Properties

Label 729.2.g.c.703.6
Level $729$
Weight $2$
Character 729.703
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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 703.6
Character \(\chi\) \(=\) 729.703
Dual form 729.2.g.c.28.6

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{27}\right)\)

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 \(-0.174587\pi\)
−0.140769 + 0.990042i \(0.544958\pi\)
\(3\) 0 0
\(4\) −0.215977 0.500690i −0.107988 0.250345i
\(5\) 2.69736 + 2.85904i 1.20630 + 1.27860i 0.950089 + 0.311979i \(0.100992\pi\)
0.256208 + 0.966622i \(0.417527\pi\)
\(6\) 0 0
\(7\) −1.84676 + 0.215855i −0.698010 + 0.0815857i −0.457695 0.889109i \(-0.651325\pi\)
−0.240315 + 0.970695i \(0.577251\pi\)
\(8\) 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 0.863322 + 0.504654i \(0.168380\pi\)
−0.443983 + 0.896035i \(0.646435\pi\)
\(12\) 0 0
\(13\) 0.0180985 + 0.310740i 0.00501963 + 0.0861838i 0.999888 0.0149987i \(-0.00477443\pi\)
−0.994868 + 0.101183i \(0.967737\pi\)
\(14\) −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 \(-0.254483\pi\)
0.0731188 + 0.997323i \(0.476705\pi\)
\(18\) 0 0
\(19\) 1.05997 0.385798i 0.243174 0.0885081i −0.217558 0.976047i \(-0.569809\pi\)
0.460732 + 0.887539i \(0.347587\pi\)
\(20\) 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 \(-0.539304\pi\)
−0.348703 + 0.937233i \(0.613378\pi\)
\(24\) 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 \(-0.562423\pi\)
0.670391 + 0.742008i \(0.266126\pi\)
\(30\) 0 0
\(31\) −2.90267 + 3.89896i −0.521334 + 0.700273i −0.982336 0.187126i \(-0.940083\pi\)
0.461002 + 0.887399i \(0.347490\pi\)
\(32\) −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 0.483519 0.875334i \(-0.339358\pi\)
0.945998 0.324173i \(-0.105086\pi\)
\(38\) 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 \(-0.721169\pi\)
0.451753 + 0.892143i \(0.350799\pi\)
\(42\) 0 0
\(43\) 4.35354 + 1.03181i 0.663908 + 0.157349i 0.548735 0.835996i \(-0.315110\pi\)
0.115173 + 0.993345i \(0.463258\pi\)
\(44\) 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 \(-0.296225\pi\)
−0.939616 + 0.342230i \(0.888818\pi\)
\(48\) 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 \(-0.202285\pi\)
−0.916442 + 0.400168i \(0.868952\pi\)
\(54\) 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 −0.541190 0.840900i \(-0.682026\pi\)
0.914240 0.405173i \(-0.132789\pi\)
\(60\) 0 0
\(61\) −0.302918 + 0.702244i −0.0387847 + 0.0899131i −0.936507 0.350648i \(-0.885961\pi\)
0.897723 + 0.440561i \(0.145221\pi\)
\(62\) −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 0.488569 0.872525i \(-0.337519\pi\)
−0.408120 + 0.912928i \(0.633816\pi\)
\(68\) −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 0.971147 + 0.238481i \(0.0766493\pi\)
−0.831015 + 0.556250i \(0.812240\pi\)
\(72\) 0 0
\(73\) −0.692009 + 3.92458i −0.0809935 + 0.459337i 0.917156 + 0.398529i \(0.130479\pi\)
−0.998149 + 0.0608086i \(0.980632\pi\)
\(74\) 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 −0.190483 0.981691i \(-0.561005\pi\)
−0.976850 + 0.213923i \(0.931376\pi\)
\(80\) 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 \(-0.448004\pi\)
−0.841581 + 0.540131i \(0.818375\pi\)
\(84\) 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 −0.893015 0.450027i \(-0.851414\pi\)
0.993078 0.117458i \(-0.0374744\pi\)
\(90\) 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 −0.867645 0.497185i \(-0.834367\pi\)
0.546792 + 0.837268i \(0.315849\pi\)
\(98\) −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 −0.564277 0.825586i \(-0.690845\pi\)
