LMFDB - Embedded newform 240.2.bf.a.77.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(53,240)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("240.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bf (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.15
Character	$\chi$	$=$	240.77
Dual form			240.2.bf.a.53.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.685419 - 1.23701i) q^{2} +(1.72806 - 0.117548i) q^{3} +(-1.06040 + 1.69575i) q^{4} +(1.91324 - 1.15738i) q^{5} +(-1.32985 - 2.05706i) q^{6} +(-0.912923 + 0.912923i) q^{7} +(2.82448 + 0.149432i) q^{8} +(2.97237 - 0.406258i) q^{9} +(-2.74306 - 1.57341i) q^{10} +(-1.03554 - 1.03554i) q^{11} +(-1.63310 + 3.05499i) q^{12} +2.08132 q^{13} +(1.75503 + 0.503562i) q^{14} +(3.17014 - 2.22491i) q^{15} +(-1.75110 - 3.59634i) q^{16} +(-1.49126 + 1.49126i) q^{17} +(-2.53986 - 3.39840i) q^{18} +(2.35078 - 2.35078i) q^{19} +(-0.0661763 + 4.47165i) q^{20} +(-1.47027 + 1.68489i) q^{21} +(-0.571195 + 1.99075i) q^{22} +(-4.27105 + 4.27105i) q^{23} +(4.89842 - 0.0737840i) q^{24} +(2.32095 - 4.42868i) q^{25} +(-1.42658 - 2.57462i) q^{26} +(5.08866 - 1.05143i) q^{27} +(-0.580021 - 2.51615i) q^{28} +(-2.58251 - 2.58251i) q^{29} +(-4.92512 - 2.39650i) q^{30} -5.18620 q^{31} +(-3.24847 + 4.63114i) q^{32} +(-1.91119 - 1.66774i) q^{33} +(2.86685 + 0.822570i) q^{34} +(-0.690039 + 2.80323i) q^{35} +(-2.46299 + 5.47117i) q^{36} -10.8954 q^{37} +(-4.51922 - 1.29667i) q^{38} +(3.59664 - 0.244654i) q^{39} +(5.57684 - 2.98309i) q^{40} +9.82802 q^{41} +(3.09199 + 0.663884i) q^{42} -0.814988i q^{43} +(2.85409 - 0.657923i) q^{44} +(5.21664 - 4.21742i) q^{45} +(8.21081 + 2.35588i) q^{46} +(-6.63331 + 6.63331i) q^{47} +(-3.44875 - 6.00884i) q^{48} +5.33314i q^{49} +(-7.06915 + 0.164463i) q^{50} +(-2.40169 + 2.75228i) q^{51} +(-2.20703 + 3.52938i) q^{52} +7.26025 q^{53} +(-4.78850 - 5.57407i) q^{54} +(-3.17974 - 0.782718i) q^{55} +(-2.71495 + 2.44211i) q^{56} +(3.78596 - 4.33861i) q^{57} +(-1.42449 + 4.96470i) q^{58} +(-6.09835 + 6.09835i) q^{59} +(0.411275 + 7.73504i) q^{60} +(9.87198 + 9.87198i) q^{61} +(3.55472 + 6.41539i) q^{62} +(-2.34266 + 3.08442i) q^{63} +(7.95534 + 0.844133i) q^{64} +(3.98205 - 2.40887i) q^{65} +(-0.753050 + 3.50727i) q^{66} +10.8038i q^{67} +(-0.947466 - 4.11014i) q^{68} +(-6.87857 + 7.88268i) q^{69} +(3.94060 - 1.06780i) q^{70} -2.57569 q^{71} +(8.45608 - 0.703301i) q^{72} +(-7.40366 - 7.40366i) q^{73} +(7.46794 + 13.4778i) q^{74} +(3.49015 - 7.92584i) q^{75} +(1.49356 + 6.47909i) q^{76} +1.89073 q^{77} +(-2.76785 - 4.28139i) q^{78} -8.54920i q^{79} +(-7.51260 - 4.85395i) q^{80} +(8.66991 - 2.41509i) q^{81} +(-6.73632 - 12.1574i) q^{82} +11.5636i q^{83} +(-1.29808 - 4.27987i) q^{84} +(-1.12718 + 4.57909i) q^{85} +(-1.00815 + 0.558608i) q^{86} +(-4.76629 - 4.15916i) q^{87} +(-2.77011 - 3.07959i) q^{88} -9.67152i q^{89} +(-8.79259 - 3.56235i) q^{90} +(-1.90008 + 1.90008i) q^{91} +(-2.71359 - 11.7716i) q^{92} +(-8.96205 + 0.609625i) q^{93} +(12.7521 + 3.65889i) q^{94} +(1.77685 - 7.21834i) q^{95} +(-5.06917 + 8.38472i) q^{96} +(-6.58488 - 6.58488i) q^{97} +(6.59717 - 3.65544i) q^{98} +(-3.49869 - 2.65730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{10} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} - 4 q^{21} - 4 q^{22} + 12 q^{24} - 4 q^{27} - 4 q^{28} - 28 q^{30} - 16 q^{31} - 4 q^{33}+ \cdots + 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^10 - 8 * q^12 - 8 * q^13 - 4 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 - 4 * q^21 - 4 * q^22 + 12 * q^24 - 4 * q^27 - 4 * q^28 - 28 * q^30 - 16 * q^31 - 4 * q^33 - 28 * q^34 - 20 * q^36 - 8 * q^37 - 24 * q^39 - 44 * q^40 + 40 * q^42 + 8 * q^45 - 36 * q^46 + 32 * q^48 - 4 * q^51 - 48 * q^52 + 24 * q^54 - 12 * q^57 - 20 * q^58 + 28 * q^60 - 24 * q^61 - 32 * q^63 + 28 * q^64 + 12 * q^66 + 12 * q^69 - 76 * q^70 + 24 * q^72 - 36 * q^75 - 36 * q^76 + 60 * q^78 - 8 * q^81 + 64 * q^82 - 48 * q^84 + 16 * q^85 + 12 * q^87 + 44 * q^88 - 56 * q^90 - 8 * q^91 - 16 * q^93 + 20 * q^94 + 48 * q^96 - 8 * q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.685419	−	1.23701i	−0.484665	−	0.874700i
$2$	−0.685419	−	1.23701i	−0.484665	−	0.874700i
$3$	1.72806	−	0.117548i	0.997694	−	0.0678662i
$3$	1.72806	−	0.117548i	0.997694	−	0.0678662i
$4$	−1.06040	+	1.69575i	−0.530200	+	0.847873i
$5$	1.91324	−	1.15738i	0.855625	−	0.517596i
$5$	1.91324	−	1.15738i	0.855625	−	0.517596i
$6$	−1.32985	−	2.05706i	−0.542910	−	0.839791i
$7$	−0.912923	+	0.912923i	−0.345052	+	0.345052i	−0.858263	−	0.513210i	$-0.828456\pi$
$7$	−0.912923	+	0.912923i	−0.345052	+	0.345052i	0.513210	+	0.858263i	$0.328456\pi$
$8$	2.82448	+	0.149432i	0.998603	+	0.0528321i
$9$	2.97237	−	0.406258i	0.990788	−	0.135419i
$10$	−2.74306	−	1.57341i	−0.867432	−	0.497555i
$11$	−1.03554	−	1.03554i	−0.312226	−	0.312226i	0.533545	−	0.845771i	$-0.320859\pi$
$11$	−1.03554	−	1.03554i	−0.312226	−	0.312226i	−0.845771	+	0.533545i	$0.820859\pi$
$12$	−1.63310	+	3.05499i	−0.471436	+	0.881900i
$13$	2.08132			0.577254			0.288627	−	0.957442i	$-0.406801\pi$
$13$	2.08132			0.577254			0.288627	+	0.957442i	$0.406801\pi$
$14$	1.75503	+	0.503562i	0.469052	+	0.134583i
$15$	3.17014	−	2.22491i	0.818525	−	0.574470i
$16$	−1.75110	−	3.59634i	−0.437776	−	0.899084i
$17$	−1.49126	+	1.49126i	−0.361684	+	0.361684i	−0.864433	−	0.502749i	$-0.832322\pi$
$17$	−1.49126	+	1.49126i	−0.361684	+	0.361684i	0.502749	+	0.864433i	$0.332322\pi$
$18$	−2.53986	−	3.39840i	−0.598652	−	0.801010i
$19$	2.35078	−	2.35078i	0.539306	−	0.539306i	−0.384019	−	0.923325i	$-0.625460\pi$
$19$	2.35078	−	2.35078i	0.539306	−	0.539306i	0.923325	+	0.384019i	$0.125460\pi$
$20$	−0.0661763	+	4.47165i	−0.0147975	+	0.999891i
$21$	−1.47027	+	1.68489i	−0.320839	+	0.367674i
$22$	−0.571195	+	1.99075i	−0.121779	+	0.424429i
$23$	−4.27105	+	4.27105i	−0.890576	+	0.890576i	−0.994577	−	0.104001i	$-0.966835\pi$
$23$	−4.27105	+	4.27105i	−0.890576	+	0.890576i	0.104001	+	0.994577i	$0.466835\pi$
$24$	4.89842	−	0.0737840i	0.999887	−	0.0150611i
$25$	2.32095	−	4.42868i	0.464189	−	0.885736i
$26$	−1.42658	−	2.57462i	−0.279775	−	0.504924i
$27$	5.08866	−	1.05143i	0.979314	−	0.202348i
$28$	−0.580021	−	2.51615i	−0.109614	−	0.475507i
$29$	−2.58251	−	2.58251i	−0.479560	−	0.479560i	0.425431	−	0.904991i	$-0.360122\pi$
$29$	−2.58251	−	2.58251i	−0.479560	−	0.479560i	−0.904991	+	0.425431i	$0.860122\pi$
$30$	−4.92512	−	2.39650i	−0.899200	−	0.437539i
$31$	−5.18620			−0.931469			−0.465734	−	0.884925i	$-0.654210\pi$
$31$	−5.18620			−0.931469			−0.465734	+	0.884925i	$0.654210\pi$
$32$	−3.24847	+	4.63114i	−0.574255	+	0.818677i
$33$	−1.91119	−	1.66774i	−0.332696	−	0.290317i
$34$	2.86685	+	0.822570i	0.491661	+	0.141070i
$35$	−0.690039	+	2.80323i	−0.116638	+	0.473833i
$36$	−2.46299	+	5.47117i	−0.410498	+	0.911862i
$37$	−10.8954			−1.79120			−0.895599	−	0.444863i	$-0.853253\pi$
$37$	−10.8954			−1.79120			−0.895599	+	0.444863i	$0.853253\pi$
$38$	−4.51922	−	1.29667i	−0.733114	−	0.210348i
$39$	3.59664	−	0.244654i	0.575923	−	0.0391760i
$40$	5.57684	−	2.98309i	0.881776	−	0.471668i
$41$	9.82802			1.53488			0.767439	−	0.641122i	$-0.221531\pi$
$41$	9.82802			1.53488			0.767439	+	0.641122i	$0.221531\pi$
$42$	3.09199	+	0.663884i	0.477104	+	0.102440i
$43$		−	0.814988i		−	0.124284i	−0.998067	−	0.0621422i	$-0.980207\pi$
$43$		−	0.814988i		−	0.124284i	0.998067	−	0.0621422i	$-0.0197932\pi$
$44$	2.85409	−	0.657923i	0.430270	−	0.0991856i
$45$	5.21664	−	4.21742i	0.777651	−	0.628696i
$46$	8.21081	+	2.35588i	1.21062	+	0.347356i
$47$	−6.63331	+	6.63331i	−0.967568	+	0.967568i	−0.999490	−	0.0319224i	$-0.989837\pi$
$47$	−6.63331	+	6.63331i	−0.967568	+	0.967568i	0.0319224	+	0.999490i	$0.489837\pi$
$48$	−3.44875	−	6.00884i	−0.497784	−	0.867301i
$49$			5.33314i			0.761878i
$50$	−7.06915	+	0.164463i	−0.999729	+	0.0232586i
$51$	−2.40169	+	2.75228i	−0.336304	+	0.385396i
$52$	−2.20703	+	3.52938i	−0.306060	+	0.489438i
$53$	7.26025			0.997273			0.498636	−	0.866811i	$-0.333834\pi$
$53$	7.26025			0.997273			0.498636	+	0.866811i	$0.333834\pi$
$54$	−4.78850	−	5.57407i	−0.651633	−	0.758535i
$55$	−3.17974	−	0.782718i	−0.428756	−	0.105542i
$56$	−2.71495	+	2.44211i	−0.362800	+	0.326341i
$57$	3.78596	−	4.33861i	0.501462	−	0.574663i
$58$	−1.42449	+	4.96470i	−0.187045	+	0.651897i
$59$	−6.09835	+	6.09835i	−0.793938	+	0.793938i	−0.982132	−	0.188194i	$-0.939737\pi$
$59$	−6.09835	+	6.09835i	−0.793938	+	0.793938i	0.188194	+	0.982132i	$0.439737\pi$
$60$	0.411275	+	7.73504i	0.0530954	+	0.998589i
$61$	9.87198	+	9.87198i	1.26398	+	1.26398i	0.949148	+	0.314829i	$0.101947\pi$
$61$	9.87198	+	9.87198i	1.26398	+	1.26398i	0.314829	+	0.949148i	$0.398053\pi$
$62$	3.55472	+	6.41539i	0.451450	+	0.814756i
$63$	−2.34266	+	3.08442i	−0.295147	+	0.388601i
$64$	7.95534	+	0.844133i	0.994418	+	0.105517i
$65$	3.98205	−	2.40887i	0.493913	−	0.298784i
$66$	−0.753050	+	3.50727i	−0.0926940	+	0.431715i
$67$			10.8038i			1.31990i	0.751310	+	0.659949i	$0.229422\pi$
$67$			10.8038i			1.31990i	−0.751310	+	0.659949i	$0.770578\pi$
$68$	−0.947466	−	4.11014i	−0.114897	−	0.498427i
$69$	−6.87857	+	7.88268i	−0.828083	+	0.948963i
$70$	3.94060	−	1.06780i	0.470992	−	0.127627i
