Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [833,2,Mod(31,833)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(833, base_ring=CyclotomicField(48))
chi = DirichletCharacter(H, H._module([8, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("833.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 833 = 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 833.bc (of order \(48\), degree \(16\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.65153848837\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{48})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{48}]$ |
Embedding invariants
Embedding label | 80.2 | ||
Character | \(\chi\) | \(=\) | 833.80 |
Dual form | 833.2.bc.a.656.2 |
$q$-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 \(\left(\mathbb{Z}/833\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{16}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08860 | + | 1.41869i | −0.769755 | + | 1.00316i | 0.229797 | + | 0.973239i | \(0.426194\pi\) |
−0.999552 | + | 0.0299259i | \(0.990473\pi\) | |||||||
\(3\) | −0.543906 | + | 0.0356495i | −0.314024 | + | 0.0205822i | −0.221601 | − | 0.975138i | \(-0.571128\pi\) |
−0.0924238 | + | 0.995720i | \(0.529461\pi\) | |||||||
\(4\) | −0.309994 | − | 1.15691i | −0.154997 | − | 0.578457i | ||||
\(5\) | −2.53857 | + | 0.861728i | −1.13528 | + | 0.385376i | −0.824924 | − | 0.565243i | \(-0.808782\pi\) |
−0.310358 | + | 0.950620i | \(0.600449\pi\) | |||||||
\(6\) | 0.541520 | − | 0.810442i | 0.221075 | − | 0.330861i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.32544 | − | 0.549014i | −0.468613 | − | 0.194106i | ||||
\(9\) | −2.67977 | + | 0.352799i | −0.893257 | + | 0.117600i | ||||
\(10\) | 1.54096 | − | 4.53951i | 0.487293 | − | 1.43552i | ||||
\(11\) | −2.21771 | − | 4.49707i | −0.668665 | − | 1.35592i | −0.921488 | − | 0.388406i | \(-0.873026\pi\) |
0.252824 | − | 0.967512i | \(-0.418641\pi\) | |||||||
\(12\) | 0.209851 | + | 0.618201i | 0.0605788 | + | 0.178459i | ||||
\(13\) | −4.70535 | + | 4.70535i | −1.30503 | + | 1.30503i | −0.380072 | + | 0.924957i | \(0.624101\pi\) |
−0.924957 | + | 0.380072i | \(0.875899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35002 | − | 0.559198i | 0.348574 | − | 0.144384i | ||||
\(16\) | 4.29627 | − | 2.48045i | 1.07407 | − | 0.620113i | ||||
\(17\) | 4.12294 | − | 0.0371267i | 0.999959 | − | 0.00900454i | ||||
\(18\) | 2.41668 | − | 4.18582i | 0.569618 | − | 0.986607i | ||||
\(19\) | 4.21946 | + | 3.23771i | 0.968011 | + | 0.742781i | 0.966354 | − | 0.257218i | \(-0.0828057\pi\) |
0.00165754 | + | 0.999999i | \(0.499472\pi\) | |||||||
\(20\) | 1.78388 | + | 2.66977i | 0.398889 | + | 0.596979i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.79414 | + | 1.74926i | 1.87492 | + | 0.372944i | ||||
\(23\) | −0.267530 | + | 4.08172i | −0.0557839 | + | 0.851098i | 0.874677 | + | 0.484706i | \(0.161074\pi\) |
−0.930461 | + | 0.366391i | \(0.880593\pi\) | |||||||
\(24\) | 0.740486 | + | 0.251361i | 0.151151 | + | 0.0513089i | ||||
\(25\) | 1.73498 | − | 1.33130i | 0.346997 | − | 0.266260i | ||||
\(26\) | −1.55319 | − | 11.7977i | −0.304606 | − | 2.31371i | ||||
\(27\) | 3.04877 | − | 0.606437i | 0.586735 | − | 0.116709i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.90098 | − | 9.55688i | 0.353004 | − | 1.77467i | −0.241323 | − | 0.970445i | \(-0.577581\pi\) |
0.594327 | − | 0.804224i | \(-0.297419\pi\) | |||||||
\(30\) | −0.676305 | + | 2.52400i | −0.123476 | + | 0.460818i | ||||
\(31\) | −0.0502494 | − | 0.766657i | −0.00902505 | − | 0.137696i | −0.999994 | − | 0.00360059i | \(-0.998854\pi\) |
0.990968 | − | 0.134095i | \(-0.0428128\pi\) | |||||||
\(32\) | −0.783404 | + | 5.95055i | −0.138488 | + | 1.05192i | ||||
\(33\) | 1.36654 | + | 2.36692i | 0.237885 | + | 0.412029i | ||||
\(34\) | −4.43555 | + | 5.88958i | −0.760691 | + | 1.01006i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.23887 | + | 2.99090i | 0.206478 | + | 0.498483i | ||||
\(37\) | −5.32156 | − | 2.62430i | −0.874859 | − | 0.431433i | −0.0513132 | − | 0.998683i | \(-0.516341\pi\) |
−0.823546 | + | 0.567250i | \(0.808007\pi\) | |||||||
\(38\) | −9.18660 | + | 2.46154i | −1.49026 | + | 0.399315i | ||||
\(39\) | 2.39153 | − | 2.72701i | 0.382950 | − | 0.436671i | ||||
\(40\) | 3.83781 | + | 0.251544i | 0.606812 | + | 0.0397725i | ||||
\(41\) | 0.0510695 | + | 0.256744i | 0.00797571 | + | 0.0400966i | 0.984568 | − | 0.175001i | \(-0.0559930\pi\) |
−0.976593 | + | 0.215098i | \(0.930993\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.397620 | − | 0.959941i | 0.0606365 | − | 0.146390i | −0.890657 | − | 0.454675i | \(-0.849755\pi\) |
0.951294 | + | 0.308286i | \(0.0997553\pi\) | |||||||
\(44\) | −4.51524 | + | 3.95976i | −0.680699 | + | 0.596957i | ||||
\(45\) | 6.49877 | − | 3.20484i | 0.968779 | − | 0.477749i | ||||
\(46\) | −5.49946 | − | 4.82290i | −0.810851 | − | 0.711098i | ||||
\(47\) | 8.29355 | + | 2.22225i | 1.20974 | + | 0.324148i | 0.806659 | − | 0.591017i | \(-0.201273\pi\) |
0.403079 | + | 0.915165i | \(0.367940\pi\) | |||||||
\(48\) | −2.24834 | + | 1.50229i | −0.324520 | + | 0.216837i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.91066i | 0.553050i | ||||||||
\(51\) | −2.24117 | + | 0.167174i | −0.313826 | + | 0.0234091i | ||||
\(52\) | 6.90231 | + | 3.98505i | 0.957178 | + | 0.552627i | ||||
\(53\) | 1.81423 | + | 0.238848i | 0.249203 | + | 0.0328083i | 0.254093 | − | 0.967180i | \(-0.418223\pi\) |
−0.00488954 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(54\) | −2.45854 | + | 4.98542i | −0.334564 | + | 0.678429i | ||||
\(55\) | 9.50506 | + | 9.50506i | 1.28166 | + | 1.28166i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.41041 | − | 1.61059i | −0.319267 | − | 0.213327i | ||||
\(58\) | 11.4888 | + | 13.1005i | 1.50856 | + | 1.72018i | ||||
\(59\) | −3.63474 | − | 4.73689i | −0.473203 | − | 0.616691i | 0.494379 | − | 0.869246i | \(-0.335396\pi\) |
−0.967582 | + | 0.252556i | \(0.918729\pi\) | |||||||
\(60\) | −1.06544 | − | 1.38851i | −0.137548 | − | 0.179256i | ||||
\(61\) | −0.999567 | − | 1.13979i | −0.127981 | − | 0.145935i | 0.684300 | − | 0.729201i | \(-0.260108\pi\) |
−0.812281 | + | 0.583266i | \(0.801775\pi\) | |||||||
\(62\) | 1.14235 | + | 0.763294i | 0.145079 | + | 0.0969384i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.573383 | − | 0.573383i | −0.0716728 | − | 0.0716728i | ||||
\(65\) | 7.89012 | − | 15.9996i | 0.978649 | − | 1.98450i | ||||
\(66\) | −4.84555 | − | 0.637929i | −0.596446 | − | 0.0785236i | ||||
\(67\) | 10.7106 | + | 6.18377i | 1.30851 | + | 0.755467i | 0.981847 | − | 0.189674i | \(-0.0607433\pi\) |
0.326661 | + | 0.945142i | \(0.394077\pi\) | |||||||
\(68\) | −1.32104 | − | 4.75837i | −0.160199 | − | 0.577037i | ||||
\(69\) | − | 2.22961i | − | 0.268414i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.95416 | + | 2.64209i | −0.469273 | + | 0.313558i | −0.767627 | − | 0.640897i | \(-0.778562\pi\) |
0.298354 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(72\) | 3.74556 | + | 1.00362i | 0.441419 | + | 0.118278i | ||||
\(73\) | −0.852445 | − | 0.747574i | −0.0997711 | − | 0.0874969i | 0.608007 | − | 0.793931i | \(-0.291969\pi\) |
−0.707778 | + | 0.706435i | \(0.750302\pi\) | |||||||
\(74\) | 9.51611 | − | 4.69283i | 1.10623 | − | 0.545530i | ||||
\(75\) | −0.896209 | + | 0.785954i | −0.103485 | + | 0.0907542i | ||||
\(76\) | 2.43774 | − | 5.88522i | 0.279628 | − | 0.675081i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.26537 | + | 6.36145i | 0.143275 | + | 0.720292i | ||||
\(79\) | 12.0747 | + | 0.791417i | 1.35851 | + | 0.0890414i | 0.727166 | − | 0.686462i | \(-0.240837\pi\) |
0.631343 | + | 0.775503i | \(0.282504\pi\) | |||||||
\(80\) | −8.76890 | + | 9.99901i | −0.980393 | + | 1.11792i | ||||
\(81\) | 6.19577 | − | 1.66015i | 0.688418 | − | 0.184461i | ||||
\(82\) | −0.419833 | − | 0.207039i | −0.0463628 | − | 0.0228636i | ||||
\(83\) | −5.11069 | − | 12.3383i | −0.560971 | − | 1.35430i | −0.908990 | − | 0.416817i | \(-0.863146\pi\) |
0.348019 | − | 0.937488i | \(-0.386854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4344 | + | 3.64710i | −1.13177 | + | 0.395583i | ||||
\(86\) | 0.929008 | + | 1.60909i | 0.100178 | + | 0.173513i | ||||
\(87\) | −0.693258 | + | 5.26582i | −0.0743250 | + | 0.564555i | ||||
\(88\) | 0.470480 | + | 7.17814i | 0.0501534 | + | 0.765193i | ||||
\(89\) | −0.507083 | + | 1.89246i | −0.0537506 | + | 0.200600i | −0.987580 | − | 0.157120i | \(-0.949779\pi\) |
0.933829 | + | 0.357720i | \(0.116446\pi\) | |||||||
\(90\) | −2.52788 | + | 12.7085i | −0.266462 | + | 1.33959i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.80513 | − | 0.955800i | 0.500969 | − | 0.0996490i | ||||
\(93\) | 0.0546619 | + | 0.415198i | 0.00566817 | + | 0.0430541i | ||||
\(94\) | −12.1810 | + | 9.34683i | −1.25638 | + | 0.964052i | ||||
\(95\) | −13.5014 | − | 4.58311i | −1.38522 | − | 0.470217i | ||||
\(96\) | 0.213964 | − | 3.26447i | 0.0218377 | − | 0.333178i | ||||
\(97\) | −9.84825 | − | 1.95894i | −0.999938 | − | 0.198900i | −0.332130 | − | 0.943234i | \(-0.607767\pi\) |
−0.667808 | + | 0.744334i | \(0.732767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.52952 | + | 11.2687i | 0.756745 | + | 1.13255i | ||||
\(100\) | −2.07803 | − | 1.59453i | −0.207803 | − | 0.159453i | ||||
\(101\) | −2.60445 | + | 4.51103i | −0.259152 | + | 0.448865i | −0.966015 | − | 0.258486i | \(-0.916776\pi\) |
0.706863 | + | 0.707351i | \(0.250110\pi\) | |||||||
\(102\) | 2.20256 | − | 3.36151i | 0.218086 | − | 0.332839i | ||||
\(103\) | −5.55189 | + | 3.20538i | −0.547044 | + | 0.315836i | −0.747929 | − | 0.663779i | \(-0.768952\pi\) |
0.200885 | + | 0.979615i | \(0.435618\pi\) | |||||||
\(104\) | 8.81995 | − | 3.65334i | 0.864867 | − | 0.358240i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.31382 | + | 2.31382i | −0.224738 | + | 0.224738i | ||||
\(107\) | −1.74168 | − | 5.13082i | −0.168375 | − | 0.496016i | 0.829688 | − | 0.558227i | \(-0.188518\pi\) |
−0.998063 | + | 0.0622112i | \(0.980185\pi\) | |||||||
