LMFDB - Embedded newform 1470.2.d.e.1469.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1470,2,Mod(1469,1470)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1470.1469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1470, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.4
Root			$1.01575 + 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.e.1469.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(-1.41421 + 1.73205i) q^{5} +(0.707107 - 1.58114i) q^{6} -1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +(1.41421 - 1.73205i) q^{10} +0.213422i q^{11} +(-0.707107 + 1.58114i) q^{12} -6.70141 q^{13} +(-1.73861 - 3.46081i) q^{15} +1.00000 q^{16} +3.16228i q^{17} +(2.00000 + 2.23607i) q^{18} -4.89433i q^{19} +(-1.41421 + 1.73205i) q^{20} -0.213422i q^{22} +6.47723 q^{23} +(0.707107 - 1.58114i) q^{24} +(-1.00000 - 4.89898i) q^{25} +6.70141 q^{26} +(4.94975 - 1.58114i) q^{27} -2.02265i q^{29} +(1.73861 + 3.46081i) q^{30} -0.301824i q^{31} -1.00000 q^{32} +(-0.337449 - 0.150912i) q^{33} -3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} -7.13505i q^{37} +4.89433i q^{38} +(4.73861 - 10.5959i) q^{39} +(1.41421 - 1.73205i) q^{40} -6.70141 q^{41} +2.02265i q^{43} +0.213422i q^{44} +(6.70141 - 0.301824i) q^{45} -6.47723 q^{46} +7.75478i q^{47} +(-0.707107 + 1.58114i) q^{48} +(1.00000 + 4.89898i) q^{50} +(-5.00000 - 2.23607i) q^{51} -6.70141 q^{52} -5.00000 q^{53} +(-4.94975 + 1.58114i) q^{54} +(-0.369657 - 0.301824i) q^{55} +(7.73861 + 3.46081i) q^{57} +2.02265i q^{58} +4.91754 q^{59} +(-1.73861 - 3.46081i) q^{60} -3.46410i q^{61} +0.301824i q^{62} +1.00000 q^{64} +(9.47723 - 11.6072i) q^{65} +(0.337449 + 0.150912i) q^{66} +5.32582i q^{67} +3.16228i q^{68} +(-4.58009 + 10.2414i) q^{69} +2.02265i q^{71} +(2.00000 + 2.23607i) q^{72} +11.9886 q^{73} +7.13505i q^{74} +(8.45307 + 1.88296i) q^{75} -4.89433i q^{76} +(-4.73861 + 10.5959i) q^{78} +0.522774 q^{79} +(-1.41421 + 1.73205i) q^{80} +(-1.00000 + 8.94427i) q^{81} +6.70141 q^{82} -16.7169i q^{83} +(-5.47723 - 4.47214i) q^{85} -2.02265i q^{86} +(3.19808 + 1.43023i) q^{87} -0.213422i q^{88} +10.5744 q^{89} +(-6.70141 + 0.301824i) q^{90} +6.47723 q^{92} +(0.477226 + 0.213422i) q^{93} -7.75478i q^{94} +(8.47723 + 6.92163i) q^{95} +(0.707107 - 1.58114i) q^{96} +3.50333 q^{97} +(0.477226 - 0.426844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 16 q^{9} + 8 q^{15} + 8 q^{16} + 16 q^{18} + 8 q^{23} - 8 q^{25} - 8 q^{30} - 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} + 8 q^{50} - 40 q^{51} - 40 q^{53} + 40 q^{57}+ \cdots - 40 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 16 * q^9 + 8 * q^15 + 8 * q^16 + 16 * q^18 + 8 * q^23 - 8 * q^25 - 8 * q^30 - 8 * q^32 - 16 * q^36 + 16 * q^39 - 8 * q^46 + 8 * q^50 - 40 * q^51 - 40 * q^53 + 40 * q^57 + 8 * q^60 + 8 * q^64 + 32 * q^65 + 16 * q^72 - 16 * q^78 + 48 * q^79 - 8 * q^81 + 8 * q^92 - 40 * q^93 + 24 * q^95 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	+	1.58114i	−0.408248	+	0.912871i
$3$	−0.707107	+	1.58114i	−0.408248	+	0.912871i
$4$	1.00000			0.500000
$5$	−1.41421	+	1.73205i	−0.632456	+	0.774597i
$5$	−1.41421	+	1.73205i	−0.632456	+	0.774597i
$6$	0.707107	−	1.58114i	0.288675	−	0.645497i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.00000	−	2.23607i	−0.666667	−	0.745356i
$10$	1.41421	−	1.73205i	0.447214	−	0.547723i
$11$			0.213422i			0.0643491i	0.999482	+	0.0321745i	$0.0102432\pi$
$11$			0.213422i			0.0643491i	−0.999482	+	0.0321745i	$0.989757\pi$
$12$	−0.707107	+	1.58114i	−0.204124	+	0.456435i
$13$	−6.70141			−1.85864			−0.929318	−	0.369279i	$-0.879605\pi$
$13$	−6.70141			−1.85864			−0.929318	+	0.369279i	$0.879605\pi$
$14$		0			0
$15$	−1.73861	−	3.46081i	−0.448908	−	0.893578i
$16$	1.00000			0.250000
$17$			3.16228i			0.766965i	0.923548	+	0.383482i	$0.125275\pi$
$17$			3.16228i			0.766965i	−0.923548	+	0.383482i	$0.874725\pi$
$18$	2.00000	+	2.23607i	0.471405	+	0.527046i
$19$		−	4.89433i		−	1.12284i	−0.827532	−	0.561418i	$-0.810256\pi$
$19$		−	4.89433i		−	1.12284i	0.827532	−	0.561418i	$-0.189744\pi$
$20$	−1.41421	+	1.73205i	−0.316228	+	0.387298i
$21$		0			0
$22$		−	0.213422i		−	0.0455017i
$23$	6.47723			1.35059			0.675297	−	0.737545i	$-0.264015\pi$
$23$	6.47723			1.35059			0.675297	+	0.737545i	$0.264015\pi$
$24$	0.707107	−	1.58114i	0.144338	−	0.322749i
$25$	−1.00000	−	4.89898i	−0.200000	−	0.979796i
$26$	6.70141			1.31425
$27$	4.94975	−	1.58114i	0.952579	−	0.304290i
$28$		0			0
$29$		−	2.02265i		−	0.375596i	−0.982208	−	0.187798i	$-0.939865\pi$
$29$		−	2.02265i		−	0.375596i	0.982208	−	0.187798i	$-0.0601350\pi$
$30$	1.73861	+	3.46081i	0.317426	+	0.631855i
$31$		−	0.301824i		−	0.0542092i	−0.999633	−	0.0271046i	$-0.991371\pi$
$31$		−	0.301824i		−	0.0542092i	0.999633	−	0.0271046i	$-0.00862872\pi$
$32$	−1.00000			−0.176777
$33$	−0.337449	−	0.150912i	−0.0587424	−	0.0262704i
$34$		−	3.16228i		−	0.542326i
$35$		0			0
$36$	−2.00000	−	2.23607i	−0.333333	−	0.372678i
$37$		−	7.13505i		−	1.17299i	−0.809951	−	0.586497i	$-0.800506\pi$
$37$		−	7.13505i		−	1.17299i	0.809951	−	0.586497i	$-0.199494\pi$
$38$			4.89433i			0.793965i
$39$	4.73861	−	10.5959i	0.758785	−	1.69670i
$40$	1.41421	−	1.73205i	0.223607	−	0.273861i
$41$	−6.70141			−1.04658			−0.523292	−	0.852153i	$-0.675296\pi$
$41$	−6.70141			−1.04658			−0.523292	+	0.852153i	$0.675296\pi$
$42$		0			0
$43$			2.02265i			0.308451i	0.988036	+	0.154225i	$0.0492882\pi$
$43$			2.02265i			0.308451i	−0.988036	+	0.154225i	$0.950712\pi$
$44$			0.213422i			0.0321745i
$45$	6.70141	−	0.301824i	0.998987	−	0.0449933i
$46$	−6.47723			−0.955015
$47$			7.75478i			1.13115i	0.824696	+	0.565576i	$0.191346\pi$
$47$			7.75478i			1.13115i	−0.824696	+	0.565576i	$0.808654\pi$
$48$	−0.707107	+	1.58114i	−0.102062	+	0.228218i
$49$		0			0
$50$	1.00000	+	4.89898i	0.141421	+	0.692820i
$51$	−5.00000	−	2.23607i	−0.700140	−	0.313112i
$52$	−6.70141			−0.929318
$53$	−5.00000			−0.686803			−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000			−0.686803			−0.343401	+	0.939189i	$0.611579\pi$
$54$	−4.94975	+	1.58114i	−0.673575	+	0.215166i
$55$	−0.369657	−	0.301824i	−0.0498446	−	0.0406979i
$56$		0			0
$57$	7.73861	+	3.46081i	1.02500	+	0.458396i
$58$			2.02265i			0.265586i
$59$	4.91754			0.640209			0.320105	−	0.947382i	$-0.396282\pi$
$59$	4.91754			0.640209			0.320105	+	0.947382i	$0.396282\pi$
$60$	−1.73861	−	3.46081i	−0.224454	−	0.446789i
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$			0.301824i			0.0383317i
$63$		0			0
$64$	1.00000			0.125000
$65$	9.47723	−	11.6072i	1.17551	−	1.43969i
$66$	0.337449	+	0.150912i	0.0415372	+	0.0185760i
$67$			5.32582i			0.650653i	0.945602	+	0.325326i	$0.105474\pi$
$67$			5.32582i			0.650653i	−0.945602	+	0.325326i	$0.894526\pi$
$68$			3.16228i			0.383482i
$69$	−4.58009	+	10.2414i	−0.551378	+	1.23292i
$70$		0			0
$71$			2.02265i			0.240044i	0.992771	+	0.120022i	$0.0382965\pi$
$71$			2.02265i			0.240044i	−0.992771	+	0.120022i	$0.961703\pi$
$72$	2.00000	+	2.23607i	0.235702	+	0.263523i
$73$	11.9886			1.40316			0.701580	−	0.712591i	$-0.252478\pi$
$73$	11.9886			1.40316			0.701580	+	0.712591i	$0.252478\pi$
$74$			7.13505i			0.829432i
$75$	8.45307	+	1.88296i	0.976077	+	0.217426i
$76$		−	4.89433i		−	0.561418i
