LMFDB - Embedded newform 552.2.x.a.35.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			35.14
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28558 - 0.589316i) q^{2} +(-1.72832 - 0.113594i) q^{3} +(1.30541 + 1.51522i) q^{4} +(-0.988646 + 0.290293i) q^{5} +(2.15495 + 1.16456i) q^{6} +(-3.80564 + 3.29760i) q^{7} +(-0.785267 - 2.71723i) q^{8} +(2.97419 + 0.392655i) q^{9} +O(q^{10})$	\(q+(-1.28558 - 0.589316i) q^{2} +(-1.72832 - 0.113594i) q^{3} +(1.30541 + 1.51522i) q^{4} +(-0.988646 + 0.290293i) q^{5} +(2.15495 + 1.16456i) q^{6} +(-3.80564 + 3.29760i) q^{7} +(-0.785267 - 2.71723i) q^{8} +(2.97419 + 0.392655i) q^{9} +(1.44205 + 0.209431i) q^{10} +(-2.09985 + 3.26743i) q^{11} +(-2.08406 - 2.76708i) q^{12} +(-2.13088 - 1.84641i) q^{13} +(6.83576 - 1.99660i) q^{14} +(1.74167 - 0.389414i) q^{15} +(-0.591786 + 3.95598i) q^{16} +(3.90952 - 1.78542i) q^{17} +(-3.59215 - 2.25753i) q^{18} +(2.74706 - 6.01522i) q^{19} +(-1.73045 - 1.11906i) q^{20} +(6.95195 - 5.26702i) q^{21} +(4.62507 - 2.96306i) q^{22} +(-2.36551 + 4.17185i) q^{23} +(1.04853 + 4.78546i) q^{24} +(-3.31312 + 2.12921i) q^{25} +(1.65128 + 3.62947i) q^{26} +(-5.09576 - 1.01649i) q^{27} +(-9.96453 - 1.46164i) q^{28} +(0.540101 + 1.18266i) q^{29} +(-2.46854 - 0.525773i) q^{30} +(6.59993 - 0.948927i) q^{31} +(3.09211 - 4.73697i) q^{32} +(4.00038 - 5.40864i) q^{33} +(-6.07817 - 0.00864931i) q^{34} +(2.80516 - 4.36491i) q^{35} +(3.28759 + 5.01914i) q^{36} +(1.57422 - 5.36130i) q^{37} +(-7.07642 + 6.11414i) q^{38} +(3.47310 + 3.43325i) q^{39} +(1.56514 + 2.45842i) q^{40} +(-1.70429 - 5.80428i) q^{41} +(-12.0412 + 2.67426i) q^{42} +(0.782590 - 5.44303i) q^{43} +(-7.69205 + 1.08362i) q^{44} +(-3.05441 + 0.475189i) q^{45} +(5.49958 - 3.96920i) q^{46} -0.253681 q^{47} +(1.47217 - 6.76999i) q^{48} +(2.61248 - 18.1702i) q^{49} +(5.51404 - 0.784793i) q^{50} +(-6.95973 + 2.64168i) q^{51} +(0.0160490 - 5.63908i) q^{52} +(-3.61274 - 4.16933i) q^{53} +(5.95196 + 4.30978i) q^{54} +(1.12750 - 3.83990i) q^{55} +(11.9488 + 7.75130i) q^{56} +(-5.43110 + 10.0842i) q^{57} +(0.00261648 - 1.83869i) q^{58} +(-1.51523 - 1.31295i) q^{59} +(2.86365 + 2.13067i) q^{60} +(-8.56608 + 1.23162i) q^{61} +(-9.04394 - 2.66952i) q^{62} +(-12.6135 + 8.31340i) q^{63} +(-6.76671 + 4.26751i) q^{64} +(2.64268 + 1.20687i) q^{65} +(-8.33019 + 4.59574i) q^{66} +(0.595835 - 0.382920i) q^{67} +(7.80885 + 3.59308i) q^{68} +(4.56226 - 6.94160i) q^{69} +(-6.17855 + 3.95830i) q^{70} +(2.11184 - 1.35720i) q^{71} +(-1.26860 - 8.38991i) q^{72} +(-4.18049 + 9.15399i) q^{73} +(-5.18328 + 5.96465i) q^{74} +(5.96800 - 3.30361i) q^{75} +(12.7004 - 3.68996i) q^{76} +(-2.78342 - 19.3591i) q^{77} +(-2.44166 - 6.46046i) q^{78} +(-3.84921 - 3.33536i) q^{79} +(-0.563325 - 4.08285i) q^{80} +(8.69164 + 2.33566i) q^{81} +(-1.22956 + 8.46622i) q^{82} +(2.91564 - 9.92977i) q^{83} +(17.0559 + 3.65810i) q^{84} +(-3.34684 + 2.90005i) q^{85} +(-4.21374 + 6.53624i) q^{86} +(-0.799126 - 2.10536i) q^{87} +(10.5273 + 3.13998i) q^{88} +(18.1542 + 2.61018i) q^{89} +(4.20671 + 1.18912i) q^{90} +14.1981 q^{91} +(-9.40925 + 1.86173i) q^{92} +(-11.5146 + 0.890336i) q^{93} +(0.326126 + 0.149498i) q^{94} +(-0.969694 + 6.74437i) q^{95} +(-5.88225 + 7.83576i) q^{96} +(1.41934 - 0.416756i) q^{97} +(-14.0665 + 21.8196i) q^{98} +(-7.52833 + 8.89345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.28558	−	0.589316i	−0.909040	−	0.416709i
$2$	−1.28558	−	0.589316i	−0.909040	−	0.416709i
$3$	−1.72832	−	0.113594i	−0.997847	−	0.0655837i
$3$	−1.72832	−	0.113594i	−0.997847	−	0.0655837i
$4$	1.30541	+	1.51522i	0.652707	+	0.757610i
$5$	−0.988646	+	0.290293i	−0.442136	+	0.129823i	−0.495221	−	0.868767i	$-0.664913\pi$
$5$	−0.988646	+	0.290293i	−0.442136	+	0.129823i	0.0530849	+	0.998590i	$0.483095\pi$
$6$	2.15495	+	1.16456i	0.879754	+	0.475430i
$7$	−3.80564	+	3.29760i	−1.43840	+	1.24638i	−0.518004	+	0.855378i	$0.673325\pi$
$7$	−3.80564	+	3.29760i	−1.43840	+	1.24638i	−0.920391	+	0.390998i	$0.872130\pi$
$8$	−0.785267	−	2.71723i	−0.277634	−	0.960687i
$9$	2.97419	+	0.392655i	0.991398	+	0.130885i
$10$	1.44205	+	0.209431i	0.456017	+	0.0662279i
$11$	−2.09985	+	3.26743i	−0.633129	+	0.985168i	0.365395	+	0.930853i	$0.380934\pi$
$11$	−2.09985	+	3.26743i	−0.633129	+	0.985168i	−0.998524	+	0.0543151i	$0.982702\pi$
$12$	−2.08406	−	2.76708i	−0.601615	−	0.798786i
$13$	−2.13088	−	1.84641i	−0.590999	−	0.512103i	0.307228	−	0.951636i	$-0.400599\pi$
$13$	−2.13088	−	1.84641i	−0.590999	−	0.512103i	−0.898227	+	0.439533i	$0.855144\pi$
$14$	6.83576	−	1.99660i	1.82694	−	0.533614i
$15$	1.74167	−	0.389414i	0.449698	−	0.100546i
$16$	−0.591786	+	3.95598i	−0.147947	+	0.988995i
$17$	3.90952	−	1.78542i	0.948198	−	0.433028i	0.119569	−	0.992826i	$-0.461849\pi$
$17$	3.90952	−	1.78542i	0.948198	−	0.433028i	0.828629	+	0.559798i	$0.189121\pi$
$18$	−3.59215	−	2.25753i	−0.846679	−	0.532104i
$19$	2.74706	−	6.01522i	0.630219	−	1.37999i	−0.277630	−	0.960688i	$-0.589549\pi$
$19$	2.74706	−	6.01522i	0.630219	−	1.37999i	0.907848	−	0.419298i	$-0.137724\pi$
$20$	−1.73045	−	1.11906i	−0.386940	−	0.250230i
$21$	6.95195	−	5.26702i	1.51704	−	1.14936i
$22$	4.62507	−	2.96306i	0.986068	−	0.631726i
$23$	−2.36551	+	4.17185i	−0.493243	+	0.869892i
$23$	−2.36551	+	4.17185i	−0.493243	+	0.869892i
$24$	1.04853	+	4.78546i	0.214031	+	0.976827i
$25$	−3.31312	+	2.12921i	−0.662623	+	0.425842i
$26$	1.65128	+	3.62947i	0.323843	+	0.711797i
$27$	−5.09576	−	1.01649i	−0.980679	−	0.195623i
$28$	−9.96453	−	1.46164i	−1.88312	−	0.276224i
$29$	0.540101	+	1.18266i	0.100294	+	0.219614i	0.953127	−	0.302570i	$-0.0978447\pi$
$29$	0.540101	+	1.18266i	0.100294	+	0.219614i	−0.852833	+	0.522184i	$0.825117\pi$
$30$	−2.46854	−	0.525773i	−0.450692	−	0.0959926i
$31$	6.59993	−	0.948927i	1.18538	−	0.170432i	0.478710	−	0.877973i	$-0.341104\pi$
$31$	6.59993	−	0.948927i	1.18538	−	0.170432i	0.706673	+	0.707541i	$0.250195\pi$
$32$	3.09211	−	4.73697i	0.546613	−	0.837386i
$33$	4.00038	−	5.40864i	0.696377	−	0.941524i
$34$	−6.07817	−	0.00864931i	−1.04240	−	0.00148334i
$35$	2.80516	−	4.36491i	0.474158	−	0.737804i
$36$	3.28759	+	5.01914i	0.547932	+	0.836523i
$37$	1.57422	−	5.36130i	0.258800	−	0.881393i	−0.722899	−	0.690954i	$-0.757191\pi$
$37$	1.57422	−	5.36130i	0.258800	−	0.881393i	0.981699	−	0.190439i	$-0.0609911\pi$
$38$	−7.07642	+	6.11414i	−1.14795	+	0.991845i
$39$	3.47310	+	3.43325i	0.556141	+	0.549761i
$40$	1.56514	+	2.45842i	0.247471	+	0.388711i
$41$	−1.70429	−	5.80428i	−0.266166	−	0.906477i	−0.978779	−	0.204920i	$-0.934307\pi$
$41$	−1.70429	−	5.80428i	−0.266166	−	0.906477i	0.712613	−	0.701557i	$-0.247511\pi$
$42$	−12.0412	+	2.67426i	−1.85800	+	0.412648i
$43$	0.782590	−	5.44303i	0.119344	−	0.830055i	−0.838937	−	0.544228i	$-0.816823\pi$
$43$	0.782590	−	5.44303i	0.119344	−	0.830055i	0.958281	−	0.285827i	$-0.0922682\pi$
$44$	−7.69205	+	1.08362i	−1.15962	+	0.163361i
$45$	−3.05441	+	0.475189i	−0.455324	+	0.0708370i
$46$	5.49958	−	3.96920i	0.810869	−	0.585227i
$47$	−0.253681			−0.0370032			−0.0185016	−	0.999829i	$-0.505890\pi$
$47$	−0.253681			−0.0370032			−0.0185016	+	0.999829i	$0.505890\pi$
$48$	1.47217	−	6.76999i	0.212490	−	0.977163i
$49$	2.61248	−	18.1702i	0.373211	−	2.59574i
$50$	5.51404	−	0.784793i	0.779804	−	0.110986i
$51$	−6.95973	+	2.64168i	−0.974557	+	0.369909i
$52$	0.0160490	−	5.63908i	0.00222560	−	0.782000i
$53$	−3.61274	−	4.16933i	−0.496249	−	0.572701i	0.451276	−	0.892384i	$-0.350969\pi$
$53$	−3.61274	−	4.16933i	−0.496249	−	0.572701i	−0.947525	+	0.319683i	$0.896424\pi$
$54$	5.95196	+	4.30978i	0.809959	+	0.586487i
$55$	1.12750	−	3.83990i	0.152032	−	0.517772i
$56$	11.9488	+	7.75130i	1.59672	+	1.03581i
$57$	−5.43110	+	10.0842i	−0.719367	+	1.33568i
$58$	0.00261648	−	1.83869i	0.000343560	−	0.241431i
$59$	−1.51523	−	1.31295i	−0.197266	−	0.170932i	0.550627	−	0.834752i	$-0.314389\pi$
$59$	−1.51523	−	1.31295i	−0.197266	−	0.170932i	−0.747893	+	0.663820i	$0.768934\pi$
$60$	2.86365	+	2.13067i	0.369696	+	0.275069i
$61$	−8.56608	+	1.23162i	−1.09677	+	0.157692i	−0.666864	−	0.745179i	$-0.732364\pi$
$61$	−8.56608	+	1.23162i	−1.09677	+	0.157692i	−0.429910	+	0.902872i	$0.641455\pi$
$62$	−9.04394	−	2.66952i	−1.14858	−	0.339030i
$63$	−12.6135	+	8.31340i	−1.58915	+	1.04739i
$64$	−6.76671	+	4.26751i	−0.845839	+	0.533439i
$65$	2.64268	+	1.20687i	0.327784	+	0.149694i
$66$	−8.33019	+	4.59574i	−1.02538	+	0.565696i
$67$	0.595835	−	0.382920i	0.0727928	−	0.0467811i	−0.503738	−	0.863856i	$-0.668042\pi$
$67$	0.595835	−	0.382920i	0.0727928	−	0.0467811i	0.576531	+	0.817075i	$0.304406\pi$
$68$	7.80885	+	3.59308i	0.946962	+	0.435725i
$69$	4.56226	−	6.94160i	0.549232	−	0.835670i
$70$	−6.17855	+	3.95830i	−0.738478	+	0.473107i
$71$	2.11184	−	1.35720i	0.250629	−	0.161070i	−0.409294	−	0.912402i	$-0.634225\pi$
$71$	2.11184	−	1.35720i	0.250629	−	0.161070i	0.659924	+	0.751333i	$0.270589\pi$
$72$	−1.26860	−	8.38991i	−0.149506	−	0.988761i
$73$	−4.18049	+	9.15399i	−0.489289	+	1.07139i	0.490515	+	0.871433i	$0.336809\pi$
$73$	−4.18049	+	9.15399i	−0.489289	+	1.07139i	−0.979804	+	0.199960i	$0.935919\pi$
$74$	−5.18328	+	5.96465i	−0.602544	+	0.693377i
$75$	5.96800	−	3.30361i	0.689125	−	0.381468i
$76$	12.7004	−	3.68996i	1.45684	−	0.423267i
$77$	−2.78342	−	19.3591i	−0.317200	−	2.20618i
$78$	−2.44166	−	6.46046i	−0.276464	−	0.731503i
$79$	−3.84921	−	3.33536i	−0.433070	−	0.375257i	0.410871	−	0.911693i	$-0.365225\pi$
