LMFDB - Embedded newform 630.2.bf.f.209.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(209,630)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			209.1
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.f.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.71915 - 0.210974i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00815 + 1.99591i) q^{5} +(-1.04229 + 1.38334i) q^{6} +(-2.45843 - 0.977807i) q^{7} -1.00000 q^{8} +(2.91098 + 0.725392i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71915 - 0.210974i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00815 + 1.99591i) q^{5} +(-1.04229 + 1.38334i) q^{6} +(-2.45843 - 0.977807i) q^{7} -1.00000 q^{8} +(2.91098 + 0.725392i) q^{9} +(2.23258 + 0.124872i) q^{10} +(-1.44107 - 0.832005i) q^{11} +(0.676868 + 1.59432i) q^{12} +(-1.04814 - 1.81544i) q^{13} +(-2.07602 + 1.64016i) q^{14} +(-1.31208 - 3.64396i) q^{15} +(-0.500000 + 0.866025i) q^{16} +7.45463i q^{17} +(2.08370 - 2.15829i) q^{18} +4.66141i q^{19} +(1.22443 - 1.87103i) q^{20} +(4.02013 + 2.19967i) q^{21} +(-1.44107 + 0.832005i) q^{22} +(2.82486 + 4.89279i) q^{23} +(1.71915 + 0.210974i) q^{24} +(-2.96728 + 4.02433i) q^{25} -2.09629 q^{26} +(-4.85138 - 1.86120i) q^{27} +(0.382411 + 2.61797i) q^{28} +(-4.10738 - 2.37140i) q^{29} +(-3.81180 - 0.685689i) q^{30} +(-1.73402 + 1.00114i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.30190 + 1.73437i) q^{33} +(6.45590 + 3.72732i) q^{34} +(-0.526851 - 5.89257i) q^{35} +(-0.827282 - 2.88368i) q^{36} +4.86789i q^{37} +(4.03690 + 2.33070i) q^{38} +(1.41891 + 3.34215i) q^{39} +(-1.00815 - 1.99591i) q^{40} +(4.07169 + 7.05238i) q^{41} +(3.91503 - 2.38170i) q^{42} +(2.25274 + 1.30062i) q^{43} +1.66401i q^{44} +(1.48688 + 6.54134i) q^{45} +5.64971 q^{46} +(-8.90154 - 5.13931i) q^{47} +(1.04229 - 1.38334i) q^{48} +(5.08779 + 4.80775i) q^{49} +(2.00154 + 4.58191i) q^{50} +(1.57273 - 12.8157i) q^{51} +(-1.04814 + 1.81544i) q^{52} +13.8374 q^{53} +(-4.03754 + 3.27082i) q^{54} +(0.207788 - 3.71503i) q^{55} +(2.45843 + 0.977807i) q^{56} +(0.983434 - 8.01368i) q^{57} +(-4.10738 + 2.37140i) q^{58} +(0.0862901 + 0.149459i) q^{59} +(-2.49972 + 2.95827i) q^{60} +(-5.17503 - 2.98781i) q^{61} +2.00228i q^{62} +(-6.44716 - 4.62971i) q^{63} +1.00000 q^{64} +(2.56676 - 3.92222i) q^{65} +(2.65296 - 1.12632i) q^{66} +(-4.70611 + 2.71707i) q^{67} +(6.45590 - 3.72732i) q^{68} +(-3.82411 - 9.00744i) q^{69} +(-5.36654 - 2.49002i) q^{70} -12.0450i q^{71} +(-2.91098 - 0.725392i) q^{72} -4.79644 q^{73} +(4.21571 + 2.43394i) q^{74} +(5.95024 - 6.29243i) q^{75} +(4.03690 - 2.33070i) q^{76} +(2.72924 + 3.45452i) q^{77} +(3.60384 + 0.442261i) q^{78} +(-6.30891 + 10.9273i) q^{79} +(-2.23258 - 0.124872i) q^{80} +(7.94761 + 4.22320i) q^{81} +8.14339 q^{82} +(2.24015 + 1.29335i) q^{83} +(-0.105101 - 4.58137i) q^{84} +(-14.8787 + 7.51536i) q^{85} +(2.25274 - 1.30062i) q^{86} +(6.56091 + 4.94334i) q^{87} +(1.44107 + 0.832005i) q^{88} -11.2248 q^{89} +(6.40841 + 1.98299i) q^{90} +(0.801642 + 5.48801i) q^{91} +(2.82486 - 4.89279i) q^{92} +(3.19227 - 1.35528i) q^{93} +(-8.90154 + 5.13931i) q^{94} +(-9.30373 + 4.69938i) q^{95} +(-0.676868 - 1.59432i) q^{96} +(-4.73188 + 8.19586i) q^{97} +(6.70752 - 2.00228i) q^{98} +(-3.59141 - 3.46729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9} - 24 q^{11} - 12 q^{15} - 16 q^{16} - 6 q^{18} + 2 q^{21} - 24 q^{22} + 24 q^{23} + 50 q^{25} - 36 q^{29} - 18 q^{30} + 16 q^{32} + 48 q^{35} - 66 q^{39} - 2 q^{42} + 54 q^{43} + 48 q^{46} + 32 q^{49} + 58 q^{50} - 26 q^{51} + 24 q^{53} - 110 q^{57} - 36 q^{58} - 6 q^{60} - 20 q^{63} + 32 q^{64} - 66 q^{65} + 66 q^{67} + 12 q^{70} + 6 q^{72} + 12 q^{74} - 18 q^{77} - 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} - 32 q^{85} + 54 q^{86} + 24 q^{88} + 16 q^{91} + 24 q^{92} - 28 q^{93} - 24 q^{95} + 64 q^{98} + 58 q^{99}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9 - 24 * q^11 - 12 * q^15 - 16 * q^16 - 6 * q^18 + 2 * q^21 - 24 * q^22 + 24 * q^23 + 50 * q^25 - 36 * q^29 - 18 * q^30 + 16 * q^32 + 48 * q^35 - 66 * q^39 - 2 * q^42 + 54 * q^43 + 48 * q^46 + 32 * q^49 + 58 * q^50 - 26 * q^51 + 24 * q^53 - 110 * q^57 - 36 * q^58 - 6 * q^60 - 20 * q^63 + 32 * q^64 - 66 * q^65 + 66 * q^67 + 12 * q^70 + 6 * q^72 + 12 * q^74 - 18 * q^77 - 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 - 32 * q^85 + 54 * q^86 + 24 * q^88 + 16 * q^91 + 24 * q^92 - 28 * q^93 - 24 * q^95 + 64 * q^98 + 58 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−1.71915	−	0.210974i	−0.992554	−	0.121806i
$3$	−1.71915	−	0.210974i	−0.992554	−	0.121806i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00815	+	1.99591i	0.450857	+	0.892596i
$5$	1.00815	+	1.99591i	0.450857	+	0.892596i
$6$	−1.04229	+	1.38334i	−0.425511	+	0.564748i
$7$	−2.45843	−	0.977807i	−0.929200	−	0.369576i
$7$	−2.45843	−	0.977807i	−0.929200	−	0.369576i
$8$	−1.00000			−0.353553
$9$	2.91098	+	0.725392i	0.970327	+	0.241797i
$10$	2.23258	+	0.124872i	0.706003	+	0.0394879i
$11$	−1.44107	−	0.832005i	−0.434500	−	0.250859i	0.266762	−	0.963763i	$-0.414046\pi$
$11$	−1.44107	−	0.832005i	−0.434500	−	0.250859i	−0.701262	+	0.712904i	$0.747380\pi$
$12$	0.676868	+	1.59432i	0.195395	+	0.460240i
$13$	−1.04814	−	1.81544i	−0.290703	−	0.503512i	0.683273	−	0.730163i	$-0.260556\pi$
$13$	−1.04814	−	1.81544i	−0.290703	−	0.503512i	−0.973976	+	0.226651i	$0.927222\pi$
$14$	−2.07602	+	1.64016i	−0.554840	+	0.438352i
$15$	−1.31208	−	3.64396i	−0.338777	−	0.940867i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			7.45463i			1.80801i	0.427518	+	0.904007i	$0.359388\pi$
$17$			7.45463i			1.80801i	−0.427518	+	0.904007i	$0.640612\pi$
$18$	2.08370	−	2.15829i	0.491132	−	0.508713i
$19$			4.66141i			1.06940i	0.845042	+	0.534700i	$0.179575\pi$
$19$			4.66141i			1.06940i	−0.845042	+	0.534700i	$0.820425\pi$
$20$	1.22443	−	1.87103i	0.273791	−	0.418376i
$21$	4.02013	+	2.19967i	0.877265	+	0.480006i
$22$	−1.44107	+	0.832005i	−0.307238	+	0.177384i
$23$	2.82486	+	4.89279i	0.589023	+	1.02022i	0.994361	+	0.106051i	$0.0338207\pi$
$23$	2.82486	+	4.89279i	0.589023	+	1.02022i	−0.405337	+	0.914167i	$0.632846\pi$
$24$	1.71915	+	0.210974i	0.350921	+	0.0430648i
$25$	−2.96728	+	4.02433i	−0.593456	+	0.804867i
$26$	−2.09629			−0.411116
$27$	−4.85138	−	1.86120i	−0.933649	−	0.358188i
$28$	0.382411	+	2.61797i	0.0722688	+	0.494750i
$29$	−4.10738	−	2.37140i	−0.762721	−	0.440357i	0.0675508	−	0.997716i	$-0.478482\pi$
$29$	−4.10738	−	2.37140i	−0.762721	−	0.440357i	−0.830272	+	0.557359i	$0.811815\pi$
$30$	−3.81180	−	0.685689i	−0.695937	−	0.125189i
$31$	−1.73402	+	1.00114i	−0.311440	+	0.179810i	−0.647571	−	0.762005i	$-0.724215\pi$
$31$	−1.73402	+	1.00114i	−0.311440	+	0.179810i	0.336131	+	0.941815i	$0.390882\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.30190	+	1.73437i	0.400709	+	0.301915i
$34$	6.45590	+	3.72732i	1.10718	+	0.639229i
$35$	−0.526851	−	5.89257i	−0.0890541	−	0.996027i
$36$	−0.827282	−	2.88368i	−0.137880	−	0.480613i
$37$			4.86789i			0.800276i	0.916455	+	0.400138i	$0.131038\pi$
$37$			4.86789i			0.800276i	−0.916455	+	0.400138i	$0.868962\pi$
$38$	4.03690	+	2.33070i	0.654871	+	0.378090i
$39$	1.41891	+	3.34215i	0.227207	+	0.535172i
$40$	−1.00815	−	1.99591i	−0.159402	−	0.315580i
$41$	4.07169	+	7.05238i	0.635892	+	1.10140i	0.986325	+	0.164809i	$0.0527008\pi$
$41$	4.07169	+	7.05238i	0.635892	+	1.10140i	−0.350434	+	0.936587i	$0.613966\pi$
$42$	3.91503	−	2.38170i	0.604103	−	0.367505i
$43$	2.25274	+	1.30062i	0.343540	+	0.198343i	0.661836	−	0.749648i	$-0.269777\pi$
$43$	2.25274	+	1.30062i	0.343540	+	0.198343i	−0.318296	+	0.947991i	$0.603111\pi$
$44$			1.66401i			0.250859i
$45$	1.48688	+	6.54134i	0.221651	+	0.975126i
$46$	5.64971			0.833005
$47$	−8.90154	−	5.13931i	−1.29842	−	0.749645i	−0.318292	−	0.947993i	$-0.603109\pi$
$47$	−8.90154	−	5.13931i	−1.29842	−	0.749645i	−0.980132	+	0.198348i	$0.936442\pi$
$48$	1.04229	−	1.38334i	0.150441	−	0.199669i
$49$	5.08779	+	4.80775i	0.726827	+	0.686821i
$50$	2.00154	+	4.58191i	0.283060	+	0.647979i
$51$	1.57273	−	12.8157i	0.220226	−	1.79455i
$52$	−1.04814	+	1.81544i	−0.145351	+	0.251756i
$53$	13.8374			1.90071			0.950354	−	0.311170i	$-0.100721\pi$
$53$	13.8374			1.90071			0.950354	+	0.311170i	$0.100721\pi$
$54$	−4.03754	+	3.27082i	−0.549440	+	0.445102i
$55$	0.207788	−	3.71503i	0.0280181	−	0.500935i
$56$	2.45843	+	0.977807i	0.328522	+	0.130665i
$57$	0.983434	−	8.01368i	0.130259	−	1.06144i
$58$	−4.10738	+	2.37140i	−0.539325	+	0.311380i
$59$	0.0862901	+	0.149459i	0.0112340	+	0.0194579i	0.871588	−	0.490240i	$-0.163091\pi$
$59$	0.0862901	+	0.149459i	0.0112340	+	0.0194579i	−0.860354	+	0.509697i	$0.829757\pi$
$60$	−2.49972	+	2.95827i	−0.322713	+	0.381911i
$61$	−5.17503	−	2.98781i	−0.662595	−	0.382550i	0.130670	−	0.991426i	$-0.458287\pi$
$61$	−5.17503	−	2.98781i	−0.662595	−	0.382550i	−0.793265	+	0.608876i	$0.791621\pi$
$62$			2.00228i			0.254290i
$63$	−6.44716	−	4.62971i	−0.812265	−	0.583288i
$64$	1.00000			0.125000
$65$	2.56676	−	3.92222i	0.318367	−	0.486492i
$66$	2.65296	−	1.12632i	0.326557	−	0.138640i
$67$	−4.70611	+	2.71707i	−0.574943	+	0.331943i	−0.759121	−	0.650949i	$-0.774371\pi$
$67$	−4.70611	+	2.71707i	−0.574943	+	0.331943i	0.184178	+	0.982893i	$0.441038\pi$
