Properties

Label 243.2.e.c.55.2
Level $243$
Weight $2$
Character 243.55
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.e (of order \(9\), degree \(6\), 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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 55.2
Root \(0.500000 + 2.22827i\) of defining polynomial
Character \(\chi\) \(=\) 243.55
Dual form 243.2.e.c.190.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.98897 - 0.723928i) q^{2} +(1.89986 - 1.59417i) q^{4} +(-0.465915 - 2.64234i) q^{5} +(0.744850 + 0.625003i) q^{7} +(0.508086 - 0.880031i) q^{8} +O(q^{10})\) \(q+(1.98897 - 0.723928i) q^{2} +(1.89986 - 1.59417i) q^{4} +(-0.465915 - 2.64234i) q^{5} +(0.744850 + 0.625003i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-2.83955 - 4.91825i) q^{10} +(-0.0550295 + 0.312088i) q^{11} +(1.42272 + 0.517829i) q^{13} +(1.93395 + 0.703898i) q^{14} +(-0.487835 + 2.76665i) q^{16} +(-0.587342 - 1.01731i) q^{17} +(-3.11040 + 5.38737i) q^{19} +(-5.09751 - 4.27732i) q^{20} +(0.116477 + 0.660572i) q^{22} +(1.65676 - 1.39018i) q^{23} +(-2.06640 + 0.752107i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(4.13926 - 1.50657i) q^{29} +(-6.64408 + 5.57504i) q^{31} +(1.38548 + 7.85742i) q^{32} +(-1.90466 - 1.59820i) q^{34} +(1.30443 - 2.25934i) q^{35} +(2.23332 + 3.86823i) q^{37} +(-2.28644 + 12.9671i) q^{38} +(-2.56206 - 0.932515i) q^{40} +(-5.49268 - 1.99917i) q^{41} +(0.970865 - 5.50605i) q^{43} +(0.392973 + 0.680649i) q^{44} +(2.28885 - 3.96441i) q^{46} +(-1.89678 - 1.59159i) q^{47} +(-1.05136 - 5.96259i) q^{49} +(-3.56554 + 2.99184i) q^{50} +(3.52848 - 1.28426i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(0.928471 - 0.337936i) q^{56} +(7.14224 - 5.99305i) q^{58} +(-0.299406 - 1.69802i) q^{59} +(0.777365 + 0.652287i) q^{61} +(-9.17898 + 15.8985i) q^{62} +(5.63455 + 9.75933i) q^{64} +(0.705410 - 4.00058i) q^{65} +(-0.804895 - 0.292958i) q^{67} +(-2.73763 - 0.996416i) q^{68} +(0.958882 - 5.43809i) q^{70} +(4.79788 + 8.31018i) q^{71} +(7.62091 - 13.1998i) q^{73} +(7.24234 + 6.07705i) q^{74} +(2.67907 + 15.1938i) q^{76} +(-0.236045 + 0.198065i) q^{77} +(10.5375 - 3.83533i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(-4.40239 + 1.60234i) q^{83} +(-2.41441 + 2.02593i) q^{85} +(-2.05496 - 11.6542i) q^{86} +(0.246687 + 0.206995i) q^{88} +(7.74976 - 13.4230i) q^{89} +(0.736071 + 1.27491i) q^{91} +(0.931414 - 5.28231i) q^{92} +(-4.92484 - 1.79249i) q^{94} +(15.6844 + 5.70867i) q^{95} +(-0.963658 + 5.46518i) q^{97} +(-6.40762 - 11.0983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 3 q^{13} + 6 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} - 21 q^{20} - 15 q^{22} + 24 q^{23} - 15 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 15 q^{31} - 27 q^{32} - 9 q^{34} + 12 q^{35} - 3 q^{37} - 12 q^{38} - 6 q^{40} - 21 q^{41} + 12 q^{43} + 3 q^{44} - 3 q^{46} + 3 q^{47} + 21 q^{49} + 12 q^{50} + 36 q^{52} - 18 q^{53} - 12 q^{55} + 3 q^{56} + 30 q^{58} + 15 q^{59} + 21 q^{61} - 12 q^{62} + 12 q^{64} - 24 q^{65} + 21 q^{67} - 18 q^{68} + 30 q^{70} + 27 q^{71} + 6 q^{73} - 12 q^{74} + 42 q^{76} - 3 q^{77} + 21 q^{79} + 42 q^{80} - 12 q^{82} - 33 q^{83} - 9 q^{85} - 30 q^{86} - 12 q^{88} + 9 q^{89} + 6 q^{91} + 42 q^{92} - 33 q^{94} + 30 q^{95} - 42 q^{97} - 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.98897 0.723928i 1.40642 0.511894i 0.476341 0.879261i \(-0.341963\pi\)
0.930076 + 0.367366i \(0.119740\pi\)
\(3\) 0 0
\(4\) 1.89986 1.59417i 0.949930 0.797086i
\(5\) −0.465915 2.64234i −0.208364 1.18169i −0.892058 0.451920i \(-0.850739\pi\)
0.683695 0.729768i \(-0.260372\pi\)
\(6\) 0 0
\(7\) 0.744850 + 0.625003i 0.281527 + 0.236229i 0.772606 0.634886i \(-0.218953\pi\)
−0.491079 + 0.871115i \(0.663397\pi\)
\(8\) 0.508086 0.880031i 0.179636 0.311138i
\(9\) 0 0
\(10\) −2.83955 4.91825i −0.897945 1.55529i
\(11\) −0.0550295 + 0.312088i −0.0165920 + 0.0940980i −0.991979 0.126401i \(-0.959657\pi\)
0.975387 + 0.220499i \(0.0707685\pi\)
\(12\) 0 0
\(13\) 1.42272 + 0.517829i 0.394592 + 0.143620i 0.531693 0.846937i \(-0.321556\pi\)
−0.137100 + 0.990557i \(0.543778\pi\)
\(14\) 1.93395 + 0.703898i 0.516869 + 0.188125i
\(15\) 0 0
\(16\) −0.487835 + 2.76665i −0.121959 + 0.691662i
\(17\) −0.587342 1.01731i −0.142451 0.246733i 0.785968 0.618267i \(-0.212165\pi\)
−0.928419 + 0.371534i \(0.878832\pi\)
\(18\) 0 0
\(19\) −3.11040 + 5.38737i −0.713575 + 1.23595i 0.249931 + 0.968264i \(0.419592\pi\)
−0.963507 + 0.267685i \(0.913741\pi\)
\(20\) −5.09751 4.27732i −1.13984 0.956438i
\(21\) 0 0
\(22\) 0.116477 + 0.660572i 0.0248329 + 0.140834i
\(23\) 1.65676 1.39018i 0.345458 0.289873i −0.453505 0.891254i \(-0.649827\pi\)
0.798963 + 0.601380i \(0.205382\pi\)
\(24\) 0 0
\(25\) −2.06640 + 0.752107i −0.413280 + 0.150421i
\(26\) 3.20463 0.628480
\(27\) 0 0
\(28\) 2.41147 0.455726
\(29\) 4.13926 1.50657i 0.768642 0.279763i 0.0722135 0.997389i \(-0.476994\pi\)
0.696428 + 0.717627i \(0.254771\pi\)
\(30\) 0 0
\(31\) −6.64408 + 5.57504i −1.19331 + 1.00131i −0.193516 + 0.981097i \(0.561989\pi\)
−0.999796 + 0.0202102i \(0.993566\pi\)
\(32\) 1.38548 + 7.85742i 0.244920 + 1.38901i
\(33\) 0 0
\(34\) −1.90466 1.59820i −0.326647 0.274090i
\(35\) 1.30443 2.25934i 0.220489 0.381899i
\(36\) 0 0
\(37\) 2.23332 + 3.86823i 0.367156 + 0.635933i 0.989120 0.147113i \(-0.0469982\pi\)
−0.621964 + 0.783046i \(0.713665\pi\)
\(38\) −2.28644 + 12.9671i −0.370910 + 2.10353i
\(39\) 0 0
\(40\) −2.56206 0.932515i −0.405098 0.147443i
\(41\) −5.49268 1.99917i −0.857812 0.312218i −0.124591 0.992208i \(-0.539762\pi\)
−0.733221 + 0.679990i \(0.761984\pi\)
\(42\) 0 0
\(43\) 0.970865 5.50605i 0.148056 0.839665i −0.816807 0.576911i \(-0.804258\pi\)
0.964863 0.262754i \(-0.0846308\pi\)
\(44\) 0.392973 + 0.680649i 0.0592429 + 0.102612i
\(45\) 0 0
\(46\) 2.28885 3.96441i 0.337473 0.584521i
\(47\) −1.89678 1.59159i −0.276674 0.232157i 0.493883 0.869528i \(-0.335577\pi\)
−0.770556 + 0.637372i \(0.780022\pi\)
\(48\) 0 0
\(49\) −1.05136 5.96259i −0.150195 0.851798i
\(50\) −3.56554 + 2.99184i −0.504244 + 0.423111i
\(51\) 0 0
\(52\) 3.52848 1.28426i 0.489313 0.178095i
\(53\) −10.8920 −1.49613 −0.748063 0.663628i \(-0.769016\pi\)
−0.748063 + 0.663628i \(0.769016\pi\)
\(54\) 0 0
\(55\) 0.850279 0.114652
\(56\) 0.928471 0.337936i 0.124072 0.0451586i
\(57\) 0 0
\(58\) 7.14224 5.99305i 0.937822 0.786926i
\(59\) −0.299406 1.69802i −0.0389793 0.221063i 0.959096 0.283082i \(-0.0913570\pi\)
−0.998075 + 0.0620196i \(0.980246\pi\)
\(60\) 0 0
