.309017 | + | 0.224514i | −0.0104051 | + | 0.00755978i | ||||
\(883\) | 10.6246 | + | 32.6992i | 0.357547 | + | 1.10042i | 0.954518 | + | 0.298153i | \(0.0963706\pi\) |
−0.596971 | + | 0.802262i | \(0.703629\pi\) | |||||||
\(884\) | −0.145898 | + | 0.449028i | −0.00490708 | + | 0.0151024i | ||||
\(885\) | 1.80902 | + | 1.31433i | 0.0608094 | + | 0.0441806i | ||||
\(886\) | −21.3435 | − | 15.5069i | −0.717048 | − | 0.520966i | ||||
\(887\) | −6.79837 | + | 20.9232i | −0.228267 | + | 0.702534i | 0.769676 | + | 0.638434i | \(0.220418\pi\) |
−0.997944 | + | 0.0640996i | \(0.979582\pi\) | |||||||
\(888\) | −1.85410 | − | 5.70634i | −0.0622196 | − | 0.191492i | ||||
\(889\) | 6.61803 | − | 4.80828i | 0.221962 | − | 0.161265i | ||||
\(890\) | 3.14590 | 0.105451 | ||||||||
\(891\) | −9.52786 | + | 23.7234i | −0.319195 | + | 0.794764i | ||||
\(892\) | −22.9443 | −0.768231 | ||||||||
\(893\) | −23.7984 | + | 17.2905i | −0.796382 | + | 0.578606i | ||||
\(894\) | −3.85410 | − | 11.8617i | −0.128900 | − | 0.396715i | ||||
\(895\) | 2.51722 | − | 7.74721i | 0.0841414 | − | 0.258961i | ||||
\(896\) | 0.809017 | + | 0.587785i | 0.0270274 | + | 0.0196365i | ||||
\(897\) | −0.472136 | − | 0.343027i | −0.0157642 | − | 0.0114533i | ||||
\(898\) | −8.57295 | + | 26.3848i | −0.286083 | + | 0.880473i | ||||
\(899\) | 5.52786 | + | 17.0130i | 0.184365 | + | 0.567416i | ||||
\(900\) | 0.309017 | − | 0.224514i | 0.0103006 | − | 0.00748380i | ||||
\(901\) | 1.52786 | 0.0509005 | ||||||||
\(902\) | 16.2426 | + | 13.5721i | 0.540821 | + | 0.451900i | ||||
\(903\) | 3.85410 | 0.128256 | ||||||||
\(904\) | −8.73607 | + | 6.34712i | −0.290557 | + | 0.211102i | ||||
\(905\) | 7.14590 | + | 21.9928i | 0.237538 | + | 0.731066i | ||||
\(906\) | 10.0902 | − | 31.0543i | 0.335223 | − | 1.03171i | ||||
\(907\) | −16.8262 | − | 12.2250i | −0.558706 | − | 0.405924i | 0.272279 | − | 0.962218i | \(-0.412223\pi\) |
−0.830985 | + | 0.556295i | \(0.812223\pi\) | |||||||
\(908\) | 9.35410 | + | 6.79615i | 0.310427 | + | 0.225538i | ||||
\(909\) | −1.50658 | + | 4.63677i | −0.0499700 | + | 0.153792i | ||||
\(910\) | −0.236068 | − | 0.726543i | −0.00782558 | − | 0.0240847i | ||||
\(911\) | 21.0902 | − | 15.3229i | 0.698749 | − | 0.507671i | −0.180776 | − | 0.983524i | \(-0.557861\pi\) |
0.879524 | + | 0.475854i | \(0.157861\pi\) | |||||||
\(912\) | 4.23607 | 0.140270 | ||||||||
\(913\) | 0.229490 | + | 0.191758i | 0.00759502 | + | 0.00634626i | ||||
\(914\) | 5.43769 | 0.179863 | ||||||||
\(915\) | 10.4721 | − | 7.60845i | 0.346198 | − | 0.251528i | ||||
\(916\) | 2.38197 | + | 7.33094i | 0.0787024 | + | 0.242221i | ||||
\(917\) | 2.51722 | − | 7.74721i | 0.0831260 | − | 0.255835i | ||||
\(918\) | 2.73607 | + | 1.98787i | 0.0903037 | + | 0.0656095i | ||||
\(919\) | 17.1803 | + | 12.4822i | 0.566727 | + | 0.411751i | 0.833915 | − | 0.551893i | \(-0.186094\pi\) |
−0.267188 | + | 0.963645i | \(0.586094\pi\) | |||||||
\(920\) | 0.145898 | − | 0.449028i | 0.00481012 | − | 0.0148040i | ||||
\(921\) | 1.75329 | + | 5.39607i | 0.0577728 | + | 0.177806i | ||||
\(922\) | 31.6525 | − | 22.9969i | 1.04242 | − | 0.757362i | ||||
\(923\) | 4.94427 | 0.162743 | ||||||||
