LMFDB - Embedded newform 297.2.x.a.2.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(2,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(90)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.x (of order $90$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	297.2
Dual form			297.2.x.a.149.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.85576 - 0.986723i) q^{2} +(-1.57006 + 0.731366i) q^{3} +(1.35182 + 2.00416i) q^{4} +(2.23335 - 3.57411i) q^{5} +(3.63531 + 0.191982i) q^{6} +(-0.641535 + 2.23730i) q^{7} +(-0.0917117 - 0.872579i) q^{8} +(1.93021 - 2.29658i) q^{9} +(-7.67120 + 4.42897i) q^{10} +(0.754763 + 3.22960i) q^{11} +(-3.58822 - 2.15798i) q^{12} +(-0.216980 + 1.54389i) q^{13} +(3.39812 - 3.51886i) q^{14} +(-0.892523 + 7.24497i) q^{15} +(1.12039 - 2.77305i) q^{16} +(1.79691 - 1.99567i) q^{17} +(-5.84808 + 2.35732i) q^{18} +(2.39149 - 0.251356i) q^{19} +(10.1822 - 0.355569i) q^{20} +(-0.629032 - 3.98190i) q^{21} +(1.78607 - 6.73809i) q^{22} +(2.11845 - 5.82039i) q^{23} +(0.782168 + 1.30293i) q^{24} +(-5.59453 - 11.4705i) q^{25} +(1.92605 - 2.65098i) q^{26} +(-1.35091 + 5.01747i) q^{27} +(-5.35113 + 1.73869i) q^{28} +(6.02780 - 5.82098i) q^{29} +(8.80508 - 12.5642i) q^{30} +(1.34723 - 1.72438i) q^{31} +(-6.15963 + 5.16854i) q^{32} +(-3.54705 - 4.51868i) q^{33} +(-5.30380 + 1.93043i) q^{34} +(6.56357 + 7.28958i) q^{35} +(7.21201 + 0.763868i) q^{36} +(-0.780772 + 7.42855i) q^{37} +(-4.68604 - 1.89328i) q^{38} +(-0.788477 - 2.58270i) q^{39} +(-3.32351 - 1.62099i) q^{40} +(-1.64764 - 1.59111i) q^{41} +(-2.76170 + 8.01011i) q^{42} +(5.27201 - 6.28293i) q^{43} +(-5.45233 + 5.87851i) q^{44} +(-3.89741 - 12.0278i) q^{45} +(-9.67443 + 8.71089i) q^{46} +(-4.72012 - 3.18376i) q^{47} +(0.269038 + 5.17329i) q^{48} +(1.34240 + 0.838828i) q^{49} +(-0.936109 + 26.8067i) q^{50} +(-1.36170 + 4.44753i) q^{51} +(-3.38752 + 1.65220i) q^{52} +(-2.90214 - 0.942963i) q^{53} +(7.45781 - 7.97823i) q^{54} +(13.2286 + 4.51523i) q^{55} +(2.01105 + 0.354603i) q^{56} +(-3.57096 + 2.14370i) q^{57} +(-16.9298 + 4.85454i) q^{58} +(-0.606488 - 8.67318i) q^{59} +(-15.7266 + 8.00515i) q^{60} +(5.91017 - 4.61753i) q^{61} +(-4.20161 + 1.87068i) q^{62} +(3.89985 + 5.79179i) q^{63} +(10.6797 - 2.27005i) q^{64} +(5.03344 + 4.22356i) q^{65} +(2.12377 + 11.8855i) q^{66} +(0.00943758 + 0.0535232i) q^{67} +(6.42874 + 0.903500i) q^{68} +(0.930733 + 10.6877i) q^{69} +(-4.98758 - 20.0041i) q^{70} +(0.520742 + 0.468878i) q^{71} +(-2.18097 - 1.47363i) q^{72} +(4.03548 + 9.06384i) q^{73} +(8.77884 - 13.0152i) q^{74} +(17.1729 + 13.9178i) q^{75} +(3.73662 + 4.45313i) q^{76} +(-7.70979 - 0.383274i) q^{77} +(-1.08519 + 5.57087i) q^{78} +(-6.19132 + 11.6442i) q^{79} +(-7.40898 - 10.1976i) q^{80} +(-1.54860 - 8.86577i) q^{81} +(1.48764 + 4.57847i) q^{82} +(-2.62381 + 0.368752i) q^{83} +(7.13001 - 6.64349i) q^{84} +(-3.11961 - 10.8794i) q^{85} +(-15.9831 + 6.45758i) q^{86} +(-5.20677 + 13.5478i) q^{87} +(2.74886 - 0.954782i) q^{88} +(11.6287 + 6.71382i) q^{89} +(-4.63551 + 26.1664i) q^{90} +(-3.31494 - 1.47591i) q^{91} +(14.5287 - 3.62242i) q^{92} +(-0.854089 + 3.69270i) q^{93} +(5.61790 + 10.5657i) q^{94} +(4.44266 - 9.10880i) q^{95} +(5.89092 - 12.6199i) q^{96} +(3.84112 - 2.40020i) q^{97} +(-1.66348 - 2.88124i) q^{98} +(8.87390 + 4.50043i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 30 q^{2} - 18 q^{3} - 18 q^{4} - 21 q^{5} - 30 q^{6} - 30 q^{7} - 45 q^{8} - 36 q^{9} - 33 q^{11} - 30 q^{12} - 30 q^{13} - 18 q^{14} - 21 q^{15} - 30 q^{16} - 45 q^{17} - 15 q^{19} - 60 q^{20}+ \cdots + 3 q^{99}+O(q^{100}) $ 816 * q - 30 * q^2 - 18 * q^3 - 18 * q^4 - 21 * q^5 - 30 * q^6 - 30 * q^7 - 45 * q^8 - 36 * q^9 - 33 * q^11 - 30 * q^12 - 30 * q^13 - 18 * q^14 - 21 * q^15 - 30 * q^16 - 45 * q^17 - 15 * q^19 - 60 * q^20 - 15 * q^22 - 84 * q^23 - 30 * q^24 - 27 * q^25 + 36 * q^27 - 60 * q^28 + 60 * q^29 - 75 * q^30 - 9 * q^31 - 63 * q^33 - 42 * q^34 - 45 * q^35 + 36 * q^36 - 9 * q^37 - 18 * q^38 - 150 * q^39 - 90 * q^40 - 30 * q^41 - 66 * q^42 - 108 * q^44 + 24 * q^45 - 15 * q^46 - 6 * q^47 + 174 * q^48 - 18 * q^49 - 105 * q^50 - 30 * q^51 - 30 * q^52 - 48 * q^55 + 54 * q^56 - 75 * q^57 - 18 * q^58 + 81 * q^59 - 72 * q^60 - 30 * q^61 - 45 * q^62 - 30 * q^63 + 51 * q^64 - 75 * q^66 + 6 * q^67 - 225 * q^68 + 9 * q^69 - 93 * q^70 - 27 * q^71 - 30 * q^72 - 15 * q^73 - 30 * q^74 + 42 * q^75 - 141 * q^77 + 30 * q^78 - 30 * q^79 + 48 * q^81 - 36 * q^82 + 15 * q^83 + 90 * q^84 - 30 * q^85 + 93 * q^86 - 108 * q^88 + 54 * q^89 - 15 * q^90 - 9 * q^91 + 276 * q^92 + 87 * q^93 - 30 * q^94 + 90 * q^95 + 90 * q^96 - 81 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.85576	−	0.986723i	−1.31222	−	0.697718i	−0.341942	−	0.939721i	$-0.611085\pi$
$2$	−1.85576	−	0.986723i	−1.31222	−	0.697718i	−0.970276	+	0.242003i	$0.922196\pi$
$3$	−1.57006	+	0.731366i	−0.906477	+	0.422254i
$3$	−1.57006	+	0.731366i	−0.906477	+	0.422254i
$4$	1.35182	+	2.00416i	0.675910	+	1.00208i
$5$	2.23335	−	3.57411i	0.998784	−	1.59839i	0.215713	−	0.976457i	$-0.430793\pi$
$5$	2.23335	−	3.57411i	0.998784	−	1.59839i	0.783071	−	0.621932i	$-0.213652\pi$
$6$	3.63531	+	0.191982i	1.48411	+	0.0783764i
$7$	−0.641535	+	2.23730i	−0.242477	+	0.845619i	0.742044	+	0.670352i	$0.233857\pi$
$7$	−0.641535	+	2.23730i	−0.242477	+	0.845619i	−0.984521	+	0.175267i	$0.943921\pi$
$8$	−0.0917117	−	0.872579i	−0.0324250	−	0.308503i
$9$	1.93021	−	2.29658i	0.643402	−	0.765528i
$10$	−7.67120	+	4.42897i	−2.42585	+	1.40056i
$11$	0.754763	+	3.22960i	0.227570	+	0.973762i
$11$	0.754763	+	3.22960i	0.227570	+	0.973762i
$12$	−3.58822	−	2.15798i	−1.03583	−	0.622955i
$13$	−0.216980	+	1.54389i	−0.0601793	+	0.428198i	0.936757	+	0.349981i	$0.113812\pi$
$13$	−0.216980	+	1.54389i	−0.0601793	+	0.428198i	−0.996936	+	0.0782177i	$0.975077\pi$
$14$	3.39812	−	3.51886i	0.908187	−	0.940455i
$15$	−0.892523	+	7.24497i	−0.230449	+	1.87064i
$16$	1.12039	−	2.77305i	0.280097	−	0.693264i
$17$	1.79691	−	1.99567i	0.435815	−	0.484021i	−0.484727	−	0.874666i	$-0.661081\pi$
$17$	1.79691	−	1.99567i	0.435815	−	0.484021i	0.920542	+	0.390644i	$0.127748\pi$
$18$	−5.84808	+	2.35732i	−1.37841	+	0.555625i
$19$	2.39149	−	0.251356i	0.548645	−	0.0576649i	0.173849	−	0.984772i	$-0.444379\pi$
$19$	2.39149	−	0.251356i	0.548645	−	0.0576649i	0.374796	+	0.927107i	$0.377713\pi$
$20$	10.1822	−	0.355569i	2.27680	−	0.0795076i
$21$	−0.629032	−	3.98190i	−0.137266	−	0.868921i
$22$	1.78607	−	6.73809i	0.380791	−	1.43657i
$23$	2.11845	−	5.82039i	0.441727	−	1.21363i	−0.496629	−	0.867963i	$-0.665429\pi$
$23$	2.11845	−	5.82039i	0.441727	−	1.21363i	0.938356	−	0.345671i	$-0.112349\pi$
$24$	0.782168	+	1.30293i	0.159659	+	0.265960i
$25$	−5.59453	−	11.4705i	−1.11891	−	2.29410i
$26$	1.92605	−	2.65098i	0.377730	−	0.519901i
$27$	−1.35091	+	5.01747i	−0.259982	+	0.965613i
$28$	−5.35113	+	1.73869i	−1.01127	+	0.328581i
$29$	6.02780	−	5.82098i	1.11933	−	1.08093i	0.123262	−	0.992374i	$-0.460664\pi$
$29$	6.02780	−	5.82098i	1.11933	−	1.08093i	0.996071	−	0.0885538i	$-0.0282245\pi$
$30$	8.80508	−	12.5642i	1.60758	−	2.29390i
$31$	1.34723	−	1.72438i	0.241970	−	0.309707i	−0.651661	−	0.758510i	$-0.725927\pi$
$31$	1.34723	−	1.72438i	0.241970	−	0.309707i	0.893630	+	0.448803i	$0.148150\pi$
$32$	−6.15963	+	5.16854i	−1.08888	+	0.913678i
$33$	−3.54705	−	4.51868i	−0.617462	−	0.786601i
$34$	−5.30380	+	1.93043i	−0.909594	+	0.331065i
$35$	6.56357	+	7.28958i	1.10945	+	1.23216i
$36$	7.21201	+	0.763868i	1.20200	+	0.127311i
$37$	−0.780772	+	7.42855i	−0.128358	+	1.22125i	0.720814	+	0.693129i	$0.243768\pi$
$37$	−0.780772	+	7.42855i	−0.128358	+	1.22125i	−0.849172	+	0.528117i	$0.822898\pi$
$38$	−4.68604	−	1.89328i	−0.760175	−	0.307131i
$39$	−0.788477	−	2.58270i	−0.126257	−	0.413563i
$40$	−3.32351	−	1.62099i	−0.525493	−	0.256300i
$41$	−1.64764	−	1.59111i	−0.257318	−	0.248489i	0.554798	−	0.831985i	$-0.312796\pi$
$41$	−1.64764	−	1.59111i	−0.257318	−	0.248489i	−0.812116	+	0.583496i	$0.801684\pi$
$42$	−2.76170	+	8.01011i	−0.426139	+	1.23599i
$43$	5.27201	−	6.28293i	0.803974	−	0.958139i	−0.195773	−	0.980649i	$-0.562722\pi$
$43$	5.27201	−	6.28293i	0.803974	−	0.958139i	0.999747	+	0.0225107i	$0.00716597\pi$
$44$	−5.45233	+	5.87851i	−0.821969	+	0.886218i
$45$	−3.89741	−	12.0278i	−0.580991	−	1.79300i
$46$	−9.67443	+	8.71089i	−1.42642	+	1.28435i
$47$	−4.72012	−	3.18376i	−0.688500	−	0.464399i	0.164454	−	0.986385i	$-0.447414\pi$
$47$	−4.72012	−	3.18376i	−0.688500	−	0.464399i	−0.852954	+	0.521986i	$0.825191\pi$
$48$	0.269038	+	5.17329i	0.0388323	+	0.746700i
$49$	1.34240	+	0.838828i	0.191772	+	0.119833i
$50$	−0.936109	+	26.8067i	−0.132386	+	3.79103i
$51$	−1.36170	+	4.44753i	−0.190676	+	0.622779i
$52$	−3.38752	+	1.65220i	−0.469764	+	0.229119i
$53$	−2.90214	−	0.942963i	−0.398640	−	0.129526i	0.102835	−	0.994698i	$-0.467209\pi$
$53$	−2.90214	−	0.942963i	−0.398640	−	0.129526i	−0.501474	+	0.865173i	$0.667209\pi$
$54$	7.45781	−	7.97823i	1.01488	−	1.08570i
$55$	13.2286	+	4.51523i	1.78374	+	0.608833i
$56$	2.01105	+	0.354603i	0.268738	+	0.0473858i
$57$	−3.57096	+	2.14370i	−0.472985	+	0.283940i
$58$	−16.9298	+	4.85454i	−2.22299	+	0.637433i
$59$	−0.606488	−	8.67318i	−0.0789580	−	1.12915i	−0.861907	−	0.507066i	$-0.830730\pi$
$59$	−0.606488	−	8.67318i	−0.0789580	−	1.12915i	0.782949	−	0.622086i	$-0.213715\pi$
$60$	−15.7266	+	8.00515i	−2.03029	+	1.03346i
$61$	5.91017	−	4.61753i	0.756719	−	0.591214i	−0.161692	−	0.986841i	$-0.551695\pi$
$61$	5.91017	−	4.61753i	0.756719	−	0.591214i	0.918411	+	0.395627i	$0.129473\pi$
$62$	−4.20161	+	1.87068i	−0.533605	+	0.237576i
$63$	3.89985	+	5.79179i	0.491334	+	0.729696i
$64$	10.6797	−	2.27005i	1.33497	−	0.283756i
$65$	5.03344	+	4.22356i	0.624321	+	0.523868i
