LMFDB - Embedded newform 224.2.be.a.115.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			115.25
Character	$\chi$	$=$	224.115
Dual form			224.2.be.a.187.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08037 + 0.912577i) q^{2} +(0.906063 + 1.18080i) q^{3} +(0.334408 + 1.97184i) q^{4} +(1.00532 - 1.31016i) q^{5} +(-0.0986893 + 2.10256i) q^{6} +(-2.23554 + 1.41505i) q^{7} +(-1.43817 + 2.43550i) q^{8} +(0.203108 - 0.758010i) q^{9} +O(q^{10})$	\(q+(1.08037 + 0.912577i) q^{2} +(0.906063 + 1.18080i) q^{3} +(0.334408 + 1.97184i) q^{4} +(1.00532 - 1.31016i) q^{5} +(-0.0986893 + 2.10256i) q^{6} +(-2.23554 + 1.41505i) q^{7} +(-1.43817 + 2.43550i) q^{8} +(0.203108 - 0.758010i) q^{9} +(2.28173 - 0.498026i) q^{10} +(0.146082 - 1.10960i) q^{11} +(-2.02537 + 2.18149i) q^{12} +(0.522112 - 1.26049i) q^{13} +(-3.70656 - 0.511320i) q^{14} +2.45792 q^{15} +(-3.77634 + 1.31880i) q^{16} +(1.92977 - 3.34246i) q^{17} +(0.911175 - 0.633581i) q^{18} +(-0.0505153 - 0.383702i) q^{19} +(2.91961 + 1.54420i) q^{20} +(-3.69644 - 1.35761i) q^{21} +(1.17042 - 1.06547i) q^{22} +(-3.87109 - 1.03726i) q^{23} +(-4.17893 + 0.508512i) q^{24} +(0.588252 + 2.19538i) q^{25} +(1.71437 - 0.885331i) q^{26} +(5.20432 - 2.15570i) q^{27} +(-3.53784 - 3.93493i) q^{28} +(-0.846917 + 2.04464i) q^{29} +(2.65547 + 2.24304i) q^{30} +(-1.81828 + 3.14935i) q^{31} +(-5.28336 - 2.02141i) q^{32} +(1.44258 - 0.832875i) q^{33} +(5.13513 - 1.85004i) q^{34} +(-0.393491 + 4.35148i) q^{35} +(1.56260 + 0.147014i) q^{36} +(-3.40805 - 2.61509i) q^{37} +(0.295582 - 0.460640i) q^{38} +(1.96146 - 0.525571i) q^{39} +(1.74506 + 4.33268i) q^{40} +(3.82713 - 3.82713i) q^{41} +(-2.75460 - 4.84001i) q^{42} +(1.98296 - 0.821369i) q^{43} +(2.23681 - 0.0830085i) q^{44} +(-0.788923 - 1.02814i) q^{45} +(-3.23564 - 4.65329i) q^{46} +(8.69324 - 5.01904i) q^{47} +(-4.97885 - 3.26421i) q^{48} +(2.99527 - 6.32680i) q^{49} +(-1.36793 + 2.90866i) q^{50} +(5.69529 - 0.749800i) q^{51} +(2.66009 + 0.608007i) q^{52} +(-11.4501 - 1.50744i) q^{53} +(7.58984 + 2.42038i) q^{54} +(-1.30689 - 1.30689i) q^{55} +(-0.231256 - 7.47974i) q^{56} +(0.407307 - 0.407307i) q^{57} +(-2.78088 + 1.43609i) q^{58} +(-1.42227 + 10.8032i) q^{59} +(0.821947 + 4.84663i) q^{60} +(1.01451 + 7.70596i) q^{61} +(-4.83844 + 1.74315i) q^{62} +(0.618566 + 1.98197i) q^{63} +(-3.86331 - 7.00535i) q^{64} +(-1.12655 - 1.95124i) q^{65} +(2.31859 + 0.416652i) q^{66} +(-10.8729 + 8.34305i) q^{67} +(7.23615 + 2.68747i) q^{68} +(-2.28266 - 5.51082i) q^{69} +(-4.39617 + 4.34212i) q^{70} +(4.38876 + 4.38876i) q^{71} +(1.55403 + 1.58482i) q^{72} +(-3.29273 - 12.2886i) q^{73} +(-1.29549 - 5.93538i) q^{74} +(-2.05933 + 2.68377i) q^{75} +(0.739708 - 0.227921i) q^{76} +(1.24357 + 2.68727i) q^{77} +(2.59873 + 1.22217i) q^{78} +(-5.09615 - 8.82678i) q^{79} +(-2.06859 + 6.27341i) q^{80} +(5.22206 + 3.01496i) q^{81} +(7.62727 - 0.642174i) q^{82} +(1.46558 + 0.607064i) q^{83} +(1.44088 - 7.74279i) q^{84} +(-2.43911 - 5.88854i) q^{85} +(2.89190 + 0.922219i) q^{86} +(-3.18168 + 0.852529i) q^{87} +(2.49234 + 1.95158i) q^{88} +(-3.10664 + 11.5941i) q^{89} +(0.0859303 - 1.83073i) q^{90} +(0.616455 + 3.55669i) q^{91} +(0.750785 - 7.98006i) q^{92} +(-5.36624 + 0.706479i) q^{93} +(13.9722 + 2.51081i) q^{94} +(-0.553493 - 0.319560i) q^{95} +(-2.40017 - 8.07014i) q^{96} -3.79460i q^{97} +(9.00969 - 4.10188i) q^{98} +(-0.811419 - 0.336101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.08037	+	0.912577i	0.763938	+	0.645289i
$2$	1.08037	+	0.912577i	0.763938	+	0.645289i
$3$	0.906063	+	1.18080i	0.523116	+	0.681738i	0.977950	−	0.208838i	$-0.0669682\pi$
$3$	0.906063	+	1.18080i	0.523116	+	0.681738i	−0.454834	+	0.890576i	$0.650302\pi$
$4$	0.334408	+	1.97184i	0.167204	+	0.985922i
$5$	1.00532	−	1.31016i	0.449592	−	0.585919i	−0.512486	−	0.858696i	$-0.671275\pi$
$5$	1.00532	−	1.31016i	0.449592	−	0.585919i	0.962077	+	0.272776i	$0.0879419\pi$
$6$	−0.0986893	+	2.10256i	−0.0402898	+	0.858367i
$7$	−2.23554	+	1.41505i	−0.844954	+	0.534839i
$7$	−2.23554	+	1.41505i	−0.844954	+	0.534839i
$8$	−1.43817	+	2.43550i	−0.508472	+	0.861079i
$9$	0.203108	−	0.758010i	0.0677027	−	0.252670i
$10$	2.28173	−	0.498026i	0.721548	−	0.157490i
$11$	0.146082	−	1.10960i	0.0440453	−	0.334557i	−0.955208	−	0.295934i	$-0.904369\pi$
$11$	0.146082	−	1.10960i	0.0440453	−	0.334557i	0.999254	−	0.0386238i	$-0.0122974\pi$
$12$	−2.02537	+	2.18149i	−0.584674	+	0.629741i
$13$	0.522112	−	1.26049i	0.144808	−	0.349597i	−0.834789	−	0.550570i	$-0.814410\pi$
$13$	0.522112	−	1.26049i	0.144808	−	0.349597i	0.979597	+	0.200973i	$0.0644104\pi$
$14$	−3.70656	−	0.511320i	−0.990619	−	0.136656i
$15$	2.45792			0.634632
$16$	−3.77634	+	1.31880i	−0.944086	+	0.329700i
$17$	1.92977	−	3.34246i	0.468039	−	0.810667i	−0.531294	−	0.847187i	$-0.678294\pi$
$17$	1.92977	−	3.34246i	0.468039	−	0.810667i	0.999333	+	0.0365206i	$0.0116275\pi$
$18$	0.911175	−	0.633581i	0.214766	−	0.149337i
$19$	−0.0505153	−	0.383702i	−0.0115890	−	0.0880273i	0.984673	−	0.174411i	$-0.0558022\pi$
$19$	−0.0505153	−	0.383702i	−0.0115890	−	0.0880273i	−0.996262	+	0.0863839i	$0.972469\pi$
$20$	2.91961	+	1.54420i	0.652844	+	0.345295i
$21$	−3.69644	−	1.35761i	−0.806629	−	0.296255i
$22$	1.17042	−	1.06547i	0.249534	−	0.227159i
$23$	−3.87109	−	1.03726i	−0.807178	−	0.216283i	−0.168445	−	0.985711i	$-0.553875\pi$
$23$	−3.87109	−	1.03726i	−0.807178	−	0.216283i	−0.638733	+	0.769428i	$0.720541\pi$
$24$	−4.17893	+	0.508512i	−0.853020	+	0.103800i
$25$	0.588252	+	2.19538i	0.117650	+	0.439077i
$26$	1.71437	−	0.885331i	0.336215	−	0.173628i
$27$	5.20432	−	2.15570i	1.00157	−	0.414865i
$28$	−3.53784	−	3.93493i	−0.668589	−	0.743632i
$29$	−0.846917	+	2.04464i	−0.157269	+	0.379680i	−0.982799	−	0.184677i	$-0.940876\pi$
$29$	−0.846917	+	2.04464i	−0.157269	+	0.379680i	0.825531	+	0.564357i	$0.190876\pi$
$30$	2.65547	+	2.24304i	0.484820	+	0.409521i
$31$	−1.81828	+	3.14935i	−0.326572	+	0.565640i	−0.981829	−	0.189766i	$-0.939227\pi$
$31$	−1.81828	+	3.14935i	−0.326572	+	0.565640i	0.655257	+	0.755406i	$0.272560\pi$
$32$	−5.28336	−	2.02141i	−0.933975	−	0.357338i
$33$	1.44258	−	0.832875i	0.251121	−	0.144985i
$34$	5.13513	−	1.85004i	0.880667	−	0.317279i
$35$	−0.393491	+	4.35148i	−0.0665122	+	0.735534i
$36$	1.56260	+	0.147014i	0.260433	+	0.0245023i
$37$	−3.40805	−	2.61509i	−0.560281	−	0.429918i	0.289406	−	0.957206i	$-0.406542\pi$
$37$	−3.40805	−	2.61509i	−0.560281	−	0.429918i	−0.849687	+	0.527288i	$0.823209\pi$
$38$	0.295582	−	0.460640i	0.0479498	−	0.0747257i
$39$	1.96146	−	0.525571i	0.314085	−	0.0841588i
$40$	1.74506	+	4.33268i	0.275918	+	0.685057i
$41$	3.82713	−	3.82713i	0.597697	−	0.597697i	−0.342002	−	0.939699i	$-0.611105\pi$
$41$	3.82713	−	3.82713i	0.597697	−	0.597697i	0.939699	+	0.342002i	$0.111105\pi$
$42$	−2.75460	−	4.84001i	−0.425045	−	0.746829i
$43$	1.98296	−	0.821369i	0.302399	−	0.125258i	−0.226325	−	0.974052i	$-0.572671\pi$
$43$	1.98296	−	0.821369i	0.302399	−	0.125258i	0.528723	+	0.848794i	$0.322671\pi$
$44$	2.23681	−	0.0830085i	0.337212	−	0.0125140i
$45$	−0.788923	−	1.02814i	−0.117606	−	0.153267i
$46$	−3.23564	−	4.65329i	−0.477070	−	0.686090i
$47$	8.69324	−	5.01904i	1.26804	−	0.732103i	0.293423	−	0.955983i	$-0.405206\pi$
$47$	8.69324	−	5.01904i	1.26804	−	0.732103i	0.974617	+	0.223880i	$0.0718723\pi$
$48$	−4.97885	−	3.26421i	−0.718635	−	0.471148i
$49$	2.99527	−	6.32680i	0.427895	−	0.903828i
$50$	−1.36793	+	2.90866i	−0.193454	+	0.411346i
$51$	5.69529	−	0.749800i	0.797501	−	0.104993i
$52$	2.66009	+	0.608007i	0.368888	+	0.0843153i
$53$	−11.4501	−	1.50744i	−1.57280	−	0.207063i	−0.706910	−	0.707304i	$-0.749911\pi$
$53$	−11.4501	−	1.50744i	−1.57280	−	0.207063i	−0.865886	+	0.500241i	$0.833245\pi$
$54$	7.58984	+	2.42038i	1.03285	+	0.329372i
$55$	−1.30689	−	1.30689i	−0.176221	−	0.176221i
$56$	−0.231256	−	7.47974i	−0.0309029	−	0.999522i
$57$	0.407307	−	0.407307i	0.0539492	−	0.0539492i
$58$	−2.78088	+	1.43609i	−0.365147	+	0.188568i
$59$	−1.42227	+	10.8032i	−0.185164	+	1.40646i	0.606296	+	0.795239i	$0.292655\pi$
$59$	−1.42227	+	10.8032i	−0.185164	+	1.40646i	−0.791460	+	0.611221i	$0.790679\pi$
$60$	0.821947	+	4.84663i	0.106113	+	0.625698i
$61$	1.01451	+	7.70596i	0.129895	+	0.986648i	0.924944	+	0.380103i	$0.124111\pi$
$61$	1.01451	+	7.70596i	0.129895	+	0.986648i	−0.795050	+	0.606545i	$0.792555\pi$
$62$	−4.83844	+	1.74315i	−0.614482	+	0.221380i
$63$	0.618566	+	1.98197i	0.0779320	+	0.249705i
$64$	−3.86331	−	7.00535i	−0.482913	−	0.875668i
$65$	−1.12655	−	1.95124i	−0.139731	−	0.242022i
$66$	2.31859	+	0.416652i	0.285398	+	0.0512863i
$67$	−10.8729	+	8.34305i	−1.32833	+	1.01927i	−0.331203	+	0.943559i	$0.607455\pi$
$67$	−10.8729	+	8.34305i	−1.32833	+	1.01927i	−0.997130	+	0.0757068i	$0.975879\pi$
$68$	7.23615	+	2.68747i	0.877512	+	0.325903i
$69$	−2.28266	−	5.51082i	−0.274800	−	0.663425i
$70$	−4.39617	+	4.34212i	−0.525443	+	0.518983i
$71$	4.38876	+	4.38876i	0.520849	+	0.520849i	0.917828	−	0.396978i	$-0.129941\pi$
$71$	4.38876	+	4.38876i	0.520849	+	0.520849i	−0.396978	+	0.917828i	$0.629941\pi$
$72$	1.55403	+	1.58482i	0.183144	+	0.186773i
$73$	−3.29273	−	12.2886i	−0.385385	−	1.43828i	−0.837559	−	0.546347i	$-0.816018\pi$
$73$	−3.29273	−	12.2886i	−0.385385	−	1.43828i	0.452173	−	0.891930i	$-0.350649\pi$
$74$	−1.29549	−	5.93538i	−0.150598	−	0.689974i
$75$	−2.05933	+	2.68377i	−0.237791	+	0.309895i
$76$	0.739708	−	0.227921i	0.0848504	−	0.0261444i
