Properties

Label 546.2.bz.b.31.4
Level $546$
Weight $2$
Character 546.31
Analytic conductor $4.360$
Analytic rank $0$
Dimension $40$
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] = [546,2,Mod(31,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bz (of order \(12\), degree \(4\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 31.4
Character \(\chi\) \(=\) 546.31
Dual form 546.2.bz.b.229.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.466002 - 1.73914i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.0195352 + 2.64568i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.466002 - 1.73914i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.0195352 + 2.64568i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.900247 + 1.55927i) q^{10} +(-3.06668 + 0.821714i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.35673 + 2.72871i) q^{13} +(0.703622 - 2.55047i) q^{14} +(-1.27314 + 1.27314i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.111696 + 0.193463i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.205632 - 0.767427i) q^{19} +(1.27314 - 1.27314i) q^{20} +(1.33976 - 2.28146i) q^{21} +3.17486 q^{22} +(-2.65409 + 1.53234i) q^{23} +(0.258819 + 0.965926i) q^{24} +(1.52266 + 0.879111i) q^{25} +(2.98266 - 2.02576i) q^{26} -1.00000i q^{27} +(-1.33976 + 2.28146i) q^{28} +1.94847 q^{29} +(1.55927 - 0.900247i) q^{30} +(-7.00225 + 1.87625i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(3.06668 + 0.821714i) q^{33} +(0.157962 - 0.157962i) q^{34} +(4.59211 + 1.26687i) q^{35} +1.00000i q^{36} +(-1.56149 + 5.82755i) q^{37} +(-0.397250 + 0.688056i) q^{38} +(3.40534 - 1.18477i) q^{39} +(-1.55927 + 0.900247i) q^{40} +(7.12025 + 7.12025i) q^{41} +(-1.88459 + 1.85696i) q^{42} +11.7777i q^{43} +(-3.06668 - 0.821714i) q^{44} +(1.73914 - 0.466002i) q^{45} +(2.96026 - 0.793198i) q^{46} +(-0.218962 - 0.0586707i) q^{47} -1.00000i q^{48} +(-6.99924 - 0.103368i) q^{49} +(-1.24325 - 1.24325i) q^{50} +(0.193463 - 0.111696i) q^{51} +(-3.40534 + 1.18477i) q^{52} +(0.0417568 - 0.0723248i) q^{53} +(-0.258819 + 0.965926i) q^{54} +5.71632i q^{55} +(1.88459 - 1.85696i) q^{56} +(-0.561796 + 0.561796i) q^{57} +(-1.88208 - 0.504302i) q^{58} +(-1.23841 - 4.62180i) q^{59} +(-1.73914 + 0.466002i) q^{60} +(5.64039 - 3.25648i) q^{61} +7.24926 q^{62} +(-2.30099 + 1.30592i) q^{63} +1.00000i q^{64} +(3.64737 + 5.37027i) q^{65} +(-2.74951 - 1.58743i) q^{66} +(0.753079 + 2.81053i) q^{67} +(-0.193463 + 0.111696i) q^{68} +3.06468 q^{69} +(-4.10775 - 2.41223i) q^{70} +(-8.47774 + 8.47774i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-1.28643 - 4.80103i) q^{73} +(3.01656 - 5.22484i) q^{74} +(-0.879111 - 1.52266i) q^{75} +(0.561796 - 0.561796i) q^{76} +(-2.11408 - 8.12950i) q^{77} +(-3.59594 + 0.263030i) q^{78} +(2.88905 + 5.00398i) q^{79} +(1.73914 - 0.466002i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.03478 - 8.72049i) q^{82} +(2.38179 + 2.38179i) q^{83} +(2.30099 - 1.30592i) q^{84} +(0.284410 + 0.284410i) q^{85} +(3.04828 - 11.3763i) q^{86} +(-1.68743 - 0.974236i) q^{87} +(2.74951 + 1.58743i) q^{88} +(-9.21651 - 2.46956i) q^{89} -1.80049 q^{90} +(-7.17324 - 6.28845i) q^{91} -3.06468 q^{92} +(7.00225 + 1.87625i) q^{93} +(0.196316 + 0.113343i) q^{94} +(-1.23884 - 0.715246i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(8.45484 + 8.45484i) q^{97} +(6.73399 + 1.91138i) q^{98} +(-2.24497 - 2.24497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0.466002 1.73914i 0.208402 0.777769i −0.779983 0.625801i \(-0.784772\pi\)
0.988385 0.151968i \(-0.0485610\pi\)
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) −0.0195352 + 2.64568i −0.00738360 + 0.999973i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −0.900247 + 1.55927i −0.284683 + 0.493086i
\(11\) −3.06668 + 0.821714i −0.924639 + 0.247756i −0.689567 0.724222i \(-0.742199\pi\)
−0.235072 + 0.971978i \(0.575532\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −2.35673 + 2.72871i −0.653638 + 0.756807i
\(14\) 0.703622 2.55047i 0.188051 0.681643i
\(15\) −1.27314 + 1.27314i −0.328724 + 0.328724i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −0.111696 + 0.193463i −0.0270903 + 0.0469217i −0.879253 0.476356i \(-0.841957\pi\)
0.852162 + 0.523277i \(0.175291\pi\)
\(18\) −0.258819 0.965926i −0.0610042 0.227671i
\(19\) 0.205632 0.767427i 0.0471751 0.176060i −0.938319 0.345772i \(-0.887617\pi\)
0.985494 + 0.169712i \(0.0542838\pi\)
\(20\) 1.27314 1.27314i 0.284683 0.284683i
\(21\) 1.33976 2.28146i 0.292359 0.497855i
\(22\) 3.17486 0.676882
\(23\) −2.65409 + 1.53234i −0.553417 + 0.319515i −0.750499 0.660872i \(-0.770187\pi\)
0.197082 + 0.980387i \(0.436853\pi\)
\(24\) 0.258819 + 0.965926i 0.0528312 + 0.197169i
\(25\) 1.52266 + 0.879111i 0.304533 + 0.175822i
\(26\) 2.98266 2.02576i 0.584949 0.397285i
\(27\) 1.00000i 0.192450i
\(28\) −1.33976 + 2.28146i −0.253190 + 0.431155i
\(29\) 1.94847 0.361822 0.180911 0.983499i \(-0.442095\pi\)
0.180911 + 0.983499i \(0.442095\pi\)
\(30\) 1.55927 0.900247i 0.284683 0.164362i
\(31\) −7.00225 + 1.87625i −1.25764 + 0.336984i −0.825284 0.564718i \(-0.808985\pi\)
−0.432358 + 0.901702i \(0.642318\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) 3.06668 + 0.821714i 0.533840 + 0.143042i
\(34\) 0.157962 0.157962i 0.0270903 0.0270903i
\(35\) 4.59211 + 1.26687i 0.776209 + 0.214140i
\(36\) 1.00000i 0.166667i
\(37\) −1.56149 + 5.82755i −0.256707 + 0.958043i 0.710426 + 0.703772i \(0.248502\pi\)
−0.967133 + 0.254271i \(0.918164\pi\)
\(38\) −0.397250 + 0.688056i −0.0644424 + 0.111617i
\(39\) 3.40534 1.18477i 0.545291 0.189714i
\(40\) −1.55927 + 0.900247i −0.246543 + 0.142342i
\(41\) 7.12025 + 7.12025i 1.11200 + 1.11200i 0.992880 + 0.119116i \(0.0380059\pi\)
0.119116 + 0.992880i \(0.461994\pi\)
\(42\) −1.88459 + 1.85696i −0.290799 + 0.286536i
\(43\) 11.7777i 1.79608i 0.439917 + 0.898038i \(0.355008\pi\)
−0.439917 + 0.898038i \(0.644992\pi\)
\(44\) −3.06668 0.821714i −0.462319 0.123878i
\(45\) 1.73914 0.466002i 0.259256 0.0694675i
\(46\) 2.96026 0.793198i 0.436466 0.116951i
\(47\) −0.218962 0.0586707i −0.0319389 0.00855800i 0.242814 0.970073i \(-0.421929\pi\)
−0.274753 + 0.961515i \(0.588596\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.99924 0.103368i −0.999891 0.0147668i
\(50\) −1.24325 1.24325i −0.175822 0.175822i
\(51\) 0.193463 0.111696i 0.0270903 0.0156406i
\(52\) −3.40534 + 1.18477i −0.472235 + 0.164298i
\(53\) 0.0417568 0.0723248i 0.00573573 0.00993458i −0.863143 0.504959i \(-0.831508\pi\)
0.868879 + 0.495024i \(0.164841\pi\)
\(54\) −0.258819 + 0.965926i −0.0352208 + 0.131446i
\(55\) 5.71632i 0.770788i
\(56\) 1.88459 1.85696i 0.251839 0.248147i
\(57\) −0.561796 + 0.561796i −0.0744117 + 0.0744117i
\(58\) −1.88208 0.504302i −0.247129 0.0662181i
\(59\) −1.23841 4.62180i −0.161227 0.601708i −0.998491 0.0549091i \(-0.982513\pi\)
0.837264 0.546798i \(-0.184154\pi\)
\(60\) −1.73914 + 0.466002i −0.224522 + 0.0601606i
\(61\) 5.64039 3.25648i 0.722178 0.416949i −0.0933761 0.995631i \(-0.529766\pi\)
0.815554 + 0.578682i \(0.196433\pi\)
\(62\) 7.24926 0.920657
\(63\) −2.30099 + 1.30592i −0.289898 + 0.164531i
\(64\) 1.00000i 0.125000i
\(65\) 3.64737 + 5.37027i 0.452401 + 0.666100i
\(66\) −2.74951 1.58743i −0.338441 0.195399i
\(67\) 0.753079 + 2.81053i 0.0920032 + 0.343361i 0.996548 0.0830178i \(-0.0264559\pi\)
−0.904545 + 0.426378i \(0.859789\pi\)
\(68\) −0.193463 + 0.111696i −0.0234609 + 0.0135451i
\(69\) 3.06468 0.368945
\(70\) −4.10775 2.41223i −0.490970 0.288316i
\(71\) −8.47774 + 8.47774i −1.00612 + 1.00612i −0.00614143 + 0.999981i \(0.501955\pi\)
−0.999981 + 0.00614143i \(0.998045\pi\)
\(72\) 0.258819 0.965926i 0.0305021 0.113835i
\(73\) −1.28643 4.80103i −0.150566 0.561918i −0.999444 0.0333308i \(-0.989389\pi\)