$66$	2.12377	+	11.8855i	0.261418	+	1.46301i
$67$	0.00943758	+	0.0535232i	0.00115298	+	0.00653890i	0.985379	−	0.170378i	$-0.0544988\pi$
$67$	0.00943758	+	0.0535232i	0.00115298	+	0.00653890i	−0.984226	+	0.176917i	$0.943388\pi$
$68$	6.42874	+	0.903500i	0.779599	+	0.109566i
$69$	0.930733	+	10.6877i	0.112047	+	1.28665i
$70$	−4.98758	−	20.0041i	−0.596130	−	2.39095i
$71$	0.520742	+	0.468878i	0.0618007	+	0.0556456i	0.699452	−	0.714679i	$-0.253427\pi$
$71$	0.520742	+	0.468878i	0.0618007	+	0.0556456i	−0.637652	+	0.770325i	$0.720094\pi$
$72$	−2.18097	−	1.47363i	−0.257030	−	0.173669i
$73$	4.03548	+	9.06384i	0.472317	+	1.06084i	0.979945	+	0.199266i	$0.0638557\pi$
$73$	4.03548	+	9.06384i	0.472317	+	1.06084i	−0.507628	+	0.861576i	$0.669478\pi$
$74$	8.77884	−	13.0152i	1.02052	−	1.51298i
$75$	17.1729	+	13.9178i	1.98295	+	1.60708i
$76$	3.73662	+	4.45313i	0.428620	+	0.510809i
$77$	−7.70979	−	0.383274i	−0.878612	−	0.0436781i
$78$	−1.08519	+	5.57087i	−0.122873	+	0.630777i
$79$	−6.19132	+	11.6442i	−0.696578	+	1.31007i	0.243761	+	0.969835i	$0.421619\pi$
$79$	−6.19132	+	11.6442i	−0.696578	+	1.31007i	−0.940339	+	0.340238i	$0.889492\pi$
$80$	−7.40898	−	10.1976i	−0.828349	−	1.14012i
$81$	−1.54860	−	8.86577i	−0.172067	−	0.985085i
$82$	1.48764	+	4.57847i	0.164282	+	0.505607i
$83$	−2.62381	+	0.368752i	−0.288000	+	0.0404758i	−0.281694	−	0.959504i	$-0.590896\pi$
$83$	−2.62381	+	0.368752i	−0.288000	+	0.0404758i	−0.00630630	+	0.999980i	$0.502007\pi$
$84$	7.13001	−	6.64349i	0.777948	−	0.724864i
$85$	−3.11961	−	10.8794i	−0.338369	−	1.18003i
$86$	−15.9831	+	6.45758i	−1.72350	+	0.696339i
$87$	−5.20677	+	13.5478i	−0.558224	+	1.45248i
$88$	2.74886	−	0.954782i	0.293030	−	0.101780i
$89$	11.6287	+	6.71382i	1.23264	+	0.711664i	0.967579	−	0.252569i	$-0.0812754\pi$
$89$	11.6287	+	6.71382i	1.23264	+	0.711664i	0.265058	+	0.964232i	$0.414609\pi$
$90$	−4.63551	+	26.1664i	−0.488625	+	2.75818i
$91$	−3.31494	−	1.47591i	−0.347500	−	0.154717i
$92$	14.5287	−	3.62242i	1.51472	−	0.377663i
$93$	−0.854089	+	3.69270i	−0.0885649	+	0.382915i
$94$	5.61790	+	10.5657i	0.579442	+	1.08977i
$95$	4.44266	−	9.10880i	0.455807	−	0.934543i
$96$	5.89092	−	12.6199i	0.601240	−	1.28801i
$97$	3.84112	−	2.40020i	0.390006	−	0.243703i	−0.320716	−	0.947175i	$-0.603924\pi$
$97$	3.84112	−	2.40020i	0.390006	−	0.243703i	0.710723	+	0.703472i	$0.248368\pi$
$98$	−1.66348	−	2.88124i	−0.168037	−	0.291049i
$99$	8.87390	+	4.50043i	0.891861	+	0.452310i
$100$	15.4258	−	26.7183i	1.54258	−	2.67183i
$101$	−0.104569	−	2.99445i	−0.0104050	−	0.297959i	−0.993427	−	0.114470i	$-0.963483\pi$
$101$	−0.104569	−	2.99445i	−0.0104050	−	0.297959i	0.983022	−	0.183489i	$-0.0587392\pi$
$102$	6.91546	−	6.90991i	0.684733	−	0.684183i
$103$	11.7408	−	0.820993i	1.15685	−	0.0808949i	0.521593	−	0.853195i	$-0.325338\pi$
$103$	11.7408	−	0.820993i	1.15685	−	0.0808949i	0.635258	+	0.772300i	$0.280894\pi$
$104$	1.36707	+	0.0477390i	0.134052	+	0.00468119i
$105$	−15.6366	−	6.64474i	−1.52597	−	0.648460i
$106$	4.45522	+	4.61352i	0.432729	+	0.448104i
$107$	−8.64278	+	6.27935i	−0.835529	+	0.607047i	−0.921118	−	0.389283i	$-0.872723\pi$
$107$	−8.64278	+	6.27935i	−0.835529	+	0.607047i	0.0855891	+	0.996331i	$0.472723\pi$
$108$	−11.8820	+	4.07530i	−1.14335	+	0.392146i
$109$			0.513862i			0.0492190i	0.999697	+	0.0246095i	$0.00783424\pi$
$109$			0.513862i			0.0492190i	−0.999697	+	0.0246095i	$0.992166\pi$
$110$	−20.0937	−	21.4321i	−1.91586	−	2.04347i
$111$	−4.20713	−	12.2343i	−0.399323	−	1.16123i
$112$	5.48538	+	4.28565i	0.518320	+	0.404956i
$113$	0.620171	+	0.154626i	0.0583408	+	0.0145460i	0.270983	−	0.962584i	$-0.412651\pi$
$113$	0.620171	+	0.154626i	0.0583408	+	0.0145460i	−0.212642	+	0.977130i	$0.568207\pi$
$114$	8.74206	−	0.454633i	0.818769	−	0.0425803i
$115$	−16.0714	−	20.5705i	−1.49867	−	1.91821i
$116$	19.8146	+	4.21173i	1.83974	+	0.391050i
$117$	3.12686	+	3.47834i	0.289078	+	0.321573i
$118$	−7.43253	+	16.6937i	−0.684220	+	1.53678i
$119$	3.31213	+	5.30051i	0.303622	+	0.485897i
$120$	6.40366	+	0.114348i	0.584572	+	0.0104385i
$121$	−9.86067	+	4.87517i	−0.896424	+	0.443197i
$122$	−15.5240	+	2.73731i	−1.40548	+	0.247824i
$123$	3.75058	+	1.29311i	0.338179	+	0.116596i
$124$	5.27713	+	0.369013i	0.473901	+	0.0331384i
$125$	−32.5341	−	3.41948i	−2.90994	−	0.305847i
$126$	−1.52227	−	14.5962i	−0.135615	−	1.30033i
$127$	1.77451	−	8.34840i	0.157462	−	0.740801i	−0.826573	−	0.562829i	$-0.809713\pi$
$127$	1.77451	−	8.34840i	0.157462	−	0.740801i	0.984036	−	0.177972i	$-0.0569537\pi$
$128$	−6.60020	−	1.89258i	−0.583381	−	0.167282i
$129$	−3.68227	+	13.7204i	−0.324206	+	1.20801i
$130$	−5.17335	−	12.8045i	−0.453733	−	1.12303i
$131$	−15.6451	−	5.69435i	−1.36692	−	0.497518i	−0.448732	−	0.893666i	$-0.648124\pi$
$131$	−15.6451	−	5.69435i	−1.36692	−	0.497518i	−0.918186	+	0.396149i	$0.870346\pi$
$132$	4.26117	−	13.2173i	0.370887	−	1.15042i
$133$	−0.971866	+	5.51172i	−0.0842714	+	0.477927i
$134$	0.0352987	−	0.108638i	0.00304934	−	0.00938491i
$135$	14.9159	+	16.0341i	1.28376	+	1.37999i
$136$	−1.90618	−	1.38492i	−0.163453	−	0.118756i
$137$	2.75065	+	19.5719i	0.235004	+	1.67214i	0.648178	+	0.761489i	$0.275531\pi$
$137$	2.75065	+	19.5719i	0.235004	+	1.67214i	−0.413174	+	0.910652i	$0.635580\pi$
$138$	8.81863	−	20.7522i	0.750691	−	1.76655i
$139$	1.70158	−	1.14773i	0.144326	−	0.0973493i	−0.484907	−	0.874566i	$-0.661147\pi$
$139$	1.70158	−	1.14773i	0.144326	−	0.0973493i	0.629234	+	0.777216i	$0.283369\pi$
$140$	−5.73669	+	23.0086i	−0.484839	+	1.94458i
$141$	9.73938	+	1.54657i	0.820204	+	0.130245i
$142$	−0.503717	−	1.38395i	−0.0422710	−	0.116139i
$143$	−5.14992	+	0.464513i	−0.430658	+	0.0388445i
$144$	−4.20597	−	7.92563i	−0.350498	−	0.660469i
$145$	−7.34261	−	34.5443i	−0.609770	−	2.86874i
$146$	1.45463	−	20.8022i	0.120386	−	1.72160i
$147$	−2.72115	−	0.335225i	−0.224437	−	0.0276489i
$148$	−15.9434	+	8.47728i	−1.31054	+	0.696828i
$149$	4.79614	−	2.55015i	0.392915	−	0.208917i	−0.261245	−	0.965272i	$-0.584133\pi$
$149$	4.79614	−	2.55015i	0.392915	−	0.208917i	0.654161	+	0.756356i	$0.273022\pi$
$150$	−18.1357	−	42.7728i	−1.48078	−	3.49239i
$151$	−0.917536	+	13.1214i	−0.0746680	+	1.06780i	0.805331	+	0.592826i	$0.201988\pi$
$151$	−0.917536	+	13.1214i	−0.0746680	+	1.06780i	−0.879999	+	0.474976i	$0.842457\pi$
$152$	−0.438655	−	2.06371i	−0.0355796	−	0.167389i
$153$	−1.11482	−	7.97882i	−0.0901276	−	0.645049i
$154$	13.9293	+	8.31868i	1.12245	+	0.670339i
$155$	−3.15427	−	8.66627i	−0.253357	−	0.696092i
$156$	4.11026	−	5.07158i	0.329084	−	0.406051i
$157$	0.109438	−	0.438932i	0.00873411	−	0.0350306i	−0.965771	−	0.259398i	$-0.916476\pi$
$157$	0.109438	−	0.438932i	0.00873411	−	0.0350306i	0.974505	+	0.224367i	$0.0720315\pi$
$158$	22.9792	−	15.4996i	1.82812	−	1.23309i
$159$	5.24620	−	0.642015i	0.416051	−	0.0509151i
$160$	4.71632	+	33.5583i	0.372858	+	2.65302i
$161$	11.6629	+	8.47357i	0.919163	+	0.667811i
$162$	−5.87423	+	17.9807i	−0.461523	+	1.41270i
$163$	3.78489	−	11.6487i	0.296455	−	0.912396i	−0.686273	−	0.727344i	$-0.740755\pi$
$163$	3.78489	−	11.6487i	0.296455	−	0.912396i	0.982729	−	0.185052i	$-0.0592454\pi$
$164$	0.961515	−	5.45302i	0.0750817	−	0.425809i
$165$	−24.0720	+	2.58574i	−1.87400	+	0.201300i
$166$	5.23300	+	1.90466i	0.406159	+	0.147830i
$167$	2.70058	+	6.68418i	0.208978	+	0.517238i	0.994874	−	0.101120i	$-0.0322427\pi$
$167$	2.70058	+	6.68418i	0.208978	+	0.517238i	−0.785897	+	0.618358i	$0.787798\pi$
$168$	−3.41683	+	0.914067i	−0.263614	+	0.0705218i
$169$	10.1599	+	2.91330i	0.781530	+	0.224100i
$170$	−4.94569	+	23.2677i	−0.379317	+	1.78455i
$171$	4.03881	−	5.97742i	0.308856	−	0.457105i
$172$	19.7188	+	2.07253i	1.50354	+	0.158029i
$173$	4.94680	+	0.345914i	0.376098	+	0.0262993i	0.256555	−	0.966530i	$-0.417413\pi$
$173$	4.94680	+	0.345914i	0.376098	+	0.0262993i	0.119543	+	0.992829i	$0.461857\pi$
$174$	23.0304	−	20.0038i	1.74593	−	1.51649i
$175$	29.2520	−	5.15791i	2.21124	−	0.389901i
$176$	9.80149	+	1.52541i	0.738815	+	0.114982i
$177$	7.29550	+	13.1739i	0.548363	+	0.990211i
$178$	−14.9553	−	23.9335i	−1.12095	−	1.79389i
$179$	2.28680	−	5.13623i	0.170923	−	0.383900i	−0.807690	−	0.589607i	$-0.799283\pi$
$179$	2.28680	−	5.13623i	0.170923	−	0.383900i	0.978614	+	0.205707i	$0.0659493\pi$
$180$	18.8371	−	24.0705i	1.40403	−	1.79411i
$181$	2.84214	+	0.604116i	0.211255	+	0.0449036i	0.312323	−	0.949976i	$-0.398893\pi$
$181$	2.84214	+	0.604116i	0.211255	+	0.0449036i	−0.101069	+	0.994879i	$0.532226\pi$
$182$	4.69541	+	6.00985i	0.348047	+	0.445480i
$183$	−5.90224	+	11.5723i	−0.436306	+	0.855450i
$184$	−5.27303	−	1.31471i	−0.388733	−	0.0969220i
$185$	24.8067	+	19.3811i	1.82382	+	1.42493i
$186$	5.22865	−	6.01000i	0.383383	−	0.440675i
$187$	7.80147	+	4.29705i	0.570500	+	0.314231i
$188$		−	13.7637i		−	1.00382i
$189$	−10.3589	−	6.24126i	−0.753501	−	0.453985i
$190$	−17.2323	+	12.5200i	−1.25017	+	0.908298i
$191$	13.9354	+	14.4306i	1.00833	+	1.04416i	0.999023	+	0.0442035i	$0.0140750\pi$
$191$	13.9354	+	14.4306i	1.00833	+	1.04416i	0.00931117	+	0.999957i	$0.497036\pi$
$192$	−15.1076	+	11.3749i	−1.09030	+	0.820914i
$193$	−17.0549	−	0.595571i	−1.22764	−	0.0428702i	−0.586279	−	0.810109i	$-0.699408\pi$
$193$	−17.0549	−	0.595571i	−1.22764	−	0.0428702i	−0.641362	+	0.767239i	$0.721630\pi$
$194$	−9.49650	+	0.664060i	−0.681809	+	0.0476767i
$195$	−10.9918	−	2.94997i	−0.787138	−	0.211252i
$196$	0.133549	+	3.82433i	0.00953919	+	0.273167i
$197$	−0.802906	+	1.39067i	−0.0572047	+	0.0990814i	−0.893210	−	0.449641i	$-0.851552\pi$
$197$	−0.802906	+	1.39067i	−0.0572047	+	0.0990814i	0.836005	+	0.548722i	$0.184885\pi$
$198$	−12.0271	−	17.1078i	−0.854730	−	1.21580i
$199$	−2.00192	−	3.46742i	−0.141912	−	0.245799i	0.786304	−	0.617839i	$-0.211992\pi$
$199$	−2.00192	−	3.46742i	−0.141912	−	0.245799i	−0.928217	+	0.372040i	$0.878658\pi$
