Properties

Label 360.2.br.d.317.1
Level $360$
Weight $2$
Character 360.317
Analytic conductor $2.875$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(77,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.br (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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 317.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 360.317
Dual form 360.2.br.d.293.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-4.23205 + 1.13397i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-4.23205 + 1.13397i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.09808 + 2.36603i) q^{10} +(1.00000 - 1.73205i) q^{11} -3.46410i q^{12} +(-0.464102 + 1.73205i) q^{13} +6.19615i q^{14} +(-3.86603 - 0.232051i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 + 3.00000i) q^{17} +(3.00000 + 3.00000i) q^{18} +4.73205 q^{19} +(4.00000 - 2.00000i) q^{20} +(-5.36603 - 5.36603i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(0.232051 - 0.866025i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(-1.96410 - 4.59808i) q^{25} +(2.19615 + 1.26795i) q^{26} -5.19615 q^{27} +(8.46410 + 2.26795i) q^{28} +(-2.76795 - 1.59808i) q^{29} +(-1.73205 + 5.19615i) q^{30} +(4.09808 + 7.09808i) q^{31} +(5.46410 - 1.46410i) q^{32} +3.46410 q^{33} +(3.00000 + 5.19615i) q^{34} +(3.09808 - 9.29423i) q^{35} +(5.19615 - 3.00000i) q^{36} +(0.464102 - 0.464102i) q^{37} +(1.73205 - 6.46410i) q^{38} +(-3.00000 + 0.803848i) q^{39} +(-1.26795 - 6.19615i) q^{40} +(-5.59808 + 3.23205i) q^{41} +(-9.29423 + 5.36603i) q^{42} +(8.83013 - 2.36603i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(-3.00000 - 6.00000i) q^{45} +(-1.09808 - 0.633975i) q^{46} +(-0.401924 - 1.50000i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(10.5622 - 6.09808i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(-7.09808 - 1.90192i) q^{51} +(2.53590 - 2.53590i) q^{52} +(-5.19615 + 5.19615i) q^{53} +(-1.90192 + 7.09808i) q^{54} +(2.00000 + 4.00000i) q^{55} +(6.19615 - 10.7321i) q^{56} +(4.09808 + 7.09808i) q^{57} +(-3.19615 + 3.19615i) q^{58} +(-1.56218 + 0.901924i) q^{59} +(6.46410 + 4.26795i) q^{60} +(12.6962 + 7.33013i) q^{61} +(11.1962 - 3.00000i) q^{62} +(3.40192 - 12.6962i) q^{63} -8.00000i q^{64} +(-2.66025 - 3.00000i) q^{65} +(1.26795 - 4.73205i) q^{66} +(7.33013 + 1.96410i) q^{67} +(8.19615 - 2.19615i) q^{68} +(1.50000 - 0.401924i) q^{69} +(-11.5622 - 7.63397i) q^{70} -12.0000i q^{71} +(-2.19615 - 8.19615i) q^{72} +(-10.1962 + 10.1962i) q^{73} +(-0.464102 - 0.803848i) q^{74} +(5.19615 - 6.92820i) q^{75} +(-8.19615 - 4.73205i) q^{76} +(-2.26795 + 8.46410i) q^{77} +4.39230i q^{78} +(-1.90192 - 1.09808i) q^{79} +(-8.92820 - 0.535898i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.36603 + 8.83013i) q^{82} +(3.03590 + 11.3301i) q^{83} +(3.92820 + 14.6603i) q^{84} +(-1.90192 - 9.29423i) q^{85} -12.9282i q^{86} -5.53590i q^{87} +(1.46410 + 5.46410i) q^{88} -2.66025 q^{89} +(-9.29423 + 1.90192i) q^{90} -7.85641i q^{91} +(-1.26795 + 1.26795i) q^{92} +(-7.09808 + 12.2942i) q^{93} -2.19615 q^{94} +(-5.83013 + 8.83013i) q^{95} +(6.92820 + 6.92820i) q^{96} +(-6.83013 + 1.83013i) q^{97} +(-4.46410 - 16.6603i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{5} + 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 2 q^{5} + 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} - 2 q^{10} + 4 q^{11} + 12 q^{13} - 12 q^{15} + 8 q^{16} - 12 q^{17} + 12 q^{18} + 12 q^{19} + 16 q^{20} - 18 q^{21} - 8 q^{22} - 6 q^{23} - 12 q^{24} + 6 q^{25} - 12 q^{26} + 20 q^{28} - 18 q^{29} + 6 q^{31} + 8 q^{32} + 12 q^{34} + 2 q^{35} - 12 q^{37} - 12 q^{39} - 12 q^{40} - 12 q^{41} - 6 q^{42} + 18 q^{43} - 12 q^{45} + 6 q^{46} - 12 q^{47} + 18 q^{49} - 28 q^{50} - 18 q^{51} + 24 q^{52} - 18 q^{54} + 8 q^{55} + 4 q^{56} + 6 q^{57} + 8 q^{58} + 18 q^{59} + 12 q^{60} + 30 q^{61} + 24 q^{62} + 24 q^{63} + 24 q^{65} + 12 q^{66} + 12 q^{67} + 12 q^{68} + 6 q^{69} - 22 q^{70} + 12 q^{72} - 20 q^{73} + 12 q^{74} - 12 q^{76} - 16 q^{77} - 18 q^{79} - 8 q^{80} - 18 q^{81} + 6 q^{82} + 26 q^{83} - 12 q^{84} - 18 q^{85} - 8 q^{88} + 24 q^{89} - 6 q^{90} - 12 q^{92} - 18 q^{93} + 12 q^{94} - 6 q^{95} - 10 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) 0.866025 + 1.50000i 0.500000 + 0.866025i
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) −1.23205 + 1.86603i −0.550990 + 0.834512i
\(6\) 2.36603 0.633975i 0.965926 0.258819i
\(7\) −4.23205 + 1.13397i −1.59956 + 0.428602i −0.944911 0.327327i \(-0.893852\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 2.09808 + 2.36603i 0.663470 + 0.748203i
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 3.46410i 1.00000i
\(13\) −0.464102 + 1.73205i −0.128719 + 0.480384i −0.999945 0.0104972i \(-0.996659\pi\)
0.871226 + 0.490882i \(0.163325\pi\)
\(14\) 6.19615i 1.65599i
\(15\) −3.86603 0.232051i −0.998203 0.0599153i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −3.00000 + 3.00000i −0.727607 + 0.727607i −0.970143 0.242536i \(-0.922021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 4.73205 1.08561 0.542803 0.839860i \(-0.317363\pi\)
0.542803 + 0.839860i \(0.317363\pi\)
\(20\) 4.00000 2.00000i 0.894427 0.447214i
\(21\) −5.36603 5.36603i −1.17096 1.17096i
\(22\) −2.00000 2.00000i −0.426401 0.426401i
\(23\) 0.232051 0.866025i 0.0483859 0.180579i −0.937504 0.347975i \(-0.886869\pi\)
0.985890 + 0.167396i \(0.0535360\pi\)
\(24\) −4.73205 1.26795i −0.965926 0.258819i
\(25\) −1.96410 4.59808i −0.392820 0.919615i
\(26\) 2.19615 + 1.26795i 0.430701 + 0.248665i
\(27\) −5.19615 −1.00000
\(28\) 8.46410 + 2.26795i 1.59956 + 0.428602i
\(29\) −2.76795 1.59808i −0.513995 0.296755i 0.220479 0.975392i \(-0.429238\pi\)
−0.734474 + 0.678636i \(0.762571\pi\)
\(30\) −1.73205 + 5.19615i −0.316228 + 0.948683i
\(31\) 4.09808 + 7.09808i 0.736036 + 1.27485i 0.954267 + 0.298955i \(0.0966380\pi\)
−0.218231 + 0.975897i \(0.570029\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) 3.46410 0.603023
\(34\) 3.00000 + 5.19615i 0.514496 + 0.891133i
\(35\) 3.09808 9.29423i 0.523670 1.57101i
\(36\) 5.19615 3.00000i 0.866025 0.500000i
\(37\) 0.464102 0.464102i 0.0762978 0.0762978i −0.667928 0.744226i \(-0.732819\pi\)
0.744226 + 0.667928i \(0.232819\pi\)
\(38\) 1.73205 6.46410i 0.280976 1.04862i
\(39\) −3.00000 + 0.803848i −0.480384 + 0.128719i
\(40\) −1.26795 6.19615i −0.200480 0.979698i
\(41\) −5.59808 + 3.23205i −0.874273 + 0.504762i −0.868766 0.495223i \(-0.835086\pi\)
−0.00550690 + 0.999985i \(0.501753\pi\)
\(42\) −9.29423 + 5.36603i −1.43413 + 0.827996i
\(43\) 8.83013 2.36603i 1.34658 0.360815i 0.487710 0.873006i \(-0.337832\pi\)
0.858872 + 0.512190i \(0.171166\pi\)
\(44\) −3.46410 + 2.00000i −0.522233 + 0.301511i
\(45\) −3.00000 6.00000i −0.447214 0.894427i
\(46\) −1.09808 0.633975i −0.161903 0.0934745i
\(47\) −0.401924 1.50000i −0.0586266 0.218797i 0.930397 0.366552i \(-0.119462\pi\)
−0.989024 + 0.147755i \(0.952795\pi\)
\(48\) −3.46410 + 6.00000i −0.500000 + 0.866025i
\(49\) 10.5622 6.09808i 1.50888 0.871154i
\(50\) −7.00000 + 1.00000i −0.989949 + 0.141421i
\(51\) −7.09808 1.90192i −0.993929 0.266323i
\(52\) 2.53590 2.53590i 0.351666 0.351666i
\(53\) −5.19615 + 5.19615i −0.713746 + 0.713746i −0.967317 0.253570i \(-0.918395\pi\)
0.253570 + 0.967317i \(0.418395\pi\)
\(54\) −1.90192 + 7.09808i −0.258819 + 0.965926i
\(55\) 2.00000 + 4.00000i 0.269680 + 0.539360i
\(56\) 6.19615 10.7321i 0.827996 1.43413i
\(57\) 4.09808 + 7.09808i 0.542803 + 0.940163i
\(58\) −3.19615 + 3.19615i −0.419675 + 0.419675i
\(59\) −1.56218 + 0.901924i −0.203378 + 0.117420i −0.598230 0.801324i \(-0.704129\pi\)
0.394852 + 0.918745i \(0.370796\pi\)
