LMFDB - Embedded newform 961.2.d.q.388.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			388.1
Root			$-0.333129i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.q.374.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67638 + 1.21796i) q^{2} +(-1.73080 - 1.25750i) q^{3} +(0.708788 - 2.18143i) q^{4} +2.34791 q^{5} +4.43308 q^{6} +(-1.13550 + 3.49470i) q^{7} +(0.188054 + 0.578772i) q^{8} +(0.487319 + 1.49981i) q^{9} +(-3.93600 + 2.85967i) q^{10} +(1.32279 - 4.07113i) q^{11} +(-3.96992 + 2.88432i) q^{12} +(-1.68858 - 1.22682i) q^{13} +(-2.35288 - 7.24144i) q^{14} +(-4.06377 - 2.95251i) q^{15} +(2.69109 + 1.95519i) q^{16} +(-0.657617 - 2.02394i) q^{17} +(-2.64365 - 1.92072i) q^{18} +(0.501603 - 0.364436i) q^{19} +(1.66417 - 5.12180i) q^{20} +(6.35991 - 4.62075i) q^{21} +(2.74098 + 8.43588i) q^{22} +(1.03640 + 3.18973i) q^{23} +(0.402322 - 1.23822i) q^{24} +0.512688 q^{25} +4.32493 q^{26} +(-0.940760 + 2.89536i) q^{27} +(6.81860 + 4.95400i) q^{28} +(-1.11435 + 0.809625i) q^{29} +10.4085 q^{30} -8.10976 q^{32} +(-7.40895 + 5.38292i) q^{33} +(3.56749 + 2.59194i) q^{34} +(-2.66604 + 8.20524i) q^{35} +3.61714 q^{36} -0.274477 q^{37} +(-0.397009 + 1.22187i) q^{38} +(1.37986 + 4.24679i) q^{39} +(0.441535 + 1.35890i) q^{40} +(3.46091 - 2.51449i) q^{41} +(-5.03374 + 15.4923i) q^{42} +(0.218186 - 0.158521i) q^{43} +(-7.94330 - 5.77114i) q^{44} +(1.14418 + 3.52143i) q^{45} +(-5.62238 - 4.08489i) q^{46} +(-4.35183 - 3.16179i) q^{47} +(-2.19909 - 6.76811i) q^{48} +(-5.26043 - 3.82193i) q^{49} +(-0.859461 + 0.624435i) q^{50} +(-1.40690 + 4.32999i) q^{51} +(-3.87307 + 2.81395i) q^{52} +(-2.93835 - 9.04330i) q^{53} +(-1.94937 - 5.99954i) q^{54} +(3.10580 - 9.55866i) q^{55} -2.23617 q^{56} -1.32646 q^{57} +(0.881988 - 2.71448i) q^{58} +(4.71450 + 3.42528i) q^{59} +(-9.32103 + 6.77212i) q^{60} -2.22719 q^{61} -5.79474 q^{63} +(8.21287 - 5.96700i) q^{64} +(-3.96464 - 2.88048i) q^{65} +(5.86404 - 18.0477i) q^{66} -13.6144 q^{67} -4.88118 q^{68} +(2.21728 - 6.82407i) q^{69} +(-5.52437 - 17.0022i) q^{70} +(-0.412823 - 1.27054i) q^{71} +(-0.776406 + 0.564092i) q^{72} +(4.37754 - 13.4727i) q^{73} +(0.460128 - 0.334303i) q^{74} +(-0.887363 - 0.644707i) q^{75} +(-0.439460 - 1.35252i) q^{76} +(12.7253 + 9.24551i) q^{77} +(-7.48561 - 5.43861i) q^{78} +(-2.68122 - 8.25195i) q^{79} +(6.31845 + 4.59062i) q^{80} +(9.09665 - 6.60910i) q^{81} +(-2.73924 + 8.43051i) q^{82} +(-4.19514 + 3.04795i) q^{83} +(-5.57199 - 17.1488i) q^{84} +(-1.54403 - 4.75202i) q^{85} +(-0.172690 + 0.531484i) q^{86} +2.94683 q^{87} +2.60501 q^{88} +(-1.54897 + 4.76725i) q^{89} +(-6.20705 - 4.50968i) q^{90} +(6.20475 - 4.50802i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(1.17772 - 0.855663i) q^{95} +(14.0364 + 10.1980i) q^{96} +(2.07474 - 6.38538i) q^{97} +13.4735 q^{98} +6.75055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} - 9 q^{13} - 18 q^{14} - 4 q^{15} - 2 q^{16} - 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 - 9 * q^13 - 18 * q^14 - 4 * q^15 - 2 * q^16 - 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 - 2 * q^21 + 8 * q^22 - 21 * q^23 - 5 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 + 56 * q^34 + 21 * q^35 - 2 * q^36 - 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 - 12 * q^42 + 16 * q^43 - 37 * q^44 - 5 * q^45 + 16 * q^46 + 4 * q^47 - 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 + 18 * q^52 - 3 * q^53 - 39 * q^54 - 29 * q^55 + 60 * q^56 - 34 * q^57 - 10 * q^58 - 3 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 9 * q^65 + 20 * q^66 - 26 * q^67 + 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 + 9 * q^73 - 64 * q^74 - 19 * q^75 + 9 * q^76 + 42 * q^77 + 15 * q^78 - 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 - 67 * q^83 - 39 * q^84 + 63 * q^85 + 23 * q^86 - 30 * q^87 - 34 * q^88 - 26 * q^89 - 24 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 4 * q^96 - 37 * q^97 + 20 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−1.67638	+	1.21796i	−1.18538	+	0.861230i	−0.992768	−	0.120045i	$-0.961696\pi$
$2$	−1.67638	+	1.21796i	−1.18538	+	0.861230i	−0.192612	+	0.981275i	$0.561696\pi$
$3$	−1.73080	−	1.25750i	−0.999280	−	0.726020i	−0.0373465	−	0.999302i	$-0.511891\pi$
$3$	−1.73080	−	1.25750i	−0.999280	−	0.726020i	−0.961934	+	0.273283i	$0.911891\pi$
$4$	0.708788	−	2.18143i	0.354394	−	1.09071i
$5$	2.34791			1.05002			0.525009	−	0.851097i	$-0.324062\pi$
$5$	2.34791			1.05002			0.525009	+	0.851097i	$0.324062\pi$
$6$	4.43308			1.80980
$7$	−1.13550	+	3.49470i	−0.429177	+	1.32087i	0.469760	+	0.882794i	$0.344340\pi$
$7$	−1.13550	+	3.49470i	−0.429177	+	1.32087i	−0.898937	+	0.438077i	$0.855660\pi$
$8$	0.188054	+	0.578772i	0.0664872	+	0.204627i
$9$	0.487319	+	1.49981i	0.162440	+	0.499937i
$10$	−3.93600	+	2.85967i	−1.24467	+	0.904306i
$11$	1.32279	−	4.07113i	0.398836	−	1.22749i	−0.527097	−	0.849805i	$-0.676719\pi$
$11$	1.32279	−	4.07113i	0.398836	−	1.22749i	0.925933	−	0.377687i	$-0.123281\pi$
$12$	−3.96992	+	2.88432i	−1.14602	+	0.832631i
$13$	−1.68858	−	1.22682i	−0.468328	−	0.340260i	0.328462	−	0.944517i	$-0.393470\pi$
$13$	−1.68858	−	1.22682i	−0.468328	−	0.340260i	−0.796789	+	0.604257i	$0.793470\pi$
$14$	−2.35288	−	7.24144i	−0.628835	−	1.93536i
$15$	−4.06377	−	2.95251i	−1.04926	−	0.762334i
$16$	2.69109	+	1.95519i	0.672773	+	0.488798i
$17$	−0.657617	−	2.02394i	−0.159495	−	0.490876i	0.839093	−	0.543988i	$-0.183086\pi$
$17$	−0.657617	−	2.02394i	−0.159495	−	0.490876i	−0.998589	+	0.0531113i	$0.983086\pi$
$18$	−2.64365	−	1.92072i	−0.623113	−	0.452718i
$19$	0.501603	−	0.364436i	0.115076	−	0.0836073i	−0.528759	−	0.848772i	$-0.677342\pi$
$19$	0.501603	−	0.364436i	0.115076	−	0.0836073i	0.643835	+	0.765165i	$0.277342\pi$
$20$	1.66417	−	5.12180i	0.372120	−	1.14527i
$21$	6.35991	−	4.62075i	1.38785	−	1.00833i
$22$	2.74098	+	8.43588i	0.584380	+	1.79854i
$23$	1.03640	+	3.18973i	0.216105	+	0.665104i	0.999073	+	0.0430417i	$0.0137048\pi$
$23$	1.03640	+	3.18973i	0.216105	+	0.665104i	−0.782968	+	0.622062i	$0.786295\pi$
$24$	0.402322	−	1.23822i	0.0821236	−	0.252750i
$25$	0.512688			0.102538
$26$	4.32493			0.848189
$27$	−0.940760	+	2.89536i	−0.181049	+	0.557213i
$28$	6.81860	+	4.95400i	1.28859	+	0.936218i
$29$	−1.11435	+	0.809625i	−0.206930	+	0.150344i	−0.686424	−	0.727202i	$-0.740820\pi$
$29$	−1.11435	+	0.809625i	−0.206930	+	0.150344i	0.479493	+	0.877545i	$0.340820\pi$
$30$	10.4085			1.90032
$31$		0			0
$31$		0			0
$32$	−8.10976			−1.43362
$33$	−7.40895	+	5.38292i	−1.28973	+	0.937046i
$34$	3.56749	+	2.59194i	0.611820	+	0.444513i
$35$	−2.66604	+	8.20524i	−0.450644	+	1.38694i
$36$	3.61714			0.602856
$37$	−0.274477			−0.0451238			−0.0225619	−	0.999745i	$-0.507182\pi$
$37$	−0.274477			−0.0451238			−0.0225619	+	0.999745i	$0.507182\pi$
$38$	−0.397009	+	1.22187i	−0.0644033	+	0.198213i
$39$	1.37986	+	4.24679i	0.220955	+	0.680030i
$40$	0.441535	+	1.35890i	0.0698128	+	0.214862i
$41$	3.46091	−	2.51449i	0.540503	−	0.392698i	−0.283769	−	0.958893i	$-0.591585\pi$
$41$	3.46091	−	2.51449i	0.540503	−	0.392698i	0.824272	+	0.566195i	$0.191585\pi$
$42$	−5.03374	+	15.4923i	−0.776723	+	2.39051i
$43$	0.218186	−	0.158521i	0.0332730	−	0.0241743i	−0.571024	−	0.820933i	$-0.693454\pi$
$43$	0.218186	−	0.158521i	0.0332730	−	0.0241743i	0.604297	+	0.796759i	$0.293454\pi$
$44$	−7.94330	−	5.77114i	−1.19750	−	0.870033i
$45$	1.14418	+	3.52143i	0.170564	+	0.524943i
$46$	−5.62238	−	4.08489i	−0.828974	−	0.602285i
$47$	−4.35183	−	3.16179i	−0.634780	−	0.461195i	0.223273	−	0.974756i	$-0.428326\pi$
$47$	−4.35183	−	3.16179i	−0.634780	−	0.461195i	−0.858053	+	0.513561i	$0.828326\pi$
$48$	−2.19909	−	6.76811i	−0.317412	−	0.976893i
$49$	−5.26043	−	3.82193i	−0.751490	−	0.545990i
$50$	−0.859461	+	0.624435i	−0.121546	+	0.0883084i
$51$	−1.40690	+	4.32999i	−0.197005	+	0.606320i
$52$	−3.87307	+	2.81395i	−0.537099	+	0.390225i
$53$	−2.93835	−	9.04330i	−0.403613	−	1.24219i	−0.922048	−	0.387075i	$-0.873485\pi$
$53$	−2.93835	−	9.04330i	−0.403613	−	1.24219i	0.518435	−	0.855117i	$-0.326515\pi$
$54$	−1.94937	−	5.99954i	−0.265276	−	0.816434i
$55$	3.10580	−	9.55866i	0.418785	−	1.28889i
$56$	−2.23617			−0.298820
$57$	−1.32646			−0.175693
$58$	0.881988	−	2.71448i	0.115811	−	0.356429i
$59$	4.71450	+	3.42528i	0.613775	+	0.445934i	0.850742	−	0.525584i	$-0.176153\pi$
$59$	4.71450	+	3.42528i	0.613775	+	0.445934i	−0.236967	+	0.971518i	$0.576153\pi$
$60$	−9.32103	+	6.77212i	−1.20334	+	0.874278i
$61$	−2.22719			−0.285162			−0.142581	−	0.989783i	$-0.545540\pi$
$61$	−2.22719			−0.285162			−0.142581	+	0.989783i	$0.545540\pi$
$62$		0			0
$63$	−5.79474			−0.730068
$64$	8.21287	−	5.96700i	1.02661	−	0.745875i
$65$	−3.96464	−	2.88048i	−0.491752	−	0.357279i
$66$	5.86404	−	18.0477i	0.721813	−	2.22151i
$67$	−13.6144			−1.66326			−0.831631	−	0.555328i	$-0.812593\pi$
$67$	−13.6144			−1.66326			−0.831631	+	0.555328i	$0.812593\pi$
$68$	−4.88118			−0.591930
$69$	2.21728	−	6.82407i	0.266929	−	0.821522i
$70$	−5.52437	−	17.0022i	−0.660288	−	2.03216i
$71$	−0.412823	−	1.27054i	−0.0489931	−	0.150785i	0.923567	−	0.383437i	$-0.125260\pi$
$71$	−0.412823	−	1.27054i	−0.0489931	−	0.150785i	−0.972560	+	0.232652i	$0.925260\pi$
