Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(39,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.39");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.n (of order \(10\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 134.10 | ||
Character | \(\chi\) | \(=\) | 475.134 |
Dual form | 475.2.n.b.39.10 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.262787 | + | 0.361695i | −0.185819 | + | 0.255757i | −0.891756 | − | 0.452517i | \(-0.850526\pi\) |
0.705937 | + | 0.708275i | \(0.250526\pi\) | |||||||
\(3\) | 2.64793 | − | 0.860365i | 1.52878 | − | 0.496732i | 0.580528 | − | 0.814240i | \(-0.302846\pi\) |
0.948255 | + | 0.317509i | \(0.102846\pi\) | |||||||
\(4\) | 0.556267 | + | 1.71202i | 0.278134 | + | 0.856008i | ||||
\(5\) | 0.0123725 | − | 2.23603i | 0.00553315 | − | 0.999985i | ||||
\(6\) | −0.384652 | + | 1.18384i | −0.157033 | + | 0.483299i | ||||
\(7\) | 4.32436i | 1.63445i | 0.576315 | + | 0.817227i | \(0.304490\pi\) | ||||
−0.576315 | + | 0.817227i | \(0.695510\pi\) | |||||||
\(8\) | −1.61580 | − | 0.525007i | −0.571273 | − | 0.185618i | ||||
\(9\) | 3.84426 | − | 2.79302i | 1.28142 | − | 0.931005i | ||||
\(10\) | 0.805512 | + | 0.592076i | 0.254725 | + | 0.187231i | ||||
\(11\) | −0.742900 | − | 0.539748i | −0.223993 | − | 0.162740i | 0.470129 | − | 0.882598i | \(-0.344207\pi\) |
−0.694122 | + | 0.719857i | \(0.744207\pi\) | |||||||
\(12\) | 2.94591 | + | 4.05470i | 0.850412 | + | 1.17049i | ||||
\(13\) | 1.76879 | + | 2.43454i | 0.490575 | + | 0.675219i | 0.980494 | − | 0.196549i | \(-0.0629736\pi\) |
−0.489919 | + | 0.871768i | \(0.662974\pi\) | |||||||
\(14\) | −1.56410 | − | 1.13639i | −0.418024 | − | 0.303712i | ||||
\(15\) | −1.89104 | − | 5.93151i | −0.488265 | − | 1.53151i | ||||
\(16\) | −2.29815 | + | 1.66970i | −0.574537 | + | 0.417426i | ||||
\(17\) | 2.92059 | + | 0.948958i | 0.708348 | + | 0.230156i | 0.640964 | − | 0.767571i | \(-0.278535\pi\) |
0.0673839 | + | 0.997727i | \(0.478535\pi\) | |||||||
\(18\) | 2.12442i | 0.500730i | ||||||||
\(19\) | 0.309017 | − | 0.951057i | 0.0708934 | − | 0.218187i | ||||
\(20\) | 3.83501 | − | 1.22265i | 0.857533 | − | 0.273393i | ||||
\(21\) | 3.72053 | + | 11.4506i | 0.811886 | + | 2.49873i | ||||
\(22\) | 0.390449 | − | 0.126865i | 0.0832440 | − | 0.0270476i | ||||
\(23\) | 3.67850 | − | 5.06302i | 0.767021 | − | 1.05571i | −0.229577 | − | 0.973291i | \(-0.573734\pi\) |
0.996597 | − | 0.0824230i | \(-0.0262658\pi\) | |||||||
\(24\) | −4.73024 | −0.965555 | ||||||||
\(25\) | −4.99969 | − | 0.0553306i | −0.999939 | − | 0.0110661i | ||||
\(26\) | −1.34538 | −0.263850 | ||||||||
\(27\) | 2.86678 | − | 3.94578i | 0.551711 | − | 0.759365i | ||||
\(28\) | −7.40337 | + | 2.40550i | −1.39911 | + | 0.454597i | ||||
\(29\) | −1.90347 | − | 5.85826i | −0.353465 | − | 1.08785i | −0.956894 | − | 0.290436i | \(-0.906200\pi\) |
0.603430 | − | 0.797416i | \(-0.293800\pi\) | |||||||
\(30\) | 2.64234 | + | 0.874742i | 0.482423 | + | 0.159705i | ||||
\(31\) | −0.458081 | + | 1.40983i | −0.0822738 | + | 0.253213i | −0.983729 | − | 0.179660i | \(-0.942500\pi\) |
0.901455 | + | 0.432873i | \(0.142500\pi\) | |||||||
\(32\) | − | 4.66792i | − | 0.825180i | ||||||
\(33\) | −2.43153 | − | 0.790051i | −0.423275 | − | 0.137530i | ||||
\(34\) | −1.11073 | + | 0.806991i | −0.190488 | + | 0.138398i | ||||
\(35\) | 9.66942 | + | 0.0535031i | 1.63443 | + | 0.00904368i | ||||
\(36\) | 6.92012 | + | 5.02776i | 1.15335 | + | 0.837960i | ||||
\(37\) | −3.89637 | − | 5.36289i | −0.640559 | − | 0.881653i | 0.358087 | − | 0.933688i | \(-0.383429\pi\) |
−0.998645 | + | 0.0520350i | \(0.983429\pi\) | |||||||
\(38\) | 0.262787 | + | 0.361695i | 0.0426297 | + | 0.0586747i | ||||
\(39\) | 6.77823 | + | 4.92467i | 1.08539 | + | 0.788579i | ||||
\(40\) | −1.19392 | + | 3.60650i | −0.188776 | + | 0.570237i | ||||
\(41\) | 1.95642 | − | 1.42142i | 0.305541 | − | 0.221989i | −0.424440 | − | 0.905456i | \(-0.639529\pi\) |
0.729981 | + | 0.683467i | \(0.239529\pi\) | |||||||
\(42\) | −5.11934 | − | 1.66337i | −0.789931 | − | 0.256664i | ||||
\(43\) | − | 9.63799i | − | 1.46978i | −0.678186 | − | 0.734890i | \(-0.737234\pi\) | ||
0.678186 | − | 0.734890i | \(-0.262766\pi\) | |||||||
\(44\) | 0.510806 | − | 1.57210i | 0.0770070 | − | 0.237003i | ||||
\(45\) | −6.19771 | − | 8.63044i | −0.923901 | − | 1.28655i | ||||
\(46\) | 0.864610 | + | 2.66099i | 0.127480 | + | 0.392342i | ||||
\(47\) | −10.0778 | + | 3.27449i | −1.47000 | + | 0.477633i | −0.931109 | − | 0.364741i | \(-0.881158\pi\) |
−0.538894 | + | 0.842374i | \(0.681158\pi\) | |||||||
\(48\) | −4.64878 | + | 6.39850i | −0.670994 | + | 0.923544i | ||||
\(49\) | −11.7001 | −1.67144 | ||||||||
\(50\) | 1.33387 | − | 1.79383i | 0.188637 | − | 0.253685i | ||||
\(51\) | 8.54998 | 1.19724 | ||||||||
\(52\) | −3.18404 | + | 4.38245i | −0.441547 | + | 0.607737i | ||||
\(53\) | −4.90441 | + | 1.59354i | −0.673673 | + | 0.218890i | −0.625823 | − | 0.779965i | \(-0.715237\pi\) |
−0.0478496 | + | 0.998855i | \(0.515237\pi\) | |||||||
\(54\) | 0.673818 | + | 2.07380i | 0.0916951 | + | 0.282208i | ||||
\(55\) | −1.21609 | + | 1.65447i | −0.163977 | + | 0.223089i | ||||
\(56\) | 2.27032 | − | 6.98732i | 0.303384 | − | 0.933720i | ||||
\(57\) | − | 2.78420i | − | 0.368776i | ||||||
\(58\) | 2.61911 | + | 0.851001i | 0.343906 | + | 0.111742i | ||||
\(59\) | −5.68224 | + | 4.12839i | −0.739764 | + | 0.537470i | −0.892637 | − | 0.450776i | \(-0.851147\pi\) |
0.152873 | + | 0.988246i | \(0.451147\pi\) | |||||||
\(60\) | 9.10290 | − | 6.53700i | 1.17518 | − | 0.843923i | ||||
\(61\) | 6.29954 | + | 4.57688i | 0.806573 | + | 0.586010i | 0.912835 | − | 0.408329i | \(-0.133888\pi\) |
−0.106262 | + | 0.994338i | \(0.533888\pi\) | |||||||
\(62\) | −0.389551 | − | 0.536171i | −0.0494730 | − | 0.0680937i | ||||
\(63\) | 12.0780 | + | 16.6240i | 1.52169 | + | 2.09442i | ||||
\(64\) | −2.90793 | − | 2.11274i | −0.363492 | − | 0.264092i | ||||
\(65\) | 5.46559 | − | 3.92496i | 0.677923 | − | 0.486831i | ||||
\(66\) | 0.924732 | − | 0.671857i | 0.113827 | − | 0.0826999i | ||||
\(67\) | 8.04870 | + | 2.61518i | 0.983305 | + | 0.319495i | 0.756175 | − | 0.654369i | \(-0.227066\pi\) |
0.227130 | + | 0.973864i | \(0.427066\pi\) | |||||||
\(68\) | 5.52798i | 0.670365i | ||||||||
\(69\) | 5.38437 | − | 16.5714i | 0.648202 | − | 1.99496i | ||||
\(70\) | −2.56035 | + | 3.48332i | −0.306020 | + | 0.416337i | ||||
\(71\) | 3.62351 | + | 11.1520i | 0.430031 | + | 1.32350i | 0.898094 | + | 0.439804i | \(0.144952\pi\) |
−0.468063 | + | 0.883695i | \(0.655048\pi\) | |||||||
\(72\) | −7.67792 | + | 2.49471i | −0.904851 | + | 0.294004i | ||||
\(73\) | 7.55504 | − | 10.3986i | 0.884250 | − | 1.21707i | −0.0909755 | − | 0.995853i | \(-0.528999\pi\) |
0.975226 | − | 0.221213i | \(-0.0710015\pi\) | |||||||
\(74\) | 2.96365 | 0.344517 | ||||||||
\(75\) | −13.2864 | + | 4.15505i | −1.53419 | + | 0.479784i | ||||
\(76\) | 1.80012 | 0.206488 | ||||||||
\(77\) | 2.33407 | − | 3.21257i | 0.265992 | − | 0.366106i | ||||
\(78\) | −3.56246 | + | 1.15751i | −0.403369 | + | 0.131063i | ||||
\(79\) | 3.35067 | + | 10.3123i | 0.376980 | + | 1.16023i | 0.942133 | + | 0.335239i | \(0.108817\pi\) |
−0.565153 | + | 0.824986i | \(0.691183\pi\) | |||||||
\(80\) | 3.70508 | + | 5.15940i | 0.414240 | + | 0.576838i | ||||
\(81\) | −0.208911 | + | 0.642961i | −0.0232123 | + | 0.0714401i | ||||
\(82\) | 1.08116i | 0.119394i | ||||||||
\(83\) | −10.0710 | − | 3.27228i | −1.10544 | − | 0.359179i | −0.301246 | − | 0.953546i | \(-0.597403\pi\) |
−0.804194 | + | 0.594367i | \(0.797403\pi\) | |||||||
\(84\) | −17.5340 | + | 12.7392i | −1.91312 | + | 1.38996i | ||||
\(85\) | 2.15804 | − | 6.51880i | 0.234072 | − | 0.707064i | ||||
\(86\) | 3.48602 | + | 2.53274i | 0.375907 | + | 0.273112i | ||||
\(87\) | −10.0805 | − | 13.8746i | −1.08074 | − | 1.48751i | ||||
\(88\) | 0.917010 | + | 1.26216i | 0.0977536 | + | 0.134546i | ||||
\(89\) | −3.85580 | − | 2.80140i | −0.408714 | − | 0.296948i | 0.364367 | − | 0.931256i | \(-0.381285\pi\) |
−0.773081 | + | 0.634307i | \(0.781285\pi\) | |||||||
\(90\) | 4.75027 | + | 0.0262843i | 0.500722 | + | 0.00277061i | ||||
\(91\) | −10.5278 | + | 7.64890i | −1.10361 | + | 0.801823i | ||||
\(92\) | 10.7142 | + | 3.48126i | 1.11703 | + | 0.362946i | ||||
\(93\) | 4.12724i | 0.427975i | ||||||||
\(94\) | 1.46396 | − | 4.50560i | 0.150996 | − | 0.464717i | ||||
\(95\) | −2.12277 | − | 0.702739i | −0.217792 | − | 0.0720995i | ||||
\(96\) | −4.01611 | − | 12.3603i | −0.409893 | − | 1.26152i | ||||
\(97\) | −0.493676 | + | 0.160405i | −0.0501252 | + | 0.0162867i | −0.333972 | − | 0.942583i | \(-0.608389\pi\) |
0.283847 | + | 0.958870i | \(0.408389\pi\) | |||||||
\(98\) | 3.07464 | − | 4.23187i | 0.310585 | − | 0.427484i | ||||
\(99\) | −4.36342 | −0.438541 | ||||||||
\(100\) | −2.68644 | − | 8.59033i | −0.268644 | − | 0.859033i | ||||
\(101\) | −14.8247 | −1.47511 | −0.737557 | − | 0.675284i | \(-0.764021\pi\) | ||||
−0.737557 | + | 0.675284i | \(0.764021\pi\) | |||||||
\(102\) | −2.24682 | + | 3.09249i | −0.222469 | + | 0.306202i | ||||
\(103\) | 3.98724 | − | 1.29553i | 0.392875 | − | 0.127653i | −0.105916 | − | 0.994375i | \(-0.533778\pi\) |
0.498791 | + | 0.866722i | \(0.333778\pi\) | |||||||
\(104\) | −1.57988 | − | 4.86236i | −0.154920 | − | 0.476794i | ||||
\(105\) | 25.6500 | − | 8.17755i | 2.50318 | − | 0.798047i | ||||
\(106\) | 0.712440 | − | 2.19266i | 0.0691983 | − | 0.212970i | ||||
\(107\) | − | 2.34479i | − | 0.226679i | −0.993556 | − | 0.113340i | \(-0.963845\pi\) | ||
0.993556 | − | 0.113340i | \(-0.0361548\pi\) | |||||||
\(108\) | 8.34993 | + | 2.71306i | 0.803472 | + | 0.261064i | ||||
\(109\) | −6.43598 | + | 4.67601i | −0.616455 | + | 0.447881i | −0.851682 | − | 0.524060i | \(-0.824417\pi\) |
0.235226 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(110\) | −0.278843 | − | 0.874627i | −0.0265866 | − | 0.0833924i | ||||
\(111\) | −14.9313 | − | 10.8483i | −1.41722 | − | 1.02967i | ||||
\(112\) | −7.22040 | − | 9.93803i | −0.682264 | − | 0.939055i | ||||
\(113\) | 3.18196 | + | 4.37959i | 0.299334 | + | 0.411997i | 0.932018 | − | 0.362413i | \(-0.118047\pi\) |
