LMFDB - Embedded newform 1155.2.l.f.1121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.3
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50847 q^{2} +(1.71957 - 0.207558i) q^{3} +4.29243 q^{4} +1.00000i q^{5} +(-4.31349 + 0.520654i) q^{6} +1.00000i q^{7} -5.75050 q^{8} +(2.91384 - 0.713822i) q^{9} +O(q^{10})$	\(q-2.50847 q^{2} +(1.71957 - 0.207558i) q^{3} +4.29243 q^{4} +1.00000i q^{5} +(-4.31349 + 0.520654i) q^{6} +1.00000i q^{7} -5.75050 q^{8} +(2.91384 - 0.713822i) q^{9} -2.50847i q^{10} +(3.26280 - 0.595079i) q^{11} +(7.38113 - 0.890930i) q^{12} +2.68588i q^{13} -2.50847i q^{14} +(0.207558 + 1.71957i) q^{15} +5.84011 q^{16} +1.44967 q^{17} +(-7.30928 + 1.79060i) q^{18} -7.09255i q^{19} +4.29243i q^{20} +(0.207558 + 1.71957i) q^{21} +(-8.18465 + 1.49274i) q^{22} +0.250518i q^{23} +(-9.88839 + 1.19356i) q^{24} -1.00000 q^{25} -6.73745i q^{26} +(4.86239 - 1.83226i) q^{27} +4.29243i q^{28} +4.88936 q^{29} +(-0.520654 - 4.31349i) q^{30} -4.26213 q^{31} -3.14874 q^{32} +(5.48710 - 1.70050i) q^{33} -3.63646 q^{34} -1.00000 q^{35} +(12.5075 - 3.06403i) q^{36} +7.50495 q^{37} +17.7915i q^{38} +(0.557477 + 4.61856i) q^{39} -5.75050i q^{40} +1.94404 q^{41} +(-0.520654 - 4.31349i) q^{42} +7.29209i q^{43} +(14.0054 - 2.55433i) q^{44} +(0.713822 + 2.91384i) q^{45} -0.628417i q^{46} -1.14684i q^{47} +(10.0425 - 1.21216i) q^{48} -1.00000 q^{49} +2.50847 q^{50} +(2.49281 - 0.300891i) q^{51} +11.5290i q^{52} +2.58049i q^{53} +(-12.1972 + 4.59617i) q^{54} +(0.595079 + 3.26280i) q^{55} -5.75050i q^{56} +(-1.47212 - 12.1961i) q^{57} -12.2648 q^{58} +11.7965i q^{59} +(0.890930 + 7.38113i) q^{60} -13.2914i q^{61} +10.6914 q^{62} +(0.713822 + 2.91384i) q^{63} -3.78168 q^{64} -2.68588 q^{65} +(-13.7642 + 4.26566i) q^{66} -5.66647 q^{67} +6.22261 q^{68} +(0.0519970 + 0.430783i) q^{69} +2.50847 q^{70} -4.04494i q^{71} +(-16.7560 + 4.10483i) q^{72} +0.248236i q^{73} -18.8260 q^{74} +(-1.71957 + 0.207558i) q^{75} -30.4443i q^{76} +(0.595079 + 3.26280i) q^{77} +(-1.39842 - 11.5855i) q^{78} +14.3043i q^{79} +5.84011i q^{80} +(7.98092 - 4.15993i) q^{81} -4.87656 q^{82} -3.49679 q^{83} +(0.890930 + 7.38113i) q^{84} +1.44967i q^{85} -18.2920i q^{86} +(8.40759 - 1.01483i) q^{87} +(-18.7627 + 3.42200i) q^{88} -11.0019i q^{89} +(-1.79060 - 7.30928i) q^{90} -2.68588 q^{91} +1.07533i q^{92} +(-7.32904 + 0.884642i) q^{93} +2.87683i q^{94} +7.09255 q^{95} +(-5.41448 + 0.653547i) q^{96} -2.11638 q^{97} +2.50847 q^{98} +(9.08250 - 4.06302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−2.50847			−1.77376			−0.886879	−	0.462002i	$-0.847131\pi$
$2$	−2.50847			−1.77376			−0.886879	+	0.462002i	$0.847131\pi$
$3$	1.71957	−	0.207558i	0.992794	−	0.119834i
$3$	1.71957	−	0.207558i	0.992794	−	0.119834i
$4$	4.29243			2.14622
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−4.31349	+	0.520654i	−1.76098	+	0.212556i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−5.75050			−2.03311
$9$	2.91384	−	0.713822i	0.971280	−	0.237941i
$10$		−	2.50847i		−	0.793248i
$11$	3.26280	−	0.595079i	0.983772	−	0.179423i
$11$	3.26280	−	0.595079i	0.983772	−	0.179423i
$12$	7.38113	−	0.890930i	2.13075	−	0.257189i
$13$			2.68588i			0.744929i	0.928046	+	0.372465i	$0.121487\pi$
$13$			2.68588i			0.744929i	−0.928046	+	0.372465i	$0.878513\pi$
$14$		−	2.50847i		−	0.670417i
$15$	0.207558	+	1.71957i	0.0535913	+	0.443991i
$16$	5.84011			1.46003
$17$	1.44967			0.351597			0.175798	−	0.984426i	$-0.443749\pi$
$17$	1.44967			0.351597			0.175798	+	0.984426i	$0.443749\pi$
$18$	−7.30928	+	1.79060i	−1.72281	+	0.422049i
$19$		−	7.09255i		−	1.62714i	−0.581465	−	0.813572i	$-0.697520\pi$
$19$		−	7.09255i		−	1.62714i	0.581465	−	0.813572i	$-0.302480\pi$
$20$			4.29243i			0.959817i
$21$	0.207558	+	1.71957i	0.0452929	+	0.375241i
$22$	−8.18465	+	1.49274i	−1.74497	+	0.318253i
$23$			0.250518i			0.0522365i	0.999659	+	0.0261183i	$0.00831465\pi$
$23$			0.250518i			0.0522365i	−0.999659	+	0.0261183i	$0.991685\pi$
$24$	−9.88839	+	1.19356i	−2.01846	+	0.243635i
$25$	−1.00000			−0.200000
$26$		−	6.73745i		−	1.32132i
$27$	4.86239	−	1.83226i	0.935767	−	0.352618i
$28$			4.29243i			0.811193i
$29$	4.88936			0.907931			0.453965	−	0.891019i	$-0.350009\pi$
$29$	4.88936			0.907931			0.453965	+	0.891019i	$0.350009\pi$
$30$	−0.520654	−	4.31349i	−0.0950580	−	0.787532i
$31$	−4.26213			−0.765502			−0.382751	−	0.923852i	$-0.625023\pi$
$31$	−4.26213			−0.765502			−0.382751	+	0.923852i	$0.625023\pi$
$32$	−3.14874			−0.556624
$33$	5.48710	−	1.70050i	0.955182	−	0.296019i
$34$	−3.63646			−0.623647
$35$	−1.00000			−0.169031
$36$	12.5075	−	3.06403i	2.08458	−	0.510672i
$37$	7.50495			1.23381			0.616903	−	0.787039i	$-0.288387\pi$
$37$	7.50495			1.23381			0.616903	+	0.787039i	$0.288387\pi$
$38$			17.7915i			2.88616i
$39$	0.557477	+	4.61856i	0.0892677	+	0.739561i
$40$		−	5.75050i		−	0.909234i
$41$	1.94404			0.303608			0.151804	−	0.988411i	$-0.451492\pi$
$41$	1.94404			0.303608			0.151804	+	0.988411i	$0.451492\pi$
$42$	−0.520654	−	4.31349i	−0.0803387	−	0.665586i
$43$			7.29209i			1.11203i	0.831171	+	0.556016i	$0.187671\pi$
$43$			7.29209i			1.11203i	−0.831171	+	0.556016i	$0.812329\pi$
$44$	14.0054	−	2.55433i	2.11139	−	0.385080i
$45$	0.713822	+	2.91384i	0.106410	+	0.434369i
$46$		−	0.628417i		−	0.0926550i
$47$		−	1.14684i		−	0.167284i	−0.996496	−	0.0836422i	$-0.973345\pi$
$47$		−	1.14684i		−	0.167284i	0.996496	−	0.0836422i	$-0.0266553\pi$
$48$	10.0425	−	1.21216i	1.44951	−	0.174961i
$49$	−1.00000			−0.142857
$50$	2.50847			0.354752
$51$	2.49281	−	0.300891i	0.349063	−	0.0421332i
$52$			11.5290i			1.59878i
$53$			2.58049i			0.354458i	0.984170	+	0.177229i	$0.0567133\pi$
$53$			2.58049i			0.354458i	−0.984170	+	0.177229i	$0.943287\pi$
$54$	−12.1972	+	4.59617i	−1.65982	+	0.625459i
$55$	0.595079	+	3.26280i	0.0802404	+	0.439956i
$56$		−	5.75050i		−	0.768443i
$57$	−1.47212	−	12.1961i	−0.194987	−	1.61542i
$58$	−12.2648			−1.61045
$59$			11.7965i			1.53577i	0.640587	+	0.767886i	$0.278691\pi$
$59$			11.7965i			1.53577i	−0.640587	+	0.767886i	$0.721309\pi$
$60$	0.890930	+	7.38113i	0.115019	+	0.952900i
$61$		−	13.2914i		−	1.70179i	−0.525336	−	0.850895i	$-0.676060\pi$
$61$		−	13.2914i		−	1.70179i	0.525336	−	0.850895i	$-0.323940\pi$
$62$	10.6914			1.35781
$63$	0.713822	+	2.91384i	0.0899331	+	0.367109i
$64$	−3.78168			−0.472711
$65$	−2.68588			−0.333142
$66$	−13.7642	+	4.26566i	−1.69426	+	0.525066i
$67$	−5.66647			−0.692270			−0.346135	−	0.938185i	$-0.612506\pi$
$67$	−5.66647			−0.692270			−0.346135	+	0.938185i	$0.612506\pi$
$68$	6.22261			0.754603
$69$	0.0519970	+	0.430783i	0.00625971	+	0.0518601i
$70$	2.50847			0.299820
$71$		−	4.04494i		−	0.480047i	−0.970767	−	0.240023i	$-0.922845\pi$
$71$		−	4.04494i		−	0.480047i	0.970767	−	0.240023i	$-0.0771551\pi$
$72$	−16.7560	+	4.10483i	−1.97472	+	0.483759i
$73$			0.248236i			0.0290538i	0.999894	+	0.0145269i	$0.00462422\pi$
$73$			0.248236i			0.0290538i	−0.999894	+	0.0145269i	$0.995376\pi$
$74$	−18.8260			−2.18847
$75$	−1.71957	+	0.207558i	−0.198559	+	0.0239668i
$76$		−	30.4443i		−	3.49220i
$77$	0.595079	+	3.26280i	0.0678155	+	0.371831i
$78$	−1.39842	−	11.5855i	−0.158339	−	1.31180i
$79$			14.3043i			1.60936i	0.593710	+	0.804679i	$0.297662\pi$
$79$			14.3043i			1.60936i	−0.593710	+	0.804679i	$0.702338\pi$
$80$			5.84011i			0.652944i
