Properties

Label 504.2.br.a.155.8
Level $504$
Weight $2$
Character 504.155
Analytic conductor $4.024$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(155,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.br (of order \(6\), degree \(2\), 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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(72\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 155.8
Character \(\chi\) \(=\) 504.155
Dual form 504.2.br.a.491.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33761 + 0.459123i) q^{2} +(0.847856 - 1.51034i) q^{3} +(1.57841 - 1.22826i) q^{4} +(0.551827 + 0.955792i) q^{5} +(-0.440668 + 2.40953i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.54738 + 2.36762i) q^{8} +(-1.56228 - 2.56111i) q^{9} +O(q^{10})\) \(q+(-1.33761 + 0.459123i) q^{2} +(0.847856 - 1.51034i) q^{3} +(1.57841 - 1.22826i) q^{4} +(0.551827 + 0.955792i) q^{5} +(-0.440668 + 2.40953i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.54738 + 2.36762i) q^{8} +(-1.56228 - 2.56111i) q^{9} +(-1.17696 - 1.02512i) q^{10} +(-4.37593 - 2.52645i) q^{11} +(-0.516827 - 3.42533i) q^{12} +(3.85751 - 2.22713i) q^{13} +(1.38797 + 0.271193i) q^{14} +(1.91144 - 0.0230745i) q^{15} +(0.982764 - 3.87739i) q^{16} -2.89070i q^{17} +(3.26559 + 2.70849i) q^{18} -2.04644 q^{19} +(2.04497 + 0.830847i) q^{20} +(-1.48944 + 0.884069i) q^{21} +(7.01325 + 1.37031i) q^{22} +(0.713863 + 1.23645i) q^{23} +(2.26396 + 4.34448i) q^{24} +(1.89097 - 3.27526i) q^{25} +(-4.13732 + 4.75011i) q^{26} +(-5.19275 + 0.188130i) q^{27} +(-1.98107 + 0.274497i) q^{28} +(0.314341 - 0.544454i) q^{29} +(-2.54618 + 0.908454i) q^{30} +(-2.12729 + 1.22819i) q^{31} +(0.465645 + 5.63766i) q^{32} +(-7.52596 + 4.46710i) q^{33} +(1.32719 + 3.86663i) q^{34} -1.10365i q^{35} +(-5.61162 - 2.12360i) q^{36} -9.44610i q^{37} +(2.73735 - 0.939570i) q^{38} +(-0.0931273 - 7.71446i) q^{39} +(-3.11684 - 0.172458i) q^{40} +(3.45334 - 1.99379i) q^{41} +(1.58639 - 1.86638i) q^{42} +(0.376249 - 0.651683i) q^{43} +(-10.0101 + 1.38700i) q^{44} +(1.58578 - 2.90650i) q^{45} +(-1.52255 - 1.32613i) q^{46} +(-4.96806 + 8.60493i) q^{47} +(-5.02296 - 4.77178i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.02564 + 5.24922i) q^{50} +(-4.36595 - 2.45090i) q^{51} +(3.35324 - 8.25335i) q^{52} -0.509103 q^{53} +(6.85950 - 2.63576i) q^{54} -5.57664i q^{55} +(2.52388 - 1.27673i) q^{56} +(-1.73509 + 3.09083i) q^{57} +(-0.170494 + 0.872590i) q^{58} +(11.0827 - 6.39860i) q^{59} +(2.98870 - 2.38417i) q^{60} +(1.50179 + 0.867059i) q^{61} +(2.28160 - 2.61953i) q^{62} +(0.0724201 + 2.99913i) q^{63} +(-3.21123 - 7.32721i) q^{64} +(4.25735 + 2.45798i) q^{65} +(8.01587 - 9.43060i) q^{66} +(-2.45861 - 4.25843i) q^{67} +(-3.55053 - 4.56271i) q^{68} +(2.47271 - 0.0298501i) q^{69} +(0.506713 + 1.47626i) q^{70} -5.16985 q^{71} +(8.48117 + 0.264124i) q^{72} +3.07080 q^{73} +(4.33693 + 12.6352i) q^{74} +(-3.34350 - 5.63298i) q^{75} +(-3.23013 + 2.51356i) q^{76} +(2.52645 + 4.37593i) q^{77} +(3.66646 + 10.2762i) q^{78} +(10.1848 + 5.88019i) q^{79} +(4.24830 - 1.20033i) q^{80} +(-4.11856 + 8.00234i) q^{81} +(-3.70384 + 4.25242i) q^{82} +(-5.59514 - 3.23036i) q^{83} +(-1.26508 + 3.22484i) q^{84} +(2.76291 - 1.59517i) q^{85} +(-0.204073 + 1.04444i) q^{86} +(-0.555798 - 0.936382i) q^{87} +(12.7529 - 6.45117i) q^{88} +6.63971i q^{89} +(-0.786713 + 4.61584i) q^{90} -4.45427 q^{91} +(2.64544 + 1.07481i) q^{92} +(0.0513566 + 4.25427i) q^{93} +(2.69461 - 13.7910i) q^{94} +(-1.12928 - 1.95597i) q^{95} +(8.90960 + 4.07664i) q^{96} +(-0.323290 + 0.559955i) q^{97} +(-1.06642 - 0.928844i) q^{98} +(0.365931 + 15.1543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33761 + 0.459123i −0.945834 + 0.324649i
\(3\) 0.847856 1.51034i 0.489510 0.871998i
\(4\) 1.57841 1.22826i 0.789206 0.614129i
\(5\) 0.551827 + 0.955792i 0.246784 + 0.427443i 0.962632 0.270814i \(-0.0872927\pi\)
−0.715847 + 0.698257i \(0.753959\pi\)
\(6\) −0.440668 + 2.40953i −0.179902 + 0.983685i
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) −1.54738 + 2.36762i −0.547081 + 0.837079i
\(9\) −1.56228 2.56111i −0.520760 0.853703i
\(10\) −1.17696 1.02512i −0.372186 0.324172i
\(11\) −4.37593 2.52645i −1.31939 0.761752i −0.335762 0.941947i \(-0.608994\pi\)
−0.983631 + 0.180195i \(0.942327\pi\)
\(12\) −0.516827 3.42533i −0.149195 0.988808i
\(13\) 3.85751 2.22713i 1.06988 0.617696i 0.141732 0.989905i \(-0.454733\pi\)
0.928149 + 0.372209i \(0.121400\pi\)
\(14\) 1.38797 + 0.271193i 0.370950 + 0.0724795i
\(15\) 1.91144 0.0230745i 0.493533 0.00595782i
\(16\) 0.982764 3.87739i 0.245691 0.969348i
\(17\) 2.89070i 0.701098i −0.936544 0.350549i \(-0.885995\pi\)
0.936544 0.350549i \(-0.114005\pi\)
\(18\) 3.26559 + 2.70849i 0.769707 + 0.638397i
\(19\) −2.04644 −0.469486 −0.234743 0.972057i \(-0.575425\pi\)
−0.234743 + 0.972057i \(0.575425\pi\)
\(20\) 2.04497 + 0.830847i 0.457269 + 0.185783i
\(21\) −1.48944 + 0.884069i −0.325022 + 0.192920i
\(22\) 7.01325 + 1.37031i 1.49523 + 0.292151i
\(23\) 0.713863 + 1.23645i 0.148851 + 0.257817i 0.930803 0.365521i \(-0.119109\pi\)
−0.781952 + 0.623338i \(0.785776\pi\)
\(24\) 2.26396 + 4.34448i 0.462130 + 0.886812i
\(25\) 1.89097 3.27526i 0.378195 0.655053i
\(26\) −4.13732 + 4.75011i −0.811395 + 0.931574i
\(27\) −5.19275 + 0.188130i −0.999344 + 0.0362057i
\(28\) −1.98107 + 0.274497i −0.374388 + 0.0518751i
\(29\) 0.314341 0.544454i 0.0583716 0.101103i −0.835363 0.549699i \(-0.814742\pi\)
0.893735 + 0.448596i \(0.148076\pi\)
\(30\) −2.54618 + 0.908454i −0.464866 + 0.165860i
\(31\) −2.12729 + 1.22819i −0.382072 + 0.220590i −0.678719 0.734398i \(-0.737465\pi\)
0.296647 + 0.954987i \(0.404131\pi\)
\(32\) 0.465645 + 5.63766i 0.0823151 + 0.996606i
\(33\) −7.52596 + 4.46710i −1.31010 + 0.777623i
\(34\) 1.32719 + 3.86663i 0.227611 + 0.663122i
\(35\) 1.10365i 0.186551i
\(36\) −5.61162 2.12360i −0.935271 0.353933i
\(37\) 9.44610i 1.55293i −0.630161 0.776464i \(-0.717011\pi\)
0.630161 0.776464i \(-0.282989\pi\)
\(38\) 2.73735 0.939570i 0.444056 0.152418i
\(39\) −0.0931273 7.71446i −0.0149123 1.23530i
\(40\) −3.11684 0.172458i −0.492815 0.0272680i
\(41\) 3.45334 1.99379i 0.539321 0.311377i −0.205482 0.978661i \(-0.565876\pi\)
0.744804 + 0.667283i \(0.232543\pi\)
\(42\) 1.58639 1.86638i 0.244786 0.287988i
\(43\) 0.376249 0.651683i 0.0573775 0.0993807i −0.835910 0.548867i \(-0.815059\pi\)
0.893287 + 0.449486i \(0.148393\pi\)
\(44\) −10.0101 + 1.38700i −1.50909 + 0.209099i
\(45\) 1.58578 2.90650i 0.236394 0.433276i
\(46\) −1.52255 1.32613i −0.224488 0.195528i
\(47\) −4.96806 + 8.60493i −0.724666 + 1.25516i 0.234446 + 0.972129i \(0.424672\pi\)
−0.959111 + 0.283029i \(0.908661\pi\)
\(48\) −5.02296 4.77178i −0.725001 0.688748i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −1.02564 + 5.24922i −0.145047 + 0.742352i
\(51\) −4.36595 2.45090i −0.611356 0.343194i
\(52\) 3.35324 8.25335i 0.465011 1.14453i
\(53\) −0.509103 −0.0699306 −0.0349653 0.999389i \(-0.511132\pi\)
−0.0349653 + 0.999389i \(0.511132\pi\)
\(54\) 6.85950 2.63576i 0.933460 0.358681i
\(55\) 5.57664i 0.751954i
\(56\) 2.52388 1.27673i 0.337268 0.170610i
\(57\) −1.73509 + 3.09083i −0.229818 + 0.409391i
\(58\) −0.170494 + 0.872590i −0.0223870 + 0.114577i
\(59\) 11.0827 6.39860i 1.44284 0.833027i 0.444806 0.895627i \(-0.353273\pi\)
0.998039 + 0.0626002i \(0.0199393\pi\)
\(60\) 2.98870 2.38417i 0.385840 0.307795i
\(61\) 1.50179 + 0.867059i 0.192285 + 0.111016i 0.593052 0.805164i \(-0.297923\pi\)
−0.400767 + 0.916180i \(0.631256\pi\)
\(62\) 2.28160 2.61953i 0.289763 0.332681i
\(63\) 0.0724201 + 2.99913i 0.00912408 + 0.377854i
\(64\) −3.21123 7.32721i −0.401404 0.915901i
\(65\) 4.25735 + 2.45798i 0.528060 + 0.304875i
\(66\) 8.01587 9.43060i 0.986685 1.16083i
