Properties

Label 287.2.r.c.9.17
Level $287$
Weight $2$
Character 287.9
Analytic conductor $2.292$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,2,Mod(9,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.r (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 9.17
Character \(\chi\) \(=\) 287.9
Dual form 287.2.r.c.32.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.12292 + 0.648320i) q^{2} +(0.752557 - 2.80858i) q^{3} +(-0.159362 - 0.276022i) q^{4} +(-1.50273 - 0.867599i) q^{5} +(2.66592 - 2.66592i) q^{6} +(-0.701479 + 2.55106i) q^{7} -3.00655i q^{8} +(-4.72371 - 2.72723i) q^{9} +O(q^{10})\) \(q+(1.12292 + 0.648320i) q^{2} +(0.752557 - 2.80858i) q^{3} +(-0.159362 - 0.276022i) q^{4} +(-1.50273 - 0.867599i) q^{5} +(2.66592 - 2.66592i) q^{6} +(-0.701479 + 2.55106i) q^{7} -3.00655i q^{8} +(-4.72371 - 2.72723i) q^{9} +(-1.12496 - 1.94850i) q^{10} +(0.603332 - 2.25167i) q^{11} +(-0.895160 + 0.239857i) q^{12} +(3.55754 + 3.55754i) q^{13} +(-2.44161 + 2.40987i) q^{14} +(-3.56761 + 3.56761i) q^{15} +(1.63048 - 2.82408i) q^{16} +(1.30217 + 0.348914i) q^{17} +(-3.53624 - 6.12495i) q^{18} +(0.586080 + 2.18728i) q^{19} +0.553048i q^{20} +(6.63697 + 3.88998i) q^{21} +(2.13730 - 2.13730i) q^{22} +(3.47726 - 6.02278i) q^{23} +(-8.44414 - 2.26260i) q^{24} +(-0.994543 - 1.72260i) q^{25} +(1.68842 + 6.30128i) q^{26} +(-5.04644 + 5.04644i) q^{27} +(0.815940 - 0.212918i) q^{28} +(0.651898 + 0.651898i) q^{29} +(-6.31911 + 1.69320i) q^{30} +(2.55565 + 4.42652i) q^{31} +(-1.54568 + 0.892398i) q^{32} +(-5.86994 - 3.38901i) q^{33} +(1.23603 + 1.23603i) q^{34} +(3.26743 - 3.22495i) q^{35} +1.73847i q^{36} +(3.37484 - 5.84540i) q^{37} +(-0.759935 + 2.83612i) q^{38} +(12.6689 - 7.31439i) q^{39} +(-2.60848 + 4.51802i) q^{40} +(5.82327 - 2.66262i) q^{41} +(4.93085 + 8.67103i) q^{42} +11.9603i q^{43} +(-0.717658 + 0.192296i) q^{44} +(4.73229 + 8.19657i) q^{45} +(7.80938 - 4.50875i) q^{46} +(2.86486 + 10.6918i) q^{47} +(-6.70463 - 6.70463i) q^{48} +(-6.01586 - 3.57903i) q^{49} -2.57913i q^{50} +(1.95991 - 3.39466i) q^{51} +(0.415026 - 1.54890i) q^{52} +(-2.38438 + 8.89863i) q^{53} +(-8.93847 + 2.39506i) q^{54} +(-2.86019 + 2.86019i) q^{55} +(7.66990 + 2.10903i) q^{56} +6.58421 q^{57} +(0.309393 + 1.15467i) q^{58} +(-0.182785 - 0.316594i) q^{59} +(1.55328 + 0.416200i) q^{60} +(-1.12490 - 0.649464i) q^{61} +6.62752i q^{62} +(10.2709 - 10.1374i) q^{63} -8.83618 q^{64} +(-2.25949 - 8.43253i) q^{65} +(-4.39433 - 7.61121i) q^{66} +(-15.2010 - 4.07309i) q^{67} +(-0.111207 - 0.415031i) q^{68} +(-14.2986 - 14.2986i) q^{69} +(5.75988 - 1.50303i) q^{70} +(-2.32467 - 2.32467i) q^{71} +(-8.19956 + 14.2021i) q^{72} +(-4.26864 + 2.46450i) q^{73} +(7.57938 - 4.37596i) q^{74} +(-5.58651 + 1.49690i) q^{75} +(0.510340 - 0.510340i) q^{76} +(5.32092 + 3.11863i) q^{77} +18.9683 q^{78} +(0.101951 - 0.0273178i) q^{79} +(-4.90034 + 2.82921i) q^{80} +(2.19390 + 3.79994i) q^{81} +(8.26532 + 0.785429i) q^{82} +6.06355 q^{83} +(0.0160440 - 2.45187i) q^{84} +(-1.65408 - 1.65408i) q^{85} +(-7.75408 + 13.4305i) q^{86} +(2.32150 - 1.34032i) q^{87} +(-6.76975 - 1.81395i) q^{88} +(2.82332 - 0.756506i) q^{89} +12.2722i q^{90} +(-11.5711 + 6.57998i) q^{91} -2.21656 q^{92} +(14.3555 - 3.84655i) q^{93} +(-3.71470 + 13.8634i) q^{94} +(1.01696 - 3.79536i) q^{95} +(1.34316 + 5.01275i) q^{96} +(-0.441870 + 0.441870i) q^{97} +(-4.43499 - 7.91918i) q^{98} +(-8.99078 + 8.99078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7} - 28 q^{10} + 12 q^{12} - 8 q^{13} + 8 q^{14} - 20 q^{15} - 40 q^{16} - 20 q^{17} - 16 q^{18} - 8 q^{19} - 12 q^{22} + 12 q^{23} - 30 q^{24} + 40 q^{25} + 8 q^{26} - 4 q^{27} - 20 q^{28} - 72 q^{29} + 14 q^{30} + 24 q^{31} + 40 q^{34} + 20 q^{35} + 16 q^{37} - 18 q^{38} + 80 q^{40} - 88 q^{41} - 76 q^{42} + 4 q^{44} - 16 q^{45} + 14 q^{47} - 24 q^{48} - 8 q^{51} + 10 q^{52} - 4 q^{53} + 16 q^{54} - 60 q^{55} + 36 q^{56} + 128 q^{57} - 16 q^{58} - 8 q^{59} + 54 q^{60} + 30 q^{63} - 16 q^{64} + 48 q^{66} + 14 q^{67} - 30 q^{68} + 56 q^{69} - 34 q^{70} - 68 q^{71} + 112 q^{72} - 62 q^{75} - 84 q^{76} - 96 q^{78} - 26 q^{79} - 32 q^{81} + 14 q^{82} + 56 q^{83} - 92 q^{85} + 36 q^{86} + 6 q^{88} + 40 q^{89} - 160 q^{92} - 78 q^{93} + 96 q^{94} + 72 q^{95} + 24 q^{96} + 60 q^{97} - 116 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.12292 + 0.648320i 0.794027 + 0.458432i 0.841378 0.540447i \(-0.181745\pi\)
−0.0473514 + 0.998878i \(0.515078\pi\)
\(3\) 0.752557 2.80858i 0.434489 1.62153i −0.307798 0.951452i \(-0.599592\pi\)
0.742286 0.670083i \(-0.233741\pi\)
\(4\) −0.159362 0.276022i −0.0796808 0.138011i
\(5\) −1.50273 0.867599i −0.672040 0.388002i 0.124809 0.992181i \(-0.460168\pi\)
−0.796849 + 0.604179i \(0.793501\pi\)
\(6\) 2.66592 2.66592i 1.08836 1.08836i
\(7\) −0.701479 + 2.55106i −0.265134 + 0.964212i
\(8\) 3.00655i 1.06298i
\(9\) −4.72371 2.72723i −1.57457 0.909078i
\(10\) −1.12496 1.94850i −0.355745 0.616168i
\(11\) 0.603332 2.25167i 0.181911 0.678903i −0.813359 0.581762i \(-0.802364\pi\)
0.995271 0.0971409i \(-0.0309698\pi\)
\(12\) −0.895160 + 0.239857i −0.258410 + 0.0692409i
\(13\) 3.55754 + 3.55754i 0.986685 + 0.986685i 0.999913 0.0132276i \(-0.00421058\pi\)
−0.0132276 + 0.999913i \(0.504211\pi\)
\(14\) −2.44161 + 2.40987i −0.652549 + 0.644064i
\(15\) −3.56761 + 3.56761i −0.921153 + 0.921153i
\(16\) 1.63048 2.82408i 0.407621 0.706020i
\(17\) 1.30217 + 0.348914i 0.315822 + 0.0846242i 0.413248 0.910619i \(-0.364394\pi\)
−0.0974261 + 0.995243i \(0.531061\pi\)
\(18\) −3.53624 6.12495i −0.833500 1.44366i
\(19\) 0.586080 + 2.18728i 0.134456 + 0.501796i 1.00000 0.000962780i \(0.000306462\pi\)
−0.865544 + 0.500834i \(0.833027\pi\)
\(20\) 0.553048i 0.123665i
\(21\) 6.63697 + 3.88998i 1.44830 + 0.848863i
\(22\) 2.13730 2.13730i 0.455673 0.455673i
\(23\) 3.47726 6.02278i 0.725058 1.25584i −0.233892 0.972262i \(-0.575146\pi\)
0.958950 0.283574i \(-0.0915203\pi\)
\(24\) −8.44414 2.26260i −1.72365 0.461851i
\(25\) −0.994543 1.72260i −0.198909 0.344520i
\(26\) 1.68842 + 6.30128i 0.331127 + 1.23578i
\(27\) −5.04644 + 5.04644i −0.971188 + 0.971188i
\(28\) 0.815940 0.212918i 0.154198 0.0402377i
\(29\) 0.651898 + 0.651898i 0.121054 + 0.121054i 0.765039 0.643984i \(-0.222720\pi\)
−0.643984 + 0.765039i \(0.722720\pi\)
\(30\) −6.31911 + 1.69320i −1.15371 + 0.309134i
\(31\) 2.55565 + 4.42652i 0.459009 + 0.795026i 0.998909 0.0467027i \(-0.0148713\pi\)
−0.539900 + 0.841729i \(0.681538\pi\)
\(32\) −1.54568 + 0.892398i −0.273240 + 0.157755i
\(33\) −5.86994 3.38901i −1.02183 0.589951i
\(34\) 1.23603 + 1.23603i 0.211977 + 0.211977i
\(35\) 3.26743 3.22495i 0.552297 0.545116i
\(36\) 1.73847i 0.289744i
\(37\) 3.37484 5.84540i 0.554821 0.960977i −0.443097 0.896474i \(-0.646120\pi\)
0.997917 0.0645037i \(-0.0205464\pi\)
\(38\) −0.759935 + 2.83612i −0.123278 + 0.460079i
\(39\) 12.6689 7.31439i 2.02865 1.17124i
\(40\) −2.60848 + 4.51802i −0.412437 + 0.714362i
\(41\) 5.82327 2.66262i 0.909442 0.415831i
\(42\) 4.93085 + 8.67103i 0.760847 + 1.33797i
\(43\) 11.9603i 1.82392i 0.410276 + 0.911961i \(0.365432\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(44\) −0.717658 + 0.192296i −0.108191 + 0.0289897i
\(45\) 4.73229 + 8.19657i 0.705448 + 1.22187i
\(46\) 7.80938 4.50875i 1.15143 0.664779i
\(47\) 2.86486 + 10.6918i 0.417883 + 1.55956i 0.778990 + 0.627037i \(0.215732\pi\)
−0.361107 + 0.932525i \(0.617601\pi\)
\(48\) −6.70463 6.70463i −0.967730 0.967730i
\(49\) −6.01586 3.57903i −0.859408 0.511291i
\(50\) 2.57913i 0.364744i
\(51\) 1.95991 3.39466i 0.274442 0.475348i
\(52\) 0.415026 1.54890i 0.0575537 0.214793i
\(53\) −2.38438 + 8.89863i −0.327520 + 1.22232i 0.584235 + 0.811585i \(0.301395\pi\)
−0.911755 + 0.410736i \(0.865272\pi\)
\(54\) −8.93847 + 2.39506i −1.21637 + 0.325926i