$72$	−0.776406	+	0.564092i	−0.0915004	+	0.0664789i
$73$	4.37754	−	13.4727i	0.512352	−	1.57686i	−0.275696	−	0.961245i	$-0.588908\pi$
$73$	4.37754	−	13.4727i	0.512352	−	1.57686i	0.788048	−	0.615614i	$-0.211092\pi$
$74$	0.460128	−	0.334303i	0.0534888	−	0.0388619i
$75$	−0.887363	−	0.644707i	−0.102464	−	0.0744443i
$76$	−0.439460	−	1.35252i	−0.0504095	−	0.155144i
$77$	12.7253	+	9.24551i	1.45019	+	1.05362i
$78$	−7.48561	−	5.43861i	−0.847578	−	0.615801i
$79$	−2.68122	−	8.25195i	−0.301661	−	0.928417i	−0.980902	−	0.194502i	$-0.937691\pi$
$79$	−2.68122	−	8.25195i	−0.301661	−	0.928417i	0.679241	−	0.733915i	$-0.262309\pi$
$80$	6.31845	+	4.59062i	0.706424	+	0.513247i
$81$	9.09665	−	6.60910i	1.01074	−	0.734344i
$82$	−2.73924	+	8.43051i	−0.302498	+	0.930994i
$83$	−4.19514	+	3.04795i	−0.460477	+	0.334556i	−0.793718	−	0.608286i	$-0.791858\pi$
$83$	−4.19514	+	3.04795i	−0.460477	+	0.334556i	0.333242	+	0.942841i	$0.391858\pi$
$84$	−5.57199	−	17.1488i	−0.607954	−	1.87109i
$85$	−1.54403	−	4.75202i	−0.167473	−	0.515429i
$86$	−0.172690	+	0.531484i	−0.0186216	+	0.0573114i
$87$	2.94683			0.315934
$88$	2.60501			0.277695
$89$	−1.54897	+	4.76725i	−0.164191	+	0.505327i	−0.998976	−	0.0452489i	$-0.985592\pi$
$89$	−1.54897	+	4.76725i	−0.164191	+	0.505327i	0.834785	+	0.550576i	$0.185592\pi$
$90$	−6.20705	−	4.50968i	−0.654280	−	0.475362i
$91$	6.20475	−	4.50802i	0.650435	−	0.472569i
$92$	7.69274			0.802024
$93$		0			0
$94$	11.1463			1.14965
$95$	1.17772	−	0.855663i	0.120831	−	0.0877892i
$96$	14.0364	+	10.1980i	1.43258	+	1.04083i
$97$	2.07474	−	6.38538i	0.210657	−	0.648337i	−0.788776	−	0.614681i	$-0.789285\pi$
$97$	2.07474	−	6.38538i	0.210657	−	0.648337i	0.999433	−	0.0336562i	$-0.0107151\pi$
$98$	13.4735			1.36102
$99$	6.75055			0.678456
$100$	0.363388	−	1.11839i	0.0363388	−	0.111839i
$101$	−5.58165	−	17.1786i	−0.555395	−	1.70933i	−0.694898	−	0.719108i	$-0.744550\pi$
$101$	−5.58165	−	17.1786i	−0.555395	−	1.70933i	0.139503	−	0.990222i	$-0.455450\pi$
$102$	−2.91527	−	8.97227i	−0.288654	−	0.888387i
$103$	−3.16756	+	2.30137i	−0.312109	+	0.226760i	−0.732801	−	0.680443i	$-0.761787\pi$
$103$	−3.16756	+	2.30137i	−0.312109	+	0.226760i	0.420692	+	0.907204i	$0.361787\pi$
$104$	0.392507	−	1.20801i	0.0384885	−	0.118455i
$105$	14.9325	−	10.8491i	1.45726	−	1.05876i
$106$	15.9402	+	11.5812i	1.54825	+	1.12487i
$107$	3.43492	+	10.5716i	0.332066	+	1.02199i	0.968149	+	0.250374i	$0.0805534\pi$
$107$	3.43492	+	10.5716i	0.332066	+	1.02199i	−0.636083	+	0.771620i	$0.719447\pi$
$108$	5.64922	+	4.10440i	0.543596	+	0.394946i
$109$	−14.6379	−	10.6350i	−1.40205	−	1.01865i	−0.994419	−	0.105505i	$-0.966354\pi$
$109$	−14.6379	−	10.6350i	−1.40205	−	1.01865i	−0.407633	−	0.913146i	$-0.633646\pi$
$110$	6.43559	+	19.8067i	0.613609	+	1.88849i
$111$	0.475066	+	0.345156i	0.0450913	+	0.0327607i
$112$	−9.88853	+	7.18444i	−0.934378	+	0.678865i
$113$	5.41977	−	16.6803i	0.509849	−	1.56915i	−0.282613	−	0.959234i	$-0.591201\pi$
$113$	5.41977	−	16.6803i	0.509849	−	1.56915i	0.792462	−	0.609921i	$-0.208799\pi$
$114$	2.22365	−	1.61557i	0.208263	−	0.151312i
$115$	2.43339	+	7.48919i	0.226914	+	0.698371i
$116$	0.976297	+	3.00473i	0.0906469	+	0.278982i
$117$	1.01713	−	3.13041i	0.0940338	−	0.289406i
$118$	−12.0752			−1.11161
$119$	7.81976			0.716836
$120$	0.944616	−	2.90723i	0.0862312	−	0.265392i
$121$	−5.92515	−	4.30488i	−0.538650	−	0.391352i
$122$	3.73362	−	2.71263i	0.338026	−	0.245590i
$123$	−9.15213			−0.825220
$124$		0			0
$125$	−10.5358			−0.942352
$126$	9.71419	−	7.05777i	0.865409	−	0.628756i
$127$	−11.4866	−	8.34554i	−1.01928	−	0.740547i	−0.0531411	−	0.998587i	$-0.516923\pi$
$127$	−11.4866	−	8.34554i	−1.01928	−	0.740547i	−0.966134	+	0.258040i	$0.916923\pi$
$128$	−1.48821	+	4.58025i	−0.131541	+	0.404841i
$129$	−0.576978			−0.0508000
$130$	10.1546			0.890613
$131$	2.22137	−	6.83668i	0.194082	−	0.597324i	−0.805904	−	0.592046i	$-0.798320\pi$
$131$	2.22137	−	6.83668i	0.194082	−	0.597324i	0.999986	−	0.00527721i	$-0.00167980\pi$
$132$	6.49106	+	19.9774i	0.564974	+	1.73881i
$133$	0.704025	+	2.16677i	0.0610467	+	0.187882i
$134$	22.8229	−	16.5818i	1.97160	−	1.43245i
$135$	−2.20882	+	6.79805i	−0.190105	+	0.585083i
$136$	1.04773	−	0.761220i	0.0898420	−	0.0652740i
$137$	6.13045	+	4.45403i	0.523760	+	0.380534i	0.818018	−	0.575192i	$-0.195073\pi$
$137$	6.13045	+	4.45403i	0.523760	+	0.380534i	−0.294259	+	0.955726i	$0.595073\pi$
$138$	4.59446	+	14.1403i	0.391107	+	1.20370i
$139$	−16.2598	−	11.8134i	−1.37914	−	1.00200i	−0.996960	−	0.0779138i	$-0.975174\pi$
$139$	−16.2598	−	11.8134i	−1.37914	−	1.00200i	−0.382178	−	0.924089i	$-0.624826\pi$
$140$	16.0095	+	11.6316i	1.35305	+	0.983046i
$141$	3.55621	+	10.9449i	0.299487	+	0.921726i
$142$	2.23952	+	1.62711i	0.187936	+	0.136544i
$143$	−7.22820	+	5.25160i	−0.604453	+	0.439161i
$144$	−1.62100	+	4.98893i	−0.135084	+	0.415744i
$145$	−2.61640	+	1.90093i	−0.217280	+	0.157863i
$146$	9.07080	+	27.9170i	0.750704	+	2.31043i
$147$	4.29869	+	13.2300i	0.354550	+	1.09119i
$148$	−0.194546	+	0.598752i	−0.0159916	+	0.0492171i
$149$	12.3150			1.00888			0.504441	−	0.863446i	$-0.331699\pi$
$149$	12.3150			1.00888			0.504441	+	0.863446i	$0.331699\pi$
$150$	2.27279			0.185572
$151$	6.14232	−	18.9041i	0.499855	−	1.53840i	−0.309397	−	0.950933i	$-0.600127\pi$
$151$	6.14232	−	18.9041i	0.499855	−	1.53840i	0.809252	−	0.587462i	$-0.199873\pi$
$152$	0.305254	+	0.221780i	0.0247593	+	0.0179887i
$153$	2.71505	−	1.97260i	0.219499	−	0.159475i
$154$	−32.5932			−2.62644
$155$		0			0
$156$	10.2421			0.820023
$157$	4.69603	−	3.41187i	0.374784	−	0.272297i	−0.384408	−	0.923163i	$-0.625594\pi$
$157$	4.69603	−	3.41187i	0.374784	−	0.272297i	0.759192	+	0.650867i	$0.225594\pi$
$158$	14.5453	+	10.5678i	1.15716	+	0.840728i
$159$	−6.28627	+	19.3472i	−0.498534	+	1.53433i
$160$	−19.0410			−1.50532
$161$	−12.3240			−0.971264
$162$	−7.19981	+	22.1587i	−0.565671	+	1.74096i
$163$	5.49535	+	16.9129i	0.430429	+	1.32472i	0.897699	+	0.440610i	$0.145238\pi$
$163$	5.49535	+	16.9129i	0.430429	+	1.32472i	−0.467270	+	0.884115i	$0.654762\pi$
$164$	−3.03214	−	9.33196i	−0.236770	−	0.728703i
$165$	−17.3956	+	12.6386i	−1.35424	+	0.983915i
$166$	3.32037	−	10.2190i	0.257711	−	0.793152i
$167$	1.76530	−	1.28257i	0.136603	−	0.0992479i	−0.517385	−	0.855753i	$-0.673095\pi$
$167$	1.76530	−	1.28257i	0.136603	−	0.0992479i	0.653988	+	0.756505i	$0.273095\pi$
$168$	3.87036	+	2.81198i	0.298605	+	0.216949i
$169$	−2.67102	−	8.22055i	−0.205463	−	0.632350i
$170$	8.37616	+	6.08564i	0.642422	+	0.466747i
$171$	0.791026	+	0.574714i	0.0604912	+	0.0439495i
$172$	−0.191155	−	0.588314i	−0.0145754	−	0.0448585i
$173$	4.45601	+	3.23748i	0.338784	+	0.246141i	0.744149	−	0.668014i	$-0.232855\pi$
$173$	4.45601	+	3.23748i	0.338784	+	0.246141i	−0.405365	+	0.914155i	$0.632855\pi$
$174$	−4.94002	+	3.58913i	−0.374502	+	0.272091i
$175$	−0.582155	+	1.79169i	−0.0440068	+	0.135439i
$176$	11.5196	−	8.36948i	0.868322	−	0.630873i
$177$	−3.85257	−	11.8570i	−0.289577	−	0.891225i
$178$	−3.20966	−	9.87832i	−0.240574	−	0.740411i
$179$	−3.74958	+	11.5400i	−0.280257	+	0.862541i	0.707524	+	0.706689i	$0.249812\pi$
$179$	−3.74958	+	11.5400i	−0.280257	+	0.862541i	−0.987780	+	0.155852i	$0.950188\pi$
$180$	8.49271			0.633010
$181$	−9.64687			−0.717046			−0.358523	−	0.933521i	$-0.616720\pi$
$181$	−9.64687			−0.717046			−0.358523	+	0.933521i	$0.616720\pi$
$182$	−4.91094	+	15.1143i	−0.364023	+	1.12035i
$183$	3.85483	+	2.80070i	0.284957	+	0.207033i
$184$	−1.65122	+	1.19968i	−0.121730	+	0.0884418i
$185$	−0.644448			−0.0473808
$186$		0			0
$187$	−9.10960			−0.666160
$188$	−9.98175	+	7.25216i	−0.727994	+	0.528918i
$189$	−9.05018	−	6.57534i	−0.658304	−	0.478286i
$190$	−0.932141	+	2.86884i	−0.0676246	+	0.208127i
$191$	10.4654			0.757250			0.378625	−	0.925550i	$-0.376397\pi$
$191$	10.4654			0.757250			0.378625	+	0.925550i	$0.376397\pi$
$192$	−21.7184			−1.56739
$193$	−0.553341	+	1.70301i	−0.0398304	+	0.122585i	−0.968995	−	0.247082i	$-0.920528\pi$
$193$	−0.553341	+	1.70301i	−0.0398304	+	0.122585i	0.929164	+	0.369667i	$0.120528\pi$
$194$	4.29910	+	13.2313i	0.308658	+	0.949951i
$195$	3.23980	+	9.97108i	0.232007	+	0.714044i
$196$	−12.0658	+	8.76631i	−0.861842	+	0.626165i
$197$	−1.97677	+	6.08387i	−0.140839	+	0.433458i	−0.996452	−	0.0841575i	$-0.973180\pi$
$197$	−1.97677	+	6.08387i	−0.140839	+	0.433458i	0.855614	+	0.517615i	$0.173180\pi$
$198$	−11.3165	+	8.22192i	−0.804229	+	0.584306i
$199$	0.750085	+	0.544969i	0.0531721	+	0.0386318i	0.614054	−	0.789264i	$-0.289538\pi$
$199$	0.750085	+	0.544969i	0.0531721	+	0.0386318i	−0.560882	+	0.827896i	$0.689538\pi$
$200$	0.0964132	+	0.296729i	0.00681744	+	0.0209819i
$201$	23.5638	+	17.1201i	1.66207	+	1.20756i
$202$	30.2798	+	21.9996i	2.13048	+	1.54788i
$203$	−1.56405	−	4.81365i	−0.109775	−	0.337852i
$204$	8.44836	+	6.13809i	0.591504	+	0.429753i
$205$	8.12590	−	5.90381i	0.567537	−	0.412340i
$206$	2.50706	−	7.71594i	0.174675	−	0.537595i
$207$	−4.27893	+	3.10882i	−0.297406	+	0.216078i
$208$	−2.14544	−	6.60300i	−0.148760	−	0.457835i
$209$	−0.820151	−	2.52416i	−0.0567310	−	0.174600i
$210$	−11.8188	+	36.3745i	−0.815573	+	2.51008i
