Properties

Label 729.2.g.b.28.3
Level $729$
Weight $2$
Character 729.28
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 28.3
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.b.703.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00769 + 0.662771i) q^{2} +(-0.215977 + 0.500690i) q^{4} +(-2.69736 + 2.85904i) q^{5} +(-1.84676 - 0.215855i) q^{7} +(-0.533084 - 3.02327i) q^{8} +O(q^{10})\) \(q+(-1.00769 + 0.662771i) q^{2} +(-0.215977 + 0.500690i) q^{4} +(-2.69736 + 2.85904i) q^{5} +(-1.84676 - 0.215855i) q^{7} +(-0.533084 - 3.02327i) q^{8} +(0.823230 - 4.66877i) q^{10} +(-1.39079 + 4.64556i) q^{11} +(0.0180985 - 0.310740i) q^{13} +(2.00403 - 1.00646i) q^{14} +(1.79253 + 1.89997i) q^{16} +(-3.17561 + 1.15583i) q^{17} +(1.05997 + 0.385798i) q^{19} +(-0.848924 - 1.96803i) q^{20} +(-1.67745 - 5.60308i) q^{22} +(2.26299 - 0.264506i) q^{23} +(-0.607605 - 10.4322i) q^{25} +(0.187712 + 0.325126i) q^{26} +(0.506934 - 0.878035i) q^{28} +(-2.56086 - 1.28611i) q^{29} +(-2.90267 - 3.89896i) q^{31} +(2.90875 + 0.689387i) q^{32} +(2.43399 - 3.26942i) q^{34} +(5.59852 - 4.69772i) q^{35} +(8.69541 + 7.29632i) q^{37} +(-1.32382 + 0.313752i) q^{38} +(10.0816 + 6.63075i) q^{40} +(1.20697 + 0.793835i) q^{41} +(4.35354 - 1.03181i) q^{43} +(-2.02561 - 1.69969i) q^{44} +(-2.10510 + 1.76639i) q^{46} +(2.34655 - 3.15196i) q^{47} +(-3.44738 - 0.817044i) q^{49} +(7.52643 + 10.1097i) q^{50} +(0.151676 + 0.0761743i) q^{52} +(0.812932 - 1.40804i) q^{53} +(-9.53037 - 16.5071i) q^{55} +(0.331890 + 5.69833i) q^{56} +(3.43296 - 0.401256i) q^{58} +(-2.86545 - 9.57127i) q^{59} +(-0.302918 - 0.702244i) q^{61} +(5.50912 + 2.00515i) q^{62} +(-8.29717 + 3.01992i) q^{64} +(0.839599 + 0.889923i) q^{65} +(0.658500 - 0.330711i) q^{67} +(0.107146 - 1.83963i) q^{68} +(-2.52809 + 8.44441i) q^{70} +(-1.18078 + 6.69652i) q^{71} +(-0.692009 - 3.92458i) q^{73} +(-13.5981 - 1.58939i) q^{74} +(-0.422094 + 0.447393i) q^{76} +(3.57123 - 8.27903i) q^{77} +(-10.3755 + 6.82406i) q^{79} -10.2672 q^{80} -1.74239 q^{82} +(6.18560 - 4.06833i) q^{83} +(5.26121 - 12.1969i) q^{85} +(-3.70318 + 3.92515i) q^{86} +(14.7862 + 1.72826i) q^{88} +(-0.943990 - 5.35363i) q^{89} +(-0.100499 + 0.569956i) q^{91} +(-0.356318 + 1.19018i) q^{92} +(-0.275575 + 4.73143i) q^{94} +(-3.96214 + 1.98986i) q^{95} +(-3.16003 - 3.34944i) q^{97} +(4.01542 - 1.46149i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{22}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00769 + 0.662771i −0.712548 + 0.468650i −0.853317 0.521392i \(-0.825413\pi\)
0.140769 + 0.990042i \(0.455042\pi\)
\(3\) 0 0
\(4\) −0.215977 + 0.500690i −0.107988 + 0.250345i
\(5\) −2.69736 + 2.85904i −1.20630 + 1.27860i −0.256208 + 0.966622i \(0.582473\pi\)
−0.950089 + 0.311979i \(0.899008\pi\)
\(6\) 0 0
\(7\) −1.84676 0.215855i −0.698010 0.0815857i −0.240315 0.970695i \(-0.577251\pi\)
−0.457695 + 0.889109i \(0.651325\pi\)
\(8\) −0.533084 3.02327i −0.188474 1.06889i
\(9\) 0 0
\(10\) 0.823230 4.66877i 0.260328 1.47640i
\(11\) −1.39079 + 4.64556i −0.419339 + 1.40069i 0.443983 + 0.896035i \(0.353565\pi\)
−0.863322 + 0.504654i \(0.831620\pi\)
\(12\) 0 0
\(13\) 0.0180985 0.310740i 0.00501963 0.0861838i −0.994868 0.101183i \(-0.967737\pi\)
0.999888 + 0.0149987i \(0.00477443\pi\)
\(14\) 2.00403 1.00646i 0.535601 0.268989i
\(15\) 0 0
\(16\) 1.79253 + 1.89997i 0.448132 + 0.474992i
\(17\) −3.17561 + 1.15583i −0.770198 + 0.280329i −0.697079 0.716994i \(-0.745517\pi\)
−0.0731188 + 0.997323i \(0.523295\pi\)
\(18\) 0 0
\(19\) 1.05997 + 0.385798i 0.243174 + 0.0885081i 0.460732 0.887539i \(-0.347587\pi\)
−0.217558 + 0.976047i \(0.569809\pi\)
\(20\) −0.848924 1.96803i −0.189825 0.440064i
\(21\) 0 0
\(22\) −1.67745 5.60308i −0.357634 1.19458i
\(23\) 2.26299 0.264506i 0.471866 0.0551532i 0.123163 0.992386i \(-0.460696\pi\)
0.348703 + 0.937233i \(0.386622\pi\)
\(24\) 0 0
\(25\) −0.607605 10.4322i −0.121521 2.08644i
\(26\) 0.187712 + 0.325126i 0.0368133 + 0.0637625i
\(27\) 0 0
\(28\) 0.506934 0.878035i 0.0958015 0.165933i
\(29\) −2.56086 1.28611i −0.475540 0.238825i 0.194852 0.980833i \(-0.437577\pi\)
−0.670391 + 0.742008i \(0.733874\pi\)
\(30\) 0 0
\(31\) −2.90267 3.89896i −0.521334 0.700273i 0.461002 0.887399i \(-0.347490\pi\)
−0.982336 + 0.187126i \(0.940083\pi\)
\(32\) 2.90875 + 0.689387i 0.514200 + 0.121868i
\(33\) 0 0
\(34\) 2.43399 3.26942i 0.417427 0.560701i
\(35\) 5.59852 4.69772i 0.946323 0.794059i
\(36\) 0 0
\(37\) 8.69541 + 7.29632i 1.42952 + 1.19951i 0.945998 + 0.324173i \(0.105086\pi\)
0.483519 + 0.875334i \(0.339358\pi\)
\(38\) −1.32382 + 0.313752i −0.214752 + 0.0508973i
\(39\) 0 0
\(40\) 10.0816 + 6.63075i 1.59403 + 1.04841i
\(41\) 1.20697 + 0.793835i 0.188497 + 0.123976i 0.640250 0.768167i \(-0.278831\pi\)
−0.451753 + 0.892143i \(0.649201\pi\)
\(42\) 0 0
\(43\) 4.35354 1.03181i 0.663908 0.157349i 0.115173 0.993345i \(-0.463258\pi\)
0.548735 + 0.835996i \(0.315110\pi\)
\(44\) −2.02561 1.69969i −0.305372 0.256237i
\(45\) 0 0
\(46\) −2.10510 + 1.76639i −0.310380 + 0.260439i
\(47\) 2.34655 3.15196i 0.342279 0.459760i −0.597337 0.801990i \(-0.703775\pi\)
0.939616 + 0.342230i \(0.111182\pi\)
\(48\) 0 0
\(49\) −3.44738 0.817044i −0.492483 0.116721i
\(50\) 7.52643 + 10.1097i 1.06440 + 1.42973i
\(51\) 0 0
\(52\) 0.151676 + 0.0761743i 0.0210336 + 0.0105635i
\(53\) 0.812932 1.40804i 0.111665 0.193409i −0.804777 0.593577i \(-0.797715\pi\)
0.916442 + 0.400168i \(0.131048\pi\)
\(54\) 0 0
\(55\) −9.53037 16.5071i −1.28507 2.22581i
\(56\) 0.331890 + 5.69833i 0.0443506 + 0.761471i
\(57\) 0 0
\(58\) 3.43296 0.401256i 0.450770 0.0526875i
\(59\) −2.86545 9.57127i −0.373050 1.24607i −0.914240 0.405173i \(-0.867211\pi\)
0.541190 0.840900i \(-0.317974\pi\)
\(60\) 0 0
\(61\) −0.302918 0.702244i −0.0387847 0.0899131i 0.897723 0.440561i \(-0.145221\pi\)
−0.936507 + 0.350648i \(0.885961\pi\)
\(62\) 5.50912 + 2.00515i 0.699659 + 0.254655i
\(63\) 0 0
\(64\) −8.29717 + 3.01992i −1.03715 + 0.377490i
\(65\) 0.839599 + 0.889923i 0.104139 + 0.110381i
\(66\) 0 0
\(67\) 0.658500 0.330711i 0.0804486 0.0404028i −0.408120 0.912928i \(-0.633816\pi\)
0.488569 + 0.872525i \(0.337519\pi\)
\(68\) 0.107146 1.83963i 0.0129934 0.223088i
\(69\) 0 0
\(70\) −2.52809 + 8.44441i −0.302164 + 1.00930i
\(71\) −1.18078 + 6.69652i −0.140133 + 0.794731i 0.831015 + 0.556250i \(0.187760\pi\)
−0.971147 + 0.238481i \(0.923351\pi\)
\(72\) 0 0
\(73\) −0.692009 3.92458i −0.0809935 0.459337i −0.998149 0.0608086i \(-0.980632\pi\)