\(67\) −2.45861 4.25843i −0.300367 0.520251i 0.675852 0.737037i \(-0.263776\pi\)
−0.976219 + 0.216787i \(0.930442\pi\)
\(68\) −3.55053 4.56271i −0.430564 0.553310i
\(69\) 2.47271 0.0298501i 0.297680 0.00359352i
\(70\) 0.506713 + 1.47626i 0.0605638 + 0.176447i
\(71\) −5.16985 −0.613548 −0.306774 0.951782i \(-0.599250\pi\)
−0.306774 + 0.951782i \(0.599250\pi\)
\(72\) 8.48117 + 0.264124i 0.999515 + 0.0311273i
\(73\) 3.07080 0.359410 0.179705 0.983721i \(-0.442486\pi\)
0.179705 + 0.983721i \(0.442486\pi\)
\(74\) 4.33693 + 12.6352i 0.504157 + 1.46881i
\(75\) −3.34350 5.63298i −0.386074 0.650440i
\(76\) −3.23013 + 2.51356i −0.370521 + 0.288325i
\(77\) 2.52645 + 4.37593i 0.287915 + 0.498684i
\(78\) 3.66646 + 10.2762i 0.415144 + 1.16355i
\(79\) 10.1848 + 5.88019i 1.14588 + 0.661573i 0.947880 0.318629i \(-0.103222\pi\)
0.197999 + 0.980202i \(0.436556\pi\)
\(80\) 4.24830 1.20033i 0.474974 0.134201i
\(81\) −4.11856 + 8.00234i −0.457618 + 0.889149i
\(82\) −3.70384 + 4.25242i −0.409020 + 0.469602i
\(83\) −5.59514 3.23036i −0.614146 0.354578i 0.160440 0.987046i \(-0.448709\pi\)
−0.774586 + 0.632468i \(0.782042\pi\)
\(84\) −1.26508 + 3.22484i −0.138032 + 0.351859i
\(85\) 2.76291 1.59517i 0.299679 0.173020i
\(86\) −0.204073 + 1.04444i −0.0220057 + 0.112625i
\(87\) −0.555798 0.936382i −0.0595878 0.100391i
\(88\) 12.7529 6.45117i 1.35946 0.687697i
\(89\) 6.63971i 0.703808i 0.936036 + 0.351904i \(0.114466\pi\)
−0.936036 + 0.351904i \(0.885534\pi\)
\(90\) −0.786713 + 4.61584i −0.0829268 + 0.486552i
\(91\) −4.45427 −0.466934
\(92\) 2.64544 + 1.07481i 0.275807 + 0.112057i
\(93\) 0.0513566 + 4.25427i 0.00532543 + 0.441147i
\(94\) 2.69461 13.7910i 0.277928 1.42243i
\(95\) −1.12928 1.95597i −0.115862 0.200679i
\(96\) 8.90960 + 4.07664i 0.909333 + 0.416070i
\(97\) −0.323290 + 0.559955i −0.0328251 + 0.0568548i −0.881971 0.471303i \(-0.843784\pi\)
0.849146 + 0.528158i \(0.177117\pi\)
\(98\) −1.06642 0.928844i −0.107725 0.0938274i
\(99\) 0.365931 + 15.1543i 0.0367775 + 1.52306i
\(100\) −1.03813 7.49232i −0.103813 0.749232i
\(101\) 4.30714 7.46018i 0.428576 0.742316i −0.568171 0.822911i \(-0.692349\pi\)
0.996747 + 0.0805948i \(0.0256820\pi\)
\(102\) 6.96522 + 1.27384i 0.689659 + 0.126129i
\(103\) −5.91810 + 3.41682i −0.583128 + 0.336669i −0.762375 0.647135i \(-0.775967\pi\)
0.179248 + 0.983804i \(0.442634\pi\)
\(104\) −0.696028 + 12.5793i −0.0682512 + 1.23351i
\(105\) −1.66690 0.935739i −0.162672 0.0913188i
\(106\) 0.680982 0.233741i 0.0661428 0.0227029i
\(107\) 17.5169i 1.69342i −0.532054 0.846710i \(-0.678580\pi\)
0.532054 0.846710i \(-0.321420\pi\)
\(108\) −7.96522 + 6.67498i −0.766453 + 0.642300i
\(109\) 18.7050i 1.79161i 0.444443 + 0.895807i \(0.353401\pi\)
−0.444443 + 0.895807i \(0.646599\pi\)
\(110\) 2.56037 + 7.45938i 0.244121 + 0.711224i
\(111\) −14.2669 8.00893i −1.35415 0.760174i
\(112\) −2.78980 + 2.86654i −0.263611 + 0.270862i
\(113\) −10.7371 + 6.19906i −1.01006 + 0.583158i −0.911209 0.411944i \(-0.864850\pi\)
−0.0988505 + 0.995102i \(0.531517\pi\)
\(114\) 0.901801 4.93096i 0.0844614 0.461826i
\(115\) −0.787857 + 1.36461i −0.0734680 + 0.127250i
\(116\) −0.172571 1.24546i −0.0160228 0.115638i
\(117\) −11.7304 6.40009i −1.08448 0.591689i
\(118\) −11.8866 + 13.6472i −1.09425 + 1.25632i
\(119\) −1.44535 + 2.50342i −0.132495 + 0.229488i
\(120\) −2.90310 + 4.56128i −0.265015 + 0.416386i
\(121\) 7.26586 + 12.5848i 0.660533 + 1.14408i
\(122\) −2.40690 0.470281i −0.217910 0.0425773i
\(123\) −0.0833699 6.90618i −0.00751721 0.622709i
\(124\) −1.84920 + 4.55145i −0.166063 + 0.408732i
\(125\) 9.69223 0.866899
\(126\) −1.47384 3.97842i −0.131300 0.354426i
\(127\) 12.2831i 1.08995i 0.838453 + 0.544974i \(0.183460\pi\)
−0.838453 + 0.544974i \(0.816540\pi\)
\(128\) 7.65948 + 8.32661i 0.677008 + 0.735975i
\(129\) −0.665260 1.12080i −0.0585729 0.0986809i
\(130\) −6.82320 1.33318i −0.598435 0.116927i
\(131\) 19.6423 11.3405i 1.71616 0.990825i 0.790505 0.612455i \(-0.209818\pi\)
0.925654 0.378370i \(-0.123515\pi\)
\(132\) −6.39231 + 16.2948i −0.556379 + 1.41828i
\(133\) 1.77227 + 1.02322i 0.153675 + 0.0887245i
\(134\) 5.24381 + 4.56733i 0.452996 + 0.394557i
\(135\) −3.04531 4.85937i −0.262098 0.418228i
\(136\) 6.84407 + 4.47301i 0.586875 + 0.383557i
\(137\) 5.46474 + 3.15507i 0.466884 + 0.269556i 0.714934 0.699192i \(-0.246457\pi\)
−0.248050 + 0.968747i \(0.579790\pi\)
\(138\) −3.29383 + 1.17521i −0.280389 + 0.100040i
\(139\) 10.2915 + 17.8254i 0.872913 + 1.51193i 0.858970 + 0.512027i \(0.171105\pi\)
0.0139432 + 0.999903i \(0.495562\pi\)
\(140\) −1.35557 1.74202i −0.114567 0.147227i
\(141\) 8.78421 + 14.7992i 0.739764 + 1.24632i
\(142\) 6.91525 2.37360i 0.580315 0.199188i
\(143\) −22.5069 −1.88212
\(144\) −11.4658 + 3.54061i −0.955482 + 0.295051i
\(145\) 0.693847 0.0576208
\(146\) −4.10754 + 1.40988i −0.339943 + 0.116682i
\(147\) 1.73192 0.0209074i 0.142847 0.00172441i
\(148\) −11.6022 14.9098i −0.953699 1.22558i
\(149\) 10.2993 + 17.8389i 0.843750 + 1.46142i 0.886702 + 0.462341i \(0.152990\pi\)
−0.0429519 + 0.999077i \(0.513676\pi\)
\(150\) 7.05854 + 5.99965i 0.576327 + 0.489870i
\(151\) 15.3304 + 8.85102i 1.24757 + 0.720286i 0.970625 0.240599i \(-0.0773439\pi\)
0.276947 + 0.960885i \(0.410677\pi\)
\(152\) 3.16662 4.84520i 0.256847 0.392997i
\(153\) −7.40340 + 4.51608i −0.598529 + 0.365104i
\(154\) −5.38850 4.69335i −0.434218 0.378201i
\(155\) −2.34779 1.35550i −0.188579 0.108876i
\(156\) −9.62234 12.0622i −0.770404 0.965749i
\(157\) −15.0881 + 8.71112i −1.20416 + 0.695223i −0.961478 0.274883i \(-0.911361\pi\)
−0.242683 + 0.970106i \(0.578028\pi\)
\(158\) −16.3230 3.18934i −1.29859 0.253730i
\(159\) −0.431646 + 0.768920i −0.0342317 + 0.0609793i
\(160\) −5.13147 + 3.55607i −0.405678 + 0.281132i
\(161\) 1.42773i 0.112521i
\(162\) 1.83497 12.5950i 0.144169 0.989553i
\(163\) 15.5817 1.22046 0.610228 0.792226i \(-0.291078\pi\)
0.610228 + 0.792226i \(0.291078\pi\)
\(164\) 3.00191 7.38861i 0.234410 0.576954i
\(165\) −8.42265 4.72819i −0.655702 0.368089i
\(166\) 8.96726 + 1.75210i 0.695994 + 0.135989i
\(167\) 0.892269 + 1.54545i 0.0690458 + 0.119591i 0.898482 0.439011i \(-0.144671\pi\)
−0.829436 + 0.558602i \(0.811338\pi\)
\(168\) 0.211587 4.89441i 0.0163243 0.377612i
\(169\) 3.42025 5.92405i 0.263097 0.455697i
\(170\) −2.96332 + 3.40223i −0.227276 + 0.260939i
\(171\) 3.19712 + 5.24116i 0.244490 + 0.400802i
\(172\) −0.206559 1.49075i −0.0157499 0.113669i
\(173\) 5.23200 9.06208i 0.397781 0.688978i −0.595671 0.803229i \(-0.703114\pi\)
0.993452 + 0.114251i \(0.0364469\pi\)
\(174\) 1.17336 + 0.997336i 0.0889519 + 0.0756078i
\(175\) −3.27526 + 1.89097i −0.247587 + 0.142944i
\(176\) −14.0965 + 14.4843i −1.06257 + 1.09180i
\(177\) −0.267556 22.1638i −0.0201108 1.66593i
\(178\) −3.04845 8.88136i −0.228491 0.665686i
\(179\) 3.28458i 0.245501i −0.992438 0.122751i \(-0.960829\pi\)
0.992438 0.122751i \(-0.0391715\pi\)
\(180\) −1.06692 6.53540i −0.0795239 0.487120i
\(181\) 22.2835i 1.65632i −0.560491 0.828160i \(-0.689388\pi\)
0.560491 0.828160i \(-0.310612\pi\)
\(182\) 5.95808 2.04506i 0.441642 0.151590i
\(183\) 2.58286 1.53308i 0.190930 0.113328i
\(184\) −4.03205 0.223098i −0.297247 0.0164470i
\(185\) 9.02850 5.21261i 0.663789 0.383239i
\(186\) −2.02193 5.66698i −0.148255 0.415523i
\(187\) −7.30320 + 12.6495i −0.534063 + 0.925024i
\(188\) 2.72743 + 19.6842i 0.198919 + 1.43562i
\(189\) 4.59111 + 2.43345i 0.333954 + 0.177007i
\(190\) 2.40857 + 2.09785i 0.174736 + 0.152194i
\(191\) 6.07042 10.5143i 0.439240 0.760786i −0.558391 0.829578i \(-0.688581\pi\)
0.997631 + 0.0687916i \(0.0219143\pi\)
\(192\) −13.7893 1.36235i −0.995155 0.0983192i
\(193\) 12.1747 + 21.0872i 0.876354 + 1.51789i 0.855313 + 0.518111i \(0.173365\pi\)
0.0210410 + 0.999779i \(0.493302\pi\)