0.987740 0.156111i \(-0.0498958\pi\)
\(102\) 0 0
\(103\) 3.36931 11.2543i 0.331988 1.10892i −0.615235 0.788344i \(-0.710939\pi\)
0.947223 0.320575i \(-0.103876\pi\)
\(104\) 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 \(-0.732903\pi\)
0.978428 + 0.206589i \(0.0662363\pi\)
\(108\) 0 0
\(109\) −1.72147 2.98167i −0.164887 0.285592i 0.771728 0.635952i \(-0.219393\pi\)
−0.936615 + 0.350360i \(0.886059\pi\)
\(110\) −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 \(-0.313971\pi\)
0.867348 + 0.497702i \(0.165823\pi\)
\(114\) 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 0.146093 0.989271i \(-0.453330\pi\)
−0.948873 + 0.315659i \(0.897775\pi\)
\(128\) −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 0.0476433 + 0.998864i \(0.484829\pi\)
−0.970566 + 0.240836i \(0.922578\pi\)
\(132\) 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 −0.935712 0.352765i \(-0.885242\pi\)
0.970339 0.241750i \(-0.0777213\pi\)
\(138\) 0 0
\(139\) −6.26136 0.731848i −0.531081 0.0620745i −0.153674 0.988122i \(-0.549110\pi\)
−0.377408 + 0.926047i \(0.623184\pi\)
\(140\) −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 −0.423710 0.905798i \(-0.639272\pi\)
0.315688 0.948863i \(-0.397765\pi\)
\(150\) 0 0
\(151\) −4.15613 13.8824i −0.338221 1.12974i −0.942847 0.333227i \(-0.891862\pi\)
0.604625 0.796510i \(-0.293323\pi\)
\(152\) −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 0.336682 0.941618i \(-0.390695\pi\)
−0.959602 + 0.281363i \(0.909214\pi\)
\(158\) −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 \(-0.168636\pi\)
−0.554668 + 0.832071i \(0.687155\pi\)
\(168\) 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 \(-0.0503907\pi\)
−0.911669 + 0.410926i \(0.865206\pi\)
\(174\) 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 \(-0.294537\pi\)
−0.0526260 + 0.998614i \(0.516759\pi\)
\(180\) 0 0
\(181\) −10.9891 + 3.99971i −0.816815 + 0.297296i −0.716436 0.697653i \(-0.754228\pi\)
−0.100379 + 0.994949i \(0.532006\pi\)
\(182\) 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 \(-0.471671\pi\)
0.852024 + 0.523502i \(0.175375\pi\)
\(192\) 0 0
\(193\) 10.1622 13.6503i 0.731494 0.982568i −0.268320 0.963330i \(-0.586469\pi\)
0.999815 0.0192379i \(-0.00612399\pi\)
\(194\) −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 \(-0.131495\pi\)
−0.236315 + 0.971676i \(0.575940\pi\)
\(198\) 0 0
\(199\) −16.5214 + 13.8631i −1.17117 + 0.982731i −0.999997 0.00250896i \(-0.999201\pi\)
−0.171177 + 0.985240i \(0.554757\pi\)
\(200\) 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 −0.632121 0.774870i \(-0.717815\pi\)
−0.217123 + 0.976144i \(0.569667\pi\)
\(212\) −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 −0.970958 0.239251i \(-0.923098\pi\)
0.840336 + 0.542065i \(0.182357\pi\)
\(224\) 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 \(-0.690847\pi\)
0.856995 + 0.515324i \(0.172328\pi\)
\(228\) 0 0
\(229\) 26.5744 + 13.3462i 1.75608 + 0.881939i 0.961509 + 0.274773i \(0.0886026\pi\)
0.794575 + 0.607166i \(0.207694\pi\)
\(230\) −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 0.815087 + 0.579339i \(0.196689\pi\)
−0.567786 + 0.823176i \(0.692200\pi\)
\(234\) 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 \(-0.0680099\pi\)
−0.824868 + 0.565325i \(0.808751\pi\)
\(240\) 0 0
\(241\) 0.990937 + 0.651749i 0.0638318 + 0.0419829i 0.581024 0.813887i \(-0.302652\pi\)
−0.517192 + 0.855869i \(0.673023\pi\)
\(242\) −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 −0.816789 0.576937i \(-0.804248\pi\)
0.964854 0.262785i \(-0.0846410\pi\)