\(60\) 6.46410 + 4.26795i 0.834512 + 0.550990i
\(61\) 12.6962 + 7.33013i 1.62558 + 0.938527i 0.985391 + 0.170305i \(0.0544754\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 11.1962 3.00000i 1.42191 0.381000i
\(63\) 3.40192 12.6962i 0.428602 1.59956i
\(64\) 8.00000i 1.00000i
\(65\) −2.66025 3.00000i −0.329964 0.372104i
\(66\) 1.26795 4.73205i 0.156074 0.582475i
\(67\) 7.33013 + 1.96410i 0.895518 + 0.239953i 0.677090 0.735900i \(-0.263241\pi\)
0.218427 + 0.975853i \(0.429907\pi\)
\(68\) 8.19615 2.19615i 0.993929 0.266323i
\(69\) 1.50000 0.401924i 0.180579 0.0483859i
\(70\) −11.5622 7.63397i −1.38194 0.912434i
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) −2.19615 8.19615i −0.258819 0.965926i
\(73\) −10.1962 + 10.1962i −1.19337 + 1.19337i −0.217254 + 0.976115i \(0.569710\pi\)
−0.976115 + 0.217254i \(0.930290\pi\)
\(74\) −0.464102 0.803848i −0.0539507 0.0934454i
\(75\) 5.19615 6.92820i 0.600000 0.800000i
\(76\) −8.19615 4.73205i −0.940163 0.542803i
\(77\) −2.26795 + 8.46410i −0.258457 + 0.964574i
\(78\) 4.39230i 0.497331i
\(79\) −1.90192 1.09808i −0.213983 0.123543i 0.389178 0.921163i \(-0.372759\pi\)
−0.603161 + 0.797619i \(0.706092\pi\)
\(80\) −8.92820 0.535898i −0.998203 0.0599153i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 2.36603 + 8.83013i 0.261284 + 0.975124i
\(83\) 3.03590 + 11.3301i 0.333233 + 1.24364i 0.905772 + 0.423765i \(0.139292\pi\)
−0.572539 + 0.819878i \(0.694041\pi\)
\(84\) 3.92820 + 14.6603i 0.428602 + 1.59956i
\(85\) −1.90192 9.29423i −0.206293 1.00810i
\(86\) 12.9282i 1.39408i
\(87\) 5.53590i 0.593511i
\(88\) 1.46410 + 5.46410i 0.156074 + 0.582475i
\(89\) −2.66025 −0.281986 −0.140993 0.990011i \(-0.545030\pi\)
−0.140993 + 0.990011i \(0.545030\pi\)
\(90\) −9.29423 + 1.90192i −0.979698 + 0.200480i
\(91\) 7.85641i 0.823575i
\(92\) −1.26795 + 1.26795i −0.132193 + 0.132193i
\(93\) −7.09808 + 12.2942i −0.736036 + 1.27485i
\(94\) −2.19615 −0.226516
\(95\) −5.83013 + 8.83013i −0.598158 + 0.905952i
\(96\) 6.92820 + 6.92820i 0.707107 + 0.707107i
\(97\) −6.83013 + 1.83013i −0.693494 + 0.185821i −0.588315 0.808632i \(-0.700208\pi\)
−0.105180 + 0.994453i \(0.533542\pi\)
\(98\) −4.46410 16.6603i −0.450942 1.68294i
\(99\) 3.00000 + 5.19615i 0.301511 + 0.522233i
\(100\) −1.19615 + 9.92820i −0.119615 + 0.992820i
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) −5.19615 + 9.00000i −0.514496 + 0.891133i
\(103\) −15.5622 4.16987i −1.53339 0.410870i −0.609265 0.792967i \(-0.708535\pi\)
−0.924122 + 0.382097i \(0.875202\pi\)
\(104\) −2.53590 4.39230i −0.248665 0.430701i
\(105\) 16.6244 3.40192i 1.62237 0.331994i
\(106\) 5.19615 + 9.00000i 0.504695 + 0.874157i
\(107\) −6.09808 6.09808i −0.589523 0.589523i 0.347979 0.937502i \(-0.386868\pi\)
−0.937502 + 0.347979i \(0.886868\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) −8.66025 −0.829502 −0.414751 0.909935i \(-0.636131\pi\)
−0.414751 + 0.909935i \(0.636131\pi\)
\(110\) 6.19615 1.26795i 0.590780 0.120894i
\(111\) 1.09808 + 0.294229i 0.104225 + 0.0279269i
\(112\) −12.3923 12.3923i −1.17096 1.17096i
\(113\) 0.464102 1.73205i 0.0436590 0.162938i −0.940655 0.339366i \(-0.889788\pi\)
0.984314 + 0.176428i \(0.0564543\pi\)
\(114\) 11.1962 3.00000i 1.04862 0.280976i
\(115\) 1.33013 + 1.50000i 0.124035 + 0.139876i
\(116\) 3.19615 + 5.53590i 0.296755 + 0.513995i
\(117\) −3.80385 3.80385i −0.351666 0.351666i
\(118\) 0.660254 + 2.46410i 0.0607813 + 0.226839i
\(119\) 9.29423 16.0981i 0.852001 1.47571i
\(120\) 8.19615 7.26795i 0.748203 0.663470i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 14.6603 14.6603i 1.32728 1.32728i
\(123\) −9.69615 5.59808i −0.874273 0.504762i
\(124\) 16.3923i 1.47207i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) −16.0981 9.29423i −1.43413 0.827996i
\(127\) 5.90192 + 5.90192i 0.523711 + 0.523711i 0.918690 0.394979i \(-0.129248\pi\)
−0.394979 + 0.918690i \(0.629248\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) 11.1962 + 11.1962i 0.985766 + 0.985766i
\(130\) −5.07180 + 2.53590i −0.444826 + 0.222413i
\(131\) 3.90192 + 6.75833i 0.340913 + 0.590478i 0.984602 0.174808i \(-0.0559306\pi\)
−0.643690 + 0.765287i \(0.722597\pi\)
\(132\) −6.00000 3.46410i −0.522233 0.301511i
\(133\) −20.0263 + 5.36603i −1.73650 + 0.465293i
\(134\) 5.36603 9.29423i 0.463554 0.802899i
\(135\) 6.40192 9.69615i 0.550990 0.834512i
\(136\) 12.0000i 1.02899i
\(137\) 3.46410 + 12.9282i 0.295958 + 1.10453i 0.940453 + 0.339923i \(0.110401\pi\)
−0.644495 + 0.764608i \(0.722932\pi\)
\(138\) 2.19615i 0.186949i
\(139\) 3.46410 + 6.00000i 0.293821 + 0.508913i 0.974710 0.223474i \(-0.0717396\pi\)
−0.680889 + 0.732387i \(0.738406\pi\)
\(140\) −14.6603 + 13.0000i −1.23902 + 1.09870i
\(141\) 1.90192 1.90192i 0.160171 0.160171i
\(142\) −16.3923 4.39230i −1.37561 0.368594i
\(143\) 2.53590 + 2.53590i 0.212062 + 0.212062i
\(144\) −12.0000 −1.00000
\(145\) 6.39230 3.19615i 0.530852 0.265426i
\(146\) 10.1962 + 17.6603i 0.843840 + 1.46157i
\(147\) 18.2942 + 10.5622i 1.50888 + 0.871154i
\(148\) −1.26795 + 0.339746i −0.104225 + 0.0279269i
\(149\) 6.06218 3.50000i 0.496633 0.286731i −0.230689 0.973028i \(-0.574098\pi\)
0.727322 + 0.686296i \(0.240765\pi\)
\(150\) −7.56218 9.63397i −0.617449 0.786611i
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) −9.46410 + 9.46410i −0.767640 + 0.767640i
\(153\) −3.29423 12.2942i −0.266323 0.993929i
\(154\) 10.7321 + 6.19615i 0.864813 + 0.499300i
\(155\) −18.2942 1.09808i −1.46943 0.0881996i
\(156\) 6.00000 + 1.60770i 0.480384 + 0.128719i
\(157\) 12.2942 + 3.29423i 0.981186 + 0.262908i 0.713544 0.700610i \(-0.247089\pi\)
0.267642 + 0.963518i \(0.413756\pi\)
\(158\) −2.19615 + 2.19615i −0.174717 + 0.174717i
\(159\) −12.2942 3.29423i −0.974996 0.261249i
\(160\) −4.00000 + 12.0000i −0.316228 + 0.948683i
\(161\) 3.92820i 0.309586i
\(162\) −12.2942 + 3.29423i −0.965926 + 0.258819i
\(163\) −6.46410 6.46410i −0.506308 0.506308i 0.407083 0.913391i \(-0.366546\pi\)
−0.913391 + 0.407083i \(0.866546\pi\)
\(164\) 12.9282 1.00952
\(165\) −4.26795 + 6.46410i −0.332259 + 0.503230i
\(166\) 16.5885 1.28751
\(167\) 17.8923 + 4.79423i 1.38455 + 0.370989i 0.872771 0.488130i \(-0.162321\pi\)
0.511777 + 0.859118i \(0.328987\pi\)
\(168\) 21.4641 1.65599
\(169\) 8.47372 + 4.89230i 0.651825 + 0.376331i
\(170\) −13.3923 0.803848i −1.02714 0.0616523i
\(171\) −7.09808 + 12.2942i −0.542803 + 0.940163i
\(172\) −17.6603 4.73205i −1.34658 0.360815i
\(173\) −0.732051 2.73205i −0.0556568 0.207714i 0.932498 0.361176i \(-0.117625\pi\)
−0.988155 + 0.153462i \(0.950958\pi\)
\(174\) −7.56218 2.02628i −0.573287 0.153612i
\(175\) 13.5263 + 17.2321i 1.02249 + 1.30262i
\(176\) 8.00000 0.603023
\(177\) −2.70577 1.56218i −0.203378 0.117420i
\(178\) −0.973721 + 3.63397i −0.0729834 + 0.272378i
\(179\) 6.39230i 0.477783i 0.971046 + 0.238892i \(0.0767841\pi\)
−0.971046 + 0.238892i \(0.923216\pi\)
\(180\) −0.803848 + 13.3923i −0.0599153 + 0.998203i
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) −10.7321 2.87564i −0.795513 0.213157i
\(183\) 25.3923i 1.87705i
\(184\) 1.26795 + 2.19615i 0.0934745 + 0.161903i
\(185\) 0.294229 + 1.43782i 0.0216321 + 0.105711i
\(186\) 14.1962 + 14.1962i 1.04091 + 1.04091i
\(187\) 2.19615 + 8.19615i 0.160599 + 0.599362i
\(188\) −0.803848 + 3.00000i −0.0586266 + 0.218797i
\(189\) 21.9904 5.89230i 1.59956 0.428602i
\(190\) 9.92820 + 11.1962i 0.720268 + 0.812254i
\(191\) −16.0981 9.29423i −1.16482 0.672507i −0.212362 0.977191i \(-0.568116\pi\)
−0.952453 + 0.304684i \(0.901449\pi\)
\(192\) 12.0000 6.92820i 0.866025 0.500000i
\(193\) 13.6603 + 3.66025i 0.983287 + 0.263471i 0.714428 0.699709i \(-0.246687\pi\)