\(924\) | −2.00000 | + | 4.97980i | −0.0657952 | + | 0.163823i | ||||
\(925\) | −3.70820 | −0.121925 | ||||||||
\(926\) | −24.7984 | + | 18.0171i | −0.814925 | + | 0.592078i | ||||
\(927\) | −1.61803 | − | 4.97980i | −0.0531432 | − | 0.163558i | ||||
\(928\) | −1.23607 | + | 3.80423i | −0.0405759 | + | 0.124880i | ||||
\(929\) | −15.9164 | − | 11.5639i | −0.522200 | − | 0.379401i | 0.295232 | − | 0.955426i | \(-0.404603\pi\) |
−0.817432 | + | 0.576025i | \(0.804603\pi\) | |||||||
\(930\) | 5.85410 | + | 4.25325i | 0.191964 | + | 0.139470i | ||||
\(931\) | −0.809017 | + | 2.48990i | −0.0265145 | + | 0.0816031i | ||||
\(932\) | 5.97214 | + | 18.3803i | 0.195624 | + | 0.602068i | ||||
\(933\) | −1.61803 | + | 1.17557i | −0.0529721 | + | 0.0384865i | ||||
\(934\) | 0.944272 | 0.0308975 | ||||||||
\(935\) | −0.500000 | − | 1.98787i | −0.0163517 | − | 0.0650103i | ||||
\(936\) | −0.291796 | −0.00953765 | ||||||||
\(937\) | 22.9721 | − | 16.6902i | 0.750467 | − | 0.545246i | −0.145505 | − | 0.989358i | \(-0.546481\pi\) |
0.895972 | + | 0.444111i | \(0.146481\pi\) | |||||||
\(938\) | −1.57295 | − | 4.84104i | −0.0513586 | − | 0.158066i | ||||
\(939\) | 6.16312 | − | 18.9681i | 0.201126 | − | 0.619002i | ||||
\(940\) | −9.09017 | − | 6.60440i | −0.296489 | − | 0.215412i | ||||
\(941\) | −43.5066 | − | 31.6094i | −1.41827 | − | 1.03044i | −0.992053 | − | 0.125817i | \(-0.959845\pi\) |
−0.426220 | − | 0.904619i | \(-0.640155\pi\) | |||||||
\(942\) | −3.09017 | + | 9.51057i | −0.100683 | + | 0.309871i | ||||
\(943\) | 0.931116 | + | 2.86568i | 0.0303213 | + | 0.0933194i | ||||
\(944\) | 1.11803 | − | 0.812299i | 0.0363889 | − | 0.0264381i | ||||
\(945\) | −5.47214 | −0.178009 | ||||||||
\(946\) | −6.69098 | + | 4.20025i | −0.217543 | + | 0.136562i | ||||
\(947\) | 51.3394 | 1.66831 | 0.834153 | − | 0.551533i | \(-0.185957\pi\) | ||||
0.834153 | + | 0.551533i | \(0.185957\pi\) | |||||||
\(948\) | −15.3262 | + | 11.1352i | −0.497773 | + | 0.361653i | ||||
\(949\) | 2.67376 | + | 8.22899i | 0.0867940 | + | 0.267124i | ||||
\(950\) | 0.809017 | − | 2.48990i | 0.0262480 | − | 0.0807830i | ||||
\(951\) | 23.4164 | + | 17.0130i | 0.759329 | + | 0.551685i | ||||
\(952\) | 0.500000 | + | 0.363271i | 0.0162051 | + | 0.0117737i | ||||
\(953\) | 8.38854 | − | 25.8173i | 0.271732 | − | 0.836304i | −0.718334 | − | 0.695698i | \(-0.755095\pi\) |
0.990066 | − | 0.140606i | \(-0.0449049\pi\) | |||||||
\(954\) | 0.291796 | + | 0.898056i | 0.00944725 | + | 0.0290756i | ||||
\(955\) | −1.61803 | + | 1.17557i | −0.0523584 | + | 0.0380406i | ||||
\(956\) | 4.29180 | 0.138807 | ||||||||
\(957\) | −21.4164 | − | 1.45309i | −0.692294 | − | 0.0469716i | ||||
\(958\) | −23.1246 | −0.747122 | ||||||||
\(959\) | 10.3992 | − | 7.55545i | 0.335807 | − | 0.243978i | ||||
\(960\) | 0.500000 | + | 1.53884i | 0.0161374 | + | 0.0496659i | ||||
\(961\) | −3.39919 | + | 10.4616i | −0.109651 | + | 0.337472i | ||||
\(962\) | 2.29180 | + | 1.66509i | 0.0738905 | + | 0.0536846i | ||||
\(963\) | 2.50000 | + | 1.81636i | 0.0805614 | + | 0.0585313i | ||||
\(964\) | −4.28115 | + | 13.1760i | −0.137887 | + | 0.424371i | ||||
\(965\) | 1.09017 | + | 3.35520i | 0.0350938 | + | 0.108008i | ||||