\(55\) −2.86019 + 2.86019i −0.385667 + 0.385667i
\(56\) 7.66990 + 2.10903i 1.02493 + 0.281831i
\(57\) 6.58421 0.872100
\(58\) 0.309393 + 1.15467i 0.0406253 + 0.151616i
\(59\) −0.182785 0.316594i −0.0237966 0.0412170i 0.853882 0.520467i \(-0.174242\pi\)
−0.877678 + 0.479250i \(0.840909\pi\)
\(60\) 1.55328 + 0.416200i 0.200528 + 0.0537312i
\(61\) −1.12490 0.649464i −0.144029 0.0831553i 0.426254 0.904604i \(-0.359833\pi\)
−0.570283 + 0.821448i \(0.693166\pi\)
\(62\) 6.62752i 0.841696i
\(63\) 10.2709 10.1374i 1.29401 1.27719i
\(64\) −8.83618 −1.10452
\(65\) −2.25949 8.43253i −0.280255 1.04593i
\(66\) −4.39433 7.61121i −0.540905 0.936875i
\(67\) −15.2010 4.07309i −1.85710 0.497607i −0.857245 0.514909i \(-0.827826\pi\)
−0.999850 + 0.0173020i \(0.994492\pi\)
\(68\) −0.111207 0.415031i −0.0134859 0.0503299i
\(69\) −14.2986 14.2986i −1.72135 1.72135i
\(70\) 5.75988 1.50303i 0.688437 0.179646i
\(71\) −2.32467 2.32467i −0.275888 0.275888i 0.555577 0.831465i \(-0.312497\pi\)
−0.831465 + 0.555577i \(0.812497\pi\)
\(72\) −8.19956 + 14.2021i −0.966328 + 1.67373i
\(73\) −4.26864 + 2.46450i −0.499606 + 0.288448i −0.728551 0.684992i \(-0.759806\pi\)
0.228945 + 0.973439i \(0.426472\pi\)
\(74\) 7.57938 4.37596i 0.881085 0.508695i
\(75\) −5.58651 + 1.49690i −0.645074 + 0.172847i
\(76\) 0.510340 0.510340i 0.0585400 0.0585400i
\(77\) 5.32092 + 3.11863i 0.606375 + 0.355401i
\(78\) 18.9683 2.14773
\(79\) 0.101951 0.0273178i 0.0114704 0.00307349i −0.253079 0.967446i \(-0.581443\pi\)
0.264550 + 0.964372i \(0.414777\pi\)
\(80\) −4.90034 + 2.82921i −0.547875 + 0.316316i
\(81\) 2.19390 + 3.79994i 0.243766 + 0.422216i
\(82\) 8.26532 + 0.785429i 0.912751 + 0.0867362i
\(83\) 6.06355 0.665561 0.332781 0.943004i \(-0.392013\pi\)
0.332781 + 0.943004i \(0.392013\pi\)
\(84\) 0.0160440 2.45187i 0.00175054 0.267520i
\(85\) −1.65408 1.65408i −0.179410 0.179410i
\(86\) −7.75408 + 13.4305i −0.836144 + 1.44824i
\(87\) 2.32150 1.34032i 0.248891 0.143697i
\(88\) −6.76975 1.81395i −0.721657 0.193368i
\(89\) 2.82332 0.756506i 0.299271 0.0801895i −0.106059 0.994360i \(-0.533823\pi\)
0.405330 + 0.914170i \(0.367157\pi\)
\(90\) 12.2722i 1.29360i
\(91\) −11.5711 + 6.57998i −1.21298 + 0.689769i
\(92\) −2.21656 −0.231093
\(93\) 14.3555 3.84655i 1.48860 0.398868i
\(94\) −3.71470 + 13.8634i −0.383142 + 1.42990i
\(95\) 1.01696 3.79536i 0.104338 0.389396i
\(96\) 1.34316 + 5.01275i 0.137086 + 0.511611i
\(97\) −0.441870 + 0.441870i −0.0448651 + 0.0448651i −0.729183 0.684318i \(-0.760100\pi\)
0.684318 + 0.729183i \(0.260100\pi\)
\(98\) −4.43499 7.91918i −0.448001 0.799958i
\(99\) −8.99078 + 8.99078i −0.903607 + 0.903607i
\(100\) −0.316984 + 0.549032i −0.0316984 + 0.0549032i
\(101\) −4.32172 1.15800i −0.430027 0.115225i 0.0373117 0.999304i \(-0.488121\pi\)
−0.467339 + 0.884078i \(0.654787\pi\)
\(102\) 4.40166 2.54130i 0.435829 0.251626i
\(103\) −14.3033 8.25799i −1.40934 0.813684i −0.414018 0.910269i \(-0.635875\pi\)
−0.995325 + 0.0965846i \(0.969208\pi\)
\(104\) 10.6959 10.6959i 1.04882 1.04882i
\(105\) −6.59860 11.6038i −0.643957 1.13241i
\(106\) −8.44664 + 8.44664i −0.820410 + 0.820410i
\(107\) −5.56803 + 9.64410i −0.538281 + 0.932331i 0.460715 + 0.887548i \(0.347593\pi\)
−0.998997 + 0.0447828i \(0.985740\pi\)
\(108\) 2.19714 + 0.588722i 0.211420 + 0.0566498i
\(109\) 11.4776 + 3.07541i 1.09935 + 0.294571i 0.762501 0.646987i \(-0.223971\pi\)
0.336852 + 0.941557i \(0.390638\pi\)
\(110\) −5.06609 + 1.35745i −0.483032 + 0.129428i
\(111\) −13.8775 13.8775i −1.31719 1.31719i
\(112\) 6.06066 + 6.14050i 0.572679 + 0.580223i
\(113\) −1.53669 −0.144559 −0.0722796 0.997384i \(-0.523027\pi\)
−0.0722796 + 0.997384i \(0.523027\pi\)
\(114\) 7.39356 + 4.26868i 0.692471 + 0.399798i
\(115\) −10.4507 + 6.03373i −0.974535 + 0.562648i
\(116\) 0.0760509 0.283826i 0.00706115 0.0263526i
\(117\) −7.10254 26.5070i −0.656630 2.45058i
\(118\) 0.474014i 0.0436365i
\(119\) −1.80355 + 3.07715i −0.165331 + 0.282082i
\(120\) 10.7262 + 10.7262i 0.979163 + 0.979163i
\(121\) 4.82029 + 2.78300i 0.438208 + 0.253000i
\(122\) −0.842121 1.45860i −0.0762420 0.132055i
\(123\) −3.09583 18.3589i −0.279142 1.65537i
\(124\) 0.814546 1.41084i 0.0731484 0.126697i
\(125\) 12.1275i 1.08471i
\(126\) 18.1057 4.72466i 1.61299 0.420906i
\(127\) 14.6097 1.29640 0.648202 0.761468i \(-0.275521\pi\)
0.648202 + 0.761468i \(0.275521\pi\)
\(128\) −6.83099 3.94388i −0.603780 0.348593i
\(129\) 33.5914 + 9.00078i 2.95755 + 0.792474i
\(130\) 2.92975 10.9340i 0.256956 0.958972i
\(131\) −2.35463 1.35945i −0.205725 0.118775i 0.393598 0.919283i \(-0.371230\pi\)
−0.599323 + 0.800507i \(0.704564\pi\)
\(132\) 2.16031i 0.188031i
\(133\) −5.99101 0.0392027i −0.519487 0.00339931i
\(134\) −14.4289 14.4289i −1.24646 1.24646i
\(135\) 11.9617 3.20513i 1.02950 0.275854i
\(136\) 1.04903 3.91503i 0.0899535 0.335711i
\(137\) 17.2371 + 4.61866i 1.47266 + 0.394599i 0.903843 0.427863i \(-0.140734\pi\)
0.568820 + 0.822462i \(0.307400\pi\)
\(138\) −6.78618 25.3264i −0.577678 2.15592i
\(139\) −10.8708 −0.922048 −0.461024 0.887388i \(-0.652518\pi\)
−0.461024 + 0.887388i \(0.652518\pi\)
\(140\) −1.41086 0.387952i −0.119240 0.0327879i
\(141\) 32.1848 2.71045
\(142\) −1.10330 4.11756i −0.0925866 0.345538i
\(143\) 10.1568 5.86402i 0.849352 0.490374i
\(144\) −15.4039 + 8.89342i −1.28365 + 0.741118i
\(145\) −0.414038 1.54521i −0.0343839 0.128323i
\(146\) −6.39114 −0.528934
\(147\) −14.5793 + 14.2026i −1.20248 + 1.17141i
\(148\) −2.15128 −0.176834
\(149\) 1.11656 + 4.16705i 0.0914720 + 0.341378i 0.996461 0.0840568i \(-0.0267877\pi\)
−0.904989 + 0.425435i \(0.860121\pi\)
\(150\) −7.24369 1.94094i −0.591445 0.158477i
\(151\) −2.04974 + 7.64975i −0.166806 + 0.622528i 0.830997 + 0.556277i \(0.187770\pi\)
−0.997803 + 0.0662510i \(0.978896\pi\)
\(152\) 6.57617 1.76208i 0.533398 0.142923i
\(153\) −5.19948 5.19948i −0.420353 0.420353i
\(154\) 3.95311 + 6.95165i 0.318551 + 0.560180i
\(155\) 8.86913i 0.712386i
\(156\) −4.03787 2.33127i −0.323289 0.186651i
\(157\) 3.27922 12.2382i 0.261710 0.976716i −0.702523 0.711661i \(-0.747943\pi\)
0.964233 0.265055i \(-0.0853902\pi\)
\(158\) 0.132194 + 0.0354214i 0.0105168 + 0.00281797i
\(159\) 23.1981 + 13.3934i 1.83973 + 1.06217i
\(160\) 3.09698 0.244838
\(161\) 12.9253 + 13.0956i 1.01866 + 1.03207i
\(162\) 5.68939i 0.447001i
\(163\) −2.49791 + 4.32651i −0.195651 + 0.338878i −0.947114 0.320898i \(-0.896015\pi\)
0.751462 + 0.659776i \(0.229349\pi\)
\(164\) −1.66295 1.18303i −0.129854 0.0923795i
\(165\) 5.88061 + 10.1855i 0.457805 + 0.792941i
\(166\) 6.80891 + 3.93112i 0.528474 + 0.305114i
\(167\) −3.22374 3.22374i −0.249460 0.249460i 0.571289 0.820749i \(-0.306444\pi\)
−0.820749 + 0.571289i \(0.806444\pi\)
\(168\) 11.6954 19.9544i 0.902321 1.53951i
\(169\) 12.3122i 0.947094i
\(170\) −0.785033 2.92978i −0.0602093 0.224704i
\(171\) 3.19675 11.9304i 0.244462 0.912344i
\(172\) 3.30130 1.90601i 0.251722 0.145332i
\(173\) −0.243704 0.140703i −0.0185285 0.0106974i 0.490707 0.871325i \(-0.336738\pi\)
−0.509236 + 0.860627i \(0.670072\pi\)
\(174\) 3.47582 0.263501
\(175\) 5.09211 1.32878i 0.384927 0.100446i
\(176\) −5.37516 5.37516i −0.405168 0.405168i
\(177\) −1.02674 + 0.275113i −0.0771741 + 0.0206787i
\(178\) 3.66083 + 0.980916i 0.274391 + 0.0735228i
\(179\) −21.1456 5.66594i −1.58049 0.423492i −0.641416 0.767194i \(-0.721653\pi\)
−0.939079 + 0.343701i \(0.888319\pi\)
\(180\) 1.50829 2.61244i 0.112421 0.194720i
\(181\) 1.98291 1.98291i 0.147389 0.147389i −0.629562 0.776951i \(-0.716765\pi\)
0.776951 + 0.629562i \(0.216765\pi\)
\(182\) −17.2594 0.112938i −1.27935 0.00837153i
\(183\) −2.67062 + 2.67062i −0.197418 + 0.197418i
\(184\) −18.1078 10.4545i −1.33492 0.770719i
\(185\) −10.1429 + 5.85602i −0.745723 + 0.430543i
