LMFDB - Embedded newform 552.2.bf.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(5,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bf (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.18

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15945 - 0.809745i) q^{2} +(1.35636 - 1.07716i) q^{3} +(0.688626 + 1.87771i) q^{4} +(-1.97986 - 0.284661i) q^{5} +(-2.44486 + 0.150603i) q^{6} +(2.90361 - 1.32603i) q^{7} +(0.722042 - 2.73471i) q^{8} +(0.679440 - 2.92205i) q^{9} +O(q^{10})$	\(q+(-1.15945 - 0.809745i) q^{2} +(1.35636 - 1.07716i) q^{3} +(0.688626 + 1.87771i) q^{4} +(-1.97986 - 0.284661i) q^{5} +(-2.44486 + 0.150603i) q^{6} +(2.90361 - 1.32603i) q^{7} +(0.722042 - 2.73471i) q^{8} +(0.679440 - 2.92205i) q^{9} +(2.06503 + 1.93323i) q^{10} +(0.0155140 + 0.0528360i) q^{11} +(2.95663 + 1.80509i) q^{12} +(6.52515 + 2.97994i) q^{13} +(-4.44033 - 0.813720i) q^{14} +(-2.99203 + 1.74653i) q^{15} +(-3.05159 + 2.58608i) q^{16} +(-0.218352 + 0.140326i) q^{17} +(-3.15389 + 2.83778i) q^{18} +(-4.96870 - 3.19319i) q^{19} +(-0.828872 - 3.91362i) q^{20} +(2.50999 - 4.92625i) q^{21} +(0.0247960 - 0.0738228i) q^{22} +(3.59799 + 3.17088i) q^{23} +(-1.96638 - 4.48702i) q^{24} +(-0.958658 - 0.281487i) q^{25} +(-5.15257 - 8.73879i) q^{26} +(-2.22595 - 4.69522i) q^{27} +(4.48941 + 4.53900i) q^{28} +(6.21239 - 3.99246i) q^{29} +(4.88334 + 0.397781i) q^{30} +(-4.18469 - 4.82939i) q^{31} +(5.63221 - 0.527410i) q^{32} +(0.0779556 + 0.0549536i) q^{33} +(0.366795 + 0.0141087i) q^{34} +(-6.12621 + 1.79882i) q^{35} +(5.95464 - 0.736407i) q^{36} +(-0.947989 - 6.59341i) q^{37} +(3.17526 + 7.72570i) q^{38} +(12.0604 - 2.98678i) q^{39} +(-2.20801 + 5.20881i) q^{40} +(-0.898237 - 0.129147i) q^{41} +(-6.89920 + 3.67926i) q^{42} +(0.831631 - 0.959753i) q^{43} +(-0.0885272 + 0.0655151i) q^{44} +(-2.17699 + 5.59183i) q^{45} +(-1.60407 - 6.58991i) q^{46} +0.188785i q^{47} +(-1.35343 + 6.79472i) q^{48} +(2.08856 - 2.41033i) q^{49} +(0.883578 + 1.10264i) q^{50} +(-0.145010 + 0.425533i) q^{51} +(-1.10207 + 14.3044i) q^{52} +(-8.20646 + 3.74777i) q^{53} +(-1.22106 + 7.24631i) q^{54} +(-0.0156753 - 0.109024i) q^{55} +(-1.52980 - 8.89799i) q^{56} +(-10.1789 + 1.02098i) q^{57} +(-10.4358 - 0.401412i) q^{58} +(4.21225 - 9.22355i) q^{59} +(-5.33986 - 4.41546i) q^{60} +(8.61910 + 9.94698i) q^{61} +(0.941345 + 8.98794i) q^{62} +(-1.90191 - 9.38545i) q^{63} +(-6.95731 - 3.94915i) q^{64} +(-12.0706 - 7.75731i) q^{65} +(-0.0458869 - 0.126840i) q^{66} +(4.09784 + 1.20324i) q^{67} +(-0.413854 - 0.313369i) q^{68} +(8.29573 + 0.425234i) q^{69} +(8.55959 + 2.87504i) q^{70} +(-0.594995 + 2.02637i) q^{71} +(-7.50038 - 3.96791i) q^{72} +(-2.56222 - 1.64664i) q^{73} +(-4.23984 + 8.41232i) q^{74} +(-1.60350 + 0.650832i) q^{75} +(2.57430 - 11.5287i) q^{76} +(0.115109 + 0.132843i) q^{77} +(-16.4018 - 6.30281i) q^{78} +(-2.82384 - 1.28960i) q^{79} +(6.77787 - 4.25141i) q^{80} +(-8.07672 - 3.97071i) q^{81} +(0.936880 + 0.877081i) q^{82} +(8.96634 - 1.28917i) q^{83} +(10.9785 + 1.32070i) q^{84} +(0.472251 - 0.215670i) q^{85} +(-1.74139 + 0.439372i) q^{86} +(4.12572 - 12.1070i) q^{87} +(0.155693 - 0.00427668i) q^{88} +(-11.4022 + 13.1589i) q^{89} +(7.05205 - 4.72062i) q^{90} +22.8980 q^{91} +(-3.47631 + 8.93953i) q^{92} +(-10.8780 - 2.04281i) q^{93} +(0.152867 - 0.218885i) q^{94} +(8.92834 + 7.73645i) q^{95} +(7.07122 - 6.78217i) q^{96} +(5.29925 + 0.761917i) q^{97} +(-4.37333 + 1.10344i) q^{98} +(0.164930 - 0.00943389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$	$-1$	$1$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.15945	−	0.809745i	−0.819852	−	0.572576i
$2$	−1.15945	−	0.809745i	−0.819852	−	0.572576i
$3$	1.35636	−	1.07716i	0.783096	−	0.621900i
$3$	1.35636	−	1.07716i	0.783096	−	0.621900i
$4$	0.688626	+	1.87771i	0.344313	+	0.938855i
$5$	−1.97986	−	0.284661i	−0.885420	−	0.127304i	−0.315423	−	0.948951i	$-0.602146\pi$
$5$	−1.97986	−	0.284661i	−0.885420	−	0.127304i	−0.569997	+	0.821647i	$0.693055\pi$
$6$	−2.44486	+	0.150603i	−0.998108	+	0.0614836i
$7$	2.90361	−	1.32603i	1.09746	−	0.501194i	0.217414	−	0.976079i	$-0.430238\pi$
$7$	2.90361	−	1.32603i	1.09746	−	0.501194i	0.880048	+	0.474885i	$0.157511\pi$
$8$	0.722042	−	2.73471i	0.255280	−	0.966867i
$9$	0.679440	−	2.92205i	0.226480	−	0.974016i
$10$	2.06503	+	1.93323i	0.653021	+	0.611341i
$11$	0.0155140	+	0.0528360i	0.00467766	+	0.0159306i	0.961799	−	0.273758i	$-0.0882666\pi$
$11$	0.0155140	+	0.0528360i	0.00467766	+	0.0159306i	−0.957121	+	0.289688i	$0.906448\pi$
$12$	2.95663	+	1.80509i	0.853504	+	0.521085i
$13$	6.52515	+	2.97994i	1.80975	+	0.826486i	0.947300	+	0.320348i	$0.103800\pi$
$13$	6.52515	+	2.97994i	1.80975	+	0.826486i	0.862452	+	0.506138i	$0.168927\pi$
$14$	−4.44033	−	0.813720i	−1.18673	−	0.217476i
$15$	−2.99203	+	1.74653i	−0.772539	+	0.450951i
$16$	−3.05159	+	2.58608i	−0.762897	+	0.646520i
$17$	−0.218352	+	0.140326i	−0.0529580	+	0.0340341i	−0.566852	−	0.823820i	$-0.691839\pi$
$17$	−0.218352	+	0.140326i	−0.0529580	+	0.0340341i	0.513894	+	0.857854i	$0.328202\pi$
$18$	−3.15389	+	2.83778i	−0.743378	+	0.668871i
$19$	−4.96870	−	3.19319i	−1.13990	−	0.732567i	−0.172295	−	0.985045i	$-0.555118\pi$
$19$	−4.96870	−	3.19319i	−1.13990	−	0.732567i	−0.967603	+	0.252478i	$0.918754\pi$
$20$	−0.828872	−	3.91362i	−0.185341	−	0.875113i
$21$	2.50999	−	4.92625i	0.547726	−	1.07500i
$22$	0.0247960	−	0.0738228i	0.00528652	−	0.0157391i
$23$	3.59799	+	3.17088i	0.750233	+	0.661173i
$23$	3.59799	+	3.17088i	0.750233	+	0.661173i
$24$	−1.96638	−	4.48702i	−0.401386	−	0.915909i
$25$	−0.958658	−	0.281487i	−0.191732	−	0.0562975i
$26$	−5.15257	−	8.73879i	−1.01050	−	1.71382i
$27$	−2.22595	−	4.69522i	−0.428385	−	0.903596i
$28$	4.48941	+	4.53900i	0.848419	+	0.857790i
$29$	6.21239	−	3.99246i	1.15361	−	0.741381i	0.183256	−	0.983065i	$-0.441336\pi$
$29$	6.21239	−	3.99246i	1.15361	−	0.741381i	0.970355	+	0.241684i	$0.0776998\pi$
$30$	4.88334	+	0.397781i	0.891572	+	0.0726245i
$31$	−4.18469	−	4.82939i	−0.751592	−	0.867384i	0.243129	−	0.969994i	$-0.421826\pi$
$31$	−4.18469	−	4.82939i	−0.751592	−	0.867384i	−0.994722	+	0.102610i	$0.967281\pi$
$32$	5.63221	−	0.527410i	0.995644	−	0.0932339i
$33$	0.0779556	+	0.0549536i	0.0135703	+	0.00956619i
$34$	0.366795	+	0.0141087i	0.0629048	+	0.00241963i
$35$	−6.12621	+	1.79882i	−1.03552	+	0.304056i
$36$	5.95464	−	0.736407i	0.992440	−	0.122735i
$37$	−0.947989	−	6.59341i	−0.155848	−	1.08395i	−0.906181	−	0.422889i	$-0.861016\pi$
$37$	−0.947989	−	6.59341i	−0.155848	−	1.08395i	0.750333	−	0.661060i	$-0.229893\pi$
$38$	3.17526	+	7.72570i	0.515096	+	1.25327i
$39$	12.0604	−	2.98678i	1.93120	−	0.478267i
$40$	−2.20801	+	5.20881i	−0.349116	+	0.823585i
$41$	−0.898237	−	0.129147i	−0.140281	−	0.0201694i	0.0718166	−	0.997418i	$-0.477120\pi$
$41$	−0.898237	−	0.129147i	−0.140281	−	0.0201694i	−0.212098	+	0.977248i	$0.568029\pi$
$42$	−6.89920	+	3.67926i	−1.06457	+	0.567722i
$43$	0.831631	−	0.959753i	0.126823	−	0.146361i	−0.688787	−	0.724964i	$-0.741856\pi$
$43$	0.831631	−	0.959753i	0.126823	−	0.146361i	0.815609	+	0.578603i	$0.196402\pi$
$44$	−0.0885272	+	0.0655151i	−0.0133460	+	0.00987677i
$45$	−2.17699	+	5.59183i	−0.324526	+	0.833581i
$46$	−1.60407	−	6.58991i	−0.236508	−	0.971630i
$47$			0.188785i			0.0275371i	0.999905	+	0.0137685i	$0.00438280\pi$
$47$			0.188785i			0.0275371i	−0.999905	+	0.0137685i	$0.995617\pi$
$48$	−1.35343	+	6.79472i	−0.195351	+	0.980733i
$49$	2.08856	−	2.41033i	0.298366	−	0.344333i
$50$	0.883578	+	1.10264i	0.124957	+	0.155936i
$51$	−0.145010	+	0.425533i	−0.0203055	+	0.0595866i
$52$	−1.10207	+	14.3044i	−0.152829	+	1.98366i
$53$	−8.20646	+	3.74777i	−1.12724	+	0.514795i	−0.889684	−	0.456578i	$-0.849075\pi$
$53$	−8.20646	+	3.74777i	−1.12724	+	0.514795i	−0.237561	+	0.971373i	$0.576348\pi$
$54$	−1.22106	+	7.24631i	−0.166166	+	0.986098i
$55$	−0.0156753	−	0.109024i	−0.00211365	−	0.0147008i
$56$	−1.52980	−	8.89799i	−0.204428	−	1.18904i
$57$	−10.1789	+	1.02098i	−1.34823	+	0.135231i
$58$	−10.4358	−	0.401412i	−1.37029	−	0.0527080i
$59$	4.21225	−	9.22355i	0.548388	−	1.20080i	−0.409142	−	0.912471i	$-0.634172\pi$
$59$	4.21225	−	9.22355i	0.548388	−	1.20080i	0.957530	−	0.288333i	$-0.0931008\pi$
$60$	−5.33986	−	4.41546i	−0.689373	−	0.570034i
$61$	8.61910	+	9.94698i	1.10356	+	1.27358i	0.958790	+	0.284115i	$0.0916997\pi$
$61$	8.61910	+	9.94698i	1.10356	+	1.27358i	0.144773	+	0.989465i	$0.453755\pi$
$62$	0.941345	+	8.98794i	0.119551	+	1.14147i
$63$	−1.90191	−	9.38545i	−0.239618	−	1.18246i
$64$	−6.95731	−	3.94915i	−0.869664	−	0.493644i
$65$	−12.0706	−	7.75731i	−1.49717	−	0.962176i
$66$	−0.0458869	−	0.126840i	−0.00564828	−	0.0156129i
$67$	4.09784	+	1.20324i	0.500631	+	0.146999i	0.522292	−	0.852767i	$-0.325077\pi$
$67$	4.09784	+	1.20324i	0.500631	+	0.146999i	−0.0216607	+	0.999765i	$0.506895\pi$
$68$	−0.413854	−	0.313369i	−0.0501872	−	0.0380015i
$69$	8.29573	+	0.425234i	0.998689	+	0.0511921i
$70$	8.55959	+	2.87504i	1.02307	+	0.343633i
$71$	−0.594995	+	2.02637i	−0.0706129	+	0.240485i	−0.987235	−	0.159269i	$-0.949086\pi$
$71$	−0.594995	+	2.02637i	−0.0706129	+	0.240485i	0.916622	+	0.399754i	$0.130905\pi$
$72$	−7.50038	−	3.96791i	−0.883928	−	0.467623i
$73$	−2.56222	−	1.64664i	−0.299885	−	0.192725i	0.382041	−	0.924145i	$-0.375221\pi$
$73$	−2.56222	−	1.64664i	−0.299885	−	0.192725i	−0.681927	+	0.731421i	$0.738858\pi$
$74$	−4.23984	+	8.41232i	−0.492871	+	0.977913i
$75$	−1.60350	+	0.650832i	−0.185156	+	0.0751516i