$211$	−6.18144			−0.425548			−0.212774	−	0.977101i	$-0.568250\pi$
$211$	−6.18144			−0.425548			−0.212774	+	0.977101i	$0.568250\pi$
$212$	−21.8100			−1.49791
$213$	−0.883191	+	2.71818i	−0.0605152	+	0.186247i
$214$	−18.6340	−	13.5384i	−1.27380	−	0.925467i
$215$	0.512281	−	0.372194i	0.0349373	−	0.0253834i
$216$	−1.85267			−0.126058
$217$		0			0
$218$	37.4917			2.53926
$219$	−24.5186	+	17.8138i	−1.65681	+	1.20375i
$220$	−18.6502	−	13.5501i	−1.25739	−	0.913550i
$221$	−1.37258	+	4.22436i	−0.0923295	+	0.284161i
$222$	−1.21678			−0.0816648
$223$	−15.8978			−1.06460			−0.532298	−	0.846557i	$-0.678671\pi$
$223$	−15.8978			−1.06460			−0.532298	+	0.846557i	$0.678671\pi$
$224$	9.20860	−	28.3411i	0.615275	−	1.89362i
$225$	0.249842	+	0.768936i	0.0166562	+	0.0512624i
$226$	11.2304	+	34.5637i	0.747037	+	2.29914i
$227$	3.75785	−	2.73024i	0.249417	−	0.181212i	−0.456051	−	0.889954i	$-0.650737\pi$
$227$	3.75785	−	2.73024i	0.249417	−	0.181212i	0.705469	+	0.708741i	$0.250737\pi$
$228$	−0.940176	+	2.89357i	−0.0622647	+	0.191631i
$229$	−15.7098	+	11.4138i	−1.03813	+	0.754247i	−0.969920	−	0.243424i	$-0.921729\pi$
$229$	−15.7098	+	11.4138i	−1.03813	+	0.754247i	−0.0682122	+	0.997671i	$0.521729\pi$
$230$	−13.2008	−	9.59097i	−0.870438	−	0.632410i
$231$	−10.3988	−	32.0043i	−0.684193	−	2.10573i
$232$	−0.678147	−	0.492703i	−0.0445225	−	0.0323475i
$233$	11.5273	+	8.37505i	0.755176	+	0.548667i	0.897427	−	0.441163i	$-0.145434\pi$
$233$	11.5273	+	8.37505i	0.755176	+	0.548667i	−0.142251	+	0.989831i	$0.545434\pi$
$234$	2.10762	+	6.48658i	0.137779	+	0.424041i
$235$	−10.2177	−	7.42361i	−0.666531	−	0.484263i
$236$	10.8136	−	7.85653i	0.703904	−	0.511416i
$237$	−5.73618	+	17.6542i	−0.372605	+	1.14676i
$238$	−13.1089	+	9.52417i	−0.849724	+	0.617361i
$239$	2.10178	+	6.46863i	0.135953	+	0.418421i	0.995737	−	0.0922373i	$-0.0294018\pi$
$239$	2.10178	+	6.46863i	0.135953	+	0.418421i	−0.859784	+	0.510658i	$0.829402\pi$
$240$	−5.16327	−	15.8909i	−0.333288	−	1.02575i
$241$	3.55528	−	10.9420i	0.229016	−	0.704837i	−0.768844	−	0.639437i	$-0.779168\pi$
$241$	3.55528	−	10.9420i	0.229016	−	0.704837i	0.997859	−	0.0654005i	$-0.0208325\pi$
$242$	15.1760			0.975550
$243$	−14.9224			−0.957271
$244$	−1.57861	+	4.85845i	−0.101060	+	0.311030i
$245$	−12.3510	−	8.97355i	−0.789078	−	0.573299i
$246$	15.3425	−	11.1470i	0.978200	−	0.710704i
$247$	−1.29410			−0.0823413
$248$		0			0
$249$	11.0938			0.703039
$250$	17.6620	−	12.8322i	1.11705	−	0.811581i
$251$	−5.90130	−	4.28755i	−0.372487	−	0.270627i	0.385755	−	0.922601i	$-0.373941\pi$
$251$	−5.90130	−	4.28755i	−0.372487	−	0.270627i	−0.758241	+	0.651974i	$0.773941\pi$
$252$	−4.10724	+	12.6408i	−0.258732	+	0.796295i
$253$	14.3567			0.902600
$254$	29.4206			1.84601
$255$	−3.30327	+	10.1664i	−0.206859	+	0.636647i
$256$	3.19031	+	9.81877i	0.199395	+	0.613673i
$257$	−7.61903	−	23.4490i	−0.475262	−	1.46271i	−0.845604	−	0.533810i	$-0.820760\pi$
$257$	−7.61903	−	23.4490i	−0.475262	−	1.46271i	0.370342	−	0.928895i	$-0.379240\pi$
$258$	0.967235	−	0.702737i	0.0602174	−	0.0437505i
$259$	0.311668	−	0.959214i	0.0193661	−	0.0596027i
$260$	−9.09363	+	6.60691i	−0.563963	+	0.409743i
$261$	−1.75733	−	1.27678i	−0.108776	−	0.0790304i
$262$	4.60295	+	14.1664i	0.284371	+	0.875205i
$263$	−21.2666	−	15.4511i	−1.31136	−	0.952757i	−0.999997	−	0.00246465i	$-0.999215\pi$
$263$	−21.2666	−	15.4511i	−1.31136	−	0.952757i	−0.311360	−	0.950292i	$-0.600785\pi$
$264$	−4.50877	−	3.27581i	−0.277495	−	0.201612i
$265$	−6.89897	−	21.2329i	−0.423801	−	1.30432i
$266$	−3.81925	−	2.77485i	−0.234173	−	0.170137i
$267$	8.67580	−	6.30333i	0.530950	−	0.385758i
$268$	−9.64972	+	29.6988i	−0.589451	+	1.81414i
$269$	−16.8921	+	12.2728i	−1.02993	+	0.748288i	−0.968295	−	0.249811i	$-0.919632\pi$
$269$	−16.8921	+	12.2728i	−1.02993	+	0.748288i	−0.0616353	+	0.998099i	$0.519632\pi$
$270$	−4.57695	−	14.0864i	−0.278544	−	0.857270i
$271$	6.49271	+	19.9825i	0.394404	+	1.21385i	0.929425	+	0.369012i	$0.120304\pi$
$271$	6.49271	+	19.9825i	0.394404	+	1.21385i	−0.535021	+	0.844839i	$0.679696\pi$
$272$	2.18748	−	6.73236i	0.132635	−	0.408209i
$273$	−16.4081			−0.993061
$274$	−15.7018			−0.948581
$275$	0.678179	−	2.08722i	0.0408958	−	0.125864i
$276$	−13.3146	−	9.67365i	−0.801447	−	0.582285i
$277$	−3.85034	+	2.79744i	−0.231345	+	0.168082i	−0.697418	−	0.716664i	$-0.745668\pi$
$277$	−3.85034	+	2.79744i	−0.231345	+	0.168082i	0.466074	+	0.884746i	$0.345668\pi$
$278$	41.6459			2.49776
$279$		0			0
$280$	−5.25032			−0.313767
$281$	5.38386	−	3.91160i	0.321174	−	0.233347i	−0.415502	−	0.909592i	$-0.636394\pi$
$281$	5.38386	−	3.91160i	0.321174	−	0.233347i	0.736676	+	0.676246i	$0.236394\pi$
$282$	−19.2920	−	14.0165i	−1.14882	−	0.834669i
$283$	−2.23921	+	6.89159i	−0.133107	+	0.409662i	−0.995291	−	0.0969338i	$-0.969096\pi$
$283$	−2.23921	+	6.89159i	−0.133107	+	0.409662i	0.862183	+	0.506596i	$0.169096\pi$
$284$	−3.06419			−0.181826
$285$	−3.11440			−0.184481
$286$	5.72098	−	17.6074i	0.338289	−	1.04115i
$287$	4.85755	+	14.9500i	0.286732	+	0.882471i
$288$	−3.95204	−	12.1631i	−0.232876	−	0.716719i
$289$	10.0894	−	7.33040i	0.593496	−	0.431200i
$290$	2.07083	−	6.37336i	0.121603	−	0.374257i
$291$	−11.6206	+	8.44285i	−0.681211	+	0.494929i
$292$	−26.2869	−	19.0986i	−1.53833	−	1.11766i
$293$	4.17529	+	12.8502i	0.243923	+	0.750718i	0.995812	+	0.0914278i	$0.0291431\pi$
$293$	4.17529	+	12.8502i	0.243923	+	0.750718i	−0.751889	+	0.659290i	$0.770857\pi$
$294$	−23.3199	−	16.9429i	−1.36004	−	0.988131i
$295$	11.0692	+	8.04226i	0.644475	+	0.468238i
$296$	−0.0516166	−	0.158860i	−0.00300015	−	0.00923352i
$297$	10.5430	+	7.65992i	0.611765	+	0.444473i
$298$	−20.6446	+	14.9992i	−1.19591	+	0.868879i
$299$	2.16318	−	6.65759i	0.125100	−	0.385018i
$300$	−2.03533	+	1.47876i	−0.117510	+	0.0853760i
$301$	0.306235	+	0.942493i	0.0176511	+	0.0543244i
$302$	12.7276	+	39.1716i	0.732393	+	2.25407i
$303$	−11.9413	+	36.7517i	−0.686012	+	2.11133i
$304$	2.06240			0.118287
$305$	−5.22924			−0.299425
$306$	−2.14891	+	6.61367i	−0.122845	+	0.378078i
$307$	18.3856	+	13.3579i	1.04932	+	0.762376i	0.972083	−	0.234637i	$-0.0753901\pi$
$307$	18.3856	+	13.3579i	1.04932	+	0.762376i	0.0772373	+	0.997013i	$0.475390\pi$
$308$	29.1880	−	21.2063i	1.66314	−	1.20834i
$309$	8.37640			0.476517
$310$		0			0
$311$	9.49330			0.538315			0.269158	−	0.963096i	$-0.413255\pi$
$311$	9.49330			0.538315			0.269158	+	0.963096i	$0.413255\pi$
$312$	−2.19843	+	1.59725i	−0.124462	+	0.0904266i
$313$	22.7310	+	16.5150i	1.28483	+	0.933485i	0.999687	−	0.0249998i	$-0.00795851\pi$
$313$	22.7310	+	16.5150i	1.28483	+	0.933485i	0.285144	+	0.958485i	$0.407959\pi$
$314$	−3.71682	+	11.4392i	−0.209752	+	0.645551i
$315$	−13.6055			−0.766585
$316$	−19.9014			−1.11954
$317$	−4.88767	+	15.0427i	−0.274519	+	0.844882i	0.714828	+	0.699301i	$0.246505\pi$
$317$	−4.88767	+	15.0427i	−0.274519	+	0.844882i	−0.989346	+	0.145581i	$0.953495\pi$
$318$	−13.0259	−	40.0896i	−0.730457	−	2.24812i
$319$	1.82203	+	5.60764i	0.102014	+	0.313968i
$320$	19.2831	−	14.0100i	1.07796	−	0.783182i
$321$	7.34863	−	22.6168i	0.410161	−	1.26234i
$322$	20.6596	−	15.0101i	1.15132	−	0.836481i
$323$	−1.06746	−	0.775553i	−0.0593949	−	0.0431529i
$324$	−7.96967	−	24.5281i	−0.442759	−	1.36267i
$325$	−0.865715	−	0.628979i	−0.0480212	−	0.0348895i
$326$	−29.8116	−	21.6594i	−1.65111	−	1.19960i
$327$	11.9617	+	36.8143i	0.661483	+	2.03583i
$328$	2.10616	+	1.53021i	0.116293	+	0.0844918i
$329$	15.9910	−	11.6181i	0.881612	−	0.640529i
$330$	13.7682	−	42.3743i	0.757917	−	2.33263i
$331$	10.4720	−	7.60836i	0.575594	−	0.418194i	−0.261539	−	0.965193i	$-0.584230\pi$
$331$	10.4720	−	7.60836i	0.575594	−	0.418194i	0.837133	+	0.546999i	$0.184230\pi$
$332$	3.67541	+	11.3117i	0.201714	+	0.620812i
$333$	−0.133758	−	0.411664i	−0.00732988	−	0.0225591i
$334$	−1.39720	+	4.30014i	−0.0764514	+	0.235293i
$335$	−31.9654			−1.74646
$336$	26.1495			1.42657
$337$	8.61116	−	26.5024i	0.469080	−	1.44368i	−0.384698	−	0.923042i	$-0.625694\pi$
$337$	8.61116	−	26.5024i	0.469080	−	1.44368i	0.853778	−	0.520637i	$-0.174306\pi$
$338$	14.4900	+	10.5276i	0.788151	+	0.572625i
$339$	−30.3561	+	22.0550i	−1.64872	+	1.19786i
$340$	−11.4606			−0.621537
$341$		0			0
$342$	−2.02604			−0.109556
$343$	−1.47969	+	1.07506i	−0.0798956	+	0.0580476i
$344$	0.132778	+	0.0964691i	0.00715893	+	0.00520127i
$345$	5.20597	−	16.0223i	0.280280	−	0.862612i
$346$	−11.4131			−0.613572
$347$	−5.32351			−0.285781			−0.142890	−	0.989739i	$-0.545640\pi$
$347$	−5.32351			−0.285781			−0.142890	+	0.989739i	$0.545640\pi$
$348$	2.08868	−	6.42830i	0.111965	−	0.344593i
$349$	−1.26632	−	3.89734i	−0.0677847	−	0.208620i	0.911427	−	0.411463i	$-0.134982\pi$
$349$	−1.26632	−	3.89734i	−0.0677847	−	0.208620i	−0.979211	+	0.202843i	$0.934982\pi$
$350$	−1.20630	−	3.71260i	−0.0644793	−	0.198447i
$351$	5.14065	−	3.73490i	0.274388	−	0.199354i
$352$	−10.7275	+	33.0159i	−0.571779	+	1.75975i
$353$	17.6280	−	12.8075i	0.938242	−	0.681673i	−0.00975494	−	0.999952i	$-0.503105\pi$
$353$	17.6280	−	12.8075i	0.938242	−	0.681673i	0.947997	+	0.318280i	$0.103105\pi$
$354$	20.8997	+	15.1845i	1.11081	+	0.807050i
$355$	−0.969272	−	2.98311i	−0.0514436	−	0.158327i