$77$		0			0
$78$	−4.73861	+	10.5959i	−0.536542	+	1.19974i
$79$	0.522774			0.0588167			0.0294084	−	0.999567i	$-0.490638\pi$
$79$	0.522774			0.0588167			0.0294084	+	0.999567i	$0.490638\pi$
$80$	−1.41421	+	1.73205i	−0.158114	+	0.193649i
$81$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$82$	6.70141			0.740047
$83$		−	16.7169i		−	1.83491i	−0.397835	−	0.917457i	$-0.630238\pi$
$83$		−	16.7169i		−	1.83491i	0.397835	−	0.917457i	$-0.369762\pi$
$84$		0			0
$85$	−5.47723	−	4.47214i	−0.594089	−	0.485071i
$86$		−	2.02265i		−	0.218108i
$87$	3.19808	+	1.43023i	0.342871	+	0.153336i
$88$		−	0.213422i		−	0.0227508i
$89$	10.5744			1.12088			0.560442	−	0.828194i	$-0.310631\pi$
$89$	10.5744			1.12088			0.560442	+	0.828194i	$0.310631\pi$
$90$	−6.70141	+	0.301824i	−0.706391	+	0.0318150i
$91$		0			0
$92$	6.47723			0.675297
$93$	0.477226	+	0.213422i	0.0494860	+	0.0221308i
$94$		−	7.75478i		−	0.799845i
$95$	8.47723	+	6.92163i	0.869745	+	0.710144i
$96$	0.707107	−	1.58114i	0.0721688	−	0.161374i
$97$	3.50333			0.355709			0.177854	−	0.984057i	$-0.443084\pi$
$97$	3.50333			0.355709			0.177854	+	0.984057i	$0.443084\pi$
$98$		0			0
$99$	0.477226	−	0.426844i	0.0479630	−	0.0428994i
$100$	−1.00000	−	4.89898i	−0.100000	−	0.489898i
$101$	11.3137			1.12576			0.562878	−	0.826540i	$-0.309694\pi$
$101$	11.3137			1.12576			0.562878	+	0.826540i	$0.309694\pi$
$102$	5.00000	+	2.23607i	0.495074	+	0.221404i
$103$	−10.5744			−1.04193			−0.520963	−	0.853579i	$-0.674427\pi$
$103$	−10.5744			−1.04193			−0.520963	+	0.853579i	$0.674427\pi$
$104$	6.70141			0.657127
$105$		0			0
$106$	5.00000			0.485643
$107$	−5.47723			−0.529503			−0.264752	−	0.964317i	$-0.585290\pi$
$107$	−5.47723			−0.529503			−0.264752	+	0.964317i	$0.585290\pi$
$108$	4.94975	−	1.58114i	0.476290	−	0.152145i
$109$	12.4317			1.19074			0.595369	−	0.803452i	$-0.297006\pi$
$109$	12.4317			1.19074			0.595369	+	0.803452i	$0.297006\pi$
$110$	0.369657	+	0.301824i	0.0352454	+	0.0287778i
$111$	11.2815	+	5.04524i	1.07079	+	0.478873i
$112$		0			0
$113$	−6.52277			−0.613611			−0.306806	−	0.951772i	$-0.599260\pi$
$113$	−6.52277			−0.613611			−0.306806	+	0.951772i	$0.599260\pi$
$114$	−7.73861	−	3.46081i	−0.724787	−	0.324135i
$115$	−9.16018	+	11.2189i	−0.854191	+	1.04617i
$116$		−	2.02265i		−	0.187798i
$117$	13.4028	+	14.9848i	1.23909	+	1.38535i
$118$	−4.91754			−0.452696
$119$		0			0
$120$	1.73861	+	3.46081i	0.158713	+	0.315928i
$121$	10.9545			0.995859
$122$			3.46410i			0.313625i
$123$	4.73861	−	10.5959i	0.427266	−	0.955397i
$124$		−	0.301824i		−	0.0271046i
$125$	9.89949	+	5.19615i	0.885438	+	0.464758i
$126$		0			0
$127$		−	13.6298i		−	1.20945i	−0.796434	−	0.604726i	$-0.793283\pi$
$127$		−	13.6298i		−	1.20945i	0.796434	−	0.604726i	$-0.206717\pi$
$128$	−1.00000			−0.0883883
$129$	−3.19808	−	1.43023i	−0.281576	−	0.125924i
$130$	−9.47723	+	11.6072i	−0.831208	+	1.01802i
$131$	−6.02651			−0.526539			−0.263269	−	0.964722i	$-0.584801\pi$
$131$	−6.02651			−0.526539			−0.263269	+	0.964722i	$0.584801\pi$
$132$	−0.337449	−	0.150912i	−0.0293712	−	0.0131352i
$133$		0			0
$134$		−	5.32582i		−	0.460081i
$135$	−4.26139	+	10.8093i	−0.366762	+	0.930315i
$136$		−	3.16228i		−	0.271163i
$137$	−7.47723			−0.638822			−0.319411	−	0.947616i	$-0.603485\pi$
$137$	−7.47723			−0.638822			−0.319411	+	0.947616i	$0.603485\pi$
$138$	4.58009	−	10.2414i	0.389883	−	0.871805i
$139$		−	7.53185i		−	0.638843i	−0.947613	−	0.319422i	$-0.896511\pi$
$139$		−	7.53185i		−	0.638843i	0.947613	−	0.319422i	$-0.103489\pi$
$140$		0			0
$141$	−12.2614	−	5.48346i	−1.03260	−	0.461791i
$142$		−	2.02265i		−	0.169737i
$143$		−	1.43023i		−	0.119602i
$144$	−2.00000	−	2.23607i	−0.166667	−	0.186339i
$145$	3.50333	+	2.86045i	0.290935	+	0.237548i
$146$	−11.9886			−0.992184
$147$		0			0
$148$		−	7.13505i		−	0.586497i
$149$		−	2.44949i		−	0.200670i	−0.994954	−	0.100335i	$-0.968009\pi$
$149$		−	2.44949i		−	0.200670i	0.994954	−	0.100335i	$-0.0319915\pi$
$150$	−8.45307	−	1.88296i	−0.690191	−	0.153743i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$			4.89433i			0.396982i
$153$	7.07107	−	6.32456i	0.571662	−	0.511310i
$154$		0			0
$155$	0.522774	+	0.426844i	0.0419903	+	0.0342849i
$156$	4.73861	−	10.5959i	0.379393	−	0.848348i
$157$	8.79052			0.701560			0.350780	−	0.936458i	$-0.385916\pi$
$157$	8.79052			0.701560			0.350780	+	0.936458i	$0.385916\pi$
$158$	−0.522774			−0.0415897
$159$	3.53553	−	7.90569i	0.280386	−	0.626962i
$160$	1.41421	−	1.73205i	0.111803	−	0.136931i
$161$		0			0
$162$	1.00000	−	8.94427i	0.0785674	−	0.702728i
$163$		−	14.6969i		−	1.15115i	−0.817748	−	0.575577i	$-0.804778\pi$
$163$		−	14.6969i		−	1.15115i	0.817748	−	0.575577i	$-0.195222\pi$
$164$	−6.70141			−0.523292
$165$	0.738613	−	0.371058i	0.0575009	−	0.0288868i
$166$			16.7169i			1.29748i
$167$			14.6830i			1.13620i	0.822958	+	0.568102i	$0.192322\pi$
$167$			14.6830i			1.13620i	−0.822958	+	0.568102i	$0.807678\pi$
$168$		0			0
$169$	31.9089			2.45453
$170$	5.47723	+	4.47214i	0.420084	+	0.342997i
$171$	−10.9441	+	9.78866i	−0.836913	+	0.748557i
$172$			2.02265i			0.154225i
$173$		−	11.5207i		−	0.875903i	−0.898999	−	0.437952i	$-0.855704\pi$
$173$		−	11.5207i		−	0.875903i	0.898999	−	0.437952i	$-0.144296\pi$
$174$	−3.19808	−	1.43023i	−0.242446	−	0.108425i
$175$		0			0
$176$			0.213422i			0.0160873i
$177$	−3.47723	+	7.77531i	−0.261364	+	0.584428i
$178$	−10.5744			−0.792584
$179$		−	14.9104i		−	1.11445i	−0.830361	−	0.557226i	$-0.811866\pi$
$179$		−	14.9104i		−	1.11445i	0.830361	−	0.557226i	$-0.188134\pi$
$180$	6.70141	−	0.301824i	0.499494	−	0.0224966i
$181$			3.16228i			0.235050i	0.993070	+	0.117525i	$0.0374961\pi$
$181$			3.16228i			0.235050i	−0.993070	+	0.117525i	$0.962504\pi$
$182$		0			0
$183$	5.47723	+	2.44949i	0.404888	+	0.181071i
$184$	−6.47723			−0.477507
$185$	12.3583	+	10.0905i	0.908598	+	0.741867i
$186$	−0.477226	−	0.213422i	−0.0349919	−	0.0156488i
$187$	−0.674899			−0.0493535
$188$			7.75478i			0.565576i
$189$		0			0
$190$	−8.47723	−	6.92163i	−0.615003	−	0.502148i
$191$			1.59580i			0.115468i	0.998332	+	0.0577341i	$0.0183876\pi$
$191$			1.59580i			0.115468i	−0.998332	+	0.0577341i	$0.981612\pi$
$192$	−0.707107	+	1.58114i	−0.0510310	+	0.114109i
$193$			7.34847i			0.528954i	0.964392	+	0.264477i	$0.0851994\pi$
$193$			7.34847i			0.528954i	−0.964392	+	0.264477i	$0.914801\pi$
$194$	−3.50333			−0.251524
$195$	11.6512	+	23.1923i	0.834357	+	1.66084i
$196$		0			0
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$	−0.477226	+	0.426844i	−0.0339149	+	0.0303344i
$199$		−	22.4378i		−	1.59057i	−0.606235	−	0.795286i	$-0.707321\pi$
$199$		−	22.4378i		−	1.59057i	0.606235	−	0.795286i	$-0.292679\pi$
$200$	1.00000	+	4.89898i	0.0707107	+	0.346410i
$201$	−8.42087	−	3.76593i	−0.593962	−	0.265628i
$202$	−11.3137			−0.796030
$203$		0			0
$204$	−5.00000	−	2.23607i	−0.350070	−	0.156556i
$205$	9.47723	−	11.6072i	0.661918	−	0.810681i
$206$	10.5744			0.736753
$207$	−12.9545	−	14.4835i	−0.900397	−	1.00667i
$208$	−6.70141			−0.464659
$209$	1.04456			0.0722535
$210$		0			0
$211$	13.5228			0.930946			0.465473	−	0.885062i	$-0.345884\pi$
$211$	13.5228			0.930946			0.465473	+	0.885062i	$0.345884\pi$
$212$	−5.00000			−0.343401
$213$	−3.19808	−	1.43023i	−0.219129	−	0.0979975i
$214$	5.47723			0.374415