$76$	2.57430	−	11.5287i	0.295293	−	1.32243i
$77$	0.115109	+	0.132843i	0.0131179	+	0.0151389i
$78$	−16.4018	−	6.30281i	−1.85714	−	0.713652i
$79$	−2.82384	−	1.28960i	−0.317706	−	0.145092i	0.250178	−	0.968200i	$-0.419511\pi$
$79$	−2.82384	−	1.28960i	−0.317706	−	0.145092i	−0.567885	+	0.823108i	$0.692238\pi$
$80$	6.77787	−	4.25141i	0.757789	−	0.475322i
$81$	−8.07672	−	3.97071i	−0.897414	−	0.441190i
$82$	0.936880	+	0.877081i	0.103461	+	0.0968574i
$83$	8.96634	−	1.28917i	0.984184	−	0.141504i	0.368611	−	0.929584i	$-0.379834\pi$
$83$	8.96634	−	1.28917i	0.984184	−	0.141504i	0.615573	+	0.788080i	$0.288924\pi$
$84$	10.9785	+	1.32070i	1.19785	+	0.144100i
$85$	0.472251	−	0.215670i	0.0512228	−	0.0233927i
$86$	−1.74139	+	0.439372i	−0.187778	+	0.0473787i
$87$	4.12572	−	12.1070i	0.442324	−	1.29800i
$88$	0.155693	−	0.00427668i	0.0165969	−	0.000455895i
$89$	−11.4022	+	13.1589i	−1.20863	+	1.39484i	−0.313175	+	0.949696i	$0.601393\pi$
$89$	−11.4022	+	13.1589i	−1.20863	+	1.39484i	−0.895460	+	0.445143i	$0.853153\pi$
$90$	7.05205	−	4.72062i	0.743352	−	0.497597i
$91$	22.8980			2.40036
$92$	−3.47631	+	8.93953i	−0.362431	+	0.932011i
$93$	−10.8780	−	2.04281i	−1.12800	−	0.211830i
$94$	0.152867	−	0.218885i	0.0157671	−	0.0225763i
$95$	8.92834	+	7.73645i	0.916028	+	0.793743i
$96$	7.07122	−	6.78217i	0.721703	−	0.692203i
$97$	5.29925	+	0.761917i	0.538057	+	0.0773609i	0.405986	−	0.913879i	$-0.366928\pi$
$97$	5.29925	+	0.761917i	0.538057	+	0.0773609i	0.132071	+	0.991240i	$0.457837\pi$
$98$	−4.37333	+	1.10344i	−0.441773	+	0.111465i
$99$	0.164930	−	0.00943389i	0.0165761	−	0.000948141i
$100$	−0.131605	−	1.99392i	−0.0131605	−	0.199392i
$101$	2.25826	+	15.7065i	0.224705	+	1.56286i	0.719902	+	0.694076i	$0.244187\pi$
$101$	2.25826	+	15.7065i	0.224705	+	1.56286i	−0.495197	+	0.868781i	$0.664904\pi$
$102$	0.512705	−	0.375961i	0.0507653	−	0.0372257i
$103$	2.05661	+	7.00418i	0.202644	+	0.690142i	0.996617	+	0.0821887i	$0.0261910\pi$
$103$	2.05661	+	7.00418i	0.202644	+	0.690142i	−0.793973	+	0.607953i	$0.791991\pi$
$104$	12.8607	−	15.6928i	1.26110	−	1.53880i
$105$	−6.37174	+	9.03877i	−0.621818	+	0.882094i
$106$	12.5497	+	2.29981i	1.21893	+	0.223378i
$107$	−2.28968	+	1.98402i	−0.221352	+	0.191802i	−0.758476	−	0.651700i	$-0.774056\pi$
$107$	−2.28968	+	1.98402i	−0.221352	+	0.191802i	0.537125	+	0.843503i	$0.319510\pi$
$108$	7.28342	−	7.41295i	0.700847	−	0.713311i
$109$	−14.4636	+	9.29518i	−1.38536	+	0.890317i	−0.999480	−	0.0322317i	$-0.989739\pi$
$109$	−14.4636	+	9.29518i	−1.38536	+	0.890317i	−0.385880	+	0.922549i	$0.626102\pi$
$110$	−0.0701070	+	0.139100i	−0.00668444	+	0.0132627i
$111$	−8.38799	−	7.92191i	−0.796153	−	0.751915i
$112$	−5.43139	+	11.5555i	−0.513218	+	1.09189i
$113$	−8.05933	−	2.36643i	−0.758158	−	0.222615i	−0.120267	−	0.992742i	$-0.538375\pi$
$113$	−8.05933	−	2.36643i	−0.758158	−	0.222615i	−0.637891	+	0.770126i	$0.720193\pi$
$114$	12.6287	+	7.05858i	1.18278	+	0.661097i
$115$	−6.22089	−	7.30209i	−0.580101	−	0.680924i
$116$	11.7747	+	8.91575i	1.09325	+	0.827807i
$117$	13.1410	−	17.0421i	1.21488	−	1.57554i
$118$	−12.3526	+	7.28335i	−1.13715	+	0.670486i
$119$	−0.447931	+	0.696994i	−0.0410618	+	0.0638933i
$120$	2.61588	+	9.44341i	0.238796	+	0.862062i
$121$	9.25124	−	5.94541i	0.841022	−	0.540492i
$122$	−1.93886	−	18.5122i	−0.175537	−	1.67602i
$123$	−1.35745	+	0.792377i	−0.122397	+	0.0714462i
$124$	6.18650	−	11.1833i	0.555564	−	1.00429i
$125$	10.9152	+	4.98480i	0.976284	+	0.445854i
$126$	−5.39466	+	12.4220i	−0.480595	+	1.10664i
$127$	11.0253	−	3.23733i	0.978341	−	0.287267i	0.246802	−	0.969066i	$-0.420620\pi$
$127$	11.0253	−	3.23733i	0.978341	−	0.287267i	0.731539	+	0.681799i	$0.238802\pi$
$128$	4.86881	+	10.2125i	0.430346	+	0.902664i
$129$	0.0941826	−	2.19758i	0.00829232	−	0.193486i
$130$	7.71377	+	18.7683i	0.676542	+	1.64609i
$131$	4.83007	+	10.5764i	0.422006	+	0.924063i	0.994557	+	0.104194i	$0.0332264\pi$
$131$	4.83007	+	10.5764i	0.422006	+	0.924063i	−0.572551	+	0.819869i	$0.694046\pi$
$132$	−0.0495046	+	0.184220i	−0.00430882	+	0.0160343i
$133$	−18.6614	−	2.68311i	−1.61815	−	0.232655i
$134$	−3.77691	−	4.71329i	−0.326275	−	0.407166i
$135$	3.07053	+	9.92952i	0.264269	+	0.854597i
$136$	0.226093	+	0.698450i	0.0193873	+	0.0598916i
$137$	2.12677			0.181702			0.0908512	−	0.995864i	$-0.471041\pi$
$137$	2.12677			0.181702			0.0908512	+	0.995864i	$0.471041\pi$
$138$	−9.27412	−	7.21046i	−0.789465	−	0.613795i
$139$			5.52420i			0.468556i	0.972170	+	0.234278i	$0.0752727\pi$
$139$			5.52420i			0.468556i	−0.972170	+	0.234278i	$0.924727\pi$
$140$	−7.59632	−	10.2645i	−0.642007	−	0.867511i
$141$	0.203352	+	0.256060i	0.0171253	+	0.0215642i
$142$	2.33070	−	1.86767i	0.195588	−	0.156731i
$143$	−0.0562164	+	0.390994i	−0.00470105	+	0.0326965i
$144$	5.48328	+	10.6740i	0.456940	+	0.889498i
$145$	−13.4361	+	6.13608i	−1.11581	+	0.509574i
$146$	1.63740	+	3.98393i	0.135512	+	0.329713i
$147$	0.236531	−	5.51900i	0.0195087	−	0.455200i
$148$	11.7277	−	6.32044i	0.964011	−	0.519537i
$149$	0.375378	+	1.27842i	0.0307522	+	0.104732i	0.973439	−	0.228946i	$-0.0735281\pi$
$149$	0.375378	+	1.27842i	0.0307522	+	0.104732i	−0.942687	+	0.333679i	$0.891710\pi$
$150$	2.38617	+	0.543819i	0.194830	+	0.0444026i
$151$	−2.97813	+	6.52120i	−0.242357	+	0.530688i	−0.991249	−	0.132004i	$-0.957859\pi$
$151$	−2.97813	+	6.52120i	−0.242357	+	0.530688i	0.748892	+	0.662692i	$0.230586\pi$
$152$	−12.3201	+	11.2823i	−0.999289	+	0.915119i
$153$	0.261683	+	0.733377i	0.0211558	+	0.0592900i
$154$	−0.0258937	−	0.247233i	−0.00208658	−	0.0199226i
$155$	6.91036	+	10.7527i	0.555053	+	0.863679i
$156$	13.9134	+	20.5891i	1.11396	+	1.64845i
$157$	−4.35713	−	2.80016i	−0.347737	−	0.223477i	0.355099	−	0.934829i	$-0.384447\pi$
$157$	−4.35713	−	2.80016i	−0.347737	−	0.223477i	−0.702836	+	0.711352i	$0.748083\pi$
$158$	2.22983	+	3.78181i	0.177396	+	0.300865i
$159$	−7.09399	+	13.9230i	−0.562590	+	1.10417i
$160$	−11.3011	−	0.559072i	−0.893432	−	0.0441985i
$161$	14.6519	+	4.43593i	1.15473	+	0.349600i
$162$	6.14925	+	11.1439i	0.483131	+	0.875548i
$163$	−3.85714	+	13.1362i	−0.302115	+	1.02891i	0.658859	+	0.752267i	$0.271040\pi$
$163$	−3.85714	+	13.1362i	−0.302115	+	1.02891i	−0.960973	+	0.276641i	$0.910779\pi$
$164$	−0.376049	−	1.77556i	−0.0293645	−	0.138648i
$165$	−0.138698	−	0.130991i	−0.0107976	−	0.0101977i
$166$	−11.4399	−	5.76573i	−0.887907	−	0.447508i
$167$	5.91488	+	9.20373i	0.457707	+	0.712206i	0.991020	−	0.133712i	$-0.0426896\pi$
$167$	5.91488	+	9.20373i	0.457707	+	0.712206i	−0.533313	+	0.845918i	$0.679053\pi$
$168$	−11.6595	−	10.4211i	−0.899554	−	0.804003i
$169$	25.1844	+	29.0644i	1.93726	+	2.23572i
$170$	−0.722186	−	0.132345i	−0.0553891	−	0.0101504i
$171$	−12.7066	+	12.3492i	−0.971696	+	0.944366i
$172$	2.37482	+	0.900650i	0.181078	+	0.0686739i
$173$	4.60226	−	1.35135i	0.349903	−	0.102741i	−0.102058	−	0.994778i	$-0.532543\pi$
$173$	4.60226	−	1.35135i	0.349903	−	0.102741i	0.451961	+	0.892038i	$0.350725\pi$
$174$	−14.5871	+	10.6966i	−1.10585	+	0.810907i
$175$	−3.15683	+	0.453884i	−0.238634	+	0.0343104i
$176$	−0.183980	−	0.121113i	−0.0138681	−	0.00912924i
$177$	−4.22192	−	17.0478i	−0.317339	−	1.28139i
$178$	23.8756	−	6.02410i	1.78955	−	0.451525i
$179$	−0.276056	+	1.92001i	−0.0206334	+	0.143508i	−0.997534	−	0.0701862i	$-0.977641\pi$
$179$	−0.276056	+	1.92001i	−0.0206334	+	0.143508i	0.976901	+	0.213695i	$0.0685498\pi$
$180$	−11.9990	−	0.237069i	−0.894350	−	0.0176701i
$181$	−7.63190	+	8.80768i	−0.567275	+	0.654670i	−0.964820	−	0.262913i	$-0.915317\pi$
$181$	−7.63190	+	8.80768i	−0.567275	+	0.654670i	0.397545	+	0.917583i	$0.369862\pi$
$182$	−26.5490	−	18.5415i	−1.96794	−	1.37439i
$183$	22.4051	+	4.20753i	1.65624	+	0.311030i
$184$	11.2693	−	7.54997i	0.830786	−	0.556591i
$185$			13.3239i			0.979590i
$186$	10.9583	+	11.1769i	0.803500	+	0.819532i
$187$	−0.0108018	−	0.00935979i	−0.000789904	−	0.000684456i
$188$	−0.354483	+	0.130002i	−0.0258533	+	0.00948137i
$189$	−12.6893	−	10.6814i	−0.923013	−	0.776958i
$190$	−4.08737	−	16.1997i	−0.296529	−	1.17525i
$191$	−5.48466	−	12.0097i	−0.396856	−	0.868993i	−0.997579	−	0.0695361i	$-0.977848\pi$
$191$	−5.48466	−	12.0097i	−0.396856	−	0.868993i	0.600724	−	0.799457i	$-0.294879\pi$
$192$	−13.6905	+	2.13767i	−0.988028	+	0.154273i
$193$	2.00407	+	13.9386i	0.144256	+	1.00332i	0.925406	+	0.378978i	$0.123724\pi$
$193$	2.00407	+	13.9386i	0.144256	+	1.00332i	−0.781150	+	0.624343i	$0.785367\pi$
$194$	−5.52723	−	5.17444i	−0.396832	−	0.371503i
$195$	−24.7280	+	2.48029i	−1.77081	+	0.177617i
$196$	5.96414	+	2.26190i	0.426010	+	0.161564i
$197$	7.78755	−	17.0524i	0.554840	−	1.21493i	−0.399644	−	0.916670i	$-0.630866\pi$
$197$	7.78755	−	17.0524i	0.554840	−	1.21493i	0.954485	−	0.298260i	$-0.0964063\pi$
$198$	−0.198866	−	0.122613i	−0.0141328	−	0.00871374i
$199$	11.6411	−	10.0871i	0.825214	−	0.715052i	−0.136044	−	0.990703i	$-0.543439\pi$
$199$	11.6411	−	10.0871i	0.825214	−	0.715052i	0.961258	+	0.275651i	$0.0888933\pi$
$200$	−1.46198	+	2.41841i	−0.103377	+	0.171007i
$201$	6.85424	−	2.78202i	0.483461	−	0.196229i
$202$	10.0999	−	20.0395i	0.710630	−	1.40997i
$203$	12.7442	−	19.8304i	0.894469	−	1.39182i
$204$	−0.898886	+	0.0207467i	−0.0629346	+	0.00145256i
$205$	1.74162	+	0.511385i	0.121640	+	0.0357167i
$206$	3.28707	−	9.78629i	0.229021	−	0.681843i
$207$	11.7101	−	8.35908i	0.813906	−	0.580997i
$208$	−27.6184	+	7.78103i	−1.91499	+	0.539517i
$209$	0.0916306	−	0.312065i	0.00633822	−	0.0215860i
$210$	14.7068	−	5.32048i	1.01486	−	0.367148i
