LMFDB - Embedded newform 429.2.p.b.230.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(230,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("429.230");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.p (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			230.19
Character	$\chi$	$=$	429.230
Dual form			429.2.p.b.263.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.400235 + 0.693228i) q^{2} +(-1.18152 + 1.26649i) q^{3} +(0.679624 + 1.17714i) q^{4} -2.49177i q^{5} +(-0.405079 - 1.32596i) q^{6} +(-0.533256 + 0.307876i) q^{7} -2.68898 q^{8} +(-0.207999 - 2.99278i) q^{9} +O(q^{10})$	\(q+(-0.400235 + 0.693228i) q^{2} +(-1.18152 + 1.26649i) q^{3} +(0.679624 + 1.17714i) q^{4} -2.49177i q^{5} +(-0.405079 - 1.32596i) q^{6} +(-0.533256 + 0.307876i) q^{7} -2.68898 q^{8} +(-0.207999 - 2.99278i) q^{9} +(1.72737 + 0.997295i) q^{10} +(-3.17941 + 0.944117i) q^{11} +(-2.29383 - 0.530086i) q^{12} +(-2.90515 - 2.13544i) q^{13} -0.492891i q^{14} +(3.15581 + 2.94409i) q^{15} +(-0.283023 + 0.490211i) q^{16} +(-2.03186 - 3.51928i) q^{17} +(2.15793 + 1.05363i) q^{18} +(-5.18322 + 2.99253i) q^{19} +(2.93317 - 1.69347i) q^{20} +(0.240134 - 1.03913i) q^{21} +(0.618024 - 2.58192i) q^{22} +(0.318813 + 0.184067i) q^{23} +(3.17709 - 3.40557i) q^{24} -1.20893 q^{25} +(2.64309 - 1.15925i) q^{26} +(4.03609 + 3.27262i) q^{27} +(-0.724827 - 0.418479i) q^{28} +(1.24579 - 2.15778i) q^{29} +(-3.30399 + 1.00936i) q^{30} -2.67384 q^{31} +(-2.91553 - 5.04985i) q^{32} +(2.56084 - 5.14219i) q^{33} +3.25288 q^{34} +(0.767156 + 1.32875i) q^{35} +(3.38157 - 2.27881i) q^{36} +(3.81325 - 6.60475i) q^{37} -4.79087i q^{38} +(6.13702 - 1.15628i) q^{39} +6.70032i q^{40} +(-4.02997 + 6.98010i) q^{41} +(0.624241 + 0.582362i) q^{42} +(5.27705 - 3.04671i) q^{43} +(-3.27216 - 3.10097i) q^{44} +(-7.45733 + 0.518286i) q^{45} +(-0.255200 + 0.147340i) q^{46} -0.492431i q^{47} +(-0.286448 - 0.937642i) q^{48} +(-3.31043 + 5.73382i) q^{49} +(0.483855 - 0.838061i) q^{50} +(6.85782 + 1.58479i) q^{51} +(0.539306 - 4.87107i) q^{52} -7.11354i q^{53} +(-3.88405 + 1.48811i) q^{54} +(2.35252 + 7.92236i) q^{55} +(1.43391 - 0.827871i) q^{56} +(2.33409 - 10.1003i) q^{57} +(0.997221 + 1.72724i) q^{58} +(-8.67632 + 5.00927i) q^{59} +(-1.32085 + 5.71571i) q^{60} +(2.96548 - 1.71212i) q^{61} +(1.07016 - 1.85358i) q^{62} +(1.03232 + 1.53188i) q^{63} +3.53550 q^{64} +(-5.32102 + 7.23897i) q^{65} +(2.53977 + 3.83333i) q^{66} +(-1.28542 + 2.22641i) q^{67} +(2.76179 - 4.78357i) q^{68} +(-0.609804 + 0.186294i) q^{69} -1.22817 q^{70} +(-12.6355 + 7.29512i) q^{71} +(0.559304 + 8.04752i) q^{72} +15.9862i q^{73} +(3.05240 + 5.28691i) q^{74} +(1.42838 - 1.53109i) q^{75} +(-7.04528 - 4.06759i) q^{76} +(1.40477 - 1.48232i) q^{77} +(-1.65469 + 4.71714i) q^{78} -8.77299i q^{79} +(1.22149 + 0.705229i) q^{80} +(-8.91347 + 1.24499i) q^{81} +(-3.22587 - 5.58737i) q^{82} +1.41718 q^{83} +(1.38640 - 0.423543i) q^{84} +(-8.76923 + 5.06292i) q^{85} +4.87760i q^{86} +(1.26087 + 4.12725i) q^{87} +(8.54936 - 2.53871i) q^{88} +(-0.846297 - 0.488610i) q^{89} +(2.62539 - 5.37706i) q^{90} +(2.20664 + 0.244310i) q^{91} +0.500384i q^{92} +(3.15920 - 3.38639i) q^{93} +(0.341367 + 0.197088i) q^{94} +(7.45671 + 12.9154i) q^{95} +(9.84035 + 2.27403i) q^{96} +(5.19256 + 8.99377i) q^{97} +(-2.64990 - 4.58976i) q^{98} +(3.48685 + 9.31890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9}+O(q^{10}) $ 96 * q + 2 * q^3 - 60 * q^4 - 2 * q^9	$ 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9} + 28 q^{12} - 8 q^{15} - 44 q^{16} + 16 q^{22} - 56 q^{25} + 44 q^{27} - 40 q^{31} - 16 q^{33} - 56 q^{34} + 40 q^{36} + 28 q^{37} - 22 q^{42} - 10 q^{45} + 24 q^{48} - 8 q^{49} - 12 q^{55} - 16 q^{58} - 76 q^{60} + 104 q^{64} + 68 q^{66} - 24 q^{67} + 30 q^{69} + 88 q^{70} - 66 q^{75} - 28 q^{78} - 66 q^{81} + 32 q^{82} - 8 q^{88} - 80 q^{91} + 30 q^{93} - 80 q^{97} - 68 q^{99}+O(q^{100}) $ 96 * q + 2 * q^3 - 60 * q^4 - 2 * q^9 + 28 * q^12 - 8 * q^15 - 44 * q^16 + 16 * q^22 - 56 * q^25 + 44 * q^27 - 40 * q^31 - 16 * q^33 - 56 * q^34 + 40 * q^36 + 28 * q^37 - 22 * q^42 - 10 * q^45 + 24 * q^48 - 8 * q^49 - 12 * q^55 - 16 * q^58 - 76 * q^60 + 104 * q^64 + 68 * q^66 - 24 * q^67 + 30 * q^69 + 88 * q^70 - 66 * q^75 - 28 * q^78 - 66 * q^81 + 32 * q^82 - 8 * q^88 - 80 * q^91 + 30 * q^93 - 80 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.400235	+	0.693228i	−0.283009	+	0.490186i	−0.972124	−	0.234466i	$-0.924666\pi$
$2$	−0.400235	+	0.693228i	−0.283009	+	0.490186i	0.689115	+	0.724652i	$0.257999\pi$
$3$	−1.18152	+	1.26649i	−0.682154	+	0.731209i
$3$	−1.18152	+	1.26649i	−0.682154	+	0.731209i
$4$	0.679624	+	1.17714i	0.339812	+	0.588571i
$5$		−	2.49177i		−	1.11435i	−0.830394	−	0.557177i	$-0.811884\pi$
$5$		−	2.49177i		−	1.11435i	0.830394	−	0.557177i	$-0.188116\pi$
$6$	−0.405079	−	1.32596i	−0.165373	−	0.541321i
$7$	−0.533256	+	0.307876i	−0.201552	+	0.116366i	−0.597379	−	0.801959i	$-0.703791\pi$
$7$	−0.533256	+	0.307876i	−0.201552	+	0.116366i	0.395827	+	0.918325i	$0.370458\pi$
$8$	−2.68898			−0.950697
$9$	−0.207999	−	2.99278i	−0.0693329	−	0.997594i
$10$	1.72737	+	0.997295i	0.546241	+	0.315372i
$11$	−3.17941	+	0.944117i	−0.958628	+	0.284662i
$11$	−3.17941	+	0.944117i	−0.958628	+	0.284662i
$12$	−2.29383	−	0.530086i	−0.662172	−	0.153023i
$13$	−2.90515	−	2.13544i	−0.805744	−	0.592264i
$13$	−2.90515	−	2.13544i	−0.805744	−	0.592264i
$14$		−	0.492891i		−	0.131731i
$15$	3.15581	+	2.94409i	0.814826	+	0.760161i
$16$	−0.283023	+	0.490211i	−0.0707558	+	0.122553i
$17$	−2.03186	−	3.51928i	−0.492797	−	0.853550i	0.507168	−	0.861847i	$-0.330692\pi$
$17$	−2.03186	−	3.51928i	−0.492797	−	0.853550i	−0.999966	+	0.00829700i	$0.997359\pi$
$18$	2.15793	+	1.05363i	0.508628	+	0.248342i
$19$	−5.18322	+	2.99253i	−1.18911	+	0.686534i	−0.958105	−	0.286418i	$-0.907536\pi$
$19$	−5.18322	+	2.99253i	−1.18911	+	0.686534i	−0.231007	+	0.972952i	$0.574202\pi$
$20$	2.93317	−	1.69347i	0.655877	−	0.378671i
$21$	0.240134	−	1.03913i	0.0524015	−	0.226756i
$22$	0.618024	−	2.58192i	0.131763	−	0.550468i
$23$	0.318813	+	0.184067i	0.0664771	+	0.0383805i	0.532870	−	0.846197i	$-0.321113\pi$
$23$	0.318813	+	0.184067i	0.0664771	+	0.0383805i	−0.466393	+	0.884578i	$0.654447\pi$
$24$	3.17709	−	3.40557i	0.648522	−	0.695158i
$25$	−1.20893			−0.241785
$26$	2.64309	−	1.15925i	0.518352	−	0.227348i
$27$	4.03609	+	3.27262i	0.776745	+	0.629815i
$28$	−0.724827	−	0.418479i	−0.136979	−	0.0790851i
$29$	1.24579	−	2.15778i	0.231338	−	0.400689i	−0.726864	−	0.686781i	$-0.759023\pi$
$29$	1.24579	−	2.15778i	0.231338	−	0.400689i	0.958202	+	0.286092i	$0.0923563\pi$
$30$	−3.30399	+	1.00936i	−0.603223	+	0.184284i
$31$	−2.67384			−0.480235			−0.240118	−	0.970744i	$-0.577186\pi$
$31$	−2.67384			−0.480235			−0.240118	+	0.970744i	$0.577186\pi$
$32$	−2.91553	−	5.04985i	−0.515398	−	0.892695i
$33$	2.56084	−	5.14219i	0.445784	−	0.895140i
$34$	3.25288			0.557864
$35$	0.767156	+	1.32875i	0.129673	+	0.224600i
$36$	3.38157	−	2.27881i	0.563595	−	0.379801i
$37$	3.81325	−	6.60475i	0.626895	−	1.08581i	−0.361276	−	0.932459i	$-0.617659\pi$
$37$	3.81325	−	6.60475i	0.626895	−	1.08581i	0.988171	−	0.153355i	$-0.0490078\pi$
$38$		−	4.79087i		−	0.777182i
$39$	6.13702	−	1.15628i	0.982710	−	0.185152i
$40$			6.70032i			1.05941i
$41$	−4.02997	+	6.98010i	−0.629375	+	1.09011i	0.358303	+	0.933606i	$0.383356\pi$
$41$	−4.02997	+	6.98010i	−0.629375	+	1.09011i	−0.987677	+	0.156504i	$0.949978\pi$
$42$	0.624241	+	0.582362i	0.0963226	+	0.0898605i
$43$	5.27705	−	3.04671i	0.804743	−	0.464619i	−0.0403838	−	0.999184i	$-0.512858\pi$
$43$	5.27705	−	3.04671i	0.804743	−	0.464619i	0.845127	+	0.534566i	$0.179525\pi$
$44$	−3.27216	−	3.10097i	−0.493297	−	0.467489i
$45$	−7.45733	+	0.518286i	−1.11167	+	0.0772614i
$46$	−0.255200	+	0.147340i	−0.0376272	+	0.0217241i
$47$		−	0.492431i		−	0.0718284i	−0.999355	−	0.0359142i	$-0.988566\pi$
$47$		−	0.492431i		−	0.0718284i	0.999355	−	0.0359142i	$-0.0114343\pi$
$48$	−0.286448	−	0.937642i	−0.0413453	−	0.135337i
$49$	−3.31043	+	5.73382i	−0.472918	+	0.819118i
$50$	0.483855	−	0.838061i	0.0684274	−	0.118520i
$51$	6.85782	+	1.58479i	0.960287	+	0.221914i
$52$	0.539306	−	4.87107i	0.0747882	−	0.675496i
$53$		−	7.11354i		−	0.977120i	−0.872530	−	0.488560i	$-0.837522\pi$
$53$		−	7.11354i		−	0.977120i	0.872530	−	0.488560i	$-0.162478\pi$
$54$	−3.88405	+	1.48811i	−0.528552	+	0.202506i
$55$	2.35252	+	7.92236i	0.317214	+	1.06825i
