LMFDB - Embedded newform 630.2.bf.e.209.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(209,630)] 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("630.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.14
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.e.419.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.42161 + 0.989450i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.07274 + 1.96195i) q^{5} +(-1.56770 + 0.736429i) q^{6} +(-2.59656 + 0.507832i) q^{7} +1.00000 q^{8} +(1.04198 + 2.81323i) q^{9} +(-1.16272 - 1.90999i) q^{10} +(4.30527 + 2.48565i) q^{11} +(0.146082 - 1.72588i) q^{12} +(-1.15117 - 1.99388i) q^{13} +(0.858483 - 2.50260i) q^{14} +(-3.46627 + 1.72771i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.05745i q^{17} +(-2.95732 - 0.504240i) q^{18} +1.63818i q^{19} +(2.23546 - 0.0519524i) q^{20} +(-4.19378 - 1.84722i) q^{21} +(-4.30527 + 2.48565i) q^{22} +(-3.70342 - 6.41451i) q^{23} +(1.42161 + 0.989450i) q^{24} +(-2.69846 - 4.20931i) q^{25} +2.30233 q^{26} +(-1.30227 + 5.03032i) q^{27} +(1.73807 + 1.99477i) q^{28} +(-6.86211 - 3.96184i) q^{29} +(0.236897 - 3.86573i) q^{30} +(-6.00511 + 3.46705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.66101 + 7.79349i) q^{33} +(-3.51386 - 2.02873i) q^{34} +(1.78909 - 5.63907i) q^{35} +(1.91534 - 2.30899i) q^{36} +10.4902i q^{37} +(-1.41871 - 0.819090i) q^{38} +(0.336330 - 3.97355i) q^{39} +(-1.07274 + 1.96195i) q^{40} +(-2.40962 - 4.17358i) q^{41} +(3.69663 - 2.70831i) q^{42} +(-2.31707 - 1.33776i) q^{43} -4.97130i q^{44} +(-6.63718 - 0.973570i) q^{45} +7.40684 q^{46} +(9.03708 + 5.21756i) q^{47} +(-1.56770 + 0.736429i) q^{48} +(6.48421 - 2.63723i) q^{49} +(4.99460 - 0.232276i) q^{50} +(-4.01465 + 5.76813i) q^{51} +(-1.15117 + 1.99388i) q^{52} +12.4295 q^{53} +(-3.70525 - 3.64296i) q^{54} +(-9.49514 + 5.78025i) q^{55} +(-2.59656 + 0.507832i) q^{56} +(-1.62090 + 2.32886i) q^{57} +(6.86211 - 3.96184i) q^{58} +(5.82902 + 10.0962i) q^{59} +(3.22937 + 2.13802i) q^{60} +(3.89175 + 2.24690i) q^{61} -6.93411i q^{62} +(-4.13420 - 6.77557i) q^{63} +1.00000 q^{64} +(5.14679 - 0.119612i) q^{65} +(-8.57986 - 0.726217i) q^{66} +(-0.266411 + 0.153812i) q^{67} +(3.51386 - 2.02873i) q^{68} +(1.08201 - 12.7833i) q^{69} +(3.98904 + 4.36894i) q^{70} -7.38341i q^{71} +(1.04198 + 2.81323i) q^{72} -3.95051 q^{73} +(-9.08477 - 5.24509i) q^{74} +(0.328742 - 8.65401i) q^{75} +(1.41871 - 0.819090i) q^{76} +(-12.4412 - 4.26777i) q^{77} +(3.27303 + 2.27805i) q^{78} +(-1.42332 + 2.46526i) q^{79} +(-1.16272 - 1.90999i) q^{80} +(-6.82857 + 5.86264i) q^{81} +4.81924 q^{82} +(9.60784 + 5.54709i) q^{83} +(0.497147 + 4.55553i) q^{84} +(-7.96050 - 4.35259i) q^{85} +(2.31707 - 1.33776i) q^{86} +(-5.83523 - 12.4219i) q^{87} +(4.30527 + 2.48565i) q^{88} +5.77755 q^{89} +(4.16173 - 5.26118i) q^{90} +(4.00163 + 4.59262i) q^{91} +(-3.70342 + 6.41451i) q^{92} +(-11.9674 - 1.01295i) q^{93} +(-9.03708 + 5.21756i) q^{94} +(-3.21402 - 1.75734i) q^{95} +(0.146082 - 1.72588i) q^{96} +(4.81542 - 8.34056i) q^{97} +(-0.958199 + 6.93411i) q^{98} +(-2.50673 + 14.7017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39}+ \cdots + 58 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.42161	+	0.989450i	0.820770	+	0.571259i
$3$	1.42161	+	0.989450i	0.820770	+	0.571259i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.07274	+	1.96195i	−0.479744	+	0.877409i
$5$	−1.07274	+	1.96195i	−0.479744	+	0.877409i
$6$	−1.56770	+	0.736429i	−0.640009	+	0.300646i
$7$	−2.59656	+	0.507832i	−0.981406	+	0.191943i
$7$	−2.59656	+	0.507832i	−0.981406	+	0.191943i
$8$	1.00000			0.353553
$9$	1.04198	+	2.81323i	0.347325	+	0.937745i
$10$	−1.16272	−	1.90999i	−0.367686	−	0.603993i
$11$	4.30527	+	2.48565i	1.29809	+	0.749451i	0.980074	−	0.198635i	$-0.0636507\pi$
$11$	4.30527	+	2.48565i	1.29809	+	0.749451i	0.318014	+	0.948086i	$0.396984\pi$
$12$	0.146082	−	1.72588i	0.0421702	−	0.498218i
$13$	−1.15117	−	1.99388i	−0.319276	−	0.553003i	0.661061	−	0.750332i	$-0.270106\pi$
$13$	−1.15117	−	1.99388i	−0.319276	−	0.553003i	−0.980337	+	0.197329i	$0.936773\pi$
$14$	0.858483	−	2.50260i	0.229439	−	0.668848i
$15$	−3.46627	+	1.72771i	−0.894987	+	0.446092i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			4.05745i			0.984077i	0.870574	+	0.492038i	$0.163748\pi$
$17$			4.05745i			0.984077i	−0.870574	+	0.492038i	$0.836252\pi$
$18$	−2.95732	−	0.504240i	−0.697047	−	0.118850i
$19$			1.63818i			0.375824i	0.982186	+	0.187912i	$0.0601720\pi$
$19$			1.63818i			0.375824i	−0.982186	+	0.187912i	$0.939828\pi$
$20$	2.23546	−	0.0519524i	0.499865	−	0.0116169i
$21$	−4.19378	−	1.84722i	−0.915157	−	0.403097i
$22$	−4.30527	+	2.48565i	−0.917887	+	0.529942i
$23$	−3.70342	−	6.41451i	−0.772216	−	1.33752i	−0.936346	−	0.351079i	$-0.885815\pi$
$23$	−3.70342	−	6.41451i	−0.772216	−	1.33752i	0.164130	−	0.986439i	$-0.447518\pi$
$24$	1.42161	+	0.989450i	0.290186	+	0.201971i
$25$	−2.69846	−	4.20931i	−0.539692	−	0.841863i
$26$	2.30233			0.451525
$27$	−1.30227	+	5.03032i	−0.250622	+	0.968085i
$28$	1.73807	+	1.99477i	0.328465	+	0.376976i
$29$	−6.86211	−	3.96184i	−1.27426	−	0.735696i	−0.298475	−	0.954417i	$-0.596478\pi$
$29$	−6.86211	−	3.96184i	−1.27426	−	0.735696i	−0.975787	+	0.218721i	$0.929811\pi$
$30$	0.236897	−	3.86573i	0.0432514	−	0.705783i
$31$	−6.00511	+	3.46705i	−1.07855	+	0.622701i	−0.930505	−	0.366279i	$-0.880631\pi$
$31$	−6.00511	+	3.46705i	−1.07855	+	0.622701i	−0.148045	+	0.988981i	$0.547298\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.66101	+	7.79349i	0.637300	+	1.35667i
$34$	−3.51386	−	2.02873i	−0.602621	−	0.347924i
$35$	1.78909	−	5.63907i	0.302412	−	0.953177i
$36$	1.91534	−	2.30899i	0.319224	−	0.384832i
$37$			10.4902i			1.72458i	0.506419	+	0.862288i	$0.330969\pi$
$37$			10.4902i			1.72458i	−0.506419	+	0.862288i	$0.669031\pi$
$38$	−1.41871	−	0.819090i	−0.230145	−	0.132874i
$39$	0.336330	−	3.97355i	0.0538558	−	0.636277i
$40$	−1.07274	+	1.96195i	−0.169615	+	0.310211i
$41$	−2.40962	−	4.17358i	−0.376319	−	0.651804i	0.614204	−	0.789147i	$-0.289477\pi$
$41$	−2.40962	−	4.17358i	−0.376319	−	0.651804i	−0.990524	+	0.137343i	$0.956144\pi$
$42$	3.69663	−	2.70831i	0.570402	−	0.417901i
$43$	−2.31707	−	1.33776i	−0.353350	−	0.204007i	0.312810	−	0.949816i	$-0.398730\pi$
$43$	−2.31707	−	1.33776i	−0.353350	−	0.204007i	−0.666160	+	0.745809i	$0.732063\pi$
$44$		−	4.97130i		−	0.749451i
$45$	−6.63718	−	0.973570i	−0.989412	−	0.145131i
$46$	7.40684			1.09208
$47$	9.03708	+	5.21756i	1.31819	+	0.761059i	0.983438	−	0.181246i	$-0.0580130\pi$
$47$	9.03708	+	5.21756i	1.31819	+	0.761059i	0.334755	+	0.942305i	$0.391346\pi$
$48$	−1.56770	+	0.736429i	−0.226277	+	0.106294i
$49$	6.48421	−	2.63723i	0.926316	−	0.376747i
$50$	4.99460	−	0.232276i	0.706343	−	0.0328487i
$51$	−4.01465	+	5.76813i	−0.562163	+	0.807700i
$52$	−1.15117	+	1.99388i	−0.159638	+	0.276501i
$53$	12.4295			1.70733			0.853665	−	0.520823i	$-0.174375\pi$
$53$	12.4295			1.70733			0.853665	+	0.520823i	$0.174375\pi$
$54$	−3.70525	−	3.64296i	−0.504220	−	0.495744i
$55$	−9.49514	+	5.78025i	−1.28032	+	0.779409i
$56$	−2.59656	+	0.507832i	−0.346979	+	0.0678619i
$57$	−1.62090	+	2.32886i	−0.214693	+	0.308465i
$58$	6.86211	−	3.96184i	0.901040	−	0.520216i
$59$	5.82902	+	10.0962i	0.758874	+	1.31441i	0.943425	+	0.331585i	$0.107583\pi$
$59$	5.82902	+	10.0962i	0.758874	+	1.31441i	−0.184552	+	0.982823i	$0.559083\pi$
$60$	3.22937	+	2.13802i	0.416910	+	0.276018i
$61$	3.89175	+	2.24690i	0.498287	+	0.287686i	0.728006	−	0.685571i	$-0.240447\pi$
$61$	3.89175	+	2.24690i	0.498287	+	0.287686i	−0.229719	+	0.973257i	$0.573781\pi$
$62$		−	6.93411i		−	0.880633i
$63$	−4.13420	−	6.77557i	−0.520860	−	0.853642i
$64$	1.00000			0.125000
$65$	5.14679	−	0.119612i	0.638380	−	0.0148360i
$66$	−8.57986	−	0.726217i	−1.05611	−	0.0893911i
$67$	−0.266411	+	0.153812i	−0.0325472	+	0.0187912i	−0.516185	−	0.856477i	$-0.672648\pi$
$67$	−0.266411	+	0.153812i	−0.0325472	+	0.0187912i	0.483638	+	0.875268i	$0.339315\pi$
$68$	3.51386	−	2.02873i	0.426118	−	0.246019i
$69$	1.08201	−	12.7833i	0.130258	−	1.53893i
$70$	3.98904	+	4.36894i	0.476781	+	0.522188i
$71$		−	7.38341i		−	0.876249i	−0.898914	−	0.438125i	$-0.855643\pi$
$71$		−	7.38341i		−	0.876249i	0.898914	−	0.438125i	$-0.144357\pi$
$72$	1.04198	+	2.81323i	0.122798	+	0.331543i
$73$	−3.95051			−0.462372			−0.231186	−	0.972910i	$-0.574261\pi$
$73$	−3.95051			−0.462372			−0.231186	+	0.972910i	$0.574261\pi$
$74$	−9.08477	−	5.24509i	−1.05608	−	0.609730i
$75$	0.328742	−	8.65401i	0.0379598	−	0.999279i
$76$	1.41871	−	0.819090i	0.162737	−	0.0939561i
$77$	−12.4412	−	4.26777i	−1.41780	−	0.486358i
$78$	3.27303	+	2.27805i	0.370598	+	0.257938i
$79$	−1.42332	+	2.46526i	−0.160136	+	0.277364i	−0.934917	−	0.354865i	$-0.884527\pi$
$79$	−1.42332	+	2.46526i	−0.160136	+	0.277364i	0.774781	+	0.632229i	$0.217860\pi$
$80$	−1.16272	−	1.90999i	−0.129997	−	0.213544i
$81$	−6.82857	+	5.86264i	−0.758730	+	0.651405i
$82$	4.81924			0.532196