−0.632684 | + | 0.774410i | \(0.718047\pi\) | |||||||
\(114\) | 1.00703 | + | 0.731651i | 0.0943172 | + | 0.0685254i | ||||
\(115\) | −11.2756 | − | 8.28790i | −1.05145 | − | 0.772850i | ||||
\(116\) | 8.97060 | − | 6.51752i | 0.832899 | − | 0.605137i | ||||
\(117\) | 13.5994 | + | 4.41871i | 1.25726 | + | 0.408510i | ||||
\(118\) | − | 3.14013i | − | 0.289072i | ||||||
\(119\) | −4.10364 | + | 12.6297i | −0.376180 | + | 1.15776i | ||||
\(120\) | −0.0585248 | + | 10.5770i | −0.00534256 | + | 0.965540i | ||||
\(121\) | −3.13861 | − | 9.65966i | −0.285329 | − | 0.878151i | ||||
\(122\) | −3.31087 | + | 1.07577i | −0.299752 | + | 0.0973955i | ||||
\(123\) | 3.95752 | − | 5.44706i | 0.356838 | − | 0.491145i | ||||
\(124\) | −2.66846 | −0.239635 | ||||||||
\(125\) | −0.185580 | + | 11.1788i | −0.0165988 | + | 0.999862i | ||||
\(126\) | −9.18675 | −0.818421 | ||||||||
\(127\) | 5.13130 | − | 7.06262i | 0.455329 | − | 0.626706i | −0.518203 | − | 0.855258i | \(-0.673399\pi\) |
0.973532 | + | 0.228551i | \(0.0733988\pi\) | |||||||
\(128\) | 10.4072 | − | 3.38152i | 0.919880 | − | 0.298887i | ||||
\(129\) | −8.29219 | − | 25.5207i | −0.730087 | − | 2.24698i | ||||
\(130\) | −0.0166457 | + | 3.00831i | −0.00145992 | + | 0.263846i | ||||
\(131\) | 0.623982 | − | 1.92042i | 0.0545176 | − | 0.167788i | −0.920090 | − | 0.391706i | \(-0.871885\pi\) |
0.974608 | + | 0.223918i | \(0.0718849\pi\) | |||||||
\(132\) | − | 4.60229i | − | 0.400578i | ||||||
\(133\) | 4.11271 | + | 1.33630i | 0.356617 | + | 0.115872i | ||||
\(134\) | −3.06099 | + | 2.22394i | −0.264430 | + | 0.192119i | ||||
\(135\) | −8.78743 | − | 6.45903i | −0.756301 | − | 0.555905i | ||||
\(136\) | −4.22090 | − | 3.06666i | −0.361939 | − | 0.262964i | ||||
\(137\) | −10.9877 | − | 15.1233i | −0.938744 | − | 1.29207i | −0.956350 | − | 0.292225i | \(-0.905604\pi\) |
0.0176055 | − | 0.999845i | \(-0.494396\pi\) | |||||||
\(138\) | 4.57885 | + | 6.30225i | 0.389778 | + | 0.536483i | ||||
\(139\) | 13.6831 | + | 9.94137i | 1.16059 | + | 0.843216i | 0.989852 | − | 0.142101i | \(-0.0453857\pi\) |
0.170735 | + | 0.985317i | \(0.445386\pi\) | |||||||
\(140\) | 5.28718 | + | 16.5840i | 0.446849 | + | 1.40160i | ||||
\(141\) | −23.8681 | + | 17.3412i | −2.01006 | + | 1.46039i | ||||
\(142\) | −4.98584 | − | 1.62000i | −0.418402 | − | 0.135947i | ||||
\(143\) | − | 2.76332i | − | 0.231080i | ||||||
\(144\) | −4.17117 | + | 12.8375i | −0.347597 | + | 1.06979i | ||||
\(145\) | −13.1228 | + | 4.18373i | −1.08979 | + | 0.347440i | ||||
\(146\) | 1.77577 | + | 5.46524i | 0.146963 | + | 0.452307i | ||||
\(147\) | −30.9811 | + | 10.0664i | −2.55527 | + | 0.830259i | ||||
\(148\) | 7.01392 | − | 9.65384i | 0.576541 | − | 0.793541i | ||||
\(149\) | −2.74494 | −0.224874 | −0.112437 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112437 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(150\) | 1.98864 | − | 5.89754i | 0.162372 | − | 0.481532i | ||||
\(151\) | −16.7075 | −1.35964 | −0.679818 | − | 0.733380i | \(-0.737941\pi\) | ||||
−0.679818 | + | 0.733380i | \(0.737941\pi\) | |||||||
\(152\) | −0.998622 | + | 1.37449i | −0.0809990 | + | 0.111486i | ||||
\(153\) | 13.8780 | − | 4.50922i | 1.12197 | − | 0.364549i | ||||
\(154\) | 0.548608 | + | 1.68844i | 0.0442081 | + | 0.136059i | ||||
\(155\) | 3.14676 | + | 1.04173i | 0.252754 | + | 0.0836736i | ||||
\(156\) | −4.66061 | + | 14.3439i | −0.373147 | + | 1.14843i | ||||
\(157\) | 2.41292i | 0.192572i | 0.995354 | + | 0.0962859i | \(0.0306963\pi\) | ||||
−0.995354 | + | 0.0962859i | \(0.969304\pi\) | |||||||
\(158\) | −4.61043 | − | 1.49802i | −0.366786 | − | 0.119176i | ||||
\(159\) | −11.6155 | + | 8.43916i | −0.921170 | + | 0.669269i | ||||
\(160\) | −10.4376 | − | 0.0577538i | −0.825167 | − | 0.00456584i | ||||
\(161\) | 21.8943 | + | 15.9072i | 1.72552 | + | 1.25366i | ||||
\(162\) | −0.177657 | − | 0.244524i | −0.0139581 | − | 0.0192116i | ||||
\(163\) | −8.97603 | − | 12.3544i | −0.703057 | − | 0.967675i | −0.999919 | − | 0.0127543i | \(-0.995940\pi\) |
0.296862 | − | 0.954920i | \(-0.404060\pi\) | |||||||
\(164\) | 3.52179 | + | 2.55873i | 0.275005 | + | 0.199803i | ||||
\(165\) | −1.79667 | + | 5.42720i | −0.139870 | + | 0.422507i | ||||
\(166\) | 3.83011 | − | 2.78274i | 0.297274 | − | 0.215982i | ||||
\(167\) | 21.7786 | + | 7.07628i | 1.68528 | + | 0.547579i | 0.985923 | − | 0.167198i | \(-0.0534720\pi\) |
0.699352 | + | 0.714777i | \(0.253472\pi\) | |||||||
\(168\) | − | 20.4552i | − | 1.57816i | ||||||
\(169\) | 1.21889 | − | 3.75135i | 0.0937607 | − | 0.288566i | ||||
\(170\) | 1.79072 | + | 2.49361i | 0.137342 | + | 0.191251i | ||||
\(171\) | −1.46837 | − | 4.51919i | −0.112289 | − | 0.345591i | ||||
\(172\) | 16.5004 | − | 5.36130i | 1.25814 | − | 0.408796i | ||||
\(173\) | 4.16344 | − | 5.73048i | 0.316540 | − | 0.435681i | −0.620867 | − | 0.783916i | \(-0.713219\pi\) |
0.937407 | + | 0.348236i | \(0.113219\pi\) | |||||||
\(174\) | 7.66740 | 0.581264 | ||||||||
\(175\) | 0.239270 | − | 21.6205i | 0.0180871 | − | 1.63435i | ||||
\(176\) | 2.60851 | 0.196624 | ||||||||
\(177\) | −11.4942 | + | 15.8205i | −0.863961 | + | 1.18914i | ||||
\(178\) | 2.02651 | − | 0.658453i | 0.151893 | − | 0.0493531i | ||||
\(179\) | 0.217238 | + | 0.668589i | 0.0162371 | + | 0.0499727i | 0.958847 | − | 0.283924i | \(-0.0916363\pi\) |
−0.942610 | + | 0.333897i | \(0.891636\pi\) | |||||||
\(180\) | 11.3279 | − | 15.4114i | 0.844329 | − | 1.14870i | ||||
\(181\) | 2.23789 | − | 6.88752i | 0.166341 | − | 0.511945i | −0.832791 | − | 0.553587i | \(-0.813259\pi\) |
0.999133 | + | 0.0416414i | \(0.0132587\pi\) | |||||||
\(182\) | − | 5.81789i | − | 0.431251i | ||||||
\(183\) | 20.6185 | + | 6.69936i | 1.52416 | + | 0.495231i | ||||
\(184\) | −8.60186 | + | 6.24962i | −0.634138 | + | 0.460728i | ||||
\(185\) | −12.0398 | + | 8.64605i | −0.885184 | + | 0.635671i | ||||
\(186\) | −1.49281 | − | 1.08459i | −0.109458 | − | 0.0795257i | ||||
\(187\) | −1.65751 | − | 2.28137i | −0.121209 | − | 0.166830i | ||||
\(188\) | −11.2119 | − | 15.4319i | −0.817715 | − | 1.12549i | ||||
\(189\) | 17.0630 | + | 12.3970i | 1.24115 | + | 0.901747i | ||||
\(190\) | 0.812014 | − | 0.583126i | 0.0589097 | − | 0.0423044i | ||||
\(191\) | −0.408127 | + | 0.296522i | −0.0295310 | + | 0.0214556i | −0.602453 | − | 0.798154i | \(-0.705810\pi\) |
0.572922 | + | 0.819610i | \(0.305810\pi\) | |||||||
\(192\) | −9.51773 | − | 3.09250i | −0.686883 | − | 0.223182i | ||||
\(193\) | 23.3193i | 1.67856i | 0.543700 | + | 0.839280i | \(0.317023\pi\) | ||||
−0.543700 | + | 0.839280i | \(0.682977\pi\) | |||||||
\(194\) | 0.0717140 | − | 0.220713i | 0.00514876 | − | 0.0158463i | ||||
\(195\) | 11.0956 | − | 15.0954i | 0.794572 | − | 1.08101i | ||||
\(196\) | −6.50839 | − | 20.0308i | −0.464885 | − | 1.43077i | ||||
\(197\) | 7.55921 | − | 2.45614i | 0.538572 | − | 0.174993i | −0.0270854 | − | 0.999633i | \(-0.508623\pi\) |
0.565657 | + | 0.824641i | \(0.308623\pi\) | |||||||
\(198\) | 1.14665 | − | 1.57823i | 0.0814890 | − | 0.112160i | ||||
\(199\) | 4.56505 | 0.323608 | 0.161804 | − | 0.986823i | \(-0.448269\pi\) | ||||
0.161804 | + | 0.986823i | \(0.448269\pi\) | |||||||
\(200\) | 8.04948 | + | 2.71428i | 0.569184 | + | 0.191928i | ||||
\(201\) | 23.5624 | 1.66196 | ||||||||
\(202\) | 3.89575 | − | 5.36203i | 0.274104 | − | 0.377271i | ||||
\(203\) | 25.3333 | − | 8.23127i | 1.77805 | − | 0.577722i | ||||
\(204\) | 4.75607 | + | 14.6377i | 0.332992 | + | 1.02484i | ||||
\(205\) | −3.15414 | − | 4.39221i | −0.220295 | − | 0.306765i | ||||
\(206\) | −0.579207 | + | 1.78262i | −0.0403553 | + | 0.124201i | ||||
\(207\) | − | 29.7377i | − | 2.06691i | ||||||
\(208\) | −8.12990 | − | 2.64157i | −0.563707 | − | 0.183160i | ||||
\(209\) | −0.742900 | + | 0.539748i | −0.0513875 | + | 0.0373352i | ||||
\(210\) | −3.78270 | + | 11.4264i | −0.261031 | + | 0.788499i | ||||
\(211\) | 9.74433 | + | 7.07967i | 0.670828 | + | 0.487385i | 0.870302 | − | 0.492518i | \(-0.163924\pi\) |
−0.199474 | + | 0.979903i | \(0.563924\pi\) | |||||||
\(212\) | −5.45633 | − | 7.50999i | −0.374742 | − | 0.515788i | ||||
\(213\) | 19.1896 | + | 26.4122i | 1.31485 | + | 1.80973i | ||||
\(214\) | 0.848099 | + | 0.616180i | 0.0579748 | + | 0.0421212i | ||||
\(215\) | −21.5509 | − | 0.119246i | −1.46976 | − | 0.00813251i | ||||
\(216\) | −6.70371 | + | 4.87053i | −0.456130 | + | 0.331398i | ||||
\(217\) | −6.09661 | − | 1.98091i | −0.413865 | − | 0.134473i | ||||
\(218\) | − | 3.55666i | − | 0.240887i | ||||||
\(219\) | 11.0586 | − | 34.0349i | 0.747271 | − | 2.29986i | ||||
\(220\) | −3.50895 | − | 1.16163i | −0.236573 | − | 0.0783172i | ||||
\(221\) | 2.85565 | + | 8.78880i | 0.192092 | + | 0.591199i | ||||
\(222\) | 7.84753 | − | 2.54982i | 0.526692 | − | 0.171133i | ||||
\(223\) | −13.3137 | + | 18.3248i | −0.891553 | + | 1.22712i | 0.0815321 | + | 0.996671i | \(0.474019\pi\) |
−0.973085 | + | 0.230447i | \(0.925981\pi\) | |||||||
\(224\) | 20.1858 | 1.34872 | ||||||||
\(225\) | −19.3746 | + | 13.7515i | −1.29164 | + | 0.916768i | ||||
\(226\) | −2.42026 | −0.160993 | ||||||||
\(227\) | 14.8797 | − | 20.4801i | 0.987599 | − | 1.35931i | 0.0549659 | − | 0.998488i | \(-0.482495\pi\) |
0.932633 | − | 0.360825i | \(-0.117505\pi\) | |||||||
\(228\) | 4.76659 | − | 1.54876i | 0.315675 | − | 0.102569i | ||||
\(229\) | 7.95002 | + | 24.4676i | 0.525352 | + | 1.61687i | 0.763619 | + | 0.645667i | \(0.223421\pi\) |
−0.238267 | + | 0.971200i | \(0.576579\pi\) | |||||||
\(230\) | 5.96077 | − | 1.90037i | 0.393042 | − | 0.125307i | ||||
\(231\) | 3.41647 | − | 10.5148i | 0.224787 | − | 0.691823i | ||||
\(232\) | 10.4651i | 0.687070i | ||||||||
\(233\) | 8.25006 | + | 2.68061i | 0.540479 | + | 0.175612i | 0.566519 | − | 0.824049i | \(-0.308290\pi\) |
−0.0260400 | + | 0.999661i | \(0.508290\pi\) | |||||||
\(234\) | −5.17197 | + | 3.75766i | −0.338102 | + | 0.245646i | ||||
\(235\) | 7.19717 | + | 22.5749i | 0.469492 | + | 1.47262i | ||||
\(236\) | −10.2287 | − | 7.43159i | −0.665832 | − | 0.483755i | ||||
\(237\) | 17.7447 | + | 24.4235i | 1.15264 | + | 1.58648i | ||||