\(252\) 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 \(-0.628363\pi\)
−0.972120 + 0.234486i \(0.924659\pi\)
\(258\) 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 0.417795 + 0.908541i \(0.362803\pi\)
−0.947557 + 0.319586i \(0.896456\pi\)
\(264\) 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 \(-0.889333\pi\)
0.765148 + 0.643855i \(0.222666\pi\)
\(270\) 0 0
\(271\) 7.23998 + 12.5400i 0.439798 + 0.761752i 0.997674 0.0681726i \(-0.0217169\pi\)
−0.557876 + 0.829924i \(0.688384\pi\)
\(272\) 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 0.962182 0.272408i \(-0.0878202\pi\)
−0.536921 + 0.843632i \(0.680413\pi\)
\(278\) −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 \(-0.575619\pi\)
−0.646498 + 0.762915i \(0.723767\pi\)
\(282\) 0 0
\(283\) −20.8426 + 13.7084i −1.23896 + 0.814880i −0.988200 0.153168i \(-0.951052\pi\)
−0.250764 + 0.968048i \(0.580682\pi\)
\(284\) 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 \(-0.876891\pi\)
0.626962 + 0.779050i \(0.284298\pi\)
\(294\) 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 0.392891 0.919585i \(-0.371475\pi\)
−0.290126 + 0.956989i \(0.593697\pi\)
\(308\) −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 0.925270 + 0.379310i \(0.123838\pi\)
−0.874978 + 0.484162i \(0.839124\pi\)
\(312\) 0 0
\(313\) 8.80754 + 29.4192i 0.497832 + 1.66287i 0.724790 + 0.688969i \(0.241937\pi\)
−0.226959 + 0.973904i \(0.572878\pi\)
\(314\) −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 \(-0.314075\pi\)
0.728966 + 0.684549i \(0.240001\pi\)
\(318\) 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 −0.0914610 0.995809i \(-0.529154\pi\)
0.140654 + 0.990059i \(0.455080\pi\)
\(332\) −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 0.342885 + 0.939377i \(0.388596\pi\)
−0.231511 + 0.972832i \(0.574367\pi\)
\(338\) 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 \(-0.329425\pi\)
0.298545 + 0.954396i \(0.403499\pi\)
\(348\) 0 0
\(349\) 1.64660 28.2711i 0.0881406 1.51332i −0.607151 0.794587i \(-0.707688\pi\)
0.695291 0.718728i \(-0.255275\pi\)
\(350\) 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 \(-0.793931\pi\)
0.00743042 + 0.999972i \(0.497635\pi\)
\(354\) 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 \(-0.398640\pi\)
−0.880934 + 0.473239i \(0.843085\pi\)
\(360\) 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 0.367173 0.930153i \(-0.380326\pi\)
−0.0893336 + 0.996002i \(0.528474\pi\)
\(368\) −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 0.555805 0.831313i \(-0.312410\pi\)
0.869778 + 0.493443i \(0.164262\pi\)
\(374\) −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 −0.995595 0.0937537i \(-0.970113\pi\)
0.578991 + 0.815334i \(0.303447\pi\)
\(380\) 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 −0.778220 0.627992i \(-0.783877\pi\)
0.995280 0.0970408i \(-0.0309377\pi\)
\(384\) 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 \(-0.698630\pi\)
0.844141 + 0.536121i \(0.180111\pi\)
\(390\) 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 0.517876 + 0.855455i \(0.326723\pi\)
−0.779228 + 0.626741i \(0.784388\pi\)
\(398\) −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 \(-0.181938\pi\)
−0.970642 + 0.240529i \(0.922679\pi\)
\(402\) 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 0.934809 0.355150i \(-0.115570\pi\)
−0.899832 + 0.436237i \(0.856311\pi\)
\(410\) −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 \(-0.182924\pi\)
0.0652339 + 0.997870i \(0.479221\pi\)
\(420\) 0 0
\(421\) −13.0106 + 13.7904i −0.634097 + 0.672103i −0.962139 0.272560i \(-0.912130\pi\)
