Properties

Label 729.2.g.a.28.6
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 28.6
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.a.703.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26928 - 0.834819i) q^{2} +(0.121992 - 0.282809i) q^{4} +(-0.0546290 + 0.0579033i) q^{5} +(0.848729 + 0.0992022i) q^{7} +(0.446364 + 2.53145i) q^{8} +O(q^{10})\) \(q+(1.26928 - 0.834819i) q^{2} +(0.121992 - 0.282809i) q^{4} +(-0.0546290 + 0.0579033i) q^{5} +(0.848729 + 0.0992022i) q^{7} +(0.446364 + 2.53145i) q^{8} +(-0.0210007 + 0.119101i) q^{10} +(1.14520 - 3.82522i) q^{11} +(0.117949 - 2.02511i) q^{13} +(1.16009 - 0.582620i) q^{14} +(3.10259 + 3.28855i) q^{16} +(1.92609 - 0.701038i) q^{17} +(5.26032 + 1.91460i) q^{19} +(0.00971128 + 0.0225133i) q^{20} +(-1.73979 - 5.81131i) q^{22} +(7.45312 - 0.871145i) q^{23} +(0.290356 + 4.98521i) q^{25} +(-1.54089 - 2.66890i) q^{26} +(0.131593 - 0.227926i) q^{28} +(-0.993107 - 0.498757i) q^{29} +(3.57847 + 4.80672i) q^{31} +(1.68097 + 0.398397i) q^{32} +(1.85950 - 2.49775i) q^{34} +(-0.0521094 + 0.0437249i) q^{35} +(-0.782274 - 0.656406i) q^{37} +(8.27517 - 1.96125i) q^{38} +(-0.170964 - 0.112445i) q^{40} +(-3.65733 - 2.40547i) q^{41} +(-11.6846 + 2.76930i) q^{43} +(-0.942101 - 0.790516i) q^{44} +(8.73286 - 7.32774i) q^{46} +(-3.07256 + 4.12716i) q^{47} +(-6.10081 - 1.44592i) q^{49} +(4.53030 + 6.08524i) q^{50} +(-0.558330 - 0.280404i) q^{52} +(5.16096 - 8.93905i) q^{53} +(0.158932 + 0.275278i) q^{55} +(0.127716 + 2.19280i) q^{56} +(-1.67690 + 0.196002i) q^{58} +(-3.14185 - 10.4945i) q^{59} +(-4.21089 - 9.76194i) q^{61} +(8.55483 + 3.11370i) q^{62} +(-6.03074 + 2.19501i) q^{64} +(0.110817 + 0.117459i) q^{65} +(-4.10628 + 2.06225i) q^{67} +(0.0367070 - 0.630234i) q^{68} +(-0.0296390 + 0.0990011i) q^{70} +(0.963622 - 5.46497i) q^{71} +(0.267464 + 1.51686i) q^{73} +(-1.54091 - 0.180106i) q^{74} +(1.18318 - 1.25410i) q^{76} +(1.35143 - 3.13297i) q^{77} +(-11.4068 + 7.50239i) q^{79} -0.359909 q^{80} -6.65031 q^{82} +(-5.24973 + 3.45280i) q^{83} +(-0.0646276 + 0.149824i) q^{85} +(-12.5192 + 13.2696i) q^{86} +(10.1945 + 1.19157i) q^{88} +(1.79520 + 10.1811i) q^{89} +(0.301002 - 1.70707i) q^{91} +(0.662852 - 2.21408i) q^{92} +(-0.454506 + 7.80356i) q^{94} +(-0.398228 + 0.199997i) q^{95} +(9.42786 + 9.99295i) q^{97} +(-8.95073 + 3.25780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26928 0.834819i 0.897517 0.590306i −0.0147548 0.999891i \(-0.504697\pi\)
0.912272 + 0.409585i \(0.134326\pi\)
\(3\) 0 0
\(4\) 0.121992 0.282809i 0.0609959 0.141404i
\(5\) −0.0546290 + 0.0579033i −0.0244308 + 0.0258952i −0.739474 0.673185i \(-0.764926\pi\)
0.715043 + 0.699080i \(0.246407\pi\)
\(6\) 0 0
\(7\) 0.848729 + 0.0992022i 0.320790 + 0.0374949i 0.274964 0.961455i \(-0.411334\pi\)
0.0458256 + 0.998949i \(0.485408\pi\)
\(8\) 0.446364 + 2.53145i 0.157813 + 0.895004i
\(9\) 0 0
\(10\) −0.0210007 + 0.119101i −0.00664101 + 0.0376630i
\(11\) 1.14520 3.82522i 0.345289 1.15335i −0.592333 0.805693i \(-0.701793\pi\)
0.937623 0.347654i \(-0.113022\pi\)
\(12\) 0 0
\(13\) 0.117949 2.02511i 0.0327132 0.561664i −0.941637 0.336629i \(-0.890713\pi\)
0.974351 0.225035i \(-0.0722498\pi\)
\(14\) 1.16009 0.582620i 0.310048 0.155712i
\(15\) 0 0
\(16\) 3.10259 + 3.28855i 0.775647 + 0.822138i
\(17\) 1.92609 0.701038i 0.467144 0.170027i −0.0977140 0.995215i \(-0.531153\pi\)
0.564858 + 0.825188i \(0.308931\pi\)
\(18\) 0 0
\(19\) 5.26032 + 1.91460i 1.20680 + 0.439239i 0.865593 0.500749i \(-0.166942\pi\)
0.341207 + 0.939988i \(0.389164\pi\)
\(20\) 0.00971128 + 0.0225133i 0.00217151 + 0.00503412i
\(21\) 0 0
\(22\) −1.73979 5.81131i −0.370925 1.23898i
\(23\) 7.45312 0.871145i 1.55408 0.181646i 0.704732 0.709474i \(-0.251067\pi\)
0.849352 + 0.527827i \(0.176993\pi\)
\(24\) 0 0
\(25\) 0.290356 + 4.98521i 0.0580711 + 0.997043i
\(26\) −1.54089 2.66890i −0.302193 0.523414i
\(27\) 0 0
\(28\) 0.131593 0.227926i 0.0248688 0.0430740i
\(29\) −0.993107 0.498757i −0.184415 0.0926169i 0.354196 0.935171i \(-0.384755\pi\)
−0.538611 + 0.842554i \(0.681051\pi\)
\(30\) 0 0
\(31\) 3.57847 + 4.80672i 0.642712 + 0.863313i 0.997429 0.0716613i \(-0.0228301\pi\)
−0.354717 + 0.934974i \(0.615423\pi\)
\(32\) 1.68097 + 0.398397i 0.297156 + 0.0704274i
\(33\) 0 0
\(34\) 1.85950 2.49775i 0.318902 0.428360i
\(35\) −0.0521094 + 0.0437249i −0.00880809 + 0.00739086i
\(36\) 0 0
\(37\) −0.782274 0.656406i −0.128605 0.107913i 0.576216 0.817297i \(-0.304529\pi\)
−0.704822 + 0.709385i \(0.748973\pi\)
\(38\) 8.27517 1.96125i 1.34241 0.318157i
\(39\) 0 0
\(40\) −0.170964 0.112445i −0.0270318 0.0177791i
\(41\) −3.65733 2.40547i −0.571180 0.375671i 0.230819 0.972997i \(-0.425859\pi\)
−0.801999 + 0.597326i \(0.796230\pi\)
\(42\) 0 0
\(43\) −11.6846 + 2.76930i −1.78189 + 0.422315i −0.983659 0.180043i \(-0.942376\pi\)
−0.798227 + 0.602357i \(0.794228\pi\)
\(44\) −0.942101 0.790516i −0.142027 0.119175i
\(45\) 0 0
\(46\) 8.73286 7.32774i 1.28759 1.08042i
\(47\) −3.07256 + 4.12716i −0.448179 + 0.602008i −0.967593 0.252514i \(-0.918743\pi\)
0.519415 + 0.854522i \(0.326150\pi\)
\(48\) 0 0
\(49\) −6.10081 1.44592i −0.871545 0.206560i
\(50\) 4.53030 + 6.08524i 0.640681 + 0.860583i
\(51\) 0 0
\(52\) −0.558330 0.280404i −0.0774264 0.0388850i
\(53\) 5.16096 8.93905i 0.708913 1.22787i −0.256348 0.966584i \(-0.582519\pi\)
0.965261 0.261288i \(-0.0841473\pi\)
\(54\) 0 0
\(55\) 0.158932 + 0.275278i 0.0214304 + 0.0371185i
\(56\) 0.127716 + 2.19280i 0.0170668 + 0.293025i
\(57\) 0 0
\(58\) −1.67690 + 0.196002i −0.220188 + 0.0257363i
\(59\) −3.14185 10.4945i −0.409034 1.36627i −0.876136 0.482064i \(-0.839887\pi\)
0.467102 0.884203i \(-0.345298\pi\)
\(60\) 0 0
\(61\) −4.21089 9.76194i −0.539149 1.24989i −0.942304 0.334757i \(-0.891346\pi\)
0.403155 0.915132i \(-0.367914\pi\)
\(62\) 8.55483 + 3.11370i 1.08646 + 0.395441i
\(63\) 0 0
\(64\) −6.03074 + 2.19501i −0.753842 + 0.274376i
\(65\) 0.110817 + 0.117459i 0.0137452 + 0.0145690i
\(66\) 0 0
\(67\) −4.10628 + 2.06225i −0.501662 + 0.251944i −0.681588 0.731736i \(-0.738710\pi\)
0.179926 + 0.983680i \(0.442414\pi\)
\(68\) 0.0367070 0.630234i 0.00445137 0.0764271i
\(69\) 0 0
\(70\) −0.0296390 + 0.0990011i −0.00354254 + 0.0118329i
\(71\) 0.963622 5.46497i 0.114361 0.648573i −0.872704 0.488250i \(-0.837635\pi\)
0.987065 0.160323i \(-0.0512535\pi\)
\(72\) 0 0
\(73\) 0.267464 + 1.51686i 0.0313043 + 0.177536i 0.996451 0.0841735i \(-0.0268250\pi\)
−0.965147 + 0.261709i \(0.915714\pi\)
\(74\) −1.54091 0.180106i −0.179127 0.0209369i
\(75\) 0 0