$77$	1.24357	+	2.68727i	0.141718	+	0.306243i
$78$	2.59873	+	1.22217i	0.294248	+	0.138383i
$79$	−5.09615	−	8.82678i	−0.573361	−	0.993091i	−0.996218	−	0.0868940i	$-0.972306\pi$
$79$	−5.09615	−	8.82678i	−0.573361	−	0.993091i	0.422856	−	0.906197i	$-0.361027\pi$
$80$	−2.06859	+	6.27341i	−0.231276	+	0.701388i
$81$	5.22206	+	3.01496i	0.580229	+	0.334995i
$82$	7.62727	−	0.642174i	0.842291	−	0.0709163i
$83$	1.46558	+	0.607064i	0.160869	+	0.0666339i	0.461665	−	0.887055i	$-0.347252\pi$
$83$	1.46558	+	0.607064i	0.160869	+	0.0666339i	−0.300796	+	0.953688i	$0.597252\pi$
$84$	1.44088	−	7.74279i	0.157213	−	0.844808i
$85$	−2.43911	−	5.88854i	−0.264559	−	0.638702i
$86$	2.89190	+	0.922219i	0.311841	+	0.0994454i
$87$	−3.18168	+	0.852529i	−0.341112	+	0.0914007i
$88$	2.49234	+	1.95158i	0.265685	+	0.208039i
$89$	−3.10664	+	11.5941i	−0.329303	+	1.22898i	0.580612	+	0.814181i	$0.302813\pi$
$89$	−3.10664	+	11.5941i	−0.329303	+	1.22898i	−0.909915	+	0.414795i	$0.863853\pi$
$90$	0.0859303	−	1.83073i	0.00905785	−	0.192976i
$91$	0.616455	+	3.55669i	0.0646220	+	0.372842i
$92$	0.750785	−	7.98006i	0.0782747	−	0.831978i
$93$	−5.36624	+	0.706479i	−0.556453	+	0.0732584i
$94$	13.9722	+	2.51081i	1.44112	+	0.258971i
$95$	−0.553493	−	0.319560i	−0.0567872	−	0.0327861i
$96$	−2.40017	−	8.07014i	−0.244966	−	0.823655i
$97$		−	3.79460i		−	0.385283i	−0.981269	−	0.192642i	$-0.938294\pi$
$97$		−	3.79460i		−	0.385283i	0.981269	−	0.192642i	$-0.0617055\pi$
$98$	9.00969	−	4.10188i	0.910116	−	0.414353i
$99$	−0.811419	−	0.336101i	−0.0815507	−	0.0337794i
$100$	−4.13224	+	1.89409i	−0.413224	+	0.189409i
$101$	8.26826	+	1.08854i	0.822722	+	0.108313i	0.530122	−	0.847921i	$-0.322146\pi$
$101$	8.26826	+	1.08854i	0.822722	+	0.108313i	0.292600	+	0.956235i	$0.405479\pi$
$102$	6.83729	+	4.38733i	0.676992	+	0.434410i
$103$	−13.1687	−	3.52854i	−1.29755	−	0.347677i	−0.457026	−	0.889453i	$-0.651085\pi$
$103$	−13.1687	−	3.52854i	−1.29755	−	0.347677i	−0.840523	+	0.541776i	$0.817752\pi$
$104$	2.31903	+	3.08441i	0.227400	+	0.302451i
$105$	−5.49477	+	3.47808i	−0.536235	+	0.339426i
$106$	−10.9947	−	12.0777i	−1.06790	−	1.17309i
$107$	13.1829	+	10.1156i	1.27444	+	0.977911i	0.999866	+	0.0163441i	$0.00520271\pi$
$107$	13.1829	+	10.1156i	1.27444	+	0.977911i	0.274572	+	0.961567i	$0.411464\pi$
$108$	5.99107	+	9.54123i	0.576491	+	0.918105i
$109$	−14.9313	+	11.4572i	−1.43016	+	1.09740i	−0.451411	+	0.892316i	$0.649079\pi$
$109$	−14.9313	+	11.4572i	−1.43016	+	1.09740i	−0.978745	+	0.205082i	$0.934254\pi$
$110$	−0.219290	−	2.60457i	−0.0209085	−	0.248336i
$111$		−	6.39368i		−	0.606862i
$112$	6.57599	−	8.29194i	0.621373	−	0.783515i
$113$			14.1283i			1.32908i	0.747252	+	0.664541i	$0.231373\pi$
$113$			14.1283i			1.32908i	−0.747252	+	0.664541i	$0.768627\pi$
$114$	0.811742	−	0.0683443i	0.0760266	−	0.00640103i
$115$	−5.25064	+	4.02896i	−0.489625	+	0.375702i
$116$	−4.31493	−	0.986247i	−0.400631	−	0.0915707i
$117$	−0.849419	−	0.651782i	−0.0785288	−	0.0602573i
$118$	−11.3954	+	10.3736i	−1.04903	+	0.954965i
$119$	0.415672	+	10.2029i	0.0381046	+	0.935301i
$120$	−3.53492	+	5.98626i	−0.322692	+	0.546468i
$121$	9.41531	+	2.52282i	0.855937	+	0.229348i
$122$	−5.93624	+	9.25113i	−0.537442	+	0.837558i
$123$	7.98671	+	1.05147i	0.720138	+	0.0948079i
$124$	−6.81807	−	2.53219i	−0.612281	−	0.227398i
$125$	11.0962	+	4.59620i	0.992476	+	0.411097i
$126$	−1.14042	+	2.70575i	−0.101596	+	0.241048i
$127$		−	9.62909i		−	0.854444i	−0.904147	−	0.427222i	$-0.859492\pi$
$127$		−	9.62909i		−	0.854444i	0.904147	−	0.427222i	$-0.140508\pi$
$128$	2.21911	−	11.0939i	0.196143	−	0.980575i
$129$	2.76656	+	1.59728i	0.243582	+	0.140632i
$130$	0.563564	−	3.13613i	0.0494279	−	0.275057i
$131$	−16.2113	+	2.13426i	−1.41639	+	0.186471i	−0.799542	−	0.600610i	$-0.794925\pi$
$131$	−16.2113	+	2.13426i	−1.41639	+	0.186471i	−0.616849	+	0.787081i	$0.711591\pi$
$132$	2.12471	+	2.56603i	0.184932	+	0.223344i
$133$	0.655887	+	0.786299i	0.0568726	+	0.0681808i
$134$	−19.3604	−	0.908734i	−1.67249	−	0.0785027i
$135$	2.40769	−	8.98563i	0.207221	−	0.773360i
$136$	5.36522	+	9.50701i	0.460064	+	0.815219i
$137$	−1.61968	+	0.433992i	−0.138379	+	0.0370785i	−0.327344	−	0.944905i	$-0.606153\pi$
$137$	−1.61968	+	0.433992i	−0.138379	+	0.0370785i	0.188965	+	0.981984i	$0.439487\pi$
$138$	2.56293	−	8.03684i	0.218171	−	0.684141i
$139$	−1.99514	−	4.81670i	−0.169226	−	0.408547i	0.816401	−	0.577486i	$-0.195966\pi$
$139$	−1.99514	−	4.81670i	−0.169226	−	0.408547i	−0.985627	+	0.168939i	$0.945966\pi$
$140$	−8.71202	+	0.679264i	−0.736300	+	0.0574082i
$141$	13.8031	+	5.71745i	1.16243	+	0.481496i
$142$	0.736413	+	8.74656i	0.0617984	+	0.733995i
$143$	−1.32237	−	0.763471i	−0.110582	−	0.0638447i
$144$	0.232657	+	3.13037i	0.0193881	+	0.260864i
$145$	1.82737	+	3.16510i	0.151755	+	0.262848i
$146$	7.65696	−	16.2812i	0.633694	−	1.34744i
$147$	10.1846	−	2.19565i	0.840013	−	0.181094i
$148$	4.01688	−	7.59466i	0.330185	−	0.624277i
$149$	−10.2756	+	13.3915i	−0.841813	+	1.09707i	0.152258	+	0.988341i	$0.451345\pi$
$149$	−10.2756	+	13.3915i	−0.841813	+	1.09707i	−0.994071	+	0.108731i	$0.965321\pi$
$150$	−4.67398	+	1.02017i	−0.381629	+	0.0832968i
$151$	2.89640	+	10.8095i	0.235706	+	0.879665i	0.977830	+	0.209403i	$0.0671519\pi$
$151$	2.89640	+	10.8095i	0.235706	+	0.879665i	−0.742124	+	0.670263i	$0.766181\pi$
$152$	1.00716	+	0.428801i	0.0816911	+	0.0347803i
$153$	−2.14167	−	2.14167i	−0.173144	−	0.173144i
$154$	−1.10882	+	4.03811i	−0.0893514	+	0.325400i
$155$	2.29819	+	5.54832i	0.184595	+	0.445652i
$156$	1.69227	+	3.69194i	0.135490	+	0.295592i
$157$	1.52569	−	1.17070i	0.121763	−	0.0934321i	−0.546085	−	0.837730i	$-0.683882\pi$
$157$	1.52569	−	1.17070i	0.121763	−	0.0934321i	0.667848	+	0.744298i	$0.267216\pi$
$158$	2.54938	−	14.1868i	0.202818	−	1.12864i
$159$	−8.59455	−	14.8862i	−0.681592	−	1.18055i
$160$	−7.95982	+	4.88987i	−0.629279	+	0.386578i
$161$	10.1217	−	3.15896i	0.797705	−	0.248961i
$162$	2.89039	+	8.02281i	0.227090	+	0.630331i
$163$	−0.555029	−	4.21587i	−0.0434733	−	0.330212i	−0.999337	−	0.0364025i	$-0.988410\pi$
$163$	−0.555029	−	4.21587i	−0.0434733	−	0.330212i	0.955864	−	0.293810i	$-0.0949232\pi$
$164$	8.82632	+	6.26668i	0.689220	+	0.489346i
$165$	0.359057	−	2.72731i	0.0279526	−	0.212321i
$166$	1.02938	+	1.99331i	0.0798955	+	0.154711i
$167$	7.50770	−	7.50770i	0.580963	−	0.580963i	−0.354205	−	0.935168i	$-0.615248\pi$
$167$	7.50770	−	7.50770i	0.580963	−	0.580963i	0.935168	+	0.354205i	$0.115248\pi$
$168$	8.62258	−	7.05019i	0.665246	−	0.543934i
$169$	7.87615	+	7.87615i	0.605858	+	0.605858i
$170$	2.73859	−	8.58769i	0.210041	−	0.658646i
$171$	−0.301110	−	0.0396419i	−0.0230265	−	0.00303149i
$172$	2.28273	+	3.63542i	0.174056	+	0.277198i
$173$	12.0525	−	1.58675i	0.916337	−	0.120638i	0.342416	−	0.939549i	$-0.388755\pi$
$173$	12.0525	−	1.58675i	0.916337	−	0.120638i	0.573921	+	0.818910i	$0.305422\pi$
$174$	−4.21540	−	1.98248i	−0.319568	−	0.150291i
$175$	−4.42164	−	4.07546i	−0.334244	−	0.308076i
$176$	0.911687	+	4.38289i	0.0687210	+	0.330373i
$177$	−14.0452	+	8.10898i	−1.05570	+	0.609508i
$178$	−13.9369	+	9.69093i	−1.04461	+	0.726366i
$179$	−11.6270	−	15.1526i	−0.869044	−	1.13256i	−0.990163	−	0.139922i	$-0.955315\pi$
$179$	−11.6270	−	15.1526i	−0.869044	−	1.13256i	0.121118	−	0.992638i	$-0.461352\pi$
$180$	1.76352	−	1.89945i	0.131445	−	0.141577i
$181$	8.16126	−	3.38050i	0.606621	−	0.251271i	−0.0581617	−	0.998307i	$-0.518524\pi$
$181$	8.16126	−	3.38050i	0.606621	−	0.251271i	0.664783	+	0.747036i	$0.268524\pi$
$182$	−2.57975	+	4.40511i	−0.191224	+	0.326528i
$183$	−8.18003	+	8.18003i	−0.604685	+	0.604685i
$184$	8.09354	−	7.93628i	0.596664	−	0.585070i
$185$	−6.85235	+	1.83608i	−0.503795	+	0.134991i
$186$	−6.44225	−	4.13384i	−0.472369	−	0.303108i
$187$	−3.42690	−	2.62955i	−0.250600	−	0.192292i
$188$	12.8039	+	15.4633i	0.933818	+	1.12778i
$189$	−8.58403	+	12.1835i	−0.624397	+	0.886221i
$190$	−0.306356	−	0.850348i	−0.0222254	−	0.0616908i
$191$	14.1485	−	8.16866i	1.02375	−	0.591063i	0.108563	−	0.994090i	$-0.465375\pi$
$191$	14.1485	−	8.16866i	1.02375	−	0.591063i	0.915188	+	0.403026i	$0.132042\pi$
$192$	4.77155	−	10.9091i	0.344357	−	0.787296i
$193$	10.8534	−	18.7987i	0.781245	−	1.35316i	−0.149971	−	0.988690i	$-0.547918\pi$
$193$	10.8534	−	18.7987i	0.781245	−	1.35316i	0.931217	−	0.364466i	$-0.118749\pi$
$194$	3.46286	−	4.09958i	0.248619	−	0.294333i
$195$	1.28331	−	3.09818i	0.0918997	−	0.221865i
$196$	13.4771	+	3.79047i	0.962650	+	0.270748i
$197$	18.9198	−	7.83685i	1.34798	−	0.558353i	0.412253	−	0.911070i	$-0.364742\pi$
$197$	18.9198	−	7.83685i	1.34798	−	0.558353i	0.935730	+	0.352717i	$0.114742\pi$
$198$	−0.569917	−	1.10360i	−0.0405022	−	0.0784291i
$199$	0.236384	+	0.882197i	0.0167568	+	0.0625373i	0.973798	−	0.227415i	$-0.0730273\pi$
$199$	0.236384	+	0.882197i	0.0167568	+	0.0625373i	−0.957041	+	0.289952i	$0.906361\pi$
$200$	−6.19287	−	1.72466i	−0.437902	−	0.121952i
$201$	−19.7030	−	5.27941i	−1.38974	−	0.372381i
$202$	7.93942	+	8.72144i	0.558616	+	0.613639i
$203$	−0.999950	−	5.76930i	−0.0701827	−	0.404926i
$204$	3.38304	+	10.9795i	0.236860	+	0.768718i
$205$	−1.16665	−	8.86161i	−0.0814826	−	0.618922i
$206$	−11.0070	−	15.8296i	−0.766895	−	1.10290i
$207$	−1.57250	+	2.72365i	−0.109296	+	0.189307i
$208$	−0.309341	+	5.44860i	−0.0214489	+	0.377793i
$209$	−0.433136			−0.0299606
$210$	−9.11041	−	1.25678i	−0.628678	−	0.0867263i