$200$	−9.49581	+	5.93364i	−0.671455	+	0.419572i
$201$	−0.0539627	−	0.0771326i	−0.00380623	−	0.00544051i
$202$	−2.76064	+	5.66015i	−0.194238	+	0.398247i
$203$	9.15621	+	17.2203i	0.642640	+	1.20863i
$204$	−10.7543	+	3.28321i	−0.752953	+	0.229870i
$205$	−9.36654	+	2.33534i	−0.654188	+	0.163107i
$206$	−22.5981	−	10.0613i	−1.57448	−	0.701004i
$207$	−9.27796	−	16.0997i	−0.644863	−	1.11901i
$208$	4.03819	+	2.33145i	0.279998	+	0.161657i
$209$	2.61679	+	7.53384i	0.181007	+	0.521127i
$210$	22.4611	+	27.7600i	1.54997	+	1.91562i
$211$	−10.4946	+	4.24010i	−0.722479	+	0.291901i	−0.706245	−	0.707968i	$-0.749612\pi$
$211$	−10.4946	+	4.24010i	−0.722479	+	0.291901i	−0.0162344	+	0.999868i	$0.505168\pi$
$212$	−2.03333	−	7.09106i	−0.139650	−	0.487016i
$213$	−1.16052	−	0.355316i	−0.0795175	−	0.0243458i
$214$	22.2349	−	3.12491i	1.51994	−	0.213614i
$215$	−10.6816	−	32.8747i	−0.728482	−	2.24204i
$216$	4.50203	+	0.718612i	0.306325	+	0.0488953i
$217$	2.99365	+	4.12040i	0.203222	+	0.279711i
$218$	0.507039	−	0.953601i	0.0343410	−	0.0645860i
$219$	−12.9650	−	11.2794i	−0.876090	−	0.762191i
$220$	8.83346	+	32.6159i	0.595552	+	2.19897i
$221$	2.69120	+	3.20725i	0.181030	+	0.215743i
$222$	−4.26450	+	26.8552i	−0.286214	+	1.80240i
$223$	8.42274	−	12.4872i	0.564028	−	0.836206i	−0.433872	−	0.900974i	$-0.642853\pi$
$223$	8.42274	−	12.4872i	0.564028	−	0.836206i	0.997900	+	0.0647684i	$0.0206309\pi$
$224$	−7.61195	−	17.0967i	−0.508595	−	1.14232i
$225$	−37.1415	−	9.29210i	−2.47610	−	0.619474i
$226$	−0.998313	−	0.898885i	−0.0664068	−	0.0597929i
$227$	1.05841	+	4.24504i	0.0702490	+	0.281753i	0.995139	−	0.0984818i	$-0.0313986\pi$
$227$	1.05841	+	4.24504i	0.0702490	+	0.281753i	−0.924890	+	0.380235i	$0.875843\pi$
$228$	−9.12360	−	4.25887i	−0.604225	−	0.282050i
$229$	−10.1594	−	1.42780i	−0.671349	−	0.0943519i	−0.204741	−	0.978816i	$-0.565635\pi$
$229$	−10.1594	−	1.42780i	−0.671349	−	0.0943519i	−0.466608	+	0.884464i	$0.654524\pi$
$230$	9.52728	+	54.0319i	0.628210	+	3.56276i
$231$	12.3852	−	5.03691i	0.814885	−	0.331404i
$232$	−5.63208	−	4.72587i	−0.369764	−	0.310269i
$233$	−20.2780	+	4.31021i	−1.32845	+	0.282371i	−0.816850	−	0.576850i	$-0.804282\pi$
$233$	−20.2780	+	4.31021i	−1.32845	+	0.282371i	−0.511603	+	0.859222i	$0.670948\pi$
$234$	−2.37053	−	9.54029i	−0.154966	−	0.623669i
$235$	−21.9208	+	9.75975i	−1.42995	+	0.636656i
$236$	16.5626	−	12.9401i	1.07813	−	0.842328i
$237$	1.20462	−	22.8103i	0.0782483	−	1.48169i
$238$	−0.916364	−	13.1046i	−0.0593990	−	0.849446i
$239$	−19.5307	+	5.60033i	−1.26333	+	0.362255i	−0.839438	−	0.543456i	$-0.817116\pi$
$239$	−19.5307	+	5.60033i	−1.26333	+	0.362255i	−0.423896	+	0.905711i	$0.639338\pi$
$240$	19.0907	+	10.5922i	1.23230	+	0.683723i
$241$	−12.7541	−	2.24890i	−0.821565	−	0.144864i	−0.252962	−	0.967476i	$-0.581405\pi$
$241$	−12.7541	−	2.24890i	−0.821565	−	0.144864i	−0.568603	+	0.822612i	$0.692516\pi$
$242$	23.1094	+	0.682625i	1.48553	+	0.0438808i
$243$	8.91552	+	12.7872i	0.571931	+	0.820302i
$244$	17.2437	+	5.60283i	1.10392	+	0.358684i
$245$	5.99612	−	2.92450i	0.383078	−	0.186840i
$246$	−5.68422	−	6.10049i	−0.362413	−	0.388953i
$247$	−0.130839	+	3.74674i	−0.00832508	+	0.238399i
$248$	−1.62821	−	1.01742i	−0.103391	−	0.0646061i
$249$	3.84985	−	2.49793i	0.243975	−	0.158300i
$250$	57.0013	+	38.4479i	3.60508	+	2.43166i
$251$	−12.4617	+	11.2206i	−0.786575	+	0.708236i	−0.961034	−	0.276429i	$-0.910849\pi$
$251$	−12.4617	+	11.2206i	−0.786575	+	0.708236i	0.174459	+	0.984664i	$0.444182\pi$
$252$	−6.33575	+	15.6454i	−0.399115	+	0.985565i
$253$	20.3965	+	2.44873i	1.28231	+	0.153950i
$254$	−11.5306	+	13.7416i	−0.723495	+	0.862228i
$255$	12.8548	+	14.7998i	0.804999	+	0.926796i
$256$	−5.32706	−	5.14429i	−0.332941	−	0.321518i
$257$	−20.3237	−	9.91251i	−1.26775	−	0.618325i	−0.323092	−	0.946368i	$-0.604722\pi$
$257$	−20.3237	−	9.91251i	−1.26775	−	0.618325i	−0.944663	+	0.328042i	$0.893611\pi$
$258$	20.3716	−	21.8283i	1.26828	−	1.35897i
$259$	−16.1190	−	6.51249i	−1.00158	−	0.404666i
$260$	−1.66036	+	15.7973i	−0.102971	+	0.979706i
$261$	−1.73346	−	25.0790i	−0.107299	−	1.55235i
$262$	23.4147	+	26.0047i	1.44657	+	1.60658i
$263$	7.72560	−	2.81189i	0.476381	−	0.173388i	−0.0926599	−	0.995698i	$-0.529537\pi$
$263$	7.72560	−	2.81189i	0.476381	−	0.173388i	0.569041	+	0.822309i	$0.307315\pi$
$264$	−3.61760	+	3.50949i	−0.222648	+	0.215994i
$265$	−9.85174	+	8.26659i	−0.605188	+	0.507813i
$266$	7.24209	−	9.26945i	0.444041	−	0.568346i
$267$	−23.1680	−	2.03631i	−1.41786	−	0.124620i
$268$	−0.0945109	+	0.0912682i	−0.00577317	+	0.00557509i
$269$	20.4737	−	6.65231i	1.24830	−	0.405599i	0.390991	−	0.920394i	$-0.372132\pi$
$269$	20.4737	−	6.65231i	1.24830	−	0.405599i	0.857313	+	0.514796i	$0.172132\pi$
$270$	−11.8592	−	44.4732i	−0.721726	−	2.70655i
$271$	−15.9986	+	22.0201i	−0.971844	+	1.33763i	−0.0307338	+	0.999528i	$0.509784\pi$
$271$	−15.9986	+	22.0201i	−0.971844	+	1.33763i	−0.941110	+	0.338101i	$0.890216\pi$
$272$	−3.52087	−	7.21885i	−0.213484	−	0.437707i
$273$	6.28410	−	0.107166i	0.380331	−	0.00648597i
$274$	14.2075	−	39.0348i	0.858307	−	2.35818i
$275$	32.8226	−	26.7256i	1.97927	−	1.61161i
$276$	−20.1617	+	16.3132i	−1.21359	+	0.981942i
$277$	18.9458	−	0.661602i	1.13834	−	0.0397518i	0.540485	−	0.841354i	$-0.318241\pi$
$277$	18.9458	−	0.661602i	1.13834	−	0.0397518i	0.597858	+	0.801602i	$0.296019\pi$
$278$	−4.29021	+	0.450920i	−0.257310	+	0.0270444i
$279$	−1.35974	−	6.42243i	−0.0814056	−	0.384501i
$280$	5.75877	−	6.39577i	0.344153	−	0.382220i
$281$	−6.31736	+	15.6360i	−0.376862	+	0.932766i	0.612916	+	0.790148i	$0.289996\pi$
$281$	−6.31736	+	15.6360i	−0.376862	+	0.932766i	−0.989778	+	0.142618i	$0.954448\pi$
$282$	−16.5479	−	12.4801i	−0.985411	−	0.743181i
$283$	−4.53945	+	4.70074i	−0.269842	+	0.279430i	−0.840562	−	0.541715i	$-0.817775\pi$
$283$	−4.53945	+	4.70074i	−0.269842	+	0.279430i	0.570720	+	0.821145i	$0.306664\pi$
$284$	−0.235755	+	1.67749i	−0.0139895	+	0.0995405i
$285$	−0.313395	+	17.5506i	−0.0185639	+	1.03961i
$286$	10.0153	+	4.21952i	0.592219	+	0.249506i
$287$	4.61680	−	2.66551i	0.272521	−	0.157340i
$288$	−0.0193684	+	24.1225i	−0.00114129	+	1.42143i
$289$	1.02317	+	9.73479i	0.0601863	+	0.572635i
$290$	−20.4595	+	71.3508i	−1.20142	+	4.18986i
$291$	−4.27538	+	6.57773i	−0.250627	+	0.385593i
$292$	−12.7101	+	20.3404i	−0.743803	+	1.19033i
$293$	−1.53916	−	2.28190i	−0.0899189	−	0.133310i	0.781394	−	0.624038i	$-0.214509\pi$
$293$	−1.53916	−	2.28190i	−0.0899189	−	0.133310i	−0.871313	+	0.490727i	$0.836731\pi$
$294$	4.71902	+	3.30712i	0.275219	+	0.192875i
$295$	−32.3534	−	17.2026i	−1.88369	−	1.00157i
$296$	6.55360			0.380920
$297$	−17.2241	−	0.575891i	−0.999442	−	0.0334166i
$298$	−11.4168			−0.661355
$299$	8.52638	+	4.53356i	0.493093	+	0.262182i
$300$	−4.67869	+	53.2315i	−0.270124	+	3.07332i
$301$	10.6746	+	15.8258i	0.615275	+	0.912182i
$302$	14.6499	−	23.4447i	0.843006	−	1.34909i
$303$	2.35422	+	4.62500i	0.135246	+	0.265700i
$304$	1.98237	−	6.91334i	0.113697	−	0.396507i
$305$	−3.30407	−	31.4361i	−0.189190	−	1.80003i
$306$	−5.80405	+	15.9067i	−0.331795	+	0.909328i
$307$	−2.53606	+	1.46419i	−0.144741	+	0.0835660i	−0.570621	−	0.821213i	$-0.693298\pi$
$307$	−2.53606	+	1.46419i	−0.144741	+	0.0835660i	0.425881	+	0.904779i	$0.359964\pi$
$308$	−9.65411	−	15.9697i	−0.550094	−	0.909960i
$309$	−17.8333	+	9.87580i	−1.01450	+	0.561815i
$310$	−2.69766	+	19.1949i	−0.153217	+	1.09020i
$311$	6.29235	−	6.51592i	0.356806	−	0.369484i	−0.516809	−	0.856101i	$-0.672880\pi$
$311$	6.29235	−	6.51592i	0.356806	−	0.369484i	0.873616	+	0.486617i	$0.161769\pi$
$312$	−2.18130	+	0.924872i	−0.123492	+	0.0523606i
$313$	−2.01449	+	4.98603i	−0.113866	+	0.281827i	−0.973346	−	0.229341i	$-0.926343\pi$
$313$	−2.01449	+	4.98603i	−0.113866	+	0.281827i	0.859480	+	0.511169i	$0.170787\pi$
$314$	−0.636194	+	0.706565i	−0.0359025	+	0.0398738i
$315$	29.4102	−	1.00338i	1.65708	−	0.0565343i
$316$	−31.7063	+	3.33247i	−1.78362	+	0.187466i
$317$	−15.5115	+	0.541672i	−0.871211	+	0.0304234i	−0.467015	−	0.884249i	$-0.654671\pi$
$317$	−15.5115	+	0.541672i	−0.871211	+	0.0304234i	−0.404196	+	0.914673i	$0.632448\pi$
$318$	−10.3692	−	3.98512i	−0.581473	−	0.223475i
$319$	23.3490	+	15.0739i	1.30729	+	0.843978i
$320$	15.7382	−	43.2403i	0.879791	−	2.41721i
$321$	8.97722	−	16.1800i	0.501060	−	0.903081i
$322$	−13.2824	−	27.2329i	−0.740198	−	1.51763i
$323$	3.79567	−	5.22429i	0.211197	−	0.290687i
$324$	15.6750	−	15.0886i	0.870831	−	0.838254i
$325$	18.9231	−	6.14848i	1.04966	−	0.341056i
$326$	−18.5179	+	17.8825i	−1.02561	+	0.990419i
$327$	−0.375821	−	0.806796i	−0.0207829	−	0.0446159i
$328$	−1.23726	+	1.58362i	−0.0683162	+	0.0874407i
$329$	10.1511	−	8.51781i	0.559650	−	0.469602i
$330$	47.2232	+	18.9539i	2.59955	+	1.04338i
$331$	−5.38037	+	1.95829i	−0.295732	+	0.107638i	−0.485625	−	0.874167i	$-0.661408\pi$
$331$	−5.38037	+	1.95829i	−0.295732	+	0.107638i	0.189893	+	0.981805i	$0.439186\pi$
$332$	−4.28595	−	4.76003i	−0.235222	−	0.261241i
$333$	15.5532	+	16.1317i	0.852312	+	0.884014i
$334$	1.58381	−	15.0689i	0.0866622	−	0.824535i
$335$	0.212375	+	0.0858050i	0.0116033	+	0.00468803i
$336$	−11.7468	−	2.71693i	−0.640839	−	0.148220i
$337$	−12.5405	−	6.11642i	−0.683125	−	0.333182i	0.0639206	−	0.997955i	$-0.479640\pi$
$337$	−12.5405	−	6.11642i	−0.683125	−	0.333182i	−0.747046	+	0.664773i	$0.768528\pi$
$338$	−15.9796	−	15.4314i	−0.869178	−	0.839355i
$339$	−1.08680	+	0.210799i	−0.0590267	+	0.0114490i
$340$	17.5868	−	20.9592i	0.953779	−	1.13667i
$341$	6.58589	+	3.04952i	0.356646	+	0.165141i
$342$	−13.3931	+	7.10745i	−0.724216	+	0.384327i
$343$	−14.8454	+	13.3668i	−0.801575	+	0.721742i
$344$	−5.96586	−	4.02402i	−0.321658	−	0.216961i
$345$	40.2778	+	20.5429i	2.16848	+	1.10599i
