LMFDB - Embedded newform 558.2.bb.b.103.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(7,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 28])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.bb (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,16] 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:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	558.103
Dual form			558.2.bb.b.493.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.104528 + 0.994522i) q^{2} +(0.100069 + 1.72916i) q^{3} +(-0.978148 - 0.207912i) q^{4} +2.97916 q^{5} +(-1.73015 - 0.0812257i) q^{6} +(0.990529 + 3.04854i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.97997 + 0.346069i) q^{9} +(-0.311407 + 2.96284i) q^{10} +(-3.53963 - 0.752371i) q^{11} +(0.261630 - 1.71218i) q^{12} +(1.13523 - 0.824795i) q^{13} +(-3.13537 + 0.666444i) q^{14} +(0.298121 + 5.15144i) q^{15} +(0.913545 + 0.406737i) q^{16} +(4.08183 + 4.53333i) q^{17} +(-0.0326812 - 2.99982i) q^{18} +(-0.408444 + 0.181851i) q^{19} +(-2.91406 - 0.619403i) q^{20} +(-5.17228 + 2.01784i) q^{21} +(1.11824 - 3.44159i) q^{22} +(2.57514 + 2.85998i) q^{23} +(1.67545 + 0.439168i) q^{24} +3.87541 q^{25} +(0.701612 + 1.21523i) q^{26} +(-0.896610 - 5.11821i) q^{27} +(-0.335058 - 3.18786i) q^{28} +(0.523378 - 4.97961i) q^{29} +(-5.15438 - 0.241985i) q^{30} +(-4.92770 + 2.59186i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.946763 - 6.19586i) q^{33} +(-4.93517 + 3.58561i) q^{34} +(2.95095 + 9.08208i) q^{35} +(2.98680 + 0.281065i) q^{36} +(0.215578 - 0.373392i) q^{37} +(-0.138161 - 0.425215i) q^{38} +(1.53980 + 1.88046i) q^{39} +(0.920612 - 2.83335i) q^{40} +(-3.81891 - 2.77460i) q^{41} +(-1.46614 - 5.35487i) q^{42} +(-7.26489 - 5.27825i) q^{43} +(3.30585 + 1.47186i) q^{44} +(-8.87782 + 1.03100i) q^{45} +(-3.11349 + 2.26208i) q^{46} +(9.67057 + 4.30562i) q^{47} +(-0.611895 + 1.62037i) q^{48} +(-2.64931 + 1.92483i) q^{49} +(-0.405091 + 3.85418i) q^{50} +(-7.43038 + 7.51178i) q^{51} +(-1.28191 + 0.570743i) q^{52} +(6.98081 - 1.48382i) q^{53} +(5.18389 - 0.356699i) q^{54} +(-10.5451 - 2.24144i) q^{55} +3.20542 q^{56} +(-0.355322 - 0.688067i) q^{57} +(4.89762 + 1.04102i) q^{58} +(-8.80227 - 3.91903i) q^{59} +(0.779439 - 5.10085i) q^{60} +(1.04198 + 1.80477i) q^{61} +(-2.06258 - 5.17163i) q^{62} +(-4.00675 - 8.74176i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.38204 - 2.45720i) q^{65} +(6.06296 + 1.58922i) q^{66} -12.0679 q^{67} +(-3.05010 - 5.28293i) q^{68} +(-4.68767 + 4.73901i) q^{69} +(-9.34079 + 1.98545i) q^{70} +(13.4957 - 2.86860i) q^{71} +(-0.591731 + 2.94106i) q^{72} +(6.34935 - 7.05167i) q^{73} +(0.348812 + 0.253427i) q^{74} +(0.387807 + 6.70119i) q^{75} +(0.437328 - 0.0929568i) q^{76} +(-1.21248 - 11.5359i) q^{77} +(-2.03111 + 1.33480i) q^{78} +(-2.28103 + 7.02029i) q^{79} +(2.72160 + 1.21173i) q^{80} +(8.76047 - 2.06255i) q^{81} +(3.15859 - 3.50797i) q^{82} +(7.31296 - 3.25594i) q^{83} +(5.47879 - 0.898373i) q^{84} +(12.1604 + 13.5055i) q^{85} +(6.00872 - 6.67337i) q^{86} +(8.66290 + 0.406700i) q^{87} +(-1.80935 + 3.13389i) q^{88} +(-1.63278 - 5.02519i) q^{89} +(-0.0973627 - 8.93696i) q^{90} +(3.63890 + 2.64381i) q^{91} +(-1.92424 - 3.33288i) q^{92} +(-4.97484 - 8.26141i) q^{93} +(-5.29288 + 9.16754i) q^{94} +(-1.21682 + 0.541764i) q^{95} +(-1.54753 - 0.777917i) q^{96} +(5.09565 - 5.65929i) q^{97} +(-1.63736 - 2.83599i) q^{98} +(10.8084 + 1.01709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 2 q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 32 q^{8} - 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 20 q^{13} - q^{14} - 22 q^{15} + 16 q^{16} + 4 q^{17} - 2 q^{18} - 4 q^{19} + q^{20}+ \cdots + 15 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 32 * q^8 - 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 - 20 * q^13 - q^14 - 22 * q^15 + 16 * q^16 + 4 * q^17 - 2 * q^18 - 4 * q^19 + q^20 + 19 * q^21 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 122 * q^25 - 20 * q^26 - 37 * q^27 + 9 * q^28 - 12 * q^29 - 14 * q^30 + 25 * q^31 - 64 * q^32 + 22 * q^33 - 8 * q^34 + 6 * q^36 - 66 * q^37 - 12 * q^38 + 11 * q^39 - 2 * q^40 + 20 * q^41 + 10 * q^42 - 31 * q^43 + 2 * q^44 + 64 * q^45 + 13 * q^46 + 11 * q^47 - 3 * q^48 - 46 * q^49 + 19 * q^50 + 17 * q^51 + 10 * q^52 + 27 * q^53 - 13 * q^54 - 19 * q^55 + 2 * q^56 + 20 * q^57 + 3 * q^58 - 9 * q^59 + 11 * q^60 - 57 * q^61 + 14 * q^62 - 38 * q^63 - 32 * q^64 - 66 * q^65 - 20 * q^66 - 16 * q^67 - 16 * q^68 - 8 * q^69 - 7 * q^71 + q^72 - 7 * q^73 - 28 * q^74 + 74 * q^75 + 6 * q^76 + 46 * q^77 - 24 * q^78 - 48 * q^79 - 9 * q^80 - 64 * q^81 + 50 * q^82 - 99 * q^83 + q^84 + 27 * q^85 + 33 * q^86 + 81 * q^87 - 8 * q^88 - 52 * q^89 - 45 * q^90 + 11 * q^91 + q^92 + 30 * q^93 + 6 * q^94 + 19 * q^95 - 4 * q^96 + 35 * q^97 - 77 * q^98 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	0.100069	+	1.72916i	0.0577747	+	0.998330i
$3$	0.100069	+	1.72916i	0.0577747	+	0.998330i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	2.97916			1.33232			0.666161	−	0.745808i	$-0.267936\pi$
$5$	2.97916			1.33232			0.666161	+	0.745808i	$0.267936\pi$
$6$	−1.73015	−	0.0812257i	−0.706329	−	0.0331603i
$7$	0.990529	+	3.04854i	0.374385	+	1.15224i	0.943893	+	0.330252i	$0.107134\pi$
$7$	0.990529	+	3.04854i	0.374385	+	1.15224i	−0.569508	+	0.821986i	$0.692866\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−2.97997	+	0.346069i	−0.993324	+	0.115356i
$10$	−0.311407	+	2.96284i	−0.0984756	+	0.936933i
$11$	−3.53963	−	0.752371i	−1.06724	−	0.226848i	−0.359371	−	0.933195i	$-0.617009\pi$
$11$	−3.53963	−	0.752371i	−1.06724	−	0.226848i	−0.707867	+	0.706346i	$0.750342\pi$
$12$	0.261630	−	1.71218i	0.0755261	−	0.494263i
$13$	1.13523	−	0.824795i	0.314857	−	0.228757i	−0.419121	−	0.907930i	$-0.637662\pi$
$13$	1.13523	−	0.824795i	0.314857	−	0.228757i	0.733978	+	0.679174i	$0.237662\pi$
$14$	−3.13537	+	0.666444i	−0.837964	+	0.178115i
$15$	0.298121	+	5.15144i	0.0769745	+	1.33010i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	4.08183	+	4.53333i	0.989990	+	1.09949i	0.995037	+	0.0995076i	$0.0317268\pi$
$17$	4.08183	+	4.53333i	0.989990	+	1.09949i	−0.00504720	+	0.999987i	$0.501607\pi$
$18$	−0.0326812	−	2.99982i	−0.00770304	−	0.707065i
$19$	−0.408444	+	0.181851i	−0.0937035	+	0.0417195i	−0.453053	−	0.891484i	$-0.649665\pi$
$19$	−0.408444	+	0.181851i	−0.0937035	+	0.0417195i	0.359350	+	0.933203i	$0.382999\pi$
$20$	−2.91406	−	0.619403i	−0.651604	−	0.138503i
$21$	−5.17228	+	2.01784i	−1.12868	+	0.440330i
$22$	1.11824	−	3.44159i	0.238410	−	0.733750i
$23$	2.57514	+	2.85998i	0.536953	+	0.596347i	0.949180	−	0.314734i	$-0.101915\pi$
$23$	2.57514	+	2.85998i	0.536953	+	0.596347i	−0.412226	+	0.911081i	$0.635249\pi$
$24$	1.67545	+	0.439168i	0.342000	+	0.0896448i
$25$	3.87541			0.775082
$26$	0.701612	+	1.21523i	0.137597	+	0.238326i
$27$	−0.896610	−	5.11821i	−0.172553	−	0.985000i
$28$	−0.335058	−	3.18786i	−0.0633200	−	0.602449i
$29$	0.523378	−	4.97961i	0.0971889	−	0.924690i	−0.831923	−	0.554891i	$-0.812760\pi$
$29$	0.523378	−	4.97961i	0.0971889	−	0.924690i	0.929112	−	0.369799i	$-0.120573\pi$
$30$	−5.15438	−	0.241985i	−0.941057	−	0.0441801i
$31$	−4.92770	+	2.59186i	−0.885042	+	0.465512i
$31$	−4.92770	+	2.59186i	−0.885042	+	0.465512i
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.946763	−	6.19586i	0.164810	−	1.07856i
$34$	−4.93517	+	3.58561i	−0.846374	+	0.614927i
$35$	2.95095	+	9.08208i	0.498801	+	1.53515i
$36$	2.98680	+	0.281065i	0.497801	+	0.0468441i
$37$	0.215578	−	0.373392i	0.0354408	−	0.0613852i	−0.847761	−	0.530378i	$-0.822050\pi$
$37$	0.215578	−	0.373392i	0.0354408	−	0.0613852i	0.883202	+	0.468993i	$0.155383\pi$
$38$	−0.138161	−	0.425215i	−0.0224126	−	0.0689790i
$39$	1.53980	+	1.88046i	0.246566	+	0.301115i
$40$	0.920612	−	2.83335i	0.145562	−	0.447992i
$41$	−3.81891	−	2.77460i	−0.596414	−	0.433320i	0.248190	−	0.968711i	$-0.420164\pi$
$41$	−3.81891	−	2.77460i	−0.596414	−	0.433320i	−0.844604	+	0.535391i	$0.820164\pi$
$42$	−1.46614	−	5.35487i	−0.226230	−	0.826274i
$43$	−7.26489	−	5.27825i	−1.10789	−	0.804926i	−0.125556	−	0.992087i	$-0.540072\pi$
$43$	−7.26489	−	5.27825i	−1.10789	−	0.804926i	−0.982329	+	0.187161i	$0.940072\pi$
$44$	3.30585	+	1.47186i	0.498376	+	0.221891i
$45$	−8.87782	+	1.03100i	−1.32343	+	0.153692i
$46$	−3.11349	+	2.26208i	−0.459059	+	0.333526i
$47$	9.67057	+	4.30562i	1.41060	+	0.628039i	0.963807	−	0.266600i	$-0.0859002\pi$
$47$	9.67057	+	4.30562i	1.41060	+	0.628039i	0.446791	+	0.894639i	$0.352567\pi$
$48$	−0.611895	+	1.62037i	−0.0883194	+	0.233880i
$49$	−2.64931	+	1.92483i	−0.378472	+	0.274976i
$50$	−0.405091	+	3.85418i	−0.0572885	+	0.545063i
$51$	−7.43038	+	7.51178i	−1.04046	+	1.05186i
$52$	−1.28191	+	0.570743i	−0.177769	+	0.0791478i
$53$	6.98081	−	1.48382i	0.958889	−	0.203818i	0.298221	−	0.954497i	$-0.403607\pi$
$53$	6.98081	−	1.48382i	0.958889	−	0.203818i	0.660667	+	0.750679i	$0.270273\pi$
$54$	5.18389	−	0.356699i	0.705439	−	0.0485406i
$55$	−10.5451	−	2.24144i	−1.42190	−	0.302235i
$56$	3.20542			0.428342
$57$	−0.355322	−	0.688067i	−0.0470635	−	0.0911367i
$58$	4.89762	+	1.04102i	0.643089	+	0.136693i
$59$	−8.80227	−	3.91903i	−1.14596	−	0.510214i	−0.256190	−	0.966626i	$-0.582467\pi$
$59$	−8.80227	−	3.91903i	−1.14596	−	0.510214i	−0.889768	+	0.456413i	$0.849134\pi$
$60$	0.779439	−	5.10085i	0.100625	−	0.658517i
$61$	1.04198	+	1.80477i	0.133412	+	0.231077i	0.924990	−	0.379992i	$-0.124073\pi$
$61$	1.04198	+	1.80477i	0.133412	+	0.231077i	−0.791577	+	0.611069i	$0.790740\pi$
$62$	−2.06258	−	5.17163i	−0.261947	−	0.656798i
