LMFDB - Embedded newform 158.2.g.b.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [158,2,Mod(5,158)] 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("158.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(158, base_ring=CyclotomicField(78)) chi = DirichletCharacter(H, H._module([62])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 158 = 2 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	158.g (of order $39$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.26163635194$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$3$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	158.13
Dual form			158.2.g.b.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.692724 - 0.721202i) q^{2} +(-0.436898 - 2.14007i) q^{3} +(-0.0402659 - 0.999189i) q^{4} +(-2.26208 - 0.182614i) q^{5} +(-1.84607 - 1.16739i) q^{6} +(1.00326 + 0.334937i) q^{7} +(-0.748511 - 0.663123i) q^{8} +(-1.62908 + 0.694084i) q^{9} +(-1.69870 + 1.50492i) q^{10} +(0.105762 - 0.222888i) q^{11} +(-2.12074 + 0.522716i) q^{12} +(1.83032 - 1.15742i) q^{13} +(0.936540 - 0.491534i) q^{14} +(0.597493 + 4.92080i) q^{15} +(-0.996757 + 0.0804666i) q^{16} +(-2.02983 - 1.06534i) q^{17} +(-0.627925 + 1.65570i) q^{18} +(7.51299 - 1.22098i) q^{19} +(-0.0913813 + 2.26760i) q^{20} +(0.278466 - 2.29338i) q^{21} +(-0.0874838 - 0.230676i) q^{22} +(2.61308 + 4.52598i) q^{23} +(-1.09211 + 1.89158i) q^{24} +(0.148429 + 0.0241220i) q^{25} +(0.433169 - 2.12180i) q^{26} +(-1.52519 - 2.20962i) q^{27} +(0.294268 - 1.01593i) q^{28} +(4.25120 - 3.19457i) q^{29} +(3.96279 + 2.97784i) q^{30} +(0.706804 + 2.44017i) q^{31} +(-0.632445 + 0.774605i) q^{32} +(-0.523204 - 0.128958i) q^{33} +(-2.17444 + 0.725935i) q^{34} +(-2.20829 - 0.940866i) q^{35} +(0.759117 + 1.59981i) q^{36} +(0.670858 + 0.821652i) q^{37} +(4.32386 - 6.26419i) q^{38} +(-3.27662 - 3.41132i) q^{39} +(1.57210 + 1.63673i) q^{40} +(-0.0459625 + 0.0665881i) q^{41} +(-1.46109 - 1.78951i) q^{42} +(5.17764 + 10.9116i) q^{43} +(-0.226966 - 0.0967013i) q^{44} +(3.81186 - 1.27258i) q^{45} +(5.07429 + 1.25070i) q^{46} +(-7.28935 + 8.92784i) q^{47} +(0.607685 + 2.09797i) q^{48} +(-4.70175 - 3.53314i) q^{49} +(0.120217 - 0.0903372i) q^{50} +(-1.39307 + 4.80943i) q^{51} +(-1.23018 - 1.78223i) q^{52} +(-1.87231 + 9.17116i) q^{53} +(-2.65012 - 0.430686i) q^{54} +(-0.279945 + 0.484879i) q^{55} +(-0.528846 - 0.915988i) q^{56} +(-5.89539 - 15.5449i) q^{57} +(0.640978 - 5.27893i) q^{58} +(0.0857959 - 2.12900i) q^{59} +(4.89275 - 0.795149i) q^{60} +(2.97932 - 7.85583i) q^{61} +(2.24948 + 1.18062i) q^{62} +(-1.86686 + 0.150708i) q^{63} +(0.120537 + 0.992709i) q^{64} +(-4.35169 + 2.28394i) q^{65} +(-0.455441 + 0.288003i) q^{66} +(-9.72551 + 2.39712i) q^{67} +(-0.982741 + 2.07108i) q^{68} +(8.54426 - 7.56955i) q^{69} +(-2.20829 + 0.940866i) q^{70} +(-0.100455 - 0.0889956i) q^{71} +(1.67964 + 0.560747i) q^{72} +(0.462937 + 0.292744i) q^{73} +(1.05730 + 0.0853538i) q^{74} +(-0.0132255 - 0.328186i) q^{75} +(-1.52251 - 7.45773i) q^{76} +(0.180760 - 0.188191i) q^{77} -4.73005 q^{78} +(7.16418 + 5.26066i) q^{79} +2.26944 q^{80} +(-7.74236 + 8.06065i) q^{81} +(0.0161842 + 0.0792755i) q^{82} +(-0.463489 - 11.5014i) q^{83} +(-2.30273 - 0.185896i) q^{84} +(4.39711 + 2.78056i) q^{85} +(11.4562 + 3.82464i) q^{86} +(-8.69394 - 7.70216i) q^{87} +(-0.226966 + 0.0967013i) q^{88} +(-3.63923 + 3.22408i) q^{89} +(1.72277 - 3.63067i) q^{90} +(2.22394 - 0.548153i) q^{91} +(4.41709 - 2.79320i) q^{92} +(4.91333 - 2.57871i) q^{93} +(1.38927 + 11.4416i) q^{94} +(-17.2180 + 1.38998i) q^{95} +(1.93402 + 1.01505i) q^{96} +(4.00477 - 10.5597i) q^{97} +(-5.80513 + 0.943425i) q^{98} +(-0.0175907 + 0.436510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{2} + q^{3} + 3 q^{4} - 14 q^{5} + q^{6} - 6 q^{8} + 2 q^{9} + 2 q^{10} + 5 q^{11} - 2 q^{12} - 21 q^{13} - 13 q^{14} - 4 q^{15} + 3 q^{16} + 30 q^{17} - 4 q^{18} - 26 q^{19} - q^{20} - 8 q^{21}+ \cdots - 44 q^{99}+O(q^{100}) $ 72 * q + 3 * q^2 + q^3 + 3 * q^4 - 14 * q^5 + q^6 - 6 * q^8 + 2 * q^9 + 2 * q^10 + 5 * q^11 - 2 * q^12 - 21 * q^13 - 13 * q^14 - 4 * q^15 + 3 * q^16 + 30 * q^17 - 4 * q^18 - 26 * q^19 - q^20 - 8 * q^21 - 23 * q^22 - 5 * q^23 - 12 * q^24 - 17 * q^25 + 31 * q^26 - 59 * q^27 - 2 * q^29 - 37 * q^30 - 19 * q^31 + 3 * q^32 + 76 * q^33 + 11 * q^34 - 17 * q^35 + 2 * q^36 - 19 * q^37 - 12 * q^39 - q^40 + 18 * q^41 + 17 * q^42 - 29 * q^43 - 21 * q^44 - 65 * q^45 - 16 * q^46 - 17 * q^47 + q^48 - 23 * q^49 - 30 * q^50 - 45 * q^51 - 10 * q^52 + 60 * q^53 - 29 * q^54 - 14 * q^55 - 26 * q^56 - 52 * q^57 + 4 * q^58 - 14 * q^59 + 67 * q^60 - 33 * q^61 + 51 * q^62 - 33 * q^63 - 6 * q^64 + 28 * q^65 + 40 * q^66 - 2 * q^67 + 37 * q^68 + 172 * q^69 - 17 * q^70 + 54 * q^71 + 2 * q^72 - 91 * q^73 + 59 * q^74 + 115 * q^75 + 39 * q^76 - 98 * q^77 + 24 * q^78 + 152 * q^79 + 2 * q^80 + 77 * q^81 + 4 * q^82 - 82 * q^83 - 9 * q^84 + 175 * q^85 + 49 * q^86 + 21 * q^87 - 21 * q^88 + 74 * q^89 - 39 * q^90 + 53 * q^91 + 21 * q^92 + 8 * q^93 + 112 * q^94 - 2 * q^96 + 34 * q^97 + 16 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/158\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{17}{39}\right)$

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 $

$2$	0.692724	−	0.721202i	0.489830	−	0.509967i
$2$	0.692724	−	0.721202i	0.489830	−	0.509967i
$3$	−0.436898	−	2.14007i	−0.252243	−	1.23557i	−0.886603	−	0.462531i	$-0.846941\pi$
$3$	−0.436898	−	2.14007i	−0.252243	−	1.23557i	0.634360	−	0.773038i	$-0.281264\pi$
$4$	−0.0402659	−	0.999189i	−0.0201330	−	0.499594i
$5$	−2.26208	−	0.182614i	−1.01164	−	0.0816676i	−0.436482	−	0.899713i	$-0.643776\pi$
$5$	−2.26208	−	0.182614i	−1.01164	−	0.0816676i	−0.575153	+	0.818046i	$0.695058\pi$
$6$	−1.84607	−	1.16739i	−0.753656	−	0.476583i
$7$	1.00326	+	0.334937i	0.379196	+	0.126594i	0.499876	−	0.866097i	$-0.333379\pi$
$7$	1.00326	+	0.334937i	0.379196	+	0.126594i	−0.120679	+	0.992692i	$0.538507\pi$
$8$	−0.748511	−	0.663123i	−0.264639	−	0.234449i
$9$	−1.62908	+	0.694084i	−0.543025	+	0.231361i
$10$	−1.69870	+	1.50492i	−0.537177	+	0.475897i
$11$	0.105762	−	0.222888i	0.0318884	−	0.0672034i	−0.886881	−	0.461998i	$-0.847133\pi$
$11$	0.105762	−	0.222888i	0.0318884	−	0.0672034i	0.918770	+	0.394794i	$0.129184\pi$
$12$	−2.12074	+	0.522716i	−0.612205	+	0.150895i
$13$	1.83032	−	1.15742i	0.507638	−	0.321011i	−0.255977	−	0.966683i	$-0.582397\pi$
$13$	1.83032	−	1.15742i	0.507638	−	0.321011i	0.763615	+	0.645672i	$0.223423\pi$
$14$	0.936540	−	0.491534i	0.250301	−	0.131368i
$15$	0.597493	+	4.92080i	0.154272	+	1.27055i
$16$	−0.996757	+	0.0804666i	−0.249189	+	0.0201166i
$17$	−2.02983	−	1.06534i	−0.492307	−	0.258383i	0.200251	−	0.979745i	$-0.435824\pi$
$17$	−2.02983	−	1.06534i	−0.492307	−	0.258383i	−0.692558	+	0.721362i	$0.743516\pi$
$18$	−0.627925	+	1.65570i	−0.148003	+	0.390253i
$19$	7.51299	−	1.22098i	1.72360	−	0.280112i	0.783594	−	0.621274i	$-0.213384\pi$
$19$	7.51299	−	1.22098i	1.72360	−	0.280112i	0.940005	+	0.341161i	$0.110820\pi$
$20$	−0.0913813	+	2.26760i	−0.0204335	+	0.507052i
$21$	0.278466	−	2.29338i	0.0607663	−	0.500456i
$22$	−0.0874838	−	0.230676i	−0.0186516	−	0.0491803i
$23$	2.61308	+	4.52598i	0.544864	+	0.943732i	0.998615	+	0.0526036i	$0.0167520\pi$
$23$	2.61308	+	4.52598i	0.544864	+	0.943732i	−0.453752	+	0.891128i	$0.649915\pi$
$24$	−1.09211	+	1.89158i	−0.222925	+	0.386117i
$25$	0.148429	+	0.0241220i	0.0296857	+	0.00482440i
$26$	0.433169	−	2.12180i	0.0849514	−	0.416120i
$27$	−1.52519	−	2.20962i	−0.293523	−	0.425242i
$28$	0.294268	−	1.01593i	0.0556115	−	0.191993i
$29$	4.25120	−	3.19457i	0.789428	−	0.593216i	−0.127699	−	0.991813i	$-0.540759\pi$
$29$	4.25120	−	3.19457i	0.789428	−	0.593216i	0.917126	+	0.398597i	$0.130503\pi$
$30$	3.96279	+	2.97784i	0.723503	+	0.543678i
$31$	0.706804	+	2.44017i	0.126946	+	0.438267i	0.998660	−	0.0517467i	$-0.0164788\pi$
$31$	0.706804	+	2.44017i	0.126946	+	0.438267i	−0.871715	+	0.490014i	$0.836992\pi$
$32$	−0.632445	+	0.774605i	−0.111802	+	0.136932i
$33$	−0.523204	−	0.128958i	−0.0910781	−	0.0224487i
$34$	−2.17444	+	0.725935i	−0.372913	+	0.124497i
$35$	−2.20829	−	0.940866i	−0.373270	−	0.159035i
$36$	0.759117	+	1.59981i	0.126520	+	0.266634i
$37$	0.670858	+	0.821652i	0.110288	+	0.135079i	0.826799	−	0.562497i	$-0.190159\pi$
$37$	0.670858	+	0.821652i	0.110288	+	0.135079i	−0.716511	+	0.697576i	$0.754262\pi$
$38$	4.32386	−	6.26419i	0.701422	−	1.01619i
$39$	−3.27662	−	3.41132i	−0.524679	−	0.546249i
$40$	1.57210	+	1.63673i	0.248571	+	0.258790i
$41$	−0.0459625	+	0.0665881i	−0.00717813	+	0.0103993i	−0.826557	−	0.562854i	$-0.809703\pi$
$41$	−0.0459625	+	0.0665881i	−0.00717813	+	0.0103993i	0.819378	+	0.573253i	$0.194319\pi$
$42$	−1.46109	−	1.78951i	−0.225451	−	0.276127i
$43$	5.17764	+	10.9116i	0.789583	+	1.66401i	0.746913	+	0.664922i	$0.231535\pi$
$43$	5.17764	+	10.9116i	0.789583	+	1.66401i	0.0426699	+	0.999089i	$0.486414\pi$
$44$	−0.226966	−	0.0967013i	−0.0342164	−	0.0145783i
$45$	3.81186	−	1.27258i	0.568238	−	0.189706i
$46$	5.07429	+	1.25070i	0.748163	+	0.184406i
$47$	−7.28935	+	8.92784i	−1.06326	+	1.30226i	−0.112056	+	0.993702i	$0.535744\pi$
$47$	−7.28935	+	8.92784i	−1.06326	+	1.30226i	−0.951206	+	0.308557i	$0.900154\pi$
$48$	0.607685	+	2.09797i	0.0877118	+	0.302816i
$49$	−4.70175	−	3.53314i	−0.671679	−	0.504734i
$50$	0.120217	−	0.0903372i	0.0170013	−	0.0127756i
$51$	−1.39307	+	4.80943i	−0.195068	+	0.673454i
$52$	−1.23018	−	1.78223i	−0.170596	−	0.247150i
$53$	−1.87231	+	9.17116i	−0.257181	+	1.25976i	0.621905	+	0.783093i	$0.286359\pi$
$53$	−1.87231	+	9.17116i	−0.257181	+	1.25976i	−0.879086	+	0.476663i	$0.841846\pi$
$54$	−2.65012	−	0.430686i	−0.360636	−	0.0586090i
$55$	−0.279945	+	0.484879i	−0.0377478	+	0.0653811i
$56$	−0.528846	−	0.915988i	−0.0706700	−	0.122404i
$57$	−5.89539	−	15.5449i	−0.780864	−	2.05897i
$58$	0.640978	−	5.27893i	0.0841646	−	0.693157i