\(186\) 18.6139 + 4.98759i 1.36484 + 0.365708i
\(187\) 1.57128 2.72153i 0.114903 0.199018i
\(188\) 2.49463 2.49463i 0.181940 0.181940i
\(189\) −9.33382 16.4138i −0.678935 1.19393i
\(190\) 3.60259 3.60259i 0.261359 0.261359i
\(191\) −2.08624 7.78595i −0.150955 0.563372i −0.999418 0.0341169i \(-0.989138\pi\)
0.848463 0.529255i \(-0.177529\pi\)
\(192\) −6.64973 + 24.8171i −0.479903 + 1.79102i
\(193\) 1.45499 5.43009i 0.104732 0.390867i −0.893582 0.448899i \(-0.851816\pi\)
0.998315 + 0.0580328i \(0.0184828\pi\)
\(194\) −0.782660 + 0.209713i −0.0561917 + 0.0150565i
\(195\) −25.3838 −1.81777
\(196\) −0.0291971 + 2.23087i −0.00208551 + 0.159348i
\(197\) 27.8537i 1.98449i −0.124295 0.992245i \(-0.539667\pi\)
0.124295 0.992245i \(-0.460333\pi\)
\(198\) −15.9249 + 4.26705i −1.13173 + 0.303246i
\(199\) 20.3057 + 5.44090i 1.43943 + 0.385695i 0.892335 0.451373i \(-0.149066\pi\)
0.547098 + 0.837068i \(0.315732\pi\)
\(200\) −5.17908 + 2.99014i −0.366216 + 0.211435i
\(201\) −22.8792 + 39.6279i −1.61377 + 2.79514i
\(202\) −4.10221 4.10221i −0.288630 0.288630i
\(203\) −2.12032 + 1.20574i −0.148818 + 0.0846264i
\(204\) −1.24934 −0.0874711
\(205\) −11.0609 1.05108i −0.772524 0.0734108i
\(206\) −10.7076 18.5462i −0.746037 1.29217i
\(207\) −32.8511 + 18.9666i −2.28331 + 1.31827i
\(208\) 15.8473 4.24627i 1.09881 0.294426i
\(209\) 5.27862 0.365130
\(210\) 0.113258 17.3082i 0.00781552 1.19438i
\(211\) −3.91616 + 3.91616i −0.269599 + 0.269599i −0.828939 0.559339i \(-0.811055\pi\)
0.559339 + 0.828939i \(0.311055\pi\)
\(212\) 2.83620 0.759957i 0.194791 0.0521941i
\(213\) −8.27848 + 4.77958i −0.567232 + 0.327491i
\(214\) −12.5049 + 7.21973i −0.854820 + 0.493530i
\(215\) 10.3767 17.9730i 0.707686 1.22575i
\(216\) 15.1724 + 15.1724i 1.03235 + 1.03235i
\(217\) −13.0851 + 3.41452i −0.888272 + 0.231793i
\(218\) 10.8946 + 10.8946i 0.737876 + 0.737876i
\(219\) 3.70935 + 13.8435i 0.250655 + 0.935456i
\(220\) 1.24528 + 0.333672i 0.0839567 + 0.0224961i
\(221\) 3.39124 + 5.87379i 0.228119 + 0.395114i
\(222\) −6.58631 24.5805i −0.442044 1.64973i
\(223\) 4.00133 0.267949 0.133974 0.990985i \(-0.457226\pi\)
0.133974 + 0.990985i \(0.457226\pi\)
\(224\) −1.19230 4.56913i −0.0796642 0.305288i
\(225\) 10.8494i 0.723293i
\(226\) −1.72558 0.996264i −0.114784 0.0662705i
\(227\) 5.72532 + 1.53410i 0.380003 + 0.101821i 0.443764 0.896144i \(-0.353643\pi\)
−0.0637610 + 0.997965i \(0.520310\pi\)
\(228\) −1.04927 1.81739i −0.0694896 0.120360i
\(229\) 5.65084 + 21.0892i 0.373418 + 1.39362i 0.855642 + 0.517567i \(0.173162\pi\)
−0.482224 + 0.876048i \(0.660171\pi\)
\(230\) −15.6472 −1.03174
\(231\) 12.7632 12.5973i 0.839759 0.828840i
\(232\) 1.95996 1.95996i 0.128678 0.128678i
\(233\) 21.4605 5.75032i 1.40592 0.376716i 0.525456 0.850821i \(-0.323895\pi\)
0.880469 + 0.474105i \(0.157228\pi\)
\(234\) 9.20944 34.3701i 0.602040 2.24684i
\(235\) 4.97111 18.5524i 0.324279 1.21023i
\(236\) −0.0582580 + 0.100906i −0.00379227 + 0.00656841i
\(237\) 0.306897i 0.0199351i
\(238\) −4.02023 + 2.28613i −0.260592 + 0.148188i
\(239\) −14.7641 14.7641i −0.955011 0.955011i 0.0440196 0.999031i \(-0.485984\pi\)
−0.999031 + 0.0440196i \(0.985984\pi\)
\(240\) 4.25829 + 15.8922i 0.274871 + 1.02583i
\(241\) −23.6419 + 13.6496i −1.52291 + 0.879250i −0.523273 + 0.852165i \(0.675289\pi\)
−0.999633 + 0.0270850i \(0.991378\pi\)
\(242\) 3.60855 + 6.25018i 0.231966 + 0.401777i
\(243\) −8.35721 + 2.23931i −0.536115 + 0.143652i
\(244\) 0.413998i 0.0265035i
\(245\) 5.93502 + 10.5977i 0.379174 + 0.677060i
\(246\) 8.42606 22.6227i 0.537226 1.44237i
\(247\) −5.69634 + 9.86635i −0.362449 + 0.627781i
\(248\) 13.3086 7.68370i 0.845094 0.487915i
\(249\) 4.56317 17.0300i 0.289179 1.07923i
\(250\) −7.86247 + 13.6182i −0.497266 + 0.861291i
\(251\) 4.75952i 0.300418i −0.988654 0.150209i \(-0.952005\pi\)
0.988654 0.150209i \(-0.0479947\pi\)
\(252\) −4.43494 1.21950i −0.279375 0.0768210i
\(253\) −11.4634 11.4634i −0.720695 0.720695i
\(254\) 16.4056 + 9.47179i 1.02938 + 0.594313i
\(255\) −5.89041 + 3.40083i −0.368872 + 0.212968i
\(256\) 3.72239 + 6.44737i 0.232649 + 0.402960i
\(257\) 2.87039 0.769118i 0.179050 0.0479763i −0.168180 0.985756i \(-0.553789\pi\)
0.347230 + 0.937780i \(0.387122\pi\)
\(258\) 31.8851 + 31.8851i 1.98508 + 1.98508i
\(259\) 12.5446 + 12.7099i 0.779484 + 0.789752i
\(260\) −1.96749 + 1.96749i −0.122019 + 0.122019i
\(261\) −1.30150 4.85725i −0.0805606 0.300656i
\(262\) −1.76271 3.05311i −0.108901 0.188622i
\(263\) 13.5150 + 3.62132i 0.833368 + 0.223300i 0.650182 0.759778i \(-0.274692\pi\)
0.183185 + 0.983078i \(0.441359\pi\)
\(264\) −10.1892 + 17.6483i −0.627104 + 1.08618i
\(265\) 11.3035 11.3035i 0.694369 0.694369i
\(266\) −6.70203 3.92812i −0.410928 0.240848i
\(267\) 8.49883i 0.520120i
\(268\) 1.29819 + 4.84491i 0.0792995 + 0.295950i
\(269\) 4.18299 + 7.24516i 0.255042 + 0.441745i 0.964907 0.262593i \(-0.0845775\pi\)
−0.709865 + 0.704338i \(0.751244\pi\)
\(270\) 15.5100 + 4.15590i 0.943910 + 0.252920i
\(271\) −11.0081 + 19.0665i −0.668692 + 1.15821i 0.309578 + 0.950874i \(0.399812\pi\)
−0.978270 + 0.207335i \(0.933521\pi\)
\(272\) 3.10853 3.10853i 0.188482 0.188482i
\(273\) 9.77252 + 37.4501i 0.591460 + 2.26658i
\(274\) 16.3616 + 16.3616i 0.988438 + 0.988438i
\(275\) −4.47876 + 1.20008i −0.270079 + 0.0723675i
\(276\) −1.66809 + 6.22540i −0.100407 + 0.374725i
\(277\) 1.93858 + 3.35771i 0.116478 + 0.201745i 0.918369 0.395724i \(-0.129506\pi\)
−0.801892 + 0.597469i \(0.796173\pi\)
\(278\) −12.2071 7.04775i −0.732131 0.422696i
\(279\) 27.8794i 1.66910i
\(280\) −9.69597 9.82370i −0.579445 0.587078i
\(281\) 5.40303 5.40303i 0.322318 0.322318i −0.527338 0.849656i \(-0.676810\pi\)
0.849656 + 0.527338i \(0.176810\pi\)
\(282\) 36.1411 + 20.8660i 2.15217 + 1.24256i
\(283\) 3.28963 + 5.69781i 0.195548 + 0.338699i 0.947080 0.320997i \(-0.104018\pi\)
−0.751532 + 0.659697i \(0.770685\pi\)
\(284\) −0.271198 + 1.01213i −0.0160927 + 0.0600586i
\(285\) −9.89426 5.71245i −0.586085 0.338377i
\(286\) 15.2070 0.899212
\(287\) 2.70760 + 16.7233i 0.159825 + 0.987145i
\(288\) 9.73511 0.573647
\(289\) −13.1485 7.59131i −0.773443 0.446548i
\(290\) 0.536858 2.00358i 0.0315254 0.117654i
\(291\) 0.908495 + 1.57356i 0.0532569 + 0.0922437i
\(292\) 1.36051 + 0.785493i 0.0796181 + 0.0459675i
\(293\) −1.45657 + 1.45657i −0.0850936 + 0.0850936i −0.748372 0.663279i \(-0.769164\pi\)
0.663279 + 0.748372i \(0.269164\pi\)
\(294\) −25.5792 + 6.49638i −1.49181 + 0.378877i
\(295\) 0.634338i 0.0369326i
\(296\) −17.5745 10.1466i −1.02150 0.589761i
\(297\) 8.31821 + 14.4076i 0.482672 + 0.836012i
\(298\) −1.44777 + 5.40317i −0.0838674 + 0.312997i
\(299\) 33.7968 9.05582i 1.95452 0.523712i
\(300\) 1.30345 + 1.30345i 0.0752549 + 0.0752549i
\(301\) −30.5114 8.38987i −1.75865 0.483584i
\(302\) −7.26119 + 7.26119i −0.417835 + 0.417835i
\(303\) −6.50468 + 11.2664i −0.373684 + 0.647240i
\(304\) 7.13265 + 1.91119i 0.409086 + 0.109614i
\(305\) 1.12695 + 1.95193i 0.0645289 + 0.111767i
\(306\) −2.46769 9.20955i −0.141069 0.526475i
\(307\) 19.8352i 1.13205i −0.824386 0.566027i \(-0.808480\pi\)
0.824386 0.566027i \(-0.191520\pi\)
\(308\) 0.0128626 1.96568i 0.000732916 0.112005i
\(309\) −33.9573 + 33.9573i −1.93176 + 1.93176i
\(310\) 5.75004 9.95935i 0.326580 0.565653i
\(311\) −22.3373 5.98526i −1.26663 0.339393i −0.437892 0.899028i \(-0.644275\pi\)
−0.828739 + 0.559635i \(0.810941\pi\)
\(312\) −21.9911 38.0897i −1.24500 2.15640i
\(313\) 6.85072 + 25.5672i 0.387225 + 1.44515i 0.834629 + 0.550813i \(0.185682\pi\)
−0.447403 + 0.894332i \(0.647651\pi\)
\(314\) 11.6166 11.6166i 0.655563 0.655563i
\(315\) −24.2296 + 6.32266i −1.36518 + 0.356241i
\(316\) −0.0237875 0.0237875i −0.00133815 0.00133815i
\(317\) 12.6385 3.38647i 0.709848 0.190203i 0.114210 0.993457i \(-0.463566\pi\)
