LMFDB - Embedded newform 567.2.bm.a.104.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(20,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([25, 27]))

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

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

chi := DirichletCharacter("567.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bm (of order $54$, degree $18$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$1260$
Relative dimension:	$70$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			104.51
Character	$\chi$	$=$	567.104
Dual form			567.2.bm.a.398.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16421 + 0.866725i) q^{2} +(-1.68424 + 0.404131i) q^{3} +(0.0305746 + 0.102126i) q^{4} +(2.88972 + 1.90060i) q^{5} +(-2.31109 - 0.989281i) q^{6} +(2.57593 + 0.603817i) q^{7} +(0.939906 - 2.58237i) q^{8} +(2.67336 - 1.36131i) q^{9} +O(q^{10})$	\(q+(1.16421 + 0.866725i) q^{2} +(-1.68424 + 0.404131i) q^{3} +(0.0305746 + 0.102126i) q^{4} +(2.88972 + 1.90060i) q^{5} +(-2.31109 - 0.989281i) q^{6} +(2.57593 + 0.603817i) q^{7} +(0.939906 - 2.58237i) q^{8} +(2.67336 - 1.36131i) q^{9} +(1.71696 + 4.71730i) q^{10} +(1.50991 - 3.00647i) q^{11} +(-0.0927674 - 0.159649i) q^{12} +(-6.12402 - 2.64164i) q^{13} +(2.47559 + 2.93559i) q^{14} +(-5.63509 - 2.03325i) q^{15} +(3.51059 - 2.30895i) q^{16} +(1.24870 + 1.04778i) q^{17} +(4.29224 + 0.732208i) q^{18} +(4.77804 + 5.69425i) q^{19} +(-0.105749 + 0.353227i) q^{20} +(-4.58251 + 0.0240377i) q^{21} +(4.36364 - 2.19150i) q^{22} +(-0.137404 - 0.129634i) q^{23} +(-0.539415 + 4.72919i) q^{24} +(2.75782 + 6.39335i) q^{25} +(-4.84009 - 8.38328i) q^{26} +(-3.95244 + 3.37317i) q^{27} +(0.0170924 + 0.281531i) q^{28} +(-0.561187 + 4.80126i) q^{29} +(-4.79818 - 7.25121i) q^{30} +(1.01521 - 4.28351i) q^{31} +(0.601397 + 0.0350274i) q^{32} +(-1.32804 + 5.67384i) q^{33} +(0.545613 + 2.30212i) q^{34} +(6.29611 + 6.64068i) q^{35} +(0.220762 + 0.231398i) q^{36} +(-1.13116 + 6.41510i) q^{37} +(0.627314 + 10.7706i) q^{38} +(11.3819 + 1.97427i) q^{39} +(7.62413 - 5.67595i) q^{40} +(-3.28702 - 4.41524i) q^{41} +(-5.35586 - 3.94379i) q^{42} +(0.172505 + 2.96179i) q^{43} +(0.353205 + 0.0622795i) q^{44} +(10.3126 + 1.14717i) q^{45} +(-0.0476107 - 0.270014i) q^{46} +(0.214259 - 0.0507803i) q^{47} +(-4.97957 + 5.30758i) q^{48} +(6.27081 + 3.11078i) q^{49} +(-2.33058 + 9.83349i) q^{50} +(-2.52656 - 1.26008i) q^{51} +(0.0825418 - 0.706190i) q^{52} +(-10.0152 - 5.78225i) q^{53} +(-7.52509 + 0.501411i) q^{54} +(10.0773 - 5.81815i) q^{55} +(3.98041 - 6.08447i) q^{56} +(-10.3486 - 7.65954i) q^{57} +(-4.81471 + 5.10330i) q^{58} +(-3.16350 + 1.58877i) q^{59} +(0.0353574 - 0.637656i) q^{60} +(-3.34588 - 1.00169i) q^{61} +(4.89455 - 4.10701i) q^{62} +(7.70836 - 1.89242i) q^{63} +(-5.76780 - 4.83976i) q^{64} +(-12.6760 - 19.2729i) q^{65} +(-6.46378 + 5.45451i) q^{66} +(-8.44223 + 0.986755i) q^{67} +(-0.0688277 + 0.159560i) q^{68} +(0.283812 + 0.162806i) q^{69} +(1.57437 + 13.1882i) q^{70} +(4.32093 + 11.8716i) q^{71} +(-1.00271 - 8.18310i) q^{72} +(3.67448 - 10.0955i) q^{73} +(-6.87704 + 6.48815i) q^{74} +(-7.22859 - 9.65344i) q^{75} +(-0.435445 + 0.662062i) q^{76} +(5.70478 - 6.83275i) q^{77} +(11.5398 + 12.1635i) q^{78} +(1.20978 - 1.62501i) q^{79} +14.5330 q^{80} +(5.29367 - 7.27854i) q^{81} -7.98923i q^{82} +(3.98563 - 5.35362i) q^{83} +(-0.142563 - 0.467260i) q^{84} +(1.61698 + 5.40109i) q^{85} +(-2.36622 + 3.59767i) q^{86} +(-0.995163 - 8.31329i) q^{87} +(-6.34466 - 6.72495i) q^{88} +(-15.6638 - 5.70117i) q^{89} +(11.0118 + 10.2737i) q^{90} +(-14.1800 - 10.5025i) q^{91} +(0.00903797 - 0.0179961i) q^{92} +(0.0212373 + 7.62476i) q^{93} +(0.293456 + 0.126584i) q^{94} +(2.98472 + 25.5359i) q^{95} +(-1.02705 + 0.184048i) q^{96} +(-0.686236 - 1.04337i) q^{97} +(4.60437 + 9.05668i) q^{98} +(-0.0562237 - 10.0928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1260 q - 36 q^{2} - 36 q^{4} - 18 q^{7} - 36 q^{8} - 36 q^{9}+O(q^{10}) $ 1260 * q - 36 * q^2 - 36 * q^4 - 18 * q^7 - 36 * q^8 - 36 * q^9	$ 1260 q - 36 q^{2} - 36 q^{4} - 18 q^{7} - 36 q^{8} - 36 q^{9} - 36 q^{11} - 18 q^{14} - 36 q^{15} - 36 q^{16} - 36 q^{18} + 9 q^{21} - 36 q^{22} - 90 q^{23} - 36 q^{25} - 9 q^{28} - 36 q^{29} - 144 q^{30} - 36 q^{32} + 9 q^{35} - 36 q^{36} - 36 q^{37} - 36 q^{39} - 63 q^{42} - 36 q^{43} - 36 q^{44} - 36 q^{46} - 18 q^{49} - 36 q^{50} - 36 q^{51} - 54 q^{53} - 126 q^{56} - 36 q^{57} - 36 q^{58} - 36 q^{60} - 72 q^{63} - 36 q^{64} - 36 q^{67} + 36 q^{70} + 36 q^{71} + 180 q^{72} - 36 q^{74} - 162 q^{77} + 162 q^{78} - 90 q^{79} - 36 q^{81} - 297 q^{84} - 90 q^{85} + 108 q^{86} - 36 q^{88} - 18 q^{91} + 360 q^{92} + 36 q^{93} - 252 q^{95} - 261 q^{98} + 216 q^{99}+O(q^{100}) $ 1260 * q - 36 * q^2 - 36 * q^4 - 18 * q^7 - 36 * q^8 - 36 * q^9 - 36 * q^11 - 18 * q^14 - 36 * q^15 - 36 * q^16 - 36 * q^18 + 9 * q^21 - 36 * q^22 - 90 * q^23 - 36 * q^25 - 9 * q^28 - 36 * q^29 - 144 * q^30 - 36 * q^32 + 9 * q^35 - 36 * q^36 - 36 * q^37 - 36 * q^39 - 63 * q^42 - 36 * q^43 - 36 * q^44 - 36 * q^46 - 18 * q^49 - 36 * q^50 - 36 * q^51 - 54 * q^53 - 126 * q^56 - 36 * q^57 - 36 * q^58 - 36 * q^60 - 72 * q^63 - 36 * q^64 - 36 * q^67 + 36 * q^70 + 36 * q^71 + 180 * q^72 - 36 * q^74 - 162 * q^77 + 162 * q^78 - 90 * q^79 - 36 * q^81 - 297 * q^84 - 90 * q^85 + 108 * q^86 - 36 * q^88 - 18 * q^91 + 360 * q^92 + 36 * q^93 - 252 * q^95 - 261 * q^98 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{11}{54}\right)$

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 $a_p$)

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

$2$	1.16421	+	0.866725i	0.823223	+	0.612867i	0.924151	−	0.382027i	$-0.124774\pi$
$2$	1.16421	+	0.866725i	0.823223	+	0.612867i	−0.100928	+	0.994894i	$0.532181\pi$
$3$	−1.68424	+	0.404131i	−0.972399	+	0.233325i
$3$	−1.68424	+	0.404131i	−0.972399	+	0.233325i
$4$	0.0305746	+	0.102126i	0.0152873	+	0.0510631i
$5$	2.88972	+	1.90060i	1.29232	+	0.849975i	0.994509	−	0.104649i	$-0.0333719\pi$
$5$	2.88972	+	1.90060i	1.29232	+	0.849975i	0.297815	+	0.954624i	$0.403742\pi$
$6$	−2.31109	−	0.989281i	−0.943499	−	0.403872i
$7$	2.57593	+	0.603817i	0.973609	+	0.228221i
$7$	2.57593	+	0.603817i	0.973609	+	0.228221i
$8$	0.939906	−	2.58237i	0.332307	−	0.913006i
$9$	2.67336	−	1.36131i	0.891119	−	0.453770i
$10$	1.71696	+	4.71730i	0.542950	+	1.49174i
$11$	1.50991	−	3.00647i	0.455254	−	0.906486i	−0.542535	−	0.840033i	$-0.682535\pi$
$11$	1.50991	−	3.00647i	0.455254	−	0.906486i	0.997790	−	0.0664531i	$-0.0211683\pi$
$12$	−0.0927674	−	0.159649i	−0.0267796	−	0.0460868i
$13$	−6.12402	−	2.64164i	−1.69850	−	0.732660i	−0.999852	−	0.0171919i	$-0.994527\pi$
$13$	−6.12402	−	2.64164i	−1.69850	−	0.732660i	−0.698645	−	0.715468i	$-0.746213\pi$
$14$	2.47559	+	2.93559i	0.661628	+	0.784570i
$15$	−5.63509	−	2.03325i	−1.45497	−	0.524983i
$16$	3.51059	−	2.30895i	0.877648	−	0.577238i
$17$	1.24870	+	1.04778i	0.302854	+	0.254125i	0.781531	−	0.623866i	$-0.214439\pi$
$17$	1.24870	+	1.04778i	0.302854	+	0.254125i	−0.478677	+	0.877991i	$0.658883\pi$
$18$	4.29224	+	0.732208i	1.01169	+	0.172583i
$19$	4.77804	+	5.69425i	1.09616	+	1.30635i	0.948312	+	0.317339i	$0.102789\pi$
$19$	4.77804	+	5.69425i	1.09616	+	1.30635i	0.147845	+	0.989011i	$0.452766\pi$
$20$	−0.105749	+	0.353227i	−0.0236462	+	0.0789839i
$21$	−4.58251	+	0.0240377i	−0.999986	+	0.00524546i
$22$	4.36364	−	2.19150i	0.930332	−	0.467230i
$23$	−0.137404	−	0.129634i	−0.0286508	−	0.0270306i	0.671783	−	0.740748i	$-0.265529\pi$
$23$	−0.137404	−	0.129634i	−0.0286508	−	0.0270306i	−0.700434	+	0.713717i	$0.747010\pi$
$24$	−0.539415	+	4.72919i	−0.110108	+	0.965342i
$25$	2.75782	+	6.39335i	0.551564	+	1.27867i
$26$	−4.84009	−	8.38328i	−0.949219	−	1.64410i
$27$	−3.95244	+	3.37317i	−0.760647	+	0.649166i
$28$	0.0170924	+	0.281531i	0.00323016	+	0.0532044i
$29$	−0.561187	+	4.80126i	−0.104210	+	0.891572i	0.835475	+	0.549529i	$0.185193\pi$
$29$	−0.561187	+	4.80126i	−0.104210	+	0.891572i	−0.939684	+	0.342043i	$0.888881\pi$
$30$	−4.79818	−	7.25121i	−0.876024	−	1.32388i
$31$	1.01521	−	4.28351i	0.182337	−	0.769341i	−0.802613	−	0.596501i	$-0.796557\pi$
$31$	1.01521	−	4.28351i	0.182337	−	0.769341i	0.984950	−	0.172841i	$-0.0552946\pi$
$32$	0.601397	+	0.0350274i	0.106313	+	0.00619202i
$33$	−1.32804	+	5.67384i	−0.231183	+	0.987688i
$34$	0.545613	+	2.30212i	0.0935719	+	0.394811i
$35$	6.29611	+	6.64068i	1.06424	+	1.12248i
$36$	0.220762	+	0.231398i	0.0367937	+	0.0385664i
$37$	−1.13116	+	6.41510i	−0.185961	+	1.05464i	0.738754	+	0.673976i	$0.235415\pi$
$37$	−1.13116	+	6.41510i	−0.185961	+	1.05464i	−0.924715	+	0.380661i	$0.875696\pi$
$38$	0.627314	+	10.7706i	0.101764	+	1.74722i
$39$	11.3819	+	1.97427i	1.82256	+	0.316136i
$40$	7.62413	−	5.67595i	1.20548	−	0.897447i
$41$	−3.28702	−	4.41524i	−0.513347	−	0.689545i	0.467574	−	0.883954i	$-0.345128\pi$
$41$	−3.28702	−	4.41524i	−0.513347	−	0.689545i	−0.980920	+	0.194410i	$0.937721\pi$
$42$	−5.35586	−	3.94379i	−0.826427	−	0.608540i
$43$	0.172505	+	2.96179i	0.0263067	+	0.451669i	0.985582	+	0.169197i	$0.0541174\pi$
$43$	0.172505	+	2.96179i	0.0263067	+	0.451669i	−0.959276	+	0.282472i	$0.908846\pi$
$44$	0.353205	+	0.0622795i	0.0532476	+	0.00938899i
$45$	10.3126	+	1.14717i	1.53731	+	0.171010i
$46$	−0.0476107	−	0.270014i	−0.00701981	−	0.0398113i
$47$	0.214259	−	0.0507803i	0.0312529	−	0.00740706i	−0.214960	−	0.976623i	$-0.568962\pi$
$47$	0.214259	−	0.0507803i	0.0312529	−	0.00740706i	0.246213	+	0.969216i	$0.420814\pi$
$48$	−4.97957	+	5.30758i	−0.718739	+	0.766083i
$49$	6.27081	+	3.11078i	0.895830	+	0.444397i
$50$	−2.33058	+	9.83349i	−0.329594	+	1.39067i
$51$	−2.52656	−	1.26008i	−0.353789	−	0.176447i
$52$	0.0825418	−	0.706190i	0.0114465	−	0.0979309i
$53$	−10.0152	−	5.78225i	−1.37569	−	0.794253i	−0.384050	−	0.923312i	$-0.625471\pi$
$53$	−10.0152	−	5.78225i	−1.37569	−	0.794253i	−0.991637	+	0.129059i	$0.958804\pi$
$54$	−7.52509	+	0.501411i	−1.02403	+	0.0682334i