$68$	6.45590	−	3.72732i	0.782893	−	0.452003i
$69$	−3.82411	−	9.00744i	−0.460369	−	1.08437i
$70$	−5.36654	−	2.49002i	−0.641425	−	0.297614i
$71$		−	12.0450i		−	1.42947i	−0.699393	−	0.714737i	$-0.746546\pi$
$71$		−	12.0450i		−	1.42947i	0.699393	−	0.714737i	$-0.253454\pi$
$72$	−2.91098	−	0.725392i	−0.343062	−	0.0854883i
$73$	−4.79644			−0.561381			−0.280691	−	0.959798i	$-0.590563\pi$
$73$	−4.79644			−0.561381			−0.280691	+	0.959798i	$0.590563\pi$
$74$	4.21571	+	2.43394i	0.490067	+	0.282940i
$75$	5.95024	−	6.29243i	0.687074	−	0.726587i
$76$	4.03690	−	2.33070i	0.463064	−	0.267350i
$77$	2.72924	+	3.45452i	0.311026	+	0.393679i
$78$	3.60384	+	0.442261i	0.408054	+	0.0500762i
$79$	−6.30891	+	10.9273i	−0.709807	+	1.22942i	0.255121	+	0.966909i	$0.417885\pi$
$79$	−6.30891	+	10.9273i	−0.709807	+	1.22942i	−0.964928	+	0.262513i	$0.915449\pi$
$80$	−2.23258	−	0.124872i	−0.249610	−	0.0139611i
$81$	7.94761	+	4.22320i	0.883068	+	0.469245i
$82$	8.14339			0.899286
$83$	2.24015	+	1.29335i	0.245888	+	0.141964i	0.617880	−	0.786272i	$-0.287992\pi$
$83$	2.24015	+	1.29335i	0.245888	+	0.141964i	−0.371992	+	0.928236i	$0.621325\pi$
$84$	−0.105101	−	4.58137i	−0.0114674	−	0.499868i
$85$	−14.8787	+	7.51536i	−1.61383	+	0.815156i
$86$	2.25274	−	1.30062i	0.242919	−	0.140250i
$87$	6.56091	+	4.94334i	0.703404	+	0.529982i
$88$	1.44107	+	0.832005i	0.153619	+	0.0886920i
$89$	−11.2248			−1.18982			−0.594912	−	0.803791i	$-0.702813\pi$
$89$	−11.2248			−1.18982			−0.594912	+	0.803791i	$0.702813\pi$
$90$	6.40841	+	1.98299i	0.675506	+	0.209026i
$91$	0.801642	+	5.48801i	0.0840350	+	0.575300i
$92$	2.82486	−	4.89279i	0.294512	−	0.510109i
$93$	3.19227	−	1.35528i	0.331023	−	0.140536i
$94$	−8.90154	+	5.13931i	−0.918124	+	0.530079i
$95$	−9.30373	+	4.69938i	−0.954543	+	0.482147i
$96$	−0.676868	−	1.59432i	−0.0690826	−	0.162719i
$97$	−4.73188	+	8.19586i	−0.480450	+	0.832164i	−0.999748	−	0.0224290i	$-0.992860\pi$
$97$	−4.73188	+	8.19586i	−0.480450	+	0.832164i	0.519298	+	0.854593i	$0.326193\pi$
$98$	6.70752	−	2.00228i	0.677562	−	0.202261i
$99$	−3.59141	−	3.46729i	−0.360950	−	0.348476i
$100$	4.96881	+	0.557572i	0.496881	+	0.0557572i
$101$	5.28548	−	9.15472i	0.525925	−	0.910928i	−0.473619	−	0.880730i	$-0.657053\pi$
$101$	5.28548	−	9.15472i	0.525925	−	0.910928i	0.999544	−	0.0301987i	$-0.00961400\pi$
$102$	−10.3123	−	7.76985i	−1.02107	−	0.769330i
$103$	−7.61856	−	13.1957i	−0.750679	−	1.30021i	−0.947494	−	0.319773i	$-0.896393\pi$
$103$	−7.61856	−	13.1957i	−0.750679	−	1.30021i	0.196816	−	0.980441i	$-0.436940\pi$
$104$	1.04814	+	1.81544i	0.102779	+	0.178018i
$105$	−0.337439	+	10.2414i	−0.0329306	+	0.999458i
$106$	6.91868	−	11.9835i	0.672002	−	1.16394i
$107$	11.4163			1.10366			0.551829	−	0.833957i	$-0.313930\pi$
$107$	11.4163			1.10366			0.551829	+	0.833957i	$0.313930\pi$
$108$	0.813845	+	5.13202i	0.0783123	+	0.493829i
$109$	−10.6147			−1.01670			−0.508351	−	0.861150i	$-0.669745\pi$
$109$	−10.6147			−1.01670			−0.508351	+	0.861150i	$0.669745\pi$
$110$	−3.11342	−	2.03747i	−0.296853	−	0.194265i
$111$	1.02700	−	8.36865i	0.0974781	−	0.794317i
$112$	2.07602	−	1.64016i	0.196166	−	0.154981i
$113$	−6.87120	−	11.9013i	−0.646388	−	1.11958i	−0.983979	−	0.178284i	$-0.942945\pi$
$113$	−6.87120	−	11.9013i	−0.646388	−	1.11958i	0.337591	−	0.941293i	$-0.390388\pi$
$114$	−6.44833	−	4.85852i	−0.603942	−	0.455042i
$115$	−6.91769	+	10.5708i	−0.645078	+	0.985733i
$116$			4.74279i			0.440357i
$117$	−1.73422	−	6.04502i	−0.160329	−	0.558862i
$118$	0.172580			0.0158873
$119$	7.28919	−	18.3267i	0.668199	−	1.68001i
$120$	1.31208	+	3.64396i	0.119776	+	0.332647i
$121$	−4.11554	−	7.12832i	−0.374140	−	0.648029i
$122$	−5.17503	+	2.98781i	−0.468526	+	0.270503i
$123$	−5.51200	−	12.9831i	−0.497000	−	1.17065i
$124$	1.73402	+	1.00114i	0.155720	+	0.0899050i
$125$	−11.0236	−	1.86529i	−0.985985	−	0.166837i
$126$	−7.23302	+	3.26855i	−0.644369	+	0.291185i
$127$			14.1949i			1.25960i	0.776759	+	0.629798i	$0.216862\pi$
$127$			14.1949i			1.25960i	−0.776759	+	0.629798i	$0.783138\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.59841	−	2.71124i	−0.316823	−	0.238711i
$130$	−2.11336	−	4.18399i	−0.185354	−	0.366960i
$131$	1.14681	+	1.98633i	0.100197	+	0.173547i	0.911766	−	0.410710i	$-0.134719\pi$
$131$	1.14681	+	1.98633i	0.100197	+	0.173547i	−0.811569	+	0.584257i	$0.801386\pi$
$132$	0.351062	−	2.86069i	0.0305560	−	0.248991i
$133$	4.55796	−	11.4598i	0.395225	−	0.993687i
$134$			5.43415i			0.469439i
$135$	−1.17613	−	11.5593i	−0.101225	−	0.994864i
$136$		−	7.45463i		−	0.639229i
$137$	−5.41797	+	9.38419i	−0.462888	+	0.801746i	−0.999103	−	0.0423355i	$-0.986520\pi$
$137$	−5.41797	+	9.38419i	−0.462888	+	0.801746i	0.536215	+	0.844081i	$0.319853\pi$
$138$	−9.71273	−	1.19194i	−0.826802	−	0.101465i
$139$	7.63600	−	4.40865i	0.647677	−	0.373936i	−0.139889	−	0.990167i	$-0.544674\pi$
$139$	7.63600	−	4.40865i	0.647677	−	0.373936i	0.787566	+	0.616231i	$0.211341\pi$
$140$	−4.83969	+	3.40255i	−0.409029	+	0.287568i
$141$	14.2189	+	10.7133i	1.19744	+	0.902219i
$142$	−10.4312	−	6.02248i	−0.875371	−	0.505396i
$143$			3.48824i			0.291701i
$144$	−2.08370	+	2.15829i	−0.173642	+	0.179857i
$145$	0.592241	−	10.5887i	0.0491830	−	0.879340i
$146$	−2.39822	+	4.15384i	−0.198478	+	0.343774i
$147$	−7.73238	−	9.33865i	−0.637756	−	0.770238i
$148$	4.21571	−	2.43394i	0.346529	−	0.200069i
$149$	12.4184	−	7.16974i	1.01735	−	0.587368i	0.104016	−	0.994576i	$-0.466831\pi$
$149$	12.4184	−	7.16974i	1.01735	−	0.587368i	0.913336	+	0.407207i	$0.133497\pi$
$150$	−2.47429	−	8.29927i	−0.202025	−	0.677633i
$151$	3.45207	−	5.97917i	0.280926	−	0.486578i	−0.690687	−	0.723154i	$-0.742692\pi$
$151$	3.45207	−	5.97917i	0.280926	−	0.486578i	0.971613	+	0.236576i	$0.0760252\pi$
$152$		−	4.66141i		−	0.378090i
$153$	−5.40753	+	21.7003i	−0.437173	+	1.75436i
$154$	4.35632	−	0.636335i	0.351043	−	0.0512773i
$155$	−3.74633	−	2.45165i	−0.300913	−	0.196922i
$156$	2.18493	−	2.89989i	0.174934	−	0.232177i
$157$	7.48808	+	12.9697i	0.597614	+	1.03510i	0.993172	+	0.116657i	$0.0372177\pi$
$157$	7.48808	+	12.9697i	0.597614	+	1.03510i	−0.395559	+	0.918441i	$0.629449\pi$
$158$	6.30891	+	10.9273i	0.501910	+	0.869333i
$159$	−23.7886	−	2.91932i	−1.88656	−	0.231517i
$160$	−1.22443	+	1.87103i	−0.0967998	+	0.147918i
$161$	−2.16051	−	14.7908i	−0.170272	−	1.16568i
$162$	7.63121	−	4.77123i	0.599564	−	0.374863i
$163$			8.03539i			0.629380i	0.949194	+	0.314690i	$0.101901\pi$
$163$			8.03539i			0.629380i	−0.949194	+	0.314690i	$0.898099\pi$
$164$	4.07169	−	7.05238i	0.317946	−	0.550698i
$165$	−1.14099	+	6.34287i	−0.0888262	+	0.493792i
$166$	2.24015	−	1.29335i	0.173869	−	0.100384i
$167$	−4.12075	+	2.37911i	−0.318873	+	0.184101i	−0.650890	−	0.759172i	$-0.725604\pi$
$167$	−4.12075	+	2.37911i	−0.318873	+	0.184101i	0.332017	+	0.943273i	$0.392271\pi$
$168$	−4.02013	−	2.19967i	−0.310160	−	0.169708i
$169$	4.30279	−	7.45265i	0.330984	−	0.573281i
$170$	−0.930873	+	16.6430i	−0.0713947	+	1.27646i
$171$	−3.38135	+	13.5693i	−0.258578	+	1.03767i
$172$		−	2.60124i		−	0.198343i
$173$	14.9456	+	8.62882i	1.13629	+	0.656037i	0.945509	−	0.325595i	$-0.105565\pi$
$173$	14.9456	+	8.62882i	1.13629	+	0.656037i	0.190781	+	0.981633i	$0.438898\pi$
$174$	7.56152	−	3.21025i	0.573237	−	0.243368i
$175$	11.2299	−	6.99213i	0.848899	−	0.528555i
$176$	1.44107	−	0.832005i	0.108625	−	0.0627147i
$177$	−0.116814	−	0.275148i	−0.00878029	−	0.0206814i
$178$	−5.61239	+	9.72094i	−0.420666	+	0.728616i
$179$		−	0.602635i		−	0.0450430i	−0.999746	−	0.0225215i	$-0.992831\pi$
$179$		−	0.602635i		−	0.0450430i	0.999746	−	0.0225215i	$-0.00716943\pi$
$180$	4.92153	−	4.55835i	0.366829	−	0.339759i
$181$		−	12.7778i		−	0.949769i	−0.880048	−	0.474885i	$-0.842490\pi$
$181$		−	12.7778i		−	0.949769i	0.880048	−	0.474885i	$-0.157510\pi$
$182$	5.15358	+	2.04976i	0.382009	+	0.151939i
$183$	8.26633	+	6.22830i	0.611065	+	0.460409i
$184$	−2.82486	−	4.89279i	−0.208251	−	0.360702i
$185$	−9.71584	+	4.90754i	−0.714323	+	0.360810i
$186$	0.422428	−	3.44223i	0.0309739	−	0.252396i
$187$	6.20229	−	10.7427i	0.453556	−	0.785582i
$188$			10.2786i			0.749645i
$189$	10.1069	+	9.31936i	0.735169	+	0.677883i
$190$	−0.582079	+	10.4070i	−0.0422284	+	0.755000i
$191$	16.3178	+	9.42111i	1.18072	+	0.681687i	0.956180	−	0.292778i	$-0.0945798\pi$
$191$	16.3178	+	9.42111i	1.18072	+	0.681687i	0.224537	+	0.974466i	$0.427913\pi$
$192$	−1.71915	−	0.210974i	−0.124069	−	0.0152257i
$193$	−5.89207	+	3.40179i	−0.424120	+	0.244866i	−0.696839	−	0.717228i	$-0.745411\pi$
$193$	−5.89207	+	3.40179i	−0.424120	+	0.244866i	0.272718	+	0.962094i	$0.412077\pi$
$194$	4.73188	+	8.19586i	0.339730	+	0.588429i
$195$	−5.24014	+	6.20139i	−0.375254	+	0.444090i
$196$	1.61974	−	6.81003i	0.115696	−	0.486430i
$197$	8.58750			0.611834			0.305917	−	0.952058i	$-0.401037\pi$
$197$	8.58750			0.611834			0.305917	+	0.952058i	$0.401037\pi$
$198$	−4.79847	+	1.37661i	−0.341012	+	0.0978311i
$199$			5.10064i			0.361575i	0.983522	+	0.180788i	$0.0578646\pi$
$199$			5.10064i			0.361575i	−0.983522	+	0.180788i	$0.942135\pi$
$200$	2.96728	−	4.02433i	0.209818	−	0.284563i
$201$	8.66376	−	3.67820i	0.611094	−	0.259440i
$202$	−5.28548	−	9.15472i	−0.371885	−	0.644124i
$203$	7.77895	+	9.84614i	0.545975	+	0.691064i
$204$	−11.8851	+	5.04580i	−0.832120	+	0.353277i
$205$	−9.97102	+	15.2365i	−0.696406	+	1.06417i