0.848879 0.528588i \(-0.177278\pi\)
\(74\) 3.01656 5.22484i 0.350668 0.607375i
\(75\) −0.879111 1.52266i −0.101511 0.175822i
\(76\) 0.561796 0.561796i 0.0644424 0.0644424i
\(77\) −2.11408 8.12950i −0.240922 0.926443i
\(78\) −3.59594 + 0.263030i −0.407161 + 0.0297823i
\(79\) 2.88905 + 5.00398i 0.325044 + 0.562992i 0.981521 0.191353i \(-0.0612876\pi\)
−0.656477 + 0.754346i \(0.727954\pi\)
\(80\) 1.73914 0.466002i 0.194442 0.0521006i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.03478 8.72049i −0.555998 0.963017i
\(83\) 2.38179 + 2.38179i 0.261436 + 0.261436i 0.825637 0.564201i \(-0.190816\pi\)
−0.564201 + 0.825637i \(0.690816\pi\)
\(84\) 2.30099 1.30592i 0.251059 0.142488i
\(85\) 0.284410 + 0.284410i 0.0308486 + 0.0308486i
\(86\) 3.04828 11.3763i 0.328705 1.22674i
\(87\) −1.68743 0.974236i −0.180911 0.104449i
\(88\) 2.74951 + 1.58743i 0.293099 + 0.169221i
\(89\) −9.21651 2.46956i −0.976948 0.261772i −0.265189 0.964196i \(-0.585434\pi\)
−0.711759 + 0.702424i \(0.752101\pi\)
\(90\) −1.80049 −0.189789
\(91\) −7.17324 6.28845i −0.751960 0.659208i
\(92\) −3.06468 −0.319515
\(93\) 7.00225 + 1.87625i 0.726100 + 0.194558i
\(94\) 0.196316 + 0.113343i 0.0202484 + 0.0116904i
\(95\) −1.23884 0.715246i −0.127102 0.0733826i
\(96\) −0.258819 + 0.965926i −0.0264156 + 0.0985844i
\(97\) 8.45484 + 8.45484i 0.858459 + 0.858459i 0.991157 0.132697i \(-0.0423639\pi\)
−0.132697 + 0.991157i \(0.542364\pi\)
\(98\) 6.73399 + 1.91138i 0.680236 + 0.193079i
\(99\) −2.24497 2.24497i −0.225627 0.225627i
\(100\) 0.879111 + 1.52266i 0.0879111 + 0.152266i
\(101\) 8.66835 15.0140i 0.862533 1.49395i −0.00694320 0.999976i \(-0.502210\pi\)
0.869476 0.493975i \(-0.164457\pi\)
\(102\) −0.215780 + 0.0578181i −0.0213654 + 0.00572485i
\(103\) −0.172869 0.299418i −0.0170333 0.0295025i 0.857383 0.514679i \(-0.172089\pi\)
−0.874416 + 0.485176i \(0.838755\pi\)
\(104\) 3.59594 0.263030i 0.352611 0.0257922i
\(105\) −3.34345 3.39320i −0.326288 0.331142i
\(106\) −0.0590530 + 0.0590530i −0.00573573 + 0.00573573i
\(107\) 0.134673 + 0.233260i 0.0130193 + 0.0225501i 0.872462 0.488683i \(-0.162522\pi\)
−0.859442 + 0.511233i \(0.829189\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −4.85339 18.1131i −0.464870 1.73492i −0.657318 0.753613i \(-0.728309\pi\)
0.192448 0.981307i \(-0.438357\pi\)
\(110\) 1.47949 5.52154i 0.141064 0.526458i
\(111\) 4.26606 4.26606i 0.404917 0.404917i
\(112\) −2.30099 + 1.30592i −0.217423 + 0.123398i
\(113\) −2.10825 −0.198328 −0.0991638 0.995071i \(-0.531617\pi\)
−0.0991638 + 0.995071i \(0.531617\pi\)
\(114\) 0.688056 0.397250i 0.0644424 0.0372058i
\(115\) 1.42815 + 5.32993i 0.133176 + 0.497018i
\(116\) 1.68743 + 0.974236i 0.156674 + 0.0904556i
\(117\) −3.54149 0.676631i −0.327411 0.0625546i
\(118\) 4.78484i 0.440480i
\(119\) −0.509660 0.299291i −0.0467204 0.0274360i
\(120\) 1.80049 0.164362
\(121\) −0.796971 + 0.460131i −0.0724519 + 0.0418301i
\(122\) −6.29103 + 1.68568i −0.569563 + 0.152614i
\(123\) −2.60619 9.72644i −0.234992 0.877004i
\(124\) −7.00225 1.87625i −0.628821 0.168492i
\(125\) 8.60417 8.60417i 0.769581 0.769581i
\(126\) 2.56059 0.665883i 0.228115 0.0593215i
\(127\) 2.03102i 0.180224i 0.995932 + 0.0901120i \(0.0287225\pi\)
−0.995932 + 0.0901120i \(0.971278\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) 5.88883 10.1998i 0.518483 0.898038i
\(130\) −2.13317 6.13129i −0.187091 0.537750i
\(131\) −4.52771 + 2.61408i −0.395588 + 0.228393i −0.684579 0.728939i \(-0.740014\pi\)
0.288991 + 0.957332i \(0.406680\pi\)
\(132\) 2.24497 + 2.24497i 0.195399 + 0.195399i
\(133\) 2.02635 + 0.559027i 0.175707 + 0.0484738i
\(134\) 2.90967i 0.251357i
\(135\) −1.73914 0.466002i −0.149682 0.0401071i
\(136\) 0.215780 0.0578181i 0.0185030 0.00495786i
\(137\) −15.6336 + 4.18902i −1.33567 + 0.357892i −0.854827 0.518914i \(-0.826337\pi\)
−0.480845 + 0.876806i \(0.659670\pi\)
\(138\) −2.96026 0.793198i −0.251994 0.0675215i
\(139\) 17.2938i 1.46684i −0.679776 0.733420i \(-0.737923\pi\)
0.679776 0.733420i \(-0.262077\pi\)
\(140\) 3.34345 + 3.39320i 0.282573 + 0.286777i
\(141\) 0.160291 + 0.160291i 0.0134990 + 0.0134990i
\(142\) 10.3831 5.99467i 0.871328 0.503061i
\(143\) 4.98511 10.3046i 0.416876 0.861716i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0.907992 3.38867i 0.0754047 0.281414i
\(146\) 4.97039i 0.411353i
\(147\) 6.00983 + 3.58914i 0.495683 + 0.296027i
\(148\) −4.26606 + 4.26606i −0.350668 + 0.350668i
\(149\) −21.5172 5.76551i −1.76276 0.472329i −0.775483 0.631368i \(-0.782494\pi\)
−0.987272 + 0.159039i \(0.949160\pi\)
\(150\) 0.455061 + 1.69831i 0.0371556 + 0.138667i
\(151\) 5.80675 1.55591i 0.472546 0.126618i −0.0146835 0.999892i \(-0.504674\pi\)
0.487230 + 0.873274i \(0.338007\pi\)
\(152\) −0.688056 + 0.397250i −0.0558087 + 0.0322212i
\(153\) −0.223392 −0.0180602
\(154\) −0.0620214 + 8.39966i −0.00499783 + 0.676864i
\(155\) 13.0523i 1.04838i
\(156\) 3.54149 + 0.676631i 0.283546 + 0.0541739i
\(157\) −0.933918 0.539198i −0.0745348 0.0430327i 0.462269 0.886740i \(-0.347035\pi\)
−0.536804 + 0.843707i \(0.680369\pi\)
\(158\) −1.49548 5.58122i −0.118974 0.444018i
\(159\) −0.0723248 + 0.0417568i −0.00573573 + 0.00331153i
\(160\) −1.80049 −0.142342
\(161\) −4.00224 7.05182i −0.315420 0.555761i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 2.19931 8.20793i 0.172263 0.642894i −0.824739 0.565514i \(-0.808678\pi\)
0.997002 0.0773803i \(-0.0246556\pi\)
\(164\) 2.60619 + 9.72644i 0.203509 + 0.759507i
\(165\) 2.85816 4.95048i 0.222507 0.385394i
\(166\) −1.68418 2.91709i −0.130718 0.226410i
\(167\) −12.2305 + 12.2305i −0.946423 + 0.946423i −0.998636 0.0522134i \(-0.983372\pi\)
0.0522134 + 0.998636i \(0.483372\pi\)
\(168\) −2.56059 + 0.665883i −0.197553 + 0.0513740i
\(169\) −1.89168 12.8616i −0.145514 0.989356i
\(170\) −0.201108 0.348329i −0.0154243 0.0267156i
\(171\) 0.767427 0.205632i 0.0586866 0.0157250i
\(172\) −5.88883 + 10.1998i −0.449019 + 0.777724i
\(173\) −5.15587 8.93022i −0.391993 0.678952i 0.600719 0.799460i \(-0.294881\pi\)
−0.992712 + 0.120508i \(0.961548\pi\)
\(174\) 1.37778 + 1.37778i 0.104449 + 0.104449i
\(175\) −2.35559 + 4.01131i −0.178066 + 0.303226i
\(176\) −2.24497 2.24497i −0.169221 0.169221i
\(177\) −1.23841 + 4.62180i −0.0930845 + 0.347396i
\(178\) 8.26330 + 4.77082i 0.619360 + 0.357588i
\(179\) 12.2977 + 7.10010i 0.919176 + 0.530686i 0.883372 0.468673i \(-0.155268\pi\)
0.0358037 + 0.999359i \(0.488601\pi\)
\(180\) 1.73914 + 0.466002i 0.129628 + 0.0347337i
\(181\) 21.6559 1.60967 0.804836 0.593497i \(-0.202253\pi\)
0.804836 + 0.593497i \(0.202253\pi\)
\(182\) 5.30125 + 7.93075i 0.392955 + 0.587866i
\(183\) −6.51296 −0.481452
\(184\) 2.96026 + 0.793198i 0.218233 + 0.0584754i
\(185\) 9.40729 + 5.43130i 0.691638 + 0.399317i
\(186\) −6.27805 3.62463i −0.460329 0.265771i
\(187\) 0.183564 0.685072i 0.0134236 0.0500974i
\(188\) −0.160291 0.160291i −0.0116904 0.0116904i
\(189\) 2.64568 + 0.0195352i 0.192445 + 0.00142097i
\(190\) 1.01151 + 1.01151i 0.0733826 + 0.0733826i
\(191\) −3.13759 5.43447i −0.227028 0.393224i 0.729898 0.683556i \(-0.239568\pi\)
−0.956926 + 0.290332i \(0.906234\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −7.72155 + 2.06898i −0.555810 + 0.148929i −0.525781 0.850620i \(-0.676227\pi\)
−0.0300292 + 0.999549i \(0.509560\pi\)
\(194\) −5.97848 10.3550i −0.429230 0.743447i
\(195\) −0.473584 6.47448i −0.0339141 0.463647i
\(196\) −6.00983 3.58914i −0.429274 0.256367i
\(197\) −18.2543 + 18.2543i −1.30056 + 1.30056i −0.372553 + 0.928011i \(0.621518\pi\)
−0.928011 + 0.372553i \(0.878482\pi\)
\(198\) 1.58743 + 2.74951i 0.112814 + 0.195399i
\(199\) −11.4624 + 19.8534i −0.812547 + 1.40737i 0.0985296 + 0.995134i \(0.468586\pi\)
−0.911076 + 0.412238i \(0.864747\pi\)