$59$	0.0857959	−	2.12900i	0.0111697	−	0.277173i	−0.983947	−	0.178463i	$-0.942887\pi$
$59$	0.0857959	−	2.12900i	0.0111697	−	0.277173i	0.995116	−	0.0987096i	$-0.0314715\pi$
$60$	4.89275	−	0.795149i	0.631651	−	0.102653i
$61$	2.97932	−	7.85583i	0.381463	−	1.00584i	−0.597512	−	0.801860i	$-0.703844\pi$
$61$	2.97932	−	7.85583i	0.381463	−	1.00584i	0.978976	−	0.203977i	$-0.0653866\pi$
$62$	2.24948	+	1.18062i	0.285684	+	0.149938i
$63$	−1.86686	+	0.150708i	−0.235202	+	0.0189875i
$64$	0.120537	+	0.992709i	0.0150671	+	0.124089i
$65$	−4.35169	+	2.28394i	−0.539761	+	0.283288i
$66$	−0.455441	+	0.288003i	−0.0560609	+	0.0354508i
$67$	−9.72551	+	2.39712i	−1.18816	+	0.292855i	−0.783371	−	0.621555i	$-0.786501\pi$
$67$	−9.72551	+	2.39712i	−1.18816	+	0.292855i	−0.404790	+	0.914410i	$0.632655\pi$
$68$	−0.982741	+	2.07108i	−0.119175	+	0.251156i
$69$	8.54426	−	7.56955i	1.02861	−	0.911267i
$70$	−2.20829	+	0.940866i	−0.263942	+	0.112455i
$71$	−0.100455	−	0.0889956i	−0.0119218	−	0.0105618i	0.657141	−	0.753768i	$-0.271766\pi$
$71$	−0.100455	−	0.0889956i	−0.0119218	−	0.0105618i	−0.669063	+	0.743206i	$0.733304\pi$
$72$	1.67964	+	0.560747i	0.197948	+	0.0660847i
$73$	0.462937	+	0.292744i	0.0541827	+	0.0342631i	0.561283	−	0.827624i	$-0.310308\pi$
$73$	0.462937	+	0.292744i	0.0541827	+	0.0342631i	−0.507100	+	0.861887i	$0.669282\pi$
$74$	1.05730	+	0.0853538i	0.122908	+	0.00992218i
$75$	−0.0132255	−	0.328186i	−0.00152714	−	0.0378957i
$76$	−1.52251	−	7.45773i	−0.174644	−	0.855461i
$77$	0.180760	−	0.188191i	0.0205995	−	0.0214464i
$78$	−4.73005			−0.535573
$79$	7.16418	+	5.26066i	0.806033	+	0.591871i
$79$	7.16418	+	5.26066i	0.806033	+	0.591871i
$80$	2.26944			0.253732
$81$	−7.74236	+	8.06065i	−0.860262	+	0.895628i
$82$	0.0161842	+	0.0792755i	0.00178725	+	0.00875451i
$83$	−0.463489	−	11.5014i	−0.0508745	−	1.26244i	−0.799996	−	0.600005i	$-0.795165\pi$
$83$	−0.463489	−	11.5014i	−0.0508745	−	1.26244i	0.749122	−	0.662432i	$-0.230476\pi$
$84$	−2.30273	−	0.185896i	−0.251248	−	0.0202829i
$85$	4.39711	+	2.78056i	0.476933	+	0.301594i
$86$	11.4562	+	3.82464i	1.23535	+	0.412421i
$87$	−8.69394	−	7.70216i	−0.932088	−	0.825758i
$88$	−0.226966	+	0.0967013i	−0.0241947	+	0.0103084i
$89$	−3.63923	+	3.22408i	−0.385758	+	0.341752i	−0.833608	−	0.552357i	$-0.813728\pi$
$89$	−3.63923	+	3.22408i	−0.385758	+	0.341752i	0.447850	+	0.894109i	$0.352190\pi$
$90$	1.72277	−	3.63067i	0.181596	−	0.382706i
$91$	2.22394	−	0.548153i	0.233133	−	0.0574620i
$92$	4.41709	−	2.79320i	0.460513	−	0.291211i
$93$	4.91333	−	2.57871i	0.509488	−	0.267400i
$94$	1.38927	+	11.4416i	0.143292	+	1.18011i
$95$	−17.2180	+	1.38998i	−1.76653	+	0.142609i
$96$	1.93402	+	1.01505i	0.197390	+	0.103598i
$97$	4.00477	−	10.5597i	0.406623	−	1.07218i	−0.562759	−	0.826621i	$-0.690260\pi$
$97$	4.00477	−	10.5597i	0.406623	−	1.07218i	0.969382	−	0.245556i	$-0.0789706\pi$
$98$	−5.80513	+	0.943425i	−0.586406	+	0.0953003i
$99$	−0.0175907	+	0.436510i	−0.00176794	+	0.0438709i
$100$	0.0181258	−	0.149280i	0.00181258	−	0.0149280i
$101$	−1.56401	−	4.12395i	−0.155624	−	0.410348i	0.834415	−	0.551136i	$-0.185806\pi$
$101$	−1.56401	−	4.12395i	−0.155624	−	0.410348i	−0.990040	+	0.140788i	$0.955036\pi$
$102$	2.50356	+	4.33629i	0.247889	+	0.429357i
$103$	0.162961	−	0.282257i	0.0160570	−	0.0278116i	−0.857885	−	0.513841i	$-0.828222\pi$
$103$	0.162961	−	0.282257i	0.0160570	−	0.0278116i	0.873942	+	0.486030i	$0.161555\pi$
$104$	−2.13752	−	0.347381i	−0.209601	−	0.0340635i
$105$	−1.04872	+	5.13696i	−0.102344	+	0.501316i
$106$	5.31727	+	7.70340i	0.516459	+	0.748220i
$107$	4.51604	−	15.5912i	0.436582	−	1.50726i	−0.377225	−	0.926122i	$-0.623122\pi$
$107$	4.51604	−	15.5912i	0.436582	−	1.50726i	0.813807	−	0.581135i	$-0.197391\pi$
$108$	−2.14641	+	1.61293i	−0.206539	+	0.155204i
$109$	0.816429	+	0.613506i	0.0781997	+	0.0587633i	0.639123	−	0.769104i	$-0.279297\pi$
$109$	0.816429	+	0.613506i	0.0781997	+	0.0587633i	−0.560923	+	0.827868i	$0.689554\pi$
$110$	0.155771	+	0.537784i	0.0148522	+	0.0512757i
$111$	1.46529	−	1.79466i	0.139080	−	0.170342i
$112$	−1.02696	−	0.253122i	−0.0970383	−	0.0239178i
$113$	−18.1384	+	6.05548i	−1.70632	+	0.569652i	−0.991552	−	0.129713i	$-0.958594\pi$
$113$	−18.1384	+	6.05548i	−1.70632	+	0.569652i	−0.714765	+	0.699365i	$0.753466\pi$
$114$	−15.2949	−	6.51654i	−1.43250	−	0.610330i
$115$	−5.08449	−	10.7153i	−0.474131	−	0.999210i
$116$	−3.36316	−	4.11912i	−0.312261	−	0.382451i
$117$	−2.17837	+	3.15592i	−0.201391	+	0.291765i
$118$	−1.47601	−	1.53669i	−0.135878	−	0.141464i
$119$	−1.67963	−	1.74868i	−0.153971	−	0.160301i
$120$	2.81586	−	4.07948i	0.257052	−	0.372404i
$121$	6.91841	+	8.47351i	0.628946	+	0.770319i
$122$	−3.60180	−	7.59062i	−0.326091	−	0.687223i
$123$	0.162584	+	0.0692706i	0.0146597	+	0.00624592i
$124$	2.40973	−	0.804486i	0.216400	−	0.0722450i
$125$	10.6861	+	2.63390i	0.955797	+	0.235583i
$126$	−1.18453	+	1.45078i	−0.105526	+	0.129246i
$127$	5.57906	+	19.2612i	0.495062	+	1.70915i	0.686045	+	0.727559i	$0.259345\pi$
$127$	5.57906	+	19.2612i	0.495062	+	1.70915i	−0.190983	+	0.981593i	$0.561168\pi$
$128$	0.799443	+	0.600742i	0.0706614	+	0.0530986i
$129$	21.0896	−	15.8478i	1.85683	−	1.39532i
$130$	−1.36734	+	4.72059i	−0.119923	+	0.414023i
$131$	4.90410	+	7.10481i	0.428473	+	0.620750i	0.976450	−	0.215743i	$-0.0692173\pi$
$131$	4.90410	+	7.10481i	0.428473	+	0.620750i	−0.547977	+	0.836493i	$0.684602\pi$
$132$	−0.107786	+	0.527972i	−0.00938159	+	0.0459541i
$133$	7.94643	+	1.29142i	0.689043	+	0.111980i
$134$	−5.00829	+	8.67461i	−0.432650	+	0.749372i
$135$	3.04660	+	5.27687i	0.262210	+	0.454161i
$136$	0.812902	+	2.14345i	0.0697057	+	0.183799i
$137$	1.06375	−	8.76076i	0.0908822	−	0.748482i	−0.874023	−	0.485884i	$-0.838498\pi$
$137$	1.06375	−	8.76076i	0.0908822	−	0.748482i	0.964905	−	0.262598i	$-0.0845792\pi$
$138$	0.459636	−	11.4058i	0.0391268	−	0.970922i
$139$	−7.41583	+	1.20519i	−0.629003	+	0.102223i	−0.466552	−	0.884494i	$-0.654504\pi$
$139$	−7.41583	+	1.20519i	−0.629003	+	0.102223i	−0.162451	+	0.986717i	$0.551940\pi$
$140$	−0.851184	+	2.24439i	−0.0719382	+	0.189685i
$141$	22.2909	+	11.6992i	1.87723	+	0.985247i
$142$	−0.133772	+	0.0107992i	−0.0112259	+	0.000906245i
$143$	−0.0643982	−	0.530367i	−0.00538525	−	0.0443515i
$144$	1.56794	−	0.822919i	0.130662	−	0.0685766i
$145$	−10.1999	+	6.45006i	−0.847059	+	0.535648i
$146$	0.531815	−	0.131081i	0.0440133	−	0.0108483i
$147$	−5.50697	+	11.6057i	−0.454207	+	0.957222i
$148$	0.793973	−	0.703398i	0.0652642	−	0.0578190i
$149$	−4.90860	+	2.09136i	−0.402128	+	0.171331i	−0.583555	−	0.812074i	$-0.698339\pi$
$149$	−4.90860	+	2.09136i	−0.402128	+	0.171331i	0.181427	+	0.983404i	$0.441929\pi$
$150$	−0.245850	−	0.217804i	−0.0200736	−	0.0177837i
$151$	14.5863	+	4.86963i	1.18702	+	0.396284i	0.840527	−	0.541769i	$-0.182245\pi$
$151$	14.5863	+	4.86963i	1.18702	+	0.396284i	0.346490	+	0.938054i	$0.387374\pi$
$152$	−6.43321	−	4.06812i	−0.521803	−	0.329968i
$153$	4.04618	+	0.326642i	0.327115	+	0.0264074i
$154$	−0.0105070	−	0.260729i	−0.000846681	−	0.0210102i
$155$	−1.15324	−	5.64894i	−0.0926304	−	0.453734i
$156$	−3.27662	+	3.41132i	−0.262340	+	0.273125i
$157$	−13.7706			−1.09901			−0.549506	−	0.835490i	$-0.685184\pi$
$157$	−13.7706			−1.09901			−0.549506	+	0.835490i	$0.685184\pi$
$158$	8.75680	−	1.52263i	0.696654	−	0.121134i
$159$	20.4449			1.62139
$160$	1.57210	−	1.63673i	0.124285	−	0.129395i
$161$	1.10567	+	5.41595i	0.0871393	+	0.426836i
$162$	0.450040	+	11.1676i	0.0353585	+	0.877411i
$163$	12.1007	+	0.976870i	0.947800	+	0.0765143i	0.544690	−	0.838637i	$-0.316647\pi$
$163$	12.1007	+	0.976870i	0.947800	+	0.0765143i	0.403110	+	0.915152i	$0.367929\pi$
$164$	0.0683848	+	0.0432440i	0.00533996	+	0.00337679i
$165$	1.15998	+	0.387259i	0.0903044	+	0.0301480i
$166$	−8.61587	−	7.63300i	−0.668721	−	0.592435i
$167$	10.1265	−	4.31451i	0.783613	−	0.333866i	0.0371645	−	0.999309i	$-0.488167\pi$
$167$	10.1265	−	4.31451i	0.783613	−	0.333866i	0.746449	+	0.665443i	$0.231757\pi$
$168$	−1.72923	+	1.53196i	−0.133413	+	0.118193i
$169$	−3.56257	+	7.50797i	−0.274044	+	0.577536i
$170$	5.05133	−	1.24504i	0.387420	−	0.0954903i
$171$	−11.3918	+	7.20372i	−0.871150	+	0.550882i
$172$	10.6943	−	5.61281i	0.815434	−	0.427973i
$173$	2.12900	+	17.5339i	0.161865	+	1.33308i	0.816594	+	0.577213i	$0.195860\pi$
$173$	2.12900	+	17.5339i	0.161865	+	1.33308i	−0.654729	+	0.755864i	$0.727217\pi$
$174$	−11.5773	+	0.934617i	−0.877674	+	0.0708532i
$175$	0.140833	+	0.0739149i	0.0106460	+	0.00558744i
$176$	−0.0874838	+	0.230676i	−0.00659434	+	0.0173879i
$177$	−4.59370	+	0.746549i	−0.345284	+	0.0561140i
$178$	−0.195772	+	4.85802i	−0.0146737	+	0.364124i
$179$	0.559225	−	4.60563i	0.0417984	−	0.344241i	−0.956774	−	0.290832i	$-0.906068\pi$
$179$	0.559225	−	4.60563i	0.0417984	−	0.344241i	0.998573	−	0.0534094i	$-0.0170088\pi$
$180$	−1.42504	−	3.75752i	−0.106216	−	0.280069i
$181$	2.39629	+	4.15049i	0.178114	+	0.308503i	0.941235	−	0.337753i	$-0.109667\pi$
$181$	2.39629	+	4.15049i	0.178114	+	0.308503i	−0.763120	+	0.646257i	$0.776334\pi$
$182$	1.14525	−	1.98363i	0.0848916	−	0.147037i
$183$	−18.1137	−	2.94376i	−1.33900	−	0.217609i
$184$	1.04536	−	5.12053i	0.0770653	−	0.377491i
$185$	−1.36749	−	1.98115i	−0.100540	−	0.145657i
$186$	1.54381	−	5.32984i	0.113197	−	0.390803i
$187$	−0.452130	+	0.339754i	−0.0330631	+	0.0248453i
$188$	9.21411	+	6.92396i	0.672008	+	0.504981i
$189$	−0.790078	−	2.72766i	−0.0574697	−	0.198408i
$190$	−10.9249	+	13.3805i	−0.792573	+	0.970726i
$191$	17.2538	+	4.25269i	1.24844	+	0.307714i	0.807525	−	0.589833i	$-0.200807\pi$
$191$	17.2538	+	4.25269i	1.24844	+	0.307714i	0.440919	+	0.897547i	$0.354653\pi$
$192$	2.07180	−	0.691669i	0.149519	−	0.0499169i
$193$	−22.3289	−	9.51347i	−1.60727	−	0.684794i	−0.612843	−	0.790205i	$-0.709974\pi$
$193$	−22.3289	−	9.51347i	−1.60727	−	0.684794i	−0.994429	+	0.105410i	$0.966384\pi$
