Properties

Label 930.2.v.a.401.2
Level $930$
Weight $2$
Character 930.401
Analytic conductor $7.426$
Analytic rank $0$
Dimension $80$
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] = [930,2,Mod(401,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.401");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.v (of order \(10\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 401.2
Character \(\chi\) \(=\) 930.401
Dual form 930.2.v.a.821.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 + 0.809017i) q^{2} +(-1.71414 - 0.248453i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.20855 - 1.24073i) q^{6} +(1.53704 + 4.73053i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.87654 + 0.851766i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.809017i) q^{2} +(-1.71414 - 0.248453i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.20855 - 1.24073i) q^{6} +(1.53704 + 4.73053i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.87654 + 0.851766i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-1.90924 - 5.87605i) q^{11} +(0.293405 + 1.70702i) q^{12} +(0.906168 + 1.24723i) q^{13} +(-4.73053 - 1.53704i) q^{14} +(-0.248453 + 1.71414i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.47453 + 4.53813i) q^{17} +(-2.37988 + 1.82652i) q^{18} +(0.335667 + 0.243877i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-1.45939 - 8.49066i) q^{21} +(5.87605 + 1.90924i) q^{22} +(2.47418 - 7.61474i) q^{23} +(-1.55347 - 0.765991i) q^{24} -1.00000 q^{25} -1.54166 q^{26} +(-4.71917 - 2.17473i) q^{27} +(4.02403 - 2.92363i) q^{28} +(1.75623 + 1.27598i) q^{29} +(-1.24073 - 1.20855i) q^{30} +(4.76219 + 2.88471i) q^{31} -1.00000i q^{32} +(1.81279 + 10.5467i) q^{33} +(-2.80472 - 3.86037i) q^{34} +(4.73053 - 1.53704i) q^{35} +(-0.0788226 - 2.99896i) q^{36} +2.89843i q^{37} +(-0.394601 + 0.128214i) q^{38} +(-1.24342 - 2.36307i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-2.52980 + 3.48197i) q^{41} +(7.72690 + 3.81002i) q^{42} +(2.91877 - 4.01734i) q^{43} +(-4.99846 + 3.63160i) q^{44} +(0.851766 - 2.87654i) q^{45} +(4.70617 + 6.47748i) q^{46} +(6.07142 + 8.35659i) q^{47} +(1.53280 - 0.806543i) q^{48} +(-14.3523 + 10.4275i) q^{49} +(0.587785 - 0.809017i) q^{50} +(3.65506 - 7.41264i) q^{51} +(0.906168 - 1.24723i) q^{52} +(-3.37203 + 10.3780i) q^{53} +(4.53325 - 2.53961i) q^{54} +(-5.87605 + 1.90924i) q^{55} +4.97397i q^{56} +(-0.514788 - 0.501436i) q^{57} +(-2.06458 + 0.670821i) q^{58} +(7.94684 + 10.9379i) q^{59} +(1.70702 - 0.293405i) q^{60} +2.73514i q^{61} +(-5.13292 + 2.15710i) q^{62} +(0.392061 + 14.9168i) q^{63} +(0.809017 + 0.587785i) q^{64} +(1.24723 - 0.906168i) q^{65} +(-9.59800 - 4.73263i) q^{66} +11.5154 q^{67} +4.77168 q^{68} +(-6.13299 + 12.4380i) q^{69} +(-1.53704 + 4.73053i) q^{70} +(-5.25039 - 1.70596i) q^{71} +(2.47254 + 1.69898i) q^{72} +(-4.72751 + 1.53606i) q^{73} +(-2.34488 - 1.70365i) q^{74} +(1.71414 + 0.248453i) q^{75} +(0.128214 - 0.394601i) q^{76} +(24.8622 - 18.0635i) q^{77} +(2.64263 + 0.383032i) q^{78} +(2.36777 + 0.769334i) q^{79} +(0.587785 + 0.809017i) q^{80} +(7.54899 + 4.90028i) q^{81} +(-1.32999 - 4.09330i) q^{82} +(4.55277 + 3.30778i) q^{83} +(-7.62412 + 4.01172i) q^{84} +(4.53813 + 1.47453i) q^{85} +(1.53449 + 4.72267i) q^{86} +(-2.69341 - 2.62355i) q^{87} -6.17844i q^{88} +(2.61775 + 8.05661i) q^{89} +(1.82652 + 2.37988i) q^{90} +(-4.50725 + 6.20370i) q^{91} -8.00661 q^{92} +(-7.44634 - 6.12797i) q^{93} -10.3293 q^{94} +(0.243877 - 0.335667i) q^{95} +(-0.248453 + 1.71414i) q^{96} +(-0.828372 - 2.54947i) q^{97} -17.7404i q^{98} +(-0.487001 - 18.5289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 + 0.809017i −0.415627 + 0.572061i
\(3\) −1.71414 0.248453i −0.989658 0.143444i
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) 1.00000i 0.447214i
\(6\) 1.20855 1.24073i 0.493388 0.506526i
\(7\) 1.53704 + 4.73053i 0.580947 + 1.78797i 0.614970 + 0.788550i \(0.289168\pi\)
−0.0340234 + 0.999421i \(0.510832\pi\)
\(8\) 0.951057 + 0.309017i 0.336249 + 0.109254i
\(9\) 2.87654 + 0.851766i 0.958847 + 0.283922i
\(10\) 0.809017 + 0.587785i 0.255834 + 0.185874i
\(11\) −1.90924 5.87605i −0.575659 1.77169i −0.633926 0.773394i \(-0.718558\pi\)
0.0582675 0.998301i \(-0.481442\pi\)
\(12\) 0.293405 + 1.70702i 0.0846987 + 0.492774i
\(13\) 0.906168 + 1.24723i 0.251326 + 0.345920i 0.915975 0.401235i \(-0.131419\pi\)
−0.664649 + 0.747156i \(0.731419\pi\)
\(14\) −4.73053 1.53704i −1.26429 0.410792i
\(15\) −0.248453 + 1.71414i −0.0641503 + 0.442589i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −1.47453 + 4.53813i −0.357626 + 1.10066i 0.596845 + 0.802356i \(0.296421\pi\)
−0.954471 + 0.298303i \(0.903579\pi\)
\(18\) −2.37988 + 1.82652i −0.560944 + 0.430514i
\(19\) 0.335667 + 0.243877i 0.0770074 + 0.0559491i 0.625623 0.780126i \(-0.284845\pi\)
−0.548615 + 0.836075i \(0.684845\pi\)
\(20\) −0.951057 + 0.309017i −0.212663 + 0.0690983i
\(21\) −1.45939 8.49066i −0.318465 1.85281i
\(22\) 5.87605 + 1.90924i 1.25278 + 0.407052i
\(23\) 2.47418 7.61474i 0.515902 1.58778i −0.265733 0.964047i \(-0.585614\pi\)
0.781635 0.623736i \(-0.214386\pi\)
\(24\) −1.55347 0.765991i −0.317100 0.156357i
\(25\) −1.00000 −0.200000
\(26\) −1.54166 −0.302345
\(27\) −4.71917 2.17473i −0.908204 0.418527i
\(28\) 4.02403 2.92363i 0.760470 0.552513i
\(29\) 1.75623 + 1.27598i 0.326124 + 0.236943i 0.738784 0.673942i \(-0.235400\pi\)
−0.412660 + 0.910885i \(0.635400\pi\)
\(30\) −1.24073 1.20855i −0.226525 0.220650i
\(31\) 4.76219 + 2.88471i 0.855315 + 0.518109i
\(32\) 1.00000i 0.176777i
\(33\) 1.81279 + 10.5467i 0.315565 + 1.83595i
\(34\) −2.80472 3.86037i −0.481006 0.662047i
\(35\) 4.73053 1.53704i 0.799605 0.259807i
\(36\) −0.0788226 2.99896i −0.0131371 0.499827i
\(37\) 2.89843i 0.476498i 0.971204 + 0.238249i \(0.0765735\pi\)
−0.971204 + 0.238249i \(0.923426\pi\)
\(38\) −0.394601 + 0.128214i −0.0640127 + 0.0207990i
\(39\) −1.24342 2.36307i −0.199106 0.378394i
\(40\) 0.309017 0.951057i 0.0488599 0.150375i
\(41\) −2.52980 + 3.48197i −0.395088 + 0.543792i −0.959503 0.281699i \(-0.909102\pi\)
0.564415 + 0.825491i \(0.309102\pi\)
\(42\) 7.72690 + 3.81002i 1.19229 + 0.587898i
\(43\) 2.91877 4.01734i 0.445108 0.612639i −0.526229 0.850343i \(-0.676395\pi\)
0.971338 + 0.237704i \(0.0763947\pi\)
\(44\) −4.99846 + 3.63160i −0.753547 + 0.547484i
\(45\) 0.851766 2.87654i 0.126974 0.428810i
\(46\) 4.70617 + 6.47748i 0.693886 + 0.955053i
\(47\) 6.07142 + 8.35659i 0.885608 + 1.21893i 0.974836 + 0.222923i \(0.0715598\pi\)
−0.0892285 + 0.996011i \(0.528440\pi\)
\(48\) 1.53280 0.806543i 0.221241 0.116414i
\(49\) −14.3523 + 10.4275i −2.05032 + 1.48965i
\(50\) 0.587785 0.809017i 0.0831254 0.114412i
\(51\) 3.65506 7.41264i 0.511811 1.03798i
\(52\) 0.906168 1.24723i 0.125663 0.172960i
\(53\) −3.37203 + 10.3780i −0.463184 + 1.42553i 0.398069 + 0.917356i \(0.369681\pi\)
−0.861253 + 0.508177i \(0.830319\pi\)
\(54\) 4.53325 2.53961i 0.616897 0.345597i
\(55\) −5.87605 + 1.90924i −0.792326 + 0.257442i
\(56\) 4.97397i 0.664675i
\(57\) −0.514788 0.501436i −0.0681854 0.0664168i
\(58\) −2.06458 + 0.670821i −0.271092 + 0.0880832i
\(59\) 7.94684 + 10.9379i 1.03459 + 1.42399i 0.901444 + 0.432896i \(0.142508\pi\)
0.133147 + 0.991096i \(0.457492\pi\)
\(60\) 1.70702 0.293405i 0.220375 0.0378784i
\(61\) 2.73514i 0.350199i 0.984551 + 0.175099i \(0.0560247\pi\)
−0.984551 + 0.175099i \(0.943975\pi\)
\(62\) −5.13292 + 2.15710i −0.651882 + 0.273952i
\(63\) 0.392061 + 14.9168i 0.0493951 + 1.87934i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) 1.24723 0.906168i 0.154700 0.112396i
\(66\) −9.59800 4.73263i −1.18143 0.582546i
\(67\) 11.5154 1.40683 0.703417 0.710777i \(-0.251657\pi\)