$56$	1.43391	−	0.827871i	0.191615	−	0.110629i
$57$	2.33409	−	10.1003i	0.309157	−	1.33781i
$58$	0.997221	+	1.72724i	0.130942	+	0.226797i
$59$	−8.67632	+	5.00927i	−1.12956	+	0.652152i	−0.943824	−	0.330448i	$-0.892800\pi$
$59$	−8.67632	+	5.00927i	−1.12956	+	0.652152i	−0.185736	+	0.982600i	$0.559467\pi$
$60$	−1.32085	+	5.71571i	−0.170521	+	0.737894i
$61$	2.96548	−	1.71212i	0.379691	−	0.219214i	−0.297993	−	0.954568i	$-0.596317\pi$
$61$	2.96548	−	1.71212i	0.379691	−	0.219214i	0.677684	+	0.735354i	$0.262984\pi$
$62$	1.07016	−	1.85358i	0.135911	−	0.235405i
$63$	1.03232	+	1.53188i	0.130060	+	0.192999i
$64$	3.53550			0.441937
$65$	−5.32102	+	7.23897i	−0.659992	+	0.897884i
$66$	2.53977	+	3.83333i	0.312624	+	0.471850i
$67$	−1.28542	+	2.22641i	−0.157039	+	0.271999i	−0.933799	−	0.357797i	$-0.883528\pi$
$67$	−1.28542	+	2.22641i	−0.157039	+	0.271999i	0.776761	+	0.629796i	$0.216861\pi$
$68$	2.76179	−	4.78357i	0.334917	−	0.580093i
$69$	−0.609804	+	0.186294i	−0.0734118	+	0.0224272i
$70$	−1.22817			−0.146794
$71$	−12.6355	+	7.29512i	−1.49956	+	0.865771i	−1.00000		0.000508264i	$-0.999838\pi$
$71$	−12.6355	+	7.29512i	−1.49956	+	0.865771i	−0.499560	+	0.866279i	$0.666505\pi$
$72$	0.559304	+	8.04752i	0.0659146	+	0.948410i
$73$			15.9862i			1.87104i	0.353272	+	0.935521i	$0.385069\pi$
$73$			15.9862i			1.87104i	−0.353272	+	0.935521i	$0.614931\pi$
$74$	3.05240	+	5.28691i	0.354834	+	0.614590i
$75$	1.42838	−	1.53109i	0.164935	−	0.176795i
$76$	−7.04528	−	4.06759i	−0.808149	−	0.466585i
$77$	1.40477	−	1.48232i	0.160088	−	0.168926i
$78$	−1.65469	+	4.71714i	−0.187357	+	0.534110i
$79$		−	8.77299i		−	0.987038i	−0.869735	−	0.493519i	$-0.835710\pi$
$79$		−	8.77299i		−	0.987038i	0.869735	−	0.493519i	$-0.164290\pi$
$80$	1.22149	+	0.705229i	0.136567	+	0.0788470i
$81$	−8.91347	+	1.24499i	−0.990386	+	0.138332i
$82$	−3.22587	−	5.58737i	−0.356238	−	0.617022i
$83$	1.41718			0.155556			0.0777780	−	0.996971i	$-0.475217\pi$
$83$	1.41718			0.155556			0.0777780	+	0.996971i	$0.475217\pi$
$84$	1.38640	−	0.423543i	0.151269	−	0.0462124i
$85$	−8.76923	+	5.06292i	−0.951157	+	0.549151i
$86$			4.87760i			0.525965i
$87$	1.26087	+	4.12725i	0.135179	+	0.442488i
$88$	8.54936	−	2.53871i	0.911365	−	0.270627i
$89$	−0.846297	−	0.488610i	−0.0897073	−	0.0517925i	0.454475	−	0.890759i	$-0.349827\pi$
$89$	−0.846297	−	0.488610i	−0.0897073	−	0.0517925i	−0.544183	+	0.838967i	$0.683160\pi$
$90$	2.62539	−	5.37706i	0.276741	−	0.566792i
$91$	2.20664	+	0.244310i	0.231319	+	0.0256107i
$92$			0.500384i			0.0521686i
$93$	3.15920	−	3.38639i	0.327594	−	0.351152i
$94$	0.341367	+	0.197088i	0.0352093	+	0.0203281i
$95$	7.45671	+	12.9154i	0.765042	+	1.32509i
$96$	9.84035	+	2.27403i	1.00433	+	0.232092i
$97$	5.19256	+	8.99377i	0.527224	+	0.913179i	0.999497	+	0.0317264i	$0.0101005\pi$
$97$	5.19256	+	8.99377i	0.527224	+	0.913179i	−0.472272	+	0.881453i	$0.656566\pi$
$98$	−2.64990	−	4.58976i	−0.267680	−	0.463636i
$99$	3.48685	+	9.31890i	0.350441	+	0.936585i
$100$	−0.821614	−	1.42308i	−0.0821614	−	0.142308i
$101$	−8.02789	+	13.9047i	−0.798805	+	1.38357i	0.121590	+	0.992580i	$0.461201\pi$
$101$	−8.02789	+	13.9047i	−0.798805	+	1.38357i	−0.920395	+	0.390990i	$0.872133\pi$
$102$	−3.84336	+	4.11974i	−0.380549	+	0.407915i
$103$	−4.60515			−0.453759			−0.226879	−	0.973923i	$-0.572852\pi$
$103$	−4.60515			−0.453759			−0.226879	+	0.973923i	$0.572852\pi$
$104$	7.81189	+	5.74215i	0.766019	+	0.563064i
$105$	−2.58927	−	0.598358i	−0.252686	−	0.0583938i
$106$	4.93130	+	2.84709i	0.478971	+	0.276534i
$107$	3.06684	−	5.31191i	0.296482	−	0.513522i	−0.678846	−	0.734280i	$-0.737520\pi$
$107$	3.06684	−	5.31191i	0.296482	−	0.513522i	0.975329	+	0.220758i	$0.0708531\pi$
$108$	−1.10932	+	6.97519i	−0.106744	+	0.671188i
$109$		−	14.1446i		−	1.35481i	−0.735609	−	0.677406i	$-0.763104\pi$
$109$		−	14.1446i		−	1.35481i	0.735609	−	0.677406i	$-0.236896\pi$
$110$	−6.43356	−	1.53997i	−0.613416	−	0.146831i
$111$	3.85940	+	12.6331i	0.366318	+	1.19908i
$112$		−	0.348544i		−	0.0329343i
$113$	2.01327	−	1.16236i	0.189392	−	0.109346i	−0.402306	−	0.915505i	$-0.631791\pi$
$113$	2.01327	−	1.16236i	0.189392	−	0.109346i	0.591698	+	0.806160i	$0.298458\pi$
$114$	6.06759	+	5.66053i	0.568282	+	0.530157i
$115$	0.458652	−	0.794409i	0.0427695	−	0.0740790i
$116$	3.38668			0.314446
$117$	−5.78663	+	9.13865i	−0.534974	+	0.844868i
$118$		−	8.01955i		−	0.738260i
$119$	2.16700	+	1.25112i	0.198648	+	0.114690i
$120$	−8.48589	−	7.91659i	−0.774653	−	0.722683i
$121$	9.21729	−	6.00347i	0.837935	−	0.545770i
$122$			2.74100i			0.248159i
$123$	−4.07874	−	13.3511i	−0.367767	−	1.20383i
$124$	−1.81720	−	3.14749i	−0.163190	−	0.282653i
$125$		−	9.44649i		−	0.844920i
$126$	−1.47511	+	0.102521i	−0.131414	+	0.00913327i
$127$	−3.10405	−	1.79213i	−0.275440	−	0.159025i	0.355917	−	0.934518i	$-0.384169\pi$
$127$	−3.10405	−	1.79213i	−0.275440	−	0.159025i	−0.631357	+	0.775492i	$0.717502\pi$
$128$	4.41603	−	7.64879i	0.390325	−	0.676064i
$129$	−2.37634	+	10.2831i	−0.209225	+	0.905377i
$130$	−2.88860	−	6.58597i	−0.253347	−	0.577628i
$131$	14.9707			1.30800			0.653999	−	0.756496i	$-0.273090\pi$
$131$	14.9707			1.30800			0.653999	+	0.756496i	$0.273090\pi$
$132$	7.79349	−	0.480285i	0.678337	−	0.0418035i
$133$	1.84266	−	3.19157i	0.159779	−	0.276745i
$134$	−1.02894	−	1.78217i	−0.0888867	−	0.153956i
$135$	8.15461	−	10.0570i	0.701837	−	0.865569i
$136$	5.46362	+	9.46326i	0.468501	+	0.811468i
$137$	−11.8492	+	6.84113i	−1.01234	+	0.584478i	−0.911877	−	0.410463i	$-0.865367\pi$
$137$	−11.8492	+	6.84113i	−1.01234	+	0.584478i	−0.100467	+	0.994940i	$0.532034\pi$
$138$	0.114921	−	0.497295i	0.00978270	−	0.0423325i
$139$	−8.39569	+	4.84725i	−0.712113	+	0.411139i	−0.811843	−	0.583876i	$-0.801535\pi$
$139$	−8.39569	+	4.84725i	−0.712113	+	0.411139i	0.0997300	+	0.995015i	$0.468202\pi$
$140$	−1.04275	+	1.80610i	−0.0881288	+	0.152644i
$141$	0.623659	+	0.581819i	0.0525216	+	0.0489980i
$142$		−	11.6791i		−	0.980084i
$143$	11.2528	+	4.04663i	0.941004	+	0.338396i
$144$	1.52596	+	0.745063i	0.127163	+	0.0620886i
$145$	−5.37669	−	3.10423i	−0.446510	−	0.257792i
$146$	−11.0821	−	6.39823i	−0.917158	−	0.529522i
$147$	−3.35049	−	10.9673i	−0.276344	−	0.904566i
$148$	10.3663			0.852105
$149$	−7.10007	−	12.2977i	−0.581661	−	1.00747i	−0.995283	−	0.0970171i	$-0.969070\pi$
$149$	−7.10007	−	12.2977i	−0.581661	−	1.00747i	0.413622	−	0.910449i	$-0.364263\pi$
$150$	0.489710	+	1.60299i	0.0399847	+	0.130883i
$151$		−	7.78883i		−	0.633846i	−0.948451	−	0.316923i	$-0.897350\pi$
$151$		−	7.78883i		−	0.633846i	0.948451	−	0.316923i	$-0.102650\pi$
$152$	13.9376	−	8.04686i	1.13049	−	0.652686i
$153$	−10.1098	+	6.81290i	−0.817329	+	0.550791i
$154$	0.465346	+	1.56710i	0.0374987	+	0.126281i
$155$			6.66259i			0.535152i
$156$	5.53196	+	6.43832i	0.442912	+	0.515478i
$157$	−9.09630			−0.725964			−0.362982	−	0.931796i	$-0.618241\pi$
$157$	−9.09630			−0.725964			−0.362982	+	0.931796i	$0.618241\pi$
$158$	6.08168	+	3.51126i	0.483832	+	0.279341i
$159$	9.00924	+	8.40482i	0.714479	+	0.666546i
$160$	−12.5831	+	7.26483i	−0.994778	+	0.574336i
$161$	−0.226678			−0.0178648
$162$	2.70442	−	6.67736i	0.212480	−	0.524623i
$163$	−7.04235	−	12.1977i	−0.551599	−	0.955398i	−0.998159	−	0.0606445i	$-0.980684\pi$
$163$	−7.04235	−	12.1977i	−0.551599	−	0.955398i	0.446560	−	0.894754i	$-0.352649\pi$
$164$	−10.9554			−0.855476
$165$	−12.8132	−	6.38102i	−0.997503	−	0.496762i
$166$	−0.567206	+	0.982430i	−0.0440237	+	0.0762513i
$167$	−4.93188	+	8.54227i	−0.381640	+	0.661020i	−0.991297	−	0.131645i	$-0.957974\pi$
$167$	−4.93188	+	8.54227i	−0.381640	+	0.661020i	0.609657	+	0.792666i	$0.291307\pi$
$168$	−0.645714	+	2.79419i	−0.0498179	+	0.215576i
$169$	3.87981	+	12.4075i	0.298447	+	0.954426i
$170$		−	8.10544i		−	0.621659i
$171$	10.0341	+	14.8898i	0.767327	+	1.13865i
$172$	7.17282	+	4.14123i	0.546922	+	0.315766i
$173$	−1.41704	−	2.45439i	−0.107736	−	0.186604i	0.807117	−	0.590392i	$-0.201027\pi$
$173$	−1.41704	−	2.45439i	−0.107736	−	0.186604i	−0.914853	+	0.403788i	$0.867693\pi$
$174$	−3.36577	−	0.777802i	−0.255158	−	0.0589650i
$175$	0.644667	−	0.372199i	0.0487322	−	0.0281356i
$176$	0.437031	−	1.82579i	0.0329424	−	0.137624i
$177$	3.90708	−	16.9071i	0.293674	−	1.27081i
$178$	0.677436	−	0.391118i	0.0507759	−	0.0293155i
$179$	12.7591	+	7.36649i	0.953662	+	0.550597i	0.894217	−	0.447635i	$-0.147733\pi$
$179$	12.7591	+	7.36649i	0.953662	+	0.550597i	0.0594454	+	0.998232i	$0.481067\pi$
