LMFDB - Embedded newform 552.2.bb.a.85.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.23
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.160789 - 1.40504i) q^{2} +(0.540641 + 0.841254i) q^{3} +(-1.94829 + 0.451832i) q^{4} +(-0.0738416 + 0.0337223i) q^{5} +(1.09507 - 0.894888i) q^{6} +(-0.400719 + 0.117662i) q^{7} +(0.948109 + 2.66479i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.160789 - 1.40504i) q^{2} +(0.540641 + 0.841254i) q^{3} +(-1.94829 + 0.451832i) q^{4} +(-0.0738416 + 0.0337223i) q^{5} +(1.09507 - 0.894888i) q^{6} +(-0.400719 + 0.117662i) q^{7} +(0.948109 + 2.66479i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(0.0592543 + 0.0983284i) q^{10} +(-2.76031 + 2.39183i) q^{11} +(-1.43343 - 1.39473i) q^{12} +(-1.04525 + 3.55980i) q^{13} +(0.229751 + 0.544109i) q^{14} +(-0.0682908 - 0.0438878i) q^{15} +(3.59170 - 1.76060i) q^{16} +(-0.466666 + 3.24573i) q^{17} +(1.34487 + 0.437417i) q^{18} +(-0.956420 + 0.137512i) q^{19} +(0.128628 - 0.0990650i) q^{20} +(-0.315629 - 0.273494i) q^{21} +(3.80445 + 3.49378i) q^{22} +(-0.872942 - 4.71572i) q^{23} +(-1.72917 + 2.23829i) q^{24} +(-3.26999 + 3.77377i) q^{25} +(5.16974 + 0.896245i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(0.727555 - 0.410298i) q^{28} +(-3.25048 - 0.467348i) q^{29} +(-0.0506839 + 0.103008i) q^{30} +(4.99772 + 3.21184i) q^{31} +(-3.05123 - 4.76340i) q^{32} +(-3.50447 - 1.02901i) q^{33} +(4.63543 + 0.133806i) q^{34} +(0.0256219 - 0.0222015i) q^{35} +(0.398349 - 1.95993i) q^{36} +(8.45554 + 3.86152i) q^{37} +(0.346993 + 1.32170i) q^{38} +(-3.55980 + 1.04525i) q^{39} +(-0.159873 - 0.164800i) q^{40} +(3.21284 + 7.03514i) q^{41} +(-0.333521 + 0.487447i) q^{42} +(4.77047 + 7.42299i) q^{43} +(4.29720 - 5.90718i) q^{44} -0.0811774i q^{45} +(-6.48542 + 1.98476i) q^{46} -4.94443 q^{47} +(3.42293 + 2.06967i) q^{48} +(-5.74204 + 3.69019i) q^{49} +(5.82809 + 3.98769i) q^{50} +(-2.98278 + 1.36219i) q^{51} +(0.428024 - 7.40781i) q^{52} +(-1.01460 - 3.45540i) q^{53} +(0.359111 + 1.36786i) q^{54} +(0.123168 - 0.269700i) q^{55} +(-0.693469 - 0.956275i) q^{56} +(-0.632762 - 0.730247i) q^{57} +(-0.134002 + 4.64221i) q^{58} +(2.31899 - 7.89776i) q^{59} +(0.152880 + 0.0546504i) q^{60} +(5.62148 - 8.74720i) q^{61} +(3.70919 - 7.53844i) q^{62} +(0.0594359 - 0.413386i) q^{63} +(-6.20218 + 5.05302i) q^{64} +(-0.0428617 - 0.298110i) q^{65} +(-0.882315 + 5.08939i) q^{66} +(-4.23708 - 3.67145i) q^{67} +(-0.557325 - 6.53449i) q^{68} +(3.49516 - 3.28387i) q^{69} +(-0.0353138 - 0.0324301i) q^{70} +(6.12026 - 7.06315i) q^{71} +(-2.81783 - 0.244562i) q^{72} +(1.45635 + 10.1292i) q^{73} +(4.06604 - 12.5013i) q^{74} +(-4.94258 - 0.710636i) q^{75} +(1.80125 - 0.700056i) q^{76} +(0.824684 - 1.28323i) q^{77} +(2.04100 + 4.83361i) q^{78} +(-10.6910 - 3.13916i) q^{79} +(-0.205845 + 0.251126i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(9.36809 - 5.64536i) q^{82} +(-9.63750 - 4.40130i) q^{83} +(0.738510 + 0.390235i) q^{84} +(-0.0749943 - 0.255407i) q^{85} +(9.66259 - 7.89626i) q^{86} +(-1.36418 - 2.98714i) q^{87} +(-8.99078 - 5.08794i) q^{88} +(1.16133 - 0.746342i) q^{89} +(-0.114058 + 0.0130525i) q^{90} -1.54947i q^{91} +(3.83146 + 8.79317i) q^{92} +5.94080i q^{93} +(0.795013 + 6.94714i) q^{94} +(0.0659863 - 0.0424068i) q^{95} +(2.35761 - 5.14215i) q^{96} +(-1.88329 - 4.12384i) q^{97} +(6.10813 + 7.47448i) q^{98} +(-1.02901 - 3.50447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.160789	−	1.40504i	−0.113695	−	0.993516i
$2$	−0.160789	−	1.40504i	−0.113695	−	0.993516i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$4$	−1.94829	+	0.451832i	−0.974147	+	0.225916i
$5$	−0.0738416	+	0.0337223i	−0.0330230	+	0.0150811i	−0.431858	−	0.901942i	$-0.642142\pi$
$5$	−0.0738416	+	0.0337223i	−0.0330230	+	0.0150811i	0.398835	+	0.917023i	$0.369415\pi$
$6$	1.09507	−	0.894888i	0.447060	−	0.365337i
$7$	−0.400719	+	0.117662i	−0.151458	+	0.0444720i	−0.356583	−	0.934264i	$-0.616058\pi$
$7$	−0.400719	+	0.117662i	−0.151458	+	0.0444720i	0.205125	+	0.978736i	$0.434240\pi$
$8$	0.948109	+	2.66479i	0.335207	+	0.942144i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	0.0592543	+	0.0983284i	0.0187378	+	0.0310942i
$11$	−2.76031	+	2.39183i	−0.832266	+	0.721162i	−0.962781	−	0.270284i	$-0.912882\pi$
$11$	−2.76031	+	2.39183i	−0.832266	+	0.721162i	0.130515	+	0.991446i	$0.458337\pi$
$12$	−1.43343	−	1.39473i	−0.413796	−	0.402624i
$13$	−1.04525	+	3.55980i	−0.289901	+	0.987311i	0.677808	+	0.735239i	$0.262930\pi$
$13$	−1.04525	+	3.55980i	−0.289901	+	0.987311i	−0.967709	+	0.252072i	$0.918888\pi$
$14$	0.229751	+	0.544109i	0.0614036	+	0.145419i
$15$	−0.0682908	−	0.0438878i	−0.0176326	−	0.0113318i
$16$	3.59170	−	1.76060i	0.897924	−	0.440151i
$17$	−0.466666	+	3.24573i	−0.113183	+	0.787206i	0.851606	+	0.524182i	$0.175629\pi$
$17$	−0.466666	+	3.24573i	−0.113183	+	0.787206i	−0.964789	+	0.263024i	$0.915280\pi$
$18$	1.34487	+	0.437417i	0.316988	+	0.103100i
$19$	−0.956420	+	0.137512i	−0.219418	+	0.0315475i	−0.251147	−	0.967949i	$-0.580808\pi$
$19$	−0.956420	+	0.137512i	−0.219418	+	0.0315475i	0.0317291	+	0.999497i	$0.489899\pi$
$20$	0.128628	−	0.0990650i	0.0287621	−	0.0221516i
$21$	−0.315629	−	0.273494i	−0.0688758	−	0.0596812i
$22$	3.80445	+	3.49378i	0.811111	+	0.744876i
$23$	−0.872942	−	4.71572i	−0.182021	−	0.983295i
$23$	−0.872942	−	4.71572i	−0.182021	−	0.983295i
$24$	−1.72917	+	2.23829i	−0.352966	+	0.456890i
$25$	−3.26999	+	3.77377i	−0.653998	+	0.754754i
$26$	5.16974	+	0.896245i	1.01387	+	0.175768i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	0.727555	−	0.410298i	0.137495	−	0.0775390i
$29$	−3.25048	−	0.467348i	−0.603599	−	0.0867844i	−0.166261	−	0.986082i	$-0.553169\pi$
$29$	−3.25048	−	0.467348i	−0.603599	−	0.0867844i	−0.437338	+	0.899297i	$0.644079\pi$
$30$	−0.0506839	+	0.103008i	−0.00925356	+	0.0188066i
$31$	4.99772	+	3.21184i	0.897616	+	0.576863i	0.906082	−	0.423101i	$-0.139059\pi$
$31$	4.99772	+	3.21184i	0.897616	+	0.576863i	−0.00846621	+	0.999964i	$0.502695\pi$
$32$	−3.05123	−	4.76340i	−0.539387	−	0.842058i
$33$	−3.50447	−	1.02901i	−0.610050	−	0.179127i
$34$	4.63543	+	0.133806i	0.794970	+	0.0229476i
$35$	0.0256219	−	0.0222015i	0.00433089	−	0.00375274i
$36$	0.398349	−	1.95993i	0.0663915	−	0.326655i
$37$	8.45554	+	3.86152i	1.39008	+	0.634829i	0.963029	−	0.269397i	$-0.0868244\pi$
$37$	8.45554	+	3.86152i	1.39008	+	0.634829i	0.427053	+	0.904226i	$0.359552\pi$
$38$	0.346993	+	1.32170i	0.0562897	+	0.214408i
$39$	−3.55980	+	1.04525i	−0.570024	+	0.167374i
$40$	−0.159873	−	0.164800i	−0.0252781	−	0.0260571i
$41$	3.21284	+	7.03514i	0.501761	+	1.09870i	0.975893	+	0.218250i	$0.0700349\pi$
$41$	3.21284	+	7.03514i	0.501761	+	1.09870i	−0.474131	+	0.880454i	$0.657238\pi$
$42$	−0.333521	+	0.487447i	−0.0514634	+	0.0752147i
$43$	4.77047	+	7.42299i	0.727490	+	1.13200i	0.986122	+	0.166020i	$0.0530917\pi$
$43$	4.77047	+	7.42299i	0.727490	+	1.13200i	−0.258633	+	0.965976i	$0.583272\pi$
$44$	4.29720	−	5.90718i	0.647827	−	0.890540i
$45$		−	0.0811774i		−	0.0121012i
$46$	−6.48542	+	1.98476i	−0.956224	+	0.292637i
$47$	−4.94443			−0.721220			−0.360610	−	0.932717i	$-0.617431\pi$
$47$	−4.94443			−0.721220			−0.360610	+	0.932717i	$0.617431\pi$
$48$	3.42293	+	2.06967i	0.494058	+	0.298731i
$49$	−5.74204	+	3.69019i	−0.820292	+	0.527170i
$50$	5.82809	+	3.98769i	0.824216	+	0.563945i
$51$	−2.98278	+	1.36219i	−0.417673	+	0.190745i
$52$	0.428024	−	7.40781i	0.0593562	−	1.02728i
$53$	−1.01460	−	3.45540i	−0.139366	−	0.474636i	0.859998	−	0.510297i	$-0.170465\pi$
$53$	−1.01460	−	3.45540i	−0.139366	−	0.474636i	−0.999364	+	0.0356609i	$0.988646\pi$
$54$	0.359111	+	1.36786i	0.0488689	+	0.186142i
$55$	0.123168	−	0.269700i	0.0166080	−	0.0363664i
$56$	−0.693469	−	0.956275i	−0.0926687	−	0.127788i
$57$	−0.632762	−	0.730247i	−0.0838114	−	0.0967235i
$58$	−0.134002	+	4.64221i	−0.0175953	+	0.609552i
$59$	2.31899	−	7.89776i	0.301907	−	1.02820i	−0.659187	−	0.751979i	$-0.729099\pi$
$59$	2.31899	−	7.89776i	0.301907	−	1.02820i	0.961094	−	0.276222i	$-0.0890825\pi$
$60$	0.152880	+	0.0546504i	0.0197368	+	0.00705533i
$61$	5.62148	−	8.74720i	0.719757	−	1.11996i	−0.267917	−	0.963442i	$-0.586335\pi$
$61$	5.62148	−	8.74720i	0.719757	−	1.11996i	0.987674	−	0.156522i	$-0.0500282\pi$
$62$	3.70919	−	7.53844i	0.471068	−	0.957382i
$63$	0.0594359	−	0.413386i	0.00748822	−	0.0520817i
$64$	−6.20218	+	5.05302i	−0.775272	+	0.631627i
$65$	−0.0428617	−	0.298110i	−0.00531634	−	0.0369759i
$66$	−0.882315	+	5.08939i	−0.108605	+	0.626460i
$67$	−4.23708	−	3.67145i	−0.517642	−	0.448540i	0.356440	−	0.934318i	$-0.383991\pi$
$67$	−4.23708	−	3.67145i	−0.517642	−	0.448540i	−0.874082	+	0.485779i	$0.838536\pi$
$68$	−0.557325	−	6.53449i	−0.0675856	−	0.792424i
$69$	3.49516	−	3.28387i	0.420768	−	0.395332i
$70$	−0.0353138	−	0.0324301i	−0.00422081	−	0.00387614i
$71$	6.12026	−	7.06315i	0.726341	−	0.838242i	−0.265714	−	0.964052i	$-0.585608\pi$
$71$	6.12026	−	7.06315i	0.726341	−	0.838242i	0.992054	+	0.125810i	$0.0401530\pi$
$72$	−2.81783	−	0.244562i	−0.332085	−	0.0288219i
$73$	1.45635	+	10.1292i	0.170453	+	1.18553i	0.877929	+	0.478790i	$0.158925\pi$
$73$	1.45635	+	10.1292i	0.170453	+	1.18553i	−0.707476	+	0.706737i	$0.750166\pi$
$74$	4.06604	−	12.5013i	0.472667	−	1.45325i
$75$	−4.94258	−	0.710636i	−0.570720	−	0.0820572i
$76$	1.80125	−	0.700056i	0.206618	−	0.0803019i
$77$	0.824684	−	1.28323i	0.0939815	−	0.146238i
$78$	2.04100	+	4.83361i	0.231098	+	0.547298i