\(194\) 0.175348 0.897433i 0.0125893 0.0644319i
\(195\) 7.32202 4.34605i 0.524341 0.311227i
\(196\) 1.85291 + 0.752815i 0.132351 + 0.0537725i
\(197\) 8.49270 0.605080 0.302540 0.953137i \(-0.402165\pi\)
0.302540 + 0.953137i \(0.402165\pi\)
\(198\) −7.44715 20.1025i −0.529246 1.42862i
\(199\) 24.0323i 1.70360i −0.523865 0.851801i \(-0.675510\pi\)
0.523865 0.851801i \(-0.324490\pi\)
\(200\) 4.82852 + 9.54518i 0.341428 + 0.674946i
\(201\) −8.51625 + 0.102806i −0.600690 + 0.00725140i
\(202\) −2.33613 + 11.9563i −0.164370 + 0.841245i
\(203\) −0.544454 + 0.314341i −0.0382132 + 0.0220624i
\(204\) −9.90160 + 1.49399i −0.693251 + 0.104600i
\(205\) 3.81129 + 2.20045i 0.266192 + 0.153686i
\(206\) 6.34738 7.28752i 0.442243 0.507745i
\(207\) 2.05142 3.75996i 0.142584 0.261335i
\(208\) −4.84445 17.1458i −0.335902 1.18885i
\(209\) 8.95510 + 5.17023i 0.619437 + 0.357632i
\(210\) 2.65928 + 0.486344i 0.183508 + 0.0335609i
\(211\) −2.16736 3.75398i −0.149207 0.258435i 0.781727 0.623620i \(-0.214339\pi\)
−0.930935 + 0.365186i \(0.881006\pi\)
\(212\) −0.803573 + 0.625309i −0.0551896 + 0.0429464i
\(213\) −4.38329 + 7.80825i −0.300338 + 0.535013i
\(214\) 8.04241 + 23.4308i 0.549768 + 1.60170i
\(215\) 0.830498 0.0566395
\(216\) 7.58973 12.5855i 0.516416 0.856338i
\(217\) 2.45638 0.166750
\(218\) −8.58790 25.0200i −0.581646 1.69457i
\(219\) 2.60360 4.63797i 0.175935 0.313405i
\(220\) −6.84955 8.80223i −0.461797 0.593446i
\(221\) −6.43798 11.1509i −0.433065 0.750091i
\(222\) 22.7606 + 4.16259i 1.52759 + 0.279375i
\(223\) −13.3580 7.71226i −0.894519 0.516451i −0.0191014 0.999818i \(-0.506081\pi\)
−0.875418 + 0.483366i \(0.839414\pi\)
\(224\) 2.41557 5.11518i 0.161397 0.341772i
\(225\) −11.3425 + 0.273889i −0.756170 + 0.0182593i
\(226\) 11.5159 13.2216i 0.766027 0.879486i
\(227\) −17.4675 10.0849i −1.15936 0.669358i −0.208211 0.978084i \(-0.566764\pi\)
−0.951151 + 0.308726i \(0.900097\pi\)
\(228\) 1.05766 + 7.00974i 0.0700451 + 0.464232i
\(229\) 2.11212 1.21944i 0.139573 0.0805826i −0.428587 0.903500i \(-0.640989\pi\)
0.568161 + 0.822918i \(0.307655\pi\)
\(230\) 0.427323 2.18704i 0.0281769 0.144209i
\(231\) 8.75123 0.105643i 0.575789 0.00695079i
\(232\) 0.802655 + 1.58672i 0.0526969 + 0.104173i
\(233\) 28.8925i 1.89281i 0.322983 + 0.946405i \(0.395314\pi\)
−0.322983 + 0.946405i \(0.604686\pi\)
\(234\) 18.6292 + 3.17512i 1.21783 + 0.207564i
\(235\) −10.9660 −0.715345
\(236\) 9.63393 23.7120i 0.627115 1.54352i
\(237\) 17.5164 10.3970i 1.13781 0.675357i
\(238\) 0.783939 4.01220i 0.0508152 0.260072i
\(239\) 7.06875 + 12.2434i 0.457239 + 0.791962i 0.998814 0.0486910i \(-0.0155050\pi\)
−0.541575 + 0.840653i \(0.682172\pi\)
\(240\) 1.78903 7.43410i 0.115481 0.479869i
\(241\) 11.1867 19.3759i 0.720597 1.24811i −0.240164 0.970732i \(-0.577201\pi\)
0.960761 0.277378i \(-0.0894654\pi\)
\(242\) −15.4969 13.4977i −0.996178 0.867665i
\(243\) 8.59435 + 13.0053i 0.551328 + 0.834289i
\(244\) 3.43541 0.476010i 0.219930 0.0304734i
\(245\) −0.551827 + 0.955792i −0.0352549 + 0.0610633i
\(246\) 3.28231 + 9.19951i 0.209272 + 0.586540i
\(247\) −7.89417 + 4.55770i −0.502294 + 0.290000i
\(248\) 0.383836 6.93708i 0.0243736 0.440505i
\(249\) −9.62282 + 5.71171i −0.609822 + 0.361965i
\(250\) −12.9644 + 4.44993i −0.819943 + 0.281438i
\(251\) 4.86531i 0.307096i 0.988141 + 0.153548i \(0.0490699\pi\)
−0.988141 + 0.153548i \(0.950930\pi\)
\(252\) 3.79801 + 4.64490i 0.239252 + 0.292601i
\(253\) 7.21414i 0.453549i
\(254\) −5.63945 16.4300i −0.353851 1.03091i
\(255\) −0.0667016 5.52541i −0.00417701 0.346015i
\(256\) −14.0683 7.62113i −0.879272 0.476320i
\(257\) 17.4415 10.0698i 1.08797 0.628139i 0.154934 0.987925i \(-0.450483\pi\)
0.933035 + 0.359785i \(0.117150\pi\)
\(258\) 1.40445 + 1.19376i 0.0874370 + 0.0743201i
\(259\) −4.72305 + 8.18056i −0.293476 + 0.508315i
\(260\) 9.73889 1.34942i 0.603980 0.0836874i
\(261\) −1.88550 + 0.0455292i −0.116709 + 0.00281819i
\(262\) −21.0671 + 24.1875i −1.30153 + 1.49431i
\(263\) 11.7798 20.4033i 0.726377 1.25812i −0.232028 0.972709i \(-0.574536\pi\)
0.958405 0.285412i \(-0.0921305\pi\)
\(264\) 1.06913 24.7309i 0.0658003 1.52208i
\(265\) −0.280936 0.486596i −0.0172578 0.0298914i
\(266\) −2.84040 0.554982i −0.174156 0.0340281i
\(267\) 10.0283 + 5.62952i 0.613719 + 0.344521i
\(268\) −9.11115 3.70176i −0.556552 0.226121i
\(269\) 2.52530 0.153970 0.0769852 0.997032i \(-0.475471\pi\)
0.0769852 + 0.997032i \(0.475471\pi\)
\(270\) 6.30449 + 5.10178i 0.383679 + 0.310484i
\(271\) 28.0117i 1.70159i 0.525500 + 0.850794i \(0.323878\pi\)
−0.525500 + 0.850794i \(0.676122\pi\)
\(272\) −11.2084 2.84088i −0.679608 0.172253i
\(273\) −3.77658 + 6.72748i −0.228569 + 0.407166i
\(274\) −8.75826 1.71127i −0.529106 0.103381i
\(275\) −16.5496 + 9.55489i −0.997976 + 0.576182i
\(276\) 3.86629 3.08425i 0.232724 0.185650i
\(277\) −16.5059 9.52970i −0.991745 0.572584i −0.0859497 0.996299i \(-0.527392\pi\)
−0.905796 + 0.423715i \(0.860726\pi\)
\(278\) −21.9501 19.1184i −1.31648 1.14664i
\(279\) 6.46895 + 3.52944i 0.387286 + 0.211302i
\(280\) 2.61303 + 1.70777i 0.156158 + 0.102059i
\(281\) −19.0303 10.9871i −1.13525 0.655437i −0.190001 0.981784i \(-0.560849\pi\)
−0.945250 + 0.326346i \(0.894182\pi\)
\(282\) −18.5445 15.7626i −1.10431 0.938648i
\(283\) −0.424809 0.735791i −0.0252523 0.0437382i 0.853123 0.521710i \(-0.174706\pi\)
−0.878375 + 0.477971i \(0.841372\pi\)
\(284\) −8.16015 + 6.34991i −0.484216 + 0.376798i
\(285\) −3.91166 + 0.0472207i −0.231707 + 0.00279711i
\(286\) 30.1055 10.3335i 1.78018 0.611030i
\(287\) −3.98758 −0.235379
\(288\) 13.7112 10.0002i 0.807939 0.589266i
\(289\) 8.64385 0.508462
\(290\) −0.928098 + 0.318561i −0.0544998 + 0.0187066i
\(291\) 0.571622 + 0.963041i 0.0335090 + 0.0564545i
\(292\) 4.84699 3.77174i 0.283649 0.220724i
\(293\) −11.0407 19.1230i −0.645004 1.11718i −0.984301 0.176501i \(-0.943522\pi\)
0.339296 0.940680i \(-0.389811\pi\)
\(294\) −2.30704 + 0.823133i −0.134550 + 0.0480061i
\(295\) 12.2315 + 7.06184i 0.712143 + 0.411156i
\(296\) 22.3648 + 14.6167i 1.29992 + 0.849578i
\(297\) 23.1984 + 12.2959i 1.34611 + 0.713483i
\(298\) −21.9667 19.1329i −1.27250 1.10834i
\(299\) 5.50747 + 3.17974i 0.318505 + 0.183889i
\(300\) −12.1962 4.78447i −0.704146 0.276231i
\(301\) −0.651683 + 0.376249i −0.0375624 + 0.0216867i
\(302\) −24.5699 4.80068i −1.41384 0.276248i
\(303\) −7.61561 12.8304i −0.437506 0.737089i
\(304\) −2.01117 + 7.93486i −0.115349 + 0.455096i
\(305\) 1.91386i 0.109588i
\(306\) 7.82943 9.43984i 0.447579 0.539640i
\(307\) 1.59259 0.0908938 0.0454469 0.998967i \(-0.485529\pi\)
0.0454469 + 0.998967i \(0.485529\pi\)
\(308\) 9.36255 + 3.80389i 0.533481 + 0.216747i
\(309\) 0.142874 + 11.8353i 0.00812780 + 0.673289i
\(310\) 3.76277 + 0.735203i 0.213711 + 0.0417567i
\(311\) −3.05144 5.28525i −0.173031 0.299699i 0.766447 0.642308i \(-0.222023\pi\)
−0.939478 + 0.342609i \(0.888689\pi\)
\(312\) 18.4090 + 11.7167i 1.04220 + 0.663328i
\(313\) 2.10943 3.65364i 0.119232 0.206516i −0.800232 0.599691i \(-0.795290\pi\)
0.919464 + 0.393175i \(0.128623\pi\)
\(314\) 16.1825 18.5794i 0.913234 1.04850i
\(315\) −2.82658 + 1.72422i −0.159260 + 0.0971486i
\(316\) 23.2982 3.22819i 1.31063 0.181600i
\(317\) −8.07198 + 13.9811i −0.453368 + 0.785256i −0.998593 0.0530337i \(-0.983111\pi\)
0.545225 + 0.838290i \(0.316444\pi\)
\(318\) 0.224345 1.22670i 0.0125806 0.0687897i
\(319\) −2.75107 + 1.58833i −0.154030 + 0.0889294i
\(320\) 5.23124 7.11262i 0.292435 0.397607i
\(321\) −26.4565 14.8518i −1.47666 0.828946i
\(322\) 0.655502 + 1.90974i 0.0365297 + 0.106426i
\(323\) 5.91565i 0.329156i
\(324\) 3.32816 + 17.6896i 0.184898 + 0.982758i
\(325\) 16.8458i 0.934438i
\(326\) −20.8423 + 7.15394i −1.15435 + 0.396220i
\(327\) 28.2510 + 15.8591i 1.56228 + 0.877013i
\(328\) −0.623102 + 11.2613i −0.0344051 + 0.621804i