0.268858 + 0.963180i \(0.413354\pi\)
\(194\) 10.0000i 0.717958i
\(195\) 2.19615 6.58846i 0.157270 0.471809i
\(196\) −24.3923 −1.74231
\(197\) 12.0000 + 12.0000i 0.854965 + 0.854965i 0.990740 0.135775i \(-0.0433525\pi\)
−0.135775 + 0.990740i \(0.543352\pi\)
\(198\) 8.19615 2.19615i 0.582475 0.156074i
\(199\) 4.19615i 0.297457i 0.988878 + 0.148729i \(0.0475181\pi\)
−0.988878 + 0.148729i \(0.952482\pi\)
\(200\) 13.1244 + 5.26795i 0.928032 + 0.372500i
\(201\) 3.40192 + 12.6962i 0.239953 + 0.895518i
\(202\) 2.00000 + 2.00000i 0.140720 + 0.140720i
\(203\) 13.5263 + 3.62436i 0.949359 + 0.254380i
\(204\) 10.3923 + 10.3923i 0.727607 + 0.727607i
\(205\) 0.866025 14.4282i 0.0604858 1.00771i
\(206\) −11.3923 + 19.7321i −0.793739 + 1.37480i
\(207\) 1.90192 + 1.90192i 0.132193 + 0.132193i
\(208\) −6.92820 + 1.85641i −0.480384 + 0.128719i
\(209\) 4.73205 8.19615i 0.327323 0.566940i
\(210\) 1.43782 23.9545i 0.0992192 1.65302i
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 14.1962 3.80385i 0.974996 0.261249i
\(213\) 18.0000 10.3923i 1.23334 0.712069i
\(214\) −10.5622 + 6.09808i −0.722016 + 0.416856i
\(215\) −6.46410 + 19.3923i −0.440848 + 1.32254i
\(216\) 10.3923 10.3923i 0.707107 0.707107i
\(217\) −25.3923 25.3923i −1.72374 1.72374i
\(218\) −3.16987 + 11.8301i −0.214691 + 0.801237i
\(219\) −24.1244 6.46410i −1.63017 0.436804i
\(220\) 0.535898 8.92820i 0.0361303 0.601939i
\(221\) −3.80385 6.58846i −0.255874 0.443188i
\(222\) 0.803848 1.39230i 0.0539507 0.0934454i
\(223\) 4.42820 + 16.5263i 0.296534 + 1.10668i 0.939991 + 0.341199i \(0.110833\pi\)
−0.643457 + 0.765483i \(0.722500\pi\)
\(224\) −21.4641 + 12.3923i −1.43413 + 0.827996i
\(225\) 14.8923 + 1.79423i 0.992820 + 0.119615i
\(226\) −2.19615 1.26795i −0.146086 0.0843427i
\(227\) 10.0981 2.70577i 0.670233 0.179588i 0.0923731 0.995724i \(-0.470555\pi\)
0.577860 + 0.816136i \(0.303888\pi\)
\(228\) 16.3923i 1.08561i
\(229\) −5.76795 9.99038i −0.381157 0.660183i 0.610071 0.792347i \(-0.291141\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 2.53590 1.26795i 0.167212 0.0836061i
\(231\) −14.6603 + 3.92820i −0.964574 + 0.258457i
\(232\) 8.73205 2.33975i 0.573287 0.153612i
\(233\) −18.1244 18.1244i −1.18737 1.18737i −0.977793 0.209573i \(-0.932793\pi\)
−0.209573 0.977793i \(-0.567207\pi\)
\(234\) −6.58846 + 3.80385i −0.430701 + 0.248665i
\(235\) 3.29423 + 1.09808i 0.214892 + 0.0716306i
\(236\) 3.60770 0.234841
\(237\) 3.80385i 0.247086i
\(238\) −18.5885 18.5885i −1.20491 1.20491i
\(239\) 9.46410 + 16.3923i 0.612182 + 1.06033i 0.990872 + 0.134807i \(0.0430413\pi\)
−0.378690 + 0.925524i \(0.623625\pi\)
\(240\) −6.92820 13.8564i −0.447214 0.894427i
\(241\) 9.40192 16.2846i 0.605631 1.04898i −0.386320 0.922365i \(-0.626254\pi\)
0.991951 0.126619i \(-0.0404126\pi\)
\(242\) 9.56218 2.56218i 0.614680 0.164703i
\(243\) 7.79423 13.5000i 0.500000 0.866025i
\(244\) −14.6603 25.3923i −0.938527 1.62558i
\(245\) −1.63397 + 27.2224i −0.104391 + 1.73918i
\(246\) −11.1962 + 11.1962i −0.713841 + 0.713841i
\(247\) −2.19615 + 8.19615i −0.139738 + 0.521509i
\(248\) −22.3923 6.00000i −1.42191 0.381000i
\(249\) −14.3660 + 14.3660i −0.910410 + 0.910410i
\(250\) 6.75833 14.2942i 0.427434 0.904046i
\(251\) −26.5885 −1.67825 −0.839124 0.543940i \(-0.816932\pi\)
−0.839124 + 0.543940i \(0.816932\pi\)
\(252\) −18.5885 + 18.5885i −1.17096 + 1.17096i
\(253\) −1.26795 1.26795i −0.0797153 0.0797153i
\(254\) 10.2224 5.90192i 0.641412 0.370320i
\(255\) 12.2942 10.9019i 0.769894 0.682705i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −15.7583 4.22243i −0.982978 0.263388i −0.268680 0.963230i \(-0.586587\pi\)
−0.714298 + 0.699842i \(0.753254\pi\)
\(258\) 19.3923 11.1962i 1.20731 0.697042i
\(259\) −1.43782 + 2.49038i −0.0893419 + 0.154745i
\(260\) 1.60770 + 7.85641i 0.0997050 + 0.487234i
\(261\) 8.30385 4.79423i 0.513995 0.296755i
\(262\) 10.6603 2.85641i 0.658593 0.176469i
\(263\) 13.5622 3.63397i 0.836280 0.224080i 0.184828 0.982771i \(-0.440827\pi\)
0.651451 + 0.758690i \(0.274160\pi\)
\(264\) −6.92820 + 6.92820i −0.426401 + 0.426401i
\(265\) −3.29423 16.0981i −0.202363 0.988897i
\(266\) 29.3205i 1.79776i
\(267\) −2.30385 3.99038i −0.140993 0.244207i
\(268\) −10.7321 10.7321i −0.655564 0.655564i
\(269\) 1.00000i 0.0609711i −0.999535 0.0304855i \(-0.990295\pi\)
0.999535 0.0304855i \(-0.00970535\pi\)
\(270\) −10.9019 12.2942i −0.663470 0.748203i
\(271\) 4.58846 0.278729 0.139364 0.990241i \(-0.455494\pi\)
0.139364 + 0.990241i \(0.455494\pi\)
\(272\) −16.3923 4.39230i −0.993929 0.266323i
\(273\) 11.7846 6.80385i 0.713237 0.411788i
\(274\) 18.9282 1.14349
\(275\) −9.92820 1.19615i −0.598693 0.0721307i
\(276\) −3.00000 0.803848i −0.180579 0.0483859i
\(277\) 2.36603 + 8.83013i 0.142161 + 0.530551i 0.999865 + 0.0164083i \(0.00522314\pi\)
−0.857705 + 0.514143i \(0.828110\pi\)
\(278\) 9.46410 2.53590i 0.567619 0.152093i
\(279\) −24.5885 −1.47207
\(280\) 12.3923 + 24.7846i 0.740582 + 1.48116i
\(281\) −1.79423 1.03590i −0.107035 0.0617965i 0.445527 0.895268i \(-0.353016\pi\)
−0.552562 + 0.833472i \(0.686350\pi\)
\(282\) −1.90192 3.29423i −0.113258 0.196168i
\(283\) −1.20577 + 4.50000i −0.0716757 + 0.267497i −0.992459 0.122577i \(-0.960884\pi\)
0.920783 + 0.390074i \(0.127551\pi\)
\(284\) −12.0000 + 20.7846i −0.712069 + 1.23334i
\(285\) −18.2942 1.09808i −1.08366 0.0650444i
\(286\) 4.39230 2.53590i 0.259722 0.149951i
\(287\) 20.0263 20.0263i 1.18211 1.18211i
\(288\) −4.39230 + 16.3923i −0.258819 + 0.965926i
\(289\) 1.00000i 0.0588235i
\(290\) −2.02628 9.90192i −0.118987 0.581461i
\(291\) −8.66025 8.66025i −0.507673 0.507673i
\(292\) 27.8564 7.46410i 1.63017 0.436804i
\(293\) 1.09808 + 0.294229i 0.0641503 + 0.0171890i 0.290751 0.956799i \(-0.406095\pi\)
−0.226601 + 0.973988i \(0.572761\pi\)
\(294\) 21.1244 21.1244i 1.23200 1.23200i
\(295\) 0.241670 4.02628i 0.0140706 0.234419i
\(296\) 1.85641i 0.107901i
\(297\) −5.19615 + 9.00000i −0.301511 + 0.522233i
\(298\) −2.56218 9.56218i −0.148423 0.553922i
\(299\) 1.39230 + 0.803848i 0.0805191 + 0.0464877i
\(300\) −15.9282 + 6.80385i −0.919615 + 0.392820i
\(301\) −34.6865 + 20.0263i −1.99930 + 1.15430i
\(302\) −16.0000 16.0000i −0.920697 0.920697i
\(303\) −3.46410 −0.199007
\(304\) 9.46410 + 16.3923i 0.542803 + 0.940163i
\(305\) −29.3205 + 14.6603i −1.67889 + 0.839444i
\(306\) −18.0000 −1.02899
\(307\) 14.3660 14.3660i 0.819912 0.819912i −0.166183 0.986095i \(-0.553144\pi\)
0.986095 + 0.166183i \(0.0531441\pi\)
\(308\) 12.3923 12.3923i 0.706117 0.706117i
\(309\) −7.22243 26.9545i −0.410870 1.53339i
\(310\) −8.19615 + 24.5885i −0.465510 + 1.39653i
\(311\) 12.2942 7.09808i 0.697142 0.402495i −0.109140 0.994026i \(-0.534810\pi\)
0.806282 + 0.591531i \(0.201476\pi\)
\(312\) 4.39230 7.60770i 0.248665 0.430701i
\(313\) −3.87564 14.4641i −0.219064 0.817559i −0.984696 0.174280i \(-0.944240\pi\)
0.765632 0.643279i \(-0.222427\pi\)
\(314\) 9.00000 15.5885i 0.507899 0.879708i
\(315\) 19.5000 + 21.9904i 1.09870 + 1.23902i
\(316\) 2.19615 + 3.80385i 0.123543 + 0.213983i
\(317\) −13.6603 + 3.66025i −0.767236 + 0.205580i −0.621150 0.783692i \(-0.713334\pi\)
−0.146086 + 0.989272i \(0.546668\pi\)
\(318\) −9.00000 + 15.5885i −0.504695 + 0.874157i
\(319\) −5.53590 + 3.19615i −0.309951 + 0.178950i
\(320\) 14.9282 + 9.85641i 0.834512 + 0.550990i
\(321\) 3.86603 14.4282i 0.215780 0.805304i
\(322\) 5.36603 + 1.43782i 0.299037 + 0.0801267i
\(323\) −14.1962 + 14.1962i −0.789895 + 0.789895i
\(324\) 18.0000i 1.00000i
\(325\) 8.87564 1.26795i 0.492332 0.0703332i
\(326\) −11.1962 + 6.46410i −0.620098 + 0.358013i
\(327\) −7.50000 12.9904i −0.414751 0.718370i
\(328\) 4.73205 17.6603i 0.261284 0.975124i
