Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), degree \(4\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 215.3 | ||
Character | \(\chi\) | \(=\) | 637.215 |
Dual form | 637.2.x.b.80.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0302180 | − | 0.112775i | 0.0213674 | − | 0.0797441i | −0.954419 | − | 0.298471i | \(-0.903524\pi\) |
0.975786 | + | 0.218726i | \(0.0701902\pi\) | |||||||
\(3\) | − | 2.59871i | − | 1.50036i | −0.661231 | − | 0.750182i | \(-0.729966\pi\) | ||
0.661231 | − | 0.750182i | \(-0.270034\pi\) | |||||||
\(4\) | 1.72025 | + | 0.993184i | 0.860123 | + | 0.496592i | ||||
\(5\) | 0.456951 | + | 1.70537i | 0.204355 | + | 0.762663i | 0.989645 | + | 0.143535i | \(0.0458470\pi\) |
−0.785290 | + | 0.619128i | \(0.787486\pi\) | |||||||
\(6\) | −0.293070 | − | 0.0785278i | −0.119645 | − | 0.0320589i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.329103 | − | 0.329103i | 0.116356 | − | 0.116356i | ||||
\(9\) | −3.75328 | −1.25109 | ||||||||
\(10\) | 0.206131 | 0.0651844 | ||||||||
\(11\) | −1.38433 | + | 1.38433i | −0.417390 | + | 0.417390i | −0.884303 | − | 0.466913i | \(-0.845366\pi\) |
0.466913 | + | 0.884303i | \(0.345366\pi\) | |||||||
\(12\) | 2.58100 | − | 4.47042i | 0.745069 | − | 1.29050i | ||||
\(13\) | 1.85749 | − | 3.09026i | 0.515175 | − | 0.857085i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.43175 | − | 1.18748i | 1.14427 | − | 0.306607i | ||||
\(16\) | 1.95920 | + | 3.39343i | 0.489800 | + | 0.848358i | ||||
\(17\) | 2.13907 | − | 3.70498i | 0.518801 | − | 0.898589i | −0.480960 | − | 0.876742i | \(-0.659712\pi\) |
0.999761 | − | 0.0218471i | \(-0.00695471\pi\) | |||||||
\(18\) | −0.113417 | + | 0.423277i | −0.0267326 | + | 0.0997674i | ||||
\(19\) | 3.01787 | − | 3.01787i | 0.692346 | − | 0.692346i | −0.270402 | − | 0.962748i | \(-0.587157\pi\) |
0.962748 | + | 0.270402i | \(0.0871566\pi\) | |||||||
\(20\) | −0.907674 | + | 3.38749i | −0.202962 | + | 0.757465i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.114286 | + | 0.197949i | 0.0243659 | + | 0.0422030i | ||||
\(23\) | 5.53927 | − | 3.19810i | 1.15502 | − | 0.666850i | 0.204913 | − | 0.978780i | \(-0.434309\pi\) |
0.950105 | + | 0.311930i | \(0.100976\pi\) | |||||||
\(24\) | −0.855244 | − | 0.855244i | −0.174576 | − | 0.174576i | ||||
\(25\) | 1.63066 | − | 0.941462i | 0.326132 | − | 0.188292i | ||||
\(26\) | −0.292376 | − | 0.302861i | −0.0573396 | − | 0.0593959i | ||||
\(27\) | 1.95756i | 0.376733i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.57954 | + | 6.19995i | −0.664704 | + | 1.15130i | 0.314661 | + | 0.949204i | \(0.398109\pi\) |
−0.979365 | + | 0.202097i | \(0.935224\pi\) | |||||||
\(30\) | − | 0.535675i | − | 0.0978004i | ||||||
\(31\) | −4.13397 | − | 1.10769i | −0.742483 | − | 0.198948i | −0.132302 | − | 0.991210i | \(-0.542237\pi\) |
−0.610181 | + | 0.792262i | \(0.708903\pi\) | |||||||
\(32\) | 1.34103 | − | 0.359327i | 0.237062 | − | 0.0635206i | ||||
\(33\) | 3.59746 | + | 3.59746i | 0.626237 | + | 0.626237i | ||||
\(34\) | −0.353191 | − | 0.353191i | −0.0605718 | − | 0.0605718i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.45657 | − | 3.72770i | −1.07609 | − | 0.621284i | ||||
\(37\) | 2.73261 | + | 0.732202i | 0.449239 | + | 0.120373i | 0.476343 | − | 0.879259i | \(-0.341962\pi\) |
−0.0271042 | + | 0.999633i | \(0.508629\pi\) | |||||||
\(38\) | −0.249147 | − | 0.431534i | −0.0404169 | − | 0.0700041i | ||||
\(39\) | −8.03069 | − | 4.82707i | −1.28594 | − | 0.772951i | ||||
\(40\) | 0.711626 | + | 0.410857i | 0.112518 | + | 0.0649623i | ||||
\(41\) | 2.94901 | + | 11.0059i | 0.460558 | + | 1.71883i | 0.671212 | + | 0.741266i | \(0.265774\pi\) |
−0.210654 | + | 0.977561i | \(0.567559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.55234 | + | 0.896243i | −0.236730 | + | 0.136676i | −0.613673 | − | 0.789561i | \(-0.710309\pi\) |
0.376943 | + | 0.926236i | \(0.376975\pi\) | |||||||
\(44\) | −3.75627 | + | 1.00649i | −0.566279 | + | 0.151734i | ||||
\(45\) | −1.71507 | − | 6.40072i | −0.255667 | − | 0.954163i | ||||
\(46\) | −0.193281 | − | 0.721333i | −0.0284977 | − | 0.106355i | ||||
\(47\) | −6.40208 | + | 1.71543i | −0.933839 | + | 0.250222i | −0.693491 | − | 0.720465i | \(-0.743928\pi\) |
−0.240348 | + | 0.970687i | \(0.577262\pi\) | |||||||
\(48\) | 8.81854 | − | 5.09139i | 1.27285 | − | 0.734878i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0568982 | − | 0.212347i | −0.00804663 | − | 0.0300304i | ||||
\(51\) | −9.62816 | − | 5.55882i | −1.34821 | − | 0.778390i | ||||
\(52\) | 6.26454 | − | 3.47118i | 0.868736 | − | 0.481366i | ||||
\(53\) | −2.13896 | − | 3.70479i | −0.293809 | − | 0.508893i | 0.680898 | − | 0.732378i | \(-0.261590\pi\) |
−0.974707 | + | 0.223486i | \(0.928256\pi\) | |||||||
\(54\) | 0.220765 | + | 0.0591537i | 0.0300423 | + | 0.00804980i | ||||
\(55\) | −2.99335 | − | 1.72821i | −0.403624 | − | 0.233032i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.84255 | − | 7.84255i | −1.03877 | − | 1.03877i | ||||
\(58\) | 0.591034 | + | 0.591034i | 0.0776066 | + | 0.0776066i | ||||
\(59\) | −1.62980 | + | 0.436704i | −0.212182 | + | 0.0568541i | −0.363344 | − | 0.931655i | \(-0.618365\pi\) |
0.151162 | + | 0.988509i | \(0.451698\pi\) | |||||||
\(60\) | 8.80308 | + | 2.35878i | 1.13647 | + | 0.304517i | ||||
\(61\) | − | 3.08259i | − | 0.394685i | −0.980335 | − | 0.197342i | \(-0.936769\pi\) | ||
0.980335 | − | 0.197342i | \(-0.0632311\pi\) | |||||||
\(62\) | −0.249841 | + | 0.432737i | −0.0317298 | + | 0.0549577i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.67470i | 0.959338i | ||||||||
\(65\) | 6.11881 | + | 1.75560i | 0.758945 | + | 0.217755i | ||||
\(66\) | 0.514413 | − | 0.296996i | 0.0633198 | − | 0.0365577i | ||||
\(67\) | 0.0139368 | + | 0.0139368i | 0.00170265 | + | 0.00170265i | 0.707958 | − | 0.706255i | \(-0.249617\pi\) |
−0.706255 | + | 0.707958i | \(0.749617\pi\) | |||||||
\(68\) | 7.35945 | − | 4.24898i | 0.892465 | − | 0.515265i | ||||
\(69\) | −8.31093 | − | 14.3949i | −1.00052 | − | 1.73295i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.23109 | − | 4.59449i | 0.146104 | − | 0.545266i | −0.853600 | − | 0.520929i | \(-0.825586\pi\) |
0.999704 | − | 0.0243373i | \(-0.00774758\pi\) | |||||||
\(72\) | −1.23522 | + | 1.23522i | −0.145572 | + | 0.145572i | ||||
\(73\) | −0.255666 | + | 0.954158i | −0.0299234 | + | 0.111676i | −0.979272 | − | 0.202548i | \(-0.935078\pi\) |
0.949349 | + | 0.314224i | \(0.101744\pi\) | |||||||
\(74\) | 0.165148 | − | 0.286046i | 0.0191981 | − | 0.0332521i | ||||
\(75\) | −2.44658 | − | 4.23761i | −0.282507 | − | 0.489317i | ||||
\(76\) | 8.18877 | − | 2.19417i | 0.939316 | − | 0.251689i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.787046 | + | 0.759799i | −0.0891154 | + | 0.0860303i | ||||
\(79\) | 2.96860 | − | 5.14176i | 0.333993 | − | 0.578493i | −0.649298 | − | 0.760534i | \(-0.724937\pi\) |
0.983291 | + | 0.182041i | \(0.0582704\pi\) | |||||||
\(80\) | −4.89178 | + | 4.89178i | −0.546918 | + | 0.546918i | ||||
\(81\) | −6.17272 | −0.685857 | ||||||||
\(82\) | 1.33030 | 0.146907 | ||||||||
\(83\) | −9.87683 | + | 9.87683i | −1.08412 | + | 1.08412i | −0.0880033 | + | 0.996120i | \(0.528049\pi\) |
−0.996120 | + | 0.0880033i | \(0.971951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.29580 | + | 1.95490i | 0.791340 | + | 0.212039i | ||||
\(86\) | 0.0541654 | + | 0.202148i | 0.00584081 | + | 0.0217982i | ||||
\(87\) | 16.1119 | + | 9.30218i | 1.72737 | + | 0.997299i | ||||
\(88\) | 0.911173i | 0.0971314i | ||||||||
\(89\) | −2.07993 | + | 7.76240i | −0.220472 | + | 0.822813i | 0.763696 | + | 0.645576i | \(0.223383\pi\) |
−0.984168 | + | 0.177237i | \(0.943284\pi\) | |||||||
\(90\) | −0.773669 | −0.0815519 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.7052 | 1.32461 | ||||||||
\(93\) | −2.87857 | + | 10.7430i | −0.298494 | + | 1.11400i | ||||
\(94\) | 0.773833i | 0.0798148i | ||||||||
\(95\) | 6.52558 | + | 3.76755i | 0.669511 | + | 0.386542i | ||||
\(96\) | −0.933785 | − | 3.48493i | −0.0953041 | − | 0.355680i | ||||
\(97\) | −14.2676 | − | 3.82300i | −1.44866 | − | 0.388167i | −0.553102 | − | 0.833113i | \(-0.686556\pi\) |
−0.895557 | + | 0.444946i | \(0.853223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.19577 | − | 5.19577i | 0.522194 | − | 0.522194i | ||||
\(100\) | 3.74018 | 0.374018 | ||||||||
\(101\) | −16.0096 | −1.59301 | −0.796506 | − | 0.604630i | \(-0.793321\pi\) | ||||
−0.796506 | + | 0.604630i | \(0.793321\pi\) | |||||||
\(102\) | −0.917841 | + | 0.917841i | −0.0908798 | + | 0.0908798i | ||||
\(103\) | −5.90755 | + | 10.2322i | −0.582088 | + | 1.00821i | 0.413143 | + | 0.910666i | \(0.364431\pi\) |
−0.995232 | + | 0.0975405i | \(0.968902\pi\) | |||||||
\(104\) | −0.405710 | − | 1.62832i | −0.0397831 | − | 0.159670i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.482444 | + | 0.129271i | −0.0468591 | + | 0.0125559i | ||||
\(107\) | −3.99556 | − | 6.92051i | −0.386265 | − | 0.669031i | 0.605679 | − | 0.795709i | \(-0.292902\pi\) |
−0.991944 | + | 0.126678i | \(0.959568\pi\) | |||||||
\(108\) | −1.94422 | + | 3.36749i | −0.187083 | + | 0.324037i | ||||
\(109\) | −3.20509 | + | 11.9616i | −0.306992 | + | 1.14571i | 0.624225 | + | 0.781245i | \(0.285415\pi\) |
−0.931217 | + | 0.364465i | \(0.881252\pi\) | |||||||
\(110\) | −0.285353 | + | 0.285353i | −0.0272073 | + | 0.0272073i | ||||
\(111\) | 1.90278 | − | 7.10127i | 0.180604 | − | 0.674022i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.27217 | + | 7.39961i | 0.401892 | + | 0.696097i | 0.993954 | − | 0.109795i | \(-0.0350195\pi\) |
−0.592063 | + | 0.805892i | \(0.701686\pi\) | |||||||
\(114\) | −1.12143 | + | 0.647459i | −0.105032 | + | 0.0606401i | ||||
\(115\) | 7.98511 | + | 7.98511i | 0.744615 | + | 0.744615i | ||||