$211$	0.540538	−	1.30497i	0.0372121	−	0.0898380i	−0.904181	−	0.427150i	$-0.859518\pi$
$211$	0.540538	−	1.30497i	0.0372121	−	0.0898380i	0.941393	+	0.337312i	$0.109518\pi$
$212$	−0.856576	−	23.0820i	−0.0588299	−	1.58528i
$213$	−1.20577	+	9.15875i	−0.0826182	+	0.627547i
$214$	5.01118	+	22.9590i	0.342557	+	1.56944i
$215$	0.917384	−	3.42372i	0.0625650	−	0.233496i
$216$	−2.23452	+	15.7754i	−0.152040	+	1.07338i
$217$	−0.391656	−	9.61344i	−0.0265873	−	0.652603i
$218$	−26.5869	−	1.24793i	−1.80069	−	0.0845202i
$219$	11.5271	−	15.0224i	0.778927	−	1.01512i
$220$	2.13995	−	3.01402i	0.144276	−	0.203205i
$221$	−3.20559	−	4.17760i	−0.215631	−	0.281016i
$222$	5.83473	−	6.90756i	0.391601	−	0.463605i
$223$	−28.1962			−1.88816			−0.944079	−	0.329718i	$-0.893046\pi$
$223$	−28.1962			−1.88816			−0.944079	+	0.329718i	$0.893046\pi$
$224$	14.6716	−	2.95728i	0.980284	−	0.197592i
$225$	1.78360			0.118907
$226$	−12.8932	+	15.2639i	−0.857642	+	1.01534i
$227$	−8.52163	−	11.1056i	−0.565600	−	0.737105i	0.419751	−	0.907639i	$-0.362117\pi$
$227$	−8.52163	−	11.1056i	−0.565600	−	0.737105i	−0.985352	+	0.170534i	$0.945451\pi$
$228$	0.939353	+	0.666940i	0.0622102	+	0.0441692i
$229$	−9.19837	+	11.9876i	−0.607845	+	0.792160i	−0.991331	−	0.131387i	$-0.958057\pi$
$229$	−9.19837	+	11.9876i	−0.607845	+	0.792160i	0.383486	+	0.923547i	$0.374724\pi$
$230$	−9.34938	−	0.438838i	−0.616480	−	0.0289361i
$231$	−2.04639	+	3.90325i	−0.134642	+	0.256815i
$232$	−3.76170	−	5.00321i	−0.246968	−	0.328477i
$233$	−2.41546	+	9.01461i	−0.158242	+	0.590567i	0.840564	+	0.541712i	$0.182224\pi$
$233$	−2.41546	+	9.01461i	−0.158242	+	0.590567i	−0.998806	+	0.0488545i	$0.984443\pi$
$234$	−0.322887	−	1.47933i	−0.0211078	−	0.0967067i
$235$	2.16374	−	16.4352i	0.141147	−	1.07212i
$236$	−21.7779	+	0.808182i	−1.41762	+	0.0526082i
$237$	5.80528	−	14.0152i	0.377093	−	0.910384i
$238$	−8.86188	+	11.4023i	−0.574430	+	0.739101i
$239$	23.4830			1.51899			0.759496	−	0.650512i	$-0.225446\pi$
$239$	23.4830			1.51899			0.759496	+	0.650512i	$0.225446\pi$
$240$	−9.28194	+	3.24150i	−0.599147	+	0.209238i
$241$	11.3430	−	19.6467i	0.730669	−	1.26556i	−0.225928	−	0.974144i	$-0.572541\pi$
$241$	11.3430	−	19.6467i	0.730669	−	1.26556i	0.956598	−	0.291412i	$-0.0941252\pi$
$242$	7.86977	+	11.3178i	0.505888	+	0.727534i
$243$	−1.03437	−	7.85679i	−0.0663546	−	0.504013i
$244$	−14.8557	+	4.57739i	−0.951039	+	0.293037i
$245$	−5.27789	−	10.2847i	−0.337192	−	0.657066i
$246$	7.66907	+	8.42447i	0.488962	+	0.537124i
$247$	−0.510028	−	0.136661i	−0.0324523	−	0.00869556i
$248$	−5.05523	−	8.95772i	−0.321008	−	0.568816i
$249$	0.611086	+	2.28060i	0.0387260	+	0.144527i
$250$	7.79365	+	15.0918i	0.492914	+	0.954487i
$251$	9.64932	−	3.99688i	0.609060	−	0.252281i	−0.0567666	−	0.998387i	$-0.518079\pi$
$251$	9.64932	−	3.99688i	0.609060	−	0.252281i	0.665827	+	0.746107i	$0.268079\pi$
$252$	−3.70128	+	1.88250i	−0.233159	+	0.118586i
$253$	−1.71644	+	4.14384i	−0.107911	+	0.260521i
$254$	8.78728	−	10.4030i	0.551363	−	0.652742i
$255$	4.74322	−	8.21551i	0.297032	−	0.514475i
$256$	12.5215	−	9.96048i	0.782596	−	0.622530i
$257$	12.4485	−	7.18712i	0.776514	−	0.448321i	−0.0586795	−	0.998277i	$-0.518689\pi$
$257$	12.4485	−	7.18712i	0.776514	−	0.448321i	0.835193	+	0.549956i	$0.185356\pi$
$258$	1.53128	+	4.25035i	0.0953334	+	0.264615i
$259$	11.3193	+	1.02357i	0.703348	+	0.0636017i
$260$	3.47082	−	2.87389i	0.215251	−	0.178231i
$261$	1.37784	+	1.05726i	0.0852863	+	0.0654424i
$262$	−19.4620	−	12.4883i	−1.20236	−	0.771529i
$263$	12.1073	−	3.24415i	0.746570	−	0.200043i	0.134574	−	0.990904i	$-0.457034\pi$
$263$	12.1073	−	3.24415i	0.746570	−	0.200043i	0.611996	+	0.790861i	$0.290367\pi$
$264$	−0.0462192	+	4.71123i	−0.00284460	+	0.289956i
$265$	−13.4860	+	13.4860i	−0.828438	+	0.828438i
$266$	−0.00895675	+	1.44804i	−0.000549173	+	0.0887852i
$267$	−16.5052	+	6.83669i	−1.01010	+	0.418398i
$268$	−20.0872	−	18.6496i	−1.22702	−	1.13921i
$269$	−2.15183	−	2.80432i	−0.131199	−	0.170982i	0.723134	−	0.690708i	$-0.242701\pi$
$269$	−2.15183	−	2.80432i	−0.131199	−	0.170982i	−0.854333	+	0.519725i	$0.826034\pi$
$270$	10.8013	−	7.51062i	0.657345	−	0.457082i
$271$	3.20436	−	1.85004i	0.194651	−	0.112382i	−0.399507	−	0.916730i	$-0.630819\pi$
$271$	3.20436	−	1.85004i	0.194651	−	0.112382i	0.594158	+	0.804348i	$0.297485\pi$
$272$	−2.87944	+	15.1673i	−0.174592	+	0.919651i
$273$	−3.64121	+	3.95050i	−0.220376	+	0.239095i
$274$	−2.14591	−	1.00921i	−0.129639	−	0.0609686i
$275$	2.52194	−	0.332019i	0.152078	−	0.0200215i
$276$	10.1031	−	6.34390i	0.608138	−	0.381858i
$277$	17.2112	+	2.26589i	1.03412	+	0.136144i	0.628430	−	0.777867i	$-0.283698\pi$
$277$	17.2112	+	2.26589i	1.03412	+	0.136144i	0.405690	+	0.914011i	$0.367031\pi$
$278$	2.24011	−	7.02455i	0.134353	−	0.421304i
$279$	2.01793	+	2.01793i	0.120810	+	0.120810i
$280$	−10.0321	−	7.21653i	−0.599533	−	0.431270i
$281$	7.81895	−	7.81895i	0.466439	−	0.466439i	−0.434320	−	0.900759i	$-0.643011\pi$
$281$	7.81895	−	7.81895i	0.466439	−	0.466439i	0.900759	+	0.434320i	$0.143011\pi$
$282$	9.69491	+	18.7734i	0.577324	+	1.11794i
$283$	−0.857977	+	6.51699i	−0.0510015	+	0.387395i	0.946839	+	0.321708i	$0.104257\pi$
$283$	−0.857977	+	6.51699i	−0.0510015	+	0.387395i	−0.997840	+	0.0656864i	$0.979076\pi$
$284$	−7.18631	+	10.1216i	−0.426429	+	0.600605i
$285$	−0.124163	−	0.943109i	−0.00735476	−	0.0558649i
$286$	−0.731927	−	2.03160i	−0.0432797	−	0.120131i
$287$	−3.14012	+	13.9713i	−0.185355	+	0.824698i
$288$	−2.60534	+	3.59428i	−0.153521	+	0.211795i
$289$	1.05195	+	1.82204i	0.0618797	+	0.107179i
$290$	−0.914157	+	5.08711i	−0.0536811	+	0.298725i
$291$	4.48068	−	3.43815i	0.262662	−	0.201548i
$292$	23.1302	−	10.6022i	1.35359	−	0.620445i
$293$	−3.19328	−	7.70926i	−0.186553	−	0.450380i	0.802738	−	0.596331i	$-0.203376\pi$
$293$	−3.19328	−	7.70926i	−0.186553	−	0.450380i	−0.989292	+	0.145952i	$0.953376\pi$
$294$	13.0069	+	6.92212i	0.758576	+	0.403706i
$295$	12.7241	+	12.7241i	0.740824	+	0.740824i
$296$	11.2704	−	4.53935i	0.655080	−	0.263844i
$297$	−1.63171	−	6.08963i	−0.0946815	−	0.353356i
$298$	−23.3223	+	5.09046i	−1.35102	+	0.294883i
$299$	−3.32859	+	4.33791i	−0.192498	+	0.250868i
$300$	−5.98063	−	3.16320i	−0.345292	−	0.182628i
$301$	−3.27071	+	4.64219i	−0.188520	+	0.267571i
$302$	−6.73532	+	14.3215i	−0.387574	+	0.824108i
$303$	6.20621	+	10.7495i	0.356538	+	0.617541i
$304$	0.696790	+	1.38237i	0.0399636	+	0.0792844i
$305$	11.1159	+	6.41778i	0.636495	+	0.367481i
$306$	−0.359362	−	4.26824i	−0.0205434	−	0.243999i
$307$	−20.1868	−	8.36163i	−1.15212	−	0.477223i	−0.276876	−	0.960906i	$-0.589299\pi$
$307$	−20.1868	−	8.36163i	−1.15212	−	0.477223i	−0.875244	+	0.483682i	$0.839299\pi$
$308$	−4.88302	+	3.35077i	−0.278236	+	0.190928i
$309$	−7.76515	−	18.7467i	−0.441744	−	1.06646i
$310$	−2.58037	+	8.09152i	−0.146555	+	0.459568i
$311$	11.7920	−	3.15965i	0.668662	−	0.179167i	0.0915099	−	0.995804i	$-0.470831\pi$
$311$	11.7920	−	3.15965i	0.668662	−	0.179167i	0.577152	+	0.816637i	$0.304164\pi$
$312$	−1.54089	+	5.53299i	−0.0872359	+	0.313244i
$313$	−8.28146	+	30.9068i	−0.468096	+	1.74696i	0.178321	+	0.983972i	$0.442934\pi$
$313$	−8.28146	+	30.9068i	−0.468096	+	1.74696i	−0.646417	+	0.762985i	$0.723733\pi$
$314$	2.71666	+	0.127514i	0.153310	+	0.00719603i
$315$	3.21854	+	1.18209i	0.181344	+	0.0666033i
$316$	15.7009	−	13.0006i	0.883242	−	0.731338i
$317$	−11.9523	+	1.57355i	−0.671310	+	0.0883797i	−0.458473	−	0.888708i	$-0.651604\pi$
$317$	−11.9523	+	1.57355i	−0.671310	+	0.0883797i	−0.212837	+	0.977088i	$0.568270\pi$
$318$	4.29948	−	23.9258i	0.241103	−	1.34169i
$319$	2.14502	+	1.23843i	0.120098	+	0.0693385i
$320$	−13.0619	−	1.98107i	−0.730185	−	0.110745i
$321$			24.7318i			1.38039i
$322$	13.8180	+	5.82401i	0.770049	+	0.324559i
$323$	−1.37999	−	0.571612i	−0.0767849	−	0.0318054i
$324$	−4.19873	+	11.3053i	−0.233263	+	0.628073i
$325$	3.07439	+	0.404752i	0.170537	+	0.0224516i
$326$	3.24766	−	5.06121i	0.179871	−	0.280315i
$327$	−27.0574	−	7.25000i	−1.49627	−	0.400926i
$328$	3.81689	+	14.8250i	0.210752	+	0.818576i
$329$	−12.3319	+	23.5216i	−0.679878	+	1.29679i
$330$	2.87680	−	2.61884i	0.158362	−	0.144163i
$331$	10.2096	+	7.83414i	0.561173	+	0.430603i	0.850004	−	0.526777i	$-0.176600\pi$
$331$	10.2096	+	7.83414i	0.561173	+	0.430603i	−0.288830	+	0.957380i	$0.593266\pi$
$332$	−0.706934	+	3.09291i	−0.0387980	+	0.169745i
$333$	−2.67447	+	2.05219i	−0.146560	+	0.112459i
$334$	14.9625	−	1.25976i	0.818709	−	0.0689308i
$335$			22.6326i			1.23655i
$336$	15.7494	+	0.251941i	0.859202	+	0.0137445i
$337$		−	13.3161i		−	0.725377i	−0.931910	−	0.362688i	$-0.881859\pi$
$337$		−	13.3161i		−	0.725377i	0.931910	−	0.362688i	$-0.118141\pi$
$338$	1.32158	+	15.6968i	0.0718846	+	0.853792i
$339$	−16.6828	+	12.8012i	−0.906085	+	0.695263i
$340$	10.7956	−	6.77872i	0.585475	−	0.367628i
$341$	3.22890	+	2.47763i	0.174855	+	0.134171i
$342$	−0.289135	−	0.317614i	−0.0156346	−	0.0171746i
$343$	2.25670	+	18.3823i	0.121850	+	0.992548i
$344$	−0.851401	+	6.01077i	−0.0459044	+	0.324079i
$345$	−9.51483	−	2.54949i	−0.512261	−	0.137260i
$346$	14.4692	+	9.28458i	0.777871	+	0.499142i
$347$	−10.5082	−	1.38343i	−0.564108	−	0.0742662i	−0.156921	−	0.987611i	$-0.550157\pi$
$347$	−10.5082	−	1.38343i	−0.564108	−	0.0742662i	−0.407187	+	0.913345i	$0.633490\pi$
$348$	−2.74503	−	5.98869i	−0.147149	−	0.321027i
$349$	20.3065	+	8.41123i	1.08698	+	0.450243i	0.852954	−	0.521986i	$-0.174809\pi$