\(108\) | −1.64669 | − | 3.33917i | −0.158453 | − | 0.321311i | ||||
\(109\) | −0.751286 | + | 2.21322i | −0.0719602 | + | 0.211988i | −0.976959 | − | 0.213425i | \(-0.931538\pi\) |
0.904999 | + | 0.425413i | \(0.139871\pi\) | |||||||
\(110\) | −23.8319 | + | 3.13753i | −2.27228 | + | 0.299152i | ||||
\(111\) | 2.98798 | + | 1.23766i | 0.283607 | + | 0.117474i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3160 | − | 15.4390i | 0.970451 | − | 1.45238i | 0.0802713 | − | 0.996773i | \(-0.474421\pi\) |
0.890180 | − | 0.455610i | \(-0.150579\pi\) | |||||||
\(114\) | 4.90890 | − | 1.66635i | 0.459760 | − | 0.156068i | ||||
\(115\) | −2.83819 | − | 10.5923i | −0.264663 | − | 0.987734i | ||||
\(116\) | −11.6458 | + | 0.763304i | −1.08128 | + | 0.0708710i | ||||
\(117\) | 10.9492 | − | 14.2693i | 1.01226 | − | 1.31920i | ||||
\(118\) | 10.6769 | 0.982893 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.09638 | −0.191372 | ||||||||
\(121\) | −8.60904 | + | 11.2195i | −0.782640 | + | 1.01996i | ||||
\(122\) | 2.70513 | − | 0.177304i | 0.244911 | − | 0.0160523i | ||||
\(123\) | −0.0369298 | − | 0.137824i | −0.00332985 | − | 0.0124272i | ||||
\(124\) | −0.871379 | + | 0.295793i | −0.0782521 | + | 0.0265630i | ||||
\(125\) | 4.18982 | − | 6.27050i | 0.374748 | − | 0.560851i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.38122 | + | 0.572121i | 0.122564 | + | 0.0507675i | 0.443122 | − | 0.896461i | \(-0.353871\pi\) |
−0.320559 | + | 0.947229i | \(0.603871\pi\) | |||||||
\(128\) | −10.4635 | + | 1.37754i | −0.924848 | + | 0.121759i | ||||
\(129\) | −0.182047 | + | 0.536293i | −0.0160283 | + | 0.0472179i | ||||
\(130\) | 14.1093 | + | 28.6107i | 1.23746 | + | 2.50933i | ||||
\(131\) | −1.15391 | − | 3.39931i | −0.100818 | − | 0.296999i | 0.884805 | − | 0.465962i | \(-0.154292\pi\) |
−0.985622 | + | 0.168963i | \(0.945958\pi\) | |||||||
\(132\) | 2.31471 | − | 2.31471i | 0.201469 | − | 0.201469i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.4324 | + | 8.46337i | −1.76509 | + | 0.731124i | ||||
\(135\) | −7.21692 | + | 4.16669i | −0.621133 | + | 0.358611i | ||||
\(136\) | −5.48508 | − | 2.21434i | −0.470342 | − | 0.189878i | ||||
\(137\) | −2.44057 | + | 4.22720i | −0.208512 | + | 0.361154i | −0.951246 | − | 0.308433i | \(-0.900195\pi\) |
0.742734 | + | 0.669587i | \(0.233529\pi\) | |||||||
\(138\) | 3.16312 | + | 2.42715i | 0.269263 | + | 0.206613i | ||||
\(139\) | −2.96540 | − | 4.43803i | −0.251522 | − | 0.376429i | 0.684126 | − | 0.729364i | \(-0.260184\pi\) |
−0.935648 | + | 0.352935i | \(0.885184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.59013 | − | 0.913034i | −0.386559 | − | 0.0768914i | ||||
\(142\) | 0.556195 | − | 8.48590i | 0.0466749 | − | 0.712121i | ||||
\(143\) | 31.5954 | + | 10.7252i | 2.64214 | + | 0.896886i | ||||
\(144\) | −10.6379 | + | 8.16276i | −0.886493 | + | 0.680230i | ||||
\(145\) | 3.40966 | + | 25.8989i | 0.283157 | + | 2.15079i | ||||
\(146\) | 1.98854 | − | 0.395546i | 0.164573 | − | 0.0327356i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.38644 | + | 6.97010i | −0.113965 | + | 0.572939i | ||||
\(149\) | 1.94392 | − | 7.25482i | 0.159252 | − | 0.594338i | −0.839451 | − | 0.543435i | \(-0.817123\pi\) |
0.998704 | − | 0.0509031i | \(-0.0162100\pi\) | |||||||
\(150\) | −0.139413 | − | 2.12703i | −0.0113830 | − | 0.173671i | ||||
\(151\) | 0.750711 | − | 5.70222i | 0.0610920 | − | 0.464040i | −0.933368 | − | 0.358922i | \(-0.883145\pi\) |
0.994460 | − | 0.105118i | \(-0.0335221\pi\) | |||||||
\(152\) | −3.81509 | − | 6.60793i | −0.309444 | − | 0.535974i | ||||
\(153\) | −11.0354 | + | 1.55406i | −0.892162 | + | 0.125638i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.788211 | + | 1.90291i | 0.0633107 | + | 0.152845i | ||||
\(156\) | −3.89627 | − | 1.92143i | −0.311952 | − | 0.153837i | ||||
\(157\) | 6.69003 | − | 1.79259i | 0.533923 | − | 0.143064i | 0.0182236 | − | 0.999834i | \(-0.494199\pi\) |
0.515699 | + | 0.856770i | \(0.327532\pi\) | |||||||
\(158\) | −14.2673 | + | 16.2687i | −1.13504 | + | 1.29427i | ||||
\(159\) | −0.995285 | − | 0.0652344i | −0.0789312 | − | 0.00517343i | ||||
\(160\) | −3.13903 | − | 15.7809i | −0.248162 | − | 1.24759i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.38946 | + | 10.5971i | −0.344869 | + | 0.832587i | ||||
\(163\) | 9.48461 | − | 8.31778i | 0.742892 | − | 0.651499i | −0.201811 | − | 0.979424i | \(-0.564683\pi\) |
0.944704 | + | 0.327925i | \(0.106349\pi\) | |||||||
\(164\) | 0.281199 | − | 0.138672i | 0.0219579 | − | 0.0108285i | ||||
\(165\) | −5.50871 | − | 4.83101i | −0.428853 | − | 0.376094i | ||||
\(166\) | 23.0677 | + | 6.18097i | 1.79040 | + | 0.479737i | ||||
\(167\) | −11.1181 | + | 7.42888i | −0.860345 | + | 0.574864i | −0.905610 | − | 0.424111i | \(-0.860587\pi\) |
0.0452651 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 31.2806i | − | 2.40620i | ||||||
\(170\) | 6.18473 | − | 18.7733i | 0.474347 | − | 1.43985i | ||||
\(171\) | −12.4495 | − | 7.18770i | −0.952034 | − | 0.549657i | ||||
\(172\) | −1.23383 | − | 0.162437i | −0.0940785 | − | 0.0123857i | ||||
\(173\) | 1.56835 | − | 3.18030i | 0.119239 | − | 0.241794i | −0.829067 | − | 0.559149i | \(-0.811128\pi\) |
0.948307 | + | 0.317355i | \(0.102795\pi\) | |||||||
\(174\) | −6.71588 | − | 6.71588i | −0.509129 | − | 0.509129i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.6827 | − | 13.8197i | −1.55901 | − | 1.04170i | ||||
\(177\) | 2.14583 | + | 2.44685i | 0.161290 | + | 0.183916i | ||||
\(178\) | −2.13280 | − | 2.77952i | −0.159860 | − | 0.208334i | ||||
\(179\) | −5.21888 | − | 6.80137i | −0.390077 | − | 0.508358i | 0.556495 | − | 0.830851i | \(-0.312146\pi\) |
−0.946572 | + | 0.322493i | \(0.895479\pi\) | |||||||
\(180\) | −5.72229 | − | 6.52503i | −0.426515 | − | 0.486347i | ||||
\(181\) | 4.23355 | + | 2.82877i | 0.314677 | + | 0.210261i | 0.702871 | − | 0.711317i | \(-0.251901\pi\) |
−0.388194 | + | 0.921578i | \(0.626901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.584303 | + | 0.584303i | 0.0431930 | + | 0.0431930i | ||||
\(184\) | 2.59552 | − | 5.26319i | 0.191344 | − | 0.388008i | ||||
\(185\) | 15.7706 | + | 2.07624i | 1.15948 | + | 0.152648i | ||||
\(186\) | −0.648542 | − | 0.374436i | −0.0475534 | − | 0.0274550i | ||||
\(187\) | −9.31045 | − | 18.4588i | −0.680847 | − | 1.34984i | ||||
\(188\) | − | 10.2838i | − | 0.750023i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.1996 | − | 14.1651i | 1.53798 | − | 1.02765i | ||||
\(191\) | −23.8250 | − | 6.38390i | −1.72392 | − | 0.461923i | −0.745151 | − | 0.666896i | \(-0.767623\pi\) |
−0.978768 | + | 0.204973i | \(0.934289\pi\) | |||||||
\(192\) | 0.332307 | + | 0.291426i | 0.0239822 | + | 0.0210318i | ||||
\(193\) | 18.3146 | − | 9.03176i | 1.31831 | − | 0.650121i | 0.359232 | − | 0.933248i | \(-0.383039\pi\) |
0.959082 | + | 0.283128i | \(0.0913720\pi\) | |||||||
\(194\) | 13.4999 | − | 11.8391i | 0.969237 | − | 0.849998i | ||||
\(195\) | −3.72111 | + | 8.98355i | −0.266474 | + | 0.643325i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.66733 | + | 8.38222i | 0.118792 | + | 0.597208i | 0.993621 | + | 0.112775i | \(0.0359740\pi\) |
−0.874828 | + | 0.484433i | \(0.839026\pi\) | |||||||
\(198\) | −24.1834 | − | 1.58507i | −1.71864 | − | 0.112646i | ||||
\(199\) | 10.7161 | − | 12.2193i | 0.759641 | − | 0.866205i | −0.234741 | − | 0.972058i | \(-0.575424\pi\) |
0.994382 | + | 0.105853i | \(0.0337575\pi\) | |||||||
\(200\) | −3.03052 | + | 0.812025i | −0.214290 | + | 0.0574188i | ||||
\(201\) | −6.04601 | − | 2.98156i | −0.426452 | − | 0.210303i | ||||
\(202\) | −3.56456 | − | 8.60560i | −0.250801 | − | 0.605488i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.888154 | + | 2.54101i | 0.0621832 | + | 0.177907i | ||||
\(205\) | −0.350886 | − | 0.607753i | −0.0245070 | − | 0.0424473i | ||||
\(206\) | 1.49633 | − | 11.3658i | 0.104254 | − | 0.791891i | ||||
\(207\) | −0.723106 | − | 11.0325i | −0.0502594 | − | 0.766810i | ||||
\(208\) | −8.54405 | + | 31.8868i | −0.592424 | + | 2.21095i | ||||
\(209\) | 5.20266 | − | 26.1555i | 0.359875 | − | 1.80922i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.74454 | + | 1.93831i | −0.670842 | + | 0.133439i | −0.518748 | − | 0.854927i | \(-0.673602\pi\) |
−0.152094 | + | 0.988366i | \(0.548602\pi\) | |||||||
\(212\) | −0.286074 | − | 2.17295i | −0.0196476 | − | 0.149239i | ||||
\(213\) | 2.05650 | − | 1.57801i | 0.140909 | − | 0.108124i | ||||
\(214\) | 9.17503 | + | 3.11450i | 0.627192 | + | 0.212903i | ||||
\(215\) | −0.182179 | + | 2.77951i | −0.0124245 | + | 0.189561i | ||||
\(216\) | −4.37389 | − | 0.870022i | −0.297606 | − | 0.0591975i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.32202 | − | 3.47515i | −0.157267 | − | 0.235367i | ||||
\(219\) | 0.490301 | + | 0.376221i | 0.0331314 | + | 0.0254227i | ||||
\(220\) | 8.05002 | − | 13.9430i | 0.542732 | − | 0.940039i | ||||
\(221\) | −19.2252 | + | 19.5746i | −1.29322 | + | 1.31673i | ||||
\(222\) | −5.00857 | + | 2.89170i | −0.336153 | + | 0.194078i | ||||
\(223\) | −1.88077 | + | 0.779040i | −0.125946 | + | 0.0521684i | −0.444766 | − | 0.895647i | \(-0.646713\pi\) |
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.17968 | + | 4.17968i | −0.278645 | + | 0.278645i | ||||
\(226\) | 10.6732 | + | 31.4422i | 0.709969 | + | 2.09150i | ||||
\(227\) | 0.631956 | + | 1.28148i | 0.0419444 | + | 0.0850548i | 0.916836 | − | 0.399264i | \(-0.130734\pi\) |
−0.874892 | + | 0.484319i | \(0.839068\pi\) | |||||||
\(228\) | −1.11610 | + | 3.28791i | −0.0739152 | + | 0.217747i | ||||
\(229\) | −8.95970 | + | 1.17957i | −0.592073 | + | 0.0779479i | −0.420608 | − | 0.907242i | \(-0.638183\pi\) |
−0.171465 | + | 0.985190i | \(0.554850\pi\) | |||||||
\(230\) | 18.1168 | + | 7.50422i | 1.19459 | + | 0.494813i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.76650 | + | 11.6234i | −0.509896 | + | 0.763113i | ||||
\(233\) | 1.72102 | − | 0.584207i | 0.112748 | − | 0.0382727i | −0.264495 | − | 0.964387i | \(-0.585205\pi\) |
0.377243 | + | 0.926114i | \(0.376872\pi\) | |||||||
