LMFDB - Embedded newform 361.2.k.a.4.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(4,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(342)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.k (of order $171$, degree $108$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$3348$
Relative dimension:	$31$ over $\Q(\zeta_{171})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{171}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	361.4
Dual form			361.2.k.a.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.68057 - 0.0492526i) q^{2} +(2.14428 - 1.42921i) q^{3} +(5.18437 + 0.190579i) q^{4} +(0.225586 + 0.466865i) q^{5} +(-5.81829 + 3.72547i) q^{6} +(-1.02509 + 0.416356i) q^{7} +(-8.53377 - 0.470821i) q^{8} +(1.40091 - 3.36025i) q^{9} +(-0.581703 - 1.26257i) q^{10} +(1.44795 - 4.62936i) q^{11} +(11.3891 - 7.00087i) q^{12} +(2.03799 - 0.496214i) q^{13} +(2.76833 - 1.06558i) q^{14} +(1.15097 + 0.678683i) q^{15} +(12.5044 + 0.920578i) q^{16} +(-2.97857 - 4.74728i) q^{17} +(-3.92073 + 8.93837i) q^{18} +(-0.920943 + 4.26050i) q^{19} +(1.08054 + 2.46339i) q^{20} +(-1.60303 + 2.35785i) q^{21} +(-4.10934 + 12.3380i) q^{22} +(1.11928 - 0.553568i) q^{23} +(-18.9717 + 11.1869i) q^{24} +(2.94010 - 3.70669i) q^{25} +(-5.48742 + 1.22976i) q^{26} +(-0.316461 - 1.62011i) q^{27} +(-5.39380 + 1.96318i) q^{28} +(0.837660 + 0.270472i) q^{29} +(-3.05182 - 1.87594i) q^{30} +(5.25882 - 4.57991i) q^{31} +(-16.4522 - 1.51556i) q^{32} +(-3.51149 - 11.9961i) q^{33} +(7.75045 + 12.8721i) q^{34} +(-0.425628 - 0.384655i) q^{35} +(7.90322 - 17.1538i) q^{36} +(4.19270 + 4.55449i) q^{37} +(2.67849 - 11.3752i) q^{38} +(3.66084 - 3.97673i) q^{39} +(-1.70529 - 4.09033i) q^{40} +(2.49876 + 7.06659i) q^{41} +(4.41315 - 6.24143i) q^{42} +(-4.79986 - 6.78833i) q^{43} +(8.38898 - 23.7244i) q^{44} +(1.88481 - 0.103988i) q^{45} +(-3.02758 + 1.42875i) q^{46} +(-0.193087 - 0.0999521i) q^{47} +(28.1287 - 15.8974i) q^{48} +(-4.14002 + 4.02747i) q^{49} +(-8.06371 + 9.79123i) q^{50} +(-13.1717 - 5.92252i) q^{51} +(10.6603 - 2.18416i) q^{52} +(-0.320809 - 6.97986i) q^{53} +(0.768502 + 4.35839i) q^{54} +(2.48792 - 0.368319i) q^{55} +(8.94392 - 3.07045i) q^{56} +(4.11437 + 10.4519i) q^{57} +(-2.23208 - 0.766275i) q^{58} +(-4.33126 - 0.804810i) q^{59} +(5.83769 + 3.73789i) q^{60} +(1.58698 - 13.2262i) q^{61} +(-14.3222 + 12.0177i) q^{62} +(-0.0370005 + 4.02784i) q^{63} +(19.1023 + 2.11424i) q^{64} +(0.691407 + 0.839529i) q^{65} +(8.82194 + 32.3293i) q^{66} +(-1.93081 + 8.25934i) q^{67} +(-14.5373 - 25.1793i) q^{68} +(1.60890 - 2.78669i) q^{69} +(1.12198 + 1.05206i) q^{70} +(0.908473 + 7.57135i) q^{71} +(-13.5371 + 28.0160i) q^{72} +(-4.13787 + 7.81682i) q^{73} +(-11.0145 - 12.4151i) q^{74} +(1.00679 - 12.1502i) q^{75} +(-5.58647 + 21.9125i) q^{76} +(0.443179 + 5.34838i) q^{77} +(-10.0090 + 10.4796i) q^{78} +(12.8860 - 1.18704i) q^{79} +(2.39103 + 6.04555i) q^{80} +(4.69323 + 4.73654i) q^{81} +(-6.35005 - 19.0656i) q^{82} +(-14.3915 - 4.06952i) q^{83} +(-8.76004 + 11.9185i) q^{84} +(1.54442 - 2.46151i) q^{85} +(12.5320 + 18.4330i) q^{86} +(2.18274 - 0.617220i) q^{87} +(-14.5361 + 38.8242i) q^{88} +(3.43729 + 6.49336i) q^{89} +(-5.05748 + 0.185914i) q^{90} +(-1.88253 + 1.35720i) q^{91} +(5.90827 - 2.65659i) q^{92} +(4.73076 - 17.3366i) q^{93} +(0.512661 + 0.277438i) q^{94} +(-2.19683 + 0.531152i) q^{95} +(-37.4442 + 20.2638i) q^{96} +(-0.0159665 - 0.0682991i) q^{97} +(11.2960 - 10.5920i) q^{98} +(-13.5273 - 11.3508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) $ 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{171}\right)$

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 $

$2$	−2.68057	−	0.0492526i	−1.89545	−	0.0348269i	−0.941871	−	0.335975i	$-0.890934\pi$
$2$	−2.68057	−	0.0492526i	−1.89545	−	0.0348269i	−0.953577	+	0.301149i	$0.902630\pi$
$3$	2.14428	−	1.42921i	1.23800	−	0.825152i	0.248355	−	0.968669i	$-0.420110\pi$
$3$	2.14428	−	1.42921i	1.23800	−	0.825152i	0.989648	+	0.143517i	$0.0458412\pi$
$4$	5.18437	+	0.190579i	2.59219	+	0.0952895i
$5$	0.225586	+	0.466865i	0.100885	+	0.208789i	0.944769	−	0.327737i	$-0.106286\pi$
$5$	0.225586	+	0.466865i	0.100885	+	0.208789i	−0.843884	+	0.536526i	$0.819736\pi$
$6$	−5.81829	+	3.72547i	−2.37531	+	1.52092i
$7$	−1.02509	+	0.416356i	−0.387448	+	0.157368i	−0.561715	−	0.827331i	$-0.689858\pi$
$7$	−1.02509	+	0.416356i	−0.387448	+	0.157368i	0.174267	+	0.984698i	$0.444244\pi$
$8$	−8.53377	−	0.470821i	−3.01714	−	0.166460i
$9$	1.40091	−	3.36025i	0.466970	−	1.12008i
$10$	−0.581703	−	1.26257i	−0.183951	−	0.399261i
$11$	1.44795	−	4.62936i	0.436574	−	1.39580i	−0.432729	−	0.901524i	$-0.642449\pi$
$11$	1.44795	−	4.62936i	0.436574	−	1.39580i	0.869303	−	0.494280i	$-0.164568\pi$
$12$	11.3891	−	7.00087i	3.28776	−	2.02098i
$13$	2.03799	−	0.496214i	0.565238	−	0.137625i	0.0562775	−	0.998415i	$-0.482077\pi$
$13$	2.03799	−	0.496214i	0.565238	−	0.137625i	0.508960	+	0.860790i	$0.330030\pi$
$14$	2.76833	−	1.06558i	0.739868	−	0.284789i
$15$	1.15097	+	0.678683i	0.297178	+	0.175235i
$16$	12.5044	+	0.920578i	3.12611	+	0.230144i
$17$	−2.97857	−	4.74728i	−0.722410	−	1.15138i	−0.982583	−	0.185823i	$-0.940505\pi$
$17$	−2.97857	−	4.74728i	−0.722410	−	1.15138i	0.260174	−	0.965562i	$-0.416220\pi$
$18$	−3.92073	+	8.93837i	−0.924126	+	2.10679i
$19$	−0.920943	+	4.26050i	−0.211279	+	0.977426i
$19$	−0.920943	+	4.26050i	−0.211279	+	0.977426i
$20$	1.08054	+	2.46339i	0.241617	+	0.550832i
$21$	−1.60303	+	2.35785i	−0.349809	+	0.514525i
$22$	−4.10934	+	12.3380i	−0.876115	+	2.63047i
$23$	1.11928	−	0.553568i	0.233387	−	0.115427i	−0.322852	−	0.946449i	$-0.604642\pi$
$23$	1.11928	−	0.553568i	0.233387	−	0.115427i	0.556239	+	0.831023i	$0.312244\pi$
$24$	−18.9717	+	11.1869i	−3.87259	+	2.28352i
$25$	2.94010	−	3.70669i	0.588021	−	0.741338i
$26$	−5.48742	+	1.22976i	−1.07617	+	0.241176i
$27$	−0.316461	−	1.62011i	−0.0609030	−	0.311789i
$28$	−5.39380	+	1.96318i	−1.01933	+	0.371007i
$29$	0.837660	+	0.270472i	0.155550	+	0.0502253i	0.384016	−	0.923326i	$-0.374541\pi$
$29$	0.837660	+	0.270472i	0.155550	+	0.0502253i	−0.228467	+	0.973552i	$0.573371\pi$
$30$	−3.05182	−	1.87594i	−0.557183	−	0.342499i
$31$	5.25882	−	4.57991i	0.944512	−	0.822576i	−0.0397650	−	0.999209i	$-0.512661\pi$
$31$	5.25882	−	4.57991i	0.944512	−	0.822576i	0.984277	+	0.176633i	$0.0565206\pi$
$32$	−16.4522	−	1.51556i	−2.90837	−	0.267915i
$33$	−3.51149	−	11.9961i	−0.611272	−	2.08825i
$34$	7.75045	+	12.8721i	1.32919	+	2.20755i
$35$	−0.425628	−	0.384655i	−0.0719443	−	0.0650186i
$36$	7.90322	−	17.1538i	1.31720	−	2.85896i
$37$	4.19270	+	4.55449i	0.689276	+	0.748753i	0.977988	−	0.208663i	$-0.0669112\pi$
$37$	4.19270	+	4.55449i	0.689276	+	0.748753i	−0.288712	+	0.957416i	$0.593227\pi$
$38$	2.67849	−	11.3752i	0.434509	−	1.84530i
$39$	3.66084	−	3.97673i	0.586204	−	0.636787i
$40$	−1.70529	−	4.09033i	−0.269630	−	0.646738i
$41$	2.49876	+	7.06659i	0.390241	+	1.10362i	0.959561	+	0.281501i	$0.0908321\pi$
$41$	2.49876	+	7.06659i	0.390241	+	1.10362i	−0.569320	+	0.822116i	$0.692794\pi$
$42$	4.41315	−	6.24143i	0.680964	−	0.963073i
$43$	−4.79986	−	6.78833i	−0.731971	−	1.03521i	−0.997469	−	0.0710995i	$-0.977349\pi$
$43$	−4.79986	−	6.78833i	−0.731971	−	1.03521i	0.265498	−	0.964111i	$-0.414464\pi$
$44$	8.38898	−	23.7244i	1.26469	−	3.57658i
$45$	1.88481	−	0.103988i	0.280971	−	0.0155016i
$46$	−3.02758	+	1.42875i	−0.446392	+	0.210657i
$47$	−0.193087	−	0.0999521i	−0.0281647	−	0.0145795i	0.445570	−	0.895247i	$-0.353001\pi$
$47$	−0.193087	−	0.0999521i	−0.0281647	−	0.0145795i	−0.473735	+	0.880667i	$0.657095\pi$
$48$	28.1287	−	15.8974i	4.06003	−	2.29459i
$49$	−4.14002	+	4.02747i	−0.591431	+	0.575353i
$50$	−8.06371	+	9.79123i	−1.14038	+	1.38469i
$51$	−13.1717	−	5.92252i	−1.84441	−	0.829319i
$52$	10.6603	−	2.18416i	1.47831	−	0.302888i
$53$	−0.320809	−	6.97986i	−0.0440665	−	0.958758i	−0.898439	−	0.439097i	$-0.855298\pi$
$53$	−0.320809	−	6.97986i	−0.0440665	−	0.958758i	0.854373	−	0.519660i	$-0.173941\pi$
$54$	0.768502	+	4.35839i	0.104580	+	0.593102i
$55$	2.48792	−	0.368319i	0.335472	−	0.0496641i
$56$	8.94392	−	3.07045i	1.19518	−	0.410306i
$57$	4.11437	+	10.4519i	0.544961	+	1.38439i
$58$	−2.23208	−	0.766275i	−0.293087	−	0.100617i
$59$	−4.33126	−	0.804810i	−0.563882	−	0.104777i	−0.106927	−	0.994267i	$-0.534101\pi$
$59$	−4.33126	−	0.804810i	−0.563882	−	0.104777i	−0.456955	+	0.889490i	$0.651060\pi$
$60$	5.83769	+	3.73789i	0.753643	+	0.482560i
$61$	1.58698	−	13.2262i	0.203193	−	1.69344i	−0.416935	−	0.908936i	$-0.636896\pi$
$61$	1.58698	−	13.2262i	0.203193	−	1.69344i	0.620127	−	0.784501i	$-0.287081\pi$
$62$	−14.3222	+	12.0177i	−1.81892	+	1.52626i
$63$	−0.0370005	+	4.02784i	−0.00466163	+	0.507460i
$64$	19.1023	+	2.11424i	2.38778	+	0.264280i
$65$	0.691407	+	0.839529i	0.0857585	+	0.104131i
$66$	8.82194	+	32.3293i	1.08591	+	3.97946i
$67$	−1.93081	+	8.25934i	−0.235886	+	1.00904i	0.714909	+	0.699218i	$0.246468\pi$
$67$	−1.93081	+	8.25934i	−0.235886	+	1.00904i	−0.950795	+	0.309822i	$0.899731\pi$
$68$	−14.5373	−	25.1793i	−1.76290	−	3.05344i
$69$	1.60890	−	2.78669i	0.193688	−	0.335478i
$70$	1.12198	+	1.05206i	0.134102	+	0.125745i
$71$	0.908473	+	7.57135i	0.107816	+	0.898554i	0.939322	+	0.343038i	$0.111456\pi$
$71$	0.908473	+	7.57135i	0.107816	+	0.898554i	−0.831506	+	0.555516i	$0.812521\pi$
$72$	−13.5371	+	28.0160i	−1.59536	+	3.30172i
$73$	−4.13787	+	7.81682i	−0.484301	+	0.914889i	0.514065	+	0.857751i	$0.328139\pi$