$55$	10.0773	−	5.81815i	1.35883	−	0.784519i
$56$	3.98041	−	6.08447i	0.531905	−	0.813072i
$57$	−10.3486	−	7.65954i	−1.37071	−	1.01453i
$58$	−4.81471	+	5.10330i	−0.632203	+	0.670096i
$59$	−3.16350	+	1.58877i	−0.411852	+	0.206840i	−0.642647	−	0.766162i	$-0.722164\pi$
$59$	−3.16350	+	1.58877i	−0.411852	+	0.206840i	0.230794	+	0.973003i	$0.425867\pi$
$60$	0.0353574	−	0.637656i	0.00456463	−	0.0823211i
$61$	−3.34588	−	1.00169i	−0.428396	−	0.128253i	0.0653445	−	0.997863i	$-0.479185\pi$
$61$	−3.34588	−	1.00169i	−0.428396	−	0.128253i	−0.493740	+	0.869610i	$0.664371\pi$
$62$	4.89455	−	4.10701i	0.621608	−	0.521591i
$63$	7.70836	−	1.89242i	0.971161	−	0.238423i
$64$	−5.76780	−	4.83976i	−0.720976	−	0.604970i
$65$	−12.6760	−	19.2729i	−1.57227	−	2.39051i
$66$	−6.46378	+	5.45451i	−0.795637	+	0.671404i
$67$	−8.44223	+	0.986755i	−1.03138	+	0.120551i	−0.614910	−	0.788597i	$-0.710808\pi$
$67$	−8.44223	+	0.986755i	−1.03138	+	0.120551i	−0.416472	+	0.909148i	$0.636734\pi$
$68$	−0.0688277	+	0.159560i	−0.00834658	+	0.0193495i
$69$	0.283812	+	0.162806i	0.0341669	+	0.0195996i
$70$	1.57437	+	13.1882i	0.188174	+	1.57629i
$71$	4.32093	+	11.8716i	0.512799	+	1.40890i	0.878307	+	0.478097i	$0.158673\pi$
$71$	4.32093	+	11.8716i	0.512799	+	1.40890i	−0.365508	+	0.930808i	$0.619105\pi$
$72$	−1.00271	−	8.18310i	−0.118170	−	0.964388i
$73$	3.67448	−	10.0955i	0.430065	−	1.18159i	−0.515708	−	0.856764i	$-0.672471\pi$
$73$	3.67448	−	10.0955i	0.430065	−	1.18159i	0.945773	−	0.324829i	$-0.105307\pi$
$74$	−6.87704	+	6.48815i	−0.799439	+	0.754232i
$75$	−7.22859	−	9.65344i	−0.834686	−	1.11468i
$76$	−0.435445	+	0.662062i	−0.0499490	+	0.0759437i
$77$	5.70478	−	6.83275i	0.650119	−	0.778665i
$78$	11.5398	+	12.1635i	1.30663	+	1.37724i
$79$	1.20978	−	1.62501i	0.136111	−	0.182828i	−0.728842	−	0.684682i	$-0.759941\pi$
$79$	1.20978	−	1.62501i	0.136111	−	0.182828i	0.864952	+	0.501854i	$0.167348\pi$
$80$	14.5330			1.62484
$81$	5.29367	−	7.27854i	0.588185	−	0.808726i
$82$		−	7.98923i		−	0.882262i
$83$	3.98563	−	5.35362i	0.437479	−	0.587637i	−0.527633	−	0.849472i	$-0.676920\pi$
$83$	3.98563	−	5.35362i	0.437479	−	0.587637i	0.965112	+	0.261836i	$0.0843278\pi$
$84$	−0.142563	−	0.467260i	−0.0155549	−	0.0509822i
$85$	1.61698	+	5.40109i	0.175386	+	0.585830i
$86$	−2.36622	+	3.59767i	−0.255157	+	0.387947i
$87$	−0.995163	−	8.31329i	−0.106693	−	0.891278i
$88$	−6.34466	−	6.72495i	−0.676343	−	0.716882i
$89$	−15.6638	−	5.70117i	−1.66036	−	0.604323i	−0.669944	−	0.742411i	$-0.733682\pi$
$89$	−15.6638	−	5.70117i	−1.66036	−	0.604323i	−0.990420	+	0.138088i	$0.955904\pi$
$90$	11.0118	+	10.2737i	1.16074	+	1.08294i
$91$	−14.1800	−	10.5025i	−1.48646	−	1.10096i
$92$	0.00903797	−	0.0179961i	0.000942274	−	0.00187622i
$93$	0.0212373	+	7.62476i	0.00220220	+	0.790651i
$94$	0.293456	+	0.126584i	0.0302676	+	0.0130562i
$95$	2.98472	+	25.5359i	0.306226	+	2.61993i
$96$	−1.02705	+	0.184048i	−0.104823	+	0.0187844i
$97$	−0.686236	−	1.04337i	−0.0696768	−	0.105938i	0.798969	−	0.601373i	$-0.205379\pi$
$97$	−0.686236	−	1.04337i	−0.0696768	−	0.105938i	−0.868645	+	0.495434i	$0.835009\pi$
$98$	4.60437	+	9.05668i	0.465112	+	0.914862i
$99$	−0.0562237	−	10.0928i	−0.00565070	−	1.01437i
$100$	−0.568609	+	0.477120i	−0.0568609	+	0.0477120i
$101$	−4.24099	+	14.1659i	−0.421995	+	1.40956i	0.437870	+	0.899038i	$0.355733\pi$
$101$	−4.24099	+	14.1659i	−0.421995	+	1.40956i	−0.859865	+	0.510522i	$0.829452\pi$
$102$	−1.84930	−	3.65684i	−0.183108	−	0.362081i
$103$	−0.837882	−	1.66836i	−0.0825589	−	0.164388i	0.848565	−	0.529091i	$-0.177467\pi$
$103$	−0.837882	−	1.66836i	−0.0825589	−	0.164388i	−0.931124	+	0.364703i	$0.881171\pi$
$104$	−12.5777	+	13.3316i	−1.23335	+	1.30727i
$105$	−13.2879	−	8.64007i	−1.29676	−	0.843184i
$106$	−6.64816	−	15.4122i	−0.645726	−	1.49696i
$107$	8.41746	−	4.85982i	0.813747	−	0.469817i	−0.0345085	−	0.999404i	$-0.510987\pi$
$107$	8.41746	−	4.85982i	0.813747	−	0.469817i	0.848255	+	0.529587i	$0.177653\pi$
$108$	−0.465333	−	0.300514i	−0.0447766	−	0.0289170i
$109$	5.29486	−	9.17097i	0.507156	−	0.878419i	−0.492810	−	0.870137i	$-0.664030\pi$
$109$	5.29486	−	9.17097i	0.507156	−	0.878419i	0.999966	−	0.00828234i	$-0.00263638\pi$
$110$	16.7749	+	1.96070i	1.59942	+	0.186946i
$111$	−0.687400	−	11.2617i	−0.0652452	−	1.06892i
$112$	10.4372	−	3.82794i	0.986224	−	0.361706i
$113$	−11.9457	−	0.695761i	−1.12376	−	0.0654517i	−0.513820	−	0.857898i	$-0.671770\pi$
$113$	−11.9457	−	0.695761i	−1.12376	−	0.0654517i	−0.609942	+	0.792446i	$0.708807\pi$
$114$	−5.40927	−	17.8867i	−0.506624	−	1.67525i
$115$	−0.150677	−	0.635758i	−0.0140507	−	0.0592847i
$116$	−0.507492	+	0.0894846i	−0.0471195	+	0.00830844i
$117$	−19.9678	+	1.27464i	−1.84602	+	0.117840i
$118$	−5.06001	−	0.892217i	−0.465812	−	0.0821352i
$119$	2.58389	+	3.45300i	0.236865	+	0.316536i
$120$	−10.5471	+	12.6408i	−0.962811	+	1.15395i
$121$	−0.190322	−	0.255647i	−0.0173020	−	0.0232407i
$122$	−3.02712	−	4.06613i	−0.274063	−	0.368131i
$123$	7.32049	+	6.10795i	0.660066	+	0.550736i
$124$	0.468498	−	0.0272869i	0.0420724	−	0.00245044i
$125$	−1.17886	+	6.68563i	−0.105440	+	0.597981i
$126$	10.6144	+	4.47784i	0.945604	+	0.398918i
$127$	−1.73312	−	9.82899i	−0.153789	−	0.872182i	−0.959884	−	0.280396i	$-0.909534\pi$
$127$	−1.73312	−	9.82899i	−0.153789	−	0.872182i	0.806095	−	0.591786i	$-0.201577\pi$
$128$	−2.79807	−	11.8060i	−0.247316	−	1.04351i
$129$	−1.48749	−	4.91866i	−0.130966	−	0.433064i
$130$	1.94675	−	33.4244i	0.170741	−	2.93152i
$131$	9.74987	+	2.31076i	0.851850	+	0.201892i	0.633274	−	0.773928i	$-0.281711\pi$
$131$	9.74987	+	2.31076i	0.851850	+	0.201892i	0.218576	+	0.975820i	$0.429859\pi$
$132$	−0.620052	+	0.0378471i	−0.0539686	+	0.00329417i
$133$	8.86960	+	17.5530i	0.769092	+	1.52204i
$134$	−10.6838	−	6.16829i	−0.922940	−	0.532860i
$135$	−17.8325	+	2.23551i	−1.53478	+	0.192402i
$136$	3.87943	−	2.23979i	0.332658	−	0.192060i
$137$	−11.4315	+	4.93105i	−0.976656	+	0.421288i	−0.823750	−	0.566952i	$-0.808122\pi$
$137$	−11.4315	+	4.93105i	−0.976656	+	0.421288i	−0.152906	+	0.988241i	$0.548863\pi$
$138$	0.189309	+	0.435528i	0.0161150	+	0.0370746i
$139$	2.30954	+	2.17894i	0.195893	+	0.184815i	0.777938	−	0.628341i	$-0.216266\pi$
$139$	2.30954	+	2.17894i	0.195893	+	0.184815i	−0.582045	+	0.813157i	$0.697747\pi$
$140$	−0.485686	+	0.846033i	−0.0410480	+	0.0715028i
$141$	−0.340342	+	0.172115i	−0.0286620	+	0.0144947i
$142$	−5.25897	+	17.5662i	−0.441323	+	1.47412i
$143$	−17.1887	+	14.4231i	−1.43739	+	1.20612i
$144$	6.24186	−	10.9517i	0.520155	−	0.912638i
$145$	−10.7470	+	12.8077i	−0.892486	+	1.06362i
$146$	13.0279	−	8.56860i	1.07820	−	0.709143i
$147$	−11.8187	−	2.70508i	−0.974793	−	0.223111i
$148$	−0.689735	+	0.0806184i	−0.0566958	+	0.00662679i
$149$	−5.96649	−	2.57369i	−0.488794	−	0.210845i	0.137395	−	0.990516i	$-0.456127\pi$
$149$	−5.96649	−	2.57369i	−0.488794	−	0.210845i	−0.626189	+	0.779671i	$0.715386\pi$
$150$	−0.0487536	−	17.5039i	−0.00398072	−	1.42918i
$151$	21.7971	+	10.9469i	1.77382	+	0.890848i	0.941849	+	0.336036i	$0.109086\pi$
$151$	21.7971	+	10.9469i	1.77382	+	0.890848i	0.831976	+	0.554812i	$0.187210\pi$
$152$	19.1956	−	6.98661i	1.55697	−	0.566689i
$153$	4.76458	+	1.10123i	0.385193	+	0.0890292i
$154$	12.5637	−	3.01031i	1.01241	−	0.242578i
$155$	11.0749	−	10.4487i	0.889560	−	0.839256i
$156$	0.146373	+	1.22275i	0.0117192	+	0.0978986i
$157$	5.81445	−	8.84044i	0.464043	−	0.705544i	−0.525337	−	0.850894i	$-0.676061\pi$
$157$	5.81445	−	8.84044i	0.464043	−	0.705544i	0.989380	+	0.145351i	$0.0464311\pi$
$158$	2.81688	−	0.843318i	0.224099	−	0.0670908i
$159$	19.2048	+	5.69129i	1.52304	+	0.451348i
$160$	1.67130	+	1.24423i	0.132128	+	0.0983654i
$161$	−0.275668	−	0.416896i	−0.0217257	−	0.0328560i
$162$	12.4714	−	3.88562i	0.979849	−	0.305283i
$163$	8.12720			0.636571			0.318286	−	0.947995i	$-0.396893\pi$
$163$	8.12720			0.636571			0.318286	+	0.947995i	$0.396893\pi$
$164$	0.350412	−	0.470685i	0.0273626	−	0.0367543i
$165$	−14.6214	+	13.8717i	−1.13827	+	1.07991i
$166$	9.28024	−	2.77832i	0.720286	−	0.215640i
$167$	−1.14411	−	0.752491i	−0.0885337	−	0.0582295i	0.504470	−	0.863429i	$-0.331688\pi$
$167$	−1.14411	−	0.752491i	−0.0885337	−	0.0582295i	−0.593004	+	0.805200i	$0.702058\pi$
$168$	−4.24506	+	11.8563i	−0.327513	+	0.914737i
$169$	21.6042	+	22.8991i	1.66186	+	1.76147i
$170$	−2.79875	+	7.68949i	−0.214654	+	0.589757i
$171$	20.5250	+	8.71835i	1.56959	+	0.666709i
$172$	−0.297202	+	0.108173i	−0.0226614	+	0.00824809i
$173$	0.854049	+	0.428919i	0.0649321	+	0.0326101i	0.480969	−	0.876738i	$-0.340285\pi$
$173$	0.854049	+	0.428919i	0.0649321	+	0.0326101i	−0.416037	+	0.909348i	$0.636581\pi$
$174$	6.04675	−	10.5410i	0.458403	−	0.799109i
$175$	3.24354	+	18.1340i	0.245188	+	1.37080i
$176$	−1.64113	−	14.0408i	−0.123705	−	1.05837i
$177$	4.68603	−	3.95434i	0.352224	−	0.297227i
$178$	−13.2947	−	20.2136i	−0.996481	−	1.51508i
$179$	1.39894	−	1.66719i	0.104562	−	0.124612i	−0.711226	−	0.702964i	$-0.751860\pi$
$179$	1.39894	−	1.66719i	0.104562	−	0.124612i	0.815787	+	0.578352i	$0.196304\pi$
$180$	0.198146	+	1.08826i	0.0147689	+	0.0811139i
$181$	0.0393782	+	0.0469292i	0.00292696	+	0.00348822i	0.767506	−	0.641042i	$-0.221498\pi$
$181$	0.0393782	+	0.0469292i	0.00292696	+	0.00348822i	−0.764579	+	0.644530i	$0.777053\pi$
$182$	−7.40575	−	24.5172i	−0.548951	−	1.81734i
$183$	6.04009	+	0.334917i	0.446496	+	0.0247578i
$184$	−0.463911	+	0.232985i	−0.0342000	+	0.0171759i
$185$	−15.4613	+	16.3880i	−1.13674	+	1.20487i
$186$	−6.58384	+	8.89525i	−0.482751	+	0.652232i
$187$	5.03556	−	2.17213i	0.368236	−	0.158842i
$188$	0.0117369	+	0.0203289i	0.000855999	+	0.00148263i
$189$	−12.2180	+	6.30249i	−0.888726	+	0.458438i
$190$	−18.6578	+	32.3162i	−1.35358	+	2.34447i
$191$	−0.0760775	+	0.650885i	−0.00550477	+	0.0470964i	−0.995712	−	0.0925121i	$-0.970510\pi$
$191$	−0.0760775	+	0.650885i	−0.00550477	+	0.0470964i	0.990207	+	0.139608i	$0.0445844\pi$
$192$	11.6703	+	5.82039i	0.842231	+	0.420051i