0.595637 + 0.803254i \(0.296900\pi\)
\(318\) 17.3665 + 30.0796i 0.973864 + 1.68678i
\(319\) 1.86117 1.07454i 0.104205 0.0601630i
\(320\) 13.2784 + 7.66626i 0.742283 + 0.428557i
\(321\) 22.8960 + 22.8960i 1.27793 + 1.27793i
\(322\) 6.02399 + 23.0850i 0.335704 + 1.28648i
\(323\) 3.05269i 0.169856i
\(324\) 0.699246 1.21113i 0.0388470 0.0672850i
\(325\) 2.59009 9.66635i 0.143672 0.536193i
\(326\) −5.60992 + 3.23889i −0.310705 + 0.179386i
\(327\) 17.2751 29.9213i 0.955314 1.65465i
\(328\) −8.00529 17.5080i −0.442018 0.966715i
\(329\) −29.2851 0.191630i −1.61454 0.0105649i
\(330\) 15.2501i 0.839489i
\(331\) 15.3223 4.10559i 0.842189 0.225664i 0.188165 0.982137i \(-0.439746\pi\)
0.654024 + 0.756474i \(0.273079\pi\)
\(332\) −0.966298 1.67368i −0.0530325 0.0918550i
\(333\) −31.8835 + 18.4080i −1.74721 + 1.00875i
\(334\) −1.53000 5.71003i −0.0837177 0.312439i
\(335\) 19.3091 + 19.3091i 1.05497 + 1.05497i
\(336\) 21.8071 12.4008i 1.18967 0.676518i
\(337\) 5.49246i 0.299194i 0.988747 + 0.149597i \(0.0477975\pi\)
−0.988747 + 0.149597i \(0.952202\pi\)
\(338\) −7.98227 + 13.8257i −0.434178 + 0.752018i
\(339\) −1.15644 + 4.31590i −0.0628094 + 0.234408i
\(340\) −0.192967 + 0.720161i −0.0104651 + 0.0390562i
\(341\) 11.5089 3.08381i 0.623245 0.166998i
\(342\) 11.3245 11.3245i 0.612356 0.612356i
\(343\) 13.3503 12.8362i 0.720851 0.693091i
\(344\) 35.9591 1.93879
\(345\) 9.08145 + 33.8924i 0.488929 + 1.82471i
\(346\) −0.182441 0.315997i −0.00980807 0.0169881i
\(347\) −34.5410 9.25524i −1.85426 0.496848i −0.854515 0.519426i \(-0.826146\pi\)
−0.999745 + 0.0225788i \(0.992812\pi\)
\(348\) −0.739915 0.427190i −0.0396636 0.0228998i
\(349\) 0.658383i 0.0352424i −0.999845 0.0176212i \(-0.994391\pi\)
0.999845 0.0176212i \(-0.00560929\pi\)
\(350\) 6.57952 + 1.80920i 0.351690 + 0.0967060i
\(351\) −35.9058 −1.91651
\(352\) 1.07683 + 4.01877i 0.0573950 + 0.214201i
\(353\) −12.9827 22.4866i −0.690997 1.19684i −0.971512 0.236992i \(-0.923838\pi\)
0.280514 0.959850i \(-0.409495\pi\)
\(354\) −1.33131 0.356722i −0.0707581 0.0189596i
\(355\) 1.47646 + 5.51023i 0.0783624 + 0.292453i
\(356\) −0.658741 0.658741i −0.0349132 0.0349132i
\(357\) 7.28517 + 7.38114i 0.385572 + 0.390651i
\(358\) −20.0715 20.0715i −1.06081 1.06081i
\(359\) −2.04747 + 3.54633i −0.108061 + 0.187168i −0.914985 0.403488i \(-0.867798\pi\)
0.806923 + 0.590656i \(0.201131\pi\)
\(360\) 24.6434 14.2279i 1.29882 0.749875i
\(361\) 12.0138 6.93616i 0.632304 0.365061i
\(362\) 3.51223 0.941098i 0.184598 0.0494630i
\(363\) 11.4438 11.4438i 0.600644 0.600644i
\(364\) 3.66021 + 2.14528i 0.191847 + 0.112443i
\(365\) 8.55279 0.447673
\(366\) −4.73033 + 1.26749i −0.247258 + 0.0662526i
\(367\) −30.7196 + 17.7360i −1.60355 + 0.925811i −0.612783 + 0.790251i \(0.709950\pi\)
−0.990769 + 0.135560i \(0.956717\pi\)
\(368\) −11.3392 19.6401i −0.591098 1.02381i
\(369\) −34.7690 3.30400i −1.81000 0.171999i
\(370\) −15.1863 −0.789499
\(371\) −21.0284 12.3249i −1.09174 0.639877i
\(372\) −3.34945 3.34945i −0.173661 0.173661i
\(373\) 7.15769 12.3975i 0.370611 0.641917i −0.619048 0.785353i \(-0.712482\pi\)
0.989660 + 0.143435i \(0.0458149\pi\)
\(374\) 3.52885 2.03738i 0.182472 0.105351i
\(375\) 34.0609 + 9.12660i 1.75890 + 0.471295i
\(376\) 32.1455 8.61335i 1.65778 0.444200i
\(377\) 4.63831i 0.238885i
\(378\) 0.160205 24.4827i 0.00824004 1.25925i
\(379\) −7.86975 −0.404242 −0.202121 0.979361i \(-0.564783\pi\)
−0.202121 + 0.979361i \(0.564783\pi\)
\(380\) −1.20967 + 0.324130i −0.0620548 + 0.0166275i
\(381\) 10.9947 41.0326i 0.563273 2.10216i
\(382\) 2.70510 10.0956i 0.138405 0.516535i
\(383\) 1.78146 + 6.64848i 0.0910281 + 0.339722i 0.996387 0.0849250i \(-0.0270651\pi\)
−0.905359 + 0.424646i \(0.860398\pi\)
\(384\) −16.2174 + 16.2174i −0.827591 + 0.827591i
\(385\) −5.29016 9.30288i −0.269611 0.474119i
\(386\) 5.15428 5.15428i 0.262346 0.262346i
\(387\) 32.6184 56.4968i 1.65809 2.87189i
\(388\) 0.192383 + 0.0515489i 0.00976678 + 0.00261700i
\(389\) −24.0731 + 13.8986i −1.22056 + 0.704688i −0.965036 0.262116i \(-0.915580\pi\)
−0.255519 + 0.966804i \(0.582246\pi\)
\(390\) −28.5041 16.4569i −1.44336 0.833326i
\(391\) 6.62940 6.62940i 0.335263 0.335263i
\(392\) −10.7605 + 18.0870i −0.543490 + 0.913530i
\(393\) −5.59011 + 5.59011i −0.281984 + 0.281984i
\(394\) 18.0581 31.2775i 0.909753 1.57574i
\(395\) −0.176906 0.0474018i −0.00890110 0.00238504i
\(396\) 3.91444 + 1.04887i 0.196708 + 0.0527078i
\(397\) −11.6447 + 3.12020i −0.584432 + 0.156598i −0.538907 0.842365i \(-0.681163\pi\)
−0.0455250 + 0.998963i \(0.514496\pi\)
\(398\) 19.2743 + 19.2743i 0.966134 + 0.966134i
\(399\) −4.61868 + 16.7967i −0.231223 + 0.840889i
\(400\) −6.48635 −0.324317
\(401\) 21.6097 + 12.4764i 1.07914 + 0.623041i 0.930664 0.365875i \(-0.119230\pi\)
0.148475 + 0.988916i \(0.452564\pi\)
\(402\) −51.3832 + 29.6661i −2.56276 + 1.47961i
\(403\) −6.65569 + 24.8394i −0.331544 + 1.23734i
\(404\) 0.369082 + 1.37743i 0.0183625 + 0.0685299i
\(405\) 7.61370i 0.378328i
\(406\) −3.16267 0.0206952i −0.156961 0.00102709i
\(407\) −11.1257 11.1257i −0.551482 0.551482i
\(408\) −10.2062 5.89257i −0.505283 0.291725i
\(409\) 10.8974 + 18.8748i 0.538840 + 0.933298i 0.998967 + 0.0454446i \(0.0144704\pi\)
−0.460127 + 0.887853i \(0.652196\pi\)
\(410\) −11.7391 8.35127i −0.579751 0.412440i
\(411\) 25.9438 44.9359i 1.27971 2.21653i
\(412\) 5.26403i 0.259340i
\(413\) 0.935871 0.244214i 0.0460512 0.0120170i
\(414\) −49.1856 −2.41734
\(415\) −9.11186 5.26073i −0.447284 0.258239i
\(416\) −8.67357 2.32408i −0.425257 0.113947i
\(417\) −8.18088 + 30.5315i −0.400619 + 1.49513i
\(418\) 5.92749 + 3.42224i 0.289923 + 0.167387i
\(419\) 23.4339i 1.14482i 0.819967 + 0.572410i \(0.193991\pi\)
−0.819967 + 0.572410i \(0.806009\pi\)
\(420\) −2.15135 + 3.67056i −0.104975 + 0.179105i
\(421\) −20.2830 20.2830i −0.988532 0.988532i 0.0114029 0.999935i \(-0.496370\pi\)
−0.999935 + 0.0114029i \(0.996370\pi\)
\(422\) −6.93647 + 1.85862i −0.337662 + 0.0904763i
\(423\) 15.6263 58.3181i 0.759776 2.83552i
\(424\) 26.7542 + 7.16876i 1.29930 + 0.348146i
\(425\) −0.694021 2.59012i −0.0336650 0.125639i
\(426\) −12.3948 −0.600530
\(427\) 2.44592 2.41412i 0.118366 0.116827i
\(428\) 3.54932 0.171563
\(429\) −8.82601 32.9391i −0.426124 1.59032i
\(430\) 23.3045 13.4549i 1.12384 0.648851i
\(431\) 1.81385 1.04723i 0.0873700 0.0504431i −0.455678 0.890144i \(-0.650603\pi\)
0.543048 + 0.839701i \(0.317270\pi\)
\(432\) 6.02342 + 22.4797i 0.289802 + 1.08155i
\(433\) 3.10679 0.149303 0.0746515 0.997210i \(-0.476216\pi\)
0.0746515 + 0.997210i \(0.476216\pi\)
\(434\) −16.9072 4.64907i −0.811573 0.223162i
\(435\) −4.65143 −0.223019
\(436\) −0.980205 3.65818i −0.0469433 0.175195i
\(437\) 15.2115 + 4.07590i 0.727663 + 0.194977i
\(438\) −4.80969 + 17.9500i −0.229816 + 0.857685i
\(439\) −34.4225 + 9.22348i −1.64290 + 0.440213i −0.957611 0.288063i \(-0.906989\pi\)
−0.685284 + 0.728276i \(0.740322\pi\)
\(440\) 8.59929 + 8.59929i 0.409955 + 0.409955i
\(441\) 18.6563 + 33.3129i 0.888394 + 1.58633i
\(442\) 8.79443i 0.418308i
\(443\) −1.80535 1.04232i −0.0857746 0.0495220i 0.456499 0.889724i \(-0.349103\pi\)
−0.542274 + 0.840202i \(0.682436\pi\)
\(444\) −1.61896 + 6.04205i −0.0768325 + 0.286743i
\(445\) −4.89902 1.31269i −0.232236 0.0622274i
\(446\) 4.49318 + 2.59414i 0.212758 + 0.122836i
\(447\) 12.5438 0.593300
\(448\) 6.19839 22.5417i 0.292846 1.06499i
\(449\) 5.83364i 0.275306i 0.990480 + 0.137653i \(0.0439559\pi\)
−0.990480 + 0.137653i \(0.956044\pi\)
\(450\) −7.03389 + 12.1830i −0.331581 + 0.574314i
\(451\) −2.48196 14.7185i −0.116871 0.693067i
\(452\) 0.244889 + 0.424160i 0.0115186 + 0.0199508i
\(453\) 19.9424 + 11.5137i 0.936975 + 0.540963i
\(454\) 5.43451 + 5.43451i 0.255054 + 0.255054i
\(455\) 23.0969 + 0.151137i 1.08280 + 0.00708540i