$79$	−3.84921	−	3.33536i	−0.433070	−	0.375257i	−0.843941	+	0.536437i	$0.819770\pi$
$80$	−0.563325	−	4.08285i	−0.0629816	−	0.456477i
$81$	8.69164	+	2.33566i	0.965738	+	0.259518i
$82$	−1.22956	+	8.46622i	−0.135782	+	0.934937i
$83$	2.91564	−	9.92977i	0.320033	−	1.08993i	−0.629691	−	0.776846i	$-0.716818\pi$
$83$	2.91564	−	9.92977i	0.320033	−	1.08993i	0.949724	−	0.313088i	$-0.101363\pi$
$84$	17.0559	+	3.65810i	1.86095	+	0.399131i
$85$	−3.34684	+	2.90005i	−0.363016	+	0.314555i
$86$	−4.21374	+	6.53624i	−0.454380	+	0.704821i
$87$	−0.799126	−	2.10536i	−0.0856753	−	0.225719i
$88$	10.5273	+	3.13998i	1.12222	+	0.334723i
$89$	18.1542	+	2.61018i	1.92434	+	0.276678i	0.995574	−	0.0939843i	$-0.0299603\pi$
$89$	18.1542	+	2.61018i	1.92434	+	0.276678i	0.928768	+	0.370663i	$0.120869\pi$
$90$	4.20671	+	1.18912i	0.443426	+	0.125344i
$91$	14.1981			1.48836
$92$	−9.40925	+	1.86173i	−0.980982	+	0.194098i
$93$	−11.5146	+	0.890336i	−1.19401	+	0.0923236i
$94$	0.326126	+	0.149498i	0.0336374	+	0.0154196i
$95$	−0.969694	+	6.74437i	−0.0994886	+	0.691958i
$96$	−5.88225	+	7.83576i	−0.600355	+	0.799734i
$97$	1.41934	−	0.416756i	0.144112	−	0.0423152i	−0.208881	−	0.977941i	$-0.566982\pi$
$97$	1.41934	−	0.416756i	0.144112	−	0.0423152i	0.352993	+	0.935626i	$0.385164\pi$
$98$	−14.0665	+	21.8196i	−1.42093	+	2.20411i
$99$	−7.52833	+	8.89345i	−0.756626	+	0.893826i
$100$	−7.55122	−	2.24060i	−0.755122	−	0.224060i
$101$	7.76913	+	2.28122i	0.773057	+	0.226990i	0.644389	−	0.764698i	$-0.277112\pi$
$101$	7.76913	+	2.28122i	0.773057	+	0.226990i	0.128668	+	0.991688i	$0.458930\pi$
$102$	10.5040	+	0.705394i	1.04006	+	0.0698444i
$103$	−0.0878221	+	0.136654i	−0.00865336	+	0.0134649i	−0.845553	−	0.533891i	$-0.820729\pi$
$103$	−0.0878221	+	0.136654i	−0.00865336	+	0.0134649i	0.836900	+	0.547356i	$0.184366\pi$
$104$	−3.34383	+	7.24002i	−0.327890	+	0.709942i
$105$	−5.34404	+	7.22532i	−0.521525	+	0.705119i
$106$	2.18741	+	7.48904i	0.212460	+	0.727400i
$107$	0.479808	−	0.0689860i	0.0463848	−	0.00666913i	−0.119083	−	0.992884i	$-0.537996\pi$
$107$	0.479808	−	0.0689860i	0.0463848	−	0.00666913i	0.165468	+	0.986215i	$0.447086\pi$
$108$	−5.11188	−	9.04813i	−0.491891	−	0.870657i
$109$	7.49579	−	3.42321i	0.717966	−	0.327884i	−0.0227139	−	0.999742i	$-0.507231\pi$
$109$	7.49579	−	3.42321i	0.717966	−	0.327884i	0.740680	+	0.671858i	$0.234503\pi$
$110$	−3.71240	+	4.27204i	−0.353963	+	0.407323i
$111$	−3.32977	+	9.08723i	−0.316048	+	0.862522i
$112$	−10.7931	−	17.0065i	−1.01985	−	1.60696i
$113$	6.33006	+	9.84976i	0.595482	+	0.926588i	0.999928	+	0.0120259i	$0.00382807\pi$
$113$	6.33006	+	9.84976i	0.595482	+	0.926588i	−0.404446	+	0.914562i	$0.632536\pi$
$114$	12.9249	−	9.76337i	1.21052	−	0.914423i
$115$	1.12759	−	4.81117i	0.105149	−	0.448644i
$116$	−1.08693	+	2.36223i	−0.100919	+	0.219328i
$117$	−5.61263	−	6.32829i	−0.518888	−	0.585051i
$118$	1.17420	+	2.58085i	0.108094	+	0.237587i
$119$	−8.99062	+	19.6867i	−0.824169	+	1.80468i
$120$	−2.42581	−	4.42674i	−0.221445	−	0.404104i
$121$	−1.69717	−	3.71629i	−0.154288	−	0.337844i
$122$	11.7382	+	3.46479i	1.06272	+	0.313687i
$123$	2.28623	+	10.2253i	0.206142	+	0.921981i
$124$	10.0535	+	8.76161i	0.902829	+	0.786816i
$125$	6.03119	−	6.96037i	0.539446	−	0.622554i
$126$	21.1149	−	3.25418i	1.88106	−	0.289905i
$127$	1.08547	−	1.68903i	0.0963200	−	0.149877i	−0.789749	−	0.613430i	$-0.789789\pi$
$127$	1.08547	−	1.68903i	0.0963200	−	0.149877i	0.886069	+	0.463553i	$0.153426\pi$
$128$	11.2140	−	1.49848i	0.991190	−	0.132448i
$129$	−1.97086	+	9.31841i	−0.173525	+	0.820440i
$130$	−2.68614	−	3.10890i	−0.235590	−	0.272669i
$131$	−7.30944	+	6.33367i	−0.638629	+	0.553375i	−0.912852	−	0.408291i	$-0.866125\pi$
$131$	−7.30944	+	6.33367i	−0.638629	+	0.553375i	0.274223	+	0.961666i	$0.411579\pi$
$132$	13.4174	−	0.999062i	1.16784	−	0.0869572i
$133$	9.38150	+	31.9505i	0.813479	+	2.77046i
$134$	−0.991652	+	0.141138i	−0.0856657	+	0.0121925i
$135$	5.33298	−	0.474317i	0.458990	−	0.0408227i
$136$	−7.92142	−	9.22105i	−0.679256	−	0.790699i
$137$		−	10.8015i		−	0.922831i	−0.887184	−	0.461416i	$-0.847342\pi$
$137$		−	10.8015i		−	0.922831i	0.887184	−	0.461416i	$-0.152658\pi$
$138$	−9.95593	+	6.23534i	−0.847505	+	0.530788i
$139$	−16.2161			−1.37543			−0.687716	−	0.725980i	$-0.741386\pi$
$139$	−16.2161			−1.37543			−0.687716	+	0.725980i	$0.741386\pi$
$140$	10.2757	−	1.44758i	0.868454	−	0.122343i
$141$	0.438442	+	0.0288167i	0.0369235	+	0.00242681i
$142$	−3.51475	+	0.500241i	−0.294951	+	0.0419793i
$143$	10.5076	−	3.08530i	0.878686	−	0.258005i
$144$	−3.31342	+	11.5335i	−0.276119	+	0.961124i
$145$	−0.877285	−	1.01244i	−0.0728546	−	0.0840787i
$146$	10.7689	−	9.30453i	0.891242	−	0.770048i
$147$	−6.57924	+	31.1072i	−0.542646	+	2.56568i
$148$	10.1786	−	4.61343i	0.836673	−	0.379222i
$149$	7.86352	+	5.05358i	0.644205	+	0.414005i	0.821544	−	0.570144i	$-0.193113\pi$
$149$	7.86352	+	5.05358i	0.644205	+	0.414005i	−0.177340	+	0.984150i	$0.556749\pi$
$150$	−9.61919	+	0.730010i	−0.785404	+	0.0596051i
$151$	−7.91929	−	6.86211i	−0.644463	−	0.558430i	0.270121	−	0.962826i	$-0.412936\pi$
$151$	−7.91929	−	6.86211i	−0.644463	−	0.558430i	−0.914584	+	0.404396i	$0.867482\pi$
$152$	−18.5019	−	2.74084i	−1.50071	−	0.222312i
$153$	12.3287	−	3.77509i	0.996718	−	0.305198i
$154$	−7.83033	+	26.5280i	−0.630986	+	2.13768i
$155$	−6.24953	+	2.85406i	−0.501974	+	0.229244i
$156$	−0.668306	+	9.74433i	−0.0535073	+	0.780171i
$157$	20.1495	+	9.20198i	1.60811	+	0.734398i	0.998307	−	0.0581576i	$-0.0185226\pi$
$157$	20.1495	+	9.20198i	1.60811	+	0.734398i	0.609800	+	0.792556i	$0.291250\pi$
$158$	2.98287	+	6.55625i	0.237305	+	0.521587i
$159$	5.77037	+	7.61633i	0.457620	+	0.604014i
$160$	−1.68189	+	5.58080i	−0.132965	+	0.441201i
$161$	−4.75484	−	23.6771i	−0.374734	−	1.86601i
$162$	−9.79733	−	8.12480i	−0.769751	−	0.638344i
$163$	−0.464227	+	0.298341i	−0.0363611	+	0.0233679i	−0.558695	−	0.829373i	$-0.688698\pi$
$163$	−0.464227	+	0.298341i	−0.0363611	+	0.0233679i	0.522334	+	0.852741i	$0.325061\pi$
$164$	6.56996	−	10.1594i	0.513028	−	0.793314i
$165$	−2.38487	+	6.50851i	−0.185662	+	0.506687i
$166$	−9.60005	+	11.0472i	−0.745108	+	0.857432i
$167$	−6.57113	−	14.3888i	−0.508490	−	1.11344i	−0.973616	−	0.228193i	$-0.926718\pi$
$167$	−6.57113	−	14.3888i	−0.508490	−	1.11344i	0.465126	−	0.885244i	$-0.346009\pi$
$168$	−19.7709	−	14.7541i	−1.52535	−	1.13830i
$169$	−0.718707	−	4.99872i	−0.0552851	−	0.384517i
$170$	6.01166	−	1.75589i	0.461073	−	0.134671i
$171$	10.5322	−	16.8118i	0.805417	−	1.28563i
$172$	9.26900	−	5.91962i	0.706754	−	0.451366i
$173$	−14.0571	−	9.03393i	−1.06874	−	0.686837i	−0.116810	−	0.993154i	$-0.537267\pi$
$173$	−14.0571	−	9.03393i	−1.06874	−	0.686837i	−0.951929	+	0.306317i	$0.900903\pi$
$174$	−0.213386	+	3.17755i	−0.0161768	+	0.240889i
$175$	5.58723	−	19.0283i	0.422355	−	1.43841i
$176$	−11.6832	−	10.2406i	−0.880657	−	0.771914i
$177$	2.46966	+	2.44133i	0.185631	+	0.183502i
$178$	−21.8004	−	14.0541i	−1.63401	−	1.05340i
$179$	1.59883	+	5.44512i	0.119502	+	0.406988i	0.997417	−	0.0718297i	$-0.0228838\pi$
$179$	1.59883	+	5.44512i	0.119502	+	0.406988i	−0.877915	+	0.478817i	$0.841066\pi$
$180$	−4.70728	−	4.00778i	−0.350860	−	0.298722i
$181$	−23.8945	−	3.43551i	−1.77606	−	0.255359i	−0.825171	−	0.564883i	$-0.808921\pi$
$181$	−23.8945	−	3.43551i	−1.77606	−	0.255359i	−0.950892	+	0.309523i	$0.899831\pi$
$182$	−18.2527	−	8.36715i	−1.35298	−	0.620214i
$183$	14.9449	−	1.15557i	1.10476	−	0.0854223i
$184$	13.1935	+	3.15162i	0.972634	+	0.232341i
$185$			5.75741i			0.423293i
$186$	15.3276	+	5.64114i	1.12387	+	0.413628i
$187$	−2.37568	+	16.5232i	−0.173727	+	1.20830i
$188$	−0.331159	−	0.384383i	−0.0241522	−	0.0280340i
$189$	22.7446	−	12.9354i	1.65442	−	0.940913i
$190$	5.22118	−	8.09895i	0.378784	−	0.587560i
$191$	−3.21695	−	3.71256i	−0.232770	−	0.268631i	0.627333	−	0.778751i	$-0.284146\pi$
$191$	−3.21695	−	3.71256i	−0.232770	−	0.268631i	−0.860103	+	0.510120i	$0.829601\pi$
$192$	12.1798	−	6.60697i	0.879003	−	0.476817i
$193$	−14.2749	−	4.19150i	−1.02753	−	0.301711i	−0.275825	−	0.961208i	$-0.588951\pi$
$193$	−14.2749	−	4.19150i	−1.02753	−	0.301711i	−0.751707	+	0.659497i	$0.770769\pi$
$194$	−2.07027	−	0.300668i	−0.148637	−	0.0215867i
$195$	−4.43031	−	2.38606i	−0.317261	−	0.170869i
$196$	30.9422	−	19.7612i	2.21016	−	1.41151i
$197$	−1.85145	+	2.13669i	−0.131910	+	0.152233i	−0.817862	−	0.575415i	$-0.804841\pi$
$197$	−1.85145	+	2.13669i	−0.131910	+	0.152233i	0.685952	+	0.727647i	$0.259386\pi$
$198$	14.9193	−	6.99665i	1.06027	−	0.497230i
$199$	7.52629	−	1.08212i	0.533524	−	0.0767092i	0.129713	−	0.991552i	$-0.458594\pi$
$199$	7.52629	−	1.08212i	0.533524	−	0.0767092i	0.403811	+	0.914842i	$0.367685\pi$
$200$	8.38725	+	7.33051i	0.593068	+	0.518345i
$201$	−1.07329	+	0.594125i	−0.0757042	+	0.0419064i
$202$	−8.64345	−	7.51116i	−0.608151	−	0.528483i
$203$	−5.95536	−	2.71972i	−0.417985	−	0.190887i
$204$	−13.0881	−	7.09703i	−0.916347	−	0.496892i
$205$	3.36988	+	5.24364i	0.235363	+	0.366231i
$206$	0.193434	−	0.123924i	0.0134772	−	0.00863419i
$207$	−8.67358	+	11.4791i	−0.602856	+	0.797850i
$208$	8.56541	−	7.33702i	0.593904	−	0.508731i
$209$	13.8859	+	21.6069i	0.960508	+	1.49458i
$210$	11.1282	−	6.13937i	0.767916	−	0.423657i
$211$	−0.253944	+	0.556060i	−0.0174822	+	0.0382807i	−0.918172	−	0.396183i	$-0.870335\pi$
$211$	−0.253944	+	0.556060i	−0.0174822	+	0.0382807i	0.900689	+	0.434463i	$0.143062\pi$