\(76\) 1.18318 1.25410i 0.135720 0.143855i
\(77\) 1.35143 3.13297i 0.154010 0.357035i
\(78\) 0 0
\(79\) −11.4068 + 7.50239i −1.28337 + 0.844085i −0.993594 0.113009i \(-0.963951\pi\)
−0.289775 + 0.957095i \(0.593581\pi\)
\(80\) −0.359909 −0.0402391
\(81\) 0 0
\(82\) −6.65031 −0.734404
\(83\) −5.24973 + 3.45280i −0.576232 + 0.378994i −0.803917 0.594741i \(-0.797255\pi\)
0.227685 + 0.973735i \(0.426884\pi\)
\(84\) 0 0
\(85\) −0.0646276 + 0.149824i −0.00700985 + 0.0162507i
\(86\) −12.5192 + 13.2696i −1.34998 + 1.43089i
\(87\) 0 0
\(88\) 10.1945 + 1.19157i 1.08674 + 0.127022i
\(89\) 1.79520 + 10.1811i 0.190291 + 1.07919i 0.918967 + 0.394334i \(0.129025\pi\)
−0.728676 + 0.684858i \(0.759864\pi\)
\(90\) 0 0
\(91\) 0.301002 1.70707i 0.0315536 0.178950i
\(92\) 0.662852 2.21408i 0.0691071 0.230834i
\(93\) 0 0
\(94\) −0.454506 + 7.80356i −0.0468787 + 0.804876i
\(95\) −0.398228 + 0.199997i −0.0408573 + 0.0205193i
\(96\) 0 0
\(97\) 9.42786 + 9.99295i 0.957254 + 1.01463i 0.999879 + 0.0155391i \(0.00494645\pi\)
−0.0426250 + 0.999091i \(0.513572\pi\)
\(98\) −8.95073 + 3.25780i −0.904160 + 0.329087i
\(99\) 0 0
\(100\) 1.44528 + 0.526040i 0.144528 + 0.0526040i
\(101\) 3.38133 + 7.83881i 0.336455 + 0.779991i 0.999506 + 0.0314167i \(0.0100019\pi\)
−0.663051 + 0.748574i \(0.730739\pi\)
\(102\) 0 0
\(103\) −2.36031 7.88398i −0.232568 0.776832i −0.991999 0.126244i \(-0.959708\pi\)
0.759431 0.650588i \(-0.225477\pi\)
\(104\) 5.17912 0.605352i 0.507855 0.0593597i
\(105\) 0 0
\(106\) −0.911779 15.6546i −0.0885598 1.52051i
\(107\) −2.93755 5.08798i −0.283984 0.491874i 0.688379 0.725352i \(-0.258323\pi\)
−0.972362 + 0.233478i \(0.924989\pi\)
\(108\) 0 0
\(109\) −5.21293 + 9.02906i −0.499308 + 0.864827i −1.00000 0.000798944i \(-0.999746\pi\)
0.500692 + 0.865626i \(0.333079\pi\)
\(110\) 0.431537 + 0.216726i 0.0411455 + 0.0206640i
\(111\) 0 0
\(112\) 2.30703 + 3.09888i 0.217994 + 0.292816i
\(113\) 2.69864 + 0.639589i 0.253867 + 0.0601675i 0.355579 0.934646i \(-0.384284\pi\)
−0.101712 + 0.994814i \(0.532432\pi\)
\(114\) 0 0
\(115\) −0.356714 + 0.479150i −0.0332638 + 0.0446810i
\(116\) −0.262204 + 0.220015i −0.0243450 + 0.0204279i
\(117\) 0 0
\(118\) −12.7489 10.6976i −1.17363 0.984793i
\(119\) 1.70427 0.403919i 0.156230 0.0370272i
\(120\) 0 0
\(121\) −4.13047 2.71665i −0.375497 0.246968i
\(122\) −13.4943 8.87532i −1.22171 0.803534i
\(123\) 0 0
\(124\) 1.79593 0.425642i 0.161279 0.0382238i
\(125\) −0.609431 0.511373i −0.0545092 0.0457386i
\(126\) 0 0
\(127\) −8.52362 + 7.15216i −0.756349 + 0.634652i −0.937174 0.348863i \(-0.886568\pi\)
0.180825 + 0.983515i \(0.442123\pi\)
\(128\) −7.88549 + 10.5921i −0.696986 + 0.936214i
\(129\) 0 0
\(130\) 0.238715 + 0.0565766i 0.0209367 + 0.00496210i
\(131\) −5.93022 7.96566i −0.518125 0.695963i 0.463648 0.886020i \(-0.346540\pi\)
−0.981773 + 0.190056i \(0.939133\pi\)
\(132\) 0 0
\(133\) 4.27466 + 2.14681i 0.370660 + 0.186152i
\(134\) −3.49042 + 6.04558i −0.301526 + 0.522259i
\(135\) 0 0
\(136\) 2.63438 + 4.56288i 0.225896 + 0.391264i
\(137\) −0.934938 16.0523i −0.0798772 1.37144i −0.765479 0.643461i \(-0.777498\pi\)
0.685601 0.727977i \(-0.259539\pi\)
\(138\) 0 0
\(139\) 20.1578 2.35611i 1.70976 0.199843i 0.795778 0.605588i \(-0.207062\pi\)
0.913986 + 0.405745i \(0.132988\pi\)
\(140\) 0.00600888 + 0.0200711i 0.000507843 + 0.00169631i
\(141\) 0 0
\(142\) −3.33916 7.74104i −0.280216 0.649613i
\(143\) −7.61142 2.77033i −0.636499 0.231667i
\(144\) 0 0
\(145\) 0.0831321 0.0302576i 0.00690375 0.00251276i
\(146\) 1.60580 + 1.70204i 0.132897 + 0.140862i
\(147\) 0 0
\(148\) −0.281068 + 0.141158i −0.0231037 + 0.0116031i
\(149\) −0.297275 + 5.10402i −0.0243538 + 0.418138i 0.963994 + 0.265924i \(0.0856772\pi\)
−0.988348 + 0.152213i \(0.951360\pi\)
\(150\) 0 0
\(151\) 5.09479 17.0178i 0.414608 1.38489i −0.454712 0.890638i \(-0.650258\pi\)
0.869320 0.494249i \(-0.164557\pi\)
\(152\) −2.49871 + 14.1709i −0.202672 + 1.14941i
\(153\) 0 0
\(154\) −0.900118 5.10482i −0.0725336 0.411358i
\(155\) −0.473813 0.0553808i −0.0380576 0.00444830i
\(156\) 0 0
\(157\) 4.95262 5.24948i 0.395262 0.418954i −0.498926 0.866645i \(-0.666272\pi\)
0.894188 + 0.447691i \(0.147754\pi\)
\(158\) −8.21534 + 19.0453i −0.653577 + 1.51516i
\(159\) 0 0
\(160\) −0.114898 + 0.0755698i −0.00908350 + 0.00597431i
\(161\) 6.41210 0.505345
\(162\) 0 0
\(163\) 4.94597 0.387398 0.193699 0.981061i \(-0.437951\pi\)
0.193699 + 0.981061i \(0.437951\pi\)
\(164\) −1.12645 + 0.740878i −0.0879610 + 0.0578529i
\(165\) 0 0
\(166\) −3.78091 + 8.76515i −0.293456 + 0.680307i
\(167\) −12.2989 + 13.0361i −0.951717 + 1.00876i 0.0482337 + 0.998836i \(0.484641\pi\)
−0.999951 + 0.00992510i \(0.996841\pi\)
\(168\) 0 0
\(169\) 8.82494 + 1.03149i 0.678842 + 0.0793452i
\(170\) 0.0430451 + 0.244121i 0.00330141 + 0.0187232i
\(171\) 0 0
\(172\) −0.642242 + 3.64234i −0.0489705 + 0.277726i
\(173\) 0.494173 1.65065i 0.0375713 0.125497i −0.937147 0.348936i \(-0.886543\pi\)
0.974718 + 0.223439i \(0.0717283\pi\)
\(174\) 0 0
\(175\) −0.248111 + 4.25990i −0.0187554 + 0.322018i
\(176\) 16.1325 8.10205i 1.21603 0.610715i
\(177\) 0 0
\(178\) 10.7780 + 11.4240i 0.807843 + 0.856264i
\(179\) −11.6071 + 4.22465i −0.867558 + 0.315765i −0.737178 0.675699i \(-0.763842\pi\)
−0.130380 + 0.991464i \(0.541620\pi\)
\(180\) 0 0
\(181\) −0.0341083 0.0124144i −0.00253525 0.000922757i 0.340752 0.940153i \(-0.389318\pi\)
−0.343287 + 0.939230i \(0.611541\pi\)
\(182\) −1.04304 2.41803i −0.0773151 0.179237i
\(183\) 0 0
\(184\) 5.53207 + 18.4784i 0.407829 + 1.36225i
\(185\) 0.0807430 0.00943750i 0.00593634 0.000693859i
\(186\) 0 0
\(187\) −0.475879 8.17052i −0.0347997 0.597488i
\(188\) 0.792370 + 1.37243i 0.0577895 + 0.100094i
\(189\) 0 0
\(190\) −0.338501 + 0.586301i −0.0245574 + 0.0425347i
\(191\) −23.7317 11.9185i −1.71716 0.862391i −0.983044 0.183370i \(-0.941299\pi\)
−0.734118 0.679021i \(-0.762404\pi\)
\(192\) 0 0
\(193\) −0.0270102 0.0362809i −0.00194423 0.00261156i 0.801150 0.598464i \(-0.204222\pi\)
−0.803094 + 0.595852i \(0.796814\pi\)
\(194\) 20.3089 + 4.81330i 1.45809 + 0.345575i
\(195\) 0 0
\(196\) −1.15317 + 1.54897i −0.0823691 + 0.110641i
\(197\) −9.33211 + 7.83057i −0.664885 + 0.557905i −0.911547 0.411197i \(-0.865111\pi\)
0.246661 + 0.969102i \(0.420666\pi\)
\(198\) 0 0
\(199\) 9.63166 + 8.08192i 0.682770 + 0.572912i 0.916814 0.399314i \(-0.130752\pi\)
−0.234044 + 0.972226i \(0.575196\pi\)
\(200\) −12.4902 + 2.96024i −0.883193 + 0.209321i
\(201\) 0 0
\(202\) 10.8359 + 7.12685i 0.762408 + 0.501443i