\(329\) 3.40192 + 5.89230i 0.187554 + 0.324853i
\(330\) 7.26795 + 8.19615i 0.400087 + 0.451183i
\(331\) 0.509619 + 0.294229i 0.0280112 + 0.0161723i 0.513940 0.857826i \(-0.328185\pi\)
−0.485929 + 0.873998i \(0.661519\pi\)
\(332\) 6.07180 22.6603i 0.333233 1.24364i
\(333\) 0.509619 + 1.90192i 0.0279269 + 0.104225i
\(334\) 13.0981 22.6865i 0.716695 1.24135i
\(335\) −12.6962 + 11.2583i −0.693665 + 0.615108i
\(336\) 7.85641 29.3205i 0.428602 1.59956i
\(337\) 0.0717968 0.267949i 0.00391102 0.0145961i −0.963943 0.266110i \(-0.914262\pi\)
0.967854 + 0.251514i \(0.0809283\pi\)
\(338\) 9.78461 9.78461i 0.532213 0.532213i
\(339\) 3.00000 0.803848i 0.162938 0.0436590i
\(340\) −6.00000 + 18.0000i −0.325396 + 0.976187i
\(341\) 16.3923 0.887693
\(342\) 14.1962 + 14.1962i 0.767640 + 0.767640i
\(343\) −16.0981 + 16.0981i −0.869214 + 0.869214i
\(344\) −12.9282 + 22.3923i −0.697042 + 1.20731i
\(345\) −1.09808 + 3.29423i −0.0591184 + 0.177355i
\(346\) −4.00000 −0.215041
\(347\) 1.90192 7.09808i 0.102101 0.381045i −0.895899 0.444257i \(-0.853468\pi\)
0.998000 + 0.0632121i \(0.0201345\pi\)
\(348\) −5.53590 + 9.58846i −0.296755 + 0.513995i
\(349\) 18.2321 31.5788i 0.975939 1.69038i 0.299139 0.954209i \(-0.403300\pi\)
0.676800 0.736167i \(-0.263366\pi\)
\(350\) 28.4904 12.1699i 1.52287 0.650507i
\(351\) 2.41154 9.00000i 0.128719 0.480384i
\(352\) 2.92820 10.9282i 0.156074 0.582475i
\(353\) 12.9282 3.46410i 0.688099 0.184376i 0.102205 0.994763i \(-0.467410\pi\)
0.585894 + 0.810388i \(0.300744\pi\)
\(354\) −3.12436 + 3.12436i −0.166058 + 0.166058i
\(355\) 22.3923 + 14.7846i 1.18846 + 0.784686i
\(356\) 4.60770 + 2.66025i 0.244207 + 0.140993i
\(357\) 32.1962 1.70400
\(358\) 8.73205 + 2.33975i 0.461503 + 0.123659i
\(359\) 2.19615 0.115908 0.0579542 0.998319i \(-0.481542\pi\)
0.0579542 + 0.998319i \(0.481542\pi\)
\(360\) 18.0000 + 6.00000i 0.948683 + 0.316228i
\(361\) 3.39230 0.178542
\(362\) −4.09808 1.09808i −0.215390 0.0577136i
\(363\) −6.06218 + 10.5000i −0.318182 + 0.551107i
\(364\) −7.85641 + 13.6077i −0.411788 + 0.713237i
\(365\) −6.46410 31.5885i −0.338347 1.65342i
\(366\) 34.6865 + 9.29423i 1.81309 + 0.485817i
\(367\) −9.56218 + 2.56218i −0.499142 + 0.133745i −0.499602 0.866255i \(-0.666520\pi\)
0.000459976 1.00000i \(0.499854\pi\)
\(368\) 3.46410 0.928203i 0.180579 0.0483859i
\(369\) 19.3923i 1.00952i
\(370\) 2.07180 + 0.124356i 0.107708 + 0.00646494i
\(371\) 16.0981 27.8827i 0.835770 1.44760i
\(372\) 24.5885 14.1962i 1.27485 0.736036i
\(373\) −0.973721 + 3.63397i −0.0504173 + 0.188160i −0.986542 0.163508i \(-0.947719\pi\)
0.936125 + 0.351669i \(0.114386\pi\)
\(374\) 12.0000 0.620505
\(375\) 6.52628 + 18.2321i 0.337016 + 0.941499i
\(376\) 3.80385 + 2.19615i 0.196168 + 0.113258i
\(377\) 4.05256 4.05256i 0.208717 0.208717i
\(378\) 32.1962i 1.65599i
\(379\) −33.1244 −1.70148 −0.850742 0.525584i \(-0.823847\pi\)
−0.850742 + 0.525584i \(0.823847\pi\)
\(380\) 18.9282 9.46410i 0.970996 0.485498i
\(381\) −3.74167 + 13.9641i −0.191692 + 0.715403i
\(382\) −18.5885 + 18.5885i −0.951068 + 0.951068i
\(383\) 7.43782 27.7583i 0.380055 1.41838i −0.465761 0.884910i \(-0.654220\pi\)
0.845816 0.533474i \(-0.179114\pi\)
\(384\) −5.07180 18.9282i −0.258819 0.965926i
\(385\) −13.0000 14.6603i −0.662541 0.747156i
\(386\) 10.0000 17.3205i 0.508987 0.881591i
\(387\) −7.09808 + 26.4904i −0.360815 + 1.34658i
\(388\) 13.6603 + 3.66025i 0.693494 + 0.185821i
\(389\) 15.0622 + 8.69615i 0.763683 + 0.440912i 0.830616 0.556845i \(-0.187988\pi\)
−0.0669337 + 0.997757i \(0.521322\pi\)
\(390\) −8.19615 5.41154i −0.415028 0.274024i
\(391\) 1.90192 + 3.29423i 0.0961844 + 0.166596i
\(392\) −8.92820 + 33.3205i −0.450942 + 1.68294i
\(393\) −6.75833 + 11.7058i −0.340913 + 0.590478i
\(394\) 20.7846 12.0000i 1.04711 0.604551i
\(395\) 4.39230 2.19615i 0.221001 0.110500i
\(396\) 12.0000i 0.603023i
\(397\) −0.803848 + 0.803848i −0.0403440 + 0.0403440i −0.726991 0.686647i \(-0.759082\pi\)
0.686647 + 0.726991i \(0.259082\pi\)
\(398\) 5.73205 + 1.53590i 0.287322 + 0.0769876i
\(399\) −25.3923 25.3923i −1.27121 1.27121i
\(400\) 12.0000 16.0000i 0.600000 0.800000i
\(401\) −31.3923 + 18.1244i −1.56766 + 0.905087i −0.571215 + 0.820800i \(0.693528\pi\)
−0.996442 + 0.0842869i \(0.973139\pi\)
\(402\) 18.5885 0.927108
\(403\) −14.1962 + 3.80385i −0.707161 + 0.189483i
\(404\) 3.46410 2.00000i 0.172345 0.0995037i
\(405\) 20.0885 + 1.20577i 0.998203 + 0.0599153i
\(406\) 9.90192 17.1506i 0.491424 0.851172i
\(407\) −0.339746 1.26795i −0.0168406 0.0628499i
\(408\) 18.0000 10.3923i 0.891133 0.514496i
\(409\) −5.19615 + 3.00000i −0.256933 + 0.148340i −0.622935 0.782274i \(-0.714060\pi\)
0.366002 + 0.930614i \(0.380726\pi\)
\(410\) −19.3923 6.46410i −0.957718 0.319239i
\(411\) −16.3923 + 16.3923i −0.808573 + 0.808573i
\(412\) 22.7846 + 22.7846i 1.12252 + 1.12252i
\(413\) 5.58846 5.58846i 0.274990 0.274990i
\(414\) 3.29423 1.90192i 0.161903 0.0934745i
\(415\) −24.8827 8.29423i −1.22144 0.407148i
\(416\) 10.1436i 0.497331i
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) −9.46410 9.46410i −0.462904 0.462904i
\(419\) −10.7321 + 6.19615i −0.524295 + 0.302702i −0.738690 0.674045i \(-0.764555\pi\)
0.214395 + 0.976747i \(0.431222\pi\)
\(420\) −32.1962 10.7321i −1.57101 0.523670i
\(421\) 4.60770 + 2.66025i 0.224565 + 0.129653i 0.608062 0.793889i \(-0.291947\pi\)
−0.383497 + 0.923542i \(0.625280\pi\)
\(422\) 0 0
\(423\) 4.50000 + 1.20577i 0.218797 + 0.0586266i
\(424\) 20.7846i 1.00939i
\(425\) 19.6865 + 7.90192i 0.954937 + 0.383300i
\(426\) −7.60770 28.3923i −0.368594 1.37561i
\(427\) −62.0429 16.6244i −3.00247 0.804509i
\(428\) 4.46410 + 16.6603i 0.215780 + 0.805304i
\(429\) −1.60770 + 6.00000i −0.0776203 + 0.289683i
\(430\) 24.1244 + 15.9282i 1.16338 + 0.768126i
\(431\) 22.0526i 1.06223i 0.847298 + 0.531117i \(0.178228\pi\)
−0.847298 + 0.531117i \(0.821772\pi\)
\(432\) −10.3923 18.0000i −0.500000 0.866025i
\(433\) −15.3923 + 15.3923i −0.739707 + 0.739707i −0.972521 0.232814i \(-0.925207\pi\)
0.232814 + 0.972521i \(0.425207\pi\)
\(434\) −43.9808 + 25.3923i −2.11114 + 1.21887i
\(435\) 10.3301 + 6.82051i 0.495292 + 0.327018i
\(436\) 15.0000 + 8.66025i 0.718370 + 0.414751i
\(437\) 1.09808 4.09808i 0.0525281 0.196038i
\(438\) −17.6603 + 30.5885i −0.843840 + 1.46157i
\(439\) −16.2679 9.39230i −0.776427 0.448270i 0.0587356 0.998274i \(-0.481293\pi\)
−0.835162 + 0.550003i \(0.814626\pi\)
\(440\) −12.0000 4.00000i −0.572078 0.190693i
\(441\) 36.5885i 1.74231i
\(442\) −10.3923 + 2.78461i −0.494312 + 0.132450i
\(443\) −9.99038 37.2846i −0.474657 1.77145i −0.622696 0.782464i \(-0.713963\pi\)
0.148039 0.988982i \(-0.452704\pi\)
\(444\) −1.60770 1.60770i −0.0762978 0.0762978i
\(445\) 3.27757 4.96410i 0.155372 0.235321i
\(446\) 24.1962 1.14572
\(447\) 10.5000 + 6.06218i 0.496633 + 0.286731i
\(448\) 9.07180 + 33.8564i 0.428602 + 1.59956i
\(449\) 32.7846 1.54720 0.773601 0.633673i \(-0.218454\pi\)
0.773601 + 0.633673i \(0.218454\pi\)
\(450\) 7.90192 19.6865i 0.372500 0.928032i
\(451\) 12.9282i 0.608765i
\(452\) −2.53590 + 2.53590i −0.119279 + 0.119279i
\(453\) 27.7128 1.30206
\(454\) 14.7846i 0.693876i
\(455\) 14.6603 + 9.67949i 0.687283 + 0.453782i
\(456\) −22.3923 6.00000i −1.04862 0.280976i
\(457\) 9.83013 2.63397i 0.459834 0.123212i −0.0214632 0.999770i \(-0.506832\pi\)
0.481297 + 0.876558i \(0.340166\pi\)
\(458\) −15.7583 + 4.22243i −0.736338 + 0.197301i
\(459\) 15.5885 15.5885i 0.727607 0.727607i
\(460\) −0.803848 3.92820i −0.0374796 0.183153i
\(461\) 6.79423 11.7679i 0.316439 0.548088i −0.663304 0.748350i \(-0.730846\pi\)
0.979742 + 0.200262i \(0.0641795\pi\)
\(462\) 21.4641i 0.998600i