\(456\) 19.7958i 0.927021i
\(457\) −1.19605 4.46373i −0.0559489 0.208804i 0.932293 0.361705i \(-0.117805\pi\)
−0.988242 + 0.152901i \(0.951139\pi\)
\(458\) −7.32711 + 27.3451i −0.342373 + 1.27775i
\(459\) −8.33208 + 4.81053i −0.388908 + 0.224536i
\(460\) 3.33089 + 1.92309i 0.155304 + 0.0896645i
\(461\) −25.7304 −1.19838 −0.599192 0.800605i \(-0.704511\pi\)
−0.599192 + 0.800605i \(0.704511\pi\)
\(462\) 22.4992 5.87112i 1.04676 0.273149i
\(463\) −3.19464 3.19464i −0.148468 0.148468i 0.628965 0.777433i \(-0.283479\pi\)
−0.777433 + 0.628965i \(0.783479\pi\)
\(464\) 2.90392 0.778103i 0.134811 0.0361225i
\(465\) −24.9097 6.67452i −1.15516 0.309524i
\(466\) 27.8266 + 7.45610i 1.28904 + 0.345397i
\(467\) 3.24397 5.61871i 0.150113 0.260003i −0.781156 0.624336i \(-0.785370\pi\)
0.931269 + 0.364333i \(0.118703\pi\)
\(468\) −6.18467 + 6.18467i −0.285886 + 0.285886i
\(469\) 21.0539 35.9215i 0.972178 1.65870i
\(470\) 17.6101 17.6101i 0.812292 0.812292i
\(471\) −31.9042 18.4199i −1.47007 0.848745i
\(472\) −0.951855 + 0.549554i −0.0438127 + 0.0252953i
\(473\) 26.9305 + 7.21601i 1.23827 + 0.331792i
\(474\) 0.198968 0.344622i 0.00913888 0.0158290i
\(475\) 3.18492 3.18492i 0.146134 0.146134i
\(476\) 1.13678 + 0.00743862i 0.0521042 + 0.000340949i
\(477\) 35.5317 35.5317i 1.62689 1.62689i
\(478\) −7.00710 26.1508i −0.320497 1.19611i
\(479\) 7.70857 28.7688i 0.352213 1.31448i −0.531742 0.846906i \(-0.678462\pi\)
0.883955 0.467572i \(-0.154871\pi\)
\(480\) 2.33065 8.69811i 0.106379 0.397013i
\(481\) 32.8014 8.78911i 1.49562 0.400749i
\(482\) −35.3973 −1.61230
\(483\) 46.5069 26.4466i 2.11614 1.20336i
\(484\) 1.77401i 0.0806369i
\(485\) 1.04738 0.280644i 0.0475589 0.0127434i
\(486\) −10.8363 2.90358i −0.491544 0.131709i
\(487\) 31.4171 18.1386i 1.42364 0.821941i 0.427035 0.904235i \(-0.359558\pi\)
0.996608 + 0.0822946i \(0.0262248\pi\)
\(488\) −1.95265 + 3.38208i −0.0883921 + 0.153100i
\(489\) 10.2715 + 10.2715i 0.464494 + 0.464494i
\(490\) −0.206108 + 15.7482i −0.00931100 + 0.711429i
\(491\) −24.4115 −1.10167 −0.550837 0.834613i \(-0.685691\pi\)
−0.550837 + 0.834613i \(0.685691\pi\)
\(492\) −4.57411 + 3.78022i −0.206217 + 0.170426i
\(493\) 0.621423 + 1.07634i 0.0279875 + 0.0484757i
\(494\) −12.7931 + 7.38610i −0.575589 + 0.332316i
\(495\) 21.3111 5.71028i 0.957861 0.256658i
\(496\) 16.6678 0.748407
\(497\) 7.56110 4.29968i 0.339161 0.192867i
\(498\) 16.1650 16.1650i 0.724369 0.724369i
\(499\) −30.8207 + 8.25839i −1.37973 + 0.369696i −0.871021 0.491245i \(-0.836542\pi\)
−0.508704 + 0.860941i \(0.669875\pi\)
\(500\) 3.34745 1.93265i 0.149702 0.0864308i
\(501\) −11.4802 + 6.62808i −0.512896 + 0.296121i
\(502\) 3.08569 5.34457i 0.137721 0.238540i
\(503\) 10.8501 + 10.8501i 0.483782 + 0.483782i 0.906337 0.422555i \(-0.138867\pi\)
−0.422555 + 0.906337i \(0.638867\pi\)
\(504\) −30.4785 30.8801i −1.35762 1.37551i
\(505\) 5.48968 + 5.48968i 0.244288 + 0.244288i
\(506\) −5.44055 20.3044i −0.241862 0.902640i
\(507\) 34.5799 + 9.26565i 1.53575 + 0.411502i
\(508\) −2.32823 4.03262i −0.103299 0.178918i
\(509\) 7.62385 + 28.4526i 0.337921 + 1.26114i 0.900667 + 0.434509i \(0.143078\pi\)
−0.562746 + 0.826630i \(0.690255\pi\)
\(510\) −8.81931 −0.390526
\(511\) −3.29274 12.6184i −0.145662 0.558203i
\(512\) 25.4287i 1.12380i
\(513\) −13.9956 8.08036i −0.617920 0.356756i
\(514\) 3.72186 + 0.997270i 0.164164 + 0.0439877i
\(515\) 14.3293 + 24.8190i 0.631423 + 1.09366i
\(516\) −2.86876 10.7063i −0.126290 0.471321i
\(517\) 25.8029 1.13481
\(518\) 5.84657 + 22.4051i 0.256884 + 0.984425i
\(519\) −0.578576 + 0.578576i −0.0253967 + 0.0253967i
\(520\) −25.3528 + 6.79327i −1.11180 + 0.297905i
\(521\) 9.71074 36.2410i 0.425435 1.58775i −0.337536 0.941313i \(-0.609593\pi\)
0.762971 0.646433i \(-0.223740\pi\)
\(522\) 1.68757 6.29811i 0.0738630 0.275661i
\(523\) 5.12856 8.88292i 0.224256 0.388423i −0.731840 0.681477i \(-0.761338\pi\)
0.956096 + 0.293054i \(0.0946714\pi\)
\(524\) 0.866574i 0.0378565i
\(525\) 0.100127 15.3016i 0.00436991 0.667816i
\(526\) 12.8285 + 12.8285i 0.559349 + 0.559349i
\(527\) 1.78341 + 6.65577i 0.0776865 + 0.289930i
\(528\) −19.1417 + 11.0515i −0.833036 + 0.480953i
\(529\) −12.6826 21.9669i −0.551418 0.955083i
\(530\) 20.0213 5.36468i 0.869669 0.233027i
\(531\) 1.99399i 0.0865319i
\(532\) 0.943917 + 1.65990i 0.0409240 + 0.0719659i
\(533\) 30.1889 + 11.2442i 1.30763 + 0.487039i
\(534\) 5.50996 9.54354i 0.238439 0.412989i
\(535\) 16.7344 9.66163i 0.723493 0.417709i
\(536\) −12.2460 + 45.7025i −0.528945 + 1.97405i
\(537\) −31.8265 + 55.1251i −1.37341 + 2.37882i
\(538\) 10.8477i 0.467677i
\(539\) −11.6883 + 11.3864i −0.503453 + 0.490445i
\(540\) −2.79092 2.79092i −0.120102 0.120102i
\(541\) 2.14432 + 1.23802i 0.0921914 + 0.0532267i 0.545387 0.838184i \(-0.316383\pi\)
−0.453196 + 0.891411i \(0.649716\pi\)
\(542\) −24.7224 + 14.2735i −1.06192 + 0.613100i
\(543\) −4.07692 7.06143i −0.174957 0.303035i
\(544\) −2.32410 + 0.622742i −0.0996451 + 0.0266998i
\(545\) −14.5795 14.5795i −0.624515 0.624515i
\(546\) −13.3058 + 48.3893i −0.569437 + 2.07087i
\(547\) −9.26238 + 9.26238i −0.396031 + 0.396031i −0.876830 0.480800i \(-0.840346\pi\)
0.480800 + 0.876830i \(0.340346\pi\)
\(548\) −1.47208 5.49386i −0.0628839 0.234686i
\(549\) 3.54248 + 6.13575i 0.151189 + 0.261867i
\(550\) −5.80734 1.55607i −0.247626 0.0663511i
\(551\) −1.04382 + 1.80795i −0.0444682 + 0.0770211i
\(552\) −42.9896 + 42.9896i −1.82976 + 1.82976i
\(553\) −0.00182728 + 0.279247i −7.77039e−5 + 0.0118748i
\(554\) 5.02727i 0.213588i
\(555\) 8.81398 + 32.8942i 0.374132 + 1.39628i
\(556\) 1.73239 + 3.00058i 0.0734695 + 0.127253i
\(557\) 34.7097 + 9.30045i 1.47070 + 0.394073i 0.903171 0.429281i \(-0.141233\pi\)
0.567528 + 0.823354i \(0.307900\pi\)
\(558\) 18.0748 31.3065i 0.765167 1.32531i
\(559\) −42.5492 + 42.5492i −1.79964 + 1.79964i
\(560\) −3.78002 14.4857i −0.159735 0.612133i
\(561\) −6.46117 6.46117i −0.272791 0.272791i
\(562\) 9.57009 2.56430i 0.403690 0.108168i
\(563\) −5.30917 + 19.8141i −0.223755 + 0.835065i 0.759144 + 0.650922i \(0.225618\pi\)
−0.982899 + 0.184143i \(0.941049\pi\)
\(564\) −5.12902 8.88372i −0.215971 0.374072i
\(565\) 2.30922 + 1.33323i 0.0971495 + 0.0560893i
\(566\) 8.53094i 0.358582i
\(567\) −11.2329 + 2.93120i −0.471736 + 0.123099i
\(568\) −6.98924 + 6.98924i −0.293262 + 0.293262i
\(569\) −7.92536 4.57571i −0.332248 0.191824i 0.324591 0.945855i \(-0.394774\pi\)
−0.656839 + 0.754031i \(0.728107\pi\)
\(570\) −7.40700 12.8293i −0.310245 0.537360i
\(571\) −7.50156 + 27.9962i −0.313931 + 1.17160i 0.611050 + 0.791592i \(0.290747\pi\)
−0.924981 + 0.380013i \(0.875919\pi\)
\(572\) −3.23720 1.86900i −0.135354 0.0781468i
\(573\) −23.4375 −0.979115
\(574\) −7.80162 + 20.5344i −0.325633 + 0.857089i
\(575\) −13.8331 −0.576881
\(576\) 41.7395 + 24.0983i 1.73915 + 1.00410i
\(577\) 6.68254 24.9396i 0.278198 1.03825i −0.675470 0.737387i \(-0.736059\pi\)
0.953668 0.300861i \(-0.0972740\pi\)
\(578\) −9.84320 17.0489i −0.409423 0.709142i
\(579\) −14.1559 8.17291i −0.588299 0.339654i
\(580\) −0.360531 + 0.360531i −0.0149702 + 0.0149702i
\(581\) −4.25345 + 15.4685i −0.176463 + 0.641742i
\(582\) 2.35598i 0.0976587i
\(583\) 18.5982 + 10.7377i 0.770257 + 0.444708i
\(584\) 7.40964 + 12.8339i 0.306613 + 0.531069i
\(585\) −12.3243 + 45.9950i −0.509548 + 1.90166i
\(586\) −2.57994 + 0.691292i −0.106576 + 0.0285570i
\(587\) −29.5099 29.5099i −1.21800 1.21800i −0.968330 0.249673i \(-0.919677\pi\)
−0.249673 0.968330i \(-0.580323\pi\)
\(588\) 6.24361 + 1.76086i 0.257482 + 0.0726167i
\(589\) −8.18422 + 8.18422i −0.337225 + 0.337225i
\(590\) −0.411254 + 0.712313i −0.0169311 + 0.0293255i
\(591\) −78.2292 20.9615i −3.21792 0.862239i
\(592\) −11.0053 19.0617i −0.452313 0.783429i