$215$	−3.50333	−	2.86045i	−0.238925	−	0.195081i
$216$	−4.94975	+	1.58114i	−0.336788	+	0.107583i
$217$		0			0
$218$	−12.4317			−0.841979
$219$	−8.47723	+	18.9557i	−0.572838	+	1.28090i
$220$	−0.369657	−	0.301824i	−0.0249223	−	0.0203490i
$221$		−	21.1917i		−	1.42551i
$222$	−11.2815	−	5.04524i	−0.757165	−	0.338614i
$223$	−6.39617			−0.428319			−0.214160	−	0.976799i	$-0.568701\pi$
$223$	−6.39617			−0.428319			−0.214160	+	0.976799i	$0.568701\pi$
$224$		0			0
$225$	−8.95445	+	12.0340i	−0.596963	+	0.802268i
$226$	6.52277			0.433889
$227$		−	10.3923i		−	0.689761i	−0.938647	−	0.344881i	$-0.887919\pi$
$227$		−	10.3923i		−	0.689761i	0.938647	−	0.344881i	$-0.112081\pi$
$228$	7.73861	+	3.46081i	0.512502	+	0.229198i
$229$			7.23003i			0.477774i	0.971047	+	0.238887i	$0.0767825\pi$
$229$			7.23003i			0.477774i	−0.971047	+	0.238887i	$0.923218\pi$
$230$	9.16018	−	11.2189i	0.604004	−	0.739751i
$231$		0			0
$232$			2.02265i			0.132793i
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$	−13.4028	−	14.9848i	−0.876170	−	0.979588i
$235$	−13.4317	−	10.9669i	−0.876186	−	0.715403i
$236$	4.91754			0.320105
$237$	−0.369657	+	0.826579i	−0.0240118	+	0.0536921i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−1.73861	−	3.46081i	−0.112227	−	0.223395i
$241$			3.98886i			0.256945i	0.991713	+	0.128472i	$0.0410074\pi$
$241$			3.98886i			0.256945i	−0.991713	+	0.128472i	$0.958993\pi$
$242$	−10.9545			−0.704179
$243$	−13.4350	−	7.90569i	−0.861858	−	0.507151i
$244$		−	3.46410i		−	0.221766i
$245$		0			0
$246$	−4.73861	+	10.5959i	−0.302123	+	0.675567i
$247$			32.7989i			2.08694i
$248$			0.301824i			0.0191658i
$249$	26.4317	+	11.8206i	1.67504	+	0.749100i
$250$	−9.89949	−	5.19615i	−0.626099	−	0.328634i
$251$	16.6009			1.04784			0.523920	−	0.851768i	$-0.324469\pi$
$251$	16.6009			1.04784			0.523920	+	0.851768i	$0.324469\pi$
$252$		0			0
$253$			1.38238i			0.0869095i
$254$			13.6298i			0.855212i
$255$	10.9441	−	5.49798i	0.685343	−	0.344297i
$256$	1.00000			0.0625000
$257$		−	23.6451i		−	1.47494i	−0.675381	−	0.737469i	$-0.736021\pi$
$257$		−	23.6451i		−	1.47494i	0.675381	−	0.737469i	$-0.263979\pi$
$258$	3.19808	+	1.43023i	0.199104	+	0.0890420i
$259$		0			0
$260$	9.47723	−	11.6072i	0.587753	−	0.719847i
$261$	−4.52277	+	4.04529i	−0.279953	+	0.250397i
$262$	6.02651			0.372319
$263$	2.00000			0.123325			0.0616626	−	0.998097i	$-0.480360\pi$
$263$	2.00000			0.123325			0.0616626	+	0.998097i	$0.480360\pi$
$264$	0.337449	+	0.150912i	0.0207686	+	0.00928799i
$265$	7.07107	−	8.66025i	0.434372	−	0.531995i
$266$		0			0
$267$	−7.47723	+	16.7196i	−0.457599	+	1.02322i
$268$			5.32582i			0.325326i
$269$	−28.8948			−1.76174			−0.880872	−	0.473354i	$-0.843043\pi$
$269$	−28.8948			−1.76174			−0.880872	+	0.473354i	$0.843043\pi$
$270$	4.26139	−	10.8093i	0.259340	−	0.657832i
$271$		−	6.32456i		−	0.384189i	−0.981376	−	0.192095i	$-0.938472\pi$
$271$		−	6.32456i		−	0.384189i	0.981376	−	0.192095i	$-0.0615281\pi$
$272$			3.16228i			0.191741i
$273$		0			0
$274$	7.47723			0.451716
$275$	1.04555	−	0.213422i	0.0630490	−	0.0128698i
$276$	−4.58009	+	10.2414i	−0.275689	+	0.616459i
$277$		−	9.79796i		−	0.588702i	−0.955697	−	0.294351i	$-0.904896\pi$
$277$		−	9.79796i		−	0.588702i	0.955697	−	0.294351i	$-0.0951035\pi$
$278$			7.53185i			0.451730i
$279$	−0.674899	+	0.603648i	−0.0404051	+	0.0361395i
$280$		0			0
$281$			11.6072i			0.692427i	0.938156	+	0.346213i	$0.112533\pi$
$281$			11.6072i			0.692427i	−0.938156	+	0.346213i	$0.887467\pi$
$282$	12.2614	+	5.48346i	0.730155	+	0.326535i
$283$	−24.7165			−1.46925			−0.734623	−	0.678476i	$-0.762641\pi$
$283$	−24.7165			−1.46925			−0.734623	+	0.678476i	$0.762641\pi$
$284$			2.02265i			0.120022i
$285$	−16.9384	+	8.50934i	−1.00334	+	0.504050i
$286$			1.43023i			0.0845711i
$287$		0			0
$288$	2.00000	+	2.23607i	0.117851	+	0.131762i
$289$	7.00000			0.411765
$290$	−3.50333	−	2.86045i	−0.205722	−	0.167972i
$291$	−2.47723	+	5.53924i	−0.145218	+	0.324716i
$292$	11.9886			0.701580
$293$		−	4.59250i		−	0.268297i	−0.990961	−	0.134148i	$-0.957170\pi$
$293$		−	4.59250i		−	0.268297i	0.990961	−	0.134148i	$-0.0428299\pi$
$294$		0			0
$295$	−6.95445	+	8.51743i	−0.404904	+	0.495904i
$296$			7.13505i			0.414716i
$297$	0.337449	+	1.05638i	0.0195808	+	0.0612976i
$298$			2.44949i			0.141895i
$299$	−43.4065			−2.51027
$300$	8.45307	+	1.88296i	0.488038	+	0.108713i
$301$		0			0
$302$	2.00000			0.115087
$303$	−8.00000	+	17.8885i	−0.459588	+	1.02767i
$304$		−	4.89433i		−	0.280709i
$305$	6.00000	+	4.89898i	0.343559	+	0.280515i
$306$	−7.07107	+	6.32456i	−0.404226	+	0.361551i
$307$	−3.50333			−0.199945			−0.0999727	−	0.994990i	$-0.531876\pi$
$307$	−3.50333			−0.199945			−0.0999727	+	0.994990i	$0.531876\pi$
$308$		0			0
$309$	7.47723	−	16.7196i	0.425365	−	0.951144i
$310$	−0.522774	−	0.426844i	−0.0296916	−	0.0242431i
$311$	−28.8948			−1.63847			−0.819236	−	0.573457i	$-0.805602\pi$
$311$	−28.8948			−1.63847			−0.819236	+	0.573457i	$0.805602\pi$
$312$	−4.73861	+	10.5959i	−0.268271	+	0.599872i
$313$	23.2379			1.31348			0.656742	−	0.754115i	$-0.271934\pi$
$313$	23.2379			1.31348			0.656742	+	0.754115i	$0.271934\pi$
$314$	−8.79052			−0.496078
$315$		0			0
$316$	0.522774			0.0294084
$317$	−33.9089			−1.90451			−0.952257	−	0.305298i	$-0.901244\pi$
$317$	−33.9089			−1.90451			−0.952257	+	0.305298i	$0.901244\pi$
$318$	−3.53553	+	7.90569i	−0.198263	+	0.443329i
$319$	0.431677			0.0241693
$320$	−1.41421	+	1.73205i	−0.0790569	+	0.0968246i
$321$	3.87298	−	8.66025i	0.216169	−	0.483368i
$322$		0			0
$323$	15.4772			0.861176
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$	6.70141	+	32.8301i	0.371727	+	1.82108i
$326$			14.6969i			0.813988i
$327$	−8.79052	+	19.6562i	−0.486117	+	1.08699i
$328$	6.70141			0.370023
$329$		0			0
$330$	−0.738613	+	0.371058i	−0.0406593	+	0.0204261i
$331$	−11.4317			−0.628342			−0.314171	−	0.949366i	$-0.601726\pi$
$331$	−11.4317			−0.628342			−0.314171	+	0.949366i	$0.601726\pi$
$332$		−	16.7169i		−	0.917457i
$333$	−15.9545	+	14.2701i	−0.874299	+	0.781996i
$334$		−	14.6830i		−	0.803417i
$335$	−9.22460	−	7.53185i	−0.503994	−	0.411509i
$336$		0			0
$337$		−	17.1464i		−	0.934025i	−0.884251	−	0.467013i	$-0.845330\pi$
$337$		−	17.1464i		−	0.934025i	0.884251	−	0.467013i	$-0.154670\pi$
$338$	−31.9089			−1.73562
$339$	4.61230	−	10.3134i	0.250506	−	0.560148i
$340$	−5.47723	−	4.47214i	−0.297044	−	0.242536i
$341$	0.0644158			0.00348831
$342$	10.9441	−	9.78866i	0.591787	−	0.529310i
$343$		0			0
$344$		−	2.02265i		−	0.109054i
$345$	−11.2614	−	22.4165i	−0.606293	−	1.20686i
$346$			11.5207i			0.619357i
$347$	6.52277			0.350161			0.175080	−	0.984554i	$-0.443981\pi$
$347$	6.52277			0.350161			0.175080	+	0.984554i	$0.443981\pi$
$348$	3.19808	+	1.43023i	0.171435	+	0.0766682i
$349$		−	32.5282i		−	1.74120i	−0.491994	−	0.870599i	$-0.663732\pi$
$349$		−	32.5282i		−	1.74120i	0.491994	−	0.870599i	$-0.336268\pi$
$350$		0			0
$351$	−33.1703	+	10.5959i	−1.77050	+	0.565565i
$352$		−	0.213422i		−	0.0113754i
$353$		−	13.2528i		−	0.705373i	−0.935742	−	0.352687i	$-0.885268\pi$
$353$		−	13.2528i		−	0.705373i	0.935742	−	0.352687i	$-0.114732\pi$
$354$	3.47723	−	7.77531i	0.184812	−	0.413253i
$355$	−3.50333	−	2.86045i	−0.185937	−	0.151817i
$356$	10.5744			0.560442