\(463\) 6.56218 + 1.75833i 0.304970 + 0.0817165i 0.408059 0.912956i \(-0.366206\pi\)
−0.103089 + 0.994672i \(0.532873\pi\)
\(464\) 12.7846i 0.593511i
\(465\) −14.1962 28.3923i −0.658331 1.31666i
\(466\) −31.3923 + 18.1244i −1.45422 + 0.839595i
\(467\) −8.60770 8.60770i −0.398317 0.398317i 0.479322 0.877639i \(-0.340882\pi\)
−0.877639 + 0.479322i \(0.840882\pi\)
\(468\) 2.78461 + 10.3923i 0.128719 + 0.480384i
\(469\) −33.2487 −1.53528
\(470\) 2.70577 4.09808i 0.124808 0.189030i
\(471\) 5.70577 + 21.2942i 0.262908 + 0.981186i
\(472\) 1.32051 4.92820i 0.0607813 0.226839i
\(473\) 4.73205 17.6603i 0.217580 0.812019i
\(474\) −5.19615 1.39230i −0.238667 0.0639507i
\(475\) −9.29423 21.7583i −0.426448 0.998341i
\(476\) −32.1962 + 18.5885i −1.47571 + 0.852001i
\(477\) −5.70577 21.2942i −0.261249 0.974996i
\(478\) 25.8564 6.92820i 1.18264 0.316889i
\(479\) −10.5622 + 18.2942i −0.482598 + 0.835885i −0.999800 0.0199786i \(-0.993640\pi\)
0.517202 + 0.855863i \(0.326974\pi\)
\(480\) −21.4641 + 4.39230i −0.979698 + 0.200480i
\(481\) 0.588457 + 1.01924i 0.0268313 + 0.0464732i
\(482\) −18.8038 18.8038i −0.856492 0.856492i
\(483\) −5.89230 + 3.40192i −0.268109 + 0.154793i
\(484\) 14.0000i 0.636364i
\(485\) 5.00000 15.0000i 0.227038 0.681115i
\(486\) −15.5885 15.5885i −0.707107 0.707107i
\(487\) 3.39230 + 3.39230i 0.153720 + 0.153720i 0.779777 0.626057i \(-0.215332\pi\)
−0.626057 + 0.779777i \(0.715332\pi\)
\(488\) −40.0526 + 10.7321i −1.81309 + 0.485817i
\(489\) 4.09808 15.2942i 0.185321 0.691629i
\(490\) 36.5885 + 12.1962i 1.65290 + 0.550966i
\(491\) 12.3923 + 21.4641i 0.559257 + 0.968661i 0.997559 + 0.0698335i \(0.0222468\pi\)
−0.438302 + 0.898828i \(0.644420\pi\)
\(492\) 11.1962 + 19.3923i 0.504762 + 0.874273i
\(493\) 13.0981 3.50962i 0.589908 0.158065i
\(494\) 10.3923 + 6.00000i 0.467572 + 0.269953i
\(495\) −13.3923 0.803848i −0.601939 0.0361303i
\(496\) −16.3923 + 28.3923i −0.736036 + 1.27485i
\(497\) 13.6077 + 50.7846i 0.610389 + 2.27800i
\(498\) 14.3660 + 24.8827i 0.643757 + 1.11502i
\(499\) 13.3923 + 23.1962i 0.599522 + 1.03840i 0.992892 + 0.119022i \(0.0379759\pi\)
−0.393370 + 0.919380i \(0.628691\pi\)
\(500\) −17.0526 14.4641i −0.762614 0.646854i
\(501\) 8.30385 + 30.9904i 0.370989 + 1.38455i
\(502\) −9.73205 + 36.3205i −0.434363 + 1.62106i
\(503\) 3.97372 + 3.97372i 0.177179 + 0.177179i 0.790125 0.612946i \(-0.210016\pi\)
−0.612946 + 0.790125i \(0.710016\pi\)
\(504\) 18.5885 + 32.1962i 0.827996 + 1.43413i
\(505\) −2.00000 4.00000i −0.0889988 0.177998i
\(506\) −2.19615 + 1.26795i −0.0976309 + 0.0563672i
\(507\) 16.9474i 0.752662i
\(508\) −4.32051 16.1244i −0.191692 0.715403i
\(509\) 6.57180 3.79423i 0.291290 0.168176i −0.347234 0.937779i \(-0.612879\pi\)
0.638523 + 0.769602i \(0.279546\pi\)
\(510\) −10.3923 20.7846i −0.460179 0.920358i
\(511\) 31.5885 54.7128i 1.39739 2.42035i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) −24.5885 −1.08561
\(514\) −11.5359 + 19.9808i −0.508827 + 0.881314i
\(515\) 26.9545 23.9019i 1.18776 1.05324i
\(516\) −8.19615 30.5885i −0.360815 1.34658i
\(517\) −3.00000 0.803848i −0.131940 0.0353532i
\(518\) 2.87564 + 2.87564i 0.126349 + 0.126349i
\(519\) 3.46410 3.46410i 0.152057 0.152057i
\(520\) 11.3205 + 0.679492i 0.496437 + 0.0297977i
\(521\) 14.6603i 0.642277i −0.947032 0.321139i \(-0.895934\pi\)
0.947032 0.321139i \(-0.104066\pi\)
\(522\) −3.50962 13.0981i −0.153612 0.573287i
\(523\) −1.56218 1.56218i −0.0683093 0.0683093i 0.672127 0.740436i \(-0.265381\pi\)
−0.740436 + 0.672127i \(0.765381\pi\)
\(524\) 15.6077i 0.681825i
\(525\) −14.1340 + 35.2128i −0.616857 + 1.53681i
\(526\) 19.8564i 0.865780i
\(527\) −33.5885 9.00000i −1.46314 0.392046i
\(528\) 6.92820 + 12.0000i 0.301511 + 0.522233i
\(529\) 19.2224 + 11.0981i 0.835758 + 0.482525i
\(530\) −23.1962 1.39230i −1.00758 0.0604779i
\(531\) 5.41154i 0.234841i
\(532\) 40.0526 + 10.7321i 1.73650 + 0.465293i
\(533\) −3.00000 11.1962i −0.129944 0.484959i
\(534\) −6.29423 + 1.68653i −0.272378 + 0.0729834i
\(535\) 18.8923 3.86603i 0.816786 0.167143i
\(536\) −18.5885 + 10.7321i −0.802899 + 0.463554i
\(537\) −9.58846 + 5.53590i −0.413772 + 0.238892i
\(538\) −1.36603 0.366025i −0.0588935 0.0157805i
\(539\) 24.3923i 1.05065i
\(540\) −20.7846 + 10.3923i −0.894427 + 0.447214i
\(541\) 12.4641i 0.535874i 0.963436 + 0.267937i \(0.0863418\pi\)
−0.963436 + 0.267937i \(0.913658\pi\)
\(542\) 1.67949 6.26795i 0.0721404 0.269231i
\(543\) 4.50000 2.59808i 0.193113 0.111494i
\(544\) −12.0000 + 20.7846i −0.514496 + 0.891133i
\(545\) 10.6699 16.1603i 0.457047 0.692229i
\(546\) −4.98076 18.5885i −0.213157 0.795513i
\(547\) −7.11474 26.5526i −0.304204 1.13531i −0.933628 0.358243i \(-0.883376\pi\)
0.629424 0.777062i \(-0.283291\pi\)
\(548\) 6.92820 25.8564i 0.295958 1.10453i
\(549\) −38.0885 + 21.9904i −1.62558 + 0.938527i
\(550\) −5.26795 + 13.1244i −0.224626 + 0.559624i
\(551\) −13.0981 7.56218i −0.557997 0.322160i
\(552\) −2.19615 + 3.80385i −0.0934745 + 0.161903i
\(553\) 9.29423 + 2.49038i 0.395231 + 0.105902i
\(554\) 12.9282 0.549267
\(555\) −1.90192 + 1.68653i −0.0807322 + 0.0715894i
\(556\) 13.8564i 0.587643i
\(557\) 0.803848 + 0.803848i 0.0340601 + 0.0340601i 0.723932 0.689872i \(-0.242333\pi\)
−0.689872 + 0.723932i \(0.742333\pi\)
\(558\) −9.00000 + 33.5885i −0.381000 + 1.42191i
\(559\) 16.3923i 0.693321i
\(560\) 38.3923 7.85641i 1.62237 0.331994i
\(561\) −10.3923 + 10.3923i −0.438763 + 0.438763i
\(562\) −2.07180 + 2.07180i −0.0873935 + 0.0873935i
\(563\) 32.0885 + 8.59808i 1.35237 + 0.362366i 0.861008 0.508591i \(-0.169834\pi\)
0.491359 + 0.870957i \(0.336500\pi\)
\(564\) −5.19615 + 1.39230i −0.218797 + 0.0586266i
\(565\) 2.66025 + 3.00000i 0.111918 + 0.126211i
\(566\) 5.70577 + 3.29423i 0.239831 + 0.138467i
\(567\) 27.8827 + 27.8827i 1.17096 + 1.17096i
\(568\) 24.0000 + 24.0000i 1.00702 + 1.00702i
\(569\) 1.26795 2.19615i 0.0531552 0.0920675i −0.838223 0.545327i \(-0.816406\pi\)
0.891379 + 0.453259i \(0.149739\pi\)
\(570\) −8.19615 + 24.5885i −0.343299 + 1.02990i
\(571\) 3.00000 1.73205i 0.125546 0.0724841i −0.435912 0.899989i \(-0.643574\pi\)
0.561458 + 0.827505i \(0.310241\pi\)
\(572\) −1.85641 6.92820i −0.0776203 0.289683i
\(573\) 32.1962i 1.34501i
\(574\) −20.0263 34.6865i −0.835881 1.44779i
\(575\) −4.43782 + 0.633975i −0.185070 + 0.0264386i
\(576\) 20.7846 + 12.0000i 0.866025 + 0.500000i
\(577\) 5.39230 + 5.39230i 0.224485 + 0.224485i 0.810384 0.585899i \(-0.199259\pi\)
−0.585899 + 0.810384i \(0.699259\pi\)
\(578\) −1.36603 0.366025i −0.0568192 0.0152246i
\(579\) 6.33975 + 23.6603i 0.263471 + 0.983287i
\(580\) −14.2679 0.856406i −0.592444 0.0355603i
\(581\) −25.6962 44.5070i −1.06606 1.84646i
\(582\) −15.0000 + 8.66025i −0.621770 + 0.358979i
\(583\) 3.80385 + 14.1962i 0.157539 + 0.587945i
\(584\) 40.7846i 1.68768i
\(585\) 11.7846 2.41154i 0.487234 0.0997050i
\(586\) 0.803848 1.39230i 0.0332066 0.0575156i
\(587\) 32.6506 8.74871i 1.34764 0.361098i 0.488374 0.872634i \(-0.337590\pi\)
0.859262 + 0.511536i \(0.170923\pi\)
\(588\) −21.1244 36.5885i −0.871154 1.50888i
\(589\) 19.3923 + 33.5885i 0.799046 + 1.38399i
\(590\) −5.41154 1.80385i −0.222790 0.0742632i
\(591\) −7.60770 + 28.3923i −0.312939 + 1.16790i
\(592\) 2.53590 + 0.679492i 0.104225 + 0.0279269i
\(593\) 14.6603 + 14.6603i 0.602024 + 0.602024i 0.940849 0.338825i \(-0.110029\pi\)
−0.338825 + 0.940849i \(0.610029\pi\)
\(594\) 10.3923 + 10.3923i 0.426401 + 0.426401i
\(595\) 18.5885 + 37.1769i 0.762052 + 1.52410i
\(596\) −14.0000 −0.573462
\(597\) −6.29423 + 3.63397i −0.257606 + 0.148729i
\(598\) 1.60770 1.60770i 0.0657435 0.0657435i