\(329\) 8.60493 4.96806i 0.474405 0.273898i
\(330\) 13.4371 + 2.45744i 0.739686 + 0.135278i
\(331\) −14.6729 + 25.4142i −0.806495 + 1.39689i 0.108783 + 0.994066i \(0.465305\pi\)
−0.915277 + 0.402824i \(0.868029\pi\)
\(332\) −12.7991 + 1.77345i −0.702444 + 0.0973305i
\(333\) −24.1925 + 14.7575i −1.32574 + 0.808704i
\(334\) −1.90306 1.65756i −0.104131 0.0906975i
\(335\) 2.71345 4.69983i 0.148252 0.256779i
\(336\) 1.96412 + 6.64396i 0.107151 + 0.362458i
\(337\) 2.19627 + 3.80406i 0.119639 + 0.207220i 0.919625 0.392799i \(-0.128493\pi\)
−0.799986 + 0.600019i \(0.795160\pi\)
\(338\) −1.85510 + 9.49441i −0.100904 + 0.516428i
\(339\) 0.259213 + 21.4726i 0.0140785 + 1.16623i
\(340\) 2.40173 5.91139i 0.130252 0.320590i
\(341\) 12.4118 0.672138
\(342\) −6.68284 5.54277i −0.361367 0.299719i
\(343\) 1.00000i 0.0539949i
\(344\) 0.960736 + 1.89922i 0.0517994 + 0.102399i
\(345\) 1.39304 + 2.34693i 0.0749987 + 0.126354i
\(346\) −2.83777 + 14.5237i −0.152559 + 0.780798i
\(347\) 4.88761 2.82186i 0.262380 0.151485i −0.363040 0.931774i \(-0.618261\pi\)
0.625420 + 0.780288i \(0.284928\pi\)
\(348\) −2.02740 0.795333i −0.108680 0.0426343i
\(349\) −25.4757 14.7084i −1.36368 0.787321i −0.373569 0.927602i \(-0.621866\pi\)
−0.990112 + 0.140281i \(0.955199\pi\)
\(350\) 3.51284 4.03314i 0.187769 0.215580i
\(351\) −19.6121 + 12.2907i −1.04682 + 0.656027i
\(352\) 12.2056 25.8464i 0.650561 1.37762i
\(353\) −18.3067 10.5694i −0.974365 0.562550i −0.0738007 0.997273i \(-0.523513\pi\)
−0.900564 + 0.434723i \(0.856846\pi\)
\(354\) 10.5338 + 29.5237i 0.559865 + 1.56917i
\(355\) −2.85286 4.94130i −0.151414 0.262257i
\(356\) 8.15528 + 10.4802i 0.432229 + 0.555450i
\(357\) 2.55558 + 4.30552i 0.135256 + 0.227872i
\(358\) 1.50803 + 4.39349i 0.0797017 + 0.232203i
\(359\) 11.5283 0.608440 0.304220 0.952602i \(-0.401604\pi\)
0.304220 + 0.952602i \(0.401604\pi\)
\(360\) 4.42769 + 8.25198i 0.233360 + 0.434918i
\(361\) −14.8121 −0.779583
\(362\) 10.2309 + 29.8067i 0.537723 + 1.56661i
\(363\) 25.1678 0.303821i 1.32097 0.0159464i
\(364\) −7.03067 + 5.47099i −0.368507 + 0.286758i
\(365\) 1.69455 + 2.93505i 0.0886969 + 0.153627i
\(366\) −2.75099 + 3.23652i −0.143797 + 0.169175i
\(367\) 11.4483 + 6.60966i 0.597594 + 0.345021i 0.768095 0.640336i \(-0.221205\pi\)
−0.170500 + 0.985358i \(0.554538\pi\)
\(368\) 5.49575 1.55279i 0.286486 0.0809448i
\(369\) −10.5014 5.72953i −0.546681 0.298267i
\(370\) −9.68340 + 11.1176i −0.503416 + 0.577979i
\(371\) 0.440896 + 0.254551i 0.0228902 + 0.0132156i
\(372\) 5.30640 + 6.65190i 0.275124 + 0.344885i
\(373\) −17.8798 + 10.3229i −0.925782 + 0.534501i −0.885475 0.464687i \(-0.846167\pi\)
−0.0403072 + 0.999187i \(0.512834\pi\)
\(374\) 3.96116 20.2732i 0.204827 1.04830i
\(375\) 8.21761 14.6386i 0.424356 0.755934i
\(376\) −12.6857 25.0776i −0.654216 1.29328i
\(377\) 2.80032i 0.144224i
\(378\) −7.25838 1.14712i −0.373331 0.0590015i
\(379\) 3.39883 0.174586 0.0872932 0.996183i \(-0.472178\pi\)
0.0872932 + 0.996183i \(0.472178\pi\)
\(380\) −4.18491 1.70028i −0.214681 0.0872226i
\(381\) 18.5517 + 10.4143i 0.950432 + 0.533540i
\(382\) −3.29252 + 16.8511i −0.168460 + 0.862177i
\(383\) −9.61525 16.6541i −0.491316 0.850985i 0.508634 0.860983i \(-0.330151\pi\)
−0.999950 + 0.00999820i \(0.996817\pi\)
\(384\) 19.0702 4.50868i 0.973171 0.230083i
\(385\) −2.78832 + 4.82951i −0.142106 + 0.246135i
\(386\) −25.9667 22.6168i −1.32167 1.15116i
\(387\) −2.25684 + 0.0544961i −0.114722 + 0.00277019i
\(388\) 0.177484 + 1.28092i 0.00901041 + 0.0650290i
\(389\) 10.0678 17.4380i 0.510458 0.884140i −0.489468 0.872021i \(-0.662809\pi\)
0.999927 0.0121188i \(-0.00385764\pi\)
\(390\) −7.79865 + 9.17505i −0.394900 + 0.464596i
\(391\) 3.57420 2.06356i 0.180755 0.104359i
\(392\) −2.82411 0.156261i −0.142639 0.00789237i
\(393\) −0.474202 39.2818i −0.0239203 1.98151i
\(394\) −11.3599 + 3.89920i −0.572305 + 0.196439i
\(395\) 12.9794i 0.653064i
\(396\) 19.1909 + 23.4702i 0.964380 + 1.17942i
\(397\) 13.1516i 0.660059i 0.943971 + 0.330029i \(0.107059\pi\)
−0.943971 + 0.330029i \(0.892941\pi\)
\(398\) 11.0338 + 32.1458i 0.553073 + 1.61133i
\(399\) 3.04805 1.80920i 0.152593 0.0905731i
\(400\) −10.8411 10.5509i −0.542055 0.527543i
\(401\) 3.21456 1.85593i 0.160527 0.0926805i −0.417584 0.908638i \(-0.637123\pi\)
0.578112 + 0.815958i \(0.303790\pi\)
\(402\) 11.3442 4.04752i 0.565799 0.201872i
\(403\) −5.47069 + 9.47551i −0.272514 + 0.472009i
\(404\) −2.36459 17.0655i −0.117643 0.849041i
\(405\) −9.92130 + 0.479421i −0.492993 + 0.0238226i
\(406\) 0.583947 0.670438i 0.0289808 0.0332733i
\(407\) −23.8651 + 41.3355i −1.18295 + 2.04892i
\(408\) 12.5586 6.54444i 0.621742 0.323998i
\(409\) −0.231006 0.400115i −0.0114225 0.0197844i 0.860258 0.509860i \(-0.170303\pi\)
−0.871680 + 0.490075i \(0.836969\pi\)
\(410\) −6.10831 1.19350i −0.301668 0.0589425i
\(411\) 9.39855 5.57859i 0.463596 0.275172i
\(412\) −5.14446 + 12.6621i −0.253450 + 0.623817i
\(413\) −12.7972 −0.629709
\(414\) −1.01772 + 5.97122i −0.0500182 + 0.293469i
\(415\) 7.13038i 0.350017i
\(416\) 14.3520 + 20.7103i 0.703667 + 1.01540i
\(417\) 35.6482 0.430337i 1.74570 0.0210737i
\(418\) −14.3522 2.80426i −0.701990 0.137161i
\(419\) 6.77061 3.90901i 0.330766 0.190968i −0.325415 0.945571i \(-0.605504\pi\)
0.656181 + 0.754603i \(0.272171\pi\)
\(420\) −3.78038 + 0.570398i −0.184464 + 0.0278326i
\(421\) −18.8054 10.8573i −0.916519 0.529153i −0.0339963 0.999422i \(-0.510823\pi\)
−0.882523 + 0.470269i \(0.844157\pi\)
\(422\) 4.62263 + 4.02628i 0.225026 + 0.195996i
\(423\) 29.7997 0.719575i 1.44891 0.0349869i
\(424\) 0.787775 1.20536i 0.0382577 0.0585375i
\(425\) −9.46781 5.46624i −0.459256 0.265152i
\(426\) 2.27819 12.4569i 0.110378 0.603538i
\(427\) −0.867059 1.50179i −0.0419599 0.0726767i
\(428\) −21.5153 27.6488i −1.03998 1.33646i
\(429\) −19.0826 + 33.9932i −0.921319 + 1.64121i
\(430\) −1.11088 + 0.381301i −0.0535716 + 0.0183880i
\(431\) 19.0335 0.916814 0.458407 0.888743i \(-0.348420\pi\)
0.458407 + 0.888743i \(0.348420\pi\)
\(432\) −4.37379 + 20.3192i −0.210434 + 0.977608i
\(433\) 1.41692 0.0680929 0.0340465 0.999420i \(-0.489161\pi\)
0.0340465 + 0.999420i \(0.489161\pi\)
\(434\) −3.28568 + 1.12778i −0.157718 + 0.0541353i
\(435\) 0.588282 1.04795i 0.0282060 0.0502452i
\(436\) 22.9746 + 29.5242i 1.10028 + 1.41395i
\(437\) −1.46088 2.53032i −0.0698833 0.121041i
\(438\) −1.35320 + 7.39918i −0.0646586 + 0.353546i
\(439\) 16.7024 + 9.64312i 0.797161 + 0.460241i 0.842477 0.538732i \(-0.181096\pi\)
−0.0453165 + 0.998973i \(0.514430\pi\)
\(440\) 13.2034 + 8.62918i 0.629445 + 0.411380i
\(441\) 1.43685 2.63353i 0.0684212 0.125406i
\(442\) 13.7312 + 11.9598i 0.653125 + 0.568868i
\(443\) −25.5813 14.7694i −1.21540 0.701713i −0.251472 0.967865i \(-0.580915\pi\)
−0.963931 + 0.266152i \(0.914248\pi\)
\(444\) −32.3560 + 4.88200i −1.53555 + 0.231690i
\(445\) −6.34618 + 3.66397i −0.300838 + 0.173689i
\(446\) 21.4087 + 4.18303i 1.01373 + 0.198072i
\(447\) 35.6752 0.430663i 1.68738 0.0203697i
\(448\) −0.882595 + 7.95117i −0.0416987 + 0.375657i
\(449\) 2.41176i 0.113818i 0.998379 + 0.0569090i \(0.0181245\pi\)
−0.998379 + 0.0569090i \(0.981876\pi\)
\(450\) 15.0462 5.57399i 0.709283 0.262760i
\(451\) −20.1488 −0.948769
\(452\) −9.33349 + 22.9726i −0.439010 + 1.08054i
\(453\) 26.3661 15.6498i 1.23879 0.735293i
\(454\) 27.9950 + 5.46991i 1.31387 + 0.256716i
\(455\) −2.45798 4.25735i −0.115232 0.199588i
\(456\) −4.63307 8.89072i −0.216964 0.416346i
\(457\) 13.4246 23.2520i 0.627975 1.08768i −0.359983 0.932959i \(-0.617217\pi\)
0.987958 0.154725i \(-0.0494492\pi\)
\(458\) −2.26533 + 2.60086i −0.105852 + 0.121530i
\(459\) 0.543828 + 15.0107i 0.0253837 + 0.700638i
\(460\) 0.432529 + 3.12160i 0.0201668 + 0.145546i