\(200\) −0.455061 1.69831i −0.0321777 0.120089i
\(201\) 0.753079 2.81053i 0.0531181 0.198239i
\(202\) −12.2589 + 12.2589i −0.862533 + 0.862533i
\(203\) −0.0380637 + 5.15503i −0.00267155 + 0.361812i
\(204\) 0.223392 0.0156406
\(205\) 15.7012 9.06508i 1.09662 0.633133i
\(206\) 0.0894836 + 0.333957i 0.00623462 + 0.0232679i
\(207\) −2.65409 1.53234i −0.184472 0.106505i
\(208\) −3.54149 0.676631i −0.245558 0.0469159i
\(209\) 2.52242i 0.174480i
\(210\) 2.35130 + 4.14292i 0.162255 + 0.285889i
\(211\) −0.357942 −0.0246417 −0.0123209 0.999924i \(-0.503922\pi\)
−0.0123209 + 0.999924i \(0.503922\pi\)
\(212\) 0.0723248 0.0417568i 0.00496729 0.00286787i
\(213\) 11.5808 3.10307i 0.793504 0.212619i
\(214\) −0.0697118 0.260168i −0.00476540 0.0177847i
\(215\) 20.4830 + 5.48842i 1.39693 + 0.374307i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) −4.82716 18.5624i −0.327689 1.26010i
\(218\) 18.7521i 1.27005i
\(219\) −1.28643 + 4.80103i −0.0869291 + 0.324424i
\(220\) −2.85816 + 4.95048i −0.192697 + 0.333761i
\(221\) −0.264667 0.760726i −0.0178035 0.0511719i
\(222\) −5.22484 + 3.01656i −0.350668 + 0.202458i
\(223\) 11.6892 + 11.6892i 0.782765 + 0.782765i 0.980297 0.197532i \(-0.0632925\pi\)
−0.197532 + 0.980297i \(0.563292\pi\)
\(224\) 2.56059 0.665883i 0.171086 0.0444912i
\(225\) 1.75822i 0.117215i
\(226\) 2.03641 + 0.545656i 0.135460 + 0.0362965i
\(227\) 5.48817 1.47055i 0.364262 0.0976038i −0.0720453 0.997401i \(-0.522953\pi\)
0.436308 + 0.899798i \(0.356286\pi\)
\(228\) −0.767427 + 0.205632i −0.0508241 + 0.0136183i
\(229\) 18.5532 + 4.97132i 1.22603 + 0.328514i 0.813033 0.582217i \(-0.197815\pi\)
0.412999 + 0.910732i \(0.364481\pi\)
\(230\) 5.51794i 0.363842i
\(231\) −2.23390 + 8.09740i −0.146980 + 0.532770i
\(232\) −1.37778 1.37778i −0.0904556 0.0904556i
\(233\) 9.32849 5.38580i 0.611129 0.352836i −0.162278 0.986745i \(-0.551884\pi\)
0.773407 + 0.633909i \(0.218551\pi\)
\(234\) 3.24569 + 1.57018i 0.212178 + 0.102646i
\(235\) −0.204073 + 0.353466i −0.0133123 + 0.0230576i
\(236\) 1.23841 4.62180i 0.0806135 0.300854i
\(237\) 5.77810i 0.375328i
\(238\) 0.414831 + 0.421003i 0.0268895 + 0.0272896i
\(239\) 3.09622 3.09622i 0.200278 0.200278i −0.599841 0.800119i \(-0.704770\pi\)
0.800119 + 0.599841i \(0.204770\pi\)
\(240\) −1.73914 0.466002i −0.112261 0.0300803i
\(241\) −5.09930 19.0309i −0.328475 1.22589i −0.910772 0.412909i \(-0.864513\pi\)
0.582297 0.812976i \(-0.302154\pi\)
\(242\) 0.888905 0.238181i 0.0571410 0.0153109i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 6.51296 0.416949
\(245\) −3.44143 + 12.1245i −0.219865 + 0.774606i
\(246\) 10.0696i 0.642011i
\(247\) 1.60947 + 2.36972i 0.102408 + 0.150782i
\(248\) 6.27805 + 3.62463i 0.398656 + 0.230164i
\(249\) −0.871797 3.25359i −0.0552479 0.206188i
\(250\) −10.5379 + 6.08407i −0.666476 + 0.384790i
\(251\) 9.94217 0.627544 0.313772 0.949498i \(-0.398407\pi\)
0.313772 + 0.949498i \(0.398407\pi\)
\(252\) −2.64568 0.0195352i −0.166662 0.00123060i
\(253\) 6.88011 6.88011i 0.432549 0.432549i
\(254\) 0.525667 1.96182i 0.0329833 0.123095i
\(255\) −0.104101 0.388511i −0.00651907 0.0243295i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 12.3991 + 21.4758i 0.773432 + 1.33962i 0.935672 + 0.352872i \(0.114795\pi\)
−0.162240 + 0.986751i \(0.551872\pi\)
\(258\) −8.32807 + 8.32807i −0.518483 + 0.518483i
\(259\) −15.3873 4.24504i −0.956122 0.263774i
\(260\) 0.473584 + 6.47448i 0.0293704 + 0.401530i
\(261\) 0.974236 + 1.68743i 0.0603037 + 0.104449i
\(262\) 5.05001 1.35314i 0.311990 0.0835976i
\(263\) 5.98709 10.3699i 0.369180 0.639438i −0.620258 0.784398i \(-0.712972\pi\)
0.989438 + 0.144960i \(0.0463053\pi\)
\(264\) −1.58743 2.74951i −0.0976996 0.169221i
\(265\) −0.106325 0.106325i −0.00653146 0.00653146i
\(266\) −1.81262 1.06444i −0.111139 0.0652648i
\(267\) 6.74695 + 6.74695i 0.412907 + 0.412907i
\(268\) −0.753079 + 2.81053i −0.0460016 + 0.171680i
\(269\) −4.24198 2.44911i −0.258638 0.149325i 0.365075 0.930978i \(-0.381043\pi\)
−0.623713 + 0.781653i \(0.714377\pi\)
\(270\) 1.55927 + 0.900247i 0.0948944 + 0.0547873i
\(271\) −18.8780 5.05835i −1.14676 0.307273i −0.365093 0.930971i \(-0.618963\pi\)
−0.781666 + 0.623698i \(0.785630\pi\)
\(272\) −0.223392 −0.0135451
\(273\) 3.06799 + 9.03258i 0.185683 + 0.546676i
\(274\) 16.1851 0.977779
\(275\) −5.39190 1.44476i −0.325144 0.0871220i
\(276\) 2.65409 + 1.53234i 0.159758 + 0.0922361i
\(277\) 19.4967 + 11.2564i 1.17144 + 0.676332i 0.954019 0.299745i \(-0.0969017\pi\)
0.217422 + 0.976078i \(0.430235\pi\)
\(278\) −4.47596 + 16.7045i −0.268450 + 1.00187i
\(279\) −5.12600 5.12600i −0.306886 0.306886i
\(280\) −2.35130 4.14292i −0.140517 0.247587i
\(281\) 12.6136 + 12.6136i 0.752467 + 0.752467i 0.974939 0.222472i \(-0.0714127\pi\)
−0.222472 + 0.974939i \(0.571413\pi\)
\(282\) −0.113343 0.196316i −0.00674948 0.0116904i
\(283\) 0.872513 1.51124i 0.0518655 0.0898337i −0.838927 0.544244i \(-0.816817\pi\)
0.890793 + 0.454410i \(0.150150\pi\)
\(284\) −11.5808 + 3.10307i −0.687194 + 0.184133i
\(285\) 0.715246 + 1.23884i 0.0423675 + 0.0733826i
\(286\) −7.48228 + 8.66326i −0.442436 + 0.512270i
\(287\) −18.9770 + 18.6988i −1.12018 + 1.10376i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 8.47505 + 14.6792i 0.498532 + 0.863483i
\(290\) −1.75411 + 3.03820i −0.103005 + 0.178409i
\(291\) −3.09469 11.5495i −0.181414 0.677045i
\(292\) 1.28643 4.80103i 0.0752828 0.280959i
\(293\) −20.0462 + 20.0462i −1.17111 + 1.17111i −0.189170 + 0.981944i \(0.560580\pi\)
−0.981944 + 0.189170i \(0.939420\pi\)
\(294\) −4.87612 5.02230i −0.284381 0.292906i
\(295\) −8.61508 −0.501589
\(296\) 5.22484 3.01656i 0.303688 0.175334i
\(297\) 0.821714 + 3.06668i 0.0476807 + 0.177947i
\(298\) 19.2918 + 11.1381i 1.11754 + 0.645213i
\(299\) 2.07366 10.8536i 0.119923 0.627677i
\(300\) 1.75822i 0.101511i
\(301\) −31.1599 0.230079i −1.79603 0.0132615i
\(302\) −6.01159 −0.345928
\(303\) −15.0140 + 8.66835i −0.862533 + 0.497984i
\(304\) 0.767427 0.205632i 0.0440150 0.0117938i
\(305\) −3.03505 11.3270i −0.173787 0.648580i
\(306\) 0.215780 + 0.0578181i 0.0123353 + 0.00330524i
\(307\) 8.60761 8.60761i 0.491262 0.491262i −0.417442 0.908704i \(-0.637073\pi\)
0.908704 + 0.417442i \(0.137073\pi\)
\(308\) 2.23390 8.09740i 0.127288 0.461392i
\(309\) 0.345738i 0.0196683i
\(310\) 3.37817 12.6075i 0.191867 0.716059i
\(311\) 1.72235 2.98320i 0.0976655 0.169162i −0.813052 0.582190i \(-0.802196\pi\)
0.910718 + 0.413029i \(0.135529\pi\)
\(312\) −3.24569 1.57018i −0.183751 0.0888940i
\(313\) 8.77092 5.06389i 0.495762 0.286228i −0.231200 0.972906i \(-0.574265\pi\)
0.726962 + 0.686678i \(0.240932\pi\)
\(314\) 0.762541 + 0.762541i 0.0430327 + 0.0430327i
\(315\) 1.19892 + 4.61032i 0.0675514 + 0.259762i
\(316\) 5.77810i 0.325044i
\(317\) −11.9496 3.20189i −0.671158 0.179836i −0.0928814 0.995677i \(-0.529608\pi\)
−0.578276 + 0.815841i \(0.696274\pi\)
\(318\) 0.0806679 0.0216149i 0.00452363 0.00121210i
\(319\) −5.97534 + 1.60109i −0.334555 + 0.0896437i
\(320\) 1.73914 + 0.466002i 0.0972211 + 0.0260503i
\(321\) 0.269346i 0.0150334i
\(322\) 2.04072 + 7.84739i 0.113725 + 0.437318i
\(323\) 0.125501 + 0.125501i 0.00698305 + 0.00698305i
\(324\) −0.866025 + 0.500000i −0.0481125 + 0.0277778i
\(325\) −5.98734 + 2.08308i −0.332118 + 0.115549i
\(326\) −4.24874 + 7.35903i −0.235316 + 0.407579i
\(327\) −4.85339 + 18.1131i −0.268393 + 1.00166i
\(328\) 10.0696i 0.555998i
\(329\) 0.159501 0.578157i 0.00879359 0.0318748i
\(330\) −4.04205 + 4.04205i −0.222507 + 0.222507i
\(331\) −24.1448 6.46959i −1.32712 0.355601i −0.475479 0.879727i \(-0.657725\pi\)
−0.851640 + 0.524127i \(0.824392\pi\)
\(332\) 0.871797 + 3.25359i 0.0478461 + 0.178564i
\(333\) −5.82755 + 1.56149i −0.319348 + 0.0855690i