$71$	−2.57569			−0.305678			−0.152839	−	0.988251i	$-0.548842\pi$
$71$	−2.57569			−0.305678			−0.152839	+	0.988251i	$0.548842\pi$
$72$	8.45608	−	0.703301i	0.996559	−	0.0828848i
$73$	−7.40366	−	7.40366i	−0.866533	−	0.866533i	0.125554	−	0.992087i	$-0.459929\pi$
$73$	−7.40366	−	7.40366i	−0.866533	−	0.866533i	−0.992087	+	0.125554i	$0.959929\pi$
$74$	7.46794	+	13.4778i	0.868130	+	1.56676i
$75$	3.49015	−	7.92584i	0.403008	−	0.915197i
$76$	1.49356	+	6.47909i	0.171323	+	0.743203i
$77$	1.89073			0.215469
$78$	−2.76785	−	4.28139i	−0.313397	−	0.484773i
$79$		−	8.54920i		−	0.961861i	−0.876759	−	0.480930i	$-0.840299\pi$
$79$		−	8.54920i		−	0.961861i	0.876759	−	0.480930i	$-0.159701\pi$
$80$	−7.51260	−	4.85395i	−0.839934	−	0.542688i
$81$	8.66991	−	2.41509i	0.963323	−	0.268344i
$82$	−6.73632	−	12.1574i	−0.743902	−	1.34256i
$83$			11.5636i			1.26927i	0.772812	+	0.634635i	$0.218849\pi$
$83$			11.5636i			1.26927i	−0.772812	+	0.634635i	$0.781151\pi$
$84$	−1.29808	−	4.27987i	−0.141632	−	0.466972i
$85$	−1.12718	+	4.57909i	−0.122260	+	0.496672i
$86$	−1.00815	+	0.558608i	−0.108712	+	0.0602363i
$87$	−4.76629	−	4.15916i	−0.511000	−	0.445908i
$88$	−2.77011	−	3.07959i	−0.295295	−	0.328286i
$89$		−	9.67152i		−	1.02518i	−0.858634	−	0.512590i	$-0.828686\pi$
$89$		−	9.67152i		−	1.02518i	0.858634	−	0.512590i	$-0.171314\pi$
$90$	−8.79259	−	3.56235i	−0.926821	−	0.375505i
$91$	−1.90008	+	1.90008i	−0.199183	+	0.199183i
$92$	−2.71359	−	11.7716i	−0.282911	−	1.22728i
$93$	−8.96205	+	0.609625i	−0.929321	+	0.0632152i
$94$	12.7521	+	3.65889i	1.31528	+	0.377386i
$95$	1.77685	−	7.21834i	0.182301	−	0.740586i
$96$	−5.06917	+	8.38472i	−0.517370	+	0.855762i
$97$	−6.58488	−	6.58488i	−0.668593	−	0.668593i	0.288797	−	0.957390i	$-0.406745\pi$
$97$	−6.58488	−	6.58488i	−0.668593	−	0.668593i	−0.957390	+	0.288797i	$0.906745\pi$
$98$	6.59717	−	3.65544i	0.666414	−	0.369255i
$99$	−3.49869	−	2.65730i	−0.351632	−	0.267069i
$100$	5.04878	+	8.63191i	0.504878	+	0.863191i
$101$	−4.86989	−	4.86989i	−0.484572	−	0.484572i	0.422016	−	0.906588i	$-0.361322\pi$
$101$	−4.86989	−	4.86989i	−0.484572	−	0.484572i	−0.906588	+	0.422016i	$0.861322\pi$
$102$	5.05077	+	1.08446i	0.500101	+	0.107377i
$103$	−4.41364	−	4.41364i	−0.434888	−	0.434888i	0.455399	−	0.890287i	$-0.349497\pi$
$103$	−4.41364	−	4.41364i	−0.434888	−	0.434888i	−0.890287	+	0.455399i	$0.849497\pi$
$104$	5.87864	+	0.311015i	0.576448	+	0.0304975i
$105$	−0.862914	+	4.92526i	−0.0842118	+	0.480657i
$106$	−4.97632	−	8.98103i	−0.483343	−	0.872314i
$107$		−	8.76918i		−	0.847748i	−0.905721	−	0.423874i	$-0.860670\pi$
$107$		−	8.76918i		−	0.847748i	0.905721	−	0.423874i	$-0.139330\pi$
$108$	−3.61306	+	9.74401i	−0.347667	+	0.937618i
$109$	−5.82689	+	5.82689i	−0.558115	+	0.558115i	−0.928770	−	0.370656i	$-0.879133\pi$
$109$	−5.82689	+	5.82689i	−0.558115	+	0.558115i	0.370656	+	0.928770i	$0.379133\pi$
$110$	1.21122	+	4.46986i	0.115485	+	0.426185i
$111$	−18.8279	+	1.28073i	−1.78707	+	0.121562i
$112$	4.88180	+	1.68456i	0.461287	+	0.159176i
$113$	6.67807	+	6.67807i	0.628220	+	0.628220i	0.947620	−	0.319400i	$-0.103481\pi$
$113$	6.67807	+	6.67807i	0.628220	+	0.628220i	−0.319400	+	0.947620i	$0.603481\pi$
$114$	−7.96189	−	1.70950i	−0.745699	−	0.160110i
$115$	−3.22831	+	13.1148i	−0.301041	+	1.22296i
$116$	7.11777	−	1.64078i	0.660868	−	0.152343i
$117$	6.18644	−	0.845552i	0.571936	−	0.0781713i
$118$	11.7237	+	3.36381i	1.07925	+	0.309664i
$119$		−	2.72281i		−	0.249600i
$120$	9.28645	−	5.81050i	0.847733	−	0.530424i
$121$		−	8.85533i		−	0.805030i
$122$	5.44532	−	18.9782i	0.492996	−	1.71821i
$123$	16.9834	−	1.15526i	1.53134	−	0.104166i
$124$	5.49945	−	8.79447i	0.493865	−	0.789767i
$125$	−0.685142	−	11.1593i	−0.0612810	−	0.998121i
$126$	5.42117	+	0.783774i	0.482956	+	0.0698241i
$127$	−4.03563	−	4.03563i	−0.358105	−	0.358105i	0.505009	−	0.863114i	$-0.331489\pi$
$127$	−4.03563	−	4.03563i	−0.358105	−	0.358105i	−0.863114	+	0.505009i	$0.831489\pi$
$128$	−4.40854	−	10.4194i	−0.389664	−	0.920957i
$129$	−0.0957999	−	1.40835i	−0.00843471	−	0.123998i
$130$	−5.70918	−	3.27476i	−0.500729	−	0.287216i
$131$	12.4730	−	12.4730i	1.08977	−	1.08977i	0.0942236	−	0.995551i	$-0.469963\pi$
$131$	12.4730	−	12.4730i	1.08977	−	1.08977i	0.995551	−	0.0942236i	$-0.0300369\pi$
$132$	4.85470	−	1.47242i	0.422547	−	0.128158i
$133$			4.29216i			0.372178i
$134$	13.3645	−	7.40516i	1.15452	−	0.639708i
$135$	8.51891	−	7.90115i	0.733191	−	0.680023i
$136$	−4.43488	+	3.98919i	−0.380288	+	0.342071i
$137$	−2.68828	−	2.68828i	−0.229675	−	0.229675i	0.582882	−	0.812557i	$-0.301925\pi$
$137$	−2.68828	−	2.68828i	−0.229675	−	0.229675i	−0.812557	+	0.582882i	$0.801925\pi$
$138$	14.4657	+	3.10594i	1.23140	+	0.264395i
$139$	4.14179	+	4.14179i	0.351302	+	0.351302i	0.860594	−	0.509292i	$-0.170093\pi$
$139$	4.14179	+	4.14179i	0.351302	+	0.351302i	−0.509292	+	0.860594i	$0.670093\pi$
$140$	−4.02185	−	4.14268i	−0.339909	−	0.350121i
$141$	−10.6830	+	12.2425i	−0.899672	+	1.03100i
$142$	1.76543	+	3.18616i	0.148151	+	0.267377i
$143$	−2.15528	−	2.15528i	−0.180234	−	0.180234i
$144$	−6.66596	−	9.97823i	−0.555496	−	0.831519i
$145$	−7.92989	−	1.95201i	−0.658542	−	0.162105i
$146$	−4.08381	+	14.2330i	−0.337978	+	1.17793i
$147$	0.626898	+	9.21598i	0.0517057	+	0.760121i
$148$	11.5535	−	18.4759i	0.949693	−	1.51871i
$149$	3.27529	−	3.27529i	0.268322	−	0.268322i	−0.560102	−	0.828424i	$-0.689238\pi$
$149$	3.27529	−	3.27529i	0.268322	−	0.268322i	0.828424	+	0.560102i	$0.189238\pi$
$150$	−12.1966	+	1.11516i	−0.995846	+	0.0910528i
$151$		−	11.4102i		−	0.928548i	−0.885692	−	0.464274i	$-0.846315\pi$
$151$		−	11.4102i		−	0.928548i	0.885692	−	0.464274i	$-0.153685\pi$
$152$	6.99101	−	6.28845i	0.567046	−	0.510060i
$153$	−3.82674	+	5.03841i	−0.309373	+	0.407332i
$154$	−1.29594	−	2.33886i	−0.104430	−	0.188471i
$155$	−9.92242	+	6.00240i	−0.796988	+	0.482124i
$156$	−3.39900	+	6.35841i	−0.272138	+	0.509080i
$157$			3.40961i			0.272116i	0.990701	+	0.136058i	$0.0434434\pi$
$157$			3.40961i			0.272116i	−0.990701	+	0.136058i	$0.956557\pi$
$158$	−10.5755	+	5.85979i	−0.841339	+	0.466180i
$159$	12.5461	−	0.853426i	0.994973	−	0.0676811i
$160$	−0.855119	+	12.6202i	−0.0676031	+	0.997712i
$161$		−	7.79828i		−	0.614591i
$162$	−8.93003	−	9.06943i	−0.701609	−	0.712562i
$163$	4.71686			0.369453			0.184727	−	0.982790i	$-0.440860\pi$
$163$	4.71686			0.369453			0.184727	+	0.982790i	$0.440860\pi$
$164$	−10.4216	+	16.6658i	−0.813793	+	1.30138i
$165$	−5.58677	−	0.978811i	−0.434930	−	0.0762004i
$166$	14.3043	−	7.92591i	1.11023	−	0.615170i
$167$	14.7875	+	14.7875i	1.14429	+	1.14429i	0.987657	+	0.156635i	$0.0500647\pi$
$167$	14.7875	+	14.7875i	1.14429	+	1.14429i	0.156635	+	0.987657i	$0.449935\pi$
$168$	−4.40452	+	4.53924i	−0.339816	+	0.350210i
$169$	−8.66811			−0.666778
$170$	6.43699	−	1.74426i	0.493694	−	0.133779i
$171$	6.03236	−	7.94240i	0.461306	−	0.607371i
$172$	1.38201	+	0.864213i	0.105377	+	0.0658956i
$173$			20.6855i			1.57269i	0.617790	+	0.786343i	$0.288028\pi$
$173$			20.6855i			1.57269i	−0.617790	+	0.786343i	$0.711972\pi$
$174$	−1.87802	+	8.74673i	−0.142372	+	0.663088i
$175$	1.92420	+	6.16189i	0.145456	+	0.465795i
$176$	−1.91081	+	5.53747i	−0.144033	+	0.417403i
$177$	−9.82146	+	11.2552i	−0.738226	+	0.845989i
$178$	−11.9638	+	6.62905i	−0.896724	+	0.496868i
$179$	−15.0062	−	15.0062i	−1.12162	−	1.12162i	−0.991499	−	0.130118i	$-0.958464\pi$
$179$	−15.0062	−	15.0062i	−1.12162	−	1.12162i	−0.130118	−	0.991499i	$-0.541536\pi$
$180$	1.61994	+	13.3183i	0.120743	+	0.992684i
$181$	2.48233	−	2.48233i	0.184510	−	0.184510i	−0.608808	−	0.793318i	$-0.708352\pi$
$181$	2.48233	−	2.48233i	0.184510	−	0.184510i	0.793318	+	0.608808i	$0.208352\pi$
$182$	3.65278	+	1.04807i	0.270762	+	0.0776883i
$183$	18.2198	+	15.8989i	1.34684	+	1.17528i
$184$	−12.7017	+	11.4253i	−0.936383	+	0.842281i
$185$	−20.8455	+	12.6101i	−1.53259	+	0.927116i
$186$	6.89688	+	10.6683i	0.505703	+	0.782239i
$187$	3.08851			0.225855
$188$	−4.21444	−	18.2824i	−0.307370	−	1.33338i
$189$	−3.68568	+	5.60543i	−0.268094	+	0.407735i
$190$	−10.1471	+	2.74960i	−0.736146	+	0.199477i
$191$		−	14.6164i		−	1.05761i	−0.848744	−	0.528804i	$-0.822641\pi$
$191$		−	14.6164i		−	1.05761i	0.848744	−	0.528804i	$-0.177359\pi$
$192$	13.8465	+	0.523579i	0.999286	+	0.0377860i
$193$	−5.06820	+	5.06820i	−0.364817	+	0.364817i	−0.865583	−	0.500766i	$-0.833052\pi$
$193$	−5.06820	+	5.06820i	−0.364817	+	0.364817i	0.500766	+	0.865583i	$0.333052\pi$
$194$	−3.63217	+	12.6590i	−0.260775	+	0.908862i
$195$	6.59806	−	4.63075i	0.472497	−	0.331615i
$196$	−9.04365	−	5.65527i	−0.645975	−	0.403948i
$197$		−	4.73103i		−	0.337072i	−0.985696	−	0.168536i	$-0.946096\pi$
$197$		−	4.73103i		−	0.337072i	0.985696	−	0.168536i	$-0.0539039\pi$
$198$	−0.889042	+	6.14929i	−0.0631815	+	0.437011i
$199$	7.61133			0.539553			0.269776	−	0.962923i	$-0.413050\pi$
$199$	7.61133			0.539553			0.269776	+	0.962923i	$0.413050\pi$
$200$	7.21725	−	12.1619i	0.510336	−	0.859975i
$201$	1.26997	+	18.6696i	0.0895764	+	1.31686i
$202$	−2.68620	+	9.36202i	−0.189000	+	0.658710i
$203$	4.71526			0.330946
$204$	−2.12041	−	6.99118i	−0.148459	−	0.489480i
$205$	18.8033	−	11.3747i	1.31328	−	0.794447i