$194$	−4.84149	−	10.2032i	−0.347599	−	0.732549i
$195$	6.78904	+	8.31506i	0.486173	+	0.595454i
$196$	−3.34095	+	4.84021i	−0.238639	+	0.345729i
$197$	−17.6692	−	18.3956i	−1.25888	−	1.31063i	−0.930592	−	0.366058i	$-0.880707\pi$
$197$	−17.6692	−	18.3956i	−1.25888	−	1.31063i	−0.328290	−	0.944577i	$-0.606472\pi$
$198$	0.302626	+	0.315067i	0.0215067	+	0.0223909i
$199$	7.08973	−	10.2713i	0.502578	−	0.728110i	−0.486794	−	0.873517i	$-0.661834\pi$
$199$	7.08973	−	10.2713i	0.502578	−	0.728110i	0.989372	+	0.145407i	$0.0464492\pi$
$200$	−0.0951046	−	0.116482i	−0.00672491	−	0.00823652i
$201$	9.37907	+	19.7660i	0.661548	+	1.39418i
$202$	−4.05762	−	1.72879i	−0.285493	−	0.121637i
$203$	5.33503	−	1.78110i	0.374446	−	0.125008i
$204$	4.86162	+	1.19828i	0.340381	+	0.0838965i
$205$	0.116131	−	0.142235i	0.00811094	−	0.00993409i
$206$	−0.0906773	−	0.313054i	−0.00631779	−	0.0218115i
$207$	−7.39831	−	5.55947i	−0.514218	−	0.386410i
$208$	−1.73125	+	1.30095i	−0.120040	+	0.0902045i
$209$	0.522446	−	1.80369i	0.0361383	−	0.124764i
$210$	2.97832	+	4.31484i	0.205523	+	0.297752i
$211$	2.99614	−	14.6761i	0.206263	−	1.01034i	−0.736388	−	0.676560i	$-0.763470\pi$
$211$	2.99614	−	14.6761i	0.206263	−	1.01034i	0.942650	−	0.333782i	$-0.108325\pi$
$212$	9.23911	+	1.50150i	0.634545	+	0.103124i
$213$	−0.146568	+	0.253863i	−0.0100427	+	0.0173944i
$214$	−8.11603	−	14.0574i	−0.554800	−	0.960942i
$215$	−9.71964	−	25.6286i	−0.662874	−	1.74786i
$216$	−0.323628	+	2.66531i	−0.0220201	+	0.181352i
$217$	−0.108196	+	2.68486i	−0.00734482	+	0.182260i
$218$	1.00802	−	0.163820i	0.0682719	−	0.0110953i
$219$	0.424235	−	1.11862i	0.0286672	−	0.0755891i
$220$	0.495758	+	0.260194i	0.0334240	+	0.0175423i
$221$	−4.94828	+	0.399466i	−0.332857	+	0.0268710i
$222$	−0.279268	−	2.29998i	−0.0187432	−	0.154364i
$223$	−12.5855	+	6.60540i	−0.842790	+	0.442330i	−0.830117	−	0.557589i	$-0.811726\pi$
$223$	−12.5855	+	6.60540i	−0.842790	+	0.442330i	−0.0126731	+	0.999920i	$0.504034\pi$
$224$	−0.893951	+	0.565300i	−0.0597296	+	0.0377707i
$225$	−0.258544	+	0.0637254i	−0.0172363	+	0.00424836i
$226$	−8.19767	+	17.2762i	−0.545301	+	1.14920i
$227$	0.225976	−	0.200198i	0.0149986	−	0.0132876i	−0.655590	−	0.755117i	$-0.727580\pi$
$227$	0.225976	−	0.200198i	0.0149986	−	0.0132876i	0.670589	+	0.741829i	$0.266042\pi$
$228$	−15.2949	+	6.51654i	−1.01293	+	0.431568i
$229$	−12.2196	−	10.8256i	−0.807494	−	0.715377i	0.154635	−	0.987972i	$-0.450580\pi$
$229$	−12.2196	−	10.8256i	−0.807494	−	0.715377i	−0.962129	+	0.272594i	$0.912118\pi$
$230$	−11.2501	−	3.75583i	−0.741808	−	0.247652i
$231$	−0.481716	−	0.304619i	−0.0316946	−	0.0200424i
$232$	−5.30046	−	0.427897i	−0.347992	−	0.0280928i
$233$	0.189790	+	4.70960i	0.0124336	+	0.308536i	0.993425	+	0.114485i	$0.0365217\pi$
$233$	0.189790	+	4.70960i	0.0124336	+	0.308536i	−0.980991	+	0.194051i	$0.937837\pi$
$234$	0.767044	+	3.75723i	0.0501432	+	0.245618i
$235$	18.1195	−	18.8644i	1.18199	−	1.23058i
$236$	−2.13073			−0.138699
$237$	8.12816	−	17.6302i	0.527981	−	1.14520i
$238$	−2.42467			−0.157168
$239$	−6.79323	+	7.07250i	−0.439417	+	0.457482i	−0.903675	−	0.428218i	$-0.859142\pi$
$239$	−6.79323	+	7.07250i	−0.439417	+	0.457482i	0.464258	+	0.885700i	$0.346321\pi$
$240$	−0.991516	−	4.85677i	−0.0640021	−	0.313503i
$241$	−0.664256	−	16.4833i	−0.0427885	−	1.06179i	−0.867876	−	0.496781i	$-0.834515\pi$
$241$	−0.664256	−	16.4833i	−0.0427885	−	1.06179i	0.825088	−	0.565005i	$-0.191126\pi$
$242$	10.9037	+	0.880235i	0.700914	+	0.0565836i
$243$	13.8252	+	8.74255i	0.886890	+	0.560835i
$244$	−7.96943	−	2.66059i	−0.510190	−	0.170327i
$245$	9.99056	+	8.85087i	0.638274	+	0.565461i
$246$	0.162584	−	0.0692706i	0.0103660	−	0.00441653i
$247$	12.3380	−	10.9305i	0.785045	−	0.695489i
$248$	1.08908	−	2.29519i	0.0691567	−	0.145745i
$249$	−24.4112	+	6.01682i	−1.54700	+	0.381300i
$250$	9.30212	−	5.88230i	0.588318	−	0.372030i
$251$	−19.0641	+	10.0056i	−1.20331	+	0.631547i	−0.942618	−	0.333874i	$-0.891644\pi$
$251$	−19.0641	+	10.0056i	−1.20331	+	0.631547i	−0.260695	+	0.965421i	$0.583952\pi$
$252$	0.225757	+	1.85928i	0.0142214	+	0.117123i
$253$	1.28515	−	0.103748i	0.0807968	−	0.00652259i
$254$	17.7560	+	9.31904i	1.11411	+	0.584729i
$255$	4.02951	−	10.6249i	0.252337	−	0.665359i
$256$	0.987050	−	0.160411i	0.0616906	−	0.0100257i
$257$	0.0737722	−	1.83064i	0.00460178	−	0.114192i	−0.995255	−	0.0972962i	$-0.968981\pi$
$257$	0.0737722	−	1.83064i	0.00460178	−	0.114192i	0.999857	−	0.0168959i	$-0.00537839\pi$
$258$	3.17980	−	26.1880i	0.197966	−	1.63039i
$259$	0.397843	+	1.04903i	0.0247207	+	0.0651832i
$260$	2.45732	+	4.25620i	0.152396	+	0.263958i
$261$	−4.70822	+	8.15488i	−0.291432	+	0.504775i
$262$	8.52120	+	1.38483i	0.526441	+	0.0855550i
$263$	3.42610	−	16.7822i	0.211263	−	1.03483i	−0.726396	−	0.687276i	$-0.758806\pi$
$263$	3.42610	−	16.7822i	0.211263	−	1.03483i	0.937659	−	0.347557i	$-0.112989\pi$
$264$	0.306109	+	0.443475i	0.0188397	+	0.0272940i
$265$	5.91010	−	20.4040i	0.363055	−	1.25341i
$266$	6.43606	−	4.83639i	0.394620	−	0.296538i
$267$	8.48973	+	6.37962i	0.519563	+	0.390426i
$268$	2.78679	+	9.62110i	0.170230	+	0.587702i
$269$	1.87004	−	2.29038i	0.114018	−	0.139647i	−0.714443	−	0.699694i	$-0.753320\pi$
$269$	1.87004	−	2.29038i	0.114018	−	0.139647i	0.828461	+	0.560047i	$0.189217\pi$
$270$	5.91615	+	1.45820i	0.360045	+	0.0887432i
$271$	−20.3789	+	6.80349i	−1.23793	+	0.413282i	−0.858920	−	0.512109i	$-0.828864\pi$
$271$	−20.3789	+	6.80349i	−1.23793	+	0.413282i	−0.379012	+	0.925392i	$0.623736\pi$
$272$	2.10897	+	0.898550i	0.127875	+	0.0544826i
$273$	−2.14472	−	4.51991i	−0.129804	−	0.273557i
$274$	−5.58139	−	6.83597i	−0.337184	−	0.412976i
$275$	0.0210746	−	0.0305318i	0.00127085	−	0.00184114i
$276$	−7.90746	−	8.23253i	−0.475973	−	0.495540i
$277$	−19.1141	−	19.8999i	−1.14846	−	1.19567i	−0.977622	−	0.210371i	$-0.932533\pi$
$277$	−19.1141	−	19.8999i	−1.14846	−	1.19567i	−0.170836	−	0.985300i	$-0.554647\pi$
$278$	−4.26794	+	6.18318i	−0.255974	+	0.370843i
$279$	−2.84512	−	3.48464i	−0.170333	−	0.208620i
$280$	1.02902	+	2.16862i	0.0614958	+	0.129600i
$281$	29.8944	+	12.7368i	1.78335	+	0.759815i	0.988155	+	0.153462i	$0.0490422\pi$
$281$	29.8944	+	12.7368i	1.78335	+	0.759815i	0.795196	+	0.606353i	$0.207368\pi$
$282$	23.8789	−	7.97195i	1.42197	−	0.474723i
$283$	−7.10251	−	1.75061i	−0.422201	−	0.104063i	0.0224906	−	0.999747i	$-0.492840\pi$
$283$	−7.10251	−	1.75061i	−0.422201	−	0.104063i	−0.444691	+	0.895684i	$0.646687\pi$
$284$	−0.0848785	+	0.103957i	−0.00503661	+	0.00616873i
$285$	10.4972	+	36.2404i	0.621798	+	2.14670i
$286$	−0.427112	−	0.320954i	−0.0252557	−	0.0189784i
$287$	−0.0684151	+	0.0514106i	−0.00403842	+	0.00303467i
$288$	0.492660	−	1.70086i	0.0290303	−	0.100224i
$289$	−6.67183	−	9.66581i	−0.392460	−	0.568577i
$290$	−2.41396	+	11.8243i	−0.141752	+	0.694349i
$291$	−24.3482	−	3.95697i	−1.42732	−	0.231962i
$292$	0.273866	−	0.474349i	0.0160268	−	0.0277592i
$293$	6.60211	+	11.4352i	0.385700	+	0.668051i	0.991866	−	0.127287i	$-0.0406268\pi$
$293$	6.60211	+	11.4352i	0.385700	+	0.668051i	−0.606166	+	0.795338i	$0.707293\pi$
$294$	4.55524	+	12.0112i	0.265667	+	0.700507i
$295$	−0.582864	+	4.80032i	−0.0339357	+	0.279485i
$296$	0.0427116	−	1.05988i	0.00248256	−	0.0616041i
$297$	−0.653806	+	0.106254i	−0.0379377	+	0.00616547i
$298$	−1.89201	+	4.98883i	−0.109601	+	0.288995i
$299$	10.0212	+	5.25954i	0.579542	+	0.304167i
$300$	−0.327388	+	0.0264295i	−0.0189017	+	0.00152591i
$301$	1.53980	+	12.6814i	0.0887526	+	0.730944i
$302$	13.6163	−	7.14637i	0.783529	−	0.411228i
$303$	−8.14221	+	5.14882i	−0.467758	+	0.295792i
$304$	−7.39038	+	1.82157i	−0.423867	+	0.104474i
$305$	−8.17407	+	17.2265i	−0.468046	+	0.986386i
$306$	3.03847	−	2.69185i	0.173698	−	0.153883i
$307$	−10.1401	+	4.32029i	−0.578726	+	0.246572i	−0.661436	−	0.750002i	$-0.730053\pi$
$307$	−10.1401	+	4.32029i	−0.578726	+	0.246572i	0.0827100	+	0.996574i	$0.473642\pi$
$308$	−0.195317	−	0.173036i	−0.0111292	−	0.00985963i
$309$	−0.675247	−	0.225431i	−0.0384135	−	0.0128243i
$310$	−4.87291	−	3.08144i	−0.276763	−	0.175014i
$311$	−5.12458	−	0.413699i	−0.290589	−	0.0234587i	−0.0656872	−	0.997840i	$-0.520924\pi$
$311$	−5.12458	−	0.413699i	−0.290589	−	0.0234587i	−0.224901	+	0.974382i	$0.572206\pi$
$312$	0.190460	+	4.72622i	0.0107827	+	0.267569i
$313$	3.49484	+	17.1189i	0.197540	+	0.967615i	0.950779	+	0.309869i	$0.100285\pi$
$313$	3.49484	+	17.1189i	0.197540	+	0.967615i	−0.753239	+	0.657746i	$0.771510\pi$
$314$	−9.53921	+	9.93137i	−0.538329	+	0.560459i
$315$	4.25052			0.239489
$316$	4.96792	−	7.37019i	0.279468	−	0.414606i
$317$	7.08173			0.397750			0.198875	−	0.980025i	$-0.436271\pi$
$317$	7.08173			0.397750			0.198875	+	0.980025i	$0.436271\pi$
$318$	14.1627	−	14.7449i	0.794205	−	0.826855i
$319$	−0.262418	−	1.28541i	−0.0146926	−	0.0719689i
$320$	−0.0913813	−	2.26760i	−0.00510837	−	0.126763i
$321$	−35.3393	−	2.85288i	−1.97244	−	0.159232i
$322$	4.67192	+	2.95434i	0.260356	+	0.164639i
$323$	−16.5509	−	5.52549i	−0.920915	−	0.307447i
$324$	8.36587	+	7.41151i	0.464770	+	0.411751i
$325$	0.299591	−	0.127644i	0.0166183	−	0.00708039i
$326$	9.08697	−	8.05036i	0.503281	−	0.445868i
$327$	0.956250	−	2.01525i	0.0528807	−	0.111444i
$328$	0.0785595	−	0.0193632i	0.00433772	−	0.00106915i
$329$	−10.3034	+	6.51546i	−0.568044	+	0.359209i
$330$	1.08284	−	0.568318i	0.0596083	−	0.0312849i
$331$	0.722908	+	5.95368i	0.0397346	+	0.327244i	0.998999	+	0.0447339i	$0.0142440\pi$
$331$	0.722908	+	5.95368i	0.0397346	+	0.327244i	−0.959264	+	0.282510i	$0.908833\pi$
$332$	−11.4734	+	0.926225i	−0.629682	+	0.0508332i
$333$	−1.66317	−	0.872901i	−0.0911413	−	0.0478347i
$334$	3.90325	−	10.2920i	0.213576	−	0.563155i
$335$	22.4377	−	3.64648i	1.22590	−	0.199228i
$336$	−0.0930232	+	2.30835i	−0.00507483	+	0.125931i
$337$	−3.68569	+	30.3544i	−0.200773	+	1.65351i	0.449110	+	0.893476i	$0.351741\pi$