$63$	−4.00675	−	8.74176i	−0.504804	−	1.10136i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.38204	−	2.45720i	0.419491	−	0.304778i
$66$	6.06296	+	1.58922i	0.746299	+	0.195619i
$67$	−12.0679			−1.47433			−0.737165	−	0.675713i	$-0.763836\pi$
$67$	−12.0679			−1.47433			−0.737165	+	0.675713i	$0.763836\pi$
$68$	−3.05010	−	5.28293i	−0.369879	−	0.640649i
$69$	−4.68767	+	4.73901i	−0.564329	+	0.570510i
$70$	−9.34079	+	1.98545i	−1.11644	+	0.237306i
$71$	13.4957	−	2.86860i	1.60165	−	0.340440i	0.681440	−	0.731874i	$-0.261354\pi$
$71$	13.4957	−	2.86860i	1.60165	−	0.340440i	0.920206	+	0.391434i	$0.128021\pi$
$72$	−0.591731	+	2.94106i	−0.0697362	+	0.346608i
$73$	6.34935	−	7.05167i	0.743135	−	0.825335i	−0.246469	−	0.969151i	$-0.579271\pi$
$73$	6.34935	−	7.05167i	0.743135	−	0.825335i	0.989605	+	0.143815i	$0.0459372\pi$
$74$	0.348812	+	0.253427i	0.0405486	+	0.0294603i
$75$	0.387807	+	6.70119i	0.0447801	+	0.773787i
$76$	0.437328	−	0.0929568i	0.0501649	−	0.0106629i
$77$	−1.21248	−	11.5359i	−0.138174	−	1.31464i
$78$	−2.03111	+	1.33480i	−0.229978	+	0.151137i
$79$	−2.28103	+	7.02029i	−0.256636	+	0.789844i	0.736867	+	0.676038i	$0.236304\pi$
$79$	−2.28103	+	7.02029i	−0.256636	+	0.789844i	−0.993503	+	0.113806i	$0.963696\pi$
$80$	2.72160	+	1.21173i	0.304284	+	0.135476i
$81$	8.76047	−	2.06255i	0.973386	−	0.229172i
$82$	3.15859	−	3.50797i	0.348808	−	0.387390i
$83$	7.31296	−	3.25594i	0.802702	−	0.357386i	0.0359696	−	0.999353i	$-0.488548\pi$
$83$	7.31296	−	3.25594i	0.802702	−	0.357386i	0.766732	+	0.641967i	$0.221881\pi$
$84$	5.47879	−	0.898373i	0.597785	−	0.0980205i
$85$	12.1604	+	13.5055i	1.31898	+	1.46488i
$86$	6.00872	−	6.67337i	0.647937	−	0.719607i
$87$	8.66290	+	0.406700i	0.928761	+	0.0436029i
$88$	−1.80935	+	3.13389i	−0.192878	+	0.334074i
$89$	−1.63278	−	5.02519i	−0.173075	−	0.532669i	0.826466	−	0.562987i	$-0.190348\pi$
$89$	−1.63278	−	5.02519i	−0.173075	−	0.532669i	−0.999540	+	0.0303182i	$0.990348\pi$
$90$	−0.0973627	−	8.93696i	−0.0102629	−	0.942038i
$91$	3.63890	+	2.64381i	0.381460	+	0.277147i
$92$	−1.92424	−	3.33288i	−0.200616	−	0.347477i
$93$	−4.97484	−	8.26141i	−0.515867	−	0.856669i
$94$	−5.29288	+	9.16754i	−0.545919	+	0.945559i
$95$	−1.21682	+	0.541764i	−0.124843	+	0.0555838i
$96$	−1.54753	−	0.777917i	−0.157944	−	0.0793958i
$97$	5.09565	−	5.65929i	0.517385	−	0.574614i	−0.426668	−	0.904408i	$-0.640313\pi$
$97$	5.09565	−	5.65929i	0.517385	−	0.574614i	0.944053	+	0.329794i	$0.106979\pi$
$98$	−1.63736	−	2.83599i	−0.165398	−	0.286478i
$99$	10.8084	+	1.01709i	1.08628	+	0.102221i
$100$	−3.79072	−	0.805743i	−0.379072	−	0.0805743i
$101$	6.94458	−	1.47612i	0.691012	−	0.146879i	0.150996	−	0.988534i	$-0.451752\pi$
$101$	6.94458	−	1.47612i	0.691012	−	0.146879i	0.540015	+	0.841655i	$0.318418\pi$
$102$	−6.69394	−	8.17487i	−0.662799	−	0.809433i
$103$	9.06126	+	6.58339i	0.892833	+	0.648681i	0.936615	−	0.350360i	$-0.113941\pi$
$103$	9.06126	+	6.58339i	0.892833	+	0.648681i	−0.0437822	+	0.999041i	$0.513941\pi$
$104$	−0.433620	−	1.33455i	−0.0425200	−	0.130863i
$105$	−15.4091	+	6.01149i	−1.50377	+	0.586661i
$106$	0.745996	+	7.09767i	0.0724575	+	0.689387i
$107$	13.2479	+	14.7132i	1.28072	+	1.42238i	0.855930	+	0.517091i	$0.172985\pi$
$107$	13.2479	+	14.7132i	1.28072	+	1.42238i	0.424789	+	0.905292i	$0.360348\pi$
$108$	−0.187119	+	5.19278i	−0.0180056	+	0.499676i
$109$	−3.43550	+	2.49604i	−0.329061	+	0.239077i	−0.740032	−	0.672571i	$-0.765190\pi$
$109$	−3.43550	+	2.49604i	−0.329061	+	0.239077i	0.410971	+	0.911648i	$0.365190\pi$
$110$	3.33142	−	10.2531i	0.317639	−	0.977592i
$111$	0.667225	+	0.335403i	0.0633302	+	0.0318350i
$112$	−0.335058	+	3.18786i	−0.0316600	+	0.301225i
$113$	5.02836	+	15.4757i	0.473028	+	1.45583i	0.848599	+	0.529037i	$0.177447\pi$
$113$	5.02836	+	15.4757i	0.473028	+	1.45583i	−0.375570	+	0.926794i	$0.622553\pi$
$114$	0.721439	−	0.281453i	0.0675689	−	0.0263604i
$115$	7.67175	+	8.52035i	0.715395	+	0.794526i
$116$	−1.54726	+	4.76198i	−0.143660	+	0.442138i
$117$	−3.09753	+	2.85073i	−0.286366	+	0.263550i
$118$	4.81764	−	8.34441i	0.443500	−	0.768165i
$119$	−9.77686	+	16.9340i	−0.896243	+	1.55234i
$120$	4.99144	+	1.30835i	0.455654	+	0.119436i
$121$	1.91391	+	0.852126i	0.173991	+	0.0774660i
$122$	−1.90380	+	0.847626i	−0.172362	+	0.0767405i
$123$	4.41557	−	6.88115i	0.398139	−	0.620452i
$124$	5.35890	−	1.51069i	0.481243	−	0.135664i
$125$	−3.35034			−0.299663
$126$	9.11269	−	3.07104i	0.811823	−	0.273590i
$127$	0.644566	+	6.13264i	0.0571960	+	0.544183i	0.985175	+	0.171551i	$0.0548780\pi$
$127$	0.644566	+	6.13264i	0.0571960	+	0.544183i	−0.927979	+	0.372632i	$0.878455\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	8.39994	−	13.0903i	0.739574	−	1.15254i
$130$	2.09022	+	3.62036i	0.183324	+	0.317527i
$131$	12.5426	−	13.9300i	1.09586	−	1.21707i	0.121372	−	0.992607i	$-0.461270\pi$
$131$	12.5426	−	13.9300i	1.09586	−	1.21707i	0.974483	−	0.224463i	$-0.0720629\pi$
$132$	−2.21427	+	5.86363i	−0.192727	+	0.510363i
$133$	−0.958955	−	1.06503i	−0.0831520	−	0.0923496i
$134$	1.26144	−	12.0018i	0.108972	−	1.03680i
$135$	−2.67115	−	15.2480i	−0.229896	−	1.31234i
$136$	5.57281	−	2.48118i	0.477865	−	0.212759i
$137$	−1.89593	−	18.0385i	−0.161980	−	1.54114i	−0.709718	−	0.704486i	$-0.751178\pi$
$137$	−1.89593	−	18.0385i	−0.161980	−	1.54114i	0.547738	−	0.836650i	$-0.315489\pi$
$138$	−4.22306	−	5.15735i	−0.359491	−	0.439023i
$139$	−1.34693	−	12.8152i	−0.114245	−	1.08697i	−0.890008	−	0.455945i	$-0.849301\pi$
$139$	−1.34693	−	12.8152i	−0.114245	−	1.08697i	0.775763	−	0.631025i	$-0.217365\pi$
$140$	−0.998191	−	9.49716i	−0.0843626	−	0.802656i
$141$	−6.47737	+	17.1528i	−0.545493	+	1.44453i
$142$	1.44220	+	13.7216i	0.121027	+	1.15149i
$143$	−4.63885	+	2.06535i	−0.387920	+	0.172713i
$144$	−2.86310	−	0.895914i	−0.238592	−	0.0746595i
$145$	1.55923	−	14.8351i	0.129487	−	1.23199i
$146$	6.34935	+	7.05167i	0.525476	+	0.583600i
$147$	−3.59345	−	4.38845i	−0.296383	−	0.361953i
$148$	−0.288499	+	0.320411i	−0.0237145	+	0.0263376i
$149$	10.1796	+	17.6316i	0.833944	+	1.44443i	0.894887	+	0.446293i	$0.147256\pi$
$149$	10.1796	+	17.6316i	0.833944	+	1.44443i	−0.0609424	+	0.998141i	$0.519411\pi$
$150$	−6.70502	−	0.314783i	−0.547463	−	0.0257019i
$151$	1.44955	−	1.60989i	0.117963	−	0.131011i	−0.681271	−	0.732031i	$-0.738572\pi$
$151$	1.44955	−	1.60989i	0.117963	−	0.131011i	0.799234	+	0.601021i	$0.205239\pi$
$152$	0.0467344	+	0.444648i	0.00379066	+	0.0360658i
$153$	−13.7326	−	12.0966i	−1.11021	−	0.977953i
$154$	11.5995			0.934712
$155$	−14.6804	+	7.72157i	−1.17916	+	0.620211i
$156$	−1.11518	−	2.15951i	−0.0892861	−	0.172899i
$157$	0.318467	−	0.141791i	0.0254164	−	0.0113161i	−0.393989	−	0.919115i	$-0.628905\pi$
$157$	0.318467	−	0.141791i	0.0254164	−	0.0113161i	0.419405	+	0.907799i	$0.362239\pi$
$158$	−6.74340	−	3.00235i	−0.536476	−	0.238855i
$159$	3.26432	+	11.9224i	0.258877	+	0.945511i
$160$	−1.48958	+	2.58003i	−0.117762	+	0.203969i
$161$	−6.16800	+	10.6833i	−0.486107	+	0.841962i
$162$	1.13553	+	8.92808i	0.0892160	+	0.701456i
$163$	5.05743	−	15.5652i	0.396128	−	1.21916i	−0.531951	−	0.846775i	$-0.678541\pi$
$163$	5.05743	−	15.5652i	0.396128	−	1.21916i	0.928079	−	0.372382i	$-0.121459\pi$
$164$	3.15859	+	3.50797i	0.246644	+	0.273926i
$165$	2.82056	−	18.4585i	0.219580	−	1.43699i
$166$	2.47369	+	7.61324i	0.191996	+	0.590902i
$167$	−0.474222	+	4.51192i	−0.0366964	+	0.349143i	0.960732	+	0.277477i	$0.0894983\pi$
$167$	−0.474222	+	4.51192i	−0.0366964	+	0.349143i	−0.997429	+	0.0716661i	$0.977168\pi$
$168$	0.320762	+	5.54268i	0.0247473	+	0.427627i
$169$	−3.40875	+	10.4911i	−0.262212	+	0.807005i
$170$	−14.7027	+	10.6821i	−1.12764	+	0.819280i
$171$	1.15422	−	0.683261i	0.0882653	−	0.0522503i
$172$	6.00872	+	6.67337i	0.458161	+	0.508839i
$173$	0.310347	+	2.95275i	0.0235952	+	0.224493i	0.999965	+	0.00838614i	$0.00266942\pi$
$173$	0.310347	+	2.95275i	0.0235952	+	0.224493i	−0.976370	+	0.216107i	$0.930664\pi$
$174$	−1.30999	+	8.57294i	−0.0993103	+	0.649913i
$175$	3.83871	+	11.8143i	0.290179	+	0.893079i
$176$	−2.92759	−	2.12702i	−0.220676	−	0.160330i
$177$	5.89578	−	15.6127i	0.443154	−	1.17352i
$178$	5.16833	−	1.09856i	0.387383	−	0.0823408i
$179$	−5.05100	−	1.07362i	−0.377529	−	0.0802464i	0.0152387	−	0.999884i	$-0.495149\pi$
$179$	−5.05100	−	1.07362i	−0.377529	−	0.0802464i	−0.392768	+	0.919638i	$0.628483\pi$
$180$	8.89818	+	0.837337i	0.663231	+	0.0624114i
$181$	−6.59657	−	11.4256i	−0.490319	−	0.849257i	0.509619	−	0.860400i	$-0.329786\pi$
$181$	−6.59657	−	11.4256i	−0.490319	−	0.849257i	−0.999938	+	0.0111428i	$0.996453\pi$
$182$	−3.00970	+	3.34261i	−0.223094	+	0.247771i
$183$	−3.01646	+	1.98236i	−0.222983	+	0.146540i
$184$	3.51576	−	1.56532i	0.259186	−	0.115397i
$185$	0.642241	−	1.11239i	0.0472185	−	0.0817848i
$186$	8.73617	−	4.08404i	0.640567	−	0.299456i
$187$	−11.0374	−	19.1174i	−0.807136	−	1.39800i
$188$	−8.56406	−	6.22215i	−0.624598	−	0.453797i
$189$	14.7149	−	7.80309i	1.07035	−	0.567591i
$190$	−0.411603	−	1.26679i	−0.0298609	−	0.0919023i
$191$	2.81163	−	4.86989i	0.203443	−	0.352373i	−0.746193	−	0.665730i	$-0.768120\pi$
$191$	2.81163	−	4.86989i	0.203443	−	0.352373i	0.949635	+	0.313357i	$0.101454\pi$
$192$	0.935416	−	1.45774i	0.0675078	−	0.105203i
$193$	−6.99525	+	7.76901i	−0.503529	+	0.559226i	−0.940300	−	0.340347i	$-0.889455\pi$
$193$	−6.99525	+	7.76901i	−0.503529	+	0.559226i	0.436771	+	0.899573i	$0.356122\pi$
$194$	5.09565	+	5.65929i	0.365846	+	0.406314i
$195$	4.58732	+	5.60220i	0.328505	+	0.401182i
$196$	2.99161	−	1.33195i	0.213686	−	0.0951392i
$197$	7.49425	−	8.32320i	0.533943	−	0.593004i	−0.414462	−	0.910067i	$-0.636030\pi$
$197$	7.49425	−	8.32320i	0.533943	−	0.593004i	0.948404	+	0.317063i	$0.102697\pi$
$198$	−2.14130	+	10.6428i	−0.152176	+	0.756354i