\(61\) 0.777365 + 0.652287i 0.0995314 + 0.0835168i 0.691195 0.722668i \(-0.257084\pi\)
−0.591664 + 0.806185i \(0.701529\pi\)
\(62\) −9.17898 + 15.8985i −1.16573 + 2.01911i
\(63\) 0 0
\(64\) 5.63455 + 9.75933i 0.704319 + 1.21992i
\(65\) 0.705410 4.00058i 0.0874953 0.496210i
\(66\) 0 0
\(67\) −0.804895 0.292958i −0.0983335 0.0357905i 0.292385 0.956301i \(-0.405551\pi\)
−0.390718 + 0.920510i \(0.627773\pi\)
\(68\) −2.73763 0.996416i −0.331986 0.120833i
\(69\) 0 0
\(70\) 0.958882 5.43809i 0.114608 0.649976i
\(71\) 4.79788 + 8.31018i 0.569404 + 0.986237i 0.996625 + 0.0820894i \(0.0261593\pi\)
−0.427221 + 0.904147i \(0.640507\pi\)
\(72\) 0 0
\(73\) 7.62091 13.1998i 0.891960 1.54492i 0.0544385 0.998517i \(-0.482663\pi\)
0.837522 0.546404i \(-0.184004\pi\)
\(74\) 7.24234 + 6.07705i 0.841905 + 0.706442i
\(75\) 0 0
\(76\) 2.67907 + 15.1938i 0.307311 + 1.74285i
\(77\) −0.236045 + 0.198065i −0.0268998 + 0.0225716i
\(78\) 0 0
\(79\) 10.5375 3.83533i 1.18556 0.431509i 0.327398 0.944887i \(-0.393828\pi\)
0.858163 + 0.513378i \(0.171606\pi\)
\(80\) 7.53771 0.842741
\(81\) 0 0
\(82\) −12.3721 −1.36626
\(83\) −4.40239 + 1.60234i −0.483226 + 0.175880i −0.572134 0.820160i \(-0.693884\pi\)
0.0889086 + 0.996040i \(0.471662\pi\)
\(84\) 0 0
\(85\) −2.41441 + 2.02593i −0.261880 + 0.219743i
\(86\) −2.05496 11.6542i −0.221592 1.25671i
\(87\) 0 0
\(88\) 0.246687 + 0.206995i 0.0262969 + 0.0220657i
\(89\) 7.74976 13.4230i 0.821473 1.42283i −0.0831130 0.996540i \(-0.526486\pi\)
0.904586 0.426292i \(-0.140180\pi\)
\(90\) 0 0
\(91\) 0.736071 + 1.27491i 0.0771612 + 0.133647i
\(92\) 0.931414 5.28231i 0.0971066 0.550719i
\(93\) 0 0
\(94\) −4.92484 1.79249i −0.507958 0.184882i
\(95\) 15.6844 + 5.70867i 1.60919 + 0.585697i
\(96\) 0 0
\(97\) −0.963658 + 5.46518i −0.0978446 + 0.554905i 0.895994 + 0.444066i \(0.146465\pi\)
−0.993838 + 0.110838i \(0.964647\pi\)
\(98\) −6.40762 11.0983i −0.647267 1.12110i
\(99\) 0 0
\(100\) −2.72688 + 4.72309i −0.272688 + 0.472309i
\(101\) −7.76696 6.51725i −0.772841 0.648491i 0.168594 0.985686i \(-0.446077\pi\)
−0.941435 + 0.337195i \(0.890522\pi\)
\(102\) 0 0
\(103\) −1.71101 9.70360i −0.168590 0.956124i −0.945285 0.326246i \(-0.894216\pi\)
0.776694 0.629878i \(-0.216895\pi\)
\(104\) 1.17857 0.988939i 0.115568 0.0969734i
\(105\) 0 0
\(106\) −21.6638 + 7.88499i −2.10418 + 0.765858i
\(107\) 5.17080 0.499880 0.249940 0.968261i \(-0.419589\pi\)
0.249940 + 0.968261i \(0.419589\pi\)
\(108\) 0 0
\(109\) −7.31065 −0.700234 −0.350117 0.936706i \(-0.613858\pi\)
−0.350117 + 0.936706i \(0.613858\pi\)
\(110\) 1.69118 0.615541i 0.161248 0.0586895i
\(111\) 0 0
\(112\) −2.09253 + 1.75584i −0.197725 + 0.165911i
\(113\) 1.80171 + 10.2180i 0.169491 + 0.961230i 0.944313 + 0.329050i \(0.106728\pi\)
−0.774822 + 0.632180i \(0.782160\pi\)
\(114\) 0 0
\(115\) −4.44524 3.73000i −0.414521 0.347824i
\(116\) 5.46229 9.46096i 0.507161 0.878428i
\(117\) 0 0
\(118\) −1.82475 3.16056i −0.167982 0.290953i
\(119\) 0.198338 1.12483i 0.0181816 0.103113i
\(120\) 0 0
\(121\) 10.2422 + 3.72787i 0.931113 + 0.338898i
\(122\) 2.01837 + 0.734626i 0.182734 + 0.0665099i
\(123\) 0 0
\(124\) −3.73524 + 21.1836i −0.335435 + 1.90234i
\(125\) −3.75766 6.50846i −0.336095 0.582134i
\(126\) 0 0
\(127\) −2.61372 + 4.52709i −0.231930 + 0.401714i −0.958376 0.285509i \(-0.907837\pi\)
0.726446 + 0.687223i \(0.241171\pi\)
\(128\) 6.04805 + 5.07491i 0.534577 + 0.448563i
\(129\) 0 0
\(130\) −1.49309 8.46771i −0.130952 0.742667i
\(131\) −5.54180 + 4.65012i −0.484189 + 0.406283i −0.851938 0.523642i \(-0.824573\pi\)
0.367749 + 0.929925i \(0.380128\pi\)
\(132\) 0 0
\(133\) −5.68391 + 2.06877i −0.492858 + 0.179385i
\(134\) −1.81300 −0.156619
\(135\) 0 0
\(136\) −1.19368 −0.102357
\(137\) −10.5709 + 3.84749i −0.903133 + 0.328714i −0.751508 0.659724i \(-0.770673\pi\)
−0.151626 + 0.988438i \(0.548451\pi\)
\(138\) 0 0
\(139\) 7.18562 6.02945i 0.609477 0.511412i −0.284999 0.958528i \(-0.591993\pi\)
0.894476 + 0.447116i \(0.147549\pi\)
\(140\) −1.12354 6.37192i −0.0949566 0.538526i
\(141\) 0 0
\(142\) 15.5588 + 13.0554i 1.30567 + 1.09559i
\(143\) −0.239900 + 0.415518i −0.0200614 + 0.0347474i
\(144\) 0 0
\(145\) −5.90940 10.2354i −0.490749 0.850003i
\(146\) 5.60210 31.7711i 0.463633 2.62939i
\(147\) 0 0
\(148\) 10.4096 + 3.78879i 0.855666 + 0.311437i
\(149\) −17.9023 6.51591i −1.46661 0.533804i −0.519436 0.854509i \(-0.673858\pi\)
−0.947179 + 0.320705i \(0.896080\pi\)
\(150\) 0 0
\(151\) 0.697024 3.95302i 0.0567230 0.321692i −0.943222 0.332163i \(-0.892222\pi\)
0.999945 + 0.0104703i \(0.00333286\pi\)
\(152\) 3.16070 + 5.47450i 0.256367 + 0.444041i
\(153\) 0 0
\(154\) −0.326102 + 0.564825i −0.0262780 + 0.0455149i
\(155\) 17.8267 + 14.9584i 1.43188 + 1.20149i
\(156\) 0 0
\(157\) 1.26345 + 7.16538i 0.100834 + 0.571860i 0.992803 + 0.119762i \(0.0382131\pi\)
−0.891968 + 0.452098i \(0.850676\pi\)
\(158\) 18.1823 15.2568i 1.44651 1.21376i
\(159\) 0 0
\(160\) 20.1164 7.32178i 1.59034 0.578838i
\(161\) 2.10290 0.165732
\(162\) 0 0
\(163\) 12.4492 0.975094 0.487547 0.873097i \(-0.337892\pi\)
0.487547 + 0.873097i \(0.337892\pi\)
\(164\) −13.6223 + 4.95813i −1.06373 + 0.387165i
\(165\) 0 0
\(166\) −7.59627 + 6.37403i −0.589585 + 0.494721i
\(167\) −0.404928 2.29646i −0.0313343 0.177705i 0.965124 0.261793i \(-0.0843137\pi\)
−0.996458 + 0.0840872i \(0.973203\pi\)
\(168\) 0 0
\(169\) −8.20258 6.88278i −0.630968 0.529445i
\(170\) −3.33558 + 5.77739i −0.255827 + 0.443106i
\(171\) 0 0
\(172\) −6.93308 12.0085i −0.528643 0.915636i
\(173\) −0.622055 + 3.52785i −0.0472939 + 0.268217i −0.999281 0.0379219i \(-0.987926\pi\)
0.951987 + 0.306139i \(0.0990373\pi\)
\(174\) 0 0
\(175\) −2.00923 0.731298i −0.151883 0.0552810i
\(176\) −0.836592 0.304494i −0.0630605 0.0229521i
\(177\) 0 0
\(178\) 5.69681 32.3082i 0.426994 2.42160i
\(179\) 9.99785 + 17.3168i 0.747275 + 1.29432i 0.949124 + 0.314901i \(0.101971\pi\)
−0.201850 + 0.979416i \(0.564695\pi\)
\(180\) 0 0
\(181\) −4.86616 + 8.42844i −0.361699 + 0.626481i −0.988241 0.152907i \(-0.951136\pi\)
0.626542 + 0.779388i \(0.284470\pi\)
\(182\) 2.38697 + 2.00291i 0.176934 + 0.148465i
\(183\) 0 0
\(184\) −0.381630 2.16433i −0.0281341 0.159557i
\(185\) 9.18062 7.70346i 0.674973 0.566369i
\(186\) 0 0
\(187\) 0.349810 0.127320i 0.0255806 0.00931059i
\(188\) −6.14088 −0.447869
\(189\) 0 0
\(190\) 35.3286 2.56301
\(191\) 16.6857 6.07309i 1.20733 0.439433i 0.341555 0.939862i \(-0.389046\pi\)
0.865778 + 0.500428i \(0.166824\pi\)
\(192\) 0 0
