Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(267,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.267");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 267.23 | ||
Character | \(\chi\) | \(=\) | 380.267 |
Dual form | 380.2.k.c.343.23 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25747 | + | 0.647117i | 0.889168 | + | 0.457581i | ||||
\(3\) | 1.78847 | + | 1.78847i | 1.03257 | + | 1.03257i | 0.999451 | + | 0.0331206i | \(0.0105445\pi\) |
0.0331206 | + | 0.999451i | \(0.489455\pi\) | |||||||
\(4\) | 1.16248 | + | 1.62746i | 0.581240 | + | 0.813732i | ||||
\(5\) | 0.0829302 | − | 2.23453i | 0.0370875 | − | 0.999312i | ||||
\(6\) | 1.09160 | + | 3.40630i | 0.445645 | + | 1.39061i | ||||
\(7\) | 0.904221 | − | 0.904221i | 0.341763 | − | 0.341763i | −0.515267 | − | 0.857030i | \(-0.672307\pi\) |
0.857030 | + | 0.515267i | \(0.172307\pi\) | |||||||
\(8\) | 0.408628 | + | 2.79875i | 0.144472 | + | 0.989509i | ||||
\(9\) | 3.39723i | 1.13241i | ||||||||
\(10\) | 1.55028 | − | 2.75620i | 0.490243 | − | 0.871586i | ||||
\(11\) | − | 4.92807i | − | 1.48587i | −0.669365 | − | 0.742934i | \(-0.733434\pi\) | ||
0.669365 | − | 0.742934i | \(-0.266566\pi\) | |||||||
\(12\) | −0.831610 | + | 4.98972i | −0.240065 | + | 1.44041i | ||||
\(13\) | −4.64598 | + | 4.64598i | −1.28856 | + | 1.28856i | −0.352902 | + | 0.935660i | \(0.614805\pi\) |
−0.935660 | + | 0.352902i | \(0.885195\pi\) | |||||||
\(14\) | 1.72217 | − | 0.551898i | 0.460270 | − | 0.147501i | ||||
\(15\) | 4.14470 | − | 3.84806i | 1.07016 | − | 0.993566i | ||||
\(16\) | −1.29728 | + | 3.78379i | −0.324320 | + | 0.945947i | ||||
\(17\) | −3.50664 | − | 3.50664i | −0.850485 | − | 0.850485i | 0.139707 | − | 0.990193i | \(-0.455384\pi\) |
−0.990193 | + | 0.139707i | \(0.955384\pi\) | |||||||
\(18\) | −2.19840 | + | 4.27193i | −0.518169 | + | 1.00690i | ||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.73302 | − | 2.46263i | 0.834729 | − | 0.550661i | ||||
\(21\) | 3.23434 | 0.705791 | ||||||||
\(22\) | 3.18903 | − | 6.19691i | 0.679905 | − | 1.32119i | ||||
\(23\) | −2.65546 | − | 2.65546i | −0.553701 | − | 0.553701i | 0.373806 | − | 0.927507i | \(-0.378053\pi\) |
−0.927507 | + | 0.373806i | \(0.878053\pi\) | |||||||
\(24\) | −4.27466 | + | 5.73630i | −0.872562 | + | 1.17092i | ||||
\(25\) | −4.98625 | − | 0.370620i | −0.997249 | − | 0.0741240i | ||||
\(26\) | −8.84868 | + | 2.83570i | −1.73537 | + | 0.556127i | ||||
\(27\) | −0.710431 | + | 0.710431i | −0.136722 | + | 0.136722i | ||||
\(28\) | 2.52273 | + | 0.420449i | 0.476751 | + | 0.0794574i | ||||
\(29\) | 4.23410i | 0.786253i | 0.919484 | + | 0.393126i | \(0.128606\pi\) | ||||
−0.919484 | + | 0.393126i | \(0.871394\pi\) | |||||||
\(30\) | 7.70200 | − | 2.15673i | 1.40619 | − | 0.393764i | ||||
\(31\) | 6.52947i | 1.17273i | 0.810048 | + | 0.586364i | \(0.199441\pi\) | ||||
−0.810048 | + | 0.586364i | \(0.800559\pi\) | |||||||
\(32\) | −4.07985 | + | 3.91852i | −0.721223 | + | 0.692703i | ||||
\(33\) | 8.81369 | − | 8.81369i | 1.53427 | − | 1.53427i | ||||
\(34\) | −2.14030 | − | 6.67871i | −0.367059 | − | 1.14539i | ||||
\(35\) | −1.94552 | − | 2.09550i | −0.328853 | − | 0.354204i | ||||
\(36\) | −5.52887 | + | 3.94921i | −0.921478 | + | 0.658202i | ||||
\(37\) | −4.68490 | − | 4.68490i | −0.770193 | − | 0.770193i | 0.207947 | − | 0.978140i | \(-0.433322\pi\) |
−0.978140 | + | 0.207947i | \(0.933322\pi\) | |||||||
\(38\) | 1.25747 | + | 0.647117i | 0.203989 | + | 0.104976i | ||||
\(39\) | −16.6184 | −2.66107 | ||||||||
\(40\) | 6.28779 | − | 0.680990i | 0.994186 | − | 0.107674i | ||||
\(41\) | 3.99527 | 0.623956 | 0.311978 | − | 0.950089i | \(-0.399008\pi\) | ||||
0.311978 | + | 0.950089i | \(0.399008\pi\) | |||||||
\(42\) | 4.06710 | + | 2.09300i | 0.627567 | + | 0.322956i | ||||
\(43\) | 1.41043 | + | 1.41043i | 0.215088 | + | 0.215088i | 0.806425 | − | 0.591337i | \(-0.201400\pi\) |
−0.591337 | + | 0.806425i | \(0.701400\pi\) | |||||||
\(44\) | 8.02025 | − | 5.72878i | 1.20910 | − | 0.863646i | ||||
\(45\) | 7.59121 | + | 0.281733i | 1.13163 | + | 0.0419983i | ||||
\(46\) | −1.62078 | − | 5.05756i | −0.238971 | − | 0.745697i | ||||
\(47\) | 0.801371 | − | 0.801371i | 0.116892 | − | 0.116892i | −0.646241 | − | 0.763133i | \(-0.723660\pi\) |
0.763133 | + | 0.646241i | \(0.223660\pi\) | |||||||
\(48\) | −9.08733 | + | 4.44704i | −1.31164 | + | 0.641874i | ||||
\(49\) | 5.36477i | 0.766395i | ||||||||
\(50\) | −6.03024 | − | 3.69273i | −0.852804 | − | 0.522231i | ||||
\(51\) | − | 12.5430i | − | 1.75637i | ||||||
\(52\) | −12.9620 | − | 2.16031i | −1.79751 | − | 0.299581i | ||||
\(53\) | −2.72848 | + | 2.72848i | −0.374785 | + | 0.374785i | −0.869217 | − | 0.494431i | \(-0.835376\pi\) |
0.494431 | + | 0.869217i | \(0.335376\pi\) | |||||||
\(54\) | −1.35308 | + | 0.433616i | −0.184131 | + | 0.0590077i | ||||
\(55\) | −11.0119 | − | 0.408686i | −1.48485 | − | 0.0551072i | ||||
\(56\) | 2.90018 | + | 2.16120i | 0.387553 | + | 0.288803i | ||||
\(57\) | 1.78847 | + | 1.78847i | 0.236888 | + | 0.236888i | ||||
\(58\) | −2.73996 | + | 5.32427i | −0.359774 | + | 0.699111i | ||||
\(59\) | 13.9835 | 1.82050 | 0.910248 | − | 0.414063i | \(-0.135891\pi\) | ||||
0.910248 | + | 0.414063i | \(0.135891\pi\) | |||||||
\(60\) | 11.0807 | + | 2.27206i | 1.43051 | + | 0.293321i | ||||
\(61\) | 6.61259 | 0.846655 | 0.423327 | − | 0.905977i | \(-0.360862\pi\) | ||||
0.423327 | + | 0.905977i | \(0.360862\pi\) | |||||||
\(62\) | −4.22533 | + | 8.21063i | −0.536617 | + | 1.04275i | ||||
\(63\) | 3.07185 | + | 3.07185i | 0.387016 | + | 0.387016i | ||||
\(64\) | −7.66605 | + | 2.28730i | −0.958256 | + | 0.285912i | ||||
\(65\) | 9.99628 | + | 10.7669i | 1.23989 | + | 1.33547i | ||||
\(66\) | 16.7865 | − | 5.37949i | 2.06627 | − | 0.662170i | ||||
\(67\) | 1.41268 | − | 1.41268i | 0.172586 | − | 0.172586i | −0.615528 | − | 0.788115i | \(-0.711057\pi\) |
0.788115 | + | 0.615528i | \(0.211057\pi\) | |||||||
\(68\) | 1.63053 | − | 9.78333i | 0.197731 | − | 1.18640i | ||||
\(69\) | − | 9.49840i | − | 1.14347i | ||||||
\(70\) | −1.09041 | − | 3.89401i | −0.130329 | − | 0.465423i | ||||
\(71\) | − | 0.666584i | − | 0.0791089i | −0.999217 | − | 0.0395545i | \(-0.987406\pi\) | ||
0.999217 | − | 0.0395545i | \(-0.0125939\pi\) | |||||||
\(72\) | −9.50801 | + | 1.38820i | −1.12053 | + | 0.163601i | ||||
\(73\) | 9.09755 | − | 9.09755i | 1.06479 | − | 1.06479i | 0.0670369 | − | 0.997750i | \(-0.478645\pi\) |
0.997750 | − | 0.0670369i | \(-0.0213545\pi\) | |||||||
\(74\) | −2.85946 | − | 8.92281i | −0.332406 | − | 1.03726i | ||||
\(75\) | −8.25489 | − | 9.58058i | −0.953193 | − | 1.10627i | ||||
\(76\) | 1.16248 | + | 1.62746i | 0.133346 | + | 0.186683i | ||||
\(77\) | −4.45606 | − | 4.45606i | −0.507815 | − | 0.507815i | ||||
\(78\) | −20.8971 | − | 10.7540i | −2.36614 | − | 1.21765i | ||||
\(79\) | 7.09809 | 0.798598 | 0.399299 | − | 0.916821i | \(-0.369254\pi\) | ||||
0.399299 | + | 0.916821i | \(0.369254\pi\) | |||||||
\(80\) | 8.34741 | + | 3.21260i | 0.933268 | + | 0.359180i | ||||
\(81\) | 7.65052 | 0.850058 | ||||||||
\(82\) | 5.02395 | + | 2.58541i | 0.554802 | + | 0.285510i | ||||
\(83\) | 6.54308 | + | 6.54308i | 0.718196 | + | 0.718196i | 0.968236 | − | 0.250039i | \(-0.0804435\pi\) |
−0.250039 | + | 0.968236i | \(0.580444\pi\) | |||||||
\(84\) | 3.75985 | + | 5.26377i | 0.410234 | + | 0.574325i | ||||
\(85\) | −8.12650 | + | 7.54489i | −0.881443 | + | 0.818358i | ||||
\(86\) | 0.860863 | + | 2.68628i | 0.0928293 | + | 0.289669i | ||||
\(87\) | −7.57255 | + | 7.57255i | −0.811862 | + | 0.811862i | ||||
\(88\) | 13.7924 | − | 2.01375i | 1.47028 | − | 0.214666i | ||||
\(89\) | − | 6.08572i | − | 0.645085i | −0.946555 | − | 0.322542i | \(-0.895462\pi\) | ||
0.946555 | − | 0.322542i | \(-0.104538\pi\) | |||||||
\(90\) | 9.36343 | + | 5.26667i | 0.986992 | + | 0.555156i | ||||
\(91\) | 8.40198i | 0.880767i | ||||||||
\(92\) | 1.23475 | − | 7.40858i | 0.128731 | − | 0.772398i | ||||
\(93\) | −11.6777 | + | 11.6777i | −1.21092 | + | 1.21092i | ||||
\(94\) | 1.52628 | − | 0.489122i | 0.157424 | − | 0.0504491i | ||||
\(95\) | 0.0829302 | − | 2.23453i | 0.00850846 | − | 0.229258i | ||||
\(96\) | −14.3048 | − | 0.288531i | −1.45998 | − | 0.0294480i | ||||
\(97\) | 1.52334 | + | 1.52334i | 0.154672 | + | 0.154672i | 0.780201 | − | 0.625529i | \(-0.215117\pi\) |
−0.625529 | + | 0.780201i | \(0.715117\pi\) | |||||||
\(98\) | −3.47163 | + | 6.74605i | −0.350688 | + | 0.681454i | ||||
\(99\) | 16.7418 | 1.68261 | ||||||||
\(100\) | −5.19324 | − | 8.54578i | −0.519324 | − | 0.854578i | ||||
\(101\) | −0.349073 | −0.0347341 | −0.0173670 | − | 0.999849i | \(-0.505528\pi\) | ||||
−0.0173670 | + | 0.999849i | \(0.505528\pi\) | |||||||
\(102\) | 8.11680 | − | 15.7725i | 0.803683 | − | 1.56171i | ||||
\(103\) | −6.13616 | − | 6.13616i | −0.604613 | − | 0.604613i | 0.336920 | − | 0.941533i | \(-0.390615\pi\) |
−0.941533 | + | 0.336920i | \(0.890615\pi\) | |||||||
\(104\) | −14.9014 | − | 11.1045i | −1.46120 | − | 1.08888i | ||||
\(105\) | 0.268225 | − | 7.22723i | 0.0261760 | − | 0.705305i | ||||
\(106\) | −5.19663 | + | 1.66535i | −0.504742 | + | 0.161753i | ||||
\(107\) | −7.72854 | + | 7.72854i | −0.747146 | + | 0.747146i | −0.973942 | − | 0.226796i | \(-0.927175\pi\) |
0.226796 | + | 0.973942i | \(0.427175\pi\) | |||||||
\(108\) | −1.98206 | − | 0.330339i | −0.190724 | − | 0.0317869i | ||||
\(109\) | − | 1.11697i | − | 0.106986i | −0.998568 | − | 0.0534931i | \(-0.982964\pi\) | ||
0.998568 | − | 0.0534931i | \(-0.0170355\pi\) | |||||||
\(110\) | −13.5827 | − | 7.63990i | −1.29506 | − | 0.728436i | ||||
\(111\) | − | 16.7576i | − | 1.59056i | ||||||
\(112\) | 2.24835 | + | 4.59441i | 0.212449 | + | 0.434131i | ||||
\(113\) | −7.06685 | + | 7.06685i | −0.664794 | + | 0.664794i | −0.956506 | − | 0.291712i | \(-0.905775\pi\) |
0.291712 | + | 0.956506i | \(0.405775\pi\) | |||||||
\(114\) | 1.09160 | + | 3.40630i | 0.102238 | + | 0.319029i | ||||