\(238\) | −3.48972 | − | 4.80319i | −0.226205 | − | 0.311345i | ||||
\(239\) | 0.768449 | + | 0.558311i | 0.0497068 | + | 0.0361141i | 0.612361 | − | 0.790578i | \(-0.290220\pi\) |
−0.562654 | + | 0.826692i | \(0.690220\pi\) | |||||||
\(240\) | 14.2498 | + | 10.4740i | 0.919818 | + | 0.676094i | ||||
\(241\) | 1.74154 | − | 1.26531i | 0.112183 | − | 0.0815055i | −0.530279 | − | 0.847823i | \(-0.677913\pi\) |
0.642462 | + | 0.766317i | \(0.277913\pi\) | |||||||
\(242\) | 4.31864 | + | 1.40321i | 0.277613 | + | 0.0902019i | ||||
\(243\) | 16.5140i | 1.05937i | ||||||||
\(244\) | −4.33146 | + | 13.3309i | −0.277294 | + | 0.853422i | ||||
\(245\) | −0.144759 | + | 26.1618i | −0.00924834 | + | 1.67142i | ||||
\(246\) | 0.930191 | + | 2.86283i | 0.0593068 | + | 0.182528i | ||||
\(247\) | 2.86197 | − | 0.929910i | 0.182103 | − | 0.0591687i | ||||
\(248\) | 1.48034 | − | 2.03751i | 0.0940016 | − | 0.129382i | ||||
\(249\) | −29.4828 | −1.86839 | ||||||||
\(250\) | −3.99455 | − | 3.00477i | −0.252638 | − | 0.190038i | ||||
\(251\) | 8.34465 | 0.526709 | 0.263355 | − | 0.964699i | \(-0.415171\pi\) | ||||
0.263355 | + | 0.964699i | \(0.415171\pi\) | |||||||
\(252\) | −21.7419 | + | 29.9251i | −1.36961 | + | 1.88510i | ||||
\(253\) | −5.46552 | + | 1.77585i | −0.343614 | + | 0.111647i | ||||
\(254\) | 1.20608 | + | 3.71193i | 0.0756762 | + | 0.232907i | ||||
\(255\) | 0.105785 | − | 19.1180i | 0.00662448 | − | 1.19722i | ||||
\(256\) | 0.709652 | − | 2.18409i | 0.0443533 | − | 0.136505i | ||||
\(257\) | 21.5289i | 1.34294i | 0.741034 | + | 0.671468i | \(0.234336\pi\) | ||||
−0.741034 | + | 0.671468i | \(0.765664\pi\) | |||||||
\(258\) | 11.4098 | + | 3.70727i | 0.710344 | + | 0.230805i | ||||
\(259\) | 23.1911 | − | 16.8493i | 1.44102 | − | 1.04696i | ||||
\(260\) | 9.75992 | + | 7.17384i | 0.605285 | + | 0.444903i | ||||
\(261\) | −23.6796 | − | 17.2043i | −1.46573 | − | 1.06492i | ||||
\(262\) | 0.530632 | + | 0.730353i | 0.0327826 | + | 0.0451213i | ||||
\(263\) | 10.3428 | + | 14.2356i | 0.637764 | + | 0.877807i | 0.998494 | − | 0.0548634i | \(-0.0174723\pi\) |
−0.360730 | + | 0.932670i | \(0.617472\pi\) | |||||||
\(264\) | 3.51409 | + | 2.55314i | 0.216277 | + | 0.157135i | ||||
\(265\) | 3.50253 | + | 10.9861i | 0.215159 | + | 0.674874i | ||||
\(266\) | −1.56410 | + | 1.13639i | −0.0959012 | + | 0.0696763i | ||||
\(267\) | −12.6201 | − | 4.10053i | −0.772339 | − | 0.250948i | ||||
\(268\) | 15.2342i | 0.930579i | ||||||||
\(269\) | 5.46680 | − | 16.8251i | 0.333317 | − | 1.02584i | −0.634228 | − | 0.773146i | \(-0.718682\pi\) |
0.967545 | − | 0.252698i | \(-0.0813179\pi\) | |||||||
\(270\) | 4.64542 | − | 1.48102i | 0.282711 | − | 0.0901321i | ||||
\(271\) | 7.01444 | + | 21.5882i | 0.426097 | + | 1.31139i | 0.901940 | + | 0.431862i | \(0.142143\pi\) |
−0.475843 | + | 0.879530i | \(0.657857\pi\) | |||||||
\(272\) | −8.29644 | + | 2.69568i | −0.503045 | + | 0.163449i | ||||
\(273\) | −21.2961 | + | 29.3115i | −1.28890 | + | 1.77401i | ||||
\(274\) | 8.35746 | 0.504892 | ||||||||
\(275\) | 3.68441 | + | 2.73968i | 0.222178 | + | 0.165209i | ||||
\(276\) | 31.3656 | 1.88799 | ||||||||
\(277\) | 12.2108 | − | 16.8067i | 0.733673 | − | 1.00981i | −0.265284 | − | 0.964170i | \(-0.585466\pi\) |
0.998958 | − | 0.0456446i | \(-0.0145342\pi\) | |||||||
\(278\) | −7.19150 | + | 2.33666i | −0.431317 | + | 0.140143i | ||||
\(279\) | 2.17669 | + | 6.69917i | 0.130315 | + | 0.401069i | ||||
\(280\) | −15.5958 | − | 5.16296i | −0.932027 | − | 0.308546i | ||||
\(281\) | 0.910488 | − | 2.80219i | 0.0543152 | − | 0.167165i | −0.920219 | − | 0.391404i | \(-0.871990\pi\) |
0.974534 | + | 0.224239i | \(0.0719896\pi\) | |||||||
\(282\) | − | 13.1900i | − | 0.785456i | ||||||
\(283\) | −20.1731 | − | 6.55465i | −1.19917 | − | 0.389633i | −0.359713 | − | 0.933063i | \(-0.617126\pi\) |
−0.839455 | + | 0.543429i | \(0.817126\pi\) | |||||||
\(284\) | −17.0768 | + | 12.4070i | −1.01332 | + | 0.736220i | ||||
\(285\) | −6.22556 | − | 0.0344475i | −0.368770 | − | 0.00204049i | ||||
\(286\) | 0.999480 | + | 0.726165i | 0.0591005 | + | 0.0429390i | ||||
\(287\) | 6.14674 | + | 8.46026i | 0.362831 | + | 0.499394i | ||||
\(288\) | −13.0376 | − | 17.9447i | −0.768247 | − | 1.05740i | ||||
\(289\) | −6.12394 | − | 4.44931i | −0.360232 | − | 0.261724i | ||||
\(290\) | 1.93527 | − | 5.84590i | 0.113643 | − | 0.343283i | ||||
\(291\) | −1.16921 | + | 0.849484i | −0.0685405 | + | 0.0497976i | ||||
\(292\) | 22.0052 | + | 7.14993i | 1.28776 | + | 0.418418i | ||||
\(293\) | 19.8597i | 1.16022i | 0.814540 | + | 0.580108i | \(0.196989\pi\) | ||||
−0.814540 | + | 0.580108i | \(0.803011\pi\) | |||||||
\(294\) | 4.50047 | − | 13.8510i | 0.262473 | − | 0.807807i | ||||
\(295\) | 9.16091 | + | 12.7568i | 0.533369 | + | 0.742727i | ||||
\(296\) | 3.48021 | + | 10.7110i | 0.202283 | + | 0.622564i | ||||
\(297\) | −4.25946 | + | 1.38398i | −0.247159 | + | 0.0803067i | ||||
\(298\) | 0.721335 | − | 0.992832i | 0.0417858 | − | 0.0575132i | ||||
\(299\) | 18.8326 | 1.08912 | ||||||||
\(300\) | −14.5043 | − | 20.4353i | −0.837407 | − | 1.17983i | ||||
\(301\) | 41.6782 | 2.40229 | ||||||||
\(302\) | 4.39051 | − | 6.04303i | 0.252646 | − | 0.347737i | ||||
\(303\) | −39.2548 | + | 12.7547i | −2.25513 | + | 0.732736i | ||||
\(304\) | 0.877815 | + | 2.70164i | 0.0503461 | + | 0.154949i | ||||
\(305\) | 10.3120 | − | 14.0293i | 0.590464 | − | 0.803318i | ||||
\(306\) | −2.01598 | + | 6.20456i | −0.115246 | + | 0.354691i | ||||
\(307\) | − | 22.5851i | − | 1.28900i | −0.764605 | − | 0.644499i | \(-0.777066\pi\) | ||
0.764605 | − | 0.644499i | \(-0.222934\pi\) | |||||||
\(308\) | 6.79833 | + | 2.20891i | 0.387371 | + | 0.125864i | ||||
\(309\) | 9.44331 | − | 6.86097i | 0.537211 | − | 0.390307i | ||||
\(310\) | −1.20372 | + | 0.864415i | −0.0683664 | + | 0.0490955i | ||||
\(311\) | 8.53985 | + | 6.20456i | 0.484250 | + | 0.351828i | 0.802969 | − | 0.596021i | \(-0.203252\pi\) |
−0.318719 | + | 0.947849i | \(0.603252\pi\) | |||||||
\(312\) | −8.36681 | − | 11.5159i | −0.473677 | − | 0.651961i | ||||
\(313\) | −16.2695 | − | 22.3931i | −0.919607 | − | 1.26573i | −0.963778 | − | 0.266706i | \(-0.914065\pi\) |
0.0441712 | − | 0.999024i | \(-0.485935\pi\) | |||||||
\(314\) | −0.872741 | − | 0.634084i | −0.0492516 | − | 0.0357834i | ||||
\(315\) | 37.3211 | − | 26.8012i | 2.10281 | − | 1.51007i | ||||
\(316\) | −15.7910 | + | 11.4728i | −0.888311 | + | 0.645396i | ||||
\(317\) | −24.1290 | − | 7.83999i | −1.35522 | − | 0.440338i | −0.460776 | − | 0.887517i | \(-0.652429\pi\) |
−0.894445 | + | 0.447179i | \(0.852429\pi\) | |||||||
\(318\) | − | 6.41898i | − | 0.359959i | ||||||
\(319\) | −1.74790 | + | 5.37950i | −0.0978639 | + | 0.301194i | ||||
\(320\) | −4.76013 | + | 6.47610i | −0.266099 | + | 0.362025i | ||||
\(321\) | −2.01737 | − | 6.20883i | −0.112599 | − | 0.346543i | ||||
\(322\) | −11.5071 | + | 3.73888i | −0.641266 | + | 0.208360i | ||||
\(323\) | 1.80503 | − | 2.48441i | 0.100434 | − | 0.138236i | ||||
\(324\) | −1.21697 | −0.0676094 | ||||||||
\(325\) | −8.70872 | − | 12.2698i | −0.483073 | − | 0.680606i | ||||
\(326\) | 6.82733 | 0.378131 | ||||||||
\(327\) | −13.0190 | + | 17.9190i | −0.719950 | + | 0.990926i | ||||
\(328\) | −3.90745 | + | 1.26961i | −0.215753 | + | 0.0701023i | ||||
\(329\) | −14.1601 | − | 43.5802i | −0.780670 | − | 2.40265i | ||||
\(330\) | −1.49085 | − | 2.07604i | −0.0820688 | − | 0.114282i | ||||
\(331\) | −1.04782 | + | 3.22485i | −0.0575932 | + | 0.177254i | −0.975715 | − | 0.219045i | \(-0.929706\pi\) |
0.918121 | + | 0.396299i | \(0.129706\pi\) | |||||||
\(332\) | − | 19.0620i | − | 1.04617i | ||||||
\(333\) | −29.9573 | − | 9.73370i | −1.64165 | − | 0.533404i | ||||
\(334\) | −8.28258 | + | 6.01765i | −0.453203 | + | 0.329271i | ||||
\(335\) | 5.94722 | − | 17.9648i | 0.324931 | − | 0.981523i | ||||
\(336\) | −27.6694 | − | 20.1030i | −1.50949 | − | 1.09671i | ||||
\(337\) | 5.92137 | + | 8.15007i | 0.322558 | + | 0.443963i | 0.939246 | − | 0.343245i | \(-0.111526\pi\) |
−0.616688 | + | 0.787207i | \(0.711526\pi\) | |||||||
\(338\) | 1.03654 | + | 1.42667i | 0.0563803 | + | 0.0776008i | ||||
\(339\) | 12.1937 | + | 8.85921i | 0.662268 | + | 0.481166i | ||||
\(340\) | 12.3607 | + | 0.0683948i | 0.670355 | + | 0.00370923i | ||||
\(341\) | 1.10126 | − | 0.800113i | 0.0596366 | − | 0.0433286i | ||||
\(342\) | 2.02044 | + | 0.656481i | 0.109253 | + | 0.0354984i | ||||
\(343\) | − | 20.3249i | − | 1.09744i | ||||||
\(344\) | −5.06001 | + | 15.5731i | −0.272818 | + | 0.839646i | ||||
\(345\) | −36.9876 | − | 12.2447i | −1.99134 | − | 0.659231i | ||||
\(346\) | 0.978591 | + | 3.01179i | 0.0526094 | + | 0.161915i | ||||
\(347\) | 11.3207 | − | 3.67832i | 0.607727 | − | 0.197463i | 0.0110436 | − | 0.999939i | \(-0.496485\pi\) |
0.596684 | + | 0.802476i | \(0.296485\pi\) | |||||||
\(348\) | 18.1461 | − | 24.9759i | 0.972732 | − | 1.33885i | ||||
\(349\) | 9.35956 | 0.501006 | 0.250503 | − | 0.968116i | \(-0.419404\pi\) | ||||
0.250503 | + | 0.968116i | \(0.419404\pi\) | |||||||
\(350\) | 7.75715 | + | 5.76813i | 0.414637 | + | 0.308319i | ||||
\(351\) | 14.6769 | 0.783394 | ||||||||
\(352\) | −2.51950 | + | 3.46780i | −0.134290 | + | 0.184834i | ||||
\(353\) | −5.18894 | + | 1.68599i | −0.276179 | + | 0.0897361i | −0.443832 | − | 0.896110i | \(-0.646381\pi\) |
0.167653 | + | 0.985846i | \(0.446381\pi\) | |||||||
\(354\) | −2.70165 | − | 8.31483i | −0.143591 | − | 0.441928i | ||||
\(355\) | 24.9811 | − | 7.96430i | 1.32586 | − | 0.422701i | ||||
\(356\) | 2.65119 | − | 8.15952i | 0.140513 | − | 0.432454i | ||||
\(357\) | 36.9732i | 1.95683i | ||||||||
\(358\) | −0.298913 | − | 0.0971226i | −0.0157980 | − | 0.00513309i | ||||
\(359\) | −23.0491 | + | 16.7461i | −1.21648 | + | 0.883828i | −0.995803 | − | 0.0915182i | \(-0.970828\pi\) |
−0.220681 | + | 0.975346i | \(0.570828\pi\) | |||||||
\(360\) | 5.48325 | + | 17.1990i | 0.288993 | + | 0.906464i | ||||
\(361\) | −0.809017 | − | 0.587785i | −0.0425798 | − | 0.0309361i | ||||
\(362\) | 1.90310 | + | 2.61939i | 0.100024 | + | 0.137672i | ||||
\(363\) | −16.6217 | − | 22.8778i | −0.872411 | − | 1.20077i | ||||