\(461\) −14.3966 + 24.9356i −0.670515 + 1.16137i 0.307243 + 0.951631i \(0.400594\pi\)
−0.977758 + 0.209735i \(0.932740\pi\)
\(462\) −11.6572 + 4.15920i −0.542344 + 0.193504i
\(463\) 8.70983 5.02862i 0.404780 0.233700i −0.283764 0.958894i \(-0.591583\pi\)
0.688544 + 0.725194i \(0.258250\pi\)
\(464\) −1.80214 1.75389i −0.0836623 0.0814225i
\(465\) −4.03785 + 2.39670i −0.187251 + 0.111144i
\(466\) −13.2652 38.6469i −0.614499 1.79028i
\(467\) 7.49126i 0.346654i −0.984864 0.173327i \(-0.944548\pi\)
0.984864 0.173327i \(-0.0554518\pi\)
\(468\) −26.3764 + 4.30603i −1.21925 + 0.199046i
\(469\) 4.91722i 0.227056i
\(470\) 14.6683 5.03476i 0.676598 0.232236i
\(471\) 0.364254 + 30.1740i 0.0167839 + 1.39034i
\(472\) −1.99970 + 36.1407i −0.0920438 + 1.66351i
\(473\) −3.29288 + 1.90115i −0.151407 + 0.0874148i
\(474\) −18.6566 + 21.9493i −0.856925 + 1.00817i
\(475\) −3.86977 + 6.70264i −0.177557 + 0.307538i
\(476\) 0.793489 + 5.72669i 0.0363695 + 0.262482i
\(477\) 0.795361 + 1.30387i 0.0364171 + 0.0597000i
\(478\) −15.0765 13.1315i −0.689583 0.600622i
\(479\) 0.829109 1.43606i 0.0378830 0.0656152i −0.846462 0.532449i \(-0.821272\pi\)
0.884345 + 0.466833i \(0.154605\pi\)
\(480\) 1.02014 + 10.7653i 0.0465628 + 0.491367i
\(481\) −21.0377 36.4384i −0.959238 1.66145i
\(482\) −6.06750 + 31.0535i −0.276367 + 1.41445i
\(483\) −2.15636 1.21051i −0.0981177 0.0550799i
\(484\) 26.9259 + 10.9397i 1.22391 + 0.497259i
\(485\) −0.713601 −0.0324029
\(486\) −17.4669 13.4501i −0.792316 0.610111i
\(487\) 10.8329i 0.490886i −0.969411 0.245443i \(-0.921067\pi\)
0.969411 0.245443i \(-0.0789333\pi\)
\(488\) −4.37670 + 2.21400i −0.198124 + 0.100223i
\(489\) 13.2111 23.5338i 0.597425 1.06423i
\(490\) 0.299303 1.53183i 0.0135212 0.0692012i
\(491\) −9.25970 + 5.34609i −0.417884 + 0.241266i −0.694172 0.719809i \(-0.744229\pi\)
0.276287 + 0.961075i \(0.410896\pi\)
\(492\) −8.61416 10.7984i −0.388357 0.486829i
\(493\) −1.57385 0.908665i −0.0708828 0.0409242i
\(494\) 8.46679 9.72084i 0.380939 0.437361i
\(495\) −14.2824 + 8.71228i −0.641945 + 0.391588i
\(496\) 2.67155 + 9.45535i 0.119956 + 0.424558i
\(497\) 4.47722 + 2.58492i 0.200831 + 0.115950i
\(498\) 10.2492 12.0581i 0.459279 0.540337i
\(499\) 1.67543 + 2.90194i 0.0750027 + 0.129909i 0.901087 0.433637i \(-0.142770\pi\)
−0.826085 + 0.563546i \(0.809437\pi\)
\(500\) 15.2983 11.9046i 0.684162 0.532388i
\(501\) 3.09068 0.0373101i 0.138082 0.00166689i
\(502\) −2.23378 6.50790i −0.0996984 0.290462i
\(503\) −35.2168 −1.57024 −0.785119 0.619345i \(-0.787398\pi\)
−0.785119 + 0.619345i \(0.787398\pi\)
\(504\) −7.21285 4.46932i −0.321286 0.199079i
\(505\) 9.50717 0.423064
\(506\) 3.31218 + 9.64972i 0.147244 + 0.428983i
\(507\) −6.04748 10.1885i −0.268578 0.452488i
\(508\) 15.0868 + 19.3878i 0.669368 + 0.860193i
\(509\) −4.24020 7.34425i −0.187944 0.325528i 0.756621 0.653854i \(-0.226849\pi\)
−0.944565 + 0.328326i \(0.893516\pi\)
\(510\) 2.62607 + 7.36023i 0.116284 + 0.325917i
\(511\) −2.65939 1.53540i −0.117645 0.0679222i
\(512\) 22.3170 + 3.73500i 0.986283 + 0.165065i
\(513\) 10.6267 0.384998i 0.469178 0.0169981i
\(514\) −18.7066 + 21.4773i −0.825114 + 0.947324i
\(515\) −6.53153 3.77098i −0.287814 0.166169i
\(516\) −2.42669 0.951971i −0.106829 0.0419082i
\(517\) 43.4798 25.1031i 1.91224 1.10403i
\(518\) 2.56172 13.1109i 0.112555 0.576059i
\(519\) −9.25089 15.5855i −0.406069 0.684126i
\(520\) −12.4073 + 6.27635i −0.544096 + 0.275236i
\(521\) 35.6466i 1.56171i 0.624715 + 0.780853i \(0.285215\pi\)
−0.624715 + 0.780853i \(0.714785\pi\)
\(522\) 2.50116 0.926576i 0.109473 0.0405551i
\(523\) 30.4799 1.33279 0.666397 0.745598i \(-0.267836\pi\)
0.666397 + 0.745598i \(0.267836\pi\)
\(524\) 17.0746 42.0259i 0.745908 1.83591i
\(525\) 0.0790708 + 6.55005i 0.00345093 + 0.285868i
\(526\) −6.38923 + 32.7001i −0.278584 + 1.42579i
\(527\) 3.55033 + 6.14935i 0.154655 + 0.267870i
\(528\) 9.92447 + 33.5712i 0.431907 + 1.46100i
\(529\) 10.4808 18.1533i 0.455687 0.789273i
\(530\) 0.599191 + 0.521892i 0.0260272 + 0.0226695i
\(531\) −33.7018 18.3876i −1.46253 0.797954i
\(532\) 4.05415 0.561742i 0.175770 0.0243546i
\(533\) 8.88087 15.3821i 0.384673 0.666273i
\(534\) −15.9986 2.92591i −0.692325 0.126616i
\(535\) 16.7425 9.66628i 0.723841 0.417910i
\(536\) 13.8867 + 0.768369i 0.599816 + 0.0331885i
\(537\) −4.96085 2.78485i −0.214076 0.120175i
\(538\) −3.37788 + 1.15943i −0.145631 + 0.0499864i
\(539\) 5.05289i 0.217643i
\(540\) −10.7753 3.92966i −0.463695 0.169105i
\(541\) 25.3260i 1.08885i 0.838809 + 0.544426i \(0.183252\pi\)
−0.838809 + 0.544426i \(0.816748\pi\)
\(542\) −12.8608 37.4687i −0.552419 1.60942i
\(543\) −33.6558 18.8932i −1.44431 0.810785i
\(544\) 16.2968 1.34604i 0.698718 0.0577110i
\(545\) −17.8781 + 10.3219i −0.765813 + 0.442142i
\(546\) 1.96285 10.7327i 0.0840023 0.459316i
\(547\) 13.1464 22.7703i 0.562101 0.973587i −0.435212 0.900328i \(-0.643327\pi\)
0.997313 0.0732594i \(-0.0233401\pi\)
\(548\) 12.5008 1.73211i 0.534009 0.0739922i
\(549\) −0.125585 5.20084i −0.00535984 0.221966i
\(550\) 17.7500 20.3790i 0.756863 0.868965i
\(551\) −0.643281 + 1.11419i −0.0274047 + 0.0474663i
\(552\) −3.75555 + 5.90063i −0.159847 + 0.251147i
\(553\) −5.88019 10.1848i −0.250051 0.433101i
\(554\) 26.4538 + 5.16878i 1.12392 + 0.219601i
\(555\) −0.217964 18.0557i −0.00925207 0.766421i
\(556\) 38.1384 + 15.4952i 1.61743 + 0.657142i
\(557\) 36.1604 1.53216 0.766082 0.642742i \(-0.222203\pi\)
0.766082 + 0.642742i \(0.222203\pi\)
\(558\) −10.2734 1.75097i −0.434907 0.0741246i
\(559\) 3.35183i 0.141767i
\(560\) −4.27930 1.08463i −0.180833 0.0458340i
\(561\) 12.9131 + 21.7553i 0.545190 + 0.918510i
\(562\) 30.4996 + 5.95928i 1.28655 + 0.251377i
\(563\) 27.0427 15.6131i 1.13971 0.658014i 0.193355 0.981129i \(-0.438063\pi\)
0.946360 + 0.323114i \(0.104730\pi\)
\(564\) 32.0424 + 12.5700i 1.34923 + 0.529292i
\(565\) −11.8500 6.84161i −0.498534 0.287829i
\(566\) 0.906048 + 0.789163i 0.0380840 + 0.0331710i
\(567\) 7.56795 4.87095i 0.317824 0.204561i
\(568\) 7.99972 12.2402i 0.335661 0.513589i
\(569\) −21.6173 12.4808i −0.906246 0.523222i −0.0270248 0.999635i \(-0.508603\pi\)
−0.879222 + 0.476413i \(0.841937\pi\)
\(570\) 5.21060 1.85910i 0.218248 0.0778691i
\(571\) −13.6541 23.6496i −0.571406 0.989705i −0.996422 0.0845188i \(-0.973065\pi\)
0.425016 0.905186i \(-0.360269\pi\)
\(572\) −35.5252 + 27.6443i −1.48538 + 1.15587i
\(573\) −10.7333 18.0830i −0.448392 0.755429i
\(574\) 5.33383 1.83079i 0.222630 0.0764157i
\(575\) 5.39959 0.225178
\(576\) −13.7489 + 19.6715i −0.572872 + 0.819645i
\(577\) −28.5837 −1.18995 −0.594977 0.803743i \(-0.702839\pi\)
−0.594977 + 0.803743i \(0.702839\pi\)
\(578\) −11.5621 + 3.96860i −0.480921 + 0.165072i
\(579\) 42.1713 0.509083i 1.75258 0.0211568i
\(580\) 1.09518 0.852223i 0.0454747 0.0353866i
\(581\) 3.23036 + 5.59514i 0.134018 + 0.232126i
\(582\) −1.20676 1.02573i −0.0500219 0.0425179i
\(583\) 2.22780 + 1.28622i 0.0922660 + 0.0532698i
\(584\) −4.75170 + 7.27049i −0.196627 + 0.300855i
\(585\) −0.356015 14.7436i −0.0147194 0.609573i
\(586\) 23.5480 + 20.5102i 0.972759 + 0.847267i
\(587\) −4.64634 2.68257i −0.191775 0.110721i 0.401038 0.916061i \(-0.368649\pi\)
−0.592813 + 0.805340i \(0.701983\pi\)
\(588\) 2.70801 2.16025i 0.111676 0.0890872i
\(589\) 4.35337 2.51342i 0.179378 0.103564i
\(590\) −19.6032 3.83025i −0.807051 0.157689i
\(591\) 7.20059 12.8269i 0.296193 0.527628i
\(592\) −36.6262 9.28329i −1.50533 0.381541i
\(593\) 2.71179i 0.111360i 0.998449 + 0.0556799i \(0.0177326\pi\)
−0.998449 + 0.0556799i \(0.982267\pi\)
\(594\) −36.6758 5.79627i −1.50483 0.237824i
\(595\) −3.19033 −0.130791
\(596\) 38.1673 + 15.5069i 1.56339 + 0.635188i
\(597\) −36.2970 20.3759i −1.48554 0.833930i
\(598\) −8.82674 1.72465i −0.360952 0.0705261i