0.328042 + 0.944663i \(0.393611\pi\)
\(422\) −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 \(-0.837232\pi\)
0.859836 + 0.510570i \(0.170566\pi\)
\(432\) 0 0
\(433\) 10.9606 + 18.9844i 0.526734 + 0.912330i 0.999515 + 0.0311498i \(0.00991689\pi\)
−0.472781 + 0.881180i \(0.656750\pi\)
\(434\) 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 −0.957441 0.288629i \(-0.906801\pi\)
−0.00190618 0.999998i \(-0.500607\pi\)
\(440\) 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 \(-0.519982\pi\)
−0.503976 + 0.863717i \(0.668130\pi\)
\(444\) 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 \(-0.518477\pi\)
0.973075 + 0.230490i \(0.0740328\pi\)
\(450\) 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 −0.939216 0.343327i \(-0.888446\pi\)
−0.285470 + 0.958388i \(0.592150\pi\)
\(458\) 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 0.935441 + 0.353484i \(0.115003\pi\)
−0.970152 + 0.242496i \(0.922034\pi\)
\(462\) 0 0
\(463\) −10.2547 1.19861i −0.476578 0.0557040i −0.125587 0.992083i \(-0.540081\pi\)
−0.350992 + 0.936379i \(0.614155\pi\)
\(464\) 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 \(-0.662668\pi\)
0.186005 + 0.982549i \(0.440446\pi\)
\(468\) 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 \(-0.260347\pi\)
0.833605 + 0.552361i \(0.186273\pi\)
\(480\) 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 \(-0.358902\pi\)
−0.926763 + 0.375646i \(0.877421\pi\)
\(492\) 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 −0.993325 0.115351i \(-0.963201\pi\)
0.973217 0.229889i \(-0.0738365\pi\)
\(500\) 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 \(-0.130885\pi\)
0.445272 + 0.895395i \(0.353107\pi\)
\(504\) 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 \(-0.471778\pi\)
−0.143550 + 0.989643i \(0.545852\pi\)
\(510\) 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 \(-0.449444\pi\)
−0.944948 + 0.327220i \(0.893888\pi\)
\(522\) 0 0
\(523\) 26.2642 22.0383i 1.14845 0.963666i 0.148770 0.988872i \(-0.452469\pi\)
0.999682 + 0.0252058i \(0.00802411\pi\)
\(524\) 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 −0.665132 0.746726i \(-0.731625\pi\)
0.979250 + 0.202658i \(0.0649580\pi\)
\(542\) −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 −0.997056 0.0766801i \(-0.975568\pi\)
0.739996 + 0.672611i \(0.234827\pi\)
\(548\) −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 0.991744 + 0.128234i \(0.0409309\pi\)
−0.888076 + 0.459697i \(0.847958\pi\)
\(558\) 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 −0.901302 0.433192i \(-0.857387\pi\)
0.303418 0.952858i \(-0.401872\pi\)
\(564\) 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 \(-0.515056\pi\)
−0.935917 + 0.352221i \(0.885427\pi\)
\(570\) 0 0
\(571\) −18.5275 42.9516i −0.775353 1.79747i −0.575817 0.817579i \(-0.695316\pi\)
−0.199536 0.979890i \(-0.563943\pi\)
\(572\) 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 0.974247 + 0.225485i \(0.0723966\pi\)
−0.838372 + 0.545098i \(0.816492\pi\)
\(578\) −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 \(-0.863949\pi\)
0.926019 + 0.377476i \(0.123208\pi\)
\(588\) 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 0.125592 + 0.992082i \(0.459917\pi\)
−0.921964 + 0.387276i \(0.873416\pi\)
\(594\) 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 \(-0.336152\pi\)
0.830589 + 0.556886i \(0.188004\pi\)
\(600\) 0 0
\(601\) −12.1572 16.3299i −0.495901 0.666111i 0.481759 0.876304i \(-0.339998\pi\)
−0.977660 + 0.210193i \(0.932591\pi\)