\(234\) | 8.32440 | + | 31.0671i | 0.544183 | + | 2.03092i | ||||
\(235\) | −22.9687 | + | 1.50545i | −1.49831 | + | 0.0982046i | ||||
\(236\) | −4.35342 | + | 5.67349i | −0.283384 | + | 0.369313i | ||||
\(237\) | −6.59571 | −0.428438 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.77316 | −0.308750 | −0.154375 | − | 0.988012i | \(-0.549336\pi\) | ||||
−0.154375 | + | 0.988012i | \(0.549336\pi\) | |||||||
\(240\) | 4.41300 | − | 5.75113i | 0.284858 | − | 0.371234i | ||||
\(241\) | −14.4316 | + | 0.945895i | −0.929619 | + | 0.0609304i | −0.522684 | − | 0.852527i | \(-0.675069\pi\) |
−0.406935 | + | 0.913457i | \(0.633402\pi\) | |||||||
\(242\) | −6.54522 | − | 24.4271i | −0.420743 | − | 1.57023i | ||||
\(243\) | −12.1413 | + | 4.12142i | −0.778866 | + | 0.264389i | ||||
\(244\) | −1.00878 | + | 1.50974i | −0.0645802 | + | 0.0966512i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.235731 | + | 0.0976429i | 0.0150296 | + | 0.00622548i | ||||
\(247\) | −35.0886 | + | 4.61950i | −2.23263 | + | 0.293932i | ||||
\(248\) | −0.354303 | + | 1.04374i | −0.0224983 | + | 0.0662778i | ||||
\(249\) | 3.21959 | + | 6.52869i | 0.204033 | + | 0.413739i | ||||
\(250\) | 4.33487 | + | 12.7701i | 0.274161 | + | 0.807652i | ||||
\(251\) | 22.0951 | − | 22.0951i | 1.39463 | − | 1.39463i | 0.580038 | − | 0.814589i | \(-0.303037\pi\) |
0.814589 | − | 0.580038i | \(-0.196963\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9491 | − | 7.84898i | 1.19132 | − | 0.493461i | ||||
\(254\) | −2.31526 | + | 1.33671i | −0.145272 | + | 0.0838730i | ||||
\(255\) | 5.54530 | − | 2.35566i | 0.347260 | − | 0.147517i | ||||
\(256\) | 10.2471 | − | 17.7485i | 0.640443 | − | 1.10928i | ||||
\(257\) | 17.7380 | + | 13.6109i | 1.10647 | + | 0.849023i | 0.989560 | − | 0.144120i | \(-0.0460350\pi\) |
0.116908 | + | 0.993143i | \(0.462702\pi\) | |||||||
\(258\) | −0.562657 | − | 0.842075i | −0.0350295 | − | 0.0524253i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −20.9560 | − | 4.16841i | −1.29964 | − | 0.258514i | ||||
\(261\) | −1.72254 | + | 26.2809i | −0.106623 | + | 1.62675i | ||||
\(262\) | 6.07870 | + | 2.06344i | 0.375543 | + | 0.127480i | ||||
\(263\) | 5.58330 | − | 4.28422i | 0.344281 | − | 0.264176i | −0.422118 | − | 0.906541i | \(-0.638713\pi\) |
0.766399 | + | 0.642365i | \(0.222047\pi\) | |||||||
\(264\) | −0.511794 | − | 3.88746i | −0.0314988 | − | 0.239257i | ||||
\(265\) | −4.81136 | + | 0.957040i | −0.295560 | + | 0.0587905i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.208340 | − | 1.04740i | 0.0127502 | − | 0.0640996i | ||||
\(268\) | 3.83386 | − | 14.3082i | 0.234190 | − | 0.874010i | ||||
\(269\) | −0.274950 | − | 4.19493i | −0.0167640 | − | 0.255769i | −0.998012 | − | 0.0630208i | \(-0.979927\pi\) |
0.981248 | − | 0.192748i | \(-0.0617401\pi\) | |||||||
\(270\) | 1.94509 | − | 14.7744i | 0.118374 | − | 0.899142i | ||||
\(271\) | −2.14798 | − | 3.72042i | −0.130481 | − | 0.225999i | 0.793381 | − | 0.608725i | \(-0.208319\pi\) |
−0.923862 | + | 0.382726i | \(0.874985\pi\) | |||||||
\(272\) | 17.6212 | − | 10.3863i | 1.06844 | − | 0.629759i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.34027 | − | 8.06414i | −0.201793 | − | 0.487172i | ||||
\(275\) | −9.83465 | − | 4.84991i | −0.593052 | − | 0.292461i | ||||
\(276\) | −2.57947 | + | 0.691166i | −0.155266 | + | 0.0416033i | ||||
\(277\) | 8.23070 | − | 9.38532i | 0.494535 | − | 0.563909i | −0.449701 | − | 0.893179i | \(-0.648469\pi\) |
0.944236 | + | 0.329270i | \(0.106803\pi\) | |||||||
\(278\) | 9.52432 | + | 0.624257i | 0.571231 | + | 0.0374404i | ||||
\(279\) | 0.405133 | + | 2.03674i | 0.0242546 | + | 0.121936i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.91965 | + | 7.04865i | −0.174172 | + | 0.420487i | −0.986725 | − | 0.162399i | \(-0.948077\pi\) |
0.812554 | + | 0.582887i | \(0.198077\pi\) | |||||||
\(282\) | 6.29212 | − | 5.51804i | 0.374691 | − | 0.328595i | ||||
\(283\) | 6.42883 | − | 3.17035i | 0.382154 | − | 0.188458i | −0.241057 | − | 0.970511i | \(-0.577494\pi\) |
0.623212 | + | 0.782053i | \(0.285827\pi\) | |||||||
\(284\) | 4.28243 | + | 3.75559i | 0.254116 | + | 0.222853i | ||||
\(285\) | 7.50689 | + | 2.01146i | 0.444670 | + | 0.119149i | ||||
\(286\) | −49.6104 | + | 33.1486i | −2.93352 | + | 1.96012i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 16.2225i | − | 0.955919i | ||||||
\(289\) | 16.9972 | − | 0.306142i | 0.999838 | − | 0.0180084i | ||||
\(290\) | −40.4543 | − | 23.3563i | −2.37556 | − | 1.37153i | ||||
\(291\) | 5.42636 | + | 0.714394i | 0.318099 | + | 0.0418785i | ||||
\(292\) | −0.600625 | + | 1.21795i | −0.0351489 | + | 0.0712750i | ||||
\(293\) | 4.15110 | + | 4.15110i | 0.242510 | + | 0.242510i | 0.817888 | − | 0.575378i | \(-0.195145\pi\) |
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.3090 | + | 8.89276i | 0.774877 | + | 0.517756i | ||||
\(296\) | 5.61262 | + | 6.39996i | 0.326227 | + | 0.371990i | ||||
\(297\) | −9.48847 | − | 12.3656i | −0.550577 | − | 0.717526i | ||||
\(298\) | 8.17618 | + | 10.6554i | 0.473634 | + | 0.617251i | ||||
\(299\) | −17.9471 | − | 20.4648i | −1.03791 | − | 1.18351i | ||||
\(300\) | 1.18710 | + | 0.793195i | 0.0685372 | + | 0.0457951i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.27245 | + | 7.27245i | 0.418482 | + | 0.418482i | ||||
\(303\) | 1.25576 | − | 2.54643i | 0.0721414 | − | 0.146288i | ||||
\(304\) | 26.1589 | + | 3.44389i | 1.50032 | + | 0.197521i | ||||
\(305\) | 3.51965 | + | 2.03207i | 0.201535 | + | 0.116356i | ||||
\(306\) | 9.80843 | − | 17.3476i | 0.560711 | − | 0.991696i | ||||
\(307\) | − | 24.0844i | − | 1.37457i | −0.726387 | − | 0.687286i | \(-0.758802\pi\) | ||
0.726387 | − | 0.687286i | \(-0.241198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.90544 | − | 1.94135i | 0.165284 | − | 0.110440i | ||||
\(310\) | −3.55768 | − | 0.953278i | −0.202063 | − | 0.0541426i | ||||
\(311\) | 2.43224 | + | 2.13301i | 0.137920 | + | 0.120952i | 0.725526 | − | 0.688195i | \(-0.241596\pi\) |
−0.587607 | + | 0.809147i | \(0.699930\pi\) | |||||||
\(312\) | −4.66699 | + | 2.30150i | −0.264216 | + | 0.130297i | ||||
\(313\) | −4.98316 | + | 4.37011i | −0.281665 | + | 0.247013i | −0.788507 | − | 0.615025i | \(-0.789146\pi\) |
0.506843 | + | 0.862039i | \(0.330813\pi\) | |||||||
\(314\) | −4.73963 | + | 11.4425i | −0.267473 | + | 0.645737i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.82748 | − | 14.2147i | −0.159058 | − | 0.799639i | ||||
\(317\) | −11.3232 | − | 0.742161i | −0.635974 | − | 0.0416839i | −0.255993 | − | 0.966679i | \(-0.582403\pi\) |
−0.379980 | + | 0.924995i | \(0.624069\pi\) | |||||||
\(318\) | 1.17601 | − | 1.34099i | 0.0659475 | − | 0.0751987i | ||||
\(319\) | −47.1938 | + | 12.6455i | −2.64235 | + | 0.708015i | ||||
\(320\) | 1.94967 | + | 0.961471i | 0.108990 | + | 0.0537479i | ||||
\(321\) | 1.13022 | + | 2.72860i | 0.0630828 | + | 0.152295i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.5168 | + | 13.1922i | 0.974660 | + | 0.734034i | ||||
\(324\) | −3.84130 | − | 6.65332i | −0.213405 | − | 0.369629i | ||||
\(325\) | −1.89947 | + | 14.4279i | −0.105364 | + | 0.800318i | ||||
\(326\) | 1.47541 | + | 22.5104i | 0.0817155 | + | 1.24674i | ||||
\(327\) | 0.329729 | − | 1.23057i | 0.0182341 | − | 0.0680505i | ||||
\(328\) | 0.0732665 | − | 0.368335i | 0.00404546 | − | 0.0203379i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12.8505 | − | 2.55612i | 0.707395 | − | 0.140710i | ||||
\(331\) | −3.20682 | − | 24.3582i | −0.176263 | − | 1.33885i | −0.819455 | − | 0.573144i | \(-0.805724\pi\) |
0.643192 | − | 0.765705i | \(-0.277610\pi\) | |||||||
\(332\) | −12.6901 | + | 9.73743i | −0.696458 | + | 0.534411i | ||||
\(333\) | 15.1864 | + | 5.15509i | 0.832210 | + | 0.282497i | ||||
\(334\) | 1.56388 | − | 23.8602i | 0.0855718 | − | 1.30557i | ||||
\(335\) | −32.5183 | − | 6.46829i | −1.77666 | − | 0.353401i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.83989 | + | 4.25020i | 0.154699 | + | 0.231523i | 0.900721 | − | 0.434398i | \(-0.143039\pi\) |
−0.746022 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(338\) | 44.3775 | + | 34.0520i | 2.41382 | + | 1.85219i | ||||
\(339\) | −5.06056 | + | 8.76515i | −0.274852 | + | 0.476058i | ||||
\(340\) | 7.45397 | + | 10.9411i | 0.404248 | + | 0.593363i | ||||
\(341\) | −3.33627 | + | 1.92620i | −0.180669 | + | 0.104310i | ||||
\(342\) | 23.7496 | − | 9.83739i | 1.28423 | − | 0.531945i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.05404 | + | 1.05404i | −0.0568302 | + | 0.0568302i | ||||
\(345\) | 1.92132 | + | 5.66002i | 0.103440 | + | 0.304725i | ||||
\(346\) | 2.80455 | + | 5.68707i | 0.150774 | + | 0.305739i | ||||
\(347\) | 6.75895 | − | 19.9112i | 0.362839 | − | 1.06889i | −0.600274 | − | 0.799794i | \(-0.704942\pi\) |
0.963113 | − | 0.269096i | \(-0.0867249\pi\) | |||||||
\(348\) | 6.30700 | − | 0.830332i | 0.338091 | − | 0.0445105i | ||||
\(349\) | 26.1712 | + | 10.8405i | 1.40091 | + | 0.580276i | 0.949988 | − | 0.312287i | \(-0.101095\pi\) |
0.450923 | + | 0.892563i | \(0.351095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4920 | + | 17.1990i | −0.613398 | + | 0.918015i | ||||
\(352\) | 28.4974 | − | 9.67356i | 1.51892 | − | 0.515603i | ||||
\(353\) | 1.48164 | + | 5.52956i | 0.0788598 | + | 0.294309i | 0.994081 | − | 0.108644i | \(-0.0346507\pi\) |
−0.915221 | + | 0.402952i | \(0.867984\pi\) | |||||||
\(354\) | −5.80726 | + | 0.380628i | −0.308652 | + | 0.0202301i | ||||
\(355\) | 7.76115 | − | 10.1145i | 0.411919 | − | 0.536823i | ||||
\(356\) | 2.34660 | 0.124370 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.3303 | 0.810231 | ||||||||
\(359\) | −13.4900 | + | 17.5806i | −0.711977 | + | 0.927866i | −0.999553 | − | 0.0298914i | \(-0.990484\pi\) |
0.287576 | + | 0.957758i | \(0.407151\pi\) | |||||||
\(360\) | −10.3732 | + | 0.679896i | −0.546716 | + | 0.0358337i | ||||
\(361\) | 2.40355 | + | 8.97018i | 0.126503 | + | 0.472115i | ||||
\(362\) | −8.62178 | + | 2.92670i | −0.453151 | + | 0.153824i | ||||