\(334\) 14.9792 8.64825i 0.819626 0.473211i
\(335\) 5.23885 0.286229
\(336\) 2.64568 + 0.0195352i 0.144334 + 0.00106573i
\(337\) 3.20762i 0.174730i −0.996176 0.0873650i \(-0.972155\pi\)
0.996176 0.0873650i \(-0.0278446\pi\)
\(338\) −1.50161 + 12.9130i −0.0816767 + 0.702374i
\(339\) 1.82580 + 1.05413i 0.0991638 + 0.0572523i
\(340\) 0.104101 + 0.388511i 0.00564568 + 0.0210700i
\(341\) 19.9319 11.5077i 1.07937 0.623177i
\(342\) −0.794499 −0.0429616
\(343\) 0.410209 18.5157i 0.0221492 0.999755i
\(344\) 8.32807 8.32807i 0.449019 0.449019i
\(345\) 1.42815 5.32993i 0.0768890 0.286954i
\(346\) 2.66887 + 9.96037i 0.143480 + 0.535473i
\(347\) −12.6696 + 21.9443i −0.680138 + 1.17803i 0.294800 + 0.955559i \(0.404747\pi\)
−0.974938 + 0.222475i \(0.928586\pi\)
\(348\) −0.974236 1.68743i −0.0522246 0.0904556i
\(349\) 6.74898 6.74898i 0.361265 0.361265i −0.503014 0.864278i \(-0.667776\pi\)
0.864278 + 0.503014i \(0.167776\pi\)
\(350\) 3.31353 3.26495i 0.177116 0.174519i
\(351\) 2.72871 + 2.35673i 0.145648 + 0.125793i
\(352\) 1.58743 + 2.74951i 0.0846103 + 0.146549i
\(353\) −4.83670 + 1.29599i −0.257431 + 0.0689785i −0.385226 0.922822i \(-0.625877\pi\)
0.127795 + 0.991801i \(0.459210\pi\)
\(354\) 2.39242 4.14380i 0.127156 0.220240i
\(355\) 10.7934 + 18.6947i 0.572852 + 0.992209i
\(356\) −6.74695 6.74695i −0.357588 0.357588i
\(357\) 0.291733 + 0.514024i 0.0154401 + 0.0272050i
\(358\) −10.0411 10.0411i −0.530686 0.530686i
\(359\) 0.349207 1.30326i 0.0184304 0.0687833i −0.956098 0.293047i \(-0.905331\pi\)
0.974529 + 0.224263i \(0.0719976\pi\)
\(360\) −1.55927 0.900247i −0.0821809 0.0474472i
\(361\) 15.9078 + 9.18439i 0.837254 + 0.483389i
\(362\) −20.9180 5.60497i −1.09943 0.294591i
\(363\) 0.920262 0.0483013
\(364\) −3.06799 9.03258i −0.160806 0.473436i
\(365\) −8.94917 −0.468421
\(366\) 6.29103 + 1.68568i 0.328838 + 0.0881118i
\(367\) 2.58864 + 1.49455i 0.135126 + 0.0780150i 0.566039 0.824378i \(-0.308475\pi\)
−0.430913 + 0.902393i \(0.641808\pi\)
\(368\) −2.65409 1.53234i −0.138354 0.0798788i
\(369\) −2.60619 + 9.72644i −0.135673 + 0.506338i
\(370\) −7.68102 7.68102i −0.399317 0.399317i
\(371\) 0.190533 + 0.111888i 0.00989196 + 0.00580893i
\(372\) 5.12600 + 5.12600i 0.265771 + 0.265771i
\(373\) 7.22112 + 12.5073i 0.373895 + 0.647606i 0.990161 0.139933i \(-0.0446886\pi\)
−0.616266 + 0.787538i \(0.711355\pi\)
\(374\) −0.354619 + 0.614219i −0.0183369 + 0.0317605i
\(375\) −11.7535 + 3.14935i −0.606949 + 0.162632i
\(376\) 0.113343 + 0.196316i 0.00584522 + 0.0101242i
\(377\) −4.59202 + 5.31681i −0.236501 + 0.273830i
\(378\) −2.55047 0.703622i −0.131182 0.0361904i
\(379\) 16.0441 16.0441i 0.824130 0.824130i −0.162568 0.986697i \(-0.551978\pi\)
0.986697 + 0.162568i \(0.0519776\pi\)
\(380\) −0.715246 1.23884i −0.0366913 0.0635512i
\(381\) 1.01551 1.75892i 0.0520262 0.0901120i
\(382\) 1.62414 + 6.06136i 0.0830980 + 0.310126i
\(383\) 7.16979 26.7580i 0.366359 1.36727i −0.499210 0.866481i \(-0.666376\pi\)
0.865569 0.500790i \(-0.166957\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −15.1235 0.111669i −0.770767 0.00569119i
\(386\) 7.99394 0.406881
\(387\) −10.1998 + 5.88883i −0.518483 + 0.299346i
\(388\) 3.09469 + 11.5495i 0.157109 + 0.586339i
\(389\) 5.73080 + 3.30868i 0.290563 + 0.167757i 0.638196 0.769874i \(-0.279681\pi\)
−0.347633 + 0.937631i \(0.613014\pi\)
\(390\) −1.21827 + 6.37644i −0.0616895 + 0.322883i
\(391\) 0.684626i 0.0346230i
\(392\) 4.87612 + 5.02230i 0.246281 + 0.253664i
\(393\) 5.22815 0.263725
\(394\) 22.3568 12.9077i 1.12632 0.650282i
\(395\) 10.0490 2.69261i 0.505618 0.135480i
\(396\) −0.821714 3.06668i −0.0412927 0.154106i
\(397\) −21.6404 5.79852i −1.08610 0.291019i −0.329007 0.944328i \(-0.606714\pi\)
−0.757092 + 0.653308i \(0.773380\pi\)
\(398\) 16.2103 16.2103i 0.812547 0.812547i
\(399\) −1.47536 1.49731i −0.0738602 0.0749591i
\(400\) 1.75822i 0.0879111i
\(401\) −8.06709 + 30.1068i −0.402851 + 1.50346i 0.405133 + 0.914258i \(0.367225\pi\)
−0.807985 + 0.589204i \(0.799442\pi\)
\(402\) −1.45484 + 2.51985i −0.0725606 + 0.125679i
\(403\) 11.3827 23.5289i 0.567011 1.17206i
\(404\) 15.0140 8.66835i 0.746975 0.431266i
\(405\) 1.27314 + 1.27314i 0.0632629 + 0.0632629i
\(406\) 1.37099 4.96953i 0.0680410 0.246634i
\(407\) 19.1543i 0.949445i
\(408\) −0.215780 0.0578181i −0.0106827 0.00286242i
\(409\) 17.4925 4.68709i 0.864946 0.231762i 0.201045 0.979582i \(-0.435566\pi\)
0.663901 + 0.747820i \(0.268900\pi\)
\(410\) −17.5124 + 4.69243i −0.864876 + 0.231743i
\(411\) 15.6336 + 4.18902i 0.771150 + 0.206629i
\(412\) 0.345738i 0.0170333i
\(413\) 12.2520 3.18614i 0.602882 0.156780i
\(414\) 2.16706 + 2.16706i 0.106505 + 0.106505i
\(415\) 5.25220 3.03236i 0.257820 0.148853i
\(416\) 3.24569 + 1.57018i 0.159133 + 0.0769845i
\(417\) −8.64690 + 14.9769i −0.423440 + 0.733420i
\(418\) 0.652851 2.43647i 0.0319320 0.119172i
\(419\) 26.9996i 1.31902i −0.751697 0.659508i \(-0.770764\pi\)
0.751697 0.659508i \(-0.229236\pi\)
\(420\) −1.19892 4.61032i −0.0585012 0.224961i
\(421\) 22.4347 22.4347i 1.09340 1.09340i 0.0982373 0.995163i \(-0.468680\pi\)
0.995163 0.0982373i \(-0.0313204\pi\)
\(422\) 0.345745 + 0.0926421i 0.0168306 + 0.00450975i
\(423\) −0.0586707 0.218962i −0.00285267 0.0106463i
\(424\) −0.0806679 + 0.0216149i −0.00391758 + 0.00104971i
\(425\) −0.340151 + 0.196386i −0.0164998 + 0.00952614i
\(426\) −11.9893 −0.580885
\(427\) 8.50541 + 14.9863i 0.411606 + 0.725236i
\(428\) 0.269346i 0.0130193i
\(429\) −9.46954 + 6.43151i −0.457194 + 0.310516i
\(430\) −18.3646 10.6028i −0.885620 0.511313i
\(431\) 4.32782 + 16.1516i 0.208464 + 0.777998i 0.988366 + 0.152096i \(0.0486022\pi\)
−0.779902 + 0.625902i \(0.784731\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 29.7090 1.42772 0.713861 0.700288i \(-0.246945\pi\)
0.713861 + 0.700288i \(0.246945\pi\)
\(434\) −0.141616 + 19.1792i −0.00679777 + 0.920632i
\(435\) −2.48068 + 2.48068i −0.118940 + 0.118940i
\(436\) 4.85339 18.1131i 0.232435 0.867460i
\(437\) 0.630196 + 2.35192i 0.0301463 + 0.112508i
\(438\) 2.48520 4.30449i 0.118747 0.205676i
\(439\) 3.78193 + 6.55050i 0.180502 + 0.312638i 0.942052 0.335468i \(-0.108895\pi\)
−0.761550 + 0.648106i \(0.775561\pi\)
\(440\) 4.04205 4.04205i 0.192697 0.192697i
\(441\) −3.41010 6.11320i −0.162386 0.291105i
\(442\) 0.0587589 + 0.803306i 0.00279487 + 0.0382093i
\(443\) 1.91884 + 3.32353i 0.0911669 + 0.157906i 0.908002 0.418965i \(-0.137607\pi\)
−0.816835 + 0.576871i \(0.804274\pi\)
\(444\) 5.82755 1.56149i 0.276563 0.0741049i
\(445\) −8.58983 + 14.8780i −0.407197 + 0.705286i
\(446\) −8.26549 14.3163i −0.391383 0.677894i
\(447\) 15.7517 + 15.7517i 0.745028 + 0.745028i
\(448\) −2.64568 0.0195352i −0.124997 0.000922950i
\(449\) 24.4225 + 24.4225i 1.15257 + 1.15257i 0.986036 + 0.166534i \(0.0532576\pi\)
0.166534 + 0.986036i \(0.446742\pi\)
\(450\) 0.455061 1.69831i 0.0214518 0.0800592i
\(451\) −27.6863 15.9847i −1.30370 0.752691i
\(452\) −1.82580 1.05413i −0.0858784 0.0495819i
\(453\) −5.80675 1.55591i −0.272825 0.0731032i
\(454\) −5.68177 −0.266659
\(455\) −14.2793 + 9.54487i −0.669422 + 0.447471i
\(456\) 0.794499 0.0372058
\(457\) 22.5178 + 6.03362i 1.05334 + 0.282241i 0.743630 0.668591i \(-0.233102\pi\)
0.309707 + 0.950832i \(0.399769\pi\)
\(458\) −16.6344 9.60386i −0.777273 0.448759i
\(459\) 0.193463 + 0.111696i 0.00903009 + 0.00521353i
\(460\) −1.42815 + 5.32993i −0.0665878 + 0.248509i
\(461\) −4.28776 4.28776i −0.199701 0.199701i 0.600171 0.799872i \(-0.295099\pi\)
−0.799872 + 0.600171i \(0.795099\pi\)
\(462\) 4.25354 7.24331i 0.197893 0.336989i
\(463\) −28.2642 28.2642i −1.31355 1.31355i −0.918781 0.394767i \(-0.870825\pi\)
−0.394767 0.918781i \(-0.629175\pi\)
\(464\) 0.974236 + 1.68743i 0.0452278 + 0.0783368i