\(203\) −0.793401 0.521828i −0.0556859 0.0366252i
\(204\) 0 0
\(205\) 0.339081 0.0803636i 0.0236824 0.00561284i
\(206\) −9.57760 8.03656i −0.667303 0.559934i
\(207\) 0 0
\(208\) 7.02563 5.89520i 0.487140 0.408759i
\(209\) 13.3479 17.9293i 0.923291 1.24019i
\(210\) 0 0
\(211\) 13.3553 + 3.16527i 0.919418 + 0.217906i 0.662965 0.748651i \(-0.269298\pi\)
0.256453 + 0.966557i \(0.417446\pi\)
\(212\) −1.89844 2.55005i −0.130386 0.175138i
\(213\) 0 0
\(214\) −7.97612 4.00576i −0.545236 0.273828i
\(215\) 0.477966 0.827862i 0.0325970 0.0564597i
\(216\) 0 0
\(217\) 2.56032 + 4.43460i 0.173806 + 0.301040i
\(218\) 0.920959 + 15.8123i 0.0623752 + 1.07094i
\(219\) 0 0
\(220\) 0.0972395 0.0113657i 0.00655589 0.000766273i
\(221\) −1.19250 3.98322i −0.0802161 0.267940i
\(222\) 0 0
\(223\) −1.16339 2.69705i −0.0779066 0.180608i 0.874811 0.484464i \(-0.160985\pi\)
−0.952718 + 0.303856i \(0.901726\pi\)
\(224\) 1.38717 + 0.504888i 0.0926840 + 0.0337342i
\(225\) 0 0
\(226\) 3.95927 1.44106i 0.263367 0.0958578i
\(227\) 2.72165 + 2.88478i 0.180642 + 0.191469i 0.811367 0.584537i \(-0.198724\pi\)
−0.630725 + 0.776006i \(0.717242\pi\)
\(228\) 0 0
\(229\) −9.13092 + 4.58572i −0.603388 + 0.303033i −0.724143 0.689649i \(-0.757765\pi\)
0.120755 + 0.992682i \(0.461468\pi\)
\(230\) −0.0527667 + 0.905969i −0.00347933 + 0.0597378i
\(231\) 0 0
\(232\) 0.819294 2.73663i 0.0537893 0.179669i
\(233\) −0.443423 + 2.51478i −0.0290496 + 0.164748i −0.995881 0.0906654i \(-0.971101\pi\)
0.966832 + 0.255414i \(0.0822117\pi\)
\(234\) 0 0
\(235\) −0.0711257 0.403374i −0.00463973 0.0263132i
\(236\) −3.35121 0.391701i −0.218145 0.0254975i
\(237\) 0 0
\(238\) 1.82600 1.93544i 0.118362 0.125456i
\(239\) 1.84643 4.28050i 0.119435 0.276883i −0.848002 0.529993i \(-0.822194\pi\)
0.967437 + 0.253111i \(0.0814537\pi\)
\(240\) 0 0
\(241\) −1.26850 + 0.834304i −0.0817112 + 0.0537423i −0.589707 0.807617i \(-0.700757\pi\)
0.507996 + 0.861359i \(0.330386\pi\)
\(242\) −7.51064 −0.482802
\(243\) 0 0
\(244\) −3.27446 −0.209626
\(245\) 0.417005 0.274268i 0.0266415 0.0175224i
\(246\) 0 0
\(247\) 4.49773 10.4269i 0.286183 0.663448i
\(248\) −10.5707 + 11.2043i −0.671240 + 0.711473i
\(249\) 0 0
\(250\) −1.20044 0.140312i −0.0759227 0.00887410i
\(251\) −3.80000 21.5509i −0.239854 1.36028i −0.832146 0.554556i \(-0.812888\pi\)
0.592293 0.805723i \(-0.298223\pi\)
\(252\) 0 0
\(253\) 5.20296 29.5075i 0.327107 1.85512i
\(254\) −4.84810 + 16.1938i −0.304197 + 1.01609i
\(255\) 0 0
\(256\) −0.420134 + 7.21342i −0.0262584 + 0.450839i
\(257\) 6.36081 3.19452i 0.396776 0.199269i −0.239212 0.970967i \(-0.576889\pi\)
0.635988 + 0.771699i \(0.280593\pi\)
\(258\) 0 0
\(259\) −0.598822 0.634715i −0.0372090 0.0394392i
\(260\) 0.0467373 0.0170110i 0.00289852 0.00105498i
\(261\) 0 0
\(262\) −14.1770 5.16001i −0.875858 0.318786i
\(263\) 6.65013 + 15.4167i 0.410064 + 0.950636i 0.990649 + 0.136436i \(0.0435649\pi\)
−0.580584 + 0.814200i \(0.697176\pi\)
\(264\) 0 0
\(265\) 0.235663 + 0.787168i 0.0144766 + 0.0483553i
\(266\) 7.21794 0.843656i 0.442560 0.0517279i
\(267\) 0 0
\(268\) 0.0822903 + 1.41287i 0.00502668 + 0.0863047i
\(269\) 10.3000 + 17.8402i 0.628003 + 1.08773i 0.987952 + 0.154762i \(0.0494610\pi\)
−0.359948 + 0.932972i \(0.617206\pi\)
\(270\) 0 0
\(271\) −1.75375 + 3.03758i −0.106533 + 0.184520i −0.914363 0.404895i \(-0.867308\pi\)
0.807831 + 0.589414i \(0.200641\pi\)
\(272\) 8.28125 + 4.15900i 0.502125 + 0.252176i
\(273\) 0 0
\(274\) −14.5874 19.5943i −0.881260 1.18374i
\(275\) 19.4021 + 4.59837i 1.16999 + 0.277292i
\(276\) 0 0
\(277\) −9.69997 + 13.0293i −0.582815 + 0.782856i −0.991540 0.129802i \(-0.958566\pi\)
0.408725 + 0.912657i \(0.365973\pi\)
\(278\) 23.6190 19.8187i 1.41657 1.18865i
\(279\) 0 0
\(280\) −0.133947 0.112395i −0.00800489 0.00671690i
\(281\) 0.396059 0.0938677i 0.0236269 0.00559968i −0.218785 0.975773i \(-0.570209\pi\)
0.242412 + 0.970173i \(0.422061\pi\)
\(282\) 0 0
\(283\) −15.6157 10.2706i −0.928258 0.610525i −0.00721029 0.999974i \(-0.502295\pi\)
−0.921048 + 0.389449i \(0.872665\pi\)
\(284\) −1.42799 0.939202i −0.0847354 0.0557314i
\(285\) 0 0
\(286\) −11.9738 + 2.83783i −0.708023 + 0.167804i
\(287\) −2.86546 2.40441i −0.169143 0.141928i
\(288\) 0 0
\(289\) −9.80441 + 8.22687i −0.576730 + 0.483934i
\(290\) 0.0802584 0.107806i 0.00471293 0.00633057i
\(291\) 0 0
\(292\) 0.461611 + 0.109404i 0.0270137 + 0.00640237i
\(293\) −7.69020 10.3297i −0.449266 0.603469i 0.518575 0.855032i \(-0.326463\pi\)
−0.967841 + 0.251563i \(0.919055\pi\)
\(294\) 0 0
\(295\) 0.779302 + 0.391380i 0.0453727 + 0.0227870i
\(296\) 1.31248 2.27329i 0.0762865 0.132132i
\(297\) 0 0
\(298\) 3.88361 + 6.72661i 0.224972 + 0.389662i
\(299\) −0.885075 15.1961i −0.0511852 0.878816i
\(300\) 0 0
\(301\) −10.1918 + 1.19125i −0.587445 + 0.0686625i
\(302\) −7.74005 25.8536i −0.445390 1.48771i
\(303\) 0 0
\(304\) 10.0243 + 23.2391i 0.574936 + 1.33285i
\(305\) 0.795286 + 0.289460i 0.0455379 + 0.0165745i
\(306\) 0 0
\(307\) 8.20971 2.98809i 0.468553 0.170539i −0.0969439 0.995290i \(-0.530907\pi\)
0.565497 + 0.824751i \(0.308685\pi\)
\(308\) −0.721168 0.764393i −0.0410923 0.0435553i
\(309\) 0 0
\(310\) −0.647635 + 0.325255i −0.0367832 + 0.0184732i
\(311\) −1.08085 + 18.5575i −0.0612894 + 1.05230i 0.817758 + 0.575563i \(0.195217\pi\)
−0.879047 + 0.476735i \(0.841820\pi\)
\(312\) 0 0
\(313\) 6.03398 20.1549i 0.341061 1.13922i −0.599721 0.800209i \(-0.704722\pi\)
0.940782 0.339013i \(-0.110093\pi\)
\(314\) 1.90391 10.7976i 0.107444 0.609344i
\(315\) 0 0
\(316\) 0.730202 + 4.14118i 0.0410771 + 0.232960i
\(317\) 16.0918 + 1.88086i 0.903805 + 0.105640i 0.555283 0.831661i \(-0.312610\pi\)
0.348521 + 0.937301i \(0.386684\pi\)
\(318\) 0 0
\(319\) −3.04516 + 3.22768i −0.170496 + 0.180715i
\(320\) 0.202355 0.469111i 0.0113120 0.0262241i
\(321\) 0 0
\(322\) 8.13876 5.35295i 0.453556 0.298308i
\(323\) 11.4740 0.638432
\(324\) 0 0
\(325\) 10.1299 0.561903
\(326\) 6.27783 4.12899i 0.347697 0.228684i
\(327\) 0 0
\(328\) 4.45683 10.3321i 0.246087 0.570494i
\(329\) −3.01719 + 3.19804i −0.166343 + 0.176314i
\(330\) 0 0
\(331\) −18.9254 2.21206i −1.04023 0.121586i −0.421214 0.906961i \(-0.638396\pi\)
−0.619020 + 0.785375i \(0.712470\pi\)
\(332\) 0.336058 + 1.90588i 0.0184436 + 0.104599i
\(333\) 0 0
\(334\) −4.72799 + 26.8138i −0.258704 + 1.46719i
\(335\) 0.104911 0.350426i 0.00573188 0.0191458i
\(336\) 0 0
\(337\) 0.635590 10.9127i 0.0346228 0.594450i −0.935724 0.352733i \(-0.885252\pi\)
0.970347 0.241717i \(-0.0777106\pi\)