$211$	10.0471	−	15.6336i	0.691669	−	1.07626i	−0.300791	−	0.953690i	$-0.597251\pi$
$211$	10.0471	−	15.6336i	0.691669	−	1.07626i	0.992460	−	0.122568i	$-0.0391130\pi$
$212$	−12.6884	−	12.8285i	−0.871443	−	0.881068i
$213$	1.37570	+	3.38939i	0.0942612	+	0.232237i
$214$	4.26131	−	0.446305i	0.291297	−	0.0305088i
$215$	−1.91972	+	1.66344i	−0.130923	+	0.113446i
$216$	−14.4473	+	2.69720i	−0.983016	+	0.183521i
$217$	−18.5546	−	8.47362i	−1.25957	−	0.575227i
$218$	24.2965	+	0.934562i	1.64556	+	0.0632965i
$219$	−5.24900	+	0.526489i	−0.354695	+	0.0355768i
$220$	0.193921	−	0.104510i	0.0130741	−	0.00704609i
$221$	−1.84294	+	0.264975i	−0.123970	+	0.0178241i
$222$	3.31069	+	15.9772i	0.222199	+	1.07232i
$223$	2.50053	+	5.47540i	0.167448	+	0.366660i	0.974690	−	0.223561i	$-0.0717680\pi$
$223$	2.50053	+	5.47540i	0.167448	+	0.366660i	−0.807242	+	0.590221i	$0.799041\pi$
$224$	15.6544	−	8.99991i	1.04595	−	0.601331i
$225$	−1.47387	+	2.60999i	−0.0982580	+	0.173999i
$226$	7.42815	+	9.26975i	0.494113	+	0.616615i
$227$	−12.6652	−	10.9745i	−0.840620	−	0.728402i	0.123933	−	0.992291i	$-0.460449\pi$
$227$	−12.6652	−	10.9745i	−0.840620	−	0.728402i	−0.964553	+	0.263889i	$0.914995\pi$
$228$	−8.92658	−	18.4100i	−0.591177	−	1.21923i
$229$	−8.28742			−0.547648			−0.273824	−	0.961780i	$-0.588289\pi$
$229$	−8.28742			−0.547648			−0.273824	+	0.961780i	$0.588289\pi$
$230$	1.29995	+	13.5037i	0.0857162	+	0.890408i
$231$	0.299223	+	0.0561920i	0.0196874	+	0.00369716i
$232$	−6.43263	−	19.8718i	−0.422323	−	1.30465i
$233$	−4.88566	−	4.23345i	−0.320070	−	0.277342i	0.479975	−	0.877282i	$-0.340646\pi$
$233$	−4.88566	−	4.23345i	−0.320070	−	0.277342i	−0.800045	+	0.599940i	$0.795191\pi$
$234$	−29.0360	+	9.11857i	−1.89814	+	0.596100i
$235$	0.0537395	−	0.373767i	0.00350558	−	0.0243819i
$236$	20.2198	+	1.55781i	1.31620	+	0.101405i
$237$	−5.21926	+	1.29256i	−0.339027	+	0.0839610i
$238$	1.08374	−	0.445417i	0.0702484	−	0.0288721i
$239$	13.2711	−	1.90810i	0.858437	−	0.123425i	0.300980	−	0.953631i	$-0.402686\pi$
$239$	13.2711	−	1.90810i	0.858437	−	0.123425i	0.557457	+	0.830206i	$0.311777\pi$
$240$	4.61379	−	13.0673i	0.297819	−	0.843492i
$241$	−6.06198	−	20.6452i	−0.390486	−	1.32987i	−0.886970	−	0.461828i	$-0.847194\pi$
$241$	−6.06198	−	20.6452i	−0.390486	−	1.32987i	0.496483	−	0.868046i	$-0.334624\pi$
$242$	−15.5406	−	0.597767i	−0.998986	−	0.0384259i
$243$	−15.2321	+	3.31422i	−0.977138	+	0.212607i
$244$	−12.7422	+	23.0339i	−0.815735	+	1.47460i
$245$	−4.82118	+	4.17758i	−0.308014	+	0.266896i
$246$	2.21551	+	0.180468i	0.141256	+	0.0115062i
$247$	−22.9060	−	35.6425i	−1.45747	−	2.26787i
$248$	−16.2285	+	7.95691i	−1.03051	+	0.505264i
$249$	10.7730	−	11.4068i	0.682709	−	0.722876i
$250$	−8.61915	−	14.6181i	−0.545123	−	0.924531i
$251$	3.97193	−	13.5271i	0.250706	−	0.853825i	−0.733933	−	0.679222i	$-0.762317\pi$
$251$	3.97193	−	13.5271i	0.250706	−	0.853825i	0.984639	−	0.174604i	$-0.0558644\pi$
$252$	16.3134	−	10.0343i	1.02765	−	0.632101i
$253$	−0.111717	+	0.239296i	−0.00702358	+	0.0150444i
$254$	−15.4047	−	5.17421i	−0.966577	−	0.324659i
$255$	0.408232	−	0.801217i	0.0255645	−	0.0501742i
$256$	2.62438	−	15.7833i	0.164024	−	0.986456i
$257$	−8.63035	+	13.4291i	−0.538346	+	0.837683i	−0.998748	−	0.0500274i	$-0.984069\pi$
$257$	−8.63035	+	13.4291i	−0.538346	+	0.837683i	0.460401	+	0.887711i	$0.347705\pi$
$258$	−1.88867	+	2.47170i	−0.117584	+	0.153882i
$259$	−11.4957	−	17.8876i	−0.714307	−	1.11148i
$260$	6.25384	−	28.0070i	0.387847	−	1.73692i
$261$	−7.44521	−	20.8655i	−0.460847	−	1.29154i
$262$	2.96397	−	16.1739i	0.183115	−	0.999225i
$263$	−4.95594	+	10.8520i	−0.305597	+	0.669163i	−0.998662	−	0.0517114i	$-0.983532\pi$
$263$	−4.95594	+	10.8520i	−0.305597	+	0.669163i	0.693065	+	0.720875i	$0.256260\pi$
$264$	0.206569	−	0.173507i	0.0127135	−	0.0106786i
$265$	17.3145	−	5.08399i	1.06362	−	0.312307i
$266$	19.4643	+	18.2219i	1.19343	+	1.11726i
$267$	−1.29131	+	30.1303i	−0.0790268	+	1.84394i
$268$	0.562555	+	8.52314i	0.0343635	+	0.520634i
$269$	3.38101	+	7.40338i	0.206144	+	0.451392i	0.984260	−	0.176729i	$-0.0565516\pi$
$269$	3.38101	+	7.40338i	0.206144	+	0.451392i	−0.778116	+	0.628121i	$0.783824\pi$
$270$	4.48027	−	13.9991i	0.272661	−	0.851957i
$271$	0.0765703	−	0.532558i	0.00465131	−	0.0323506i	−0.987364	−	0.158471i	$-0.949344\pi$
$271$	0.0765703	−	0.532558i	0.00465131	−	0.0323506i	0.992015	+	0.126121i	$0.0402526\pi$
$272$	0.303425	−	0.992892i	0.0183978	−	0.0602029i
$273$	31.0580	−	24.6649i	1.87972	−	1.49279i
$274$	−2.46588	−	1.72214i	−0.148969	−	0.104038i
$275$		−	0.0550186i		−	0.00331775i
$276$	4.91419	+	15.8698i	0.295800	+	0.955250i
$277$			16.3196i			0.980550i	0.871568	+	0.490275i	$0.163104\pi$
$277$			16.3196i			0.980550i	−0.871568	+	0.490275i	$0.836896\pi$
$278$	4.47319	−	6.40500i	0.268284	−	0.384147i
$279$	−16.9550	+	8.94658i	−1.01507	+	0.535618i
$280$	0.495871	+	18.0522i	0.0296339	+	1.07883i
$281$	−2.91601	+	20.2813i	−0.173955	+	1.20988i	0.696472	+	0.717584i	$0.254752\pi$
$281$	−2.91601	+	20.2813i	−0.173955	+	1.20988i	−0.870427	+	0.492298i	$0.836157\pi$
$282$	−0.0284316	−	0.461551i	−0.00169308	−	0.0274850i
$283$	−2.82248	−	6.18038i	−0.167779	−	0.367385i	0.807002	−	0.590549i	$-0.201089\pi$
$283$	−2.82248	−	6.18038i	−0.167779	−	0.367385i	−0.974781	+	0.223164i	$0.928362\pi$
$284$	−4.21466	+	0.278181i	−0.250094	+	0.0165070i
$285$	20.4435	+	0.876157i	1.21097	+	0.0518991i
$286$	0.381785	−	0.407815i	0.0225754	−	0.0241146i
$287$	−2.77938	+	0.816100i	−0.164062	+	0.0481729i
$288$	2.28563	−	16.8159i	0.134682	−	0.990889i
$289$	−7.03407	+	15.4025i	−0.413769	+	0.906027i
$290$	20.5471	+	3.76540i	1.20657	+	0.221112i
$291$	8.00841	−	4.67472i	0.469461	−	0.274037i
$292$	1.32750	−	5.94503i	0.0776860	−	0.347906i
$293$	−2.26890	−	3.53049i	−0.132551	−	0.206253i	0.768633	−	0.639690i	$-0.220937\pi$
$293$	−2.26890	−	3.53049i	−0.132551	−	0.206253i	−0.901184	+	0.433437i	$0.857301\pi$
$294$	−4.74323	+	6.20745i	−0.276631	+	0.362026i
$295$	−10.9652	+	17.0623i	−0.638421	+	0.993403i
$296$	−18.7156	−	2.16824i	−1.08782	−	0.126026i
$297$	0.213543	−	0.190452i	0.0123910	−	0.0110512i
$298$	0.599965	−	1.78622i	0.0347550	−	0.103473i
$299$	14.0284	+	31.4122i	0.811286	+	1.81662i
$300$	−2.32628	−	2.56272i	−0.134308	−	0.147959i
$301$	1.14207	−	3.88952i	0.0658276	−	0.224188i
$302$	8.73349	−	5.14945i	0.502556	−	0.296317i
$303$	19.9815	+	18.8712i	1.14791	+	1.08412i
$304$	23.4203	−	3.10516i	1.34324	−	0.178093i
$305$	−14.2331	−	22.1471i	−0.814984	−	1.26814i
$306$	0.290442	−	1.06221i	0.0166034	−	0.0607223i
$307$	9.03845	−	7.83186i	0.515852	−	0.446988i	−0.357617	−	0.933868i	$-0.616411\pi$
$307$	9.03845	−	7.83186i	0.515852	−	0.446988i	0.873469	+	0.486880i	$0.161865\pi$
$308$	−0.170173	+	0.307620i	−0.00969653	+	0.0175283i
$309$	10.3342	+	7.28490i	0.587889	+	0.414423i
$310$	0.694785	−	18.0628i	0.0394611	−	1.02590i
$311$	−4.40419	−	14.9993i	−0.249739	−	0.850531i	−0.984972	−	0.172717i	$-0.944745\pi$
$311$	−4.40419	−	14.9993i	−0.249739	−	0.850531i	0.735233	−	0.677815i	$-0.237073\pi$
$312$	0.540101	−	35.1382i	0.0305772	−	1.98931i
$313$	−17.7415	+	2.55084i	−1.00281	+	0.144182i	−0.624108	−	0.781338i	$-0.714538\pi$
$313$	−17.7415	+	2.55084i	−1.00281	+	0.144182i	−0.378699	+	0.925520i	$0.623628\pi$
$314$	2.78444	+	6.77480i	0.157135	+	0.382324i
$315$	1.09384	+	19.1233i	0.0616308	+	1.07747i
$316$	0.476932	−	6.19040i	0.0268295	−	0.348237i
$317$	0.000574710	−	0.00399720i	3.22789e−5	−	0.000224505i	−0.989805	−	0.142427i	$-0.954509\pi$
$317$	0.000574710	−	0.00399720i	3.22789e−5	−	0.000224505i	0.989838	+	0.142203i	$0.0454184\pi$
$318$	19.4992	−	10.3987i	1.09346	−	0.583128i
$319$	0.307325	+	0.266298i	0.0172069	+	0.0149098i
$320$	12.6503	+	9.79924i	0.707175	+	0.547794i
$321$	−0.968526	+	5.15741i	−0.0540578	+	0.287859i
$322$	−13.3961	−	17.0075i	−0.746533	−	0.947790i
$323$	1.53301			0.0852990
$324$	1.89400	−	17.9001i	0.105222	−	0.994449i
$325$	−5.41657	−	4.69349i	−0.300458	−	0.260348i
$326$	15.1091	−	12.1074i	0.836817	−	0.670568i
$327$	−9.60545	+	28.1873i	−0.531182	+	1.55876i
$328$	−1.00174	+	2.36317i	−0.0553121	+	0.130484i
$329$	0.250335	+	0.548157i	0.0138014	+	0.0302209i
$330$	0.0547432	+	0.264187i	0.00301351	+	0.0145430i
$331$	−10.3915	+	1.49407i	−0.571167	+	0.0821215i	−0.421846	−	0.906667i	$-0.638618\pi$
$331$	−10.3915	+	1.49407i	−0.571167	+	0.0821215i	−0.149321	+	0.988789i	$0.547709\pi$
$332$	8.59514	+	15.9484i	0.471719	+	0.875284i
$333$	−19.9104	−	1.70976i	−1.09108	−	0.0936941i
$334$	0.594697	−	15.4608i	0.0325404	−	0.845976i
$335$	−7.77063	−	3.54873i	−0.424555	−	0.193888i
$336$	5.08020	+	21.5239i	0.277148	+	1.17423i
$337$	−1.56676	+	1.35760i	−0.0853468	+	0.0739534i	−0.696489	−	0.717567i	$-0.745256\pi$
$337$	−1.56676	+	1.35760i	−0.0853468	+	0.0739534i	0.611143	+	0.791521i	$0.290710\pi$
$338$	−5.66523	−	54.0915i	−0.308148	−	2.94219i
$339$	−13.4804	+	5.47147i	−0.732155	+	0.297170i
$340$	0.730169	+	0.738234i	0.0395990	+	0.0400363i
$341$	0.190244	−	0.296025i	0.0103023	−	0.0160307i
$342$	24.7323	−	4.02912i	1.33737	−	0.217870i
$343$	−3.42698	+	11.6712i	−0.185040	+	0.630187i
$344$	−2.02418	−	2.96725i	−0.109136	−	0.159984i
$345$	−16.3033	−	3.20337i	−0.877742	−	0.172464i
$346$	−6.43031	−	2.15985i	−0.345696	−	0.116114i
$347$	−31.7336	−	9.31783i	−1.70355	−	0.500208i	−0.722078	−	0.691811i	$-0.756813\pi$
$347$	−31.7336	−	9.31783i	−1.70355	−	0.500208i	−0.981472	+	0.191604i	$0.938631\pi$
$348$	25.5745	−	0.590272i	1.37094	−	0.0316419i