$356$	9.30151	+	6.75794i	0.492979	+	0.358170i
$357$	−13.5345	−	9.83337i	−0.716320	−	0.520437i
$358$	−7.76958	−	23.9123i	−0.410635	−	1.26381i
$359$	5.72900	+	4.16236i	0.302365	+	0.219681i	0.728613	−	0.684925i	$-0.240165\pi$
$359$	5.72900	+	4.16236i	0.302365	+	0.219681i	−0.426249	+	0.904606i	$0.640165\pi$
$360$	−1.82293	+	1.32444i	−0.0960770	+	0.0698040i
$361$	−5.75253	+	17.7045i	−0.302765	+	0.931814i
$362$	16.1718	−	11.7495i	0.849973	−	0.617541i
$363$	4.84189	+	14.9018i	0.254133	+	0.782141i
$364$	−5.43605	−	16.7304i	−0.284927	−	0.876914i
$365$	10.2781	−	31.6327i	0.537979	−	1.65573i
$366$	−9.87330			−0.516086
$367$	16.1177			0.841336			0.420668	−	0.907215i	$-0.361796\pi$
$367$	16.1177			0.841336			0.420668	+	0.907215i	$0.361796\pi$
$368$	−3.44747	+	10.6102i	−0.179712	+	0.553096i
$369$	5.45783	+	3.96535i	0.284123	+	0.206428i
$370$	1.08034	−	0.784913i	0.0561642	−	0.0408057i
$371$	34.9401			1.81400
$372$		0			0
$373$	−9.81895			−0.508406			−0.254203	−	0.967151i	$-0.581813\pi$
$373$	−9.81895			−0.508406			−0.254203	+	0.967151i	$0.581813\pi$
$374$	15.2712	−	11.0951i	0.789653	−	0.573716i
$375$	18.2354	+	13.2488i	0.941673	+	0.684166i
$376$	1.01157	−	3.11331i	0.0521680	−	0.160557i
$377$	2.87494			0.148067
$378$	23.1801			1.19225
$379$	−4.26926	+	13.1394i	−0.219297	+	0.674928i	0.779523	+	0.626373i	$0.215461\pi$
$379$	−4.26926	+	13.1394i	−0.219297	+	0.674928i	−0.998821	+	0.0485544i	$0.984539\pi$
$380$	−1.03181	−	3.17559i	−0.0529309	−	0.162904i
$381$	9.38660	+	28.8890i	0.480890	+	1.48003i
$382$	−17.5440	+	12.7465i	−0.897630	+	0.652166i
$383$	−3.18474	+	9.80161i	−0.162732	+	0.500839i	−0.998862	−	0.0476930i	$-0.984813\pi$
$383$	−3.18474	+	9.80161i	−0.162732	+	0.500839i	0.836130	+	0.548532i	$0.184813\pi$
$384$	8.33549	−	6.05609i	0.425369	−	0.309048i
$385$	29.8780	+	21.7076i	1.52272	+	1.10632i
$386$	−1.14659	−	3.52884i	−0.0583599	−	0.179613i
$387$	0.344078	+	0.249987i	0.0174905	+	0.0127076i
$388$	−12.4587	−	9.05177i	−0.632494	−	0.459534i
$389$	7.83834	+	24.1239i	0.397420	+	1.22313i	0.927061	+	0.374910i	$0.122327\pi$
$389$	7.83834	+	24.1239i	0.397420	+	1.22313i	−0.529641	+	0.848222i	$0.677673\pi$
$390$	−17.5755	−	12.7694i	−0.889972	−	0.646603i
$391$	5.77424	−	4.19523i	0.292016	−	0.212162i
$392$	1.22278	−	3.76332i	0.0617595	−	0.190076i
$393$	−12.4419	+	9.03957i	−0.627611	+	0.455986i
$394$	−4.09610	−	12.6065i	−0.206359	−	0.635107i
$395$	−6.29527	−	19.3749i	−0.316749	−	0.974855i
$396$	4.78471	−	14.7258i	0.240441	−	0.740001i
$397$	16.7588			0.841101			0.420550	−	0.907269i	$-0.361837\pi$
$397$	16.7588			0.841101			0.420550	+	0.907269i	$0.361837\pi$
$398$	−1.92118			−0.0963001
$399$	1.50618	−	4.63556i	0.0754035	−	0.232068i
$400$	1.37969	+	1.00240i	0.0689846	+	0.0501202i
$401$	−22.3479	+	16.2367i	−1.11600	+	0.810823i	−0.983598	−	0.180372i	$-0.942270\pi$
$401$	−22.3479	+	16.2367i	−1.11600	+	0.810823i	−0.132404	+	0.991196i	$0.542270\pi$
$402$	−60.3537			−3.01017
$403$		0			0
$404$	−41.4300			−2.06122
$405$	21.3581	−	15.5176i	1.06129	−	0.771075i
$406$	8.48479	+	6.16456i	0.421093	+	0.305942i
$407$	−0.363076	+	1.11743i	−0.0179970	+	0.0553891i
$408$	−2.77065			−0.137168
$409$	22.6107			1.11803			0.559013	−	0.829159i	$-0.311180\pi$
$409$	22.6107			1.11803			0.559013	+	0.829159i	$0.311180\pi$
$410$	−6.43149	+	19.7941i	−0.317628	+	0.977560i
$411$	−5.00965	−	15.4181i	−0.247108	−	0.760519i
$412$	2.77513	+	8.54098i	0.136721	+	0.420784i
$413$	−17.3236	+	12.5863i	−0.852439	+	0.619333i
$414$	3.38669	−	10.4232i	0.166447	−	0.512270i
$415$	−9.84982	+	7.15631i	−0.483509	+	0.351290i
$416$	13.6940	+	9.94926i	0.671402	+	0.487802i
$417$	13.2871	+	40.8935i	0.650672	+	2.00256i
$418$	4.44922	+	3.23255i	0.217619	+	0.158109i
$419$	5.00860	+	3.63896i	0.244686	+	0.177775i	0.703368	−	0.710825i	$-0.251678\pi$
$419$	5.00860	+	3.63896i	0.244686	+	0.177775i	−0.458682	+	0.888600i	$0.651678\pi$
$420$	−13.0825	−	40.2639i	−0.638362	−	1.96468i
$421$	−5.30662	−	3.85548i	−0.258629	−	0.187905i	0.450914	−	0.892568i	$-0.351098\pi$
$421$	−5.30662	−	3.85548i	−0.258629	−	0.187905i	−0.709542	+	0.704663i	$0.751098\pi$
$422$	10.3624	−	7.52876i	0.504436	−	0.366494i
$423$	2.62137	−	8.06773i	0.127455	−	0.392267i
$424$	4.68143	−	3.40126i	0.227351	−	0.165180i
$425$	−0.337152	−	1.03765i	−0.0163543	−	0.0503333i
$426$	−1.83008	−	5.63240i	−0.0886676	−	0.272891i
$427$	2.52896	−	7.78335i	0.122385	−	0.376663i
$428$	25.4958			1.23238
$429$	19.1145			0.922857
$430$	−0.405460	+	1.24788i	−0.0195530	+	0.0601780i
$431$	−18.9858	−	13.7940i	−0.914513	−	0.664432i	0.0276396	−	0.999618i	$-0.491201\pi$
$431$	−18.9858	−	13.7940i	−0.914513	−	0.664432i	−0.942152	+	0.335186i	$0.891201\pi$
$432$	−8.19266	+	5.95232i	−0.394170	+	0.286381i
$433$	−24.3130			−1.16841			−0.584203	−	0.811607i	$-0.698593\pi$
$433$	−24.3130			−1.16841			−0.584203	+	0.811607i	$0.698593\pi$
$434$		0			0
$435$	6.91890			0.331736
$436$	−33.5747	+	24.3934i	−1.60793	+	1.16823i
$437$	1.68231	+	1.22227i	0.0804760	+	0.0584692i
$438$	19.4060	−	59.7255i	0.927254	−	2.85379i
$439$	14.5064			0.692350			0.346175	−	0.938170i	$-0.387480\pi$
$439$	14.5064			0.692350			0.346175	+	0.938170i	$0.387480\pi$
$440$	6.11634			0.291585
$441$	3.16867	−	9.75216i	0.150889	−	0.464388i
$442$	−2.84415	−	8.75338i	−0.135282	−	0.416356i
$443$	−5.11917	−	15.7552i	−0.243219	−	0.748552i	−0.995924	−	0.0901938i	$-0.971251\pi$
$443$	−5.11917	−	15.7552i	−0.243219	−	0.748552i	0.752705	−	0.658358i	$-0.228749\pi$
$444$	1.08965	−	0.791679i	0.0517126	−	0.0375714i
$445$	−3.63685	+	11.1931i	−0.172403	+	0.530603i
$446$	26.6508	−	19.3629i	1.26195	−	0.916862i
$447$	−21.3148	−	15.4861i	−1.00816	−	0.732468i
$448$	11.5272	+	35.4770i	0.544608	+	1.67613i
$449$	5.51532	+	4.00712i	0.260284	+	0.189107i	0.710272	−	0.703927i	$-0.248572\pi$
$449$	5.51532	+	4.00712i	0.260284	+	0.189107i	−0.449988	+	0.893035i	$0.648572\pi$
$450$	−1.35537	−	0.984731i	−0.0638926	−	0.0464207i
$451$	−5.65879	−	17.4160i	−0.266462	−	0.820085i
$452$	−32.5455	−	23.6457i	−1.53081	−	1.11220i
$453$	−34.4031	+	24.9953i	−1.61640	+	1.17438i
$454$	−2.97426	+	9.15384i	−0.139589	+	0.429611i
$455$	14.5682	−	10.5844i	0.682968	−	0.496206i
$456$	−0.249446	−	0.767715i	−0.0116814	−	0.0359515i
$457$	−6.62154	−	20.3790i	−0.309742	−	0.953289i	−0.977865	−	0.209238i	$-0.932902\pi$
$457$	−6.62154	−	20.3790i	−0.309742	−	0.953289i	0.668122	−	0.744051i	$-0.267098\pi$
$458$	12.4340	−	38.2679i	0.581002	−	1.78814i
$459$	6.47868			0.302399
$460$	18.0619			0.842139
$461$	2.68057	−	8.24994i	0.124847	−	0.384238i	−0.869027	−	0.494766i	$-0.835254\pi$
$461$	2.68057	−	8.24994i	0.124847	−	0.384238i	0.993873	+	0.110527i	$0.0352540\pi$
$462$	56.4125	+	40.9861i	2.62455	+	1.90684i
$463$	2.95281	−	2.14534i	0.137229	−	0.0997025i	−0.517053	−	0.855953i	$-0.672971\pi$
$463$	2.95281	−	2.14534i	0.137229	−	0.0997025i	0.654282	+	0.756251i	$0.272971\pi$
$464$	−4.58180			−0.212705
$465$		0			0
$466$	−29.5246			−1.36770
$467$	2.49267	−	1.81103i	0.115347	−	0.0838045i	−0.528616	−	0.848861i	$-0.677289\pi$
$467$	2.49267	−	1.81103i	0.115347	−	0.0838045i	0.643963	+	0.765056i	$0.277289\pi$
$468$	−6.10782	−	4.43759i	−0.282334	−	0.205128i
$469$	15.4591	−	47.5782i	0.713834	−	2.19696i
$470$	26.1705			1.20715
$471$	−12.4183			−0.572207
$472$	−1.09587	+	3.37276i	−0.0504417	+	0.155244i
$473$	−0.356747	−	1.09795i	−0.0164032	−	0.0504839i
$474$	−11.8861	−	36.5816i	−0.545945	−	1.68025i
$475$	0.257166	−	0.186842i	0.0117996	−	0.00857290i
$476$	5.54256	−	17.0582i	0.254043	−	0.781863i
$477$	12.1313	−	8.81393i	0.555456	−	0.403562i
$478$	−11.4019	−	8.28399i	−0.521513	−	0.378901i
$479$	−5.38006	−	16.5581i	−0.245821	−	0.756559i	−0.995500	−	0.0947581i	$-0.969792\pi$
$479$	−5.38006	−	16.5581i	−0.245821	−	0.756559i	0.749679	−	0.661801i	$-0.230208\pi$
$480$	32.9562	+	23.9441i	1.50424	+	1.09289i
$481$	0.463476	+	0.336735i	0.0211327	+	0.0153538i
$482$	7.36697	+	22.6732i	0.335556	+	1.03274i
$483$	21.3303	+	15.4974i	0.970564	+	0.705156i
$484$	−13.5905	+	9.87404i	−0.617748	+	0.448820i
$485$	4.87129	−	14.9923i	0.221194	−	0.680765i
$486$	25.0156	−	18.1749i	1.13473	−	0.824430i
$487$	−8.89154	−	27.3653i	−0.402914	−	1.24004i	−0.922624	−	0.385699i	$-0.873960\pi$
$487$	−8.89154	−	27.3653i	−0.402914	−	1.24004i	0.519710	−	0.854342i	$-0.326040\pi$
$488$	−0.418832	−	1.28903i	−0.0189596	−	0.0583518i
$489$	11.7567	−	36.1834i	0.531657	−	1.63627i
$490$	31.6345			1.42910
$491$	9.82568			0.443427			0.221713	−	0.975112i	$-0.428835\pi$
$491$	9.82568			0.443427			0.221713	+	0.975112i	$0.428835\pi$
$492$	−6.48693	+	19.9647i	−0.292453	+	0.900078i
$493$	2.37145	+	1.72296i	0.106805	+	0.0775980i
$494$	2.16940	−	1.57616i	0.0976058	−	0.0709148i
$495$	15.8497			0.712391
$496$		0			0
$497$	4.90891			0.220195
$498$	−18.5974	+	13.5118i	−0.833369	+	0.605478i
$499$	−8.77622	−	6.37630i	−0.392878	−	0.285442i	0.373756	−	0.927527i	$-0.378070\pi$
$499$	−8.77622	−	6.37630i	−0.392878	−	0.285442i	−0.766634	+	0.642085i	$0.778070\pi$
$500$	−7.46766	+	22.9831i	−0.333964	+	1.02784i
$501$	−4.66822			−0.208561
$502$	15.1149			0.674611
$503$	2.64548	−	8.14195i	0.117956	−	0.363031i	−0.874596	−	0.484852i	$-0.838873\pi$