$193$	−13.9031	−	3.29509i	−1.00076	−	0.237186i	−0.302596	−	0.953119i	$-0.597853\pi$
$193$	−13.9031	−	3.29509i	−1.00076	−	0.237186i	−0.698169	+	0.715933i	$0.746001\pi$
$194$	0.105391	−	1.80949i	0.00756660	−	0.129913i
$195$	29.1383	+	27.3376i	2.08664	+	1.95768i
$196$	−0.125964	+	0.735525i	−0.00899746	+	0.0525375i
$197$	−19.5486	+	3.44694i	−1.39278	+	0.245584i	−0.819172	−	0.573548i	$-0.805567\pi$
$197$	−19.5486	+	3.44694i	−1.39278	+	0.245584i	−0.573605	+	0.819132i	$0.694456\pi$
$198$	8.68225	−	11.7989i	0.617021	−	0.838514i
$199$	−17.1314	−	3.02074i	−1.21442	−	0.214134i	−0.470496	−	0.882402i	$-0.655925\pi$
$199$	−17.1314	−	3.02074i	−1.21442	−	0.214134i	−0.743921	+	0.668268i	$0.767036\pi$
$200$	19.1021	−	1.11257i	1.35072	−	0.0786706i
$201$	13.8200	−	5.07370i	0.974787	−	0.357871i
$202$	−17.2154	+	12.8164i	−1.21127	+	0.901756i
$203$	−4.34466	+	12.0288i	−0.304935	+	0.844260i
$204$	0.0514392	−	0.296554i	0.00360147	−	0.0207629i
$205$	−1.10698	−	19.0061i	−0.0773150	−	1.32745i
$206$	0.470536	−	2.66854i	0.0327838	−	0.185926i
$207$	−0.543803	−	0.159509i	−0.0377969	−	0.0110866i
$208$	−27.5983	+	4.86633i	−1.91360	+	0.337420i
$209$	24.3340	−	5.76727i	1.68322	−	0.398930i
$210$	−7.98137	−	21.5758i	−0.550767	−	1.48887i
$211$	0.550253	−	9.44748i	0.0378810	−	0.650391i	−0.924917	−	0.380169i	$-0.875866\pi$
$211$	0.550253	−	9.44748i	0.0378810	−	0.650391i	0.962798	−	0.270222i	$-0.0870972\pi$
$212$	0.284310	−	1.19960i	0.0195265	−	0.0823888i
$213$	−12.0752	−	18.2485i	−0.827379	−	1.25037i
$214$	14.0119	+	1.63775i	0.957831	+	0.111954i
$215$	−5.13069	+	8.88662i	−0.349910	+	0.606062i
$216$	4.99585	+	13.3771i	0.339924	+	0.910197i
$217$	5.20157	−	10.4210i	0.353105	−	0.707425i
$218$	14.1130	−	6.08778i	0.955856	−	0.412316i
$219$	−2.10879	+	18.4883i	−0.142499	+	1.24932i
$220$	0.902295	+	0.851272i	0.0608327	+	0.0573927i
$221$	−4.87919	−	9.71527i	−0.328210	−	0.653520i
$222$	8.96055	−	13.7069i	0.601392	−	0.919944i
$223$	7.99603	+	2.39385i	0.535454	+	0.160304i	0.543103	−	0.839666i	$-0.317249\pi$
$223$	7.99603	+	2.39385i	0.535454	+	0.160304i	−0.00764871	+	0.999971i	$0.502435\pi$
$224$	1.52800	+	0.453361i	0.102094	+	0.0302915i
$225$	16.0760	+	13.3374i	1.07173	+	0.889163i
$226$	−13.3044	−	11.1637i	−0.884993	−	0.742598i
$227$	−11.6153	+	7.63952i	−0.770937	+	0.507053i	−0.872997	−	0.487725i	$-0.837827\pi$
$227$	−11.6153	+	7.63952i	−0.770937	+	0.507053i	0.102061	+	0.994778i	$0.467456\pi$
$228$	0.465836	−	1.29105i	0.0308507	−	0.0855019i
$229$	3.19700	+	27.3521i	0.211264	+	1.80748i	0.517675	+	0.855578i	$0.326798\pi$
$229$	3.19700	+	27.3521i	0.211264	+	1.80748i	−0.306411	+	0.951899i	$0.599128\pi$
$230$	0.375607	−	0.870754i	0.0247668	−	0.0574158i
$231$	−6.84691	+	13.8135i	−0.450493	+	0.908862i
$232$	11.8712	+	5.96193i	0.779381	+	0.391420i
$233$	−3.78908	−	10.4104i	−0.248231	−	0.682009i	−0.999751	−	0.0222989i	$-0.992901\pi$
$233$	−3.78908	−	10.4104i	−0.248231	−	0.682009i	0.751520	−	0.659710i	$-0.229321\pi$
$234$	−24.3515	−	15.8226i	−1.59191	−	1.03436i
$235$	0.715662	+	0.260480i	0.0466846	+	0.0169918i
$236$	−0.258978	−	0.274500i	−0.0168580	−	0.0178684i
$237$	−1.38084	+	3.22583i	−0.0896953	+	0.209540i
$238$	0.0153997	+	6.25955i	0.000998213	+	0.405747i
$239$	−1.17244	+	0.351007i	−0.0758391	+	0.0227047i	−0.324498	−	0.945886i	$-0.605195\pi$
$239$	−1.17244	+	0.351007i	−0.0758391	+	0.0227047i	0.248659	+	0.968591i	$0.420010\pi$
$240$	−24.4772	+	5.87325i	−1.57999	+	0.379117i
$241$	−0.691762	−	0.514998i	−0.0445603	−	0.0331739i	0.574648	−	0.818401i	$-0.305139\pi$
$241$	−0.691762	−	0.514998i	−0.0445603	−	0.0331739i	−0.619208	+	0.785227i	$0.712546\pi$
$242$		−	0.462585i		−	0.0297361i
$243$	−5.97434	+	14.3982i	−0.383254	+	0.923643i
$244$		−	0.372328i		−	0.0238358i
$245$	12.2086	+	20.9076i	0.779977	+	1.33574i
$246$	3.22869	+	13.4558i	0.205854	+	0.857911i
$247$	−14.2186	−	47.4935i	−0.904710	−	3.02194i
$248$	−10.1074	−	6.64775i	−0.641821	−	0.422133i
$249$	−4.54920	+	10.6275i	−0.288294	+	0.673492i
$250$	−7.16704	+	6.76175i	−0.453283	+	0.427651i
$251$	−8.71945	−	3.17362i	−0.550367	−	0.200317i	0.0518426	−	0.998655i	$-0.483491\pi$
$251$	−8.71945	−	3.17362i	−0.550367	−	0.200317i	−0.602209	+	0.798338i	$0.705713\pi$
$252$	0.428945	+	0.729365i	0.0270210	+	0.0459457i
$253$	−0.597210	+	0.217367i	−0.0375463	+	0.0136657i
$254$	6.50131	−	12.9452i	0.407929	−	0.812253i
$255$	−4.90613	−	8.44328i	−0.307234	−	0.528738i
$256$	1.01055	−	2.34271i	0.0631592	−	0.146419i
$257$	4.30290	−	0.502936i	0.268407	−	0.0313723i	0.0191753	−	0.999816i	$-0.493896\pi$
$257$	4.30290	−	0.502936i	0.268407	−	0.0313723i	0.249232	+	0.968444i	$0.419822\pi$
$258$	2.53137	−	7.01562i	0.157596	−	0.436773i
$259$	−6.78732	+	15.8418i	−0.421744	+	0.984364i
$260$	1.58071	−	1.88381i	0.0980314	−	0.116829i
$261$	5.03576	+	13.5994i	0.311705	+	0.841784i
$262$	9.34814	+	11.1407i	0.577530	+	0.688273i
$263$	1.07463	+	0.321723i	0.0662644	+	0.0198383i	0.319764	−	0.947497i	$-0.396396\pi$
$263$	1.07463	+	0.321723i	0.0662644	+	0.0198383i	−0.253499	+	0.967336i	$0.581582\pi$
$264$	13.4037	+	8.76238i	0.824942	+	0.539287i
$265$	−17.9513	−	35.7439i	−1.10274	−	2.19573i
$266$	−4.88753	+	28.1230i	−0.299674	+	1.72433i
$267$	28.6858	+	3.27192i	1.75554	+	0.200238i
$268$	−0.358891	−	0.832003i	−0.0219228	−	0.0508227i
$269$	−4.37457	−	7.57697i	−0.266722	−	0.461976i	0.701291	−	0.712875i	$-0.252607\pi$
$269$	−4.37457	−	7.57697i	−0.266722	−	0.461976i	−0.968013	+	0.250899i	$0.919274\pi$
$270$	−22.6984	−	12.8533i	−1.38138	−	0.782224i
$271$	−3.25215	−	1.87763i	−0.197554	−	0.114058i	0.397960	−	0.917403i	$-0.369718\pi$
$271$	−3.25215	−	1.87763i	−0.197554	−	0.114058i	−0.595514	+	0.803345i	$0.703052\pi$
$272$	6.80295	+	0.795151i	0.412490	+	0.0482131i
$273$	28.1269	+	11.9582i	1.70232	+	0.723741i
$274$	−17.5825	−	4.16714i	−1.06220	−	0.251746i
$275$	23.3855	+	1.36205i	1.41020	+	0.0821347i
$276$	−0.00794938	+	0.0339623i	−0.000478496	+	0.00204429i
$277$	−13.7280	+	3.25358i	−0.824833	+	0.195489i	−0.621294	−	0.783578i	$-0.713393\pi$
$277$	−13.7280	+	3.25358i	−0.824833	+	0.195489i	−0.203539	+	0.979067i	$0.565244\pi$
$278$	0.800258	+	4.53849i	0.0479963	+	0.272201i
$279$	−3.11717	−	12.8334i	−0.186620	−	0.768314i
$280$	23.0664	−	10.0173i	1.37848	−	0.598646i
$281$	−7.45494	+	0.434201i	−0.444724	+	0.0259022i	−0.279046	−	0.960278i	$-0.590018\pi$
$281$	−7.45494	+	0.434201i	−0.444724	+	0.0259022i	−0.165678	+	0.986180i	$0.552981\pi$
$282$	−0.545407	−	0.0946045i	−0.0324785	−	0.00563361i
$283$	−0.267139	+	0.198878i	−0.0158798	+	0.0118221i	−0.605069	−	0.796173i	$-0.706855\pi$
$283$	−0.267139	+	0.198878i	−0.0158798	+	0.0118221i	0.589189	+	0.807995i	$0.299447\pi$
$284$	−1.08030	+	0.804250i	−0.0641037	+	0.0477235i
$285$	−15.3469	−	41.8025i	−0.909070	−	2.47617i
$286$	−32.5122	+	1.89362i	−1.92249	+	0.111972i
$287$	−5.80114	−	13.3581i	−0.342431	−	0.788504i
$288$	1.65543	−	0.725047i	0.0975472	−	0.0427238i
$289$	−2.49062	−	14.1250i	−0.146507	−	0.830882i
$290$	−23.6125	+	5.59627i	−1.38658	+	0.328624i
$291$	1.57745	+	1.47996i	0.0924717	+	0.0867570i
$292$	1.14336	+	0.0665934i	0.0669103	+	0.00389708i
$293$	−16.9098	−	4.00770i	−0.987882	−	0.234132i	−0.295247	−	0.955421i	$-0.595402\pi$
$293$	−16.9098	−	4.00770i	−0.987882	−	0.234132i	−0.692635	+	0.721288i	$0.743550\pi$
$294$	−11.4150	−	13.3929i	−0.665735	−	0.781089i
$295$	−12.1613	−	1.42145i	−0.708056	−	0.0827598i
$296$	15.5030	+	8.95066i	0.901094	+	0.520247i
$297$	4.17352	+	16.9761i	0.242172	+	0.985052i
$298$	−4.71558	−	8.16763i	−0.273166	−	0.473138i
$299$	0.499019	+	1.15686i	0.0288590	+	0.0669027i
$300$	0.764857	−	1.03338i	0.0441591	−	0.0596621i
$301$	−1.34402	+	7.73352i	−0.0774680	+	0.445753i
$302$	15.8885	+	31.6367i	0.914282	+	1.82049i
$303$	1.41799	−	25.5728i	0.0814612	−	1.46912i
$304$	29.9215	+	8.95790i	1.71611	+	0.513771i
$305$	−7.76485	−	9.25378i	−0.444614	−	0.529870i
$306$	4.59252	+	5.41164i	0.262537	+	0.309363i
$307$	−8.61796	+	10.2705i	−0.491853	+	0.586168i	−0.953688	−	0.300798i	$-0.902747\pi$
$307$	−8.61796	+	10.2705i	−0.491853	+	0.586168i	0.461835	+	0.886966i	$0.347191\pi$
$308$	0.872224	+	0.373698i	0.0496996	+	0.0212934i
$309$	2.08543	+	2.47131i	0.118636	+	0.140588i
$310$	21.9497	−	2.56555i	1.24666	−	0.145713i
$311$	1.63839	−	3.79821i	0.0929045	−	0.215377i	−0.865427	−	0.501035i	$-0.832953\pi$
$311$	1.63839	−	3.79821i	0.0929045	−	0.215377i	0.958332	+	0.285658i	$0.0922121\pi$
$312$	15.7962	−	27.5367i	0.894285	−	1.55896i
$313$	−0.173469	+	0.345405i	−0.00980506	+	0.0195235i	−0.898482	−	0.439011i	$-0.855329\pi$
$313$	−0.173469	+	0.345405i	−0.00980506	+	0.0195235i	0.888677	+	0.458534i	$0.151625\pi$
$314$	14.4315	−	5.25263i	0.814416	−	0.296423i
$315$	25.8718	+	9.18194i	1.45771	+	0.517344i
$316$	0.202945	+	0.0738659i	0.0114165	+	0.00415528i
$317$	8.75413	−	8.25910i	0.491681	−	0.463877i	−0.400017	−	0.916508i	$-0.630996\pi$
$317$	8.75413	−	8.25910i	0.491681	−	0.463877i	0.891698	+	0.452631i	$0.149514\pi$
$318$	17.4256	+	23.2711i	0.977182	+	1.30498i
$319$	13.5875	+	8.93666i	0.760756	+	0.500357i
$320$	−7.46890	−	24.9479i	−0.417524	−	1.39463i
$321$	−12.2131	+	11.5869i	−0.681666	+	0.646717i
$322$	0.0403971	−	0.724284i	0.00225124	−	0.0403628i
$323$			12.1168i			0.674194i
$324$	0.905181	+	0.318084i	0.0502878	+	0.0176713i
$325$		−	46.4382i		−	2.57593i
$326$	9.46179	+	7.04404i	0.524040	+	0.390134i
$327$	−5.21156	+	17.5860i	−0.288200	+	0.972506i
$328$	−14.4913	+	4.33840i	−0.800147	+	0.239548i
$329$	0.582577	−	0.00143325i	0.0321185	−	7.90176e-5i
$330$	−29.0454	+	3.47695i	−1.59890	+	0.191400i
$331$	9.79810	+	10.3854i	0.538552	+	0.570832i	0.938313	−	0.345787i	$-0.112388\pi$
$331$	9.79810	+	10.3854i	0.538552	+	0.570832i	−0.399760	+	0.916620i	$0.630907\pi$
$332$	0.668604	+	0.243352i	0.0366944	+	0.0133557i
$333$	5.70897	+	18.6897i	0.312850	+	1.02419i
$334$	−0.679783	−	1.86769i	−0.0371960	−	0.102195i
$335$	−26.2711	−	13.1939i	−1.43535	−	0.720858i
$336$	−16.0318	+	10.6652i	−0.874608	+	0.581834i