\(364\) | −18.9513 | − | 13.7689i | −0.993319 | − | 0.721688i | ||||
\(365\) | −23.1582 | − | 17.0220i | −1.21215 | − | 0.890971i | ||||
\(366\) | −7.84141 | + | 5.69712i | −0.409877 | + | 0.297793i | ||||
\(367\) | 22.9990 | + | 7.47283i | 1.20054 | + | 0.390078i | 0.839959 | − | 0.542650i | \(-0.182579\pi\) |
0.360579 | + | 0.932729i | \(0.382579\pi\) | |||||||
\(368\) | 17.7776i | 0.926721i | ||||||||
\(369\) | 3.55092 | − | 10.9286i | 0.184854 | − | 0.568921i | ||||
\(370\) | 0.0366677 | − | 6.62681i | 0.00190626 | − | 0.344512i | ||||
\(371\) | −6.89104 | − | 21.2084i | −0.357765 | − | 1.10109i | ||||
\(372\) | −7.06591 | + | 2.29585i | −0.366350 | + | 0.119034i | ||||
\(373\) | 2.97740 | − | 4.09804i | 0.154164 | − | 0.212188i | −0.724948 | − | 0.688803i | \(-0.758136\pi\) |
0.879112 | + | 0.476615i | \(0.158136\pi\) | |||||||
\(374\) | 1.26073 | 0.0651909 | ||||||||
\(375\) | 9.12644 | + | 29.7603i | 0.471287 | + | 1.53682i | ||||
\(376\) | 18.0029 | 0.928431 | ||||||||
\(377\) | 10.8953 | − | 14.9961i | 0.561137 | − | 0.772339i | ||||
\(378\) | −8.96786 | + | 2.91383i | −0.461257 | + | 0.149871i | ||||
\(379\) | 8.59922 | + | 26.4657i | 0.441712 | + | 1.35945i | 0.886049 | + | 0.463591i | \(0.153439\pi\) |
−0.444337 | + | 0.895860i | \(0.646561\pi\) | |||||||
\(380\) | 0.0222720 | − | 4.02513i | 0.00114253 | − | 0.206485i | ||||
\(381\) | 7.51088 | − | 23.1161i | 0.384794 | − | 1.18427i | ||||
\(382\) | − | 0.225540i | − | 0.0115396i | ||||||
\(383\) | 9.24435 | + | 3.00367i | 0.472364 | + | 0.153480i | 0.535519 | − | 0.844523i | \(-0.320116\pi\) |
−0.0631546 | + | 0.998004i | \(0.520116\pi\) | |||||||
\(384\) | 24.6483 | − | 17.9081i | 1.25783 | − | 0.913867i | ||||
\(385\) | −7.15453 | − | 5.25880i | −0.364629 | − | 0.268013i | ||||
\(386\) | −8.43448 | − | 6.12801i | −0.429304 | − | 0.311907i | ||||
\(387\) | −26.9191 | − | 37.0509i | −1.36837 | − | 1.88340i | ||||
\(388\) | −0.549232 | − | 0.755953i | −0.0278830 | − | 0.0383777i | ||||
\(389\) | 3.64753 | + | 2.65008i | 0.184937 | + | 0.134365i | 0.676402 | − | 0.736533i | \(-0.263538\pi\) |
−0.491465 | + | 0.870897i | \(0.663538\pi\) | |||||||
\(390\) | 2.54416 | + | 7.98011i | 0.128829 | + | 0.404088i | ||||
\(391\) | 15.5480 | − | 11.2963i | 0.786297 | − | 0.571278i | ||||
\(392\) | 18.9051 | + | 6.14263i | 0.954851 | + | 0.310250i | ||||
\(393\) | − | 5.62199i | − | 0.283592i | ||||||
\(394\) | −1.09809 | + | 3.37957i | −0.0553210 | + | 0.170260i | ||||
\(395\) | 23.1001 | − | 7.36463i | 1.16229 | − | 0.370555i | ||||
\(396\) | −2.42723 | − | 7.47025i | −0.121973 | − | 0.375394i | ||||
\(397\) | 19.7046 | − | 6.40241i | 0.988945 | − | 0.321328i | 0.230505 | − | 0.973071i | \(-0.425962\pi\) |
0.758440 | + | 0.651743i | \(0.225962\pi\) | |||||||
\(398\) | −1.19964 | + | 1.65116i | −0.0601324 | + | 0.0827651i | ||||
\(399\) | 12.0399 | 0.602748 | ||||||||
\(400\) | 11.5824 | − | 8.22085i | 0.579121 | − | 0.411042i | ||||
\(401\) | −7.91289 | −0.395151 | −0.197575 | − | 0.980288i | \(-0.563307\pi\) | ||||
−0.197575 | + | 0.980288i | \(0.563307\pi\) | |||||||
\(402\) | −6.19190 | + | 8.52242i | −0.308824 | + | 0.425059i | ||||
\(403\) | −4.24253 | + | 1.37848i | −0.211335 | + | 0.0686670i | ||||
\(404\) | −8.24651 | − | 25.3801i | −0.410279 | − | 1.26271i | ||||
\(405\) | 1.43510 | + | 0.475087i | 0.0713106 | + | 0.0236072i | ||||
\(406\) | −3.68004 | + | 11.3260i | −0.182637 | + | 0.562100i | ||||
\(407\) | 6.08715i | 0.301729i | ||||||||
\(408\) | −13.8151 | − | 4.48880i | −0.683949 | − | 0.222229i | ||||
\(409\) | −26.5157 | + | 19.2648i | −1.31112 | + | 0.952583i | −0.311121 | + | 0.950370i | \(0.600704\pi\) |
−0.999998 | + | 0.00221288i | \(0.999296\pi\) | |||||||
\(410\) | 2.41751 | + | 0.0133766i | 0.119392 | + | 0.000660625i | ||||
\(411\) | −42.1063 | − | 30.5920i | −2.07695 | − | 1.50899i | ||||
\(412\) | 4.43595 | + | 6.10556i | 0.218543 | + | 0.300799i | ||||
\(413\) | −17.8526 | − | 24.5720i | −0.878471 | − | 1.20911i | ||||
\(414\) | 10.7560 | + | 7.81468i | 0.528628 | + | 0.384070i | ||||
\(415\) | −7.44153 | + | 22.4787i | −0.365290 | + | 1.10344i | ||||
\(416\) | 11.3642 | − | 8.25659i | 0.557177 | − | 0.404813i | ||||
\(417\) | 44.7852 | + | 14.5516i | 2.19314 | + | 0.712594i | ||||
\(418\) | − | 0.410542i | − | 0.0200803i | ||||||
\(419\) | 4.01813 | − | 12.3665i | 0.196298 | − | 0.604145i | −0.803661 | − | 0.595088i | \(-0.797117\pi\) |
0.999959 | − | 0.00905653i | \(-0.00288282\pi\) | |||||||
\(420\) | 28.2683 | + | 39.3642i | 1.37935 | + | 1.92078i | ||||
\(421\) | 10.7403 | + | 33.0553i | 0.523452 | + | 1.61102i | 0.767357 | + | 0.641220i | \(0.221571\pi\) |
−0.243905 | + | 0.969799i | \(0.578429\pi\) | |||||||
\(422\) | −5.12137 | + | 1.66403i | −0.249304 | + | 0.0810039i | ||||
\(423\) | −29.5961 | + | 40.7355i | −1.43901 | + | 1.98063i | ||||
\(424\) | 8.76119 | 0.425481 | ||||||||
\(425\) | −14.5496 | − | 4.90610i | −0.705758 | − | 0.237981i | ||||
\(426\) | −14.5959 | −0.707176 | ||||||||
\(427\) | −19.7921 | + | 27.2415i | −0.957806 | + | 1.31831i | ||||
\(428\) | 4.01431 | − | 1.30433i | 0.194039 | − | 0.0630471i | ||||
\(429\) | −2.37746 | − | 7.31708i | −0.114785 | − | 0.353272i | ||||
\(430\) | 5.70642 | − | 7.76352i | 0.275188 | − | 0.374390i | ||||
\(431\) | −5.31757 | + | 16.3658i | −0.256138 | + | 0.788312i | 0.737465 | + | 0.675385i | \(0.236023\pi\) |
−0.993603 | + | 0.112927i | \(0.963977\pi\) | |||||||
\(432\) | 13.8547i | 0.666582i | ||||||||
\(433\) | −29.6654 | − | 9.63887i | −1.42563 | − | 0.463215i | −0.508242 | − | 0.861214i | \(-0.669705\pi\) |
−0.917386 | + | 0.397999i | \(0.869705\pi\) | |||||||
\(434\) | 2.31860 | − | 1.68456i | 0.111296 | − | 0.0808614i | ||||
\(435\) | −31.1488 | + | 22.3686i | −1.49347 | + | 1.07249i | ||||
\(436\) | −11.5855 | − | 8.41738i | −0.554846 | − | 0.403120i | ||||
\(437\) | −3.67850 | − | 5.06302i | −0.175967 | − | 0.242197i | ||||
\(438\) | 9.40420 | + | 12.9438i | 0.449350 | + | 0.618478i | ||||
\(439\) | −12.8137 | − | 9.30970i | −0.611565 | − | 0.444328i | 0.238400 | − | 0.971167i | \(-0.423377\pi\) |
−0.849965 | + | 0.526839i | \(0.823377\pi\) | |||||||
\(440\) | 2.83357 | − | 2.03485i | 0.135085 | − | 0.0970076i | ||||
\(441\) | −44.9782 | + | 32.6786i | −2.14182 | + | 1.55612i | ||||
\(442\) | −3.92930 | − | 1.27671i | −0.186898 | − | 0.0607267i | ||||
\(443\) | − | 10.5951i | − | 0.503388i | −0.967807 | − | 0.251694i | \(-0.919012\pi\) | ||
0.967807 | − | 0.251694i | \(-0.0809876\pi\) | |||||||
\(444\) | 10.2666 | − | 31.5972i | 0.487229 | − | 1.49954i | ||||
\(445\) | −6.31174 | + | 8.58704i | −0.299205 | + | 0.407065i | ||||
\(446\) | −3.12931 | − | 9.63103i | −0.148177 | − | 0.456042i | ||||
\(447\) | −7.26841 | + | 2.36165i | −0.343784 | + | 0.111702i | ||||
\(448\) | 9.13624 | − | 12.5750i | 0.431647 | − | 0.594111i | ||||
\(449\) | −19.3596 | −0.913636 | −0.456818 | − | 0.889560i | \(-0.651011\pi\) | ||||
−0.456818 | + | 0.889560i | \(0.651011\pi\) | |||||||
\(450\) | 0.117545 | − | 10.6214i | 0.00554114 | − | 0.500699i | ||||
\(451\) | −2.22063 | −0.104566 | ||||||||
\(452\) | −5.72791 | + | 7.88379i | −0.269418 | + | 0.370822i | ||||
\(453\) | −44.2403 | + | 14.3745i | −2.07859 | + | 0.675375i | ||||
\(454\) | 3.49738 | + | 10.7638i | 0.164140 | + | 0.505171i | ||||
\(455\) | 16.9729 | + | 23.6352i | 0.795704 | + | 1.10803i | ||||
\(456\) | −1.46172 | + | 4.49872i | −0.0684515 | + | 0.210672i | ||||
\(457\) | 2.56820i | 0.120135i | 0.998194 | + | 0.0600676i | \(0.0191316\pi\) | ||||
−0.998194 | + | 0.0600676i | \(0.980868\pi\) | |||||||
\(458\) | −10.9390 | − | 3.55429i | −0.511145 | − | 0.166081i | ||||
\(459\) | 12.1171 | − | 8.80356i | 0.565576 | − | 0.410915i | ||||
\(460\) | 7.91677 | − | 23.9143i | 0.369121 | − | 1.11501i | ||||
\(461\) | 8.00363 | + | 5.81498i | 0.372766 | + | 0.270831i | 0.758357 | − | 0.651839i | \(-0.226002\pi\) |
−0.385591 | + | 0.922670i | \(0.626002\pi\) | |||||||
\(462\) | 2.90535 | + | 3.99888i | 0.135169 | + | 0.186045i | ||||
\(463\) | −17.3898 | − | 23.9349i | −0.808170 | − | 1.11235i | −0.991603 | − | 0.129319i | \(-0.958721\pi\) |
0.183433 | − | 0.983032i | \(-0.441279\pi\) | |||||||
\(464\) | 14.1560 | + | 10.2849i | 0.657176 | + | 0.477466i | ||||
\(465\) | 9.22866 | + | 0.0510643i | 0.427969 | + | 0.00236805i | ||||
\(466\) | −3.13757 | + | 2.27958i | −0.145345 | + | 0.105599i | ||||
\(467\) | 12.7024 | + | 4.12726i | 0.587797 | + | 0.190987i | 0.587791 | − | 0.809013i | \(-0.299998\pi\) |
6.54700e−6 | 1.00000i | \(0.499998\pi\) | ||||||||
\(468\) | 25.7403i | 1.18985i | ||||||||
\(469\) | −11.3090 | + | 34.8055i | −0.522201 | + | 1.60717i | ||||
\(470\) | −10.0566 | − | 3.32920i | −0.463874 | − | 0.153565i | ||||
\(471\) | 2.07599 | + | 6.38924i | 0.0956565 | + | 0.294400i | ||||
\(472\) | 11.3488 | − | 3.68745i | 0.522372 | − | 0.169729i | ||||
\(473\) | −5.20209 | + | 7.16007i | −0.239192 | + | 0.329220i | ||||
\(474\) | −13.4969 | −0.619935 | ||||||||
\(475\) | −1.59761 | + | 4.73789i | −0.0733035 | + | 0.217389i | ||||
\(476\) | −23.9050 | −1.09568 | ||||||||
\(477\) | −14.4030 | + | 19.8241i | −0.659469 | + | 0.907682i | ||||
\(478\) | −0.403877 | + | 0.131228i | −0.0184729 | + | 0.00600221i | ||||
\(479\) | −0.406052 | − | 1.24970i | −0.0185530 | − | 0.0571003i | 0.941351 | − | 0.337428i | \(-0.109557\pi\) |
−0.959904 | + | 0.280328i | \(0.909557\pi\) | |||||||
\(480\) | −27.6878 | + | 8.82724i | −1.26377 | + | 0.402907i | ||||
\(481\) | 6.16427 | − | 18.9717i | 0.281067 | − | 0.865034i | ||||
\(482\) | 0.962415i | 0.0438368i | ||||||||
\(483\) | 71.6607 | + | 23.2840i | 3.26067 | + | 1.05946i | ||||
\(484\) | 14.7916 | − | 10.7467i | 0.672345 | − | 0.488487i | ||||
\(485\) | 0.352563 | + | 1.10586i | 0.0160091 | + | 0.0502146i | ||||
\(486\) | −5.97304 | − | 4.33967i | −0.270943 | − | 0.196851i | ||||
\(487\) | 10.3577 | + | 14.2562i | 0.469353 | + | 0.646010i | 0.976415 | − | 0.215900i | \(-0.0692685\pi\) |
−0.507062 | + | 0.861910i | \(0.669269\pi\) | |||||||
\(488\) | −7.77593 | − | 10.7026i | −0.352000 | − | 0.484486i | ||||