0.703417 + 0.710777i \(0.251657\pi\)
\(68\) 4.77168 0.578651
\(69\) −6.13299 + 12.4380i −0.738325 + 1.49736i
\(70\) −1.53704 + 4.73053i −0.183712 + 0.565406i
\(71\) −5.25039 1.70596i −0.623107 0.202460i −0.0195876 0.999808i \(-0.506235\pi\)
−0.603519 + 0.797348i \(0.706235\pi\)
\(72\) 2.47254 + 1.69898i 0.291392 + 0.200227i
\(73\) −4.72751 + 1.53606i −0.553313 + 0.179782i −0.572310 0.820037i \(-0.693953\pi\)
0.0189972 + 0.999820i \(0.493953\pi\)
\(74\) −2.34488 1.70365i −0.272586 0.198046i
\(75\) 1.71414 + 0.248453i 0.197932 + 0.0286889i
\(76\) 0.128214 0.394601i 0.0147071 0.0452638i
\(77\) 24.8622 18.0635i 2.83331 2.05852i
\(78\) 2.64263 + 0.383032i 0.299219 + 0.0433698i
\(79\) 2.36777 + 0.769334i 0.266394 + 0.0865568i 0.439169 0.898405i \(-0.355273\pi\)
−0.172774 + 0.984961i \(0.555273\pi\)
\(80\) 0.587785 + 0.809017i 0.0657164 + 0.0904508i
\(81\) 7.54899 + 4.90028i 0.838777 + 0.544476i
\(82\) −1.32999 4.09330i −0.146873 0.452029i
\(83\) 4.55277 + 3.30778i 0.499732 + 0.363076i 0.808915 0.587926i \(-0.200055\pi\)
−0.309183 + 0.951003i \(0.600055\pi\)
\(84\) −7.62412 + 4.01172i −0.831860 + 0.437714i
\(85\) 4.53813 + 1.47453i 0.492230 + 0.159935i
\(86\) 1.53449 + 4.72267i 0.165468 + 0.509259i
\(87\) −2.69341 2.62355i −0.288763 0.281274i
\(88\) 6.17844i 0.658624i
\(89\) 2.61775 + 8.05661i 0.277481 + 0.853999i 0.988552 + 0.150879i \(0.0482103\pi\)
−0.711071 + 0.703120i \(0.751790\pi\)
\(90\) 1.82652 + 2.37988i 0.192532 + 0.250862i
\(91\) −4.50725 + 6.20370i −0.472488 + 0.650325i
\(92\) −8.00661 −0.834747
\(93\) −7.44634 6.12797i −0.772149 0.635441i
\(94\) −10.3293 −1.06539
\(95\) 0.243877 0.335667i 0.0250212 0.0344387i
\(96\) −0.248453 + 1.71414i −0.0253576 + 0.174949i
\(97\) −0.828372 2.54947i −0.0841084 0.258859i 0.900154 0.435572i \(-0.143454\pi\)
−0.984263 + 0.176712i \(0.943454\pi\)
\(98\) 17.7404i 1.79205i
\(99\) −0.487001 18.5289i −0.0489454 1.86223i
\(100\) 0.309017 + 0.951057i 0.0309017 + 0.0951057i
\(101\) 4.39854 + 1.42917i 0.437671 + 0.142208i 0.519561 0.854433i \(-0.326096\pi\)
−0.0818898 + 0.996641i \(0.526096\pi\)
\(102\) 3.84856 + 7.31405i 0.381064 + 0.724198i
\(103\) 9.78248 + 7.10738i 0.963896 + 0.700311i 0.954052 0.299640i \(-0.0968666\pi\)
0.00984364 + 0.999952i \(0.496867\pi\)
\(104\) 0.476401 + 1.46621i 0.0467149 + 0.143774i
\(105\) −8.49066 + 1.45939i −0.828604 + 0.142422i
\(106\) −6.41398 8.82808i −0.622981 0.857459i
\(107\) −13.0750 4.24834i −1.26401 0.410703i −0.401090 0.916039i \(-0.631369\pi\)
−0.862923 + 0.505336i \(0.831369\pi\)
\(108\) −0.609989 + 5.16022i −0.0586962 + 0.496543i
\(109\) 2.99968 2.17939i 0.287317 0.208748i −0.434786 0.900534i \(-0.643176\pi\)
0.722103 + 0.691786i \(0.243176\pi\)
\(110\) 1.90924 5.87605i 0.182039 0.560259i
\(111\) 0.720123 4.96831i 0.0683511 0.471571i
\(112\) −4.02403 2.92363i −0.380235 0.276257i
\(113\) −10.7180 + 3.48250i −1.00827 + 0.327606i −0.766165 0.642644i \(-0.777838\pi\)
−0.242104 + 0.970250i \(0.577838\pi\)
\(114\) 0.708255 0.121736i 0.0663342 0.0114016i
\(115\) −7.61474 2.47418i −0.710078 0.230718i
\(116\) 0.670821 2.06458i 0.0622842 0.191691i
\(117\) 1.54428 + 4.35956i 0.142769 + 0.403042i
\(118\) −13.5200 −1.24461
\(119\) −23.7342 −2.17571
\(120\) −0.765991 + 1.55347i −0.0699251 + 0.141811i
\(121\) −21.9835 + 15.9720i −1.99850 + 1.45200i
\(122\) −2.21278 1.60768i −0.200335 0.145552i
\(123\) 5.20153 5.34004i 0.469006 0.481495i
\(124\) 1.27192 5.42054i 0.114222 0.486778i
\(125\) 1.00000i 0.0894427i
\(126\) −12.2984 8.45067i −1.09563 0.752845i
\(127\) 3.60213 + 4.95791i 0.319637 + 0.439943i 0.938356 0.345669i \(-0.112348\pi\)
−0.618719 + 0.785612i \(0.712348\pi\)
\(128\) −0.951057 + 0.309017i −0.0840623 + 0.0273135i
\(129\) −6.00130 + 6.16110i −0.528385 + 0.542455i
\(130\) 1.54166i 0.135213i
\(131\) 10.1759 3.30634i 0.889070 0.288876i 0.171351 0.985210i \(-0.445187\pi\)
0.717718 + 0.696334i \(0.245187\pi\)
\(132\) 9.47034 4.98318i 0.824287 0.433730i
\(133\) −0.637730 + 1.96273i −0.0552982 + 0.170190i
\(134\) −6.76860 + 9.31618i −0.584718 + 0.804795i
\(135\) −2.17473 + 4.71917i −0.187171 + 0.406161i
\(136\) −2.80472 + 3.86037i −0.240503 + 0.331024i
\(137\) −0.250780 + 0.182202i −0.0214256 + 0.0155666i −0.598447 0.801163i \(-0.704215\pi\)
0.577021 + 0.816729i \(0.304215\pi\)
\(138\) −6.45767 12.2726i −0.549713 1.04471i
\(139\) −3.54416 4.87812i −0.300612 0.413756i 0.631813 0.775121i \(-0.282311\pi\)
−0.932425 + 0.361364i \(0.882311\pi\)
\(140\) −2.92363 4.02403i −0.247092 0.340092i
\(141\) −8.33103 15.8328i −0.701599 1.33336i
\(142\) 4.46625 3.24492i 0.374799 0.272308i
\(143\) 5.59871 7.70596i 0.468187 0.644404i
\(144\) −2.82783 + 1.00170i −0.235652 + 0.0834746i
\(145\) 1.27598 1.75623i 0.105964 0.145847i
\(146\) 1.53606 4.72751i 0.127125 0.391251i
\(147\) 27.1925 14.3084i 2.24280 1.18013i
\(148\) 2.75657 0.895663i 0.226588 0.0736231i
\(149\) 11.1030i 0.909589i −0.890596 0.454795i \(-0.849713\pi\)
0.890596 0.454795i \(-0.150287\pi\)
\(150\) −1.20855 + 1.24073i −0.0986775 + 0.101305i
\(151\) 14.5776 4.73655i 1.18631 0.385455i 0.351601 0.936150i \(-0.385637\pi\)
0.834706 + 0.550695i \(0.185637\pi\)
\(152\) 0.243877 + 0.335667i 0.0197810 + 0.0272262i
\(153\) −8.10697 + 11.7982i −0.655410 + 0.953826i
\(154\) 30.7314i 2.47641i
\(155\) 2.88471 4.76219i 0.231705 0.382508i
\(156\) −1.86318 + 1.91279i −0.149173 + 0.153146i
\(157\) 17.5339 + 12.7391i 1.39936 + 1.01669i 0.994764 + 0.102197i \(0.0325873\pi\)
0.404594 + 0.914496i \(0.367413\pi\)
\(158\) −2.01414 + 1.46336i −0.160237 + 0.116419i
\(159\) 8.35858 16.9516i 0.662878 1.34435i
\(160\) −1.00000 −0.0790569
\(161\) 39.8246 3.13862
\(162\) −8.40160 + 3.22695i −0.660092 + 0.253533i
\(163\) −1.79214 + 5.51565i −0.140372 + 0.432019i −0.996387 0.0849313i \(-0.972933\pi\)
0.856015 + 0.516951i \(0.172933\pi\)
\(164\) 4.09330 + 1.32999i 0.319633 + 0.103855i
\(165\) 10.5467 1.81279i 0.821061 0.141125i
\(166\) −5.35211 + 1.73900i −0.415404 + 0.134973i
\(167\) −9.92944 7.21416i −0.768363 0.558248i 0.133101 0.991102i \(-0.457507\pi\)
−0.901464 + 0.432854i \(0.857507\pi\)
\(168\) 1.23580 8.52607i 0.0953439 0.657801i
\(169\) 3.28277 10.1033i 0.252521 0.777179i
\(170\) −3.86037 + 2.80472i −0.296077 + 0.215112i
\(171\) 0.757835 + 0.987431i 0.0579531 + 0.0755108i
\(172\) −4.72267 1.53449i −0.360100 0.117004i
\(173\) −7.88064 10.8468i −0.599154 0.824665i 0.396476 0.918045i \(-0.370233\pi\)
−0.995631 + 0.0933799i \(0.970233\pi\)
\(174\) 3.70564 0.636930i 0.280924 0.0482856i
\(175\) −1.53704 4.73053i −0.116189 0.357594i
\(176\) 4.99846 + 3.63160i 0.376773 + 0.273742i
\(177\) −10.9044 20.7235i −0.819628 1.55767i
\(178\) −8.05661 2.61775i −0.603868 0.196209i
\(179\) 0.286458 + 0.881626i 0.0214108 + 0.0658958i 0.961191 0.275884i \(-0.0889704\pi\)
−0.939780 + 0.341779i \(0.888970\pi\)
\(180\) −2.99896 + 0.0788226i −0.223530 + 0.00587509i
\(181\) 17.2187i 1.27985i −0.768436 0.639926i \(-0.778965\pi\)
0.768436 0.639926i \(-0.221035\pi\)
\(182\) −2.36960 7.29289i −0.175647 0.540585i
\(183\) 0.679554 4.68841i 0.0502341 0.346577i
\(184\) 4.70617 6.47748i 0.346943 0.477526i
\(185\) 2.89843 0.213097
\(186\) 9.33448 2.42228i 0.684437 0.177610i
\(187\) 29.4815 2.15590
\(188\) 6.07142 8.35659i 0.442804 0.609467i
\(189\) 3.03407 25.6668i 0.220696 1.86699i
\(190\) 0.128214 + 0.394601i 0.00930159 + 0.0286273i
\(191\) 10.8765i 0.786996i 0.919326 + 0.393498i \(0.128735\pi\)
−0.919326 + 0.393498i \(0.871265\pi\)
\(192\) −1.24073 1.20855i −0.0895420 0.0872195i
\(193\) 6.31102 + 19.4233i 0.454277 + 1.39812i 0.871982 + 0.489538i \(0.162835\pi\)
−0.417705 + 0.908583i \(0.637165\pi\)
\(194\) 2.54947 + 0.828372i 0.183041 + 0.0594736i
\(195\) −2.36307 + 1.24342i −0.169223 + 0.0890430i