$337$	−3.47007	+	8.04452i	−0.189027	+	0.438213i	−0.986204	−	0.165532i	$-0.947066\pi$
$337$	−3.47007	+	8.04452i	−0.189027	+	0.438213i	0.797178	+	0.603745i	$0.206325\pi$
$338$	5.30467	+	45.3843i	0.288536	+	2.46858i
$339$	20.4007	−	3.65582i	1.10802	−	0.198557i
$340$	−0.502154	+	0.330272i	−0.0272331	+	0.0179115i
$341$	−11.3454	−	9.51992i	−0.614388	−	0.515532i
$342$	16.3391	+	27.9396i	0.883518	+	1.51080i
$343$	14.2748	+	11.7996i	0.770768	+	0.637116i
$344$	7.81058	+	2.33833i	0.421118	+	0.126074i
$345$	0.510707	+	1.00988i	0.0274955	+	0.0543700i
$346$	0.622540	+	1.23958i	0.0334679	+	0.0666402i
$347$	−22.0738	−	20.8255i	−1.18498	−	1.11797i	−0.990564	−	0.137053i	$-0.956237\pi$
$347$	−22.0738	−	20.8255i	−1.18498	−	1.11797i	−0.194418	−	0.980919i	$-0.562282\pi$
$348$	0.818578	−	0.355807i	0.0438804	−	0.0190733i
$349$	0.858702	−	0.370408i	0.0459653	−	0.0198275i	−0.372973	−	0.927842i	$-0.621662\pi$
$349$	0.858702	−	0.370408i	0.0459653	−	0.0198275i	0.418938	+	0.908015i	$0.362402\pi$
$350$	−11.9410	+	23.9231i	−0.638275	+	1.27874i
$351$	33.1155	−	10.2164i	1.76757	−	0.545311i
$352$	1.01336	−	1.75520i	0.0540124	−	0.0935522i
$353$	28.7623	+	3.36183i	1.53086	+	0.178932i	0.839414	−	0.543492i	$-0.182898\pi$
$353$	28.7623	+	3.36183i	1.53086	+	0.178932i	0.691450	+	0.722425i	$0.256972\pi$
$354$	8.88287	−	0.542198i	0.472119	−	0.0288175i
$355$	−10.0770	+	42.5181i	−0.534831	+	2.25663i
$356$	0.103324	−	1.77400i	0.00547615	−	0.0940218i
$357$	−5.74737	−	4.77147i	−0.304183	−	0.252533i
$358$	3.07366	−	0.728472i	0.162448	−	0.0385009i
$359$	−17.4161	+	3.07092i	−0.919185	+	0.162077i	−0.613171	−	0.789950i	$-0.710106\pi$
$359$	−17.4161	+	3.07092i	−0.919185	+	0.162077i	−0.306014	+	0.952027i	$0.598995\pi$
$360$	12.6553	−	25.5527i	0.666991	−	1.34674i
$361$	−6.29546	+	35.7033i	−0.331340	+	1.87912i
$362$	0.00517001	+	0.0887657i	0.000271730	+	0.00466542i
$363$	0.423864	+	0.353657i	0.0222471	+	0.0185622i
$364$	0.639031	−	1.76925i	0.0334943	−	0.0927341i
$365$	29.8058	−	22.1896i	1.56011	−	1.16146i
$366$	6.74167	+	5.62501i	0.352393	+	0.294024i
$367$	5.90005	−	0.343639i	0.307980	−	0.0179378i	0.0965411	−	0.995329i	$-0.469222\pi$
$367$	5.90005	−	0.343639i	0.307980	−	0.0179378i	0.211439	+	0.977391i	$0.432185\pi$
$368$	−0.781689	−	0.137833i	−0.0407484	−	0.00718504i
$369$	−14.7979	−	7.32885i	−0.770348	−	0.381525i
$370$	−32.2041	+	5.67846i	−1.67421	+	0.295209i
$371$	−22.3069	−	20.9420i	−1.15812	−	1.08725i
$372$	−0.778038	+	0.235293i	−0.0403394	+	0.0121994i
$373$	−1.73235	+	29.7432i	−0.0896975	+	1.54005i	0.590512	+	0.807029i	$0.298926\pi$
$373$	−1.73235	+	29.7432i	−0.0896975	+	1.54005i	−0.680210	+	0.733018i	$0.738111\pi$
$374$	7.74510	+	1.83562i	0.400490	+	0.0949178i
$375$	−0.716388	−	11.7366i	−0.0369941	−	0.606077i
$376$	0.0702497	−	0.601024i	0.00362285	−	0.0309955i
$377$	16.1199	−	27.9206i	0.830219	−	1.43798i
$378$	−19.6868	−	3.25218i	−1.01258	−	0.167274i
$379$	8.00931	+	13.8725i	0.411411	+	0.712584i	0.995044	−	0.0994330i	$-0.0317029\pi$
$379$	8.00931	+	13.8725i	0.411411	+	0.712584i	−0.583634	+	0.812017i	$0.698370\pi$
$380$	−2.51663	+	1.08557i	−0.129100	+	0.0556885i
$381$	6.89119	+	15.8540i	0.353046	+	0.812226i
$382$	−0.652708	+	0.691830i	−0.0333955	+	0.0353971i
$383$	19.5250	−	9.80584i	0.997683	−	0.501055i	0.126475	−	0.991970i	$-0.459634\pi$
$383$	19.5250	−	9.80584i	0.997683	−	0.501055i	0.871208	+	0.490915i	$0.163337\pi$
$384$	9.48379	+	18.7534i	0.483967	+	0.957003i
$385$	29.4716	−	8.90227i	1.50201	−	0.453702i
$386$	−13.3302	−	15.8863i	−0.678489	−	0.808592i
$387$	4.49308	+	7.68309i	0.228396	+	0.390553i
$388$	0.0855742	−	0.101983i	0.00434437	−	0.00517742i
$389$	10.1214	+	15.3888i	0.513174	+	0.780244i	0.995400	−	0.0958032i	$-0.0305419\pi$
$389$	10.1214	+	15.3888i	0.513174	+	0.780244i	−0.482226	+	0.876047i	$0.660172\pi$
$390$	10.2290	+	57.0816i	0.517968	+	2.89044i
$391$	−0.0357481	−	0.305844i	−0.00180786	−	0.0154672i
$392$	13.9272	−	13.2697i	0.703428	−	0.670222i
$393$	−17.3550	+	0.0483390i	−0.875445	+	0.00243838i
$394$	−25.7462	−	12.9302i	−1.29708	−	0.651417i
$395$	6.58442	−	2.39653i	0.331298	−	0.120583i
$396$	1.02902	−	0.314326i	0.0517104	−	0.0157955i
$397$	−5.15711	+	14.1690i	−0.258828	+	0.711124i	0.740412	+	0.672153i	$0.234630\pi$
$397$	−5.15711	+	14.1690i	−0.258828	+	0.711124i	−0.999240	+	0.0389710i	$0.987592\pi$
$398$	−17.3265	−	18.3650i	−0.868500	−	0.920556i
$399$	−22.0323	−	25.9791i	−1.10299	−	1.30058i
$400$	24.4435	+	16.0767i	1.22218	+	0.803837i
$401$	−13.7396	+	4.11336i	−0.686122	+	0.205412i	−0.610844	−	0.791751i	$-0.709170\pi$
$401$	−13.7396	+	4.11336i	−0.686122	+	0.205412i	−0.0752783	+	0.997163i	$0.523985\pi$
$402$	20.4869	+	6.07126i	1.02180	+	0.302807i
$403$	−17.5327	+	23.5505i	−0.873365	+	1.17313i
$404$	−1.57638			−0.0784277
$405$	29.1308	−	10.9718i	1.44752	−	0.545194i
$406$	−15.4838	+	10.2385i	−0.768449	+	0.508129i
$407$	17.5789	+	13.0870i	0.871354	+	0.648699i
$408$	−5.62873	+	5.34015i	−0.278664	+	0.264377i
$409$	32.2350	−	9.65053i	1.59392	−	0.477188i	0.637808	−	0.770195i	$-0.279841\pi$
$409$	32.2350	−	9.65053i	1.59392	−	0.477188i	0.956110	+	0.293007i	$0.0946559\pi$
$410$	15.1843	−	23.0867i	0.749901	−	1.14017i
$411$	17.2606	−	12.9249i	0.851402	−	0.637539i
$412$	0.144765	−	0.136579i	0.00713208	−	0.00672877i
$413$	−9.10827	+	2.18238i	−0.448189	+	0.107388i
$414$	−0.494853	−	0.657030i	−0.0243207	−	0.0322912i
$415$	21.6925	−	7.89541i	1.06484	−	0.387571i
$416$	−3.59043	−	1.80318i	−0.176036	−	0.0884084i
$417$	−4.77041	−	2.73651i	−0.233608	−	0.134008i
$418$	33.3286	+	14.3766i	1.63016	+	0.703180i
$419$	−2.23804	+	0.261589i	−0.109335	+	0.0127795i	−0.170585	−	0.985343i	$-0.554566\pi$
$419$	−2.23804	+	0.261589i	−0.109335	+	0.0127795i	0.0612493	+	0.998122i	$0.480492\pi$
$420$	0.476106	−	1.62121i	0.0232316	−	0.0791068i
$421$	31.6928	−	20.8447i	1.54461	−	1.01591i	0.562678	−	0.826676i	$-0.309771\pi$
$421$	31.6928	−	20.8447i	1.54461	−	1.01591i	0.981933	−	0.189230i	$-0.0605993\pi$
$422$	8.82898	−	10.5220i	0.429788	−	0.512201i
$423$	0.503662	−	0.427427i	0.0244889	−	0.0207822i
$424$	−24.3452	+	20.4281i	−1.18231	+	0.992075i
$425$	−3.25515	+	10.8730i	−0.157898	+	0.527417i
$426$	1.75835	−	31.7110i	0.0851922	−	1.53641i
$427$	−8.01390	−	4.60058i	−0.387820	−	0.222638i
$428$	0.753676	+	0.711056i	0.0364303	+	0.0343702i
$429$	23.1212	−	31.2385i	1.11630	−	1.50821i
$430$	−13.6755	+	5.89902i	−0.659490	+	0.284476i
$431$	6.18216	−	3.56927i	0.297784	−	0.171926i	−0.343663	−	0.939093i	$-0.611668\pi$
$431$	6.18216	−	3.56927i	0.297784	−	0.171926i	0.641447	+	0.767167i	$0.278334\pi$
$432$	−6.08691	+	20.9678i	−0.292856	+	1.00881i
$433$	24.9229	+	14.3892i	1.19772	+	0.691503i	0.960046	−	0.279842i	$-0.0902822\pi$
$433$	24.9229	+	14.3892i	1.19772	+	0.691503i	0.237672	+	0.971345i	$0.423616\pi$
$434$	15.0879	−	7.62396i	0.724242	−	0.365962i
$435$	12.9245	−	25.9145i	0.619682	−	1.24251i
$436$	1.09848	+	0.260345i	0.0526078	+	0.0124683i
$437$	0.0816462	−	1.40181i	0.00390567	−	0.0670577i
$438$	−18.4794	+	19.6966i	−0.882978	+	0.941140i
$439$	0.694553	+	2.93055i	0.0331492	+	0.139867i	0.987103	−	0.160086i	$-0.0511771\pi$
$439$	0.694553	+	2.93055i	0.0331492	+	0.139867i	−0.953954	+	0.299953i	$0.903029\pi$
$440$	−5.55287	−	31.4919i	−0.264723	−	1.50132i
$441$	20.9988	−	0.220306i	0.999945	−	0.0104908i
$442$	2.74004	−	15.5396i	0.130331	−	0.739141i
$443$	−17.7469	+	1.03364i	−0.843183	+	0.0491098i	−0.474297	−	0.880365i	$-0.657298\pi$
$443$	−17.7469	+	1.03364i	−0.843183	+	0.0491098i	−0.368886	+	0.929475i	$0.620261\pi$
$444$	1.12910	−	0.414524i	0.0535848	−	0.0196725i
$445$	−34.4285	−	46.2455i	−1.63207	−	2.19225i
$446$	7.23427	+	9.71731i	0.342553	+	0.460128i
$447$	11.0891	+	1.92348i	0.524498	+	0.0909776i
$448$	−11.9351	−	15.9496i	−0.563881	−	0.753547i
$449$	29.2399	+	5.15578i	1.37991	+	0.243316i	0.813864	−	0.581055i	$-0.197360\pi$
$449$	29.2399	+	5.15578i	1.37991	+	0.243316i	0.566050	+	0.824371i	$0.308471\pi$
$450$	7.15597	+	29.4611i	0.337336	+	1.38881i
$451$	−18.2374	+	3.21575i	−0.858766	+	0.151424i
$452$	−0.294181	−	1.24125i	−0.0138371	−	0.0583833i
$453$	−41.1357	−	9.62840i	−1.93272	−	0.452382i
$454$	−20.1441	−	1.17326i	−0.945409	−	0.0550638i
$455$	−21.0152	−	57.2997i	−0.985207	−	2.68625i
$456$	−29.5065	+	19.5247i	−1.38177	+	0.914327i
$457$	16.8781	+	1.97277i	0.789525	+	0.0922823i	0.501292	−	0.865278i	$-0.332858\pi$
$457$	16.8781	+	1.97277i	0.789525	+	0.0922823i	0.288233	+	0.957560i	$0.406932\pi$
$458$	−19.9847	+	34.6146i	−0.933826	+	1.61743i
$459$	−8.46975	+	0.0707741i	−0.395334	+	0.00330345i
$460$	0.0603206	−	0.0348261i	0.00281246	−	0.00162378i
$461$	−0.198213	−	0.459510i	−0.00923172	−	0.0214015i	0.913538	−	0.406754i	$-0.133339\pi$
$461$	−0.198213	−	0.459510i	−0.00923172	−	0.0214015i	−0.922770	+	0.385352i	$0.874080\pi$
$462$	−19.9438	+	10.1475i	−0.927868	+	0.472104i
$463$	11.3027	−	11.9802i	0.525281	−	0.556765i	−0.409353	−	0.912376i	$-0.634246\pi$
$463$	11.3027	−	11.9802i	0.525281	−	0.556765i	0.934634	+	0.355611i	$0.115727\pi$
$464$	9.11578	+	18.1510i	0.423190	+	0.842640i
$465$	−14.4303	+	22.0738i	−0.669187	+	1.02365i
$466$	4.61166	−	15.4040i	0.213631	−	0.713578i
$467$	10.9673	−	9.20264i	0.507505	−	0.425848i	−0.352745	−	0.935720i	$-0.614752\pi$
$467$	10.9673	−	9.20264i	0.507505	−	0.425848i	0.860250	+	0.509872i	$0.170307\pi$
$468$	−0.740680	−	2.00026i	−0.0342380	−	0.0924621i
$469$	−22.3424	−	2.55575i	−1.03168	−	0.118014i
$470$	0.607419	+	0.923536i	0.0280182	+	0.0425995i
$471$	−6.22025	+	17.2392i	−0.286614	+	0.794343i
$472$	1.12940	+	9.66262i	0.0519848	+	0.444758i
$473$	9.16501	+	3.95340i	0.421408	+	0.181778i
$474$	−4.40350	+	2.55874i	−0.202259	+	0.117527i
$475$	−23.2283	+	46.2514i	−1.06579	+	2.12216i
$476$	−0.273640	+	0.369457i	−0.0125423	+	0.0169340i
$477$	−34.6455	−	1.82428i	−1.58631	−	0.0835281i
$478$	−1.66920	−	0.607540i	−0.0763475	−	0.0277882i
$479$	−3.95776	−	4.19498i	−0.180835	−	0.191674i	0.630615	−	0.776096i	$-0.282803\pi$
$479$	−3.95776	−	4.19498i	−0.180835	−	0.191674i	−0.811450	+	0.584422i	$0.801321\pi$