$180$	−5.67827	−	8.42610i	−0.423233	−	0.628044i
$181$	−1.44843			−0.107661			−0.0538306	−	0.998550i	$-0.517143\pi$
$181$	−1.44843			−0.107661			−0.0538306	+	0.998550i	$0.517143\pi$
$182$	−1.05254	+	1.43192i	−0.0780193	+	0.106141i
$183$	−1.33540	+	5.77866i	−0.0987157	+	0.427171i
$184$	−0.857281	−	0.494951i	−0.0631996	−	0.0364883i
$185$	−16.4575	−	9.50175i	−1.20998	−	0.698583i
$186$	1.08311	+	3.54540i	0.0794178	+	0.259961i
$187$	9.78271	+	9.27091i	0.715383	+	0.677956i
$188$	0.579661	−	0.334667i	0.0422761	−	0.0244081i
$189$	−3.15983	−	0.502530i	−0.229843	−	0.0365537i
$190$	−11.9378			−0.866056
$191$	−17.4965	+	10.1016i	−1.26600	+	0.730926i	−0.974229	−	0.225562i	$-0.927578\pi$
$191$	−17.4965	+	10.1016i	−1.26600	+	0.730926i	−0.291772	+	0.956488i	$0.594245\pi$
$192$	−4.17728	+	4.47768i	−0.301469	+	0.323148i
$193$	13.9432	+	8.05014i	1.00366	+	0.579461i	0.909328	−	0.416080i	$-0.136596\pi$
$193$	13.9432	+	8.05014i	1.00366	+	0.579461i	0.0943286	+	0.995541i	$0.469930\pi$
$194$	−8.31297			−0.596837
$195$	−2.88117	−	15.2921i	−0.206325	−	1.09509i
$196$	−8.99937			−0.642812
$197$	2.47703	−	4.29034i	0.176481	−	0.305674i	−0.764192	−	0.644989i	$-0.776862\pi$
$197$	2.47703	−	4.29034i	0.176481	−	0.305674i	0.940673	+	0.339315i	$0.110195\pi$
$198$	−7.85568	−	1.31257i	−0.558279	−	0.0932805i
$199$	−2.51081	−	4.34885i	−0.177987	−	0.308282i	0.763204	−	0.646157i	$-0.223625\pi$
$199$	−2.51081	−	4.34885i	−0.177987	−	0.308282i	−0.941191	+	0.337876i	$0.890292\pi$
$200$	3.25077			0.229864
$201$	−1.30097	−	4.25852i	−0.0917636	−	0.300373i
$202$	−6.42609	−	11.1303i	−0.452138	−	0.783126i
$203$			1.53420i			0.107680i
$204$	2.79522	+	9.14969i	0.195704	+	0.640606i
$205$	17.3928	+	10.0418i	1.21477	+	0.701346i
$206$	1.84314	−	3.19242i	0.128418	−	0.222426i
$207$	0.484558	−	0.992422i	0.0336791	−	0.0689781i
$208$	1.86904	−	0.819757i	0.129595	−	0.0568399i
$209$	13.6543	−	14.4081i	0.944486	−	0.996626i
$210$	1.45111	−	1.55547i	0.100136	−	0.107337i
$211$	−12.9411	−	7.47157i	−0.890905	−	0.514364i	−0.0166668	−	0.999861i	$-0.505305\pi$
$211$	−12.9411	−	7.47157i	−0.890905	−	0.514364i	−0.874239	+	0.485497i	$0.838639\pi$
$212$	8.37365	−	4.83453i	0.575105	−	0.332037i
$213$	5.68997	−	24.6221i	0.389870	−	1.68708i
$214$	2.45491	+	4.25203i	0.167814	+	0.290663i
$215$	−7.59170	−	13.1492i	−0.517750	−	0.896769i
$216$	−10.8529	−	8.79999i	−0.738449	−	0.598764i
$217$	1.42584	−	0.823209i	0.0967923	−	0.0558831i
$218$	9.80546	+	5.66119i	0.664110	+	0.383424i
$219$	−20.2464	−	18.8881i	−1.36812	−	1.27634i
$220$	−7.72692	+	8.15348i	−0.520949	+	0.549707i
$221$	−1.61235	+	14.5629i	−0.108458	+	0.979609i
$222$	−10.3023	−	2.38078i	−0.691445	−	0.159787i
$223$	12.2861	−	21.2802i	0.822741	−	1.42503i	−0.0808925	−	0.996723i	$-0.525777\pi$
$223$	12.2861	−	21.2802i	0.822741	−	1.42503i	0.903634	−	0.428306i	$-0.140890\pi$
$224$	3.10945	+	1.79524i	0.207759	+	0.119950i
$225$	0.251455	+	3.61805i	0.0167637	+	0.241203i
$226$			1.86087i			0.123783i
$227$	−0.214356	−	0.371276i	−0.0142273	−	0.0246424i	0.858824	−	0.512271i	$-0.171196\pi$
$227$	−0.214356	−	0.371276i	−0.0142273	−	0.0246424i	−0.873051	+	0.487628i	$0.837862\pi$
$228$	13.4757	−	4.11682i	0.892453	−	0.272643i
$229$	3.73042			0.246513			0.123256	−	0.992375i	$-0.460666\pi$
$229$	3.73042			0.246513			0.123256	+	0.992375i	$0.460666\pi$
$230$	0.367137	+	0.635901i	0.0242083	+	0.0419300i
$231$	0.217573	+	3.53052i	0.0143153	+	0.232291i
$232$	−3.34991	+	5.80222i	−0.219932	+	0.380934i
$233$	−24.5862			−1.61069			−0.805347	−	0.592804i	$-0.798021\pi$
$233$	−24.5862			−1.61069			−0.805347	+	0.592804i	$0.798021\pi$
$234$	−4.01915	−	7.66906i	−0.262740	−	0.501342i
$235$	−1.22702			−0.0800422
$236$	−11.7933	−	6.80884i	−0.767676	−	0.443218i
$237$	11.1109	+	10.3655i	0.721731	+	0.673312i
$238$	−1.73462	+	1.00148i	−0.112439	+	0.0649165i
$239$	21.4950			1.39040			0.695199	−	0.718817i	$-0.255316\pi$
$239$	21.4950			1.39040			0.695199	+	0.718817i	$0.255316\pi$
$240$	−2.33639	+	0.713764i	−0.150813	+	0.0460733i
$241$	9.78158	−	5.64740i	0.630087	−	0.363781i	−0.150699	−	0.988580i	$-0.548152\pi$
$241$	9.78158	−	5.64740i	0.630087	−	0.363781i	0.780786	+	0.624799i	$0.214819\pi$
$242$	0.472686	+	8.79248i	0.0303854	+	0.565202i
$243$	8.95472	−	12.7598i	0.574446	−	0.818543i
$244$	4.03082	+	2.32719i	0.258047	+	0.148983i
$245$	14.2874	+	8.24882i	0.912787	+	0.526998i
$246$	10.8878	+	2.51608i	0.694180	+	0.160419i
$247$	21.4484	+	2.37468i	1.36473	+	0.151097i
$248$	7.18989			0.456558
$249$	−1.67444	+	1.79485i	−0.106113	+	0.113744i
$250$	6.54857	+	3.78082i	0.414168	+	0.239120i
$251$	−0.742803	+	0.428858i	−0.0468853	+	0.0270693i	−0.523259	−	0.852173i	$-0.675284\pi$
$251$	−0.742803	+	0.428858i	−0.0468853	+	0.0270693i	0.476374	+	0.879243i	$0.341951\pi$
$252$	−1.10165	+	2.25629i	−0.0693976	+	0.142133i
$253$	−1.18742	−	0.284227i	−0.0746522	−	0.0178692i
$254$	2.48470	−	1.43454i	0.155904	−	0.0900113i
$255$	3.94892	−	17.0881i	0.247291	−	1.07010i
$256$	7.07040	+	12.2463i	0.441900	+	0.765393i
$257$	17.0195	+	9.82620i	1.06165	+	0.612942i	0.925887	−	0.377800i	$-0.123319\pi$
$257$	17.0195	+	9.82620i	1.06165	+	0.612942i	0.135759	+	0.990742i	$0.456653\pi$
$258$	−6.17744	−	5.76301i	−0.384590	−	0.358789i
$259$			4.69603i			0.291797i
$260$	−12.1376	−	1.34383i	−0.752742	−	0.0833406i
$261$	−6.71688	−	3.27957i	−0.415764	−	0.203000i
$262$	−5.99181	+	10.3781i	−0.370175	+	0.641162i
$263$	12.0497	−	20.8706i	0.743014	−	1.28694i	−0.208103	−	0.978107i	$-0.566729\pi$
$263$	12.0497	−	20.8706i	0.743014	−	1.28694i	0.951117	−	0.308831i	$-0.0999377\pi$
$264$	−6.88603	+	13.8272i	−0.423806	+	0.851008i
$265$	−17.7253			−1.08886
$266$	1.47499	+	2.55476i	0.0904375	+	0.156642i
$267$	1.61874	−	0.494523i	0.0990653	−	0.0302643i
$268$	−3.49440			−0.213454
$269$	24.2182	−	13.9824i	1.47661	−	0.852520i	0.476956	−	0.878927i	$-0.341740\pi$
$269$	24.2182	−	13.9824i	1.47661	−	0.852520i	0.999651	+	0.0264072i	$0.00840666\pi$
$270$	3.70803	+	9.67817i	0.225664	+	0.588995i
$271$	7.96773	+	4.60017i	0.484005	+	0.279441i	0.722084	−	0.691805i	$-0.243184\pi$
$271$	7.96773	+	4.60017i	0.484005	+	0.279441i	−0.238079	+	0.971246i	$0.576518\pi$
$272$	2.30025			0.139473
$273$	−2.91662	+	2.50603i	−0.176522	+	0.151672i
$274$		−	10.9523i		−	0.661650i
$275$	3.84367	−	1.14137i	0.231782	−	0.0688270i
$276$	−0.633732	−	0.591216i	−0.0381462	−	0.0355870i
$277$	−19.3167	+	11.1525i	−1.16063	+	0.670089i	−0.951455	−	0.307789i	$-0.900411\pi$
$277$	−19.3167	+	11.1525i	−1.16063	+	0.670089i	−0.209174	+	0.977878i	$0.567078\pi$
$278$		−	7.76016i		−	0.465424i
$279$	0.556155	+	8.00221i	0.0332961	+	0.479079i
$280$	−2.06286	−	3.57299i	−0.123280	−	0.213527i
$281$	26.3512			1.57198			0.785991	−	0.618238i	$-0.212153\pi$
$281$	26.3512			1.57198			0.785991	+	0.618238i	$0.212153\pi$
$282$	−0.652943	+	0.199473i	−0.0388822	+	0.0118785i
$283$	−16.4003	−	9.46873i	−0.974898	−	0.562857i	−0.0741718	−	0.997245i	$-0.523631\pi$
$283$	−16.4003	−	9.46873i	−0.974898	−	0.562857i	−0.900726	+	0.434388i	$0.856965\pi$
$284$	−17.1748	−	9.91587i	−1.01914	−	0.588398i
$285$	−25.1675	−	5.81601i	−1.49080	−	0.344511i
$286$	−7.30899	+	6.18113i	−0.432190	+	0.365498i
$287$		−	4.96291i		−	0.292951i
$288$	−14.5067	+	9.77590i	−0.854813	+	0.576051i
$289$	0.243125	−	0.421105i	0.0143015	−	0.0247709i
$290$	4.30388	−	2.48485i	0.252733	−	0.145915i
$291$	−17.5257	−	4.05004i	−1.02737	−	0.237417i
$292$	−18.8180	+	10.8646i	−1.10124	+	0.635802i
$293$	−8.29686	−	14.3706i	−0.484708	−	0.839538i	0.515138	−	0.857107i	$-0.327741\pi$
$293$	−8.29686	−	14.3706i	−0.484708	−	0.839538i	−0.999846	+	0.0175690i	$0.994407\pi$
$294$	8.94381	+	2.06684i	0.521613	+	0.120541i
$295$	12.4820	+	21.6194i	0.726728	+	1.25873i
$296$	−10.2538	+	17.7600i	−0.595987	+	1.03228i
$297$	−15.9221	−	6.59445i	−0.923894	−	0.382649i
$298$	11.3668			0.658461
$299$	−0.533136	−	1.21555i	−0.0308321	−	0.0702969i
$300$	2.77307	+	0.640834i	0.160103	+	0.0369986i
$301$	−1.87601	+	3.24935i	−0.108132	+	0.187290i
$302$	5.39943	+	3.11736i	0.310702	+	0.179384i
$303$	−8.12504	−	26.5960i	−0.466771	−	1.52790i
$304$		−	3.38783i		−	0.194305i
$305$	−4.26621	−	7.38929i	−0.244283	−	0.423110i
$306$	−0.676595	−	9.73516i	−0.0386784	−	0.556522i
$307$		−	5.84463i		−	0.333570i	−0.985993	−	0.166785i	$-0.946661\pi$
$307$		−	5.84463i		−	0.333570i	0.985993	−	0.166785i	$-0.0533386\pi$
$308$	2.69961	+	0.646195i	0.153825	+	0.0368204i
$309$	5.44110	−	5.83238i	0.309533	−	0.331793i
$310$	−4.61869	−	2.66660i	−0.262324	−	0.151453i