$83$	9.60784	+	5.54709i	1.05460	+	0.608872i	0.923933	−	0.382554i	$-0.124956\pi$
$83$	9.60784	+	5.54709i	1.05460	+	0.608872i	0.130665	+	0.991427i	$0.458289\pi$
$84$	0.497147	+	4.55553i	0.0542432	+	0.497049i
$85$	−7.96050	−	4.35259i	−0.863437	−	0.472105i
$86$	2.31707	−	1.33776i	0.249856	−	0.144255i
$87$	−5.83523	−	12.4219i	−0.625603	−	1.33177i
$88$	4.30527	+	2.48565i	0.458943	+	0.264971i
$89$	5.77755			0.612419			0.306209	−	0.951964i	$-0.400939\pi$
$89$	5.77755			0.612419			0.306209	+	0.951964i	$0.400939\pi$
$90$	4.16173	−	5.26118i	0.438685	−	0.554577i
$91$	4.00163	+	4.59262i	0.419484	+	0.481438i
$92$	−3.70342	+	6.41451i	−0.386108	+	0.668759i
$93$	−11.9674	−	1.01295i	−1.24097	−	0.105038i
$94$	−9.03708	+	5.21756i	−0.932103	+	0.538150i
$95$	−3.21402	−	1.75734i	−0.329752	−	0.180299i
$96$	0.146082	−	1.72588i	0.0149094	−	0.176147i
$97$	4.81542	−	8.34056i	0.488932	−	0.846855i	−0.510987	−	0.859589i	$-0.670720\pi$
$97$	4.81542	−	8.34056i	0.488932	−	0.846855i	0.999919	+	0.0127332i	$0.00405323\pi$
$98$	−0.958199	+	6.93411i	−0.0967927	+	0.700451i
$99$	−2.50673	+	14.7017i	−0.251935	+	1.47758i
$100$	−2.29614	+	4.44159i	−0.229614	+	0.444159i
$101$	−6.69877	+	11.6026i	−0.666552	+	1.15450i	0.312310	+	0.949980i	$0.398897\pi$
$101$	−6.69877	+	11.6026i	−0.666552	+	1.15450i	−0.978862	+	0.204522i	$0.934436\pi$
$102$	−2.98803	−	6.36085i	−0.295859	−	0.629818i
$103$	−5.36750	−	9.29678i	−0.528875	−	0.916039i	−0.999433	−	0.0336694i	$-0.989281\pi$
$103$	−5.36750	−	9.29678i	−0.528875	−	0.916039i	0.470558	−	0.882369i	$-0.344053\pi$
$104$	−1.15117	−	1.99388i	−0.112881	−	0.195516i
$105$	8.12298	−	6.24637i	0.792722	−	0.609583i
$106$	−6.21477	+	10.7643i	−0.603632	+	1.04552i
$107$	8.66456			0.837634			0.418817	−	0.908071i	$-0.362445\pi$
$107$	8.66456			0.837634			0.418817	+	0.908071i	$0.362445\pi$
$108$	5.00752	−	1.38736i	0.481849	−	0.133499i
$109$	12.6662			1.21320			0.606600	−	0.795007i	$-0.292533\pi$
$109$	12.6662			1.21320			0.606600	+	0.795007i	$0.292533\pi$
$110$	−0.258271	−	11.1132i	−0.0246252	−	1.05960i
$111$	−10.3795	+	14.9130i	−0.985180	+	1.41548i
$112$	0.858483	−	2.50260i	0.0811190	−	0.236473i
$113$	7.96108	+	13.7890i	0.748916	+	1.29716i	0.948343	+	0.317247i	$0.102759\pi$
$113$	7.96108	+	13.7890i	0.748916	+	1.29716i	−0.199427	+	0.979913i	$0.563908\pi$
$114$	−1.20640	−	2.56817i	−0.112990	−	0.240531i
$115$	16.5577	−	0.384803i	1.54402	−	0.0358831i
$116$			7.92369i			0.735696i
$117$	4.40976	−	5.31608i	0.407683	−	0.491471i
$118$	−11.6580			−1.07321
$119$	−2.06050	−	10.5354i	−0.188886	−	0.965779i
$120$	−3.46627	+	1.72771i	−0.316426	+	0.157717i
$121$	6.85690	+	11.8765i	0.623355	+	1.07968i
$122$	−3.89175	+	2.24690i	−0.352342	+	0.203425i
$123$	0.704004	−	8.31743i	0.0634779	−	0.749957i
$124$	6.00511	+	3.46705i	0.539275	+	0.311351i
$125$	11.1532	−	0.778726i	0.997571	−	0.0696513i
$126$	7.93492	−	0.192535i	0.706899	−	0.0171524i
$127$		−	0.0958062i		−	0.00850143i	−0.999991	−	0.00425071i	$-0.998647\pi$
$127$		−	0.0958062i		−	0.00850143i	0.999991	−	0.00425071i	$-0.00135305\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.97033	−	4.19441i	−0.173478	−	0.369297i
$130$	−2.46981	+	4.51705i	−0.216616	+	0.396172i
$131$	−5.51174	−	9.54661i	−0.481563	−	0.834091i	0.518213	−	0.855251i	$-0.326597\pi$
$131$	−5.51174	−	9.54661i	−0.481563	−	0.834091i	−0.999776	+	0.0211601i	$0.993264\pi$
$132$	4.91885	−	7.06727i	0.428131	−	0.615127i
$133$	−0.831921	−	4.25363i	−0.0721367	−	0.368836i
$134$		−	0.307624i		−	0.0265747i
$135$	−8.47221	−	7.95120i	−0.729172	−	0.684331i
$136$			4.05745i			0.347924i
$137$	0.646384	−	1.11957i	0.0552243	−	0.0956513i	−0.837092	−	0.547063i	$-0.815746\pi$
$137$	0.646384	−	1.11957i	0.0552243	−	0.0956513i	0.892316	+	0.451411i	$0.149079\pi$
$138$	10.5297	+	7.32870i	0.896345	+	0.623860i
$139$	−6.11640	+	3.53131i	−0.518787	+	0.299522i	−0.736438	−	0.676505i	$-0.763494\pi$
$139$	−6.11640	+	3.53131i	−0.518787	+	0.299522i	0.217651	+	0.976027i	$0.430160\pi$
$140$	−5.77813	+	1.27014i	−0.488341	+	0.107346i
$141$	7.68472	+	16.3591i	0.647170	+	1.37768i
$142$	6.39422	+	3.69170i	0.536591	+	0.309801i
$143$		−	11.4456i		−	0.957128i
$144$	−2.95732	−	0.504240i	−0.246443	−	0.0420200i
$145$	15.1342	−	9.21306i	1.25683	−	0.765103i
$146$	1.97525	−	3.42124i	0.163473	−	0.283144i
$147$	11.8275	+	2.66668i	0.975512	+	0.219944i
$148$	9.08477	−	5.24509i	0.746763	−	0.431144i
$149$	7.16878	−	4.13890i	0.587289	−	0.339072i	−0.176736	−	0.984258i	$-0.556554\pi$
$149$	7.16878	−	4.13890i	0.587289	−	0.339072i	0.764025	+	0.645187i	$0.223220\pi$
$150$	7.33022	+	4.61170i	0.598510	+	0.376544i
$151$	0.0473069	−	0.0819379i	0.00384978	−	0.00666801i	−0.864094	−	0.503330i	$-0.832108\pi$
$151$	0.0473069	−	0.0819379i	0.00384978	−	0.00666801i	0.867944	+	0.496662i	$0.165441\pi$
$152$			1.63818i			0.132874i
$153$	−11.4146	+	4.22777i	−0.922813	+	0.341795i
$154$	9.91659	−	8.64048i	0.799101	−	0.696270i
$155$	−0.360244	−	15.5010i	−0.0289355	−	1.24507i
$156$	−3.60936	+	1.69551i	−0.288980	+	0.135749i
$157$	0.938382	+	1.62532i	0.0748910	+	0.129715i	0.901039	−	0.433738i	$-0.142806\pi$
$157$	0.938382	+	1.62532i	0.0748910	+	0.129715i	−0.826148	+	0.563453i	$0.809472\pi$
$158$	−1.42332	−	2.46526i	−0.113233	−	0.196126i
$159$	17.6700	+	12.2984i	1.40132	+	0.975328i
$160$	2.23546	−	0.0519524i	0.176729	−	0.00410720i
$161$	12.8736	+	14.7749i	1.01458	+	1.16443i
$162$	−1.66291	−	8.84504i	−0.130651	−	0.694932i
$163$		−	2.36790i		−	0.185468i	−0.995691	−	0.0927341i	$-0.970439\pi$
$163$		−	2.36790i		−	0.185468i	0.995691	−	0.0927341i	$-0.0295606\pi$
$164$	−2.40962	+	4.17358i	−0.188160	+	0.325902i
$165$	−19.2177	−	1.17769i	−1.49610	−	0.0916829i
$166$	−9.60784	+	5.54709i	−0.745713	+	0.430538i
$167$	−6.32518	+	3.65184i	−0.489457	+	0.282588i	−0.724349	−	0.689433i	$-0.757860\pi$
$167$	−6.32518	+	3.65184i	−0.489457	+	0.282588i	0.234892	+	0.972021i	$0.424526\pi$
$168$	−4.19378	−	1.84722i	−0.323557	−	0.142516i
$169$	3.84963	−	6.66775i	0.296125	−	0.512904i
$170$	7.74970	−	4.71770i	0.594375	−	0.361831i
$171$	−4.60859	+	1.70694i	−0.352427	+	0.130533i
$172$			2.67552i			0.204007i
$173$	16.4983	+	9.52529i	1.25434	+	0.724194i	0.971969	−	0.235111i	$-0.0755453\pi$
$173$	16.4983	+	9.52529i	1.25434	+	0.724194i	0.282372	+	0.959305i	$0.408879\pi$
$174$	13.6753	+	1.15751i	1.03672	+	0.0877505i
$175$	9.14432	+	9.55936i	0.691246	+	0.722620i
$176$	−4.30527	+	2.48565i	−0.324522	+	0.187363i
$177$	−1.70303	+	20.1204i	−0.128008	+	1.51234i
$178$	−2.88877	+	5.00350i	−0.216523	+	0.375028i
$179$			8.19441i			0.612479i	0.951955	+	0.306239i	$0.0990708\pi$
$179$			8.19441i			0.612479i	−0.951955	+	0.306239i	$0.900929\pi$
$180$	2.47545	+	6.23475i	0.184509	+	0.464711i
$181$			6.03316i			0.448441i	0.974538	+	0.224221i	$0.0719837\pi$
$181$			6.03316i			0.448441i	−0.974538	+	0.224221i	$0.928016\pi$
$182$	−5.97814	+	1.16920i	−0.443129	+	0.0866668i
$183$	3.30937	+	7.04492i	0.244635	+	0.520775i
$184$	−3.70342	−	6.41451i	−0.273020	−	0.472884i
$185$	−20.5812	−	11.2532i	−1.51316	−	0.827355i
$186$	6.86096	−	9.85763i	0.503070	−	0.722796i
$187$	−10.0854	+	17.4684i	−0.737518	+	1.27742i
$188$		−	10.4351i		−	0.761059i
$189$	0.826857	−	13.7228i	0.0601450	−	0.998190i
$190$	3.12891	−	1.90475i	0.226995	−	0.138185i
$191$	1.19518	+	0.690038i	0.0864803	+	0.0499294i	0.542617	−	0.839981i	$-0.317434\pi$
$191$	1.19518	+	0.690038i	0.0864803	+	0.0499294i	−0.456136	+	0.889910i	$0.650767\pi$
$192$	1.42161	+	0.989450i	0.102596	+	0.0714074i
$193$	−5.06489	+	2.92422i	−0.364579	+	0.210490i	−0.671088	−	0.741378i	$-0.734173\pi$
$193$	−5.06489	+	2.92422i	−0.364579	+	0.210490i	0.306509	+	0.951868i	$0.400839\pi$
$194$	4.81542	+	8.34056i	0.345727	+	0.598817i
$195$	7.43510	+	4.92245i	0.532438	+	0.352504i
$196$	−5.52601	−	4.29688i	−0.394715	−	0.306920i
$197$	12.3268			0.878249			0.439124	−	0.898426i	$-0.355289\pi$
$197$	12.3268			0.878249			0.439124	+	0.898426i	$0.355289\pi$
$198$	−11.4787	−	9.52175i	−0.815756	−	0.676681i
$199$			4.62044i			0.327534i	0.986499	+	0.163767i	$0.0523646\pi$
$199$			4.62044i			0.327534i	−0.986499	+	0.163767i	$0.947635\pi$
$200$	−2.69846	−	4.20931i	−0.190810	−	0.297643i
$201$	−0.530923	−	0.0449384i	−0.0374484	−	0.00316971i
$202$	−6.69877	−	11.6026i	−0.471323	−	0.816356i
$203$	19.8298	+	6.80235i	1.39178	+	0.477431i
$204$	7.00267	+	0.592721i	0.490285	+	0.0414987i
$205$	10.7732	−	0.250371i	0.752436	−	0.0174867i
$206$	10.7350			0.747942
$207$	14.1866	−	17.1023i	0.986040	−	1.18870i
$208$	2.30233			0.159638
$209$	−4.07194	+	7.05281i	−0.281662	+	0.487853i
$210$	1.34802	+	10.1579i	0.0930226	+	0.700961i
$211$	−1.35443	−	2.34594i	−0.0932428	−	0.161501i	0.815631	−	0.578572i	$-0.196390\pi$
$211$	−1.35443	−	2.34594i	−0.0932428	−	0.161501i	−0.908874	+	0.417071i	$0.863057\pi$
$212$	−6.21477	−	10.7643i	−0.426832	−	0.739295i
$213$	7.30551	−	10.4964i	0.500566	−	0.719198i
$214$	−4.33228	+	7.50373i	−0.296148	+	0.512944i
$215$	5.11023	−	3.11090i	0.348515	−	0.212161i
$216$	−1.30227	+	5.03032i	−0.0886081	+	0.342270i