0.917156 0.398529i \(-0.130479\pi\)
\(74\) −13.5981 1.58939i −1.58075 0.184763i
\(75\) 0 0
\(76\) −0.422094 + 0.447393i −0.0484175 + 0.0513196i
\(77\) 3.57123 8.27903i 0.406979 0.943483i
\(78\) 0 0
\(79\) −10.3755 + 6.82406i −1.16733 + 0.767767i −0.976850 0.213923i \(-0.931376\pi\)
−0.190483 + 0.981691i \(0.561005\pi\)
\(80\) −10.2672 −1.14790
\(81\) 0 0
\(82\) −1.74239 −0.192414
\(83\) 6.18560 4.06833i 0.678958 0.446558i −0.162623 0.986688i \(-0.551996\pi\)
0.841581 + 0.540131i \(0.181625\pi\)
\(84\) 0 0
\(85\) 5.26121 12.1969i 0.570659 1.32294i
\(86\) −3.70318 + 3.92515i −0.399325 + 0.423259i
\(87\) 0 0
\(88\) 14.7862 + 1.72826i 1.57621 + 0.184233i
\(89\) −0.943990 5.35363i −0.100063 0.567484i −0.993078 0.117458i \(-0.962526\pi\)
0.893015 0.450027i \(-0.148586\pi\)
\(90\) 0 0
\(91\) −0.100499 + 0.569956i −0.0105351 + 0.0597476i
\(92\) −0.356318 + 1.19018i −0.0371487 + 0.124085i
\(93\) 0 0
\(94\) −0.275575 + 4.73143i −0.0284234 + 0.488010i
\(95\) −3.96214 + 1.98986i −0.406507 + 0.204155i
\(96\) 0 0
\(97\) −3.16003 3.34944i −0.320852 0.340084i 0.546792 0.837268i \(-0.315849\pi\)
−0.867645 + 0.497185i \(0.834367\pi\)
\(98\) 4.01542 1.46149i 0.405619 0.147633i
\(99\) 0 0
\(100\) 5.35452 + 1.94888i 0.535452 + 0.194888i
\(101\) −4.25575 9.86593i −0.423463 0.981697i −0.987740 0.156111i \(-0.950104\pi\)
0.564277 0.825586i \(-0.309155\pi\)
\(102\) 0 0
\(103\) 3.36931 + 11.2543i 0.331988 + 1.10892i 0.947223 + 0.320575i \(0.103876\pi\)
−0.615235 + 0.788344i \(0.710939\pi\)
\(104\) −0.949099 + 0.110934i −0.0930668 + 0.0108779i
\(105\) 0 0
\(106\) 0.114021 + 1.95766i 0.0110747 + 0.190145i
\(107\) −3.20979 5.55953i −0.310302 0.537460i 0.668125 0.744049i \(-0.267097\pi\)
−0.978428 + 0.206589i \(0.933764\pi\)
\(108\) 0 0
\(109\) −1.72147 + 2.98167i −0.164887 + 0.285592i −0.936615 0.350360i \(-0.886059\pi\)
0.771728 + 0.635952i \(0.219393\pi\)
\(110\) 20.5441 + 10.3176i 1.95881 + 0.983749i
\(111\) 0 0
\(112\) −2.90025 3.89571i −0.274048 0.368110i
\(113\) −15.0849 3.57519i −1.41907 0.336326i −0.551722 0.834028i \(-0.686029\pi\)
−0.867348 + 0.497702i \(0.834177\pi\)
\(114\) 0 0
\(115\) −5.34788 + 7.18344i −0.498692 + 0.669859i
\(116\) 1.19703 1.00443i 0.111141 0.0932587i
\(117\) 0 0
\(118\) 9.23106 + 7.74578i 0.849788 + 0.713057i
\(119\) 6.11408 1.44906i 0.560477 0.132835i
\(120\) 0 0
\(121\) −10.4566 6.87740i −0.950598 0.625218i
\(122\) 0.770676 + 0.506882i 0.0697738 + 0.0458909i
\(123\) 0 0
\(124\) 2.57908 0.611252i 0.231608 0.0548921i
\(125\) 16.4097 + 13.7694i 1.46773 + 1.23157i
\(126\) 0 0
\(127\) −9.04687 + 7.59122i −0.802780 + 0.673612i −0.948873 0.315659i \(-0.897775\pi\)
0.146093 + 0.989271i \(0.453330\pi\)
\(128\) 2.78929 3.74666i 0.246540 0.331161i
\(129\) 0 0
\(130\) −1.43587 0.340309i −0.125935 0.0298470i
\(131\) 10.5633 + 14.1890i 0.922923 + 1.23970i 0.970566 + 0.240836i \(0.0774215\pi\)
−0.0476433 + 0.998864i \(0.515171\pi\)
\(132\) 0 0
\(133\) −1.87424 0.941277i −0.162517 0.0816191i
\(134\) −0.444381 + 0.769691i −0.0383887 + 0.0664911i
\(135\) 0 0
\(136\) 5.18724 + 8.98457i 0.444802 + 0.770420i
\(137\) −0.405293 6.95861i −0.0346265 0.594514i −0.970339 0.241750i \(-0.922279\pi\)
0.935712 0.352765i \(-0.114758\pi\)
\(138\) 0 0
\(139\) −6.26136 + 0.731848i −0.531081 + 0.0620745i −0.377408 0.926047i \(-0.623184\pi\)
−0.153674 + 0.988122i \(0.549110\pi\)
\(140\) 1.14295 + 3.81772i 0.0965970 + 0.322656i
\(141\) 0 0
\(142\) −3.24840 7.53064i −0.272600 0.631957i
\(143\) 1.41839 + 0.516252i 0.118612 + 0.0431712i
\(144\) 0 0
\(145\) 10.5846 3.85248i 0.879004 0.319931i
\(146\) 3.29843 + 3.49613i 0.272980 + 0.289342i
\(147\) 0 0
\(148\) −5.53120 + 2.77787i −0.454662 + 0.228340i
\(149\) 1.31857 22.6390i 0.108022 1.85466i −0.315688 0.948863i \(-0.602235\pi\)
0.423710 0.905798i \(-0.360728\pi\)
\(150\) 0 0
\(151\) −4.15613 + 13.8824i −0.338221 + 1.12974i 0.604625 + 0.796510i \(0.293323\pi\)
−0.942847 + 0.333227i \(0.891862\pi\)
\(152\) 0.601317 3.41024i 0.0487733 0.276607i
\(153\) 0 0
\(154\) 1.88840 + 10.7096i 0.152172 + 0.863008i
\(155\) 18.9768 + 2.21807i 1.52425 + 0.178160i
\(156\) 0 0
\(157\) −7.80515 + 8.27298i −0.622919 + 0.660256i −0.959602 0.281363i \(-0.909214\pi\)
0.336682 + 0.941618i \(0.390695\pi\)
\(158\) 5.93253 13.7531i 0.471967 1.09414i
\(159\) 0 0
\(160\) −9.81695 + 6.45671i −0.776098 + 0.510448i
\(161\) −4.23630 −0.333867
\(162\) 0 0
\(163\) −0.789620 −0.0618478 −0.0309239 0.999522i \(-0.509845\pi\)
−0.0309239 + 0.999522i \(0.509845\pi\)
\(164\) −0.658142 + 0.432867i −0.0513923 + 0.0338012i
\(165\) 0 0
\(166\) −3.53682 + 8.19928i −0.274511 + 0.636387i
\(167\) −3.98342 + 4.22218i −0.308246 + 0.326722i −0.862915 0.505349i \(-0.831364\pi\)
0.554668 + 0.832071i \(0.312845\pi\)
\(168\) 0 0
\(169\) 12.8159 + 1.49796i 0.985836 + 0.115228i
\(170\) 2.78203 + 15.7777i 0.213372 + 1.21009i
\(171\) 0 0
\(172\) −0.423646 + 2.40262i −0.0323027 + 0.183198i
\(173\) −0.997345 + 3.33136i −0.0758267 + 0.253279i −0.987496 0.157647i \(-0.949609\pi\)
0.911669 + 0.410926i \(0.134794\pi\)
\(174\) 0 0
\(175\) −1.12974 + 19.3969i −0.0854004 + 1.46627i
\(176\) −11.3194 + 5.68484i −0.853235 + 0.428511i
\(177\) 0 0
\(178\) 4.49949 + 4.76918i 0.337251 + 0.357465i
\(179\) −7.34454 + 2.67320i −0.548957 + 0.199804i −0.601583 0.798810i \(-0.705463\pi\)
0.0526260 + 0.998614i \(0.483241\pi\)
\(180\) 0 0
\(181\) −10.9891 3.99971i −0.816815 0.297296i −0.100379 0.994949i \(-0.532006\pi\)
−0.716436 + 0.697653i \(0.754228\pi\)
\(182\) −0.276478 0.640949i −0.0204939 0.0475103i
\(183\) 0 0
\(184\) −2.00604 6.70063i −0.147887 0.493977i
\(185\) −44.3151 + 5.17969i −3.25811 + 0.380819i
\(186\) 0 0
\(187\) −0.952861 16.3600i −0.0696801 1.19636i
\(188\) 1.07135 + 1.85564i 0.0781366 + 0.135337i
\(189\) 0 0
\(190\) 2.67380 4.63116i 0.193978 0.335980i
\(191\) −13.0036 6.53063i −0.940904 0.472540i −0.0888801 0.996042i \(-0.528329\pi\)
−0.852024 + 0.523502i \(0.824625\pi\)
\(192\) 0 0
\(193\) 10.1622 + 13.6503i 0.731494 + 0.982568i 0.999815 + 0.0192379i \(0.00612399\pi\)
−0.268320 + 0.963330i \(0.586469\pi\)
\(194\) 5.40425 + 1.28083i 0.388003 + 0.0919584i
\(195\) 0 0
\(196\) 1.15364 1.54961i 0.0824028 0.110686i
\(197\) −9.53813 + 8.00344i −0.679563 + 0.570221i −0.915879 0.401455i \(-0.868505\pi\)
0.236315 + 0.971676i \(0.424060\pi\)
\(198\) 0 0
\(199\) −16.5214 13.8631i −1.17117 0.982731i −0.171177 0.985240i \(-0.554757\pi\)
−0.999997 + 0.00250896i \(0.999201\pi\)