\(363\) | 4.28254 | − | 6.40927i | 0.224775 | − | 0.336400i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.80819 | + | 1.16319i | 0.146988 | + | 0.0608843i | ||||
\(366\) | −1.46502 | + | 0.192873i | −0.0765776 | + | 0.0100816i | ||||
\(367\) | −8.89760 | + | 26.2115i | −0.464451 | + | 1.36823i | 0.422499 | + | 0.906363i | \(0.361153\pi\) |
−0.886950 | + | 0.461865i | \(0.847180\pi\) | |||||||
\(368\) | 8.97514 | + | 18.1998i | 0.467861 | + | 0.948729i | ||||
\(369\) | −0.227433 | − | 0.669997i | −0.0118397 | − | 0.0348786i | ||||
\(370\) | −20.1134 | + | 20.1134i | −1.04564 | + | 1.04564i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.463403 | − | 0.191948i | 0.0240264 | − | 0.00995204i | ||||
\(373\) | 22.6098 | − | 13.0538i | 1.17069 | − | 0.675899i | 0.216849 | − | 0.976205i | \(-0.430422\pi\) |
0.953843 | + | 0.300306i | \(0.0970889\pi\) | |||||||
\(374\) | 36.3227 | + | 6.88561i | 1.87820 | + | 0.356046i | ||||
\(375\) | −2.05533 | + | 3.55993i | −0.106137 | + | 0.183834i | ||||
\(376\) | −9.77254 | − | 7.49873i | −0.503980 | − | 0.386718i | ||||
\(377\) | 36.0237 | + | 53.9132i | 1.85531 | + | 2.77667i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.55946 | + | 1.30476i | 0.336937 | + | 0.0670209i | 0.360659 | − | 0.932698i | \(-0.382552\pi\) |
−0.0237224 | + | 0.999719i | \(0.507552\pi\) | |||||||
\(380\) | −1.11691 | + | 17.0407i | −0.0572961 | + | 0.874169i | ||||
\(381\) | −0.771651 | − | 0.261940i | −0.0395329 | − | 0.0134196i | ||||
\(382\) | 34.9927 | − | 26.8508i | 1.79038 | − | 1.37381i | ||||
\(383\) | 1.90614 | + | 14.4786i | 0.0973992 | + | 0.739820i | 0.968553 | + | 0.248809i | \(0.0800392\pi\) |
−0.871153 | + | 0.491011i | \(0.836627\pi\) | |||||||
\(384\) | 5.64203 | − | 1.12227i | 0.287919 | − | 0.0572706i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.12399 | + | 35.8147i | −0.362601 | + | 1.82292i | ||||
\(387\) | −0.726866 | + | 2.71270i | −0.0369487 | + | 0.137894i | ||||
\(388\) | 0.786576 | + | 12.0008i | 0.0399323 | + | 0.609250i | ||||
\(389\) | 1.64849 | − | 12.5215i | 0.0835817 | − | 0.634866i | −0.897464 | − | 0.441088i | \(-0.854593\pi\) |
0.981045 | − | 0.193778i | \(-0.0620741\pi\) | |||||||
\(390\) | −8.69407 | − | 15.0586i | −0.440241 | − | 0.762520i | ||||
\(391\) | −0.951470 | + | 16.8386i | −0.0481179 | + | 0.851566i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.748802 | + | 1.80777i | 0.0377721 | + | 0.0911898i | ||||
\(394\) | −13.7068 | − | 6.75945i | −0.690539 | − | 0.340536i | ||||
\(395\) | −31.3344 | + | 8.39603i | −1.57661 | + | 0.422450i | ||||
\(396\) | 10.7028 | − | 12.2042i | 0.537837 | − | 0.613286i | ||||
\(397\) | −3.82001 | − | 0.250377i | −0.191721 | − | 0.0125660i | −0.0307598 | − | 0.999527i | \(-0.509793\pi\) |
−0.160961 | + | 0.986961i | \(0.551459\pi\) | |||||||
\(398\) | 5.66993 | + | 28.5047i | 0.284208 | + | 1.42881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.15174 | − | 10.0232i | 0.207587 | − | 0.501159i | ||||
\(401\) | 8.93141 | − | 7.83264i | 0.446014 | − | 0.391143i | −0.406667 | − | 0.913577i | \(-0.633309\pi\) |
0.852680 | + | 0.522433i | \(0.174976\pi\) | |||||||
\(402\) | 10.8116 | − | 5.33168i | 0.539233 | − | 0.265920i | ||||
\(403\) | 3.84383 | + | 3.37095i | 0.191475 | + | 0.167919i | ||||
\(404\) | 6.02623 | + | 1.61472i | 0.299816 | + | 0.0803356i | ||||
\(405\) | −14.2978 | + | 9.55347i | −0.710462 | + | 0.474716i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.7514i | 1.47472i | ||||||||
\(408\) | 3.06231 | + | 1.00885i | 0.151607 | + | 0.0499457i | ||||
\(409\) | 2.12696 | + | 1.22800i | 0.105171 | + | 0.0607207i | 0.551663 | − | 0.834067i | \(-0.313993\pi\) |
−0.446492 | + | 0.894788i | \(0.647327\pi\) | |||||||
\(410\) | 1.24419 | + | 0.163800i | 0.0614460 | + | 0.00808952i | ||||
\(411\) | 1.17675 | − | 2.38620i | 0.0580446 | − | 0.117703i | ||||
\(412\) | 5.42940 | + | 5.42940i | 0.267487 | + | 0.267487i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.4388 | + | 10.9841i | 0.807924 | + | 0.539837i | ||||
\(415\) | 23.6061 | + | 26.9176i | 1.15878 | + | 1.32133i | ||||
\(416\) | −24.3132 | − | 31.6856i | −1.19205 | − | 1.55351i | ||||
\(417\) | 1.77111 | + | 2.30816i | 0.0867318 | + | 0.113031i | ||||
\(418\) | 31.4429 | + | 35.8538i | 1.53792 | + | 1.75367i | ||||
\(419\) | 28.3283 | + | 18.9283i | 1.38393 | + | 0.924710i | 0.999999 | + | 0.00134678i | \(0.000428695\pi\) |
0.383927 | + | 0.923363i | \(0.374571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.501993 | − | 0.501993i | −0.0244656 | − | 0.0244656i | 0.694768 | − | 0.719234i | \(-0.255507\pi\) |
−0.719234 | + | 0.694768i | \(0.755507\pi\) | |||||||
\(422\) | 7.85803 | − | 15.9345i | 0.382523 | − | 0.775680i | ||||
\(423\) | −23.0088 | − | 3.02917i | −1.11873 | − | 0.147283i | ||||
\(424\) | −2.27352 | − | 1.31262i | −0.110412 | − | 0.0637462i | ||||
\(425\) | 7.10381 | − | 5.55329i | 0.344585 | − | 0.269374i | ||||
\(426\) | 4.63536i | 0.224584i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.39601 | + | 3.60550i | −0.260826 | + | 0.174278i | ||||
\(429\) | −17.5673 | − | 4.70714i | −0.848156 | − | 0.227263i | ||||
\(430\) | −3.74495 | − | 3.28423i | −0.180597 | − | 0.158380i | ||||
\(431\) | 10.0870 | − | 4.97433i | 0.485871 | − | 0.239605i | −0.182819 | − | 0.983147i | \(-0.558522\pi\) |
0.668690 | + | 0.743541i | \(0.266855\pi\) | |||||||
\(432\) | 11.5941 | − | 10.1677i | 0.557821 | − | 0.489196i | ||||
\(433\) | 2.47687 | − | 5.97968i | 0.119031 | − | 0.287365i | −0.853123 | − | 0.521710i | \(-0.825294\pi\) |
0.972154 | + | 0.234345i | \(0.0752944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.77782 | − | 13.9650i | −0.133186 | − | 0.669572i | ||||
\(436\) | 2.79340 | + | 0.183089i | 0.133779 | + | 0.00876836i | ||||
\(437\) | −14.3443 | + | 16.3565i | −0.686179 | + | 0.782437i | ||||
\(438\) | −1.06748 | + | 0.286031i | −0.0510062 | + | 0.0136671i | ||||
\(439\) | 19.3112 | + | 9.52324i | 0.921675 | + | 0.454520i | 0.840274 | − | 0.542162i | \(-0.182394\pi\) |
0.0814006 | + | 0.996681i | \(0.474061\pi\) | |||||||
\(440\) | −7.37995 | − | 17.8168i | −0.351825 | − | 0.849382i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.84172 | − | 48.5834i | −0.325427 | − | 2.31088i | ||||
\(443\) | 16.1621 | + | 27.9936i | 0.767886 | + | 1.33002i | 0.938707 | + | 0.344715i | \(0.112024\pi\) |
−0.170822 | + | 0.985302i | \(0.554642\pi\) | |||||||
\(444\) | 0.505612 | − | 3.84051i | 0.0239953 | − | 0.182262i | ||||
\(445\) | −0.343520 | − | 5.24110i | −0.0162844 | − | 0.248452i | ||||
\(446\) | 0.942186 | − | 3.51629i | 0.0446138 | − | 0.166501i | ||||
\(447\) | −0.798681 | + | 4.01524i | −0.0377763 | + | 0.189914i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1303 | + | 4.20309i | −0.997203 | + | 0.198356i | −0.666601 | − | 0.745415i | \(-0.732252\pi\) |
−0.330601 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(450\) | −1.37967 | − | 10.4797i | −0.0650385 | − | 0.494016i | ||||
\(451\) | 1.04134 | − | 0.799046i | 0.0490346 | − | 0.0376256i | ||||
\(452\) | −21.0595 | − | 7.14875i | −0.990557 | − | 0.336249i | ||||
\(453\) | −0.205035 | + | 3.12823i | −0.00963340 | + | 0.146977i | ||||
\(454\) | −2.50597 | − | 0.498468i | −0.117611 | − | 0.0233943i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.31062 | + | 3.45809i | 0.108205 | + | 0.161940i | ||||
\(457\) | −3.35760 | − | 2.57638i | −0.157062 | − | 0.120518i | 0.527241 | − | 0.849716i | \(-0.323227\pi\) |
−0.684303 | + | 0.729198i | \(0.739893\pi\) | |||||||
\(458\) | 8.08007 | − | 13.9951i | 0.377557 | − | 0.653948i | ||||
\(459\) | 12.5474 | − | 2.61349i | 0.585661 | − | 0.121987i | ||||
\(460\) | −11.3745 | + | 6.56708i | −0.530339 | + | 0.306192i | ||||
\(461\) | −33.5138 | + | 13.8819i | −1.56089 | + | 0.646544i | −0.985245 | − | 0.171152i | \(-0.945251\pi\) |
−0.575650 | + | 0.817696i | \(0.695251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.81782 | − | 9.81782i | 0.456273 | − | 0.456273i | −0.441157 | − | 0.897430i | \(-0.645432\pi\) |
0.897430 | + | 0.441157i | \(0.145432\pi\) | |||||||
\(464\) | −15.5383 | − | 45.7742i | −0.721346 | − | 2.12502i | ||||
\(465\) | −0.496551 | − | 1.00691i | −0.0230270 | − | 0.0466941i | ||||
\(466\) | −1.04469 | + | 3.07756i | −0.0483943 | + | 0.142565i | ||||
\(467\) | −35.1543 | + | 4.62815i | −1.62675 | + | 0.214165i | −0.888009 | − | 0.459826i | \(-0.847912\pi\) |
−0.738739 | + | 0.673991i | \(0.764578\pi\) | |||||||
\(468\) | −19.9025 | − | 8.24390i | −0.919995 | − | 0.381074i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 22.8679 | − | 34.2243i | 1.05482 | − | 1.57865i | ||||
\(471\) | −3.57484 | + | 1.21350i | −0.164720 | + | 0.0559150i | ||||
\(472\) | 2.21701 | + | 8.27398i | 0.102046 | + | 0.380841i | ||||
\(473\) | −5.19873 | + | 0.340743i | −0.239038 | + | 0.0156674i | ||||
\(474\) | 7.18008 | − | 9.35726i | 0.329792 | − | 0.429793i | ||||
\(475\) | 11.6311 | 0.533670 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.94598 | −0.226461 | ||||||||
\(478\) | 5.19605 | − | 6.77162i | 0.237662 | − | 0.309727i | ||||
\(479\) | −11.5459 | + | 0.756757i | −0.527545 | + | 0.0345771i | −0.326849 | − | 0.945077i | \(-0.605987\pi\) |
−0.200696 | + | 0.979654i | \(0.564320\pi\) | |||||||
\(480\) | 2.26992 | + | 8.47145i | 0.103607 | + | 0.386667i | ||||
\(481\) | 37.3881 | − | 12.6915i | 1.70475 | − | 0.578684i | ||||
\(482\) | 14.3682 | − | 21.5036i | 0.654456 | − | 0.979462i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6488 | + | 6.48193i | 0.711307 | + | 0.294633i | ||||
\(485\) | 26.6885 | − | 3.51361i | 1.21186 | − | 0.159545i | ||||
\(486\) | 7.37000 | − | 21.7113i | 0.334310 | − | 0.984846i | ||||
\(487\) | 11.9424 | + | 24.2167i | 0.541160 | + | 1.09736i | 0.980037 | + | 0.198817i | \(0.0637099\pi\) |
−0.438876 | + | 0.898547i | \(0.644623\pi\) | |||||||
\(488\) | 0.699104 | + | 2.05949i | 0.0316470 | + | 0.0932289i | ||||
\(489\) | −4.86221 | + | 4.86221i | −0.219877 | + | 0.219877i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.96262 | + | 2.46980i | −0.269089 | + | 0.111460i | −0.513148 | − | 0.858300i | \(-0.671521\pi\) |