$480$	−3.31771	−	1.42017i	−0.151432	−	0.0648217i
$481$	23.8736	−	36.2981i	1.08854	−	1.65505i
$482$	−0.358997	−	1.19913i	−0.0163519	−	0.0546191i
$483$	0.632773	+	0.590748i	0.0287922	+	0.0268800i
$484$	0.0202893	−	0.0272532i	0.000922239	−	0.00123878i
$485$		−	4.31932i		−	0.196130i
$486$	−19.4347	+	11.5844i	−0.881574	+	0.525480i
$487$	−11.3429			−0.513995			−0.256997	−	0.966412i	$-0.582733\pi$
$487$	−11.3429			−0.513995			−0.256997	+	0.966412i	$0.582733\pi$
$488$	−5.73154	+	7.69880i	−0.259455	+	0.348508i
$489$	−13.6882	+	3.28445i	−0.619001	+	0.148528i
$490$	−3.90776	+	34.9224i	−0.176535	+	1.57763i
$491$	8.25305	−	12.5482i	0.372455	−	0.566290i	−0.599819	−	0.800136i	$-0.704761\pi$
$491$	8.25305	−	12.5482i	0.372455	−	0.566290i	0.972274	+	0.233846i	$0.0751311\pi$
$492$	−0.399961	+	0.934361i	−0.0180316	+	0.0421243i
$493$	−5.73144	+	5.40733i	−0.258131	+	0.243534i
$494$	24.6103	−	67.6163i	1.10727	−	3.04220i
$495$	19.0200	−	29.2724i	0.854885	−	1.31569i
$496$	−6.32643	−	17.3817i	−0.284065	−	0.780463i
$497$	3.96209	+	33.1895i	0.177724	+	1.48875i
$498$	−14.5074	+	8.42980i	−0.650091	+	0.377749i
$499$	7.00248	−	16.2336i	0.313474	−	0.726715i	−0.686526	−	0.727105i	$-0.740865\pi$
$499$	7.00248	−	16.2336i	0.313474	−	0.726715i	1.00000		0.000390769i	$0.000124386\pi$
$500$	−0.718820	+	0.0840181i	−0.0321466	+	0.00375740i
$501$	2.23106	+	0.805010i	0.0996765	+	0.0359652i
$502$	−7.40065	−	11.2521i	−0.330307	−	0.502207i
$503$	−3.57602	−	3.00064i	−0.159447	−	0.133792i	0.559574	−	0.828781i	$-0.310965\pi$
$503$	−3.57602	−	3.00064i	−0.159447	−	0.133792i	−0.719021	+	0.694989i	$0.755409\pi$
$504$	2.35820	−	21.6845i	0.105042	−	0.965906i
$505$	−39.1791	+	32.8751i	−1.74344	+	1.46292i
$506$	−0.883677	−	0.264555i	−0.0392842	−	0.0117609i
$507$	−45.6410	−	29.8368i	−2.02699	−	1.32510i
$508$	0.950808	−	0.477514i	0.0421853	−	0.0211862i
$509$	10.3001	−	10.9174i	0.456542	−	0.483906i	−0.457682	−	0.889116i	$-0.651320\pi$
$509$	10.3001	−	10.9174i	0.456542	−	0.483906i	0.914224	+	0.405210i	$0.132802\pi$
$510$	1.60621	−	14.0820i	0.0711241	−	0.623563i
$511$	15.5610	−	23.7867i	0.688380	−	1.05226i
$512$	−17.8080	+	10.2815i	−0.787011	+	0.454381i
$513$	−38.0925	−	6.38902i	−1.68183	−	0.282082i
$514$	5.44540	+	3.14390i	0.240186	+	0.138672i
$515$	0.749640	−	6.41358i	0.0330331	−	0.282616i
$516$	0.456845	−	0.302298i	0.0201115	−	0.0133079i
$517$	0.170842	−	0.720837i	0.00751360	−	0.0317024i
$518$	−21.6324	+	12.5605i	−0.950473	+	0.551878i
$519$	−1.61177	−	0.377257i	−0.0707487	−	0.0165598i
$520$	−61.6842	+	14.6194i	−2.70503	+	0.641104i
$521$	−2.60525	−	14.7751i	−0.114138	−	0.647310i	−0.987173	−	0.159653i	$-0.948963\pi$
$521$	−2.60525	−	14.7751i	−0.114138	−	0.647310i	0.873035	−	0.487658i	$-0.162149\pi$
$522$	−5.92427	+	20.1973i	−0.259298	+	0.884010i
$523$	32.3314	+	5.70090i	1.41375	+	0.249283i	0.827783	−	0.561048i	$-0.189602\pi$
$523$	32.3314	+	5.70090i	1.41375	+	0.249283i	0.585972	+	0.810332i	$0.300713\pi$
$524$	0.0621088	+	1.06637i	0.00271324	+	0.0465845i
$525$	−12.7914	−	29.2313i	−0.558264	−	1.27576i
$526$	0.972252	+	1.30596i	0.0423922	+	0.0569426i
$527$	5.75589	−	4.28510i	0.250730	−	0.186662i
$528$	8.43840	+	22.9849i	0.367234	+	1.00029i
$529$	−1.33526	−	22.9255i	−0.0580546	−	0.996759i
$530$	10.0810	−	57.1724i	0.437892	−	2.48341i
$531$	−6.29435	+	8.55385i	−0.273152	+	0.371205i
$532$	−1.52144	+	1.44250i	−0.0659628	+	0.0625401i
$533$	8.46631	+	35.7222i	0.366717	+	1.54730i
$534$	30.5605	+	28.6719i	1.32248	+	1.24075i
$535$	33.5607	+	1.95469i	1.45096	+	0.0845086i
$536$	−5.38673	+	22.7284i	−0.232672	+	0.981718i
$537$	−1.68239	+	3.37332i	−0.0726006	+	0.145569i
$538$	1.47422	−	12.6128i	0.0635581	−	0.543774i
$539$	18.8208	−	14.1560i	0.810670	−	0.609744i
$540$	−0.773525	−	1.75281i	−0.0332872	−	0.0754291i
$541$	20.8276	+	36.0745i	0.895449	+	1.55096i	0.833248	+	0.552899i	$0.186479\pi$
$541$	20.8276	+	36.0745i	0.895449	+	1.55096i	0.0622010	+	0.998064i	$0.480188\pi$
$542$	−2.15881	−	5.00468i	−0.0927288	−	0.214970i
$543$	−0.0852881	−	0.0631262i	−0.00366006	−	0.00270900i
$544$	0.714263	+	0.673872i	0.0306238	+	0.0288920i
$545$	32.7310	−	16.4381i	1.40204	−	0.704133i
$546$	22.3813	+	38.3001i	0.957830	+	1.63909i
$547$	2.22559	−	7.43399i	0.0951594	−	0.317855i	−0.897135	−	0.441756i	$-0.854356\pi$
$547$	2.22559	−	7.43399i	0.0951594	−	0.317855i	0.992294	+	0.123902i	$0.0395408\pi$
$548$	−0.853102	−	1.01669i	−0.0364427	−	0.0434307i
$549$	−10.3083	+	1.87690i	−0.439949	+	0.0801043i
$550$	26.0452	+	21.8545i	1.11057	+	0.931879i
$551$	−30.0209	+	19.7451i	−1.27893	+	0.841169i
$552$	0.687183	−	0.579884i	0.0292484	−	0.0246815i
$553$	4.09751	−	3.45543i	0.174244	−	0.146940i
$554$	−18.8022	−	8.11049i	−0.798830	−	0.344582i
$555$	19.4177	−	33.8498i	0.824235	−	1.43684i
$556$	−0.151914	+	0.302485i	−0.00644258	+	0.0128282i
$557$	2.34742	+	6.44948i	0.0994633	+	0.273273i	0.979437	−	0.201749i	$-0.0646624\pi$
$557$	2.34742	+	6.44948i	0.0994633	+	0.273273i	−0.879974	+	0.475022i	$0.842440\pi$
$558$	7.49395	−	17.6425i	0.317244	−	0.746867i
$559$	6.76757	−	18.5938i	0.286238	−	0.786432i
$560$	37.4360	+	8.77529i	1.58196	+	0.370824i
$561$	−7.60328	+	5.69342i	−0.321011	+	0.240376i
$562$	−9.05547	−	5.95588i	−0.381982	−	0.251233i
$563$	6.91716	+	23.1049i	0.291524	+	0.973757i	0.970803	+	0.239877i	$0.0771071\pi$
$563$	6.91716	+	23.1049i	0.291524	+	0.973757i	−0.679280	+	0.733879i	$0.737708\pi$
$564$	−0.0279833	−	0.0294955i	−0.00117831	−	0.00124199i
$565$	−33.1976	−	24.7147i	−1.39663	−	1.03975i
$566$	−0.483379			−0.0203179
$567$	18.0310	−	15.5526i	0.757231	−	0.653147i
$568$	34.7183			1.45675
$569$	−29.0543	−	21.6301i	−1.21802	−	0.906783i	−0.220379	−	0.975414i	$-0.570729\pi$
$569$	−29.0543	−	21.6301i	−1.21802	−	0.906783i	−0.997642	+	0.0686316i	$0.978137\pi$
$570$	18.3643	−	61.9686i	0.769195	−	2.59558i
$571$	6.51109	+	21.7485i	0.272481	+	0.910148i	0.979242	+	0.202696i	$0.0649703\pi$
$571$	6.51109	+	21.7485i	0.272481	+	0.910148i	−0.706761	+	0.707452i	$0.749844\pi$
$572$	−1.99851	−	1.31444i	−0.0835620	−	0.0549596i
$573$	−0.134910	−	1.12699i	−0.00563593	−	0.0470808i
$574$	4.82403	−	20.5797i	0.201351	−	0.858979i
$575$	0.449860	−	1.23598i	0.0187605	−	0.0515440i
$576$	−22.0078	−	5.08663i	−0.916992	−	0.211943i
$577$	12.0866	+	33.2076i	0.503171	+	1.38245i	0.888162	+	0.459531i	$0.151983\pi$
$577$	12.0866	+	33.2076i	0.503171	+	1.38245i	−0.384990	+	0.922921i	$0.625795\pi$
$578$	9.34287	−	18.6032i	0.388612	−	0.773791i
$579$	24.7478	−	0.0689302i	1.02848	−	0.00286464i
$580$	−1.63659	−	0.705955i	−0.0679556	−	0.0293132i
$581$	13.4993	−	11.3840i	0.560045	−	0.472286i
$582$	0.553766	+	3.09021i	0.0229543	+	0.128093i
$583$	−32.5062	+	21.3796i	−1.34627	+	0.885454i
$584$	−22.6168	−	18.9777i	−0.935888	−	0.785304i
$585$	−60.1240	−	34.2674i	−2.48582	−	1.41678i
$586$	−16.2131	−	19.3220i	−0.669756	−	0.798184i
$587$	−12.3307	+	41.1875i	−0.508943	+	1.69999i	0.187403	+	0.982283i	$0.439993\pi$
$587$	−12.3307	+	41.1875i	−0.508943	+	1.69999i	−0.696346	+	0.717706i	$0.745192\pi$
$588$	−0.0850935	−	1.28971i	−0.00350919	−	0.0531867i
$589$	29.2421	−	14.6859i	1.20490	−	0.605123i
$590$	−12.9263	−	12.1953i	−0.532167	−	0.502074i
$591$	31.5315	−	13.7057i	1.29703	−	0.563776i
$592$	10.8411	+	25.1326i	0.445568	+	1.03294i
$593$	−11.1767	−	19.3586i	−0.458971	−	0.794962i	0.539936	−	0.841706i	$-0.318449\pi$
$593$	−11.1767	−	19.3586i	−0.458971	−	0.794962i	−0.998907	+	0.0467447i	$0.985115\pi$
$594$	−9.85471	+	23.3811i	−0.404344	+	0.959337i
$595$	0.903955	+	14.8892i	0.0370585	+	0.610396i
$596$	0.0804185	−	0.688024i	0.00329407	−	0.0281826i
$597$	30.0743	−	1.83569i	1.23086	−	0.0751299i
$598$	−0.421711	+	1.77934i	−0.0172450	+	0.0727626i
$599$	−34.6794	−	2.01985i	−1.41696	−	0.0825287i	−0.667517	−	0.744595i	$-0.732643\pi$
$599$	−34.6794	−	2.01985i	−1.41696	−	0.0825287i	−0.749446	+	0.662066i	$0.769680\pi$
$600$	−31.7230	+	9.59359i	−1.29508	+	0.391657i
$601$	5.90030	+	24.8953i	0.240678	+	1.01550i	0.950403	+	0.311022i	$0.100671\pi$
$601$	5.90030	+	24.8953i	0.240678	+	1.01550i	−0.709724	+	0.704479i	$0.751181\pi$
$602$	−8.26756	+	7.83857i	−0.336960	+	0.319476i
$603$	−21.2258	+	14.1304i	−0.864381	+	0.575436i
$604$	−0.451530	+	2.56075i	−0.0183725	+	0.104196i
$605$	−0.0640955	−	1.10048i	−0.00260585	−	0.0447408i
$606$	23.8154	−	28.5432i	0.967434	−	1.15949i
$607$	−12.7112	+	9.46314i	−0.515932	+	0.384097i	−0.823400	−	0.567461i	$-0.807926\pi$
$607$	−12.7112	+	9.46314i	−0.515932	+	0.384097i	0.307468	+	0.951558i	$0.400518\pi$
$608$	2.67404	+	3.59186i	0.108447	+	0.145669i
$609$	2.45623	−	22.0153i	0.0995317	−	0.892106i
$610$	−1.01945	−	17.5034i	−0.0412765	−	0.708691i
$611$	−1.44627	−	0.255016i	−0.0585098	−	0.0103169i
$612$	0.0332105	+	0.520258i	0.00134246	+	0.0210302i
$613$	3.78161	+	21.4466i	0.152738	+	0.866219i	0.960825	+	0.277156i	$0.0893918\pi$
$613$	3.78161	+	21.4466i	0.152738	+	0.866219i	−0.808087	+	0.589063i	$0.799497\pi$
$614$	−18.9348	+	4.48764i	−0.764148	+	0.181106i
$615$	9.54540	+	31.5636i	0.384908	+	1.27277i
$616$	−12.2828	−	21.1540i	−0.494886	−	0.852319i
$617$	7.96315	−	33.5992i	0.320584	−	1.35265i	−0.539279	−	0.842127i	$-0.681303\pi$
$617$	7.96315	−	33.5992i	0.320584	−	1.35265i	0.859863	−	0.510524i	$-0.170549\pi$
$618$	0.285943	+	4.68463i	0.0115023	+	0.188443i
$619$	0.849298	−	7.26621i	0.0341362	−	0.292054i	−0.965377	−	0.260858i	$-0.915994\pi$
$619$	0.849298	−	7.26621i	0.0341362	−	0.292054i	0.999513	−	0.0311955i	$-0.00993145\pi$
$620$	1.40569	+	0.811577i	0.0564540	+	0.0325937i
$621$	0.980359	+	0.0488837i	0.0393405	+	0.00196163i
$622$	5.19944	−	3.00190i	0.208478	−	0.120365i
$623$	−36.9065	−	24.1439i	−1.47863	−	0.967305i
$624$	44.5157	−	19.3494i	1.78206	−	0.774598i
$625$	7.77751	−	8.24368i	0.311100	−	0.329747i
$626$	−0.501327	+	0.251776i	−0.0200370	+	0.0100630i
$627$	−38.6537	+	19.5476i	−1.54368	+	0.780656i
$628$	1.08061	+	0.323515i	0.0431212	+	0.0129096i
$629$	−8.13412	+	6.82533i	−0.324328	+	0.272144i
$630$	22.1620	+	33.1134i	0.882957	+	1.31927i