$311$			33.1390i			1.87914i	0.342355	+	0.939571i	$0.388775\pi$
$311$			33.1390i			1.87914i	−0.342355	+	0.939571i	$0.611225\pi$
$312$	−16.5023	+	3.10920i	−0.934260	+	0.176024i
$313$	−27.9123			−1.57770			−0.788848	−	0.614589i	$-0.789322\pi$
$313$	−27.9123			−1.57770			−0.788848	+	0.614589i	$0.789322\pi$
$314$	3.64066	−	6.30581i	0.205454	−	0.355857i
$315$	3.81710	−	2.57231i	0.215069	−	0.144933i
$316$	10.3271	−	5.96233i	0.580942	−	0.335407i
$317$			8.06428i			0.452935i	0.974019	+	0.226468i	$0.0727177\pi$
$317$			8.06428i			0.452935i	−0.974019	+	0.226468i	$0.927282\pi$
$318$	−9.43227	+	2.88155i	−0.528935	+	0.161589i
$319$	−1.92369	+	8.03663i	−0.107706	+	0.449965i
$320$		−	8.80965i		−	0.492475i
$321$	3.10395	+	10.1603i	0.173246	+	0.567091i
$322$	0.0907247	−	0.157140i	0.00505589	−	0.00875706i
$323$	21.0631	+	12.1608i	1.17198	+	0.676645i
$324$	−7.52334	−	9.64630i	−0.417963	−	0.535906i
$325$	3.51211	+	2.58159i	0.194817	+	0.143201i
$326$	11.2744			0.624431
$327$	17.9141	+	16.7123i	0.990650	+	0.924190i
$328$	10.8365	−	18.7693i	0.598345	−	1.03636i
$329$	0.151607	+	0.262592i	0.00835838	+	0.0144771i
$330$	9.55178	−	6.32853i	0.525808	−	0.348374i
$331$	−7.28170	−	12.6123i	−0.400239	−	0.693233i	0.593516	−	0.804822i	$-0.297739\pi$
$331$	−7.28170	−	12.6123i	−0.400239	−	0.693233i	−0.993754	+	0.111589i	$0.964406\pi$
$332$	0.963150	+	1.66822i	0.0528597	+	0.0915557i
$333$	−20.5597	−	10.0384i	−1.12667	−	0.550104i
$334$	−3.94782	−	6.83783i	−0.216015	−	0.374150i
$335$	5.54770	+	3.20297i	0.303103	+	0.174997i
$336$	0.441427	+	0.411813i	0.0240818	+	0.0224662i
$337$			9.46350i			0.515510i	0.966210	+	0.257755i	$0.0829827\pi$
$337$			9.46350i			0.515510i	−0.966210	+	0.257755i	$0.917017\pi$
$338$	−10.1541	−	2.27634i	−0.552310	−	0.123817i
$339$	−0.906606	+	3.92314i	−0.0492401	+	0.213076i
$340$	−11.9196	−	6.88176i	−0.646429	−	0.373216i
$341$	8.50122	−	2.52441i	0.460367	−	0.136705i
$342$	−14.3380	+	0.996495i	−0.775311	+	0.0538843i
$343$		−	8.38705i		−	0.452858i
$344$	−14.1899	+	8.19253i	−0.765067	+	0.441712i
$345$	0.464203	+	1.51949i	0.0249918	+	0.0818067i
$346$	2.26860			0.121961
$347$	9.49861	+	16.4521i	0.509912	+	0.883193i	0.999934	+	0.0114834i	$0.00365535\pi$
$347$	9.49861	+	16.4521i	0.509912	+	0.883193i	−0.490022	+	0.871710i	$0.663011\pi$
$348$	−4.00145	+	4.28920i	−0.214500	+	0.229925i
$349$	−16.6870	−	9.63426i	−0.893236	−	0.515710i	−0.0182363	−	0.999834i	$-0.505805\pi$
$349$	−16.6870	−	9.63426i	−0.893236	−	0.515710i	−0.875000	+	0.484124i	$0.839138\pi$
$350$			0.595868i			0.0318505i
$351$	−4.73697	−	18.1263i	−0.252841	−	0.967508i
$352$	14.0373	+	13.3029i	0.748191	+	0.709048i
$353$	−4.32646	−	2.49788i	−0.230274	−	0.132949i	0.380424	−	0.924812i	$-0.375778\pi$
$353$	−4.32646	−	2.49788i	−0.230274	−	0.132949i	−0.610699	+	0.791863i	$0.709111\pi$
$354$	10.1567	+	9.47530i	0.539822	+	0.503606i
$355$	18.1778	+	31.4848i	0.964776	+	1.67104i
$356$		−	1.32828i		−	0.0703988i
$357$	−4.14489	+	1.26626i	−0.219371	+	0.0670175i
$358$	−10.2133	+	5.89665i	−0.539790	+	0.311648i
$359$	12.9015			0.680915			0.340457	−	0.940260i	$-0.389418\pi$
$359$	12.9015			0.680915			0.340457	+	0.940260i	$0.389418\pi$
$360$	20.0526	−	1.39366i	1.05686	−	0.0734522i
$361$	8.41052	−	14.5674i	0.442659	−	0.766707i
$362$	0.579714	−	1.00409i	0.0304691	−	0.0527741i
$363$	−3.28712	+	18.7669i	−0.172529	+	0.985004i
$364$	1.21210	+	2.76357i	0.0635311	+	0.144850i
$365$	39.8339			2.08500
$366$	−3.47145	−	3.23856i	−0.181456	−	0.169282i
$367$	−2.46499	+	4.26949i	−0.128671	+	0.222865i	−0.923162	−	0.384411i	$-0.874405\pi$
$367$	−2.46499	+	4.26949i	−0.128671	+	0.222865i	0.794491	+	0.607276i	$0.207738\pi$
$368$	−0.180463	+	0.104190i	−0.00940728	+	0.00543129i
$369$	21.7281	+	10.6089i	1.13112	+	0.552280i
$370$	13.1738	−	7.60587i	0.684871	−	0.395411i
$371$	2.19009	+	3.79334i	0.113704	+	0.196940i
$372$	6.13333	+	1.41736i	0.317998	+	0.0734868i
$373$	7.21454	−	4.16532i	0.373555	−	0.215672i	−0.301456	−	0.953480i	$-0.597473\pi$
$373$	7.21454	−	4.16532i	0.373555	−	0.215672i	0.675010	+	0.737808i	$0.264139\pi$
$374$	−10.3422	+	3.07110i	−0.534785	+	0.158803i
$375$	11.9639	+	11.1613i	0.617813	+	0.576365i
$376$			1.32413i			0.0682870i
$377$	−8.22702	+	3.60836i	−0.423713	+	0.185840i
$378$	1.61304	−	1.98935i	0.0829659	−	0.102321i
$379$	10.4160	−	18.0410i	0.535032	−	0.926703i	−0.464129	−	0.885767i	$-0.653633\pi$
$379$	10.4160	−	18.0410i	0.535032	−	0.926703i	0.999162	−	0.0409359i	$-0.0130339\pi$
$380$	−10.1355	+	17.5552i	−0.519941	+	0.900564i
$381$	5.93723	−	1.81381i	0.304173	−	0.0929245i
$382$		−	16.1721i		−	0.827435i
$383$	−1.09145	+	0.630147i	−0.0557703	+	0.0321990i	−0.527626	−	0.849477i	$-0.676918\pi$
$383$	−1.09145	+	0.630147i	−0.0557703	+	0.0321990i	0.471856	+	0.881676i	$0.343584\pi$
$384$	4.46947	+	14.6301i	0.228082	+	0.746589i
$385$	−3.69360	−	3.50036i	−0.188243	−	0.178395i
$386$	−11.1612	+	6.44390i	−0.568088	+	0.327986i
$387$	−10.2158	−	15.1594i	−0.519296	−	0.770593i
$388$	−7.05797	+	12.2248i	−0.358314	+	0.620618i
$389$			38.7801i			1.96623i	0.182989	+	0.983115i	$0.441423\pi$
$389$			38.7801i			1.96623i	−0.182989	+	0.983115i	$0.558577\pi$
$390$	11.7540	+	4.12311i	0.595188	+	0.208782i
$391$		−	1.49599i		−	0.0756553i
$392$	8.90166	−	15.4181i	0.449602	−	0.778733i
$393$	−17.6883	+	18.9603i	−0.892255	+	0.956420i
$394$	1.98279	+	3.43429i	0.0998914	+	0.173017i
$395$	−21.8603			−1.09991
$396$	−8.59993	+	10.4379i	−0.432163	+	0.524522i
$397$	16.9512	+	29.3603i	0.850755	+	1.47355i	0.880528	+	0.473995i	$0.157188\pi$
$397$	16.9512	+	29.3603i	0.850755	+	1.47355i	−0.0297724	+	0.999557i	$0.509478\pi$
$398$	4.01966			0.201487
$399$	1.86496	+	6.10463i	0.0933646	+	0.305614i
$400$	0.342154	−	0.592628i	0.0171077	−	0.0296314i
$401$	−20.8560	−	12.0412i	−1.04150	−	0.601310i	−0.121241	−	0.992623i	$-0.538688\pi$
$401$	−20.8560	−	12.0412i	−1.04150	−	0.601310i	−0.920257	+	0.391313i	$0.872021\pi$
$402$	3.47282	+	0.802541i	0.173209	+	0.0400271i
$403$	7.76790	+	5.70981i	0.386947	+	0.284426i
$404$	−21.8238			−1.08577
$405$	3.10223	+	22.2103i	0.154151	+	1.10364i
$406$	−1.06355	−	0.614040i	−0.0527830	−	0.0304743i
$407$	−5.88824	+	24.5994i	−0.291869	+	1.21934i
$408$	−18.4405	−	4.26145i	−0.912942	−	0.210973i
$409$	9.55481	−	5.51647i	0.472455	−	0.272772i	−0.244812	−	0.969571i	$-0.578726\pi$
$409$	9.55481	−	5.51647i	0.472455	−	0.272772i	0.717267	+	0.696799i	$0.245393\pi$
$410$	−13.9224	+	8.03813i	−0.687580	+	0.396975i
$411$	5.33588	−	23.0899i	0.263199	−	1.13894i
$412$	−3.12977	−	5.42092i	−0.154193	−	0.267069i
$413$	3.08447	−	5.34245i	0.151777	−	0.262885i
$414$	0.494037	+	0.733112i	0.0242806	+	0.0360305i
$415$		−	3.53129i		−	0.173344i
$416$	−2.31358	+	20.8965i	−0.113432	+	1.02454i
$417$	3.78071	−	16.3602i	0.185142	−	0.801163i
$418$	4.52314	+	15.2321i	0.221234	+	0.745028i
$419$	−10.0282	−	5.78976i	−0.489908	−	0.282848i	0.234628	−	0.972085i	$-0.424613\pi$
$419$	−10.0282	−	5.78976i	−0.489908	−	0.282848i	−0.724536	+	0.689237i	$0.757946\pi$
$420$	−1.05537	−	3.45459i	−0.0514969	−	0.168567i
$421$	7.91744			0.385873			0.192936	−	0.981211i	$-0.438199\pi$
$421$	7.91744			0.385873			0.192936	+	0.981211i	$0.438199\pi$
$422$	10.3590	−	5.98078i	0.504269	−	0.291140i
$423$	−1.47374	+	0.102425i	−0.0716555	+	0.00498007i
$424$			19.1282i			0.928945i
$425$	2.45636	+	4.25454i	0.119151	+	0.206376i
$426$	14.7914	+	13.7991i	0.716646	+	0.668568i
$427$	−1.05424	+	1.82600i	−0.0510182	+	0.0883662i
$428$	8.33717			0.402992
$429$	−18.4204	+	9.47033i	−0.889347	+	0.457232i
$430$	12.1539			0.586112
$431$	5.66604	−	9.81388i	0.272924	−	0.472718i	−0.696685	−	0.717377i	$-0.745343\pi$
$431$	5.66604	−	9.81388i	0.272924	−	0.472718i	0.969609	+	0.244659i	$0.0786760\pi$
$432$	−2.74658	+	1.05231i	−0.132145	+	0.0506291i
$433$	−4.06126	−	7.03431i	−0.195172	−	0.338048i	0.751785	−	0.659408i	$-0.229193\pi$
$433$	−4.06126	−	7.03431i	−0.195172	−	0.338048i	−0.946957	+	0.321361i	$0.895860\pi$
$434$			1.31791i			0.0632616i
$435$	10.2842	−	3.14180i	0.493088	−	0.150638i
$436$	16.6503	−	9.61304i	0.797403	−	0.460381i
$437$	−2.20330			−0.105398
$438$	21.1970	−	6.47567i	1.01283	−	0.309419i
$439$	0.749036	+	0.432456i	0.0357495	+	0.0206400i	0.517768	−	0.855521i	$-0.326763\pi$
$439$	0.749036	+	0.432456i	0.0357495	+	0.0206400i	−0.482019	+	0.876161i	$0.660096\pi$
$440$	−6.32588	−	21.3031i	−0.301575	−	1.01558i
$441$	17.8486	+	8.71475i	0.849935	+	0.414988i
$442$	−9.45011	−	6.94633i	−0.449496	−	0.330403i