$206$	−15.2371			−1.06162
$207$	4.67391	+	16.2920i	0.324859	+	1.13237i
$208$	2.09629			0.145351
$209$	3.87831	−	6.71743i	0.268268	−	0.464655i
$210$	8.70059	+	5.41293i	0.600398	+	0.373527i
$211$	5.01715	+	8.68995i	0.345395	+	0.598241i	0.985425	−	0.170108i	$-0.0544118\pi$
$211$	5.01715	+	8.68995i	0.345395	+	0.598241i	−0.640031	+	0.768349i	$0.721078\pi$
$212$	−6.91868	−	11.9835i	−0.475177	−	0.823031i
$213$	−2.54117	+	20.7072i	−0.174118	+	1.41883i
$214$	5.70816	−	9.88683i	0.390202	−	0.675850i
$215$	−0.324822	+	5.80748i	−0.0221527	+	0.396067i
$216$	4.85138	+	1.86120i	0.330095	+	0.126639i
$217$	5.24190	−	0.765693i	0.355844	−	0.0519786i
$218$	−5.30734	+	9.19258i	−0.359458	+	0.622600i
$219$	8.24582	+	1.01192i	0.557201	+	0.0683794i
$220$	−3.32121	+	1.67757i	−0.223916	+	0.113101i
$221$	13.5334	−	7.81352i	0.910356	−	0.525594i
$222$	−6.73396	−	5.07373i	−0.451954	−	0.340526i
$223$	8.87226	−	15.3672i	0.594131	−	1.02906i	−0.399538	−	0.916717i	$-0.630829\pi$
$223$	8.87226	−	15.3672i	0.594131	−	1.02906i	0.993669	−	0.112348i	$-0.0358372\pi$
$224$	−0.382411	−	2.61797i	−0.0255509	−	0.174920i
$225$	−11.5569	+	9.56231i	−0.770461	+	0.637488i
$226$	−13.7424			−0.914131
$227$	0.411273	+	0.237449i	0.0272972	+	0.0157600i	0.513586	−	0.858038i	$-0.328317\pi$
$227$	0.411273	+	0.237449i	0.0272972	+	0.0157600i	−0.486289	+	0.873798i	$0.661650\pi$
$228$	−7.43177	+	3.15516i	−0.492181	+	0.208956i
$229$	−9.51279	+	5.49221i	−0.628623	+	0.362936i	−0.780219	−	0.625507i	$-0.784892\pi$
$229$	−9.51279	+	5.49221i	−0.628623	+	0.362936i	0.151596	+	0.988443i	$0.451559\pi$
$230$	5.69574	+	11.2763i	0.375566	+	0.743537i
$231$	−3.96318	−	6.51465i	−0.260758	−	0.428633i
$232$	4.10738	+	2.37140i	0.269663	+	0.155690i
$233$	−21.4794			−1.40716			−0.703582	−	0.710614i	$-0.748417\pi$
$233$	−21.4794			−1.40716			−0.703582	+	0.710614i	$0.748417\pi$
$234$	−6.10225	−	1.52063i	−0.398916	−	0.0994067i
$235$	1.28351	−	22.9478i	0.0837269	−	1.49695i
$236$	0.0862901	−	0.149459i	0.00561701	−	0.00972894i
$237$	13.1514	−	17.4548i	0.854273	−	1.13381i
$238$	−12.2268	−	15.4760i	−0.792546	−	1.00316i
$239$	−14.6228	+	8.44250i	−0.945873	+	0.546100i	−0.891797	−	0.452437i	$-0.850555\pi$
$239$	−14.6228	+	8.44250i	−0.945873	+	0.546100i	−0.0540768	+	0.998537i	$0.517222\pi$
$240$	3.81180	+	0.685689i	0.246051	+	0.0442610i
$241$	8.00911	+	4.62406i	0.515912	+	0.297862i	0.735261	−	0.677784i	$-0.237060\pi$
$241$	8.00911	+	4.62406i	0.515912	+	0.297862i	−0.219348	+	0.975647i	$0.570393\pi$
$242$	−8.23107			−0.529113
$243$	−12.7722	−	8.93707i	−0.819336	−	0.573314i
$244$			5.97562i			0.382550i
$245$	−4.46657	+	15.0017i	−0.285359	+	0.958421i
$246$	−13.9997	−	1.71804i	−0.892590	−	0.109538i
$247$	8.46249	−	4.88582i	0.538456	−	0.310877i
$248$	1.73402	−	1.00114i	0.110111	−	0.0635724i
$249$	−3.57830	−	2.69608i	−0.226766	−	0.170857i
$250$	−7.12721	+	8.61411i	−0.450764	+	0.544804i
$251$	−9.36996			−0.591426			−0.295713	−	0.955277i	$-0.595557\pi$
$251$	−9.36996			−0.591426			−0.295713	+	0.955277i	$0.595557\pi$
$252$	−0.785864	+	7.89825i	−0.0495048	+	0.497543i
$253$		−	9.40117i		−	0.591047i
$254$	12.2932	+	7.09746i	0.771342	+	0.445334i
$255$	27.1644	−	9.78105i	1.70110	−	0.612513i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.62239	−	3.24609i	0.350715	−	0.202485i	−0.314285	−	0.949329i	$-0.601765\pi$
$257$	5.62239	−	3.24609i	0.350715	−	0.202485i	0.665000	+	0.746843i	$0.268431\pi$
$258$	−4.14721	+	1.76070i	−0.258194	+	0.109616i
$259$	4.75985	−	11.9674i	0.295763	−	0.743616i
$260$	−4.68012	−	0.261767i	−0.290249	−	0.0162341i
$261$	−10.2363	−	9.88255i	−0.633612	−	0.611714i
$262$	2.29362			0.141700
$263$	4.41420	−	7.64563i	0.272192	−	0.471450i	−0.697231	−	0.716846i	$-0.745585\pi$
$263$	4.41420	−	7.64563i	0.272192	−	0.471450i	0.969423	+	0.245397i	$0.0789182\pi$
$264$	−2.30190	−	1.73437i	−0.141672	−	0.106743i
$265$	13.9501	+	27.6181i	0.856948	+	1.69657i
$266$	−7.64546	−	9.67719i	−0.468773	−	0.593346i
$267$	19.2971	+	2.36813i	1.18096	+	0.144927i
$268$	4.70611	+	2.71707i	0.287471	+	0.165972i
$269$	11.6257			0.708833			0.354416	−	0.935088i	$-0.384680\pi$
$269$	11.6257			0.708833			0.354416	+	0.935088i	$0.384680\pi$
$270$	−10.5987	−	4.76108i	−0.645015	−	0.289750i
$271$			16.8123i			1.02128i	0.859796	+	0.510638i	$0.170591\pi$
$271$			16.8123i			1.02128i	−0.859796	+	0.510638i	$0.829409\pi$
$272$	−6.45590	−	3.72732i	−0.391446	−	0.226002i
$273$	−0.220321	−	9.60386i	−0.0133344	−	0.581252i
$274$	5.41797	+	9.38419i	0.327311	+	0.566920i
$275$	7.62433	−	3.33057i	0.459765	−	0.200841i
$276$	−5.88861	+	7.81550i	−0.354453	+	0.470438i
$277$	1.93149	+	1.11514i	0.116052	+	0.0670026i	0.556902	−	0.830578i	$-0.311990\pi$
$277$	1.93149	+	1.11514i	0.116052	+	0.0670026i	−0.440850	+	0.897581i	$0.645323\pi$
$278$		−	8.81729i		−	0.528826i
$279$	−5.77393	+	1.65645i	−0.345676	+	0.0991690i
$280$	0.526851	+	5.89257i	0.0314854	+	0.352149i
$281$	−2.79869	−	1.61582i	−0.166956	−	0.0963919i	0.414194	−	0.910189i	$-0.364064\pi$
$281$	−2.79869	−	1.61582i	−0.166956	−	0.0963919i	−0.581150	+	0.813797i	$0.697397\pi$
$282$	16.3874	−	6.95727i	0.975854	−	0.414299i
$283$	−3.23291	−	5.59957i	−0.192177	−	0.332860i	0.753795	−	0.657110i	$-0.228221\pi$
$283$	−3.23291	−	5.59957i	−0.192177	−	0.332860i	−0.945971	+	0.324250i	$0.894888\pi$
$284$	−10.4312	+	6.02248i	−0.618981	+	0.357369i
$285$	16.9860	−	6.11612i	1.00616	−	0.362288i
$286$	3.02090	+	1.74412i	0.178630	+	0.103132i
$287$	−3.11412	−	21.3191i	−0.183821	−	1.25843i
$288$	0.827282	+	2.88368i	0.0487481	+	0.169922i
$289$	−38.5715			−2.26891
$290$	−8.87393	−	5.80722i	−0.521095	−	0.341012i
$291$	9.86395	−	13.0917i	0.578235	−	0.767446i
$292$	2.39822	+	4.15384i	0.140345	+	0.243085i
$293$	16.0415	−	9.26155i	0.937153	−	0.541066i	0.0480865	−	0.998843i	$-0.484688\pi$
$293$	16.0415	−	9.26155i	0.937153	−	0.541066i	0.889067	+	0.457777i	$0.151354\pi$
$294$	−11.9537	+	2.02712i	−0.697154	+	0.118224i
$295$	−0.211313	+	0.322903i	−0.0123031	+	0.0188002i
$296$		−	4.86789i		−	0.282940i
$297$	5.44268	+	6.71850i	0.315816	+	0.389847i
$298$		−	14.3395i		−	0.830664i
$299$	5.92171	−	10.2567i	0.342461	−	0.593160i
$300$	−8.42452	−	2.00684i	−0.486390	−	0.115865i
$301$	−4.26646	−	5.40024i	−0.245915	−	0.311264i
$302$	−3.45207	−	5.97917i	−0.198645	−	0.344062i
$303$	−11.0180	+	14.6233i	−0.632965	+	0.840085i
$304$	−4.03690	−	2.33070i	−0.231532	−	0.133675i
$305$	0.746186	−	13.3410i	0.0427265	−	0.763905i
$306$	16.0892	+	15.5332i	0.919760	+	0.887974i
$307$	3.44142			0.196412			0.0982062	−	0.995166i	$-0.468690\pi$
$307$	3.44142			0.196412			0.0982062	+	0.995166i	$0.468690\pi$
$308$	1.62708	−	4.09086i	0.0927115	−	0.233098i
$309$	10.3135	+	24.2928i	0.586716	+	1.38197i
$310$	−3.99636	+	2.01859i	−0.226978	+	0.114648i
$311$	16.6186	+	28.7842i	0.942352	+	1.63220i	0.760967	+	0.648790i	$0.224725\pi$
$311$	16.6186	+	28.7842i	0.942352	+	1.63220i	0.181385	+	0.983412i	$0.441942\pi$
$312$	−1.41891	−	3.34215i	−0.0803300	−	0.189212i
$313$	−0.967111	+	1.67509i	−0.0546644	+	0.0946815i	−0.892063	−	0.451912i	$-0.850742\pi$
$313$	−0.967111	+	1.67509i	−0.0546644	+	0.0946815i	0.837398	+	0.546593i	$0.184076\pi$
$314$	14.9762			0.845153
$315$	2.74077	−	17.5353i	0.154425	−	0.988005i
$316$	12.6178			0.709807
$317$	−5.12038	+	8.86877i	−0.287589	+	0.498120i	−0.973234	−	0.229817i	$-0.926187\pi$
$317$	−5.12038	+	8.86877i	−0.287589	+	0.498120i	0.685644	+	0.727937i	$0.259521\pi$
$318$	−14.4225	+	19.1418i	−0.808773	+	1.07342i
$319$	3.94603	+	6.83472i	0.220935	+	0.382671i
$320$	1.00815	+	1.99591i	0.0563571	+	0.111575i
$321$	−19.6264	−	2.40854i	−1.09544	−	0.134432i
$322$	−13.8894	−	5.52433i	−0.774028	−	0.307859i
$323$	−34.7491			−1.93349
$324$	−0.316404	−	8.99444i	−0.0175780	−	0.499691i
$325$	10.4161	+	1.16883i	0.577779	+	0.0648351i
$326$	6.95885	+	4.01770i	0.385415	+	0.222520i
$327$	18.2483	+	2.23942i	1.00913	+	0.123840i
$328$	−4.07169	−	7.05238i	−0.224822	−	0.389402i
$329$	16.8586	+	21.3386i	0.929444	+	1.17644i
$330$	4.92259	+	4.15956i	0.270980	+	0.228977i
$331$	−2.81788	+	4.88070i	−0.154884	+	0.268268i	−0.933017	−	0.359832i	$-0.882834\pi$
$331$	−2.81788	+	4.88070i	−0.154884	+	0.268268i	0.778133	+	0.628100i	$0.216167\pi$
$332$		−	2.58670i		−	0.141964i
$333$	−3.53113	+	14.1703i	−0.193505	+	0.776529i
$334$			4.75823i			0.260359i
$335$	−10.1675	−	6.65374i	−0.555508	−	0.363533i
$336$	−3.91503	+	2.38170i	−0.213583	+	0.129933i
$337$	11.8563	−	6.84524i	0.645854	−	0.372884i	−0.141012	−	0.990008i	$-0.545036\pi$
$337$	11.8563	−	6.84524i	0.645854	−	0.372884i	0.786866	+	0.617124i	$0.211702\pi$
$338$	−4.30279	−	7.45265i	−0.234041	−	0.405371i
$339$	9.30180	+	21.9098i	0.505204	+	1.18997i
$340$	13.9479	+	9.12768i	0.756429	+	0.495018i
$341$	3.33181			0.180428
$342$	10.0607	+	9.71297i	0.544018	+	0.525217i
$343$	−7.80693	−	16.7944i	−0.421535	−	0.906812i
$344$	−2.25274	−	1.30062i	−0.121460	−	0.0701248i
$345$	14.1227	−	16.7134i	0.760342	−	0.899819i
$346$	14.9456	−	8.62882i	0.803478	−	0.463888i
$347$	−4.89520	−	8.47874i	−0.262788	−	0.455163i	0.704193	−	0.710008i	$-0.251309\pi$
$347$	−4.89520	−	8.47874i	−0.262788	−	0.455163i	−0.966982	+	0.254845i	$0.917975\pi$
$348$	1.00060	−	8.15359i	0.0536380	−	0.437078i
$349$	14.0539	+	8.11400i	0.752286	+	0.434332i	0.826519	−	0.562909i	$-0.190318\pi$