$81$	7.98092	−	4.15993i	0.886768	−	0.462214i
$82$	−4.87656			−0.538526
$83$	−3.49679			−0.383822			−0.191911	−	0.981412i	$-0.561469\pi$
$83$	−3.49679			−0.383822			−0.191911	+	0.981412i	$0.561469\pi$
$84$	0.890930	+	7.38113i	0.0972084	+	0.805348i
$85$			1.44967i			0.157239i
$86$		−	18.2920i		−	1.97248i
$87$	8.40759	−	1.01483i	0.901388	−	0.108801i
$88$	−18.7627	+	3.42200i	−2.00012	+	0.364786i
$89$		−	11.0019i		−	1.16619i	−0.812402	−	0.583097i	$-0.801841\pi$
$89$		−	11.0019i		−	1.16619i	0.812402	−	0.583097i	$-0.198159\pi$
$90$	−1.79060	−	7.30928i	−0.188746	−	0.770466i
$91$	−2.68588			−0.281557
$92$			1.07533i			0.112111i
$93$	−7.32904	+	0.884642i	−0.759986	+	0.0917331i
$94$			2.87683i			0.296722i
$95$	7.09255			0.727681
$96$	−5.41448	+	0.653547i	−0.552613	+	0.0667024i
$97$	−2.11638			−0.214886			−0.107443	−	0.994211i	$-0.534266\pi$
$97$	−2.11638			−0.214886			−0.107443	+	0.994211i	$0.534266\pi$
$98$	2.50847			0.253394
$99$	9.08250	−	4.06302i	0.912826	−	0.408349i
$100$	−4.29243			−0.429243
$101$	−2.83756			−0.282348			−0.141174	−	0.989985i	$-0.545088\pi$
$101$	−2.83756			−0.282348			−0.141174	+	0.989985i	$0.545088\pi$
$102$	−6.25314	+	0.754777i	−0.619153	+	0.0747341i
$103$	17.6307			1.73721			0.868604	−	0.495506i	$-0.165018\pi$
$103$	17.6307			1.73721			0.868604	+	0.495506i	$0.165018\pi$
$104$		−	15.4452i		−	1.51452i
$105$	−1.71957	+	0.207558i	−0.167813	+	0.0202556i
$106$		−	6.47309i		−	0.628722i
$107$	−11.0415			−1.06742			−0.533712	−	0.845666i	$-0.679203\pi$
$107$	−11.0415			−1.06742			−0.533712	+	0.845666i	$0.679203\pi$
$108$	20.8715	−	7.86484i	2.00836	−	0.756795i
$109$			13.7920i			1.32104i	0.750811	+	0.660518i	$0.229663\pi$
$109$			13.7920i			1.32104i	−0.750811	+	0.660518i	$0.770337\pi$
$110$	−1.49274	−	8.18465i	−0.142327	−	0.780376i
$111$	12.9053	−	1.55772i	1.22492	−	0.147852i
$112$			5.84011i			0.551838i
$113$			15.6587i			1.47305i	0.676413	+	0.736523i	$0.263533\pi$
$113$			15.6587i			1.47305i	−0.676413	+	0.736523i	$0.736467\pi$
$114$	3.69277	+	30.5937i	0.345860	+	2.86536i
$115$	−0.250518			−0.0233609
$116$	20.9872			1.94861
$117$	1.91724	+	7.82622i	0.177249	+	0.723535i
$118$		−	29.5912i		−	2.72409i
$119$			1.44967i			0.132891i
$120$	−1.19356	−	9.88839i	−0.108957	−	0.902682i
$121$	10.2918	−	3.88325i	0.935615	−	0.353023i
$122$			33.3411i			3.01856i
$123$	3.34291	−	0.403501i	0.301420	−	0.0363825i
$124$	−18.2949			−1.64293
$125$		−	1.00000i		−	0.0894427i
$126$	−1.79060	−	7.30928i	−0.159520	−	0.651163i
$127$			9.71047i			0.861665i	0.902432	+	0.430832i	$0.141780\pi$
$127$			9.71047i			0.861665i	−0.902432	+	0.430832i	$0.858220\pi$
$128$	15.7837			1.39510
$129$	1.51353	+	12.5392i	0.133259	+	1.10402i
$130$	6.73745			0.590914
$131$	19.8187			1.73157			0.865785	−	0.500416i	$-0.166820\pi$
$131$	19.8187			1.73157			0.865785	+	0.500416i	$0.166820\pi$
$132$	23.5530	−	7.29929i	2.05003	−	0.635321i
$133$	7.09255			0.615002
$134$	14.2142			1.22792
$135$	1.83226	+	4.86239i	0.157696	+	0.418488i
$136$	−8.33633			−0.714834
$137$		−	16.1946i		−	1.38360i	−0.722090	−	0.691799i	$-0.756819\pi$
$137$		−	16.1946i		−	1.38360i	0.722090	−	0.691799i	$-0.243181\pi$
$138$	−0.130433	−	1.08061i	−0.0111032	−	0.0919873i
$139$		−	4.98300i		−	0.422652i	−0.977416	−	0.211326i	$-0.932222\pi$
$139$		−	4.98300i		−	0.422652i	0.977416	−	0.211326i	$-0.0677782\pi$
$140$	−4.29243			−0.362777
$141$	−0.238037	−	1.97208i	−0.0200463	−	0.166079i
$142$			10.1466i			0.851486i
$143$	1.59831	+	8.76350i	0.133657	+	0.732840i
$144$	17.0171	−	4.16880i	1.41809	−	0.347400i
$145$			4.88936i			0.406039i
$146$		−	0.622692i		−	0.0515344i
$147$	−1.71957	+	0.207558i	−0.141828	+	0.0171191i
$148$	32.2145			2.64801
$149$	2.67404			0.219066			0.109533	−	0.993983i	$-0.465064\pi$
$149$	2.67404			0.219066			0.109533	+	0.993983i	$0.465064\pi$
$150$	4.31349	−	0.520654i	0.352195	−	0.0425112i
$151$		−	3.80740i		−	0.309841i	−0.987927	−	0.154921i	$-0.950488\pi$
$151$		−	3.80740i		−	0.309841i	0.987927	−	0.154921i	$-0.0495122\pi$
$152$			40.7857i			3.30816i
$153$	4.22411	−	1.03481i	0.341499	−	0.0836592i
$154$	−1.49274	−	8.18465i	−0.120288	−	0.659538i
$155$		−	4.26213i		−	0.342343i
$156$	2.39293	+	19.8248i	0.191588	+	1.58726i
$157$	3.66952			0.292860			0.146430	−	0.989221i	$-0.453222\pi$
$157$	3.66952			0.292860			0.146430	+	0.989221i	$0.453222\pi$
$158$		−	35.8819i		−	2.85461i
$159$	0.535603	+	4.43734i	0.0424761	+	0.351904i
$160$		−	3.14874i		−	0.248930i
$161$	−0.250518			−0.0197436
$162$	−20.0199	+	10.4351i	−1.57291	+	0.819855i
$163$	−18.6555			−1.46121			−0.730605	−	0.682800i	$-0.760762\pi$
$163$	−18.6555			−1.46121			−0.730605	+	0.682800i	$0.760762\pi$
$164$	8.34465			0.651608
$165$	1.70050	+	5.48710i	0.132384	+	0.427170i
$166$	8.77160			0.680808
$167$	20.9675			1.62252			0.811258	−	0.584688i	$-0.198783\pi$
$167$	20.9675			1.62252			0.811258	+	0.584688i	$0.198783\pi$
$168$	−1.19356	−	9.88839i	−0.0920855	−	0.762905i
$169$	5.78605			0.445081
$170$		−	3.63646i		−	0.278904i
$171$	−5.06282	−	20.6666i	−0.387164	−	1.58041i
$172$			31.3008i			2.38666i
$173$	−11.8304			−0.899445			−0.449723	−	0.893168i	$-0.648477\pi$
$173$	−11.8304			−0.899445			−0.449723	+	0.893168i	$0.648477\pi$
$174$	−21.0902	+	2.54566i	−1.59884	+	0.192986i
$175$		−	1.00000i		−	0.0755929i
$176$	19.0551	−	3.47532i	1.43633	−	0.261962i
$177$	2.44846	+	20.2849i	0.184037	+	1.52470i
$178$			27.5979i			2.06855i
$179$		−	21.1328i		−	1.57954i	−0.613402	−	0.789771i	$-0.710199\pi$
$179$		−	21.1328i		−	1.57954i	0.613402	−	0.789771i	$-0.289801\pi$
$180$	3.06403	+	12.5075i	0.228379	+	0.932251i
$181$	16.6359			1.23654			0.618268	−	0.785968i	$-0.287835\pi$
$181$	16.6359			1.23654			0.618268	+	0.785968i	$0.287835\pi$
$182$	6.73745			0.499413
$183$	−2.75874	−	22.8555i	−0.203932	−	1.68953i
$184$		−	1.44060i		−	0.106203i
$185$			7.50495i			0.551775i
$186$	18.3847	−	2.21910i	1.34803	−	0.162712i
$187$	4.72999	−	0.862668i	0.345891	−	0.0630845i
$188$		−	4.92275i		−	0.359029i
$189$	1.83226	+	4.86239i	0.133277	+	0.353687i
$190$	−17.7915			−1.29073
$191$			25.0566i			1.81303i	0.422171	+	0.906516i	$0.361268\pi$
$191$			25.0566i			1.81303i	−0.422171	+	0.906516i	$0.638732\pi$
$192$	−6.50287	+	0.784920i	−0.469304	+	0.0566467i
$193$			13.7658i			0.990882i	0.868642	+	0.495441i	$0.164994\pi$
$193$			13.7658i			0.990882i	−0.868642	+	0.495441i	$0.835006\pi$
$194$	5.30888			0.381155
$195$	−4.61856	+	0.557477i	−0.330742	+	0.0399217i
$196$	−4.29243			−0.306602
$197$	−1.57492			−0.112209			−0.0561044	−	0.998425i	$-0.517868\pi$
$197$	−1.57492			−0.112209			−0.0561044	+	0.998425i	$0.517868\pi$
$198$	−22.7832	+	10.1920i	−1.61913	+	0.724313i
$199$	13.8639			0.982788			0.491394	−	0.870937i	$-0.336487\pi$
$199$	13.8639			0.982788			0.491394	+	0.870937i	$0.336487\pi$
$200$	5.75050			0.406622
$201$	−9.74389	+	1.17612i	−0.687281	+	0.0829573i
$202$	7.11793			0.500816
$203$			4.88936i			0.343165i
$204$	10.7002	−	1.29156i	0.749165	−	0.0904269i
$205$			1.94404i			0.135777i
$206$	−44.2262			−3.08139
$207$	0.178825	+	0.729968i	0.0124292	+	0.0507363i
$208$			15.6858i			1.08762i
$209$	−4.22063	−	23.1416i	−0.291947	−	1.60074i
$210$	4.31349	−	0.520654i	0.297659	−	0.0359286i
$211$		−	17.1325i		−	1.17945i	−0.807604	−	0.589725i	$-0.799236\pi$
$211$		−	17.1325i		−	1.17945i	0.807604	−	0.589725i	$-0.200764\pi$
$212$			11.0766i			0.760743i
$213$	−0.839562	−	6.95556i	−0.0575258	−	0.476587i