\(116\) | −12.3154 | + | 7.11029i | −1.14345 | + | 0.660174i | ||||
\(117\) | −6.97169 | + | 11.5986i | −0.644533 | + | 1.07229i | ||||
\(118\) | 0.196998i | 0.0181351i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.06770 | − | 1.84931i | 0.0974671 | − | 0.168818i | ||||
\(121\) | 7.16728i | 0.651571i | ||||||||
\(122\) | −0.347640 | − | 0.0931497i | −0.0314738 | − | 0.00843338i | ||||
\(123\) | 28.6010 | − | 7.66362i | 2.57887 | − | 0.691005i | ||||
\(124\) | −6.01130 | − | 6.01130i | −0.539831 | − | 0.539831i | ||||
\(125\) | 8.59274 | + | 8.59274i | 0.768558 | + | 0.768558i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.29483 | − | 3.05697i | −0.469840 | − | 0.271262i | 0.246333 | − | 0.969185i | \(-0.420774\pi\) |
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(128\) | 3.54757 | + | 0.950568i | 0.313564 | + | 0.0840191i | ||||
\(129\) | 2.32907 | + | 4.03408i | 0.205064 | + | 0.355181i | ||||
\(130\) | 0.382887 | − | 0.637000i | 0.0335814 | − | 0.0558686i | ||||
\(131\) | 4.99207 | + | 2.88218i | 0.436159 | + | 0.251817i | 0.701967 | − | 0.712209i | \(-0.252305\pi\) |
−0.265808 | + | 0.964026i | \(0.585639\pi\) | |||||||
\(132\) | 2.61557 | + | 9.76146i | 0.227657 | + | 0.849626i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.00199287 | − | 0.00115058i | 0.000172157 | − | 9.93951e-5i | ||||
\(135\) | −3.33836 | + | 0.894511i | −0.287320 | + | 0.0769872i | ||||
\(136\) | −0.515346 | − | 1.92330i | −0.0441905 | − | 0.164921i | ||||
\(137\) | 1.62427 | + | 6.06188i | 0.138771 | + | 0.517901i | 0.999954 | + | 0.00960548i | \(0.00305757\pi\) |
−0.861183 | + | 0.508296i | \(0.830276\pi\) | |||||||
\(138\) | −1.87453 | + | 0.502280i | −0.159571 | + | 0.0427569i | ||||
\(139\) | 18.1314 | − | 10.4682i | 1.53789 | − | 0.887900i | 0.538927 | − | 0.842353i | \(-0.318830\pi\) |
0.998962 | − | 0.0455477i | \(-0.0145033\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.45791 | + | 16.6371i | 0.375424 | + | 1.40110i | ||||
\(142\) | −0.480944 | − | 0.277673i | −0.0403599 | − | 0.0233018i | ||||
\(143\) | 1.70656 | + | 6.84931i | 0.142710 | + | 0.572768i | ||||
\(144\) | −7.35343 | − | 12.7365i | −0.612786 | − | 1.06138i | ||||
\(145\) | −12.2089 | − | 3.27135i | −1.01389 | − | 0.271671i | ||||
\(146\) | 0.0998797 | + | 0.0576656i | 0.00826610 | + | 0.00477244i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.97356 | + | 3.97356i | 0.326624 | + | 0.326624i | ||||
\(149\) | 10.9301 | + | 10.9301i | 0.895431 | + | 0.895431i | 0.995028 | − | 0.0995972i | \(-0.0317554\pi\) |
−0.0995972 | + | 0.995028i | \(0.531755\pi\) | |||||||
\(150\) | −0.551828 | + | 0.147862i | −0.0450566 | + | 0.0120729i | ||||
\(151\) | −4.27019 | − | 1.14419i | −0.347503 | − | 0.0931131i | 0.0808459 | − | 0.996727i | \(-0.474238\pi\) |
−0.428349 | + | 0.903614i | \(0.640905\pi\) | |||||||
\(152\) | − | 1.98638i | − | 0.161117i | ||||||
\(153\) | −8.02854 | + | 13.9058i | −0.649069 | + | 1.12422i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.55609i | − | 0.606920i | ||||||
\(156\) | −9.02059 | − | 16.2797i | −0.722225 | − | 1.30342i | ||||
\(157\) | −6.00211 | + | 3.46532i | −0.479020 | + | 0.276563i | −0.720008 | − | 0.693966i | \(-0.755862\pi\) |
0.240988 | + | 0.970528i | \(0.422529\pi\) | |||||||
\(158\) | −0.490158 | − | 0.490158i | −0.0389949 | − | 0.0389949i | ||||
\(159\) | −9.62768 | + | 5.55854i | −0.763525 | + | 0.440821i | ||||
\(160\) | 1.22557 | + | 2.12274i | 0.0968896 | + | 0.167818i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.186527 | + | 0.696129i | −0.0146550 | + | 0.0546931i | ||||
\(163\) | 9.14651 | − | 9.14651i | 0.716410 | − | 0.716410i | −0.251458 | − | 0.967868i | \(-0.580910\pi\) |
0.967868 | + | 0.251458i | \(0.0809101\pi\) | |||||||
\(164\) | −5.85782 | + | 21.8617i | −0.457419 | + | 1.70711i | ||||
\(165\) | −4.49112 | + | 7.77885i | −0.349633 | + | 0.605583i | ||||
\(166\) | 0.815404 | + | 1.41232i | 0.0632876 | + | 0.109617i | ||||
\(167\) | 0.900490 | − | 0.241286i | 0.0696820 | − | 0.0186712i | −0.223810 | − | 0.974633i | \(-0.571849\pi\) |
0.293492 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.09946 | − | 11.4803i | −0.469189 | − | 0.883098i | ||||
\(170\) | 0.440929 | − | 0.763712i | 0.0338177 | − | 0.0585740i | ||||
\(171\) | −11.3269 | + | 11.3269i | −0.866190 | + | 0.866190i | ||||
\(172\) | −3.56054 | −0.271489 | ||||||||
\(173\) | −0.527560 | −0.0401096 | −0.0200548 | − | 0.999799i | \(-0.506384\pi\) | ||||
−0.0200548 | + | 0.999799i | \(0.506384\pi\) | |||||||
\(174\) | 1.53592 | − | 1.53592i | 0.116438 | − | 0.116438i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.40979 | − | 1.98545i | −0.558534 | − | 0.149659i | ||||
\(177\) | 1.13487 | + | 4.23538i | 0.0853018 | + | 0.318351i | ||||
\(178\) | 0.812555 | + | 0.469129i | 0.0609036 | + | 0.0351627i | ||||
\(179\) | − | 8.27003i | − | 0.618131i | −0.951041 | − | 0.309066i | \(-0.899984\pi\) | ||
0.951041 | − | 0.309066i | \(-0.100016\pi\) | |||||||
\(180\) | 3.40676 | − | 12.7142i | 0.253925 | − | 0.947660i | ||||
\(181\) | −14.9785 | −1.11334 | −0.556672 | − | 0.830732i | \(-0.687922\pi\) | ||||
−0.556672 | + | 0.830732i | \(0.687922\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.01075 | −0.592171 | ||||||||
\(184\) | 0.770488 | − | 2.87550i | 0.0568011 | − | 0.211985i | ||||
\(185\) | 4.99469i | 0.367217i | ||||||||
\(186\) | 1.12456 | + | 0.649263i | 0.0824565 | + | 0.0476063i | ||||
\(187\) | 2.16773 | + | 8.09007i | 0.158520 | + | 0.591605i | ||||
\(188\) | −12.7169 | − | 3.40748i | −0.927475 | − | 0.248516i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.622076 | − | 0.622076i | 0.0451301 | − | 0.0451301i | ||||
\(191\) | −14.5292 | −1.05130 | −0.525649 | − | 0.850702i | \(-0.676177\pi\) | ||||
−0.525649 | + | 0.850702i | \(0.676177\pi\) | |||||||
\(192\) | 19.9443 | 1.43936 | ||||||||
\(193\) | 13.8436 | − | 13.8436i | 0.996483 | − | 0.996483i | −0.00351052 | − | 0.999994i | \(-0.501117\pi\) |
0.999994 | + | 0.00351052i | \(0.00111744\pi\) | |||||||
\(194\) | −0.862280 | + | 1.49351i | −0.0619081 | + | 0.107228i | ||||
\(195\) | 4.56229 | − | 15.9010i | 0.326712 | − | 1.13869i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.0175 | + | 5.63163i | −1.49744 | + | 0.401237i | −0.912240 | − | 0.409655i | \(-0.865649\pi\) |
−0.585196 | + | 0.810892i | \(0.698982\pi\) | |||||||
\(198\) | −0.428948 | − | 0.742960i | −0.0304840 | − | 0.0527999i | ||||
\(199\) | 9.64065 | − | 16.6981i | 0.683408 | − | 1.18370i | −0.290527 | − | 0.956867i | \(-0.593830\pi\) |
0.973934 | − | 0.226830i | \(-0.0728362\pi\) | |||||||
\(200\) | 0.226817 | − | 0.846494i | 0.0160384 | − | 0.0598562i | ||||
\(201\) | 0.0362176 | − | 0.0362176i | 0.00255459 | − | 0.00255459i | ||||
\(202\) | −0.483778 | + | 1.80548i | −0.0340385 | + | 0.127033i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.0419 | − | 19.1251i | −0.773085 | − | 1.33902i | ||||
\(205\) | −17.4215 | + | 10.0583i | −1.21677 | + | 0.702501i | ||||
\(206\) | 0.975422 | + | 0.975422i | 0.0679609 | + | 0.0679609i | ||||
\(207\) | −20.7905 | + | 12.0034i | −1.44504 | + | 0.834292i | ||||
\(208\) | 14.1258 | + | 0.248825i | 0.979447 | + | 0.0172529i | ||||
\(209\) | 8.35542i | 0.577957i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.51130 | − | 2.61764i | 0.104042 | − | 0.180206i | −0.809304 | − | 0.587389i | \(-0.800156\pi\) |
0.913346 | + | 0.407184i | \(0.133489\pi\) | |||||||
\(212\) | − | 8.49754i | − | 0.583614i | ||||||
\(213\) | −11.9397 | − | 3.19925i | −0.818098 | − | 0.219209i | ||||
\(214\) | −0.901200 | + | 0.241476i | −0.0616048 | + | 0.0165070i | ||||
\(215\) | −2.23777 | − | 2.23777i | −0.152614 | − | 0.152614i | ||||
\(216\) | 0.644241 | + | 0.644241i | 0.0438350 | + | 0.0438350i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.25212 | + | 0.722910i | 0.0848040 | + | 0.0489616i | ||||
\(219\) | 2.47958 | + | 0.664401i | 0.167554 | + | 0.0448961i | ||||
\(220\) | −3.43287 | − | 5.94590i | −0.231444 | − | 0.400873i | ||||
\(221\) | −7.47606 | − | 13.4923i | −0.502894 | − | 0.907587i | ||||
\(222\) | −0.743349 | − | 0.429173i | −0.0498903 | − | 0.0288042i | ||||
\(223\) | −1.13865 | − | 4.24949i | −0.0762495 | − | 0.284567i | 0.917264 | − | 0.398279i | \(-0.130392\pi\) |
−0.993514 | + | 0.113712i | \(0.963726\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.12033 | + | 3.53357i | −0.408022 | + | 0.235571i | ||||
\(226\) | 0.963589 | − | 0.258193i | 0.0640970 | − | 0.0171747i | ||||
\(227\) | −1.06086 | − | 3.95917i | −0.0704116 | − | 0.262780i | 0.921742 | − | 0.387803i | \(-0.126766\pi\) |
−0.992154 | + | 0.125024i | \(0.960099\pi\) | |||||||
\(228\) | −5.70202 | − | 21.2802i | −0.377625 | − | 1.40932i | ||||
\(229\) | 13.1144 | − | 3.51399i | 0.866623 | − | 0.232211i | 0.201996 | − | 0.979386i | \(-0.435257\pi\) |
0.664627 | + | 0.747176i | \(0.268591\pi\) | |||||||
\(230\) | 1.14182 | − | 0.659228i | 0.0752892 | − | 0.0434682i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.862385 | + | 3.21846i | 0.0566183 | + | 0.211303i | ||||
\(233\) | 14.1595 | + | 8.17501i | 0.927622 | + | 0.535563i | 0.886059 | − | 0.463573i | \(-0.153433\pi\) |
0.0415633 | + | 0.999136i | \(0.486766\pi\) | |||||||
\(234\) | 1.09737 | + | 1.13672i | 0.0717372 | + | 0.0743098i | ||||
\(235\) | −5.85088 | − | 10.1340i | −0.381669 | − | 0.661071i | ||||
\(236\) | −3.23739 | − | 0.867456i | −0.210736 | − | 0.0564666i | ||||
\(237\) | −13.3619 | − | 7.71452i | −0.867951 | − | 0.501112i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.11495 | + | 6.11495i | 0.395543 | + | 0.395543i | 0.876658 | − | 0.481115i | \(-0.159768\pi\) |
−0.481115 | + | 0.876658i | \(0.659768\pi\) | |||||||
\(240\) | 12.7123 | + | 12.7123i | 0.820577 | + | 0.820577i | ||||