$73$	−4.13787	+	7.81682i	−0.484301	+	0.914889i	−0.998366	+	0.0571381i	$0.981802\pi$
$74$	−11.0145	−	12.4151i	−1.28041	−	1.44323i
$75$	1.00679	−	12.1502i	0.116255	−	1.40298i
$76$	−5.58647	+	21.9125i	−0.640812	+	2.51354i
$77$	0.443179	+	5.34838i	0.0505050	+	0.609504i
$78$	−10.0090	+	10.4796i	−1.13330	+	1.18658i
$79$	12.8860	−	1.18704i	1.44979	−	0.133553i	0.662003	−	0.749501i	$-0.269707\pi$
$79$	12.8860	−	1.18704i	1.44979	−	0.133553i	0.787786	+	0.615949i	$0.211227\pi$
$80$	2.39103	+	6.04555i	0.267326	+	0.675913i
$81$	4.69323	+	4.73654i	0.521470	+	0.526283i
$82$	−6.35005	−	19.0656i	−0.701245	−	2.10544i
$83$	−14.3915	−	4.06952i	−1.57967	−	0.446688i	−0.634408	−	0.772999i	$-0.718756\pi$
$83$	−14.3915	−	4.06952i	−1.57967	−	0.446688i	−0.945263	+	0.326310i	$0.894195\pi$
$84$	−8.76004	+	11.9185i	−0.955799	+	1.30041i
$85$	1.54442	−	2.46151i	0.167516	−	0.266988i
$86$	12.5320	+	18.4330i	1.35136	+	1.98768i
$87$	2.18274	−	0.617220i	0.234014	−	0.0661729i
$88$	−14.5361	+	38.8242i	−1.54955	+	4.13867i
$89$	3.43729	+	6.49336i	0.364352	+	0.688294i	0.996228	−	0.0867753i	$-0.0276562\pi$
$89$	3.43729	+	6.49336i	0.364352	+	0.688294i	−0.631876	+	0.775070i	$0.717715\pi$
$90$	−5.05748	+	0.185914i	−0.533105	+	0.0195971i
$91$	−1.88253	+	1.35720i	−0.197342	+	0.142273i
$92$	5.90827	−	2.65659i	0.615980	−	0.276968i
$93$	4.73076	−	17.3366i	0.490557	−	1.79772i
$94$	0.512661	+	0.277438i	0.0528770	+	0.0286156i
$95$	−2.19683	+	0.531152i	−0.225390	+	0.0544950i
$96$	−37.4442	+	20.2638i	−3.82163	+	2.06817i
$97$	−0.0159665	−	0.0682991i	−0.00162115	−	0.00693472i	0.972930	−	0.231101i	$-0.0742329\pi$
$97$	−0.0159665	−	0.0682991i	−0.00162115	−	0.00693472i	−0.974551	+	0.224167i	$0.928034\pi$
$98$	11.2960	−	10.5920i	1.14106	−	1.06995i
$99$	−13.5273	−	11.3508i	−1.35955	−	1.14080i
$100$	15.9490	−	18.6565i	1.59490	−	1.86565i
$101$	11.8522	+	15.5197i	1.17934	+	1.54427i	0.777907	+	0.628380i	$0.216282\pi$
$101$	11.8522	+	15.5197i	1.17934	+	1.54427i	0.401429	+	0.915890i	$0.368514\pi$
$102$	35.0160	+	16.5245i	3.46711	+	1.63617i
$103$	−12.8535	−	5.22064i	−1.26649	−	0.514405i	−0.358555	−	0.933508i	$-0.616731\pi$
$103$	−12.8535	−	5.22064i	−1.26649	−	0.514405i	−0.907939	+	0.419103i	$0.862345\pi$
$104$	−17.6254	+	3.27505i	−1.72831	+	0.321145i
$105$	−1.46242	−	0.216500i	−0.142717	−	0.0211283i
$106$	0.516173	+	18.7258i	0.0501352	+	1.81881i
$107$	−2.06319	+	10.5624i	−0.199456	+	1.02110i	0.738475	+	0.674281i	$0.235546\pi$
$107$	−2.06319	+	10.5624i	−0.199456	+	1.02110i	−0.937931	+	0.346822i	$0.887261\pi$
$108$	−1.33189	−	8.45954i	−0.128162	−	0.814019i
$109$	0.0863441	−	1.87860i	0.00827027	−	0.179937i	−0.990751	−	0.135695i	$-0.956673\pi$
$109$	0.0863441	−	1.87860i	0.00827027	−	0.179937i	0.999021	−	0.0442414i	$-0.0140871\pi$
$110$	−6.68719	+	0.864767i	−0.637599	+	0.0824523i
$111$	15.4996	+	3.77388i	1.47116	+	0.358201i
$112$	−13.2015	+	4.26262i	−1.24742	+	0.402780i
$113$	−9.41889	+	7.33102i	−0.886055	+	0.689644i	−0.951314	−	0.308224i	$-0.900265\pi$
$113$	−9.41889	+	7.33102i	−0.886055	+	0.689644i	0.0652590	+	0.997868i	$0.479213\pi$
$114$	−10.5141	−	28.2198i	−0.984732	−	2.64302i
$115$	0.510936	+	0.397677i	0.0476450	+	0.0370836i
$116$	4.29119	+	1.56187i	0.398427	+	0.145016i
$117$	1.18764	−	7.54331i	0.109797	−	0.697379i
$118$	11.5706	+	2.37067i	1.06516	+	0.218238i
$119$	5.02987	+	3.62625i	0.461087	+	0.332418i
$120$	−9.50254	−	6.33363i	−0.867459	−	0.578178i
$121$	−10.2949	−	7.13829i	−0.935896	−	0.648936i
$122$	−4.90544	+	35.3755i	−0.444118	+	3.20275i
$123$	15.4577	+	11.5815i	1.39377	+	1.04427i
$124$	28.1365	−	22.7417i	2.52673	−	2.04227i
$125$	4.92357	+	1.10340i	0.440377	+	0.0986909i
$126$	0.297564	−	10.7951i	0.0265091	−	0.961701i
$127$	−2.36553	+	13.4156i	−0.209906	+	1.19044i	0.679623	+	0.733561i	$0.262143\pi$
$127$	−2.36553	+	13.4156i	−0.209906	+	1.19044i	−0.889530	+	0.456877i	$0.848968\pi$
$128$	−18.3299	−	2.37037i	−1.62015	−	0.209513i
$129$	−19.9942	−	7.69612i	−1.76039	−	0.677606i
$130$	−1.81202	−	2.28447i	−0.158924	−	0.200361i
$131$	1.43901	+	1.16310i	0.125727	+	0.101621i	0.689413	−	0.724369i	$-0.257869\pi$
$131$	1.43901	+	1.16310i	0.125727	+	0.101621i	−0.563686	+	0.825989i	$0.690617\pi$
$132$	−15.9187	−	62.8613i	−1.38554	−	5.47138i
$133$	−0.829835	−	4.75084i	−0.0719558	−	0.411950i
$134$	5.58246	−	22.0446i	0.482251	−	1.90437i
$135$	0.684982	−	0.513217i	0.0589539	−	0.0441707i
$136$	23.1833	+	41.9146i	1.98795	+	3.59415i
$137$	14.6295	−	4.42865i	1.24989	−	0.378365i	0.405497	−	0.914096i	$-0.367098\pi$
$137$	14.6295	−	4.42865i	1.24989	−	0.378365i	0.844389	+	0.535731i	$0.179964\pi$
$138$	−4.45001	+	7.39067i	−0.378810	+	0.629136i
$139$	12.0379	+	3.16636i	1.02104	+	0.268568i	0.726570	−	0.687092i	$-0.241113\pi$
$139$	12.0379	+	3.16636i	1.02104	+	0.268568i	0.294473	+	0.955660i	$0.404856\pi$
$140$	−2.13331	−	2.07531i	−0.180297	−	0.175396i
$141$	−0.556886	+	0.0616362i	−0.0468983	+	0.00519070i
$142$	−2.06231	−	20.3403i	−0.173066	−	1.70692i
$143$	0.653762	−	10.1531i	0.0546703	−	0.849045i
$144$	20.6109	−	40.7283i	1.71758	−	3.39403i
$145$	0.0626902	+	0.452089i	0.00520614	+	0.0375439i
$146$	11.4768	−	20.7497i	0.949831	−	1.71726i
$147$	−3.12129	+	14.5530i	−0.257439	+	1.20031i
$148$	20.8685	+	24.4112i	1.71538	+	2.00659i
$149$	0.138535	+	15.0808i	0.0113492	+	1.23546i	0.792010	+	0.610508i	$0.209035\pi$
$149$	0.138535	+	15.0808i	0.0113492	+	1.23546i	−0.780661	+	0.624955i	$0.785117\pi$
$150$	−3.29721	+	32.5199i	−0.269216	+	2.65524i
$151$	−14.1602	−	2.36292i	−1.15234	−	0.192292i	−0.442577	−	0.896730i	$-0.645936\pi$
$151$	−14.1602	−	2.36292i	−1.15234	−	0.192292i	−0.709765	+	0.704438i	$0.751199\pi$
$152$	9.86505	−	35.9245i	0.800161	−	2.91386i
$153$	−20.1247	+	3.35823i	−1.62699	+	0.271496i
$154$	−0.924551	−	14.3585i	−0.0745024	−	1.15704i
$155$	3.32452	+	1.42200i	0.267031	+	0.114218i
$156$	19.7370	−	19.9192i	1.58023	−	1.59481i
$157$	7.48057	+	3.69969i	0.597014	+	0.295268i	0.716521	−	0.697566i	$-0.245734\pi$
$157$	7.48057	+	3.69969i	0.597014	+	0.295268i	−0.119506	+	0.992833i	$0.538131\pi$
$158$	−34.6003	+	2.54728i	−2.75265	+	0.202650i
$159$	−10.6636	−	14.5083i	−0.845675	−	1.15058i
$160$	−3.00382	−	8.02285i	−0.237473	−	0.634262i
$161$	−0.916885	+	1.03348i	−0.0722607	+	0.0814494i
$162$	−12.3472	−	12.9278i	−0.970091	−	1.01570i
$163$	−0.631237	−	0.549745i	−0.0494423	−	0.0430594i	0.631678	−	0.775231i	$-0.282367\pi$
$163$	−0.631237	−	0.549745i	−0.0494423	−	0.0430594i	−0.681120	+	0.732172i	$0.738507\pi$
$164$	11.6077	+	37.1120i	0.906413	+	2.89796i
$165$	4.80841	−	4.34554i	0.374334	−	0.338299i
$166$	38.3769	+	11.6175i	2.97863	+	0.901689i
$167$	−2.66769	−	12.4381i	−0.206432	−	0.962489i	−0.954348	−	0.298696i	$-0.903448\pi$
$167$	−2.66769	−	12.4381i	−0.206432	−	0.962489i	0.747916	−	0.663793i	$-0.231055\pi$
$168$	14.7900	−	19.3666i	1.14107	−	1.49417i
$169$	−7.63771	+	3.95367i	−0.587516	+	0.304129i
$170$	−4.26115	+	6.52218i	−0.326815	+	0.500228i
$171$	13.0262	+	9.06317i	0.996137	+	0.693078i
$172$	−23.5905	−	36.1080i	−1.79876	−	2.75321i
$173$	8.83129	+	4.99115i	0.671430	+	0.379470i	0.789684	−	0.613513i	$-0.210244\pi$
$173$	8.83129	+	4.99115i	0.671430	+	0.379470i	−0.118254	+	0.992983i	$0.537730\pi$
$174$	−5.88138	+	1.54699i	−0.445866	+	0.117277i
$175$	−1.47057	+	5.02382i	−0.111165	+	0.379765i
$176$	22.3675	−	56.5546i	1.68601	−	4.26296i
$177$	−10.4377	+	4.46452i	−0.784545	+	0.335574i
$178$	−8.89408	−	17.5752i	−0.666639	−	1.31732i
$179$	17.2689	−	11.9740i	1.29073	−	0.894976i	0.292613	−	0.956231i	$-0.405475\pi$
$179$	17.2689	−	11.9740i	1.29073	−	0.894976i	0.998122	+	0.0612554i	$0.0195104\pi$
$180$	9.79136	−	0.179906i	0.729805	−	0.0134094i
$181$	−1.47809	+	0.0271584i	−0.109866	+	0.00201867i	−0.0732759	−	0.997312i	$-0.523345\pi$
$181$	−1.47809	+	0.0271584i	−0.109866	+	0.00201867i	−0.0365897	+	0.999330i	$0.511649\pi$
$182$	5.11309	−	3.54534i	0.379007	−	0.262798i
$183$	−15.5000	−	30.6288i	−1.14579	−	2.26414i
$184$	−9.81233	+	4.19704i	−0.723375	+	0.309410i
$185$	−1.18052	+	2.98485i	−0.0867935	+	0.219451i
$186$	−13.5350	+	46.2388i	−0.992435	+	3.39039i
$187$	−26.2897	+	6.91505i	−1.92249	+	0.505678i
$188$	−0.981988	−	0.554987i	−0.0716189	−	0.0404766i
$189$	0.998942	+	1.52900i	0.0726624	+	0.111218i
$190$	5.91492	−	1.31559i	0.429113	−	0.0954428i
$191$	−10.6796	+	16.3464i	−0.772750	+	1.18278i	0.206166	+	0.978517i	$0.433901\pi$
$191$	−10.6796	+	16.3464i	−0.772750	+	1.18278i	−0.978916	+	0.204265i	$0.934520\pi$
$192$	43.9823	−	22.7675i	3.17415	−	1.64311i
$193$	−5.11927	+	6.70338i	−0.368493	+	0.482520i	−0.941492	−	0.337037i	$-0.890575\pi$
$193$	−5.11927	+	6.70338i	−0.368493	+	0.482520i	0.572999	+	0.819556i	$0.305780\pi$
$194$	0.0394353	+	0.183867i	0.00283129	+	0.0132009i
$195$	2.68243	+	0.812026i	0.192093	+	0.0581504i
$196$	−22.2309	+	20.0909i	−1.58792	+	1.43506i
$197$	3.69173	+	11.8031i	0.263025	+	0.840938i	0.988306	+	0.152485i	$0.0487276\pi$
$197$	3.69173	+	11.8031i	0.263025	+	0.840938i	−0.725281	+	0.688453i	$0.758290\pi$
$198$	35.7019	+	31.0928i	2.53722	+	2.20967i
$199$	8.73032	+	9.14080i	0.618876	+	0.647974i	0.955959	−	0.293501i	$-0.0948203\pi$
$199$	8.73032	+	9.14080i	0.618876	+	0.647974i	−0.337083	+	0.941475i	$0.609440\pi$
$200$	−26.8354	+	30.2478i	−1.89755	+	2.13884i
$201$	7.66410	+	20.4699i	0.540584	+	1.44383i
$202$	−31.0062	−	42.1854i	−2.18159	−	2.96816i
$203$	−0.971290	+	0.0715065i	−0.0681712	+	0.00501877i
$204$	−67.1585	−	33.2148i	−4.70203	−	2.32550i