$217$	13.8319	−	12.0520i	0.938973	−	0.818143i
$218$	−6.33309	+	10.9692i	−0.428931	+	0.742930i
$219$	−5.61610	−	3.90883i	−0.379501	−	0.264134i
$220$	9.75341	+	5.33291i	0.657575	+	0.359545i
$221$	8.09007	−	4.67081i	0.544197	−	0.314192i
$222$	−7.72528	−	16.4454i	−0.518487	−	1.10374i
$223$	−2.64289	+	4.57762i	−0.176981	+	0.306540i	−0.940845	−	0.338837i	$-0.889966\pi$
$223$	−2.64289	+	4.57762i	−0.176981	+	0.306540i	0.763864	+	0.645377i	$0.223300\pi$
$224$	1.73807	+	1.99477i	0.116130	+	0.133281i
$225$	9.03006	−	11.9774i	0.602004	−	0.798493i
$226$	−15.9222			−1.05913
$227$	−16.0790	−	9.28322i	−1.06720	−	0.616149i	−0.139786	−	0.990182i	$-0.544641\pi$
$227$	−16.0790	−	9.28322i	−1.06720	−	0.616149i	−0.927416	+	0.374033i	$0.877975\pi$
$228$	2.82730	+	0.239309i	0.187243	+	0.0158486i
$229$	7.82193	−	4.51600i	0.516888	−	0.298425i	−0.218773	−	0.975776i	$-0.570205\pi$
$229$	7.82193	−	4.51600i	0.516888	−	0.298425i	0.735660	+	0.677351i	$0.236872\pi$
$230$	−7.94561	+	14.5318i	−0.523918	+	0.958199i
$231$	−13.4638	−	18.3771i	−0.885853	−	1.20912i
$232$	−6.86211	−	3.96184i	−0.450520	−	0.260108i
$233$	2.62042			0.171669			0.0858346	−	0.996309i	$-0.472644\pi$
$233$	2.62042			0.171669			0.0858346	+	0.996309i	$0.472644\pi$
$234$	2.39898	+	6.47701i	0.156826	+	0.423415i
$235$	−19.9310	+	12.1332i	−1.30015	+	0.791480i
$236$	5.82902	−	10.0962i	0.379437	−	0.657204i
$237$	−4.46267	+	2.09635i	−0.289882	+	0.136173i
$238$	10.1542	+	3.48325i	0.658198	+	0.225786i
$239$	4.21909	−	2.43589i	0.272910	−	0.157565i	−0.357299	−	0.933990i	$-0.616302\pi$
$239$	4.21909	−	2.43589i	0.272910	−	0.157565i	0.630210	+	0.776425i	$0.282969\pi$
$240$	0.236897	−	3.86573i	0.0152917	−	0.249532i
$241$	−12.6051	−	7.27755i	−0.811965	−	0.468788i	0.0356728	−	0.999364i	$-0.488643\pi$
$241$	−12.6051	−	7.27755i	−0.811965	−	0.468788i	−0.847638	+	0.530575i	$0.821976\pi$
$242$	−13.7138			−0.881557
$243$	−15.5084	+	1.57788i	−0.994864	+	0.101221i
$244$		−	4.49380i		−	0.287686i
$245$	−1.78177	+	15.5507i	−0.113833	+	0.993500i
$246$	6.85110	+	4.76840i	0.436810	+	0.304022i
$247$	3.26634	−	1.88582i	0.207832	−	0.119992i
$248$	−6.00511	+	3.46705i	−0.381325	+	0.220158i
$249$	8.17008	+	17.3923i	0.517758	+	1.10219i
$250$	−4.90220	+	10.0483i	−0.310042	+	0.635511i
$251$	−20.6043			−1.30053			−0.650265	−	0.759707i	$-0.725342\pi$
$251$	−20.6043			−1.30053			−0.650265	+	0.759707i	$0.725342\pi$
$252$	−3.80072	+	6.96811i	−0.239423	+	0.438950i
$253$		−	36.8216i		−	2.31495i
$254$	0.0829706	+	0.0479031i	0.00520604	+	0.00300571i
$255$	−7.01009	−	14.0642i	−0.438989	−	0.880736i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.274796	−	0.158654i	0.0171413	−	0.00989654i	−0.491405	−	0.870931i	$-0.663516\pi$
$257$	0.274796	−	0.158654i	0.0171413	−	0.00989654i	0.508546	+	0.861035i	$0.330183\pi$
$258$	4.61763	+	0.390846i	0.287481	+	0.0243330i
$259$	−5.32725	−	27.2384i	−0.331019	−	1.69251i
$260$	−2.67698	−	4.39744i	−0.166019	−	0.272718i
$261$	3.99544	−	23.4329i	0.247311	−	1.45046i
$262$	11.0235			0.681033
$263$	−13.8308	+	23.9556i	−0.852841	+	1.47716i	0.0257917	+	0.999667i	$0.491789\pi$
$263$	−13.8308	+	23.9556i	−0.852841	+	1.47716i	−0.878633	+	0.477497i	$0.841544\pi$
$264$	3.66101	+	7.79349i	0.225319	+	0.479656i
$265$	−13.3337	+	24.3861i	−0.819081	+	1.49803i
$266$	4.09971	+	1.40635i	0.251369	+	0.0862288i
$267$	8.21344	+	5.71660i	0.502655	+	0.349850i
$268$	0.266411	+	0.153812i	0.0162736	+	0.00939558i
$269$	−15.6998			−0.957235			−0.478618	−	0.878023i	$-0.658862\pi$
$269$	−15.6998			−0.957235			−0.478618	+	0.878023i	$0.658862\pi$
$270$	11.1220	−	3.36155i	0.676866	−	0.204577i
$271$		−	13.2951i		−	0.807622i	−0.914842	−	0.403811i	$-0.867685\pi$
$271$		−	13.2951i		−	0.807622i	0.914842	−	0.403811i	$-0.132315\pi$
$272$	−3.51386	−	2.02873i	−0.213059	−	0.123010i
$273$	1.14460	+	10.4883i	0.0692742	+	0.634784i
$274$	0.646384	+	1.11957i	0.0390495	+	0.0676357i
$275$	−1.15471	−	24.8297i	−0.0696317	−	1.49728i
$276$	−11.6117	+	5.45461i	−0.698941	+	0.328329i
$277$	15.3861	+	8.88318i	0.924462	+	0.533739i	0.885056	−	0.465485i	$-0.154120\pi$
$277$	15.3861	+	8.88318i	0.924462	+	0.533739i	0.0394064	+	0.999223i	$0.487453\pi$
$278$		−	7.06261i		−	0.423587i
$279$	−16.0108	−	13.2812i	−0.958543	−	0.795125i
$280$	1.78909	−	5.63907i	0.106919	−	0.336999i
$281$	5.91512	+	3.41510i	0.352867	+	0.203728i	0.665947	−	0.745999i	$-0.268028\pi$
$281$	5.91512	+	3.41510i	0.352867	+	0.203728i	−0.313080	+	0.949727i	$0.601361\pi$
$282$	−18.0098	−	1.52438i	−1.07247	−	0.0907757i
$283$	−11.4981	−	19.9152i	−0.683488	−	1.18384i	−0.973909	−	0.226937i	$-0.927129\pi$
$283$	−11.4981	−	19.9152i	−0.683488	−	1.18384i	0.290421	−	0.956899i	$-0.406205\pi$
$284$	−6.39422	+	3.69170i	−0.379427	+	0.219062i
$285$	−2.83030	−	5.67838i	−0.167652	−	0.336358i
$286$	9.91217	+	5.72279i	0.586119	+	0.338396i
$287$	8.37619	+	9.61327i	0.494431	+	0.567453i
$288$	1.91534	−	2.30899i	0.112863	−	0.136059i
$289$	0.537081			0.0315930
$290$	0.411655	+	17.7131i	0.0241732	+	1.04015i
$291$	15.0982	−	7.09244i	0.885075	−	0.415766i
$292$	1.97525	+	3.42124i	0.115593	+	0.200213i
$293$	12.6365	−	7.29571i	0.738235	−	0.426220i	−0.0831923	−	0.996534i	$-0.526512\pi$
$293$	12.6365	−	7.29571i	0.738235	−	0.426220i	0.821427	+	0.570313i	$0.193178\pi$
$294$	−8.22315	+	8.90954i	−0.479584	+	0.519615i
$295$	−26.0611	+	0.605663i	−1.51734	+	0.0352631i
$296$			10.4902i			0.609730i
$297$	−18.1102	+	18.4199i	−1.05086	+	1.06883i
$298$			8.27779i			0.479520i
$299$	−8.52651	+	14.7683i	−0.493101	+	0.854075i
$300$	−7.65897	+	4.04231i	−0.442191	+	0.233383i
$301$	6.69576	+	2.29689i	0.385937	+	0.132391i
$302$	0.0473069	+	0.0819379i	0.00272220	+	0.00471499i
$303$	−21.0033	+	9.86633i	−1.20661	+	0.566806i
$304$	−1.41871	−	0.819090i	−0.0813684	−	0.0469781i
$305$	−8.58313	+	5.22505i	−0.491469	+	0.299186i
$306$	2.04593	−	11.9992i	0.116958	−	0.685948i
$307$	8.23143			0.469792			0.234896	−	0.972020i	$-0.424525\pi$
$307$	8.23143			0.469792			0.234896	+	0.972020i	$0.424525\pi$
$308$	2.52458	+	12.9083i	0.143852	+	0.735516i
$309$	1.56819	−	18.5273i	0.0892112	−	1.05398i
$310$	13.6043	+	7.43850i	0.772675	+	0.422478i
$311$	5.27741	+	9.14075i	0.299255	+	0.518324i	0.975966	−	0.217924i	$-0.0699286\pi$
$311$	5.27741	+	9.14075i	0.299255	+	0.518324i	−0.676711	+	0.736249i	$0.736595\pi$
$312$	0.336330	−	3.97355i	0.0190409	−	0.224958i
$313$	9.20310	−	15.9402i	0.520190	−	0.900996i	−0.479534	−	0.877523i	$-0.659194\pi$
$313$	9.20310	−	15.9402i	0.520190	−	0.900996i	0.999724	−	0.0234725i	$-0.00747222\pi$
$314$	−1.87676			−0.105912
$315$	17.7282	−	0.842643i	0.998872	−	0.0474776i
$316$	2.84664			0.160136
$317$	13.6314	−	23.6102i	0.765613	−	1.32608i	−0.174309	−	0.984691i	$-0.555769\pi$
$317$	13.6314	−	23.6102i	0.765613	−	1.32608i	0.939922	−	0.341390i	$-0.110898\pi$
$318$	−19.4858	+	9.15348i	−1.09271	+	0.513302i
$319$	−19.6955	−	34.1136i	−1.10274	−	1.91000i
$320$	−1.07274	+	1.96195i	−0.0599680	+	0.109676i
$321$	12.3177	+	8.57315i	0.687505	+	0.478507i
$322$	−19.2323	+	3.76143i	−1.07177	+	0.209616i
$323$	−6.64684			−0.369840
$324$	8.49148	+	2.98240i	0.471749	+	0.165689i
$325$	−5.28649	+	10.2260i	−0.293242	+	0.567238i
$326$	2.05066	+	1.18395i	0.113576	+	0.0655729i
$327$	18.0064	+	12.5326i	0.995758	+	0.693052i
$328$	−2.40962	−	4.17358i	−0.133049	−	0.230448i
$329$	−26.1149	−	8.95837i	−1.43976	−	0.493891i
$330$	10.6288	−	16.0542i	0.585094	−	0.883753i
$331$	−9.19875	+	15.9327i	−0.505609	+	0.875740i	0.494370	+	0.869252i	$0.335399\pi$
$331$	−9.19875	+	15.9327i	−0.505609	+	0.875740i	−0.999979	+	0.00648873i	$0.997935\pi$
$332$		−	11.0942i		−	0.608872i
$333$	−29.5113	+	10.9305i	−1.61721	+	0.598989i
$334$		−	7.30368i		−	0.399640i
$335$	−0.0159818	−	0.687684i	−0.000873181	−	0.0375722i
$336$	3.69663	−	2.70831i	0.201668	−	0.147750i
$337$	−12.5155	+	7.22584i	−0.681764	+	0.393617i	−0.800519	−	0.599307i	$-0.795443\pi$
$337$	−12.5155	+	7.22584i	−0.681764	+	0.393617i	0.118755	+	0.992924i	$0.462110\pi$
$338$	3.84963	+	6.66775i	0.209392	+	0.362678i
$339$	−2.32594	+	27.4797i	−0.126328	+	1.49249i
$340$	0.210795	+	9.07029i	0.0114319	+	0.491906i
$341$	−34.4715			−1.86674
$342$	0.826036	−	4.84462i	0.0446669	−	0.261967i
$343$	−15.4974	+	10.1406i	−0.836779	+	0.547541i
$344$	−2.31707	−	1.33776i	−0.124928	−	0.0721273i
$345$	23.9194	+	15.8360i	1.28778	+	0.852582i
$346$	−16.4983	+	9.52529i	−0.886953	+	0.512083i
$347$	−9.03284	−	15.6453i	−0.484908	−	0.839886i	0.514941	−	0.857225i	$-0.327814\pi$
$347$	−9.03284	−	15.6453i	−0.484908	−	0.839886i	−0.999850	+	0.0173396i	$0.994480\pi$
$348$	−7.84010	+	11.2644i	−0.420273	+	0.603837i
$349$	−7.58926	−	4.38166i	−0.406244	−	0.234545i	0.282931	−	0.959140i	$-0.408693\pi$
$349$	−7.58926	−	4.38166i	−0.406244	−	0.234545i	−0.689175	+	0.724595i	$0.742027\pi$
$350$	−12.8508	+	3.13954i	−0.686905	+	0.167815i
$351$	11.5290	−	3.19417i	0.615371	−	0.170492i
$352$		−	4.97130i		−	0.264971i
$353$	9.23289	+	5.33061i	0.491417	+	0.283720i	0.725162	−	0.688578i	$-0.241765\pi$