\(115\) | −6.15392 | + | 5.71348i | −0.573856 | + | 0.532785i | ||||
\(116\) | −6.89085 | + | 4.92206i | −0.639799 | + | 0.457001i | ||||
\(117\) | −15.7834 | − | 15.7834i | −1.45918 | − | 1.45918i | ||||
\(118\) | 17.5839 | + | 9.04896i | 1.61873 | + | 0.833024i | ||||
\(119\) | −6.34156 | −0.581330 | ||||||||
\(120\) | 12.4634 | + | 10.0276i | 1.13775 | + | 0.915388i | ||||
\(121\) | −13.2858 | −1.20780 | ||||||||
\(122\) | 8.31515 | + | 4.27912i | 0.752818 | + | 0.387413i | ||||
\(123\) | 7.14541 | + | 7.14541i | 0.644280 | + | 0.644280i | ||||
\(124\) | −10.6265 | + | 7.59037i | −0.954286 | + | 0.681636i | ||||
\(125\) | −1.24167 | + | 11.1112i | −0.111059 | + | 0.993814i | ||||
\(126\) | 1.87492 | + | 5.85061i | 0.167031 | + | 0.521214i | ||||
\(127\) | 0.443269 | − | 0.443269i | 0.0393338 | − | 0.0393338i | −0.687166 | − | 0.726500i | \(-0.741146\pi\) |
0.726500 | + | 0.687166i | \(0.241146\pi\) | |||||||
\(128\) | −11.1200 | − | 2.08461i | −0.982878 | − | 0.184255i | ||||
\(129\) | 5.04500i | 0.444188i | ||||||||
\(130\) | 5.60264 | + | 20.0078i | 0.491384 | + | 1.75480i | ||||
\(131\) | − | 19.8615i | − | 1.73531i | −0.497166 | − | 0.867655i | \(-0.665626\pi\) | ||
0.497166 | − | 0.867655i | \(-0.334374\pi\) | |||||||
\(132\) | 24.5897 | + | 4.09823i | 2.14026 | + | 0.356705i | ||||
\(133\) | 0.904221 | − | 0.904221i | 0.0784059 | − | 0.0784059i | ||||
\(134\) | 2.69057 | − | 0.862238i | 0.232430 | − | 0.0744860i | ||||
\(135\) | 1.52856 | + | 1.64639i | 0.131558 | + | 0.141699i | ||||
\(136\) | 8.38131 | − | 11.2471i | 0.718692 | − | 0.964434i | ||||
\(137\) | −10.4985 | − | 10.4985i | −0.896951 | − | 0.896951i | 0.0982139 | − | 0.995165i | \(-0.468687\pi\) |
−0.995165 | + | 0.0982139i | \(0.968687\pi\) | |||||||
\(138\) | 6.14658 | − | 11.9440i | 0.523231 | − | 1.01674i | ||||
\(139\) | −18.2723 | −1.54984 | −0.774920 | − | 0.632060i | \(-0.782210\pi\) | ||||
−0.774920 | + | 0.632060i | \(0.782210\pi\) | |||||||
\(140\) | 1.14872 | − | 5.60224i | 0.0970842 | − | 0.473476i | ||||
\(141\) | 2.86645 | 0.241399 | ||||||||
\(142\) | 0.431358 | − | 0.838212i | 0.0361987 | − | 0.0703411i | ||||
\(143\) | 22.8957 | + | 22.8957i | 1.91463 | + | 1.91463i | ||||
\(144\) | −12.8544 | − | 4.40716i | −1.07120 | − | 0.367264i | ||||
\(145\) | 9.46122 | + | 0.351135i | 0.785712 | + | 0.0291602i | ||||
\(146\) | 17.3271 | − | 5.55275i | 1.43400 | − | 0.459549i | ||||
\(147\) | −9.59471 | + | 9.59471i | −0.791358 | + | 0.791358i | ||||
\(148\) | 2.17841 | − | 13.0706i | 0.179064 | − | 1.07440i | ||||
\(149\) | 20.0334i | 1.64120i | 0.571501 | + | 0.820601i | \(0.306361\pi\) | ||||
−0.571501 | + | 0.820601i | \(0.693639\pi\) | |||||||
\(150\) | −4.18056 | − | 17.3892i | −0.341341 | − | 1.41982i | ||||
\(151\) | 0.536358i | 0.0436482i | 0.999762 | + | 0.0218241i | \(0.00694738\pi\) | ||||
−0.999762 | + | 0.0218241i | \(0.993053\pi\) | |||||||
\(152\) | 0.408628 | + | 2.79875i | 0.0331441 | + | 0.227009i | ||||
\(153\) | 11.9129 | − | 11.9129i | 0.963098 | − | 0.963098i | ||||
\(154\) | −2.71979 | − | 8.48697i | −0.219167 | − | 0.683900i | ||||
\(155\) | 14.5903 | + | 0.541490i | 1.17192 | + | 0.0434936i | ||||
\(156\) | −19.3185 | − | 27.0458i | −1.54672 | − | 2.16540i | ||||
\(157\) | −3.05908 | − | 3.05908i | −0.244141 | − | 0.244141i | 0.574420 | − | 0.818561i | \(-0.305228\pi\) |
−0.818561 | + | 0.574420i | \(0.805228\pi\) | |||||||
\(158\) | 8.92567 | + | 4.59330i | 0.710088 | + | 0.365423i | ||||
\(159\) | −9.75959 | −0.773985 | ||||||||
\(160\) | 8.41771 | + | 9.44151i | 0.665478 | + | 0.746417i | ||||
\(161\) | −4.80224 | −0.378470 | ||||||||
\(162\) | 9.62033 | + | 4.95078i | 0.755845 | + | 0.388970i | ||||
\(163\) | 4.16638 | + | 4.16638i | 0.326336 | + | 0.326336i | 0.851191 | − | 0.524856i | \(-0.175881\pi\) |
−0.524856 | + | 0.851191i | \(0.675881\pi\) | |||||||
\(164\) | 4.64442 | + | 6.50216i | 0.362668 | + | 0.507734i | ||||
\(165\) | −18.9635 | − | 20.4254i | −1.47631 | − | 1.59011i | ||||
\(166\) | 3.99361 | + | 12.4619i | 0.309965 | + | 0.967230i | ||||
\(167\) | 1.58055 | − | 1.58055i | 0.122307 | − | 0.122307i | −0.643304 | − | 0.765611i | \(-0.722437\pi\) |
0.765611 | + | 0.643304i | \(0.222437\pi\) | |||||||
\(168\) | 1.32164 | + | 9.05212i | 0.101967 | + | 0.698386i | ||||
\(169\) | − | 30.1702i | − | 2.32079i | ||||||
\(170\) | −15.1013 | + | 4.22870i | −1.15822 | + | 0.324327i | ||||
\(171\) | 3.39723i | 0.259793i | ||||||||
\(172\) | −0.655827 | + | 3.93501i | −0.0500063 | + | 0.300042i | ||||
\(173\) | −8.52546 | + | 8.52546i | −0.648179 | + | 0.648179i | −0.952553 | − | 0.304374i | \(-0.901553\pi\) |
0.304374 | + | 0.952553i | \(0.401553\pi\) | |||||||
\(174\) | −14.4226 | + | 4.62196i | −1.09337 | + | 0.350390i | ||||
\(175\) | −4.84379 | + | 4.17355i | −0.366156 | + | 0.315490i | ||||
\(176\) | 18.6468 | + | 6.39309i | 1.40555 | + | 0.481897i | ||||
\(177\) | 25.0090 | + | 25.0090i | 1.87979 | + | 1.87979i | ||||
\(178\) | 3.93817 | − | 7.65263i | 0.295178 | − | 0.573589i | ||||
\(179\) | 15.0799 | 1.12713 | 0.563564 | − | 0.826073i | \(-0.309430\pi\) | ||||
0.563564 | + | 0.826073i | \(0.309430\pi\) | |||||||
\(180\) | 8.36612 | + | 12.6819i | 0.623573 | + | 0.945255i | ||||
\(181\) | −7.85061 | −0.583531 | −0.291765 | − | 0.956490i | \(-0.594243\pi\) | ||||
−0.291765 | + | 0.956490i | \(0.594243\pi\) | |||||||
\(182\) | −5.43706 | + | 10.5653i | −0.403022 | + | 0.783150i | ||||
\(183\) | 11.8264 | + | 11.8264i | 0.874232 | + | 0.874232i | ||||
\(184\) | 6.34688 | − | 8.51707i | 0.467898 | − | 0.627887i | ||||
\(185\) | −10.8571 | + | 10.0800i | −0.798227 | + | 0.741098i | ||||
\(186\) | −22.2413 | + | 7.12759i | −1.63081 | + | 0.522620i | ||||
\(187\) | −17.2810 | + | 17.2810i | −1.26371 | + | 1.26371i | ||||
\(188\) | 2.23578 | + | 0.372625i | 0.163061 | + | 0.0271765i | ||||
\(189\) | 1.28477i | 0.0934535i | ||||||||
\(190\) | 1.55028 | − | 2.75620i | 0.112469 | − | 0.199956i | ||||
\(191\) | − | 9.49299i | − | 0.686889i | −0.939173 | − | 0.343444i | \(-0.888406\pi\) | ||
0.939173 | − | 0.343444i | \(-0.111594\pi\) | |||||||
\(192\) | −17.8012 | − | 9.61971i | −1.28469 | − | 0.694243i | ||||
\(193\) | −6.06821 | + | 6.06821i | −0.436800 | + | 0.436800i | −0.890933 | − | 0.454134i | \(-0.849949\pi\) |
0.454134 | + | 0.890933i | \(0.349949\pi\) | |||||||
\(194\) | 0.929783 | + | 2.90134i | 0.0667545 | + | 0.208304i | ||||
\(195\) | −1.37816 | + | 37.1342i | −0.0986924 | + | 2.65924i | ||||
\(196\) | −8.73097 | + | 6.23643i | −0.623641 | + | 0.445460i | ||||
\(197\) | 12.5816 | + | 12.5816i | 0.896402 | + | 0.896402i | 0.995116 | − | 0.0987143i | \(-0.0314730\pi\) |
−0.0987143 | + | 0.995116i | \(0.531473\pi\) | |||||||
\(198\) | 21.0523 | + | 10.8339i | 1.49612 | + | 0.769930i | ||||
\(199\) | 9.07658 | 0.643422 | 0.321711 | − | 0.946838i | \(-0.395742\pi\) | ||||
0.321711 | + | 0.946838i | \(0.395742\pi\) | |||||||
\(200\) | −1.00024 | − | 14.1067i | −0.0707280 | − | 0.997496i | ||||
\(201\) | 5.05306 | 0.356415 | ||||||||
\(202\) | −0.438950 | − | 0.225891i | −0.0308844 | − | 0.0158936i | ||||
\(203\) | 3.82856 | + | 3.82856i | 0.268712 | + | 0.268712i | ||||
\(204\) | 20.4133 | − | 14.5810i | 1.42922 | − | 1.02088i | ||||
\(205\) | 0.331329 | − | 8.92755i | 0.0231410 | − | 0.623527i | ||||
\(206\) | −3.74524 | − | 11.6869i | −0.260944 | − | 0.814262i | ||||
\(207\) | 9.02120 | − | 9.02120i | 0.627017 | − | 0.627017i | ||||
\(208\) | −11.5523 | − | 23.6065i | −0.801005 | − | 1.63682i | ||||
\(209\) | − | 4.92807i | − | 0.340882i | ||||||
\(210\) | 5.01415 | − | 8.91448i | 0.346009 | − | 0.615157i | ||||
\(211\) | 21.5273i | 1.48200i | 0.671506 | + | 0.740999i | \(0.265648\pi\) | ||||
−0.671506 | + | 0.740999i | \(0.734352\pi\) | |||||||
\(212\) | −7.61230 | − | 1.26870i | −0.522815 | − | 0.0871347i | ||||
\(213\) | 1.19216 | − | 1.19216i | 0.0816857 | − | 0.0816857i | ||||
\(214\) | −14.7197 | + | 4.71717i | −1.00622 | + | 0.322459i | ||||
\(215\) | 3.26861 | − | 3.03467i | 0.222917 | − | 0.206963i | ||||
\(216\) | −2.27862 | − | 1.69802i | −0.155041 | − | 0.115536i | ||||
\(217\) | 5.90408 | + | 5.90408i | 0.400795 | + | 0.400795i | ||||
\(218\) | 0.722809 | − | 1.40456i | 0.0489548 | − | 0.0951287i | ||||
\(219\) | 32.5413 | 2.19894 | ||||||||
\(220\) | −12.1360 | − | 18.3966i | −0.818209 | − | 1.24030i | ||||
\(221\) | 32.5836 | 2.19181 | ||||||||
\(222\) | 10.8441 | − | 21.0722i | 0.727809 | − | 1.41427i | ||||
\(223\) | −11.2136 | − | 11.2136i | −0.750919 | − | 0.750919i | 0.223732 | − | 0.974651i | \(-0.428176\pi\) |
−0.974651 | + | 0.223732i | \(0.928176\pi\) | |||||||
\(224\) | −0.145877 | + | 7.23230i | −0.00974679 | + | 0.483228i | ||||
\(225\) | 1.25908 | − | 16.9394i | 0.0839388 | − | 1.12929i | ||||
\(226\) | −13.4595 | + | 4.31330i | −0.895310 | + | 0.286917i | ||||
\(227\) | 10.4346 | − | 10.4346i | 0.692570 | − | 0.692570i | −0.270227 | − | 0.962797i | \(-0.587099\pi\) |
0.962797 | + | 0.270227i | \(0.0870986\pi\) | |||||||
\(228\) | −0.831610 | + | 4.98972i | −0.0550747 | + | 0.330453i | ||||
\(229\) | − | 3.99464i | − | 0.263973i | −0.991252 | − | 0.131987i | \(-0.957864\pi\) | ||
0.991252 | − | 0.131987i | \(-0.0421356\pi\) | |||||||
\(230\) | −11.4357 | + | 3.20225i | −0.754047 | + | 0.211150i | ||||
\(231\) | − | 15.9390i | − | 1.04871i | ||||||
\(232\) | −11.8502 | + | 1.73017i | −0.778004 | + | 0.113591i | ||||
\(233\) | −12.5036 | + | 12.5036i | −0.819139 | + | 0.819139i | −0.985983 | − | 0.166844i | \(-0.946642\pi\) |
0.166844 | + | 0.985983i | \(0.446642\pi\) | |||||||
\(234\) | −9.63354 | − | 30.0610i | −0.629764 | − | 1.96515i | ||||
\(235\) | −1.72423 | − | 1.85715i | −0.112476 | − | 0.121147i | ||||
\(236\) | 16.2555 | + | 22.7576i | 1.05814 | + | 1.48140i | ||||
\(237\) | 12.6947 | + | 12.6947i | 0.824610 | + | 0.824610i | ||||
\(238\) | −7.97434 | − | 4.10373i | −0.516900 | − | 0.266005i | ||||
\(239\) | −10.1130 | −0.654153 | −0.327077 | − | 0.944998i | \(-0.606064\pi\) | ||||