$337$	−3.68569	+	30.3544i	−0.200773	+	1.65351i	−0.649883	+	0.760034i	$0.725182\pi$
$338$	2.94688	+	7.77029i	0.160289	+	0.422648i
$339$	20.8838	+	36.1718i	1.13425	+	1.96458i
$340$	2.60125	−	4.50550i	0.141073	−	0.244345i
$341$	0.618638	+	0.100538i	0.0335011	+	0.00544446i
$342$	−2.69602	+	13.2060i	−0.145784	+	0.714096i
$343$	−7.73956	−	11.2127i	−0.417897	−	0.605428i
$344$	3.36024	−	11.6009i	0.181172	−	0.625479i
$345$	−20.7101	+	15.5627i	−1.11500	+	0.837866i
$346$	14.1203	+	10.6107i	0.759111	+	0.570435i
$347$	2.08283	+	7.19077i	0.111812	+	0.386021i	0.996832	−	0.0795321i	$-0.0253426\pi$
$347$	2.08283	+	7.19077i	0.111812	+	0.386021i	−0.885020	+	0.465553i	$0.845855\pi$
$348$	−7.34584	+	8.99702i	−0.393778	+	0.482291i
$349$	1.36608	+	0.336707i	0.0731243	+	0.0180235i	0.275708	−	0.961241i	$-0.411088\pi$
$349$	1.36608	+	0.336707i	0.0731243	+	0.0180235i	−0.202584	+	0.979265i	$0.564934\pi$
$350$	0.150866	−	0.0503665i	0.00806413	−	0.00269220i
$351$	−5.34904	−	2.27901i	−0.285511	−	0.121645i
$352$	0.105762	+	0.222888i	0.00563713	+	0.0118800i
$353$	12.6741	+	15.5229i	0.674572	+	0.826201i	0.992542	−	0.121900i	$-0.0388986\pi$
$353$	12.6741	+	15.5229i	0.674572	+	0.826201i	−0.317970	+	0.948101i	$0.603001\pi$
$354$	−2.64375	+	3.83014i	−0.140514	+	0.203570i
$355$	0.210986	+	0.219660i	0.0111980	+	0.0116583i
$356$	3.36800	+	3.50646i	0.178504	+	0.185842i
$357$	−3.00846	+	4.35851i	−0.159225	+	0.230677i
$358$	−2.93420	−	3.59375i	−0.155077	−	0.189935i
$359$	4.76544	+	10.0430i	0.251510	+	0.530047i	0.989460	−	0.144809i	$-0.0462569\pi$
$359$	4.76544	+	10.0430i	0.251510	+	0.530047i	−0.737949	+	0.674856i	$0.764206\pi$
$360$	−3.69709	−	1.57518i	−0.194854	−	0.0830195i
$361$	36.9321	−	12.3297i	1.94379	−	0.648933i
$362$	4.65331	+	1.14694i	0.244572	+	0.0602817i
$363$	15.1113	−	18.5079i	0.793135	−	0.971414i
$364$	−0.637258	−	2.20007i	−0.0334014	−	0.115315i
$365$	−0.993744	−	0.746750i	−0.0520149	−	0.0390867i
$366$	−14.6708	+	11.0244i	−0.766857	+	0.576256i
$367$	8.80655	−	30.4037i	0.459698	−	1.58706i	−0.311357	−	0.950293i	$-0.600784\pi$
$367$	8.80655	−	30.4037i	0.459698	−	1.58706i	0.771055	−	0.636768i	$-0.219729\pi$
$368$	−2.96879	−	4.30104i	−0.154759	−	0.224207i
$369$	0.0286586	−	0.140379i	0.00149190	−	0.00730783i
$370$	−2.37611	−	0.386155i	−0.123528	−	0.0200753i
$371$	−4.95017	+	8.57395i	−0.257000	+	0.445137i
$372$	−2.77446	−	4.80551i	−0.143849	−	0.249154i
$373$	0.323925	+	0.854121i	0.0167722	+	0.0442247i	0.943141	−	0.332393i	$-0.107856\pi$
$373$	0.323925	+	0.854121i	0.0167722	+	0.0442247i	−0.926369	+	0.376618i	$0.877087\pi$
$374$	−0.0681704	+	0.561434i	−0.00352501	+	0.0290310i
$375$	0.967965	−	24.0198i	0.0499855	−	1.24038i
$376$	11.3764	−	1.84885i	0.586694	−	0.0953470i
$377$	4.08357	−	10.7675i	0.210315	−	0.554554i
$378$	−2.51450	−	1.31971i	−0.129332	−	0.0678788i
$379$	−18.3041	+	1.47766i	−0.940218	+	0.0759022i	−0.541064	−	0.840982i	$-0.681978\pi$
$379$	−18.3041	+	1.47766i	−0.940218	+	0.0759022i	−0.399154	+	0.916884i	$0.630696\pi$
$380$	2.08215	+	17.1481i	0.106812	+	0.879677i
$381$	38.7827	−	20.3547i	1.98690	−	1.04281i
$382$	15.0192	−	9.49757i	0.768449	−	0.485938i
$383$	22.4994	−	5.54560i	1.14967	−	0.283367i	0.381966	−	0.924177i	$-0.375247\pi$
$383$	22.4994	−	5.54560i	1.14967	−	0.283367i	0.767700	+	0.640809i	$0.221401\pi$
$384$	0.936355	−	1.97333i	0.0477831	−	0.100701i
$385$	−0.443261	+	0.392695i	−0.0225907	+	0.0200136i
$386$	−22.3289	+	9.51347i	−1.13651	+	0.484223i
$387$	−16.0084	−	14.1822i	−0.813751	−	0.720921i
$388$	−10.7124	−	3.57633i	−0.543840	−	0.181561i
$389$	30.6528	+	19.3837i	1.55416	+	0.982791i	0.987280	+	0.158990i	$0.0508238\pi$
$389$	30.6528	+	19.3837i	1.55416	+	0.982791i	0.566879	+	0.823801i	$0.308151\pi$
$390$	10.6998	+	0.863775i	0.541804	+	0.0437390i
$391$	−0.482406	−	11.9708i	−0.0243963	−	0.605389i
$392$	1.17641	+	5.76243i	0.0594176	+	0.291047i
$393$	13.0622	−	13.5992i	0.658901	−	0.685988i
$394$	−25.5069			−1.28502
$395$	−15.2453	−	13.2083i	−0.767074	−	0.664584i
$396$	0.436864			0.0219532
$397$	−13.4400	+	13.9925i	−0.674533	+	0.702263i	−0.967218	−	0.253946i	$-0.918272\pi$
$397$	−13.4400	+	13.9925i	−0.674533	+	0.702263i	0.292686	+	0.956209i	$0.405451\pi$
$398$	−2.49642	−	12.2283i	−0.125134	−	0.612948i
$399$	−0.708052	−	17.5701i	−0.0354469	−	0.879606i
$400$	−0.149888	−	0.0121002i	−0.00749442	−	0.000605012i
$401$	−30.3992	−	19.2233i	−1.51806	−	0.959965i	−0.994129	−	0.108206i	$-0.965489\pi$
$401$	−30.3992	−	19.2233i	−1.51806	−	0.959965i	−0.523934	−	0.851759i	$-0.675536\pi$
$402$	20.7524	+	6.92816i	1.03503	+	0.345545i
$403$	4.11798	+	3.64821i	0.205131	+	0.181730i
$404$	−4.05762	+	1.72879i	−0.201874	+	0.0860106i
$405$	18.9859	−	16.8200i	0.943415	−	0.835793i
$406$	2.41118	−	5.08145i	0.119665	−	0.252188i
$407$	0.254088	−	0.0626270i	0.0125947	−	0.00310431i
$408$	4.23196	−	2.67613i	0.209513	−	0.132488i
$409$	−1.55672	+	0.817030i	−0.0769749	+	0.0403995i	−0.502771	−	0.864419i	$-0.667686\pi$
$409$	−1.55672	+	0.817030i	−0.0769749	+	0.0403995i	0.425797	+	0.904819i	$0.359994\pi$
$410$	−0.0221332	−	0.182283i	−0.00109308	−	0.00900233i
$411$	−19.2134	+	1.55106i	−0.947726	+	0.0765083i
$412$	−0.288590	−	0.151464i	−0.0142178	−	0.00746208i
$413$	0.799158	−	2.10721i	0.0393240	−	0.103689i
$414$	−9.13449	+	1.48450i	−0.448936	+	0.0729591i
$415$	−1.05186	+	26.1017i	−0.0516338	+	1.28128i
$416$	−0.261030	+	2.14978i	−0.0127981	+	0.105401i
$417$	5.81915	+	15.3438i	0.284965	+	0.751391i
$418$	−0.938916	−	1.62625i	−0.0459239	−	0.0795425i
$419$	−4.11943	+	7.13505i	−0.201247	+	0.348570i	−0.948931	−	0.315485i	$-0.897833\pi$
$419$	−4.11943	+	7.13505i	−0.201247	+	0.348570i	0.747683	+	0.664055i	$0.231166\pi$
$420$	5.17502	+	0.841023i	0.252515	+	0.0410377i
$421$	−1.48427	+	7.27043i	−0.0723388	+	0.354339i	−0.999809	−	0.0195589i	$-0.993774\pi$
$421$	−1.48427	+	7.27043i	−0.0723388	+	0.354339i	0.927470	+	0.373898i	$0.121979\pi$
$422$	−8.50891	−	12.3273i	−0.414207	−	0.600083i
$423$	5.67824	−	19.6035i	0.276085	−	0.953157i
$424$	7.48305	−	5.62314i	0.363409	−	0.273084i
$425$	−0.275587	−	0.207090i	−0.0133679	−	0.0100454i
$426$	0.0815555	+	0.281562i	0.00395138	+	0.0136417i
$427$	5.62024	−	6.88355i	0.271983	−	0.333118i
$428$	−15.7604	−	3.88459i	−0.761807	−	0.187769i
$429$	−1.10689	+	0.369533i	−0.0534410	+	0.0178412i
$430$	−25.2164	−	10.7437i	−1.21604	−	0.518108i
$431$	−2.72220	−	5.73691i	−0.131124	−	0.276337i	0.827261	−	0.561818i	$-0.189898\pi$
$431$	−2.72220	−	5.73691i	−0.131124	−	0.276337i	−0.958384	+	0.285481i	$0.907847\pi$
$432$	1.69805	+	2.07973i	0.0816973	+	0.100061i
$433$	10.4428	−	15.1290i	0.501847	−	0.727051i	−0.487420	−	0.873167i	$-0.662062\pi$
$433$	10.4428	−	15.1290i	0.501847	−	0.727051i	0.989267	+	0.146116i	$0.0466774\pi$
$434$	1.86138	+	1.93790i	0.0893489	+	0.0930220i
$435$	18.2599	+	19.0106i	0.875495	+	0.911487i
$436$	0.580135	−	0.840470i	0.0277834	−	0.0402512i
$437$	25.1581	+	30.8131i	1.20348	+	1.47399i
$438$	−0.512871	−	1.08085i	−0.0245059	−	0.0516451i
$439$	−23.7817	−	10.1324i	−1.13504	−	0.483595i	−0.259021	−	0.965872i	$-0.583400\pi$
$439$	−23.7817	−	10.1324i	−1.13504	−	0.483595i	−0.876019	+	0.482276i	$0.839810\pi$
$440$	0.531076	−	0.177299i	0.0253181	−	0.00845241i
$441$	10.1118	+	2.49234i	0.481515	+	0.118683i
$442$	−3.13970	+	3.84543i	−0.149340	+	0.182908i
$443$	−4.85498	−	16.7614i	−0.230667	−	0.796356i	−0.989433	−	0.144992i	$-0.953684\pi$
$443$	−4.85498	−	16.7614i	−0.230667	−	0.796356i	0.758766	−	0.651364i	$-0.225803\pi$
$444$	−1.85221	−	1.39184i	−0.0879018	−	0.0660539i
$445$	8.82102	−	6.62857i	0.418156	−	0.314224i
$446$	−3.95448	+	13.6524i	−0.187250	+	0.646462i
$447$	6.62021	+	9.59104i	0.313125	+	0.453640i
$448$	−0.211566	+	1.03632i	−0.00999553	+	0.0489614i
$449$	4.23269	+	0.687879i	0.199753	+	0.0324630i	0.259464	−	0.965753i	$-0.416454\pi$
$449$	4.23269	+	0.687879i	0.199753	+	0.0324630i	−0.0597114	+	0.998216i	$0.519018\pi$
$450$	−0.133141	+	0.230607i	−0.00627632	+	0.0108709i
$451$	0.00998065	+	0.0172870i	0.000469970	+	0.000814012i
$452$	6.78093	+	17.8798i	0.318948	+	0.840997i
$453$	4.04860	−	33.3432i	0.190220	−	1.56660i
$454$	0.0121563	−	0.301657i	0.000570526	−	0.0141574i
$455$	−5.13085	+	0.833844i	−0.240538	+	0.0390912i
$456$	−5.89539	+	15.5449i	−0.276077	+	0.727955i
$457$	−32.9888	−	17.3139i	−1.54315	−	0.809908i	−0.543585	−	0.839354i	$-0.682934\pi$
$457$	−32.9888	−	17.3139i	−1.54315	−	0.809908i	−0.999566	+	0.0294455i	$0.990626\pi$
$458$	−16.2723	+	1.31363i	−0.760354	+	0.0613821i
$459$	0.741889	+	6.11000i	0.0346284	+	0.285191i
$460$	−10.5019	+	5.51183i	−0.489654	+	0.256990i
$461$	−15.9728	+	10.1006i	−0.743927	+	0.470431i	−0.851888	−	0.523724i	$-0.824542\pi$
$461$	−15.9728	+	10.1006i	−0.743927	+	0.470431i	0.107961	+	0.994155i	$0.465568\pi$
$462$	−0.553388	+	0.136398i	−0.0257459	+	0.00634581i
$463$	−8.88389	+	18.7224i	−0.412869	+	0.870103i	0.585369	+	0.810767i	$0.300950\pi$
$463$	−8.88389	+	18.7224i	−0.412869	+	0.870103i	−0.998238	+	0.0593362i	$0.981102\pi$
$464$	−3.98036	+	3.52629i	−0.184783	+	0.163704i
$465$	−11.5853	+	4.93602i	−0.537254	+	0.228903i
$466$	3.52804	+	3.12558i	0.163434	+	0.144789i
$467$	2.54156	+	0.848496i	0.117609	+	0.0392637i	0.374863	−	0.927080i	$-0.377690\pi$
$467$	2.54156	+	0.848496i	0.117609	+	0.0392637i	−0.257254	+	0.966344i	$0.582818\pi$
$468$	3.24107	+	2.04953i	0.149819	+	0.0947396i
$469$	−10.5601	−	0.852499i	−0.487620	−	0.0393647i
$470$	−1.05323	−	26.1356i	−0.0485819	−	1.20555i
$471$	6.01634	+	29.4700i	0.277218	+	1.35790i
$472$	−1.47601	+	1.53669i	−0.0679389	+	0.0707319i
$473$	2.97968			0.137006
$474$	−7.08437	−	18.0749i	−0.325396	−	0.830209i
$475$	1.14460			0.0525177
$476$	−1.67963	+	1.74868i	−0.0769856	+	0.0801505i
$477$	−3.31543	−	16.2401i	−0.151803	−	0.743581i
$478$	0.394870	+	9.79859i	0.0180609	+	0.448177i
$479$	−6.03085	−	0.486860i	−0.275556	−	0.0222452i	−0.0580841	−	0.998312i	$-0.518499\pi$
$479$	−6.03085	−	0.486860i	−0.275556	−	0.0222452i	−0.217472	+	0.976066i	$0.569781\pi$