$214$	27.6973			1.89335
$215$	−7.29209			−0.497316
$216$	−27.9612	+	10.5364i	−1.90252	+	0.716911i
$217$		−	4.26213i		−	0.289333i
$218$		−	34.5969i		−	2.34320i
$219$	0.0515234	+	0.426858i	0.00348163	+	0.0288444i
$220$	2.55433	+	14.0054i	0.172213	+	0.944241i
$221$			3.89364i			0.261915i
$222$	−32.3725	+	3.90749i	−2.17270	+	0.262253i
$223$	−14.4492			−0.967593			−0.483797	−	0.875181i	$-0.660743\pi$
$223$	−14.4492			−0.967593			−0.483797	+	0.875181i	$0.660743\pi$
$224$		−	3.14874i		−	0.210384i
$225$	−2.91384	+	0.713822i	−0.194256	+	0.0475881i
$226$		−	39.2794i		−	2.61282i
$227$	−18.7742			−1.24609			−0.623043	−	0.782187i	$-0.714104\pi$
$227$	−18.7742			−1.24609			−0.623043	+	0.782187i	$0.714104\pi$
$228$	−6.31897	−	52.3511i	−0.418484	−	3.46704i
$229$	−10.4680			−0.691746			−0.345873	−	0.938281i	$-0.612417\pi$
$229$	−10.4680			−0.691746			−0.345873	+	0.938281i	$0.612417\pi$
$230$	0.628417			0.0414366
$231$	1.70050	+	5.48710i	0.111885	+	0.361025i
$232$	−28.1162			−1.84592
$233$	−3.22233			−0.211102			−0.105551	−	0.994414i	$-0.533661\pi$
$233$	−3.22233			−0.211102			−0.105551	+	0.994414i	$0.533661\pi$
$234$	−4.80934	−	19.6319i	−0.314397	−	1.28337i
$235$	1.14684			0.0748119
$236$			50.6356i			3.29610i
$237$	2.96897	+	24.5972i	0.192856	+	1.59776i
$238$		−	3.63646i		−	0.235717i
$239$	−10.4063			−0.673128			−0.336564	−	0.941661i	$-0.609265\pi$
$239$	−10.4063			−0.673128			−0.336564	+	0.941661i	$0.609265\pi$
$240$	1.21216	+	10.0425i	0.0782448	+	0.648238i
$241$		−	22.8403i		−	1.47127i	−0.677376	−	0.735637i	$-0.736883\pi$
$241$		−	22.8403i		−	1.47127i	0.677376	−	0.735637i	$-0.263117\pi$
$242$	−25.8166	+	9.74102i	−1.65955	+	0.626177i
$243$	12.8603	−	8.80979i	0.824989	−	0.565148i
$244$		−	57.0524i		−	3.65241i
$245$		−	1.00000i		−	0.0638877i
$246$	−8.38559	+	1.01217i	−0.534646	+	0.0645337i
$247$	19.0498			1.21211
$248$	24.5094			1.55635
$249$	−6.01297	+	0.725788i	−0.381057	+	0.0459949i
$250$			2.50847i			0.158650i
$251$			9.05738i			0.571697i	0.958275	+	0.285848i	$0.0922754\pi$
$251$			9.05738i			0.571697i	−0.958275	+	0.285848i	$0.907725\pi$
$252$	3.06403	+	12.5075i	0.193016	+	0.787896i
$253$	0.149078	+	0.817390i	0.00937244	+	0.0513889i
$254$		−	24.3584i		−	1.52838i
$255$	0.300891	+	2.49281i	0.0188425	+	0.156106i
$256$	−32.0297			−2.00185
$257$		−	10.8959i		−	0.679665i	−0.940486	−	0.339832i	$-0.889630\pi$
$257$		−	10.8959i		−	0.679665i	0.940486	−	0.339832i	$-0.110370\pi$
$258$	−3.79666	−	31.4544i	−0.236369	−	1.95826i
$259$			7.50495i			0.466335i
$260$	−11.5290			−0.714996
$261$	14.2468	−	3.49013i	0.881854	−	0.216034i
$262$	−49.7147			−3.07139
$263$	−10.7666			−0.663896			−0.331948	−	0.943298i	$-0.607706\pi$
$263$	−10.7666			−0.663896			−0.331948	+	0.943298i	$0.607706\pi$
$264$	−31.5536	+	9.77873i	−1.94199	+	0.601839i
$265$	−2.58049			−0.158518
$266$	−17.7915			−1.09087
$267$	−2.28353	−	18.9185i	−0.139750	−	1.15779i
$268$	−24.3229			−1.48576
$269$			4.98201i			0.303758i	0.988399	+	0.151879i	$0.0485325\pi$
$269$			4.98201i			0.303758i	−0.988399	+	0.151879i	$0.951468\pi$
$270$	−4.59617	−	12.1972i	−0.279714	−	0.742296i
$271$			2.07649i			0.126138i	0.998009	+	0.0630690i	$0.0200888\pi$
$271$			2.07649i			0.126138i	−0.998009	+	0.0630690i	$0.979911\pi$
$272$	8.46623			0.513341
$273$	−4.61856	+	0.557477i	−0.279528	+	0.0337400i
$274$			40.6237i			2.45417i
$275$	−3.26280	+	0.595079i	−0.196754	+	0.0358846i
$276$	0.223194	+	1.84910i	0.0134347	+	0.111303i
$277$		−	20.3297i		−	1.22150i	−0.791825	−	0.610748i	$-0.790869\pi$
$277$		−	20.3297i		−	1.22150i	0.791825	−	0.610748i	$-0.209131\pi$
$278$			12.4997i			0.749683i
$279$	−12.4192	+	3.04241i	−0.743517	+	0.182144i
$280$	5.75050			0.343658
$281$	−13.0224			−0.776853			−0.388426	−	0.921480i	$-0.626981\pi$
$281$	−13.0224			−0.776853			−0.388426	+	0.921480i	$0.626981\pi$
$282$	0.597110	+	4.94691i	0.0355574	+	0.294584i
$283$		−	2.71534i		−	0.161410i	−0.996738	−	0.0807052i	$-0.974283\pi$
$283$		−	2.71534i		−	0.161410i	0.996738	−	0.0807052i	$-0.0257172\pi$
$284$		−	17.3626i		−	1.03028i
$285$	12.1961	−	1.47212i	0.722437	−	0.0872008i
$286$	−4.00932	−	21.9830i	−0.237076	−	1.29988i
$287$			1.94404i			0.114753i
$288$	−9.17492	+	2.24764i	−0.540637	+	0.132443i
$289$	−14.8985			−0.876380
$290$		−	12.2648i		−	0.720215i
$291$	−3.63926	+	0.439272i	−0.213337	+	0.0257506i
$292$			1.06553i			0.0623557i
$293$	−2.56104			−0.149617			−0.0748087	−	0.997198i	$-0.523835\pi$
$293$	−2.56104			−0.149617			−0.0748087	+	0.997198i	$0.523835\pi$
$294$	4.31349	−	0.520654i	0.251568	−	0.0303652i
$295$	−11.7965			−0.686818
$296$	−43.1572			−2.50846
$297$	14.7747	−	8.87180i	0.857314	−	0.514794i
$298$	−6.70776			−0.388570
$299$	−0.672860			−0.0389125
$300$	−7.38113	+	0.890930i	−0.426150	+	0.0514379i
$301$	−7.29209			−0.420309
$302$			9.55075i			0.549584i
$303$	−4.87938	+	0.588959i	−0.280313	+	0.0338348i
$304$		−	41.4213i		−	2.37567i
$305$	13.2914			0.761064
$306$	−10.5961	+	2.59578i	−0.605736	+	0.148391i
$307$		−	15.7629i		−	0.899634i	−0.893121	−	0.449817i	$-0.851489\pi$
$307$		−	15.7629i		−	0.899634i	0.893121	−	0.449817i	$-0.148511\pi$
$308$	2.55433	+	14.0054i	0.145547	+	0.798029i
$309$	30.3173	−	3.65941i	1.72469	−	0.208176i
$310$			10.6914i			0.607233i
$311$			22.0502i			1.25035i	0.780485	+	0.625175i	$0.214972\pi$
$311$			22.0502i			1.25035i	−0.780485	+	0.625175i	$0.785028\pi$
$312$	−3.20577	−	26.5590i	−0.181491	−	1.50361i
$313$	12.1670			0.687717			0.343858	−	0.939022i	$-0.388266\pi$
$313$	12.1670			0.687717			0.343858	+	0.939022i	$0.388266\pi$
$314$	−9.20489			−0.519462
$315$	−2.91384	+	0.713822i	−0.164176	+	0.0402193i
$316$			61.4002i			3.45403i
$317$		−	12.5163i		−	0.702984i	−0.936191	−	0.351492i	$-0.885674\pi$
$317$		−	12.5163i		−	0.702984i	0.936191	−	0.351492i	$-0.114326\pi$
$318$	−1.34354	−	11.1309i	−0.0753422	−	0.624192i
$319$	15.9530	−	2.90955i	0.893197	−	0.162904i
$320$		−	3.78168i		−	0.211403i
$321$	−18.9867	+	2.29176i	−1.05973	+	0.127913i
$322$	0.628417			0.0350203
$323$		−	10.2819i		−	0.572098i
$324$	34.2575	−	17.8562i	1.90320	−	0.992011i
$325$		−	2.68588i		−	0.148986i
$326$	46.7968			2.59183
$327$	2.86265	+	23.7163i	0.158305	+	1.31152i
$328$	−11.1792			−0.617267
$329$	1.14684			0.0632276
$330$	−4.26566	−	13.7642i	−0.234817	−	0.757697i
$331$	−1.89425			−0.104117			−0.0520586	−	0.998644i	$-0.516578\pi$
$331$	−1.89425			−0.104117			−0.0520586	+	0.998644i	$0.516578\pi$
$332$	−15.0097			−0.823766
$333$	21.8682	−	5.35720i	1.19837	−	0.293573i
$334$	−52.5965			−2.87795
$335$		−	5.66647i		−	0.309592i
$336$	1.21216	+	10.0425i	0.0661289	+	0.547862i
$337$			5.71137i			0.311118i	0.987827	+	0.155559i	$0.0497179\pi$
$337$			5.71137i			0.311118i	−0.987827	+	0.155559i	$0.950282\pi$
$338$	−14.5141			−0.789465
$339$	3.25009	+	26.9262i	0.176521	+	1.46243i
$340$			6.22261i			0.337469i
$341$	−13.9065	+	2.53631i	−0.753079	+	0.137349i
$342$	12.6999	+	51.8415i	0.686734	+	2.80327i
$343$		−	1.00000i		−	0.0539949i
$344$		−	41.9331i		−	2.26088i
$345$	−0.430783	+	0.0519970i	−0.0231926	+	0.00279943i
$346$	29.6761			1.59540
$347$	−22.4093			−1.20299			−0.601496	−	0.798876i	$-0.705429\pi$
$347$	−22.4093			−1.20299			−0.601496	+	0.798876i	$0.705429\pi$
$348$	36.0890	−	4.35607i	1.93457	−	0.233510i
$349$			25.7825i			1.38011i	0.723759	+	0.690053i	$0.242413\pi$