−0.327077 | + | 0.944998i | \(0.606064\pi\) | |||||||
\(240\) | 9.18342 | + | 20.6747i | 0.592787 | + | 1.33455i | ||||
\(241\) | −21.6620 | −1.39537 | −0.697687 | − | 0.716402i | \(-0.745787\pi\) | ||||
−0.697687 | + | 0.716402i | \(0.745787\pi\) | |||||||
\(242\) | −16.7066 | − | 8.59749i | −1.07394 | − | 0.552668i | ||||
\(243\) | 15.8140 | + | 15.8140i | 1.01447 | + | 1.01447i | ||||
\(244\) | 7.68700 | + | 10.7617i | 0.492110 | + | 0.688950i | ||||
\(245\) | 11.9877 | + | 0.444902i | 0.765868 | + | 0.0284237i | ||||
\(246\) | 4.36125 | + | 13.6091i | 0.278063 | + | 0.867683i | ||||
\(247\) | −4.64598 | + | 4.64598i | −0.295616 | + | 0.295616i | ||||
\(248\) | −18.2744 | + | 2.66812i | −1.16042 | + | 0.169426i | ||||
\(249\) | 23.4042i | 1.48318i | ||||||||
\(250\) | −8.75160 | + | 13.1685i | −0.553500 | + | 0.832849i | ||||
\(251\) | − | 2.50042i | − | 0.157825i | −0.996882 | − | 0.0789125i | \(-0.974855\pi\) | ||
0.996882 | − | 0.0789125i | \(-0.0251448\pi\) | |||||||
\(252\) | −1.42836 | + | 8.57028i | −0.0899783 | + | 0.539877i | ||||
\(253\) | −13.0863 | + | 13.0863i | −0.822727 | + | 0.822727i | ||||
\(254\) | 0.844246 | − | 0.270552i | 0.0529727 | − | 0.0169760i | ||||
\(255\) | −28.0278 | − | 1.04020i | −1.75517 | − | 0.0651396i | ||||
\(256\) | −12.6341 | − | 9.81728i | −0.789633 | − | 0.613580i | ||||
\(257\) | 3.26731 | + | 3.26731i | 0.203809 | + | 0.203809i | 0.801630 | − | 0.597821i | \(-0.203966\pi\) |
−0.597821 | + | 0.801630i | \(0.703966\pi\) | |||||||
\(258\) | −3.26470 | + | 6.34396i | −0.203252 | + | 0.394957i | ||||
\(259\) | −8.47237 | −0.526447 | ||||||||
\(260\) | −5.90222 | + | 28.7849i | −0.366040 | + | 1.78516i | ||||
\(261\) | −14.3842 | −0.890360 | ||||||||
\(262\) | 12.8527 | − | 24.9754i | 0.794044 | − | 1.54298i | ||||
\(263\) | −17.4522 | − | 17.4522i | −1.07615 | − | 1.07615i | −0.996851 | − | 0.0792985i | \(-0.974732\pi\) |
−0.0792985 | − | 0.996851i | \(-0.525268\pi\) | |||||||
\(264\) | 28.2689 | + | 21.0658i | 1.73983 | + | 1.29651i | ||||
\(265\) | 5.87059 | + | 6.32314i | 0.360628 | + | 0.388427i | ||||
\(266\) | 1.72217 | − | 0.551898i | 0.105593 | − | 0.0338390i | ||||
\(267\) | 10.8841 | − | 10.8841i | 0.666097 | − | 0.666097i | ||||
\(268\) | 3.94129 | + | 0.656874i | 0.240753 | + | 0.0401250i | ||||
\(269\) | − | 13.8165i | − | 0.842410i | −0.906965 | − | 0.421205i | \(-0.861607\pi\) | ||
0.906965 | − | 0.421205i | \(-0.138393\pi\) | |||||||
\(270\) | 0.856717 | + | 3.05946i | 0.0521381 | + | 0.186193i | ||||
\(271\) | − | 1.41089i | − | 0.0857053i | −0.999081 | − | 0.0428526i | \(-0.986355\pi\) | ||
0.999081 | − | 0.0428526i | \(-0.0136446\pi\) | |||||||
\(272\) | 17.8175 | − | 8.71929i | 1.08034 | − | 0.528685i | ||||
\(273\) | −15.0267 | + | 15.0267i | −0.909455 | + | 0.909455i | ||||
\(274\) | −6.40786 | − | 19.9954i | −0.387113 | − | 1.20797i | ||||
\(275\) | −1.82644 | + | 24.5726i | −0.110139 | + | 1.48178i | ||||
\(276\) | 15.4583 | − | 11.0417i | 0.930481 | − | 0.664632i | ||||
\(277\) | 10.5953 | + | 10.5953i | 0.636609 | + | 0.636609i | 0.949717 | − | 0.313108i | \(-0.101370\pi\) |
−0.313108 | + | 0.949717i | \(0.601370\pi\) | |||||||
\(278\) | −22.9770 | − | 11.8243i | −1.37807 | − | 0.709176i | ||||
\(279\) | −22.1821 | −1.32801 | ||||||||
\(280\) | 5.06978 | − | 6.30131i | 0.302978 | − | 0.376576i | ||||
\(281\) | 3.69749 | 0.220574 | 0.110287 | − | 0.993900i | \(-0.464823\pi\) | ||||
0.110287 | + | 0.993900i | \(0.464823\pi\) | |||||||
\(282\) | 3.60449 | + | 1.85493i | 0.214644 | + | 0.110459i | ||||
\(283\) | −10.5387 | − | 10.5387i | −0.626458 | − | 0.626458i | 0.320717 | − | 0.947175i | \(-0.396076\pi\) |
−0.947175 | + | 0.320717i | \(0.896076\pi\) | |||||||
\(284\) | 1.08484 | − | 0.774890i | 0.0643735 | − | 0.0459813i | ||||
\(285\) | 4.14470 | − | 3.84806i | 0.245511 | − | 0.227940i | ||||
\(286\) | 13.9745 | + | 43.6069i | 0.826332 | + | 2.57853i | ||||
\(287\) | 3.61261 | − | 3.61261i | 0.213246 | − | 0.213246i | ||||
\(288\) | −13.3121 | − | 13.8602i | −0.784424 | − | 0.816719i | ||||
\(289\) | 7.59306i | 0.446651i | ||||||||
\(290\) | 11.6700 | + | 6.56406i | 0.685287 | + | 0.385455i | ||||
\(291\) | 5.44890i | 0.319420i | ||||||||
\(292\) | 25.3817 | + | 4.23022i | 1.48535 | + | 0.247555i | ||||
\(293\) | 0.294186 | − | 0.294186i | 0.0171865 | − | 0.0171865i | −0.698461 | − | 0.715648i | \(-0.746132\pi\) |
0.715648 | + | 0.698461i | \(0.246132\pi\) | |||||||
\(294\) | −18.2740 | + | 5.85620i | −1.06576 | + | 0.341540i | ||||
\(295\) | 1.15965 | − | 31.2465i | 0.0675177 | − | 1.81924i | ||||
\(296\) | 11.1975 | − | 15.0263i | 0.650841 | − | 0.873384i | ||||
\(297\) | 3.50105 | + | 3.50105i | 0.203152 | + | 0.203152i | ||||
\(298\) | −12.9640 | + | 25.1915i | −0.750983 | + | 1.45931i | ||||
\(299\) | 24.6744 | 1.42696 | ||||||||
\(300\) | 5.99590 | − | 24.5718i | 0.346174 | − | 1.41865i | ||||
\(301\) | 2.55067 | 0.147018 | ||||||||
\(302\) | −0.347086 | + | 0.674456i | −0.0199726 | + | 0.0388106i | ||||
\(303\) | −0.624306 | − | 0.624306i | −0.0358654 | − | 0.0358654i | ||||
\(304\) | −1.29728 | + | 3.78379i | −0.0744042 | + | 0.217015i | ||||
\(305\) | 0.548383 | − | 14.7760i | 0.0314003 | − | 0.846072i | ||||
\(306\) | 22.6891 | − | 7.27110i | 1.29705 | − | 0.415661i | ||||
\(307\) | 0.725482 | − | 0.725482i | 0.0414055 | − | 0.0414055i | −0.686101 | − | 0.727506i | \(-0.740679\pi\) |
0.727506 | + | 0.686101i | \(0.240679\pi\) | |||||||
\(308\) | 2.07200 | − | 12.4322i | 0.118063 | − | 0.708388i | ||||
\(309\) | − | 21.9486i | − | 1.24861i | ||||||
\(310\) | 17.9965 | + | 10.1225i | 1.02213 | + | 0.574921i | ||||
\(311\) | − | 13.6716i | − | 0.775247i | −0.921818 | − | 0.387624i | \(-0.873296\pi\) | ||
0.921818 | − | 0.387624i | \(-0.126704\pi\) | |||||||
\(312\) | −6.79073 | − | 46.5107i | −0.384449 | − | 2.63315i | ||||
\(313\) | 4.09570 | − | 4.09570i | 0.231502 | − | 0.231502i | −0.581817 | − | 0.813320i | \(-0.697658\pi\) |
0.813320 | + | 0.581817i | \(0.197658\pi\) | |||||||
\(314\) | −1.86713 | − | 5.82629i | −0.105368 | − | 0.328797i | ||||
\(315\) | 7.11888 | − | 6.60938i | 0.401103 | − | 0.372397i | ||||
\(316\) | 8.25139 | + | 11.5519i | 0.464177 | + | 0.649845i | ||||
\(317\) | 1.42470 | + | 1.42470i | 0.0800191 | + | 0.0800191i | 0.745983 | − | 0.665964i | \(-0.231980\pi\) |
−0.665964 | + | 0.745983i | \(0.731980\pi\) | |||||||
\(318\) | −12.2724 | − | 6.31559i | −0.688203 | − | 0.354161i | ||||
\(319\) | 20.8659 | 1.16827 | ||||||||
\(320\) | 4.47529 | + | 17.3197i | 0.250176 | + | 0.968200i | ||||
\(321\) | −27.6445 | −1.54296 | ||||||||
\(322\) | −6.03870 | − | 3.10761i | −0.336523 | − | 0.173181i | ||||
\(323\) | −3.50664 | − | 3.50664i | −0.195115 | − | 0.195115i | ||||
\(324\) | 8.89358 | + | 12.4510i | 0.494088 | + | 0.691720i | ||||
\(325\) | 24.8879 | − | 21.4441i | 1.38053 | − | 1.18950i | ||||
\(326\) | 2.54298 | + | 7.93524i | 0.140842 | + | 0.439492i | ||||
\(327\) | 1.99766 | − | 1.99766i | 0.110471 | − | 0.110471i | ||||
\(328\) | 1.63258 | + | 11.1818i | 0.0901441 | + | 0.617411i | ||||
\(329\) | − | 1.44923i | − | 0.0798988i | ||||||
\(330\) | −10.6285 | − | 37.9560i | −0.585081 | − | 2.08941i | ||||
\(331\) | 7.52474i | 0.413597i | 0.978384 | + | 0.206799i | \(0.0663045\pi\) | ||||
−0.978384 | + | 0.206799i | \(0.933696\pi\) | |||||||
\(332\) | −3.04243 | + | 18.2548i | −0.166975 | + | 1.00186i | ||||
\(333\) | 15.9157 | − | 15.9157i | 0.872174 | − | 0.872174i | ||||
\(334\) | 3.01030 | − | 0.964700i | 0.164716 | − | 0.0527860i | ||||
\(335\) | −3.03952 | − | 3.27383i | −0.166067 | − | 0.178868i | ||||
\(336\) | −4.19585 | + | 12.2381i | −0.228902 | + | 0.667641i | ||||
\(337\) | 13.7139 | + | 13.7139i | 0.747045 | + | 0.747045i | 0.973923 | − | 0.226878i | \(-0.0728518\pi\) |
−0.226878 | + | 0.973923i | \(0.572852\pi\) | |||||||
\(338\) | 19.5237 | − | 37.9382i | 1.06195 | − | 2.06357i | ||||
\(339\) | −25.2777 | −1.37289 | ||||||||
\(340\) | −21.7259 | − | 4.45481i | −1.17825 | − | 0.241596i | ||||
\(341\) | 32.1777 | 1.74252 | ||||||||
\(342\) | −2.19840 | + | 4.27193i | −0.118876 | + | 0.230999i | ||||
\(343\) | 11.1805 | + | 11.1805i | 0.603689 | + | 0.603689i | ||||
\(344\) | −3.37110 | + | 4.52377i | −0.181757 | + | 0.243906i | ||||
\(345\) | −21.2245 | − | 0.787705i | −1.14269 | − | 0.0424086i | ||||
\(346\) | −16.2375 | + | 5.20357i | −0.872934 | + | 0.279746i | ||||
\(347\) | 22.6242 | − | 22.6242i | 1.21453 | − | 1.21453i | 0.245012 | − | 0.969520i | \(-0.421208\pi\) |
0.969520 | − | 0.245012i | \(-0.0787919\pi\) | |||||||
\(348\) | −21.1270 | − | 3.52112i | −1.13253 | − | 0.188752i | ||||
\(349\) | 1.72511i | 0.0923432i | 0.998934 | + | 0.0461716i | \(0.0147021\pi\) | ||||
−0.998934 | + | 0.0461716i | \(0.985298\pi\) | |||||||
\(350\) | −8.79171 | + | 2.11363i | −0.469937 | + | 0.112978i | ||||
\(351\) | − | 6.60129i | − | 0.352351i | ||||||
\(352\) | 19.3107 | + | 20.1058i | 1.02927 | + | 1.07164i | ||||
\(353\) | 10.9581 | − | 10.9581i | 0.583240 | − | 0.583240i | −0.352552 | − | 0.935792i | \(-0.614686\pi\) |
0.935792 | + | 0.352552i | \(0.114686\pi\) | |||||||
\(354\) | 15.2644 | + | 47.6319i | 0.811295 | + | 2.53161i | ||||
\(355\) | −1.48950 | − | 0.0552800i | −0.0790545 | − | 0.00293396i | ||||
\(356\) | 9.90429 | − | 7.07453i | 0.524926 | − | 0.374949i | ||||
\(357\) | −11.3417 | − | 11.3417i | −0.600265 | − | 0.600265i | ||||
\(358\) | 18.9626 | + | 9.75848i | 1.00221 | + | 0.515752i | ||||
\(359\) | −26.0612 | −1.37546 | −0.687728 | − | 0.725968i | \(-0.741392\pi\) | ||||
−0.687728 | + | 0.725968i | \(0.741392\pi\) | |||||||
\(360\) | 2.31348 | + | 21.3610i | 0.121931 | + | 1.12583i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.87193 | − | 5.08026i | −0.518857 | − | 0.267012i | ||||
\(363\) | −23.7613 | − | 23.7613i | −1.24714 | − | 1.24714i | ||||
\(364\) | −13.6739 | + | 9.76713i | −0.716709 | + | 0.511937i | ||||
\(365\) | −19.5743 | − | 21.0832i | −1.02456 | − | 1.10355i | ||||
\(366\) | 7.21832 | + | 22.5244i | 0.377308 | + | 1.17737i | ||||