\(196\) 14.3523 + 10.4275i 1.02516 + 0.744824i
\(197\) 2.27012 + 6.98672i 0.161740 + 0.497783i 0.998781 0.0493559i \(-0.0157169\pi\)
−0.837042 + 0.547139i \(0.815717\pi\)
\(198\) 15.2765 + 10.4970i 1.08565 + 0.745992i
\(199\) −4.77730 6.57539i −0.338654 0.466117i 0.605394 0.795926i \(-0.293016\pi\)
−0.944048 + 0.329809i \(0.893016\pi\)
\(200\) −0.951057 0.309017i −0.0672499 0.0218508i
\(201\) −19.7390 2.86105i −1.39229 0.201803i
\(202\) −3.74162 + 2.71845i −0.263260 + 0.191269i
\(203\) −3.33665 + 10.2691i −0.234187 + 0.720752i
\(204\) −8.17931 1.18554i −0.572666 0.0830043i
\(205\) 3.48197 + 2.52980i 0.243191 + 0.176689i
\(206\) −11.5000 + 3.73657i −0.801242 + 0.260339i
\(207\) 13.6031 19.7967i 0.945478 1.37597i
\(208\) −1.46621 0.476401i −0.101663 0.0330324i
\(209\) 0.792160 2.43802i 0.0547948 0.168641i
\(210\) 3.81002 7.72690i 0.262916 0.533206i
\(211\) −19.2768 −1.32707 −0.663536 0.748145i \(-0.730945\pi\)
−0.663536 + 0.748145i \(0.730945\pi\)
\(212\) 10.9121 0.749447
\(213\) 8.57605 + 4.22872i 0.587621 + 0.289747i
\(214\) 11.1223 8.08082i 0.760305 0.552394i
\(215\) −4.01734 2.91877i −0.273981 0.199058i
\(216\) −3.81617 3.52660i −0.259657 0.239954i
\(217\) −6.32651 + 26.9616i −0.429472 + 1.83027i
\(218\) 3.70781i 0.251124i
\(219\) 8.48524 1.45846i 0.573380 0.0985533i
\(220\) 3.63160 + 4.99846i 0.244842 + 0.336996i
\(221\) −6.99628 + 2.27323i −0.470621 + 0.152914i
\(222\) 3.59617 + 3.50289i 0.241359 + 0.235098i
\(223\) 15.1815i 1.01663i −0.861172 0.508314i \(-0.830269\pi\)
0.861172 0.508314i \(-0.169731\pi\)
\(224\) 4.73053 1.53704i 0.316072 0.102698i
\(225\) −2.87654 0.851766i −0.191769 0.0567844i
\(226\) 3.48250 10.7180i 0.231653 0.712954i
\(227\) −6.92359 + 9.52950i −0.459535 + 0.632495i −0.974412 0.224769i \(-0.927837\pi\)
0.514878 + 0.857264i \(0.327837\pi\)
\(228\) −0.317815 + 0.644545i −0.0210478 + 0.0426860i
\(229\) 4.68042 6.44204i 0.309291 0.425702i −0.625869 0.779928i \(-0.715256\pi\)
0.935160 + 0.354226i \(0.115256\pi\)
\(230\) 6.47748 4.70617i 0.427113 0.310315i
\(231\) −47.1052 + 24.7862i −3.09929 + 1.63081i
\(232\) 1.27598 + 1.75623i 0.0837721 + 0.115302i
\(233\) 7.25371 + 9.98387i 0.475206 + 0.654065i 0.977575 0.210588i \(-0.0675379\pi\)
−0.502369 + 0.864654i \(0.667538\pi\)
\(234\) −4.43466 1.31314i −0.289903 0.0858425i
\(235\) 8.35659 6.07142i 0.545124 0.396056i
\(236\) 7.94684 10.9379i 0.517295 0.711996i
\(237\) −3.86753 1.90702i −0.251223 0.123874i
\(238\) 13.9506 19.2014i 0.904283 1.24464i
\(239\) 1.25885 3.87436i 0.0814285 0.250611i −0.902051 0.431629i \(-0.857939\pi\)
0.983480 + 0.181017i \(0.0579391\pi\)
\(240\) −0.806543 1.53280i −0.0520621 0.0989421i
\(241\) 9.61347 3.12360i 0.619258 0.201209i 0.0174470 0.999848i \(-0.494446\pi\)
0.601811 + 0.798639i \(0.294446\pi\)
\(242\) 27.1731i 1.74676i
\(243\) −11.7225 10.2753i −0.752000 0.659163i
\(244\) 2.60127 0.845205i 0.166529 0.0541087i
\(245\) 10.4275 + 14.3523i 0.666191 + 0.916933i
\(246\) 1.26280 + 7.34692i 0.0805132 + 0.468423i
\(247\) 0.639649i 0.0406999i
\(248\) 3.63769 + 4.21512i 0.230993 + 0.267660i
\(249\) −6.98225 6.80115i −0.442482 0.431005i
\(250\) −0.809017 0.587785i −0.0511667 0.0371748i
\(251\) −7.91101 + 5.74769i −0.499339 + 0.362791i −0.808764 0.588133i \(-0.799863\pi\)
0.309426 + 0.950924i \(0.399863\pi\)
\(252\) 14.0655 4.98240i 0.886045 0.313862i
\(253\) −49.4684 −3.11005
\(254\) −6.12831 −0.384524
\(255\) −7.41264 3.65506i −0.464197 0.228889i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 10.3089 + 3.34957i 0.643053 + 0.208940i 0.612348 0.790588i \(-0.290225\pi\)
0.0307043 + 0.999529i \(0.490225\pi\)
\(258\) −1.45696 8.47656i −0.0907066 0.527727i
\(259\) −13.7111 + 4.45500i −0.851966 + 0.276820i
\(260\) −1.24723 0.906168i −0.0773501 0.0561981i
\(261\) 3.96504 + 5.16631i 0.245430 + 0.319786i
\(262\) −3.30634 + 10.1759i −0.204266 + 0.628667i
\(263\) 9.65517 7.01489i 0.595363 0.432557i −0.248867 0.968538i \(-0.580058\pi\)
0.844230 + 0.535981i \(0.180058\pi\)
\(264\) −1.53505 + 10.5907i −0.0944760 + 0.651813i
\(265\) 10.3780 + 3.37203i 0.637518 + 0.207142i
\(266\) −1.21303 1.66960i −0.0743759 0.102370i
\(267\) −2.48550 14.4605i −0.152110 0.884970i
\(268\) −3.55846 10.9518i −0.217368 0.668989i
\(269\) 11.1253 + 8.08301i 0.678322 + 0.492830i 0.872801 0.488077i \(-0.162301\pi\)
−0.194479 + 0.980907i \(0.562301\pi\)
\(270\) −2.53961 4.53325i −0.154556 0.275885i
\(271\) −28.0531 9.11499i −1.70410 0.553696i −0.714768 0.699361i \(-0.753468\pi\)
−0.989334 + 0.145665i \(0.953468\pi\)
\(272\) −1.47453 4.53813i −0.0894064 0.275165i
\(273\) 9.26738 9.51416i 0.560888 0.575823i
\(274\) 0.309981i 0.0187266i
\(275\) 1.90924 + 5.87605i 0.115132 + 0.354339i
\(276\) 13.7244 + 1.98927i 0.826114 + 0.119740i
\(277\) −4.76140 + 6.55350i −0.286085 + 0.393762i −0.927737 0.373234i \(-0.878249\pi\)
0.641653 + 0.766995i \(0.278249\pi\)
\(278\) 6.02968 0.361636
\(279\) 11.2415 + 12.3543i 0.673013 + 0.739630i
\(280\) 4.97397 0.297252
\(281\) 4.36193 6.00369i 0.260211 0.358150i −0.658843 0.752280i \(-0.728954\pi\)
0.919055 + 0.394130i \(0.128954\pi\)
\(282\) 17.7059 + 2.56635i 1.05437 + 0.152824i
\(283\) −5.43167 16.7170i −0.322879 0.993720i −0.972389 0.233367i \(-0.925026\pi\)
0.649509 0.760354i \(-0.274974\pi\)
\(284\) 5.52059i 0.327587i
\(285\) −0.501436 + 0.514788i −0.0297025 + 0.0304934i
\(286\) 2.94341 + 9.05890i 0.174048 + 0.535664i
\(287\) −20.3599 6.61535i −1.20181 0.390492i
\(288\) 0.851766 2.87654i 0.0501908 0.169502i
\(289\) −4.66713 3.39087i −0.274537 0.199463i
\(290\) 0.670821 + 2.06458i 0.0393920 + 0.121236i
\(291\) 0.786521 + 4.57595i 0.0461067 + 0.268247i
\(292\) 2.92176 + 4.02146i 0.170983 + 0.235338i
\(293\) −20.3437 6.61007i −1.18849 0.386164i −0.352976 0.935632i \(-0.614830\pi\)
−0.835515 + 0.549468i \(0.814830\pi\)
\(294\) −4.40765 + 30.4095i −0.257060 + 1.77352i
\(295\) 10.9379 7.94684i 0.636829 0.462683i
\(296\) −0.895663 + 2.75657i −0.0520594 + 0.160222i
\(297\) −3.76878 + 31.8821i −0.218687 + 1.84999i
\(298\) 8.98248 + 6.52615i 0.520341 + 0.378050i
\(299\) 11.7394 3.81435i 0.678906 0.220590i
\(300\) −0.293405 1.70702i −0.0169397 0.0985548i
\(301\) 23.4904 + 7.63250i 1.35397 + 0.439930i
\(302\) −4.73655 + 14.5776i −0.272558 + 0.838846i
\(303\) −7.18463 3.54263i −0.412746 0.203519i
\(304\) −0.414908 −0.0237966
\(305\) 2.73514 0.156614
\(306\) −4.77977 13.4935i −0.273241 0.771371i
\(307\) −7.47487 + 5.43081i −0.426613 + 0.309953i −0.780293 0.625414i \(-0.784930\pi\)
0.353680 + 0.935366i \(0.384930\pi\)
\(308\) −24.8622 18.0635i −1.41666 1.02926i
\(309\) −15.0027 14.6135i −0.853472 0.831335i
\(310\) 2.15710 + 5.13292i 0.122515 + 0.291530i
\(311\) 10.4798i 0.594255i −0.954838 0.297127i \(-0.903971\pi\)
0.954838 0.297127i \(-0.0960286\pi\)
\(312\) −0.452332 2.63165i −0.0256083 0.148988i
\(313\) 9.99563 + 13.7578i 0.564986 + 0.777637i 0.991950 0.126632i \(-0.0404167\pi\)
−0.426963 + 0.904269i \(0.640417\pi\)
\(314\) −20.6124 + 6.69736i −1.16322 + 0.377954i
\(315\) 14.9168 0.392061i 0.840464 0.0220901i
\(316\) 2.48962i 0.140052i
\(317\) 4.02776 1.30870i 0.226221 0.0735038i −0.193713 0.981058i \(-0.562053\pi\)
0.419934 + 0.907554i \(0.362053\pi\)
\(318\) 8.80108 + 16.7261i 0.493540 + 0.937955i
\(319\) 4.14463 12.7559i 0.232055 0.714191i
\(320\) 0.587785 0.809017i 0.0328582 0.0452254i
\(321\) 21.3569 + 10.5308i 1.19203 + 0.587771i
\(322\) −23.4083 + 32.2188i −1.30450 + 1.79548i
\(323\) −1.60170 + 1.16370i −0.0891207 + 0.0647500i
\(324\) 2.32768 8.69379i 0.129316 0.482988i
\(325\) −0.906168 1.24723i −0.0502652 0.0691840i
\(326\) −3.40886 4.69189i −0.188799 0.259860i
\(327\) −5.68334 + 2.99050i −0.314289 + 0.165375i
\(328\) −3.48197 + 2.52980i −0.192260 + 0.139685i
