Properties

Label 546.2.bx.a.97.5
Level $546$
Weight $2$
Character 546.97
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(97,546)]
 
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, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bx (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 97.5
Character \(\chi\) \(=\) 546.97
Dual form 546.2.bx.a.349.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.52974 + 2.52974i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.48229 - 0.915557i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.52974 + 2.52974i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.48229 - 0.915557i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.78880 - 3.09829i) q^{10} +(-0.141178 + 0.0378284i) q^{11} +1.00000 q^{12} +(-3.09703 + 1.84618i) q^{13} +(-0.241896 + 2.63467i) q^{14} +(-0.925950 - 3.45569i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.55049 + 4.41758i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-1.37483 + 5.13093i) q^{19} +(-3.45569 - 0.925950i) q^{20} +(1.69195 + 2.03404i) q^{21} +(0.0730789 + 0.126576i) q^{22} +(-4.87674 - 2.81559i) q^{23} +(-0.258819 - 0.965926i) q^{24} +7.79920i q^{25} +(2.58485 + 2.51368i) q^{26} -1.00000i q^{27} +(2.60750 - 0.448249i) q^{28} +(-1.83299 + 3.17482i) q^{29} +(-3.09829 + 1.78880i) q^{30} +(7.04095 + 7.04095i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.141178 + 0.0378284i) q^{33} +(3.60694 - 3.60694i) q^{34} +(-3.96343 - 8.59568i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.66064 - 0.980866i) q^{37} +5.31193 q^{38} +(3.60520 - 0.0503243i) q^{39} +3.57760i q^{40} +(-6.98851 + 1.87256i) q^{41} +(1.52682 - 2.16074i) q^{42} +(2.79434 - 1.61331i) q^{43} +(0.103349 - 0.103349i) q^{44} +(-0.925950 + 3.45569i) q^{45} +(-1.45746 + 5.43930i) q^{46} +(1.81311 - 1.81311i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(5.32351 + 4.54535i) q^{49} +(7.53345 - 2.01858i) q^{50} -5.10098i q^{51} +(1.75902 - 3.14736i) q^{52} +7.13879 q^{53} +(-0.965926 + 0.258819i) q^{54} +(-0.452839 - 0.261447i) q^{55} +(-1.10785 - 2.40264i) q^{56} +(3.75610 - 3.75610i) q^{57} +(3.54106 + 0.948823i) q^{58} +(-4.08824 - 1.09544i) q^{59} +(2.52974 + 2.52974i) q^{60} +(9.62468 - 5.55681i) q^{61} +(4.97871 - 8.62337i) q^{62} +(-0.448249 - 2.60750i) q^{63} +1.00000i q^{64} +(-12.5051 - 3.16433i) q^{65} -0.146158i q^{66} +(1.29264 + 4.82420i) q^{67} +(-4.41758 - 2.55049i) q^{68} +(2.81559 + 4.87674i) q^{69} +(-7.27697 + 6.05310i) q^{70} +(6.47842 + 1.73589i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-7.91676 + 7.91676i) q^{73} +(-1.89489 - 3.28204i) q^{74} +(3.89960 - 6.75431i) q^{75} +(-1.37483 - 5.13093i) q^{76} +(0.385078 + 0.0353550i) q^{77} +(-0.981704 - 3.46933i) q^{78} -8.03063 q^{79} +(3.45569 - 0.925950i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.61752 + 6.26572i) q^{82} +(-5.59369 - 5.59369i) q^{83} +(-2.48229 - 0.915557i) q^{84} +(-4.72326 + 17.6274i) q^{85} +(-2.28157 - 2.28157i) q^{86} +(3.17482 - 1.83299i) q^{87} +(-0.126576 - 0.0730789i) q^{88} +(-3.28299 - 12.2523i) q^{89} +3.57760 q^{90} +(9.37801 - 1.74725i) q^{91} +5.63117 q^{92} +(-2.57717 - 9.61812i) q^{93} +(-2.22059 - 1.28206i) q^{94} +(-16.4579 + 9.50198i) q^{95} +(0.707107 + 0.707107i) q^{96} +(1.80716 - 6.74442i) q^{97} +(3.01265 - 6.31854i) q^{98} +(-0.103349 - 0.103349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 2.52974 + 2.52974i 1.13134 + 1.13134i 0.989955 + 0.141380i \(0.0451540\pi\)
0.141380 + 0.989955i \(0.454846\pi\)
\(6\) −0.258819 + 0.965926i −0.105662 + 0.394338i
\(7\) −2.48229 0.915557i −0.938217 0.346048i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.78880 3.09829i 0.565668 0.979765i
\(11\) −0.141178 + 0.0378284i −0.0425667 + 0.0114057i −0.280040 0.959988i \(-0.590348\pi\)
0.237473 + 0.971394i \(0.423681\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.09703 + 1.84618i −0.858962 + 0.512039i
\(14\) −0.241896 + 2.63467i −0.0646495 + 0.704145i
\(15\) −0.925950 3.45569i −0.239079 0.892256i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 2.55049 + 4.41758i 0.618585 + 1.07142i 0.989744 + 0.142851i \(0.0456271\pi\)
−0.371159 + 0.928569i \(0.621040\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −1.37483 + 5.13093i −0.315408 + 1.17712i 0.608202 + 0.793782i \(0.291891\pi\)
−0.923609 + 0.383335i \(0.874776\pi\)
\(20\) −3.45569 0.925950i −0.772717 0.207049i
\(21\) 1.69195 + 2.03404i 0.369213 + 0.443864i
\(22\) 0.0730789 + 0.126576i 0.0155805 + 0.0269862i
\(23\) −4.87674 2.81559i −1.01687 0.587090i −0.103675 0.994611i \(-0.533060\pi\)
−0.913196 + 0.407521i \(0.866393\pi\)
\(24\) −0.258819 0.965926i −0.0528312 0.197169i
\(25\) 7.79920i 1.55984i
\(26\) 2.58485 + 2.51368i 0.506930 + 0.492973i
\(27\) 1.00000i 0.192450i
\(28\) 2.60750 0.448249i 0.492772 0.0847111i
\(29\) −1.83299 + 3.17482i −0.340377 + 0.589550i −0.984503 0.175370i \(-0.943888\pi\)
0.644126 + 0.764920i \(0.277221\pi\)
\(30\) −3.09829 + 1.78880i −0.565668 + 0.326588i
\(31\) 7.04095 + 7.04095i 1.26459 + 1.26459i 0.948842 + 0.315750i \(0.102256\pi\)
0.315750 + 0.948842i \(0.397744\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 0.141178 + 0.0378284i 0.0245759 + 0.00658508i
\(34\) 3.60694 3.60694i 0.618585 0.618585i
\(35\) −3.96343 8.59568i −0.669942 1.45293i
\(36\) −0.866025 0.500000i −0.144338 0.0833333i
\(37\) 3.66064 0.980866i 0.601806 0.161253i 0.0549627 0.998488i \(-0.482496\pi\)
0.546843 + 0.837235i \(0.315829\pi\)
\(38\) 5.31193 0.861710
\(39\) 3.60520 0.0503243i 0.577294 0.00805834i
\(40\) 3.57760i 0.565668i
\(41\) −6.98851 + 1.87256i −1.09142 + 0.292445i −0.759267 0.650780i \(-0.774442\pi\)
−0.332155 + 0.943225i \(0.607776\pi\)
\(42\) 1.52682 2.16074i 0.235594 0.333410i
\(43\) 2.79434 1.61331i 0.426132 0.246028i −0.271565 0.962420i \(-0.587541\pi\)
0.697698 + 0.716392i \(0.254208\pi\)
\(44\) 0.103349 0.103349i 0.0155805 0.0155805i
\(45\) −0.925950 + 3.45569i −0.138033 + 0.515144i
\(46\) −1.45746 + 5.43930i −0.214890 + 0.801981i
\(47\) 1.81311 1.81311i 0.264469 0.264469i −0.562398 0.826867i \(-0.690121\pi\)
0.826867 + 0.562398i \(0.190121\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) 5.32351 + 4.54535i 0.760502 + 0.649336i
\(50\) 7.53345 2.01858i 1.06539 0.285471i
\(51\) 5.10098i 0.714281i
\(52\) 1.75902 3.14736i 0.243932 0.436460i
\(53\) 7.13879 0.980589 0.490294 0.871557i \(-0.336889\pi\)
0.490294 + 0.871557i \(0.336889\pi\)
\(54\) −0.965926 + 0.258819i −0.131446 + 0.0352208i
\(55\) −0.452839 0.261447i −0.0610608 0.0352535i
\(56\) −1.10785 2.40264i −0.148042 0.321066i
\(57\) 3.75610 3.75610i 0.497508 0.497508i
\(58\) 3.54106 + 0.948823i 0.464963 + 0.124587i
\(59\) −4.08824 1.09544i −0.532244 0.142614i −0.0173194 0.999850i \(-0.505513\pi\)
−0.514924 + 0.857236i \(0.672180\pi\)
\(60\) 2.52974 + 2.52974i 0.326588 + 0.326588i
\(61\) 9.62468 5.55681i 1.23231 0.711477i 0.264803 0.964303i \(-0.414693\pi\)
0.967512 + 0.252825i \(0.0813599\pi\)
\(62\) 4.97871 8.62337i 0.632296 1.09517i
\(63\) −0.448249 2.60750i −0.0564741 0.328515i
\(64\) 1.00000i 0.125000i
\(65\) −12.5051 3.16433i −1.55106 0.392487i
\(66\) 0.146158i 0.0179908i
\(67\) 1.29264 + 4.82420i 0.157921 + 0.589370i 0.998837 + 0.0482049i \(0.0153500\pi\)
−0.840916 + 0.541165i \(0.817983\pi\)
\(68\) −4.41758 2.55049i −0.535710 0.309293i
\(69\) 2.81559 + 4.87674i 0.338957 + 0.587090i
\(70\) −7.27697 + 6.05310i −0.869765 + 0.723484i
\(71\) 6.47842 + 1.73589i 0.768847 + 0.206012i 0.621862 0.783127i \(-0.286376\pi\)
0.146985 + 0.989139i \(0.453043\pi\)
\(72\) −0.258819 + 0.965926i −0.0305021 + 0.113835i
\(73\) −7.91676 + 7.91676i −0.926587 + 0.926587i −0.997484 0.0708965i \(-0.977414\pi\)