\(489\) | −34.3972 | − | 24.9910i | −1.55550 | − | 1.13013i | ||||
\(490\) | −9.42457 | − | 6.92735i | −0.425759 | − | 0.312946i | ||||
\(491\) | 27.4410 | − | 19.9371i | 1.23839 | − | 0.899747i | 0.240905 | − | 0.970549i | \(-0.422556\pi\) |
0.997490 | + | 0.0708023i | \(0.0225559\pi\) | |||||||
\(492\) | 11.5269 | + | 3.74531i | 0.519672 | + | 0.168852i | ||||
\(493\) | − | 18.9159i | − | 0.851930i | ||||||
\(494\) | −0.415744 | + | 1.27953i | −0.0187052 | + | 0.0575687i | ||||
\(495\) | −0.0539864 | + | 9.75676i | −0.00242651 | + | 0.438534i | ||||
\(496\) | −1.30126 | − | 4.00486i | −0.0584281 | − | 0.179823i | ||||
\(497\) | −48.2253 | + | 15.6693i | −2.16320 | + | 0.702866i | ||||
\(498\) | 7.74769 | − | 10.6638i | 0.347182 | − | 0.477855i | ||||
\(499\) | −1.30681 | −0.0585011 | −0.0292505 | − | 0.999572i | \(-0.509312\pi\) | ||||
−0.0292505 | + | 0.999572i | \(0.509312\pi\) | |||||||
\(500\) | −19.2415 | + | 5.90069i | −0.860506 | + | 0.263887i | ||||
\(501\) | 63.7563 | 2.84842 | ||||||||
\(502\) | −2.19286 | + | 3.01822i | −0.0978724 | + | 0.134710i | ||||
\(503\) | 27.6699 | − | 8.99049i | 1.23374 | − | 0.400866i | 0.381671 | − | 0.924298i | \(-0.375349\pi\) |
0.852067 | + | 0.523432i | \(0.175349\pi\) | |||||||
\(504\) | −10.7880 | − | 33.2021i | −0.480536 | − | 1.47894i | ||||
\(505\) | −0.183419 | + | 33.1486i | −0.00816203 | + | 1.47509i | ||||
\(506\) | 0.793949 | − | 2.44352i | 0.0352954 | − | 0.108628i | ||||
\(507\) | − | 10.9820i | − | 0.487728i | ||||||
\(508\) | 14.9457 | + | 4.85615i | 0.663108 | + | 0.215457i | ||||
\(509\) | 33.7617 | − | 24.5293i | 1.49646 | − | 1.08724i | 0.524699 | − | 0.851288i | \(-0.324178\pi\) |
0.971764 | − | 0.235957i | \(-0.0758223\pi\) | |||||||
\(510\) | 6.88711 | + | 5.06224i | 0.304966 | + | 0.224160i | ||||
\(511\) | 44.9674 | + | 32.6707i | 1.98924 | + | 1.44527i | ||||
\(512\) | 13.4676 | + | 18.5365i | 0.595187 | + | 0.819205i | ||||
\(513\) | −2.86678 | − | 3.94578i | −0.126571 | − | 0.174210i | ||||
\(514\) | −7.78690 | − | 5.65752i | −0.343466 | − | 0.249542i | ||||
\(515\) | −2.84753 | − | 8.93164i | −0.125477 | − | 0.393575i | ||||
\(516\) | 39.0792 | − | 28.3927i | 1.72037 | − | 1.24992i | ||||
\(517\) | 9.25422 | + | 3.00688i | 0.407000 | + | 0.132242i | ||||
\(518\) | 12.8159i | 0.563097i | ||||||||
\(519\) | 6.09419 | − | 18.7560i | 0.267505 | − | 0.823297i | ||||
\(520\) | −10.8920 | + | 3.47250i | −0.477644 | + | 0.152279i | ||||
\(521\) | −2.29698 | − | 7.06938i | −0.100633 | − | 0.309715i | 0.888048 | − | 0.459751i | \(-0.152061\pi\) |
−0.988681 | + | 0.150036i | \(0.952061\pi\) | |||||||
\(522\) | 12.4454 | − | 4.04376i | 0.544720 | − | 0.176990i | ||||
\(523\) | −9.24536 | + | 12.7251i | −0.404271 | + | 0.556432i | −0.961810 | − | 0.273720i | \(-0.911746\pi\) |
0.557538 | + | 0.830151i | \(0.311746\pi\) | |||||||
\(524\) | 3.63489 | 0.158791 | ||||||||
\(525\) | −17.9679 | − | 57.4554i | −0.784185 | − | 2.50756i | ||||
\(526\) | −7.86692 | −0.343014 | ||||||||
\(527\) | −2.67574 | + | 3.68284i | −0.116557 | + | 0.160427i | ||||
\(528\) | 6.90716 | − | 2.24427i | 0.300596 | − | 0.0976695i | ||||
\(529\) | −4.99544 | − | 15.3744i | −0.217193 | − | 0.668452i | ||||
\(530\) | −4.89406 | − | 1.62017i | −0.212584 | − | 0.0703756i | ||||
\(531\) | −10.3133 | + | 31.7411i | −0.447560 | + | 1.37745i | ||||
\(532\) | 7.78437i | 0.337495i | ||||||||
\(533\) | 6.92100 | + | 2.24877i | 0.299782 | + | 0.0974051i | ||||
\(534\) | 4.79955 | − | 3.48708i | 0.207697 | − | 0.150901i | ||||
\(535\) | −5.24302 | − | 0.0290109i | −0.226676 | − | 0.00125425i | ||||
\(536\) | −11.6321 | − | 8.45125i | −0.502432 | − | 0.365038i | ||||
\(537\) | 1.15046 | + | 1.58347i | 0.0496460 | + | 0.0683319i | ||||
\(538\) | 4.64895 | + | 6.39873i | 0.200431 | + | 0.275869i | ||||
\(539\) | 8.69201 | + | 6.31511i | 0.374391 | + | 0.272011i | ||||
\(540\) | 6.16979 | − | 18.6372i | 0.265506 | − | 0.802015i | ||||
\(541\) | −7.76452 | + | 5.64125i | −0.333823 | + | 0.242536i | −0.742051 | − | 0.670344i | \(-0.766147\pi\) |
0.408228 | + | 0.912880i | \(0.366147\pi\) | |||||||
\(542\) | −9.65167 | − | 3.13602i | −0.414575 | − | 0.134704i | ||||
\(543\) | − | 20.1631i | − | 0.865280i | ||||||
\(544\) | 4.42966 | − | 13.6331i | 0.189920 | − | 0.584514i | ||||
\(545\) | 10.3761 | + | 14.4489i | 0.444463 | + | 0.618924i | ||||
\(546\) | −5.00551 | − | 15.4054i | −0.214216 | − | 0.659289i | ||||
\(547\) | 14.4631 | − | 4.69934i | 0.618396 | − | 0.200929i | 0.0169681 | − | 0.999856i | \(-0.494599\pi\) |
0.601428 | + | 0.798927i | \(0.294599\pi\) | |||||||
\(548\) | 19.7792 | − | 27.2237i | 0.844926 | − | 1.16294i | ||||
\(549\) | 37.0003 | 1.57914 | ||||||||
\(550\) | −1.95915 | + | 0.612680i | −0.0835382 | + | 0.0261248i | ||||
\(551\) | −6.15974 | −0.262414 | ||||||||
\(552\) | −17.4002 | + | 23.9493i | −0.740601 | + | 1.01935i | ||||
\(553\) | −44.5942 | + | 14.4895i | −1.89634 | + | 0.616157i | ||||
\(554\) | 2.87006 | + | 8.83315i | 0.121937 | + | 0.375285i | ||||
\(555\) | −24.4418 | + | 33.2528i | −1.03750 | + | 1.41150i | ||||
\(556\) | −9.40830 | + | 28.9558i | −0.399001 | + | 1.22800i | ||||
\(557\) | 36.8412i | 1.56101i | 0.625149 | + | 0.780506i | \(0.285038\pi\) | ||||
−0.625149 | + | 0.780506i | \(0.714962\pi\) | |||||||
\(558\) | −2.99506 | − | 0.973156i | −0.126791 | − | 0.0411970i | ||||
\(559\) | 23.4640 | − | 17.0476i | 0.992423 | − | 0.721038i | ||||
\(560\) | −22.3111 | + | 16.0221i | −0.942816 | + | 0.677057i | ||||
\(561\) | −6.35178 | − | 4.61484i | −0.268172 | − | 0.194839i | ||||
\(562\) | 0.774276 | + | 1.06570i | 0.0326609 | + | 0.0449538i | ||||
\(563\) | 23.6267 | + | 32.5193i | 0.995746 | + | 1.37053i | 0.927899 | + | 0.372831i | \(0.121613\pi\) |
0.0678467 | + | 0.997696i | \(0.478387\pi\) | |||||||
\(564\) | −42.9655 | − | 31.2163i | −1.80917 | − | 1.31444i | ||||
\(565\) | 9.83228 | − | 7.06078i | 0.413647 | − | 0.297049i | ||||
\(566\) | 7.67202 | − | 5.57405i | 0.322479 | − | 0.234295i | ||||
\(567\) | −2.78040 | − | 0.903406i | −0.116766 | − | 0.0379395i | ||||
\(568\) | − | 19.9218i | − | 0.835901i | ||||||
\(569\) | −6.47592 | + | 19.9308i | −0.271485 | + | 0.835544i | 0.718643 | + | 0.695379i | \(0.244763\pi\) |
−0.990128 | + | 0.140165i | \(0.955237\pi\) | |||||||
\(570\) | 1.64846 | − | 2.24270i | 0.0690463 | − | 0.0939366i | ||||
\(571\) | 9.46988 | + | 29.1453i | 0.396302 | + | 1.21969i | 0.927943 | + | 0.372723i | \(0.121576\pi\) |
−0.531641 | + | 0.846970i | \(0.678424\pi\) | |||||||
\(572\) | 4.73085 | − | 1.53715i | 0.197807 | − | 0.0642713i | ||||
\(573\) | −0.825575 | + | 1.13631i | −0.0344889 | + | 0.0474699i | ||||
\(574\) | −4.67532 | −0.195144 | ||||||||
\(575\) | −18.6715 | + | 25.1100i | −0.778656 | + | 1.04716i | ||||
\(576\) | −17.0797 | −0.711656 | ||||||||
\(577\) | −14.8081 | + | 20.3817i | −0.616471 | + | 0.848499i | −0.997090 | − | 0.0762324i | \(-0.975711\pi\) |
0.380619 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(578\) | 3.21859 | − | 1.04578i | 0.133876 | − | 0.0434988i | ||||
\(579\) | 20.0631 | + | 61.7479i | 0.833794 | + | 2.56615i | ||||
\(580\) | −14.4624 | − | 20.1392i | −0.600519 | − | 0.836235i | ||||
\(581\) | 14.1505 | − | 43.5508i | 0.587063 | − | 1.80679i | ||||
\(582\) | − | 0.646133i | − | 0.0267831i | ||||||
\(583\) | 4.50360 | + | 1.46331i | 0.186520 | + | 0.0606040i | ||||
\(584\) | −17.6668 | + | 12.8357i | −0.731058 | + | 0.531144i | ||||
\(585\) | 10.0486 | − | 30.3540i | 0.415460 | − | 1.25498i | ||||
\(586\) | −7.18316 | − | 5.21887i | −0.296733 | − | 0.215589i | ||||
\(587\) | −27.7123 | − | 38.1427i | −1.14381 | − | 1.57432i | −0.758694 | − | 0.651447i | \(-0.774162\pi\) |
−0.385113 | − | 0.922869i | \(-0.625838\pi\) | |||||||
\(588\) | −34.4675 | − | 47.4404i | −1.42142 | − | 1.95641i | ||||
\(589\) | 1.19927 | + | 0.871322i | 0.0494151 | + | 0.0359022i | ||||
\(590\) | −7.02143 | − | 0.0388512i | −0.289068 | − | 0.00159948i | ||||
\(591\) | 17.9031 | − | 13.0074i | 0.736435 | − | 0.535051i | ||||
\(592\) | 17.9089 | + | 5.81894i | 0.736050 | + | 0.239157i | ||||
\(593\) | − | 4.27977i | − | 0.175749i | −0.996132 | − | 0.0878746i | \(-0.971993\pi\) | ||
0.996132 | − | 0.0878746i | \(-0.0280075\pi\) | |||||||
\(594\) | 0.618750 | − | 1.90432i | 0.0253876 | − | 0.0781351i | ||||
\(595\) | 28.1897 | + | 9.33214i | 1.15566 | + | 0.382580i | ||||
\(596\) | −1.52692 | − | 4.69938i | −0.0625451 | − | 0.192494i | ||||
\(597\) | 12.0879 | − | 3.92761i | 0.494726 | − | 0.160746i | ||||
\(598\) | −4.94897 | + | 6.81167i | −0.202378 | + | 0.278550i | ||||
\(599\) | −39.6614 | −1.62052 | −0.810260 | − | 0.586071i | \(-0.800674\pi\) | ||||
−0.810260 | + | 0.586071i | \(0.800674\pi\) | |||||||
\(600\) | 23.6497 | + | 0.261727i | 0.965496 | + | 0.0106850i | ||||
\(601\) | −26.2384 | −1.07029 | −0.535143 | − | 0.844762i | \(-0.679742\pi\) | ||||
−0.535143 | + | 0.844762i | \(0.679742\pi\) | |||||||
\(602\) | −10.9525 | + | 15.0748i | −0.446390 | + | 0.614403i | ||||
\(603\) | 38.2455 | − | 12.4267i | 1.55748 | − | 0.506055i | ||||
\(604\) | −9.29384 | − | 28.6035i | −0.378161 | − | 1.16386i | ||||
\(605\) | −21.6382 | + | 6.89853i | −0.879717 | + | 0.280465i | ||||
\(606\) | 5.70236 | − | 17.5501i | 0.231642 | − | 0.712922i | ||||
\(607\) | − | 16.7230i | − | 0.678767i | −0.940648 | − | 0.339383i | \(-0.889782\pi\) | ||
0.940648 | − | 0.339383i | \(-0.110218\pi\) | |||||||
\(608\) | −4.43946 | − | 1.44247i | −0.180044 | − | 0.0584998i | ||||
\(609\) | 59.9988 | − | 43.5917i | 2.43127 | − | 1.76642i | ||||
\(610\) | 2.36449 | + | 7.41654i | 0.0957354 | + | 0.300287i | ||||
\(611\) | −25.7975 | − | 18.7430i | −1.04365 | − | 0.758259i | ||||
\(612\) | 15.4397 | + | 21.2509i | 0.624114 | + | 0.859019i | ||||
\(613\) | 6.23766 | + | 8.58540i | 0.251937 | + | 0.346761i | 0.916188 | − | 0.400748i | \(-0.131250\pi\) |
−0.664252 | + | 0.747509i | \(0.731250\pi\) | |||||||
\(614\) | 8.16892 | + | 5.93507i | 0.329671 | + | 0.239520i | ||||
\(615\) | −12.1308 | − | 8.91654i | −0.489163 | − | 0.359550i | ||||
\(616\) | −5.45802 | + | 3.96548i | −0.219910 | + | 0.159774i | ||||