$199$	−17.1061	−	7.61612i	−1.21262	−	0.539892i	−0.302066	−	0.953287i	$-0.597676\pi$
$199$	−17.1061	−	7.61612i	−1.21262	−	0.539892i	−0.910552	+	0.413395i	$0.864343\pi$
$200$	1.19757	−	3.68573i	0.0846808	−	0.260621i
$201$	−1.20762	−	20.8673i	−0.0851789	−	1.47187i
$202$	0.742124	+	7.06083i	0.0522156	+	0.496799i
$203$	15.6989	−	3.33691i	1.10185	−	0.234205i
$204$	8.82980	−	5.80276i	0.618210	−	0.406275i
$205$	−11.3772	−	8.26599i	−0.794615	−	0.577322i
$206$	−7.49449	+	8.32347i	−0.522166	+	0.579924i
$207$	−8.66359	−	7.63149i	−0.602161	−	0.530425i
$208$	1.37256	−	0.291747i	0.0951700	−	0.0202290i
$209$	1.58256	−	0.336383i	0.109468	−	0.0232681i
$210$	−4.36787	−	15.9530i	−0.301412	−	1.10086i
$211$	8.51303	+	14.7450i	0.586061	+	1.01509i	0.994742	+	0.102410i	$0.0326554\pi$
$211$	8.51303	+	14.7450i	0.586061	+	1.01509i	−0.408681	+	0.912677i	$0.634011\pi$
$212$	−7.13677			−0.490155
$213$	6.31076	+	23.0492i	0.432406	+	1.57930i
$214$	−16.0174	+	11.6373i	−1.09493	+	0.795512i
$215$	−21.6433	−	15.7248i	−1.47606	−	1.07242i
$216$	−5.14478	−	0.728888i	−0.350058	−	0.0495945i
$217$	−12.7824	−	12.4550i	−0.867727	−	0.845499i
$218$	−2.12326	−	3.67759i	−0.143805	−	0.249078i
$219$	12.8288	+	10.2734i	0.866891	+	0.694210i
$220$	9.84867	+	4.38491i	0.663997	+	0.295631i
$221$	8.37290	+	1.77971i	0.563222	+	0.119717i
$222$	−0.403310	+	0.628511i	−0.0270684	+	0.0421829i
$223$	7.82055			0.523703			0.261851	−	0.965108i	$-0.415667\pi$
$223$	7.82055			0.523703			0.261851	+	0.965108i	$0.415667\pi$
$224$	−3.13537	−	0.666444i	−0.209491	−	0.0445287i
$225$	−11.5486	+	1.34116i	−0.769907	+	0.0894106i
$226$	−15.9165	+	3.38316i	−1.05875	+	0.225045i
$227$	−18.5709	+	8.26830i	−1.23259	+	0.548786i	−0.916535	−	0.399954i	$-0.869026\pi$
$227$	−18.5709	+	8.26830i	−1.23259	+	0.548786i	−0.316058	+	0.948740i	$0.602360\pi$
$228$	0.204500	+	0.746906i	0.0135433	+	0.0494651i
$229$	1.97823	−	18.8216i	0.130725	−	1.24377i	−0.710739	−	0.703456i	$-0.751639\pi$
$229$	1.97823	−	18.8216i	0.130725	−	1.24377i	0.841464	−	0.540313i	$-0.181694\pi$
$230$	−9.27559	+	6.73911i	−0.611614	+	0.444364i
$231$	19.8261	−	3.25095i	1.30446	−	0.213897i
$232$	−4.57416	−	2.03655i	−0.300308	−	0.133706i
$233$	−0.523339	+	0.380228i	−0.0342851	+	0.0249096i	−0.604796	−	0.796381i	$-0.706745\pi$
$233$	−0.523339	+	0.380228i	−0.0342851	+	0.0249096i	0.570511	+	0.821290i	$0.306745\pi$
$234$	−2.51134	−	3.37854i	−0.164171	−	0.220862i
$235$	28.8102	+	12.8271i	1.87937	+	0.836750i
$236$	7.79511	+	5.66348i	0.507419	+	0.368661i
$237$	−12.3674	−	3.24175i	−0.803352	−	0.210574i
$238$	−15.8193	−	11.4934i	−1.02541	−	0.745005i
$239$	2.70878	−	8.33676i	0.175216	−	0.539260i	−0.824427	−	0.565968i	$-0.808502\pi$
$239$	2.70878	−	8.33676i	0.175216	−	0.539260i	0.999643	+	0.0267080i	$0.00850243\pi$
$240$	−1.82293	+	4.82733i	−0.117670	+	0.311603i
$241$	−4.48000	−	13.7880i	−0.288582	−	0.888165i	−0.985302	−	0.170822i	$-0.945358\pi$
$241$	−4.48000	−	13.7880i	−0.288582	−	0.888165i	0.696720	−	0.717344i	$-0.254642\pi$
$242$	−1.04752	+	1.81435i	−0.0673369	+	0.116631i
$243$	4.44313	+	14.9418i	0.285027	+	0.958520i
$244$	−0.643982	−	1.98197i	−0.0412267	−	0.126883i
$245$	−7.89271	+	5.73439i	−0.504247	+	0.366357i
$246$	6.38190	+	5.11066i	0.406895	+	0.325844i
$247$	−0.313689	+	0.543326i	−0.0199596	+	0.0345710i
$248$	0.942260	+	5.48745i	0.0598336	+	0.348454i
$249$	6.36183	+	12.3194i	0.403165	+	0.780713i
$250$	0.350206	−	3.33199i	0.0221490	−	0.210733i
$251$	−0.659584	−	6.27552i	−0.0416325	−	0.396107i	−0.995418	−	0.0956188i	$-0.969517\pi$
$251$	−0.659584	−	6.27552i	−0.0416325	−	0.396107i	0.953785	−	0.300488i	$-0.0971497\pi$
$252$	2.10168	+	9.38379i	0.132394	+	0.591123i
$253$	−6.96326	−	12.0607i	−0.437777	−	0.758251i
$254$	−6.16642			−0.386915
$255$	−22.1363	+	22.3788i	−1.38623	+	1.40141i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−2.89555	+	8.91158i	−0.180619	+	0.555889i	−0.999845	−	0.0175817i	$-0.994403\pi$
$257$	−2.89555	+	8.91158i	−0.180619	+	0.555889i	0.819226	+	0.573470i	$0.194403\pi$
$258$	12.1406	+	9.72224i	0.755840	+	0.605280i
$259$	1.35183	+	0.287341i	0.0839989	+	0.0178545i
$260$	−3.81902	+	1.70034i	−0.236845	+	0.105450i
$261$	0.163636	+	15.0202i	0.0101288	+	0.929729i
$262$	12.5426	+	13.9300i	0.774887	+	0.860599i
$263$	−17.4725	−	7.77926i	−1.07740	−	0.479690i	−0.210205	−	0.977657i	$-0.567413\pi$
$263$	−17.4725	−	7.77926i	−1.07740	−	0.479690i	−0.867196	+	0.497967i	$0.834080\pi$
$264$	−5.60005	−	2.81505i	−0.344659	−	0.173254i
$265$	20.7970	−	4.42053i	1.27755	−	0.271551i
$266$	1.15943	−	0.842376i	0.0710893	−	0.0516494i
$267$	8.52595	−	3.32620i	0.521780	−	0.203560i
$268$	11.8042	+	2.50906i	0.721056	+	0.153265i
$269$	−0.758379	+	7.21550i	−0.0462392	+	0.439937i	0.946771	+	0.321908i	$0.104324\pi$
$269$	−0.758379	+	7.21550i	−0.0462392	+	0.439937i	−0.993010	+	0.118029i	$0.962343\pi$
$270$	15.4437	−	1.06266i	0.939872	−	0.0646717i
$271$	4.32586	−	13.3136i	0.262777	−	0.808745i	−0.729420	−	0.684066i	$-0.760210\pi$
$271$	4.32586	−	13.3136i	0.262777	−	0.808745i	0.992197	−	0.124679i	$-0.0397900\pi$
$272$	1.88507	+	5.80164i	0.114299	+	0.351776i
$273$	−4.20743	+	6.55679i	−0.254645	+	0.396835i
$274$	18.1379			1.09575
$275$	−13.7175	−	2.91575i	−0.827197	−	0.175826i
$276$	5.57053	−	3.66083i	0.335306	−	0.220356i
$277$	−2.24374	+	21.3478i	−0.134813	+	1.28266i	0.692703	+	0.721223i	$0.256420\pi$
$277$	−2.24374	+	21.3478i	−0.134813	+	1.28266i	−0.827517	+	0.561441i	$0.810247\pi$
$278$	12.8858			0.772838
$279$	13.7875	−	9.42899i	0.825434	−	0.564499i
$280$	9.54947			0.570690
$281$	2.07970	−	19.7871i	0.124065	−	1.18040i	−0.738430	−	0.674330i	$-0.764432\pi$
$281$	2.07970	−	19.7871i	0.124065	−	1.18040i	0.862494	−	0.506066i	$-0.168901\pi$
$282$	−16.3818	−	8.23484i	−0.975520	−	0.490378i
$283$	−6.47250	−	1.37577i	−0.384750	−	0.0817812i	0.0114759	−	0.999934i	$-0.496347\pi$
$283$	−6.47250	−	1.37577i	−0.384750	−	0.0817812i	−0.396226	+	0.918153i	$0.629680\pi$
$284$	−13.7972			−0.818714
$285$	−1.05856	−	2.04986i	−0.0627037	−	0.121423i
$286$	−1.56914	−	4.82933i	−0.0927854	−	0.285564i
$287$	4.67573	−	14.3904i	0.276000	−	0.849439i
$288$	1.19028	−	2.75377i	0.0701380	−	0.162267i
$289$	−2.11278	+	20.1017i	−0.124281	+	1.18246i
$290$	14.5908	+	3.10137i	0.856802	+	0.182119i
$291$	10.2957	+	8.24487i	0.603546	+	0.483323i
$292$	−7.67672	+	5.57747i	−0.449246	+	0.326397i
$293$	−31.6184	+	6.72070i	−1.84717	+	0.392627i	−0.992054	−	0.125815i	$-0.959846\pi$
$293$	−31.6184	+	6.72070i	−1.84717	+	0.392627i	−0.855113	+	0.518442i	$0.826512\pi$
$294$	4.74003	−	3.11505i	0.276444	−	0.181673i
$295$	−26.2234	−	11.6754i	−1.52679	−	0.679769i
$296$	−0.288499	−	0.320411i	−0.0167687	−	0.0186235i
$297$	−0.677130	+	18.7912i	−0.0392911	+	1.09037i
$298$	−18.5990	+	8.28082i	−1.07741	+	0.479695i
$299$	5.28228	+	1.12278i	0.305482	+	0.0649322i
$300$	1.01392	−	6.63539i	0.0585389	−	0.383094i
$301$	8.89485	−	27.3755i	0.512691	−	1.57790i
$302$	1.44955	+	1.60989i	0.0834123	+	0.0926387i
$303$	3.24737	+	11.8606i	0.186557	+	0.681372i
$304$	−0.447098			−0.0256428
$305$	3.10424	+	5.37670i	0.177748	+	0.307869i
$306$	13.4658	−	12.3929i	0.769788	−	0.708456i
$307$	1.61499	+	15.3656i	0.0921726	+	0.876963i	0.938727	+	0.344661i	$0.112006\pi$
$307$	1.61499	+	15.3656i	0.0921726	+	0.876963i	−0.846555	+	0.532302i	$0.821327\pi$
$308$	−1.21248	+	11.5359i	−0.0690872	+	0.657321i
$309$	−10.4770	+	16.3271i	−0.596014	+	0.928819i
$310$	−6.14475	−	15.4071i	−0.348998	−	0.875066i
$311$	8.83409	−	15.3011i	0.500935	−	0.867645i	−0.499064	−	0.866565i	$-0.666323\pi$
$311$	8.83409	−	15.3011i	0.500935	−	0.867645i	0.999999	−	0.00108025i	$-0.000343854\pi$
$312$	2.26425	−	0.883344i	0.128188	−	0.0500095i
$313$	−7.78057	+	5.65291i	−0.439784	+	0.319521i	−0.785549	−	0.618800i	$-0.787619\pi$
$313$	−7.78057	+	5.65291i	−0.439784	+	0.319521i	0.345765	+	0.938321i	$0.387619\pi$
$314$	0.107725	+	0.331543i	0.00607927	+	0.0187101i
$315$	−11.9368	−	26.0431i	−0.672561	−	1.46736i
$316$	3.69078	−	6.39263i	0.207623	−	0.359613i
$317$	−2.62665	−	8.08398i	−0.147527	−	0.454042i	0.849800	−	0.527105i	$-0.176723\pi$
$317$	−2.62665	−	8.08398i	−0.147527	−	0.454042i	−0.997327	+	0.0730631i	$0.976723\pi$
$318$	−12.1983	+	2.00020i	−0.684049	+	0.112166i
$319$	−5.59908	+	17.2322i	−0.313488	+	0.964818i
$320$	−2.41019	−	1.75111i	−0.134734	−	0.0978899i
$321$	−24.1158	+	24.3800i	−1.34601	+	1.36076i
$322$	−9.98004	−	7.25092i	−0.556166	−	0.404078i
$323$	−2.49159	−	1.10933i	−0.138636	−	0.0617247i
$324$	−8.99786	+	0.196076i	−0.499881	+	0.0108931i
$325$	4.39949	−	3.19642i	0.244040	−	0.177305i
$326$	14.9512	+	6.65672i	0.828073	+	0.368682i
$327$	−4.65983	−	5.69075i	−0.257689	−	0.314699i
$328$	−3.81891	+	2.77460i	−0.210864	+	0.153202i
$329$	−3.54684	+	33.7459i	−0.195544	+	1.86047i
$330$	18.0625	+	4.73455i	0.994310	+	0.260628i
$331$	−2.58578	+	1.15127i	−0.142128	+	0.0632793i	−0.476568	−	0.879138i	$-0.658119\pi$
$331$	−2.58578	+	1.15127i	−0.142128	+	0.0632793i	0.334440	+	0.942417i	$0.391453\pi$
$332$	−7.83010	+	1.66434i	−0.429733	+	0.0913425i
$333$	−0.513196	+	1.18730i	−0.0281230	+	0.0650637i
$334$	−4.43764	−	0.943249i	−0.242817	−	0.0516123i
$335$	−35.9523			−1.96428
$336$	−5.54584	−	0.260363i	−0.302551	−	0.0142039i
$337$	−15.9741	−	3.39540i	−0.870165	−	0.184959i	−0.248871	−	0.968537i	$-0.580059\pi$
$337$	−15.9741	−	3.39540i	−0.870165	−	0.184959i	−0.621294	+	0.783577i	$0.713393\pi$
$338$	−10.0773	−	4.48670i	−0.548132	−	0.244044i
$339$	−26.2567	+	10.2435i	−1.42607	+	0.556348i
$340$	−9.08675	−	15.7387i	−0.492798	−	0.853551i
$341$	19.3923	−	5.46675i	1.05015	−	0.296041i
$342$	0.558869	+	1.21932i	0.0302202	+	0.0659331i
$343$	9.66054	+	7.01879i	0.521620	+	0.378979i