$480$	−4.18956	−	2.64932i	−0.191226	−	0.120924i
$481$	2.17888	+	0.727417i	0.0993483	+	0.0331673i
$482$	−12.3480	−	10.9394i	−0.562435	−	0.498274i
$483$	11.1074	−	4.73243i	0.505406	−	0.215333i
$484$	8.18806	−	7.25399i	0.372185	−	0.329727i
$485$	−10.9875	+	23.1557i	−0.498916	+	1.05144i
$486$	15.8822	−	3.91462i	0.720433	−	0.177571i
$487$	−21.4502	+	13.5643i	−0.972003	+	0.614658i	−0.923269	−	0.384154i	$-0.874493\pi$
$487$	−21.4502	+	13.5643i	−0.972003	+	0.614658i	−0.0487342	+	0.998812i	$0.515519\pi$
$488$	−7.43944	+	3.90452i	−0.336767	+	0.176749i
$489$	−3.19621	−	26.3231i	−0.144537	−	1.19037i
$490$	13.3040	−	1.07401i	0.601012	−	0.0485187i
$491$	−3.28400	−	1.72358i	−0.148205	−	0.0777840i	0.388990	−	0.921242i	$-0.372824\pi$
$491$	−3.28400	−	1.72358i	−0.148205	−	0.0777840i	−0.537195	+	0.843458i	$0.680516\pi$
$492$	0.0626678	−	0.165241i	0.00282528	−	0.00744966i
$493$	−12.0325	+	1.95547i	−0.541917	+	0.0880701i
$494$	0.663717	−	16.4700i	0.0298620	−	0.741019i
$495$	0.119505	−	0.984209i	0.00537134	−	0.0442369i
$496$	−0.900864	−	2.37538i	−0.0404500	−	0.106658i
$497$	−0.0709747	−	0.122932i	−0.00318365	−	0.00551425i
$498$	−12.5709	+	21.7734i	−0.563315	+	0.975689i
$499$	−36.3964	−	5.91499i	−1.62933	−	0.264791i	−0.724091	−	0.689704i	$-0.757741\pi$
$499$	−36.3964	−	5.91499i	−1.62933	−	0.264791i	−0.905234	+	0.424913i	$0.860305\pi$
$500$	2.20147	−	10.7835i	0.0984529	−	0.482254i
$501$	−13.6576	−	19.7864i	−0.610176	−	0.883993i
$502$	−5.99008	+	20.6802i	−0.267351	+	0.923001i
$503$	−9.60161	+	7.21514i	−0.428114	+	0.321707i	−0.792864	−	0.609398i	$-0.791411\pi$
$503$	−9.60161	+	7.21514i	−0.428114	+	0.321707i	0.364750	+	0.931106i	$0.381155\pi$
$504$	1.49730	+	1.12515i	0.0666952	+	0.0501182i
$505$	2.78482	+	9.61432i	0.123923	+	0.427832i
$506$	0.815433	−	0.998724i	0.0362504	−	0.0443987i
$507$	17.6240	+	4.34394i	0.782711	+	0.192921i
$508$	19.0209	−	6.35011i	0.843916	−	0.281741i
$509$	17.9009	+	7.62687i	0.793445	+	0.338055i	0.750371	−	0.661017i	$-0.229875\pi$
$509$	17.9009	+	7.62687i	0.793445	+	0.338055i	0.0430735	+	0.999072i	$0.486285\pi$
$510$	−4.87139	−	10.2662i	−0.215709	−	0.454597i
$511$	0.366395	+	0.448753i	0.0162084	+	0.0198516i
$512$	0.568065	−	0.822984i	0.0251052	−	0.0363711i
$513$	−14.1566	−	14.7386i	−0.625031	−	0.650726i
$514$	−1.26916	−	1.32133i	−0.0559801	−	0.0582815i
$515$	−0.420176	+	0.608730i	−0.0185152	+	0.0268239i
$516$	−16.6841	−	20.4343i	−0.734478	−	0.899572i
$517$	1.21898	+	2.56894i	0.0536105	+	0.112982i
$518$	1.03215	+	0.439760i	0.0453503	+	0.0193219i
$519$	36.5936	−	12.2167i	1.60628	−	0.536255i
$520$	4.77182	+	1.17615i	0.209258	+	0.0515775i
$521$	1.23197	−	1.50889i	0.0539737	−	0.0661058i	−0.746913	−	0.664922i	$-0.768465\pi$
$521$	1.23197	−	1.50889i	0.0539737	−	0.0661058i	0.800886	+	0.598816i	$0.204362\pi$
$522$	2.61982	+	9.04467i	0.114666	+	0.395874i
$523$	21.5592	+	16.2007i	0.942719	+	0.708407i	0.956572	−	0.291497i	$-0.0941533\pi$
$523$	21.5592	+	16.2007i	0.942719	+	0.708407i	−0.0138530	+	0.999904i	$0.504410\pi$
$524$	6.90158	−	5.18620i	0.301497	−	0.226560i
$525$	0.0966532	−	0.333686i	0.00421829	−	0.0145632i
$526$	−9.72999	−	14.0963i	−0.424248	−	0.614629i
$527$	1.16491	−	5.70612i	0.0507444	−	0.248562i
$528$	0.531884	+	0.0864395i	0.0231473	+	0.00376180i
$529$	−2.15632	+	3.73486i	−0.0937532	+	0.162385i
$530$	−10.6214	−	18.3968i	−0.461363	−	0.799104i
$531$	1.33794	+	3.52786i	0.0580616	+	0.153096i
$532$	0.970403	−	7.99199i	0.0420723	−	0.346497i
$533$	−0.00705529	+	0.175075i	−0.000305598	+	0.00758335i
$534$	10.4820	−	1.70350i	0.453602	−	0.0737175i
$535$	−13.0628	+	34.4439i	−0.564756	+	1.48914i
$536$	8.86924	+	4.65493i	0.383093	+	0.201063i
$537$	−10.1007	+	0.815412i	−0.435877	+	0.0351876i
$538$	−0.356407	−	2.93527i	−0.0153658	−	0.126549i
$539$	−1.28476	+	0.674295i	−0.0553386	+	0.0290439i
$540$	5.14992	−	3.25661i	0.221617	−	0.140142i
$541$	15.2158	−	3.75037i	0.654180	−	0.161241i	0.101763	−	0.994809i	$-0.467552\pi$
$541$	15.2158	−	3.75037i	0.654180	−	0.161241i	0.552417	+	0.833568i	$0.313706\pi$
$542$	−9.21029	+	19.4103i	−0.395616	+	0.833743i
$543$	7.83540	−	6.94156i	0.336249	−	0.297891i
$544$	2.10897	−	0.898550i	0.0904215	−	0.0385250i
$545$	−1.73480	−	1.53690i	−0.0743105	−	0.0658334i
$546$	−4.74547	−	1.58427i	−0.203087	−	0.0678005i
$547$	25.9194	+	16.3904i	1.10823	+	0.700803i	0.957690	−	0.287800i	$-0.0929239\pi$
$547$	25.9194	+	16.3904i	1.10823	+	0.700803i	0.150541	+	0.988604i	$0.451898\pi$
$548$	−8.79648	−	0.710126i	−0.375767	−	0.0303351i
$549$	0.599065	+	14.8656i	0.0255675	+	0.634450i
$550$	−0.00742074	−	0.0363492i	−0.000316422	−	0.00154994i
$551$	28.0387	−	29.1914i	1.19449	−	1.24360i
$552$	−11.4150			−0.485855
$553$	5.42553	+	7.67736i	0.230717	+	0.326474i
$554$	−27.5927			−1.17230
$555$	−3.64235	+	3.79209i	−0.154609	+	0.160965i
$556$	1.50282	+	7.36129i	0.0637337	+	0.312188i
$557$	−1.11204	−	27.5951i	−0.0471188	−	1.16924i	−0.833866	−	0.551967i	$-0.813878\pi$
$557$	−1.11204	−	27.5951i	−0.0471188	−	1.16924i	0.786747	−	0.617275i	$-0.211764\pi$
$558$	−4.48401	−	0.361987i	−0.189823	−	0.0153241i
$559$	22.1061	+	13.9790i	0.934988	+	0.591251i
$560$	2.27684	+	0.760121i	0.0962141	+	0.0321210i
$561$	0.924632	+	0.819152i	0.0390380	+	0.0345846i
$562$	29.8944	−	12.7368i	1.26102	−	0.537270i
$563$	32.9132	−	29.1586i	1.38713	−	1.22889i	0.444181	−	0.895937i	$-0.353495\pi$
$563$	32.9132	−	29.1586i	1.38713	−	1.22889i	0.942945	−	0.332950i	$-0.108044\pi$
$564$	10.7921	−	22.7439i	0.454430	−	0.957691i
$565$	42.1364	−	10.3857i	1.77269	−	0.436929i
$566$	−6.18263	+	3.90966i	−0.259875	+	0.164335i
$567$	−10.4674	+	5.49372i	−0.439590	+	0.230714i
$568$	0.0161768	+	0.133228i	0.000678765	+	0.00559013i
$569$	14.2927	−	1.15383i	0.599182	−	0.0483710i	0.222845	−	0.974854i	$-0.428466\pi$
$569$	14.2927	−	1.15383i	0.599182	−	0.0483710i	0.376337	+	0.926483i	$0.377183\pi$
$570$	33.4083	+	17.5340i	1.39932	+	0.734420i
$571$	2.12360	−	5.59948i	0.0888700	−	0.234331i	−0.883211	−	0.468975i	$-0.844623\pi$
$571$	2.12360	−	5.59948i	0.0888700	−	0.234331i	0.972081	+	0.234644i	$0.0753925\pi$
$572$	−0.527344	+	0.0857017i	−0.0220494	+	0.00358337i
$573$	1.56288	−	38.7824i	0.0652901	−	1.62016i
$574$	−0.0103153	+	0.0849545i	−0.000430554	+	0.00354593i
$575$	0.278680	+	0.734818i	0.0116217	+	0.0306440i
$576$	−0.885387	−	1.53353i	−0.0368911	−	0.0638973i
$577$	−3.44350	+	5.96431i	−0.143355	+	0.248297i	−0.928758	−	0.370687i	$-0.879122\pi$
$577$	−3.44350	+	5.96431i	−0.143355	+	0.248297i	0.785403	+	0.618984i	$0.212456\pi$
$578$	−11.5927	−	1.88400i	−0.482194	−	0.0783642i
$579$	−10.6040	+	51.9419i	−0.440688	+	2.15863i
$580$	6.85553	+	9.93196i	0.284661	+	0.412402i
$581$	3.38723	−	11.6941i	0.140526	−	0.485152i
$582$	−19.7204	+	14.8189i	−0.817436	+	0.614263i
$583$	1.84613	+	1.38727i	0.0764588	+	0.0574550i
$584$	−0.152388	−	0.526106i	−0.00630588	−	0.0217704i
$585$	5.50398	−	6.74115i	0.227562	−	0.278712i
$586$	12.8205	+	3.15998i	0.529611	+	0.130537i
$587$	−23.2966	+	7.77756i	−0.961555	+	0.321014i	−0.753754	−	0.657157i	$-0.771759\pi$
$587$	−23.2966	+	7.77756i	−0.961555	+	0.321014i	−0.207801	+	0.978171i	$0.566631\pi$
$588$	11.8180	+	5.03519i	0.487367	+	0.207648i
$589$	8.28961	+	17.4700i	0.341567	+	0.719838i
$590$	3.05824	+	3.74566i	0.125906	+	0.154206i
$591$	−31.6483	+	45.8504i	−1.30184	+	1.88603i
$592$	−0.734798	−	0.765006i	−0.0302000	−	0.0314415i
$593$	22.8865	+	23.8274i	0.939835	+	0.978472i	0.999805	−	0.0197279i	$-0.00628000\pi$
$593$	22.8865	+	23.8274i	0.939835	+	0.978472i	−0.0599700	+	0.998200i	$0.519101\pi$
$594$	−0.376277	+	0.545131i	−0.0154388	+	0.0223670i
$595$	3.48013	+	4.26238i	0.142671	+	0.174741i
$596$	2.28731	+	4.82041i	0.0936920	+	0.197452i
$597$	−25.0787	−	10.6850i	−1.02640	−	0.437309i
$598$	10.7351	−	3.58391i	0.438992	−	0.146557i
$599$	−1.84316	−	0.454299i	−0.0753096	−	0.0185621i	0.201481	−	0.979492i	$-0.435425\pi$
$599$	−1.84316	−	0.454299i	−0.0753096	−	0.0185621i	−0.276790	+	0.960930i	$0.589271\pi$
$600$	−0.207728	+	0.254421i	−0.00848048	+	0.0103867i
$601$	−1.07839	−	3.72302i	−0.0439883	−	0.151865i	0.935518	−	0.353279i	$-0.114933\pi$
$601$	−1.07839	−	3.72302i	−0.0439883	−	0.151865i	−0.979506	+	0.201414i	$0.935446\pi$
$602$	10.2125	+	7.67420i	0.416231	+	0.312777i
$603$	14.1798	−	10.6554i	0.577446	−	0.433922i
$604$	4.27834	−	14.7706i	0.174083	−	0.601006i
$605$	−14.1026	−	20.4312i	−0.573354	−	0.830646i
$606$	−1.92697	+	9.43890i	−0.0782776	+	0.383429i
$607$	3.80208	+	0.617898i	0.154322	+	0.0250797i	0.237081	−	0.971490i	$-0.423809\pi$
$607$	3.80208	+	0.617898i	0.154322	+	0.0250797i	−0.0827596	+	0.996570i	$0.526373\pi$
$608$	−3.80578	+	6.59180i	−0.154345	+	0.267333i
$609$	−6.14253	−	10.6392i	−0.248908	−	0.431121i
$610$	6.76141	+	17.8284i	0.273761	+	0.721850i
$611$	−3.00855	+	24.7776i	−0.121713	+	1.00239i
$612$	0.163453	−	4.05606i	0.00660721	−	0.163956i
$613$	−7.52514	+	1.22295i	−0.303938	+	0.0493947i	−0.310467	−	0.950584i	$-0.600486\pi$
$613$	−7.52514	+	1.22295i	−0.303938	+	0.0493947i	0.00652984	+	0.999979i	$0.497921\pi$
$614$	−3.90849	+	10.3058i	−0.157734	+	0.415910i
$615$	−0.355129	−	0.186386i	−0.0143202	−	0.00751582i
$616$	−0.260095	+	0.0209970i	−0.0104795	+	0.000845994i
$617$	−1.74098	−	14.3382i	−0.0700891	−	0.577235i	−0.984871	−	0.173288i	$-0.944561\pi$
$617$	−1.74098	−	14.3382i	−0.0700891	−	0.577235i	0.914782	−	0.403948i	$-0.132362\pi$
$618$	−0.630341	+	0.330828i	−0.0253560	+	0.0133079i
$619$	−15.2435	+	9.63938i	−0.612686	+	0.387439i	−0.804466	−	0.593999i	$-0.797548\pi$
$619$	−15.2435	+	9.63938i	−0.612686	+	0.387439i	0.191780	+	0.981438i	$0.438574\pi$
$620$	−5.59792	+	1.37976i	−0.224818	+	0.0554127i
$621$	6.01526	−	12.6769i	0.241384	−	0.508706i
$622$	−3.84829	+	3.40928i	−0.154302	+	0.136700i
$623$	−4.73096	+	2.01567i	−0.189542	+	0.0807563i
$624$	3.54049	+	3.13660i	0.141733	+	0.125565i
$625$	−24.4051	−	8.14764i	−0.976206	−	0.325905i