\(241\) | 12.9736 | − | 3.47625i | 0.835700 | − | 0.223925i | 0.184501 | − | 0.982832i | \(-0.440933\pi\) |
0.651199 | + | 0.758907i | \(0.274266\pi\) | |||||||
\(242\) | 0.808292 | + | 0.216581i | 0.0519590 | + | 0.0139224i | ||||
\(243\) | 21.9138i | 1.40577i | ||||||||
\(244\) | 3.06158 | − | 5.30281i | 0.195997 | − | 0.339478i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 3.45707i | − | 0.220414i | ||||||
\(247\) | −3.72034 | − | 14.9317i | −0.236720 | − | 0.950078i | ||||
\(248\) | −1.72505 | + | 0.995958i | −0.109541 | + | 0.0632434i | ||||
\(249\) | 25.6670 | + | 25.6670i | 1.62658 | + | 1.62658i | ||||
\(250\) | 1.22870 | − | 0.709393i | 0.0777101 | − | 0.0448659i | ||||
\(251\) | 1.74301 | + | 3.01899i | 0.110018 | + | 0.190557i | 0.915777 | − | 0.401686i | \(-0.131576\pi\) |
−0.805759 | + | 0.592243i | \(0.798242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.24095 | + | 12.0954i | −0.203756 | + | 0.760430i | ||||
\(254\) | −0.504750 | + | 0.504750i | −0.0316708 | + | 0.0316708i | ||||
\(255\) | 5.08022 | − | 18.9596i | 0.318136 | − | 1.18730i | ||||
\(256\) | −7.46030 | + | 12.9216i | −0.466269 | + | 0.807601i | ||||
\(257\) | −6.72396 | − | 11.6462i | −0.419429 | − | 0.726472i | 0.576453 | − | 0.817130i | \(-0.304436\pi\) |
−0.995882 | + | 0.0906578i | \(0.971103\pi\) | |||||||
\(258\) | 0.525324 | − | 0.140760i | 0.0327052 | − | 0.00876334i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.78223 | + | 9.09717i | 0.544651 | + | 0.564183i | ||||
\(261\) | 13.4350 | − | 23.2702i | 0.831608 | − | 1.44039i | ||||
\(262\) | 0.475889 | − | 0.475889i | 0.0294005 | − | 0.0294005i | ||||
\(263\) | 20.5358 | 1.26629 | 0.633147 | − | 0.774032i | \(-0.281763\pi\) | ||||
0.633147 | + | 0.774032i | \(0.281763\pi\) | |||||||
\(264\) | 2.36787 | 0.145733 | ||||||||
\(265\) | 5.34063 | − | 5.34063i | 0.328072 | − | 0.328072i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.1722 | + | 5.40513i | 1.23452 | + | 0.330788i | ||||
\(268\) | 0.0101329 | + | 0.0378165i | 0.000618965 | + | 0.00231001i | ||||
\(269\) | −9.29875 | − | 5.36864i | −0.566955 | − | 0.327332i | 0.188977 | − | 0.981981i | \(-0.439483\pi\) |
−0.755932 | + | 0.654650i | \(0.772816\pi\) | |||||||
\(270\) | 0.403515i | 0.0245571i | ||||||||
\(271\) | −0.387901 | + | 1.44767i | −0.0235633 | + | 0.0879396i | −0.976706 | − | 0.214581i | \(-0.931161\pi\) |
0.953143 | + | 0.302521i | \(0.0978281\pi\) | |||||||
\(272\) | 16.7635 | 1.01643 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.732712 | 0.0442647 | ||||||||
\(275\) | −0.954075 | + | 3.56065i | −0.0575329 | + | 0.214716i | ||||
\(276\) | − | 33.0171i | − | 1.98740i | ||||||
\(277\) | −4.07919 | − | 2.35512i | −0.245095 | − | 0.141506i | 0.372421 | − | 0.928064i | \(-0.378528\pi\) |
−0.617516 | + | 0.786558i | \(0.711861\pi\) | |||||||
\(278\) | −0.632656 | − | 2.36111i | −0.0379442 | − | 0.141610i | ||||
\(279\) | 15.5160 | + | 4.15749i | 0.928916 | + | 0.248902i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.01227 | − | 8.01227i | 0.477972 | − | 0.477972i | −0.426511 | − | 0.904483i | \(-0.640257\pi\) |
0.904483 | + | 0.426511i | \(0.140257\pi\) | |||||||
\(282\) | 2.01097 | 0.119751 | ||||||||
\(283\) | −7.87867 | −0.468338 | −0.234169 | − | 0.972196i | \(-0.575237\pi\) | ||||
−0.234169 | + | 0.972196i | \(0.575237\pi\) | |||||||
\(284\) | 6.68096 | − | 6.68096i | 0.396442 | − | 0.396442i | ||||
\(285\) | 9.79075 | − | 16.9581i | 0.579954 | − | 1.00451i | ||||
\(286\) | 0.824001 | + | 0.0145147i | 0.0487242 | + | 0.000858275i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.03325 | + | 1.34865i | −0.296587 | + | 0.0794703i | ||||
\(289\) | −0.651246 | − | 1.12799i | −0.0383086 | − | 0.0663525i | ||||
\(290\) | −0.737855 | + | 1.27800i | −0.0433284 | + | 0.0750469i | ||||
\(291\) | −9.93487 | + | 37.0774i | −0.582392 | + | 2.17352i | ||||
\(292\) | −1.38746 | + | 1.38746i | −0.0811951 | + | 0.0811951i | ||||
\(293\) | −3.16216 | + | 11.8013i | −0.184735 | + | 0.689442i | 0.809952 | + | 0.586497i | \(0.199493\pi\) |
−0.994687 | + | 0.102945i | \(0.967173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.48948 | − | 2.57986i | −0.0867210 | − | 0.150205i | ||||
\(296\) | 1.14028 | − | 0.658343i | 0.0662776 | − | 0.0382654i | ||||
\(297\) | −2.70991 | − | 2.70991i | −0.157245 | − | 0.157245i | ||||
\(298\) | 1.56293 | − | 0.902360i | 0.0905383 | − | 0.0522723i | ||||
\(299\) | 0.406170 | − | 23.0582i | 0.0234894 | − | 1.33349i | ||||
\(300\) | − | 9.71963i | − | 0.561163i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.258073 | + | 0.446996i | −0.0148504 | + | 0.0257217i | ||||
\(303\) | 41.6042i | 2.39010i | ||||||||
\(304\) | 16.1535 | + | 4.32832i | 0.926468 | + | 0.248246i | ||||
\(305\) | 5.25694 | − | 1.40859i | 0.301011 | − | 0.0806558i | ||||
\(306\) | 1.32563 | + | 1.32563i | 0.0757811 | + | 0.0757811i | ||||
\(307\) | 7.97207 | + | 7.97207i | 0.454990 | + | 0.454990i | 0.897007 | − | 0.442017i | \(-0.145737\pi\) |
−0.442017 | + | 0.897007i | \(0.645737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.5904 | + | 15.3520i | 1.51268 | + | 0.873345i | ||||
\(310\) | −0.852140 | − | 0.228330i | −0.0483983 | − | 0.0129683i | ||||
\(311\) | −6.52139 | − | 11.2954i | −0.369794 | − | 0.640502i | 0.619739 | − | 0.784808i | \(-0.287238\pi\) |
−0.989533 | + | 0.144306i | \(0.953905\pi\) | |||||||
\(312\) | −4.23154 | + | 1.05432i | −0.239564 | + | 0.0596892i | ||||
\(313\) | −3.09510 | − | 1.78696i | −0.174945 | − | 0.101005i | 0.409970 | − | 0.912099i | \(-0.365539\pi\) |
−0.584916 | + | 0.811094i | \(0.698872\pi\) | |||||||
\(314\) | 0.209430 | + | 0.781604i | 0.0118188 | + | 0.0441085i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2134 | − | 5.89673i | 0.574551 | − | 0.331717i | ||||
\(317\) | −32.0422 | + | 8.58569i | −1.79967 | + | 0.482220i | −0.993927 | − | 0.110045i | \(-0.964901\pi\) |
−0.805743 | + | 0.592265i | \(0.798234\pi\) | |||||||
\(318\) | 0.335936 | + | 1.25373i | 0.0188384 | + | 0.0703058i | ||||
\(319\) | −3.62750 | − | 13.5380i | −0.203101 | − | 0.757983i | ||||
\(320\) | −13.0882 | + | 3.50697i | −0.731651 | + | 0.196045i | ||||
\(321\) | −17.9844 | + | 10.3833i | −1.00379 | + | 0.579539i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.72570 | − | 17.6366i | −0.262945 | − | 0.981324i | ||||
\(324\) | −10.6186 | − | 6.13064i | −0.589921 | − | 0.340591i | ||||
\(325\) | 0.119569 | − | 6.78792i | 0.00663249 | − | 0.376526i | ||||
\(326\) | −0.755110 | − | 1.30789i | −0.0418217 | − | 0.0724373i | ||||
\(327\) | 31.0846 | + | 8.32910i | 1.71898 | + | 0.460600i | ||||
\(328\) | 4.59260 | + | 2.65154i | 0.253584 | + | 0.146407i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.741549 | + | 0.741549i | 0.0408209 | + | 0.0408209i | ||||
\(331\) | −0.670431 | − | 0.670431i | −0.0368502 | − | 0.0368502i | 0.688442 | − | 0.725292i | \(-0.258295\pi\) |
−0.725292 | + | 0.688442i | \(0.758295\pi\) | |||||||
\(332\) | −26.8001 | + | 7.18106i | −1.47085 | + | 0.394112i | ||||
\(333\) | −10.2563 | − | 2.74816i | −0.562040 | − | 0.150598i | ||||
\(334\) | − | 0.108844i | − | 0.00595569i | ||||||
\(335\) | −0.0173989 | + | 0.0301357i | −0.000950602 | + | 0.00164649i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.1901i | − | 0.772982i | −0.922293 | − | 0.386491i | \(-0.873687\pi\) | ||
0.922293 | − | 0.386491i | \(-0.126313\pi\) | |||||||
\(338\) | −1.47900 | + | 0.340957i | −0.0804472 | + | 0.0185456i | ||||
\(339\) | 19.2294 | − | 11.1021i | 1.04440 | − | 0.602984i | ||||
\(340\) | 10.6090 | + | 10.6090i | 0.575353 | + | 0.575353i | ||||
\(341\) | 7.25617 | − | 4.18935i | 0.392944 | − | 0.226866i | ||||
\(342\) | 0.935117 | + | 1.61967i | 0.0505654 | + | 0.0875818i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.215923 | + | 0.805837i | −0.0116418 | + | 0.0434478i | ||||
\(345\) | 20.7510 | − | 20.7510i | 1.11719 | − | 1.11719i | ||||
\(346\) | −0.0159418 | + | 0.0594957i | −0.000857038 | + | 0.00319851i | ||||
\(347\) | −6.92103 | + | 11.9876i | −0.371540 | + | 0.643527i | −0.989803 | − | 0.142445i | \(-0.954504\pi\) |
0.618262 | + | 0.785972i | \(0.287837\pi\) | |||||||
\(348\) | 18.4776 | + | 32.0041i | 0.990502 | + | 1.71560i | ||||
\(349\) | −14.7875 | + | 3.96231i | −0.791559 | + | 0.212098i | −0.631875 | − | 0.775071i | \(-0.717714\pi\) |
−0.159684 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.04939 | + | 3.63615i | 0.322892 | + | 0.194084i | ||||
\(352\) | −1.35899 | + | 2.35384i | −0.0724345 | + | 0.125460i | ||||
\(353\) | 11.1372 | − | 11.1372i | 0.592773 | − | 0.592773i | −0.345607 | − | 0.938379i | \(-0.612327\pi\) |
0.938379 | + | 0.345607i | \(0.112327\pi\) | |||||||
\(354\) | 0.511940 | 0.0272093 | ||||||||
\(355\) | 8.39784 | 0.445711 | ||||||||
\(356\) | −11.2875 | + | 11.2875i | −0.598235 | + | 0.598235i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.932655 | − | 0.249904i | −0.0492924 | − | 0.0132078i | ||||
\(359\) | −1.71588 | − | 6.40375i | −0.0905607 | − | 0.337977i | 0.905748 | − | 0.423816i | \(-0.139310\pi\) |
−0.996309 | + | 0.0858388i | \(0.972643\pi\) | |||||||
\(360\) | −2.67093 | − | 1.54206i | −0.140771 | − | 0.0812739i | ||||
\(361\) | 0.784981i | 0.0413148i | ||||||||
\(362\) | −0.452621 | + | 1.68920i | −0.0237892 | + | 0.0887826i | ||||
\(363\) | 18.6257 | 0.977594 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.74402 | −0.0912859 | ||||||||
\(366\) | −0.242069 | + | 0.903414i | −0.0126531 | + | 0.0472222i | ||||
\(367\) | 32.8567i | 1.71511i | 0.514396 | + | 0.857553i | \(0.328016\pi\) | ||||
−0.514396 | + | 0.857553i | \(0.671984\pi\) | |||||||
\(368\) | 21.7051 | + | 12.5314i | 1.13145 | + | 0.653246i | ||||
\(369\) | −11.0685 | − | 41.3081i | −0.576202 | − | 2.15041i | ||||