$357$		0			0
$358$			14.9104i			0.788037i
$359$		−	6.49478i		−	0.342781i	−0.985203	−	0.171391i	$-0.945174\pi$
$359$		−	6.49478i		−	0.342781i	0.985203	−	0.171391i	$-0.0548261\pi$
$360$	−6.70141	+	0.301824i	−0.353195	+	0.0159075i
$361$	−4.95445			−0.260761
$362$		−	3.16228i		−	0.166206i
$363$	−7.74597	+	17.3205i	−0.406558	+	0.909091i
$364$		0			0
$365$	−16.9545	+	20.7649i	−0.887437	+	1.08688i
$366$	−5.47723	−	2.44949i	−0.286299	−	0.128037i
$367$	−8.11562			−0.423632			−0.211816	−	0.977310i	$-0.567938\pi$
$367$	−8.11562			−0.423632			−0.211816	+	0.977310i	$0.567938\pi$
$368$	6.47723			0.337649
$369$	13.4028	+	14.9848i	0.697723	+	0.780078i
$370$	−12.3583	−	10.0905i	−0.642476	−	0.524579i
$371$		0			0
$372$	0.477226	+	0.213422i	0.0247430	+	0.0110654i
$373$		−	3.61845i		−	0.187356i	−0.995603	−	0.0936781i	$-0.970138\pi$
$373$		−	3.61845i		−	0.187356i	0.995603	−	0.0936781i	$-0.0298624\pi$
$374$	0.674899			0.0348982
$375$	−15.2158	+	11.9782i	−0.785743	+	0.618554i
$376$		−	7.75478i		−	0.399922i
$377$			13.5546i			0.698097i
$378$		0			0
$379$	−9.52277			−0.489152			−0.244576	−	0.969630i	$-0.578649\pi$
$379$	−9.52277			−0.489152			−0.244576	+	0.969630i	$0.578649\pi$
$380$	8.47723	+	6.92163i	0.434872	+	0.355072i
$381$	21.5507	+	9.63774i	1.10407	+	0.493757i
$382$		−	1.59580i		−	0.0816484i
$383$		−	0.826579i		−	0.0422362i	−0.999777	−	0.0211181i	$-0.993277\pi$
$383$		−	0.826579i		−	0.0422362i	0.999777	−	0.0211181i	$-0.00672260\pi$
$384$	0.707107	−	1.58114i	0.0360844	−	0.0806872i
$385$		0			0
$386$		−	7.34847i		−	0.374027i
$387$	4.52277	−	4.04529i	0.229906	−	0.205634i
$388$	3.50333			0.177854
$389$		−	7.34847i		−	0.372582i	−0.982495	−	0.186291i	$-0.940353\pi$
$389$		−	7.34847i		−	0.372582i	0.982495	−	0.186291i	$-0.0596468\pi$
$390$	−11.6512	−	23.1923i	−0.589979	−	1.17439i
$391$			20.4828i			1.03586i
$392$		0			0
$393$	4.26139	−	9.52875i	0.214959	−	0.480662i
$394$	9.00000			0.453413
$395$	−0.739315	+	0.905472i	−0.0371990	+	0.0455592i
$396$	0.477226	−	0.426844i	0.0239815	−	0.0214497i
$397$	−30.3734			−1.52440			−0.762198	−	0.647344i	$-0.775880\pi$
$397$	−30.3734			−1.52440			−0.762198	+	0.647344i	$0.775880\pi$
$398$			22.4378i			1.12470i
$399$		0			0
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$			30.3494i			1.51558i	0.652500	+	0.757789i	$0.273720\pi$
$401$			30.3494i			1.51558i	−0.652500	+	0.757789i	$0.726280\pi$
$402$	8.42087	+	3.76593i	0.419995	+	0.187827i
$403$			2.02265i			0.100755i
$404$	11.3137			0.562878
$405$	−14.0777	−	14.3812i	−0.699528	−	0.714606i
$406$		0			0
$407$	1.52277			0.0754811
$408$	5.00000	+	2.23607i	0.247537	+	0.110702i
$409$		−	22.4378i		−	1.10948i	−0.832025	−	0.554738i	$-0.812818\pi$
$409$		−	22.4378i		−	1.10948i	0.832025	−	0.554738i	$-0.187182\pi$
$410$	−9.47723	+	11.6072i	−0.468047	+	0.573238i
$411$	5.28720	−	11.8225i	0.260798	−	0.583162i
$412$	−10.5744			−0.520963
$413$		0			0
$414$	12.9545	+	14.4835i	0.636677	+	0.711826i
$415$	28.9545	+	23.6412i	1.42132	+	1.16050i
$416$	6.70141			0.328564
$417$	11.9089	+	5.32582i	0.583181	+	0.260807i
$418$	−1.04456			−0.0510909
$419$	−16.6009			−0.811007			−0.405504	−	0.914093i	$-0.632904\pi$
$419$	−16.6009			−0.811007			−0.405504	+	0.914093i	$0.632904\pi$
$420$		0			0
$421$	−2.95445			−0.143991			−0.0719956	−	0.997405i	$-0.522937\pi$
$421$	−2.95445			−0.143991			−0.0719956	+	0.997405i	$0.522937\pi$
$422$	−13.5228			−0.658278
$423$	17.3402	−	15.5096i	0.843110	−	0.754101i
$424$	5.00000			0.242821
$425$	15.4919	−	3.16228i	0.751469	−	0.153393i
$426$	3.19808	+	1.43023i	0.154948	+	0.0692947i
$427$		0			0
$428$	−5.47723			−0.264752
$429$	2.26139	+	1.01132i	0.109181	+	0.0488271i
$430$	3.50333	+	2.86045i	0.168945	+	0.137943i
$431$			37.0576i			1.78500i	0.451045	+	0.892501i	$0.351051\pi$
$431$			37.0576i			1.78500i	−0.451045	+	0.892501i	$0.648949\pi$
$432$	4.94975	−	1.58114i	0.238145	−	0.0760726i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	−7.00000	+	3.51660i	−0.335624	+	0.168608i
$436$	12.4317			0.595369
$437$		−	31.7017i		−	1.51650i
$438$	8.47723	−	18.9557i	0.405058	−	0.905736i
$439$		−	22.7396i		−	1.08530i	−0.839958	−	0.542651i	$-0.817421\pi$
$439$		−	22.7396i		−	1.08530i	0.839958	−	0.542651i	$-0.182579\pi$
$440$	0.369657	+	0.301824i	0.0176227	+	0.0143889i
$441$		0			0
$442$			21.1917i			1.00799i
$443$	36.9545			1.75576			0.877879	−	0.478882i	$-0.158958\pi$
$443$	36.9545			1.75576			0.877879	+	0.478882i	$0.158958\pi$
$444$	11.2815	+	5.04524i	0.535396	+	0.239437i
$445$	−14.9545	+	18.3154i	−0.708909	+	0.868233i
$446$	6.39617			0.302867
$447$	3.87298	+	1.73205i	0.183186	+	0.0819232i
$448$		0			0
$449$		−	3.51660i		−	0.165959i	−0.996551	−	0.0829793i	$-0.973556\pi$
$449$		−	3.51660i		−	0.165959i	0.996551	−	0.0829793i	$-0.0264435\pi$
$450$	8.95445	−	12.0340i	0.422117	−	0.567289i
$451$		−	1.43023i		−	0.0673468i
$452$	−6.52277			−0.306806
$453$	1.41421	−	3.16228i	0.0664455	−	0.148577i
$454$			10.3923i			0.487735i
$455$		0			0
$456$	−7.73861	−	3.46081i	−0.362394	−	0.162067i
$457$		−	37.9113i		−	1.77342i	−0.462330	−	0.886708i	$-0.652986\pi$
$457$		−	37.9113i		−	1.77342i	0.462330	−	0.886708i	$-0.347014\pi$
$458$		−	7.23003i		−	0.337837i
$459$	5.00000	+	15.6525i	0.233380	+	0.730595i
$460$	−9.16018	+	11.2189i	−0.427096	+	0.523083i
$461$	−16.2957			−0.758965			−0.379482	−	0.925199i	$-0.623898\pi$
$461$	−16.2957			−0.758965			−0.379482	+	0.925199i	$0.623898\pi$
$462$		0			0
$463$		−	17.6751i		−	0.821433i	−0.911763	−	0.410716i	$-0.865279\pi$
$463$		−	17.6751i		−	0.821433i	0.911763	−	0.410716i	$-0.134721\pi$
$464$		−	2.02265i		−	0.0938990i
$465$	−1.04456	+	0.524755i	−0.0484401	+	0.0243349i
$466$	−4.00000			−0.185296
$467$		−	34.3392i		−	1.58903i	−0.607246	−	0.794514i	$-0.707726\pi$
$467$		−	34.3392i		−	1.58903i	0.607246	−	0.794514i	$-0.292274\pi$
$468$	13.4028	+	14.9848i	0.619546	+	0.692673i
$469$		0			0
$470$	13.4317	+	10.9669i	0.619557	+	0.505866i
$471$	−6.21584	+	13.8990i	−0.286411	+	0.640434i
$472$	−4.91754			−0.226348
$473$	−0.431677			−0.0198485
$474$	0.369657	−	0.826579i	0.0169789	−	0.0379660i
$475$	−23.9772	+	4.89433i	−1.10015	+	0.224567i
$476$		0			0
$477$	10.0000	+	11.1803i	0.457869	+	0.511913i
$478$		0			0
$479$	−11.3781			−0.519880			−0.259940	−	0.965625i	$-0.583703\pi$
$479$	−11.3781			−0.519880			−0.259940	+	0.965625i	$0.583703\pi$
$480$	1.73861	+	3.46081i	0.0793565	+	0.157964i
$481$			47.8149i			2.18017i
$482$		−	3.98886i		−	0.181687i
$483$		0			0
$484$	10.9545			0.497930
$485$	−4.95445	+	6.06794i	−0.224970	+	0.275531i
$486$	13.4350	+	7.90569i	0.609425	+	0.358610i
$487$			36.6308i			1.65990i	0.557839	+	0.829949i	$0.311631\pi$
$487$			36.6308i			1.65990i	−0.557839	+	0.829949i	$0.688369\pi$
$488$			3.46410i			0.156813i
$489$	23.2379	+	10.3923i	1.05085	+	0.469956i
$490$		0			0
$491$		−	4.04529i		−	0.182561i	−0.995825	−	0.0912807i	$-0.970904\pi$
$491$		−	4.04529i		−	0.182561i	0.995825	−	0.0912807i	$-0.0290961\pi$
$492$	4.73861	−	10.5959i	0.213633	−	0.477698i
$493$	6.39617			0.288069
$494$		−	32.7989i		−	1.47569i
$495$	0.0644158	+	1.43023i	0.00289527	+	0.0642839i
$496$		−	0.301824i		−	0.0135523i
$497$		0			0
$498$	−26.4317	−	11.8206i	−1.18443	−	0.529694i
$499$	−41.9089			−1.87610			−0.938050	−	0.346500i	$-0.887370\pi$