$353$	9.23289	+	5.33061i	0.491417	+	0.283720i	−0.233745	+	0.972298i	$0.575098\pi$
$354$	−16.5732	−	11.5351i	−0.880858	−	0.613081i
$355$	14.4858	+	7.92047i	0.768828	+	0.420375i
$356$	−2.88877	−	5.00350i	−0.153105	−	0.265185i
$357$	7.49502	−	17.0161i	0.396678	−	0.900585i
$358$	−7.09657	−	4.09720i	−0.375065	−	0.216544i
$359$			16.4960i			0.870628i	0.900279	+	0.435314i	$0.143363\pi$
$359$			16.4960i			0.870628i	−0.900279	+	0.435314i	$0.856637\pi$
$360$	−6.63718	−	0.973570i	−0.349810	−	0.0513117i
$361$	16.3164			0.858756
$362$	−5.22487	−	3.01658i	−0.274613	−	0.158548i
$363$	−2.00334	+	23.6684i	−0.105148	+	1.24227i
$364$	1.97651	−	5.76182i	0.103597	−	0.302002i
$365$	4.23787	−	7.75068i	0.221820	−	0.405689i
$366$	−7.75576	−	0.656464i	−0.405400	−	0.0343139i
$367$	−0.205646	+	0.356189i	−0.0107346	+	0.0185929i	−0.871343	−	0.490675i	$-0.836750\pi$
$367$	−0.205646	+	0.356189i	−0.0107346	+	0.0185929i	0.860608	+	0.509268i	$0.170084\pi$
$368$	7.40684			0.386108
$369$	9.23050	−	11.1276i	0.480521	−	0.579280i
$370$	20.0362	−	12.1972i	1.04163	−	0.634102i
$371$	−32.2740	+	6.31212i	−1.67558	+	0.327709i
$372$	5.10648	+	10.8706i	0.264759	+	0.563613i
$373$	9.38126	−	5.41627i	0.485743	−	0.280444i	−0.237064	−	0.971494i	$-0.576185\pi$
$373$	9.38126	−	5.41627i	0.485743	−	0.280444i	0.722807	+	0.691050i	$0.242852\pi$
$374$	−10.0854	−	17.4684i	−0.521504	−	0.903271i
$375$	16.6260	+	9.92848i	0.858565	+	0.512704i
$376$	9.03708	+	5.21756i	0.466052	+	0.269075i
$377$			18.2430i			0.939561i
$378$	11.4709	+	7.57750i	0.589999	+	0.389744i
$379$	−20.7547			−1.06610			−0.533049	−	0.846084i	$-0.678954\pi$
$379$	−20.7547			−1.06610			−0.533049	+	0.846084i	$0.678954\pi$
$380$	0.0851075	+	3.66209i	0.00436592	+	0.187861i
$381$	0.0947955	−	0.136200i	0.00485652	−	0.00697771i
$382$	−1.19518	+	0.690038i	−0.0611508	+	0.0353054i
$383$	−29.5240	+	17.0457i	−1.50860	+	0.870993i	−0.508655	+	0.860971i	$0.669857\pi$
$383$	−29.5240	+	17.0457i	−1.50860	+	0.870993i	−0.999950	+	0.0100224i	$0.996810\pi$
$384$	−1.56770	+	0.736429i	−0.0800012	+	0.0375807i
$385$	21.7193	−	19.8307i	1.10692	−	1.01067i
$386$		−	5.84844i		−	0.297678i
$387$	1.34911	−	7.91238i	0.0685789	−	0.402209i
$388$	−9.63085			−0.488932
$389$	15.5200	+	8.96050i	0.786897	+	0.454315i	0.838869	−	0.544333i	$-0.183217\pi$
$389$	15.5200	+	8.96050i	0.786897	+	0.454315i	−0.0519719	+	0.998649i	$0.516551\pi$
$390$	−7.98051	+	3.97776i	−0.404109	+	0.201422i
$391$	26.0266	−	15.0264i	1.31622	−	0.759920i
$392$	6.48421	−	2.63723i	0.327502	−	0.133200i
$393$	1.61033	−	19.0252i	0.0812305	−	0.959694i
$394$	−6.16341	+	10.6753i	−0.310508	+	0.537815i
$395$	−3.30986	−	5.43707i	−0.166537	−	0.273568i
$396$	13.9854	−	5.17997i	0.702794	−	0.260303i
$397$	1.13391			0.0569091			0.0284546	−	0.999595i	$-0.490941\pi$
$397$	1.13391			0.0569091			0.0284546	+	0.999595i	$0.490941\pi$
$398$	−4.00142	−	2.31022i	−0.200573	−	0.115801i
$399$	3.02608	−	6.87016i	0.151494	−	0.343938i
$400$	4.99460	−	0.232276i	0.249730	−	0.0116138i
$401$	−7.01673	+	4.05111i	−0.350399	+	0.202303i	−0.664861	−	0.746967i	$-0.731509\pi$
$401$	−7.01673	+	4.05111i	−0.350399	+	0.202303i	0.314462	+	0.949270i	$0.398176\pi$
$402$	0.304379	−	0.437323i	0.0151811	−	0.0218117i
$403$	13.8258	+	7.98232i	0.688711	+	0.397628i
$404$	13.3975			0.666552
$405$	−4.17690	−	19.6864i	−0.207552	−	0.978224i
$406$	−15.8059	+	13.7720i	−0.784435	+	0.683491i
$407$	−26.0749	+	45.1631i	−1.29249	+	2.23865i
$408$	−4.01465	+	5.76813i	−0.198755	+	0.285565i
$409$	12.6764	−	7.31875i	0.626810	−	0.361889i	−0.152706	−	0.988272i	$-0.548799\pi$
$409$	12.6764	−	7.31875i	0.626810	−	0.361889i	0.779516	+	0.626383i	$0.215465\pi$
$410$	−5.16979	+	9.45508i	−0.255318	+	0.466953i
$411$	2.02667	−	0.952032i	0.0999681	−	0.0469603i
$412$	−5.36750	+	9.29678i	−0.264438	+	0.458019i
$413$	−20.2625	−	23.2551i	−0.997054	−	1.14431i
$414$	7.71774	+	20.8372i	0.379306	+	1.02409i
$415$	−21.1898	+	12.8995i	−1.04017	+	0.633210i
$416$	−1.15117	+	1.99388i	−0.0564406	+	0.0977580i
$417$	−12.1892	−	1.03172i	−0.596909	−	0.0505236i
$418$	−4.07194	−	7.05281i	−0.199165	−	0.344964i
$419$	5.84160	+	10.1179i	0.285381	+	0.494294i	0.972701	−	0.232060i	$-0.0745466\pi$
$419$	5.84160	+	10.1179i	0.285381	+	0.494294i	−0.687321	+	0.726354i	$0.741213\pi$
$420$	−9.47101	−	3.91152i	−0.462138	−	0.190863i
$421$	12.5853	−	21.7984i	0.613370	−	1.06239i	−0.377298	−	0.926092i	$-0.623147\pi$
$421$	12.5853	−	21.7984i	0.613370	−	1.06239i	0.990668	−	0.136296i	$-0.0435199\pi$
$422$	2.70886			0.131865
$423$	−5.26180	+	30.8600i	−0.255838	+	1.50046i
$424$	12.4295			0.603632
$425$	17.0791	−	10.9489i	0.828458	−	0.531098i
$426$	5.43735	+	11.5749i	0.263441	+	0.560808i
$427$	−11.2462	−	3.85785i	−0.544241	−	0.186695i
$428$	−4.33228	−	7.50373i	−0.209409	−	0.362706i
$429$	11.3248	−	16.2712i	0.546769	−	0.785582i
$430$	0.139000	+	5.98104i	0.00670317	+	0.288431i
$431$		−	0.681468i		−	0.0328252i	−0.999865	−	0.0164126i	$-0.994775\pi$
$431$		−	0.681468i		−	0.0328252i	0.999865	−	0.0164126i	$-0.00522452\pi$
$432$	−3.70525	−	3.64296i	−0.178269	−	0.175272i
$433$	1.64024			0.0788247			0.0394124	−	0.999223i	$-0.487451\pi$
$433$	1.64024			0.0788247			0.0394124	+	0.999223i	$0.487451\pi$
$434$	3.52136	+	18.0048i	0.169031	+	0.864258i
$435$	30.6308	+	1.87710i	1.46864	+	0.0900001i
$436$	−6.33309	−	10.9692i	−0.303300	−	0.525331i
$437$	10.5081	−	6.06687i	0.502672	−	0.290218i
$438$	6.19320	−	2.90927i	0.295922	−	0.139010i
$439$	−14.2849	−	8.24739i	−0.681781	−	0.393627i	0.118744	−	0.992925i	$-0.462113\pi$
$439$	−14.2849	−	8.24739i	−0.681781	−	0.393627i	−0.800526	+	0.599298i	$0.795446\pi$
$440$	−9.49514	+	5.78025i	−0.452663	+	0.275563i
$441$	14.1755	+	15.4937i	0.675026	+	0.737794i
$442$			9.34161i			0.444335i
$443$	11.5504	−	20.0059i	0.548775	−	0.950507i	−0.449583	−	0.893238i	$-0.648428\pi$
$443$	11.5504	−	20.0059i	0.548775	−	0.950507i	0.998359	−	0.0572684i	$-0.0182391\pi$
$444$	18.1048	+	1.53243i	0.859215	+	0.0727258i
$445$	−6.19780	+	11.3352i	−0.293804	+	0.537341i
$446$	−2.64289	−	4.57762i	−0.125144	−	0.216757i
$447$	14.2865	+	1.20924i	0.675727	+	0.0571949i
$448$	−2.59656	+	0.507832i	−0.122676	+	0.0239928i
$449$		−	16.0497i		−	0.757430i	−0.925513	−	0.378715i	$-0.876366\pi$
$449$		−	16.0497i		−	0.757430i	0.925513	−	0.378715i	$-0.123634\pi$
$450$	5.85770	+	13.8090i	0.276135	+	0.650961i
$451$		−	23.9579i		−	1.12813i
$452$	7.96108	−	13.7890i	0.374458	−	0.648580i
$453$	0.148326	−	0.0696763i	0.00696894	−	0.00327368i
$454$	16.0790	−	9.28322i	0.754625	−	0.435683i
$455$	−13.3032	+	2.92428i	−0.623663	+	0.137092i
$456$	−1.62090	+	2.32886i	−0.0759055	+	0.109059i
$457$	0.692830	+	0.400006i	0.0324092	+	0.0187115i	0.516117	−	0.856518i	$-0.327377\pi$
$457$	0.692830	+	0.400006i	0.0324092	+	0.0187115i	−0.483708	+	0.875230i	$0.660710\pi$
$458$			9.03199i			0.422037i
$459$	−20.4103	−	5.28389i	−0.952670	−	0.246631i
$460$	−8.61211	−	14.1470i	−0.401542	−	0.659608i
$461$	3.10910	−	5.38511i	0.144805	−	0.250810i	−0.784495	−	0.620135i	$-0.787078\pi$
$461$	3.10910	−	5.38511i	0.144805	−	0.250810i	0.929300	+	0.369325i	$0.120411\pi$
$462$	22.6469	−	2.47147i	1.05363	−	0.114983i
$463$	11.7010	−	6.75560i	0.543793	−	0.313959i	−0.202822	−	0.979216i	$-0.565011\pi$
$463$	11.7010	−	6.75560i	0.543793	−	0.313959i	0.746615	+	0.665256i	$0.231678\pi$
$464$	6.86211	−	3.96184i	0.318566	−	0.183924i
$465$	14.8253	−	22.3928i	0.687507	−	1.03844i
$466$	−1.31021	+	2.26935i	−0.0606942	+	0.105125i
$467$		−	14.0650i		−	0.650853i	−0.945567	−	0.325426i	$-0.894492\pi$
$467$		−	14.0650i		−	0.650853i	0.945567	−	0.325426i	$-0.105508\pi$
$468$	−6.80874	−	1.16093i	−0.314734	−	0.0536639i
$469$	0.613639	−	0.534674i	0.0283352	−	0.0246890i
$470$	−0.542130	−	23.3273i	−0.0250066	−	1.07601i
$471$	−0.274161	+	3.23907i	−0.0126327	+	0.149248i
$472$	5.82902	+	10.0962i	0.268302	+	0.464713i
$473$	−6.65041	−	11.5188i	−0.305786	−	0.529637i
$474$	0.415843	−	4.91296i	0.0191003	−	0.225660i
$475$	6.89562	−	4.42056i	0.316393	−	0.202829i
$476$	−8.09368	+	7.05215i	−0.370973	+	0.323235i
$477$	12.9513	+	34.9672i	0.592999	+	1.60104i
$478$			4.87179i			0.222830i
$479$	2.52248	−	4.36907i	0.115255	−	0.199628i	−0.802627	−	0.596482i	$-0.796565\pi$
$479$	2.52248	−	4.36907i	0.115255	−	0.199628i	0.917882	+	0.396854i	$0.129898\pi$
$480$	3.22937	+	2.13802i	0.147400	+	0.0975870i
$481$	20.9162	−	12.0760i	0.953695	−	0.550616i
$482$	12.6051	−	7.27755i	0.574146	−	0.331483i
$483$	3.68229	+	33.7421i	0.167550	+	1.53532i
$484$	6.85690	−	11.8765i	0.311677	−	0.539841i
$485$	11.1980	+	18.3948i	0.508476	+	0.835267i
$486$	6.38771	−	14.2196i	0.289752	−	0.645014i
$487$		−	27.6648i		−	1.25361i	−0.779176	−	0.626806i	$-0.784362\pi$
$487$		−	27.6648i		−	1.25361i	0.779176	−	0.626806i	$-0.215638\pi$
$488$	3.89175	+	2.24690i	0.176171	+	0.101712i
$489$	2.34292	−	3.36624i	0.105950	−	0.152227i
$490$	−12.5764	−	9.31843i	−0.568146	−	0.420964i
$491$	13.4050	−	7.73941i	0.604961	−	0.349275i	−0.166030	−	0.986121i	$-0.553095\pi$
$491$	13.4050	−	7.73941i	0.604961	−	0.349275i	0.770991	+	0.636846i	$0.219761\pi$