\(370\) | 0.563277 | + | 0.150930i | 0.0292834 | + | 0.00784646i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −15.6216 | + | 15.6216i | −0.809943 | + | 0.809943i | ||||
\(373\) | 7.87973 | 0.407997 | 0.203998 | − | 0.978971i | \(-0.434606\pi\) | ||||
0.203998 | + | 0.978971i | \(0.434606\pi\) | |||||||
\(374\) | 0.977864 | 0.0505642 | ||||||||
\(375\) | 22.3300 | − | 22.3300i | 1.15312 | − | 1.15312i | ||||
\(376\) | −1.54239 | + | 2.67150i | −0.0795428 | + | 0.137772i | ||||
\(377\) | 12.5105 | + | 22.5781i | 0.644324 | + | 1.16283i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.8095 | − | 2.89639i | 0.555245 | − | 0.148778i | 0.0297243 | − | 0.999558i | \(-0.490537\pi\) |
0.525521 | + | 0.850781i | \(0.323870\pi\) | |||||||
\(380\) | 7.48374 | + | 12.9622i | 0.383908 | + | 0.664947i | ||||
\(381\) | −7.94417 | + | 13.7597i | −0.406992 | + | 0.704931i | ||||
\(382\) | −0.439044 | + | 1.63854i | −0.0224635 | + | 0.0838348i | ||||
\(383\) | 1.70452 | − | 1.70452i | 0.0870968 | − | 0.0870968i | −0.662216 | − | 0.749313i | \(-0.730384\pi\) |
0.749313 | + | 0.662216i | \(0.230384\pi\) | |||||||
\(384\) | 2.47025 | − | 9.21909i | 0.126059 | − | 0.470460i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.14289 | − | 1.97954i | −0.0581715 | − | 0.100756i | ||||
\(387\) | 5.82637 | − | 3.36386i | 0.296171 | − | 0.170994i | ||||
\(388\) | −20.7469 | − | 20.7469i | −1.05326 | − | 1.05326i | ||||
\(389\) | −14.5674 | + | 8.41049i | −0.738596 | + | 0.426429i | −0.821559 | − | 0.570124i | \(-0.806895\pi\) |
0.0829624 | + | 0.996553i | \(0.473562\pi\) | |||||||
\(390\) | −1.65538 | − | 0.995011i | −0.0838232 | − | 0.0503843i | ||||
\(391\) | − | 27.3638i | − | 1.38385i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.48993 | − | 12.9729i | 0.377817 | − | 0.654398i | ||||
\(394\) | 2.54043i | 0.127985i | ||||||||
\(395\) | 10.1251 | + | 2.71301i | 0.509448 | + | 0.136506i | ||||
\(396\) | 14.0984 | − | 3.77764i | 0.708469 | − | 0.189834i | ||||
\(397\) | 16.6347 | + | 16.6347i | 0.834873 | + | 0.834873i | 0.988179 | − | 0.153306i | \(-0.0489921\pi\) |
−0.153306 | + | 0.988179i | \(0.548992\pi\) | |||||||
\(398\) | −1.59181 | − | 1.59181i | −0.0797903 | − | 0.0797903i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.38957 | + | 3.68902i | 0.319479 | + | 0.184451i | ||||
\(401\) | −8.33434 | − | 2.23318i | −0.416197 | − | 0.111520i | 0.0446427 | − | 0.999003i | \(-0.485785\pi\) |
−0.460840 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(402\) | −0.00299003 | − | 0.00517888i | −0.000149129 | − | 0.000258299i | ||||
\(403\) | −11.1019 | + | 10.7175i | −0.553024 | + | 0.533878i | ||||
\(404\) | −27.5404 | − | 15.9005i | −1.37019 | − | 0.791078i | ||||
\(405\) | −2.82063 | − | 10.5267i | −0.140158 | − | 0.523078i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.79644 | + | 2.76922i | −0.237751 | + | 0.137265i | ||||
\(408\) | −4.99809 | + | 1.33923i | −0.247442 | + | 0.0663019i | ||||
\(409\) | −3.47744 | − | 12.9780i | −0.171948 | − | 0.641720i | −0.997051 | − | 0.0767375i | \(-0.975550\pi\) |
0.825103 | − | 0.564982i | \(-0.191117\pi\) | |||||||
\(410\) | 0.607883 | + | 2.26865i | 0.0300212 | + | 0.112041i | ||||
\(411\) | 15.7530 | − | 4.22102i | 0.777040 | − | 0.208207i | ||||
\(412\) | −20.3249 | + | 11.7346i | −1.00133 | + | 0.578121i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.725437 | + | 2.70737i | 0.0356533 | + | 0.133060i | ||||
\(415\) | −21.3568 | − | 12.3304i | −1.04837 | − | 0.605275i | ||||
\(416\) | 1.38053 | − | 4.81157i | 0.0676859 | − | 0.235907i | ||||
\(417\) | −27.2038 | − | 47.1183i | −1.33217 | − | 2.30739i | ||||
\(418\) | 0.942285 | + | 0.252484i | 0.0460886 | + | 0.0123494i | ||||
\(419\) | 15.0514 | + | 8.68991i | 0.735308 | + | 0.424530i | 0.820361 | − | 0.571846i | \(-0.193773\pi\) |
−0.0850532 | + | 0.996376i | \(0.527106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.2490 | − | 21.2490i | −1.03561 | − | 1.03561i | −0.999342 | − | 0.0362722i | \(-0.988452\pi\) |
−0.0362722 | − | 0.999342i | \(-0.511548\pi\) | |||||||
\(422\) | −0.249537 | − | 0.249537i | −0.0121473 | − | 0.0121473i | ||||
\(423\) | 24.0288 | − | 6.43850i | 1.16832 | − | 0.313051i | ||||
\(424\) | −1.92320 | − | 0.515320i | −0.0933989 | − | 0.0250262i | ||||
\(425\) | − | 8.05541i | − | 0.390745i | ||||||
\(426\) | −0.721591 | + | 1.24983i | −0.0349612 | + | 0.0605546i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 15.8733i | − | 0.767265i | ||||||
\(429\) | 17.7993 | − | 4.43485i | 0.859361 | − | 0.214117i | ||||
\(430\) | −0.319986 | + | 0.184744i | −0.0154311 | + | 0.00890913i | ||||
\(431\) | −17.0631 | − | 17.0631i | −0.821902 | − | 0.821902i | 0.164479 | − | 0.986381i | \(-0.447406\pi\) |
−0.986381 | + | 0.164479i | \(0.947406\pi\) | |||||||
\(432\) | −6.64286 | + | 3.83525i | −0.319605 | + | 0.184524i | ||||
\(433\) | 2.27124 | + | 3.93391i | 0.109149 | + | 0.189051i | 0.915426 | − | 0.402487i | \(-0.131854\pi\) |
−0.806277 | + | 0.591538i | \(0.798521\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.50129 | + | 31.7273i | −0.407606 | + | 1.52121i | ||||
\(436\) | −17.3936 | + | 17.3936i | −0.833001 | + | 0.833001i | ||||
\(437\) | 7.06534 | − | 26.3682i | 0.337981 | − | 1.26136i | ||||
\(438\) | 0.149856 | − | 0.259558i | 0.00716039 | − | 0.0124022i | ||||
\(439\) | −8.50036 | − | 14.7231i | −0.405700 | − | 0.702693i | 0.588703 | − | 0.808350i | \(-0.299639\pi\) |
−0.994403 | + | 0.105657i | \(0.966306\pi\) | |||||||
\(440\) | −1.55388 | + | 0.416362i | −0.0740785 | + | 0.0198493i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.74750 | + | 0.435405i | −0.0831203 | + | 0.0207101i | ||||
\(443\) | 18.3082 | − | 31.7108i | 0.869851 | − | 1.50663i | 0.00770183 | − | 0.999970i | \(-0.497548\pi\) |
0.862149 | − | 0.506655i | \(-0.169118\pi\) | |||||||
\(444\) | 10.3261 | − | 10.3261i | 0.490056 | − | 0.490056i | ||||
\(445\) | −14.1882 | −0.672583 | ||||||||
\(446\) | −0.513645 | −0.0243218 | ||||||||
\(447\) | 28.4042 | − | 28.4042i | 1.34347 | − | 1.34347i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.7480 | − | 8.77481i | −1.54547 | − | 0.414109i | −0.617445 | − | 0.786614i | \(-0.711832\pi\) |
−0.928030 | + | 0.372505i | \(0.878499\pi\) | |||||||
\(450\) | 0.213555 | + | 0.796999i | 0.0100671 | + | 0.0375709i | ||||
\(451\) | −19.3181 | − | 11.1533i | −0.909654 | − | 0.525189i | ||||
\(452\) | 16.9722i | 0.798305i | ||||||||
\(453\) | −2.97342 | + | 11.0970i | −0.139704 | + | 0.521381i | ||||
\(454\) | −0.478554 | −0.0224596 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.16202 | −0.241734 | ||||||||
\(457\) | 0.585644 | − | 2.18565i | 0.0273953 | − | 0.102241i | −0.950874 | − | 0.309577i | \(-0.899813\pi\) |
0.978270 | + | 0.207336i | \(0.0664793\pi\) | |||||||
\(458\) | − | 1.58516i | − | 0.0740698i | ||||||
\(459\) | 7.25273 | + | 4.18737i | 0.338528 | + | 0.195449i | ||||
\(460\) | 5.80566 | + | 21.6670i | 0.270690 | + | 1.01023i | ||||
\(461\) | 24.5455 | + | 6.57694i | 1.14320 | + | 0.306319i | 0.780235 | − | 0.625486i | \(-0.215099\pi\) |
0.362961 | + | 0.931804i | \(0.381766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.6265 | + | 22.6265i | −1.05154 | + | 1.05154i | −0.0529442 | + | 0.998597i | \(0.516861\pi\) |
−0.998597 | + | 0.0529442i | \(0.983139\pi\) | |||||||
\(464\) | −28.0521 | −1.30229 | ||||||||
\(465\) | −19.6361 | −0.910601 | ||||||||
\(466\) | 1.34981 | − | 1.34981i | 0.0625288 | − | 0.0625288i | ||||
\(467\) | −5.64704 | + | 9.78095i | −0.261314 | + | 0.452609i | −0.966591 | − | 0.256323i | \(-0.917489\pi\) |
0.705278 | + | 0.708931i | \(0.250822\pi\) | |||||||
\(468\) | −23.5126 | + | 13.0283i | −1.08687 | + | 0.602235i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.31967 | + | 0.353604i | −0.0608718 | + | 0.0163105i | ||||
\(471\) | 9.00535 | + | 15.5977i | 0.414945 | + | 0.718705i | ||||
\(472\) | −0.392653 | + | 0.680095i | −0.0180733 | + | 0.0313039i | ||||
\(473\) | 0.908251 | − | 3.38964i | 0.0417614 | − | 0.155856i | ||||
\(474\) | −1.27378 | + | 1.27378i | −0.0585066 | + | 0.0585066i | ||||
\(475\) | 2.07991 | − | 7.76231i | 0.0954326 | − | 0.356159i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.02814 | + | 13.9051i | 0.367583 | + | 0.636673i | ||||
\(478\) | 0.874396 | − | 0.504833i | 0.0399939 | − | 0.0230905i | ||||
\(479\) | 14.1810 | + | 14.1810i | 0.647945 | + | 0.647945i | 0.952496 | − | 0.304551i | \(-0.0985064\pi\) |
−0.304551 | + | 0.952496i | \(0.598506\pi\) | |||||||
\(480\) | 5.51639 | − | 3.18489i | 0.251788 | − | 0.145370i | ||||
\(481\) | 7.33850 | − | 7.08444i | 0.334607 | − | 0.323023i | ||||
\(482\) | − | 1.56814i | − | 0.0714269i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.11843 | + | 12.3295i | −0.323565 | + | 0.560431i | ||||
\(485\) | − | 26.0785i | − | 1.18416i | ||||||
\(486\) | 2.47133 | + | 0.662191i | 0.112102 | + | 0.0300376i | ||||
\(487\) | 30.3456 | − | 8.13109i | 1.37509 | − | 0.368455i | 0.505756 | − | 0.862676i | \(-0.331213\pi\) |
0.869336 | + | 0.494221i | \(0.164547\pi\) | |||||||
\(488\) | −1.01449 | − | 1.01449i | −0.0459238 | − | 0.0459238i | ||||
\(489\) | −23.7691 | − | 23.7691i | −1.07488 | − | 1.07488i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8341 | − | 9.71919i | −0.759714 | − | 0.438621i | 0.0694792 | − | 0.997583i | \(-0.477866\pi\) |
−0.829193 | + | 0.558962i | \(0.811200\pi\) | |||||||
\(492\) | 56.8122 | + | 15.2228i | 2.56129 | + | 0.686296i | ||||
\(493\) | 15.3138 | + | 26.5243i | 0.689698 | + | 1.19459i | ||||
\(494\) | −1.79634 | − | 0.0316425i | −0.0808213 | − | 0.00142366i | ||||
\(495\) | 11.2349 | + | 6.48647i | 0.504971 | + | 0.291545i | ||||
\(496\) | −4.34038 | − | 16.1985i | −0.194889 | − | 0.727336i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.67021 | − | 2.11900i | 0.164466 | − | 0.0949545i | ||||