$206$	−2.43453	+	8.48492i	−0.169622	+	0.591172i
$207$	−10.9600	+	14.4303i	−0.761771	+	1.00297i
$208$	−3.64460	−	7.48512i	−0.252708	−	0.519000i
$209$	−4.86864			−0.336771
$210$	6.68407	−	2.30844i	0.461245	−	0.159297i
$211$	−7.48648	−	7.48648i	−0.515391	−	0.515391i	0.400783	−	0.916173i	$-0.368738\pi$
$211$	−7.48648	−	7.48648i	−0.515391	−	0.515391i	−0.916173	+	0.400783i	$0.868738\pi$
$212$	−7.69878	+	12.3115i	−0.528754	+	0.845560i
$213$	−4.45094	+	0.302766i	−0.304973	+	0.0207452i
$214$	−10.8476	+	6.01056i	−0.741525	+	0.410874i
$215$	−0.943250	−	1.55926i	−0.0643291	−	0.106341i
$216$	14.5299	−	2.20934i	0.988636	−	0.150326i
$217$	4.73460	−	4.73460i	0.321405	−	0.321405i
$218$	11.2018	+	3.21407i	0.758681	+	0.217684i
$219$	−13.6642	−	11.9237i	−0.923343	−	0.805727i
$220$	4.69908	−	4.56203i	0.316812	−	0.307572i
$221$	−3.10379	+	3.10379i	−0.208784	+	0.208784i
$222$	14.4893	+	22.4125i	0.972459	+	1.50423i
$223$	14.9484	−	14.9484i	1.00102	−	1.00102i	0.00101699	−	0.999999i	$-0.499676\pi$
$223$	14.9484	−	14.9484i	1.00102	−	1.00102i	0.999999	−	0.00101699i	$-0.000323717\pi$
$224$	−1.26226	−	7.19348i	−0.0843385	−	0.480634i
$225$	5.09951	−	14.1066i	0.339968	−	0.940437i
$226$	3.68358	−	12.8381i	0.245028	−	0.853980i
$227$	5.12514			0.340167			0.170084	−	0.985430i	$-0.445596\pi$
$227$	5.12514			0.340167			0.170084	+	0.985430i	$0.445596\pi$
$228$	3.34255	+	11.0207i	0.221366	+	0.729862i
$229$	1.86356	+	1.86356i	0.123148	+	0.123148i	0.765995	−	0.642847i	$-0.222247\pi$
$229$	1.86356	+	1.86356i	0.123148	+	0.123148i	−0.642847	+	0.765995i	$0.722247\pi$
$230$	18.4359	−	4.99566i	1.21563	−	0.329404i
$231$	3.26729	−	0.222251i	0.214972	−	0.0146230i
$232$	−6.90833	−	7.68014i	−0.453554	−	0.504226i
$233$	5.48648	−	5.48648i	0.359431	−	0.359431i	−0.504172	−	0.863603i	$-0.668202\pi$
$233$	5.48648	−	5.48648i	0.359431	−	0.359431i	0.863603	+	0.504172i	$0.168202\pi$
$234$	−5.28626	−	7.07314i	−0.345574	−	0.462386i
$235$	−5.01384	+	20.3684i	−0.327067	+	1.32868i
$236$	−3.87456	−	16.8079i	−0.252212	−	1.09410i
$237$	−1.00494	−	14.7735i	−0.0652778	−	0.959643i
$238$	−3.36816	+	1.86627i	−0.218325	+	0.120972i
$239$	9.45252			0.611433			0.305716	−	0.952123i	$-0.401104\pi$
$239$	9.45252			0.611433			0.305716	+	0.952123i	$0.401104\pi$
$240$	−13.5528	−	7.50482i	−0.874828	−	0.484434i
$241$	10.3530			0.666894			0.333447	−	0.942769i	$-0.391788\pi$
$241$	10.3530			0.666894			0.333447	+	0.942769i	$0.391788\pi$
$242$	−10.9541	+	6.06961i	−0.704159	+	0.390170i
$243$	14.6982	−	5.19255i	0.942891	−	0.333102i
$244$	−27.2086	+	6.27211i	−1.74185	+	0.401531i
$245$	6.17247	+	10.2036i	0.394345	+	0.651882i
$246$	−13.0698	−	20.2168i	−0.833301	−	1.28898i
$247$	4.89272	−	4.89272i	0.311316	−	0.311316i
$248$	−14.6483	−	0.774982i	−0.930168	−	0.0492114i
$249$	1.35927	+	19.9826i	0.0861404	+	1.26634i
$250$	−13.3346	+	8.49635i	−0.843355	+	0.537356i
$251$	18.5502	+	18.5502i	1.17088	+	1.17088i	0.982001	+	0.188874i	$0.0604838\pi$
$251$	18.5502	+	18.5502i	1.17088	+	1.17088i	0.188874	+	0.982001i	$0.439516\pi$
$252$	−2.74624	−	7.24327i	−0.172997	−	0.456283i
$253$	8.84567			0.556122
$254$	−2.22603	+	7.75823i	−0.139673	+	0.486795i
$255$	−1.40957	+	8.04543i	−0.0882708	+	0.503825i
$256$	−9.86728	+	12.5951i	−0.616705	+	0.787194i
$257$	−5.32881	+	5.32881i	−0.332402	+	0.332402i	−0.853498	−	0.521096i	$-0.825523\pi$
$257$	−5.32881	+	5.32881i	−0.332402	+	0.332402i	0.521096	+	0.853498i	$0.325523\pi$
$258$	−1.67648	+	1.08381i	−0.104373	+	0.0674753i
$259$	9.94669	−	9.94669i	0.618057	−	0.618057i
$260$	−0.137734	+	9.30692i	−0.00854189	+	0.577191i
$261$	−8.72532	−	6.62699i	−0.540084	−	0.410201i
$262$	−23.9786	−	6.88004i	−1.48140	−	0.425051i
$263$	6.84521	−	6.84521i	0.422094	−	0.422094i	−0.463830	−	0.885924i	$-0.653525\pi$
$263$	6.84521	−	6.84521i	0.422094	−	0.422094i	0.885924	+	0.463830i	$0.153525\pi$
$264$	−5.14891	−	4.99609i	−0.316893	−	0.307488i
$265$	13.8906	−	8.40287i	0.853292	−	0.516184i
$266$	5.30946	−	2.94193i	0.325544	−	0.180381i
$267$	−1.13686	−	16.7129i	−0.0695750	−	1.02282i
$268$	−18.3205	−	11.4564i	−1.11911	−	0.699810i
$269$	0.0586414	+	0.0586414i	0.00357543	+	0.00357543i	0.708892	−	0.705317i	$-0.249195\pi$
$269$	0.0586414	+	0.0586414i	0.00357543	+	0.00357543i	−0.705317	+	0.708892i	$0.749195\pi$
$270$	−15.6128	−	5.12240i	−0.950168	−	0.311739i
$271$	14.7531			0.896185			0.448093	−	0.893987i	$-0.352103\pi$
$271$	14.7531			0.896185			0.448093	+	0.893987i	$0.352103\pi$
$272$	7.97443	+	2.75173i	0.483521	+	0.166848i
$273$	−3.06010	+	3.50680i	−0.185206	+	0.212241i
$274$	−1.48284	+	5.16804i	−0.0895815	+	0.312213i
$275$	−6.98949	+	2.18264i	−0.421482	+	0.131618i
$276$	−6.07297	−	20.0231i	−0.365550	−	1.20525i
$277$	12.2040			0.733266			0.366633	−	0.930366i	$-0.380510\pi$
$277$	12.2040			0.733266			0.366633	+	0.930366i	$0.380510\pi$
$278$	2.28458	−	7.96232i	0.137020	−	0.477548i
$279$	−15.4153	+	2.10693i	−0.922888	+	0.126139i
$280$	−2.36789	+	7.81456i	−0.141509	+	0.467009i
$281$	2.18598			0.130404			0.0652022	−	0.997872i	$-0.479231\pi$
$281$	2.18598			0.130404			0.0652022	+	0.997872i	$0.479231\pi$
$282$	22.4664	+	4.82379i	1.33786	+	0.287253i
$283$			10.8232i			0.643373i	0.946846	+	0.321686i	$0.104250\pi$
$283$			10.8232i			0.643373i	−0.946846	+	0.321686i	$0.895750\pi$
$284$	2.73126	−	4.36771i	0.162071	−	0.259176i
$285$	2.22201	−	12.6826i	0.131620	−	0.751251i
$286$	−1.18884	+	4.14338i	−0.0702975	+	0.245003i
$287$	−8.97222	+	8.97222i	−0.529614	+	0.529614i
$288$	−7.77421	+	15.0851i	−0.458100	+	0.888901i
$289$			12.5523i			0.738369i
$290$	3.02064	+	11.1473i	0.177378	+	0.654593i
$291$	−12.1531	−	10.6050i	−0.712427	−	0.621677i
$292$	20.4056	−	4.70388i	1.19415	−	0.275274i
$293$	−13.0105			−0.760084			−0.380042	−	0.924969i	$-0.624090\pi$
$293$	−13.0105			−0.760084			−0.380042	+	0.924969i	$0.624090\pi$
$294$	10.9706	−	7.09229i	0.639818	−	0.413631i
$295$	−4.60948	+	18.7257i	−0.268375	+	1.09025i
$296$	−30.7739	−	1.62812i	−1.78870	−	0.0946327i
$297$	−6.35830	−	4.18070i	−0.368946	−	0.242589i
$298$	−6.29652	−	1.80663i	−0.364747	−	0.104655i
$299$	−8.88942	+	8.88942i	−0.514088	+	0.514088i
$300$	9.73924	+	14.3230i	0.562295	+	0.826936i
$301$	0.744021	+	0.744021i	0.0428846	+	0.0428846i
$302$	−14.1145	+	7.82077i	−0.812201	+	0.450035i
$303$	−8.98789	−	7.84300i	−0.516341	−	0.450568i
$304$	−12.5707	−	4.33774i	−0.720977	−	0.248787i
$305$	30.3131	+	7.46181i	1.73572	+	0.427262i
$306$	8.85550	+	1.28030i	0.506235	+	0.0731897i
$307$		−	34.3297i		−	1.95930i	−0.200718	−	0.979649i	$-0.564328\pi$
$307$		−	34.3297i		−	1.95930i	0.200718	−	0.979649i	$-0.435672\pi$
$308$	−2.00493	+	3.20620i	−0.114242	+	0.182690i
$309$	−8.14583	−	7.10820i	−0.463400	−	0.404372i
$310$	14.2261	+	8.16000i	0.807986	+	0.463457i
$311$	−19.7120			−1.11777			−0.558883	−	0.829247i	$-0.688770\pi$
$311$	−19.7120			−1.11777			−0.558883	+	0.829247i	$0.688770\pi$
$312$	10.1952	−	0.153568i	0.577188	−	0.00869407i
$313$	8.82647	+	8.82647i	0.498902	+	0.498902i	0.911096	−	0.412194i	$-0.135237\pi$
$313$	8.82647	+	8.82647i	0.498902	+	0.498902i	−0.412194	+	0.911096i	$0.635237\pi$
$314$	4.21773	−	2.33701i	0.238020	−	0.131885i
$315$	−0.912212	+	8.61257i	−0.0513973	+	0.485263i
$316$	14.4973	+	9.06558i	0.815535	+	0.509979i
$317$	27.9576			1.57026			0.785128	−	0.619334i	$-0.212597\pi$
$317$	27.9576			1.57026			0.785128	+	0.619334i	$0.212597\pi$
$318$	−9.65506	−	14.9348i	−0.541429	−	0.837501i
$319$			5.34857i			0.299462i
$320$	16.1974	−	7.59232i	0.905464	−	0.424424i
$321$	−1.03080	−	15.1536i	−0.0575334	−	0.845794i
$322$	−9.64657	+	5.34510i	−0.537583	+	0.297871i
$323$			7.01126i			0.390117i
$324$	−5.09819	+	17.2629i	−0.283233	+	0.959051i
$325$	4.83063	−	9.21749i	0.267955	−	0.511294i
$326$	−3.23303	−	5.83482i	−0.179061	−	0.323161i
$327$	−9.38426	+	10.7541i	−0.518951	+	0.594705i
$328$	27.7590	+	1.46862i	1.53274	+	0.0810909i
$329$		−	12.1114i		−	0.667723i
$330$	2.61848	+	7.58181i	0.144143	+	0.417365i
$331$	−11.7945	+	11.7945i	−0.648285	+	0.648285i	−0.952578	−	0.304293i	$-0.901580\pi$
$331$	−11.7945	+	11.7945i	−0.648285	+	0.648285i	0.304293	+	0.952578i	$0.401580\pi$
$332$	−19.6089	−	12.2620i	−1.07618	−	0.672967i
$333$	−32.3852	+	4.42636i	−1.77470	+	0.242563i
$334$	8.15669	−	28.4280i	0.446314	−	1.55551i
$335$	12.5041	+	20.6703i	0.683174	+	1.12934i
$336$	8.63405	+	2.33717i	0.471026	+	0.127503i
$337$	1.70964	+	1.70964i	0.0931298	+	0.0931298i	0.752137	−	0.659007i	$-0.229023\pi$
$337$	1.70964	+	1.70964i	0.0931298	+	0.0931298i	−0.659007	+	0.752137i	$0.729023\pi$
$338$	5.94129	+	10.7226i	0.323164	+	0.583231i
$339$	12.3251	+	10.7551i	0.669407	+	0.584137i
$340$	−6.56971	−	6.76708i	−0.356293	−	0.366997i
$341$	5.37050	+	5.37050i	0.290829	+	0.290829i
$342$	−13.9595	−	2.01822i	−0.754846	−	0.109133i
$343$	−11.2592	−	11.2592i	−0.607940	−	0.607940i
$344$	0.121785	−	2.30191i	0.00656621	−	0.124111i
$345$	−4.03709	+	23.0425i	−0.217350	+	1.24057i
$346$	25.5882	−	14.1782i	1.37563	−	0.762226i
$347$		−	19.6676i		−	1.05581i	−0.849304	−	0.527905i	$-0.822978\pi$
$347$		−	19.6676i		−	1.05581i	0.849304	−	0.527905i	$-0.177022\pi$
$348$	12.1070	−	3.67204i	0.649006	−	0.196842i
$349$	5.38375	−	5.38375i	0.288186	−	0.288186i	−0.548177	−	0.836362i	$-0.684678\pi$