\(193\) 8.10807 6.80348i 0.583632 0.489725i −0.302506 0.953148i \(-0.597823\pi\)
0.886138 + 0.463422i \(0.153379\pi\)
\(194\) 2.03970 + 11.5677i 0.146442 + 0.830514i
\(195\) 0 0
\(196\) −11.5028 9.65202i −0.821631 0.689430i
\(197\) −7.07945 + 12.2620i −0.504390 + 0.873628i 0.495597 + 0.868552i \(0.334949\pi\)
−0.999987 + 0.00507615i \(0.998384\pi\)
\(198\) 0 0
\(199\) −3.77010 6.53000i −0.267255 0.462899i 0.700897 0.713263i \(-0.252783\pi\)
−0.968152 + 0.250363i \(0.919450\pi\)
\(200\) −0.388030 + 2.20063i −0.0274379 + 0.155608i
\(201\) 0 0
\(202\) −20.1663 7.33993i −1.41890 0.516436i
\(203\) 4.02474 + 1.46489i 0.282481 + 0.102815i
\(204\) 0 0
\(205\) −2.72336 + 15.4449i −0.190208 + 1.07872i
\(206\) −10.4278 18.0616i −0.726543 1.25841i
\(207\) 0 0
\(208\) −2.12670 + 3.68356i −0.147460 + 0.255409i
\(209\) −1.51017 1.26718i −0.104461 0.0876528i
\(210\) 0 0
\(211\) 0.905339 + 5.13443i 0.0623261 + 0.353469i 0.999983 + 0.00590544i \(0.00187977\pi\)
−0.937656 + 0.347563i \(0.887009\pi\)
\(212\) −20.6932 + 17.3637i −1.42121 + 1.19254i
\(213\) 0 0
\(214\) 10.2846 3.74329i 0.703040 0.255886i
\(215\) −15.0012 −1.02307
\(216\) 0 0
\(217\) −8.43326 −0.572487
\(218\) −14.5407 + 5.29238i −0.984821 + 0.358445i
\(219\) 0 0
\(220\) 1.61541 1.35549i 0.108911 0.0913872i
\(221\) −0.308835 1.75149i −0.0207745 0.117818i
\(222\) 0 0
\(223\) 13.5542 + 11.3734i 0.907659 + 0.761616i 0.971672 0.236333i \(-0.0759456\pi\)
−0.0640133 + 0.997949i \(0.520390\pi\)
\(224\) −3.87894 + 6.71853i −0.259173 + 0.448901i
\(225\) 0 0
\(226\) 10.9807 + 19.0191i 0.730423 + 1.26513i
\(227\) −2.73878 + 15.5324i −0.181779 + 1.03092i 0.748245 + 0.663422i \(0.230897\pi\)
−0.930024 + 0.367498i \(0.880215\pi\)
\(228\) 0 0
\(229\) 1.66031 + 0.604303i 0.109716 + 0.0399335i 0.396295 0.918123i \(-0.370296\pi\)
−0.286579 + 0.958057i \(0.592518\pi\)
\(230\) −11.5417 4.20084i −0.761038 0.276995i
\(231\) 0 0
\(232\) 0.777275 4.40815i 0.0510306 0.289409i
\(233\) 6.94920 + 12.0364i 0.455257 + 0.788529i 0.998703 0.0509157i \(-0.0162140\pi\)
−0.543446 + 0.839444i \(0.682881\pi\)
\(234\) 0 0
\(235\) −3.32177 + 5.75347i −0.216688 + 0.375315i
\(236\) −3.27576 2.74869i −0.213234 0.178924i
\(237\) 0 0
\(238\) −0.419807 2.38084i −0.0272120 0.154327i
\(239\) −15.1927 + 12.7482i −0.982735 + 0.824613i −0.984500 0.175386i \(-0.943883\pi\)
0.00176451 + 0.999998i \(0.499438\pi\)
\(240\) 0 0
\(241\) −18.2063 + 6.62654i −1.17277 + 0.426853i −0.853642 0.520859i \(-0.825612\pi\)
−0.319126 + 0.947712i \(0.603389\pi\)
\(242\) 23.0703 1.48301
\(243\) 0 0
\(244\) 2.51674 0.161118
\(245\) −15.2653 + 5.55612i −0.975265 + 0.354967i
\(246\) 0 0
\(247\) −7.21498 + 6.05409i −0.459078 + 0.385212i
\(248\) 1.53045 + 8.67960i 0.0971835 + 0.551155i
\(249\) 0 0
\(250\) −12.1855 10.2249i −0.770681 0.646678i
\(251\) 2.73786 4.74212i 0.172812 0.299320i −0.766590 0.642137i \(-0.778048\pi\)
0.939402 + 0.342818i \(0.111381\pi\)
\(252\) 0 0
\(253\) 0.342689 + 0.593554i 0.0215447 + 0.0373164i
\(254\) −1.92133 + 10.8964i −0.120555 + 0.683701i
\(255\) 0 0
\(256\) −5.47570 1.99299i −0.342231 0.124562i
\(257\) 10.8677 + 3.95552i 0.677909 + 0.246739i 0.657949 0.753062i \(-0.271424\pi\)
0.0199594 + 0.999801i \(0.493646\pi\)
\(258\) 0 0
\(259\) −0.754166 + 4.27709i −0.0468616 + 0.265765i
\(260\) −5.03743 8.72508i −0.312408 0.541107i
\(261\) 0 0
\(262\) −7.65614 + 13.2608i −0.472998 + 0.819257i
\(263\) 4.96239 + 4.16394i 0.305994 + 0.256759i 0.782834 0.622231i \(-0.213773\pi\)
−0.476840 + 0.878990i \(0.658218\pi\)
\(264\) 0 0
\(265\) 5.07473 + 28.7802i 0.311738 + 1.76795i
\(266\) −9.80751 + 8.22948i −0.601337 + 0.504582i
\(267\) 0 0
\(268\) −1.99621 + 0.726562i −0.121938 + 0.0443818i
\(269\) −13.8387 −0.843758 −0.421879 0.906652i \(-0.638629\pi\)
−0.421879 + 0.906652i \(0.638629\pi\)
\(270\) 0 0
\(271\) 1.94536 0.118172 0.0590860 0.998253i \(-0.481181\pi\)
0.0590860 + 0.998253i \(0.481181\pi\)
\(272\) 3.10106 1.12869i 0.188029 0.0684370i
\(273\) 0 0
\(274\) −18.2399 + 15.3051i −1.10192 + 0.924617i
\(275\) −0.121011 0.686285i −0.00729721 0.0413846i
\(276\) 0 0
\(277\) 9.55463 + 8.01729i 0.574082 + 0.481712i 0.882998 0.469377i \(-0.155522\pi\)
−0.308915 + 0.951090i \(0.599966\pi\)
\(278\) 9.92713 17.1943i 0.595390 1.03125i
\(279\) 0 0
\(280\) −1.32553 2.29588i −0.0792154 0.137205i
\(281\) 1.69409 9.60766i 0.101061 0.573145i −0.891660 0.452706i \(-0.850459\pi\)
0.992721 0.120439i \(-0.0384301\pi\)
\(282\) 0 0
\(283\) −24.9688 9.08790i −1.48424 0.540220i −0.532315 0.846547i \(-0.678678\pi\)
−0.951926 + 0.306327i \(0.900900\pi\)
\(284\) 22.3632 + 8.13953i 1.32701 + 0.482992i
\(285\) 0 0
\(286\) −0.176349 + 1.00013i −0.0104277 + 0.0591387i
\(287\) −2.84173 4.92202i −0.167742 0.290538i
\(288\) 0 0
\(289\) 7.81006 13.5274i 0.459415 0.795730i
\(290\) −19.1633 16.0799i −1.12531 0.944247i
\(291\) 0 0
\(292\) −6.56410 37.2268i −0.384135 2.17854i
\(293\) 9.38976 7.87895i 0.548556 0.460293i −0.325896 0.945406i \(-0.605666\pi\)
0.874452 + 0.485113i \(0.161221\pi\)
\(294\) 0 0
\(295\) −4.34723 + 1.58226i −0.253106 + 0.0921229i
\(296\) 4.53888 0.263817
\(297\) 0 0
\(298\) −40.3243 −2.33592
\(299\) 3.07698 1.11993i 0.177947 0.0647672i
\(300\) 0 0
\(301\) 4.16445 3.49439i 0.240035 0.201413i
\(302\) −1.47534 8.36705i −0.0848961 0.481470i
\(303\) 0 0
\(304\) −13.3876 11.2335i −0.767832 0.644288i
\(305\) 1.36137 2.35797i 0.0779521 0.135017i
\(306\) 0 0
\(307\) 13.2370 + 22.9271i 0.755475 + 1.30852i 0.945138 + 0.326671i \(0.105927\pi\)
−0.189663 + 0.981849i \(0.560740\pi\)
\(308\) −0.132702 + 0.752591i −0.00756141 + 0.0428829i
\(309\) 0 0
\(310\) 46.2857 + 16.8466i 2.62885 + 0.956823i
\(311\) 16.5945 + 6.03990i 0.940987 + 0.342491i 0.766556 0.642178i \(-0.221969\pi\)
0.174432 + 0.984669i \(0.444191\pi\)
\(312\) 0 0
\(313\) 1.67522 9.50064i 0.0946890 0.537008i −0.900153 0.435574i \(-0.856546\pi\)
0.994842 0.101435i \(-0.0323433\pi\)
\(314\) 7.70019 + 13.3371i 0.434547 + 0.752657i
\(315\) 0 0
\(316\) 13.9056 24.0852i 0.782250 1.35490i
\(317\) −2.84240 2.38506i −0.159645 0.133958i 0.559466 0.828853i \(-0.311006\pi\)
−0.719111 + 0.694895i \(0.755451\pi\)
\(318\) 0 0
\(319\) 0.242400 + 1.37472i 0.0135718 + 0.0769694i
\(320\) 23.1622 19.4354i 1.29481 1.08647i
\(321\) 0 0
\(322\) 4.18262 1.52235i 0.233089 0.0848373i
\(323\) 7.30748 0.406599
\(324\) 0 0
\(325\) −3.32937 −0.184680
\(326\) 24.7611 9.01229i 1.37139 0.499145i
\(327\) 0 0
\(328\) −4.55009 + 3.81798i −0.251236 + 0.210812i
\(329\) −0.418069 2.37099i −0.0230489 0.130717i