$79$	−10.6910	−	3.13916i	−1.20283	−	0.353184i	−0.381897	−	0.924205i	$-0.624729\pi$
$79$	−10.6910	−	3.13916i	−1.20283	−	0.353184i	−0.820935	+	0.571021i	$0.806547\pi$
$80$	−0.205845	+	0.251126i	−0.0230141	+	0.0280767i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	9.36809	−	5.64536i	1.03453	−	0.623425i
$83$	−9.63750	−	4.40130i	−1.05785	−	0.483105i	−0.190959	−	0.981598i	$-0.561160\pi$
$83$	−9.63750	−	4.40130i	−1.05785	−	0.483105i	−0.866894	+	0.498493i	$0.833887\pi$
$84$	0.738510	+	0.390235i	0.0805781	+	0.0425781i
$85$	−0.0749943	−	0.255407i	−0.00813427	−	0.0277028i
$86$	9.66259	−	7.89626i	1.04194	−	0.851475i
$87$	−1.36418	−	2.98714i	−0.146256	−	0.320255i
$88$	−8.99078	−	5.08794i	−0.958421	−	0.542376i
$89$	1.16133	−	0.746342i	0.123101	−	0.0791121i	−0.477641	−	0.878555i	$-0.658508\pi$
$89$	1.16133	−	0.746342i	0.123101	−	0.0791121i	0.600742	+	0.799443i	$0.294872\pi$
$90$	−0.114058	+	0.0130525i	−0.0120227	+	0.00137585i
$91$		−	1.54947i		−	0.162428i
$92$	3.83146	+	8.79317i	0.399457	+	0.916752i
$93$			5.94080i			0.616032i
$94$	0.795013	+	6.94714i	0.0819993	+	0.716543i
$95$	0.0659863	−	0.0424068i	0.00677005	−	0.00435085i
$96$	2.35761	−	5.14215i	0.240622	−	0.524818i
$97$	−1.88329	−	4.12384i	−0.191220	−	0.418713i	0.789602	−	0.613619i	$-0.210287\pi$
$97$	−1.88329	−	4.12384i	−0.191220	−	0.418713i	−0.980822	+	0.194906i	$0.937560\pi$
$98$	6.10813	+	7.47448i	0.617015	+	0.755036i
$99$	−1.02901	−	3.50447i	−0.103419	−	0.352212i
$100$	4.66579	−	8.82989i	0.466579	−	0.882989i
$101$	−0.319064	−	0.145712i	−0.0317481	−	0.0144989i	0.399478	−	0.916743i	$-0.369191\pi$
$101$	−0.319064	−	0.145712i	−0.0317481	−	0.0144989i	−0.431226	+	0.902244i	$0.641919\pi$
$102$	2.39354	+	3.97191i	0.236996	+	0.393278i
$103$	3.20140	+	3.69461i	0.315443	+	0.364041i	0.891224	−	0.453563i	$-0.149847\pi$
$103$	3.20140	+	3.69461i	0.315443	+	0.364041i	−0.575781	+	0.817604i	$0.695302\pi$
$104$	−10.4771	+	0.589706i	−1.02737	+	0.0578255i
$105$	0.0325294	+	0.00955148i	0.00317454	+	0.000932129i
$106$	−4.69186	+	1.98115i	−0.455713	+	0.192426i
$107$	6.89871	−	10.7346i	0.666924	−	1.03775i	−0.328712	−	0.944430i	$-0.606615\pi$
$107$	6.89871	−	10.7346i	0.666924	−	1.03775i	0.995636	−	0.0933235i	$-0.0297491\pi$
$108$	1.86416	−	0.724504i	0.179379	−	0.0697155i
$109$	10.7097	+	1.53982i	1.02580	+	0.147488i	0.634619	−	0.772825i	$-0.281157\pi$
$109$	10.7097	+	1.53982i	1.02580	+	0.147488i	0.391183	+	0.920313i	$0.372066\pi$
$110$	−0.398745	−	0.129691i	−0.0380188	−	0.0123656i
$111$	1.32290	+	9.20095i	0.125564	+	0.873315i
$112$	−1.23211	+	1.12811i	−0.116423	+	0.106597i
$113$	−6.87962	+	7.93951i	−0.647180	+	0.746886i	−0.980627	−	0.195883i	$-0.937243\pi$
$113$	−6.87962	+	7.93951i	−0.647180	+	0.746886i	0.333447	+	0.942769i	$0.391788\pi$
$114$	−0.924287	+	1.00647i	−0.0865674	+	0.0942650i
$115$	0.223484	+	0.318778i	0.0208400	+	0.0297262i
$116$	6.54405	−	0.558140i	0.607600	−	0.0518220i
$117$	−2.80389	−	2.42959i	−0.259220	−	0.224616i
$118$	−11.4696	−	1.98841i	−1.05586	−	0.183048i
$119$	−0.194897	−	1.35554i	−0.0178662	−	0.124262i
$120$	0.0522046	−	0.223591i	0.00476560	−	0.0204110i
$121$	0.333040	−	2.31634i	0.0302763	−	0.210576i
$122$	−13.1941	−	6.49197i	−1.19453	−	0.587755i
$123$	−4.18134	+	6.50630i	−0.377019	+	0.586653i
$124$	−11.1882	−	3.99947i	−1.00473	−	0.359163i
$125$	0.228553	−	0.778378i	0.0204424	−	0.0696203i
$126$	−0.590381	−	0.0170419i	−0.0525953	−	0.00151822i
$127$	−6.51042	−	7.51343i	−0.577707	−	0.666709i	0.389403	−	0.921067i	$-0.372681\pi$
$127$	−6.51042	−	7.51343i	−0.577707	−	0.666709i	−0.967110	+	0.254358i	$0.918136\pi$
$128$	8.09695	+	7.90186i	0.715676	+	0.698432i
$129$	−3.66551	+	8.02635i	−0.322730	+	0.706681i
$130$	−0.411965	+	0.108155i	−0.0361317	+	0.00948586i
$131$	−1.97500	−	6.72622i	−0.172556	−	0.587672i	−0.999671	−	0.0256397i	$-0.991838\pi$
$131$	−1.97500	−	6.72622i	−0.172556	−	0.587672i	0.827115	−	0.562033i	$-0.189980\pi$
$132$	7.29267	+	0.421371i	0.634746	+	0.0366757i
$133$	0.367076	−	0.167638i	0.0318295	−	0.0145360i
$134$	−4.47727	+	6.54362i	−0.386778	+	0.565283i
$135$	0.0682908	−	0.0438878i	0.00587754	−	0.00377726i
$136$	−9.09164	+	1.83374i	−0.779601	+	0.157242i
$137$	10.7474			0.918209			0.459105	−	0.888382i	$-0.348170\pi$
$137$	10.7474			0.918209			0.459105	+	0.888382i	$0.348170\pi$
$138$	−5.17597	−	4.38285i	−0.440608	−	0.373093i
$139$			17.1535i			1.45494i	0.686139	+	0.727470i	$0.259304\pi$
$139$			17.1535i			1.45494i	−0.686139	+	0.727470i	$0.740696\pi$
$140$	−0.0398876	+	0.0548319i	−0.00337112	+	0.00463414i
$141$	−2.67316	−	4.15952i	−0.225121	−	0.350295i
$142$	−10.9081	−	7.46354i	−0.915388	−	0.626327i
$143$	−5.62920	−	12.3262i	−0.470737	−	1.03077i
$144$	0.109458	+	3.99850i	0.00912148	+	0.333209i
$145$	0.255780	−	0.0751039i	0.0212414	−	0.00623704i
$146$	13.9977	−	3.67490i	1.15846	−	0.304137i
$147$	−6.20877	−	2.83545i	−0.512090	−	0.233864i
$148$	−18.2186	−	3.70288i	−1.49756	−	0.304375i
$149$	−4.82923	+	4.18455i	−0.395626	+	0.342812i	−0.829843	−	0.557996i	$-0.811570\pi$
$149$	−4.82923	+	4.18455i	−0.395626	+	0.342812i	0.434218	+	0.900808i	$0.357025\pi$
$150$	−0.203759	+	7.05881i	−0.0166369	+	0.576349i
$151$	−12.5486	−	3.68459i	−1.02119	−	0.299848i	−0.272064	−	0.962279i	$-0.587706\pi$
$151$	−12.5486	−	3.68459i	−1.02119	−	0.299848i	−0.749122	+	0.662431i	$0.769525\pi$
$152$	−1.27323	−	2.41828i	−0.103273	−	0.196148i
$153$	−2.75856	−	1.77282i	−0.223017	−	0.143324i
$154$	−1.93560	−	0.952387i	−0.155975	−	0.0767455i
$155$	−0.477350	−	0.0686325i	−0.0383417	−	0.00551270i
$156$	6.46326	−	3.64489i	0.517475	−	0.291825i
$157$	22.6001	−	3.24940i	1.80368	−	0.259330i	0.843185	−	0.537624i	$-0.180678\pi$
$157$	22.6001	−	3.24940i	1.80368	−	0.259330i	0.960496	+	0.278294i	$0.0897688\pi$
$158$	−2.69166	+	15.5261i	−0.214137	+	1.23519i
$159$	2.35834	−	2.72167i	0.187028	−	0.215842i
$160$	0.385941	+	0.248842i	0.0305113	+	0.0196727i
$161$	0.904664	+	1.78697i	0.0712975	+	0.140833i
$162$	−0.956566	+	1.04162i	−0.0751549	+	0.0818377i
$163$	0.976815	+	0.846415i	0.0765100	+	0.0662963i	0.692276	−	0.721633i	$-0.256608\pi$
$163$	0.976815	+	0.846415i	0.0765100	+	0.0662963i	−0.615766	+	0.787929i	$0.711153\pi$
$164$	−9.43826	−	12.2549i	−0.737004	−	0.956943i
$165$	0.293476	−	0.0421955i	0.0228471	−	0.00328491i
$166$	−4.63441	+	14.2488i	−0.359700	+	1.10592i
$167$	0.189110	−	1.31529i	0.0146338	−	0.101780i	−0.981195	−	0.193017i	$-0.938173\pi$
$167$	0.189110	−	1.31529i	0.0146338	−	0.101780i	0.995829	+	0.0912366i	$0.0290820\pi$
$168$	0.429552	−	1.10038i	0.0331407	−	0.0848965i
$169$	−0.643328	−	0.413442i	−0.0494868	−	0.0318032i
$170$	−0.346800	+	0.146437i	−0.0265983	+	0.0112312i
$171$	0.272225	−	0.927115i	0.0208176	−	0.0708982i
$172$	−12.6482	−	12.3067i	−0.964418	−	0.938379i
$173$	−8.91183	+	7.72215i	−0.677554	+	0.587104i	−0.924157	−	0.382013i	$-0.875231\pi$
$173$	−8.91183	+	7.72215i	−0.677554	+	0.587104i	0.246603	+	0.969117i	$0.420686\pi$
$174$	−3.97772	+	2.39704i	−0.301550	+	0.181719i
$175$	0.866319	−	1.89697i	0.0654876	−	0.143398i
$176$	−5.70315	+	13.4505i	−0.429891	+	1.01387i
$177$	7.89776	−	2.31899i	0.593632	−	0.174306i
$178$	−1.23537	−	1.51172i	−0.0925951	−	0.113308i
$179$	−15.2945	+	6.98478i	−1.14317	+	0.522067i	−0.894742	−	0.446584i	$-0.852641\pi$
$179$	−15.2945	+	6.98478i	−1.14317	+	0.522067i	−0.248426	+	0.968651i	$0.579913\pi$
$180$	0.0366786	+	0.158157i	0.00273386	+	0.0117884i
$181$	3.54406	+	5.51466i	0.263428	+	0.409901i	0.947620	−	0.319400i	$-0.103481\pi$
$181$	3.54406	+	5.51466i	0.263428	+	0.409901i	−0.684192	+	0.729302i	$0.739845\pi$
$182$	−2.17707	+	0.249138i	−0.161375	+	0.0184673i
$183$	10.3978			0.768628
$184$	11.7387	−	6.79722i	0.865391	−	0.501097i
$185$	−0.754590			−0.0554786
$186$	8.34708	−	0.955217i	0.612037	−	0.0700399i
$187$	−6.47508	−	10.0754i	−0.473505	−	0.736788i
$188$	9.63321	−	2.23406i	0.702574	−	0.162935i
$189$	0.379896	−	0.173492i	0.0276333	−	0.0126197i
$190$	−0.0701933	−	0.0858950i	−0.00509236	−	0.00623148i
$191$	8.57529	−	2.51793i	0.620486	−	0.182191i	0.0436445	−	0.999047i	$-0.486103\pi$
$191$	8.57529	−	2.51793i	0.620486	−	0.182191i	0.576842	+	0.816856i	$0.304285\pi$
$192$	−7.60402	−	2.48574i	−0.548773	−	0.179393i
$193$	5.75025	−	12.5913i	0.413912	−	0.906341i	−0.581756	−	0.813363i	$-0.697634\pi$
$193$	5.75025	−	12.5913i	0.413912	−	0.906341i	0.995668	−	0.0929779i	$-0.0296386\pi$
$194$	−5.49136	+	3.30918i	−0.394257	+	0.237585i
$195$	0.227613	−	0.197228i	0.0162997	−	0.0141238i
$196$	9.51984	−	9.78401i	0.679989	−	0.698858i
$197$	−2.90767	+	9.90262i	−0.207163	+	0.705532i	0.788709	+	0.614766i	$0.210750\pi$
$197$	−2.90767	+	9.90262i	−0.207163	+	0.705532i	−0.995872	+	0.0907659i	$0.971069\pi$
$198$	−4.75848	+	2.00928i	−0.338170	+	0.142793i
$199$	9.47549	+	6.08953i	0.671699	+	0.431675i	0.831538	−	0.555468i	$-0.187461\pi$
$199$	9.47549	+	6.08953i	0.671699	+	0.431675i	−0.159838	+	0.987143i	$0.551097\pi$
$200$	−13.1566	−	5.13588i	−0.930312	−	0.363161i
$201$	0.797883	−	5.54940i	0.0562784	−	0.391425i
$202$	−0.153429	+	0.471728i	−0.0107952	+	0.0331907i
$203$	1.35752	−	0.195182i	0.0952791	−	0.0136991i
$204$	5.19585	−	4.00167i	0.363783	−	0.280173i
$205$	−0.474482	−	0.411141i	−0.0331393	−	0.0287154i
$206$	4.67634	−	5.09216i	0.325816	−	0.354788i
$207$	4.65220	+	1.16492i	0.323350	+	0.0809678i
$208$	2.51317	+	14.6260i	0.174257	+	1.01413i
$209$	2.31111	−	2.66717i	0.159863	−	0.184492i
$210$	0.00818987	−	0.0472409i	0.000565154	−	0.00325993i
