LMFDB - Embedded newform 352.2.bf.a.5.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(5,352)] 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("352.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([0, 5, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.bf (of order $40$, degree $16$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$736$
Relative dimension:	$46$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	352.5
Dual form			352.2.bf.a.141.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34285 - 0.443581i) q^{2} +(-0.229576 + 0.956251i) q^{3} +(1.60647 + 1.19132i) q^{4} +(-0.0398970 + 0.0467134i) q^{5} +(0.732459 - 1.18226i) q^{6} +(3.01590 + 0.477672i) q^{7} +(-1.62880 - 2.31236i) q^{8} +(1.81131 + 0.922908i) q^{9} +(0.0742968 - 0.0450314i) q^{10} +(-3.06783 - 1.26032i) q^{11} +(-1.50801 + 1.26269i) q^{12} +(0.0472126 + 0.0552789i) q^{13} +(-3.83800 - 1.97924i) q^{14} +(-0.0355104 - 0.0488758i) q^{15} +(1.16150 + 3.82765i) q^{16} +(2.65125 + 0.861442i) q^{17} +(-2.02292 - 2.04279i) q^{18} +(0.616817 + 0.148085i) q^{19} +(-0.119744 + 0.0275136i) q^{20} +(-1.14915 + 2.77430i) q^{21} +(3.56057 + 3.05325i) q^{22} +(0.933262 - 0.933262i) q^{23} +(2.58513 - 1.02668i) q^{24} +(0.781582 + 4.93471i) q^{25} +(-0.0388786 - 0.0951737i) q^{26} +(-3.21441 + 3.76359i) q^{27} +(4.27590 + 4.36027i) q^{28} +(3.04702 + 1.86721i) q^{29} +(0.0260046 + 0.0813845i) q^{30} +(1.70553 + 5.24910i) q^{31} +(0.138155 - 5.65517i) q^{32} +(1.90948 - 2.64428i) q^{33} +(-3.17810 - 2.33283i) q^{34} +(-0.142639 + 0.121825i) q^{35} +(1.81034 + 3.64048i) q^{36} +(2.80584 - 0.673624i) q^{37} +(-0.762603 - 0.472463i) q^{38} +(-0.0636994 + 0.0324564i) q^{39} +(0.173003 + 0.0161698i) q^{40} +(4.96424 - 0.786258i) q^{41} +(2.77376 - 3.21571i) q^{42} +(2.23884 - 5.40504i) q^{43} +(-3.42693 - 5.67945i) q^{44} +(-0.115378 + 0.0477911i) q^{45} +(-1.66720 + 0.839250i) q^{46} +(-5.48180 + 7.54505i) q^{47} +(-3.92685 + 0.231952i) q^{48} +(2.21008 + 0.718100i) q^{49} +(1.13940 - 6.97326i) q^{50} +(-1.43242 + 2.33749i) q^{51} +(0.00999078 + 0.145049i) q^{52} +(5.51277 + 0.433865i) q^{53} +(5.98592 - 3.62807i) q^{54} +(0.181271 - 0.0930257i) q^{55} +(-3.80774 - 7.75188i) q^{56} +(-0.283212 + 0.555835i) q^{57} +(-3.26341 - 3.85898i) q^{58} +(-9.61859 + 2.30922i) q^{59} +(0.00118047 - 0.120822i) q^{60} +(5.52132 - 0.434537i) q^{61} +(0.0381291 - 7.80527i) q^{62} +(5.02188 + 3.64861i) q^{63} +(-2.69405 + 7.53274i) q^{64} -0.00446591 q^{65} +(-3.73709 + 2.70385i) q^{66} +(-3.11765 - 7.52668i) q^{67} +(3.23290 + 4.54237i) q^{68} +(0.678179 + 1.10669i) q^{69} +(0.245582 - 0.100321i) q^{70} +(-0.945767 + 0.481892i) q^{71} +(-0.816154 - 5.69163i) q^{72} +(1.14532 - 7.23128i) q^{73} +(-4.06662 - 0.340047i) q^{74} +(-4.89826 - 0.385501i) q^{75} +(0.814483 + 0.972722i) q^{76} +(-8.65025 - 5.26642i) q^{77} +(0.0999355 - 0.0153282i) q^{78} +(-13.0543 + 4.24161i) q^{79} +(-0.225143 - 0.0984542i) q^{80} +(0.723702 + 0.996090i) q^{81} +(-7.01498 - 1.14622i) q^{82} +(-0.622825 - 7.91374i) q^{83} +(-5.15116 + 3.08782i) q^{84} +(-0.146018 + 0.0894798i) q^{85} +(-5.40399 + 6.26503i) q^{86} +(-2.48505 + 2.48505i) q^{87} +(2.08255 + 9.14675i) q^{88} +(-9.76648 - 9.76648i) q^{89} +(0.176134 - 0.0129966i) q^{90} +(0.115983 + 0.189268i) q^{91} +(2.61108 - 0.387443i) q^{92} +(-5.41100 + 0.425855i) q^{93} +(10.7081 - 7.70022i) q^{94} +(-0.0315267 + 0.0229055i) q^{95} +(5.37604 + 1.43040i) q^{96} +(-4.60684 - 14.1784i) q^{97} +(-2.64927 - 1.94465i) q^{98} +(-4.39363 - 5.11416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100}) $ 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.34285	−	0.443581i	−0.949536	−	0.313659i
$2$	−1.34285	−	0.443581i	−0.949536	−	0.313659i
$3$	−0.229576	+	0.956251i	−0.132546	+	0.552092i	0.866091	+	0.499887i	$0.166625\pi$
$3$	−0.229576	+	0.956251i	−0.132546	+	0.552092i	−0.998636	+	0.0522052i	$0.983375\pi$
$4$	1.60647	+	1.19132i	0.803236	+	0.595661i
$5$	−0.0398970	+	0.0467134i	−0.0178425	+	0.0208909i	−0.769255	−	0.638941i	$-0.779373\pi$
$5$	−0.0398970	+	0.0467134i	−0.0178425	+	0.0208909i	0.751413	+	0.659832i	$0.229373\pi$
$6$	0.732459	−	1.18226i	0.299025	−	0.482657i
$7$	3.01590	+	0.477672i	1.13990	+	0.180543i	0.697712	−	0.716378i	$-0.254201\pi$
$7$	3.01590	+	0.477672i	1.13990	+	0.180543i	0.442191	+	0.896921i	$0.354201\pi$
$8$	−1.62880	−	2.31236i	−0.575866	−	0.817544i
$9$	1.81131	+	0.922908i	0.603770	+	0.307636i
$10$	0.0742968	−	0.0450314i	0.0234947	−	0.0142402i
$11$	−3.06783	−	1.26032i	−0.924986	−	0.380002i
$11$	−3.06783	−	1.26032i	−0.924986	−	0.380002i
$12$	−1.50801	+	1.26269i	−0.435325	+	0.364508i
$13$	0.0472126	+	0.0552789i	0.0130944	+	0.0153316i	0.766915	−	0.641749i	$-0.221791\pi$
$13$	0.0472126	+	0.0552789i	0.0130944	+	0.0153316i	−0.753820	+	0.657081i	$0.771791\pi$
$14$	−3.83800	−	1.97924i	−1.02575	−	0.528973i
$15$	−0.0355104	−	0.0488758i	−0.00916874	−	0.0126197i
$16$	1.16150	+	3.82765i	0.290376	+	0.956913i
$17$	2.65125	+	0.861442i	0.643022	+	0.208930i	0.612335	−	0.790599i	$-0.290230\pi$
$17$	2.65125	+	0.861442i	0.643022	+	0.208930i	0.0306871	+	0.999529i	$0.490230\pi$
$18$	−2.02292	−	2.04279i	−0.476808	−	0.481489i
$19$	0.616817	+	0.148085i	0.141508	+	0.0339730i	0.303580	−	0.952806i	$-0.401818\pi$
$19$	0.616817	+	0.148085i	0.141508	+	0.0339730i	−0.162073	+	0.986779i	$0.551818\pi$
$20$	−0.119744	+	0.0275136i	−0.0267756	+	0.00615222i
$21$	−1.14915	+	2.77430i	−0.250765	+	0.605401i
$22$	3.56057	+	3.05325i	0.759116	+	0.650956i
$23$	0.933262	−	0.933262i	0.194599	−	0.194599i	−0.603081	−	0.797680i	$-0.706061\pi$
$23$	0.933262	−	0.933262i	0.194599	−	0.194599i	0.797680	+	0.603081i	$0.206061\pi$
$24$	2.58513	−	1.02668i	0.527688	−	0.209569i
$25$	0.781582	+	4.93471i	0.156316	+	0.986943i
$26$	−0.0388786	−	0.0951737i	−0.00762473	−	0.0186651i
$27$	−3.21441	+	3.76359i	−0.618614	+	0.724303i
$28$	4.27590	+	4.36027i	0.808068	+	0.824014i
$29$	3.04702	+	1.86721i	0.565817	+	0.346733i	0.775807	−	0.630971i	$-0.217343\pi$
$29$	3.04702	+	1.86721i	0.565817	+	0.346733i	−0.209990	+	0.977704i	$0.567343\pi$
$30$	0.0260046	+	0.0813845i	0.00474776	+	0.0148587i
$31$	1.70553	+	5.24910i	0.306323	+	0.942765i	0.979180	+	0.202993i	$0.0650669\pi$
$31$	1.70553	+	5.24910i	0.306323	+	0.942765i	−0.672857	+	0.739772i	$0.734933\pi$
$32$	0.138155	−	5.65517i	0.0244226	−	0.999702i
$33$	1.90948	−	2.64428i	0.332399	−	0.460309i
$34$	−3.17810	−	2.33283i	−0.545039	−	0.400077i
$35$	−0.142639	+	0.121825i	−0.0241104	+	0.0205922i
$36$	1.81034	+	3.64048i	0.301723	+	0.606746i
$37$	2.80584	−	0.673624i	0.461278	−	0.110743i	0.00385549	−	0.999993i	$-0.498773\pi$
$37$	2.80584	−	0.673624i	0.461278	−	0.110743i	0.457422	+	0.889250i	$0.348773\pi$
$38$	−0.762603	−	0.472463i	−0.123711	−	0.0766437i
$39$	−0.0636994	+	0.0324564i	−0.0102001	+	0.00519719i
$40$	0.173003	+	0.0161698i	0.0273541	+	0.00255667i
$41$	4.96424	−	0.786258i	0.775284	−	0.122793i	0.243759	−	0.969836i	$-0.421619\pi$
$41$	4.96424	−	0.786258i	0.775284	−	0.122793i	0.531525	+	0.847043i	$0.321619\pi$
$42$	2.77376	−	3.21571i	0.428000	−	0.496195i
$43$	2.23884	−	5.40504i	0.341420	−	0.824261i	−0.656153	−	0.754628i	$-0.727817\pi$
$43$	2.23884	−	5.40504i	0.341420	−	0.824261i	0.997573	−	0.0696329i	$-0.0221828\pi$
$44$	−3.42693	−	5.67945i	−0.516629	−	0.856209i
$45$	−0.115378	+	0.0477911i	−0.0171995	+	0.00712428i
$46$	−1.66720	+	0.839250i	−0.245816	+	0.123741i
$47$	−5.48180	+	7.54505i	−0.799602	+	1.10056i	0.193243	+	0.981151i	$0.438099\pi$
$47$	−5.48180	+	7.54505i	−0.799602	+	1.10056i	−0.992845	+	0.119407i	$0.961901\pi$
$48$	−3.92685	+	0.231952i	−0.566792	+	0.0334794i
$49$	2.21008	+	0.718100i	0.315726	+	0.102586i
$50$	1.13940	−	6.97326i	0.161136	−	0.986167i
$51$	−1.43242	+	2.33749i	−0.200578	+	0.327314i
$52$	0.00999078	+	0.145049i	0.00138547	+	0.0201147i
$53$	5.51277	+	0.433865i	0.757238	+	0.0595959i	0.451199	−	0.892423i	$-0.350996\pi$
$53$	5.51277	+	0.433865i	0.757238	+	0.0595959i	0.306039	+	0.952019i	$0.400996\pi$
$54$	5.98592	−	3.62807i	0.814580	−	0.493718i
$55$	0.181271	−	0.0930257i	0.0244426	−	0.0125436i
$56$	−3.80774	−	7.75188i	−0.508830	−	1.03589i
$57$	−0.283212	+	0.555835i	−0.0375124	+	0.0736222i
$58$	−3.26341	−	3.85898i	−0.428507	−	0.506709i
$59$	−9.61859	+	2.30922i	−1.25223	+	0.300635i	−0.804727	−	0.593646i	$-0.797688\pi$
$59$	−9.61859	+	2.30922i	−1.25223	+	0.300635i	−0.447507	+	0.894280i	$0.647688\pi$
$60$	0.00118047	−	0.120822i	0.000152398	−	0.0155980i
$61$	5.52132	−	0.434537i	0.706933	−	0.0556368i	0.280105	−	0.959970i	$-0.409631\pi$
$61$	5.52132	−	0.434537i	0.706933	−	0.0556368i	0.426828	+	0.904333i	$0.359631\pi$
$62$	0.0381291	−	7.80527i	0.00484240	−	0.991270i
$63$	5.02188	+	3.64861i	0.632697	+	0.459681i
$64$	−2.69405	+	7.53274i	−0.336756	+	0.941592i
$65$	−0.00446591			−0.000553928
$66$	−3.73709	+	2.70385i	−0.460005	+	0.332820i
$67$	−3.11765	−	7.52668i	−0.380882	−	0.919530i	−0.991796	−	0.127833i	$-0.959198\pi$
$67$	−3.11765	−	7.52668i	−0.380882	−	0.919530i	0.610914	−	0.791697i	$-0.290802\pi$
$68$	3.23290	+	4.54237i	0.392046	+	0.550844i
$69$	0.678179	+	1.10669i	0.0816431	+	0.133229i
$70$	0.245582	−	0.100321i	0.0293526	−	0.0119906i
$71$	−0.945767	+	0.481892i	−0.112242	+	0.0571901i	−0.509210	−	0.860642i	$-0.670062\pi$
$71$	−0.945767	+	0.481892i	−0.112242	+	0.0571901i	0.396968	+	0.917832i	$0.370062\pi$
$72$	−0.816154	−	5.69163i	−0.0961847	−	0.670765i
$73$	1.14532	−	7.23128i	0.134050	−	0.846357i	−0.825415	−	0.564527i	$-0.809059\pi$
$73$	1.14532	−	7.23128i	0.134050	−	0.846357i	0.959464	−	0.281830i	$-0.0909414\pi$