\(599\) −15.2942 26.4904i −0.624905 1.08237i −0.988559 0.150834i \(-0.951804\pi\)
0.363654 0.931534i \(-0.381529\pi\)
\(600\) 3.46410 + 24.2487i 0.141421 + 0.989949i
\(601\) −21.1962 + 36.7128i −0.864609 + 1.49755i 0.00282571 + 0.999996i \(0.499101\pi\)
−0.867435 + 0.497551i \(0.834233\pi\)
\(602\) 14.6603 + 54.7128i 0.597507 + 2.22993i
\(603\) −16.0981 + 16.0981i −0.655564 + 0.655564i
\(604\) −27.7128 + 16.0000i −1.12762 + 0.651031i
\(605\) −15.6244 0.937822i −0.635220 0.0381279i
\(606\) −1.26795 + 4.73205i −0.0515069 + 0.192226i
\(607\) 7.57180 28.2583i 0.307330 1.14697i −0.623592 0.781750i \(-0.714327\pi\)
0.930921 0.365220i \(-0.119006\pi\)
\(608\) 25.8564 6.92820i 1.04862 0.280976i
\(609\) 6.27757 + 23.4282i 0.254380 + 0.949359i
\(610\) 9.29423 + 45.4186i 0.376312 + 1.83894i
\(611\) 2.78461 0.112653
\(612\) −6.58846 + 24.5885i −0.266323 + 0.993929i
\(613\) 23.7846 + 23.7846i 0.960651 + 0.960651i 0.999255 0.0386033i \(-0.0122909\pi\)
−0.0386033 + 0.999255i \(0.512291\pi\)
\(614\) −14.3660 24.8827i −0.579766 1.00418i
\(615\) 22.3923 11.1962i 0.902945 0.451472i
\(616\) −12.3923 21.4641i −0.499300 0.864813i
\(617\) 28.0526 + 7.51666i 1.12935 + 0.302609i 0.774663 0.632374i \(-0.217920\pi\)
0.354691 + 0.934984i \(0.384586\pi\)
\(618\) −39.4641 −1.58748
\(619\) −1.90192 + 3.29423i −0.0764448 + 0.132406i −0.901714 0.432334i \(-0.857690\pi\)
0.825269 + 0.564740i \(0.191024\pi\)
\(620\) 30.5885 + 20.1962i 1.22846 + 0.811097i
\(621\) −1.20577 + 4.50000i −0.0483859 + 0.180579i
\(622\) −5.19615 19.3923i −0.208347 0.777561i
\(623\) 11.2583 3.01666i 0.451055 0.120860i
\(624\) −8.78461 8.78461i −0.351666 0.351666i
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) −21.1769 −0.846400
\(627\) 16.3923 0.654646
\(628\) −18.0000 18.0000i −0.718278 0.718278i
\(629\) 2.78461i 0.111030i
\(630\) 37.1769 18.5885i 1.48116 0.740582i
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 6.00000 1.60770i 0.238667 0.0639507i
\(633\) 0 0
\(634\) 20.0000i 0.794301i
\(635\) −18.2846 + 3.74167i −0.725603 + 0.148484i
\(636\) 18.0000 + 18.0000i 0.713746 + 0.713746i
\(637\) 5.66025 + 21.1244i 0.224267 + 0.836977i
\(638\) 2.33975 + 8.73205i 0.0926314 + 0.345705i
\(639\) 31.1769 + 18.0000i 1.23334 + 0.712069i
\(640\) 18.9282 16.7846i 0.748203 0.663470i
\(641\) −36.1865 20.8923i −1.42928 0.825196i −0.432218 0.901769i \(-0.642269\pi\)
−0.997064 + 0.0765727i \(0.975602\pi\)
\(642\) −18.2942 10.5622i −0.722016 0.416856i
\(643\) 6.91154 25.7942i 0.272565 1.01723i −0.684891 0.728645i \(-0.740150\pi\)
0.957456 0.288580i \(-0.0931830\pi\)
\(644\) 3.92820 6.80385i 0.154793 0.268109i
\(645\) −34.6865 + 7.09808i −1.36578 + 0.279486i
\(646\) 14.1962 + 24.5885i 0.558540 + 0.967420i
\(647\) −19.6865 + 19.6865i −0.773957 + 0.773957i −0.978796 0.204838i \(-0.934333\pi\)
0.204838 + 0.978796i \(0.434333\pi\)
\(648\) 24.5885 + 6.58846i 0.965926 + 0.258819i
\(649\) 3.60770i 0.141614i
\(650\) 1.51666 12.5885i 0.0594883 0.493760i
\(651\) 16.0981 60.0788i 0.630933 2.35468i
\(652\) 4.73205 + 17.6603i 0.185321 + 0.691629i
\(653\) −29.2224 7.83013i −1.14356 0.306417i −0.363180 0.931719i \(-0.618309\pi\)
−0.780382 + 0.625303i \(0.784976\pi\)
\(654\) −20.4904 + 5.49038i −0.801237 + 0.214691i
\(655\) −17.4186 1.04552i −0.680600 0.0408517i
\(656\) −22.3923 12.9282i −0.874273 0.504762i
\(657\) −11.1962 41.7846i −0.436804 1.63017i
\(658\) 9.29423 2.49038i 0.362327 0.0970852i
\(659\) 10.7321 + 6.19615i 0.418061 + 0.241368i 0.694248 0.719736i \(-0.255737\pi\)
−0.276186 + 0.961104i \(0.589071\pi\)
\(660\) 13.8564 6.92820i 0.539360 0.269680i
\(661\) −6.00000 + 3.46410i −0.233373 + 0.134738i −0.612127 0.790759i \(-0.709686\pi\)
0.378754 + 0.925497i \(0.376353\pi\)
\(662\) 0.588457 0.588457i 0.0228710 0.0228710i
\(663\) 6.58846 11.4115i 0.255874 0.443188i
\(664\) −28.7321 16.5885i −1.11502 0.643757i
\(665\) 14.6603 43.9808i 0.568500 1.70550i
\(666\) 2.78461 0.107901
\(667\) −2.02628 + 2.02628i −0.0784579 + 0.0784579i
\(668\) −26.1962 26.1962i −1.01356 1.01356i
\(669\) −20.9545 + 20.9545i −0.810147 + 0.810147i
\(670\) 10.7321 + 21.4641i 0.414615 + 0.829231i
\(671\) 25.3923 14.6603i 0.980259 0.565953i
\(672\) −37.1769 21.4641i −1.43413 0.827996i
\(673\) −1.24871 4.66025i −0.0481343 0.179640i 0.937674 0.347517i \(-0.112975\pi\)
−0.985808 + 0.167878i \(0.946309\pi\)
\(674\) −0.339746 0.196152i −0.0130865 0.00755551i
\(675\) 10.2058 + 23.8923i 0.392820 + 0.919615i
\(676\) −9.78461 16.9474i −0.376331 0.651825i
\(677\) −39.3205 + 10.5359i −1.51121 + 0.404927i −0.916837 0.399262i \(-0.869266\pi\)
−0.594373 + 0.804189i \(0.702600\pi\)
\(678\) 4.39230i 0.168685i
\(679\) 26.8301 15.4904i 1.02965 0.594466i
\(680\) 22.3923 + 14.7846i 0.858706 + 0.566964i
\(681\) 12.8038 + 12.8038i 0.490645 + 0.490645i
\(682\) 6.00000 22.3923i 0.229752 0.857446i
\(683\) −7.00000 + 7.00000i −0.267848 + 0.267848i −0.828232 0.560385i \(-0.810653\pi\)
0.560385 + 0.828232i \(0.310653\pi\)
\(684\) 24.5885 14.1962i 0.940163 0.542803i
\(685\) −28.3923 9.46410i −1.08481 0.361605i
\(686\) 16.0981 + 27.8827i 0.614627 + 1.06457i
\(687\) 9.99038 17.3038i 0.381157 0.660183i
\(688\) 25.8564 + 25.8564i 0.985766 + 0.985766i
\(689\) −6.58846 11.4115i −0.251000 0.434745i
\(690\) 4.09808 + 2.70577i 0.156011 + 0.103007i
\(691\) 40.4711 + 23.3660i 1.53959 + 0.888885i 0.998862 + 0.0476910i \(0.0151863\pi\)
0.540733 + 0.841194i \(0.318147\pi\)
\(692\) −1.46410 + 5.46410i −0.0556568 + 0.207714i
\(693\) −18.5885 18.5885i −0.706117 0.706117i
\(694\) −9.00000 5.19615i −0.341635 0.197243i
\(695\) −15.4641 0.928203i −0.586587 0.0352088i
\(696\) 11.0718 + 11.0718i 0.419675 + 0.419675i
\(697\) 7.09808 26.4904i 0.268859 1.00339i
\(698\) −36.4641 36.4641i −1.38019 1.38019i
\(699\) 11.4904 42.8827i 0.434606 1.62197i
\(700\) −6.19615 43.3731i −0.234193 1.63935i
\(701\) 50.1769 1.89516 0.947578 0.319525i \(-0.103523\pi\)
0.947578 + 0.319525i \(0.103523\pi\)
\(702\) −11.4115 6.58846i −0.430701 0.248665i
\(703\) 2.19615 2.19615i 0.0828295 0.0828295i
\(704\) −13.8564 8.00000i −0.522233 0.301511i
\(705\) 1.20577 + 5.89230i 0.0454120 + 0.221917i
\(706\) 18.9282i 0.712372i
\(707\) 2.26795 8.46410i 0.0852950 0.318325i
\(708\) 3.12436 + 5.41154i 0.117420 + 0.203378i
\(709\) −9.57180 + 16.5788i −0.359476 + 0.622631i −0.987873 0.155261i \(-0.950378\pi\)
0.628397 + 0.777893i \(0.283711\pi\)
\(710\) 28.3923 25.1769i 1.06554 0.944873i
\(711\) 5.70577 3.29423i 0.213983 0.123543i
\(712\) 5.32051 5.32051i 0.199394 0.199394i
\(713\) 7.09808 1.90192i 0.265825 0.0712276i
\(714\) 11.7846 43.9808i 0.441028 1.64594i
\(715\) −7.85641 + 1.60770i −0.293813 + 0.0601244i
\(716\) 6.39230 11.0718i 0.238892 0.413772i
\(717\) −16.3923 + 28.3923i −0.612182 + 1.06033i
\(718\) 0.803848 3.00000i 0.0299993 0.111959i
\(719\) 1.51666 0.0565619 0.0282809 0.999600i \(-0.490997\pi\)
0.0282809 + 0.999600i \(0.490997\pi\)
\(720\) 14.7846 22.3923i 0.550990 0.834512i
\(721\) 70.5885 2.62885
\(722\) 1.24167 4.63397i 0.0462102 0.172459i
\(723\) 32.5692 1.21126
\(724\) −3.00000 + 5.19615i −0.111494 + 0.193113i
\(725\) −1.91154 + 15.8660i −0.0709929 + 0.589249i
\(726\) 12.1244 + 12.1244i 0.449977 + 0.449977i
\(727\) 2.86603 0.767949i 0.106295 0.0284817i −0.205279 0.978703i \(-0.565810\pi\)
0.311574 + 0.950222i \(0.399144\pi\)
\(728\) 15.7128 + 15.7128i 0.582356 + 0.582356i
\(729\) 27.0000 1.00000
\(730\) −45.5167 2.73205i −1.68465 0.101118i
\(731\) −19.3923 + 33.5885i −0.717250 + 1.24231i
\(732\) 25.3923 43.9808i 0.938527 1.62558i
\(733\) 2.83013 10.5622i 0.104533 0.390123i −0.893759 0.448548i \(-0.851941\pi\)
0.998292 + 0.0584252i \(0.0186079\pi\)
\(734\) 14.0000i 0.516749i
\(735\) −42.2487 + 21.1244i −1.55837 + 0.779184i