$212$	1.60132	−	10.9168i	0.109979	−	0.749769i
$213$	−3.80411	+	2.10578i	−0.260653	+	0.144286i
$214$	−0.657485	−	0.194072i	−0.0449447	−	0.0132665i
$215$	0.806367	+	5.60841i	0.0549938	+	0.382490i
$216$	1.23950	+	14.6446i	0.0843376	+	0.996437i
$217$	−21.9878	+	25.3752i	−1.49263	+	1.72258i
$218$	−11.6538	−	0.0165835i	−0.789292	−	0.00112317i
$219$	8.26507	−	15.3462i	0.558501	−	1.03700i
$220$	7.29015	−	3.30426i	0.491502	−	0.222773i
$221$	−11.6273	−	3.41409i	−0.782139	−	0.229657i
$222$	9.63593	−	9.72005i	0.646721	−	0.652367i
$223$	9.94480	−	8.61722i	0.665953	−	0.577052i	−0.254897	−	0.966968i	$-0.582042\pi$
$223$	9.94480	−	8.61722i	0.665953	−	0.577052i	0.920850	+	0.389916i	$0.127496\pi$
$224$	3.85320	+	28.2237i	0.257453	+	1.88578i
$225$	−10.6899	+	5.03177i	−0.712660	+	0.335451i
$226$	−2.33316	−	16.3930i	−0.155199	−	1.09045i
$227$	15.0417	+	2.16266i	0.998350	+	0.143541i	0.622067	−	0.782964i	$-0.286293\pi$
$227$	15.0417	+	2.16266i	0.998350	+	0.143541i	0.376283	+	0.926505i	$0.377202\pi$
$228$	−22.3696	+	4.93473i	−1.48146	+	0.326811i
$229$			4.59746i			0.303808i	0.988395	+	0.151904i	$0.0485405\pi$
$229$			4.59746i			0.303808i	−0.988395	+	0.151904i	$0.951459\pi$
$230$	−4.28491	+	5.52062i	−0.282538	+	0.364019i
$231$	2.61156	+	33.7750i	0.171828	+	2.22223i
$232$	2.78943	−	2.39628i	0.183135	−	0.157324i
$233$	−25.2397	−	3.62892i	−1.65351	−	0.237738i	−0.748499	−	0.663136i	$-0.769225\pi$
$233$	−25.2397	−	3.62892i	−1.65351	−	0.237738i	−0.905006	+	0.425398i	$0.860134\pi$
$234$	3.48611	+	11.4431i	0.227894	+	0.748060i
$235$	0.250801	−	0.0736417i	0.0163604	−	0.00480385i
$236$	0.0114122	−	4.00986i	0.000742870	−	0.261019i
$237$	6.27379	+	6.20182i	0.407526	+	0.402851i
$238$	23.1598	−	20.0105i	1.50123	−	1.29709i
$239$	−16.9620	−	4.98048i	−1.09718	−	0.322161i	−0.317448	−	0.948276i	$-0.602826\pi$
$239$	−16.9620	−	4.98048i	−1.09718	−	0.322161i	−0.779731	+	0.626115i	$0.784644\pi$
$240$	0.509817	+	7.12048i	0.0329086	+	0.459625i
$241$	13.2640	+	8.52428i	0.854412	+	0.549097i	0.892948	−	0.450160i	$-0.148633\pi$
$241$	13.2640	+	8.52428i	0.854412	+	0.549097i	−0.0385358	+	0.999257i	$0.512269\pi$
$242$	−0.00822180	+	5.77774i	−0.000528517	+	0.371407i
$243$	−14.7566	−	5.02410i	−0.946639	−	0.322296i
$244$	−13.0485	−	11.3717i	−0.835342	−	0.728001i
$245$	2.69186	+	18.7223i	0.171976	+	1.19612i
$246$	3.08678	−	14.4927i	0.196806	−	0.924019i
$247$	−16.9602	+	7.74548i	−1.07915	+	0.492833i
$248$	−7.76117	−	17.1884i	−0.492835	−	1.09146i
$249$	−6.16713	+	16.8306i	−0.390826	+	1.06660i
$250$	−11.8554	+	5.39381i	−0.749802	+	0.341134i
$251$	−7.13812	−	11.1071i	−0.450554	−	0.701076i	0.539465	−	0.842008i	$-0.318626\pi$
$251$	−7.13812	−	11.1071i	−0.450554	−	0.701076i	−0.990019	+	0.140932i	$0.954990\pi$
$252$	−29.0625	−	8.25982i	−1.83077	−	0.520320i
$253$	−8.66403	−	16.4894i	−0.544703	−	1.03668i
$254$	−2.39083	+	1.53169i	−0.150014	+	0.0961067i
$255$	6.11384	−	4.63204i	0.382864	−	0.290070i
$256$	−15.2996	−	4.68219i	−0.956224	−	0.292637i
$257$	−10.8472	−	4.95377i	−0.676632	−	0.309008i	0.0472980	−	0.998881i	$-0.484939\pi$
$257$	−10.8472	−	4.95377i	−0.676632	−	0.309008i	−0.723930	+	0.689873i	$0.757666\pi$
$258$	8.02518	−	10.8181i	0.499626	−	0.673504i
$259$	11.6885	+	25.5943i	0.726290	+	1.59035i
$260$	1.62112	+	5.57971i	0.100537	+	0.346039i
$261$	1.14199	+	3.72952i	0.0706874	+	0.230852i
$262$	13.1294	−	3.83485i	0.811136	−	0.236918i
$263$	16.6127	−	19.1721i	1.02438	−	1.18220i	0.0412798	−	0.999148i	$-0.486856\pi$
$263$	16.6127	−	19.1721i	1.02438	−	1.18220i	0.983103	−	0.183053i	$-0.0585981\pi$
$264$	−17.8379	−	6.62273i	−1.09785	−	0.407601i
$265$	4.78205	+	3.07324i	0.293759	+	0.188787i
$266$	6.76826	−	46.6034i	0.414989	−	2.85744i
$267$	−31.0798	−	6.57344i	−1.90205	−	0.402288i
$268$	1.35802	+	0.402952i	0.0829543	+	0.0246142i
$269$	−7.87136	−	9.08404i	−0.479925	−	0.553863i	0.463220	−	0.886243i	$-0.346694\pi$
$269$	−7.87136	−	9.08404i	−0.479925	−	0.553863i	−0.943146	+	0.332380i	$0.892148\pi$
$270$	−7.13547	−	2.53304i	−0.434251	−	0.154156i
$271$	−7.53257	−	25.6536i	−0.457571	−	1.55834i	−0.788713	−	0.614762i	$-0.789252\pi$
$271$	−7.53257	−	25.6536i	−0.457571	−	1.55834i	0.331142	−	0.943581i	$-0.392566\pi$
$272$	4.74948	+	16.5226i	0.287980	+	1.00183i
$273$	−24.5389	−	1.61282i	−1.48516	−	0.0976124i
$274$	−6.36547	+	13.8861i	−0.384552	+	0.838891i
$275$		−	15.2964i		−	0.922408i
$276$	16.4737	−	2.14883i	0.991600	−	0.129344i
$277$			4.53202i			0.272302i	0.990688	+	0.136151i	$0.0434733\pi$
$277$			4.53202i			0.272302i	−0.990688	+	0.136151i	$0.956527\pi$
$278$	20.8470	+	9.55640i	1.25032	+	0.573155i
$279$	20.0021	−	0.230795i	1.19749	−	0.0138173i
$280$	−14.0633	−	4.19464i	−0.840441	−	0.250678i
$281$	−1.82483	−	6.21478i	−0.108860	−	0.370743i	0.886986	−	0.461796i	$-0.152795\pi$
$281$	−1.82483	−	6.21478i	−0.108860	−	0.370743i	−0.995846	+	0.0910532i	$0.970977\pi$
$282$	−0.546669	−	0.295427i	−0.0325537	−	0.0175924i
$283$	6.72634	+	7.76261i	0.399839	+	0.461439i	0.919590	−	0.392879i	$-0.128521\pi$
$283$	6.72634	+	7.76261i	0.399839	+	0.461439i	−0.519751	+	0.854318i	$0.673975\pi$
$284$	4.81328	+	1.42820i	0.285616	+	0.0847480i
$285$	2.44207	−	11.5463i	0.144656	−	0.683944i
$286$	−15.3265	−	2.22588i	−0.906274	−	0.131619i
$287$	25.6261	+	16.4689i	1.51266	+	0.972129i
$288$	11.0565	−	12.8745i	0.651512	−	0.758639i
$289$	0.964011	−	1.11253i	0.0567066	−	0.0654429i
$290$	0.531170	+	1.81857i	0.0311914	+	0.106790i
$291$	−2.50042	+	0.559060i	−0.146577	+	0.0327727i
$292$	−19.3276	+	5.61539i	−1.13106	+	0.328616i
$293$	−2.60765	−	5.70996i	−0.152341	−	0.333580i	0.818040	−	0.575162i	$-0.195061\pi$
$293$	−2.60765	−	5.70996i	−0.152341	−	0.333580i	−0.970380	+	0.241582i	$0.922334\pi$
$294$	26.7901	−	36.1134i	1.56243	−	2.10618i
$295$	1.87917	+	0.858186i	0.109409	+	0.0499655i
$296$	−15.8041	−	0.0674687i	−0.918594	−	0.00392154i
$297$	14.0216	−	14.5156i	0.813618	−	0.842279i
$298$	−7.13101	−	11.1309i	−0.413088	−	0.644793i
$299$	12.7436	−	4.52199i	0.736980	−	0.261513i
$300$	12.7964	+	4.73025i	0.738801	+	0.273101i
$301$	14.9707	+	23.2949i	0.862897	+	1.34269i
$302$	6.13691	+	13.4887i	0.353140	+	0.776189i
$303$	−13.1684	−	4.82522i	−0.756506	−	0.277201i
$304$	22.1704	+	14.4270i	1.27156	+	0.827448i
$305$	8.11129	−	3.70430i	0.464451	−	0.212108i
$306$	−18.0742	−	2.41235i	−1.03324	−	0.137905i
$307$	2.29138	+	15.9369i	0.130776	+	0.909565i	0.944546	+	0.328379i	$0.106502\pi$
$307$	2.29138	+	15.9369i	0.130776	+	0.909565i	−0.813770	+	0.581187i	$0.802589\pi$
$308$	25.6998	−	29.4892i	1.46438	−	1.68030i
$309$	0.167308	−	0.226206i	0.00951781	−	0.0128684i
$310$	9.71619	+	0.0138263i	0.551842	+	0.000785279i
$311$	−17.5461	−	11.2762i	−0.994946	−	0.639413i	−0.0614911	−	0.998108i	$-0.519586\pi$
$311$	−17.5461	−	11.2762i	−0.994946	−	0.639413i	−0.933455	+	0.358695i	$0.883222\pi$
$312$	6.60164	−	12.1332i	0.373744	−	0.686909i
$313$	4.71488	+	1.38441i	0.266501	+	0.0782517i	0.412253	−	0.911069i	$-0.364742\pi$
$313$	4.71488	+	1.38441i	0.266501	+	0.0782517i	−0.145752	+	0.989321i	$0.546560\pi$
$314$	−20.4809	−	23.7043i	−1.15580	−	1.33771i
$315$	10.0570	−	11.8806i	0.566646	−	0.669397i
$316$	0.0289909	−	10.1864i	0.00163086	−	0.573031i
$317$	6.84377	−	2.00951i	0.384384	−	0.112865i	−0.0838306	−	0.996480i	$-0.526715\pi$
$317$	6.84377	−	2.00951i	0.384384	−	0.112865i	0.468215	+	0.883615i	$0.344897\pi$
$318$	−2.92983	−	13.1919i	−0.164297	−	0.739768i
$319$	−4.99838	−	0.718659i	−0.279856	−	0.0402372i
$320$	5.45105	−	6.18338i	0.304723	−	0.345661i
$321$	−0.837099	+	0.0647265i	−0.0467223	+	0.00361268i
$322$	−7.84055	+	33.2408i	−0.436937	+	1.85244i
$323$		−	28.4213i		−	1.58140i
$324$	7.80715	+	16.2188i	0.433731	+	0.901043i
$325$	10.9913	+	1.58030i	0.609685	+	0.0876595i
$326$	0.772617	−	0.109964i	0.0427913	−	0.00609032i
$327$	−13.3440	+	5.06493i	−0.737924	+	0.280091i
$328$	−14.4333	+	9.18887i	−0.796944	+	0.507370i
$329$	0.965417	−	0.836539i	0.0532252	−	0.0461199i
$330$	6.90150	−	6.96175i	0.379915	−	0.383232i
$331$	−16.3973	−	4.81469i	−0.901278	−	0.264639i	−0.201913	−	0.979404i	$-0.564716\pi$
$331$	−16.3973	−	4.81469i	−0.901278	−	0.264639i	−0.699365	+	0.714764i	$0.746534\pi$
$332$	18.8519	−	8.54462i	1.03463	−	0.468947i
$333$	6.78718	−	15.3274i	0.371935	−	0.839938i
$334$	−0.0318333	+	22.3703i	−0.00174184	+	1.22405i
$335$	−0.477911	+	0.551539i	−0.0261111	+	0.0301338i
$336$	16.7222	+	30.6187i	0.912269	+	1.67039i
$337$	−1.31809	−	9.16751i	−0.0718009	−	0.499386i	−0.993710	−	0.111981i	$-0.964280\pi$
$337$	−1.31809	−	9.16751i	−0.0718009	−	0.499386i	0.921909	−	0.387405i	$-0.126629\pi$
$338$	−2.02187	+	6.84978i	−0.109975	+	0.372579i
$339$	−9.82150	−	17.7426i	−0.533431	−	0.963647i
$340$	−8.76323	−	1.28543i	−0.475253	−	0.0697121i
$341$	−10.7583	+	23.5574i	−0.582596	+	1.27571i
$342$	−23.4474	+	15.4060i	−1.26789	+	0.833064i
$343$	30.9189	+	48.1107i	1.66946	+	2.59773i
$344$	−15.4045	+	2.14776i	−0.830556	+	0.115799i
$345$	−2.49537	+	8.18717i	−0.134346	+	0.440782i
$346$	12.7476	+	19.8979i	0.685315	+	1.06972i
$347$	6.44321	+	10.0258i	0.345889	+	0.538214i	0.969995	−	0.243126i	$-0.0781728\pi$
$347$	6.44321	+	10.0258i	0.345889	+	0.538214i	−0.624105	+	0.781340i	$0.714536\pi$
$348$	2.14690	−	3.95923i	0.115086	−	0.212237i
$349$	2.45922	+	1.12309i	0.131639	+	0.0601175i	0.480146	−	0.877189i	$-0.340584\pi$
$349$	2.45922	+	1.12309i	0.131639	+	0.0601175i	−0.348507	+	0.937306i	$0.613311\pi$