\(465\) 6.52613 11.3036i 0.302642 0.524191i
\(466\) −10.4046 + 2.78790i −0.481983 + 0.129147i
\(467\) 0.523058 + 0.905963i 0.0242042 + 0.0419230i 0.877874 0.478892i \(-0.158961\pi\)
−0.853670 + 0.520815i \(0.825628\pi\)
\(468\) −2.72871 2.35673i −0.126135 0.108940i
\(469\) −7.45047 + 1.93750i −0.344031 + 0.0894655i
\(470\) 0.288603 0.288603i 0.0133123 0.0133123i
\(471\) 0.539198 + 0.933918i 0.0248449 + 0.0430327i
\(472\) −2.39242 + 4.14380i −0.110120 + 0.190734i
\(473\) −9.67787 36.1183i −0.444989 1.66072i
\(474\) −1.49548 + 5.58122i −0.0686898 + 0.256354i
\(475\) 0.987761 0.987761i 0.0453216 0.0453216i
\(476\) −0.291733 0.514024i −0.0133715 0.0235602i
\(477\) 0.0835135 0.00382382
\(478\) −3.79208 + 2.18936i −0.173446 + 0.100139i
\(479\) −3.53184 13.1810i −0.161374 0.602256i −0.998475 0.0552075i \(-0.982418\pi\)
0.837101 0.547049i \(-0.184249\pi\)
\(480\) 1.55927 + 0.900247i 0.0711708 + 0.0410905i
\(481\) −12.2217 17.9948i −0.557261 0.820491i
\(482\) 19.7022i 0.897411i
\(483\) −0.0598691 + 8.10817i −0.00272414 + 0.368934i
\(484\) −0.920262 −0.0418301
\(485\) 18.6442 10.7642i 0.846588 0.488778i
\(486\) −0.965926 + 0.258819i −0.0438153 + 0.0117403i
\(487\) 9.59413 + 35.8058i 0.434752 + 1.62252i 0.741660 + 0.670776i \(0.234039\pi\)
−0.306908 + 0.951739i \(0.599294\pi\)
\(488\) −6.29103 1.68568i −0.284782 0.0763070i
\(489\) −6.00862 + 6.00862i −0.271719 + 0.271719i
\(490\) 6.46222 10.8207i 0.291933 0.488828i
\(491\) 29.9158i 1.35008i −0.737781 0.675040i \(-0.764126\pi\)
0.737781 0.675040i \(-0.235874\pi\)
\(492\) 2.60619 9.72644i 0.117496 0.438502i
\(493\) −0.217637 + 0.376958i −0.00980186 + 0.0169773i
\(494\) −0.941296 2.70554i −0.0423509 0.121728i
\(495\) −4.95048 + 2.85816i −0.222507 + 0.128465i
\(496\) −5.12600 5.12600i −0.230164 0.230164i
\(497\) −22.2638 22.5950i −0.998666 1.01352i
\(498\) 3.36836i 0.150940i
\(499\) −10.6303 2.84837i −0.475876 0.127510i 0.0129059 0.999917i \(-0.495892\pi\)
−0.488781 + 0.872406i \(0.662558\pi\)
\(500\) 11.7535 3.14935i 0.525633 0.140843i
\(501\) 16.7071 4.47666i 0.746420 0.200003i
\(502\) −9.60340 2.57322i −0.428621 0.114849i
\(503\) 19.1890i 0.855597i −0.903874 0.427798i \(-0.859289\pi\)
0.903874 0.427798i \(-0.140711\pi\)
\(504\) 2.55047 + 0.703622i 0.113607 + 0.0313418i
\(505\) −22.0721 22.0721i −0.982194 0.982194i
\(506\) −8.42638 + 4.86497i −0.374598 + 0.216274i
\(507\) −4.79257 + 12.0843i −0.212845 + 0.536684i
\(508\) −1.01551 + 1.75892i −0.0450560 + 0.0780393i
\(509\) 1.37973 5.14921i 0.0611553 0.228235i −0.928583 0.371124i \(-0.878973\pi\)
0.989739 + 0.142889i \(0.0456392\pi\)
\(510\) 0.402216i 0.0178104i
\(511\) 12.7271 3.30970i 0.563015 0.146412i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −0.767427 0.205632i −0.0338827 0.00907885i
\(514\) −6.41822 23.9531i −0.283096 1.05653i
\(515\) −0.601288 + 0.161115i −0.0264959 + 0.00709956i
\(516\) 10.1998 5.88883i 0.449019 0.259241i
\(517\) 0.719696 0.0316522
\(518\) 13.7643 + 8.08292i 0.604769 + 0.355143i
\(519\) 10.3117i 0.452635i
\(520\) 1.21827 6.37644i 0.0534247 0.279625i
\(521\) −6.90031 3.98390i −0.302308 0.174538i 0.341171 0.940001i \(-0.389176\pi\)
−0.643479 + 0.765463i \(0.722510\pi\)
\(522\) −0.504302 1.88208i −0.0220727 0.0823764i
\(523\) −7.92947 + 4.57808i −0.346731 + 0.200185i −0.663245 0.748403i \(-0.730821\pi\)
0.316513 + 0.948588i \(0.397488\pi\)
\(524\) −5.22815 −0.228393
\(525\) 4.04565 2.29610i 0.176567 0.100210i
\(526\) −8.46702 + 8.46702i −0.369180 + 0.369180i
\(527\) 0.419139 1.56425i 0.0182580 0.0681397i
\(528\) 0.821714 + 3.06668i 0.0357605 + 0.133460i
\(529\) −6.80386 + 11.7846i −0.295820 + 0.512375i
\(530\) 0.0751828 + 0.130220i 0.00326573 + 0.00565641i
\(531\) 3.38339 3.38339i 0.146827 0.146827i
\(532\) 1.47536 + 1.49731i 0.0639648 + 0.0649165i
\(533\) −36.2095 + 2.64860i −1.56841 + 0.114723i
\(534\) −4.77082 8.26330i −0.206453 0.357588i
\(535\) 0.468431 0.125516i 0.0202520 0.00542651i
\(536\) 1.45484 2.51985i 0.0628394 0.108841i
\(537\) −7.10010 12.2977i −0.306392 0.530686i
\(538\) 3.46356 + 3.46356i 0.149325 + 0.149325i
\(539\) 21.5494 5.43438i 0.928196 0.234075i
\(540\) −1.27314 1.27314i −0.0547873 0.0547873i
\(541\) −4.22877 + 15.7820i −0.181809 + 0.678520i 0.813482 + 0.581590i \(0.197569\pi\)
−0.995291 + 0.0969303i \(0.969098\pi\)
\(542\) 16.9256 + 9.77199i 0.727016 + 0.419743i
\(543\) −18.7546 10.8280i −0.804836 0.464672i
\(544\) 0.215780 + 0.0578181i 0.00925150 + 0.00247893i
\(545\) −33.7630 −1.44625
\(546\) −0.625646 9.51885i −0.0267752 0.407369i
\(547\) 31.4974 1.34673 0.673365 0.739310i \(-0.264848\pi\)
0.673365 + 0.739310i \(0.264848\pi\)
\(548\) −15.6336 4.18902i −0.667836 0.178946i
\(549\) 5.64039 + 3.25648i 0.240726 + 0.138983i
\(550\) 4.83425 + 2.79105i 0.206133 + 0.119011i
\(551\) 0.400667 1.49531i 0.0170690 0.0637024i
\(552\) −2.16706 2.16706i −0.0922361 0.0922361i
\(553\) −13.2954 + 7.54575i −0.565377 + 0.320878i
\(554\) −15.9190 15.9190i −0.676332 0.676332i
\(555\) −5.43130 9.40729i −0.230546 0.399317i
\(556\) 8.64690 14.9769i 0.366710 0.635161i
\(557\) 21.5789 5.78205i 0.914327 0.244993i 0.229168 0.973387i \(-0.426399\pi\)
0.685159 + 0.728394i \(0.259733\pi\)
\(558\) 3.62463 + 6.27805i 0.153443 + 0.265771i
\(559\) −32.1378 27.7567i −1.35928 1.17398i
\(560\) 1.19892 + 4.61032i 0.0506635 + 0.194822i
\(561\) −0.501508 + 0.501508i −0.0211737 + 0.0211737i
\(562\) −8.91919 15.4485i −0.376233 0.651655i
\(563\) −4.23343 + 7.33251i −0.178418 + 0.309029i −0.941339 0.337463i \(-0.890431\pi\)
0.762921 + 0.646492i \(0.223764\pi\)
\(564\) 0.0586707 + 0.218962i 0.00247048 + 0.00921996i
\(565\) −0.982450 + 3.66655i −0.0413320 + 0.154253i
\(566\) −1.23392 + 1.23392i −0.0518655 + 0.0518655i
\(567\) −2.28146 1.33976i −0.0958122 0.0562645i
\(568\) 11.9893 0.503061
\(569\) 3.69891 2.13556i 0.155066 0.0895275i −0.420459 0.907312i \(-0.638131\pi\)
0.575525 + 0.817784i \(0.304798\pi\)
\(570\) −0.370238 1.38175i −0.0155076 0.0578751i
\(571\) 22.5530 + 13.0210i 0.943813 + 0.544911i 0.891154 0.453702i \(-0.149897\pi\)
0.0526598 + 0.998613i \(0.483230\pi\)
\(572\) 9.46954 6.43151i 0.395941 0.268915i
\(573\) 6.27518i 0.262149i
\(574\) 23.1700 13.1500i 0.967096 0.548872i
\(575\) −5.38839 −0.224711
\(576\) −0.866025 + 0.500000i −0.0360844 + 0.0208333i
\(577\) −9.85848 + 2.64157i −0.410414 + 0.109970i −0.458118 0.888891i \(-0.651476\pi\)
0.0477039 + 0.998862i \(0.484810\pi\)
\(578\) −4.38701 16.3725i −0.182475 0.681008i
\(579\) 7.72155 + 2.06898i 0.320897 + 0.0859841i
\(580\) 2.48068 2.48068i 0.103005 0.103005i
\(581\) −6.34799 + 6.25493i −0.263359 + 0.259498i
\(582\) 11.9570i 0.495632i
\(583\) −0.0686243 + 0.256109i −0.00284213 + 0.0106070i
\(584\) −2.48520 + 4.30449i −0.102838 + 0.178121i
\(585\) −2.82710 + 5.84385i −0.116886 + 0.241614i
\(586\) 24.5515 14.1748i 1.01421 0.585557i
\(587\) 14.6950 + 14.6950i 0.606529 + 0.606529i 0.942037 0.335508i \(-0.108908\pi\)
−0.335508 + 0.942037i \(0.608908\pi\)
\(588\) 3.41010 + 6.11320i 0.140630 + 0.252104i
\(589\) 5.75953i 0.237317i
\(590\) 8.32153 + 2.22975i 0.342592 + 0.0917972i
\(591\) 24.9358 6.68153i 1.02572 0.274842i
\(592\) −5.82755 + 1.56149i −0.239511 + 0.0641767i
\(593\) 29.4230 + 7.88387i 1.20826 + 0.323752i 0.806078 0.591809i \(-0.201586\pi\)
0.402179 + 0.915561i \(0.368253\pi\)
\(594\) 3.17486i 0.130266i
\(595\) −0.758013 + 0.746901i −0.0310755 + 0.0306200i
\(596\) −15.7517 15.7517i −0.645213 0.645213i
\(597\) 19.8534 11.4624i 0.812547 0.469124i
\(598\) −4.81211 + 9.94703i −0.196782 + 0.406764i
\(599\) −19.2665 + 33.3706i −0.787208 + 1.36348i 0.140463 + 0.990086i \(0.455141\pi\)
−0.927671 + 0.373398i \(0.878193\pi\)
\(600\) −0.455061 + 1.69831i −0.0185778 + 0.0693333i
\(601\) 18.4547i 0.752783i −0.926461 0.376392i \(-0.877165\pi\)