$344$	−7.26489	+	5.27825i	−0.391697	+	0.284584i
$345$	−13.9653	+	14.1183i	−0.751868	+	0.760103i
$346$	−2.96901			−0.159615
$347$	−5.22676	−	9.05301i	−0.280587	−	0.485991i	0.690942	−	0.722910i	$-0.257196\pi$
$347$	−5.22676	−	9.05301i	−0.280587	−	0.485991i	−0.971529	+	0.236919i	$0.923863\pi$
$348$	−8.38904	−	2.19893i	−0.449700	−	0.117875i
$349$	−1.50275	+	0.319419i	−0.0804403	+	0.0170981i	−0.247956	−	0.968771i	$-0.579759\pi$
$349$	−1.50275	+	0.319419i	−0.0804403	+	0.0170981i	0.167516	+	0.985869i	$0.446426\pi$
$350$	−12.1509	+	2.58274i	−0.649491	+	0.138054i
$351$	−5.23933	−	5.07084i	−0.279655	−	0.270662i
$352$	2.42139	−	2.68922i	0.129060	−	0.143336i
$353$	−13.7310	−	9.97618i	−0.730829	−	0.530978i	0.158997	−	0.987279i	$-0.449174\pi$
$353$	−13.7310	−	9.97618i	−0.730829	−	0.530978i	−0.889826	+	0.456301i	$0.849174\pi$
$354$	14.9109	+	7.49545i	0.792505	+	0.398379i
$355$	40.2059	−	8.54603i	2.13391	−	0.453576i
$356$	0.552307	+	5.25485i	0.0292722	+	0.278507i
$357$	−30.2599	−	15.2112i	−1.60153	−	0.805060i
$358$	1.59571	−	4.91111i	0.0843361	−	0.259560i
$359$	18.7555	+	8.35049i	0.989878	+	0.440722i	0.836810	−	0.547493i	$-0.184418\pi$
$359$	18.7555	+	8.35049i	0.989878	+	0.440722i	0.153068	+	0.988216i	$0.451085\pi$
$360$	−1.76286	+	8.76191i	−0.0929110	+	0.461793i
$361$	−12.5797	+	13.9712i	−0.662091	+	0.735326i
$362$	12.0525	−	5.36613i	0.633467	−	0.282038i
$363$	−1.28194	+	3.39472i	−0.0672843	+	0.178176i
$364$	−3.00970	−	3.34261i	−0.157751	−	0.175200i
$365$	18.9157	−	21.0081i	0.990095	−	1.09961i
$366$	−1.65619	−	3.20715i	−0.0865704	−	0.167640i
$367$	−8.15694	+	14.1282i	−0.425789	+	0.737487i	−0.996494	−	0.0836677i	$-0.973337\pi$
$367$	−8.15694	+	14.1282i	−0.425789	+	0.737487i	0.570705	+	0.821155i	$0.306670\pi$
$368$	1.18925	+	3.66013i	0.0619938	+	0.190797i
$369$	12.3405	+	6.94663i	0.642418	+	0.361627i
$370$	1.03917	+	0.755000i	0.0540238	+	0.0392506i
$371$	11.4382	+	19.8115i	0.593840	+	1.02856i
$372$	3.14848	+	9.11521i	0.163241	+	0.472602i
$373$	13.9938	−	24.2380i	0.724573	−	1.25500i	−0.234577	−	0.972098i	$-0.575370\pi$
$373$	13.9938	−	24.2380i	0.724573	−	1.25500i	0.959150	−	0.282899i	$-0.0912962\pi$
$374$	20.1664	−	8.97864i	1.04278	−	0.464275i
$375$	−0.335264	−	5.79327i	−0.0173130	−	0.299163i
$376$	7.08326	−	7.86675i	0.365291	−	0.405697i
$377$	−3.51300	−	6.08469i	−0.180929	−	0.313378i
$378$	6.22221	+	15.4500i	0.320036	+	0.794661i
$379$	−30.5785	−	6.49966i	−1.57071	−	0.333865i	−0.661417	−	0.750018i	$-0.730045\pi$
$379$	−30.5785	−	6.49966i	−1.57071	−	0.333865i	−0.909294	+	0.416153i	$0.863378\pi$
$380$	1.30287	−	0.276934i	0.0668358	−	0.0142064i
$381$	−10.5398	+	1.72824i	−0.539970	+	0.0885405i
$382$	4.54932	+	3.30527i	0.232763	+	0.169113i
$383$	1.85880	+	5.72080i	0.0949803	+	0.292319i	0.987249	−	0.159186i	$-0.0508871\pi$
$383$	1.85880	+	5.72080i	0.0949803	+	0.292319i	−0.892268	+	0.451506i	$0.850887\pi$
$384$	1.35197	+	1.08267i	0.0689926	+	0.0552496i
$385$	−3.61216	−	34.3674i	−0.184093	−	1.75153i
$386$	−6.99525	−	7.76901i	−0.356049	−	0.395432i
$387$	23.4758	+	13.2149i	1.19334	+	0.671751i
$388$	−6.16093	+	4.47618i	−0.312774	+	0.227244i
$389$	5.29123	−	16.2847i	0.268276	−	0.825669i	−0.722644	−	0.691220i	$-0.757074\pi$
$389$	5.29123	−	16.2847i	0.268276	−	0.825669i	0.990921	−	0.134449i	$-0.0429264\pi$
$390$	−6.05101	+	3.97660i	−0.306405	+	0.201363i
$391$	−2.45396	+	23.3479i	−0.124102	+	1.18075i
$392$	1.01194	+	3.11445i	0.0511109	+	0.157303i
$393$	25.3423	+	20.2942i	1.27835	+	1.02371i
$394$	7.49425	+	8.32320i	0.377555	+	0.419317i
$395$	−6.79556	+	20.9146i	−0.341922	+	1.05233i
$396$	−10.3607	−	3.24205i	−0.520645	−	0.162919i
$397$	−1.46679	+	2.54055i	−0.0736160	+	0.127507i	−0.900484	−	0.434890i	$-0.856787\pi$
$397$	−1.46679	+	2.54055i	−0.0736160	+	0.127507i	0.826868	+	0.562397i	$0.190121\pi$
$398$	9.36247	−	16.2163i	0.469298	−	0.812848i
$399$	1.74564	−	1.76476i	0.0873913	−	0.0883485i
$400$	3.54036	+	1.57627i	0.177018	+	0.0788135i
$401$	−19.4271	+	8.64950i	−0.970143	+	0.431935i	−0.829734	−	0.558158i	$-0.811508\pi$
$401$	−19.4271	+	8.64950i	−0.970143	+	0.431935i	−0.140408	+	0.990094i	$0.544841\pi$
$402$	20.8792	+	0.980224i	1.04136	+	0.0488891i
$403$	−3.45634	+	7.00671i	−0.172172	+	0.349029i
$404$	−7.09973			−0.353225
$405$	26.0989	−	6.14468i	1.29686	−	0.305332i
$406$	1.67765	+	15.9617i	0.0832602	+	0.792168i
$407$	−1.04399	+	1.15947i	−0.0517489	+	0.0574729i
$408$	4.84801	+	9.38798i	0.240012	+	0.464774i
$409$	2.19778	+	3.80667i	0.108673	+	0.188228i	0.915233	−	0.402925i	$-0.132006\pi$
$409$	2.19778	+	3.80667i	0.108673	+	0.188228i	−0.806560	+	0.591153i	$0.798673\pi$
$410$	9.40994	−	10.4508i	0.464724	−	0.516128i
$411$	31.0017	−	5.08345i	1.52920	−	0.250748i
$412$	−7.49449	−	8.32347i	−0.369227	−	0.410068i
$413$	3.22838	−	30.7160i	0.158858	−	1.51143i
$414$	8.49527	−	7.81842i	0.417520	−	0.384255i
$415$	21.7865	−	9.69998i	1.06946	−	0.476153i
$416$	0.146677	+	1.39554i	0.00719143	+	0.0684219i
$417$	22.0247	−	3.61146i	1.07855	−	0.176854i
$418$	0.169118	+	1.60905i	0.00827184	+	0.0787013i
$419$	3.49734	+	33.2749i	0.170856	+	1.62559i	0.658526	+	0.752558i	$0.271180\pi$
$419$	3.49734	+	33.2749i	0.170856	+	1.62559i	−0.487670	+	0.873028i	$0.662153\pi$
$420$	16.3222	−	2.67640i	0.796441	−	0.130595i
$421$	−1.60338	−	15.2552i	−0.0781441	−	0.743491i	−0.961503	−	0.274794i	$-0.911390\pi$
$421$	−1.60338	−	15.2552i	−0.0781441	−	0.743491i	0.883359	−	0.468697i	$-0.155276\pi$
$422$	−15.5541	+	6.92512i	−0.757160	+	0.337110i
$423$	−30.3081	−	9.48393i	−1.47363	−	0.461125i
$424$	0.745996	−	7.09767i	0.0362287	−	0.344694i
$425$	15.8188	+	17.5685i	0.767323	+	0.852198i
$426$	−23.5825	+	3.86690i	−1.14258	+	0.187352i
$427$	−4.46979	+	4.96420i	−0.216308	+	0.240235i
$428$	−9.89931	−	17.1461i	−0.478501	−	0.828789i
$429$	−4.03552	−	7.81463i	−0.194837	−	0.377294i
$430$	17.9010	−	19.8810i	0.863261	−	0.958749i
$431$	−2.32932	−	22.1620i	−0.112199	−	1.06750i	−0.895255	−	0.445553i	$-0.853007\pi$
$431$	−2.32932	−	22.1620i	−0.112199	−	1.06750i	0.783056	−	0.621951i	$-0.213660\pi$
$432$	1.26267	−	5.04040i	0.0607503	−	0.242507i
$433$	35.5312			1.70752			0.853760	−	0.520667i	$-0.174317\pi$
$433$	35.5312			1.70752			0.853760	+	0.520667i	$0.174317\pi$
$434$	13.7229	−	11.4105i	0.658719	−	0.547721i
$435$	25.8082	+	1.21163i	1.23741	+	0.0580930i
$436$	3.87938	−	1.72721i	0.185789	−	0.0827184i
$437$	−1.57189	−	0.699851i	−0.0751937	−	0.0334784i
$438$	−11.5581	+	11.6847i	−0.552266	+	0.558315i
$439$	−2.66297	+	4.61240i	−0.127097	+	0.220138i	−0.922551	−	0.385876i	$-0.873899\pi$
$439$	−2.66297	+	4.61240i	−0.127097	+	0.220138i	0.795454	+	0.606014i	$0.207232\pi$
$440$	−5.39036	+	9.33637i	−0.256975	+	0.445094i
$441$	7.22873	−	6.65279i	0.344225	−	0.316800i
$442$	−2.64517	+	8.14100i	−0.125818	+	0.387228i
$443$	4.03417	+	4.48039i	0.191669	+	0.212870i	0.831318	−	0.555797i	$-0.187587\pi$
$443$	4.03417	+	4.48039i	0.191669	+	0.212870i	−0.639649	+	0.768667i	$0.720920\pi$
$444$	−0.582911	−	0.466798i	−0.0276637	−	0.0221532i
$445$	−4.86433	−	14.9709i	−0.230591	−	0.709687i
$446$	−0.817470	+	7.77771i	−0.0387083	+	0.368285i
$447$	−29.4691	+	19.3665i	−1.39384	+	0.916003i
$448$	0.990529	−	3.04854i	0.0467981	−	0.144030i
$449$	−19.4979	+	14.1661i	−0.920165	+	0.668539i	−0.943565	−	0.331187i	$-0.892551\pi$
$449$	−19.4979	+	14.1661i	−0.920165	+	0.668539i	0.0234002	+	0.999726i	$0.492551\pi$
$450$	−0.126653	−	11.6255i	−0.00597049	−	0.548033i
$451$	11.4300	+	12.6943i	0.538218	+	0.597751i
$452$	−1.70090	−	16.1830i	−0.0800035	−	0.761183i
$453$	2.92881	+	2.34540i	0.137607	+	0.110197i
$454$	−6.28181	−	19.3334i	−0.294820	−	0.907363i
$455$	10.8409	+	7.87635i	0.508228	+	0.369249i
$456$	−0.764191	+	0.125307i	−0.0357865	+	0.00586802i
$457$	−1.93978	+	0.412312i	−0.0907390	+	0.0192872i	−0.253057	−	0.967451i	$-0.581436\pi$
$457$	−1.93978	+	0.412312i	−0.0907390	+	0.0192872i	0.162318	+	0.986738i	$0.448103\pi$
$458$	18.5117	+	3.93479i	0.864997	+	0.183861i
$459$	19.5427	−	24.9563i	0.912177	−	1.16486i
$460$	−5.73263	−	9.92920i	−0.267285	−	0.462952i
$461$	11.1974	−	12.4360i	0.521517	−	0.579203i	−0.423636	−	0.905833i	$-0.639246\pi$
$461$	11.1974	−	12.4360i	0.521517	−	0.579203i	0.945152	+	0.326630i	$0.105913\pi$
$462$	1.16074	+	20.0573i	0.0540027	+	0.933151i
$463$	3.08014	−	1.37137i	0.143146	−	0.0637328i	−0.333913	−	0.942604i	$-0.608369\pi$
$463$	3.08014	−	1.37137i	0.143146	−	0.0637328i	0.477060	+	0.878871i	$0.341703\pi$
$464$	2.50352	−	4.33622i	0.116223	−	0.201304i
$465$	−14.8209	−	24.6121i	−0.687301	−	1.14136i
$466$	−0.323441	−	0.560217i	−0.0149831	−	0.0259515i
$467$	−31.5458	−	22.9194i	−1.45976	−	1.06058i	−0.983424	−	0.181320i	$-0.941963\pi$
$467$	−31.5458	−	22.9194i	−1.45976	−	1.06058i	−0.476340	−	0.879261i	$-0.658037\pi$
$468$	3.62254	−	2.14443i	0.167452	−	0.0991262i
$469$	−11.9536	−	36.7894i	−0.551967	−	1.69878i
$470$	−15.7683	+	27.3116i	−0.727340	+	1.25979i
$471$	0.277047	+	0.536491i	0.0127656	+	0.0247202i
$472$	−6.44727	+	7.16042i	−0.296760	+	0.329585i
$473$	21.7438	+	24.1489i	0.999781	+	1.11037i
$474$	4.51674	−	11.9608i	0.207461	−	0.549380i
$475$	−1.58289	+	0.704747i	−0.0726279	+	0.0323360i
$476$	13.0840	−	14.5312i	0.599704	−	0.666038i
$477$	−20.2891	+	6.83758i	−0.928976	+	0.313071i
$478$	8.00795	+	3.56537i	0.366275	+	0.163076i
$479$	2.44407	−	7.52208i	0.111673	−	0.343693i	−0.879566	−	0.475777i	$-0.842167\pi$
$479$	2.44407	−	7.52208i	0.111673	−	0.343693i	0.991239	+	0.132084i	$0.0421669\pi$
$480$	−4.61034	−	2.31754i	−0.210432	−	0.105781i
$481$	−0.0632405	−	0.601694i	−0.00288352	−	0.0274349i
$482$	14.1808	−	3.01422i	0.645917	−	0.137294i
$483$	−19.0903	−	9.59639i	−0.868640	−	0.436651i