\(617\) | 46.5002 | + | 15.1088i | 1.87203 | + | 0.608258i | 0.990758 | + | 0.135643i | \(0.0433101\pi\) |
0.881269 | + | 0.472615i | \(0.156690\pi\) | |||||||
\(618\) | 5.21858i | 0.209922i | ||||||||
\(619\) | 0.894829 | − | 2.75400i | 0.0359662 | − | 0.110693i | −0.931462 | − | 0.363840i | \(-0.881466\pi\) |
0.967428 | + | 0.253147i | \(0.0814656\pi\) | |||||||
\(620\) | −0.0330155 | + | 5.96677i | −0.00132594 | + | 0.239631i | ||||
\(621\) | −9.43213 | − | 29.0291i | −0.378498 | − | 1.16490i | ||||
\(622\) | −4.48832 | + | 1.45834i | −0.179965 | + | 0.0584743i | ||||
\(623\) | 12.1143 | − | 16.6739i | 0.485349 | − | 0.668025i | ||||
\(624\) | −23.8001 | −0.952767 | ||||||||
\(625\) | 24.9939 | + | 0.553272i | 0.999755 | + | 0.0221309i | ||||
\(626\) | 12.3749 | 0.494600 | ||||||||
\(627\) | −1.50277 | + | 2.06838i | −0.0600147 | + | 0.0826032i | ||||
\(628\) | −4.13095 | + | 1.34223i | −0.164843 | + | 0.0535607i | ||||
\(629\) | −6.29054 | − | 19.3603i | −0.250820 | − | 0.771946i | ||||
\(630\) | −0.113663 | + | 20.5419i | −0.00452844 | + | 0.818408i | ||||
\(631\) | 7.18553 | − | 22.1148i | 0.286051 | − | 0.880376i | −0.700030 | − | 0.714113i | \(-0.746830\pi\) |
0.986082 | − | 0.166262i | \(-0.0531699\pi\) | |||||||
\(632\) | − | 18.4218i | − | 0.732780i | ||||||
\(633\) | 31.8934 | + | 10.3628i | 1.26765 | + | 0.411884i | ||||
\(634\) | 9.17648 | − | 6.66710i | 0.364445 | − | 0.264785i | ||||
\(635\) | −15.7288 | − | 11.5611i | −0.624177 | − | 0.458790i | ||||
\(636\) | −20.9093 | − | 15.1915i | −0.829108 | − | 0.602382i | ||||
\(637\) | −20.6951 | − | 28.4843i | −0.819968 | − | 1.12859i | ||||
\(638\) | −1.48641 | − | 2.04587i | −0.0588476 | − | 0.0809968i | ||||
\(639\) | 45.0774 | + | 32.7506i | 1.78323 | + | 1.29560i | ||||
\(640\) | −7.43243 | − | 23.3128i | −0.293793 | − | 0.921519i | ||||
\(641\) | −35.8071 | + | 26.0153i | −1.41429 | + | 1.02754i | −0.421613 | + | 0.906776i | \(0.638536\pi\) |
−0.992681 | + | 0.120769i | \(0.961464\pi\) | |||||||
\(642\) | 2.77585 | + | 0.901927i | 0.109554 | + | 0.0355962i | ||||
\(643\) | − | 15.2181i | − | 0.600143i | −0.953917 | − | 0.300072i | \(-0.902989\pi\) | ||
0.953917 | − | 0.300072i | \(-0.0970105\pi\) | |||||||
\(644\) | −15.0542 | + | 46.3321i | −0.593219 | + | 1.82574i | ||||
\(645\) | −57.1678 | + | 18.2259i | −2.25098 | + | 0.717643i | ||||
\(646\) | 0.424260 | + | 1.30574i | 0.0166923 | + | 0.0513736i | ||||
\(647\) | 14.3779 | − | 4.67165i | 0.565252 | − | 0.183661i | −0.0124310 | − | 0.999923i | \(-0.503957\pi\) |
0.577683 | + | 0.816261i | \(0.303957\pi\) | |||||||
\(648\) | 0.675118 | − | 0.929220i | 0.0265211 | − | 0.0365032i | ||||
\(649\) | 6.44962 | 0.253170 | ||||||||
\(650\) | 6.72647 | + | 0.0744405i | 0.263834 | + | 0.00291980i | ||||
\(651\) | −17.8477 | −0.699506 | ||||||||
\(652\) | 16.1579 | − | 22.2395i | 0.632793 | − | 0.870965i | ||||
\(653\) | −29.9088 | + | 9.71794i | −1.17042 | + | 0.380293i | −0.828800 | − | 0.559545i | \(-0.810976\pi\) |
−0.341620 | + | 0.939838i | \(0.610976\pi\) | |||||||
\(654\) | −3.06003 | − | 9.41779i | −0.119656 | − | 0.368265i | ||||
\(655\) | −4.28640 | − | 1.41901i | −0.167484 | − | 0.0554451i | ||||
\(656\) | −2.12279 | + | 6.53328i | −0.0828811 | + | 0.255082i | ||||
\(657\) | − | 61.0763i | − | 2.38281i | ||||||
\(658\) | 19.4838 | + | 6.33068i | 0.759559 | + | 0.246796i | ||||
\(659\) | 8.16136 | − | 5.92957i | 0.317921 | − | 0.230983i | −0.417367 | − | 0.908738i | \(-0.637047\pi\) |
0.735288 | + | 0.677755i | \(0.237047\pi\) | |||||||
\(660\) | −10.2909 | − | 0.0569418i | −0.400572 | − | 0.00221646i | ||||
\(661\) | −13.9774 | − | 10.1552i | −0.543660 | − | 0.394992i | 0.281783 | − | 0.959478i | \(-0.409074\pi\) |
−0.825442 | + | 0.564486i | \(0.809074\pi\) | |||||||
\(662\) | −0.891061 | − | 1.22644i | −0.0346321 | − | 0.0476669i | ||||
\(663\) | 15.1231 | + | 20.8152i | 0.587334 | + | 0.808396i | ||||
\(664\) | 14.5549 | + | 10.5747i | 0.564838 | + | 0.410379i | ||||
\(665\) | 3.03890 | − | 9.17963i | 0.117843 | − | 0.355971i | ||||
\(666\) | 11.3930 | − | 8.27751i | 0.441470 | − | 0.320747i | ||||
\(667\) | −36.6624 | − | 11.9123i | −1.41958 | − | 0.461248i | ||||
\(668\) | 41.2215i | 1.59491i | ||||||||
\(669\) | −19.4878 | + | 59.9774i | −0.753443 | + | 2.31886i | ||||
\(670\) | 4.93494 | + | 6.87200i | 0.190653 | + | 0.265489i | ||||
\(671\) | −2.20956 | − | 6.80033i | −0.0852992 | − | 0.262524i | ||||
\(672\) | 53.4505 | − | 17.3671i | 2.06190 | − | 0.669952i | ||||
\(673\) | −18.4091 | + | 25.3380i | −0.709619 | + | 0.976707i | 0.290186 | + | 0.956970i | \(0.406283\pi\) |
−0.999805 | + | 0.0197365i | \(0.993717\pi\) | |||||||
\(674\) | −4.50390 | −0.173484 | ||||||||
\(675\) | −14.5513 | + | 19.5691i | −0.560081 | + | 0.753214i | ||||
\(676\) | 7.10040 | 0.273092 | ||||||||
\(677\) | −19.6780 | + | 27.0844i | −0.756285 | + | 1.04094i | 0.241228 | + | 0.970468i | \(0.422450\pi\) |
−0.997514 | + | 0.0704693i | \(0.977550\pi\) | |||||||
\(678\) | −6.40867 | + | 2.08230i | −0.246123 | + | 0.0799704i | ||||
\(679\) | −0.693650 | − | 2.13484i | −0.0266198 | − | 0.0819275i | ||||
\(680\) | −6.90938 | + | 9.40013i | −0.264963 | + | 0.360479i | ||||
\(681\) | 21.7800 | − | 67.0319i | 0.834611 | − | 2.56867i | ||||
\(682\) | 0.608581i | 0.0233038i | ||||||||
\(683\) | 5.31100 | + | 1.72565i | 0.203220 | + | 0.0660302i | 0.408858 | − | 0.912598i | \(-0.365927\pi\) |
−0.205638 | + | 0.978628i | \(0.565927\pi\) | |||||||
\(684\) | 6.92012 | − | 5.02776i | 0.264597 | − | 0.192241i | ||||
\(685\) | −33.9521 | + | 24.3818i | −1.29724 | + | 0.931580i | ||||
\(686\) | 7.35144 | + | 5.34113i | 0.280679 | + | 0.203925i | ||||
\(687\) | 42.1022 | + | 57.9487i | 1.60630 | + | 2.21088i | ||||
\(688\) | 16.0926 | + | 22.1495i | 0.613524 | + | 0.844444i | ||||
\(689\) | −12.5544 | − | 9.12132i | −0.478285 | − | 0.347495i | ||||
\(690\) | 14.1487 | − | 10.1605i | 0.538632 | − | 0.386803i | ||||
\(691\) | −7.70620 | + | 5.59888i | −0.293158 | + | 0.212992i | −0.724636 | − | 0.689132i | \(-0.757992\pi\) |
0.431478 | + | 0.902123i | \(0.357992\pi\) | |||||||
\(692\) | 12.1267 | + | 3.94019i | 0.460986 | + | 0.149784i | ||||
\(693\) | − | 18.8690i | − | 0.716775i | ||||||
\(694\) | −1.64450 | + | 5.06126i | −0.0624245 | + | 0.192123i | ||||
\(695\) | 22.3985 | − | 30.4729i | 0.849625 | − | 1.15590i | ||||
\(696\) | 9.00384 | + | 27.7110i | 0.341290 | + | 1.05038i | ||||
\(697\) | 7.06278 | − | 2.29483i | 0.267522 | − | 0.0869231i | ||||
\(698\) | −2.45957 | + | 3.38531i | −0.0930961 | + | 0.128136i | ||||
\(699\) | 24.1519 | 0.913508 | ||||||||
\(700\) | 37.1477 | − | 11.6171i | 1.40405 | − | 0.439087i | ||||
\(701\) | −9.07800 | −0.342871 | −0.171436 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171436 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(702\) | −3.85689 | + | 5.30856i | −0.145569 | + | 0.200359i | ||||
\(703\) | −6.30445 | + | 2.04844i | −0.237777 | + | 0.0772584i | ||||
\(704\) | 1.01996 | + | 3.13910i | 0.0384411 | + | 0.118309i | ||||
\(705\) | 38.4802 | + | 53.5845i | 1.44925 | + | 2.01811i | ||||
\(706\) | 0.753772 | − | 2.31987i | 0.0283686 | − | 0.0873095i | ||||
\(707\) | − | 64.1074i | − | 2.41101i | ||||||
\(708\) | −33.4788 | − | 10.8779i | −1.25821 | − | 0.408817i | ||||
\(709\) | 20.2899 | − | 14.7415i | 0.762005 | − | 0.553629i | −0.137520 | − | 0.990499i | \(-0.543913\pi\) |
0.899525 | + | 0.436870i | \(0.143913\pi\) | |||||||
\(710\) | −3.68406 | + | 11.1285i | −0.138260 | + | 0.417644i | ||||
\(711\) | 41.6833 | + | 30.2847i | 1.56325 | + | 1.13576i | ||||
\(712\) | 4.75947 | + | 6.55085i | 0.178369 | + | 0.245503i | ||||
\(713\) | 5.45294 | + | 7.50533i | 0.204214 | + | 0.281077i | ||||
\(714\) | −13.3730 | − | 9.71608i | −0.500473 | − | 0.363615i | ||||
\(715\) | −6.17888 | − | 0.0341892i | −0.231077 | − | 0.00127860i | ||||
\(716\) | −1.02379 | + | 0.743828i | −0.0382609 | + | 0.0277982i | ||||
\(717\) | 2.51515 | + | 0.817222i | 0.0939300 | + | 0.0305197i | ||||
\(718\) | − | 12.7374i | − | 0.475356i | ||||||
\(719\) | −4.95854 | + | 15.2608i | −0.184922 | + | 0.569133i | −0.999947 | − | 0.0102936i | \(-0.996723\pi\) |
0.815025 | + | 0.579426i | \(0.196723\pi\) | |||||||
\(720\) | 28.6535 | + | 9.48570i | 1.06785 | + | 0.353511i | ||||
\(721\) | 5.60236 | + | 17.2423i | 0.208643 | + | 0.642136i | ||||
\(722\) | 0.425198 | − | 0.138155i | 0.0158242 | − | 0.00514161i | ||||
\(723\) | 3.52286 | − | 4.84881i | 0.131017 | − | 0.180329i | ||||
\(724\) | 13.0364 | 0.484494 | ||||||||
\(725\) | 9.19260 | + | 29.3948i | 0.341405 | + | 1.09170i | ||||
\(726\) | 12.6427 | 0.469216 | ||||||||
\(727\) | −7.74716 | + | 10.6631i | −0.287326 | + | 0.395471i | −0.928143 | − | 0.372223i | \(-0.878596\pi\) |
0.640817 | + | 0.767694i | \(0.278596\pi\) | |||||||
\(728\) | 21.0266 | − | 6.83196i | 0.779298 | − | 0.253209i | ||||
\(729\) | 13.5813 | + | 41.7991i | 0.503012 | + | 1.54811i | ||||
\(730\) | 12.2424 | − | 3.90305i | 0.453113 | − | 0.144458i | ||||
\(731\) | 9.14605 | − | 28.1487i | 0.338279 | − | 1.04112i | ||||
\(732\) | 39.0259i | 1.44244i | ||||||||
\(733\) | −45.3997 | − | 14.7513i | −1.67688 | − | 0.544850i | −0.692575 | − | 0.721346i | \(-0.743524\pi\) |
−0.984301 | + | 0.176496i | \(0.943524\pi\) | |||||||
\(734\) | −8.74673 | + | 6.35487i | −0.322848 | + | 0.234563i | ||||
\(735\) | 22.1254 | + | 69.3992i | 0.816107 | + | 2.55983i | ||||
\(736\) | −23.6338 | − | 17.1710i | −0.871154 | − | 0.632930i | ||||
\(737\) | −4.56784 | − | 6.28709i | −0.168259 | − | 0.231588i | ||||
\(738\) | 3.01969 | + | 4.15625i | 0.111156 | + | 0.152994i | ||||
\(739\) | 5.32735 | + | 3.87054i | 0.195970 | + | 0.142380i | 0.681443 | − | 0.731871i | \(-0.261353\pi\) |
−0.485473 | + | 0.874251i | \(0.661353\pi\) | |||||||
\(740\) | −21.4995 | − | 15.8028i | −0.790338 | − | 0.580923i | ||||
\(741\) | 6.77823 | − | 4.92467i | 0.249004 | − | 0.180912i | ||||
\(742\) | 9.48188 | + | 3.08085i | 0.348091 | + | 0.113101i | ||||
\(743\) | − | 32.4303i | − | 1.18975i | −0.803818 | − | 0.594876i | \(-0.797201\pi\) | ||
0.803818 | − | 0.594876i | \(-0.202799\pi\) | |||||||
\(744\) | 2.16683 | − | 6.66882i | 0.0794399 | − | 0.244491i | ||||