$205$	−2.73546	+	2.76071i	−0.191053	+	0.192816i
$206$	34.1976	+	14.6274i	2.38266	+	1.01914i
$207$	−0.292111	−	4.53656i	−0.0203031	−	0.315313i
$208$	25.9407	−	4.32874i	1.79867	−	0.300144i
$209$	18.3899	+	10.4324i	1.27206	+	0.721623i
$210$	3.90945	+	0.652372i	0.269778	+	0.0450179i
$211$	−0.959756	+	9.46592i	−0.0660724	+	0.651661i	0.906995	+	0.421141i	$0.138370\pi$
$211$	−0.959756	+	9.46592i	−0.0660724	+	0.651661i	−0.973068	+	0.230520i	$0.925957\pi$
$212$	−0.332975	−	36.2473i	−0.0228688	−	2.48948i
$213$	12.7690	+	14.9367i	0.874920	+	1.02345i
$214$	6.05074	−	28.2115i	0.413620	−	1.92850i
$215$	2.08646	−	3.77224i	0.142295	−	0.257264i
$216$	1.93783	+	13.9746i	0.131853	+	0.950852i
$217$	−3.48390	+	6.88437i	−0.236502	+	0.467341i
$218$	−0.323977	+	5.03145i	−0.0219425	+	0.340773i
$219$	2.29907	+	22.6753i	0.155357	+	1.53226i
$220$	12.9685	−	1.43536i	0.874337	−	0.0967716i
$221$	−8.42598	−	8.19692i	−0.566792	−	0.551384i
$222$	−41.3620	−	10.8795i	−2.77603	−	0.730187i
$223$	0.152995	−	0.254097i	0.0102453	−	0.0170156i	−0.851529	−	0.524308i	$-0.824324\pi$
$223$	0.152995	−	0.254097i	0.0102453	−	0.0170156i	0.861774	+	0.507292i	$0.169353\pi$
$224$	17.4960	−	5.29639i	1.16900	−	0.353880i
$225$	−8.33657	−	15.0722i	−0.555771	−	1.00481i
$226$	25.6091	−	19.1874i	1.70349	−	1.27633i
$227$	3.00312	−	11.8591i	0.199324	−	0.787114i	−0.786255	−	0.617902i	$-0.787983\pi$
$227$	3.00312	−	11.8591i	0.199324	−	0.787114i	0.985580	−	0.169212i	$-0.0541222\pi$
$228$	19.3385	+	54.9708i	1.28072	+	3.64053i
$229$	−3.31091	−	13.0745i	−0.218791	−	0.863986i	−0.977220	−	0.212230i	$-0.931927\pi$
$229$	−3.31091	−	13.0745i	−0.218791	−	0.863986i	0.758429	−	0.651756i	$-0.225967\pi$
$230$	−1.35001	−	1.09117i	−0.0890171	−	0.0719494i
$231$	8.59423	+	10.8350i	0.565459	+	0.712894i
$232$	−7.02105	−	2.70253i	−0.460955	−	0.177430i
$233$	15.1575	+	1.96012i	0.993003	+	0.128412i	0.607521	−	0.794303i	$-0.292164\pi$
$233$	15.1575	+	1.96012i	0.993003	+	0.128412i	0.385482	+	0.922716i	$0.374035\pi$
$234$	−3.55508	+	20.1619i	−0.232403	+	1.31802i
$235$	0.00310638	−	0.112694i	0.000202638	−	0.00735132i
$236$	−22.3015	−	4.99788i	−1.45170	−	0.325334i
$237$	25.9347	−	20.9621i	1.68464	−	1.36164i
$238$	−13.3043	−	9.96814i	−0.862389	−	0.646139i
$239$	0.421238	−	3.03775i	0.0272476	−	0.196496i	−0.972014	−	0.234924i	$-0.924516\pi$
$239$	0.421238	−	3.03775i	0.0272476	−	0.196496i	0.999261	+	0.0384284i	$0.0122351\pi$
$240$	13.7674	+	9.54610i	0.888681	+	0.616198i
$241$	3.03209	+	2.02094i	0.195314	+	0.130180i	0.648439	−	0.761266i	$-0.275422\pi$
$241$	3.03209	+	2.02094i	0.195314	+	0.130180i	−0.453125	+	0.891447i	$0.649691\pi$
$242$	27.2445	+	19.6417i	1.75134	+	1.26262i
$243$	21.6845	+	4.44289i	1.39106	+	0.285011i
$244$	10.7481	−	68.2669i	0.688080	−	4.37034i
$245$	−2.81422	−	1.02429i	−0.179794	−	0.0654395i
$246$	−40.8649	−	31.8064i	−2.60545	−	2.02790i
$247$	0.237246	+	9.13986i	0.0150956	+	0.581555i
$248$	−47.0339	+	36.6079i	−2.98665	+	2.32461i
$249$	−36.6756	+	11.8422i	−2.32422	+	0.750467i
$250$	−13.1436	−	3.20023i	−0.831275	−	0.202400i
$251$	−12.4801	+	1.61388i	−0.787735	+	0.101867i	−0.511569	−	0.859242i	$-0.670935\pi$
$251$	−12.4801	+	1.61388i	−0.787735	+	0.101867i	−0.276166	+	0.961110i	$0.589064\pi$
$252$	−0.959446	+	20.8747i	−0.0604394	+	1.31498i
$253$	−0.941997	−	5.98310i	−0.0592229	−	0.376154i
$254$	7.00170	−	35.8448i	0.439326	−	2.24910i
$255$	−0.206335	−	7.48546i	−0.0129212	−	0.468758i
$256$	10.9945	+	1.62766i	0.687157	+	0.101728i
$257$	−15.9899	+	2.97116i	−0.997425	+	0.185336i	−0.656152	−	0.754628i	$-0.727817\pi$
$257$	−15.9899	+	2.97116i	−0.997425	+	0.185336i	−0.341273	+	0.939964i	$0.610858\pi$
$258$	53.2167	+	21.6148i	3.31313	+	1.34568i
$259$	−6.19419	−	2.92311i	−0.384888	−	0.181633i
$260$	3.42451	+	4.48420i	0.212379	+	0.278098i
$261$	2.08234	−	2.43584i	0.128893	−	0.150775i
$262$	−3.80009	−	3.18865i	−0.234770	−	0.196996i
$263$	6.30188	−	5.90915i	0.388591	−	0.364374i	−0.465007	−	0.885307i	$-0.653948\pi$
$263$	6.30188	−	5.90915i	0.388591	−	0.364374i	0.853597	+	0.520933i	$0.174416\pi$
$264$	24.3182	+	104.025i	1.49668	+	6.40230i
$265$	3.18629	−	1.72433i	0.195732	−	0.105925i
$266$	1.99044	+	12.7758i	0.122042	+	0.783336i
$267$	16.6509	+	9.01100i	1.01902	+	0.551464i
$268$	−11.5841	+	42.4515i	−0.707611	+	2.59314i
$269$	−4.76553	+	2.14277i	−0.290560	+	0.130647i	−0.550134	−	0.835076i	$-0.685423\pi$
$269$	−4.76553	+	2.14277i	−0.290560	+	0.130647i	0.259575	+	0.965723i	$0.416418\pi$
$270$	−1.86142	+	1.34198i	−0.113282	+	0.0816701i
$271$	−14.0321	+	0.515823i	−0.852386	+	0.0313340i	−0.459420	−	0.888219i	$-0.651943\pi$
$271$	−14.0321	+	0.515823i	−0.852386	+	0.0313340i	−0.392966	+	0.919553i	$0.628551\pi$
$272$	−32.8751	−	62.1040i	−1.99335	−	3.76561i
$273$	−2.09696	+	5.60073i	−0.126914	+	0.338971i
$274$	−39.4336	+	11.1508i	−2.38227	+	0.673642i
$275$	−12.9025	−	18.9779i	−0.778048	−	1.14441i
$276$	8.87220	−	14.1406i	0.534044	−	0.851165i
$277$	−3.37005	+	4.58512i	−0.202487	+	0.275493i	−0.895147	−	0.445771i	$-0.852930\pi$
$277$	−3.37005	+	4.58512i	−0.202487	+	0.275493i	0.692660	+	0.721264i	$0.256438\pi$
$278$	−32.1125	−	9.08056i	−1.92598	−	0.544616i
$279$	−8.02250	−	24.0870i	−0.480294	−	1.44205i
$280$	3.45111	+	3.48296i	0.206243	+	0.208146i
$281$	−2.33894	−	5.91383i	−0.139529	−	0.352790i	0.843264	−	0.537500i	$-0.180631\pi$
$281$	−2.33894	−	5.91383i	−0.139529	−	0.352790i	−0.982793	+	0.184711i	$0.940865\pi$
$282$	1.49581	−	0.137792i	0.0890740	−	0.00820538i
$283$	17.3424	−	18.1578i	1.03090	−	1.07937i	0.0340987	−	0.999418i	$-0.489144\pi$
$283$	17.3424	−	18.1578i	1.03090	−	1.07937i	0.996799	−	0.0799496i	$-0.0254760\pi$
$284$	3.26692	+	39.4258i	0.193856	+	2.33949i
$285$	−3.95150	+	4.27866i	−0.234067	+	0.253446i
$286$	−2.25252	+	27.1839i	−0.133194	+	1.60742i
$287$	−5.50367	−	6.20353i	−0.324872	−	0.366183i
$288$	−28.1407	+	53.1603i	−1.65821	+	3.13250i
$289$	−6.26867	+	12.9735i	−0.368745	+	0.763144i
$290$	−0.145779	−	1.21494i	−0.00856042	−	0.0713439i
$291$	−0.131850	−	0.123633i	−0.00772919	−	0.00724751i
$292$	−22.9420	+	39.7367i	−1.34258	+	2.32541i
$293$	8.69847	+	15.0662i	0.508170	+	0.880176i	0.999955	+	0.00945947i	$0.00301109\pi$
$293$	8.69847	+	15.0662i	0.508170	+	0.880176i	−0.491785	+	0.870716i	$0.663656\pi$
$294$	9.08359	−	38.8565i	0.529766	−	2.26616i
$295$	−0.601333	−	2.20367i	−0.0350110	−	0.128303i
$296$	−33.6352	−	40.8410i	−1.95501	−	2.37383i
$297$	−7.95827	−	0.880822i	−0.461786	−	0.0511104i
$298$	0.371415	−	40.4318i	0.0215155	−	2.34215i
$299$	2.00640	−	1.68357i	0.116033	−	0.0973634i
$300$	7.53517	−	62.7993i	0.435043	−	3.62572i
$301$	7.74665	+	4.96021i	0.446510	+	0.285902i
$302$	37.8411	+	7.03140i	2.17751	+	0.404612i
$303$	47.5953	+	16.3395i	2.73428	+	0.938679i
$304$	−15.4380	+	52.4273i	−0.885429	+	3.00691i
$305$	6.53284	−	2.24273i	0.374069	−	0.128418i
$306$	54.1111	−	8.01076i	3.09333	−	0.457944i
$307$	−2.66284	−	15.1017i	−0.151977	−	0.861902i	−0.961498	−	0.274812i	$-0.911385\pi$
$307$	−2.66284	−	15.1017i	−0.151977	−	0.861902i	0.809522	−	0.587090i	$-0.199727\pi$
$308$	1.27832	+	27.8124i	0.0728388	+	1.58476i
$309$	−35.0229	+	7.17577i	−1.99239	+	0.408215i
$310$	−8.84155	−	3.97550i	−0.502166	−	0.225793i
$311$	11.8096	−	14.3396i	0.669663	−	0.813127i	−0.321340	−	0.946964i	$-0.604133\pi$
$311$	11.8096	−	14.3396i	0.669663	−	0.813127i	0.991003	+	0.133837i	$0.0427299\pi$
$312$	−33.1131	+	32.2129i	−1.87466	+	1.82370i
$313$	14.3414	−	8.10530i	0.810625	−	0.458138i	−0.0301350	−	0.999546i	$-0.509594\pi$
$313$	14.3414	−	8.10530i	0.810625	−	0.458138i	0.840760	+	0.541407i	$0.182108\pi$
$314$	−19.8700	−	10.2857i	−1.12133	−	0.580457i
$315$	−1.88880	+	0.891348i	−0.106422	+	0.0502218i
$316$	67.0321	−	3.69826i	3.77085	−	0.208043i
$317$	−11.8154	+	33.4143i	−0.663617	+	1.87673i	−0.240548	+	0.970637i	$0.577327\pi$
$317$	−11.8154	+	33.4143i	−0.663617	+	1.87673i	−0.423068	+	0.906098i	$0.639047\pi$
$318$	27.8698	+	39.4157i	1.56286	+	2.21032i
$319$	2.46500	−	3.48620i	0.138014	−	0.195190i
$320$	3.32213	+	9.39513i	0.185713	+	0.525203i
$321$	10.6717	+	25.5974i	0.595638	+	1.42871i
$322$	2.50868	−	2.72515i	0.139803	−	0.151867i
$323$	22.9689	−	8.31823i	1.27802	−	0.462839i
$324$	23.4288	+	25.4504i	1.30160	+	1.41391i
$325$	4.15260	−	9.01313i	0.230345	−	0.499958i
$326$	1.66500	+	1.50472i	0.0922157	+	0.0833387i
$327$	−2.49975	−	4.15164i	−0.138237	−	0.229586i
$328$	−17.9967	−	61.4812i	−0.993704	−	3.39473i
$329$	0.239548	+	0.0220668i	0.0132067	+	0.00121658i
$330$	−13.1033	+	11.4117i	−0.721313	+	0.628192i
$331$	−15.1694	−	9.32457i	−0.833783	−	0.512525i	0.0397953	−	0.999208i	$-0.487329\pi$
$331$	−15.1694	−	9.32457i	−0.833783	−	0.512525i	−0.873579	+	0.486683i	$0.838207\pi$
$332$	−73.8352	−	23.8406i	−4.05223	−	1.30842i
$333$	21.1778	−	7.70809i	1.16054	−	0.422400i
$334$	6.53832	+	33.4726i	0.357761	+	1.83154i
$335$	−4.29156	+	0.961762i	−0.234473	+	0.0525467i
$336$	−22.2155	+	28.0079i	−1.21196	+	1.52795i
$337$	3.29002	−	1.94001i	0.179219	−	0.105679i	−0.415569	−	0.909562i	$-0.636417\pi$
$337$	3.29002	−	1.94001i	0.179219	−	0.105679i	0.594788	+	0.803883i	$0.297236\pi$
$338$	20.6681	−	10.2219i	1.12420	−	0.555999i
$339$	−9.71924	+	29.1813i	−0.527877	+	1.58491i
$340$	8.47594	−	12.4670i	0.459673	−	0.676121i
$341$	−13.5875	−	30.9765i	−0.735806	−	1.67747i
$342$	−34.4712	−	24.9360i	−1.86399	−	1.34839i
$343$	5.67814	−	12.9449i	0.306591	−	0.698956i
$344$	37.7648	+	60.1900i	2.03614	+	3.24522i