0.244059 | + | 0.969760i | \(0.421521\pi\) | |||||||
\(492\) | −0.148002 | + | 0.0854491i | −0.00667245 | + | 0.00385234i | ||||
\(493\) | 7.48282 | − | 39.4730i | 0.337009 | − | 1.77778i | ||||
\(494\) | 31.6437 | − | 54.8086i | 1.42372 | − | 2.46595i | ||||
\(495\) | −28.8248 | − | 22.1180i | −1.29558 | − | 0.994131i | ||||
\(496\) | −2.11754 | − | 3.16913i | −0.0950804 | − | 0.142298i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.7670 | − | 2.53952i | −0.572104 | − | 0.113798i | ||||
\(499\) | −2.12358 | + | 32.3996i | −0.0950647 | + | 1.45041i | 0.637889 | + | 0.770128i | \(0.279808\pi\) |
−0.732954 | + | 0.680278i | \(0.761859\pi\) | |||||||
\(500\) | −8.55324 | − | 2.90343i | −0.382513 | − | 0.129846i | ||||
\(501\) | 5.78237 | − | 4.43697i | 0.258337 | − | 0.198229i | ||||
\(502\) | 7.29337 | + | 55.3987i | 0.325519 | + | 2.47256i | ||||
\(503\) | −27.8736 | + | 5.54441i | −1.24282 | + | 0.247213i | −0.772348 | − | 0.635200i | \(-0.780918\pi\) |
−0.470476 | + | 0.882413i | \(0.655918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.72428 | − | 13.6959i | 0.121229 | − | 0.609459i | ||||
\(506\) | −9.49271 | + | 35.4273i | −0.422002 | + | 1.57493i | ||||
\(507\) | 1.11514 | + | 17.0137i | 0.0495250 | + | 0.755606i | ||||
\(508\) | 0.233724 | − | 1.77531i | 0.0103698 | − | 0.0787666i | ||||
\(509\) | −18.1377 | − | 31.4154i | −0.803939 | − | 1.39246i | −0.917005 | − | 0.398876i | \(-0.869400\pi\) |
0.113065 | − | 0.993588i | \(-0.463933\pi\) | |||||||
\(510\) | −2.69465 | + | 10.4314i | −0.119321 | + | 0.461911i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.94712 | + | 14.3576i | 0.262828 | + | 0.634523i | ||||
\(513\) | 14.8276 | + | 7.31217i | 0.654656 | + | 0.322840i | ||||
\(514\) | −38.6192 | + | 10.3480i | −1.70342 | + | 0.456430i | ||||
\(515\) | 11.3317 | − | 12.9213i | 0.499333 | − | 0.569380i | ||||
\(516\) | 0.676877 | + | 0.0443649i | 0.0297979 | + | 0.00195306i | ||||
\(517\) | −8.39907 | − | 42.2250i | −0.369391 | − | 1.85705i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.739659 | + | 1.78570i | −0.0324674 | + | 0.0783834i | ||||
\(520\) | −19.2419 | + | 16.8747i | −0.843811 | + | 0.740003i | ||||
\(521\) | 23.7780 | − | 11.7260i | 1.04173 | − | 0.513726i | 0.160811 | − | 0.986985i | \(-0.448589\pi\) |
0.880923 | + | 0.473259i | \(0.156922\pi\) | |||||||
\(522\) | −35.4093 | − | 31.0531i | −1.54982 | − | 1.35916i | ||||
\(523\) | −20.1594 | − | 5.40169i | −0.881508 | − | 0.236199i | −0.210450 | − | 0.977605i | \(-0.567493\pi\) |
−0.671058 | + | 0.741405i | \(0.734160\pi\) | |||||||
\(524\) | −3.57500 | + | 2.38874i | −0.156174 | + | 0.104352i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.5848i | 0.548721i | ||||||||
\(527\) | −0.235639 | − | 3.15902i | −0.0102646 | − | 0.137609i | ||||
\(528\) | 11.7421 | + | 6.77930i | 0.511009 | + | 0.295031i | ||||
\(529\) | 6.21435 | + | 0.818134i | 0.270189 | + | 0.0355711i | ||||
\(530\) | 3.87990 | − | 7.86766i | 0.168532 | − | 0.341749i | ||||
\(531\) | 11.4115 | + | 11.4115i | 0.495215 | + | 0.495215i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.44837 | − | 0.967768i | −0.0627358 | − | 0.0419187i | ||||
\(534\) | 1.25913 | + | 1.43576i | 0.0544879 | + | 0.0621316i | ||||
\(535\) | 8.84275 | + | 11.5241i | 0.382305 | + | 0.498230i | ||||
\(536\) | −10.8013 | − | 14.0765i | −0.466543 | − | 0.608011i | ||||
\(537\) | 3.08104 | + | 3.51326i | 0.132957 | + | 0.151608i | ||||
\(538\) | 6.25061 | + | 4.17652i | 0.269483 | + | 0.180063i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.05770 | + | 7.05770i | 0.303715 | + | 0.303715i | ||||
\(541\) | 15.4385 | − | 31.3062i | 0.663752 | − | 1.34596i | −0.260982 | − | 0.965344i | \(-0.584046\pi\) |
0.924734 | − | 0.380613i | \(-0.124287\pi\) | |||||||
\(542\) | 7.61640 | + | 1.00272i | 0.327152 | + | 0.0430704i | ||||
\(543\) | −2.40350 | − | 1.38766i | −0.103144 | − | 0.0595502i | ||||
\(544\) | −3.00900 | + | 24.5628i | −0.129010 | + | 1.05312i | ||||
\(545\) | − | 6.26581i | − | 0.268398i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.70359 | − | 2.47466i | 0.158354 | − | 0.105809i | −0.473869 | − | 0.880596i | \(-0.657143\pi\) |
0.632223 | + | 0.774787i | \(0.282143\pi\) | |||||||
\(548\) | 5.64706 | + | 1.51313i | 0.241231 | + | 0.0646376i | ||||
\(549\) | 3.08073 | + | 2.70172i | 0.131482 | + | 0.115307i | ||||
\(550\) | 17.5865 | − | 8.67270i | 0.749891 | − | 0.369805i | ||||
\(551\) | 38.9635 | − | 34.1701i | 1.65990 | − | 1.45569i | ||||
\(552\) | −1.22409 | + | 2.95521i | −0.0521007 | + | 0.125782i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.35492 | + | 21.8937i | 0.185023 | + | 0.930172i | ||||
\(555\) | −8.65173 | − | 0.567064i | −0.367245 | − | 0.0240705i | ||||
\(556\) | −4.21516 | + | 4.80647i | −0.178763 | + | 0.203840i | ||||
\(557\) | 8.03526 | − | 2.15304i | 0.340465 | − | 0.0912273i | −0.0845355 | − | 0.996420i | \(-0.526941\pi\) |
0.425000 | + | 0.905193i | \(0.360274\pi\) | |||||||
\(558\) | −3.33053 | − | 1.64243i | −0.140992 | − | 0.0695297i | ||||
\(559\) | 2.64591 | + | 6.38780i | 0.111910 | + | 0.270175i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.72206 | + | 9.70795i | 0.241585 | + | 0.409870i | ||||
\(562\) | −6.82152 | − | 11.8152i | −0.287749 | − | 0.498395i | ||||
\(563\) | −4.71686 | + | 35.8281i | −0.198792 | + | 1.50998i | 0.543221 | + | 0.839590i | \(0.317205\pi\) |
−0.742013 | + | 0.670386i | \(0.766129\pi\) | |||||||
\(564\) | 0.366612 | + | 5.59342i | 0.0154372 | + | 0.235526i | ||||
\(565\) | −12.8837 | + | 48.0827i | −0.542022 | + | 2.02285i | ||||
\(566\) | −2.50068 | + | 12.5718i | −0.105111 | + | 0.528430i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.69154 | − | 1.33103i | 0.280771 | − | 0.0558488i | ||||
\(569\) | −1.10714 | − | 8.40959i | −0.0464139 | − | 0.352549i | −0.998856 | − | 0.0478277i | \(-0.984770\pi\) |
0.952442 | − | 0.304721i | \(-0.0985632\pi\) | |||||||
\(570\) | −11.0256 | + | 8.46026i | −0.461813 | + | 0.354361i | ||||
\(571\) | −19.1472 | − | 6.49961i | −0.801287 | − | 0.272000i | −0.109392 | − | 0.993999i | \(-0.534891\pi\) |
−0.691895 | + | 0.721998i | \(0.743224\pi\) | |||||||
\(572\) | 2.61373 | − | 39.8779i | 0.109286 | − | 1.66738i | ||||
\(573\) | 13.1862 | + | 2.62289i | 0.550860 | + | 0.109573i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.96984 | + | 7.43789i | 0.207257 | + | 0.310181i | ||||
\(576\) | 1.73882 | + | 1.33425i | 0.0724510 | + | 0.0555936i | ||||
\(577\) | 18.0046 | − | 31.1850i | 0.749543 | − | 1.29825i | −0.198499 | − | 0.980101i | \(-0.563607\pi\) |
0.948042 | − | 0.318146i | \(-0.103060\pi\) | |||||||
\(578\) | −18.0688 | + | 24.4471i | −0.751565 | + | 1.01686i | ||||
\(579\) | −9.63945 | + | 5.56534i | −0.400602 | + | 0.231288i | ||||
\(580\) | 28.9058 | − | 11.9732i | 1.20025 | − | 0.497159i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.92063 | + | 6.92063i | −0.286869 | + | 0.286869i | ||||
\(583\) | −2.94932 | − | 8.68841i | −0.122148 | − | 0.359837i | ||||
\(584\) | 0.719434 | + | 1.45887i | 0.0297704 | + | 0.0603684i | ||||
\(585\) | −15.4991 | + | 45.6588i | −0.640808 | + | 1.88776i | ||||
\(586\) | −10.4080 | + | 1.37024i | −0.429951 | + | 0.0566041i | ||||
\(587\) | −18.6945 | − | 7.74352i | −0.771605 | − | 0.319609i | −0.0380824 | − | 0.999275i | \(-0.512125\pi\) |
−0.733522 | + | 0.679666i | \(0.762125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27019 | − | 3.39757i | 0.0935414 | − | 0.139995i | ||||
\(590\) | −27.1042 | + | 9.20062i | −1.11586 | + | 0.378784i | ||||
\(591\) | −1.20569 | − | 4.49970i | −0.0495955 | − | 0.185093i | ||||
\(592\) | −29.3723 | + | 1.92516i | −1.20719 | + | 0.0791237i | ||||
\(593\) | −15.1704 | + | 19.7704i | −0.622973 | + | 0.811874i | −0.993120 | − | 0.117099i | \(-0.962640\pi\) |
0.370148 | + | 0.928973i | \(0.379307\pi\) | |||||||
\(594\) | 27.8721 | 1.14361 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.99580 | −0.368482 | ||||||||
\(597\) | −5.39292 | + | 7.02818i | −0.220717 | + | 0.287644i | ||||
\(598\) | 48.5703 | − | 3.18347i | 1.98619 | − | 0.130182i | ||||
\(599\) | −2.94729 | − | 10.9994i | −0.120423 | − | 0.449425i | 0.879212 | − | 0.476430i | \(-0.158070\pi\) |
−0.999635 | + | 0.0270052i | \(0.991403\pi\) | |||||||
\(600\) | 1.61937 | − | 0.549702i | 0.0661105 | − | 0.0224415i | ||||
\(601\) | 10.4548 | − | 15.6467i | 0.426460 | − | 0.638243i | −0.554561 | − | 0.832143i | \(-0.687114\pi\) |
0.981021 | + | 0.193900i | \(0.0621138\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.8836 | − | 12.7924i | −1.25768 | − | 0.520947i | ||||
\(604\) | −6.82969 | + | 0.899145i | −0.277896 | + | 0.0365857i | ||||
\(605\) | 12.1865 | − | 35.9002i | 0.495450 | − | 1.45955i | ||||
\(606\) | 2.24557 | + | 4.55356i | 0.0912200 | + | 0.184976i | ||||
\(607\) | −11.7318 | − | 34.5608i | −0.476179 | − | 1.40278i | −0.874274 | − | 0.485433i | \(-0.838662\pi\) |
0.398095 | − | 0.917344i | \(-0.369672\pi\) | |||||||
\(608\) | −22.5717 | + | 22.5717i | −0.915402 | + | 0.915402i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.71437 | + | 2.78118i | −0.271857 | + | 0.112607i | ||||
\(611\) | −49.4805 | + | 28.5676i | −2.00177 | + | 1.15572i | ||||
\(612\) | 5.21883 | + | 12.2853i | 0.210959 | + | 0.496603i | ||||
\(613\) | 1.74342 | − | 3.01970i | 0.0704162 | − | 0.121965i | −0.828668 | − | 0.559741i | \(-0.810901\pi\) |
0.899084 | + | 0.437777i | \(0.144234\pi\) | |||||||
\(614\) | 34.1683 | + | 26.2183i | 1.37892 | + | 1.05808i | ||||
\(615\) | 0.212515 | + | 0.318052i | 0.00856944 | + | 0.0128251i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.2155 | + | 9.19283i | 1.86057 | + | 0.370089i | 0.992078 | − | 0.125622i | \(-0.0400928\pi\) |
0.868487 | + | 0.495712i | \(0.165093\pi\) | |||||||
\(618\) | −0.408681 | + | 6.23526i | −0.0164395 | + | 0.250819i | ||||
\(619\) | 3.78417 | + | 1.28455i | 0.152098 | + | 0.0516305i | 0.396450 | − | 0.918056i | \(-0.370242\pi\) |
−0.244352 | + | 0.969687i | \(0.578575\pi\) | |||||||
\(620\) | 1.95716 | − | 1.50178i | 0.0786015 | − | 0.0603130i | ||||