$499$	−41.9089			−1.87610			−0.938050	+	0.346500i	$0.887370\pi$
$500$	9.89949	+	5.19615i	0.442719	+	0.232379i
$501$	−23.2158	−	10.3824i	−1.03721	−	0.463853i
$502$	−16.6009			−0.740935
$503$		−	22.4378i		−	1.00045i	−0.865895	−	0.500225i	$-0.833251\pi$
$503$		−	22.4378i		−	1.00045i	0.865895	−	0.500225i	$-0.166749\pi$
$504$		0			0
$505$	−16.0000	+	19.5959i	−0.711991	+	0.872007i
$506$		−	1.38238i		−	0.0614543i
$507$	−22.5630	+	50.4524i	−1.00206	+	2.24067i
$508$		−	13.6298i		−	0.604726i
$509$	−9.22460			−0.408873			−0.204437	−	0.978880i	$-0.565536\pi$
$509$	−9.22460			−0.408873			−0.204437	+	0.978880i	$0.565536\pi$
$510$	−10.9441	+	5.49798i	−0.484611	+	0.243454i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−7.73861	−	24.2257i	−0.341668	−	1.06959i
$514$			23.6451i			1.04294i
$515$	14.9545	−	18.3154i	0.658972	−	0.807072i
$516$	−3.19808	−	1.43023i	−0.140788	−	0.0629622i
$517$	−1.65504			−0.0727885
$518$		0			0
$519$	18.2158	+	8.14637i	0.799587	+	0.357586i
$520$	−9.47723	+	11.6072i	−0.415604	+	0.509009i
$521$	18.6256			0.816002			0.408001	−	0.912981i	$-0.366226\pi$
$521$	18.6256			0.816002			0.408001	+	0.912981i	$0.366226\pi$
$522$	4.52277	−	4.04529i	0.197956	−	0.177058i
$523$	−14.0777			−0.615576			−0.307788	−	0.951455i	$-0.599589\pi$
$523$	−14.0777			−0.615576			−0.307788	+	0.951455i	$0.599589\pi$
$524$	−6.02651			−0.263269
$525$		0			0
$526$	−2.00000			−0.0872041
$527$	0.954451			0.0415765
$528$	−0.337449	−	0.150912i	−0.0146856	−	0.00656760i
$529$	18.9545			0.824107
$530$	−7.07107	+	8.66025i	−0.307148	+	0.376177i
$531$	−9.83508	−	10.9960i	−0.426806	−	0.477184i
$532$		0			0
$533$	44.9089			1.94522
$534$	7.47723	−	16.7196i	0.323571	−	0.723527i
$535$	7.74597	−	9.48683i	0.334887	−	0.410152i
$536$		−	5.32582i		−	0.230041i
$537$	23.5753	+	10.5432i	1.01735	+	0.454973i
$538$	28.8948			1.24574
$539$		0			0
$540$	−4.26139	+	10.8093i	−0.183381	+	0.465157i
$541$	19.4772			0.837391			0.418696	−	0.908127i	$-0.362487\pi$
$541$	19.4772			0.837391			0.418696	+	0.908127i	$0.362487\pi$
$542$			6.32456i			0.271663i
$543$	−5.00000	−	2.23607i	−0.214571	−	0.0959589i
$544$		−	3.16228i		−	0.135582i
$545$	−17.5810	+	21.5323i	−0.753089	+	0.922342i
$546$		0			0
$547$			23.2144i			0.992575i	0.868158	+	0.496287i	$0.165304\pi$
$547$			23.2144i			0.992575i	−0.868158	+	0.496287i	$0.834696\pi$
$548$	−7.47723			−0.319411
$549$	−7.74597	+	6.92820i	−0.330590	+	0.295689i
$550$	−1.04555	+	0.213422i	−0.0445824	+	0.00910033i
$551$	−9.89949			−0.421733
$552$	4.58009	−	10.2414i	0.194942	−	0.435903i
$553$		0			0
$554$			9.79796i			0.416275i
$555$	−24.6931	+	12.4051i	−1.04816	+	0.526567i
$556$		−	7.53185i		−	0.319422i
$557$	37.8634			1.60432			0.802161	−	0.597108i	$-0.203684\pi$
$557$	37.8634			1.60432			0.802161	+	0.597108i	$0.203684\pi$
$558$	0.674899	−	0.603648i	0.0285707	−	0.0255545i
$559$		−	13.5546i		−	0.573298i
$560$		0			0
$561$	0.477226	−	1.06711i	0.0201485	−	0.0450534i
$562$		−	11.6072i		−	0.489619i
$563$		−	10.3923i		−	0.437983i	−0.975727	−	0.218992i	$-0.929723\pi$
$563$		−	10.3923i		−	0.437983i	0.975727	−	0.218992i	$-0.0702768\pi$
$564$	−12.2614	−	5.48346i	−0.516298	−	0.230895i
$565$	9.22460	−	11.2978i	0.388082	−	0.475301i
$566$	24.7165			1.03891
$567$		0			0
$568$		−	2.02265i		−	0.0848683i
$569$		−	12.0340i		−	0.504493i	−0.967663	−	0.252246i	$-0.918831\pi$
$569$		−	12.0340i		−	0.504493i	0.967663	−	0.252246i	$-0.0811693\pi$
$570$	16.9384	−	8.50934i	0.709470	−	0.356417i
$571$	−6.95445			−0.291035			−0.145517	−	0.989356i	$-0.546485\pi$
$571$	−6.95445			−0.291035			−0.145517	+	0.989356i	$0.546485\pi$
$572$		−	1.43023i		−	0.0598008i
$573$	−2.52319	−	1.12840i	−0.105408	−	0.0471397i
$574$		0			0
$575$	−6.47723	−	31.7318i	−0.270119	−	1.32331i
$576$	−2.00000	−	2.23607i	−0.0833333	−	0.0931695i
$577$	−14.8170			−0.616841			−0.308421	−	0.951250i	$-0.599800\pi$
$577$	−14.8170			−0.616841			−0.308421	+	0.951250i	$0.599800\pi$
$578$	−7.00000			−0.291162
$579$	−11.6190	−	5.19615i	−0.482867	−	0.215945i
$580$	3.50333	+	2.86045i	0.145468	+	0.118774i
$581$		0			0
$582$	2.47723	−	5.53924i	0.102684	−	0.229609i
$583$		−	1.06711i		−	0.0441951i
$584$	−11.9886			−0.496092
$585$	−44.9089	+	2.02265i	−1.85675	+	0.0836261i
$586$			4.59250i			0.189715i
$587$		−	27.4110i		−	1.13137i	−0.824621	−	0.565686i	$-0.808611\pi$
$587$		−	27.4110i		−	1.13137i	0.824621	−	0.565686i	$-0.191389\pi$
$588$		0			0
$589$	−1.47723			−0.0608680
$590$	6.95445	−	8.51743i	0.286310	−	0.350657i
$591$	6.36396	−	14.2302i	0.261778	−	0.585354i
$592$		−	7.13505i		−	0.293249i
$593$			36.2942i			1.49042i	0.666828	+	0.745212i	$0.267652\pi$
$593$			36.2942i			1.49042i	−0.666828	+	0.745212i	$0.732348\pi$
$594$	−0.337449	−	1.05638i	−0.0138457	−	0.0433440i
$595$		0			0
$596$		−	2.44949i		−	0.100335i
$597$	35.4772	+	15.8659i	1.45199	+	0.649348i
$598$	43.4065			1.77503
$599$			5.75267i			0.235048i	0.993070	+	0.117524i	$0.0374956\pi$
$599$			5.75267i			0.235048i	−0.993070	+	0.117524i	$0.962504\pi$
$600$	−8.45307	−	1.88296i	−0.345095	−	0.0768716i
$601$			16.7169i			0.681895i	0.940082	+	0.340947i	$0.110748\pi$
$601$			16.7169i			0.681895i	−0.940082	+	0.340947i	$0.889252\pi$
$602$		0			0
$603$	11.9089	−	10.6516i	0.484968	−	0.433769i
$604$	−2.00000			−0.0813788
$605$	−15.4919	+	18.9737i	−0.629837	+	0.771389i
$606$	8.00000	−	17.8885i	0.324978	−	0.726672i
$607$	26.4360			1.07300			0.536502	−	0.843899i	$-0.319745\pi$
$607$	26.4360			1.07300			0.536502	+	0.843899i	$0.319745\pi$
$608$			4.89433i			0.198491i
$609$		0			0
$610$	−6.00000	−	4.89898i	−0.242933	−	0.198354i
$611$		−	51.9680i		−	2.10240i
$612$	7.07107	−	6.32456i	0.285831	−	0.255655i
$613$		−	25.4504i		−	1.02793i	−0.857810	−	0.513967i	$-0.828175\pi$
$613$		−	25.4504i		−	1.02793i	0.857810	−	0.513967i	$-0.171825\pi$
$614$	3.50333			0.141383
$615$	11.6512	+	23.1923i	0.469820	+	0.935205i
$616$		0			0
$617$	−25.4772			−1.02567			−0.512837	−	0.858486i	$-0.671406\pi$
$617$	−25.4772			−1.02567			−0.512837	+	0.858486i	$0.671406\pi$
$618$	−7.47723	+	16.7196i	−0.300778	+	0.672560i
$619$		−	26.7284i		−	1.07431i	−0.843484	−	0.537154i	$-0.819500\pi$
$619$		−	26.7284i		−	1.07431i	0.843484	−	0.537154i	$-0.180500\pi$
$620$	0.522774	+	0.426844i	0.0209951	+	0.0171424i
$621$	32.0606	−	10.2414i	1.28655	−	0.410973i
$622$	28.8948			1.15857
$623$		0			0
$624$	4.73861	−	10.5959i	0.189696	−	0.424174i
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$	−23.2379			−0.928773
$627$	−0.738613	+	1.65159i	−0.0294974	+	0.0659581i
$628$	8.79052			0.350780
$629$	22.5630			0.899646
$630$		0			0
$631$	−7.47723			−0.297664			−0.148832	−	0.988863i	$-0.547551\pi$
$631$	−7.47723			−0.297664			−0.148832	+	0.988863i	$0.547551\pi$
$632$	−0.522774			−0.0207949
$633$	−9.56205	+	21.3814i	−0.380057	+	0.849834i
$634$	33.9089			1.34669
$635$	23.6076	+	19.2755i	0.936837	+	0.764924i
$636$	3.53553	−	7.90569i	0.140193	−	0.313481i
$637$		0			0
$638$	−0.431677			−0.0170902
$639$	4.52277	−	4.04529i	0.178918	−	0.160029i
$640$	1.41421	−	1.73205i	0.0559017	−	0.0684653i
$641$			6.28136i			0.248099i	0.992276	+	0.124049i	$0.0395881\pi$
$641$			6.28136i			0.248099i	−0.992276	+	0.124049i	$0.960412\pi$
$642$	−3.87298	+	8.66025i	−0.152854	+	0.341793i
$643$	20.4095			0.804871			0.402436	−	0.915448i	$-0.368164\pi$