$443$		−	19.2142i		−	0.912893i	−0.889751	−	0.456447i	$-0.849122\pi$
$443$		−	19.2142i		−	0.912893i	0.889751	−	0.456447i	$-0.150878\pi$
$444$	−12.2480	+	13.1288i	−0.581267	+	0.623067i
$445$	−1.21750	+	2.10878i	−0.0577152	+	0.0999657i
$446$	9.83470	+	17.0342i	0.465686	+	0.806592i
$447$	23.9638	+	5.53784i	1.13345	+	0.261931i
$448$	−1.88533	+	1.08849i	−0.0890733	+	0.0514265i
$449$	−5.75404	+	3.32209i	−0.271550	+	0.156779i	−0.629592	−	0.776926i	$-0.716778\pi$
$449$	−5.75404	+	3.32209i	−0.271550	+	0.156779i	0.358042	+	0.933706i	$0.383444\pi$
$450$	−2.60877	−	1.27375i	−0.122979	−	0.0600454i
$451$	6.22288	−	25.9974i	0.293024	−	1.22417i
$452$	2.73653	+	1.57994i	0.128715	+	0.0743139i
$453$	9.86448	+	9.20269i	0.463474	+	0.432380i
$454$	0.343172			0.0161058
$455$	0.608766	−	5.49844i	0.0285394	−	0.257771i
$456$	−6.27631	+	27.1594i	−0.293915	+	1.27185i
$457$	−10.9909	−	6.34560i	−0.514133	−	0.296835i	0.220398	−	0.975410i	$-0.429264\pi$
$457$	−10.9909	−	6.34560i	−0.514133	−	0.296835i	−0.734531	+	0.678575i	$0.762598\pi$
$458$	−1.49304	+	2.58603i	−0.0697654	+	0.120837i
$459$	3.31650	−	20.8536i	0.154801	−	0.973362i
$460$	1.24684			0.0581343
$461$	14.6871	+	25.4388i	0.684047	+	1.18480i	0.973735	+	0.227684i	$0.0731152\pi$
$461$	14.6871	+	25.4388i	0.684047	+	1.18480i	−0.289688	+	0.957121i	$0.593551\pi$
$462$	−2.53454	−	1.26221i	−0.117917	−	0.0587234i
$463$	7.91720			0.367944			0.183972	−	0.982932i	$-0.441104\pi$
$463$	7.91720			0.367944			0.183972	+	0.982932i	$0.441104\pi$
$464$	0.705177	+	1.22140i	0.0327370	+	0.0567022i
$465$	−8.43811	−	7.87201i	−0.391308	−	0.365056i
$466$	9.84025	−	17.0438i	0.455841	−	0.789539i
$467$		−	7.29551i		−	0.337596i	−0.985651	−	0.168798i	$-0.946011\pi$
$467$		−	7.29551i		−	0.337596i	0.985651	−	0.168798i	$-0.0539885\pi$
$468$	−14.6902	−	0.600847i	−0.679056	−	0.0277742i
$469$		−	1.58299i		−	0.0730959i
$470$	0.491098	−	0.850607i	0.0226527	−	0.0392356i
$471$	10.7475	−	11.5204i	0.495219	−	0.530831i
$472$	23.3304	−	13.4698i	1.07387	−	0.619999i
$473$	−13.9015	+	14.6689i	−0.639190	+	0.674476i
$474$	−11.6326	+	3.55375i	−0.534305	+	0.163229i
$475$	6.26613	−	3.61775i	0.287510	−	0.165994i
$476$			3.40116i			0.155892i
$477$	−21.2893	+	1.47961i	−0.974769	+	0.0677466i
$478$	−8.60307	+	14.9010i	−0.393495	+	0.681554i
$479$	−9.26574	+	16.0487i	−0.423362	+	0.733285i	−0.996266	−	0.0863377i	$-0.972484\pi$
$479$	−9.26574	+	16.0487i	−0.423362	+	0.733285i	0.572904	+	0.819623i	$0.305817\pi$
$480$	5.66635	−	24.5199i	0.258632	−	1.11918i
$481$	−25.1821	+	11.0448i	−1.14821	+	0.503601i
$482$			9.04115i			0.411813i
$483$	0.267826	−	0.287086i	0.0121865	−	0.0130629i
$484$	13.3312	+	6.76996i	0.605965	+	0.307726i
$485$	22.4104	−	12.9387i	1.01760	−	0.587514i
$486$	5.26147	+	11.3146i	0.238665	+	0.513240i
$487$	−19.4499	−	33.6882i	−0.881359	−	1.52656i	−0.849831	−	0.527056i	$-0.823296\pi$
$487$	−19.4499	−	33.6882i	−0.881359	−	1.52656i	−0.0315281	−	0.999503i	$-0.510037\pi$
$488$	−7.97410	+	4.60385i	−0.360971	+	0.208407i
$489$	23.7690	+	5.49282i	1.07487	+	0.248394i
$490$	−11.4366	+	6.60294i	−0.516654	+	0.298290i
$491$	−10.3218	+	17.8778i	−0.465815	+	0.806815i	−0.999238	−	0.0390338i	$-0.987572\pi$
$491$	−10.3218	+	17.8778i	−0.465815	+	0.806815i	0.533423	+	0.845849i	$0.320905\pi$
$492$	12.9441	−	13.8750i	0.583566	−	0.625532i
$493$	−10.1251			−0.456011
$494$	−10.2306	+	13.9182i	−0.460297	+	0.626209i
$495$	23.2206	−	8.68843i	1.04369	−	0.390516i
$496$	0.756758	−	1.31074i	0.0339794	−	0.0588541i
$497$	4.49198	−	7.78033i	0.201493	−	0.348996i
$498$	−0.574070	−	1.87913i	−0.0257247	−	0.0842057i
$499$	−7.02320			−0.314402			−0.157201	−	0.987567i	$-0.550247\pi$
$499$	−7.02320			−0.314402			−0.157201	+	0.987567i	$0.550247\pi$
$500$	11.1199	−	6.42006i	0.497296	−	0.287114i
$501$	−4.99157	−	16.3391i	−0.223007	−	0.729976i
$502$		−	0.686576i		−	0.0306434i
$503$	−8.21137	−	14.2225i	−0.366127	−	0.634150i	0.622829	−	0.782358i	$-0.285983\pi$
$503$	−8.21137	−	14.2225i	−0.366127	−	0.634150i	−0.988956	+	0.148207i	$0.952650\pi$
$504$	−2.77589	−	4.11919i	−0.123648	−	0.183483i
$505$	34.6474	+	20.0037i	1.54179	+	0.890151i
$506$	0.672280	−	0.709393i	0.0298865	−	0.0315363i
$507$	−20.2981	−	9.74607i	−0.901472	−	0.432838i
$508$		−	4.87188i		−	0.216155i
$509$	−20.3675	−	11.7592i	−0.902773	−	0.521216i	−0.0246741	−	0.999696i	$-0.507855\pi$
$509$	−20.3675	−	11.7592i	−0.902773	−	0.521216i	−0.878099	+	0.478479i	$0.841188\pi$
$510$	10.2655	+	9.57677i	0.454562	+	0.424067i
$511$	−4.92175	−	8.52473i	−0.217726	−	0.377112i
$512$	6.34482			0.280404
$513$	−30.7133	−	4.88457i	−1.35603	−	0.215659i
$514$	−13.6236	+	7.86559i	−0.600911	+	0.346936i
$515$			11.4750i			0.505648i
$516$	−13.7197	+	4.19135i	−0.603976	+	0.184514i
$517$	0.464912	+	1.56564i	0.0204468	+	0.0688567i
$518$	−3.25542	−	1.87952i	−0.143035	−	0.0825812i
$519$	4.78273	+	1.10525i	0.209938	+	0.0485151i
$520$	14.3081	−	19.4654i	0.627452	−	0.853616i
$521$		−	41.1443i		−	1.80257i	−0.433231	−	0.901283i	$-0.642627\pi$
$521$		−	41.1443i		−	1.80257i	0.433231	−	0.901283i	$-0.357373\pi$
$522$	4.96182	−	3.34373i	0.217173	−	0.146351i
$523$	−28.5384	−	16.4766i	−1.24790	−	0.720473i	−0.277206	−	0.960810i	$-0.589409\pi$
$523$	−28.5384	−	16.4766i	−1.24790	−	0.720473i	−0.970689	+	0.240337i	$0.922742\pi$
$524$	10.1745	+	17.6227i	0.444473	+	0.769850i
$525$	−0.290304	+	1.25623i	−0.0126699	+	0.0548262i
$526$	9.64540	+	16.7063i	0.420559	+	0.728430i
$527$	5.43285	+	9.40997i	0.236659	+	0.409905i
$528$	1.79598	+	2.71071i	0.0781600	+	0.117968i
$529$	−11.4322	−	19.8012i	−0.497054	−	0.860923i
$530$	7.09430	−	12.2877i	0.308157	−	0.533743i
$531$	16.7963	+	24.9244i	0.728898	+	1.08163i
$532$	5.00925			0.217178
$533$	26.6132	−	11.6725i	1.15275	−	0.505593i
$534$	−0.305060	+	1.32008i	−0.0132012	+	0.0571255i
$535$	−13.2361	−	7.64185i	−0.572246	−	0.330386i
$536$	3.45646	−	5.98676i	0.149296	−	0.258589i
$537$	−24.4048	+	7.45564i	−1.05315	+	0.321734i
$538$			22.3849i			0.965083i
$539$	5.11180	−	21.3556i	0.220181	−	0.919851i
$540$	17.3806	+	2.76416i	0.747942	+	0.118951i
$541$			12.9448i			0.556540i	0.960503	+	0.278270i	$0.0897610\pi$
$541$			12.9448i			0.556540i	−0.960503	+	0.278270i	$0.910239\pi$
$542$	−6.37793	+	3.68230i	−0.273956	+	0.158168i
$543$	1.71136	−	1.83443i	0.0734415	−	0.0787229i
$544$	−11.8479	+	20.5211i	−0.507973	+	0.879836i
$545$	−35.2452			−1.50974
$546$	−0.569917	−	3.02488i	−0.0243902	−	0.129453i
$547$			40.8248i			1.74554i	0.488130	+	0.872771i	$0.337679\pi$
$547$			40.8248i			1.74554i	−0.488130	+	0.872771i	$0.662321\pi$
$548$	−16.1060	−	9.29879i	−0.688013	−	0.397225i
$549$	−5.74081	−	8.51891i	−0.245012	−	0.363578i
$550$	−0.747145	+	3.12135i	−0.0318584	+	0.133095i
$551$			14.9123i			0.635286i
$552$	1.63975	−	0.500941i	0.0697924	−	0.0213215i
$553$	2.70099	+	4.67825i	0.114858	+	0.198939i
$554$		−	17.8545i		−	0.758565i
$555$	31.4789	−	9.61675i	1.33620	−	0.408208i
$556$	−11.4118	−	6.58861i	−0.483969	−	0.279419i
$557$	13.7274	−	23.7765i	0.581648	−	1.00744i	−0.413636	−	0.910442i	$-0.635741\pi$
$557$	13.7274	−	23.7765i	0.581648	−	1.00744i	0.995284	−	0.0970016i	$-0.0309252\pi$
$558$	−5.76994	−	2.81722i	−0.244261	−	0.119263i
$559$	−21.8367	−	2.41767i	−0.923594	−	0.102257i
$560$	−0.868491			−0.0367005
$561$	−23.3000	+	1.43590i	−0.983729	+	0.0606237i
$562$	−10.5467	+	18.2674i	−0.444885	+	0.770564i
$563$	−15.1086	−	26.1688i	−0.636750	−	1.10288i	−0.986141	−	0.165907i	$-0.946945\pi$
$563$	−15.1086	−	26.1688i	−0.636750	−	1.10288i	0.349391	−	0.936977i	$-0.386389\pi$
$564$	−0.261030	+	1.12955i	−0.0109914	+	0.0475628i
$565$	−2.89634	−	5.01660i	−0.121850	−	0.211050i
$566$	13.1280	−	7.57944i	0.551810	−	0.318587i
$567$	4.36986	−	3.40814i	0.183517	−	0.143128i
$568$	33.9766	−	19.6164i	1.42563	−	0.823086i
$569$	−12.3086	+	21.3191i	−0.516002	+	0.893742i	0.483825	+	0.875165i	$0.339247\pi$
$569$	−12.3086	+	21.3191i	−0.516002	+	0.893742i	−0.999827	+	0.0185774i	$0.994086\pi$
$570$	14.1047	−	15.1191i	0.590783	−	0.633268i
$571$			28.4076i			1.18882i	0.804162	+	0.594410i	$0.202614\pi$
$571$			28.4076i			1.18882i	−0.804162	+	0.594410i	$0.797386\pi$
$572$	2.88418	+	15.9963i	0.120594	+	0.668839i
$573$	7.87894	−	34.0944i	0.329147	−	1.42431i
$574$	3.44043	+	1.98633i	0.143601	+	0.0829079i
$575$	−0.385421	−	0.222523i	−0.0160732	−	0.00927984i
$576$	−0.735379	−	10.5810i	−0.0306408	−	0.440874i
$577$	11.0945			0.461870			0.230935	−	0.972969i	$-0.425821\pi$
$577$	11.0945			0.461870			0.230935	+	0.972969i	$0.425821\pi$