\(330\) 0 0
\(331\) −1.08226 0.908128i −0.0594866 0.0499152i 0.612560 0.790424i \(-0.290140\pi\)
−0.672046 + 0.740509i \(0.734584\pi\)
\(332\) −5.80953 + 10.0624i −0.318839 + 0.552246i
\(333\) 0 0
\(334\) −2.46786 4.27446i −0.135035 0.233888i
\(335\) −0.399080 + 2.26330i −0.0218041 + 0.123657i
\(336\) 0 0
\(337\) 12.2067 + 4.44287i 0.664940 + 0.242018i 0.652368 0.757903i \(-0.273776\pi\)
0.0125722 + 0.999921i \(0.495998\pi\)
\(338\) −21.2974 7.75161i −1.15842 0.421632i
\(339\) 0 0
\(340\) −1.35736 + 7.69798i −0.0736133 + 0.417482i
\(341\) −1.37428 2.38033i −0.0744215 0.128902i
\(342\) 0 0
\(343\) 6.34669 10.9928i 0.342689 0.593555i
\(344\) −4.35221 3.65194i −0.234656 0.196899i
\(345\) 0 0
\(346\) 1.31665 + 7.46712i 0.0707838 + 0.401435i
\(347\) −3.67737 + 3.08568i −0.197411 + 0.165648i −0.736135 0.676835i \(-0.763351\pi\)
0.538724 + 0.842483i \(0.318907\pi\)
\(348\) 0 0
\(349\) 21.2160 7.72198i 1.13567 0.413348i 0.295319 0.955399i \(-0.404574\pi\)
0.840346 + 0.542050i \(0.182352\pi\)
\(350\) −4.52571 −0.241909
\(351\) 0 0
\(352\) −2.52845 −0.134767
\(353\) 27.9150 10.1602i 1.48577 0.540775i 0.533436 0.845840i \(-0.320900\pi\)
0.952331 + 0.305065i \(0.0986783\pi\)
\(354\) 0 0
\(355\) 19.7229 16.5495i 1.04678 0.878354i
\(356\) −6.67507 37.8562i −0.353778 2.00638i
\(357\) 0 0
\(358\) 32.4216 + 27.2049i 1.71353 + 1.43783i
\(359\) −6.70991 + 11.6219i −0.354136 + 0.613381i −0.986970 0.160906i \(-0.948558\pi\)
0.632834 + 0.774288i \(0.281892\pi\)
\(360\) 0 0
\(361\) −9.84920 17.0593i −0.518379 0.897858i
\(362\) −3.57709 + 20.2867i −0.188008 + 1.06625i
\(363\) 0 0
\(364\) 3.43086 + 1.24873i 0.179826 + 0.0654513i
\(365\) −38.4290 13.9870i −2.01147 0.732114i
\(366\) 0 0
\(367\) −1.38050 + 7.82920i −0.0720615 + 0.408681i 0.927344 + 0.374209i \(0.122086\pi\)
−0.999406 + 0.0344715i \(0.989025\pi\)
\(368\) 3.03793 + 5.26184i 0.158363 + 0.274293i
\(369\) 0 0
\(370\) 12.6833 21.9681i 0.659372 1.14207i
\(371\) −8.11288 6.80751i −0.421200 0.353428i
\(372\) 0 0
\(373\) −1.98315 11.2470i −0.102684 0.582348i −0.992120 0.125289i \(-0.960014\pi\)
0.889437 0.457059i \(-0.151097\pi\)
\(374\) 0.603592 0.506474i 0.0312110 0.0261891i
\(375\) 0 0
\(376\) −2.36437 + 0.860561i −0.121933 + 0.0443801i
\(377\) 6.66917 0.343480
\(378\) 0 0
\(379\) −24.1705 −1.24155 −0.620777 0.783987i \(-0.713183\pi\)
−0.620777 + 0.783987i \(0.713183\pi\)
\(380\) 38.8988 14.1580i 1.99547 0.726291i
\(381\) 0 0
\(382\) 28.7909 24.1584i 1.47307 1.23605i
\(383\) 1.63981 + 9.29982i 0.0837903 + 0.475199i 0.997611 + 0.0690808i \(0.0220066\pi\)
−0.913821 + 0.406118i \(0.866882\pi\)
\(384\) 0 0
\(385\) 0.633331 + 0.531428i 0.0322775 + 0.0270841i
\(386\) 11.2015 19.4016i 0.570143 0.987516i
\(387\) 0 0
\(388\) 6.88162 + 11.9193i 0.349361 + 0.605111i
\(389\) −0.442405 + 2.50900i −0.0224308 + 0.127211i −0.993967 0.109680i \(-0.965017\pi\)
0.971536 + 0.236891i \(0.0761285\pi\)
\(390\) 0 0
\(391\) −2.38733 0.868915i −0.120732 0.0439429i
\(392\) −5.78145 2.10427i −0.292007 0.106282i
\(393\) 0 0
\(394\) −5.20407 + 29.5137i −0.262177 + 1.48688i
\(395\) −15.0438 26.0567i −0.756937 1.31105i
\(396\) 0 0
\(397\) −1.83759 + 3.18279i −0.0922258 + 0.159740i −0.908447 0.417999i \(-0.862731\pi\)
0.816222 + 0.577739i \(0.196065\pi\)
\(398\) −12.2259 10.2587i −0.612828 0.514223i
\(399\) 0 0
\(400\) −1.07276 6.08390i −0.0536378 0.304195i
\(401\) 12.3706 10.3802i 0.617760 0.518362i −0.279338 0.960193i \(-0.590115\pi\)
0.897099 + 0.441830i \(0.145671\pi\)
\(402\) 0 0
\(403\) −12.3396 + 4.49125i −0.614679 + 0.223725i
\(404\) −25.1458 −1.25105
\(405\) 0 0
\(406\) 9.06558 0.449917
\(407\) −1.33013 + 0.484126i −0.0659319 + 0.0239972i
\(408\) 0 0
\(409\) 7.03380 5.90206i 0.347799 0.291838i −0.452107 0.891964i \(-0.649327\pi\)
0.799906 + 0.600126i \(0.204883\pi\)
\(410\) 5.76432 + 32.6911i 0.284680 + 1.61450i
\(411\) 0 0
\(412\) −18.7199 15.7078i −0.922262 0.773870i
\(413\) 0.838253 1.45190i 0.0412477 0.0714432i
\(414\) 0 0
\(415\) 6.28506 + 10.8860i 0.308522 + 0.534375i
\(416\) −2.09765 + 11.8964i −0.102846 + 0.583268i
\(417\) 0 0
\(418\) −3.92104 1.42714i −0.191784 0.0698037i
\(419\) 6.55800 + 2.38692i 0.320379 + 0.116608i 0.497204 0.867634i \(-0.334360\pi\)
−0.176824 + 0.984242i \(0.556582\pi\)
\(420\) 0 0
\(421\) 5.35021 30.3425i 0.260753 1.47880i −0.520108 0.854100i \(-0.674108\pi\)
0.780861 0.624704i \(-0.214781\pi\)
\(422\) 5.51765 + 9.55686i 0.268595 + 0.465221i
\(423\) 0 0
\(424\) −5.53405 + 9.58526i −0.268757 + 0.465502i
\(425\) 1.97881 + 1.66042i 0.0959862 + 0.0805420i
\(426\) 0 0
\(427\) 0.171339 + 0.971712i 0.00829167 + 0.0470244i
\(428\) 9.82380 8.24315i 0.474851 0.398448i
\(429\) 0 0
\(430\) −29.8370 + 10.8598i −1.43887 + 0.523704i
\(431\) 27.8971 1.34376 0.671879 0.740661i \(-0.265487\pi\)
0.671879 + 0.740661i \(0.265487\pi\)
\(432\) 0 0
\(433\) 19.1706 0.921278 0.460639 0.887588i \(-0.347620\pi\)
0.460639 + 0.887588i \(0.347620\pi\)
\(434\) −16.7735 + 6.10507i −0.805156 + 0.293053i
\(435\) 0 0
\(436\) −13.8892 + 11.6544i −0.665173 + 0.558146i
\(437\) 2.33626 + 13.2496i 0.111759 + 0.633814i
\(438\) 0 0
\(439\) −18.1928 15.2656i −0.868294 0.728585i 0.0954443 0.995435i \(-0.469573\pi\)
−0.963738 + 0.266850i \(0.914017\pi\)
\(440\) 0.432015 0.748272i 0.0205955 0.0356725i
\(441\) 0 0
\(442\) −1.88221 3.26009i −0.0895278 0.155067i
\(443\) 4.05612 23.0034i 0.192712 1.09292i −0.722927 0.690924i \(-0.757204\pi\)
0.915639 0.402000i \(-0.131685\pi\)
\(444\) 0 0
\(445\) −39.0787 14.2235i −1.85251 0.674258i
\(446\) 35.1925 + 12.8090i 1.66641 + 0.606525i
\(447\) 0 0
\(448\) −1.90272 + 10.7908i −0.0898950 + 0.509820i
\(449\) −2.40953 4.17343i −0.113713 0.196956i 0.803552 0.595235i \(-0.202941\pi\)
−0.917264 + 0.398279i \(0.869608\pi\)
\(450\) 0 0
\(451\) 0.926176 1.60418i 0.0436119 0.0755380i
\(452\) 19.7123 + 16.5406i 0.927187 + 0.778002i
\(453\) 0 0
\(454\) 5.79696 + 32.8762i 0.272065 + 1.54296i
\(455\) 3.02580 2.53895i 0.141852 0.119028i
\(456\) 0 0
\(457\) 4.59848 1.67371i 0.215108 0.0782929i −0.232219 0.972664i \(-0.574598\pi\)
0.447326 + 0.894371i \(0.352376\pi\)
\(458\) 3.73978 0.174749
\(459\) 0 0
\(460\) −14.3916 −0.671012
\(461\) −26.3024 + 9.57330i −1.22503 + 0.445873i −0.871891 0.489699i \(-0.837107\pi\)
−0.353135 + 0.935572i \(0.614884\pi\)
\(462\) 0 0
\(463\) −21.0473 + 17.6608i −0.978152 + 0.820767i −0.983810 0.179217i \(-0.942644\pi\)
0.00565725 + 0.999984i \(0.498199\pi\)
\(464\) 2.14887 + 12.1868i 0.0997587 + 0.565760i
\(465\) 0 0