$643$	20.4095			0.804871			0.402436	+	0.915448i	$0.368164\pi$
$644$		0			0
$645$	7.00000	−	3.51660i	0.275625	−	0.138466i
$646$	−15.4772			−0.608943
$647$			23.8680i			0.938348i	0.883106	+	0.469174i	$0.155448\pi$
$647$			23.8680i			0.938348i	−0.883106	+	0.469174i	$0.844552\pi$
$648$	1.00000	−	8.94427i	0.0392837	−	0.351364i
$649$			1.04951i			0.0411969i
$650$	−6.70141	−	32.8301i	−0.262851	−	1.28770i
$651$		0			0
$652$		−	14.6969i		−	0.575577i
$653$	25.8634			1.01211			0.506056	−	0.862501i	$-0.331103\pi$
$653$	25.8634			1.01211			0.506056	+	0.862501i	$0.331103\pi$
$654$	8.79052	−	19.6562i	0.343737	−	0.768619i
$655$	8.52277	−	10.4382i	0.333012	−	0.407855i
$656$	−6.70141			−0.261646
$657$	−23.9772	−	26.8073i	−0.935440	−	1.04585i
$658$		0			0
$659$		−	34.2929i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$	0.738613	−	0.371058i	0.0287505	−	0.0144434i
$661$			13.2528i			0.515473i	0.966215	+	0.257736i	$0.0829766\pi$
$661$			13.2528i			0.515473i	−0.966215	+	0.257736i	$0.917023\pi$
$662$	11.4317			0.444305
$663$	33.5071	+	14.9848i	1.30131	+	0.581962i
$664$			16.7169i			0.648740i
$665$		0			0
$666$	15.9545	−	14.2701i	0.618222	−	0.552955i
$667$		−	13.1011i		−	0.507278i
$668$			14.6830i			0.568102i
$669$	4.52277	−	10.1132i	0.174861	−	0.391000i
$670$	9.22460	+	7.53185i	0.356377	+	0.290981i
$671$	0.739315			0.0285409
$672$		0			0
$673$		−	48.4514i		−	1.86766i	−0.357713	−	0.933832i	$-0.616443\pi$
$673$		−	48.4514i		−	1.86766i	0.357713	−	0.933832i	$-0.383557\pi$
$674$			17.1464i			0.660456i
$675$	−12.6957	−	22.6676i	−0.488658	−	0.872475i
$676$	31.9089			1.22727
$677$		−	32.9090i		−	1.26479i	−0.774644	−	0.632397i	$-0.782071\pi$
$677$		−	32.9090i		−	1.26479i	0.774644	−	0.632397i	$-0.217929\pi$
$678$	−4.61230	+	10.3134i	−0.177134	+	0.396084i
$679$		0			0
$680$	5.47723	+	4.47214i	0.210042	+	0.171499i
$681$	16.4317	+	7.34847i	0.629663	+	0.281594i
$682$	−0.0644158			−0.00246661
$683$	−2.95445			−0.113049			−0.0565245	−	0.998401i	$-0.518002\pi$
$683$	−2.95445			−0.113049			−0.0565245	+	0.998401i	$0.518002\pi$
$684$	−10.9441	+	9.78866i	−0.418456	+	0.374279i
$685$	10.5744	−	12.9509i	0.404027	−	0.494830i
$686$		0			0
$687$	−11.4317	−	5.11240i	−0.436146	−	0.195050i
$688$			2.02265i			0.0771127i
$689$	33.5071			1.27652
$690$	11.2614	+	22.4165i	0.428714	+	0.853380i
$691$		−	3.46410i		−	0.131781i	−0.997827	−	0.0658903i	$-0.979011\pi$
$691$		−	3.46410i		−	0.131781i	0.997827	−	0.0658903i	$-0.0209887\pi$
$692$		−	11.5207i		−	0.437952i
$693$		0			0
$694$	−6.52277			−0.247601
$695$	13.0455	+	10.6516i	0.494846	+	0.404040i
$696$	−3.19808	−	1.43023i	−0.121223	−	0.0542126i
$697$		−	21.1917i		−	0.802694i
$698$			32.5282i			1.23121i
$699$	−2.82843	+	6.32456i	−0.106981	+	0.239217i
$700$		0			0
$701$			7.03320i			0.265640i	0.991140	+	0.132820i	$0.0424033\pi$
$701$			7.03320i			0.265640i	−0.991140	+	0.132820i	$0.957597\pi$
$702$	33.1703	−	10.5959i	1.25193	−	0.399915i
$703$	−34.9213			−1.31708
$704$			0.213422i			0.00804364i
$705$	26.8378	−	13.4826i	1.01077	−	0.507783i
$706$			13.2528i			0.498774i
$707$		0			0
$708$	−3.47723	+	7.77531i	−0.130682	+	0.292214i
$709$	10.4317			0.391770			0.195885	−	0.980627i	$-0.437242\pi$
$709$	10.4317			0.391770			0.195885	+	0.980627i	$0.437242\pi$
$710$	3.50333	+	2.86045i	0.131477	+	0.107351i
$711$	−1.04555	−	1.16896i	−0.0392111	−	0.0438394i
$712$	−10.5744			−0.396292
$713$		−	1.95498i		−	0.0732146i
$714$		0			0
$715$	2.47723	+	2.02265i	0.0926430	+	0.0756427i
$716$		−	14.9104i		−	0.557226i
$717$		0			0
$718$			6.49478i			0.242383i
$719$	47.2795			1.76323			0.881614	−	0.471970i	$-0.156457\pi$
$719$	47.2795			1.76323			0.881614	+	0.471970i	$0.156457\pi$
$720$	6.70141	−	0.301824i	0.249747	−	0.0112483i
$721$		0			0
$722$	4.95445			0.184386
$723$	−6.30694	−	2.82055i	−0.234557	−	0.104897i
$724$			3.16228i			0.117525i
$725$	−9.90890	+	2.02265i	−0.368007	+	0.0751192i
$726$	7.74597	−	17.3205i	0.287480	−	0.642824i
$727$	23.6076			0.875556			0.437778	−	0.899083i	$-0.355766\pi$
$727$	23.6076			0.875556			0.437778	+	0.899083i	$0.355766\pi$
$728$		0			0
$729$	22.0000	−	15.6525i	0.814815	−	0.579721i
$730$	16.9545	−	20.7649i	0.627512	−	0.768543i
$731$	−6.39617			−0.236571
$732$	5.47723	+	2.44949i	0.202444	+	0.0905357i
$733$	36.3355			1.34208			0.671041	−	0.741420i	$-0.265848\pi$
$733$	36.3355			1.34208			0.671041	+	0.741420i	$0.265848\pi$
$734$	8.11562			0.299553
$735$		0			0
$736$	−6.47723			−0.238754
$737$	−1.13665			−0.0418689
$738$	−13.4028	−	14.9848i	−0.493365	−	0.551598i
$739$	−4.47723			−0.164697			−0.0823487	−	0.996604i	$-0.526242\pi$
$739$	−4.47723			−0.164697			−0.0823487	+	0.996604i	$0.526242\pi$
$740$	12.3583	+	10.0905i	0.454299	+	0.370933i
$741$	−51.8596	−	23.1923i	−1.90511	−	0.851991i
$742$		0			0
$743$	19.4317			0.712879			0.356440	−	0.934318i	$-0.383991\pi$
$743$	19.4317			0.712879			0.356440	+	0.934318i	$0.383991\pi$
$744$	−0.477226	−	0.213422i	−0.0174959	−	0.00782442i
$745$	4.24264	+	3.46410i	0.155438	+	0.126915i
$746$			3.61845i			0.132481i
$747$	−37.3800	+	33.4337i	−1.36766	+	1.22328i
$748$	−0.674899			−0.0246767
$749$		0			0
$750$	15.2158	−	11.9782i	0.555604	−	0.437384i
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$			7.75478i			0.282788i
$753$	−11.7386	+	26.2483i	−0.427779	+	0.956543i
$754$		−	13.5546i		−	0.493629i
$755$	2.82843	−	3.46410i	0.102937	−	0.126072i
$756$		0			0
$757$			30.2476i			1.09937i	0.835373	+	0.549683i	$0.185252\pi$
$757$			30.2476i			1.09937i	−0.835373	+	0.549683i	$0.814748\pi$
$758$	9.52277			0.345883
$759$	−2.18574	−	0.977491i	−0.0793372	−	0.0354807i
$760$	−8.47723	−	6.92163i	−0.307501	−	0.251074i
$761$	−9.52984			−0.345456			−0.172728	−	0.984970i	$-0.555258\pi$
$761$	−9.52984			−0.345456			−0.172728	+	0.984970i	$0.555258\pi$
$762$	−21.5507	−	9.63774i	−0.780698	−	0.349139i
$763$		0			0
$764$			1.59580i			0.0577341i
$765$	0.954451	+	21.1917i	0.0345083	+	0.766188i
$766$			0.826579i			0.0298655i
$767$	−32.9545			−1.18992
$768$	−0.707107	+	1.58114i	−0.0255155	+	0.0570544i
$769$			28.8412i			1.04004i	0.854154	+	0.520020i	$0.174076\pi$
$769$			28.8412i			1.04004i	−0.854154	+	0.520020i	$0.825924\pi$
$770$		0			0
$771$	37.3861	+	16.7196i	1.34643	+	0.602141i
$772$			7.34847i			0.264477i
$773$			28.8412i			1.03735i	0.854973	+	0.518673i	$0.173574\pi$
$773$			28.8412i			1.03735i	−0.854973	+	0.518673i	$0.826426\pi$
$774$	−4.52277	+	4.04529i	−0.162568	+	0.145405i
$775$	−1.47863	+	0.301824i	−0.0531139	+	0.0108418i
$776$	−3.50333			−0.125762
$777$		0			0
$778$			7.34847i			0.263455i
$779$			32.7989i			1.17514i
$780$	11.6512	+	23.1923i	0.417178	+	0.830419i
$781$	−0.431677			−0.0154466
$782$		−	20.4828i		−	0.732463i
$783$	−3.19808	−	10.0116i	−0.114290	−	0.357785i
$784$		0			0
$785$	−12.4317	+	15.2256i	−0.443706	+	0.543426i
$786$	−4.26139	+	9.52875i	−0.151999	+	0.339879i
$787$	34.6804			1.23622			0.618112	−	0.786090i	$-0.287898\pi$
$787$	34.6804			1.23622			0.618112	+	0.786090i	$0.287898\pi$
$788$	−9.00000			−0.320612
$789$	−1.41421	+	3.16228i	−0.0503473	+	0.112580i
$790$	0.739315	−	0.905472i	0.0263036	−	0.0322152i
$791$		0			0
$792$	−0.477226	+	0.426844i	−0.0169575	+	0.0151672i
$793$			23.2144i			0.824366i
$794$	30.3734			1.07791