\(499\) | −16.1261 | + | 4.32098i | −0.721904 | + | 0.193434i | −0.601021 | − | 0.799233i | \(-0.705239\pi\) |
−0.120883 | + | 0.992667i | \(0.538573\pi\) | |||||||
\(500\) | 6.24745 | + | 23.3158i | 0.279394 | + | 1.04271i | ||||
\(501\) | −0.627031 | − | 2.34011i | −0.0280137 | − | 0.104548i | ||||
\(502\) | 0.393138 | − | 0.105341i | 0.0175466 | − | 0.00470160i | ||||
\(503\) | −25.9585 | + | 14.9871i | −1.15743 | + | 0.668243i | −0.950687 | − | 0.310153i | \(-0.899620\pi\) |
−0.206743 | + | 0.978395i | \(0.566287\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.31560 | − | 27.3022i | −0.325540 | − | 1.21493i | ||||
\(506\) | 1.26612 | + | 0.730997i | 0.0562861 | + | 0.0324968i | ||||
\(507\) | −29.8339 | + | 15.8507i | −1.32497 | + | 0.703955i | ||||
\(508\) | −6.07227 | − | 10.5175i | −0.269413 | − | 0.466638i | ||||
\(509\) | −13.5446 | − | 3.62928i | −0.600356 | − | 0.160865i | −0.0541739 | − | 0.998532i | \(-0.517253\pi\) |
−0.546182 | + | 0.837667i | \(0.683919\pi\) | |||||||
\(510\) | −1.98466 | − | 1.14585i | −0.0878824 | − | 0.0507389i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.42580 | + | 6.42580i | 0.283983 | + | 0.283983i | ||||
\(513\) | 5.90766 | + | 5.90766i | 0.260830 | + | 0.260830i | ||||
\(514\) | −1.51659 | + | 0.406370i | −0.0668940 | + | 0.0179242i | ||||
\(515\) | −20.1491 | − | 5.39893i | −0.887874 | − | 0.237905i | ||||
\(516\) | 9.25280i | 0.407332i | ||||||||
\(517\) | 6.48785 | − | 11.2373i | 0.285335 | − | 0.494215i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.37097i | 0.0601791i | ||||||||
\(520\) | 2.59150 | − | 1.43595i | 0.113645 | − | 0.0629705i | ||||
\(521\) | −0.757986 | + | 0.437623i | −0.0332080 | + | 0.0191726i | −0.516512 | − | 0.856280i | \(-0.672770\pi\) |
0.483304 | + | 0.875453i | \(0.339437\pi\) | |||||||
\(522\) | −2.21832 | − | 2.21832i | −0.0970931 | − | 0.0970931i | ||||
\(523\) | −11.7198 | + | 6.76640i | −0.512469 | + | 0.295874i | −0.733848 | − | 0.679314i | \(-0.762278\pi\) |
0.221379 | + | 0.975188i | \(0.428944\pi\) | |||||||
\(524\) | 5.72506 | + | 9.91610i | 0.250100 | + | 0.433187i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.620553 | − | 2.31593i | 0.0270574 | − | 0.100980i | ||||
\(527\) | −12.9468 | + | 12.9468i | −0.563973 | + | 0.563973i | ||||
\(528\) | −5.15960 | + | 19.2559i | −0.224543 | + | 0.838004i | ||||
\(529\) | 8.95568 | − | 15.5117i | 0.389377 | − | 0.674421i | ||||
\(530\) | −0.440907 | − | 0.763674i | −0.0191518 | − | 0.0331719i | ||||
\(531\) | 6.11711 | − | 1.63908i | 0.265460 | − | 0.0711298i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.4888 | + | 11.3301i | 1.71045 | + | 0.490759i | ||||
\(534\) | 1.21913 | − | 2.11159i | 0.0527569 | − | 0.0913776i | ||||
\(535\) | 9.97623 | − | 9.97623i | 0.431310 | − | 0.431310i | ||||
\(536\) | 0.00917329 | 0.000396226 | ||||||||
\(537\) | −21.4914 | −0.927423 | ||||||||
\(538\) | −0.886440 | + | 0.886440i | −0.0382171 | + | 0.0382171i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.63121 | − | 1.77683i | −0.285362 | − | 0.0764625i | ||||
\(541\) | 3.18000 | + | 11.8679i | 0.136719 | + | 0.510241i | 0.999985 | + | 0.00549222i | \(0.00174824\pi\) |
−0.863266 | + | 0.504749i | \(0.831585\pi\) | |||||||
\(542\) | 0.151539 | + | 0.0874914i | 0.00650918 | + | 0.00375808i | ||||
\(543\) | 38.9248i | 1.67042i | ||||||||
\(544\) | 1.53725 | − | 5.73710i | 0.0659091 | − | 0.245976i | ||||
\(545\) | −21.8634 | −0.936526 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2786 | 0.696022 | 0.348011 | − | 0.937490i | \(-0.386857\pi\) | ||||
0.348011 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(548\) | −3.22641 | + | 12.0411i | −0.137825 | + | 0.514371i | ||||
\(549\) | 11.5698i | 0.493788i | ||||||||
\(550\) | 0.372723 | + | 0.215192i | 0.0158930 | + | 0.00917582i | ||||
\(551\) | 7.90803 | + | 29.5132i | 0.336894 | + | 1.25730i | ||||
\(552\) | −7.47258 | − | 2.00227i | −0.318054 | − | 0.0852224i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.388865 | + | 0.388865i | −0.0165213 | + | 0.0165213i | ||||
\(555\) | 12.9797 | 0.550959 | ||||||||
\(556\) | 41.5874 | 1.76370 | ||||||||
\(557\) | 5.84312 | − | 5.84312i | 0.247581 | − | 0.247581i | −0.572396 | − | 0.819977i | \(-0.693986\pi\) |
0.819977 | + | 0.572396i | \(0.193986\pi\) | |||||||
\(558\) | 0.937724 | − | 1.62418i | 0.0396970 | − | 0.0687572i | ||||
\(559\) | −0.113826 | + | 6.46190i | −0.00481433 | + | 0.273309i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.0237 | − | 5.63329i | 0.887623 | − | 0.237838i | ||||
\(562\) | −0.661470 | − | 1.14570i | −0.0279024 | − | 0.0483285i | ||||
\(563\) | −14.0767 | + | 24.3815i | −0.593261 | + | 1.02756i | 0.400528 | + | 0.916284i | \(0.368827\pi\) |
−0.993790 | + | 0.111274i | \(0.964507\pi\) | |||||||
\(564\) | −8.85505 | + | 33.0475i | −0.372865 | + | 1.39155i | ||||
\(565\) | −10.6669 | + | 10.6669i | −0.448759 | + | 0.448759i | ||||
\(566\) | −0.238078 | + | 0.888519i | −0.0100072 | + | 0.0373472i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.10691 | − | 1.91722i | −0.0464448 | − | 0.0804447i | ||||
\(569\) | 8.62645 | − | 4.98048i | 0.361640 | − | 0.208793i | −0.308160 | − | 0.951335i | \(-0.599713\pi\) |
0.669800 | + | 0.742542i | \(0.266380\pi\) | |||||||
\(570\) | −1.61659 | − | 1.61659i | −0.0677117 | − | 0.0677117i | ||||
\(571\) | −4.46188 | + | 2.57607i | −0.186724 | + | 0.107805i | −0.590448 | − | 0.807076i | \(-0.701049\pi\) |
0.403724 | + | 0.914881i | \(0.367716\pi\) | |||||||
\(572\) | −3.86692 | + | 13.4774i | −0.161684 | + | 0.563519i | ||||
\(573\) | 37.7572i | 1.57733i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.02177 | − | 10.4300i | 0.251125 | − | 0.434962i | ||||
\(576\) | − | 28.8053i | − | 1.20022i | ||||||
\(577\) | −12.9819 | − | 3.47849i | −0.540444 | − | 0.144812i | −0.0217373 | − | 0.999764i | \(-0.506920\pi\) |
−0.518707 | + | 0.854952i | \(0.673586\pi\) | |||||||
\(578\) | −0.146889 | + | 0.0393588i | −0.00610978 | + | 0.00163711i | ||||
\(579\) | −35.9754 | − | 35.9754i | −1.49509 | − | 1.49509i | ||||
\(580\) | −17.7532 | − | 17.7532i | −0.737161 | − | 0.737161i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.88120 | + | 2.24081i | 0.160881 | + | 0.0928847i | ||||
\(583\) | 8.08967 | + | 2.16762i | 0.335040 | + | 0.0897737i | ||||
\(584\) | 0.229876 | + | 0.398157i | 0.00951234 | + | 0.0164759i | ||||
\(585\) | −22.9656 | − | 6.58926i | −0.949512 | − | 0.272433i | ||||
\(586\) | 1.23535 | + | 0.713227i | 0.0510317 | + | 0.0294631i | ||||
\(587\) | −9.73498 | − | 36.3314i | −0.401806 | − | 1.49956i | −0.809872 | − | 0.586607i | \(-0.800463\pi\) |
0.408066 | − | 0.912952i | \(-0.366203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.8186 | + | 9.13289i | −0.651795 | + | 0.376314i | ||||
\(590\) | −0.335953 | + | 0.0900184i | −0.0138310 | + | 0.00370600i | ||||
\(591\) | 14.6350 | + | 54.6184i | 0.602001 | + | 2.24670i | ||||
\(592\) | 2.86906 | + | 10.7075i | 0.117918 | + | 0.440074i | ||||
\(593\) | 35.2975 | − | 9.45795i | 1.44950 | − | 0.388391i | 0.553648 | − | 0.832751i | \(-0.313235\pi\) |
0.895848 | + | 0.444360i | \(0.146569\pi\) | |||||||
\(594\) | −0.387498 | + | 0.223722i | −0.0158992 | + | 0.00917944i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.94687 | + | 29.6581i | 0.325517 | + | 1.21484i | ||||
\(597\) | −43.3935 | − | 25.0532i | −1.77598 | − | 1.02536i | ||||
\(598\) | −2.58813 | − | 0.742581i | −0.105836 | − | 0.0303664i | ||||
\(599\) | −2.66014 | − | 4.60749i | −0.108690 | − | 0.188257i | 0.806550 | − | 0.591166i | \(-0.201332\pi\) |
−0.915240 | + | 0.402909i | \(0.867999\pi\) | |||||||
\(600\) | −2.19979 | − | 0.589432i | −0.0898061 | − | 0.0240635i | ||||
\(601\) | 21.4564 | + | 12.3879i | 0.875225 | + | 0.505312i | 0.869081 | − | 0.494669i | \(-0.164711\pi\) |
0.00614424 | + | 0.999981i | \(0.498044\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0523087 | − | 0.0523087i | −0.00213017 | − | 0.00213017i | ||||
\(604\) | −6.20937 | − | 6.20937i | −0.252656 | − | 0.252656i | ||||
\(605\) | −12.2228 | + | 3.27510i | −0.496929 | + | 0.133152i | ||||
\(606\) | 4.69193 | + | 1.25720i | 0.190596 | + | 0.0510702i | ||||
\(607\) | − | 22.5591i | − | 0.915644i | −0.889044 | − | 0.457822i | \(-0.848630\pi\) | ||
0.889044 | − | 0.457822i | \(-0.151370\pi\) | |||||||
\(608\) | 2.96263 | − | 5.13143i | 0.120151 | − | 0.208107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 0.635418i | − | 0.0257273i | ||||||
\(611\) | −6.59066 | + | 22.9705i | −0.266630 | + | 0.929288i | ||||
\(612\) | −27.6221 | + | 15.9476i | −1.11656 | + | 0.644645i | ||||
\(613\) | 16.2662 | + | 16.2662i | 0.656986 | + | 0.656986i | 0.954666 | − | 0.297680i | \(-0.0962128\pi\) |
−0.297680 | + | 0.954666i | \(0.596213\pi\) | |||||||
\(614\) | 1.13995 | − | 0.658151i | 0.0460047 | − | 0.0265608i | ||||
\(615\) | 26.1385 | + | 45.2733i | 1.05401 | + | 1.82560i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.79350 | − | 29.0858i | 0.313755 | − | 1.17095i | −0.611389 | − | 0.791330i | \(-0.709389\pi\) |
0.925143 | − | 0.379618i | \(-0.123945\pi\) | |||||||
\(618\) | 2.53484 | − | 2.53484i | 0.101966 | − | 0.101966i | ||||
\(619\) | −2.76561 | + | 10.3214i | −0.111159 | + | 0.414852i | −0.998971 | − | 0.0453549i | \(-0.985558\pi\) |
0.887812 | + | 0.460207i | \(0.152225\pi\) | |||||||
\(620\) | 7.50459 | − | 12.9983i | 0.301392 | − | 0.522026i | ||||
\(621\) | 6.26048 | + | 10.8435i | 0.251224 | + | 0.435133i | ||||
\(622\) | −1.47090 | + | 0.394127i | −0.0589778 | + | 0.0158031i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.646624 | − | 36.7088i | 0.0258857 | − | 1.46953i | ||||
\(625\) | −6.01999 | + | 10.4269i | −0.240800 | + | 0.417077i | ||||
\(626\) | −0.295052 | + | 0.295052i | −0.0117927 | + | 0.0117927i | ||||
\(627\) | 21.7133 | 0.867146 | ||||||||