\(466\) 22.5352 + 18.9093i 1.04392 + 0.875957i
\(467\) 10.6232 18.4000i 0.491585 0.851450i −0.508368 0.861140i \(-0.669751\pi\)
0.999953 + 0.00968963i \(0.00308435\pi\)
\(468\) 0 0
\(469\) −0.416426 0.721272i −0.0192288 0.0333052i
\(470\) −2.44182 + 13.8482i −0.112633 + 0.638771i
\(471\) 0 0
\(472\) −1.64643 0.599252i −0.0757831 0.0275828i
\(473\) 1.66494 + 0.605990i 0.0765542 + 0.0278635i
\(474\) 0 0
\(475\) 2.37544 13.4718i 0.108993 0.618129i
\(476\) −1.41636 2.45321i −0.0649188 0.112443i
\(477\) 0 0
\(478\) −20.9892 + 36.3543i −0.960022 + 1.66281i
\(479\) −31.9278 26.7906i −1.45882 1.22410i −0.925811 0.377986i \(-0.876617\pi\)
−0.533009 0.846109i \(-0.678939\pi\)
\(480\) 0 0
\(481\) 1.17432 + 6.65990i 0.0535444 + 0.303665i
\(482\) −31.4147 + 26.3600i −1.43090 + 1.20067i
\(483\) 0 0
\(484\) 25.4017 9.24547i 1.15462 0.420249i
\(485\) 14.8898 0.676112
\(486\) 0 0
\(487\) 4.02801 0.182527 0.0912634 0.995827i \(-0.470909\pi\)
0.0912634 + 0.995827i \(0.470909\pi\)
\(488\) 0.969001 0.352688i 0.0438646 0.0159654i
\(489\) 0 0
\(490\) −26.3401 + 22.1020i −1.18992 + 0.998465i
\(491\) −6.70653 38.0346i −0.302661 1.71648i −0.634313 0.773076i \(-0.718717\pi\)
0.331652 0.943402i \(-0.392394\pi\)
\(492\) 0 0
\(493\) −3.96380 3.32603i −0.178521 0.149797i
\(494\) −9.96769 + 17.2645i −0.448468 + 0.776769i
\(495\) 0 0
\(496\) −12.1830 21.1015i −0.547032 0.947487i
\(497\) −1.62019 + 9.18853i −0.0726753 + 0.412162i
\(498\) 0 0
\(499\) 3.82629 + 1.39266i 0.171288 + 0.0623439i 0.426241 0.904610i \(-0.359838\pi\)
−0.254952 + 0.966954i \(0.582060\pi\)
\(500\) −17.5146 6.37480i −0.783278 0.285090i
\(501\) 0 0
\(502\) 2.01259 11.4140i 0.0898263 0.509430i
\(503\) 1.71297 + 2.96695i 0.0763775 + 0.132290i 0.901684 0.432395i \(-0.142331\pi\)
−0.825307 + 0.564684i \(0.808998\pi\)
\(504\) 0 0
\(505\) −13.6020 + 23.5594i −0.605282 + 1.04838i
\(506\) 1.11129 + 0.932483i 0.0494028 + 0.0414539i
\(507\) 0 0
\(508\) 2.25126 + 12.7675i 0.0998837 + 0.566468i
\(509\) −9.39432 + 7.88277i −0.416396 + 0.349398i −0.826790 0.562511i \(-0.809836\pi\)
0.410394 + 0.911908i \(0.365391\pi\)
\(510\) 0 0
\(511\) 13.9264 5.06878i 0.616066 0.224230i
\(512\) −28.1241 −1.24292
\(513\) 0 0
\(514\) 24.4791 1.07973
\(515\) −24.8430 + 9.04210i −1.09471 + 0.398443i
\(516\) 0 0
\(517\) 0.601093 0.504377i 0.0264360 0.0221825i
\(518\) 1.59628 + 9.05298i 0.0701367 + 0.397765i
\(519\) 0 0
\(520\) −3.16222 2.65342i −0.138673 0.116360i
\(521\) −7.04117 + 12.1957i −0.308479 + 0.534302i −0.978030 0.208465i \(-0.933153\pi\)
0.669551 + 0.742766i \(0.266487\pi\)
\(522\) 0 0
\(523\) −4.88956 8.46897i −0.213806 0.370322i 0.739097 0.673599i \(-0.235253\pi\)
−0.952902 + 0.303277i \(0.901919\pi\)
\(524\) −3.11555 + 17.6692i −0.136103 + 0.771881i
\(525\) 0 0
\(526\) 12.8845 + 4.68956i 0.561789 + 0.204474i
\(527\) 9.57387 + 3.48460i 0.417044 + 0.151792i
\(528\) 0 0
\(529\) −3.18168 + 18.0442i −0.138334 + 0.784530i
\(530\) 30.9283 + 53.5694i 1.34344 + 2.32691i
\(531\) 0 0
\(532\) −7.50065 + 12.9915i −0.325195 + 0.563254i
\(533\) −6.77933 5.68853i −0.293645 0.246398i
\(534\) 0 0
\(535\) −2.40915 13.6630i −0.104157 0.590703i
\(536\) −0.666768 + 0.559485i −0.0288000 + 0.0241661i
\(537\) 0 0
\(538\) −27.5247 + 10.0182i −1.18668 + 0.431915i
\(539\) 1.91871 0.0826445
\(540\) 0 0
\(541\) 40.9454 1.76038 0.880189 0.474623i \(-0.157416\pi\)
0.880189 + 0.474623i \(0.157416\pi\)
\(542\) 3.86927 1.40830i 0.166199 0.0604916i
\(543\) 0 0
\(544\) 7.17966 6.02445i 0.307825 0.258296i
\(545\) 3.40614 + 19.3172i 0.145903 + 0.827458i
\(546\) 0 0
\(547\) 0.850521 + 0.713672i 0.0363657 + 0.0305144i 0.660789 0.750571i \(-0.270222\pi\)
−0.624424 + 0.781086i \(0.714666\pi\)
\(548\) −13.9497 + 24.1615i −0.595900 + 1.03213i
\(549\) 0 0
\(550\) −0.737508 1.27740i −0.0314474 0.0544686i
\(551\) −4.75832 + 26.9858i −0.202711 + 1.14963i
\(552\) 0 0
\(553\) 10.2459 + 3.72922i 0.435702 + 0.158583i
\(554\) 24.8079 + 9.02932i 1.05399 + 0.383619i
\(555\) 0 0
\(556\) 4.03969 22.9102i 0.171321 0.971610i
\(557\) −17.5201 30.3458i −0.742352 1.28579i −0.951422 0.307890i \(-0.900377\pi\)
0.209070 0.977901i \(-0.432956\pi\)
\(558\) 0 0
\(559\) 4.23247 7.33084i 0.179014 0.310062i
\(560\) 5.61446 + 4.71109i 0.237254 + 0.199080i
\(561\) 0 0
\(562\) −3.58575 20.3358i −0.151256 0.857813i
\(563\) −29.7005 + 24.9216i −1.25172 + 1.05032i −0.255212 + 0.966885i \(0.582145\pi\)
−0.996513 + 0.0834367i \(0.973410\pi\)
\(564\) 0 0
\(565\) 26.1600 9.52145i 1.10056 0.400570i
\(566\) −56.2413 −2.36400
\(567\) 0 0
\(568\) 9.75095 0.409141
\(569\) 31.9198 11.6179i 1.33815 0.487046i 0.428919 0.903343i \(-0.358895\pi\)
0.909229 + 0.416297i \(0.136672\pi\)
\(570\) 0 0
\(571\) 7.72852 6.48500i 0.323428 0.271389i −0.466587 0.884475i \(-0.654517\pi\)
0.790016 + 0.613086i \(0.210072\pi\)
\(572\) 0.206632 + 1.17187i 0.00863972 + 0.0489983i
\(573\) 0 0
\(574\) −9.21532 7.73257i −0.384640 0.322751i
\(575\) −2.37795 + 4.11873i −0.0991674 + 0.171763i
\(576\) 0 0
\(577\) 6.06615 + 10.5069i 0.252537 + 0.437407i 0.964224 0.265090i \(-0.0854017\pi\)
−0.711687 + 0.702497i \(0.752068\pi\)
\(578\) 5.74114 32.5596i 0.238800 1.35430i
\(579\) 0 0
\(580\) −27.5440 10.0252i −1.14370 0.416274i
\(581\) −4.28059 1.55801i −0.177589 0.0646371i
\(582\) 0 0
\(583\) 0.599379 3.39925i 0.0248237 0.140782i
\(584\) −7.74416 13.4133i −0.320456 0.555046i
\(585\) 0 0
\(586\) 12.9722 22.4685i 0.535877 0.928167i
\(587\) 24.3213 + 20.4080i 1.00385 + 0.842328i 0.987513 0.157539i \(-0.0503559\pi\)
0.0163344 + 0.999867i \(0.494800\pi\)
\(588\) 0 0
\(589\) −9.36909 53.1348i −0.386047 2.18938i
\(590\) −7.50109 + 6.29416i −0.308815 + 0.259126i
\(591\) 0 0
\(592\) −11.7915 + 4.29176i −0.484629 + 0.176390i
\(593\) 13.4906 0.553993 0.276996 0.960871i \(-0.410661\pi\)
0.276996 + 0.960871i \(0.410661\pi\)
\(594\) 0 0
\(595\) −3.06459 −0.125636
\(596\) −44.3994 + 16.1601i −1.81867 + 0.661942i
\(597\) 0 0
\(598\) 5.30929 4.45503i 0.217113 0.182180i
\(599\) −7.36796 41.7858i −0.301047 1.70732i −0.641554 0.767078i \(-0.721710\pi\)
0.340507 0.940242i \(-0.389401\pi\)
\(600\) 0 0
\(601\) −15.1713 12.7302i −0.618851 0.519277i 0.278591 0.960410i \(-0.410132\pi\)
−0.897442 + 0.441132i \(0.854577\pi\)
\(602\) 5.75330 9.96501i 0.234487 0.406144i
\(603\) 0 0
\(604\) −4.97755 8.62136i −0.202533 0.350798i
\(605\) 5.07828 28.8003i 0.206461 1.17090i
\(606\) 0 0
\(607\) 33.8280 + 12.3124i 1.37304 + 0.499745i 0.920060 0.391778i \(-0.128140\pi\)
0.452977 + 0.891522i \(0.350362\pi\)