$349$			25.7825i			1.38011i	−0.723759	+	0.690053i	$0.757587\pi$
$350$			2.50847i			0.134083i
$351$	4.92123	+	13.0598i	0.262676	+	0.697080i
$352$	−10.2737	+	1.87375i	−0.547591	+	0.0998711i
$353$			18.6096i			0.990491i	0.868753	+	0.495245i	$0.164922\pi$
$353$			18.6096i			0.990491i	−0.868753	+	0.495245i	$0.835078\pi$
$354$	−6.14189	−	50.8840i	−0.326438	−	2.70446i
$355$	4.04494			0.214683
$356$		−	47.2247i		−	2.50291i
$357$	0.300891	+	2.49281i	0.0159249	+	0.131933i
$358$			53.0111i			2.80172i
$359$	−23.6464			−1.24801			−0.624004	−	0.781421i	$-0.714495\pi$
$359$	−23.6464			−1.24801			−0.624004	+	0.781421i	$0.714495\pi$
$360$	−4.10483	−	16.7560i	−0.216344	−	0.883120i
$361$	−31.3043			−1.64760
$362$	−41.7307			−2.19331
$363$	16.8914	−	8.81366i	0.886569	−	0.462597i
$364$	−11.5290			−0.604282
$365$	−0.248236			−0.0129932
$366$	6.92023	+	57.3324i	0.361726	+	2.99681i
$367$	−30.6598			−1.60043			−0.800214	−	0.599715i	$-0.795281\pi$
$367$	−30.6598			−1.60043			−0.800214	+	0.599715i	$0.795281\pi$
$368$			1.46305i			0.0762667i
$369$	5.66461	−	1.38770i	0.294888	−	0.0722406i
$370$		−	18.8260i		−	0.978715i
$371$	−2.58049			−0.133972
$372$	−31.4594	+	3.79726i	−1.63109	+	0.196879i
$373$		−	1.91693i		−	0.0992550i	−0.998768	−	0.0496275i	$-0.984197\pi$
$373$		−	1.91693i		−	0.0992550i	0.998768	−	0.0496275i	$-0.0158034\pi$
$374$	−11.8650	+	2.16398i	−0.613527	+	0.111897i
$375$	−0.207558	−	1.71957i	−0.0107183	−	0.0887982i
$376$			6.59493i			0.340108i
$377$			13.1322i			0.676344i
$378$	−4.59617	−	12.1972i	−0.236401	−	0.627355i
$379$	−16.0365			−0.823739			−0.411869	−	0.911243i	$-0.635124\pi$
$379$	−16.0365			−0.823739			−0.411869	+	0.911243i	$0.635124\pi$
$380$	30.4443			1.56176
$381$	2.01549	+	16.6978i	0.103257	+	0.855455i
$382$		−	62.8538i		−	3.21588i
$383$		−	19.4876i		−	0.995769i	−0.867243	−	0.497885i	$-0.834110\pi$
$383$		−	19.4876i		−	0.995769i	0.867243	−	0.497885i	$-0.165890\pi$
$384$	27.1412	−	3.27605i	1.38504	−	0.167180i
$385$	−3.26280	+	0.595079i	−0.166288	+	0.0303280i
$386$		−	34.5311i		−	1.75758i
$387$	5.20525	+	21.2480i	0.264598	+	1.08009i
$388$	−9.08442			−0.461191
$389$			24.7426i			1.25450i	0.778818	+	0.627250i	$0.215820\pi$
$389$			24.7426i			1.25450i	−0.778818	+	0.627250i	$0.784180\pi$
$390$	11.5855	−	1.39842i	0.586656	−	0.0708115i
$391$			0.363168i			0.0183662i
$392$	5.75050			0.290444
$393$	34.0797	−	4.11354i	1.71909	−	0.207501i
$394$	3.95066			0.199031
$395$	−14.3043			−0.719727
$396$	38.9860	−	17.4403i	1.95912	−	0.876406i
$397$	8.78434			0.440874			0.220437	−	0.975401i	$-0.429252\pi$
$397$	8.78434			0.440874			0.220437	+	0.975401i	$0.429252\pi$
$398$	−34.7773			−1.74323
$399$	12.1961	−	1.47212i	0.610571	−	0.0736981i
$400$	−5.84011			−0.292005
$401$		−	32.3374i		−	1.61485i	−0.589967	−	0.807427i	$-0.700859\pi$
$401$		−	32.3374i		−	1.61485i	0.589967	−	0.807427i	$-0.299141\pi$
$402$	24.4423	−	2.95027i	1.21907	−	0.147146i
$403$		−	11.4476i		−	0.570245i
$404$	−12.1800			−0.605979
$405$	4.15993	+	7.98092i	0.206708	+	0.396575i
$406$		−	12.2648i		−	0.608692i
$407$	24.4872	−	4.46604i	1.21378	−	0.221373i
$408$	−14.3349	+	1.73028i	−0.709683	+	0.0856614i
$409$			10.1943i			0.504076i	0.967717	+	0.252038i	$0.0811008\pi$
$409$			10.1943i			0.504076i	−0.967717	+	0.252038i	$0.918899\pi$
$410$		−	4.87656i		−	0.240836i
$411$	−3.36132	−	27.8477i	−0.165802	−	1.37363i
$412$	75.6787			3.72842
$413$	−11.7965			−0.580467
$414$	−0.448578	−	1.83110i	−0.0220464	−	0.0899939i
$415$		−	3.49679i		−	0.171651i
$416$		−	8.45714i		−	0.414645i
$417$	−1.03426	−	8.56861i	−0.0506481	−	0.419607i
$418$	10.5873	+	58.0501i	0.517843	+	2.83932i
$419$			16.1021i			0.786641i	0.919401	+	0.393321i	$0.128674\pi$
$419$			16.1021i			0.786641i	−0.919401	+	0.393321i	$0.871326\pi$
$420$	−7.38113	+	0.890930i	−0.360162	+	0.0434729i
$421$	8.86925			0.432261			0.216130	−	0.976365i	$-0.430656\pi$
$421$	8.86925			0.432261			0.216130	+	0.976365i	$0.430656\pi$
$422$			42.9764i			2.09206i
$423$	−0.818643	−	3.34172i	−0.0398038	−	0.162480i
$424$		−	14.8391i		−	0.720651i
$425$	−1.44967			−0.0703194
$426$	2.10602	+	17.4478i	0.102037	+	0.845350i
$427$	13.2914			0.643216
$428$	−47.3949			−2.29092
$429$	4.56734	+	14.7377i	0.220513	+	0.711543i
$430$	18.2920			0.882118
$431$	1.42921			0.0688424			0.0344212	−	0.999407i	$-0.489041\pi$
$431$	1.42921			0.0688424			0.0344212	+	0.999407i	$0.489041\pi$
$432$	28.3969	−	10.7006i	1.36624	−	0.514832i
$433$	−33.4982			−1.60982			−0.804909	−	0.593398i	$-0.797786\pi$
$433$	−33.4982			−1.60982			−0.804909	+	0.593398i	$0.797786\pi$
$434$			10.6914i			0.513206i
$435$	1.01483	+	8.40759i	0.0486572	+	0.403113i
$436$			59.2013i			2.83523i
$437$	1.77681			0.0849964
$438$	−0.129245	−	1.07076i	−0.00617556	−	0.0511630i
$439$			12.2749i			0.585849i	0.956136	+	0.292925i	$0.0946285\pi$
$439$			12.2749i			0.585849i	−0.956136	+	0.292925i	$0.905372\pi$
$440$	−3.42200	−	18.7627i	−0.163137	−	0.894479i
$441$	−2.91384	+	0.713822i	−0.138754	+	0.0339915i
$442$		−	9.76709i		−	0.464573i
$443$		−	13.8146i		−	0.656353i	−0.944616	−	0.328176i	$-0.893566\pi$
$443$		−	13.8146i		−	0.656353i	0.944616	−	0.328176i	$-0.106434\pi$
$444$	55.3951	−	6.68639i	2.62893	−	0.317322i
$445$	11.0019			0.521538
$446$	36.2455			1.71628
$447$	4.59820	−	0.555020i	0.217487	−	0.0262515i
$448$		−	3.78168i		−	0.178668i
$449$		−	39.6878i		−	1.87298i	−0.350688	−	0.936492i	$-0.614052\pi$
$449$		−	39.6878i		−	1.87298i	0.350688	−	0.936492i	$-0.385948\pi$
$450$	7.30928	−	1.79060i	0.344563	−	0.0844098i
$451$	6.34301	−	1.15686i	0.298681	−	0.0544742i
$452$			67.2138i			3.16147i
$453$	−0.790257	−	6.54708i	−0.0371295	−	0.307609i
$454$	47.0945			2.21026
$455$		−	2.68588i		−	0.125916i
$456$	8.46542	+	70.1339i	0.396430	+	3.28432i
$457$		−	40.2033i		−	1.88063i	−0.340304	−	0.940315i	$-0.610530\pi$
$457$		−	40.2033i		−	1.88063i	0.340304	−	0.940315i	$-0.389470\pi$
$458$	26.2587			1.22699
$459$	7.04886	−	2.65617i	0.329013	−	0.123979i
$460$	−1.07533			−0.0501375
$461$	−30.1028			−1.40203			−0.701013	−	0.713148i	$-0.747269\pi$
$461$	−30.1028			−1.40203			−0.701013	+	0.713148i	$0.747269\pi$
$462$	−4.26566	−	13.7642i	−0.198456	−	0.640371i
$463$	11.4031			0.529949			0.264975	−	0.964255i	$-0.414636\pi$
$463$	11.4031			0.529949			0.264975	+	0.964255i	$0.414636\pi$
$464$	28.5544			1.32560
$465$	−0.884642	−	7.32904i	−0.0410243	−	0.339876i
$466$	8.08313			0.374444
$467$		−	3.89223i		−	0.180111i	−0.995937	−	0.0900554i	$-0.971296\pi$
$467$		−	3.89223i		−	0.180111i	0.995937	−	0.0900554i	$-0.0287044\pi$
$468$	8.22962	+	33.5935i	0.380414	+	1.55286i
$469$		−	5.66647i		−	0.261653i
$470$	−2.87683			−0.132698
$471$	6.30999	−	0.761640i	0.290749	−	0.0350945i
$472$		−	67.8357i		−	3.12239i
$473$	4.33937	+	23.7926i	0.199524	+	1.09399i
$474$	−7.44759	−	61.7014i	−0.342079	−	2.83404i
$475$			7.09255i			0.325429i
$476$			6.22261i			0.285213i
$477$	1.84201	+	7.51914i	0.0843400	+	0.344278i
$478$	26.1039			1.19397
$479$	0.960796			0.0438999			0.0219500	−	0.999759i	$-0.493013\pi$
$479$	0.960796			0.0438999			0.0219500	+	0.999759i	$0.493013\pi$
$480$	−0.653547	−	5.41448i	−0.0298302	−	0.247136i
$481$			20.1574i			0.919098i
$482$			57.2943i			2.60968i
$483$	−0.430783	+	0.0519970i	−0.0196013	+	0.00236595i
$484$	44.1767	−	16.6686i	2.00803	−	0.757663i
$485$		−	2.11638i		−	0.0960999i
$486$	−32.2597	+	22.0991i	−1.46333	+	1.00244i