\(628\) | −13.7668 | −0.549355 | ||||||||
\(629\) | 8.55805 | − | 8.55805i | 0.341232 | − | 0.341232i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6759 | + | 3.66444i | 0.544428 | + | 0.145879i | 0.520543 | − | 0.853836i | \(-0.325730\pi\) |
0.0238855 | + | 0.999715i | \(0.492396\pi\) | |||||||
\(632\) | −0.715196 | − | 2.66915i | −0.0284490 | − | 0.106173i | ||||
\(633\) | −6.80249 | − | 3.92742i | −0.270375 | − | 0.156101i | ||||
\(634\) | 3.87301i | 0.153817i | ||||||||
\(635\) | 2.79377 | − | 10.4265i | 0.110867 | − | 0.413763i | ||||
\(636\) | −22.0826 | −0.875633 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.63637 | −0.0647844 | ||||||||
\(639\) | −4.62063 | + | 17.2444i | −0.182789 | + | 0.682179i | ||||
\(640\) | 6.48426i | 0.256313i | ||||||||
\(641\) | 32.0667 | + | 18.5137i | 1.26656 | + | 0.731248i | 0.974335 | − | 0.225102i | \(-0.0722714\pi\) |
0.292224 | + | 0.956350i | \(0.405605\pi\) | |||||||
\(642\) | 0.627525 | + | 2.34196i | 0.0247664 | + | 0.0924296i | ||||
\(643\) | 33.2886 | + | 8.91965i | 1.31277 | + | 0.351757i | 0.846266 | − | 0.532761i | \(-0.178845\pi\) |
0.466507 | + | 0.884517i | \(0.345512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.81530 | + | 5.81530i | −0.228977 | + | 0.228977i | ||||
\(646\) | −2.13177 | −0.0838733 | ||||||||
\(647\) | 6.06726 | 0.238529 | 0.119264 | − | 0.992863i | \(-0.461946\pi\) | ||||
0.119264 | + | 0.992863i | \(0.461946\pi\) | |||||||
\(648\) | −2.03146 | + | 2.03146i | −0.0798034 | + | 0.0798034i | ||||
\(649\) | 1.65164 | − | 2.86072i | 0.0648325 | − | 0.112293i | ||||
\(650\) | −0.761896 | − | 0.218602i | −0.0298840 | − | 0.00857428i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.8184 | − | 6.65007i | 0.971964 | − | 0.260437i | ||||
\(653\) | −15.1009 | − | 26.1555i | −0.590943 | − | 1.02354i | −0.994106 | − | 0.108416i | \(-0.965422\pi\) |
0.403162 | − | 0.915129i | \(-0.367911\pi\) | |||||||
\(654\) | 1.87863 | − | 3.25389i | 0.0734603 | − | 0.127237i | ||||
\(655\) | −2.63403 | + | 9.83033i | −0.102920 | + | 0.384103i | ||||
\(656\) | −31.5699 | + | 31.5699i | −1.23260 | + | 1.23260i | ||||
\(657\) | 0.959586 | − | 3.58123i | 0.0374370 | − | 0.139717i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.37179 | + | 7.57216i | 0.170301 | + | 0.294969i | 0.938525 | − | 0.345211i | \(-0.112193\pi\) |
−0.768224 | + | 0.640181i | \(0.778859\pi\) | |||||||
\(660\) | −15.4517 | + | 8.92102i | −0.601455 | + | 0.347250i | ||||
\(661\) | 12.7006 | + | 12.7006i | 0.493996 | + | 0.493996i | 0.909563 | − | 0.415566i | \(-0.136417\pi\) |
−0.415566 | + | 0.909563i | \(0.636417\pi\) | |||||||
\(662\) | −0.0958671 | + | 0.0553489i | −0.00372598 | + | 0.00215120i | ||||
\(663\) | −35.0624 | + | 19.4281i | −1.36171 | + | 0.754525i | ||||
\(664\) | 6.50100i | 0.252288i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.619849 | + | 1.07361i | −0.0240187 | + | 0.0416015i | ||||
\(667\) | 45.7909i | 1.77303i | ||||||||
\(668\) | 1.78870 | + | 0.479282i | 0.0692071 | + | 0.0185440i | ||||
\(669\) | −11.0432 | + | 2.95901i | −0.426954 | + | 0.114402i | ||||
\(670\) | 0.00287281 | + | 0.00287281i | 0.000110986 | + | 0.000110986i | ||||
\(671\) | 4.26731 | + | 4.26731i | 0.164738 | + | 0.164738i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0524 | + | 12.7319i | 0.850057 | + | 0.490780i | 0.860670 | − | 0.509163i | \(-0.170045\pi\) |
−0.0106133 | + | 0.999944i | \(0.503378\pi\) | |||||||
\(674\) | −1.60029 | − | 0.428796i | −0.0616408 | − | 0.0165166i | ||||
\(675\) | 1.84297 | + | 3.19212i | 0.0709359 | + | 0.122865i | ||||
\(676\) | 0.909453 | − | 25.8068i | 0.0349790 | − | 0.992568i | ||||
\(677\) | 18.9268 | + | 10.9274i | 0.727415 | + | 0.419973i | 0.817476 | − | 0.575963i | \(-0.195373\pi\) |
−0.0900609 | + | 0.995936i | \(0.528706\pi\) | |||||||
\(678\) | −0.670968 | − | 2.50409i | −0.0257684 | − | 0.0961689i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.04444 | − | 1.75771i | 0.116749 | − | 0.0674050i | ||||
\(681\) | −10.2887 | + | 2.75686i | −0.394265 | + | 0.105643i | ||||
\(682\) | −0.253188 | − | 0.944911i | −0.00969507 | − | 0.0361825i | ||||
\(683\) | −8.29515 | − | 30.9579i | −0.317405 | − | 1.18457i | −0.921729 | − | 0.387833i | \(-0.873224\pi\) |
0.604324 | − | 0.796738i | \(-0.293443\pi\) | |||||||
\(684\) | −30.7348 | + | 8.23535i | −1.17517 | + | 0.314887i | ||||
\(685\) | −9.59550 | + | 5.53997i | −0.366625 | + | 0.211671i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.13183 | − | 34.0804i | −0.348401 | − | 1.30025i | ||||
\(688\) | −6.08268 | − | 3.51184i | −0.231900 | − | 0.133888i | ||||
\(689\) | −15.4219 | − | 0.271656i | −0.587527 | − | 0.0103493i | ||||
\(690\) | −1.71314 | − | 2.96725i | −0.0652182 | − | 0.112961i | ||||
\(691\) | −27.1642 | − | 7.27863i | −1.03337 | − | 0.276892i | −0.298010 | − | 0.954563i | \(-0.596323\pi\) |
−0.735365 | + | 0.677671i | \(0.762989\pi\) | |||||||
\(692\) | −0.907533 | − | 0.523964i | −0.0344992 | − | 0.0199181i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.14276 | + | 1.14276i | 0.0433786 | + | 0.0433786i | ||||
\(695\) | 26.1373 | + | 26.1373i | 0.991444 | + | 0.991444i | ||||
\(696\) | 8.36385 | − | 2.24109i | 0.317031 | − | 0.0849482i | ||||
\(697\) | 47.0846 | + | 12.6163i | 1.78346 | + | 0.477876i | ||||
\(698\) | 1.78740i | 0.0676542i | ||||||||
\(699\) | 21.2445 | − | 36.7965i | 0.803540 | − | 1.39177i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.8411i | 1.58032i | 0.612904 | + | 0.790158i | \(0.290001\pi\) | ||||
−0.612904 | + | 0.790158i | \(0.709999\pi\) | |||||||
\(702\) | 0.592869 | − | 0.572343i | 0.0223764 | − | 0.0216017i | ||||
\(703\) | 10.4563 | − | 6.03698i | 0.394369 | − | 0.227689i | ||||
\(704\) | −10.6243 | − | 10.6243i | −0.400418 | − | 0.400418i | ||||
\(705\) | −26.3354 | + | 15.2047i | −0.991847 | + | 0.572643i | ||||
\(706\) | −0.919455 | − | 1.59254i | −0.0346041 | − | 0.0599361i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.25426 | + | 8.41303i | −0.0847204 | + | 0.316181i | ||||
\(709\) | 26.4279 | − | 26.4279i | 0.992520 | − | 0.992520i | −0.00745226 | − | 0.999972i | \(-0.502372\pi\) |
0.999972 | + | 0.00745226i | \(0.00237215\pi\) | |||||||
\(710\) | 0.253766 | − | 0.947068i | 0.00952368 | − | 0.0355428i | ||||
\(711\) | −11.1420 | + | 19.2985i | −0.417857 | + | 0.723750i | ||||
\(712\) | 1.87012 | + | 3.23914i | 0.0700857 | + | 0.121392i | ||||
\(713\) | −26.4417 | + | 7.08503i | −0.990249 | + | 0.265336i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.9008 | + | 6.04011i | −0.407665 | + | 0.225887i | ||||
\(716\) | 8.21367 | − | 14.2265i | 0.306959 | − | 0.531669i | ||||
\(717\) | 15.8910 | − | 15.8910i | 0.593459 | − | 0.593459i | ||||
\(718\) | −0.774035 | −0.0288867 | ||||||||
\(719\) | 29.4939 | 1.09994 | 0.549968 | − | 0.835186i | \(-0.314640\pi\) | ||||
0.549968 | + | 0.835186i | \(0.314640\pi\) | |||||||
\(720\) | 18.3602 | − | 18.3602i | 0.684246 | − | 0.684246i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.0885265 | + | 0.0237206i | 0.00329461 | + | 0.000882789i | ||||
\(723\) | −9.03377 | − | 33.7145i | −0.335969 | − | 1.25386i | ||||
\(724\) | −25.7667 | − | 14.8764i | −0.957612 | − | 0.552878i | ||||
\(725\) | 13.4800i | 0.500635i | ||||||||
\(726\) | 0.562831 | − | 2.10051i | 0.0208886 | − | 0.0779574i | ||||
\(727\) | 3.04387 | 0.112891 | 0.0564455 | − | 0.998406i | \(-0.482023\pi\) | ||||
0.0564455 | + | 0.998406i | \(0.482023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.4293 | 1.42331 | ||||||||
\(730\) | −0.0527007 | + | 0.196682i | −0.00195054 | + | 0.00727952i | ||||
\(731\) | 7.66851i | 0.283630i | ||||||||
\(732\) | −13.7805 | − | 7.95615i | −0.509340 | − | 0.294068i | ||||
\(733\) | −0.339796 | − | 1.26813i | −0.0125506 | − | 0.0468396i | 0.959367 | − | 0.282163i | \(-0.0910518\pi\) |
−0.971917 | + | 0.235323i | \(0.924385\pi\) | |||||||
\(734\) | 3.70542 | + | 0.992865i | 0.136770 | + | 0.0366473i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.27914 | − | 6.27914i | 0.231452 | − | 0.231452i | ||||
\(737\) | −0.0385861 | −0.00142134 | ||||||||
\(738\) | −4.99300 | −0.183795 | ||||||||
\(739\) | −21.2184 | + | 21.2184i | −0.780533 | + | 0.780533i | −0.979921 | − | 0.199388i | \(-0.936105\pi\) |
0.199388 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(740\) | −4.96065 | + | 8.59209i | −0.182357 | + | 0.315852i | ||||
\(741\) | −38.8030 | + | 9.66809i | −1.42546 | + | 0.355166i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.4397 | + | 10.5678i | −1.44690 | + | 0.387697i | −0.894946 | − | 0.446175i | \(-0.852786\pi\) |
−0.551958 | + | 0.833872i | \(0.686119\pi\) | |||||||
\(744\) | 2.58820 | + | 4.48290i | 0.0948881 | + | 0.164351i | ||||
\(745\) | −13.6453 | + | 23.6344i | −0.499926 | + | 0.865897i | ||||
\(746\) | 0.238110 | − | 0.888638i | 0.00871782 | − | 0.0325354i | ||||
\(747\) | 37.0706 | − | 37.0706i | 1.35634 | − | 1.35634i | ||||
\(748\) | −4.30591 | + | 16.0699i | −0.157440 | + | 0.587573i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.84350 | − | 3.19304i | −0.0673153 | − | 0.116593i | ||||
\(751\) | 31.0690 | − | 17.9377i | 1.13372 | − | 0.654556i | 0.188856 | − | 0.982005i | \(-0.439522\pi\) |
0.944869 | + | 0.327448i | \(0.106189\pi\) | |||||||
\(752\) | −18.3642 | − | 18.3642i | −0.669672 | − | 0.669672i | ||||
\(753\) | 7.84547 | − | 4.52958i | 0.285905 | − | 0.165067i | ||||
\(754\) | 2.92429 | − | 0.728611i | 0.106496 | − | 0.0265345i | ||||
\(755\) | − | 7.80507i | − | 0.284056i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.439138 | + | 0.760610i | −0.0159607 | + | 0.0276448i | −0.873895 | − | 0.486114i | \(-0.838414\pi\) |
0.857935 | + | 0.513759i | \(0.171747\pi\) | |||||||
\(758\) | − | 1.30656i | − | 0.0474566i | ||||||