$484$	−1.69492	−	1.23143i	−0.0770416	−	0.0559740i
$485$	15.1808	−	16.8600i	0.689323	−	0.765571i
$486$	−15.3244	+	2.85694i	−0.695130	+	0.129593i
$487$	41.1644	−	8.74977i	1.86534	−	0.396490i	0.870010	−	0.493035i	$-0.164112\pi$
$487$	41.1644	−	8.74977i	1.86534	−	0.396490i	0.995329	+	0.0965447i	$0.0307791\pi$
$488$	2.03843	−	0.433281i	0.0922753	−	0.0196137i
$489$	27.4207	+	7.18750i	1.24001	+	0.325030i
$490$	−4.87796	−	8.44888i	−0.220364	−	0.381682i
$491$	18.5945			0.839159			0.419579	−	0.907719i	$-0.362178\pi$
$491$	18.5945			0.839159			0.419579	+	0.907719i	$0.362178\pi$
$492$	−5.74975	+	5.81273i	−0.259219	+	0.262058i
$493$	24.7106	−	17.9533i	1.11291	−	0.808575i
$494$	−0.507560	−	0.368764i	−0.0228362	−	0.0165915i
$495$	32.1999	+	3.03008i	1.44728	+	0.136192i
$496$	−5.55589	+	0.363503i	−0.249467	+	0.0163218i
$497$	22.1129	+	38.3007i	0.991901	+	1.71802i
$498$	−12.9170	+	5.03925i	−0.578822	+	0.225814i
$499$	29.4625	+	13.1176i	1.31892	+	0.587222i	0.940935	−	0.338588i	$-0.109949\pi$
$499$	29.4625	+	13.1176i	1.31892	+	0.587222i	0.377988	+	0.925810i	$0.376616\pi$
$500$	3.27713	+	0.696575i	0.146558	+	0.0311518i
$501$	−7.84928	−	0.368503i	−0.350680	−	0.0164635i
$502$	6.31009			0.281633
$503$	−28.4904	−	6.05582i	−1.27032	−	0.270016i	−0.477048	−	0.878877i	$-0.658293\pi$
$503$	−28.4904	−	6.05582i	−1.27032	−	0.270016i	−0.793276	+	0.608862i	$0.791626\pi$
$504$	−9.55207	+	1.10930i	−0.425483	+	0.0494120i
$505$	20.6890	−	4.39759i	0.920650	−	0.195690i
$506$	12.7225	−	5.66443i	0.565585	−	0.251815i
$507$	−18.4818	−	4.84445i	−0.820806	−	0.215149i
$508$	0.644566	−	6.13264i	0.0285980	−	0.272092i
$509$	−30.1854	+	21.9310i	−1.33795	+	0.972075i	−0.338429	+	0.940992i	$0.609896\pi$
$509$	−30.1854	+	21.9310i	−1.33795	+	0.972075i	−0.999517	+	0.0310826i	$0.990104\pi$
$510$	−19.9423	−	24.3543i	−0.883061	−	1.07843i
$511$	27.7865	+	12.3713i	1.22920	+	0.547276i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.29697	+	1.92745i	0.0572625	+	0.0850992i
$514$	−8.56009	−	3.81120i	−0.377569	−	0.168105i
$515$	26.9950	+	19.6130i	1.18954	+	0.864252i
$516$	−10.9380	+	11.0578i	−0.481519	+	0.486794i
$517$	−30.9908	−	22.5161i	−1.36297	−	0.990259i
$518$	−0.427072	+	1.31439i	−0.0187645	+	0.0577511i
$519$	−5.07471	+	0.832116i	−0.222755	+	0.0365258i
$520$	−1.29183	−	3.97583i	−0.0566503	−	0.174352i
$521$	5.30094	−	9.18150i	0.232239	−	0.402249i	−0.726228	−	0.687454i	$-0.758728\pi$
$521$	5.30094	−	9.18150i	0.232239	−	0.402249i	0.958467	+	0.285205i	$0.0920617\pi$
$522$	−14.9550	−	1.40730i	−0.654565	−	0.0615959i
$523$	−8.01325	−	24.6623i	−0.350395	−	1.07841i	−0.958632	−	0.284649i	$-0.908123\pi$
$523$	−8.01325	−	24.6623i	−0.350395	−	1.07841i	0.608237	−	0.793756i	$-0.291877\pi$
$524$	−15.1648	+	11.0178i	−0.662476	+	0.481317i
$525$	−20.0447	+	7.81997i	−0.874822	+	0.341292i
$526$	9.56302	−	16.5636i	0.416967	−	0.722209i
$527$	−31.8638	−	11.7594i	−1.38801	−	0.512247i
$528$	3.38500	−	5.27512i	0.147313	−	0.229570i
$529$	0.856002	−	8.14432i	0.0372175	−	0.354101i
$530$	2.22244	+	21.1451i	0.0965367	+	0.918485i
$531$	27.5868	+	8.63239i	1.19716	+	0.374614i
$532$	0.716568	+	1.24113i	0.0310672	+	0.0538099i
$533$	−6.62383			−0.286910
$534$	2.41678	+	8.82693i	0.104584	+	0.381979i
$535$	39.4675	+	43.8332i	1.70633	+	1.89507i
$536$	−3.72919	+	11.4773i	−0.161076	+	0.495742i
$537$	1.35102	−	8.84141i	0.0583007	−	0.381535i
$538$	−7.09670	−	1.50845i	−0.305960	−	0.0650339i
$539$	10.8257	−	4.81993i	0.466298	−	0.207609i
$540$	−0.557459	+	15.4701i	−0.0239892	+	0.665729i
$541$	−13.1059	−	14.5555i	−0.563465	−	0.625792i	0.392330	−	0.919825i	$-0.371669\pi$
$541$	−13.1059	−	14.5555i	−0.563465	−	0.625792i	−0.955795	+	0.294033i	$0.905002\pi$
$542$	12.7885	+	5.69381i	0.549313	+	0.244570i
$543$	19.0965	−	12.5498i	0.819511	−	0.538566i
$544$	−5.96690	+	1.26830i	−0.255829	+	0.0543781i
$545$	−10.2349	+	7.43610i	−0.438416	+	0.318528i
$546$	−6.08108	−	4.86975i	−0.260246	−	0.208406i
$547$	−36.0168	−	7.65561i	−1.53997	−	0.327330i	−0.641761	−	0.766905i	$-0.721796\pi$
$547$	−36.0168	−	7.65561i	−1.53997	−	0.327330i	−0.898206	+	0.439575i	$0.855129\pi$
$548$	−1.89593	+	18.0385i	−0.0809900	+	0.770568i
$549$	−3.72966	−	5.01756i	−0.159178	−	0.214144i
$550$	4.33364	−	13.3376i	0.184787	−	0.568716i
$551$	0.691776	+	2.12907i	0.0294707	+	0.0907014i
$552$	3.05850	+	5.92267i	0.130178	+	0.252086i
$553$	−23.6610			−1.00617
$554$	−20.9963	−	4.46290i	−0.892048	−	0.189611i
$555$	1.98777	+	0.999220i	0.0843763	+	0.0424145i
$556$	−1.34693	+	12.8152i	−0.0571226	+	0.543485i
$557$	−6.13161			−0.259805			−0.129902	−	0.991527i	$-0.541466\pi$
$557$	−6.13161			−0.259805			−0.129902	+	0.991527i	$0.541466\pi$
$558$	7.93616	+	14.6975i	0.335964	+	0.622196i
$559$	−12.6008			−0.532958
$560$	−0.998191	+	9.49716i	−0.0421813	+	0.401328i
$561$	31.9524	−	20.9985i	1.34903	−	0.886557i
$562$	19.4613	+	4.13662i	0.820924	+	0.174493i
$563$	−5.98434			−0.252210			−0.126105	−	0.992017i	$-0.540248\pi$
$563$	−5.98434			−0.252210			−0.126105	+	0.992017i	$0.540248\pi$
$564$	9.90209	−	15.4313i	0.416953	−	0.649773i
$565$	14.9803	+	46.1046i	0.630226	+	1.93964i
$566$	2.04480	−	6.29323i	0.0859492	−	0.264524i
$567$	14.9653	+	24.6636i	0.628482	+	1.03577i
$568$	1.44220	−	13.7216i	0.0605134	−	0.575747i
$569$	−44.0709	−	9.36756i	−1.84755	−	0.392709i	−0.855420	−	0.517935i	$-0.826701\pi$
$569$	−44.0709	−	9.36756i	−1.84755	−	0.392709i	−0.992128	+	0.125226i	$0.960034\pi$
$570$	2.14928	−	0.838493i	0.0900235	−	0.0351206i
$571$	22.3677	−	16.2511i	0.936060	−	0.680087i	−0.0114094	−	0.999935i	$-0.503632\pi$
$571$	22.3677	−	16.2511i	0.936060	−	0.680087i	0.947469	+	0.319848i	$0.103632\pi$
$572$	4.96689	−	1.05575i	0.207676	−	0.0441430i
$573$	8.70217	+	4.37444i	0.363538	+	0.182745i
$574$	13.8228	+	6.15432i	0.576954	+	0.256876i
$575$	9.97971	+	11.0836i	0.416183	+	0.462218i
$576$	2.61426	+	1.47161i	0.108928	+	0.0613170i
$577$	−21.3370	+	9.49986i	−0.888272	+	0.395484i	−0.799569	−	0.600574i	$-0.794939\pi$
$577$	−21.3370	+	9.49986i	−0.888272	+	0.395484i	−0.0887028	+	0.996058i	$0.528272\pi$
$578$	−19.7708	−	4.20241i	−0.822356	−	0.174797i
$579$	−14.1339	−	11.3185i	−0.587383	−	0.470379i
$580$	−4.60954	+	14.1867i	−0.191401	+	0.589071i
$581$	17.1696	+	19.0687i	0.712313	+	0.791104i
$582$	−9.27590	+	9.37750i	−0.384498	+	0.388710i
$583$	−25.8259			−1.06960
$584$	−4.74448	−	8.21767i	−0.196328	−	0.340050i
$585$	−9.22803	+	8.49280i	−0.381532	+	0.351134i
$586$	−3.37886	−	32.1477i	−0.139579	−	1.32801i
$587$	−0.428776	+	4.07953i	−0.0176975	+	0.168380i	−0.999801	−	0.0199631i	$-0.993645\pi$
$587$	−0.428776	+	4.07953i	−0.0176975	+	0.168380i	0.982103	+	0.188343i	$0.0603118\pi$
$588$	2.60252	+	5.03967i	0.107326	+	0.207833i
$589$	1.54136	−	1.95474i	0.0635106	−	0.0805436i
$590$	14.3525	−	24.8593i	0.590885	−	1.02344i
$591$	15.1421	+	12.1258i	0.622861	+	0.498790i
$592$	0.348812	−	0.253427i	0.0143361	−	0.0104158i
$593$	10.4643	+	32.2059i	0.429719	+	1.32254i	0.898403	+	0.439173i	$0.144728\pi$
$593$	10.4643	+	32.2059i	0.429719	+	1.32254i	−0.468684	+	0.883366i	$0.655272\pi$
$594$	−18.6174	−	2.63763i	−0.763882	−	0.108223i
$595$	−29.1268	+	50.4492i	−1.19408	+	2.06821i
$596$	−6.29133	−	19.3627i	−0.257703	−	0.793128i
$597$	11.4577	−	30.3412i	0.468932	−	1.24178i
$598$	−1.66878	+	5.13598i	−0.0682415	+	0.210026i
$599$	−35.2247	−	25.5922i	−1.43924	−	1.04567i	−0.988201	−	0.153166i	$-0.951053\pi$
$599$	−35.2247	−	25.5922i	−1.43924	−	1.04567i	−0.451040	−	0.892504i	$-0.648947\pi$
$600$	6.49305	+	1.70196i	0.265078	+	0.0694821i
$601$	30.4659	+	22.1347i	1.24273	+	0.902895i	0.997777	−	0.0666404i	$-0.0212280\pi$
$601$	30.4659	+	22.1347i	1.24273	+	0.902895i	0.244951	+	0.969535i	$0.421228\pi$
$602$	26.2958	+	11.7077i	1.07174	+	0.477168i
$603$	35.9620	−	4.17633i	1.46449	−	0.170073i
$604$	−1.75259	+	1.27333i	−0.0713118	+	0.0518111i
$605$	5.70184	+	2.53862i	0.231813	+	0.103210i
$606$	−12.1350	+	1.98982i	−0.492952	+	0.0808308i
$607$	−26.0927	+	18.9574i	−1.05907	+	0.769458i	−0.973916	−	0.226910i	$-0.927138\pi$
$607$	−26.0927	+	18.9574i	−1.05907	+	0.769458i	−0.0851524	+	0.996368i	$0.527138\pi$
$608$	0.0467344	−	0.444648i	0.00189533	−	0.0180329i
$609$	7.34102	+	26.8120i	0.297473	+	1.08648i
$610$	−5.67173	+	2.52522i	−0.229642	+	0.102243i
$611$	14.5296	−	3.08836i	0.587805	−	0.124942i
$612$	10.9175	+	14.6874i	0.441313	+	0.593705i
$613$	22.0071	+	4.67776i	0.888859	+	0.188933i	0.629641	−	0.776886i	$-0.283202\pi$
$613$	22.0071	+	4.67776i	0.888859	+	0.188933i	0.259218	+	0.965819i	$0.416535\pi$
$614$	−15.4503			−0.623523
$615$	13.1547	−	20.5001i	0.530449	−	0.826642i
$616$	−11.3460	−	2.41167i	−0.457143	−	0.0971688i
$617$	12.0367	+	5.35907i	0.484578	+	0.215748i	0.634460	−	0.772956i	$-0.281223\pi$
$617$	12.0367	+	5.35907i	0.484578	+	0.215748i	−0.149882	+	0.988704i	$0.547889\pi$
$618$	−15.1426	−	12.1262i	−0.609123	−	0.487789i
$619$	−10.0454	−	17.3991i	−0.403757	−	0.699328i	0.590419	−	0.807097i	$-0.298963\pi$
$619$	−10.0454	−	17.3991i	−0.403757	−	0.699328i	−0.994176	+	0.107769i	$0.965629\pi$
$620$	15.9650	−	4.50060i	0.641171	−	0.180748i
$621$	12.3291	−	15.7444i	0.494749	−	0.631800i
$622$	14.2939	+	10.3851i	0.573131	+	0.416404i
$623$	13.7022	−	9.95520i	0.548965	−	0.398846i
$624$	0.641827	+	2.34418i	0.0256936	+	0.0938423i
$625$	−29.3583			−1.17433
$626$	−4.80865	−	8.32883i	−0.192192	−	0.332887i
$627$	0.740025	+	2.70283i	0.0295537	+	0.107941i
$628$	−0.340987	+	0.0724791i	−0.0136069	+	0.00289223i
$629$	2.57266	−	0.546836i	0.102579	−	0.0218038i
$630$	27.1482	−	9.14913i	1.08161	−	0.364510i
$631$	−29.2212	+	32.4534i	−1.16328	+	1.29195i	−0.214240	+	0.976781i	$0.568727\pi$
$631$	−29.2212	+	32.4534i	−1.16328	+	1.29195i	−0.949036	+	0.315168i	$0.897939\pi$