\(599\) −2.82360 4.89061i −0.115369 0.199825i 0.802558 0.596574i \(-0.203472\pi\)
−0.917927 + 0.396749i \(0.870138\pi\)
\(600\) 18.5104 + 0.800213i 0.755684 + 0.0326685i
\(601\) 17.4149 30.1635i 0.710369 1.23040i −0.254350 0.967112i \(-0.581861\pi\)
0.964719 0.263283i \(-0.0848053\pi\)
\(602\) 0.698954 0.802479i 0.0284872 0.0327066i
\(603\) −7.06528 + 12.9496i −0.287720 + 0.527350i
\(604\) 35.0691 4.85916i 1.42694 0.197716i
\(605\) −8.01899 + 13.8893i −0.326018 + 0.564680i
\(606\) 16.0775 + 13.6656i 0.653103 + 0.555128i
\(607\) −36.7066 + 21.1926i −1.48988 + 0.860181i −0.999933 0.0115734i \(-0.996316\pi\)
−0.489944 + 0.871754i \(0.662983\pi\)
\(608\) −0.952915 11.5371i −0.0386458 0.467893i
\(609\) 0.0131441 + 1.08883i 0.000532626 + 0.0441216i
\(610\) −0.878700 2.56001i −0.0355775 0.103652i
\(611\) 44.2581i 1.79049i
\(612\) −6.13869 + 16.2215i −0.248142 + 0.655716i
\(613\) 30.3276i 1.22492i 0.790502 + 0.612459i \(0.209820\pi\)
−0.790502 + 0.612459i \(0.790180\pi\)
\(614\) −2.13027 + 0.731195i −0.0859705 + 0.0295086i
\(615\) 6.55486 3.89070i 0.264318 0.156888i
\(616\) −14.2699 0.789570i −0.574951 0.0318127i
\(617\) 0.167922 0.0969498i 0.00676028 0.00390305i −0.496616 0.867970i \(-0.665424\pi\)
0.503376 + 0.864067i \(0.332091\pi\)
\(618\) −5.62499 15.7655i −0.226270 0.634181i
\(619\) 3.37036 5.83763i 0.135466 0.234634i −0.790309 0.612708i \(-0.790080\pi\)
0.925775 + 0.378074i \(0.123413\pi\)
\(620\) −5.37068 + 0.744159i −0.215692 + 0.0298862i
\(621\) −3.93952 6.28625i −0.158088 0.252259i
\(622\) 6.50822 + 5.66862i 0.260956 + 0.227291i
\(623\) 3.31986 5.75016i 0.133007 0.230375i
\(624\) −30.0035 7.22040i −1.20110 0.289047i
\(625\) −4.10645 7.11257i −0.164258 0.284503i
\(626\) −1.14413 + 5.85564i −0.0457285 + 0.234039i
\(627\) 15.4015 9.14167i 0.615075 0.365083i
\(628\) −13.1157 + 32.2818i −0.523374 + 1.28818i
\(629\) −27.3058 −1.08876
\(630\) 2.98923 3.60408i 0.119094 0.143590i
\(631\) 35.5601i 1.41562i −0.706401 0.707812i \(-0.749682\pi\)
0.706401 0.707812i \(-0.250318\pi\)
\(632\) −29.6818 + 15.0148i −1.18068 + 0.597257i
\(633\) −7.50741 + 0.0906279i −0.298393 + 0.00360213i
\(634\) 4.37814 22.4073i 0.173878 0.889908i
\(635\) −11.7401 + 6.77813i −0.465890 + 0.268982i
\(636\) 0.263118 + 1.74384i 0.0104333 + 0.0691479i
\(637\) 3.85751 + 2.22713i 0.152840 + 0.0882423i
\(638\) 2.95062 3.38765i 0.116816 0.134118i
\(639\) 8.07675 + 13.2405i 0.319511 + 0.523788i
\(640\) −3.73180 + 11.9157i −0.147512 + 0.471010i
\(641\) 21.4710 + 12.3963i 0.848055 + 0.489625i 0.859994 0.510304i \(-0.170467\pi\)
−0.0119388 + 0.999929i \(0.503800\pi\)
\(642\) 42.2074 + 7.71912i 1.66579 + 0.304649i
\(643\) −4.24703 7.35607i −0.167486 0.290095i 0.770049 0.637985i \(-0.220232\pi\)
−0.937535 + 0.347890i \(0.886898\pi\)
\(644\) −1.75362 2.25354i −0.0691021 0.0888018i
\(645\) 0.704142 1.25434i 0.0277256 0.0493895i
\(646\) −2.71601 7.91285i −0.106860 0.311327i
\(647\) −12.9279 −0.508247 −0.254124 0.967172i \(-0.581787\pi\)
−0.254124 + 0.967172i \(0.581787\pi\)
\(648\) −12.5735 22.1338i −0.493934 0.869499i
\(649\) −64.6629 −2.53824
\(650\) 7.73431 + 22.5332i 0.303365 + 0.883824i
\(651\) 2.08266 3.70998i 0.0816258 0.145406i
\(652\) 24.5944 19.1384i 0.963190 0.749517i
\(653\) 9.71807 + 16.8322i 0.380297 + 0.658695i 0.991105 0.133085i \(-0.0424883\pi\)
−0.610807 + 0.791779i \(0.709155\pi\)
\(654\) −45.0702 8.24269i −1.76238 0.322315i
\(655\) 21.6783 + 12.5160i 0.847043 + 0.489040i
\(656\) −4.33688 15.3494i −0.169327 0.599293i
\(657\) −4.79746 7.86466i −0.187167 0.306830i
\(658\) −9.22910 + 10.5961i −0.359788 + 0.413077i
\(659\) 38.9399 + 22.4819i 1.51688 + 0.875772i 0.999803 + 0.0198335i \(0.00631360\pi\)
0.517078 + 0.855938i \(0.327020\pi\)
\(660\) −19.1018 + 2.88216i −0.743538 + 0.112188i
\(661\) 2.20738 1.27443i 0.0858571 0.0495696i −0.456457 0.889746i \(-0.650882\pi\)
0.542314 + 0.840176i \(0.317548\pi\)
\(662\) 7.95838 40.7310i 0.309311 1.58305i
\(663\) −22.3002 + 0.269203i −0.866067 + 0.0104550i
\(664\) 16.3061 8.24857i 0.632798 0.320107i
\(665\) 2.25856i 0.0875833i
\(666\) 25.5847 30.8471i 0.991386 1.19530i
\(667\) 0.897585 0.0347546
\(668\) 3.30658 + 1.34343i 0.127936 + 0.0519788i
\(669\) −22.9738 + 13.6363i −0.888220 + 0.527211i
\(670\) −1.47174 + 7.53236i −0.0568583 + 0.291001i
\(671\) −4.38116 7.58838i −0.169133 0.292946i
\(672\) −5.67762 7.98527i −0.219019 0.308039i
\(673\) −6.35177 + 11.0016i −0.244843 + 0.424080i −0.962087 0.272741i \(-0.912070\pi\)
0.717245 + 0.696821i \(0.245403\pi\)
\(674\) −4.68429 4.07999i −0.180432 0.157155i
\(675\) −9.20318 + 17.3634i −0.354230 + 0.668316i
\(676\) −1.87770 13.5515i −0.0722192 0.521213i
\(677\) 6.23807 10.8046i 0.239748 0.415256i −0.720894 0.693046i \(-0.756268\pi\)
0.960642 + 0.277789i \(0.0896017\pi\)
\(678\) −10.2053 28.6030i −0.391932 1.09849i
\(679\) 0.559955 0.323290i 0.0214891 0.0124067i
\(680\) −0.498524 + 9.00984i −0.0191175 + 0.345511i
\(681\) −30.0416 + 17.8315i −1.15120 + 0.683304i
\(682\) −16.6022 + 5.69856i −0.635731 + 0.218209i
\(683\) 7.01037i 0.268244i 0.990965 + 0.134122i \(0.0428214\pi\)
−0.990965 + 0.134122i \(0.957179\pi\)
\(684\) 11.4839 + 4.34583i 0.439097 + 0.166167i
\(685\) 6.96420i 0.266088i
\(686\) 0.459123 + 1.33761i 0.0175294 + 0.0510703i
\(687\) −0.0509905 4.22394i −0.00194541 0.161153i
\(688\) −2.15707 2.09932i −0.0822374 0.0800357i
\(689\) −1.96387 + 1.13384i −0.0748174 + 0.0431959i
\(690\) −2.94087 2.49970i −0.111957 0.0951619i
\(691\) −18.6471 + 32.2977i −0.709369 + 1.22866i 0.255723 + 0.966750i \(0.417687\pi\)
−0.965092 + 0.261913i \(0.915647\pi\)
\(692\) −2.87234 20.7299i −0.109190 0.788034i
\(693\) 7.26022 13.3069i 0.275793 0.505489i
\(694\) −5.24214 + 6.01857i −0.198989 + 0.228462i
\(695\) −11.3582 + 19.6730i −0.430842 + 0.746241i
\(696\) 3.07703 + 0.133021i 0.116634 + 0.00504215i
\(697\) −5.76344 9.98258i −0.218306 0.378117i
\(698\) 40.8295 + 7.97763i 1.54542 + 0.301958i
\(699\) 43.6376 + 24.4967i 1.65053 + 0.926549i
\(700\) −2.84711 + 7.00761i −0.107611 + 0.264863i
\(701\) −10.0719 −0.380412 −0.190206 0.981744i \(-0.560916\pi\)
−0.190206 + 0.981744i \(0.560916\pi\)
\(702\) 20.5904 25.4445i 0.777135 0.960340i
\(703\) 19.3309i 0.729079i
\(704\) −4.45966 + 40.1764i −0.168080 + 1.51420i
\(705\) −9.29761 + 16.5625i −0.350168 + 0.623779i
\(706\) 29.3398 + 5.73268i 1.10422 + 0.215752i
\(707\) −7.46018 + 4.30714i −0.280569 + 0.161987i
\(708\) −27.6452 34.6549i −1.03897 1.30241i
\(709\) 20.2799 + 11.7086i 0.761626 + 0.439725i 0.829879 0.557943i \(-0.188409\pi\)
−0.0682530 + 0.997668i \(0.521743\pi\)
\(710\) 6.08469 + 5.29973i 0.228354 + 0.198895i
\(711\) −0.851689 35.2709i −0.0319408 1.32276i
\(712\) −15.7203 10.2742i −0.589144 0.385040i
\(713\) −3.03718 1.75352i −0.113743 0.0656698i
\(714\) −5.39513 4.58578i −0.201908 0.171619i
\(715\) −12.4199 21.5119i −0.464479 0.804501i
\(716\) −4.03431 5.18442i −0.150769 0.193751i
\(717\) 24.4851 0.295579i 0.914412 0.0110386i
\(718\) −15.4204 + 5.29291i −0.575483 + 0.197529i
\(719\) 51.2688 1.91201 0.956003 0.293358i \(-0.0947729\pi\)
0.956003 + 0.293358i \(0.0947729\pi\)
\(720\) −9.71121 9.00509i −0.361915 0.335600i
\(721\) 6.83364 0.254498
\(722\) 19.8128 6.80057i 0.737356 0.253091i
\(723\) −19.7796 33.3237i −0.735610 1.23932i
\(724\) −27.3699 35.1726i −1.01719 1.30718i
\(725\) −1.18882 2.05910i −0.0441517 0.0764730i
\(726\) −33.5253 + 11.9615i −1.24424 + 0.443934i
\(727\) −23.7413 13.7071i −0.880517 0.508367i −0.00968817 0.999953i \(-0.503084\pi\)
−0.870829 + 0.491586i \(0.836417\pi\)
\(728\) 6.89244 10.5460i 0.255451 0.390861i
\(729\) 26.9292 1.95382i 0.997378 0.0723639i
\(730\) −3.61420 3.14795i −0.133768 0.116511i
\(731\) −1.88382 1.08762i −0.0696756 0.0402272i
\(732\) 2.19380 5.59225i 0.0810851 0.206695i
\(733\) 38.7813 22.3904i 1.43242 0.827009i 0.435116 0.900374i \(-0.356707\pi\)