\(329\) −30.1991 + 41.5654i −1.66493 + 2.29158i
\(330\) −4.73263 + 9.59800i −0.260523 + 0.528353i
\(331\) −4.60862 + 6.34322i −0.253312 + 0.348655i −0.916668 0.399650i \(-0.869132\pi\)
0.663355 + 0.748304i \(0.269132\pi\)
\(332\) 1.73900 5.35211i 0.0954403 0.293735i
\(333\) −2.46878 + 8.33745i −0.135288 + 0.456889i
\(334\) 11.6728 3.79271i 0.638705 0.207528i
\(335\) 11.5154i 0.629155i
\(336\) 6.17136 + 6.01128i 0.336675 + 0.327942i
\(337\) −16.4253 + 5.33692i −0.894745 + 0.290720i −0.720066 0.693905i \(-0.755889\pi\)
−0.174679 + 0.984625i \(0.555889\pi\)
\(338\) 6.24420 + 8.59441i 0.339640 + 0.467474i
\(339\) 19.2375 3.30656i 1.04484 0.179588i
\(340\) 4.77168i 0.258780i
\(341\) 7.85851 33.4905i 0.425562 1.81361i
\(342\) −1.24429 + 0.0327041i −0.0672837 + 0.00176843i
\(343\) −43.2196 31.4009i −2.33364 1.69549i
\(344\) 4.01734 2.91877i 0.216601 0.157370i
\(345\) 12.4380 + 6.13299i 0.669639 + 0.330189i
\(346\) 13.4074 0.720784
\(347\) −13.0825 −0.702307 −0.351154 0.936318i \(-0.614210\pi\)
−0.351154 + 0.936318i \(0.614210\pi\)
\(348\) −1.66283 + 3.37230i −0.0891371 + 0.180774i
\(349\) 2.68402 8.26056i 0.143672 0.442178i −0.853166 0.521640i \(-0.825320\pi\)
0.996838 + 0.0794623i \(0.0253203\pi\)
\(350\) 4.73053 + 1.53704i 0.252857 + 0.0821583i
\(351\) −1.56396 7.85657i −0.0834781 0.419353i
\(352\) −5.87605 + 1.90924i −0.313194 + 0.101763i
\(353\) 11.3776 + 8.26633i 0.605570 + 0.439972i 0.847852 0.530234i \(-0.177896\pi\)
−0.242282 + 0.970206i \(0.577896\pi\)
\(354\) 23.1751 + 3.35908i 1.23174 + 0.178533i
\(355\) −1.70596 + 5.25039i −0.0905427 + 0.278662i
\(356\) 6.85336 4.97926i 0.363227 0.263900i
\(357\) 40.6837 + 5.89683i 2.15321 + 0.312093i
\(358\) −0.881626 0.286458i −0.0465954 0.0151398i
\(359\) −2.21446 3.04794i −0.116875 0.160864i 0.746571 0.665305i \(-0.231699\pi\)
−0.863446 + 0.504441i \(0.831699\pi\)
\(360\) 1.69898 2.47254i 0.0895440 0.130315i
\(361\) −5.81813 17.9064i −0.306217 0.942440i
\(362\) 13.9302 + 10.1209i 0.732154 + 0.531941i
\(363\) 41.6511 21.9163i 2.18612 1.15031i
\(364\) 7.29289 + 2.36960i 0.382251 + 0.124201i
\(365\) 1.53606 + 4.72751i 0.0804011 + 0.247449i
\(366\) 3.39357 + 3.30555i 0.177385 + 0.172784i
\(367\) 15.7839i 0.823910i −0.911204 0.411955i \(-0.864846\pi\)
0.911204 0.411955i \(-0.135154\pi\)
\(368\) 2.47418 + 7.61474i 0.128975 + 0.396946i
\(369\) −10.2429 + 7.86123i −0.533224 + 0.409239i
\(370\) −1.70365 + 2.34488i −0.0885687 + 0.121904i
\(371\) −54.2765 −2.81790
\(372\) −3.52700 + 8.97554i −0.182867 + 0.465360i
\(373\) 10.4998 0.543657 0.271828 0.962346i \(-0.412372\pi\)
0.271828 + 0.962346i \(0.412372\pi\)
\(374\) −17.3288 + 23.8510i −0.896051 + 1.23331i
\(375\) 0.248453 1.71414i 0.0128301 0.0885177i
\(376\) 3.19193 + 9.82376i 0.164611 + 0.506622i
\(377\) 3.34668i 0.172363i
\(378\) 18.9815 + 17.5412i 0.976303 + 0.902221i
\(379\) 2.38916 + 7.35309i 0.122723 + 0.377703i 0.993479 0.114012i \(-0.0363703\pi\)
−0.870756 + 0.491715i \(0.836370\pi\)
\(380\) −0.394601 0.128214i −0.0202426 0.00657721i
\(381\) −4.94274 9.39350i −0.253224 0.481244i
\(382\) −8.79927 6.39304i −0.450210 0.327097i
\(383\) 6.38754 + 19.6588i 0.326388 + 1.00452i 0.970810 + 0.239849i \(0.0770979\pi\)
−0.644422 + 0.764670i \(0.722902\pi\)
\(384\) 1.70702 0.293405i 0.0871109 0.0149728i
\(385\) −18.0635 24.8622i −0.920599 1.26710i
\(386\) −19.4233 6.31102i −0.988621 0.321222i
\(387\) 11.8178 9.06995i 0.600733 0.461051i
\(388\) −2.16871 + 1.57566i −0.110099 + 0.0799919i
\(389\) 7.30062 22.4690i 0.370156 1.13922i −0.576533 0.817074i \(-0.695595\pi\)
0.946689 0.322149i \(-0.104405\pi\)
\(390\) 0.383032 2.64263i 0.0193956 0.133815i
\(391\) 30.9085 + 22.4563i 1.56311 + 1.13566i
\(392\) −16.8721 + 5.48208i −0.852170 + 0.276887i
\(393\) −18.2643 + 3.13930i −0.921313 + 0.158357i
\(394\) −6.98672 2.27012i −0.351986 0.114367i
\(395\) 0.769334 2.36777i 0.0387094 0.119135i
\(396\) −17.4716 + 6.18892i −0.877979 + 0.311005i
\(397\) 26.9416 1.35216 0.676081 0.736827i \(-0.263677\pi\)
0.676081 + 0.736827i \(0.263677\pi\)
\(398\) 8.12762 0.407401
\(399\) 1.58080 3.20595i 0.0791392 0.160498i
\(400\) 0.809017 0.587785i 0.0404508 0.0293893i
\(401\) 30.8503 + 22.4140i 1.54059 + 1.11930i 0.949964 + 0.312358i \(0.101119\pi\)
0.590625 + 0.806946i \(0.298881\pi\)
\(402\) 13.9170 14.2875i 0.694115 0.712598i
\(403\) 0.717438 + 8.55359i 0.0357381 + 0.426085i
\(404\) 4.62490i 0.230097i
\(405\) 4.90028 7.54899i 0.243497 0.375112i
\(406\) −6.34668 8.73545i −0.314980 0.433533i
\(407\) 17.0313 5.53380i 0.844210 0.274300i
\(408\) 5.76680 5.92036i 0.285499 0.293102i
\(409\) 23.8854i 1.18106i −0.807017 0.590529i \(-0.798919\pi\)
0.807017 0.590529i \(-0.201081\pi\)
\(410\) −4.09330 + 1.32999i −0.202154 + 0.0656837i
\(411\) 0.475140 0.250013i 0.0234370 0.0123322i
\(412\) 3.73657 11.5000i 0.184088 0.566564i
\(413\) −39.5274 + 54.4048i −1.94501 + 2.67708i
\(414\) 8.02019 + 22.6413i 0.394171 + 1.11276i
\(415\) 3.30778 4.55277i 0.162373 0.223487i
\(416\) 1.24723 0.906168i 0.0611506 0.0444285i
\(417\) 4.86320 + 9.24232i 0.238152 + 0.452599i
\(418\) 1.50678 + 2.07390i 0.0736989 + 0.101438i
\(419\) −20.8835 28.7436i −1.02022 1.40422i −0.912047 0.410086i \(-0.865499\pi\)
−0.108177 0.994132i \(-0.534501\pi\)
\(420\) 4.01172 + 7.62412i 0.195752 + 0.372019i
\(421\) 10.3621 7.52850i 0.505017 0.366917i −0.305913 0.952060i \(-0.598962\pi\)
0.810930 + 0.585143i \(0.198962\pi\)
\(422\) 11.3306 15.5953i 0.551566 0.759166i
\(423\) 10.3468 + 29.2095i 0.503080 + 1.42022i
\(424\) −6.41398 + 8.82808i −0.311490 + 0.428730i
\(425\) 1.47453 4.53813i 0.0715252 0.220132i
\(426\) −8.46198 + 4.45259i −0.409984 + 0.215729i
\(427\) −12.9387 + 4.20403i −0.626146 + 0.203447i
\(428\) 13.7479i 0.664531i
\(429\) −11.5115 + 11.8181i −0.555782 + 0.570581i
\(430\) 4.72267 1.53449i 0.227747 0.0739996i
\(431\) 24.0560 + 33.1102i 1.15874 + 1.59486i 0.715790 + 0.698316i \(0.246067\pi\)
0.442947 + 0.896548i \(0.353933\pi\)
\(432\) 5.09616 1.01446i 0.245189 0.0488084i
\(433\) 15.4169i 0.740889i −0.928855 0.370445i \(-0.879205\pi\)
0.928855 0.370445i \(-0.120795\pi\)
\(434\) −18.0937 20.9659i −0.868528 1.00639i
\(435\) −2.62355 + 2.69341i −0.125789 + 0.129139i
\(436\) −2.99968 2.17939i −0.143658 0.104374i
\(437\) 2.68756 1.95262i 0.128563 0.0934067i
\(438\) −3.80758 + 7.72196i −0.181933 + 0.368970i
\(439\) −32.0714 −1.53069 −0.765343 0.643622i \(-0.777431\pi\)
−0.765343 + 0.643622i \(0.777431\pi\)
\(440\) −6.17844 −0.294546
\(441\) −50.1667 + 17.7705i −2.38889 + 0.846213i
\(442\) 2.27323 6.99628i 0.108127 0.332779i
\(443\) −17.9621 5.83624i −0.853405 0.277288i −0.150534 0.988605i \(-0.548099\pi\)
−0.702872 + 0.711317i \(0.748099\pi\)
\(444\) −4.94767 + 0.850413i −0.234806 + 0.0403588i
\(445\) 8.05661 2.61775i 0.381920 0.124093i
\(446\) 12.2821 + 8.92346i 0.581574 + 0.422538i
\(447\) −2.75856 + 19.0320i −0.130476 + 0.900183i
\(448\) −1.53704 + 4.73053i −0.0726184 + 0.223496i
\(449\) 0.284048 0.206373i 0.0134050 0.00973933i −0.581063 0.813859i \(-0.697363\pi\)
0.594468 + 0.804120i \(0.297363\pi\)
\(450\) 2.37988 1.82652i 0.112189 0.0861028i
\(451\) 25.2902 + 8.21729i 1.19087 + 0.386937i
\(452\) 6.62412 + 9.11731i 0.311572 + 0.428842i
\(453\) −26.1648 + 4.49725i −1.22933 + 0.211299i
\(454\) −3.63994 11.2026i −0.170831 0.525764i
\(455\) 6.20370 + 4.50725i 0.290834 + 0.211303i
\(456\) −0.334641 0.635972i −0.0156710 0.0297821i
\(457\) −25.1067 8.15765i −1.17444 0.381599i −0.344142 0.938918i \(-0.611830\pi\)
−0.830299 + 0.557319i \(0.811830\pi\)
\(458\) 2.46064 + 7.57308i 0.114978 + 0.353867i
\(459\) 16.8278 18.2095i 0.785453 0.849947i
\(460\) 8.00661i 0.373310i
\(461\) 0.639110 + 1.96698i 0.0297663 + 0.0916114i 0.964836 0.262853i \(-0.0846633\pi\)