$349$	5.38375	−	5.38375i	0.288186	−	0.288186i	0.836362	+	0.548177i	$0.184678\pi$
$350$	6.30345	−	6.60373i	0.336934	−	0.352984i
$351$	10.5911	−	2.18836i	0.565313	−	0.116806i
$352$	8.15963	−	1.43180i	0.434910	−	0.0763150i
$353$	−25.3482	−	25.3482i	−1.34915	−	1.34915i	−0.886590	−	0.462556i	$-0.846933\pi$
$353$	−25.3482	−	25.3482i	−1.34915	−	1.34915i	−0.462556	−	0.886590i	$-0.653067\pi$
$354$	20.6546	+	4.43477i	1.09778	+	0.235705i
$355$	−4.92790	+	2.98105i	−0.261546	+	0.158218i
$356$	16.4004	+	10.2557i	0.869222	+	0.543550i
$357$	−0.320060	−	4.70518i	−0.0169394	−	0.249025i
$358$	−8.27732	+	28.8484i	−0.437470	+	1.52469i
$359$		−	22.5488i		−	1.19008i	−0.803696	−	0.595040i	$-0.797136\pi$
$359$		−	22.5488i		−	1.19008i	0.803696	−	0.595040i	$-0.202864\pi$
$360$	15.3645	−	11.1325i	0.809780	−	0.586733i
$361$			7.94766i			0.418298i
$362$	−4.77211	−	1.36923i	−0.250816	−	0.0719654i
$363$	−1.04092	−	15.3025i	−0.0546343	−	0.803174i
$364$	−1.20721	−	5.23690i	−0.0632749	−	0.274488i
$365$	−22.7338	−	5.59611i	−1.18994	−	0.292914i
$366$	7.17898	−	33.4355i	0.375251	−	1.74770i
$367$	16.5406	+	16.5406i	0.863411	+	0.863411i	0.991733	−	0.128322i	$-0.0409591\pi$
$367$	16.5406	+	16.5406i	0.863411	+	0.863411i	−0.128322	+	0.991733i	$0.540959\pi$
$368$	22.8392	+	7.88109i	1.19058	+	0.410830i
$369$	29.2125	−	3.99271i	1.52074	−	0.207852i
$370$	29.8868	+	17.1429i	1.55374	+	0.891219i
$371$	−6.62805	+	6.62805i	−0.344111	+	0.344111i
$372$	8.46959	−	15.8438i	0.439128	−	0.821462i
$373$			7.24873i			0.375325i	0.982234	+	0.187663i	$0.0600911\pi$
$373$			7.24873i			0.375325i	−0.982234	+	0.187663i	$0.939909\pi$
$374$	−2.11693	−	3.82053i	−0.109464	−	0.197555i
$375$	−2.49572	−	19.2034i	−0.128878	−	0.991660i
$376$	−19.7269	+	17.7444i	−1.01734	+	0.915098i
$377$	−5.37502	−	5.37502i	−0.276828	−	0.276828i
$378$	9.46023	+	0.717160i	0.486582	+	0.0368867i
$379$	6.48173	+	6.48173i	0.332944	+	0.332944i	0.853703	−	0.520759i	$-0.174351\pi$
$379$	6.48173	+	6.48173i	0.332944	+	0.332944i	−0.520759	+	0.853703i	$0.674351\pi$
$380$	10.3563	+	10.6674i	0.531267	+	0.547227i
$381$	−7.44819	−	6.49943i	−0.381582	−	0.332976i
$382$	−18.0807	+	10.0184i	−0.925089	+	0.512585i
$383$	−13.1911	−	13.1911i	−0.674035	−	0.674035i	0.284609	−	0.958644i	$-0.408136\pi$
$383$	−13.1911	−	13.1911i	−0.674035	−	0.674035i	−0.958644	+	0.284609i	$0.908136\pi$
$384$	−8.84299	−	17.4872i	−0.451267	−	0.892389i
$385$	3.61741	−	2.18829i	0.184361	−	0.111526i
$386$	9.74326	+	2.79558i	0.495919	+	0.142291i
$387$	−0.331095	−	2.42244i	−0.0168305	−	0.123140i
$388$	18.1489	−	4.18367i	0.921370	−	0.212394i
$389$	1.04217	−	1.04217i	0.0528401	−	0.0528401i	−0.680193	−	0.733033i	$-0.738104\pi$
$389$	1.04217	−	1.04217i	0.0528401	−	0.0528401i	0.733033	+	0.680193i	$0.238104\pi$
$390$	−10.2507	−	4.98787i	−0.519066	−	0.252571i
$391$		−	12.7385i		−	0.644215i
$392$	−0.796941	+	15.0633i	−0.0402516	+	0.760814i
$393$	20.0880	−	23.0203i	1.01330	−	1.16122i
$394$	−5.85234	+	3.24274i	−0.294837	+	0.163367i
$395$	−9.89467	−	16.3566i	−0.497855	−	0.822992i
$396$	8.21611	−	3.11509i	0.412875	−	0.156539i
$397$			0.837780i			0.0420470i	0.999779	+	0.0210235i	$0.00669248\pi$
$397$			0.837780i			0.0420470i	−0.999779	+	0.0210235i	$0.993308\pi$
$398$	−5.21695	−	9.41531i	−0.261502	−	0.471947i
$399$	0.504534	+	7.41710i	0.0252583	+	0.371320i
$400$	−19.9912	−	0.591834i	−0.999562	−	0.0295917i
$401$			23.6742i			1.18223i	0.806587	+	0.591116i	$0.201312\pi$
$401$			23.6742i			1.18223i	−0.806587	+	0.591116i	$0.798688\pi$
$402$	22.2241	−	14.3675i	1.10844	−	0.716586i
$403$	−10.7941			−0.537694
$404$	13.4221	−	3.09406i	0.667775	−	0.153935i
$405$	13.7924	−	14.6550i	0.685350	−	0.728214i
$406$	−3.23193	−	5.83284i	−0.160398	−	0.289479i
$407$	11.2826	+	11.2826i	0.559259	+	0.559259i
$408$	−7.19480	+	7.41487i	−0.356196	+	0.367091i
$409$	−25.7330			−1.27242			−0.636208	−	0.771517i	$-0.719498\pi$
$409$	−25.7330			−1.27242			−0.636208	+	0.771517i	$0.719498\pi$
$410$	−26.9589	−	15.4635i	−1.33140	−	0.763687i
$411$	−4.96151	−	4.32950i	−0.244733	−	0.213559i
$412$	12.1646	−	2.80418i	0.599308	−	0.138152i
$413$		−	11.1347i		−	0.547900i
$414$	25.3626	+	3.66684i	1.24650	+	0.180215i
$415$	13.3835	+	22.1239i	0.656968	+	1.08602i
$416$	−6.76111	+	9.63887i	−0.331491	+	0.472584i
$417$	7.64411	+	6.67040i	0.374334	+	0.326651i
$418$	3.33706	+	6.02257i	0.163221	+	0.294574i
$419$	13.8036	+	13.8036i	0.674351	+	0.674351i	0.958716	−	0.284365i	$-0.0917829\pi$
$419$	13.8036	+	13.8036i	0.674351	+	0.674351i	−0.284365	+	0.958716i	$0.591783\pi$
$420$	−7.43696	−	6.68603i	−0.362886	−	0.326245i
$421$	13.7845	−	13.7845i	0.671817	−	0.671817i	−0.286318	−	0.958135i	$-0.592431\pi$
$421$	13.7845	−	13.7845i	0.671817	−	0.671817i	0.958135	+	0.286318i	$0.0924314\pi$
$422$	−4.12949	+	14.3923i	−0.201021	+	0.700604i
$423$	−17.0218	+	22.4115i	−0.827628	+	1.08968i
$424$	20.5064	+	1.08491i	0.995880	+	0.0526880i
$425$	3.14318	+	10.0655i	0.152467	+	0.488247i
$426$	3.42528	+	5.29834i	0.165956	+	0.256706i
$427$	−18.0247			−0.872277
$428$	14.8703	+	9.29884i	0.718782	+	0.449476i
$429$	−3.97780	−	3.47110i	−0.192050	−	0.167586i
$430$	−1.28231	+	2.23556i	−0.0618384	+	0.107808i
$431$			2.16037i			0.104061i	0.998645	+	0.0520307i	$0.0165694\pi$
$431$			2.16037i			0.104061i	−0.998645	+	0.0520307i	$0.983431\pi$
$432$	−12.6921	−	16.4594i	−0.610648	−	0.791902i
$433$	−17.6860	+	17.6860i	−0.849935	+	0.849935i	−0.990125	−	0.140189i	$-0.955229\pi$
$433$	−17.6860	+	17.6860i	−0.849935	+	0.849935i	0.140189	+	0.990125i	$0.455229\pi$
$434$	−9.10194	−	2.61157i	−0.436907	−	0.125359i
$435$	−13.9328	−	2.44104i	−0.668025	−	0.117039i
$436$	−3.70208	−	16.0598i	−0.177298	−	0.769123i
$437$			20.0806i			0.960586i
$438$	−5.38399	+	25.0755i	−0.257257	+	1.19816i
$439$	11.2105			0.535049			0.267525	−	0.963551i	$-0.413794\pi$
$439$	11.2105			0.535049			0.267525	+	0.963551i	$0.413794\pi$
$440$	−8.86413	−	2.68592i	−0.422581	−	0.128046i
$441$	2.16663	+	15.8521i	0.103173	+	0.754860i
$442$	5.96683	+	1.71203i	0.283813	+	0.0814329i
$443$	−5.63824			−0.267881			−0.133940	−	0.990989i	$-0.542763\pi$
$443$	−5.63824			−0.267881			−0.133940	+	0.990989i	$0.542763\pi$
$444$	17.7933	−	33.2855i	0.844435	−	1.57966i
$445$	−11.1936	−	18.5039i	−0.530629	−	0.877170i
$446$	−28.7372	−	8.24541i	−1.36075	−	0.390432i
$447$	5.27488	−	6.04489i	0.249493	−	0.285913i
$448$	−8.03324	+	6.49198i	−0.379535	+	0.306717i
$449$	−9.38457			−0.442885			−0.221443	−	0.975173i	$-0.571077\pi$
$449$	−9.38457			−0.442885			−0.221443	+	0.975173i	$0.571077\pi$
$450$	−20.9453	+	3.36075i	−0.987371	+	0.158427i
$451$	−10.1773	−	10.1773i	−0.479229	−	0.479229i
$452$	−18.4057	+	4.24288i	−0.865733	+	0.199568i
$453$	−1.34124	−	19.7175i	−0.0630170	−	0.926407i
$454$	−3.51287	−	6.33986i	−0.164867	−	0.297544i
$455$	−1.43619	+	5.83442i	−0.0673297	+	0.273522i
$456$	11.3417	−	11.6886i	0.531122	−	0.547367i
$457$	−16.2317	+	16.2317i	−0.759289	+	0.759289i	−0.976193	−	0.216904i	$-0.930404\pi$
$457$	−16.2317	+	16.2317i	−0.759289	+	0.759289i	0.216904	+	0.976193i	$0.430404\pi$
$458$	1.02793	−	3.58258i	0.0480320	−	0.167403i
$459$	−6.02057	+	9.15649i	−0.281016	+	0.427388i
$460$	−18.8160	−	19.3813i	−0.877300	−	0.903657i
$461$	−7.62591	+	7.62591i	−0.355174	+	0.355174i	−0.862030	−	0.506857i	$-0.830807\pi$
$461$	−7.62591	+	7.62591i	−0.355174	+	0.355174i	0.506857	+	0.862030i	$0.330807\pi$
$462$	−2.51439	−	3.88935i	−0.116980	−	0.180949i
$463$	10.9986	−	10.9986i	0.511149	−	0.511149i	−0.403730	−	0.914878i	$-0.632286\pi$
$463$	10.9986	−	10.9986i	0.511149	−	0.511149i	0.914878	+	0.403730i	$0.132286\pi$
$464$	−4.76533	+	13.8098i	−0.221225	+	0.641104i
$465$	−16.4409	+	11.5388i	−0.762431	+	0.535101i
$466$	−10.5474	−	3.02630i	−0.488598	−	0.140191i
$467$	9.64270			0.446211			0.223105	−	0.974794i	$-0.428381\pi$
$467$	9.64270			0.446211			0.223105	+	0.974794i	$0.428381\pi$
$468$	−5.12626	+	11.3872i	−0.236961	+	0.526376i
$469$	−9.86307	−	9.86307i	−0.455434	−	0.455434i
$470$	28.6325	−	7.75869i	1.32072	−	0.357881i
$471$	0.400791	+	5.89200i	0.0184675	+	0.271489i
$472$	−18.1359	+	16.3134i	−0.834775	+	0.750884i
$473$	−0.843950	+	0.843950i	−0.0388049	+	0.0388049i
$474$	−17.5862	+	11.3692i	−0.807762	+	0.522204i
$475$	−4.95482	−	15.8669i	−0.227343	−	0.728023i
$476$	4.61720	+	2.88727i	0.211629	+	0.132338i
$477$	21.5801	−	2.94954i	0.988086	−	0.135050i
$478$	−6.47894	−	11.6929i	−0.296340	−	0.534820i
$479$	−0.350518			−0.0160156			−0.00800779	−	0.999968i	$-0.502549\pi$
$479$	−0.350518			−0.0160156			−0.00800779	+	0.999968i	$0.502549\pi$
$480$	0.00577642	+	21.9089i	0.000263656	+	1.00000i
$481$	−22.6769			−1.03398
$482$	−7.09613	−	12.8068i	−0.323220	−	0.583332i
$483$	−0.916670	−	13.4759i	−0.0417099	−	0.613174i
$484$	15.0164	+	9.39019i	0.682563	+	0.426827i
$485$	−20.2196	−	4.97723i	−0.918126	−	0.226004i
$486$	−16.4977	−	14.6228i	−0.748350	−	0.663304i
$487$	−3.32822	+	3.32822i	−0.150816	+	0.150816i	−0.778482	−	0.627666i	$-0.784010\pi$
$487$	−3.32822	+	3.32822i	−0.150816	+	0.150816i	0.627666	+	0.778482i	$0.284010\pi$
$488$	26.4080	+	29.3584i	1.19543	+	1.32899i
$489$	8.15101	−	0.554456i	0.368601	−	0.0250734i
$490$	8.39121	−	14.6291i	0.379076	−	0.660877i