$492$	−7.55511	+	3.54903i	−0.340610	+	0.160003i
$493$	16.0750	−	27.8427i	0.723981	−	1.25397i
$494$			3.77164i			0.169694i
$495$	−26.1549	−	20.6892i	−1.17558	−	0.929910i
$496$		−	6.93411i		−	0.311351i
$497$	3.74953	+	19.1714i	0.168189	+	0.859956i
$498$	−19.1472	−	1.62066i	−0.858007	−	0.0726235i
$499$	7.72566	+	13.3812i	0.345848	+	0.599026i	0.985507	−	0.169632i	$-0.0542580\pi$
$499$	7.72566	+	13.3812i	0.345848	+	0.599026i	−0.639660	+	0.768658i	$0.720925\pi$
$500$	−6.25099	−	9.26958i	−0.279553	−	0.414548i
$501$	−12.6053	−	1.06694i	−0.563162	−	0.0476672i
$502$	10.3021	−	17.8438i	0.459807	−	0.796409i
$503$		−	25.7705i		−	1.14905i	−0.818487	−	0.574524i	$-0.805187\pi$
$503$		−	25.7705i		−	1.14905i	0.818487	−	0.574524i	$-0.194813\pi$
$504$	−4.13420	−	6.77557i	−0.184152	−	0.301808i
$505$	−15.5776	−	25.5892i	−0.693196	−	1.13870i
$506$	31.8884	+	18.4108i	1.41761	+	0.818460i
$507$	12.0701	−	5.66996i	0.536052	−	0.251812i
$508$	−0.0829706	+	0.0479031i	−0.00368123	+	0.00212536i
$509$	10.0008	+	17.3218i	0.443276	+	0.767777i	0.997930	−	0.0643043i	$-0.0204828\pi$
$509$	10.0008	+	17.3218i	0.443276	+	0.767777i	−0.554654	+	0.832081i	$0.687149\pi$
$510$	15.6850	+	0.961200i	0.694544	+	0.0425627i
$511$	10.2577	−	2.00619i	0.453775	−	0.0887488i
$512$	1.00000			0.0441942
$513$	−8.24057	−	2.13335i	−0.363830	−	0.0941897i
$514$			0.317307i			0.0139958i
$515$	23.9977	−	0.557709i	1.05746	−	0.0245756i
$516$	−2.64730	+	3.80356i	−0.116541	+	0.167442i
$517$	25.9380	+	44.9260i	1.14075	+	1.97584i
$518$	26.2527	+	9.00564i	1.15348	+	0.395685i
$519$	14.0294	+	29.8655i	0.615822	+	1.31095i
$520$	5.14679	−	0.119612i	0.225701	−	0.00524533i
$521$	38.6845			1.69480			0.847400	−	0.530956i	$-0.178167\pi$
$521$	38.6845			1.69480			0.847400	+	0.530956i	$0.178167\pi$
$522$	18.2958	+	15.1766i	0.800783	+	0.664261i
$523$	−24.2102			−1.05864			−0.529318	−	0.848423i	$-0.677552\pi$
$523$	−24.2102			−1.05864			−0.529318	+	0.848423i	$0.677552\pi$
$524$	−5.51174	+	9.54661i	−0.240781	+	0.417046i
$525$	3.54119	+	22.6376i	0.154550	+	0.987985i
$526$	−13.8308	−	23.9556i	−0.603050	−	1.04451i
$527$	−14.0674	−	24.3655i	−0.612786	−	1.06138i
$528$	−8.57986	−	0.726217i	−0.373391	−	0.0316045i
$529$	−15.9306	+	27.5926i	−0.692636	+	1.19968i
$530$	−14.4521	−	23.7403i	−0.627761	−	1.03121i
$531$	−22.3292	+	26.9183i	−0.969003	+	1.16816i
$532$	−3.26779	+	2.84728i	−0.141677	+	0.123445i
$533$	−5.54775	+	9.60899i	−0.240300	+	0.416211i
$534$	−9.05744	+	4.25475i	−0.391954	+	0.184121i
$535$	−9.29482	+	16.9994i	−0.401850	+	0.734948i
$536$	−0.266411	+	0.153812i	−0.0115072	+	0.00664368i
$537$	−8.10796	+	11.6493i	−0.349884	+	0.502704i
$538$	7.84991	−	13.5964i	0.338434	−	0.586185i
$539$	34.4715	+	4.76349i	1.48479	+	0.205178i
$540$	−2.64984	+	11.3128i	−0.114031	+	0.486823i
$541$	−44.0407			−1.89346			−0.946729	−	0.322030i	$-0.895635\pi$
$541$	−44.0407			−1.89346			−0.946729	+	0.322030i	$0.895635\pi$
$542$	11.5139	+	6.64757i	0.494566	+	0.285538i
$543$	−5.96952	+	8.57683i	−0.256176	+	0.368067i
$544$	3.51386	−	2.02873i	0.150655	−	0.0869809i
$545$	−13.5875	+	24.8504i	−0.582026	+	1.06447i
$546$	−9.65548	−	4.25292i	−0.413216	−	0.182008i
$547$	−6.01282	−	3.47150i	−0.257089	−	0.148431i	0.365917	−	0.930648i	$-0.380756\pi$
$547$	−6.01282	−	3.47150i	−0.257089	−	0.148431i	−0.623006	+	0.782217i	$0.714089\pi$
$548$	−1.29277			−0.0552243
$549$	−2.26595	+	13.2896i	−0.0967086	+	0.567187i
$550$	22.0805	+	11.4148i	0.941514	+	0.486729i
$551$	6.49022	−	11.2414i	0.276492	−	0.478899i
$552$	1.08201	−	12.7833i	0.0460532	−	0.544094i
$553$	2.44379	−	7.12401i	0.103921	−	0.302944i
$554$	−15.3861	+	8.88318i	−0.653694	+	0.377410i
$555$	−18.1240	−	36.3618i	−0.769319	−	1.54347i
$556$	6.11640	+	3.53131i	0.259393	+	0.149761i
$557$	23.0000			0.974542			0.487271	−	0.873251i	$-0.337992\pi$
$557$	23.0000			0.974542			0.487271	+	0.873251i	$0.337992\pi$
$558$	19.5073	−	7.22517i	0.825809	−	0.305866i
$559$			6.15995i			0.260538i
$560$	3.98904	+	4.36894i	0.168568	+	0.184621i
$561$	−31.6217	+	14.8544i	−1.33507	+	0.627152i
$562$	−5.91512	+	3.41510i	−0.249514	+	0.144057i
$563$	34.1966	−	19.7434i	1.44121	−	0.832085i	0.443283	−	0.896382i	$-0.353814\pi$
$563$	34.1966	−	19.7434i	1.44121	−	0.832085i	0.997931	+	0.0642966i	$0.0204804\pi$
$564$	10.3250	−	14.8347i	0.434762	−	0.624654i
$565$	−35.5934	+	0.827195i	−1.49743	+	0.0348004i
$566$	22.9961			0.966598
$567$	14.7535	−	18.6905i	0.619590	−	0.784925i
$568$		−	7.38341i		−	0.309801i
$569$	18.2142	+	10.5160i	0.763579	+	0.440853i	0.830579	−	0.556900i	$-0.188009\pi$
$569$	18.2142	+	10.5160i	0.763579	+	0.440853i	−0.0670000	+	0.997753i	$0.521343\pi$
$570$	6.33277	+	0.388081i	0.265250	+	0.0162549i
$571$	−0.697417	−	1.20796i	−0.0291860	−	0.0505516i	0.851063	−	0.525063i	$-0.175958\pi$
$571$	−0.697417	−	1.20796i	−0.0291860	−	0.0505516i	−0.880249	+	0.474511i	$0.842625\pi$
$572$	−9.91217	+	5.72279i	−0.414449	+	0.239282i
$573$	1.01633	+	2.16354i	0.0424577	+	0.0903832i
$574$	−12.5134	+	2.44736i	−0.522300	+	0.102151i
$575$	−17.0072	+	32.8981i	−0.709248	+	1.37195i
$576$	1.04198	+	2.81323i	0.0434156	+	0.117218i
$577$	−32.0089			−1.33255			−0.666273	−	0.745708i	$-0.732111\pi$
$577$	−32.0089			−1.33255			−0.666273	+	0.745708i	$0.732111\pi$
$578$	−0.268541	+	0.465126i	−0.0111698	+	0.0193467i
$579$	−10.0937	−	0.854351i	−0.419480	−	0.0355056i
$580$	−15.5458	−	8.50006i	−0.645506	−	0.352946i
$581$	−27.7643	−	9.52416i	−1.15186	−	0.395129i
$582$	−1.40689	+	16.6217i	−0.0583176	+	0.688991i
$583$	53.5126	+	30.8955i	2.21626	+	1.27956i
$584$	−3.95051			−0.163473
$585$	5.69932	+	14.3545i	0.235638	+	0.593485i
$586$			14.5914i			0.602766i
$587$	−8.54969	−	4.93616i	−0.352883	−	0.203737i	0.313071	−	0.949730i	$-0.398642\pi$
$587$	−8.54969	−	4.93616i	−0.352883	−	0.203737i	−0.665954	+	0.745992i	$0.731975\pi$
$588$	−3.60431	−	11.5762i	−0.148639	−	0.477395i
$589$	−5.67966	−	9.83746i	−0.234026	−	0.405346i
$590$	12.5060	−	22.8724i	0.514866	−	0.941643i
$591$	17.5240	+	12.1968i	0.720840	+	0.501708i
$592$	−9.08477	−	5.24509i	−0.373382	−	0.215572i
$593$		−	6.53202i		−	0.268238i	−0.990965	−	0.134119i	$-0.957180\pi$
$593$		−	6.53202i		−	0.268238i	0.990965	−	0.134119i	$-0.0428204\pi$
$594$	−6.89699	−	24.8939i	−0.282987	−	1.02141i
$595$	22.8803	+	7.25915i	0.938000	+	0.297596i
$596$	−7.16878	−	4.13890i	−0.293645	−	0.169536i
$597$	−4.57170	+	6.56849i	−0.187107	+	0.268830i
$598$	−8.52651	−	14.7683i	−0.348675	−	0.603923i
$599$	−3.97020	+	2.29220i	−0.162218	+	0.0936565i	−0.578911	−	0.815391i	$-0.696522\pi$
$599$	−3.97020	+	2.29220i	−0.162218	+	0.0936565i	0.416693	+	0.909047i	$0.363189\pi$
$600$	0.328742	−	8.65401i	0.0134208	−	0.353299i
$601$	−13.3073	−	7.68298i	−0.542816	−	0.313395i	0.203403	−	0.979095i	$-0.434800\pi$
$601$	−13.3073	−	7.68298i	−0.542816	−	0.313395i	−0.746220	+	0.665700i	$0.768133\pi$
$602$	−5.33705	+	4.65026i	−0.217522	+	0.189530i
$603$	−0.710303	−	0.589207i	−0.0289258	−	0.0239944i
$604$	−0.0946137			−0.00384978
$605$	−30.6567	+	0.712466i	−1.24637	+	0.0289658i
$606$	1.95714	−	23.1225i	0.0795033	−	0.939288i
$607$	0.113970	+	0.197402i	0.00462591	+	0.00801230i	0.868329	−	0.495988i	$-0.165194\pi$
$607$	0.113970	+	0.197402i	0.00462591	+	0.00801230i	−0.863703	+	0.504001i	$0.831861\pi$
$608$	1.41871	−	0.819090i	0.0575361	−	0.0332185i
$609$	21.4598	+	29.2909i	0.869594	+	1.18693i
$610$	−0.233464	−	10.0457i	−0.00945268	−	0.406740i
$611$		−	24.0251i		−	0.971953i
$612$	9.36863	+	7.77142i	0.378705	+	0.314141i
$613$		−	26.7256i		−	1.07944i	−0.841845	−	0.539719i	$-0.818531\pi$
$613$		−	26.7256i		−	1.07944i	0.841845	−	0.539719i	$-0.181469\pi$
$614$	−4.11571	+	7.12863i	−0.166097	+	0.287688i
$615$	15.5631	+	10.3037i	0.627566	+	0.415483i
$616$	−12.4412	−	4.26777i	−0.501269	−	0.171954i
$617$	18.8600	+	32.6665i	0.759276	+	1.31510i	0.943220	+	0.332167i	$0.107780\pi$
$617$	18.8600	+	32.6665i	0.759276	+	1.31510i	−0.183945	+	0.982937i	$0.558887\pi$
$618$	15.2610	+	10.6217i	0.613888	+	0.427269i
$619$	−8.46555	−	4.88759i	−0.340259	−	0.196449i	0.320127	−	0.947374i	$-0.396274\pi$
$619$	−8.46555	−	4.88759i	−0.340259	−	0.196449i	−0.660387	+	0.750926i	$0.729608\pi$
$620$	−13.2441	+	8.06246i	−0.531896	+	0.323796i
$621$	37.0899	−	10.2760i	1.48837	−	0.412360i
$622$	−10.5548			−0.423210
$623$	−15.0017	+	2.93402i	−0.601031	+	0.117549i
$624$	3.27303	+	2.27805i	0.131026	+	0.0911948i
$625$	−10.4367	+	22.7173i	−0.417466	+	0.908692i
$626$	9.20310	+	15.9402i	0.367830	+	0.637100i
$627$	−12.7671	+	5.99739i	−0.509870	+	0.239513i
$628$	0.938382	−	1.62532i	0.0374455	−	0.0648575i
$629$	−42.5634			−1.69711
$630$	−8.13436	+	15.7744i	−0.324081	+	0.628468i
$631$	5.47839			0.218091			0.109046	−	0.994037i	$-0.465221\pi$
$631$	5.47839			0.218091			0.109046	+	0.994037i	$0.465221\pi$
$632$	−1.42332	+	2.46526i	−0.0566167	+	0.0980630i
$633$	0.395715	−	4.67516i	0.0157283	−	0.185821i
$634$	13.6314	+	23.6102i	0.541370	+	0.937681i
$635$	0.187967	+	0.102775i	0.00745923	+	0.00407851i