\(338\) 12.0624 6.05798i 0.656110 0.329511i
\(339\) 0 0
\(340\) 0.0344874 + 0.0365545i 0.00187034 + 0.00198245i
\(341\) 22.4848 8.18380i 1.21762 0.443178i
\(342\) 0 0
\(343\) −10.6553 3.87822i −0.575333 0.209404i
\(344\) −12.2259 28.3429i −0.659179 1.52815i
\(345\) 0 0
\(346\) −0.750753 2.50769i −0.0403607 0.134814i
\(347\) −22.1659 + 2.59082i −1.18993 + 0.139083i −0.687924 0.725783i \(-0.741478\pi\)
−0.502004 + 0.864865i \(0.667404\pi\)
\(348\) 0 0
\(349\) 1.35928 + 23.3379i 0.0727606 + 1.24925i 0.815137 + 0.579268i \(0.196662\pi\)
−0.742377 + 0.669983i \(0.766301\pi\)
\(350\) 3.24133 + 5.61414i 0.173256 + 0.300088i
\(351\) 0 0
\(352\) 3.44900 5.97384i 0.183832 0.318407i
\(353\) 28.4906 + 14.3085i 1.51640 + 0.761566i 0.995741 0.0921962i \(-0.0293887\pi\)
0.520663 + 0.853763i \(0.325685\pi\)
\(354\) 0 0
\(355\) 0.263798 + 0.354343i 0.0140010 + 0.0188066i
\(356\) 3.09830 + 0.734310i 0.164209 + 0.0389183i
\(357\) 0 0
\(358\) −11.2059 + 15.0521i −0.592250 + 0.795530i
\(359\) −8.66761 + 7.27299i −0.457459 + 0.383854i −0.842195 0.539173i \(-0.818737\pi\)
0.384736 + 0.923027i \(0.374292\pi\)
\(360\) 0 0
\(361\) 9.45042 + 7.92984i 0.497391 + 0.417360i
\(362\) −0.0536569 + 0.0127169i −0.00282014 + 0.000668386i
\(363\) 0 0
\(364\) −0.446054 0.293374i −0.0233796 0.0153770i
\(365\) −0.102443 0.0673777i −0.00536210 0.00352671i
\(366\) 0 0
\(367\) −0.660094 + 0.156445i −0.0344566 + 0.00816637i −0.247808 0.968809i \(-0.579710\pi\)
0.213351 + 0.976976i \(0.431562\pi\)
\(368\) 25.9888 + 21.8072i 1.35476 + 1.13678i
\(369\) 0 0
\(370\) 0.0946069 0.0793846i 0.00491838 0.00412701i
\(371\) 5.26703 7.07485i 0.273451 0.367308i
\(372\) 0 0
\(373\) −10.8528 2.57217i −0.561939 0.133182i −0.0601770 0.998188i \(-0.519167\pi\)
−0.501762 + 0.865006i \(0.667315\pi\)
\(374\) −7.42494 9.97342i −0.383934 0.515713i
\(375\) 0 0
\(376\) −11.8192 5.93583i −0.609529 0.306117i
\(377\) −1.12717 + 1.95232i −0.0580524 + 0.100550i
\(378\) 0 0
\(379\) −9.99112 17.3051i −0.513209 0.888905i −0.999883 0.0153206i \(-0.995123\pi\)
0.486673 0.873584i \(-0.338210\pi\)
\(380\) 0.00798052 + 0.137020i 0.000409392 + 0.00702899i
\(381\) 0 0
\(382\) −40.0719 + 4.68374i −2.05026 + 0.239641i
\(383\) −6.75310 22.5569i −0.345067 1.15260i −0.937791 0.347199i \(-0.887133\pi\)
0.592724 0.805405i \(-0.298052\pi\)
\(384\) 0 0
\(385\) 0.107582 + 0.249403i 0.00548289 + 0.0127108i
\(386\) −0.0645715 0.0235021i −0.00328660 0.00119623i
\(387\) 0 0
\(388\) 3.97621 1.44722i 0.201862 0.0734716i
\(389\) −4.28568 4.54255i −0.217292 0.230317i 0.609554 0.792745i \(-0.291349\pi\)
−0.826846 + 0.562428i \(0.809867\pi\)
\(390\) 0 0
\(391\) 13.7446 6.90282i 0.695097 0.349091i
\(392\) 0.937097 16.0893i 0.0473306 0.812634i
\(393\) 0 0
\(394\) −5.30796 + 17.7298i −0.267411 + 0.893215i
\(395\) 0.188730 1.07034i 0.00949604 0.0538547i
\(396\) 0 0
\(397\) −0.194836 1.10497i −0.00977853 0.0554568i 0.979528 0.201308i \(-0.0645191\pi\)
−0.989307 + 0.145851i \(0.953408\pi\)
\(398\) 18.9722 + 2.21754i 0.950992 + 0.111155i
\(399\) 0 0
\(400\) −15.4933 + 16.4219i −0.774664 + 0.821096i
\(401\) −1.67881 + 3.89191i −0.0838356 + 0.194353i −0.954977 0.296679i \(-0.904121\pi\)
0.871142 + 0.491032i \(0.163380\pi\)
\(402\) 0 0
\(403\) 10.1562 6.67985i 0.505917 0.332747i
\(404\) 2.62938 0.130816
\(405\) 0 0
\(406\) −1.44268 −0.0715991
\(407\) −3.40676 + 2.24066i −0.168867 + 0.111065i
\(408\) 0 0
\(409\) −0.756884 + 1.75465i −0.0374255 + 0.0867621i −0.935904 0.352256i \(-0.885414\pi\)
0.898478 + 0.439019i \(0.144674\pi\)
\(410\) 0.363300 0.385075i 0.0179421 0.0190175i
\(411\) 0 0
\(412\) −2.51760 0.294265i −0.124033 0.0144974i
\(413\) −1.62550 9.21867i −0.0799856 0.453621i
\(414\) 0 0
\(415\) 0.0868586 0.492600i 0.00426372 0.0241808i
\(416\) 1.00507 3.35716i 0.0492775 0.164598i
\(417\) 0 0
\(418\) 1.97447 33.9004i 0.0965745 1.65812i
\(419\) −2.21787 + 1.11386i −0.108350 + 0.0544156i −0.502149 0.864781i \(-0.667457\pi\)
0.393799 + 0.919197i \(0.371161\pi\)
\(420\) 0 0
\(421\) −11.9853 12.7037i −0.584128 0.619140i 0.366145 0.930558i \(-0.380678\pi\)
−0.950273 + 0.311418i \(0.899196\pi\)
\(422\) 19.5941 7.13166i 0.953825 0.347164i
\(423\) 0 0
\(424\) 24.9325 + 9.07467i 1.21083 + 0.440705i
\(425\) 4.05407 + 9.39840i 0.196651 + 0.455889i
\(426\) 0 0
\(427\) −2.60550 8.70298i −0.126089 0.421167i
\(428\) −1.79728 + 0.210072i −0.0868749 + 0.0101542i
\(429\) 0 0
\(430\) −0.0844415 1.44980i −0.00407213 0.0699158i
\(431\) −11.6850 20.2390i −0.562845 0.974877i −0.997247 0.0741572i \(-0.976373\pi\)
0.434401 0.900719i \(-0.356960\pi\)
\(432\) 0 0
\(433\) 15.2874 26.4785i 0.734664 1.27247i −0.220207 0.975453i \(-0.570673\pi\)
0.954871 0.297021i \(-0.0959933\pi\)
\(434\) 6.95185 + 3.49135i 0.333699 + 0.167590i
\(435\) 0 0
\(436\) 1.91756 + 2.57573i 0.0918345 + 0.123355i
\(437\) 40.8737 + 9.68724i 1.95525 + 0.463404i
\(438\) 0 0
\(439\) 7.40966 9.95290i 0.353644 0.475026i −0.589330 0.807892i \(-0.700608\pi\)
0.942974 + 0.332866i \(0.108016\pi\)
\(440\) −0.625913 + 0.525204i −0.0298392 + 0.0250381i
\(441\) 0 0
\(442\) −4.83889 4.06031i −0.230162 0.193129i
\(443\) −3.37497 + 0.799883i −0.160350 + 0.0380036i −0.310007 0.950734i \(-0.600331\pi\)
0.149657 + 0.988738i \(0.452183\pi\)
\(444\) 0 0
\(445\) −0.687588 0.452234i −0.0325948 0.0214379i
\(446\) −3.72822 2.45209i −0.176537 0.116110i
\(447\) 0 0
\(448\) −5.33621 + 1.26471i −0.252112 + 0.0597517i
\(449\) −2.37761 1.99505i −0.112206 0.0941523i 0.584958 0.811063i \(-0.301111\pi\)
−0.697165 + 0.716911i \(0.745555\pi\)
\(450\) 0 0
\(451\) −13.3898 + 11.2354i −0.630501 + 0.529053i
\(452\) 0.510093 0.685174i 0.0239928 0.0322279i
\(453\) 0 0
\(454\) 5.86280 + 1.38951i 0.275155 + 0.0652129i
\(455\) 0.0824016 + 0.110685i 0.00386305 + 0.00518897i
\(456\) 0 0
\(457\) 31.7054 + 15.9230i 1.48312 + 0.744848i 0.991999 0.126246i \(-0.0402928\pi\)
0.491116 + 0.871094i \(0.336589\pi\)
\(458\) −7.76145 + 13.4432i −0.362669 + 0.628161i
\(459\) 0 0
\(460\) 0.0919917 + 0.159334i 0.00428913 + 0.00742900i
\(461\) 1.48196 + 25.4443i 0.0690217 + 1.18506i 0.837959 + 0.545733i \(0.183749\pi\)
−0.768937 + 0.639324i \(0.779214\pi\)
\(462\) 0 0
\(463\) 9.25377 1.08161i 0.430059 0.0502667i 0.101690 0.994816i \(-0.467575\pi\)
0.328369 + 0.944549i \(0.393501\pi\)
\(464\) −1.44101 4.81332i −0.0668974 0.223453i
\(465\) 0 0
\(466\) 1.53656 + 3.56214i 0.0711795 + 0.165013i
\(467\) −11.6612 4.24434i −0.539617 0.196404i 0.0578105 0.998328i \(-0.481588\pi\)
−0.597427 + 0.801923i \(0.703810\pi\)
\(468\) 0 0