$349$	14.0539	+	8.11400i	0.752286	+	0.434332i	−0.0742335	+	0.997241i	$0.523651\pi$
$350$	−0.440421	−	13.2214i	−0.0235415	−	0.706715i
$351$	1.70605	+	10.7582i	0.0910624	+	0.574230i
$352$		−	1.66401i		−	0.0886920i
$353$	20.9960	+	12.1220i	1.11750	+	0.645191i	0.940762	−	0.339066i	$-0.110111\pi$
$353$	20.9960	+	12.1220i	1.11750	+	0.645191i	0.176741	+	0.984257i	$0.443444\pi$
$354$	−0.296692	−	0.0364099i	−0.0157690	−	0.00193516i
$355$	24.0406	−	12.1431i	1.27594	−	0.644489i
$356$	5.61239	+	9.72094i	0.297456	+	0.515209i
$357$	−16.3977	+	29.9686i	−0.867858	+	1.58611i
$358$	−0.521897	−	0.301317i	−0.0275831	−	0.0159251i
$359$			31.3617i			1.65521i	0.561313	+	0.827604i	$0.310296\pi$
$359$			31.3617i			1.65521i	−0.561313	+	0.827604i	$0.689704\pi$
$360$	−1.48688	−	6.54134i	−0.0783656	−	0.344759i
$361$	−2.72872			−0.143617
$362$	−11.0659	−	6.38892i	−0.581612	−	0.335794i
$363$	5.57135	+	13.1229i	0.292420	+	0.688776i
$364$	4.35194	−	3.43825i	0.228103	−	0.180213i
$365$	−4.83552	−	9.57325i	−0.253103	−	0.501087i
$366$	9.52703	−	4.04471i	0.497986	−	0.211420i
$367$	−0.616195	+	1.06728i	−0.0321651	+	0.0557116i	−0.881660	−	0.471885i	$-0.843574\pi$
$367$	−0.616195	+	1.06728i	−0.0321651	+	0.0557116i	0.849495	+	0.527597i	$0.176907\pi$
$368$	−5.64971			−0.294512
$369$	6.73688	+	23.4829i	0.350708	+	1.22247i
$370$	−0.607862	+	10.8679i	−0.0316012	+	0.564997i
$371$	−34.0182	−	13.5303i	−1.76614	−	0.702457i
$372$	−2.76984	−	2.08695i	−0.143610	−	0.108203i
$373$	23.9159	−	13.8079i	1.23832	−	0.714944i	0.269569	−	0.962981i	$-0.413119\pi$
$373$	23.9159	−	13.8079i	1.23832	−	0.714944i	0.968751	+	0.248037i	$0.0797855\pi$
$374$	−6.20229	−	10.7427i	−0.320713	−	0.555491i
$375$	18.5578	+	5.53242i	0.958321	+	0.285693i
$376$	8.90154	+	5.13931i	0.459062	+	0.265040i
$377$			9.94225i			0.512052i
$378$	13.1243	−	4.09316i	0.675039	−	0.210530i
$379$	23.2265			1.19307			0.596533	−	0.802589i	$-0.296545\pi$
$379$	23.2265			1.19307			0.596533	+	0.802589i	$0.296545\pi$
$380$	8.72165	+	5.70757i	0.447411	+	0.292792i
$381$	2.99475	−	24.4033i	0.153426	−	1.25022i
$382$	16.3178	−	9.42111i	0.834893	−	0.482026i
$383$	20.6052	−	11.8964i	1.05288	−	0.607880i	0.129425	−	0.991589i	$-0.458687\pi$
$383$	20.6052	−	11.8964i	1.05288	−	0.607880i	0.923454	+	0.383709i	$0.125354\pi$
$384$	−1.04229	+	1.38334i	−0.0531889	+	0.0705935i
$385$	−4.14342	+	8.92998i	−0.211168	+	0.455114i
$386$			6.80357i			0.346293i
$387$	5.61423	+	5.42020i	0.285387	+	0.275524i
$388$	9.46377			0.480450
$389$	−8.18328	−	4.72462i	−0.414909	−	0.239548i	0.277988	−	0.960585i	$-0.410332\pi$
$389$	−8.18328	−	4.72462i	−0.414909	−	0.239548i	−0.692897	+	0.721037i	$0.743666\pi$
$390$	2.75049	+	7.63879i	0.139276	+	0.386805i
$391$	−36.4740	+	21.0583i	−1.84457	+	1.06496i
$392$	−5.08779	−	4.80775i	−0.256972	−	0.242828i
$393$	−1.55248	−	3.65676i	−0.0783122	−	0.184459i
$394$	4.29375	−	7.43699i	0.216316	−	0.374670i
$395$	−28.1703	−	1.57561i	−1.41740	−	0.0792775i
$396$	−1.20706	+	4.84390i	−0.0606570	+	0.243415i
$397$	−21.7234			−1.09026			−0.545132	−	0.838350i	$-0.683521\pi$
$397$	−21.7234			−1.09026			−0.545132	+	0.838350i	$0.683521\pi$
$398$	4.41729	+	2.55032i	0.221419	+	0.127836i
$399$	−10.2535	+	18.7395i	−0.513319	+	0.938148i
$400$	−2.00154	−	4.58191i	−0.100077	−	0.229095i
$401$	−10.6544	+	6.15134i	−0.532057	+	0.307183i	−0.741854	−	0.670562i	$-0.766053\pi$
$401$	−10.6544	+	6.15134i	−0.532057	+	0.307183i	0.209797	+	0.977745i	$0.432720\pi$
$402$	1.14646	−	9.34214i	0.0571803	−	0.465943i
$403$	3.63501	+	2.09867i	0.181073	+	0.104542i
$404$	−10.5710			−0.525925
$405$	−0.416755	+	20.1203i	−0.0207087	+	0.999786i
$406$	12.4165	−	1.81369i	0.616220	−	0.0900122i
$407$	4.05010	−	7.01498i	0.200756	−	0.347720i
$408$	−1.57273	+	12.8157i	−0.0778617	+	0.634470i
$409$	−2.50285	+	1.44502i	−0.123758	+	0.0714517i	−0.560601	−	0.828086i	$-0.689430\pi$
$409$	−2.50285	+	1.44502i	−0.123758	+	0.0714517i	0.436843	+	0.899538i	$0.356097\pi$
$410$	8.20973	+	16.2534i	0.405450	+	0.802700i
$411$	11.2941	−	14.9898i	0.557099	−	0.739393i
$412$	−7.61856	+	13.1957i	−0.375339	+	0.650107i
$413$	−0.0659965	−	0.451810i	−0.00324748	−	0.0222321i
$414$	16.4462	+	4.09826i	0.808287	+	0.201418i
$415$	−0.323006	+	5.77502i	−0.0158558	+	0.283484i
$416$	1.04814	−	1.81544i	0.0513894	−	0.0890091i
$417$	−14.0576	+	5.96815i	−0.688402	+	0.292261i
$418$	−3.87831	−	6.71743i	−0.189694	−	0.328560i
$419$	−12.7397	−	22.0658i	−0.622374	−	1.07798i	−0.989042	−	0.147632i	$-0.952835\pi$
$419$	−12.7397	−	22.0658i	−0.622374	−	1.07798i	0.366668	−	0.930352i	$-0.380499\pi$
$420$	9.03803	−	4.82847i	0.441011	−	0.235605i
$421$	−2.96965	+	5.14359i	−0.144732	+	0.250683i	−0.929273	−	0.369394i	$-0.879565\pi$
$421$	−2.96965	+	5.14359i	−0.144732	+	0.250683i	0.784541	+	0.620077i	$0.212899\pi$
$422$	10.0343			0.488462
$423$	−22.1842	−	21.4175i	−1.07863	−	1.04136i
$424$	−13.8374			−0.672002
$425$	−29.9999	−	22.1200i	−1.45521	−	1.07298i
$426$	16.6623	+	12.5543i	0.807293	+	0.608258i
$427$	9.80098	+	12.4055i	0.474303	+	0.600345i
$428$	−5.70816	−	9.88683i	−0.275914	−	0.477898i
$429$	0.735926	−	5.99682i	0.0355309	−	0.289529i
$430$	4.86701	+	3.18504i	0.234708	+	0.153596i
$431$			29.4344i			1.41781i	0.705306	+	0.708903i	$0.250810\pi$
$431$			29.4344i			1.41781i	−0.705306	+	0.708903i	$0.749190\pi$
$432$	4.03754	−	3.27082i	0.194256	−	0.157367i
$433$	−14.2559			−0.685093			−0.342546	−	0.939501i	$-0.611289\pi$
$433$	−14.2559			−0.685093			−0.342546	+	0.939501i	$0.611289\pi$
$434$	1.95784	−	4.92247i	0.0939795	−	0.236286i
$435$	−3.25208	+	18.0786i	−0.155925	+	0.866802i
$436$	5.30734	+	9.19258i	0.254176	+	0.440245i
$437$	−22.8073	+	13.1678i	−1.09102	+	0.629902i
$438$	4.99926	−	6.63513i	0.238874	−	0.317039i
$439$	−9.41191	−	5.43397i	−0.449206	−	0.259349i	0.258289	−	0.966068i	$-0.416841\pi$
$439$	−9.41191	−	5.43397i	−0.449206	−	0.259349i	−0.707495	+	0.706719i	$0.750175\pi$
$440$	−0.207788	+	3.71503i	−0.00990590	+	0.177107i
$441$	11.3229	+	17.6859i	0.539188	+	0.842186i
$442$		−	15.6270i		−	0.743303i
$443$	−5.24859	+	9.09083i	−0.249368	+	0.431918i	−0.963351	−	0.268245i	$-0.913556\pi$
$443$	−5.24859	+	9.09083i	−0.249368	+	0.431918i	0.713983	+	0.700164i	$0.246890\pi$
$444$	−7.76096	+	3.29492i	−0.368319	+	0.156370i
$445$	−11.3162	−	22.4036i	−0.536441	−	1.06203i
$446$	−8.87226	−	15.3672i	−0.420114	−	0.727659i
$447$	−22.8617	+	9.70595i	−1.08132	+	0.459076i
$448$	−2.45843	−	0.977807i	−0.116150	−	0.0461970i
$449$		−	37.0684i		−	1.74937i	−0.484695	−	0.874683i	$-0.661070\pi$
$449$		−	37.0684i		−	1.74937i	0.484695	−	0.874683i	$-0.338930\pi$
$450$	2.50275	+	14.7897i	0.117981	+	0.697195i
$451$		−	13.5507i		−	0.638076i
$452$	−6.87120	+	11.9013i	−0.323194	+	0.559789i
$453$	−7.19609	+	9.55081i	−0.338102	+	0.448736i
$454$	0.411273	−	0.237449i	0.0193020	−	0.0111440i
$455$	−10.1454	+	7.13273i	−0.475623	+	0.334387i
$456$	−0.983434	+	8.01368i	−0.0460535	+	0.375275i
$457$	17.5211	+	10.1158i	0.819601	+	0.473197i	0.850279	−	0.526333i	$-0.176433\pi$
$457$	17.5211	+	10.1158i	0.819601	+	0.473197i	−0.0306780	+	0.999529i	$0.509767\pi$
$458$			10.9844i			0.513269i
$459$	13.8746	−	36.1653i	0.647609	−	1.68805i
$460$	12.6134	+	0.705490i	0.588104	+	0.0328936i
$461$	6.80701	−	11.7901i	0.317034	−	0.549119i	−0.662834	−	0.748766i	$-0.730646\pi$
$461$	6.80701	−	11.7901i	0.317034	−	0.549119i	0.979868	+	0.199648i	$0.0639798\pi$
$462$	−7.62344	+	0.174888i	−0.354675	+	0.00813654i
$463$	−19.8188	+	11.4424i	−0.921057	+	0.531773i	−0.883972	−	0.467539i	$-0.845141\pi$
$463$	−19.8188	+	11.4424i	−0.921057	+	0.531773i	−0.0370852	+	0.999312i	$0.511807\pi$
$464$	4.10738	−	2.37140i	0.190680	−	0.110089i
$465$	5.92329	+	5.00515i	0.274686	+	0.232108i
$466$	−10.7397	+	18.6017i	−0.497507	+	0.861708i
$467$			3.34545i			0.154809i	0.997000	+	0.0774044i	$0.0246633\pi$
$467$			3.34545i			0.154809i	−0.997000	+	0.0774044i	$0.975337\pi$
$468$	−4.36803	+	4.52439i	−0.201912	+	0.209140i
$469$	14.2264	−	2.07808i	0.656916	−	0.0959567i
$470$	−19.2316	−	12.5855i	−0.887089	−	0.580524i
$471$	−10.1369	−	23.8768i	−0.467083	−	1.10018i
$472$	−0.0862901	−	0.149459i	−0.00397182	−	0.00687940i
$473$	−2.16425	−	3.74858i	−0.0995121	−	0.172360i
$474$	−8.54060	−	20.1168i	−0.392283	−	0.923995i
$475$	−18.7591	−	13.8317i	−0.860725	−	0.634642i
$476$	−19.5160	+	2.85073i	−0.894514	+	0.130663i
$477$	40.2803	+	10.0375i	1.84431	+	0.459586i
$478$			16.8850i			0.772302i
$479$	−8.15257	+	14.1207i	−0.372500	+	0.645189i	−0.989949	−	0.141421i	$-0.954833\pi$
$479$	−8.15257	+	14.1207i	−0.372500	+	0.645189i	0.617449	+	0.786611i	$0.288166\pi$
$480$	2.49972	−	2.95827i	0.114096	−	0.135026i
$481$	8.83734	−	5.10224i	0.402948	−	0.232642i
$482$	8.00911	−	4.62406i	0.364805	−	0.210620i
$483$	0.593788	+	25.8834i	0.0270183	+	1.17774i
$484$	−4.11554	+	7.12832i	−0.187070	+	0.324014i
$485$	−21.1286	−	1.18176i	−0.959401	−	0.0536609i
$486$	−14.1258	+	6.59250i	−0.640760	+	0.299042i
$487$		−	5.20248i		−	0.235747i	−0.993029	−	0.117873i	$-0.962392\pi$
$487$		−	5.20248i		−	0.235747i	0.993029	−	0.117873i	$-0.0376077\pi$
$488$	5.17503	+	2.98781i	0.234263	+	0.135252i
$489$	1.69525	−	13.8141i	0.0766621	−	0.624694i
$490$	10.7585	+	11.3690i	0.486021	+	0.513599i
$491$	−20.6633	+	11.9299i	−0.932521	+	0.538391i	−0.887608	−	0.460600i	$-0.847634\pi$
$491$	−20.6633	+	11.9299i	−0.932521	+	0.538391i	−0.0449127	+	0.998991i	$0.514301\pi$