$636$	1.81573	−	21.4519i	0.0719985	−	0.850623i
$637$	−12.7227	−	9.89285i	−0.504093	−	0.391969i
$638$	39.3910			1.55951
$639$	20.7712	−	7.69333i	0.821698	−	0.304343i
$640$	−1.16272	−	1.90999i	−0.0459607	−	0.0754991i
$641$	−5.91036	−	3.41235i	−0.233445	−	0.134780i	0.378715	−	0.925513i	$-0.376366\pi$
$641$	−5.91036	−	3.41235i	−0.233445	−	0.134780i	−0.612160	+	0.790734i	$0.709699\pi$
$642$	−13.5834	+	6.38083i	−0.536094	+	0.251831i
$643$	9.33848	+	16.1747i	0.368274	+	0.637869i	0.989296	−	0.145924i	$-0.0466156\pi$
$643$	9.33848	+	16.1747i	0.368274	+	0.637869i	−0.621022	+	0.783793i	$0.713282\pi$
$644$	6.35864	−	18.5364i	0.250566	−	0.730435i
$645$	10.3429	+	0.633824i	0.407249	+	0.0249568i
$646$	3.32342	−	5.75633i	0.130758	−	0.226480i
$647$		−	6.15085i		−	0.241815i	−0.992664	−	0.120907i	$-0.961420\pi$
$647$		−	6.15085i		−	0.241815i	0.992664	−	0.120907i	$-0.0385804\pi$
$648$	−6.82857	+	5.86264i	−0.268252	+	0.230306i
$649$			57.9556i			2.27496i
$650$	−6.21275	−	9.69125i	−0.243684	−	0.380122i
$651$	31.5885	−	3.44727i	1.23805	−	0.135109i
$652$	−2.05066	+	1.18395i	−0.0803100	+	0.0463670i
$653$	4.62276	+	8.00685i	0.180902	+	0.313332i	0.942188	−	0.335084i	$-0.108765\pi$
$653$	4.62276	+	8.00685i	0.180902	+	0.313332i	−0.761286	+	0.648417i	$0.775432\pi$
$654$	−19.8567	+	9.32775i	−0.776460	+	0.364744i
$655$	24.6426	−	0.572697i	0.962866	−	0.0223771i
$656$	4.81924			0.188160
$657$	−4.11633	−	11.1137i	−0.160593	−	0.433587i
$658$	20.8156	−	18.1370i	0.811478	−	0.707054i
$659$	−11.1622	−	6.44447i	−0.434816	−	0.251041i	0.266580	−	0.963813i	$-0.414106\pi$
$659$	−11.1622	−	6.44447i	−0.434816	−	0.251041i	−0.701396	+	0.712772i	$0.747440\pi$
$660$	8.58894	+	17.2319i	0.334324	+	0.670749i
$661$	29.4904	−	17.0263i	1.14704	−	0.662245i	0.198878	−	0.980024i	$-0.436270\pi$
$661$	29.4904	−	17.0263i	1.14704	−	0.662245i	0.948165	+	0.317779i	$0.102937\pi$
$662$	−9.19875	−	15.9327i	−0.357519	−	0.619242i
$663$	16.1225	+	1.36464i	0.626146	+	0.0529983i
$664$	9.60784	+	5.54709i	0.372857	+	0.215269i
$665$	9.23782	+	2.93086i	0.358227	+	0.113654i
$666$	5.28957	−	31.0228i	0.204967	−	1.20211i
$667$			58.6895i			2.27247i
$668$	6.32518	+	3.65184i	0.244728	+	0.141294i
$669$	−8.28650	+	3.89260i	−0.320375	+	0.150497i
$670$	0.603542	+	0.330001i	0.0233169	+	0.0127491i
$671$	11.1700	+	19.3470i	0.431214	+	0.746884i
$672$	0.497147	+	4.55553i	0.0191779	+	0.175733i
$673$	−21.9800	−	12.6901i	−0.847265	−	0.489169i	0.0124618	−	0.999922i	$-0.496033\pi$
$673$	−21.9800	−	12.6901i	−0.847265	−	0.489169i	−0.859727	+	0.510753i	$0.829367\pi$
$674$		−	14.4517i		−	0.556658i
$675$	24.6883	−	8.09244i	0.950253	−	0.311478i
$676$	−7.69926			−0.296125
$677$	−28.8703	−	16.6683i	−1.10958	−	0.640613i	−0.170856	−	0.985296i	$-0.554653\pi$
$677$	−28.8703	−	16.6683i	−1.10958	−	0.640613i	−0.938719	+	0.344683i	$0.887987\pi$
$678$	−22.6352	−	15.7542i	−0.869299	−	0.605036i
$679$	−8.26792	+	24.1022i	−0.317294	+	0.924956i
$680$	−7.96050	−	4.35259i	−0.305271	−	0.166914i
$681$	−13.6729	−	29.1065i	−0.523945	−	1.11537i
$682$	17.2358	−	29.8532i	0.659991	−	1.14314i
$683$	−4.53570			−0.173554			−0.0867769	−	0.996228i	$-0.527657\pi$
$683$	−4.53570			−0.173554			−0.0867769	+	0.996228i	$0.527657\pi$
$684$	3.78255	+	3.13768i	0.144629	+	0.119972i
$685$	1.50313	+	2.46918i	0.0574317	+	0.0943424i
$686$	−1.03335	−	18.4914i	−0.0394533	−	0.706005i
$687$	15.5881	+	1.31941i	0.594724	+	0.0503387i
$688$	2.31707	−	1.33776i	0.0883375	−	0.0510017i
$689$	−14.3085	−	24.7830i	−0.545110	−	0.944158i
$690$	−25.6741	+	12.7968i	−0.977396	+	0.487167i
$691$	−8.08693	−	4.66899i	−0.307641	−	0.177617i	0.338229	−	0.941064i	$-0.390172\pi$
$691$	−8.08693	−	4.66899i	−0.307641	−	0.177617i	−0.645871	+	0.763447i	$0.723505\pi$
$692$		−	19.0506i		−	0.724194i
$693$	−0.957148	−	39.4468i	−0.0363591	−	1.49846i
$694$	18.0657			0.685764
$695$	−0.366920	−	15.7882i	−0.0139181	−	0.598881i
$696$	−5.83523	−	12.4219i	−0.221184	−	0.470852i
$697$	16.9341	−	9.77692i	0.641425	−	0.370327i
$698$	7.58926	−	4.38166i	0.287258	−	0.165848i
$699$	3.72522	+	2.59277i	0.140901	+	0.0980677i
$700$	3.70649	−	12.6989i	0.140092	−	0.479973i
$701$		−	5.36231i		−	0.202532i	−0.994859	−	0.101266i	$-0.967711\pi$
$701$		−	5.36231i		−	0.202532i	0.994859	−	0.101266i	$-0.0322892\pi$
$702$	−2.99826	+	11.5815i	−0.113162	+	0.437115i
$703$	−17.1848			−0.648138
$704$	4.30527	+	2.48565i	0.162261	+	0.0936814i
$705$	−40.3394	−	2.47205i	−1.51927	−	0.0931029i
$706$	−9.23289	+	5.33061i	−0.347484	+	0.200620i
$707$	11.5015	−	33.5287i	0.432560	−	1.26098i
$708$	18.2763	−	8.58532i	0.686864	−	0.322656i
$709$	−16.7421	+	28.9982i	−0.628764	+	1.08905i	0.359036	+	0.933324i	$0.383106\pi$
$709$	−16.7421	+	28.9982i	−0.628764	+	1.08905i	−0.987800	+	0.155728i	$0.950228\pi$
$710$	−14.1023	+	8.58487i	−0.529248	+	0.322184i
$711$	−8.41843	−	1.43539i	−0.315716	−	0.0538313i
$712$	5.77755			0.216523
$713$	44.4789	+	25.6799i	1.66575	+	0.961720i
$714$	10.9888	+	14.9989i	0.411246	+	0.561320i
$715$	22.4556	+	12.2781i	0.839793	+	0.459176i
$716$	7.09657	−	4.09720i	0.265211	−	0.153120i
$717$	8.40812	+	0.711681i	0.314007	+	0.0265782i
$718$	−14.2860	−	8.24802i	−0.533149	−	0.307813i
$719$	2.15051			0.0802004			0.0401002	−	0.999196i	$-0.487232\pi$
$719$	2.15051			0.0802004			0.0401002	+	0.999196i	$0.487232\pi$
$720$	4.16173	−	5.26118i	0.155098	−	0.196073i
$721$	18.6582	+	21.4138i	0.694868	+	0.797492i
$722$	−8.15818	+	14.1304i	−0.303616	+	0.525879i
$723$	−10.7188	−	22.8180i	−0.398636	−	0.848610i
$724$	5.22487	−	3.01658i	0.194181	−	0.112110i
$725$	1.84048	+	39.5757i	0.0683537	+	1.46980i
$726$	−19.4957	−	13.5691i	−0.723555	−	0.503598i
$727$	5.44298	−	9.42752i	0.201869	−	0.349647i	−0.747262	−	0.664530i	$-0.768632\pi$
$727$	5.44298	−	9.42752i	0.201869	−	0.349647i	0.949131	+	0.314883i	$0.101965\pi$
$728$	4.00163	+	4.59262i	0.148310	+	0.170214i
$729$	−23.6082	−	13.1016i	−0.874378	−	0.485246i
$730$	4.59335	+	7.54544i	0.170008	+	0.279269i
$731$	5.42790	−	9.40140i	0.200758	−	0.347723i
$732$	4.44639	−	6.38845i	0.164343	−	0.236124i
$733$	−18.0386	−	31.2438i	−0.666271	−	1.15402i	−0.978939	−	0.204153i	$-0.934556\pi$
$733$	−18.0386	−	31.2438i	−0.666271	−	1.15402i	0.312668	−	0.949863i	$-0.398777\pi$
$734$	−0.205646	−	0.356189i	−0.00759053	−	0.0131472i
$735$	−17.9197	+	20.3442i	−0.660977	+	0.750406i
$736$	−3.70342	+	6.41451i	−0.136510	+	0.236442i
$737$	−1.52929			−0.0563322
$738$	5.02153	+	13.5577i	0.184845	+	0.499064i
$739$	−8.61728			−0.316992			−0.158496	−	0.987360i	$-0.550664\pi$
$739$	−8.61728			−0.316992			−0.158496	+	0.987360i	$0.550664\pi$
$740$	0.544991	+	23.4504i	0.0200343	+	0.862055i
$741$	6.50939	+	0.550969i	0.239129	+	0.0202403i
$742$	10.6706	−	31.1062i	0.391728	−	1.14194i
$743$	15.2682	+	26.4453i	0.560135	+	0.970183i	0.997484	+	0.0708907i	$0.0225842\pi$
$743$	15.2682	+	26.4453i	0.560135	+	0.970183i	−0.437349	+	0.899292i	$0.644083\pi$
$744$	−11.9674	−	1.01295i	−0.438747	−	0.0371365i
$745$	0.430052	+	18.5047i	0.0157559	+	0.677960i
$746$			10.8325i			0.396608i
$747$	−5.59413	+	32.8090i	−0.204678	+	1.20042i
$748$	20.1708			0.737518
$749$	−22.4980	+	4.40014i	−0.822060	+	0.160778i
$750$	−16.9113	+	9.43434i	−0.617515	+	0.344493i
$751$	3.78106	+	6.54899i	0.137973	+	0.238976i	0.926729	−	0.375730i	$-0.122608\pi$
$751$	3.78106	+	6.54899i	0.137973	+	0.238976i	−0.788756	+	0.614706i	$0.789275\pi$
$752$	−9.03708	+	5.21756i	−0.329548	+	0.190265i
$753$	−29.2913	−	20.3869i	−1.06744	−	0.742940i
$754$	−15.7989	−	9.12149i	−0.575361	−	0.332185i
$755$	0.110010	+	0.180711i	0.00400366	+	0.00657676i
$756$	−12.2978	+	6.14534i	−0.447265	+	0.223504i
$757$			16.4905i			0.599358i	0.954040	+	0.299679i	$0.0968795\pi$
$757$			16.4905i			0.599358i	−0.954040	+	0.299679i	$0.903121\pi$
$758$	10.3774	−	17.9741i	0.376923	−	0.652850i
$759$	36.4331	−	52.3461i	1.32244	−	1.90004i
$760$	−3.21402	−	1.75734i	−0.116585	−	0.0637455i
$761$	7.56857	+	13.1092i	0.274361	+	0.475206i	0.969974	−	0.243210i	$-0.0782005\pi$
$761$	7.56857	+	13.1092i	0.274361	+	0.475206i	−0.695613	+	0.718417i	$0.744867\pi$
$762$	0.0705545	+	0.150195i	0.00255592	+	0.00544099i
$763$	−32.8885	+	6.43229i	−1.19064	+	0.232865i
$764$		−	1.38008i		−	0.0499294i
$765$	3.95021	−	26.9300i	0.142820	−	0.973658i
$766$		−	34.0913i		−	1.23177i
$767$	13.4203	−	23.2447i	0.484581	−	0.839318i
$768$	0.146082	−	1.72588i	0.00527128	−	0.0622773i
$769$	23.8050	−	13.7438i	0.858430	−	0.495615i	−0.00505613	−	0.999987i	$-0.501609\pi$
$769$	23.8050	−	13.7438i	0.858430	−	0.495615i	0.863486	+	0.504372i	$0.168276\pi$
$770$	6.31423	+	28.7248i	0.227549	+	1.03517i
$771$	0.547634	+	0.0463529i	0.0197226	+	0.00166936i
$772$	5.06489	+	2.92422i	0.182290	+	0.105245i
$773$			40.9642i			1.47338i	0.676230	+	0.736691i	$0.263613\pi$
$773$			40.9642i			1.47338i	−0.676230	+	0.736691i	$0.736387\pi$
$774$	6.17777	+	5.12455i	0.222055	+	0.184198i
$775$	30.7985	+	15.9217i	1.10631	+	0.571925i
$776$	4.81542	−	8.34056i	0.172864	−	0.299409i
$777$	19.3777	−	43.9935i	0.695171	−	1.57826i