$346$	−8.83873	−	5.52305i	−0.475173	−	0.296921i
$347$	0.236896	−	6.78381i	0.0127172	−	0.364174i	−0.976304	−	0.216402i	$-0.930568\pi$
$347$	0.236896	−	6.78381i	0.0127172	−	0.364174i	0.989022	−	0.147772i	$-0.0472100\pi$
$348$	−34.1906	+	7.87907i	−1.83281	+	0.422362i
$349$	5.50343	−	2.68420i	0.294592	−	0.143682i	−0.285148	−	0.958483i	$-0.592043\pi$
$349$	5.50343	−	2.68420i	0.294592	−	0.143682i	0.579740	+	0.814801i	$0.303154\pi$
$350$	−59.3739	−	19.2918i	−3.17367	−	1.03119i
$351$	−7.45331	−	3.17434i	−0.397828	−	0.169434i
$352$	−21.3414	−	15.9921i	−1.13750	−	0.852384i
$353$	−7.75996	−	1.36829i	−0.413021	−	0.0728267i	−0.0367231	−	0.999325i	$-0.511692\pi$
$353$	−7.75996	−	1.36829i	−0.413021	−	0.0728267i	−0.376298	+	0.926499i	$0.622803\pi$
$354$	−0.539677	−	31.6462i	−0.0286835	−	1.68197i
$355$	2.83882	−	0.814018i	0.150669	−	0.0432036i
$356$	2.26434	+	32.3816i	0.120010	+	1.71622i
$357$	−9.07687	−	5.89977i	−0.480399	−	0.312249i
$358$	−9.31178	+	7.27516i	−0.492143	+	0.384504i
$359$	29.0209	−	12.9209i	1.53167	−	0.681941i	0.544081	−	0.839032i	$-0.316878\pi$
$359$	29.0209	−	12.9209i	1.53167	−	0.681941i	0.987584	+	0.157091i	$0.0502116\pi$
$360$	−10.1378	+	4.50389i	−0.534309	+	0.237376i
$361$	−12.9288	+	2.74809i	−0.680461	+	0.144637i
$362$	−4.67822	−	3.92549i	−0.245882	−	0.206319i
$363$	11.9164	−	14.8661i	0.625446	−	0.780267i
$364$	−1.52326	−	8.63883i	−0.0798404	−	0.452798i
$365$	41.4078	+	5.81948i	2.16738	+	0.304606i
$366$	22.3718	−	15.6515i	1.16939	−	0.818118i
$367$	0.424818	+	1.70385i	0.0221753	+	0.0889404i	0.980364	−	0.197197i	$-0.0631840\pi$
$367$	0.424818	+	1.70385i	0.0221753	+	0.0889404i	−0.958188	+	0.286138i	$0.907628\pi$
$368$	−13.7668	−	12.3957i	−0.717642	−	0.646168i
$369$	−6.83440	+	0.712777i	−0.355785	+	0.0371057i
$370$	−26.9114	−	60.4439i	−1.39906	−	3.14233i
$371$	3.97151	−	5.88801i	0.206191	−	0.305690i
$372$	−8.55532	+	3.28014i	−0.443573	+	0.170067i
$373$	−15.9386	−	18.9949i	−0.825269	−	0.983517i	0.174730	−	0.984616i	$-0.444095\pi$
$373$	−15.9386	−	18.9949i	−0.825269	−	0.983517i	−0.999999	+	0.00109903i	$0.999650\pi$
$374$	−10.2376	−	15.6722i	−0.529375	−	0.810388i
$375$	53.5816	−	18.4256i	2.76694	−	0.951492i
$376$	−2.34519	+	4.41066i	−0.120944	+	0.227462i
$377$	7.67904	+	10.5693i	0.395491	+	0.544346i
$378$	13.0652	+	21.8036i	0.672003	+	1.12146i
$379$	2.54960	+	7.84685i	0.130964	+	0.403066i	0.994940	−	0.100467i	$-0.0320335\pi$
$379$	2.54960	+	7.84685i	0.130964	+	0.403066i	−0.863976	+	0.503532i	$0.832034\pi$
$380$	24.2611	−	3.40968i	1.24457	−	0.174913i
$381$	3.31965	+	14.4053i	0.170071	+	0.738008i
$382$	−11.6218	−	40.5301i	−0.594623	−	2.07370i
$383$	4.07494	−	1.64638i	0.208220	−	0.0841263i	−0.268128	−	0.963383i	$-0.586405\pi$
$383$	4.07494	−	1.64638i	0.208220	−	0.0841263i	0.476347	+	0.879257i	$0.341960\pi$
$384$	11.7469	−	1.85569i	0.599457	−	0.0946980i
$385$	−18.5885	+	26.6996i	−0.947358	+	1.36074i
$386$	31.0621	+	17.9337i	1.58102	+	0.912802i
$387$	−4.25322	−	24.2350i	−0.216203	−	1.23193i
$388$	10.0029	+	4.45356i	0.507819	+	0.226095i
$389$	−33.6153	+	8.38123i	−1.70436	+	0.424945i	−0.967860	−	0.251491i	$-0.919079\pi$
$389$	−33.6153	+	8.38123i	−1.70436	+	0.424945i	−0.736502	+	0.676436i	$0.763524\pi$
$390$	17.4873	+	16.3203i	0.885502	+	0.826409i
$391$	−7.80892	−	14.6864i	−0.394914	−	0.742725i
$392$	0.608829	−	1.24828i	0.0307505	−	0.0630479i
$393$	28.7285	−	2.50179i	1.44916	−	0.126199i
$394$	2.86221	−	1.78850i	0.144196	−	0.0901036i
$395$	27.7902	+	48.1340i	1.39828	+	2.42188i
$396$	2.97637	+	23.8685i	0.149568	+	1.19944i
$397$	16.7033	−	28.9310i	0.838316	−	1.45201i	−0.0529861	−	0.998595i	$-0.516874\pi$
$397$	16.7033	−	28.9310i	0.838316	−	1.45201i	0.891302	−	0.453410i	$-0.149793\pi$
$398$	0.293685	+	8.41003i	0.0147211	+	0.421557i
$399$	−2.50520	−	9.36455i	−0.125417	−	0.468814i
$400$	−38.0763	+	2.66255i	−1.90382	+	0.133128i
$401$	−10.2609	−	0.358319i	−0.512406	−	0.0178936i	−0.222470	−	0.974940i	$-0.571412\pi$
$401$	−10.2609	−	0.358319i	−0.512406	−	0.0178936i	−0.289936	+	0.957046i	$0.593634\pi$
$402$	0.0240331	+	0.196385i	0.00119866	+	0.00979481i
$403$	2.36993	+	2.45413i	0.118054	+	0.122249i
$404$	5.85999	−	4.25753i	0.291545	−	0.211820i
$405$	−35.1458	−	14.2655i	−1.74641	−	0.708858i
$406$		−	40.9914i		−	2.03437i
$407$	−24.5806	+	3.08521i	−1.21841	+	0.152928i
$408$	4.00571	+	0.780299i	0.198312	+	0.0386306i
$409$	19.9480	+	15.5851i	0.986364	+	0.770632i	0.973360	−	0.229283i	$-0.0736383\pi$
$409$	19.9480	+	15.5851i	0.986364	+	0.770632i	0.0130043	+	0.999915i	$0.495861\pi$
$410$	19.6863	+	4.90836i	0.972239	+	0.242406i
$411$	−18.6329	−	28.7174i	−0.919095	−	1.41653i
$412$	17.5168	+	22.4205i	0.862990	+	1.10458i
$413$	19.7936	+	4.20725i	0.973978	+	0.207025i
$414$	1.33165	+	39.0320i	0.0654470	+	1.91832i
$415$	−4.54192	+	10.2013i	−0.222954	+	0.500763i
$416$	−6.64315	−	10.6313i	−0.325707	−	0.521241i
$417$	−1.83218	+	3.04649i	−0.0897223	+	0.149187i
$418$	2.57770	−	16.5630i	0.126080	−	0.810123i
$419$	−35.4813	+	6.25632i	−1.73338	+	0.305641i	−0.949148	−	0.314831i	$-0.898052\pi$
$419$	−35.4813	+	6.25632i	−1.73338	+	0.305641i	−0.784229	+	0.620472i	$0.786941\pi$
$420$	−7.82074	−	40.3206i	−0.381613	−	1.96745i
$421$	10.4903	+	0.733551i	0.511264	+	0.0357511i	0.323059	−	0.946379i	$-0.395289\pi$
$421$	10.4903	+	0.733551i	0.511264	+	0.0357511i	0.188205	+	0.982130i	$0.439733\pi$
$422$	23.6592	+	2.48669i	1.15171	+	0.121050i
$423$	−16.4226	+	4.69483i	−0.798493	+	0.228270i
$424$	−0.556649	+	2.61883i	−0.0270333	+	0.127181i
$425$	−32.9442	−	9.44659i	−1.59803	−	0.458227i
$426$	1.80304	+	1.80449i	0.0873577	+	0.0874279i
$427$	6.53921	+	16.1851i	0.316454	+	0.783252i
$428$	−24.2683	−	8.83293i	−1.17305	−	0.426956i
$429$	7.74598	−	4.49579i	0.373980	−	0.217059i
$430$	−12.6157	+	71.5472i	−0.608383	+	3.45031i
$431$	−10.7144	+	32.9755i	−0.516094	+	1.58838i	0.265188	+	0.964197i	$0.414566\pi$
$431$	−10.7144	+	32.9755i	−0.516094	+	1.58838i	−0.781282	+	0.624178i	$0.785434\pi$
$432$	12.4002	+	9.36765i	0.596605	+	0.450701i
$433$	−1.32278	−	0.961056i	−0.0635687	−	0.0461854i	0.555547	−	0.831485i	$-0.312509\pi$
$433$	−1.32278	−	0.961056i	−0.0635687	−	0.0461854i	−0.619116	+	0.785300i	$0.712509\pi$
$434$	−1.48978	−	10.6004i	−0.0715119	−	0.508833i
$435$	36.7929	+	48.8666i	1.76408	+	2.34297i
$436$	−1.02986	+	0.694649i	−0.0493213	+	0.0332676i
$437$	3.60326	−	14.4519i	0.172367	−	0.691327i
$438$	12.9301	+	33.7246i	0.617826	+	1.61142i
$439$	2.00744	+	5.51540i	0.0958100	+	0.263236i	0.978334	−	0.207031i	$-0.0663800\pi$
$439$	2.00744	+	5.51540i	0.0958100	+	0.263236i	−0.882524	+	0.470266i	$0.844158\pi$
$440$	2.72668	−	11.9571i	0.129989	−	0.570032i
$441$	4.51756	−	1.46383i	0.215122	−	0.0697064i
$442$	−1.82955	−	8.60735i	−0.0870228	−	0.409410i
$443$	−0.122837	+	1.75665i	−0.00583617	+	0.0834611i	−0.999609	−	0.0279649i	$-0.991097\pi$
$443$	−0.122837	+	1.75665i	−0.00583617	+	0.0834611i	0.993773	+	0.111426i	$0.0355418\pi$
$444$	18.8322	−	24.9704i	0.893739	−	1.18504i
$445$	49.9668	−	26.5678i	2.36865	−	1.25944i
$446$	−27.9520	+	14.8623i	−1.32356	+	0.703751i
$447$	−5.66516	+	7.51164i	−0.267953	+	0.355288i
$448$	−1.77265	+	25.3500i	−0.0837497	+	1.19768i
$449$	−4.77961	−	22.4863i	−0.225564	−	1.06119i	−0.934511	−	0.355933i	$-0.884163\pi$
$449$	−4.77961	−	22.4863i	−0.225564	−	1.06119i	0.708947	−	0.705261i	$-0.249170\pi$
$450$	59.7569	+	53.8923i	2.81697	+	2.54051i
$451$	3.89507	−	6.52213i	0.183412	−	0.307115i
$452$	0.528465	+	1.45195i	0.0248569	+	0.0682938i
$453$	−8.15594	−	21.2725i	−0.383199	−	0.999468i
$454$	2.22453	−	8.92212i	0.104403	−	0.418736i
$455$	−12.6785	+	8.55174i	−0.594376	+	0.400912i
$456$	2.19804	+	2.91934i	0.102933	+	0.136711i
$457$	−3.56823	−	25.3893i	−0.166915	−	1.18766i	−0.875920	−	0.482457i	$-0.839745\pi$
$457$	−3.56823	−	25.3893i	−0.166915	−	1.18766i	0.709005	−	0.705203i	$-0.249144\pi$
$458$	17.4444	+	12.6741i	0.815125	+	0.592223i
$459$	7.58577	+	11.7119i	0.354073	+	0.546666i
$460$	19.5008	−	60.0173i	0.909230	−	2.79832i
$461$	−6.13465	+	34.7913i	−0.285719	+	1.62039i	0.416987	+	0.908912i	$0.363086\pi$
$461$	−6.13465	+	34.7913i	−0.285719	+	1.62039i	−0.702706	+	0.711480i	$0.748025\pi$
$462$	−27.9539	−	2.87346i	−1.30053	−	0.133685i
$463$	11.6430	+	4.23770i	0.541095	+	0.196943i	0.598086	−	0.801432i	$-0.295928\pi$
$463$	11.6430	+	4.23770i	0.541095	+	0.196943i	−0.0569904	+	0.998375i	$0.518150\pi$
$464$	−9.38842	−	23.2372i	−0.435846	−	1.07876i
$465$	11.2906	+	11.2997i	0.523590	+	0.524011i
$466$	41.8839	+	12.0100i	1.94024	+	0.556353i
$467$	5.14581	−	24.2091i	0.238119	−	1.12026i	−0.682829	−	0.730579i	$-0.739250\pi$
$467$	5.14581	−	24.2091i	0.238119	−	1.12026i	0.920948	−	0.389685i	$-0.127416\pi$
$468$	−2.74419	+	10.9688i	−0.126850	+	0.507033i
$469$	−0.125802	−	0.0132223i	−0.00580899	−	0.000610549i
$470$	50.3097	+	3.51800i	2.32062	+	0.162273i
$471$	0.149195	+	0.769191i	0.00687455	+	0.0354424i
$472$	−7.51241	+	1.32464i	−0.345787	+	0.0609715i
$473$	24.2705	+	12.2844i	1.11596	+	0.564836i
$474$	−24.7429	+	41.1416i	−1.13648	+	1.88970i
$475$	−16.2624	−	26.0253i	−0.746171	−	1.19412i
$476$	−6.14566	+	13.8034i	−0.281686	+	0.632677i
$477$	−7.76733	+	4.84490i	−0.355641	+	0.221833i
$478$	41.7701	+	8.87851i	1.91052	+	0.406094i
$479$	15.6947	+	20.0883i	0.717110	+	0.917859i	0.999137	−	0.0415477i	$-0.0132288\pi$
$479$	15.6947	+	20.0883i	0.717110	+	0.917859i	−0.282027	+	0.959407i	$0.591007\pi$
$480$	−31.9484	−	49.2394i	−1.45824	−	2.24746i
$481$	−11.2995	−	2.81727i	−0.515211	−	0.128456i
$482$	21.4495	+	16.7582i	0.976998	+	0.763314i
$483$	−24.5088	−	4.77423i	−1.11519	−	0.217235i
$484$	−23.1005	−	13.1720i	−1.05002	−	0.598726i
$485$		−	19.0890i		−	0.866788i
$486$	−3.92757	−	32.5271i	−0.178158	−	1.47546i
$487$	−16.4506	+	11.9521i	−0.745447	+	0.541599i	−0.894412	−	0.447243i	$-0.852406\pi$