$491$	20.7903	+	20.7903i	0.938255	+	0.938255i	0.998202	−	0.0599467i	$-0.0190931\pi$
$491$	20.7903	+	20.7903i	0.938255	+	0.938255i	−0.0599467	+	0.998202i	$0.519093\pi$
$492$	−16.0502	+	30.0245i	−0.723597	+	1.35361i
$493$	7.70239			0.346898
$494$	−9.40593	−	2.69879i	−0.423193	−	0.121424i
$495$	−9.76932	−	1.03473i	−0.439098	−	0.0465077i
$496$	9.08156	+	18.6513i	0.407774	+	0.837469i
$497$	2.35140	−	2.35140i	0.105475	−	0.105475i
$498$	23.7870	−	15.3779i	1.06592	−	0.689099i
$499$	−2.98889	+	2.98889i	−0.133801	+	0.133801i	−0.770835	−	0.637034i	$-0.780161\pi$
$499$	−2.98889	+	2.98889i	−0.133801	+	0.133801i	0.637034	+	0.770835i	$0.280161\pi$
$500$	19.6499	+	10.6715i	0.878770	+	0.477245i
$501$	27.2919	+	23.8154i	1.21931	+	1.06399i
$502$	10.2321	−	35.6614i	0.456683	−	1.59165i
$503$	−11.0899	+	11.0899i	−0.494475	+	0.494475i	−0.909713	−	0.415238i	$-0.863698\pi$
$503$	−11.0899	+	11.0899i	−0.494475	+	0.494475i	0.415238	+	0.909713i	$0.363698\pi$
$504$	−7.07769	+	8.36181i	−0.315265	+	0.372465i
$505$	−14.9535	−	3.68094i	−0.665424	−	0.163800i
$506$	−6.06299	−	10.9422i	−0.269533	−	0.486440i
$507$	−14.9790	+	1.01892i	−0.665241	+	0.0452517i
$508$	11.1228	−	2.56402i	0.493494	−	0.113760i
$509$	−16.8263	−	16.8263i	−0.745811	−	0.745811i	0.227879	−	0.973690i	$-0.426821\pi$
$509$	−16.8263	−	16.8263i	−0.745811	−	0.745811i	−0.973690	+	0.227879i	$0.926821\pi$
$510$	10.9185	−	3.77084i	0.483477	−	0.166976i
$511$	13.5179			0.597998
$512$	22.3435	+	3.57301i	0.987454	+	0.157906i
$513$	9.49065	−	14.4340i	0.419022	−	0.637277i
$514$	10.2443	+	2.93933i	0.451855	+	0.129648i
$515$	−13.5526	−	3.33608i	−0.597198	−	0.147005i
$516$	2.48978	+	1.33096i	0.109606	+	0.0585921i
$517$	13.7381			0.604200
$518$	−19.1218	−	5.48652i	−0.840165	−	0.241064i
$519$	2.43153	+	35.7457i	0.106732	+	1.56906i
$520$	11.6072	−	6.20876i	0.509009	−	0.272272i
$521$	30.3997			1.33184			0.665918	−	0.746025i	$-0.268040\pi$
$521$	30.3997			1.33184			0.665918	+	0.746025i	$0.268040\pi$
$522$	−2.21717	+	15.3356i	−0.0970428	+	0.671221i
$523$		−	8.45346i		−	0.369644i	−0.982772	−	0.184822i	$-0.940829\pi$
$523$		−	8.45346i		−	0.369644i	0.982772	−	0.184822i	$-0.0591709\pi$
$524$	7.92468	+	34.3775i	0.346191	+	1.50179i
$525$	4.04944	+	10.4219i	0.176732	+	0.454850i
$526$	−13.1595	−	3.77577i	−0.573779	−	0.164631i
$527$	7.73398	−	7.73398i	0.336897	−	0.336897i
$528$	−2.65107	+	9.79368i	−0.115373	+	0.426215i
$529$		−	13.4838i		−	0.586252i
$530$	−19.9153	−	11.4233i	−0.865067	−	0.496198i
$531$	−15.6490	+	20.6040i	−0.679110	+	0.894139i
$532$	−7.27841	−	4.55141i	−0.315559	−	0.197329i
$533$	20.4552			0.886015
$534$	−19.8949	+	12.8617i	−0.860936	+	0.556580i
$535$	−10.1493	−	16.7775i	−0.438791	−	0.725355i
$536$	−1.61444	+	30.5152i	−0.0697330	+	1.31806i
$537$	−27.6955	−	24.1676i	−1.19515	−	1.04291i
$538$	0.0323462	−	0.112734i	0.00139454	−	0.00486031i
$539$	5.52267	−	5.52267i	0.237878	−	0.237878i
$540$	4.36488	+	22.8243i	0.187835	+	0.982201i
$541$	−7.99141	−	7.99141i	−0.343578	−	0.343578i	0.514133	−	0.857710i	$-0.328114\pi$
$541$	−7.99141	−	7.99141i	−0.343578	−	0.343578i	−0.857710	+	0.514133i	$0.828114\pi$
$542$	−10.1120	−	18.2497i	−0.434349	−	0.783893i
$543$	3.99781	−	4.58140i	0.171563	−	0.196607i
$544$	−2.06191	−	11.7506i	−0.0884037	−	0.503801i
$545$	−4.40430	+	17.8921i	−0.188659	+	0.766415i
$546$	6.43541	+	1.38175i	0.275410	+	0.0591336i
$547$			19.6579i			0.840511i	0.907406	+	0.420255i	$0.138060\pi$
$547$			19.6579i			0.840511i	−0.907406	+	0.420255i	$0.861940\pi$
$548$	7.40929	−	1.70799i	0.316509	−	0.0729615i
$549$	33.3537	+	25.3326i	1.42350	+	1.08117i
$550$	7.49068	+	7.15006i	0.319404	+	0.304880i
$551$	−12.1418			−0.517259
$552$	−20.6063	+	21.2366i	−0.877062	+	0.903888i
$553$	7.80476	+	7.80476i	0.331892	+	0.331892i
$554$	−8.36485	−	15.0965i	−0.355388	−	0.641388i
$555$	−34.5400	+	24.2414i	−1.46614	+	1.02899i
$556$	−11.4154	+	2.63147i	−0.484120	+	0.111599i
$557$	32.6270			1.38245			0.691225	−	0.722640i	$-0.257072\pi$
$557$	32.6270			1.38245			0.691225	+	0.722640i	$0.257072\pi$
$558$	13.1722	+	17.6248i	0.557625	+	0.746115i
$559$		−	1.69625i		−	0.0717437i
$560$	11.2897	−	2.42714i	0.477077	−	0.102565i
$561$	5.33713	−	0.363048i	0.225334	−	0.0153279i
$562$	−1.49831	−	2.70408i	−0.0632024	−	0.114065i
$563$		−	22.9635i		−	0.967798i	−0.875124	−	0.483899i	$-0.839220\pi$
$563$		−	22.9635i		−	0.967798i	0.875124	−	0.483899i	$-0.160780\pi$
$564$	−9.43184	−	31.0976i	−0.397152	−	1.30944i
$565$	20.5058	+	5.04767i	0.862685	+	0.212357i
$566$	13.3884	−	7.41844i	0.562758	−	0.311820i
$567$	−5.71016	+	10.1198i	−0.239804	+	0.424990i
$568$	−7.27497	−	0.384890i	−0.305251	−	0.0161496i
$569$			42.0779i			1.76400i	0.471254	+	0.881998i	$0.343802\pi$
$569$			42.0779i			1.76400i	−0.471254	+	0.881998i	$0.656198\pi$
$570$	−17.2115	+	5.94424i	−0.720911	+	0.248977i
$571$	−12.9520	+	12.9520i	−0.542026	+	0.542026i	−0.924122	−	0.382096i	$-0.875202\pi$
$571$	−12.9520	+	12.9520i	−0.542026	+	0.542026i	0.382096	+	0.924122i	$0.375202\pi$
$572$	5.94027	−	1.36935i	0.248375	−	0.0572553i
$573$	−1.71813	−	25.2580i	−0.0717758	−	1.05517i
$574$	17.2485	+	4.94902i	0.719938	+	0.206568i
$575$	9.00224	+	28.8280i	0.375419	+	1.20221i
$576$	23.9891	−	0.722850i	0.999546	−	0.0301188i
$577$	6.79698	+	6.79698i	0.282962	+	0.282962i	0.834289	−	0.551327i	$-0.185878\pi$
$577$	6.79698	+	6.79698i	0.282962	+	0.282962i	−0.551327	+	0.834289i	$0.685878\pi$
$578$	15.5273	−	8.60357i	0.645851	−	0.357861i
$579$	−8.16238	+	9.35389i	−0.339217	+	0.388734i
$580$	11.7190	−	11.3772i	0.486604	−	0.472411i
$581$	−10.5567	−	10.5567i	−0.437964	−	0.437964i
$582$	−4.78857	+	22.3024i	−0.198493	+	0.924465i
$583$	−7.51826	−	7.51826i	−0.311375	−	0.311375i
$584$	−19.8051	−	22.0178i	−0.819542	−	0.911103i
$585$	10.8575	−	8.77780i	0.448902	−	0.362917i
$586$	8.91768	+	16.0942i	0.368386	+	0.664845i
$587$		−	37.8077i		−	1.56049i	−0.625474	−	0.780245i	$-0.715094\pi$
$587$		−	37.8077i		−	1.56049i	0.625474	−	0.780245i	$-0.284906\pi$
$588$	−16.2927	−	8.70957i	−0.671900	−	0.359176i
$589$	−12.1916	+	12.1916i	−0.502347	+	0.502347i
$590$	26.3234	−	7.13297i	1.08372	−	0.293660i
$591$	−0.556121	−	8.17549i	−0.0228758	−	0.336295i
$592$	19.0790	+	39.1836i	0.784143	+	1.61044i
$593$	−21.2191	−	21.2191i	−0.871365	−	0.871365i	0.121256	−	0.992621i	$-0.461308\pi$
$593$	−21.2191	−	21.2191i	−0.871365	−	0.871365i	−0.992621	+	0.121256i	$0.961308\pi$
$594$	−0.813482	+	10.7308i	−0.0333776	+	0.440291i
$595$	−3.15133	−	5.20939i	−0.129192	−	0.213564i
$596$	2.08094	+	9.02717i	0.0852385	+	0.369767i
$597$	13.1528	−	0.894694i	0.538309	−	0.0366174i
$598$	17.0893	+	4.90334i	0.698834	+	0.200513i
$599$		−	17.6257i		−	0.720165i	−0.932920	−	0.360083i	$-0.882749\pi$
$599$		−	17.6257i		−	0.720165i	0.932920	−	0.360083i	$-0.117251\pi$
$600$	11.0422	−	21.8648i	0.450797	−	0.892627i
$601$			1.46847i			0.0599003i	0.999551	+	0.0299501i	$0.00953485\pi$
$601$			1.46847i			0.0599003i	−0.999551	+	0.0299501i	$0.990465\pi$
$602$	0.410397	−	1.43033i	0.0167265	−	0.0582959i
$603$	4.38915	+	32.1129i	0.178740	+	1.30774i
$604$	19.3488	+	12.0994i	0.787290	+	0.492316i
$605$	−10.2490	−	16.9423i	−0.416680	−	0.688804i
$606$	−3.54142	+	16.4939i	−0.143860	+	0.670018i
$607$	−12.7986	−	12.7986i	−0.519479	−	0.519479i	0.397935	−	0.917414i	$-0.369727\pi$
$607$	−12.7986	−	12.7986i	−0.519479	−	0.519479i	−0.917414	+	0.397935i	$0.869727\pi$
$608$	3.25033	+	18.5232i	0.131818	+	0.751216i
$609$	8.14824	−	0.554268i	0.330183	−	0.0224601i
$610$	−11.5468	−	42.6121i	−0.467517	−	1.72531i
$611$	−13.8060	+	13.8060i	−0.558532	+	0.558532i
$612$	−4.48599	−	11.8319i	−0.181335	−	0.478276i
$613$			8.91389i			0.360029i	0.983664	+	0.180014i	$0.0576144\pi$
$613$			8.91389i			0.360029i	−0.983664	+	0.180014i	$0.942386\pi$
$614$	−42.4662	+	23.5302i	−1.71380	+	0.949603i
$615$	31.1561	−	21.8665i	1.25634	−	0.881742i
$616$	5.34033	+	0.282535i	0.215168	+	0.0113837i
$617$	−1.81921	−	1.81921i	−0.0732388	−	0.0732388i	0.669539	−	0.742777i	$-0.266492\pi$
$617$	−1.81921	−	1.81921i	−0.0732388	−	0.0732388i	−0.742777	+	0.669539i	$0.766492\pi$
$618$	−3.20963	+	14.9486i	−0.129110	+	0.601321i
$619$	0.786785	+	0.786785i	0.0316236	+	0.0316236i	0.722742	−	0.691118i	$-0.242882\pi$
$619$	0.786785	+	0.786785i	0.0316236	+	0.0316236i	−0.691118	+	0.722742i	$0.742882\pi$
$620$	0.343203	−	23.1908i	0.0137834	−	0.931367i
$621$	−17.2432	+	26.2247i	−0.691947	+	1.05236i
$622$	13.5110	+	24.3840i	0.541742	+	0.977710i
$623$	8.82935	+	8.82935i	0.353741	+	0.353741i
$624$	−7.17794	−	12.5063i	−0.287348	−	0.500653i
$625$	−14.2264	−	20.5575i	−0.569056	−	0.822298i
$626$	4.86862	−	16.9683i	0.194589	−	0.678190i
$627$	−8.41329	+	0.572297i	−0.335995	+	0.0228554i
$628$	−5.78183	−	3.61555i	−0.230720	−	0.144276i
$629$	16.2479	−	16.2479i	0.647848	−	0.647848i
$630$	11.2791	−	4.77481i	0.449370	−	0.190233i
$631$			39.2718i			1.56339i	0.623663	+	0.781693i	$0.285644\pi$
$631$			39.2718i			1.56339i	−0.623663	+	0.781693i	$0.714356\pi$
$632$	1.27752	−	24.1470i	0.0508171	−	0.960517i
$633$	−13.8171	−	12.0571i	−0.549180	−	0.479225i
$634$	−19.1627	−	34.5839i	−0.761048	−	1.37350i
$635$	−12.3919	−	3.05036i	−0.491757	−	0.121050i
$636$	−11.8567	+	22.1800i	−0.470150	+	0.879495i
$637$			11.1000i			0.439797i