$492$	−8.48773	+	11.2651i	−0.382656	+	0.507870i
$493$	17.6779	−	30.6190i	0.796172	−	1.37901i
$494$		−	9.77165i		−	0.439647i
$495$	3.29972	−	10.6637i	0.148311	−	0.479296i
$496$		−	2.00228i		−	0.0899050i
$497$	−11.7777	+	29.6117i	−0.528300	+	1.32827i
$498$	−4.12403	+	1.75086i	−0.184802	+	0.0784578i
$499$	16.1660	+	28.0003i	0.723688	+	1.25346i	0.959512	+	0.281668i	$0.0908877\pi$
$499$	16.1660	+	28.0003i	0.723688	+	1.25346i	−0.235824	+	0.971796i	$0.575779\pi$
$500$	3.89643	+	10.4794i	0.174254	+	0.468653i
$501$	7.58613	−	3.22069i	0.338923	−	0.143890i
$502$	−4.68498	+	8.11462i	−0.209101	+	0.362173i
$503$			10.0768i			0.449301i	0.974439	+	0.224651i	$0.0721241\pi$
$503$			10.0768i			0.449301i	−0.974439	+	0.224651i	$0.927876\pi$
$504$	6.44716	+	4.62971i	0.287179	+	0.206223i
$505$	23.6005	+	1.32001i	1.05021	+	0.0587399i
$506$	−8.14166	−	4.70059i	−0.361941	−	0.208967i
$507$	−8.96947	+	11.9045i	−0.398348	+	0.528697i
$508$	12.2932	−	7.09746i	0.545421	−	0.314899i
$509$	10.5573	+	18.2858i	0.467944	+	0.810503i	0.999329	−	0.0366275i	$-0.0116615\pi$
$509$	10.5573	+	18.2858i	0.467944	+	0.810503i	−0.531385	+	0.847131i	$0.678328\pi$
$510$	5.11156	−	28.4156i	0.226344	−	1.25826i
$511$	11.7917	+	4.69000i	0.521636	+	0.207473i
$512$	−1.00000			−0.0441942
$513$	8.67582	−	22.6143i	0.383047	−	0.998445i
$514$		−	6.49218i		−	0.286358i
$515$	18.6568	−	28.5092i	0.822117	−	1.25626i
$516$	−0.548793	+	4.47194i	−0.0241593	+	0.196866i
$517$	8.55186	+	14.8122i	0.376110	+	0.651442i
$518$	−7.98412	−	10.1058i	−0.350802	−	0.444025i
$519$	−23.8733	−	17.9874i	−1.04792	−	0.789559i
$520$	−2.56676	+	3.92222i	−0.112560	+	0.172001i
$521$	21.9402			0.961216			0.480608	−	0.876936i	$-0.340416\pi$
$521$	21.9402			0.961216			0.480608	+	0.876936i	$0.340416\pi$
$522$	−13.6767	+	3.92363i	−0.598613	+	0.171733i
$523$	−7.10550			−0.310702			−0.155351	−	0.987859i	$-0.549651\pi$
$523$	−7.10550			−0.310702			−0.155351	+	0.987859i	$0.549651\pi$
$524$	1.14681	−	1.98633i	0.0500986	−	0.0867733i
$525$	−20.7810	+	9.65133i	−0.906959	+	0.421219i
$526$	−4.41420	−	7.64563i	−0.192468	−	0.333365i
$527$	−7.46313	−	12.9265i	−0.325099	−	0.563088i
$528$	−2.65296	+	1.12632i	−0.115455	+	0.0490166i
$529$	−4.45963	+	7.72430i	−0.193897	+	0.335839i
$530$	30.8930	+	1.72790i	1.34191	+	0.0750551i
$531$	0.142773	+	0.497666i	0.00619580	+	0.0215969i
$532$	−12.2034	+	1.78257i	−0.529085	+	0.0772843i
$533$	8.53543	−	14.7838i	0.369711	−	0.640358i
$534$	11.6994	−	15.5277i	0.506284	−	0.671951i
$535$	11.5093	+	22.7859i	0.497592	+	0.985121i
$536$	4.70611	−	2.71707i	0.203273	−	0.117360i
$537$	−0.127140	+	1.03602i	−0.00548650	+	0.0447076i
$538$	5.81286	−	10.0682i	0.250610	−	0.434070i
$539$	−3.33181	−	11.1614i	−0.143511	−	0.480755i
$540$	−9.42256	+	6.79819i	−0.405482	+	0.292548i
$541$	−36.7965			−1.58200			−0.791002	−	0.611813i	$-0.790441\pi$
$541$	−36.7965			−1.58200			−0.791002	+	0.611813i	$0.790441\pi$
$542$	14.5599	+	8.40617i	0.625402	+	0.361076i
$543$	−2.69579	+	21.9671i	−0.115687	+	0.942697i
$544$	−6.45590	+	3.72732i	−0.276794	+	0.159807i
$545$	−10.7012	−	21.1859i	−0.458387	−	0.907504i
$546$	−8.42735	−	4.61113i	−0.360657	−	0.197338i
$547$	14.6902	+	8.48140i	0.628108	+	0.362638i	0.780019	−	0.625756i	$-0.215209\pi$
$547$	14.6902	+	8.48140i	0.628108	+	0.362638i	−0.151911	+	0.988394i	$0.548543\pi$
$548$	10.8359			0.462888
$549$	−12.8971	−	12.4514i	−0.550434	−	0.531412i
$550$	0.927806	−	8.26815i	0.0395618	−	0.352555i
$551$	11.0540	−	19.1462i	0.470918	−	0.815654i
$552$	3.82411	+	9.00744i	0.162765	+	0.383382i
$553$	26.1949	−	20.6953i	1.11392	−	0.880052i
$554$	1.93149	−	1.11514i	0.0820610	−	0.0473780i
$555$	17.7384	−	6.38704i	0.752953	−	0.271115i
$556$	−7.63600	−	4.40865i	−0.323839	−	0.186968i
$557$	−2.63451			−0.111628			−0.0558139	−	0.998441i	$-0.517775\pi$
$557$	−2.63451			−0.111628			−0.0558139	+	0.998441i	$0.517775\pi$
$558$	−1.45244	+	5.82859i	−0.0614866	+	0.246744i
$559$		−	5.45295i		−	0.230635i
$560$	5.36654	+	2.49002i	0.226778	+	0.105223i
$561$	−12.9291	+	17.1598i	−0.545867	+	0.724487i
$562$	−2.79869	+	1.61582i	−0.118055	+	0.0681594i
$563$	20.7641	−	11.9882i	0.875104	−	0.505242i	0.00606320	−	0.999982i	$-0.498070\pi$
$563$	20.7641	−	11.9882i	0.875104	−	0.505242i	0.869041	+	0.494740i	$0.164737\pi$
$564$	2.16852	−	17.6705i	0.0913110	−	0.744063i
$565$	16.8266	−	25.7125i	0.707902	−	1.08173i
$566$	−6.46583			−0.271779
$567$	−15.4092	−	18.1537i	−0.647125	−	0.762384i
$568$			12.0450i			0.505396i
$569$	36.5400	+	21.0964i	1.53184	+	0.884407i	0.999277	+	0.0380144i	$0.0121033\pi$
$569$	36.5400	+	21.0964i	1.53184	+	0.884407i	0.532560	+	0.846392i	$0.321230\pi$
$570$	3.19628	−	17.7684i	0.133877	−	0.744235i
$571$	12.7469	+	22.0783i	0.533441	+	0.923947i	0.999237	+	0.0390547i	$0.0124347\pi$
$571$	12.7469	+	22.0783i	0.533441	+	0.923947i	−0.465796	+	0.884892i	$0.654232\pi$
$572$	3.02090	−	1.74412i	0.126310	−	0.0729253i
$573$	−26.0653	−	19.6390i	−1.08889	−	0.820429i
$574$	−20.0200	−	7.96266i	−0.835617	−	0.332355i
$575$	−28.0724	−	3.15012i	−1.17070	−	0.131369i
$576$	2.91098	+	0.725392i	0.121291	+	0.0302247i
$577$	−32.7696			−1.36422			−0.682108	−	0.731251i	$-0.738937\pi$
$577$	−32.7696			−1.36422			−0.682108	+	0.731251i	$0.738937\pi$
$578$	−19.2858	+	33.4039i	−0.802182	+	1.38942i
$579$	10.8471	−	4.60512i	0.450788	−	0.191382i
$580$	−9.46617	+	4.78143i	−0.393061	+	0.198538i
$581$	−4.24261	−	5.37005i	−0.176013	−	0.222787i
$582$	−6.40573	−	15.0883i	−0.265526	−	0.625428i
$583$	−19.9407	−	11.5128i	−0.825858	−	0.476810i
$584$	4.79644			0.198478
$585$	10.3169	−	9.55561i	0.426553	−	0.395076i
$586$		−	18.5231i		−	0.765182i
$587$	−19.1726	−	11.0693i	−0.791337	−	0.456879i	0.0490959	−	0.998794i	$-0.484366\pi$
$587$	−19.1726	−	11.0693i	−0.791337	−	0.456879i	−0.840433	+	0.541915i	$0.817699\pi$
$588$	−4.22131	+	11.3658i	−0.174084	+	0.468716i
$589$	−4.66672	−	8.08300i	−0.192289	−	0.333054i
$590$	0.173986	+	0.344454i	0.00716290	+	0.0141809i
$591$	−14.7632	−	1.81174i	−0.607278	−	0.0745249i
$592$	−4.21571	−	2.43394i	−0.173265	−	0.100034i
$593$			26.0392i			1.06930i	0.845073	+	0.534650i	$0.179557\pi$
$593$			26.0392i			1.06930i	−0.845073	+	0.534650i	$0.820443\pi$
$594$	8.53973	−	1.35425i	0.350389	−	0.0555654i
$595$	43.9270	−	3.92748i	1.80083	−	0.161011i
$596$	−12.4184	−	7.16974i	−0.508676	−	0.293684i
$597$	1.07610	−	8.76879i	0.0440419	−	0.358883i
$598$	−5.92171	−	10.2567i	−0.242157	−	0.419428i
$599$	18.1227	−	10.4631i	0.740472	−	0.427512i	−0.0817689	−	0.996651i	$-0.526057\pi$
$599$	18.1227	−	10.4631i	0.740472	−	0.427512i	0.822241	+	0.569140i	$0.192724\pi$
$600$	−5.95024	+	6.29243i	−0.242917	+	0.256887i
$601$	−25.4768	−	14.7091i	−1.03922	−	0.599995i	−0.119609	−	0.992821i	$-0.538164\pi$
$601$	−25.4768	−	14.7091i	−1.03922	−	0.599995i	−0.919613	+	0.392826i	$0.871497\pi$
$602$	−6.80997	+	0.994743i	−0.277554	+	0.0405427i
$603$	−15.6703	+	4.49557i	−0.638146	+	0.183074i
$604$	−6.90415			−0.280926
$605$	10.0784	−	15.4006i	0.409745	−	0.626124i
$606$	7.15515	+	16.8535i	0.290658	+	0.684625i
$607$	6.62507	+	11.4750i	0.268903	+	0.465754i	0.968579	−	0.248707i	$-0.0800055\pi$
$607$	6.62507	+	11.4750i	0.268903	+	0.465754i	−0.699676	+	0.714461i	$0.746672\pi$
$608$	−4.03690	+	2.33070i	−0.163718	+	0.0945225i
$609$	−11.2959	−	18.5682i	−0.457734	−	0.752421i
$610$	−11.1806	−	7.31673i	−0.452688	−	0.296246i
$611$			21.5469i			0.871695i
$612$	21.4968	−	6.16708i	0.868955	−	0.249290i
$613$		−	17.3252i		−	0.699759i	−0.936795	−	0.349880i	$-0.886222\pi$
$613$		−	17.3252i		−	0.699759i	0.936795	−	0.349880i	$-0.113778\pi$
$614$	1.72071	−	2.98036i	0.0694423	−	0.120278i
$615$	20.3562	−	24.0904i	0.820842	−	0.971417i
$616$	−2.72924	−	3.45452i	−0.109964	−	0.139187i
$617$	−9.93911	−	17.2150i	−0.400133	−	0.693052i	0.593608	−	0.804754i	$-0.297703\pi$
$617$	−9.93911	−	17.2150i	−0.400133	−	0.693052i	−0.993742	+	0.111703i	$0.964370\pi$
$618$	26.1949	+	3.21463i	1.05371	+	0.129311i
$619$	30.8618	+	17.8181i	1.24044	+	0.716168i	0.969184	−	0.246339i	$-0.0792276\pi$
$619$	30.8618	+	17.8181i	1.24044	+	0.716168i	0.271256	+	0.962507i	$0.412561\pi$
$620$	−0.250028	+	4.47025i	−0.0100414	+	0.179529i
$621$	−4.59799	−	28.9945i	−0.184511	−	1.16351i
$622$	33.2371			1.33269
$623$	27.5954	+	10.9757i	1.10559	+	0.439731i
$624$	−3.60384	−	0.442261i	−0.144269	−	0.0177046i
$625$	−7.39051	−	23.8826i	−0.295620	−	0.955305i
$626$	0.967111	+	1.67509i	0.0386535	+	0.0669499i
$627$	−8.08462	+	10.7301i	−0.322869	+	0.428518i
$628$	7.48808	−	12.9697i	0.298807	−	0.517549i
$629$	−36.2883			−1.44691
$630$	−13.8157	−	11.1412i	−0.550429	−	0.443878i
$631$	28.1609			1.12107			0.560533	−	0.828132i	$-0.310596\pi$
$631$	28.1609			1.12107			0.560533	+	0.828132i	$0.310596\pi$
$632$	6.30891	−	10.9273i	0.250955	−	0.434666i
$633$	−6.79189	−	15.9978i	−0.269954	−	0.635857i
$634$	5.12038	+	8.86877i	0.203356	+	0.352224i
$635$	−28.3317	+	14.3106i	−1.12431	+	0.567898i
$636$	9.36608	+	22.0612i	0.371389	+	0.874782i
$637$	3.39543	−	14.2758i	0.134532	−	0.565626i
$638$	7.89205			0.312449
$639$	8.73732	−	35.0627i	0.345643	−	1.38706i
$640$	2.23258	+	0.124872i	0.0882504	+	0.00493599i
$641$	25.4170	+	14.6745i	1.00391	+	0.579608i	0.909403	−	0.415916i	$-0.136539\pi$
$641$	25.4170	+	14.6745i	1.00391	+	0.579608i	0.0945076	+	0.995524i	$0.469872\pi$