$74$	−4.06662	−	0.340047i	−0.472735	−	0.0395296i
$75$	−4.89826	−	0.385501i	−0.565602	−	0.0445138i
$76$	0.814483	+	0.972722i	0.0934276	+	0.111579i
$77$	−8.65025	−	5.26642i	−0.985787	−	0.600165i
$78$	0.0999355	−	0.0153282i	0.0113155	−	0.00173557i
$79$	−13.0543	+	4.24161i	−1.46873	+	0.477218i	−0.930723	−	0.365725i	$-0.880821\pi$
$79$	−13.0543	+	4.24161i	−1.46873	+	0.477218i	−0.538003	+	0.842943i	$0.680821\pi$
$80$	−0.225143	−	0.0984542i	−0.0251718	−	0.0110075i
$81$	0.723702	+	0.996090i	0.0804113	+	0.110677i
$82$	−7.01498	−	1.14622i	−0.774675	−	0.126579i
$83$	−0.622825	−	7.91374i	−0.0683639	−	0.868646i	−0.931516	−	0.363701i	$-0.881513\pi$
$83$	−0.622825	−	7.91374i	−0.0683639	−	0.868646i	0.863152	−	0.504945i	$-0.168487\pi$
$84$	−5.15116	+	3.08782i	−0.562037	+	0.336909i
$85$	−0.146018	+	0.0894798i	−0.0158379	+	0.00970545i
$86$	−5.40399	+	6.26503i	−0.582728	+	0.675576i
$87$	−2.48505	+	2.48505i	−0.266425	+	0.266425i
$88$	2.08255	+	9.14675i	0.222000	+	0.975047i
$89$	−9.76648	−	9.76648i	−1.03524	−	1.03524i	−0.999356	−	0.0358890i	$-0.988574\pi$
$89$	−9.76648	−	9.76648i	−1.03524	−	1.03524i	−0.0358890	−	0.999356i	$-0.511426\pi$
$90$	0.176134	−	0.0129966i	0.0185662	−	0.00136997i
$91$	0.115983	+	0.189268i	0.0121584	+	0.0198406i
$92$	2.61108	−	0.387443i	0.272223	−	0.0403937i
$93$	−5.41100	+	0.425855i	−0.561095	+	0.0441591i
$94$	10.7081	−	7.70022i	1.10445	−	0.794217i
$95$	−0.0315267	+	0.0229055i	−0.00323457	+	0.00235005i
$96$	5.37604	+	1.43040i	0.548690	+	0.145989i
$97$	−4.60684	−	14.1784i	−0.467753	−	1.43960i	−0.855486	−	0.517825i	$-0.826742\pi$
$97$	−4.60684	−	14.1784i	−0.467753	−	1.43960i	0.387733	−	0.921772i	$-0.373258\pi$
$98$	−2.64927	−	1.94465i	−0.267616	−	0.196439i
$99$	−4.39363	−	5.11416i	−0.441576	−	0.513992i
$100$	−4.62325	+	8.85859i	−0.462325	+	0.885859i
$101$	−0.217473	+	2.76326i	−0.0216394	+	0.274955i	0.976573	+	0.215187i	$0.0690361\pi$
$101$	−0.217473	+	2.76326i	−0.0216394	+	0.274955i	−0.998212	+	0.0597679i	$0.980964\pi$
$102$	2.96038	−	2.50350i	0.293122	−	0.247883i
$103$	2.09789	+	0.332273i	0.206711	+	0.0327398i	0.258931	−	0.965896i	$-0.416630\pi$
$103$	2.09789	+	0.332273i	0.206711	+	0.0327398i	−0.0522201	+	0.998636i	$0.516630\pi$
$104$	0.0509251	−	0.199211i	0.00499362	−	0.0195342i
$105$	−0.0837491	−	0.164367i	−0.00817308	−	0.0160406i
$106$	−7.21035	−	3.02798i	−0.700331	−	0.294103i
$107$	7.72419	−	4.73339i	0.746726	−	0.457594i	−0.0963782	−	0.995345i	$-0.530726\pi$
$107$	7.72419	−	4.73339i	0.746726	−	0.457594i	0.843104	+	0.537751i	$0.180726\pi$
$108$	−9.64751	+	2.21670i	−0.928332	+	0.213302i
$109$	−13.5651	+	5.61884i	−1.29930	+	0.538187i	−0.921744	−	0.387799i	$-0.873235\pi$
$109$	−13.5651	+	5.61884i	−1.29930	+	0.538187i	−0.377556	+	0.925987i	$0.623235\pi$
$110$	−0.284684	+	0.0445107i	−0.0271436	+	0.00424393i
$111$			2.83774i			0.269346i
$112$	1.67461	+	12.0986i	0.158236	+	1.14321i
$113$	6.92185	−	9.52711i	0.651153	−	0.896235i	−0.347995	−	0.937496i	$-0.613138\pi$
$113$	6.92185	−	9.52711i	0.651153	−	0.896235i	0.999148	+	0.0412610i	$0.0131375\pi$
$114$	0.626869	−	0.620774i	0.0587116	−	0.0581408i
$115$	0.00636148	+	0.0808303i	0.000593211	+	0.00753746i
$116$	2.67049	+	6.62960i	0.247949	+	0.615543i
$117$	0.0344993	+	0.143700i	0.00318946	+	0.0132851i
$118$	13.9406	+	1.16570i	1.28334	+	0.107311i
$119$	7.58441	+	3.86445i	0.695262	+	0.354253i
$120$	−0.0551795	+	0.161722i	−0.00503718	+	0.0147631i
$121$	7.82317	+	7.73292i	0.711197	+	0.702993i
$122$	−7.60704	−	1.86564i	−0.688709	−	0.168907i
$123$	−0.387808	+	4.92756i	−0.0349674	+	0.444304i
$124$	−3.51347	+	10.4644i	−0.315519	+	0.939728i
$125$	−0.523598	−	0.320861i	−0.0468320	−	0.0286987i
$126$	−5.12516	−	7.12713i	−0.456585	−	0.634935i
$127$	5.41794	−	16.6747i	0.480764	−	1.47964i	−0.357259	−	0.934005i	$-0.616289\pi$
$127$	5.41794	−	16.6747i	0.480764	−	1.47964i	0.838023	−	0.545634i	$-0.183711\pi$
$128$	6.95907	−	8.92028i	0.615101	−	0.788449i
$129$	4.65459	+	3.38176i	0.409814	+	0.297747i
$130$	0.00599703	+	0.00198099i	0.000525974	+	0.000173745i
$131$	−5.39082	−	13.0146i	−0.470998	−	1.13709i	−0.963723	−	0.266905i	$-0.913999\pi$
$131$	−5.39082	−	13.0146i	−0.470998	−	1.13709i	0.492725	−	0.870185i	$-0.336001\pi$
$132$	6.21772	−	1.97314i	0.541183	−	0.171740i
$133$	1.78952	+	0.741245i	0.155171	+	0.0642741i
$134$	0.847835	+	11.4901i	0.0732418	+	0.992594i
$135$	−0.0475648	−	0.300312i	−0.00409372	−	0.0258468i
$136$	−2.32637	−	7.53376i	−0.199485	−	0.646015i
$137$	3.61193	+	7.08881i	0.308588	+	0.605638i	0.992264	−	0.124148i	$-0.0396198\pi$
$137$	3.61193	+	7.08881i	0.308588	+	0.605638i	−0.683676	+	0.729786i	$0.739620\pi$
$138$	−0.419784	−	1.78694i	−0.0357344	−	0.152114i
$139$	3.14903	+	13.1167i	0.267097	+	1.11254i	0.931087	+	0.364798i	$0.118862\pi$
$139$	3.14903	+	13.1167i	0.267097	+	1.11254i	−0.663989	+	0.747742i	$0.731138\pi$
$140$	−0.374279	+	0.0257797i	−0.0316323	+	0.00217879i
$141$	−5.95647	−	6.97413i	−0.501625	−	0.587328i
$142$	1.48378	−	0.227583i	0.124516	−	0.0190983i
$143$	−0.0751711	−	0.229089i	−0.00628612	−	0.0191574i
$144$	−1.42873	+	8.00502i	−0.119061	+	0.667085i
$145$	−0.208791	+	0.0678403i	−0.0173391	+	0.00563383i
$146$	−4.74565	+	9.20245i	−0.392753	+	0.761600i
$147$	−1.19406	+	1.94854i	−0.0984848	+	0.160713i
$148$	5.31001	+	2.26051i	0.436480	+	0.185813i
$149$	8.65383	+	7.39107i	0.708950	+	0.605500i	0.929040	−	0.369979i	$-0.120635\pi$
$149$	8.65383	+	7.39107i	0.708950	+	0.605500i	−0.220090	+	0.975479i	$0.570635\pi$
$150$	6.40661	+	2.69044i	0.523097	+	0.219674i
$151$	12.5350	−	1.98535i	1.02008	−	0.161566i	0.376080	−	0.926587i	$-0.377272\pi$
$151$	12.5350	−	1.98535i	1.02008	−	0.161566i	0.644005	+	0.765022i	$0.277272\pi$
$152$	−0.662244	−	1.66750i	−0.0537151	−	0.135253i
$153$	4.00719	+	4.00719i	0.323963	+	0.323963i
$154$	9.27987	+	10.9091i	0.747793	+	0.879079i
$155$	−0.313249	−	0.129752i	−0.0251608	−	0.0104219i
$156$	−0.140997	−	0.0237461i	−0.0112888	−	0.00190121i
$157$	1.22542	−	5.10423i	0.0977989	−	0.407362i	−0.901899	−	0.431947i	$-0.857827\pi$
$157$	1.22542	−	5.10423i	0.0977989	−	0.407362i	0.999698	+	0.0245857i	$0.00782665\pi$
$158$	19.4114	+	0.0948257i	1.54429	+	0.00754393i
$159$	−1.68048	+	5.17199i	−0.133271	+	0.410166i
$160$	0.258660	+	0.232078i	0.0204489	+	0.0183474i
$161$	3.26042	−	2.36883i	0.256957	−	0.186690i
$162$	−0.529974	−	1.65862i	−0.0416387	−	0.130313i
$163$	−1.20950	+	1.03301i	−0.0947354	+	0.0809117i	−0.695554	−	0.718473i	$-0.744841\pi$
$163$	−1.20950	+	1.03301i	−0.0947354	+	0.0809117i	0.600819	+	0.799385i	$0.294841\pi$
$164$	8.91160	+	4.65091i	0.695879	+	0.363175i
$165$	0.0473405	+	0.194697i	0.00368545	+	0.0151572i
$166$	−2.67403	+	10.9032i	−0.207545	+	0.846253i
$167$	6.63277	−	13.0175i	0.513259	−	1.00733i	−0.478364	−	0.878162i	$-0.658770\pi$
$167$	6.63277	−	13.0175i	0.513259	−	1.00733i	0.991623	−	0.129166i	$-0.0412301\pi$
$168$	8.28691	−	1.86151i	0.639349	−	0.143618i
$169$	2.03282	−	12.8347i	0.156371	−	0.987287i
$170$	0.235771	−	0.0553869i	0.0180828	−	0.00424798i
$171$	0.980578	+	0.837492i	0.0749866	+	0.0640446i
$172$	10.0358	−	6.01586i	0.765221	−	0.458705i
$173$	−16.2049	−	3.89046i	−1.23204	−	0.295786i	−0.435396	−	0.900239i	$-0.643392\pi$
$173$	−16.2049	−	3.89046i	−1.23204	−	0.295786i	−0.796641	+	0.604453i	$0.793392\pi$
$174$	4.43935	−	2.23471i	0.336546	−	0.169413i
$175$			15.2559i			1.15324i
$176$	1.26079	−	13.2065i	0.0950354	−	0.995474i
$177$		−	9.72792i		−	0.731196i
$178$	8.78265	+	17.4471i	0.658288	+	1.30772i
$179$	−5.72848	−	1.37529i	−0.428167	−	0.102794i	0.0136337	−	0.999907i	$-0.495660\pi$
$179$	−5.72848	−	1.37529i	−0.428167	−	0.102794i	−0.441801	+	0.897113i	$0.645660\pi$
$180$	−0.242286	−	0.0606773i	−0.0180589	−	0.00452262i
$181$	18.4163	+	15.7290i	1.36887	+	1.16913i	0.967399	+	0.253257i	$0.0815019\pi$
$181$	18.4163	+	15.7290i	1.36887	+	1.16913i	0.401474	+	0.915871i	$0.368498\pi$
$182$	−0.0717923	−	0.305605i	−0.00532160	−	0.0226530i
$183$	−0.852034	+	5.37953i	−0.0629841	+	0.397666i
$184$	−3.67813	−	0.637947i	−0.271156	−	0.0470301i
$185$	−0.0804776	+	0.157946i	−0.00591683	+	0.0116124i
$186$	7.45504	+	1.82836i	0.546630	+	0.134062i
$187$	−7.04788	−	5.98419i	−0.515392	−	0.437607i
$188$	−17.7949	+	5.59032i	−1.29783	+	0.407716i
$189$	−11.4921	+	9.81518i	−0.835927	+	0.713949i
$190$	0.0524960	−	0.0167739i	0.00380846	−	0.00121691i
$191$	−2.81883	+	2.04800i	−0.203963	+	0.148188i	−0.685078	−	0.728470i	$-0.740232\pi$
$191$	−2.81883	+	2.04800i	−0.203963	+	0.148188i	0.481115	+	0.876658i	$0.340232\pi$
$192$	−6.58470	−	4.30552i	−0.475210	−	0.310724i
$193$	3.55134	−	10.9299i	0.255631	−	0.786752i	−0.738073	−	0.674720i	$-0.764264\pi$
$193$	3.55134	−	10.9299i	0.255631	−	0.786752i	0.993705	−	0.112032i	$-0.0357358\pi$
$194$	−0.102991	+	21.0829i	−0.00739432	+	1.51366i
$195$	0.00102526	−	0.00427053i	7.34207e−5	−	0.000305819i
$196$	2.69495	+	3.78653i	0.192496	+	0.270466i
$197$	−18.5054	−	7.66518i	−1.31845	−	0.546122i	−0.391115	−	0.920342i	$-0.627910\pi$
$197$	−18.5054	−	7.66518i	−1.31845	−	0.546122i	−0.927340	+	0.374220i	$0.877910\pi$
$198$	3.63142	+	8.81646i	0.258074	+	0.626558i
$199$	−5.60885	−	5.60885i	−0.397601	−	0.397601i	0.479785	−	0.877386i	$-0.340715\pi$
$199$	−5.60885	−	5.60885i	−0.397601	−	0.397601i	−0.877386	+	0.479785i	$0.840715\pi$
$200$	10.1378	−	9.84494i	0.716852	−	0.696143i
$201$	7.91313	−	1.25332i	0.558149	−	0.0884021i
$202$	1.51776	−	3.61417i	0.106789	−	0.254292i
$203$	8.29758	+	7.08680i	0.582376	+	0.497396i
$204$	−5.08584	+	2.04864i	−0.356080	+	0.143434i
$205$	−0.161330	+	0.263266i	−0.0112677	+	0.0183873i
$206$	−2.66975	−	1.37677i	−0.186010	−	0.0959244i