\(200\) −31.2154 + 7.39818i −2.20726 + 0.523131i
\(201\) 0 0
\(202\) 10.8273 + 7.12126i 0.761809 + 0.501050i
\(203\) 4.45168 + 2.92792i 0.312447 + 0.205499i
\(204\) 0 0
\(205\) −5.52524 + 1.30950i −0.385899 + 0.0914598i
\(206\) −10.8543 9.10781i −0.756252 0.634571i
\(207\) 0 0
\(208\) 0.622838 0.522623i 0.0431860 0.0362374i
\(209\) −3.26644 + 4.38760i −0.225945 + 0.303496i
\(210\) 0 0
\(211\) −12.3360 2.92368i −0.849244 0.201275i −0.217123 0.976144i \(-0.569667\pi\)
−0.632121 + 0.774870i \(0.717815\pi\)
\(212\) 0.529417 + 0.711130i 0.0363605 + 0.0488406i
\(213\) 0 0
\(214\) 6.91919 + 3.47495i 0.472986 + 0.237542i
\(215\) −8.79309 + 15.2301i −0.599684 + 1.03868i
\(216\) 0 0
\(217\) 4.51892 + 7.82700i 0.306764 + 0.531331i
\(218\) −0.241451 4.14555i −0.0163531 0.280772i
\(219\) 0 0
\(220\) 10.3233 1.20662i 0.695995 0.0813501i
\(221\) 0.301688 + 1.00771i 0.0202937 + 0.0677857i
\(222\) 0 0
\(223\) −1.95059 4.52199i −0.130622 0.302815i 0.840336 0.542065i \(-0.182357\pi\)
−0.970958 + 0.239251i \(0.923098\pi\)
\(224\) −5.22297 1.90100i −0.348974 0.127016i
\(225\) 0 0
\(226\) 17.5705 6.39515i 1.16877 0.425399i
\(227\) −4.41017 4.67451i −0.292713 0.310258i 0.564282 0.825582i \(-0.309153\pi\)
−0.856995 + 0.515324i \(0.827672\pi\)
\(228\) 0 0
\(229\) 26.5744 13.3462i 1.75608 0.881939i 0.794575 0.607166i \(-0.207694\pi\)
0.961509 0.274773i \(-0.0886026\pi\)
\(230\) 0.628046 10.7831i 0.0414121 0.711019i
\(231\) 0 0
\(232\) −2.52311 + 8.42777i −0.165650 + 0.553310i
\(233\) −3.77489 + 21.4085i −0.247301 + 1.40252i 0.567786 + 0.823176i \(0.307800\pi\)
−0.815087 + 0.579339i \(0.803311\pi\)
\(234\) 0 0
\(235\) 2.68208 + 15.2108i 0.174960 + 0.992245i
\(236\) 5.41111 + 0.632468i 0.352233 + 0.0411702i
\(237\) 0 0
\(238\) −5.20073 + 5.51245i −0.337113 + 0.357319i
\(239\) −2.35595 + 5.46170i −0.152394 + 0.353288i −0.977262 0.212037i \(-0.931990\pi\)
0.824868 + 0.565325i \(0.191249\pi\)
\(240\) 0 0
\(241\) 0.990937 0.651749i 0.0638318 0.0419829i −0.517192 0.855869i \(-0.673023\pi\)
0.581024 + 0.813887i \(0.302652\pi\)
\(242\) 15.0952 0.970355
\(243\) 0 0
\(244\) 0.417030 0.0266976
\(245\) 11.6348 7.65233i 0.743320 0.488889i
\(246\) 0 0
\(247\) 0.139067 0.322393i 0.00884861 0.0205134i
\(248\) −10.2402 + 10.8540i −0.650255 + 0.689230i
\(249\) 0 0
\(250\) −25.6620 2.99945i −1.62301 0.189702i
\(251\) −2.34580 13.3037i −0.148066 0.839722i −0.964854 0.262785i \(-0.915359\pi\)
0.816789 0.576937i \(-0.195752\pi\)
\(252\) 0 0
\(253\) −1.91857 + 10.8807i −0.120619 + 0.684066i
\(254\) 4.08524 13.6456i 0.256331 0.856204i
\(255\) 0 0
\(256\) 0.699229 12.0053i 0.0437018 0.750331i
\(257\) 21.8753 10.9862i 1.36454 0.685299i 0.392423 0.919785i \(-0.371637\pi\)
0.972120 + 0.234486i \(0.0753406\pi\)
\(258\) 0 0
\(259\) −14.4834 15.3515i −0.899955 0.953896i
\(260\) −0.626909 + 0.228176i −0.0388793 + 0.0141509i
\(261\) 0 0
\(262\) −20.0487 7.29712i −1.23861 0.450818i
\(263\) 8.59130 + 19.9169i 0.529762 + 1.22813i 0.947557 + 0.319586i \(0.103544\pi\)
−0.417795 + 0.908541i \(0.637197\pi\)
\(264\) 0 0
\(265\) 1.83286 + 6.12219i 0.112592 + 0.376083i
\(266\) 2.51251 0.293670i 0.154052 0.0180061i
\(267\) 0 0
\(268\) 0.0233632 + 0.401130i 0.00142713 + 0.0245029i
\(269\) 2.87056 + 4.97195i 0.175021 + 0.303145i 0.940169 0.340710i \(-0.110667\pi\)
−0.765148 + 0.643855i \(0.777334\pi\)
\(270\) 0 0
\(271\) 7.23998 12.5400i 0.439798 0.761752i −0.557876 0.829924i \(-0.688384\pi\)
0.997674 + 0.0681726i \(0.0217169\pi\)
\(272\) −7.88839 3.96170i −0.478304 0.240213i
\(273\) 0 0
\(274\) 5.02038 + 6.74354i 0.303292 + 0.407392i
\(275\) 49.3084 + 11.6863i 2.97341 + 0.704711i
\(276\) 0 0
\(277\) 7.07774 9.50706i 0.425260 0.571224i −0.536921 0.843632i \(-0.680413\pi\)
0.962182 + 0.272408i \(0.0878202\pi\)
\(278\) 5.82449 4.88733i 0.349330 0.293122i
\(279\) 0 0
\(280\) −17.1870 14.4216i −1.02712 0.861853i
\(281\) 14.7822 3.50346i 0.881835 0.208999i 0.235336 0.971914i \(-0.424381\pi\)
0.646498 + 0.762915i \(0.276233\pi\)
\(282\) 0 0
\(283\) −20.8426 13.7084i −1.23896 0.814880i −0.250764 0.968048i \(-0.580682\pi\)
−0.988200 + 0.153168i \(0.951052\pi\)
\(284\) −3.09786 2.03750i −0.183824 0.120903i
\(285\) 0 0
\(286\) −1.77146 + 0.419844i −0.104749 + 0.0248259i
\(287\) −2.05763 1.72655i −0.121458 0.101915i
\(288\) 0 0
\(289\) −4.27421 + 3.58648i −0.251424 + 0.210970i
\(290\) −8.11274 + 10.8973i −0.476396 + 0.639912i
\(291\) 0 0
\(292\) 2.11446 + 0.501135i 0.123739 + 0.0293267i
\(293\) 5.12105 + 6.87876i 0.299175 + 0.401862i 0.926136 0.377189i \(-0.123109\pi\)
−0.626962 + 0.779050i \(0.715702\pi\)
\(294\) 0 0
\(295\) 35.0938 + 17.6248i 2.04324 + 1.02615i
\(296\) 17.4233 30.1781i 1.01271 1.75407i
\(297\) 0 0
\(298\) 13.6758 + 23.6871i 0.792216 + 1.37216i
\(299\) −0.0412357 0.707989i −0.00238472 0.0409441i
\(300\) 0 0
\(301\) −8.26266 + 0.965767i −0.476252 + 0.0556659i
\(302\) −5.01277 16.7438i −0.288453 0.963499i
\(303\) 0 0
\(304\) 1.16702 + 2.70546i 0.0669333 + 0.155169i
\(305\) 2.82482 + 1.02815i 0.161749 + 0.0588718i
\(306\) 0 0
\(307\) 1.80059 0.655362i 0.102765 0.0374035i −0.290126 0.956989i \(-0.593697\pi\)
0.392891 + 0.919585i \(0.371475\pi\)
\(308\) 3.37393 + 3.57615i 0.192247 + 0.203770i
\(309\) 0 0
\(310\) −20.5929 + 10.3421i −1.16960 + 0.587394i
\(311\) −0.886900 + 15.2275i −0.0502915 + 0.863472i 0.874978 + 0.484162i \(0.160876\pi\)
−0.925270 + 0.379310i \(0.876162\pi\)
\(312\) 0 0
\(313\) 8.80754 29.4192i 0.497832 1.66287i −0.226959 0.973904i \(-0.572878\pi\)
0.724790 0.688969i \(-0.241937\pi\)
\(314\) 2.38212 13.5097i 0.134431 0.762395i
\(315\) 0 0
\(316\) −1.17588 6.66874i −0.0661484 0.375146i
\(317\) −22.7971 2.66460i −1.28042 0.149659i −0.551449 0.834209i \(-0.685925\pi\)
−0.728966 + 0.684549i \(0.759999\pi\)
\(318\) 0 0
\(319\) 9.53633 10.1079i 0.533932 0.565935i
\(320\) 13.7464 31.8677i 0.768447 1.78146i
\(321\) 0 0
\(322\) 4.26890 2.80770i 0.237896 0.156467i
\(323\) −3.81197 −0.212104
\(324\) 0 0
\(325\) −3.25269 −0.180427
\(326\) 0.795696 0.523337i 0.0440695 0.0289850i
\(327\) 0 0
\(328\) 1.75656 4.07217i 0.0969900 0.224848i
\(329\) −5.01388 + 5.31440i −0.276424 + 0.292992i
\(330\) 0 0
\(331\) 0.894983 + 0.104608i 0.0491927 + 0.00574980i 0.140654 0.990059i \(-0.455080\pi\)
−0.0914610 + 0.995809i \(0.529154\pi\)
\(332\) 0.701029 + 3.97573i 0.0384740 + 0.218197i
\(333\) 0 0
\(334\) 1.21573 6.89476i 0.0665219 0.377265i
\(335\) −0.830698 + 2.77472i −0.0453859 + 0.151599i
\(336\) 0 0
\(337\) 2.04455 35.1035i 0.111374 1.91221i −0.231511 0.972832i \(-0.574367\pi\)