$631$	−28.4108	−	23.8395i	−1.13102	−	0.949035i	−0.131908	−	0.991262i	$-0.542110\pi$
$631$	−28.4108	−	23.8395i	−1.13102	−	0.949035i	−0.999108	+	0.0422265i	$0.986555\pi$
$632$	−3.05931	−	4.65145i	−0.121693	−	0.185025i
$633$	2.89126	+	16.1342i	0.114917	+	0.641278i
$634$	17.3500	−	2.02793i	0.689058	−	0.0805394i
$635$	13.6728	−	31.6970i	0.542587	−	1.25786i
$636$	0.00594751	+	2.13532i	0.000235834	+	0.0846708i
$637$	−30.1850	−	35.6157i	−1.19597	−	1.41115i
$638$	8.07316	+	22.1808i	0.319619	+	0.878147i
$639$	27.7124	+	25.8550i	1.09628	+	1.02281i
$640$	14.3528	−	39.4340i	0.567344	−	1.55877i
$641$	2.74305	−	2.58793i	0.108344	−	0.102217i	−0.630164	−	0.776462i	$-0.717012\pi$
$641$	2.74305	−	2.58793i	0.108344	−	0.102217i	0.738508	+	0.674245i	$0.235531\pi$
$642$	−24.2612	+	2.90425i	−0.957515	+	0.114622i
$643$	−13.6446	+	20.7456i	−0.538090	+	0.818127i	−0.997542	−	0.0700763i	$-0.977676\pi$
$643$	−13.6446	+	20.7456i	−0.538090	+	0.818127i	0.459451	+	0.888203i	$0.348046\pi$
$644$	0.0341475	−	0.0408993i	0.00134560	−	0.00161166i
$645$	5.04998	−	17.0407i	0.198843	−	0.670977i
$646$	−10.5019	+	14.1065i	−0.413191	+	0.555012i
$647$	−5.41990			−0.213078			−0.106539	−	0.994309i	$-0.533977\pi$
$647$	−5.41990			−0.213078			−0.106539	+	0.994309i	$0.533977\pi$
$648$	−13.8203	−	20.5114i	−0.542914	−	0.805762i
$649$			11.9099i			0.467503i
$650$	40.2491	−	54.0639i	1.57870	−	2.12056i
$651$	−4.54925	+	19.6537i	−0.178299	+	0.770287i
$652$	0.248486	+	0.830000i	0.00973145	+	0.0325053i
$653$	−17.5403	+	26.6688i	−0.686406	+	1.04363i	0.309292	+	0.950967i	$0.399908\pi$
$653$	−17.5403	+	26.6688i	−0.686406	+	1.04363i	−0.995698	+	0.0926619i	$0.970462\pi$
$654$	−21.3096	+	15.9568i	−0.833270	+	0.623961i
$655$	23.7826	+	25.2081i	0.929263	+	0.984961i
$656$	−21.7340	−	7.91052i	−0.848569	−	0.308854i
$657$	−3.91998	−	31.9911i	−0.152933	−	1.24809i
$658$	0.679487	+	0.503266i	0.0264891	+	0.0196193i
$659$	4.68286	−	9.32434i	0.182418	−	0.363225i	−0.783774	−	0.621046i	$-0.786708\pi$
$659$	4.68286	−	9.32434i	0.182418	−	0.363225i	0.966193	+	0.257821i	$0.0830044\pi$
$660$	−1.86371	−	1.06910i	−0.0725448	−	0.0416148i
$661$	−5.17460	−	2.23211i	−0.201269	−	0.0868189i	0.293059	−	0.956094i	$-0.405327\pi$
$661$	−5.17460	−	2.23211i	−0.201269	−	0.0868189i	−0.494328	+	0.869275i	$0.664586\pi$
$662$	2.40581	+	20.5831i	0.0935046	+	0.799983i
$663$	12.1440	+	14.3910i	0.471633	+	0.558902i
$664$	−10.0789	−	15.3243i	−0.391138	−	0.594697i
$665$	−7.73060	+	67.5810i	−0.299780	+	2.62068i
$666$	−9.55238	+	26.7069i	−0.370147	+	1.03487i
$667$	0.699517	−	0.586965i	0.0270854	−	0.0227274i
$668$	0.0418685	−	0.139850i	0.00161994	−	0.00541098i
$669$	−14.4347	−	0.800390i	−0.558078	−	0.0309449i
$670$	−19.1498	−	38.1303i	−0.739820	−	1.47310i
$671$	−8.06352	+	8.54683i	−0.311289	+	0.329947i
$672$	−2.75675	−	0.146057i	−0.106344	−	0.00563428i
$673$	1.70680	+	3.95680i	0.0657922	+	0.152524i	0.947940	−	0.318450i	$-0.103162\pi$
$673$	1.70680	+	3.95680i	0.0657922	+	0.152524i	−0.882148	+	0.470973i	$0.843903\pi$
$674$	−11.0123	+	6.35795i	−0.424177	+	0.244899i
$675$	−32.4659	−	15.9667i	−1.24961	−	0.614559i
$676$	−1.67806	+	2.90648i	−0.0645407	+	0.111788i
$677$	28.3713	+	3.31613i	1.09040	+	0.127449i	0.642239	−	0.766505i	$-0.278006\pi$
$677$	28.3713	+	3.31613i	1.09040	+	0.127449i	0.448159	+	0.893954i	$0.352080\pi$
$678$	26.9194	+	13.4257i	1.03383	+	0.515610i
$679$	−1.13769	−	3.10201i	−0.0436605	−	0.119044i
$680$	15.4674	+	0.900874i	0.593148	+	0.0345470i
$681$	16.4757	−	17.5609i	0.631349	−	0.672937i
$682$	−4.95731	−	20.9165i	−0.189825	−	0.800936i
$683$	47.6469	−	8.40144i	1.82316	−	0.321472i	0.845871	−	0.533388i	$-0.179081\pi$
$683$	47.6469	−	8.40144i	1.82316	−	0.321472i	0.977288	+	0.211916i	$0.0679703\pi$
$684$	−0.262827	+	2.36270i	−0.0100495	+	0.0903402i
$685$	−42.4058	−	7.47728i	−1.62024	−	0.285692i
$686$	6.39196	+	26.1095i	0.244046	+	0.996867i
$687$	−16.4384	−	44.7756i	−0.627162	−	1.70830i
$688$	7.44422	+	9.99933i	0.283808	+	0.381221i
$689$	46.0583	+	61.8671i	1.75468	+	2.35695i
$690$	−0.280714	+	1.61836i	−0.0106866	+	0.0616098i
$691$	−5.85904	+	0.341250i	−0.222888	+	0.0129818i	−0.169225	−	0.985577i	$-0.554127\pi$
$691$	−5.85904	+	0.341250i	−0.222888	+	0.0129818i	−0.0536627	+	0.998559i	$0.517090\pi$
$692$	−0.0176917	+	0.100335i	−0.000672538	+	0.00381415i
$693$	5.94939	−	26.0324i	0.225999	−	0.988887i
$694$	−7.64857	−	43.3772i	−0.290336	−	1.64658i
$695$	2.53264	+	10.6861i	0.0960686	+	0.405345i
$696$	−22.4034	−	5.24383i	−0.849197	−	0.198767i
$697$	0.521709	−	8.95740i	0.0197611	−	0.339286i
$698$	1.32075	+	0.313024i	0.0499913	+	0.0118481i
$699$	10.5889	+	16.0024i	0.400509	+	0.605266i
$700$	−1.75279	+	0.885690i	−0.0662492	+	0.0334759i
$701$	−27.7208	−	16.0046i	−1.04700	−	0.604486i	−0.125193	−	0.992132i	$-0.539955\pi$
$701$	−27.7208	−	16.0046i	−1.04700	−	0.604486i	−0.921808	+	0.387646i	$0.873288\pi$
$702$	47.4083	+	16.8079i	1.78931	+	0.634375i
$703$	−41.9339	+	24.2105i	−1.58157	+	0.913118i
$704$	−23.2595	+	10.0332i	−0.876625	+	0.378139i
$705$	−1.31062	−	0.149490i	−0.0493607	−	0.00563012i
$706$	30.5717	+	28.8429i	1.15058	+	1.08552i
$707$	−19.4781	+	33.9296i	−0.732550	+	1.27605i
$708$	0.547115	+	0.357664i	0.0205619	+	0.0134418i
$709$	3.14312	−	10.4987i	0.118042	−	0.394289i	−0.878464	−	0.477809i	$-0.841431\pi$
$709$	3.14312	−	10.4987i	0.118042	−	0.394289i	0.996506	+	0.0835203i	$0.0266163\pi$
$710$	−48.5833	+	40.7662i	−1.82330	+	1.52993i
$711$	1.02202	−	5.99112i	0.0383287	−	0.224685i
$712$	−29.4451	+	35.0913i	−1.10350	+	1.31510i
$713$	−0.694784	+	0.456967i	−0.0260199	+	0.0171135i
$714$	−2.55562	−	10.5364i	−0.0956415	−	0.394315i
$715$	−77.0832	+	9.00974i	−2.88275	+	0.336945i
$716$	0.213036	+	0.0918948i	0.00796153	+	0.00343427i
$717$	1.83283	−	1.06500i	0.0684483	−	0.0397732i
$718$	−22.9377	−	11.5197i	−0.856026	−	0.429912i
$719$	2.72860	−	0.993131i	0.101760	−	0.0370375i	−0.290639	−	0.956833i	$-0.593868\pi$
$719$	2.72860	−	0.993131i	0.101760	−	0.0370375i	0.392398	+	0.919795i	$0.371645\pi$
$720$	38.8520	−	19.7840i	1.44793	−	0.737305i
$721$	−1.15094	−	4.80350i	−0.0428632	−	0.178892i
$722$	−38.2742	+	36.1098i	−1.42442	+	1.34387i
$723$	1.37322	+	0.587819i	0.0510707	+	0.0218612i
$724$	−0.00358872	+	0.00545639i	−0.000133374	+	0.000202785i
$725$	−32.2438	+	9.65316i	−1.19750	+	0.358509i
$726$	0.186945	+	0.779106i	0.00693818	+	0.0289153i
$727$	−16.3830	−	12.1967i	−0.607611	−	0.452349i	0.248864	−	0.968538i	$-0.419943\pi$
$727$	−16.3830	−	12.1967i	−0.607611	−	0.452349i	−0.856475	+	0.516189i	$0.827350\pi$
$728$	−40.4491	+	26.7466i	−1.49914	+	0.991295i
$729$	4.24350	−	26.6644i	0.157167	−	0.987572i
$730$	53.9326			1.99614
$731$	−2.88791	+	3.87913i	−0.106813	+	0.143475i
$732$	0.150469	+	0.627091i	0.00556150	+	0.0231779i
$733$	1.02920	−	0.308121i	0.0380142	−	0.0113807i	−0.267740	−	0.963491i	$-0.586277\pi$
$733$	1.02920	−	0.308121i	0.0380142	−	0.0113807i	0.305754	+	0.952111i	$0.401092\pi$
$734$	7.16676	+	4.71365i	0.264530	+	0.173984i
$735$	−29.0116	−	30.2796i	−1.07011	−	1.11688i
$736$	−0.0780937	−	0.0827745i	−0.00287857	−	0.00305111i
$737$	−9.78034	+	26.8713i	−0.360263	+	0.989815i
$738$	−10.8758	−	21.3580i	−0.400344	−	0.786201i
$739$	−30.9852	+	11.2777i	−1.13981	+	0.414857i	−0.841845	−	0.539720i	$-0.818530\pi$
$739$	−30.9852	+	11.2777i	−1.13981	+	0.414857i	−0.297965	+	0.954577i	$0.596308\pi$
$740$	−2.14637	−	1.07795i	−0.0789020	−	0.0396261i
$741$	43.1413	+	74.2445i	1.58483	+	2.72744i
$742$	−7.81905	−	43.7149i	−0.287046	−	1.60482i
$743$	−1.10075	−	9.41755i	−0.0403827	−	0.345496i	−0.998292	−	0.0584247i	$-0.981392\pi$
$743$	−1.10075	−	9.41755i	−0.0403827	−	0.345496i	0.957909	−	0.287072i	$-0.0926818\pi$
$744$	19.7099	+	7.11171i	0.722600	+	0.260728i
$745$	−12.3499	−	18.7772i	−0.452467	−	0.687943i
$746$	−27.7960	+	33.1260i	−1.01768	+	1.21283i
$747$	3.36705	−	19.7378i	0.123194	−	0.722169i
$748$	0.375791	+	0.447850i	0.0137403	+	0.0163750i
$749$	24.6172	−	7.43595i	0.899494	−	0.271704i
$750$	9.33841	−	14.2849i	0.340990	−	0.521609i
$751$	29.8286	−	14.9805i	1.08846	−	0.546645i	0.188259	−	0.982119i	$-0.439716\pi$
$751$	29.8286	−	14.9805i	1.08846	−	0.546645i	0.900201	+	0.435474i	$0.143419\pi$
$752$	0.634926	−	0.672982i	0.0231534	−	0.0245411i
$753$	15.9682	+	1.82135i	0.581915	+	0.0663737i
$754$	42.9665	−	18.5339i	1.56475	−	0.674966i
$755$	42.1819	+	73.0612i	1.53516	+	2.65897i
$756$	−1.01721	−	1.05508i	−0.0369955	−	0.0383728i
$757$	14.2604	−	24.6997i	0.518303	−	0.897727i	−0.481471	−	0.876462i	$-0.659897\pi$
$757$	14.2604	−	24.6997i	0.518303	−	0.897727i	0.999774	−	0.0212647i	$-0.00676926\pi$
$758$	−2.69912	+	23.0925i	−0.0980365	+	0.838756i
$759$	0.918003	−	0.607450i	0.0333214	−	0.0220490i
$760$	68.7487	+	16.2937i	2.49378	+	0.591036i
$761$	0.476342	−	8.17847i	0.0172674	−	0.296469i	−0.978608	−	0.205735i	$-0.934042\pi$
$761$	0.476342	−	8.17847i	0.0172674	−	0.296469i	0.995875	−	0.0907344i	$-0.0289214\pi$
$762$	−5.71825	+	24.4302i	−0.207150	+	0.885013i
$763$	19.1768	−	20.4266i	0.694245	−	0.739493i
$764$	−0.0687984	+	0.0121310i	−0.00248904	+	0.000438885i
$765$	11.6753	+	12.2378i	0.422122	+	0.442459i
$766$	31.2303	+	5.50674i	1.12840	+	0.198967i
$767$	23.5703	−	1.37281i	0.851074	−	0.0495694i
$768$	−0.755245	+	4.35409i	−0.0272526	+	0.157115i
$769$	43.7813	−	32.5940i	1.57879	−	1.17537i	0.683446	−	0.730001i	$-0.260480\pi$
$769$	43.7813	−	32.5940i	1.57879	−	1.17537i	0.895348	−	0.445368i	$-0.146927\pi$
$770$	42.0270	+	15.1796i	1.51455	+	0.547035i
$771$	−7.04387	+	2.58600i	−0.253679	+	0.0931326i
$772$	−0.0885656	−	1.52061i	−0.00318755	−	0.0547281i
$773$	−3.91574	+	22.2073i	−0.140839	+	0.798740i	0.829775	+	0.558099i	$0.188469\pi$
$773$	−3.91574	+	22.2073i	−0.140839	+	0.798740i	−0.970614	+	0.240641i	$0.922642\pi$
$774$	−1.42821	+	12.8390i	−0.0513361	+	0.461489i
$775$	30.1858	−	5.32256i	1.08430	−	0.191192i
$776$	−3.33937	+	0.791445i	−0.119876	+	0.0284112i
$777$	5.02933	−	29.4245i	0.180426	−	1.05560i
$778$	−1.55442	+	26.6883i	−0.0557286	+	0.956822i