\(608\) −46.6403 16.9757i −1.89151 0.688454i
\(609\) 0 0
\(610\) 1.00074 5.67548i 0.0405188 0.229793i
\(611\) −1.87442 3.24659i −0.0758310 0.131343i
\(612\) 0 0
\(613\) −13.2314 + 22.9175i −0.534411 + 0.925627i 0.464780 + 0.885426i \(0.346133\pi\)
−0.999192 + 0.0402013i \(0.987200\pi\)
\(614\) 42.9256 + 36.0189i 1.73234 + 1.45360i
\(615\) 0 0
\(616\) 0.0543723 + 0.308361i 0.00219072 + 0.0124242i
\(617\) 37.6256 31.5716i 1.51475 1.27103i 0.660943 0.750436i \(-0.270157\pi\)
0.853807 0.520590i \(-0.174288\pi\)
\(618\) 0 0
\(619\) 22.7464 8.27901i 0.914255 0.332762i 0.158304 0.987390i \(-0.449397\pi\)
0.755950 + 0.654629i \(0.227175\pi\)
\(620\) 57.7145 2.31787
\(621\) 0 0
\(622\) 37.3785 1.49874
\(623\) 14.1618 5.15448i 0.567381 0.206510i
\(624\) 0 0
\(625\) −23.8695 + 20.0289i −0.954780 + 0.801155i
\(626\) −3.54581 20.1093i −0.141719 0.803728i
\(627\) 0 0
\(628\) 13.8232 + 11.5991i 0.551607 + 0.462853i
\(629\) 2.62345 4.54395i 0.104604 0.181179i
\(630\) 0 0
\(631\) −8.84842 15.3259i −0.352250 0.610115i 0.634393 0.773010i \(-0.281250\pi\)
−0.986643 + 0.162895i \(0.947917\pi\)
\(632\) 1.97874 11.2220i 0.0787101 0.446387i
\(633\) 0 0
\(634\) −7.38007 2.68613i −0.293100 0.106680i
\(635\) 13.1799 + 4.79708i 0.523027 + 0.190366i
\(636\) 0 0
\(637\) 1.59180 9.02754i 0.0630693 0.357684i
\(638\) 1.47732 + 2.55880i 0.0584878 + 0.101304i
\(639\) 0 0
\(640\) 10.5917 18.3454i 0.418676 0.725167i
\(641\) 29.1483 + 24.4583i 1.15129 + 0.966046i 0.999749 0.0224050i \(-0.00713234\pi\)
0.151540 + 0.988451i \(0.451577\pi\)
\(642\) 0 0
\(643\) 8.15148 + 46.2293i 0.321463 + 1.82311i 0.533447 + 0.845834i \(0.320896\pi\)
−0.211984 + 0.977273i \(0.567992\pi\)
\(644\) 3.99523 3.35239i 0.157434 0.132103i
\(645\) 0 0
\(646\) 14.5344 5.29009i 0.571848 0.208136i
\(647\) −28.2333 −1.10997 −0.554983 0.831862i \(-0.687275\pi\)
−0.554983 + 0.831862i \(0.687275\pi\)
\(648\) 0 0
\(649\) 0.546406 0.0214483
\(650\) −6.62204 + 2.41023i −0.259738 + 0.0945368i
\(651\) 0 0
\(652\) 23.6517 19.8461i 0.926271 0.777234i
\(653\) 6.13103 + 34.7708i 0.239926 + 1.36069i 0.831988 + 0.554794i \(0.187203\pi\)
−0.592062 + 0.805893i \(0.701686\pi\)
\(654\) 0 0
\(655\) 14.8692 + 12.4767i 0.580987 + 0.487506i
\(656\) 8.21052 14.2210i 0.320567 0.555239i
\(657\) 0 0
\(658\) −2.54795 4.41318i −0.0993295 0.172044i
\(659\) 7.24004 41.0603i 0.282032 1.59948i −0.433667 0.901073i \(-0.642781\pi\)
0.715699 0.698409i \(-0.246108\pi\)
\(660\) 0 0
\(661\) −1.19709 0.435704i −0.0465613 0.0169469i 0.318635 0.947878i \(-0.396776\pi\)
−0.365196 + 0.930931i \(0.618998\pi\)
\(662\) −2.81002 1.02276i −0.109214 0.0397508i
\(663\) 0 0
\(664\) −0.826686 + 4.68837i −0.0320817 + 0.181944i
\(665\) 8.11461 + 14.0549i 0.314671 + 0.545027i
\(666\) 0 0
\(667\) 4.76334 8.25035i 0.184437 0.319455i
\(668\) −4.43026 3.71743i −0.171412 0.143832i
\(669\) 0 0
\(670\) 0.844702 + 4.79054i 0.0326337 + 0.185075i
\(671\) −0.246349 + 0.206711i −0.00951018 + 0.00797999i
\(672\) 0 0
\(673\) −33.4838 + 12.1871i −1.29071 + 0.469779i −0.893959 0.448149i \(-0.852084\pi\)
−0.396748 + 0.917928i \(0.629861\pi\)
\(674\) 27.4951 1.05907
\(675\) 0 0
\(676\) −26.5561 −1.02139
\(677\) −16.9162 + 6.15701i −0.650144 + 0.236633i −0.645975 0.763358i \(-0.723549\pi\)
−0.00416861 + 0.999991i \(0.501327\pi\)
\(678\) 0 0
\(679\) −4.13353 + 3.46845i −0.158630 + 0.133107i
\(680\) 0.556154 + 3.15411i 0.0213275 + 0.120955i
\(681\) 0 0
\(682\) −4.45660 3.73953i −0.170652 0.143194i
\(683\) −19.8807 + 34.4344i −0.760715 + 1.31760i 0.181768 + 0.983341i \(0.441818\pi\)
−0.942483 + 0.334255i \(0.891515\pi\)
\(684\) 0 0
\(685\) 15.0915 + 26.1393i 0.576617 + 0.998730i
\(686\) 4.66542 26.4589i 0.178127 1.01021i
\(687\) 0 0
\(688\) 14.7597 + 5.37209i 0.562708 + 0.204809i
\(689\) −15.4962 5.64017i −0.590360 0.214873i
\(690\) 0 0
\(691\) −2.92436 + 16.5849i −0.111248 + 0.630918i 0.877292 + 0.479957i \(0.159348\pi\)
−0.988540 + 0.150961i \(0.951763\pi\)
\(692\) 4.44218 + 7.69408i 0.168866 + 0.292485i
\(693\) 0 0
\(694\) −5.08038 + 8.79948i −0.192849 + 0.334024i
\(695\) −19.2797 16.1776i −0.731322 0.613652i
\(696\) 0 0
\(697\) 1.19231 + 6.76193i 0.0451620 + 0.256126i
\(698\) 36.6079 30.7177i 1.38563 1.16268i
\(699\) 0 0
\(700\) −4.98306 + 1.81369i −0.188342 + 0.0685509i
\(701\) −8.96921 −0.338762 −0.169381 0.985551i \(-0.554177\pi\)
−0.169381 + 0.985551i \(0.554177\pi\)
\(702\) 0 0
\(703\) −27.7861 −1.04797
\(704\) −3.35583 + 1.22142i −0.126478 + 0.0460341i
\(705\) 0 0
\(706\) 48.1670 40.4169i 1.81279 1.52111i
\(707\) −1.71191 9.70875i −0.0643832 0.365135i
\(708\) 0 0
\(709\) 13.8973 + 11.6612i 0.521924 + 0.437946i 0.865302 0.501251i \(-0.167127\pi\)
−0.343378 + 0.939197i \(0.611571\pi\)
\(710\) 27.2477 47.1944i 1.02259 1.77117i
\(711\) 0 0
\(712\) −7.87509 13.6401i −0.295131 0.511183i
\(713\) −3.25728 + 18.4730i −0.121986 + 0.691818i
\(714\) 0 0
\(715\) 1.20971 + 0.440299i 0.0452407 + 0.0164663i
\(716\) 46.6005 + 16.9612i 1.74154 + 0.633869i
\(717\) 0 0
\(718\) −4.93243 + 27.9732i −0.184077 + 1.04395i
\(719\) −15.7860 27.3421i −0.588718 1.01969i −0.994401 0.105675i \(-0.966300\pi\)
0.405683 0.914014i \(-0.367034\pi\)
\(720\) 0 0
\(721\) 4.79034 8.29711i 0.178402 0.309001i
\(722\) −31.9395 26.8004i −1.18867 0.997409i
\(723\) 0 0
\(724\) 4.19135 + 23.7704i 0.155770 + 0.883418i
\(725\) −7.42026 + 6.22634i −0.275582 + 0.231240i
\(726\) 0 0
\(727\) −36.0929 + 13.1367i −1.33861 + 0.487215i −0.909375 0.415977i \(-0.863440\pi\)
−0.429237 + 0.903192i \(0.641217\pi\)
\(728\) 1.49595 0.0554436
\(729\) 0 0
\(730\) −86.5599 −3.20373
\(731\) −6.17157 + 2.24627i −0.228264 + 0.0830812i
\(732\) 0 0
\(733\) −23.2344 + 19.4959i −0.858181 + 0.720099i −0.961575 0.274541i \(-0.911474\pi\)
0.103395 + 0.994640i \(0.467030\pi\)
\(734\) 2.92200 + 16.5715i 0.107853 + 0.611664i
\(735\) 0 0
\(736\) 13.2187 + 11.0918i 0.487246 + 0.408848i
\(737\) 0.135721 0.235076i 0.00499936 0.00865915i
\(738\) 0 0
\(739\) −5.00127 8.66245i −0.183975 0.318653i 0.759256 0.650792i \(-0.225563\pi\)
−0.943230 + 0.332139i \(0.892230\pi\)
\(740\) 5.16126 29.2710i 0.189732 1.07602i
\(741\) 0 0
\(742\) −21.0645 7.66683i −0.773300 0.281458i
\(743\) −34.0862 12.4064i −1.25050 0.455145i −0.369931 0.929059i \(-0.620619\pi\)
−0.880571 + 0.473914i \(0.842841\pi\)
\(744\) 0 0
\(745\) −8.87626 + 50.3398i −0.325201 + 1.84431i
\(746\) −12.0865 20.9344i −0.442517 0.766461i
\(747\) 0 0
\(748\) 0.461619 0.799548i 0.0168785 0.0292344i
\(749\) 3.85147 + 3.23177i 0.140730 + 0.118086i
\(750\) 0 0