$207$	2.55174	−	0.829111i	0.177358	−	0.0576272i
$208$	−0.156751	+	0.244920i	−0.0108687	+	0.0169821i
$209$	−1.70566	−	1.23169i	−0.117983	−	0.0851976i
$210$	0.0395521	+	0.257869i	0.00272936	+	0.0177947i
$211$	−18.3279	−	21.4593i	−1.26175	−	1.47732i	−0.811433	−	0.584446i	$-0.801312\pi$
$211$	−18.3279	−	21.4593i	−1.26175	−	1.47732i	−0.450314	−	0.892870i	$-0.648688\pi$
$212$	8.33924	+	7.26448i	0.572742	+	0.498927i
$213$	−0.243685	−	1.01502i	−0.0166970	−	0.0695481i
$214$	−12.4720	+	2.92991i	−0.852571	+	0.200285i
$215$	0.163165	+	0.320229i	0.0111278	+	0.0218394i
$216$	13.9384	+	1.30276i	0.948388	+	0.0886417i
$217$	2.63638	+	16.6454i	0.178969	+	1.12997i
$218$	20.7082	−	1.52803i	1.40254	−	0.103491i
$219$	6.65198	+	2.75534i	0.449499	+	0.186189i
$220$	0.402031	+	0.0665095i	0.0271049	+	0.00448407i
$221$	0.0775528	+	0.187229i	0.00521676	+	0.0125944i
$222$	1.25877	−	3.81065i	0.0844829	−	0.255754i
$223$	−5.06803	−	3.68214i	−0.339380	−	0.246574i	0.405020	−	0.914308i	$-0.367265\pi$
$223$	−5.06803	−	3.68214i	−0.339380	−	0.246574i	−0.744400	+	0.667734i	$0.767265\pi$
$224$	3.11797	−	16.9894i	0.208328	−	1.13515i
$225$	−3.13860	+	9.65962i	−0.209240	+	0.643975i
$226$	−13.5210	+	9.72304i	−0.899405	+	0.646767i
$227$	13.1798	+	8.07658i	0.874773	+	0.536062i	0.885900	−	0.463877i	$-0.153542\pi$
$227$	13.1798	+	8.07658i	0.874773	+	0.536062i	−0.0111269	+	0.999938i	$0.503542\pi$
$228$	−1.11715	+	0.555537i	−0.0739852	+	0.0367913i
$229$	−1.00593	+	12.7816i	−0.0664739	+	0.844630i	0.869810	+	0.493387i	$0.164241\pi$
$229$	−1.00593	+	12.7816i	−0.0664739	+	0.844630i	−0.936284	+	0.351244i	$0.885759\pi$
$230$	0.0273123	−	0.111364i	0.00180092	−	0.00734315i
$231$	7.02191	−	7.06277i	0.462008	−	0.464696i
$232$	−0.645292	−	10.0871i	−0.0423655	−	0.662252i
$233$	−7.55176	−	3.84781i	−0.494732	−	0.252079i	0.188778	−	0.982020i	$-0.439547\pi$
$233$	−7.55176	−	3.84781i	−0.494732	−	0.252079i	−0.683510	+	0.729941i	$0.739547\pi$
$234$	0.0174153	−	0.208270i	0.00113848	−	0.0136151i
$235$	−0.133748	−	0.557099i	−0.00872473	−	0.0363411i
$236$	−18.2030	−	7.74915i	−1.18492	−	0.504426i
$237$	−1.05909	−	13.4570i	−0.0687951	−	0.874124i
$238$	−8.47050	−	8.55366i	−0.549061	−	0.554452i
$239$	−5.07313	+	6.98257i	−0.328154	+	0.451665i	−0.940935	−	0.338588i	$-0.890051\pi$
$239$	−5.07313	+	6.98257i	−0.328154	+	0.451665i	0.612781	+	0.790253i	$0.290051\pi$
$240$	0.145834	−	0.192691i	0.00941356	−	0.0124381i
$241$		−	1.66475i		−	0.107236i	−0.998562	−	0.0536181i	$-0.982925\pi$
$241$		−	1.66475i		−	0.107236i	0.998562	−	0.0536181i	$-0.0170754\pi$
$242$	−7.07514	−	13.8543i	−0.454807	−	0.890590i
$243$	−14.8367	+	6.14558i	−0.951777	+	0.394239i
$244$	9.38752	+	5.87960i	0.600974	+	0.376403i
$245$	−0.121721	+	0.0745905i	−0.00777645	+	0.00476541i
$246$	2.70654	−	6.44494i	0.172563	−	0.410914i
$247$	0.0209356	+	0.0410884i	0.00133210	+	0.00261439i
$248$	9.35985	−	12.4935i	0.594351	−	0.793339i
$249$	7.71051	+	1.22122i	0.488634	+	0.0773920i
$250$	0.560784	+	0.663126i	0.0354671	+	0.0419397i
$251$	0.353038	−	4.48577i	0.0222835	−	0.283139i	−0.975672	−	0.219234i	$-0.929644\pi$
$251$	0.353038	−	4.48577i	0.0222835	−	0.283139i	0.997956	−	0.0639057i	$-0.0203557\pi$
$252$	3.72084	+	11.8441i	0.234391	+	0.746106i
$253$	−4.03930	+	1.68688i	−0.253949	+	0.106053i
$254$	−14.6720	+	19.9883i	−0.920605	+	1.25417i
$255$	−0.0520431	−	0.160172i	−0.00325906	−	0.0100304i
$256$	−13.3018	+	8.89165i	−0.831364	+	0.555728i
$257$	−1.75372	+	1.27415i	−0.109394	+	0.0794793i	−0.641137	−	0.767426i	$-0.721537\pi$
$257$	−1.75372	+	1.27415i	−0.109394	+	0.0794793i	0.531743	+	0.846906i	$0.321537\pi$
$258$	−4.75032	−	6.60587i	−0.295742	−	0.411264i
$259$	8.78391	−	0.691309i	0.545806	−	0.0429559i
$260$	−0.00717436	−	0.00532034i	−0.000444935	−	0.000329953i
$261$	3.79582	+	6.19421i	0.234955	+	0.383412i
$262$	1.46601	+	19.8679i	0.0905707	+	1.22744i
$263$	16.5135	+	16.5135i	1.01827	+	1.01827i	0.999830	+	0.0184378i	$0.00586925\pi$
$263$	16.5135	+	16.5135i	1.01827	+	1.01827i	0.0184378	+	0.999830i	$0.494131\pi$
$264$	−9.22469	−	0.108434i	−0.567740	−	0.00667363i
$265$	−0.240211	+	0.240211i	−0.0147560	+	0.0147560i
$266$	−2.07425	−	1.78918i	−0.127181	−	0.109701i
$267$	11.5814	−	7.09706i	0.708767	−	0.434333i
$268$	3.95828	−	15.8055i	0.241790	−	0.965476i
$269$	1.30831	+	16.6237i	0.0797693	+	1.01357i	0.898381	+	0.439217i	$0.144744\pi$
$269$	1.30831	+	16.6237i	0.0797693	+	1.01357i	−0.818611	+	0.574348i	$0.805256\pi$
$270$	−0.0693406	+	0.424372i	−0.00421994	+	0.0258265i
$271$	−18.9871	−	26.1335i	−1.15338	−	1.58750i	−0.733127	−	0.680091i	$-0.761940\pi$
$271$	−18.9871	−	26.1335i	−1.15338	−	1.58750i	−0.420257	−	0.907405i	$-0.638060\pi$
$272$	−0.217872	+	11.1486i	−0.0132104	+	0.675984i
$273$	−0.207614	+	0.0674580i	−0.0125654	+	0.00408274i
$274$	−1.70580	−	11.1214i	−0.103051	−	0.671866i
$275$	3.82157	−	16.1239i	0.230450	−	0.972309i
$276$	−0.228946	+	2.58579i	−0.0137809	+	0.155646i
$277$	−5.34175	−	0.420405i	−0.320955	−	0.0252597i	−0.0830415	−	0.996546i	$-0.526463\pi$
$277$	−5.34175	−	0.420405i	−0.320955	−	0.0252597i	−0.237913	+	0.971286i	$0.576463\pi$
$278$	1.58964	−	19.0105i	0.0953401	−	1.14017i
$279$	−1.75518	+	11.0818i	−0.105080	+	0.663449i
$280$	0.514034	+	0.131405i	0.0307194	+	0.00785294i
$281$	−25.4949	+	12.9903i	−1.52090	+	0.774936i	−0.997041	−	0.0768706i	$-0.975507\pi$
$281$	−25.4949	+	12.9903i	−1.52090	+	0.774936i	−0.523856	+	0.851807i	$0.675507\pi$
$282$	4.90503	+	12.0074i	0.292090	+	0.715028i
$283$	13.0841	+	21.3513i	0.777769	+	1.26920i	0.958337	+	0.285640i	$0.0922063\pi$
$283$	13.0841	+	21.3513i	0.777769	+	1.26920i	−0.180568	+	0.983562i	$0.557794\pi$
$284$	−2.09344	−	0.352567i	−0.124223	−	0.0209210i
$285$	−0.0146656	−	0.0354060i	−0.000868718	−	0.00209727i
$286$	−0.000676556		0.340976i	−4.00056e−5		0.0201624i
$287$	15.3472			0.905918
$288$	5.46944	−	10.1157i	0.322290	−	0.596076i
$289$	−7.46626	−	5.42456i	−0.439192	−	0.319091i
$290$	0.310467	+	0.00151664i	0.0182312	+	8.90604e-5i
$291$	14.6157	−	1.15028i	0.856788	−	0.0674307i
$292$	10.4547	−	10.2524i	0.611816	−	0.599976i
$293$	−19.9604	+	4.79207i	−1.16610	+	0.279956i	−0.769873	−	0.638197i	$-0.779680\pi$
$293$	−19.9604	+	4.79207i	−1.16610	+	0.279956i	−0.396226	+	0.918153i	$0.629680\pi$
$294$	2.46778	−	2.08692i	0.143924	−	0.121712i
$295$	0.275882	−	0.541448i	0.0160624	−	0.0315243i
$296$	−6.12781	−	5.39093i	−0.356172	−	0.313342i
$297$	14.6046	−	7.49486i	0.847445	−	0.434896i
$298$	−8.34223	−	13.7637i	−0.483252	−	0.797313i
$299$	0.0956515	+	0.00752793i	0.00553167	+	0.000435352i
$300$	−7.40966	−	6.45470i	−0.427797	−	0.372662i
$301$	9.33396	−	15.2316i	0.538000	−	0.877937i
$302$	−17.7133	−	2.89427i	−1.01928	−	0.166547i
$303$	−2.59244	−	0.842336i	−0.148932	−	0.0483910i
$304$	0.149618	+	2.53296i	0.00858117	+	0.145275i
$305$	−0.199986	+	0.275257i	−0.0114511	+	0.0157611i
$306$	−3.60353	−	7.15856i	−0.206000	−	0.409228i
$307$	−4.94764	+	2.04938i	−0.282377	+	0.116964i	−0.519377	−	0.854545i	$-0.673836\pi$
$307$	−4.94764	+	2.04938i	−0.282377	+	0.116964i	0.237000	+	0.971510i	$0.423836\pi$
$308$	−7.62237	−	18.7656i	−0.434325	−	1.06927i
$309$	−0.799359	+	1.92982i	−0.0454740	+	0.109784i
$310$	0.363090	+	0.313188i	0.0206221	+	0.0177879i
$311$	23.6640	−	3.74801i	1.34186	−	0.212530i	0.556130	−	0.831096i	$-0.312286\pi$
$311$	23.6640	−	3.74801i	1.34186	−	0.212530i	0.785733	+	0.618565i	$0.212286\pi$
$312$	0.178804	+	0.0944311i	0.0101228	+	0.00534611i
$313$	−22.2673	+	11.3458i	−1.25862	+	0.641300i	−0.950700	−	0.310111i	$-0.899634\pi$
$313$	−22.2673	+	11.3458i	−1.25862	+	0.641300i	−0.307922	+	0.951411i	$0.599634\pi$
$314$	−3.90968	+	6.31062i	−0.220636	+	0.356129i
$315$	−0.370797	+	0.0890205i	−0.0208920	+	0.00501574i
$316$	−26.0245	−	8.73788i	−1.46399	−	0.491544i
$317$	−16.3390	+	13.9548i	−0.917689	+	0.783780i	−0.976729	−	0.214476i	$-0.931196\pi$
$317$	−16.3390	+	13.9548i	−0.917689	+	0.783780i	0.0590408	+	0.998256i	$0.481196\pi$
$318$	4.55083	−	6.19976i	0.255198	−	0.347665i
$319$	−6.99444	−	9.56852i	−0.391613	−	0.535734i
$320$	−0.244395	−	0.426382i	−0.0136621	−	0.0238355i
$321$	2.75302	+	8.47294i	0.153659	+	0.472913i
$322$	−5.42901	+	1.73472i	−0.302547	+	0.0966720i
$323$	1.50777	+	0.923962i	0.0838945	+	0.0514106i
$324$	−0.0240580	+	2.46235i	−0.00133655	+	0.136797i
$325$	−0.235885	+	0.276186i	−0.0130845	+	0.0153200i
$326$	2.08240	−	0.850663i	0.115333	−	0.0471139i
$327$	−2.25881	−	14.2616i	−0.124913	−	0.788667i
$328$	−9.90385	−	10.1985i	−0.546849	−	0.563116i
$329$	−20.1366	+	20.1366i	−1.11017	+	1.11017i
$330$	0.0227931	−	0.282448i	0.00125472	−	0.0155482i
$331$	8.81569	−	21.2830i	0.484554	−	1.16982i	−0.472870	−	0.881132i	$-0.656782\pi$
$331$	8.81569	−	21.2830i	0.484554	−	1.16982i	0.957424	−	0.288685i	$-0.0932181\pi$
$332$	8.42727	−	13.4552i	0.462506	−	0.738449i
$333$	5.70394	+	1.36940i	0.312574	+	0.0750424i
$334$	−14.6811	+	14.5384i	−0.803316	+	0.795505i
$335$	0.475982	+	0.154656i	0.0260057	+	0.00844976i
$336$	−11.9538	−	1.17620i	−0.652132	−	0.0641669i
$337$	−12.2366	−	16.8423i	−0.666572	−	0.917458i	0.333104	−	0.942890i	$-0.391904\pi$
$337$	−12.2366	−	16.8423i	−0.666572	−	0.917458i	−0.999677	+	0.0254320i	$0.991904\pi$
$338$	−8.42301	+	16.3333i	−0.458151	+	0.888417i
$339$	7.52122	+	8.80622i	0.408497	+	0.478288i
$340$	−0.341173	−	0.0302075i	−0.0185027	−	0.00163823i
$341$	1.38327	−	18.2529i	0.0749081	−	0.988448i
$342$	−0.945269	−	1.55959i	−0.0511143	−	0.0843329i
$343$	−12.7224	−	6.48239i	−0.686945	−	0.350016i
$344$	−16.1450	+	3.62670i	−0.870482	+	0.195538i
$345$	−0.0787545	−	0.0124735i	−0.00424000	−	0.000671550i
$346$	20.0350	+	12.4125i	1.07709	+	0.667299i