$345$	1.66395	+	0.122500i	0.0895842	+	0.00659520i
$346$	−23.4270	−	13.8141i	−1.25945	−	0.742650i
$347$	9.23817	−	3.55594i	0.495931	−	0.190893i	−0.0983478	−	0.995152i	$-0.531356\pi$
$347$	9.23817	−	3.55594i	0.495931	−	0.190893i	0.594279	+	0.804259i	$0.297438\pi$
$348$	11.4338	−	2.78391i	0.612914	−	0.149233i
$349$	−5.68570	+	3.49499i	−0.304349	+	0.187083i	−0.667425	−	0.744677i	$-0.732604\pi$
$349$	−5.68570	+	3.49499i	−0.304349	+	0.187083i	0.363076	+	0.931759i	$0.381726\pi$
$350$	4.18941	−	13.3943i	0.223933	−	0.715954i
$351$	−1.44887	−	3.14473i	−0.0773347	−	0.167853i
$352$	−30.8380	+	73.9687i	−1.64367	+	3.94255i
$353$	−31.5556	−	1.74097i	−1.67953	−	0.0926624i	−0.809966	−	0.586477i	$-0.800514\pi$
$353$	−31.5556	−	1.74097i	−1.67953	−	0.0926624i	−0.869567	+	0.493815i	$0.835602\pi$
$354$	28.1988	−	11.4534i	1.49875	−	0.608740i
$355$	−3.32986	+	2.13212i	−0.176731	+	0.113161i
$356$	16.5827	+	34.3190i	0.878881	+	1.81891i
$357$	15.9681	+	0.586993i	0.845122	+	0.0310670i
$358$	−46.8801	+	31.2465i	−2.47769	+	1.65143i
$359$	−3.34227	−	0.0614107i	−0.176398	−	0.00324113i	−0.0698998	−	0.997554i	$-0.522268\pi$
$359$	−3.34227	−	0.0614107i	−0.176398	−	0.00324113i	−0.106498	+	0.994313i	$0.533964\pi$
$360$	−16.1335			−0.850309
$361$	−17.3037	−	7.84735i	−0.910723	−	0.413019i
$362$	3.96346			0.208315
$363$	−32.2772	−	0.593059i	−1.69411	−	0.0311275i
$364$	−10.0184	+	6.67743i	−0.525105	+	0.349993i
$365$	−4.58285	−	0.168467i	−0.239877	−	0.00881796i
$366$	40.0402	+	82.8660i	2.09293	+	4.33147i
$367$	11.3002	−	7.23555i	0.589865	−	0.377693i	−0.210153	−	0.977668i	$-0.567396\pi$
$367$	11.3002	−	7.23555i	0.589865	−	0.377693i	0.800018	+	0.599976i	$0.204823\pi$
$368$	14.5056	−	5.89166i	0.756156	−	0.307124i
$369$	27.2460	+	1.50321i	1.41837	+	0.0782537i
$370$	3.31147	−	7.94296i	0.172155	−	0.412935i
$371$	3.23497	+	7.02142i	0.167951	+	0.364534i
$372$	27.8300	−	88.9775i	1.44292	−	4.61327i
$373$	−18.3499	+	11.2796i	−0.950122	+	0.584038i	−0.909754	−	0.415147i	$-0.863730\pi$
$373$	−18.3499	+	11.2796i	−0.950122	+	0.584038i	−0.0403679	+	0.999185i	$0.512853\pi$
$374$	70.8119	−	17.2414i	3.66160	−	0.891532i
$375$	12.1345	−	4.67079i	0.626623	−	0.241199i
$376$	1.60071	+	0.943878i	0.0825501	+	0.0486768i
$377$	1.84136	+	0.135561i	0.0948347	+	0.00698174i
$378$	−2.60243	−	4.14778i	−0.133854	−	0.213339i
$379$	10.2701	−	23.4135i	0.527541	−	1.20267i	−0.426907	−	0.904295i	$-0.640397\pi$
$379$	10.2701	−	23.4135i	0.527541	−	1.20267i	0.954448	−	0.298377i	$-0.0964451\pi$
$380$	−11.4904	+	2.33502i	−0.589446	+	0.119784i
$381$	14.1012	+	32.1476i	0.722428	+	1.64697i
$382$	29.4325	−	43.2916i	1.50590	−	2.21499i
$383$	9.23735	−	27.7345i	0.472006	−	1.41716i	−0.394914	−	0.918718i	$-0.629226\pi$
$383$	9.23735	−	27.7345i	0.472006	−	1.41716i	0.866920	−	0.498447i	$-0.166096\pi$
$384$	−42.6923	+	21.1145i	−2.17863	+	1.07750i
$385$	−2.39700	+	1.41342i	−0.122162	+	0.0720347i
$386$	14.0527	−	17.7167i	0.715264	−	0.901758i
$387$	−29.5346	+	6.61887i	−1.50133	+	0.336456i
$388$	−0.0697597	−	0.357131i	−0.00354151	−	0.0181306i
$389$	1.35047	−	0.491531i	0.0684716	−	0.0249216i	−0.307557	−	0.951530i	$-0.599512\pi$
$389$	1.35047	−	0.491531i	0.0684716	−	0.0249216i	0.376029	+	0.926608i	$0.377289\pi$
$390$	−7.15045	−	2.30881i	−0.362077	−	0.116911i
$391$	−5.96181	−	3.66471i	−0.301501	−	0.185332i
$392$	37.2262	−	32.4203i	1.88021	−	1.63747i
$393$	4.74797	+	0.437376i	0.239503	+	0.0220627i
$394$	−9.31461	−	31.8209i	−0.469263	−	1.60312i
$395$	3.46109	+	5.74825i	0.174146	+	0.289226i
$396$	−67.9675	−	61.4247i	−3.41550	−	3.08671i
$397$	14.6753	−	31.8525i	0.736534	−	1.59863i	−0.0630027	−	0.998013i	$-0.520068\pi$
$397$	14.6753	−	31.8525i	0.736534	−	1.59863i	0.799536	−	0.600618i	$-0.205079\pi$
$398$	−22.9520	−	24.9325i	−1.15048	−	1.24976i
$399$	−8.56933	−	9.00114i	−0.429003	−	0.450621i
$400$	40.1766	−	43.6434i	2.00883	−	2.18217i
$401$	5.12623	+	12.2959i	0.255992	+	0.614027i	0.998438	−	0.0558794i	$-0.0177962\pi$
$401$	5.12623	+	12.2959i	0.255992	+	0.614027i	−0.742446	+	0.669906i	$0.766334\pi$
$402$	−19.5359	−	55.2484i	−0.974364	−	2.75554i
$403$	8.44482	−	11.9433i	0.420666	−	0.594939i
$404$	58.4883	+	82.7188i	2.90990	+	4.11541i
$405$	−1.15260	+	3.25960i	−0.0572732	+	0.161971i
$406$	2.60713	−	0.143839i	0.129390	−	0.00713863i
$407$	27.1552	−	12.8148i	1.34603	−	0.635208i
$408$	109.616	+	56.7430i	5.42681	+	2.80920i
$409$	−4.72307	+	2.66932i	−0.233541	+	0.131989i	−0.604348	−	0.796720i	$-0.706566\pi$
$409$	−4.72307	+	2.66932i	−0.233541	+	0.131989i	0.370807	+	0.928710i	$0.379081\pi$
$410$	7.46857	−	7.26553i	0.368846	−	0.358819i
$411$	25.0404	−	30.4049i	1.23515	−	1.49976i
$412$	−65.6424	−	29.5154i	−3.23397	−	1.45412i
$413$	4.77503	−	0.978344i	0.234964	−	0.0481411i
$414$	0.559586	+	12.1750i	0.0275021	+	0.598366i
$415$	−1.34659	−	7.63691i	−0.0661017	−	0.374881i
$416$	−34.2815	+	5.07513i	−1.68079	+	0.248828i
$417$	30.3381	−	10.4151i	1.48566	−	0.510029i
$418$	−48.7816	−	28.8704i	−2.38599	−	1.41210i
$419$	−17.1898	−	5.90128i	−0.839778	−	0.288296i	−0.128941	−	0.991652i	$-0.541158\pi$
$419$	−17.1898	−	5.90128i	−0.839778	−	0.288296i	−0.710838	+	0.703356i	$0.751684\pi$
$420$	−7.54046	−	1.40112i	−0.367937	−	0.0683679i
$421$	−15.6093	−	9.99467i	−0.760749	−	0.487110i	0.100723	−	0.994914i	$-0.467884\pi$
$421$	−15.6093	−	9.99467i	−0.760749	−	0.487110i	−0.861473	+	0.507804i	$0.830457\pi$
$422$	3.03891	−	25.3268i	0.147932	−	1.23289i
$423$	−0.606362	+	0.508798i	−0.0294823	+	0.0247386i
$424$	−0.548560	+	59.7156i	−0.0266404	+	2.90005i
$425$	−26.3540	−	2.91686i	−1.27836	−	0.141489i
$426$	−33.4926	−	40.6678i	−1.62272	−	1.97036i
$427$	3.87999	+	14.2188i	0.187766	+	0.688095i
$428$	−12.7093	+	54.3660i	−0.614327	+	2.62788i
$429$	−13.1090	−	22.7055i	−0.632909	−	1.09623i
$430$	−5.77868	+	10.0090i	−0.278673	+	0.482676i
$431$	11.0905	+	10.3993i	0.534208	+	0.500917i	0.903612	−	0.428352i	$-0.140906\pi$
$431$	11.0905	+	10.3993i	0.534208	+	0.500917i	−0.369404	+	0.929269i	$0.620438\pi$
$432$	−2.46574	−	20.5498i	−0.118633	−	0.988704i
$433$	−15.2892	+	31.6422i	−0.734754	+	1.52063i	0.114953	+	0.993371i	$0.463328\pi$
$433$	−15.2892	+	31.6422i	−0.734754	+	1.52063i	−0.849707	+	0.527254i	$0.823221\pi$
$434$	9.67789	−	18.2824i	0.464554	−	0.877584i
$435$	0.780553	+	0.879809i	0.0374247	+	0.0421836i
$436$	0.805661	−	9.72288i	0.0385842	−	0.465642i
$437$	1.32768	+	5.27851i	0.0635116	+	0.252505i
$438$	−5.04599	−	60.8960i	−0.241107	−	2.90972i
$439$	12.4259	−	13.0102i	0.593058	−	0.620942i	−0.356590	−	0.934261i	$-0.616061\pi$
$439$	12.4259	−	13.0102i	0.593058	−	0.620942i	0.949648	+	0.313319i	$0.101441\pi$
$440$	−21.4048	+	1.97178i	−1.02043	+	0.0940010i
$441$	7.73351	+	19.5536i	0.368262	+	0.931124i
$442$	22.1827	+	22.3874i	1.05512	+	1.06486i
$443$	−8.11057	−	24.3514i	−0.385345	−	1.15697i	−0.944670	−	0.328021i	$-0.893618\pi$
$443$	−8.11057	−	24.3514i	−0.385345	−	1.15697i	0.559326	−	0.828948i	$-0.311060\pi$
$444$	79.6366	+	22.5191i	3.77939	+	1.06871i
$445$	−2.25612	+	3.06956i	−0.106950	+	0.145511i
$446$	−0.422628	+	0.673590i	−0.0200120	+	0.0318954i
$447$	21.8505	+	32.1394i	1.03350	+	1.52014i
$448$	−20.4618	+	5.78606i	−0.966731	+	0.273365i
$449$	1.70239	−	4.54687i	0.0803406	−	0.214580i	−0.890175	−	0.455619i	$-0.849418\pi$
$449$	1.70239	−	4.54687i	0.0803406	−	0.214580i	0.970515	+	0.241039i	$0.0774881\pi$
$450$	21.6044	+	40.8127i	1.01844	+	1.92393i
$451$	36.3319	−	1.33557i	1.71080	−	0.0628896i
$452$	−50.2282	+	36.2117i	−2.36253	+	1.70325i
$453$	−33.7406	+	15.1711i	−1.58527	+	0.712800i
$454$	−8.63416	+	31.6411i	−0.405221	+	1.48499i
$455$	−1.05830	−	0.572723i	−0.0496138	−	0.0268496i
$456$	−30.1901	−	91.1316i	−1.41378	−	4.26763i
$457$	−13.7263	+	7.42831i	−0.642090	+	0.347482i	−0.764148	−	0.645041i	$-0.776840\pi$
$457$	−13.7263	+	7.42831i	−0.642090	+	0.347482i	0.122058	+	0.992523i	$0.461051\pi$
$458$	8.23116	+	35.2101i	0.384617	+	1.64526i
$459$	−6.74849	+	6.32793i	−0.314993	+	0.295363i
$460$	2.57309	+	2.15908i	0.119971	+	0.100668i
$461$	−8.62102	+	10.0845i	−0.401521	+	0.469684i	−0.923680	−	0.383164i	$-0.874834\pi$
$461$	−8.62102	+	10.0845i	−0.401521	+	0.469684i	0.522159	+	0.852848i	$0.325127\pi$
$462$	−22.5038	−	29.4674i	−1.04697	−	1.37095i
$463$	10.2981	+	4.85978i	0.478592	+	0.225853i	0.650861	−	0.759197i	$-0.274408\pi$
$463$	10.2981	+	4.85978i	0.478592	+	0.225853i	−0.172269	+	0.985050i	$0.555110\pi$
$464$	10.2255	+	4.15323i	0.474705	+	0.192809i
$465$	9.16103	−	1.70225i	0.424833	−	0.0789399i
$466$	−40.5342	−	6.00080i	−1.87771	−	0.277982i
$467$	1.02227	+	37.0862i	0.0473052	+	1.71614i	0.536441	+	0.843938i	$0.319768\pi$
$467$	1.02227	+	37.0862i	0.0473052	+	1.71614i	−0.489136	+	0.872207i	$0.662688\pi$
$468$	7.59477	−	38.8810i	0.351068	−	1.79727i
$469$	−1.45957	−	9.27048i	−0.0673968	−	0.428071i
$470$	−0.0138773	+	0.301930i	−0.000640113	+	0.0139270i
$471$	21.3281	−	2.75808i	0.982746	−	0.127086i
$472$	36.5831	+	8.90731i	1.68387	+	0.409992i
$473$	−38.3756	+	12.3911i	−1.76451	+	0.569743i
$474$	−70.5522	+	54.9130i	−3.24057	+	2.52224i
$475$	13.0847	+	15.9400i	0.600367	+	0.731376i
$476$	25.3856	+	19.7584i	1.16355	+	0.905625i
$477$	−23.9035	−	8.70016i	−1.09447	−	0.398353i
$478$	−1.27877	+	8.12215i	−0.0584898	+	0.371498i
$479$	−32.1614	−	6.58947i	−1.46949	−	0.301080i	−0.601985	−	0.798508i	$-0.705623\pi$
$479$	−32.1614	−	6.58947i	−1.46949	−	0.301080i	−0.867506	+	0.497427i	$0.834278\pi$
$480$	−17.9073	−	12.9102i	−0.817355	−	0.589267i