\(593\) −6.90024 25.7520i −0.283359 1.05751i −0.950030 0.312158i \(-0.898948\pi\)
0.666671 0.745352i \(-0.267718\pi\)
\(594\) 21.5715i 0.885088i
\(595\) 5.37997 3.05937i 0.220557 0.125422i
\(596\) 0.972264 0.972264i 0.0398255 0.0398255i
\(597\) 30.5624 52.9356i 1.25084 2.16651i
\(598\) 43.8223 + 11.7421i 1.79203 + 0.480172i
\(599\) 23.7851 + 41.1970i 0.971832 + 1.68326i 0.690017 + 0.723793i \(0.257603\pi\)
0.281815 + 0.959469i \(0.409064\pi\)
\(600\) 4.50051 + 16.7961i 0.183732 + 0.685699i
\(601\) 9.72081 9.72081i 0.396520 0.396520i −0.480484 0.877004i \(-0.659539\pi\)
0.877004 + 0.480484i \(0.159539\pi\)
\(602\) −28.8226 29.2023i −1.17472 1.19020i
\(603\) 60.6967 + 60.6967i 2.47176 + 2.47176i
\(604\) 2.43815 0.653301i 0.0992070 0.0265824i
\(605\) −4.82905 8.36416i −0.196329 0.340051i
\(606\) −14.6085 + 8.43423i −0.593431 + 0.342617i
\(607\) 17.3466 + 10.0151i 0.704078 + 0.406500i 0.808864 0.587995i \(-0.200083\pi\)
−0.104787 + 0.994495i \(0.533416\pi\)
\(608\) −2.85782 2.85782i −0.115900 0.115900i
\(609\) 1.79075 + 6.86249i 0.0725650 + 0.278082i
\(610\) 2.92249i 0.118328i
\(611\) −27.8447 + 48.2285i −1.12648 + 1.95111i
\(612\) −0.606576 + 2.26377i −0.0245194 + 0.0915075i
\(613\) 15.3595 8.86778i 0.620362 0.358166i −0.156648 0.987655i \(-0.550069\pi\)
0.777010 + 0.629488i \(0.216735\pi\)
\(614\) 12.8596 22.2734i 0.518970 0.898882i
\(615\) −11.2760 + 30.2743i −0.454691 + 1.22078i
\(616\) 9.37633 15.9976i 0.377783 0.644562i
\(617\) 35.8613i 1.44372i −0.692038 0.721861i \(-0.743287\pi\)
0.692038 0.721861i \(-0.256713\pi\)
\(618\) −60.1466 + 16.1162i −2.41945 + 0.648290i
\(619\) 20.8682 + 36.1448i 0.838764 + 1.45278i 0.890928 + 0.454144i \(0.150055\pi\)
−0.0521642 + 0.998639i \(0.516612\pi\)
\(620\) −2.44808 + 1.41340i −0.0983172 + 0.0567635i
\(621\) 12.8458 + 47.9414i 0.515486 + 1.92382i
\(622\) −21.2027 21.2027i −0.850151 0.850151i
\(623\) −0.0506025 + 7.73314i −0.00202735 + 0.309822i
\(624\) 47.7040i 1.90969i
\(625\) 5.54905 9.61124i 0.221962 0.384450i
\(626\) −8.88292 + 33.1515i −0.355033 + 1.32500i
\(627\) 3.97246 14.8254i 0.158645 0.592071i
\(628\) −3.90061 + 1.04516i −0.155651 + 0.0417066i
\(629\) 6.43415 6.43415i 0.256546 0.256546i
\(630\) −31.3071 8.60866i −1.24730 0.342977i
\(631\) 33.4051 1.32984 0.664918 0.746916i \(-0.268466\pi\)
0.664918 + 0.746916i \(0.268466\pi\)
\(632\) −0.0821324 0.306522i −0.00326705 0.0121928i
\(633\) 8.05171 + 13.9460i 0.320027 + 0.554303i
\(634\) 16.3876 + 4.39103i 0.650833 + 0.174390i
\(635\) −21.9544 12.6754i −0.871235 0.503008i
\(636\) 8.53761i 0.338538i
\(637\) −8.66910 34.1342i −0.343482 1.35245i
\(638\) 2.78660 0.110322
\(639\) 4.64114 + 17.3210i 0.183601 + 0.685208i
\(640\) 6.84341 + 11.8531i 0.270509 + 0.468536i
\(641\) −16.9079 4.53047i −0.667824 0.178943i −0.0910494 0.995846i \(-0.529022\pi\)
−0.576774 + 0.816904i \(0.695689\pi\)
\(642\) 10.8665 + 40.5544i 0.428867 + 1.60055i
\(643\) 4.80939 + 4.80939i 0.189664 + 0.189664i 0.795551 0.605887i \(-0.207182\pi\)
−0.605887 + 0.795551i \(0.707182\pi\)
\(644\) 1.55487 5.65460i 0.0612706 0.222822i
\(645\) −42.6695 42.6695i −1.68011 1.68011i
\(646\) −1.97912 + 3.42794i −0.0778676 + 0.134871i
\(647\) 7.55243 4.36039i 0.296916 0.171425i −0.344140 0.938918i \(-0.611830\pi\)
0.641057 + 0.767493i \(0.278496\pi\)
\(648\) 11.4247 6.59607i 0.448805 0.259118i
\(649\) −0.823143 + 0.220561i −0.0323112 + 0.00865776i
\(650\) 9.17536 9.17536i 0.359887 0.359887i
\(651\) −0.257295 + 39.3201i −0.0100842 + 1.54108i
\(652\) 1.59228 0.0623587
\(653\) 24.4080 6.54011i 0.955160 0.255934i 0.252609 0.967568i \(-0.418711\pi\)
0.702550 + 0.711634i \(0.252045\pi\)
\(654\) 38.7972 22.3996i 1.51709 0.875892i
\(655\) 2.35891 + 4.08575i 0.0921702 + 0.159643i
\(656\) 1.97531 20.7867i 0.0771227 0.811586i
\(657\) 26.8850 1.04889
\(658\) −32.7607 19.2013i −1.27715 0.748546i
\(659\) −6.02808 6.02808i −0.234821 0.234821i 0.579881 0.814701i \(-0.303099\pi\)
−0.814701 + 0.579881i \(0.803099\pi\)
\(660\) 1.87429 3.24636i 0.0729565 0.126364i
\(661\) 14.9735 8.64495i 0.582402 0.336250i −0.179686 0.983724i \(-0.557508\pi\)
0.762087 + 0.647474i \(0.224175\pi\)
\(662\) 19.8675 + 5.32348i 0.772172 + 0.206903i
\(663\) 19.0491 5.10420i 0.739806 0.198231i
\(664\) 18.2304i 0.707476i
\(665\) 8.96884 + 5.25671i 0.347797 + 0.203846i
\(666\) −47.7370 −1.84977
\(667\) 6.19305 1.65942i 0.239796 0.0642531i
\(668\) −0.376084 + 1.40356i −0.0145511 + 0.0543055i
\(669\) 3.01123 11.2380i 0.116421 0.434488i
\(670\) 9.16416 + 34.2011i 0.354042 + 1.32130i
\(671\) −2.14107 + 2.14107i −0.0826549 + 0.0826549i
\(672\) −13.7300 0.0898437i −0.529648 0.00346580i
\(673\) 14.5515 14.5515i 0.560921 0.560921i −0.368648 0.929569i \(-0.620179\pi\)
0.929569 + 0.368648i \(0.120179\pi\)
\(674\) −3.56088 + 6.16762i −0.137160 + 0.237568i
\(675\) 13.7119 + 3.67409i 0.527771 + 0.141416i
\(676\) 3.39845 1.96210i 0.130710 0.0754653i
\(677\) 12.4288 + 7.17578i 0.477678 + 0.275788i 0.719449 0.694546i \(-0.244395\pi\)
−0.241770 + 0.970334i \(0.577728\pi\)
\(678\) −4.09669 + 4.09669i −0.157332 + 0.157332i
\(679\) −0.817277 1.43720i −0.0313642 0.0551547i
\(680\) −4.97308 + 4.97308i −0.190709 + 0.190709i
\(681\) 8.61726 14.9255i 0.330214 0.571948i
\(682\) 14.9230 + 3.99860i 0.571430 + 0.153114i
\(683\) 39.1901 + 10.5010i 1.49957 + 0.401808i 0.912956 0.408059i \(-0.133794\pi\)
0.586613 + 0.809867i \(0.300461\pi\)
\(684\) −3.80251 + 1.01888i −0.145393 + 0.0389578i
\(685\) −21.8955 21.8955i −0.836583 0.836583i
\(686\) 23.3134 5.75880i 0.890109 0.219872i
\(687\) 63.4834 2.42204
\(688\) 33.7768 + 19.5010i 1.28773 + 0.743469i
\(689\) −40.1398 + 23.1747i −1.52920 + 0.882886i
\(690\) −11.7754 + 43.9463i −0.448281 + 1.67301i
\(691\) −12.4668 46.5267i −0.474259 1.76996i −0.624201 0.781263i \(-0.714576\pi\)
0.149943 0.988695i \(-0.452091\pi\)
\(692\) 0.0896904i 0.00340952i
\(693\) −16.6292 29.2429i −0.631692 1.11085i
\(694\) −32.7866 32.7866i −1.24456 1.24456i
\(695\) 16.3358 + 9.43148i 0.619652 + 0.357757i
\(696\) −4.02973 6.97970i −0.152747 0.264565i
\(697\) 8.51189 1.43535i 0.322411 0.0543676i
\(698\) 0.426843 0.739313i 0.0161562 0.0279834i
\(699\) 64.6010i 2.44343i
\(700\) −1.17826 1.19378i −0.0445340 0.0451207i
\(701\) −5.13213 −0.193838 −0.0969190 0.995292i \(-0.530899\pi\)
−0.0969190 + 0.995292i \(0.530899\pi\)
\(702\) −40.3195 23.2785i −1.52176 0.878590i
\(703\) 14.7634 + 3.95585i 0.556814 + 0.149198i
\(704\) −5.33115 + 19.8961i −0.200925 + 0.749863i
\(705\) −48.3649 27.9235i −1.82153 1.05166i
\(706\) 33.6677i 1.26710i
\(707\) 5.98573 10.2127i 0.225117 0.384087i
\(708\) 0.239560 + 0.239560i 0.00900320 + 0.00900320i
\(709\) −5.11166 + 1.36967i −0.191973 + 0.0514389i −0.353524 0.935425i \(-0.615017\pi\)
0.161552 + 0.986864i \(0.448350\pi\)
\(710\) −1.91444 + 7.14479i −0.0718476 + 0.268139i
\(711\) −0.556090 0.149004i −0.0208550 0.00558809i
\(712\) −2.27447 8.48845i −0.0852395 0.318118i
\(713\) 35.5466 1.33123
\(714\) 3.39534 + 13.0116i 0.127068 + 0.486946i
\(715\) −20.3505 −0.761065
\(716\) 1.80587 + 6.73959i 0.0674884 + 0.251870i
\(717\) −52.5770 + 30.3554i −1.96353 + 1.13364i
\(718\) −4.59831 + 2.65484i −0.171607 + 0.0990776i
\(719\) −0.698868 2.60821i −0.0260634 0.0972698i 0.951669 0.307126i \(-0.0993672\pi\)
−0.977732 + 0.209856i \(0.932701\pi\)
\(720\) 30.8637 1.15022
\(721\) 31.1001 30.6957i 1.15823 1.14317i
\(722\) 17.9874 0.669422
\(723\) 20.5443 + 76.6722i 0.764049 + 2.85147i
\(724\) −0.863330 0.231328i −0.0320854 0.00859726i
\(725\) 0.474618 1.77130i 0.0176269 0.0657844i
\(726\) 20.2698 5.43127i 0.752282 0.201573i
\(727\) −0.305010 0.305010i −0.0113122 0.0113122i 0.701428 0.712740i \(-0.252546\pi\)
−0.712740 + 0.701428i \(0.752546\pi\)
\(728\) 19.7830 + 34.7890i 0.733208 + 1.28937i
\(729\) 38.3205i 1.41928i