$349$	−8.04540	+	12.5189i	−0.430660	+	0.670121i	−0.986979	−	0.160848i	$-0.948577\pi$
$349$	−8.04540	+	12.5189i	−0.430660	+	0.670121i	0.556319	+	0.830969i	$0.312213\pi$
$350$	4.02770	+	2.02997i	0.215290	+	0.108507i
$351$	−0.533216	−	37.2703i	−0.0284610	−	1.98934i
$352$	0.115245	+	0.289401i	0.00614256	+	0.0154251i
$353$	0.584494	−	0.506467i	0.0311095	−	0.0269565i	−0.639167	−	0.769068i	$-0.720721\pi$
$353$	0.584494	−	0.506467i	0.0311095	−	0.0269565i	0.670277	+	0.742111i	$0.266175\pi$
$354$	−8.90925	+	23.1846i	−0.473521	+	1.23225i
$355$	1.75483	−	3.84255i	0.0931368	−	0.203941i
$356$	−32.5604	−	12.3485i	−1.72570	−	0.654471i
$357$	0.143219	+	1.42787i	0.00757997	+	0.0755710i
$358$	1.87479	−	2.00261i	0.0990859	−	0.105841i
$359$	−1.57852	−	10.9788i	−0.0833110	−	0.579441i	−0.988127	−	0.153638i	$-0.950901\pi$
$359$	−1.57852	−	10.9788i	−0.0833110	−	0.579441i	0.904816	−	0.425802i	$-0.140008\pi$
$360$	13.7202	+	9.99097i	0.723117	+	0.526570i
$361$	6.59862	+	14.4490i	0.347296	+	0.760471i
$362$	15.9807	−	4.03213i	0.839929	−	0.211924i
$363$	6.14386	−	18.0292i	0.322469	−	0.946289i
$364$	15.7682	+	42.9958i	0.826477	+	2.25359i
$365$	4.60410	+	3.98948i	0.240990	+	0.208819i
$366$	−22.5705	−	23.0209i	−1.17978	−	1.20332i
$367$			27.3870i			1.42959i	0.699333	+	0.714796i	$0.253480\pi$
$367$			27.3870i			1.42959i	−0.699333	+	0.714796i	$0.746520\pi$
$368$	−19.1797	−	0.371509i	−0.999812	−	0.0193662i
$369$	−0.987671	+	2.53694i	−0.0514161	+	0.132068i
$370$	10.7889	−	15.4483i	0.560890	−	0.803119i
$371$	−18.8587	+	21.7641i	−0.979095	+	1.12994i
$372$	−3.65507	−	21.8325i	−0.189506	−	1.13196i
$373$	−3.85672	+	26.8241i	−0.199693	+	1.38890i	0.605481	+	0.795860i	$0.292981\pi$
$373$	−3.85672	+	26.8241i	−0.199693	+	1.38890i	−0.805174	+	0.593039i	$0.797928\pi$
$374$	0.00494502	+	0.0195989i	0.000255701	+	0.00101343i
$375$	20.1744	−	4.99624i	1.04180	−	0.258005i
$376$	0.516272	+	0.136310i	0.0266247	+	0.00702967i
$377$	52.4341	−	7.53888i	2.70049	−	0.388272i
$378$	6.06337	+	22.6596i	0.311866	+	1.16549i
$379$	4.81820	−	1.41475i	0.247494	−	0.0726708i	−0.155633	−	0.987815i	$-0.549742\pi$
$379$	4.81820	−	1.41475i	0.247494	−	0.0726708i	0.403127	+	0.915144i	$0.367923\pi$
$380$	−8.37852	+	22.0924i	−0.429809	+	1.13331i
$381$	11.4672	−	16.2671i	0.587484	−	0.833388i
$382$	−3.36565	+	18.3658i	−0.172202	+	0.939675i
$383$	13.6411	+	15.7427i	0.697027	+	0.804412i	0.988348	−	0.152213i	$-0.0486401\pi$
$383$	13.6411	+	15.7427i	0.697027	+	0.804412i	−0.291321	+	0.956625i	$0.594095\pi$
$384$	17.6044	+	8.60732i	0.898370	+	0.439240i
$385$	−0.190084	−	0.295777i	−0.00968760	−	0.0150742i
$386$	8.96309	−	17.7838i	0.456209	−	0.905172i
$387$	−2.23940	−	3.08216i	−0.113835	−	0.156675i
$388$	2.21854	+	10.4751i	0.112629	+	0.531794i
$389$	−7.99687	+	27.2348i	−0.405457	+	1.38086i	0.463554	+	0.886069i	$0.346574\pi$
$389$	−7.99687	+	27.2348i	−0.405457	+	1.38086i	−0.869011	+	0.494792i	$0.835244\pi$
$390$	30.6792	+	17.1476i	1.55350	+	0.868304i
$391$	−1.23058	−	0.187474i	−0.0622333	−	0.00948095i
$392$	−5.08353	−	7.45198i	−0.256757	−	0.376382i
$393$	17.9438	+	9.14264i	0.905146	+	0.461185i
$394$	−22.8373	+	13.4653i	−1.15053	+	0.678374i
$395$	5.22370	+	3.35707i	0.262833	+	0.168912i
$396$	0.131289	+	0.303194i	0.00659753	+	0.0152361i
$397$	−10.4403	−	16.2455i	−0.523986	−	0.815337i	0.473883	−	0.880588i	$-0.342852\pi$
$397$	−10.4403	−	16.2455i	−0.523986	−	0.815337i	−0.997869	+	0.0652502i	$0.979215\pi$
$398$	−21.6651	+	2.26908i	−1.08597	+	0.113739i
$399$	−28.2018	+	16.4621i	−1.41186	+	0.824138i
$400$	3.65338	−	1.62018i	0.182669	−	0.0810091i
$401$	13.4396	−	29.4286i	0.671142	−	1.46960i	−0.200622	−	0.979669i	$-0.564296\pi$
$401$	13.4396	−	29.4286i	0.671142	−	1.46960i	0.871764	−	0.489927i	$-0.162976\pi$
$402$	−10.1998	−	2.32459i	−0.508722	−	0.115940i
$403$	−12.9145	−	43.9826i	−0.643315	−	2.19093i
$404$	−27.9372	+	15.0563i	−1.38993	+	0.749077i
$405$	14.8605	+	10.1606i	0.738422	+	0.504883i
$406$	−30.8338	+	12.6727i	−1.53025	+	0.628935i
$407$	0.333662	−	0.152378i	0.0165390	−	0.00755311i
$408$	1.05901	+	0.703813i	0.0524287	+	0.0348440i
$409$	−0.117692	+	0.818568i	−0.00581951	+	0.0404756i	−0.992524	−	0.122047i	$-0.961054\pi$
$409$	−0.117692	+	0.818568i	−0.00581951	+	0.0404756i	0.986705	+	0.162523i	$0.0519631\pi$
$410$	−1.60522	−	2.00319i	−0.0792761	−	0.0989305i
$411$	2.88467	−	2.29088i	0.142290	−	0.113001i
$412$	−11.7356	+	8.68498i	−0.578170	+	0.427878i
$413$		−	32.3672i		−	1.59268i
$414$	−20.3459	+	0.209730i	−0.999947	+	0.0103077i
$415$	−18.1191			−0.889430
$416$	38.3227	+	13.3422i	1.87893	+	0.654156i
$417$	5.95046	+	7.49282i	0.291395	+	0.366925i
$418$	−0.358934	+	0.287625i	−0.0175560	+	0.0140682i
$419$	−4.26622	−	0.613390i	−0.208419	−	0.0299661i	0.0373146	−	0.999304i	$-0.488120\pi$
$419$	−4.26622	−	0.613390i	−0.208419	−	0.0299661i	−0.245733	+	0.969337i	$0.579029\pi$
$420$	−21.3599	−	5.73995i	−1.04226	−	0.280081i
$421$	3.95796	+	8.66672i	0.192899	+	0.422390i	0.981225	−	0.192868i	$-0.0617790\pi$
$421$	3.95796	+	8.66672i	0.192899	+	0.422390i	−0.788326	+	0.615258i	$0.789052\pi$
$422$	−24.3082	+	9.99068i	−1.18331	+	0.486339i
$423$	0.551638	+	0.128268i	0.0268215	+	0.00623659i
$424$	4.32366	+	25.1484i	0.209975	+	1.22131i
$425$	0.248824	−	0.0730615i	0.0120698	−	0.00354400i
$426$	1.14950	−	5.04378i	0.0556934	−	0.244372i
$427$	38.2166	+	17.4529i	1.84943	+	0.844606i
$428$	−5.30215	−	2.93311i	−0.256289	−	0.141777i
$429$	0.344914	+	0.590884i	0.0166526	+	0.0285281i
$430$	3.57277	−	0.374191i	0.172294	−	0.0180451i
$431$	−12.0562	+	7.74805i	−0.580727	+	0.373211i	−0.797779	−	0.602949i	$-0.793992\pi$
$431$	−12.0562	+	7.74805i	−0.580727	+	0.373211i	0.217052	+	0.976160i	$0.430356\pi$
$432$	18.9349	+	8.57139i	0.911007	+	0.412391i
$433$	2.06454	−	3.21248i	0.0992154	−	0.154382i	−0.788097	−	0.615551i	$-0.788933\pi$
$433$	2.06454	−	3.21248i	0.0992154	−	0.154382i	0.887312	+	0.461169i	$0.152570\pi$
$434$	14.6516	+	24.8492i	0.703300	+	1.19280i
$435$	−11.6147	+	22.7957i	−0.556883	+	1.09297i
$436$	−27.4137	−	20.7575i	−1.31288	−	0.994105i
$437$	−7.75213	−	27.2442i	−0.370835	−	1.30327i
$438$	6.51225	+	3.63992i	0.311167	+	0.173922i
$439$	−10.4357	−	3.06419i	−0.498068	−	0.146246i	0.0230439	−	0.999734i	$-0.492664\pi$
$439$	−10.4357	−	3.06419i	−0.498068	−	0.146246i	−0.521112	+	0.853489i	$0.674482\pi$
$440$	−0.309467	−	0.0358525i	−0.0147533	−	0.00170920i
$441$	−5.62405	−	7.74055i	−0.267812	−	0.368598i
$442$	2.35135	+	1.18509i	0.111842	+	0.0563689i
$443$	−27.0293	+	17.3707i	−1.28420	+	0.825307i	−0.991400	−	0.130866i	$-0.958224\pi$
$443$	−27.0293	+	17.3707i	−1.28420	+	0.825307i	−0.292803	+	0.956173i	$0.594588\pi$
$444$	9.09886	−	21.2054i	0.431813	−	1.00637i
$445$	26.3206	−	22.8069i	1.24772	−	1.08115i
$446$	1.53445	−	8.37322i	0.0726583	−	0.396484i
$447$	1.88622	+	1.32966i	0.0892150	+	0.0628907i
$448$	−25.4380	−	2.24117i	−1.20183	−	0.105885i
$449$	1.63100	+	5.55467i	0.0769715	+	0.262141i	0.988984	−	0.148021i	$-0.0472903\pi$
$449$	1.63100	+	5.55467i	0.0769715	+	0.262141i	−0.912013	+	0.410162i	$0.865472\pi$
$450$	3.82230	−	1.83268i	0.180185	−	0.0863934i
$451$	−0.00711168	−	0.0494628i	−0.000334876	−	0.00232911i
$452$	−1.10639	−	16.7627i	−0.0520403	−	0.788450i
$453$	2.98497	+	12.0531i	0.140246	+	0.566302i
$454$	5.79810	+	22.9799i	0.272118	+	1.07850i
$455$	−45.3348	−	6.51816i	−2.12533	−	0.305576i
$456$	−4.55754	+	28.5737i	−0.213427	+	1.33808i
$457$	−15.5557	−	13.4791i	−0.727665	−	0.630526i	0.210146	−	0.977670i	$-0.432606\pi$
$457$	−15.5557	−	13.4791i	−0.727665	−	0.630526i	−0.937812	+	0.347144i	$0.887151\pi$
$458$	9.60881	+	6.71070i	0.448990	+	0.313570i
$459$	1.14490	+	0.712850i	0.0534395	+	0.0332730i
$460$	9.42734	−	16.7094i	0.439552	−	0.779082i
$461$	−2.99612			−0.139543			−0.0697717	−	0.997563i	$-0.522227\pi$
$461$	−2.99612			−0.139543			−0.0697717	+	0.997563i	$0.522227\pi$
$462$	−0.301432	−	0.307446i	−0.0140239	−	0.0143037i
$463$	9.21742	−	10.6375i	0.428370	−	0.494365i	−0.499999	−	0.866026i	$-0.666666\pi$
$463$	9.21742	−	10.6375i	0.428370	−	0.494365i	0.928368	+	0.371661i	$0.121212\pi$
$464$	−8.63283	+	28.2491i	−0.400769	+	1.31143i
$465$	20.9554	+	7.14101i	0.971783	+	0.331157i
$466$	2.23664	+	8.86459i	0.103610	+	0.410644i
$467$	23.5846	−	10.7707i	1.09137	−	0.498411i	0.213319	−	0.976983i	$-0.431573\pi$
$467$	23.5846	−	10.7707i	1.09137	−	0.498411i	0.878048	+	0.478572i	$0.158845\pi$
$468$	41.0494	+	12.9393i	1.89751	+	0.598118i
$469$	13.4941	−	1.94015i	0.623098	−	0.0895880i
$470$	−0.364964	+	0.389847i	−0.0168345	+	0.0179823i
$471$	−8.92608	+	0.895310i	−0.411292	+	0.0412537i
$472$	−22.1823	−	18.1791i	−1.02102	−	0.836760i
$473$	0.0636114	+	0.0290504i	0.00292486	+	0.00133574i
$474$	7.09809	+	2.72761i	0.326026	+	0.125283i
$475$	3.86444	+	4.45980i	0.177313	+	0.204630i
$476$	−1.61721	−	0.361116i	−0.0741247	−	0.0165517i
$477$	5.37535	+	26.5261i	0.246120	+	1.21454i
$478$	−16.9322	−	8.53388i	−0.774461	−	0.390331i
$479$	−16.0401	−	10.3083i	−0.732890	−	0.471000i	0.120209	−	0.992749i	$-0.461644\pi$
$479$	−16.0401	−	10.3083i	−0.732890	−	0.471000i	−0.853099	+	0.521749i	$0.825280\pi$
$480$	−15.9306	+	11.4148i	−0.727130	+	0.521014i
$481$	13.4622	−	45.8480i	0.613822	−	2.09049i
$482$	−9.68881	+	28.8456i	−0.441313	+	1.31388i
$483$	24.6515	−	9.76571i	1.12168	−	0.444355i
$484$	17.5344	+	13.2770i	0.797018	+	0.603499i
$485$	−10.2749	−	3.01698i	−0.466558	−	0.136994i
$486$	20.3444	+	8.49144i	0.922842	+	0.385179i
$487$	−3.96837	−	2.55032i	−0.179824	−	0.115566i	0.447632	−	0.894218i	$-0.352267\pi$