0.342885 0.939377i \(-0.388596\pi\)
\(338\) −13.9073 + 6.98450i −0.756457 + 0.379907i
\(339\) 0 0
\(340\) 4.97055 + 5.26848i 0.269566 + 0.285723i
\(341\) 22.1498 8.06188i 1.19948 0.436575i
\(342\) 0 0
\(343\) 18.4205 + 6.70453i 0.994616 + 0.362010i
\(344\) −5.44023 12.6119i −0.293318 0.679987i
\(345\) 0 0
\(346\) −1.20291 4.01801i −0.0646690 0.216010i
\(347\) −15.0726 + 1.76174i −0.809142 + 0.0945751i −0.510597 0.859820i \(-0.670575\pi\)
−0.298545 + 0.954396i \(0.596501\pi\)
\(348\) 0 0
\(349\) 1.64660 + 28.2711i 0.0881406 + 1.51332i 0.695291 + 0.718728i \(0.255275\pi\)
−0.607151 + 0.794587i \(0.707688\pi\)
\(350\) −11.7173 20.2949i −0.626315 1.08481i
\(351\) 0 0
\(352\) −7.24806 + 12.5540i −0.386323 + 0.669131i
\(353\) 14.8471 + 7.45651i 0.790233 + 0.396870i 0.797664 0.603102i \(-0.206069\pi\)
−0.00743042 + 0.999972i \(0.502365\pi\)
\(354\) 0 0
\(355\) −15.9606 21.4388i −0.847102 1.13786i
\(356\) 2.88439 + 0.683613i 0.152872 + 0.0362314i
\(357\) 0 0
\(358\) 5.62934 7.56152i 0.297520 0.399639i
\(359\) 10.7593 9.02816i 0.567856 0.476488i −0.313077 0.949728i \(-0.601360\pi\)
0.880934 + 0.473239i \(0.156915\pi\)
\(360\) 0 0
\(361\) −13.5801 11.3951i −0.714745 0.599742i
\(362\) 13.7246 3.25278i 0.721348 0.170963i
\(363\) 0 0
\(364\) −0.263666 0.173416i −0.0138198 0.00908946i
\(365\) 13.0871 + 8.60753i 0.685011 + 0.450539i
\(366\) 0 0
\(367\) 5.32264 1.26149i 0.277840 0.0658492i −0.0893336 0.996002i \(-0.528474\pi\)
0.367173 + 0.930153i \(0.380326\pi\)
\(368\) 4.55902 + 3.82547i 0.237656 + 0.199417i
\(369\) 0 0
\(370\) 41.2232 34.5903i 2.14309 1.79827i
\(371\) −1.80522 + 2.42484i −0.0937225 + 0.125891i
\(372\) 0 0
\(373\) 27.5326 + 6.52534i 1.42558 + 0.337869i 0.869778 0.493443i \(-0.164262\pi\)
0.555805 + 0.831313i \(0.312410\pi\)
\(374\) 11.8031 + 15.8544i 0.610325 + 0.819809i
\(375\) 0 0
\(376\) −10.7801 5.41398i −0.555942 0.279205i
\(377\) −0.445994 + 0.772485i −0.0229699 + 0.0397850i
\(378\) 0 0
\(379\) −8.11043 14.0477i −0.416605 0.721580i 0.578991 0.815334i \(-0.303447\pi\)
−0.995595 + 0.0937537i \(0.970113\pi\)
\(380\) −0.140574 2.41356i −0.00721130 0.123813i
\(381\) 0 0
\(382\) 17.4319 2.03750i 0.891895 0.104248i
\(383\) −4.24796 14.1892i −0.217061 0.725033i −0.995280 0.0970408i \(-0.969062\pi\)
0.778220 0.627992i \(-0.216123\pi\)
\(384\) 0 0
\(385\) 14.0372 + 32.5418i 0.715401 + 1.65848i
\(386\) −19.2874 7.02006i −0.981705 0.357311i
\(387\) 0 0
\(388\) 2.35952 0.858795i 0.119787 0.0435987i
\(389\) −5.12493 5.43211i −0.259844 0.275419i 0.584297 0.811540i \(-0.301370\pi\)
−0.844141 + 0.536121i \(0.819889\pi\)
\(390\) 0 0
\(391\) −6.88065 + 3.45559i −0.347969 + 0.174757i
\(392\) −0.632402 + 10.8579i −0.0319411 + 0.548408i
\(393\) 0 0
\(394\) 4.30707 14.3866i 0.216987 0.724787i
\(395\) 8.47619 48.0709i 0.426484 2.41871i
\(396\) 0 0
\(397\) −5.20739 29.5326i −0.261351 1.48220i −0.779228 0.626741i \(-0.784388\pi\)
0.517876 0.855455i \(-0.326723\pi\)
\(398\) 25.8367 + 3.01987i 1.29507 + 0.151372i
\(399\) 0 0
\(400\) 18.7317 19.8544i 0.936583 0.992720i
\(401\) 2.59509 6.01608i 0.129592 0.300429i −0.841050 0.540958i \(-0.818062\pi\)
0.970642 + 0.240529i \(0.0773210\pi\)
\(402\) 0 0
\(403\) −1.26410 + 0.831409i −0.0629691 + 0.0414154i
\(404\) 5.85891 0.291492
\(405\) 0 0
\(406\) −6.42647 −0.318941
\(407\) −45.9890 + 30.2474i −2.27959 + 1.49931i
\(408\) 0 0
\(409\) 0.707379 1.63989i 0.0349776 0.0810873i −0.899832 0.436237i \(-0.856311\pi\)
0.934809 + 0.355150i \(0.115570\pi\)
\(410\) 4.69985 4.98155i 0.232109 0.246021i
\(411\) 0 0
\(412\) −6.36261 0.743682i −0.313463 0.0366386i
\(413\) 3.22579 + 18.2944i 0.158731 + 0.900207i
\(414\) 0 0
\(415\) −5.05329 + 28.6586i −0.248056 + 1.40680i
\(416\) 0.266864 0.891389i 0.0130841 0.0437040i
\(417\) 0 0
\(418\) 0.383606 6.58626i 0.0187628 0.322145i
\(419\) −18.5168 + 9.29947i −0.904603 + 0.454309i −0.839370 0.543561i \(-0.817076\pi\)
−0.0652339 + 0.997870i \(0.520779\pi\)
\(420\) 0 0
\(421\) −13.0106 13.7904i −0.634097 0.672103i 0.328042 0.944663i \(-0.393611\pi\)
−0.962139 + 0.272560i \(0.912130\pi\)
\(422\) 14.3686 5.22976i 0.699454 0.254581i
\(423\) 0 0
\(424\) −4.69024 1.70711i −0.227778 0.0829045i
\(425\) 13.9873 + 32.4262i 0.678484 + 1.57290i
\(426\) 0 0
\(427\) 0.407835 + 1.36226i 0.0197365 + 0.0659245i
\(428\) 3.47684 0.406384i 0.168059 0.0196433i
\(429\) 0 0
\(430\) −1.23331 21.1751i −0.0594754 1.02115i
\(431\) 0.254281 + 0.440427i 0.0122483 + 0.0212146i 0.872085 0.489355i \(-0.162768\pi\)
−0.859836 + 0.510570i \(0.829434\pi\)
\(432\) 0 0
\(433\) 10.9606 18.9844i 0.526734 0.912330i −0.472781 0.881180i \(-0.656750\pi\)
0.999515 0.0311498i \(-0.00991689\pi\)
\(434\) −9.74120 4.89221i −0.467593 0.234834i
\(435\) 0 0
\(436\) −1.12110 1.50589i −0.0536908 0.0721192i
\(437\) 2.50075 + 0.592689i 0.119627 + 0.0283521i
\(438\) 0 0
\(439\) −20.1006 + 26.9997i −0.959347 + 1.28863i −0.00190618 + 0.999998i \(0.500607\pi\)
−0.957441 + 0.288629i \(0.906801\pi\)
\(440\) −44.8249 + 37.6125i −2.13694 + 1.79311i
\(441\) 0 0
\(442\) −0.971889 0.815511i −0.0462280 0.0387899i
\(443\) 11.9279 2.82696i 0.566711 0.134313i 0.0627341 0.998030i \(-0.480018\pi\)
0.503976 + 0.863717i \(0.331870\pi\)
\(444\) 0 0
\(445\) 17.8525 + 11.7418i 0.846291 + 0.556614i
\(446\) 4.96265 + 3.26398i 0.234988 + 0.154554i
\(447\) 0 0
\(448\) 15.9748 3.78609i 0.754736 0.178876i
\(449\) −19.3898 16.2699i −0.915060 0.767826i 0.0580153 0.998316i \(-0.481523\pi\)
−0.973075 + 0.230490i \(0.925967\pi\)
\(450\) 0 0
\(451\) −5.36645 + 4.50299i −0.252696 + 0.212037i
\(452\) 5.04805 6.78071i 0.237440 0.318938i
\(453\) 0 0
\(454\) 7.54224 + 1.78754i 0.353975 + 0.0838935i
\(455\) −1.35844 1.82471i −0.0636848 0.0855436i
\(456\) 0 0
\(457\) −26.1808 13.1485i −1.22469 0.615060i −0.285470 0.958388i \(-0.592150\pi\)
−0.939216 + 0.343327i \(0.888446\pi\)
\(458\) −17.9334 + 31.0616i −0.837973 + 1.45141i
\(459\) 0 0
\(460\) −2.44166 4.22908i −0.113843 0.197182i
\(461\) 0.745295 + 12.7962i 0.0347119 + 0.595980i 0.970152 + 0.242496i \(0.0779661\pi\)
−0.935441 + 0.353484i \(0.884997\pi\)
\(462\) 0 0
\(463\) −10.2547 + 1.19861i −0.476578 + 0.0557040i −0.350992 0.936379i \(-0.614155\pi\)
−0.125587 + 0.992083i \(0.540081\pi\)
\(464\) −2.14684 7.17094i −0.0996645 0.332902i
\(465\) 0 0
\(466\) −10.3850 24.0751i −0.481075 1.11526i
\(467\) 6.54957 + 2.38385i 0.303078 + 0.110311i 0.489083 0.872238i \(-0.337332\pi\)
−0.186005 + 0.982549i \(0.559554\pi\)