$503$	2.64548	−	8.14195i	0.117956	−	0.363031i	0.992552	+	0.121821i	$0.0388734\pi$
$504$	−1.08973	−	3.35383i	−0.0485402	−	0.149391i
$505$	−13.1052	−	40.3337i	−0.583175	−	1.79483i
$506$	−24.0674	+	17.4860i	−1.06993	+	0.777346i
$507$	−5.71436	+	17.5870i	−0.253783	+	0.781065i
$508$	−26.3468	+	19.1421i	−1.16895	+	0.849292i
$509$	−32.0228	−	23.2659i	−1.41938	−	1.03124i	−0.991873	−	0.127233i	$-0.959390\pi$
$509$	−32.0228	−	23.2659i	−1.41938	−	1.03124i	−0.427512	−	0.904010i	$-0.640610\pi$
$510$	−6.84479	−	21.0661i	−0.303092	−	0.932822i
$511$	42.1123	+	30.5963i	1.86294	+	1.35350i
$512$	−25.0995	−	18.2358i	−1.10925	−	0.805918i
$513$	0.583286	+	1.79517i	0.0257527	+	0.0792586i
$514$	41.3324	+	30.0297i	1.82309	+	1.32455i
$515$	−7.43715	+	5.40341i	−0.327720	+	0.238103i
$516$	−0.408955	+	1.25863i	−0.0180032	+	0.0554083i
$517$	−18.6286	+	13.5345i	−0.819287	+	0.595247i
$518$	0.645813	+	1.98761i	0.0283754	+	0.0873305i
$519$	−3.64134	−	11.2069i	−0.159837	−	0.491927i
$520$	0.921571	−	2.83630i	0.0404136	−	0.124380i
$521$	−1.34932			−0.0591148			−0.0295574	−	0.999563i	$-0.509410\pi$
$521$	−1.34932			−0.0591148			−0.0295574	+	0.999563i	$0.509410\pi$
$522$	4.50102			0.197004
$523$	−8.79861	+	27.0793i	−0.384736	+	1.18410i	0.551935	+	0.833887i	$0.313890\pi$
$523$	−8.79861	+	27.0793i	−0.384736	+	1.18410i	−0.936671	+	0.350210i	$0.886110\pi$
$524$	−13.3392	−	9.69152i	−0.582727	−	0.423376i
$525$	3.26065	−	2.36900i	0.142306	−	0.103392i
$526$	54.4699			2.37500
$527$		0			0
$528$	−30.4628			−1.32572
$529$	9.50718	−	6.90737i	0.413356	−	0.300320i
$530$	37.4261	+	27.1917i	1.62569	+	1.18113i
$531$	−2.83982	+	8.74006i	−0.123238	+	0.379286i
$532$	5.22564			0.226560
$533$	−8.92886			−0.386752
$534$	−6.86672	+	21.1336i	−0.297152	+	0.914540i
$535$	8.06488	+	24.8211i	0.348675	+	1.07311i
$536$	−2.56024	−	7.87962i	−0.110586	−	0.340348i
$537$	21.0014	−	15.2584i	0.906277	−	0.658449i
$538$	13.3698	−	41.1479i	0.576412	−	1.77401i
$539$	−22.5180	+	16.3603i	−0.969920	+	0.704688i
$540$	13.2639	+	9.63676i	0.570786	+	0.414700i
$541$	−4.42191	−	13.6092i	−0.190113	−	0.585107i	0.809886	−	0.586587i	$-0.199529\pi$
$541$	−4.42191	−	13.6092i	−0.190113	−	0.585107i	−0.999999	+	0.00148020i	$0.999529\pi$
$542$	−35.2222	−	25.5904i	−1.51292	−	1.09920i
$543$	16.6968	+	12.1310i	0.716530	+	0.520590i
$544$	5.33311	+	16.4136i	0.228655	+	0.703729i
$545$	−34.3684	−	24.9701i	−1.47218	−	1.06960i
$546$	27.5062	−	19.9844i	1.17716	−	0.855253i
$547$	13.0921	−	40.2933i	0.559778	−	1.72282i	−0.123203	−	0.992382i	$-0.539317\pi$
$547$	13.0921	−	40.2933i	0.559778	−	1.72282i	0.682980	−	0.730437i	$-0.260683\pi$
$548$	14.0613	−	10.2162i	0.600670	−	0.436413i
$549$	−1.08535	−	3.34036i	−0.0463216	−	0.142563i
$550$	1.40527	+	4.32498i	0.0599209	+	0.184418i
$551$	−0.263906	+	0.812221i	−0.0112428	+	0.0346018i
$552$	4.36655			0.185853
$553$	31.8826			1.35579
$554$	3.04747	−	9.37914i	0.129474	−	0.398481i
$555$	1.11541	+	0.810395i	0.0473466	+	0.0343994i
$556$	−37.2949	+	27.0963i	−1.58166	+	1.14914i
$557$	−27.3019			−1.15682			−0.578409	−	0.815747i	$-0.696326\pi$
$557$	−27.3019			−1.15682			−0.578409	+	0.815747i	$0.696326\pi$
$558$		0			0
$559$	−0.562902			−0.0238082
$560$	−23.2174	+	16.8684i	−0.981114	+	0.712821i
$561$	15.7669	+	11.4553i	0.665680	+	0.483645i
$562$	−4.26122	+	13.1147i	−0.179749	+	0.553209i
$563$	5.18799			0.218648			0.109324	−	0.994006i	$-0.465131\pi$
$563$	5.18799			0.218648			0.109324	+	0.994006i	$0.465131\pi$
$564$	26.3961			1.11147
$565$	12.7251	−	39.1640i	0.535351	−	1.64764i
$566$	−4.63992	−	14.2802i	−0.195030	−	0.600242i
$567$	12.7676	+	39.2946i	0.536189	+	1.65022i
$568$	0.657719	−	0.477861i	0.0275973	−	0.0200506i
$569$	−0.731700	+	2.25194i	−0.0306745	+	0.0944063i	−0.965222	−	0.261433i	$-0.915805\pi$
$569$	−0.731700	+	2.25194i	−0.0306745	+	0.0944063i	0.934547	+	0.355839i	$0.115805\pi$
$570$	5.22092	−	3.79322i	0.218680	−	0.158881i
$571$	16.4732	+	11.9684i	0.689380	+	0.500864i	0.876456	−	0.481482i	$-0.159901\pi$
$571$	16.4732	+	11.9684i	0.689380	+	0.500864i	−0.187076	+	0.982345i	$0.559901\pi$
$572$	6.33271	+	19.4901i	0.264784	+	0.814921i
$573$	−18.1136	−	13.1603i	−0.756705	−	0.549778i
$574$	−26.3517	−	19.1456i	−1.09990	−	0.799122i
$575$	0.531352	+	1.63533i	0.0221589	+	0.0681982i
$576$	12.9517	+	9.40993i	0.539653	+	0.392081i
$577$	−20.6961	+	15.0366i	−0.861589	+	0.625981i	−0.928317	−	0.371790i	$-0.878744\pi$
$577$	−20.6961	+	15.0366i	−0.861589	+	0.625981i	0.0667280	+	0.997771i	$0.478744\pi$
$578$	−7.98558	+	24.5771i	−0.332157	+	1.02227i
$579$	3.09926	−	2.25175i	0.128801	−	0.0935794i
$580$	2.29226	+	7.05485i	0.0951809	+	0.292937i
$581$	−5.88809	−	18.1217i	−0.244279	−	0.751814i
$582$	9.19747	−	28.3069i	0.381247	−	1.17336i
$583$	−40.7033			−1.68576
$584$	8.62082			0.356732
$585$	2.38813	−	7.34992i	0.0987371	−	0.303882i
$586$	−22.6505	−	16.4565i	−0.935682	−	0.679813i
$587$	32.3299	−	23.4890i	1.33440	−	0.969495i	0.334766	−	0.942301i	$-0.391343\pi$
$587$	32.3299	−	23.4890i	1.33440	−	0.969495i	0.999630	−	0.0271941i	$-0.00865722\pi$
$588$	31.9072			1.31583
$589$		0			0
$590$	−28.3514			−1.16721
$591$	11.0719	−	8.04419i	0.455436	−	0.330894i
$592$	−0.738643	−	0.536656i	−0.0303580	−	0.0220564i
$593$	−6.48230	+	19.9505i	−0.266196	+	0.819268i	0.725219	+	0.688518i	$0.241738\pi$
$593$	−6.48230	+	19.9505i	−0.266196	+	0.819268i	−0.991415	+	0.130750i	$0.958262\pi$
$594$	−27.0035			−1.10797
$595$	18.3601			0.752691
$596$	8.72871	−	26.8642i	0.357542	−	1.10040i
$597$	−0.612951	−	1.88647i	−0.0250864	−	0.0772080i
$598$	4.48238	+	13.7953i	0.183298	+	0.564133i
$599$	−16.9419	+	12.3090i	−0.692228	+	0.502933i	−0.877392	−	0.479775i	$-0.840718\pi$
$599$	−16.9419	+	12.3090i	−0.692228	+	0.502933i	0.185164	+	0.982708i	$0.440718\pi$
$600$	0.206266	−	0.634820i	0.00842076	−	0.0259164i
$601$	−13.4448	+	9.76821i	−0.548424	+	0.398454i	−0.827204	−	0.561901i	$-0.810070\pi$
$601$	−13.4448	+	9.76821i	−0.548424	+	0.398454i	0.278780	+	0.960355i	$0.410070\pi$
$602$	−1.66129	−	1.20700i	−0.0677090	−	0.0491935i
$603$	−6.63454	−	20.4190i	−0.270180	−	0.831527i
$604$	−36.8843	−	26.7980i	−1.50080	−	1.09040i
$605$	−13.9117	−	10.1075i	−0.565592	−	0.410927i
$606$	−24.7439	−	76.1539i	−1.00515	−	3.09354i
$607$	−23.9075	−	17.3698i	−0.970377	−	0.705020i	−0.0148397	−	0.999890i	$-0.504724\pi$
$607$	−23.9075	−	17.3698i	−0.970377	−	0.705020i	−0.955538	+	0.294870i	$0.904724\pi$
$608$	−4.06788	+	2.95549i	−0.164974	+	0.119861i
$609$	−3.34612	+	10.2983i	−0.135591	+	0.417308i
$610$	8.76620	−	6.36902i	0.354933	−	0.257874i
$611$	3.46945	+	10.6779i	0.140359	+	0.431981i
$612$	−2.37869	−	7.32085i	−0.0961528	−	0.295928i
$613$	−11.4645	+	35.2840i	−0.463046	+	1.42511i	0.398377	+	0.917222i	$0.369573\pi$
$613$	−11.4645	+	35.2840i	−0.463046	+	1.42511i	−0.861423	+	0.507888i	$0.830427\pi$
$614$	−47.0907			−1.90042
$615$	−21.4884			−0.866496
$616$	−2.95798	+	9.10373i	−0.119180	+	0.366800i
$617$	21.3120	+	15.4841i	0.857991	+	0.623367i	0.927338	−	0.374226i	$-0.122092\pi$
$617$	21.3120	+	15.4841i	0.857991	+	0.623367i	−0.0693470	+	0.997593i	$0.522092\pi$
$618$	−14.0420	+	10.2021i	−0.564854	+	0.410390i
$619$	26.3796			1.06029			0.530144	−	0.847908i	$-0.322138\pi$
$619$	26.3796			1.06029			0.530144	+	0.847908i	$0.322138\pi$
$620$		0			0
$621$	−10.2104			−0.409730
$622$	−15.9144	+	11.5625i	−0.638109	+	0.463613i
$623$	−14.9012	−	10.8264i	−0.597005	−	0.433750i
$624$	−4.58994	+	14.1264i	−0.183745	+	0.565508i
$625$	−27.3006			−1.09202
$626$	−58.2205			−2.32696
$627$	−1.75462	+	5.40018i	−0.0700729	+	0.215662i
$628$	−4.11425	−	12.6623i	−0.164176	−	0.505283i
$629$	0.180501	+	0.555524i	0.00719703	+	0.0221502i
$630$	22.8081	−	16.5710i	0.908695	−	0.660205i
$631$	−6.17145	+	18.9938i	−0.245682	+	0.756131i	0.749842	+	0.661617i	$0.230130\pi$
$631$	−6.17145	+	18.9938i	−0.245682	+	0.756131i	−0.995524	+	0.0945134i	$0.969870\pi$
$632$	4.27178	−	3.10363i	0.169922	−	0.123456i
$633$	10.6989	+	7.77317i	0.425241	+	0.308956i
$634$	−10.1278	−	31.1703i	−0.402228	−	1.23793i
$635$	−26.9696	−	19.5946i	−1.07026	−	0.777587i
$636$	37.7488	+	27.4261i	1.49684	+	1.08751i
$637$	4.19382	+	12.9073i	0.166165	+	0.511404i
$638$	−9.88432	−	7.18138i	−0.391324	−	0.284314i
$639$	1.70439	−	1.23831i	0.0674248	−	0.0489870i
$640$	−3.49420	+	10.7540i	−0.138120	+	0.425090i
$641$	18.8460	−	13.6924i	0.744373	−	0.540818i	−0.149705	−	0.988731i	$-0.547832\pi$
$641$	18.8460	−	13.6924i	0.744373	−	0.540818i	0.894077	+	0.447912i	$0.147832\pi$
$642$	15.2273	+	46.8647i	0.600972	+	1.84960i
$643$	12.0189	+	36.9903i	0.473978	+	1.45875i	0.847332	+	0.531064i	$0.178208\pi$
$643$	12.0189	+	36.9903i	0.473978	+	1.45875i	−0.373354	+	0.927689i	$0.621792\pi$
$644$	−8.73508	+	26.8838i	−0.344210	+	1.05937i
$645$	−1.35469			−0.0533410
$646$	2.73406			0.107570
$647$	0.689235	−	2.12125i	0.0270966	−	0.0833948i	−0.936594	−	0.350417i	$-0.886040\pi$
$647$	0.689235	−	2.12125i	0.0270966	−	0.0833948i	0.963690	+	0.267022i	$0.0860398\pi$
$648$	5.53582	+	4.02201i	0.217468	+	0.157999i
$649$	20.1811	−	14.6624i	0.792176	−	0.575550i
$650$	2.21734			0.0869713
$651$		0			0
$652$	40.7894			1.59744
$653$	23.1162	−	16.7949i	0.904607	−	0.657235i	−0.0350384	−	0.999386i	$-0.511155\pi$