\(730\) 9.60413 + 5.54495i 0.355465 + 0.205228i
\(731\) −4.17311 + 15.5743i −0.154348 + 0.576035i
\(732\) 1.16275 + 0.311557i 0.0429764 + 0.0115155i
\(733\) −28.3091 16.3443i −1.04562 0.603690i −0.124201 0.992257i \(-0.539637\pi\)
−0.921420 + 0.388568i \(0.872970\pi\)
\(734\) −45.9944 −1.69768
\(735\) 34.2308 8.69363i 1.26262 0.320669i
\(736\) 12.4124i 0.457527i
\(737\) −18.3425 + 31.7701i −0.675654 + 1.17027i
\(738\) −36.9009 26.2516i −1.35834 0.966334i
\(739\) −10.2066 17.6784i −0.375457 0.650310i 0.614938 0.788575i \(-0.289181\pi\)
−0.990395 + 0.138265i \(0.955848\pi\)
\(740\) 3.23279 + 1.86645i 0.118840 + 0.0686121i
\(741\) 23.4236 + 23.4236i 0.860488 + 0.860488i
\(742\) −15.6228 27.4730i −0.573530 1.00857i
\(743\) 2.34864i 0.0861632i −0.999072 0.0430816i \(-0.986282\pi\)
0.999072 0.0430816i \(-0.0137176\pi\)
\(744\) −11.5648 43.1606i −0.423988 1.58234i
\(745\) 1.93745 7.23066i 0.0709827 0.264911i
\(746\) 16.0751 9.28095i 0.588551 0.339800i
\(747\) −28.6424 16.5367i −1.04797 0.605047i
\(748\) −1.00161 −0.0366223
\(749\) −20.6969 20.9695i −0.756247 0.766210i
\(750\) 32.3309 + 32.3309i 1.18056 + 1.18056i
\(751\) −40.8938 + 10.9575i −1.49224 + 0.399844i −0.910492 0.413527i \(-0.864297\pi\)
−0.581745 + 0.813371i \(0.697630\pi\)
\(752\) 34.8657 + 9.34223i 1.27142 + 0.340676i
\(753\) −13.3675 3.58181i −0.487138 0.130528i
\(754\) −3.00711 + 5.20847i −0.109512 + 0.189681i
\(755\) 9.71712 9.71712i 0.353642 0.353642i
\(756\) −3.04311 + 5.19207i −0.110677 + 0.188834i
\(757\) 3.67155 3.67155i 0.133445 0.133445i −0.637229 0.770674i \(-0.719920\pi\)
0.770674 + 0.637229i \(0.219920\pi\)
\(758\) −8.83713 5.10212i −0.320979 0.185317i
\(759\) −40.8226 + 23.5689i −1.48177 + 0.855498i
\(760\) −11.4110 3.05756i −0.413919 0.110909i
\(761\) −1.54564 + 2.67713i −0.0560295 + 0.0970460i −0.892680 0.450692i \(-0.851177\pi\)
0.836650 + 0.547738i \(0.184511\pi\)
\(762\) 38.9484 38.9484i 1.41095 1.41095i
\(763\) −15.8969 + 27.1227i −0.575505 + 0.981909i
\(764\) −1.81663 + 1.81663i −0.0657234 + 0.0657234i
\(765\) 3.30233 + 12.3245i 0.119396 + 0.445592i
\(766\) −2.30991 + 8.62069i −0.0834603 + 0.311478i
\(767\) 0.476029 1.77656i 0.0171884 0.0641480i
\(768\) 20.9093 5.60262i 0.754498 0.202167i
\(769\) −37.3814 −1.34801 −0.674003 0.738728i \(-0.735427\pi\)
−0.674003 + 0.738728i \(0.735427\pi\)
\(770\) 0.0907998 13.8761i 0.00327220 0.500061i
\(771\) 8.64052i 0.311181i
\(772\) −1.73070 + 0.463739i −0.0622891 + 0.0166903i
\(773\) −26.5321 7.10926i −0.954293 0.255702i −0.252110 0.967699i \(-0.581125\pi\)
−0.702183 + 0.711996i \(0.747791\pi\)
\(774\) 73.2560 42.2944i 2.63313 1.52024i
\(775\) 5.08341 8.80473i 0.182602 0.316275i
\(776\) 1.32851 + 1.32851i 0.0476906 + 0.0476906i
\(777\) 45.1372 25.6676i 1.61929 0.920821i
\(778\) −36.0430 −1.29221
\(779\) 9.23679 + 11.1766i 0.330942 + 0.400444i
\(780\) 4.04521 + 7.00651i 0.144842 + 0.250873i
\(781\) −6.63693 + 3.83184i −0.237488 + 0.137114i
\(782\) 11.7423 3.14634i 0.419903 0.112513i
\(783\) −6.57952 −0.235133
\(784\) −19.9162 + 11.1537i −0.711294 + 0.398347i
\(785\) −15.5456 + 15.5456i −0.554848 + 0.554848i
\(786\) −9.90144 + 2.65308i −0.353173 + 0.0946324i
\(787\) 29.9696 17.3029i 1.06830 0.616783i 0.140583 0.990069i \(-0.455102\pi\)
0.927716 + 0.373286i \(0.121769\pi\)
\(788\) −7.68823 + 4.43880i −0.273882 + 0.158126i
\(789\) 20.3415 35.2326i 0.724178 1.25431i
\(790\) −0.167920 0.167920i −0.00597434 0.00597434i
\(791\) 1.07795 3.92018i 0.0383276 0.139386i
\(792\) 27.0312 + 27.0312i 0.960513 + 0.960513i
\(793\) −1.69140 6.31239i −0.0600634 0.224160i
\(794\) −15.0990 4.04577i −0.535845 0.143579i
\(795\) −23.2403 40.2533i −0.824248 1.42764i
\(796\) −1.73414 6.47190i −0.0614650 0.229390i
\(797\) −41.3243 −1.46378 −0.731892 0.681421i \(-0.761362\pi\)
−0.731892 + 0.681421i \(0.761362\pi\)
\(798\) −16.0761 + 15.8671i −0.569088 + 0.561688i
\(799\) 14.9221i 0.527906i
\(800\) 3.07449 + 1.77506i 0.108700 + 0.0627578i
\(801\) −15.3997 4.12633i −0.544121 0.145797i
\(802\) 16.1774 + 28.0201i 0.571244 + 0.989423i
\(803\) 2.97382 + 11.0985i 0.104944 + 0.391656i
\(804\) 14.5843 0.514348
\(805\) −8.06147 30.8930i −0.284129 1.08884i
\(806\) −23.5777 + 23.5777i −0.830489 + 0.830489i
\(807\) 23.4965 6.29588i 0.827118 0.221625i
\(808\) −3.48159 + 12.9935i −0.122482 + 0.457109i
\(809\) −6.21924 + 23.2105i −0.218657 + 0.816038i 0.766191 + 0.642613i \(0.222150\pi\)
−0.984847 + 0.173424i \(0.944517\pi\)
\(810\) 4.93611 8.54960i 0.173437 0.300402i
\(811\) 11.9437i 0.419401i 0.977766 + 0.209700i \(0.0672488\pi\)
−0.977766 + 0.209700i \(0.932751\pi\)
\(812\) 0.670710 + 0.393109i 0.0235373 + 0.0137954i
\(813\) 45.2657 + 45.2657i 1.58754 + 1.58754i
\(814\) −5.28031 19.7064i −0.185075 0.690708i
\(815\) 7.50735 4.33437i 0.262971 0.151826i
\(816\) −6.39120 11.0699i −0.223737 0.387524i
\(817\) −26.1604 + 7.00967i −0.915238 + 0.245237i
\(818\) 28.2599i 0.988084i
\(819\) 72.6034 + 0.475087i 2.53697 + 0.0166009i
\(820\) 1.47256 + 3.22055i 0.0514239 + 0.112466i
\(821\) 14.1541 24.5157i 0.493983 0.855603i −0.505993 0.862537i \(-0.668874\pi\)
0.999976 + 0.00693445i \(0.00220732\pi\)
\(822\) 58.2657 33.6397i 2.03225 1.17332i
\(823\) 8.35759 31.1910i 0.291327 1.08725i −0.652763 0.757562i \(-0.726390\pi\)
0.944091 0.329686i \(-0.106943\pi\)
\(824\) −24.8281 + 43.0035i −0.864927 + 1.49810i
\(825\) 13.4821i 0.469386i
\(826\) 1.20924 + 0.332511i 0.0420748 + 0.0115695i
\(827\) 15.1277 + 15.1277i 0.526040 + 0.526040i 0.919389 0.393349i \(-0.128684\pi\)
−0.393349 + 0.919389i \(0.628684\pi\)
\(828\) 10.4704 + 6.04509i 0.363872 + 0.210081i
\(829\) 2.80397 1.61887i 0.0973858 0.0562257i −0.450516 0.892768i \(-0.648760\pi\)
0.547902 + 0.836543i \(0.315427\pi\)
\(830\) −6.82128 11.8148i −0.236770 0.410098i
\(831\) 10.8893 2.91778i 0.377745 0.101217i
\(832\) −31.4351 31.4351i −1.08982 1.08982i
\(833\) −6.58487 6.75952i −0.228152 0.234203i
\(834\) −28.9807 + 28.9807i −1.00352 + 1.00352i
\(835\) 2.04748 + 7.64131i 0.0708561 + 0.264438i
\(836\) −0.841210 1.45702i −0.0290939 0.0503920i
\(837\) −35.2351 9.44122i −1.21790 0.326336i
\(838\) −15.1927 + 26.3145i −0.524822 + 0.909018i
\(839\) 19.0538 19.0538i 0.657810 0.657810i −0.297051 0.954862i \(-0.596003\pi\)
0.954862 + 0.297051i \(0.0960032\pi\)
\(840\) −34.8874 + 19.8390i −1.20373 + 0.684511i
\(841\) 28.1501i 0.970692i
\(842\) −9.62637 35.9261i −0.331747 1.23810i
\(843\) −11.1088 19.2409i −0.382606 0.662693i
\(844\) 1.70503 + 0.456862i 0.0586897 + 0.0157258i
\(845\) 10.6821 18.5019i 0.367475 0.636485i
\(846\) 55.3560 55.3560i 1.90318 1.90318i
\(847\) −10.4809 + 10.3447i −0.360129 + 0.355447i
\(848\) 21.2428 + 21.2428i 0.729479 + 0.729479i
\(849\) 18.4784 4.95127i 0.634176 0.169927i
\(850\) 0.899896 3.35846i 0.0308662 0.115194i
\(851\) −23.4704 40.6519i −0.804554 1.39353i
\(852\) 2.63854 + 1.52336i 0.0903950 + 0.0521896i
\(853\) 36.9504i 1.26516i 0.774496 + 0.632578i \(0.218003\pi\)
−0.774496 + 0.632578i \(0.781997\pi\)
\(854\) 4.31170 1.12513i 0.147543 0.0385012i
\(855\) −15.1547 + 15.1547i −0.518279 + 0.518279i
\(856\) 28.9955 + 16.7406i 0.991045 + 0.572180i
\(857\) −14.8528 25.7258i −0.507363 0.878778i −0.999964 0.00852251i \(-0.997287\pi\)
0.492601 0.870255i \(-0.336046\pi\)
\(858\) 11.4442 42.7102i 0.390697 1.45810i
\(859\) −2.52829 1.45971i −0.0862643 0.0498047i 0.456247 0.889853i \(-0.349193\pi\)
−0.542512 + 0.840048i \(0.682527\pi\)
\(860\) −6.61460 −0.225556
\(861\) 49.0064 + 4.98071i 1.67013 + 0.169742i
\(862\) 2.71575 0.0924988
\(863\) −29.2924 16.9120i −0.997123 0.575690i −0.0897276 0.995966i \(-0.528600\pi\)
−0.907396 + 0.420277i \(0.861933\pi\)
\(864\) 3.29674 12.3036i 0.112157 0.418577i
\(865\) 0.244147 + 0.422875i 0.00830124 + 0.0143782i
\(866\) 3.48869 + 2.01420i 0.118551 + 0.0684452i