$487$	−16.4506	+	11.9521i	−0.745447	+	0.541599i	0.148965	+	0.988842i	$0.452406\pi$
$488$	−4.57119	−	4.73360i	−0.206928	−	0.214280i
$489$	2.57694	+	21.0573i	0.116533	+	0.952246i
$490$	−14.0130	−	0.489345i	−0.633043	−	0.0221063i
$491$	−31.7619	+	2.22101i	−1.43339	+	0.100233i	−0.765218	−	0.643771i	$-0.777369\pi$
$491$	−31.7619	+	2.22101i	−1.43339	+	0.100233i	−0.668175	+	0.744004i	$0.732924\pi$
$492$	2.47851	+	9.26482i	0.111740	+	0.417690i
$493$	−0.785343	−	22.4893i	−0.0353701	−	1.01287i
$494$	3.93979	−	6.82392i	0.177260	−	0.307023i
$495$	35.9035	−	21.6652i	1.61374	−	0.973780i
$496$	−3.27237	−	5.66791i	−0.146934	−	0.254497i
$497$	−1.38309	+	0.864252i	−0.0620402	+	0.0387670i
$498$	−9.60915	+	0.836804i	−0.430596	+	0.0374981i
$499$	−6.22252	+	12.7581i	−0.278558	+	0.571129i	−0.991502	−	0.130092i	$-0.958473\pi$
$499$	−6.22252	+	12.7581i	−0.278558	+	0.571129i	0.712944	+	0.701221i	$0.247362\pi$
$500$	−37.1272	−	69.8260i	−1.66038	−	3.12272i
$501$	−9.12868	−	8.51948i	−0.407839	−	0.380622i
$502$	34.1974	−	8.52638i	1.52631	−	0.380551i
$503$	18.3244	+	8.15853i	0.817043	+	0.363771i	0.772324	−	0.635229i	$-0.219094\pi$
$503$	18.3244	+	8.15853i	0.817043	+	0.363771i	0.0447187	+	0.999000i	$0.485761\pi$
$504$	4.69613	−	3.93410i	0.209182	−	0.175239i
$505$	−10.9360	−	6.31392i	−0.486647	−	0.280966i
$506$	−35.4346	−	24.6699i	−1.57526	−	1.09671i
$507$	−18.0824	+	2.85652i	−0.803066	+	0.126863i
$508$	19.1303	−	7.72915i	0.848771	−	0.342926i
$509$	−3.58651	−	12.5076i	−0.158969	−	0.554392i	−0.999912	−	0.0132676i	$-0.995777\pi$
$509$	−3.58651	−	12.5076i	−0.158969	−	0.554392i	0.840943	−	0.541124i	$-0.182001\pi$
$510$	−9.25211	−	40.1488i	−0.409691	−	1.77782i
$511$	−22.8674	+	3.21380i	−1.01159	+	0.142170i
$512$	9.05328	+	27.8631i	0.400102	+	1.23139i
$513$	−1.96951	+	12.3388i	−0.0869559	+	0.544771i
$514$	27.9348	+	38.4490i	1.23215	+	1.69591i
$515$	23.2869	−	43.7963i	1.02614	−	1.92989i
$516$	−32.4756	+	11.1677i	−1.42966	+	0.491629i
$517$	6.71971	−	17.6471i	0.295532	−	0.776118i
$518$	23.4869	+	27.9906i	1.03195	+	1.22983i
$519$	−8.01978	+	3.07481i	−0.352029	+	0.134969i
$520$	3.22376	−	4.77942i	0.141371	−	0.209591i
$521$	17.0811	+	38.3648i	0.748336	+	1.68079i	0.732359	+	0.680918i	$0.238419\pi$
$521$	17.0811	+	38.3648i	0.748336	+	1.68079i	0.0159767	+	0.999872i	$0.494914\pi$
$522$	−21.5292	+	48.2510i	−0.942306	+	2.11189i
$523$	23.2581	+	20.9417i	1.01701	+	0.915717i	0.996460	−	0.0840718i	$-0.0267925\pi$
$523$	23.2581	+	20.9417i	1.01701	+	0.915717i	0.0205471	+	0.999789i	$0.493459\pi$
$524$	−9.73700	−	39.0530i	−0.425363	−	1.70604i
$525$	−42.1552	+	29.4921i	−1.83980	+	1.28714i
$526$	−17.1114	−	2.40485i	−0.746091	−	0.104856i
$527$	−1.02044	−	5.78718i	−0.0444509	−	0.252093i
$528$	−16.5046	+	4.77349i	−0.718271	+	0.207740i
$529$	−11.7700	−	9.87624i	−0.511741	−	0.429402i
$530$	26.4393	−	5.61984i	1.14845	−	0.244110i
$531$	−21.0893	−	15.3482i	−0.915200	−	0.666055i
$532$	−12.3601	+	5.50309i	−0.535880	+	0.238589i
$533$	2.81400	−	2.19854i	0.121888	−	0.0952293i
$534$	40.9849	+	26.6393i	1.77359	+	1.15280i
$535$	3.14071	+	44.9142i	0.135785	+	1.94181i
$536$	0.0458377	−	0.0131437i	0.00197989	−	0.000567723i
$537$	0.166045	+	9.73671i	0.00716536	+	0.420170i
$538$	−44.5582	−	7.85681i	−1.92104	−	0.338731i
$539$	−1.69588	+	4.96855i	−0.0730468	+	0.214011i
$540$	−11.9711	+	51.5690i	−0.515154	+	2.21918i
$541$	−34.4714	−	11.2004i	−1.48204	−	0.481544i	−0.547319	−	0.836924i	$-0.684352\pi$
$541$	−34.4714	−	11.2004i	−1.48204	−	0.481544i	−0.934722	+	0.355379i	$0.884352\pi$
$542$	51.4172	−	25.0778i	2.20856	−	1.07719i
$543$	−4.90417	+	1.13014i	−0.210458	+	0.0484991i
$544$	−0.753591	+	21.5800i	−0.0323099	+	0.925235i
$545$	1.83660	+	1.14763i	0.0786711	+	0.0491592i
$546$	−11.7675	−	6.00179i	−0.503603	−	0.256853i
$547$	3.37987	+	2.27975i	0.144513	+	0.0974750i	0.629321	−	0.777145i	$-0.283333\pi$
$547$	3.37987	+	2.27975i	0.144513	+	0.0974750i	−0.484809	+	0.874620i	$0.661111\pi$
$548$	−35.5068	+	31.9704i	−1.51677	+	1.36571i
$549$	0.803305	−	22.4860i	0.0342842	−	0.959678i
$550$	−87.2814	+	17.2094i	−3.72169	+	0.733811i
$551$	12.9523	−	15.4359i	0.551785	−	0.657592i
$552$	9.24054	−	1.79233i	0.393303	−	0.0762866i
$553$	−22.0796	−	21.3220i	−0.938918	−	0.906703i
$554$	−35.8116	−	17.4665i	−1.52149	−	0.742080i
$555$	−53.1228	−	12.2868i	−2.25494	−	0.521547i
$556$	4.60047	+	1.85871i	0.195103	+	0.0788268i
$557$	3.01471	−	28.6830i	0.127737	−	1.21534i	−0.723412	−	0.690416i	$-0.757427\pi$
$557$	3.01471	−	28.6830i	0.127737	−	1.21534i	0.851150	−	0.524923i	$-0.175906\pi$
$558$	−3.81381	+	13.2601i	−0.161451	+	0.561347i
$559$	8.55625	+	9.50267i	0.361891	+	0.401920i
$560$	27.5681	−	10.0340i	1.16497	−	0.424013i
$561$	−15.3915	−	1.04092i	−0.649831	−	0.0439476i
$562$	27.1519	−	22.7831i	1.14533	−	0.961048i
$563$	−0.777615	+	0.995302i	−0.0327726	+	0.0419470i	−0.804118	−	0.594470i	$-0.797362\pi$
$563$	−0.777615	+	0.995302i	−0.0327726	+	0.0419470i	0.771345	+	0.636417i	$0.219584\pi$
$564$	10.0663	+	21.6099i	0.423869	+	0.909943i
$565$	1.93771	−	1.87122i	0.0815200	−	0.0787229i
$566$	13.0624	−	4.24424i	0.549055	−	0.178399i
$567$	20.8288	+	2.22302i	0.874729	+	0.0933581i
$568$	0.361375	−	0.497390i	0.0151629	−	0.0208700i
$569$	9.45478	+	19.3852i	0.396365	+	0.812669i	0.999883	+	0.0153191i	$0.00487640\pi$
$569$	9.45478	+	19.3852i	0.396365	+	0.812669i	−0.603518	+	0.797350i	$0.706235\pi$
$570$	17.8992	−	32.2604i	0.749714	−	1.35124i
$571$	5.16666	−	14.1953i	0.216218	−	0.594054i	−0.783405	−	0.621512i	$-0.786519\pi$
$571$	5.16666	−	14.1953i	0.216218	−	0.594054i	0.999623	+	0.0274575i	$0.00874110\pi$
$572$	−7.89273	−	9.69331i	−0.330012	−	0.405298i
$573$	−32.4336	−	12.4650i	−1.35493	−	0.520734i
$574$	−11.1978	+	0.391035i	−0.467386	+	0.0163215i
$575$	−78.6143	+	8.26270i	−3.27844	+	0.344578i
$576$	15.4007	−	28.9086i	0.641698	−	1.20452i
$577$	23.2602	−	25.8331i	0.968335	−	1.07545i	−0.0287835	−	0.999586i	$-0.509163\pi$
$577$	23.2602	−	25.8331i	0.968335	−	1.07545i	0.997119	−	0.0758593i	$-0.0241700\pi$
$578$	7.70679	−	19.0750i	0.320560	−	0.793414i
$579$	27.2129	−	11.5383i	1.13093	−	0.479516i
$580$	59.3062	−	61.4134i	2.46256	−	2.55005i
$581$	0.858255	−	6.10680i	0.0356064	−	0.253353i
$582$	14.4245	−	7.98804i	0.597913	−	0.331115i
$583$	0.854967	−	10.0845i	0.0354091	−	0.417656i
$584$	7.53881	−	4.35253i	0.311958	−	0.180109i
$585$	19.4153	−	3.40737i	0.802725	−	0.140878i
$586$	0.604705	+	5.75338i	0.0249801	+	0.237670i
$587$	11.6460	−	40.6145i	0.480682	−	1.67634i	−0.230293	−	0.973121i	$-0.573968\pi$
$587$	11.6460	−	40.6145i	0.480682	−	1.67634i	0.710975	−	0.703217i	$-0.248254\pi$
$588$	−3.00667	−	5.90678i	−0.123993	−	0.243592i
$589$	2.78845	−	4.46246i	0.114896	−	0.183872i
$590$	43.0658	+	63.8476i	1.77299	+	2.62856i
$591$	0.243523	−	2.77067i	0.0100172	−	0.113970i
$592$	19.7250	+	10.4880i	0.810693	+	0.431053i
$593$	35.0501			1.43934			0.719668	−	0.694318i	$-0.244294\pi$
$593$	35.0501			1.43934			0.719668	+	0.694318i	$0.244294\pi$
$594$	31.3954	+	18.0641i	1.28817	+	0.741178i
$595$	26.3417			1.07991
$596$	11.5944	+	6.16487i	0.474926	+	0.252523i
$597$	5.67910	+	3.97995i	0.232430	+	0.162888i
$598$	−11.3495	−	16.8263i	−0.464116	−	0.688080i
$599$	2.65258	−	4.24502i	0.108382	−	0.173447i	−0.789411	−	0.613865i	$-0.789614\pi$
$599$	2.65258	−	4.24502i	0.108382	−	0.173447i	0.897793	+	0.440418i	$0.145170\pi$
$600$	10.5694	−	16.2611i	0.431493	−	0.663857i
$601$	11.6924	−	40.7762i	0.476942	−	1.66329i	−0.243594	−	0.969877i	$-0.578326\pi$
$601$	11.6924	−	40.7762i	0.476942	−	1.66329i	0.720536	−	0.693417i	$-0.243896\pi$
$602$	−4.19383	−	39.9016i	−0.170928	−	1.62627i
$603$	0.141137	+	0.0816367i	0.00574754	+	0.00332450i
$604$	−27.5376	+	15.8989i	−1.12049	+	0.646916i
$605$	−4.59795	+	46.1310i	−0.186933	+	1.87549i
$606$	0.194742	−	10.9058i	0.00791084	−	0.443019i
$607$	0.0292096	−	0.207837i	0.00118558	−	0.00843586i	−0.989666	−	0.143390i	$-0.954200\pi$
$607$	0.0292096	−	0.207837i	0.00118558	−	0.00843586i	0.990852	+	0.134954i	$0.0430886\pi$
$608$	−13.4315	+	13.9088i	−0.544721	+	0.564075i
$609$	−26.9702	−	20.3405i	−1.09289	−	0.824238i
$610$	−24.8872	+	61.5979i	−1.00765	+	2.49403i
$611$	5.93954	−	6.59653i	0.240288	−	0.266867i
$612$	14.4838	−	13.0202i	0.585471	−	0.526310i
$613$	−17.6289	+	1.85287i	−0.712023	+	0.0748366i	−0.453613	−	0.891199i	$-0.649865\pi$
$613$	−17.6289	+	1.85287i	−0.712023	+	0.0748366i	−0.258410	+	0.966035i	$0.583199\pi$
$614$	6.15106	−	0.214800i	0.248237	−	0.00866861i
$615$	12.9981	−	10.5170i	0.524134	−	0.424087i
$616$	0.372641	+	6.76255i	0.0150142	+	0.272471i
$617$	−4.11436	+	11.3041i	−0.165638	+	0.455087i	−0.994546	−	0.104298i	$-0.966740\pi$
$617$	−4.11436	+	11.3041i	−0.165638	+	0.455087i	0.828908	+	0.559385i	$0.188963\pi$
$618$	42.8389	−	0.730553i	1.72323	−	0.0293871i
$619$	7.67156	+	15.7290i	0.308346	+	0.632203i	0.995547	−	0.0942639i	$-0.0300498\pi$
$619$	7.67156	+	15.7290i	0.308346	+	0.632203i	−0.687201	+	0.726467i	$0.741161\pi$
$620$	13.1046	−	18.0369i	0.526292	−	0.724379i
$621$	26.3418	+	18.4921i	1.05706	+	0.742061i
$622$	−18.1065	+	5.88315i	−0.726003	+	0.235893i
$623$	−22.4810	+	21.7097i	−0.900683	+	0.869779i
$624$	−8.04537	−	0.707133i	−0.322072	−	0.0283080i
$625$	−45.5961	+	58.3603i	−1.82384	+	2.33441i
$626$	8.65823	−	7.26512i	0.346052	−	0.290372i
$627$	−9.61852	−	9.91480i	−0.384127	−	0.395959i
$628$	1.02763	−	0.374026i	0.0410069	−	0.0149253i
$629$	13.4220	+	14.9066i	0.535169	+	0.594365i
$630$	−55.5682	−	27.1577i	−2.21389	−	1.08199i
$631$	−3.21151	+	30.5555i	−0.127848	+	1.21640i	0.722949	+	0.690901i	$0.242786\pi$
$631$	−3.21151	+	30.5555i	−0.127848	+	1.21640i	−0.850797	+	0.525494i	$0.823881\pi$
$632$	10.7283	+	4.33451i	0.426748	+	0.172418i
$633$	13.3762	−	14.3326i	0.531655	−	0.569671i