$481$	10.8047	+	7.20153i	0.492652	+	0.328362i
$482$	−8.02818	−	5.56662i	−0.365674	−	0.253553i
$483$	−0.489010	+	3.52649i	−0.0222507	+	0.160461i
$484$	−52.0119	−	38.9695i	−2.36418	−	1.77134i
$485$	0.0282847	−	0.0228615i	0.00128434	−	0.00103809i
$486$	−57.9080	−	12.9775i	−2.62676	−	0.588670i
$487$	−0.411480	+	14.9277i	−0.0186459	+	0.676440i	0.931341	+	0.364149i	$0.118640\pi$
$487$	−0.411480	+	14.9277i	−0.0186459	+	0.676440i	−0.949987	+	0.312291i	$0.898904\pi$
$488$	−19.7701	+	112.122i	−0.894952	+	5.07552i
$489$	−2.13925	−	0.276641i	−0.0967402	−	0.0125101i
$490$	7.49325	+	2.88429i	0.338510	+	0.130299i
$491$	−4.81928	−	6.07583i	−0.217491	−	0.274199i	0.662631	−	0.748946i	$-0.269440\pi$
$491$	−4.81928	−	6.07583i	−0.217491	−	0.274199i	−0.880122	+	0.474748i	$0.842539\pi$
$492$	77.9310	+	62.9889i	3.51340	+	2.83976i
$493$	−1.21102	−	4.78223i	−0.0545418	−	0.215381i
$494$	−0.185792	−	24.5117i	−0.00835917	−	1.10283i
$495$	2.24771	−	8.87602i	0.101027	−	0.398948i
$496$	69.9747	−	52.4280i	3.14196	−	2.35409i
$497$	−4.08365	−	7.38308i	−0.183177	−	0.331176i
$498$	98.8947	−	29.9374i	4.43158	−	1.34153i
$499$	−13.9631	+	23.1902i	−0.625075	+	1.03814i	0.368999	+	0.929430i	$0.379700\pi$
$499$	−13.9631	+	23.1902i	−0.625075	+	1.03814i	−0.994074	+	0.108708i	$0.965329\pi$
$500$	25.3153	+	6.65875i	1.13214	+	0.297788i
$501$	−23.4969	−	22.8581i	−1.04976	−	1.02123i
$502$	33.5332	−	3.71145i	1.49666	−	0.165650i
$503$	−1.50417	−	14.8354i	−0.0670676	−	0.661477i	−0.971850	−	0.235602i	$-0.924294\pi$
$503$	−1.50417	−	14.8354i	−0.0670676	−	0.661477i	0.904782	−	0.425875i	$-0.140034\pi$
$504$	2.21214	−	34.3552i	0.0985368	−	1.53030i
$505$	−4.57194	+	9.03440i	−0.203449	+	0.402025i
$506$	2.23040	+	16.0845i	0.0991536	+	0.715044i
$507$	−10.7268	+	19.3936i	−0.476394	+	0.861302i
$508$	−14.8205	+	69.1004i	−0.657553	+	3.06584i
$509$	2.52618	+	2.95503i	0.111971	+	0.130979i	0.813267	−	0.581891i	$-0.197687\pi$
$509$	2.52618	+	2.95503i	0.111971	+	0.130979i	−0.701296	+	0.712871i	$0.747395\pi$
$510$	0.184417	+	20.0755i	0.00816613	+	0.888956i
$511$	0.987117	−	9.73578i	0.0436675	−	0.430686i
$512$	7.06962	+	1.17971i	0.312436	+	0.0521364i
$513$	7.19390	+	0.143741i	0.317619	+	0.00634631i
$514$	43.0085	−	7.17685i	1.89702	−	0.316557i
$515$	−0.462230	−	7.17856i	−0.0203683	−	0.316325i
$516$	−102.190	−	43.7100i	−4.49868	−	1.92423i
$517$	−0.742296	+	0.749146i	−0.0326461	+	0.0329474i
$518$	16.4600	+	8.14067i	0.723210	+	0.357680i
$519$	26.0702	−	1.91929i	1.14435	−	0.0842474i
$520$	−5.50504	−	7.48988i	−0.241412	−	0.328453i
$521$	−7.26161	−	19.3949i	−0.318137	−	0.849706i	−0.993666	−	0.112373i	$-0.964155\pi$
$521$	−7.26161	−	19.3949i	−0.318137	−	0.849706i	0.675529	−	0.737333i	$-0.263915\pi$
$522$	−5.70182	+	6.42687i	−0.249562	+	0.281296i
$523$	1.65833	+	1.73630i	0.0725138	+	0.0759233i	0.758417	−	0.651769i	$-0.225973\pi$
$523$	1.65833	+	1.73630i	0.0725138	+	0.0759233i	−0.685904	+	0.727692i	$0.740593\pi$
$524$	7.23872	+	6.30420i	0.316225	+	0.275400i
$525$	4.02675	+	12.8743i	0.175742	+	0.561878i
$526$	−17.1837	+	15.5295i	−0.749243	+	0.677118i
$527$	−37.4059	−	11.3235i	−1.62943	−	0.493260i
$528$	−32.8658	−	153.237i	−1.43030	−	6.66877i
$529$	−13.0132	+	17.0400i	−0.565792	+	0.740871i
$530$	−8.62598	+	4.46526i	−0.374689	+	0.193958i
$531$	−8.77206	+	13.4266i	−0.380675	+	0.582667i
$532$	−3.39676	−	24.7883i	−0.147268	−	1.07471i
$533$	8.59900	+	13.1617i	0.372464	+	0.570099i
$534$	−44.1900	−	24.9747i	−1.91229	−	1.08076i
$535$	−5.39663	+	1.41949i	−0.233317	+	0.0613698i
$536$	20.3658	−	69.5743i	0.879667	−	3.00515i
$537$	19.9161	−	50.3563i	0.859442	−	2.17303i
$538$	12.8799	−	5.50912i	0.555291	−	0.237515i
$539$	12.6501	+	24.9972i	0.544877	+	1.07671i
$540$	3.64901	−	2.53017i	0.157028	−	0.108881i
$541$	27.0088	−	0.496259i	1.16120	−	0.0213359i	0.565644	−	0.824649i	$-0.308627\pi$
$541$	27.0088	−	0.496259i	1.16120	−	0.0213359i	0.595557	+	0.803313i	$0.296932\pi$
$542$	37.6393	−	0.691582i	1.61675	−	0.0297060i
$543$	−3.13063	+	2.17073i	−0.134348	+	0.0931550i
$544$	41.8093	+	82.6174i	1.79256	+	3.54219i
$545$	0.896529	−	0.383473i	0.0384031	−	0.0164262i
$546$	5.89689	−	14.9099i	0.252364	−	0.638083i
$547$	−0.333092	+	1.13792i	−0.0142420	+	0.0486541i	−0.966541	−	0.256514i	$-0.917426\pi$
$547$	−0.333092	+	1.13792i	−0.0142420	+	0.0486541i	0.952299	+	0.305168i	$0.0987126\pi$
$548$	76.6889	−	20.1717i	3.27599	−	0.861691i
$549$	−42.2200	−	23.8613i	−1.80190	−	1.01838i
$550$	33.6512	+	51.5071i	1.43489	+	2.19627i
$551$	−1.92378	+	3.31976i	−0.0819559	+	0.141427i
$552$	−15.0420	+	23.0235i	−0.640230	+	0.979944i
$553$	−12.7151	+	6.58199i	−0.540701	+	0.279895i
$554$	9.25949	−	12.1248i	0.393398	−	0.515131i
$555$	1.73460	+	8.08757i	0.0736298	+	0.343298i
$556$	61.8056	+	18.7098i	2.62114	+	0.793472i
$557$	−11.2607	+	10.1767i	−0.477130	+	0.431200i	−0.873451	−	0.486912i	$-0.838123\pi$
$557$	−11.2607	+	10.1767i	−0.477130	+	0.431200i	0.396321	+	0.918112i	$0.370287\pi$
$558$	20.3185	+	64.9619i	0.860151	+	2.75006i
$559$	−13.1505	−	11.4528i	−0.556209	−	0.484403i
$560$	−4.96813	−	5.20172i	−0.209942	−	0.219813i
$561$	−46.4895	+	52.4012i	−1.96279	+	2.21238i
$562$	5.97841	+	15.9676i	0.252184	+	0.673554i
$563$	−5.57536	−	7.58555i	−0.234973	−	0.319693i	0.672264	−	0.740311i	$-0.265322\pi$
$563$	−5.57536	−	7.58555i	−0.234973	−	0.319693i	−0.907238	+	0.420618i	$0.861813\pi$
$564$	−2.89885	+	0.213414i	−0.122064	+	0.00898634i
$565$	−5.54736	−	2.74358i	−0.233379	−	0.115423i
$566$	−47.3818	+	47.8190i	−1.99160	+	2.00998i
$567$	−6.78308	−	2.90133i	−0.284863	−	0.121845i
$568$	−4.18795	−	65.0399i	−0.175722	−	2.72901i
$569$	13.7578	−	2.29577i	0.576756	−	0.0962436i	0.130975	−	0.991386i	$-0.458189\pi$
$569$	13.7578	−	2.29577i	0.576756	−	0.0962436i	0.445781	+	0.895142i	$0.352926\pi$
$570$	10.8030	−	11.2746i	0.452488	−	0.472242i
$571$	−21.8415	−	3.64471i	−0.914040	−	0.152526i	−0.311160	−	0.950358i	$-0.600717\pi$
$571$	−21.8415	−	3.64471i	−0.914040	−	0.152526i	−0.602881	+	0.797831i	$0.705981\pi$
$572$	5.32431	−	52.5128i	0.222621	−	2.19567i
$573$	0.462200	+	50.3146i	0.0193087	+	2.10192i
$574$	14.4474	+	16.9000i	0.603024	+	0.705394i
$575$	1.23890	−	5.77638i	0.0516659	−	0.240892i
$576$	33.8649	−	61.2265i	1.41104	−	2.55110i
$577$	−0.963241	−	6.94639i	−0.0401002	−	0.289182i	−0.999962	−	0.00870870i	$-0.997228\pi$
$577$	−0.963241	−	6.94639i	−0.0401002	−	0.289182i	0.959862	−	0.280473i	$-0.0904914\pi$
$578$	17.4426	−	34.4675i	0.725516	−	1.43366i
$579$	−1.39665	+	21.6904i	−0.0580430	+	0.901423i
$580$	0.238850	+	2.35574i	0.00991772	+	0.0978169i
$581$	16.4470	−	1.82035i	0.682334	−	0.0755208i
$582$	0.347344	+	0.337901i	0.0143979	+	0.0140065i
$583$	−32.7768	−	8.62137i	−1.35748	−	0.357061i
$584$	38.9920	−	64.7587i	1.61350	−	2.67974i
$585$	3.78962	−	1.14719i	0.156682	−	0.0474307i
$586$	−22.5748	−	40.8144i	−0.932556	−	1.68603i
$587$	−5.97007	+	4.47303i	−0.246411	+	0.184622i	−0.715669	−	0.698439i	$-0.753878\pi$
$587$	−5.97007	+	4.47303i	−0.246411	+	0.184622i	0.469258	+	0.883061i	$0.344521\pi$
$588$	−18.9554	+	74.8532i	−0.781707	+	3.08689i
$589$	14.6696	+	26.6230i	0.604452	+	1.09698i
$590$	1.50338	+	5.93670i	0.0618931	+	0.244410i
$591$	24.7852	+	20.0330i	1.01953	+	0.824048i
$592$	48.2346	+	60.8110i	1.98243	+	2.49932i
$593$	3.21925	+	1.23915i	0.132199	+	0.0508857i	0.424423	−	0.905464i	$-0.360477\pi$
$593$	3.21925	+	1.23915i	0.132199	+	0.0508857i	−0.292224	+	0.956350i	$0.594395\pi$
$594$	21.2893	+	2.75307i	0.873511	+	0.112960i
$595$	−0.558304	+	3.16630i	−0.0228882	+	0.129806i
$596$	−2.15586	+	78.2106i	−0.0883075	+	3.20363i
$597$	31.7844	+	7.12304i	1.30085	+	0.291527i
$598$	−5.46122	+	4.41411i	−0.223326	+	0.180506i
$599$	−2.16295	−	1.62057i	−0.0883756	−	0.0662147i	0.554509	−	0.832177i	$-0.312906\pi$
$599$	−2.16295	−	1.62057i	−0.0883756	−	0.0662147i	−0.642885	+	0.765963i	$0.722263\pi$
$600$	−14.3123	+	103.213i	−0.584298	+	4.21366i
$601$	26.3774	+	18.2897i	1.07596	+	0.746051i	0.968713	−	0.248182i	$-0.0798330\pi$
$601$	26.3774	+	18.2897i	1.07596	+	0.746051i	0.107242	+	0.994233i	$0.465798\pi$
$602$	−20.5211	−	13.6777i	−0.836379	−	0.557462i
$603$	25.0485	+	18.0586i	1.02006	+	0.735402i
$604$	−72.9615	−	14.9489i	−2.96876	−	0.608263i
$605$	1.01025	−	6.41661i	0.0410725	−	0.260872i
$606$	−126.778	−	46.1433i	−5.14999	−	1.87444i
$607$	3.39329	+	2.64110i	0.137729	+	0.107199i	0.680734	−	0.732530i	$-0.261661\pi$
$607$	3.39329	+	2.64110i	0.137729	+	0.107199i	−0.543005	+	0.839730i	$0.682713\pi$
$608$	21.6086	−	68.6989i	0.876343	−	2.78611i
$609$	−1.98052	+	1.54150i	−0.0802548	+	0.0624649i
$610$	−17.6222	+	5.69002i	−0.713502	+	0.230382i
$611$	−0.443109	−	0.107889i	−0.0179263	−	0.00436472i
$612$	−104.974	+	13.5749i	−4.24333	+	0.548734i
$613$	1.61956	−	35.2370i	0.0654135	−	1.42321i	−0.668372	−	0.743827i	$-0.733009\pi$
$613$	1.61956	−	35.2370i	0.0654135	−	1.42321i	0.733786	−	0.679381i	$-0.237752\pi$
$614$	6.39414	+	40.6124i	0.258046	+	1.63898i
$615$	−1.91999	+	9.82927i	−0.0774214	+	0.396355i
$616$	−1.26386	−	45.8505i	−0.0509224	−	1.84737i
$617$	37.4982	+	5.55134i	1.50962	+	0.223488i	0.849468	−	0.527641i	$-0.176923\pi$
$617$	37.4982	+	5.55134i	1.50962	+	0.223488i	0.660155	+	0.751129i	$0.270491\pi$
$618$	94.2348	−	17.5102i	3.79068	−	0.704362i
$619$	−22.6159	−	9.18578i	−0.909009	−	0.369208i	−0.126587	−	0.991956i	$-0.540402\pi$
$619$	−22.6159	−	9.18578i	−0.909009	−	0.369208i	−0.782423	+	0.622748i	$0.786016\pi$
$620$	16.9645	+	8.00575i	0.681311	+	0.321519i