$211$	5.94714	−	0.855069i	0.409418	−	0.0588654i	0.0654709	−	0.997854i	$-0.479145\pi$
$211$	5.94714	−	0.855069i	0.409418	−	0.0588654i	0.343947	+	0.938989i	$0.388236\pi$
$212$	3.53800	+	6.27371i	0.242991	+	0.430880i
$213$	9.25076	+	1.33006i	0.633852	+	0.0911341i
$214$	−16.1918	−	7.96698i	−1.10685	−	0.544612i
$215$	−0.602580	−	0.387254i	−0.0410956	−	0.0264105i
$216$	−1.31770	−	2.50273i	−0.0896580	−	0.170289i
$217$	−2.38059	−	0.699005i	−0.161605	−	0.0474515i
$218$	0.441510	−	15.2952i	0.0299028	−	1.03592i
$219$	−7.73382	+	6.70139i	−0.522603	+	0.452838i
$220$	−0.118108	+	0.581107i	−0.00796285	+	0.0391782i
$221$	−11.0664	−	5.05384i	−0.744405	−	0.339958i
$222$	12.7150	−	3.33814i	0.853376	−	0.224041i
$223$	16.6931	−	4.90154i	1.11785	−	0.328231i	0.329930	−	0.944005i	$-0.392975\pi$
$223$	16.6931	−	4.90154i	1.11785	−	0.328231i	0.787923	+	0.615774i	$0.211157\pi$
$224$	1.78316	+	1.54977i	0.119142	+	0.103549i
$225$	−2.07434	−	4.54217i	−0.138289	−	0.302811i
$226$	12.2615	+	8.38958i	0.815624	+	0.558066i
$227$	4.96071	+	7.71901i	0.329254	+	0.512329i	0.965930	−	0.258802i	$-0.0833277\pi$
$227$	4.96071	+	7.71901i	0.329254	+	0.512329i	−0.636677	+	0.771131i	$0.719691\pi$
$228$	1.56276	+	1.13683i	0.103496	+	0.0752885i
$229$			1.16837i			0.0772081i	0.999255	+	0.0386041i	$0.0122911\pi$
$229$			1.16837i			0.0772081i	−0.999255	+	0.0386041i	$0.987709\pi$
$230$	0.411963	−	0.365261i	0.0271641	−	0.0240846i
$231$	1.52538			0.100363
$232$	−1.83642	−	9.10493i	−0.120567	−	0.597768i
$233$	20.9682	−	13.4755i	1.37368	−	0.882807i	0.374659	−	0.927163i	$-0.377760\pi$
$233$	20.9682	−	13.4755i	1.37368	−	0.882807i	0.999016	+	0.0443552i	$0.0141233\pi$
$234$	−2.96284	+	4.33025i	−0.193687	+	0.283077i
$235$	0.365105	−	0.166738i	0.0238168	−	0.0108768i
$236$	−0.949613	+	16.4350i	−0.0618145	+	1.06982i
$237$	−3.13916	−	10.6910i	−0.203911	−	0.694456i
$238$	−1.87325	+	0.491794i	−0.121425	+	0.0318783i
$239$	4.26306	−	9.33479i	0.275754	−	0.603818i	−0.720191	−	0.693776i	$-0.755946\pi$
$239$	4.26306	−	9.33479i	0.275754	−	0.603818i	0.995946	+	0.0899579i	$0.0286733\pi$
$240$	−0.322549	−	0.0373986i	−0.0208204	−	0.00241407i
$241$	−7.63040	−	8.80595i	−0.491517	−	0.567241i	0.454753	−	0.890618i	$-0.349728\pi$
$241$	−7.63040	−	8.80595i	−0.491517	−	0.567241i	−0.946270	+	0.323376i	$0.895182\pi$
$242$	−3.30811	−	0.0954917i	−0.212653	−	0.00613844i
$243$	0.281733	−	0.959493i	0.0180732	−	0.0615515i
$244$	−7.00003	+	19.5821i	−0.448131	+	1.25361i
$245$	0.299560	−	0.466124i	0.0191382	−	0.0297796i
$246$	9.81395	+	4.82882i	0.625714	+	0.307875i
$247$	0.510182	−	3.54840i	0.0324621	−	0.225779i
$248$	−3.82048	+	16.3630i	−0.242601	+	1.03905i
$249$	−1.50782	−	10.4871i	−0.0955540	−	0.664593i
$250$	−1.13040	−	0.195971i	−0.0714930	−	0.0123943i
$251$	14.1507	+	12.2616i	0.893184	+	0.773948i	0.974885	−	0.222709i	$-0.0714898\pi$
$251$	14.1507	+	12.2616i	0.893184	+	0.773948i	−0.0817011	+	0.996657i	$0.526035\pi$
$252$	0.0709825	+	0.832251i	0.00447147	+	0.0524269i
$253$	13.6888	+	10.9289i	0.860605	+	0.687096i
$254$	−9.50989	+	10.3555i	−0.596703	+	0.649762i
$255$	0.174317	−	0.201173i	0.0109162	−	0.0125979i
$256$	9.80055	−	12.6471i	0.612534	−	0.790444i
$257$	4.10469	+	28.5487i	0.256044	+	1.78082i	0.560358	+	0.828250i	$0.310663\pi$
$257$	4.10469	+	28.5487i	0.256044	+	1.78082i	−0.304315	+	0.952572i	$0.598427\pi$
$258$	11.8667	+	3.85965i	0.738791	+	0.240291i
$259$	−3.84265	−	0.552490i	−0.238771	−	0.0343301i
$260$	0.218203	+	0.561439i	0.0135324	+	0.0348189i
$261$	1.77541	−	2.76260i	0.109895	−	0.171000i
$262$	−9.13307	+	3.85646i	−0.564243	+	0.238253i
$263$	−11.0888	−	3.25595i	−0.683762	−	0.200771i	−0.0786396	−	0.996903i	$-0.525058\pi$
$263$	−11.0888	−	3.25595i	−0.683762	−	0.200771i	−0.605122	+	0.796132i	$0.706876\pi$
$264$	−0.580540	−	10.3143i	−0.0357298	−	0.634800i
$265$	0.191444	+	0.220938i	0.0117603	+	0.0135721i
$266$	−0.294560	−	0.488803i	−0.0180607	−	0.0299704i
$267$	1.25573	+	0.573471i	0.0768492	+	0.0350959i
$268$	9.91397	+	5.23862i	0.605592	+	0.320000i
$269$	0.777445	+	2.64774i	0.0474017	+	0.161435i	0.979793	−	0.200016i	$-0.0640995\pi$
$269$	0.777445	+	2.64774i	0.0474017	+	0.161435i	−0.932391	+	0.361452i	$0.882281\pi$
$270$	−0.0726447	−	0.0888948i	−0.00442102	−	0.00540997i
$271$	10.7453	+	23.5290i	0.652733	+	1.42929i	0.889141	+	0.457633i	$0.151302\pi$
$271$	10.7453	+	23.5290i	0.652733	+	1.42929i	−0.236408	+	0.971654i	$0.575970\pi$
$272$	4.03833	+	12.4793i	0.244860	+	0.756668i
$273$	1.30349	−	0.837705i	0.0788911	−	0.0507002i
$274$	−1.72806	−	15.1005i	−0.104396	−	0.912255i
$275$		−	18.2380i		−	1.09979i
$276$	−5.32585	+	7.97718i	−0.320578	+	0.480170i
$277$			0.0265049i			0.00159252i	1.00000		0.000796262i	$0.000253458\pi$
$277$			0.0265049i			0.00159252i	−1.00000		0.000796262i	$0.999747\pi$
$278$	24.1014	−	2.75810i	1.44551	−	0.165420i
$279$	−4.99772	+	3.21184i	−0.299205	+	0.192288i
$280$	0.0834547	+	0.0472275i	0.00498737	+	0.00282238i
$281$	8.50823	+	18.6304i	0.507558	+	1.11140i	0.973938	+	0.226813i	$0.0728306\pi$
$281$	8.50823	+	18.6304i	0.507558	+	1.11140i	−0.466380	+	0.884584i	$0.654442\pi$
$282$	−5.41449	+	4.42472i	−0.322428	+	0.263488i
$283$	5.20722	+	17.7342i	0.309537	+	1.05419i	0.956516	+	0.291679i	$0.0942138\pi$
$283$	5.20722	+	17.7342i	0.309537	+	1.05419i	−0.646979	+	0.762508i	$0.723968\pi$
$284$	−8.73269	+	16.5264i	−0.518190	+	0.980663i
$285$	0.0713498	+	0.0325843i	0.00422640	+	0.00193013i
$286$	−16.4138	+	9.89119i	−0.970566	+	0.584879i
$287$	−2.11521	−	2.44109i	−0.124857	−	0.144093i
$288$	5.60047	−	0.796710i	0.330011	−	0.0469466i
$289$	5.99438	+	1.76011i	0.352610	+	0.103536i
$290$	−0.146651	−	0.347307i	−0.00861165	−	0.0203946i
$291$	2.45101	−	3.81385i	0.143681	−	0.223572i
$292$	−7.41408	−	19.0765i	−0.433876	−	1.11637i
$293$	24.2588	+	3.48789i	1.41721	+	0.203764i	0.807972	−	0.589221i	$-0.200565\pi$
$293$	24.2588	+	3.48789i	1.41721	+	0.203764i	0.609241	+	0.792985i	$0.291474\pi$
$294$	−2.98562	+	9.17950i	−0.174125	+	0.535359i
$295$	0.0950928	+	0.661385i	0.00553652	+	0.0385073i
$296$	−2.27334	+	26.1934i	−0.132135	+	1.52246i
$297$	2.39183	−	2.76031i	0.138788	−	0.160170i
$298$	6.65596	+	6.11244i	0.385570	+	0.354084i
$299$	17.6994	+	1.82161i	1.02359	+	0.105347i
$300$	9.95069	−	0.848691i	0.574504	−	0.0489992i
$301$	−2.78502	−	2.41324i	−0.160526	−	0.139097i
$302$	−3.15933	+	18.2237i	−0.181799	+	1.04866i
$303$	−0.0499186	−	0.347192i	−0.00286775	−	0.0199456i
$304$	−3.19306	+	2.17778i	−0.183135	+	0.124904i
$305$	−0.120123	+	0.835476i	−0.00687824	+	0.0478392i
$306$	−2.04734	+	4.16095i	−0.117039	+	0.237866i
$307$	11.4266	−	17.7801i	0.652150	−	1.01477i	−0.344947	−	0.938622i	$-0.612103\pi$
$307$	11.4266	−	17.7801i	0.652150	−	1.01477i	0.997097	−	0.0761431i	$-0.0242606\pi$
$308$	−1.02692	+	2.87274i	−0.0585142	+	0.163689i
$309$	−1.37730	+	4.69065i	−0.0783517	+	0.266842i
$310$	−0.0196789	+	0.681733i	−0.00111768	+	0.0387198i
$311$	5.19068	+	5.99036i	0.294336	+	0.339682i	0.883586	−	0.468269i	$-0.155122\pi$
$311$	5.19068	+	5.99036i	0.294336	+	0.339682i	−0.589250	+	0.807951i	$0.700577\pi$
$312$	−6.16045	−	8.49510i	−0.348767	−	0.480940i
$313$	11.6598	−	25.5315i	0.659053	−	1.44312i	−0.224350	−	0.974509i	$-0.572026\pi$
$313$	11.6598	−	25.5315i	0.659053	−	1.44312i	0.883402	−	0.468615i	$-0.155247\pi$
$314$	−8.19940	−	31.2316i	−0.462719	−	1.76250i
$315$	0.00955148	+	0.0325294i	0.000538165	+	0.00183282i
$316$	22.2476	+	1.28547i	1.25153	+	0.0723132i
$317$	−19.1193	+	8.73150i	−1.07385	+	0.490410i	−0.872251	−	0.489059i	$-0.837340\pi$
$317$	−19.1193	+	8.73150i	−1.07385	+	0.490410i	−0.201597	+	0.979469i	$0.564613\pi$
$318$	−4.20326	−	2.87595i	−0.235707	−	0.161275i
$319$	10.0902	−	6.48455i	0.564940	−	0.363065i
$320$	0.287579	−	0.582275i	0.0160762	−	0.0325501i
$321$	12.7603			0.712208
$322$	2.36530	−	1.55842i	0.131813	−	0.0868472i
$323$		−	3.16845i		−	0.176298i
$324$	1.61733	+	1.17653i	0.0898518	+	0.0653630i
$325$	−10.0159	−	15.5850i	−0.555582	−	0.864502i
$326$	1.03219	−	1.50856i	0.0571676	−	0.0835515i
$327$	4.49471	+	9.84205i	0.248558	+	0.544267i
$328$	−15.7010	+	15.2316i	−0.866944	+	0.841025i
$329$	1.98133	−	0.581771i	0.109234	−	0.0320741i
$330$	−0.106474	−	0.405562i	−0.00586122	−	0.0223254i
$331$	8.39818	+	3.83532i	0.461606	+	0.210808i	0.632623	−	0.774460i	$-0.281978\pi$
$331$	8.39818	+	3.83532i	0.461606	+	0.210808i	−0.171018	+	0.985268i	$0.554705\pi$
$332$	20.7653	+	4.22049i	1.13965	+	0.231629i
$333$	−7.02512	+	6.08730i	−0.384974	+	0.333582i
$334$	−1.87844	−	0.0542231i	−0.102784	−	0.00296695i
$335$	0.436683	+	0.128222i	0.0238585	+	0.00700550i
$336$	−1.61516	−	0.426609i	−0.0881140	−	0.0232734i
$337$	6.73140	+	4.32601i	0.366683	+	0.235653i	0.710987	−	0.703206i	$-0.248249\pi$
$337$	6.73140	+	4.32601i	0.366683	+	0.235653i	−0.344304	+	0.938858i	$0.611885\pi$
$338$	−0.477463	+	0.970381i	−0.0259706	+	0.0527818i
$339$	−10.3985	−	1.49508i	−0.564771	−	0.0812019i
$340$	0.261512	+	0.463723i	0.0141825	+	0.0251489i
$341$	−21.4774	+	3.08799i	−1.16307	+	0.167224i
$342$	−1.34641	−	0.233418i	−0.0728054	−	0.0126218i
$343$	3.78121	−	4.36375i	0.204166	−	0.235620i
$344$	−15.2578	+	19.7501i	−0.822644	+	1.06485i
$345$	−0.147349	+	0.360351i	−0.00793298	+	0.0194007i
$346$	12.2829	+	11.2799i	0.660332	+	0.606410i
$347$	13.9472	+	12.0853i	0.748723	+	0.648772i	0.943234	−	0.332128i	$-0.107767\pi$
$347$	13.9472	+	12.0853i	0.748723	+	0.648772i	−0.194511	+	0.980900i	$0.562312\pi$
$348$	4.00752	+	5.20345i	0.214825	+	0.278934i