$487$	−3.96837	−	2.55032i	−0.179824	−	0.115566i	−0.627456	+	0.778652i	$0.715904\pi$
$488$	33.4255	−	16.3886i	1.51310	−	0.741879i
$489$	8.91816	+	21.9722i	0.403293	+	0.993619i
$490$	8.97267	−	0.939745i	0.405344	−	0.0424534i
$491$	7.75644	+	8.95141i	0.350043	+	0.403971i	0.903279	−	0.429053i	$-0.141153\pi$
$491$	7.75644	+	8.95141i	0.350043	+	0.403971i	−0.553236	+	0.833025i	$0.686607\pi$
$492$	−2.42263	−	2.00324i	−0.109221	−	0.0903130i
$493$	−0.796239	+	1.74352i	−0.0358608	+	0.0785242i
$494$	−2.30303	+	59.8735i	−0.103618	+	2.69384i
$495$	−0.329224	−	0.0282713i	−0.0147975	−	0.00127070i
$496$	25.2591	+	3.91536i	1.13417	+	0.175805i
$497$	0.959398	+	6.67276i	0.0430349	+	0.299314i
$498$	−21.7273	+	4.50219i	−0.973622	+	0.201748i
$499$	35.2232	−	16.0859i	1.57681	−	0.720105i	0.581204	−	0.813758i	$-0.302582\pi$
$499$	35.2232	−	16.0859i	1.57681	−	0.720105i	0.995605	+	0.0936531i	$0.0298545\pi$
$500$	−1.84352	+	23.9282i	−0.0824448	+	1.07010i
$501$	17.9366	+	6.11231i	0.801350	+	0.273078i
$502$	−15.5588	+	12.4677i	−0.694422	+	0.556462i
$503$	26.8470	−	30.9831i	1.19705	−	1.38147i	0.291862	−	0.956460i	$-0.405725\pi$
$503$	26.8470	−	30.9831i	1.19705	−	1.38147i	0.905189	−	0.425010i	$-0.139729\pi$
$504$	−27.0398	−	1.57552i	−1.20445	−	0.0701791i
$505$		−	31.7395i		−	1.41239i
$506$	0.323299	−	0.186989i	0.0143724	−	0.00831267i
$507$	65.4663	+	12.2941i	2.90746	+	0.546000i
$508$	13.6711	+	18.4731i	0.606558	+	0.819611i
$509$	3.49008	−	4.02776i	0.154695	−	0.178528i	−0.673112	−	0.739541i	$-0.735043\pi$
$509$	3.49008	−	4.02776i	0.154695	−	0.178528i	0.827807	+	0.561013i	$0.189588\pi$
$510$	−1.12210	+	0.598404i	−0.0496876	+	0.0264978i
$511$	−9.62320	−	1.38361i	−0.425705	−	0.0612072i
$512$	−15.8233	+	16.1748i	−0.699296	+	0.714832i
$513$	−3.93264	+	30.4370i	−0.173630	+	1.34383i
$514$	20.8806	−	8.58191i	0.921002	−	0.378532i
$515$	−2.07799	−	14.4527i	−0.0915670	−	0.636863i
$516$	4.19126	−	1.33646i	0.184510	−	0.0588344i
$517$	−0.00997462	+	0.00292881i	−0.000438683	+	0.000128809i
$518$	−1.15581	+	30.0483i	−0.0507832	+	1.32025i
$519$	4.78672	−	6.79030i	0.210113	−	0.298061i
$520$	−29.9295	+	27.4086i	−1.31250	+	1.20194i
$521$	23.3345	+	26.9294i	1.02230	+	1.17980i	0.983566	+	0.180549i	$0.0577876\pi$
$521$	23.3345	+	26.9294i	1.02230	+	1.17980i	0.0387356	+	0.999249i	$0.487667\pi$
$522$	−8.26344	+	30.2212i	−0.361681	+	1.32274i
$523$	−21.1877	+	13.6165i	−0.926471	+	0.595407i	−0.914528	−	0.404522i	$-0.867438\pi$
$523$	−21.1877	+	13.6165i	−0.926471	+	0.595407i	−0.0119430	+	0.999929i	$0.503802\pi$
$524$	−16.5333	+	16.3527i	−0.722259	+	0.714369i
$525$	−3.79290	+	4.01605i	−0.165536	+	0.175275i
$526$	14.5335	−	8.56925i	0.633691	−	0.373637i
$527$	1.59142	+	0.467284i	0.0693235	+	0.0203552i
$528$	−0.380003	+	0.0339038i	−0.0165375	+	0.00147547i
$529$	2.89110	+	22.8176i	0.125700	+	0.992068i
$530$	−24.1919	−	8.12570i	−1.05083	−	0.352958i
$531$	−24.0897	−	18.5752i	−1.04540	−	0.806097i
$532$	−7.81265	−	36.8884i	−0.338722	−	1.59932i
$533$	−5.47628	−	3.51939i	−0.237204	−	0.152442i
$534$	25.8950	−	33.8888i	1.12059	−	1.46651i
$535$	5.09802	−	3.27630i	0.220407	−	0.141647i
$536$	6.24932	−	10.3376i	0.269929	−	0.446518i
$537$	1.69373	+	2.90159i	0.0730900	+	0.125213i
$538$	2.07475	−	11.3216i	0.0894490	−	0.488108i
$539$	0.159754	+	0.0729573i	0.00688110	+	0.00314249i
$540$	−16.5303	+	12.6033i	−0.711351	+	0.542359i
$541$	−7.42659	−	25.2926i	−0.319294	−	1.08742i	−0.950222	−	0.311574i	$-0.899144\pi$
$541$	−7.42659	−	25.2926i	−0.319294	−	1.08742i	0.630928	−	0.775841i	$-0.282674\pi$
$542$	−0.520015	+	0.555469i	−0.0223366	+	0.0238595i
$543$	−0.864316	+	20.1672i	−0.0370914	+	0.865458i
$544$	−1.15579	+	0.905507i	−0.0495542	+	0.0388233i
$545$	31.2818	−	14.2859i	1.33997	−	0.611942i
$546$	−55.9823	+	3.44852i	−2.39582	+	0.147583i
$547$	−31.5039	−	4.52958i	−1.34701	−	0.193671i	−0.569215	−	0.822189i	$-0.692753\pi$
$547$	−31.5039	−	4.52958i	−1.34701	−	0.193671i	−0.777795	+	0.628518i	$0.783662\pi$
$548$	1.46455	+	3.99346i	0.0625625	+	0.170592i
$549$	34.9217	−	18.4271i	1.49042	−	0.786448i
$550$	−0.0445510	+	0.0637911i	−0.00189966	+	0.00272006i
$551$	−43.6161			−1.85811
$552$	7.15276	−	22.3794i	0.304442	−	0.952531i
$553$	−9.90938			−0.421390
$554$	13.2147	−	18.9217i	0.561439	−	0.803905i
$555$	14.3520	+	18.0720i	0.609207	+	0.767114i
$556$	−10.3728	+	3.80411i	−0.439906	+	0.161330i
$557$	−11.2631	−	1.61939i	−0.477233	−	0.0686157i	−0.100499	−	0.994937i	$-0.532044\pi$
$557$	−11.2631	−	1.61939i	−0.477233	−	0.0686157i	−0.376734	+	0.926321i	$0.622953\pi$
$558$	26.9028	+	3.35612i	1.13889	+	0.142076i
$559$	8.28652	−	3.78433i	0.350483	−	0.160060i
$560$	14.0428	−	21.3321i	0.593416	−	0.901446i
$561$	−0.0247332	−	0.00106000i	−0.00104423	−	4.47533e-5i
$562$	19.8037	−	21.1539i	0.835367	−	0.892321i
$563$	−4.88057	−	16.6217i	−0.205692	−	0.700521i	−0.996123	−	0.0879707i	$-0.971962\pi$
$563$	−4.88057	−	16.6217i	−0.205692	−	0.700521i	0.790431	−	0.612550i	$-0.209856\pi$
$564$	−0.340774	+	0.558165i	−0.0143492	+	0.0235030i
$565$	15.2827	+	6.97938i	0.642948	+	0.293625i
$566$	−1.73201	+	9.45130i	−0.0728020	+	0.397268i
$567$	−28.7170	−	0.819389i	−1.20600	−	0.0344111i
$568$	5.11192	+	3.09026i	0.214491	+	0.129664i
$569$	0.347448	−	0.223291i	0.0145658	−	0.00936086i	−0.533338	−	0.845902i	$-0.679062\pi$
$569$	0.347448	−	0.223291i	0.0145658	−	0.00936086i	0.547903	+	0.836542i	$0.315426\pi$
$570$	−22.9936	−	17.5699i	−0.963098	−	0.735921i
$571$	25.4115	+	16.3310i	1.06344	+	0.683430i	0.950674	−	0.310192i	$-0.100393\pi$
$571$	25.4115	+	16.3310i	1.06344	+	0.683430i	0.112764	+	0.993622i	$0.464030\pi$
$572$	−0.772885	+	0.163690i	−0.0323159	+	0.00684424i
$573$	−20.3756	−	10.3817i	−0.851203	−	0.433700i
$574$	3.88338	+	1.30437i	0.162089	+	0.0544433i
$575$	−2.55668	−	4.05257i	−0.106621	−	0.169004i
$576$	−16.2667	+	17.6464i	−0.677779	+	0.735266i
$577$	24.5892	+	7.22005i	1.02366	+	0.300575i	0.750132	−	0.661289i	$-0.229990\pi$
$577$	24.5892	+	7.22005i	1.02366	+	0.300575i	0.273531	+	0.961863i	$0.411808\pi$
$578$	20.6277	−	12.1625i	0.857999	−	0.505894i
$579$	17.7324	+	16.7471i	0.736932	+	0.695985i
$580$	−20.7743	−	21.0037i	−0.862604	−	0.872132i
$581$	24.3253	−	15.6329i	1.00918	−	0.648563i
$582$	−13.0706	−	1.06469i	−0.541796	−	0.0441329i
$583$	−0.325332	−	0.375453i	−0.0134739	−	0.0155497i
$584$	−6.35312	+	5.81800i	−0.262894	+	0.240750i
$585$	−30.8685	+	30.0003i	−1.27625	+	1.24036i
$586$	−0.228122	+	5.93064i	−0.00942361	+	0.244992i
$587$	26.9524	−	7.91395i	1.11245	−	0.326644i	0.326660	−	0.945142i	$-0.394077\pi$
$587$	26.9524	−	7.91395i	1.11245	−	0.326644i	0.785786	+	0.618498i	$0.212259\pi$
$588$	10.5260	−	3.35639i	0.434084	−	0.138415i
$589$	5.37131	+	37.3583i	0.221321	+	1.53932i
$590$	26.5297	−	10.9037i	1.09221	−	0.448898i
$591$	−7.80543	−	31.5177i	−0.321072	−	1.29646i
$592$	19.9440	+	17.6688i	0.819691	+	0.726183i
$593$	9.38536	+	1.34941i	0.385410	+	0.0554137i	0.332297	−	0.943175i	$-0.392176\pi$
$593$	9.38536	+	1.34941i	0.385410	+	0.0554137i	0.0531135	+	0.998588i	$0.483085\pi$
$594$	−0.401809	+	0.0479035i	−0.0164864	+	0.00196551i
$595$	1.08525	−	1.25244i	0.0444908	−	0.0513451i
$596$	−2.14201	+	1.58521i	−0.0877401	+	0.0649326i
$597$	4.92413	−	26.2210i	0.201531	−	1.07316i
$598$	9.17070	−	47.7802i	0.375018	−	1.95388i
$599$		−	13.9967i		−	0.571889i	−0.958246	−	0.285944i	$-0.907693\pi$
$599$		−	13.9967i		−	0.571889i	0.958246	−	0.285944i	$-0.0923072\pi$
$600$	0.622047	+	4.85503i	0.0253950	+	0.198206i
$601$	5.37903	−	6.20774i	0.219415	−	0.253219i	−0.635361	−	0.772215i	$-0.719149\pi$
$601$	5.37903	−	6.20774i	0.219415	−	0.253219i	0.854776	+	0.518996i	$0.173694\pi$
$602$	−4.47368	+	3.58490i	−0.182334	+	0.146110i
$603$	6.30015	−	11.1566i	0.256562	−	0.454330i
$604$	−14.2957	−	1.10140i	−0.581686	−	0.0448153i
$605$	−20.0086	+	9.13761i	−0.813464	+	0.371496i
$606$	−7.88656	−	38.0601i	−0.320370	−	1.54608i
$607$	−3.92066	−	27.2688i	−0.159135	−	1.10681i	−0.900233	−	0.435409i	$-0.856604\pi$
$607$	−3.92066	−	27.2688i	−0.159135	−	1.10681i	0.741098	−	0.671397i	$-0.234305\pi$
$608$	−29.6689	−	15.3642i	−1.20323	−	0.623100i
$609$	−4.07478	−	40.6248i	−0.165118	−	1.64620i
$610$	−1.43103	+	37.2035i	−0.0579408	+	1.50633i
$611$	−0.562566	+	1.23185i	−0.0227590	+	0.0498353i
$612$	−1.19687	+	0.996387i	−0.0483805	+	0.0402765i
$613$	−15.3882	−	17.7589i	−0.621523	−	0.717276i	0.354472	−	0.935067i	$-0.384661\pi$
$613$	−15.3882	−	17.7589i	−0.621523	−	0.717276i	−0.975996	+	0.217790i	$0.930115\pi$
$614$	−16.8214	+	1.76177i	−0.678856	+	0.0710994i
$615$	2.91311	−	1.18238i	0.117468	−	0.0476783i
$616$	0.446401	−	0.218872i	0.0179860	−	0.00881861i
$617$	−34.7823	−	22.3532i	−1.40028	−	0.899908i	−0.400418	−	0.916332i	$-0.631135\pi$
$617$	−34.7823	−	22.3532i	−1.40028	−	0.899908i	−0.999865	+	0.0164249i	$0.994772\pi$
$618$	−6.08297	−	16.8145i	−0.244693	−	0.676377i
$619$	11.9988	+	3.52317i	0.482273	+	0.141608i	0.513827	−	0.857894i	$-0.328227\pi$
$619$	11.9988	+	3.52317i	0.482273	+	0.141608i	−0.0315538	+	0.999502i	$0.510046\pi$
$620$	−15.4318	+	20.3802i	−0.619758	+	0.818490i
$621$	6.87901	−	23.9516i	0.276045	−	0.961145i
$622$	−7.03918	+	20.9571i	−0.282245	+	0.840304i
$623$	−15.6585	+	53.3280i	−0.627345	+	2.13654i
$624$	−29.0792	+	40.3035i	−1.16410	+	1.61343i
$625$	−15.9889	−	10.2755i	−0.639558	−	0.411019i
$626$	22.6358	+	11.4085i	0.904708	+	0.455976i
$627$	−0.211861	−	0.521975i	−0.00846090	−	0.0208457i
$628$	2.25745	−	10.1097i	0.0900821	−	0.403421i
$629$	1.13222	+	1.30665i	0.0451446	+	0.0520997i