$621$	−1.25105	−	1.63817i	−0.0502028	−	0.0657376i
$622$	−32.3628	+	37.8567i	−1.29763	+	1.51792i
$623$	−6.22708	−	5.22514i	−0.249483	−	0.209341i
$624$	49.4376	−	46.3567i	1.97909	−	1.85575i
$625$	−4.78933	−	20.4871i	−0.191573	−	0.819486i
$626$	−38.8424	+	21.0204i	−1.55245	+	0.840146i
$627$	54.3432	−	3.91299i	2.17026	−	0.156270i
$628$	38.0769	+	20.6062i	1.51944	+	0.822277i
$629$	9.13317	−	33.4698i	0.364163	−	1.33453i
$630$	5.10697	−	2.29629i	0.203466	−	0.0914864i
$631$	29.7321	−	21.4352i	1.18362	−	0.853321i	0.191856	−	0.981423i	$-0.438549\pi$
$631$	29.7321	−	21.4352i	1.18362	−	0.853321i	0.991761	+	0.128102i	$0.0408885\pi$
$632$	−110.525	+	4.06294i	−4.39645	+	0.161615i
$633$	11.4708	+	21.6693i	0.455922	+	0.861278i
$634$	33.3176	−	88.9874i	1.32321	−	3.53414i
$635$	−6.79689	+	1.92198i	−0.269726	+	0.0762713i
$636$	−52.5189	−	77.2486i	−2.08251	−	3.06311i
$637$	−6.43884	+	10.2623i	−0.255116	+	0.406607i
$638$	−6.77931	+	9.22358i	−0.268395	+	0.365165i
$639$	26.7143	+	7.55408i	1.05680	+	0.298835i
$640$	−3.02833	−	9.09234i	−0.119705	−	0.359406i
$641$	−15.9581	−	16.1054i	−0.630308	−	0.636125i	0.320006	−	0.947415i	$-0.396315\pi$
$641$	−15.9581	−	16.1054i	−0.630308	−	0.636125i	−0.950315	+	0.311290i	$0.899239\pi$
$642$	−27.3456	−	69.1412i	−1.07924	−	2.72879i
$643$	16.3051	−	1.50201i	0.643011	−	0.0592333i	0.234688	−	0.972071i	$-0.424593\pi$
$643$	16.3051	−	1.50201i	0.643011	−	0.0592333i	0.408323	+	0.912837i	$0.366114\pi$
$644$	−4.95043	+	5.18319i	−0.195074	+	0.204246i
$645$	−0.917346	−	11.0707i	−0.0361205	−	0.435909i
$646$	−61.9794	+	21.1663i	−2.43855	+	0.832777i
$647$	−1.56802	+	18.9231i	−0.0616451	+	0.743945i	0.893741	+	0.448584i	$0.148072\pi$
$647$	−1.56802	+	18.9231i	−0.0616451	+	0.743945i	−0.955386	+	0.295361i	$0.904560\pi$
$648$	−37.8209	−	42.6303i	−1.48575	−	1.67467i
$649$	−9.99721	+	18.8856i	−0.392425	+	0.741326i
$650$	−11.5752	+	23.9558i	−0.454019	+	0.939623i
$651$	2.36871	+	19.7412i	0.0928372	+	0.773720i
$652$	−3.16780	−	2.97038i	−0.124061	−	0.116329i
$653$	−8.16024	+	14.1339i	−0.319335	+	0.553104i	−0.980349	−	0.197269i	$-0.936793\pi$
$653$	−8.16024	+	14.1339i	−0.319335	+	0.553104i	0.661015	+	0.750373i	$0.270126\pi$
$654$	6.49628	+	11.2519i	0.254025	+	0.439984i
$655$	−0.218392	+	0.934205i	−0.00853327	+	0.0365024i
$656$	24.7402	+	90.6640i	0.965943	+	3.53983i
$657$	20.4697	+	24.8549i	0.798597	+	0.969683i
$658$	−0.641038	−	0.0709500i	−0.0249903	−	0.00276592i
$659$	0.356538	−	38.8124i	0.0138888	−	1.51192i	−0.647612	−	0.761970i	$-0.724232\pi$
$659$	0.356538	−	38.8124i	0.0138888	−	1.51192i	0.661501	−	0.749945i	$-0.269920\pi$
$660$	25.7568	−	21.6125i	1.00258	−	0.841265i
$661$	−1.32646	+	11.0549i	−0.0515934	+	0.429988i	0.943525	+	0.331301i	$0.107488\pi$
$661$	−1.32646	+	11.0549i	−0.0515934	+	0.429988i	−0.995119	+	0.0986866i	$0.968536\pi$
$662$	40.2032	+	25.7423i	1.56254	+	1.00050i
$663$	−29.7828	−	5.53406i	−1.15667	−	0.214925i
$664$	120.898	+	41.5042i	4.69174	+	1.61068i
$665$	2.03080	−	1.45914i	0.0787512	−	0.0565831i
$666$	−57.1482	+	19.6190i	−2.21445	+	0.760220i
$667$	1.08730	−	0.160967i	0.0421005	−	0.00623267i
$668$	−11.4599	−	64.9921i	−0.443396	−	2.51462i
$669$	−0.0350928	−	0.763517i	−0.00135677	−	0.0295193i
$670$	11.5512	−	2.36670i	0.446262	−	0.0914335i
$671$	−58.9308	−	26.4976i	−2.27500	−	1.02293i
$672$	29.9468	−	36.3624i	1.15522	−	1.40271i
$673$	17.9452	−	17.4573i	0.691735	−	0.672930i	−0.264881	−	0.964281i	$-0.585333\pi$
$673$	17.9452	−	17.4573i	0.691735	−	0.672930i	0.956616	+	0.291351i	$0.0941047\pi$
$674$	−8.91468	+	5.03828i	−0.343380	+	0.194067i
$675$	−6.93566	−	3.59026i	−0.266954	−	0.138189i
$676$	−40.3502	+	19.0417i	−1.55193	+	0.732374i
$677$	−23.1633	+	1.27796i	−0.890239	+	0.0491159i	−0.494430	−	0.869217i	$-0.664623\pi$
$677$	−23.1633	+	1.27796i	−0.890239	+	0.0491159i	−0.395809	+	0.918333i	$0.629536\pi$
$678$	27.4903	−	77.7438i	1.05576	−	2.98573i
$679$	0.0448038	+	0.0633651i	0.00171941	+	0.00243173i
$680$	−14.3386	+	20.2788i	−0.549862	+	0.777657i
$681$	−10.5095	−	29.7213i	−0.402725	−	1.13892i
$682$	34.8966	+	83.7037i	1.33626	+	3.20518i
$683$	18.7602	−	20.3790i	0.717840	−	0.779782i	−0.264999	−	0.964249i	$-0.585372\pi$
$683$	18.7602	−	20.3790i	0.717840	−	0.779782i	0.982839	+	0.184467i	$0.0590559\pi$
$684$	65.8053	+	49.4693i	2.51613	+	1.89151i
$685$	5.36780	+	5.83098i	0.205093	+	0.222790i
$686$	−15.8582	+	34.4199i	−0.605469	+	1.31416i
$687$	−25.7856	−	23.3034i	−0.983783	−	0.889081i
$688$	−53.7703	−	89.3029i	−2.04997	−	3.40464i
$689$	−4.11731	−	14.0657i	−0.156857	−	0.535861i
$690$	−4.45431	−	0.410325i	−0.169573	−	0.0156208i
$691$	19.4606	−	16.9482i	0.740314	−	0.644740i	−0.202032	−	0.979379i	$-0.564755\pi$
$691$	19.4606	−	16.9482i	0.740314	−	0.644740i	0.942347	+	0.334639i	$0.108614\pi$
$692$	44.8335	+	27.5590i	1.70431	+	1.04764i
$693$	18.5927	+	6.00340i	0.706279	+	0.228050i
$694$	−24.9387	+	9.07694i	−0.946659	+	0.344556i
$695$	1.23732	+	6.33438i	0.0469341	+	0.240277i
$696$	−18.9176	+	4.23953i	−0.717070	+	0.160699i
$697$	26.1044	−	32.9107i	0.988773	−	1.24658i
$698$	15.4131	−	9.08852i	0.583393	−	0.344006i
$699$	35.3035	−	17.4602i	1.33530	−	0.660404i
$700$	−8.58143	+	25.7651i	−0.324347	+	0.973829i
$701$	22.0336	−	32.4087i	0.832199	−	1.22406i	−0.140058	−	0.990143i	$-0.544729\pi$
$701$	22.0336	−	32.4087i	0.832199	−	1.22406i	0.972257	−	0.233916i	$-0.0751542\pi$
$702$	3.72890	+	8.50103i	0.140738	+	0.320851i
$703$	−23.2656	+	13.6686i	−0.877480	+	0.515520i
$704$	37.4467	−	85.3699i	1.41133	−	3.21750i
$705$	−0.154401	−	0.246087i	−0.00581509	−	0.00926816i
$706$	84.5011	+	6.22098i	3.18024	+	0.234130i
$707$	−18.6113	−	10.9744i	−0.699950	−	0.412735i
$708$	−54.9637	+	21.1565i	−2.06566	+	0.795111i
$709$	17.2752	−	4.20620i	0.648785	−	0.157967i	0.101397	−	0.994846i	$-0.467669\pi$
$709$	17.2752	−	4.20620i	0.648785	−	0.157967i	0.547388	+	0.836879i	$0.315622\pi$
$710$	9.03094	−	5.55130i	0.338925	−	0.208336i
$711$	14.0634	−	44.9631i	0.527418	−	1.68625i
$712$	−26.2759	−	57.0312i	−0.984729	−	2.13733i
$713$	3.35081	−	8.03733i	0.125489	−	0.301000i
$714$	−42.7747	−	2.35995i	−1.60080	−	0.0883188i
$715$	4.88761	−	1.98518i	0.182786	−	0.0742413i
$716$	91.8101	−	58.7863i	3.43111	−	2.19695i
$717$	−3.43831	−	7.11583i	−0.128406	−	0.265746i
$718$	8.95615	+	0.329231i	0.334241	+	0.0122868i
$719$	−12.1691	+	8.11092i	−0.453830	+	0.302486i	−0.760510	−	0.649326i	$-0.775051\pi$
$719$	−12.1691	+	8.11092i	−0.453830	+	0.302486i	0.306680	+	0.951813i	$0.400782\pi$
$720$	23.6642	+	0.434804i	0.881912	+	0.0162042i
$721$	15.3497			0.571651
$722$	45.9973	+	21.8876i	1.71184	+	0.814573i
$723$	9.39000			0.349218
$724$	−7.66815	−	0.140894i	−0.284984	−	0.00523629i
$725$	3.46536	−	2.30973i	0.128700	−	0.0857812i
$726$	86.4920	+	3.17947i	3.21002	+	0.118001i
$727$	−8.46689	−	17.5228i	−0.314020	−	0.649885i	0.682711	−	0.730689i	$-0.260801\pi$
$727$	−8.46689	−	17.5228i	−0.314020	−	0.649885i	−0.996730	+	0.0808037i	$0.974251\pi$
$728$	16.7040	−	10.6957i	0.619093	−	0.396408i
$729$	34.3141	−	13.9372i	1.27089	−	0.516192i
$730$	12.2763	+	0.677304i	0.454368	+	0.0250682i
$731$	−17.9294	+	43.0058i	−0.663143	+	1.59063i
$732$	−74.5204	−	161.745i	−2.75435	−	5.97826i
$733$	3.97016	−	12.6933i	0.146641	−	0.468839i	−0.851848	−	0.523790i	$-0.824518\pi$
$733$	3.97016	−	12.6933i	0.146641	−	0.468839i	0.998489	+	0.0549510i	$0.0175003\pi$
$734$	−30.6473	+	18.8388i	−1.13121	+	0.695354i
$735$	−7.49840	+	1.82572i	−0.276583	+	0.0673428i
$736$	−19.2536	+	7.41107i	−0.709698	+	0.273176i
$737$	35.4398	+	20.8975i	1.30544	+	0.769771i
$738$	−72.9608	−	5.37138i	−2.68572	−	0.197723i
$739$	−9.93364	−	15.8324i	−0.365415	−	0.582402i	0.612739	−	0.790286i	$-0.290068\pi$
$739$	−9.93364	−	15.8324i	−0.365415	−	0.582402i	−0.978154	+	0.207883i	$0.933343\pi$
$740$	−6.68910	+	15.2496i	−0.245896	+	0.560587i
$741$	13.5715	+	19.2594i	0.498560	+	0.707510i
$742$	−8.32572	−	18.9807i	−0.305647	−	0.696805i
$743$	−1.90177	+	2.79726i	−0.0697691	+	0.102622i	−0.860269	−	0.509841i	$-0.829704\pi$
$743$	−1.90177	+	2.79726i	−0.0697691	+	0.102622i	0.790499	+	0.612463i	$0.209821\pi$
$744$	−48.5337	+	145.719i	−1.77933	+	5.34231i
$745$	−7.00943	+	3.46668i	−0.256806	+	0.127009i
$746$	49.7437	−	29.3321i	1.82125	−	1.07392i
$747$	−33.8358	+	42.6579i	−1.23799	+	1.56077i
$748$	−137.613	+	30.8399i	−5.03164	+	1.12762i
$749$	−2.28275	−	11.6864i	−0.0834099	−	0.427012i
$750$	−32.7574	+	11.9227i	−1.19613	+	0.435356i
$751$	44.4856	+	14.3639i	1.62330	+	0.524147i	0.972062	−	0.234725i	$-0.0754191\pi$
$751$	44.4856	+	14.3639i	1.62330	+	0.524147i	0.651239	+	0.758873i	$0.274249\pi$
$752$	−2.32244	−	1.42760i	−0.0846905	−	0.0520591i
$753$	−24.4542	+	21.2972i	−0.891161	+	0.776113i
$754$	−4.92921	−	0.454072i	−0.179511	−	0.0165363i
$755$	−2.09118	−	7.14396i	−0.0761057	−	0.259995i
$756$	4.88749	+	8.11725i	0.177756	+	0.295222i
$757$	9.53402	+	8.61624i	0.346520	+	0.313162i	0.825215	−	0.564819i	$-0.191054\pi$
$757$	9.53402	+	8.61624i	0.346520	+	0.313162i	−0.478695	+	0.877981i	$0.658890\pi$
$758$	−28.6829	+	62.2557i	−1.04181	+	2.26123i
$759$	−10.5710	−	11.4832i	−0.383703	−	0.416812i
$760$	18.9973	−	3.49841i	0.689106	−	0.126901i
$761$	10.6913	−	11.6139i	0.387560	−	0.421002i	−0.511188	−	0.859469i	$-0.670794\pi$
$761$	10.6913	−	11.6139i	0.387560	−	0.421002i	0.898747	+	0.438467i	$0.144478\pi$
$762$	−36.2160	−	86.8683i	−1.31197	−	3.14691i
$763$	0.693654	+	1.96168i	0.0251120	+	0.0710177i
$764$	−58.4824	+	82.7103i	−2.11582	+	2.99235i