\(367\) | −2.92099 | + | 2.92099i | −0.152474 | + | 0.152474i | −0.779222 | − | 0.626748i | \(-0.784386\pi\) |
0.626748 | + | 0.779222i | \(0.284386\pi\) | |||||||
\(368\) | 13.4926 | − | 6.60282i | 0.703349 | − | 0.344196i | ||||
\(369\) | 13.5728i | 0.706574i | ||||||||
\(370\) | −20.1754 | + | 5.64958i | −1.04887 | + | 0.293708i | ||||
\(371\) | 4.93429i | 0.256176i | ||||||||
\(372\) | −32.5802 | − | 5.42997i | −1.68921 | − | 0.281531i | ||||
\(373\) | −9.00352 | + | 9.00352i | −0.466185 | + | 0.466185i | −0.900676 | − | 0.434491i | \(-0.856928\pi\) |
0.434491 | + | 0.900676i | \(0.356928\pi\) | |||||||
\(374\) | −32.9132 | + | 10.5476i | −1.70190 | + | 0.545401i | ||||
\(375\) | −22.0927 | + | 17.6513i | −1.14086 | + | 0.911508i | ||||
\(376\) | 2.57030 | + | 1.91538i | 0.132553 | + | 0.0987781i | ||||
\(377\) | −19.6715 | − | 19.6715i | −1.01314 | − | 1.01314i | ||||
\(378\) | −0.831398 | + | 1.61557i | −0.0427625 | + | 0.0830959i | ||||
\(379\) | −11.5138 | −0.591425 | −0.295713 | − | 0.955277i | \(-0.595557\pi\) | ||||
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(380\) | 3.73302 | − | 2.46263i | 0.191500 | − | 0.126330i | ||||
\(381\) | 1.58554 | 0.0812299 | ||||||||
\(382\) | 6.14307 | − | 11.9372i | 0.314307 | − | 0.610760i | ||||
\(383\) | −19.1866 | − | 19.1866i | −0.980387 | − | 0.980387i | 0.0194239 | − | 0.999811i | \(-0.493817\pi\) |
−0.999811 | + | 0.0194239i | \(0.993817\pi\) | |||||||
\(384\) | −16.1595 | − | 23.6160i | −0.824636 | − | 1.20515i | ||||
\(385\) | −10.3267 | + | 9.58766i | −0.526300 | + | 0.488632i | ||||
\(386\) | −11.5575 | + | 3.70378i | −0.588259 | + | 0.188517i | ||||
\(387\) | −4.79154 | + | 4.79154i | −0.243568 | + | 0.243568i | ||||
\(388\) | −0.708331 | + | 4.25004i | −0.0359601 | + | 0.215763i | ||||
\(389\) | − | 19.3955i | − | 0.983390i | −0.870767 | − | 0.491695i | \(-0.836377\pi\) | ||
0.870767 | − | 0.491695i | \(-0.163623\pi\) | |||||||
\(390\) | −25.7632 | + | 45.8035i | −1.30457 | + | 2.31935i | ||||
\(391\) | 18.6235i | 0.941830i | ||||||||
\(392\) | −15.0147 | + | 2.19219i | −0.758355 | + | 0.110723i | ||||
\(393\) | 35.5217 | − | 35.5217i | 1.79183 | − | 1.79183i | ||||
\(394\) | 7.67926 | + | 23.9628i | 0.386876 | + | 1.20723i | ||||
\(395\) | 0.588647 | − | 15.8609i | 0.0296180 | − | 0.798049i | ||||
\(396\) | 19.4620 | + | 27.2466i | 0.978001 | + | 1.36920i | ||||
\(397\) | 7.98711 | + | 7.98711i | 0.400862 | + | 0.400862i | 0.878537 | − | 0.477675i | \(-0.158520\pi\) |
−0.477675 | + | 0.878537i | \(0.658520\pi\) | |||||||
\(398\) | 11.4136 | + | 5.87361i | 0.572110 | + | 0.294417i | ||||
\(399\) | 3.23434 | 0.161920 | ||||||||
\(400\) | 7.87091 | − | 18.3861i | 0.393546 | − | 0.919305i | ||||
\(401\) | −21.8145 | −1.08936 | −0.544682 | − | 0.838643i | \(-0.683350\pi\) | ||||
−0.544682 | + | 0.838643i | \(0.683350\pi\) | |||||||
\(402\) | 6.35409 | + | 3.26992i | 0.316913 | + | 0.163089i | ||||
\(403\) | −30.3358 | − | 30.3358i | −1.51113 | − | 1.51113i | ||||
\(404\) | −0.405791 | − | 0.568104i | −0.0201888 | − | 0.0282642i | ||||
\(405\) | 0.634460 | − | 17.0953i | 0.0315266 | − | 0.849473i | ||||
\(406\) | 2.33679 | + | 7.29184i | 0.115973 | + | 0.361888i | ||||
\(407\) | −23.0875 | + | 23.0875i | −1.14440 | + | 1.14440i | ||||
\(408\) | 35.1048 | − | 5.12543i | 1.73795 | − | 0.253747i | ||||
\(409\) | − | 26.8043i | − | 1.32539i | −0.748890 | − | 0.662694i | \(-0.769413\pi\) | ||
0.748890 | − | 0.662694i | \(-0.230587\pi\) | |||||||
\(410\) | 6.19381 | − | 11.0118i | 0.305890 | − | 0.543832i | ||||
\(411\) | − | 37.5526i | − | 1.85233i | ||||||
\(412\) | 2.85322 | − | 17.1195i | 0.140568 | − | 0.843419i | ||||
\(413\) | 12.6442 | − | 12.6442i | 0.622179 | − | 0.622179i | ||||
\(414\) | 17.1817 | − | 5.50615i | 0.844434 | − | 0.270613i | ||||
\(415\) | 15.1633 | − | 14.0781i | 0.744338 | − | 0.691066i | ||||
\(416\) | 0.749528 | − | 37.1603i | 0.0367487 | − | 1.82193i | ||||
\(417\) | −32.6795 | − | 32.6795i | −1.60032 | − | 1.60032i | ||||
\(418\) | 3.18903 | − | 6.19691i | 0.155981 | − | 0.303101i | ||||
\(419\) | 22.9547 | 1.12141 | 0.560706 | − | 0.828015i | \(-0.310530\pi\) | ||||
0.560706 | + | 0.828015i | \(0.310530\pi\) | |||||||
\(420\) | 12.0739 | − | 7.96498i | 0.589144 | − | 0.388651i | ||||
\(421\) | −22.1889 | −1.08142 | −0.540710 | − | 0.841209i | \(-0.681844\pi\) | ||||
−0.540710 | + | 0.841209i | \(0.681844\pi\) | |||||||
\(422\) | −13.9307 | + | 27.0700i | −0.678134 | + | 1.31775i | ||||
\(423\) | 2.72244 | + | 2.72244i | 0.132370 | + | 0.132370i | ||||
\(424\) | −8.75127 | − | 6.52141i | −0.424999 | − | 0.316707i | ||||
\(425\) | 16.1853 | + | 18.7846i | 0.785104 | + | 0.911187i | ||||
\(426\) | 2.27058 | − | 0.727645i | 0.110010 | − | 0.0352545i | ||||
\(427\) | 5.97924 | − | 5.97924i | 0.289356 | − | 0.289356i | ||||
\(428\) | −21.5622 | − | 3.59365i | −1.04225 | − | 0.173706i | ||||
\(429\) | 81.8964i | 3.95399i | ||||||||
\(430\) | 6.07397 | − | 1.70085i | 0.292913 | − | 0.0820223i | ||||
\(431\) | − | 3.20599i | − | 0.154427i | −0.997015 | − | 0.0772135i | \(-0.975398\pi\) | ||
0.997015 | − | 0.0772135i | \(-0.0246023\pi\) | |||||||
\(432\) | −1.76649 | − | 3.60975i | −0.0849903 | − | 0.173674i | ||||
\(433\) | −16.1866 | + | 16.1866i | −0.777880 | + | 0.777880i | −0.979470 | − | 0.201590i | \(-0.935389\pi\) |
0.201590 | + | 0.979470i | \(0.435389\pi\) | |||||||
\(434\) | 3.60360 | + | 11.2449i | 0.172978 | + | 0.539771i | ||||
\(435\) | 16.2931 | + | 17.5491i | 0.781194 | + | 0.841414i | ||||
\(436\) | 1.81783 | − | 1.29845i | 0.0870581 | − | 0.0621847i | ||||
\(437\) | −2.65546 | − | 2.65546i | −0.127028 | − | 0.127028i | ||||
\(438\) | 40.9199 | + | 21.0580i | 1.95523 | + | 1.00619i | ||||
\(439\) | 33.4711 | 1.59749 | 0.798745 | − | 0.601669i | \(-0.205498\pi\) | ||||
0.798745 | + | 0.601669i | \(0.205498\pi\) | |||||||
\(440\) | −3.35596 | − | 30.9866i | −0.159989 | − | 1.47723i | ||||
\(441\) | −18.2253 | −0.867874 | ||||||||
\(442\) | 40.9730 | + | 21.0854i | 1.94888 | + | 1.00293i | ||||
\(443\) | −6.99853 | − | 6.99853i | −0.332510 | − | 0.332510i | 0.521029 | − | 0.853539i | \(-0.325548\pi\) |
−0.853539 | + | 0.521029i | \(0.825548\pi\) | |||||||
\(444\) | 27.2724 | − | 19.4803i | 1.29429 | − | 0.924496i | ||||
\(445\) | −13.5987 | − | 0.504690i | −0.644641 | − | 0.0239246i | ||||
\(446\) | −6.84431 | − | 21.3573i | −0.324087 | − | 1.01130i | ||||
\(447\) | −35.8291 | + | 35.8291i | −1.69466 | + | 1.69466i | ||||
\(448\) | −4.86358 | + | 9.00003i | −0.229782 | + | 0.425211i | ||||
\(449\) | 10.8774i | 0.513334i | 0.966500 | + | 0.256667i | \(0.0826244\pi\) | ||||
−0.966500 | + | 0.256667i | \(0.917376\pi\) | |||||||
\(450\) | 12.5450 | − | 20.4861i | 0.591379 | − | 0.965724i | ||||
\(451\) | − | 19.6890i | − | 0.927117i | ||||||
\(452\) | −19.7161 | − | 3.28598i | −0.927369 | − | 0.154559i | ||||
\(453\) | −0.959259 | + | 0.959259i | −0.0450699 | + | 0.0450699i | ||||
\(454\) | 19.8737 | − | 6.36884i | 0.932718 | − | 0.298905i | ||||
\(455\) | 18.7745 | + | 0.696778i | 0.880161 | + | 0.0326655i | ||||
\(456\) | −4.27466 | + | 5.73630i | −0.200179 | + | 0.268627i | ||||
\(457\) | −2.21461 | − | 2.21461i | −0.103595 | − | 0.103595i | 0.653409 | − | 0.757005i | \(-0.273338\pi\) |
−0.757005 | + | 0.653409i | \(0.773338\pi\) | |||||||
\(458\) | 2.58500 | − | 5.02315i | 0.120789 | − | 0.234716i | ||||
\(459\) | 4.98245 | 0.232561 | ||||||||
\(460\) | −16.4523 | − | 3.37348i | −0.767092 | − | 0.157289i | ||||
\(461\) | 32.4654 | 1.51207 | 0.756033 | − | 0.654534i | \(-0.227135\pi\) | ||||
0.756033 | + | 0.654534i | \(0.227135\pi\) | |||||||
\(462\) | 10.3144 | − | 20.0429i | 0.479870 | − | 0.932481i | ||||
\(463\) | −17.6213 | − | 17.6213i | −0.818933 | − | 0.818933i | 0.167020 | − | 0.985953i | \(-0.446586\pi\) |
−0.985953 | + | 0.167020i | \(0.946586\pi\) | |||||||
\(464\) | −16.0209 | − | 5.49282i | −0.743754 | − | 0.254998i | ||||
\(465\) | 25.1258 | + | 27.0627i | 1.16518 | + | 1.25500i | ||||
\(466\) | −23.8143 | + | 7.63167i | −1.10317 | + | 0.353530i | ||||
\(467\) | 4.04114 | − | 4.04114i | 0.187002 | − | 0.187002i | −0.607397 | − | 0.794399i | \(-0.707786\pi\) |
0.794399 | + | 0.607397i | \(0.207786\pi\) | |||||||
\(468\) | 7.33906 | − | 44.0349i | 0.339248 | − | 2.03552i | ||||
\(469\) | − | 2.55475i | − | 0.117967i | ||||||
\(470\) | −0.966383 | − | 3.45109i | −0.0445759 | − | 0.159187i | ||||
\(471\) | − | 10.9421i | − | 0.504187i | ||||||
\(472\) | 5.71405 | + | 39.1364i | 0.263010 | + | 1.80140i | ||||
\(473\) | 6.95067 | − | 6.95067i | 0.319592 | − | 0.319592i | ||||
\(474\) | 7.74830 | + | 24.1782i | 0.355891 | + | 1.11054i | ||||
\(475\) | −4.98625 | − | 0.370620i | −0.228785 | − | 0.0170052i | ||||
\(476\) | −7.37193 | − | 10.3207i | −0.337892 | − | 0.473047i | ||||
\(477\) | −9.26926 | − | 9.26926i | −0.424410 | − | 0.424410i | ||||
\(478\) | −12.7168 | − | 6.54427i | −0.581652 | − | 0.299328i | ||||
\(479\) | 41.6363 | 1.90241 | 0.951205 | − | 0.308559i | \(-0.0998468\pi\) | ||||
0.951205 | + | 0.308559i | \(0.0998468\pi\) | |||||||
\(480\) | −1.83103 | + | 31.9406i | −0.0835748 | + | 1.45788i | ||||
\(481\) | 43.5319 | 1.98488 | ||||||||
\(482\) | −27.2394 | − | 14.0179i | −1.24072 | − | 0.638496i | ||||
\(483\) | −8.58866 | − | 8.58866i | −0.390797 | − | 0.390797i | ||||
\(484\) | −15.4445 | − | 21.6222i | −0.702024 | − | 0.982829i | ||||
\(485\) | 3.53029 | − | 3.27762i | 0.160302 | − | 0.148829i | ||||
\(486\) | 9.65218 | + | 30.1192i | 0.437832 | + | 1.36623i | ||||
\(487\) | −20.9898 | + | 20.9898i | −0.951140 | + | 0.951140i | −0.998861 | − | 0.0477211i | \(-0.984804\pi\) |
0.0477211 | + | 0.998861i | \(0.484804\pi\) | |||||||
\(488\) | 2.70209 | + | 18.5070i | 0.122318 | + | 0.837772i | ||||
\(489\) | 14.9029i | 0.673930i | ||||||||
\(490\) | 14.7864 | + | 8.31692i | 0.667979 | + | 0.375720i | ||||
\(491\) | 26.4536i | 1.19384i | 0.802302 | + | 0.596918i | \(0.203608\pi\) | ||||