\(621\) | 1.65967 | + | 12.6065i | 0.0666003 | + | 0.505880i | ||||
\(622\) | −5.67381 | + | 1.12859i | −0.227499 | + | 0.0452524i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.51041 | − | 17.6480i | 0.140529 | − | 0.706487i | ||||
\(625\) | −8.06272 | + | 30.0905i | −0.322509 | + | 1.20362i | ||||
\(626\) | −0.775173 | − | 11.8269i | −0.0309821 | − | 0.472696i | ||||
\(627\) | −1.89733 | + | 14.4116i | −0.0757719 | + | 0.575545i | ||||
\(628\) | −4.14774 | − | 7.18409i | −0.165513 | − | 0.286677i | ||||
\(629\) | −22.0379 | − | 10.6223i | −0.878708 | − | 0.423537i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.89828 | − | 4.58286i | −0.0755694 | − | 0.182441i | 0.881580 | − | 0.472034i | \(-0.156480\pi\) |
−0.957150 | + | 0.289593i | \(0.906480\pi\) | |||||||
\(632\) | −15.5698 | − | 7.67815i | −0.619332 | − | 0.305421i | ||||
\(633\) | 5.23101 | − | 1.40165i | 0.207914 | − | 0.0557104i | ||||
\(634\) | 13.3793 | − | 15.2562i | 0.531360 | − | 0.605900i | ||||
\(635\) | −3.99934 | − | 0.262131i | −0.158709 | − | 0.0104023i | ||||
\(636\) | 0.233062 | + | 1.17168i | 0.00924150 | + | 0.0464602i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 33.4350 | − | 80.7193i | 1.32370 | − | 3.19571i | ||||
\(639\) | 9.66413 | − | 8.47521i | 0.382307 | − | 0.335274i | ||||
\(640\) | 25.3751 | − | 12.5136i | 1.00304 | − | 0.494645i | ||||
\(641\) | −25.0628 | − | 21.9795i | −0.989921 | − | 0.868138i | 0.00134697 | − | 0.999999i | \(-0.499571\pi\) |
−0.991268 | + | 0.131862i | \(0.957905\pi\) | |||||||
\(642\) | −5.10139 | − | 1.36691i | −0.201336 | − | 0.0539477i | ||||
\(643\) | 27.9715 | − | 18.6900i | 1.10309 | − | 0.737061i | 0.135800 | − | 0.990736i | \(-0.456639\pi\) |
0.967289 | + | 0.253675i | \(0.0816394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.51829i | − | 0.0597826i | ||||||
\(646\) | −37.7844 | + | 10.4899i | −1.48661 | + | 0.412718i | ||||
\(647\) | 30.0850 | + | 17.3696i | 1.18276 | + | 0.682868i | 0.956652 | − | 0.291234i | \(-0.0940658\pi\) |
0.226110 | + | 0.974102i | \(0.427399\pi\) | |||||||
\(648\) | −9.12355 | − | 1.20114i | −0.358407 | − | 0.0471852i | ||||
\(649\) | −13.2413 | + | 26.8508i | −0.519768 | + | 1.05398i | ||||
\(650\) | −18.4010 | − | 18.4010i | −0.721747 | − | 0.721747i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.5631 | − | 8.39441i | −0.492010 | − | 0.328750i | ||||
\(653\) | −23.6554 | − | 26.9739i | −0.925709 | − | 1.05557i | −0.998305 | − | 0.0582070i | \(-0.981462\pi\) |
0.0725958 | − | 0.997361i | \(-0.476872\pi\) | |||||||
\(654\) | 1.38685 | + | 1.80738i | 0.0542300 | + | 0.0706740i | ||||
\(655\) | 5.85855 | + | 7.63501i | 0.228913 | + | 0.298325i | ||||
\(656\) | 0.856248 | + | 0.976364i | 0.0334309 | + | 0.0381206i | ||||
\(657\) | 2.54810 | + | 1.70259i | 0.0994109 | + | 0.0664242i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.30369 | − | 4.30369i | −0.167648 | − | 0.167648i | 0.618297 | − | 0.785945i | \(-0.287823\pi\) |
−0.785945 | + | 0.618297i | \(0.787823\pi\) | |||||||
\(660\) | −3.88139 | + | 7.87068i | −0.151083 | + | 0.306366i | ||||
\(661\) | −32.7821 | − | 4.31585i | −1.27508 | − | 0.167867i | −0.537577 | − | 0.843215i | \(-0.680660\pi\) |
−0.737499 | + | 0.675348i | \(0.763994\pi\) | |||||||
\(662\) | 38.0477 | + | 21.9668i | 1.47877 | + | 0.853766i | ||||
\(663\) | 9.75887 | − | 11.3321i | 0.379003 | − | 0.440102i | ||||
\(664\) | 19.1595i | 0.743533i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.8454 | + | 15.9330i | −0.923990 | + | 0.617390i | ||||
\(667\) | 38.5000 | + | 10.3160i | 1.49072 | + | 0.399438i | ||||
\(668\) | 12.0411 | + | 10.5598i | 0.465885 | + | 0.408570i | ||||
\(669\) | 0.995189 | − | 0.490773i | 0.0384762 | − | 0.0189744i | ||||
\(670\) | 44.5759 | − | 39.0920i | 1.72212 | − | 1.51025i | ||||
\(671\) | −2.90896 | + | 7.02284i | −0.112299 | + | 0.271114i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.94208 | − | 19.8182i | −0.151956 | − | 0.763934i | −0.979328 | − | 0.202279i | \(-0.935165\pi\) |
0.827372 | − | 0.561654i | \(-0.189835\pi\) | |||||||
\(674\) | −9.12121 | − | 0.597835i | −0.351336 | − | 0.0230278i | ||||
\(675\) | 4.48221 | − | 5.11098i | 0.172520 | − | 0.196722i | ||||
\(676\) | −36.1890 | + | 9.69680i | −1.39188 | + | 0.372954i | ||||
\(677\) | 23.0645 | + | 11.3742i | 0.886441 | + | 0.437144i | 0.827727 | − | 0.561131i | \(-0.189633\pi\) |
0.0587135 | + | 0.998275i | \(0.481300\pi\) | |||||||
\(678\) | −6.92610 | − | 16.7211i | −0.265995 | − | 0.642170i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.8324 | + | 0.894614i | 0.607145 | + | 0.0343069i | ||||
\(681\) | −0.389409 | − | 0.674476i | −0.0149222 | − | 0.0258460i | ||||
\(682\) | 0.899186 | − | 6.82999i | 0.0344316 | − | 0.261534i | ||||
\(683\) | 1.71419 | + | 26.1535i | 0.0655916 | + | 1.00073i | 0.896135 | + | 0.443781i | \(0.146363\pi\) |
−0.830544 | + | 0.556953i | \(0.811970\pi\) | |||||||
\(684\) | −4.45628 | + | 16.6311i | −0.170390 | + | 0.635905i | ||||
\(685\) | 2.55287 | − | 12.8341i | 0.0975401 | − | 0.490367i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.83118 | − | 0.960982i | 0.184321 | − | 0.0366637i | ||||
\(688\) | −0.672803 | − | 5.11044i | −0.0256504 | − | 0.194834i | ||||
\(689\) | −9.66044 | + | 7.41272i | −0.368033 | + | 0.282402i | ||||
\(690\) | −10.1213 | − | 3.43574i | −0.385313 | − | 0.130796i | ||||
\(691\) | 2.59734 | − | 39.6277i | 0.0988073 | − | 1.50751i | −0.604490 | − | 0.796613i | \(-0.706623\pi\) |
0.703298 | − | 0.710896i | \(-0.251710\pi\) | |||||||
\(692\) | −4.16551 | − | 0.828572i | −0.158349 | − | 0.0314976i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.8901 | + | 31.2642i | 0.792975 | + | 1.18677i | ||||
\(695\) | 11.3522 | + | 8.71088i | 0.430615 | + | 0.330423i | ||||
\(696\) | 3.80988 | − | 6.59890i | 0.144413 | − | 0.250131i | ||||
\(697\) | 0.220088 | + | 1.05664i | 0.00833644 | + | 0.0400232i | ||||
\(698\) | −43.8691 | + | 25.3279i | −1.66047 | + | 0.958673i | ||||
\(699\) | −0.915246 | + | 0.379107i | −0.0346178 | + | 0.0143392i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.39878 | − | 9.39878i | 0.354987 | − | 0.354987i | −0.506974 | − | 0.861961i | \(-0.669236\pi\) |
0.861961 | + | 0.506974i | \(0.169236\pi\) | |||||||
\(702\) | −11.8899 | − | 35.0264i | −0.448754 | − | 1.32199i | ||||
\(703\) | −13.9574 | − | 28.3028i | −0.526413 | − | 1.06746i | ||||
\(704\) | −1.30695 | + | 3.85014i | −0.0492574 | + | 0.145108i | ||||
\(705\) | 12.4392 | − | 1.63765i | 0.468486 | − | 0.0616773i | ||||
\(706\) | −9.45764 | − | 3.91748i | −0.355943 | − | 0.147436i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.16560 | − | 3.24104i | 0.0813881 | − | 0.121806i | ||||
\(709\) | 40.2328 | − | 13.6572i | 1.51098 | − | 0.512907i | 0.561697 | − | 0.827343i | \(-0.310149\pi\) |
0.949279 | + | 0.314436i | \(0.101815\pi\) | |||||||
\(710\) | 5.90059 | + | 22.0213i | 0.221445 | + | 0.826445i | ||||
\(711\) | −32.6366 | + | 2.13912i | −1.22397 | + | 0.0802232i | ||||
\(712\) | 1.71109 | − | 2.22994i | 0.0641259 | − | 0.0835705i | ||||
\(713\) | 3.14273 | 0.117696 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −89.4492 | −3.34521 | ||||||||
\(716\) | −6.25078 | + | 8.14617i | −0.233602 | + | 0.304437i | ||||
\(717\) | 2.59615 | − | 0.170161i | 0.0969550 | − | 0.00635476i | ||||
\(718\) | −10.2561 | − | 38.2763i | −0.382755 | − | 1.42846i | ||||
\(719\) | 19.0741 | − | 6.47478i | 0.711343 | − | 0.241468i | 0.0577679 | − | 0.998330i | \(-0.481602\pi\) |
0.653575 | + | 0.756862i | \(0.273268\pi\) | |||||||
\(720\) | 19.9710 | − | 29.8887i | 0.744275 | − | 1.11389i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.3424 | − | 6.35503i | −0.570985 | − | 0.236510i | ||||
\(723\) | 7.81570 | − | 1.02896i | 0.290669 | − | 0.0382673i | ||||
\(724\) | 1.96026 | − | 5.77475i | 0.0728526 | − | 0.214617i | ||||
\(725\) | −9.42491 | − | 19.1118i | −0.350032 | − | 0.709795i | ||||
\(726\) | 4.43080 | + | 13.0527i | 0.164442 | + | 0.484432i | ||||
\(727\) | −15.6585 | + | 15.6585i | −0.580743 | + | 0.580743i | −0.935107 | − | 0.354364i | \(-0.884697\pi\) |
0.354364 | + | 0.935107i | \(0.384697\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.3214 | + | 4.68947i | −0.419311 | + | 0.173684i | ||||
\(730\) | −4.70720 | + | 2.71770i | −0.174221 | + | 0.100587i | ||||
\(731\) | 1.60373 | − | 3.97254i | 0.0593159 | − | 0.146930i | ||||
\(732\) | 0.494858 | − | 0.857119i | 0.0182905 | − | 0.0316800i | ||||
\(733\) | 26.1840 | + | 20.0917i | 0.967127 | + | 0.742103i | 0.966173 | − | 0.257897i | \(-0.0830294\pi\) |
0.000954952 | 1.00000i | \(0.499696\pi\) | ||||||||
\(734\) | −27.5000 | − | 41.1567i | −1.01505 | − | 1.51912i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0789 | − | 4.78959i | −0.887560 | − | 0.176547i | ||||
\(737\) | 4.05584 | − | 61.8801i | 0.149399 | − | 2.27938i | ||||
\(738\) | 1.19810 | + | 0.406700i | 0.0441027 | + | 0.0149708i | ||||
\(739\) | −18.3573 | + | 14.0860i | −0.675282 | + | 0.518162i | −0.888520 | − | 0.458838i | \(-0.848266\pi\) |
0.213238 | + | 0.977000i | \(0.431599\pi\) | |||||||
\(740\) | −2.48676 | − | 18.8888i | −0.0914150 | − | 0.694366i | ||||
\(741\) | 18.9202 | − | 3.76346i | 0.695051 | − | 0.138254i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.30776 | + | 21.6566i | −0.158037 | + | 0.794503i | 0.817715 | + | 0.575623i | \(0.195240\pi\) |
−0.975752 | + | 0.218880i | \(0.929760\pi\) | |||||||
\(744\) | 0.155499 | − | 0.580330i | 0.00570087 | − | 0.0212759i | ||||
\(745\) | 1.31690 | + | 20.0920i | 0.0482474 | + | 0.736114i | ||||
\(746\) | −6.09375 | + | 46.2866i | −0.223108 | + | 1.69467i | ||||
\(747\) | 18.0484 | + | 31.2608i | 0.660357 | + | 1.14377i | ||||
\(748\) | −18.4691 | + | 16.4935i | −0.675296 | + | 0.603062i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.81301 | − | 6.79120i | −0.102717 | − | 0.247980i | ||||
\(751\) | 2.28253 | + | 1.12562i | 0.0832908 | + | 0.0410745i | 0.483457 | − | 0.875368i | \(-0.339381\pi\) |
−0.400166 | + | 0.916443i | \(0.631048\pi\) | |||||||