$653$	23.1162	−	16.7949i	0.904607	−	0.657235i	0.939645	+	0.342151i	$0.111155\pi$
$654$	−64.8908	−	47.1459i	−2.53743	−	1.84355i
$655$	5.21559	−	16.0519i	0.203790	−	0.627201i
$656$	14.2299			0.555586
$657$	22.3398			0.871557
$658$	−12.6566	+	38.9529i	−0.493404	+	1.51854i
$659$	1.58766	+	4.88632i	0.0618466	+	0.190344i	0.977206	−	0.212294i	$-0.0680934\pi$
$659$	1.58766	+	4.88632i	0.0618466	+	0.190344i	−0.915359	+	0.402638i	$0.868093\pi$
$660$	15.2404	+	46.9052i	0.593233	+	1.82578i
$661$	4.76952	−	3.46526i	0.185513	−	0.134783i	−0.491153	−	0.871073i	$-0.663424\pi$
$661$	4.76952	−	3.46526i	0.185513	−	0.134783i	0.676666	+	0.736291i	$0.263424\pi$
$662$	−8.28839	+	25.5090i	−0.322137	+	0.991437i
$663$	7.68780	−	5.58551i	0.298569	−	0.216923i
$664$	−2.55298	−	1.85485i	−0.0990748	−	0.0719821i
$665$	1.65299	+	5.08737i	0.0641001	+	0.197280i
$666$	0.725620	+	0.527194i	0.0281172	+	0.0204284i
$667$	−3.73740	−	2.71538i	−0.144713	−	0.105140i
$668$	−1.54660	−	4.75994i	−0.0598397	−	0.184168i
$669$	27.5160	+	19.9915i	1.06383	+	0.772918i
$670$	53.5862	−	38.9326i	2.07021	−	1.50410i
$671$	−2.94610	+	9.06718i	−0.113733	+	0.350034i
$672$	−51.5774	+	37.4731i	−1.98964	+	1.44556i
$673$	−8.42483	−	25.9290i	−0.324753	−	0.999488i	−0.971552	−	0.236827i	$-0.923893\pi$
$673$	−8.42483	−	25.9290i	−0.324753	−	0.999488i	0.646799	−	0.762661i	$-0.276107\pi$
$674$	17.8434	+	54.9163i	0.687301	+	2.11530i
$675$	−0.482317	+	1.48442i	−0.0185644	+	0.0571353i
$676$	−19.8257			−0.762528
$677$	2.63022			0.101088			0.0505438	−	0.998722i	$-0.483905\pi$
$677$	2.63022			0.101088			0.0505438	+	0.998722i	$0.483905\pi$
$678$	24.0263	−	73.9453i	0.922724	−	2.83985i
$679$	19.9591	+	14.5011i	0.765960	+	0.556503i
$680$	2.45997	−	1.78728i	0.0943357	−	0.0685389i
$681$	−9.93738			−0.380801
$682$		0			0
$683$	29.5859			1.13207			0.566037	−	0.824380i	$-0.308476\pi$
$683$	29.5859			1.13207			0.566037	+	0.824380i	$0.308476\pi$
$684$	1.81437	−	1.31821i	0.0693740	−	0.0504032i
$685$	14.3938	+	10.4577i	0.549957	+	0.399567i
$686$	1.17114	−	3.60441i	0.0447145	−	0.137617i
$687$	41.5435			1.58498
$688$	0.897097			0.0342015
$689$	−6.13291	+	18.8752i	−0.233645	+	0.719086i
$690$	10.7874	+	33.2002i	0.410669	+	1.26391i
$691$	5.20564	+	16.0213i	0.198032	+	0.609480i	0.999928	+	0.0120160i	$0.00382489\pi$
$691$	5.20564	+	16.0213i	0.198032	+	0.609480i	−0.801896	+	0.597464i	$0.796175\pi$
$692$	10.2207	−	7.42576i	0.388532	−	0.282285i
$693$	−7.66522	+	23.5911i	−0.291178	+	0.896153i
$694$	8.92423	−	6.48383i	0.338759	−	0.246123i
$695$	−38.1766	−	27.7369i	−1.44812	−	1.05212i
$696$	0.554165	+	1.70554i	0.0210056	+	0.0646484i
$697$	−7.36512	−	5.35108i	−0.278974	−	0.202686i
$698$	6.86966	+	4.99110i	0.260020	+	0.188916i
$699$	−9.41979	−	28.9911i	−0.356289	−	1.09655i
$700$	3.49581	+	2.53986i	0.132129	+	0.0959976i
$701$	−17.1708	+	12.4753i	−0.648534	+	0.471187i	−0.862771	−	0.505594i	$-0.831273\pi$
$701$	−17.1708	+	12.4753i	−0.648534	+	0.471187i	0.214238	+	0.976782i	$0.431273\pi$
$702$	−4.06872	+	12.5222i	−0.153564	+	0.472621i
$703$	−0.137679	+	0.100029i	−0.00519264	+	0.00377268i
$704$	−13.4285	−	41.3288i	−0.506107	−	1.55764i
$705$	8.34966	+	25.6976i	0.314467	+	0.967828i
$706$	−13.9522	+	42.9404i	−0.525097	+	1.61608i
$707$	66.3718			2.49617
$708$	−28.5958			−1.07470
$709$	−15.8662	+	48.8313i	−0.595869	+	1.83390i	−0.0455172	+	0.998964i	$0.514494\pi$
$709$	−15.8662	+	48.8313i	−0.595869	+	1.83390i	−0.550352	+	0.834933i	$0.685506\pi$
$710$	5.25819	+	3.82030i	0.197336	+	0.143373i
$711$	11.0698	−	8.04266i	0.415149	−	0.301623i
$712$	−3.05044			−0.114320
$713$		0			0
$714$	34.6656			1.29733
$715$	−16.9712	+	12.3303i	−0.634686	+	0.461127i
$716$	22.5160	+	16.3589i	0.841464	+	0.611359i
$717$	4.49654	−	13.8389i	0.167926	−	0.516824i
$718$	−14.6736			−0.547613
$719$	40.1999			1.49920			0.749601	−	0.661890i	$-0.230245\pi$
$719$	40.1999			1.49920			0.749601	+	0.661890i	$0.230245\pi$
$720$	−3.80597	+	11.7136i	−0.141840	+	0.436539i
$721$	−4.44583	−	13.6829i	−0.165571	−	0.509576i
$722$	−11.9199	−	36.6858i	−0.443614	−	1.36530i
$723$	−19.9131	+	14.4677i	−0.740577	+	0.538060i
$724$	−6.83759	+	21.0439i	−0.254117	+	0.782092i
$725$	−0.571316	+	0.415085i	−0.0212181	+	0.0154159i
$726$	−26.2667	−	19.0839i	−0.974848	−	0.708268i
$727$	−6.63887	−	20.4324i	−0.246222	−	0.757794i	−0.995433	−	0.0954624i	$-0.969567\pi$
$727$	−6.63887	−	20.4324i	−0.246222	−	0.757794i	0.749211	−	0.662332i	$-0.230433\pi$
$728$	3.77594	+	2.74338i	0.139946	+	0.101677i
$729$	−1.46222	−	1.06236i	−0.0541562	−	0.0393468i
$730$	21.2974	+	65.5467i	0.788253	+	2.42599i
$731$	−0.464319	−	0.337348i	−0.0171735	−	0.0124773i
$732$	8.84177	−	6.42392i	0.326801	−	0.237435i
$733$	6.94402	−	21.3715i	0.256483	−	0.789375i	−0.737050	−	0.675838i	$-0.763782\pi$
$733$	6.94402	−	21.3715i	0.256483	−	0.789375i	0.993534	−	0.113537i	$-0.0362180\pi$
$734$	−27.0194	+	19.6307i	−0.997304	+	0.724584i
$735$	10.0930	+	31.0629i	0.372284	+	1.14577i
$736$	−8.40499	−	25.8679i	−0.309812	−	0.953504i
$737$	−18.0090	+	55.4260i	−0.663370	+	2.04164i
$738$	−13.9791			−0.514576
$739$	−52.5500			−1.93308			−0.966542	−	0.256507i	$-0.917428\pi$
$739$	−52.5500			−1.93308			−0.966542	+	0.256507i	$0.917428\pi$
$740$	−0.456777	+	1.40582i	−0.0167915	+	0.0516788i
$741$	2.23983	+	1.62733i	0.0822820	+	0.0597814i
$742$	−58.5729	+	42.5557i	−2.15028	+	1.56227i
$743$	17.4032			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$743$	17.4032			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$744$		0			0
$745$	28.9145			1.05934
$746$	16.4603	−	11.9591i	0.602655	−	0.437854i
$747$	−6.61572	−	4.80660i	−0.242057	−	0.175864i
$748$	−6.45678	+	19.8719i	−0.236083	+	0.726589i
$749$	−40.8448			−1.49244
$750$	−46.7061			−1.70546
$751$	−6.93557	+	21.3455i	−0.253082	+	0.778908i	0.741119	+	0.671374i	$0.234295\pi$
$751$	−6.93557	+	21.3455i	−0.253082	+	0.778908i	−0.994201	+	0.107534i	$0.965705\pi$
$752$	−5.52927	−	17.0173i	−0.201632	−	0.620559i
$753$	4.82239	+	14.8418i	0.175738	+	0.540865i
$754$	−4.81950	+	3.50157i	−0.175516	+	0.127520i
$755$	14.4216	−	44.3852i	0.524857	−	1.61534i
$756$	−20.7583	+	15.0818i	−0.754972	+	0.548519i
$757$	−11.9677	−	8.69501i	−0.434972	−	0.316025i	0.348662	−	0.937248i	$-0.386636\pi$
$757$	−11.9677	−	8.69501i	−0.434972	−	0.316025i	−0.783634	+	0.621223i	$0.786636\pi$
$758$	−8.84643	−	27.2265i	−0.321317	−	0.988912i
$759$	−24.8487	−	18.0536i	−0.901951	−	0.655306i
$760$	0.716709	+	0.520719i	0.0259978	+	0.0188885i
$761$	6.14983	+	18.9272i	0.222931	+	0.686111i	0.998495	+	0.0548422i	$0.0174656\pi$
$761$	6.14983	+	18.9272i	0.222931	+	0.686111i	−0.775564	+	0.631269i	$0.782534\pi$
$762$	−50.9212	−	36.9964i	−1.84468	−	1.34024i
$763$	53.7874	−	39.0788i	1.94723	−	1.41475i
$764$	7.41776	−	22.8295i	0.268365	−	0.825943i
$765$	6.37471	−	4.63150i	0.230478	−	0.167452i
$766$	−6.59916	−	20.3101i	−0.238437	−	0.733835i
$767$	−3.75858	−	11.5677i	−0.135714	−	0.417686i
$768$	6.82533	−	21.0062i	0.246288	−	0.757996i
$769$	4.19707			0.151350			0.0756751	−	0.997133i	$-0.475889\pi$
$769$	4.19707			0.151350			0.0756751	+	0.997133i	$0.475889\pi$
$770$	−76.5260			−2.75780
$771$	−16.3001	+	50.1665i	−0.587033	+	1.80670i
$772$	3.32279	+	2.41415i	0.119590	+	0.0868870i
$773$	9.61002	−	6.98209i	0.345648	−	0.251128i	−0.401393	−	0.915906i	$-0.631474\pi$
$773$	9.61002	−	6.98209i	0.345648	−	0.251128i	0.747041	+	0.664778i	$0.231474\pi$
$774$	−0.881281			−0.0316770
$775$		0			0
$776$	4.08584			0.146673
$777$	−1.74565	+	1.26829i	−0.0626248	+	0.0454996i
$778$	−42.5221	−	30.8941i	−1.52449	−	1.10761i
$779$	0.819628	−	2.52256i	0.0293662	−	0.0903799i
$780$	24.0475			0.861039
$781$	−5.71861			−0.204628
$782$	−4.57020	+	14.0656i	−0.163430	+	0.502986i
$783$	−1.29582	−	3.98812i	−0.0463088	−	0.142524i
$784$	−6.68370	−	20.5703i	−0.238704	−	0.734654i
$785$	11.0259	−	8.01076i	0.393530	−	0.285916i
$786$	9.84752	−	30.3075i	0.351249	−	1.08103i
$787$	1.60511	−	1.16618i	0.0572162	−	0.0415700i	−0.558810	−	0.829296i	$-0.688742\pi$
$787$	1.60511	−	1.16618i	0.0572162	−	0.0415700i	0.616026	+	0.787726i	$0.288742\pi$
$788$	11.8704	+	8.62435i	0.422866	+	0.307230i
$789$	17.3786	+	53.4857i	0.618693	+	1.90414i
$790$	34.1511	+	24.8122i	1.21504	+	0.882780i
$791$	52.1386	+	37.8809i	1.85384	+	1.34689i
$792$	1.26947	+	3.90703i	0.0451087	+	0.138830i
$793$	3.76078	+	2.73237i	0.133549	+	0.0970293i
$794$	−28.0942	+	20.4116i	−0.997025	+	0.724381i
$795$	−14.7596	+	45.4254i	−0.523469	+	1.61107i
$796$	1.72046	−	1.24999i	0.0609801	−	0.0443047i
$797$	15.5702	+	47.9203i	0.551526	+	1.69742i	0.704946	+	0.709261i	$0.250971\pi$
$797$	15.5702	+	47.9203i	0.551526	+	1.69742i	−0.153420	+	0.988161i	$0.549029\pi$
$798$	3.12100	+	9.60544i	0.110482	+	0.340029i
$799$	−3.53743	+	10.8871i	−0.125145	+	0.385157i
$800$	−4.15778			−0.147000
$801$	−7.90482			−0.279303
$802$	17.6879	−	54.4379i	0.624583	−	1.92227i
$803$	−49.0585	−	35.6431i	−1.73124	−	1.25782i
$804$	54.0481	−	39.2682i	1.90613	−	1.38488i
$805$	−28.9356			−1.01984
$806$		0			0
$807$	44.6701			1.57246
$808$	8.89281	−	6.46100i	0.312848	−	0.227297i
$809$	−12.5983	−	9.15324i	−0.442934	−	0.321811i	0.343865	−	0.939019i	$-0.388264\pi$