$349$	20.3065	+	8.41123i	1.08698	+	0.450243i	0.234029	+	0.972230i	$0.424809\pi$
$350$	−1.05784	−	8.43810i	−0.0565441	−	0.451035i
$351$		−	7.68551i		−	0.410222i
$352$	−3.01476	+	5.56714i	−0.160687	+	0.296729i
$353$	−4.91322	−	2.83665i	−0.261504	−	0.150980i	0.363516	−	0.931588i	$-0.381576\pi$
$353$	−4.91322	−	2.83665i	−0.261504	−	0.150980i	−0.625021	+	0.780608i	$0.714909\pi$
$354$	−22.5741	−	4.05658i	−1.19980	−	0.215605i
$355$	10.1620	−	1.33786i	0.539345	−	0.0710062i
$356$	−23.9007	−	2.24864i	−1.26674	−	0.119178i
$357$	−11.6710	+	9.73533i	−0.617697	+	0.515248i
$358$	1.26643	−	26.9810i	0.0669327	−	1.42599i
$359$	−2.40629	+	8.98041i	−0.126999	+	0.473968i	−0.999903	−	0.0139247i	$-0.995567\pi$
$359$	−2.40629	+	8.98041i	−0.126999	+	0.473968i	0.872904	+	0.487892i	$0.162234\pi$
$360$	3.63865	−	0.442769i	0.191774	−	0.0233360i
$361$	18.2079	−	4.87880i	0.958311	−	0.256779i
$362$	11.9022	+	3.79557i	0.625564	+	0.199491i
$363$	5.55190	+	13.4035i	0.291399	+	0.703500i
$364$	−6.80709	+	2.40494i	−0.356789	+	0.126053i
$365$	−19.4103	−	8.04000i	−1.01598	−	0.420833i
$366$	−16.3024	+	1.37257i	−0.852139	+	0.0717454i
$367$	0.684236	+	0.395044i	0.0357168	+	0.0206211i	0.517752	−	0.855531i	$-0.326769\pi$
$367$	0.684236	+	0.395044i	0.0357168	+	0.0206211i	−0.482035	+	0.876152i	$0.660102\pi$
$368$	15.9865	−	1.18816i	0.833354	−	0.0619371i
$369$	−2.12368	−	3.67832i	−0.110554	−	0.191486i
$370$	−9.07866	−	4.26964i	−0.471977	−	0.221968i
$371$	27.7303	−	12.8326i	1.43969	−	0.666234i
$372$	−3.18758	−	10.3451i	−0.165268	−	0.536370i
$373$	0.658939	−	0.858746i	0.0341186	−	0.0444642i	−0.775982	−	0.630754i	$-0.782746\pi$
$373$	0.658939	−	0.858746i	0.0341186	−	0.0444642i	0.810101	+	0.586290i	$0.199412\pi$
$374$	−1.30266	−	5.96820i	−0.0673588	−	0.308608i
$375$	4.62666	+	17.2669i	0.238919	+	0.891660i
$376$	−0.278525	+	28.3906i	−0.0143638	+	1.46414i
$377$	2.13506	+	2.13506i	0.109961	+	0.109961i
$378$	−20.3923	+	5.32915i	−1.04887	+	0.274102i
$379$	1.93491	+	4.67129i	0.0993897	+	0.239948i	0.965751	−	0.259469i	$-0.0835476\pi$
$379$	1.93491	+	4.67129i	0.0993897	+	0.239948i	−0.866362	+	0.499417i	$0.833548\pi$
$380$	0.445029	−	1.19827i	0.0228295	−	0.0614698i
$381$	11.3701	−	8.72457i	0.582507	−	0.446973i
$382$	22.7402	+	4.08643i	1.16349	+	0.209080i
$383$	15.7126	+	27.2150i	0.802877	+	1.39062i	0.917715	+	0.397239i	$0.130032\pi$
$383$	15.7126	+	27.2150i	0.802877	+	1.39062i	−0.114838	+	0.993384i	$0.536635\pi$
$384$	15.1104	−	7.43148i	0.771101	−	0.379236i
$385$	4.77092	+	1.07229i	0.243149	+	0.0546490i
$386$	28.8809	−	10.4050i	1.47000	−	0.529599i
$387$	−0.219851	−	1.66993i	−0.0111756	−	0.0848874i
$388$	7.48236	−	1.26894i	0.379860	−	0.0644208i
$389$	0.0876149	−	0.665501i	0.00444225	−	0.0337423i	−0.989080	−	0.147378i	$-0.952916\pi$
$389$	0.0876149	−	0.665501i	0.00444225	−	0.0337423i	0.993522	+	0.113636i	$0.0362498\pi$
$390$	4.21378	−	2.17607i	0.213373	−	0.110190i
$391$	−10.9373	+	10.9373i	−0.553124	+	0.553124i
$392$	11.1012	+	16.3940i	0.560695	+	0.828023i
$393$	−17.2086	−	17.2086i	−0.868062	−	0.868062i
$394$	27.5922	+	8.79909i	1.39007	+	0.443292i
$395$	−16.6877	−	2.19698i	−0.839649	−	0.110542i
$396$	0.391394	−	1.71239i	0.0196683	−	0.0860507i
$397$	25.8536	−	3.40369i	1.29755	−	0.170826i	0.550076	−	0.835114i	$-0.314599\pi$
$397$	25.8536	−	3.40369i	1.29755	−	0.170826i	0.747477	+	0.664288i	$0.231265\pi$
$398$	−0.549690	+	1.16882i	−0.0275535	+	0.0585876i
$399$	−0.334191	+	1.48691i	−0.0167305	+	0.0744387i
$400$	−5.11671	−	7.51474i	−0.255836	−	0.375737i
$401$	−14.3098	+	8.26177i	−0.714597	+	0.412573i	−0.812761	−	0.582597i	$-0.802037\pi$
$401$	−14.3098	+	8.26177i	−0.714597	+	0.412573i	0.0981636	+	0.995170i	$0.468703\pi$
$402$	−16.4687	−	23.6843i	−0.821386	−	1.18126i
$403$	3.02038	+	3.93623i	0.150456	+	0.196078i
$404$	0.618542	+	16.6677i	0.0307736	+	0.829251i
$405$	9.19989	−	3.81072i	0.457146	−	0.189356i
$406$	4.18461	−	7.14552i	0.207679	−	0.354626i
$407$	−3.39956	+	3.39956i	−0.168510	+	0.168510i
$408$	−6.36469	+	14.9492i	−0.315099	+	0.740097i
$409$	−2.33918	+	0.626781i	−0.115665	+	0.0309923i	−0.316187	−	0.948697i	$-0.602403\pi$
$409$	−2.33918	+	0.626781i	−0.115665	+	0.0309923i	0.200522	+	0.979689i	$0.435736\pi$
$410$	6.82648	−	10.6385i	0.337136	−	0.525398i
$411$	−1.97999	−	1.51930i	−0.0976659	−	0.0749417i
$412$	2.55402	−	27.1466i	0.125828	−	1.33742i
$413$	−12.1076	−	26.1636i	−0.595774	−	1.28743i
$414$	−4.18443	+	1.50753i	−0.205653	+	0.0740910i
$415$	2.26872	−	1.30985i	0.111367	−	0.0642979i
$416$	−5.30647	+	5.60422i	−0.260171	+	0.274770i
$417$	3.87985	−	6.72010i	0.189997	−	0.329085i
$418$	−0.467948	−	0.395270i	−0.0228881	−	0.0193333i
$419$	5.90675	−	14.2602i	0.288564	−	0.696654i	−0.711418	−	0.702769i	$-0.751947\pi$
$419$	5.90675	−	14.2602i	0.288564	−	0.696654i	0.999981	+	0.00611536i	$0.00194659\pi$
$420$	−8.69572	−	9.67174i	−0.424308	−	0.471933i
$421$	−0.800818	+	0.331710i	−0.0390295	+	0.0161665i	−0.402113	−	0.915590i	$-0.631724\pi$
$421$	−0.800818	+	0.331710i	−0.0390295	+	0.0161665i	0.363083	+	0.931757i	$0.381724\pi$
$422$	1.77487	−	0.916574i	0.0863993	−	0.0446181i
$423$	−2.03882	−	7.60897i	−0.0991307	−	0.369961i
$424$	20.1386	−	25.7188i	0.978019	−	1.24902i
$425$	8.47319	+	2.27038i	0.411010	+	0.110130i
$426$	−9.66075	+	8.79450i	−0.468065	+	0.426095i
$427$	−13.1723	−	15.7914i	−0.637452	−	0.764199i
$428$	−15.5379	+	29.3773i	−0.751053	+	1.42001i
$429$	−0.296641	−	2.25321i	−0.0143220	−	0.108786i
$430$	4.11552	−	2.86171i	0.198468	−	0.138004i
$431$	−2.29200	+	3.96987i	−0.110402	+	0.191222i	−0.915932	−	0.401333i	$-0.868547\pi$
$431$	−2.29200	+	3.96987i	−0.110402	+	0.191222i	0.805530	+	0.592554i	$0.201880\pi$
$432$	−16.8104	+	15.0041i	−0.808789	+	0.721886i
$433$	−12.5378			−0.602528			−0.301264	−	0.953541i	$-0.597409\pi$
$433$	−12.5378			−0.602528			−0.301264	+	0.953541i	$0.597409\pi$
$434$	8.34987	−	10.7435i	0.400806	−	0.515705i
$435$	−2.08165	+	5.02556i	−0.0998077	+	0.240957i
$436$	−27.5849	−	25.6108i	−1.32108	−	1.22653i
$437$	−0.202448	+	1.53774i	−0.00968439	+	0.0735602i
$438$	26.1626	−	5.71041i	1.25010	−	0.272854i
$439$	7.54474	−	28.1573i	0.360091	−	1.34388i	−0.513865	−	0.857871i	$-0.671787\pi$
$439$	7.54474	−	28.1573i	0.360091	−	1.34388i	0.873956	−	0.486006i	$-0.161547\pi$
$440$	5.06247	−	1.30339i	0.241344	−	0.0621369i
$441$	−4.18741	−	3.55547i	−0.199401	−	0.169308i
$442$	0.349156	−	7.43871i	0.0166076	−	0.353823i
$443$	−5.94436	+	7.74684i	−0.282425	+	0.368064i	−0.912926	−	0.408125i	$-0.866183\pi$
$443$	−5.94436	+	7.74684i	−0.282425	+	0.368064i	0.630501	+	0.776188i	$0.282849\pi$
$444$	12.6074	−	2.13810i	0.598318	−	0.101470i
$445$	12.0670	+	15.7260i	0.572029	+	0.745482i
$446$	−30.4624	−	25.7312i	−1.44244	−	1.21841i
$447$	−25.1231			−1.18828
$448$	18.5495	+	10.1940i	0.876381	+	0.481619i
$449$	−37.0103			−1.74662			−0.873311	−	0.487163i	$-0.838032\pi$
$449$	−37.0103			−1.74662			−0.873311	+	0.487163i	$0.838032\pi$
$450$	1.92695	+	1.62767i	0.0908375	+	0.0767293i
$451$	−3.68751	−	4.80566i	−0.173638	−	0.226290i
$452$	−27.8589	+	4.72462i	−1.31037	+	0.222227i
$453$	−10.1396	+	13.2142i	−0.476400	+	0.620856i
$454$	0.928185	−	19.7748i	0.0435619	−	0.928079i
$455$	5.27955	+	2.76795i	0.247509	+	0.129764i
$456$	0.406217	+	1.57778i	0.0190229	+	0.0738861i
$457$	−0.872935	+	3.25784i	−0.0408342	+	0.152395i	−0.983333	−	0.181815i	$-0.941803\pi$
$457$	−0.872935	+	3.25784i	−0.0408342	+	0.152395i	0.942499	+	0.334210i	$0.108470\pi$
$458$	−20.8772	+	4.55680i	−0.975529	+	0.212925i
$459$	2.83780	−	21.5553i	0.132457	−	1.00611i
$460$	−9.70034	−	9.00613i	−0.452280	−	0.419913i
$461$	3.14709	−	7.59775i	0.146575	−	0.353863i	−0.833492	−	0.552532i	$-0.813662\pi$
$461$	3.14709	−	7.59775i	0.146575	−	0.353863i	0.980067	+	0.198669i	$0.0636619\pi$
$462$	−5.77288	+	2.34948i	−0.268579	+	0.109308i
$463$	−37.3652			−1.73651			−0.868254	−	0.496120i	$-0.834758\pi$
$463$	−37.3652			−1.73651			−0.868254	+	0.496120i	$0.834758\pi$
$464$	0.501781	−	8.83817i	0.0232946	−	0.410302i
$465$	−4.46918	+	7.74084i	−0.207253	+	0.358973i
$466$	−10.8361	+	7.53484i	−0.501973	+	0.349045i
$467$	1.40775	+	10.6929i	0.0651427	+	0.494808i	0.992652	+	0.121007i	$0.0386124\pi$
$467$	1.40775	+	10.6929i	0.0651427	+	0.494808i	−0.927509	+	0.373801i	$0.878054\pi$
$468$	1.00116	−	1.89288i	0.0462787	−	0.0874986i
$469$	12.5009	−	34.0369i	0.577238	−	1.57168i
$470$	17.3360	−	15.7816i	0.799652	−	0.727950i
$471$	2.76474	+	0.740809i	0.127392	+	0.0341347i
$472$	−24.2658	−	19.0009i	−1.11692	−	0.874586i
$473$	−0.621718	−	2.32028i	−0.0285866	−	0.106687i
$474$	19.0618	−	9.84385i	0.875537	−	0.452143i
$475$	0.812658	−	0.336614i	0.0372873	−	0.0154449i
$476$	−19.9796	+	4.23158i	−0.915763	+	0.193954i
$477$	−3.46827	+	8.37314i	−0.158801	+	0.383380i
$478$	25.3704	+	21.4301i	1.16042	+	0.980189i
$479$	2.74811	−	4.75986i	0.125564	−	0.217484i	−0.796389	−	0.604785i	$-0.793259\pi$
$479$	2.74811	−	4.75986i	0.125564	−	0.217484i	0.921953	+	0.387301i	$0.126593\pi$
$480$	−12.9861	−	4.96846i	−0.592730	−	0.226778i
$481$	−5.07568	+	2.93045i	−0.231431	+	0.133617i
$482$	30.1838	−	10.8744i	1.37484	−	0.495314i
$483$	12.9011	+	9.08958i	0.587018	+	0.413590i
$484$	−1.82607	+	19.4092i	−0.0830031	+	0.882235i
$485$	−4.97152	−	3.81478i	−0.225745	−	0.173220i
$486$	6.05242	−	9.43219i	0.274543	−	0.427853i
$487$	−5.50269	+	1.47444i	−0.249351	+	0.0668133i	−0.381329	−	0.924439i	$-0.624534\pi$
$487$	−5.50269	+	1.47444i	−0.249351	+	0.0668133i	0.131979	+	0.991253i	$0.457867\pi$