0.926461 0.376392i \(-0.122835\pi\)
\(602\) 30.0386 + 8.28702i 1.22428 + 0.337754i
\(603\) −2.05745 + 2.05745i −0.0837858 + 0.0837858i
\(604\) 5.80675 + 1.55591i 0.236273 + 0.0633092i
\(605\) 0.428844 + 1.60047i 0.0174350 + 0.0650683i
\(606\) 16.7460 4.48707i 0.680258 0.182275i
\(607\) −16.2326 + 9.37191i −0.658862 + 0.380394i −0.791843 0.610725i \(-0.790878\pi\)
0.132981 + 0.991119i \(0.457545\pi\)
\(608\) −0.794499 −0.0322212
\(609\) 2.61048 4.44536i 0.105782 0.180135i
\(610\) 11.7265i 0.474794i
\(611\) 0.676128 0.459212i 0.0273532 0.0185777i
\(612\) −0.193463 0.111696i −0.00782029 0.00451505i
\(613\) 9.52923 + 35.5636i 0.384882 + 1.43640i 0.838353 + 0.545128i \(0.183519\pi\)
−0.453471 + 0.891271i \(0.649814\pi\)
\(614\) −10.5421 + 6.08650i −0.425445 + 0.245631i
\(615\) −18.1302 −0.731079
\(616\) −4.25354 + 7.24331i −0.171380 + 0.291841i
\(617\) −21.8442 + 21.8442i −0.879415 + 0.879415i −0.993474 0.114059i \(-0.963615\pi\)
0.114059 + 0.993474i \(0.463615\pi\)
\(618\) 0.0894836 0.333957i 0.00359956 0.0134337i
\(619\) 10.0041 + 37.3360i 0.402100 + 1.50066i 0.809341 + 0.587339i \(0.199824\pi\)
−0.407241 + 0.913321i \(0.633509\pi\)
\(620\) −6.52613 + 11.3036i −0.262096 + 0.453963i
\(621\) 1.53234 + 2.65409i 0.0614908 + 0.106505i
\(622\) −2.43577 + 2.43577i −0.0976655 + 0.0976655i
\(623\) 6.71370 24.3357i 0.268979 0.974988i
\(624\) 2.72871 + 2.35673i 0.109236 + 0.0943446i
\(625\) −6.55878 11.3601i −0.262351 0.454405i
\(626\) −9.78269 + 2.62126i −0.390995 + 0.104767i
\(627\) 1.26121 2.18448i 0.0503680 0.0872399i
\(628\) −0.539198 0.933918i −0.0215163 0.0372674i
\(629\) −0.953005 0.953005i −0.0379988 0.0379988i
\(630\) 0.0351730 4.76353i 0.00140132 0.189784i
\(631\) 11.8545 + 11.8545i 0.471922 + 0.471922i 0.902536 0.430614i \(-0.141703\pi\)
−0.430614 + 0.902536i \(0.641703\pi\)
\(632\) 1.49548 5.58122i 0.0594871 0.222009i
\(633\) 0.309986 + 0.178971i 0.0123209 + 0.00711345i
\(634\) 10.7137 + 6.18558i 0.425497 + 0.245661i
\(635\) 3.53224 + 0.946460i 0.140173 + 0.0375591i
\(636\) −0.0835135 −0.00331153
\(637\) 16.7773 18.8553i 0.664743 0.747072i
\(638\) 6.18613 0.244911
\(639\) −11.5808 3.10307i −0.458130 0.122755i
\(640\) −1.55927 0.900247i −0.0616357 0.0355854i
\(641\) −18.2477 10.5353i −0.720741 0.416120i 0.0942844 0.995545i \(-0.469944\pi\)
−0.815025 + 0.579425i \(0.803277\pi\)
\(642\) −0.0697118 + 0.260168i −0.00275130 + 0.0102680i
\(643\) −1.79630 1.79630i −0.0708392 0.0708392i 0.670800 0.741639i \(-0.265951\pi\)
−0.741639 + 0.670800i \(0.765951\pi\)
\(644\) 0.0598691 8.10817i 0.00235917 0.319507i
\(645\) −14.9946 14.9946i −0.590413 0.590413i
\(646\) −0.0887424 0.153706i −0.00349152 0.00604750i
\(647\) 15.2874 26.4786i 0.601010 1.04098i −0.391658 0.920111i \(-0.628098\pi\)
0.992668 0.120869i \(-0.0385683\pi\)
\(648\) 0.965926 0.258819i 0.0379452 0.0101674i
\(649\) 7.59560 + 13.1560i 0.298154 + 0.516417i
\(650\) 6.32247 0.462465i 0.247987 0.0181394i
\(651\) −5.10074 + 18.4891i −0.199914 + 0.724643i
\(652\) 6.00862 6.00862i 0.235316 0.235316i
\(653\) 3.40705 + 5.90119i 0.133328 + 0.230931i 0.924958 0.380070i \(-0.124100\pi\)
−0.791629 + 0.611002i \(0.790767\pi\)
\(654\) 9.37603 16.2398i 0.366632 0.635025i
\(655\) 2.43633 + 9.09250i 0.0951953 + 0.355274i
\(656\) −2.60619 + 9.72644i −0.101755 + 0.379754i
\(657\) 3.51460 3.51460i 0.137118 0.137118i
\(658\) −0.303704 + 0.517175i −0.0118396 + 0.0201616i
\(659\) 48.5714 1.89207 0.946037 0.324060i \(-0.105048\pi\)
0.946037 + 0.324060i \(0.105048\pi\)
\(660\) 4.95048 2.85816i 0.192697 0.111254i
\(661\) 6.21976 + 23.2125i 0.241921 + 0.902860i 0.974906 + 0.222616i \(0.0714595\pi\)
−0.732986 + 0.680244i \(0.761874\pi\)
\(662\) 21.6477 + 12.4983i 0.841360 + 0.485759i
\(663\) −0.151154 + 0.791141i −0.00587034 + 0.0307254i
\(664\) 3.36836i 0.130718i
\(665\) 1.91651 3.26360i 0.0743191 0.126557i
\(666\) 6.03312 0.233779
\(667\) −5.17143 + 2.98573i −0.200239 + 0.115608i
\(668\) −16.7071 + 4.47666i −0.646419 + 0.173207i
\(669\) −4.27853 15.9677i −0.165418 0.617347i
\(670\) −5.06034 1.35591i −0.195498 0.0523835i
\(671\) −14.6214 + 14.6214i −0.564451 + 0.564451i
\(672\) −2.55047 0.703622i −0.0983867 0.0271428i
\(673\) 12.5415i 0.483441i −0.970346 0.241721i \(-0.922288\pi\)
0.970346 0.241721i \(-0.0777117\pi\)
\(674\) −0.830192 + 3.09832i −0.0319778 + 0.119343i
\(675\) 0.879111 1.52266i 0.0338370 0.0586074i
\(676\) 4.79257 12.0843i 0.184330 0.464782i
\(677\) −32.6149 + 18.8302i −1.25349 + 0.723704i −0.971801 0.235801i \(-0.924229\pi\)
−0.281691 + 0.959505i \(0.590895\pi\)
\(678\) −1.49076 1.49076i −0.0572523 0.0572523i
\(679\) −22.5340 + 22.2036i −0.864774 + 0.852097i
\(680\) 0.402216i 0.0154243i
\(681\) −5.48817 1.47055i −0.210307 0.0563516i
\(682\) −22.2312 + 5.95682i −0.851276 + 0.228099i
\(683\) 48.6984 13.0487i 1.86339 0.499295i 0.863406 0.504509i \(-0.168326\pi\)
0.999986 + 0.00521439i \(0.00165980\pi\)
\(684\) 0.767427 + 0.205632i 0.0293433 + 0.00786252i
\(685\) 29.1412i 1.11343i
\(686\) −5.18845 + 17.7786i −0.198096 + 0.678792i
\(687\) −13.5819 13.5819i −0.518182 0.518182i
\(688\) −10.1998 + 5.88883i −0.388862 + 0.224510i
\(689\) 0.0989440 + 0.284392i 0.00376947 + 0.0108345i
\(690\) −2.75897 + 4.77868i −0.105032 + 0.181921i
\(691\) −4.46289 + 16.6557i −0.169776 + 0.633614i 0.827606 + 0.561309i \(0.189702\pi\)
−0.997383 + 0.0723050i \(0.976965\pi\)
\(692\) 10.3117i 0.391993i
\(693\) 5.98331 5.89560i 0.227287 0.223955i
\(694\) 17.9175 17.9175i 0.680138 0.680138i
\(695\) −30.0764 8.05895i −1.14086 0.305693i
\(696\) 0.504302 + 1.88208i 0.0191155 + 0.0713401i
\(697\) −2.17281 + 0.582203i −0.0823010 + 0.0220525i
\(698\) −8.26578 + 4.77225i −0.312864 + 0.180632i
\(699\) −10.7716 −0.407420
\(700\) −4.04565 + 2.29610i −0.152911 + 0.0867844i
\(701\) 23.8179i 0.899591i 0.893132 + 0.449796i \(0.148503\pi\)
−0.893132 + 0.449796i \(0.851497\pi\)
\(702\) −2.02576 2.98266i −0.0764575 0.112573i
\(703\) 4.15113 + 2.39666i 0.156563 + 0.0903916i
\(704\) −0.821714 3.06668i −0.0309695 0.115580i
\(705\) 0.353466 0.204073i 0.0133123 0.00768585i
\(706\) 5.00732 0.188453
\(707\) 39.5529 + 23.2270i 1.48754 + 0.873540i
\(708\) −3.38339 + 3.38339i −0.127156 + 0.127156i
\(709\) −10.0704 + 37.5831i −0.378201 + 1.41146i 0.470411 + 0.882448i \(0.344106\pi\)
−0.848611 + 0.529017i \(0.822561\pi\)
\(710\) −5.58706 20.8512i −0.209678 0.782531i
\(711\) −2.88905 + 5.00398i −0.108348 + 0.187664i
\(712\) 4.77082 + 8.26330i 0.178794 + 0.309680i
\(713\) 15.7096 15.7096i 0.588328 0.588328i
\(714\) −0.148753 0.572015i −0.00556694 0.0214071i
\(715\) −15.5982 13.4718i −0.583338 0.503817i
\(716\) 7.10010 + 12.2977i 0.265343 + 0.459588i
\(717\) −4.22951 + 1.13329i −0.157954 + 0.0423237i
\(718\) −0.674616 + 1.16847i −0.0251764 + 0.0436069i
\(719\) 19.8247 + 34.3373i 0.739336 + 1.28057i 0.952795 + 0.303615i \(0.0981937\pi\)
−0.213459 + 0.976952i \(0.568473\pi\)
\(720\) 1.27314 + 1.27314i 0.0474472 + 0.0474472i
\(721\) 0.795541 0.451507i 0.0296275 0.0168150i
\(722\) −12.9887 12.9887i −0.483389 0.483389i
\(723\) −5.09930 + 19.0309i −0.189645 + 0.707765i
\(724\) 18.7546 + 10.8280i 0.697009 + 0.402418i
\(725\) 2.96687 + 1.71292i 0.110187 + 0.0636164i
\(726\) −0.888905 0.238181i −0.0329904 0.00883974i
\(727\) −49.4576 −1.83428 −0.917140 0.398565i \(-0.869508\pi\)
−0.917140 + 0.398565i \(0.869508\pi\)
\(728\) 0.625646 + 9.51885i 0.0231880 + 0.352792i
\(729\) −1.00000 −0.0370370
\(730\) 8.64423 + 2.31621i 0.319937 + 0.0857269i
\(731\) −2.27854 1.31552i −0.0842750 0.0486562i
\(732\) −5.64039 3.25648i −0.208475 0.120363i
\(733\) 6.93687 25.8888i 0.256219 0.956223i −0.711189 0.703001i \(-0.751843\pi\)
0.967408 0.253222i \(-0.0814904\pi\)
\(734\) −2.11362 2.11362i −0.0780150 0.0780150i
\(735\) 9.04262 8.77942i 0.333542 0.323834i