$638$	6.61624	−	3.66601i	0.261940	−	0.145139i
$639$	−7.65589	+	1.04639i	−0.302862	+	0.0413947i
$640$	−20.4938	−	14.8325i	−0.810090	−	0.586306i
$641$		−	26.9846i		−	1.06583i	−0.846170	−	0.532914i	$-0.821097\pi$
$641$		−	26.9846i		−	1.06583i	0.846170	−	0.532914i	$-0.178903\pi$
$642$	−18.0387	+	11.6617i	−0.711931	+	0.460251i
$643$	−18.7886			−0.740949			−0.370474	−	0.928843i	$-0.620805\pi$
$643$	−18.7886			−0.740949			−0.370474	+	0.928843i	$0.620805\pi$
$644$	13.2239	+	8.26930i	0.521095	+	0.325856i
$645$	−1.81328	−	2.58362i	−0.0713977	−	0.101730i
$646$	8.67302	−	4.80566i	0.341235	−	0.189076i
$647$	−4.74385	−	4.74385i	−0.186500	−	0.186500i	0.607681	−	0.794181i	$-0.292100\pi$
$647$	−4.74385	−	4.74385i	−0.186500	−	0.186500i	−0.794181	+	0.607681i	$0.792100\pi$
$648$	24.8488	−	5.52582i	0.976155	−	0.217075i
$649$	12.6301			0.495776
$650$	−14.7132	+	0.342300i	−0.577098	+	0.0134261i
$651$	7.62512	−	8.73820i	0.298852	−	0.342477i
$652$	−5.00176	+	7.99860i	−0.195884	+	0.313249i
$653$			37.7676i			1.47796i	0.673726	+	0.738981i	$0.264693\pi$
$653$			37.7676i			1.47796i	−0.673726	+	0.738981i	$0.735307\pi$
$654$	19.7352	+	4.23736i	0.771706	+	0.165694i
$655$	9.42784	−	38.2999i	0.368376	−	1.49650i
$656$	−17.2099	−	35.3449i	−0.671933	−	1.37999i
$657$	−25.0142	−	18.9986i	−0.975896	−	0.741205i
$658$	−14.9820	+	8.30139i	−0.584058	+	0.323622i
$659$	13.5538	+	13.5538i	0.527980	+	0.527980i	0.919970	−	0.391990i	$-0.128213\pi$
$659$	13.5538	+	13.5538i	0.527980	+	0.527980i	−0.391990	+	0.919970i	$0.628213\pi$
$660$	7.58403	−	8.43581i	0.295208	−	0.328364i
$661$	−16.9462	+	16.9462i	−0.659132	+	0.659132i	−0.955175	−	0.296043i	$-0.904333\pi$
$661$	−16.9462	+	16.9462i	−0.659132	+	0.659132i	0.296043	+	0.955175i	$0.404333\pi$
$662$	22.6741	+	6.50577i	0.881256	+	0.252854i
$663$	−4.99869	+	5.72837i	−0.194133	+	0.222472i
$664$	−1.72797	+	32.6611i	−0.0670582	+	1.26750i
$665$	4.96766	+	8.21192i	0.192638	+	0.318445i
$666$	27.6729	+	37.0270i	1.07230	+	1.43477i
$667$	22.0601			0.854169
$668$	−40.7565	+	9.39517i	−1.57692	+	0.363510i
$669$	24.0745	−	27.5888i	0.930773	−	1.06664i
$670$	16.9988	−	29.6356i	0.656722	−	1.14492i
$671$		−	20.4456i		−	0.789294i
$672$	−3.02684	−	12.2824i	−0.116763	−	0.473802i
$673$	26.0839	−	26.0839i	1.00546	−	1.00546i	0.00547515	−	0.999985i	$-0.498257\pi$
$673$	26.0839	−	26.0839i	1.00546	−	1.00546i	0.999985	−	0.00547515i	$-0.00174280\pi$
$674$	0.943023	−	3.28666i	0.0363239	−	0.126597i
$675$	7.15406	−	24.9764i	0.275360	−	0.961341i
$676$	9.19167	−	14.6989i	0.353526	−	0.565343i
$677$			6.41910i			0.246706i	0.992363	+	0.123353i	$0.0393648\pi$
$677$			6.41910i			0.246706i	−0.992363	+	0.123353i	$0.960635\pi$
$678$	4.85634	−	22.6180i	0.186507	−	0.868641i
$679$	12.0230			0.461399
$680$	−3.86796	+	12.7651i	−0.148329	+	0.489519i
$681$	8.85653	−	0.602448i	0.339383	−	0.0230858i
$682$	2.96233	−	10.3244i	0.113433	−	0.395343i
$683$	14.6529			0.560679			0.280340	−	0.959901i	$-0.409553\pi$
$683$	14.6529			0.560679			0.280340	+	0.959901i	$0.409553\pi$
$684$	7.07158	+	18.6515i	0.270389	+	0.713156i
$685$	−8.25468	−	2.03196i	−0.315395	−	0.0776371i
$686$	−6.21050	+	21.6451i	−0.237118	+	0.826412i
$687$	3.43940	+	3.00129i	0.131221	+	0.114506i
$688$	−2.93097	+	1.42713i	−0.111742	+	0.0544087i
$689$	15.1109			0.575679
$690$	31.2710	−	10.7999i	1.19047	−	0.411144i
$691$	28.3072	+	28.3072i	1.07686	+	1.07686i	0.996789	+	0.0800692i	$0.0255141\pi$
$691$	28.3072	+	28.3072i	1.07686	+	1.07686i	0.0800692	+	0.996789i	$0.474486\pi$
$692$	−35.0773	−	21.9349i	−1.33344	−	0.833839i
$693$	5.61994	−	0.768125i	0.213484	−	0.0291786i
$694$	−24.3290	+	13.4805i	−0.923517	+	0.511714i
$695$	12.7179	+	3.13060i	0.482416	+	0.118751i
$696$	−12.8408	−	12.4597i	−0.486728	−	0.472283i
$697$	−14.6562	+	14.6562i	−0.555141	+	0.555141i
$698$	−10.3499	−	2.96964i	−0.391749	−	0.112403i
$699$	8.83603	−	10.1259i	0.334209	−	0.382996i
$700$	−12.4894	−	3.27112i	−0.472055	−	0.123637i
$701$	23.7655	−	23.7655i	0.897612	−	0.897612i	−0.0976124	−	0.995225i	$-0.531121\pi$
$701$	23.7655	−	23.7655i	0.897612	−	0.897612i	0.995225	+	0.0976124i	$0.0311205\pi$
$702$	−9.96640	−	11.6014i	−0.376157	−	0.437867i
$703$	−25.6128	+	25.6128i	−0.966004	+	0.966004i
$704$	−7.36392	−	9.11218i	−0.277538	−	0.343428i
$705$	−6.26995	+	35.7870i	−0.236140	+	1.34782i
$706$	−13.9819	+	48.7301i	−0.526214	+	1.83398i
$707$	8.89166			0.334405
$708$	−8.67119	−	28.5897i	−0.325883	−	1.07447i
$709$	5.81334	+	5.81334i	0.218325	+	0.218325i	0.807792	−	0.589468i	$-0.200662\pi$
$709$	5.81334	+	5.81334i	0.218325	+	0.218325i	−0.589468	+	0.807792i	$0.700662\pi$
$710$	7.06527	+	4.05261i	0.265155	+	0.152092i
$711$	−3.47318	−	25.4114i	−0.130255	−	0.953000i
$712$	1.44523	−	27.3170i	0.0541624	−	1.02375i
$713$	22.1505	−	22.1505i	0.829544	−	0.829544i
$714$	−5.60099	+	3.62094i	−0.209612	+	0.135510i
$715$	−6.61804	−	1.62909i	−0.247501	−	0.0609243i
$716$	41.3593	−	9.53411i	1.54567	−	0.356307i
$717$	16.3345	−	1.11112i	0.610023	−	0.0414956i
$718$	−27.8931	+	15.4554i	−1.04096	+	0.576790i
$719$	−2.88200			−0.107480			−0.0537402	−	0.998555i	$-0.517114\pi$
$719$	−2.88200			−0.107480			−0.0537402	+	0.998555i	$0.517114\pi$
$720$	−24.3021	−	11.3757i	−0.905687	−	0.423946i
$721$	8.05862			0.300119
$722$	9.83135	−	5.44748i	0.365885	−	0.202734i
$723$	17.8905	−	1.21697i	0.665356	−	0.0452595i
$724$	1.57713	+	6.84166i	0.0586137	+	0.254268i
$725$	−17.4310	+	5.44324i	−0.647370	+	0.202157i
$726$	−18.2159	+	11.7763i	−0.676057	+	0.437059i
$727$	24.4474	−	24.4474i	0.906704	−	0.906704i	−0.0893004	−	0.996005i	$-0.528463\pi$
$727$	24.4474	−	24.4474i	0.906704	−	0.906704i	0.996005	+	0.0893004i	$0.0284631\pi$
$728$	−5.65067	+	5.08281i	−0.209428	+	0.188381i
$729$	24.7890	−	10.7008i	0.918110	−	0.396325i
$730$	8.65973	+	31.9577i	0.320511	+	1.18281i
$731$	1.21536	+	1.21536i	0.0449517	+	0.0449517i
$732$	−46.2808	+	14.0369i	−1.71059	+	0.518818i
$733$	17.2734			0.638007			0.319003	−	0.947754i	$-0.396652\pi$
$733$	17.2734			0.638007			0.319003	+	0.947754i	$0.396652\pi$
$734$	9.12366	−	31.7981i	0.336761	−	1.17369i
$735$	11.8658	+	16.9068i	0.437676	+	0.623616i
$736$	−5.90542	−	33.6542i	−0.217677	−	1.24051i
$737$	11.1878	−	11.1878i	0.412107	−	0.412107i
$738$	−24.9618	−	33.3995i	−0.918857	−	1.22945i
$739$	7.62856	−	7.62856i	0.280621	−	0.280621i	−0.552736	−	0.833357i	$-0.686416\pi$
$739$	7.62856	−	7.62856i	0.280621	−	0.280621i	0.833357	+	0.552736i	$0.186416\pi$
$740$	0.721019	−	48.7205i	0.0265052	−	1.79100i
$741$	7.87978	−	9.03003i	0.289471	−	0.331727i
$742$	12.7420	+	3.65599i	0.467773	+	0.134216i
$743$	21.3182	−	21.3182i	0.782090	−	0.782090i	−0.198093	−	0.980183i	$-0.563475\pi$
$743$	21.3182	−	21.3182i	0.782090	−	0.782090i	0.980183	+	0.198093i	$0.0634749\pi$
$744$	−25.4042	+	0.382658i	−0.931363	+	0.0140289i
$745$	2.47565	−	10.0571i	0.0907008	−	0.368465i
$746$	8.96677	−	4.96842i	0.328297	−	0.181907i
$747$	4.69780	+	34.3712i	0.171884	+	1.25758i
$748$	−3.27506	+	5.23733i	−0.119748	+	0.191496i
$749$	8.00558	+	8.00558i	0.292518	+	0.292518i
$750$	−22.0443	+	16.2496i	−0.804943	+	0.593353i
$751$	−26.1007			−0.952430			−0.476215	−	0.879329i	$-0.657992\pi$
$751$	−26.1007			−0.952430			−0.476215	+	0.879329i	$0.657992\pi$
$752$	35.4712	+	12.2400i	1.29350	+	0.446347i
$753$	34.2363	+	29.8752i	1.24764	+	1.08871i
$754$	−2.96482	+	10.3331i	−0.107973	+	0.376310i
$755$	−13.2059	−	21.8304i	−0.480612	−	0.794489i
$756$	−5.59709	−	12.1940i	−0.203564	−	0.443491i
$757$	−42.5694			−1.54721			−0.773605	−	0.633668i	$-0.781548\pi$
$757$	−42.5694			−1.54721			−0.773605	+	0.633668i	$0.781548\pi$
$758$	3.57528	−	12.4607i	0.129860	−	0.452592i
$759$	15.2858	−	1.03979i	0.554840	−	0.0377419i
$760$	6.09733	−	20.1225i	0.221174	−	0.729921i
$761$	−51.8643			−1.88008			−0.940040	−	0.341065i	$-0.889212\pi$
$761$	−51.8643			−1.88008			−0.940040	+	0.341065i	$0.889212\pi$
$762$	−2.93474	+	13.6683i	−0.106314	+	0.495152i
$763$		−	10.6390i		−	0.385158i
$764$	24.7857	+	15.4993i	0.896716	+	0.560744i
$765$	−1.49010	+	14.0687i	−0.0538747	+	0.508654i
$766$	−7.27614	+	25.3591i	−0.262897	+	0.916260i
$767$	−12.6926	+	12.6926i	−0.458304	+	0.458304i
$768$	−15.5707	+	22.9249i	−0.561859	+	0.827233i
$769$		−	4.33991i		−	0.156501i	−0.996934	−	0.0782506i	$-0.975067\pi$
$769$		−	4.33991i		−	0.156501i	0.996934	−	0.0782506i	$-0.0249334\pi$
$770$	−5.18639	−	2.97489i	−0.186905	−	0.107208i
$771$	−8.58210	+	9.83487i	−0.309077	+	0.354194i
$772$	−3.22005	−	13.9687i	−0.115892	−	0.502744i
$773$	−39.7001			−1.42791			−0.713957	−	0.700190i	$-0.753099\pi$
$773$	−39.7001			−1.42791			−0.713957	+	0.700190i	$0.753099\pi$
$774$	−2.76965	+	2.06996i	−0.0995530	+	0.0744031i
$775$	−12.0369	+	22.9680i	−0.432378	+	0.825035i
$776$	−17.6149	−	19.5828i	−0.632336	−	0.702983i
$777$	16.0192	−	18.3577i	0.574687	−	0.658577i
$778$	−2.00350	−	0.574853i	−0.0718289	−	0.0206095i
$779$	23.1035	−	23.1035i	0.827769	−	0.827769i
$780$	0.855994	+	16.0991i	0.0306495	+	0.576440i
$781$	2.66722	+	2.66722i	0.0954407	+	0.0954407i
$782$	−15.7577	+	8.73123i	−0.563495	+	0.312228i
$783$	−15.8568	−	10.4262i	−0.566677	−	0.372601i
$784$	19.1798	−	9.33888i	0.684992	−	0.333532i
$785$	3.94621	+	6.52339i	0.140846	+	0.232830i