$487$	−18.8757			−0.855338			−0.427669	−	0.903935i	$-0.640665\pi$
$487$	−18.8757			−0.855338			−0.427669	+	0.903935i	$0.640665\pi$
$488$			76.4322i			3.45992i
$489$	−32.0794	+	3.87210i	−1.45068	+	0.175103i
$490$			2.50847i			0.113321i
$491$	−10.0458			−0.453362			−0.226681	−	0.973969i	$-0.572787\pi$
$491$	−10.0458			−0.453362			−0.226681	+	0.973969i	$0.572787\pi$
$492$	14.3492	−	1.73200i	0.646912	−	0.0780847i
$493$	7.08796			0.319225
$494$	−47.7858			−2.14998
$495$	4.06302	+	9.08250i	0.182619	+	0.408228i
$496$	−24.8913			−1.11765
$497$	4.04494			0.181441
$498$	15.0834	−	1.82062i	0.675902	−	0.0815839i
$499$	−30.5995			−1.36982			−0.684910	−	0.728627i	$-0.740159\pi$
$499$	−30.5995			−1.36982			−0.684910	+	0.728627i	$0.740159\pi$
$500$		−	4.29243i		−	0.191963i
$501$	36.0551	−	4.35199i	1.61082	−	0.194432i
$502$		−	22.7202i		−	1.01405i
$503$	−15.2551			−0.680191			−0.340096	−	0.940391i	$-0.610459\pi$
$503$	−15.2551			−0.680191			−0.340096	+	0.940391i	$0.610459\pi$
$504$	−4.10483	−	16.7560i	−0.182844	−	0.746373i
$505$		−	2.83756i		−	0.126270i
$506$	−0.373957	−	2.05040i	−0.0166244	−	0.0911514i
$507$	9.94951	−	1.20094i	0.441873	−	0.0533357i
$508$			41.6815i			1.84932i
$509$		−	42.8456i		−	1.89910i	−0.313621	−	0.949548i	$-0.601542\pi$
$509$		−	42.8456i		−	1.89910i	0.313621	−	0.949548i	$-0.398458\pi$
$510$	−0.754777	−	6.25314i	−0.0334221	−	0.276894i
$511$	−0.248236			−0.0109813
$512$	48.7781			2.15571
$513$	−12.9954	−	34.4868i	−0.573761	−	1.52263i
$514$			27.3319i			1.20556i
$515$			17.6307i			0.776903i
$516$	6.49674	+	53.8239i	0.286003	+	2.36946i
$517$	−0.682463	−	3.74193i	−0.0300147	−	0.164570i
$518$		−	18.8260i		−	0.827165i
$519$	−20.3431	+	2.45549i	−0.892964	+	0.107784i
$520$	15.4452			0.677315
$521$		−	22.2681i		−	0.975585i	−0.872960	−	0.487793i	$-0.837802\pi$
$521$		−	22.2681i		−	0.975585i	0.872960	−	0.487793i	$-0.162198\pi$
$522$	−35.7377	+	8.75489i	−1.56420	+	0.383191i
$523$			1.45840i			0.0637714i	0.999492	+	0.0318857i	$0.0101513\pi$
$523$			1.45840i			0.0637714i	−0.999492	+	0.0318857i	$0.989849\pi$
$524$	85.0705			3.71632
$525$	−0.207558	−	1.71957i	−0.00905859	−	0.0750482i
$526$	27.0077			1.17759
$527$	−6.17869			−0.269148
$528$	32.0453	−	9.93111i	1.39459	−	0.432196i
$529$	22.9372			0.997271
$530$	6.47309			0.281173
$531$	8.42059	+	34.3731i	0.365423	+	1.49166i
$532$	30.4443			1.31993
$533$			5.22145i			0.226166i
$534$	5.72817	+	47.4564i	0.247882	+	2.05364i
$535$		−	11.0415i		−	0.477366i
$536$	32.5850			1.40746
$537$	−4.38630	−	36.3394i	−0.189283	−	1.56816i
$538$		−	12.4972i		−	0.538794i
$539$	−3.26280	+	0.595079i	−0.140539	+	0.0256319i
$540$	7.86484	+	20.8715i	0.338449	+	0.898165i
$541$			4.45340i			0.191467i	0.995407	+	0.0957333i	$0.0305196\pi$
$541$			4.45340i			0.191467i	−0.995407	+	0.0957333i	$0.969480\pi$
$542$		−	5.20883i		−	0.223738i
$543$	28.6066	−	3.45292i	1.22763	−	0.148179i
$544$	−4.56464			−0.195707
$545$	−13.7920			−0.590785
$546$	11.5855	−	1.39842i	0.495815	−	0.0598466i
$547$		−	10.2347i		−	0.437604i	−0.975769	−	0.218802i	$-0.929785\pi$
$547$		−	10.2347i		−	0.437604i	0.975769	−	0.218802i	$-0.0702149\pi$
$548$		−	69.5142i		−	2.96950i
$549$	−9.48770	−	38.7290i	−0.404925	−	1.65291i
$550$	8.18465	−	1.49274i	0.348995	−	0.0636506i
$551$		−	34.6780i		−	1.47733i
$552$	−0.299009	−	2.47722i	−0.0127267	−	0.105437i
$553$	−14.3043			−0.608280
$554$			50.9966i			2.16664i
$555$	1.55772	+	12.9053i	0.0661213	+	0.547799i
$556$		−	21.3892i		−	0.907103i
$557$	−44.7074			−1.89431			−0.947157	−	0.320770i	$-0.896058\pi$
$557$	−44.7074			−1.89431			−0.947157	+	0.320770i	$0.896058\pi$
$558$	31.1532	−	7.63179i	1.31882	−	0.323079i
$559$	−19.5857			−0.828385
$560$	−5.84011			−0.246789
$561$	7.95449	−	2.46517i	0.335839	−	0.104079i
$562$	32.6664			1.37795
$563$	43.9008			1.85020			0.925099	−	0.379726i	$-0.123982\pi$
$563$	43.9008			1.85020			0.925099	+	0.379726i	$0.123982\pi$
$564$	−1.02176	−	8.46502i	−0.0430238	−	0.356441i
$565$	−15.6587			−0.658766
$566$			6.81136i			0.286303i
$567$	4.15993	+	7.98092i	0.174700	+	0.335167i
$568$			23.2605i			0.975987i
$569$	27.5969			1.15692			0.578461	−	0.815710i	$-0.303653\pi$
$569$	27.5969			1.15692			0.578461	+	0.815710i	$0.303653\pi$
$570$	−30.5937	+	3.69277i	−1.28143	+	0.154673i
$571$			8.29392i			0.347090i	0.984826	+	0.173545i	$0.0555222\pi$
$571$			8.29392i			0.347090i	−0.984826	+	0.173545i	$0.944478\pi$
$572$	6.86064	+	37.6167i	0.286858	+	1.57283i
$573$	5.20071	+	43.0866i	0.217263	+	1.79997i
$574$		−	4.87656i		−	0.203544i
$575$		−	0.250518i		−	0.0104473i
$576$	−11.0192	+	2.69945i	−0.459134	+	0.112477i
$577$	−7.94135			−0.330603			−0.165301	−	0.986243i	$-0.552860\pi$
$577$	−7.94135			−0.330603			−0.165301	+	0.986243i	$0.552860\pi$
$578$	37.3724			1.55449
$579$	2.85720	+	23.6712i	0.118741	+	0.983742i
$580$			20.9872i			0.871447i
$581$		−	3.49679i		−	0.145071i
$582$	9.12899	−	1.10190i	0.378409	−	0.0456753i
$583$	1.53560	+	8.41964i	0.0635979	+	0.348706i
$584$		−	1.42748i		−	0.0590695i
$585$	−7.82622	+	1.91724i	−0.323574	+	0.0792681i
$586$	6.42429			0.265385
$587$		−	40.1364i		−	1.65660i	−0.560281	−	0.828302i	$-0.689307\pi$
$587$		−	40.1364i		−	1.65660i	0.560281	−	0.828302i	$-0.310693\pi$
$588$	−7.38113	+	0.890930i	−0.304393	+	0.0367413i
$589$			30.2294i			1.24558i
$590$	29.5912			1.21825
$591$	−2.70819	+	0.326889i	−0.111400	+	0.0134464i
$592$	43.8297			1.80139
$593$	−35.7849			−1.46951			−0.734755	−	0.678333i	$-0.762703\pi$
$593$	−35.7849			−1.46951			−0.734755	+	0.678333i	$0.762703\pi$
$594$	−37.0619	+	22.2547i	−1.52067	+	0.913120i
$595$	−1.44967			−0.0594307
$596$	11.4781			0.470163
$597$	23.8400	−	2.87758i	0.975706	−	0.117771i
$598$	1.68785			0.0690214
$599$			26.2084i			1.07085i	0.844584	+	0.535423i	$0.179848\pi$
$599$			26.2084i			1.07085i	−0.844584	+	0.535423i	$0.820152\pi$
$600$	9.88839	−	1.19356i	0.403692	−	0.0487271i
$601$			14.5437i			0.593250i	0.954994	+	0.296625i	$0.0958612\pi$
$601$			14.5437i			0.593250i	−0.954994	+	0.296625i	$0.904139\pi$
$602$	18.2920			0.745526
$603$	−16.5112	+	4.04485i	−0.672387	+	0.164719i
$604$		−	16.3430i		−	0.664987i
$605$	3.88325	+	10.2918i	0.157877	+	0.418420i
$606$	12.2398	−	1.47739i	0.497207	−	0.0600147i
$607$		−	32.4654i		−	1.31773i	−0.752262	−	0.658864i	$-0.771037\pi$
$607$		−	32.4654i		−	1.31773i	0.752262	−	0.658864i	$-0.228963\pi$
$608$			22.3326i			0.905707i
$609$	1.01483	+	8.40759i	0.0411228	+	0.340693i
$610$	−33.3411			−1.34994
$611$	3.08029			0.124615
$612$	18.1317	−	4.44184i	0.732930	−	0.179551i
$613$		−	33.4972i		−	1.35294i	−0.736470	−	0.676471i	$-0.763509\pi$
$613$		−	33.4972i		−	1.35294i	0.736470	−	0.676471i	$-0.236491\pi$
$614$			39.5407i			1.59573i
$615$	0.403501	+	3.34291i	0.0162707	+	0.134799i
$616$	−3.42200	−	18.7627i	−0.137876	−	0.755973i
$617$			12.0479i			0.485029i	0.970148	+	0.242515i	$0.0779723\pi$
$617$			12.0479i			0.485029i	−0.970148	+	0.242515i	$0.922028\pi$
$618$	−76.0501	+	9.17952i	−3.05918	+	0.369255i
$619$	−10.5568			−0.424312			−0.212156	−	0.977236i	$-0.568048\pi$
$619$	−10.5568			−0.424312			−0.212156	+	0.977236i	$0.568048\pi$
$620$		−	18.2949i		−	0.734742i
$621$	0.459013	+	1.21811i	0.0184196	+	0.0488812i
$622$		−	55.3122i		−	2.21782i
$623$	11.0019			0.440780
$624$	3.25572	+	26.9729i	0.130333	+	1.07978i
$625$	1.00000			0.0400000
$626$	−30.5205			−1.21984