\(602\) −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 −0.522322 0.852748i \(-0.674934\pi\)
0.576126 + 0.817361i \(0.304564\pi\)
\(608\) −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 0.530903 0.847433i \(-0.321853\pi\)
−0.742368 + 0.669992i \(0.766297\pi\)
\(614\) 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 \(-0.798904\pi\)
0.797204 + 0.603710i \(0.206311\pi\)
\(618\) 0 0
\(619\) 8.95900 4.49938i 0.360093 0.180845i −0.259550 0.965730i \(-0.583574\pi\)
0.619642 + 0.784885i \(0.287278\pi\)
\(620\) 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 0.0307388 0.999527i \(-0.490214\pi\)
−0.618937 + 0.785441i \(0.712436\pi\)
\(632\) −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 \(-0.587821\pi\)
−0.0431744 + 0.999068i \(0.513747\pi\)
\(642\) 0 0
\(643\) 6.55424 + 6.94709i 0.258474 + 0.273966i 0.843595 0.536979i \(-0.180435\pi\)
−0.585121 + 0.810946i \(0.698953\pi\)
\(644\) −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 \(-0.243873\pi\)
0.720586 + 0.693365i \(0.243873\pi\)
\(648\) 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 \(-0.364159\pi\)
−0.932840 + 0.360292i \(0.882677\pi\)
\(654\) 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 0.938159 + 0.346205i \(0.112530\pi\)
−0.593577 + 0.804777i \(0.702285\pi\)
\(660\) 0 0
\(661\) −0.928413 15.9402i −0.0361111 0.620003i −0.967012 0.254731i \(-0.918013\pi\)
0.930901 0.365272i \(-0.119024\pi\)
\(662\) 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 −0.627223 0.778840i \(-0.715808\pi\)
0.713399 0.700758i \(-0.247155\pi\)
\(674\) −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 \(-0.567446\pi\)
0.658599 + 0.752494i \(0.271150\pi\)
\(678\) 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 \(-0.333503\pi\)
−0.766387 + 0.642379i \(0.777947\pi\)
\(684\) 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 0.446080 0.894993i \(-0.352820\pi\)
−0.00304009 + 0.999995i \(0.500968\pi\)
\(692\) 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 \(-0.161356\pi\)
−0.857563 + 0.514379i \(0.828023\pi\)
\(702\) 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 −0.646593 0.762835i \(-0.723807\pi\)
0.998585 0.0531741i \(-0.0169338\pi\)
\(710\) −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 0.955407 + 0.295293i \(0.0954174\pi\)
−0.796792 + 0.604253i \(0.793471\pi\)
\(720\) 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 0.671079 0.741386i \(-0.265831\pi\)
−0.414952 + 0.909843i \(0.636202\pi\)
\(728\) −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 0.769668 0.638444i \(-0.220422\pi\)
−0.992566 + 0.121710i \(0.961162\pi\)
\(734\) 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 0.928545 + 0.371219i \(0.121060\pi\)
−0.745583 + 0.666413i \(0.767829\pi\)
\(740\) −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 \(-0.264605\pi\)
−0.190162 + 0.981753i \(0.560901\pi\)
\(744\) 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 −0.910183 0.414207i \(-0.864059\pi\)
0.988057 + 0.154089i \(0.0492443\pi\)
\(752\) −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 0.750821 0.660506i \(-0.229658\pi\)
−0.947425 + 0.319977i \(0.896325\pi\)
\(758\) −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 \(-0.607002\pi\)
0.128906 + 0.991657i \(0.458853\pi\)
\(762\) 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 −0.276152 0.961114i \(-0.589059\pi\)
0.773132 + 0.634245i \(0.218689\pi\)
\(770\) 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 \(-0.731685\pi\)
0.619734 + 0.784812i \(0.287241\pi\)
\(774\) 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