$578$	0.194615	+	0.337082i	0.00809490	+	0.0140208i
$579$	−26.6697	+	8.14756i	−1.10836	+	0.338601i
$580$		−	8.43884i		−	0.350404i
$581$	−0.755721	+	0.436316i	−0.0313526	+	0.0181014i
$582$	9.82198	−	10.5283i	0.407134	−	0.436412i
$583$	6.71601	+	22.6169i	0.278149	+	0.936695i
$584$		−	42.9865i		−	1.77879i
$585$	22.7714	+	14.4190i	0.941483	+	0.596151i
$586$	13.2828			0.548707
$587$	2.07698	+	1.19914i	0.0857260	+	0.0494939i	0.542250	−	0.840217i	$-0.317572\pi$
$587$	2.07698	+	1.19914i	0.0857260	+	0.0494939i	−0.456524	+	0.889711i	$0.650906\pi$
$588$	10.6330	−	11.3976i	0.438497	−	0.470030i
$589$	13.8591	−	8.00154i	0.571054	−	0.329698i
$590$	−19.9829			−0.822683
$591$	2.50701	+	8.20628i	0.103124	+	0.337561i
$592$	2.15848	+	3.73859i	0.0887129	+	0.153655i
$593$	−33.2913			−1.36711			−0.683554	−	0.729900i	$-0.739567\pi$
$593$	−33.2913			−1.36711			−0.683554	+	0.729900i	$0.739567\pi$
$594$	10.9440	−	8.39831i	0.449039	−	0.344587i
$595$	3.11750	−	5.39967i	0.127805	−	0.221365i
$596$	9.65075	−	16.7156i	0.395310	−	0.684697i
$597$	8.47436	+	1.95836i	0.346832	+	0.0801501i
$598$	1.05603	+	0.116920i	0.0431843	+	0.00478120i
$599$		−	14.9090i		−	0.609167i	−0.952486	−	0.304583i	$-0.901483\pi$
$599$		−	14.9090i		−	0.609167i	0.952486	−	0.304583i	$-0.0985172\pi$
$600$	−3.84087	+	4.11708i	−0.156803	+	0.168079i
$601$	−12.9291	−	7.46462i	−0.527389	−	0.304488i	0.212564	−	0.977147i	$-0.431819\pi$
$601$	−12.9291	−	7.46462i	−0.527389	−	0.304488i	−0.739953	+	0.672659i	$0.765152\pi$
$602$	−1.50169	−	2.60101i	−0.0612045	−	0.106009i
$603$	6.93052	+	3.38388i	0.282232	+	0.137802i
$604$	9.16856	−	5.29347i	0.373063	−	0.215388i
$605$	−14.9593	−	22.9674i	−0.608181	−	0.933757i
$606$	21.6890	+	5.01215i	0.881056	+	0.203605i
$607$	17.6233	−	10.1748i	0.715308	−	0.412984i	−0.0977150	−	0.995214i	$-0.531153\pi$
$607$	17.6233	−	10.1748i	0.715308	−	0.412984i	0.813023	+	0.582231i	$0.197820\pi$
$608$	30.2237	+	17.4496i	1.22573	+	0.707676i
$609$	−1.94305	−	1.81269i	−0.0787362	−	0.0734540i
$610$	6.82995			0.276537
$611$	−1.05155	+	1.43059i	−0.0425414	+	0.0578753i
$612$	−14.8906	−	7.27047i	−0.601918	−	0.293891i
$613$	−39.5365	−	22.8264i	−1.59686	−	0.921949i	−0.992087	−	0.125554i	$-0.959929\pi$
$613$	−39.5365	−	22.8264i	−1.59686	−	0.921949i	−0.604776	−	0.796396i	$-0.706737\pi$
$614$	4.05166	+	2.33922i	0.163512	+	0.0944034i
$615$	−33.2678	+	10.1633i	−1.34149	+	0.409823i
$616$	−3.77739	+	3.98592i	−0.152196	+	0.160597i
$617$	−7.83944	+	4.52610i	−0.315604	+	0.182214i	−0.649431	−	0.760420i	$-0.724993\pi$
$617$	−7.83944	+	4.52610i	−0.315604	+	0.182214i	0.333828	+	0.942634i	$0.391660\pi$
$618$	1.86545	+	6.10625i	0.0750394	+	0.245629i
$619$	−44.7782			−1.79979			−0.899895	−	0.436107i	$-0.856357\pi$
$619$	−44.7782			−1.79979			−0.899895	+	0.436107i	$0.856357\pi$
$620$	−7.84282	+	4.52805i	−0.314975	+	0.181851i
$621$	0.684376	+	1.78626i	0.0274631	+	0.0716802i
$622$	−22.9729	−	13.2634i	−0.921129	−	0.531814i
$623$	0.601724			0.0241076
$624$	−1.17010	+	3.33569i	−0.0468415	+	0.133534i
$625$	−29.5831			−1.18333
$626$	11.1715	−	19.3496i	0.446502	−	0.773364i
$627$	2.11480	+	34.3165i	0.0844571	+	1.37047i
$628$	−6.18206	−	10.7076i	−0.246691	−	0.427281i
$629$	−30.9919			−1.23573
$630$	0.255458	+	3.67565i	0.0101777	+	0.146441i
$631$	9.99644	+	17.3143i	0.397952	+	0.689273i	0.993473	−	0.114067i	$-0.0363878\pi$
$631$	9.99644	+	17.3143i	0.397952	+	0.689273i	−0.595521	+	0.803340i	$0.703054\pi$
$632$			23.5904i			0.938375i
$633$	24.7530	−	7.56200i	0.983842	−	0.300562i
$634$	−5.59038	−	3.22761i	−0.222022	−	0.128185i
$635$	−4.46557	+	7.73459i	−0.177211	+	0.306938i
$636$	−3.77079	+	16.3173i	−0.149521	+	0.647022i
$637$	21.8615	−	9.58842i	0.866185	−	0.379907i
$638$	−4.80129	−	4.55010i	−0.190085	−	0.180140i
$639$	24.4609	+	36.2979i	0.967657	+	1.43592i
$640$	−19.0590	−	11.0037i	−0.753374	−	0.434961i
$641$	25.3668	−	14.6455i	1.00193	−	0.578463i	0.0931090	−	0.995656i	$-0.470319\pi$
$641$	25.3668	−	14.6455i	1.00193	−	0.578463i	0.908818	+	0.417193i	$0.136986\pi$
$642$	−8.28570	−	1.91476i	−0.327010	−	0.0755694i
$643$	0.760803	+	1.31775i	0.0300031	+	0.0519669i	0.880637	−	0.473791i	$-0.157115\pi$
$643$	0.760803	+	1.31775i	0.0300031	+	0.0519669i	−0.850634	+	0.525758i	$0.823782\pi$
$644$	−0.154056	−	0.266833i	−0.00607066	−	0.0105147i
$645$	25.6231	+	5.92130i	1.00891	+	0.233151i
$646$	−16.8604	+	9.73436i	−0.663364	+	0.382993i
$647$	−27.8452	−	16.0764i	−1.09471	−	0.632029i	−0.159881	−	0.987136i	$-0.551111\pi$
$647$	−27.8452	−	16.0764i	−1.09471	−	0.632029i	−0.934826	+	0.355107i	$0.884444\pi$
$648$	23.9681	−	3.34775i	0.941557	−	0.131512i
$649$	22.8562	−	24.1180i	0.897185	−	0.946714i
$650$	−3.19530	+	1.40145i	−0.125330	+	0.0549695i
$651$	−0.642078	+	2.77845i	−0.0251650	+	0.108896i
$652$	9.57229	−	16.5797i	0.374880	−	0.649311i
$653$	−23.7703	−	13.7238i	−0.930202	−	0.537052i	−0.0433265	−	0.999061i	$-0.513796\pi$
$653$	−23.7703	−	13.7238i	−0.930202	−	0.537052i	−0.886875	+	0.462009i	$0.847129\pi$
$654$	−18.7552	+	5.72970i	−0.733388	+	0.224049i
$655$		−	37.3036i		−	1.45757i
$656$	−2.28115	−	3.95106i	−0.0890638	−	0.154263i
$657$	47.8431	−	3.32511i	1.86654	−	0.129725i
$658$	−0.242714			−0.00946199
$659$	−10.4106	−	18.0317i	−0.405539	−	0.702415i	0.588845	−	0.808246i	$-0.299583\pi$
$659$	−10.4106	−	18.0317i	−0.405539	−	0.702415i	−0.994384	+	0.105831i	$0.966250\pi$
$660$	−1.19676	−	19.4196i	−0.0465838	−	0.755907i
$661$	2.82643	−	4.89553i	0.109936	−	0.190414i	−0.805808	−	0.592176i	$-0.798269\pi$
$661$	2.82643	−	4.89553i	0.109936	−	0.190414i	0.915744	+	0.401762i	$0.131602\pi$
$662$	11.6576			0.453084
$663$	−16.5388	−	19.2485i	−0.642314	−	0.747550i
$664$	−3.81077			−0.147887
$665$	−7.95267	−	4.59148i	−0.308391	−	0.178050i
$666$	15.1877	−	10.2348i	0.588510	−	0.396591i
$667$	0.794350	−	0.458618i	0.0307573	−	0.0177578i
$668$	−13.4073			−0.518743
$669$	12.4348	+	40.7034i	0.480758	+	1.57368i
$670$	−4.44077	+	2.56388i	−0.171562	+	0.0990513i
$671$	−7.81203	+	8.24329i	−0.301580	+	0.318228i
$672$	−5.94755	+	1.81697i	−0.229432	+	0.0700910i
$673$	16.2597	+	9.38754i	0.626765	+	0.361863i	0.779498	−	0.626404i	$-0.215474\pi$
$673$	16.2597	+	9.38754i	0.626765	+	0.361863i	−0.152733	+	0.988267i	$0.548807\pi$
$674$	−6.56036	−	3.78763i	−0.252696	−	0.145894i
$675$	−4.87933	−	3.95635i	−0.187805	−	0.152280i
$676$	−11.9686	+	12.9995i	−0.460332	+	0.499982i
$677$	12.2724			0.471668			0.235834	−	0.971793i	$-0.424218\pi$
$677$	12.2724			0.471668			0.235834	+	0.971793i	$0.424218\pi$
$678$	−2.35678	−	2.19866i	−0.0905114	−	0.0844392i
$679$	−5.53792	−	3.19732i	−0.212526	−	0.122702i
$680$	23.5803	−	13.6141i	0.904262	−	0.522076i
$681$	0.723485	+	0.167191i	0.0277240	+	0.00640679i
$682$	−1.65249	+	6.90364i	−0.0632773	+	0.264354i
$683$	34.5652	−	19.9562i	1.32260	−	0.763603i	0.338457	−	0.940982i	$-0.390095\pi$
$683$	34.5652	−	19.9562i	1.32260	−	0.763603i	0.984143	+	0.177378i	$0.0567617\pi$
$684$	−10.7080	+	21.9310i	−0.409431	+	0.838554i
$685$	17.0465	+	29.5255i	0.651315	+	1.12811i
$686$	5.81414	+	3.35679i	0.221985	+	0.128163i
$687$	−4.40758	+	4.72454i	−0.168160	+	0.180252i
$688$			3.44916i			0.131498i
$689$	−15.1905	+	20.6659i	−0.578713	+	0.787309i
$690$	−1.23914	−	0.286356i	−0.0471734	−	0.0109014i
$691$	−1.50702	+	2.61023i	−0.0573296	+	0.0992978i	−0.893266	−	0.449529i	$-0.851592\pi$
$691$	−1.50702	+	2.61023i	−0.0573296	+	0.0992978i	0.835936	+	0.548827i	$0.184925\pi$
$692$	1.92611	−	3.33612i	0.0732197	−	0.126820i
$693$	−4.72844	−	3.89585i	−0.179619	−	0.147991i
$694$	−15.2067			−0.577239
$695$	12.0782	+	20.9201i	0.458154	+	0.793546i
$696$	−3.39045	−	11.0981i	−0.128515	−	0.420672i
$697$	32.7532			1.24062
$698$	13.3575	−	7.71194i	0.505588	−	0.291901i
$699$	29.0492	−	31.1382i	1.09874	−	1.17775i
$700$	0.876261	+	0.505910i	0.0331196	+	0.0191216i
$701$	17.9497			0.677953			0.338976	−	0.940795i	$-0.389919\pi$
$701$	17.9497			0.677953			0.338976	+	0.940795i	$0.389919\pi$
$702$	14.4615	+	3.97097i	0.545815	+	0.149874i
$703$			45.6452i			1.72154i
$704$	−11.2408	+	3.33792i	−0.423653	+	0.125803i
$705$	1.44976	−	1.55402i	0.0546011	−	0.0585276i
$706$	3.46320	−	1.99948i	0.130339	−	0.0752514i
$707$		−	9.88636i		−	0.371815i
$708$	22.5574	−	6.89124i	0.847758	−	0.258989i
$709$	−15.3343	−	26.5598i	−0.575891	−	0.997473i	−0.995944	−	0.0899733i	$-0.971322\pi$
$709$	−15.3343	−	26.5598i	−0.575891	−	0.997473i	0.420053	−	0.907500i	$-0.362011\pi$
$710$	−29.1015			−1.09216
$711$	−26.2556	+	1.82477i	−0.984663	+	0.0684343i