\(736\) 5.07180i 0.186949i
\(737\) 10.7321 10.7321i 0.395320 0.395320i
\(738\) −26.4904 7.09808i −0.975124 0.261284i
\(739\) 22.7321 0.836212 0.418106 0.908398i \(-0.362694\pi\)
0.418106 + 0.908398i \(0.362694\pi\)
\(740\) 0.928203 2.78461i 0.0341214 0.102364i
\(741\) −14.1962 + 3.80385i −0.521509 + 0.139738i
\(742\) −32.1962 32.1962i −1.18196 1.18196i
\(743\) −6.82051 + 25.4545i −0.250220 + 0.933834i 0.720467 + 0.693489i \(0.243927\pi\)
−0.970687 + 0.240345i \(0.922739\pi\)
\(744\) −10.3923 38.7846i −0.381000 1.42191i
\(745\) −0.937822 + 15.6244i −0.0343591 + 0.572432i
\(746\) 4.60770 + 2.66025i 0.168700 + 0.0973988i
\(747\) −33.9904 9.10770i −1.24364 0.333233i
\(748\) 4.39230 16.3923i 0.160599 0.599362i
\(749\) 32.7224 + 18.8923i 1.19565 + 0.690310i
\(750\) 27.2942 2.24167i 0.996644 0.0818542i
\(751\) −6.80385 11.7846i −0.248276 0.430027i 0.714772 0.699358i \(-0.246531\pi\)
−0.963048 + 0.269331i \(0.913197\pi\)
\(752\) 4.39230 4.39230i 0.160171 0.160171i
\(753\) −23.0263 39.8827i −0.839124 1.45341i
\(754\) −4.05256 7.01924i −0.147585 0.255626i
\(755\) 16.0000 + 32.0000i 0.582300 + 1.16460i
\(756\) −43.9808 11.7846i −1.59956 0.428602i
\(757\) 34.0526 34.0526i 1.23766 1.23766i 0.276707 0.960954i \(-0.410757\pi\)
0.960954 0.276707i \(-0.0892431\pi\)
\(758\) −12.1244 + 45.2487i −0.440376 + 1.64351i
\(759\) 0.803848 3.00000i 0.0291778 0.108893i
\(760\) −6.00000 29.3205i −0.217643 1.06357i
\(761\) 21.4808 12.4019i 0.778677 0.449569i −0.0572842 0.998358i \(-0.518244\pi\)
0.835961 + 0.548789i \(0.184911\pi\)
\(762\) 17.7058 + 10.2224i 0.641412 + 0.370320i
\(763\) 36.6506 9.82051i 1.32684 0.355526i
\(764\) 18.5885 + 32.1962i 0.672507 + 1.16482i
\(765\) 27.0000 + 9.00000i 0.976187 + 0.325396i
\(766\) −35.1962 20.3205i −1.27169 0.734210i
\(767\) −0.837169 3.12436i −0.0302284 0.112814i
\(768\) −27.7128 −1.00000
\(769\) −29.9378 + 17.2846i −1.07959 + 0.623299i −0.930785 0.365568i \(-0.880875\pi\)
−0.148801 + 0.988867i \(0.547541\pi\)
\(770\) −24.7846 + 12.3923i −0.893175 + 0.446588i
\(771\) −7.31347 27.2942i −0.263388 0.982978i
\(772\) −20.0000 20.0000i −0.719816 0.719816i
\(773\) −16.1962 + 16.1962i −0.582535 + 0.582535i −0.935599 0.353064i \(-0.885140\pi\)
0.353064 + 0.935599i \(0.385140\pi\)
\(774\) 33.5885 + 19.3923i 1.20731 + 0.697042i
\(775\) 24.5885 32.7846i 0.883243 1.17766i
\(776\) 10.0000 17.3205i 0.358979 0.621770i
\(777\) −4.98076 −0.178684
\(778\) 17.3923 17.3923i 0.623544 0.623544i
\(779\) −26.4904 + 15.2942i −0.949116 + 0.547973i
\(780\) −10.3923 + 9.21539i −0.372104 + 0.329964i
\(781\) −20.7846 12.0000i −0.743732 0.429394i
\(782\) 5.19615 1.39230i 0.185814 0.0497887i
\(783\) 14.3827 + 8.30385i 0.513995 + 0.296755i
\(784\) 42.2487 + 24.3923i 1.50888 + 0.871154i
\(785\) −21.2942 + 18.8827i −0.760024 + 0.673952i
\(786\) 13.5167 + 13.5167i 0.482123 + 0.482123i
\(787\) −38.9545 10.4378i −1.38858 0.372068i −0.514348 0.857582i \(-0.671966\pi\)
−0.874229 + 0.485513i \(0.838633\pi\)
\(788\) −8.78461 32.7846i −0.312939 1.16790i
\(789\) 17.1962 + 17.1962i 0.612199 + 0.612199i
\(790\) −1.39230 6.80385i −0.0495360 0.242070i
\(791\) 7.85641i 0.279342i
\(792\) −16.3923 4.39230i −0.582475 0.156074i
\(793\) −18.5885 + 18.5885i −0.660095 + 0.660095i
\(794\) 0.803848 + 1.39230i 0.0285275 + 0.0494111i
\(795\) 21.2942 18.8827i 0.755228 0.669700i
\(796\) 4.19615 7.26795i 0.148729 0.257606i
\(797\) −5.92820 + 22.1244i −0.209988 + 0.783685i 0.777883 + 0.628409i \(0.216293\pi\)
−0.987871 + 0.155276i \(0.950373\pi\)
\(798\) −43.9808 + 25.3923i −1.55690 + 0.898878i
\(799\) 5.70577 + 3.29423i 0.201856 + 0.116541i
\(800\) −17.4641 22.2487i −0.617449 0.786611i
\(801\) 3.99038 6.91154i 0.140993 0.244207i
\(802\) 13.2679 + 49.5167i 0.468508 + 1.74849i
\(803\) 7.46410 + 27.8564i 0.263402 + 0.983031i
\(804\) 6.80385 25.3923i 0.239953 0.895518i
\(805\) −7.33013 4.83975i −0.258353 0.170579i
\(806\) 20.7846i 0.732107i
\(807\) 1.50000 0.866025i 0.0528025 0.0304855i
\(808\) −1.46410 5.46410i −0.0515069 0.192226i
\(809\) 45.7128 1.60718 0.803588 0.595185i \(-0.202921\pi\)
0.803588 + 0.595185i \(0.202921\pi\)
\(810\) 9.00000 27.0000i 0.316228 0.948683i
\(811\) 16.7321i 0.587542i 0.955876 + 0.293771i \(0.0949103\pi\)
−0.955876 + 0.293771i \(0.905090\pi\)
\(812\) −19.8038 19.8038i −0.694979 0.694979i
\(813\) 3.97372 + 6.88269i 0.139364 + 0.241386i
\(814\) −1.85641 −0.0650670
\(815\) 20.0263 4.09808i 0.701490 0.143549i
\(816\) −7.60770 28.3923i −0.266323 0.993929i
\(817\) 41.7846 11.1962i 1.46186 0.391704i
\(818\) 2.19615 + 8.19615i 0.0767867 + 0.286572i
\(819\) 20.4115 + 11.7846i 0.713237 + 0.411788i
\(820\) −15.9282 + 24.1244i −0.556237 + 0.842459i
\(821\) 14.2846 24.7417i 0.498536 0.863490i −0.501462 0.865180i \(-0.667204\pi\)
0.999999 + 0.00168929i \(0.000537719\pi\)
\(822\) 16.3923 + 28.3923i 0.571747 + 0.990295i
\(823\) −11.0622 2.96410i −0.385603 0.103322i 0.0608092 0.998149i \(-0.480632\pi\)
−0.446412 + 0.894827i \(0.647299\pi\)
\(824\) 39.4641 22.7846i 1.37480 0.793739i
\(825\) −6.80385 15.9282i −0.236880 0.554549i
\(826\) −5.58846 9.67949i −0.194447 0.336793i
\(827\) −9.29423 9.29423i −0.323192 0.323192i 0.526798 0.849990i \(-0.323392\pi\)
−0.849990 + 0.526798i \(0.823392\pi\)
\(828\) −1.39230 5.19615i −0.0483859 0.180579i
\(829\) 25.0526 0.870111 0.435056 0.900404i \(-0.356729\pi\)
0.435056 + 0.900404i \(0.356729\pi\)
\(830\) −20.4378 + 30.9545i −0.709407 + 1.07445i
\(831\) −11.1962 + 11.1962i −0.388390 + 0.388390i
\(832\) 13.8564 + 3.71281i 0.480384 + 0.128719i
\(833\) −13.3923 + 49.9808i −0.464016 + 1.73173i
\(834\) 12.0000 + 12.0000i 0.415526 + 0.415526i
\(835\) −30.9904 + 27.4808i −1.07247 + 0.951011i
\(836\) −16.3923 + 9.46410i −0.566940 + 0.327323i
\(837\) −21.2942 36.8827i −0.736036 1.27485i
\(838\) 4.53590 + 16.9282i 0.156690 + 0.584775i
\(839\) −14.0263 + 24.2942i −0.484241 + 0.838730i −0.999836 0.0181024i \(-0.994238\pi\)
0.515595 + 0.856832i \(0.327571\pi\)
\(840\) −26.4449 + 40.0526i −0.912434 + 1.38194i
\(841\) −9.39230 16.2679i −0.323873 0.560964i
\(842\) 5.32051 5.32051i 0.183357 0.183357i
\(843\) 3.58846i 0.123593i
\(844\) 0 0
\(845\) −19.5692 + 9.78461i −0.673202 + 0.336601i
\(846\) 3.29423 5.70577i 0.113258 0.196168i
\(847\) −21.6865 21.6865i −0.745158 0.745158i
\(848\) −28.3923 7.60770i −0.974996 0.261249i
\(849\) −7.79423 + 2.08846i −0.267497 + 0.0716757i
\(850\) 18.0000 24.0000i 0.617395 0.823193i
\(851\) −0.294229 0.509619i −0.0100860 0.0174695i
\(852\) −41.5692 −1.42414
\(853\) −44.7846 + 12.0000i −1.53340 + 0.410872i −0.924125 0.382090i \(-0.875204\pi\)
−0.609271 + 0.792962i \(0.708538\pi\)
\(854\) −45.4186 + 78.6673i −1.55419 + 2.69194i
\(855\) −14.1962 28.3923i −0.485498 0.970996i
\(856\) 24.3923 0.833712
\(857\) −7.48334 27.9282i −0.255626 0.954009i −0.967741 0.251947i \(-0.918929\pi\)
0.712115 0.702063i \(-0.247737\pi\)
\(858\) 7.60770 + 4.39230i 0.259722 + 0.149951i
\(859\) 8.66025 + 15.0000i 0.295484 + 0.511793i 0.975097 0.221777i \(-0.0711857\pi\)
−0.679613 + 0.733571i \(0.737852\pi\)
\(860\) 30.5885 27.1244i 1.04306 0.924933i
\(861\) 47.3827 + 12.6962i 1.61480 + 0.432684i
\(862\) 30.1244 + 8.07180i 1.02604 + 0.274926i
\(863\) 12.4186 + 12.4186i 0.422734 + 0.422734i 0.886144 0.463410i \(-0.153374\pi\)
−0.463410 + 0.886144i \(0.653374\pi\)
\(864\) −28.3923 + 7.60770i −0.965926 + 0.258819i
\(865\) 6.00000 + 2.00000i 0.204006 + 0.0680020i
\(866\) 15.3923 + 26.6603i 0.523052 + 0.905952i
\(867\) 1.50000 0.866025i 0.0509427 0.0294118i
\(868\) 18.5885 + 69.3731i 0.630933 + 2.35468i
\(869\) −3.80385 + 2.19615i −0.129037 + 0.0744994i
\(870\) 13.0981 11.6147i 0.444066 0.393776i
\(871\) −6.80385 + 11.7846i −0.230540 + 0.399306i