\(966\) | −0.618034 | + | 0.449028i | −0.0198849 | + | 0.0144472i | ||||
\(967\) | −26.0000 | −0.836104 | −0.418052 | − | 0.908423i | \(-0.637287\pi\) | ||||
−0.418052 | + | 0.908423i | \(0.637287\pi\) | |||||||
\(968\) | −1.95492 | − | 10.8249i | −0.0628333 | − | 0.347925i | ||||
\(969\) | 2.61803 | 0.0841034 | ||||||||
\(970\) | −11.1631 | + | 8.11048i | −0.358426 | + | 0.260412i | ||||
\(971\) | −6.58359 | − | 20.2622i | −0.211278 | − | 0.650245i | −0.999397 | − | 0.0347230i | \(-0.988945\pi\) |
0.788119 | − | 0.615522i | \(-0.211055\pi\) | |||||||
\(972\) | −1.21885 | + | 3.75123i | −0.0390945 | + | 0.120321i | ||||
\(973\) | 1.23607 | + | 0.898056i | 0.0396265 | + | 0.0287904i | ||||
\(974\) | −27.3262 | − | 19.8537i | −0.875589 | − | 0.636153i | ||||
\(975\) | 0.381966 | − | 1.17557i | 0.0122327 | − | 0.0376484i | ||||
\(976\) | −2.47214 | − | 7.60845i | −0.0791311 | − | 0.243541i | ||||
\(977\) | −25.5066 | + | 18.5316i | −0.816028 | + | 0.592879i | −0.915572 | − | 0.402154i | \(-0.868262\pi\) |
0.0995442 | + | 0.995033i | \(0.468262\pi\) | |||||||
\(978\) | −36.5967 | −1.17023 | ||||||||
\(979\) | 10.4098 | + | 0.706298i | 0.332700 | + | 0.0225734i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 3.14590 | − | 2.28563i | 0.100441 | − | 0.0729745i | ||||
\(982\) | −8.31966 | − | 25.6053i | −0.265491 | − | 0.817097i | ||||
\(983\) | 9.65248 | − | 29.7073i | 0.307866 | − | 0.947515i | −0.670726 | − | 0.741705i | \(-0.734017\pi\) |
0.978592 | − | 0.205809i | \(-0.0659827\pi\) | |||||||
\(984\) | −8.35410 | − | 6.06961i | −0.266319 | − | 0.193492i | ||||
\(985\) | −4.38197 | − | 3.18368i | −0.139621 | − | 0.101441i | ||||
\(986\) | −0.763932 | + | 2.35114i | −0.0243286 | + | 0.0748756i | ||||
\(987\) | 5.61803 | + | 17.2905i | 0.178824 | + | 0.550364i | ||||
\(988\) | −1.61803 | + | 1.17557i | −0.0514765 | + | 0.0373999i | ||||
\(989\) | −1.12461 | −0.0357606 | ||||||||
\(990\) | 1.07295 | − | 0.673542i | 0.0341006 | − | 0.0214066i | ||||
\(991\) | −61.2361 | −1.94523 | −0.972614 | − | 0.232427i | \(-0.925333\pi\) | ||||
−0.972614 | + | 0.232427i | \(0.925333\pi\) | |||||||
\(992\) | 3.61803 | − | 2.62866i | 0.114873 | − | 0.0834599i | ||||
\(993\) | 1.66312 | + | 5.11855i | 0.0527775 | + | 0.162432i | ||||
\(994\) | 2.00000 | − | 6.15537i | 0.0634361 | − | 0.195236i | ||||
\(995\) | 2.61803 | + | 1.90211i | 0.0829973 | + | 0.0603010i | ||||
\(996\) | −0.118034 | − | 0.0857567i | −0.00374005 | − | 0.00271731i | ||||
\(997\) | 3.97871 | − | 12.2452i | 0.126007 | − | 0.387810i | −0.868076 | − | 0.496431i | \(-0.834644\pi\) |
0.994083 | + | 0.108621i | \(0.0346435\pi\) | |||||||
\(998\) | 0.500000 | + | 1.53884i | 0.0158272 | + | 0.0487112i | ||||
\(999\) | 16.4164 | − | 11.9272i | 0.519392 | − | 0.377360i |
(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 | 770.2.n.c.421.1 | ✓ | 4 | |
11.2 | odd | 10 | 8470.2.a.bx.1.1 | 2 | |||
11.4 | even | 5 | inner | 770.2.n.c.631.1 | yes | 4 | |
11.9 | even | 5 | 8470.2.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.c.421.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
770.2.n.c.631.1 | yes | 4 | 11.4 | even | 5 | inner | |
8470.2.a.bk.1.1 | 2 | 11.9 | even | 5 | |||
8470.2.a.bx.1.1 | 2 | 11.2 | odd | 10 |