0.0708965 + 0.997484i \(0.477414\pi\)
\(74\) −1.89489 3.28204i −0.220276 0.381530i
\(75\) 3.89960 6.75431i 0.450287 0.779920i
\(76\) −1.37483 5.13093i −0.157704 0.588559i
\(77\) 0.385078 + 0.0353550i 0.0438837 + 0.00402908i
\(78\) −0.981704 3.46933i −0.111156 0.392824i
\(79\) −8.03063 −0.903517 −0.451758 0.892140i \(-0.649203\pi\)
−0.451758 + 0.892140i \(0.649203\pi\)
\(80\) 3.45569 0.925950i 0.386358 0.103524i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.61752 + 6.26572i 0.399488 + 0.691933i
\(83\) −5.59369 5.59369i −0.613988 0.613988i 0.329995 0.943983i \(-0.392953\pi\)
−0.943983 + 0.329995i \(0.892953\pi\)
\(84\) −2.48229 0.915557i −0.270840 0.0998954i
\(85\) −4.72326 + 17.6274i −0.512309 + 1.91196i
\(86\) −2.28157 2.28157i −0.246028 0.246028i
\(87\) 3.17482 1.83299i 0.340377 0.196517i
\(88\) −0.126576 0.0730789i −0.0134931 0.00779024i
\(89\) −3.28299 12.2523i −0.347997 1.29874i −0.889072 0.457767i \(-0.848649\pi\)
0.541075 0.840974i \(-0.318017\pi\)
\(90\) 3.57760 0.377112
\(91\) 9.37801 1.74725i 0.983083 0.183161i
\(92\) 5.63117 0.587090
\(93\) −2.57717 9.61812i −0.267240 0.997353i
\(94\) −2.22059 1.28206i −0.229037 0.132234i
\(95\) −16.4579 + 9.50198i −1.68855 + 0.974883i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 1.80716 6.74442i 0.183489 0.684792i −0.811460 0.584409i \(-0.801327\pi\)
0.994949 0.100383i \(-0.0320068\pi\)
\(98\) 3.01265 6.31854i 0.304323 0.638269i
\(99\) −0.103349 0.103349i −0.0103870 0.0103870i
\(100\) −3.89960 6.75431i −0.389960 0.675431i
\(101\) −5.05039 + 8.74753i −0.502532 + 0.870411i 0.497463 + 0.867485i \(0.334265\pi\)
−0.999996 + 0.00292646i \(0.999068\pi\)
\(102\) −4.92717 + 1.32023i −0.487863 + 0.130722i
\(103\) −8.14972 −0.803016 −0.401508 0.915855i \(-0.631514\pi\)
−0.401508 + 0.915855i \(0.631514\pi\)
\(104\) −3.49538 0.884485i −0.342750 0.0867309i
\(105\) −0.865407 + 9.42579i −0.0844551 + 0.919863i
\(106\) −1.84766 6.89555i −0.179460 0.669755i
\(107\) 0.0773176 0.133918i 0.00747457 0.0129463i −0.862264 0.506459i \(-0.830954\pi\)
0.869738 + 0.493513i \(0.164287\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −5.77656 + 5.77656i −0.553294 + 0.553294i −0.927390 0.374096i \(-0.877953\pi\)
0.374096 + 0.927390i \(0.377953\pi\)
\(110\) −0.135335 + 0.505077i −0.0129037 + 0.0481572i
\(111\) −3.66064 0.980866i −0.347453 0.0930997i
\(112\) −2.03404 + 1.69195i −0.192199 + 0.159874i
\(113\) −0.0357767 0.0619671i −0.00336559 0.00582937i 0.864338 0.502912i \(-0.167738\pi\)
−0.867703 + 0.497082i \(0.834405\pi\)
\(114\) −4.60027 2.65597i −0.430855 0.248754i
\(115\) −5.21419 19.4596i −0.486225 1.81462i
\(116\) 3.66597i 0.340377i
\(117\) −3.14736 1.75902i −0.290973 0.162621i
\(118\) 4.23246i 0.389629i
\(119\) −2.28651 13.3008i −0.209604 1.21929i
\(120\) 1.78880 3.09829i 0.163294 0.282834i
\(121\) −9.50778 + 5.48932i −0.864344 + 0.499029i
\(122\) −7.85852 7.85852i −0.711477 0.711477i
\(123\) 6.98851 + 1.87256i 0.630132 + 0.168843i
\(124\) −9.61812 2.57717i −0.863733 0.231436i
\(125\) −7.08126 + 7.08126i −0.633367 + 0.633367i
\(126\) −2.40264 + 1.10785i −0.214044 + 0.0986948i
\(127\) −6.70337 3.87019i −0.594828 0.343424i 0.172176 0.985066i \(-0.444920\pi\)
−0.767004 + 0.641642i \(0.778254\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −3.22662 −0.284088
\(130\) 0.180040 + 12.8980i 0.0157906 + 1.13123i
\(131\) 1.11889i 0.0977578i −0.998805 0.0488789i \(-0.984435\pi\)
0.998805 0.0488789i \(-0.0155648\pi\)
\(132\) −0.141178 + 0.0378284i −0.0122879 + 0.00329254i
\(133\) 8.11038 11.4777i 0.703260 0.995245i
\(134\) 4.32526 2.49719i 0.373646 0.215724i
\(135\) 2.52974 2.52974i 0.217726 0.217726i
\(136\) −1.32023 + 4.92717i −0.113209 + 0.422501i
\(137\) 3.69259 13.7809i 0.315479 1.17738i −0.608064 0.793888i \(-0.708054\pi\)
0.923543 0.383495i \(-0.125280\pi\)
\(138\) 3.98184 3.98184i 0.338957 0.338957i
\(139\) 13.4946 7.79111i 1.14460 0.660834i 0.197032 0.980397i \(-0.436870\pi\)
0.947565 + 0.319563i \(0.103536\pi\)
\(140\) 7.73027 + 5.46236i 0.653327 + 0.461654i
\(141\) −2.47675 + 0.663644i −0.208580 + 0.0558889i
\(142\) 6.70695i 0.562835i
\(143\) 0.367394 0.377795i 0.0307230 0.0315928i
\(144\) 1.00000 0.0833333
\(145\) −12.6685 + 3.39451i −1.05206 + 0.281898i
\(146\) 9.69602 + 5.59800i 0.802448 + 0.463294i
\(147\) −2.33762 6.59815i −0.192804 0.544206i
\(148\) −2.67978 + 2.67978i −0.220276 + 0.220276i
\(149\) 17.7313 + 4.75108i 1.45260 + 0.389224i 0.896928 0.442176i \(-0.145793\pi\)
0.555675 + 0.831400i \(0.312460\pi\)
\(150\) −7.53345 2.01858i −0.615104 0.164817i
\(151\) 12.9899 + 12.9899i 1.05710 + 1.05710i 0.998268 + 0.0588357i \(0.0187388\pi\)
0.0588357 + 0.998268i \(0.481261\pi\)
\(152\) −4.60027 + 2.65597i −0.373131 + 0.215427i
\(153\) −2.55049 + 4.41758i −0.206195 + 0.357140i
\(154\) −0.0655151 0.381107i −0.00527936 0.0307105i
\(155\) 35.6236i 2.86136i
\(156\) −3.09703 + 1.84618i −0.247961 + 0.147813i
\(157\) 14.7243i 1.17513i −0.809178 0.587564i \(-0.800087\pi\)
0.809178 0.587564i \(-0.199913\pi\)
\(158\) 2.07848 + 7.75700i 0.165355 + 0.617114i
\(159\) −6.18238 3.56940i −0.490294 0.283072i
\(160\) −1.78880 3.09829i −0.141417 0.244941i
\(161\) 9.52765 + 11.4540i 0.750884 + 0.902704i
\(162\) 0.965926 + 0.258819i 0.0758903 + 0.0203347i
\(163\) −3.21246 + 11.9891i −0.251619 + 0.939055i 0.718321 + 0.695712i \(0.244911\pi\)
−0.969940 + 0.243343i \(0.921756\pi\)
\(164\) 5.11594 5.11594i 0.399488 0.399488i
\(165\) 0.261447 + 0.452839i 0.0203536 + 0.0352535i
\(166\) −3.95534 + 6.85085i −0.306994 + 0.531729i
\(167\) 2.88019 + 10.7490i 0.222876 + 0.831783i 0.983244 + 0.182292i \(0.0583516\pi\)
−0.760369 + 0.649492i \(0.774982\pi\)
\(168\) −0.241896 + 2.63467i −0.0186627 + 0.203269i
\(169\) 6.18322 11.4354i 0.475633 0.879644i
\(170\) 18.2493 1.39965
\(171\) −5.13093 + 1.37483i −0.392372 + 0.105136i
\(172\) −1.61331 + 2.79434i −0.123014 + 0.213066i
\(173\) −6.62282 11.4711i −0.503523 0.872128i −0.999992 0.00407317i \(-0.998703\pi\)
0.496468 0.868055i \(-0.334630\pi\)
\(174\) −2.59223 2.59223i −0.196517 0.196517i
\(175\) 7.14061 19.3599i 0.539779 1.46347i
\(176\) −0.0378284 + 0.141178i −0.00285143 + 0.0106417i
\(177\) 2.99280 + 2.99280i 0.224953 + 0.224953i
\(178\) −10.9851 + 6.34226i −0.823369 + 0.475372i
\(179\) 13.1577 + 7.59659i 0.983451 + 0.567796i 0.903310 0.428988i \(-0.141130\pi\)
0.0801407 + 0.996784i \(0.474463\pi\)
\(180\) −0.925950 3.45569i −0.0690163 0.257572i
\(181\) −1.51565 −0.112658 −0.0563288 0.998412i \(-0.517940\pi\)
−0.0563288 + 0.998412i \(0.517940\pi\)
\(182\) −4.11492 8.60624i −0.305018 0.637937i
\(183\) −11.1136 −0.821543
\(184\) −1.45746 5.43930i −0.107445 0.400990i
\(185\) 11.7418 + 6.77915i 0.863276 + 0.498413i
\(186\) −8.62337 + 4.97871i −0.632296 + 0.365056i
\(187\) −0.527182 0.527182i −0.0385514 0.0385514i
\(188\) −0.663644 + 2.47675i −0.0484012 + 0.180636i
\(189\) −0.915557 + 2.48229i −0.0665969 + 0.180560i
\(190\) 13.4378 + 13.4378i 0.974883 + 0.974883i
\(191\) −7.50536 12.9997i −0.543069 0.940623i −0.998726 0.0504674i \(-0.983929\pi\)
0.455657 0.890156i \(-0.349404\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 19.8473 5.31807i 1.42864 0.382803i 0.540100 0.841601i \(-0.318386\pi\)
0.888541 + 0.458797i \(0.151720\pi\)
\(194\) −6.98233 −0.501302
\(195\) 9.24754 + 8.99292i 0.662230 + 0.643997i
\(196\) −6.88297 1.27463i −0.491641 0.0910452i
\(197\) −3.60071 13.4380i −0.256540 0.957420i −0.967227 0.253912i \(-0.918283\pi\)
0.710687 0.703508i \(-0.248384\pi\)
\(198\) −0.0730789 + 0.126576i −0.00519349 + 0.00899539i
\(199\) 4.61379 + 7.99132i 0.327063 + 0.566490i 0.981928 0.189256i \(-0.0606077\pi\)
−0.654865 + 0.755746i \(0.727274\pi\)