$778$	−15.5200	+	8.96050i	−0.556420	+	0.321249i
$779$	6.83708	−	3.94739i	0.244964	−	0.141430i
$780$	0.545417	−	8.90021i	0.0195291	−	0.318678i
$781$	18.3526	−	31.7876i	0.656706	−	1.13745i
$782$			30.0529i			1.07469i
$783$	28.8656	−	29.3592i	1.03157	−	1.04921i
$784$	−0.958199	+	6.93411i	−0.0342214	+	0.247647i
$785$	−4.19544	+	0.0975024i	−0.149742	+	0.00348001i
$786$	15.6711	+	10.9072i	0.558971	+	0.389046i
$787$	16.9398	+	29.3406i	0.603839	+	1.04588i	0.992234	+	0.124387i	$0.0396963\pi$
$787$	16.9398	+	29.3406i	0.603839	+	1.04588i	−0.388395	+	0.921493i	$0.626970\pi$
$788$	−6.16341	−	10.6753i	−0.219562	−	0.380293i
$789$	−43.3649	+	20.3708i	−1.54383	+	0.725218i
$790$	6.36357	−	0.147890i	0.226406	−	0.00526169i
$791$	−27.6739	−	31.7610i	−0.983971	−	1.12929i
$792$	−2.50673	+	14.7017i	−0.0890726	+	0.522403i
$793$		−	10.3462i		−	0.367406i
$794$	−0.566953	+	0.981991i	−0.0201204	+	0.0348496i
$795$	−43.0842	+	21.4746i	−1.52804	+	0.761626i
$796$	4.00142	−	2.31022i	0.141827	−	0.0818836i
$797$	−44.1099	+	25.4669i	−1.56245	+	0.902083i	−0.565445	+	0.824786i	$0.691295\pi$
$797$	−44.1099	+	25.4669i	−1.56245	+	0.902083i	−0.997008	+	0.0772962i	$0.975371\pi$
$798$	4.43670	+	6.05575i	0.157057	+	0.214371i
$799$	−21.1700	+	36.6675i	−0.748941	+	1.29720i
$800$	−2.29614	+	4.44159i	−0.0811810	+	0.157034i
$801$	6.02006	+	16.2536i	0.212708	+	0.574292i
$802$		−	8.10222i		−	0.286099i
$803$	−17.0080	−	9.81958i	−0.600199	−	0.346525i
$804$	0.226544	+	0.482262i	0.00798958	+	0.0170081i
$805$	−42.7976	+	9.40771i	−1.50842	+	0.331578i
$806$	−13.8258	+	7.98232i	−0.486992	+	0.281165i
$807$	−22.3191	−	15.5342i	−0.785670	−	0.546830i
$808$	−6.69877	+	11.6026i	−0.235662	+	0.408178i
$809$		−	3.46980i		−	0.121992i	−0.998138	−	0.0609959i	$-0.980572\pi$
$809$		−	3.46980i		−	0.121992i	0.998138	−	0.0609959i	$-0.0194277\pi$
$810$	19.1374	+	6.22589i	0.672418	+	0.218755i
$811$		−	38.8069i		−	1.36270i	−0.731960	−	0.681348i	$-0.761394\pi$
$811$		−	38.8069i		−	1.36270i	0.731960	−	0.681348i	$-0.238606\pi$
$812$	−4.02390	−	20.5743i	−0.141211	−	0.722017i
$813$	13.1549	−	18.9006i	0.461362	−	0.662872i
$814$	−26.0749	−	45.1631i	−0.913925	−	1.58297i
$815$	4.64569	+	2.54014i	0.162731	+	0.0889772i
$816$	−2.98803	−	6.36085i	−0.104602	−	0.222674i
$817$	2.19149	−	3.79578i	0.0766707	−	0.132798i
$818$			14.6375i			0.511788i
$819$	−8.75053	+	16.0429i	−0.305768	+	0.560585i
$820$	−5.60345	−	9.20471i	−0.195681	−	0.321443i
$821$	−35.8129	−	20.6766i	−1.24988	−	0.721617i	−0.278792	−	0.960351i	$-0.589934\pi$
$821$	−35.8129	−	20.6766i	−1.24988	−	0.721617i	−0.971085	+	0.238735i	$0.923267\pi$
$822$	−0.188850	+	2.23116i	−0.00658690	+	0.0778207i
$823$	46.7302	−	26.9797i	1.62891	−	0.940453i	0.644494	−	0.764609i	$-0.277068\pi$
$823$	46.7302	−	26.9797i	1.62891	−	0.940453i	0.984418	−	0.175844i	$-0.0562654\pi$
$824$	−5.36750	−	9.29678i	−0.186986	−	0.323869i
$825$	22.9262	−	36.4407i	0.798186	−	1.26870i
$826$	30.2708	−	5.92033i	1.05325	−	0.205994i
$827$	−20.1603			−0.701044			−0.350522	−	0.936555i	$-0.613996\pi$
$827$	−20.1603			−0.701044			−0.350522	+	0.936555i	$0.613996\pi$
$828$	−21.9044	−	3.73482i	−0.761230	−	0.129794i
$829$			34.6201i			1.20241i	0.799097	+	0.601203i	$0.205311\pi$
$829$			34.6201i			1.20241i	−0.799097	+	0.601203i	$0.794689\pi$
$830$	−0.576370	−	24.8006i	−0.0200061	−	0.860843i
$831$	13.0837	+	27.8523i	0.453867	+	0.966184i
$832$	−1.15117	−	1.99388i	−0.0399095	−	0.0691253i
$833$	10.7004	+	26.3094i	0.370748	+	0.911566i
$834$	6.98811	−	10.0403i	0.241978	−	0.347668i
$835$	−0.379444	−	16.3271i	−0.0131312	−	0.565023i
$836$	8.14388			0.281662
$837$	−9.62011	−	34.7227i	−0.332520	−	1.20019i
$838$	−11.6832			−0.403590
$839$	18.3497	−	31.7826i	0.633501	−	1.09726i	−0.353329	−	0.935499i	$-0.614950\pi$
$839$	18.3497	−	31.7826i	0.633501	−	1.09726i	0.986831	−	0.161758i	$-0.0517162\pi$
$840$	8.12298	−	6.24637i	0.280270	−	0.215520i
$841$	16.8924	+	29.2585i	0.582497	+	1.00891i
$842$	12.5853	+	21.7984i	0.433718	+	0.751222i
$843$	5.02996	+	10.7077i	0.173241	+	0.368792i
$844$	−1.35443	+	2.34594i	−0.0466214	+	0.0807506i
$845$	8.95211	+	14.7055i	0.307962	+	0.505885i
$846$	−24.0946	−	19.9868i	−0.828390	−	0.687162i
$847$	−23.8356	−	27.3559i	−0.819001	−	0.939958i
$848$	−6.21477	+	10.7643i	−0.213416	+	0.369648i
$849$	3.35932	−	39.6885i	0.115291	−	1.36211i
$850$	0.942447	+	20.2654i	0.0323257	+	0.695096i
$851$	67.2894	−	38.8495i	2.30665	−	1.33175i
$852$	−12.7429	−	1.07858i	−0.436563	−	0.0369516i
$853$	−12.5798	+	21.7888i	−0.430723	+	0.746034i	−0.996936	−	0.0782251i	$-0.975075\pi$
$853$	−12.5798	+	21.7888i	−0.430723	+	0.746034i	0.566213	+	0.824259i	$0.308408\pi$
$854$	8.96409	−	7.81056i	0.306745	−	0.267272i
$855$	1.59488	−	10.8729i	0.0545439	−	0.371845i
$856$	8.66456			0.296148
$857$	−15.3574	−	8.86660i	−0.524599	−	0.302877i	0.214215	−	0.976786i	$-0.431281\pi$
$857$	−15.3574	−	8.86660i	−0.524599	−	0.302877i	−0.738814	+	0.673909i	$0.764614\pi$
$858$	8.42886	+	17.9432i	0.287757	+	0.612571i
$859$	26.6331	−	15.3766i	0.908710	−	0.524644i	0.0286940	−	0.999588i	$-0.490865\pi$
$859$	26.6331	−	15.3766i	0.908710	−	0.524644i	0.880016	+	0.474944i	$0.157532\pi$
$860$	−5.24923	−	2.87014i	−0.178997	−	0.0978710i
$861$	2.39587	+	21.9542i	0.0816510	+	0.748197i
$862$	0.590169	+	0.340734i	0.0201012	+	0.0116054i
$863$	−20.1050			−0.684381			−0.342190	−	0.939631i	$-0.611169\pi$
$863$	−20.1050			−0.684381			−0.342190	+	0.939631i	$0.611169\pi$
$864$	5.00752	−	1.38736i	0.170359	−	0.0471990i
$865$	−36.3865	+	22.1506i	−1.23718	+	0.753142i
$866$	−0.820118	+	1.42049i	−0.0278687	+	0.0482701i
$867$	0.763522	+	0.531415i	0.0259306	+	0.0180478i
$868$	−17.3533	−	5.95281i	−0.589009	−	0.202052i
$869$	−12.2556	+	7.07575i	−0.415742	+	0.240029i
$870$	−16.9410	+	25.5885i	−0.574355	+	0.867533i
$871$	0.613366	+	0.354127i	0.0207831	+	0.0119991i
$872$	12.6662			0.428931
$873$	28.4815	+	4.85626i	0.963953	+	0.164359i
$874$			12.1337i			0.410430i
$875$	−28.5644	+	7.68595i	−0.965654	+	0.259833i
$876$	−0.577098	+	6.81810i	−0.0194983	+	0.230362i
$877$	20.1511	−	11.6342i	0.680454	−	0.392860i	−0.119572	−	0.992825i	$-0.538152\pi$
$877$	20.1511	−	11.6342i	0.680454	−	0.392860i	0.800026	+	0.599965i	$0.204819\pi$
$878$	14.2849	−	8.24739i	0.482092	−	0.278336i
$879$	25.1830	+	2.13154i	0.849403	+	0.0718952i
$880$	−0.258271	−	11.1132i	−0.00870632	−	0.374625i
$881$	14.6821			0.494653			0.247326	−	0.968932i	$-0.420448\pi$
$881$	14.6821			0.494653			0.247326	+	0.968932i	$0.420448\pi$
$882$	−20.5057	+	4.52953i	−0.690462	+	0.152517i
$883$			25.8044i			0.868386i	0.900820	+	0.434193i	$0.142966\pi$
$883$			25.8044i			0.868386i	−0.900820	+	0.434193i	$0.857034\pi$
$884$	−8.09007	−	4.67081i	−0.272099	−	0.157096i
$885$	−37.6482	−	24.9252i	−1.26553	−	0.837851i
$886$	11.5504	+	20.0059i	0.388043	+	0.672110i
$887$	11.3367	−	6.54525i	0.380649	−	0.219768i	−0.297451	−	0.954737i	$-0.596137\pi$
$887$	11.3367	−	6.54525i	0.380649	−	0.219768i	0.678101	+	0.734969i	$0.262803\pi$
$888$	−10.3795	+	14.9130i	−0.348314	+	0.500447i
$889$	0.0486535	+	0.248766i	0.00163179	+	0.00834335i
$890$	−6.71769	−	11.0351i	−0.225178	−	0.369896i
$891$	−43.9713	+	8.26682i	−1.47309	+	0.276949i
$892$	5.28578			0.176981
$893$	−8.54730	+	14.8044i	−0.286025	+	0.495409i
$894$	−8.19047	+	11.7678i	−0.273930	+	0.393575i
$895$	−16.0770	−	8.79047i	−0.537394	−	0.293833i
$896$	0.858483	−	2.50260i	0.0286799	−	0.0836060i
$897$	−26.7340	+	12.5583i	−0.892621	+	0.419311i
$898$	13.8994	+	8.02483i	0.463829	+	0.267792i
$899$	54.9437			1.83248
$900$	−14.8878	−	1.83156i	−0.496259	−	0.0610521i
$901$			50.4323i			1.68014i
$902$	20.7481	+	11.9789i	0.690837	+	0.398855i
$903$	7.24614	+	9.89042i	0.241136	+	0.329133i
$904$	7.96108	+	13.7890i	0.264782	+	0.458615i
$905$	−11.8367	−	6.47202i	−0.393466	−	0.215137i
$906$	−0.0138214	+	0.163292i	−0.000459184	+	0.00542501i
$907$	10.9875	+	6.34364i	0.364834	+	0.210637i	0.671199	−	0.741277i	$-0.265780\pi$
$907$	10.9875	+	6.34364i	0.364834	+	0.210637i	−0.306365	+	0.951914i	$0.599113\pi$
$908$			18.5664i			0.616149i
$909$	−39.6208	−	6.75557i	−1.31414	−	0.224068i
$910$	4.11909	−	12.9830i	0.136546	−	0.430383i
$911$	−43.7132	−	25.2378i	−1.44828	−	0.836167i	−0.449904	−	0.893077i	$-0.648542\pi$
$911$	−43.7132	−	25.2378i	−1.44828	−	0.836167i	−0.998379	+	0.0569104i	$0.981875\pi$
$912$	−1.20640	−	2.56817i	−0.0399480	−	0.0850406i
$913$	27.5762	+	47.7635i	0.912640	+	1.58074i
$914$	−0.692830	+	0.400006i	−0.0229168	+	0.0132310i
$915$	−17.3718	−	1.06457i	−0.574295	−	0.0351936i
$916$	−7.82193	−	4.51600i	−0.258444	−	0.149213i
$917$	19.1596	+	21.9893i	0.632706	+	0.726150i
$918$	14.7811	−	15.0339i	0.487850	−	0.496192i
$919$	38.5621			1.27205			0.636024	−	0.771670i	$-0.280578\pi$
$919$	38.5621			1.27205			0.636024	+	0.771670i	$0.280578\pi$
$920$	16.5577	−	0.384803i	0.545892	−	0.0126866i
$921$	11.7019	+	8.14459i	0.385591	+	0.268373i
$922$	3.10910	+	5.38511i	0.102393	+	0.177349i
$923$	−14.7216	+	8.49953i	−0.484568	+	0.279766i
$924$	−9.18309	+	20.8485i	−0.302102	+	0.685866i