\(468\) 0 0
\(469\) −1.28748 + 0.468604i −0.0594502 + 0.0216381i
\(470\) −12.7840 13.5503i −0.589683 0.625027i
\(471\) 0 0
\(472\) −27.4090 + 13.7653i −1.26160 + 0.633600i
\(473\) −1.26153 + 21.6596i −0.0580053 + 0.995912i
\(474\) 0 0
\(475\) 3.38067 11.2922i 0.155116 0.518123i
\(476\) −0.594967 + 3.37422i −0.0272702 + 0.154657i
\(477\) 0 0
\(478\) −1.24578 7.06518i −0.0569807 0.323154i
\(479\) −33.2090 3.88157i −1.51736 0.177354i −0.683752 0.729714i \(-0.739653\pi\)
−0.833605 + 0.552361i \(0.813727\pi\)
\(480\) 0 0
\(481\) 2.42463 2.56996i 0.110554 0.117180i
\(482\) −0.566601 + 1.31353i −0.0258080 + 0.0598296i
\(483\) 0 0
\(484\) 5.70182 3.75015i 0.259174 0.170461i
\(485\) 18.0999 0.821874
\(486\) 0 0
\(487\) −8.67546 −0.393122 −0.196561 0.980492i \(-0.562977\pi\)
−0.196561 + 0.980492i \(0.562977\pi\)
\(488\) −1.96159 + 1.29016i −0.0887971 + 0.0584028i
\(489\) 0 0
\(490\) −6.65258 + 15.4224i −0.300533 + 0.696714i
\(491\) 11.0320 11.6932i 0.497866 0.527707i −0.428897 0.903353i \(-0.641098\pi\)
0.926763 + 0.375646i \(0.122579\pi\)
\(492\) 0 0
\(493\) 9.61881 + 1.12428i 0.433209 + 0.0506349i
\(494\) 0.0735360 + 0.417043i 0.00330854 + 0.0187637i
\(495\) 0 0
\(496\) 2.20478 12.5040i 0.0989977 0.561444i
\(497\) 3.62609 12.1120i 0.162653 0.543297i
\(498\) 0 0
\(499\) −0.449179 + 7.71210i −0.0201080 + 0.345241i 0.973217 + 0.229889i \(0.0738365\pi\)
−0.993325 + 0.115351i \(0.963201\pi\)
\(500\) −10.4383 + 5.24232i −0.466816 + 0.234444i
\(501\) 0 0
\(502\) 11.1812 + 11.8513i 0.499040 + 0.528951i
\(503\) −30.5447 + 11.1174i −1.36192 + 0.495698i −0.916647 0.399697i \(-0.869115\pi\)
−0.445272 + 0.895395i \(0.646893\pi\)
\(504\) 0 0
\(505\) 39.6864 + 14.4447i 1.76602 + 0.642778i
\(506\) −5.27811 12.2360i −0.234641 0.543958i
\(507\) 0 0
\(508\) −1.84694 6.16920i −0.0819446 0.273714i
\(509\) 1.24093 0.145044i 0.0550034 0.00642898i −0.0885467 0.996072i \(-0.528222\pi\)
0.143550 + 0.989643i \(0.454148\pi\)
\(510\) 0 0
\(511\) 0.430834 + 7.39713i 0.0190590 + 0.327230i
\(512\) 11.9231 + 20.6514i 0.526931 + 0.912671i
\(513\) 0 0
\(514\) −14.7623 + 25.5690i −0.651136 + 1.12780i
\(515\) −41.2647 20.7239i −1.81834 0.913205i
\(516\) 0 0
\(517\) 11.3791 + 15.2847i 0.500451 + 0.672222i
\(518\) 24.7694 + 5.87045i 1.08830 + 0.257933i
\(519\) 0 0
\(520\) 2.24290 3.01274i 0.0983577 0.132117i
\(521\) 17.9588 15.0692i 0.786787 0.660193i −0.158161 0.987413i \(-0.550556\pi\)
0.944948 + 0.327220i \(0.106112\pi\)
\(522\) 0 0
\(523\) 26.2642 + 22.0383i 1.14845 + 0.963666i 0.999682 0.0252058i \(-0.00802411\pi\)
0.148770 + 0.988872i \(0.452469\pi\)
\(524\) −9.38573 + 2.22446i −0.410018 + 0.0971760i
\(525\) 0 0
\(526\) −21.8577 14.3761i −0.953043 0.626826i
\(527\) 13.7242 + 9.02658i 0.597838 + 0.393204i
\(528\) 0 0
\(529\) −17.3289 + 4.10702i −0.753429 + 0.178566i
\(530\) −5.90458 4.95453i −0.256479 0.215211i
\(531\) 0 0
\(532\) 0.876079 0.735118i 0.0379828 0.0318714i
\(533\) 0.268521 0.360686i 0.0116309 0.0156230i
\(534\) 0 0
\(535\) 24.5529 + 5.81914i 1.06151 + 0.251583i
\(536\) −1.35086 1.81453i −0.0583485 0.0783756i
\(537\) 0 0
\(538\) −6.18791 3.10769i −0.266780 0.133982i
\(539\) 8.59021 14.8787i 0.370007 0.640870i
\(540\) 0 0
\(541\) 7.30619 + 12.6547i 0.314118 + 0.544068i 0.979250 0.202658i \(-0.0649580\pi\)
−0.665132 + 0.746726i \(0.731625\pi\)
\(542\) 1.01547 + 17.4350i 0.0436182 + 0.748896i
\(543\) 0 0
\(544\) −10.0339 + 1.17279i −0.430199 + 0.0502830i
\(545\) −3.88128 12.9644i −0.166256 0.555334i
\(546\) 0 0
\(547\) −6.01211 13.9376i −0.257059 0.595931i 0.739996 0.672611i \(-0.234827\pi\)
−0.997056 + 0.0766801i \(0.975568\pi\)
\(548\) 3.57164 + 1.29997i 0.152573 + 0.0555320i
\(549\) 0 0
\(550\) −57.4331 + 20.9040i −2.44896 + 0.891348i
\(551\) −2.21826 2.35121i −0.0945009 0.100165i
\(552\) 0 0
\(553\) 20.6341 10.3628i 0.877449 0.440672i
\(554\) −0.831199 + 14.2711i −0.0353143 + 0.606323i
\(555\) 0 0
\(556\) 0.985878 3.29306i 0.0418105 0.139657i
\(557\) −2.44666 + 13.8757i −0.103668 + 0.587931i 0.888076 + 0.459697i \(0.152042\pi\)
−0.991744 + 0.128234i \(0.959069\pi\)
\(558\) 0 0
\(559\) −0.241831 1.37149i −0.0102284 0.0580079i
\(560\) 18.9610 + 2.21622i 0.801249 + 0.0936526i
\(561\) 0 0
\(562\) −12.5740 + 13.3277i −0.530402 + 0.562193i
\(563\) 14.1864 32.8877i 0.597884 1.38605i −0.303418 0.952858i \(-0.598128\pi\)
0.901302 0.433192i \(-0.142613\pi\)
\(564\) 0 0
\(565\) 50.9111 33.4848i 2.14185 1.40871i
\(566\) 30.0885 1.26471
\(567\) 0 0
\(568\) 20.8748 0.875889
\(569\) 23.4530 15.4253i 0.983200 0.646661i 0.0472828 0.998882i \(-0.484944\pi\)
0.935917 + 0.352221i \(0.114573\pi\)
\(570\) 0 0
\(571\) −18.5275 + 42.9516i −0.775353 + 1.79747i −0.199536 + 0.979890i \(0.563943\pi\)
−0.575817 + 0.817579i \(0.695316\pi\)
\(572\) −0.564821 + 0.598676i −0.0236164 + 0.0250319i
\(573\) 0 0
\(574\) 3.21777 + 0.376104i 0.134307 + 0.0156983i
\(575\) −4.13438 23.4472i −0.172415 0.977816i
\(576\) 0 0
\(577\) 3.26382 18.5100i 0.135875 0.770583i −0.838372 0.545098i \(-0.816492\pi\)
0.974247 0.225485i \(-0.0723966\pi\)
\(578\) 1.93008 6.44690i 0.0802806 0.268156i
\(579\) 0 0
\(580\) −0.357128 + 6.13165i −0.0148289 + 0.254603i
\(581\) −12.3015 + 6.17804i −0.510352 + 0.256308i
\(582\) 0 0
\(583\) 5.41051 + 5.73481i 0.224081 + 0.237512i
\(584\) −11.4962 + 4.18426i −0.475714 + 0.173146i
\(585\) 0 0
\(586\) −9.71950 3.53761i −0.401509 0.146137i
\(587\) −0.387163 0.897546i −0.0159799 0.0370457i 0.910039 0.414522i \(-0.136051\pi\)
−0.926019 + 0.377476i \(0.876792\pi\)
\(588\) 0 0
\(589\) −1.57253 5.25262i −0.0647950 0.216431i
\(590\) −47.0450 + 5.49877i −1.93681 + 0.226381i
\(591\) 0 0
\(592\) 1.72399 + 29.5998i 0.0708557 + 1.21655i
\(593\) 19.3929 + 33.5896i 0.796372 + 1.37936i 0.921964 + 0.387276i \(0.126584\pi\)
−0.125592 + 0.992082i \(0.540083\pi\)
\(594\) 0 0
\(595\) −12.3490 + 21.3890i −0.506258 + 0.876865i
\(596\) 11.0504 + 5.54970i 0.452640 + 0.227324i
\(597\) 0 0
\(598\) 0.510788 + 0.686107i 0.0208877 + 0.0280570i
\(599\) −32.3773 7.67356i −1.32290 0.313533i −0.492312 0.870419i \(-0.663848\pi\)
−0.830589 + 0.556886i \(0.811996\pi\)
\(600\) 0 0
\(601\) −12.1572 + 16.3299i −0.495901 + 0.666111i −0.977660 0.210193i \(-0.932591\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(602\) 7.68616 6.44945i 0.313264 0.262860i
\(603\) 0 0
\(604\) −6.05317 5.07922i −0.246300 0.206670i
\(605\) 47.8679 11.3449i 1.94611 0.461236i
\(606\) 0 0
\(607\) 1.32559 + 0.871857i 0.0538042 + 0.0353876i 0.576126 0.817361i \(-0.304564\pi\)