\(200\) −5.51487 + 5.51487i −0.389960 + 0.389960i
\(201\) 1.29264 4.82420i 0.0911759 0.340273i
\(202\) 9.75660 + 2.61427i 0.686472 + 0.183940i
\(203\) 7.45673 6.20263i 0.523360 0.435339i
\(204\) 2.55049 + 4.41758i 0.178570 + 0.309293i
\(205\) −22.4162 12.9420i −1.56562 0.903910i
\(206\) 2.10930 + 7.87203i 0.146962 + 0.548470i
\(207\) 5.63117i 0.391394i
\(208\) 0.0503243 + 3.60520i 0.00348936 + 0.249976i
\(209\) 0.776381i 0.0537034i
\(210\) 9.32860 1.60365i 0.643734 0.110663i
\(211\) 7.84722 13.5918i 0.540225 0.935697i −0.458666 0.888609i \(-0.651673\pi\)
0.998891 0.0470880i \(-0.0149941\pi\)
\(212\) −6.18238 + 3.56940i −0.424607 + 0.245147i
\(213\) −4.74253 4.74253i −0.324953 0.324953i
\(214\) −0.149366 0.0400225i −0.0102105 0.00273588i
\(215\) 11.1502 + 2.98769i 0.760439 + 0.203759i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) −11.0313 23.9241i −0.748852 1.62407i
\(218\) 7.07481 + 4.08464i 0.479167 + 0.276647i
\(219\) 10.8145 2.89774i 0.730776 0.195811i
\(220\) 0.522894 0.0352535
\(221\) −16.0546 8.97272i −1.07995 0.603571i
\(222\) 3.78978i 0.254353i
\(223\) 3.98854 1.06873i 0.267092 0.0715672i −0.122787 0.992433i \(-0.539183\pi\)
0.389880 + 0.920866i \(0.372517\pi\)
\(224\) 2.16074 + 1.52682i 0.144371 + 0.102015i
\(225\) −6.75431 + 3.89960i −0.450287 + 0.259973i
\(226\) −0.0505959 + 0.0505959i −0.00336559 + 0.00336559i
\(227\) 6.88324 25.6886i 0.456857 1.70501i −0.225715 0.974193i \(-0.572472\pi\)
0.682572 0.730819i \(-0.260861\pi\)
\(228\) −1.37483 + 5.13093i −0.0910503 + 0.339804i
\(229\) −14.2644 + 14.2644i −0.942616 + 0.942616i −0.998441 0.0558250i \(-0.982221\pi\)
0.0558250 + 0.998441i \(0.482221\pi\)
\(230\) −17.4470 + 10.0730i −1.15042 + 0.664196i
\(231\) −0.315810 0.223157i −0.0207787 0.0146827i
\(232\) −3.54106 + 0.948823i −0.232482 + 0.0622933i
\(233\) 13.2012i 0.864839i −0.901673 0.432419i \(-0.857660\pi\)
0.901673 0.432419i \(-0.142340\pi\)
\(234\) −0.884485 + 3.49538i −0.0578206 + 0.228500i
\(235\) 9.17339 0.598406
\(236\) 4.08824 1.09544i 0.266122 0.0713071i
\(237\) 6.95473 + 4.01532i 0.451758 + 0.260823i
\(238\) −12.2558 + 5.65111i −0.794427 + 0.366307i
\(239\) −16.1493 + 16.1493i −1.04461 + 1.04461i −0.0456558 + 0.998957i \(0.514538\pi\)
−0.998957 + 0.0456558i \(0.985462\pi\)
\(240\) −3.45569 0.925950i −0.223064 0.0597698i
\(241\) 26.0443 + 6.97856i 1.67766 + 0.449529i 0.967161 0.254165i \(-0.0818007\pi\)
0.710503 + 0.703694i \(0.248467\pi\)
\(242\) 7.76307 + 7.76307i 0.499029 + 0.499029i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −5.55681 + 9.62468i −0.355739 + 0.616157i
\(245\) 1.96855 + 24.9657i 0.125766 + 1.59500i
\(246\) 7.23503i 0.461289i
\(247\) −5.21475 18.4289i −0.331806 1.17260i
\(248\) 9.95741i 0.632296i
\(249\) 2.04743 + 7.64113i 0.129751 + 0.484237i
\(250\) 8.67274 + 5.00721i 0.548512 + 0.316684i
\(251\) −14.9142 25.8321i −0.941374 1.63051i −0.762853 0.646572i \(-0.776202\pi\)
−0.178522 0.983936i \(-0.557131\pi\)
\(252\) 1.69195 + 2.03404i 0.106583 + 0.128132i
\(253\) 0.794996 + 0.213018i 0.0499810 + 0.0133924i
\(254\) −2.00336 + 7.47664i −0.125702 + 0.469126i
\(255\) 12.9042 12.9042i 0.808091 0.808091i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.14454 15.8388i 0.570421 0.987997i −0.426102 0.904675i \(-0.640114\pi\)
0.996523 0.0833222i \(-0.0265531\pi\)
\(258\) 0.835111 + 3.11668i 0.0519918 + 0.194036i
\(259\) −9.98481 0.916732i −0.620426 0.0569630i
\(260\) 12.4119 3.51214i 0.769751 0.217814i
\(261\) −3.66597 −0.226918
\(262\) −1.08076 + 0.289590i −0.0667698 + 0.0178909i
\(263\) −7.04212 + 12.1973i −0.434236 + 0.752119i −0.997233 0.0743403i \(-0.976315\pi\)
0.562997 + 0.826459i \(0.309648\pi\)
\(264\) 0.0730789 + 0.126576i 0.00449770 + 0.00779024i
\(265\) 18.0593 + 18.0593i 1.10938 + 1.10938i
\(266\) −13.1858 4.86338i −0.808470 0.298193i
\(267\) −3.28299 + 12.2523i −0.200916 + 0.749829i
\(268\) −3.53156 3.53156i −0.215724 0.215724i
\(269\) −18.5454 + 10.7072i −1.13074 + 0.652830i −0.944120 0.329603i \(-0.893085\pi\)
−0.186616 + 0.982433i \(0.559752\pi\)
\(270\) −3.09829 1.78880i −0.188556 0.108863i
\(271\) 8.10518 + 30.2489i 0.492355 + 1.83749i 0.544368 + 0.838846i \(0.316769\pi\)
−0.0520136 + 0.998646i \(0.516564\pi\)
\(272\) 5.10098 0.309293
\(273\) −8.99522 3.17584i −0.544416 0.192211i
\(274\) −14.2671 −0.861905
\(275\) −0.295032 1.10107i −0.0177911 0.0663972i
\(276\) −4.87674 2.81559i −0.293545 0.169478i
\(277\) 1.43943 0.831056i 0.0864870 0.0499333i −0.456133 0.889912i \(-0.650766\pi\)
0.542620 + 0.839978i \(0.317432\pi\)
\(278\) −11.0183 11.0183i −0.660834 0.660834i
\(279\) −2.57717 + 9.61812i −0.154291 + 0.575822i
\(280\) 3.27549 8.88063i 0.195748 0.530719i
\(281\) 7.44786 + 7.44786i 0.444302 + 0.444302i 0.893455 0.449153i \(-0.148274\pi\)
−0.449153 + 0.893455i \(0.648274\pi\)
\(282\) 1.28206 + 2.22059i 0.0763456 + 0.132234i
\(283\) −5.72365 + 9.91366i −0.340236 + 0.589306i −0.984476 0.175517i \(-0.943840\pi\)
0.644240 + 0.764823i \(0.277174\pi\)
\(284\) −6.47842 + 1.73589i −0.384423 + 0.103006i
\(285\) 19.0040 1.12570
\(286\) −0.460011 0.257094i −0.0272010 0.0152023i
\(287\) 19.0619 + 1.75013i 1.12519 + 0.103307i
\(288\) −0.258819 0.965926i −0.0152511 0.0569177i
\(289\) −4.51001 + 7.81157i −0.265295 + 0.459504i
\(290\) 6.55768 + 11.3582i 0.385080 + 0.666979i
\(291\) −4.93725 + 4.93725i −0.289427 + 0.289427i
\(292\) 2.89774 10.8145i 0.169577 0.632871i
\(293\) 26.4297 + 7.08181i 1.54404 + 0.413724i 0.927568 0.373654i \(-0.121895\pi\)
0.616471 + 0.787378i \(0.288562\pi\)
\(294\) −5.76830 + 3.96569i −0.336414 + 0.231284i
\(295\) −7.57101 13.1134i −0.440801 0.763491i
\(296\) 3.28204 + 1.89489i 0.190765 + 0.110138i
\(297\) 0.0378284 + 0.141178i 0.00219503 + 0.00819196i
\(298\) 18.3568i 1.06338i
\(299\) 20.3015 0.283385i 1.17407 0.0163886i
\(300\) 7.79920i 0.450287i
\(301\) −8.41343 + 1.44633i −0.484942 + 0.0833651i
\(302\) 9.18525 15.9093i 0.528552 0.915478i
\(303\) 8.74753 5.05039i 0.502532 0.290137i
\(304\) 3.75610 + 3.75610i 0.215427 + 0.215427i
\(305\) 38.4053 + 10.2907i 2.19908 + 0.589242i
\(306\) 4.92717 + 1.32023i 0.281668 + 0.0754726i
\(307\) 17.1877 17.1877i 0.980952 0.980952i −0.0188701 0.999822i \(-0.506007\pi\)
0.999822 + 0.0188701i \(0.00600689\pi\)
\(308\) −0.351165 + 0.161920i −0.0200095 + 0.00922628i
\(309\) 7.05787 + 4.07486i 0.401508 + 0.231811i
\(310\) 34.4098 9.22007i 1.95434 0.523665i
\(311\) 12.9484 0.734237 0.367118 0.930174i \(-0.380344\pi\)
0.367118 + 0.930174i \(0.380344\pi\)
\(312\) 2.58485 + 2.51368i 0.146338 + 0.142309i
\(313\) 14.9687i 0.846084i 0.906110 + 0.423042i \(0.139038\pi\)
−0.906110 + 0.423042i \(0.860962\pi\)
\(314\) −14.2226 + 3.81093i −0.802628 + 0.215063i
\(315\) 5.46236 7.73027i 0.307769 0.435551i
\(316\) 6.95473 4.01532i 0.391234 0.225879i
\(317\) −6.93196 + 6.93196i −0.389338 + 0.389338i −0.874451 0.485113i \(-0.838778\pi\)
0.485113 + 0.874451i \(0.338778\pi\)
\(318\) −1.84766 + 6.89555i −0.103611 + 0.386683i
\(319\) 0.138678 0.517553i 0.00776447 0.0289774i
\(320\) −2.52974 + 2.52974i −0.141417 + 0.141417i
\(321\) −0.133918 + 0.0773176i −0.00747457 + 0.00431545i
\(322\) 8.59781 12.1675i 0.479137 0.678069i
\(323\) −26.1728 + 7.01298i −1.45629 + 0.390213i
\(324\) 1.00000i 0.0555556i
\(325\) −14.3987 24.1544i −0.798699 1.33984i
\(326\) 12.4120 0.687436
\(327\) 7.89092 2.11437i 0.436369 0.116925i
\(328\) −6.26572 3.61752i −0.345967 0.199744i
\(329\) −6.16066 + 2.84065i −0.339648 + 0.156610i
\(330\) 0.369742 0.369742i 0.0203536 0.0203536i
\(331\) 33.2990 + 8.92245i 1.83028 + 0.490422i 0.997958 0.0638711i \(-0.0203447\pi\)
0.832322 + 0.554293i \(0.187011\pi\)
\(332\) 7.64113 + 2.04743i 0.419361 + 0.112368i
\(333\) 2.67978 + 2.67978i 0.146851 + 0.146851i