$925$	44.1565	−	28.3073i	1.45186	−	0.930739i
$926$			13.5112i			0.444005i
$927$	20.5612	−	24.7870i	0.675319	−	0.814113i
$928$			7.92369i			0.260108i
$929$	20.4721	−	35.4587i	0.671667	−	1.16336i	−0.305764	−	0.952107i	$-0.598912\pi$
$929$	20.4721	−	35.4587i	0.671667	−	1.16336i	0.977431	−	0.211254i	$-0.0677546\pi$
$930$	11.9801	+	24.0355i	0.392843	+	0.788155i
$931$	4.32026	+	10.6223i	0.141591	+	0.348132i
$932$	−1.31021	−	2.26935i	−0.0429173	−	0.0743350i
$933$	−1.54187	+	18.2164i	−0.0504786	+	0.596377i
$934$	12.1807	+	7.03252i	0.398564	+	0.230111i
$935$	−23.4531	−	38.5261i	−0.766998	−	1.25994i
$936$	4.40976	−	5.31608i	0.144138	−	0.173761i
$937$	−21.5005			−0.702390			−0.351195	−	0.936302i	$-0.614225\pi$
$937$	−21.5005			−0.702390			−0.351195	+	0.936302i	$0.614225\pi$
$938$	0.156222	+	0.798764i	0.00510082	+	0.0260806i
$939$	28.8553	−	13.5549i	0.941658	−	0.442346i
$940$	20.4731	+	11.1942i	0.667760	+	0.365114i
$941$	−19.3545	−	33.5229i	−0.630937	−	1.09282i	−0.987360	−	0.158491i	$-0.949337\pi$
$941$	−19.3545	−	33.5229i	−0.630937	−	1.09282i	0.356423	−	0.934325i	$-0.383996\pi$
$942$	−2.66803	−	1.85696i	−0.0869292	−	0.0605032i
$943$	−17.8477	+	30.9131i	−0.581200	+	1.00667i
$944$	−11.6580			−0.379437
$945$	26.0365	+	16.3433i	0.846966	+	0.531647i
$946$	13.3008			0.432447
$947$	−12.9866	+	22.4934i	−0.422007	+	0.730937i	−0.996136	−	0.0878280i	$-0.972007\pi$
$947$	−12.9866	+	22.4934i	−0.422007	+	0.730937i	0.574129	+	0.818765i	$0.305341\pi$
$948$	4.04683	+	2.81661i	0.131435	+	0.0914793i
$949$	4.54769	+	7.87684i	0.147624	+	0.255693i
$950$	0.380509	+	8.18206i	0.0123454	+	0.265461i
$951$	42.7396	−	20.0770i	1.38593	−	0.651043i
$952$	−2.06050	−	10.5354i	−0.0667813	−	0.341454i
$953$	−9.34565			−0.302735			−0.151368	−	0.988478i	$-0.548368\pi$
$953$	−9.34565			−0.302735			−0.151368	+	0.988478i	$0.548368\pi$
$954$	−36.7581	−	6.26747i	−1.19009	−	0.202917i
$955$	−2.63594	+	1.60465i	−0.0852969	+	0.0519252i
$956$	−4.21909	−	2.43589i	−0.136455	−	0.0787825i
$957$	5.75432	−	67.9841i	0.186011	−	2.19762i
$958$	2.52248	+	4.36907i	0.0814977	+	0.141158i
$959$	−1.10982	+	3.23528i	−0.0358379	+	0.104473i
$960$	−3.46627	+	1.72771i	−0.111873	+	0.0557615i
$961$	8.54093	−	14.7933i	0.275514	−	0.477204i
$962$			24.1519i			0.778689i
$963$	9.02826	+	24.3754i	0.290931	+	0.785487i
$964$			14.5551i			0.468788i
$965$	−0.303840	−	13.0740i	−0.00978097	−	0.420866i
$966$	−31.0626	−	13.6821i	−0.999424	−	0.440214i
$967$	−52.6756	+	30.4123i	−1.69393	+	0.977993i	−0.742647	+	0.669683i	$0.766430\pi$
$967$	−52.6756	+	30.4123i	−1.69393	+	0.977993i	−0.951286	+	0.308310i	$0.900237\pi$
$968$	6.85690	+	11.8765i	0.220389	+	0.381725i
$969$	−9.44924	−	6.57672i	−0.303553	−	0.211275i
$970$	−21.5294	+	0.500346i	−0.691268	+	0.0160651i
$971$	−23.3430			−0.749111			−0.374556	−	0.927204i	$-0.622205\pi$
$971$	−23.3430			−0.749111			−0.374556	+	0.927204i	$0.622205\pi$
$972$	9.12068	+	12.6417i	0.292546	+	0.405483i
$973$	14.0883	−	12.2753i	0.451649	−	0.393530i
$974$	23.9584	+	13.8324i	0.767677	+	0.443219i
$975$	−17.6335	+	9.30674i	−0.564724	+	0.298054i
$976$	−3.89175	+	2.24690i	−0.124572	+	0.0719216i
$977$	−10.2509	−	17.7551i	−0.327955	−	0.568035i	0.654151	−	0.756364i	$-0.273026\pi$
$977$	−10.2509	−	17.7551i	−0.327955	−	0.568035i	−0.982106	+	0.188329i	$0.939693\pi$
$978$	1.74379	+	3.71215i	0.0557602	+	0.118701i
$979$	24.8739	+	14.3610i	0.794973	+	0.458978i
$980$	14.3582	−	6.23230i	0.458656	−	0.199084i
$981$	13.1979	+	35.6329i	0.421375	+	1.13767i
$982$			15.4788i			0.493949i
$983$	18.5257	+	10.6958i	0.590877	+	0.341143i	0.765444	−	0.643502i	$-0.222519\pi$
$983$	18.5257	+	10.6958i	0.590877	+	0.341143i	−0.174567	+	0.984645i	$0.555853\pi$
$984$	0.704004	−	8.31743i	0.0224428	−	0.265150i
$985$	−13.2235	+	24.1845i	−0.421335	+	0.770583i
$986$	16.0750	+	27.8427i	0.511932	+	0.886692i
$987$	−28.2615	−	38.5748i	−0.899573	−	1.22785i
$988$	−3.26634	−	1.88582i	−0.103916	−	0.0599959i
$989$			19.8172i			0.630149i
$990$	30.9948	−	12.3062i	0.985080	−	0.391117i
$991$	−8.23001			−0.261435			−0.130717	−	0.991420i	$-0.541728\pi$
$991$	−8.23001			−0.261435			−0.130717	+	0.991420i	$0.541728\pi$
$992$	6.00511	+	3.46705i	0.190663	+	0.110079i
$993$	−28.8417	+	13.5484i	−0.915263	+	0.429947i
$994$	−18.4777	−	6.33853i	−0.586077	−	0.201046i
$995$	−9.06505	−	4.95653i	−0.287382	−	0.157133i
$996$	10.9771	−	15.7716i	0.347824	−	0.499744i
$997$	−0.0357929	+	0.0619952i	−0.00113357	+	0.00196341i	−0.866592	−	0.499018i	$-0.833694\pi$
$997$	−0.0357929	+	0.0619952i	−0.00113357	+	0.00196341i	0.865458	+	0.500981i	$0.167027\pi$
$998$	−15.4513			−0.489103
$999$	−52.7690	−	13.6610i	−1.66954	−	0.432216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.e.209.14	yes	32
3.2	odd	2		1890.2.bf.f.629.12		32
5.4	even	2		630.2.bf.f.209.3	yes	32
7.6	odd	2	inner	630.2.bf.e.209.3	✓	32
9.4	even	3		1890.2.bf.e.1259.16		32
9.5	odd	6		630.2.bf.f.419.14	yes	32
15.14	odd	2		1890.2.bf.e.629.1		32
21.20	even	2		1890.2.bf.f.629.5		32
35.34	odd	2		630.2.bf.f.209.14	yes	32
45.4	even	6		1890.2.bf.f.1259.5		32
45.14	odd	6	inner	630.2.bf.e.419.3	yes	32
63.13	odd	6		1890.2.bf.e.1259.1		32
63.41	even	6		630.2.bf.f.419.3	yes	32
105.104	even	2		1890.2.bf.e.629.16		32
315.104	even	6	inner	630.2.bf.e.419.14	yes	32
315.139	odd	6		1890.2.bf.f.1259.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.3	✓	32	7.6	odd	2	inner
630.2.bf.e.209.14	yes	32	1.1	even	1	trivial
630.2.bf.e.419.3	yes	32	45.14	odd	6	inner
630.2.bf.e.419.14	yes	32	315.104	even	6	inner
630.2.bf.f.209.3	yes	32	5.4	even	2
630.2.bf.f.209.14	yes	32	35.34	odd	2
630.2.bf.f.419.3	yes	32	63.41	even	6
630.2.bf.f.419.14	yes	32	9.5	odd	6
1890.2.bf.e.629.1		32	15.14	odd	2
1890.2.bf.e.629.16		32	105.104	even	2
1890.2.bf.e.1259.1		32	63.13	odd	6
1890.2.bf.e.1259.16		32	9.4	even	3
1890.2.bf.f.629.5		32	21.20	even	2
1890.2.bf.f.629.12		32	3.2	odd	2
1890.2.bf.f.1259.5		32	45.4	even	6
1890.2.bf.f.1259.12		32	315.139	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.42161 + 0.989450i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.07274 + 1.96195i) q^{5} +(-1.56770 + 0.736429i) q^{6} +(-2.59656 + 0.507832i) q^{7} +1.00000 q^{8} +(1.04198 + 2.81323i) q^{9} +(-1.16272 - 1.90999i) q^{10} +(4.30527 + 2.48565i) q^{11} +(0.146082 - 1.72588i) q^{12} +(-1.15117 - 1.99388i) q^{13} +(0.858483 - 2.50260i) q^{14} +(-3.46627 + 1.72771i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.05745i q^{17} +(-2.95732 - 0.504240i) q^{18} +1.63818i q^{19} +(2.23546 - 0.0519524i) q^{20} +(-4.19378 - 1.84722i) q^{21} +(-4.30527 + 2.48565i) q^{22} +(-3.70342 - 6.41451i) q^{23} +(1.42161 + 0.989450i) q^{24} +(-2.69846 - 4.20931i) q^{25} +2.30233 q^{26} +(-1.30227 + 5.03032i) q^{27} +(1.73807 + 1.99477i) q^{28} +(-6.86211 - 3.96184i) q^{29} +(0.236897 - 3.86573i) q^{30} +(-6.00511 + 3.46705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.66101 + 7.79349i) q^{33} +(-3.51386 - 2.02873i) q^{34} +(1.78909 - 5.63907i) q^{35} +(1.91534 - 2.30899i) q^{36} +10.4902i q^{37} +(-1.41871 - 0.819090i) q^{38} +(0.336330 - 3.97355i) q^{39} +(-1.07274 + 1.96195i) q^{40} +(-2.40962 - 4.17358i) q^{41} +(3.69663 - 2.70831i) q^{42} +(-2.31707 - 1.33776i) q^{43} -4.97130i q^{44} +(-6.63718 - 0.973570i) q^{45} +7.40684 q^{46} +(9.03708 + 5.21756i) q^{47} +(-1.56770 + 0.736429i) q^{48} +(6.48421 - 2.63723i) q^{49} +(4.99460 - 0.232276i) q^{50} +(-4.01465 + 5.76813i) q^{51} +(-1.15117 + 1.99388i) q^{52} +12.4295 q^{53} +(-3.70525 - 3.64296i) q^{54} +(-9.49514 + 5.78025i) q^{55} +(-2.59656 + 0.507832i) q^{56} +(-1.62090 + 2.32886i) q^{57} +(6.86211 - 3.96184i) q^{58} +(5.82902 + 10.0962i) q^{59} +(3.22937 + 2.13802i) q^{60} +(3.89175 + 2.24690i) q^{61} -6.93411i q^{62} +(-4.13420 - 6.77557i) q^{63} +1.00000 q^{64} +(5.14679 - 0.119612i) q^{65} +(-8.57986 - 0.726217i) q^{66} +(-0.266411 + 0.153812i) q^{67} +(3.51386 - 2.02873i) q^{68} +(1.08201 - 12.7833i) q^{69} +(3.98904 + 4.36894i) q^{70} -7.38341i q^{71} +(1.04198 + 2.81323i) q^{72} -3.95051 q^{73} +(-9.08477 - 5.24509i) q^{74} +(0.328742 - 8.65401i) q^{75} +(1.41871 - 0.819090i) q^{76} +(-12.4412 - 4.26777i) q^{77} +(3.27303 + 2.27805i) q^{78} +(-1.42332 + 2.46526i) q^{79} +(-1.16272 - 1.90999i) q^{80} +(-6.82857 + 5.86264i) q^{81} +4.81924 q^{82} +(9.60784 + 5.54709i) q^{83} +(0.497147 + 4.55553i) q^{84} +(-7.96050 - 4.35259i) q^{85} +(2.31707 - 1.33776i) q^{86} +(-5.83523 - 12.4219i) q^{87} +(4.30527 + 2.48565i) q^{88} +5.77755 q^{89} +(4.16173 - 5.26118i) q^{90} +(4.00163 + 4.59262i) q^{91} +(-3.70342 + 6.41451i) q^{92} +(-11.9674 - 1.01295i) q^{93} +(-9.03708 + 5.21756i) q^{94} +(-3.21402 - 1.75734i) q^{95} +(0.146082 - 1.72588i) q^{96} +(4.81542 - 8.34056i) q^{97} +(-0.958199 + 6.93411i) q^{98} +(-2.50673 + 14.7017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39}+ \cdots + 58 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Introduction

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