$632$	5.97181	+	4.33878i	0.237546	+	0.172587i
$633$	−24.6445	+	16.1959i	−0.979532	+	0.643728i
$634$	8.31426	−	1.76725i	0.330201	−	0.0701865i
$635$	1.92027	+	18.2701i	0.0762035	+	0.725027i
$636$	−0.714167	−	12.3406i	−0.0283186	−	0.489337i
$637$	−1.41999	+	4.37027i	−0.0562619	+	0.173156i
$638$	−16.5525	−	7.36966i	−0.655321	−	0.291768i
$639$	−39.2241	+	13.2188i	−1.55168	+	0.522928i
$640$	1.99345	−	2.21395i	0.0787980	−	0.0875140i
$641$	24.9683	−	11.1166i	0.986187	−	0.439079i	0.150694	−	0.988580i	$-0.451849\pi$
$641$	24.9683	−	11.1166i	0.986187	−	0.439079i	0.835493	+	0.549502i	$0.185182\pi$
$642$	−21.7256	−	26.5321i	−0.857443	−	1.04714i
$643$	−17.0857	−	18.9756i	−0.673794	−	0.748324i	0.305183	−	0.952294i	$-0.401282\pi$
$643$	−17.0857	−	18.9756i	−0.673794	−	0.748324i	−0.978977	+	0.203970i	$0.934616\pi$
$644$	8.25440	−	9.16744i	0.325269	−	0.361248i
$645$	25.0248	−	38.9982i	0.985350	−	1.53555i
$646$	1.36369	−	2.36199i	0.0536538	−	0.0929311i
$647$	−6.02029	−	18.5286i	−0.236682	−	0.728433i	−0.996894	−	0.0787572i	$-0.974905\pi$
$647$	−6.02029	−	18.5286i	−0.236682	−	0.728433i	0.760212	−	0.649675i	$-0.225095\pi$
$648$	0.745531	−	8.96907i	0.0292872	−	0.352338i
$649$	28.2082	+	20.4945i	1.10727	+	0.804478i
$650$	2.71903	+	4.70951i	0.106649	+	0.184722i
$651$	20.2575	−	23.3492i	0.793954	−	0.915126i
$652$	−8.18309	+	14.1735i	−0.320474	+	0.555078i
$653$	14.1956	−	6.32030i	0.555518	−	0.247333i	−0.109722	−	0.993962i	$-0.534996\pi$
$653$	14.1956	−	6.32030i	0.555518	−	0.247333i	0.665240	+	0.746630i	$0.268329\pi$
$654$	6.14666	−	4.03946i	0.240353	−	0.157955i
$655$	37.3665	−	41.4998i	1.46003	−	1.62153i
$656$	−2.36022	−	4.08802i	−0.0921510	−	0.159610i
$657$	−16.4805	+	23.2111i	−0.642966	+	0.905551i
$658$	−33.1903	−	7.05482i	−1.29389	−	0.275026i
$659$	−30.1910	+	6.41729i	−1.17607	+	0.249982i	−0.754183	−	0.656665i	$-0.771967\pi$
$659$	−30.1910	+	6.41729i	−1.17607	+	0.249982i	−0.421890	+	0.906647i	$0.638633\pi$
$660$	−6.59666	+	17.4687i	−0.256775	+	0.679968i
$661$	4.62440	+	3.35982i	0.179868	+	0.130682i	0.674076	−	0.738662i	$-0.264542\pi$
$661$	4.62440	+	3.35982i	0.179868	+	0.130682i	−0.494208	+	0.869344i	$0.664542\pi$
$662$	−0.874670	−	2.69196i	−0.0339950	−	0.104626i
$663$	−2.23954	+	14.6562i	−0.0869766	+	0.569198i
$664$	−0.836754	−	7.96118i	−0.0324723	−	0.308954i
$665$	−2.85688	−	3.17289i	−0.110785	−	0.123039i
$666$	−1.12715	−	0.634492i	−0.0436763	−	0.0245861i
$667$	15.5894	−	11.3263i	0.603622	−	0.438557i
$668$	1.40194	−	4.31473i	0.0542427	−	0.166942i
$669$	0.782592	+	13.5230i	0.0302567	+	0.522828i
$670$	3.75803	−	35.7553i	0.145186	−	1.38135i
$671$	−2.33038	−	7.17217i	−0.0899633	−	0.276879i
$672$	0.838635	−	5.48825i	0.0323510	−	0.211714i
$673$	20.4249	+	22.6841i	0.787320	+	0.874408i	0.994590	−	0.103876i	$-0.0331245\pi$
$673$	20.4249	+	22.6841i	0.787320	+	0.874408i	−0.207270	+	0.978284i	$0.566458\pi$
$674$	5.04655	−	15.5317i	0.194386	−	0.598258i
$675$	−3.47473	−	19.8352i	−0.133742	−	0.763456i
$676$	5.51548	−	9.55309i	0.212134	−	0.367427i
$677$	13.4891	−	23.3639i	0.518429	−	0.897946i	−0.481341	−	0.876533i	$-0.659850\pi$
$677$	13.4891	−	23.3639i	0.518429	−	0.897946i	0.999771	−	0.0214128i	$-0.00681643\pi$
$678$	−7.44277	−	27.1836i	−0.285838	−	1.04398i
$679$	22.3000	+	9.92858i	0.855794	+	0.381024i
$680$	16.6023	−	7.39183i	0.636670	−	0.283464i
$681$	−16.1556	−	31.2846i	−0.619082	−	1.19883i
$682$	3.40976	+	19.8575i	0.130567	+	0.760382i
$683$	−17.1654			−0.656814			−0.328407	−	0.944536i	$-0.606512\pi$
$683$	−17.1654			−0.656814			−0.328407	+	0.944536i	$0.606512\pi$
$684$	−1.27105	+	0.428354i	−0.0486000	+	0.0163785i
$685$	−5.64827	−	53.7397i	−0.215809	−	2.05329i
$686$	−7.99014	+	8.87395i	−0.305065	+	0.338809i
$687$	32.7435	+	1.53722i	1.24924	+	0.0586487i
$688$	−4.48995	−	7.77682i	−0.171178	−	0.296488i
$689$	6.70100	−	7.44222i	0.255288	−	0.283526i
$690$	−12.5812	−	15.3646i	−0.478957	−	0.584920i
$691$	−13.4830	−	14.9744i	−0.512919	−	0.569654i	0.429935	−	0.902860i	$-0.358536\pi$
$691$	−13.4830	−	14.9744i	−0.512919	−	0.569654i	−0.942854	+	0.333205i	$0.891870\pi$
$692$	0.310347	−	2.95275i	0.0117976	−	0.112247i
$693$	7.60537	+	33.9572i	0.288904	+	1.28993i
$694$	9.54976	−	4.25183i	0.362504	−	0.161397i
$695$	−4.01273	−	38.1785i	−0.152211	−	1.44819i
$696$	3.06378	−	8.11323i	0.116132	−	0.307531i
$697$	−3.00996	−	28.6379i	−0.114010	−	1.08474i
$698$	−0.160589	−	1.52791i	−0.00607840	−	0.0578321i
$699$	−0.709844	−	0.866887i	−0.0268488	−	0.0327887i
$700$	−1.29849	−	12.3543i	−0.0490781	−	0.466947i
$701$	1.06138	−	0.472556i	0.0400877	−	0.0178482i	−0.386595	−	0.922250i	$-0.626349\pi$
$701$	1.06138	−	0.472556i	0.0400877	−	0.0178482i	0.426683	+	0.904401i	$0.359682\pi$
$702$	5.59072	−	4.68059i	0.211008	−	0.176657i
$703$	−0.0201498	+	0.191713i	−0.000759964	+	0.00723058i
$704$	2.42139	+	2.68922i	0.0912594	+	0.101354i
$705$	−19.2971	+	51.1010i	−0.726772	+	1.92457i
$706$	11.3568	−	12.6130i	0.427419	−	0.474697i
$707$	11.3788	+	19.7087i	0.427944	+	0.741221i
$708$	−9.01301	+	14.0457i	−0.338729	+	0.527870i
$709$	−19.2205	+	21.3465i	−0.721841	+	0.801685i	−0.986691	−	0.162604i	$-0.948011\pi$
$709$	−19.2205	+	21.3465i	−0.721841	+	0.801685i	0.264851	+	0.964289i	$0.414677\pi$
$710$	4.29655	+	40.8790i	0.161247	+	1.53416i
$711$	4.36790	−	21.7097i	0.163809	−	0.814176i
$712$	−5.28380			−0.198019
$713$	−20.1022	−	7.41874i	−0.752833	−	0.277834i
$714$	18.2909	−	28.5042i	0.684518	−	1.06674i
$715$	−13.8199	+	6.15301i	−0.516835	+	0.230110i
$716$	4.71740	+	2.10032i	0.176298	+	0.0784928i
$717$	14.6866	+	3.84966i	0.548483	+	0.143768i
$718$	−10.2652	+	17.7799i	−0.383095	+	0.663540i
$719$	23.6725	−	41.0020i	0.882836	−	1.52912i	0.0346616	−	0.999399i	$-0.488965\pi$
$719$	23.6725	−	41.0020i	0.882836	−	1.52912i	0.848174	−	0.529717i	$-0.177702\pi$
$720$	−8.52964	−	2.66907i	−0.317881	−	0.0994705i
$721$	−11.0943	+	34.1446i	−0.413172	+	1.27161i
$722$	−12.5797	−	13.9712i	−0.468169	−	0.519954i
$723$	23.3934	−	9.12638i	0.870009	−	0.339414i
$724$	4.07690	+	12.5474i	0.151517	+	0.466321i
$725$	2.02830	−	19.2980i	0.0753293	−	0.716711i
$726$	−3.24212	−	1.62976i	−0.120326	−	0.0604861i
$727$	−9.48197	+	29.1825i	−0.351667	+	1.08232i	0.606250	+	0.795274i	$0.292673\pi$
$727$	−9.48197	+	29.1825i	−0.351667	+	1.08232i	−0.957917	+	0.287045i	$0.907327\pi$
$728$	3.63890	−	2.64381i	0.134867	−	0.0979863i
$729$	−25.3922	+	9.17808i	−0.940451	+	0.339929i
$730$	18.9157	+	21.0081i	0.700103	+	0.777543i
$731$	−5.72598	−	54.4791i	−0.211783	−	2.01498i
$732$	3.36270	−	1.31188i	0.124289	−	0.0484884i
$733$	0.745376	+	2.29403i	0.0275311	+	0.0847320i	0.963878	−	0.266344i	$-0.0858158\pi$
$733$	0.745376	+	2.29403i	0.0275311	+	0.0847320i	−0.936347	+	0.351076i	$0.885816\pi$
$734$	−13.1982	−	9.58905i	−0.487154	−	0.353938i
$735$	−10.7055	−	13.0739i	−0.394878	−	0.482238i
$736$	−3.76438	+	0.800145i	−0.138757	+	0.0294937i
$737$	42.7159	+	9.07955i	1.57346	+	0.334449i
$738$	−8.19850	+	11.5467i	−0.301791	+	0.425041i
$739$	−1.70400	−	2.95141i	−0.0626825	−	0.108569i	0.832981	−	0.553301i	$-0.186632\pi$
$739$	−1.70400	−	2.95141i	−0.0626825	−	0.108569i	−0.895664	+	0.444732i	$0.853299\pi$
$740$	−0.859486	+	0.954556i	−0.0315953	+	0.0350902i
$741$	−0.970886	−	0.488048i	−0.0356664	−	0.0179289i
$742$	−20.8986	+	9.30465i	−0.767211	+	0.341584i
$743$	11.3988	−	19.7433i	0.418180	−	0.724310i	−0.577576	−	0.816337i	$-0.696001\pi$
$743$	11.3988	−	19.7433i	0.418180	−	0.724310i	0.995757	+	0.0920271i	$0.0293346\pi$
$744$	−9.39438	+	2.17844i	−0.344415	+	0.0798654i
$745$	30.3267	+	52.5273i	1.11108	+	1.92445i
$746$	22.6425	+	16.4507i	0.829000	+	0.602304i
$747$	−20.6656	+	12.2334i	−0.756116	+	0.447597i
$748$	6.82150	+	20.9944i	0.249419	+	0.767632i
$749$	−31.7315	+	54.9605i	−1.15944	+	2.00821i
$750$	5.79657	+	0.272134i	0.211661	+	0.00993692i
$751$	−3.93046	+	4.36522i	−0.143425	+	0.159289i	−0.810577	−	0.585632i	$-0.800846\pi$
$751$	−3.93046	+	4.36522i	−0.143425	+	0.159289i	0.667152	+	0.744921i	$0.267513\pi$
$752$	7.08326	+	7.86675i	0.258300	+	0.286871i
$753$	10.7854	−	1.76851i	0.393040	−	0.0644480i
$754$	6.41857	−	2.85773i	0.233751	−	0.104072i
$755$	4.31845	−	4.79612i	0.157164	−	0.174549i
$756$	−16.0157	+	4.57316i	−0.582487	+	0.166324i
$757$	−47.0409	−	20.9440i	−1.70973	−	0.761221i	−0.998289	−	0.0584752i	$-0.981376\pi$
$757$	−47.0409	−	20.9440i	−1.70973	−	0.761221i	−0.711441	−	0.702746i	$-0.751957\pi$
$758$	9.66037	−	29.7316i	0.350881	−	1.07990i
$759$	20.1581	−	13.2475i	0.731692	−	0.480853i
$760$	0.139229	+	1.32468i	0.00505038	+	0.0480512i
$761$	−0.406545	+	0.0864139i	−0.0147373	+	0.00313250i	−0.215274	−	0.976554i	$-0.569065\pi$
$761$	−0.406545	+	0.0864139i	−0.0147373	+	0.00313250i	0.200537	+	0.979686i	$0.435731\pi$
$762$	−0.617065	−	10.6627i	−0.0223539	−	0.386269i
$763$	−11.0122	−	8.00085i	−0.398669	−	0.289650i
$764$	−3.76270	+	4.17890i	−0.136130	+	0.151187i
$765$	−40.9116	−	36.0378i	−1.47916	−	1.30295i
$766$	−5.88376	+	1.25063i	−0.212589	+	0.0451872i
$767$	−13.2250	+	2.81106i	−0.477528	+	0.101502i
$768$	−1.21806	+	1.23140i	−0.0439528	+	0.0444342i
$769$	9.93847	+	17.2139i	0.358390	+	0.620750i	0.987692	−	0.156411i	$-0.0499924\pi$
$769$	9.93847	+	17.2139i	0.358390	+	0.620750i	−0.629302	+	0.777161i	$0.716659\pi$
$770$	34.5567			1.24534
$771$	−15.6993	−	4.11509i	−0.565395	−	0.148201i
$772$	8.45766	−	6.14485i	0.304398	−	0.221158i
$773$	0.874552	+	0.635399i	0.0314555	+	0.0228537i	0.603402	−	0.797437i	$-0.293811\pi$
$773$	0.874552	+	0.635399i	0.0314555	+	0.0228537i	−0.571946	+	0.820291i	$0.693811\pi$
$774$	−15.5964	+	21.9659i	−0.560601	+	0.789547i
$775$	−19.0969	+	10.0445i	−0.685980	+	0.360810i
$776$	−3.80767	−	6.59507i	−0.136687	−	0.236749i