\(469\) −3.68970 + 1.34294i −0.170375 + 0.0620113i
\(470\) −0.427023 0.452618i −0.0196971 0.0208777i
\(471\) 0 0
\(472\) 25.1639 12.6378i 1.15826 0.581702i
\(473\) −2.78797 + 47.8676i −0.128191 + 2.20095i
\(474\) 0 0
\(475\) −8.01733 + 26.7797i −0.367860 + 1.22874i
\(476\) 0.0936749 0.531257i 0.00429358 0.0243501i
\(477\) 0 0
\(478\) −1.22981 6.97459i −0.0562501 0.319010i
\(479\) −34.5296 4.03593i −1.57770 0.184406i −0.718306 0.695727i \(-0.755082\pi\)
−0.859390 + 0.511321i \(0.829156\pi\)
\(480\) 0 0
\(481\) −1.42156 + 1.50677i −0.0648177 + 0.0687028i
\(482\) −0.913587 + 2.11793i −0.0416128 + 0.0964692i
\(483\) 0 0
\(484\) −1.27217 + 0.836723i −0.0578261 + 0.0380328i
\(485\) −1.09366 −0.0496605
\(486\) 0 0
\(487\) 4.53564 0.205529 0.102765 0.994706i \(-0.467231\pi\)
0.102765 + 0.994706i \(0.467231\pi\)
\(488\) 22.8323 15.0171i 1.03357 0.679790i
\(489\) 0 0
\(490\) 0.300332 0.696247i 0.0135676 0.0314532i
\(491\) 20.5553 21.7873i 0.927648 0.983249i −0.0722525 0.997386i \(-0.523019\pi\)
0.999900 + 0.0141374i \(0.00450023\pi\)
\(492\) 0 0
\(493\) −2.26246 0.264443i −0.101896 0.0119099i
\(494\) −2.99570 16.9895i −0.134783 0.764392i
\(495\) 0 0
\(496\) −4.70463 + 26.6813i −0.211244 + 1.19802i
\(497\) 1.35999 4.54269i 0.0610040 0.203767i
\(498\) 0 0
\(499\) −0.396814 + 6.81303i −0.0177638 + 0.304993i 0.977710 + 0.209959i \(0.0673331\pi\)
−0.995474 + 0.0950342i \(0.969704\pi\)
\(500\) −0.218966 + 0.109969i −0.00979247 + 0.00491796i
\(501\) 0 0
\(502\) −22.8144 24.1818i −1.01825 1.07929i
\(503\) 5.01364 1.82482i 0.223547 0.0813646i −0.227818 0.973704i \(-0.573159\pi\)
0.451366 + 0.892339i \(0.350937\pi\)
\(504\) 0 0
\(505\) −0.638612 0.232436i −0.0284179 0.0103433i
\(506\) −18.0294 41.7968i −0.801504 1.85809i
\(507\) 0 0
\(508\) 0.982883 + 3.28306i 0.0436084 + 0.145662i
\(509\) 44.4079 5.19054i 1.96834 0.230066i 0.968522 0.248928i \(-0.0800782\pi\)
0.999822 + 0.0188613i \(0.00600410\pi\)
\(510\) 0 0
\(511\) 0.0765284 + 1.31394i 0.00338541 + 0.0581253i
\(512\) −7.71639 13.3652i −0.341019 0.590663i
\(513\) 0 0
\(514\) 5.40681 9.36487i 0.238484 0.413067i
\(515\) 0.585450 + 0.294024i 0.0257980 + 0.0129563i
\(516\) 0 0
\(517\) 12.2686 + 16.4796i 0.539573 + 0.724773i
\(518\) −1.28995 0.305723i −0.0566770 0.0134327i
\(519\) 0 0
\(520\) −0.247878 + 0.332958i −0.0108702 + 0.0146012i
\(521\) −7.56500 + 6.34779i −0.331429 + 0.278102i −0.793282 0.608855i \(-0.791629\pi\)
0.461853 + 0.886956i \(0.347185\pi\)
\(522\) 0 0
\(523\) 29.0347 + 24.3630i 1.26960 + 1.06532i 0.994590 + 0.103880i \(0.0331258\pi\)
0.275010 + 0.961441i \(0.411319\pi\)
\(524\) −2.97619 + 0.705371i −0.130016 + 0.0308143i
\(525\) 0 0
\(526\) 21.3111 + 14.0165i 0.929207 + 0.611149i
\(527\) 10.2621 + 6.74951i 0.447026 + 0.294013i
\(528\) 0 0
\(529\) 32.4101 7.68134i 1.40914 0.333971i
\(530\) 0.956265 + 0.802402i 0.0415375 + 0.0348541i
\(531\) 0 0
\(532\) 1.12861 0.947016i 0.0489314 0.0410583i
\(533\) −5.30271 + 7.12278i −0.229686 + 0.308522i
\(534\) 0 0
\(535\) 0.455086 + 0.107857i 0.0196751 + 0.00466308i
\(536\) −7.05339 9.47435i −0.304660 0.409230i
\(537\) 0 0
\(538\) 27.9669 + 14.0455i 1.20574 + 0.605546i
\(539\) −12.5176 + 21.6811i −0.539171 + 0.933871i
\(540\) 0 0
\(541\) −22.1922 38.4380i −0.954116 1.65258i −0.736378 0.676570i \(-0.763466\pi\)
−0.217737 0.976007i \(-0.569868\pi\)
\(542\) 0.309832 + 5.31960i 0.0133084 + 0.228496i
\(543\) 0 0
\(544\) 3.51698 0.411077i 0.150789 0.0176248i
\(545\) −0.238036 0.795094i −0.0101963 0.0340581i
\(546\) 0 0
\(547\) 1.26392 + 2.93009i 0.0540413 + 0.125282i 0.943098 0.332516i \(-0.107898\pi\)
−0.889056 + 0.457798i \(0.848638\pi\)
\(548\) −4.65378 1.69384i −0.198799 0.0723571i
\(549\) 0 0
\(550\) 28.4655 10.3606i 1.21377 0.441777i
\(551\) −4.26914 4.52502i −0.181871 0.192772i
\(552\) 0 0
\(553\) −10.4256 + 5.23592i −0.443340 + 0.222654i
\(554\) −1.43486 + 24.6356i −0.0609613 + 1.04667i
\(555\) 0 0
\(556\) 1.79276 5.98823i 0.0760299 0.253958i
\(557\) 4.44633 25.2164i 0.188397 1.06845i −0.733116 0.680104i \(-0.761935\pi\)
0.921513 0.388348i \(-0.126954\pi\)
\(558\) 0 0
\(559\) 4.22995 + 23.9892i 0.178908 + 1.01464i
\(560\) −0.305466 0.0357038i −0.0129083 0.00150876i
\(561\) 0 0
\(562\) 0.424347 0.449782i 0.0179000 0.0189729i
\(563\) −6.05077 + 14.0273i −0.255010 + 0.591179i −0.996842 0.0794062i \(-0.974698\pi\)
0.741833 + 0.670585i \(0.233957\pi\)
\(564\) 0 0
\(565\) −0.184458 + 0.121320i −0.00776022 + 0.00510398i
\(566\) −28.3949 −1.19352
\(567\) 0 0
\(568\) 14.2645 0.598523
\(569\) −13.4404 + 8.83989i −0.563451 + 0.370587i −0.799052 0.601262i \(-0.794665\pi\)
0.235601 + 0.971850i \(0.424294\pi\)
\(570\) 0 0
\(571\) −7.24317 + 16.7916i −0.303117 + 0.702705i −0.999894 0.0145837i \(-0.995358\pi\)
0.696776 + 0.717288i \(0.254617\pi\)
\(572\) −1.71200 + 1.81462i −0.0715824 + 0.0758729i
\(573\) 0 0
\(574\) −5.64432 0.659726i −0.235589 0.0275364i
\(575\) 6.50690 + 36.9025i 0.271357 + 1.53894i
\(576\) 0 0
\(577\) 1.90472 10.8022i 0.0792945 0.449702i −0.919148 0.393912i \(-0.871121\pi\)
0.998443 0.0557894i \(-0.0177675\pi\)
\(578\) −5.57659 + 18.6271i −0.231956 + 0.774786i
\(579\) 0 0
\(580\) 0.00158432 0.0272017i 6.57851e−5 0.00112949i
\(581\) −4.79812 + 2.40971i −0.199060 + 0.0999715i
\(582\) 0 0
\(583\) −28.2835 29.9788i −1.17138 1.24159i
\(584\) −3.72049 + 1.35415i −0.153955 + 0.0560350i
\(585\) 0 0
\(586\) −18.3845 6.69140i −0.759456 0.276419i
\(587\) 6.21258 + 14.4024i 0.256421 + 0.594450i 0.996990 0.0775302i \(-0.0247034\pi\)
−0.740569 + 0.671980i \(0.765444\pi\)
\(588\) 0 0
\(589\) 9.62095 + 32.1362i 0.396425 + 1.32415i
\(590\) 1.31589 0.153805i 0.0541742 0.00633205i
\(591\) 0 0
\(592\) −0.268450 4.60911i −0.0110332 0.189433i
\(593\) 20.4416 + 35.4058i 0.839434 + 1.45394i 0.890369 + 0.455240i \(0.150447\pi\)
−0.0509346 + 0.998702i \(0.516220\pi\)
\(594\) 0 0
\(595\) −0.0697142 + 0.120749i −0.00285800 + 0.00495021i
\(596\) 1.40720 + 0.706721i 0.0576410 + 0.0289484i
\(597\) 0 0
\(598\) −13.8094 18.5493i −0.564710 0.758537i
\(599\) −26.3190 6.23772i −1.07537 0.254867i −0.345474 0.938428i \(-0.612282\pi\)
−0.729893 + 0.683562i \(0.760430\pi\)
\(600\) 0 0
\(601\) 9.97163 13.3942i 0.406751 0.546362i −0.550795 0.834640i \(-0.685675\pi\)
0.957547 + 0.288279i \(0.0930829\pi\)
\(602\) −11.9418 + 10.0203i −0.486710 + 0.408398i
\(603\) 0 0
\(604\) −4.19125 3.51688i −0.170540 0.143100i
\(605\) 0.382946 0.0907599i 0.0155690 0.00368992i
\(606\) 0 0
\(607\) 38.1367 + 25.0829i 1.54792 + 1.01808i 0.980930 + 0.194362i \(0.0622635\pi\)