$627$	−12.0609	−	38.9176i	−0.481666	−	1.55422i
$628$	15.7512			0.628540
$629$	10.8797			0.433802
$630$	7.30928	−	1.79060i	0.291209	−	0.0713393i
$631$	−21.7226			−0.864762			−0.432381	−	0.901691i	$-0.642326\pi$
$631$	−21.7226			−0.864762			−0.432381	+	0.901691i	$0.642326\pi$
$632$		−	82.2568i		−	3.27200i
$633$	−3.55599	−	29.4605i	−0.141338	−	1.17095i
$634$			31.3967i			1.24692i
$635$	−9.71047			−0.385348
$636$	2.29904	+	19.0470i	0.0911628	+	0.755261i
$637$		−	2.68588i		−	0.106418i
$638$	−40.0177	+	7.29853i	−1.58431	+	0.288952i
$639$	−2.88737	−	11.7863i	−0.114223	−	0.466259i
$640$			15.7837i			0.623907i
$641$			43.5811i			1.72135i	0.509155	+	0.860675i	$0.329958\pi$
$641$			43.5811i			1.72135i	−0.509155	+	0.860675i	$0.670042\pi$
$642$	47.6275	−	5.74881i	1.87971	−	0.226887i
$643$	−22.1708			−0.874329			−0.437165	−	0.899382i	$-0.644017\pi$
$643$	−22.1708			−0.874329			−0.437165	+	0.899382i	$0.644017\pi$
$644$	−1.07533			−0.0423739
$645$	−12.5392	+	1.51353i	−0.493732	+	0.0595953i
$646$			25.7918i			1.01476i
$647$			0.403114i			0.0158480i	0.999969	+	0.00792402i	$0.00252232\pi$
$647$			0.403114i			0.0158480i	−0.999969	+	0.00792402i	$0.997478\pi$
$648$	−45.8943	+	23.9217i	−1.80290	+	0.939731i
$649$	7.01984	+	38.4896i	0.275553	+	1.51085i
$650$			6.73745i			0.264265i
$651$	−0.884642	−	7.32904i	−0.0346718	−	0.287248i
$652$	−80.0774			−3.13607
$653$			9.15952i			0.358440i	0.983809	+	0.179220i	$0.0573573\pi$
$653$			9.15952i			0.358440i	−0.983809	+	0.179220i	$0.942643\pi$
$654$	−7.18087	−	59.4917i	−0.280794	−	2.32631i
$655$			19.8187i			0.774382i
$656$	11.3534			0.443275
$657$	0.177196	+	0.723319i	0.00691308	+	0.0282194i
$658$	−2.87683			−0.112150
$659$	−36.6315			−1.42696			−0.713481	−	0.700675i	$-0.752883\pi$
$659$	−36.6315			−1.42696			−0.713481	+	0.700675i	$0.752883\pi$
$660$	7.29929	+	23.5530i	0.284124	+	0.916800i
$661$	37.5235			1.45949			0.729747	−	0.683718i	$-0.239638\pi$
$661$	37.5235			1.45949			0.729747	+	0.683718i	$0.239638\pi$
$662$	4.75167			0.184679
$663$	0.808158	+	6.69539i	0.0313862	+	0.260027i
$664$	20.1083			0.780353
$665$			7.09255i			0.275037i
$666$	−54.8558	+	13.4384i	−2.12562	+	0.520727i
$667$			1.22487i			0.0474272i
$668$	90.0017			3.48227
$669$	−24.8465	+	2.99906i	−0.960621	+	0.115950i
$670$			14.2142i			0.549142i
$671$	−7.90943	−	43.3672i	−0.305340	−	1.67417i
$672$	−0.653547	−	5.41448i	−0.0252111	−	0.208868i
$673$		−	0.708445i		−	0.0273085i	−0.999907	−	0.0136543i	$-0.995654\pi$
$673$		−	0.708445i		−	0.0273085i	0.999907	−	0.0136543i	$-0.00434642\pi$
$674$		−	14.3268i		−	0.551848i
$675$	−4.86239	+	1.83226i	−0.187153	+	0.0705237i
$676$	24.8362			0.955239
$677$	37.1482			1.42772			0.713861	−	0.700287i	$-0.246945\pi$
$677$	37.1482			1.42772			0.713861	+	0.700287i	$0.246945\pi$
$678$	−8.15276	−	67.5436i	−0.313105	−	2.59400i
$679$		−	2.11638i		−	0.0812192i
$680$		−	8.33633i		−	0.319684i
$681$	−32.2835	+	3.89674i	−1.23711	+	0.149323i
$682$	34.8841	−	6.36225i	1.33578	−	0.243623i
$683$			47.6468i			1.82315i	0.411131	+	0.911576i	$0.365134\pi$
$683$			47.6468i			1.82315i	−0.411131	+	0.911576i	$0.634866\pi$
$684$	−21.7318	−	88.7098i	−0.830937	−	3.39190i
$685$	16.1946			0.618764
$686$			2.50847i			0.0957739i
$687$	−18.0005	+	2.17272i	−0.686761	+	0.0828946i
$688$			42.5865i			1.62360i
$689$	−6.93089			−0.264046
$690$	1.08061	−	0.130433i	0.0411380	−	0.00496550i
$691$	−40.5974			−1.54440			−0.772199	−	0.635381i	$-0.780843\pi$
$691$	−40.5974			−1.54440			−0.772199	+	0.635381i	$0.780843\pi$
$692$	−50.7810			−1.93040
$693$	4.06302	+	9.08250i	0.154342	+	0.345016i
$694$	56.2130			2.13382
$695$	4.98300			0.189016
$696$	−48.3478	+	5.83576i	−1.83262	+	0.221204i
$697$	2.81821			0.106747
$698$		−	64.6747i		−	2.44797i
$699$	−5.54102	+	0.668822i	−0.209581	+	0.0252972i
$700$		−	4.29243i		−	0.162239i
$701$	−12.8918			−0.486915			−0.243458	−	0.969912i	$-0.578282\pi$
$701$	−12.8918			−0.486915			−0.243458	+	0.969912i	$0.578282\pi$
$702$	−12.3448	−	32.7601i	−0.465923	−	1.23645i
$703$		−	53.2293i		−	2.00758i
$704$	−12.3389	+	2.25040i	−0.465039	+	0.0848152i
$705$	1.97208	−	0.238037i	0.0742728	−	0.00896500i
$706$		−	46.6817i		−	1.75689i
$707$		−	2.83756i		−	0.106717i
$708$	10.5098	+	87.0715i	0.394984	+	3.27235i
$709$	10.1320			0.380515			0.190257	−	0.981734i	$-0.439068\pi$
$709$	10.1320			0.380515			0.190257	+	0.981734i	$0.439068\pi$
$710$	−10.1466			−0.380796
$711$	10.2107	+	41.6804i	0.382932	+	1.56314i
$712$			63.2662i			2.37100i
$713$		−	1.06774i		−	0.0399872i
$714$	−0.754777	−	6.25314i	−0.0282468	−	0.234018i
$715$	−8.76350	+	1.59831i	−0.327736	+	0.0597734i
$716$		−	90.7112i		−	3.39004i
$717$	−17.8944	+	2.15992i	−0.668278	+	0.0806636i
$718$	59.3163			2.21366
$719$			26.6064i			0.992253i	0.868250	+	0.496126i	$0.165245\pi$
$719$			26.6064i			0.992253i	−0.868250	+	0.496126i	$0.834755\pi$
$720$	4.16880	+	17.0171i	0.155362	+	0.634191i
$721$			17.6307i			0.656603i
$722$	78.5260			2.92244
$723$	−4.74070	−	39.2755i	−0.176308	−	1.46067i
$724$	71.4084			2.65387
$725$	−4.88936			−0.181586
$726$	−42.3716	+	22.1088i	−1.57256	+	0.820535i
$727$	11.9810			0.444349			0.222175	−	0.975007i	$-0.428684\pi$
$727$	11.9810			0.444349			0.222175	+	0.975007i	$0.428684\pi$
$728$	15.4452			0.572435
$729$	20.2857	−	17.8183i	0.751321	−	0.659937i
$730$	0.622692			0.0230469
$731$			10.5711i			0.390987i
$732$	−11.8417	−	98.1057i	−0.437682	−	3.62609i
$733$		−	24.8213i		−	0.916795i	−0.888747	−	0.458397i	$-0.848424\pi$
$733$		−	24.8213i		−	0.916795i	0.888747	−	0.458397i	$-0.151576\pi$
$734$	76.9092			2.83877
$735$	−0.207558	−	1.71957i	−0.00765591	−	0.0634273i
$736$		−	0.788815i		−	0.0290761i
$737$	−18.4886	+	3.37200i	−0.681035	+	0.124209i
$738$	−14.2095	+	3.48100i	−0.523060	+	0.128137i
$739$			45.0502i			1.65720i	0.559843	+	0.828599i	$0.310861\pi$
$739$			45.0502i			1.65720i	−0.559843	+	0.828599i	$0.689139\pi$
$740$			32.2145i			1.18423i
$741$	32.7574	−	3.95393i	1.20337	−	0.145251i
$742$	6.47309			0.237635
$743$	18.4894			0.678312			0.339156	−	0.940730i	$-0.389859\pi$
$743$	18.4894			0.678312			0.339156	+	0.940730i	$0.389859\pi$
$744$	42.1456	−	5.08713i	1.54513	−	0.186503i
$745$			2.67404i			0.0979693i
$746$			4.80857i			0.176054i
$747$	−10.1891	+	2.49609i	−0.372799	+	0.0913270i
$748$	20.3032	−	3.70294i	0.742357	−	0.135393i
$749$		−	11.0415i		−	0.403448i
$750$	0.520654	+	4.31349i	0.0190116	+	0.157506i
$751$	−16.3173			−0.595427			−0.297713	−	0.954655i	$-0.596224\pi$
$751$	−16.3173			−0.595427			−0.297713	+	0.954655i	$0.596224\pi$
$752$		−	6.69769i		−	0.244240i
$753$	1.87993	+	15.5748i	0.0685086	+	0.567577i
$754$		−	32.9418i		−	1.19967i
$755$	3.80740			0.138565
$756$	7.86484	+	20.8715i	0.286042	+	0.759088i
$757$	14.9994			0.545162			0.272581	−	0.962133i	$-0.412123\pi$
$757$	14.9994			0.545162			0.272581	+	0.962133i	$0.412123\pi$
$758$	40.2271			1.46111
$759$	0.426006	+	1.37462i	0.0154630	+	0.0498954i
$760$	−40.7857			−1.47945
$761$	37.2801			1.35140			0.675701	−	0.737176i	$-0.263841\pi$
$761$	37.2801			1.35140			0.675701	+	0.737176i	$0.263841\pi$
$762$	−5.05580	−	41.8860i	−0.183152	−	1.51737i
$763$	−13.7920			−0.499304
$764$			107.554i			3.89116i
$765$	1.03481	+	4.22411i	0.0374135	+	0.152723i
$766$			48.8841i			1.76625i
$767$	−31.6839			−1.14404
$768$	−55.0773	+	6.64803i	−1.98743	+	0.239890i
$769$			26.8497i			0.968224i	0.875006	+	0.484112i	$0.160857\pi$