$809$	−12.5983	−	9.15324i	−0.442934	−	0.321811i	−0.786800	+	0.617208i	$0.788264\pi$
$810$	−16.9045	+	52.0268i	−0.593964	+	1.82803i
$811$	20.7388			0.728239			0.364119	−	0.931352i	$-0.381370\pi$
$811$	20.7388			0.728239			0.364119	+	0.931352i	$0.381370\pi$
$812$	−11.6092			−0.407403
$813$	13.8904	−	42.7504i	0.487159	−	1.49932i
$814$	−0.752337	−	2.31546i	−0.0263694	−	0.0811567i
$815$	12.9026	+	39.7101i	0.451958	+	1.39098i
$816$	−12.2521	+	8.90164i	−0.428908	+	0.311620i
$817$	0.0516718	−	0.159029i	0.00180777	−	0.00556373i
$818$	−37.9041	+	27.5390i	−1.32529	+	0.962877i
$819$	9.78487	+	7.10913i	0.341911	+	0.248413i
$820$	−7.11919	−	21.9106i	−0.248613	−	0.765152i
$821$	15.8525	+	11.5175i	0.553256	+	0.401964i	0.828984	−	0.559272i	$-0.188919\pi$
$821$	15.8525	+	11.5175i	0.553256	+	0.401964i	−0.275729	+	0.961235i	$0.588919\pi$
$822$	27.1768	+	19.7451i	0.947899	+	0.688689i
$823$	−0.649127	−	1.99781i	−0.0226272	−	0.0696392i	0.939105	−	0.343629i	$-0.111656\pi$
$823$	−0.649127	−	1.99781i	−0.0226272	−	0.0696392i	−0.961732	+	0.273990i	$0.911656\pi$
$824$	−1.92764	−	1.40051i	−0.0671525	−	0.0487891i
$825$	−3.79848	+	2.75976i	−0.132246	+	0.0960825i
$826$	13.7113	−	42.1990i	0.477077	−	1.46829i
$827$	−2.83572	+	2.06027i	−0.0986076	+	0.0716426i	−0.635997	−	0.771692i	$-0.719411\pi$
$827$	−2.83572	+	2.06027i	−0.0986076	+	0.0716426i	0.537389	+	0.843335i	$0.319411\pi$
$828$	3.74882	+	11.5377i	0.130280	+	0.400962i
$829$	0.645411	+	1.98637i	0.0224161	+	0.0689895i	0.961639	−	0.274319i	$-0.0884524\pi$
$829$	0.645411	+	1.98637i	0.0224161	+	0.0689895i	−0.939223	+	0.343308i	$0.888452\pi$
$830$	7.79593	−	23.9934i	0.270601	−	0.832824i
$831$	10.1820			0.353209
$832$	−21.1885			−0.734581
$833$	−4.27599	+	13.1601i	−0.148154	+	0.455972i
$834$	−72.0810	−	52.3699i	−2.49596	−	1.81342i
$835$	4.14477	−	3.01135i	0.143436	−	0.104212i
$836$	−6.08759			−0.210544
$837$		0			0
$838$	−12.8284			−0.443151
$839$	8.71583	−	6.33242i	0.300904	−	0.218620i	−0.427080	−	0.904214i	$-0.640458\pi$
$839$	8.71583	−	6.33242i	0.300904	−	0.218620i	0.727984	+	0.685594i	$0.240458\pi$
$840$	9.08727	+	6.60229i	0.313541	+	0.227801i
$841$	−8.37520	+	25.7762i	−0.288800	+	0.888835i
$842$	13.5917			0.468402
$843$	−14.2373			−0.490357
$844$	−4.38133	+	13.4844i	−0.150812	+	0.464151i
$845$	−6.27132	−	19.3011i	−0.215740	−	0.663979i
$846$	5.43179	+	16.7173i	0.186749	+	0.574753i
$847$	21.7722	−	15.8184i	0.748102	−	0.543528i
$848$	9.77403	−	30.0814i	0.335642	−	1.03300i
$849$	12.5418	−	9.11217i	0.430435	−	0.312729i
$850$	1.82901	+	1.32886i	0.0627346	+	0.0455794i
$851$	−0.284469	−	0.875506i	−0.00975148	−	0.0300120i
$852$	5.30352	+	3.85323i	0.181695	+	0.132010i
$853$	−26.4147	−	19.1914i	−0.904423	−	0.657102i	0.0351753	−	0.999381i	$-0.488801\pi$
$853$	−26.4147	−	19.1914i	−0.904423	−	0.657102i	−0.939598	+	0.342280i	$0.888801\pi$
$854$	5.24032	+	16.1280i	0.179320	+	0.551890i
$855$	1.85726	+	1.34938i	0.0635169	+	0.0461477i
$856$	−5.47258	+	3.97606i	−0.187049	+	0.135899i
$857$	−13.5145	+	41.5933i	−0.461646	+	1.42080i	0.401506	+	0.915856i	$0.368487\pi$
$857$	−13.5145	+	41.5933i	−0.461646	+	1.42080i	−0.863152	+	0.504944i	$0.831513\pi$
$858$	−32.0432	+	23.2807i	−1.09394	+	0.794792i
$859$	7.52960	+	23.1737i	0.256907	+	0.790678i	0.993448	+	0.114285i	$0.0364577\pi$
$859$	7.52960	+	23.1737i	0.256907	+	0.790678i	−0.736541	+	0.676393i	$0.763542\pi$
$860$	−0.448815	−	1.38131i	−0.0153045	−	0.0471023i
$861$	10.3922	−	31.9839i	0.354165	−	1.09001i
$862$	48.6279			1.65627
$863$	43.5140			1.48123			0.740616	−	0.671928i	$-0.234534\pi$
$863$	43.5140			1.48123			0.740616	+	0.671928i	$0.234534\pi$
$864$	7.62934	−	23.4807i	0.259555	−	0.798829i
$865$	10.4623	+	7.60131i	0.355729	+	0.258452i
$866$	40.7578	−	29.6123i	1.38501	−	1.00627i
$867$	−26.6808			−0.906129
$868$		0			0
$869$	−37.1415			−1.25994
$870$	−11.5987	+	8.42696i	−0.393233	+	0.285701i
$871$	22.9890	+	16.7025i	0.778952	+	0.565942i
$872$	3.40254	−	10.4719i	0.115224	−	0.354625i
$873$	10.5879			0.358347
$874$	−4.30888			−0.145750
$875$	11.9634	−	36.8195i	0.404436	−	1.24472i
$876$	21.4810	+	66.1118i	0.725776	+	2.23371i
$877$	−11.8180	−	36.3720i	−0.399065	−	1.22820i	−0.925750	−	0.378136i	$-0.876565\pi$
$877$	−11.8180	−	36.3720i	−0.399065	−	1.22820i	0.526685	−	0.850061i	$-0.323435\pi$
$878$	−24.3182	+	17.6682i	−0.820699	+	0.596273i
$879$	8.93258	−	27.4917i	0.301288	−	0.927270i
$880$	27.0470	−	19.6508i	0.911754	−	0.662428i
$881$	32.9605	+	23.9472i	1.11047	+	0.806802i	0.982737	−	0.185007i	$-0.0592308\pi$
$881$	32.9605	+	23.9472i	1.11047	+	0.806802i	0.127730	+	0.991809i	$0.459231\pi$
$882$	6.56586	+	20.2077i	0.221084	+	0.680427i
$883$	26.7914	+	19.4651i	0.901604	+	0.655054i	0.938877	−	0.344252i	$-0.111867\pi$
$883$	26.7914	+	19.4651i	0.901604	+	0.655054i	−0.0372736	+	0.999305i	$0.511867\pi$
$884$	8.24226	+	5.98835i	0.277217	+	0.201410i
$885$	−9.04549	−	27.8391i	−0.304061	−	0.935803i
$886$	27.7709	+	20.1768i	0.932982	+	0.677851i
$887$	−10.0864	+	7.32822i	−0.338669	+	0.246058i	−0.744100	−	0.668068i	$-0.767121\pi$
$887$	−10.0864	+	7.32822i	−0.338669	+	0.246058i	0.405431	+	0.914126i	$0.367121\pi$
$888$	−0.110428	+	0.339863i	−0.00370572	+	0.0114050i
$889$	42.2082	−	30.6660i	1.41562	−	1.02851i
$890$	−7.53600	−	23.1934i	−0.252607	−	0.777445i
$891$	−14.8736	−	45.7761i	−0.498283	−	1.53356i
$892$	−11.2682	+	34.6799i	−0.377287	+	1.16117i
$893$	−3.33516			−0.111607
$894$	54.5932			1.82587
$895$	−8.80368	+	27.0949i	−0.294274	+	0.905684i
$896$	−14.3167	−	10.4017i	−0.478288	−	0.347497i
$897$	−12.1160	+	8.80278i	−0.404541	+	0.293916i
$898$	−14.1263			−0.471401
$899$		0			0
$900$	1.85446			0.0618154
$901$	−16.3707	+	11.8940i	−0.545389	+	0.396248i
$902$	30.6983	+	22.3036i	1.02214	+	0.742628i
$903$	0.655156	−	2.01636i	0.0218022	−	0.0671003i
$904$	10.6733			0.354989
$905$	−22.6500			−0.752912
$906$	27.2294	−	83.8034i	0.904636	−	2.78418i
$907$	5.22278	+	16.0741i	0.173419	+	0.533730i	0.999558	−	0.0297372i	$-0.00946703\pi$
$907$	5.22278	+	16.0741i	0.173419	+	0.533730i	−0.826138	+	0.563467i	$0.809467\pi$
$908$	−3.29229	−	10.1326i	−0.109259	−	0.336263i
$909$	23.0446	−	16.7429i	0.764340	−	0.555325i
$910$	−11.5305	+	35.4871i	−0.382231	+	1.17639i
$911$	−44.0669	+	32.0165i	−1.46000	+	1.06075i	−0.476638	+	0.879100i	$0.658145\pi$
$911$	−44.0669	+	32.0165i	−1.46000	+	1.06075i	−0.983363	+	0.181653i	$0.941855\pi$
$912$	−3.56961	−	2.59348i	−0.118202	−	0.0858786i
$913$	6.85930	+	21.1108i	0.227010	+	0.698665i
$914$	35.9211	+	26.0982i	1.18816	+	0.863251i
$915$	9.05079	+	6.57578i	0.299210	+	0.217389i
$916$	13.7635	+	42.3597i	0.454759	+	1.39961i
$917$	21.3698	+	15.5260i	0.705692	+	0.512715i
$918$	−10.8607	+	7.89079i	−0.358458	+	0.260435i
$919$	−2.70925	+	8.33821i	−0.0893699	+	0.275052i	−0.985746	−	0.168243i	$-0.946191\pi$
$919$	−2.70925	+	8.33821i	−0.0893699	+	0.275052i	0.896376	+	0.443295i	$0.146191\pi$
$920$	−3.87692	+	2.81675i	−0.127818	+	0.0928655i
$921$	−15.0242	−	46.2398i	−0.495065	−	1.52365i
$922$	5.55447	+	17.0949i	0.182927	+	0.562990i
$923$	−0.861644	+	2.65187i	−0.0283614	+	0.0872873i
$924$	−77.1856			−2.53922
$925$	−0.140721			−0.00462688
$926$	−2.33709	+	7.19283i	−0.0768016	+	0.236371i
$927$	−4.99523	−	3.62925i	−0.164065	−	0.119200i
$928$	9.03714	−	6.56587i	0.296659	−	0.215535i
$929$	44.2868			1.45300			0.726501	−	0.687165i	$-0.241145\pi$
$929$	44.2868			1.45300			0.726501	+	0.687165i	$0.241145\pi$
$930$		0			0
$931$	−4.03150			−0.132127
$932$	26.4399	−	19.2097i	0.866069	−	0.629236i
$933$	−16.4310	−	11.9378i	−0.537928	−	0.390828i
$934$	−1.97290	+	6.07196i	−0.0645552	+	0.198681i
$935$	−21.3885			−0.699480
$936$	2.00307			0.0654723
$937$	−15.9195	+	48.9952i	−0.520067	+	1.60060i	0.253802	+	0.967256i	$0.418319\pi$
$937$	−15.9195	+	48.9952i	−0.520067	+	1.60060i	−0.773869	+	0.633346i	$0.781681\pi$
$938$	32.0331	+	98.5877i	1.04592	+	3.21900i
$939$	−18.5752	−	57.1686i	−0.606179	−	1.86563i
$940$	−23.4363	+	17.0274i	−0.764406	+	0.555374i
$941$	−12.1125	+	37.2786i	−0.394858	+	1.21525i	0.534215	+	0.845349i	$0.320607\pi$
$941$	−12.1125	+	37.2786i	−0.394858	+	1.21525i	−0.929072	+	0.369898i	$0.879393\pi$
$942$	20.8179	−	15.1251i	0.678283	−	0.492802i
$943$	11.6074	+	8.43330i	0.377990	+	0.274626i
$944$	5.99006	+	18.4355i	0.194960	+	0.600024i
$945$	−21.2490	−	15.4383i	−0.691231	−	0.502208i
$946$	1.93531	+	1.40608i	0.0629223	+	0.0457158i
$947$	−17.5881	−	54.1306i	−0.571537	−	1.75901i	−0.647680	−	0.761912i	$-0.724261\pi$
$947$	−17.5881	−	54.1306i	−0.571537	−	1.75901i	0.0761432	−	0.997097i	$-0.475739\pi$
$948$	34.4455	+	25.0261i	1.11874	+	0.812811i
$949$	−23.9204	+	17.3792i	−0.776491	+	0.564153i
$950$	−0.203542	+	0.626437i	−0.00660376	+	0.0203243i
$951$	27.3758	−	19.8897i	0.887722	−	0.644968i
$952$	1.47054	+	4.52586i	0.0476605	+	0.146684i
$953$	4.71987	+	14.5263i	0.152892	+	0.470552i	0.997941	−	0.0641360i	$-0.0204292\pi$
$953$	4.71987	+	14.5263i	0.152892	+	0.470552i	−0.845050	+	0.534688i	$0.820429\pi$
$954$	−9.60171	+	29.5510i	−0.310867	+	0.956750i
$955$	24.5718			0.795126
$956$	15.6006			0.504558
$957$	3.89804	−	11.9969i	0.126006	−	0.387806i
$958$	29.1862	+	21.2050i	0.942963	+	0.685103i
$959$	−22.5266	+	16.3665i	−0.727421	+	0.528503i