\(759\) | 31.4323 | + | 8.42227i | 1.14092 | + | 0.305709i | ||||
\(760\) | 3.38750 | − | 0.907679i | 0.122878 | − | 0.0329250i | ||||
\(761\) | 25.8663 | + | 25.8663i | 0.937654 | + | 0.937654i | 0.998167 | − | 0.0605137i | \(-0.0192739\pi\) |
−0.0605137 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(762\) | 1.31170 | + | 1.31170i | 0.0475178 | + | 0.0475178i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.9938 | − | 14.4302i | −0.904245 | − | 0.522066i | ||||
\(765\) | −27.3832 | − | 7.33730i | −0.990041 | − | 0.265281i | ||||
\(766\) | −0.140720 | − | 0.243735i | −0.00508443 | − | 0.00880649i | ||||
\(767\) | −1.67781 | + | 5.84769i | −0.0605822 | + | 0.211148i | ||||
\(768\) | 33.5795 | + | 19.3871i | 1.21170 | + | 0.699573i | ||||
\(769\) | −7.85943 | − | 29.3318i | −0.283418 | − | 1.05773i | −0.949987 | − | 0.312288i | \(-0.898904\pi\) |
0.666569 | − | 0.745443i | \(-0.267762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.2652 | + | 17.4736i | −1.08997 | + | 0.629297i | ||||
\(772\) | 37.5636 | − | 10.0651i | 1.35194 | − | 0.362252i | ||||
\(773\) | −5.13389 | − | 19.1599i | −0.184653 | − | 0.689134i | −0.994705 | − | 0.102776i | \(-0.967228\pi\) |
0.810052 | − | 0.586359i | \(-0.199439\pi\) | |||||||
\(774\) | −0.203298 | − | 0.758719i | −0.00730740 | − | 0.0272716i | ||||
\(775\) | −7.78395 | + | 2.08570i | −0.279608 | + | 0.0749206i | ||||
\(776\) | −5.95369 | + | 3.43737i | −0.213725 | + | 0.123394i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.508297 | + | 1.89699i | 0.0182233 | + | 0.0680104i | ||||
\(779\) | 42.1139 | + | 24.3145i | 1.50889 | + | 0.871157i | ||||
\(780\) | 23.6409 | − | 22.8224i | 0.846480 | − | 0.817175i | ||||
\(781\) | 4.65605 | + | 8.06451i | 0.166606 | + | 0.288571i | ||||
\(782\) | −3.08596 | − | 0.826882i | −0.110354 | − | 0.0295692i | ||||
\(783\) | −12.1368 | − | 7.00718i | −0.433733 | − | 0.250416i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.65231 | − | 8.65231i | −0.308814 | − | 0.308814i | ||||
\(786\) | −1.23670 | − | 1.23670i | −0.0441115 | − | 0.0441115i | ||||
\(787\) | 8.48989 | − | 2.27486i | 0.302632 | − | 0.0810900i | −0.104308 | − | 0.994545i | \(-0.533263\pi\) |
0.406940 | + | 0.913455i | \(0.366596\pi\) | |||||||
\(788\) | −41.7485 | − | 11.1865i | −1.48723 | − | 0.398502i | ||||
\(789\) | − | 53.3666i | − | 1.89990i | ||||||
\(790\) | 0.611921 | − | 1.05988i | 0.0217712 | − | 0.0377087i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 3.41989i | − | 0.121521i | ||||||
\(793\) | −9.52601 | − | 5.72588i | −0.338279 | − | 0.203332i | ||||
\(794\) | 2.37865 | − | 1.37332i | 0.0844152 | − | 0.0487372i | ||||
\(795\) | −13.8787 | − | 13.8787i | −0.492228 | − | 0.492228i | ||||
\(796\) | 33.1686 | − | 19.1499i | 1.17563 | − | 0.678750i | ||||
\(797\) | −12.3887 | − | 21.4579i | −0.438832 | − | 0.760079i | 0.558768 | − | 0.829324i | \(-0.311274\pi\) |
−0.997600 | + | 0.0692450i | \(0.977941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.33886 | + | 27.3890i | −0.259630 | + | 0.968953i | ||||
\(800\) | 1.84846 | − | 1.84846i | 0.0653531 | − | 0.0653531i | ||||
\(801\) | 7.80656 | − | 29.1345i | 0.275831 | − | 1.02942i | ||||
\(802\) | −0.503695 | + | 0.872425i | −0.0177861 | + | 0.0308064i | ||||
\(803\) | −0.966941 | − | 1.67479i | −0.0341226 | − | 0.0591021i | ||||
\(804\) | 0.0982740 | − | 0.0263324i | 0.00346586 | − | 0.000928674i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.873195 | + | 1.57588i | 0.0307570 | + | 0.0555080i | ||||
\(807\) | −13.9515 | + | 24.1647i | −0.491117 | + | 0.850639i | ||||
\(808\) | −5.26881 | + | 5.26881i | −0.185356 | + | 0.185356i | ||||
\(809\) | 7.50747 | 0.263949 | 0.131974 | − | 0.991253i | \(-0.457868\pi\) | ||||
0.131974 | + | 0.991253i | \(0.457868\pi\) | |||||||
\(810\) | −1.27239 | −0.0447072 | ||||||||
\(811\) | −32.4572 | + | 32.4572i | −1.13973 | + | 1.13973i | −0.151229 | + | 0.988499i | \(0.548323\pi\) |
−0.988499 | + | 0.151229i | \(0.951677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.76207 | + | 1.00804i | 0.131941 | + | 0.0353536i | ||||
\(814\) | 0.167361 | + | 0.624600i | 0.00586600 | + | 0.0218922i | ||||
\(815\) | 19.7777 | + | 11.4186i | 0.692781 | + | 0.399977i | ||||
\(816\) | − | 43.5633i | − | 1.52502i | ||||||
\(817\) | −1.98001 | + | 7.38949i | −0.0692717 | + | 0.258526i | ||||
\(818\) | −1.56868 | −0.0548475 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39.9589 | −1.39543 | ||||||||
\(821\) | −8.15549 | + | 30.4367i | −0.284629 | + | 1.06225i | 0.664482 | + | 0.747305i | \(0.268652\pi\) |
−0.949110 | + | 0.314944i | \(0.898014\pi\) | |||||||
\(822\) | − | 1.90410i | − | 0.0664133i | ||||||
\(823\) | −27.4139 | − | 15.8274i | −0.955590 | − | 0.551710i | −0.0607767 | − | 0.998151i | \(-0.519358\pi\) |
−0.894813 | + | 0.446442i | \(0.852691\pi\) | |||||||
\(824\) | 1.42325 | + | 5.31164i | 0.0495813 | + | 0.185040i | ||||
\(825\) | 9.25310 | + | 2.47936i | 0.322152 | + | 0.0863203i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1824 | − | 25.1824i | 0.875678 | − | 0.875678i | −0.117406 | − | 0.993084i | \(-0.537458\pi\) |
0.993084 | + | 0.117406i | \(0.0374580\pi\) | |||||||
\(828\) | −47.6862 | −1.65721 | ||||||||
\(829\) | 2.10865 | 0.0732364 | 0.0366182 | − | 0.999329i | \(-0.488341\pi\) | ||||
0.0366182 | + | 0.999329i | \(0.488341\pi\) | |||||||
\(830\) | −2.03592 | + | 2.03592i | −0.0706679 | + | 0.0706679i | ||||
\(831\) | −6.12027 | + | 10.6006i | −0.212310 | + | 0.367732i | ||||
\(832\) | 23.7169 | + | 14.2557i | 0.822234 | + | 0.494227i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.13582 | + | 1.64409i | −0.212466 | + | 0.0569302i | ||||
\(835\) | 0.822960 | + | 1.42541i | 0.0284797 | + | 0.0493283i | ||||
\(836\) | −8.29847 | + | 14.3734i | −0.287009 | + | 0.497114i | ||||
\(837\) | 2.16838 | − | 8.09251i | 0.0749502 | − | 0.279718i | ||||
\(838\) | 1.43483 | − | 1.43483i | 0.0495654 | − | 0.0495654i | ||||
\(839\) | 6.14897 | − | 22.9483i | 0.212286 | − | 0.792262i | −0.774818 | − | 0.632184i | \(-0.782159\pi\) |
0.987104 | − | 0.160078i | \(-0.0511746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1262 | − | 19.2712i | −0.383663 | − | 0.664525i | ||||
\(842\) | −3.03847 | + | 1.75426i | −0.104713 | + | 0.0604558i | ||||
\(843\) | −20.8215 | − | 20.8215i | −0.717132 | − | 0.717132i | ||||
\(844\) | 5.19960 | − | 3.00199i | 0.178978 | − | 0.103333i | ||||
\(845\) | 16.7909 | − | 15.6477i | 0.577625 | − | 0.538298i | ||||
\(846\) | − | 2.90442i | − | 0.0998559i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.38131 | − | 14.5169i | 0.287815 | − | 0.498511i | ||||
\(849\) | 20.4744i | 0.702678i | ||||||||
\(850\) | −0.908451 | − | 0.243419i | −0.0311596 | − | 0.00834919i | ||||
\(851\) | 17.4783 | − | 4.68331i | 0.599150 | − | 0.160542i | ||||
\(852\) | −17.3619 | − | 17.3619i | −0.594807 | − | 0.594807i | ||||
\(853\) | 4.73993 | + | 4.73993i | 0.162292 | + | 0.162292i | 0.783581 | − | 0.621289i | \(-0.213391\pi\) |
−0.621289 | + | 0.783581i | \(0.713391\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.4924 | − | 14.1407i | −0.837621 | − | 0.483601i | ||||
\(856\) | −3.59252 | − | 0.962612i | −0.122790 | − | 0.0329014i | ||||
\(857\) | −5.66099 | − | 9.80512i | −0.193376 | − | 0.334936i | 0.752991 | − | 0.658031i | \(-0.228610\pi\) |
−0.946367 | + | 0.323094i | \(0.895277\pi\) | |||||||
\(858\) | 0.0377196 | − | 2.14134i | 0.00128773 | − | 0.0731041i | ||||
\(859\) | −41.9548 | − | 24.2226i | −1.43148 | − | 0.826465i | −0.434246 | − | 0.900794i | \(-0.642985\pi\) |
−0.997234 | + | 0.0743295i | \(0.976318\pi\) | |||||||
\(860\) | −1.62699 | − | 6.07202i | −0.0554800 | − | 0.207054i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.43991 | + | 1.40868i | −0.0831038 | + | 0.0479800i | ||||
\(863\) | 18.1110 | − | 4.85283i | 0.616506 | − | 0.165192i | 0.0629669 | − | 0.998016i | \(-0.479944\pi\) |
0.553539 | + | 0.832823i | \(0.313277\pi\) | |||||||
\(864\) | 0.703405 | + | 2.62514i | 0.0239303 | + | 0.0893091i | ||||
\(865\) | −0.241069 | − | 0.899682i | −0.00819660 | − | 0.0305901i | ||||
\(866\) | 0.512280 | − | 0.137265i | 0.0174080 | − | 0.00466445i | ||||
\(867\) | −2.93132 | + | 1.69240i | −0.0995529 | + | 0.0574769i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00837 | + | 11.2274i | 0.102052 | + | 0.380863i | ||||
\(870\) | 3.32116 | + | 1.91747i | 0.112598 | + | 0.0650083i | ||||
\(871\) | 0.0689558 | − | 0.0171809i | 0.00233648 | − | 0.000582153i | ||||
\(872\) | 2.88179 | + | 4.99140i | 0.0975896 | + | 0.169030i | ||||
\(873\) | 53.5505 | + | 14.3488i | 1.81241 | + | 0.485634i | ||||
\(874\) | −2.76018 | − | 1.59359i | −0.0933645 | − | 0.0539040i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.60561 | + | 3.60561i | 0.121822 | + | 0.121822i | ||||
\(877\) | 5.01143 | + | 5.01143i | 0.169224 | + | 0.169224i | 0.786638 | − | 0.617414i | \(-0.211820\pi\) |
−0.617414 | + | 0.786638i | \(0.711820\pi\) | |||||||
\(878\) | −1.91726 | + | 0.513728i | −0.0647044 | + | 0.0173375i | ||||
\(879\) | 30.6683 | + | 8.21753i | 1.03441 | + | 0.277171i | ||||
\(880\) | − | 13.5437i | − | 0.456556i | ||||||
\(881\) | 12.1808 | − | 21.0977i | 0.410380 | − | 0.710800i | −0.584551 | − | 0.811357i | \(-0.698729\pi\) |
0.994931 | + | 0.100557i | \(0.0320626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.51673i | 0.152000i | 0.997108 | + | 0.0760000i | \(0.0242149\pi\) | ||||
−0.997108 | + | 0.0760000i | \(0.975785\pi\) | |||||||
\(884\) | 0.539636 | − | 30.6351i | 0.0181499 | − | 1.03037i | ||||
\(885\) | −6.70430 | + | 3.87073i | −0.225362 | + | 0.130113i | ||||
\(886\) | −3.02295 | − | 3.02295i | −0.101558 | − | 0.101558i | ||||
\(887\) | 38.3035 | − | 22.1145i | 1.28611 | − | 0.742533i | 0.308148 | − | 0.951338i | \(-0.400291\pi\) |