$769$			26.8497i			0.968224i	−0.875006	+	0.484112i	$0.839143\pi$
$770$	8.18465	−	1.49274i	0.294954	−	0.0537946i
$771$	−2.26153	−	18.7362i	−0.0814468	−	0.674767i
$772$			59.0886i			2.12665i
$773$			16.1938i			0.582450i	0.956655	+	0.291225i	$0.0940628\pi$
$773$			16.1938i			0.582450i	−0.956655	+	0.291225i	$0.905937\pi$
$774$	−13.0572	−	53.2999i	−0.469332	−	1.91583i
$775$	4.26213			0.153100
$776$	12.1702			0.436886
$777$	1.55772	+	12.9053i	0.0558827	+	0.462975i
$778$		−	62.0662i		−	2.22518i
$779$		−	13.7882i		−	0.494013i
$780$	−19.8248	+	2.39293i	−0.709843	+	0.0856807i
$781$	−2.40706	−	13.1979i	−0.0861314	−	0.472256i
$782$		−	0.910997i		−	0.0325772i
$783$	23.7739	−	8.95856i	0.849612	−	0.320153i
$784$	−5.84011			−0.208575
$785$			3.66952i			0.130971i
$786$	−85.4879	+	10.3187i	−3.04925	+	0.368056i
$787$		−	42.7501i		−	1.52387i	−0.647651	−	0.761937i	$-0.724248\pi$
$787$		−	42.7501i		−	1.52387i	0.647651	−	0.761937i	$-0.275752\pi$
$788$	−6.76026			−0.240824
$789$	−18.5139	+	2.23470i	−0.659112	+	0.0795573i
$790$	35.8819			1.27662
$791$	−15.6587			−0.556759
$792$	−52.2289	+	23.3644i	−1.85587	+	0.830219i
$793$	35.6991			1.26771
$794$	−22.0353			−0.782003
$795$	−4.43734	+	0.535603i	−0.157376	+	0.0189959i
$796$	59.5100			2.10928
$797$		−	46.0499i		−	1.63117i	−0.578637	−	0.815585i	$-0.696415\pi$
$797$		−	46.0499i		−	1.63117i	0.578637	−	0.815585i	$-0.303585\pi$
$798$	−30.5937	+	3.69277i	−1.08300	+	0.130723i
$799$		−	1.66255i		−	0.0588167i
$800$	3.14874			0.111325
$801$	−7.85337	−	32.0576i	−0.277485	−	1.13270i
$802$			81.1175i			2.86436i
$803$	0.147720	+	0.809944i	0.00521292	+	0.0285823i
$804$	−41.8250	+	5.04843i	−1.47505	+	0.178044i
$805$		−	0.250518i		−	0.00882959i
$806$			28.7159i			1.01148i
$807$	1.03406	+	8.56691i	0.0364005	+	0.301569i
$808$	16.3174			0.574043
$809$	8.80950			0.309726			0.154863	−	0.987936i	$-0.450506\pi$
$809$	8.80950			0.309726			0.154863	+	0.987936i	$0.450506\pi$
$810$	−10.4351	−	20.0199i	−0.366650	−	0.703428i
$811$			31.7595i			1.11523i	0.830101	+	0.557613i	$0.188283\pi$
$811$			31.7595i			1.11523i	−0.830101	+	0.557613i	$0.811717\pi$
$812$			20.9872i			0.736507i
$813$	0.430994	+	3.57068i	0.0151156	+	0.125229i
$814$	−61.4254	+	11.2029i	−2.15296	+	0.392662i
$815$		−	18.6555i		−	0.653473i
$816$	14.5583	−	1.75724i	0.509641	−	0.0615156i
$817$	51.7195			1.80944
$818$		−	25.5721i		−	0.894109i
$819$	−7.82622	+	1.91724i	−0.273470	+	0.0669938i
$820$			8.34465i			0.291408i
$821$	0.498906			0.0174119			0.00870597	−	0.999962i	$-0.497229\pi$
$821$	0.498906			0.0174119			0.00870597	+	0.999962i	$0.497229\pi$
$822$	8.43178	+	69.8552i	0.294092	+	2.43648i
$823$	−30.1667			−1.05155			−0.525773	−	0.850625i	$-0.676224\pi$
$823$	−30.1667			−1.05155			−0.525773	+	0.850625i	$0.676224\pi$
$824$	−101.386			−3.53193
$825$	−5.48710	+	1.70050i	−0.191036	+	0.0592039i
$826$	29.5912			1.02961
$827$	−11.1224			−0.386763			−0.193381	−	0.981124i	$-0.561945\pi$
$827$	−11.1224			−0.386763			−0.193381	+	0.981124i	$0.561945\pi$
$828$	0.767594	+	3.13334i	0.0266757	+	0.108891i
$829$	51.3365			1.78299			0.891496	−	0.453029i	$-0.149657\pi$
$829$	51.3365			1.78299			0.891496	+	0.453029i	$0.149657\pi$
$830$			8.77160i			0.304467i
$831$	−4.21961	−	34.9584i	−0.146377	−	1.21269i
$832$		−	10.1572i		−	0.352136i
$833$	−1.44967			−0.0502281
$834$	2.59442	+	21.4941i	0.0898374	+	0.744280i
$835$			20.9675i			0.725611i
$836$	−18.1168	−	99.3338i	−0.626581	−	3.43553i
$837$	−20.7242	+	7.80933i	−0.716332	+	0.269930i
$838$		−	40.3918i		−	1.39531i
$839$		−	8.42213i		−	0.290764i	−0.989376	−	0.145382i	$-0.953559\pi$
$839$		−	8.42213i		−	0.290764i	0.989376	−	0.145382i	$-0.0464412\pi$
$840$	9.88839	−	1.19356i	0.341182	−	0.0411819i
$841$	−5.09420			−0.175662
$842$	−22.2483			−0.766726
$843$	−22.3930	+	2.70291i	−0.771255	+	0.0930933i
$844$		−	73.5401i		−	2.53135i
$845$			5.78605i			0.199046i
$846$	2.05354	+	8.38261i	0.0706023	+	0.288200i
$847$	3.88325	+	10.2918i	0.133430	+	0.353629i
$848$			15.0703i			0.517518i
$849$	−0.563592	−	4.66922i	−0.0193424	−	0.160247i
$850$	3.63646			0.124729
$851$			1.88012i			0.0644498i
$852$	−3.60376	−	29.8563i	−0.123463	−	1.02286i
$853$			27.5842i			0.944464i	0.881474	+	0.472232i	$0.156551\pi$
$853$			27.5842i			0.944464i	−0.881474	+	0.472232i	$0.843449\pi$
$854$	−33.3411			−1.14091
$855$	20.6666	−	5.06282i	0.706781	−	0.173145i
$856$	63.4942			2.17019
$857$	34.8713			1.19118			0.595590	−	0.803288i	$-0.296918\pi$
$857$	34.8713			1.19118			0.595590	+	0.803288i	$0.296918\pi$
$858$	−11.4571	−	36.9691i	−0.391137	−	1.26210i
$859$	−45.2531			−1.54402			−0.772008	−	0.635613i	$-0.780747\pi$
$859$	−45.2531			−1.54402			−0.772008	+	0.635613i	$0.780747\pi$
$860$	−31.3008			−1.06735
$861$	0.403501	+	3.34291i	0.0137513	+	0.113926i
$862$	−3.58512			−0.122110
$863$			35.7352i			1.21644i	0.793768	+	0.608220i	$0.208116\pi$
$863$			35.7352i			1.21644i	−0.793768	+	0.608220i	$0.791884\pi$
$864$	−15.3104	+	5.76931i	−0.520870	+	0.196276i
$865$		−	11.8304i		−	0.402244i
$866$	84.0292			2.85543
$867$	−25.6189	+	3.09230i	−0.870064	+	0.105020i
$868$		−	18.2949i		−	0.620970i
$869$	8.51218	+	46.6721i	0.288756	+	1.58324i
$870$	−2.54566	−	21.0902i	−0.0863061	−	0.715025i
$871$		−	15.2195i		−	0.515692i
$872$		−	79.3110i		−	2.68581i
$873$	−6.16679	+	1.51072i	−0.208714	+	0.0511301i
$874$	−4.45708			−0.150763
$875$	1.00000			0.0338062
$876$	0.221161	+	1.83226i	0.00747232	+	0.0619064i
$877$			27.3508i			0.923570i	0.886992	+	0.461785i	$0.152791\pi$
$877$			27.3508i			0.923570i	−0.886992	+	0.461785i	$0.847209\pi$
$878$		−	30.7912i		−	1.03915i
$879$	−4.40388	+	0.531565i	−0.148539	+	0.0179292i
$880$	3.47532	+	19.0551i	0.117153	+	0.642348i
$881$		−	4.32369i		−	0.145669i	−0.997344	−	0.0728344i	$-0.976796\pi$
$881$		−	4.32369i		−	0.145669i	0.997344	−	0.0728344i	$-0.0232045\pi$
$882$	7.30928	−	1.79060i	0.246116	−	0.0602927i
$883$	28.7867			0.968748			0.484374	−	0.874861i	$-0.339047\pi$
$883$	28.7867			0.968748			0.484374	+	0.874861i	$0.339047\pi$
$884$			16.7132i			0.562125i
$885$	−20.2849	+	2.44846i	−0.681869	+	0.0823041i
$886$			34.6536i			1.16421i
$887$	17.2875			0.580458			0.290229	−	0.956957i	$-0.406268\pi$
$887$	17.2875			0.580458			0.290229	+	0.956957i	$0.406268\pi$
$888$	−74.2118	+	8.95764i	−2.49039	+	0.300599i
$889$	−9.71047			−0.325679
$890$	−27.5979			−0.925082
$891$	23.5647	−	18.3223i	0.789446	−	0.613820i
$892$	−62.0224			−2.07666
$893$	−8.13406			−0.272196
$894$	−11.5345	+	1.39225i	−0.385770	+	0.0465639i
$895$	21.1328			0.706393
$896$			15.7837i			0.527297i
$897$	−1.15703	+	0.139658i	−0.0386321	+	0.00466304i
$898$			99.5558i			3.32222i
$899$	−20.8391			−0.695023
$900$	−12.5075	+	3.06403i	−0.416915	+	0.102134i
$901$			3.74086i			0.124626i
$902$	−15.9113	+	2.90194i	−0.529787	+	0.0966240i
$903$	−12.5392	+	1.51353i	−0.417280	+	0.0503672i
$904$		−	90.0453i		−	2.99486i
$905$			16.6359i			0.552996i
$906$	1.98234	+	16.4232i	0.0658587	+	0.545623i
$907$	−20.4962			−0.680566			−0.340283	−	0.940323i	$-0.610523\pi$
$907$	−20.4962			−0.680566			−0.340283	+	0.940323i	$0.610523\pi$
$908$	−80.5869			−2.67437
$909$	−8.26819	+	2.02551i	−0.274238	+	0.0671820i
$910$			6.73745i			0.223344i
$911$		−	7.19986i		−	0.238542i	−0.992862	−	0.119271i	$-0.961944\pi$
$911$		−	7.19986i		−	0.238542i	0.992862	−	0.119271i	$-0.0380558\pi$