$630$	14.2167	−	23.0581i	0.566408	−	0.918657i
$631$	26.5893	+	12.1429i	1.05851	+	0.483403i	0.867113	−	0.498111i	$-0.165973\pi$
$631$	26.5893	+	12.1429i	1.05851	+	0.483403i	0.191392	+	0.981514i	$0.438700\pi$
$632$	−5.56562	+	6.79124i	−0.221389	+	0.270141i
$633$	−3.21241	−	32.0271i	−0.127682	−	1.27296i
$634$	−0.00390306	+	0.00416916i	−0.000155010	+	0.000165579i
$635$	−22.7502	+	3.27098i	−0.902813	+	0.129805i
$636$	−31.0285	−	3.73268i	−1.23036	−	0.148011i
$637$	20.8108	−	9.50399i	0.824555	−	0.376562i
$638$	−0.140692	−	0.557613i	−0.00557006	−	0.0220761i
$639$	5.51687	+	3.11540i	0.218244	+	0.123243i
$640$	−6.73247	−	21.6052i	−0.266124	−	0.854021i
$641$	5.25986	−	6.07020i	0.207752	−	0.239758i	−0.642305	−	0.766449i	$-0.722022\pi$
$641$	5.25986	−	6.07020i	0.207752	−	0.239758i	0.850057	+	0.526690i	$0.176567\pi$
$642$	5.29914	−	5.19548i	0.209140	−	0.205049i
$643$	−30.1495			−1.18898			−0.594490	−	0.804103i	$-0.702646\pi$
$643$	−30.1495			−1.18898			−0.594490	+	0.804103i	$0.702646\pi$
$644$	1.76027	+	30.5666i	0.0693644	+	1.20449i
$645$	−0.812031	+	4.32408i	−0.0319737	+	0.170260i
$646$	−1.77744	−	1.24135i	−0.0699325	−	0.0488402i
$647$	12.5040	+	10.8348i	0.491584	+	0.425960i	0.865051	−	0.501683i	$-0.167286\pi$
$647$	12.5040	+	10.8348i	0.491584	+	0.425960i	−0.373467	+	0.927643i	$0.621831\pi$
$648$	−16.6905	+	19.2205i	−0.655664	+	0.755053i
$649$	0.552684	+	0.0794640i	0.0216947	+	0.00311923i
$650$	2.47969	+	9.82789i	0.0972615	+	0.385481i
$651$	−34.2943	+	8.49307i	−1.34410	+	0.332870i
$652$	−27.3221	+	1.80335i	−1.07002	+	0.0706247i
$653$	4.52439	+	31.4678i	0.177053	+	1.23143i	0.863537	+	0.504286i	$0.168244\pi$
$653$	4.52439	+	31.4678i	0.177053	+	1.23143i	−0.686483	+	0.727145i	$0.740847\pi$
$654$	33.9615	−	24.9036i	1.32800	−	0.973810i
$655$	−6.55218	−	22.3147i	−0.256015	−	0.871907i
$656$	3.07503	−	1.92881i	0.120060	−	0.0753073i
$657$	−6.55244	+	6.36814i	−0.255635	+	0.248445i
$658$	0.153618	−	0.838265i	0.00598864	−	0.0326790i
$659$	−14.1322	+	12.2456i	−0.550514	+	0.477023i	−0.885138	−	0.465329i	$-0.845936\pi$
$659$	−14.1322	+	12.2456i	−0.550514	+	0.477023i	0.334624	+	0.942352i	$0.391391\pi$
$660$	0.150452	−	0.350638i	0.00585635	−	0.0136486i
$661$	1.09180	−	0.701659i	0.0424662	−	0.0272914i	−0.519235	−	0.854631i	$-0.673783\pi$
$661$	1.09180	−	0.701659i	0.0424662	−	0.0272914i	0.561702	+	0.827340i	$0.310147\pi$
$662$	13.2582	+	6.68216i	0.515293	+	0.259709i
$663$	−2.21428	+	2.34455i	−0.0859953	+	0.0910548i
$664$	2.94858	−	25.4512i	0.114427	−	0.987698i
$665$	36.1832	+	10.6244i	1.40313	+	0.411995i
$666$	21.7005	+	18.1047i	0.840877	+	0.701542i
$667$	35.0117	+	5.33387i	1.35566	+	0.206528i
$668$	−13.2088	+	17.4444i	−0.511064	+	0.674943i
$669$	9.28953	+	4.73315i	0.359154	+	0.182994i
$670$	6.13606	+	10.4068i	0.237057	+	0.402049i
$671$	−0.391841	+	0.609716i	−0.0151269	+	0.0235378i
$672$	11.5387	−	29.0695i	0.445114	−	1.12138i
$673$	−6.29948	+	4.04843i	−0.242827	+	0.156055i	−0.656394	−	0.754418i	$-0.727919\pi$
$673$	−6.29948	+	4.04843i	−0.242827	+	0.156055i	0.413567	+	0.910474i	$0.364283\pi$
$674$	2.91588	−	0.305393i	0.112316	−	0.0117633i
$675$	0.812282	+	5.12769i	0.0312647	+	0.197365i
$676$	−37.2318	+	67.3035i	−1.43199	+	2.58860i
$677$	12.8312	+	5.85982i	0.493144	+	0.225211i	0.646434	−	0.762970i	$-0.276260\pi$
$677$	12.8312	+	5.85982i	0.493144	+	0.225211i	−0.153290	+	0.988181i	$0.548987\pi$
$678$	20.0603	+	4.57182i	0.770411	+	0.175580i
$679$	16.3973	−	4.81468i	0.629270	−	0.184770i
$680$	−0.248810	−	1.44719i	−0.00954142	−	0.0554973i
$681$	−28.9999	−	1.24286i	−1.11128	−	0.0476267i
$682$	−0.460283	+	0.189176i	−0.0176251	+	0.00724393i
$683$	−6.31761	−	13.8336i	−0.241736	−	0.529329i	0.749409	−	0.662107i	$-0.230338\pi$
$683$	−6.31761	−	13.8336i	−0.241736	−	0.529329i	−0.991146	+	0.132778i	$0.957610\pi$
$684$	−31.9383	−	15.3553i	−1.22119	−	0.587124i
$685$	−4.21071	−	0.605408i	−0.160883	−	0.0231315i
$686$	13.4241	−	10.7572i	0.512535	−	0.410711i
$687$	−11.2407	+	8.92690i	−0.428861	+	0.340583i
$688$	−0.0557959	+	5.07943i	−0.00212720	+	0.193652i
$689$	−64.7165			−2.46550
$690$	16.3089	+	16.9157i	0.620869	+	0.643969i
$691$		−	12.6547i		−	0.481409i	−0.970598	−	0.240704i	$-0.922622\pi$
$691$		−	12.6547i		−	0.481409i	0.970598	−	0.240704i	$-0.0773785\pi$
$692$	5.70667	+	7.71114i	0.216935	+	0.293133i
$693$	0.466383	−	0.246095i	0.0177164	−	0.00934839i
$694$	29.2483	+	36.4997i	1.11025	+	1.38551i
$695$	1.57252	−	10.9371i	0.0596492	−	0.414869i
$696$	−30.1302	−	20.0244i	−1.14208	−	0.759023i
$697$	0.214254	−	0.0978466i	0.00811545	−	0.00370620i
$698$	19.4653	−	8.00024i	0.736773	−	0.302814i
$699$	−11.1868	−	0.479440i	−0.423125	−	0.0181341i
$700$	−3.02614	−	5.61506i	−0.114377	−	0.212229i
$701$	−6.77345	−	23.0683i	−0.255830	−	0.871276i	−0.982810	−	0.184618i	$-0.940895\pi$
$701$	−6.77345	−	23.0683i	−0.255830	−	0.871276i	0.726981	−	0.686658i	$-0.240923\pi$
$702$	−29.5612	+	43.6446i	−1.11571	+	1.64726i
$703$	−16.3437	+	35.7877i	−0.616415	+	1.34976i
$704$	0.100721	−	0.428864i	0.00379608	−	0.0161634i
$705$	−0.329717	−	0.564850i	−0.0124179	−	0.0212735i
$706$	−1.08780	+	0.113930i	−0.0409398	+	0.00428780i
$707$	27.3845	+	42.6111i	1.02990	+	1.60255i
$708$	29.1034	−	19.6671i	1.09377	−	0.739134i
$709$	16.2304	+	10.4306i	0.609544	+	0.391730i	0.808686	−	0.588240i	$-0.200179\pi$
$709$	16.2304	+	10.4306i	0.609544	+	0.391730i	−0.199142	+	0.979971i	$0.563815\pi$
$710$	−5.14611	+	3.03426i	−0.193130	+	0.113874i
$711$	−5.68691	+	7.37518i	−0.213276	+	0.276591i
$712$	27.7529	+	40.6831i	1.04008	+	1.52466i
$713$	0.256912	−	30.6452i	0.00962143	−	1.14767i
$714$	0.990157	−	1.77151i	0.0370557	−	0.0662971i
$715$	0.222601	−	0.758110i	0.00832481	−	0.0283517i
$716$	−3.79533	+	0.803818i	−0.141838	+	0.0300401i
$717$	15.9451	−	16.8832i	0.595481	−	0.630515i
$718$	−7.05985	+	14.0076i	−0.263471	+	0.522757i
$719$	26.5692	+	41.3425i	0.990865	+	1.54182i	0.832194	+	0.554485i	$0.187085\pi$
$719$	26.5692	+	41.3425i	0.990865	+	1.54182i	0.158672	+	0.987331i	$0.449279\pi$
$720$	−7.81765	−	22.6938i	−0.291347	−	0.845749i
$721$	15.2594	+	17.6103i	0.568289	+	0.655841i
$722$	4.04923	−	22.0960i	0.150697	−	0.822327i
$723$	−30.4605	−	21.4726i	−1.13284	−	0.798576i
$724$	−21.7938	−	8.26529i	−0.809960	−	0.307177i
$725$	−7.07938	+	2.07869i	−0.262922	+	0.0772007i
$726$	−21.7225	+	15.9289i	−0.806199	+	0.591178i
$727$	39.9591	−	5.74525i	1.48200	−	0.213079i	0.646645	−	0.762791i	$-0.276171\pi$
$727$	39.9591	−	5.74525i	1.48200	−	0.213079i	0.835355	+	0.549711i	$0.185262\pi$
$728$	16.5333	−	62.6195i	0.612766	−	2.32083i
$729$	−17.0903	+	20.9027i	−0.632973	+	0.774174i
$730$	−2.10774	−	8.35373i	−0.0780111	−	0.309185i
$731$	−0.0469096	+	0.326263i	−0.00173501	+	0.0120673i
$732$	7.52825	+	44.9678i	0.278252	+	1.66206i
$733$	13.7800	−	15.9030i	0.508977	−	0.587390i	−0.441860	−	0.897084i	$-0.645681\pi$
$733$	13.7800	−	15.9030i	0.508977	−	0.587390i	0.950836	+	0.309694i	$0.100227\pi$
$734$	22.1765	−	31.7538i	0.818550	−	1.17205i
$735$	−2.03934	+	10.8595i	−0.0752222	+	0.400559i
$736$	21.9370	+	15.9614i	0.808609	+	0.588346i
$737$			0.235181i			0.00866299i
$738$	3.19943	−	2.14168i	0.117773	−	0.0788365i
$739$	8.49777	+	7.36336i	0.312595	+	0.270866i	0.797001	−	0.603978i	$-0.206419\pi$
$739$	8.49777	+	7.36336i	0.312595	+	0.270866i	−0.484405	+	0.874844i	$0.660964\pi$
$740$	−25.0184	+	9.17516i	−0.919693	+	0.337286i
$741$	−69.4616	−	23.6706i	−2.55174	−	0.869561i
$742$	39.4890	−	9.96355i	1.44969	−	0.365773i
$743$	4.47602	+	9.80111i	0.164209	+	0.359568i	0.973793	−	0.227437i	$-0.0730344\pi$
$743$	4.47602	+	9.80111i	0.164209	+	0.359568i	−0.809584	+	0.587004i	$0.800307\pi$
$744$	−13.4409	+	28.2732i	−0.492766	+	1.03655i
$745$	−0.379280	−	2.63795i	−0.0138957	−	0.0966470i
$746$	26.1923	−	27.9781i	0.958969	−	1.02435i
$747$	2.32509	−	27.0760i	0.0850706	−	0.990659i
$748$	0.0101366	−	0.0267280i	0.000370630	−	0.000977273i
$749$	−4.01746	+	8.79702i	−0.146795	+	0.321436i
$750$	−27.4368	−	10.5432i	−1.00185	−	0.384985i
$751$	−12.1309	+	10.5115i	−0.442662	+	0.383569i	−0.847479	−	0.530829i	$-0.821881\pi$
$751$	−12.1309	+	10.5115i	−0.442662	+	0.383569i	0.404817	+	0.914398i	$0.367335\pi$
$752$	−0.488212	−	0.576093i	−0.0178033	−	0.0210079i
$753$	−9.18356	−	22.6261i	−0.334667	−	0.824542i
$754$	−66.8990	−	33.7173i	−2.43632	−	1.22791i
$755$	7.75261	−	12.0633i	0.282146	−	0.439028i
$756$	11.3184	−	31.1824i	0.411646	−	1.13409i
$757$	−33.3100	−	9.78071i	−1.21067	−	0.355486i	−0.386749	−	0.922185i	$-0.626402\pi$
$757$	−33.3100	−	9.78071i	−1.21067	−	0.355486i	−0.823925	+	0.566699i	$0.808220\pi$
$758$	−6.73202	−	2.26118i	−0.244518	−	0.0821299i
$759$	0.106233	+	0.444910i	0.00385600	+	0.0161492i
$760$	27.6036	−	18.8304i	1.00129	−	0.683051i
$761$	7.30750	−	24.8871i	0.264897	−	0.902155i	−0.714402	−	0.699735i	$-0.753301\pi$
$761$	7.30750	−	24.8871i	0.264897	−	0.902155i	0.979299	−	0.202420i	$-0.0648805\pi$
$762$	−26.4678	+	9.57527i	−0.958828	+	0.346875i
$763$	−29.6709	+	46.1688i	−1.07416	+	1.67142i
$764$	18.7739	−	18.5688i	0.679216	−	0.671796i
$765$	−0.309331	−	1.52647i	−0.0111839	−	0.0551898i
$766$	−3.06856	−	29.2985i	−0.110872	−	1.05860i
$767$	54.9712	−	47.6328i	1.98489	−	1.71992i
$768$	−13.4416	−	24.2348i	−0.485031	−	0.874497i
$769$	−28.6177	−	13.0693i	−1.03198	−	0.471290i	−0.173878	−	0.984767i	$-0.555630\pi$
$769$	−28.6177	−	13.0693i	−1.03198	−	0.471290i	−0.858103	+	0.513477i	$0.828357\pi$
$770$	−0.0191116	+	0.496857i	−0.000688734	+	0.0179055i
$771$	2.75943	+	27.5110i	0.0993784	+	0.990785i