$347$	−5.47684	+	6.41256i	−0.294012	+	0.344244i	−0.887676	−	0.460469i	$-0.847681\pi$
$347$	−5.47684	+	6.41256i	−0.294012	+	0.344244i	0.593663	+	0.804714i	$0.297681\pi$
$348$	−6.95264	+	1.03166i	−0.372701	+	0.0553030i
$349$	−0.0824693	+	0.343509i	−0.00441448	+	0.0183876i	−0.974534	−	0.224241i	$-0.928010\pi$
$349$	−0.0824693	+	0.343509i	−0.00441448	+	0.0183876i	0.970119	+	0.242629i	$0.0780097\pi$
$350$	6.76725	−	20.4864i	0.361725	−	1.09504i
$351$	−0.359808			−0.0192051
$352$	−7.55118	+	17.1750i	−0.402479	+	0.915429i
$353$	8.18000			0.435377			0.217689	−	0.976018i	$-0.430148\pi$
$353$	8.18000			0.435377			0.217689	+	0.976018i	$0.430148\pi$
$354$	−4.31512	+	13.0631i	−0.229346	+	0.694296i
$355$	0.0152225	−	0.0634061i	0.000807924	−	0.00336524i
$356$	−4.05455	−	27.3246i	−0.214891	−	1.44820i
$357$	−5.43658	+	6.36542i	−0.287734	+	0.336893i
$358$	7.08242	+	4.38784i	0.374317	+	0.231905i
$359$	17.6914	+	2.80204i	0.933717	+	0.147886i	0.604714	−	0.796443i	$-0.293287\pi$
$359$	17.6914	+	2.80204i	0.933717	+	0.147886i	0.329003	+	0.944329i	$0.393287\pi$
$360$	0.298438	+	0.188954i	0.0157291	+	0.00995874i
$361$	−16.5706	−	8.44314i	−0.872136	−	0.444376i
$362$	−17.7532	−	29.2908i	−0.933086	−	1.53949i
$363$	−9.19062	+	5.70562i	−0.482382	+	0.299468i
$364$	−0.0391548	+	0.442227i	−0.00205227	+	0.0231790i
$365$	0.292103	+	0.342008i	0.0152894	+	0.0179015i
$366$	3.53041	−	6.84593i	0.184537	−	0.357843i
$367$	11.7661	+	16.1946i	0.614184	+	0.845352i	0.996913	−	0.0785087i	$-0.0250158\pi$
$367$	11.7661	+	16.1946i	0.614184	+	0.845352i	−0.382729	+	0.923860i	$0.625016\pi$
$368$	4.65619	+	2.48822i	0.242721	+	0.129707i
$369$	9.71741	+	3.15738i	0.505868	+	0.164367i
$370$	0.178131	−	0.176399i	0.00926059	−	0.00917055i
$371$	16.4187	+	3.94179i	0.852418	+	0.204647i
$372$	−9.19995	−	5.76212i	−0.476995	−	0.298752i
$373$	5.66665	−	13.6805i	0.293408	−	0.708350i	−0.706591	−	0.707622i	$-0.749768\pi$
$373$	5.66665	−	13.6805i	0.293408	−	0.708350i	1.00000		0.000728482i	$-0.000231883\pi$
$374$	6.80975	+	11.1622i	0.352124	+	0.577181i
$375$	0.427029	−	0.427029i	0.0220517	−	0.0220517i
$376$	26.3756	+	0.386563i	1.36022	+	0.0199355i
$377$	0.0406401	+	0.256592i	0.00209307	+	0.0132151i
$378$	19.7859	−	8.08260i	1.01768	−	0.415724i
$379$	0.220928	−	0.258674i	0.0113483	−	0.0132872i	−0.754703	−	0.656067i	$-0.772219\pi$
$379$	0.220928	−	0.258674i	0.0113483	−	0.0132872i	0.766051	+	0.642780i	$0.222219\pi$
$380$	−0.0779346		0.000761446i	−0.00399796		3.90614e-5i
$381$	14.7014	+	9.00901i	0.753174	+	0.461545i
$382$	4.69371	−	1.49977i	0.240151	−	0.0767348i
$383$	4.58569	+	14.1133i	0.234318	+	0.721156i	0.997211	+	0.0746314i	$0.0237780\pi$
$383$	4.58569	+	14.1133i	0.234318	+	0.721156i	−0.762894	+	0.646524i	$0.776222\pi$
$384$	6.93239	+	8.70249i	0.353767	+	0.444097i
$385$	0.591132	−	0.193968i	0.0301269	−	0.00988553i
$386$	−9.61721	+	13.1019i	−0.489503	+	0.666868i
$387$	9.04359	−	7.72395i	0.459711	−	0.392631i
$388$	9.49028	−	28.2654i	0.481796	−	1.43496i
$389$	29.9378	−	7.18744i	1.51791	−	0.364418i	0.613020	−	0.790067i	$-0.289954\pi$
$389$	29.9378	−	7.18744i	1.51791	−	0.364418i	0.904888	+	0.425649i	$0.139954\pi$
$390$	−0.00327110	+	0.00527988i	−0.000165639	+	0.000267357i
$391$	3.27826	−	1.67036i	0.165789	−	0.0844736i
$392$	−1.93927	−	6.28015i	−0.0979479	−	0.317196i
$393$	13.6828	−	2.16714i	0.690207	−	0.109318i
$394$	21.4498	+	18.5018i	1.08062	+	0.932108i
$395$	0.322689	−	0.779039i	0.0162362	−	0.0391977i
$396$	−0.965622	−	13.4500i	−0.0485244	−	0.675887i
$397$	31.6105	−	13.0935i	1.58649	−	0.657145i	0.597063	−	0.802194i	$-0.296334\pi$
$397$	31.6105	−	13.0935i	1.58649	−	0.657145i	0.989424	+	0.145050i	$0.0463342\pi$
$398$	5.04384	+	10.0198i	0.252825	+	0.502247i
$399$	−1.11965	+	1.54106i	−0.0560524	+	0.0771496i
$400$	−17.9806	+	8.72330i	−0.899028	+	0.436165i
$401$	27.7164	+	9.00559i	1.38409	+	0.449718i	0.904011	−	0.427509i	$-0.140609\pi$
$401$	27.7164	+	9.00559i	1.38409	+	0.449718i	0.480077	+	0.877226i	$0.340609\pi$
$402$	−11.1821	−	1.82710i	−0.557711	−	0.0911276i
$403$	−0.209641	+	0.342104i	−0.0104430	+	0.0170414i
$404$	−3.64130	+	4.18002i	−0.181161	+	0.207964i
$405$	−0.0754043	−	0.00593445i	−0.00374687	−	0.000294885i
$406$	−7.99880	−	13.1971i	−0.396974	−	0.654963i
$407$	−9.45684	−	1.46971i	−0.468758	−	0.0728507i
$408$	7.73824	−	0.495030i	0.383100	−	0.0245076i
$409$	−4.26885	+	8.37810i	−0.211081	+	0.414270i	−0.972136	−	0.234417i	$-0.924682\pi$
$409$	−4.26885	+	8.37810i	−0.211081	+	0.414270i	0.761055	+	0.648688i	$0.224682\pi$
$410$	0.333421	−	0.281963i	0.0164665	−	0.0139252i
$411$	−7.60789	+	1.82649i	−0.375270	+	0.0900942i
$412$	2.97435	+	3.03305i	0.146536	+	0.149427i
$413$	−30.1117	+	2.36985i	−1.48170	+	0.116612i
$414$	−3.79437	−	0.0185357i	−0.186483	−	0.000910979i
$415$	0.394527	+	0.286641i	0.0193666	+	0.0140706i
$416$	0.319134	−	0.259358i	0.0156468	−	0.0127161i
$417$	−13.2658			−0.649627
$418$	1.74408	+	2.41056i	0.0853057	+	0.117905i
$419$	5.96042	+	14.3897i	0.291186	+	0.702984i	0.999997	−	0.00241364i	$-0.000768286\pi$
$419$	5.96042	+	14.3897i	0.291186	+	0.702984i	−0.708811	+	0.705398i	$0.750768\pi$
$420$	0.0612734	−	0.363823i	0.00298984	−	0.0177527i
$421$	−0.677612	−	1.10576i	−0.0330248	−	0.0538916i	0.835702	−	0.549183i	$-0.185061\pi$
$421$	−0.677612	−	1.10576i	−0.0330248	−	0.0538916i	−0.868727	+	0.495292i	$0.835061\pi$
$422$	15.0927	+	36.9464i	0.734700	+	1.79852i
$423$	−16.8926	+	8.60721i	−0.821347	+	0.418497i
$424$	−7.97593	−	13.4542i	−0.387346	−	0.653394i
$425$	−2.17881	+	13.7564i	−0.105688	+	0.667285i
$426$	−0.123013	+	1.47111i	−0.00595998	+	0.0712756i
$427$	16.8593	+	1.32686i	0.815880	+	0.0642111i
$428$	18.0477	+	1.59794i	0.872368	+	0.0772395i
$429$	0.236324	−	0.0192891i	0.0114099	−	0.000931286i
$430$	−0.0770578	−	0.502395i	−0.00371605	−	0.0242277i
$431$	5.50643	−	1.78915i	0.265235	−	0.0861802i	−0.173380	−	0.984855i	$-0.555469\pi$
$431$	5.50643	−	1.78915i	0.265235	−	0.0861802i	0.438616	+	0.898675i	$0.355469\pi$
$432$	−18.1393	−	7.93222i	−0.872725	−	0.381639i
$433$	8.25898	+	11.3675i	0.396901	+	0.546288i	0.959963	−	0.280127i	$-0.0903767\pi$
$433$	8.25898	+	11.3675i	0.396901	+	0.546288i	−0.563062	+	0.826415i	$0.690377\pi$
$434$	3.84335	−	23.5217i	0.184487	−	1.12908i
$435$	−0.0169390	−	0.215231i	−0.000812165	−	0.0103195i
$436$	−28.4858	−	7.13388i	−1.36422	−	0.341651i
$437$	0.713854	−	0.437450i	0.0341483	−	0.0209261i
$438$	−7.71037	−	6.65069i	−0.368416	−	0.317782i
$439$	−13.1692	+	13.1692i	−0.628530	+	0.628530i	−0.947698	−	0.319168i	$-0.896597\pi$
$439$	−13.1692	+	13.1692i	−0.628530	+	0.628530i	0.319168	+	0.947698i	$0.396597\pi$
$440$	−0.510363	−	0.267645i	−0.0243306	−	0.0127595i
$441$	3.34040	+	3.34040i	0.159067	+	0.159067i
$442$	−0.0210902	−	0.285821i	−0.00100316	−	0.0135951i
$443$	18.5418	+	30.2575i	0.880949	+	1.43758i	0.899100	+	0.437743i	$0.144222\pi$
$443$	18.5418	+	30.2575i	0.880949	+	1.43758i	−0.0181513	+	0.999835i	$0.505778\pi$
$444$	−3.38066	+	4.55875i	−0.160439	+	0.216349i
$445$	0.845879	−	0.0665721i	0.0400985	−	0.00315582i
$446$	5.17225	+	7.19262i	0.244913	+	0.340581i
$447$	−9.05443	+	6.57843i	−0.428260	+	0.311149i
$448$	−11.7231	+	21.4311i	−0.553867	+	1.01252i
$449$	−12.8594	−	39.5770i	−0.606870	−	1.86775i	−0.483384	−	0.875408i	$-0.660593\pi$
$449$	−12.8594	−	39.5770i	−0.606870	−	1.86775i	−0.123486	−	0.992346i	$-0.539407\pi$
$450$	8.49948	−	11.5792i	0.400669	−	0.545847i
$451$	−16.2204	−	3.84444i	−0.763788	−	0.181028i
$452$	22.4696	−	7.05888i	1.05688	−	0.332022i
$453$	−0.979238	+	12.4424i	−0.0460086	+	0.584595i
$454$	−14.1158	−	16.6919i	−0.662487	−	0.783390i
$455$	−0.0134687	−	0.00213324i	−0.000631424	−	0.000100008i
$456$	1.74659	−	0.250453i	0.0817915	−	0.0117285i
$457$	−4.54302	−	8.91618i	−0.212514	−	0.417081i	0.760001	−	0.649921i	$-0.225198\pi$
$457$	−4.54302	−	8.91618i	−0.212514	−	0.417081i	−0.972515	+	0.232840i	$0.925198\pi$
$458$	7.02048	−	16.7175i	0.328045	−	0.781157i
$459$	−11.7643	+	7.20918i	−0.549111	+	0.336496i
$460$	−0.0860754	+	0.137430i	−0.00401328	+	0.00640771i
$461$	−15.6894	+	6.49876i	−0.730728	+	0.302677i	−0.716851	−	0.697226i	$-0.754417\pi$
$461$	−15.6894	+	6.49876i	−0.730728	+	0.302677i	−0.0138767	+	0.999904i	$0.504417\pi$
$462$	−12.5623	+	6.36942i	−0.584449	+	0.296332i
$463$		−	11.2042i		−	0.520706i	−0.965514	−	0.260353i	$-0.916161\pi$
$463$		−	11.2042i		−	0.520706i	0.965514	−	0.260353i	$-0.0838389\pi$
$464$	−3.60793	+	13.8317i	−0.167494	+	0.642120i
$465$	0.195990	−	0.269757i	0.00908881	−	0.0125097i
$466$	8.43404	+	8.51684i	0.390699	+	0.394535i
$467$	−1.75421	−	22.2893i	−0.0811750	−	1.03143i	−0.893749	−	0.448568i	$-0.851934\pi$
$467$	−1.75421	−	22.2893i	−0.0811750	−	1.03143i	0.812574	−	0.582859i	$-0.198066\pi$
$468$	−0.115771	+	0.271950i	−0.00535151	+	0.0125709i
$469$	−5.80725	−	24.1889i	−0.268154	−	1.11694i
$470$	−0.0675160	+	0.807425i	−0.00311428	+	0.0372438i
$471$	4.59960	+	2.34361i	0.211938	+	0.107988i
$472$	21.0065	+	18.4804i	0.966901	+	0.850630i
$473$	−13.6805	+	13.7601i	−0.629030	+	0.632690i
$474$	−4.54707	+	18.5404i	−0.208854	+	0.851590i
$475$	−0.248662	+	3.15956i	−0.0114094	+	0.144970i
$476$	7.58033	+	15.2436i	0.347444	+	0.698689i
$477$	9.58492	+	5.87365i	0.438863	+	0.268936i
$478$	9.90978	−	7.12617i	0.453263	−	0.325943i
$479$	−6.96840	+	21.4465i	−0.318394	+	0.979917i	0.655940	+	0.754813i	$0.272272\pi$
$479$	−6.96840	+	21.4465i	−0.318394	+	0.979917i	−0.974335	+	0.225105i	$0.927728\pi$
$480$	−0.281307	+	0.194065i	−0.0128398	+	0.00885780i
$481$	0.169708	+	0.123300i	0.00773804	+	0.00562201i
$482$	−0.738453	+	2.23551i	−0.0336356	+	0.101825i