$350$	−18.3965	+	21.1698i	−0.983335	+	1.13157i
$351$	8.98158	+	11.5749i	0.479401	+	0.617822i
$352$	8.98475	+	20.0502i	0.478889	+	1.06868i
$353$	4.35108	−	0.625591i	0.231585	−	0.0332968i	−0.0255454	−	0.999674i	$-0.508132\pi$
$353$	4.35108	−	0.625591i	0.231585	−	0.0332968i	0.257130	+	0.966377i	$0.417223\pi$
$354$	−1.73623	−	4.59392i	−0.0922793	−	0.244164i
$355$	−1.69388	+	1.95484i	−0.0899017	+	0.103752i
$356$	19.7438	+	30.9150i	1.04642	+	1.63849i
$357$	17.7750	−	33.0037i	0.940752	−	1.74674i
$358$	1.15347	−	7.94234i	0.0609630	−	0.419766i
$359$	−3.08850	−	0.906864i	−0.163005	−	0.0478625i	0.199212	−	0.979956i	$-0.436162\pi$
$359$	−3.08850	−	0.906864i	−0.163005	−	0.0478625i	−0.362217	+	0.932094i	$0.617980\pi$
$360$	3.68973	+	7.92639i	0.194466	+	0.417757i
$361$	−16.1942	−	18.6891i	−0.852326	−	0.983637i
$362$	28.6936	+	18.4980i	1.50810	+	0.972233i
$363$	2.51111	+	6.61573i	0.131799	+	0.347236i
$364$	18.5344	+	21.5132i	0.971465	+	1.12760i
$365$	1.47568	−	10.2636i	0.0772409	−	0.537222i
$366$	−19.8938	−	7.32166i	−1.03986	−	0.382709i
$367$		−	28.5605i		−	1.49084i	−0.666592	−	0.745422i	$-0.732248\pi$
$367$		−	28.5605i		−	1.49084i	0.666592	−	0.745422i	$-0.267752\pi$
$368$	−15.1039	−	11.8268i	−0.787345	−	0.616513i
$369$	−2.78981	−	17.9323i	−0.145232	−	0.933516i
$370$	3.39293	−	7.40160i	0.176390	−	0.384791i
$371$	27.4976	+	3.95355i	1.42760	+	0.205258i
$372$	−16.3804	−	16.2849i	−0.849283	−	0.844333i
$373$	−6.82886	−	23.2570i	−0.353585	−	1.20420i	−0.923855	−	0.382743i	$-0.874980\pi$
$373$	−6.82886	−	23.2570i	−0.353585	−	1.20420i	0.570270	−	0.821457i	$-0.306839\pi$
$374$	12.7915	−	19.8418i	0.661433	−	1.02600i
$375$	−11.2145	+	11.3446i	−0.579114	+	0.585835i
$376$	0.199207	+	0.689310i	0.0102733	+	0.0355485i
$377$	1.03279	−	3.51735i	0.0531912	−	0.181153i
$378$	−36.8629	+	3.22574i	−1.89602	+	0.165914i
$379$	10.9319	+	7.02552i	0.561535	+	0.360877i	0.790409	−	0.612579i	$-0.209868\pi$
$379$	10.9319	+	7.02552i	0.561535	+	0.360877i	−0.228874	+	0.973456i	$0.573504\pi$
$380$	−11.4851	+	7.33490i	−0.589171	+	0.376272i
$381$	−2.06791	+	2.79588i	−0.105942	+	0.143237i
$382$	1.94777	+	6.66857i	0.0996564	+	0.341194i
$383$	0.979060	+	6.80951i	0.0500276	+	0.347950i	0.999426	+	0.0338755i	$0.0107850\pi$
$383$	0.979060	+	6.80951i	0.0500276	+	0.347950i	−0.949398	+	0.314074i	$0.898306\pi$
$384$	−19.5517	+	1.31601i	−0.997742	+	0.0671572i
$385$	8.37163	+	18.3313i	0.426658	+	0.934250i
$386$	15.8814	+	13.8009i	0.808342	+	0.702449i
$387$	4.46481	−	15.8813i	0.226959	−	0.807294i
$388$	2.48431	+	1.60658i	0.126122	+	0.0815616i
$389$	−20.0032	+	12.8553i	−1.01420	+	0.651789i	−0.938478	−	0.345339i	$-0.887764\pi$
$389$	−20.0032	+	12.8553i	−1.01420	+	0.651789i	−0.0757260	+	0.997129i	$0.524127\pi$
$390$	4.28936	+	5.67831i	0.217200	+	0.287532i
$391$	−1.79951	+	20.5334i	−0.0910052	+	1.03842i
$392$	−51.4242	+	7.16974i	−2.59731	+	0.362127i
$393$	13.3525	−	10.1163i	0.673546	−	0.510300i
$394$	3.63936	−	1.65579i	0.183348	−	0.0834173i
$395$	4.77373	+	2.18009i	0.240192	+	0.109692i
$396$	−23.3031	+	0.202556i	−1.17103	+	0.0101788i
$397$	−31.9123	+	14.5739i	−1.60163	+	0.731442i	−0.997840	−	0.0656986i	$-0.979072\pi$
$397$	−31.9123	+	14.5739i	−1.60163	+	0.731442i	−0.603794	+	0.797140i	$0.706345\pi$
$398$	−10.3133	−	3.04421i	−0.516960	−	0.152593i
$399$	−12.5849	−	56.2864i	−0.630031	−	2.81784i
$400$	−6.46246	−	14.3667i	−0.323123	−	0.718333i
$401$	−17.0849	−	14.8041i	−0.853178	−	0.739283i	0.113973	−	0.993484i	$-0.463642\pi$
$401$	−17.0849	−	14.8041i	−0.853178	−	0.739283i	−0.967152	+	0.254200i	$0.918188\pi$
$402$	1.72993	−	0.131286i	0.0862809	−	0.00654795i
$403$	−15.8158	−	10.1642i	−0.787839	−	0.506313i
$404$	6.68538	+	14.7499i	0.332610	+	0.733834i
$405$	−9.27098	+	0.213976i	−0.460679	+	0.0106325i
$406$	6.05330	+	7.00600i	0.300420	+	0.347702i
$407$	14.2121	+	16.4016i	0.704466	+	0.812997i
$408$	12.6433	+	16.8368i	0.625937	+	0.833545i
$409$	26.9704	−	7.91921i	1.33360	−	0.391580i	0.464217	−	0.885722i	$-0.346336\pi$
$409$	26.9704	−	7.91921i	1.33360	−	0.391580i	0.869381	+	0.494142i	$0.164518\pi$
$410$	−1.24208	−	8.72702i	−0.0613421	−	0.430997i
$411$	−1.22698	+	18.6684i	−0.0605227	+	0.920845i
$412$	−0.321705	+	0.0453200i	−0.0158493	+	0.00223276i
$413$	10.0960			0.496792
$414$	17.9153	−	9.64574i	0.880491	−	0.474062i
$415$			10.6634i			0.523446i
$416$	−15.3353	+	4.38458i	−0.751875	+	0.214972i
$417$	28.0266	+	1.84206i	1.37247	+	0.0902059i
$418$	−5.11812	−	35.9605i	−0.250335	−	1.75889i
$419$	5.37186	+	18.2949i	0.262432	+	0.893763i	0.980289	+	0.197571i	$0.0633054\pi$
$419$	5.37186	+	18.2949i	0.262432	+	0.893763i	−0.717856	+	0.696191i	$0.754876\pi$
$420$	−17.9241	+	1.33463i	−0.874608	+	0.0651233i
$421$	−2.83308	+	2.45488i	−0.138076	+	0.119643i	−0.721161	−	0.692768i	$-0.756391\pi$
$421$	−2.83308	+	2.45488i	−0.138076	+	0.119643i	0.583085	+	0.812411i	$0.301846\pi$
$422$	0.654159	−	0.565204i	0.0318440	−	0.0275137i
$423$	−0.754496	−	0.0996091i	−0.0366849	−	0.00484316i
$424$	−8.49207	+	13.0907i	−0.412411	+	0.635741i
$425$	−9.15117	+	14.2395i	−0.443897	+	0.690717i
$426$	6.13144	−	0.465322i	0.297069	−	0.0225449i
$427$	28.5380	−	32.9346i	1.38105	−	1.59382i
$428$	0.730878	+	0.636960i	0.0353283	+	0.0307886i
$429$	−18.5109	+	4.13879i	−0.893715	+	0.199823i
$430$	2.26848	−	7.68524i	0.109396	−	0.370615i
$431$	−13.5784	−	29.7325i	−0.654048	−	1.43216i	−0.887966	−	0.459909i	$-0.847882\pi$
$431$	−13.5784	−	29.7325i	−0.654048	−	1.43216i	0.233918	−	0.972256i	$-0.424845\pi$
$432$	7.03680	−	19.5572i	0.338558	−	0.940945i
$433$	−14.3616	+	31.4476i	−0.690177	+	1.51128i	0.161312	+	0.986903i	$0.448427\pi$
$433$	−14.3616	+	31.4476i	−0.690177	+	1.51128i	−0.851489	+	0.524373i	$0.824300\pi$
$434$	43.2210	−	19.6641i	2.07467	−	0.943905i
$435$	1.40122	+	1.84948i	0.0671835	+	0.0886757i
$436$	14.9720	+	6.88906i	0.717030	+	0.329926i
$437$	18.5964	+	25.6894i	0.889588	+	1.22889i
$438$	−19.6691	+	14.8579i	−0.939826	+	0.709939i
$439$	5.97694	+	9.30029i	0.285264	+	0.443879i	0.954081	−	0.299548i	$-0.0968357\pi$
$439$	5.97694	+	9.30029i	0.285264	+	0.443879i	−0.668818	+	0.743426i	$0.733199\pi$
$440$	−11.3193	−	0.0483228i	−0.539626	−	0.00230370i
$441$	14.9046	−	53.0159i	0.709745	−	2.52457i
$442$	12.9358	+	11.2412i	0.615296	+	0.534692i
$443$	−35.5313	+	16.2266i	−1.68814	+	0.770949i	−0.689221	+	0.724551i	$0.742047\pi$
$443$	−35.5313	+	16.2266i	−1.68814	+	0.770949i	−0.998923	+	0.0463982i	$0.985226\pi$
$444$	−18.1159	+	6.81727i	−0.859742	+	0.323533i
$445$	−18.7058	+	2.68949i	−0.886739	+	0.127494i
$446$	−17.8631	+	5.21747i	−0.845841	+	0.247054i
$447$	−13.0166	−	9.62746i	−0.615666	−	0.455363i
$448$	11.6791	−	38.5545i	0.551785	−	1.82153i
$449$	−1.69501	+	2.63749i	−0.0799926	+	0.124471i	−0.878945	−	0.476924i	$-0.841752\pi$
$449$	−1.69501	+	2.63749i	−0.0799926	+	0.124471i	0.798952	+	0.601395i	$0.205388\pi$
$450$	16.7080	−	0.169008i	0.787622	−	0.00796709i
$451$	22.5439	+	6.61947i	1.06155	+	0.311699i
$452$	−6.66121	+	22.4495i	−0.313317	+	1.05593i
$453$	12.9076	+	12.7595i	0.606451	+	0.599494i
$454$	−18.0627	−	11.6446i	−0.847725	−	0.546506i
$455$	−14.0369	+	4.12160i	−0.658059	+	0.193223i
$456$	31.6660	+	6.83878i	1.48289	+	0.320255i
$457$	0.406202	−	2.82520i	0.0190013	−	0.132157i	−0.978113	−	0.208076i	$-0.933280\pi$
$457$	0.406202	−	2.82520i	0.0190013	−	0.132157i	0.997114	+	0.0759188i	$0.0241890\pi$
$458$	2.70935	−	5.91038i	0.126600	−	0.276174i
$459$	−21.7368	+	5.12409i	−1.01459	+	0.239172i
$460$	8.76197	−	4.57202i	0.408529	−	0.213172i
$461$	34.5869			1.61087			0.805436	−	0.592683i	$-0.201931\pi$
$461$	34.5869			1.61087			0.805436	+	0.592683i	$0.201931\pi$
$462$	16.5468	−	44.9594i	0.769825	−	2.09170i
$463$	10.3132	+	1.48281i	0.479295	+	0.0689122i	0.377728	−	0.925917i	$-0.376705\pi$
$463$	10.3132	+	1.48281i	0.479295	+	0.0689122i	0.101567	+	0.994829i	$0.467614\pi$
$464$	−4.99819	+	1.43675i	−0.232035	+	0.0666995i
$465$	11.1254	−	4.22283i	0.515928	−	0.195829i
$466$	30.3089	+	19.5394i	1.40403	+	0.905144i
$467$	8.87980	−	7.69439i	0.410908	−	0.356054i	−0.424744	−	0.905314i	$-0.639636\pi$
$467$	8.87980	−	7.69439i	0.410908	−	0.356054i	0.835652	+	0.549260i	$0.185090\pi$
$468$	2.26195	−	16.7654i	0.104559	−	0.774982i
$469$	−1.00481	+	3.42208i	−0.0463980	+	0.158017i
$470$	−0.365822	−	0.0531286i	−0.0168741	−	0.00245064i
$471$	−33.7796	−	18.1929i	−1.55648	−	0.838282i
$472$	−2.37774	+	5.14825i	−0.109444	+	0.236968i
$473$	16.1414	+	13.9866i	0.742183	+	0.643105i
$474$	−4.41061	−	11.6702i	−0.202586	−	0.536028i
$475$	3.70635	+	25.7782i	0.170059	+	1.18279i
$476$	−41.5662	+	12.0765i	−1.90518	+	0.553527i
$477$	−9.10789	−	13.8189i	−0.417022	−	0.632726i
$478$	18.8708	+	16.3987i	0.863132	+	0.750061i
$479$	7.56418	−	16.5632i	0.345616	−	0.756794i	−0.654384	−	0.756163i	$-0.727072\pi$
$479$	7.56418	−	16.5632i	0.345616	−	0.756794i	1.00000		0.000630981i	$-0.000200848\pi$
$480$	3.54080	−	9.45436i	0.161615	−	0.431531i
$481$	−13.2537	+	8.51761i	−0.604315	+	0.388370i
$482$	−12.0285	−	18.7753i	−0.547881	−	0.855193i
$483$	5.52831	+	41.4617i	0.251547	+	1.88657i
$484$	3.41548	−	7.42288i	0.155249	−	0.337404i
$485$	−1.28224	+	0.824049i	−0.0582237	+	0.0374181i
$486$	16.0100	+	15.1552i	0.726229	+	0.687453i
$487$	−22.5309	−	10.2895i	−1.02097	−	0.466263i	−0.166656	−	0.986015i	$-0.553297\pi$
$487$	−22.5309	−	10.2895i	−1.02097	−	0.466263i	−0.854317	+	0.519753i	$0.826024\pi$
$488$	10.0733	+	22.3089i	0.455995	+	1.00988i