\(334\) 9.63730 5.56410i 0.527330 0.304454i
\(335\) −8.93395 + 15.4740i −0.488114 + 0.845437i
\(336\) 2.60750 0.448249i 0.142251 0.0244540i
\(337\) 36.1304i 1.96815i 0.177751 + 0.984075i \(0.443118\pi\)
−0.177751 + 0.984075i \(0.556882\pi\)
\(338\) −12.6461 3.01284i −0.687855 0.163877i
\(339\) 0.0715534i 0.00388625i
\(340\) −4.72326 17.6274i −0.256155 0.955982i
\(341\) −1.26037 0.727677i −0.0682530 0.0394059i
\(342\) 2.65597 + 4.60027i 0.143618 + 0.248754i
\(343\) −9.05297 16.1568i −0.488814 0.872388i
\(344\) 3.11668 + 0.835111i 0.168040 + 0.0450262i
\(345\) −5.21419 + 19.4596i −0.280722 + 1.04767i
\(346\) −9.36608 + 9.36608i −0.503523 + 0.503523i
\(347\) 5.51197 + 9.54701i 0.295898 + 0.512510i 0.975193 0.221355i \(-0.0710478\pi\)
−0.679295 + 0.733865i \(0.737715\pi\)
\(348\) −1.83299 + 3.17482i −0.0982583 + 0.170188i
\(349\) 1.93308 + 7.21435i 0.103475 + 0.386175i 0.998168 0.0605076i \(-0.0192719\pi\)
−0.894692 + 0.446683i \(0.852605\pi\)
\(350\) −20.5483 1.88660i −1.09835 0.100843i
\(351\) 1.84618 + 3.09703i 0.0985419 + 0.165307i
\(352\) 0.146158 0.00779024
\(353\) −11.9077 + 3.19067i −0.633785 + 0.169822i −0.561387 0.827554i \(-0.689732\pi\)
−0.0723982 + 0.997376i \(0.523065\pi\)
\(354\) 2.11623 3.66542i 0.112476 0.194815i
\(355\) 11.9974 + 20.7801i 0.636755 + 1.10289i
\(356\) 8.96931 + 8.96931i 0.475372 + 0.475372i
\(357\) −4.67024 + 12.6621i −0.247175 + 0.670150i
\(358\) 3.93228 14.6755i 0.207828 0.775623i
\(359\) −2.29322 2.29322i −0.121031 0.121031i 0.643997 0.765028i \(-0.277275\pi\)
−0.765028 + 0.643997i \(0.777275\pi\)
\(360\) −3.09829 + 1.78880i −0.163294 + 0.0942780i
\(361\) −7.98185 4.60832i −0.420097 0.242543i
\(362\) 0.392280 + 1.46401i 0.0206178 + 0.0769466i
\(363\) 10.9786 0.576229
\(364\) −7.24797 + 6.20217i −0.379897 + 0.325082i
\(365\) −40.0548 −2.09656
\(366\) 2.87642 + 10.7349i 0.150353 + 0.561124i
\(367\) −0.769489 0.444265i −0.0401670 0.0231904i 0.479782 0.877388i \(-0.340716\pi\)
−0.519949 + 0.854197i \(0.674049\pi\)
\(368\) −4.87674 + 2.81559i −0.254218 + 0.146773i
\(369\) −5.11594 5.11594i −0.266325 0.266325i
\(370\) 3.50914 13.0963i 0.182432 0.680845i
\(371\) −17.7205 6.53597i −0.920005 0.339331i
\(372\) 7.04095 + 7.04095i 0.365056 + 0.365056i
\(373\) 2.90414 + 5.03012i 0.150371 + 0.260450i 0.931364 0.364090i \(-0.118620\pi\)
−0.780993 + 0.624540i \(0.785287\pi\)
\(374\) −0.372774 + 0.645664i −0.0192757 + 0.0333865i
\(375\) 9.67318 2.59192i 0.499521 0.133846i
\(376\) 2.56412 0.132234
\(377\) −0.184487 13.2166i −0.00950158 0.680687i
\(378\) 2.63467 + 0.241896i 0.135513 + 0.0124418i
\(379\) −5.36510 20.0228i −0.275586 1.02850i −0.955447 0.295162i \(-0.904627\pi\)
0.679861 0.733341i \(-0.262040\pi\)
\(380\) 9.50198 16.4579i 0.487441 0.844273i
\(381\) 3.87019 + 6.70337i 0.198276 + 0.343424i
\(382\) −10.6142 + 10.6142i −0.543069 + 0.543069i
\(383\) −1.97902 + 7.38580i −0.101123 + 0.377397i −0.997877 0.0651339i \(-0.979253\pi\)
0.896753 + 0.442531i \(0.145919\pi\)
\(384\) −0.965926 0.258819i −0.0492922 0.0132078i
\(385\) 0.884708 + 1.06359i 0.0450889 + 0.0542054i
\(386\) −10.2737 17.7946i −0.522919 0.905722i
\(387\) 2.79434 + 1.61331i 0.142044 + 0.0820092i
\(388\) 1.80716 + 6.74442i 0.0917447 + 0.342396i
\(389\) 14.5405i 0.737234i 0.929581 + 0.368617i \(0.120169\pi\)
−0.929581 + 0.368617i \(0.879831\pi\)
\(390\) 6.29306 11.2600i 0.318661 0.570171i
\(391\) 28.7245i 1.45266i
\(392\) 0.550243 + 6.97834i 0.0277915 + 0.352459i
\(393\) −0.559445 + 0.968986i −0.0282202 + 0.0488789i
\(394\) −12.0482 + 6.95604i −0.606980 + 0.350440i
\(395\) −20.3154 20.3154i −1.02218 1.02218i
\(396\) 0.141178 + 0.0378284i 0.00709444 + 0.00190095i
\(397\) 8.47081 + 2.26975i 0.425138 + 0.113915i 0.465043 0.885288i \(-0.346039\pi\)
−0.0399051 + 0.999203i \(0.512706\pi\)
\(398\) 6.52489 6.52489i 0.327063 0.327063i
\(399\) −12.7627 + 5.88481i −0.638932 + 0.294609i
\(400\) 6.75431 + 3.89960i 0.337715 + 0.194980i
\(401\) 24.9872 6.69529i 1.24780 0.334347i 0.426313 0.904576i \(-0.359812\pi\)
0.821486 + 0.570229i \(0.193145\pi\)
\(402\) −4.99438 −0.249097
\(403\) −34.8049 8.80718i −1.73376 0.438717i
\(404\) 10.1008i 0.502532i
\(405\) −3.45569 + 0.925950i −0.171715 + 0.0460108i
\(406\) −7.92122 5.59729i −0.393124 0.277789i
\(407\) −0.479696 + 0.276953i −0.0237777 + 0.0137280i
\(408\) 3.60694 3.60694i 0.178570 0.178570i
\(409\) −5.40561 + 20.1740i −0.267290 + 0.997541i 0.693543 + 0.720415i \(0.256049\pi\)
−0.960834 + 0.277126i \(0.910618\pi\)
\(410\) −6.69928 + 25.0021i −0.330854 + 1.23476i
\(411\) −10.0883 + 10.0883i −0.497621 + 0.497621i
\(412\) 7.05787 4.07486i 0.347716 0.200754i
\(413\) 9.14525 + 6.46221i 0.450008 + 0.317985i
\(414\) −5.43930 + 1.45746i −0.267327 + 0.0716300i
\(415\) 28.3012i 1.38925i
\(416\) 3.46933 0.981704i 0.170098 0.0481320i
\(417\) −15.5822 −0.763065
\(418\) −0.749926 + 0.200942i −0.0366801 + 0.00982840i
\(419\) −14.7014 8.48788i −0.718212 0.414660i 0.0958821 0.995393i \(-0.469433\pi\)
−0.814094 + 0.580733i \(0.802766\pi\)
\(420\) −3.96343 8.59568i −0.193396 0.419426i
\(421\) 16.0883 16.0883i 0.784096 0.784096i −0.196423 0.980519i \(-0.562933\pi\)
0.980519 + 0.196423i \(0.0629327\pi\)
\(422\) −15.1597 4.06202i −0.737961 0.197736i
\(423\) 2.47675 + 0.663644i 0.120424 + 0.0322675i
\(424\) 5.04789 + 5.04789i 0.245147 + 0.245147i
\(425\) −34.4536 + 19.8918i −1.67125 + 0.964894i
\(426\) −3.35348 + 5.80839i −0.162476 + 0.281418i
\(427\) −28.9788 + 4.98167i −1.40238 + 0.241080i
\(428\) 0.154635i 0.00747457i
\(429\) −0.507070 + 0.143484i −0.0244816 + 0.00692746i
\(430\) 11.5436i 0.556680i
\(431\) −0.746143 2.78464i −0.0359404 0.134131i 0.945625 0.325260i \(-0.105452\pi\)
−0.981565 + 0.191129i \(0.938785\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) −16.0890 27.8670i −0.773189 1.33920i −0.935807 0.352513i \(-0.885327\pi\)
0.162618 0.986689i \(-0.448006\pi\)
\(434\) −20.2538 + 16.8474i −0.972212 + 0.808701i
\(435\) 12.6685 + 3.39451i 0.607407 + 0.162754i
\(436\) 2.11437 7.89092i 0.101260 0.377907i
\(437\) 21.1513 21.1513i 1.01180 1.01180i
\(438\) −5.59800 9.69602i −0.267483 0.463294i
\(439\) −9.52788 + 16.5028i −0.454741 + 0.787635i −0.998673 0.0514945i \(-0.983602\pi\)
0.543932 + 0.839129i \(0.316935\pi\)
\(440\) −0.135335 0.505077i −0.00645184 0.0240786i
\(441\) −1.27463 + 6.88297i −0.0606968 + 0.327761i
\(442\) −4.51174 + 17.8299i −0.214602 + 0.848081i
\(443\) −15.5732 −0.739904 −0.369952 0.929051i \(-0.620626\pi\)
−0.369952 + 0.929051i \(0.620626\pi\)
\(444\) 3.66064 0.980866i 0.173726 0.0465499i
\(445\) 22.6900 39.3003i 1.07561 1.86301i
\(446\) −2.06462 3.57603i −0.0977626 0.169330i
\(447\) −12.9802 12.9802i −0.613942 0.613942i
\(448\) 0.915557 2.48229i 0.0432560 0.117277i
\(449\) 6.58392 24.5715i 0.310714 1.15960i −0.617199 0.786807i \(-0.711733\pi\)
0.927914 0.372795i \(-0.121600\pi\)
\(450\) 5.51487 + 5.51487i 0.259973 + 0.259973i
\(451\) 0.915784 0.528728i 0.0431226 0.0248968i
\(452\) 0.0619671 + 0.0357767i 0.00291469 + 0.00168279i
\(453\) −4.75463 17.7445i −0.223392 0.833711i
\(454\) −26.5948 −1.24816
\(455\) 28.1441 + 19.3039i 1.31941 + 0.904980i
\(456\) 5.31193 0.248754
\(457\) 7.14603 + 26.6694i 0.334277 + 1.24754i 0.904650 + 0.426154i \(0.140132\pi\)
−0.570373 + 0.821386i \(0.693201\pi\)
\(458\) 17.4702 + 10.0864i 0.816329 + 0.471308i
\(459\) 4.41758 2.55049i 0.206195 0.119047i
\(460\) 14.2454 + 14.2454i 0.664196 + 0.664196i
\(461\) −7.08637 + 26.4467i −0.330045 + 1.23174i 0.579097 + 0.815259i \(0.303405\pi\)
−0.909142 + 0.416486i \(0.863261\pi\)
\(462\) −0.133816 + 0.362806i −0.00622567 + 0.0168793i
\(463\) 13.3036 + 13.3036i 0.618271 + 0.618271i 0.945088 0.326817i \(-0.105976\pi\)