0.997305 + 0.0733653i \(0.0233739\pi\)
\(734\) −18.3480 3.58499i −0.677236 0.132324i
\(735\) 0.975705 + 1.64382i 0.0359894 + 0.0606333i
\(736\) −6.63826 + 4.60026i −0.244689 + 0.169568i
\(737\) 24.8462i 0.915220i
\(738\) 16.6774 + 2.84245i 0.613902 + 0.104632i
\(739\) −36.2365 −1.33298 −0.666491 0.745513i \(-0.732205\pi\)
−0.666491 + 0.745513i \(0.732205\pi\)
\(740\) 7.84826 19.3170i 0.288508 0.710106i
\(741\) 0.190580 + 15.7872i 0.00700112 + 0.579957i
\(742\) −0.706618 0.138065i −0.0259408 0.00506853i
\(743\) 2.11326 + 3.66028i 0.0775281 + 0.134283i 0.902183 0.431354i \(-0.141964\pi\)
−0.824655 + 0.565636i \(0.808631\pi\)
\(744\) −10.1519 6.46137i −0.372188 0.236885i
\(745\) −11.3668 + 19.6879i −0.416449 + 0.721310i
\(746\) 19.1768 22.0171i 0.702112 0.806104i
\(747\) 0.467886 + 19.3765i 0.0171190 + 0.708949i
\(748\) 4.00941 + 28.9363i 0.146599 + 1.05802i
\(749\) −8.75844 + 15.1701i −0.320026 + 0.554302i
\(750\) −4.27105 + 23.3537i −0.155957 + 0.852755i
\(751\) 13.9626 8.06131i 0.509503 0.294162i −0.223127 0.974789i \(-0.571626\pi\)
0.732629 + 0.680628i \(0.238293\pi\)
\(752\) 28.4823 + 27.7197i 1.03864 + 1.01083i
\(753\) 7.34829 + 4.12508i 0.267787 + 0.150326i
\(754\) 1.28569 + 3.74574i 0.0468221 + 0.136412i
\(755\) 19.5369i 0.711021i
\(756\) 10.2356 1.79809i 0.372264 0.0653960i
\(757\) 0.476439i 0.0173165i 0.999963 + 0.00865824i \(0.00275604\pi\)
−0.999963 + 0.00865824i \(0.997244\pi\)
\(758\) −4.54632 + 1.56048i −0.165130 + 0.0566793i
\(759\) −10.8958 6.11655i −0.395494 0.222017i
\(760\) 6.37842 + 0.352925i 0.231370 + 0.0128019i
\(761\) −14.0087 + 8.08794i −0.507816 + 0.293188i −0.731935 0.681374i \(-0.761383\pi\)
0.224120 + 0.974562i \(0.428049\pi\)
\(762\) −29.5964 5.41276i −1.07216 0.196084i
\(763\) 9.35250 16.1990i 0.338583 0.586443i
\(764\) −3.33263 24.0519i −0.120570 0.870167i
\(765\) −8.40183 4.58401i −0.303769 0.165735i
\(766\) 20.5078 + 17.8621i 0.740976 + 0.645385i
\(767\) 28.5011 49.3653i 1.02911 1.78248i
\(768\) −23.4385 + 14.7864i −0.845763 + 0.533560i
\(769\) 6.02178 + 10.4300i 0.217151 + 0.376117i 0.953936 0.300011i \(-0.0969903\pi\)
−0.736785 + 0.676127i \(0.763657\pi\)
\(770\) 1.51235 7.74020i 0.0545012 0.278937i
\(771\) −0.421069 34.8804i −0.0151644 1.25619i
\(772\) 45.1172 + 18.3306i 1.62380 + 0.659733i
\(773\) −34.3563 −1.23571 −0.617856 0.786291i \(-0.711999\pi\)
−0.617856 + 0.786291i \(0.711999\pi\)
\(774\) 2.99375 1.10906i 0.107608 0.0398644i
\(775\) 9.28991i 0.333703i
\(776\) −0.825507 1.63189i −0.0296340 0.0585815i
\(777\) 8.35100 + 14.0694i 0.299590 + 0.504736i
\(778\) −5.46065 + 27.9476i −0.195774 + 1.00197i
\(779\) −7.06707 + 4.08017i −0.253204 + 0.146187i
\(780\) 6.21909 15.8532i 0.222679 0.567635i
\(781\) 22.6229 + 13.0613i 0.809511 + 0.467372i
\(782\) −3.83346 + 4.40124i −0.137084 + 0.157388i
\(783\) −1.52986 + 2.88635i −0.0546729 + 0.103150i
\(784\) 3.84930 1.08760i 0.137475 0.0388428i
\(785\) −16.6520 9.61405i −0.594336 0.343140i
\(786\) 18.6695 + 52.3261i 0.665919 + 1.86641i
\(787\) −16.0580 27.8133i −0.572406 0.991436i −0.996318 0.0857330i \(-0.972677\pi\)
0.423912 0.905703i \(-0.360657\pi\)
\(788\) 13.4050 10.4312i 0.477532 0.371597i
\(789\) −20.8284 35.0907i −0.741510 1.24926i
\(790\) −5.95914 17.3614i −0.212017 0.617690i
\(791\) 12.3981 0.440826
\(792\) −36.4457 22.5830i −1.29504 0.802452i
\(793\) 7.72423 0.274295
\(794\) −6.03820 17.5917i −0.214288 0.624306i
\(795\) −0.973121 + 0.0117473i −0.0345130 + 0.000416634i
\(796\) −29.5178 37.9328i −1.04623 1.34449i
\(797\) 20.0884 + 34.7941i 0.711566 + 1.23247i 0.964269 + 0.264925i \(0.0853473\pi\)
−0.252703 + 0.967544i \(0.581319\pi\)
\(798\) −3.24646 + 3.81943i −0.114923 + 0.135206i
\(799\) 24.8743 + 14.3612i 0.879988 + 0.508062i
\(800\) 19.3453 + 9.13556i 0.683961 + 0.322991i
\(801\) 17.0050 10.3731i 0.600843 0.366515i
\(802\) −3.44773 + 3.95839i −0.121744 + 0.139776i
\(803\) −13.4376 7.75822i −0.474204 0.273782i
\(804\) −13.3159 + 10.6224i −0.469614 + 0.374624i
\(805\) 1.36461 0.787857i 0.0480961 0.0277683i
\(806\) 2.96723 15.1863i 0.104516 0.534914i
\(807\) 2.14109 3.81408i 0.0753701 0.134262i
\(808\) 10.9981 + 21.7414i 0.386911 + 0.764860i
\(809\) 14.8351i 0.521575i −0.965396 0.260788i \(-0.916018\pi\)
0.965396 0.260788i \(-0.0839822\pi\)
\(810\) 13.0507 5.19638i 0.458556 0.182582i
\(811\) −5.81300 −0.204122 −0.102061 0.994778i \(-0.532544\pi\)
−0.102061 + 0.994778i \(0.532544\pi\)
\(812\) −0.473281 + 1.16489i −0.0166089 + 0.0408796i
\(813\) 42.3073 + 23.7499i 1.48378 + 0.832944i
\(814\) 12.9441 66.2478i 0.453690 2.32199i
\(815\) 8.59841 + 14.8929i 0.301189 + 0.521675i
\(816\) −13.7938 + 14.5199i −0.482879 + 0.508297i
\(817\) −0.769973 + 1.33363i −0.0269379 + 0.0466579i
\(818\) 0.492699 + 0.429138i 0.0172268 + 0.0150045i
\(819\) 6.95882 + 11.4079i 0.243161 + 0.398623i
\(820\) 8.71851 1.20803i 0.304463 0.0421864i
\(821\) 16.6085 28.7668i 0.579642 1.00397i −0.415878 0.909420i \(-0.636526\pi\)
0.995520 0.0945492i \(-0.0301410\pi\)
\(822\) −10.0103 + 11.7771i −0.349151 + 0.410773i
\(823\) −29.8670 + 17.2437i −1.04110 + 0.601078i −0.920144 0.391580i \(-0.871929\pi\)
−0.120954 + 0.992658i \(0.538595\pi\)
\(824\) 1.06783 19.2989i 0.0371996 0.672310i
\(825\) 0.399536 + 33.0967i 0.0139101 + 1.15228i
\(826\) 17.1177 5.87549i 0.595601 0.204435i
\(827\) 5.17402i 0.179918i 0.995945 + 0.0899592i \(0.0286737\pi\)
−0.995945 + 0.0899592i \(0.971326\pi\)
\(828\) −1.38021 8.45443i −0.0479657 0.293812i
\(829\) 13.7946i 0.479107i 0.970883 + 0.239553i \(0.0770010\pi\)
−0.970883 + 0.239553i \(0.922999\pi\)
\(830\) 3.27373 + 9.53769i 0.113633 + 0.331058i
\(831\) −28.3878 + 16.8498i −0.984761 + 0.584514i
\(832\) −28.7060 21.1129i −0.995203 0.731959i
\(833\) 2.50342 1.44535i 0.0867384 0.0500784i
\(834\) −47.4858 + 16.9425i −1.64430 + 0.586672i
\(835\) −0.984755 + 1.70565i −0.0340789 + 0.0590263i
\(836\) 20.4852 2.83842i 0.708495 0.0981689i
\(837\) 10.8154 6.77789i 0.373835 0.234278i
\(838\) −7.26173 + 8.33729i −0.250852 + 0.288007i
\(839\) −5.68556 + 9.84768i −0.196287 + 0.339980i −0.947322 0.320283i \(-0.896222\pi\)
0.751034 + 0.660263i \(0.229555\pi\)
\(840\) 4.79479 2.49863i 0.165436 0.0862110i
\(841\) 14.3024 + 24.7724i 0.493186 + 0.854222i
\(842\) 30.1392 + 5.88886i 1.03866 + 0.202943i
\(843\) −32.7293 + 19.4268i −1.12726 + 0.669093i
\(844\) −8.03184 3.26325i −0.276467 0.112326i
\(845\) 7.54955 0.259712
\(846\) −39.5300 + 14.6442i −1.35907 + 0.503479i
\(847\) 14.5317i 0.499316i
\(848\) −0.500328 + 1.97399i −0.0171813 + 0.0677871i
\(849\) −1.47147 + 0.0177633i −0.0505009 + 0.000609635i
\(850\) 15.1739 + 2.96482i 0.520462 + 0.101692i
\(851\) 11.6796 6.74322i 0.400371 0.231155i
\(852\) 2.67192 + 17.7084i 0.0915384 + 0.606681i
\(853\) −2.92490 1.68869i −0.100147 0.0578197i 0.449090 0.893486i \(-0.351748\pi\)
−0.549237 + 0.835667i \(0.685082\pi\)
\(854\) 1.84930 + 1.61073i 0.0632816 + 0.0551179i
\(855\) −3.24521 + 5.94799i −0.110984 + 0.203417i
\(856\) 41.4733 + 27.1053i 1.41753 + 0.926439i
\(857\) 29.3238 + 16.9301i 1.00168 + 0.578321i 0.908745 0.417351i \(-0.137042\pi\)
0.0929358 + 0.995672i \(0.470375\pi\)
\(858\) 9.91808 54.2310i 0.338598 1.85142i
\(859\) −0.105328 0.182433i −0.00359373 0.00622453i 0.864223 0.503109i \(-0.167811\pi\)
−0.867817 + 0.496885i \(0.834477\pi\)
\(860\) 1.31087 1.02007i 0.0447002 0.0347839i
\(861\) −3.38089 + 6.02261i −0.115220 + 0.205250i
\(862\) −25.4595 + 8.73875i −0.867154 + 0.297643i
\(863\) 7.00845 0.238570 0.119285 0.992860i \(-0.461940\pi\)
0.119285 + 0.992860i \(0.461940\pi\)
\(864\) −3.47859 29.1873i −0.118344 0.992973i
\(865\) 11.5486 0.392665
\(866\) −1.89529 + 0.650542i −0.0644047 + 0.0221063i
\(867\) 7.32874 13.0552i 0.248897 0.443378i
\(868\) 3.87718 3.01707i 0.131600 0.102406i