−0.935070 + 0.354464i \(0.884663\pi\)
\(462\) 7.63531 52.6779i 0.355227 2.45080i
\(463\) −2.37049 + 3.26270i −0.110166 + 0.151631i −0.860540 0.509383i \(-0.829874\pi\)
0.750374 + 0.661014i \(0.229874\pi\)
\(464\) −2.17082 −0.100778
\(465\) −6.12797 + 7.44634i −0.284178 + 0.345316i
\(466\) −12.3407 −0.571674
\(467\) 5.69016 7.83183i 0.263309 0.362414i −0.656808 0.754058i \(-0.728094\pi\)
0.920117 + 0.391644i \(0.128094\pi\)
\(468\) 3.66898 2.81588i 0.169599 0.130164i
\(469\) 17.6997 + 54.4741i 0.817296 + 2.51538i
\(470\) 10.3293i 0.476456i
\(471\) −26.8905 26.1930i −1.23905 1.20691i
\(472\) 4.17790 + 12.8583i 0.192304 + 0.591850i
\(473\) −29.1787 9.48075i −1.34164 0.435925i
\(474\) 3.81609 2.00798i 0.175279 0.0922296i
\(475\) −0.335667 0.243877i −0.0154015 0.0111898i
\(476\) 7.33426 + 22.5725i 0.336165 + 1.03461i
\(477\) −18.5394 + 26.9807i −0.848863 + 1.23536i
\(478\) 2.39448 + 3.29572i 0.109521 + 0.150743i
\(479\) −14.0772 4.57395i −0.643203 0.208989i −0.0307880 0.999526i \(-0.509802\pi\)
−0.612415 + 0.790537i \(0.709802\pi\)
\(480\) 1.71414 + 0.248453i 0.0782394 + 0.0113403i
\(481\) −3.61501 + 2.62646i −0.164830 + 0.119756i
\(482\) −3.12360 + 9.61347i −0.142276 + 0.437881i
\(483\) −68.2650 9.89456i −3.10616 0.450218i
\(484\) 21.9835 + 15.9720i 0.999251 + 0.725999i
\(485\) −2.54947 + 0.828372i −0.115765 + 0.0376144i
\(486\) 15.2032 3.44403i 0.689633 0.156224i
\(487\) 7.09578 + 2.30556i 0.321541 + 0.104475i 0.465340 0.885132i \(-0.345932\pi\)
−0.143799 + 0.989607i \(0.545932\pi\)
\(488\) −0.845205 + 2.60127i −0.0382606 + 0.117754i
\(489\) 4.44236 9.00933i 0.200891 0.407416i
\(490\) −17.7404 −0.801429
\(491\) 27.7032 1.25023 0.625115 0.780533i \(-0.285052\pi\)
0.625115 + 0.780533i \(0.285052\pi\)
\(492\) −6.68604 3.29679i −0.301430 0.148631i
\(493\) −8.38018 + 6.08855i −0.377424 + 0.274215i
\(494\) −0.517487 0.375976i −0.0232828 0.0169160i
\(495\) −18.5289 + 0.487001i −0.832813 + 0.0218890i
\(496\) −5.54828 + 0.465366i −0.249125 + 0.0208955i
\(497\) 27.4592i 1.23172i
\(498\) 9.60631 1.65115i 0.430469 0.0739897i
\(499\) 7.13113 + 9.81516i 0.319233 + 0.439387i 0.938233 0.346004i \(-0.112462\pi\)
−0.619000 + 0.785391i \(0.712462\pi\)
\(500\) 0.951057 0.309017i 0.0425325 0.0138197i
\(501\) 15.2281 + 14.8331i 0.680339 + 0.662693i
\(502\) 9.77855i 0.436438i
\(503\) −0.819893 + 0.266399i −0.0365572 + 0.0118782i −0.327239 0.944942i \(-0.606118\pi\)
0.290681 + 0.956820i \(0.406118\pi\)
\(504\) −4.23666 + 14.3078i −0.188716 + 0.637322i
\(505\) 1.42917 4.39854i 0.0635973 0.195732i
\(506\) 29.0768 40.0207i 1.29262 1.77914i
\(507\) −8.13733 + 16.5029i −0.361391 + 0.732919i
\(508\) 3.60213 4.95791i 0.159819 0.219972i
\(509\) 8.99676 6.53653i 0.398775 0.289727i −0.370267 0.928925i \(-0.620734\pi\)
0.769042 + 0.639199i \(0.220734\pi\)
\(510\) 7.31405 3.84856i 0.323871 0.170417i
\(511\) −14.5328 20.0026i −0.642891 0.884864i
\(512\) 0.587785 + 0.809017i 0.0259767 + 0.0357538i
\(513\) −1.05370 1.88088i −0.0465222 0.0830429i
\(514\) −8.76929 + 6.37126i −0.386797 + 0.281024i
\(515\) 7.10738 9.78248i 0.313189 0.431067i
\(516\) 7.71406 + 3.80369i 0.339593 + 0.167448i
\(517\) 37.5119 51.6307i 1.64977 2.27072i
\(518\) 4.45500 13.7111i 0.195742 0.602431i
\(519\) 10.8136 + 20.5508i 0.474664 + 0.902082i
\(520\) 1.46621 0.476401i 0.0642976 0.0208916i
\(521\) 6.42111i 0.281314i −0.990058 0.140657i \(-0.955079\pi\)
0.990058 0.140657i \(-0.0449215\pi\)
\(522\) −6.51022 + 0.171110i −0.284945 + 0.00748928i
\(523\) 38.7267 12.5831i 1.69340 0.550219i 0.705965 0.708247i \(-0.250514\pi\)
0.987435 + 0.158028i \(0.0505137\pi\)
\(524\) −6.28903 8.65611i −0.274738 0.378144i
\(525\) 1.45939 + 8.49066i 0.0636929 + 0.370563i
\(526\) 11.9344i 0.520366i
\(527\) −20.1132 + 17.3579i −0.876144 + 0.756120i
\(528\) −7.66578 7.46694i −0.333610 0.324957i
\(529\) −33.2553 24.1614i −1.44588 1.05049i
\(530\) −8.82808 + 6.41398i −0.383467 + 0.278605i
\(531\) 13.5429 + 38.2322i 0.587712 + 1.65913i
\(532\) 2.06374 0.0894744
\(533\) −6.63525 −0.287404
\(534\) 13.1598 + 6.48888i 0.569478 + 0.280801i
\(535\) −4.24834 + 13.0750i −0.183672 + 0.565284i
\(536\) 10.9518 + 3.55846i 0.473047 + 0.153702i
\(537\) −0.271985 1.58240i −0.0117370 0.0682856i
\(538\) −13.0786 + 4.24949i −0.563858 + 0.183209i
\(539\) 88.6747 + 64.4259i 3.81949 + 2.77502i
\(540\) 5.16022 + 0.609989i 0.222061 + 0.0262498i
\(541\) 2.76029 8.49529i 0.118674 0.365241i −0.874022 0.485887i \(-0.838497\pi\)
0.992696 + 0.120646i \(0.0384966\pi\)
\(542\) 23.8634 17.3377i 1.02502 0.744720i
\(543\) −4.27803 + 29.5152i −0.183588 + 1.26662i
\(544\) 4.53813 + 1.47453i 0.194571 + 0.0632199i
\(545\) −2.17939 2.99968i −0.0933549 0.128492i
\(546\) 2.24989 + 13.0898i 0.0962863 + 0.560190i
\(547\) −0.642969 1.97885i −0.0274914 0.0846097i 0.936369 0.351016i \(-0.114164\pi\)
−0.963861 + 0.266406i \(0.914164\pi\)
\(548\) 0.250780 + 0.182202i 0.0107128 + 0.00778330i
\(549\) −2.32970 + 7.86775i −0.0994292 + 0.335787i
\(550\) −5.87605 1.90924i −0.250555 0.0814104i
\(551\) 0.278329 + 0.856608i 0.0118572 + 0.0364927i
\(552\) −9.67637 + 9.93404i −0.411854 + 0.422821i
\(553\) 12.3833i 0.526590i
\(554\) −2.50321 7.70410i −0.106351 0.327316i
\(555\) −4.96831 0.720123i −0.210893 0.0305675i
\(556\) −3.54416 + 4.87812i −0.150306 + 0.206878i
\(557\) −29.1860 −1.23665 −0.618324 0.785923i \(-0.712188\pi\)
−0.618324 + 0.785923i \(0.712188\pi\)
\(558\) −16.6024 + 1.83295i −0.702836 + 0.0775948i
\(559\) 7.65546 0.323791
\(560\) −2.92363 + 4.02403i −0.123546 + 0.170046i
\(561\) −50.5354 7.32478i −2.13361 0.309252i
\(562\) 2.29320 + 7.05776i 0.0967330 + 0.297714i
\(563\) 11.3902i 0.480040i −0.970768 0.240020i \(-0.922846\pi\)
0.970768 0.240020i \(-0.0771541\pi\)
\(564\) −12.4835 + 12.8159i −0.525649 + 0.539646i
\(565\) 3.48250 + 10.7180i 0.146510 + 0.450912i
\(566\) 16.7170 + 5.43167i 0.702666 + 0.228310i
\(567\) −11.5778 + 43.2426i −0.486222 + 1.81602i
\(568\) −4.46625 3.24492i −0.187400 0.136154i
\(569\) −3.64257 11.2107i −0.152704 0.469975i 0.845217 0.534424i \(-0.179471\pi\)
−0.997921 + 0.0644482i \(0.979471\pi\)
\(570\) −0.121736 0.708255i −0.00509896 0.0296655i
\(571\) 13.3757 + 18.4100i 0.559754 + 0.770435i 0.991295 0.131658i \(-0.0420301\pi\)
−0.431541 + 0.902093i \(0.642030\pi\)
\(572\) −9.05890 2.94341i −0.378771 0.123070i
\(573\) 2.70230 18.6438i 0.112890 0.778857i
\(574\) 17.3192 12.5831i 0.722890 0.525210i
\(575\) −2.47418 + 7.61474i −0.103180 + 0.317557i
\(576\) 1.82652 + 2.37988i 0.0761048 + 0.0991618i
\(577\) −19.7210 14.3282i −0.820997 0.596489i 0.0960008 0.995381i \(-0.469395\pi\)
−0.916998 + 0.398892i \(0.869395\pi\)
\(578\) 5.48654 1.78269i 0.228210 0.0741499i
\(579\) −5.99218 34.8623i −0.249026 1.44883i
\(580\) −2.06458 0.670821i −0.0857269 0.0278543i
\(581\) −8.64976 + 26.6212i −0.358852 + 1.10443i
\(582\) −4.16433 2.05337i −0.172617 0.0851148i
\(583\) 67.4198 2.79224
\(584\) −4.97080 −0.205693
\(585\) 4.35956 1.54428i 0.180246 0.0638481i
\(586\) 17.3054 12.5731i 0.714879 0.519390i
\(587\) −22.0050 15.9876i −0.908244 0.659878i 0.0323262 0.999477i \(-0.489708\pi\)
−0.940570 + 0.339600i \(0.889708\pi\)
\(588\) −22.0110 21.4401i −0.907720 0.884175i
\(589\) 0.894998 + 2.12969i 0.0368778 + 0.0877523i
\(590\) 13.5200i 0.556609i
\(591\) −2.15543 12.5402i −0.0886627 0.515836i
\(592\) −1.70365 2.34488i −0.0700197 0.0963738i
\(593\) 36.6070 11.8943i 1.50327 0.488442i 0.562301 0.826933i \(-0.309916\pi\)
0.940970 + 0.338490i \(0.109916\pi\)
\(594\) −23.5780 21.7889i −0.967415 0.894008i
\(595\) 23.7342i 0.973006i
\(596\) −10.5595 + 3.43100i −0.432535 + 0.140539i
\(597\) 6.55527 + 12.4581i 0.268290 + 0.509874i
\(598\) −3.81435 + 11.7394i −0.155981 + 0.480059i