−0.326817 + 0.945088i \(0.605976\pi\)
\(464\) 1.83299 + 3.17482i 0.0850942 + 0.147387i
\(465\) 17.8118 30.8509i 0.826003 1.43068i
\(466\) −12.7514 + 3.41672i −0.590696 + 0.158276i
\(467\) 32.2700 1.49328 0.746640 0.665229i \(-0.231666\pi\)
0.746640 + 0.665229i \(0.231666\pi\)
\(468\) 3.60520 0.0503243i 0.166650 0.00232624i
\(469\) 1.20812 13.1586i 0.0557859 0.607605i
\(470\) −2.37425 8.86082i −0.109516 0.408719i
\(471\) −7.36216 + 12.7516i −0.339230 + 0.587564i
\(472\) −2.11623 3.66542i −0.0974073 0.168714i
\(473\) −0.333469 + 0.333469i −0.0153329 + 0.0153329i
\(474\) 2.07848 7.75700i 0.0954678 0.356291i
\(475\) −40.0172 10.7226i −1.83611 0.491985i
\(476\) 8.63059 + 10.3756i 0.395583 + 0.475565i
\(477\) 3.56940 + 6.18238i 0.163431 + 0.283072i
\(478\) 19.7788 + 11.4193i 0.904661 + 0.522307i
\(479\) 6.91383 + 25.8028i 0.315901 + 1.17896i 0.923148 + 0.384445i \(0.125607\pi\)
−0.607247 + 0.794513i \(0.707726\pi\)
\(480\) 3.57760i 0.163294i
\(481\) −9.52627 + 9.79599i −0.434361 + 0.446659i
\(482\) 26.9631i 1.22814i
\(483\) −2.52417 14.6833i −0.114854 0.668113i
\(484\) 5.48932 9.50778i 0.249514 0.432172i
\(485\) 21.6333 12.4900i 0.982317 0.567141i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) 7.81258 + 2.09337i 0.354022 + 0.0948598i 0.431447 0.902138i \(-0.358003\pi\)
−0.0774252 + 0.996998i \(0.524670\pi\)
\(488\) 10.7349 + 2.87642i 0.485948 + 0.130209i
\(489\) 8.77660 8.77660i 0.396891 0.396891i
\(490\) 23.6055 8.36307i 1.06639 0.377805i
\(491\) −24.2765 14.0161i −1.09558 0.632536i −0.160527 0.987031i \(-0.551319\pi\)
−0.935058 + 0.354495i \(0.884653\pi\)
\(492\) −6.98851 + 1.87256i −0.315066 + 0.0844217i
\(493\) −18.7001 −0.842208
\(494\) −16.4512 + 9.80680i −0.740176 + 0.441229i
\(495\) 0.522894i 0.0235023i
\(496\) 9.61812 2.57717i 0.431866 0.115718i
\(497\) −14.4920 10.2403i −0.650055 0.459342i
\(498\) 6.85085 3.95534i 0.306994 0.177243i
\(499\) 16.4680 16.4680i 0.737210 0.737210i −0.234827 0.972037i \(-0.575452\pi\)
0.972037 + 0.234827i \(0.0754524\pi\)
\(500\) 2.59192 9.67318i 0.115914 0.432598i
\(501\) 2.88019 10.7490i 0.128677 0.480230i
\(502\) −21.0918 + 21.0918i −0.941374 + 0.941374i
\(503\) −25.2775 + 14.5940i −1.12707 + 0.650713i −0.943196 0.332237i \(-0.892197\pi\)
−0.183872 + 0.982950i \(0.558863\pi\)
\(504\) 1.52682 2.16074i 0.0680101 0.0962471i
\(505\) −34.9052 + 9.35281i −1.55326 + 0.416195i
\(506\) 0.823040i 0.0365886i
\(507\) −11.0725 + 6.81171i −0.491748 + 0.302519i
\(508\) 7.74039 0.343424
\(509\) 17.2162 4.61306i 0.763093 0.204470i 0.143775 0.989610i \(-0.454076\pi\)
0.619318 + 0.785140i \(0.287409\pi\)
\(510\) −15.8043 9.12463i −0.699827 0.404045i
\(511\) 26.8999 12.4034i 1.18998 0.548696i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 5.13093 + 1.37483i 0.226536 + 0.0607002i
\(514\) −17.6659 4.73356i −0.779209 0.208788i
\(515\) −20.6167 20.6167i −0.908481 0.908481i
\(516\) 2.79434 1.61331i 0.123014 0.0710221i
\(517\) −0.187383 + 0.324557i −0.00824110 + 0.0142740i
\(518\) 1.69876 + 9.88186i 0.0746394 + 0.434184i
\(519\) 13.2456i 0.581419i
\(520\) −6.60490 11.0799i −0.289644 0.485887i
\(521\) 23.2693i 1.01944i −0.860339 0.509722i \(-0.829748\pi\)
0.860339 0.509722i \(-0.170252\pi\)
\(522\) 0.948823 + 3.54106i 0.0415289 + 0.154988i
\(523\) −22.0867 12.7518i −0.965785 0.557596i −0.0678360 0.997696i \(-0.521609\pi\)
−0.897949 + 0.440101i \(0.854943\pi\)
\(524\) 0.559445 + 0.968986i 0.0244394 + 0.0423304i
\(525\) −15.8639 + 13.1958i −0.692357 + 0.575913i
\(526\) 13.6043 + 3.64527i 0.593177 + 0.158941i
\(527\) −13.1461 + 49.0619i −0.572653 + 2.13717i
\(528\) 0.103349 0.103349i 0.00449770 0.00449770i
\(529\) 4.35506 + 7.54319i 0.189350 + 0.327965i
\(530\) 12.7699 22.1181i 0.554688 0.960747i
\(531\) −1.09544 4.08824i −0.0475381 0.177415i
\(532\) −1.28494 + 13.9952i −0.0557091 + 0.606769i
\(533\) 18.1865 18.7014i 0.787746 0.810050i
\(534\) 12.6845 0.548913
\(535\) 0.534372 0.143184i 0.0231029 0.00619040i
\(536\) −2.49719 + 4.32526i −0.107862 + 0.186823i
\(537\) −7.59659 13.1577i −0.327817 0.567796i
\(538\) 15.1423 + 15.1423i 0.652830 + 0.652830i
\(539\) −0.923504 0.440322i −0.0397781 0.0189660i
\(540\) −0.925950 + 3.45569i −0.0398466 + 0.148709i
\(541\) −8.39604 8.39604i −0.360974 0.360974i 0.503197 0.864171i \(-0.332157\pi\)
−0.864171 + 0.503197i \(0.832157\pi\)
\(542\) 27.1205 15.6580i 1.16492 0.672569i
\(543\) 1.31259 + 0.757827i 0.0563288 + 0.0325215i
\(544\) −1.32023 4.92717i −0.0566045 0.211251i
\(545\) −29.2264 −1.25192
\(546\) −0.739496 + 9.51069i −0.0316475 + 0.407020i
\(547\) −16.6366 −0.711330 −0.355665 0.934613i \(-0.615746\pi\)
−0.355665 + 0.934613i \(0.615746\pi\)
\(548\) 3.69259 + 13.7809i 0.157739 + 0.588692i
\(549\) 9.62468 + 5.55681i 0.410772 + 0.237159i
\(550\) −0.987195 + 0.569957i −0.0420941 + 0.0243031i
\(551\) −13.7698 13.7698i −0.586612 0.586612i
\(552\) −1.45746 + 5.43930i −0.0620334 + 0.231512i
\(553\) 19.9343 + 7.35250i 0.847695 + 0.312660i
\(554\) −1.17529 1.17529i −0.0499333 0.0499333i
\(555\) −6.77915 11.7418i −0.287759 0.498413i
\(556\) −7.79111 + 13.4946i −0.330417 + 0.572299i
\(557\) 40.4995 10.8518i 1.71602 0.459806i 0.739132 0.673561i \(-0.235236\pi\)
0.976887 + 0.213755i \(0.0685694\pi\)
\(558\) 9.95741 0.421531
\(559\) −5.67569 + 10.1553i −0.240056 + 0.429525i
\(560\) −9.42579 0.865407i −0.398312 0.0365701i
\(561\) 0.192962 + 0.720145i 0.00814687 + 0.0304045i
\(562\) 5.26643 9.12173i 0.222151 0.384777i
\(563\) 4.65785 + 8.06763i 0.196305 + 0.340010i 0.947327 0.320266i \(-0.103772\pi\)
−0.751023 + 0.660276i \(0.770439\pi\)
\(564\) 1.81311 1.81311i 0.0763456 0.0763456i
\(565\) 0.0662549 0.247267i 0.00278737 0.0104026i
\(566\) 11.0573 + 2.96278i 0.464771 + 0.124535i
\(567\) 2.03404 1.69195i 0.0854216 0.0710551i
\(568\) 3.35348 + 5.80839i 0.140709 + 0.243715i
\(569\) 1.41738 + 0.818326i 0.0594198 + 0.0343060i 0.529416 0.848363i \(-0.322411\pi\)
−0.469996 + 0.882669i \(0.655745\pi\)
\(570\) −4.91859 18.3564i −0.206017 0.768866i
\(571\) 12.7108i 0.531931i 0.963983 + 0.265966i \(0.0856908\pi\)
−0.963983 + 0.265966i \(0.914309\pi\)
\(572\) −0.129274 + 0.510877i −0.00540523 + 0.0213608i
\(573\) 15.0107i 0.627082i
\(574\) −3.24310 18.8654i −0.135364 0.787426i
\(575\) 21.9593 38.0347i 0.915767 1.58616i
\(576\) −0.866025 + 0.500000i −0.0360844 + 0.0208333i
\(577\) 31.8482 + 31.8482i 1.32586 + 1.32586i 0.908948 + 0.416910i \(0.136887\pi\)
0.416910 + 0.908948i \(0.363113\pi\)
\(578\) 8.71268 + 2.33456i 0.362400 + 0.0971047i
\(579\) −19.8473 5.31807i −0.824826 0.221012i
\(580\) 9.27396 9.27396i 0.385080 0.385080i
\(581\) 8.76382 + 19.0065i 0.363585 + 0.788523i
\(582\) 6.04688 + 3.49117i 0.250651 + 0.144713i
\(583\) −1.00784 + 0.270049i −0.0417404 + 0.0111843i
\(584\) −11.1960 −0.463294
\(585\) −3.51214 12.4119i −0.145209 0.513168i
\(586\) 27.3620i 1.13031i
\(587\) 25.6092 6.86196i 1.05700 0.283224i 0.311861 0.950128i \(-0.399048\pi\)
0.745144 + 0.666904i \(0.232381\pi\)
\(588\) 5.32351 + 4.54535i 0.219538 + 0.187447i
\(589\) −45.8068 + 26.4466i −1.88744 + 1.08971i
\(590\) −10.7070 + 10.7070i −0.440801 + 0.440801i
\(591\) −3.60071 + 13.4380i −0.148113 + 0.552767i
\(592\) 0.980866 3.66064i 0.0403134 0.150452i
\(593\) −5.45292 + 5.45292i −0.223925 + 0.223925i −0.810149 0.586224i \(-0.800614\pi\)
0.586224 + 0.810149i \(0.300614\pi\)
\(594\) 0.126576 0.0730789i 0.00519349 0.00299846i
\(595\) 27.8634 39.4320i 1.14229 1.61655i
\(596\) −17.7313 + 4.75108i −0.726302 + 0.194612i
\(597\) 9.22759i 0.377660i
\(598\) −5.52815 19.5364i −0.226063 0.798903i
\(599\) −1.76811 −0.0722431 −0.0361216 0.999347i \(-0.511500\pi\)
−0.0361216 + 0.999347i \(0.511500\pi\)
\(600\) 7.53345 2.01858i 0.307552 0.0824083i