−0.802302 | + | 0.596918i | \(0.796392\pi\) | |||||||
\(492\) | −3.32251 | + | 19.9353i | −0.149790 | + | 0.898753i | ||||
\(493\) | 14.8475 | − | 14.8475i | 0.668696 | − | 0.668696i | ||||
\(494\) | −8.84868 | + | 2.83570i | −0.398121 | + | 0.127584i | ||||
\(495\) | 1.38840 | − | 37.4100i | 0.0624039 | − | 1.68145i | ||||
\(496\) | −24.7061 | − | 8.47056i | −1.10934 | − | 0.380339i | ||||
\(497\) | −0.602739 | − | 0.602739i | −0.0270365 | − | 0.0270365i | ||||
\(498\) | −15.1452 | + | 29.4301i | −0.678674 | + | 1.31880i | ||||
\(499\) | 15.2356 | 0.682041 | 0.341021 | − | 0.940056i | \(-0.389227\pi\) | ||||
0.341021 | + | 0.940056i | \(0.389227\pi\) | |||||||
\(500\) | −19.5265 | + | 10.8957i | −0.873250 | + | 0.487272i | ||||
\(501\) | 5.65353 | 0.252581 | ||||||||
\(502\) | 1.61806 | − | 3.14421i | 0.0722176 | − | 0.140333i | ||||
\(503\) | 12.4917 | + | 12.4917i | 0.556977 | + | 0.556977i | 0.928445 | − | 0.371469i | \(-0.121146\pi\) |
−0.371469 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(504\) | −7.34210 | + | 9.85258i | −0.327043 | + | 0.438869i | ||||
\(505\) | −0.0289487 | + | 0.780014i | −0.00128820 | + | 0.0347102i | ||||
\(506\) | −24.9240 | + | 7.98730i | −1.10801 | + | 0.355079i | ||||
\(507\) | 53.9584 | − | 53.9584i | 2.39638 | − | 2.39638i | ||||
\(508\) | 1.23670 | + | 0.206113i | 0.0548695 | + | 0.00914480i | ||||
\(509\) | 17.6173i | 0.780873i | 0.920630 | + | 0.390437i | \(0.127676\pi\) | ||||
−0.920630 | + | 0.390437i | \(0.872324\pi\) | |||||||
\(510\) | −34.5710 | − | 19.4453i | −1.53083 | − | 0.861050i | ||||
\(511\) | − | 16.4524i | − | 0.727811i | ||||||
\(512\) | −9.53415 | − | 20.5207i | −0.421354 | − | 0.906896i | ||||
\(513\) | −0.710431 | + | 0.710431i | −0.0313663 | + | 0.0313663i | ||||
\(514\) | 1.99423 | + | 6.22289i | 0.0879616 | + | 0.274480i | ||||
\(515\) | −14.2203 | + | 13.2025i | −0.626621 | + | 0.581774i | ||||
\(516\) | −8.21056 | + | 5.86471i | −0.361450 | + | 0.258180i | ||||
\(517\) | −3.94921 | − | 3.94921i | −0.173686 | − | 0.173686i | ||||
\(518\) | −10.6538 | − | 5.48261i | −0.468100 | − | 0.240892i | ||||
\(519\) | −30.4950 | −1.33858 | ||||||||
\(520\) | −26.0490 | + | 32.3768i | −1.14233 | + | 1.41982i | ||||
\(521\) | 11.6663 | 0.511111 | 0.255555 | − | 0.966794i | \(-0.417742\pi\) | ||||
0.255555 | + | 0.966794i | \(0.417742\pi\) | |||||||
\(522\) | −18.0878 | − | 9.30826i | −0.791680 | − | 0.407412i | ||||
\(523\) | 11.2249 | + | 11.2249i | 0.490833 | + | 0.490833i | 0.908569 | − | 0.417736i | \(-0.137176\pi\) |
−0.417736 | + | 0.908569i | \(0.637176\pi\) | |||||||
\(524\) | 32.3239 | − | 23.0886i | 1.41208 | − | 1.00863i | ||||
\(525\) | −16.1272 | − | 1.19871i | −0.703849 | − | 0.0523161i | ||||
\(526\) | −10.6521 | − | 33.2393i | −0.464453 | − | 1.44930i | ||||
\(527\) | 22.8965 | − | 22.8965i | 0.997387 | − | 0.997387i | ||||
\(528\) | 21.9153 | + | 44.7830i | 0.953741 | + | 1.94893i | ||||
\(529\) | − | 8.89707i | − | 0.386829i | ||||||
\(530\) | 3.29030 | + | 11.7501i | 0.142922 | + | 0.510393i | ||||
\(531\) | 47.5051i | 2.06155i | ||||||||
\(532\) | 2.52273 | + | 0.420449i | 0.109374 | + | 0.0182288i | ||||
\(533\) | −18.5619 | + | 18.5619i | −0.804007 | + | 0.804007i | ||||
\(534\) | 20.7298 | − | 6.64319i | 0.897065 | − | 0.287479i | ||||
\(535\) | 16.6287 | + | 17.9106i | 0.718922 | + | 0.774342i | ||||
\(536\) | 4.53100 | + | 3.37648i | 0.195709 | + | 0.145842i | ||||
\(537\) | 26.9700 | + | 26.9700i | 1.16384 | + | 1.16384i | ||||
\(538\) | 8.94092 | − | 17.3739i | 0.385470 | − | 0.749044i | ||||
\(539\) | 26.4379 | 1.13876 | ||||||||
\(540\) | −0.902526 | + | 4.40158i | −0.0388385 | + | 0.189414i | ||||
\(541\) | 11.7416 | 0.504811 | 0.252405 | − | 0.967622i | \(-0.418778\pi\) | ||||
0.252405 | + | 0.967622i | \(0.418778\pi\) | |||||||
\(542\) | 0.913008 | − | 1.77415i | 0.0392171 | − | 0.0762064i | ||||
\(543\) | −14.0405 | − | 14.0405i | −0.602538 | − | 0.602538i | ||||
\(544\) | 28.0474 | + | 0.565721i | 1.20252 | + | 0.0242551i | ||||
\(545\) | −2.49590 | − | 0.0926305i | −0.106913 | − | 0.00396786i | ||||
\(546\) | −28.6196 | + | 9.17163i | −1.22481 | + | 0.392510i | ||||
\(547\) | −4.80032 | + | 4.80032i | −0.205247 | + | 0.205247i | −0.802244 | − | 0.596997i | \(-0.796361\pi\) |
0.596997 | + | 0.802244i | \(0.296361\pi\) | |||||||
\(548\) | 4.88166 | − | 29.2904i | 0.208534 | − | 1.25122i | ||||
\(549\) | 22.4645i | 0.958760i | ||||||||
\(550\) | −18.1980 | + | 29.7174i | −0.775966 | + | 1.26715i | ||||
\(551\) | 4.23410i | 0.180379i | ||||||||
\(552\) | 26.5837 | − | 3.88131i | 1.13148 | − | 0.165200i | ||||
\(553\) | 6.41825 | − | 6.41825i | 0.272932 | − | 0.272932i | ||||
\(554\) | 6.46691 | + | 20.1797i | 0.274753 | + | 0.857353i | ||||
\(555\) | −37.4453 | − | 1.38971i | −1.58946 | − | 0.0589899i | ||||
\(556\) | −21.2412 | − | 29.7376i | −0.900828 | − | 1.26115i | ||||
\(557\) | 23.5262 | + | 23.5262i | 0.996839 | + | 0.996839i | 0.999995 | − | 0.00315589i | \(-0.00100455\pi\) |
−0.00315589 | + | 0.999995i | \(0.501005\pi\) | |||||||
\(558\) | −27.8934 | − | 14.3544i | −1.18082 | − | 0.607670i | ||||
\(559\) | −13.1056 | −0.554308 | ||||||||
\(560\) | 10.4528 | − | 4.64300i | 0.441712 | − | 0.196202i | ||||
\(561\) | −61.8129 | −2.60974 | ||||||||
\(562\) | 4.64950 | + | 2.39271i | 0.196127 | + | 0.100930i | ||||
\(563\) | 16.6377 | + | 16.6377i | 0.701194 | + | 0.701194i | 0.964667 | − | 0.263473i | \(-0.0848679\pi\) |
−0.263473 | + | 0.964667i | \(0.584868\pi\) | |||||||
\(564\) | 3.33219 | + | 4.66505i | 0.140311 | + | 0.196434i | ||||
\(565\) | 15.2050 | + | 16.3771i | 0.639681 | + | 0.688992i | ||||
\(566\) | −6.43234 | − | 20.0718i | −0.270371 | − | 0.843682i | ||||
\(567\) | 6.91776 | − | 6.91776i | 0.290519 | − | 0.290519i | ||||
\(568\) | 1.86560 | − | 0.272385i | 0.0782790 | − | 0.0114290i | ||||
\(569\) | − | 34.4084i | − | 1.44247i | −0.692689 | − | 0.721237i | \(-0.743574\pi\) | ||
0.692689 | − | 0.721237i | \(-0.256426\pi\) | |||||||
\(570\) | 7.70200 | − | 2.15673i | 0.322601 | − | 0.0903357i | ||||
\(571\) | 46.0355i | 1.92652i | 0.268563 | + | 0.963262i | \(0.413451\pi\) | ||||
−0.268563 | + | 0.963262i | \(0.586549\pi\) | |||||||
\(572\) | −10.6461 | + | 63.8777i | −0.445138 | + | 2.67086i | ||||
\(573\) | 16.9779 | − | 16.9779i | 0.709262 | − | 0.709262i | ||||
\(574\) | 6.88054 | − | 2.20498i | 0.287188 | − | 0.0920341i | ||||
\(575\) | 12.2566 | + | 14.2249i | 0.511136 | + | 0.593221i | ||||
\(576\) | −7.77048 | − | 26.0433i | −0.323770 | − | 1.08514i | ||||
\(577\) | −20.6188 | − | 20.6188i | −0.858372 | − | 0.858372i | 0.132775 | − | 0.991146i | \(-0.457611\pi\) |
−0.991146 | + | 0.132775i | \(0.957611\pi\) | |||||||
\(578\) | −4.91360 | + | 9.54808i | −0.204379 | + | 0.397148i | ||||
\(579\) | −21.7056 | −0.902054 | ||||||||
\(580\) | 10.4270 | + | 15.8060i | 0.432958 | + | 0.656308i | ||||
\(581\) | 11.8328 | 0.490907 | ||||||||
\(582\) | −3.52607 | + | 6.85185i | −0.146160 | + | 0.284018i | ||||
\(583\) | 13.4461 | + | 13.4461i | 0.556881 | + | 0.556881i | ||||
\(584\) | 29.1793 | + | 21.7443i | 1.20745 | + | 0.899785i | ||||
\(585\) | −36.5775 | + | 33.9597i | −1.51229 | + | 1.40406i | ||||
\(586\) | 0.560303 | − | 0.179558i | 0.0231459 | − | 0.00741749i | ||||
\(587\) | −10.5267 | + | 10.5267i | −0.434482 | + | 0.434482i | −0.890150 | − | 0.455668i | \(-0.849401\pi\) |
0.455668 | + | 0.890150i | \(0.349401\pi\) | |||||||
\(588\) | −26.7687 | − | 4.46139i | −1.10392 | − | 0.183985i | ||||
\(589\) | 6.52947i | 0.269042i | ||||||||
\(590\) | 21.6784 | − | 38.5413i | 0.892485 | − | 1.58672i | ||||
\(591\) | 45.0035i | 1.85120i | ||||||||
\(592\) | 23.8043 | − | 11.6490i | 0.978351 | − | 0.478773i | ||||
\(593\) | 1.48897 | − | 1.48897i | 0.0611445 | − | 0.0611445i | −0.675873 | − | 0.737018i | \(-0.736233\pi\) |
0.737018 | + | 0.675873i | \(0.236233\pi\) | |||||||
\(594\) | 2.13689 | + | 6.66807i | 0.0876777 | + | 0.273594i | ||||
\(595\) | −0.525907 | + | 14.1704i | −0.0215601 | + | 0.580930i | ||||
\(596\) | −32.6037 | + | 23.2885i | −1.33550 | + | 0.953933i | ||||
\(597\) | 16.2332 | + | 16.2332i | 0.664379 | + | 0.664379i | ||||
\(598\) | 31.0274 | + | 15.9672i | 1.26881 | + | 0.652948i | ||||
\(599\) | −40.1937 | −1.64227 | −0.821134 | − | 0.570735i | \(-0.806658\pi\) | ||||
−0.821134 | + | 0.570735i | \(0.806658\pi\) | |||||||
\(600\) | 23.4405 | − | 27.0183i | 0.956954 | − | 1.10302i | ||||
\(601\) | −36.4888 | −1.48841 | −0.744204 | − | 0.667953i | \(-0.767171\pi\) | ||||
−0.744204 | + | 0.667953i | \(0.767171\pi\) | |||||||
\(602\) | 3.20741 | + | 1.65058i | 0.130724 | + | 0.0672728i | ||||
\(603\) | 4.79919 | + | 4.79919i | 0.195438 | + | 0.195438i | ||||
\(604\) | −0.872904 | + | 0.623505i | −0.0355179 | + | 0.0253701i | ||||
\(605\) | −1.10180 | + | 29.6876i | −0.0447945 | + | 1.20697i | ||||
\(606\) | −0.381049 | − | 1.18905i | −0.0154791 | − | 0.0483017i | ||||
\(607\) | 1.97147 | − | 1.97147i | 0.0800195 | − | 0.0800195i | −0.665964 | − | 0.745984i | \(-0.731980\pi\) |
0.745984 | + | 0.665964i | \(0.231980\pi\) | |||||||
\(608\) | −4.07985 | + | 3.91852i | −0.165460 | + | 0.158917i | ||||
\(609\) | 13.6945i | 0.554930i | ||||||||
\(610\) | 10.2514 | − | 18.2256i | 0.415067 | − | 0.737932i | ||||
\(611\) | 7.44631i | 0.301245i | ||||||||
\(612\) | 33.2362 | + | 5.53930i | 1.34349 | + | 0.223913i | ||||
\(613\) | 28.7912 | − | 28.7912i | 1.16286 | − | 1.16286i | 0.179019 | − | 0.983846i | \(-0.442708\pi\) |
0.983846 | − | 0.179019i | \(-0.0572924\pi\) | |||||||
\(614\) | 1.38175 | − | 0.442803i | 0.0557627 | − | 0.0178701i | ||||
\(615\) | 16.5592 | − | 15.3741i | 0.667731 | − | 0.619942i | ||||
\(616\) | 10.6506 | − | 14.2923i | 0.429123 | − | 0.575853i | ||||
\(617\) | −0.750563 | − | 0.750563i | −0.0302165 | − | 0.0302165i | 0.691837 | − | 0.722054i | \(-0.256802\pi\) |
−0.722054 | + | 0.691837i | \(0.756802\pi\) | |||||||
\(618\) | 14.2033 | − | 27.5998i | 0.571341 | − | 1.11023i | ||||