$489$	0.836224	−	0.462895i	0.0378154	−	0.0209328i
$490$	7.57274	−	25.6553i	0.342101	−	1.15899i
$491$	−24.8654	+	3.57511i	−1.12216	+	0.161342i	−0.678322	−	0.734765i	$-0.737293\pi$
$491$	−24.8654	+	3.57511i	−1.12216	+	0.161342i	−0.443838	+	0.896107i	$0.646383\pi$
$492$	−12.5091	+	16.8124i	−0.563952	+	0.757959i
$493$	4.22308	+	3.65932i	0.190198	+	0.164807i
$494$	26.3682	+	0.0375223i	1.18636	+	0.00168821i
$495$	4.86115	−	10.9779i	0.218492	−	0.493420i
$496$	−0.151813	+	26.6708i	−0.00681660	+	1.19755i
$497$	−3.56140	+	12.1290i	−0.159751	+	0.544060i
$498$	17.8469	−	18.0027i	0.799738	−	0.806719i
$499$	−15.1135	−	17.4419i	−0.676573	−	0.780807i	0.308816	−	0.951122i	$-0.400067\pi$
$499$	−15.1135	−	17.4419i	−0.676573	−	0.780807i	−0.985390	+	0.170314i	$0.945522\pi$
$500$	18.4197	+	0.0524230i	0.823754	+	0.00234443i
$501$	9.72255	+	25.6149i	0.434372	+	1.14439i
$502$	2.63099	+	18.4857i	0.117427	+	0.825056i
$503$	1.87841	−	13.0646i	0.0837542	−	0.582523i	−0.904121	−	0.427276i	$-0.859473\pi$
$503$	1.87841	−	13.0646i	0.0837542	−	0.582523i	0.987876	−	0.155247i	$-0.0496175\pi$
$504$	32.4944	+	27.7456i	1.44742	+	1.23589i
$505$	−8.34314			−0.371265
$506$	1.42080	+	26.3042i	0.0631623	+	1.16937i
$507$	0.674331	+	8.72103i	0.0299481	+	0.387315i
$508$	3.97624	−	0.560151i	0.176417	−	0.0248527i
$509$	−2.89809	+	20.1567i	−0.128456	+	0.893429i	0.819057	+	0.573712i	$0.194497\pi$
$509$	−2.89809	+	20.1567i	−0.128456	+	0.893429i	−0.947513	+	0.319717i	$0.896412\pi$
$510$	−10.5895	+	2.35186i	−0.468913	+	0.104142i
$511$	−14.2768	−	48.6223i	−0.631569	−	2.15092i
$512$	16.9095	+	15.0356i	0.747301	+	0.664486i
$513$	−20.1127	+	27.8598i	−0.887999	+	1.23004i
$514$	11.0256	+	12.7609i	0.486319	+	0.562859i
$515$	0.0471553	−	0.160596i	0.00207791	−	0.00707672i
$516$	−16.6922	+	9.17810i	−0.734835	+	0.404043i
$517$	0.532692	−	0.828885i	0.0234278	−	0.0364543i
$518$	0.0566241	−	39.7917i	0.00248792	−	1.74835i
$519$	23.2689	+	17.2103i	1.02139	+	0.755450i
$520$	1.20414	−	8.12850i	0.0528051	−	0.356458i
$521$	11.1811	−	1.60760i	0.489853	−	0.0704302i	0.107037	−	0.994255i	$-0.465864\pi$
$521$	11.1811	−	1.60760i	0.489853	−	0.0704302i	0.382815	+	0.923825i	$0.374955\pi$
$522$	0.729751	−	5.46758i	0.0319404	−	0.239310i
$523$	−2.82533	−	6.18660i	−0.123543	−	0.270521i	0.837748	−	0.546057i	$-0.183872\pi$
$523$	−2.82533	−	6.18660i	−0.123543	−	0.270521i	−0.961291	+	0.275536i	$0.911145\pi$
$524$	−19.1388	−	2.80736i	−0.836080	−	0.122640i
$525$	−11.8180	+	32.2524i	−0.515781	+	1.40761i
$526$	−32.6553	+	14.8571i	−1.42384	+	0.647798i
$527$	24.1083	−	15.4935i	1.05018	−	0.674907i
$528$	19.0291	+	19.0262i	0.828136	+	0.828009i
$529$	−11.8087	−	19.7371i	−0.513423	−	0.858136i
$530$	−4.33658	−	6.76902i	−0.188369	−	0.294027i
$531$	−3.99105	−	4.49994i	−0.173197	−	0.195281i
$532$	−36.1652	+	55.9236i	−1.56796	+	2.42460i
$533$	−7.08548	+	15.5150i	−0.306906	+	0.672031i
$534$	36.0816	+	26.7665i	1.56140	+	1.15830i
$535$	−0.454334	+	0.207487i	−0.0196426	+	0.00897046i
$536$	−1.50837	−	1.31833i	−0.0651518	−	0.0569431i
$537$	−2.14476	−	9.59254i	−0.0925533	−	0.413949i
$538$	4.76588	+	16.3169i	0.205471	+	0.703473i
$539$	53.8841	+	46.6908i	2.32095	+	2.01112i
$540$	7.68044	+	7.46146i	0.330514	+	0.321090i
$541$	8.90516	−	13.8567i	0.382863	−	0.595746i	−0.595321	−	0.803488i	$-0.702975\pi$
$541$	8.90516	−	13.8567i	0.382863	−	0.595746i	0.978184	+	0.207742i	$0.0666114\pi$
$542$	−5.43435	+	37.4187i	−0.233425	+	1.60727i
$543$	40.9071	+	8.65194i	1.75549	+	0.371290i
$544$	3.63119	−	24.0400i	0.155686	−	1.03071i
$545$	−6.41694	+	5.56031i	−0.274872	+	0.238178i
$546$	30.5961	+	16.5345i	1.30939	+	0.707613i
$547$	11.8265	−	3.47257i	0.505664	−	0.148476i	−0.0189437	−	0.999821i	$-0.506030\pi$
$547$	11.8265	−	3.47257i	0.505664	−	0.148476i	0.524607	+	0.851344i	$0.324212\pi$
$548$	16.3666	−	14.1004i	0.699147	−	0.602339i
$549$	−25.9608	+	0.299550i	−1.10798	+	0.0127845i
$550$	−9.01441	+	19.6647i	−0.384376	+	0.838506i
$551$	8.59764			0.366272
$552$	−22.4445	−	6.94572i	−0.955303	−	0.295630i
$553$	25.6474			1.09064
$554$	2.67079	−	5.82625i	0.113471	−	0.247534i
$555$	0.654009	−	9.95066i	0.0277611	−	0.422382i
$556$	−21.1687	−	24.5710i	−0.897754	−	1.04204i
$557$	8.98745	−	2.63895i	0.380810	−	0.111816i	−0.0857243	−	0.996319i	$-0.527320\pi$
$557$	8.98745	−	2.63895i	0.380810	−	0.111816i	0.466535	+	0.884503i	$0.345502\pi$
$558$	−25.8502	−	11.4908i	−1.09433	−	0.486445i
$559$	−11.7177	+	10.1534i	−0.495606	+	0.429445i
$560$	15.6074	+	13.6802i	0.659535	+	0.578096i
$561$	5.98288	−	28.2876i	0.252597	−	1.19430i
$562$	−1.31652	+	9.06498i	−0.0555339	+	0.382383i
$563$	8.67155	−	13.4932i	0.365462	−	0.568670i	−0.609014	−	0.793159i	$-0.708435\pi$
$563$	8.67155	−	13.4932i	0.365462	−	0.568670i	0.974477	+	0.224489i	$0.0720712\pi$
$564$	0.528685	+	0.701955i	0.0222617	+	0.0295576i
$565$	−9.11750	−	7.90036i	−0.383576	−	0.332371i
$566$	−4.07260	−	13.9434i	−0.171184	−	0.586083i
$567$	−40.7793	+	19.7729i	−1.71257	+	0.830384i
$568$	−5.34618	−	4.67260i	−0.224321	−	0.196058i
$569$	−28.0229	+	12.7976i	−1.17478	+	0.536505i	−0.904582	−	0.426300i	$-0.859817\pi$
$569$	−28.0229	+	12.7976i	−1.17478	+	0.536505i	−0.270199	+	0.962804i	$0.587090\pi$
$570$	−9.94387	+	13.4045i	−0.416503	+	0.561453i
$571$	13.0430	−	28.5601i	0.545832	−	1.19520i	−0.412870	−	0.910790i	$-0.635474\pi$
$571$	13.0430	−	28.5601i	0.545832	−	1.19520i	0.958701	−	0.284415i	$-0.0917992\pi$
$572$	18.3916	+	11.8937i	0.768992	+	0.497299i
$573$	5.13820	+	6.78192i	0.214651	+	0.283319i
$574$	−23.2390	−	36.2739i	−0.969976	−	1.51404i
$575$	−1.04554	−	18.8585i	−0.0436021	−	0.786454i
$576$	−21.8012	+	10.0354i	−0.908382	+	0.418142i
$577$	−19.0271	+	12.2280i	−0.792109	+	0.509058i	−0.873032	−	0.487663i	$-0.837850\pi$
$577$	−19.0271	+	12.2280i	−0.792109	+	0.509058i	0.0809229	+	0.996720i	$0.474213\pi$
$578$	−1.89494	+	0.862134i	−0.0788192	+	0.0358600i
$579$	24.1956	+	8.86581i	1.00553	+	0.368451i
$580$	0.388851	−	2.65094i	0.0161462	−	0.110074i
$581$	21.6486	+	47.4037i	0.898133	+	1.96664i
$582$	3.54395	+	0.754822i	0.146901	+	0.0312884i
$583$	21.2092	−	3.04943i	0.878396	−	0.126294i
$584$	28.1563	+	4.17103i	1.16512	+	0.172598i
$585$	7.38596	+	4.62713i	0.305372	+	0.191308i
$586$	−0.0126325	+	8.87732i	−0.000521846	+	0.366719i
$587$	−17.6673	+	27.4909i	−0.729207	+	1.13467i	0.256556	+	0.966529i	$0.417412\pi$
$587$	−17.6673	+	27.4909i	−0.729207	+	1.13467i	−0.985763	+	0.168139i	$0.946224\pi$
$588$	−55.7229	+	30.6388i	−2.29797	+	1.26352i
$589$	12.4224	−	42.3068i	0.511856	−	1.74322i
$590$	−1.91007	−	2.21069i	−0.0786363	−	0.0910125i
$591$	3.44262	−	3.48257i	0.141610	−	0.143254i
$592$	20.2776	+	9.40033i	0.833405	+	0.386351i
$593$	8.06417	+	27.4640i	0.331156	+	1.12781i	0.941874	+	0.335965i	$0.109062\pi$
$593$	8.06417	+	27.4640i	0.331156	+	1.12781i	−0.610719	+	0.791848i	$0.709119\pi$
$594$	−26.5801	+	10.3977i	−1.09060	+	0.426624i
$595$	3.17363	−	22.0731i	0.130106	−	0.904908i
$596$	2.60787	+	18.5120i	0.106822	+	0.758280i
$597$	−13.1308	+	1.01530i	−0.537407	+	0.0415536i
$598$	−19.0477	−	1.69663i	−0.778920	−	0.0693802i
$599$	14.4736			0.591375			0.295687	−	0.955285i	$-0.404451\pi$
$599$	14.4736			0.591375			0.295687	+	0.955285i	$0.404451\pi$
$600$	−13.6632	−	13.6222i	−0.557796	−	0.556125i
$601$	2.29630	−	15.9711i	0.0936682	−	0.651477i	−0.887854	−	0.460126i	$-0.847804\pi$
$601$	2.29630	−	15.9711i	0.0936682	−	0.651477i	0.981522	−	0.191350i	$-0.0612867\pi$
$602$	−5.51796	−	38.7698i	−0.224895	−	1.58014i
$603$	1.92248	−	0.904920i	0.0782896	−	0.0368512i
$604$	0.0596453	−	20.9574i	0.00242693	−	0.852743i
$605$	2.75671	+	3.18141i	0.112076	+	0.129343i
$606$	14.0854	+	13.9635i	0.572182	+	0.567230i
$607$	7.93711	−	27.0313i	0.322157	−	1.09717i	−0.626121	−	0.779726i	$-0.715358\pi$
$607$	7.93711	−	27.0313i	0.322157	−	1.09717i	0.948278	−	0.317441i	$-0.102823\pi$
$608$	−19.9997	−	31.6124i	−0.811095	−	1.28205i
$609$	9.98384	+	5.37705i	0.404566	+	0.217889i
$610$	−12.6107	−	0.0179452i	−0.510592	−	0.000726579i
$611$	0.540563	+	0.468400i	0.0218688	+	0.0189494i
$612$	21.8142	+	13.7527i	0.881786	+	0.555919i
$613$	30.9683	−	4.45257i	1.25080	−	0.179838i	0.515090	−	0.857136i	$-0.327759\pi$
$613$	30.9683	−	4.45257i	1.25080	−	0.179838i	0.735708	+	0.677299i	$0.236850\pi$
$614$	6.44611	−	21.8384i	0.260144	−	0.881327i
$615$	−5.22859	−	9.44549i	−0.210837	−	0.380879i
$616$	−50.4175	+	22.7653i	−2.03138	+	0.917240i
$617$	4.40601	+	2.01216i	0.177379	+	0.0810065i	0.502125	−	0.864795i	$-0.332552\pi$
$617$	4.40601	+	2.01216i	0.177379	+	0.0810065i	−0.324746	+	0.945801i	$0.605279\pi$
$618$	−0.348394	+	0.192208i	−0.0140144	+	0.00773172i
$619$	19.0459	−	12.2401i	0.765520	−	0.491970i	−0.0986791	−	0.995119i	$-0.531462\pi$
$619$	19.0459	−	12.2401i	0.765520	−	0.491970i	0.864200	+	0.503149i	$0.167825\pi$
$620$	−12.4828	−	5.74368i	−0.501320	−	0.230672i
$621$	16.2947	−	18.8542i	0.653884	−	0.756595i
$622$	15.9116	+	24.8365i	0.637997	+	0.995855i
$623$	−77.6956	+	49.9319i	−3.11281	+	2.00048i
$624$	−15.6372	+	11.7078i	−0.625990	+	0.468685i
$625$	4.23800	−	9.27992i	0.169520	−	0.371197i
$626$	−5.24549	−	4.55832i	−0.209652	−	0.182187i
$627$	−21.5449	−	38.9210i	−0.860420	−	1.55436i
$628$	12.3605	+	42.5434i	0.493236	+	1.69767i
$629$	−3.41772	−	23.7708i	−0.136273	−	0.947803i
$630$	−19.9304	+	9.34671i	−0.794048	+	0.372382i
$631$	17.4340	+	15.1066i	0.694036	+	0.601386i	0.928762	−	0.370676i	$-0.120874\pi$