$483$	1.51669	+	3.66160i	0.0690116	+	0.166609i
$484$	3.35530	+	21.7426i	0.152514	+	0.988301i
$485$	0.846120	+	0.350474i	0.0384203	+	0.0159142i
$486$	22.6495	−	1.67127i	1.02740	−	0.0758103i
$487$	−2.47151	−	15.6045i	−0.111995	−	0.707107i	−0.978238	−	0.207485i	$-0.933472\pi$
$487$	−2.47151	−	15.6045i	−0.111995	−	0.707107i	0.866243	−	0.499622i	$-0.166528\pi$
$488$	−9.99792	−	12.0595i	−0.452584	−	0.545909i
$489$	−0.710146	−	1.39374i	−0.0321139	−	0.0630271i
$490$	0.196539	−	0.0461706i	0.00887873	−	0.00208578i
$491$	3.20721	+	13.3590i	0.144739	+	0.602883i	0.996835	+	0.0794972i	$0.0253315\pi$
$491$	3.20721	+	13.3590i	0.144739	+	0.602883i	−0.852096	+	0.523386i	$0.824669\pi$
$492$	−6.49332	+	7.45399i	−0.292741	+	0.336052i
$493$	6.46990	+	7.57527i	0.291389	+	0.341173i
$494$	−0.00988724	−	0.0644621i	−0.000444848	−	0.00290029i
$495$	0.414193	−	0.00120151i	0.0186166	−	5.40038e-5i
$496$	−18.1107	+	12.6250i	−0.813196	+	0.566880i
$497$	−3.08252	+	1.00157i	−0.138270	+	0.0449267i
$498$	−9.81231	−	5.06015i	−0.439700	−	0.226751i
$499$	−6.00261	+	9.79536i	−0.268714	+	0.438501i	−0.958326	−	0.285678i	$-0.907781\pi$
$499$	−6.00261	+	9.79536i	−0.268714	+	0.438501i	0.689612	+	0.724179i	$0.257781\pi$
$500$	−0.458896	−	1.13923i	−0.0205225	−	0.0509479i
$501$	10.9253	+	9.33110i	0.488107	+	0.416883i
$502$	−2.46388	+	5.86710i	−0.109968	+	0.261861i
$503$	30.0383	−	4.75760i	1.33934	−	0.212131i	0.554685	−	0.832060i	$-0.312839\pi$
$503$	30.0383	−	4.75760i	1.33934	−	0.212131i	0.784658	+	0.619929i	$0.212839\pi$
$504$	0.257291	−	17.5552i	0.0114606	−	0.781973i
$505$	−0.120405	−	0.120405i	−0.00535795	−	0.00535795i
$506$	6.17243	−	0.473460i	0.274398	−	0.0210478i
$507$	11.8065	+	4.89043i	0.524347	+	0.217191i
$508$	28.5687	−	20.3329i	1.26753	−	0.902127i
$509$	0.891992	−	3.71542i	0.0395369	−	0.164683i	−0.949109	−	0.314948i	$-0.898013\pi$
$509$	0.891992	−	3.71542i	0.0395369	−	0.164683i	0.988646	+	0.150265i	$0.0480128\pi$
$510$	−0.00116348	+	0.238172i	−5.15197e−5	+	0.0105464i
$511$	6.90835	−	21.2617i	0.305607	−	0.940563i
$512$	21.8065	−	6.03968i	0.963719	−	0.266919i
$513$	−2.54003	+	1.84544i	−0.112145	+	0.0814783i
$514$	2.92016	−	0.933072i	0.128803	−	0.0411560i
$515$	−0.0992210	+	0.0847428i	−0.00437220	+	0.00373421i
$516$	3.44871	+	10.9778i	0.151821	+	0.483272i
$517$	26.3264	−	16.2381i	1.15783	−	0.714150i
$518$	−12.1021	−	2.96806i	−0.531736	−	0.130409i
$519$	7.44051	−	14.6028i	0.326602	−	0.640992i
$520$	0.00727406	+	0.0103268i	0.000318989	+	0.000452860i
$521$	−5.77883	+	36.4861i	−0.253175	+	1.59848i	0.453706	+	0.891152i	$0.350102\pi$
$521$	−5.77883	+	36.4861i	−0.253175	+	1.59848i	−0.706881	+	0.707333i	$0.749898\pi$
$522$	−2.34957	−	10.0016i	−0.102838	−	0.437760i
$523$	−16.3787	−	13.9887i	−0.716189	−	0.611683i	0.214831	−	0.976651i	$-0.431080\pi$
$523$	−16.3787	−	13.9887i	−0.716189	−	0.611683i	−0.931020	+	0.364968i	$0.881080\pi$
$524$	6.84437	−	27.3298i	0.298998	−	1.19391i
$525$	−14.5885	−	3.50239i	−0.636695	−	0.152857i
$526$	−14.8500	−	29.5002i	−0.647492	−	1.28627i
$527$			15.3859i			0.670219i
$528$	12.3392	+	4.23751i	0.536996	+	0.184414i
$529$			21.2580i			0.924263i
$530$	0.429119	−	0.216013i	0.0186397	−	0.00938301i
$531$	−19.5534	−	4.69436i	−0.848547	−	0.203718i
$532$	1.99176	+	3.32269i	0.0863536	+	0.144057i
$533$	0.277838	+	0.237296i	0.0120345	+	0.0102784i
$534$	−18.7001	+	4.39299i	−0.809232	+	0.190103i
$535$	−0.0870594	+	0.549672i	−0.00376391	+	0.0237644i
$536$	−12.3264	+	19.4686i	−0.532419	+	0.840914i
$537$	2.63024	−	5.16213i	0.113503	−	0.222763i
$538$	5.61710	−	22.9034i	0.242170	−	0.987437i
$539$	−5.87513	−	4.98843i	−0.253060	−	0.214867i
$540$	0.281357	−	0.539108i	0.0121077	−	0.0231995i
$541$	20.9746	−	17.9140i	0.901766	−	0.770181i	−0.0720776	−	0.997399i	$-0.522963\pi$
$541$	20.9746	−	17.9140i	0.901766	−	0.770181i	0.973844	+	0.227218i	$0.0729629\pi$
$542$	13.9044	+	43.5156i	0.597246	+	1.86915i
$543$	−19.2688	+	13.9996i	−0.826904	+	0.600781i
$544$	5.23788	−	14.8742i	0.224572	−	0.637727i
$545$	0.278731	−	0.857847i	0.0119395	−	0.0367461i
$546$	0.308717	+	0.00150810i	0.0132119	+	6.45406e-5i
$547$	−2.65295	+	11.0503i	−0.113432	+	0.472477i	0.886520	+	0.462690i	$0.153116\pi$
$547$	−2.65295	+	11.0503i	−0.113432	+	0.472477i	−0.999952	+	0.00978776i	$0.996884\pi$
$548$	−2.64260	+	15.6909i	−0.112886	+	0.670284i
$549$	10.4019	+	4.30859i	0.443940	+	0.183886i
$550$	−12.2841	+	19.9568i	−0.523794	+	0.850959i
$551$	1.60295	+	1.60295i	0.0682878	+	0.0682878i
$552$	1.45445	−	3.37076i	0.0619054	−	0.143469i
$553$	−41.3966	+	6.55658i	−1.76036	+	0.278814i
$554$	6.98667	+	2.93404i	0.296835	+	0.124655i
$555$	−0.132560	−	0.113217i	−0.00562688	−	0.00480581i
$556$	−10.5673	+	24.8231i	−0.448155	+	1.05273i
$557$	−1.01129	+	1.65028i	−0.0428499	+	0.0699247i	−0.873348	−	0.487097i	$-0.838056\pi$
$557$	−1.01129	+	1.65028i	−0.0428499	+	0.0699247i	0.830498	+	0.557021i	$0.188056\pi$
$558$	7.27261	−	14.1026i	0.307874	−	0.597009i
$559$	0.404486	−	0.131426i	0.0171079	−	0.00555871i
$560$	−0.631980	−	0.404472i	−0.0267060	−	0.0170921i
$561$	7.34041	−	5.36572i	0.309912	−	0.226541i
$562$	39.9980	−	6.13492i	1.68721	−	0.258786i
$563$	−11.5846	−	13.5639i	−0.488234	−	0.571649i	0.460526	−	0.887646i	$-0.347661\pi$
$563$	−11.5846	−	13.5639i	−0.488234	−	0.571649i	−0.948760	+	0.315998i	$0.897661\pi$
$564$	−1.26046	−	18.2998i	−0.0530751	−	0.770562i
$565$	0.168883	+	0.703447i	0.00710495	+	0.0295942i
$566$	−8.09889	−	34.4754i	−0.340422	−	1.44911i
$567$	1.70681	+	3.34980i	0.0716792	+	0.140678i
$568$	2.65477	+	1.40205i	0.111392	+	0.0588288i
$569$	−3.43574	−	21.6924i	−0.144034	−	0.909393i	−0.948818	−	0.315825i	$-0.897719\pi$
$569$	−3.43574	−	21.6924i	−0.144034	−	0.909393i	0.804784	−	0.593568i	$-0.202281\pi$
$570$	0.00398827	+	0.0540502i	0.000167050	+	0.00226391i
$571$	17.1010	+	7.08345i	0.715653	+	0.296433i	0.710641	−	0.703554i	$-0.248405\pi$
$571$	17.1010	+	7.08345i	0.715653	+	0.296433i	0.00501121	+	0.999987i	$0.498405\pi$
$572$	0.152159	−	0.457579i	0.00636210	−	0.0191323i
$573$	−1.31127	−	3.16568i	−0.0547790	−	0.132248i
$574$	−20.6090	−	6.80774i	−0.860201	−	0.284149i
$575$	5.33480	+	3.87596i	0.222477	+	0.161639i
$576$	−11.8318	+	11.1578i	−0.492990	+	0.464906i
$577$	−5.12329	+	15.7679i	−0.213285	+	0.656425i	0.785986	+	0.618245i	$0.212156\pi$
$577$	−5.12329	+	15.7679i	−0.213285	+	0.656425i	−0.999271	+	0.0381799i	$0.987844\pi$
$578$	7.61981	+	10.5962i	0.316942	+	0.440745i
$579$	9.63644	+	5.90522i	0.400477	+	0.245412i
$580$	−0.416236	−	0.139754i	−0.0172833	−	0.00580296i
$581$	1.90179	−	24.1646i	0.0788996	−	1.00251i
$582$	−20.1369	−	4.93860i	−0.834701	−	0.204712i
$583$	−16.3654	−	8.27890i	−0.677788	−	0.342877i
$584$	−18.5868	+	9.12988i	−0.769129	+	0.377797i
$585$	−0.00808914	−	0.00412162i	−0.000334445	−	0.000170408i
$586$	28.9294	+	2.41905i	1.19506	+	0.0999299i
$587$	6.59715	+	27.4791i	0.272294	+	1.13418i	0.926026	+	0.377459i	$0.123202\pi$
$587$	6.59715	+	27.4791i	0.272294	+	1.13418i	−0.653733	+	0.756725i	$0.726798\pi$
$588$	−4.23957	+	1.70775i	−0.174837	+	0.0704265i
$589$	0.274692	+	3.49030i	0.0113185	+	0.143815i
$590$	−0.610643	+	0.604706i	−0.0251398	+	0.0248953i
$591$	11.5782	−	15.9361i	0.476265	−	0.655522i
$592$	5.83739	+	9.95738i	0.239915	+	0.409246i
$593$		−	6.34987i		−	0.260758i	−0.991464	−	0.130379i	$-0.958381\pi$
$593$		−	6.34987i		−	0.260758i	0.991464	−	0.130379i	$-0.0416194\pi$
$594$	−22.9363	+	3.58612i	−0.941089	+	0.147140i
$595$	−0.483117	+	0.200114i	−0.0198059	+	0.00820386i
$596$	5.09699	+	22.1831i	0.208781	+	0.908653i
$597$	6.65112	−	4.07581i	0.272212	−	0.166812i
$598$	−0.125106	−	0.0525380i	−0.00511596	−	0.00214844i
$599$	−11.3988	−	22.3715i	−0.465743	−	0.914073i	−0.997731	−	0.0673210i	$-0.978555\pi$
$599$	−11.3988	−	22.3715i	−0.465743	−	0.914073i	0.531988	−	0.846752i	$-0.321445\pi$
$600$	7.08684	+	11.9545i	0.289319	+	0.488038i
$601$	12.2875	+	1.94614i	0.501216	+	0.0793849i	0.401923	−	0.915673i	$-0.368342\pi$
$601$	12.2875	+	1.94614i	0.501216	+	0.0793849i	0.0992932	+	0.995058i	$0.468342\pi$
$602$	−19.2905	+	16.3134i	−0.786223	+	0.664883i
$603$	1.29940	−	16.5104i	0.0529157	−	0.672357i
$604$	22.5023	+	11.7438i	0.915607	+	0.477850i
$605$	−0.673352	+	0.0569266i	−0.0273757	+	0.00231439i
$606$	3.10761	+	2.28109i	0.126238	+	0.0926629i
$607$	−10.6625	−	32.8158i	−0.432777	−	1.33195i	−0.895347	−	0.445369i	$-0.853073\pi$
$607$	−10.6625	−	32.8158i	−0.432777	−	1.33195i	0.462570	−	0.886583i	$-0.346927\pi$
$608$	0.922660	−	3.46775i	0.0374188	−	0.140636i
$609$	−8.68168	+	6.30761i	−0.351800	+	0.255597i
$610$	0.390649	−	0.280917i	0.0158169	−	0.0113740i
$611$	−0.675892	+	0.0531938i	−0.0273437	+	0.00215199i
$612$	1.66358	+	11.2113i	0.0672464	+	0.453190i
$613$	−9.38822	−	15.3202i	−0.379187	−	0.618776i	0.604934	−	0.796275i	$-0.293199\pi$
$613$	−9.38822	−	15.3202i	−0.379187	−	0.618776i	−0.984121	+	0.177499i	$0.943199\pi$
$614$	7.55298	−	0.557322i	0.304814	−	0.0224917i
$615$	−0.214711	−	0.214711i	−0.00865798	−	0.00865798i
$616$	1.91161	+	28.5804i	0.0770208	+	1.15154i
$617$	0.0837823	−	0.0837823i	0.00337295	−	0.00337295i	−0.705418	−	0.708791i	$-0.749241\pi$
$617$	0.0837823	−	0.0837823i	0.00337295	−	0.00337295i	0.708791	+	0.705418i	$0.249241\pi$
$618$	1.92945	−	2.23688i	0.0776139	−	0.0899804i
$619$	−4.75368	+	2.91306i	−0.191067	+	0.117086i	−0.614742	−	0.788728i	$-0.710740\pi$
$619$	−4.75368	+	2.91306i	−0.191067	+	0.117086i	0.423675	+	0.905814i	$0.360740\pi$
$620$	−0.348649	−	0.581623i	−0.0140021	−	0.0233586i
$621$	0.512529	+	6.51230i	0.0205671	+	0.261330i
$622$	−33.4397	−	5.46391i	−1.34081	−	0.219083i
$623$	−24.7896	−	34.1199i	−0.993172	−	1.36698i