$349$	−21.6980	+	3.11970i	−1.16147	+	0.166994i	−0.695980	−	0.718062i	$-0.745030\pi$
$349$	−21.6980	+	3.11970i	−1.16147	+	0.166994i	−0.465486	+	0.885055i	$0.654121\pi$
$350$	−2.80463	−	0.912202i	−0.149914	−	0.0487593i
$351$	0.528000	−	3.67232i	0.0281826	−	0.196014i
$352$	19.8156	+	5.85047i	1.05617	+	0.311831i
$353$	−17.8282	−	11.4575i	−0.948901	−	0.609822i	−0.0279957	−	0.999608i	$-0.508912\pi$
$353$	−17.8282	−	11.4575i	−0.948901	−	0.609822i	−0.920905	+	0.389786i	$0.872549\pi$
$354$	−4.52816	−	10.7238i	−0.240669	−	0.569965i
$355$	−0.213743	+	0.727943i	−0.0113443	+	0.0386352i
$356$	−1.92539	+	1.97882i	−0.102046	+	0.104877i
$357$	1.03498	−	0.896816i	0.0547770	−	0.0474645i
$358$	12.2731	+	20.3664i	0.648655	+	1.07640i
$359$	−1.37581	+	3.01260i	−0.0726123	+	0.158999i	−0.942457	−	0.334326i	$-0.891491\pi$
$359$	−1.37581	+	3.01260i	−0.0726123	+	0.158999i	0.869845	+	0.493325i	$0.164219\pi$
$360$	0.216321	−	0.0769651i	0.0114011	−	0.00405641i
$361$	−17.3345	+	5.08988i	−0.912344	+	0.267888i
$362$	7.17849	−	5.86625i	0.377293	−	0.308323i
$363$	2.12868	−	0.972138i	0.111727	−	0.0510240i
$364$	0.700099	+	3.01882i	0.0366952	+	0.158229i
$365$	−0.449118	−	0.698841i	−0.0235079	−	0.0365790i
$366$	−1.67186	−	14.6094i	−0.0873895	−	0.763644i
$367$	17.4284			0.909755			0.454877	−	0.890554i	$-0.349683\pi$
$367$	17.4284			0.909755			0.454877	+	0.890554i	$0.349683\pi$
$368$	−11.4378	−	15.4005i	−0.596239	−	0.802807i
$369$	−7.73405			−0.402619
$370$	0.121330	+	1.06023i	0.00630765	+	0.0551188i
$371$	0.813138	+	1.26527i	0.0422160	+	0.0656894i
$372$	−2.68424	−	11.5744i	−0.139172	−	0.600105i
$373$	−6.87640	+	3.14035i	−0.356047	+	0.162601i	−0.585405	−	0.810741i	$-0.699064\pi$
$373$	−6.87640	+	3.14035i	−0.356047	+	0.162601i	0.229358	+	0.973342i	$0.426337\pi$
$374$	−13.1153	+	10.7178i	−0.678175	+	0.554204i
$375$	0.778378	−	0.228553i	0.0401953	−	0.0118024i
$376$	−4.68786	−	13.1759i	−0.241758	−	0.679493i
$377$	5.06123	−	11.0826i	0.260667	−	0.570781i
$378$	−0.304848	−	0.505874i	−0.0156797	−	0.0260193i
$379$	3.54656	−	3.07311i	0.182174	−	0.157855i	−0.559000	−	0.829168i	$-0.688815\pi$
$379$	3.54656	−	3.07311i	0.182174	−	0.157855i	0.741174	+	0.671313i	$0.234269\pi$
$380$	−0.109400	+	0.112436i	−0.00561210	+	0.00576783i
$381$	2.80090	−	9.53898i	0.143494	−	0.488697i
$382$	−4.91662	−	11.6438i	−0.251556	−	0.595749i
$383$	−25.8124	−	16.5886i	−1.31895	−	0.847639i	−0.323814	−	0.946121i	$-0.604965\pi$
$383$	−25.8124	−	16.5886i	−1.31895	−	0.847639i	−0.995139	+	0.0984816i	$0.968601\pi$
$384$	−2.26992	+	11.0837i	−0.115836	+	0.565611i
$385$	−0.0176224	+	0.122566i	−0.000898119	+	0.00624656i
$386$	−18.6159	−	6.05481i	−0.947524	−	0.308181i
$387$	−8.73392	+	1.25575i	−0.443970	+	0.0638333i
$388$	5.53250	+	7.18352i	0.280870	+	0.364688i
$389$	−15.9604	−	13.8298i	−0.809226	−	0.701198i	0.148490	−	0.988914i	$-0.452559\pi$
$389$	−15.9604	−	13.8298i	−0.809226	−	0.701198i	−0.957716	+	0.287716i	$0.907104\pi$
$390$	−0.313711	−	0.288094i	−0.0158854	−	0.0145882i
$391$	15.7133	−	0.632671i	0.794657	−	0.0319956i
$392$	−15.2776	−	11.8026i	−0.771638	−	0.596122i
$393$	4.59069	−	5.29794i	0.231570	−	0.267246i
$394$	14.3811	+	2.49317i	0.724511	+	0.125604i
$395$	0.895301	−	0.128725i	0.0450475	−	0.00647685i
$396$	3.58824	+	6.36280i	0.180316	+	0.319743i
$397$	−15.2976	−	2.19946i	−0.767763	−	0.110388i	−0.252705	−	0.967543i	$-0.581320\pi$
$397$	−15.2976	−	2.19946i	−0.767763	−	0.110388i	−0.515057	+	0.857156i	$0.672229\pi$
$398$	7.03249	−	14.2926i	0.352507	−	0.716423i
$399$	0.339482	+	0.218172i	0.0169954	+	0.0109223i
$400$	−5.10069	+	19.3114i	−0.255034	+	0.965569i
$401$	−7.00943	−	2.05815i	−0.350034	−	0.102779i	0.101989	−	0.994786i	$-0.467479\pi$
$401$	−7.00943	−	2.05815i	−0.350034	−	0.102779i	−0.452023	+	0.892006i	$0.649298\pi$
$402$	−7.92544	−	0.228775i	−0.395285	−	0.0114103i
$403$	−16.6574	+	14.4337i	−0.829762	+	0.718993i
$404$	0.687468	+	0.139726i	0.0342028	+	0.00695161i
$405$	0.0738416	+	0.0337223i	0.00366922	+	0.00167568i
$406$	−0.492513	−	1.87599i	−0.0244430	−	0.0931038i
$407$	−32.5760	+	9.56518i	−1.61473	+	0.474129i
$408$	−6.45795	−	6.65697i	−0.319716	−	0.329569i
$409$	4.50641	+	9.86765i	0.222827	+	0.487924i	0.987720	−	0.156234i	$-0.0499353\pi$
$409$	4.50641	+	9.86765i	0.222827	+	0.487924i	−0.764893	+	0.644158i	$0.777208\pi$
$410$	−0.501380	+	0.732776i	−0.0247614	+	0.0361892i
$411$	5.81046	+	9.04126i	0.286609	+	0.445972i
$412$	−7.90661	−	5.75169i	−0.389531	−	0.283366i
$413$			3.43764i			0.169155i
$414$	0.888743	−	6.72385i	0.0436794	−	0.330459i
$415$	0.860070			0.0422192
$416$	20.1461	−	5.88282i	0.987742	−	0.288429i
$417$	−14.4304	+	9.27388i	−0.706662	+	0.454144i
$418$	−4.11909	−	2.81836i	−0.201471	−	0.137851i
$419$	1.17137	−	0.534946i	0.0572251	−	0.0261338i	−0.386597	−	0.922249i	$-0.626350\pi$
$419$	1.17137	−	0.534946i	0.0572251	−	0.0261338i	0.443822	+	0.896115i	$0.353622\pi$
$420$	−0.0676924	−	0.00391127i	−0.00330305	−	0.000190851i
$421$	−3.78079	−	12.8762i	−0.184265	−	0.627548i	−0.998870	−	0.0475317i	$-0.984864\pi$
$421$	−3.78079	−	12.8762i	−0.184265	−	0.627548i	0.814605	−	0.580016i	$-0.196954\pi$
$422$	−2.15765	−	8.21850i	−0.105033	−	0.400070i
$423$	2.05399	−	4.49762i	0.0998685	−	0.218682i
$424$	8.24597	−	5.97979i	0.400459	−	0.290404i
$425$	−10.7226	−	12.3746i	−0.520125	−	0.600256i
$426$	0.381365	−	13.2116i	0.0184772	−	0.640103i
$427$	−1.22343	+	4.16660i	−0.0592057	+	0.201636i
$428$	−8.59048	+	24.0312i	−0.415236	+	1.16159i
$429$	7.32610	−	11.3996i	0.353708	−	0.550380i
$430$	−0.447221	+	0.908917i	−0.0215669	+	0.0438319i
$431$	−2.31149	+	16.0768i	−0.111341	+	0.774391i	0.855278	+	0.518170i	$0.173387\pi$
$431$	−2.31149	+	16.0768i	−0.111341	+	0.774391i	−0.966618	+	0.256221i	$0.917522\pi$
$432$	−3.30458	+	2.25384i	−0.158992	+	0.108438i
$433$	−2.67096	−	18.5769i	−0.128358	−	0.892749i	−0.947636	−	0.319353i	$-0.896535\pi$
$433$	−2.67096	−	18.5769i	−0.128358	−	0.892749i	0.819278	−	0.573397i	$-0.194375\pi$
$434$	−0.599358	+	3.45723i	−0.0287701	+	0.165952i
$435$	0.201467	+	0.174572i	0.00965959	+	0.00837009i
$436$	−21.5614	+	1.83896i	−1.03260	+	0.0880703i
$437$	1.48337	+	4.39016i	0.0709591	+	0.210010i
$438$	10.6593	+	9.78884i	0.509319	+	0.467729i
$439$	−9.22337	+	10.6443i	−0.440207	+	0.508026i	−0.931886	−	0.362750i	$-0.881838\pi$
$439$	−9.22337	+	10.6443i	−0.440207	+	0.508026i	0.491679	+	0.870776i	$0.336383\pi$
$440$	0.835471	+	0.0725112i	0.0398295	+	0.00345683i
$441$	−0.971381	−	6.75611i	−0.0462563	−	0.321719i
$442$	−5.32151	+	16.3613i	−0.253119	+	0.778230i
$443$	35.0848	+	5.04444i	1.66693	+	0.239669i	0.910233	−	0.414096i	$-0.135902\pi$
$443$	35.0848	+	5.04444i	1.66693	+	0.239669i	0.756698	+	0.653764i	$0.226811\pi$
$444$	−6.73468	−	17.3284i	−0.319614	−	0.822370i
$445$	−0.0605861	+	0.0942739i	−0.00287206	+	0.00446901i
$446$	−9.57095	−	22.6664i	−0.453197	−	1.07329i
$447$	−6.13115	−	1.80027i	−0.289993	−	0.0851497i
$448$	1.89079	−	2.75460i	0.0893312	−	0.130143i
$449$	9.08480	+	10.4844i	0.428738	+	0.494790i	0.928479	−	0.371385i	$-0.121117\pi$
$449$	9.08480	+	10.4844i	0.428738	+	0.494790i	−0.499741	+	0.866175i	$0.666571\pi$
$450$	−6.04841	+	3.64487i	−0.285125	+	0.171821i
$451$	−25.6953	−	11.7346i	−1.20994	−	0.552563i
$452$	9.81620	−	18.5769i	0.461715	−	0.873785i
$453$	−3.68459	−	12.5486i	−0.173117	−	0.589583i
$454$	10.0479	−	8.21115i	0.471572	−	0.385368i
$455$	0.0522516	+	0.114415i	0.00244959	+	0.00536386i
$456$	1.34602	−	2.37853i	0.0630333	−	0.111385i
$457$	30.4756	−	19.5855i	1.42559	−	0.916171i	0.425654	−	0.904886i	$-0.360044\pi$
$457$	30.4756	−	19.5855i	1.42559	−	0.916171i	0.999936	−	0.0112848i	$-0.00359215\pi$
$458$	1.64161	−	0.187862i	0.0767075	−	0.00877820i
$459$		−	3.27911i		−	0.153056i
$460$	−0.579447	−	0.520096i	−0.0270169	−	0.0242496i
$461$			34.9091i			1.62588i	0.582349	+	0.812939i	$0.302134\pi$
$461$			34.9091i			1.62588i	−0.582349	+	0.812939i	$0.697866\pi$
$462$	−0.245266	−	2.14323i	−0.0114108	−	0.0997121i
$463$	−29.4229	+	18.9090i	−1.36740	+	0.878775i	−0.998710	−	0.0507774i	$-0.983830\pi$
$463$	−29.4229	+	18.9090i	−1.36740	+	0.878775i	−0.368690	+	0.929552i	$0.620194\pi$
$464$	−12.4975	+	4.04423i	−0.580184	+	0.187749i
$465$	−0.200337	−	0.438678i	−0.00929042	−	0.0203432i
$466$	−22.3051	−	27.2946i	−1.03326	−	1.26440i
$467$	1.46374	+	4.98503i	0.0677337	+	0.230680i	0.986402	−	0.164350i	$-0.0525526\pi$
$467$	1.46374	+	4.98503i	0.0677337	+	0.230680i	−0.918668	+	0.395029i	$0.870734\pi$
$468$	6.56058	+	3.46666i	0.303263	+	0.160246i
$469$	2.12987	+	0.972680i	0.0983483	+	0.0449142i
$470$	−0.292979	−	0.486178i	−0.0135141	−	0.0224257i
$471$	14.9521	+	17.2556i	0.688956	+	0.795097i
$472$	23.2445	−	1.30832i	1.06992	−	0.0602204i
$473$	−30.9225	−	9.07966i	−1.42182	−	0.417483i
$474$	−14.5166	+	6.12966i	−0.666769	+	0.281545i
$475$	2.60854	−	4.05897i	0.119688	−	0.186238i
$476$	0.992191	+	2.55292i	0.0454770	+	0.117013i
$477$	3.56463	+	0.512516i	0.163213	+	0.0234665i
$478$	−13.8012	−	4.48884i	−0.631254	−	0.205315i
$479$	0.778949	+	5.41771i	0.0355911	+	0.247541i	0.999848	−	0.0174271i	$-0.00554751\pi$
$479$	0.778949	+	5.41771i	0.0355911	+	0.247541i	−0.964257	+	0.264969i	$0.914638\pi$
$480$	−0.000684257		0.459208i	−3.12319e−5		0.0209599i
$481$	−22.5844	+	26.0638i	−1.02976	+	1.18841i
$482$	−11.1459	+	12.1370i	−0.507680	+	0.552823i
$483$	−1.01419	+	1.72716i	−0.0461474	+	0.0785884i
$484$	0.397739	+	4.66339i	0.0180790	+	0.211972i
$485$	0.278131	+	0.241002i	0.0126293	+	0.0109433i
$486$	−1.39343	−	0.241570i	−0.0632072	−	0.0109578i