$488$	−20.2269	−	8.61169i	−0.915629	−	0.389833i
$489$	4.47522	−	4.47522i	0.202377	−	0.202377i
$490$	3.68350	−	15.9278i	0.166403	−	0.719544i
$491$	−12.0158	+	4.97710i	−0.542265	+	0.224614i	−0.636966	−	0.770892i	$-0.719811\pi$
$491$	−12.0158	+	4.97710i	−0.542265	+	0.224614i	0.0947005	+	0.995506i	$0.469811\pi$
$492$	0.597480	+	16.1002i	0.0269365	+	0.725852i
$493$	5.19978	+	6.77648i	0.234186	+	0.305197i
$494$	−0.426305	−	0.613084i	−0.0191804	−	0.0275840i
$495$	−1.25608	+	0.725197i	−0.0564565	+	0.0325952i
$496$	2.71308	−	14.2910i	0.121821	−	0.641683i
$497$	−16.0215	−	3.60093i	−0.718664	−	0.161524i
$498$	−1.42103	+	3.02156i	−0.0636777	+	0.135400i
$499$	−30.5468	+	4.02157i	−1.36746	+	0.180030i	−0.778254	−	0.627950i	$-0.783894\pi$
$499$	−30.5468	+	4.02157i	−1.36746	+	0.180030i	−0.589210	+	0.807980i	$0.700561\pi$
$500$	−5.35234	+	23.4170i	−0.239364	+	1.04724i
$501$	15.6676	+	2.06268i	0.699976	+	0.0921535i
$502$	14.0723	+	4.48763i	0.628078	+	0.200293i
$503$	−1.54756	−	1.54756i	−0.0690023	−	0.0690023i	0.671763	−	0.740766i	$-0.265537\pi$
$503$	−1.54756	−	1.54756i	−0.0690023	−	0.0690023i	−0.740766	+	0.671763i	$0.765537\pi$
$504$	−5.71669	−	1.34390i	−0.254642	−	0.0598622i
$505$	9.73838	−	9.73838i	0.433352	−	0.433352i
$506$	−5.63597	+	2.91051i	−0.250549	+	0.129388i
$507$	−2.16391	+	16.4365i	−0.0961024	+	0.729970i
$508$	18.9871	−	3.22004i	0.842415	−	0.142866i
$509$	−0.116012	−	0.881200i	−0.00514215	−	0.0390585i	0.988681	−	0.150030i	$-0.0479371\pi$
$509$	−0.116012	−	0.881200i	−0.00514215	−	0.0390585i	−0.993824	+	0.110972i	$0.964604\pi$
$510$	12.6217	−	4.54725i	0.558899	−	0.201355i
$511$	24.7501	+	22.8124i	1.09488	+	1.00916i
$512$	22.6176	+	0.665837i	0.999567	+	0.0294261i
$513$	−1.09004	−	1.88801i	−0.0481266	−	0.0833578i
$514$	20.0078	+	3.59541i	0.882505	+	0.158587i
$515$	−17.8616	+	13.7057i	−0.787078	+	0.603946i
$516$	−2.22442	+	5.98937i	−0.0979247	+	0.263668i
$517$	−4.29922	−	10.3792i	−0.189079	−	0.456478i
$518$	11.2950	+	11.4356i	0.496273	+	0.502451i
$519$	12.7940	+	12.7940i	0.561594	+	0.561594i
$520$	6.37242	+	0.0625162i	0.279449	+	0.00274152i
$521$	−9.27490	−	34.6144i	−0.406341	−	1.51648i	−0.801570	−	0.597901i	$-0.796001\pi$
$521$	−9.27490	−	34.6144i	−0.406341	−	1.51648i	0.395229	−	0.918583i	$-0.370665\pi$
$522$	0.523755	+	2.39961i	0.0229241	+	0.105028i
$523$	17.4057	−	22.6835i	0.761098	−	0.991882i	−0.238686	−	0.971097i	$-0.576717\pi$
$523$	17.4057	−	22.6835i	0.761098	−	0.991882i	0.999784	−	0.0207849i	$-0.00661652\pi$
$524$	−9.62963	−	31.2525i	−0.420672	−	1.36527i
$525$	0.806041	−	8.91372i	0.0351785	−	0.389027i
$526$	16.0409	+	7.54398i	0.699419	+	0.328933i
$527$	7.01772	+	12.1551i	0.305697	+	0.529482i
$528$	−4.34929	+	5.04770i	−0.189279	+	0.219673i
$529$	−6.00914	−	3.46938i	−0.261267	−	0.150843i
$530$	−26.8769	+	2.26289i	−1.16746	+	0.0982935i
$531$	7.90008	+	3.27232i	0.342834	+	0.142007i
$532$	−1.33113	+	1.55625i	−0.0577117	+	0.0674721i
$533$	−2.82587	−	6.82225i	−0.122402	−	0.295504i
$534$	−24.0708	−	7.67611i	−1.04164	−	0.332178i
$535$	26.5060	−	7.10226i	1.14595	−	0.307057i
$536$	−4.68239	−	38.4796i	−0.202249	−	1.66207i
$537$	7.35747	−	27.4585i	0.317498	−	1.18492i
$538$	0.234379	−	4.99342i	0.0101048	−	0.215281i
$539$	−6.58267	−	4.24778i	−0.283536	−	0.182965i
$540$	18.5234	+	1.74273i	0.797121	+	0.0749953i
$541$	28.0690	−	3.69536i	1.20678	−	0.158876i	0.499821	−	0.866129i	$-0.333399\pi$
$541$	28.0690	−	3.69536i	1.20678	−	0.158876i	0.706961	+	0.707253i	$0.250066\pi$
$542$	5.15020	+	0.925494i	0.221220	+	0.0397534i
$543$	11.3863	+	6.57390i	0.488634	+	0.282113i
$544$	−16.9522	+	13.7586i	−0.726818	+	0.589895i
$545$			31.0804i			1.33134i
$546$	−7.53899	+	0.945126i	−0.322639	+	0.0404476i
$547$	7.43036	+	3.07776i	0.317699	+	0.131595i	0.535834	−	0.844323i	$-0.319997\pi$
$547$	7.43036	+	3.07776i	0.317699	+	0.131595i	−0.218135	+	0.975919i	$0.569997\pi$
$548$	−1.39740	−	3.04863i	−0.0596939	−	0.130231i
$549$	6.04726	+	0.796136i	0.258091	+	0.0339783i
$550$	3.02762	+	1.94276i	0.129098	+	0.0828394i
$551$	0.827315	+	0.221678i	0.0352448	+	0.00944381i
$552$	16.7045	+	2.36612i	0.710989	+	0.100709i
$553$	23.8830	+	12.5213i	1.01561	+	0.532461i
$554$	16.5267	+	18.1545i	0.702151	+	0.771312i
$555$	−8.37672	−	6.42768i	−0.355572	−	0.272840i
$556$	8.83059	−	5.54485i	0.374500	−	0.235154i
$557$	−20.6447	+	15.8412i	−0.874742	+	0.671213i	−0.945267	−	0.326297i	$-0.894199\pi$
$557$	−20.6447	+	15.8412i	−0.874742	+	0.671213i	0.0705254	+	0.997510i	$0.477532\pi$
$558$	0.338599	+	4.02163i	0.0143341	+	0.170249i
$559$		−	2.92835i		−	0.123856i
$560$	−4.25277	−	16.9516i	−0.179712	−	0.716336i
$561$		−	6.42904i		−	0.271434i
$562$	15.5828	−	1.31198i	0.657319	−	0.0553427i
$563$	−6.39317	+	4.90565i	−0.269440	+	0.206749i	−0.734640	−	0.678457i	$-0.762649\pi$
$563$	−6.39317	+	4.90565i	−0.269440	+	0.206749i	0.465200	+	0.885205i	$0.345982\pi$
$564$	−6.65804	+	29.1296i	−0.280354	+	1.22658i
$565$	18.5103	+	14.2035i	0.778734	+	0.597544i
$566$	−6.87418	+	6.25780i	−0.288944	+	0.263035i
$567$	−15.9404	+	0.649421i	−0.669436	+	0.0272731i
$568$	−17.0006	+	4.37701i	−0.713330	+	0.183655i
$569$	3.34721	+	0.896883i	0.140322	+	0.0375993i	0.328297	−	0.944575i	$-0.393525\pi$
$569$	3.34721	+	0.896883i	0.140322	+	0.0375993i	−0.187974	+	0.982174i	$0.560192\pi$
$570$	0.726517	−	1.13222i	0.0304305	−	0.0474233i
$571$	−20.3843	−	2.68364i	−0.853055	−	0.112307i	−0.308698	−	0.951160i	$-0.599893\pi$
$571$	−20.3843	−	2.68364i	−0.853055	−	0.112307i	−0.544357	+	0.838853i	$0.683226\pi$
$572$	1.06324	−	2.86282i	0.0444561	−	0.119701i
$573$	22.4651	+	9.30533i	0.938491	+	0.388736i
$574$	−16.1424	+	12.2286i	−0.673769	+	0.510411i
$575$		−	9.10870i		−	0.379859i
$576$	−6.09479	+	1.50558i	−0.253950	+	0.0627326i
$577$	−17.4195	−	10.0572i	−0.725185	−	0.418686i	0.0914731	−	0.995808i	$-0.470842\pi$
$577$	−17.4195	−	10.0572i	−0.725185	−	0.418686i	−0.816658	+	0.577122i	$0.804176\pi$
$578$	−0.526248	+	2.92847i	−0.0218890	+	0.121808i
$579$	32.0314	−	4.21702i	1.33118	−	0.175253i
$580$	−5.63001	+	4.66173i	−0.233773	+	0.193568i
$581$	−4.13539	+	0.716757i	−0.171565	+	0.0297361i
$582$	7.97838	+	0.374487i	0.330714	+	0.0155230i
$583$	−3.34531	+	12.4849i	−0.138549	+	0.517071i
$584$	34.6645	+	9.65378i	1.43443	+	0.399476i
$585$	−1.70787	+	0.457623i	−0.0706118	+	0.0189204i
$586$	3.58536	−	11.2430i	0.148110	−	0.464443i
$587$	15.5167	+	37.4607i	0.640444	+	1.54617i	0.826082	+	0.563551i	$0.190565\pi$
$587$	15.5167	+	37.4607i	0.640444	+	1.54617i	−0.185638	+	0.982618i	$0.559435\pi$
$588$	7.73530	+	19.3482i	0.318998	+	0.797908i
$589$	1.30026	+	0.538586i	0.0535764	+	0.0221921i
$590$	2.13504	+	25.3584i	0.0878982	+	1.04399i
$591$	26.3964	+	15.2399i	1.08580	+	0.626888i
$592$	16.3188	+	5.38094i	0.670697	+	0.221155i
$593$	−2.09011	−	3.62017i	−0.0858304	−	0.148663i	0.819914	−	0.572486i	$-0.194021\pi$
$593$	−2.09011	−	3.62017i	−0.0858304	−	0.148663i	−0.905745	+	0.423824i	$0.860688\pi$
$594$	3.79440	−	8.06813i	0.155686	−	0.331039i
$595$	13.7853	+	9.71259i	0.565143	+	0.398178i
$596$	−29.8421	−	15.7837i	−1.22238	−	0.646528i
$597$	−0.827523	+	1.07845i	−0.0338683	+	0.0441380i
$598$	−7.55479	+	1.64896i	−0.308938	+	0.0674309i
$599$	−4.32895	−	16.1559i	−0.176876	−	0.660111i	−0.996224	−	0.0868148i	$-0.972331\pi$
$599$	−4.32895	−	16.1559i	−0.176876	−	0.660111i	0.819348	−	0.573296i	$-0.194336\pi$
$600$	−3.57464	−	8.87522i	−0.145934	−	0.362329i
$601$	−22.2051	−	22.2051i	−0.905767	−	0.905767i	0.0901604	−	0.995927i	$-0.471262\pi$
$601$	−22.2051	−	22.2051i	−0.905767	−	0.905767i	−0.995927	+	0.0901604i	$0.971262\pi$
$602$	−7.76993	+	2.03052i	−0.316679	+	0.0827579i
$603$	4.11575	+	9.93630i	0.167606	+	0.404637i
$604$	−20.3461	+	9.32603i	−0.827871	+	0.379471i
$605$	12.7707	−	9.79928i	0.519201	−	0.398397i
$606$	−3.10470	+	17.2771i	−0.126120	+	0.701834i
$607$	5.96268	+	10.3277i	0.242018	+	0.419187i	0.961289	−	0.275542i	$-0.0888575\pi$
$607$	5.96268	+	10.3277i	0.242018	+	0.419187i	−0.719271	+	0.694729i	$0.755524\pi$
$608$	−0.508728	+	2.12935i	−0.0206316	+	0.0863565i
$609$	5.90640	−	6.40810i	0.239339	−	0.259669i
$610$	6.15261	+	17.0777i	0.249112	+	0.691456i
$611$	−1.78761	−	13.5782i	−0.0723190	−	0.549317i
$612$	3.50685	−	4.93923i	0.141756	−	0.199657i
$613$	−2.58410	+	19.6282i	−0.104371	+	0.792775i	0.856572	+	0.516028i	$0.172590\pi$
$613$	−2.58410	+	19.6282i	−0.104371	+	0.792775i	−0.960943	+	0.276747i	$0.910743\pi$
$614$	−14.1786	−	27.4556i	−0.572201	−	1.10802i
$615$	9.40677	−	9.40677i	0.379318	−	0.379318i
$616$	−8.33331	−	0.836052i	−0.335759	−	0.0336855i
$617$	21.0742	+	21.0742i	0.848416	+	0.848416i	0.989935	−	0.141520i	$-0.0451988\pi$
$617$	21.0742	+	21.0742i	0.848416	+	0.848416i	−0.141520	+	0.989935i	$0.545199\pi$
$618$	8.71857	−	27.3397i	0.350713	−	1.09977i
$619$	3.67918	+	0.484373i	0.147879	+	0.0194686i	0.204102	−	0.978950i	$-0.434573\pi$
$619$	3.67918	+	0.484373i	0.147879	+	0.0194686i	−0.0562234	+	0.998418i	$0.517906\pi$
$620$	−10.1719	+	6.38707i	−0.408513	+	0.256511i
$621$	−22.3824	+	2.94670i	−0.898175	+	0.118247i
$622$	15.6232	+	7.34749i	0.626431	+	0.294607i
$623$	−9.46127	−	30.3152i	−0.379058	−	1.21455i
$624$	−6.71402	+	4.57151i	−0.268776	+	0.183007i
$625$	7.33532	−	4.23505i	0.293413	−	0.169402i
$626$	−37.1519	+	25.8334i	−1.48489	+	1.03251i
$627$	−0.392449	−	0.511449i	−0.0156729	−	0.0204253i
$628$	2.81864	+	2.61693i	0.112476	+	0.104427i
$629$	−15.3176	+	6.34477i	−0.610753	+	0.252982i