$642$	−11.8991	+	15.7927i	−0.469619	+	0.623288i
$643$	−16.7337	−	28.9836i	−0.659912	−	1.14300i	−0.980638	−	0.195830i	$-0.937260\pi$
$643$	−16.7337	−	28.9836i	−0.659912	−	1.14300i	0.320726	−	0.947172i	$-0.396073\pi$
$644$	−11.7289	+	9.26644i	−0.462185	+	0.365149i
$645$	1.78364	−	9.91542i	0.0702309	−	0.390419i
$646$	−17.3745	+	30.0936i	−0.683592	+	1.18402i
$647$		−	19.6226i		−	0.771445i	−0.922615	−	0.385723i	$-0.873952\pi$
$647$		−	19.6226i		−	0.771445i	0.922615	−	0.385723i	$-0.126048\pi$
$648$	−7.94761	−	4.22320i	−0.312212	−	0.165903i
$649$		−	0.287175i		−	0.0112726i
$650$	6.22027	−	8.43615i	0.243979	−	0.330893i
$651$	−9.17318	+	0.210441i	−0.359525	+	0.00824782i
$652$	6.95885	−	4.01770i	0.272530	−	0.157345i
$653$	9.70880	+	16.8161i	0.379935	+	0.658066i	0.991052	−	0.133474i	$-0.0426131\pi$
$653$	9.70880	+	16.8161i	0.379935	+	0.658066i	−0.611118	+	0.791540i	$0.709280\pi$
$654$	11.0635	−	14.6838i	0.432618	−	0.574180i
$655$	−2.80838	+	4.29144i	−0.109732	+	0.167680i
$656$	−8.14339			−0.317946
$657$	−13.9624	−	3.47930i	−0.544723	−	0.135741i
$658$	26.9091	−	3.93065i	1.04903	−	0.153233i
$659$	−10.8291	−	6.25219i	−0.421842	−	0.243551i	0.274023	−	0.961723i	$-0.411646\pi$
$659$	−10.8291	−	6.25219i	−0.421842	−	0.243551i	−0.695865	+	0.718172i	$0.744979\pi$
$660$	6.06359	−	2.18331i	0.236025	−	0.0849851i
$661$	3.75358	−	2.16713i	0.145997	−	0.0842916i	−0.425222	−	0.905089i	$-0.639804\pi$
$661$	3.75358	−	2.16713i	0.145997	−	0.0842916i	0.571219	+	0.820798i	$0.306471\pi$
$662$	2.81788	+	4.88070i	0.109520	+	0.189694i
$663$	−24.9145	+	10.5775i	−0.967598	+	0.410794i
$664$	−2.24015	−	1.29335i	−0.0869347	−	0.0501918i
$665$	27.4677	−	2.45587i	1.06515	−	0.0952345i
$666$	10.5063	+	10.1432i	0.407111	+	0.393041i
$667$		−	26.7954i		−	1.03752i
$668$	4.12075	+	2.37911i	0.159436	+	0.0920507i
$669$	−18.4949	+	24.5468i	−0.715053	+	0.949034i
$670$	−10.8460	+	5.47842i	−0.419019	+	0.211650i
$671$	4.97174	+	8.61131i	0.191932	+	0.332436i
$672$	0.105101	+	4.58137i	0.00405434	+	0.176730i
$673$	1.47592	+	0.852124i	0.0568926	+	0.0328470i	0.528177	−	0.849135i	$-0.322876\pi$
$673$	1.47592	+	0.852124i	0.0568926	+	0.0328470i	−0.471284	+	0.881982i	$0.656209\pi$
$674$		−	13.6905i		−	0.527338i
$675$	21.8855	−	14.0009i	0.842373	−	0.538894i
$676$	−8.60558			−0.330984
$677$	−5.08519	−	2.93594i	−0.195440	−	0.112837i	0.399087	−	0.916913i	$-0.369327\pi$
$677$	−5.08519	−	2.93594i	−0.195440	−	0.112837i	−0.594527	+	0.804076i	$0.702661\pi$
$678$	23.6253	+	2.89928i	0.907324	+	0.111346i
$679$	19.6470	−	15.5221i	0.753983	−	0.595684i
$680$	14.8787	−	7.51536i	0.570574	−	0.288201i
$681$	−0.656947	−	0.494979i	−0.0251742	−	0.0189676i
$682$	1.66591	−	2.88543i	0.0637908	−	0.110489i
$683$	−10.9483			−0.418926			−0.209463	−	0.977817i	$-0.567172\pi$
$683$	−10.9483			−0.418926			−0.209463	+	0.977817i	$0.567172\pi$
$684$	13.4420	−	3.85630i	0.513968	−	0.147449i
$685$	−24.1921	−	1.35310i	−0.924332	−	0.0516994i
$686$	−18.4478	−	1.63620i	−0.704342	−	0.0624702i
$687$	17.5127	−	7.43501i	0.668150	−	0.283663i
$688$	−2.25274	+	1.30062i	−0.0858850	+	0.0495857i
$689$	−14.5035	−	25.1209i	−0.552541	−	0.957029i
$690$	−7.41286	−	20.5873i	−0.282203	−	0.783746i
$691$	−34.4759	−	19.9047i	−1.31153	−	0.757210i	−0.329177	−	0.944268i	$-0.606771\pi$
$691$	−34.4759	−	19.9047i	−1.31153	−	0.757210i	−0.982349	+	0.187058i	$0.940105\pi$
$692$		−	17.2576i		−	0.656037i
$693$	5.43890	+	12.0358i	0.206607	+	0.457203i
$694$	−9.79041			−0.371639
$695$	16.4975	+	10.7962i	0.625784	+	0.409522i
$696$	−6.56091	−	4.94334i	−0.248691	−	0.187377i
$697$	−52.5729	+	30.3530i	−1.99134	+	1.14970i
$698$	14.0539	−	8.11400i	0.531946	−	0.307119i
$699$	36.9264	+	4.53159i	1.39669	+	0.171400i
$700$	−11.6703	−	6.22930i	−0.441096	−	0.235445i
$701$		−	7.84396i		−	0.296262i	−0.988968	−	0.148131i	$-0.952674\pi$
$701$		−	7.84396i		−	0.296262i	0.988968	−	0.148131i	$-0.0473258\pi$
$702$	10.1699	+	3.90161i	0.383838	+	0.147257i
$703$	−22.6912			−0.855815
$704$	−1.44107	−	0.832005i	−0.0543125	−	0.0313574i
$705$	−7.04793	+	39.1800i	−0.265441	+	1.47561i
$706$	20.9960	−	12.1220i	0.790194	−	0.456219i
$707$	−21.9455	+	17.3381i	−0.825347	+	0.652066i
$708$	−0.179878	+	0.238738i	−0.00676022	+	0.00897232i
$709$	10.3461	−	17.9200i	0.388557	−	0.673001i	−0.603698	−	0.797213i	$-0.706307\pi$
$709$	10.3461	−	17.9200i	0.388557	−	0.673001i	0.992256	+	0.124212i	$0.0396402\pi$
$710$	1.50408	−	26.8913i	0.0564470	−	1.00921i
$711$	−26.2917	+	27.2329i	−0.986016	+	1.02131i
$712$	11.2248			0.420666
$713$	−9.79674	−	5.65615i	−0.366891	−	0.211825i
$714$	17.7547	+	29.1851i	0.664454	+	1.09223i
$715$	−6.96220	+	3.51666i	−0.260371	+	0.131516i
$716$	−0.521897	+	0.301317i	−0.0195042	+	0.0112608i
$717$	26.9201	−	11.4289i	1.00535	−	0.426821i
$718$	27.1600	+	15.6809i	1.01360	+	0.585204i
$719$	−21.2881			−0.793910			−0.396955	−	0.917838i	$-0.629933\pi$
$719$	−21.2881			−0.793910			−0.396955	+	0.917838i	$0.629933\pi$
$720$	−6.40841	−	1.98299i	−0.238827	−	0.0739018i
$721$	5.82684	+	39.8903i	0.217003	+	1.48559i
$722$	−1.36436	+	2.36314i	−0.0507763	+	0.0879471i
$723$	−12.7933	−	9.63919i	−0.475790	−	0.358485i
$724$	−11.0659	+	6.38892i	−0.411262	+	0.237442i
$725$	21.7310	−	9.49287i	0.807070	−	0.352556i
$726$	14.1505	+	1.73654i	0.525174	+	0.0644490i
$727$	−4.79802	+	8.31041i	−0.177949	+	0.308216i	−0.941178	−	0.337912i	$-0.890279\pi$
$727$	−4.79802	+	8.31041i	−0.177949	+	0.308216i	0.763229	+	0.646128i	$0.223613\pi$
$728$	−0.801642	−	5.48801i	−0.0297108	−	0.203399i
$729$	20.0719	+	18.0588i	0.743402	+	0.668844i
$730$	−10.7084	−	0.598941i	−0.396337	−	0.0221678i
$731$	−9.69565	+	16.7934i	−0.358607	+	0.621125i
$732$	1.26070	−	10.2730i	0.0465967	−	0.379701i
$733$	22.1972	+	38.4466i	0.819871	+	1.42006i	0.905777	+	0.423754i	$0.139288\pi$
$733$	22.1972	+	38.4466i	0.819871	+	1.42006i	−0.0859066	+	0.996303i	$0.527379\pi$
$734$	0.616195	+	1.06728i	0.0227442	+	0.0393941i
$735$	10.8437	−	24.8478i	0.399975	−	0.916526i
$736$	−2.82486	+	4.89279i	−0.104126	+	0.180351i
$737$	9.04247			0.333084
$738$	23.7052	+	5.90715i	0.872602	+	0.217445i
$739$	−17.8223			−0.655603			−0.327801	−	0.944747i	$-0.606308\pi$
$739$	−17.8223			−0.655603			−0.327801	+	0.944747i	$0.606308\pi$
$740$	9.10798	+	5.96039i	0.334816	+	0.219108i
$741$	−15.5791	+	6.61412i	−0.572313	+	0.242976i
$742$	−28.7267	+	22.6955i	−1.05459	+	0.833179i
$743$	25.2903	+	43.8041i	0.927811	+	1.60702i	0.786976	+	0.616983i	$0.211645\pi$
$743$	25.2903	+	43.8041i	0.927811	+	1.60702i	0.140835	+	0.990033i	$0.455021\pi$
$744$	−3.19227	+	1.35528i	−0.117034	+	0.0496870i
$745$	26.8297	+	17.5577i	0.982963	+	0.643265i
$746$		−	27.6157i		−	1.01108i
$747$	5.58285	+	5.38991i	0.204266	+	0.197206i
$748$	−12.4046			−0.453556
$749$	−28.0663	−	11.1630i	−1.02552	−	0.407886i
$750$	14.0701	−	13.3053i	0.513768	−	0.485842i
$751$	−22.2173	−	38.4816i	−0.810722	−	1.40421i	−0.912359	−	0.409390i	$-0.865741\pi$
$751$	−22.2173	−	38.4816i	−0.810722	−	1.40421i	0.101637	−	0.994822i	$-0.467592\pi$
$752$	8.90154	−	5.13931i	0.324606	−	0.187411i
$753$	16.1084	+	1.97681i	0.587023	+	0.0720391i
$754$	8.61024	+	4.97113i	0.313567	+	0.181038i
$755$	15.4140	+	0.862134i	0.560975	+	0.0313763i
$756$	3.01734	−	13.4125i	0.109740	−	0.487809i
$757$		−	26.2968i		−	0.955774i	−0.878421	−	0.477887i	$-0.841403\pi$
$757$		−	26.2968i		−	0.955774i	0.878421	−	0.477887i	$-0.158597\pi$
$758$	11.6133	−	20.1148i	0.421812	−	0.730601i
$759$	−1.98340	+	16.1621i	−0.0719928	+	0.586646i
$760$	9.30373	−	4.69938i	0.337482	−	0.170465i
$761$	−11.6947	−	20.2558i	−0.423932	−	0.734272i	0.572388	−	0.819983i	$-0.306017\pi$
$761$	−11.6947	−	20.2558i	−0.423932	−	0.734272i	−0.996320	+	0.0857107i	$0.972684\pi$
$762$	−19.6365	−	14.7952i	−0.711354	−	0.535972i
$763$	26.0955	+	10.3791i	0.944720	+	0.375749i
$764$		−	18.8422i		−	0.681687i
$765$	−48.7633	+	11.0842i	−1.76304	+	0.400749i
$766$		−	23.7929i		−	0.859672i
$767$	0.180889	−	0.313309i	0.00653152	−	0.0113129i
$768$	0.676868	+	1.59432i	0.0244244	+	0.0575300i
$769$	−21.6845	+	12.5196i	−0.781963	+	0.451467i	−0.837126	−	0.547011i	$-0.815766\pi$
$769$	−21.6845	+	12.5196i	−0.781963	+	0.451467i	0.0551625	+	0.998477i	$0.482432\pi$
$770$	5.66188	+	8.05329i	0.204040	+	0.290221i
$771$	−10.3506	+	4.39435i	−0.372768	+	0.158259i
$772$	5.89207	+	3.40179i	0.212060	+	0.122433i
$773$		−	55.5416i		−	1.99769i	−0.0480317	−	0.998846i	$-0.515295\pi$
$773$		−	55.5416i		−	1.99769i	0.0480317	−	0.998846i	$-0.484705\pi$
$774$	7.50115	−	2.15196i	0.269623	−	0.0773506i
$775$	1.11642	−	9.94895i	0.0401028	−	0.357377i
$776$	4.73188	−	8.19586i	0.169865	−	0.294214i
$777$	−10.7077	+	19.5696i	−0.384137	+	0.702054i
$778$	−8.18328	+	4.72462i	−0.293385	+	0.169386i
$779$	−32.8740	+	18.9798i	−1.17783	+	0.680023i
$780$	7.99063	+	1.43740i	0.286110	+	0.0514672i
$781$	−10.0215	+	17.3577i	−0.358596	+	0.621107i
$782$			42.1165i			1.50608i
$783$	15.5128	+	19.1492i	0.554383	+	0.684337i
$784$	−6.70752	+	2.00228i	−0.239554	+	0.0715100i
$785$	−18.3373	+	28.0209i	−0.654485	+	1.00011i
$786$	−3.94308	−	0.483893i	−0.140645	−	0.0172599i
$787$	−7.49527	−	12.9822i	−0.267177	−	0.462765i	0.700954	−	0.713206i	$-0.252758\pi$
$787$	−7.49527	−	12.9822i	−0.267177	−	0.462765i	−0.968132	+	0.250441i	$0.919424\pi$
$788$	−4.29375	−	7.43699i	−0.152959	−	0.264932i