\(872\) 17.3205 17.3205i 0.586546 0.586546i
\(873\) 5.49038 20.4904i 0.185821 0.693494i
\(874\) −5.19615 3.00000i −0.175762 0.101477i
\(875\) −48.8205 + 4.00962i −1.65043 + 0.135550i
\(876\) 35.3205 + 35.3205i 1.19337 + 1.19337i
\(877\) 24.1244 + 6.46410i 0.814622 + 0.218277i 0.641994 0.766710i \(-0.278108\pi\)
0.172628 + 0.984987i \(0.444774\pi\)
\(878\) −18.7846 + 18.7846i −0.633950 + 0.633950i
\(879\) 0.509619 + 1.90192i 0.0171890 + 0.0641503i
\(880\) −9.85641 + 14.9282i −0.332259 + 0.503230i
\(881\) 2.07180i 0.0698006i −0.999391 0.0349003i \(-0.988889\pi\)
0.999391 0.0349003i \(-0.0111114\pi\)
\(882\) 49.9808 + 13.3923i 1.68294 + 0.450942i
\(883\) −27.4186 27.4186i −0.922709 0.922709i 0.0745113 0.997220i \(-0.476260\pi\)
−0.997220 + 0.0745113i \(0.976260\pi\)
\(884\) 15.2154i 0.511749i
\(885\) 6.24871 3.12436i 0.210048 0.105024i
\(886\) −54.5885 −1.83394
\(887\) −1.56218 0.418584i −0.0524528 0.0140547i 0.232497 0.972597i \(-0.425310\pi\)
−0.284950 + 0.958542i \(0.591977\pi\)
\(888\) −2.78461 + 1.60770i −0.0934454 + 0.0539507i
\(889\) −31.6699 18.2846i −1.06217 0.613246i
\(890\) −5.58142 6.29423i −0.187089 0.210983i
\(891\) −18.0000 −0.603023
\(892\) 8.85641 33.0526i 0.296534 1.10668i
\(893\) −1.90192 7.09808i −0.0636455 0.237528i
\(894\) 12.1244 12.1244i 0.405499 0.405499i
\(895\) −11.9282 7.87564i −0.398716 0.263254i
\(896\) 49.5692 1.65599
\(897\) 2.78461i 0.0929754i
\(898\) 12.0000 44.7846i 0.400445 1.49448i
\(899\) 26.1962i 0.873691i
\(900\) −24.0000 18.0000i −0.800000 0.600000i
\(901\) 31.1769i 1.03865i
\(902\) 17.6603 + 4.73205i 0.588022 + 0.157560i
\(903\) −60.0788 34.6865i −1.99930 1.15430i
\(904\) 2.53590 + 4.39230i 0.0843427 + 0.146086i
\(905\) 5.59808 + 3.69615i 0.186086 + 0.122864i
\(906\) 10.1436 37.8564i 0.336998 1.25769i
\(907\) −0.944864 3.52628i −0.0313737 0.117088i 0.948463 0.316887i \(-0.102638\pi\)
−0.979837 + 0.199799i \(0.935971\pi\)
\(908\) −20.1962 5.41154i −0.670233 0.179588i
\(909\) −3.00000 5.19615i −0.0995037 0.172345i
\(910\) 18.5885 16.4833i 0.616201 0.546417i
\(911\) 23.4904 + 13.5622i 0.778271 + 0.449335i 0.835817 0.549008i \(-0.184994\pi\)
−0.0575461 + 0.998343i \(0.518328\pi\)
\(912\) −16.3923 + 28.3923i −0.542803 + 0.940163i
\(913\) 22.6603 + 6.07180i 0.749945 + 0.200947i
\(914\) 14.3923i 0.476055i
\(915\) −47.3827 31.2846i −1.56642 1.03424i
\(916\) 23.0718i 0.762314i
\(917\) −24.1769 24.1769i −0.798392 0.798392i
\(918\) −15.5885 27.0000i −0.514496 0.891133i
\(919\) 20.1962i 0.666210i −0.942890 0.333105i \(-0.891904\pi\)
0.942890 0.333105i \(-0.108096\pi\)
\(920\) −5.66025 0.339746i −0.186613 0.0112011i
\(921\) 33.9904 + 9.10770i 1.12002 + 0.300109i
\(922\) −13.5885 13.5885i −0.447512 0.447512i
\(923\) 20.7846 + 5.56922i 0.684134 + 0.183313i
\(924\) 29.3205 + 7.85641i 0.964574 + 0.258457i
\(925\) −3.04552 1.22243i −0.100136 0.0401933i
\(926\) 4.80385 8.32051i 0.157864 0.273429i
\(927\) 34.1769 34.1769i 1.12252 1.12252i
\(928\) −17.4641 4.67949i −0.573287 0.153612i
\(929\) −2.19615 + 3.80385i −0.0720534 + 0.124800i −0.899801 0.436300i \(-0.856289\pi\)
0.827748 + 0.561100i \(0.189622\pi\)
\(930\) −43.9808 + 9.00000i −1.44219 + 0.295122i
\(931\) 49.9808 28.8564i 1.63805 0.945731i
\(932\) 13.2679 + 49.5167i 0.434606 + 1.62197i
\(933\) 21.2942 + 12.2942i 0.697142 + 0.402495i
\(934\) −14.9090 + 8.60770i −0.487836 + 0.281652i
\(935\) −18.0000 6.00000i −0.588663 0.196221i
\(936\) 15.2154 0.497331
\(937\) −4.58846 4.58846i −0.149898 0.149898i 0.628174 0.778073i \(-0.283802\pi\)
−0.778073 + 0.628174i \(0.783802\pi\)
\(938\) −12.1699 + 45.4186i −0.397360 + 1.48297i
\(939\) 18.3397 18.3397i 0.598495 0.598495i
\(940\) −4.60770 5.19615i −0.150286 0.169480i
\(941\) 4.40192 + 7.62436i 0.143499 + 0.248547i 0.928812 0.370552i \(-0.120831\pi\)
−0.785313 + 0.619099i \(0.787498\pi\)
\(942\) 31.1769 1.01580
\(943\) 1.50000 + 5.59808i 0.0488467 + 0.182298i
\(944\) −6.24871 3.60770i −0.203378 0.117420i
\(945\) −16.0981 + 48.2942i −0.523670 + 1.57101i
\(946\) −22.3923 12.9282i −0.728037 0.420332i
\(947\) 23.0885 6.18653i 0.750274 0.201035i 0.136634 0.990622i \(-0.456371\pi\)
0.613640 + 0.789586i \(0.289705\pi\)
\(948\) −3.80385 + 6.58846i −0.123543 + 0.213983i
\(949\) −12.9282 22.3923i −0.419667 0.726885i
\(950\) −33.1244 + 4.73205i −1.07470 + 0.153528i
\(951\) −17.3205 17.3205i −0.561656 0.561656i
\(952\) 13.6077 + 50.7846i 0.441028 + 1.64594i
\(953\) 24.9282 + 24.9282i 0.807504 + 0.807504i 0.984255 0.176752i \(-0.0565590\pi\)
−0.176752 + 0.984255i \(0.556559\pi\)
\(954\) −31.1769 −1.00939
\(955\) 37.1769 18.5885i 1.20302 0.601508i
\(956\) 37.8564i 1.22436i
\(957\) −9.58846 5.53590i −0.309951 0.178950i
\(958\) 21.1244 + 21.1244i 0.682497 + 0.682497i
\(959\) −29.3205 50.7846i −0.946809 1.63992i
\(960\) −1.85641 + 30.9282i −0.0599153 + 0.998203i
\(961\) −18.0885 + 31.3301i −0.583499 + 1.01065i
\(962\) 1.60770 0.430781i 0.0518342 0.0138889i
\(963\) 24.9904 6.69615i 0.805304 0.215780i
\(964\) −32.5692 + 18.8038i −1.04898 + 0.605631i
\(965\) −23.6603 + 20.9808i −0.761651 + 0.675395i
\(966\) 2.49038 + 9.29423i 0.0801267 + 0.299037i
\(967\) −4.27757 + 15.9641i −0.137557 + 0.513371i 0.862417 + 0.506199i \(0.168950\pi\)
−0.999974 + 0.00717234i \(0.997717\pi\)
\(968\) −19.1244 5.12436i −0.614680 0.164703i
\(969\) −33.5885 9.00000i −1.07902 0.289122i
\(970\) −18.6603 12.3205i −0.599145 0.395588i
\(971\) 29.8038 0.956451 0.478225 0.878237i \(-0.341280\pi\)
0.478225 + 0.878237i \(0.341280\pi\)
\(972\) −27.0000 + 15.5885i −0.866025 + 0.500000i
\(973\) −21.4641 21.4641i −0.688108 0.688108i
\(974\) 5.87564 3.39230i 0.188268 0.108696i
\(975\) 9.58846 + 12.2154i 0.307076 + 0.391206i
\(976\) 58.6410i 1.87705i
\(977\) −40.0526 10.7321i −1.28139 0.343349i −0.447009 0.894529i \(-0.647511\pi\)
−0.834386 + 0.551181i \(0.814177\pi\)
\(978\) −19.3923 11.1962i −0.620098 0.358013i
\(979\) −2.66025 + 4.60770i −0.0850221 + 0.147263i
\(980\) 30.0526 45.5167i 0.959994 1.45398i
\(981\) 12.9904 22.5000i 0.414751 0.718370i
\(982\) 33.8564 9.07180i 1.08040 0.289493i
\(983\) 13.3301 3.57180i 0.425165 0.113923i −0.0398907 0.999204i \(-0.512701\pi\)
0.465056 + 0.885281i \(0.346034\pi\)
\(984\) 30.5885 8.19615i 0.975124 0.261284i
\(985\) −37.1769 + 7.60770i −1.18455 + 0.242401i
\(986\) 19.1769i 0.610717i
\(987\) −5.89230 + 10.2058i −0.187554 + 0.324853i
\(988\) 12.0000 12.0000i 0.381771 0.381771i
\(989\) 8.19615i 0.260622i
\(990\) −6.00000 + 18.0000i −0.190693 + 0.572078i
\(991\) 10.1962 0.323891 0.161946 0.986800i \(-0.448223\pi\)
0.161946 + 0.986800i \(0.448223\pi\)
\(992\) 32.7846 + 32.7846i 1.04091 + 1.04091i
\(993\) 1.01924i 0.0323445i
\(994\) 74.3538 2.35836
\(995\) −7.83013 5.16987i −0.248232 0.163896i
\(996\) 39.2487 10.5167i 1.24364 0.333233i
\(997\) −1.77757 6.63397i −0.0562961 0.210100i 0.932048 0.362334i \(-0.118020\pi\)
−0.988345 + 0.152234i \(0.951353\pi\)
\(998\) 36.5885 9.80385i 1.15819 0.310335i
\(999\) −2.41154 + 2.41154i −0.0762978 + 0.0762978i
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 360.2.br.d.317.1 yes 4
5.3 odd 4 360.2.br.c.173.1 yes 4
8.5 even 2 360.2.br.a.317.1 yes 4
9.5 odd 6 360.2.br.b.77.1 yes 4
40.13 odd 4 360.2.br.b.173.1 yes 4
45.23 even 12 360.2.br.a.293.1 4
72.5 odd 6 360.2.br.c.77.1 yes 4
360.293 even 12 inner 360.2.br.d.293.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.br.a.293.1 4 45.23 even 12
360.2.br.a.317.1 yes 4 8.5 even 2
360.2.br.b.77.1 yes 4 9.5 odd 6
360.2.br.b.173.1 yes 4 40.13 odd 4
360.2.br.c.77.1 yes 4 72.5 odd 6
360.2.br.c.173.1 yes 4 5.3 odd 4
360.2.br.d.293.1 yes 4 360.293 even 12 inner
360.2.br.d.317.1 yes 4 1.1 even 1 trivial