$487$	4.61813	+	32.1198i	0.209268	+	1.45549i	0.775555	+	0.631280i	$0.217470\pi$
$487$	4.61813	+	32.1198i	0.209268	+	1.45549i	−0.566287	+	0.824208i	$0.691621\pi$
$488$	28.6392	+	6.68675i	1.29644	+	0.302695i
$489$	−0.183944	+	1.27936i	−0.00831821	+	0.0578544i
$490$	−0.703091	−	0.345947i	−0.0317624	−	0.0156283i
$491$	7.55992	−	11.7635i	0.341175	−	0.530878i	−0.627692	−	0.778462i	$-0.716000\pi$
$491$	7.55992	−	11.7635i	0.341175	−	0.530878i	0.968866	+	0.247584i	$0.0796366\pi$
$492$	5.20673	−	14.5654i	0.234737	−	0.656661i
$493$	3.03377	−	10.3321i	0.136634	−	0.465334i
$494$	−5.06768	−	0.146284i	−0.228006	−	0.00658161i
$495$	0.194162	+	0.224075i	0.00872694	+	0.0100714i
$496$	23.6050	+	2.73694i	1.05990	+	0.122892i
$497$	−1.62144	+	3.55046i	−0.0727316	+	0.159260i
$498$	−14.4924	+	3.80476i	−0.649419	+	0.170496i
$499$	−3.22165	−	10.9719i	−0.144221	−	0.491171i	0.855421	−	0.517933i	$-0.173299\pi$
$499$	−3.22165	−	10.9719i	−0.144221	−	0.491171i	−0.999642	+	0.0267621i	$0.991480\pi$
$500$	−0.0935908	+	1.61978i	−0.00418551	+	0.0724386i
$501$	1.20873	−	0.552009i	0.0540021	−	0.0246619i
$502$	14.9529	−	21.8539i	0.667379	−	0.975387i
$503$	27.4202	−	17.6219i	1.22260	−	0.785720i	0.239881	−	0.970802i	$-0.422891\pi$
$503$	27.4202	−	17.6219i	1.22260	−	0.785720i	0.982723	+	0.185082i	$0.0592551\pi$
$504$	1.15794	−	0.233551i	0.0515786	−	0.0104032i
$505$	0.0284739			0.00126707
$506$	13.1546	−	20.9906i	0.584794	−	0.933144i
$507$		−	0.764726i		−	0.0339627i
$508$	16.0790	+	11.6967i	0.713391	+	0.518959i
$509$	−11.5640	−	17.9940i	−0.512567	−	0.797570i	0.484445	−	0.874822i	$-0.339022\pi$
$509$	−11.5640	−	17.9940i	−0.512567	−	0.797570i	−0.997012	+	0.0772523i	$0.975385\pi$
$510$	−0.310685	−	0.212577i	−0.0137574	−	0.00941305i
$511$	−1.77540	−	3.88759i	−0.0785392	−	0.171977i
$512$	−19.3456	−	11.7367i	−0.854961	−	0.518692i
$513$	0.927115	−	0.272225i	0.0409331	−	0.0120190i
$514$	39.4522	−	10.3576i	1.74016	−	0.456854i
$515$	−0.360987	−	0.164857i	−0.0159070	−	0.00726448i
$516$	3.51493	−	17.2939i	0.154736	−	0.761321i
$517$	13.6482	−	11.8262i	0.600247	−	0.520117i
$518$	−0.158414	+	5.48793i	−0.00696032	+	0.241126i
$519$	−11.3144	−	3.32220i	−0.496646	−	0.145829i
$520$	0.753761	−	0.396858i	0.0330546	−	0.0174034i
$521$	−26.0516	−	16.7423i	−1.14134	−	0.733495i	−0.173444	−	0.984844i	$-0.555490\pi$
$521$	−26.0516	−	16.7423i	−1.14134	−	0.733495i	−0.967897	+	0.251349i	$0.919126\pi$
$522$	−4.16703	−	2.05033i	−0.182386	−	0.0897407i
$523$	36.2445	+	5.21117i	1.58486	+	0.227868i	0.877709	−	0.479195i	$-0.159071\pi$
$523$	36.2445	+	5.21117i	1.58486	+	0.227868i	0.707151	+	0.707063i	$0.249980\pi$
$524$	6.88699	+	12.2123i	0.300860	+	0.533496i
$525$	2.06420	−	0.296788i	0.0900892	−	0.0129529i
$526$	−2.79180	+	16.1037i	−0.121728	+	0.702155i
$527$	−12.7570	+	14.7224i	−0.555705	+	0.641318i
$528$	−14.3987	+	2.47411i	−0.626621	+	0.107672i
$529$	−21.4759	+	8.23309i	−0.933737	+	0.357960i
$530$	0.279645	−	0.304511i	0.0121470	−	0.0132271i
$531$	6.22071	+	5.39028i	0.269956	+	0.233918i
$532$	−0.639427	+	0.492465i	−0.0277227	+	0.0213510i
$533$	−28.4019	+	4.08358i	−1.23022	+	0.176879i
$534$	0.603844	−	1.85656i	0.0261309	−	0.0803411i
$535$	−0.147416	+	1.02530i	−0.00637335	+	0.0443276i
$536$	5.76643	−	14.7719i	0.249072	−	0.638047i
$537$	−14.1448	−	9.09033i	−0.610394	−	0.392277i
$538$	3.59518	−	1.51807i	0.154999	−	0.0654487i
$539$	7.02356	−	23.9200i	0.302526	−	1.03031i
$540$	−0.113221	+	0.116362i	−0.00487224	+	0.00500744i
$541$	−8.03192	+	6.95970i	−0.345319	+	0.299221i	−0.810201	−	0.586152i	$-0.800642\pi$
$541$	−8.03192	+	6.95970i	−0.345319	+	0.299221i	0.464882	+	0.885373i	$0.346097\pi$
$542$	31.3316	−	18.8809i	1.34581	−	0.811004i
$543$	−2.72317	+	5.96290i	−0.116862	+	0.255893i
$544$	16.8846	−	7.68057i	0.723923	−	0.329302i
$545$	−0.842746	+	0.247453i	−0.0360993	+	0.0105997i
$546$	−1.38660	−	1.69677i	−0.0593410	−	0.0726151i
$547$	−35.4106	+	16.1715i	−1.51405	+	0.691442i	−0.987342	−	0.158606i	$-0.949300\pi$
$547$	−35.4106	+	16.1715i	−1.51405	+	0.691442i	−0.526705	+	0.850048i	$0.676573\pi$
$548$	−20.9390	+	4.85601i	−0.894471	+	0.207438i
$549$	5.62148	+	8.74720i	0.239919	+	0.373321i
$550$	−25.6252	+	2.93248i	−1.09266	+	0.125041i
$551$	3.17309			0.135178
$552$	12.0646	+	6.20040i	0.513504	+	0.263906i
$553$	4.65345			0.197885
$554$	0.0372405	−	0.00426170i	0.00158220	−	0.000181062i
$555$	−0.407962	−	0.634801i	−0.0173170	−	0.0269458i
$556$	−7.75050	−	33.4200i	−0.328695	−	1.41733i
$557$	28.8649	−	13.1821i	1.22304	−	0.558545i	0.303989	−	0.952676i	$-0.401681\pi$
$557$	28.8649	−	13.1821i	1.22304	−	0.558545i	0.919055	+	0.394130i	$0.128954\pi$
$558$	5.31635	+	6.50558i	0.225059	+	0.275403i
$559$	−31.4107	+	9.22302i	−1.32853	+	0.390092i
$560$	0.0529380	−	0.124851i	0.00223704	−	0.00527592i
$561$	4.97529	−	10.8944i	0.210057	−	0.459961i
$562$	24.8085	−	14.9500i	1.04648	−	0.630628i
$563$	24.0353	−	20.8267i	1.01297	−	0.877740i	0.0204425	−	0.999791i	$-0.493493\pi$
$563$	24.0353	−	20.8267i	1.01297	−	0.877740i	0.992524	+	0.122051i	$0.0389470\pi$
$564$	7.08751	+	6.89615i	0.298438	+	0.290380i
$565$	0.240264	−	0.818263i	0.0101080	−	0.0344246i
$566$	24.0800	−	10.1678i	1.01216	−	0.427386i
$567$	0.351338	+	0.225791i	0.0147548	+	0.00948234i
$568$	24.6245	+	9.61254i	1.03322	+	0.403333i
$569$	−5.81034	+	40.4118i	−0.243582	+	1.69415i	0.390272	+	0.920700i	$0.372381\pi$
$569$	−5.81034	+	40.4118i	−0.243582	+	1.69415i	−0.633854	+	0.773453i	$0.718528\pi$
$570$	0.0343101	−	0.105489i	0.00143709	−	0.00441844i
$571$	11.4283	−	1.64314i	0.478260	−	0.0687634i	0.101031	−	0.994883i	$-0.467786\pi$
$571$	11.4283	−	1.64314i	0.478260	−	0.0687634i	0.377229	+	0.926120i	$0.376877\pi$
$572$	16.5367	+	21.4716i	0.691435	+	0.897775i
$573$	6.75437	+	5.85270i	0.282168	+	0.244500i
$574$	−3.08973	+	3.36447i	−0.128963	+	0.140430i
$575$	20.6505	+	12.1261i	0.861186	+	0.505691i
$576$	−2.01991	−	7.74080i	−0.0841629	−	0.322533i
$577$	14.8710	−	17.1620i	0.619086	−	0.714463i	−0.356447	−	0.934315i	$-0.616012\pi$
$577$	14.8710	−	17.1620i	0.619086	−	0.714463i	0.975533	+	0.219852i	$0.0705575\pi$
$578$	1.50920	−	8.70537i	0.0627742	−	0.362096i
$579$	13.7013	−	1.96995i	0.569406	−	0.0818683i
$580$	−0.464401	+	0.261894i	−0.0192832	+	0.0108746i
$581$	4.37980	+	0.629719i	0.181705	+	0.0261252i
$582$	−5.75271	−	2.83055i	−0.238458	−	0.117330i
$583$	11.0653	+	7.11126i	0.458279	+	0.294518i
$584$	−25.6112	+	13.4844i	−1.05980	+	0.557989i
$585$	0.288975	+	0.0848508i	0.0119477	+	0.00350815i
$586$	1.00007	−	34.6454i	0.0413127	−	1.43119i
$587$	1.78630	−	1.54784i	0.0737285	−	0.0638861i	−0.617217	−	0.786793i	$-0.711740\pi$
$587$	1.78630	−	1.54784i	0.0737285	−	0.0638861i	0.690945	+	0.722907i	$0.257194\pi$
$588$	13.3776	+	2.71896i	0.551685	+	0.112128i
$589$	−5.22158	−	2.38462i	−0.215151	−	0.0982564i
$590$	0.913985	−	0.239953i	0.0376282	−	0.00987872i
$591$	−9.90262	+	2.90767i	−0.407339	+	0.119606i
$592$	37.1683	−	1.01747i	1.52761	−	0.0418178i
$593$	9.15153	+	20.0391i	0.375808	+	0.822906i	0.999161	+	0.0409645i	$0.0130431\pi$
$593$	9.15153	+	20.0391i	0.375808	+	0.822906i	−0.623352	+	0.781941i	$0.714230\pi$
$594$	−4.26294	−	2.91679i	−0.174911	−	0.119677i
$595$	0.0601033	+	0.0935226i	0.00246400	+	0.00383405i
$596$	7.51804	−	10.3347i	0.307951	−	0.423327i
$597$			11.2635i			0.460986i
$598$	−0.286441	−	25.1614i	−0.0117135	−	1.02893i
$599$	−36.0652			−1.47358			−0.736792	−	0.676119i	$-0.763660\pi$
$599$	−36.0652			−1.47358			−0.736792	+	0.676119i	$0.763660\pi$
$600$	−2.79242	−	13.8447i	−0.114000	−	0.565207i
$601$	−11.6410	+	7.48121i	−0.474846	+	0.305165i	−0.756086	−	0.654473i	$-0.772891\pi$
$601$	−11.6410	+	7.48121i	−0.474846	+	0.305165i	0.281240	+	0.959637i	$0.409254\pi$
$602$	−2.94290	+	4.30110i	−0.119944	+	0.175300i
$603$	5.09982	−	2.32901i	0.207681	−	0.0948446i
$604$	26.1131	+	1.50882i	1.06253	+	0.0613928i
$605$	0.0535202	+	0.182273i	0.00217591	+	0.00741046i
$606$	−0.479793	+	0.125963i	−0.0194903	+	0.00511688i
$607$	−0.953205	+	2.08723i	−0.0386894	+	0.0847179i	−0.927990	−	0.372605i	$-0.878465\pi$
$607$	−0.953205	+	2.08723i	−0.0386894	+	0.0847179i	0.889301	+	0.457323i	$0.151192\pi$
$608$	3.57328	+	4.13623i	0.144916	+	0.167746i
$609$	0.898127	+	1.03649i	0.0363939	+	0.0420008i
$610$	1.19319	+	0.0344427i	0.0483110	+	0.00139454i
$611$	5.16818	−	17.6012i	0.209082	−	0.712068i
$612$	6.17551	+	2.20757i	0.249630	+	0.0892356i
$613$	−3.45864	+	5.38175i	−0.139693	+	0.217367i	−0.904050	−	0.427426i	$-0.859420\pi$
$613$	−3.45864	+	5.38175i	−0.139693	+	0.217367i	0.764357	+	0.644794i	$0.223057\pi$
$614$	−26.8191	−	13.1960i	−1.08233	−	0.532547i
$615$	0.0893496	−	0.621440i	0.00360292	−	0.0250589i
$616$	4.20144	+	0.980962i	0.169281	+	0.0395241i
$617$	0.742587	+	5.16480i	0.0298954	+	0.207927i	0.999294	−	0.0375641i	$-0.0119598\pi$
$617$	0.742587	+	5.16480i	0.0298954	+	0.207927i	−0.969399	+	0.245491i	$0.921051\pi$
$618$	6.81202	+	1.18096i	0.274019	+	0.0475050i
$619$	−12.1510	−	10.5289i	−0.488390	−	0.423193i	0.375538	−	0.926807i	$-0.377458\pi$
$619$	−12.1510	−	10.5289i	−0.488390	−	0.423193i	−0.863929	+	0.503614i	$0.832003\pi$
$620$	0.961028	−	0.0819658i	0.0385958	−	0.00329182i
$621$	1.53517	+	4.54348i	0.0616044	+	0.182324i
$622$	7.58211	−	8.25631i	0.304015	−	0.331048i
$623$	−0.377552	+	0.435718i	−0.0151263	+	0.0174567i
$624$	−10.9454	+	10.0216i	−0.438168	+	0.401186i
$625$	−3.54381	−	24.6477i	−0.141752	−	0.985910i
$626$	−37.7476	−	12.2774i	−1.50870	−	0.490703i