$789$	−9.20172	+	12.2127i	−0.327590	+	0.434785i
$790$	−15.4496	+	23.6084i	−0.549674	+	0.839947i
$791$	5.25524	+	35.9772i	0.186855	+	1.27920i
$792$	3.59141	+	3.46729i	0.127615	+	0.123205i
$793$			12.5266i			0.444833i
$794$	−10.8617	+	18.8130i	−0.385467	+	0.667648i
$795$	−18.1557	−	50.4228i	−0.643916	−	1.78831i
$796$	4.41729	−	2.55032i	0.156567	−	0.0903938i
$797$	43.9990	−	25.4028i	1.55852	−	0.899814i	0.561124	−	0.827732i	$-0.310369\pi$
$797$	43.9990	−	25.4028i	1.55852	−	0.899814i	0.997399	−	0.0720822i	$-0.0229644\pi$
$798$	11.1021	+	18.2496i	0.393010	+	0.646028i
$799$	38.3116	−	66.3577i	1.35537	−	2.34757i
$800$	−4.96881	−	0.557572i	−0.175674	−	0.0197132i
$801$	−32.6751	−	8.14237i	−1.15452	−	0.287696i
$802$			12.3027i			0.434423i
$803$	6.91203	+	3.99066i	0.243920	+	0.140827i
$804$	−7.51730	−	5.66393i	−0.265115	−	0.199752i
$805$	27.3429	−	19.2235i	0.963710	−	0.677538i
$806$	3.63501	−	2.09867i	0.128038	−	0.0739227i
$807$	−19.9864	−	2.45272i	−0.703555	−	0.0863398i
$808$	−5.28548	+	9.15472i	−0.185942	+	0.322062i
$809$			38.3573i			1.34857i	0.738471	+	0.674285i	$0.235548\pi$
$809$			38.3573i			1.34857i	−0.738471	+	0.674285i	$0.764452\pi$
$810$	17.2163	+	10.4211i	0.604919	+	0.366159i
$811$		−	0.237330i		−	0.00833379i	−0.999991	−	0.00416689i	$-0.998674\pi$
$811$		−	0.237330i		−	0.00833379i	0.999991	−	0.00416689i	$-0.00132637\pi$
$812$	4.63754	−	11.6598i	0.162746	−	0.409180i
$813$	3.54696	−	28.9030i	0.124397	−	1.01367i
$814$	−4.05010	−	7.01498i	−0.141956	−	0.245875i
$815$	−16.0379	+	8.10086i	−0.561782	+	0.283761i
$816$	10.3123	+	7.76985i	0.361003	+	0.271999i
$817$	−6.06273	+	10.5009i	−0.212108	+	0.367382i
$818$			2.89004i			0.101048i
$819$	−1.64740	+	16.5570i	−0.0575647	+	0.578548i
$820$	18.1807	+	1.01688i	0.634899	+	0.0355110i
$821$	34.0959	+	19.6853i	1.18995	+	0.687020i	0.958296	−	0.285777i	$-0.0922516\pi$
$821$	34.0959	+	19.6853i	1.18995	+	0.687020i	0.231658	+	0.972797i	$0.425585\pi$
$822$	−7.33450	−	17.2759i	−0.255820	−	0.602567i
$823$	−12.0228	+	6.94134i	−0.419087	+	0.241960i	−0.694687	−	0.719312i	$-0.744457\pi$
$823$	−12.0228	+	6.94134i	−0.419087	+	0.241960i	0.275600	+	0.961273i	$0.411124\pi$
$824$	7.61856	+	13.1957i	0.265405	+	0.459695i
$825$	−13.8101	+	4.11723i	−0.480805	+	0.143344i
$826$	−0.424277	−	0.168750i	−0.0147625	−	0.00587157i
$827$	53.7207			1.86805			0.934027	−	0.357204i	$-0.116270\pi$
$827$	53.7207			1.86805			0.934027	+	0.357204i	$0.116270\pi$
$828$	11.7723	−	12.1937i	0.409116	−	0.423760i
$829$		−	40.2685i		−	1.39858i	−0.714836	−	0.699292i	$-0.753499\pi$
$829$		−	40.2685i		−	1.39858i	0.714836	−	0.699292i	$-0.246501\pi$
$830$	4.83981	+	3.16724i	0.167992	+	0.109936i
$831$	−3.08526	−	2.32460i	−0.107026	−	0.0806394i
$832$	−1.04814	−	1.81544i	−0.0363378	−	0.0629390i
$833$	−35.8400	+	37.9276i	−1.24178	+	1.31411i
$834$	−1.86022	+	15.1583i	−0.0644140	+	0.524888i
$835$	−8.90281	−	5.82612i	−0.308094	−	0.201621i
$836$	−7.75663			−0.268268
$837$	10.2757	−	1.62955i	0.355182	−	0.0563253i
$838$	−25.4794			−0.880170
$839$	−12.6898	+	21.9794i	−0.438100	+	0.758812i	−0.997543	−	0.0700572i	$-0.977682\pi$
$839$	−12.6898	+	21.9794i	−0.438100	+	0.758812i	0.559443	+	0.828869i	$0.311015\pi$
$840$	0.337439	−	10.2414i	0.0116427	−	0.353362i
$841$	−3.25296	−	5.63429i	−0.112171	−	0.194286i
$842$	2.96965	+	5.14359i	0.102341	+	0.177260i
$843$	4.47048	+	3.36830i	0.153971	+	0.116010i
$844$	5.01715	−	8.68995i	0.172697	−	0.299120i
$845$	19.2126	+	1.07460i	0.660935	+	0.0369672i
$846$	−29.6402	+	8.50332i	−1.01905	+	0.292350i
$847$	3.14765	+	21.5487i	0.108155	+	0.740422i
$848$	−6.91868	+	11.9835i	−0.237589	+	0.411516i
$849$	4.37652	+	10.3086i	0.150202	+	0.353790i
$850$	−34.1564	+	14.9207i	−1.17156	+	0.511776i
$851$	−23.8176	+	13.7511i	−0.816456	+	0.471381i
$852$	19.2035	−	8.15286i	0.657901	−	0.279312i
$853$	17.2962	−	29.9580i	0.592212	−	1.02574i	−0.401722	−	0.915762i	$-0.631588\pi$
$853$	17.2962	−	29.9580i	0.592212	−	1.02574i	0.993934	−	0.109979i	$-0.0350785\pi$
$854$	15.6440	−	2.28514i	0.535326	−	0.0781959i
$855$	−30.4919	+	6.93096i	−1.04280	+	0.237034i
$856$	−11.4163			−0.390202
$857$	−16.9137	−	9.76512i	−0.577761	−	0.333570i	0.182482	−	0.983209i	$-0.441587\pi$
$857$	−16.9137	−	9.76512i	−0.577761	−	0.333570i	−0.760243	+	0.649639i	$0.774920\pi$
$858$	−4.82544	−	3.63574i	−0.164738	−	0.124122i
$859$	43.4126	−	25.0643i	1.48122	−	0.855182i	0.481446	−	0.876476i	$-0.340112\pi$
$859$	43.4126	−	25.0643i	1.48122	−	0.855182i	0.999773	+	0.0212940i	$0.00677859\pi$
$860$	5.19183	−	2.62243i	0.177040	−	0.0894243i
$861$	0.855875	+	37.3079i	0.0291681	+	1.27145i
$862$	25.4910	+	14.7172i	0.868225	+	0.501270i
$863$	17.7867			0.605465			0.302733	−	0.953076i	$-0.402101\pi$
$863$	17.7867			0.605465			0.302733	+	0.953076i	$0.402101\pi$
$864$	−0.813845	−	5.13202i	−0.0276876	−	0.174595i
$865$	−2.15499	+	38.5290i	−0.0732720	+	1.31003i
$866$	−7.12793	+	12.3459i	−0.242217	+	0.419532i
$867$	66.3104	+	8.13757i	2.25202	+	0.276366i
$868$	−3.28406	−	4.15678i	−0.111468	−	0.141090i
$869$	18.1832	−	10.4981i	0.616823	−	0.356123i
$870$	14.0305	+	11.8557i	0.475678	+	0.401945i
$871$	9.86535	+	5.69576i	0.334275	+	0.192994i
$872$	10.6147			0.359458
$873$	−19.7196	+	20.4255i	−0.667409	+	0.691299i
$874$			26.3356i			0.890815i
$875$	25.2770	+	15.3647i	0.854518	+	0.519421i
$876$	−3.24656	−	7.64705i	−0.109691	−	0.258370i
$877$	−18.1879	+	10.5008i	−0.614163	+	0.354587i	−0.774593	−	0.632460i	$-0.782045\pi$
$877$	−18.1879	+	10.5008i	−0.614163	+	0.354587i	0.160430	+	0.987047i	$0.448712\pi$
$878$	−9.41191	+	5.43397i	−0.317637	+	0.183388i
$879$	−29.5317	+	12.5377i	−0.996080	+	0.422886i
$880$	3.11342	+	2.03747i	0.104953	+	0.0686829i
$881$	57.9674			1.95297			0.976486	−	0.215580i	$-0.0691642\pi$
$881$	57.9674			1.95297			0.976486	+	0.215580i	$0.0691642\pi$
$882$	20.9779	−	0.963010i	0.706363	−	0.0324262i
$883$			42.6213i			1.43432i	0.696908	+	0.717161i	$0.254559\pi$
$883$			42.6213i			1.43432i	−0.696908	+	0.717161i	$0.745441\pi$
$884$	−13.5334	−	7.81352i	−0.455178	−	0.262797i
$885$	0.431403	−	0.510539i	0.0145015	−	0.0171616i
$886$	5.24859	+	9.09083i	0.176330	+	0.305412i
$887$	−3.27263	+	1.88945i	−0.109884	+	0.0634416i	−0.553935	−	0.832560i	$-0.686874\pi$
$887$	−3.27263	+	1.88945i	−0.109884	+	0.0634416i	0.444051	+	0.896002i	$0.353541\pi$
$888$	−1.02700	+	8.36865i	−0.0344637	+	0.280833i
$889$	13.8799	−	34.8973i	0.465517	−	1.17042i
$890$	−25.0602	−	1.40166i	−0.840020	−	0.0469837i
$891$	−7.93937	−	12.6984i	−0.265979	−	0.425412i
$892$	−17.7445			−0.594131
$893$	23.9564	−	41.4937i	0.801671	−	1.38853i
$894$	−3.02525	+	24.6518i	−0.101180	+	0.824479i
$895$	1.20280	−	0.607544i	0.0402052	−	0.0203080i
$896$	−2.07602	+	1.64016i	−0.0693550	+	0.0547940i
$897$	−12.3442	+	16.3835i	−0.412161	+	0.547030i
$898$	−32.1022	−	18.5342i	−1.07126	−	0.618494i
$899$	9.49639			0.316722
$900$	14.0597	+	5.22742i	0.468655	+	0.174247i
$901$			103.152i			3.43651i
$902$	−11.7352	−	6.77533i	−0.390740	−	0.225594i
$903$	6.19539	+	10.1839i	0.206170	+	0.338901i
$904$	6.87120	+	11.9013i	0.228533	+	0.395830i
$905$	25.5034	−	12.8819i	0.847760	−	0.428210i
$906$	4.67320	+	11.0074i	0.155257	+	0.365696i
$907$	−43.9682	−	25.3850i	−1.45994	−	0.842896i	−0.460932	−	0.887436i	$-0.652485\pi$
$907$	−43.9682	−	25.3850i	−1.45994	−	0.842896i	−0.999008	+	0.0445394i	$0.985818\pi$
$908$		−	0.474897i		−	0.0157600i
$909$	22.0267	−	22.8152i	0.730579	−	0.756731i
$910$	1.10443	+	12.3525i	0.0366115	+	0.409482i
$911$	−6.59422	−	3.80717i	−0.218476	−	0.126137i	0.386768	−	0.922177i	$-0.373591\pi$
$911$	−6.59422	−	3.80717i	−0.218476	−	0.126137i	−0.605244	+	0.796040i	$0.706925\pi$
$912$	6.44833	+	4.85852i	0.213526	+	0.160882i
$913$	−2.15215	−	3.72763i	−0.0712257	−	0.123367i
$914$	17.5211	−	10.1158i	0.579545	−	0.334601i
$915$	−4.09741	+	22.7779i	−0.135456	+	0.753013i
$916$	9.51279	+	5.49221i	0.314312	+	0.181468i
$917$	−0.877104	−	6.00462i	−0.0289645	−	0.198290i
$918$	−24.3828	−	30.0984i	−0.804751	−	0.993394i
$919$	−10.4157			−0.343581			−0.171791	−	0.985133i	$-0.554955\pi$
$919$	−10.4157			−0.343581			−0.171791	+	0.985133i	$0.554955\pi$
$920$	6.91769	−	10.5708i	0.228069	−	0.348509i
$921$	−5.91634	−	0.726049i	−0.194950	−	0.0239241i
$922$	−6.80701	−	11.7901i	−0.224177	−	0.388286i
$923$	−21.8669	+	12.6249i	−0.719757	+	0.415552i
$924$	−3.66026	+	6.68954i	−0.120414	+	0.220070i
$925$	−19.5900	−	14.4444i	−0.644115	−	0.474928i
$926$			22.8848i			0.752040i
$927$	−12.6054	−	43.9389i	−0.414015	−	1.44314i
$928$		−	4.74279i		−	0.155690i
$929$	−21.5567	+	37.3374i	−0.707253	+	1.22500i	0.258619	+	0.965980i	$0.416733\pi$
$929$	−21.5567	+	37.3374i	−0.707253	+	1.22500i	−0.965872	+	0.259019i	$0.916601\pi$
$930$	7.29623	−	2.62714i	0.239253	−	0.0861474i
$931$	−22.4109	+	23.7162i	−0.734487	+	0.777269i
$932$	10.7397	+	18.6017i	0.351791	+	0.609320i
$933$	−22.4972	−	52.9905i	−0.736524	−	1.73483i
$934$	2.89724	+	1.67272i	0.0948006	+	0.0547332i
$935$	27.6942	+	1.54898i	0.905697	+	0.0506571i
$936$	1.73422	+	6.04502i	0.0566848	+	0.197588i
$937$	−16.2891			−0.532140			−0.266070	−	0.963954i	$-0.585725\pi$
$937$	−16.2891			−0.532140			−0.266070	+	0.963954i	$0.585725\pi$
$938$	5.31355	−	13.3595i	0.173494	−	0.436203i
$939$	2.01601	−	2.67570i	0.0657901	−	0.0873180i
$940$	−20.5151	+	10.3624i	−0.669130	+	0.337983i