$634$	29.3200	+	14.3003i	1.16444	+	0.567938i
$635$	−25.8750	−	24.9872i	−1.02682	−	0.991586i
$636$	8.37862	+	9.64632i	0.332234	+	0.382501i
$637$	−1.58633	+	1.89052i	−0.0628528	+	0.0749050i
$638$	−28.4562	−	51.0125i	−1.12659	−	2.01960i
$639$	2.08196	−	0.290896i	0.0823610	−	0.0115076i
$640$	−21.5048	+	19.3630i	−0.850052	+	0.765391i
$641$	13.0132	+	8.77752i	0.513991	+	0.346691i	0.788642	−	0.614853i	$-0.210785\pi$
$641$	13.0132	+	8.77752i	0.513991	+	0.346691i	−0.274651	+	0.961544i	$0.588562\pi$
$642$	−32.6247	+	21.1681i	−1.28760	+	0.835439i
$643$	29.3894	+	18.3645i	1.15901	+	0.724227i	0.966398	−	0.257049i	$-0.0827502\pi$
$643$	29.3894	+	18.3645i	1.15901	+	0.724227i	0.192607	+	0.981276i	$0.438306\pi$
$644$	−1.21625	+	34.8290i	−0.0479272	+	1.37245i
$645$	40.8143	+	43.8032i	1.60706	+	1.72475i
$646$	−12.1988	+	5.94973i	−0.479954	+	0.234089i
$647$	−13.5611	−	4.40627i	−0.533142	−	0.173228i	0.0300594	−	0.999548i	$-0.490430\pi$
$647$	−13.5611	−	4.40627i	−0.533142	−	0.173228i	−0.563201	+	0.826320i	$0.690430\pi$
$648$	−7.59405	+	2.16437i	−0.298323	+	0.0850244i
$649$	27.5532	−	8.50491i	1.08156	−	0.333847i
$650$	−41.1834	−	7.26175i	−1.61535	−	0.284829i
$651$	−7.71374	−	4.27984i	−0.302325	−	0.167740i
$652$	28.4623	−	8.16143i	1.11467	−	0.319626i
$653$	2.15052	+	30.7539i	0.0841563	+	1.20349i	0.837714	+	0.546109i	$0.183892\pi$
$653$	2.15052	+	30.7539i	0.0841563	+	1.20349i	−0.753558	+	0.657382i	$0.771664\pi$
$654$	−0.0986522	+	1.86805i	−0.00385761	+	0.0730464i
$655$	−55.2932	+	43.1998i	−2.16048	+	1.68795i
$656$	−6.25822	+	2.78634i	−0.244343	+	0.108788i
$657$	28.6052	+	8.22727i	1.11599	+	0.320976i
$658$	−27.2427	+	5.79062i	−1.06203	+	0.225742i
$659$	−8.62254	−	7.23517i	−0.335886	−	0.281842i	0.459207	−	0.888329i	$-0.348134\pi$
$659$	−8.62254	−	7.23517i	−0.335886	−	0.281842i	−0.795093	+	0.606487i	$0.792578\pi$
$660$	−37.7233	−	44.7487i	−1.46838	−	1.74184i
$661$	5.43460	+	30.8211i	0.211381	+	1.19880i	0.887077	+	0.461622i	$0.152732\pi$
$661$	5.43460	+	30.8211i	0.211381	+	1.19880i	−0.675695	+	0.737181i	$0.736157\pi$
$662$	11.9169	+	1.67482i	0.463165	+	0.0650936i
$663$	−6.57104	−	3.06734i	−0.255198	−	0.119126i
$664$	0.562399	+	2.25566i	0.0218253	+	0.0875365i
$665$	17.5290	+	15.7832i	0.679744	+	0.612044i
$666$	−12.9454	−	45.2833i	−0.501626	−	1.75469i
$667$	−21.1108	−	47.4155i	−0.817412	−	1.83594i
$668$	−9.74544	+	14.4482i	−0.377062	+	0.559018i
$669$	−4.09151	+	25.7658i	−0.158187	+	0.996165i
$670$	−0.309450	−	0.368788i	−0.0119551	−	0.0142475i
$671$	19.3736	+	15.6024i	0.747908	+	0.602322i
$672$	24.4552	+	21.2758i	0.943381	+	0.820734i
$673$	−10.1244	+	19.0412i	−0.390267	+	0.733985i	−0.998198	−	0.0600043i	$-0.980889\pi$
$673$	−10.1244	+	19.0412i	−0.390267	+	0.733985i	0.607931	+	0.793990i	$0.292000\pi$
$674$	17.2369	+	23.7246i	0.663941	+	0.913837i
$675$	65.1105	−	12.5748i	2.50611	−	0.484006i
$676$	7.89563	+	24.3003i	0.303678	+	0.934625i
$677$	−14.9264	+	2.09776i	−0.573667	+	0.0806236i	−0.420040	−	0.907505i	$-0.637984\pi$
$677$	−14.9264	+	2.09776i	−0.573667	+	0.0806236i	−0.153626	+	0.988129i	$0.549095\pi$
$678$	2.22483	+	0.681175i	0.0854441	+	0.0261604i
$679$	2.90574	+	10.1335i	0.111512	+	0.388889i
$680$	−9.20701	+	3.71987i	−0.353073	+	0.142651i
$681$	−4.76645	−	5.89091i	−0.182651	−	0.225740i
$682$	−9.21276	−	12.1576i	−0.352775	−	0.465539i
$683$	−18.9326	−	10.9307i	−0.724436	−	0.418253i	0.0919472	−	0.995764i	$-0.470691\pi$
$683$	−18.9326	−	10.9307i	−0.724436	−	0.418253i	−0.816383	+	0.577511i	$0.804024\pi$
$684$	17.4394	+	0.0140025i	0.666814	+	0.000535398i
$685$	76.0952	+	33.8798i	2.90745	+	1.29448i
$686$	40.7388	−	10.1573i	1.55541	−	0.387808i
$687$	16.9951	−	5.18846i	0.648403	−	0.197952i
$688$	−11.5162	−	21.6589i	−0.439052	−	0.825737i
$689$	2.08554	−	4.27598i	0.0794526	−	0.162902i
$690$	−54.4755	−	77.8656i	−2.07385	−	2.96429i
$691$	−0.0633352	+	0.0395762i	−0.00240938	+	0.00150555i	−0.531123	−	0.847294i	$-0.678230\pi$
$691$	−0.0633352	+	0.0395762i	−0.00240938	+	0.00150555i	0.528714	+	0.848800i	$0.322674\pi$
$692$	5.99392	+	10.3818i	0.227855	+	0.394656i
$693$	−15.7617	+	16.9664i	−0.598738	+	0.644499i
$694$	−7.13336	+	12.3553i	−0.270778	+	0.469002i
$695$	−0.301887	−	8.64492i	−0.0114512	−	0.327920i
$696$	12.2991	+	3.30082i	0.466195	+	0.125117i
$697$	−6.13599	+	0.429070i	−0.232417	+	0.0162522i
$698$	−12.8616	−	0.449136i	−0.486818	−	0.0170001i
$699$	28.6854	−	21.5979i	1.08498	−	0.816909i
$700$	49.8807	+	51.6529i	1.88531	+	1.95230i
$701$	−19.6625	+	14.2856i	−0.742642	+	0.539561i	−0.893537	−	0.448989i	$-0.851784\pi$
$701$	−19.6625	+	14.2856i	−0.742642	+	0.539561i	0.150896	+	0.988550i	$0.451784\pi$
$702$	10.6993	+	13.2452i	0.403820	+	0.499906i
$703$			17.9615i			0.677432i
$704$	15.3920	+	32.7779i	0.580108	+	1.23537i
$705$	27.2791	−	31.3555i	1.02739	−	1.18092i
$706$	13.0505	+	10.1961i	0.491161	+	0.383737i
$707$	6.76656	+	1.68709i	0.254483	+	0.0634497i
$708$	−16.5403	+	32.4301i	−0.621624	+	1.21880i
$709$	4.64217	+	5.94171i	0.174340	+	0.223145i	0.867242	−	0.497886i	$-0.165890\pi$
$709$	4.64217	+	5.94171i	0.174340	+	0.223145i	−0.692902	+	0.721032i	$0.743668\pi$
$710$	−6.07136	−	1.29051i	−0.227854	−	0.0484319i
$711$	14.7913	+	36.6946i	0.554718	+	1.37615i
$712$	4.79185	−	10.7627i	0.179582	−	0.403348i
$713$	−7.18250	−	11.4944i	−0.268987	−	0.430468i
$714$	11.0230	+	19.9049i	0.412526	+	0.744922i
$715$	−9.84135	+	19.4438i	−0.368046	+	0.727156i
$716$	13.3852	−	2.36016i	0.500227	−	0.0882035i
$717$	26.5685	−	23.0769i	0.992220	−	0.861824i
$718$	−66.6051	−	4.65748i	−2.48568	−	0.173816i
$719$	24.4313	+	2.56784i	0.911135	+	0.0957642i	0.548484	−	0.836161i	$-0.315205\pi$
$719$	24.4313	+	2.56784i	0.911135	+	0.0957642i	0.362651	+	0.931925i	$0.381872\pi$
$720$	−37.7205	−	2.66811i	−1.40576	−	0.0994345i
$721$	−5.69529	+	26.7942i	−0.212104	+	0.997870i
$722$	26.7042	+	7.65732i	0.993829	+	0.284976i
$723$	21.6696	−	5.79702i	0.805900	−	0.215593i
$724$	2.63132	+	6.51275i	0.0977923	+	0.242044i
$725$	−100.492	−	36.5761i	−3.73218	−	1.35840i
$726$	−36.7825	+	15.8297i	−1.36513	+	0.587495i
$727$	−2.22693	+	12.6296i	−0.0825924	+	0.468405i	0.915258	+	0.402869i	$0.131987\pi$
$727$	−2.22693	+	12.6296i	−0.0825924	+	0.468405i	−0.997850	+	0.0655360i	$0.979124\pi$
$728$	−0.983826	+	3.02791i	−0.0364630	+	0.112222i
$729$	−23.3501	−	13.5563i	−0.864819	−	0.502085i
$730$	−71.1005	−	51.6575i	−2.63155	−	1.91193i
$731$	−3.06535	−	21.8111i	−0.113376	−	0.806711i
$732$	−31.1715	+	3.81468i	−1.15213	+	0.140995i
$733$	11.3585	−	7.66143i	0.419537	−	0.282981i	−0.331228	−	0.943551i	$-0.607463\pi$
$733$	11.3585	−	7.66143i	0.419537	−	0.282981i	0.750765	+	0.660569i	$0.229685\pi$
$734$	0.892872	−	3.58111i	0.0329565	−	0.132181i
$735$	−7.27541	+	8.97701i	−0.268358	+	0.331122i
$736$	17.0341	+	46.8007i	0.627884	+	1.72510i
$737$	−0.165735	+	0.0708769i	−0.00610495	+	0.00261079i
$738$	13.3863	+	5.42092i	0.492756	+	0.199547i
$739$	−9.46607	−	44.5344i	−0.348215	−	1.63822i	−0.708737	−	0.705473i	$-0.750735\pi$
$739$	−9.46607	−	44.5344i	−0.348215	−	1.63822i	0.360522	−	0.932751i	$-0.382599\pi$
$740$	−5.30858	+	75.9163i	−0.195147	+	2.79074i
$741$	−2.53481	−	5.97831i	−0.0931186	−	0.219619i
$742$	−13.1800	+	7.00792i	−0.483852	+	0.257269i
$743$	46.1084	−	24.5163i	1.69155	−	0.899415i	0.710993	−	0.703199i	$-0.248246\pi$
$743$	46.1084	−	24.5163i	1.69155	−	0.899415i	0.980561	−	0.196216i	$-0.0628654\pi$
$744$	3.30050	+	0.406596i	0.121002	+	0.0149065i
$745$	1.59694	−	22.8373i	0.0585073	−	0.836694i
$746$	10.8355	+	50.9768i	0.396714	+	1.86639i
$747$	−4.21762	+	6.73756i	−0.154315	+	0.246514i
$748$	1.93423	+	21.4442i	0.0707223	+	0.784078i
$749$	−8.50412	−	23.3649i	−0.310734	−	0.853734i
$750$	−117.615	−	18.6768i	−4.29470	−	0.681982i
$751$	−1.22810	+	4.92564i	−0.0448140	+	0.179739i	−0.988532	−	0.151012i	$-0.951747\pi$
$751$	−1.22810	+	4.92564i	−0.0448140	+	0.179739i	0.943718	+	0.330752i	$0.107302\pi$
$752$	−14.1171	+	9.52210i	−0.514797	+	0.347235i
$753$	11.3593	−	26.7311i	0.413957	−	0.974134i
$754$	−3.82146	−	27.1911i	−0.139169	−	0.990242i
$755$	44.8480	+	32.5840i	1.63219	+	1.18585i
$756$	−1.49494	−	29.1980i	−0.0543705	−	1.06192i
$757$	−11.3779	+	35.0174i	−0.413535	+	1.27273i	0.500019	+	0.866014i	$0.333326\pi$
$757$	−11.3779	+	35.0174i	−0.413535	+	1.27273i	−0.913555	+	0.406716i	$0.866674\pi$
$758$	3.01124	−	17.0776i	0.109373	−	0.620286i
$759$	−33.8147	+	11.0726i	−1.22740	+	0.401910i
$760$	−8.35559	−	3.04118i	−0.303089	−	0.110315i
$761$	−12.6870	−	31.4014i	−0.459904	−	1.13830i	−0.961893	−	0.273428i	$-0.911843\pi$
$761$	−12.6870	−	31.4014i	−0.459904	−	1.13830i	0.501989	−	0.864874i	$-0.332602\pi$
$762$	8.05363	−	30.0084i	0.291752	−	1.08709i
$763$	−1.14966	−	0.329660i	−0.0416205	−	0.0119345i
$764$	−10.0829	+	47.4364i	−0.364787	+	1.71619i
$765$	−31.0069	−	13.8350i	−1.12106	−	0.500206i
$766$	−9.18662	−	0.965553i	−0.331926	−	0.0348868i
$767$	13.5220	+	0.945553i	0.488253	+	0.0341419i
$768$	12.1262	+	4.18083i	0.437566	+	0.150863i
$769$	−3.78007	+	0.666529i	−0.136313	+	0.0240356i	−0.241388	−	0.970429i	$-0.577603\pi$
$769$	−3.78007	+	0.666529i	−0.136313	+	0.0240356i	0.105075	+	0.994464i	$0.466492\pi$
$770$	60.8408	−	31.2062i	2.19255	−	1.12460i
$771$	39.1591	+	0.699251i	1.41028	+	0.0251829i
$772$	−21.8616	−	34.9859i	−0.786816	−	1.25917i
$773$	−11.4630	+	25.7464i	−0.412296	+	0.926033i	0.581367	+	0.813641i	$0.302518\pi$
$773$	−11.4630	+	25.7464i	−0.412296	+	0.926033i	−0.993664	+	0.112392i	$0.964149\pi$
$774$	−16.0203	+	49.1709i	−0.575837	+	1.76741i
$775$	−27.3165	−	5.80631i	−0.981239	−	0.208569i
$776$	−2.44663	−	3.13155i	−0.0878291	−	0.112416i
$777$	30.0709	−	1.56384i	1.07879	−	0.0561025i
$778$	70.6516	+	17.6154i	2.53298	+	0.631544i
$779$	−4.34025	−	3.39097i	−0.155505	−	0.121494i
$780$	−8.94672	−	26.0171i	−0.320344	−	0.931562i