$630$	2.39848	+	4.21427i	0.0955575	+	0.167900i
$631$	16.5441	−	16.5441i	0.658611	−	0.658611i	−0.296441	−	0.955051i	$-0.595800\pi$
$631$	16.5441	−	16.5441i	0.658611	−	0.658611i	0.955051	+	0.296441i	$0.0957996\pi$
$632$	28.8268	+	0.282803i	1.14667	+	0.0112493i
$633$	2.03068	−	0.544119i	0.0807123	−	0.0216268i
$634$	−14.3490	−	9.20740i	−0.569870	−	0.365673i
$635$	−12.6156	−	9.68029i	−0.500635	−	0.384151i
$636$	26.4792	−	21.9252i	1.04997	−	0.869390i
$637$	−6.41100	−	7.07880i	−0.254013	−	0.280472i
$638$	1.18726	+	3.29545i	0.0470040	+	0.130468i
$639$	4.21811	−	2.43533i	0.166866	−	0.0963401i
$640$	−12.3039	−	14.0603i	−0.486354	−	0.555783i
$641$	−9.55416	+	16.5483i	−0.377367	+	0.653618i	−0.990678	−	0.136223i	$-0.956504\pi$
$641$	−9.55416	+	16.5483i	−0.377367	+	0.653618i	0.613312	+	0.789841i	$0.289837\pi$
$642$	−22.5696	+	26.7195i	−0.890753	+	1.05454i
$643$	−8.74458	+	21.1113i	−0.344852	+	0.832548i	0.652358	+	0.757911i	$0.273780\pi$
$643$	−8.74458	+	21.1113i	−0.344852	+	0.832548i	−0.997211	+	0.0746368i	$0.976220\pi$
$644$	9.61377	+	18.9021i	0.378836	+	0.744848i
$645$	4.87395	−	2.01886i	0.191912	−	0.0794925i
$646$	−0.969267	−	1.87690i	−0.0381353	−	0.0738458i
$647$	−3.07573	−	11.4788i	−0.120919	−	0.451277i	0.878742	−	0.477297i	$-0.158383\pi$
$647$	−3.07573	−	11.4788i	−0.120919	−	0.451277i	−0.999661	+	0.0260197i	$0.991717\pi$
$648$	−14.8532	+	8.38229i	−0.583487	+	0.329287i
$649$	11.7795	+	3.15631i	0.462386	+	0.123896i
$650$	2.95212	+	3.24290i	0.115792	+	0.127197i
$651$	10.9967	−	9.17285i	0.430996	−	0.359513i
$652$	8.12743	−	2.50425i	0.318295	−	0.0980740i
$653$	−2.38658	−	18.1279i	−0.0933940	−	0.709398i	−0.972522	−	0.232812i	$-0.925207\pi$
$653$	−2.38658	−	18.1279i	−0.0933940	−	0.709398i	0.879128	−	0.476586i	$-0.158126\pi$
$654$	−22.6158	−	32.5246i	−0.884349	−	1.27181i
$655$	−13.5013	+	23.3850i	−0.527541	+	0.913727i
$656$	−9.40534	+	19.4998i	−0.367217	+	0.761338i
$657$	−9.98370			−0.389501
$658$	−34.7883	+	14.1583i	−1.35619	+	0.551949i
$659$	4.15938	−	10.0416i	0.162026	−	0.391166i	−0.821927	−	0.569593i	$-0.807101\pi$
$659$	4.15938	−	10.0416i	0.162026	−	0.391166i	0.983953	+	0.178427i	$0.0571008\pi$
$660$	5.49790	−	0.204028i	0.214006	−	0.00794179i
$661$	−5.76008	+	43.7521i	−0.224041	+	1.70176i	0.396866	+	0.917877i	$0.370098\pi$
$661$	−5.76008	+	43.7521i	−0.224041	+	1.70176i	−0.620907	+	0.783884i	$0.713235\pi$
$662$	3.88097	+	17.7809i	0.150838	+	0.691073i
$663$	2.02847	−	7.57034i	0.0787791	−	0.294008i
$664$	−3.58627	+	2.69636i	−0.139174	+	0.104639i
$665$	1.68955	−	0.0688330i	0.0655179	−	0.00266923i
$666$	−4.76221	−	0.223527i	−0.184532	−	0.00866149i
$667$	5.39931	−	7.03651i	0.209062	−	0.272455i
$668$	17.3146	+	12.2934i	0.669924	+	0.475645i
$669$	−25.5476	−	33.2942i	−0.987726	−	1.28723i
$670$	−20.6540	+	24.4516i	−0.797932	+	0.944648i
$671$	8.69875			0.335812
$672$	16.7853	+	14.6448i	0.647508	+	0.564934i
$673$	−50.1367			−1.93263			−0.966314	−	0.257367i	$-0.917145\pi$
$673$	−50.1367			−1.93263			−0.966314	+	0.257367i	$0.917145\pi$
$674$	12.1520	−	14.3864i	0.468078	−	0.554143i
$675$	7.79404	+	10.1574i	0.299993	+	0.390958i
$676$	−12.8967	+	18.1644i	−0.496027	+	0.698631i
$677$	21.4326	−	27.9316i	0.823724	−	1.07350i	−0.172356	−	0.985035i	$-0.555138\pi$
$677$	21.4326	−	27.9316i	0.823724	−	1.07350i	0.996079	−	0.0884628i	$-0.0281954\pi$
$678$	−29.7057	−	1.39432i	−1.14084	−	0.0535484i
$679$	5.36955	+	8.48298i	0.206064	+	0.325547i
$680$	17.8494	+	2.52829i	0.684493	+	0.0969557i
$681$	5.39241	−	20.1248i	0.206638	−	0.771182i
$682$	1.22739	+	5.62338i	0.0469994	+	0.215330i
$683$	4.46939	−	33.9484i	0.171016	−	1.29900i	−0.663567	−	0.748117i	$-0.730958\pi$
$683$	4.46939	−	33.9484i	0.171016	−	1.29900i	0.834583	−	0.550882i	$-0.185709\pi$
$684$	−0.0225258	−	0.606999i	−0.000861297	−	0.0232092i
$685$	−1.05970	+	2.55833i	−0.0404889	+	0.0977489i
$686$	−14.3371	+	21.9191i	−0.547395	+	0.836875i
$687$	−22.4893			−0.858019
$688$	−6.40512	+	5.71690i	−0.244193	+	0.217955i
$689$	−7.87836	+	13.6457i	−0.300142	+	0.519861i
$690$	−7.95295	−	11.4374i	−0.302764	−	0.435415i
$691$	2.57013	+	19.5221i	0.0977723	+	0.742655i	0.968168	+	0.250302i	$0.0805298\pi$
$691$	2.57013	+	19.5221i	0.0977723	+	0.742655i	−0.870396	+	0.492353i	$0.836137\pi$
$692$	7.15927	+	23.2351i	0.272155	+	0.883266i
$693$	2.28956	−	0.396832i	0.0869731	−	0.0150744i
$694$	−10.0902	−	11.0841i	−0.383020	−	0.420747i
$695$	−8.31637	−	2.22837i	−0.315458	−	0.0845267i
$696$	2.49948	−	8.97506i	0.0947426	−	0.340199i
$697$	−5.40655	−	20.1775i	−0.204788	−	0.764278i
$698$	14.2627	+	27.6185i	0.539851	+	1.04538i
$699$	−12.8331	+	5.31562i	−0.485391	+	0.201055i
$700$	6.55755	−	10.0816i	0.247852	−	0.381051i
$701$	−10.6296	+	25.6621i	−0.401474	+	0.969243i	0.585835	+	0.810430i	$0.300767\pi$
$701$	−10.6296	+	25.6621i	−0.401474	+	0.969243i	−0.987309	+	0.158813i	$0.949233\pi$
$702$	7.01362	−	8.30321i	0.264712	−	0.313384i
$703$	−0.831257	+	1.43978i	−0.0313515	+	0.0543023i
$704$	−8.33750	+	3.26338i	−0.314231	+	0.122993i
$705$	21.3673	−	12.3364i	0.804738	−	0.464616i
$706$	−2.71945	−	7.54832i	−0.102348	−	0.284085i
$707$	−20.0243	+	9.26653i	−0.753093	+	0.348504i
$708$	−20.6865	−	24.9832i	−0.777445	−	0.938926i
$709$	−0.421403	−	0.323354i	−0.0158261	−	0.0121438i	0.600818	−	0.799386i	$-0.294842\pi$
$709$	−0.421403	−	0.323354i	−0.0158261	−	0.0121438i	−0.616644	+	0.787242i	$0.711508\pi$
$710$	12.1997	+	7.82826i	0.457846	+	0.293789i
$711$	−7.72586	+	2.07014i	−0.289742	+	0.0776363i
$712$	−23.7696	−	24.2406i	−0.890804	−	0.908455i
$713$	10.3054	−	10.3054i	0.385940	−	0.385940i
$714$	−21.4933	−	0.132945i	−0.804367	−	0.00497534i
$715$	−2.32967	+	0.964980i	−0.0871247	+	0.0360882i
$716$	25.9905	−	27.9938i	0.971309	−	1.04618i
$717$	21.2771	+	27.7289i	0.794608	+	1.03555i
$718$	−10.7950	+	7.50625i	−0.402866	+	0.280131i
$719$	27.2910	−	15.7565i	1.01778	−	0.587617i	0.104321	−	0.994544i	$-0.466733\pi$
$719$	27.2910	−	15.7565i	1.01778	−	0.587617i	0.913461	+	0.406927i	$0.133400\pi$
$720$	4.33516	+	2.84219i	0.161562	+	0.105922i
$721$	34.4322	−	10.7462i	1.28232	−	0.400208i
$722$	24.1236	+	11.3452i	0.897787	+	0.422225i
$723$	33.4764	−	4.40726i	1.24500	−	0.163908i
$724$	9.39501	+	14.9623i	0.349163	+	0.556068i
$725$	−4.98697	−	0.656547i	−0.185211	−	0.0243835i
$726$	−6.23358	+	19.5473i	−0.231350	+	0.725468i
$727$	−28.9262	−	28.9262i	−1.07281	−	1.07281i	−0.997132	−	0.0756807i	$-0.975887\pi$
$727$	−28.9262	−	28.9262i	−1.07281	−	1.07281i	−0.0756807	−	0.997132i	$-0.524113\pi$
$728$	−9.54888	−	3.61377i	−0.353905	−	0.133935i
$729$	21.1315	−	21.1315i	0.782649	−	0.782649i
$730$	−13.6332	−	26.3996i	−0.504588	−	0.977092i
$731$	1.08127	−	8.21303i	0.0399921	−	0.303770i
$732$	−18.8652	−	13.3943i	−0.697278	−	0.495067i
$733$	−6.92243	−	52.5811i	−0.255686	−	1.94213i	−0.327842	−	0.944732i	$-0.606322\pi$
$733$	−6.92243	−	52.5811i	−0.255686	−	1.94213i	0.0721568	−	0.997393i	$-0.477012\pi$
$734$	0.378722	+	1.05121i	0.0139789	+	0.0388010i
$735$	7.36212	−	15.5508i	0.271556	−	0.573598i
$736$	18.3557	+	13.3053i	0.676598	+	0.490438i
$737$	7.66914	+	13.2833i	0.282496	+	0.489298i
$738$	1.06239	−	5.91198i	0.0391070	−	0.217623i
$739$	19.0808	−	14.6412i	0.701898	−	0.538585i	−0.195011	−	0.980801i	$-0.562474\pi$
$739$	19.0808	−	14.6412i	0.701898	−	0.538585i	0.896909	+	0.442216i	$0.145808\pi$
$740$	−5.91195	−	12.8978i	−0.217328	−	0.474132i
$741$	−0.300747	−	0.726067i	−0.0110482	−	0.0266727i
$742$	41.6697	+	11.4421i	1.52974	+	0.420052i
$743$	−10.7198	−	10.7198i	−0.393272	−	0.393272i	0.482580	−	0.875852i	$-0.339700\pi$
$743$	−10.7198	−	10.7198i	−0.393272	−	0.393272i	−0.875852	+	0.482580i	$0.839700\pi$
$744$	5.99696	−	14.0855i	0.219859	−	0.516400i
$745$	7.21463	+	26.9254i	0.264324	+	0.986469i
$746$	1.49557	−	0.326433i	0.0547567	−	0.0119516i
$747$	0.757832	−	0.987626i	0.0277276	−	0.0361354i
$748$	4.03909	−	7.63666i	0.147684	−	0.279224i
$749$	−43.7849	−	3.95934i	−1.59987	−	0.144671i
$750$	−10.7589	+	22.8769i	−0.392859	+	0.835345i
$751$	−14.4281	−	24.9903i	−0.526490	−	0.911907i	−0.999524	−	0.0308630i	$-0.990174\pi$
$751$	−14.4281	−	24.9903i	−0.526490	−	0.911907i	0.473034	−	0.881044i	$-0.343159\pi$
$752$	−26.2095	+	30.4183i	−0.955764	+	1.10924i
$753$	13.4624	+	7.77254i	0.490598	+	0.283247i
$754$	0.358253	+	4.25507i	0.0130468	+	0.154960i
$755$	17.0739	+	7.07226i	0.621384	+	0.257386i
$756$	−26.8946	−	12.8521i	−0.978146	−	0.467427i
$757$	8.94997	+	21.6072i	0.325292	+	0.785325i	0.998929	+	0.0462628i	$0.0147312\pi$
$757$	8.94997	+	21.6072i	0.325292	+	0.785325i	−0.673637	+	0.739062i	$0.735269\pi$
$758$	−2.17248	+	6.81248i	−0.0789082	+	0.247440i
$759$	−6.44827	+	1.72781i	−0.234057	+	0.0627155i
$760$	1.57431	−	0.888450i	0.0571061	−	0.0322275i
$761$	−12.1671	+	45.4083i	−0.441057	+	1.64605i	0.285084	+	0.958503i	$0.407979\pi$
$761$	−12.1671	+	45.4083i	−0.441057	+	1.64605i	−0.726141	+	0.687546i	$0.758688\pi$
$762$	20.2457	+	0.950289i	0.733426	+	0.0344253i
$763$	17.1670	−	46.7414i	0.621486	−	1.69215i
$764$	20.8387	+	25.1670i	0.753918	+	0.910512i
$765$	−4.95898	+	0.652862i	−0.179292	+	0.0236043i
$766$	−7.86035	+	43.7413i	−0.284006	+	1.58044i
$767$	12.8748	+	7.43326i	0.464881	+	0.268399i
$768$	23.1067	+	5.76066i	0.833791	+	0.207870i
$769$			54.0999i			1.95089i	0.220242	+	0.975445i	$0.429315\pi$
$769$			54.0999i			1.95089i	−0.220242	+	0.975445i	$0.570685\pi$
$770$	4.17583	+	5.51231i	0.150486	+	0.198650i
$771$	19.7657	+	8.18722i	0.711844	+	0.294855i