$912$	−8.59733	−	71.2267i	−0.284686	−	2.35855i
$913$	−11.4093	+	2.08086i	−0.377594	+	0.0688666i
$914$			100.849i			3.33578i
$915$	22.8555	−	2.75874i	0.755579	−	0.0912012i
$916$	−44.9332			−1.48464
$917$			19.8187i			0.654472i
$918$	−17.6819	+	6.66293i	−0.583589	+	0.219909i
$919$		−	44.3314i		−	1.46236i	−0.682185	−	0.731179i	$-0.738970\pi$
$919$		−	44.3314i		−	1.46236i	0.682185	−	0.731179i	$-0.261030\pi$
$920$	1.44060			0.0474952
$921$	−3.27171	−	27.1053i	−0.107807	−	0.893151i
$922$	75.5120			2.48685
$923$	10.8642			0.357601
$924$	7.29929	+	23.5530i	0.240129	+	0.774837i
$925$	−7.50495			−0.246761
$926$	−28.6045			−0.940002
$927$	51.3731	−	12.5852i	1.68732	−	0.413353i
$928$	−15.3953			−0.505376
$929$		−	36.0092i		−	1.18143i	−0.806882	−	0.590713i	$-0.798847\pi$
$929$		−	36.0092i		−	1.18143i	0.806882	−	0.590713i	$-0.201153\pi$
$930$	2.21910	+	18.3847i	0.0727671	+	0.602858i
$931$			7.09255i			0.232449i
$932$	−13.8316			−0.453070
$933$	4.57669	+	37.9168i	0.149834	+	1.24134i
$934$			9.76354i			0.319473i
$935$	0.862668	+	4.72999i	0.0282123	+	0.154687i
$936$	−11.0251	−	45.0047i	−0.360366	−	1.47102i
$937$			12.6717i			0.413965i	0.978345	+	0.206983i	$0.0663643\pi$
$937$			12.6717i			0.413965i	−0.978345	+	0.206983i	$0.933636\pi$
$938$			14.2142i			0.464109i
$939$	20.9219	−	2.52535i	0.682761	−	0.0824118i
$940$	4.92275			0.160562
$941$	5.27370			0.171918			0.0859588	−	0.996299i	$-0.472605\pi$
$941$	5.27370			0.171918			0.0859588	+	0.996299i	$0.472605\pi$
$942$	−15.8284	+	1.91055i	−0.515719	+	0.0622491i
$943$			0.487016i			0.0158594i
$944$			68.8927i			2.24227i
$945$	−4.86239	+	1.83226i	−0.158174	+	0.0596034i
$946$	−10.8852	−	59.6832i	−0.353908	−	1.94047i
$947$		−	3.90019i		−	0.126739i	−0.997990	−	0.0633695i	$-0.979815\pi$
$947$		−	3.90019i		−	0.126739i	0.997990	−	0.0633695i	$-0.0201847\pi$
$948$	12.7441	+	105.582i	0.413910	+	3.42914i
$949$	−0.666731			−0.0216430
$950$		−	17.7915i		−	0.577232i
$951$	−2.59786	−	21.5226i	−0.0842413	−	0.697918i
$952$		−	8.33633i		−	0.270182i
$953$	−53.6607			−1.73824			−0.869121	−	0.494600i	$-0.835315\pi$
$953$	−53.6607			−1.73824			−0.869121	+	0.494600i	$0.835315\pi$
$954$	−4.62064	−	18.8616i	−0.149599	−	0.610665i
$955$	−25.0566			−0.810813
$956$	−44.6684			−1.44468
$957$	26.8284	−	8.31436i	0.867239	−	0.268765i
$958$	−2.41013			−0.0778678
$959$	16.1946			0.522951
$960$	−0.784920	−	6.50287i	−0.0253332	−	0.209879i
$961$	−12.8342			−0.414007
$962$		−	50.5643i		−	1.63026i
$963$	−32.1732	+	7.88168i	−1.03677	+	0.253983i
$964$		−	98.0405i		−	3.15767i
$965$	−13.7658			−0.443136
$966$	1.08061	−	0.130433i	0.0347679	−	0.00419662i
$967$		−	13.7242i		−	0.441341i	−0.975348	−	0.220671i	$-0.929175\pi$
$967$		−	13.7242i		−	0.441341i	0.975348	−	0.220671i	$-0.0708246\pi$
$968$	−59.1828	+	22.3306i	−1.90221	+	0.717733i
$969$	−2.13409	−	17.6804i	−0.0685568	−	0.567976i
$970$			5.30888i			0.170458i
$971$		−	50.9981i		−	1.63661i	−0.574787	−	0.818303i	$-0.694915\pi$
$971$		−	50.9981i		−	1.63661i	0.574787	−	0.818303i	$-0.305085\pi$
$972$	55.2020	−	37.8154i	1.77061	−	1.21293i
$973$	4.98300			0.159748
$974$	47.3491			1.51716
$975$	−0.557477	−	4.61856i	−0.0178535	−	0.147912i
$976$		−	77.6232i		−	2.48466i
$977$			54.7412i			1.75133i	0.482922	+	0.875664i	$0.339576\pi$
$977$			54.7412i			1.75133i	−0.482922	+	0.875664i	$0.660424\pi$
$978$	80.4703	−	9.71306i	2.57316	−	0.310589i
$979$	−6.54697	−	35.8969i	−0.209242	−	1.14727i
$980$		−	4.29243i		−	0.137117i
$981$	9.84504	+	40.1877i	0.314328	+	1.28309i
$982$	25.1997			0.804154
$983$		−	30.7577i		−	0.981017i	−0.871436	−	0.490508i	$-0.836811\pi$
$983$		−	30.7577i		−	0.981017i	0.871436	−	0.490508i	$-0.163189\pi$
$984$	−19.2234	+	2.32033i	−0.612819	+	0.0739696i
$985$		−	1.57492i		−	0.0501813i
$986$	−17.7799			−0.566229
$987$	1.97208	−	0.238037i	0.0627720	−	0.00757681i
$988$	81.7697			2.60144
$989$	−1.82680			−0.0580887
$990$	−10.1920	−	22.7832i	−0.323922	−	0.724098i
$991$	11.8257			0.375656			0.187828	−	0.982202i	$-0.439855\pi$
$991$	11.8257			0.375656			0.187828	+	0.982202i	$0.439855\pi$
$992$	13.4204			0.426097
$993$	−3.25729	+	0.393167i	−0.103367	+	0.0124768i
$994$	−10.1466			−0.321832
$995$			13.8639i			0.439516i
$996$	−25.8103	+	3.11539i	−0.817830	+	0.0987150i
$997$		−	7.10146i		−	0.224906i	−0.993657	−	0.112453i	$-0.964129\pi$
$997$		−	7.10146i		−	0.224906i	0.993657	−	0.112453i	$-0.0358707\pi$
$998$	76.7579			2.42973
$999$	36.4920	−	13.7510i	1.15456	−	0.435063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.3	yes	40
3.2	odd	2		1155.2.l.e.1121.38	yes	40
11.10	odd	2		1155.2.l.e.1121.37	✓	40
33.32	even	2	inner	1155.2.l.f.1121.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.37	✓	40	11.10	odd	2
1155.2.l.e.1121.38	yes	40	3.2	odd	2
1155.2.l.f.1121.3	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.4	yes	40	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.50847 q^{2} +(1.71957 - 0.207558i) q^{3} +4.29243 q^{4} +1.00000i q^{5} +(-4.31349 + 0.520654i) q^{6} +1.00000i q^{7} -5.75050 q^{8} +(2.91384 - 0.713822i) q^{9} +O(q^{10})\)	\(q-2.50847 q^{2} +(1.71957 - 0.207558i) q^{3} +4.29243 q^{4} +1.00000i q^{5} +(-4.31349 + 0.520654i) q^{6} +1.00000i q^{7} -5.75050 q^{8} +(2.91384 - 0.713822i) q^{9} -2.50847i q^{10} +(3.26280 - 0.595079i) q^{11} +(7.38113 - 0.890930i) q^{12} +2.68588i q^{13} -2.50847i q^{14} +(0.207558 + 1.71957i) q^{15} +5.84011 q^{16} +1.44967 q^{17} +(-7.30928 + 1.79060i) q^{18} -7.09255i q^{19} +4.29243i q^{20} +(0.207558 + 1.71957i) q^{21} +(-8.18465 + 1.49274i) q^{22} +0.250518i q^{23} +(-9.88839 + 1.19356i) q^{24} -1.00000 q^{25} -6.73745i q^{26} +(4.86239 - 1.83226i) q^{27} +4.29243i q^{28} +4.88936 q^{29} +(-0.520654 - 4.31349i) q^{30} -4.26213 q^{31} -3.14874 q^{32} +(5.48710 - 1.70050i) q^{33} -3.63646 q^{34} -1.00000 q^{35} +(12.5075 - 3.06403i) q^{36} +7.50495 q^{37} +17.7915i q^{38} +(0.557477 + 4.61856i) q^{39} -5.75050i q^{40} +1.94404 q^{41} +(-0.520654 - 4.31349i) q^{42} +7.29209i q^{43} +(14.0054 - 2.55433i) q^{44} +(0.713822 + 2.91384i) q^{45} -0.628417i q^{46} -1.14684i q^{47} +(10.0425 - 1.21216i) q^{48} -1.00000 q^{49} +2.50847 q^{50} +(2.49281 - 0.300891i) q^{51} +11.5290i q^{52} +2.58049i q^{53} +(-12.1972 + 4.59617i) q^{54} +(0.595079 + 3.26280i) q^{55} -5.75050i q^{56} +(-1.47212 - 12.1961i) q^{57} -12.2648 q^{58} +11.7965i q^{59} +(0.890930 + 7.38113i) q^{60} -13.2914i q^{61} +10.6914 q^{62} +(0.713822 + 2.91384i) q^{63} -3.78168 q^{64} -2.68588 q^{65} +(-13.7642 + 4.26566i) q^{66} -5.66647 q^{67} +6.22261 q^{68} +(0.0519970 + 0.430783i) q^{69} +2.50847 q^{70} -4.04494i q^{71} +(-16.7560 + 4.10483i) q^{72} +0.248236i q^{73} -18.8260 q^{74} +(-1.71957 + 0.207558i) q^{75} -30.4443i q^{76} +(0.595079 + 3.26280i) q^{77} +(-1.39842 - 11.5855i) q^{78} +14.3043i q^{79} +5.84011i q^{80} +(7.98092 - 4.15993i) q^{81} -4.87656 q^{82} -3.49679 q^{83} +(0.890930 + 7.38113i) q^{84} +1.44967i q^{85} -18.2920i q^{86} +(8.40759 - 1.01483i) q^{87} +(-18.7627 + 3.42200i) q^{88} -11.0019i q^{89} +(-1.79060 - 7.30928i) q^{90} -2.68588 q^{91} +1.07533i q^{92} +(-7.32904 + 0.884642i) q^{93} +2.87683i q^{94} +7.09255 q^{95} +(-5.41448 + 0.653547i) q^{96} -2.11638 q^{97} +2.50847 q^{98} +(9.08250 - 4.06302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

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