$624$	−0.198219	−	0.206121i	−0.00793511	−	0.00825143i
$625$	−23.7226	+	7.70794i	−0.948904	+	0.308317i
$626$	34.9343	−	5.35825i	1.39626	−	0.214159i
$627$	1.56938	−	1.34827i	0.0626750	−	0.0538447i
$628$	8.04938	−	6.73993i	0.321205	−	0.268952i
$629$	8.01927	+	0.631131i	0.319749	+	0.0251648i
$630$	0.537411	+	0.0449377i	0.0214110	+	0.00179036i
$631$	−1.10427	+	6.97209i	−0.0439603	+	0.277554i	−0.999870	−	0.0161054i	$-0.994873\pi$
$631$	−1.10427	+	6.97209i	−0.0439603	+	0.277554i	0.955910	+	0.293660i	$0.0948733\pi$
$632$	31.0710	+	23.2776i	1.23594	+	0.925934i
$633$	24.7281	−	12.5996i	0.982853	−	0.500789i
$634$	28.1308	−	11.4915i	1.11722	−	0.456386i
$635$	0.562772	+	0.918361i	0.0223329	+	0.0364440i
$636$	−8.86116	+	6.30666i	−0.351368	+	0.250075i
$637$	0.0646481	+	0.156074i	0.00256145	+	0.00618389i
$638$	5.14804	+	15.9517i	0.203813	+	0.631532i
$639$	−2.15782			−0.0853619
$640$	0.139051	+	0.680975i	0.00549645	+	0.0269179i
$641$	3.70055	+	2.68861i	0.146163	+	0.106194i	0.658464	−	0.752613i	$-0.271207\pi$
$641$	3.70055	+	2.68861i	0.146163	+	0.106194i	−0.512301	+	0.858806i	$0.671207\pi$
$642$	0.0615469	−	12.5990i	0.00242906	−	0.497244i
$643$	4.58897	−	0.361160i	0.180971	−	0.0142428i	0.0123504	−	0.999924i	$-0.496069\pi$
$643$	4.58897	−	0.361160i	0.180971	−	0.0142428i	0.168621	+	0.985681i	$0.446069\pi$
$644$	8.05981	+	0.0787470i	0.317601	+	0.00310306i
$645$	−0.343678	+	0.0825098i	−0.0135323	+	0.00324882i
$646$	−1.61485	−	1.90956i	−0.0635354	−	0.0751305i
$647$	−18.4823	+	36.2735i	−0.726612	+	1.42606i	0.171000	+	0.985271i	$0.445300\pi$
$647$	−18.4823	+	36.2735i	−0.726612	+	1.42606i	−0.897612	+	0.440786i	$0.854700\pi$
$648$	1.12456	−	3.29589i	0.0441769	−	0.129475i
$649$	32.4186	+	5.03824i	1.27254	+	0.197768i
$650$	0.439268	−	0.266241i	0.0172295	−	0.0104428i
$651$	−16.5225	−	1.30035i	−0.647566	−	0.0509646i
$652$	−3.17368	+	0.218598i	−0.124291	+	0.00856095i
$653$	20.3099	−	33.1428i	0.794788	−	1.29698i	−0.156192	−	0.987727i	$-0.549922\pi$
$653$	20.3099	−	33.1428i	0.794788	−	1.29698i	0.950981	−	0.309250i	$-0.100078\pi$
$654$	−3.29293	+	20.1531i	−0.128764	+	0.788047i
$655$	0.823034	+	0.267420i	0.0321586	+	0.0104490i
$656$	8.77550	+	18.0881i	0.342626	+	0.706223i
$657$	8.74833	−	12.0410i	0.341305	−	0.469766i
$658$	35.9726	−	18.1081i	1.40236	−	0.705929i
$659$	7.44481	−	3.08374i	0.290009	−	0.120126i	−0.232936	−	0.972492i	$-0.574833\pi$
$659$	7.44481	−	3.08374i	0.290009	−	0.120126i	0.522945	+	0.852366i	$0.324833\pi$
$660$	−0.155896	+	0.369174i	−0.00606825	+	0.0143701i
$661$	5.91733	−	14.2857i	0.230157	−	0.555649i	−0.766038	−	0.642795i	$-0.777775\pi$
$661$	5.91733	−	14.2857i	0.230157	−	0.555649i	0.996196	+	0.0871461i	$0.0277747\pi$
$662$	−21.2788	+	24.6693i	−0.827026	+	0.958799i
$663$	−0.196842	+	0.0311767i	−0.00764471	+	0.00121080i
$664$	−17.2850	+	14.3301i	−0.670788	+	0.556115i
$665$	−0.106023	+	0.0540213i	−0.00411138	+	0.00209486i
$666$	−7.05208	−	4.36905i	−0.273262	−	0.169297i
$667$	4.58626	−	1.10106i	0.177581	−	0.0426334i
$668$	26.1635	−	13.0106i	1.01229	−	0.503393i
$669$	4.68454	−	4.00098i	0.181115	−	0.154687i
$670$	−0.570568	−	0.418816i	−0.0220430	−	0.0161803i
$671$	−17.4861	−	5.62556i	−0.675045	−	0.217172i
$672$	15.5303	+	6.88192i	0.599096	+	0.265476i
$673$	3.14400	+	9.67622i	0.121192	+	0.372991i	0.993188	−	0.116522i	$-0.0371746\pi$
$673$	3.14400	+	9.67622i	0.121192	+	0.372991i	−0.871996	+	0.489513i	$0.837175\pi$
$674$	8.96100	+	28.0445i	0.345165	+	1.08024i
$675$	−21.0846	−	12.9206i	−0.811545	−	0.497316i
$676$	18.5560	−	18.1969i	0.713691	−	0.699880i
$677$	−28.2163	+	33.0371i	−1.08444	+	1.26972i	−0.123686	+	0.992321i	$0.539472\pi$
$677$	−28.2163	+	33.0371i	−1.08444	+	1.26972i	−0.960755	+	0.277397i	$0.910528\pi$
$678$	−6.19357	−	15.1617i	−0.237863	−	0.582280i
$679$	−7.12115	−	44.9611i	−0.273284	−	1.72545i
$680$	0.444743	+	0.191902i	0.0170551	+	0.00735910i
$681$	−10.7490	+	10.7490i	−0.411902	+	0.411902i
$682$	−9.95414	+	23.8972i	−0.381164	+	0.915071i
$683$	3.17048	−	7.65423i	0.121315	−	0.292881i	−0.851542	−	0.524286i	$-0.824332\pi$
$683$	3.17048	−	7.65423i	0.121315	−	0.292881i	0.972857	+	0.231405i	$0.0743323\pi$
$684$	0.577547	+	2.51359i	0.0220831	+	0.0961096i
$685$	−0.475248	−	0.114097i	−0.0181583	−	0.00435942i
$686$	14.2088	+	14.3483i	0.542493	+	0.547819i
$687$	−11.9915	−	3.89626i	−0.457503	−	0.148652i
$688$	23.2890	+	2.29154i	0.887886	+	0.0873640i
$689$	0.236289	+	0.325224i	0.00900190	+	0.0123900i
$690$	0.100222	+	0.0516840i	0.00381539	+	0.00196757i
$691$	30.7297	+	35.9799i	1.16901	+	1.36874i	0.915951	+	0.401289i	$0.131438\pi$
$691$	30.7297	+	35.9799i	1.16901	+	1.36874i	0.253063	+	0.967450i	$0.418562\pi$
$692$	−21.3980	−	25.5552i	−0.813428	−	0.971462i
$693$	−10.8078	−	17.5225i	−0.410556	−	0.665625i
$694$	10.1990	−	6.18166i	0.387151	−	0.234652i
$695$	−0.738361	−	0.376214i	−0.0280076	−	0.0142706i
$696$	9.79396	+	1.69869i	0.371239	+	0.0643889i
$697$	13.8387	+	2.19184i	0.524180	+	0.0830219i
$698$	0.263118	−	0.424698i	0.00995916	−	0.0160751i
$699$	5.41318	−	6.33802i	0.204745	−	0.239726i
$700$	−18.1747	+	24.5082i	−0.686941	+	0.926324i
$701$	10.2251	−	42.5905i	0.386195	−	1.60862i	−0.353335	−	0.935497i	$-0.614953\pi$
$701$	10.2251	−	42.5905i	0.386195	−	1.60862i	0.739531	−	0.673123i	$-0.235047\pi$
$702$	0.483167	+	0.159604i	0.0182359	+	0.00602386i
$703$	1.83045			0.0690366
$704$	17.7586	−	19.7138i	0.669301	−	0.742991i
$705$	0.563431			0.0212200
$706$	−10.9845	−	3.62849i	−0.413406	−	0.136560i
$707$	−1.97581	+	8.22984i	−0.0743080	+	0.309515i
$708$	11.5891	−	15.6276i	0.435545	−	0.587322i
$709$	15.2204	−	17.8208i	0.571614	−	0.669274i	−0.397007	−	0.917816i	$-0.629951\pi$
$709$	15.2204	−	17.8208i	0.571614	−	0.669274i	0.968621	+	0.248541i	$0.0799512\pi$
$710$	−0.0485671	+	0.0783922i	−0.00182269	+	0.00294201i
$711$	−27.5600	−	4.36508i	−1.03358	−	0.163703i
$712$	−6.67604	+	38.4913i	−0.250195	+	1.44252i
$713$	6.49049	+	3.30707i	0.243071	+	0.123851i
$714$	10.1241	−	6.13621i	0.378884	−	0.229642i
$715$	0.0137007	+	0.00562849i	0.000512375	+	0.000210494i
$716$	−7.56423	−	9.03383i	−0.282689	−	0.337610i
$717$	−5.51242	−	6.45422i	−0.205865	−	0.241037i
$718$	−22.5139	−	11.6103i	−0.840212	−	0.433292i
$719$	−0.578637	−	0.796425i	−0.0215795	−	0.0297017i	0.798091	−	0.602537i	$-0.205843\pi$
$719$	−0.578637	−	0.796425i	−0.0215795	−	0.0297017i	−0.819670	+	0.572835i	$0.805843\pi$
$720$	−0.316940	−	0.386117i	−0.0118116	−	0.0143897i
$721$	6.16830	+	2.00420i	0.229719	+	0.0746404i
$722$	18.5065	+	18.6882i	0.688742	+	0.695504i
$723$	1.59192	+	0.382187i	0.0592042	+	0.0142137i
$724$	10.8469	+	47.2079i	0.403124	+	1.75447i
$725$	−6.83267	+	16.4955i	−0.253759	+	0.612629i
$726$	14.8725	−	3.58499i	0.551970	−	0.133052i
$727$	−13.2489	+	13.2489i	−0.491374	+	0.491374i	−0.908739	−	0.417365i	$-0.862954\pi$
$727$	−13.2489	+	13.2489i	−0.491374	+	0.491374i	0.417365	+	0.908739i	$0.362954\pi$
$728$	0.248742	−	0.576474i	0.00921900	−	0.0213656i
$729$	−1.89274	−	11.9503i	−0.0701015	−	0.442603i
$730$	−0.240541	−	0.588836i	−0.00890281	−	0.0217938i
$731$	10.5919	−	12.4015i	0.391754	−	0.458685i
$732$	−7.77752	+	7.62701i	−0.287465	+	0.281903i
$733$	15.7309	+	9.63990i	0.581034	+	0.356058i	0.781750	−	0.623591i	$-0.214327\pi$
$733$	15.7309	+	9.63990i	0.581034	+	0.356058i	−0.200717	+	0.979649i	$0.564327\pi$
$734$	−8.61640	−	26.9661i	−0.318037	−	0.995336i
$735$	−0.0433832	−	0.133520i	−0.00160021	−	0.00492495i
$736$	−5.14882	−	5.40669i	−0.189788	−	0.199293i
$737$	0.0783803	+	27.0198i	0.00288718	+	0.995288i
$738$	−11.6484	−	8.55034i	−0.428785	−	0.314742i
$739$	−21.8523	+	18.6637i	−0.803851	+	0.686554i	−0.953237	−	0.302225i	$-0.902271\pi$
$739$	−21.8523	+	18.6637i	−0.803851	+	0.686554i	0.149385	+	0.988779i	$0.452271\pi$
$740$	−0.317450	+	0.157861i	−0.0116697	+	0.00580310i
$741$	−0.0440972	+	0.0105868i	−0.00161995	+	0.000388915i
$742$	−20.2993	−	12.5763i	−0.745212	−	0.461689i
$743$	−8.83512	+	4.50172i	−0.324129	+	0.165152i	−0.608482	−	0.793568i	$-0.708221\pi$
$743$	−8.83512	+	4.50172i	−0.324129	+	0.165152i	0.284353	+	0.958720i	$0.408221\pi$
$744$	9.79815	+	11.8186i	0.359218	+	0.433290i
$745$	−0.690525	+	0.109368i	−0.0252989	+	0.00400695i
$746$	−13.6779	+	15.8572i	−0.500782	+	0.580574i
$747$	6.17553	−	14.9090i	0.225951	−	0.545493i
$748$	−4.19312	−	18.0097i	−0.153316	−	0.658501i
$749$	25.5564	−	10.5858i	0.933810	−	0.386797i
$750$	−0.762857	+	0.384012i	−0.0278556	+	0.0140222i
$751$	25.2748	−	34.7878i	0.922292	−	1.26943i	−0.0404998	−	0.999180i	$-0.512895\pi$
$751$	25.2748	−	34.7878i	0.922292	−	1.26943i	0.962791	−	0.270246i	$-0.0871050\pi$
$752$	−35.2469	−	12.2188i	−1.28532	−	0.445575i
$753$	4.20847	+	1.36742i	0.153365	+	0.0498314i
$754$	0.0592458	−	0.362590i	0.00215760	−	0.0132048i
$755$	−0.407367	+	0.664763i	−0.0148256	+	0.0241932i
$756$	−30.1548	+	2.07701i	−1.09672	+	0.0755402i
$757$	31.3688	+	2.46878i	1.14012	+	0.0897292i	0.634425	−	0.772985i	$-0.281237\pi$
$757$	31.3688	+	2.46878i	1.14012	+	0.0897292i	0.505692	+	0.862714i	$0.331237\pi$
$758$	−0.411415	+	0.249359i	−0.0149433	+	0.00905714i
$759$	−0.685754	−	4.24985i	−0.0248913	−	0.154260i
$760$	0.104316	+	0.0355928i	0.00378395	+	0.00129109i
$761$	14.0930	−	27.6591i	0.510872	−	1.00264i	−0.481158	−	0.876634i	$-0.659784\pi$
$761$	14.0930	−	27.6591i	0.510872	−	1.00264i	0.992029	−	0.126008i	$-0.0402165\pi$
$762$	−15.7454	−	18.6190i	−0.570397	−	0.674494i
$763$	−43.5949	+	10.4662i	−1.57824	+	0.378902i
$764$	−6.96820	−	0.0680815i	−0.252101	−	0.00246310i
$765$	−0.347065	+	0.0273146i	−0.0125482	+	0.000987562i
$766$	0.102518	−	20.9861i	0.00370413	−	0.758259i