$626$	14.7671	+	9.33816i	0.590213	+	0.373228i
$627$	−4.08828	−	0.330040i	−0.163270	−	0.0131805i
$628$	0.554485	+	13.7594i	0.0221264	+	0.549060i
$629$	−0.486392	−	2.38251i	−0.0193937	−	0.0949968i
$630$	2.94444	−	3.06548i	0.117309	−	0.122132i
$631$	−0.941344			−0.0374743			−0.0187372	−	0.999824i	$-0.505965\pi$
$631$	−0.941344			−0.0374743			−0.0187372	+	0.999824i	$0.505965\pi$
$632$	−1.87400	−	8.68839i	−0.0745436	−	0.345606i
$633$	−32.7168			−1.30038
$634$	4.90569	−	5.10736i	0.194830	−	0.202839i
$635$	−9.10295	−	44.5892i	−0.361240	−	1.76947i
$636$	−0.823234	−	20.4283i	−0.0326434	−	0.810036i
$637$	−12.6950	−	1.02485i	−0.502995	−	0.0406059i
$638$	−1.10882	−	0.701176i	−0.0438987	−	0.0277598i
$639$	0.225420	+	0.0752561i	0.00891746	+	0.00297709i
$640$	−1.69870	−	1.50492i	−0.0671471	−	0.0594872i
$641$	31.2325	−	13.3069i	1.23361	−	0.525592i	0.325986	−	0.945375i	$-0.394304\pi$
$641$	31.2325	−	13.3069i	1.23361	−	0.525592i	0.907625	+	0.419783i	$0.137894\pi$
$642$	−26.5379	+	23.5105i	−1.04737	+	0.927885i
$643$	−4.72740	+	9.96278i	−0.186430	+	0.392894i	−0.975049	−	0.221989i	$-0.928745\pi$
$643$	−4.72740	+	9.96278i	−0.186430	+	0.392894i	0.788619	+	0.614882i	$0.210796\pi$
$644$	5.36703	−	1.32285i	0.211491	−	0.0521278i
$645$	−50.6004	+	31.9978i	−1.99239	+	1.25991i
$646$	−15.4502	+	8.10889i	−0.607880	+	0.319040i
$647$	1.80497	+	14.8653i	0.0709607	+	0.584414i	0.984209	+	0.177010i	$0.0566426\pi$
$647$	1.80497	+	14.8653i	0.0709607	+	0.584414i	−0.913248	+	0.407403i	$0.866434\pi$
$648$	11.1404	−	0.899349i	0.437638	−	0.0353298i
$649$	−0.465456	−	0.244290i	−0.0182708	−	0.00958924i
$650$	0.115477	−	0.304487i	0.00452937	−	0.0119430i
$651$	5.79305	−	0.941462i	0.227047	−	0.0368988i
$652$	0.488831	−	12.1302i	0.0191441	−	0.475056i
$653$	1.69901	−	13.9926i	0.0664874	−	0.547573i	−0.920964	−	0.389648i	$-0.872597\pi$
$653$	1.69901	−	13.9926i	0.0664874	−	0.547573i	0.987451	−	0.157925i	$-0.0504804\pi$
$654$	−0.790988	−	2.08566i	−0.0309301	−	0.0815559i
$655$	−9.79605	−	16.9673i	−0.382763	−	0.662965i
$656$	0.0404553	−	0.0700706i	0.00157951	−	0.00273580i
$657$	−0.957348	−	0.155584i	−0.0373497	−	0.00606992i
$658$	−2.43843	+	11.9442i	−0.0950601	+	0.465635i
$659$	19.6885	+	28.5237i	0.766956	+	1.11113i	0.990645	+	0.136467i	$0.0435747\pi$
$659$	19.6885	+	28.5237i	0.766956	+	1.11113i	−0.223689	+	0.974661i	$0.571810\pi$
$660$	0.340237	−	1.17463i	0.0132437	−	0.0457226i
$661$	0.938442	−	0.705193i	0.0365012	−	0.0274288i	−0.582335	−	0.812949i	$-0.697861\pi$
$661$	0.938442	−	0.705193i	0.0365012	−	0.0274288i	0.618836	+	0.785520i	$0.287604\pi$
$662$	4.79459	+	3.60290i	0.186347	+	0.140031i
$663$	3.01678	+	10.4151i	0.117162	+	0.404490i
$664$	−7.27988	+	8.91623i	−0.282514	+	0.346017i
$665$	−17.7397	−	4.37244i	−0.687915	−	0.169556i
$666$	−1.78166	+	0.594805i	−0.0690379	+	0.0230482i
$667$	25.5672	+	10.8932i	0.989968	+	0.421786i
$668$	−4.71876	−	9.94458i	−0.182574	−	0.384767i
$669$	19.6346	+	24.0480i	0.759118	+	0.929750i
$670$	12.9133	−	18.7081i	0.498884	−	0.722758i
$671$	−1.43588	−	1.49490i	−0.0554313	−	0.0577101i
$672$	1.60035	+	1.66614i	0.0617347	+	0.0642726i
$673$	7.12608	−	10.3239i	0.274690	−	0.397957i	−0.661222	−	0.750190i	$-0.729962\pi$
$673$	7.12608	−	10.3239i	0.274690	−	0.397957i	0.935913	+	0.352233i	$0.114577\pi$
$674$	19.3385	+	23.6854i	0.744892	+	0.912327i
$675$	−0.173082	−	0.364762i	−0.00666191	−	0.0140397i
$676$	7.64533	+	3.25737i	0.294051	+	0.125283i
$677$	−35.1028	+	11.7191i	−1.34911	+	0.450400i	−0.897185	−	0.441655i	$-0.854391\pi$
$677$	−35.1028	+	11.7191i	−1.34911	+	0.450400i	−0.451927	+	0.892055i	$0.649263\pi$
$678$	40.5539	+	9.99563i	1.55746	+	0.383880i
$679$	7.55467	−	9.25279i	0.289922	−	0.355089i
$680$	−1.44743	−	4.99710i	−0.0555063	−	0.191630i
$681$	−0.527165	−	0.396139i	−0.0202010	−	0.0151801i
$682$	0.501054	−	0.376518i	0.0191864	−	0.0144176i
$683$	1.07313	−	3.70488i	0.0410622	−	0.141763i	−0.937368	−	0.348341i	$-0.886745\pi$
$683$	1.07313	−	3.70488i	0.0410622	−	0.141763i	0.978430	+	0.206577i	$0.0662325\pi$
$684$	7.65657	+	11.0925i	0.292756	+	0.424131i
$685$	−4.00613	+	19.6233i	−0.153066	+	0.749768i
$686$	−13.4480	−	2.18551i	−0.513447	−	0.0834433i
$687$	−17.8289	+	30.8805i	−0.680213	+	1.17816i
$688$	−6.03888	−	10.4596i	−0.230230	−	0.398770i
$689$	7.18799	+	18.9532i	0.273840	+	0.722058i
$690$	−3.12259	+	25.7168i	−0.118875	+	0.979023i
$691$	1.10399	−	27.3952i	0.0419978	−	1.04216i	−0.831557	−	0.555439i	$-0.812550\pi$
$691$	1.10399	−	27.3952i	0.0419978	−	1.04216i	0.873555	−	0.486725i	$-0.161809\pi$
$692$	17.4339	−	2.83329i	0.662739	−	0.107706i
$693$	−0.163851	+	0.432041i	−0.00622420	+	0.0164119i
$694$	6.62883	+	3.47908i	0.251627	+	0.132064i
$695$	16.9953	−	1.37200i	0.644669	−	0.0520431i
$696$	1.40003	+	11.5303i	0.0530680	+	0.437055i
$697$	0.164235	−	0.0861972i	0.00622084	−	0.00326495i
$698$	1.18915	−	0.751972i	0.0450099	−	0.0284625i
$699$	9.99594	−	2.46378i	0.378081	−	0.0931886i
$700$	0.0681842	−	0.143695i	0.00257712	−	0.00543116i
$701$	16.1817	−	14.3357i	0.611173	−	0.541452i	−0.299755	−	0.954016i	$-0.596905\pi$
$701$	16.1817	−	14.3357i	0.611173	−	0.541452i	0.910929	+	0.412564i	$0.135367\pi$
$702$	−5.34904	+	2.27901i	−0.201887	+	0.0860158i
$703$	6.04337	+	5.35396i	0.227930	+	0.201928i
$704$	0.234011	+	0.0781245i	0.00881964	+	0.00294443i
$705$	−48.2875	−	30.5351i	−1.81861	−	1.15002i
$706$	19.9748	+	1.61253i	0.751761	+	0.0606884i
$707$	−0.187841	−	4.66123i	−0.00706449	−	0.175304i
$708$	0.930913	+	4.55991i	0.0349858	+	0.171372i
$709$	25.6263	−	26.6798i	0.962415	−	1.00198i	−0.0375811	−	0.999294i	$-0.511965\pi$
$709$	25.6263	−	26.6798i	0.962415	−	1.00198i	0.999996	−	0.00268685i	$-0.000855252\pi$
$710$	0.304575			0.0114305
$711$	−15.3223	−	3.59748i	−0.574632	−	0.134916i
$712$	4.86197			0.182210
$713$	−9.19722	+	9.57532i	−0.344439	+	0.358599i
$714$	1.05933	+	5.18896i	0.0396445	+	0.194192i
$715$	0.0488216	+	1.21150i	0.00182582	+	0.0453074i
$716$	−4.62441	−	0.373321i	−0.172822	−	0.0139517i
$717$	18.1036	+	11.4480i	0.676091	+	0.427534i
$718$	10.5441	+	3.52015i	0.393504	+	0.131371i
$719$	16.0582	+	14.2264i	0.598871	+	0.530554i	0.907185	−	0.420731i	$-0.138226\pi$
$719$	16.0582	+	14.2264i	0.598871	+	0.530554i	−0.308314	+	0.951285i	$0.599765\pi$
$720$	−3.69709	+	1.57518i	−0.137783	+	0.0587037i
$721$	0.258031	−	0.228595i	0.00960956	−	0.00851333i
$722$	16.6915	−	35.1766i	0.621193	−	1.30914i
$723$	−34.9853	+	8.62310i	−1.30112	+	0.320696i
$724$	4.05063	−	2.56147i	0.150541	−	0.0951961i
$725$	0.708059	−	0.371618i	0.0262967	−	0.0138015i
$726$	−2.88003	−	23.7192i	−0.106888	−	0.880301i
$727$	9.40192	−	0.759002i	0.348698	−	0.0281498i	0.0951230	−	0.995466i	$-0.469676\pi$
$727$	9.40192	−	0.759002i	0.348698	−	0.0281498i	0.253575	+	0.967316i	$0.418394\pi$
$728$	−2.02814	−	1.06445i	−0.0751678	−	0.0394511i
$729$	0.779524	−	2.05544i	0.0288713	−	0.0761272i
$730$	−1.22695	+	0.199399i	−0.0454114	+	0.00738007i
$731$	1.11485	−	27.6648i	0.0412343	−	1.02322i
$732$	−2.21201	+	18.2175i	−0.0817582	+	0.673339i
$733$	15.0924	+	39.7955i	0.557452	+	1.46988i	0.856756	+	0.515722i	$0.172476\pi$
$733$	15.0924	+	39.7955i	0.557452	+	1.46988i	−0.299305	+	0.954158i	$0.596755\pi$
$734$	−15.8267	−	27.4127i	−0.584175	−	1.01182i
$735$	14.5766	−	25.2474i	0.537666	−	0.931265i
$736$	−5.15847	−	0.838333i	−0.190144	−	0.0309014i
$737$	−0.494297	+	2.42123i	−0.0182077	+	0.0891871i
$738$	−0.0813891	−	0.117912i	−0.00299597	−	0.00434042i
$739$	4.45578	−	15.3831i	0.163909	−	0.565878i	−0.835946	−	0.548812i	$-0.815080\pi$
$739$	4.45578	−	15.3831i	0.163909	−	0.565878i	0.999854	−	0.0170660i	$-0.00543255\pi$
$740$	−1.92448	+	1.44616i	−0.0707455	+	0.0531618i
$741$	−28.7824	−	21.6286i	−1.05735	−	0.794545i
$742$	2.75445	+	9.50946i	0.101119	+	0.349103i
$743$	−8.52973	+	10.4470i	−0.312925	+	0.383264i	−0.906989	−	0.421154i	$-0.861625\pi$
$743$	−8.52973	+	10.4470i	−0.312925	+	0.383264i	0.594064	+	0.804418i	$0.297523\pi$
$744$	−5.38768	−	1.32794i	−0.197522	−	0.0486848i
$745$	11.4856	−	3.83445i	0.420799	−	0.140484i
$746$	0.840385	+	0.358054i	0.0307687	+	0.0131093i
$747$	8.73796	+	18.4149i	0.319705	+	0.673765i
$748$	0.357684	+	0.438083i	0.0130782	+	0.0160179i
$749$	9.75283	−	14.1294i	0.356361	−	0.516277i
$750$	−16.6526	−	17.3372i	−0.608067	−	0.633065i
$751$	7.91963	+	8.24521i	0.288992	+	0.300872i	0.849834	−	0.527051i	$-0.176702\pi$
$751$	7.91963	+	8.24521i	0.288992	+	0.300872i	−0.560842	+	0.827923i	$0.689523\pi$
$752$	6.54733	−	9.48544i	0.238756	−	0.345898i
$753$	29.7417	+	36.4270i	1.08385	+	1.32747i
$754$	−4.93675	−	10.4040i	−0.179786	−	0.378891i
$755$	−32.1062	−	13.6792i	−1.16846	−	0.497836i
$756$	−2.69364	+	0.899269i	−0.0979667	+	0.0327061i
$757$	−27.0152	−	6.65864i	−0.981882	−	0.242012i	−0.284472	−	0.958684i	$-0.591818\pi$
$757$	−27.0152	−	6.65864i	−0.981882	−	0.242012i	−0.697410	+	0.716672i	$0.745664\pi$
$758$	−11.6140	+	14.2246i	−0.421839	+	0.516659i
$759$	−0.783509	−	2.70499i	−0.0284396	−	0.0981848i
$760$	13.8096	+	10.3772i	0.500926	+	0.376422i
$761$	22.7893	−	17.1251i	0.826113	−	0.620784i	−0.101286	−	0.994857i	$-0.532296\pi$
$761$	22.7893	−	17.1251i	0.826113	−	0.620784i	0.927399	+	0.374074i	$0.122039\pi$
$762$	12.1858	−	42.0704i	0.441447	−	1.52405i
$763$	0.613604	+	0.888958i	0.0222139	+	0.0321825i
$764$	3.55450	−	17.4111i	0.128597	−	0.629911i
$765$	−9.09316	−	1.47778i	−0.328764	−	0.0534294i
$766$	11.5864	−	20.0682i	0.418633	−	0.725093i
$767$	−2.30712	−	3.99605i	−0.0833053	−	0.144289i
$768$	−0.774532	−	2.04227i	−0.0279485	−	0.0736941i
$769$	4.08481	−	33.6414i	0.147302	−	1.21314i	−0.712189	−	0.701988i	$-0.752296\pi$
$769$	4.08481	−	33.6414i	0.147302	−	1.21314i	0.859490	−	0.511152i	$-0.170781\pi$
$770$	−0.0238451	+	0.591711i	−0.000859319	+	0.0213238i
$771$	−3.94992	+	0.641925i	−0.142253	+	0.0231184i
$772$	−8.60666	+	22.6939i	−0.309760	+	0.816771i
$773$	−42.6940	−	22.4076i	−1.53560	−	0.805944i	−0.536323	−	0.844013i	$-0.680187\pi$