$941$	14.8611	+	25.7402i	0.484458	+	0.839106i	0.999841	−	0.0178543i	$-0.00568350\pi$
$941$	14.8611	+	25.7402i	0.484458	+	0.839106i	−0.515383	+	0.856960i	$0.672350\pi$
$942$	−25.7463	−	3.15957i	−0.838860	−	0.102944i
$943$	−23.0039	+	39.8439i	−0.749110	+	1.29750i
$944$	−0.172580			−0.00561701
$945$	−8.41130	+	29.5677i	−0.273620	+	0.961838i
$946$	−4.32849			−0.140731
$947$	−12.6233	+	21.8642i	−0.410202	+	0.710490i	−0.994912	−	0.100752i	$-0.967875\pi$
$947$	−12.6233	+	21.8642i	−0.410202	+	0.710490i	0.584710	+	0.811243i	$0.301208\pi$
$948$	−21.6920	−	2.66202i	−0.704522	−	0.0864585i
$949$	5.02736	+	8.70764i	0.163195	+	0.282662i
$950$	−21.3581	+	9.32997i	−0.692949	+	0.302704i
$951$	10.6738	−	14.1665i	0.346122	−	0.459381i
$952$	−7.28919	+	18.3267i	−0.236244	+	0.593972i
$953$	46.4580			1.50492			0.752461	−	0.658636i	$-0.228866\pi$
$953$	46.4580			1.50492			0.752461	+	0.658636i	$0.228866\pi$
$954$	28.8329	−	29.8650i	0.933500	−	0.966915i
$955$	−2.35286	+	42.0667i	−0.0761368	+	1.36125i
$956$	14.6228	+	8.44250i	0.472937	+	0.273050i
$957$	−5.34188	−	12.5824i	−0.172678	−	0.406732i
$958$	8.15257	+	14.1207i	0.263397	+	0.456218i
$959$	22.4956	−	17.7727i	0.726422	−	0.573910i
$960$	−1.31208	−	3.64396i	−0.0423471	−	0.117608i
$961$	−13.4954	+	23.3748i	−0.435337	+	0.754025i
$962$		−	10.2045i		−	0.329006i
$963$	33.2327	+	8.28131i	1.07091	+	0.266862i
$964$		−	9.24813i		−	0.297862i
$965$	−12.7297	−	8.33051i	−0.409784	−	0.268169i
$966$	22.7126	+	12.4275i	0.730766	+	0.399848i
$967$	38.7680	−	22.3827i	1.24670	−	0.719780i	0.276246	−	0.961087i	$-0.410909\pi$
$967$	38.7680	−	22.3827i	1.24670	−	0.719780i	0.970449	+	0.241307i	$0.0775761\pi$
$968$	4.11554	+	7.12832i	0.132278	+	0.229113i
$969$	59.7390	+	7.33114i	1.91909	+	0.235510i
$970$	−11.5877	+	17.7070i	−0.372060	+	0.568539i
$971$	5.45198			0.174962			0.0874812	−	0.996166i	$-0.472118\pi$
$971$	5.45198			0.174962			0.0874812	+	0.996166i	$0.472118\pi$
$972$	−1.35364	+	15.5296i	−0.0434181	+	0.498111i
$973$	−23.0834	+	3.37183i	−0.740020	+	0.108096i
$974$	−4.50548	−	2.60124i	−0.144365	−	0.0833491i
$975$	−17.6602	−	4.20691i	−0.565579	−	0.134729i
$976$	5.17503	−	2.98781i	0.165649	−	0.0956374i
$977$	−9.53359	−	16.5127i	−0.305007	−	0.528287i	0.672256	−	0.740319i	$-0.265325\pi$
$977$	−9.53359	−	16.5127i	−0.305007	−	0.528287i	−0.977263	+	0.212032i	$0.931992\pi$
$978$	−11.1157	−	8.37517i	−0.355441	−	0.267808i
$979$	16.1757	+	9.33907i	0.516979	+	0.298478i
$980$	15.2251	−	3.63266i	0.486348	−	0.116041i
$981$	−30.8991	−	7.69981i	−0.986533	−	0.245836i
$982$			23.8599i			0.761400i
$983$	26.7964	+	15.4709i	0.854674	+	0.493446i	0.862225	−	0.506525i	$-0.169070\pi$
$983$	26.7964	+	15.4709i	0.854674	+	0.493446i	−0.00755133	+	0.999971i	$0.502404\pi$
$984$	5.51200	+	12.9831i	0.175716	+	0.413887i
$985$	8.65746	+	17.1398i	0.275850	+	0.546121i
$986$	−17.6779	−	30.6190i	−0.562979	−	0.975107i
$987$	−24.4806	−	40.2411i	−0.779227	−	1.28089i
$988$	−8.46249	−	4.88582i	−0.269228	−	0.155439i
$989$			14.6963i			0.467314i
$990$	−7.58514	−	8.18947i	−0.241071	−	0.260278i
$991$	21.5926			0.685912			0.342956	−	0.939351i	$-0.388572\pi$
$991$	21.5926			0.685912			0.342956	+	0.939351i	$0.388572\pi$
$992$	−1.73402	−	1.00114i	−0.0550553	−	0.0317862i
$993$	5.87406	−	7.79618i	0.186408	−	0.247404i
$994$	19.7557	+	25.0056i	0.626613	+	0.793130i
$995$	−10.1804	+	5.14220i	−0.322741	+	0.163019i
$996$	−0.545726	+	4.44694i	−0.0172920	+	0.140907i
$997$	26.8955	−	46.5843i	0.851788	−	1.47534i	−0.0278059	−	0.999613i	$-0.508852\pi$
$997$	26.8955	−	46.5843i	0.851788	−	1.47534i	0.879593	−	0.475726i	$-0.157815\pi$
$998$	32.3319			1.02345
$999$	9.06011	−	23.6160i	0.286649	−	0.747177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.f.209.1	yes	32
3.2	odd	2		1890.2.bf.e.629.7		32
5.4	even	2		630.2.bf.e.209.16	yes	32
7.6	odd	2	inner	630.2.bf.f.209.16	yes	32
9.4	even	3		1890.2.bf.f.1259.13		32
9.5	odd	6		630.2.bf.e.419.1	yes	32
15.14	odd	2		1890.2.bf.f.629.4		32
21.20	even	2		1890.2.bf.e.629.10		32
35.34	odd	2		630.2.bf.e.209.1	✓	32
45.4	even	6		1890.2.bf.e.1259.10		32
45.14	odd	6	inner	630.2.bf.f.419.16	yes	32
63.13	odd	6		1890.2.bf.f.1259.4		32
63.41	even	6		630.2.bf.e.419.16	yes	32
105.104	even	2		1890.2.bf.f.629.13		32
315.104	even	6	inner	630.2.bf.f.419.1	yes	32
315.139	odd	6		1890.2.bf.e.1259.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.1	✓	32	35.34	odd	2
630.2.bf.e.209.16	yes	32	5.4	even	2
630.2.bf.e.419.1	yes	32	9.5	odd	6
630.2.bf.e.419.16	yes	32	63.41	even	6
630.2.bf.f.209.1	yes	32	1.1	even	1	trivial
630.2.bf.f.209.16	yes	32	7.6	odd	2	inner
630.2.bf.f.419.1	yes	32	315.104	even	6	inner
630.2.bf.f.419.16	yes	32	45.14	odd	6	inner
1890.2.bf.e.629.7		32	3.2	odd	2
1890.2.bf.e.629.10		32	21.20	even	2
1890.2.bf.e.1259.7		32	315.139	odd	6
1890.2.bf.e.1259.10		32	45.4	even	6
1890.2.bf.f.629.4		32	15.14	odd	2
1890.2.bf.f.629.13		32	105.104	even	2
1890.2.bf.f.1259.4		32	63.13	odd	6
1890.2.bf.f.1259.13		32	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71915 - 0.210974i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00815 + 1.99591i) q^{5} +(-1.04229 + 1.38334i) q^{6} +(-2.45843 - 0.977807i) q^{7} -1.00000 q^{8} +(2.91098 + 0.725392i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71915 - 0.210974i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00815 + 1.99591i) q^{5} +(-1.04229 + 1.38334i) q^{6} +(-2.45843 - 0.977807i) q^{7} -1.00000 q^{8} +(2.91098 + 0.725392i) q^{9} +(2.23258 + 0.124872i) q^{10} +(-1.44107 - 0.832005i) q^{11} +(0.676868 + 1.59432i) q^{12} +(-1.04814 - 1.81544i) q^{13} +(-2.07602 + 1.64016i) q^{14} +(-1.31208 - 3.64396i) q^{15} +(-0.500000 + 0.866025i) q^{16} +7.45463i q^{17} +(2.08370 - 2.15829i) q^{18} +4.66141i q^{19} +(1.22443 - 1.87103i) q^{20} +(4.02013 + 2.19967i) q^{21} +(-1.44107 + 0.832005i) q^{22} +(2.82486 + 4.89279i) q^{23} +(1.71915 + 0.210974i) q^{24} +(-2.96728 + 4.02433i) q^{25} -2.09629 q^{26} +(-4.85138 - 1.86120i) q^{27} +(0.382411 + 2.61797i) q^{28} +(-4.10738 - 2.37140i) q^{29} +(-3.81180 - 0.685689i) q^{30} +(-1.73402 + 1.00114i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.30190 + 1.73437i) q^{33} +(6.45590 + 3.72732i) q^{34} +(-0.526851 - 5.89257i) q^{35} +(-0.827282 - 2.88368i) q^{36} +4.86789i q^{37} +(4.03690 + 2.33070i) q^{38} +(1.41891 + 3.34215i) q^{39} +(-1.00815 - 1.99591i) q^{40} +(4.07169 + 7.05238i) q^{41} +(3.91503 - 2.38170i) q^{42} +(2.25274 + 1.30062i) q^{43} +1.66401i q^{44} +(1.48688 + 6.54134i) q^{45} +5.64971 q^{46} +(-8.90154 - 5.13931i) q^{47} +(1.04229 - 1.38334i) q^{48} +(5.08779 + 4.80775i) q^{49} +(2.00154 + 4.58191i) q^{50} +(1.57273 - 12.8157i) q^{51} +(-1.04814 + 1.81544i) q^{52} +13.8374 q^{53} +(-4.03754 + 3.27082i) q^{54} +(0.207788 - 3.71503i) q^{55} +(2.45843 + 0.977807i) q^{56} +(0.983434 - 8.01368i) q^{57} +(-4.10738 + 2.37140i) q^{58} +(0.0862901 + 0.149459i) q^{59} +(-2.49972 + 2.95827i) q^{60} +(-5.17503 - 2.98781i) q^{61} +2.00228i q^{62} +(-6.44716 - 4.62971i) q^{63} +1.00000 q^{64} +(2.56676 - 3.92222i) q^{65} +(2.65296 - 1.12632i) q^{66} +(-4.70611 + 2.71707i) q^{67} +(6.45590 - 3.72732i) q^{68} +(-3.82411 - 9.00744i) q^{69} +(-5.36654 - 2.49002i) q^{70} -12.0450i q^{71} +(-2.91098 - 0.725392i) q^{72} -4.79644 q^{73} +(4.21571 + 2.43394i) q^{74} +(5.95024 - 6.29243i) q^{75} +(4.03690 - 2.33070i) q^{76} +(2.72924 + 3.45452i) q^{77} +(3.60384 + 0.442261i) q^{78} +(-6.30891 + 10.9273i) q^{79} +(-2.23258 - 0.124872i) q^{80} +(7.94761 + 4.22320i) q^{81} +8.14339 q^{82} +(2.24015 + 1.29335i) q^{83} +(-0.105101 - 4.58137i) q^{84} +(-14.8787 + 7.51536i) q^{85} +(2.25274 - 1.30062i) q^{86} +(6.56091 + 4.94334i) q^{87} +(1.44107 + 0.832005i) q^{88} -11.2248 q^{89} +(6.40841 + 1.98299i) q^{90} +(0.801642 + 5.48801i) q^{91} +(2.82486 - 4.89279i) q^{92} +(3.19227 - 1.35528i) q^{93} +(-8.90154 + 5.13931i) q^{94} +(-9.30373 + 4.69938i) q^{95} +(-0.676868 - 1.59432i) q^{96} +(-4.73188 + 8.19586i) q^{97} +(6.70752 - 2.00228i) q^{98} +(-3.59141 - 3.46729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9} - 24 q^{11} - 12 q^{15} - 16 q^{16} - 6 q^{18} + 2 q^{21} - 24 q^{22} + 24 q^{23} + 50 q^{25} - 36 q^{29} - 18 q^{30} + 16 q^{32} + 48 q^{35} - 66 q^{39} - 2 q^{42} + 54 q^{43} + 48 q^{46} + 32 q^{49} + 58 q^{50} - 26 q^{51} + 24 q^{53} - 110 q^{57} - 36 q^{58} - 6 q^{60} - 20 q^{63} + 32 q^{64} - 66 q^{65} + 66 q^{67} + 12 q^{70} + 6 q^{72} + 12 q^{74} - 18 q^{77} - 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} - 32 q^{85} + 54 q^{86} + 24 q^{88} + 16 q^{91} + 24 q^{92} - 28 q^{93} - 24 q^{95} + 64 q^{98} + 58 q^{99}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9 - 24 * q^11 - 12 * q^15 - 16 * q^16 - 6 * q^18 + 2 * q^21 - 24 * q^22 + 24 * q^23 + 50 * q^25 - 36 * q^29 - 18 * q^30 + 16 * q^32 + 48 * q^35 - 66 * q^39 - 2 * q^42 + 54 * q^43 + 48 * q^46 + 32 * q^49 + 58 * q^50 - 26 * q^51 + 24 * q^53 - 110 * q^57 - 36 * q^58 - 6 * q^60 - 20 * q^63 + 32 * q^64 - 66 * q^65 + 66 * q^67 + 12 * q^70 + 6 * q^72 + 12 * q^74 - 18 * q^77 - 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 - 32 * q^85 + 54 * q^86 + 24 * q^88 + 16 * q^91 + 24 * q^92 - 28 * q^93 - 24 * q^95 + 64 * q^98 + 58 * q^99

Introduction

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