\(867\) −31.2158 + 31.2158i −1.06015 + 1.06015i
\(868\) 3.02774 + 3.06763i 0.102768 + 0.104122i
\(869\) 0.246042i 0.00834641i
\(870\) −5.22320 3.01562i −0.177083 0.102239i
\(871\) −39.5879 68.5683i −1.34139 2.32335i
\(872\) 9.24638 34.5080i 0.313122 1.16859i
\(873\) 3.29235 0.882182i 0.111429 0.0298573i
\(874\) 14.4388 + 14.4388i 0.488400 + 0.488400i
\(875\) −30.9379 8.50715i −1.04589 0.287594i
\(876\) 3.22998 3.22998i 0.109131 0.109131i
\(877\) −1.40238 + 2.42900i −0.0473551 + 0.0820214i −0.888731 0.458428i \(-0.848413\pi\)
0.841376 + 0.540450i \(0.181746\pi\)
\(878\) −44.6336 11.9595i −1.50631 0.403615i
\(879\) 2.99474 + 5.18704i 0.101010 + 0.174954i
\(880\) 3.41391 + 12.7409i 0.115083 + 0.429495i
\(881\) 35.4462i 1.19421i 0.802163 + 0.597106i \(0.203683\pi\)
−0.802163 + 0.597106i \(0.796317\pi\)
\(882\) −0.647884 + 49.5031i −0.0218154 + 1.66686i
\(883\) −16.4704 + 16.4704i −0.554272 + 0.554272i −0.927671 0.373399i \(-0.878192\pi\)
0.373399 + 0.927671i \(0.378192\pi\)
\(884\) 1.08087 1.87211i 0.0363535 0.0629660i
\(885\) 1.78159 + 0.477375i 0.0598875 + 0.0160468i
\(886\) −1.35151 2.34088i −0.0454049 0.0786435i
\(887\) −3.38084 12.6175i −0.113518 0.423653i 0.885654 0.464345i \(-0.153710\pi\)
−0.999172 + 0.0406921i \(0.987044\pi\)
\(888\) −41.7234 + 41.7234i −1.40015 + 1.40015i
\(889\) −10.2484 + 37.2704i −0.343721 + 1.25001i
\(890\) −4.65018 4.65018i −0.155874 0.155874i
\(891\) 9.87985 2.64730i 0.330987 0.0886878i
\(892\) −0.637658 1.10446i −0.0213504 0.0369799i
\(893\) −21.7069 + 12.5325i −0.726395 + 0.419384i
\(894\) 14.0857 + 8.13238i 0.471096 + 0.271988i
\(895\) 26.8602 + 26.8602i 0.897839 + 0.897839i
\(896\) 14.8529 14.6598i 0.496200 0.489748i
\(897\) 101.736i 3.39687i
\(898\) −3.78207 + 6.55073i −0.126209 + 0.218601i
\(899\) −1.21961 + 4.55166i −0.0406764 + 0.151806i
\(900\) 2.99468 1.72898i 0.0998226 0.0576326i
\(901\) −6.20972 + 10.7555i −0.206876 + 0.358319i
\(902\) 6.75525 18.1369i 0.224925 0.603891i
\(903\) −46.5252 + 79.3799i −1.54826 + 2.64160i
\(904\) 4.62012i 0.153663i
\(905\) −4.70015 + 1.25940i −0.156238 + 0.0418639i
\(906\) 14.9292 + 25.8581i 0.495989 + 0.859078i
\(907\) −11.9377 + 6.89225i −0.396386 + 0.228854i −0.684923 0.728615i \(-0.740164\pi\)
0.288537 + 0.957469i \(0.406831\pi\)
\(908\) −0.488952 1.82479i −0.0162264 0.0605579i
\(909\) 17.2564 + 17.2564i 0.572359 + 0.572359i
\(910\) 25.8381 + 15.1439i 0.856524 + 0.502016i
\(911\) 1.37279i 0.0454827i 0.999741 + 0.0227413i \(0.00723941\pi\)
−0.999741 + 0.0227413i \(0.992761\pi\)
\(912\) 10.7354 18.5943i 0.355486 0.615720i
\(913\) 3.65834 13.6531i 0.121073 0.451851i
\(914\) 1.55085 5.78785i 0.0512975 0.191445i
\(915\) 6.33025 1.69619i 0.209272 0.0560742i
\(916\) 4.92057 4.92057i 0.162580 0.162580i
\(917\) 5.11976 5.05319i 0.169069 0.166871i
\(918\) −12.4751 −0.411738
\(919\) −9.19225 34.3059i −0.303224 1.13165i −0.934463 0.356060i \(-0.884120\pi\)
0.631239 0.775588i \(-0.282547\pi\)
\(920\) 18.1407 + 31.4206i 0.598081 + 1.03591i
\(921\) −55.7088 14.9271i −1.83567 0.491865i
\(922\) −28.8933 16.6815i −0.951549 0.549377i
\(923\) 16.5402i 0.544429i
\(924\) −5.51110 1.51541i −0.181302 0.0498535i
\(925\) −13.4257 −0.441434
\(926\) −1.51619 5.65849i −0.0498251 0.185950i
\(927\) 45.0429 + 78.0167i 1.47940 + 2.56240i
\(928\) −1.58938 0.425872i −0.0521739 0.0139799i
\(929\) −9.70884 36.2339i −0.318537 1.18879i −0.920652 0.390385i \(-0.872342\pi\)
0.602115 0.798409i \(-0.294325\pi\)
\(930\) −23.6444 23.6444i −0.775331 0.775331i
\(931\) 4.30258 15.2560i 0.141011 0.499994i
\(932\) −5.00720 5.00720i −0.164016 0.164016i
\(933\) −33.6202 + 58.2318i −1.10067 + 1.90642i
\(934\) 7.28545 4.20626i 0.238387 0.137633i
\(935\) −4.72240 + 2.72648i −0.154439 + 0.0891654i
\(936\) −79.6947 + 21.3541i −2.60490 + 0.697982i
\(937\) −11.3197 + 11.3197i −0.369797 + 0.369797i −0.867403 0.497606i \(-0.834213\pi\)
0.497606 + 0.867403i \(0.334213\pi\)
\(938\) 46.9305 26.6874i 1.53234 0.871375i
\(939\) 76.9632 2.51160
\(940\) −5.91309 + 1.58441i −0.192864 + 0.0516777i
\(941\) 22.1857 12.8089i 0.723233 0.417559i −0.0927084 0.995693i \(-0.529552\pi\)
0.815942 + 0.578134i \(0.196219\pi\)
\(942\) −23.8840 41.3683i −0.778183 1.34785i
\(943\) 4.21264 44.3309i 0.137182 1.44361i
\(944\) −1.19212 −0.0388000
\(945\) −0.214390 + 32.7634i −0.00697411 + 1.06579i
\(946\) 25.5626 + 25.5626i 0.831113 + 0.831113i
\(947\) 4.48354 7.76572i 0.145695 0.252352i −0.783937 0.620841i \(-0.786791\pi\)
0.929632 + 0.368489i \(0.120125\pi\)
\(948\) −0.0847105 + 0.0489076i −0.00275127 + 0.00158845i
\(949\) −23.9534 6.41830i −0.777561 0.208347i
\(950\) 5.64128 1.51158i 0.183027 0.0490420i
\(951\) 38.0447i 1.23368i
\(952\) 9.25162 + 5.42245i 0.299847 + 0.175743i
\(953\) −2.17990 −0.0706139 −0.0353069 0.999377i \(-0.511241\pi\)
−0.0353069 + 0.999377i \(0.511241\pi\)
\(954\) 62.9354 16.8635i 2.03761 0.545975i
\(955\) −3.62004 + 13.5102i −0.117142 + 0.437179i
\(956\) −1.72239 + 6.42806i −0.0557062 + 0.207898i
\(957\) −1.61731 6.03589i −0.0522803 0.195113i
\(958\) 27.3075 27.3075i 0.882265 0.882265i
\(959\) −23.8739 + 40.7330i −0.770930 + 1.31534i
\(960\) 31.5240 31.5240i 1.01743 1.01743i
\(961\) 2.43728 4.22150i 0.0786220 0.136177i
\(962\) 42.5316 + 11.3963i 1.37127 + 0.367432i
\(963\) 52.6034 30.3706i 1.69512 0.978679i
\(964\) 7.53521 + 4.35046i 0.242693 + 0.140119i
\(965\) −6.89759 + 6.89759i −0.222041 + 0.222041i
\(966\) 69.3696 + 0.453926i 2.23193 + 0.0146048i
\(967\) −29.4467 + 29.4467i −0.946942 + 0.946942i −0.998662 0.0517200i \(-0.983530\pi\)
0.0517200 + 0.998662i \(0.483530\pi\)
\(968\) 8.36722 14.4924i 0.268933 0.465805i
\(969\) 8.57374 + 2.29733i 0.275428 + 0.0738007i
\(970\) 1.35807 + 0.363894i 0.0436050 + 0.0116839i
\(971\) −31.4440 + 8.42540i −1.00909 + 0.270384i −0.725248 0.688488i \(-0.758275\pi\)
−0.283839 + 0.958872i \(0.591608\pi\)
\(972\) 1.94992 + 1.94992i 0.0625437 + 0.0625437i
\(973\) 7.62562 27.7321i 0.244466 0.889049i
\(974\) 47.0386 1.50721
\(975\) −25.1995 14.5490i −0.807031 0.465939i
\(976\) −3.66828 + 2.11788i −0.117419 + 0.0677917i
\(977\) 9.25790 34.5510i 0.296187 1.10538i −0.644084 0.764955i \(-0.722761\pi\)
0.940270 0.340428i \(-0.110572\pi\)
\(978\) 4.87490 + 18.1934i 0.155882 + 0.581760i
\(979\) 6.81359i 0.217763i
\(980\) 1.97938 3.32706i 0.0632289 0.106279i
\(981\) −45.8294 45.8294i −1.46322 1.46322i
\(982\) −27.4122 15.8265i −0.874759 0.505042i
\(983\) 9.06056 + 15.6934i 0.288987 + 0.500540i 0.973568 0.228396i \(-0.0733482\pi\)
−0.684581 + 0.728937i \(0.740015\pi\)
\(984\) −55.1969 + 9.30777i −1.75961 + 0.296721i
\(985\) −24.1658 + 41.8564i −0.769987 + 1.33366i
\(986\) 1.61152i 0.0513214i
\(987\) −22.5769 + 82.1054i −0.718632 + 2.61345i
\(988\) 3.63111 0.115521
\(989\) 72.0341 + 41.5889i 2.29055 + 1.32245i
\(990\) 27.6328 + 7.40419i 0.878228 + 0.235320i
\(991\) −11.7496 + 43.8500i −0.373238 + 1.39294i 0.482665 + 0.875805i \(0.339669\pi\)
−0.855903 + 0.517137i \(0.826998\pi\)
\(992\) −7.90044 4.56132i −0.250839 0.144822i
\(993\) 46.1236i 1.46369i
\(994\) 11.2781 + 0.0737993i 0.357720 + 0.00234077i
\(995\) −25.7934 25.7934i −0.817706 0.817706i
\(996\) −5.42785 + 1.45439i −0.171988 + 0.0460840i
\(997\) −5.84676 + 21.8204i −0.185169 + 0.691059i 0.809426 + 0.587223i \(0.199779\pi\)
−0.994594 + 0.103837i \(0.966888\pi\)
\(998\) −39.9634 10.7082i −1.26502 0.338961i
\(999\) 12.4675 + 46.5294i 0.394454 + 1.47212i
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 287.2.r.c.9.17 96
7.4 even 3 inner 287.2.r.c.214.8 yes 96
41.32 even 4 inner 287.2.r.c.114.8 yes 96
287.32 even 12 inner 287.2.r.c.32.17 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.r.c.9.17 96 1.1 even 1 trivial
287.2.r.c.32.17 yes 96 287.32 even 12 inner
287.2.r.c.114.8 yes 96 41.32 even 4 inner
287.2.r.c.214.8 yes 96 7.4 even 3 inner