$777$	−0.361582	+	2.36629i	−0.0129717	+	0.0848901i
$778$	15.6424	+	6.96446i	0.560809	+	0.249688i
$779$	2.06438	+	0.438797i	0.0739639	+	0.0157215i
$780$	−3.32231	−	6.43353i	−0.118958	−	0.230357i
$781$	−49.9280			−1.78657
$782$	−22.9635	−	4.88104i	−0.821173	−	0.174546i
$783$	−25.9560	+	1.78601i	−0.927590	+	0.0638267i
$784$	−3.20316	+	0.680853i	−0.114399	+	0.0243162i
$785$	0.948764	−	0.422417i	0.0338629	−	0.0150767i
$786$	−22.8321	+	23.0821i	−0.814392	+	0.823313i
$787$	−2.29151	+	21.8022i	−0.0816833	+	0.777165i	0.874624	+	0.484802i	$0.161108\pi$
$787$	−2.29151	+	21.8022i	−0.0816833	+	0.777165i	−0.956307	+	0.292363i	$0.905558\pi$
$788$	−9.06097	+	6.58318i	−0.322784	+	0.234516i
$789$	11.7031	−	30.9912i	0.416642	−	1.10332i
$790$	−20.0897	−	8.94450i	−0.714759	−	0.318231i
$791$	−42.1975	+	30.6583i	−1.50037	+	1.09008i
$792$	4.30728	−	9.96507i	0.153053	−	0.354093i
$793$	2.67146	+	1.18941i	0.0948663	+	0.0422372i
$794$	−2.37331	−	1.72431i	−0.0842257	−	0.0611936i
$795$	9.72493	+	35.5189i	0.344908	+	1.25973i
$796$	15.1488	+	11.0062i	0.536935	+	0.390106i
$797$	−9.73711	+	29.9677i	−0.344906	+	1.06151i	0.616728	+	0.787176i	$0.288458\pi$
$797$	−9.73711	+	29.9677i	−0.344906	+	1.06151i	−0.961634	+	0.274335i	$0.911542\pi$
$798$	1.57262	+	1.92054i	0.0556703	+	0.0679865i
$799$	19.9549	+	61.4147i	0.705952	+	2.17270i
$800$	−1.93770	+	3.35620i	−0.0685082	+	0.118660i
$801$	6.60471	+	14.4099i	0.233366	+	0.509148i
$802$	−6.57143	−	20.2248i	−0.232045	−	0.714162i
$803$	−27.7798	+	20.1832i	−0.980328	+	0.712250i
$804$	−3.15733	+	20.6624i	−0.111350	+	0.728706i
$805$	−18.3755	+	31.8273i	−0.647651	+	1.12176i
$806$	−6.60704	−	4.16980i	−0.232723	−	0.146875i
$807$	−12.5526	−	0.589312i	−0.441873	−	0.0207448i
$808$	0.742124	−	7.06083i	0.0261078	−	0.248399i
$809$	0.675378	+	6.42579i	0.0237450	+	0.225919i	0.999959	+	0.00910739i	$0.00289901\pi$
$809$	0.675378	+	6.42579i	0.0237450	+	0.225919i	−0.976214	+	0.216811i	$0.930434\pi$
$810$	3.38294	+	26.5982i	0.118864	+	0.934565i
$811$	7.53574	+	13.0523i	0.264616	+	0.458328i	0.967463	−	0.253013i	$-0.0814216\pi$
$811$	7.53574	+	13.0523i	0.264616	+	0.458328i	−0.702847	+	0.711341i	$0.748088\pi$
$812$	−16.0497			−0.563233
$813$	23.4542	+	6.14781i	0.822576	+	0.215613i
$814$	−1.04399	−	1.15947i	−0.0365920	−	0.0406395i
$815$	15.0669	−	46.3711i	0.527770	−	1.62431i
$816$	−9.84331	+	3.84014i	−0.344585	+	0.134432i
$817$	3.92716	+	0.834743i	0.137394	+	0.0292040i
$818$	−4.01555	+	1.78784i	−0.140400	+	0.0625103i
$819$	−11.7588	−	6.61918i	−0.410884	−	0.231293i
$820$	9.40994	+	10.4508i	0.328610	+	0.364958i
$821$	32.9122	+	14.6535i	1.14864	+	0.511409i	0.890628	−	0.454732i	$-0.150265\pi$
$821$	32.9122	+	14.6535i	1.14864	+	0.511409i	0.258015	+	0.966141i	$0.416932\pi$
$822$	1.81503	+	31.3633i	0.0633066	+	1.09392i
$823$	−44.3639	+	9.42984i	−1.54643	+	0.328703i	−0.900555	−	0.434742i	$-0.856840\pi$
$823$	−44.3639	+	9.42984i	−1.54643	+	0.328703i	−0.645873	+	0.763445i	$0.723506\pi$
$824$	9.06126	−	6.58339i	0.315664	−	0.229343i
$825$	3.66909	−	24.0115i	0.127741	−	0.835973i
$826$	30.2102	+	6.42139i	1.05115	+	0.223429i
$827$	3.97334	−	37.8038i	0.138166	−	1.31457i	−0.677277	−	0.735728i	$-0.736840\pi$
$827$	3.97334	−	37.8038i	0.138166	−	1.31457i	0.815443	−	0.578837i	$-0.196493\pi$
$828$	6.88760	+	9.26598i	0.239360	+	0.322015i
$829$	−8.64776	+	26.6151i	−0.300349	+	0.924380i	0.681023	+	0.732262i	$0.261535\pi$
$829$	−8.64776	+	26.6151i	−0.300349	+	0.924380i	−0.981372	+	0.192117i	$0.938465\pi$
$830$	7.36953	+	22.6811i	0.255800	+	0.787272i
$831$	−37.1382	−	1.74354i	−1.28831	−	0.0604828i
$832$	−1.40322			−0.0486481
$833$	−19.5399	−	4.15334i	−0.677018	−	0.143905i
$834$	1.28946	+	22.2815i	0.0446504	+	0.771547i
$835$	−1.41279	+	13.4418i	−0.0488915	+	0.465171i
$836$	−1.61792			−0.0559568
$837$	17.6839	+	22.8971i	0.611245	+	0.791441i
$838$	−33.4582			−1.15579
$839$	−3.96677	+	37.7413i	−0.136948	+	1.30298i	0.682950	+	0.730465i	$0.260697\pi$
$839$	−3.96677	+	37.7413i	−0.136948	+	1.30298i	−0.819898	+	0.572510i	$0.805970\pi$
$840$	0.955603	+	16.5125i	0.0329714	+	0.569737i
$841$	3.84369	+	0.817001i	0.132541	+	0.0281725i
$842$	15.3392			0.528624
$843$	34.4231	+	1.61607i	1.18559	+	0.0556604i
$844$	−5.26134	−	16.1927i	−0.181103	−	0.557377i
$845$	−10.1552	+	31.2546i	−0.349351	+	1.07519i
$846$	12.6000	−	29.1507i	0.433198	−	1.00222i
$847$	−0.701956	+	6.67867i	−0.0241195	+	0.229482i
$848$	6.98081	+	1.48382i	0.239722	+	0.0509545i
$849$	1.73123	−	11.3296i	0.0594158	−	0.388832i
$850$	−19.1258	+	13.8957i	−0.656009	+	0.476619i
$851$	1.62303	−	0.344987i	0.0556369	−	0.0118260i
$852$	−1.38067	−	23.8576i	−0.0473009	−	0.817346i
$853$	19.4702	+	8.66867i	0.666646	+	0.296810i	0.712019	−	0.702160i	$-0.247781\pi$
$853$	19.4702	+	8.66867i	0.666646	+	0.296810i	−0.0453733	+	0.998970i	$0.514448\pi$
$854$	−4.46979	−	4.96420i	−0.152953	−	0.169872i
$855$	3.43861	−	2.03555i	0.117598	−	0.0696142i
$856$	18.0869	−	8.05283i	0.618199	−	0.275240i
$857$	30.1014	+	6.39826i	1.02825	+	0.218560i	0.690999	−	0.722856i	$-0.257171\pi$
$857$	30.1014	+	6.39826i	1.02825	+	0.218560i	0.337247	+	0.941416i	$0.390504\pi$
$858$	8.19365	−	3.19656i	0.279727	−	0.109129i
$859$	13.5778	−	41.7881i	0.463268	−	1.42579i	−0.397879	−	0.917438i	$-0.630254\pi$
$859$	13.5778	−	41.7881i	0.463268	−	1.42579i	0.861147	−	0.508355i	$-0.169746\pi$
$860$	17.9010	+	19.8810i	0.610418	+	0.677938i
$861$	25.3512	+	6.64504i	0.863966	+	0.226462i
$862$	22.2840			0.758998
$863$	−6.17167	−	10.6896i	−0.210086	−	0.363880i	0.741655	−	0.670781i	$-0.234041\pi$
$863$	−6.17167	−	10.6896i	−0.210086	−	0.363880i	−0.951741	+	0.306902i	$0.900708\pi$
$864$	4.88081	+	1.78262i	0.166048	+	0.0606459i
$865$	0.924573	+	8.79672i	0.0314364	+	0.299097i
$866$	−3.71402	+	35.3365i	−0.126208	+	1.20078i
$867$	−34.9705	−	1.64177i	−1.18766	−	0.0557575i
$868$	9.91355	+	14.8404i	0.336488	+	0.503716i
$869$	13.3559	−	23.1330i	0.453067	−	0.784734i
$870$	−3.90268	+	25.5402i	−0.132313	+	0.865893i
$871$	−13.6999	+	9.95355i	−0.464203	+	0.337263i
$872$	1.31224	+	4.03867i	0.0444382	+	0.136767i
$873$	−13.2264	+	18.6280i	−0.447646	+	0.630462i
$874$	0.860324	−	1.49012i	0.0291009	−	0.0504042i
$875$	−3.31861	−	10.2136i	−0.112189	−	0.345284i
$876$	−10.4125	−	12.7161i	−0.351806	−	0.429638i
$877$	−8.07861	+	24.8634i	−0.272795	+	0.839578i	0.716999	+	0.697074i	$0.245515\pi$
$877$	−8.07861	+	24.8634i	−0.272795	+	0.839578i	−0.989794	+	0.142503i	$0.954485\pi$
$878$	−4.30877	−	3.13051i	−0.145414	−	0.105649i
$879$	−14.7852	−	54.0007i	−0.498691	−	1.82140i
$880$	−8.72178	−	6.33674i	−0.294011	−	0.213612i
$881$	−14.3517	−	6.38979i	−0.483521	−	0.215277i	0.150475	−	0.988614i	$-0.451920\pi$
$881$	−14.3517	−	6.38979i	−0.483521	−	0.215277i	−0.633996	+	0.773336i	$0.718586\pi$
$882$	5.86074	+	7.88454i	0.197341	+	0.265486i
$883$	−43.0014	+	31.2423i	−1.44711	+	1.05139i	−0.460615	+	0.887600i	$0.652371\pi$
$883$	−43.0014	+	31.2423i	−1.44711	+	1.05139i	−0.986496	+	0.163788i	$0.947629\pi$
$884$	−7.81991	−	3.48165i	−0.263012	−	0.117100i
$885$	17.5645	−	46.5127i	0.590424	−	1.56351i
$886$	−4.87754	+	3.54374i	−0.163864	+	0.119054i
$887$	0.955726	−	9.09313i	0.0320901	−	0.305317i	−0.966690	−	0.255948i	$-0.917612\pi$
$887$	0.955726	−	9.09313i	0.0320901	−	0.305317i	0.998781	−	0.0493690i	$-0.0157210\pi$
$888$	0.525171	−	0.530924i	0.0176236	−	0.0178166i
$889$	−18.0571	+	8.03954i	−0.605616	+	0.269637i
$890$	15.3973	−	3.27280i	0.516119	−	0.109704i
$891$	−32.5606	+	0.709541i	−1.09082	+	0.0237705i
$892$	−7.64965	−	1.62598i	−0.256129	−	0.0544419i
$893$	−4.73287			−0.158379
$894$	−16.1800	−	31.3320i	−0.541141	−	1.04790i
$895$	−15.0477	−	3.19850i	−0.502991	−	0.106914i
$896$	2.92830	+	1.30376i	0.0978276	+	0.0435556i
$897$	−1.41288	+	9.24625i	−0.0471746	+	0.308723i
$898$	−12.0504	−	20.8719i	−0.402127	−	0.696504i
$899$	10.3274	+	25.8946i	0.344438	+	0.863632i
$900$	11.5751	+	1.08924i	0.385836	+	0.0363080i
$901$	35.2212	+	25.5897i	1.17339	+	0.852515i
$902$	−13.8195	+	10.0405i	−0.460140	+	0.334311i
$903$	48.2267	+	12.6412i	1.60489	+	0.420672i
$904$	16.2721			0.541202
$905$	−19.6522	−	34.0387i	−0.653263	−	1.13148i
$906$	−2.63870	+	2.66760i	−0.0876648	+	0.0886251i
$907$	21.3024	−	4.52796i	0.707334	−	0.150348i	0.159821	−	0.987146i	$-0.448908\pi$
$907$	21.3024	−	4.52796i	0.707334	−	0.150348i	0.547512	+	0.836798i	$0.315575\pi$
$908$	19.8842	−	4.22651i	0.659879	−	0.140262i
$909$	−20.1838	+	6.80209i	−0.669455	+	0.225611i
$910$	−8.96638	+	9.95818i	−0.297233	+	0.330110i
$911$	−15.2288	−	11.0644i	−0.504552	−	0.366578i	0.306201	−	0.951967i	$-0.400942\pi$
$911$	−15.2288	−	11.0644i	−0.504552	−	0.366578i	−0.810753	+	0.585388i	$0.800942\pi$
$912$	−0.0447405	−	0.773102i	−0.00148151	−	0.0256000i
$913$	−28.3348	+	6.02276i	−0.937746	+	0.199324i
$914$	−0.207292	−	1.97225i	−0.00685660	−	0.0652362i
$915$	−8.98653	+	5.90576i	−0.297085	+	0.195238i
$916$	−5.84824	+	17.9990i	−0.193231	+	0.594705i
$917$	54.8900	+	24.4386i	1.81263	+	0.807033i
$918$	22.7768	+	22.0443i	0.751747	+	0.727572i
$919$	−8.56840	+	9.51618i	−0.282646	+	0.313910i	−0.867704	−	0.497082i	$-0.834405\pi$
$919$	−8.56840	+	9.51618i	−0.282646	+	0.313910i	0.585058	+	0.810991i	$0.301072\pi$
$920$	10.4740	−	4.66334i	0.345319	−	0.153746i
$921$	−26.4080	+	4.33020i	−0.870173	+	0.142685i
$922$	11.1974	+	12.4360i	0.368768	+	0.409558i
$923$	12.9548	−	14.3877i	0.426411	−	0.473578i
$924$	−20.0688	−	0.942176i	−0.660214	−	0.0309953i
$925$	0.835452	−	1.44704i	0.0274695	−	0.0475785i
$926$	1.04189	+	3.20661i	0.0342387	+	0.105376i
$927$	−29.2806	−	16.4825i	−0.961702	−	0.541357i
$928$	4.05078	+	2.94306i	0.132973	+	0.0966108i
$929$	14.3184	+	24.8002i	0.469772	+	0.813669i	0.999403	−	0.0345592i	$-0.0110027\pi$