$781$	−1.12125	+	2.03568i	−0.0401216	+	0.0728424i
$782$			34.9597i			1.25016i
$783$	21.0636	+	38.1079i	0.752752	+	1.36187i
$784$	3.83013	−	2.78275i	0.136790	−	0.0993839i
$785$	−1.32438	−	1.37143i	−0.0472690	−	0.0489485i
$786$	−55.7816	−	23.7043i	−1.98966	−	0.845505i
$787$	−7.05225	−	0.246270i	−0.251385	−	0.00877857i	−0.0910704	−	0.995844i	$-0.529029\pi$
$787$	−7.05225	−	0.246270i	−0.251385	−	0.00877857i	−0.160315	+	0.987066i	$0.551251\pi$
$788$	−3.87251	+	0.270792i	−0.137953	+	0.00964658i
$789$	−10.0732	+	10.0651i	−0.358614	+	0.358326i
$790$	−4.07686	−	116.746i	−0.145048	−	4.15364i
$791$	−0.743805	+	1.28831i	−0.0264467	+	0.0458070i
$792$	3.11314	−	8.15592i	0.110620	−	0.289808i
$793$	5.84657	+	10.1266i	0.207618	+	0.359605i
$794$	−59.5442	+	37.2073i	−2.11314	+	1.32044i
$795$	9.42197	−	20.1843i	0.334163	−	0.715864i
$796$	4.24303	−	8.69949i	0.150390	−	0.308345i
$797$	16.0456	+	30.1774i	0.568365	+	1.06894i	0.986990	+	0.160780i	$0.0514008\pi$
$797$	16.0456	+	30.1774i	0.568365	+	1.06894i	−0.418626	+	0.908159i	$0.637488\pi$
$798$	−4.59119	+	19.8503i	−0.162526	+	0.702691i
$799$	−14.8354	+	3.69887i	−0.524837	+	0.130857i
$800$	93.7459	+	41.7384i	3.31442	+	1.47567i
$801$	37.8646	−	13.7472i	1.33788	−	0.485732i
$802$	18.6882	+	10.7896i	0.659903	+	0.380995i
$803$	−26.2268	+	19.8740i	−0.925523	+	0.701340i
$804$	0.0816379	−	0.212419i	0.00287915	−	0.00749144i
$805$	56.3327	−	22.7599i	1.98547	−	0.802181i
$806$	−1.97646	−	6.89272i	−0.0696177	−	0.242786i
$807$	−27.2798	+	25.4183i	−0.960294	+	0.894768i
$808$	−2.60330	+	0.365870i	−0.0915839	+	0.0128713i
$809$	−5.95529	−	18.3285i	−0.209377	−	0.644395i	−0.999505	−	0.0314541i	$-0.989986\pi$
$809$	−5.95529	−	18.3285i	−0.209377	−	0.644395i	0.790128	−	0.612941i	$-0.210014\pi$
$810$	51.1458	+	61.1524i	1.79708	+	2.14868i
$811$	−18.0724	−	24.8745i	−0.634607	−	0.873462i	0.363706	−	0.931514i	$-0.381511\pi$
$811$	−18.0724	−	24.8745i	−0.634607	−	0.873462i	−0.998314	+	0.0580517i	$0.981511\pi$
$812$	−22.1347	+	41.6293i	−0.776775	+	1.46090i
$813$	9.01401	−	46.2739i	0.316135	−	1.62289i
$814$	48.6598	+	18.5288i	1.70552	+	0.649434i
$815$	−33.1807	−	39.5432i	−1.16227	−	1.38514i
$816$	10.8076	+	8.75902i	0.378342	+	0.306627i
$817$	11.0287	−	16.3507i	0.385845	−	0.572039i
$818$	−21.6404	−	48.6052i	−0.756640	−	1.69944i
$819$	−9.78807	+	4.76424i	−0.342023	+	0.166476i
$820$	−17.3423	−	15.6151i	−0.605619	−	0.545301i
$821$	−5.34985	−	21.4571i	−0.186711	−	0.748857i	−0.988496	−	0.151245i	$-0.951672\pi$
$821$	−5.34985	−	21.4571i	−0.186711	−	0.748857i	0.801785	−	0.597612i	$-0.203884\pi$
$822$	6.24202	+	71.6781i	0.217716	+	2.50006i
$823$	36.2907	+	5.10033i	1.26502	+	0.177786i	0.739592	−	0.673055i	$-0.235018\pi$
$823$	36.2907	+	5.10033i	1.26502	+	0.177786i	0.525423	+	0.850841i	$0.323907\pi$
$824$	−1.79315	−	10.1694i	−0.0624672	−	0.354269i
$825$	−31.9874	+	65.9662i	−1.11366	+	2.29665i
$826$	−32.5806	−	27.3384i	−1.13363	−	0.951224i
$827$	10.3206	−	2.19370i	0.358881	−	0.0762824i	−0.0249429	−	0.999689i	$-0.507940\pi$
$827$	10.3206	−	2.19370i	0.358881	−	0.0762824i	0.383824	+	0.923406i	$0.374607\pi$
$828$	19.7243	−	40.3585i	0.685466	−	1.40255i
$829$	13.8218	−	6.15385i	0.480050	−	0.213732i	−0.152421	−	0.988316i	$-0.548707\pi$
$829$	13.8218	−	6.15385i	0.480050	−	0.213732i	0.632472	+	0.774583i	$0.282040\pi$
$830$	18.4946	−	14.4495i	0.641955	−	0.501551i
$831$	−29.2623	+	14.8951i	−1.01510	+	0.516704i
$832$	1.18742	+	16.9809i	0.0411664	+	0.588707i
$833$	4.08621	−	1.17170i	0.141579	−	0.0405970i
$834$	6.40612	−	3.84569i	0.221826	−	0.133165i
$835$	29.9213	+	5.27594i	1.03547	+	0.182581i
$836$	−11.5616	+	15.4289i	−0.399866	+	0.533618i
$837$	6.83203	+	9.08916i	0.236149	+	0.314167i
$838$	72.0179	+	23.4000i	2.48782	+	0.808341i
$839$	−8.55387	+	4.17200i	−0.295313	+	0.144034i	−0.580071	−	0.814566i	$-0.696975\pi$
$839$	−8.55387	+	4.17200i	−0.295313	+	0.144034i	0.284759	+	0.958599i	$0.408086\pi$
$840$	−4.36400	+	14.2535i	−0.150572	+	0.491794i
$841$	1.43849	−	41.1930i	0.0496031	−	1.42045i
$842$	−18.7436	−	11.7123i	−0.645946	−	0.403632i
$843$	−1.51698	−	29.1698i	−0.0522477	−	1.00466i
$844$	−22.6847	−	15.3010i	−0.780838	−	0.526682i
$845$	33.1030	−	29.8061i	1.13878	−	1.02536i
$846$	35.1088	+	7.49207i	1.20706	+	0.257583i
$847$	−4.58124	−	25.1888i	−0.157413	−	0.865498i
$848$	−5.86641	+	6.99131i	−0.201453	+	0.240083i
$849$	3.68927	−	10.7005i	0.126615	−	0.367239i
$850$	51.8152	+	50.0373i	1.77725	+	1.71627i
$851$	41.5830	+	20.2814i	1.42545	+	0.695237i
$852$	−0.856706	−	2.80619i	−0.0293503	−	0.0961384i
$853$	36.4356	+	14.7209i	1.24753	+	0.504035i	0.900924	−	0.433976i	$-0.142890\pi$
$853$	36.4356	+	14.7209i	1.24753	+	0.504035i	0.346605	+	0.938011i	$0.387334\pi$
$854$	3.83504	−	36.4880i	0.131232	−	1.24859i
$855$	−12.3439	−	27.7848i	−0.422151	−	0.950220i
$856$	6.27187	+	6.96562i	0.214368	+	0.238080i
$857$	−28.9432	+	10.5345i	−0.988683	+	0.359851i	−0.785210	−	0.619230i	$-0.787445\pi$
$857$	−28.9432	+	10.5345i	−0.988683	+	0.359851i	−0.203473	+	0.979081i	$0.565223\pi$
$858$	−18.8107	+	0.699957i	−0.642188	+	0.0238961i
$859$	9.76693	−	8.19542i	0.333243	−	0.279624i	−0.460777	−	0.887516i	$-0.652429\pi$
$859$	9.76693	−	8.19542i	0.333243	−	0.279624i	0.794020	+	0.607892i	$0.207985\pi$
$860$	51.4464	−	65.8484i	1.75431	−	2.24541i
$861$	−5.29921	+	7.56159i	−0.180597	+	0.257698i
$862$	52.4210	−	50.6224i	1.78547	−	1.72420i
$863$	−41.6339	+	13.5277i	−1.41723	+	0.460487i	−0.914722	−	0.404084i	$-0.867590\pi$
$863$	−41.6339	+	13.5277i	−1.41723	+	0.460487i	−0.502511	+	0.864571i	$0.667590\pi$
$864$	−17.6120	−	37.8880i	−0.599171	−	1.28898i
$865$	12.2843	−	16.9078i	0.417677	−	0.574884i
$866$	1.50646	+	3.08870i	0.0511916	+	0.104958i
$867$	−8.72613	−	14.5359i	−0.296355	−	0.493666i
$868$	−4.21106	+	11.5698i	−0.142933	+	0.392704i
$869$	−42.2791	−	11.2069i	−1.43422	−	0.380169i
$870$	−20.0608	−	126.989i	−0.680124	−	4.30532i
$871$	−0.0846817	+	0.00295715i	−0.00286933	+	0.000100199i
$872$	0.448385	−	0.0471271i	0.0151842	−	0.00159593i
$873$	1.90190	−	13.4543i	0.0643695	−	0.455360i
$874$	−20.9467	+	23.2637i	−0.708534	+	0.786907i
$875$	28.5222	−	70.5948i	0.964225	−	2.38654i
$876$	5.07940	−	41.2315i	0.171617	−	1.39308i
$877$	3.24435	−	3.35963i	0.109554	−	0.113447i	−0.662323	−	0.749219i	$-0.730429\pi$
$877$	3.24435	−	3.35963i	0.109554	−	0.113447i	0.771877	+	0.635772i	$0.219318\pi$
$878$	1.71685	−	12.2160i	0.0579409	−	0.412271i
$879$	4.08549	+	2.45705i	0.137800	+	0.0828741i
$880$	27.3421	−	31.6248i	0.921702	−	1.06607i
$881$	−18.7549	+	10.8281i	−0.631869	+	0.364809i	−0.781475	−	0.623936i	$-0.785533\pi$
$881$	−18.7549	+	10.8281i	−0.631869	+	0.364809i	0.149607	+	0.988746i	$0.452199\pi$
$882$	−9.82788	−	1.74106i	−0.330922	−	0.0586245i
$883$	0.306232	+	2.91361i	0.0103055	+	0.0980507i	0.998466	−	0.0553760i	$-0.0176358\pi$
$883$	0.306232	+	2.91361i	0.0103055	+	0.0980507i	−0.988160	+	0.153427i	$0.950969\pi$
$884$	−2.78981	+	9.72923i	−0.0938315	+	0.327229i
$885$	63.3783	+	3.34703i	2.13044	+	0.112509i
$886$	1.96129	−	3.13871i	0.0658907	−	0.105447i
$887$	−10.9726	−	16.2676i	−0.368424	−	0.546211i	0.598550	−	0.801085i	$-0.295744\pi$
$887$	−10.9726	−	16.2676i	−0.368424	−	0.546211i	−0.966974	+	0.254874i	$0.917966\pi$
$888$	−10.2896	+	4.79308i	−0.345296	+	0.160845i
$889$	17.5394	+	9.32589i	0.588254	+	0.312780i
$890$	−118.941			−3.98692
$891$	27.4641	−	11.6929i	0.920081	−	0.391727i
$892$	36.4124			1.21918
$893$	−12.0884	−	6.42750i	−0.404522	−	0.215088i
$894$	17.9251	−	8.34983i	0.599503	−	0.279260i
$895$	−13.2502	−	19.6443i	−0.442906	−	0.656635i
$896$	8.46851	−	13.5525i	0.282913	−	0.452756i
$897$	−16.7027	−	0.882073i	−0.557685	−	0.0294516i
$898$	−13.3180	+	46.4453i	−0.444426	+	1.54990i
$899$	−1.91672	−	18.2364i	−0.0639262	−	0.608217i
$900$	−31.5859	−	86.9987i	−1.05286	−	2.89996i
$901$	−7.09673	+	4.09730i	−0.236426	+	0.136501i
$902$	−13.6638	+	8.26013i	−0.454956	+	0.275032i
$903$	−28.3343	−	17.0404i	−0.942905	−	0.567070i
$904$	0.0780464	−	0.555329i	0.00259578	−	0.0184700i
$905$	8.50666	−	8.80891i	0.282771	−	0.292818i
$906$	−5.85460	+	47.5241i	−0.194506	+	1.57888i
$907$	−11.1676	+	27.6407i	−0.370814	+	0.917796i	0.620250	+	0.784404i	$0.287031\pi$
$907$	−11.1676	+	27.6407i	−0.370814	+	0.917796i	−0.991063	+	0.133391i	$0.957413\pi$
$908$	−7.07695	+	7.85975i	−0.234857	+	0.260835i
$909$	−7.07885	−	5.53976i	−0.234791	−	0.183742i
$910$	31.9663	−	3.35980i	1.05967	−	0.111376i
$911$	3.44213	−	0.120202i	0.114043	−	0.00398246i	0.0221788	−	0.999754i	$-0.492940\pi$
$911$	3.44213	−	0.120202i	0.114043	−	0.00398246i	0.0918641	+	0.995772i	$0.470717\pi$
$912$	1.94374	+	12.3042i	0.0643635	+	0.407434i
$913$	−3.17127	−	8.19553i	−0.104954	−	0.271233i
$914$	−18.4304	+	50.6371i	−0.609624	+	1.67493i
$915$	28.1789	+	46.9403i	0.931566	+	1.55180i
$916$	−10.8721	−	22.2911i	−0.359224	−	0.736518i
$917$	22.7768	−	31.3496i	0.752157	−	1.03526i
$918$	−2.52092	−	29.2195i	−0.0832027	−	0.964387i
$919$	−14.3430	+	4.66032i	−0.473131	+	0.153730i	−0.535870	−	0.844300i	$-0.680016\pi$
$919$	−14.3430	+	4.66032i	−0.473131	+	0.153730i	0.0627391	+	0.998030i	$0.480016\pi$
$920$	−16.4754	+	15.9102i	−0.543179	+	0.524542i
$921$	2.91091	−	4.15367i	0.0959179	−	0.136868i
$922$	45.7138	−	58.5110i	1.50550	−	1.92696i
$923$	−0.836887	+	0.702231i	−0.0275465	+	0.0231142i
$924$	26.8373	+	18.0128i	0.882883	+	0.592579i
$925$	89.5771	−	32.6034i	2.94528	−	1.07199i
$926$	−17.4251	−	19.3525i	−0.572624	−	0.635964i
$927$	20.7766	−	28.5483i	0.682393	−	0.937650i
$928$	−7.04303	+	67.0100i	−0.231199	+	2.19971i
$929$	28.5309	+	11.5272i	0.936068	+	0.378196i	0.791410	−	0.611286i	$-0.209347\pi$
$929$	28.5309	+	11.5272i	0.936068	+	0.378196i	0.144658	+	0.989482i	$0.453792\pi$
$930$	−9.80297	−	32.1102i	−0.321452	−	1.05293i