\(869\) −29.7120 51.4627i −1.00791 1.74575i
\(870\) −0.305756 + 1.67184i −0.0103661 + 0.0566807i
\(871\) −18.9682 10.9513i −0.642713 0.371071i
\(872\) −44.2863 28.9437i −1.49972 0.980158i
\(873\) 1.93918 0.0468254i 0.0656312 0.00158480i
\(874\) 3.11582 + 2.71386i 0.105394 + 0.0917976i
\(875\) −8.39371 4.84611i −0.283759 0.163829i
\(876\) −1.58708 10.5185i −0.0536223 0.355388i
\(877\) 29.1484 16.8288i 0.984270 0.568269i 0.0807135 0.996737i \(-0.474280\pi\)
0.903557 + 0.428469i \(0.140947\pi\)
\(878\) −26.7687 5.23030i −0.903399 0.176514i
\(879\) −38.2433 + 0.461665i −1.28991 + 0.0155716i
\(880\) −21.6228 5.48052i −0.728905 0.184748i
\(881\) 14.4562i 0.487043i 0.969896 + 0.243521i \(0.0783026\pi\)
−0.969896 + 0.243521i \(0.921697\pi\)
\(882\) −0.712826 + 4.18233i −0.0240021 + 0.140826i
\(883\) 16.9272 0.569646 0.284823 0.958580i \(-0.408065\pi\)
0.284823 + 0.958580i \(0.408065\pi\)
\(884\) −23.8580 9.69322i −0.802430 0.326018i
\(885\) 21.0363 12.4863i 0.707128 0.419722i
\(886\) 40.9988 + 8.01070i 1.37738 + 0.269125i
\(887\) −1.09959 1.90454i −0.0369205 0.0639482i 0.846975 0.531633i \(-0.178421\pi\)
−0.883895 + 0.467685i \(0.845088\pi\)
\(888\) 41.0383 21.3856i 1.37716 0.717655i
\(889\) 6.14154 10.6375i 0.205981 0.356769i
\(890\) 6.80652 7.81465i 0.228155 0.261948i
\(891\) 38.2400 24.6124i 1.28109 0.824546i
\(892\) −30.5571 + 4.23398i −1.02313 + 0.141764i
\(893\) 10.1668 17.6095i 0.340221 0.589279i
\(894\) −47.5218 + 16.9554i −1.58937 + 0.567072i
\(895\) 3.13937 1.81252i 0.104938 0.0605858i
\(896\) −2.47000 11.0408i −0.0825168 0.368847i
\(897\) 9.47203 5.62221i 0.316262 0.187720i
\(898\) −1.10730 3.22600i −0.0369509 0.107653i
\(899\) 1.54428i 0.0515047i
\(900\) −17.5668 + 14.3639i −0.585560 + 0.478796i
\(901\) 1.47166i 0.0490282i
\(902\) 26.9513 9.25078i 0.897379 0.308017i
\(903\) 0.0157328 + 1.30327i 0.000523555 + 0.0433701i
\(904\) 1.93734 35.0136i 0.0644350 1.16454i
\(905\) 21.2984 12.2966i 0.707983 0.408754i
\(906\) −28.0824 + 33.0387i −0.932975 + 1.09764i
\(907\) 14.9355 25.8690i 0.495925 0.858967i −0.504064 0.863666i \(-0.668163\pi\)
0.999989 + 0.00469938i \(0.00149587\pi\)
\(908\) −39.9578 + 5.53655i −1.32605 + 0.183737i
\(909\) −25.8353 + 0.623847i −0.856903 + 0.0206917i
\(910\) 5.24248 + 4.56617i 0.173786 + 0.151367i
\(911\) −27.0077 + 46.7787i −0.894806 + 1.54985i −0.0607608 + 0.998152i \(0.519353\pi\)
−0.834045 + 0.551697i \(0.813981\pi\)
\(912\) 10.2792 + 9.76518i 0.340378 + 0.323357i
\(913\) 16.3226 + 28.2716i 0.540200 + 0.935655i
\(914\) −7.28131 + 37.2657i −0.240844 + 1.23264i
\(915\) 2.89059 + 1.62268i 0.0955601 + 0.0536442i
\(916\) 1.83602 4.51900i 0.0606638 0.149312i
\(917\) −22.6810 −0.748994
\(918\) −7.61918 19.8288i −0.251470 0.654447i
\(919\) 48.1303i 1.58767i −0.608132 0.793836i \(-0.708081\pi\)
0.608132 0.793836i \(-0.291919\pi\)
\(920\) −2.01176 3.97691i −0.0663257 0.131115i
\(921\) 1.35029 2.40536i 0.0444934 0.0792592i
\(922\) 7.80851 39.9640i 0.257160 1.31614i
\(923\) −19.9427 + 11.5139i −0.656423 + 0.378986i
\(924\) 13.6833 10.9155i 0.450147 0.359094i
\(925\) −30.9385 17.8623i −1.01725 0.587310i
\(926\) −9.34161 + 10.7252i −0.306985 + 0.352453i
\(927\) 17.9966 + 9.81888i 0.591085 + 0.322494i
\(928\) 3.21582 + 1.51862i 0.105564 + 0.0498513i
\(929\) 11.9516 + 6.90027i 0.392120 + 0.226391i 0.683078 0.730345i \(-0.260641\pi\)
−0.290958 + 0.956736i \(0.593974\pi\)
\(930\) 4.30070 5.05973i 0.141025 0.165915i
\(931\) −1.02322 1.77227i −0.0335347 0.0580838i
\(932\) 35.4874 + 45.6042i 1.16243 + 1.49382i
\(933\) −10.5697 + 0.127595i −0.346037 + 0.00417729i
\(934\) 3.43942 + 10.0204i 0.112541 + 0.327878i
\(935\) −16.1204 −0.527193
\(936\) 33.3044 17.8698i 1.08859 0.584094i
\(937\) 17.4540 0.570198 0.285099 0.958498i \(-0.407974\pi\)
0.285099 + 0.958498i \(0.407974\pi\)
\(938\) −2.25761 6.57733i −0.0737136 0.214757i
\(939\) −3.72976 6.28373i −0.121716 0.205062i
\(940\) −17.3089 + 13.4691i −0.564554 + 0.439314i
\(941\) 12.8593 + 22.2730i 0.419202 + 0.726078i 0.995859 0.0909074i \(-0.0289767\pi\)
−0.576658 + 0.816986i \(0.695643\pi\)
\(942\) −14.3408 40.1939i −0.467249 1.30959i
\(943\) 4.93042 + 2.84658i 0.160557 + 0.0926975i
\(944\) −13.9182 49.2603i −0.452999 1.60329i
\(945\) 0.207630 + 5.73099i 0.00675422 + 0.186429i
\(946\) 3.53174 4.05484i 0.114827 0.131834i
\(947\) 24.0210 + 13.8686i 0.780579 + 0.450667i 0.836635 0.547760i \(-0.184519\pi\)
−0.0560565 + 0.998428i \(0.517853\pi\)
\(948\) 14.8778 37.9253i 0.483209 1.23176i
\(949\) 11.8457 6.83909i 0.384526 0.222006i
\(950\) 2.09891 10.7422i 0.0680977 0.348524i
\(951\) 14.2724 + 24.0454i 0.462814 + 0.779726i
\(952\) −3.69064 7.29578i −0.119614 0.236458i
\(953\) 22.4861i 0.728397i −0.931321 0.364198i \(-0.881343\pi\)
0.931321 0.364198i \(-0.118657\pi\)
\(954\) −1.66252 1.37890i −0.0538261 0.0446435i
\(955\) 13.3993 0.433590
\(956\) 26.1955 + 10.6429i 0.847223 + 0.344217i
\(957\) 0.0664158 + 5.50174i 0.00214692 + 0.177846i
\(958\) −0.449698 + 2.30155i −0.0145291 + 0.0743598i
\(959\) −3.15507 5.46474i −0.101882 0.176466i
\(960\) −6.30716 13.9315i −0.203563 0.449636i
\(961\) −12.4831 + 21.6214i −0.402681 + 0.697463i
\(962\) 44.8700 + 39.0815i 1.44667 + 1.26004i
\(963\) −44.8626 + 27.3663i −1.44568 + 0.881866i
\(964\) −6.14142 44.3232i −0.197802 1.42756i
\(965\) −13.4366 + 23.2730i −0.432541 + 0.749183i
\(966\) 3.44014 + 0.629152i 0.110685 + 0.0202426i
\(967\) −2.79666 + 1.61465i −0.0899344 + 0.0519237i −0.544293 0.838895i \(-0.683202\pi\)
0.454358 + 0.890819i \(0.349869\pi\)
\(968\) −41.0391 2.27074i −1.31905 0.0729843i
\(969\) 8.93467 + 5.01562i 0.287023 + 0.161125i
\(970\) 0.954521 0.327631i 0.0306478 0.0105196i
\(971\) 40.0685i 1.28586i 0.765925 + 0.642930i \(0.222281\pi\)
−0.765925 + 0.642930i \(0.777719\pi\)
\(972\) 29.5392 + 9.97160i 0.947472 + 0.319839i
\(973\) 20.5830i 0.659860i
\(974\) 4.97364 + 14.4902i 0.159366 + 0.464296i
\(975\) −25.4430 14.2828i −0.814828 0.457417i
\(976\) 4.83783 4.97092i 0.154855 0.159115i
\(977\) 14.0968 8.13881i 0.450998 0.260384i −0.257254 0.966344i \(-0.582818\pi\)
0.708252 + 0.705960i \(0.249484\pi\)
\(978\) −6.86636 + 37.5446i −0.219562 + 1.20054i
\(979\) 16.7749 29.0549i 0.536127 0.928600i
\(980\) 0.302950 + 2.18642i 0.00967737 + 0.0698426i
\(981\) 47.9055 29.2225i 1.52951 0.933001i
\(982\) 9.93137 11.4023i 0.316923 0.363863i
\(983\) −17.0746 + 29.5741i −0.544596 + 0.943267i 0.454037 + 0.890983i \(0.349983\pi\)
−0.998632 + 0.0522842i \(0.983350\pi\)
\(984\) 16.4802 + 10.4891i 0.525370 + 0.334380i
\(985\) 4.68650 + 8.11725i 0.149324 + 0.258637i
\(986\) 2.52240 + 0.492848i 0.0803295 + 0.0156955i
\(987\) −0.207739 17.2086i −0.00661239 0.547756i
\(988\) −6.86222 + 16.8900i −0.218316 + 0.537343i
\(989\) 1.07436 0.0341627
\(990\) 15.1043 18.2110i 0.480045 0.578784i
\(991\) 48.3771i 1.53675i 0.640000 + 0.768375i \(0.278934\pi\)
−0.640000 + 0.768375i \(0.721066\pi\)
\(992\) −7.91468 11.4210i −0.251291 0.362618i
\(993\) 25.9437 + 43.7087i 0.823298 + 1.38705i
\(994\) −7.17558 1.40203i −0.227596 0.0444697i
\(995\) 22.9698 13.2616i 0.728193 0.420422i
\(996\) −8.17331 + 20.8347i −0.258981 + 0.660174i
\(997\) −30.0080 17.3251i −0.950362 0.548692i −0.0571687 0.998365i \(-0.518207\pi\)
−0.893193 + 0.449673i \(0.851541\pi\)
\(998\) −3.57343 3.11243i −0.113115 0.0985224i
\(999\) 1.77710 + 49.0512i 0.0562248 + 1.55191i
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 504.2.br.a.155.8 144
8.3 odd 2 inner 504.2.br.a.155.31 yes 144
9.5 odd 6 inner 504.2.br.a.491.31 yes 144
72.59 even 6 inner 504.2.br.a.491.8 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.br.a.155.8 144 1.1 even 1 trivial
504.2.br.a.155.31 yes 144 8.3 odd 2 inner
504.2.br.a.491.8 yes 144 72.59 even 6 inner
504.2.br.a.491.31 yes 144 9.5 odd 6 inner