\(619\) | −26.8459 | −1.07903 | −0.539514 | − | 0.841977i | \(-0.681392\pi\) | ||||
−0.539514 | + | 0.841977i | \(0.681392\pi\) | |||||||
\(620\) | 16.0797 | + | 24.3746i | 0.645775 | + | 0.978909i | ||||
\(621\) | 3.77304 | 0.151407 | ||||||||
\(622\) | 8.84715 | − | 17.1917i | 0.354738 | − | 0.689325i | ||||
\(623\) | −5.50284 | − | 5.50284i | −0.220466 | − | 0.220466i | ||||
\(624\) | 21.5587 | − | 62.8804i | 0.863038 | − | 2.51723i | ||||
\(625\) | 24.7253 | + | 3.69601i | 0.989011 | + | 0.147840i | ||||
\(626\) | 7.80063 | − | 2.49984i | 0.311776 | − | 0.0999136i | ||||
\(627\) | 8.81369 | − | 8.81369i | 0.351985 | − | 0.351985i | ||||
\(628\) | 1.42243 | − | 8.53466i | 0.0567610 | − | 0.340570i | ||||
\(629\) | 32.8565i | 1.31008i | ||||||||
\(630\) | 13.2288 | − | 3.70438i | 0.527050 | − | 0.147586i | ||||
\(631\) | − | 0.106404i | − | 0.00423588i | −0.999998 | − | 0.00211794i | \(-0.999326\pi\) | ||
0.999998 | − | 0.00211794i | \(-0.000674162\pi\) | |||||||
\(632\) | 2.90048 | + | 19.8658i | 0.115375 | + | 0.790220i | ||||
\(633\) | −38.5008 | + | 38.5008i | −1.53027 | + | 1.53027i | ||||
\(634\) | 0.869575 | + | 2.71347i | 0.0345352 | + | 0.107766i | ||||
\(635\) | −0.953738 | − | 1.02726i | −0.0378479 | − | 0.0407655i | ||||
\(636\) | −11.3453 | − | 15.8834i | −0.449871 | − | 0.629817i | ||||
\(637\) | −24.9246 | − | 24.9246i | −0.987548 | − | 0.987548i | ||||
\(638\) | 26.2384 | + | 13.5027i | 1.03879 | + | 0.534577i | ||||
\(639\) | 2.26454 | 0.0895837 | ||||||||
\(640\) | −5.58031 | + | 24.6751i | −0.220581 | + | 0.975369i | ||||
\(641\) | −13.7498 | −0.543084 | −0.271542 | − | 0.962427i | \(-0.587534\pi\) | ||||
−0.271542 | + | 0.962427i | \(0.587534\pi\) | |||||||
\(642\) | −34.7622 | − | 17.8892i | −1.37195 | − | 0.706030i | ||||
\(643\) | 23.5125 | + | 23.5125i | 0.927244 | + | 0.927244i | 0.997527 | − | 0.0702828i | \(-0.0223902\pi\) |
−0.0702828 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(644\) | −5.58251 | − | 7.81548i | −0.219982 | − | 0.307973i | ||||
\(645\) | 11.2732 | + | 0.418383i | 0.443882 | + | 0.0164738i | ||||
\(646\) | −2.14030 | − | 6.67871i | −0.0842091 | − | 0.262771i | ||||
\(647\) | 14.0408 | − | 14.0408i | 0.552002 | − | 0.552002i | −0.375016 | − | 0.927018i | \(-0.622363\pi\) |
0.927018 | + | 0.375016i | \(0.122363\pi\) | |||||||
\(648\) | 3.12622 | + | 21.4119i | 0.122809 | + | 0.841140i | ||||
\(649\) | − | 68.9116i | − | 2.70502i | ||||||
\(650\) | 45.1727 | − | 10.8600i | 1.77182 | − | 0.425965i | ||||
\(651\) | 21.1185i | 0.827700i | ||||||||
\(652\) | −1.93730 | + | 11.6240i | −0.0758706 | + | 0.455229i | ||||
\(653\) | −5.12437 | + | 5.12437i | −0.200532 | + | 0.200532i | −0.800228 | − | 0.599696i | \(-0.795288\pi\) |
0.599696 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(654\) | 3.80473 | − | 1.21929i | 0.148777 | − | 0.0476779i | ||||
\(655\) | −44.3812 | − | 1.64712i | −1.73412 | − | 0.0643584i | ||||
\(656\) | −5.18299 | + | 15.1173i | −0.202362 | + | 0.590230i | ||||
\(657\) | 30.9064 | + | 30.9064i | 1.20578 | + | 1.20578i | ||||
\(658\) | 0.937823 | − | 1.82237i | 0.0365602 | − | 0.0710435i | ||||
\(659\) | 3.86388 | 0.150515 | 0.0752576 | − | 0.997164i | \(-0.476022\pi\) | ||||
0.0752576 | + | 0.997164i | \(0.476022\pi\) | |||||||
\(660\) | 11.1968 | − | 54.6065i | 0.435837 | − | 2.12556i | ||||
\(661\) | 15.1842 | 0.590596 | 0.295298 | − | 0.955405i | \(-0.404581\pi\) | ||||
0.295298 | + | 0.955405i | \(0.404581\pi\) | |||||||
\(662\) | −4.86939 | + | 9.46216i | −0.189254 | + | 0.367757i | ||||
\(663\) | 58.2746 | + | 58.2746i | 2.26320 | + | 2.26320i | ||||
\(664\) | −15.6388 | + | 20.9862i | −0.606903 | + | 0.814421i | ||||
\(665\) | −1.94552 | − | 2.09550i | −0.0754441 | − | 0.0812599i | ||||
\(666\) | 30.3128 | − | 9.71424i | 1.17460 | − | 0.376419i | ||||
\(667\) | 11.2435 | − | 11.2435i | 0.435349 | − | 0.435349i | ||||
\(668\) | 4.40965 | + | 0.734932i | 0.170614 | + | 0.0284354i | ||||
\(669\) | − | 40.1104i | − | 1.55076i | ||||||
\(670\) | −1.70357 | − | 6.08367i | −0.0658145 | − | 0.235033i | ||||
\(671\) | − | 32.5873i | − | 1.25802i | ||||||
\(672\) | −13.1956 | + | 12.6738i | −0.509032 | + | 0.488904i | ||||
\(673\) | 16.4676 | − | 16.4676i | 0.634778 | − | 0.634778i | −0.314485 | − | 0.949262i | \(-0.601832\pi\) |
0.949262 | + | 0.314485i | \(0.101832\pi\) | |||||||
\(674\) | 8.37039 | + | 26.1194i | 0.322415 | + | 1.00608i | ||||
\(675\) | 3.80568 | − | 3.27908i | 0.146481 | − | 0.126212i | ||||
\(676\) | 49.1010 | − | 35.0723i | 1.88850 | − | 1.34893i | ||||
\(677\) | −13.1053 | − | 13.1053i | −0.503676 | − | 0.503676i | 0.408902 | − | 0.912578i | \(-0.365912\pi\) |
−0.912578 | + | 0.408902i | \(0.865912\pi\) | |||||||
\(678\) | −31.7860 | − | 16.3576i | −1.22073 | − | 0.628210i | ||||
\(679\) | 2.75488 | 0.105723 | ||||||||
\(680\) | −24.4370 | − | 19.6610i | −0.937116 | − | 0.753966i | ||||
\(681\) | 37.3240 | 1.43026 | ||||||||
\(682\) | 40.4626 | + | 20.8227i | 1.54939 | + | 0.797342i | ||||
\(683\) | 10.6014 | + | 10.6014i | 0.405652 | + | 0.405652i | 0.880219 | − | 0.474567i | \(-0.157395\pi\) |
−0.474567 | + | 0.880219i | \(0.657395\pi\) | |||||||
\(684\) | −5.52887 | + | 3.94921i | −0.211402 | + | 0.151002i | ||||
\(685\) | −24.3300 | + | 22.5887i | −0.929600 | + | 0.863069i | ||||
\(686\) | 6.82409 | + | 21.2942i | 0.260545 | + | 0.813018i | ||||
\(687\) | 7.14428 | − | 7.14428i | 0.272571 | − | 0.272571i | ||||
\(688\) | −7.16647 | + | 3.50703i | −0.273219 | + | 0.133704i | ||||
\(689\) | − | 25.3529i | − | 0.965868i | ||||||
\(690\) | −26.1795 | − | 14.7252i | −0.996635 | − | 0.560580i | ||||
\(691\) | 16.8100i | 0.639483i | 0.947505 | + | 0.319742i | \(0.103596\pi\) | ||||
−0.947505 | + | 0.319742i | \(0.896404\pi\) | |||||||
\(692\) | −23.7856 | − | 3.96421i | −0.904192 | − | 0.150697i | ||||
\(693\) | 15.1383 | − | 15.1383i | 0.575055 | − | 0.575055i | ||||
\(694\) | 43.0899 | − | 13.8088i | 1.63567 | − | 0.524177i | ||||
\(695\) | −1.51533 | + | 40.8301i | −0.0574797 | + | 1.54877i | ||||
\(696\) | −24.2881 | − | 18.0993i | −0.920636 | − | 0.686054i | ||||
\(697\) | −14.0100 | − | 14.0100i | −0.530666 | − | 0.530666i | ||||
\(698\) | −1.11635 | + | 2.16928i | −0.0422545 | + | 0.0821086i | ||||
\(699\) | −44.7246 | −1.69164 | ||||||||
\(700\) | −12.4231 | − | 3.03144i | −0.469549 | − | 0.114577i | ||||
\(701\) | −19.1823 | −0.724505 | −0.362253 | − | 0.932080i | \(-0.617992\pi\) | ||||
−0.362253 | + | 0.932080i | \(0.617992\pi\) | |||||||
\(702\) | 4.27181 | − | 8.30095i | 0.161229 | − | 0.313299i | ||||
\(703\) | −4.68490 | − | 4.68490i | −0.176694 | − | 0.176694i | ||||
\(704\) | 11.2720 | + | 37.7788i | 0.424828 | + | 1.42384i | ||||
\(705\) | 0.237716 | − | 6.40517i | 0.00895289 | − | 0.241233i | ||||
\(706\) | 20.8707 | − | 6.68835i | 0.785478 | − | 0.251719i | ||||
\(707\) | −0.315639 | + | 0.315639i | −0.0118708 | + | 0.0118708i | ||||
\(708\) | −11.6288 | + | 69.7738i | −0.437038 | + | 2.62226i | ||||
\(709\) | 22.4644i | 0.843668i | 0.906673 | + | 0.421834i | \(0.138613\pi\) | ||||
−0.906673 | + | 0.421834i | \(0.861387\pi\) | |||||||
\(710\) | −1.83724 | − | 1.03339i | −0.0689502 | − | 0.0387826i | ||||
\(711\) | 24.1139i | 0.904340i | ||||||||
\(712\) | 17.0324 | − | 2.48680i | 0.638317 | − | 0.0931966i | ||||
\(713\) | 17.3387 | − | 17.3387i | 0.649341 | − | 0.649341i | ||||
\(714\) | −6.92246 | − | 21.6012i | −0.259067 | − | 0.808406i | ||||
\(715\) | 53.0598 | − | 49.2624i | 1.98433 | − | 1.84231i | ||||
\(716\) | 17.5301 | + | 24.5421i | 0.655131 | + | 0.917180i | ||||
\(717\) | −18.0867 | − | 18.0867i | −0.675460 | − | 0.675460i | ||||
\(718\) | −32.7712 | − | 16.8646i | −1.22301 | − | 0.629382i | ||||
\(719\) | 45.9737 | 1.71453 | 0.857265 | − | 0.514876i | \(-0.172162\pi\) | ||||
0.857265 | + | 0.514876i | \(0.172162\pi\) | |||||||
\(720\) | −10.9140 | + | 28.3580i | −0.406739 | + | 1.05684i | ||||
\(721\) | −11.0969 | −0.413270 | ||||||||
\(722\) | 1.25747 | + | 0.647117i | 0.0467983 | + | 0.0240832i | ||||
\(723\) | −38.7418 | − | 38.7418i | −1.44082 | − | 1.44082i | ||||
\(724\) | −9.12617 | − | 12.7766i | −0.339171 | − | 0.474838i | ||||
\(725\) | 1.56924 | − | 21.1123i | 0.0582802 | − | 0.784090i | ||||
\(726\) | −14.5029 | − | 45.2555i | −0.538252 | − | 1.67959i | ||||
\(727\) | 19.6989 | − | 19.6989i | 0.730592 | − | 0.730592i | −0.240145 | − | 0.970737i | \(-0.577195\pi\) |
0.970737 | + | 0.240145i | \(0.0771950\pi\) | |||||||
\(728\) | −23.5151 | + | 3.43329i | −0.871527 | + | 0.127246i | ||||
\(729\) | 33.6141i | 1.24497i | ||||||||
\(730\) | −10.9708 | − | 39.1784i | −0.406049 | − | 1.45006i | ||||
\(731\) | − | 9.89172i | − | 0.365858i | ||||||
\(732\) | −5.49909 | + | 32.9950i | −0.203252 | + | 1.21953i | ||||
\(733\) | −26.8457 | + | 26.8457i | −0.991567 | + | 0.991567i | −0.999965 | − | 0.00839797i | \(-0.997327\pi\) |
0.00839797 | + | 0.999965i | \(0.497327\pi\) | |||||||
\(734\) | −5.56328 | + | 1.78284i | −0.205345 | + | 0.0658060i | ||||
\(735\) | 20.6440 | + | 22.2354i | 0.761464 | + | 0.820164i | ||||
\(736\) | 21.2394 | + | 0.428401i | 0.782893 | + | 0.0157911i | ||||
\(737\) | −6.96178 | − | 6.96178i | −0.256440 | − | 0.256440i | ||||
\(738\) | −8.78322 | + | 17.0675i | −0.323315 | + | 0.628263i | ||||
\(739\) | 40.4662 | 1.48857 | 0.744286 | − | 0.667861i | \(-0.232790\pi\) | ||||
0.744286 | + | 0.667861i | \(0.232790\pi\) | |||||||
\(740\) | −29.0260 | − | 5.95166i | −1.06702 | − | 0.218788i | ||||
\(741\) | −16.6184 | −0.610491 | ||||||||
\(742\) | −3.19307 | + | 6.20475i | −0.117221 | + | 0.227783i | ||||
\(743\) | −22.3693 | − | 22.3693i | −0.820650 | − | 0.820650i | 0.165551 | − | 0.986201i | \(-0.447060\pi\) |
−0.986201 | + | 0.165551i | \(0.947060\pi\) | |||||||
\(744\) | −37.4550 | − | 27.9113i | −1.37317 | − | 1.02328i | ||||
\(745\) | 44.7653 | + | 1.66138i | 1.64007 | + | 0.0608682i | ||||
\(746\) | −17.1480 | + | 5.49536i | −0.627834 | + | 0.201199i | ||||
\(747\) | −22.2283 | + | 22.2283i | −0.813292 | + | 0.813292i | ||||