−0.522322 + 0.852748i \(0.674934\pi\)
\(608\) 2.81723 + 1.85292i 0.114254 + 0.0751459i
\(609\) 0 0
\(610\) −3.52799 + 0.836148i −0.142844 + 0.0338547i
\(611\) −0.936970 0.786211i −0.0379058 0.0318067i
\(612\) 0 0
\(613\) −5.23563 + 4.39322i −0.211465 + 0.177440i −0.742368 0.669992i \(-0.766297\pi\)
0.530903 + 0.847433i \(0.321853\pi\)
\(614\) −1.38009 + 1.85379i −0.0556960 + 0.0748127i
\(615\) 0 0
\(616\) −26.9335 6.38336i −1.08518 0.257193i
\(617\) 0.243038 + 0.326456i 0.00978434 + 0.0131426i 0.806988 0.590567i \(-0.201096\pi\)
−0.797204 + 0.603710i \(0.793689\pi\)
\(618\) 0 0
\(619\) 8.95900 + 4.49938i 0.360093 + 0.180845i 0.619642 0.784885i \(-0.287278\pi\)
−0.259550 + 0.965730i \(0.583574\pi\)
\(620\) −5.20911 + 9.02245i −0.209203 + 0.362350i
\(621\) 0 0
\(622\) −9.19862 15.9325i −0.368831 0.638834i
\(623\) 0.587713 + 10.0906i 0.0235462 + 0.404273i
\(624\) 0 0
\(625\) −31.7342 + 3.70920i −1.26937 + 0.148368i
\(626\) 10.6229 + 35.4830i 0.424577 + 1.41819i
\(627\) 0 0
\(628\) −2.45647 5.69473i −0.0980237 0.227245i
\(629\) −36.0465 13.1199i −1.43727 0.523123i
\(630\) 0 0
\(631\) −14.7754 + 5.37779i −0.588198 + 0.214086i −0.618937 0.785441i \(-0.712436\pi\)
0.0307388 + 0.999527i \(0.490214\pi\)
\(632\) 26.1620 + 27.7301i 1.04067 + 1.10304i
\(633\) 0 0
\(634\) 24.7386 12.4242i 0.982495 0.493428i
\(635\) 2.69909 46.3416i 0.107110 1.83901i
\(636\) 0 0
\(637\) −0.316281 + 1.05645i −0.0125315 + 0.0418581i
\(638\) −2.91047 + 16.5061i −0.115227 + 0.653483i
\(639\) 0 0
\(640\) 3.18813 + 18.0808i 0.126022 + 0.714706i
\(641\) 7.99000 + 0.933897i 0.315586 + 0.0368867i 0.272412 0.962181i \(-0.412179\pi\)
0.0431744 + 0.999068i \(0.486253\pi\)
\(642\) 0 0
\(643\) 6.55424 6.94709i 0.258474 0.273966i −0.585121 0.810946i \(-0.698953\pi\)
0.843595 + 0.536979i \(0.180435\pi\)
\(644\) 0.914941 2.12107i 0.0360537 0.0835820i
\(645\) 0 0
\(646\) 3.84130 2.52646i 0.151134 0.0994023i
\(647\) −36.6579 −1.44117 −0.720586 0.693365i \(-0.756127\pi\)
−0.720586 + 0.693365i \(0.756127\pi\)
\(648\) 0 0
\(649\) 48.4492 1.90180
\(650\) 3.27772 2.15579i 0.128563 0.0845571i
\(651\) 0 0
\(652\) 0.170539 0.395355i 0.00667884 0.0154833i
\(653\) 13.2604 14.0552i 0.518918 0.550021i −0.413922 0.910312i \(-0.635841\pi\)
0.932840 + 0.360292i \(0.117323\pi\)
\(654\) 0 0
\(655\) −69.0601 8.07196i −2.69840 0.315398i
\(656\) 0.655261 + 3.71617i 0.0255836 + 0.145092i
\(657\) 0 0
\(658\) 1.53023 8.67834i 0.0596544 0.338317i
\(659\) −8.84575 + 29.5469i −0.344582 + 1.15098i 0.593577 + 0.804777i \(0.297715\pi\)
−0.938159 + 0.346205i \(0.887470\pi\)
\(660\) 0 0
\(661\) −0.928413 + 15.9402i −0.0361111 + 0.620003i 0.930901 + 0.365272i \(0.119024\pi\)
−0.967012 + 0.254731i \(0.918013\pi\)
\(662\) −0.971201 + 0.487755i −0.0377468 + 0.0189572i
\(663\) 0 0
\(664\) −15.5971 16.5320i −0.605285 0.641565i
\(665\) 7.74664 2.81955i 0.300402 0.109337i
\(666\) 0 0
\(667\) −6.13538 2.23310i −0.237563 0.0864659i
\(668\) −1.25368 2.90635i −0.0485062 0.112450i
\(669\) 0 0
\(670\) −1.00192 3.34664i −0.0387074 0.129292i
\(671\) 3.68361 0.430553i 0.142204 0.0166213i
\(672\) 0 0
\(673\) 2.23562 + 38.3841i 0.0861768 + 1.47960i 0.713399 + 0.700758i \(0.247155\pi\)
−0.627223 + 0.778840i \(0.715808\pi\)
\(674\) 21.2053 + 36.7287i 0.816798 + 1.41474i
\(675\) 0 0
\(676\) −3.51794 + 6.09325i −0.135305 + 0.234356i
\(677\) −11.6642 5.85800i −0.448293 0.225141i 0.210305 0.977636i \(-0.432554\pi\)
−0.658599 + 0.752494i \(0.728850\pi\)
\(678\) 0 0
\(679\) 5.11283 + 6.86772i 0.196212 + 0.263559i
\(680\) −39.6791 9.40411i −1.52162 0.360631i
\(681\) 0 0
\(682\) −16.9771 + 22.8042i −0.650087 + 0.873218i
\(683\) 6.97390 5.85180i 0.266849 0.223913i −0.499538 0.866292i \(-0.666497\pi\)
0.766387 + 0.642379i \(0.222053\pi\)
\(684\) 0 0
\(685\) 20.9882 + 17.6112i 0.801916 + 0.672888i
\(686\) −23.0058 + 5.45249i −0.878367 + 0.208177i
\(687\) 0 0
\(688\) 9.76423 + 6.42203i 0.372258 + 0.244838i
\(689\) −0.422821 0.278094i −0.0161082 0.0105945i
\(690\) 0 0
\(691\) 11.6461 2.76019i 0.443040 0.105002i −0.00304009 0.999995i \(-0.500968\pi\)
0.446080 + 0.894993i \(0.352820\pi\)
\(692\) −1.45258 1.21886i −0.0552187 0.0463340i
\(693\) 0 0
\(694\) 14.0210 11.7650i 0.532229 0.446594i
\(695\) 14.7968 19.8755i 0.561273 0.753921i
\(696\) 0 0
\(697\) −4.75039 1.12586i −0.179934 0.0426451i
\(698\) −20.3965 27.3973i −0.772020 1.03700i
\(699\) 0 0
\(700\) −9.46784 4.75493i −0.357851 0.179719i
\(701\) −0.441721 + 0.765084i −0.0166836 + 0.0288968i −0.874247 0.485482i \(-0.838644\pi\)
0.857563 + 0.514379i \(0.171977\pi\)
\(702\) 0 0
\(703\) 6.40198 + 11.0886i 0.241455 + 0.418213i
\(704\) −2.48962 42.7451i −0.0938310 1.61102i
\(705\) 0 0
\(706\) −19.9033 + 2.32637i −0.749072 + 0.0875540i
\(707\) 5.72973 + 19.1386i 0.215489 + 0.719783i
\(708\) 0 0
\(709\) 9.37251 + 21.7279i 0.351992 + 0.816009i 0.998585 + 0.0531741i \(0.0169338\pi\)
−0.646593 + 0.762835i \(0.723807\pi\)
\(710\) 30.2925 + 11.0256i 1.13686 + 0.413782i
\(711\) 0 0
\(712\) −15.6823 + 5.70787i −0.587717 + 0.213912i
\(713\) −7.60000 8.05553i −0.284622 0.301682i
\(714\) 0 0
\(715\) −5.30190 + 2.66271i −0.198280 + 0.0995798i
\(716\) 0.247807 4.25469i 0.00926100 0.159005i
\(717\) 0 0
\(718\) −4.85853 + 16.2286i −0.181319 + 0.605647i
\(719\) −4.25311 + 24.1206i −0.158614 + 0.899547i 0.796792 + 0.604253i \(0.206529\pi\)
−0.955407 + 0.295293i \(0.904583\pi\)
\(720\) 0 0
\(721\) −3.79302 21.5113i −0.141259 0.801122i
\(722\) 21.2370 + 2.48225i 0.790359 + 0.0923797i
\(723\) 0 0
\(724\) 4.37601 4.63830i 0.162633 0.172381i
\(725\) −11.8610 + 27.4968i −0.440505 + 1.02121i
\(726\) 0 0
\(727\) 6.90593 4.54210i 0.256127 0.168457i −0.414952 0.909843i \(-0.636202\pi\)
0.671079 + 0.741386i \(0.265831\pi\)
\(728\) 1.77670 0.0658490
\(729\) 0 0
\(730\) −18.8926 −0.699248
\(731\) −12.6325 + 8.30855i −0.467231 + 0.307303i
\(732\) 0 0
\(733\) −6.03471 + 13.9900i −0.222897 + 0.516734i −0.992566 0.121710i \(-0.961162\pi\)
0.769668 + 0.638444i \(0.220422\pi\)
\(734\) −4.52752 + 4.79889i −0.167114 + 0.177130i
\(735\) 0 0
\(736\) 6.76483 + 0.790695i 0.249355 + 0.0291454i
\(737\) 0.620504 + 3.51905i 0.0228565 + 0.129626i
\(738\) 0 0
\(739\) 4.97375 28.2075i 0.182962 1.03763i −0.745583 0.666413i \(-0.767829\pi\)
0.928545 0.371219i \(-0.121060\pi\)
\(740\) 6.97761 23.3068i 0.256502 0.856776i
\(741\) 0 0
\(742\) 0.212003 3.63994i 0.00778286 0.133627i
\(743\) −13.1865 + 6.62253i −0.483767 + 0.242957i −0.673929 0.738796i \(-0.735395\pi\)