\(751\) −2.52734 14.3332i −0.0922239 0.523028i −0.995563 0.0941000i \(-0.970003\pi\)
0.903339 0.428928i \(-0.141108\pi\)
\(752\) 5.32868 4.47129i 0.194317 0.163051i
\(753\) 0 0
\(754\) 13.2648 4.82799i 0.483076 0.175825i
\(755\) −10.7700 −0.391959
\(756\) 0 0
\(757\) −45.5754 −1.65646 −0.828232 0.560385i \(-0.810653\pi\)
−0.828232 + 0.560385i \(0.810653\pi\)
\(758\) −48.0745 + 17.4977i −1.74614 + 0.635544i
\(759\) 0 0
\(760\) 12.9928 10.9023i 0.471300 0.395468i
\(761\) 3.86290 + 21.9076i 0.140030 + 0.794150i 0.971224 + 0.238167i \(0.0765467\pi\)
−0.831194 + 0.555982i \(0.812342\pi\)
\(762\) 0 0
\(763\) −5.44534 4.56918i −0.197135 0.165416i
\(764\) 22.0189 38.1379i 0.796616 1.37978i
\(765\) 0 0
\(766\) 9.99393 + 17.3100i 0.361096 + 0.625436i
\(767\) 0.453310 2.57085i 0.0163681 0.0928279i
\(768\) 0 0
\(769\) −12.8408 4.67368i −0.463053 0.168537i 0.0999501 0.994992i \(-0.468132\pi\)
−0.563003 + 0.826455i \(0.690354\pi\)
\(770\) 1.64439 + 0.598510i 0.0592598 + 0.0215688i
\(771\) 0 0
\(772\) 4.55829 25.8513i 0.164056 0.930410i
\(773\) 10.3270 + 17.8869i 0.371436 + 0.643345i 0.989787 0.142557i \(-0.0455323\pi\)
−0.618351 + 0.785902i \(0.712199\pi\)
\(774\) 0 0
\(775\) 9.53628 16.5173i 0.342553 0.593319i
\(776\) 4.31990 + 3.62483i 0.155076 + 0.130124i
\(777\) 0 0
\(778\) 0.936404 + 5.31061i 0.0335717 + 0.190395i
\(779\) 27.8547 23.3729i 0.997999 0.837420i
\(780\) 0 0
\(781\) −2.85753 + 1.04006i −0.102250 + 0.0372161i
\(782\) −5.37736 −0.192294
\(783\) 0 0
\(784\) 17.0093 0.607474
\(785\) 18.3447 6.67692i 0.654750 0.238309i
\(786\) 0 0
\(787\) −18.9239 + 15.8790i −0.674564 + 0.566026i −0.914412 0.404784i \(-0.867347\pi\)
0.239849 + 0.970810i \(0.422902\pi\)
\(788\) 6.09772 + 34.5819i 0.217222 + 1.23193i
\(789\) 0 0
\(790\) −48.7849 40.9354i −1.73569 1.45642i
\(791\) −5.04429 + 8.73696i −0.179354 + 0.310651i
\(792\) 0 0
\(793\) 0.768202 + 1.33057i 0.0272797 + 0.0472498i
\(794\) −1.35080 + 7.66077i −0.0479381 + 0.271871i
\(795\) 0 0
\(796\) −17.5726 6.39590i −0.622844 0.226697i
\(797\) 28.7224 + 10.4541i 1.01740 + 0.370304i 0.796271 0.604940i \(-0.206803\pi\)
0.221131 + 0.975244i \(0.429025\pi\)
\(798\) 0 0
\(799\) −0.505073 + 2.86441i −0.0178682 + 0.101336i
\(800\) −8.77257 15.1945i −0.310157 0.537208i
\(801\) 0 0
\(802\) 17.0904 29.6014i 0.603482 1.04526i
\(803\) 3.70012 + 3.10477i 0.130574 + 0.109565i
\(804\) 0 0
\(805\) −0.979775 5.55658i −0.0345325 0.195844i
\(806\) −21.2918 + 17.8660i −0.749972 + 0.629301i
\(807\) 0 0
\(808\) −9.68167 + 3.52384i −0.340600 + 0.123968i
\(809\) 46.8599 1.64751 0.823753 0.566949i \(-0.191876\pi\)
0.823753 + 0.566949i \(0.191876\pi\)
\(810\) 0 0
\(811\) 10.9984 0.386206 0.193103 0.981178i \(-0.438145\pi\)
0.193103 + 0.981178i \(0.438145\pi\)
\(812\) 9.98172 3.63305i 0.350290 0.127495i
\(813\) 0 0
\(814\) −2.29511 + 1.92583i −0.0804437 + 0.0675003i
\(815\) −5.80025 32.8949i −0.203174 1.15226i
\(816\) 0 0
\(817\) 26.6434 + 22.3564i 0.932134 + 0.782153i
\(818\) 9.71738 16.8310i 0.339760 0.588482i
\(819\) 0 0
\(820\) 19.4479 + 33.6847i 0.679150 + 1.17632i
\(821\) −6.24844 + 35.4367i −0.218072 + 1.23675i 0.657423 + 0.753521i \(0.271646\pi\)
−0.875495 + 0.483226i \(0.839465\pi\)
\(822\) 0 0
\(823\) 46.0324 + 16.7544i 1.60459 + 0.584022i 0.980359 0.197219i \(-0.0631912\pi\)
0.624229 + 0.781242i \(0.285413\pi\)
\(824\) −9.40881 3.42453i −0.327771 0.119299i
\(825\) 0 0
\(826\) 0.616196 3.49462i 0.0214402 0.121593i
\(827\) 7.80533 + 13.5192i 0.271418 + 0.470109i 0.969225 0.246176i \(-0.0791742\pi\)
−0.697807 + 0.716286i \(0.745841\pi\)
\(828\) 0 0
\(829\) −5.73541 + 9.93401i −0.199199 + 0.345023i −0.948269 0.317468i \(-0.897167\pi\)
0.749070 + 0.662491i \(0.230501\pi\)
\(830\) 20.3815 + 17.1021i 0.707454 + 0.593624i
\(831\) 0 0
\(832\) 2.96274 + 16.8026i 0.102715 + 0.582524i
\(833\) −5.44827 + 4.57164i −0.188771 + 0.158398i
\(834\) 0 0
\(835\) −5.87936 + 2.13991i −0.203464 + 0.0740547i
\(836\) −4.88922 −0.169097
\(837\) 0 0
\(838\) 14.7716 0.510278
\(839\) 0.634597 0.230975i 0.0219087 0.00797413i −0.331043 0.943616i \(-0.607400\pi\)
0.352951 + 0.935642i \(0.385178\pi\)
\(840\) 0 0
\(841\) −7.35155 + 6.16868i −0.253502 + 0.212713i
\(842\) −11.3244 64.2237i −0.390264 2.21329i
\(843\) 0 0
\(844\) 9.90519 + 8.31144i 0.340951 + 0.286092i
\(845\) −14.3649 + 24.8808i −0.494168 + 0.855925i
\(846\) 0 0
\(847\) 5.29901 + 9.17815i 0.182076 + 0.315365i
\(848\) 5.31348 30.1342i 0.182466 1.03481i
\(849\) 0 0
\(850\) 5.13781 + 1.87001i 0.176226 + 0.0641409i
\(851\) 9.07762 + 3.30398i 0.311177 + 0.113259i
\(852\) 0 0
\(853\) 6.83405 38.7578i 0.233994 1.32704i −0.610729 0.791839i \(-0.709124\pi\)
0.844723 0.535204i \(-0.179765\pi\)
\(854\) 1.04424 + 1.80867i 0.0357331 + 0.0618915i
\(855\) 0 0
\(856\) 2.62721 4.55047i 0.0897963 0.155532i
\(857\) 25.0206 + 20.9948i 0.854688 + 0.717169i 0.960817 0.277184i \(-0.0894011\pi\)
−0.106129 + 0.994352i \(0.533846\pi\)
\(858\) 0 0
\(859\) −5.76454 32.6923i −0.196683 1.11545i −0.910001 0.414606i \(-0.863919\pi\)
0.713318 0.700841i \(-0.247192\pi\)
\(860\) −28.5001 + 23.9145i −0.971847 + 0.815476i
\(861\) 0 0
\(862\) 55.4867 20.1955i 1.88988 0.687862i
\(863\) 22.6796 0.772024 0.386012 0.922494i \(-0.373852\pi\)
0.386012 + 0.922494i \(0.373852\pi\)
\(864\) 0 0
\(865\) 9.61158 0.326804
\(866\) 38.1297 13.8781i 1.29570 0.471597i
\(867\) 0 0
\(868\) −16.0220 + 13.4441i −0.543823 + 0.456322i
\(869\) 0.617088 + 3.49968i 0.0209333 + 0.118718i
\(870\) 0 0
\(871\) −0.993440 0.833595i −0.0336614 0.0282453i
\(872\) −3.71444 + 6.43360i −0.125787 + 0.217869i
\(873\) 0 0
\(874\) 14.2385 + 24.6618i 0.481625 + 0.834199i
\(875\) 1.26892 7.19637i 0.0428972 0.243282i
\(876\) 0 0
\(877\) −8.68629 3.16155i −0.293315 0.106758i 0.191171 0.981557i \(-0.438771\pi\)
−0.484487 + 0.874799i \(0.660994\pi\)
\(878\) −47.2361 17.1925i −1.59414 0.580220i
\(879\) 0 0
\(880\) −0.414796 + 2.35242i −0.0139828 + 0.0793002i
\(881\) −3.89378 6.74422i −0.131185 0.227219i 0.792949 0.609288i \(-0.208545\pi\)
−0.924134 + 0.382070i \(0.875211\pi\)
\(882\) 0 0
\(883\) 16.2309 28.1127i 0.546213 0.946068i −0.452317 0.891857i \(-0.649402\pi\)
0.998530 0.0542106i \(-0.0172642\pi\)
\(884\) −3.37892 2.83525i −0.113645 0.0953597i
\(885\) 0 0
\(886\) −8.58527 48.6895i −0.288428 1.63576i
\(887\) −25.9288 + 21.7569i −0.870604 + 0.730524i −0.964225 0.265084i \(-0.914600\pi\)
0.0936209 + 0.995608i \(0.470156\pi\)
\(888\) 0 0
\(889\) −4.77627 + 1.73842i −0.160191 + 0.0583048i
\(890\) −88.0234 −2.95055
\(891\) 0 0