$767$	−0.581770	−	0.422681i	−0.0210065	−	0.0152621i
$768$	−5.44887	−	14.7612i	−0.196619	−	0.532649i
$769$	−33.7549			−1.21723			−0.608617	−	0.793464i	$-0.708275\pi$
$769$	−33.7549			−1.21723			−0.608617	+	0.793464i	$0.708275\pi$
$770$	−0.879840	−	0.00174575i	−0.0317072	−	6.29126e-5i
$771$	−0.815797	−	1.96951i	−0.0293802	−	0.0709301i
$772$	18.7262	−	13.3278i	0.673970	−	0.479678i
$773$	1.69941	+	2.77318i	0.0611234	+	0.0997443i	0.881742	−	0.471732i	$-0.156371\pi$
$773$	1.69941	+	2.77318i	0.0611234	+	0.0997443i	−0.820619	+	0.571476i	$0.806371\pi$
$774$	−15.5703	+	6.36052i	−0.559665	+	0.228624i
$775$	−24.5698	+	12.5189i	−0.882572	+	0.449693i
$776$	−25.2820	+	33.7464i	−0.907570	+	1.21142i
$777$	−1.35551	+	8.55833i	−0.0486285	+	0.307029i
$778$	−43.3901	−	3.62823i	−1.55561	−	0.130078i
$779$	3.17846	+	0.250150i	0.113880	+	0.00896256i
$780$	0.00673464	−	0.00563907i	0.000241139	−	0.000201911i
$781$	3.50879	−	0.286392i	0.125554	−	0.0102479i
$782$	−5.14314	+	0.788858i	−0.183918	+	0.0282095i
$783$	−16.8218	+	5.46573i	−0.601162	+	0.195329i
$784$	−0.181618	+	9.29350i	−0.00648637	+	0.331911i
$785$	0.189545	+	0.260887i	0.00676517	+	0.00931145i
$786$	−19.3352	−	3.15929i	−0.689664	−	0.112688i
$787$	0.698562	+	8.87607i	0.0249010	+	0.316398i	0.996736	+	0.0807339i	$0.0257264\pi$
$787$	0.698562	+	8.87607i	0.0249010	+	0.316398i	−0.971835	+	0.235664i	$0.924274\pi$
$788$	−20.5967	−	34.3598i	−0.733726	−	1.22402i
$789$	−19.5822	+	12.0000i	−0.697144	+	0.427210i
$790$	−0.778888	+	0.902991i	−0.0277116	+	0.0321270i
$791$	25.4264	−	25.4264i	0.904060	−	0.904060i
$792$	−4.66947	+	18.4896i	−0.165923	+	0.656999i
$793$	0.284697	+	0.284697i	0.0101099	+	0.0101099i
$794$	−48.2561	+	3.56074i	−1.71255	+	0.126366i
$795$	−0.174555	−	0.284848i	−0.00619083	−	0.0101025i
$796$	−2.32851	−	15.6924i	−0.0825319	−	0.556203i
$797$	−20.1874	+	1.58878i	−0.715074	+	0.0562776i	−0.430777	−	0.902459i	$-0.641760\pi$
$797$	−20.1874	+	1.58878i	−0.715074	+	0.0562776i	−0.284297	+	0.958736i	$0.591760\pi$
$798$	2.18710	−	1.57275i	0.0774224	−	0.0556749i
$799$	−21.0332	+	15.2815i	−0.744102	+	0.540622i
$800$	28.0146	−	3.73822i	0.990466	−	0.132166i
$801$	−8.67655	−	26.7037i	−0.306571	−	0.943528i
$802$	−33.2241	−	24.3876i	−1.17318	−	0.861155i
$803$	−12.6274	+	20.7409i	−0.445611	+	0.731929i
$804$	14.2053	+	7.41367i	0.500983	+	0.261460i
$805$	−0.0194247	+	0.246815i	−0.000684632	+	0.00869907i
$806$	0.433267	−	0.366400i	0.0152612	−	0.0129059i
$807$	−16.1968	−	2.56532i	−0.570154	−	0.0903035i
$808$	6.74388	−	3.99791i	0.237249	−	0.140646i
$809$	−6.34937	−	12.4613i	−0.223232	−	0.438117i	0.752043	−	0.659115i	$-0.229069\pi$
$809$	−6.34937	−	12.4613i	−0.223232	−	0.438117i	−0.975274	+	0.220997i	$0.929069\pi$
$810$	0.0986240	+	0.0414170i	0.00346529	+	0.00145524i
$811$	−34.5327	+	21.1617i	−1.21261	+	0.743086i	−0.973673	−	0.227949i	$-0.926798\pi$
$811$	−34.5327	+	21.1617i	−1.21261	+	0.743086i	−0.238934	+	0.971036i	$0.576798\pi$
$812$	4.88716	+	21.2698i	0.171506	+	0.746425i
$813$	29.3492	−	12.1568i	1.02932	−	0.426358i
$814$	12.0471	+	6.16847i	0.422252	+	0.216205i
$815$		−	0.0977140i		−	0.00342277i
$816$	−10.6109	−	2.76779i	−0.371454	−	0.0968920i
$817$	2.18136	−	3.00238i	0.0763161	−	0.105040i
$818$	9.44878	−	9.35692i	0.330369	−	0.327157i
$819$	0.0354051	+	0.449864i	0.00123715	+	0.0157195i
$820$	−0.572806	+	0.230734i	−0.0200033	+	0.00805757i
$821$	9.64044	+	40.1553i	0.336454	+	1.40143i	0.842394	+	0.538862i	$0.181145\pi$
$821$	9.64044	+	40.1553i	0.336454	+	1.40143i	−0.505941	+	0.862568i	$0.668855\pi$
$822$	11.0264	+	0.922017i	0.384591	+	0.0321590i
$823$	−30.7413	−	15.6635i	−1.07157	−	0.545994i	−0.173047	−	0.984914i	$-0.555361\pi$
$823$	−30.7413	−	15.6635i	−1.07157	−	0.545994i	−0.898526	+	0.438919i	$0.855361\pi$
$824$	−2.64869	−	5.39228i	−0.0922717	−	0.187849i
$825$	14.5412	+	7.35604i	0.506258	+	0.256104i
$826$	41.4867	+	10.1747i	1.44351	+	0.354022i
$827$	2.31485	−	29.4130i	0.0804953	−	1.02279i	−0.815509	−	0.578745i	$-0.803543\pi$
$827$	2.31485	−	29.4130i	0.0804953	−	1.02279i	0.896004	−	0.444046i	$-0.146457\pi$
$828$	5.08704	+	1.70800i	0.176787	+	0.0593572i
$829$	−4.78366	−	2.93143i	−0.166144	−	0.101813i	0.436941	−	0.899490i	$-0.356062\pi$
$829$	−4.78366	−	2.93143i	−0.166144	−	0.101813i	−0.603085	+	0.797677i	$0.706062\pi$
$830$	−0.402641	−	0.559919i	−0.0139759	−	0.0194351i
$831$	1.62835	−	5.01154i	0.0564868	−	0.173848i
$832$	−0.543594	+	0.206716i	−0.0188457	+	0.00716660i
$833$	5.24088	+	3.80772i	0.181586	+	0.131930i
$834$	17.8139	+	5.88444i	0.616844	+	0.203761i
$835$	0.343466	+	0.829201i	0.0118861	+	0.0286957i
$836$	−1.27275	−	4.01066i	−0.0440190	−	0.138711i
$837$	−25.2377	−	10.4538i	−0.872344	−	0.361337i
$838$	−1.62092	−	21.9671i	−0.0559936	−	0.758842i
$839$	3.41558	+	21.5652i	0.117919	+	0.744512i	0.973811	+	0.227358i	$0.0730086\pi$
$839$	3.41558	+	21.5652i	0.117919	+	0.744512i	−0.855892	+	0.517154i	$0.826991\pi$
$840$	−0.243666	+	0.461379i	−0.00840727	+	0.0159191i
$841$	−7.36791	−	14.4603i	−0.254066	−	0.498632i
$842$	0.419434	+	1.78545i	0.0144546	+	0.0615305i
$843$	−6.56898	−	27.3618i	−0.226248	−	0.942389i
$844$	−3.87842	−	56.3082i	−0.133501	−	1.93821i
$845$	0.518451	+	0.607028i	0.0178352	+	0.0208824i
$846$	26.5022	−	4.06492i	0.911164	−	0.139755i
$847$	19.9001	+	27.0586i	0.683776	+	0.929745i
$848$	4.74242	+	21.6049i	0.162855	+	0.741916i
$849$	−23.4210	+	7.60994i	−0.803806	+	0.261172i
$850$	9.02790	−	17.5063i	0.309654	−	0.600461i
$851$	1.98992	−	3.24726i	0.0682136	−	0.111314i
$852$	0.817744	−	1.92091i	0.0280155	−	0.0658093i
$853$	−1.52929	−	1.30614i	−0.0523620	−	0.0447214i	0.622882	−	0.782316i	$-0.285962\pi$
$853$	−1.52929	−	1.30614i	−0.0523620	−	0.0447214i	−0.675244	+	0.737594i	$0.735962\pi$
$854$	−22.0509	−	9.26024i	−0.754566	−	0.316879i
$855$	−0.0782443	+	0.0123927i	−0.00267590	+	0.000423821i
$856$	−23.5264	−	10.1514i	−0.804117	−	0.346968i
$857$	−6.65747	−	6.65747i	−0.227415	−	0.227415i	0.584197	−	0.811612i	$-0.301410\pi$
$857$	−6.65747	−	6.65747i	−0.227415	−	0.227415i	−0.811612	+	0.584197i	$0.801410\pi$
$858$	−0.325904	−	0.0789268i	−0.0111262	−	0.00269452i
$859$	1.81311	+	0.751015i	0.0618625	+	0.0256243i	0.413400	−	0.910549i	$-0.364341\pi$
$859$	1.81311	+	0.751015i	0.0618625	+	0.0256243i	−0.351538	+	0.936174i	$0.614341\pi$
$860$	−0.119376	+	0.708821i	−0.00407070	+	0.0241706i
$861$	−3.52335	+	14.6758i	−0.120075	+	0.500150i
$862$	−8.18792	−	0.0399983i	−0.278882	−	0.00136235i
$863$	4.97162	−	15.3011i	0.169236	−	0.520855i	−0.830087	−	0.557633i	$-0.811710\pi$
$863$	4.97162	−	15.3011i	0.169236	−	0.520855i	0.999323	+	0.0367783i	$0.0117095\pi$
$864$	20.8396	+	18.6980i	0.708979	+	0.636118i
$865$	0.828265	−	0.601769i	0.0281618	−	0.0204608i
$866$	−6.04813	−	18.9283i	−0.205524	−	0.643211i
$867$	6.90131	−	5.89427i	0.234381	−	0.200180i
$868$	−15.5948	+	29.8812i	−0.529322	+	1.01423i
$869$	45.3942	+	3.44014i	1.53989	+	0.116699i
$870$	−0.0727258	+	0.296536i	−0.00246564	+	0.0100535i
$871$	0.268874	−	0.527695i	0.00911044	−	0.0178803i
$872$	35.0876	+	22.2155i	1.18821	+	0.752310i
$873$	4.74094	−	29.9331i	0.160457	−	1.01308i
$874$	−1.15264	+	0.270776i	−0.0389887	+	0.00915914i
$875$	−1.42585	−	1.21779i	−0.0482026	−	0.0411689i
$876$	7.40372	+	12.3510i	0.250148	+	0.417303i
$877$	−29.0690	−	6.97885i	−0.981591	−	0.235659i	−0.289269	−	0.957248i	$-0.593412\pi$
$877$	−29.0690	−	6.97885i	−0.981591	−	0.235659i	−0.692322	+	0.721589i	$0.743412\pi$
$878$	23.5258	−	11.8426i	0.793956	−	0.399668i
$879$		−	20.1873i		−	0.680901i
$880$	0.566617	+	0.585794i	0.0191007	+	0.0197471i
$881$			6.17808i			0.208145i	0.994570	+	0.104072i	$0.0331874\pi$
$881$			6.17808i			0.208145i	−0.994570	+	0.104072i	$0.966813\pi$
$882$	−3.00391	−	5.96739i	−0.101147	−	0.200932i
$883$	−9.90802	−	2.37870i	−0.333431	−	0.0800498i	0.0632729	−	0.997996i	$-0.479846\pi$
$883$	−9.90802	−	2.37870i	−0.333431	−	0.0800498i	−0.396704	+	0.917946i	$0.629846\pi$
$884$	−0.0984637	+	0.393168i	−0.00331169	+	0.0132237i
$885$	0.454425	+	0.388115i	0.0152753	+	0.0130464i
$886$	−11.4772	−	48.8560i	−0.385583	−	1.64135i
$887$	−4.17184	+	26.3400i	−0.140077	+	0.884409i	0.813128	+	0.582084i	$0.197763\pi$
$887$	−4.17184	+	26.3400i	−0.140077	+	0.884409i	−0.953205	+	0.302325i	$0.902237\pi$
$888$	6.56188	−	4.62210i	0.220202	−	0.155107i
$889$	24.3050	−	47.7012i	0.815163	−	1.59985i
$890$	−1.16542	−	0.285820i	−0.0390648	−	0.00958071i
$891$	−0.964799	−	3.96793i	−0.0323220	−	0.132931i
$892$	−3.75503	−	11.9529i	−0.125728	−	0.400213i
$893$	−4.49857	+	3.84214i	−0.150539	+	0.128572i
$894$	15.0768	−	4.81744i	0.504243	−	0.161119i
$895$	0.292794	−	0.212727i	0.00978702	−	0.00711068i
$896$	25.2488	−	23.5785i	0.843504	−	0.787703i
$897$	−0.0291578	+	0.0897386i	−0.000973552	+	0.00299628i
$898$	−0.287485	+	58.8500i	−0.00959350	+	1.96385i
$899$	−4.60439	+	19.1787i	−0.153565	+	0.639645i
$900$	−16.5498	+	11.7788i	−0.551660	+	0.392627i
$901$	14.2420	+	5.89922i	0.474469	+	0.196532i
$902$	20.0762	+	12.3575i	0.668463	+	0.411461i
$903$	12.4224	+	12.4224i	0.413392	+	0.413392i
$904$	−33.3044	−	0.488112i	−1.10769	−	0.0162344i
$905$	−1.46951	+	0.232748i	−0.0488482	+	0.00773680i
$906$	6.83418	−	16.2739i	0.227050	−	0.540663i
$907$	43.1238	+	36.8312i	1.43190	+	1.22296i	0.934756	+	0.355291i	$0.115618\pi$
$907$	43.1238	+	36.8312i	1.43190	+	1.22296i	0.497145	+	0.867667i	$0.334382\pi$
$908$	11.5511	+	28.6762i	0.383338	+	0.951652i
$909$	−2.94415	+	4.80441i	−0.0976512	+	0.159352i
$910$	0.0171402	+	0.00883909i	0.000568191	+	0.000293013i
$911$	−43.3047	+	14.0706i	−1.43475	+	0.466178i	−0.920256	−	0.391316i	$-0.872020\pi$