0.566993 + 0.823723i \(0.308107\pi\)
\(608\) 8.07967 + 5.31408i 0.327674 + 0.215515i
\(609\) 0 0
\(610\) 1.25109 0.296513i 0.0506551 0.0120055i
\(611\) 7.99555 + 6.70906i 0.323465 + 0.271420i
\(612\) 0 0
\(613\) 30.0949 25.2526i 1.21552 1.01994i 0.216476 0.976288i \(-0.430544\pi\)
0.999047 0.0436562i \(-0.0139006\pi\)
\(614\) 7.92591 10.6463i 0.319864 0.429652i
\(615\) 0 0
\(616\) 8.53420 + 2.02264i 0.343853 + 0.0814946i
\(617\) 1.51537 + 2.03549i 0.0610065 + 0.0819459i 0.831579 0.555406i \(-0.187437\pi\)
−0.770573 + 0.637352i \(0.780030\pi\)
\(618\) 0 0
\(619\) −10.9596 5.50411i −0.440503 0.221229i 0.214703 0.976679i \(-0.431122\pi\)
−0.655206 + 0.755451i \(0.727418\pi\)
\(620\) −0.0734635 + 0.127242i −0.00295036 + 0.00511018i
\(621\) 0 0
\(622\) 14.1202 + 24.4570i 0.566170 + 0.980635i
\(623\) 0.513652 + 8.81907i 0.0205790 + 0.353329i
\(624\) 0 0
\(625\) −24.7366 + 2.89129i −0.989463 + 0.115652i
\(626\) −9.16688 30.6195i −0.366382 1.22380i
\(627\) 0 0
\(628\) −0.880418 2.04104i −0.0351325 0.0814463i
\(629\) −1.96689 0.715890i −0.0784251 0.0285444i
\(630\) 0 0
\(631\) −38.1004 + 13.8674i −1.51675 + 0.552053i −0.960335 0.278848i \(-0.910047\pi\)
−0.556419 + 0.830902i \(0.687825\pi\)
\(632\) −24.0836 25.5271i −0.957993 1.01541i
\(633\) 0 0
\(634\) 21.9952 11.0464i 0.873540 0.438708i
\(635\) 0.0515023 0.884261i 0.00204381 0.0350908i
\(636\) 0 0
\(637\) −3.64773 + 12.1843i −0.144528 + 0.482758i
\(638\) −1.17063 + 6.63899i −0.0463458 + 0.262840i
\(639\) 0 0
\(640\) −0.182539 1.03523i −0.00721548 0.0409210i
\(641\) −29.9887 3.50518i −1.18448 0.138446i −0.499045 0.866576i \(-0.666316\pi\)
−0.685439 + 0.728130i \(0.740390\pi\)
\(642\) 0 0
\(643\) 0.305055 0.323340i 0.0120302 0.0127513i −0.721331 0.692591i \(-0.756469\pi\)
0.733361 + 0.679840i \(0.237951\pi\)
\(644\) 0.782224 1.81340i 0.0308239 0.0714579i
\(645\) 0 0
\(646\) 14.5638 9.57874i 0.573004 0.376871i
\(647\) −38.0107 −1.49436 −0.747178 0.664624i \(-0.768592\pi\)
−0.747178 + 0.664624i \(0.768592\pi\)
\(648\) 0 0
\(649\) −43.7418 −1.71702
\(650\) 12.8576 8.45660i 0.504318 0.331695i
\(651\) 0 0
\(652\) 0.603367 1.39876i 0.0236297 0.0547798i
\(653\) −9.27699 + 9.83304i −0.363037 + 0.384796i −0.882985 0.469401i \(-0.844470\pi\)
0.519948 + 0.854198i \(0.325951\pi\)
\(654\) 0 0
\(655\) 0.785200 + 0.0917767i 0.0306803 + 0.00358601i
\(656\) −3.43670 19.4905i −0.134181 0.760977i
\(657\) 0 0
\(658\) −1.15988 + 6.57802i −0.0452169 + 0.256438i
\(659\) 7.46974 24.9507i 0.290980 0.971940i −0.680087 0.733132i \(-0.738058\pi\)
0.971067 0.238809i \(-0.0767569\pi\)
\(660\) 0 0
\(661\) −0.139876 + 2.40158i −0.00544055 + 0.0934106i −0.999935 0.0113759i \(-0.996379\pi\)
0.994495 + 0.104786i \(0.0334159\pi\)
\(662\) −25.8683 + 12.9916i −1.00540 + 0.504932i
\(663\) 0 0
\(664\) −11.0839 11.7482i −0.430138 0.455920i
\(665\) −0.357828 + 0.130239i −0.0138760 + 0.00505044i
\(666\) 0 0
\(667\) −7.83624 2.85216i −0.303420 0.110436i
\(668\) 2.18635 + 5.06853i 0.0845924 + 0.196107i
\(669\) 0 0
\(670\) −0.159381 0.532371i −0.00615744 0.0205673i
\(671\) −42.1639 + 4.92825i −1.62772 + 0.190253i
\(672\) 0 0
\(673\) 0.766718 + 13.1640i 0.0295548 + 0.507437i 0.980306 + 0.197483i \(0.0632766\pi\)
−0.950752 + 0.309954i \(0.899686\pi\)
\(674\) −8.30335 14.3818i −0.319833 0.553967i
\(675\) 0 0
\(676\) 1.36828 2.36994i 0.0526263 0.0911514i
\(677\) 10.3129 + 5.17933i 0.396357 + 0.199058i 0.635802 0.771852i \(-0.280669\pi\)
−0.239446 + 0.970910i \(0.576966\pi\)
\(678\) 0 0
\(679\) 7.01038 + 9.41658i 0.269034 + 0.361375i
\(680\) −0.408119 0.0967260i −0.0156507 0.00370927i
\(681\) 0 0
\(682\) 21.7076 29.1583i 0.831225 1.11653i
\(683\) 7.16633 6.01327i 0.274212 0.230091i −0.495302 0.868721i \(-0.664943\pi\)
0.769514 + 0.638629i \(0.220498\pi\)
\(684\) 0 0
\(685\) 0.980555 + 0.822783i 0.0374651 + 0.0314369i
\(686\) −16.7622 + 3.97272i −0.639984 + 0.151679i
\(687\) 0 0
\(688\) −45.3595 29.8334i −1.72932 1.13739i
\(689\) −17.4938 11.5059i −0.666462 0.438339i
\(690\) 0 0
\(691\) 14.6182 3.46458i 0.556103 0.131799i 0.0570515 0.998371i \(-0.481830\pi\)
0.499051 + 0.866572i \(0.333682\pi\)
\(692\) −0.406534 0.341122i −0.0154541 0.0129675i
\(693\) 0 0
\(694\) −25.9719 + 21.7930i −0.985880 + 0.827251i
\(695\) −0.964775 + 1.29592i −0.0365960 + 0.0491569i
\(696\) 0 0
\(697\) −8.73066 2.06920i −0.330697 0.0783767i
\(698\) 21.2083 + 28.4876i 0.802745 + 1.07827i
\(699\) 0 0
\(700\) 1.17447 + 0.589841i 0.0443908 + 0.0222939i
\(701\) 8.41328 14.5722i 0.317765 0.550385i −0.662256 0.749277i \(-0.730401\pi\)
0.980021 + 0.198892i \(0.0637343\pi\)
\(702\) 0 0
\(703\) −2.85826 4.95065i −0.107801 0.186717i
\(704\) 1.49002 + 25.5826i 0.0561571 + 0.964181i
\(705\) 0 0
\(706\) 48.1077 5.62298i 1.81056 0.211624i
\(707\) 2.09221 + 6.98846i 0.0786856 + 0.262828i
\(708\) 0 0
\(709\) 3.80953 + 8.83147i 0.143070 + 0.331673i 0.974651 0.223730i \(-0.0718233\pi\)
−0.831581 + 0.555403i \(0.812564\pi\)
\(710\) 0.630647 + 0.229537i 0.0236677 + 0.00861435i
\(711\) 0 0
\(712\) −24.9716 + 9.08893i −0.935851 + 0.340622i
\(713\) 30.8581 + 32.7077i 1.15565 + 1.22491i
\(714\) 0 0
\(715\) 0.576215 0.289386i 0.0215492 0.0108224i
\(716\) −0.221207 + 3.79797i −0.00826688 + 0.141937i
\(717\) 0 0
\(718\) −4.93000 + 16.4674i −0.183986 + 0.614556i
\(719\) −3.87901 + 21.9989i −0.144663 + 0.820422i 0.822975 + 0.568078i \(0.192313\pi\)
−0.967638 + 0.252344i \(0.918798\pi\)
\(720\) 0 0
\(721\) −1.22116 6.92552i −0.0454782 0.257920i
\(722\) 18.6152 + 2.17581i 0.692787 + 0.0809752i
\(723\) 0 0
\(724\) −0.00767184 + 0.00813167i −0.000285122 + 0.000302211i
\(725\) 2.19806 5.09567i 0.0816338 0.189248i
\(726\) 0 0
\(727\) 34.1335 22.4500i 1.26594 0.832623i 0.274300 0.961644i \(-0.411554\pi\)
0.991642 + 0.129021i \(0.0411835\pi\)
\(728\) 4.45573 0.165140
\(729\) 0 0
\(730\) −0.186277 −0.00689442
\(731\) −20.5642 + 13.5253i −0.760593 + 0.500250i
\(732\) 0 0
\(733\) −10.8312 + 25.1094i −0.400058 + 0.927439i 0.592489 + 0.805578i \(0.298145\pi\)
−0.992547 + 0.121860i \(0.961114\pi\)
\(734\) −0.707241 + 0.749632i −0.0261048 + 0.0276694i
\(735\) 0 0
\(736\) 12.8755 + 1.50494i 0.474599 + 0.0554727i
\(737\) 3.18607 + 18.0691i 0.117360 + 0.665584i
\(738\) 0 0
\(739\) −1.54918 + 8.78585i −0.0569876 + 0.323193i −0.999953 0.00969806i \(-0.996913\pi\)
0.942965 + 0.332891i \(0.108024\pi\)
\(740\) 0.00718097 0.0239861i 0.000263978 0.000881746i
\(741\) 0 0
\(742\) 0.779122 13.3770i 0.0286025 0.491085i
\(743\) −13.7851 + 6.92316i −0.505728 + 0.253986i −0.683321 0.730118i \(-0.739465\pi\)