$786$	−42.2451	−	9.07049i	−1.50683	−	0.323534i
$787$		−	5.30056i		−	0.188945i	−0.995527	−	0.0944723i	$-0.969884\pi$
$787$		−	5.30056i		−	0.188945i	0.995527	−	0.0944723i	$-0.0301164\pi$
$788$	8.02262	+	5.01678i	0.285794	+	0.178716i
$789$	11.0243	−	12.6336i	0.392475	−	0.449767i
$790$	−13.4514	+	23.4510i	−0.478579	+	0.834349i
$791$	−12.1931			−0.433538
$792$	−9.48488	−	8.02829i	−0.337031	−	0.285273i
$793$	20.5467	+	20.5467i	0.729636	+	0.729636i
$794$	1.03634	−	0.574231i	0.0367785	−	0.0203787i
$795$	23.0160	−	16.1534i	0.816293	−	0.572904i
$796$	−8.07105	+	12.9069i	−0.286071	+	0.457472i
$797$	−17.4862			−0.619394			−0.309697	−	0.950835i	$-0.600228\pi$
$797$	−17.4862			−0.619394			−0.309697	+	0.950835i	$0.600228\pi$
$798$	8.82923	−	5.70794i	0.312551	−	0.202059i
$799$		−	19.7840i		−	0.699908i
$800$	12.9703	+	25.1351i	0.458569	+	0.888659i
$801$	−3.92914	−	28.7473i	−0.138829	−	1.01574i
$802$	29.2852	−	16.2267i	1.03410	−	0.572986i
$803$			15.3335i			0.541108i
$804$	−33.0056	−	17.6438i	−1.16402	−	0.622247i
$805$	−9.02557	−	14.9200i	−0.318110	−	0.525859i
$806$	7.39851	+	13.3525i	0.260601	+	0.470321i
$807$	0.108229	+	0.0944426i	0.00380984	+	0.00332454i
$808$	−13.0272	−	14.4826i	−0.458294	−	0.509496i
$809$			37.4327i			1.31606i	0.752991	+	0.658031i	$0.228611\pi$
$809$			37.4327i			1.31606i	−0.752991	+	0.658031i	$0.771389\pi$
$810$	−27.5820	−	7.01654i	−0.969134	−	0.246536i
$811$	7.78970	−	7.78970i	0.273533	−	0.273533i	−0.556987	−	0.830521i	$-0.688043\pi$
$811$	7.78970	−	7.78970i	0.273533	−	0.273533i	0.830521	+	0.556987i	$0.188043\pi$
$812$	−5.00006	+	7.99588i	−0.175468	+	0.280600i
$813$	25.4942	−	1.73419i	0.894119	−	0.0608206i
$814$	6.22342	−	21.6901i	0.218131	−	0.760237i
$815$	9.02447	−	5.45920i	0.316113	−	0.191227i
$816$	14.1037	+	3.81777i	0.493730	+	0.133649i
$817$	−1.91586	−	1.91586i	−0.0670274	−	0.0670274i
$818$	17.6379	+	31.8321i	0.616696	+	1.11298i
$819$	−4.87582	+	6.41966i	−0.170375	+	0.224321i
$820$	−0.650382	+	43.9474i	−0.0227123	+	1.53471i
$821$	−12.3460	−	12.3460i	−0.430879	−	0.430879i	0.458049	−	0.888927i	$-0.348549\pi$
$821$	−12.3460	−	12.3460i	−0.430879	−	0.430879i	−0.888927	+	0.458049i	$0.848549\pi$
$822$	−1.95494	+	9.10497i	−0.0681863	+	0.317572i
$823$	10.6014	+	10.6014i	0.369542	+	0.369542i	0.867310	−	0.497768i	$-0.165847\pi$
$823$	10.6014	+	10.6014i	0.369542	+	0.369542i	−0.497768	+	0.867310i	$0.665847\pi$
$824$	−11.8067	−	13.1258i	−0.411305	−	0.457257i
$825$	−11.8217	+	4.59332i	−0.411578	+	0.159919i
$826$	−13.7737	+	7.63191i	−0.479248	+	0.265548i
$827$			18.5764i			0.645966i	0.946405	+	0.322983i	$0.104686\pi$
$827$			18.5764i			0.645966i	−0.946405	+	0.322983i	$0.895314\pi$
$828$	−12.8481	−	33.8872i	−0.446503	−	1.17766i
$829$	14.7854	−	14.7854i	0.513517	−	0.513517i	−0.402085	−	0.915602i	$-0.631714\pi$
$829$	14.7854	−	14.7854i	0.513517	−	0.513517i	0.915602	+	0.402085i	$0.131714\pi$
$830$	18.1942	−	31.7197i	0.631531	−	1.10101i
$831$	21.0892	−	1.43455i	0.731575	−	0.0497640i
$832$	16.5576	+	1.75691i	0.574031	+	0.0609099i
$833$	−7.95312	−	7.95312i	−0.275559	−	0.275559i
$834$	3.01194	−	14.0279i	0.104295	−	0.485746i
$835$	45.4067	+	11.1772i	1.57137	+	0.386804i
$836$	5.16271	−	8.25597i	0.178556	−	0.285539i
$837$	−26.3908	+	5.45293i	−0.912200	+	0.188481i
$838$	7.61398	−	26.5365i	0.263021	−	0.916689i
$839$		−	33.8653i		−	1.16916i	−0.811336	−	0.584580i	$-0.801259\pi$
$839$		−	33.8653i		−	1.16916i	0.811336	−	0.584580i	$-0.198741\pi$
$840$	−3.17327	+	13.7823i	−0.109488	+	0.475536i
$841$		−	15.6613i		−	0.540045i
$842$	−26.4998	−	7.60345i	−0.913244	−	0.262032i
$843$	3.77749	−	0.256956i	0.130104	−	0.00885004i
$844$	20.6338	−	4.75650i	0.710246	−	0.163725i
$845$	−16.5842	+	10.0323i	−0.570512	+	0.345121i
$846$	39.3903	+	5.69491i	1.35427	+	0.195795i
$847$	8.08423	+	8.08423i	0.277777	+	0.277777i
$848$	−12.7135	−	26.1103i	−0.436582	−	0.896632i
$849$	1.27224	+	18.7031i	0.0436632	+	0.641889i
$850$	10.2967	−	10.7872i	0.353174	−	0.369999i
$851$	46.5350	−	46.5350i	1.59520	−	1.59520i
$852$	4.20636	−	7.86871i	0.144108	−	0.269578i
$853$		−	27.4595i		−	0.940194i	−0.882615	−	0.470097i	$-0.844219\pi$
$853$		−	27.4595i		−	0.940194i	0.882615	−	0.470097i	$-0.155781\pi$
$854$	12.3545	+	22.2968i	0.422762	+	0.762981i
$855$	2.34895	−	22.1774i	0.0803324	−	0.758452i
$856$	1.31039	−	24.7683i	0.0447883	−	0.846564i
$857$	−17.7906	−	17.7906i	−0.607715	−	0.607715i	0.334634	−	0.942348i	$-0.391387\pi$
$857$	−17.7906	−	17.7906i	−0.607715	−	0.607715i	−0.942348	+	0.334634i	$0.891387\pi$
$858$	−1.56734	+	7.29975i	−0.0535080	+	0.249209i
$859$	−4.90738	−	4.90738i	−0.167438	−	0.167438i	0.618414	−	0.785852i	$-0.287775\pi$
$859$	−4.90738	−	4.90738i	−0.167438	−	0.167438i	−0.785852	+	0.618414i	$0.787775\pi$
$860$	3.64434	+	0.0539328i	0.124271	+	0.00183909i
$861$	−14.4499	+	16.5592i	−0.492450	+	0.564335i
$862$	2.67241	−	1.48076i	0.0910226	−	0.0504349i
$863$	−4.91101	−	4.91101i	−0.167173	−	0.167173i	0.618563	−	0.785735i	$-0.287715\pi$
$863$	−4.91101	−	4.91101i	−0.167173	−	0.167173i	−0.785735	+	0.618563i	$0.787715\pi$
$864$	−11.6611	+	26.9818i	−0.396718	+	0.917941i
$865$	23.9409	+	39.5762i	0.814016	+	1.34563i
$866$	34.0002	+	9.75548i	1.15537	+	0.331505i
$867$	1.47549	+	21.6911i	0.0501103	+	0.736667i
$868$	3.00810	+	13.0492i	0.102102	+	0.442920i
$869$	−8.85302	+	8.85302i	−0.300318	+	0.300318i
$870$	6.53019	+	18.9081i	0.221394	+	0.641046i
$871$			22.4862i			0.761916i
$872$	−17.3286	+	15.5872i	−0.586822	+	0.527849i
$873$	−22.2478	−	16.8975i	−0.752975	−	0.571894i
$874$	24.8400	−	13.7636i	0.840225	−	0.465562i
$875$	10.8131	+	9.56212i	0.365549	+	0.323259i
$876$	34.7091	−	10.5272i	1.17271	−	0.355681i
$877$			20.1399i			0.680076i	0.940412	+	0.340038i	$0.110440\pi$
$877$			20.1399i			0.680076i	−0.940412	+	0.340038i	$0.889560\pi$
$878$	−7.68392	−	13.8676i	−0.259320	−	0.468008i
$879$	−22.4830	+	1.52936i	−0.758331	+	0.0515840i
$880$	2.75313	+	12.8060i	0.0928079	+	0.431691i
$881$			36.5232i			1.23050i	0.788333	+	0.615249i	$0.210944\pi$
$881$			36.5232i			1.23050i	−0.788333	+	0.615249i	$0.789056\pi$
$882$	18.1241	−	13.5455i	0.610271	−	0.456099i
$883$	−28.7937			−0.968985			−0.484493	−	0.874795i	$-0.660996\pi$
$883$	−28.7937			−0.968985			−0.484493	+	0.874795i	$0.660996\pi$
$884$	−1.97198	−	8.55450i	−0.0663248	−	0.287719i
$885$	−5.76429	+	32.9009i	−0.193765	+	1.10595i
$886$	3.86456	+	6.97457i	0.129832	+	0.234315i
$887$	28.4788	+	28.4788i	0.956224	+	0.956224i	0.999081	−	0.0428570i	$-0.0136460\pi$
$887$	28.4788	+	28.4788i	0.956224	+	0.956224i	−0.0428570	+	0.999081i	$0.513646\pi$
$888$	−53.3704	+	0.803908i	−1.79099	+	0.0269774i
$889$	7.36844			0.247130
$890$	−15.2172	+	26.5296i	−0.510083	+	0.889274i
$891$	−11.4789	−	6.47709i	−0.384559	−	0.216991i
$892$	9.49737	+	41.1999i	0.317995	+	1.37947i
$893$			31.1869i			1.04363i
$894$	−11.0931	−	2.38181i	−0.371009	−	0.0796597i
$895$	−46.0783	−	11.3425i	−1.54023	−	0.379139i
$896$	13.5368	+	5.48749i	0.452233	+	0.183324i
$897$	−14.3165	+	16.4064i	−0.478014	+	0.547792i
$898$	6.43237	+	11.6088i	0.214651	+	0.387392i
$899$	13.3934	+	13.3934i	0.446695	+	0.446695i
$900$	18.5136	+	23.6061i	0.617120	+	0.786869i
$901$	−10.8269	+	10.8269i	−0.360698	+	0.360698i
$902$	−5.61372	+	19.5651i	−0.186916	+	0.651447i
$903$	1.37317	+	1.19825i	0.0456962	+	0.0398754i
$904$	17.8641	+	19.8600i	0.594153	+	0.660533i
$905$	1.87629	−	7.62227i	0.0623698	−	0.253373i
$906$	−23.4714	+	15.1739i	−0.779786	+	0.504118i
$907$	21.8599			0.725846			0.362923	−	0.931819i	$-0.381779\pi$
$907$	21.8599			0.725846			0.362923	+	0.931819i	$0.381779\pi$
$908$	−5.43470	+	8.69093i	−0.180357	+	0.288418i
$909$	−16.4535	−	12.4966i	−0.545728	−	0.414488i
$910$	8.20165	−	2.22244i	0.271882	−	0.0736732i
$911$		−	26.5894i		−	0.880945i	−0.897766	−	0.440473i	$-0.854811\pi$
$911$		−	26.5894i		−	0.880945i	0.897766	−	0.440473i	$-0.145189\pi$
$912$	−22.2327	−	6.01822i	−0.736199	−	0.199283i
$913$	11.9745	−	11.9745i	0.396299	−	0.396299i
$914$	31.2044	+	8.95331i	1.03215	+	0.296149i
$915$	53.2598	+	9.33120i	1.76072	+	0.308480i
$916$	−5.13625	+	1.18401i	−0.169707	+	0.0391207i
$917$			22.7738i			0.752059i
$918$	15.4533	+	1.17148i	0.510035	+	0.0386647i
$919$	−46.8512			−1.54548			−0.772739	−	0.634723i	$-0.781114\pi$
$919$	−46.8512			−1.54548			−0.772739	+	0.634723i	$0.781114\pi$
$920$	−11.0780	+	36.5599i	−0.365232	+	1.20535i
$921$	−4.03537	−	59.3237i	−0.132970	−	1.95478i
$922$	14.6603	+	4.20640i	0.482811	+	0.138530i
$923$	−5.36083			−0.176454
$924$	−3.08776	+	5.77617i	−0.101580	+	0.190022i
$925$	−25.2877	+	48.2524i	−0.831455	+	1.58653i
$926$	−21.1441	−	6.06676i	−0.694838	−	0.199366i
$927$	−14.9120	−	11.3259i	−0.489775	−	0.371990i
$928$	20.3492	−	3.57073i	0.667994	−	0.117215i
$929$	−20.5659			−0.674747			−0.337373	−	0.941371i	$-0.609538\pi$
$929$	−20.5659			−0.674747			−0.337373	+	0.941371i	$0.609538\pi$
$930$	25.5426	+	12.4287i	0.837576	+	0.407553i
$931$	12.5371	+	12.5371i	0.410885	+	0.410885i
$932$	3.48581	+	15.1215i	0.114181	+	0.495322i
$933$	−34.0635	+	2.31710i	−1.11519	+	0.0758585i
$934$	−6.60929	−	11.9281i	−0.216263	−	0.390301i
$935$	5.90906	−	3.57458i	0.193247	−	0.116901i
$936$	17.5998	−	1.46379i	0.575268	−	0.0478456i