\(748\) | −48.2129 | − | 8.03538i | −1.76284 | − | 0.293803i | ||||
\(749\) | 13.9766i | 0.510694i | ||||||||
\(750\) | −39.2034 | + | 7.89949i | −1.43151 | + | 0.288449i | ||||
\(751\) | − | 51.1851i | − | 1.86777i | −0.357573 | − | 0.933885i | \(-0.616396\pi\) | ||
0.357573 | − | 0.933885i | \(-0.383604\pi\) | |||||||
\(752\) | 1.99262 | + | 4.07182i | 0.0726632 | + | 0.148484i | ||||
\(753\) | 4.47191 | − | 4.47191i | 0.162966 | − | 0.162966i | ||||
\(754\) | −12.0067 | − | 37.4662i | −0.437257 | − | 1.36444i | ||||
\(755\) | 1.19851 | + | 0.0444803i | 0.0436182 | + | 0.00161880i | ||||
\(756\) | −2.09092 | + | 1.49352i | −0.0760461 | + | 0.0543189i | ||||
\(757\) | −4.56094 | − | 4.56094i | −0.165770 | − | 0.165770i | 0.619347 | − | 0.785117i | \(-0.287397\pi\) |
−0.785117 | + | 0.619347i | \(0.787397\pi\) | |||||||
\(758\) | −14.4783 | − | 7.45078i | −0.525876 | − | 0.270625i | ||||
\(759\) | −46.8088 | −1.69905 | ||||||||
\(760\) | 6.28779 | − | 0.680990i | 0.228082 | − | 0.0247021i | ||||
\(761\) | −16.9886 | −0.615835 | −0.307918 | − | 0.951413i | \(-0.599632\pi\) | ||||
−0.307918 | + | 0.951413i | \(0.599632\pi\) | |||||||
\(762\) | 1.99378 | + | 1.02603i | 0.0722270 | + | 0.0371692i | ||||
\(763\) | −1.00999 | − | 1.00999i | −0.0365640 | − | 0.0365640i | ||||
\(764\) | 15.4495 | − | 11.0354i | 0.558944 | − | 0.399247i | ||||
\(765\) | −25.6317 | − | 27.6076i | −0.926716 | − | 0.998154i | ||||
\(766\) | −11.7106 | − | 36.5425i | −0.423123 | − | 1.32034i | ||||
\(767\) | −64.9670 | + | 64.9670i | −2.34582 | + | 2.34582i | ||||
\(768\) | −5.03783 | − | 40.1536i | −0.181787 | − | 1.44892i | ||||
\(769\) | 34.8444i | 1.25652i | 0.778004 | + | 0.628260i | \(0.216233\pi\) | ||||
−0.778004 | + | 0.628260i | \(0.783767\pi\) | |||||||
\(770\) | −19.1899 | + | 5.37362i | −0.691558 | + | 0.193652i | ||||
\(771\) | 11.6870i | 0.420896i | ||||||||
\(772\) | −16.9300 | − | 2.82163i | −0.609323 | − | 0.101553i | ||||
\(773\) | −23.5239 | + | 23.5239i | −0.846094 | + | 0.846094i | −0.989643 | − | 0.143549i | \(-0.954149\pi\) |
0.143549 | + | 0.989643i | \(0.454149\pi\) | |||||||
\(774\) | −9.12592 | + | 2.92455i | −0.328024 | + | 0.105121i | ||||
\(775\) | 2.41995 | − | 32.5575i | 0.0869273 | − | 1.16950i | ||||
\(776\) | −3.64098 | + | 4.88594i | −0.130704 | + | 0.175395i | ||||
\(777\) | −15.1526 | − | 15.1526i | −0.543595 | − | 0.543595i | ||||
\(778\) | 12.5511 | − | 24.3893i | 0.449980 | − | 0.874399i | ||||
\(779\) | 3.99527 | 0.143145 | ||||||||
\(780\) | −62.0367 | + | 40.9249i | −2.22127 | + | 1.46534i | ||||
\(781\) | −3.28497 | −0.117545 | ||||||||
\(782\) | −12.0516 | + | 23.4185i | −0.430963 | + | 0.837445i | ||||
\(783\) | −3.00803 | − | 3.00803i | −0.107498 | − | 0.107498i | ||||
\(784\) | −20.2992 | − | 6.95961i | −0.724970 | − | 0.248558i | ||||
\(785\) | −7.08929 | + | 6.58191i | −0.253028 | + | 0.234919i | ||||
\(786\) | 67.6543 | − | 21.6809i | 2.41315 | − | 0.773333i | ||||
\(787\) | 29.8804 | − | 29.8804i | 1.06512 | − | 1.06512i | 0.0673967 | − | 0.997726i | \(-0.478531\pi\) |
0.997726 | − | 0.0673967i | \(-0.0214693\pi\) | |||||||
\(788\) | −5.85025 | + | 35.1019i | −0.208407 | + | 1.25046i | ||||
\(789\) | − | 62.4254i | − | 2.22240i | ||||||
\(790\) | 11.0041 | − | 19.5637i | 0.391507 | − | 0.696047i | ||||
\(791\) | 12.7800i | 0.454404i | ||||||||
\(792\) | 6.84116 | + | 46.8561i | 0.243090 | + | 1.66496i | ||||
\(793\) | −30.7219 | + | 30.7219i | −1.09097 | + | 1.09097i | ||||
\(794\) | 4.87499 | + | 15.2122i | 0.173007 | + | 0.539860i | ||||
\(795\) | −0.809365 | + | 21.8081i | −0.0287052 | + | 0.773453i | ||||
\(796\) | 10.5513 | + | 14.7718i | 0.373982 | + | 0.523573i | ||||
\(797\) | −25.9470 | − | 25.9470i | −0.919088 | − | 0.919088i | 0.0778748 | − | 0.996963i | \(-0.475187\pi\) |
−0.996963 | + | 0.0778748i | \(0.975187\pi\) | |||||||
\(798\) | 4.06710 | + | 2.09300i | 0.143974 | + | 0.0740912i | ||||
\(799\) | −5.62024 | −0.198830 | ||||||||
\(800\) | 21.7954 | − | 18.0266i | 0.770584 | − | 0.637338i | ||||
\(801\) | 20.6746 | 0.730500 | ||||||||
\(802\) | −27.4312 | − | 14.1165i | −0.968628 | − | 0.498472i | ||||
\(803\) | −44.8333 | − | 44.8333i | −1.58213 | − | 1.58213i | ||||
\(804\) | 5.87408 | + | 8.22367i | 0.207163 | + | 0.290027i | ||||
\(805\) | −0.398251 | + | 10.7308i | −0.0140365 | + | 0.378210i | ||||
\(806\) | −18.5156 | − | 57.7772i | −0.652186 | − | 2.03511i | ||||
\(807\) | 24.7104 | − | 24.7104i | 0.869849 | − | 0.869849i | ||||
\(808\) | −0.142641 | − | 0.976970i | −0.00501810 | − | 0.0343697i | ||||
\(809\) | − | 15.6625i | − | 0.550663i | −0.961349 | − | 0.275331i | \(-0.911212\pi\) | ||
0.961349 | − | 0.275331i | \(-0.0887876\pi\) | |||||||
\(810\) | 11.8605 | − | 21.0863i | 0.416735 | − | 0.740899i | ||||
\(811\) | 35.1664i | 1.23486i | 0.786626 | + | 0.617430i | \(0.211826\pi\) | ||||
−0.786626 | + | 0.617430i | \(0.788174\pi\) | |||||||
\(812\) | −1.78022 | + | 10.6815i | −0.0624736 | + | 0.374846i | ||||
\(813\) | 2.52332 | − | 2.52332i | 0.0884968 | − | 0.0884968i | ||||
\(814\) | −43.9722 | + | 14.0916i | −1.54123 | + | 0.493911i | ||||
\(815\) | 9.65541 | − | 8.96437i | 0.338214 | − | 0.314008i | ||||
\(816\) | 47.4602 | + | 16.2718i | 1.66144 | + | 0.569628i | ||||
\(817\) | 1.41043 | + | 1.41043i | 0.0493446 | + | 0.0493446i | ||||
\(818\) | 17.3455 | − | 33.7057i | 0.606472 | − | 1.17849i | ||||
\(819\) | −28.5435 | −0.997389 | ||||||||
\(820\) | 14.9144 | − | 9.83887i | 0.520835 | − | 0.343588i | ||||
\(821\) | −49.3171 | −1.72118 | −0.860589 | − | 0.509300i | \(-0.829904\pi\) | ||||
−0.860589 | + | 0.509300i | \(0.829904\pi\) | |||||||
\(822\) | 24.3009 | − | 47.2214i | 0.847592 | − | 1.64704i | ||||
\(823\) | 31.8005 | + | 31.8005i | 1.10850 | + | 1.10850i | 0.993348 | + | 0.115148i | \(0.0367342\pi\) |
0.115148 | + | 0.993348i | \(0.463266\pi\) | |||||||
\(824\) | 14.6662 | − | 19.6810i | 0.510921 | − | 0.685620i | ||||
\(825\) | −47.2137 | + | 40.6807i | −1.64377 | + | 1.41632i | ||||
\(826\) | 24.0820 | − | 7.71746i | 0.837919 | − | 0.268525i | ||||
\(827\) | 0.00780634 | − | 0.00780634i | 0.000271453 | − | 0.000271453i | −0.706971 | − | 0.707242i | \(-0.749939\pi\) |
0.707242 | + | 0.706971i | \(0.249939\pi\) | |||||||
\(828\) | 25.1687 | + | 4.19472i | 0.874671 | + | 0.145777i | ||||
\(829\) | − | 19.7402i | − | 0.685607i | −0.939407 | − | 0.342803i | \(-0.888624\pi\) | ||
0.939407 | − | 0.342803i | \(-0.111376\pi\) | |||||||
\(830\) | 28.1776 | − | 7.89038i | 0.978060 | − | 0.273879i | ||||
\(831\) | 37.8987i | 1.31469i | ||||||||
\(832\) | 24.9895 | − | 46.2430i | 0.866356 | − | 1.60319i | ||||
\(833\) | 18.8123 | − | 18.8123i | 0.651808 | − | 0.651808i | ||||
\(834\) | −19.9461 | − | 62.2410i | −0.690678 | − | 2.15523i | ||||
\(835\) | −3.40071 | − | 3.66286i | −0.117686 | − | 0.126759i | ||||
\(836\) | 8.02025 | − | 5.72878i | 0.277386 | − | 0.198134i | ||||
\(837\) | −4.63873 | − | 4.63873i | −0.160338 | − | 0.160338i | ||||
\(838\) | 28.8650 | + | 14.8544i | 0.997123 | + | 0.513136i | ||||
\(839\) | −34.5371 | −1.19235 | −0.596176 | − | 0.802853i | \(-0.703314\pi\) | ||||
−0.596176 | + | 0.802853i | \(0.703314\pi\) | |||||||
\(840\) | 20.3368 | − | 2.20255i | 0.701687 | − | 0.0759953i | ||||
\(841\) | 11.0724 | 0.381807 | ||||||||
\(842\) | −27.9019 | − | 14.3588i | −0.961564 | − | 0.494837i | ||||
\(843\) | 6.61284 | + | 6.61284i | 0.227758 | + | 0.227758i | ||||
\(844\) | −35.0349 | + | 25.0250i | −1.20595 | + | 0.861397i | ||||
\(845\) | −67.4162 | − | 2.50202i | −2.31919 | − | 0.0860722i | ||||
\(846\) | 1.66166 | + | 5.18514i | 0.0571291 | + | 0.178269i | ||||
\(847\) | −12.0133 | + | 12.0133i | −0.412783 | + | 0.412783i | ||||
\(848\) | −6.78438 | − | 13.8636i | −0.232977 | − | 0.476078i | ||||
\(849\) | − | 37.6961i | − | 1.29373i | ||||||
\(850\) | 8.19681 | + | 34.0949i | 0.281148 | + | 1.16945i | ||||
\(851\) | 24.8811i | 0.852914i | ||||||||
\(852\) | 3.32607 | + | 0.554338i | 0.113949 | + | 0.0189913i | ||||
\(853\) | 25.5720 | − | 25.5720i | 0.875568 | − | 0.875568i | −0.117505 | − | 0.993072i | \(-0.537490\pi\) |
0.993072 | + | 0.117505i | \(0.0374895\pi\) | |||||||
\(854\) | 11.3880 | − | 3.64947i | 0.389689 | − | 0.124882i | ||||
\(855\) | 7.59121 | + | 0.281733i | 0.259614 | + | 0.00963507i | ||||
\(856\) | −24.7884 | − | 18.4722i | −0.847249 | − | 0.631366i | ||||
\(857\) | 1.88427 | + | 1.88427i | 0.0643653 | + | 0.0643653i | 0.738557 | − | 0.674191i | \(-0.235508\pi\) |
−0.674191 | + | 0.738557i | \(0.735508\pi\) | |||||||
\(858\) | −52.9965 | + | 102.983i | −1.80927 | + | 3.51577i | ||||
\(859\) | 2.53886 | 0.0866248 | 0.0433124 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433124 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(860\) | 8.73851 | + | 1.79180i | 0.297981 | + | 0.0610997i | ||||
\(861\) | 12.9221 | 0.440383 | ||||||||
\(862\) | 2.07465 | − | 4.03145i | 0.0706628 | − | 0.137312i | ||||
\(863\) | 0.510933 | + | 0.510933i | 0.0173924 | + | 0.0173924i | 0.715749 | − | 0.698357i | \(-0.246085\pi\) |
−0.698357 | + | 0.715749i | \(0.746085\pi\) | |||||||
\(864\) | 0.114613 | − | 5.68229i | 0.00389920 | − | 0.193315i | ||||
\(865\) | 18.3434 | + | 19.7574i | 0.623694 | + | 0.671772i | ||||
\(866\) | −30.8289 | + | 9.87963i | −1.04761 | + | 0.335723i | ||||
\(867\) | −13.5799 | + | 13.5799i | −0.461199 | + | 0.461199i | ||||
\(868\) | −2.74531 | + | 16.4721i | −0.0931818 | + | 0.559098i | ||||
\(869\) | − | 34.9799i | − | 1.18661i | ||||||
\(870\) | 9.13183 | + | 32.6110i | 0.309598 | + | 1.10562i | ||||
\(871\) | 13.1265i | 0.444776i | ||||||||
\(872\) | 3.12612 | − | 0.456425i | 0.105864 | − | 0.0154565i | ||||
\(873\) | −5.17515 | + | 5.17515i | −0.175152 | + | 0.175152i | ||||
\(874\) | −1.62078 | − | 5.05756i | −0.0548236 | − | 0.171075i | ||||
\(875\) | 8.92422 | + | 11.1697i | 0.301694 | + | 0.377605i | ||||
\(876\) | 37.8286 | + | 52.9599i | 1.27811 | + | 1.78935i | ||||