\(752\) | 41.1435 | − | 11.0244i | 1.50035 | − | 0.402017i | ||||
\(753\) | −11.2300 | + | 12.8053i | −0.409242 | + | 0.466652i | ||||
\(754\) | −115.701 | − | 7.58347i | −4.21360 | − | 0.276174i | ||||
\(755\) | 3.00803 | + | 15.1224i | 0.109473 | + | 0.550360i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.2277 | + | 34.3488i | −0.517115 | + | 1.24843i | 0.422552 | + | 0.906339i | \(0.361134\pi\) |
−0.939668 | + | 0.342089i | \(0.888866\pi\) | |||||||
\(758\) | −8.99166 | + | 7.88547i | −0.326592 | + | 0.286413i | ||||
\(759\) | −10.0267 | + | 4.94463i | −0.363947 | + | 0.179479i | ||||
\(760\) | 15.3791 | + | 13.4871i | 0.557858 | + | 0.489229i | ||||
\(761\) | −2.80595 | − | 0.751851i | −0.101715 | − | 0.0272546i | 0.207602 | − | 0.978213i | \(-0.433434\pi\) |
−0.309318 | + | 0.950959i | \(0.600101\pi\) | |||||||
\(762\) | 1.21163 | − | 0.809585i | 0.0438927 | − | 0.0293282i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 29.5425i | 1.06881i | ||||||||
\(765\) | 26.6750 | − | 13.4546i | 0.964438 | − | 0.486453i | ||||
\(766\) | −22.6156 | − | 13.0571i | −0.817135 | − | 0.471773i | ||||
\(767\) | 39.3915 | + | 5.18598i | 1.42234 | + | 0.187255i | ||||
\(768\) | −4.94073 | + | 10.0188i | −0.178283 | + | 0.361523i | ||||
\(769\) | −22.1893 | − | 22.1893i | −0.800166 | − | 0.800166i | 0.182955 | − | 0.983121i | \(-0.441434\pi\) |
−0.983121 | + | 0.182955i | \(0.941434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1330 | − | 6.77069i | −0.364933 | − | 0.243840i | ||||
\(772\) | −16.1264 | − | 18.3886i | −0.580401 | − | 0.661821i | ||||
\(773\) | 2.17164 | + | 2.83013i | 0.0781084 | + | 0.101793i | 0.830773 | − | 0.556611i | \(-0.187899\pi\) |
−0.752665 | + | 0.658404i | \(0.771232\pi\) | |||||||
\(774\) | −3.05721 | − | 3.98424i | −0.109889 | − | 0.143211i | ||||
\(775\) | −1.10783 | − | 1.26324i | −0.0397946 | − | 0.0453770i | ||||
\(776\) | 11.9778 | + | 8.00328i | 0.429976 | + | 0.287301i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.9696 | + | 15.9696i | 0.572538 | + | 0.572538i | ||||
\(779\) | −0.615775 | + | 1.24867i | −0.0220624 | + | 0.0447382i | ||||
\(780\) | 11.5467 | + | 1.52015i | 0.413438 | + | 0.0544302i | ||||
\(781\) | 20.6508 | + | 11.9228i | 0.738945 | + | 0.426630i | ||||
\(782\) | −22.8530 | − | 19.6803i | −0.817222 | − | 0.703767i | ||||
\(783\) | − | 30.2895i | − | 1.08246i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4384 | + | 10.3156i | −0.551019 | + | 0.368179i | ||||
\(786\) | −3.37980 | − | 0.905616i | −0.120554 | − | 0.0323022i | ||||
\(787\) | −32.3353 | − | 28.3573i | −1.15263 | − | 1.01083i | −0.999745 | − | 0.0225862i | \(-0.992810\pi\) |
−0.152886 | − | 0.988244i | \(-0.548857\pi\) | |||||||
\(788\) | 9.18064 | − | 4.52739i | 0.327047 | − | 0.161282i | ||||
\(789\) | −2.88406 | + | 2.52925i | −0.102675 | + | 0.0900438i | ||||
\(790\) | 22.1992 | − | 53.5937i | 0.789813 | − | 1.90678i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.79322 | − | 19.0698i | −0.134786 | − | 0.677616i | ||||
\(793\) | 10.0664 | + | 0.659787i | 0.357469 | + | 0.0234297i | ||||
\(794\) | 4.51366 | − | 5.14685i | 0.160184 | − | 0.182655i | ||||
\(795\) | 2.58281 | − | 0.692063i | 0.0916029 | − | 0.0245449i | ||||
\(796\) | −17.4586 | − | 8.60963i | −0.618804 | − | 0.305160i | ||||
\(797\) | −4.78470 | − | 11.5513i | −0.169483 | − | 0.409168i | 0.816202 | − | 0.577767i | \(-0.196076\pi\) |
−0.985685 | + | 0.168599i | \(0.946076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.2763 | + | 8.85429i | 1.21261 | + | 0.313242i | ||||
\(800\) | 6.56277 | + | 11.3671i | 0.232029 | + | 0.401886i | ||||
\(801\) | 0.691209 | − | 5.25025i | 0.0244227 | − | 0.185509i | ||||
\(802\) | 1.38936 | + | 21.1975i | 0.0490599 | + | 0.748510i | ||||
\(803\) | −1.47142 | + | 5.49141i | −0.0519252 | + | 0.193788i | ||||
\(804\) | −1.57518 | + | 7.91897i | −0.0555524 | + | 0.279281i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.96672 | + | 1.78359i | −0.315839 | + | 0.0628243i | ||||
\(807\) | 0.299094 | + | 2.27184i | 0.0105286 | + | 0.0799727i | ||||
\(808\) | 5.92865 | − | 4.54922i | 0.208569 | − | 0.160041i | ||||
\(809\) | 43.1172 | + | 14.6363i | 1.51592 | + | 0.514586i | 0.950636 | − | 0.310309i | \(-0.100432\pi\) |
0.565286 | + | 0.824895i | \(0.308766\pi\) | |||||||
\(810\) | 2.01113 | − | 30.6840i | 0.0706641 | − | 1.07813i | ||||
\(811\) | 22.1324 | + | 4.40241i | 0.777174 | + | 0.154590i | 0.567712 | − | 0.823227i | \(-0.307829\pi\) |
0.209462 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.30093 | + | 1.94698i | 0.0456257 | + | 0.0682836i | ||||
\(814\) | −42.2080 | − | 32.3873i | −1.47939 | − | 1.13517i | ||||
\(815\) | −16.9097 | + | 29.2884i | −0.592320 | + | 1.02593i | ||||
\(816\) | −9.21400 | + | 6.27734i | −0.322554 | + | 0.219751i | ||||
\(817\) | 4.78575 | − | 2.76305i | 0.167432 | − | 0.0966671i | ||||
\(818\) | −4.05755 | + | 1.68069i | −0.141869 | + | 0.0587641i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.594345 | + | 0.594345i | −0.0207554 | + | 0.0207554i | ||||
\(821\) | 13.5948 | + | 40.0489i | 0.474460 | + | 1.39772i | 0.876194 | + | 0.481959i | \(0.160074\pi\) |
−0.401734 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(822\) | 2.10428 | + | 4.26705i | 0.0733951 | + | 0.148831i | ||||
\(823\) | 9.16159 | − | 26.9892i | 0.319353 | − | 0.940783i | −0.662156 | − | 0.749366i | \(-0.730358\pi\) |
0.981509 | − | 0.191417i | \(-0.0613083\pi\) | |||||||
\(824\) | 9.11848 | − | 1.20047i | 0.317657 | − | 0.0418204i | ||||
\(825\) | 5.52202 | + | 2.28730i | 0.192252 | + | 0.0796335i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.50470 | + | 8.23837i | −0.191417 | + | 0.286476i | −0.914747 | − | 0.404026i | \(-0.867610\pi\) |
0.723330 | + | 0.690502i | \(0.242610\pi\) | |||||||
\(828\) | −12.5394 | + | 4.25657i | −0.435776 | + | 0.147926i | ||||
\(829\) | 10.4447 | + | 38.9802i | 0.362760 | + | 1.35384i | 0.870432 | + | 0.492288i | \(0.163839\pi\) |
−0.507672 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(830\) | −63.8852 | + | 4.18726i | −2.21749 | + | 0.145342i | ||||
\(831\) | −4.14215 | + | 5.39815i | −0.143690 | + | 0.187260i | ||||
\(832\) | 5.39593 | 0.187070 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.20259 | −0.180151 | ||||||||
\(835\) | 21.8224 | − | 28.4395i | 0.755195 | − | 0.984190i | ||||
\(836\) | −31.8725 | + | 2.08903i | −1.10233 | + | 0.0722507i | ||||
\(837\) | −0.618128 | − | 2.30689i | −0.0213656 | − | 0.0797377i | ||||
\(838\) | −57.6915 | + | 19.5836i | −1.99292 | + | 0.676506i | ||||
\(839\) | −26.4350 | + | 39.5628i | −0.912637 | + | 1.36586i | 0.0179698 | + | 0.999839i | \(0.494280\pi\) |
−0.930607 | + | 0.366020i | \(0.880720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −60.9278 | − | 25.2371i | −2.10096 | − | 0.870245i | ||||
\(842\) | 1.25864 | − | 0.165703i | 0.0433756 | − | 0.00571050i | ||||
\(843\) | 1.33673 | − | 3.93789i | 0.0460396 | − | 0.135628i | ||||
\(844\) | 5.26320 | + | 10.6727i | 0.181167 | + | 0.367370i | ||||
\(845\) | 26.9554 | + | 79.4080i | 0.927293 | + | 2.73172i | ||||
\(846\) | 29.3448 | − | 29.3448i | 1.00890 | − | 1.00890i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.38687 | − | 3.47395i | 0.288006 | − | 0.119296i | ||||
\(849\) | −3.38366 | + | 1.95356i | −0.116127 | + | 0.0670459i | ||||
\(850\) | 0.145190 | + | 16.1234i | 0.00497996 | + | 0.553028i | ||||
\(851\) | 12.1354 | − | 21.0190i | 0.415995 | − | 0.720524i | ||||
\(852\) | −2.46313 | − | 1.89002i | −0.0843853 | − | 0.0647511i | ||||
\(853\) | 2.30560 | + | 3.45057i | 0.0789422 | + | 0.118145i | 0.868840 | − | 0.495094i | \(-0.164866\pi\) |
−0.789897 | + | 0.613239i | \(0.789866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.7976 | + | 7.51841i | 1.29265 | + | 0.257124i | ||||
\(856\) | −0.508407 | + | 7.75680i | −0.0173770 | + | 0.265122i | ||||
\(857\) | −19.7744 | − | 6.71252i | −0.675482 | − | 0.229295i | −0.0374423 | − | 0.999299i | \(-0.511921\pi\) |
−0.638040 | + | 0.770004i | \(0.720254\pi\) | |||||||
\(858\) | 25.8017 | − | 19.7983i | 0.880855 | − | 0.675904i | ||||
\(859\) | −1.75392 | − | 13.3224i | −0.0598431 | − | 0.454553i | −0.994965 | − | 0.100226i | \(-0.968043\pi\) |
0.935122 | − | 0.354327i | \(-0.115290\pi\) | |||||||
\(860\) | 3.27213 | − | 0.650867i | 0.111579 | − | 0.0221944i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.92361 | + | 19.7253i | −0.133639 | + | 0.671846i | ||||
\(863\) | 6.72620 | − | 25.1025i | 0.228963 | − | 0.854500i | −0.751816 | − | 0.659374i | \(-0.770822\pi\) |
0.980778 | − | 0.195126i | \(-0.0625117\pi\) | |||||||
\(864\) | 1.22022 | + | 18.6169i | 0.0415126 | + | 0.633360i | ||||
\(865\) | −1.24081 | + | 9.42490i | −0.0421889 | + | 0.320456i | ||||
\(866\) | 5.78700 | + | 10.0234i | 0.196650 | + | 0.340608i | ||||
\(867\) | −9.23399 | + | 0.772456i | −0.313603 | + | 0.0262340i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.2191 | − | 56.0559i | −0.787654 | − | 1.90157i | ||||
\(870\) | 22.8360 | + | 11.2614i | 0.774212 | + | 0.381799i | ||||
\(871\) | −79.4939 | + | 21.3003i | −2.69355 | + | 0.721734i | ||||
\(872\) | 2.21087 | − | 2.52102i | 0.0748696 | − | 0.0853724i | ||||
\(873\) | 27.0822 | + | 1.77506i | 0.916593 | + | 0.0600766i | ||||
\(874\) | −7.58964 | − | 38.1557i | −0.256723 | − | 1.29064i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.283265 | − | 0.683861i | 0.00957063 | − | 0.0231055i | ||||
\(877\) | 21.3731 | − | 18.7437i | 0.721717 | − | 0.632929i | −0.217577 | − | 0.976043i | \(-0.569815\pi\) |
0.939294 | + | 0.343114i | \(0.111482\pi\) | |||||||
\(878\) | −34.5327 | + | 17.0296i | −1.16542 | + | 0.574723i | ||||
\(879\) | −2.40579 | − | 2.10982i | −0.0811454 | − | 0.0711626i | ||||
\(880\) | 64.4131 | + | 17.2595i | 2.17137 | + | 0.581816i | ||||
\(881\) | 2.44242 | − | 1.63198i | 0.0822873 | − | 0.0549826i | −0.513746 | − | 0.857942i | \(-0.671743\pi\) |
0.596033 | + | 0.802960i | \(0.296743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.1609i | − | 0.577509i | −0.957403 | − | 0.288755i | \(-0.906759\pi\) | ||