$772$	−24.7926	+	13.3615i	−0.892304	+	0.480892i
$773$	31.1136	−	4.47346i	1.11908	−	0.160899i	0.442145	−	0.896943i	$-0.354217\pi$
$773$	31.1136	−	4.47346i	1.11908	−	0.160899i	0.676934	+	0.736044i	$0.263308\pi$
$774$	0.100699	+	5.38694i	0.00361957	+	0.193629i
$775$	2.65227	+	5.80767i	0.0952725	+	0.208618i
$776$	5.90990	−	13.9418i	0.212153	−	0.500481i
$777$	−34.8602	−	11.8794i	−1.25060	−	0.426171i
$778$	31.3252	−	25.1019i	1.12306	−	0.899946i
$779$	4.05068	+	3.50993i	0.145130	+	0.125756i
$780$	−21.6856	−	44.7240i	−0.776470	−	1.60138i
$781$	−0.116296			−0.00416139
$782$	1.27499	+	1.21382i	0.0455935	+	0.0434063i
$783$	−32.5740	−	20.2815i	−1.16410	−	0.724802i
$784$	−0.140126	+	12.7565i	−0.00500451	+	0.455590i
$785$	7.82941	+	6.78422i	0.279444	+	0.242139i
$786$	−13.4017	−	25.1303i	−0.478022	−	0.896369i
$787$	−3.30702	+	23.0009i	−0.117883	+	0.819892i	0.841997	+	0.539482i	$0.181380\pi$
$787$	−3.30702	+	23.0009i	−0.117883	+	0.819892i	−0.959880	+	0.280411i	$0.909529\pi$
$788$	37.3821	+	2.88006i	1.33168	+	0.102598i
$789$	4.96732	+	20.0576i	0.176841	+	0.714070i
$790$	−3.33822	−	8.12220i	−0.118769	−	0.288975i
$791$	−26.5391	+	3.81575i	−0.943623	+	0.135673i
$792$	0.0932874	−	0.457848i	0.00331482	−	0.0162689i
$793$	26.5996	+	90.5900i	0.944580	+	3.21694i
$794$	−1.04970	+	27.2898i	−0.0372524	+	0.968477i
$795$	18.0084	−	25.5462i	0.638693	−	0.906032i
$796$	26.9569	+	14.9124i	0.955462	+	0.528554i
$797$	−37.6837	+	32.6531i	−1.33482	+	1.15663i	−0.360176	+	0.932884i	$0.617284\pi$
$797$	−37.6837	+	32.6531i	−1.33482	+	1.15663i	−0.974647	+	0.223747i	$0.928171\pi$
$798$	46.0286	+	3.74934i	1.62940	+	0.132725i
$799$	−0.0264914	−	0.0412214i	−0.000937198	−	0.00145831i
$800$	−5.54782	−	1.07979i	−0.196145	−	0.0381764i
$801$	30.7037	+	42.2585i	1.08486	+	1.49313i
$802$	−39.4122	+	23.2382i	−1.39169	+	0.820570i
$803$	0.0472514	−	0.160923i	0.00166747	−	0.00567887i
$804$	9.94384	+	10.9545i	0.350692	+	0.386336i
$805$	−27.7459	−	12.9533i	−0.977914	−	0.456544i
$806$	−20.6411	+	61.4529i	−0.727052	+	2.16459i
$807$	12.5605	+	6.39977i	0.442151	+	0.225283i
$808$	44.5834	+	5.16508i	1.56844	+	0.181707i
$809$	25.0021	−	38.9040i	0.879027	−	1.36779i	−0.0503776	−	0.998730i	$-0.516042\pi$
$809$	25.0021	−	38.9040i	0.879027	−	1.36779i	0.929405	−	0.369062i	$-0.120321\pi$
$810$	−9.00242	−	23.8138i	−0.316313	−	0.836732i
$811$	20.3146	+	31.6101i	0.713342	+	1.10998i	0.988883	+	0.148693i	$0.0475065\pi$
$811$	20.3146	+	31.6101i	0.713342	+	1.10998i	−0.275541	+	0.961289i	$0.588857\pi$
$812$	46.0117	+	10.2742i	1.61469	+	0.360554i
$813$	−0.469795	−	0.804821i	−0.0164764	−	0.0282263i
$814$	−0.510250	−	0.0935068i	−0.0178843	−	0.00327741i
$815$	11.3760	−	24.9099i	0.398482	−	0.872555i
$816$	−0.657953	−	1.67356i	−0.0230329	−	0.0585863i
$817$	−7.19679	+	2.11317i	−0.251784	+	0.0739304i
$818$	0.799289	−	0.853784i	0.0279465	−	0.0298519i
$819$	15.5578	−	66.9091i	0.543634	−	2.33799i
$820$	0.239091	+	3.62241i	0.00834942	+	0.126500i
$821$	−6.72843	−	14.7332i	−0.234824	−	0.514193i	0.755131	−	0.655574i	$-0.227573\pi$
$821$	−6.72843	−	14.7332i	−0.234824	−	0.514193i	−0.989955	+	0.141381i	$0.954846\pi$
$822$	−5.19965	+	0.320299i	−0.181359	+	0.0111717i
$823$	4.58527	−	31.8913i	0.159833	−	1.11166i	−0.739107	−	0.673588i	$-0.764752\pi$
$823$	4.58527	−	31.8913i	0.159833	−	1.11166i	0.898940	−	0.438072i	$-0.144339\pi$
$824$	20.6394	−	0.566936i	0.719007	−	0.0197501i
$825$	−0.0592640	−	0.0746252i	−0.00206331	−	0.00259812i
$826$	−26.2092	+	37.5280i	−0.911933	+	1.30576i
$827$		−	37.6484i		−	1.30916i	−0.755991	−	0.654582i	$-0.772845\pi$
$827$		−	37.6484i		−	1.30916i	0.755991	−	0.654582i	$-0.227155\pi$
$828$	23.7598	+	16.2318i	0.825710	+	0.564095i
$829$			26.5649i			0.922637i	0.887235	+	0.461319i	$0.152623\pi$
$829$			26.5649i			0.922637i	−0.887235	+	0.461319i	$0.847377\pi$
$830$	21.0081	+	14.6718i	0.729200	+	0.509266i
$831$	17.5789	+	22.1353i	0.609804	+	0.767865i
$832$	−33.6293	−	46.5012i	−1.16589	−	1.61214i
$833$	−0.117809	+	0.819379i	−0.00408184	+	0.0283898i
$834$	−0.831963	−	13.5059i	−0.0288085	−	0.467670i
$835$	−9.09068	−	19.9058i	−0.314596	−	0.688869i
$836$	0.649067	−	0.0428406i	0.0224484	−	0.00148167i
$837$	−13.3601	+	30.3981i	−0.461794	+	1.05071i
$838$	4.44976	+	4.16575i	0.153714	+	0.143903i
$839$	−36.7802	+	10.7996i	−1.26979	+	0.372845i	−0.846131	−	0.532976i	$-0.821074\pi$
$839$	−36.7802	+	10.7996i	−1.26979	+	0.372845i	−0.423662	+	0.905820i	$0.639256\pi$
$840$	20.1178	+	23.9513i	0.694130	+	0.826397i
$841$	10.6070	−	23.2261i	0.365758	−	0.800899i
$842$	2.42880	−	13.2535i	0.0837019	−	0.456747i
$843$	17.8911	+	30.6499i	0.616203	+	1.05564i
$844$	36.2740	+	8.09982i	1.24860	+	0.278807i
$845$	−41.5881	−	64.7124i	−1.43067	−	2.22617i
$846$	−0.535729	−	0.595405i	−0.0184188	−	0.0204705i
$847$	18.9782	−	29.5306i	0.652098	−	1.01468i
$848$	15.3507	−	32.6592i	0.527146	−	1.12152i
$849$	−10.4856	−	5.34256i	−0.359864	−	0.183356i
$850$	−0.347659	−	0.116774i	−0.0119246	−	0.00400530i
$851$	17.4960	−	26.7290i	0.599756	−	0.916258i
$852$	−5.41696	+	4.91719i	−0.185582	+	0.168460i
$853$	−11.6489	+	39.6724i	−0.398849	+	1.35836i	0.478325	+	0.878183i	$0.341244\pi$
$853$	−11.6489	+	39.6724i	−0.398849	+	1.35836i	−0.877174	+	0.480173i	$0.840574\pi$
$854$	−30.1776	−	51.1814i	−1.03266	−	1.75139i
$855$	28.6725	−	20.8326i	0.980581	−	0.712459i
$856$	3.77248	+	7.69417i	0.128941	+	0.262981i
$857$	11.3135	+	17.6042i	0.386463	+	0.601348i	0.978918	−	0.204256i	$-0.0654774\pi$
$857$	11.3135	+	17.6042i	0.386463	+	0.601348i	−0.592455	+	0.805604i	$0.701841\pi$
$858$	0.0785560	−	0.964390i	0.00268186	−	0.0329237i
$859$	26.8976	−	23.3069i	0.917736	−	0.795223i	−0.0614664	−	0.998109i	$-0.519578\pi$
$859$	26.8976	−	23.3069i	0.917736	−	0.795223i	0.979202	+	0.202886i	$0.0650322\pi$
$860$	−4.44543	−	2.45918i	−0.151588	−	0.0838573i
$861$	−2.89078	+	4.10078i	−0.0985175	+	0.139754i
$862$	20.2525	+	0.779009i	0.689801	+	0.0265332i
$863$	−6.94888	−	23.6657i	−0.236543	−	0.805590i	−0.989123	−	0.147090i	$-0.953009\pi$
$863$	−6.94888	−	23.6657i	−0.236543	−	0.805590i	0.752581	−	0.658500i	$-0.228809\pi$
$864$	−15.0134	−	25.2705i	−0.510765	−	0.859720i
$865$	−9.49650	+	1.36539i	−0.322891	+	0.0464247i
$866$	−4.99501	+	2.05295i	−0.169737	+	0.0697621i
$867$	7.05021	+	28.4682i	0.239438	+	0.966830i
$868$	3.13379	−	40.6754i	0.106368	−	1.38061i
$869$	0.0243283	−	0.169207i	0.000825281	−	0.00573996i
$870$	31.9253	−	17.0254i	1.08237	−	0.577214i
$871$	23.1535	+	20.0626i	0.784526	+	0.679796i
$872$	14.9763	+	46.2653i	0.507163	+	1.56674i
$873$	5.82688	−	14.9670i	0.197210	−	0.506556i
$874$	−13.0727	+	37.8654i	−0.442190	+	1.28082i
$875$	38.3035			1.29489
$876$	−4.60319	−	9.49355i	−0.155527	−	0.320757i
$877$	−9.90976	−	8.58686i	−0.334629	−	0.289958i	0.471296	−	0.881975i	$-0.343786\pi$
$877$	−9.90976	−	8.58686i	−0.334629	−	0.289958i	−0.805925	+	0.592017i	$0.798332\pi$
$878$	9.61838	+	12.0030i	0.324605	+	0.405082i
$879$	−6.88037	−	2.34464i	−0.232069	−	0.0790827i
$880$	0.329779	+	0.292159i	0.0111169	+	0.00984867i
$881$	10.5992	+	23.2090i	0.357097	+	0.781933i	0.999874	+	0.0158795i	$0.00505480\pi$
$881$	10.5992	+	23.2090i	0.357097	+	0.781933i	−0.642777	+	0.766053i	$0.722218\pi$
$882$	0.252897	+	13.5288i	0.00851550	+	0.455538i
$883$	−41.1951	+	5.92297i	−1.38633	+	0.199324i	−0.794756	−	0.606929i	$-0.792401\pi$
$883$	−41.1951	+	5.92297i	−1.38633	+	0.199324i	−0.591571	+	0.806253i	$0.701492\pi$
$884$	−1.76664	−	3.27804i	−0.0594187	−	0.110252i
$885$	3.50598	+	34.9540i	0.117852	+	1.17496i
$886$	45.4049	+	1.74650i	1.52541	+	0.0586747i
$887$	1.40912	+	0.643526i	0.0473138	+	0.0216075i	0.438931	−	0.898521i	$-0.355357\pi$
$887$	1.40912	+	0.643526i	0.0473138	+	0.0216075i	−0.391618	+	0.920128i	$0.628084\pi$
$888$	−27.7206	+	17.2188i	−0.930244	+	0.577825i
$889$	27.7205	−	24.0199i	0.929715	−	0.805603i
$890$	−48.9851	+	5.13042i	−1.64199	+	0.171972i
$891$	0.0844938	−	0.488343i	0.00283065	−	0.0163601i
$892$	−8.55928	+	8.46578i	−0.286586	+	0.283455i
$893$	0.602825	−	0.938013i	0.0201728	−	0.0313894i
$894$	−1.11028	−	3.06902i	−0.0371333	−	0.102643i
$895$	1.09310	−	3.72277i	0.0365384	−	0.124439i
$896$	27.6792	+	23.1968i	0.924698	+	0.774952i
$897$	52.8638	+	27.4955i	1.76507	+	0.918048i
$898$	2.60681	−	7.76102i	0.0869904	−	0.258989i
$899$	−45.2781	−	13.2948i	−1.51011	−	0.443408i
$900$	−5.91575	−	0.970192i	−0.197192	−	0.0323397i
$901$	1.26599	−	1.96991i	0.0421761	−	0.0656273i
$902$	−0.0318066	+	0.0631080i	−0.00105905	+	0.00210127i
$903$	−2.64059	−	6.50579i	−0.0878734	−	0.216499i
$904$	−12.2907	+	20.3313i	−0.408782	+	0.676209i
$905$	17.6173	−	15.2655i	0.585618	−	0.507441i
$906$	6.29899	−	16.3919i	0.209270	−	0.544585i
$907$	18.3070	−	40.0867i	0.607873	−	1.33106i	−0.316147	−	0.948710i	$-0.602389\pi$
$907$	18.3070	−	40.0867i	0.607873	−	1.33106i	0.924019	−	0.382345i	$-0.124884\pi$
$908$	11.8853	−	31.3389i	0.394427	−	1.04002i
$909$	47.4295	+	4.07290i	1.57314	+	0.135090i
$910$	47.2852	+	44.2671i	1.56749	+	1.46744i
$911$	−6.63428	−	46.1424i	−0.219803	−	1.52877i	−0.738762	−	0.673967i	$-0.764589\pi$
$911$	−6.63428	−	46.1424i	−0.219803	−	1.52877i	0.518959	−	0.854799i	$-0.326320\pi$
$912$	28.4216	−	29.4391i	0.941133	−	0.974828i
$913$	0.207218	+	0.453745i	0.00685793	+	0.0150168i
$914$	7.12136	+	28.2244i	0.235554	+	0.933581i
$915$	−43.1613	−	14.7082i	−1.42687	−	0.486237i
$916$	−5.70693	−	15.5614i	−0.188562	−	0.514162i
$917$	28.0493	+	24.3049i	0.926270	+	0.802617i
$918$	−0.750225	−	1.75359i	−0.0247611	−	0.0578771i