\(745\) | −0.0339617 | + | 6.13778i | −0.00124426 | + | 0.224871i | ||||
\(746\) | 0.699819 | + | 2.15382i | 0.0256222 | + | 0.0788570i | ||||
\(747\) | −47.8552 | + | 15.5491i | −1.75093 | + | 0.568912i | ||||
\(748\) | 2.98372 | − | 4.10673i | 0.109095 | − | 0.150157i | ||||
\(749\) | 10.1397 | 0.370497 | ||||||||
\(750\) | −13.1625 | − | 4.51964i | −0.480626 | − | 0.165034i | ||||
\(751\) | −14.7647 | −0.538773 | −0.269387 | − | 0.963032i | \(-0.586821\pi\) | ||||
−0.269387 | + | 0.963032i | \(0.586821\pi\) | |||||||
\(752\) | 17.6929 | − | 24.3522i | 0.645195 | − | 0.888035i | ||||
\(753\) | 22.0960 | − | 7.17944i | 0.805224 | − | 0.261633i | ||||
\(754\) | 2.56088 | + | 7.88157i | 0.0932617 | + | 0.287030i | ||||
\(755\) | −0.206713 | + | 37.3585i | −0.00752307 | + | 1.35962i | ||||
\(756\) | −11.7322 | + | 36.1081i | −0.426697 | + | 1.31324i | ||||
\(757\) | − | 35.6208i | − | 1.29466i | −0.762210 | − | 0.647330i | \(-0.775886\pi\) | ||
0.762210 | − | 0.647330i | \(-0.224114\pi\) | |||||||
\(758\) | −11.8323 | − | 3.84454i | −0.429768 | − | 0.139640i | ||||
\(759\) | −12.9444 | + | 9.40468i | −0.469853 | + | 0.341368i | ||||
\(760\) | 3.06104 | + | 2.24996i | 0.111036 | + | 0.0816146i | ||||
\(761\) | −0.488874 | − | 0.355188i | −0.0177217 | − | 0.0128756i | 0.578889 | − | 0.815406i | \(-0.303486\pi\) |
−0.596611 | + | 0.802531i | \(0.703486\pi\) | |||||||
\(762\) | 6.38723 | + | 8.79127i | 0.231385 | + | 0.318474i | ||||
\(763\) | −20.2208 | − | 27.8315i | −0.732041 | − | 1.00757i | ||||
\(764\) | −0.734677 | − | 0.533774i | −0.0265797 | − | 0.0193113i | ||||
\(765\) | −9.91107 | − | 31.0874i | −0.358336 | − | 1.12397i | ||||
\(766\) | −3.51571 | + | 2.55431i | −0.127028 | + | 0.0922910i | ||||
\(767\) | −20.1014 | − | 6.53134i | −0.725820 | − | 0.235833i | ||||
\(768\) | − | 6.39387i | − | 0.230719i | ||||||
\(769\) | −2.90165 | + | 8.93035i | −0.104636 | + | 0.322037i | −0.989645 | − | 0.143538i | \(-0.954152\pi\) |
0.885009 | + | 0.465574i | \(0.154152\pi\) | |||||||
\(770\) | 3.78220 | − | 1.20582i | 0.136301 | − | 0.0434546i | ||||
\(771\) | 18.5227 | + | 57.0070i | 0.667079 | + | 2.05306i | ||||
\(772\) | −39.9230 | + | 12.9718i | −1.43686 | + | 0.466864i | ||||
\(773\) | −4.06806 | + | 5.59921i | −0.146318 | + | 0.201390i | −0.875885 | − | 0.482520i | \(-0.839722\pi\) |
0.729567 | + | 0.683909i | \(0.239722\pi\) | |||||||
\(774\) | 20.4751 | 0.735963 | ||||||||
\(775\) | 2.36827 | − | 7.02337i | 0.0850708 | − | 0.252287i | ||||
\(776\) | 0.881899 | 0.0316583 | ||||||||
\(777\) | 46.9118 | − | 64.5685i | 1.68295 | − | 2.31638i | ||||
\(778\) | −1.91705 | + | 0.622886i | −0.0687294 | + | 0.0223315i | ||||
\(779\) | −0.747286 | − | 2.29991i | −0.0267743 | − | 0.0824028i | ||||
\(780\) | 32.0157 | + | 10.5987i | 1.14635 | + | 0.379496i | ||||
\(781\) | 3.32737 | − | 10.2406i | 0.119063 | − | 0.366438i | ||||
\(782\) | 8.59216i | 0.307255i | ||||||||
\(783\) | −28.5722 | − | 9.28368i | −1.02109 | − | 0.331772i | ||||
\(784\) | 26.8886 | − | 19.5357i | 0.960306 | − | 0.697703i | ||||
\(785\) | 5.39536 | + | 0.0298538i | 0.192569 | + | 0.00106553i | ||||
\(786\) | 2.03345 | + | 1.47739i | 0.0725307 | + | 0.0526966i | ||||
\(787\) | 16.7936 | + | 23.1144i | 0.598628 | + | 0.823941i | 0.995582 | − | 0.0938978i | \(-0.0299327\pi\) |
−0.396954 | + | 0.917839i | \(0.629933\pi\) | |||||||
\(788\) | 8.40989 | + | 11.5752i | 0.299590 | + | 0.412350i | ||||
\(789\) | 39.6348 | + | 28.7964i | 1.41104 | + | 1.02518i | ||||
\(790\) | −3.40666 | + | 10.2905i | −0.121204 | + | 0.366121i | ||||
\(791\) | −18.9389 | + | 13.7599i | −0.673391 | + | 0.489247i | ||||
\(792\) | 7.05044 | + | 2.29083i | 0.250526 | + | 0.0814010i | ||||
\(793\) | 23.4320i | 0.832095i | ||||||||
\(794\) | −2.86239 | + | 8.80953i | −0.101582 | + | 0.312638i | ||||
\(795\) | 18.7265 | + | 26.0771i | 0.664162 | + | 0.924859i | ||||
\(796\) | 2.53939 | + | 7.81544i | 0.0900063 | + | 0.277011i | ||||
\(797\) | −25.5813 | + | 8.31187i | −0.906136 | + | 0.294422i | −0.724767 | − | 0.688994i | \(-0.758053\pi\) |
−0.181369 | + | 0.983415i | \(0.558053\pi\) | |||||||
\(798\) | −3.16393 | + | 4.35477i | −0.112002 | + | 0.154157i | ||||
\(799\) | −32.5406 | −1.15120 | ||||||||
\(800\) | −0.258279 | + | 23.3382i | −0.00913154 | + | 0.825129i | ||||
\(801\) | −22.6471 | −0.800194 | ||||||||
\(802\) | 2.07940 | − | 2.86206i | 0.0734263 | − | 0.101063i | ||||
\(803\) | −11.2253 | + | 3.64731i | −0.396131 | + | 0.128711i | ||||
\(804\) | 13.1070 | + | 40.3392i | 0.462248 | + | 1.42265i | ||||
\(805\) | 35.8399 | − | 48.7597i | 1.26319 | − | 1.71855i | ||||
\(806\) | 0.616291 | − | 1.89675i | 0.0217079 | − | 0.0668102i | ||||
\(807\) | − | 49.2551i | − | 1.73386i | ||||||
\(808\) | 23.9539 | + | 7.78308i | 0.842694 | + | 0.273808i | ||||
\(809\) | 1.22311 | − | 0.888640i | 0.0430022 | − | 0.0312429i | −0.566077 | − | 0.824353i | \(-0.691539\pi\) |
0.609079 | + | 0.793110i | \(0.291539\pi\) | |||||||
\(810\) | −0.548962 | + | 0.394222i | −0.0192886 | + | 0.0138515i | ||||
\(811\) | −1.46105 | − | 1.06152i | −0.0513045 | − | 0.0372749i | 0.561837 | − | 0.827248i | \(-0.310095\pi\) |
−0.613142 | + | 0.789973i | \(0.710095\pi\) | |||||||
\(812\) | 28.1841 | + | 38.7921i | 0.989069 | + | 1.36134i | ||||
\(813\) | 37.1475 | + | 51.1292i | 1.30282 | + | 1.79318i | ||||
\(814\) | −2.20169 | − | 1.59962i | −0.0771693 | − | 0.0560668i | ||||
\(815\) | −27.7360 | + | 19.9179i | −0.971550 | + | 0.697692i | ||||
\(816\) | −19.6491 | + | 14.2759i | −0.687857 | + | 0.499757i | ||||
\(817\) | −9.16628 | − | 2.97830i | −0.320687 | − | 0.104198i | ||||
\(818\) | − | 14.6532i | − | 0.512336i | ||||||
\(819\) | −19.1081 | + | 58.8087i | −0.667691 | + | 2.05494i | ||||
\(820\) | 5.76498 | − | 7.84318i | 0.201322 | − | 0.273896i | ||||
\(821\) | −7.54485 | − | 23.2207i | −0.263317 | − | 0.810407i | −0.992076 | − | 0.125637i | \(-0.959903\pi\) |
0.728759 | − | 0.684770i | \(-0.240097\pi\) | |||||||
\(822\) | 22.1300 | − | 7.19046i | 0.771871 | − | 0.250796i | ||||
\(823\) | 22.4939 | − | 30.9601i | 0.784086 | − | 1.07920i | −0.210733 | − | 0.977544i | \(-0.567585\pi\) |
0.994819 | − | 0.101659i | \(-0.0324150\pi\) | |||||||
\(824\) | −7.12277 | −0.248133 | ||||||||
\(825\) | 12.1132 | + | 4.08455i | 0.421727 | + | 0.142206i | ||||
\(826\) | 13.5790 | 0.472475 | ||||||||
\(827\) | 7.03287 | − | 9.67991i | 0.244557 | − | 0.336604i | −0.669039 | − | 0.743227i | \(-0.733294\pi\) |
0.913596 | + | 0.406624i | \(0.133294\pi\) | |||||||
\(828\) | 50.9114 | − | 16.5421i | 1.76929 | − | 0.574878i | ||||
\(829\) | −4.90284 | − | 15.0894i | −0.170283 | − | 0.524076i | 0.829104 | − | 0.559094i | \(-0.188851\pi\) |
−0.999387 | + | 0.0350181i | \(0.988851\pi\) | |||||||
\(830\) | −6.17490 | − | 8.59868i | −0.214334 | − | 0.298465i | ||||
\(831\) | 17.8734 | − | 55.0086i | 0.620020 | − | 1.90823i | ||||
\(832\) | − | 10.8165i | − | 0.374993i | ||||||
\(833\) | −34.1712 | − | 11.1029i | −1.18396 | − | 0.384693i | ||||
\(834\) | −17.0322 | + | 12.3746i | −0.589777 | + | 0.428498i | ||||
\(835\) | 16.0923 | − | 48.6100i | 0.556896 | − | 1.68222i | ||||
\(836\) | −1.33731 | − | 0.971612i | −0.0462518 | − | 0.0336039i | ||||
\(837\) | 4.24966 | + | 5.84915i | 0.146890 | + | 0.202176i | ||||
\(838\) | 3.41700 | + | 4.70310i | 0.118038 | + | 0.162466i | ||||
\(839\) | 4.50180 | + | 3.27075i | 0.155419 | + | 0.112919i | 0.662777 | − | 0.748817i | \(-0.269378\pi\) |
−0.507358 | + | 0.861736i | \(0.669378\pi\) | |||||||
\(840\) | −45.7386 | − | 0.253082i | −1.57813 | − | 0.00873217i | ||||
\(841\) | −7.23459 | + | 5.25623i | −0.249468 | + | 0.181249i | ||||
\(842\) | −14.7784 | − | 4.80179i | −0.509297 | − | 0.165481i | ||||
\(843\) | − | 8.20337i | − | 0.282539i | ||||||
\(844\) | −6.70005 | + | 20.6206i | −0.230625 | + | 0.709792i | ||||
\(845\) | −8.37307 | − | 2.77189i | −0.288042 | − | 0.0953559i | ||||
\(846\) | −6.95638 | − | 21.4095i | −0.239165 | − | 0.736075i | ||||
\(847\) | 41.7719 | − | 13.5725i | 1.43530 | − | 0.466357i | ||||
\(848\) | 8.61033 | − | 11.8511i | 0.295680 | − | 0.406969i | ||||
\(849\) | −59.0564 | −2.02681 | ||||||||
\(850\) | 5.59795 | − | 3.97325i | 0.192008 | − | 0.136281i | ||||
\(851\) | −41.4852 | −1.42210 | ||||||||
\(852\) | −34.5435 | + | 47.5451i | −1.18344 | + | 1.62887i | ||||
\(853\) | −10.6450 | + | 3.45877i | −0.364478 | + | 0.118426i | −0.485530 | − | 0.874220i | \(-0.661373\pi\) |
0.121052 | + | 0.992646i | \(0.461373\pi\) | |||||||
\(854\) | −4.65201 | − | 14.3174i | −0.159189 | − | 0.489932i | ||||
\(855\) | −10.1232 | + | 3.22742i | −0.346207 | + | 0.110376i | ||||
\(856\) | −1.23103 | + | 3.78872i | −0.0420757 | + | 0.129496i | ||||
\(857\) | − | 34.7124i | − | 1.18575i | −0.805294 | − | 0.592876i | \(-0.797992\pi\) | ||
0.805294 | − | 0.592876i | \(-0.202008\pi\) | |||||||
\(858\) | 3.27132 | + | 1.06292i | 0.111681 | + | 0.0362874i | ||||
\(859\) | 44.2128 | − | 32.1224i | 1.50852 | − | 1.09600i | 0.541691 | − | 0.840578i | \(-0.317784\pi\) |
0.966829 | − | 0.255426i | \(-0.0822157\pi\) | |||||||
\(860\) | −11.7839 | − | 36.9618i | −0.401828 | − | 1.26039i | ||||
\(861\) | 23.5551 | + | 17.1137i | 0.802754 | + | 0.583235i | ||||
\(862\) | −4.52204 | − | 6.22406i | −0.154021 | − | 0.211992i | ||||
\(863\) | −15.3092 | − | 21.0713i | −0.521132 | − | 0.717276i | 0.464615 | − | 0.885513i | \(-0.346193\pi\) |
−0.985747 | + | 0.168236i | \(0.946193\pi\) | |||||||
\(864\) | −18.4186 | − | 13.3819i | −0.626613 | − | 0.455261i | ||||
\(865\) | −12.7620 | − | 9.38049i | −0.433922 | − | 0.318946i | ||||
\(866\) | 11.2820 | − | 8.19687i | 0.383379 | − | 0.278541i | ||||
\(867\) | −20.0438 | − | 6.51263i | −0.680723 | − | 0.221180i | ||||
\(868\) | − | 11.5394i | − | 0.391673i | ||||||
\(869\) | 3.07684 | − | 9.46954i | 0.104375 | − | 0.321232i | ||||
\(870\) | 0.0948649 | − | 17.1446i | 0.00321622 | − | 0.581255i | ||||
\(871\) | 7.86974 | + | 24.2206i | 0.266656 | + | 0.820683i | ||||
\(872\) | 12.8542 | − | 4.17659i | 0.435299 | − | 0.141437i | ||||
\(873\) | −1.44980 | + | 1.99548i | −0.0490684 | + | 0.0675369i | ||||