\(736\) 2.16706 + 2.16706i 0.0798788 + 0.0798788i
\(737\) −4.61890 8.00017i −0.170139 0.294690i
\(738\) 5.03478 8.72049i 0.185333 0.321006i
\(739\) −4.18261 + 1.12073i −0.153860 + 0.0412266i −0.334927 0.942244i \(-0.608712\pi\)
0.181067 + 0.983471i \(0.442045\pi\)
\(740\) 5.43130 + 9.40729i 0.199659 + 0.345819i
\(741\) −0.208977 2.85697i −0.00767697 0.104954i
\(742\) −0.155082 0.157389i −0.00569323 0.00577793i
\(743\) 15.6827 15.6827i 0.575344 0.575344i −0.358273 0.933617i \(-0.616634\pi\)
0.933617 + 0.358273i \(0.116634\pi\)
\(744\) −3.62463 6.27805i −0.132885 0.230164i
\(745\) −20.0541 + 34.7347i −0.734725 + 1.27258i
\(746\) −3.73792 13.9501i −0.136855 0.510750i
\(747\) −0.871797 + 3.25359i −0.0318974 + 0.119043i
\(748\) 0.501508 0.501508i 0.0183369 0.0183369i
\(749\) −0.619762 + 0.351744i −0.0226456 + 0.0128525i
\(750\) 12.1681 0.444318
\(751\) −7.73391 + 4.46518i −0.282214 + 0.162937i −0.634425 0.772984i \(-0.718763\pi\)
0.352211 + 0.935921i \(0.385430\pi\)
\(752\) −0.0586707 0.218962i −0.00213950 0.00798472i
\(753\) −8.61017 4.97109i −0.313772 0.181156i
\(754\) 5.81164 3.94714i 0.211647 0.143747i
\(755\) 10.8238i 0.393919i
\(756\) 2.28146 + 1.33976i 0.0829758 + 0.0487265i
\(757\) −2.78338 −0.101164 −0.0505818 0.998720i \(-0.516108\pi\)
−0.0505818 + 0.998720i \(0.516108\pi\)
\(758\) −19.6499 + 11.3449i −0.713717 + 0.412065i
\(759\) −9.39840 + 2.51829i −0.341140 + 0.0914083i
\(760\) 0.370238 + 1.38175i 0.0134300 + 0.0501213i
\(761\) 51.6620 + 13.8428i 1.87275 + 0.501801i 0.999905 + 0.0137945i \(0.00439106\pi\)
0.872840 + 0.488006i \(0.162276\pi\)
\(762\) −1.43615 + 1.43615i −0.0520262 + 0.0520262i
\(763\) 48.0163 12.4867i 1.73831 0.452048i
\(764\) 6.27518i 0.227028i
\(765\) −0.104101 + 0.388511i −0.00376379 + 0.0140466i
\(766\) −13.8510 + 23.9906i −0.500456 + 0.866815i
\(767\) 15.5301 + 7.51307i 0.560761 + 0.271281i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) −15.3644 15.3644i −0.554056 0.554056i 0.373553 0.927609i \(-0.378139\pi\)
−0.927609 + 0.373553i \(0.878139\pi\)
\(770\) 14.5793 + 4.02212i 0.525402 + 0.144947i
\(771\) 24.7981i 0.893082i
\(772\) −7.72155 2.06898i −0.277905 0.0744644i
\(773\) 38.7771 10.3903i 1.39471 0.373713i 0.518271 0.855217i \(-0.326576\pi\)
0.876444 + 0.481504i \(0.159909\pi\)
\(774\) 11.3763 3.04828i 0.408914 0.109568i
\(775\) −12.3115 3.29886i −0.442242 0.118498i
\(776\) 11.9570i 0.429230i
\(777\) 11.2033 + 11.3700i 0.401916 + 0.407895i
\(778\) −4.67918 4.67918i −0.167757 0.167757i
\(779\) 6.92842 4.00013i 0.248236 0.143319i
\(780\) 2.82710 5.84385i 0.101226 0.209244i
\(781\) 19.0322 32.9648i 0.681027 1.17957i
\(782\) −0.177194 + 0.661298i −0.00633645 + 0.0236480i
\(783\) 1.94847i 0.0696327i
\(784\) −3.41010 6.11320i −0.121789 0.218329i
\(785\) −1.37295 + 1.37295i −0.0490027 + 0.0490027i
\(786\) −5.05001 1.35314i −0.180128 0.0482651i
\(787\) 5.70392 + 21.2873i 0.203323 + 0.758810i 0.989954 + 0.141388i \(0.0451564\pi\)
−0.786632 + 0.617423i \(0.788177\pi\)
\(788\) −24.9358 + 6.68153i −0.888302 + 0.238020i
\(789\) −10.3699 + 5.98709i −0.369180 + 0.213146i
\(790\) −10.4034 −0.370138
\(791\) 0.0411851 5.57776i 0.00146437 0.198322i
\(792\) 3.17486i 0.112814i
\(793\) −4.40687 + 23.0656i −0.156493 + 0.819083i
\(794\) 19.4022 + 11.2019i 0.688559 + 0.397540i
\(795\) 0.0389175 + 0.145242i 0.00138026 + 0.00515120i
\(796\) −19.8534 + 11.4624i −0.703686 + 0.406273i
\(797\) −45.1134 −1.59800 −0.799000 0.601332i \(-0.794637\pi\)
−0.799000 + 0.601332i \(0.794637\pi\)
\(798\) 1.03755 + 1.82814i 0.0367290 + 0.0647153i
\(799\) 0.0358078 0.0358078i 0.00126679 0.00126679i
\(800\) 0.455061 1.69831i 0.0160888 0.0600444i
\(801\) −2.46956 9.21651i −0.0872575 0.325649i
\(802\) 15.5844 26.9930i 0.550305 0.953156i
\(803\) 7.89015 + 13.6661i 0.278437 + 0.482268i
\(804\) 2.05745 2.05745i 0.0725606 0.0725606i
\(805\) −14.1292 + 3.67430i −0.497988 + 0.129502i
\(806\) −17.0845 + 19.7811i −0.601777 + 0.696760i
\(807\) 2.44911 + 4.24198i 0.0862127 + 0.149325i
\(808\) −16.7460 + 4.48707i −0.589121 + 0.157854i
\(809\) 17.1277 29.6660i 0.602177 1.04300i −0.390313 0.920682i \(-0.627633\pi\)
0.992491 0.122320i \(-0.0390333\pi\)
\(810\) −0.900247 1.55927i −0.0316315 0.0547873i
\(811\) 18.2145 + 18.2145i 0.639596 + 0.639596i 0.950456 0.310860i \(-0.100617\pi\)
−0.310860 + 0.950456i \(0.600617\pi\)
\(812\) −2.61048 + 4.44536i −0.0916099 + 0.156001i
\(813\) 13.8197 + 13.8197i 0.484677 + 0.484677i
\(814\) −4.95750 + 18.5017i −0.173760 + 0.648483i
\(815\) −13.2499 7.64982i −0.464123 0.267962i
\(816\) 0.193463 + 0.111696i 0.00677257 + 0.00391014i
\(817\) 9.03850 + 2.42186i 0.316217 + 0.0847301i
\(818\) −18.1095 −0.633185
\(819\) 1.85933 9.35644i 0.0649703 0.326940i
\(820\) 18.1302 0.633133
\(821\) −27.9819 7.49771i −0.976573 0.261672i −0.264972 0.964256i \(-0.585363\pi\)
−0.711601 + 0.702584i \(0.752030\pi\)
\(822\) −14.0167 8.09256i −0.488890 0.282261i
\(823\) −5.31305 3.06749i −0.185201 0.106926i 0.404533 0.914524i \(-0.367434\pi\)
−0.589734 + 0.807597i \(0.700767\pi\)
\(824\) −0.0894836 + 0.333957i −0.00311731 + 0.0116340i
\(825\) 3.94715 + 3.94715i 0.137422 + 0.137422i
\(826\) −12.6592 0.0934727i −0.440468 0.00325233i
\(827\) 15.7475 + 15.7475i 0.547595 + 0.547595i 0.925744 0.378150i \(-0.123440\pi\)
−0.378150 + 0.925744i \(0.623440\pi\)
\(828\) −1.53234 2.65409i −0.0532526 0.0922361i
\(829\) −21.7442 + 37.6621i −0.755209 + 1.30806i 0.190062 + 0.981772i \(0.439131\pi\)
−0.945271 + 0.326287i \(0.894202\pi\)
\(830\) −5.85807 + 1.56966i −0.203337 + 0.0544839i
\(831\) −11.2564 19.4967i −0.390481 0.676332i
\(832\) −2.72871 2.35673i −0.0946009 0.0817048i
\(833\) 0.801785 1.34255i 0.0277802 0.0465166i
\(834\) 12.2286 12.2286i 0.423440 0.423440i
\(835\) 15.5711 + 26.9700i 0.538861 + 0.933335i
\(836\) −1.26121 + 2.18448i −0.0436199 + 0.0755519i
\(837\) 1.87625 + 7.00225i 0.0648526 + 0.242033i
\(838\) −6.98801 + 26.0796i −0.241397 + 0.900905i
\(839\) −20.1834 + 20.1834i −0.696808 + 0.696808i −0.963721 0.266913i \(-0.913996\pi\)
0.266913 + 0.963721i \(0.413996\pi\)
\(840\) −0.0351730 + 4.76353i −0.00121358 + 0.164357i
\(841\) −25.2035 −0.869085
\(842\) −27.4768 + 15.8637i −0.946912 + 0.546700i
\(843\) −4.61691 17.2306i −0.159015 0.593452i
\(844\) −0.309986 0.178971i −0.0106702 0.00616043i
\(845\) −23.2498 2.70364i −0.799816 0.0930080i
\(846\) 0.226686i 0.00779363i
\(847\) −1.20179 2.11752i −0.0412940 0.0727588i
\(848\) 0.0835135 0.00286787
\(849\) −1.51124 + 0.872513i −0.0518655 + 0.0299446i
\(850\) 0.379389 0.101657i 0.0130129 0.00348681i
\(851\) −4.78546 17.8596i −0.164044 0.612219i
\(852\) 11.5808 + 3.10307i 0.396752 + 0.106309i
\(853\) −2.51650 + 2.51650i −0.0861635 + 0.0861635i −0.748875 0.662711i \(-0.769406\pi\)
0.662711 + 0.748875i \(0.269406\pi\)
\(854\) −4.33687 16.6770i −0.148404 0.570675i
\(855\) 1.43049i 0.0489218i
\(856\) 0.0697118 0.260168i 0.00238270 0.00889236i
\(857\) −19.3955 + 33.5940i −0.662538 + 1.14755i 0.317409 + 0.948289i \(0.397187\pi\)
−0.979947 + 0.199260i \(0.936146\pi\)
\(858\) 10.8115 3.76147i 0.369098 0.128414i
\(859\) 50.3485 29.0687i 1.71787 0.991813i 0.795085 0.606497i \(-0.207426\pi\)
0.922785 0.385315i \(-0.125907\pi\)
\(860\) 14.9946 + 14.9946i 0.511313 + 0.511313i
\(861\) 25.7840 6.70514i 0.878715 0.228511i
\(862\) 16.7214i 0.569534i
\(863\) 36.6383 + 9.81720i 1.24718 + 0.334181i 0.821247 0.570572i \(-0.193279\pi\)
0.425935 + 0.904754i \(0.359945\pi\)
\(864\) −0.965926 + 0.258819i −0.0328615 + 0.00880520i
\(865\) −17.9336 + 4.80529i −0.609760 + 0.163385i
\(866\) −28.6966 7.68924i −0.975152 0.261291i
\(867\) 16.9501i 0.575655i
\(868\) 5.10074 18.4891i 0.173130 0.627560i
\(869\) −12.9716 12.9716i −0.440033 0.440033i
\(870\) 3.03820 1.75411i 0.103005 0.0594698i