$931$	3.42119	+	1.66863i	0.112125	+	0.0546870i
$932$	−36.0505	−	34.8136i	−1.18087	−	1.14036i
$933$	−5.11388	+	14.8324i	−0.167421	+	0.485592i
$934$	−33.4370	+	39.8487i	−1.09409	+	1.30389i
$935$	32.7815	−	18.2865i	1.07207	−	0.598031i
$936$	2.74836	−	3.04743i	0.0898328	−	0.0996085i
$937$	−13.0120	+	11.7161i	−0.425085	+	0.382748i	−0.853722	−	0.520729i	$-0.825660\pi$
$937$	−13.0120	+	11.7161i	−0.425085	+	0.382748i	0.428638	+	0.903476i	$0.358994\pi$
$938$	0.220411	+	0.148669i	0.00719666	+	0.00485421i
$939$	−0.483738	−	9.30172i	−0.0157862	−	0.303550i
$940$	−49.1930	−	30.7392i	−1.60450	−	1.00260i
$941$	−1.28456	+	36.7851i	−0.0418756	+	1.19916i	0.778616	+	0.627501i	$0.215922\pi$
$941$	−1.28456	+	36.7851i	−0.0418756	+	1.19916i	−0.820491	+	0.571659i	$0.806300\pi$
$942$	0.482108	−	1.57464i	0.0157079	−	0.0513047i
$943$	−12.7513	+	6.21922i	−0.415239	+	0.202526i
$944$	−24.7307	−	8.03549i	−0.804916	−	0.261533i
$945$	−45.4420	+	23.0850i	−1.47823	+	0.750954i
$946$	−32.9188	−	46.7450i	−1.07028	−	1.51981i
$947$	−7.70975	−	1.35944i	−0.250533	−	0.0441758i	0.0469710	−	0.998896i	$-0.485043\pi$
$947$	−7.70975	−	1.35944i	−0.250533	−	0.0441758i	−0.297504	+	0.954720i	$0.596154\pi$
$948$	47.3438	−	28.4211i	1.53765	−	0.923076i
$949$	−14.8692	+	4.26367i	−0.482674	+	0.138405i
$950$	4.49931	+	64.3431i	0.145977	+	2.08757i
$951$	23.9579	−	12.1950i	0.776887	−	0.395451i
$952$	4.32135	−	3.37621i	0.140056	−	0.109424i
$953$	−19.5799	+	8.71754i	−0.634256	+	0.282389i	−0.698571	−	0.715541i	$-0.746180\pi$
$953$	−19.5799	+	8.71754i	−0.634256	+	0.282389i	0.0643153	+	0.997930i	$0.479514\pi$
$954$	19.1948	−	1.32675i	0.621456	−	0.0429550i
$955$	82.6991	−	17.5782i	2.67608	−	0.568819i
$956$	−37.6259	−	31.5719i	−1.21691	−	1.02111i
$957$	−47.6840	−	6.59039i	−1.54140	−	0.213037i
$958$	−9.30395	−	52.7653i	−0.300597	−	1.70477i
$959$	−45.5528	−	6.40203i	−1.47098	−	0.206732i
$960$	6.91452	+	79.4004i	0.223165	+	2.56264i
$961$	6.34114	+	25.4329i	0.204553	+	0.820416i
$962$	18.1892	+	16.3776i	0.586442	+	0.528035i
$963$	−2.26131	+	31.9693i	−0.0728696	+	1.03020i
$964$	−12.7341	−	28.6014i	−0.410139	−	0.921188i
$965$	−40.2183	+	59.6260i	−1.29467	+	1.91943i
$966$	40.7714	+	33.0431i	1.31180	+	1.06315i
$967$	−19.0851	−	22.7448i	−0.613736	−	0.731423i	0.366243	−	0.930519i	$-0.380644\pi$
$967$	−19.0851	−	22.7448i	−0.613736	−	0.731423i	−0.979980	+	0.199096i	$0.936199\pi$
$968$	5.15831	+	8.15710i	0.165794	+	0.262179i
$969$	−2.13858	+	10.9785i	−0.0687010	+	0.352680i
$970$	−18.8356	+	35.4246i	−0.604774	+	1.13741i
$971$	−7.37269	−	10.1476i	−0.236601	−	0.325653i	0.674162	−	0.738584i	$-0.264505\pi$
$971$	−7.37269	−	10.1476i	−0.236601	−	0.325653i	−0.910762	+	0.412931i	$0.864505\pi$
$972$	−13.5754	+	35.1542i	−0.435433	+	1.12757i
$973$	1.47619	+	4.54325i	0.0473246	+	0.145650i
$974$	42.3216	−	5.94792i	1.35607	−	0.190584i
$975$	−25.2137	+	23.4932i	−0.807483	+	0.752384i
$976$	−6.18299	−	21.5626i	−0.197913	−	0.690203i
$977$	−16.4171	+	6.63295i	−0.525230	+	0.212207i	−0.621881	−	0.783111i	$-0.713631\pi$
$977$	−16.4171	+	6.63295i	−0.525230	+	0.212207i	0.0966509	+	0.995318i	$0.469187\pi$
$978$	15.9956	−	41.6200i	0.511483	−	1.33086i
$979$	−12.9061	+	42.6233i	−0.412480	+	1.36225i
$980$	13.9668	+	8.06376i	0.446154	+	0.257587i
$981$	1.18013	+	0.991859i	0.0376785	+	0.0316676i
$982$	61.1338	+	27.2185i	1.95086	+	0.868578i
$983$	−21.8629	+	5.45103i	−0.697318	+	0.173861i	−0.574423	−	0.818559i	$-0.694773\pi$
$983$	−21.8629	+	5.45103i	−0.697318	+	0.173861i	−0.122895	+	0.992420i	$0.539218\pi$
$984$	0.784371	−	3.39127i	0.0250048	−	0.108110i
$985$	3.17724	+	5.97553i	0.101235	+	0.190396i
$986$	−20.7333	+	42.5095i	−0.660282	+	1.35378i
$987$	−9.70830	+	20.7977i	−0.309019	+	0.661998i
$988$	−7.68592	+	4.80269i	−0.244522	+	0.152794i
$989$	−25.4006	−	43.9952i	−0.807693	−	1.39897i
$990$	−88.0057	+	4.77857i	−2.79701	+	0.151873i
$991$	−4.26598	+	7.38889i	−0.135513	+	0.234716i	−0.925793	−	0.378030i	$-0.876602\pi$
$991$	−4.26598	+	7.38889i	−0.135513	+	0.234716i	0.790280	+	0.612746i	$0.209935\pi$
$992$	0.614073	+	17.5847i	0.0194968	+	0.558316i
$993$	7.01530	−	7.00967i	0.222624	−	0.222445i
$994$	3.41946	−	0.239112i	0.108459	−	0.00758417i
$995$	−16.8639	−	0.588901i	−0.534622	−	0.0186694i
$996$	10.2106	+	4.33896i	0.323534	+	0.137485i
$997$	12.3910	+	12.8313i	0.392428	+	0.406371i	0.886261	−	0.463186i	$-0.153294\pi$
$997$	12.3910	+	12.8313i	0.392428	+	0.406371i	−0.493834	+	0.869556i	$0.664405\pi$
$998$	24.1361	−	17.5359i	0.764016	−	0.555090i
$999$	−36.2178	−	13.9528i	−1.14588	−	0.441447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.x.a.2.6	✓	816
3.2	odd	2		891.2.bb.a.332.29		816
11.6	odd	10	inner	297.2.x.a.83.6	yes	816
27.13	even	9		891.2.bb.a.233.29		816
27.14	odd	18	inner	297.2.x.a.68.6	yes	816
33.17	even	10		891.2.bb.a.413.29		816
297.94	odd	90		891.2.bb.a.314.29		816
297.149	even	90	inner	297.2.x.a.149.6	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.2.6	✓	816	1.1	even	1	trivial
297.2.x.a.68.6	yes	816	27.14	odd	18	inner
297.2.x.a.83.6	yes	816	11.6	odd	10	inner
297.2.x.a.149.6	yes	816	297.149	even	90	inner
891.2.bb.a.233.29		816	27.13	even	9
891.2.bb.a.314.29		816	297.94	odd	90
891.2.bb.a.332.29		816	3.2	odd	2
891.2.bb.a.413.29		816	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.x (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85576 - 0.986723i) q^{2} +(-1.57006 + 0.731366i) q^{3} +(1.35182 + 2.00416i) q^{4} +(2.23335 - 3.57411i) q^{5} +(3.63531 + 0.191982i) q^{6} +(-0.641535 + 2.23730i) q^{7} +(-0.0917117 - 0.872579i) q^{8} +(1.93021 - 2.29658i) q^{9} +(-7.67120 + 4.42897i) q^{10} +(0.754763 + 3.22960i) q^{11} +(-3.58822 - 2.15798i) q^{12} +(-0.216980 + 1.54389i) q^{13} +(3.39812 - 3.51886i) q^{14} +(-0.892523 + 7.24497i) q^{15} +(1.12039 - 2.77305i) q^{16} +(1.79691 - 1.99567i) q^{17} +(-5.84808 + 2.35732i) q^{18} +(2.39149 - 0.251356i) q^{19} +(10.1822 - 0.355569i) q^{20} +(-0.629032 - 3.98190i) q^{21} +(1.78607 - 6.73809i) q^{22} +(2.11845 - 5.82039i) q^{23} +(0.782168 + 1.30293i) q^{24} +(-5.59453 - 11.4705i) q^{25} +(1.92605 - 2.65098i) q^{26} +(-1.35091 + 5.01747i) q^{27} +(-5.35113 + 1.73869i) q^{28} +(6.02780 - 5.82098i) q^{29} +(8.80508 - 12.5642i) q^{30} +(1.34723 - 1.72438i) q^{31} +(-6.15963 + 5.16854i) q^{32} +(-3.54705 - 4.51868i) q^{33} +(-5.30380 + 1.93043i) q^{34} +(6.56357 + 7.28958i) q^{35} +(7.21201 + 0.763868i) q^{36} +(-0.780772 + 7.42855i) q^{37} +(-4.68604 - 1.89328i) q^{38} +(-0.788477 - 2.58270i) q^{39} +(-3.32351 - 1.62099i) q^{40} +(-1.64764 - 1.59111i) q^{41} +(-2.76170 + 8.01011i) q^{42} +(5.27201 - 6.28293i) q^{43} +(-5.45233 + 5.87851i) q^{44} +(-3.89741 - 12.0278i) q^{45} +(-9.67443 + 8.71089i) q^{46} +(-4.72012 - 3.18376i) q^{47} +(0.269038 + 5.17329i) q^{48} +(1.34240 + 0.838828i) q^{49} +(-0.936109 + 26.8067i) q^{50} +(-1.36170 + 4.44753i) q^{51} +(-3.38752 + 1.65220i) q^{52} +(-2.90214 - 0.942963i) q^{53} +(7.45781 - 7.97823i) q^{54} +(13.2286 + 4.51523i) q^{55} +(2.01105 + 0.354603i) q^{56} +(-3.57096 + 2.14370i) q^{57} +(-16.9298 + 4.85454i) q^{58} +(-0.606488 - 8.67318i) q^{59} +(-15.7266 + 8.00515i) q^{60} +(5.91017 - 4.61753i) q^{61} +(-4.20161 + 1.87068i) q^{62} +(3.89985 + 5.79179i) q^{63} +(10.6797 - 2.27005i) q^{64} +(5.03344 + 4.22356i) q^{65} +(2.12377 + 11.8855i) q^{66} +(0.00943758 + 0.0535232i) q^{67} +(6.42874 + 0.903500i) q^{68} +(0.930733 + 10.6877i) q^{69} +(-4.98758 - 20.0041i) q^{70} +(0.520742 + 0.468878i) q^{71} +(-2.18097 - 1.47363i) q^{72} +(4.03548 + 9.06384i) q^{73} +(8.77884 - 13.0152i) q^{74} +(17.1729 + 13.9178i) q^{75} +(3.73662 + 4.45313i) q^{76} +(-7.70979 - 0.383274i) q^{77} +(-1.08519 + 5.57087i) q^{78} +(-6.19132 + 11.6442i) q^{79} +(-7.40898 - 10.1976i) q^{80} +(-1.54860 - 8.86577i) q^{81} +(1.48764 + 4.57847i) q^{82} +(-2.62381 + 0.368752i) q^{83} +(7.13001 - 6.64349i) q^{84} +(-3.11961 - 10.8794i) q^{85} +(-15.9831 + 6.45758i) q^{86} +(-5.20677 + 13.5478i) q^{87} +(2.74886 - 0.954782i) q^{88} +(11.6287 + 6.71382i) q^{89} +(-4.63551 + 26.1664i) q^{90} +(-3.31494 - 1.47591i) q^{91} +(14.5287 - 3.62242i) q^{92} +(-0.854089 + 3.69270i) q^{93} +(5.61790 + 10.5657i) q^{94} +(4.44266 - 9.10880i) q^{95} +(5.89092 - 12.6199i) q^{96} +(3.84112 - 2.40020i) q^{97} +(-1.66348 - 2.88124i) q^{98} +(8.87390 + 4.50043i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 30 q^{2} - 18 q^{3} - 18 q^{4} - 21 q^{5} - 30 q^{6} - 30 q^{7} - 45 q^{8} - 36 q^{9} - 33 q^{11} - 30 q^{12} - 30 q^{13} - 18 q^{14} - 21 q^{15} - 30 q^{16} - 45 q^{17} - 15 q^{19} - 60 q^{20}+ \cdots + 3 q^{99}+O(q^{100}) \) 816 * q - 30 * q^2 - 18 * q^3 - 18 * q^4 - 21 * q^5 - 30 * q^6 - 30 * q^7 - 45 * q^8 - 36 * q^9 - 33 * q^11 - 30 * q^12 - 30 * q^13 - 18 * q^14 - 21 * q^15 - 30 * q^16 - 45 * q^17 - 15 * q^19 - 60 * q^20 - 15 * q^22 - 84 * q^23 - 30 * q^24 - 27 * q^25 + 36 * q^27 - 60 * q^28 + 60 * q^29 - 75 * q^30 - 9 * q^31 - 63 * q^33 - 42 * q^34 - 45 * q^35 + 36 * q^36 - 9 * q^37 - 18 * q^38 - 150 * q^39 - 90 * q^40 - 30 * q^41 - 66 * q^42 - 108 * q^44 + 24 * q^45 - 15 * q^46 - 6 * q^47 + 174 * q^48 - 18 * q^49 - 105 * q^50 - 30 * q^51 - 30 * q^52 - 48 * q^55 + 54 * q^56 - 75 * q^57 - 18 * q^58 + 81 * q^59 - 72 * q^60 - 30 * q^61 - 45 * q^62 - 30 * q^63 + 51 * q^64 - 75 * q^66 + 6 * q^67 - 225 * q^68 + 9 * q^69 - 93 * q^70 - 27 * q^71 - 30 * q^72 - 15 * q^73 - 30 * q^74 + 42 * q^75 - 141 * q^77 + 30 * q^78 - 30 * q^79 + 48 * q^81 - 36 * q^82 + 15 * q^83 + 90 * q^84 - 30 * q^85 + 93 * q^86 - 108 * q^88 + 54 * q^89 - 15 * q^90 - 9 * q^91 + 276 * q^92 + 87 * q^93 - 30 * q^94 + 90 * q^95 + 90 * q^96 - 81 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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