0.177593 + 0.984104i \(0.443169\pi\)
\(744\) 0 0
\(745\) −0.279300 0.296041i −0.0102328 0.0108461i
\(746\) −15.9226 + 5.79536i −0.582968 + 0.212183i
\(747\) 0 0
\(748\) −2.36875 0.862154i −0.0866100 0.0315235i
\(749\) −1.98844 4.60973i −0.0726562 0.168436i
\(750\) 0 0
\(751\) −8.39900 28.0546i −0.306484 1.02373i −0.963019 0.269432i \(-0.913164\pi\)
0.656536 0.754295i \(-0.272021\pi\)
\(752\) −23.1053 + 2.70062i −0.842563 + 0.0984815i
\(753\) 0 0
\(754\) 0.199136 + 3.41903i 0.00725211 + 0.124514i
\(755\) 0.707063 + 1.22467i 0.0257327 + 0.0445703i
\(756\) 0 0
\(757\) −16.6330 + 28.8091i −0.604536 + 1.04709i 0.387589 + 0.921832i \(0.373308\pi\)
−0.992125 + 0.125254i \(0.960025\pi\)
\(758\) −27.1282 13.6243i −0.985340 0.494856i
\(759\) 0 0
\(760\) −0.684038 0.918823i −0.0248127 0.0333292i
\(761\) −0.311406 0.0738046i −0.0112885 0.00267542i 0.224968 0.974366i \(-0.427772\pi\)
−0.236256 + 0.971691i \(0.575920\pi\)
\(762\) 0 0
\(763\) −5.32007 + 7.14609i −0.192599 + 0.258706i
\(764\) −6.26572 + 5.25756i −0.226686 + 0.190212i
\(765\) 0 0
\(766\) −27.4025 22.9935i −0.990094 0.830787i
\(767\) −21.6231 + 5.12477i −0.780765 + 0.185045i
\(768\) 0 0
\(769\) −1.73643 1.14207i −0.0626173 0.0411841i 0.517814 0.855493i \(-0.326746\pi\)
−0.580432 + 0.814309i \(0.697116\pi\)
\(770\) 0.344759 + 0.226751i 0.0124242 + 0.00817155i
\(771\) 0 0
\(772\) −0.0135556 + 0.00321273i −0.000487876 + 0.000115629i
\(773\) −5.06191 4.24745i −0.182064 0.152770i 0.547201 0.837001i \(-0.315693\pi\)
−0.729265 + 0.684231i \(0.760138\pi\)
\(774\) 0 0
\(775\) −22.9235 + 19.2351i −0.823437 + 0.690945i
\(776\) −21.0884 + 28.3267i −0.757031 + 1.01687i
\(777\) 0 0
\(778\) −9.23194 2.18801i −0.330981 0.0784440i
\(779\) −14.6332 19.6558i −0.524290 0.704244i
\(780\) 0 0
\(781\) −19.8012 9.94453i −0.708542 0.355843i
\(782\) 11.6832 20.2359i 0.417791 0.723635i
\(783\) 0 0
\(784\) −14.1733 24.5489i −0.506191 0.876748i
\(785\) 0.0334053 + 0.573547i 0.00119229 + 0.0204708i
\(786\) 0 0
\(787\) −3.13787 + 0.366764i −0.111853 + 0.0130737i −0.171835 0.985126i \(-0.554970\pi\)
0.0599822 + 0.998199i \(0.480896\pi\)
\(788\) 1.07611 + 3.59446i 0.0383349 + 0.128047i
\(789\) 0 0
\(790\) −0.653990 1.51612i −0.0232679 0.0539411i
\(791\) 2.22697 + 0.810550i 0.0791818 + 0.0288198i
\(792\) 0 0
\(793\) −20.2657 + 7.37611i −0.719656 + 0.261933i
\(794\) −1.16975 1.23986i −0.0415129 0.0440011i
\(795\) 0 0
\(796\) 3.46062 1.73799i 0.122658 0.0616014i
\(797\) 2.72242 46.7421i 0.0964329 1.65569i −0.509720 0.860341i \(-0.670251\pi\)
0.606153 0.795348i \(-0.292712\pi\)
\(798\) 0 0
\(799\) −3.02471 + 10.1032i −0.107007 + 0.357427i
\(800\) −1.49802 + 8.49568i −0.0529629 + 0.300368i
\(801\) 0 0
\(802\) 1.11817 + 6.34143i 0.0394838 + 0.223924i
\(803\) 6.10864 + 0.713998i 0.215569 + 0.0251964i
\(804\) 0 0
\(805\) −0.350287 + 0.371282i −0.0123460 + 0.0130860i
\(806\) 7.31463 16.9572i 0.257647 0.597292i
\(807\) 0 0
\(808\) −18.3343 + 12.0586i −0.644998 + 0.424222i
\(809\) 47.8251 1.68144 0.840721 0.541468i \(-0.182131\pi\)
0.840721 + 0.541468i \(0.182131\pi\)
\(810\) 0 0
\(811\) 11.3948 0.400124 0.200062 0.979783i \(-0.435886\pi\)
0.200062 + 0.979783i \(0.435886\pi\)
\(812\) −0.244366 + 0.160722i −0.00857556 + 0.00564024i
\(813\) 0 0
\(814\) −2.45359 + 5.68805i −0.0859981 + 0.199366i
\(815\) −0.270193 + 0.286388i −0.00946446 + 0.0100317i
\(816\) 0 0
\(817\) −66.7668 7.80393i −2.33588 0.273025i
\(818\) 0.504121 + 2.85901i 0.0176262 + 0.0999630i
\(819\) 0 0
\(820\) 0.0186375 0.105699i 0.000650851 0.00369116i
\(821\) −4.57244 + 15.2730i −0.159579 + 0.533032i −0.999960 0.00896476i \(-0.997146\pi\)
0.840380 + 0.541997i \(0.182332\pi\)
\(822\) 0 0
\(823\) −2.24527 + 38.5497i −0.0782651 + 1.34376i 0.699242 + 0.714885i \(0.253521\pi\)
−0.777507 + 0.628874i \(0.783516\pi\)
\(824\) 18.9044 9.49414i 0.658566 0.330744i
\(825\) 0 0
\(826\) −9.75914 10.3441i −0.339564 0.359917i
\(827\) 32.7798 11.9309i 1.13986 0.414877i 0.298000 0.954566i \(-0.403680\pi\)
0.841865 + 0.539689i \(0.181458\pi\)
\(828\) 0 0
\(829\) 25.8256 + 9.39976i 0.896961 + 0.326467i 0.749034 0.662531i \(-0.230518\pi\)
0.147927 + 0.988998i \(0.452740\pi\)
\(830\) −0.300984 0.697758i −0.0104473 0.0242196i
\(831\) 0 0
\(832\) 3.73381 + 12.4718i 0.129447 + 0.432382i
\(833\) −12.7643 + 1.49194i −0.442258 + 0.0516925i
\(834\) 0 0
\(835\) −0.0829557 1.42429i −0.00287080 0.0492897i
\(836\) −3.44223 5.96211i −0.119052 0.206204i
\(837\) 0 0
\(838\) −1.88524 + 3.26532i −0.0651244 + 0.112799i
\(839\) 20.4441 + 10.2674i 0.705808 + 0.354470i 0.765225 0.643763i \(-0.222628\pi\)
−0.0594167 + 0.998233i \(0.518924\pi\)
\(840\) 0 0
\(841\) −16.5801 22.2709i −0.571727 0.767963i
\(842\) −25.8180 6.11898i −0.889747 0.210874i
\(843\) 0 0
\(844\) 2.52440 3.39086i 0.0868935 0.116718i
\(845\) −0.541824 + 0.454644i −0.0186393 + 0.0156402i
\(846\) 0 0
\(847\) −3.23615 2.71545i −0.111195 0.0933041i
\(848\) 45.4089 10.7621i 1.55935 0.369572i
\(849\) 0 0
\(850\) 12.9917 + 8.54479i 0.445612 + 0.293084i
\(851\) −6.40221 4.21080i −0.219465 0.144344i
\(852\) 0 0
\(853\) 51.5093 12.2079i 1.76365 0.417992i 0.784333 0.620341i \(-0.213006\pi\)
0.979314 + 0.202349i \(0.0648574\pi\)
\(854\) −10.5725 8.87141i −0.361785 0.303573i
\(855\) 0 0
\(856\) 11.5688 9.70736i 0.395413 0.331791i
\(857\) 9.39722 12.6227i 0.321003 0.431182i −0.612106 0.790776i \(-0.709677\pi\)
0.933109 + 0.359594i \(0.117085\pi\)
\(858\) 0 0
\(859\) −17.4554 4.13700i −0.595570 0.141153i −0.0782339 0.996935i \(-0.524928\pi\)
−0.517336 + 0.855782i \(0.673076\pi\)
\(860\) −0.175818 0.236165i −0.00599536 0.00805317i
\(861\) 0 0
\(862\) −31.7274 15.9341i −1.08064 0.542717i
\(863\) −24.9816 + 43.2695i −0.850385 + 1.47291i 0.0304761 + 0.999535i \(0.490298\pi\)
−0.880861 + 0.473375i \(0.843036\pi\)
\(864\) 0 0
\(865\) 0.0685821 + 0.118788i 0.00233186 + 0.00403890i
\(866\) −2.70079 46.3708i −0.0917767 1.57574i
\(867\) 0 0
\(868\) 1.56648 0.183095i 0.0531698 0.00621466i
\(869\) 15.6352 + 52.2254i 0.530389 + 1.77162i
\(870\) 0 0
\(871\) 3.69195 + 8.55891i 0.125097 + 0.290008i
\(872\) −25.1835 9.16605i −0.852821 0.310401i
\(873\) 0 0
\(874\) 59.9673 21.8263i 2.02842 0.738286i
\(875\) −0.466513 0.494475i −0.0157710 0.0167163i
\(876\) 0 0
\(877\) −7.31896 + 3.67572i −0.247144 + 0.124120i −0.568060 0.822987i \(-0.692306\pi\)
0.320916 + 0.947108i \(0.396009\pi\)
\(878\) 1.09607 18.8187i 0.0369905 0.635102i
\(879\) 0 0
\(880\) −0.412167 + 1.37673i −0.0138941 + 0.0464097i