$631$	17.4340	+	15.1066i	0.694036	+	0.601386i	−0.234726	+	0.972062i	$0.575419\pi$
$632$	−6.04028	+	13.0783i	−0.240270	+	0.520228i
$633$	0.502062	−	0.932204i	0.0199552	−	0.0370518i
$634$	−9.98242	−	1.44976i	−0.396453	−	0.0575772i
$635$	−0.582835	+	1.98495i	−0.0231291	+	0.0787705i
$636$	−4.00769	+	18.6859i	−0.158915	+	0.740942i
$637$	−39.1166	+	33.8947i	−1.54986	+	1.34296i
$638$	6.00229	+	3.86952i	0.237633	+	0.153196i
$639$	6.81393	−	3.20734i	0.269555	−	0.126880i
$640$	−10.6517	+	4.73682i	−0.421046	+	0.187239i
$641$	−27.6717	−	3.97859i	−1.09297	−	0.157145i	−0.427824	−	0.903862i	$-0.640720\pi$
$641$	−27.6717	−	3.97859i	−1.09297	−	0.157145i	−0.665142	+	0.746717i	$0.731629\pi$
$642$	1.11430	+	0.410105i	0.0439779	+	0.0161855i
$643$	3.37932			0.133267			0.0666337	−	0.997778i	$-0.478774\pi$
$643$	3.37932			0.133267			0.0666337	+	0.997778i	$0.478774\pi$
$644$	29.6689	−	38.1130i	1.16912	−	1.50186i
$645$	−0.756579	−	9.78473i	−0.0297903	−	0.385274i
$646$	−16.7491	+	36.5378i	−0.658985	+	1.43756i
$647$	1.96657	−	13.6778i	0.0773138	−	0.537729i	−0.913949	−	0.405829i	$-0.866983\pi$
$647$	1.96657	−	13.6778i	0.0773138	−	0.537729i	0.991263	−	0.131900i	$-0.0421079\pi$
$648$	−0.478721	−	25.4513i	−0.0188059	−	0.999823i
$649$	7.47174	−	2.19390i	0.293292	−	0.0861182i
$650$	−13.1988	−	8.50892i	−0.517699	−	0.333747i
$651$	40.8844	−	41.3589i	1.60239	−	1.62098i
$652$	−1.05806	−	0.313948i	−0.0414369	−	0.0122952i
$653$	−22.7560	−	6.68176i	−0.890511	−	0.261478i	−0.195695	−	0.980665i	$-0.562696\pi$
$653$	−22.7560	−	6.68176i	−0.890511	−	0.261478i	−0.694816	+	0.719187i	$0.744514\pi$
$654$	20.1396	+	1.35246i	0.787519	+	0.0528855i
$655$	5.38783	−	8.38363i	0.210520	−	0.327575i
$656$	23.9702	−	3.30725i	0.935880	−	0.129126i
$657$	−16.0279	+	25.5842i	−0.625309	+	0.998136i
$658$	−1.73410	+	0.506499i	−0.0676024	+	0.0197454i
$659$	−11.4743	+	1.64976i	−0.446975	+	0.0642654i	−0.362128	−	0.932129i	$-0.617950\pi$
$659$	−11.4743	+	1.64976i	−0.446975	+	0.0642654i	−0.0848479	+	0.996394i	$0.527040\pi$
$660$	−12.9751	+	4.88270i	−0.505054	+	0.190059i
$661$	−7.03111	+	3.21100i	−0.273478	+	0.124893i	−0.547434	−	0.836849i	$-0.684395\pi$
$661$	−7.03111	+	3.21100i	−0.273478	+	0.124893i	0.273955	+	0.961742i	$0.411668\pi$
$662$	18.2426	+	15.8528i	0.709020	+	0.616138i
$663$	19.7080	+	7.22145i	0.765393	+	0.280458i
$664$	−29.2711	−	0.124960i	−1.13594	−	0.00484939i
$665$	−18.5500	−	28.8643i	−0.719336	−	1.11931i
$666$	−17.7581	+	15.7048i	−0.688113	+	0.608548i
$667$	−6.21149	−	0.544364i	−0.240510	−	0.0210779i
$668$	13.2241	−	28.7400i	0.511656	−	1.11199i
$669$	−18.1667	+	13.7637i	−0.702365	+	0.532134i
$670$	0.939421	−	0.427405i	0.0362930	−	0.0165121i
$671$	13.9633	−	30.5753i	0.539046	−	1.18035i
$672$	−3.45351	−	49.2174i	−0.133222	−	1.89860i
$673$	−6.60814	−	14.4698i	−0.254725	−	0.557770i	0.738463	−	0.674294i	$-0.235552\pi$
$673$	−6.60814	−	14.4698i	−0.254725	−	0.557770i	−0.993188	+	0.116524i	$0.962825\pi$
$674$	−3.70805	+	12.5623i	−0.142829	+	0.483882i
$675$	19.0472	−	7.48221i	0.733126	−	0.287990i
$676$	6.63595	−	7.61439i	0.255229	−	0.292861i
$677$	11.8504	−	13.6761i	0.455448	−	0.525615i	−0.480859	−	0.876798i	$-0.659675\pi$
$677$	11.8504	−	13.6761i	0.455448	−	0.525615i	0.936307	+	0.351183i	$0.114220\pi$
$678$	2.17029	+	28.5975i	0.0833495	+	1.09828i
$679$	−4.02720	+	6.26645i	−0.154550	+	0.240484i
$680$	10.5083	+	6.81682i	0.402974	+	0.261413i
$681$	−25.7512	−	5.44643i	−0.986787	−	0.208708i
$682$	27.7134	−	23.9448i	1.06120	−	0.916895i
$683$	24.3533	−	21.1023i	0.931854	−	0.807456i	−0.0496757	−	0.998765i	$-0.515819\pi$
$683$	24.3533	−	21.1023i	0.931854	−	0.807456i	0.981530	+	0.191309i	$0.0612733\pi$
$684$	39.2224	−	5.98775i	1.49971	−	0.228947i
$685$	3.13558	+	10.6788i	0.119805	+	0.408017i
$686$	−11.3962	−	80.0710i	−0.435109	−	3.05712i
$687$	0.522245	−	7.94588i	0.0199249	−	0.303154i
$688$	21.0694	+	6.31702i	0.803264	+	0.240834i
$689$			15.5549i			0.592596i
$690$	8.03281	−	9.05467i	0.305804	−	0.344706i
$691$	5.69169			0.216522			0.108261	−	0.994123i	$-0.465472\pi$
$691$	5.69169			0.216522			0.108261	+	0.994123i	$0.465472\pi$
$692$	−4.66190	−	33.0926i	−0.177219	−	1.25799i
$693$	−0.676975	−	58.6707i	−0.0257162	−	2.22872i
$694$	−2.37486	−	16.6860i	−0.0901485	−	0.633394i
$695$	16.0320	−	4.70741i	0.608127	−	0.178562i
$696$	−5.09324	+	3.82469i	−0.193059	+	0.144974i
$697$	−17.0260	−	19.6491i	−0.644907	−	0.744263i
$698$	−2.49966	−	2.89307i	−0.0946136	−	0.109504i
$699$	43.2100	+	9.13902i	1.63435	+	0.345669i
$700$	36.1258	−	16.3740i	1.36543	−	0.618879i
$701$	−38.1867	−	24.5411i	−1.44229	−	0.926904i	−0.999542	−	0.0302591i	$-0.990367\pi$
$701$	−38.1867	−	24.5411i	−1.44229	−	0.926904i	−0.442749	−	0.896645i	$-0.645997\pi$
$702$	−4.72524	−	20.1734i	−0.178343	−	0.761396i
$703$	−27.9249	−	24.1971i	−1.05321	−	0.912611i
$704$	0.265292	−	31.0709i	0.00999857	−	1.17103i
$705$	−0.441829	+	0.0987870i	−0.0166403	+	0.00372053i
$706$	−5.96232	−	1.75991i	−0.224395	−	0.0662352i
$707$	−37.0890	+	16.9380i	−1.39488	+	0.637019i
$708$	−0.475221	+	6.92903i	−0.0178599	+	0.260409i
$709$	−9.79351	−	4.47255i	−0.367803	−	0.167970i	0.222935	−	0.974833i	$-0.428436\pi$
$709$	−9.79351	−	4.47255i	−0.367803	−	0.167970i	−0.590738	+	0.806863i	$0.701163\pi$
$710$	3.32963	−	1.51487i	0.124959	−	0.0568519i
$711$	−10.1386	−	11.4314i	−0.380229	−	0.428711i
$712$	−7.16343	−	51.3789i	−0.268461	−	1.92550i
$713$	−11.6534	+	29.7786i	−0.436424	+	1.11522i
$714$	−42.3007	+	31.9537i	−1.58306	+	1.19584i
$715$	−9.49261	+	6.10053i	−0.355003	+	0.228147i
$716$	−6.16342	+	9.53073i	−0.230338	+	0.356180i
$717$	28.7500	+	10.5347i	1.07369	+	0.393424i
$718$	3.43607	+	2.98594i	0.128233	+	0.111434i
$719$	10.8666	+	23.7946i	0.405256	+	0.887388i	0.996710	+	0.0810488i	$0.0258270\pi$
$719$	10.8666	+	23.7946i	0.405256	+	0.887388i	−0.591454	+	0.806339i	$0.701446\pi$
$720$	−0.0722830	−	12.3644i	−0.00269383	−	0.460794i
$721$	−0.116411	−	0.809657i	−0.00433537	−	0.0301532i
$722$	9.80511	+	33.5698i	0.364908	+	1.24934i
$723$	−21.9562	−	16.2394i	−0.816561	−	0.603951i
$724$	−25.9867	−	40.6902i	−0.965786	−	1.51224i
$725$	−4.30755	−	2.76829i	−0.159978	−	0.102812i
$726$	0.670528	−	9.98486i	0.0248856	−	0.370573i
$727$	5.69588	−	19.3984i	0.211249	−	0.719447i	−0.783884	−	0.620907i	$-0.786765\pi$
$727$	5.69588	−	19.3984i	0.211249	−	0.719447i	0.995133	−	0.0985401i	$-0.0314173\pi$
$728$	−11.1493	−	38.5795i	−0.413220	−	1.42985i
$729$	24.9335	+	10.3595i	0.923463	+	0.383686i
$730$	−7.94561	+	12.3250i	−0.294080	+	0.456169i
$731$	−6.65854	−	22.6769i	−0.246275	−	0.838736i
$732$	21.2602	+	21.1362i	0.785799	+	0.781218i
$733$	−9.11219	−	1.31013i	−0.336566	−	0.0483909i	−0.0280402	−	0.999607i	$-0.508927\pi$
$733$	−9.11219	−	1.31013i	−0.336566	−	0.0483909i	−0.308526	+	0.951216i	$0.599836\pi$
$734$	−16.8311	+	36.7167i	−0.621248	+	1.35524i
$735$	−2.52565	−	32.6639i	−0.0931600	−	1.20483i
$736$	12.4475	+	24.1052i	0.458822	+	0.888528i
$737$			2.75092i			0.101332i
$738$	−6.98124	+	24.6974i	−0.256983	+	0.909123i
$739$	1.65254	−	11.4937i	0.0607898	−	0.422802i	−0.936588	−	0.350432i	$-0.886035\pi$
$739$	1.65254	−	11.4937i	0.0607898	−	0.422802i	0.997378	−	0.0723700i	$-0.0230562\pi$
$740$	−8.72375	+	7.51581i	−0.320691	+	0.276287i
$741$	30.1926	−	11.4601i	1.10915	−	0.420997i
$742$	−33.0204	−	21.2873i	−1.21222	−	0.781483i
$743$	32.6868	+	37.7225i	1.19916	+	1.38391i	0.903487	+	0.428616i	$0.140999\pi$
$743$	32.6868	+	37.7225i	1.19916	+	1.38391i	0.295674	+	0.955289i	$0.404456\pi$
$744$	11.4613	+	30.5887i	0.420191	+	1.12144i
$745$	−9.24125	−	2.71348i	−0.338573	−	0.0994141i
$746$	−4.92667	+	33.9230i	−0.180378	+	1.24201i
$747$	12.5707	−	28.3882i	0.459936	−	1.03867i
$748$	−28.1376	+	17.9700i	−1.02881	+	0.657047i
$749$	−1.59849	+	1.84475i	−0.0584074	+	0.0674058i
$750$	21.1027	−	7.97553i	0.770561	−	0.291225i
$751$	−13.9920	+	2.01174i	−0.510574	+	0.0734095i	−0.392787	−	0.919629i	$-0.628489\pi$
$751$	−13.9920	+	2.01174i	−0.510574	+	0.0734095i	−0.117787	+	0.993039i	$0.537580\pi$
$752$	0.150125	−	1.00356i	0.00547449	−	0.0365960i
$753$	11.0753	+	20.0075i	0.403605	+	0.729115i
$754$	−3.40055	+	3.91318i	−0.123841	+	0.142510i
$755$	9.82139	+	4.48528i	0.357437	+	0.163236i
$756$	49.2911	+	17.5770i	1.79270	+	0.639268i
$757$	19.3577	+	30.1211i	0.703566	+	1.09477i	0.990592	+	0.136847i	$0.0436969\pi$
$757$	19.3577	+	30.1211i	0.703566	+	1.09477i	−0.287026	+	0.957923i	$0.592667\pi$
$758$	−9.91358	−	15.4742i	−0.360077	−	0.562048i
$759$	13.1011	+	29.4832i	0.475541	+	1.07017i
$760$	19.0875	−	2.66125i	0.692376	−	0.0965337i
$761$	−9.88856	−	15.3869i	−0.358460	−	0.557775i	0.614451	−	0.788955i	$-0.289378\pi$
$761$	−9.88856	−	15.3869i	−0.358460	−	0.557775i	−0.972911	+	0.231180i	$0.925741\pi$
$762$	4.30611	−	2.37567i	0.155994	−	0.0860613i
$763$	−17.2378	+	37.7456i	−0.624052	+	1.36648i
$764$	1.42589	−	9.72081i	0.0515869	−	0.351687i
$765$	−11.0929	+	7.31116i	−0.401063	+	0.264336i
$766$	2.75429	−	9.33112i	0.0995167	−	0.337147i
$767$	0.804509	+	5.59549i	0.0290492	+	0.202041i
$768$	25.9107	+	9.83028i	0.934973	+	0.354720i
$769$	9.17785	−	10.5918i	0.330962	−	0.381950i	−0.565741	−	0.824583i	$-0.691410\pi$
$769$	9.17785	−	10.5918i	0.330962	−	0.381950i	0.896703	+	0.442633i	$0.145955\pi$
$770$	0.0405556	−	28.4998i	0.00146152	−	1.02706i
$771$	18.1848	+	9.79389i	0.654910	+	0.352718i
$772$	−12.2837	−	27.1013i	−0.442099	−	0.975398i