$712$	2.27567	+	1.31386i	0.0852845	+	0.0492390i
$713$	−0.852453	−	0.492164i	−0.0319246	−	0.0184317i
$714$	0.781126	−	3.38016i	0.0292329	−	0.126499i
$715$	10.0833	−	28.0393i	0.377093	−	1.04861i
$716$			20.0257i			0.748397i
$717$	−25.3969	+	27.2233i	−0.948465	+	1.01667i
$718$	−5.16363	+	8.94367i	−0.192705	+	0.333775i
$719$	2.48589	−	1.43523i	0.0927082	−	0.0535251i	−0.452929	−	0.891547i	$-0.649621\pi$
$719$	2.48589	−	1.43523i	0.0927082	−	0.0535251i	0.545637	+	0.838021i	$0.316288\pi$
$720$	1.85653	−	3.80235i	0.0691887	−	0.141705i
$721$	2.45572	−	1.41781i	0.0914560	−	0.0528021i
$722$	6.73237	+	11.6608i	0.250553	+	0.433970i
$723$	−4.40480	+	19.0608i	−0.163816	+	0.708879i
$724$	−0.984390	−	1.70501i	−0.0365846	−	0.0633663i
$725$	−1.50607	+	2.60859i	−0.0559341	+	0.0968807i
$726$	−11.6941	−	9.78988i	−0.434008	−	0.363336i
$727$	−0.553770			−0.0205382			−0.0102691	−	0.999947i	$-0.503269\pi$
$727$	−0.553770			−0.0205382			−0.0102691	+	0.999947i	$0.503269\pi$
$728$	−5.93360	−	0.656945i	−0.219914	−	0.0243480i
$729$	5.57997	+	26.4171i	0.206666	+	0.978412i
$730$	−15.9429	+	27.6140i	−0.590075	+	1.02204i
$731$	−21.4444	−	12.3809i	−0.793151	−	0.457926i
$732$	−7.70988	+	2.35536i	−0.284965	+	0.0870565i
$733$			14.8945i			0.550141i	0.961424	+	0.275070i	$0.0887011\pi$
$733$			14.8945i			0.550141i	−0.961424	+	0.275070i	$0.911299\pi$
$734$	−1.97315	−	3.41760i	−0.0728304	−	0.126146i
$735$	−27.3280	+	8.34865i	−1.00801	+	0.307945i
$736$		−	2.14661i		−	0.0791250i
$737$	1.98488	−	8.29225i	0.0731140	−	0.305449i
$738$	−16.0508	+	10.8165i	−0.590838	+	0.398160i
$739$	3.28155	+	1.89460i	0.120714	+	0.0696941i	0.559141	−	0.829073i	$-0.311131\pi$
$739$	3.28155	+	1.89460i	0.120714	+	0.0696941i	−0.438427	+	0.898767i	$0.644464\pi$
$740$		−	25.8305i		−	0.949547i
$741$	−28.3493	+	24.3585i	−1.04144	+	0.894831i
$742$	−3.50620			−0.128717
$743$	−12.4974	+	21.6462i	−0.458487	+	0.794123i	−0.998881	−	0.0472892i	$-0.984942\pi$
$743$	−12.4974	+	21.6462i	−0.458487	+	0.794123i	0.540394	+	0.841412i	$0.318275\pi$
$744$	−8.49503	+	9.10593i	−0.311443	+	0.333839i
$745$	−30.6430	+	17.6918i	−1.12267	+	0.648176i
$746$			6.66843i			0.244148i
$747$	−0.294772	−	4.24131i	−0.0107851	−	0.155182i
$748$	−4.26463	+	17.8164i	−0.155930	+	0.651431i
$749$			3.77681i			0.138002i
$750$	−12.5257	+	3.82657i	−0.457373	+	0.139727i
$751$	4.13821	−	7.16760i	0.151006	−	0.261549i	−0.780592	−	0.625041i	$-0.785082\pi$
$751$	4.13821	−	7.16760i	0.151006	−	0.261549i	0.931597	+	0.363492i	$0.118416\pi$
$752$	0.241395	+	0.139369i	0.00880276	+	0.00508227i
$753$	0.334496	−	1.44746i	0.0121897	−	0.0527484i
$754$	0.791331	−	7.14739i	0.0288186	−	0.260293i
$755$	−19.4080			−0.706329
$756$	−1.55594	−	4.06110i	−0.0565891	−	0.147701i
$757$	25.4134	−	44.0173i	0.923666	−	1.59984i	0.129973	−	0.991518i	$-0.458511\pi$
$757$	25.4134	−	44.0173i	0.923666	−	1.59984i	0.793693	−	0.608318i	$-0.208156\pi$
$758$	8.33768	+	14.4413i	0.302838	+	0.524531i
$759$	1.76293	−	1.16803i	0.0639904	−	0.0423969i
$760$	−20.0509	−	34.7292i	−0.727324	−	1.25976i
$761$	7.42885	+	12.8671i	0.269296	+	0.466434i	0.968680	−	0.248312i	$-0.0798758\pi$
$761$	7.42885	+	12.8671i	0.269296	+	0.466434i	−0.699385	+	0.714746i	$0.746542\pi$
$762$	−1.11890	+	4.84180i	−0.0405335	+	0.175400i
$763$	4.35479	+	7.54272i	0.157654	+	0.273065i
$764$	−23.7820	−	13.7306i	−0.860404	−	0.496754i
$765$	16.9762	+	25.1913i	0.613776	+	0.910794i
$766$		−	1.00883i		−	0.0364504i
$767$	35.9030	+	3.97504i	1.29638	+	0.143530i
$768$	−23.8637	−	5.51470i	−0.861106	−	0.198995i
$769$	40.5518	+	23.4126i	1.46234	+	0.844280i	0.999119	−	0.0419657i	$-0.0133620\pi$
$769$	40.5518	+	23.4126i	1.46234	+	0.844280i	0.463216	+	0.886245i	$0.346695\pi$
$770$	3.90486	−	1.15954i	0.140721	−	0.0417868i
$771$	−32.5537	+	9.94512i	−1.17239	+	0.358165i
$772$			21.8842i			0.787631i
$773$	18.4248	−	10.6376i	0.662693	−	0.382606i	−0.130609	−	0.991434i	$-0.541693\pi$
$773$	18.4248	−	10.6376i	0.662693	−	0.382606i	0.793302	+	0.608828i	$0.208360\pi$
$774$	14.5976	−	1.01454i	0.524700	−	0.0364667i
$775$	3.23247			0.116114
$776$	−13.9627	−	24.1841i	−0.501231	−	0.868157i
$777$	−5.94748	−	5.54847i	−0.213365	−	0.199050i
$778$	−26.8835	−	15.5212i	−0.963818	−	0.556461i
$779$		−	48.2392i		−	1.72835i
$780$	16.0428	−	13.7844i	0.574425	−	0.493560i
$781$	33.2860	−	35.1236i	1.19107	−	1.25682i
$782$	1.03706	+	0.598747i	0.0370852	+	0.0214111i
$783$	12.0897	−	4.63197i	0.432051	−	0.165533i
$784$	−1.87385	−	3.24561i	−0.0669234	−	0.115915i
$785$			22.6659i			0.808981i
$786$	−6.06432	−	19.8506i	−0.216307	−	0.708047i
$787$	17.3000	−	9.98816i	0.616678	−	0.356039i	−0.158896	−	0.987295i	$-0.550794\pi$
$787$	17.3000	−	9.98816i	0.616678	−	0.356039i	0.775575	+	0.631256i	$0.217460\pi$
$788$	6.73379			0.239881
$789$	12.1955	+	39.9199i	0.434171	+	1.42119i
$790$	8.74926	−	15.1542i	0.311285	−	0.539161i
$791$	−0.715725	+	1.23967i	−0.0254482	+	0.0440777i
$792$	−9.37606	−	25.0583i	−0.333164	−	0.890409i
$793$	−12.2713	−	1.35863i	−0.435766	−	0.0482463i
$794$	−27.1378			−0.963086
$795$	20.9429	−	22.4490i	0.742768	−	0.796182i
$796$	3.41281	−	5.91116i	0.120964	−	0.209515i
$797$	−23.0243	+	13.2931i	−0.815561	+	0.470864i	−0.848883	−	0.528580i	$-0.822725\pi$
$797$	−23.0243	+	13.2931i	−0.815561	+	0.470864i	0.0333224	+	0.999445i	$0.489391\pi$
$798$	−4.97832	−	1.15045i	−0.176231	−	0.0407255i
$799$	−1.73300	+	1.00055i	−0.0613091	+	0.0353968i
$800$	3.52466	+	6.10489i	0.124615	+	0.215840i
$801$	−1.28627	+	2.63441i	−0.0454482	+	0.0930823i
$802$	16.6946	−	9.63864i	0.589507	−	0.340352i
$803$	−15.0928	−	50.8266i	−0.532614	−	1.79363i
$804$	4.12872	−	4.42562i	0.145609	−	0.156080i
$805$			0.564831i			0.0199077i
$806$	−7.06719	+	3.09966i	−0.248931	+	0.109181i
$807$	−10.9058	+	47.1926i	−0.383903	+	1.66126i
$808$	21.5868	−	37.3895i	0.759421	−	1.31536i
$809$	5.55735	−	9.62561i	0.195386	−	0.338419i	−0.751641	−	0.659572i	$-0.770737\pi$
$809$	5.55735	−	9.62561i	0.195386	−	0.338419i	0.947027	+	0.321154i	$0.104071\pi$
$810$	−16.6384	−	6.73881i	−0.584615	−	0.236778i
$811$			36.5821i			1.28457i	0.766466	+	0.642285i	$0.222013\pi$
$811$			36.5821i			1.28457i	−0.766466	+	0.642285i	$0.777987\pi$
$812$	−1.80597	+	1.04268i	−0.0633771	+	0.0365908i
$813$	−15.2401	+	4.65584i	−0.534495	+	0.163288i
$814$	−14.6963	−	13.9274i	−0.515104	−	0.488156i
$815$	−30.3939	+	17.5479i	−1.06465	+	0.614677i
$816$	−2.71780	+	2.91324i	−0.0951421	+	0.101984i
$817$	−18.2348	+	31.5835i	−0.637953	+	1.10497i
$818$			8.83154i			0.308788i
$819$	0.272189	−	6.65480i	0.00951105	−	0.232538i
$820$			27.2984i			0.953303i
$821$	14.1268	−	24.4684i	0.493029	−	0.853951i	−0.506939	−	0.861982i	$-0.669223\pi$
$821$	14.1268	−	24.4684i	0.493029	−	0.853951i	0.999968	+	0.00803077i	$0.00255630\pi$
$822$	13.8709	+	12.9404i	0.483804	+	0.451347i
$823$	9.53556	+	16.5161i	0.332389	+	0.575714i	0.982980	−	0.183714i	$-0.0588121\pi$
$823$	9.53556	+	16.5161i	0.332389	+	0.575714i	−0.650591	+	0.759428i	$0.725479\pi$
$824$	12.3831			0.431387
$825$	−3.09586	+	6.21652i	−0.107784	+	0.216432i
$826$	2.46902	+	4.27648i	0.0859083	+	0.148798i
$827$	−51.1101			−1.77727			−0.888636	−	0.458614i	$-0.848346\pi$
$827$	−51.1101			−1.77727			−0.888636	+	0.458614i	$0.848346\pi$
$828$	1.49754	−	0.104079i	0.0520431	−	0.00361701i
$829$	7.99395	−	13.8459i	0.277641	−	0.480889i	−0.693157	−	0.720787i	$-0.743781\pi$
$829$	7.99395	−	13.8459i	0.277641	−	0.480889i	0.970798	+	0.239898i	$0.0771140\pi$
$830$	2.44799	+	1.41335i	0.0849710	+	0.0490580i
$831$	8.69862	−	37.6414i	0.301752	−	1.30577i
$832$	−10.2712	−	7.54984i	−0.356088	−	0.261744i
$833$	26.9052			0.932211
$834$	9.82818	+	9.16883i	0.340322	+	0.317490i
$835$	21.2854	+	12.2891i	0.736611	+	0.425282i
$836$	26.2401	+	6.28098i	0.907533	+	0.217232i
$837$	−10.7918	−	8.75044i	−0.373020	−	0.302459i
$838$	8.02725	−	4.63454i	0.277297	−	0.160097i
$839$	−17.0082	+	9.81967i	−0.587187	+	0.339013i	−0.763984	−	0.645235i	$-0.776760\pi$
$839$	−17.0082	+	9.81967i	−0.587187	+	0.339013i	0.176797	+	0.984247i	$0.443426\pi$
$840$	6.96248	+	1.60897i	0.240228	+	0.0555148i
$841$	11.3960	+	19.7384i	0.392965	+	0.680636i
$842$	−3.16884	+	5.48859i	−0.109205	+	0.189149i
$843$	−31.1346	+	33.3736i	−1.07233	+	1.14945i
$844$		−	20.3114i		−	0.699148i
$845$	30.9168	−	9.66760i	1.06357	−	0.332575i
$846$	0.518838	−	1.06263i	0.0178380	−	0.0365339i
$847$	−3.06685	+	6.03916i	−0.105378	+	0.207508i
$848$	3.48713	+	2.01330i	0.119749	+	0.0691369i