\(881\) 2.64591 15.0057i 0.0891429 0.505555i −0.907243 0.420608i \(-0.861817\pi\)
0.996385 0.0849468i \(-0.0270720\pi\)
\(882\) 0 0
\(883\) −5.32760 30.2143i −0.179288 1.01679i −0.933077 0.359677i \(-0.882887\pi\)
0.753789 0.657117i \(-0.228224\pi\)
\(884\) −1.27196 0.148671i −0.0427808 0.00500036i
\(885\) 0 0
\(886\) −3.61603 + 3.83277i −0.121483 + 0.128764i
\(887\) −9.41627 + 21.8294i −0.316168 + 0.732959i 0.683827 + 0.729644i \(0.260314\pi\)
−0.999995 + 0.00331452i \(0.998945\pi\)
\(888\) 0 0
\(889\) −7.94375 + 5.22469i −0.266425 + 0.175230i
\(890\) −1.25028 −0.0419094
\(891\) 0 0
\(892\) −0.904673 −0.0302907
\(893\) −24.0645 + 15.8275i −0.805288 + 0.529646i
\(894\) 0 0
\(895\) 0.389465 0.902880i 0.0130184 0.0301800i
\(896\) −7.74340 + 8.20753i −0.258689 + 0.274194i
\(897\) 0 0
\(898\) −4.68336 0.547407i −0.156286 0.0182672i
\(899\) −1.15642 6.55838i −0.0385687 0.218734i
\(900\) 0 0
\(901\) 3.67384 20.8354i 0.122393 0.694128i
\(902\) −7.61591 + 25.4389i −0.253582 + 0.847023i
\(903\) 0 0
\(904\) −0.414516 + 7.11697i −0.0137866 + 0.236707i
\(905\) 0.00258214 0.00129680i 8.58332e−5 4.31071e-5i
\(906\) 0 0
\(907\) 23.7090 + 25.1300i 0.787244 + 0.834429i 0.989444 0.144915i \(-0.0462908\pi\)
−0.202201 + 0.979344i \(0.564809\pi\)
\(908\) 1.14786 0.417786i 0.0380930 0.0138647i
\(909\) 0 0
\(910\) 0.196992 + 0.0716993i 0.00653023 + 0.00237681i
\(911\) 19.8378 + 45.9892i 0.657256 + 1.52369i 0.841183 + 0.540751i \(0.181860\pi\)
−0.183926 + 0.982940i \(0.558881\pi\)
\(912\) 0 0
\(913\) 7.19575 + 24.0355i 0.238145 + 0.795459i
\(914\) 53.5359 6.25745i 1.77081 0.206978i
\(915\) 0 0
\(916\) 0.182984 + 3.14172i 0.00604598 + 0.103805i
\(917\) −4.24294 7.34898i −0.140114 0.242685i
\(918\) 0 0
\(919\) 1.41443 2.44986i 0.0466577 0.0808136i −0.841753 0.539862i \(-0.818476\pi\)
0.888411 + 0.459049i \(0.151810\pi\)
\(920\) −1.37217 0.689130i −0.0452392 0.0227200i
\(921\) 0 0
\(922\) 23.1224 + 31.0588i 0.761495 + 1.02287i
\(923\) −10.9535 2.59603i −0.360539 0.0854494i
\(924\) 0 0
\(925\) 3.04519 4.09040i 0.100125 0.134491i
\(926\) 10.8427 9.09809i 0.356313 0.298982i
\(927\) 0 0
\(928\) −1.47068 1.23405i −0.0482774 0.0405096i
\(929\) −12.0166 + 2.84797i −0.394250 + 0.0934390i −0.422959 0.906149i \(-0.639009\pi\)
0.0287088 + 0.999588i \(0.490860\pi\)
\(930\) 0 0
\(931\) −29.3239 19.2866i −0.961051 0.632093i
\(932\) 0.657106 + 0.432186i 0.0215242 + 0.0141567i
\(933\) 0 0
\(934\) −18.3446 + 4.34775i −0.600254 + 0.142263i
\(935\) 0.499097 + 0.418792i 0.0163222 + 0.0136960i
\(936\) 0 0
\(937\) −4.94841 + 4.15221i −0.161658 + 0.135647i −0.720028 0.693945i \(-0.755871\pi\)
0.558371 + 0.829592i \(0.311427\pi\)
\(938\) −3.56216 + 4.78481i −0.116309 + 0.156229i
\(939\) 0 0
\(940\) −0.122754 0.0290933i −0.00400381 0.000948920i
\(941\) 7.47147 + 10.0359i 0.243563 + 0.327162i 0.907048 0.421028i \(-0.138331\pi\)
−0.663485 + 0.748190i \(0.730923\pi\)
\(942\) 0 0
\(943\) −29.3541 14.7422i −0.955900 0.480071i
\(944\) 24.7639 42.8923i 0.805995 1.39602i
\(945\) 0 0
\(946\) 36.4221 + 63.0849i 1.18418 + 2.05107i
\(947\) −2.80010 48.0759i −0.0909911 1.56226i −0.667153 0.744921i \(-0.732487\pi\)
0.576162 0.817336i \(-0.304550\pi\)
\(948\) 0 0
\(949\) 3.10337 0.362731i 0.100740 0.0117748i
\(950\) 12.1800 + 40.6840i 0.395171 + 1.31996i
\(951\) 0 0
\(952\) 1.78323 + 4.13399i 0.0577947 + 0.133983i
\(953\) 23.6434 + 8.60549i 0.765884 + 0.278759i 0.695274 0.718745i \(-0.255283\pi\)
0.0706105 + 0.997504i \(0.477505\pi\)
\(954\) 0 0
\(955\) 1.98656 0.723047i 0.0642834 0.0233973i
\(956\) −0.985313 1.04437i −0.0318673 0.0337774i
\(957\) 0 0
\(958\) −47.1970 + 23.7032i −1.52487 + 0.765816i
\(959\) 0.798912 13.7168i 0.0257982 0.442938i
\(960\) 0 0
\(961\) −1.40821 + 4.70375i −0.0454262 + 0.151734i
\(962\) −0.546484 + 3.09926i −0.0176193 + 0.0999242i
\(963\) 0 0
\(964\) 0.0812022 + 0.460520i 0.00261535 + 0.0148324i
\(965\) 0.00357632 0.000418012i 0.000115126 1.34563e-5i
\(966\) 0 0
\(967\) 32.3702 34.3105i 1.04096 1.10335i 0.0464244 0.998922i \(-0.485217\pi\)
0.994532 0.104428i \(-0.0333012\pi\)
\(968\) 5.03339 11.6687i 0.161779 0.375046i
\(969\) 0 0
\(970\) −1.38816 + 0.913008i −0.0445712 + 0.0293149i
\(971\) 26.3271 0.844876 0.422438 0.906392i \(-0.361174\pi\)
0.422438 + 0.906392i \(0.361174\pi\)
\(972\) 0 0
\(973\) 17.3423 0.555968
\(974\) 5.75700 3.78644i 0.184466 0.121325i
\(975\) 0 0
\(976\) 19.0380 44.1351i 0.609392 1.41273i
\(977\) 11.9936 12.7124i 0.383708 0.406707i −0.506516 0.862231i \(-0.669067\pi\)
0.890223 + 0.455524i \(0.150548\pi\)
\(978\) 0 0
\(979\) 41.0007 + 4.79230i 1.31039 + 0.153162i
\(980\) −0.0266943 0.151391i −0.000852719 0.00483601i
\(981\) 0 0
\(982\) 7.90196 44.8142i 0.252162 1.43008i
\(983\) 11.3960 38.0654i 0.363477 1.21410i −0.559365 0.828921i \(-0.688955\pi\)
0.922843 0.385177i \(-0.125860\pi\)
\(984\) 0 0
\(985\) 0.0563875 0.968136i 0.00179666 0.0308474i
\(986\) −3.09245 + 1.55309i −0.0984838 + 0.0494604i
\(987\) 0 0
\(988\) −2.40013 2.54399i −0.0763584 0.0809351i
\(989\) −84.6743 + 30.8189i −2.69249 + 0.979985i
\(990\) 0 0
\(991\) −11.5059 4.18780i −0.365497 0.133030i 0.152742 0.988266i \(-0.451190\pi\)
−0.518238 + 0.855236i \(0.673412\pi\)
\(992\) 4.10032 + 9.50561i 0.130185 + 0.301803i
\(993\) 0 0
\(994\) −2.06611 6.90130i −0.0655331 0.218896i
\(995\) −0.994138 + 0.116198i −0.0315163 + 0.00368373i
\(996\) 0 0
\(997\) 0.487030 + 8.36199i 0.0154244 + 0.264827i 0.997200 + 0.0747823i \(0.0238262\pi\)
−0.981775 + 0.190045i \(0.939137\pi\)
\(998\) 5.18398 + 8.97892i 0.164096 + 0.284223i
\(999\) 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.a.28.6 144
3.2 odd 2 729.2.g.d.28.3 144
9.2 odd 6 729.2.g.c.271.6 144
9.4 even 3 243.2.g.a.91.6 144
9.5 odd 6 81.2.g.a.40.3 144
9.7 even 3 729.2.g.b.271.3 144
81.2 odd 54 729.2.g.c.460.6 144
81.25 even 27 243.2.g.a.235.6 144
81.29 odd 54 729.2.g.d.703.3 144
81.32 odd 54 6561.2.a.c.1.55 72
81.49 even 27 6561.2.a.d.1.18 72
81.52 even 27 inner 729.2.g.a.703.6 144
81.56 odd 54 81.2.g.a.79.3 yes 144
81.79 even 27 729.2.g.b.460.3 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.40.3 144 9.5 odd 6
81.2.g.a.79.3 yes 144 81.56 odd 54
243.2.g.a.91.6 144 9.4 even 3
243.2.g.a.235.6 144 81.25 even 27
729.2.g.a.28.6 144 1.1 even 1 trivial
729.2.g.a.703.6 144 81.52 even 27 inner
729.2.g.b.271.3 144 9.7 even 3
729.2.g.b.460.3 144 81.79 even 27
729.2.g.c.271.6 144 9.2 odd 6
729.2.g.c.460.6 144 81.2 odd 54
729.2.g.d.28.3 144 3.2 odd 2
729.2.g.d.703.3 144 81.29 odd 54
6561.2.a.c.1.55 72 81.32 odd 54
6561.2.a.d.1.18 72 81.49 even 27