\(601\) 6.83600 + 3.94677i 0.278846 + 0.160992i 0.632901 0.774233i \(-0.281864\pi\)
−0.354055 + 0.935225i \(0.615197\pi\)
\(602\) 3.57460 + 7.75241i 0.145690 + 0.315965i
\(603\) −3.53156 + 3.53156i −0.143816 + 0.143816i
\(604\) −17.7445 4.75463i −0.722015 0.193463i
\(605\) −37.9388 10.1657i −1.54243 0.413293i
\(606\) −7.14233 7.14233i −0.290137 0.290137i
\(607\) 29.6635 17.1262i 1.20401 0.695133i 0.242562 0.970136i \(-0.422012\pi\)
0.961443 + 0.275003i \(0.0886788\pi\)
\(608\) 2.65597 4.60027i 0.107714 0.186566i
\(609\) −9.55903 + 1.64327i −0.387351 + 0.0665886i
\(610\) 39.7601i 1.60984i
\(611\) −2.26793 + 8.96258i −0.0917505 + 0.362587i
\(612\) 5.10098i 0.206195i
\(613\) −3.59944 13.4333i −0.145380 0.542565i −0.999738 0.0228806i \(-0.992716\pi\)
0.854358 0.519684i \(-0.173950\pi\)
\(614\) −21.0505 12.1535i −0.849529 0.490476i
\(615\) 12.9420 + 22.4162i 0.521873 + 0.903910i
\(616\) 0.247291 + 0.297291i 0.00996365 + 0.0119782i
\(617\) −10.0295 2.68739i −0.403772 0.108190i 0.0512170 0.998688i \(-0.483690\pi\)
−0.454989 + 0.890497i \(0.650357\pi\)
\(618\) 2.10930 7.87203i 0.0848486 0.316659i
\(619\) 0.0354371 0.0354371i 0.00142434 0.00142434i −0.706394 0.707819i \(-0.749679\pi\)
0.707819 + 0.706394i \(0.249679\pi\)
\(620\) −17.8118 30.8509i −0.715339 1.23900i
\(621\) −2.81559 + 4.87674i −0.112986 + 0.195697i
\(622\) −3.35129 12.5072i −0.134375 0.501493i
\(623\) −3.06834 + 33.4195i −0.122930 + 1.33892i
\(624\) 1.75902 3.14736i 0.0704171 0.125995i
\(625\) 3.16846 0.126738
\(626\) 14.4587 3.87420i 0.577886 0.154844i
\(627\) −0.388190 + 0.672365i −0.0155028 + 0.0268517i
\(628\) 7.36216 + 12.7516i 0.293782 + 0.508845i
\(629\) 13.6695 + 13.6695i 0.545039 + 0.545039i
\(630\) −8.88063 3.27549i −0.353813 0.130499i
\(631\) −5.82232 + 21.7292i −0.231783 + 0.865026i 0.747790 + 0.663936i \(0.231115\pi\)
−0.979573 + 0.201090i \(0.935552\pi\)
\(632\) −5.67852 5.67852i −0.225879 0.225879i
\(633\) −13.5918 + 7.84722i −0.540225 + 0.311899i
\(634\) 8.48989 + 4.90164i 0.337177 + 0.194669i
\(635\) −7.16722 26.7484i −0.284422 1.06148i
\(636\) 7.13879 0.283072
\(637\) −24.8786 4.24893i −0.985728 0.168349i
\(638\) −0.535810 −0.0212129
\(639\) 1.73589 + 6.47842i 0.0686706 + 0.256282i
\(640\) 3.09829 + 1.78880i 0.122471 + 0.0707085i
\(641\) 12.8186 7.40080i 0.506303 0.292314i −0.225010 0.974356i \(-0.572241\pi\)
0.731312 + 0.682043i \(0.238908\pi\)
\(642\) 0.109344 + 0.109344i 0.00431545 + 0.00431545i
\(643\) 1.02867 3.83904i 0.0405667 0.151397i −0.942672 0.333721i \(-0.891695\pi\)
0.983238 + 0.182325i \(0.0583622\pi\)
\(644\) −13.9782 5.15566i −0.550818 0.203161i
\(645\) −8.16253 8.16253i −0.321399 0.321399i
\(646\) 13.5480 + 23.4659i 0.533041 + 0.923254i
\(647\) −18.0664 + 31.2919i −0.710263 + 1.23021i 0.254496 + 0.967074i \(0.418091\pi\)
−0.964758 + 0.263137i \(0.915243\pi\)
\(648\) −0.965926 + 0.258819i −0.0379452 + 0.0101674i
\(649\) 0.618607 0.0242824
\(650\) −19.6047 + 20.1597i −0.768959 + 0.790730i
\(651\) −2.40866 + 26.2345i −0.0944028 + 1.02821i
\(652\) −3.21246 11.9891i −0.125810 0.469528i
\(653\) −13.0737 + 22.6443i −0.511612 + 0.886139i 0.488297 + 0.872678i \(0.337618\pi\)
−0.999909 + 0.0134612i \(0.995715\pi\)
\(654\) −4.08464 7.07481i −0.159722 0.276647i
\(655\) 2.83050 2.83050i 0.110597 0.110597i
\(656\) −1.87256 + 6.98851i −0.0731114 + 0.272855i
\(657\) −10.8145 2.89774i −0.421914 0.113051i
\(658\) 4.33836 + 5.21552i 0.169127 + 0.203322i
\(659\) 3.33965 + 5.78444i 0.130094 + 0.225330i 0.923713 0.383086i \(-0.125139\pi\)
−0.793618 + 0.608416i \(0.791805\pi\)
\(660\) −0.452839 0.261447i −0.0176267 0.0101768i
\(661\) −5.95568 22.2269i −0.231649 0.864527i −0.979631 0.200807i \(-0.935644\pi\)
0.747982 0.663719i \(-0.231023\pi\)
\(662\) 34.4737i 1.33986i
\(663\) 9.41734 + 15.7979i 0.365739 + 0.613540i
\(664\) 7.91068i 0.306994i
\(665\) 49.5529 8.51851i 1.92158 0.330334i
\(666\) 1.89489 3.28204i 0.0734254 0.127177i
\(667\) 17.8780 10.3219i 0.692238 0.399664i
\(668\) −7.86882 7.86882i −0.304454 0.304454i
\(669\) −3.98854 1.06873i −0.154206 0.0413193i
\(670\) 17.2591 + 4.62455i 0.666776 + 0.178662i
\(671\) −1.14858 + 1.14858i −0.0443406 + 0.0443406i
\(672\) −1.10785 2.40264i −0.0427361 0.0926838i
\(673\) 21.7119 + 12.5354i 0.836932 + 0.483203i 0.856220 0.516611i \(-0.172807\pi\)
−0.0192884 + 0.999814i \(0.506140\pi\)
\(674\) 34.8993 9.35125i 1.34427 0.360197i
\(675\) 7.79920 0.300191
\(676\) 0.362858 + 12.9949i 0.0139561 + 0.499805i
\(677\) 11.0346i 0.424096i −0.977259 0.212048i \(-0.931987\pi\)
0.977259 0.212048i \(-0.0680133\pi\)
\(678\) 0.0691153 0.0185194i 0.00265436 0.000711233i
\(679\) −10.6608 + 15.0870i −0.409123 + 0.578987i
\(680\) −15.8043 + 9.12463i −0.606068 + 0.349914i
\(681\) −18.8054 + 18.8054i −0.720623 + 0.720623i
\(682\) −0.376673 + 1.40576i −0.0144236 + 0.0538295i
\(683\) −3.55612 + 13.2716i −0.136071 + 0.507825i 0.863920 + 0.503629i \(0.168002\pi\)
−0.999991 + 0.00419577i \(0.998664\pi\)
\(684\) 3.75610 3.75610i 0.143618 0.143618i
\(685\) 44.2035 25.5209i 1.68893 0.975103i
\(686\) −13.2632 + 12.9262i −0.506393 + 0.493524i
\(687\) 19.4855 5.22112i 0.743417 0.199198i
\(688\) 3.22662i 0.123014i
\(689\) −22.1091 + 13.1795i −0.842289 + 0.502100i
\(690\) 20.1461 0.766948
\(691\) −33.1008 + 8.86934i −1.25922 + 0.337406i −0.825890 0.563832i \(-0.809327\pi\)
−0.433326 + 0.901237i \(0.642660\pi\)
\(692\) 11.4711 + 6.62282i 0.436064 + 0.251762i
\(693\) 0.161920 + 0.351165i 0.00615085 + 0.0133396i
\(694\) 7.79510 7.79510i 0.295898 0.295898i
\(695\) 53.8474 + 14.4284i 2.04255 + 0.547299i
\(696\) 3.54106 + 0.948823i 0.134223 + 0.0359650i
\(697\) −26.0963 26.0963i −0.988469 0.988469i
\(698\) 6.46821 3.73442i 0.244825 0.141350i
\(699\) −6.60060 + 11.4326i −0.249657 + 0.432419i
\(700\) 3.49598 + 20.3364i 0.132136 + 0.768645i
\(701\) 23.3747i 0.882848i −0.897299 0.441424i \(-0.854473\pi\)
0.897299 0.441424i \(-0.145527\pi\)
\(702\) 2.51368 2.58485i 0.0948726 0.0975587i
\(703\) 20.1310i 0.759257i
\(704\) −0.0378284 0.141178i −0.00142571 0.00532083i
\(705\) −7.94439 4.58670i −0.299203 0.172745i
\(706\) 6.16390 + 10.6762i 0.231981 + 0.401803i
\(707\) 20.5454 17.0900i 0.772688 0.642734i
\(708\) −4.08824 1.09544i −0.153645 0.0411692i
\(709\) −7.88323 + 29.4206i −0.296061 + 1.10491i 0.644310 + 0.764764i \(0.277145\pi\)
−0.940371 + 0.340150i \(0.889522\pi\)
\(710\) 16.9669 16.9669i 0.636755 0.636755i
\(711\) −4.01532 6.95473i −0.150586 0.260823i
\(712\) 6.34226 10.9851i 0.237686 0.411685i
\(713\) −14.5125 54.1613i −0.543497 2.02836i
\(714\) 13.4394 + 1.23391i 0.502957 + 0.0461779i
\(715\) 1.88514 0.0263143i 0.0705001 0.000984098i
\(716\) −15.1932 −0.567796
\(717\) 22.0604 5.91106i 0.823860 0.220753i
\(718\) −1.62155 + 2.80860i −0.0605156 + 0.104816i
\(719\) 4.79230 + 8.30051i 0.178723 + 0.309557i 0.941443 0.337171i \(-0.109470\pi\)
−0.762721 + 0.646728i \(0.776137\pi\)
\(720\) 2.52974 + 2.52974i 0.0942780 + 0.0942780i
\(721\) 20.2300 + 7.46153i 0.753403 + 0.277882i
\(722\) −2.38544 + 8.90260i −0.0887770 + 0.331320i
\(723\) −19.0658 19.0658i −0.709064 0.709064i
\(724\) 1.31259 0.757827i 0.0487822 0.0281644i
\(725\) −24.7611 14.2958i −0.919604 0.530933i
\(726\) −2.84148 10.6045i −0.105457 0.393572i
\(727\) 28.0599 1.04068 0.520341 0.853958i \(-0.325805\pi\)
0.520341 + 0.853958i \(0.325805\pi\)
\(728\) 7.86675 + 5.39577i 0.291561 + 0.199980i
\(729\) −1.00000 −0.0370370
\(730\) 10.3669 + 38.6899i 0.383697 + 1.43198i
\(731\) 14.2539 + 8.22947i 0.527198 + 0.304378i
\(732\) 9.62468 5.55681i 0.355739 0.205386i
\(733\) −24.8749 24.8749i −0.918776 0.918776i 0.0781647 0.996940i \(-0.475094\pi\)
−0.996940 + 0.0781647i \(0.975094\pi\)
\(734\) −0.229968 + 0.858254i −0.00848829 + 0.0316787i