$779$	9.43593	−	39.8133i	0.338077	−	1.42646i
$780$	−1.90099	+	3.81162i	−0.0680664	+	0.136478i
$781$	42.2160	+	4.93434i	1.51061	+	0.176565i
$782$	0.223464	−	0.387052i	0.00799107	−	0.0138409i
$783$	−13.9774	−	20.8697i	−0.499511	−	0.745821i
$784$	29.1969	−	3.55833i	1.04275	−	0.127083i
$785$	33.6043	−	14.4955i	1.19939	−	0.517366i
$786$	−20.2468	−	14.9857i	−0.722181	−	0.534524i
$787$	−10.5049	−	9.91087i	−0.374460	−	0.353284i	0.475888	−	0.879506i	$-0.342127\pi$
$787$	−10.5049	−	9.91087i	−0.374460	−	0.353284i	−0.850348	+	0.526222i	$0.823608\pi$
$788$	−0.949711	−	1.89103i	−0.0338321	−	0.0673652i
$789$	−1.93995	−	0.107569i	−0.0690642	−	0.00382954i
$790$	9.74281	+	2.91681i	0.346634	+	0.103775i
$791$	−30.3513	−	9.00527i	−1.07917	−	0.320191i
$792$	−26.1163	−	9.34112i	−0.928002	−	0.331922i
$793$	17.8441	+	14.9730i	0.633663	+	0.531706i
$794$	−18.2846	+	12.0260i	−0.648897	+	0.426787i
$795$	44.6796	+	52.9468i	1.58462	+	1.87783i
$796$	−0.215290	−	1.84193i	−0.00763077	−	0.0652854i
$797$	18.6787	−	43.3022i	0.661635	−	1.53384i	−0.174112	−	0.984726i	$-0.555705\pi$
$797$	18.6787	−	43.3022i	0.661635	−	1.53384i	0.835746	−	0.549116i	$-0.185035\pi$
$798$	−3.13357	−	49.3412i	−0.110927	−	1.74666i
$799$	0.320752	+	0.161088i	0.0113474	+	0.00569887i
$800$	1.43460	+	3.94154i	0.0507208	+	0.139354i
$801$	−49.6361	+	6.08209i	−1.75381	+	0.214900i
$802$	−19.5610	−	7.11961i	−0.690722	−	0.251402i
$803$	−24.8039	−	26.2906i	−0.875309	−	0.927773i
$804$	0.940698	+	1.25626i	0.0331759	+	0.0443048i
$805$	−0.00425280	−	1.72865i	−0.000149892	−	0.0609269i
$806$	−40.8236	+	12.2218i	−1.43795	+	0.430494i
$807$	10.4299	+	10.9936i	0.367151	+	0.386992i
$808$	32.5955	+	24.2664i	1.14671	+	0.853691i
$809$			27.1582i			0.954831i	0.878678	+	0.477415i	$0.158426\pi$
$809$			27.1582i			0.954831i	−0.878678	+	0.477415i	$0.841574\pi$
$810$	43.4241	+	12.4749i	1.52577	+	0.438323i
$811$		−	40.9437i		−	1.43773i	−0.695150	−	0.718865i	$-0.744662\pi$
$811$		−	40.9437i		−	1.43773i	0.695150	−	0.718865i	$-0.255338\pi$
$812$	−1.36130	−	0.0759266i	−0.0477721	−	0.00266450i
$813$	6.23623	+	1.84809i	0.218714	+	0.0648155i
$814$	9.12276	+	30.4721i	0.319753	+	1.06805i
$815$	23.4854	+	15.4466i	0.822656	+	0.541070i
$816$	−11.7792	+	1.41006i	−0.412354	+	0.0493618i
$817$	−16.0409	+	15.1338i	−0.561201	+	0.529466i
$818$	45.8928	+	16.7036i	1.60460	+	0.584028i
$819$	−52.2052	−	8.77351i	−1.82420	−	0.306571i
$820$	1.90718	−	0.694157i	0.0666016	−	0.0242410i
$821$	−6.88074	+	13.7007i	−0.240139	+	0.478157i	−0.981128	−	0.193361i	$-0.938061\pi$
$821$	−6.88074	+	13.7007i	−0.240139	+	0.478157i	0.740988	+	0.671518i	$0.234357\pi$
$822$	31.2973	−	0.0871727i	1.09162	−	0.00304050i
$823$	14.9237	−	34.5971i	0.520209	−	1.20598i	−0.432372	−	0.901695i	$-0.642323\pi$
$823$	14.9237	−	34.5971i	0.520209	−	1.20598i	0.952581	−	0.304285i	$-0.0984175\pi$
$824$	−5.09585	+	0.595620i	−0.177522	+	0.0207494i
$825$	−39.9373	+	7.15678i	−1.39044	+	0.249167i
$826$	−12.4955	−	5.35361i	−0.434774	−	0.186276i
$827$	16.3458	−	19.4801i	0.568398	−	0.677390i	−0.402904	−	0.915242i	$-0.631999\pi$
$827$	16.3458	−	19.4801i	0.568398	−	0.677390i	0.971301	+	0.237853i	$0.0764435\pi$
$828$	−0.000336543	−	0.0604134i	−1.16957e−5	−	0.00209951i
$829$	9.60613	+	11.4481i	0.333635	+	0.397610i	0.906615	−	0.421959i	$-0.138657\pi$
$829$	9.60613	+	11.4481i	0.333635	+	0.397610i	−0.572980	+	0.819569i	$0.694213\pi$
$830$	32.0978	+	9.60945i	1.11413	+	0.333549i
$831$	21.8063	−	11.0277i	0.756454	−	0.382547i
$832$	22.5372	+	44.8753i	0.781337	+	1.55577i
$833$	4.57094	+	10.4549i	0.158374	+	0.362240i
$834$	−3.18198	−	7.32052i	−0.110183	−	0.253489i
$835$	−1.87597	−	4.34899i	−0.0649206	−	0.150503i
$836$	1.33299	+	2.30881i	0.0461024	+	0.0798518i
$837$	10.4364	+	20.3548i	0.360736	+	0.703564i
$838$	−2.83228	−	1.63522i	−0.0978394	−	0.0564876i
$839$	−4.19371	−	0.490174i	−0.144783	−	0.0169227i	0.0433928	−	0.999058i	$-0.486183\pi$
$839$	−4.19371	−	0.490174i	−0.144783	−	0.0169227i	−0.188176	+	0.982135i	$0.560257\pi$
$840$	−34.8012	+	26.1934i	−1.20076	+	0.903758i
$841$	5.48112	+	1.29905i	0.189004	+	0.0447948i
$842$	54.9637	+	3.20127i	1.89417	+	0.110323i
$843$	12.3805	−	3.74407i	0.426406	−	0.128953i
$844$	0.981659	−	0.232657i	0.0337901	−	0.00800840i
$845$	18.9081	+	107.233i	0.650458	+	3.68893i
$846$	0.956832	−	0.0610791i	0.0328966	−	0.00209994i
$847$	−0.335893	−	0.773449i	−0.0115414	−	0.0265760i
$848$	−48.5100	+	2.82539i	−1.66584	+	0.0970242i
$849$	0.369555	−	0.442918i	0.0126831	−	0.0152009i
$850$	−13.2136	+	9.83714i	−0.453222	+	0.337411i
$851$	0.987043	−	0.734826i	0.0338354	−	0.0251895i
$852$	1.49446	−	1.79113i	0.0511993	−	0.0613632i
$853$	25.2342	−	1.46972i	0.864003	−	0.0503224i	0.379582	−	0.925158i	$-0.376068\pi$
$853$	25.2342	−	1.46972i	0.864003	−	0.0503224i	0.484420	+	0.874835i	$0.339031\pi$
$854$	−5.34246	−	12.3019i	−0.182815	−	0.420962i
$855$	42.7416	+	64.2035i	1.46173	+	2.19571i
$856$	−4.63824	−	26.3048i	−0.158532	−	0.899079i
$857$	25.5342	−	6.05172i	0.872233	−	0.206723i	0.229961	−	0.973200i	$-0.426140\pi$
$857$	25.5342	−	6.05172i	0.872233	−	0.206723i	0.642272	+	0.766477i	$0.277992\pi$
$858$	53.9932	−	16.3285i	1.84330	−	0.557446i
$859$	−35.1127	−	2.04508i	−1.19803	−	0.0697772i	−0.552500	−	0.833513i	$-0.686326\pi$
$859$	−35.1127	−	2.04508i	−1.19803	−	0.0697772i	−0.645529	+	0.763736i	$0.723363\pi$
$860$	−1.06443	−	0.252273i	−0.0362966	−	0.00860245i
$861$	15.1690	+	20.1539i	0.516957	+	0.686842i
$862$	10.2909	+	1.20284i	0.350511	+	0.0409688i
$863$	43.5373	+	25.1363i	1.48203	+	0.855649i	0.999792	−	0.0203928i	$-0.00649169\pi$
$863$	43.5373	+	25.1363i	1.48203	+	0.855649i	0.482235	+	0.876042i	$0.339825\pi$
$864$	−2.49513	+	1.89017i	−0.0848862	+	0.0643048i
$865$	1.65276	+	2.86266i	0.0561955	+	0.0973335i
$866$	16.5441	+	38.3535i	0.562190	+	1.30330i
$867$	9.90316	+	22.7834i	0.336329	+	0.773765i
$868$	1.22329	+	0.212598i	0.0415213	+	0.00721605i
$869$	−3.05891	−	6.09079i	−0.103766	−	0.206616i
$870$	37.5076	−	18.9680i	1.27163	−	0.643077i
$871$	54.3070	+	16.2585i	1.84012	+	0.550897i
$872$	−18.7062	−	22.2931i	−0.633471	−	0.754941i
$873$	−3.25491	−	1.85512i	−0.110162	−	0.0627864i
$874$	1.31004	−	1.56124i	0.0443127	−	0.0528098i
$875$	−7.07354	+	16.5099i	−0.239129	+	0.558136i
$876$	−1.95262	+	0.349910i	−0.0659728	+	0.0118223i
$877$	−35.9124	+	4.19755i	−1.21267	+	0.141741i	−0.698288	−	0.715817i	$-0.746054\pi$
$877$	−35.9124	+	4.19755i	−1.21267	+	0.141741i	−0.514387	+	0.857558i	$0.671980\pi$
$878$	−1.73137	+	4.01377i	−0.0584309	+	0.135458i
$879$	30.0999	−	0.0838375i	1.01524	−	0.00282777i
$880$	21.9435	−	43.6932i	0.739717	−	1.47290i
$881$	−47.9889	+	17.4665i	−1.61679	+	0.588463i	−0.982766	−	0.184853i	$-0.940819\pi$
$881$	−47.9889	+	17.4665i	−1.61679	+	0.588463i	−0.634022	+	0.773315i	$0.718597\pi$
$882$	24.6381	+	17.9437i	0.829607	+	0.604197i
$883$	8.95525	+	3.25945i	0.301368	+	0.109689i	0.488278	−	0.872688i	$-0.337625\pi$
$883$	8.95525	+	3.25945i	0.301368	+	0.109689i	−0.186910	+	0.982377i	$0.559847\pi$
$884$	0.843004	−	0.795333i	0.0283533	−	0.0267499i
$885$	21.0570	−	2.52068i	0.707822	−	0.0847317i
$886$	−21.5571	−	14.1783i	−0.724225	−	0.476331i
$887$	14.2064	+	47.4526i	0.477003	+	1.59330i	0.770565	+	0.637361i	$0.219974\pi$
$887$	14.2064	+	47.4526i	0.477003	+	1.59330i	−0.293562	+	0.955940i	$0.594841\pi$
$888$	−29.7281	−	8.80985i	−0.997609	−	0.295639i
$889$	1.47053	−	26.3653i	0.0493199	−	0.884262i
$890$		−	83.6798i		−	2.80495i
$891$	−13.8898	−	26.9052i	−0.465325	−	0.901358i
$892$			0.889795i			0.0297925i
$893$	1.31289	+	0.977412i	0.0439343	+	0.0327079i
$894$	11.2430	+	11.8506i	0.376022	+	0.396342i
$895$	7.21122	−	2.15890i	0.241045	−	0.0721640i
$896$	−0.0789741	−	32.1009i	−0.00263834	−	1.07241i
$897$	−1.30799	−	1.74676i	−0.0436725	−	0.0583226i
$898$	29.5728	+	31.3453i	0.986857	+	1.04601i
$899$	19.9965	+	7.27814i	0.666922	+	0.242740i
$900$	−0.870586	+	2.04956i	−0.0290195	+	0.0683188i
$901$	−6.44737	−	17.7140i	−0.214793	−	0.590139i
$902$	−24.0194	−	12.0630i	−0.799759	−	0.401654i
$903$	−0.861699	−	13.5683i	−0.0286756	−	0.451525i
$904$	−13.0246	+	30.1944i	−0.433192	+	1.00425i
$905$	0.0245986	+	0.210455i	0.000817686	+	0.00699575i
$906$	−39.5455	−	46.8628i	−1.31381	−	1.55691i
$907$	19.8982	−	13.0872i	0.660709	−	0.434555i	−0.174374	−	0.984680i	$-0.555790\pi$
$907$	19.8982	−	13.0872i	0.660709	−	0.434555i	0.835083	+	0.550125i	$0.185420\pi$
$908$	−1.13533	−	0.952654i	−0.0376772	−	0.0316149i
$909$	7.94652	+	43.6438i	0.263569	+	1.44757i
$910$	25.1969	−	84.9235i	0.835270	−	2.81519i
$911$	24.8720	+	7.44619i	0.824046	+	0.246703i	0.670945	−	0.741507i	$-0.265889\pi$
$911$	24.8720	+	7.44619i	0.824046	+	0.246703i	0.153101	+	0.988210i	$0.451074\pi$
$912$	−54.0152	−	2.99509i	−1.78862	−	0.0991775i
$913$	−10.0776	−	20.0662i	−0.333520	−	0.664093i
$914$	17.9399	+	16.9254i	0.593399	+	0.559843i
$915$	16.8176	+	12.4476i	0.555974	+	0.411505i
$916$	−2.69562	+	1.16278i	−0.0890657	+	0.0384192i
$917$	23.7197	+	11.8395i	0.783293	+	0.390974i
$918$	−9.92194	−	7.25855i	−0.327473	−	0.239568i
$919$	1.88604	−	3.26672i	0.0622148	−	0.107759i	−0.833240	−	0.552911i	$-0.813517\pi$
$919$	1.88604	−	3.26672i	0.0622148	−	0.107759i	0.895455	+	0.445152i	$0.146850\pi$
$920$	−1.78339	−	0.208448i	−0.0587965	−	0.00687232i
$921$	10.3641	−	20.7808i	0.341510	−	0.684751i
$922$	0.167506	−	0.706765i	0.00551653	−	0.0232761i
$923$	4.89923	−	84.1165i	0.161260	−	2.76873i
$924$	−1.62006	−	0.276906i	−0.0532961	−	0.00910955i
$925$	−44.1335	+	10.4598i	−1.45110	+	0.343917i
$926$	23.5423	−	4.15114i	0.773647	−	0.136415i
$927$	−4.51111	−	3.31950i	−0.148164	−	0.109027i
$928$	−0.505671	+	2.86781i	−0.0165995	+	0.0941403i
$929$	−0.515777	−	8.85555i	−0.0169221	−	0.290541i	−0.996143	−	0.0877447i	$-0.972034\pi$
$929$	−0.515777	−	8.85555i	−0.0169221	−	0.290541i	0.979221	−	0.202797i	$-0.0650030\pi$
$930$	−35.9318	+	13.1916i	−1.17825	+	0.432568i
$931$	12.2486	+	50.5710i	0.401433	+	1.65740i