\(874\) | 2.79794 | 0.0946416 | ||||||||
\(875\) | −48.3412 | − | 0.802514i | −1.63423 | − | 0.0271299i | ||||
\(876\) | 64.4198 | 2.17654 | ||||||||
\(877\) | 13.4941 | − | 18.5730i | 0.455663 | − | 0.627167i | −0.517939 | − | 0.855417i | \(-0.673301\pi\) |
0.973602 | + | 0.228251i | \(0.0733006\pi\) | |||||||
\(878\) | 6.73455 | − | 2.18819i | 0.227280 | − | 0.0738478i | ||||
\(879\) | 17.0866 | + | 52.5871i | 0.576316 | + | 1.77372i | ||||
\(880\) | 0.0322738 | − | 5.83273i | 0.00108795 | − | 0.196621i | ||||
\(881\) | 1.66227 | − | 5.11593i | 0.0560032 | − | 0.172360i | −0.919142 | − | 0.393926i | \(-0.871117\pi\) |
0.975145 | + | 0.221566i | \(0.0711167\pi\) | |||||||
\(882\) | − | 24.8559i | − | 0.836942i | ||||||
\(883\) | −31.9303 | − | 10.3748i | −1.07454 | − | 0.349139i | −0.282285 | − | 0.959331i | \(-0.591092\pi\) |
−0.792254 | + | 0.610192i | \(0.791092\pi\) | |||||||
\(884\) | −13.4581 | + | 9.77785i | −0.452643 | + | 0.328865i | ||||
\(885\) | 35.2329 | + | 25.8973i | 1.18434 | + | 0.870527i | ||||
\(886\) | 3.83219 | + | 2.78425i | 0.128745 | + | 0.0935388i | ||||
\(887\) | −30.6492 | − | 42.1850i | −1.02910 | − | 1.41644i | −0.905621 | − | 0.424088i | \(-0.860595\pi\) |
−0.123479 | − | 0.992347i | \(-0.539405\pi\) | |||||||
\(888\) | 18.4307 | + | 25.3677i | 0.618495 | + | 0.851285i | ||||
\(889\) | 30.5413 | + | 22.1896i | 1.02432 | + | 0.744215i | ||||
\(890\) | −1.44725 | − | 4.53949i | −0.0485119 | − | 0.152164i | ||||
\(891\) | 0.502237 | − | 0.364897i | 0.0168256 | − | 0.0122245i | ||||
\(892\) | −38.7783 | − | 12.5998i | −1.29839 | − | 0.421873i | ||||
\(893\) | 10.5965i | 0.354597i | ||||||||
\(894\) | 1.05585 | − | 3.24956i | 0.0353128 | − | 0.108682i | ||||
\(895\) | 1.49768 | − | 0.477479i | 0.0500618 | − | 0.0159604i | ||||
\(896\) | 14.6229 | + | 45.0047i | 0.488517 | + | 1.50350i | ||||
\(897\) | 49.8675 | − | 16.2029i | 1.66503 | − | 0.541000i | ||||
\(898\) | 5.08745 | − | 7.00228i | 0.169771 | − | 0.233669i | ||||
\(899\) | 9.13109 | 0.304539 | ||||||||
\(900\) | −34.3203 | − | 25.5202i | −1.14401 | − | 0.850672i | ||||
\(901\) | −15.8360 | −0.527574 | ||||||||
\(902\) | 0.583554 | − | 0.803193i | 0.0194302 | − | 0.0267434i | ||||
\(903\) | 110.361 | − | 35.8584i | 3.67258 | − | 1.19329i | ||||
\(904\) | −2.84211 | − | 8.74712i | −0.0945272 | − | 0.290925i | ||||
\(905\) | −15.3730 | − | 5.08922i | −0.511017 | − | 0.169171i | ||||
\(906\) | 6.42657 | − | 19.7790i | 0.213509 | − | 0.657112i | ||||
\(907\) | 24.4809i | 0.812876i | 0.913678 | + | 0.406438i | \(0.133229\pi\) | ||||
−0.913678 | + | 0.406438i | \(0.866771\pi\) | |||||||
\(908\) | 43.3394 | + | 14.0818i | 1.43827 | + | 0.467321i | ||||
\(909\) | −56.9900 | + | 41.4057i | −1.89024 | + | 1.37334i | ||||
\(910\) | −13.0090 | − | 0.0719818i | −0.431244 | − | 0.00238618i | ||||
\(911\) | 27.6130 | + | 20.0620i | 0.914859 | + | 0.664684i | 0.942239 | − | 0.334941i | \(-0.108716\pi\) |
−0.0273802 | + | 0.999625i | \(0.508716\pi\) | |||||||
\(912\) | 4.64878 | + | 6.39850i | 0.153937 | + | 0.211876i | ||||
\(913\) | 5.71557 | + | 7.86681i | 0.189158 | + | 0.260353i | ||||
\(914\) | −0.928905 | − | 0.674889i | −0.0307255 | − | 0.0223234i | ||||
\(915\) | 15.2351 | − | 46.0208i | 0.503657 | − | 1.52140i | ||||
\(916\) | −37.4666 | + | 27.2211i | −1.23793 | + | 0.899410i | ||||
\(917\) | 8.30459 | + | 2.69832i | 0.274242 | + | 0.0891065i | ||||
\(918\) | 6.69615i | 0.221006i | ||||||||
\(919\) | 5.76755 | − | 17.7507i | 0.190254 | − | 0.585542i | −0.809745 | − | 0.586782i | \(-0.800395\pi\) |
0.999999 | + | 0.00124006i | \(0.000394722\pi\) | |||||||
\(920\) | 13.8679 | + | 19.3114i | 0.457212 | + | 0.636677i | ||||
\(921\) | −19.4314 | − | 59.8037i | −0.640286 | − | 1.97060i | ||||
\(922\) | −4.20650 | + | 1.36678i | −0.138534 | + | 0.0450124i | ||||
\(923\) | −20.7407 | + | 28.5471i | −0.682689 | + | 0.939641i | ||||
\(924\) | 19.9020 | 0.654727 | ||||||||
\(925\) | 19.1839 | + | 27.0284i | 0.630763 | + | 0.888688i | ||||
\(926\) | 13.2270 | 0.434665 | ||||||||
\(927\) | 11.7095 | − | 16.1168i | 0.384592 | − | 0.529345i | ||||
\(928\) | −27.3459 | + | 8.88523i | −0.897674 | + | 0.291672i | ||||
\(929\) | −4.49659 | − | 13.8391i | −0.147528 | − | 0.454046i | 0.849799 | − | 0.527107i | \(-0.176723\pi\) |
−0.997327 | + | 0.0730609i | \(0.976723\pi\) | |||||||
\(930\) | −2.44364 | + | 3.32454i | −0.0801302 | + | 0.109016i | ||||
\(931\) | −3.61553 | + | 11.1275i | −0.118494 | + | 0.364688i | ||||
\(932\) | 15.6154i | 0.511498i | ||||||||
\(933\) | 27.9511 | + | 9.08186i | 0.915078 | + | 0.297327i | ||||
\(934\) | −4.83084 | + | 3.50981i | −0.158070 | + | 0.114844i | ||||
\(935\) | −5.12172 | + | 3.67802i | −0.167498 | + | 0.120284i | ||||
\(936\) | −19.6541 | − | 14.2795i | −0.642415 | − | 0.466741i | ||||
\(937\) | 6.08778 | + | 8.37911i | 0.198879 | + | 0.273734i | 0.896795 | − | 0.442446i | \(-0.145889\pi\) |
−0.697916 | + | 0.716180i | \(0.745889\pi\) | |||||||
\(938\) | −9.61713 | − | 13.2368i | −0.314010 | − | 0.432198i | ||||
\(939\) | −62.3467 | − | 45.2975i | −2.03461 | − | 1.47823i | ||||
\(940\) | −34.6450 | + | 24.8793i | −1.13000 | + | 0.811475i | ||||
\(941\) | −38.1340 | + | 27.7059i | −1.24313 | + | 0.903188i | −0.997803 | − | 0.0662523i | \(-0.978896\pi\) |
−0.245328 | + | 0.969440i | \(0.578896\pi\) | |||||||
\(942\) | −2.85650 | − | 0.928133i | −0.0930698 | − | 0.0302402i | ||||
\(943\) | − | 15.1341i | − | 0.492834i | ||||||
\(944\) | 6.16545 | − | 18.9753i | 0.200668 | − | 0.617593i | ||||
\(945\) | 27.9312 | − | 38.0000i | 0.908601 | − | 1.23614i | ||||
\(946\) | −1.22272 | − | 3.76315i | −0.0397541 | − | 0.122350i | ||||
\(947\) | −26.8778 | + | 8.73311i | −0.873410 | + | 0.283788i | −0.711218 | − | 0.702971i | \(-0.751856\pi\) |
−0.162191 | + | 0.986759i | \(0.551856\pi\) | |||||||
\(948\) | −31.9426 | + | 43.9652i | −1.03745 | + | 1.42792i | ||||
\(949\) | 38.6791 | 1.25558 | ||||||||
\(950\) | −1.29384 | − | 1.82291i | −0.0419778 | − | 0.0591429i | ||||
\(951\) | −70.6372 | −2.29057 | ||||||||
\(952\) | 13.2614 | − | 18.2527i | 0.429803 | − | 0.591573i | ||||
\(953\) | −8.77435 | + | 2.85096i | −0.284229 | + | 0.0923516i | −0.447662 | − | 0.894203i | \(-0.647743\pi\) |
0.163433 | + | 0.986554i | \(0.447743\pi\) | |||||||
\(954\) | −3.38534 | − | 10.4190i | −0.109605 | − | 0.337328i | ||||
\(955\) | 0.657983 | + | 0.916255i | 0.0212918 | + | 0.0296493i | ||||
\(956\) | −0.528374 | + | 1.62617i | −0.0170888 | + | 0.0525940i | ||||
\(957\) | 15.7484i | 0.509072i | ||||||||
\(958\) | 0.558716 | + | 0.181538i | 0.0180513 | + | 0.00586523i | ||||
\(959\) | 65.3986 | − | 47.5149i | 2.11183 | − | 1.53433i | ||||
\(960\) | −7.03268 | + | 21.2437i | −0.226979 | + | 0.685637i | ||||
\(961\) | 23.3017 | + | 16.9297i | 0.751669 | + | 0.546120i | ||||
\(962\) | 5.24208 | + | 7.21510i | 0.169011 | + | 0.232624i | ||||
\(963\) | −6.54903 | − | 9.01396i | −0.211039 | − | 0.290471i | ||||
\(964\) | 3.13499 | + | 2.27770i | 0.100971 | + | 0.0733599i | ||||
\(965\) | 52.1427 | + | 0.288518i | 1.67853 | + | 0.00928772i | ||||
\(966\) | −27.2532 | + | 19.8006i | −0.876857 | + | 0.637074i | ||||
\(967\) | 3.67980 | + | 1.19564i | 0.118334 | + | 0.0384492i | 0.367586 | − | 0.929990i | \(-0.380184\pi\) |
−0.249251 | + | 0.968439i | \(0.580184\pi\) | |||||||
\(968\) | 17.2559i | 0.554626i | ||||||||
\(969\) | 2.64209 | − | 8.13151i | 0.0848761 | − | 0.261222i | ||||
\(970\) | −0.492634 | − | 0.163086i | −0.0158175 | − | 0.00523636i | ||||
\(971\) | −5.90240 | − | 18.1657i | −0.189417 | − | 0.582966i | 0.810579 | − | 0.585629i | \(-0.199152\pi\) |
−0.999996 | + | 0.00266296i | \(0.999152\pi\) | |||||||
\(972\) | −28.2722 | + | 9.18621i | −0.906832 | + | 0.294648i | ||||
\(973\) | −42.9901 | + | 59.1708i | −1.37820 | + | 1.89693i | ||||
\(974\) | −7.87827 | −0.252436 | ||||||||
\(975\) | −33.6166 | − | 24.9969i | −1.07659 | − | 0.800541i | ||||
\(976\) | −22.1193 | −0.708022 | ||||||||
\(977\) | −18.6283 | + | 25.6396i | −0.595971 | + | 0.820284i | −0.995332 | − | 0.0965099i | \(-0.969232\pi\) |
0.399361 | + | 0.916794i | \(0.369232\pi\) | |||||||
\(978\) | 18.0783 | − | 5.87399i | 0.578080 | − | 0.187830i | ||||
\(979\) | 1.35242 | + | 4.16233i | 0.0432236 | + | 0.133029i | ||||
\(980\) | −44.8700 | + | 14.3051i | −1.43332 | + | 0.456961i | ||||
\(981\) | −11.6814 | + | 35.9516i | −0.372958 | + | 1.14785i | ||||
\(982\) | 15.1645i | 0.483918i | ||||||||
\(983\) | 29.8725 | + | 9.70615i | 0.952783 | + | 0.309578i | 0.743846 | − | 0.668351i | \(-0.233000\pi\) |
0.208937 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(984\) | −9.25432 | + | 6.72366i | −0.295017 | + | 0.214342i | ||||
\(985\) | −5.39848 | − | 16.9330i | −0.172010 | − | 0.539532i | ||||
\(986\) | 6.84180 | + | 4.97086i | 0.217887 | + | 0.158304i | ||||
\(987\) | −74.9897 | − | 103.214i | −2.38695 | − | 3.28535i | ||||
\(988\) | 3.18404 | + | 4.38245i | 0.101298 | + | 0.139424i | ||||
\(989\) | −48.7974 | − | 35.4534i | −1.55167 | − | 1.12735i | ||||
\(990\) | −3.51479 | − | 2.58348i | −0.111707 | − | 0.0821083i | ||||
\(991\) | −34.6265 | + | 25.1576i | −1.09995 | + | 0.799158i | −0.981051 | − | 0.193749i | \(-0.937935\pi\) |
−0.118895 | + | 0.992907i | \(0.537935\pi\) | |||||||
\(992\) | 6.58097 | + | 2.13829i | 0.208946 | + | 0.0678907i | ||||
\(993\) | 9.44068i | 0.299591i | ||||||||
\(994\) | 7.00545 | − | 21.5606i | 0.222199 | − | 0.683860i | ||||
\(995\) | 0.0564811 | − | 10.2076i | 0.00179057 | − | 0.323603i | ||||
\(996\) | −16.4003 | − | 50.4749i | −0.519664 | − | 1.59936i | ||||
\(997\) | 42.7807 | − | 13.9003i | 1.35488 | − | 0.440227i | 0.460549 | − | 0.887634i | \(-0.347653\pi\) |
0.894330 | + | 0.447408i | \(0.147653\pi\) | |||||||
\(998\) | 0.343414 | − | 0.472669i | 0.0108706 | − | 0.0149621i | ||||
\(999\) | −32.3308 | −1.02290 |
(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 | 475.2.n.b.134.10 | yes | 96 | |
25.14 | even | 10 | inner | 475.2.n.b.39.10 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.n.b.39.10 | ✓ | 96 | 25.14 | even | 10 | inner | |
475.2.n.b.134.10 | yes | 96 | 1.1 | even | 1 | trivial |