\(735\) 10.7780 22.6052i 0.397554 0.833805i
\(736\) 3.98184 + 3.98184i 0.146773 + 0.146773i
\(737\) −0.364984 0.632171i −0.0134444 0.0232863i
\(738\) −3.61752 + 6.26572i −0.133163 + 0.230644i
\(739\) −28.0890 + 7.52644i −1.03327 + 0.276864i −0.735323 0.677717i \(-0.762969\pi\)
−0.297949 + 0.954582i \(0.596303\pi\)
\(740\) −13.5583 −0.498413
\(741\) −4.69833 + 18.5672i −0.172597 + 0.682084i
\(742\) −1.72685 + 18.8084i −0.0633945 + 0.690477i
\(743\) 5.86267 + 21.8798i 0.215080 + 0.802691i 0.986138 + 0.165926i \(0.0530613\pi\)
−0.771058 + 0.636765i \(0.780272\pi\)
\(744\) 4.97871 8.62337i 0.182528 0.316148i
\(745\) 32.8366 + 56.8746i 1.20304 + 2.08372i
\(746\) 4.10708 4.10708i 0.150371 0.150371i
\(747\) 2.04743 7.64113i 0.0749117 0.279574i
\(748\) 0.720145 + 0.192962i 0.0263311 + 0.00705540i
\(749\) −0.314534 + 0.261634i −0.0114928 + 0.00955991i
\(750\) −5.00721 8.67274i −0.182837 0.316684i
\(751\) 11.5957 + 6.69480i 0.423135 + 0.244297i 0.696418 0.717637i \(-0.254776\pi\)
−0.273283 + 0.961934i \(0.588110\pi\)
\(752\) −0.663644 2.47675i −0.0242006 0.0903178i
\(753\) 29.8283i 1.08701i
\(754\) −12.7185 + 3.59890i −0.463179 + 0.131064i
\(755\) 65.7222i 2.39188i
\(756\) −0.448249 2.60750i −0.0163027 0.0948340i
\(757\) −3.11864 + 5.40165i −0.113349 + 0.196326i −0.917119 0.398615i \(-0.869491\pi\)
0.803770 + 0.594941i \(0.202824\pi\)
\(758\) −17.9520 + 10.3646i −0.652045 + 0.376458i
\(759\) −0.581977 0.581977i −0.0211244 0.0211244i
\(760\) −18.3564 4.91859i −0.665857 0.178416i
\(761\) −1.21124 0.324552i −0.0439075 0.0117650i 0.236798 0.971559i \(-0.423902\pi\)
−0.280706 + 0.959794i \(0.590569\pi\)
\(762\) 5.47328 5.47328i 0.198276 0.198276i
\(763\) 19.6278 9.05032i 0.710576 0.327643i
\(764\) 12.9997 + 7.50536i 0.470311 + 0.271534i
\(765\) −17.6274 + 4.72326i −0.637321 + 0.170770i
\(766\) 7.64634 0.276274
\(767\) 14.6838 4.15502i 0.530201 0.150029i
\(768\) 1.00000i 0.0360844i
\(769\) −14.0382 + 3.76152i −0.506230 + 0.135644i −0.502890 0.864350i \(-0.667730\pi\)
−0.00334025 + 0.999994i \(0.501063\pi\)
\(770\) 0.798366 1.12984i 0.0287711 0.0407166i
\(771\) −15.8388 + 9.14454i −0.570421 + 0.329332i
\(772\) −14.5292 + 14.5292i −0.522919 + 0.522919i
\(773\) −0.719646 + 2.68575i −0.0258839 + 0.0965999i −0.977659 0.210195i \(-0.932590\pi\)
0.951776 + 0.306795i \(0.0992567\pi\)
\(774\) 0.835111 3.11668i 0.0300175 0.112027i
\(775\) −54.9138 + 54.9138i −1.97256 + 1.97256i
\(776\) 6.04688 3.49117i 0.217070 0.125326i
\(777\) 8.18873 + 5.78632i 0.293769 + 0.207583i
\(778\) 14.0451 3.76337i 0.503540 0.134923i
\(779\) 38.4320i 1.37697i
\(780\) −12.5051 3.16433i −0.447753 0.113301i
\(781\) −0.980274 −0.0350770
\(782\) −27.7458 + 7.43445i −0.992186 + 0.265856i
\(783\) 3.17482 + 1.83299i 0.113459 + 0.0655055i
\(784\) 6.59815 2.33762i 0.235648 0.0834865i
\(785\) 37.2487 37.2487i 1.32946 1.32946i
\(786\) 1.08076 + 0.289590i 0.0385496 + 0.0103293i
\(787\) −15.6974 4.20610i −0.559551 0.149931i −0.0320508 0.999486i \(-0.510204\pi\)
−0.527500 + 0.849555i \(0.676870\pi\)
\(788\) 9.83732 + 9.83732i 0.350440 + 0.350440i
\(789\) 12.1973 7.04212i 0.434236 0.250706i
\(790\) −14.3652 + 24.8812i −0.511090 + 0.885235i
\(791\) 0.0320738 + 0.186576i 0.00114041 + 0.00663387i
\(792\) 0.146158i 0.00519349i
\(793\) −19.5491 + 34.9786i −0.694208 + 1.24212i
\(794\) 8.76963i 0.311222i
\(795\) −6.61017 24.6695i −0.234439 0.874937i
\(796\) −7.99132 4.61379i −0.283245 0.163532i
\(797\) −23.1421 40.0833i −0.819735 1.41982i −0.905878 0.423539i \(-0.860788\pi\)
0.0861432 0.996283i \(-0.472546\pi\)
\(798\) 8.98751 + 10.8047i 0.318154 + 0.382482i
\(799\) 12.6339 + 3.38523i 0.446954 + 0.119761i
\(800\) 2.01858 7.53345i 0.0713676 0.266348i
\(801\) 8.96931 8.96931i 0.316915 0.316915i
\(802\) −12.9343 22.4029i −0.456726 0.791073i
\(803\) 0.818191 1.41715i 0.0288733 0.0500101i
\(804\) 1.29264 + 4.82420i 0.0455879 + 0.170137i
\(805\) −4.87326 + 53.0783i −0.171760 + 1.87076i
\(806\) 0.501100 + 35.8985i 0.0176505 + 1.26447i
\(807\) 21.4144 0.753824
\(808\) −9.75660 + 2.61427i −0.343236 + 0.0919698i
\(809\) 27.3471 47.3666i 0.961474 1.66532i 0.242670 0.970109i \(-0.421977\pi\)
0.718804 0.695213i \(-0.244690\pi\)
\(810\) 1.78880 + 3.09829i 0.0628520 + 0.108863i
\(811\) −1.16693 1.16693i −0.0409764 0.0409764i 0.686322 0.727298i \(-0.259224\pi\)
−0.727298 + 0.686322i \(0.759224\pi\)
\(812\) −3.35640 + 9.10000i −0.117787 + 0.319347i
\(813\) 8.10518 30.2489i 0.284261 1.06088i
\(814\) 0.391670 + 0.391670i 0.0137280 + 0.0137280i
\(815\) −38.4559 + 22.2025i −1.34705 + 0.777721i
\(816\) −4.41758 2.55049i −0.154646 0.0892851i
\(817\) 4.43606 + 16.5556i 0.155198 + 0.579207i
\(818\) 20.8857 0.730251
\(819\) 6.20217 + 7.24797i 0.216721 + 0.253265i
\(820\) 25.8840 0.903910
\(821\) −0.998281 3.72564i −0.0348402 0.130026i 0.946315 0.323245i \(-0.104774\pi\)
−0.981156 + 0.193219i \(0.938107\pi\)
\(822\) 12.3556 + 7.13353i 0.430952 + 0.248810i
\(823\) −15.2505 + 8.80488i −0.531599 + 0.306919i −0.741667 0.670768i \(-0.765965\pi\)
0.210068 + 0.977687i \(0.432631\pi\)
\(824\) −5.76273 5.76273i −0.200754 0.200754i
\(825\) −0.295032 + 1.10107i −0.0102717 + 0.0383344i
\(826\) 3.87505 10.5062i 0.134830 0.365557i
\(827\) 19.8789 + 19.8789i 0.691256 + 0.691256i 0.962508 0.271252i \(-0.0874377\pi\)
−0.271252 + 0.962508i \(0.587438\pi\)
\(828\) 2.81559 + 4.87674i 0.0978484 + 0.169478i
\(829\) −14.3732 + 24.8952i −0.499203 + 0.864645i −1.00000 0.000920314i \(-0.999707\pi\)
0.500797 + 0.865565i \(0.333040\pi\)
\(830\) −27.3369 + 7.32489i −0.948877 + 0.254251i
\(831\) −1.66211 −0.0576580
\(832\) −1.84618 3.09703i −0.0640049 0.107370i
\(833\) −6.50188 + 35.1099i −0.225277 + 1.21649i
\(834\) 4.03298 + 15.0513i 0.139651 + 0.521183i
\(835\) −19.9061 + 34.4784i −0.688879 + 1.19317i
\(836\) 0.388190 + 0.672365i 0.0134258 + 0.0232542i
\(837\) 7.04095 7.04095i 0.243371 0.243371i
\(838\) −4.39365 + 16.3973i −0.151776 + 0.566436i
\(839\) 51.8462 + 13.8921i 1.78993 + 0.479610i 0.992334 0.123585i \(-0.0394392\pi\)
0.797594 + 0.603195i \(0.206106\pi\)
\(840\) −7.27697 + 6.05310i −0.251079 + 0.208852i
\(841\) 7.78033 + 13.4759i 0.268287 + 0.464687i
\(842\) −19.7041 11.3761i −0.679047 0.392048i
\(843\) −2.72611 10.1740i −0.0938921 0.350410i
\(844\) 15.6944i 0.540225i
\(845\) 44.5705 13.2866i 1.53327 0.457073i
\(846\) 2.56412i 0.0881563i
\(847\) 28.6268 4.92116i 0.983630 0.169093i
\(848\) 3.56940 6.18238i 0.122574 0.212304i
\(849\) 9.91366 5.72365i 0.340236 0.196435i
\(850\) 28.1313 + 28.1313i 0.964894 + 0.964894i
\(851\) −20.6137 5.52343i −0.706629 0.189341i
\(852\) 6.47842 + 1.73589i 0.221947 + 0.0594705i
\(853\) 7.44167 7.44167i 0.254798 0.254798i −0.568136 0.822934i \(-0.692335\pi\)
0.822934 + 0.568136i \(0.192335\pi\)
\(854\) 12.3122 + 26.7020i 0.421315 + 0.913725i
\(855\) −16.4579 9.50198i −0.562849 0.324961i
\(856\) 0.149366 0.0400225i 0.00510523 0.00136794i
\(857\) 34.4161 1.17563 0.587816 0.808995i \(-0.299988\pi\)
0.587816 + 0.808995i \(0.299988\pi\)
\(858\) 0.269834 + 0.452656i 0.00921198 + 0.0154534i
\(859\) 5.57158i 0.190100i −0.995473 0.0950500i \(-0.969699\pi\)
0.995473 0.0950500i \(-0.0303011\pi\)
\(860\) −11.1502 + 2.98769i −0.380219 + 0.101879i
\(861\) −15.6331 11.0466i −0.532773 0.376468i
\(862\) −2.49664 + 1.44144i −0.0850360 + 0.0490955i
\(863\) 12.8891 12.8891i 0.438750 0.438750i −0.452841 0.891591i \(-0.649590\pi\)
0.891591 + 0.452841i \(0.149590\pi\)
\(864\) −0.258819 + 0.965926i −0.00880520 + 0.0328615i
\(865\) 12.2648 45.7728i 0.417016 1.55632i
\(866\) −22.7533 + 22.7533i −0.773189 + 0.773189i
\(867\) 7.81157 4.51001i 0.265295 0.153168i
\(868\) 21.5154 + 15.2032i 0.730280 + 0.516030i