$627$	3.49324	+	0.502253i	0.139507	+	0.0200580i
$628$	−42.5634	+	16.5422i	−1.69846	+	0.660106i
$629$	−16.4794	+	25.6424i	−0.657075	+	1.02243i
$630$	0.0441694	−	0.0186506i	0.00175975	−	0.000743059i
$631$	−35.1839	−	10.3309i	−1.40065	−	0.411267i	−0.507741	−	0.861510i	$-0.669519\pi$
$631$	−35.1839	−	10.3309i	−1.40065	−	0.411267i	−0.892906	+	0.450243i	$0.851338\pi$
$632$	−1.77104	−	31.4655i	−0.0704483	−	1.25163i
$633$	3.93460	+	4.54077i	0.156386	+	0.180479i
$634$	15.3423	+	25.4595i	0.609321	+	1.01113i
$635$	0.734110	+	0.335257i	0.0291323	+	0.0133043i
$636$	−3.36500	+	6.36818i	−0.133431	+	0.252515i
$637$	−7.13445	−	24.2977i	−0.282677	−	0.962710i
$638$	−10.7335	−	13.1345i	−0.424942	−	0.519998i
$639$	3.88242	+	8.50132i	0.153586	+	0.336307i
$640$	−0.864361	−	0.310438i	−0.0341669	−	0.0122711i
$641$	18.8145	−	12.0914i	0.743130	−	0.477581i	−0.113483	−	0.993540i	$-0.536201\pi$
$641$	18.8145	−	12.0914i	0.743130	−	0.477581i	0.856613	+	0.515959i	$0.172564\pi$
$642$	−2.05171	−	17.9287i	−0.0809747	−	0.707590i
$643$		−	28.4271i		−	1.12105i	−0.828136	−	0.560527i	$-0.810599\pi$
$643$		−	28.4271i		−	1.12105i	0.828136	−	0.560527i	$-0.189401\pi$
$644$	−2.56996	−	3.07278i	−0.101271	−	0.121084i
$645$		−	0.716288i		−	0.0282038i
$646$	−4.45182	+	0.509454i	−0.175154	+	0.0200442i
$647$	−21.3128	+	13.6969i	−0.837894	+	0.538482i	−0.887777	−	0.460273i	$-0.847751\pi$
$647$	−21.3128	+	13.6969i	−0.837894	+	0.538482i	0.0498835	+	0.998755i	$0.484115\pi$
$648$	1.39303	−	2.46160i	0.0547235	−	0.0967007i
$649$	12.4889	+	27.3469i	0.490233	+	1.07346i
$650$	−20.2872	+	16.5787i	−0.795730	+	0.650269i
$651$	−0.699005	−	2.38059i	−0.0273962	−	0.0933027i
$652$	−2.28556	−	1.20771i	−0.0895094	−	0.0472975i
$653$	16.6957	+	7.62469i	0.653355	+	0.298377i	0.714379	−	0.699759i	$-0.246709\pi$
$653$	16.6957	+	7.62469i	0.653355	+	0.298377i	−0.0610238	+	0.998136i	$0.519437\pi$
$654$	13.1058	−	7.89777i	0.512478	−	0.308827i
$655$	0.372660	+	0.430073i	0.0145610	+	0.0168043i
$656$	23.9256	+	19.6115i	0.934139	+	0.765702i
$657$	−9.81879	−	2.88306i	−0.383068	−	0.112479i
$658$	−1.13599	−	2.69031i	−0.0442855	−	0.104879i
$659$	−21.4861	+	33.4331i	−0.836981	+	1.30237i	0.114114	+	0.993468i	$0.463597\pi$
$659$	−21.4861	+	33.4331i	−0.836981	+	1.30237i	−0.951095	+	0.308899i	$0.900039\pi$
$660$	−0.552712	+	0.214811i	−0.0215143	+	0.00836151i
$661$	−33.0372	−	4.75003i	−1.28500	−	0.184755i	−0.534240	−	0.845333i	$-0.679402\pi$
$661$	−33.0372	−	4.75003i	−1.28500	−	0.184755i	−0.750758	+	0.660578i	$0.770311\pi$
$662$	4.03845	−	12.4165i	0.156959	−	0.482580i
$663$	−1.73137	−	12.0419i	−0.0672408	−	0.467670i
$664$	2.59112	−	29.8548i	0.100555	−	1.15859i
$665$	−0.0214523	+	0.0247573i	−0.000831885	+	0.000960047i
$666$	9.68248	+	8.89182i	0.375189	+	0.344551i
$667$	0.633596	+	15.7363i	0.0245329	+	0.609312i
$668$	0.225848	+	2.64801i	0.00873832	+	0.102455i
$669$	13.1484	+	11.3932i	0.508347	+	0.440485i
$670$	0.109943	−	0.634175i	0.00424747	−	0.0245003i
$671$	5.40471	+	37.5906i	0.208647	+	1.45117i
$672$	−0.339704	+	2.33796i	−0.0131044	+	0.0901887i
$673$	5.58393	−	38.8371i	0.215245	−	1.49706i	−0.540027	−	0.841648i	$-0.681586\pi$
$673$	5.58393	−	38.8371i	0.215245	−	1.49706i	0.755271	−	0.655412i	$-0.227505\pi$
$674$	4.99589	−	10.1535i	0.192434	−	0.391098i
$675$	2.69964	−	4.20072i	0.103909	−	0.161686i
$676$	1.44020	+	0.514830i	0.0553923	+	0.0198011i
$677$	10.5351	−	35.8792i	0.404896	−	1.37895i	−0.464825	−	0.885403i	$-0.653883\pi$
$677$	10.5351	−	35.8792i	0.404896	−	1.37895i	0.869720	−	0.493545i	$-0.164299\pi$
$678$	−0.428683	+	14.8508i	−0.0164635	+	0.570341i
$679$	1.23989	+	1.43091i	0.0475827	+	0.0549133i
$680$	0.609503	−	0.441998i	0.0233734	−	0.0169498i
$681$	−3.81169	+	8.34643i	−0.146064	+	0.319836i
$682$	7.79210	+	29.6802i	0.298375	+	1.13651i
$683$	8.47249	+	28.8546i	0.324191	+	1.10409i	0.946870	+	0.321615i	$0.104226\pi$
$683$	8.47249	+	28.8546i	0.324191	+	1.10409i	−0.622680	+	0.782477i	$0.713956\pi$
$684$	−0.111475	+	1.92929i	−0.00426234	+	0.0737683i
$685$	−0.793602	+	0.362426i	−0.0303220	+	0.0138476i
$686$	−6.73923	−	4.61112i	−0.257305	−	0.176053i
$687$	−0.982896	+	0.631669i	−0.0374998	+	0.0240997i
$688$	30.2030	+	18.2622i	1.15148	+	0.696241i
$689$	13.3611			0.509016
$690$	0.530002	+	0.149090i	0.0201768	+	0.00567578i
$691$		−	1.73578i		−	0.0660321i	−0.999455	−	0.0330161i	$-0.989489\pi$
$691$		−	1.73578i		−	0.0660321i	0.999455	−	0.0330161i	$-0.0105112\pi$
$692$	13.8738	−	19.0717i	0.527401	−	0.724996i
$693$	0.824684	+	1.28323i	0.0313272	+	0.0487460i
$694$	14.7378	−	21.5396i	0.559439	−	0.817631i
$695$	−0.578456	−	1.26664i	−0.0219421	−	0.0480464i
$696$	6.66671	−	6.46739i	0.252701	−	0.245146i
$697$	−24.3335	+	7.14496i	−0.921697	+	0.270635i
$698$	7.87212	+	29.9850i	0.297964	+	1.13495i
$699$	22.6726	+	10.3542i	0.857555	+	0.391632i
$700$	−0.830729	+	4.08729i	−0.0313986	+	0.154485i
$701$	−19.3220	+	16.7426i	−0.729782	+	0.632359i	−0.938365	−	0.345645i	$-0.887660\pi$
$701$	−19.3220	+	16.7426i	−0.729782	+	0.632359i	0.208584	+	0.978005i	$0.433115\pi$
$702$	−5.24467	−	0.151392i	−0.197947	−	0.00571394i
$703$	−8.61805	−	2.53049i	−0.325036	−	0.0954392i
$704$	5.03402	−	28.7824i	0.189727	−	1.08478i
$705$	0.337659	+	0.217000i	0.0127170	+	0.00817271i
$706$	−13.2317	+	26.8917i	−0.497982	+	1.01208i
$707$	0.145000	+	0.0208478i	0.00545328	+	0.000784064i
$708$	−14.3394	+	8.08654i	−0.538906	+	0.303911i
$709$	−22.0389	+	3.16871i	−0.827687	+	0.119003i	−0.543122	−	0.839653i	$-0.682758\pi$
$709$	−22.0389	+	3.16871i	−0.827687	+	0.119003i	−0.284564	+	0.958657i	$0.591849\pi$
$710$	1.05716	+	0.183273i	0.0396745	+	0.00687812i
$711$	7.29669	−	8.42083i	0.273647	−	0.315806i
$712$	3.08991	+	2.38709i	0.115799	+	0.0894598i
$713$	10.7834	−	26.3716i	0.403841	−	0.987622i
$714$	−1.42648	−	1.30999i	−0.0533846	−	0.0490253i
$715$	0.831338	+	0.720358i	0.0310903	+	0.0269399i
$716$	26.6423	−	20.5190i	0.995670	−	0.766830i
$717$	10.1577	−	1.46046i	0.379347	−	0.0545418i
$718$	4.45404	+	1.44867i	0.166223	+	0.0540640i
$719$	2.60717	−	18.1332i	0.0972309	−	0.676256i	−0.881662	−	0.471882i	$-0.843575\pi$
$719$	2.60717	−	18.1332i	0.0972309	−	0.676256i	0.978893	−	0.204374i	$-0.0655160\pi$
$720$	−0.142921	−	0.291565i	−0.00532636	−	0.0108660i
$721$	−1.71758	−	1.10382i	−0.0639659	−	0.0411084i
$722$	9.93871	+	23.5374i	0.369881	+	0.875970i
$723$	3.28273	−	11.1800i	0.122086	−	0.415787i
$724$	−9.39657	−	9.14286i	−0.349221	−	0.339792i
$725$	12.3927	−	10.7383i	0.460253	−	0.398811i
$726$	−1.70817	−	2.83458i	−0.0633960	−	0.105201i
$727$	10.5316	−	23.0609i	0.390594	−	0.855281i	−0.607544	−	0.794286i	$-0.707845\pi$
$727$	10.5316	−	23.0609i	0.390594	−	0.855281i	0.998138	−	0.0609953i	$-0.0194275\pi$
$728$	4.12900	−	1.46906i	0.153031	−	0.0544471i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	−0.909688	+	0.743396i	−0.0336691	+	0.0275143i
$731$	−26.3193	+	12.0196i	−0.973453	+	0.444561i
$732$	−20.2580	+	4.69807i	−0.748757	+	0.173646i
$733$	−21.5709	−	33.5650i	−0.796740	−	1.23975i	−0.967107	−	0.254371i	$-0.918131\pi$
$733$	−21.5709	−	33.5650i	−0.796740	−	1.23975i	0.170366	−	0.985381i	$-0.445505\pi$
$734$	−2.80230	−	24.4876i	−0.103435	−	0.903856i
$735$	0.554083			0.0204377
$736$	−19.7993	+	18.5469i	−0.729812	+	0.683648i
$737$	20.4772			0.754286
$738$	1.24355	+	10.8667i	0.0457759	+	0.400008i
$739$	−6.18526	−	9.62445i	−0.227528	−	0.354041i	0.708654	−	0.705556i	$-0.249303\pi$
$739$	−6.18526	−	9.62445i	−0.227528	−	0.354041i	−0.936182	+	0.351515i	$0.885667\pi$
$740$	1.47016	−	0.340948i	0.0540442	−	0.0125335i
$741$	3.26093	−	1.48922i	0.119793	−	0.0547077i
$742$	1.64701	−	1.34594i	0.0604637	−	0.0494109i
$743$	32.9597	−	9.67784i	1.20917	−	0.355046i	0.385820	−	0.922574i	$-0.373918\pi$
$743$	32.9597	−	9.67784i	1.20917	−	0.355046i	0.823354	+	0.567528i	$0.192100\pi$
$744$	−15.8310	+	5.63252i	−0.580391	+	0.206498i
$745$	0.215485	−	0.471847i	0.00789477	−	0.0172871i
$746$	5.51798	+	9.15671i	0.202028	+	0.335251i
$747$	8.00712	−	6.93821i	0.292965	−	0.253856i
$748$	17.1678	+	16.7042i	0.627716	+	0.610767i
$749$	−1.50139	+	5.11328i	−0.0548598	+	0.186835i
$750$	−0.446281	−	1.05691i	−0.0162959	−	0.0385928i
$751$	16.9156	+	10.8710i	0.617260	+	0.396689i	0.811573	−	0.584251i	$-0.198612\pi$
$751$	16.9156	+	10.8710i	0.617260	+	0.396689i	−0.194314	+	0.980939i	$0.562248\pi$
$752$	−17.7589	+	8.70519i	−0.647600	+	0.317446i
$753$	−2.66471	+	18.5335i	−0.0971075	+	0.675397i
$754$	−16.3853	−	5.32929i	−0.596716	−	0.194081i
$755$	1.05086	−	0.151091i	0.0382446	−	0.00549875i
$756$	−0.661758	+	0.509663i	−0.0240679	+	0.0185363i
$757$	35.6311	+	30.8746i	1.29504	+	1.12215i	0.985208	+	0.171362i	$0.0548167\pi$
$757$	35.6311	+	30.8746i	1.29504	+	1.12215i	0.309827	+	0.950793i	$0.399729\pi$
$758$	−4.88810	−	4.48894i	−0.177544	−	0.163046i
$759$	−1.79330	+	17.4243i	−0.0650926	+	0.632464i
$760$	0.175567	+	0.135633i	0.00636850	+	0.00491993i
$761$	12.0785	−	13.9393i	0.437845	−	0.505301i	−0.493345	−	0.869834i	$-0.664226\pi$
$761$	12.0785	−	13.9393i	0.437845	−	0.505301i	0.931190	+	0.364533i	$0.118771\pi$
$762$	−13.8530	−	2.40162i	−0.501843	−	0.0870013i
$763$	−4.47276	+	0.643085i	−0.161925	+	0.0232812i
$764$	−15.5695	+	8.78027i	−0.563285	+	0.317659i
$765$	0.263480	+	0.0378827i	0.00952615	+	0.00136965i
$766$	−19.1574	+	38.9348i	−0.692184	+	1.40677i
$767$	25.6905	+	16.5103i	0.927631	+	0.596152i
$768$	15.9380	+	1.40720i	0.575113	+	0.0507780i
$769$	−43.3551	−	12.7302i	−1.56342	−	0.459063i	−0.618346	−	0.785906i	$-0.712197\pi$