$937$	34.0136	−	34.0136i	1.11118	−	1.11118i	0.118184	−	0.992992i	$-0.462293\pi$
$937$	34.0136	−	34.0136i	1.11118	−	1.11118i	0.992992	−	0.118184i	$-0.0377073\pi$
$938$	−5.44040	+	18.9611i	−0.177635	+	0.619101i
$939$	16.2902	+	14.2151i	0.531610	+	0.463893i
$940$	−29.2229	−	30.1008i	−0.953144	−	0.981780i
$941$	−12.2462	+	12.2462i	−0.399216	+	0.399216i	−0.877956	−	0.478741i	$-0.841093\pi$
$941$	−12.2462	+	12.2462i	−0.399216	+	0.399216i	0.478741	+	0.877956i	$0.341093\pi$
$942$	7.01377	−	4.53427i	0.228521	−	0.147735i
$943$	−41.9760	+	41.9760i	−1.36693	+	1.36693i
$944$	32.6106	+	11.2529i	1.06138	+	0.366250i
$945$	−0.563967	+	14.9902i	−0.0183458	+	0.487633i
$946$	1.62244	+	0.465517i	0.0527500	+	0.0151353i
$947$	−47.5663			−1.54570			−0.772848	−	0.634592i	$-0.781168\pi$
$947$	−47.5663			−1.54570			−0.772848	+	0.634592i	$0.781168\pi$
$948$	26.1178	+	13.9617i	0.848265	+	0.453456i
$949$	−15.4094	−	15.4094i	−0.500209	−	0.500209i
$950$	−16.2314	+	17.0047i	−0.526617	+	0.551704i
$951$	48.3124	−	3.28635i	1.56664	−	0.106567i
$952$	0.406875	−	7.69053i	0.0131869	−	0.249251i
$953$	−22.3066	+	22.3066i	−0.722582	+	0.722582i	−0.969131	−	0.246548i	$-0.920704\pi$
$953$	−22.3066	+	22.3066i	−0.722582	+	0.722582i	0.246548	+	0.969131i	$0.420704\pi$
$954$	−18.4401	−	24.6732i	−0.597019	−	0.798825i
$955$	−16.9167	−	27.9647i	−0.547413	−	0.904916i
$956$	−10.0235	+	16.0291i	−0.324182	+	0.518417i
$957$	0.628711	+	9.24263i	0.0203233	+	0.298772i
$958$	0.240252	+	0.433595i	0.00776219	+	0.0140088i
$959$	4.90839			0.158500
$960$	27.0976	−	15.0239i	0.874572	−	0.484895i
$961$	−4.10336			−0.132366
$962$	15.5432	+	28.0516i	0.501132	+	0.904419i
$963$	−3.56255	−	26.0652i	−0.114802	−	0.839939i
$964$	−10.9783	+	17.5560i	−0.353587	+	0.565441i
$965$	−3.83083	+	15.5625i	−0.123319	+	0.500974i
$966$	−16.0415	+	10.3706i	−0.516128	+	0.333667i
$967$	−9.83196	+	9.83196i	−0.316175	+	0.316175i	−0.847296	−	0.531121i	$-0.821771\pi$
$967$	−9.83196	+	9.83196i	−0.316175	+	0.316175i	0.531121	+	0.847296i	$0.321771\pi$
$968$	1.32327	−	25.0117i	0.0425314	−	0.803905i
$969$	0.824157	+	12.1159i	0.0264757	+	0.389218i
$970$	7.70204	+	28.4234i	0.247298	+	0.912622i
$971$	27.1430	+	27.1430i	0.871059	+	0.871059i	0.992588	−	0.121529i	$-0.0387798\pi$
$971$	27.1430	+	27.1430i	0.871059	+	0.871059i	−0.121529	+	0.992588i	$0.538780\pi$
$972$	−6.78075	+	30.4306i	−0.217493	+	0.976062i
$973$	−7.56227			−0.242435
$974$	6.39827	+	1.83582i	0.205014	+	0.0588235i
$975$	7.26411	−	16.4962i	0.232638	−	0.528301i
$976$	18.2161	−	52.7898i	0.583084	−	1.68976i
$977$	−27.0368	+	27.0368i	−0.864984	+	0.864984i	−0.991912	−	0.126928i	$-0.959488\pi$
$977$	−27.0368	+	27.0368i	−0.864984	+	0.864984i	0.126928	+	0.991912i	$0.459488\pi$
$978$	−6.27273	−	9.70287i	−0.200580	−	0.310263i
$979$	−10.0152	+	10.0152i	−0.320088	+	0.320088i
$980$	−23.8479	−	0.352928i	−0.761794	−	0.0112739i
$981$	−14.9524	+	19.6869i	−0.477394	+	0.628553i
$982$	11.4678	−	39.9680i	0.365952	−	1.27543i
$983$	15.4408	−	15.4408i	0.492484	−	0.492484i	−0.416604	−	0.909088i	$-0.636780\pi$
$983$	15.4408	−	15.4408i	0.492484	−	0.492484i	0.909088	+	0.416604i	$0.136780\pi$
$984$	48.1418	−	0.725150i	1.53470	−	0.0231169i
$985$	−5.47559	−	9.05158i	−0.174467	−	0.288407i
$986$	−5.27937	−	9.52796i	−0.168129	−	0.303432i
$987$	−1.42367	−	20.9292i	−0.0453158	−	0.666184i
$988$	3.10857	+	13.4851i	0.0988967	+	0.429017i
$989$	3.48086	+	3.48086i	0.110685	+	0.110685i
$990$	5.41611	+	12.7940i	0.172135	+	0.406620i
$991$	−9.30144			−0.295470			−0.147735	−	0.989027i	$-0.547198\pi$
$991$	−9.30144			−0.295470			−0.147735	+	0.989027i	$0.547198\pi$
$992$	16.8472	−	24.0180i	0.534900	−	0.762572i
$993$	−18.9952	+	21.7680i	−0.602794	+	0.690787i
$994$	−4.52042	−	1.29702i	−0.143379	−	0.0411389i
$995$	14.5623	−	8.80919i	0.461655	−	0.279270i
$996$	−35.3267	−	18.8845i	−1.11937	−	0.598379i
$997$	−14.4349			−0.457158			−0.228579	−	0.973525i	$-0.573408\pi$
$997$	−14.4349			−0.457158			−0.228579	+	0.973525i	$0.573408\pi$
$998$	5.74594	+	1.64865i	0.181884	+	0.0521871i
$999$	−55.4432	+	11.4558i	−1.75414	+	0.362446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bf.a.77.15	yes	88
3.2	odd	2	inner	240.2.bf.a.77.30	yes	88
4.3	odd	2		960.2.bf.a.17.4		88
5.3	odd	4		240.2.bb.a.173.8	✓	88
12.11	even	2		960.2.bf.a.17.3		88
15.8	even	4		240.2.bb.a.173.37	yes	88
16.5	even	4		240.2.bb.a.197.37	yes	88
16.11	odd	4		960.2.bb.a.497.24		88
20.3	even	4		960.2.bb.a.593.21		88
48.5	odd	4		240.2.bb.a.197.8	yes	88
48.11	even	4		960.2.bb.a.497.21		88
60.23	odd	4		960.2.bb.a.593.24		88
80.43	even	4		960.2.bf.a.113.4		88
80.53	odd	4	inner	240.2.bf.a.53.30	yes	88
240.53	even	4	inner	240.2.bf.a.53.15	yes	88
240.203	odd	4		960.2.bf.a.113.3		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.8	✓	88	5.3	odd	4
240.2.bb.a.173.37	yes	88	15.8	even	4
240.2.bb.a.197.8	yes	88	48.5	odd	4
240.2.bb.a.197.37	yes	88	16.5	even	4
240.2.bf.a.53.15	yes	88	240.53	even	4	inner
240.2.bf.a.53.30	yes	88	80.53	odd	4	inner
240.2.bf.a.77.15	yes	88	1.1	even	1	trivial
240.2.bf.a.77.30	yes	88	3.2	odd	2	inner
960.2.bb.a.497.21		88	48.11	even	4
960.2.bb.a.497.24		88	16.11	odd	4
960.2.bb.a.593.21		88	20.3	even	4
960.2.bb.a.593.24		88	60.23	odd	4
960.2.bf.a.17.3		88	12.11	even	2
960.2.bf.a.17.4		88	4.3	odd	2
960.2.bf.a.113.3		88	240.203	odd	4
960.2.bf.a.113.4		88	80.43	even	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bf (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.685419 - 1.23701i) q^{2} +(1.72806 - 0.117548i) q^{3} +(-1.06040 + 1.69575i) q^{4} +(1.91324 - 1.15738i) q^{5} +(-1.32985 - 2.05706i) q^{6} +(-0.912923 + 0.912923i) q^{7} +(2.82448 + 0.149432i) q^{8} +(2.97237 - 0.406258i) q^{9} +(-2.74306 - 1.57341i) q^{10} +(-1.03554 - 1.03554i) q^{11} +(-1.63310 + 3.05499i) q^{12} +2.08132 q^{13} +(1.75503 + 0.503562i) q^{14} +(3.17014 - 2.22491i) q^{15} +(-1.75110 - 3.59634i) q^{16} +(-1.49126 + 1.49126i) q^{17} +(-2.53986 - 3.39840i) q^{18} +(2.35078 - 2.35078i) q^{19} +(-0.0661763 + 4.47165i) q^{20} +(-1.47027 + 1.68489i) q^{21} +(-0.571195 + 1.99075i) q^{22} +(-4.27105 + 4.27105i) q^{23} +(4.89842 - 0.0737840i) q^{24} +(2.32095 - 4.42868i) q^{25} +(-1.42658 - 2.57462i) q^{26} +(5.08866 - 1.05143i) q^{27} +(-0.580021 - 2.51615i) q^{28} +(-2.58251 - 2.58251i) q^{29} +(-4.92512 - 2.39650i) q^{30} -5.18620 q^{31} +(-3.24847 + 4.63114i) q^{32} +(-1.91119 - 1.66774i) q^{33} +(2.86685 + 0.822570i) q^{34} +(-0.690039 + 2.80323i) q^{35} +(-2.46299 + 5.47117i) q^{36} -10.8954 q^{37} +(-4.51922 - 1.29667i) q^{38} +(3.59664 - 0.244654i) q^{39} +(5.57684 - 2.98309i) q^{40} +9.82802 q^{41} +(3.09199 + 0.663884i) q^{42} -0.814988i q^{43} +(2.85409 - 0.657923i) q^{44} +(5.21664 - 4.21742i) q^{45} +(8.21081 + 2.35588i) q^{46} +(-6.63331 + 6.63331i) q^{47} +(-3.44875 - 6.00884i) q^{48} +5.33314i q^{49} +(-7.06915 + 0.164463i) q^{50} +(-2.40169 + 2.75228i) q^{51} +(-2.20703 + 3.52938i) q^{52} +7.26025 q^{53} +(-4.78850 - 5.57407i) q^{54} +(-3.17974 - 0.782718i) q^{55} +(-2.71495 + 2.44211i) q^{56} +(3.78596 - 4.33861i) q^{57} +(-1.42449 + 4.96470i) q^{58} +(-6.09835 + 6.09835i) q^{59} +(0.411275 + 7.73504i) q^{60} +(9.87198 + 9.87198i) q^{61} +(3.55472 + 6.41539i) q^{62} +(-2.34266 + 3.08442i) q^{63} +(7.95534 + 0.844133i) q^{64} +(3.98205 - 2.40887i) q^{65} +(-0.753050 + 3.50727i) q^{66} +10.8038i q^{67} +(-0.947466 - 4.11014i) q^{68} +(-6.87857 + 7.88268i) q^{69} +(3.94060 - 1.06780i) q^{70} -2.57569 q^{71} +(8.45608 - 0.703301i) q^{72} +(-7.40366 - 7.40366i) q^{73} +(7.46794 + 13.4778i) q^{74} +(3.49015 - 7.92584i) q^{75} +(1.49356 + 6.47909i) q^{76} +1.89073 q^{77} +(-2.76785 - 4.28139i) q^{78} -8.54920i q^{79} +(-7.51260 - 4.85395i) q^{80} +(8.66991 - 2.41509i) q^{81} +(-6.73632 - 12.1574i) q^{82} +11.5636i q^{83} +(-1.29808 - 4.27987i) q^{84} +(-1.12718 + 4.57909i) q^{85} +(-1.00815 + 0.558608i) q^{86} +(-4.76629 - 4.15916i) q^{87} +(-2.77011 - 3.07959i) q^{88} -9.67152i q^{89} +(-8.79259 - 3.56235i) q^{90} +(-1.90008 + 1.90008i) q^{91} +(-2.71359 - 11.7716i) q^{92} +(-8.96205 + 0.609625i) q^{93} +(12.7521 + 3.65889i) q^{94} +(1.77685 - 7.21834i) q^{95} +(-5.06917 + 8.38472i) q^{96} +(-6.58488 - 6.58488i) q^{97} +(6.59717 - 3.65544i) q^{98} +(-3.49869 - 2.65730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{10} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} - 4 q^{21} - 4 q^{22} + 12 q^{24} - 4 q^{27} - 4 q^{28} - 28 q^{30} - 16 q^{31} - 4 q^{33}+ \cdots + 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^10 - 8 * q^12 - 8 * q^13 - 4 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 - 4 * q^21 - 4 * q^22 + 12 * q^24 - 4 * q^27 - 4 * q^28 - 28 * q^30 - 16 * q^31 - 4 * q^33 - 28 * q^34 - 20 * q^36 - 8 * q^37 - 24 * q^39 - 44 * q^40 + 40 * q^42 + 8 * q^45 - 36 * q^46 + 32 * q^48 - 4 * q^51 - 48 * q^52 + 24 * q^54 - 12 * q^57 - 20 * q^58 + 28 * q^60 - 24 * q^61 - 32 * q^63 + 28 * q^64 + 12 * q^66 + 12 * q^69 - 76 * q^70 + 24 * q^72 - 36 * q^75 - 36 * q^76 + 60 * q^78 - 8 * q^81 + 64 * q^82 - 48 * q^84 + 16 * q^85 + 12 * q^87 + 44 * q^88 - 56 * q^90 - 8 * q^91 - 16 * q^93 + 20 * q^94 + 48 * q^96 - 8 * q^97 + 32 * q^99

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