$795$	8.69306	+	17.3041i	0.308311	+	0.613712i
$796$		−	22.4378i		−	0.795286i
$797$			28.9201i			1.02440i	0.858865	+	0.512201i	$0.171170\pi$
$797$			28.9201i			1.02440i	−0.858865	+	0.512201i	$0.828830\pi$
$798$		0			0
$799$	−24.5228			−0.867553
$800$	1.00000	+	4.89898i	0.0353553	+	0.173205i
$801$	−21.1488	−	23.6451i	−0.747256	−	0.835457i
$802$		−	30.3494i		−	1.07168i
$803$			2.55863i			0.0902921i
$804$	−8.42087	−	3.76593i	−0.296981	−	0.132814i
$805$		0			0
$806$		−	2.02265i		−	0.0712447i
$807$	20.4317	−	45.6866i	0.719229	−	1.60825i
$808$	−11.3137			−0.398015
$809$		−	40.1474i		−	1.41151i	−0.708458	−	0.705753i	$-0.750609\pi$
$809$		−	40.1474i		−	1.41151i	0.708458	−	0.705753i	$-0.249391\pi$
$810$	14.0777	+	14.3812i	0.494641	+	0.505303i
$811$			6.70527i			0.235454i	0.993046	+	0.117727i	$0.0375608\pi$
$811$			6.70527i			0.235454i	−0.993046	+	0.117727i	$0.962439\pi$
$812$		0			0
$813$	10.0000	+	4.47214i	0.350715	+	0.156845i
$814$	−1.52277			−0.0533732
$815$	25.4558	+	20.7846i	0.891679	+	0.728053i
$816$	−5.00000	−	2.23607i	−0.175035	−	0.0782780i
$817$	9.89949			0.346339
$818$			22.4378i			0.784518i
$819$		0			0
$820$	9.47723	−	11.6072i	0.330959	−	0.405340i
$821$		−	50.9009i		−	1.77645i	−0.459406	−	0.888226i	$-0.651938\pi$
$821$		−	50.9009i		−	1.77645i	0.459406	−	0.888226i	$-0.348062\pi$
$822$	−5.28720	+	11.8225i	−0.184412	+	0.412358i
$823$			32.5855i			1.13586i	0.823077	+	0.567929i	$0.192255\pi$
$823$			32.5855i			1.13586i	−0.823077	+	0.567929i	$0.807745\pi$
$824$	10.5744			0.368376
$825$	−0.401865	+	1.80407i	−0.0139912	+	0.0628097i
$826$		0			0
$827$	−39.9089			−1.38777			−0.693884	−	0.720087i	$-0.744102\pi$
$827$	−39.9089			−1.38777			−0.693884	+	0.720087i	$0.744102\pi$
$828$	−12.9545	−	14.4835i	−0.450198	−	0.503337i
$829$		−	18.8296i		−	0.653980i	−0.945028	−	0.326990i	$-0.893966\pi$
$829$		−	18.8296i		−	0.653980i	0.945028	−	0.326990i	$-0.106034\pi$
$830$	−28.9545	−	23.6412i	−1.00502	−	0.820598i
$831$	15.4919	+	6.92820i	0.537409	+	0.240337i
$832$	−6.70141			−0.232330
$833$		0			0
$834$	−11.9089	−	5.32582i	−0.412372	−	0.184418i
$835$	−25.4317	−	20.7649i	−0.880099	−	0.718598i
$836$	1.04456			0.0361267
$837$	−0.477226	−	1.49395i	−0.0164953	−	0.0516385i
$838$	16.6009			0.573469
$839$	−37.3156			−1.28828			−0.644139	−	0.764908i	$-0.722784\pi$
$839$	−37.3156			−1.28828			−0.644139	+	0.764908i	$0.722784\pi$
$840$		0			0
$841$	24.9089			0.858928
$842$	2.95445			0.101817
$843$	−18.3526	−	8.20752i	−0.632096	−	0.282682i
$844$	13.5228			0.465473
$845$	−45.1260	+	55.2678i	−1.55238	+	1.90127i
$846$	−17.3402	+	15.5096i	−0.596169	+	0.533230i
$847$		0			0
$848$	−5.00000			−0.171701
$849$	17.4772	−	39.0803i	0.599817	−	1.34123i
$850$	−15.4919	+	3.16228i	−0.531369	+	0.108465i
$851$		−	46.2153i		−	1.58424i
$852$	−3.19808	−	1.43023i	−0.109565	−	0.0489988i
$853$	−53.9165			−1.84607			−0.923033	−	0.384720i	$-0.874298\pi$
$853$	−53.9165			−1.84607			−0.923033	+	0.384720i	$0.874298\pi$
$854$		0			0
$855$	−1.47723	−	32.7989i	−0.0505200	−	1.12170i
$856$	5.47723			0.187208
$857$		−	40.3619i		−	1.37874i	−0.724411	−	0.689369i	$-0.757888\pi$
$857$		−	40.3619i		−	1.37874i	0.724411	−	0.689369i	$-0.242112\pi$
$858$	−2.26139	−	1.01132i	−0.0772025	−	0.0345260i
$859$			17.9242i			0.611564i	0.952102	+	0.305782i	$0.0989179\pi$
$859$			17.9242i			0.611564i	−0.952102	+	0.305782i	$0.901082\pi$
$860$	−3.50333	−	2.86045i	−0.119462	−	0.0975407i
$861$		0			0
$862$		−	37.0576i		−	1.26219i
$863$	15.5228			0.528401			0.264201	−	0.964468i	$-0.414892\pi$
$863$	15.5228			0.528401			0.264201	+	0.964468i	$0.414892\pi$
$864$	−4.94975	+	1.58114i	−0.168394	+	0.0537914i
$865$	19.9545	+	16.2927i	0.678472	+	0.553970i
$866$		0			0
$867$	−4.94975	+	11.0680i	−0.168102	+	0.375888i
$868$		0			0
$869$			0.111571i			0.00378480i
$870$	7.00000	−	3.51660i	0.237322	−	0.119224i
$871$		−	35.6905i		−	1.20933i
$872$	−12.4317			−0.420990
$873$	−7.00665	−	7.83368i	−0.237139	−	0.265130i
$874$			31.7017i			1.07232i
$875$		0			0
$876$	−8.47723	+	18.9557i	−0.286419	+	0.640452i
$877$			42.2816i			1.42775i	0.700274	+	0.713874i	$0.253061\pi$
$877$			42.2816i			1.42775i	−0.700274	+	0.713874i	$0.746939\pi$
$878$			22.7396i			0.767424i
$879$	7.26139	+	3.24739i	0.244921	+	0.109532i
$880$	−0.369657	−	0.301824i	−0.0124611	−	0.0101745i
$881$	26.5004			0.892821			0.446411	−	0.894828i	$-0.352702\pi$
$881$	26.5004			0.892821			0.446411	+	0.894828i	$0.352702\pi$
$882$		0			0
$883$			29.2823i			0.985428i	0.870191	+	0.492714i	$0.163995\pi$
$883$			29.2823i			0.985428i	−0.870191	+	0.492714i	$0.836005\pi$
$884$		−	21.1917i		−	0.712755i
$885$	−8.54970	−	17.0187i	−0.287395	−	0.572077i
$886$	−36.9545			−1.24151
$887$			3.46410i			0.116313i	0.998307	+	0.0581566i	$0.0185223\pi$
$887$			3.46410i			0.116313i	−0.998307	+	0.0581566i	$0.981478\pi$
$888$	−11.2815	−	5.04524i	−0.378582	−	0.169307i
$889$		0			0
$890$	14.9545	−	18.3154i	0.501274	−	0.613933i
$891$	−1.90890	−	0.213422i	−0.0639506	−	0.00714990i
$892$	−6.39617			−0.214160
$893$	37.9545			1.27010
$894$	−3.87298	−	1.73205i	−0.129532	−	0.0579284i
$895$	25.8255	+	21.0864i	0.863251	+	0.704842i
$896$		0			0
$897$	30.6931	−	68.6318i	1.02481	−	2.29155i
$898$			3.51660i			0.117350i
$899$	−0.610483			−0.0203608
$900$	−8.95445	+	12.0340i	−0.298482	+	0.401134i
$901$		−	15.8114i		−	0.526754i
$902$			1.43023i			0.0476213i
$903$		0			0
$904$	6.52277			0.216944
$905$	−5.47723	−	4.47214i	−0.182069	−	0.148659i
$906$	−1.41421	+	3.16228i	−0.0469841	+	0.105060i
$907$		−	9.79796i		−	0.325336i	−0.986681	−	0.162668i	$-0.947990\pi$
$907$		−	9.79796i		−	0.325336i	0.986681	−	0.162668i	$-0.0520099\pi$
$908$		−	10.3923i		−	0.344881i
$909$	−22.6274	−	25.2982i	−0.750504	−	0.839089i
$910$		0			0
$911$		−	15.1238i		−	0.501073i	−0.968107	−	0.250537i	$-0.919393\pi$
$911$		−	15.1238i		−	0.501073i	0.968107	−	0.250537i	$-0.0806071\pi$
$912$	7.73861	+	3.46081i	0.256251	+	0.114599i
$913$	3.56774			0.118075
$914$			37.9113i			1.25399i
$915$	−11.9886	+	6.02273i	−0.396331	+	0.199105i
$916$			7.23003i			0.238887i
$917$		0			0
$918$	−5.00000	−	15.6525i	−0.165025	−	0.516609i
$919$	−32.4317			−1.06982			−0.534911	−	0.844908i	$-0.679655\pi$
$919$	−32.4317			−1.06982			−0.534911	+	0.844908i	$0.679655\pi$
$920$	9.16018	−	11.2189i	0.302002	−	0.369876i
$921$	2.47723	−	5.53924i	0.0816274	−	0.182524i
$922$	16.2957			0.536669
$923$		−	13.5546i		−	0.446155i
$924$		0			0
$925$	−34.9545	+	7.13505i	−1.14930	+	0.234599i
$926$			17.6751i			0.580841i
$927$	21.1488	+	23.6451i	0.694617	+	0.776606i
$928$			2.02265i			0.0663966i
$929$	23.6720			0.776652			0.388326	−	0.921522i	$-0.373053\pi$
$929$	23.6720			0.776652			0.388326	+	0.921522i	$0.373053\pi$
$930$	1.04456	−	0.524755i	0.0342523	−	0.0172074i
$931$		0			0
$932$	4.00000			0.131024
$933$	20.4317	−	45.6866i	0.668903	−	1.49571i
$934$			34.3392i			1.12361i
$935$	0.954451	−	1.16896i	0.0312139	−	0.0382291i
$936$	−13.4028	−	14.9848i	−0.438085	−	0.489794i
$937$	−22.6918			−0.741310			−0.370655	−	0.928771i	$-0.620867\pi$
$937$	−22.6918			−0.741310			−0.370655	+	0.928771i	$0.620867\pi$
$938$		0			0
$939$	−16.4317	+	36.7423i	−0.536228	+	1.19904i
$940$	−13.4317	−	10.9669i	−0.438093	−	0.357701i
$941$	−4.98196			−0.162407			−0.0812036	−	0.996698i	$-0.525876\pi$