$769$	−43.3551	−	12.7302i	−1.56342	−	0.459063i	−0.945078	+	0.326844i	$0.894015\pi$
$770$	0.175044	+	0.00505283i	0.00630816	+	0.000182091i
$771$	−21.7976	+	18.8877i	−0.785020	+	0.680224i
$772$	−5.51402	+	27.1297i	−0.198454	+	0.976419i
$773$	−4.74400	−	2.16651i	−0.170630	−	0.0779240i	0.328269	−	0.944584i	$-0.393535\pi$
$773$	−4.74400	−	2.16651i	−0.170630	−	0.0779240i	−0.498899	+	0.866660i	$0.666262\pi$
$774$	3.16870	+	12.0696i	0.113897	+	0.433834i
$775$	−28.4632	+	8.35755i	−1.02243	+	0.300212i
$776$	9.20359	−	8.92843i	0.330390	−	0.320512i
$777$	−1.61271	−	3.53134i	−0.0578557	−	0.126686i
$778$	−16.8652	+	24.6488i	−0.604646	+	0.883701i
$779$	−4.04024	−	6.28674i	−0.144757	−	0.225246i
$780$	−0.354343	+	0.487100i	−0.0126875	+	0.0174410i
$781$			34.1351i			1.22145i
$782$	−3.41547	−	21.9762i	−0.122137	−	0.785866i
$783$	3.28390			0.117357
$784$	−14.1267	+	23.3635i	−0.504525	+	0.834410i
$785$	−1.55925	+	1.00207i	−0.0556519	+	0.0357653i
$786$	−8.18197	−	5.59827i	−0.291841	−	0.199684i
$787$	−36.0796	+	16.4770i	−1.28610	+	0.587342i	−0.936864	−	0.349693i	$-0.886286\pi$
$787$	−36.0796	+	16.4770i	−1.28610	+	0.587342i	−0.349236	+	0.937035i	$0.613559\pi$
$788$	1.19067	−	20.6070i	0.0424160	−	0.734093i
$789$	−3.25595	−	11.0888i	−0.115915	−	0.394770i
$790$	−0.324819	−	1.23724i	−0.0115565	−	0.0440190i
$791$	1.82262	−	3.99098i	0.0648049	−	0.141903i
$792$	8.36306	−	6.06470i	0.297168	−	0.215500i
$793$	25.2624	+	29.1544i	0.897094	+	1.03530i
$794$	−0.630646	+	21.8474i	−0.0223808	+	0.775335i
$795$	−0.0823625	+	0.280501i	−0.00292110	+	0.00994834i
$796$	−21.2125	−	7.58285i	−0.751856	−	0.268767i
$797$	25.1990	−	39.2104i	0.892593	−	1.38890i	−0.0285138	−	0.999593i	$-0.509077\pi$
$797$	25.1990	−	39.2104i	0.892593	−	1.38890i	0.921107	−	0.389309i	$-0.127286\pi$
$798$	0.251956	−	0.512067i	0.00891914	−	0.0181270i
$799$	2.30740	−	16.0483i	0.0816299	−	0.567748i
$800$	27.9535	+	4.06162i	0.988304	+	0.143600i
$801$	0.196462	+	1.36643i	0.00694166	+	0.0482803i
$802$	−1.76475	+	10.1795i	−0.0623156	+	0.359450i
$803$	−28.2471	−	24.4763i	−0.996820	−	0.863750i
$804$	0.952888	+	11.1724i	0.0336058	+	0.394019i
$805$	−0.127062	−	0.101445i	−0.00447836	−	0.00357547i
$806$	22.9583	+	21.0835i	0.808671	+	0.742636i
$807$	−1.80710	+	2.08550i	−0.0636129	+	0.0734132i
$808$	0.0857830	−	0.988389i	0.00301784	−	0.0347714i
$809$	2.21633	+	15.4149i	0.0779221	+	0.541960i	0.990967	+	0.134102i	$0.0428151\pi$
$809$	2.21633	+	15.4149i	0.0779221	+	0.541960i	−0.913045	+	0.407858i	$0.866276\pi$
$810$	0.0355084	−	0.109173i	0.00124764	−	0.00383594i
$811$	−8.89099	−	1.27833i	−0.312205	−	0.0448883i	−0.0155685	−	0.999879i	$-0.504956\pi$
$811$	−8.89099	−	1.27833i	−0.312205	−	0.0448883i	−0.296636	+	0.954991i	$0.595865\pi$
$812$	−2.55665	+	0.993642i	−0.0897210	+	0.0348700i
$813$	−13.9845	+	21.7603i	−0.490458	+	0.763167i
$814$	18.6774	+	44.2327i	0.654642	+	1.55036i
$815$	−0.100673	−	0.0295601i	−0.00352641	−	0.00103545i
$816$	−8.31497	+	10.1441i	−0.291082	+	0.355114i
$817$	−5.58332	−	6.44350i	−0.195336	−	0.225429i
$818$	13.1399	−	7.91831i	0.459426	−	0.276857i
$819$	1.40944	+	0.643672i	0.0492500	+	0.0224917i
$820$	1.11020	+	0.586638i	0.0387698	+	0.0204863i
$821$	12.5383	+	42.7017i	0.437591	+	1.49030i	0.823262	+	0.567662i	$0.192152\pi$
$821$	12.5383	+	42.7017i	0.437591	+	1.49030i	−0.385671	+	0.922636i	$0.626030\pi$
$822$	11.7691	−	9.61769i	0.410494	−	0.335456i
$823$	−0.0853480	−	0.186886i	−0.00297504	−	0.00651444i	0.908139	−	0.418670i	$-0.137503\pi$
$823$	−0.0853480	−	0.186886i	−0.00297504	−	0.00651444i	−0.911114	+	0.412155i	$0.864776\pi$
$824$	−6.81008	+	12.0339i	−0.237240	+	0.419222i
$825$	15.3428	−	9.86022i	0.534168	−	0.343289i
$826$	4.83004	−	0.552737i	0.168058	−	0.0192322i
$827$			44.5966i			1.55078i	0.631485	+	0.775388i	$0.282446\pi$
$827$			44.5966i			1.55078i	−0.631485	+	0.775388i	$0.717554\pi$
$828$	−9.59020	−	0.167599i	−0.333282	−	0.00582446i
$829$			14.0012i			0.486283i	0.969991	+	0.243141i	$0.0781779\pi$
$829$			14.0012i			0.486283i	−0.969991	+	0.243141i	$0.921822\pi$
$830$	−0.138290	−	1.20844i	−0.00480012	−	0.0419454i
$831$	−0.0222973	+	0.0143296i	−0.000773485	+	0.000497089i
$832$	−11.5049	−	27.3602i	−0.398860	−	0.948544i
$833$	−9.29774	−	20.3592i	−0.322148	−	0.705405i
$834$	15.3505	+	18.7842i	0.531543	+	0.650445i
$835$	0.0303904	+	0.103500i	0.00105170	+	0.00358177i
$836$	−3.29761	+	6.24066i	−0.114050	+	0.215838i
$837$	−5.40394	−	2.46790i	−0.186787	−	0.0853030i
$838$	−0.939966	−	1.55981i	−0.0324706	−	0.0538827i
$839$	4.17296	+	4.81586i	0.144067	+	0.166262i	0.823197	−	0.567756i	$-0.192188\pi$
$839$	4.17296	+	4.81586i	0.144067	+	0.166262i	−0.679130	+	0.734018i	$0.737643\pi$
$840$	0.00538872	+	0.0957396i	0.000185928	+	0.00330333i
$841$	−17.4781	−	5.13203i	−0.602693	−	0.176967i
$842$	−17.4837	+	7.38254i	−0.602528	+	0.254419i
$843$	−11.0730	+	17.2299i	−0.381375	+	0.593431i
$844$	−11.2004	+	4.35304i	−0.385534	+	0.149838i
$845$	0.0614466	+	0.00883469i	0.00211383	+	0.000303922i
$846$	−6.64960	−	2.16278i	−0.228618	−	0.0743579i
$847$	0.139089	+	0.967388i	0.00477917	+	0.0332399i
$848$	−9.72773	−	10.6245i	−0.334051	−	0.364845i
$849$	−12.1037	+	13.9684i	−0.415398	+	0.479394i
$850$	−15.6628	+	17.0555i	−0.537228	+	0.584999i
$851$	10.8286	−	43.2448i	0.371200	−	1.48241i
$852$	−18.6242	+	1.58845i	−0.638053	+	0.0544194i
$853$	20.7754	+	18.0020i	0.711336	+	0.616376i	0.933477	−	0.358638i	$-0.116759\pi$
$853$	20.7754	+	18.0020i	0.711336	+	0.616376i	−0.222140	+	0.975015i	$0.571304\pi$
$854$	6.05097	+	1.04902i	0.207060	+	0.0358967i
$855$	0.0111629	+	0.0776397i	0.000381763	+	0.00265522i
$856$	35.1462	+	8.20602i	1.20127	+	0.280476i
$857$	1.07190	−	7.45521i	0.0366153	−	0.254665i	−0.963289	−	0.268465i	$-0.913484\pi$
$857$	1.07190	−	7.45521i	0.0366153	−	0.254665i	0.999905	+	0.0137999i	$0.00439277\pi$
$858$	−17.1950	−	8.46055i	−0.587026	−	0.288838i
$859$	8.32769	−	12.9581i	0.284137	−	0.442126i	−0.669620	−	0.742704i	$-0.733543\pi$
$859$	8.32769	−	12.9581i	0.284137	−	0.442126i	0.953757	+	0.300578i	$0.0971795\pi$
$860$	1.34898	+	0.482220i	0.0459997	+	0.0164436i
$861$	0.910002	−	3.09918i	0.0310128	−	0.105620i
$862$	22.9602	+	0.662769i	0.782029	+	0.0225740i
$863$	−16.6897	−	19.2610i	−0.568125	−	0.655652i	0.396883	−	0.917869i	$-0.370092\pi$
$863$	−16.6897	−	19.2610i	−0.568125	−	0.655652i	−0.965009	+	0.262217i	$0.915546\pi$
$864$	3.69808	+	4.28068i	0.125811	+	0.145632i
$865$	0.397655	−	0.870743i	0.0135207	−	0.0296062i
$866$	−25.6719	+	6.73978i	−0.872367	+	0.229027i
$867$	1.76011	+	5.99438i	0.0597764	+	0.203580i
$868$	4.95392	+	0.286238i	0.168147	+	0.00971555i
$869$	37.0189	−	16.9060i	1.25578	−	0.573495i
$870$	0.212887	−	0.311139i	0.00721756	−	0.0105486i
$871$	17.4985	−	11.2456i	0.592913	−	0.381042i
$872$	6.05066	+	29.9989i	0.204901	+	1.01589i
$873$	4.53353			0.153437
$874$	5.92986	−	2.79009i	0.200580	−	0.0943761i
$875$			0.338803i			0.0114536i
$876$	12.0398	−	16.5507i	0.406789	−	0.559195i
$877$	−9.49762	−	14.7786i	−0.320712	−	0.499037i	0.643042	−	0.765831i	$-0.277672\pi$
$877$	−9.49762	−	14.7786i	−0.320712	−	0.499037i	−0.963754	+	0.266794i	$0.914036\pi$
$878$	16.4388	+	11.2477i	0.554782	+	0.379593i
$879$	10.1811	+	22.2935i	0.343400	+	0.751940i
$880$	−0.0324536	−	1.18553i	−0.00109401	−	0.0399643i
$881$	19.8345	−	5.82394i	0.668242	−	0.196213i	0.0700218	−	0.997545i	$-0.477693\pi$
$881$	19.8345	−	5.82394i	0.668242	−	0.196213i	0.598220	+	0.801332i	$0.295875\pi$
$882$	−9.33643	+	2.45114i	−0.314374	+	0.0825343i
$883$	−15.7902	−	7.21112i	−0.531381	−	0.242674i	0.131609	−	0.991302i	$-0.457986\pi$
$883$	−15.7902	−	7.21112i	−0.531381	−	0.242674i	−0.662990	+	0.748628i	$0.730713\pi$
$884$	23.8440	+	4.84623i	0.801962	+	0.162996i
$885$	−0.504982	+	0.437569i	−0.0169748	+	0.0147087i
$886$	1.44638	−	50.1068i	0.0485921	−	1.68337i
$887$	18.6608	+	5.47931i	0.626569	+	0.183977i	0.579576	−	0.814918i	$-0.303218\pi$
$887$	18.6608	+	5.47931i	0.626569	+	0.183977i	0.0469925	+	0.998895i	$0.485036\pi$
$888$	−23.2643	+	12.2487i	−0.780699	+	0.411041i
$889$	3.49290	+	2.24475i	0.117148	+	0.0752864i
$890$	0.142200	+	0.0699679i	0.00476657	+	0.00234533i
$891$	3.61524	+	0.519793i	0.121115	+	0.0174137i
$892$	−30.3084	+	17.0921i	−1.01480	+	0.572286i
$893$	4.72895	−	0.679921i	0.158248	−	0.0227527i
$894$	−1.54363	+	8.90399i	−0.0516267	+	0.297794i
$895$	0.893830	−	1.03153i	0.0298774	−	0.0344804i
$896$	−4.17435	−	2.21372i	−0.139455	−	0.0739553i
$897$	8.03661	+	15.8746i	0.268334	+	0.530036i
$898$	13.2703	−	14.4503i	0.442837	−	0.482214i
$899$	−14.7439	−	12.7757i	−0.491737	−	0.426093i
$900$	6.09372	+	7.91222i	0.203124	+	0.263741i
$901$	11.6888	−	1.68060i	0.389410	−	0.0559887i
$902$	−12.3561	+	37.9898i	−0.411415	+	1.26492i
$903$	0.524446	−	3.64760i	0.0174525	−	0.121385i
$904$	−27.6797	−	10.8052i	−0.920614	−	0.359376i
$905$	−0.447666	−	0.287697i	−0.0148809	−	0.00956339i
$906$	−17.0388	+	7.19468i	−0.566077	+	0.239027i
$907$	−6.20737	+	21.1404i	−0.206112	+	0.701954i	0.789940	+	0.613184i	$0.210112\pi$
$907$	−6.20737	+	21.1404i	−0.206112	+	0.701954i	−0.996052	+	0.0887699i	$0.971706\pi$
$908$	−13.1526	−	12.7975i	−0.436485	−	0.424700i
$909$	0.265088	−	0.229700i	0.00879242	−	0.00761867i
$910$	0.152357	−	0.0918125i	0.00505057	−	0.00304355i
$911$	20.9050	−	45.7755i	0.692613	−	1.51661i	−0.156091	−	0.987743i	$-0.549889\pi$
$911$	20.9050	−	45.7755i	0.692613	−	1.51661i	0.848704	−	0.528868i	$-0.177383\pi$
$912$	−3.55836	−	1.50878i	−0.117829	−	0.0499607i