\(871\) −9.44391 4.56871i −0.319995 0.154805i
\(872\) −9.37603 + 16.2398i −0.317512 + 0.549948i
\(873\) −3.09469 + 11.5495i −0.104739 + 0.390892i
\(874\) 2.43489i 0.0823613i
\(875\) 22.5958 + 22.9320i 0.763877 + 0.775242i
\(876\) −3.51460 + 3.51460i −0.118747 + 0.118747i
\(877\) −15.9796 4.28173i −0.539593 0.144584i −0.0212787 0.999774i \(-0.506774\pi\)
−0.518315 + 0.855190i \(0.673440\pi\)
\(878\) −1.95767 7.30613i −0.0660682 0.246570i
\(879\) 27.3837 7.33744i 0.923629 0.247486i
\(880\) −4.95048 + 2.85816i −0.166881 + 0.0963485i
\(881\) −15.2653 −0.514301 −0.257150 0.966371i \(-0.582784\pi\)
−0.257150 + 0.966371i \(0.582784\pi\)
\(882\) 1.71169 + 6.78750i 0.0576356 + 0.228547i
\(883\) 31.6496i 1.06509i −0.846400 0.532547i \(-0.821235\pi\)
0.846400 0.532547i \(-0.178765\pi\)
\(884\) 0.151154 0.791141i 0.00508386 0.0266090i
\(885\) 7.46088 + 4.30754i 0.250795 + 0.144796i
\(886\) −0.993266 3.70692i −0.0333694 0.124536i
\(887\) −36.8469 + 21.2736i −1.23720 + 0.714297i −0.968521 0.248933i \(-0.919920\pi\)
−0.268678 + 0.963230i \(0.586587\pi\)
\(888\) −6.03312 −0.202458
\(889\) −5.37343 0.0396763i −0.180219 0.00133070i
\(890\) 12.1478 12.1478i 0.407197 0.407197i
\(891\) 0.821714 3.06668i 0.0275285 0.102738i
\(892\) 4.27853 + 15.9677i 0.143256 + 0.534638i
\(893\) −0.0900509 + 0.155973i −0.00301344 + 0.00521943i
\(894\) −11.1381 19.2918i −0.372514 0.645213i
\(895\) 18.0789 18.0789i 0.604310 0.604310i
\(896\) 2.55047 + 0.703622i 0.0852053 + 0.0235064i
\(897\) −7.22262 + 8.36262i −0.241156 + 0.279220i
\(898\) −17.2693 29.9113i −0.576285 0.998155i
\(899\) −13.6437 + 3.65582i −0.455043 + 0.121928i
\(900\) −0.879111 + 1.52266i −0.0293037 + 0.0507555i
\(901\) 0.00932813 + 0.0161568i 0.000310765 + 0.000538261i
\(902\) 22.6058 + 22.6058i 0.752691 + 0.752691i
\(903\) 26.8702 + 15.7792i 0.894186 + 0.525099i
\(904\) 1.49076 + 1.49076i 0.0495819 + 0.0495819i
\(905\) 10.0917 37.6628i 0.335460 1.25195i
\(906\) 5.20619 + 3.00579i 0.172964 + 0.0998608i
\(907\) −23.3567 13.4850i −0.775547 0.447762i 0.0593026 0.998240i \(-0.481112\pi\)
−0.834850 + 0.550478i \(0.814446\pi\)
\(908\) 5.48817 + 1.47055i 0.182131 + 0.0488019i
\(909\) 17.3367 0.575022
\(910\) 16.2631 5.52389i 0.539117 0.183115i
\(911\) 39.5322 1.30976 0.654880 0.755733i \(-0.272719\pi\)
0.654880 + 0.755733i \(0.272719\pi\)
\(912\) −0.767427 0.205632i −0.0254121 0.00680914i
\(913\) −9.26135 5.34704i −0.306506 0.176961i
\(914\) −20.1889 11.6561i −0.667789 0.385548i
\(915\) −3.03505 + 11.3270i −0.100336 + 0.374458i
\(916\) 13.5819 + 13.5819i 0.448759 + 0.448759i
\(917\) −6.82755 12.0299i −0.225466 0.397264i
\(918\) −0.157962 0.157962i −0.00521353 0.00521353i
\(919\) −22.1455 38.3570i −0.730511 1.26528i −0.956665 0.291191i \(-0.905949\pi\)
0.226154 0.974092i \(-0.427385\pi\)
\(920\) 2.75897 4.77868i 0.0909606 0.157548i
\(921\) −11.7582 + 3.15060i −0.387446 + 0.103816i
\(922\) 3.03190 + 5.25141i 0.0998504 + 0.172946i
\(923\) −3.15356 43.1130i −0.103801 1.41908i
\(924\) −5.98331 + 5.89560i −0.196837 + 0.193951i
\(925\) −7.50068 + 7.50068i −0.246621 + 0.246621i
\(926\) 19.9858 + 34.6164i 0.656774 + 1.13757i
\(927\) 0.172869 0.299418i 0.00567776 0.00983417i
\(928\) −0.504302 1.88208i −0.0165545 0.0617823i
\(929\) −8.08638 + 30.1788i −0.265306 + 0.990134i 0.696758 + 0.717307i \(0.254625\pi\)
−0.962063 + 0.272827i \(0.912041\pi\)
\(930\) −9.22934 + 9.22934i −0.302642 + 0.302642i
\(931\) −1.51859 + 5.35015i −0.0497698 + 0.175344i
\(932\) 10.7716 0.352836
\(933\) −2.98320 + 1.72235i −0.0976655 + 0.0563872i
\(934\) −0.270755 1.01047i −0.00885937 0.0330636i
\(935\) −1.10590 0.638490i −0.0361667 0.0208809i
\(936\) 2.02576 + 2.98266i 0.0662141 + 0.0974914i
\(937\) 22.7574i 0.743453i 0.928342 + 0.371726i \(0.121234\pi\)
−0.928342 + 0.371726i \(0.878766\pi\)
\(938\) 7.69806 + 0.0568409i 0.251351 + 0.00185592i
\(939\) −10.1278 −0.330508
\(940\) −0.353466 + 0.204073i −0.0115288 + 0.00665614i
\(941\) −18.6295 + 4.99176i −0.607304 + 0.162727i −0.549350 0.835593i \(-0.685125\pi\)
−0.0579545 + 0.998319i \(0.518458\pi\)
\(942\) −0.279109 1.04165i −0.00909388 0.0339388i
\(943\) −29.8085 7.98715i −0.970697 0.260097i
\(944\) 3.38339 3.38339i 0.110120 0.110120i
\(945\) 1.26687 4.59211i 0.0412112 0.149381i
\(946\) 37.3924i 1.21573i
\(947\) 3.52731 13.1641i 0.114622 0.427776i −0.884636 0.466282i \(-0.845593\pi\)
0.999258 + 0.0385061i \(0.0122599\pi\)
\(948\) 2.88905 5.00398i 0.0938320 0.162522i
\(949\) 16.1324 + 7.80442i 0.523679 + 0.253342i
\(950\) −1.20976 + 0.698453i −0.0392496 + 0.0226608i
\(951\) 8.74773 + 8.74773i 0.283665 + 0.283665i
\(952\) 0.148753 + 0.572015i 0.00482111 + 0.0185391i
\(953\) 18.1765i 0.588796i 0.955683 + 0.294398i \(0.0951192\pi\)
−0.955683 + 0.294398i \(0.904881\pi\)
\(954\) −0.0806679 0.0216149i −0.00261172 0.000699808i
\(955\) −10.9134 + 2.92425i −0.353151 + 0.0946264i
\(956\) 4.22951 1.13329i 0.136792 0.0366534i
\(957\) 5.97534 + 1.60109i 0.193155 + 0.0517558i
\(958\) 13.6460i 0.440882i
\(959\) −10.7774 41.4434i −0.348020 1.33828i
\(960\) −1.27314 1.27314i −0.0410905 0.0410905i
\(961\) 18.6644 10.7759i 0.602079 0.347610i
\(962\) 7.14784 + 20.5448i 0.230456 + 0.662392i
\(963\) −0.134673 + 0.233260i −0.00433977 + 0.00751670i
\(964\) 5.09930 19.0309i 0.164238 0.612943i
\(965\) 14.3930i 0.463329i
\(966\) 2.15638 7.81639i 0.0693803 0.251488i
\(967\) 40.1221 40.1221i 1.29024 1.29024i 0.355604 0.934637i \(-0.384275\pi\)
0.934637 0.355604i \(-0.115725\pi\)
\(968\) 0.888905 + 0.238181i 0.0285705 + 0.00765544i
\(969\) −0.0459365 0.171437i −0.00147569 0.00550736i
\(970\) −20.7949 + 5.57197i −0.667683 + 0.178905i
\(971\) −21.2164 + 12.2493i −0.680866 + 0.393098i −0.800181 0.599758i \(-0.795263\pi\)
0.119315 + 0.992856i \(0.461930\pi\)
\(972\) 1.00000 0.0320750
\(973\) 45.7538 + 0.337837i 1.46680 + 0.0108306i
\(974\) 37.0689i 1.18776i
\(975\) 6.22673 + 1.18967i 0.199415 + 0.0380998i
\(976\) 5.64039 + 3.25648i 0.180544 + 0.104237i
\(977\) −9.07108 33.8537i −0.290209 1.08308i −0.944948 0.327221i \(-0.893888\pi\)
0.654738 0.755856i \(-0.272779\pi\)
\(978\) 7.35903 4.24874i 0.235316 0.135860i
\(979\) 30.2933 0.968180
\(980\) −9.04262 + 8.77942i −0.288856 + 0.280448i
\(981\) 13.2597 13.2597i 0.423350 0.423350i
\(982\) −7.74278 + 28.8964i −0.247082 + 0.922122i
\(983\) −7.13708 26.6359i −0.227638 0.849555i −0.981331 0.192328i \(-0.938396\pi\)
0.753693 0.657226i \(-0.228271\pi\)
\(984\) −5.03478 + 8.72049i −0.160503 + 0.277999i
\(985\) 23.2403 + 40.2534i 0.740497 + 1.28258i
\(986\) 0.307785 0.307785i 0.00980186 0.00980186i
\(987\) −0.427210 + 0.420948i −0.0135983 + 0.0133989i
\(988\) 0.208977 + 2.85697i 0.00664845 + 0.0908925i
\(989\) −18.0474 31.2590i −0.573874 0.993979i
\(990\) 5.52154 1.47949i 0.175486 0.0470213i
\(991\) −29.1505 + 50.4902i −0.925997 + 1.60387i −0.136048 + 0.990702i \(0.543440\pi\)
−0.789949 + 0.613172i \(0.789893\pi\)
\(992\) 3.62463 + 6.27805i 0.115082 + 0.199328i
\(993\) 17.6752 + 17.6752i 0.560907 + 0.560907i
\(994\) 15.6571 + 27.5874i 0.496614 + 0.875018i
\(995\) 29.1865 + 29.1865i 0.925273 + 0.925273i
\(996\) 0.871797 3.25359i 0.0276239 0.103094i
\(997\) −33.7793 19.5025i −1.06980 0.617649i −0.141673 0.989913i \(-0.545248\pi\)
−0.928127 + 0.372264i \(0.878582\pi\)
\(998\) 9.53083 + 5.50262i 0.301693 + 0.174183i
\(999\) 5.82755 + 1.56149i 0.184376 + 0.0494033i
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 546.2.bz.b.31.4 yes 40
7.5 odd 6 546.2.bz.a.187.9 yes 40
13.8 odd 4 546.2.bz.a.73.9 40
91.47 even 12 inner 546.2.bz.b.229.4 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bz.a.73.9 40 13.8 odd 4
546.2.bz.a.187.9 yes 40 7.5 odd 6
546.2.bz.b.31.4 yes 40 1.1 even 1 trivial
546.2.bz.b.229.4 yes 40 91.47 even 12 inner