0.190162 + 0.981753i \(0.439099\pi\)
\(744\) 0 0
\(745\) 61.1691 + 64.8355i 2.24106 + 2.37539i
\(746\) −32.0692 + 11.6723i −1.17414 + 0.427352i
\(747\) 0 0
\(748\) 8.39708 + 3.05629i 0.307028 + 0.111749i
\(749\) 4.72767 + 10.9600i 0.172745 + 0.400468i
\(750\) 0 0
\(751\) 2.13409 + 7.12836i 0.0778741 + 0.260118i 0.988057 0.154089i \(-0.0492443\pi\)
−0.910183 + 0.414207i \(0.864059\pi\)
\(752\) 10.1949 1.19161i 0.371768 0.0434535i
\(753\) 0 0
\(754\) −0.0625546 1.07402i −0.00227810 0.0391135i
\(755\) −28.4798 49.3285i −1.03649 1.79525i
\(756\) 0 0
\(757\) −5.40930 + 9.36918i −0.196604 + 0.340529i −0.947425 0.319977i \(-0.896325\pi\)
0.750821 + 0.660506i \(0.229658\pi\)
\(758\) 17.4832 + 8.78041i 0.635019 + 0.318919i
\(759\) 0 0
\(760\) 8.12803 + 10.9178i 0.294835 + 0.396032i
\(761\) 5.54356 + 1.31385i 0.200954 + 0.0476270i 0.329860 0.944030i \(-0.392998\pi\)
−0.128906 + 0.991657i \(0.541147\pi\)
\(762\) 0 0
\(763\) 3.82275 5.13485i 0.138393 0.185894i
\(764\) 6.07829 5.10029i 0.219905 0.184522i
\(765\) 0 0
\(766\) 13.6848 + 11.4829i 0.494453 + 0.414895i
\(767\) −3.02604 + 0.717184i −0.109264 + 0.0258960i
\(768\) 0 0
\(769\) 13.7817 + 9.06435i 0.496980 + 0.326869i 0.773132 0.634245i \(-0.218689\pi\)
−0.276152 + 0.961114i \(0.589059\pi\)
\(770\) −35.7130 23.4888i −1.28701 0.846477i
\(771\) 0 0
\(772\) −9.02936 + 2.14000i −0.324974 + 0.0770202i
\(773\) 1.26612 + 1.06240i 0.0455393 + 0.0382121i 0.665273 0.746600i \(-0.268315\pi\)
−0.619734 + 0.784812i \(0.712759\pi\)
\(774\) 0 0
\(775\) −38.9109 + 32.6502i −1.39772 + 1.17283i
\(776\) −8.44168 + 11.3391i −0.303039 + 0.407052i
\(777\) 0 0
\(778\) 8.76461 + 2.07725i 0.314226 + 0.0744730i
\(779\) 0.973091 + 1.30709i 0.0348646 + 0.0468313i
\(780\) 0 0
\(781\) −29.4669 14.7988i −1.05441 0.529544i
\(782\) 4.64333 8.04248i 0.166045 0.287598i
\(783\) 0 0
\(784\) −4.62716 8.01448i −0.165256 0.286232i
\(785\) −2.59943 44.6304i −0.0927776 1.59293i
\(786\) 0 0
\(787\) 41.3885 4.83762i 1.47534 0.172443i 0.659931 0.751326i \(-0.270586\pi\)
0.815410 + 0.578884i \(0.196512\pi\)
\(788\) −1.94723 6.50420i −0.0693672 0.231703i
\(789\) 0 0
\(790\) 23.3186 + 54.0585i 0.829638 + 1.92332i
\(791\) 27.0865 + 9.85869i 0.963086 + 0.350535i
\(792\) 0 0
\(793\) −0.223698 + 0.0814193i −0.00794374 + 0.00289128i
\(794\) 24.8208 + 26.3085i 0.880857 + 0.933653i
\(795\) 0 0
\(796\) 10.5094 5.27801i 0.372495 0.187074i
\(797\) −2.70404 + 46.4266i −0.0957820 + 1.64451i 0.518247 + 0.855231i \(0.326585\pi\)
−0.614029 + 0.789283i \(0.710452\pi\)
\(798\) 0 0
\(799\) −3.80859 + 12.7216i −0.134738 + 0.450057i
\(800\) 5.42444 30.7635i 0.191783 1.08765i
\(801\) 0 0
\(802\) 1.37223 + 7.78232i 0.0484553 + 0.274803i
\(803\) 19.1943 + 2.24349i 0.677353 + 0.0791712i
\(804\) 0 0
\(805\) 11.4268 12.1117i 0.402743 0.426883i
\(806\) 0.722789 1.67561i 0.0254592 0.0590209i
\(807\) 0 0
\(808\) −27.5587 + 18.1256i −0.969511 + 0.637658i
\(809\) 25.7135 0.904038 0.452019 0.892008i \(-0.350704\pi\)
0.452019 + 0.892008i \(0.350704\pi\)
\(810\) 0 0
\(811\) −33.1951 −1.16564 −0.582818 0.812602i \(-0.698050\pi\)
−0.582818 + 0.812602i \(0.698050\pi\)
\(812\) −2.42744 + 1.59655i −0.0851864 + 0.0560280i
\(813\) 0 0
\(814\) 26.2957 60.9603i 0.921665 2.13666i
\(815\) 2.12989 2.25755i 0.0746068 0.0790786i
\(816\) 0 0
\(817\) 5.01269 + 0.585899i 0.175372 + 0.0204980i
\(818\) 0.374049 + 2.12134i 0.0130783 + 0.0741708i
\(819\) 0 0
\(820\) 0.537666 3.04925i 0.0187761 0.106485i
\(821\) 0.0625495 0.208930i 0.00218299 0.00729170i −0.956891 0.290447i \(-0.906196\pi\)
0.959074 + 0.283155i \(0.0913812\pi\)
\(822\) 0 0
\(823\) −0.900993 + 15.4695i −0.0314066 + 0.539231i 0.945508 + 0.325600i \(0.105566\pi\)
−0.976914 + 0.213631i \(0.931471\pi\)
\(824\) 32.2286 16.1858i 1.12274 0.563860i
\(825\) 0 0
\(826\) −15.3756 16.2972i −0.534986 0.567052i
\(827\) 43.9974 16.0138i 1.52994 0.556853i 0.566334 0.824176i \(-0.308361\pi\)
0.963607 + 0.267323i \(0.0861391\pi\)
\(828\) 0 0
\(829\) −12.5795 4.57858i −0.436905 0.159021i 0.114197 0.993458i \(-0.463570\pi\)
−0.551103 + 0.834438i \(0.685793\pi\)
\(830\) −13.9019 32.2283i −0.482544 1.11866i
\(831\) 0 0
\(832\) 0.788244 + 2.63292i 0.0273274 + 0.0912800i
\(833\) 11.8919 1.38996i 0.412030 0.0481594i
\(834\) 0 0
\(835\) −1.32664 22.7775i −0.0459102 0.788248i
\(836\) −1.49135 2.58309i −0.0515794 0.0893382i
\(837\) 0 0
\(838\) 12.4958 21.6434i 0.431661 0.747659i
\(839\) 21.1461 + 10.6200i 0.730045 + 0.366642i 0.774674 0.632361i \(-0.217914\pi\)
−0.0446286 + 0.999004i \(0.514210\pi\)
\(840\) 0 0
\(841\) −12.4137 16.6745i −0.428058 0.574982i
\(842\) 22.2506 + 5.27348i 0.766806 + 0.181736i
\(843\) 0 0
\(844\) 4.12814 5.54506i 0.142097 0.190869i
\(845\) −38.8518 + 32.6005i −1.33654 + 1.12149i
\(846\) 0 0
\(847\) 17.8263 + 14.9580i 0.612518 + 0.513964i
\(848\) 4.13243 0.979404i 0.141908 0.0336329i
\(849\) 0 0
\(850\) −35.5861 23.4054i −1.22059 0.802797i
\(851\) 21.6076 + 14.2115i 0.740697 + 0.487164i
\(852\) 0 0
\(853\) −29.2236 + 6.92612i −1.00060 + 0.237146i −0.698097 0.716003i \(-0.745970\pi\)
−0.302501 + 0.953149i \(0.597821\pi\)
\(854\) −1.31384 1.10244i −0.0449587 0.0377249i
\(855\) 0 0
\(856\) −15.0969 + 12.6678i −0.516000 + 0.432975i
\(857\) 7.39525 9.93354i 0.252617 0.339323i −0.657666 0.753309i \(-0.728456\pi\)
0.910283 + 0.413986i \(0.135864\pi\)
\(858\) 0 0
\(859\) −37.1696 8.80936i −1.26821 0.300571i −0.459183 0.888342i \(-0.651858\pi\)
−0.809028 + 0.587771i \(0.800006\pi\)
\(860\) −5.72645 7.69195i −0.195270 0.262293i
\(861\) 0 0
\(862\) −0.548139 0.275286i −0.0186697 0.00937628i
\(863\) −1.57263 + 2.72387i −0.0535329 + 0.0927217i −0.891550 0.452922i \(-0.850382\pi\)
0.838017 + 0.545644i \(0.183715\pi\)
\(864\) 0 0
\(865\) −6.83429 11.8373i −0.232373 0.402482i
\(866\) 1.53732 + 26.3948i 0.0522404 + 0.896932i
\(867\) 0 0
\(868\) −4.89488 + 0.572130i −0.166143 + 0.0194193i
\(869\) −17.2715 57.6908i −0.585895 1.95703i
\(870\) 0 0
\(871\) −0.0908473 0.210608i −0.00307824 0.00713617i
\(872\) 9.93208 + 3.61498i 0.336343 + 0.122419i
\(873\) 0 0
\(874\) −2.91281 + 1.06018i −0.0985272 + 0.0358610i
\(875\) −27.3327 28.9709i −0.924013 0.979396i
\(876\) 0 0
\(877\) −33.5229 + 16.8358i −1.13199 + 0.568505i −0.913299 0.407289i \(-0.866474\pi\)
−0.218688 + 0.975795i \(0.570178\pi\)
\(878\) 2.36058 40.5296i 0.0796657 1.36781i
\(879\) 0 0
\(880\) 14.2795 47.6968i 0.481361 1.60786i