$772$	40.6975	+	15.1148i	1.46473	+	0.543994i
$773$	17.9250	+	2.35987i	0.644718	+	0.0848787i	0.445793	−	0.895136i	$-0.352922\pi$
$773$	17.9250	+	2.35987i	0.644718	+	0.0848787i	0.198925	+	0.980015i	$0.436255\pi$
$774$	1.28642	−	2.00478i	0.0462394	−	0.0720602i
$775$	−7.98363	−	2.13921i	−0.286781	−	0.0768426i
$776$	9.24175	+	5.45730i	0.331759	+	0.195906i
$777$	9.04738	+	14.2933i	0.324573	+	0.512770i
$778$	0.701978	−	0.639034i	0.0251671	−	0.0229105i
$779$	−1.66181	−	1.27515i	−0.0595404	−	0.0456869i
$780$	6.53828	+	1.49443i	0.234108	+	0.0535092i
$781$	5.51089	−	4.22865i	0.197195	−	0.151313i
$782$	−21.7975	+	1.83523i	−0.779477	+	0.0656277i
$783$			12.4667i			0.445522i
$784$	−2.96738	+	27.8423i	−0.105978	+	0.994368i
$785$		−	3.17581i		−	0.113350i
$786$	−2.88753	−	34.2960i	−0.102995	−	1.22330i
$787$	−38.2002	+	29.3120i	−1.36169	+	1.04486i	−0.368345	+	0.929689i	$0.620075\pi$
$787$	−38.2002	+	29.3120i	−1.36169	+	1.04486i	−0.993346	+	0.115172i	$0.963258\pi$
$788$	21.7800	+	34.6863i	0.775880	+	1.23565i
$789$	14.8007	+	11.3570i	0.526919	+	0.404319i
$790$	−16.0240	−	17.6024i	−0.570109	−	0.626264i
$791$	−19.9923	−	31.5844i	−0.710844	−	1.12301i
$792$	1.98554	−	1.49284i	0.0705529	−	0.0530457i
$793$	10.2430	+	2.74460i	0.363739	+	0.0974635i
$794$	31.0376	+	19.9161i	1.10148	+	0.706796i
$795$	−28.1435	−	3.70516i	−0.998146	−	0.131408i
$796$	−1.66051	+	0.761126i	−0.0588551	+	0.0269774i
$797$	−41.7312	−	17.2856i	−1.47819	−	0.612288i	−0.509483	−	0.860481i	$-0.670163\pi$
$797$	−41.7312	−	17.2856i	−1.47819	−	0.612288i	−0.968711	+	0.248193i	$0.920163\pi$
$798$	−1.71797	+	1.30144i	−0.0608155	+	0.0460706i
$799$		−	38.7425i		−	1.37061i
$800$	1.32982	−	12.7881i	0.0470164	−	0.452128i
$801$	8.15749	+	4.70973i	0.288231	+	0.166410i
$802$	−22.9994	−	4.13301i	−0.812137	−	0.145942i
$803$	−14.1165	+	1.85847i	−0.498161	+	0.0655841i
$804$	3.82134	−	40.6168i	0.134768	−	1.43244i
$805$	6.03683	−	16.4368i	0.212770	−	0.579322i
$806$	−0.328983	+	7.00892i	−0.0115879	+	0.246879i
$807$	1.36166	−	5.08178i	0.0479327	−	0.178887i
$808$	−14.5423	+	18.5718i	−0.511597	+	0.653354i
$809$	35.4391	−	9.49588i	1.24597	−	0.333857i	0.425193	−	0.905103i	$-0.360206\pi$
$809$	35.4391	−	9.49588i	1.24597	−	0.333857i	0.820779	+	0.571246i	$0.193540\pi$
$810$	13.4169	+	4.27861i	0.471421	+	0.150335i
$811$	15.5294	+	37.4914i	0.545312	+	1.31650i	0.920931	+	0.389726i	$0.127430\pi$
$811$	15.5294	+	37.4914i	0.545312	+	1.31650i	−0.375619	+	0.926774i	$0.622570\pi$
$812$	11.0418	−	3.90104i	0.387490	−	0.136900i
$813$	5.08788	+	2.10747i	0.178440	+	0.0739122i
$814$	−6.77516	+	0.570431i	−0.237469	+	0.0199936i
$815$	−6.08142	−	3.51111i	−0.213023	−	0.122989i
$816$	−20.5185	+	10.3425i	−0.718293	+	0.362058i
$817$	−0.415331	−	0.719374i	−0.0145306	−	0.0251677i
$818$	−3.09917	−	1.45752i	−0.108360	−	0.0509611i
$819$	2.82121	+	0.255114i	0.0985812	+	0.00891441i
$820$	17.0836	−	5.26385i	0.596585	−	0.183822i
$821$	−4.82738	+	6.29117i	−0.168477	+	0.219563i	−0.869959	−	0.493123i	$-0.835855\pi$
$821$	−4.82738	+	6.29117i	−0.168477	+	0.219563i	0.701483	+	0.712687i	$0.252522\pi$
$822$	−0.752650	−	3.44831i	−0.0262517	−	0.120274i
$823$	−1.74155	−	6.49956i	−0.0607067	−	0.226560i	0.928907	−	0.370313i	$-0.120750\pi$
$823$	−1.74155	−	6.49956i	−0.0607067	−	0.226560i	−0.989614	+	0.143753i	$0.954083\pi$
$824$	27.5326	−	26.9977i	0.959144	−	0.940508i
$825$	2.67708	+	2.67708i	0.0932041	+	0.0932041i
$826$	10.7956	−	39.3155i	0.375628	−	1.36796i
$827$	−10.7921	−	26.0545i	−0.375279	−	0.906004i	−0.992837	−	0.119478i	$-0.961878\pi$
$827$	−10.7921	−	26.0545i	−0.375279	−	0.906004i	0.617558	−	0.786525i	$-0.288122\pi$
$828$	−5.89647	−	2.18992i	−0.204917	−	0.0761049i
$829$	−12.5842	+	9.65621i	−0.437068	+	0.335374i	−0.803745	−	0.594974i	$-0.797162\pi$
$829$	−12.5842	+	9.65621i	−0.437068	+	0.335374i	0.366677	+	0.930348i	$0.380496\pi$
$830$	3.64640	+	0.655261i	0.126568	+	0.0227444i
$831$	12.9188	+	22.3761i	0.448149	+	0.776217i
$832$	−10.8472	+	1.21208i	−0.376061	+	0.0420214i
$833$	−15.3669	−	22.2209i	−0.532432	−	0.769907i
$834$	10.3243	−	3.71955i	0.357501	−	0.128797i
$835$	−2.28863	−	17.3839i	−0.0792013	−	0.601594i
$836$	−0.144844	−	0.854077i	−0.00500953	−	0.0295389i
$837$	−2.67384	+	20.3099i	−0.0924216	+	0.702012i
$838$	19.3950	−	10.0159i	0.669988	−	0.345994i
$839$	40.4473	−	40.4473i	1.39640	−	1.39640i	0.586308	−	0.810088i	$-0.300581\pi$
$839$	40.4473	−	40.4473i	1.39640	−	1.39640i	0.810088	−	0.586308i	$-0.199419\pi$
$840$	−0.568409	−	18.3846i	−0.0196120	−	0.634329i
$841$	17.0428	+	17.0428i	0.587683	+	0.587683i
$842$	−1.16789	−	0.372438i	−0.0402482	−	0.0128351i
$843$	16.3171	+	2.14819i	0.561991	+	0.0739875i
$844$	2.75396	+	0.629463i	0.0947953	+	0.0216670i
$845$	18.2370	−	2.40095i	0.627373	−	0.0825952i
$846$	4.74109	−	10.0811i	0.163002	−	0.346595i
$847$	−24.6182	+	7.68326i	−0.845892	+	0.264000i
$848$	45.2276	−	9.40782i	1.55312	−	0.323066i
$849$	−8.47267	+	4.89170i	−0.290781	+	0.167883i
$850$	7.08230	+	10.1853i	0.242921	+	0.349353i
$851$	10.4804	+	13.6583i	0.359262	+	0.468200i
$852$	−18.4629	+	0.685160i	−0.632527	+	0.0234732i
$853$	−40.9765	+	16.9730i	−1.40301	+	0.581145i	−0.950531	−	0.310631i	$-0.899460\pi$
$853$	−40.9765	+	16.9730i	−1.40301	+	0.581145i	−0.452477	+	0.891776i	$0.649460\pi$
$854$	0.179880	−	29.0813i	0.00615537	−	0.995142i
$855$	−0.354648	+	0.354648i	−0.0121287	+	0.0121287i
$856$	−43.5958	+	17.5589i	−1.49007	+	0.600152i
$857$	17.8990	−	4.79603i	0.611420	−	0.163829i	0.0601956	−	0.998187i	$-0.480828\pi$
$857$	17.8990	−	4.79603i	0.611420	−	0.163829i	0.551224	+	0.834357i	$0.314161\pi$
$858$	1.73575	−	2.70502i	0.0592575	−	0.0923478i
$859$	−4.68537	−	3.59521i	−0.159863	−	0.122667i	0.525732	−	0.850650i	$-0.323791\pi$
$859$	−4.68537	−	3.59521i	−0.159863	−	0.122667i	−0.685595	+	0.727983i	$0.740458\pi$
$860$	7.05783	+	0.664019i	0.240670	+	0.0226429i
$861$	−19.3425	+	8.95099i	−0.659190	+	0.305049i
$862$	−6.09902	+	2.19730i	−0.207734	+	0.0748405i
$863$	−21.6096	+	12.4763i	−0.735600	+	0.424699i	−0.820467	−	0.571693i	$-0.806287\pi$
$863$	−21.6096	+	12.4763i	−0.735600	+	0.424699i	0.0848673	+	0.996392i	$0.472953\pi$
$864$	−31.8538	+	0.869285i	−1.08369	+	0.0295737i
$865$	10.0377	−	17.3859i	0.341293	−	0.591137i
$866$	−13.5455	−	11.4417i	−0.460295	−	0.388805i
$867$	−1.19833	+	2.89303i	−0.0406976	+	0.0982526i
$868$	18.8252	−	3.98709i	0.638970	−	0.135331i
$869$	−10.5387	+	4.36526i	−0.357500	+	0.148081i
$870$	−6.83517	+	3.52980i	−0.231734	+	0.119672i
$871$	4.83947	+	18.0612i	0.163979	+	0.611979i
$872$	−6.43013	−	52.8425i	−0.217752	−	1.78947i
$873$	−2.87635	−	0.770715i	−0.0973496	−	0.0260847i
$874$	−1.62203	+	1.47659i	−0.0548659	+	0.0499463i
$875$	−31.3099	+	5.42671i	−1.05847	+	0.183456i
$876$	33.4765	+	17.7060i	1.13107	+	0.598230i
$877$	1.55613	+	11.8200i	0.0525466	+	0.399131i	0.997425	+	0.0717111i	$0.0228460\pi$
$877$	1.55613	+	11.8200i	0.0525466	+	0.399131i	−0.944879	+	0.327420i	$0.893821\pi$
$878$	33.8469	−	23.5353i	1.14228	−	0.794277i
$879$	6.20981	−	10.7557i	0.209452	−	0.362781i
$880$	6.65880	+	3.21174i	0.224468	+	0.108268i
$881$	32.8782			1.10769			0.553847	−	0.832619i	$-0.313159\pi$
$881$	32.8782			1.10769			0.553847	+	0.832619i	$0.313159\pi$
$882$	−1.27933	−	7.66257i	−0.0430772	−	0.258012i
$883$	10.6736	−	25.7683i	0.359195	−	0.867173i	−0.636219	−	0.771509i	$-0.719502\pi$
$883$	10.6736	−	25.7683i	0.359195	−	0.867173i	0.995414	−	0.0956645i	$-0.0304976\pi$
$884$	7.16561	−	7.71794i	0.241005	−	0.259582i
$885$	−3.49583	+	26.5535i	−0.117511	+	0.892585i
$886$	−13.4917	+	2.94479i	−0.453263	+	0.0989321i
$887$	2.00011	−	7.46449i	0.0671570	−	0.250633i	−0.924184	−	0.381948i	$-0.875253\pi$
$887$	2.00011	−	7.46449i	0.0671570	−	0.250633i	0.991341	+	0.131315i	$0.0419199\pi$
$888$	15.5718	+	9.19524i	0.522556	+	0.308572i
$889$	13.6256	+	21.5262i	0.456989	+	0.721966i
$890$	−1.31435	+	28.0019i	−0.0440570	+	0.938627i
$891$	4.10825	−	5.35398i	0.137632	−	0.179365i
$892$	−9.42903	−	55.5986i	−0.315707	−	1.86158i
$893$	−2.36496	−	3.08208i	−0.0791404	−	0.103138i
$894$	−27.1423	−	22.9267i	−0.907774	−	0.766785i
$895$	−31.5411			−1.05430
$896$	10.7376	+	27.9411i	0.358717	+	0.933446i
$897$	−8.13814			−0.271725
$898$	−39.9849	−	33.7747i	−1.33431	−	1.12708i
$899$	−4.89935	−	6.38496i	−0.163402	−	0.212950i
$900$	0.596450	+	3.51699i	0.0198817	+	0.117233i
$901$	−27.1347	+	35.3626i	−0.903988	+	1.17810i
$902$	0.401648	−	8.55704i	0.0133734	−	0.284918i
$903$	−8.44499	+	0.344053i	−0.281032	+	0.0114494i
$904$	−34.4095	−	20.3190i	−1.14444	−	0.675800i
$905$	3.77567	−	14.0910i	0.125508	−	0.468400i
$906$	−23.0135	+	5.02307i	−0.764572	+	0.166880i
$907$	−3.94936	+	29.9984i	−0.131136	+	0.996080i	0.791706	+	0.610902i	$0.209193\pi$
$907$	−3.94936	+	29.9984i	−0.131136	+	0.996080i	−0.922842	+	0.385178i	$0.874140\pi$
$908$	19.0488	−	20.5171i	0.632158	−	0.680885i
$909$	2.50447	−	6.04633i	0.0830681	−	0.200544i
$910$	3.17791	+	7.80841i	0.105347	+	0.258846i
$911$	−45.7140			−1.51457			−0.757287	−	0.653082i	$-0.773476\pi$
$911$	−45.7140			−1.51457			−0.757287	+	0.653082i	$0.773476\pi$
$912$	−1.00098	+	2.07529i	−0.0331456	+	0.0687197i
$913$	0.887694	−	1.53753i	0.0293784	−	0.0508849i
$914$	−3.91612	+	2.72306i	−0.129534	+	0.0900707i
$915$	2.49358	+	18.9406i	0.0824353	+	0.626158i
$916$	−26.7136	−	14.1290i	−0.882642	−	0.466836i
$917$	33.2210	−	27.7111i	1.09705	−	0.915101i
$918$	22.7367	−	20.6980i	0.750423	−	0.683135i