\(892\) 43.8822 1.46929
\(893\) 14.4742 5.26818i 0.484361 0.176293i
\(894\) 0 0
\(895\) 41.0986 34.4858i 1.37378 1.15273i
\(896\) 1.33305 + 7.56010i 0.0445341 + 0.252565i
\(897\) 0 0
\(898\) −7.81376 6.55652i −0.260749 0.218794i
\(899\) −19.1024 + 33.0863i −0.637101 + 1.10349i
\(900\) 0 0
\(901\) 6.39731 + 11.0805i 0.213125 + 0.369144i
\(902\) 0.680827 3.86116i 0.0226691 0.128563i
\(903\) 0 0
\(904\) 9.90759 + 3.60607i 0.329522 + 0.119936i
\(905\) 24.5380 + 8.93109i 0.815670 + 0.296880i
\(906\) 0 0
\(907\) −1.92052 + 10.8918i −0.0637699 + 0.361657i 0.936179 + 0.351524i \(0.114337\pi\)
−0.999949 + 0.0101328i \(0.996775\pi\)
\(908\) 19.5580 + 33.8754i 0.649054 + 1.12420i
\(909\) 0 0
\(910\) 4.18022 7.24036i 0.138573 0.240016i
\(911\) 9.61016 + 8.06388i 0.318399 + 0.267168i 0.787953 0.615735i \(-0.211141\pi\)
−0.469554 + 0.882904i \(0.655585\pi\)
\(912\) 0 0
\(913\) −0.257809 1.46211i −0.00853224 0.0483887i
\(914\) 7.93462 6.65793i 0.262454 0.220225i
\(915\) 0 0
\(916\) 4.11772 1.49873i 0.136053 0.0495193i
\(917\) −7.03415 −0.232288
\(918\) 0 0
\(919\) −5.92909 −0.195583 −0.0977913 0.995207i \(-0.531178\pi\)
−0.0977913 + 0.995207i \(0.531178\pi\)
\(920\) −5.54108 + 2.01679i −0.182684 + 0.0664915i
\(921\) 0 0
\(922\) −45.3845 + 38.0821i −1.49466 + 1.25417i
\(923\) 2.52281 + 14.3076i 0.0830393 + 0.470939i
\(924\) 0 0
\(925\) −7.52426 6.31360i −0.247396 0.207590i
\(926\) −29.0775 + 50.3636i −0.955545 + 1.65505i
\(927\) 0 0
\(928\) 17.5726 + 30.4366i 0.576848 + 0.999131i
\(929\) −1.74217 + 9.88035i −0.0571588 + 0.324164i −0.999958 0.00919826i \(-0.997072\pi\)
0.942799 + 0.333362i \(0.108183\pi\)
\(930\) 0 0
\(931\) 35.3928 + 12.8819i 1.15995 + 0.422189i
\(932\) 32.3905 + 11.7892i 1.06099 + 0.386168i
\(933\) 0 0
\(934\) 7.80910 44.2876i 0.255521 1.44913i
\(935\) −0.499405 0.864995i −0.0163323 0.0282883i
\(936\) 0 0
\(937\) 11.7671 20.3811i 0.384413 0.665823i −0.607274 0.794492i \(-0.707737\pi\)
0.991688 + 0.128669i \(0.0410705\pi\)
\(938\) −1.35041 1.13313i −0.0440924 0.0369980i
\(939\) 0 0
\(940\) 2.86113 + 16.2263i 0.0933197 + 0.529242i
\(941\) −22.4448 + 18.8334i −0.731678 + 0.613951i −0.930589 0.366067i \(-0.880704\pi\)
0.198910 + 0.980018i \(0.436260\pi\)
\(942\) 0 0
\(943\) −11.8792 + 4.32369i −0.386841 + 0.140799i
\(944\) 4.84388 0.157655
\(945\) 0 0
\(946\) 3.75023 0.121930
\(947\) −50.4257 + 18.3535i −1.63862 + 0.596407i −0.986796 0.161968i \(-0.948216\pi\)
−0.651819 + 0.758375i \(0.725994\pi\)
\(948\) 0 0
\(949\) 17.6777 14.8333i 0.573842 0.481511i
\(950\) −5.02792 28.5147i −0.163127 0.925140i
\(951\) 0 0
\(952\) −0.889114 0.746055i −0.0288163 0.0241798i
\(953\) 2.44828 4.24055i 0.0793076 0.137365i −0.823644 0.567108i \(-0.808062\pi\)
0.902951 + 0.429743i \(0.141396\pi\)
\(954\) 0 0
\(955\) −23.8212 41.2596i −0.770837 1.33513i
\(956\) −8.54121 + 48.4396i −0.276243 + 1.56665i
\(957\) 0 0
\(958\) −82.8982 30.1725i −2.67832 0.974828i
\(959\) −10.2784 3.74104i −0.331908 0.120805i
\(960\) 0 0
\(961\) 7.67957 43.5530i 0.247728 1.40494i
\(962\) 7.15698 + 12.3962i 0.230750 + 0.399671i
\(963\) 0 0
\(964\) −24.0255 + 41.6134i −0.773810 + 1.34028i
\(965\) −21.7548 18.2544i −0.700310 0.587630i
\(966\) 0 0
\(967\) 2.95083 + 16.7350i 0.0948922 + 0.538160i 0.994780 + 0.102040i \(0.0325369\pi\)
−0.899888 + 0.436121i \(0.856352\pi\)
\(968\) 8.48459 7.11942i 0.272705 0.228827i
\(969\) 0 0
\(970\) 29.6155 10.7791i 0.950895 0.346098i
\(971\) −2.68374 −0.0861253 −0.0430627 0.999072i \(-0.513712\pi\)
−0.0430627 + 0.999072i \(0.513712\pi\)
\(972\) 0 0
\(973\) 9.12064 0.292394
\(974\) 8.01162 2.91599i 0.256709 0.0934344i
\(975\) 0 0
\(976\) −2.18387 + 1.83249i −0.0699041 + 0.0586565i
\(977\) 1.90892 + 10.8260i 0.0610718 + 0.346355i 0.999998 + 0.00223539i \(0.000711548\pi\)
−0.938926 + 0.344120i \(0.888177\pi\)
\(978\) 0 0
\(979\) 3.76268 + 3.15726i 0.120256 + 0.100907i
\(980\) −20.1445 + 34.8914i −0.643494 + 1.11456i
\(981\) 0 0
\(982\) −40.8734 70.7948i −1.30432 2.25915i
\(983\) −8.29615 + 47.0498i −0.264606 + 1.50066i 0.505548 + 0.862798i \(0.331290\pi\)
−0.770154 + 0.637858i \(0.779821\pi\)
\(984\) 0 0
\(985\) 35.6986 + 12.9932i 1.13745 + 0.413999i
\(986\) −10.2917 3.74588i −0.327755 0.119293i
\(987\) 0 0
\(988\) −4.05620 + 23.0038i −0.129045 + 0.731849i
\(989\) −6.04594 10.4719i −0.192250 0.332986i
\(990\) 0 0
\(991\) −27.7503 + 48.0649i −0.881517 + 1.52683i −0.0318627 + 0.999492i \(0.510144\pi\)
−0.849654 + 0.527340i \(0.823189\pi\)
\(992\) −53.0107 44.4812i −1.68309 1.41228i
\(993\) 0 0
\(994\) 3.42932 + 19.4487i 0.108771 + 0.616874i
\(995\) −15.4979 + 13.0043i −0.491317 + 0.412264i
\(996\) 0 0
\(997\) 42.3301 15.4069i 1.34061 0.487941i 0.430603 0.902541i \(-0.358301\pi\)
0.910004 + 0.414600i \(0.136079\pi\)
\(998\) 8.61859 0.272817
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 243.2.e.c.55.2 12
3.2 odd 2 243.2.e.b.55.1 12
9.2 odd 6 81.2.e.a.46.2 12
9.4 even 3 243.2.e.d.217.1 12
9.5 odd 6 243.2.e.a.217.2 12
9.7 even 3 27.2.e.a.16.1 12
27.2 odd 18 729.2.a.d.1.5 6
27.4 even 9 inner 243.2.e.c.190.2 12
27.5 odd 18 243.2.e.a.28.2 12
27.7 even 9 729.2.c.e.487.5 12
27.11 odd 18 729.2.c.b.244.2 12
27.13 even 9 27.2.e.a.22.1 yes 12
27.14 odd 18 81.2.e.a.37.2 12
27.16 even 9 729.2.c.e.244.5 12
27.20 odd 18 729.2.c.b.487.2 12
27.22 even 9 243.2.e.d.28.1 12
27.23 odd 18 243.2.e.b.190.1 12
27.25 even 9 729.2.a.a.1.2 6
36.7 odd 6 432.2.u.c.97.2 12
45.7 odd 12 675.2.u.b.124.4 24
45.34 even 6 675.2.l.c.151.2 12
45.43 odd 12 675.2.u.b.124.1 24
108.67 odd 18 432.2.u.c.49.2 12
135.13 odd 36 675.2.u.b.49.4 24
135.67 odd 36 675.2.u.b.49.1 24
135.94 even 18 675.2.l.c.76.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.1 12 9.7 even 3
27.2.e.a.22.1 yes 12 27.13 even 9
81.2.e.a.37.2 12 27.14 odd 18
81.2.e.a.46.2 12 9.2 odd 6
243.2.e.a.28.2 12 27.5 odd 18
243.2.e.a.217.2 12 9.5 odd 6
243.2.e.b.55.1 12 3.2 odd 2
243.2.e.b.190.1 12 27.23 odd 18
243.2.e.c.55.2 12 1.1 even 1 trivial
243.2.e.c.190.2 12 27.4 even 9 inner
243.2.e.d.28.1 12 27.22 even 9
243.2.e.d.217.1 12 9.4 even 3
432.2.u.c.49.2 12 108.67 odd 18
432.2.u.c.97.2 12 36.7 odd 6
675.2.l.c.76.2 12 135.94 even 18
675.2.l.c.151.2 12 45.34 even 6
675.2.u.b.49.1 24 135.67 odd 36
675.2.u.b.49.4 24 135.13 odd 36
675.2.u.b.124.1 24 45.43 odd 12
675.2.u.b.124.4 24 45.7 odd 12
729.2.a.a.1.2 6 27.25 even 9
729.2.a.d.1.5 6 27.2 odd 18
729.2.c.b.244.2 12 27.11 odd 18
729.2.c.b.487.2 12 27.20 odd 18
729.2.c.e.244.5 12 27.16 even 9
729.2.c.e.487.5 12 27.7 even 9