\(881\) 4.15332 23.5546i 0.139929 0.793576i −0.831371 0.555718i \(-0.812444\pi\)
0.971300 0.237858i \(-0.0764453\pi\)
\(882\) 0 0
\(883\) 2.98131 + 16.9078i 0.100329 + 0.568994i 0.992984 + 0.118253i \(0.0377293\pi\)
−0.892655 + 0.450742i \(0.851160\pi\)
\(884\) −0.569706 0.0665891i −0.0191613 0.00223963i
\(885\) 0 0
\(886\) −10.1460 + 10.7542i −0.340863 + 0.361293i
\(887\) −1.90630 + 4.41930i −0.0640072 + 0.148385i −0.947217 0.320592i \(-0.896118\pi\)
0.883210 + 0.468977i \(0.155377\pi\)
\(888\) 0 0
\(889\) 18.3460 12.0664i 0.615305 0.404693i
\(890\) −25.7720 −0.863880
\(891\) 0 0
\(892\) 2.68540 0.0899137
\(893\) 3.70329 2.43569i 0.123926 0.0815073i
\(894\) 0 0
\(895\) 12.1681 28.2089i 0.406736 0.942920i
\(896\) −5.95988 + 6.31711i −0.199106 + 0.211040i
\(897\) 0 0
\(898\) 30.3222 + 3.54416i 1.01187 + 0.118270i
\(899\) 2.41882 + 13.7178i 0.0806723 + 0.457515i
\(900\) 0 0
\(901\) −0.954103 + 5.41099i −0.0317858 + 0.180266i
\(902\) 2.42329 8.09436i 0.0806868 0.269513i
\(903\) 0 0
\(904\) −2.76724 + 47.5117i −0.0920370 + 1.58021i
\(905\) 41.0770 20.6296i 1.36544 0.685752i
\(906\) 0 0
\(907\) −14.4151 15.2791i −0.478646 0.507335i 0.442385 0.896825i \(-0.354133\pi\)
−0.921030 + 0.389491i \(0.872651\pi\)
\(908\) 3.29297 1.19854i 0.109281 0.0397751i
\(909\) 0 0
\(910\) 2.57826 + 0.938410i 0.0854685 + 0.0311080i
\(911\) 10.0239 + 23.2381i 0.332108 + 0.769913i 0.999678 + 0.0253663i \(0.00807520\pi\)
−0.667570 + 0.744547i \(0.732666\pi\)
\(912\) 0 0
\(913\) 10.2968 + 34.3938i 0.340775 + 1.13827i
\(914\) 35.0967 4.10222i 1.16090 0.135689i
\(915\) 0 0
\(916\) 0.942843 + 16.1880i 0.0311524 + 0.534866i
\(917\) −16.4452 28.4839i −0.543067 0.940620i
\(918\) 0 0
\(919\) −20.2378 + 35.0529i −0.667583 + 1.15629i 0.310995 + 0.950411i \(0.399338\pi\)
−0.978578 + 0.205876i \(0.933996\pi\)
\(920\) 24.5683 + 12.3387i 0.809994 + 0.406795i
\(921\) 0 0
\(922\) −9.23200 12.4007i −0.304040 0.408396i
\(923\) 2.05951 + 0.488112i 0.0677895 + 0.0160664i
\(924\) 0 0
\(925\) 70.8331 95.1454i 2.32898 3.12836i
\(926\) 9.53925 8.00438i 0.313479 0.263040i
\(927\) 0 0
\(928\) −6.56228 5.50641i −0.215417 0.180757i
\(929\) −14.6660 + 3.47591i −0.481177 + 0.114041i −0.464044 0.885812i \(-0.653602\pi\)
−0.0171330 + 0.999853i \(0.505454\pi\)
\(930\) 0 0
\(931\) −3.33891 2.19604i −0.109428 0.0719721i
\(932\) −9.90372 6.51378i −0.324407 0.213366i
\(933\) 0 0
\(934\) −8.17992 + 1.93868i −0.267655 + 0.0634354i
\(935\) 49.3440 + 41.4046i 1.61372 + 1.35407i
\(936\) 0 0
\(937\) 10.3708 8.70215i 0.338800 0.284287i −0.457474 0.889223i \(-0.651246\pi\)
0.796274 + 0.604936i \(0.206801\pi\)
\(938\) 0.986808 1.32551i 0.0322204 0.0432795i
\(939\) 0 0
\(940\) −8.19518 1.94229i −0.267297 0.0633506i
\(941\) 18.4024 + 24.7187i 0.599900 + 0.805806i 0.993543 0.113458i \(-0.0361927\pi\)
−0.393643 + 0.919264i \(0.628785\pi\)
\(942\) 0 0
\(943\) 2.94133 + 1.47719i 0.0957829 + 0.0481040i
\(944\) 13.0487 22.6010i 0.424699 0.735601i
\(945\) 0 0
\(946\) −13.0842 22.6624i −0.425403 0.736819i
\(947\) 2.88862 + 49.5957i 0.0938676 + 1.61164i 0.636230 + 0.771499i \(0.280493\pi\)
−0.542362 + 0.840145i \(0.682470\pi\)
\(948\) 0 0
\(949\) −1.23205 + 0.144006i −0.0399940 + 0.00467462i
\(950\) 4.07748 + 13.6197i 0.132291 + 0.441882i
\(951\) 0 0
\(952\) −7.64023 17.7120i −0.247621 0.574051i
\(953\) −21.4128 7.79362i −0.693629 0.252460i −0.0289406 0.999581i \(-0.509213\pi\)
−0.664688 + 0.747121i \(0.731436\pi\)
\(954\) 0 0
\(955\) 53.7466 19.5622i 1.73920 0.633017i
\(956\) −2.22579 2.35920i −0.0719872 0.0763019i
\(957\) 0 0
\(958\) 36.0371 18.0985i 1.16431 0.584737i
\(959\) −0.753575 + 12.9384i −0.0243342 + 0.417802i
\(960\) 0 0
\(961\) 2.11450 7.06294i 0.0682098 0.227837i
\(962\) −0.739993 + 4.19671i −0.0238583 + 0.135307i
\(963\) 0 0
\(964\) 0.112305 + 0.636915i 0.00361711 + 0.0205136i
\(965\) −66.4379 7.76547i −2.13871 0.249979i
\(966\) 0 0
\(967\) −39.1298 + 41.4751i −1.25833 + 1.33375i −0.338733 + 0.940883i \(0.609998\pi\)
−0.919595 + 0.392867i \(0.871483\pi\)
\(968\) −15.2180 + 35.2793i −0.489125 + 1.13392i
\(969\) 0 0
\(970\) −18.2392 + 11.9961i −0.585625 + 0.385171i
\(971\) −38.8020 −1.24521 −0.622607 0.782535i \(-0.713926\pi\)
−0.622607 + 0.782535i \(0.713926\pi\)
\(972\) 0 0
\(973\) 11.7212 0.375765
\(974\) 8.74221 5.74984i 0.280119 0.184237i
\(975\) 0 0
\(976\) 0.791251 1.83433i 0.0253273 0.0587153i
\(977\) −29.9675 + 31.7637i −0.958747 + 1.01621i 0.0411080 + 0.999155i \(0.486911\pi\)
−0.999855 + 0.0170572i \(0.994570\pi\)
\(978\) 0 0
\(979\) 26.1835 + 3.06042i 0.836829 + 0.0978113i
\(980\) 1.31860 + 7.47815i 0.0421211 + 0.238881i
\(981\) 0 0
\(982\) −3.36694 + 19.0949i −0.107443 + 0.609342i
\(983\) 10.0516 33.5745i 0.320595 1.07086i −0.634094 0.773256i \(-0.718627\pi\)
0.954689 0.297605i \(-0.0961880\pi\)
\(984\) 0 0
\(985\) 2.84566 48.8580i 0.0906702 1.55675i
\(986\) −10.4380 + 5.24214i −0.332412 + 0.166944i
\(987\) 0 0
\(988\) 0.131384 + 0.139259i 0.00417987 + 0.00443041i
\(989\) 9.57909 3.48651i 0.304597 0.110864i
\(990\) 0 0
\(991\) −0.299988 0.109187i −0.00952943 0.00346843i 0.337251 0.941415i \(-0.390503\pi\)
−0.346780 + 0.937946i \(0.612725\pi\)
\(992\) −5.75525 13.3422i −0.182729 0.423614i
\(993\) 0 0
\(994\) 4.37349 + 14.6085i 0.138719 + 0.463353i
\(995\) 84.1995 9.84151i 2.66930 0.311997i
\(996\) 0 0
\(997\) −0.625507 10.7395i −0.0198100 0.340125i −0.993621 0.112767i \(-0.964029\pi\)
0.973811 0.227357i \(-0.0730085\pi\)
\(998\) −4.65872 8.06914i −0.147469 0.255424i
\(999\) 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 729.2.g.b.28.3 144
3.2 odd 2 729.2.g.c.28.6 144
9.2 odd 6 81.2.g.a.13.3 144
9.4 even 3 729.2.g.a.514.3 144
9.5 odd 6 729.2.g.d.514.6 144
9.7 even 3 243.2.g.a.10.6 144
81.2 odd 54 81.2.g.a.25.3 yes 144
81.25 even 27 729.2.g.a.217.3 144
81.29 odd 54 729.2.g.c.703.6 144
81.32 odd 54 6561.2.a.c.1.24 72
81.49 even 27 6561.2.a.d.1.49 72
81.52 even 27 inner 729.2.g.b.703.3 144
81.56 odd 54 729.2.g.d.217.6 144
81.79 even 27 243.2.g.a.73.6 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.3 144 9.2 odd 6
81.2.g.a.25.3 yes 144 81.2 odd 54
243.2.g.a.10.6 144 9.7 even 3
243.2.g.a.73.6 144 81.79 even 27
729.2.g.a.217.3 144 81.25 even 27
729.2.g.a.514.3 144 9.4 even 3
729.2.g.b.28.3 144 1.1 even 1 trivial
729.2.g.b.703.3 144 81.52 even 27 inner
729.2.g.c.28.6 144 3.2 odd 2
729.2.g.c.703.6 144 81.29 odd 54
729.2.g.d.217.6 144 81.56 odd 54
729.2.g.d.514.6 144 9.5 odd 6
6561.2.a.c.1.24 72 81.32 odd 54
6561.2.a.d.1.49 72 81.49 even 27