$773$	−6.61086	−	1.94113i	−0.237776	−	0.0698174i	0.160673	−	0.987008i	$-0.448633\pi$
$773$	−6.61086	−	1.94113i	−0.237776	−	0.0698174i	−0.398450	+	0.917190i	$0.630452\pi$
$774$	−15.0990	+	17.7855i	−0.542721	+	0.639286i
$775$	−19.8459	+	17.1966i	−0.712885	+	0.617719i
$776$	−2.24699	−	3.52942i	−0.0806621	−	0.126699i
$777$	−17.2942	−	45.5630i	−0.620425	−	1.63456i
$778$	33.2915	−	4.73825i	1.19356	−	0.169875i
$779$	−39.5958	−	5.69302i	−1.41867	−	0.203974i
$780$	−2.16799	−	9.82769i	−0.0776264	−	0.351888i
$781$			9.75021i			0.348890i
$782$	14.4140	−	25.3368i	0.515445	−	0.906041i
$783$	−1.55007	−	6.57554i	−0.0553951	−	0.234991i
$784$	70.3349	+	21.0878i	2.51196	+	0.753136i
$785$	−22.5920	−	3.24824i	−0.806343	−	0.115935i
$786$	−23.1274	+	5.13643i	−0.824927	+	0.183210i
$787$	−12.0113	+	3.52685i	−0.428158	+	0.125719i	−0.488710	−	0.872446i	$-0.662532\pi$
$787$	−12.0113	+	3.52685i	−0.428158	+	0.125719i	0.0605514	+	0.998165i	$0.480714\pi$
$788$	−5.65446	−	0.0160928i	−0.201432	−	0.000573281i
$789$	−30.8899	+	31.2484i	−1.09971	+	1.11247i
$790$	−4.85223	−	5.61590i	−0.172635	−	0.199805i
$791$	−56.5705	−	16.6106i	−2.01142	−	0.590605i
$792$	30.0773	+	13.4725i	1.06875	+	0.478724i
$793$	20.5273	+	13.1921i	0.728947	+	0.468466i
$794$	49.6143	+	0.0706019i	1.76075	+	0.00250557i
$795$	−7.91582	−	5.85475i	−0.280745	−	0.207647i
$796$	11.4646	+	9.99137i	0.406351	+	0.354135i
$797$	2.94400	+	20.4760i	0.104282	+	0.725296i	0.973136	+	0.230229i	$0.0739475\pi$
$797$	2.94400	+	20.4760i	0.104282	+	0.725296i	−0.868855	+	0.495067i	$0.835143\pi$
$798$	−16.9916	+	79.7769i	−0.601497	+	2.82407i
$799$	−0.991771	+	0.452927i	−0.0350864	+	0.0160234i
$800$	−0.158511	+	22.2779i	−0.00560422	+	0.787642i
$801$	52.9692	+	14.8915i	1.87157	+	0.526166i
$802$	13.2396	+	29.1002i	0.467507	+	1.02757i
$803$	−21.1316	−	32.8815i	−0.745719	−	1.16036i
$804$	−2.30132	−	0.850695i	−0.0811614	−	0.0300017i
$805$	11.5741	+	22.0279i	0.407934	+	0.776383i
$806$	14.3425	+	22.3873i	0.505192	+	0.788558i
$807$	12.5724	+	16.5943i	0.442568	+	0.584146i
$808$	0.0977697	−	22.9019i	0.00343953	−	0.805686i
$809$	44.4483	+	20.2988i	1.56272	+	0.713670i	0.994053	−	0.108899i	$-0.0347326\pi$
$809$	44.4483	+	20.2988i	1.56272	+	0.713670i	0.568665	+	0.822569i	$0.307460\pi$
$810$	12.0447	+	5.18845i	0.423206	+	0.182304i
$811$	−2.28167	−	4.99617i	−0.0801204	−	0.175439i	0.865332	−	0.501198i	$-0.167107\pi$
$811$	−2.28167	−	4.99617i	−0.0801204	−	0.175439i	−0.945453	+	0.325759i	$0.894380\pi$
$812$	−3.65324	−	12.5741i	−0.128203	−	0.441263i
$813$	10.1046	+	45.1933i	0.354384	+	1.58500i
$814$	−8.60498	−	29.4609i	−0.301604	−	1.03260i
$815$	0.372350	−	0.429715i	0.0130429	−	0.0150523i
$816$	−6.33176	−	29.0959i	−0.221656	−	1.01856i
$817$	−30.5912	−	19.6598i	−1.07025	−	0.687809i
$818$	−39.3394	−	5.71330i	−1.37547	−	0.199761i
$819$	42.2278	+	5.57495i	1.47556	+	0.194804i
$820$	−3.54617	+	11.9512i	−0.123838	+	0.417355i
$821$	−10.3617	−	11.9581i	−0.361627	−	0.417340i	0.545557	−	0.838074i	$-0.316318\pi$
$821$	−10.3617	−	11.9581i	−0.361627	−	0.417340i	−0.907184	+	0.420734i	$0.861773\pi$
$822$	12.5790	−	23.2766i	0.438742	−	0.811864i
$823$	5.78979	+	19.7182i	0.201819	+	0.687334i	0.996744	+	0.0806262i	$0.0256920\pi$
$823$	5.78979	+	19.7182i	0.201819	+	0.687334i	−0.794925	+	0.606708i	$0.792490\pi$
$824$	0.440284	+	0.131323i	0.0153380	+	0.00457486i
$825$	−1.73759	+	26.4371i	−0.0604950	+	0.920422i
$826$	−12.9792	−	5.94974i	−0.451604	−	0.207018i
$827$		−	22.2119i		−	0.772385i	−0.922418	−	0.386192i	$-0.873790\pi$
$827$		−	22.2119i		−	0.772385i	0.922418	−	0.386192i	$-0.126210\pi$
$828$	−28.7159	+	1.84255i	−0.997948	+	0.0640329i
$829$			26.2362i			0.911220i	0.890179	+	0.455610i	$0.150579\pi$
$829$			26.2362i			0.911220i	−0.890179	+	0.455610i	$0.849421\pi$
$830$	6.28411	−	13.7086i	0.218125	−	0.475834i
$831$	0.514811	−	7.83278i	0.0178586	−	0.271716i
$832$	22.2986	+	3.40062i	0.773065	+	0.117895i
$833$	−22.2279	−	75.7012i	−0.770150	−	2.62289i
$834$	−34.9448	−	18.8846i	−1.21004	−	0.653921i
$835$	10.6735	+	12.3179i	0.369371	+	0.426277i
$836$	−14.6123	+	49.2462i	−0.505379	+	1.70321i
$837$	−34.5962	−	1.87323i	−1.19582	−	0.0647484i
$838$	3.87551	−	26.6852i	0.133877	−	0.921824i
$839$	6.59861	+	4.24067i	0.227809	+	0.146404i	0.649567	−	0.760305i	$-0.274950\pi$
$839$	6.59861	+	4.24067i	0.227809	+	0.146404i	−0.421758	+	0.906709i	$0.638587\pi$
$840$	23.8294	+	8.84720i	0.822191	+	0.305257i
$841$	17.8840	−	20.6392i	0.616689	−	0.711698i
$842$	5.08884	−	1.48636i	0.175373	−	0.0512232i
$843$	2.44792	+	10.9484i	0.0843109	+	0.377084i
$844$	−1.17406	+	0.341107i	−0.0404127	+	0.0117414i
$845$	2.16164	+	4.73332i	0.0743625	+	0.162831i
$846$	0.911261	+	0.572691i	0.0313298	+	0.0196895i
$847$	18.7136	+	8.54624i	0.643008	+	0.293652i
$848$	18.6318	−	11.8246i	0.639817	−	0.406058i
$849$	−10.7435	−	14.1804i	−0.368716	−	0.486669i
$850$	20.1561	−	12.9130i	0.691348	−	0.442914i
$851$	18.6427	+	19.2496i	0.639065	+	0.659869i
$852$	−8.15666	−	3.01515i	−0.279443	−	0.103297i
$853$	−23.8896	−	37.1730i	−0.817966	−	1.27278i	−0.959179	−	0.282800i	$-0.908737\pi$
$853$	−23.8896	−	37.1730i	−0.817966	−	1.27278i	0.141213	−	0.989979i	$-0.454900\pi$
$854$	−56.0967	+	25.5221i	−1.91959	+	0.873348i
$855$	−5.53227	+	19.6783i	−0.189200	+	0.672984i
$856$	−0.564229	−	1.24958i	−0.0192849	−	0.0427097i
$857$	36.7405	−	16.7788i	1.25503	−	0.573154i	0.326778	−	0.945101i	$-0.394037\pi$
$857$	36.7405	−	16.7788i	1.25503	−	0.573154i	0.928254	+	0.371947i	$0.121310\pi$
$858$	26.2362	+	5.58804i	0.895691	+	0.190773i
$859$	2.80485	+	19.5082i	0.0957002	+	0.665610i	0.980045	+	0.198775i	$0.0636965\pi$
$859$	2.80485	+	19.5082i	0.0957002	+	0.665610i	−0.884345	+	0.466834i	$0.845394\pi$
$860$	−7.44533	+	8.54312i	−0.253884	+	0.291318i
$861$	−42.4194	−	31.3746i	−1.44565	−	1.06924i
$862$	−0.0657793	+	46.2254i	−0.00224045	+	1.57444i
$863$	15.6689	+	10.0698i	0.533375	+	0.342779i	0.779443	−	0.626473i	$-0.215502\pi$
$863$	15.6689	+	10.0698i	0.533375	+	0.342779i	−0.246068	+	0.969253i	$0.579139\pi$
$864$	−20.5717	+	20.9954i	−0.699863	+	0.714277i
$865$	16.5199	+	4.85069i	0.561695	+	0.164928i
$866$	36.9956	−	31.9648i	1.25716	−	1.08621i
$867$	−1.79250	+	1.81330i	−0.0608765	+	0.0615829i
$868$	−67.1522	−	0.191117i	−2.27929	−	0.00648694i
$869$	18.9808	−	5.57327i	0.643880	−	0.189060i
$870$	−0.711454	−	3.20341i	−0.0241205	−	0.108606i
$871$	−1.97668	−	0.284204i	−0.0669772	−	0.00962987i
$872$	−15.1879	−	17.6797i	−0.514326	−	0.598709i
$873$	4.38504	−	0.682202i	0.148411	−	0.0230890i
$874$	−8.76796	−	43.9849i	−0.296581	−	1.48781i
$875$			46.3771i			1.56783i
$876$	34.0421	−	7.50970i	1.15018	−	0.253729i
$877$	33.2448	+	4.77988i	1.12260	+	0.161405i	0.678519	−	0.734583i	$-0.262622\pi$
$877$	33.2448	+	4.77988i	1.12260	+	0.161405i	0.444078	+	0.895988i	$0.353531\pi$
$878$	−2.20300	−	15.4785i	−0.0743477	−	0.522375i
$879$	3.85824	+	10.1649i	0.130135	+	0.342852i
$880$	14.5233	+	6.73276i	0.489582	+	0.226961i
$881$	−0.929376	+	0.805309i	−0.0313115	+	0.0271315i	−0.670376	−	0.742022i	$-0.733867\pi$
$881$	−0.929376	+	0.805309i	−0.0313115	+	0.0271315i	0.639064	+	0.769153i	$0.279322\pi$
$882$	−50.4041	+	59.3724i	−1.69720	+	1.99917i
$883$	34.5059	+	10.1319i	1.16122	+	0.340964i	0.804905	−	0.593403i	$-0.202216\pi$
$883$	34.5059	+	10.1319i	1.16122	+	0.340964i	0.356311	+	0.934367i	$0.384034\pi$
$884$	−10.0054	−	22.0748i	−0.336517	−	0.742455i
$885$	−3.15032	−	1.69668i	−0.105897	−	0.0570334i
$886$	55.2408	+	0.0786084i	1.85585	+	0.00264090i
$887$	24.6922	−	28.4963i	0.829084	−	0.956814i	−0.170509	−	0.985356i	$-0.554541\pi$
$887$	24.6922	−	28.4963i	0.829084	−	0.956814i	0.999593	+	0.0285425i	$0.00908661\pi$
$888$	27.3069	+	1.91186i	0.916359	+	0.0641579i
$889$	1.43883	+	10.0073i	0.0482568	+	0.335633i
$890$	25.6327	+	7.56607i	0.859209	+	0.253615i
$891$	−25.8828	+	23.4948i	−0.867106	+	0.787106i
$892$	26.0391	+	3.81952i	0.871853	+	0.127887i
$893$	−0.696877	+	1.52595i	−0.0233201	+	0.0510639i
$894$	11.0603	+	20.0477i	0.369911	+	0.670497i
$895$	−3.16136	−	4.91917i	−0.105673	−	0.164430i
$896$	−37.7351	+	42.6821i	−1.26064	+	1.42591i
$897$	−22.5387	+	6.36785i	−0.752545	+	0.212616i
$898$	3.73338	−	2.39180i	0.124585	−	0.0798154i
$899$	4.68689	+	7.29294i	0.156316	+	0.243233i
$900$	−21.5790	−	9.62900i	−0.719300	−	0.320967i
$901$	−21.5681	−	9.84982i	−0.718538	−	0.328145i
$902$	−25.0809	−	21.7953i	−0.835102	−	0.725704i
$903$	−23.2280	−	41.9616i	−0.772980	−	1.39640i
$904$	21.7933	−	24.9349i	0.724835	−	0.829324i
$905$	24.6205	−	3.53989i	0.818412	−	0.117670i
$906$	−9.07432	−	24.0100i	−0.301474	−	0.797678i
$907$	13.4354	−	15.5053i	0.446115	−	0.514844i	−0.487499	−	0.873123i	$-0.662091\pi$
$907$	13.4354	−	15.5053i	0.446115	−	0.514844i	0.933615	+	0.358279i	$0.116636\pi$
$908$	16.3587	+	25.6146i	0.542882	+	0.850051i
$909$	22.2112	+	9.83538i	0.736698	+	0.326219i
$910$	20.4744	+	2.97352i	0.678720	+	0.0985711i
$911$	−3.90891	−	1.14776i	−0.129508	−	0.0380269i	0.216336	−	0.976319i	$-0.430589\pi$
$911$	−3.90891	−	1.14776i	−0.129508	−	0.0380269i	−0.345844	+	0.938292i	$0.612407\pi$
$912$	−36.6788	−	27.4530i	−1.21456	−	0.909060i
$913$	26.3224	+	30.3777i	0.871145	+	1.00535i
$914$	−2.18714	+	3.39263i	−0.0723441	+	0.112218i
$915$	−14.4397	+	5.48083i	−0.477362	+	0.181191i
$916$	−6.96616	+	6.00158i	−0.230168	+	0.198298i
$917$	6.93116	−	48.2073i	0.228887	−	1.59194i
$918$	30.9641	+	6.22244i	1.02197	+	0.205371i