\(599\) −7.82590 + 10.7714i −0.319758 + 0.440109i −0.938393 0.345570i \(-0.887686\pi\)
0.618636 + 0.785678i \(0.287686\pi\)
\(600\) 1.55347 + 0.765991i 0.0634200 + 0.0312714i
\(601\) 0.295682 0.406972i 0.0120611 0.0166007i −0.802944 0.596055i \(-0.796734\pi\)
0.815005 + 0.579454i \(0.196734\pi\)
\(602\) −19.9821 + 14.5179i −0.814411 + 0.591705i
\(603\) 33.1246 + 9.80846i 1.34894 + 0.399431i
\(604\) −9.00945 12.4004i −0.366589 0.504567i
\(605\) 15.9720 + 21.9835i 0.649353 + 0.893757i
\(606\) 7.08907 3.73018i 0.287974 0.151528i
\(607\) 31.2607 22.7122i 1.26883 0.921860i 0.269677 0.962951i \(-0.413083\pi\)
0.999155 + 0.0410906i \(0.0130832\pi\)
\(608\) 0.243877 0.335667i 0.00989050 0.0136131i
\(609\) 8.27087 16.7737i 0.335153 0.679706i
\(610\) −1.60768 + 2.21278i −0.0650929 + 0.0895927i
\(611\) −4.92089 + 15.1450i −0.199078 + 0.612699i
\(612\) 13.7259 + 4.06435i 0.554838 + 0.164292i
\(613\) −26.8487 + 8.72368i −1.08441 + 0.352346i −0.796084 0.605186i \(-0.793099\pi\)
−0.288326 + 0.957532i \(0.593099\pi\)
\(614\) 9.23945i 0.372874i
\(615\) −5.34004 5.20153i −0.215331 0.209746i
\(616\) 29.2273 9.49652i 1.17760 0.382626i
\(617\) −18.6115 25.6166i −0.749273 1.03129i −0.998031 0.0627199i \(-0.980023\pi\)
0.248758 0.968566i \(-0.419977\pi\)
\(618\) 20.6409 3.54780i 0.830300 0.142713i
\(619\) 16.9003i 0.679279i 0.940556 + 0.339639i \(0.110305\pi\)
−0.940556 + 0.339639i \(0.889695\pi\)
\(620\) −5.42054 1.27192i −0.217694 0.0510817i
\(621\) −28.2361 + 30.5546i −1.13307 + 1.22611i
\(622\) 8.47833 + 6.15987i 0.339950 + 0.246988i
\(623\) −34.0884 + 24.7667i −1.36572 + 0.992256i
\(624\) 2.39492 + 1.18090i 0.0958737 + 0.0472739i
\(625\) 1.00000 0.0400000
\(626\) −17.0056 −0.679680
\(627\) −1.96360 + 3.98228i −0.0784188 + 0.159037i
\(628\) 6.69736 20.6124i 0.267254 0.822522i
\(629\) −13.1534 4.27381i −0.524462 0.170408i
\(630\) −8.45067 + 12.2984i −0.336683 + 0.489978i
\(631\) 13.2090 4.29188i 0.525844 0.170857i −0.0340520 0.999420i \(-0.510841\pi\)
0.559896 + 0.828563i \(0.310841\pi\)
\(632\) 2.01414 + 1.46336i 0.0801183 + 0.0582093i
\(633\) 33.0431 + 4.78939i 1.31335 + 0.190361i
\(634\) −1.30870 + 4.02776i −0.0519750 + 0.159963i
\(635\) 4.95791 3.60213i 0.196749 0.142946i
\(636\) −18.7049 2.71115i −0.741696 0.107504i
\(637\) −26.0111 8.45153i −1.03060 0.334862i
\(638\) 7.88356 + 10.8508i 0.312113 + 0.429587i
\(639\) −13.6499 9.37936i −0.539982 0.371042i
\(640\) 0.309017 + 0.951057i 0.0122150 + 0.0375938i
\(641\) 17.9902 + 13.0707i 0.710571 + 0.516260i 0.883358 0.468699i \(-0.155277\pi\)
−0.172787 + 0.984959i \(0.555277\pi\)
\(642\) −21.0729 + 11.0883i −0.831680 + 0.437620i
\(643\) 3.91668 + 1.27261i 0.154459 + 0.0501867i 0.385226 0.922822i \(-0.374124\pi\)
−0.230767 + 0.973009i \(0.574124\pi\)
\(644\) −12.3065 37.8755i −0.484944 1.49250i
\(645\) 6.16110 + 6.00130i 0.242593 + 0.236301i
\(646\) 1.97980i 0.0778944i
\(647\) 3.65270 + 11.2419i 0.143603 + 0.441963i 0.996829 0.0795779i \(-0.0253573\pi\)
−0.853226 + 0.521541i \(0.825357\pi\)
\(648\) 5.66524 + 6.99321i 0.222552 + 0.274719i
\(649\) 49.0991 67.5791i 1.92731 2.65271i
\(650\) 1.54166 0.0604691
\(651\) 17.5432 44.6441i 0.687573 1.74974i
\(652\) 5.79950 0.227126
\(653\) 0.863803 1.18892i 0.0338032 0.0465262i −0.791781 0.610805i \(-0.790846\pi\)
0.825584 + 0.564279i \(0.190846\pi\)
\(654\) 0.921216 6.35569i 0.0360224 0.248527i
\(655\) −3.30634 10.1759i −0.129189 0.397604i
\(656\) 4.30395i 0.168041i
\(657\) −14.9072 + 0.391811i −0.581587 + 0.0152860i
\(658\) −15.8766 48.8631i −0.618934 1.90488i
\(659\) 1.71853 + 0.558384i 0.0669444 + 0.0217515i 0.342298 0.939592i \(-0.388795\pi\)
−0.275353 + 0.961343i \(0.588795\pi\)
\(660\) −4.98318 9.47034i −0.193970 0.368633i
\(661\) 31.3665 + 22.7891i 1.22001 + 0.886392i 0.996101 0.0882168i \(-0.0281168\pi\)
0.223913 + 0.974609i \(0.428117\pi\)
\(662\) −2.42289 7.45690i −0.0941684 0.289821i
\(663\) 12.5574 2.15838i 0.487688 0.0838246i
\(664\) 3.30778 + 4.55277i 0.128367 + 0.176682i
\(665\) 1.96273 + 0.637730i 0.0761115 + 0.0247301i
\(666\) −5.29402 6.89792i −0.205139 0.267289i
\(667\) 14.0615 10.2163i 0.544462 0.395575i
\(668\) −3.79271 + 11.6728i −0.146744 + 0.451633i
\(669\) −3.77189 + 26.0232i −0.145830 + 1.00611i
\(670\) 9.31618 + 6.76860i 0.359915 + 0.261494i
\(671\) 16.0718 5.22205i 0.620446 0.201595i
\(672\) −8.49066 + 1.45939i −0.327534 + 0.0562971i
\(673\) −3.66883 1.19208i −0.141423 0.0459512i 0.237450 0.971400i \(-0.423688\pi\)
−0.378873 + 0.925449i \(0.623688\pi\)
\(674\) 5.33692 16.4253i 0.205570 0.632680i
\(675\) 4.71917 + 2.17473i 0.181641 + 0.0837054i
\(676\) −10.6233 −0.408587
\(677\) −26.4759 −1.01755 −0.508775 0.860900i \(-0.669901\pi\)
−0.508775 + 0.860900i \(0.669901\pi\)
\(678\) −8.63243 + 17.5070i −0.331526 + 0.672351i
\(679\) 10.7871 7.83727i 0.413970 0.300767i
\(680\) 3.86037 + 2.80472i 0.148038 + 0.107556i
\(681\) 14.2356 14.6147i 0.545510 0.560036i
\(682\) 22.4752 + 26.0429i 0.860621 + 0.997233i
\(683\) 9.77710i 0.374110i −0.982349 0.187055i \(-0.940106\pi\)
0.982349 0.187055i \(-0.0598943\pi\)
\(684\) 0.704919 1.02588i 0.0269533 0.0392254i
\(685\) 0.182202 + 0.250780i 0.00696159 + 0.00958181i
\(686\) 50.8077 16.5084i 1.93985 0.630294i
\(687\) −9.62343 + 9.87969i −0.367157 + 0.376934i
\(688\) 4.96571i 0.189316i
\(689\) −15.9995 + 5.19854i −0.609531 + 0.198049i
\(690\) −12.2726 + 6.45767i −0.467209 + 0.245839i
\(691\) −1.49593 + 4.60401i −0.0569080 + 0.175145i −0.975470 0.220132i \(-0.929351\pi\)
0.918562 + 0.395277i \(0.129351\pi\)
\(692\) −7.88064 + 10.8468i −0.299577 + 0.412333i
\(693\) 86.9030 30.7835i 3.30117 1.16937i
\(694\) 7.68972 10.5840i 0.291898 0.401763i
\(695\) −4.87812 + 3.54416i −0.185037 + 0.134438i
\(696\) −1.75086 3.32745i −0.0663662 0.126127i
\(697\) −12.0714 16.6148i −0.457236 0.629331i
\(698\) 5.10531 + 7.02686i 0.193239 + 0.265970i
\(699\) −9.95334 18.9159i −0.376470 0.715467i
\(700\) −4.02403 + 2.92363i −0.152094 + 0.110503i
\(701\) 10.1880 14.0225i 0.384795 0.529624i −0.572052 0.820217i \(-0.693853\pi\)
0.956847 + 0.290593i \(0.0938525\pi\)
\(702\) 7.27538 + 3.35271i 0.274591 + 0.126540i
\(703\) −0.706859 + 0.972907i −0.0266597 + 0.0366939i
\(704\) 1.90924 5.87605i 0.0719573 0.221462i
\(705\) −15.8328 + 8.33103i −0.596298 + 0.313765i
\(706\) −13.3752 + 4.34587i −0.503382 + 0.163559i
\(707\) 23.0041i 0.865159i
\(708\) −16.3395 + 16.7746i −0.614078 + 0.630430i
\(709\) −48.3992 + 15.7259i −1.81767 + 0.590597i −0.817785 + 0.575524i \(0.804798\pi\)
−0.999886 + 0.0150727i \(0.995202\pi\)
\(710\) −3.24492 4.46625i −0.121780 0.167615i
\(711\) 6.15568 + 4.22980i 0.230856 + 0.158630i
\(712\) 8.47122i 0.317472i
\(713\) 33.7488 29.1255i 1.26390 1.09076i
\(714\) −28.6839 + 29.4477i −1.07347 + 1.10205i
\(715\) −7.70596 5.59871i −0.288186 0.209380i
\(716\) 0.749956 0.544875i 0.0280272 0.0203629i
\(717\) −3.12045 + 6.32842i −0.116535 + 0.236339i
\(718\) 3.76747 0.140601
\(719\) 29.0222 1.08235 0.541173 0.840911i \(-0.317980\pi\)
0.541173 + 0.840911i \(0.317980\pi\)
\(720\) 1.00170 + 2.82783i 0.0373310 + 0.105387i
\(721\) −18.5856 + 57.2006i −0.692164 + 2.13026i
\(722\) 17.9064 + 5.81813i 0.666405 + 0.216528i
\(723\) −17.2549 + 2.96579i −0.641716 + 0.110299i
\(724\) −16.3759 + 5.32086i −0.608606 + 0.197748i
\(725\) −1.75623 1.27598i −0.0652249 0.0473886i
\(726\) −6.75125 + 46.5785i −0.250562 + 1.72869i
\(727\) −15.1186 + 46.5301i −0.560716 + 1.72571i 0.119632 + 0.992818i \(0.461829\pi\)
−0.680348 + 0.732889i \(0.738171\pi\)
\(728\) −6.20370 + 4.50725i −0.229924 + 0.167050i
\(729\) 17.5411 + 20.5258i 0.649670 + 0.760216i
\(730\) −4.72751 1.53606i −0.174973 0.0568521i
\(731\) 13.9274 + 19.1695i 0.515124 + 0.709008i
\(732\) −4.66894 + 0.802504i −0.172569 + 0.0296614i