$941$	−4.98196			−0.162407			−0.0812036	+	0.996698i	$0.525876\pi$
$942$	6.21584	−	13.8990i	0.202523	−	0.452855i
$943$	−43.4065			−1.41351
$944$	4.91754			0.160052
$945$		0			0
$946$	0.431677			0.0140350
$947$	32.8634			1.06792			0.533958	−	0.845511i	$-0.320704\pi$
$947$	32.8634			1.06792			0.533958	+	0.845511i	$0.320704\pi$
$948$	−0.369657	+	0.826579i	−0.0120059	+	0.0268460i
$949$	−80.3406			−2.60797
$950$	23.9772	−	4.89433i	0.777924	−	0.158793i
$951$	23.9772	−	53.6147i	0.777514	−	1.73858i
$952$		0			0
$953$	−25.0455			−0.811305			−0.405652	−	0.914027i	$-0.632956\pi$
$953$	−25.0455			−0.811305			−0.405652	+	0.914027i	$0.632956\pi$
$954$	−10.0000	−	11.1803i	−0.323762	−	0.361977i
$955$	−2.76401	−	2.25681i	−0.0894413	−	0.0730285i
$956$		0			0
$957$	−0.305242	+	0.682541i	−0.00986706	+	0.0220634i
$958$	11.3781			0.367611
$959$		0			0
$960$	−1.73861	−	3.46081i	−0.0561135	−	0.111697i
$961$	30.9089			0.997061
$962$		−	47.8149i		−	1.54161i
$963$	10.9545	+	12.2474i	0.353002	+	0.394669i
$964$			3.98886i			0.128472i
$965$	−12.7279	−	10.3923i	−0.409726	−	0.334540i
$966$		0			0
$967$			46.4287i			1.49305i	0.665359	+	0.746524i	$0.268279\pi$
$967$			46.4287i			1.49305i	−0.665359	+	0.746524i	$0.731721\pi$
$968$	−10.9545			−0.352089
$969$	−10.9441	+	24.4716i	−0.351574	+	0.786142i
$970$	4.95445	−	6.06794i	0.159078	−	0.194830i
$971$	0.980140			0.0314542			0.0157271	−	0.999876i	$-0.494994\pi$
$971$	0.980140			0.0314542			0.0157271	+	0.999876i	$0.494994\pi$
$972$	−13.4350	−	7.90569i	−0.430929	−	0.253575i
$973$		0			0
$974$		−	36.6308i		−	1.17373i
$975$	−56.6475	−	12.6185i	−1.81417	−	0.404116i
$976$		−	3.46410i		−	0.110883i
$977$	39.9089			1.27680			0.638399	−	0.769705i	$-0.279597\pi$
$977$	39.9089			1.27680			0.638399	+	0.769705i	$0.279597\pi$
$978$	−23.2379	−	10.3923i	−0.743066	−	0.332309i
$979$			2.25681i			0.0721278i
$980$		0			0
$981$	−24.8634	−	27.7981i	−0.793826	−	0.887524i
$982$			4.04529i			0.129090i
$983$			33.8144i			1.07851i	0.842142	+	0.539257i	$0.181295\pi$
$983$			33.8144i			1.07851i	−0.842142	+	0.539257i	$0.818705\pi$
$984$	−4.73861	+	10.5959i	−0.151061	+	0.337784i
$985$	12.7279	−	15.5885i	0.405545	−	0.496690i
$986$	−6.39617			−0.203696
$987$		0			0
$988$			32.7989i			1.04347i
$989$			13.1011i			0.416592i
$990$	−0.0644158	−	1.43023i	−0.00204727	−	0.0454556i
$991$	21.4772			0.682247			0.341123	−	0.940019i	$-0.389193\pi$
$991$	21.4772			0.682247			0.341123	+	0.940019i	$0.389193\pi$
$992$			0.301824i			0.00958292i
$993$	8.08342	−	18.0751i	0.256519	−	0.573595i
$994$		0			0
$995$	38.8634	+	31.7318i	1.23205	+	1.00597i
$996$	26.4317	+	11.8206i	0.837520	+	0.374550i
$997$	15.4919			0.490634			0.245317	−	0.969443i	$-0.421108\pi$
$997$	15.4919			0.490634			0.245317	+	0.969443i	$0.421108\pi$
$998$	41.9089			1.32660
$999$	−11.2815	−	35.3167i	−0.356931	−	1.11737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.e.1469.4		8
3.2	odd	2		1470.2.d.f.1469.1		8
5.4	even	2		1470.2.d.f.1469.5		8
7.4	even	3		210.2.t.f.89.4	yes	8
7.5	odd	6		210.2.t.f.59.3	yes	8
7.6	odd	2	inner	1470.2.d.e.1469.5		8
15.14	odd	2	inner	1470.2.d.e.1469.8		8
21.5	even	6		210.2.t.e.59.1	✓	8
21.11	odd	6		210.2.t.e.89.2	yes	8
21.20	even	2		1470.2.d.f.1469.8		8
35.4	even	6		210.2.t.e.89.1	yes	8
35.12	even	12		1050.2.s.i.101.4		16
35.18	odd	12		1050.2.s.i.551.3		16
35.19	odd	6		210.2.t.e.59.2	yes	8
35.32	odd	12		1050.2.s.i.551.6		16
35.33	even	12		1050.2.s.i.101.5		16
35.34	odd	2		1470.2.d.f.1469.4		8
105.32	even	12		1050.2.s.i.551.4		16
105.47	odd	12		1050.2.s.i.101.6		16
105.53	even	12		1050.2.s.i.551.5		16
105.68	odd	12		1050.2.s.i.101.3		16
105.74	odd	6		210.2.t.f.89.3	yes	8
105.89	even	6		210.2.t.f.59.4	yes	8
105.104	even	2	inner	1470.2.d.e.1469.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.1	✓	8	21.5	even	6
210.2.t.e.59.2	yes	8	35.19	odd	6
210.2.t.e.89.1	yes	8	35.4	even	6
210.2.t.e.89.2	yes	8	21.11	odd	6
210.2.t.f.59.3	yes	8	7.5	odd	6
210.2.t.f.59.4	yes	8	105.89	even	6
210.2.t.f.89.3	yes	8	105.74	odd	6
210.2.t.f.89.4	yes	8	7.4	even	3
1050.2.s.i.101.3		16	105.68	odd	12
1050.2.s.i.101.4		16	35.12	even	12
1050.2.s.i.101.5		16	35.33	even	12
1050.2.s.i.101.6		16	105.47	odd	12
1050.2.s.i.551.3		16	35.18	odd	12
1050.2.s.i.551.4		16	105.32	even	12
1050.2.s.i.551.5		16	105.53	even	12
1050.2.s.i.551.6		16	35.32	odd	12
1470.2.d.e.1469.1		8	105.104	even	2	inner
1470.2.d.e.1469.4		8	1.1	even	1	trivial
1470.2.d.e.1469.5		8	7.6	odd	2	inner
1470.2.d.e.1469.8		8	15.14	odd	2	inner
1470.2.d.f.1469.1		8	3.2	odd	2
1470.2.d.f.1469.4		8	35.34	odd	2
1470.2.d.f.1469.5		8	5.4	even	2
1470.2.d.f.1469.8		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(-1.41421 + 1.73205i) q^{5} +(0.707107 - 1.58114i) q^{6} -1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +(1.41421 - 1.73205i) q^{10} +0.213422i q^{11} +(-0.707107 + 1.58114i) q^{12} -6.70141 q^{13} +(-1.73861 - 3.46081i) q^{15} +1.00000 q^{16} +3.16228i q^{17} +(2.00000 + 2.23607i) q^{18} -4.89433i q^{19} +(-1.41421 + 1.73205i) q^{20} -0.213422i q^{22} +6.47723 q^{23} +(0.707107 - 1.58114i) q^{24} +(-1.00000 - 4.89898i) q^{25} +6.70141 q^{26} +(4.94975 - 1.58114i) q^{27} -2.02265i q^{29} +(1.73861 + 3.46081i) q^{30} -0.301824i q^{31} -1.00000 q^{32} +(-0.337449 - 0.150912i) q^{33} -3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} -7.13505i q^{37} +4.89433i q^{38} +(4.73861 - 10.5959i) q^{39} +(1.41421 - 1.73205i) q^{40} -6.70141 q^{41} +2.02265i q^{43} +0.213422i q^{44} +(6.70141 - 0.301824i) q^{45} -6.47723 q^{46} +7.75478i q^{47} +(-0.707107 + 1.58114i) q^{48} +(1.00000 + 4.89898i) q^{50} +(-5.00000 - 2.23607i) q^{51} -6.70141 q^{52} -5.00000 q^{53} +(-4.94975 + 1.58114i) q^{54} +(-0.369657 - 0.301824i) q^{55} +(7.73861 + 3.46081i) q^{57} +2.02265i q^{58} +4.91754 q^{59} +(-1.73861 - 3.46081i) q^{60} -3.46410i q^{61} +0.301824i q^{62} +1.00000 q^{64} +(9.47723 - 11.6072i) q^{65} +(0.337449 + 0.150912i) q^{66} +5.32582i q^{67} +3.16228i q^{68} +(-4.58009 + 10.2414i) q^{69} +2.02265i q^{71} +(2.00000 + 2.23607i) q^{72} +11.9886 q^{73} +7.13505i q^{74} +(8.45307 + 1.88296i) q^{75} -4.89433i q^{76} +(-4.73861 + 10.5959i) q^{78} +0.522774 q^{79} +(-1.41421 + 1.73205i) q^{80} +(-1.00000 + 8.94427i) q^{81} +6.70141 q^{82} -16.7169i q^{83} +(-5.47723 - 4.47214i) q^{85} -2.02265i q^{86} +(3.19808 + 1.43023i) q^{87} -0.213422i q^{88} +10.5744 q^{89} +(-6.70141 + 0.301824i) q^{90} +6.47723 q^{92} +(0.477226 + 0.213422i) q^{93} -7.75478i q^{94} +(8.47723 + 6.92163i) q^{95} +(0.707107 - 1.58114i) q^{96} +3.50333 q^{97} +(0.477226 - 0.426844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 16 q^{9} + 8 q^{15} + 8 q^{16} + 16 q^{18} + 8 q^{23} - 8 q^{25} - 8 q^{30} - 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} + 8 q^{50} - 40 q^{51} - 40 q^{53} + 40 q^{57}+ \cdots - 40 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 16 * q^9 + 8 * q^15 + 8 * q^16 + 16 * q^18 + 8 * q^23 - 8 * q^25 - 8 * q^30 - 8 * q^32 - 16 * q^36 + 16 * q^39 - 8 * q^46 + 8 * q^50 - 40 * q^51 - 40 * q^53 + 40 * q^57 + 8 * q^60 + 8 * q^64 + 32 * q^65 + 16 * q^72 - 16 * q^78 + 48 * q^79 - 8 * q^81 + 8 * q^92 - 40 * q^93 + 24 * q^95 - 40 * q^99

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