$932$	0.947326	−	0.705258i	0.0310307	−	0.0231015i
$933$	−1.22447	+	7.05924i	−0.0400874	+	0.231109i
$934$	20.7444	−	1.20822i	0.678778	−	0.0395343i
$935$	18.6797	+	3.29374i	0.610892	+	0.107717i
$936$	−15.4763	+	52.7623i	−0.505857	+	1.72459i
$937$	−38.8879	+	6.85699i	−1.27041	+	0.224008i	−0.767905	−	0.640564i	$-0.778701\pi$
$937$	−38.8879	+	6.85699i	−1.27041	+	0.224008i	−0.502509	+	0.864572i	$0.667589\pi$
$938$	−23.7962	−	22.3401i	−0.776973	−	0.729431i
$939$	0.152575	−	0.651851i	0.00497911	−	0.0212724i
$940$	−0.00472073	+	0.0810519i	−0.000153973	+	0.00264362i
$941$	−19.7507	−	4.68100i	−0.643854	−	0.152596i	−0.104298	−	0.994546i	$-0.533260\pi$
$941$	−19.7507	−	4.68100i	−0.643854	−	0.152596i	−0.539556	+	0.841950i	$0.681408\pi$
$942$	−22.1834	+	14.6789i	−0.722774	+	0.478265i
$943$	−0.120715	+	1.03278i	−0.00393102	+	0.0336321i
$944$	−7.43736	+	12.8819i	−0.242065	+	0.419270i
$945$	−47.2851	−	5.00904i	−1.53818	−	0.162944i
$946$	7.24352	+	12.5461i	0.235507	+	0.407910i
$947$	−17.0918	+	7.37270i	−0.555410	+	0.239580i	−0.655236	−	0.755425i	$-0.727431\pi$
$947$	−17.0918	+	7.37270i	−0.555410	+	0.239580i	0.0998259	+	0.995005i	$0.468171\pi$
$948$	−0.371660	−	0.0423918i	−0.0120710	−	0.00137682i
$949$	−49.1714	+	52.1186i	−1.59617	+	1.69184i
$950$	−67.1299	+	33.7139i	−2.17798	+	1.09382i
$951$	−11.4063	+	17.4482i	−0.369876	+	0.565795i
$952$	11.3455	−	3.42707i	0.367711	−	0.111072i
$953$	7.83985	+	9.34317i	0.253958	+	0.302655i	0.877928	−	0.478793i	$-0.158926\pi$
$953$	7.83985	+	9.34317i	0.253958	+	0.302655i	−0.623970	+	0.781448i	$0.714481\pi$
$954$	−38.7536	−	32.1520i	−1.25469	−	1.04096i
$955$	−1.45692	+	1.73628i	−0.0471447	+	0.0561848i
$956$	−0.0716940	−	0.109005i	−0.00231875	−	0.00352549i
$957$	−26.4963	−	9.56037i	−0.856504	−	0.309043i
$958$	−0.971784	−	8.31415i	−0.0313969	−	0.268618i
$959$	−32.4241	+	5.79953i	−1.04703	+	0.187276i
$960$	22.6617	+	38.9999i	0.731402	+	1.25872i
$961$	10.3848	+	5.21544i	0.334993	+	0.168240i
$962$	59.2545	−	21.5669i	1.91044	−	0.695344i
$963$	15.8871	−	24.4508i	0.511956	−	0.787917i
$964$	0.0314444	−	0.0863928i	0.00101276	−	0.00278253i
$965$	−33.9134	−	35.9461i	−1.09171	−	1.15715i
$966$	0.224667	+	1.23620i	0.00722854	+	0.0397740i
$967$	13.9068	+	9.14665i	0.447213	+	0.294137i	0.753069	−	0.657941i	$-0.228572\pi$
$967$	13.9068	+	9.14665i	0.447213	+	0.294137i	−0.305856	+	0.952078i	$0.598943\pi$
$968$	−0.839061	+	0.251198i	−0.0269684	+	0.00807382i
$969$	−4.89676	−	20.4076i	−0.157306	−	0.655586i
$970$	3.74366	−	5.02861i	0.120202	−	0.161459i
$971$	59.3834			1.90570			0.952852	−	0.303436i	$-0.0981340\pi$
$971$	59.3834			1.90570			0.952852	+	0.303436i	$0.0981340\pi$
$972$	−1.65309	−	0.169919i	−0.0530230	−	0.00545015i
$973$	4.63354	+	7.00734i	0.148544	+	0.224645i
$974$	−13.2055	−	9.83115i	−0.423132	−	0.315010i
$975$	18.7671	+	78.2132i	0.601028	+	2.50483i
$976$	−14.0589	+	4.20894i	−0.450013	+	0.134725i
$977$	−11.5984	+	17.6345i	−0.371066	+	0.564178i	−0.971959	−	0.235151i	$-0.924441\pi$
$977$	−11.5984	+	17.6345i	−0.371066	+	0.564178i	0.600893	+	0.799330i	$0.294812\pi$
$978$	−18.7827	−	8.04008i	−0.600604	−	0.257094i
$979$	−40.7914	+	38.4847i	−1.30370	+	1.22998i
$980$	−1.76194	+	1.88605i	−0.0562832	+	0.0602478i
$981$	1.67051	−	31.7252i	0.0533353	−	1.01291i
$982$	20.4841	−	7.45560i	0.653674	−	0.237918i
$983$	13.8569	+	6.95919i	0.441966	+	0.221964i	0.655844	−	0.754897i	$-0.272313\pi$
$983$	13.8569	+	6.95919i	0.441966	+	0.221964i	−0.213878	+	0.976860i	$0.568609\pi$
$984$	22.6536	−	13.1633i	0.722169	−	0.419631i
$985$	−63.0412	−	27.1933i	−2.00866	−	0.866451i
$986$	−11.3593	+	1.32771i	−0.361753	+	0.0422829i
$987$	−0.980623	+	0.237852i	−0.0312136	+	0.00757090i
$988$	4.41561	−	2.90419i	0.140479	−	0.0923946i
$989$	0.360247	−	0.429325i	0.0114552	−	0.0136517i
$990$	47.5144	−	17.5942i	1.51011	−	0.559180i
$991$	44.2397	−	37.1216i	1.40532	−	1.17920i	0.446644	−	0.894712i	$-0.352619\pi$
$991$	44.2397	−	37.1216i	1.40532	−	1.17920i	0.958678	−	0.284493i	$-0.0918252\pi$
$992$	0.760585	−	2.54053i	0.0241486	−	0.0806619i
$993$	−20.6995	−	13.5318i	−0.656877	−	0.429419i
$994$	−24.1535	+	42.0738i	−0.766102	+	1.33450i
$995$	−43.7639	−	41.2892i	−1.38741	−	1.30895i
$996$	−1.22444	−	0.139660i	−0.0387978	−	0.00442531i
$997$	−40.8872	+	17.6370i	−1.29491	+	0.558569i	−0.928309	−	0.371809i	$-0.878737\pi$
$997$	−40.8872	+	17.6370i	−1.29491	+	0.558569i	−0.366600	+	0.930379i	$0.619478\pi$
$998$	22.2224	−	12.8301i	0.703439	−	0.406130i
$999$	−17.1684	−	29.1709i	−0.543184	−	0.922925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bm.a.104.51	✓	1260
7.6	odd	2	inner	567.2.bm.a.104.52	yes	1260
81.74	odd	54	inner	567.2.bm.a.398.52	yes	1260
567.398	even	54	inner	567.2.bm.a.398.51	yes	1260

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.bm.a.104.51	✓	1260	1.1	even	1	trivial
567.2.bm.a.104.52	yes	1260	7.6	odd	2	inner
567.2.bm.a.398.51	yes	1260	567.398	even	54	inner
567.2.bm.a.398.52	yes	1260	81.74	odd	54	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bm (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16421 + 0.866725i) q^{2} +(-1.68424 + 0.404131i) q^{3} +(0.0305746 + 0.102126i) q^{4} +(2.88972 + 1.90060i) q^{5} +(-2.31109 - 0.989281i) q^{6} +(2.57593 + 0.603817i) q^{7} +(0.939906 - 2.58237i) q^{8} +(2.67336 - 1.36131i) q^{9} +O(q^{10})\)	\(q+(1.16421 + 0.866725i) q^{2} +(-1.68424 + 0.404131i) q^{3} +(0.0305746 + 0.102126i) q^{4} +(2.88972 + 1.90060i) q^{5} +(-2.31109 - 0.989281i) q^{6} +(2.57593 + 0.603817i) q^{7} +(0.939906 - 2.58237i) q^{8} +(2.67336 - 1.36131i) q^{9} +(1.71696 + 4.71730i) q^{10} +(1.50991 - 3.00647i) q^{11} +(-0.0927674 - 0.159649i) q^{12} +(-6.12402 - 2.64164i) q^{13} +(2.47559 + 2.93559i) q^{14} +(-5.63509 - 2.03325i) q^{15} +(3.51059 - 2.30895i) q^{16} +(1.24870 + 1.04778i) q^{17} +(4.29224 + 0.732208i) q^{18} +(4.77804 + 5.69425i) q^{19} +(-0.105749 + 0.353227i) q^{20} +(-4.58251 + 0.0240377i) q^{21} +(4.36364 - 2.19150i) q^{22} +(-0.137404 - 0.129634i) q^{23} +(-0.539415 + 4.72919i) q^{24} +(2.75782 + 6.39335i) q^{25} +(-4.84009 - 8.38328i) q^{26} +(-3.95244 + 3.37317i) q^{27} +(0.0170924 + 0.281531i) q^{28} +(-0.561187 + 4.80126i) q^{29} +(-4.79818 - 7.25121i) q^{30} +(1.01521 - 4.28351i) q^{31} +(0.601397 + 0.0350274i) q^{32} +(-1.32804 + 5.67384i) q^{33} +(0.545613 + 2.30212i) q^{34} +(6.29611 + 6.64068i) q^{35} +(0.220762 + 0.231398i) q^{36} +(-1.13116 + 6.41510i) q^{37} +(0.627314 + 10.7706i) q^{38} +(11.3819 + 1.97427i) q^{39} +(7.62413 - 5.67595i) q^{40} +(-3.28702 - 4.41524i) q^{41} +(-5.35586 - 3.94379i) q^{42} +(0.172505 + 2.96179i) q^{43} +(0.353205 + 0.0622795i) q^{44} +(10.3126 + 1.14717i) q^{45} +(-0.0476107 - 0.270014i) q^{46} +(0.214259 - 0.0507803i) q^{47} +(-4.97957 + 5.30758i) q^{48} +(6.27081 + 3.11078i) q^{49} +(-2.33058 + 9.83349i) q^{50} +(-2.52656 - 1.26008i) q^{51} +(0.0825418 - 0.706190i) q^{52} +(-10.0152 - 5.78225i) q^{53} +(-7.52509 + 0.501411i) q^{54} +(10.0773 - 5.81815i) q^{55} +(3.98041 - 6.08447i) q^{56} +(-10.3486 - 7.65954i) q^{57} +(-4.81471 + 5.10330i) q^{58} +(-3.16350 + 1.58877i) q^{59} +(0.0353574 - 0.637656i) q^{60} +(-3.34588 - 1.00169i) q^{61} +(4.89455 - 4.10701i) q^{62} +(7.70836 - 1.89242i) q^{63} +(-5.76780 - 4.83976i) q^{64} +(-12.6760 - 19.2729i) q^{65} +(-6.46378 + 5.45451i) q^{66} +(-8.44223 + 0.986755i) q^{67} +(-0.0688277 + 0.159560i) q^{68} +(0.283812 + 0.162806i) q^{69} +(1.57437 + 13.1882i) q^{70} +(4.32093 + 11.8716i) q^{71} +(-1.00271 - 8.18310i) q^{72} +(3.67448 - 10.0955i) q^{73} +(-6.87704 + 6.48815i) q^{74} +(-7.22859 - 9.65344i) q^{75} +(-0.435445 + 0.662062i) q^{76} +(5.70478 - 6.83275i) q^{77} +(11.5398 + 12.1635i) q^{78} +(1.20978 - 1.62501i) q^{79} +14.5330 q^{80} +(5.29367 - 7.27854i) q^{81} -7.98923i q^{82} +(3.98563 - 5.35362i) q^{83} +(-0.142563 - 0.467260i) q^{84} +(1.61698 + 5.40109i) q^{85} +(-2.36622 + 3.59767i) q^{86} +(-0.995163 - 8.31329i) q^{87} +(-6.34466 - 6.72495i) q^{88} +(-15.6638 - 5.70117i) q^{89} +(11.0118 + 10.2737i) q^{90} +(-14.1800 - 10.5025i) q^{91} +(0.00903797 - 0.0179961i) q^{92} +(0.0212373 + 7.62476i) q^{93} +(0.293456 + 0.126584i) q^{94} +(2.98472 + 25.5359i) q^{95} +(-1.02705 + 0.184048i) q^{96} +(-0.686236 - 1.04337i) q^{97} +(4.60437 + 9.05668i) q^{98} +(-0.0562237 - 10.0928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1260 q - 36 q^{2} - 36 q^{4} - 18 q^{7} - 36 q^{8} - 36 q^{9}+O(q^{10}) \) 1260 * q - 36 * q^2 - 36 * q^4 - 18 * q^7 - 36 * q^8 - 36 * q^9	\( 1260 q - 36 q^{2} - 36 q^{4} - 18 q^{7} - 36 q^{8} - 36 q^{9} - 36 q^{11} - 18 q^{14} - 36 q^{15} - 36 q^{16} - 36 q^{18} + 9 q^{21} - 36 q^{22} - 90 q^{23} - 36 q^{25} - 9 q^{28} - 36 q^{29} - 144 q^{30} - 36 q^{32} + 9 q^{35} - 36 q^{36} - 36 q^{37} - 36 q^{39} - 63 q^{42} - 36 q^{43} - 36 q^{44} - 36 q^{46} - 18 q^{49} - 36 q^{50} - 36 q^{51} - 54 q^{53} - 126 q^{56} - 36 q^{57} - 36 q^{58} - 36 q^{60} - 72 q^{63} - 36 q^{64} - 36 q^{67} + 36 q^{70} + 36 q^{71} + 180 q^{72} - 36 q^{74} - 162 q^{77} + 162 q^{78} - 90 q^{79} - 36 q^{81} - 297 q^{84} - 90 q^{85} + 108 q^{86} - 36 q^{88} - 18 q^{91} + 360 q^{92} + 36 q^{93} - 252 q^{95} - 261 q^{98} + 216 q^{99}+O(q^{100}) \) 1260 * q - 36 * q^2 - 36 * q^4 - 18 * q^7 - 36 * q^8 - 36 * q^9 - 36 * q^11 - 18 * q^14 - 36 * q^15 - 36 * q^16 - 36 * q^18 + 9 * q^21 - 36 * q^22 - 90 * q^23 - 36 * q^25 - 9 * q^28 - 36 * q^29 - 144 * q^30 - 36 * q^32 + 9 * q^35 - 36 * q^36 - 36 * q^37 - 36 * q^39 - 63 * q^42 - 36 * q^43 - 36 * q^44 - 36 * q^46 - 18 * q^49 - 36 * q^50 - 36 * q^51 - 54 * q^53 - 126 * q^56 - 36 * q^57 - 36 * q^58 - 36 * q^60 - 72 * q^63 - 36 * q^64 - 36 * q^67 + 36 * q^70 + 36 * q^71 + 180 * q^72 - 36 * q^74 - 162 * q^77 + 162 * q^78 - 90 * q^79 - 36 * q^81 - 297 * q^84 - 90 * q^85 + 108 * q^86 - 36 * q^88 - 18 * q^91 + 360 * q^92 + 36 * q^93 - 252 * q^95 - 261 * q^98 + 216 * q^99

Introduction

L-functions

Modular forms

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