\(733\) 1.91771 + 5.90211i 0.0708323 + 0.217999i 0.980206 0.197981i \(-0.0634384\pi\)
−0.909374 + 0.415981i \(0.863438\pi\)
\(734\) 12.7694 + 9.27751i 0.471327 + 0.342439i
\(735\) −14.3084 27.1925i −0.527772 1.00301i
\(736\) −7.61474 2.47418i −0.280683 0.0911994i
\(737\) −21.9858 67.6652i −0.809856 2.49248i
\(738\) −0.339248 12.9074i −0.0124879 0.475128i
\(739\) 2.85552i 0.105042i 0.998620 + 0.0525210i \(0.0167257\pi\)
−0.998620 + 0.0525210i \(0.983274\pi\)
\(740\) −0.895663 2.75657i −0.0329252 0.101333i
\(741\) 0.158923 1.09645i 0.00583817 0.0402790i
\(742\) 31.9029 43.9106i 1.17119 1.61201i
\(743\) 32.0725 1.17663 0.588313 0.808633i \(-0.299792\pi\)
0.588313 + 0.808633i \(0.299792\pi\)
\(744\) −5.18824 8.12909i −0.190210 0.298027i
\(745\) −11.1030 −0.406781
\(746\) −6.17160 + 8.49448i −0.225958 + 0.311005i
\(747\) 10.2788 + 13.3929i 0.376081 + 0.490020i
\(748\) −9.11029 28.0386i −0.333105 1.02519i
\(749\) 68.3817i 2.49861i
\(750\) 1.24073 + 1.20855i 0.0453051 + 0.0441299i
\(751\) −3.36002 10.3411i −0.122609 0.377351i 0.870849 0.491551i \(-0.163570\pi\)
−0.993458 + 0.114200i \(0.963570\pi\)
\(752\) −9.82376 3.19193i −0.358236 0.116398i
\(753\) 14.9886 7.88682i 0.546215 0.287412i
\(754\) −2.70752 1.96713i −0.0986022 0.0716387i
\(755\) −4.73655 14.5776i −0.172381 0.530533i
\(756\) −25.3482 + 5.04591i −0.921904 + 0.183518i
\(757\) 2.75556 + 3.79270i 0.100152 + 0.137848i 0.856152 0.516724i \(-0.172849\pi\)
−0.755999 + 0.654572i \(0.772849\pi\)
\(758\) −7.35309 2.38916i −0.267076 0.0867783i
\(759\) 84.7956 + 12.2906i 3.07789 + 0.446119i
\(760\) 0.335667 0.243877i 0.0121759 0.00884633i
\(761\) 1.88509 5.80172i 0.0683345 0.210312i −0.911058 0.412278i \(-0.864733\pi\)
0.979392 + 0.201966i \(0.0647331\pi\)
\(762\) 10.5048 + 1.52260i 0.380548 + 0.0551579i
\(763\) 14.9203 + 10.8402i 0.540151 + 0.392443i
\(764\) 10.3442 3.36102i 0.374239 0.121598i
\(765\) 11.7982 + 8.10697i 0.426564 + 0.293108i
\(766\) −19.6588 6.38754i −0.710302 0.230791i
\(767\) −6.44093 + 19.8231i −0.232568 + 0.715772i
\(768\) −0.765991 + 1.55347i −0.0276403 + 0.0560559i
\(769\) 29.6057 1.06761 0.533804 0.845608i \(-0.320762\pi\)
0.533804 + 0.845608i \(0.320762\pi\)
\(770\) 30.7314 1.10748
\(771\) −16.8387 8.30291i −0.606431 0.299022i
\(772\) 16.5225 12.0043i 0.594656 0.432043i
\(773\) 12.9573 + 9.41402i 0.466041 + 0.338599i 0.795897 0.605433i \(-0.207000\pi\)
−0.329855 + 0.944032i \(0.607000\pi\)
\(774\) 0.391410 + 14.8920i 0.0140689 + 0.535281i
\(775\) −4.76219 2.88471i −0.171063 0.103622i
\(776\) 2.68067i 0.0962304i
\(777\) 24.6096 4.22993i 0.882863 0.151748i
\(778\) 13.8866 + 19.1133i 0.497859 + 0.685244i
\(779\) −1.69834 + 0.551824i −0.0608494 + 0.0197712i
\(780\) 1.91279 + 1.86318i 0.0684889 + 0.0667124i
\(781\) 34.1086i 1.22050i
\(782\) −36.3351 + 11.8060i −1.29934 + 0.422181i
\(783\) −5.51305 9.84089i −0.197020 0.351685i
\(784\) 5.48208 16.8721i 0.195789 0.602575i
\(785\) 12.7391 17.5339i 0.454679 0.625812i
\(786\) 8.19575 16.6214i 0.292333 0.592865i
\(787\) 19.5535 26.9131i 0.697007 0.959348i −0.302973 0.952999i \(-0.597979\pi\)
0.999980 0.00634842i \(-0.00202078\pi\)
\(788\) 5.94326 4.31803i 0.211720 0.153823i
\(789\) −18.2932 + 9.62564i −0.651254 + 0.342682i
\(790\) 1.46336 + 2.01414i 0.0520640 + 0.0716599i
\(791\) −32.9482 45.3493i −1.17150 1.61243i
\(792\) 5.26259 17.7725i 0.186998 0.631520i
\(793\) −3.41136 + 2.47850i −0.121141 + 0.0880140i
\(794\) −15.8359 + 21.7962i −0.561995 + 0.773520i
\(795\) −16.9516 8.35858i −0.601211 0.296448i
\(796\) −4.77730 + 6.57539i −0.169327 + 0.233058i
\(797\) 2.32251 7.14796i 0.0822676 0.253194i −0.901459 0.432864i \(-0.857503\pi\)
0.983727 + 0.179670i \(0.0575030\pi\)
\(798\) 1.66449 + 3.16331i 0.0589224 + 0.111980i
\(799\) −46.8758 + 15.2309i −1.65835 + 0.538830i
\(800\) 1.00000i 0.0353553i
\(801\) 0.667723 + 25.4049i 0.0235928 + 0.897637i
\(802\) −36.2667 + 11.7838i −1.28062 + 0.416099i
\(803\) 18.0519 + 24.8463i 0.637039 + 0.876808i
\(804\) 3.37869 + 19.6571i 0.119157 + 0.693251i
\(805\) 39.8246i 1.40363i
\(806\) −7.34170 4.44726i −0.258600 0.156648i
\(807\) −17.0621 16.6195i −0.600613 0.585035i
\(808\) 3.74162 + 2.71845i 0.131630 + 0.0956346i
\(809\) −21.3018 + 15.4767i −0.748931 + 0.544130i −0.895495 0.445071i \(-0.853179\pi\)
0.146564 + 0.989201i \(0.453179\pi\)
\(810\) 3.22695 + 8.40160i 0.113383 + 0.295202i
\(811\) −16.4995 −0.579375 −0.289687 0.957121i \(-0.593551\pi\)
−0.289687 + 0.957121i \(0.593551\pi\)
\(812\) 10.7976 0.378922
\(813\) 45.8222 + 22.5942i 1.60705 + 0.792414i
\(814\) −5.53380 + 17.0313i −0.193960 + 0.596946i
\(815\) 5.51565 + 1.79214i 0.193205 + 0.0627761i
\(816\) 1.40003 + 8.14534i 0.0490110 + 0.285144i
\(817\) 1.95947 0.636671i 0.0685532 0.0222743i
\(818\) 19.3237 + 14.0395i 0.675637 + 0.490879i
\(819\) −18.2494 + 14.0061i −0.637686 + 0.489412i
\(820\) 1.32999 4.09330i 0.0464454 0.142944i
\(821\) −12.0857 + 8.78077i −0.421793 + 0.306451i −0.778359 0.627819i \(-0.783948\pi\)
0.356566 + 0.934270i \(0.383948\pi\)
\(822\) −0.0770158 + 0.531351i −0.00268623 + 0.0185330i
\(823\) −6.39386 2.07749i −0.222876 0.0724167i 0.195450 0.980714i \(-0.437383\pi\)
−0.418326 + 0.908297i \(0.637383\pi\)
\(824\) 7.10738 + 9.78248i 0.247597 + 0.340789i
\(825\) −1.81279 10.5467i −0.0631131 0.367190i
\(826\) −20.7808 63.9566i −0.723055 2.22534i
\(827\) −16.0873 11.6881i −0.559411 0.406436i 0.271832 0.962345i \(-0.412370\pi\)
−0.831243 + 0.555909i \(0.812370\pi\)
\(828\) −23.0313 6.81976i −0.800395 0.237003i
\(829\) −2.93224 0.952741i −0.101841 0.0330901i 0.257653 0.966237i \(-0.417051\pi\)
−0.359494 + 0.933147i \(0.617051\pi\)
\(830\) 1.73900 + 5.35211i 0.0603617 + 0.185774i
\(831\) 9.78993 10.0506i 0.339609 0.348652i
\(832\) 1.54166i 0.0534476i
\(833\) −26.1587 80.5082i −0.906346 2.78944i
\(834\) −10.3357 1.49809i −0.357896 0.0518747i
\(835\) −7.21416 + 9.92944i −0.249656 + 0.343622i
\(836\) −2.56348 −0.0886599
\(837\) −16.2001 23.9699i −0.559957 0.828521i
\(838\) 35.5291 1.22733
\(839\) 20.6339 28.4001i 0.712361 0.980481i −0.287382 0.957816i \(-0.592785\pi\)
0.999743 0.0226649i \(-0.00721507\pi\)
\(840\) −8.52607 1.23580i −0.294178 0.0426391i
\(841\) −7.50526 23.0988i −0.258802 0.796511i
\(842\) 12.8082i 0.441401i
\(843\) −8.96860 + 9.20742i −0.308895 + 0.317120i
\(844\) 5.95687 + 18.3333i 0.205044 + 0.631060i
\(845\) −10.1033 3.28277i −0.347565 0.112931i
\(846\) −29.7127 8.79816i −1.02154 0.302487i
\(847\) −109.345 79.4441i −3.75715 2.72973i
\(848\) −3.37203 10.3780i −0.115796 0.356383i
\(849\) 5.15725 + 30.0047i 0.176997 + 1.02976i
\(850\) 2.80472 + 3.86037i 0.0962011 + 0.132409i
\(851\) 22.0708 + 7.17123i 0.756576 + 0.245826i
\(852\) 1.37161 9.46305i 0.0469905 0.324199i
\(853\) −28.2153 + 20.4996i −0.966075 + 0.701894i −0.954554 0.298039i \(-0.903667\pi\)
−0.0115211 + 0.999934i \(0.503667\pi\)
\(854\) 4.20403 12.9387i 0.143859 0.442752i
\(855\) 0.987431 0.757835i 0.0337694 0.0259174i
\(856\) −11.1223 8.08082i −0.380152 0.276197i
\(857\) 25.1455 8.17027i 0.858954 0.279091i 0.153762 0.988108i \(-0.450861\pi\)
0.705191 + 0.709017i \(0.250861\pi\)
\(858\) −2.79471 16.2595i −0.0954097 0.555090i
\(859\) −10.1597 3.30110i −0.346646 0.112632i 0.130519 0.991446i \(-0.458336\pi\)
−0.477165 + 0.878814i \(0.658336\pi\)
\(860\) −1.53449 + 4.72267i −0.0523256 + 0.161042i
\(861\) 33.2562 + 16.3981i 1.13337 + 0.558846i
\(862\) −40.9265 −1.39396
\(863\) 7.38062 0.251239 0.125620 0.992078i \(-0.459908\pi\)
0.125620 + 0.992078i \(0.459908\pi\)
\(864\) −2.17473 + 4.71917i −0.0739859 + 0.160549i
\(865\) −10.8468 + 7.88064i −0.368801 + 0.267950i
\(866\) 12.4725 + 9.06183i 0.423834 + 0.307933i
\(867\) 7.15764 + 6.97198i 0.243086 + 0.236781i