$773$	−42.6940	−	22.4076i	−1.53560	−	0.805944i	−0.999275	+	0.0380692i	$0.987879\pi$
$774$	−21.3176	+	1.72094i	−0.766246	+	0.0618577i
$775$	0.0460481	+	0.379240i	0.00165410	+	0.0136227i
$776$	−10.0000	+	5.24841i	−0.358979	+	0.188407i
$777$	2.07117	−	1.30973i	0.0743028	−	0.0469862i
$778$	35.2135	−	8.67935i	1.26247	−	0.311170i
$779$	−0.264013	+	0.556395i	−0.00945924	+	0.0199349i
$780$	8.03495	−	7.11835i	0.287697	−	0.254878i
$781$	−0.0304604	+	0.0129780i	−0.00108996	+	0.000464388i
$782$	−8.96754	−	7.94454i	−0.320678	−	0.284096i
$783$	−13.5427	−	4.52121i	−0.483976	−	0.161575i
$784$	4.97081	+	3.14335i	0.177529	+	0.112262i
$785$	31.1502	+	2.51470i	1.11180	+	0.0897536i
$786$	−0.759265	−	18.8410i	−0.0270821	−	0.672035i
$787$	6.76122	+	33.1186i	0.241011	+	1.18055i	0.902531	+	0.430624i	$0.141707\pi$
$787$	6.76122	+	33.1186i	0.241011	+	1.18055i	−0.661520	+	0.749927i	$0.730088\pi$
$788$	−17.6692	+	18.3956i	−0.629441	+	0.655317i
$789$	−37.4118			−1.33190
$790$	−20.0867	+	1.84520i	−0.714652	+	0.0656494i
$791$	−20.2257			−0.719144
$792$	0.302626	−	0.315067i	0.0107534	−	0.0111954i
$793$	−3.63940	−	17.8270i	−0.129239	−	0.633055i
$794$	0.781224	+	19.3859i	0.0277246	+	0.687979i
$795$	−46.2482	−	3.73354i	−1.64025	−	0.132415i
$796$	−10.5484	−	6.67040i	−0.373878	−	0.236426i
$797$	−53.1171	−	17.7331i	−1.88150	−	0.628139i	−0.981238	−	0.192800i	$-0.938243\pi$
$797$	−53.1171	−	17.7331i	−1.88150	−	0.628139i	−0.900267	−	0.435338i	$-0.856629\pi$
$798$	−13.1621	−	11.6606i	−0.465933	−	0.412781i
$799$	24.3073	−	10.3564i	0.859932	−	0.366383i
$800$	−0.112558	+	0.0997177i	−0.00397953	+	0.00352555i
$801$	3.69080	−	7.77820i	0.130408	−	0.274829i
$802$	−34.9221	+	8.60753i	−1.23314	+	0.303943i
$803$	0.114210	−	0.0722222i	0.00403039	−	0.00254867i
$804$	19.3723	−	10.1674i	0.683208	−	0.358575i
$805$	−1.51210	−	12.4532i	−0.0532944	−	0.438919i
$806$	5.48372	−	0.442692i	0.193156	−	0.0155931i
$807$	−5.71858	−	3.00134i	−0.201304	−	0.105652i
$808$	−1.56401	+	4.12395i	−0.0550215	+	0.145080i
$809$	1.60940	−	0.261552i	0.0565834	−	0.00919569i	−0.132054	−	0.991243i	$-0.542157\pi$
$809$	1.60940	−	0.261552i	0.0565834	−	0.00919569i	0.188637	+	0.982047i	$0.439593\pi$
$810$	1.02134	−	25.3443i	0.0358862	−	0.890507i
$811$	2.92723	−	24.1079i	0.102789	−	0.846542i	−0.846555	−	0.532302i	$-0.821327\pi$
$811$	2.92723	−	24.1079i	0.102789	−	0.846542i	0.949344	−	0.314240i	$-0.101750\pi$
$812$	−1.99447	−	5.25899i	−0.0699922	−	0.184554i
$813$	23.4634	+	40.6399i	0.822899	+	1.42530i
$814$	0.130846	−	0.226632i	0.00458615	−	0.00794345i
$815$	−27.1944	−	4.41952i	−0.952579	−	0.154809i
$816$	1.00155	−	4.90593i	0.0350613	−	0.171742i
$817$	52.2225	+	75.6573i	1.82703	+	2.64691i
$818$	−0.489134	+	1.68869i	−0.0171022	+	0.0590436i
$819$	−3.24251	+	2.43659i	−0.113302	+	0.0851412i
$820$	−0.146795	−	0.110310i	−0.00512632	−	0.00385218i
$821$	−6.73408	−	23.2488i	−0.235021	−	0.811387i	−0.988147	−	0.153511i	$-0.950942\pi$
$821$	−6.73408	−	23.2488i	−0.235021	−	0.811387i	0.753126	−	0.657877i	$-0.228545\pi$
$822$	−12.1909	+	14.9312i	−0.425208	+	0.520785i
$823$	29.4376	+	7.25573i	1.02613	+	0.252919i	0.716241	−	0.697853i	$-0.245861\pi$
$823$	29.4376	+	7.25573i	1.02613	+	0.252919i	0.309891	+	0.950772i	$0.399707\pi$
$824$	−0.309149	+	0.103209i	−0.0107697	+	0.00359546i
$825$	−0.0745477	−	0.0317618i	−0.00259542	−	0.00110580i
$826$	−0.966126	−	2.03607i	−0.0336158	−	0.0708439i
$827$	−24.4259	−	29.9163i	−0.849372	−	1.04029i	−0.998673	−	0.0515005i	$-0.983600\pi$
$827$	−24.4259	−	29.9163i	−0.849372	−	1.04029i	0.149301	−	0.988792i	$-0.452298\pi$
$828$	−5.25706	+	7.61616i	−0.182695	+	0.264680i
$829$	−22.8028	−	23.7402i	−0.791973	−	0.824531i	0.195765	−	0.980651i	$-0.437281\pi$
$829$	−22.8028	−	23.7402i	−0.791973	−	0.824531i	−0.987738	+	0.156120i	$0.950101\pi$
$830$	18.0959	+	18.8399i	0.628119	+	0.653941i
$831$	−34.2363	+	49.5998i	−1.18764	+	1.72060i
$832$	1.36960	+	1.67746i	0.0474824	+	0.0581554i
$833$	5.77978	+	12.1806i	0.200258	+	0.422034i
$834$	15.0971	+	6.43227i	0.522769	+	0.222731i
$835$	−23.6949	+	7.91053i	−0.819997	+	0.273755i
$836$	−1.82327	−	0.449395i	−0.0630590	−	0.0155426i
$837$	4.31384	−	5.28349i	0.149108	−	0.182624i
$838$	2.29219	+	7.91357i	0.0791825	+	0.273370i
$839$	−7.48987	−	5.62827i	−0.258579	−	0.194309i	0.463545	−	0.886074i	$-0.346577\pi$
$839$	−7.48987	−	5.62827i	−0.258579	−	0.194309i	−0.722124	+	0.691764i	$0.756834\pi$
$840$	4.19141	−	3.14964i	0.144617	−	0.108673i
$841$	−0.200885	+	0.693536i	−0.00692707	+	0.0239150i
$842$	4.21526	+	6.10686i	0.145267	+	0.210456i
$843$	14.1968	−	69.5408i	0.488965	−	2.39511i
$844$	−14.7848	−	2.40276i	−0.508914	−	0.0827065i
$845$	9.42991	−	16.3331i	0.324399	−	0.561875i
$846$	−10.2047	−	17.6750i	−0.350844	−	0.607679i
$847$	4.10286	+	10.8184i	0.140976	+	0.371723i
$848$	1.12826	−	9.29208i	0.0387447	−	0.319091i
$849$	−0.643355	+	15.9647i	−0.0220799	+	0.547907i
$850$	−0.340260	+	0.0552976i	−0.0116708	+	0.00189669i
$851$	−1.96578	+	5.18333i	−0.0673860	+	0.177682i
$852$	0.259559	+	0.136227i	0.00889234	+	0.00466706i
$853$	18.6438	−	1.50508i	0.638352	−	0.0515331i	0.242946	−	0.970040i	$-0.421886\pi$
$853$	18.6438	−	1.50508i	0.638352	−	0.0515331i	0.395406	+	0.918507i	$0.370604\pi$
$854$	−1.07115	−	8.82174i	−0.0366541	−	0.301874i
$855$	27.0846	−	14.2151i	0.926275	−	0.486147i
$856$	−13.7192	+	8.67548i	−0.468912	+	0.296522i
$857$	41.8784	−	10.3221i	1.43054	−	0.352596i	0.553433	−	0.832893i	$-0.313317\pi$
$857$	41.8784	−	10.3221i	1.43054	−	0.352596i	0.877106	+	0.480297i	$0.159471\pi$
$858$	−0.500259	+	1.05427i	−0.0170786	+	0.0359923i
$859$	−7.03612	+	6.23346i	−0.240069	+	0.212683i	−0.774575	−	0.632482i	$-0.782036\pi$
$859$	−7.03612	+	6.23346i	−0.240069	+	0.212683i	0.534506	+	0.845165i	$0.320498\pi$
$860$	−25.2164	+	10.7437i	−0.859873	+	0.366358i
$861$	0.139913	+	0.123952i	0.00476821	+	0.00422427i
$862$	−6.02321	−	2.01084i	−0.205151	−	0.0684895i
$863$	5.69238	+	3.59964i	0.193771	+	0.122533i	0.627828	−	0.778352i	$-0.283944\pi$
$863$	5.69238	+	3.59964i	0.193771	+	0.122533i	−0.434057	+	0.900885i	$0.642918\pi$
$864$	2.67618	+	0.216044i	0.0910456	+	0.00734996i
$865$	−1.61404	−	40.0519i	−0.0548789	−	1.36181i
$866$	−3.67708	−	18.0115i	−0.124952	−	0.612057i
$867$	−17.7706	+	18.5011i	−0.603521	+	0.628332i
$868$	2.68704			0.0912039
$869$	1.93024	−	1.04043i	0.0654788	−	0.0352943i
$870$	26.3595			0.893672
$871$	−15.0263	+	15.6440i	−0.509146	+	0.530077i
$872$	−0.204276	−	1.00061i	−0.00691765	−	0.0338849i
$873$	0.805256	+	19.9822i	0.0272538	+	0.676296i
$874$	39.6502	+	3.20089i	1.34119	+	0.108272i
$875$	9.83878	+	6.22166i	0.332611	+	0.210331i
$876$	−1.13479	−	0.378849i	−0.0383410	−	0.0128001i
$877$	11.9102	+	10.5515i	0.402177	+	0.356298i	0.839833	−	0.542845i	$-0.182653\pi$
$877$	11.9102	+	10.5515i	0.402177	+	0.356298i	−0.437656	+	0.899143i	$0.644191\pi$
$878$	−23.7817	+	10.1324i	−0.802595	+	0.341954i
$879$	21.5876	−	19.1250i	0.728133	−	0.645070i
$880$	0.240021	−	0.505833i	0.00809109	−	0.0170516i
$881$	19.8145	−	4.88383i	0.667567	−	0.164541i	0.109054	−	0.994036i	$-0.465218\pi$
$881$	19.8145	−	4.88383i	0.667567	−	0.164541i	0.558514	+	0.829495i	$0.311372\pi$
$882$	8.80217	−	5.56616i	0.296385	−	0.187422i
$883$	28.3438	−	14.8760i	0.953845	−	0.500616i	0.0853697	−	0.996349i	$-0.472793\pi$
$883$	28.3438	−	14.8760i	0.953845	−	0.500616i	0.868475	+	0.495733i	$0.165101\pi$
$884$	0.598389	+	4.92818i	0.0201260	+	0.165753i
$885$	10.5277	−	0.849881i	0.353884	−	0.0285684i
$886$	−15.4515	−	8.10957i	−0.519103	−	0.272446i
$887$	−9.51772	+	25.0962i	−0.319574	+	0.842646i	0.674924	+	0.737887i	$0.264176\pi$
$887$	−9.51772	+	25.0962i	−0.319574	+	0.842646i	−0.994498	+	0.104759i	$0.966593\pi$
$888$	−2.28687	+	0.371652i	−0.0767423	+	0.0124718i
$889$	−0.854032	+	21.1926i	−0.0286433	+	0.710776i
$890$	1.33000	−	10.9535i	0.0445816	−	0.367163i
$891$	0.977779	+	2.57819i	0.0327568	+	0.0863727i
$892$	7.10681	+	12.3094i	0.237954	+	0.412148i
$893$	−43.8641	+	75.9749i	−1.46786	+	2.54240i
$894$	11.5031	+	1.86943i	0.384720	+	0.0625231i
$895$	−2.10607	+	10.3162i	−0.0703981	+	0.344833i
$896$	0.600837	+	0.870463i	0.0200726	+	0.0290801i
$897$	6.87752	−	23.7440i	0.229634	−	0.792788i
$898$	3.42819	−	2.57612i	0.114400	−	0.0859661i
$899$	10.8000	+	8.11571i	0.360202	+	0.270674i
$900$	0.0740843	+	0.255769i	0.00246948	+	0.00852562i
$901$	13.5709	−	16.6213i	0.452111	−	0.553735i
$902$	0.0193813	+	0.00477705i	0.000645325	+	0.000159058i
$903$	26.4663	−	8.83576i	0.880744	−	0.294036i
$904$	17.5923	+	7.49538i	0.585111	+	0.249293i
$905$	−4.66266	−	9.82635i	−0.154992	−	0.326639i
$906$	−21.2427	−	26.0175i	−0.705740	−	0.864374i
$907$	3.31374	−	4.80078i	0.110031	−	0.159407i	−0.764100	−	0.645098i	$-0.776817\pi$
$907$	3.31374	−	4.80078i	0.110031	−	0.159407i	0.874131	+	0.485691i	$0.161432\pi$
$908$	−0.209134	−	0.217732i	−0.00694037	−	0.00722569i
$909$	5.41025	+	5.63267i	0.179447	+	0.186824i
$910$	−2.95289	+	4.27801i	−0.0978875	+	0.141815i
$911$	−10.8778	−	13.3229i	−0.360397	−	0.441406i	0.562299	−	0.826934i	$-0.309917\pi$
$911$	−10.8778	−	13.3229i	−0.360397	−	0.441406i	−0.922696	+	0.385527i	$0.874020\pi$
$912$	7.12712	+	15.0201i	0.236002	+	0.497365i
$913$	−2.61254	−	1.11310i	−0.0864624	−	0.0368382i
$914$	−35.3390	+	11.7979i	−1.16891	+	0.390239i
$915$	40.4371	+	9.96685i	1.33681	+	0.329494i
$916$	−10.3248	+	12.6456i	−0.341141	+	0.417822i
$917$	2.54042	+	8.77053i	0.0838919	+	0.289629i
$918$	4.92047	+	3.69750i	0.162400	+	0.122036i
$919$	−20.6242	+	15.4981i	−0.680330	+	0.511235i	−0.883811	−	0.467844i	$-0.845031\pi$
$919$	−20.6242	+	15.4981i	−0.680330	+	0.511235i	0.203481	+	0.979079i	$0.434774\pi$
$920$	−3.29979	+	11.3922i	−0.108791	+	0.375589i
$921$	13.6759	+	19.8130i	0.450637	+	0.652860i
$922$	−3.78018	+	18.5165i	−0.124494	+	0.609810i
$923$	−0.286870	−	0.0466209i	−0.00944244	−	0.00153455i
$924$	−0.284975	+	0.493591i	−0.00937499	+	0.0162380i