$919$	8.84218	+	2.36925i	0.291676	+	0.0781545i	0.401690	−	0.915776i	$-0.368423\pi$
$919$	8.84218	+	2.36925i	0.291676	+	0.0781545i	−0.110014	+	0.993930i	$0.535090\pi$
$920$	−2.26118	−	18.5823i	−0.0745490	−	0.612639i
$921$	−8.41703	−	31.4128i	−0.277351	−	1.03509i
$922$	10.3336	−	5.33644i	0.340318	−	0.175746i
$923$	7.82341	−	3.24056i	0.257511	−	0.106664i
$924$	−8.38093	−	2.72988i	−0.275712	−	0.0898066i
$925$	3.73634	−	9.02032i	0.122850	−	0.296586i
$926$	−40.3683	−	34.0986i	−1.32659	−	1.12055i
$927$	−5.34934	+	9.26532i	−0.175695	+	0.304313i
$928$	8.60762	−	9.09060i	0.282559	−	0.298414i
$929$	−2.57564	+	1.48705i	−0.0845039	+	0.0487884i	−0.541657	−	0.840600i	$-0.682203\pi$
$929$	−2.57564	+	1.48705i	−0.0845039	+	0.0487884i	0.457153	+	0.889388i	$0.348869\pi$
$930$	−11.8925	+	4.28452i	−0.389970	+	0.140495i
$931$	−2.57891	−	0.829690i	−0.0845205	−	0.0271920i
$932$	−18.5832	−	1.74835i	−0.608712	−	0.0572692i
$933$	14.4152	+	11.0612i	0.471933	+	0.362127i
$934$	−8.23719	+	12.8370i	−0.269529	+	0.420039i
$935$	−6.89024	+	1.84624i	−0.225335	+	0.0603784i
$936$	2.80903	−	1.13138i	0.0918160	−	0.0369804i
$937$	24.3115	−	24.3115i	0.794222	−	0.794222i	−0.187955	−	0.982178i	$-0.560186\pi$
$937$	24.3115	−	24.3115i	0.794222	−	0.794222i	0.982178	+	0.187955i	$0.0601861\pi$
$938$	44.5669	−	25.3645i	1.45516	−	0.828179i
$939$	−43.9984	+	18.2248i	−1.43584	+	0.594742i
$940$	33.1313	−	1.22951i	1.08062	−	0.0401021i
$941$	7.32587	+	9.54727i	0.238817	+	0.311232i	0.897350	−	0.441320i	$-0.145489\pi$
$941$	7.32587	+	9.54727i	0.238817	+	0.311232i	−0.658533	+	0.752552i	$0.728823\pi$
$942$	2.31090	+	3.32338i	0.0752932	+	0.108282i
$943$	−18.7849	+	10.8455i	−0.611720	+	0.353176i
$944$	−8.87631	−	42.6724i	−0.288899	−	1.38887i
$945$	7.33262	+	23.4947i	0.238530	+	0.764284i
$946$	1.44575	−	3.07413i	0.0470054	−	0.0999487i
$947$	−1.46008	+	0.192223i	−0.0474461	+	0.00624640i	−0.154212	−	0.988038i	$-0.549284\pi$
$947$	−1.46008	+	0.192223i	−0.0474461	+	0.00624640i	0.106766	+	0.994284i	$0.465950\pi$
$948$	29.5771	+	6.76032i	0.960619	+	0.219565i
$949$	−17.2089	−	2.26559i	−0.558624	−	0.0735443i
$950$	1.18516	+	0.377945i	0.0384516	+	0.0122621i
$951$	−12.6876	−	12.6876i	−0.411425	−	0.411425i
$952$	−25.4470	−	13.6612i	−0.824743	−	0.442763i
$953$	−13.3797	+	13.3797i	−0.433411	+	0.433411i	−0.889787	−	0.456376i	$-0.849147\pi$
$953$	−13.3797	+	13.3797i	−0.433411	+	0.433411i	0.456376	+	0.889787i	$0.349147\pi$
$954$	−11.3882	+	5.88105i	−0.368705	+	0.190406i
$955$	3.52156	−	26.7489i	0.113955	−	0.865573i
$956$	7.85290	+	46.3049i	0.253981	+	1.49761i
$957$	0.481181	+	3.65494i	0.0155544	+	0.118147i
$958$	7.31272	−	2.63456i	0.236263	−	0.0851188i
$959$	3.00674	−	3.26214i	0.0970927	−	0.105340i
$960$	−9.49569	−	17.2186i	−0.306472	−	0.555727i
$961$	8.88774	+	15.3940i	0.286701	+	0.496581i
$962$	−8.15788	−	1.46598i	−0.263021	−	0.0472650i
$963$	10.3453	−	7.93821i	0.333372	−	0.255805i
$964$	42.5335	+	15.7967i	1.36991	+	0.508777i
$965$	−13.7180	−	33.1183i	−0.441599	−	1.06611i
$966$	5.64300	+	21.5933i	0.181561	+	0.694754i
$967$	10.1185	+	10.1185i	0.325388	+	0.325388i	0.850830	−	0.525441i	$-0.176100\pi$
$967$	10.1185	+	10.1185i	0.325388	+	0.325388i	−0.525441	+	0.850830i	$0.676100\pi$
$968$	−19.6852	+	19.3027i	−0.632706	+	0.620412i
$969$	−0.575399	−	2.14742i	−0.0184845	−	0.0689851i
$970$	−1.88981	−	8.65827i	−0.0606781	−	0.278000i
$971$	−17.0756	+	22.2534i	−0.547982	+	0.714144i	−0.982446	−	0.186545i	$-0.940271\pi$
$971$	−17.0756	+	22.2534i	−0.547982	+	0.714144i	0.434464	+	0.900689i	$0.356938\pi$
$972$	15.1465	−	4.66698i	0.485823	−	0.149693i
$973$	11.2761	+	7.94469i	0.361495	+	0.254695i
$974$	−7.29049	−	3.42868i	−0.233602	−	0.109862i
$975$	2.30766	+	3.99699i	0.0739044	+	0.128006i
$976$	−13.9938	−	27.7624i	−0.447929	−	0.888654i
$977$	22.5539	+	13.0215i	0.721562	+	0.416594i	0.815327	−	0.579000i	$-0.196557\pi$
$977$	22.5539	+	13.0215i	0.721562	+	0.416594i	−0.0937652	+	0.995594i	$0.529890\pi$
$978$	8.91889	−	0.750922i	0.285195	−	0.0240118i
$979$	12.4110	+	5.14082i	0.396659	+	0.164301i
$980$	18.5149	−	13.8465i	0.591436	−	0.442309i
$981$	5.65199	+	13.6451i	0.180454	+	0.435655i
$982$	−17.5235	−	5.58821i	−0.559198	−	0.178327i
$983$	12.9732	−	3.47615i	0.413780	−	0.110872i	−0.0459224	−	0.998945i	$-0.514623\pi$
$983$	12.9732	−	3.47615i	0.413780	−	0.110872i	0.459703	+	0.888073i	$0.347956\pi$
$984$	−14.0471	+	17.9394i	−0.447807	+	0.571888i
$985$	8.75295	−	32.6665i	0.278892	−	1.04084i
$986$	−0.566365	+	12.0663i	−0.0180367	+	0.384270i
$987$	−38.9479	+	6.75055i	−1.23973	+	0.214872i
$988$	0.0989181	−	1.05140i	0.00314700	−	0.0334494i
$989$	−8.52819	+	1.12276i	−0.271181	+	0.0357016i
$990$	−2.01883	−	0.362785i	−0.0641626	−	0.0115301i
$991$	32.8222	+	18.9499i	1.04263	+	0.601963i	0.920577	−	0.390560i	$-0.127719\pi$
$991$	32.8222	+	18.9499i	1.04263	+	0.601963i	0.122053	+	0.992524i	$0.461052\pi$
$992$	15.9727	−	12.9637i	0.507135	−	0.411597i
$993$			19.1538i			0.607828i
$994$	−14.0231	−	18.5112i	−0.444786	−	0.587140i
$995$	1.39346	+	0.577188i	0.0441755	+	0.0182981i
$996$	−4.29265	+	1.96762i	−0.136018	+	0.0623464i
$997$	−38.7823	−	5.10579i	−1.22825	−	0.161702i	−0.511654	−	0.859192i	$-0.670967\pi$
$997$	−38.7823	−	5.10579i	−1.22825	−	0.161702i	−0.716595	+	0.697490i	$0.754300\pi$
$998$	−36.6719	−	23.5315i	−1.16083	−	0.744878i
$999$	−23.3739	−	6.26303i	−0.739519	−	0.198154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.115.25	yes	240
4.3	odd	2		896.2.bi.a.367.7		240
7.5	odd	6	inner	224.2.be.a.19.17	✓	240
28.19	even	6		896.2.bi.a.495.7		240
32.5	even	8		896.2.bi.a.143.7		240
32.27	odd	8	inner	224.2.be.a.59.17	yes	240
224.5	odd	24		896.2.bi.a.271.7		240
224.187	even	24	inner	224.2.be.a.187.25	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.17	✓	240	7.5	odd	6	inner
224.2.be.a.59.17	yes	240	32.27	odd	8	inner
224.2.be.a.115.25	yes	240	1.1	even	1	trivial
224.2.be.a.187.25	yes	240	224.187	even	24	inner
896.2.bi.a.143.7		240	32.5	even	8
896.2.bi.a.271.7		240	224.5	odd	24
896.2.bi.a.367.7		240	4.3	odd	2
896.2.bi.a.495.7		240	28.19	even	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08037 + 0.912577i) q^{2} +(0.906063 + 1.18080i) q^{3} +(0.334408 + 1.97184i) q^{4} +(1.00532 - 1.31016i) q^{5} +(-0.0986893 + 2.10256i) q^{6} +(-2.23554 + 1.41505i) q^{7} +(-1.43817 + 2.43550i) q^{8} +(0.203108 - 0.758010i) q^{9} +O(q^{10})\)	\(q+(1.08037 + 0.912577i) q^{2} +(0.906063 + 1.18080i) q^{3} +(0.334408 + 1.97184i) q^{4} +(1.00532 - 1.31016i) q^{5} +(-0.0986893 + 2.10256i) q^{6} +(-2.23554 + 1.41505i) q^{7} +(-1.43817 + 2.43550i) q^{8} +(0.203108 - 0.758010i) q^{9} +(2.28173 - 0.498026i) q^{10} +(0.146082 - 1.10960i) q^{11} +(-2.02537 + 2.18149i) q^{12} +(0.522112 - 1.26049i) q^{13} +(-3.70656 - 0.511320i) q^{14} +2.45792 q^{15} +(-3.77634 + 1.31880i) q^{16} +(1.92977 - 3.34246i) q^{17} +(0.911175 - 0.633581i) q^{18} +(-0.0505153 - 0.383702i) q^{19} +(2.91961 + 1.54420i) q^{20} +(-3.69644 - 1.35761i) q^{21} +(1.17042 - 1.06547i) q^{22} +(-3.87109 - 1.03726i) q^{23} +(-4.17893 + 0.508512i) q^{24} +(0.588252 + 2.19538i) q^{25} +(1.71437 - 0.885331i) q^{26} +(5.20432 - 2.15570i) q^{27} +(-3.53784 - 3.93493i) q^{28} +(-0.846917 + 2.04464i) q^{29} +(2.65547 + 2.24304i) q^{30} +(-1.81828 + 3.14935i) q^{31} +(-5.28336 - 2.02141i) q^{32} +(1.44258 - 0.832875i) q^{33} +(5.13513 - 1.85004i) q^{34} +(-0.393491 + 4.35148i) q^{35} +(1.56260 + 0.147014i) q^{36} +(-3.40805 - 2.61509i) q^{37} +(0.295582 - 0.460640i) q^{38} +(1.96146 - 0.525571i) q^{39} +(1.74506 + 4.33268i) q^{40} +(3.82713 - 3.82713i) q^{41} +(-2.75460 - 4.84001i) q^{42} +(1.98296 - 0.821369i) q^{43} +(2.23681 - 0.0830085i) q^{44} +(-0.788923 - 1.02814i) q^{45} +(-3.23564 - 4.65329i) q^{46} +(8.69324 - 5.01904i) q^{47} +(-4.97885 - 3.26421i) q^{48} +(2.99527 - 6.32680i) q^{49} +(-1.36793 + 2.90866i) q^{50} +(5.69529 - 0.749800i) q^{51} +(2.66009 + 0.608007i) q^{52} +(-11.4501 - 1.50744i) q^{53} +(7.58984 + 2.42038i) q^{54} +(-1.30689 - 1.30689i) q^{55} +(-0.231256 - 7.47974i) q^{56} +(0.407307 - 0.407307i) q^{57} +(-2.78088 + 1.43609i) q^{58} +(-1.42227 + 10.8032i) q^{59} +(0.821947 + 4.84663i) q^{60} +(1.01451 + 7.70596i) q^{61} +(-4.83844 + 1.74315i) q^{62} +(0.618566 + 1.98197i) q^{63} +(-3.86331 - 7.00535i) q^{64} +(-1.12655 - 1.95124i) q^{65} +(2.31859 + 0.416652i) q^{66} +(-10.8729 + 8.34305i) q^{67} +(7.23615 + 2.68747i) q^{68} +(-2.28266 - 5.51082i) q^{69} +(-4.39617 + 4.34212i) q^{70} +(4.38876 + 4.38876i) q^{71} +(1.55403 + 1.58482i) q^{72} +(-3.29273 - 12.2886i) q^{73} +(-1.29549 - 5.93538i) q^{74} +(-2.05933 + 2.68377i) q^{75} +(0.739708 - 0.227921i) q^{76} +(1.24357 + 2.68727i) q^{77} +(2.59873 + 1.22217i) q^{78} +(-5.09615 - 8.82678i) q^{79} +(-2.06859 + 6.27341i) q^{80} +(5.22206 + 3.01496i) q^{81} +(7.62727 - 0.642174i) q^{82} +(1.46558 + 0.607064i) q^{83} +(1.44088 - 7.74279i) q^{84} +(-2.43911 - 5.88854i) q^{85} +(2.89190 + 0.922219i) q^{86} +(-3.18168 + 0.852529i) q^{87} +(2.49234 + 1.95158i) q^{88} +(-3.10664 + 11.5941i) q^{89} +(0.0859303 - 1.83073i) q^{90} +(0.616455 + 3.55669i) q^{91} +(0.750785 - 7.98006i) q^{92} +(-5.36624 + 0.706479i) q^{93} +(13.9722 + 2.51081i) q^{94} +(-0.553493 - 0.319560i) q^{95} +(-2.40017 - 8.07014i) q^{96} -3.79460i q^{97} +(9.00969 - 4.10188i) q^{98} +(-0.811419 - 0.336101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

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