$929$	14.3184	+	24.8002i	0.469772	+	0.813669i	−0.529631	+	0.848228i	$0.677669\pi$
$930$	26.0265	−	12.1670i	0.853441	−	0.398972i
$931$	0.732060	−	1.26797i	0.0239923	−	0.0415559i
$932$	0.590957	−	0.263111i	0.0193574	−	0.00861848i
$933$	27.3420	+	13.7444i	0.895137	+	0.449971i
$934$	26.0912	−	28.9772i	0.853731	−	0.948164i
$935$	−32.8823	−	56.9537i	−1.07536	−	1.86259i
$936$	1.75402	+	3.82685i	0.0573320	+	0.125084i
$937$	33.4859	+	7.11765i	1.09394	+	0.232524i	0.719336	−	0.694663i	$-0.244446\pi$
$937$	33.4859	+	7.11765i	1.09394	+	0.232524i	0.374601	+	0.927186i	$0.377780\pi$
$938$	37.8374	−	8.04259i	1.23544	−	0.262600i
$939$	−10.5534	−	12.8881i	−0.344396	−	0.420589i
$940$	−25.5137	−	18.5368i	−0.832166	−	0.604604i
$941$	5.40212	+	16.6260i	0.176104	+	0.541993i	0.999682	−	0.0252102i	$-0.00802550\pi$
$941$	5.40212	+	16.6260i	0.176104	+	0.541993i	−0.823578	+	0.567203i	$0.808025\pi$
$942$	−0.562511	+	0.219451i	−0.0183276	+	0.00715009i
$943$	−1.89892	−	18.0670i	−0.0618373	−	0.588342i
$944$	−6.44727	−	7.16042i	−0.209841	−	0.233052i
$945$	43.8382	−	23.2467i	1.42606	−	0.756214i
$946$	−26.2895	+	19.1004i	−0.854745	+	0.621009i
$947$	−6.90529	+	21.2523i	−0.224392	+	0.690607i	0.773961	+	0.633233i	$0.218273\pi$
$947$	−6.90529	+	21.2523i	−0.224392	+	0.690607i	−0.998353	+	0.0573737i	$0.981727\pi$
$948$	11.4232	+	5.74225i	0.371008	+	0.186500i
$949$	1.39181	−	13.2422i	0.0451801	−	0.429860i
$950$	−0.535430	−	1.64788i	−0.0173716	−	0.0534644i
$951$	13.7156	−	5.35084i	0.444760	−	0.173513i
$952$	13.0840	+	14.5312i	0.424054	+	0.470960i
$953$	−16.9721	+	52.2349i	−0.549781	+	1.69205i	0.159560	+	0.987188i	$0.448993\pi$
$953$	−16.9721	+	52.2349i	−0.549781	+	1.69205i	−0.709341	+	0.704865i	$0.751007\pi$
$954$	−4.67933	−	20.8927i	−0.151499	−	0.676426i
$955$	8.37632	−	14.5082i	0.271051	−	0.469474i
$956$	−4.38290	+	7.59140i	−0.141753	+	0.245523i
$957$	−30.3575	−	7.95729i	−0.981318	−	0.257223i
$958$	7.22540	+	3.21696i	0.233442	+	0.103935i
$959$	53.1132	−	23.6475i	1.71511	−	0.763618i
$960$	2.78676	−	4.34283i	0.0899422	−	0.140164i
$961$	17.5645	−	25.5438i	0.566598	−	0.823994i
$962$	0.605008			0.0195062
$963$	−44.5701	−	39.2604i	−1.43625	−	1.26515i
$964$	1.51541	+	14.4182i	0.0488081	+	0.464378i
$965$	−20.8400	+	23.1452i	−0.670863	+	0.745069i
$966$	11.5393	−	17.9827i	0.371271	−	0.578582i
$967$	−2.07142	−	3.58780i	−0.0666122	−	0.115376i	0.830796	−	0.556577i	$-0.187886\pi$
$967$	−2.07142	−	3.58780i	−0.0666122	−	0.115376i	−0.897408	+	0.441202i	$0.854552\pi$
$968$	1.40185	−	1.55691i	0.0450571	−	0.0500410i
$969$	1.66887	−	4.41936i	0.0536119	−	0.141970i
$970$	15.1808	+	16.8600i	0.487425	+	0.541341i
$971$	−2.85556	+	27.1689i	−0.0916393	+	0.871890i	0.848063	+	0.529896i	$0.177769\pi$
$971$	−2.85556	+	27.1689i	−0.0916393	+	0.871890i	−0.939702	+	0.341994i	$0.888898\pi$
$972$	−1.23945	−	15.5391i	−0.0397554	−	0.498417i
$973$	37.7334	−	16.8000i	1.20968	−	0.538583i
$974$	4.39898	+	41.8535i	0.140953	+	1.34107i
$975$	5.96736	+	7.28755i	0.191108	+	0.233388i
$976$	0.217834	+	2.07255i	0.00697270	+	0.0663408i
$977$	3.83766	+	36.5129i	0.122778	+	1.16815i	0.866329	+	0.499473i	$0.166473\pi$
$977$	3.83766	+	36.5129i	0.122778	+	1.16815i	−0.743552	+	0.668678i	$0.766860\pi$
$978$	−10.0144	+	26.5192i	−0.320224	+	0.847990i
$979$	1.99864	+	19.0158i	0.0638767	+	0.607746i
$980$	8.91248	−	3.96809i	0.284699	−	0.126756i
$981$	9.37390	−	8.62704i	0.299285	−	0.275440i
$982$	−1.94366	+	18.4926i	−0.0620245	+	0.590124i
$983$	−37.7456	−	41.9207i	−1.20390	−	1.33706i	−0.926494	−	0.376310i	$-0.877193\pi$
$983$	−37.7456	−	41.9207i	−1.20390	−	1.33706i	−0.277404	−	0.960753i	$-0.589474\pi$
$984$	−5.17988	−	6.32585i	−0.165128	−	0.201661i
$985$	22.3266	−	24.7962i	0.711384	−	0.790072i
$986$	15.2720	+	26.4518i	0.486359	+	0.842398i
$987$	−58.7070	−	2.75614i	−1.86866	−	0.0877288i
$988$	0.419798	−	0.466233i	0.0133556	−	0.0148329i
$989$	−3.61240	−	34.3697i	−0.114868	−	1.09289i
$990$	−6.37928	+	31.7068i	−0.202747	+	1.00771i
$991$	−30.1379			−0.957362			−0.478681	−	0.877989i	$-0.658885\pi$
$991$	−30.1379			−0.957362			−0.478681	+	0.877989i	$0.658885\pi$
$992$	0.219236	−	5.56345i	0.00696076	−	0.176640i
$993$	−2.24947	−	4.35602i	−0.0713849	−	0.138234i
$994$	−40.4023	+	17.9883i	−1.28148	+	0.570554i
$995$	−50.9618	−	22.6897i	−1.61560	−	0.719310i
$996$	−3.66145	−	13.3729i	−0.116018	−	0.423738i
$997$	7.95563	−	13.7796i	0.251957	−	0.436403i	−0.712107	−	0.702071i	$-0.752259\pi$
$997$	7.95563	−	13.7796i	0.251957	−	0.436403i	0.964065	+	0.265668i	$0.0855924\pi$
$998$	−16.1254	+	27.9300i	−0.510440	+	0.884107i
$999$	−2.10439	−	0.768586i	−0.0665798	−	0.0243170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.bb.b.103.8	yes	128
9.7	even	3		558.2.y.b.475.9	yes	128
31.28	even	15		558.2.y.b.121.9	✓	128
279.214	even	15	inner	558.2.bb.b.493.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.y.b.121.9	✓	128	31.28	even	15
558.2.y.b.475.9	yes	128	9.7	even	3
558.2.bb.b.103.8	yes	128	1.1	even	1	trivial
558.2.bb.b.493.8	yes	128	279.214	even	15	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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.bb (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.100069 + 1.72916i) q^{3} +(-0.978148 - 0.207912i) q^{4} +2.97916 q^{5} +(-1.73015 - 0.0812257i) q^{6} +(0.990529 + 3.04854i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.97997 + 0.346069i) q^{9} +(-0.311407 + 2.96284i) q^{10} +(-3.53963 - 0.752371i) q^{11} +(0.261630 - 1.71218i) q^{12} +(1.13523 - 0.824795i) q^{13} +(-3.13537 + 0.666444i) q^{14} +(0.298121 + 5.15144i) q^{15} +(0.913545 + 0.406737i) q^{16} +(4.08183 + 4.53333i) q^{17} +(-0.0326812 - 2.99982i) q^{18} +(-0.408444 + 0.181851i) q^{19} +(-2.91406 - 0.619403i) q^{20} +(-5.17228 + 2.01784i) q^{21} +(1.11824 - 3.44159i) q^{22} +(2.57514 + 2.85998i) q^{23} +(1.67545 + 0.439168i) q^{24} +3.87541 q^{25} +(0.701612 + 1.21523i) q^{26} +(-0.896610 - 5.11821i) q^{27} +(-0.335058 - 3.18786i) q^{28} +(0.523378 - 4.97961i) q^{29} +(-5.15438 - 0.241985i) q^{30} +(-4.92770 + 2.59186i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.946763 - 6.19586i) q^{33} +(-4.93517 + 3.58561i) q^{34} +(2.95095 + 9.08208i) q^{35} +(2.98680 + 0.281065i) q^{36} +(0.215578 - 0.373392i) q^{37} +(-0.138161 - 0.425215i) q^{38} +(1.53980 + 1.88046i) q^{39} +(0.920612 - 2.83335i) q^{40} +(-3.81891 - 2.77460i) q^{41} +(-1.46614 - 5.35487i) q^{42} +(-7.26489 - 5.27825i) q^{43} +(3.30585 + 1.47186i) q^{44} +(-8.87782 + 1.03100i) q^{45} +(-3.11349 + 2.26208i) q^{46} +(9.67057 + 4.30562i) q^{47} +(-0.611895 + 1.62037i) q^{48} +(-2.64931 + 1.92483i) q^{49} +(-0.405091 + 3.85418i) q^{50} +(-7.43038 + 7.51178i) q^{51} +(-1.28191 + 0.570743i) q^{52} +(6.98081 - 1.48382i) q^{53} +(5.18389 - 0.356699i) q^{54} +(-10.5451 - 2.24144i) q^{55} +3.20542 q^{56} +(-0.355322 - 0.688067i) q^{57} +(4.89762 + 1.04102i) q^{58} +(-8.80227 - 3.91903i) q^{59} +(0.779439 - 5.10085i) q^{60} +(1.04198 + 1.80477i) q^{61} +(-2.06258 - 5.17163i) q^{62} +(-4.00675 - 8.74176i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.38204 - 2.45720i) q^{65} +(6.06296 + 1.58922i) q^{66} -12.0679 q^{67} +(-3.05010 - 5.28293i) q^{68} +(-4.68767 + 4.73901i) q^{69} +(-9.34079 + 1.98545i) q^{70} +(13.4957 - 2.86860i) q^{71} +(-0.591731 + 2.94106i) q^{72} +(6.34935 - 7.05167i) q^{73} +(0.348812 + 0.253427i) q^{74} +(0.387807 + 6.70119i) q^{75} +(0.437328 - 0.0929568i) q^{76} +(-1.21248 - 11.5359i) q^{77} +(-2.03111 + 1.33480i) q^{78} +(-2.28103 + 7.02029i) q^{79} +(2.72160 + 1.21173i) q^{80} +(8.76047 - 2.06255i) q^{81} +(3.15859 - 3.50797i) q^{82} +(7.31296 - 3.25594i) q^{83} +(5.47879 - 0.898373i) q^{84} +(12.1604 + 13.5055i) q^{85} +(6.00872 - 6.67337i) q^{86} +(8.66290 + 0.406700i) q^{87} +(-1.80935 + 3.13389i) q^{88} +(-1.63278 - 5.02519i) q^{89} +(-0.0973627 - 8.93696i) q^{90} +(3.63890 + 2.64381i) q^{91} +(-1.92424 - 3.33288i) q^{92} +(-4.97484 - 8.26141i) q^{93} +(-5.29288 + 9.16754i) q^{94} +(-1.21682 + 0.541764i) q^{95} +(-1.54753 - 0.777917i) q^{96} +(5.09565 - 5.65929i) q^{97} +(-1.63736 - 2.83599i) q^{98} +(10.8084 + 1.01709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 2 q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 32 q^{8} - 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 20 q^{13} - q^{14} - 22 q^{15} + 16 q^{16} + 4 q^{17} - 2 q^{18} - 4 q^{19} + q^{20}+ \cdots + 15 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 32 * q^8 - 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 - 20 * q^13 - q^14 - 22 * q^15 + 16 * q^16 + 4 * q^17 - 2 * q^18 - 4 * q^19 + q^20 + 19 * q^21 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 122 * q^25 - 20 * q^26 - 37 * q^27 + 9 * q^28 - 12 * q^29 - 14 * q^30 + 25 * q^31 - 64 * q^32 + 22 * q^33 - 8 * q^34 + 6 * q^36 - 66 * q^37 - 12 * q^38 + 11 * q^39 - 2 * q^40 + 20 * q^41 + 10 * q^42 - 31 * q^43 + 2 * q^44 + 64 * q^45 + 13 * q^46 + 11 * q^47 - 3 * q^48 - 46 * q^49 + 19 * q^50 + 17 * q^51 + 10 * q^52 + 27 * q^53 - 13 * q^54 - 19 * q^55 + 2 * q^56 + 20 * q^57 + 3 * q^58 - 9 * q^59 + 11 * q^60 - 57 * q^61 + 14 * q^62 - 38 * q^63 - 32 * q^64 - 66 * q^65 - 20 * q^66 - 16 * q^67 - 16 * q^68 - 8 * q^69 - 7 * q^71 + q^72 - 7 * q^73 - 28 * q^74 + 74 * q^75 + 6 * q^76 + 46 * q^77 - 24 * q^78 - 48 * q^79 - 9 * q^80 - 64 * q^81 + 50 * q^82 - 99 * q^83 + q^84 + 27 * q^85 + 33 * q^86 + 81 * q^87 - 8 * q^88 - 52 * q^89 - 45 * q^90 + 11 * q^91 + q^92 + 30 * q^93 + 6 * q^94 + 19 * q^95 - 4 * q^96 + 35 * q^97 - 77 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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