0.977957 | + | 0.208805i | \(0.0669575\pi\) | |||||||
\(888\) | −1.71084 | − | 2.96326i | −0.0574121 | − | 0.0994406i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.428738 | + | 1.60007i | −0.0143713 | + | 0.0536346i | ||||
\(891\) | 8.54505 | − | 8.54505i | 0.286270 | − | 0.286270i | ||||
\(892\) | 2.26177 | − | 8.44106i | 0.0757298 | − | 0.282628i | ||||
\(893\) | −14.1437 | + | 24.4976i | −0.473300 | + | 0.819780i | ||||
\(894\) | −2.34497 | − | 4.06161i | −0.0784276 | − | 0.135841i | ||||
\(895\) | 14.1034 | − | 3.77900i | 0.471426 | − | 0.126318i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −59.9216 | − | 1.05552i | −2.00073 | − | 0.0352427i | ||||
\(898\) | −1.97916 | + | 3.42801i | −0.0660455 | + | 0.114394i | ||||
\(899\) | 21.6654 | − | 21.6654i | 0.722580 | − | 0.722580i | ||||
\(900\) | −14.0380 | −0.467932 | ||||||||
\(901\) | −18.3016 | −0.609714 | ||||||||
\(902\) | −1.84157 | + | 1.84157i | −0.0613176 | + | 0.0613176i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.84122 | + | 1.02925i | 0.127757 | + | 0.0342324i | ||||
\(905\) | −6.84445 | − | 25.5438i | −0.227517 | − | 0.849106i | ||||
\(906\) | 1.16161 | + | 0.670657i | 0.0385920 | + | 0.0222811i | ||||
\(907\) | − | 33.8866i | − | 1.12519i | −0.826734 | − | 0.562593i | \(-0.809804\pi\) | ||
0.826734 | − | 0.562593i | \(-0.190196\pi\) | |||||||
\(908\) | 2.10725 | − | 7.86438i | 0.0699317 | − | 0.260989i | ||||
\(909\) | 60.0885 | 1.99301 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.66390 | 0.154522 | 0.0772610 | − | 0.997011i | \(-0.475383\pi\) | ||||
0.0772610 | + | 0.997011i | \(0.475383\pi\) | |||||||
\(912\) | 11.2480 | − | 41.9783i | 0.372460 | − | 1.39004i | ||||
\(913\) | − | 27.3455i | − | 0.905005i | ||||||
\(914\) | −0.228791 | − | 0.132092i | −0.00756772 | − | 0.00436923i | ||||
\(915\) | −3.66052 | − | 13.6613i | −0.121013 | − | 0.451627i | ||||
\(916\) | 26.0500 | + | 6.98007i | 0.860716 | + | 0.230628i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.691394 | − | 0.691394i | 0.0228194 | − | 0.0228194i | ||||
\(919\) | 24.1800 | 0.797625 | 0.398812 | − | 0.917033i | \(-0.369422\pi\) | ||||
0.398812 | + | 0.917033i | \(0.369422\pi\) | |||||||
\(920\) | 5.25585 | 0.173280 | ||||||||
\(921\) | 20.7171 | − | 20.7171i | 0.682651 | − | 0.682651i | ||||
\(922\) | 1.48343 | − | 2.56938i | 0.0488542 | − | 0.0846180i | ||||
\(923\) | −11.9115 | − | 12.3386i | −0.392070 | − | 0.406131i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.14530 | − | 1.37868i | 0.169177 | − | 0.0453307i | ||||
\(926\) | 1.86798 | + | 3.23543i | 0.0613856 | + | 0.106323i | ||||
\(927\) | 22.1727 | − | 38.4043i | 0.728247 | − | 1.26136i | ||||
\(928\) | −2.57245 | + | 9.60051i | −0.0844448 | + | 0.315152i | ||||
\(929\) | −10.9812 | + | 10.9812i | −0.360282 | + | 0.360282i | −0.863917 | − | 0.503635i | \(-0.831996\pi\) |
0.503635 | + | 0.863917i | \(0.331996\pi\) | |||||||
\(930\) | −0.593364 | + | 2.21446i | −0.0194572 | + | 0.0726151i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.2386 | + | 28.1261i | 0.531913 | + | 0.921300i | ||||
\(933\) | −29.3534 | + | 16.9472i | −0.960987 | + | 0.554826i | ||||
\(934\) | 0.932407 | + | 0.932407i | 0.0305093 | + | 0.0305093i | ||||
\(935\) | −12.8060 | + | 7.39354i | −0.418801 | + | 0.241795i | ||||
\(936\) | 1.52274 | + | 6.11156i | 0.0497725 | + | 0.199762i | ||||
\(937\) | 25.4720i | 0.832134i | 0.909334 | + | 0.416067i | \(0.136592\pi\) | ||||
−0.909334 | + | 0.416067i | \(0.863408\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.64378 | + | 8.04326i | −0.151544 | + | 0.262482i | ||||
\(940\) | − | 23.2440i | − | 0.758136i | ||||||
\(941\) | −17.3112 | − | 4.63851i | −0.564328 | − | 0.151211i | −0.0346338 | − | 0.999400i | \(-0.511026\pi\) |
−0.529694 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(942\) | 2.03116 | − | 0.544248i | 0.0661788 | − | 0.0177326i | ||||
\(943\) | 51.5332 | + | 51.5332i | 1.67815 | + | 1.67815i | ||||
\(944\) | −4.67503 | − | 4.67503i | −0.152159 | − | 0.152159i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.354822 | − | 0.204856i | −0.0115362 | − | 0.00666046i | ||||
\(947\) | −12.0056 | − | 3.21690i | −0.390130 | − | 0.104535i | 0.0584214 | − | 0.998292i | \(-0.481393\pi\) |
−0.448552 | + | 0.893757i | \(0.648060\pi\) | |||||||
\(948\) | −15.3239 | − | 26.5417i | −0.497696 | − | 0.862035i | ||||
\(949\) | 2.47370 | + | 2.56241i | 0.0802998 | + | 0.0831795i | ||||
\(950\) | −0.812546 | − | 0.469124i | −0.0263625 | − | 0.0152204i | ||||
\(951\) | 22.3117 | + | 83.2684i | 0.723506 | + | 2.70016i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.0716 | − | 14.4751i | 0.812147 | − | 0.468893i | −0.0355538 | − | 0.999368i | \(-0.511320\pi\) |
0.847701 | + | 0.530474i | \(0.177986\pi\) | |||||||
\(954\) | 1.81075 | − | 0.485189i | 0.0586252 | − | 0.0157086i | ||||
\(955\) | −6.63914 | − | 24.7776i | −0.214838 | − | 0.801785i | ||||
\(956\) | 4.44594 | + | 16.5925i | 0.143792 | + | 0.536639i | ||||
\(957\) | −35.1813 | + | 9.42681i | −1.13725 | + | 0.304725i | ||||
\(958\) | 2.02778 | − | 1.17074i | 0.0655147 | − | 0.0378249i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.11358 | + | 34.0123i | 0.294140 | + | 1.09774i | ||||
\(961\) | −10.9841 | − | 6.34165i | −0.354325 | − | 0.204569i | ||||
\(962\) | −0.577195 | − | 1.04168i | −0.0186095 | − | 0.0335851i | ||||
\(963\) | 14.9965 | + | 25.9746i | 0.483254 | + | 0.837021i | ||||
\(964\) | 25.7703 | + | 6.90512i | 0.830004 | + | 0.222399i | ||||
\(965\) | 29.9342 | + | 17.2825i | 0.963617 | + | 0.556344i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.8937 | + | 20.8937i | 0.671895 | + | 0.671895i | 0.958153 | − | 0.286258i | \(-0.0924113\pi\) |
−0.286258 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(968\) | 2.35878 | + | 2.35878i | 0.0758140 | + | 0.0758140i | ||||
\(969\) | −45.8323 | + | 12.2807i | −1.47234 | + | 0.394513i | ||||
\(970\) | −2.94101 | − | 0.788040i | −0.0944300 | − | 0.0253024i | ||||
\(971\) | 41.0504i | 1.31737i | 0.752419 | + | 0.658685i | \(0.228887\pi\) | ||||
−0.752419 | + | 0.658685i | \(0.771113\pi\) | |||||||
\(972\) | −21.7644 | + | 37.6971i | −0.698094 | + | 1.20913i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 3.66794i | − | 0.117528i | ||||||
\(975\) | −17.6398 | − | 0.310725i | −0.564927 | − | 0.00995116i | ||||
\(976\) | 10.4606 | − | 6.03940i | 0.334834 | − | 0.193317i | ||||
\(977\) | 16.1451 | + | 16.1451i | 0.516527 | + | 0.516527i | 0.916519 | − | 0.399992i | \(-0.130987\pi\) |
−0.399992 | + | 0.916519i | \(0.630987\pi\) | |||||||
\(978\) | −3.39882 | + | 1.96231i | −0.108682 | + | 0.0627478i | ||||
\(979\) | −7.86639 | − | 13.6250i | −0.251411 | − | 0.435457i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0296 | − | 44.8951i | 0.384076 | − | 1.43339i | ||||
\(982\) | −1.60478 | + | 1.60478i | −0.0512105 | + | 0.0512105i | ||||
\(983\) | 7.70226 | − | 28.7452i | 0.245664 | − | 0.916831i | −0.727384 | − | 0.686230i | \(-0.759264\pi\) |
0.973048 | − | 0.230601i | \(-0.0740691\pi\) | |||||||
\(984\) | 6.89057 | − | 11.9348i | 0.219663 | − | 0.380468i | ||||
\(985\) | −19.2080 | − | 33.2692i | −0.612017 | − | 1.06004i | ||||
\(986\) | 3.45403 | − | 0.925505i | 0.109999 | − | 0.0294741i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.42998 | − | 29.3811i | 0.268193 | − | 0.934737i | ||||
\(989\) | −5.73255 | + | 9.92907i | −0.182285 | + | 0.315726i | ||||
\(990\) | 1.07101 | − | 1.07101i | 0.0340389 | − | 0.0340389i | ||||
\(991\) | −2.49766 | −0.0793406 | −0.0396703 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396703 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(992\) | −5.94178 | −0.188652 | ||||||||
\(993\) | −1.74225 | + | 1.74225i | −0.0552888 | + | 0.0552888i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.8817 | + | 8.81062i | 1.04242 | + | 0.279315i | ||||
\(996\) | 18.6615 | + | 69.6456i | 0.591312 | + | 2.20681i | ||||
\(997\) | −5.16724 | − | 2.98331i | −0.163648 | − | 0.0944823i | 0.415939 | − | 0.909392i | \(-0.363453\pi\) |
−0.579587 | + | 0.814910i | \(0.696786\pi\) | |||||||
\(998\) | 1.94920i | 0.0617008i | ||||||||
\(999\) | −1.43333 | + | 5.34926i | −0.0453486 | + | 0.169243i |
(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 | 637.2.x.b.215.3 | 32 | ||
7.2 | even | 3 | 91.2.bc.a.20.6 | yes | 32 | ||
7.3 | odd | 6 | 637.2.bb.b.423.4 | 32 | |||
7.4 | even | 3 | 637.2.bb.b.423.3 | 32 | |||
7.5 | odd | 6 | 91.2.bc.a.20.5 | ✓ | 32 | ||
7.6 | odd | 2 | inner | 637.2.x.b.215.4 | 32 | ||
13.2 | odd | 12 | 637.2.bb.b.509.4 | 32 | |||
21.2 | odd | 6 | 819.2.fm.g.748.3 | 32 | |||
21.5 | even | 6 | 819.2.fm.g.748.4 | 32 | |||
91.2 | odd | 12 | 91.2.bc.a.41.5 | yes | 32 | ||
91.41 | even | 12 | 637.2.bb.b.509.3 | 32 | |||
91.54 | even | 12 | 91.2.bc.a.41.6 | yes | 32 | ||
91.67 | odd | 12 | inner | 637.2.x.b.80.3 | 32 | ||
91.80 | even | 12 | inner | 637.2.x.b.80.4 | 32 | ||
273.2 | even | 12 | 819.2.fm.g.496.4 | 32 | |||
273.236 | odd | 12 | 819.2.fm.g.496.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.20.5 | ✓ | 32 | 7.5 | odd | 6 | ||
91.2.bc.a.20.6 | yes | 32 | 7.2 | even | 3 | ||
91.2.bc.a.41.5 | yes | 32 | 91.2 | odd | 12 | ||
91.2.bc.a.41.6 | yes | 32 | 91.54 | even | 12 | ||
637.2.x.b.80.3 | 32 | 91.67 | odd | 12 | inner | ||
637.2.x.b.80.4 | 32 | 91.80 | even | 12 | inner | ||
637.2.x.b.215.3 | 32 | 1.1 | even | 1 | trivial | ||
637.2.x.b.215.4 | 32 | 7.6 | odd | 2 | inner | ||
637.2.bb.b.423.3 | 32 | 7.4 | even | 3 | |||
637.2.bb.b.423.4 | 32 | 7.3 | odd | 6 | |||
637.2.bb.b.509.3 | 32 | 91.41 | even | 12 | |||
637.2.bb.b.509.4 | 32 | 13.2 | odd | 12 | |||
819.2.fm.g.496.3 | 32 | 273.236 | odd | 12 | |||
819.2.fm.g.496.4 | 32 | 273.2 | even | 12 | |||
819.2.fm.g.748.3 | 32 | 21.2 | odd | 6 | |||
819.2.fm.g.748.4 | 32 | 21.5 | even | 6 |