\(877\) | 20.6204 | + | 20.6204i | 0.696303 | + | 0.696303i | 0.963611 | − | 0.267308i | \(-0.0861343\pi\) |
−0.267308 | + | 0.963611i | \(0.586134\pi\) | |||||||
\(878\) | 42.0891 | + | 21.6597i | 1.42044 | + | 0.730981i | ||||
\(879\) | 1.05228 | 0.0354926 | ||||||||
\(880\) | 15.8319 | − | 41.1366i | 0.533694 | − | 1.38671i | ||||
\(881\) | 25.4241 | 0.856558 | 0.428279 | − | 0.903646i | \(-0.359120\pi\) | ||||
0.428279 | + | 0.903646i | \(0.359120\pi\) | |||||||
\(882\) | −22.9179 | − | 11.7939i | −0.771686 | − | 0.397122i | ||||
\(883\) | −2.45182 | − | 2.45182i | −0.0825104 | − | 0.0825104i | 0.664647 | − | 0.747157i | \(-0.268582\pi\) |
−0.747157 | + | 0.664647i | \(0.768582\pi\) | |||||||
\(884\) | 37.8777 | + | 53.0286i | 1.27397 | + | 1.78354i | ||||
\(885\) | 57.9574 | − | 53.8094i | 1.94822 | − | 1.80878i | ||||
\(886\) | −4.27160 | − | 13.3293i | −0.143507 | − | 0.447808i | ||||
\(887\) | −20.7237 | + | 20.7237i | −0.695833 | + | 0.695833i | −0.963509 | − | 0.267676i | \(-0.913744\pi\) |
0.267676 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(888\) | 46.9003 | − | 6.84762i | 1.57387 | − | 0.229791i | ||||
\(889\) | − | 0.801627i | − | 0.0268857i | ||||||
\(890\) | −16.7734 | − | 9.43459i | −0.562247 | − | 0.316248i | ||||
\(891\) | − | 37.7023i | − | 1.26307i | ||||||
\(892\) | 5.21416 | − | 31.2854i | 0.174583 | − | 1.04751i | ||||
\(893\) | 0.801371 | − | 0.801371i | 0.0268169 | − | 0.0268169i | ||||
\(894\) | −68.2398 | + | 21.8686i | −2.28228 | + | 0.731394i | ||||
\(895\) | 1.25058 | − | 33.6966i | 0.0418024 | − | 1.12635i | ||||
\(896\) | −11.9399 | + | 8.16999i | −0.398884 | + | 0.272940i | ||||
\(897\) | 44.1294 | + | 44.1294i | 1.47344 | + | 1.47344i | ||||
\(898\) | −7.03892 | + | 13.6780i | −0.234892 | + | 0.456440i | ||||
\(899\) | −27.6464 | −0.922060 | ||||||||
\(900\) | 29.0320 | − | 17.6426i | 0.967732 | − | 0.588087i | ||||
\(901\) | 19.1356 | 0.637499 | ||||||||
\(902\) | 12.7411 | − | 24.7584i | 0.424231 | − | 0.824363i | ||||
\(903\) | 4.56180 | + | 4.56180i | 0.151807 | + | 0.151807i | ||||
\(904\) | −22.6661 | − | 16.8907i | −0.753863 | − | 0.561775i | ||||
\(905\) | −0.651053 | + | 17.5424i | −0.0216417 | + | 0.583129i | ||||
\(906\) | −1.82699 | + | 0.585490i | −0.0606978 | + | 0.0194516i | ||||
\(907\) | 11.7025 | − | 11.7025i | 0.388576 | − | 0.388576i | −0.485603 | − | 0.874179i | \(-0.661400\pi\) |
0.874179 | + | 0.485603i | \(0.161400\pi\) | |||||||
\(908\) | 29.1120 | + | 4.85194i | 0.966116 | + | 0.161017i | ||||
\(909\) | − | 1.18588i | − | 0.0393332i | ||||||
\(910\) | 23.1575 | + | 13.0255i | 0.767664 | + | 0.431790i | ||||
\(911\) | − | 40.4274i | − | 1.33942i | −0.742623 | − | 0.669709i | \(-0.766419\pi\) | ||
0.742623 | − | 0.669709i | \(-0.233581\pi\) | |||||||
\(912\) | −9.08733 | + | 4.44704i | −0.300911 | + | 0.147256i | ||||
\(913\) | 32.2447 | − | 32.2447i | 1.06715 | − | 1.06715i | ||||
\(914\) | −1.35170 | − | 4.21793i | −0.0447104 | − | 0.139517i | ||||
\(915\) | 27.4072 | − | 25.4457i | 0.906054 | − | 0.841207i | ||||
\(916\) | 6.50113 | − | 4.64368i | 0.214803 | − | 0.153432i | ||||
\(917\) | −17.9592 | − | 17.9592i | −0.593066 | − | 0.593066i | ||||
\(918\) | 6.26530 | + | 3.22423i | 0.206786 | + | 0.106415i | ||||
\(919\) | −21.3527 | −0.704359 | −0.352180 | − | 0.935932i | \(-0.614559\pi\) | ||||
−0.352180 | + | 0.935932i | \(0.614559\pi\) | |||||||
\(920\) | −18.5053 | − | 14.8886i | −0.610102 | − | 0.490863i | ||||
\(921\) | 2.59500 | 0.0855082 | ||||||||
\(922\) | 40.8244 | + | 21.0089i | 1.34448 | + | 0.691892i | ||||
\(923\) | 3.09693 | + | 3.09693i | 0.101937 | + | 0.101937i | ||||
\(924\) | 25.9402 | − | 18.5288i | 0.853371 | − | 0.609553i | ||||
\(925\) | 21.6237 | + | 25.0964i | 0.710984 | + | 0.825164i | ||||
\(926\) | −10.7553 | − | 33.5614i | −0.353441 | − | 1.10290i | ||||
\(927\) | 20.8459 | − | 20.8459i | 0.684670 | − | 0.684670i | ||||
\(928\) | −16.5914 | − | 17.2745i | −0.544640 | − | 0.567063i | ||||
\(929\) | 22.6968i | 0.744659i | 0.928101 | + | 0.372330i | \(0.121441\pi\) | ||||
−0.928101 | + | 0.372330i | \(0.878559\pi\) | |||||||
\(930\) | 14.0823 | + | 50.2900i | 0.461778 | + | 1.64907i | ||||
\(931\) | 5.36477i | 0.175823i | ||||||||
\(932\) | −34.8844 | − | 5.81399i | −1.14268 | − | 0.190444i | ||||
\(933\) | 24.4513 | − | 24.4513i | 0.800499 | − | 0.800499i | ||||
\(934\) | 7.69672 | − | 2.46654i | 0.251844 | − | 0.0807076i | ||||
\(935\) | 37.1817 | + | 40.0479i | 1.21597 | + | 1.30971i | ||||
\(936\) | 37.7244 | − | 50.6235i | 1.23306 | − | 1.65468i | ||||
\(937\) | 0.0187763 | + | 0.0187763i | 0.000613396 | + | 0.000613396i | 0.707413 | − | 0.706800i | \(-0.249862\pi\) |
−0.706800 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(938\) | 1.65322 | − | 3.21253i | 0.0539796 | − | 0.104893i | ||||
\(939\) | 14.6500 | 0.478086 | ||||||||
\(940\) | 1.01806 | − | 4.96502i | 0.0332053 | − | 0.161941i | ||||
\(941\) | 52.1786 | 1.70097 | 0.850487 | − | 0.525995i | \(-0.176307\pi\) | ||||
0.850487 | + | 0.525995i | \(0.176307\pi\) | |||||||
\(942\) | 7.08083 | − | 13.7594i | 0.230706 | − | 0.448307i | ||||
\(943\) | −10.6093 | − | 10.6093i | −0.345486 | − | 0.345486i | ||||
\(944\) | −18.1405 | + | 52.9106i | −0.590424 | + | 1.72209i | ||||
\(945\) | 2.87086 | + | 0.106547i | 0.0933892 | + | 0.00346596i | ||||
\(946\) | 13.2382 | − | 4.24239i | 0.430411 | − | 0.137932i | ||||
\(947\) | 1.09987 | − | 1.09987i | 0.0357408 | − | 0.0357408i | −0.689011 | − | 0.724751i | \(-0.741955\pi\) |
0.724751 | + | 0.689011i | \(0.241955\pi\) | |||||||
\(948\) | −5.90285 | + | 35.4175i | −0.191716 | + | 1.15031i | ||||
\(949\) | 84.5340i | 2.74409i | ||||||||
\(950\) | −6.03024 | − | 3.69273i | −0.195647 | − | 0.119808i | ||||
\(951\) | 5.09605i | 0.165251i | ||||||||
\(952\) | −2.59134 | − | 17.7485i | −0.0839858 | − | 0.575231i | ||||
\(953\) | −15.6807 | + | 15.6807i | −0.507949 | + | 0.507949i | −0.913896 | − | 0.405947i | \(-0.866942\pi\) |
0.405947 | + | 0.913896i | \(0.366942\pi\) | |||||||
\(954\) | −5.65756 | − | 17.6542i | −0.183170 | − | 0.571574i | ||||
\(955\) | −21.2124 | − | 0.787256i | −0.686416 | − | 0.0254750i | ||||
\(956\) | −11.7561 | − | 16.4585i | −0.380220 | − | 0.532306i | ||||
\(957\) | 37.3180 | + | 37.3180i | 1.20632 | + | 1.20632i | ||||
\(958\) | 52.3565 | + | 26.9435i | 1.69156 | + | 0.870506i | ||||
\(959\) | −18.9860 | −0.613090 | ||||||||
\(960\) | −22.9718 | + | 38.9796i | −0.741411 | + | 1.25806i | ||||
\(961\) | −11.6339 | −0.375289 | ||||||||
\(962\) | 54.7402 | + | 28.1702i | 1.76489 | + | 0.908244i | ||||
\(963\) | −26.2556 | − | 26.2556i | −0.846075 | − | 0.846075i | ||||
\(964\) | −25.1817 | − | 35.2542i | −0.811047 | − | 1.13546i | ||||
\(965\) | 13.0564 | + | 14.0628i | 0.420299 | + | 0.452699i | ||||
\(966\) | −5.24215 | − | 16.3579i | −0.168663 | − | 0.526306i | ||||
\(967\) | −20.0380 | + | 20.0380i | −0.644379 | + | 0.644379i | −0.951629 | − | 0.307250i | \(-0.900591\pi\) |
0.307250 | + | 0.951629i | \(0.400591\pi\) | |||||||
\(968\) | −5.42897 | − | 37.1838i | −0.174494 | − | 1.19513i | ||||
\(969\) | − | 12.5430i | − | 0.402940i | ||||||
\(970\) | 6.56025 | − | 1.83702i | 0.210637 | − | 0.0589831i | ||||
\(971\) | − | 24.2537i | − | 0.778337i | −0.921167 | − | 0.389168i | \(-0.872762\pi\) | ||
0.921167 | − | 0.389168i | \(-0.127238\pi\) | |||||||
\(972\) | −7.35327 | + | 44.1202i | −0.235856 | + | 1.41516i | ||||
\(973\) | −16.5222 | + | 16.5222i | −0.529678 | + | 0.529678i | ||||
\(974\) | −39.9770 | + | 12.8113i | −1.28095 | + | 0.410500i | ||||
\(975\) | 82.8632 | + | 6.15910i | 2.65375 | + | 0.197249i | ||||
\(976\) | −8.57839 | + | 25.0206i | −0.274587 | + | 0.800891i | ||||
\(977\) | 16.0969 | + | 16.0969i | 0.514986 | + | 0.514986i | 0.916050 | − | 0.401064i | \(-0.131360\pi\) |
−0.401064 | + | 0.916050i | \(0.631360\pi\) | |||||||
\(978\) | −9.64389 | + | 18.7399i | −0.308377 | + | 0.599237i | ||||
\(979\) | −29.9908 | −0.958511 | ||||||||
\(980\) | 13.2114 | + | 20.0268i | 0.422024 | + | 0.639733i | ||||
\(981\) | 3.79460 | 0.121152 | ||||||||
\(982\) | −17.1186 | + | 33.2648i | −0.546276 | + | 1.06152i | ||||
\(983\) | −28.6174 | − | 28.6174i | −0.912755 | − | 0.912755i | 0.0837333 | − | 0.996488i | \(-0.473316\pi\) |
−0.996488 | + | 0.0837333i | \(0.973316\pi\) | |||||||
\(984\) | −17.0784 | + | 22.9181i | −0.544440 | + | 0.730601i | ||||
\(985\) | 29.1573 | − | 27.0706i | 0.929030 | − | 0.862539i | ||||
\(986\) | 28.2783 | − | 9.06225i | 0.900566 | − | 0.288601i | ||||
\(987\) | 2.59191 | − | 2.59191i | 0.0825013 | − | 0.0825013i | ||||
\(988\) | −12.9620 | − | 2.16031i | −0.412377 | − | 0.0687286i | ||||
\(989\) | − | 7.49066i | − | 0.238189i | ||||||
\(990\) | 25.9545 | − | 46.1436i | 0.824888 | − | 1.46654i | ||||
\(991\) | 28.0599i | 0.891351i | 0.895195 | + | 0.445675i | \(0.147036\pi\) | ||||
−0.895195 | + | 0.445675i | \(0.852964\pi\) | |||||||
\(992\) | −25.5859 | − | 26.6393i | −0.812352 | − | 0.845797i | ||||
\(993\) | −13.4578 | + | 13.4578i | −0.427069 | + | 0.427069i | ||||
\(994\) | −0.367886 | − | 1.14797i | −0.0116686 | − | 0.0364114i | ||||
\(995\) | 0.752723 | − | 20.2819i | 0.0238629 | − | 0.642979i | ||||
\(996\) | −38.0895 | + | 27.2069i | −1.20691 | + | 0.862083i | ||||
\(997\) | 24.0675 | + | 24.0675i | 0.762226 | + | 0.762226i | 0.976724 | − | 0.214498i | \(-0.0688117\pi\) |
−0.214498 | + | 0.976724i | \(0.568812\pi\) | |||||||
\(998\) | 19.1584 | + | 9.85924i | 0.606449 | + | 0.312089i | ||||
\(999\) | 6.65659 | 0.210605 |
(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 | 380.2.k.c.267.23 | ✓ | 52 | |
4.3 | odd | 2 | 380.2.k.d.267.17 | yes | 52 | ||
5.3 | odd | 4 | 380.2.k.d.343.17 | yes | 52 | ||
20.3 | even | 4 | inner | 380.2.k.c.343.23 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.k.c.267.23 | ✓ | 52 | 1.1 | even | 1 | trivial | |
380.2.k.c.343.23 | yes | 52 | 20.3 | even | 4 | inner | |
380.2.k.d.267.17 | yes | 52 | 4.3 | odd | 2 | ||
380.2.k.d.343.17 | yes | 52 | 5.3 | odd | 4 |