$925$	0.0797547	+	0.138139i	0.00262232	+	0.00454199i
$926$	7.34855	+	19.3765i	0.241488	+	0.636752i
$927$	−0.0695659	+	0.572927i	−0.00228484	+	0.0188174i
$928$	−0.214122	+	5.31339i	−0.00702891	+	0.174421i
$929$	50.8072	−	8.25698i	1.66693	−	0.270903i	0.747531	−	0.664227i	$-0.231239\pi$
$929$	50.8072	−	8.25698i	1.66693	−	0.270903i	0.919400	+	0.393324i	$0.128675\pi$
$930$	−4.46553	+	11.7746i	−0.146430	+	0.386105i
$931$	−39.6381	−	20.8037i	−1.29909	−	0.681813i
$932$	4.69814	−	0.379273i	0.153893	−	0.0124235i
$933$	1.35358	+	11.1477i	0.0443141	+	0.364960i
$934$	2.37253	−	1.24520i	0.0776317	−	0.0407443i
$935$	1.08480	−	0.685987i	0.0354768	−	0.0224342i
$936$	3.72330	−	0.917710i	0.121700	−	0.0299963i
$937$	14.6378	−	30.8486i	0.478197	−	1.00778i	−0.510781	−	0.859711i	$-0.670644\pi$
$937$	14.6378	−	30.8486i	0.478197	−	1.00778i	0.988977	−	0.148067i	$-0.0473052\pi$
$938$	−7.93006	+	7.02542i	−0.258926	+	0.229388i
$939$	35.1086	−	14.9584i	1.14573	−	0.488149i
$940$	−19.5787	−	17.3452i	−0.638586	−	0.565738i
$941$	−23.7970	−	7.94460i	−0.775759	−	0.258987i	−0.0988985	−	0.995098i	$-0.531532\pi$
$941$	−23.7970	−	7.94460i	−0.775759	−	0.258987i	−0.676861	+	0.736111i	$0.736660\pi$
$942$	25.4215	+	16.0756i	0.828276	+	0.523770i
$943$	−0.421480	−	0.0340254i	−0.0137253	−	0.00110802i
$944$	0.0857959	+	2.12900i	0.00279242	+	0.0692932i
$945$	1.28911	+	6.31449i	0.0419348	+	0.205410i
$946$	2.06409	−	2.14895i	0.0671095	−	0.0698684i
$947$	38.8954			1.26393			0.631965	−	0.774997i	$-0.282249\pi$
$947$	38.8954			1.26393			0.631965	+	0.774997i	$0.282249\pi$
$948$	−17.9432	−	7.41168i	−0.582768	−	0.240720i
$949$	1.18615			0.0385040
$950$	0.792889	−	0.825485i	0.0257247	−	0.0267823i
$951$	−3.09400	−	15.1554i	−0.100330	−	0.491447i
$952$	0.0976316	+	2.42270i	0.00316426	+	0.0785202i
$953$	−7.64892	−	0.617485i	−0.247773	−	0.0200023i	−0.0440438	−	0.999030i	$-0.514024\pi$
$953$	−7.64892	−	0.617485i	−0.247773	−	0.0200023i	−0.203729	+	0.979027i	$0.565306\pi$
$954$	−14.0090	−	8.85878i	−0.453560	−	0.286814i
$955$	−38.2530	−	12.7707i	−1.23784	−	0.413251i
$956$	7.34030	+	6.50294i	0.237402	+	0.210320i
$957$	−2.63621	+	1.12318i	−0.0852165	+	0.0363074i
$958$	−4.52884	+	4.01220i	−0.146320	+	0.129628i
$959$	4.00152	−	8.43302i	0.129216	−	0.272316i
$960$	−4.81290	+	1.18627i	−0.155336	+	0.0382868i
$961$	20.7460	−	13.1190i	0.669227	−	0.423194i
$962$	2.03398	−	1.06751i	0.0655780	−	0.0344180i
$963$	3.46462	+	28.5337i	0.111646	+	0.919486i
$964$	−16.4432	+	1.32743i	−0.529601	+	0.0427538i
$965$	48.7726	+	25.5979i	1.57005	+	0.824024i
$966$	4.28134	−	11.2890i	0.137750	−	0.363217i
$967$	5.51373	−	0.896068i	0.177309	−	0.0288156i	−0.0711082	−	0.997469i	$-0.522654\pi$
$967$	5.51373	−	0.896068i	0.177309	−	0.0288156i	0.248418	+	0.968653i	$0.420089\pi$
$968$	0.440475	−	10.9303i	0.0141574	−	0.351312i
$969$	−4.59389	+	37.8341i	−0.147577	+	1.21541i
$970$	9.08861	+	23.9647i	0.291818	+	0.769460i
$971$	−26.7950	−	46.4102i	−0.859891	−	1.48937i	−0.872032	−	0.489448i	$-0.837198\pi$
$971$	−26.7950	−	46.4102i	−0.859891	−	1.48937i	0.0121414	−	0.999926i	$-0.496135\pi$
$972$	8.17878	−	14.1661i	0.262334	−	0.454376i
$973$	−7.84366	−	1.27472i	−0.251456	−	0.0408656i
$974$	−5.07649	+	24.8663i	−0.162661	+	0.796767i
$975$	−0.404057	−	0.585377i	−0.0129402	−	0.0187471i
$976$	−2.33753	+	8.07009i	−0.0748226	+	0.258317i
$977$	40.2802	−	30.2686i	1.28868	−	0.968378i	0.288737	−	0.957409i	$-0.406765\pi$
$977$	40.2802	−	30.2686i	1.28868	−	0.968378i	0.999940	−	0.0109691i	$-0.00349163\pi$
$978$	−21.1984	−	15.9296i	−0.677850	−	0.509371i
$979$	0.333718	+	1.15213i	0.0106657	+	0.0368222i
$980$	8.44141	−	10.3388i	0.269651	−	0.330262i
$981$	−1.75585	−	0.432778i	−0.0560599	−	0.0138175i
$982$	−3.51796	+	1.17447i	−0.112263	+	0.0374788i
$983$	−30.3230	−	12.9194i	−0.967152	−	0.412065i	−0.150127	−	0.988667i	$-0.547968\pi$
$983$	−30.3230	−	12.9194i	−0.967152	−	0.412065i	−0.817025	+	0.576602i	$0.804378\pi$
$984$	−0.0757610	−	0.159663i	−0.00241517	−	0.00508987i
$985$	36.6100	+	44.8391i	1.16649	+	1.42869i
$986$	−6.92493	+	10.0325i	−0.220535	+	0.319499i
$987$	18.4451	+	19.2033i	0.587113	+	0.611249i
$988$	−11.4184	−	11.8878i	−0.363268	−	0.378202i
$989$	−35.8563	+	51.9469i	−1.14016	+	1.65181i
$990$	−0.627030	−	0.767973i	−0.0199283	−	0.0244078i
$991$	11.8862	+	25.0496i	0.377577	+	0.795726i	0.999916	+	0.0129780i	$0.00413115\pi$
$991$	11.8862	+	25.0496i	0.377577	+	0.795726i	−0.622339	+	0.782748i	$0.713818\pi$
$992$	−2.33718	−	0.995780i	−0.0742056	−	0.0316160i
$993$	12.4255	−	4.14822i	0.394310	−	0.131640i
$994$	−0.137825	−	0.0339707i	−0.00437153	−	0.00107749i
$995$	−17.9133	+	21.9398i	−0.567888	+	0.695537i
$996$	6.99488	+	24.1491i	0.221641	+	0.765194i
$997$	33.6431	+	25.2812i	1.06549	+	0.800662i	0.980657	−	0.195733i	$-0.0627086\pi$
$997$	33.6431	+	25.2812i	1.06549	+	0.800662i	0.0848307	+	0.996395i	$0.472965\pi$
$998$	−29.4786	+	22.1517i	−0.933127	+	0.701200i
$999$	0.792352	−	2.73552i	0.0250689	−	0.0865479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	158.2.g.b.13.1	✓	72
79.73	even	39	inner	158.2.g.b.73.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.g.b.13.1	✓	72	1.1	even	1	trivial
158.2.g.b.73.1	yes	72	79.73	even	39	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:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.g (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.692724 - 0.721202i) q^{2} +(-0.436898 - 2.14007i) q^{3} +(-0.0402659 - 0.999189i) q^{4} +(-2.26208 - 0.182614i) q^{5} +(-1.84607 - 1.16739i) q^{6} +(1.00326 + 0.334937i) q^{7} +(-0.748511 - 0.663123i) q^{8} +(-1.62908 + 0.694084i) q^{9} +(-1.69870 + 1.50492i) q^{10} +(0.105762 - 0.222888i) q^{11} +(-2.12074 + 0.522716i) q^{12} +(1.83032 - 1.15742i) q^{13} +(0.936540 - 0.491534i) q^{14} +(0.597493 + 4.92080i) q^{15} +(-0.996757 + 0.0804666i) q^{16} +(-2.02983 - 1.06534i) q^{17} +(-0.627925 + 1.65570i) q^{18} +(7.51299 - 1.22098i) q^{19} +(-0.0913813 + 2.26760i) q^{20} +(0.278466 - 2.29338i) q^{21} +(-0.0874838 - 0.230676i) q^{22} +(2.61308 + 4.52598i) q^{23} +(-1.09211 + 1.89158i) q^{24} +(0.148429 + 0.0241220i) q^{25} +(0.433169 - 2.12180i) q^{26} +(-1.52519 - 2.20962i) q^{27} +(0.294268 - 1.01593i) q^{28} +(4.25120 - 3.19457i) q^{29} +(3.96279 + 2.97784i) q^{30} +(0.706804 + 2.44017i) q^{31} +(-0.632445 + 0.774605i) q^{32} +(-0.523204 - 0.128958i) q^{33} +(-2.17444 + 0.725935i) q^{34} +(-2.20829 - 0.940866i) q^{35} +(0.759117 + 1.59981i) q^{36} +(0.670858 + 0.821652i) q^{37} +(4.32386 - 6.26419i) q^{38} +(-3.27662 - 3.41132i) q^{39} +(1.57210 + 1.63673i) q^{40} +(-0.0459625 + 0.0665881i) q^{41} +(-1.46109 - 1.78951i) q^{42} +(5.17764 + 10.9116i) q^{43} +(-0.226966 - 0.0967013i) q^{44} +(3.81186 - 1.27258i) q^{45} +(5.07429 + 1.25070i) q^{46} +(-7.28935 + 8.92784i) q^{47} +(0.607685 + 2.09797i) q^{48} +(-4.70175 - 3.53314i) q^{49} +(0.120217 - 0.0903372i) q^{50} +(-1.39307 + 4.80943i) q^{51} +(-1.23018 - 1.78223i) q^{52} +(-1.87231 + 9.17116i) q^{53} +(-2.65012 - 0.430686i) q^{54} +(-0.279945 + 0.484879i) q^{55} +(-0.528846 - 0.915988i) q^{56} +(-5.89539 - 15.5449i) q^{57} +(0.640978 - 5.27893i) q^{58} +(0.0857959 - 2.12900i) q^{59} +(4.89275 - 0.795149i) q^{60} +(2.97932 - 7.85583i) q^{61} +(2.24948 + 1.18062i) q^{62} +(-1.86686 + 0.150708i) q^{63} +(0.120537 + 0.992709i) q^{64} +(-4.35169 + 2.28394i) q^{65} +(-0.455441 + 0.288003i) q^{66} +(-9.72551 + 2.39712i) q^{67} +(-0.982741 + 2.07108i) q^{68} +(8.54426 - 7.56955i) q^{69} +(-2.20829 + 0.940866i) q^{70} +(-0.100455 - 0.0889956i) q^{71} +(1.67964 + 0.560747i) q^{72} +(0.462937 + 0.292744i) q^{73} +(1.05730 + 0.0853538i) q^{74} +(-0.0132255 - 0.328186i) q^{75} +(-1.52251 - 7.45773i) q^{76} +(0.180760 - 0.188191i) q^{77} -4.73005 q^{78} +(7.16418 + 5.26066i) q^{79} +2.26944 q^{80} +(-7.74236 + 8.06065i) q^{81} +(0.0161842 + 0.0792755i) q^{82} +(-0.463489 - 11.5014i) q^{83} +(-2.30273 - 0.185896i) q^{84} +(4.39711 + 2.78056i) q^{85} +(11.4562 + 3.82464i) q^{86} +(-8.69394 - 7.70216i) q^{87} +(-0.226966 + 0.0967013i) q^{88} +(-3.63923 + 3.22408i) q^{89} +(1.72277 - 3.63067i) q^{90} +(2.22394 - 0.548153i) q^{91} +(4.41709 - 2.79320i) q^{92} +(4.91333 - 2.57871i) q^{93} +(1.38927 + 11.4416i) q^{94} +(-17.2180 + 1.38998i) q^{95} +(1.93402 + 1.01505i) q^{96} +(4.00477 - 10.5597i) q^{97} +(-5.80513 + 0.943425i) q^{98} +(-0.0175907 + 0.436510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{2} + q^{3} + 3 q^{4} - 14 q^{5} + q^{6} - 6 q^{8} + 2 q^{9} + 2 q^{10} + 5 q^{11} - 2 q^{12} - 21 q^{13} - 13 q^{14} - 4 q^{15} + 3 q^{16} + 30 q^{17} - 4 q^{18} - 26 q^{19} - q^{20} - 8 q^{21}+ \cdots - 44 q^{99}+O(q^{100}) \) 72 * q + 3 * q^2 + q^3 + 3 * q^4 - 14 * q^5 + q^6 - 6 * q^8 + 2 * q^9 + 2 * q^10 + 5 * q^11 - 2 * q^12 - 21 * q^13 - 13 * q^14 - 4 * q^15 + 3 * q^16 + 30 * q^17 - 4 * q^18 - 26 * q^19 - q^20 - 8 * q^21 - 23 * q^22 - 5 * q^23 - 12 * q^24 - 17 * q^25 + 31 * q^26 - 59 * q^27 - 2 * q^29 - 37 * q^30 - 19 * q^31 + 3 * q^32 + 76 * q^33 + 11 * q^34 - 17 * q^35 + 2 * q^36 - 19 * q^37 - 12 * q^39 - q^40 + 18 * q^41 + 17 * q^42 - 29 * q^43 - 21 * q^44 - 65 * q^45 - 16 * q^46 - 17 * q^47 + q^48 - 23 * q^49 - 30 * q^50 - 45 * q^51 - 10 * q^52 + 60 * q^53 - 29 * q^54 - 14 * q^55 - 26 * q^56 - 52 * q^57 + 4 * q^58 - 14 * q^59 + 67 * q^60 - 33 * q^61 + 51 * q^62 - 33 * q^63 - 6 * q^64 + 28 * q^65 + 40 * q^66 - 2 * q^67 + 37 * q^68 + 172 * q^69 - 17 * q^70 + 54 * q^71 + 2 * q^72 - 91 * q^73 + 59 * q^74 + 115 * q^75 + 39 * q^76 - 98 * q^77 + 24 * q^78 + 152 * q^79 + 2 * q^80 + 77 * q^81 + 4 * q^82 - 82 * q^83 - 9 * q^84 + 175 * q^85 + 49 * q^86 + 21 * q^87 - 21 * q^88 + 74 * q^89 - 39 * q^90 + 53 * q^91 + 21 * q^92 + 8 * q^93 + 112 * q^94 - 2 * q^96 + 34 * q^97 + 16 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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