\(868\) 27.5970 2.31472i 0.936703 0.0785666i
\(869\) 15.3819i 0.521797i
\(870\) −0.636930 3.70564i −0.0215940 0.125633i
\(871\) 10.4349 + 14.3624i 0.353574 + 0.486652i
\(872\) 3.52633 1.14577i 0.119417 0.0388008i
\(873\) −0.211297 8.03923i −0.00715132 0.272087i
\(874\) 3.32200i 0.112368i
\(875\) −4.73053 + 1.53704i −0.159921 + 0.0519615i
\(876\) −4.00916 7.61926i −0.135457 0.257431i
\(877\) 12.3864 38.1213i 0.418258 1.28727i −0.491046 0.871134i \(-0.663385\pi\)
0.909304 0.416132i \(-0.136615\pi\)
\(878\) 18.8511 25.9463i 0.636195 0.875647i
\(879\) 33.2296 + 16.3850i 1.12081 + 0.552653i
\(880\) 3.63160 4.99846i 0.122421 0.168498i
\(881\) −18.7252 + 13.6046i −0.630867 + 0.458351i −0.856700 0.515814i \(-0.827489\pi\)
0.225834 + 0.974166i \(0.427489\pi\)
\(882\) 15.1107 51.0310i 0.508802 1.71830i
\(883\) 14.5289 + 19.9973i 0.488936 + 0.672962i 0.980191 0.198053i \(-0.0634619\pi\)
−0.491256 + 0.871015i \(0.663462\pi\)
\(884\) 4.32394 + 5.95139i 0.145430 + 0.200167i
\(885\) −20.7235 + 10.9044i −0.696612 + 0.366549i
\(886\) 15.2795 11.1012i 0.513324 0.372952i
\(887\) −17.5865 + 24.2058i −0.590497 + 0.812750i −0.994797 0.101877i \(-0.967515\pi\)
0.404300 + 0.914627i \(0.367515\pi\)
\(888\) 2.22017 4.50261i 0.0745040 0.151098i
\(889\) −17.9169 + 24.6605i −0.600913 + 0.827086i
\(890\) −2.61775 + 8.05661i −0.0877472 + 0.270058i
\(891\) 14.3814 53.7140i 0.481796 1.79949i
\(892\) −14.4385 + 4.69134i −0.483436 + 0.157078i
\(893\) 4.28571i 0.143416i
\(894\) −13.7758 13.4185i −0.460731 0.448780i
\(895\) 0.881626 0.286458i 0.0294695 0.00957522i
\(896\) −2.92363 4.02403i −0.0976715 0.134433i
\(897\) −21.0706 + 3.62165i −0.703527 + 0.120923i
\(898\) 0.351102i 0.0117164i
\(899\) 4.68269 + 11.1427i 0.156176 + 0.371629i
\(900\) 0.0788226 + 2.99896i 0.00262742 + 0.0999655i
\(901\) −42.1248 30.6054i −1.40338 1.01961i
\(902\) −21.5131 + 15.6302i −0.716309 + 0.520429i
\(903\) −38.3695 18.9194i −1.27686 0.629599i
\(904\) −11.2696 −0.374822
\(905\) −17.2187 −0.572367
\(906\) 11.7409 23.8112i 0.390067 0.791074i
\(907\) 15.4169 47.4483i 0.511909 1.57549i −0.276927 0.960891i \(-0.589316\pi\)
0.788836 0.614603i \(-0.210684\pi\)
\(908\) 11.2026 + 3.63994i 0.371771 + 0.120796i
\(909\) 11.4353 + 7.85760i 0.379284 + 0.260620i
\(910\) −7.29289 + 2.36960i −0.241757 + 0.0785516i
\(911\) −29.9201 21.7382i −0.991296 0.720219i −0.0310918 0.999517i \(-0.509898\pi\)
−0.960205 + 0.279298i \(0.909898\pi\)
\(912\) 0.711209 + 0.103085i 0.0235505 + 0.00341349i
\(913\) 10.7443 33.0677i 0.355586 1.09438i
\(914\) 21.3570 15.5168i 0.706427 0.513249i
\(915\) −4.68841 0.679554i −0.154994 0.0224654i
\(916\) −7.57308 2.46064i −0.250221 0.0813019i
\(917\) 31.2815 + 43.0552i 1.03300 + 1.42181i
\(918\) 4.84069 + 24.3172i 0.159766 + 0.802588i
\(919\) 0.188242 + 0.579349i 0.00620952 + 0.0191109i 0.954113 0.299446i \(-0.0968018\pi\)
−0.947904 + 0.318557i \(0.896802\pi\)
\(920\) −6.47748 4.70617i −0.213556 0.155158i
\(921\) 14.1623 7.45201i 0.466662 0.245552i
\(922\) −1.96698 0.639110i −0.0647790 0.0210480i
\(923\) −2.63001 8.09434i −0.0865679 0.266429i
\(924\) 38.1294 + 37.1404i 1.25436 + 1.22183i
\(925\) 2.89843i 0.0952997i
\(926\) −1.24624 3.83554i −0.0409541 0.126044i
\(927\) 22.0859 + 28.7771i 0.725395 + 0.945163i
\(928\) 1.27598 1.75623i 0.0418860 0.0576512i
\(929\) 8.56753 0.281091 0.140546 0.990074i \(-0.455114\pi\)
0.140546 + 0.990074i \(0.455114\pi\)
\(930\) −2.42228 9.33448i −0.0794297 0.306090i
\(931\) −7.36062 −0.241235
\(932\) 7.25371 9.98387i 0.237603 0.327033i
\(933\) −2.60374 + 17.9638i −0.0852426 + 0.588109i
\(934\) 2.99149 + 9.20687i 0.0978847 + 0.301258i
\(935\) 29.4815i 0.964149i
\(936\) 0.121518 + 4.62340i 0.00397194 + 0.151120i
\(937\) 4.07252 + 12.5339i 0.133043 + 0.409466i 0.995281 0.0970393i \(-0.0309372\pi\)
−0.862237 + 0.506505i \(0.830937\pi\)
\(938\) −54.4741 17.6997i −1.77864 0.577916i
\(939\) −13.7157 26.0662i −0.447596 0.850639i
\(940\) −8.35659 6.07142i −0.272562 0.198028i
\(941\) 3.55213 + 10.9323i 0.115796 + 0.356384i 0.992112 0.125353i \(-0.0400063\pi\)
−0.876316 + 0.481736i \(0.840006\pi\)
\(942\) 36.9964 6.35900i 1.20541 0.207187i
\(943\) 20.2551 + 27.8788i 0.659597 + 0.907857i
\(944\) −12.8583 4.17790i −0.418501 0.135979i
\(945\) −25.6668 3.03407i −0.834941 0.0986983i
\(946\) 24.8209 18.0335i 0.806998 0.586318i
\(947\) −15.2621 + 46.9718i −0.495951 + 1.52638i 0.319519 + 0.947580i \(0.396479\pi\)
−0.815470 + 0.578800i \(0.803521\pi\)
\(948\) −0.618553 + 4.26755i −0.0200897 + 0.138603i
\(949\) −6.19974 4.50438i −0.201252 0.146218i
\(950\) 0.394601 0.128214i 0.0128025 0.00415980i
\(951\) −7.22929 + 1.24258i −0.234426 + 0.0402934i
\(952\) −22.5725 7.33426i −0.731580 0.237705i
\(953\) 4.51901 13.9081i 0.146385 0.450527i −0.850801 0.525487i \(-0.823883\pi\)
0.997187 + 0.0749603i \(0.0238830\pi\)
\(954\) −10.9306 30.8576i −0.353892 0.999051i
\(955\) 10.8765 0.351955
\(956\) −4.07374 −0.131754
\(957\) −10.2737 + 20.8356i −0.332102 + 0.673518i
\(958\) 11.9748 8.70017i 0.386887 0.281090i
\(959\) −1.24737 0.906269i −0.0402798 0.0292650i
\(960\) −1.20855 + 1.24073i −0.0390057 + 0.0400444i
\(961\) 14.3569 + 27.4751i 0.463126 + 0.886293i
\(962\) 4.46840i 0.144067i
\(963\) −33.9923 23.3574i −1.09539 0.752682i
\(964\) −5.94145 8.17770i −0.191361 0.263386i
\(965\) 19.4233 6.31102i 0.625259 0.203159i
\(966\) 48.1300 49.4116i 1.54856 1.58979i
\(967\) 18.6246i 0.598928i 0.954108 + 0.299464i \(0.0968078\pi\)
−0.954108 + 0.299464i \(0.903192\pi\)
\(968\) −25.8432 + 8.39696i −0.830631 + 0.269889i
\(969\) 3.03465 1.59680i 0.0974871 0.0512965i
\(970\) 0.828372 2.54947i 0.0265974 0.0818584i
\(971\) 9.56650 13.1672i 0.307004 0.422554i −0.627440 0.778665i \(-0.715897\pi\)
0.934444 + 0.356110i \(0.115897\pi\)
\(972\) −6.14996 + 14.3240i −0.197260 + 0.459444i
\(973\) 17.6285 24.2636i 0.565145 0.777855i
\(974\) −6.03603 + 4.38544i −0.193407 + 0.140518i
\(975\) 1.24342 + 2.36307i 0.0398213 + 0.0756788i
\(976\) −1.60768 2.21278i −0.0514604 0.0708292i
\(977\) 24.6202 + 33.8868i 0.787671 + 1.08414i 0.994394 + 0.105736i \(0.0337200\pi\)
−0.206723 + 0.978399i \(0.566280\pi\)
\(978\) 4.67754 + 8.88950i 0.149571 + 0.284255i
\(979\) 42.3431 30.7641i 1.35329 0.983223i
\(980\) 10.4275 14.3523i 0.333095 0.458467i
\(981\) 10.4850 3.71409i 0.334761 0.118582i
\(982\) −16.2836 + 22.4124i −0.519629 + 0.715208i
\(983\) −4.84094 + 14.8989i −0.154402 + 0.475201i −0.998100 0.0616178i \(-0.980374\pi\)
0.843698 + 0.536819i \(0.180374\pi\)
\(984\) 6.59711 3.47132i 0.210308 0.110662i
\(985\) 6.98672 2.27012i 0.222615 0.0723321i
\(986\) 10.3585i 0.329881i
\(987\) 62.0924 63.7459i 1.97642 2.02905i
\(988\) 0.608342 0.197662i 0.0193539 0.00628847i
\(989\) −23.3695 32.1653i −0.743105 1.02280i
\(990\) 10.4970 15.2765i 0.333618 0.485518i
\(991\) 50.1682i 1.59364i −0.604214 0.796822i \(-0.706513\pi\)
0.604214 0.796822i \(-0.293487\pi\)
\(992\) 2.88471 4.76219i 0.0915896 0.151200i
\(993\) 9.47580 9.72812i 0.300705 0.308713i
\(994\) 22.2150 + 16.1401i 0.704617 + 0.511934i
\(995\) −6.57539 + 4.77730i −0.208454 + 0.151451i
\(996\) −4.31064 + 8.74219i −0.136588 + 0.277007i
\(997\) −18.5014 −0.585947 −0.292973 0.956121i \(-0.594645\pi\)
−0.292973 + 0.956121i \(0.594645\pi\)
\(998\) −12.1322 −0.384038
\(999\) 6.30330 13.6782i 0.199428 0.432758i
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 930.2.v.a.401.2 80
3.2 odd 2 inner 930.2.v.a.401.15 yes 80
31.15 odd 10 inner 930.2.v.a.821.15 yes 80
93.77 even 10 inner 930.2.v.a.821.2 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.v.a.401.2 80 1.1 even 1 trivial
930.2.v.a.401.15 yes 80 3.2 odd 2 inner
930.2.v.a.821.2 yes 80 93.77 even 10 inner
930.2.v.a.821.15 yes 80 31.15 odd 10 inner