$765$	−6.10769	−	8.63798i	−0.220824	−	0.312307i
$766$	−26.1273	+	73.8892i	−0.944019	+	2.66972i
$767$	−9.22644	+	0.509037i	−0.333147	+	0.0183803i
$768$	25.9016	−	12.2233i	0.934643	−	0.441069i
$769$	2.83702	+	1.46859i	0.102306	+	0.0529587i	0.510100	−	0.860115i	$-0.329608\pi$
$769$	2.83702	+	1.46859i	0.102306	+	0.0529587i	−0.407794	+	0.913074i	$0.633702\pi$
$770$	6.49493	−	3.67072i	0.234061	−	0.132284i
$771$	−30.0406	+	29.2239i	−1.08188	+	1.05247i
$772$	−27.8177	+	33.7772i	−1.00118	+	1.21567i
$773$	47.9274	+	21.5500i	1.72383	+	0.775100i	0.996001	+	0.0893402i	$0.0284758\pi$
$773$	47.9274	+	21.5500i	1.72383	+	0.775100i	0.727828	+	0.685760i	$0.240530\pi$
$774$	79.4956	−	16.2877i	2.85741	−	0.585448i
$775$	−1.51483	−	32.9582i	−0.0544142	−	1.18389i
$776$	0.104098	+	0.590366i	0.00373688	+	0.0211929i
$777$	−17.4598	+	2.58480i	−0.626367	+	0.0927291i
$778$	−3.64424	+	1.25107i	−0.130652	+	0.0448530i
$779$	−32.4084	+	4.13804i	−1.16115	+	0.148261i
$780$	13.7520	+	4.72106i	0.492399	+	0.169041i
$781$	36.3659	+	6.75731i	1.30128	+	0.241795i
$782$	15.8005	+	10.1171i	0.565026	+	0.361788i
$783$	0.173106	−	1.44269i	0.00618630	−	0.0515576i
$784$	−55.4762	+	46.5500i	−1.98129	+	1.66250i
$785$	−0.0397488	+	4.32702i	−0.00141870	+	0.154438i
$786$	−12.7057	−	1.40627i	−0.453198	−	0.0501599i
$787$	−28.9294	−	35.1270i	−1.03122	−	1.25214i	−0.967153	−	0.254197i	$-0.918189\pi$
$787$	−28.9294	−	35.1270i	−1.03122	−	1.25214i	−0.0640682	−	0.997946i	$-0.520408\pi$
$788$	16.8899	+	61.8954i	0.601677	+	2.20493i
$789$	5.06763	−	21.6776i	0.180412	−	0.771742i
$790$	−8.99456	−	15.5790i	−0.320012	−	0.554277i
$791$	6.60291	−	11.4366i	0.234772	−	0.406638i
$792$	110.095	+	103.234i	3.91206	+	3.66826i
$793$	−3.32875	−	27.7423i	−0.118207	−	0.985159i
$794$	−40.9070	+	84.6600i	−1.45174	+	3.00447i
$795$	4.36787	−	8.25131i	0.154913	−	0.292644i
$796$	43.5192	+	49.0531i	1.54250	+	1.73864i
$797$	−2.81805	+	34.0088i	−0.0998205	+	1.20465i	0.744056	+	0.668117i	$0.232900\pi$
$797$	−2.81805	+	34.0088i	−0.0998205	+	1.20465i	−0.843876	+	0.536538i	$0.819732\pi$
$798$	22.5273	+	24.5502i	0.797459	+	0.869069i
$799$	0.100624	+	1.21436i	0.00355983	+	0.0429608i
$800$	−53.9889	+	56.5273i	−1.90880	+	1.99854i
$801$	26.6346	−	2.45355i	0.941088	−	0.0866918i
$802$	−13.1356	−	33.2124i	−0.463835	−	1.17277i
$803$	30.1954	+	30.4741i	1.06557	+	1.07541i
$804$	35.8324	+	107.584i	1.26371	+	3.79420i
$805$	−0.689331	−	0.194924i	−0.0242957	−	0.00687018i
$806$	−23.2252	+	31.5990i	−0.818071	+	1.11303i
$807$	−7.15619	+	11.4056i	−0.251910	+	0.401497i
$808$	−93.8367	−	138.022i	−3.30117	−	4.85560i
$809$	0.647578	−	0.183118i	0.0227676	−	0.00643808i	−0.260701	−	0.965420i	$-0.583954\pi$
$809$	0.647578	−	0.183118i	0.0227676	−	0.00643808i	0.283468	+	0.958982i	$0.408515\pi$
$810$	3.25017	−	8.68082i	0.114199	−	0.305013i
$811$	2.33754	+	4.41583i	0.0820822	+	0.155061i	0.921443	−	0.388515i	$-0.127012\pi$
$811$	2.33754	+	4.41583i	0.0820822	+	0.155061i	−0.839360	+	0.543575i	$0.817070\pi$
$812$	−5.04915	+	0.185609i	−0.177191	+	0.00651358i
$813$	−29.3515	+	21.1608i	−1.02940	+	0.742140i
$814$	−73.4225	+	33.0136i	−2.57346	+	1.15713i
$815$	0.114259	−	0.418717i	0.00400231	−	0.0146670i
$816$	−159.253	−	86.1834i	−5.57497	−	3.01702i
$817$	33.3421	−	14.1981i	1.16649	−	0.496730i
$818$	12.7920	−	6.92267i	0.447261	−	0.242045i
$819$	1.92326	+	8.22706i	0.0672042	+	0.287477i
$820$	−14.7078	+	13.7912i	−0.513618	+	0.481610i
$821$	−1.23191	−	1.03370i	−0.0429940	−	0.0360763i	0.621037	−	0.783781i	$-0.286711\pi$
$821$	−1.23191	−	1.03370i	−0.0429940	−	0.0360763i	−0.664031	+	0.747705i	$0.731156\pi$
$822$	−68.6201	+	80.2691i	−2.39340	+	2.79971i
$823$	4.01188	+	5.25331i	0.139845	+	0.183119i	0.859380	−	0.511337i	$-0.170850\pi$
$823$	4.01188	+	5.25331i	0.139845	+	0.183119i	−0.719535	+	0.694456i	$0.755645\pi$
$824$	107.231	+	50.6035i	3.73557	+	1.76286i
$825$	−54.7899	−	22.2537i	−1.90754	−	0.774775i
$826$	−12.8480	+	2.38733i	−0.447038	+	0.0830660i
$827$	17.1029	+	2.53196i	0.594727	+	0.0880449i	0.437037	−	0.899444i	$-0.356028\pi$
$827$	17.1029	+	2.53196i	0.594727	+	0.0880449i	0.157690	+	0.987489i	$0.449595\pi$
$828$	−0.649838	−	23.5749i	−0.0225834	−	0.819284i
$829$	2.12055	−	10.8560i	0.0736497	−	0.377045i	−0.926350	−	0.376663i	$-0.877071\pi$
$829$	2.12055	−	10.8560i	0.0736497	−	0.377045i	1.00000		0.000382060i	$-0.000121614\pi$
$830$	3.23350	+	20.5376i	0.112236	+	0.712870i
$831$	−0.673266	+	14.6483i	−0.0233553	+	0.508144i
$832$	39.9794	−	5.17001i	1.38604	−	0.179238i
$833$	31.4509	+	7.65772i	1.08971	+	0.265324i
$834$	−81.8363	+	26.4241i	−2.83376	+	0.914992i
$835$	5.20512	−	4.05131i	0.180131	−	0.140201i
$836$	93.3519	+	57.5900i	3.22864	+	1.99179i
$837$	−9.08415	−	7.07048i	−0.313994	−	0.244391i
$838$	45.7879	+	16.6654i	1.58172	+	0.575697i
$839$	1.33169	−	8.45825i	0.0459751	−	0.292011i	−0.953994	−	0.299824i	$-0.903072\pi$
$839$	1.33169	−	8.45825i	0.0459751	−	0.292011i	0.999969	+	0.00781335i	$0.00248709\pi$
$840$	12.3780	+	2.53610i	0.427082	+	0.0875038i
$841$	−22.8954	−	16.5063i	−0.789498	−	0.569184i
$842$	41.3494	+	27.5602i	1.42500	+	0.949787i
$843$	−13.4674	−	9.33810i	−0.463843	−	0.321621i
$844$	−6.77974	+	48.8919i	−0.233368	+	1.68293i
$845$	−3.56879	−	2.67389i	−0.122770	−	0.0919846i
$846$	1.65045	−	1.33400i	0.0567438	−	0.0458639i
$847$	13.5252	+	3.03108i	0.464733	+	0.104149i
$848$	2.41397	−	87.5745i	0.0828962	−	3.00732i
$849$	11.2358	−	63.7212i	0.385611	−	2.18691i
$850$	70.5001	+	9.11685i	2.41813	+	0.312705i
$851$	7.21403	+	2.77681i	0.247294	+	0.0951880i
$852$	63.3528	+	79.8710i	2.17043	+	2.73634i
$853$	22.4594	+	18.1531i	0.768996	+	0.621552i	0.930908	−	0.365253i	$-0.119018\pi$
$853$	22.4594	+	18.1531i	0.768996	+	0.621552i	−0.161912	+	0.986805i	$0.551766\pi$
$854$	−9.70027	−	38.3055i	−0.331937	−	1.31079i
$855$	−1.29276	+	8.12599i	−0.0442115	+	0.277903i
$856$	22.5798	−	89.1654i	0.771760	−	3.04761i
$857$	10.8638	−	8.13964i	0.371101	−	0.278045i	−0.397722	−	0.917506i	$-0.630199\pi$
$857$	10.8638	−	8.13964i	0.371101	−	0.278045i	0.768823	+	0.639461i	$0.220842\pi$
$858$	34.0213	+	61.5092i	1.16147	+	2.09989i
$859$	−51.7653	+	15.6704i	−1.76621	+	0.534666i	−0.994816	−	0.101694i	$-0.967574\pi$
$859$	−51.7653	+	15.6704i	−1.76621	+	0.534666i	−0.771392	+	0.636360i	$0.780439\pi$
$860$	11.5359	−	19.1590i	0.393370	−	0.653318i
$861$	−20.6676	−	5.43624i	−0.704348	−	0.185266i
$862$	−29.2165	−	28.4223i	−0.995118	−	0.968066i
$863$	2.35952	−	0.261152i	0.0803190	−	0.00888970i	−0.0697589	−	0.997564i	$-0.522223\pi$
$863$	2.35952	−	0.261152i	0.0803190	−	0.00888970i	0.150078	+	0.988674i	$0.452048\pi$
$864$	2.75113	+	27.1339i	0.0935952	+	0.923115i
$865$	−0.337982	+	5.24895i	−0.0114917	+	0.178470i
$866$	42.5423	−	84.0659i	1.44565	−	2.85668i
$867$	5.09992	+	36.7780i	0.173202	+	1.24905i
$868$	−19.3738	+	35.0271i	−0.657590	+	1.18890i
$869$	13.1631	−	61.3727i	0.446527	−	2.08193i
$870$	−2.04899	−	2.39683i	−0.0694674	−	0.0812602i
$871$	0.163428	+	17.7906i	0.00553754	+	0.602811i
$872$	−1.62132	+	15.9909i	−0.0549050	+	0.541519i
$873$	−0.251869	−	0.0420296i	−0.00852449	−	0.00142249i
$874$	−3.29896	−	14.2148i	−0.111589	−	0.480823i
$875$	−5.50651	+	0.918874i	−0.186154	+	0.0310636i
$876$	7.59777	+	117.996i	0.256705	+	3.98670i
$877$	−41.1678	−	17.6088i	−1.39014	−	0.594605i	−0.437641	−	0.899150i	$-0.644186\pi$
$877$	−41.1678	−	17.6088i	−1.39014	−	0.594605i	−0.952498	+	0.304545i	$0.901496\pi$
$878$	−33.9494	+	34.2627i	−1.14574	+	1.15631i
$879$	40.1846	+	19.8743i	1.35539	+	0.670342i
$880$	31.4491	−	2.31529i	1.06015	−	0.0780484i
$881$	−24.4692	−	33.2916i	−0.824390	−	1.12162i	−0.990769	−	0.135561i	$-0.956716\pi$
$881$	−24.4692	−	33.2916i	−0.824390	−	1.12162i	0.166379	−	0.986062i	$-0.446792\pi$
$882$	−19.7671	−	52.7957i	−0.665594	−	1.77772i
$883$	−22.0657	+	24.8716i	−0.742570	+	0.836996i	−0.991306	−	0.131576i	$-0.957996\pi$
$883$	−22.0657	+	24.8716i	−0.742570	+	0.836996i	0.248736	+	0.968571i	$0.419985\pi$
$884$	−42.1212	−	44.1017i	−1.41669	−	1.48330i
$885$	−4.43892	−	3.86586i	−0.149213	−	0.129950i
$886$	20.5416	+	65.6750i	0.690107	+	2.20640i
$887$	−5.51140	+	4.98085i	−0.185055	+	0.167241i	−0.757787	−	0.652502i	$-0.773720\pi$
$887$	−5.51140	+	4.98085i	−0.185055	+	0.167241i	0.572733	+	0.819742i	$0.305883\pi$
$888$	−130.494	−	39.5030i	−4.37908	−	1.32563i
$889$	−3.16077	−	14.7371i	−0.106009	−	0.494266i
$890$	6.19886	−	8.11705i	0.207786	−	0.272084i
$891$	28.7227	−	14.8684i	0.962248	−	0.498109i
$892$	0.841608	−	1.28818i	0.0281791	−	0.0431313i
$893$	0.603668	−	0.730599i	0.0202010	−	0.0244486i
$894$	−56.9889	−	87.2281i	−1.90599	−	2.91734i
$895$	9.48583	+	5.36108i	0.317076	+	0.179201i
$896$	19.7768	−	5.20193i	0.660696	−	0.173784i
$897$	1.89612	−	6.47761i	0.0633098	−	0.216281i
$898$	−4.78731	+	12.1044i	−0.159755	+	0.403928i
$899$	5.64384	−	2.41404i	0.188233	−	0.0805129i
$900$	−40.3474	−	79.7287i	−1.34491	−	2.65762i
$901$	−32.1798	+	22.3130i	−1.07207	+	0.743353i
$902$	−97.4559	+	1.79065i	−3.24493	+	0.0596221i
$903$	23.7002	−	0.435466i	0.788692	−	0.0144914i
$904$	83.8303	−	58.1266i	2.78815	−	1.93326i
$905$	−0.346116	−	0.683943i	−0.0115053	−	0.0227350i
$906$	91.1913	−	39.0053i	3.02963	−	1.29587i
$907$	−21.0150	+	53.1349i	−0.697792	+	1.76432i	−0.0547306	+	0.998501i	$0.517430\pi$
$907$	−21.0150	+	53.1349i	−0.697792	+	1.76432i	−0.643062	+	0.765815i	$0.722336\pi$
$908$	17.8294	−	60.9094i	0.591689	−	2.02135i
$909$	68.7539	−	18.0845i	2.28042	−	0.599825i