$911$	−43.3047	+	14.0706i	−1.43475	+	0.466178i	−0.514493	+	0.857495i	$0.672020\pi$
$912$	−2.45650	−	0.438434i	−0.0813427	−	0.0145180i
$913$	−8.06315	+	25.0630i	−0.266851	+	0.829464i
$914$	2.14553	+	13.9883i	0.0709678	+	0.462691i
$915$	−0.217303	−	0.254429i	−0.00718380	−	0.00841115i
$916$	−16.8430	+	19.3349i	−0.556508	+	0.638842i
$917$	−10.0415	−	41.8257i	−0.331598	−	1.38121i
$918$	18.9955	−	4.46239i	0.626946	−	0.147281i
$919$	−3.79539	−	7.44887i	−0.125198	−	0.245716i	0.819896	−	0.572512i	$-0.194031\pi$
$919$	−3.79539	−	7.44887i	−0.125198	−	0.245716i	−0.945095	+	0.326796i	$0.894031\pi$
$920$	0.176547	−	0.146366i	0.00582059	−	0.00482555i
$921$	−0.823864	−	5.20167i	−0.0271472	−	0.171401i
$922$	23.9512	−	1.76732i	0.788790	−	0.0582034i
$923$	−0.0712906	−	0.0295295i	−0.00234656	−	0.000971976i
$924$	19.6945	−	2.98078i	0.647902	−	0.0980603i
$925$	5.51714	+	13.3195i	0.181402	+	0.437944i
$926$	−4.96999	+	15.0456i	−0.163324	+	0.494428i
$927$	3.49326	+	2.53800i	0.114734	+	0.0833590i
$928$	10.9804	−	16.9734i	0.360448	−	0.557180i
$929$	8.94700	−	27.5360i	0.293542	−	0.903428i	−0.690166	−	0.723651i	$-0.742462\pi$
$929$	8.94700	−	27.5360i	0.293542	−	0.903428i	0.983707	−	0.179777i	$-0.0575376\pi$
$930$	−0.382843	+	0.275304i	−0.0125539	+	0.00902759i
$931$	1.25688	+	0.770216i	0.0411925	+	0.0252428i
$932$	−7.54770	−	15.1780i	−0.247233	−	0.497172i
$933$	−1.84864	+	23.4892i	−0.0605217	+	0.769001i
$934$	−7.53149	+	30.7093i	−0.246438	+	1.00484i
$935$	0.560732	−	0.0904793i	0.0183379	−	0.00295899i
$936$	0.276094	−	0.313833i	0.00902442	−	0.0102580i
$937$	29.2917	+	14.9249i	0.956917	+	0.487574i	0.861441	−	0.507858i	$-0.169563\pi$
$937$	29.2917	+	14.9249i	0.956917	+	0.487574i	0.0954764	+	0.995432i	$0.469563\pi$
$938$	−2.93151	+	35.0580i	−0.0957172	+	1.14468i
$939$	−5.73737	−	23.8978i	−0.187232	−	0.779877i
$940$	0.448822	−	1.05430i	0.0146390	−	0.0343875i
$941$	3.37194	+	42.8446i	0.109922	+	1.39669i	0.766407	+	0.642355i	$0.222043\pi$
$941$	3.37194	+	42.8446i	0.109922	+	1.39669i	−0.656485	+	0.754339i	$0.727957\pi$
$942$	−5.13697	−	5.18740i	−0.167371	−	0.169015i
$943$	3.89915	−	5.36672i	0.126974	−	0.174765i
$944$	−20.0109	−	34.1344i	−0.651299	−	1.11098i
$945$		−	0.928432i		−	0.0302019i
$946$	24.4745	−	12.4093i	0.795735	−	0.403460i
$947$	41.0642	−	17.0094i	1.33441	−	0.552730i	0.402498	−	0.915421i	$-0.368142\pi$
$947$	41.0642	−	17.0094i	1.33441	−	0.552730i	0.931909	+	0.362691i	$0.118142\pi$
$948$	14.3302	−	22.8800i	0.465423	−	0.743107i
$949$	0.453811	−	0.278096i	0.0147313	−	0.00902736i
$950$	1.73544	−	4.13250i	0.0563049	−	0.134076i
$951$	−9.59327	−	18.8278i	−0.311083	−	0.610535i
$952$	−3.41745	−	23.8323i	−0.110760	−	0.772409i
$953$	3.09055	+	0.489496i	0.100113	+	0.0158563i	0.206290	−	0.978491i	$-0.433861\pi$
$953$	3.09055	+	0.489496i	0.100113	+	0.0158563i	−0.106177	+	0.994347i	$0.533861\pi$
$954$	−10.2656	−	12.1391i	−0.332362	−	0.393018i
$955$	0.0167939	−	0.213386i	0.000543437	−	0.00690502i
$956$	−16.4683	+	5.17356i	−0.532624	+	0.167325i
$957$	10.7557	−	4.49174i	0.347681	−	0.145197i
$958$	18.8708	−	25.7084i	0.609687	−	0.830599i
$959$	7.50709	+	23.1044i	0.242417	+	0.746081i
$960$	0.463835	−	0.135817i	0.0149702	−	0.00438346i
$961$	0.435370	−	0.316315i	0.0140442	−	0.0102037i
$962$	−0.173199	−	0.240853i	−0.00558415	−	0.00776541i
$963$	18.3594	−	1.44491i	0.591623	−	0.0465617i
$964$	1.98326	−	2.67438i	0.0638765	−	0.0861360i
$965$	0.368885	+	0.601966i	0.0118748	+	0.0193780i
$966$	−0.412458	−	5.58974i	−0.0132706	−	0.179847i
$967$	13.9683	+	13.9683i	0.449192	+	0.449192i	0.895086	−	0.445894i	$-0.147114\pi$
$967$	13.9683	+	13.9683i	0.449192	+	0.449192i	−0.445894	+	0.895086i	$0.647114\pi$
$968$	5.13896	−	30.6854i	0.165173	−	0.986265i
$969$	−1.22969	+	1.22969i	−0.0395032	+	0.0395032i
$970$	−0.980745	−	0.845956i	−0.0314898	−	0.0271620i
$971$	−1.51385	+	0.927686i	−0.0485816	+	0.0297709i	−0.546577	−	0.837409i	$-0.684070\pi$
$971$	−1.51385	+	0.927686i	−0.0485816	+	0.0297709i	0.497996	+	0.867180i	$0.334070\pi$
$972$	−31.1562	−	7.80264i	−0.999335	−	0.250270i
$973$	3.23171	+	41.0627i	0.103604	+	1.31641i
$974$	−3.60300	+	22.0508i	−0.115448	+	0.706552i
$975$	−0.209950	−	0.288971i	−0.00672377	−	0.00925447i
$976$	8.07628	+	20.6290i	0.258516	+	0.660317i
$977$	−37.0629	+	12.0425i	−1.18575	+	0.385273i	−0.834499	−	0.551009i	$-0.814243\pi$
$977$	−37.0629	+	12.0425i	−1.18575	+	0.385273i	−0.351249	+	0.936282i	$0.614243\pi$
$978$	0.335380	+	2.18659i	0.0107243	+	0.0699193i
$979$	17.6530	+	42.2708i	0.564192	+	1.35098i
$980$	−0.284402	−	0.0251810i	−0.00908490	−	0.000804378i
$981$	−29.7562	−	2.34187i	−0.950043	−	0.0747700i
$982$	1.61901	−	19.3617i	0.0516646	−	0.617858i
$983$	−6.90235	+	43.5797i	−0.220151	+	1.38998i	0.591721	+	0.806143i	$0.298449\pi$
$983$	−6.90235	+	43.5797i	−0.220151	+	1.38998i	−0.811872	+	0.583835i	$0.801551\pi$
$984$	12.0260	−	7.12925i	0.383374	−	0.227272i
$985$	1.09638	−	0.558632i	0.0349335	−	0.0177995i
$986$	−5.32783	−	13.0424i	−0.169673	−	0.415353i
$987$	−14.6328	−	23.8785i	−0.465766	−	0.760062i
$988$	−0.0153171	+	0.0909485i	−0.000487302	+	0.00289346i
$989$	−2.95490	−	7.13375i	−0.0939602	−	0.226840i
$990$	−0.556730	−	0.182115i	−0.0176940	−	0.00578798i
$991$	23.0512			0.732245			0.366123	−	0.930567i	$-0.380685\pi$
$991$	23.0512			0.732245			0.366123	+	0.930567i	$0.380685\pi$
$992$	29.9201	−	8.91989i	0.949965	−	0.283207i
$993$	18.3280	+	13.3161i	0.581621	+	0.422573i
$994$	4.58363	+	0.0223913i	0.145384	+	0.000710207i
$995$	0.485785	−	0.0382321i	0.0154004	−	0.00121204i
$996$	10.9318	+	11.1476i	0.346389	+	0.353224i
$997$	−56.5698	+	13.5812i	−1.79158	+	0.430121i	−0.986598	−	0.163172i	$-0.947828\pi$
$997$	−56.5698	+	13.5812i	−1.79158	+	0.430121i	−0.804987	+	0.593293i	$0.797828\pi$
$998$	12.4056	−	10.4910i	0.392693	−	0.332088i
$999$	−6.48389	+	12.7254i	−0.205141	+	0.402612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.bf.a.5.6	✓	736
11.9	even	5	inner	352.2.bf.a.229.32	yes	736
32.13	even	8	inner	352.2.bf.a.269.32	yes	736
352.141	even	40	inner	352.2.bf.a.141.6	yes	736

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.bf.a.5.6	✓	736	1.1	even	1	trivial
352.2.bf.a.141.6	yes	736	352.141	even	40	inner
352.2.bf.a.229.32	yes	736	11.9	even	5	inner
352.2.bf.a.269.32	yes	736	32.13	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.bf (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34285 - 0.443581i) q^{2} +(-0.229576 + 0.956251i) q^{3} +(1.60647 + 1.19132i) q^{4} +(-0.0398970 + 0.0467134i) q^{5} +(0.732459 - 1.18226i) q^{6} +(3.01590 + 0.477672i) q^{7} +(-1.62880 - 2.31236i) q^{8} +(1.81131 + 0.922908i) q^{9} +(0.0742968 - 0.0450314i) q^{10} +(-3.06783 - 1.26032i) q^{11} +(-1.50801 + 1.26269i) q^{12} +(0.0472126 + 0.0552789i) q^{13} +(-3.83800 - 1.97924i) q^{14} +(-0.0355104 - 0.0488758i) q^{15} +(1.16150 + 3.82765i) q^{16} +(2.65125 + 0.861442i) q^{17} +(-2.02292 - 2.04279i) q^{18} +(0.616817 + 0.148085i) q^{19} +(-0.119744 + 0.0275136i) q^{20} +(-1.14915 + 2.77430i) q^{21} +(3.56057 + 3.05325i) q^{22} +(0.933262 - 0.933262i) q^{23} +(2.58513 - 1.02668i) q^{24} +(0.781582 + 4.93471i) q^{25} +(-0.0388786 - 0.0951737i) q^{26} +(-3.21441 + 3.76359i) q^{27} +(4.27590 + 4.36027i) q^{28} +(3.04702 + 1.86721i) q^{29} +(0.0260046 + 0.0813845i) q^{30} +(1.70553 + 5.24910i) q^{31} +(0.138155 - 5.65517i) q^{32} +(1.90948 - 2.64428i) q^{33} +(-3.17810 - 2.33283i) q^{34} +(-0.142639 + 0.121825i) q^{35} +(1.81034 + 3.64048i) q^{36} +(2.80584 - 0.673624i) q^{37} +(-0.762603 - 0.472463i) q^{38} +(-0.0636994 + 0.0324564i) q^{39} +(0.173003 + 0.0161698i) q^{40} +(4.96424 - 0.786258i) q^{41} +(2.77376 - 3.21571i) q^{42} +(2.23884 - 5.40504i) q^{43} +(-3.42693 - 5.67945i) q^{44} +(-0.115378 + 0.0477911i) q^{45} +(-1.66720 + 0.839250i) q^{46} +(-5.48180 + 7.54505i) q^{47} +(-3.92685 + 0.231952i) q^{48} +(2.21008 + 0.718100i) q^{49} +(1.13940 - 6.97326i) q^{50} +(-1.43242 + 2.33749i) q^{51} +(0.00999078 + 0.145049i) q^{52} +(5.51277 + 0.433865i) q^{53} +(5.98592 - 3.62807i) q^{54} +(0.181271 - 0.0930257i) q^{55} +(-3.80774 - 7.75188i) q^{56} +(-0.283212 + 0.555835i) q^{57} +(-3.26341 - 3.85898i) q^{58} +(-9.61859 + 2.30922i) q^{59} +(0.00118047 - 0.120822i) q^{60} +(5.52132 - 0.434537i) q^{61} +(0.0381291 - 7.80527i) q^{62} +(5.02188 + 3.64861i) q^{63} +(-2.69405 + 7.53274i) q^{64} -0.00446591 q^{65} +(-3.73709 + 2.70385i) q^{66} +(-3.11765 - 7.52668i) q^{67} +(3.23290 + 4.54237i) q^{68} +(0.678179 + 1.10669i) q^{69} +(0.245582 - 0.100321i) q^{70} +(-0.945767 + 0.481892i) q^{71} +(-0.816154 - 5.69163i) q^{72} +(1.14532 - 7.23128i) q^{73} +(-4.06662 - 0.340047i) q^{74} +(-4.89826 - 0.385501i) q^{75} +(0.814483 + 0.972722i) q^{76} +(-8.65025 - 5.26642i) q^{77} +(0.0999355 - 0.0153282i) q^{78} +(-13.0543 + 4.24161i) q^{79} +(-0.225143 - 0.0984542i) q^{80} +(0.723702 + 0.996090i) q^{81} +(-7.01498 - 1.14622i) q^{82} +(-0.622825 - 7.91374i) q^{83} +(-5.15116 + 3.08782i) q^{84} +(-0.146018 + 0.0894798i) q^{85} +(-5.40399 + 6.26503i) q^{86} +(-2.48505 + 2.48505i) q^{87} +(2.08255 + 9.14675i) q^{88} +(-9.76648 - 9.76648i) q^{89} +(0.176134 - 0.0129966i) q^{90} +(0.115983 + 0.189268i) q^{91} +(2.61108 - 0.387443i) q^{92} +(-5.41100 + 0.425855i) q^{93} +(10.7081 - 7.70022i) q^{94} +(-0.0315267 + 0.0229055i) q^{95} +(5.37604 + 1.43040i) q^{96} +(-4.60684 - 14.1784i) q^{97} +(-2.64927 - 1.94465i) q^{98} +(-4.39363 - 5.11416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100}) \) 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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