$919$			25.5850i			0.843971i	0.906603	+	0.421986i	$0.138667\pi$
$919$			25.5850i			0.843971i	−0.906603	+	0.421986i	$0.861333\pi$
$920$	−13.9585	+	0.714122i	−0.460200	+	0.0235439i
$921$	−2.14990	−	27.8043i	−0.0708415	−	0.916184i
$922$	−44.4641	−	20.3826i	−1.46435	−	0.671265i
$923$	−7.00602	−	1.00731i	−0.230606	−	0.0331561i
$924$	−47.7674	+	48.0474i	−1.57143	+	1.58064i
$925$	6.19977	+	21.1145i	0.203847	+	0.694240i
$926$	−12.3846	−	7.98400i	−0.406982	−	0.262370i
$927$	−0.314857	+	0.371951i	−0.0103413	+	0.0122165i
$928$	7.27226	+	1.09846i	0.238724	+	0.0360587i
$929$	4.73282	−	16.1185i	0.155279	−	0.528831i	−0.844701	−	0.535239i	$-0.820221\pi$
$929$	4.73282	−	16.1185i	0.155279	−	0.528831i	0.999979	+	0.00640780i	$0.00203968\pi$
$930$	−16.7911	−	1.12760i	−0.550603	−	0.0369755i
$931$	−102.121	−	65.6293i	−3.34688	−	2.15091i
$932$	−27.4496	−	42.9809i	−0.899142	−	1.40789i
$933$	29.0443	+	21.4820i	0.950869	+	0.703289i
$934$	−15.9501	+	4.65872i	−0.521903	+	0.152438i
$935$	−2.44786	−	17.0252i	−0.0800536	−	0.556785i
$936$	−12.7880	+	20.2202i	−0.417990	+	0.660919i
$937$	−0.956313	−	2.09403i	−0.0312414	−	0.0684091i	0.893368	−	0.449326i	$-0.148336\pi$
$937$	−0.956313	−	2.09403i	−0.0312414	−	0.0684091i	−0.924609	+	0.380917i	$0.875608\pi$
$938$	3.30845	−	3.80719i	0.108025	−	0.124309i
$939$	−7.99157	−	2.92830i	−0.260795	−	0.0955614i
$940$	0.438982	+	0.283885i	0.0143180	+	0.00925932i
$941$	25.6316	−	16.4725i	0.835568	−	0.536987i	−0.0514749	−	0.998674i	$-0.516392\pi$
$941$	25.6316	−	16.4725i	0.835568	−	0.536987i	0.887043	+	0.461687i	$0.152756\pi$
$942$	32.7049	+	43.2951i	1.06558	+	1.41063i
$943$	28.2461	+	6.62004i	0.919821	+	0.215578i
$944$	6.09072	−	5.21723i	0.198236	−	0.169806i
$945$	−18.7313	+	19.3911i	−0.609328	+	0.630793i
$946$	−12.5085	−	27.4932i	−0.406686	−	0.893883i
$947$	−6.07393	−	2.77387i	−0.197376	−	0.0901387i	0.314275	−	0.949332i	$-0.398239\pi$
$947$	−6.07393	−	2.77387i	−0.197376	−	0.0901387i	−0.511651	+	0.859193i	$0.670966\pi$
$948$	−1.20722	+	17.6021i	−0.0392088	+	0.571690i
$949$	25.8102	−	11.7871i	0.837833	−	0.382626i
$950$	10.4267	−	35.3241i	0.338287	−	1.14606i
$951$	−12.0565	+	2.69567i	−0.390959	+	0.0874131i
$952$	60.5534	+	8.97028i	1.96255	+	0.290728i
$953$	−25.5226	−	22.1155i	−0.826758	−	0.716390i	0.134835	−	0.990868i	$-0.456950\pi$
$953$	−25.5226	−	22.1155i	−0.826758	−	0.716390i	−0.961593	+	0.274478i	$0.911495\pi$
$954$	3.56517	+	23.1327i	0.115427	+	0.748950i
$955$	4.25815	+	2.73655i	0.137790	+	0.0885525i
$956$	−14.5959	−	32.2027i	−0.472064	−	1.04151i
$957$	8.55718	+	1.80986i	0.276614	+	0.0585045i
$958$	−19.4853	+	16.8356i	−0.629542	+	0.543934i
$959$	35.6189	+	41.1064i	1.15020	+	1.32740i
$960$	−10.1236	+	10.0677i	−0.326737	+	0.324932i
$961$	12.9144	−	3.79200i	0.416592	−	0.122323i
$962$	22.0582	−	3.13945i	0.711183	−	0.101220i
$963$	1.45413	−	0.0167786i	0.0468587	−	0.000540681i
$964$	4.39891	+	31.2257i	0.141679	+	1.00571i
$965$	15.3296			0.493478
$966$	17.3270	−	56.5601i	0.557486	−	1.81979i
$967$		−	1.66903i		−	0.0536722i	−0.999640	−	0.0268361i	$-0.991457\pi$
$967$		−	1.66903i		−	0.0536722i	0.999640	−	0.0268361i	$-0.00854323\pi$
$968$	−8.76528	+	7.52989i	−0.281727	+	0.242020i
$969$	−3.22850	+	49.1211i	−0.103714	+	1.57800i
$970$	2.13405	−	0.303731i	0.0685202	−	0.00975221i
$971$	−9.43435	−	32.1304i	−0.302763	−	1.03112i	−0.960595	−	0.277951i	$-0.910345\pi$
$971$	−9.43435	−	32.1304i	−0.302763	−	1.03112i	0.657833	−	0.753164i	$-0.271473\pi$
$972$	−11.6509	−	28.9181i	−0.373703	−	0.927548i
$973$	61.7125	−	53.4742i	1.97841	−	1.71431i
$974$	22.9014	+	26.5058i	0.733809	+	0.849300i
$975$	−18.8169	−	3.97982i	−0.602623	−	0.127456i
$976$	0.197039	−	34.6161i	0.00630706	−	1.10804i
$977$	−2.32723	+	3.62124i	−0.0744547	+	0.115854i	−0.876484	−	0.481431i	$-0.840117\pi$
$977$	−2.32723	+	3.62124i	−0.0744547	+	0.115854i	0.802029	+	0.597284i	$0.203754\pi$
$978$	−1.34782	+	0.102288i	−0.0430986	+	0.00327080i
$979$	−46.6497	+	53.8366i	−1.49093	+	1.72063i
$980$	−24.8544	+	28.5191i	−0.793944	+	0.911008i
$981$	23.6381	−	7.23803i	0.754705	−	0.231093i
$982$	34.0732	+	10.0575i	1.08732	+	0.320948i
$983$	−11.9363	−	26.1369i	−0.380709	−	0.833637i	−0.998867	−	0.0475833i	$-0.984848\pi$
$983$	−11.9363	−	26.1369i	−0.380709	−	0.833637i	0.618158	−	0.786054i	$-0.287879\pi$
$984$	25.9891	−	14.2418i	0.828503	−	0.454012i
$985$	1.21016	−	2.64989i	0.0385590	−	0.0844324i
$986$	−3.27260	−	7.19306i	−0.104221	−	0.229074i
$987$	−1.76358	+	1.33614i	−0.0561353	+	0.0425299i
$988$	−33.8763	−	15.5874i	−1.07775	−	0.495902i
$989$	20.8563	+	16.1404i	0.663192	+	0.513235i
$990$	−12.7188	+	11.2482i	−0.404231	+	0.357490i
$991$	11.0673	+	17.2211i	0.351566	+	0.547047i	0.971328	−	0.237742i	$-0.0764074\pi$
$991$	11.0673	+	17.2211i	0.351566	+	0.547047i	−0.619763	+	0.784789i	$0.712771\pi$
$992$	15.9127	−	34.1979i	0.505228	−	1.08578i
$993$	27.7929	+	10.1840i	0.881981	+	0.323178i
$994$	11.7263	−	13.4940i	0.371934	−	0.428003i
$995$	−7.12670	+	3.25465i	−0.225932	+	0.103179i
$996$	−33.5528	+	12.6264i	−1.06316	+	0.400082i
$997$	44.9182	−	6.45827i	1.42257	−	0.204535i	0.612319	−	0.790611i	$-0.290237\pi$
$997$	44.9182	−	6.45827i	1.42257	−	0.204535i	0.810256	+	0.586076i	$0.199328\pi$
$998$	9.15078	+	31.3295i	0.289663	+	0.991719i
$999$	−13.4715	+	25.7197i	−0.426221	+	0.813736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.14	✓	920
3.2	odd	2	inner	552.2.x.a.35.79	yes	920
8.3	odd	2	inner	552.2.x.a.35.46	yes	920
23.2	even	11	inner	552.2.x.a.347.47	yes	920
24.11	even	2	inner	552.2.x.a.35.47	yes	920
69.2	odd	22	inner	552.2.x.a.347.46	yes	920
184.163	odd	22	inner	552.2.x.a.347.79	yes	920
552.347	even	22	inner	552.2.x.a.347.14	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.14	✓	920	1.1	even	1	trivial
552.2.x.a.35.46	yes	920	8.3	odd	2	inner
552.2.x.a.35.47	yes	920	24.11	even	2	inner
552.2.x.a.35.79	yes	920	3.2	odd	2	inner
552.2.x.a.347.14	yes	920	552.347	even	22	inner
552.2.x.a.347.46	yes	920	69.2	odd	22	inner
552.2.x.a.347.47	yes	920	23.2	even	11	inner
552.2.x.a.347.79	yes	920	184.163	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.28558 - 0.589316i) q^{2} +(-1.72832 - 0.113594i) q^{3} +(1.30541 + 1.51522i) q^{4} +(-0.988646 + 0.290293i) q^{5} +(2.15495 + 1.16456i) q^{6} +(-3.80564 + 3.29760i) q^{7} +(-0.785267 - 2.71723i) q^{8} +(2.97419 + 0.392655i) q^{9} +O(q^{10})\)	\(q+(-1.28558 - 0.589316i) q^{2} +(-1.72832 - 0.113594i) q^{3} +(1.30541 + 1.51522i) q^{4} +(-0.988646 + 0.290293i) q^{5} +(2.15495 + 1.16456i) q^{6} +(-3.80564 + 3.29760i) q^{7} +(-0.785267 - 2.71723i) q^{8} +(2.97419 + 0.392655i) q^{9} +(1.44205 + 0.209431i) q^{10} +(-2.09985 + 3.26743i) q^{11} +(-2.08406 - 2.76708i) q^{12} +(-2.13088 - 1.84641i) q^{13} +(6.83576 - 1.99660i) q^{14} +(1.74167 - 0.389414i) q^{15} +(-0.591786 + 3.95598i) q^{16} +(3.90952 - 1.78542i) q^{17} +(-3.59215 - 2.25753i) q^{18} +(2.74706 - 6.01522i) q^{19} +(-1.73045 - 1.11906i) q^{20} +(6.95195 - 5.26702i) q^{21} +(4.62507 - 2.96306i) q^{22} +(-2.36551 + 4.17185i) q^{23} +(1.04853 + 4.78546i) q^{24} +(-3.31312 + 2.12921i) q^{25} +(1.65128 + 3.62947i) q^{26} +(-5.09576 - 1.01649i) q^{27} +(-9.96453 - 1.46164i) q^{28} +(0.540101 + 1.18266i) q^{29} +(-2.46854 - 0.525773i) q^{30} +(6.59993 - 0.948927i) q^{31} +(3.09211 - 4.73697i) q^{32} +(4.00038 - 5.40864i) q^{33} +(-6.07817 - 0.00864931i) q^{34} +(2.80516 - 4.36491i) q^{35} +(3.28759 + 5.01914i) q^{36} +(1.57422 - 5.36130i) q^{37} +(-7.07642 + 6.11414i) q^{38} +(3.47310 + 3.43325i) q^{39} +(1.56514 + 2.45842i) q^{40} +(-1.70429 - 5.80428i) q^{41} +(-12.0412 + 2.67426i) q^{42} +(0.782590 - 5.44303i) q^{43} +(-7.69205 + 1.08362i) q^{44} +(-3.05441 + 0.475189i) q^{45} +(5.49958 - 3.96920i) q^{46} -0.253681 q^{47} +(1.47217 - 6.76999i) q^{48} +(2.61248 - 18.1702i) q^{49} +(5.51404 - 0.784793i) q^{50} +(-6.95973 + 2.64168i) q^{51} +(0.0160490 - 5.63908i) q^{52} +(-3.61274 - 4.16933i) q^{53} +(5.95196 + 4.30978i) q^{54} +(1.12750 - 3.83990i) q^{55} +(11.9488 + 7.75130i) q^{56} +(-5.43110 + 10.0842i) q^{57} +(0.00261648 - 1.83869i) q^{58} +(-1.51523 - 1.31295i) q^{59} +(2.86365 + 2.13067i) q^{60} +(-8.56608 + 1.23162i) q^{61} +(-9.04394 - 2.66952i) q^{62} +(-12.6135 + 8.31340i) q^{63} +(-6.76671 + 4.26751i) q^{64} +(2.64268 + 1.20687i) q^{65} +(-8.33019 + 4.59574i) q^{66} +(0.595835 - 0.382920i) q^{67} +(7.80885 + 3.59308i) q^{68} +(4.56226 - 6.94160i) q^{69} +(-6.17855 + 3.95830i) q^{70} +(2.11184 - 1.35720i) q^{71} +(-1.26860 - 8.38991i) q^{72} +(-4.18049 + 9.15399i) q^{73} +(-5.18328 + 5.96465i) q^{74} +(5.96800 - 3.30361i) q^{75} +(12.7004 - 3.68996i) q^{76} +(-2.78342 - 19.3591i) q^{77} +(-2.44166 - 6.46046i) q^{78} +(-3.84921 - 3.33536i) q^{79} +(-0.563325 - 4.08285i) q^{80} +(8.69164 + 2.33566i) q^{81} +(-1.22956 + 8.46622i) q^{82} +(2.91564 - 9.92977i) q^{83} +(17.0559 + 3.65810i) q^{84} +(-3.34684 + 2.90005i) q^{85} +(-4.21374 + 6.53624i) q^{86} +(-0.799126 - 2.10536i) q^{87} +(10.5273 + 3.13998i) q^{88} +(18.1542 + 2.61018i) q^{89} +(4.20671 + 1.18912i) q^{90} +14.1981 q^{91} +(-9.40925 + 1.86173i) q^{92} +(-11.5146 + 0.890336i) q^{93} +(0.326126 + 0.149498i) q^{94} +(-0.969694 + 6.74437i) q^{95} +(-5.88225 + 7.83576i) q^{96} +(1.41934 - 0.416756i) q^{97} +(-14.0665 + 21.8196i) q^{98} +(-7.52833 + 8.89345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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