$910$	2.80863	+	1.58735i	0.0931053	+	0.0526200i
$911$	−6.85742	−	10.4961i	−0.227196	−	0.347750i	0.705313	−	0.708896i	$-0.250807\pi$
$911$	−6.85742	−	10.4961i	−0.227196	−	0.347750i	−0.932509	+	0.361146i	$0.882385\pi$
$912$	41.8260	+	134.483i	1.38500	+	4.45318i
$913$	−39.6775	+	60.7309i	−1.31313	+	2.00990i
$914$	37.1602	−	19.2360i	1.22915	−	0.636271i
$915$	10.8029	−	14.1458i	0.357134	−	0.467646i
$916$	−14.6732	−	68.4139i	−0.484818	−	2.26046i
$917$	−1.95939	−	0.593145i	−0.0647046	−	0.0195874i
$918$	18.4015	−	16.6301i	0.607339	−	0.548874i
$919$	6.93109	+	22.1599i	0.228635	+	0.730988i	0.995966	+	0.0897359i	$0.0286023\pi$
$919$	6.93109	+	22.1599i	0.228635	+	0.730988i	−0.767330	+	0.641252i	$0.778415\pi$
$920$	−4.17297	−	3.63425i	−0.137579	−	0.119818i
$921$	−27.2934	−	28.5767i	−0.899347	−	0.941633i
$922$	23.6059	−	26.6077i	0.777420	−	0.876277i
$923$	5.60847	+	14.9796i	0.184605	+	0.493058i
$924$	42.4908	+	57.8108i	1.39784	+	1.90183i
$925$	29.2090	−	2.15037i	0.960388	−	0.0707038i
$926$	−27.3653	−	13.5342i	−0.899281	−	0.444761i
$927$	−35.5493	+	35.8773i	−1.16759	+	1.17837i
$928$	−13.3714	−	5.71938i	−0.438939	−	0.187748i
$929$	2.12484	+	32.9994i	0.0697139	+	1.08268i	0.873203	+	0.487356i	$0.162039\pi$
$929$	2.12484	+	32.9994i	0.0697139	+	1.08268i	−0.803489	+	0.595319i	$0.797026\pi$
$930$	−24.6406	+	4.11179i	−0.807997	+	0.134831i
$931$	−13.3463	−	21.3476i	−0.437408	−	0.699640i
$932$	78.2087	+	13.0507i	2.56181	+	0.427491i
$933$	4.82890	−	47.6266i	0.158091	−	1.55923i
$934$	−0.913682	−	99.4625i	−0.0298966	−	3.25451i
$935$	−9.15898	−	10.7138i	−0.299531	−	0.350379i
$936$	−13.6866	+	63.8137i	−0.447361	+	2.08582i
$937$	−18.2194	+	32.9401i	−0.595203	+	1.07610i	0.392498	+	0.919753i	$0.371611\pi$
$937$	−18.2194	+	32.9401i	−0.595203	+	1.07610i	−0.987701	+	0.156352i	$0.950027\pi$
$938$	3.45589	+	24.9221i	0.112839	+	0.813734i
$939$	19.1679	−	37.8769i	0.625522	−	1.23607i
$940$	0.0375817	−	0.583653i	0.00122578	−	0.0190367i
$941$	1.40797	+	13.8866i	0.0458985	+	0.452689i	0.991759	+	0.128116i	$0.0408931\pi$
$941$	1.40797	+	13.8866i	0.0458985	+	0.452689i	−0.945861	+	0.324573i	$0.894779\pi$
$942$	−57.3072	+	6.34276i	−1.86717	+	0.206658i
$943$	6.70866	+	6.52628i	0.218464	+	0.212525i
$944$	−53.4191	−	14.0509i	−1.73864	−	0.457319i
$945$	−0.488488	+	0.811291i	−0.0158905	+	0.0263913i
$946$	103.479	−	31.3251i	3.36438	−	1.01847i
$947$	−5.90839	−	10.6822i	−0.191997	−	0.347123i	0.761681	−	0.647952i	$-0.224374\pi$
$947$	−5.90839	−	10.6822i	−0.191997	−	0.347123i	−0.953678	+	0.300829i	$0.902737\pi$
$948$	138.450	−	103.733i	4.49665	−	3.36908i
$949$	−4.55414	+	17.9839i	−0.147834	+	0.583782i
$950$	−34.2893	−	43.3726i	−1.11249	−	1.40719i
$951$	22.4204	+	88.5363i	0.727033	+	2.87099i
$952$	−41.2164	−	33.3138i	−1.33583	−	1.07970i
$953$	−17.1622	−	21.6370i	−0.555939	−	0.700891i	0.422748	−	0.906247i	$-0.361065\pi$
$953$	−17.1622	−	21.6370i	−0.555939	−	0.700891i	−0.978687	+	0.205356i	$0.934165\pi$
$954$	63.6464	+	24.4987i	2.06063	+	0.793174i
$955$	−10.0407	−	1.29844i	−0.324910	−	0.0420164i
$956$	2.76279	−	15.6685i	0.0893549	−	0.506757i
$957$	0.303169	−	10.9984i	0.00980005	−	0.355527i
$958$	85.8862	+	19.2475i	2.77486	+	0.621860i
$959$	−13.1527	+	10.6309i	−0.424723	+	0.343289i
$960$	20.5512	+	15.3978i	0.663286	+	0.496962i
$961$	2.42165	−	17.4637i	0.0781176	−	0.563344i
$962$	−28.6080	−	19.8364i	−0.922360	−	0.639550i
$963$	32.6018	+	21.7297i	1.05058	+	0.700231i
$964$	15.3343	+	11.0552i	0.493885	+	0.356063i
$965$	−4.28441	−	0.877822i	−0.137920	−	0.0282581i
$966$	1.48451	−	9.42890i	0.0477634	−	0.303370i
$967$	−25.3262	−	9.21800i	−0.814437	−	0.296431i	−0.0989815	−	0.995089i	$-0.531558\pi$
$967$	−25.3262	−	9.21800i	−0.814437	−	0.296431i	−0.715455	+	0.698658i	$0.753781\pi$
$968$	84.4931	+	65.7636i	2.71571	+	2.11372i
$969$	37.3633	−	50.6639i	1.20028	−	1.62756i
$970$	−0.0769450	+	0.0598887i	−0.00247055	+	0.00192291i
$971$	−46.1825	+	14.9119i	−1.48207	+	0.478544i	−0.933811	−	0.357766i	$-0.883539\pi$
$971$	−46.1825	+	14.9119i	−1.48207	+	0.478544i	−0.548256	+	0.836310i	$0.684708\pi$
$972$	111.574	+	27.1662i	3.57873	+	0.871356i
$973$	−13.6583	+	1.76625i	−0.437865	+	0.0566234i
$974$	1.83823	−	39.9945i	0.0589007	−	1.28151i
$975$	−3.97726	−	25.2616i	−0.127374	−	0.809019i
$976$	32.0200	−	163.925i	1.02494	−	5.24710i
$977$	−0.226662	−	8.22288i	−0.00725157	−	0.263073i	−0.994554	−	0.104222i	$-0.966765\pi$
$977$	−0.226662	−	8.22288i	−0.00725157	−	0.263073i	0.987303	−	0.158851i	$-0.0507791\pi$
$978$	5.72078	+	0.846919i	0.182930	+	0.0270815i
$979$	35.0371	−	6.51039i	1.11979	−	0.208073i
$980$	−14.3947	−	5.84663i	−0.459823	−	0.186764i
$981$	−6.19159	−	2.92188i	−0.197682	−	0.0932884i
$982$	12.6192	+	16.5240i	0.402694	+	0.527304i
$983$	9.69971	−	11.3463i	0.309373	−	0.361892i	−0.583570	−	0.812063i	$-0.698344\pi$
$983$	9.69971	−	11.3463i	0.309373	−	0.361892i	0.892942	+	0.450171i	$0.148637\pi$
$984$	−126.459	−	106.112i	−4.03138	−	3.38273i
$985$	−4.67767	+	4.38616i	−0.149043	+	0.139755i
$986$	3.01070	+	12.8787i	0.0958801	+	0.410142i
$987$	0.545197	−	0.295046i	0.0173538	−	0.00939141i
$988$	−0.511895	+	47.4296i	−0.0162855	+	1.50894i
$989$	−9.13020	−	4.94102i	−0.290323	−	0.157115i
$990$	−6.46232	+	23.6821i	−0.205386	+	0.752666i
$991$	−31.0265	+	13.9507i	−0.985589	+	0.443159i	−0.837870	−	0.545870i	$-0.816199\pi$
$991$	−31.0265	+	13.9507i	−0.985589	+	0.443159i	−0.147719	+	0.989029i	$0.547193\pi$
$992$	−93.4603	+	67.3796i	−2.96737	+	2.13930i
$993$	−45.8541	+	1.68561i	−1.45514	+	0.0534913i
$994$	10.5829	+	19.9920i	0.335668	+	0.634107i
$995$	−2.29809	+	6.13792i	−0.0728543	+	0.194585i
$996$	−192.397	+	54.4046i	−6.09632	+	1.72388i
$997$	29.1791	+	42.9188i	0.924113	+	1.35925i	0.933224	+	0.359295i	$0.116983\pi$
$997$	29.1791	+	42.9188i	0.924113	+	1.35925i	−0.00911161	+	0.999958i	$0.502900\pi$
$998$	38.5712	−	61.4753i	1.22095	−	1.94597i
$999$	6.05192	−	8.23394i	0.191474	−	0.260510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.k.a.4.1	✓	3348
361.271	even	171	inner	361.2.k.a.271.1	yes	3348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.k.a.4.1	✓	3348	1.1	even	1	trivial
361.2.k.a.271.1	yes	3348	361.271	even	171	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.k (of order \(171\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68057 - 0.0492526i) q^{2} +(2.14428 - 1.42921i) q^{3} +(5.18437 + 0.190579i) q^{4} +(0.225586 + 0.466865i) q^{5} +(-5.81829 + 3.72547i) q^{6} +(-1.02509 + 0.416356i) q^{7} +(-8.53377 - 0.470821i) q^{8} +(1.40091 - 3.36025i) q^{9} +(-0.581703 - 1.26257i) q^{10} +(1.44795 - 4.62936i) q^{11} +(11.3891 - 7.00087i) q^{12} +(2.03799 - 0.496214i) q^{13} +(2.76833 - 1.06558i) q^{14} +(1.15097 + 0.678683i) q^{15} +(12.5044 + 0.920578i) q^{16} +(-2.97857 - 4.74728i) q^{17} +(-3.92073 + 8.93837i) q^{18} +(-0.920943 + 4.26050i) q^{19} +(1.08054 + 2.46339i) q^{20} +(-1.60303 + 2.35785i) q^{21} +(-4.10934 + 12.3380i) q^{22} +(1.11928 - 0.553568i) q^{23} +(-18.9717 + 11.1869i) q^{24} +(2.94010 - 3.70669i) q^{25} +(-5.48742 + 1.22976i) q^{26} +(-0.316461 - 1.62011i) q^{27} +(-5.39380 + 1.96318i) q^{28} +(0.837660 + 0.270472i) q^{29} +(-3.05182 - 1.87594i) q^{30} +(5.25882 - 4.57991i) q^{31} +(-16.4522 - 1.51556i) q^{32} +(-3.51149 - 11.9961i) q^{33} +(7.75045 + 12.8721i) q^{34} +(-0.425628 - 0.384655i) q^{35} +(7.90322 - 17.1538i) q^{36} +(4.19270 + 4.55449i) q^{37} +(2.67849 - 11.3752i) q^{38} +(3.66084 - 3.97673i) q^{39} +(-1.70529 - 4.09033i) q^{40} +(2.49876 + 7.06659i) q^{41} +(4.41315 - 6.24143i) q^{42} +(-4.79986 - 6.78833i) q^{43} +(8.38898 - 23.7244i) q^{44} +(1.88481 - 0.103988i) q^{45} +(-3.02758 + 1.42875i) q^{46} +(-0.193087 - 0.0999521i) q^{47} +(28.1287 - 15.8974i) q^{48} +(-4.14002 + 4.02747i) q^{49} +(-8.06371 + 9.79123i) q^{50} +(-13.1717 - 5.92252i) q^{51} +(10.6603 - 2.18416i) q^{52} +(-0.320809 - 6.97986i) q^{53} +(0.768502 + 4.35839i) q^{54} +(2.48792 - 0.368319i) q^{55} +(8.94392 - 3.07045i) q^{56} +(4.11437 + 10.4519i) q^{57} +(-2.23208 - 0.766275i) q^{58} +(-4.33126 - 0.804810i) q^{59} +(5.83769 + 3.73789i) q^{60} +(1.58698 - 13.2262i) q^{61} +(-14.3222 + 12.0177i) q^{62} +(-0.0370005 + 4.02784i) q^{63} +(19.1023 + 2.11424i) q^{64} +(0.691407 + 0.839529i) q^{65} +(8.82194 + 32.3293i) q^{66} +(-1.93081 + 8.25934i) q^{67} +(-14.5373 - 25.1793i) q^{68} +(1.60890 - 2.78669i) q^{69} +(1.12198 + 1.05206i) q^{70} +(0.908473 + 7.57135i) q^{71} +(-13.5371 + 28.0160i) q^{72} +(-4.13787 + 7.81682i) q^{73} +(-11.0145 - 12.4151i) q^{74} +(1.00679 - 12.1502i) q^{75} +(-5.58647 + 21.9125i) q^{76} +(0.443179 + 5.34838i) q^{77} +(-10.0090 + 10.4796i) q^{78} +(12.8860 - 1.18704i) q^{79} +(2.39103 + 6.04555i) q^{80} +(4.69323 + 4.73654i) q^{81} +(-6.35005 - 19.0656i) q^{82} +(-14.3915 - 4.06952i) q^{83} +(-8.76004 + 11.9185i) q^{84} +(1.54442 - 2.46151i) q^{85} +(12.5320 + 18.4330i) q^{86} +(2.18274 - 0.617220i) q^{87} +(-14.5361 + 38.8242i) q^{88} +(3.43729 + 6.49336i) q^{89} +(-5.05748 + 0.185914i) q^{90} +(-1.88253 + 1.35720i) q^{91} +(5.90827 - 2.65659i) q^{92} +(4.73076 - 17.3366i) q^{93} +(0.512661 + 0.277438i) q^{94} +(-2.19683 + 0.531152i) q^{95} +(-37.4442 + 20.2638i) q^{96} +(-0.0159665 - 0.0682991i) q^{97} +(11.2960 - 10.5920i) q^{98} +(-13.5273 - 11.3508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) \) 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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