$919$			41.0957i			1.35562i	0.735236	+	0.677812i	$0.237072\pi$
$919$			41.0957i			1.35562i	−0.735236	+	0.677812i	$0.762928\pi$
$920$	−24.4609	+	11.7399i	−0.806451	+	0.387054i
$921$	3.82323	−	20.3587i	0.125980	−	0.670843i
$922$	3.47384	+	2.42610i	0.114405	+	0.0798992i
$923$	−9.92088	+	11.4493i	−0.326550	+	0.376858i
$924$	0.100541	+	0.600549i	0.00330754	+	0.0197566i
$925$	−0.947164	+	6.58767i	−0.0311425	+	0.216601i
$926$	−19.3007	+	4.86980i	−0.634261	+	0.160032i
$927$	21.8639	−	1.25060i	0.718104	−	0.0410751i
$928$	32.8838	−	25.7629i	1.07946	−	0.845707i
$929$	−29.1277	+	4.18794i	−0.955650	+	0.137402i	−0.602459	−	0.798150i	$-0.705812\pi$
$929$	−29.1277	+	4.18794i	−0.955650	+	0.137402i	−0.353191	+	0.935551i	$0.614903\pi$
$930$	−18.5142	−	25.2481i	−0.607105	−	0.827919i
$931$	−18.0741	+	5.30703i	−0.592354	+	0.173931i
$932$	4.58479	−	12.0891i	0.150180	−	0.395992i
$933$	−22.1303	−	15.6004i	−0.724515	−	0.510736i
$934$	−36.0667	−	6.60946i	−1.18014	−	0.216268i
$935$	0.0187216	+	0.0216059i	0.000612263	+	0.000706589i
$936$	−37.1170	−	48.2419i	−1.21321	−	1.57684i
$937$	−7.25428	−	11.2879i	−0.236987	−	0.368759i	0.702306	−	0.711875i	$-0.252154\pi$
$937$	−7.25428	−	11.2879i	−0.236987	−	0.368759i	−0.939293	+	0.343116i	$0.888517\pi$
$938$	−17.2167	−	8.67725i	−0.562144	−	0.283322i
$939$	−21.3162	+	22.5703i	−0.695628	+	0.736555i
$940$	0.738832	−	0.156478i	0.0240980	−	0.00510376i
$941$	−5.82395	+	19.8345i	−0.189855	+	0.646588i	0.808459	+	0.588552i	$0.200302\pi$
$941$	−5.82395	+	19.8345i	−0.189855	+	0.646588i	−0.998315	+	0.0580354i	$0.981516\pi$
$942$	11.0743	+	6.18978i	0.360819	+	0.201674i
$943$	−2.82234	−	3.31287i	−0.0919080	−	0.107882i
$944$	10.9988	+	39.0397i	0.357980	+	1.27063i
$945$	22.0825	+	24.7598i	0.718344	+	0.805437i
$946$	−0.0502306	−	0.0851913i	−0.00163314	−	0.00276981i
$947$	−14.6406	−	9.40895i	−0.475756	−	0.305750i	0.280699	−	0.959796i	$-0.409434\pi$
$947$	−14.6406	−	9.40895i	−0.475756	−	0.305750i	−0.756455	+	0.654046i	$0.773070\pi$
$948$	−6.02118	−	8.91016i	−0.195559	−	0.289389i
$949$	−11.8120	−	18.3798i	−0.383434	−	0.596635i
$950$	−0.869304	−	8.30010i	−0.0282039	−	0.269291i
$951$	−0.00352612	−	0.00604071i	−0.000114342	−	0.000195883i
$952$	1.58265	+	1.72822i	0.0512941	+	0.0560120i
$953$	−3.41827	+	7.48496i	−0.110729	+	0.242462i	−0.956882	−	0.290478i	$-0.906186\pi$
$953$	−3.41827	+	7.48496i	−0.110729	+	0.242462i	0.846153	+	0.532940i	$0.178913\pi$
$954$	15.2469	−	35.1082i	0.493637	−	1.13667i
$955$	7.44015	+	25.3388i	0.240757	+	0.819945i
$956$	12.7217	+	23.6053i	0.411449	+	0.763451i
$957$	0.703690	+	0.0301584i	0.0227471	+	0.000974883i
$958$	10.2505	+	24.9403i	0.331178	+	0.805786i
$959$	6.17532	−	2.82017i	0.199411	−	0.0910681i
$960$	27.7138	−	0.335137i	0.894459	−	0.0108165i
$961$	−1.39961	+	9.73453i	−0.0451488	+	0.314017i
$962$	−52.7338	+	42.2573i	−1.70021	+	1.36243i
$963$	4.24170	+	8.03858i	0.136687	+	0.259040i
$964$	34.5912	−	25.5995i	1.11411	−	0.824503i
$965$		−	28.1669i		−	0.906725i
$966$	−36.4897	−	8.63858i	−1.17404	−	0.277942i
$967$	−26.3208			−0.846420			−0.423210	−	0.906032i	$-0.639097\pi$
$967$	−26.3208			−0.846420			−0.423210	+	0.906032i	$0.639097\pi$
$968$	−9.57921	−	29.5923i	−0.307887	−	0.951133i
$969$	2.07932	−	1.65130i	0.0667973	−	0.0530475i
$970$	9.47017	+	11.8180i	0.304069	+	0.379455i
$971$	−15.2635	−	2.19456i	−0.489829	−	0.0704268i	−0.107025	−	0.994256i	$-0.534133\pi$
$971$	−15.2635	−	2.19456i	−0.489829	−	0.0704268i	−0.382804	+	0.923829i	$0.625042\pi$
$972$	−16.7123	−	26.3191i	−0.536049	−	0.844187i
$973$	7.32528	+	16.0401i	0.234838	+	0.514223i
$974$	2.53600	+	6.17032i	0.0812587	+	0.197710i
$975$	−12.4025	−	0.531540i	−0.397198	−	0.0170229i
$976$	−52.0256	−	8.06438i	−1.66530	−	0.258134i
$977$	−31.3903	+	9.21703i	−1.00427	+	0.294879i	−0.742205	−	0.670172i	$-0.766220\pi$
$977$	−31.3903	+	9.21703i	−1.00427	+	0.294879i	−0.262060	+	0.965051i	$0.584402\pi$
$978$	7.45179	−	32.6970i	0.238282	−	1.04554i
$979$	−0.872157	−	0.398301i	−0.0278742	−	0.0127297i
$980$	−11.1643	−	6.17599i	−0.356630	−	0.197285i
$981$	17.3338	+	48.5788i	0.553427	+	1.55100i
$982$	−1.74481	−	16.6594i	−0.0556791	−	0.531623i
$983$	36.2739	−	23.3118i	1.15696	−	0.743532i	0.185946	−	0.982560i	$-0.440465\pi$
$983$	36.2739	−	23.3118i	1.15696	−	0.743532i	0.971013	+	0.239028i	$0.0768287\pi$
$984$	1.18679	+	4.28436i	0.0378335	+	0.136580i
$985$	−20.2724	+	31.5445i	−0.645932	+	1.00509i
$986$	2.33500	−	1.37677i	0.0743616	−	0.0438451i
$987$	0.929999	+	0.473848i	0.0296022	+	0.0150828i
$988$	51.1525	−	67.5552i	1.62738	−	2.14922i
$989$	6.03546	−	0.816186i	0.191916	−	0.0259532i
$990$	0.358824	+	0.299366i	0.0114042	+	0.00951448i
$991$	−52.2985	−	15.3562i	−1.66132	−	0.487806i	−0.689646	−	0.724147i	$-0.742234\pi$
$991$	−52.2985	−	15.3562i	−1.66132	−	0.487806i	−0.971670	+	0.236340i	$0.924052\pi$
$992$	−26.1161	−	24.9931i	−0.829188	−	0.793532i
$993$	−12.4853	+	13.2198i	−0.396208	+	0.419518i
$994$	4.29087	−	8.51357i	0.136098	−	0.270034i
$995$	−25.9191	+	16.6572i	−0.821690	+	0.528068i
$996$	28.8372	+	12.3735i	0.913741	+	0.392069i
$997$	22.2705	−	19.2975i	0.705313	−	0.611157i	−0.226536	−	0.974003i	$-0.572740\pi$
$997$	22.2705	−	19.2975i	0.705313	−	0.611157i	0.931849	+	0.362845i	$0.118195\pi$
$998$	−53.8649	−	9.87111i	−1.70506	−	0.312464i
$999$	−28.8473	+	19.1276i	−0.912690	+	0.605172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.18	yes	920
3.2	odd	2	inner	552.2.bf.a.5.75	yes	920
8.5	even	2	inner	552.2.bf.a.5.91	yes	920
23.14	odd	22	inner	552.2.bf.a.221.2	yes	920
24.5	odd	2	inner	552.2.bf.a.5.2	✓	920
69.14	even	22	inner	552.2.bf.a.221.91	yes	920
184.37	odd	22	inner	552.2.bf.a.221.75	yes	920
552.221	even	22	inner	552.2.bf.a.221.18	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.2	✓	920	24.5	odd	2	inner
552.2.bf.a.5.18	yes	920	1.1	even	1	trivial
552.2.bf.a.5.75	yes	920	3.2	odd	2	inner
552.2.bf.a.5.91	yes	920	8.5	even	2	inner
552.2.bf.a.221.2	yes	920	23.14	odd	22	inner
552.2.bf.a.221.18	yes	920	552.221	even	22	inner
552.2.bf.a.221.75	yes	920	184.37	odd	22	inner
552.2.bf.a.221.91	yes	920	69.14	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15945 - 0.809745i) q^{2} +(1.35636 - 1.07716i) q^{3} +(0.688626 + 1.87771i) q^{4} +(-1.97986 - 0.284661i) q^{5} +(-2.44486 + 0.150603i) q^{6} +(2.90361 - 1.32603i) q^{7} +(0.722042 - 2.73471i) q^{8} +(0.679440 - 2.92205i) q^{9} +O(q^{10})\)	\(q+(-1.15945 - 0.809745i) q^{2} +(1.35636 - 1.07716i) q^{3} +(0.688626 + 1.87771i) q^{4} +(-1.97986 - 0.284661i) q^{5} +(-2.44486 + 0.150603i) q^{6} +(2.90361 - 1.32603i) q^{7} +(0.722042 - 2.73471i) q^{8} +(0.679440 - 2.92205i) q^{9} +(2.06503 + 1.93323i) q^{10} +(0.0155140 + 0.0528360i) q^{11} +(2.95663 + 1.80509i) q^{12} +(6.52515 + 2.97994i) q^{13} +(-4.44033 - 0.813720i) q^{14} +(-2.99203 + 1.74653i) q^{15} +(-3.05159 + 2.58608i) q^{16} +(-0.218352 + 0.140326i) q^{17} +(-3.15389 + 2.83778i) q^{18} +(-4.96870 - 3.19319i) q^{19} +(-0.828872 - 3.91362i) q^{20} +(2.50999 - 4.92625i) q^{21} +(0.0247960 - 0.0738228i) q^{22} +(3.59799 + 3.17088i) q^{23} +(-1.96638 - 4.48702i) q^{24} +(-0.958658 - 0.281487i) q^{25} +(-5.15257 - 8.73879i) q^{26} +(-2.22595 - 4.69522i) q^{27} +(4.48941 + 4.53900i) q^{28} +(6.21239 - 3.99246i) q^{29} +(4.88334 + 0.397781i) q^{30} +(-4.18469 - 4.82939i) q^{31} +(5.63221 - 0.527410i) q^{32} +(0.0779556 + 0.0549536i) q^{33} +(0.366795 + 0.0141087i) q^{34} +(-6.12621 + 1.79882i) q^{35} +(5.95464 - 0.736407i) q^{36} +(-0.947989 - 6.59341i) q^{37} +(3.17526 + 7.72570i) q^{38} +(12.0604 - 2.98678i) q^{39} +(-2.20801 + 5.20881i) q^{40} +(-0.898237 - 0.129147i) q^{41} +(-6.89920 + 3.67926i) q^{42} +(0.831631 - 0.959753i) q^{43} +(-0.0885272 + 0.0655151i) q^{44} +(-2.17699 + 5.59183i) q^{45} +(-1.60407 - 6.58991i) q^{46} +0.188785i q^{47} +(-1.35343 + 6.79472i) q^{48} +(2.08856 - 2.41033i) q^{49} +(0.883578 + 1.10264i) q^{50} +(-0.145010 + 0.425533i) q^{51} +(-1.10207 + 14.3044i) q^{52} +(-8.20646 + 3.74777i) q^{53} +(-1.22106 + 7.24631i) q^{54} +(-0.0156753 - 0.109024i) q^{55} +(-1.52980 - 8.89799i) q^{56} +(-10.1789 + 1.02098i) q^{57} +(-10.4358 - 0.401412i) q^{58} +(4.21225 - 9.22355i) q^{59} +(-5.33986 - 4.41546i) q^{60} +(8.61910 + 9.94698i) q^{61} +(0.941345 + 8.98794i) q^{62} +(-1.90191 - 9.38545i) q^{63} +(-6.95731 - 3.94915i) q^{64} +(-12.0706 - 7.75731i) q^{65} +(-0.0458869 - 0.126840i) q^{66} +(4.09784 + 1.20324i) q^{67} +(-0.413854 - 0.313369i) q^{68} +(8.29573 + 0.425234i) q^{69} +(8.55959 + 2.87504i) q^{70} +(-0.594995 + 2.02637i) q^{71} +(-7.50038 - 3.96791i) q^{72} +(-2.56222 - 1.64664i) q^{73} +(-4.23984 + 8.41232i) q^{74} +(-1.60350 + 0.650832i) q^{75} +(2.57430 - 11.5287i) q^{76} +(0.115109 + 0.132843i) q^{77} +(-16.4018 - 6.30281i) q^{78} +(-2.82384 - 1.28960i) q^{79} +(6.77787 - 4.25141i) q^{80} +(-8.07672 - 3.97071i) q^{81} +(0.936880 + 0.877081i) q^{82} +(8.96634 - 1.28917i) q^{83} +(10.9785 + 1.32070i) q^{84} +(0.472251 - 0.215670i) q^{85} +(-1.74139 + 0.439372i) q^{86} +(4.12572 - 12.1070i) q^{87} +(0.155693 - 0.00427668i) q^{88} +(-11.4022 + 13.1589i) q^{89} +(7.05205 - 4.72062i) q^{90} +22.8980 q^{91} +(-3.47631 + 8.93953i) q^{92} +(-10.8780 - 2.04281i) q^{93} +(0.152867 - 0.218885i) q^{94} +(8.92834 + 7.73645i) q^{95} +(7.07122 - 6.78217i) q^{96} +(5.29925 + 0.761917i) q^{97} +(-4.37333 + 1.10344i) q^{98} +(0.164930 - 0.00943389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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