0.957403 | − | 0.288755i | \(-0.0932411\pi\) | |||||||
\(884\) | 28.6057 | + | 16.1739i | 0.962115 | + | 0.543986i | ||||
\(885\) | −7.55584 | − | 4.36237i | −0.253987 | − | 0.146639i | ||||
\(886\) | −57.3083 | − | 7.54478i | −1.92531 | − | 0.253472i | ||||
\(887\) | 3.37950 | − | 6.85296i | 0.113473 | − | 0.230100i | −0.832727 | − | 0.553684i | \(-0.813221\pi\) |
0.946199 | + | 0.323585i | \(0.104888\pi\) | |||||||
\(888\) | −3.28089 | − | 3.28089i | −0.110100 | − | 0.110100i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.80944 | + | 5.21810i | 0.261773 | + | 0.174911i | ||||
\(891\) | −21.2062 | − | 24.1811i | −0.710435 | − | 0.810096i | ||||
\(892\) | 1.48431 | + | 1.93439i | 0.0496983 | + | 0.0647681i | ||||
\(893\) | 27.7993 | + | 36.2288i | 0.930269 | + | 1.21235i | ||||
\(894\) | −4.82694 | − | 5.50407i | −0.161437 | − | 0.184084i | ||||
\(895\) | 19.1094 | + | 12.7685i | 0.638757 | + | 0.426804i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4911 | + | 10.4911i | 0.350288 | + | 0.350288i | ||||
\(898\) | 17.0396 | − | 34.5529i | 0.568618 | − | 1.15304i | ||||
\(899\) | −7.42238 | − | 0.977174i | −0.247550 | − | 0.0325906i | ||||
\(900\) | 6.13121 | + | 3.53985i | 0.204374 | + | 0.117995i | ||||
\(901\) | 7.48882 | + | 0.917398i | 0.249489 | + | 0.0305630i | ||||
\(902\) | 2.34717i | 0.0781523i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.1495 | + | 14.7998i | −0.736682 | + | 0.492235i | ||||
\(905\) | −13.1848 | − | 3.53285i | −0.438277 | − | 0.117436i | ||||
\(906\) | −4.21479 | − | 3.69627i | −0.140027 | − | 0.122800i | ||||
\(907\) | −27.1210 | + | 13.3746i | −0.900539 | + | 0.444097i | −0.832780 | − | 0.553605i | \(-0.813252\pi\) |
−0.0677599 | + | 0.997702i | \(0.521585\pi\) | |||||||
\(908\) | 1.28666 | − | 1.12837i | 0.0426992 | − | 0.0374462i | ||||
\(909\) | 5.38783 | − | 13.0074i | 0.178703 | − | 0.431428i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.758034 | + | 3.81090i | 0.0251148 | + | 0.126261i | 0.991309 | − | 0.131555i | \(-0.0419971\pi\) |
−0.966194 | + | 0.257816i | \(0.916997\pi\) | |||||||
\(912\) | −14.3508 | − | 0.940599i | −0.475202 | − | 0.0311464i | ||||
\(913\) | −44.1522 | + | 50.3459i | −1.46122 | + | 1.66621i | ||||
\(914\) | 7.31016 | − | 1.95875i | 0.241799 | − | 0.0647898i | ||||
\(915\) | −1.98680 | − | 0.979784i | −0.0656817 | − | 0.0323906i | ||||
\(916\) | 4.14211 | + | 9.99993i | 0.136859 | + | 0.330407i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −9.95130 | + | 20.6458i | −0.328442 | + | 0.681415i | ||||
\(919\) | −1.33707 | − | 2.31587i | −0.0441059 | − | 0.0763936i | 0.843130 | − | 0.537710i | \(-0.180711\pi\) |
−0.887236 | + | 0.461317i | \(0.847377\pi\) | |||||||
\(920\) | −2.05346 | + | 15.5976i | −0.0677007 | + | 0.514238i | ||||
\(921\) | 0.858598 | + | 13.0997i | 0.0282918 | + | 0.431649i | ||||
\(922\) | 16.7890 | − | 62.6575i | 0.552917 | − | 2.06351i | ||||
\(923\) | 6.17377 | − | 31.0377i | 0.203212 | − | 1.02162i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.7266 | + | 2.53147i | −0.418447 | + | 0.0832342i | ||||
\(926\) | 3.24077 | + | 24.6161i | 0.106498 | + | 0.808935i | ||||
\(927\) | 13.7469 | − | 10.5484i | 0.451509 | − | 0.346455i | ||||
\(928\) | 55.3794 | + | 18.7988i | 1.81792 | + | 0.617100i | ||||
\(929\) | 0.484105 | − | 7.38602i | 0.0158830 | − | 0.242327i | −0.982534 | − | 0.186083i | \(-0.940421\pi\) |
0.998417 | − | 0.0562445i | \(-0.0179126\pi\) | |||||||
\(930\) | 1.96903 | + | 0.391664i | 0.0645670 | + | 0.0128432i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.20938 | − | 1.80997i | −0.0396146 | − | 0.0592875i | ||||
\(933\) | −1.39895 | − | 1.07345i | −0.0457996 | − | 0.0351432i | ||||
\(934\) | 31.7030 | − | 54.9113i | 1.03735 | − | 1.79675i | ||||
\(935\) | 39.5417 | + | 38.8359i | 1.29315 | + | 1.27007i | ||||
\(936\) | −22.3466 | + | 12.9018i | −0.730420 | + | 0.421708i | ||||
\(937\) | −8.20064 | + | 3.39682i | −0.267903 | + | 0.110969i | −0.512591 | − | 0.858633i | \(-0.671314\pi\) |
0.244688 | + | 0.969602i | \(0.421314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.55458 | − | 2.55458i | 0.0833655 | − | 0.0833655i | ||||
\(940\) | 8.86183 | + | 26.1061i | 0.289041 | + | 0.851488i | ||||
\(941\) | −15.8165 | − | 32.0727i | −0.515603 | − | 1.04554i | −0.986563 | − | 0.163384i | \(-0.947759\pi\) |
0.470960 | − | 0.882155i | \(-0.343908\pi\) | |||||||
\(942\) | 2.17000 | − | 6.39260i | 0.0707023 | − | 0.208282i | ||||
\(943\) | −1.06162 | + | 0.139765i | −0.0345710 | + | 0.00455136i | ||||
\(944\) | −27.3655 | − | 11.3351i | −0.890670 | − | 0.368928i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.17592 | − | 7.74631i | 0.168284 | − | 0.251854i | ||||
\(947\) | −19.3839 | + | 6.57995i | −0.629892 | + | 0.213820i | −0.618086 | − | 0.786111i | \(-0.712092\pi\) |
−0.0118066 | + | 0.999930i | \(0.503758\pi\) | |||||||
\(948\) | 2.04463 | + | 7.63067i | 0.0664065 | + | 0.247833i | ||||
\(949\) | 7.52865 | − | 0.493454i | 0.244390 | − | 0.0160182i | ||||
\(950\) | −12.6616 | + | 16.5009i | −0.410795 | + | 0.535359i | ||||
\(951\) | 6.18521 | 0.200569 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.8889 | 0.838625 | 0.419312 | − | 0.907842i | \(-0.362271\pi\) | ||||
0.419312 | + | 0.907842i | \(0.362271\pi\) | |||||||
\(954\) | 5.38419 | − | 7.01681i | 0.174320 | − | 0.227178i | ||||
\(955\) | 65.9826 | − | 4.32473i | 2.13515 | − | 0.139945i | ||||
\(956\) | 1.47965 | + | 5.52213i | 0.0478553 | + | 0.178598i | ||||
\(957\) | 25.2182 | − | 8.56043i | 0.815189 | − | 0.276719i | ||||
\(958\) | 11.4952 | − | 17.2038i | 0.371394 | − | 0.555830i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.09471 | − | 0.453445i | −0.0353317 | − | 0.0146349i | ||||
\(961\) | 30.1496 | − | 3.96926i | 0.972566 | − | 0.128041i | ||||
\(962\) | −22.6952 | + | 66.8580i | −0.731724 | + | 2.15559i | ||||
\(963\) | 6.47745 | + | 13.1350i | 0.208733 | + | 0.423269i | ||||
\(964\) | 5.56801 | + | 16.4028i | 0.179334 | + | 0.528300i | ||||
\(965\) | −38.7099 | + | 38.7099i | −1.24612 | + | 1.24612i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4678 | − | 11.7917i | 0.915462 | − | 0.379197i | 0.125317 | − | 0.992117i | \(-0.460005\pi\) |
0.790145 | + | 0.612920i | \(0.210005\pi\) | |||||||
\(968\) | 17.5704 | − | 10.1443i | 0.564735 | − | 0.326050i | ||||
\(969\) | −9.99779 | − | 6.55086i | −0.321175 | − | 0.210444i | ||||
\(970\) | −24.0684 | + | 41.6876i | −0.772788 | + | 1.33851i | ||||
\(971\) | −47.3068 | − | 36.2998i | −1.51815 | − | 1.16492i | −0.936087 | − | 0.351770i | \(-0.885580\pi\) |
−0.582061 | − | 0.813145i | \(-0.697753\pi\) | |||||||
\(972\) | 8.53186 | + | 12.7688i | 0.273660 | + | 0.409560i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −47.3564 | − | 9.41978i | −1.51740 | − | 0.301829i | ||||
\(975\) | 0.518787 | − | 7.91516i | 0.0166145 | − | 0.253488i | ||||
\(976\) | −7.12160 | − | 2.41746i | −0.227957 | − | 0.0773809i | ||||
\(977\) | 43.0219 | − | 33.0118i | 1.37639 | − | 1.05614i | 0.385324 | − | 0.922781i | \(-0.374090\pi\) |
0.991068 | − | 0.133361i | \(-0.0425769\pi\) | |||||||
\(978\) | −1.60497 | − | 12.1910i | −0.0513213 | − | 0.389824i | ||||
\(979\) | 9.63508 | − | 1.91654i | 0.307939 | − | 0.0612528i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.23246 | − | 6.19597i | 0.0393493 | − | 0.197822i | ||||
\(982\) | 2.98702 | − | 11.1477i | 0.0953197 | − | 0.355738i | ||||
\(983\) | −2.39569 | − | 36.5512i | −0.0764106 | − | 1.16580i | −0.848112 | − | 0.529816i | \(-0.822261\pi\) |
0.771702 | − | 0.635985i | \(-0.219406\pi\) | |||||||
\(984\) | −0.0267191 | + | 0.202952i | −0.000851774 | + | 0.00646987i | ||||
\(985\) | −11.4558 | − | 19.8420i | −0.365012 | − | 0.632220i | ||||
\(986\) | 47.8541 | + | 53.5860i | 1.52399 | + | 1.70653i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.2216 | + | 39.1624i | 0.516078 | + | 1.24592i | ||||
\(989\) | 3.81184 | + | 1.87979i | 0.121209 | + | 0.0597738i | ||||
\(990\) | 62.7572 | − | 16.8157i | 1.99455 | − | 0.534439i | ||||
\(991\) | −28.5187 | + | 32.5194i | −0.905927 | + | 1.03301i | 0.0933739 | + | 0.995631i | \(0.470235\pi\) |
−0.999301 | + | 0.0373808i | \(0.988099\pi\) | |||||||
\(992\) | 4.60140 | + | 0.301591i | 0.146094 | + | 0.00957554i | ||||
\(993\) | 2.61257 | + | 13.1343i | 0.0829074 | + | 0.416803i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.6737 | + | 40.2539i | −0.528592 | + | 1.27613i | ||||
\(996\) | 6.55507 | − | 5.74864i | 0.207705 | − | 0.182153i | ||||
\(997\) | 32.8762 | − | 16.2128i | 1.04120 | − | 0.513463i | 0.160450 | − | 0.987044i | \(-0.448705\pi\) |
0.880750 | + | 0.473581i | \(0.157039\pi\) | |||||||
\(998\) | −43.6533 | − | 38.2829i | −1.38182 | − | 1.21182i | ||||
\(999\) | −17.8157 | − | 4.77369i | −0.563663 | − | 0.151033i |
(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 | 833.2.bc.a.80.2 | 144 | ||
7.2 | even | 3 | inner | 833.2.bc.a.607.8 | 144 | ||
7.3 | odd | 6 | 833.2.t.a.97.2 | ✓ | 72 | ||
7.4 | even | 3 | 833.2.t.d.97.2 | yes | 72 | ||
7.5 | odd | 6 | 833.2.bc.d.607.8 | 144 | |||
7.6 | odd | 2 | 833.2.bc.d.80.2 | 144 | |||
17.10 | odd | 16 | 833.2.bc.d.129.8 | 144 | |||
119.10 | even | 48 | 833.2.t.d.146.2 | yes | 72 | ||
119.27 | even | 16 | inner | 833.2.bc.a.129.8 | 144 | ||
119.44 | odd | 48 | 833.2.bc.d.656.2 | 144 | |||
119.61 | even | 48 | inner | 833.2.bc.a.656.2 | 144 | ||
119.95 | odd | 48 | 833.2.t.a.146.2 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
833.2.t.a.97.2 | ✓ | 72 | 7.3 | odd | 6 | ||
833.2.t.a.146.2 | yes | 72 | 119.95 | odd | 48 | ||
833.2.t.d.97.2 | yes | 72 | 7.4 | even | 3 | ||
833.2.t.d.146.2 | yes | 72 | 119.10 | even | 48 | ||
833.2.bc.a.80.2 | 144 | 1.1 | even | 1 | trivial | ||
833.2.bc.a.129.8 | 144 | 119.27 | even | 16 | inner | ||
833.2.bc.a.607.8 | 144 | 7.2 | even | 3 | inner | ||
833.2.bc.a.656.2 | 144 | 119.61 | even | 48 | inner | ||
833.2.bc.d.80.2 | 144 | 7.6 | odd | 2 | |||
833.2.bc.d.129.8 | 144 | 17.10 | odd | 16 | |||
833.2.bc.d.607.8 | 144 | 7.5 | odd | 6 | |||
833.2.bc.d.656.2 | 144 | 119.44 | odd | 48 |