\(869\) 1.13375 0.303786i 0.0384597 0.0103052i
\(870\) 13.1154i 0.444653i
\(871\) −12.9097 12.5543i −0.437429 0.425385i
\(872\) −8.16929 −0.276647
\(873\) 6.74442 1.80716i 0.228264 0.0611631i
\(874\) −25.9049 14.9562i −0.876247 0.505901i
\(875\) 24.0610 11.0944i 0.813411 0.375061i
\(876\) −7.91676 + 7.91676i −0.267483 + 0.267483i
\(877\) −7.31466 1.95996i −0.246999 0.0661831i 0.133196 0.991090i \(-0.457476\pi\)
−0.380194 + 0.924907i \(0.624143\pi\)
\(878\) 18.4065 + 4.93200i 0.621188 + 0.166447i
\(879\) −19.3479 19.3479i −0.652588 0.652588i
\(880\) −0.452839 + 0.261447i −0.0152652 + 0.00881337i
\(881\) 26.2441 45.4561i 0.884186 1.53145i 0.0375419 0.999295i \(-0.488047\pi\)
0.846644 0.532160i \(-0.178619\pi\)
\(882\) 6.97834 0.550243i 0.234973 0.0185277i
\(883\) 42.0177i 1.41401i −0.707209 0.707004i \(-0.750046\pi\)
0.707209 0.707004i \(-0.249954\pi\)
\(884\) 18.3901 0.256703i 0.618525 0.00863387i
\(885\) 15.1420i 0.508994i
\(886\) 4.03064 + 15.0425i 0.135412 + 0.505364i
\(887\) −17.3437 10.0134i −0.582345 0.336217i 0.179720 0.983718i \(-0.442481\pi\)
−0.762065 + 0.647501i \(0.775814\pi\)
\(888\) −1.89489 3.28204i −0.0635883 0.110138i
\(889\) 13.0963 + 15.7443i 0.439237 + 0.528045i
\(890\) −43.8338 11.7452i −1.46931 0.393701i
\(891\) 0.0378284 0.141178i 0.00126730 0.00472963i
\(892\) −2.91981 + 2.91981i −0.0977626 + 0.0977626i
\(893\) 6.81022 + 11.7957i 0.227895 + 0.394726i
\(894\) −9.17839 + 15.8974i −0.306971 + 0.531690i
\(895\) 14.0681 + 52.5030i 0.470246 + 1.75498i
\(896\) −2.63467 0.241896i −0.0880181 0.00808118i
\(897\) −17.7233 9.90534i −0.591764 0.330730i
\(898\) −25.4383 −0.848887
\(899\) −35.2597 + 9.44782i −1.17598 + 0.315102i
\(900\) 3.89960 6.75431i 0.129987 0.225144i
\(901\) 18.2074 + 31.5362i 0.606578 + 1.05062i
\(902\) −0.747735 0.747735i −0.0248968 0.0248968i
\(903\) 8.00941 + 2.95416i 0.266536 + 0.0983081i
\(904\) 0.0185194 0.0691153i 0.000615946 0.00229874i
\(905\) −3.83421 3.83421i −0.127454 0.127454i
\(906\) −15.9093 + 9.18525i −0.528552 + 0.305159i
\(907\) 17.8984 + 10.3337i 0.594307 + 0.343124i 0.766799 0.641888i \(-0.221848\pi\)
−0.172491 + 0.985011i \(0.555182\pi\)
\(908\) 6.88324 + 25.6886i 0.228428 + 0.852506i
\(909\) −10.1008 −0.335021
\(910\) 11.3619 32.1813i 0.376643 1.06680i
\(911\) −16.4643 −0.545486 −0.272743 0.962087i \(-0.587931\pi\)
−0.272743 + 0.962087i \(0.587931\pi\)
\(912\) −1.37483 5.13093i −0.0455252 0.169902i
\(913\) 1.00131 + 0.578104i 0.0331384 + 0.0191324i
\(914\) 23.9111 13.8051i 0.790909 0.456631i
\(915\) −28.1146 28.1146i −0.929441 0.929441i
\(916\) 5.22112 19.4855i 0.172511 0.643818i
\(917\) −1.02441 + 2.77741i −0.0338289 + 0.0917180i
\(918\) −3.60694 3.60694i −0.119047 0.119047i
\(919\) −3.06087 5.30158i −0.100969 0.174883i 0.811115 0.584886i \(-0.198861\pi\)
−0.912084 + 0.410003i \(0.865528\pi\)
\(920\) 10.0730 17.4470i 0.332098 0.575211i
\(921\) −23.4788 + 6.29112i −0.773652 + 0.207300i
\(922\) 27.3796 0.901700
\(923\) −23.2686 + 6.58424i −0.765897 + 0.216723i
\(924\) 0.385078 + 0.0353550i 0.0126681 + 0.00116309i
\(925\) 7.64998 + 28.5501i 0.251530 + 0.938721i
\(926\) 9.40707 16.2935i 0.309136 0.535439i
\(927\) −4.07486 7.05787i −0.133836 0.231811i
\(928\) 2.59223 2.59223i 0.0850942 0.0850942i
\(929\) −1.05842 + 3.95009i −0.0347257 + 0.129598i −0.981113 0.193437i \(-0.938037\pi\)
0.946387 + 0.323035i \(0.104703\pi\)
\(930\) −34.4098 9.22007i −1.12834 0.302338i
\(931\) −30.6408 + 21.0655i −1.00421 + 0.690394i
\(932\) 6.60060 + 11.4326i 0.216210 + 0.374486i
\(933\) −11.2136 6.47420i −0.367118 0.211956i
\(934\) −8.35210 31.1705i −0.273289 1.01993i
\(935\) 2.66727i 0.0872291i
\(936\) −0.981704 3.46933i −0.0320880 0.113399i
\(937\) 25.5831i 0.835763i −0.908502 0.417882i \(-0.862773\pi\)
0.908502 0.417882i \(-0.137227\pi\)
\(938\) −13.0229 + 2.23873i −0.425212 + 0.0730970i
\(939\) 7.48437 12.9633i 0.244243 0.423042i
\(940\) −7.94439 + 4.58670i −0.259118 + 0.149602i
\(941\) −4.87350 4.87350i −0.158871 0.158871i 0.623195 0.782066i \(-0.285834\pi\)
−0.782066 + 0.623195i \(0.785834\pi\)
\(942\) 14.2226 + 3.81093i 0.463397 + 0.124167i
\(943\) 39.3535 + 10.5447i 1.28153 + 0.343384i
\(944\) −2.99280 + 2.99280i −0.0974073 + 0.0974073i
\(945\) −8.59568 + 3.96343i −0.279617 + 0.128930i
\(946\) 0.408414 + 0.235798i 0.0132787 + 0.00766646i
\(947\) −40.2565 + 10.7867i −1.30816 + 0.350520i −0.844530 0.535509i \(-0.820120\pi\)
−0.463630 + 0.886029i \(0.653453\pi\)
\(948\) −8.03063 −0.260823
\(949\) 9.90269 39.1343i 0.321455 1.27035i
\(950\) 41.4288i 1.34413i
\(951\) 9.46924 2.53728i 0.307061 0.0822768i
\(952\) 7.78830 11.0219i 0.252420 0.357222i
\(953\) 4.66440 2.69299i 0.151095 0.0872347i −0.422546 0.906341i \(-0.638864\pi\)
0.573641 + 0.819107i \(0.305530\pi\)
\(954\) 5.04789 5.04789i 0.163431 0.163431i
\(955\) 13.8992 51.8725i 0.449767 1.67855i
\(956\) 5.91106 22.0604i 0.191177 0.713484i
\(957\) −0.378875 + 0.378875i −0.0122473 + 0.0122473i
\(958\) 23.1341 13.3565i 0.747429 0.431529i
\(959\) −21.7833 + 30.8274i −0.703419 + 0.995470i
\(960\) 3.45569 0.925950i 0.111532 0.0298849i
\(961\) 68.1500i 2.19839i
\(962\) 11.9278 + 6.66629i 0.384567 + 0.214930i
\(963\) 0.154635 0.00498305
\(964\) −26.0443 + 6.97856i −0.838832 + 0.224764i
\(965\) 63.6620 + 36.7553i 2.04935 + 1.18319i
\(966\) −13.5297 + 6.23848i −0.435310 + 0.200720i
\(967\) −25.0814 + 25.0814i −0.806565 + 0.806565i −0.984112 0.177548i \(-0.943184\pi\)
0.177548 + 0.984112i \(0.443184\pi\)
\(968\) −10.6045 2.84148i −0.340843 0.0913286i
\(969\) 26.1728 + 7.01298i 0.840792 + 0.225289i
\(970\) −17.6635 17.6635i −0.567141 0.567141i
\(971\) 18.2197 10.5191i 0.584697 0.337575i −0.178301 0.983976i \(-0.557060\pi\)
0.762998 + 0.646401i \(0.223727\pi\)
\(972\) −0.500000 + 0.866025i −0.0160375 + 0.0277778i
\(973\) −40.6307 + 6.98472i −1.30256 + 0.223920i
\(974\) 8.08818i 0.259162i
\(975\) 0.392489 + 28.1177i 0.0125697 + 0.900487i
\(976\) 11.1136i 0.355739i
\(977\) −8.19242 30.5745i −0.262099 0.978165i −0.964002 0.265894i \(-0.914333\pi\)
0.701904 0.712272i \(-0.252334\pi\)
\(978\) −10.7491 6.20599i −0.343718 0.198446i
\(979\) 0.926971 + 1.60556i 0.0296261 + 0.0513139i
\(980\) −14.1877 20.6366i −0.453208 0.659214i
\(981\) −7.89092 2.11437i −0.251938 0.0675065i
\(982\) −7.25525 + 27.0770i −0.231524 + 0.864060i
\(983\) 27.5835 27.5835i 0.879777 0.879777i −0.113734 0.993511i \(-0.536281\pi\)
0.993511 + 0.113734i \(0.0362811\pi\)
\(984\) 3.61752 + 6.26572i 0.115322 + 0.199744i
\(985\) 24.8859 43.1036i 0.792931 1.37340i
\(986\) 4.83993 + 18.0629i 0.154135 + 0.575239i
\(987\) 6.75561 + 0.620251i 0.215034 + 0.0197428i
\(988\) 13.7305 + 13.3525i 0.436826 + 0.424799i
\(989\) −18.1697 −0.577762
\(990\) −0.505077 + 0.135335i −0.0160524 + 0.00430122i
\(991\) −18.1434 + 31.4254i −0.576345 + 0.998259i 0.419549 + 0.907733i \(0.362188\pi\)
−0.995894 + 0.0905266i \(0.971145\pi\)
\(992\) −4.97871 8.62337i −0.158074 0.273792i
\(993\) −24.3766 24.3766i −0.773567 0.773567i
\(994\) −6.14059 + 16.6486i −0.194768 + 0.528061i
\(995\) −8.54429 + 31.8877i −0.270872 + 1.01091i
\(996\) −5.59369 5.59369i −0.177243 0.177243i
\(997\) −4.09769 + 2.36580i −0.129775 + 0.0749257i −0.563482 0.826128i \(-0.690539\pi\)
0.433707 + 0.901054i \(0.357205\pi\)
\(998\) −20.1691 11.6447i −0.638443 0.368605i
\(999\) −0.980866 3.66064i −0.0310332 0.115818i
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.bx.a.97.5 40
7.6 odd 2 546.2.bx.b.97.1 yes 40
13.11 odd 12 546.2.bx.b.349.1 yes 40
91.76 even 12 inner 546.2.bx.a.349.5 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bx.a.97.5 40 1.1 even 1 trivial
546.2.bx.a.349.5 yes 40 91.76 even 12 inner
546.2.bx.b.97.1 yes 40 7.6 odd 2
546.2.bx.b.349.1 yes 40 13.11 odd 12