$960$	−50.9928			−1.64579
$961$		0			0
$962$	−1.18709			−0.0382735
$963$	−14.1815	+	10.3035i	−0.456992	+	0.332024i
$964$	−21.3493	−	15.5112i	−0.687614	−	0.499581i
$965$	−1.29920	+	3.99852i	−0.0418226	+	0.128717i
$966$	−54.6331			−1.75779
$967$	−11.2996			−0.363370			−0.181685	−	0.983357i	$-0.558155\pi$
$967$	−11.2996			−0.363370			−0.181685	+	0.983357i	$0.558155\pi$
$968$	1.37729	−	4.23886i	0.0442678	−	0.136242i
$969$	0.872299	+	2.68466i	0.0280223	+	0.0862437i
$970$	10.0939	+	31.0659i	0.324096	+	0.997465i
$971$	12.8377	−	9.32710i	0.411980	−	0.299321i	−0.362423	−	0.932014i	$-0.618050\pi$
$971$	12.8377	−	9.32710i	0.411980	−	0.299321i	0.774403	+	0.632693i	$0.218050\pi$
$972$	−10.5768	+	32.5521i	−0.339251	+	1.04411i
$973$	59.7473	−	43.4090i	1.91541	−	1.39163i
$974$	48.2356	+	35.0452i	1.54557	+	1.12292i
$975$	0.707440	+	2.17728i	0.0226562	+	0.0697287i
$976$	−5.99357	−	4.35458i	−0.191849	−	0.139387i
$977$	13.3973	+	9.73371i	0.428617	+	0.311409i	0.781096	−	0.624411i	$-0.214661\pi$
$977$	13.3973	+	9.73371i	0.428617	+	0.311409i	−0.352478	+	0.935820i	$0.614661\pi$
$978$	24.3613	+	74.9764i	0.778989	+	2.39748i
$979$	17.3591	+	12.6121i	0.554800	+	0.403086i
$980$	−28.3294	+	20.5825i	−0.904950	+	0.657484i
$981$	8.81724	−	27.1367i	0.281513	−	0.866407i
$982$	−16.4716	+	11.9673i	−0.525630	+	0.381892i
$983$	−6.69016	−	20.5902i	−0.213383	−	0.656725i	−0.999264	−	0.0383482i	$-0.987790\pi$
$983$	−6.69016	−	20.5902i	−0.213383	−	0.656725i	0.785881	−	0.618377i	$-0.212210\pi$
$984$	−1.72110	−	5.29699i	−0.0548666	−	0.168862i
$985$	−4.64128	+	14.2844i	−0.147883	+	0.455138i
$986$	−6.07394			−0.193434
$987$	−42.2871			−1.34601
$988$	−0.917240	+	2.82297i	−0.0291813	+	0.0898108i
$989$	0.731768	+	0.531660i	0.0232689	+	0.0169058i
$990$	−26.5701	+	19.3043i	−0.844455	+	0.613532i
$991$	−32.3028			−1.02613			−0.513066	−	0.858349i	$-0.671490\pi$
$991$	−32.3028			−1.02613			−0.513066	+	0.858349i	$0.671490\pi$
$992$		0			0
$993$	−27.6925			−0.878796
$994$	−8.22920	+	5.97887i	−0.261014	+	0.189638i
$995$	1.76113	+	1.27954i	0.0558317	+	0.0405641i
$996$	7.86314	−	24.2002i	0.249153	−	0.766814i
$997$	−11.4872			−0.363803			−0.181902	−	0.983317i	$-0.558225\pi$
$997$	−11.4872			−0.363803			−0.181902	+	0.983317i	$0.558225\pi$
$998$	22.4784			0.711541
$999$	0.258217	−	0.794710i	0.00816963	−	0.0251435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.q.388.1		16
31.2	even	5	inner	961.2.d.q.374.1		16
31.3	odd	30		31.2.g.a.20.2	yes	16
31.4	even	5		961.2.d.n.628.4		16
31.5	even	3		961.2.g.n.338.1		16
31.6	odd	6		961.2.g.s.235.1		16
31.7	even	15		961.2.g.j.846.2		16
31.8	even	5		961.2.a.j.1.7		8
31.9	even	15		961.2.c.i.521.7		16
31.10	even	15		961.2.g.m.732.1		16
31.11	odd	30		31.2.g.a.14.2	✓	16
31.12	odd	30		961.2.g.t.816.1		16
31.13	odd	30		961.2.g.k.844.2		16
31.14	even	15		961.2.c.i.439.7		16
31.15	odd	10		961.2.d.o.531.4		16
31.16	even	5		961.2.d.n.531.4		16
31.17	odd	30		961.2.c.j.439.7		16
31.18	even	15		961.2.g.j.844.2		16
31.19	even	15		961.2.g.n.816.1		16
31.20	even	15		961.2.g.l.448.2		16
31.21	odd	30		961.2.g.s.732.1		16
31.22	odd	30		961.2.c.j.521.7		16
31.23	odd	10		961.2.a.i.1.7		8
31.24	odd	30		961.2.g.k.846.2		16
31.25	even	3		961.2.g.m.235.1		16
31.26	odd	6		961.2.g.t.338.1		16
31.27	odd	10		961.2.d.o.628.4		16
31.28	even	15		961.2.g.l.547.2		16
31.29	odd	10		961.2.d.p.374.1		16
31.30	odd	2		961.2.d.p.388.1		16
93.8	odd	10		8649.2.a.be.1.2		8
93.11	even	30		279.2.y.c.262.1		16
93.23	even	10		8649.2.a.bf.1.2		8
93.65	even	30		279.2.y.c.82.1		16
124.3	even	30		496.2.bg.c.113.2		16
124.11	even	30		496.2.bg.c.417.2		16
155.3	even	60		775.2.ck.a.299.3		32
155.34	odd	30		775.2.bl.a.51.1		16
155.42	even	60		775.2.ck.a.324.3		32
155.73	even	60		775.2.ck.a.324.2		32
155.104	odd	30		775.2.bl.a.76.1		16
155.127	even	60		775.2.ck.a.299.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.2	✓	16	31.11	odd	30
31.2.g.a.20.2	yes	16	31.3	odd	30
279.2.y.c.82.1		16	93.65	even	30
279.2.y.c.262.1		16	93.11	even	30
496.2.bg.c.113.2		16	124.3	even	30
496.2.bg.c.417.2		16	124.11	even	30
775.2.bl.a.51.1		16	155.34	odd	30
775.2.bl.a.76.1		16	155.104	odd	30
775.2.ck.a.299.2		32	155.127	even	60
775.2.ck.a.299.3		32	155.3	even	60
775.2.ck.a.324.2		32	155.73	even	60
775.2.ck.a.324.3		32	155.42	even	60
961.2.a.i.1.7		8	31.23	odd	10
961.2.a.j.1.7		8	31.8	even	5
961.2.c.i.439.7		16	31.14	even	15
961.2.c.i.521.7		16	31.9	even	15
961.2.c.j.439.7		16	31.17	odd	30
961.2.c.j.521.7		16	31.22	odd	30
961.2.d.n.531.4		16	31.16	even	5
961.2.d.n.628.4		16	31.4	even	5
961.2.d.o.531.4		16	31.15	odd	10
961.2.d.o.628.4		16	31.27	odd	10
961.2.d.p.374.1		16	31.29	odd	10
961.2.d.p.388.1		16	31.30	odd	2
961.2.d.q.374.1		16	31.2	even	5	inner
961.2.d.q.388.1		16	1.1	even	1	trivial
961.2.g.j.844.2		16	31.18	even	15
961.2.g.j.846.2		16	31.7	even	15
961.2.g.k.844.2		16	31.13	odd	30
961.2.g.k.846.2		16	31.24	odd	30
961.2.g.l.448.2		16	31.20	even	15
961.2.g.l.547.2		16	31.28	even	15
961.2.g.m.235.1		16	31.25	even	3
961.2.g.m.732.1		16	31.10	even	15
961.2.g.n.338.1		16	31.5	even	3
961.2.g.n.816.1		16	31.19	even	15
961.2.g.s.235.1		16	31.6	odd	6
961.2.g.s.732.1		16	31.21	odd	30
961.2.g.t.338.1		16	31.26	odd	6
961.2.g.t.816.1		16	31.12	odd	30
8649.2.a.be.1.2		8	93.8	odd	10
8649.2.a.bf.1.2		8	93.23	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67638 + 1.21796i) q^{2} +(-1.73080 - 1.25750i) q^{3} +(0.708788 - 2.18143i) q^{4} +2.34791 q^{5} +4.43308 q^{6} +(-1.13550 + 3.49470i) q^{7} +(0.188054 + 0.578772i) q^{8} +(0.487319 + 1.49981i) q^{9} +(-3.93600 + 2.85967i) q^{10} +(1.32279 - 4.07113i) q^{11} +(-3.96992 + 2.88432i) q^{12} +(-1.68858 - 1.22682i) q^{13} +(-2.35288 - 7.24144i) q^{14} +(-4.06377 - 2.95251i) q^{15} +(2.69109 + 1.95519i) q^{16} +(-0.657617 - 2.02394i) q^{17} +(-2.64365 - 1.92072i) q^{18} +(0.501603 - 0.364436i) q^{19} +(1.66417 - 5.12180i) q^{20} +(6.35991 - 4.62075i) q^{21} +(2.74098 + 8.43588i) q^{22} +(1.03640 + 3.18973i) q^{23} +(0.402322 - 1.23822i) q^{24} +0.512688 q^{25} +4.32493 q^{26} +(-0.940760 + 2.89536i) q^{27} +(6.81860 + 4.95400i) q^{28} +(-1.11435 + 0.809625i) q^{29} +10.4085 q^{30} -8.10976 q^{32} +(-7.40895 + 5.38292i) q^{33} +(3.56749 + 2.59194i) q^{34} +(-2.66604 + 8.20524i) q^{35} +3.61714 q^{36} -0.274477 q^{37} +(-0.397009 + 1.22187i) q^{38} +(1.37986 + 4.24679i) q^{39} +(0.441535 + 1.35890i) q^{40} +(3.46091 - 2.51449i) q^{41} +(-5.03374 + 15.4923i) q^{42} +(0.218186 - 0.158521i) q^{43} +(-7.94330 - 5.77114i) q^{44} +(1.14418 + 3.52143i) q^{45} +(-5.62238 - 4.08489i) q^{46} +(-4.35183 - 3.16179i) q^{47} +(-2.19909 - 6.76811i) q^{48} +(-5.26043 - 3.82193i) q^{49} +(-0.859461 + 0.624435i) q^{50} +(-1.40690 + 4.32999i) q^{51} +(-3.87307 + 2.81395i) q^{52} +(-2.93835 - 9.04330i) q^{53} +(-1.94937 - 5.99954i) q^{54} +(3.10580 - 9.55866i) q^{55} -2.23617 q^{56} -1.32646 q^{57} +(0.881988 - 2.71448i) q^{58} +(4.71450 + 3.42528i) q^{59} +(-9.32103 + 6.77212i) q^{60} -2.22719 q^{61} -5.79474 q^{63} +(8.21287 - 5.96700i) q^{64} +(-3.96464 - 2.88048i) q^{65} +(5.86404 - 18.0477i) q^{66} -13.6144 q^{67} -4.88118 q^{68} +(2.21728 - 6.82407i) q^{69} +(-5.52437 - 17.0022i) q^{70} +(-0.412823 - 1.27054i) q^{71} +(-0.776406 + 0.564092i) q^{72} +(4.37754 - 13.4727i) q^{73} +(0.460128 - 0.334303i) q^{74} +(-0.887363 - 0.644707i) q^{75} +(-0.439460 - 1.35252i) q^{76} +(12.7253 + 9.24551i) q^{77} +(-7.48561 - 5.43861i) q^{78} +(-2.68122 - 8.25195i) q^{79} +(6.31845 + 4.59062i) q^{80} +(9.09665 - 6.60910i) q^{81} +(-2.73924 + 8.43051i) q^{82} +(-4.19514 + 3.04795i) q^{83} +(-5.57199 - 17.1488i) q^{84} +(-1.54403 - 4.75202i) q^{85} +(-0.172690 + 0.531484i) q^{86} +2.94683 q^{87} +2.60501 q^{88} +(-1.54897 + 4.76725i) q^{89} +(-6.20705 - 4.50968i) q^{90} +(6.20475 - 4.50802i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(1.17772 - 0.855663i) q^{95} +(14.0364 + 10.1980i) q^{96} +(2.07474 - 6.38538i) q^{97} +13.4735 q^{98} +6.75055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} - 9 q^{13} - 18 q^{14} - 4 q^{15} - 2 q^{16} - 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 - 9 * q^13 - 18 * q^14 - 4 * q^15 - 2 * q^16 - 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 - 2 * q^21 + 8 * q^22 - 21 * q^23 - 5 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 + 56 * q^34 + 21 * q^35 - 2 * q^36 - 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 - 12 * q^42 + 16 * q^43 - 37 * q^44 - 5 * q^45 + 16 * q^46 + 4 * q^47 - 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 + 18 * q^52 - 3 * q^53 - 39 * q^54 - 29 * q^55 + 60 * q^56 - 34 * q^57 - 10 * q^58 - 3 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 9 * q^65 + 20 * q^66 - 26 * q^67 + 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 + 9 * q^73 - 64 * q^74 - 19 * q^75 + 9 * q^76 + 42 * q^77 + 15 * q^78 - 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 - 67 * q^83 - 39 * q^84 + 63 * q^85 + 23 * q^86 - 30 * q^87 - 34 * q^88 - 26 * q^89 - 24 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 4 * q^96 - 37 * q^97 + 20 * q^98 + 12 * q^99

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