$913$	37.1296	−	10.9022i	1.22881	−	0.360812i
$914$	−32.4186	−	39.6704i	−1.07231	−	1.31218i
$915$	−0.767791	+	0.350638i	−0.0253824	+	0.0115917i
$916$	−0.527908	−	2.27633i	−0.0174426	−	0.0752120i
$917$	1.58284	+	2.46294i	0.0522699	+	0.0813335i
$918$	−4.60729	+	0.527246i	−0.152063	+	0.0174017i
$919$	20.3305			0.670641			0.335320	−	0.942104i	$-0.391155\pi$
$919$	20.3305			0.670641			0.335320	+	0.942104i	$0.391155\pi$
$920$	−0.637589	+	0.897774i	−0.0210207	+	0.0295987i
$921$	21.1353			0.696431
$922$	49.0488	−	5.61301i	1.61533	−	0.184855i
$923$	18.7462	+	29.1697i	0.617039	+	0.960131i
$924$	−2.97189	+	0.689217i	−0.0977681	+	0.0226736i
$925$	−42.2220	+	19.2821i	−1.38825	+	0.633993i
$926$	31.2988	+	38.3002i	1.02854	+	1.25862i
$927$	−4.69065	+	1.37730i	−0.154061	+	0.0452364i
$928$	7.69180	+	16.9093i	0.252496	+	0.555076i
$929$	−0.840748	+	1.84098i	−0.0275841	+	0.0604006i	−0.922923	−	0.384986i	$-0.874206\pi$
$929$	−0.840748	+	1.84098i	−0.0275841	+	0.0604006i	0.895338	+	0.445386i	$0.146934\pi$
$930$	−0.584149	+	0.352018i	−0.0191550	+	0.0115431i
$931$	4.98436	−	4.31897i	0.163356	−	0.141548i
$932$	−34.7636	+	35.7283i	−1.13872	+	1.17032i
$933$	−2.23312	+	7.60531i	−0.0731091	+	0.248987i
$934$	6.76883	−	2.85815i	0.221483	−	0.0935216i
$935$	0.817897	+	0.525630i	0.0267481	+	0.0171900i
$936$	3.81594	−	9.77530i	0.124728	−	0.319516i
$937$	−7.67644	+	53.3908i	−0.250778	+	1.74420i	0.342784	+	0.939414i	$0.388630\pi$
$937$	−7.67644	+	53.3908i	−0.250778	+	1.74420i	−0.593563	+	0.804788i	$0.702279\pi$
$938$	1.02420	−	3.14896i	0.0334412	−	0.102817i
$939$	27.7822	−	3.99448i	0.906638	−	0.130355i
$940$	−0.635994	+	0.489820i	−0.0207438	+	0.0159762i
$941$	−9.84180	−	8.52797i	−0.320833	−	0.278004i	0.479522	−	0.877530i	$-0.340810\pi$
$941$	−9.84180	−	8.52797i	−0.320833	−	0.278004i	−0.800355	+	0.599526i	$0.795356\pi$
$942$	21.8408	−	23.7828i	0.711610	−	0.774887i
$943$	30.3711	−	21.2921i	0.989019	−	0.693366i
$944$	−5.57572	−	32.4492i	−0.181474	−	1.05613i
$945$	−0.0222015	+	0.0256219i	−0.000722215	+	0.000833481i
$946$	−7.78531	+	44.9074i	−0.253122	+	1.46006i
$947$	−43.2152	+	6.21341i	−1.40431	+	0.201909i	−0.802461	−	0.596705i	$-0.796476\pi$
$947$	−43.2152	+	6.21341i	−1.40431	+	0.201909i	−0.601845	+	0.798613i	$0.705567\pi$
$948$	10.9466	+	19.4109i	0.355528	+	0.630435i
$949$	−37.5800	−	5.40319i	−1.21990	−	0.175395i
$950$	−6.12245	−	3.01247i	−0.198639	−	0.0977375i
$951$	−17.6821	−	11.3636i	−0.573381	−	0.368490i
$952$	3.42743	−	1.80455i	0.111084	−	0.0584859i
$953$	26.7053	+	7.84138i	0.865069	+	0.254007i	0.684017	−	0.729466i	$-0.260231\pi$
$953$	26.7053	+	7.84138i	0.865069	+	0.254007i	0.181052	+	0.983473i	$0.442050\pi$
$954$	0.146953	−	5.09086i	0.00475777	−	0.164823i
$955$	−0.548303	+	0.475107i	−0.0177427	+	0.0153741i
$956$	−4.08792	+	20.1131i	−0.132213	+	0.650504i
$957$	10.9103	+	4.98257i	0.352680	+	0.161063i
$958$	7.48687	−	1.96557i	0.241890	−	0.0635046i
$959$	−4.30668	+	1.26455i	−0.139070	+	0.0408346i
$960$	0.645318	−	0.0728745i	0.0208275	−	0.00235201i
$961$	1.78340	+	3.90510i	0.0575290	+	0.125971i
$962$	40.2521	+	27.5413i	1.29778	+	0.887966i
$963$	6.89871	+	10.7346i	0.222308	+	0.345918i
$964$	18.8451	+	13.7089i	0.606959	+	0.441535i
$965$			1.12367i			0.0361723i
$966$	2.58980	+	1.14728i	0.0833256	+	0.0369130i
$967$	25.6060			0.823435			0.411717	−	0.911312i	$-0.364929\pi$
$967$	25.6060			0.823435			0.411717	+	0.911312i	$0.364929\pi$
$968$	6.48831	−	1.30866i	0.208542	−	0.0420621i
$969$	2.66547	−	1.71300i	0.0856273	−	0.0550294i
$970$	0.293897	−	0.429537i	0.00943648	−	0.0137916i
$971$	1.99989	−	0.913321i	0.0641796	−	0.0293099i	−0.383067	−	0.923721i	$-0.625132\pi$
$971$	1.99989	−	0.913321i	0.0641796	−	0.0293099i	0.447246	+	0.894411i	$0.352405\pi$
$972$	−0.115368	+	1.99667i	−0.00370042	+	0.0640432i
$973$	−2.01831	−	6.87374i	−0.0647041	−	0.220362i
$974$	44.3872	−	11.6532i	1.42226	−	0.373393i
$975$	7.69597	−	16.8518i	0.246468	−	0.539690i
$976$	4.79030	−	41.3145i	0.153334	−	1.32244i
$977$	24.0372	+	27.7404i	0.769019	+	0.887495i	0.996266	−	0.0863420i	$-0.0275178\pi$
$977$	24.0372	+	27.7404i	0.769019	+	0.887495i	−0.227247	+	0.973837i	$0.572972\pi$
$978$	1.82713	+	0.0527417i	0.0584250	+	0.00168649i
$979$	−1.42052	+	4.83784i	−0.0454000	+	0.154618i
$980$	−0.373021	+	1.04350i	−0.0119157	+	0.0333333i
$981$	−5.84963	+	9.10221i	−0.186764	+	0.290611i
$982$	−17.7437	−	8.73058i	−0.566226	−	0.278604i
$983$	8.19727	−	57.0133i	0.261452	−	1.81844i	−0.260509	−	0.965472i	$-0.583890\pi$
$983$	8.19727	−	57.0133i	0.261452	−	1.81844i	0.521961	−	0.852969i	$-0.325201\pi$
$984$	−21.3023	−	4.97371i	−0.679091	−	0.158556i
$985$	−0.119232	−	0.829278i	−0.00379905	−	0.0264230i
$986$	−15.0048	−	2.60129i	−0.477851	−	0.0828421i
$987$	1.56060	+	1.35227i	0.0496746	+	0.0430433i
$988$	0.609295	+	7.14384i	0.0193843	+	0.227276i
$989$	30.8404	−	28.9760i	0.980667	−	0.921384i
$990$	0.283616	−	0.308835i	0.00901391	−	0.00981543i
$991$	−33.7926	+	38.9987i	−1.07346	+	1.23884i	−0.103740	+	0.994604i	$0.533081\pi$
$991$	−33.7926	+	38.9987i	−1.07346	+	1.23884i	−0.969717	+	0.244231i	$0.921465\pi$
$992$	0.0500759	−	33.6062i	0.00158991	−	1.06700i
$993$	1.31392	+	9.13853i	0.0416961	+	0.290002i
$994$	5.24926	+	1.70732i	0.166496	+	0.0541528i
$995$	−0.905038	−	0.130125i	−0.0286916	−	0.00412523i
$996$	7.67608	+	19.7507i	0.243226	+	0.625824i
$997$	−2.59776	+	4.04219i	−0.0822718	+	0.128017i	−0.879951	−	0.475065i	$-0.842425\pi$
$997$	−2.59776	+	4.04219i	−0.0822718	+	0.128017i	0.797679	+	0.603082i	$0.206061\pi$
$998$	−14.8980	+	6.29073i	−0.471589	+	0.199130i
$999$	−8.91903	−	2.61886i	−0.282186	−	0.0828572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.23	yes	480
8.5	even	2	inner	552.2.bb.a.85.48	yes	480
23.13	even	11	inner	552.2.bb.a.13.48	yes	480
184.13	even	22	inner	552.2.bb.a.13.23	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.23	✓	480	184.13	even	22	inner
552.2.bb.a.13.48	yes	480	23.13	even	11	inner
552.2.bb.a.85.23	yes	480	1.1	even	1	trivial
552.2.bb.a.85.48	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.160789 - 1.40504i) q^{2} +(0.540641 + 0.841254i) q^{3} +(-1.94829 + 0.451832i) q^{4} +(-0.0738416 + 0.0337223i) q^{5} +(1.09507 - 0.894888i) q^{6} +(-0.400719 + 0.117662i) q^{7} +(0.948109 + 2.66479i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.160789 - 1.40504i) q^{2} +(0.540641 + 0.841254i) q^{3} +(-1.94829 + 0.451832i) q^{4} +(-0.0738416 + 0.0337223i) q^{5} +(1.09507 - 0.894888i) q^{6} +(-0.400719 + 0.117662i) q^{7} +(0.948109 + 2.66479i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(0.0592543 + 0.0983284i) q^{10} +(-2.76031 + 2.39183i) q^{11} +(-1.43343 - 1.39473i) q^{12} +(-1.04525 + 3.55980i) q^{13} +(0.229751 + 0.544109i) q^{14} +(-0.0682908 - 0.0438878i) q^{15} +(3.59170 - 1.76060i) q^{16} +(-0.466666 + 3.24573i) q^{17} +(1.34487 + 0.437417i) q^{18} +(-0.956420 + 0.137512i) q^{19} +(0.128628 - 0.0990650i) q^{20} +(-0.315629 - 0.273494i) q^{21} +(3.80445 + 3.49378i) q^{22} +(-0.872942 - 4.71572i) q^{23} +(-1.72917 + 2.23829i) q^{24} +(-3.26999 + 3.77377i) q^{25} +(5.16974 + 0.896245i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(0.727555 - 0.410298i) q^{28} +(-3.25048 - 0.467348i) q^{29} +(-0.0506839 + 0.103008i) q^{30} +(4.99772 + 3.21184i) q^{31} +(-3.05123 - 4.76340i) q^{32} +(-3.50447 - 1.02901i) q^{33} +(4.63543 + 0.133806i) q^{34} +(0.0256219 - 0.0222015i) q^{35} +(0.398349 - 1.95993i) q^{36} +(8.45554 + 3.86152i) q^{37} +(0.346993 + 1.32170i) q^{38} +(-3.55980 + 1.04525i) q^{39} +(-0.159873 - 0.164800i) q^{40} +(3.21284 + 7.03514i) q^{41} +(-0.333521 + 0.487447i) q^{42} +(4.77047 + 7.42299i) q^{43} +(4.29720 - 5.90718i) q^{44} -0.0811774i q^{45} +(-6.48542 + 1.98476i) q^{46} -4.94443 q^{47} +(3.42293 + 2.06967i) q^{48} +(-5.74204 + 3.69019i) q^{49} +(5.82809 + 3.98769i) q^{50} +(-2.98278 + 1.36219i) q^{51} +(0.428024 - 7.40781i) q^{52} +(-1.01460 - 3.45540i) q^{53} +(0.359111 + 1.36786i) q^{54} +(0.123168 - 0.269700i) q^{55} +(-0.693469 - 0.956275i) q^{56} +(-0.632762 - 0.730247i) q^{57} +(-0.134002 + 4.64221i) q^{58} +(2.31899 - 7.89776i) q^{59} +(0.152880 + 0.0546504i) q^{60} +(5.62148 - 8.74720i) q^{61} +(3.70919 - 7.53844i) q^{62} +(0.0594359 - 0.413386i) q^{63} +(-6.20218 + 5.05302i) q^{64} +(-0.0428617 - 0.298110i) q^{65} +(-0.882315 + 5.08939i) q^{66} +(-4.23708 - 3.67145i) q^{67} +(-0.557325 - 6.53449i) q^{68} +(3.49516 - 3.28387i) q^{69} +(-0.0353138 - 0.0324301i) q^{70} +(6.12026 - 7.06315i) q^{71} +(-2.81783 - 0.244562i) q^{72} +(1.45635 + 10.1292i) q^{73} +(4.06604 - 12.5013i) q^{74} +(-4.94258 - 0.710636i) q^{75} +(1.80125 - 0.700056i) q^{76} +(0.824684 - 1.28323i) q^{77} +(2.04100 + 4.83361i) q^{78} +(-10.6910 - 3.13916i) q^{79} +(-0.205845 + 0.251126i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(9.36809 - 5.64536i) q^{82} +(-9.63750 - 4.40130i) q^{83} +(0.738510 + 0.390235i) q^{84} +(-0.0749943 - 0.255407i) q^{85} +(9.66259 - 7.89626i) q^{86} +(-1.36418 - 2.98714i) q^{87} +(-8.99078 - 5.08794i) q^{88} +(1.16133 - 0.746342i) q^{89} +(-0.114058 + 0.0130525i) q^{90} -1.54947i q^{91} +(3.83146 + 8.79317i) q^{92} +5.94080i q^{93} +(0.795013 + 6.94714i) q^{94} +(0.0659863 - 0.0424068i) q^{95} +(2.35761 - 5.14215i) q^{96} +(-1.88329 - 4.12384i) q^{97} +(6.10813 + 7.47448i) q^{98} +(-1.02901 - 3.50447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

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