$849$	31.3694	−	9.58332i	1.07660	−	0.328899i
$850$	−3.93249			−0.134883
$851$	2.43143	−	1.40379i	0.0833483	−	0.0481211i
$852$	32.8508	−	10.0359i	1.12545	−	0.343823i
$853$		−	56.1566i		−	1.92276i	−0.275217	−	0.961382i	$-0.588750\pi$
$853$		−	56.1566i		−	1.92276i	0.275217	−	0.961382i	$-0.411250\pi$
$854$	−0.843888	−	1.46166i	−0.0288772	−	0.0500168i
$855$	37.1020	−	25.0027i	1.26886	−	0.855074i
$856$	−8.24665	+	14.2836i	−0.281865	+	0.488204i
$857$	4.98704			0.170354			0.0851769	−	0.996366i	$-0.472854\pi$
$857$	4.98704			0.170354			0.0851769	+	0.996366i	$0.472854\pi$
$858$	0.807412	−	16.5599i	0.0275646	−	0.565347i
$859$	48.4500			1.65309			0.826546	−	0.562869i	$-0.190303\pi$
$859$	48.4500			1.65309			0.826546	+	0.562869i	$0.190303\pi$
$860$	10.3190	−	17.8730i	0.351875	−	0.609465i
$861$	6.28548	+	5.86380i	0.214209	+	0.199838i
$862$	4.53550	+	7.85572i	0.154480	+	0.267567i
$863$			26.5270i			0.902988i	0.892274	+	0.451494i	$0.149109\pi$
$863$			26.5270i			0.902988i	−0.892274	+	0.451494i	$0.850891\pi$
$864$	4.75888	−	29.9230i	0.161900	−	1.01800i
$865$	−6.11577	+	3.53094i	−0.207943	+	0.120056i
$866$	6.50184			0.220942
$867$	0.246068	+	0.805462i	0.00835689	+	0.0273549i
$868$	1.93807	+	1.11894i	0.0657823	+	0.0379794i
$869$	8.28272	+	27.8929i	0.280972	+	0.946203i
$870$	−1.93811	+	8.38673i	−0.0657079	+	0.284337i
$871$	8.48869	−	3.72312i	0.287628	−	0.126153i
$872$			38.0347i			1.28802i
$873$	25.8363	−	17.4109i	0.874427	−	0.589269i
$874$	0.881839	−	1.52739i	0.0298287	−	0.0516648i
$875$	2.90834	+	5.03740i	0.0983200	+	0.170295i
$876$	8.47405	−	36.6696i	0.286312	−	1.23895i
$877$	−17.4168	+	10.0556i	−0.588123	+	0.339553i	−0.764355	−	0.644796i	$-0.776942\pi$
$877$	−17.4168	+	10.0556i	−0.588123	+	0.339553i	0.176232	+	0.984349i	$0.443609\pi$
$878$	−0.599581	+	0.346168i	−0.0202349	+	0.0116826i
$879$	28.0032	+	6.47130i	0.944523	+	0.218272i
$880$	−4.54944	−	1.08898i	−0.153362	−	0.0367095i
$881$	26.4366	+	15.2632i	0.890672	+	0.514230i	0.874162	−	0.485634i	$-0.161411\pi$
$881$	26.4366	+	15.2632i	0.890672	+	0.514230i	0.0165099	+	0.999864i	$0.494745\pi$
$882$	−13.1850	+	8.88523i	−0.443961	+	0.299181i
$883$	−6.94741			−0.233799			−0.116899	−	0.993144i	$-0.537296\pi$
$883$	−6.94741			−0.233799			−0.116899	+	0.993144i	$0.537296\pi$
$884$	−18.2384	+	7.99935i	−0.613425	+	0.269047i
$885$	−42.1285	−	9.73556i	−1.41613	−	0.327257i
$886$	13.3198	+	7.69019i	0.447488	+	0.258357i
$887$	−28.1993	+	48.8426i	−0.946840	+	1.63998i	−0.194815	+	0.980840i	$0.562411\pi$
$887$	−28.1993	+	48.8426i	−0.946840	+	1.63998i	−0.752025	+	0.659135i	$0.770923\pi$
$888$	−10.3778	−	33.9702i	−0.348258	−	1.13996i
$889$	2.20701			0.0740207
$890$	−0.974576	−	1.68801i	−0.0326678	−	0.0565824i
$891$	27.1642	−	12.3737i	0.910034	−	0.414534i
$892$	33.3998			1.11831
$893$	1.47362	+	2.55238i	0.0493126	+	0.0854120i
$894$	−13.4302	+	14.3959i	−0.449171	+	0.481472i
$895$	18.3556	−	31.7928i	0.613560	−	1.06272i
$896$			5.43835i			0.181682i
$897$	2.16939	+	0.760986i	0.0724339	+	0.0254086i
$898$		−	5.31848i		−	0.177480i
$899$	−3.33105	+	5.76954i	−0.111097	+	0.192425i
$900$	−4.08806	+	2.75491i	−0.136269	+	0.0918303i
$901$	−25.0345	+	14.4537i	−0.834021	+	0.481522i
$902$	15.5315	+	14.7189i	0.517142	+	0.490087i
$903$	−1.89872	−	6.21515i	−0.0631854	−	0.206827i
$904$	−5.41363	+	3.12556i	−0.180055	+	0.103955i
$905$			3.60917i			0.119973i
$906$	−10.3277	+	3.15509i	−0.343114	+	0.104821i
$907$	−28.1928	+	48.8314i	−0.936128	+	1.62142i	−0.163517	+	0.986540i	$0.552284\pi$
$907$	−28.1928	+	48.8314i	−0.936128	+	1.62142i	−0.772610	+	0.634880i	$0.781049\pi$
$908$	0.291363	−	0.504656i	0.00966922	−	0.0167476i
$909$	43.2835	+	21.1335i	1.43562	+	0.700955i
$910$	3.56802	+	2.62268i	0.118279	+	0.0869411i
$911$			49.9394i			1.65457i	0.561786	+	0.827283i	$0.310115\pi$
$911$			49.9394i			1.65457i	−0.561786	+	0.827283i	$0.689885\pi$
$912$	4.29065	+	4.00280i	0.142078	+	0.132546i
$913$	−4.50580	+	1.33798i	−0.149120	+	0.0442808i
$914$	8.79790	−	5.07947i	0.291009	−	0.168014i
$915$	14.3991	+	3.32752i	0.476020	+	0.110004i
$916$	2.53528	+	4.39123i	0.0837680	+	0.145090i
$917$	−7.98323	+	4.60912i	−0.263629	+	0.152206i
$918$	13.1289	+	10.6454i	0.433318	+	0.351352i
$919$	−4.66476	+	2.69320i	−0.153876	+	0.0888405i	−0.574961	−	0.818181i	$-0.694983\pi$
$919$	−4.66476	+	2.69320i	−0.153876	+	0.0888405i	0.421085	+	0.907021i	$0.361649\pi$
$920$	−1.23331	+	2.13615i	−0.0406609	+	0.0704267i
$921$	7.40217	+	6.90557i	0.243910	+	0.227546i
$922$	−23.5132			−0.774366
$923$	52.2864	+	5.78894i	1.72103	+	0.190545i
$924$	−4.00806	+	2.65554i	−0.131856	+	0.0873609i
$925$	−4.60994	+	7.98465i	−0.151574	+	0.262534i
$926$	−3.16874	+	5.48842i	−0.104131	+	0.180361i
$927$	0.957866	+	13.7822i	0.0314604	+	0.452667i
$928$	−14.5286			−0.476924
$929$	−2.97813	+	1.71943i	−0.0977093	+	0.0564125i	−0.548058	−	0.836440i	$-0.684633\pi$
$929$	−2.97813	+	1.71943i	−0.0977093	+	0.0564125i	0.450349	+	0.892853i	$0.351300\pi$
$930$	8.83433	−	2.69887i	0.289689	−	0.0884996i
$931$		−	39.6262i		−	1.29870i
$932$	−16.7093	−	28.9414i	−0.547332	−	0.948008i
$933$	−41.9703	−	39.1546i	−1.37404	−	1.28186i
$934$	5.05745	+	2.91992i	0.165485	+	0.0955427i
$935$	23.1010	−	24.3763i	0.755484	−	0.797189i
$936$	15.5601	−	24.5736i	0.508598	−	0.803214i
$937$		−	0.566081i		−	0.0184931i	−0.999957	−	0.00924653i	$-0.997057\pi$
$937$		−	0.566081i		−	0.0184931i	0.999957	−	0.00924653i	$-0.00294331\pi$
$938$	1.09738	+	0.633570i	0.0358306	+	0.0206868i
$939$	32.9791	−	35.3507i	1.07623	−	1.15362i
$940$	−0.833915	−	1.44438i	−0.0271993	−	0.0471106i
$941$	−27.3179			−0.890539			−0.445269	−	0.895397i	$-0.646892\pi$
$941$	−27.3179			−0.890539			−0.445269	+	0.895397i	$0.646892\pi$
$942$	3.68472	+	12.0613i	0.120055	+	0.392979i
$943$	−2.56961	+	1.48356i	−0.0836780	+	0.0483115i
$944$		−	5.67096i		−	0.184574i
$945$	−1.25219	+	7.87356i	−0.0407338	+	0.256127i
$946$	−4.60502	−	15.5079i	−0.149722	−	0.504205i
$947$	−28.3034	−	16.3410i	−0.919738	−	0.531011i	−0.0361867	−	0.999345i	$-0.511521\pi$
$947$	−28.3034	−	16.3410i	−0.919738	−	0.531011i	−0.883552	+	0.468334i	$0.844854\pi$
$948$	−4.65044	+	20.1238i	−0.151039	+	0.653590i
$949$	34.1375	−	46.4423i	1.10815	−	1.50758i
$950$			5.79180i			0.187911i
$951$	−10.2133	−	9.52815i	−0.331190	−	0.308971i
$952$	−5.82701	−	3.36423i	−0.188855	−	0.109035i
$953$	9.12430	+	15.8037i	0.295565	+	0.511934i	0.975116	−	0.221695i	$-0.0711588\pi$
$953$	9.12430	+	15.8037i	0.295565	+	0.511934i	−0.679551	+	0.733628i	$0.737825\pi$
$954$	7.49501	−	15.3505i	0.242660	−	0.496991i
$955$	25.1709	+	43.5972i	0.814510	+	1.41077i
$956$	14.6085	+	25.3027i	0.472474	+	0.818348i
$957$	−7.90543	−	11.9318i	−0.255546	−	0.385701i
$958$	−7.41695	−	12.8465i	−0.239631	−	0.415053i
$959$	4.21244	−	7.29615i	0.136027	−	0.235605i
$960$	11.1573	+	10.4088i	0.360102	+	0.335943i
$961$	−23.8506			−0.769374
$962$	2.42219	−	21.8775i	0.0780944	−	0.705358i
$963$	−16.5353	−	8.07349i	−0.532842	−	0.260165i
$964$	13.2956	+	7.67621i	0.428222	+	0.247234i
$965$	20.0591	−	34.7434i	0.645725	−	1.11843i
$966$	0.0918227	+	0.300567i	0.00295435	+	0.00967057i
$967$			15.6281i			0.502565i	0.967914	+	0.251282i	$0.0808523\pi$
$967$			15.6281i			0.502565i	−0.967914	+	0.251282i	$0.919148\pi$
$968$	−24.7851	+	16.1432i	−0.796623	+	0.518862i
$969$	−40.2881	+	12.3080i	−1.29424	+	0.395389i
$970$			20.7140i			0.665088i
$971$	−16.1836	+	9.34359i	−0.519356	+	0.299850i	−0.736671	−	0.676251i	$-0.763603\pi$
$971$	−16.1836	+	9.34359i	−0.519356	+	0.299850i	0.217315	+	0.976101i	$0.430270\pi$
$972$	21.1060	+	1.86911i	0.676974	+	0.0599517i
$973$	2.98470	−	5.16965i	0.0956851	−	0.165731i
$974$	31.1381			0.997730
$975$	−7.41920	+	1.39785i	−0.237605	+	0.0447670i
$976$			1.93828i			0.0620428i
$977$	1.52302	+	0.879315i	0.0487257	+	0.0281318i	0.524165	−	0.851617i	$-0.324378\pi$
$977$	1.52302	+	0.879315i	0.0487257	+	0.0281318i	−0.475439	+	0.879749i	$0.657711\pi$
$978$	−13.3210	+	14.2789i	−0.425958	+	0.456589i
$979$	3.15203	+	0.754487i	0.100739	+	0.0241135i
$980$			22.4244i			0.716320i
$981$	−42.3318	+	2.94207i	−1.35155	+	0.0939331i
$982$	−8.26227	−	14.3107i	−0.263660	−	0.456672i
$983$		−	28.1088i		−	0.896530i	−0.893901	−	0.448265i	$-0.852042\pi$
$983$		−	28.1088i		−	0.896530i	0.893901	−	0.448265i	$-0.147958\pi$
$984$	10.9676	+	35.9008i	0.349635	+	1.14447i
$985$	−10.6905	−	6.17219i	−0.340629	−	0.196662i
$986$	4.05242	−	7.01899i	0.129055	−	0.223530i
$987$	−0.511698	−	0.118249i	−0.0162875	−	0.00376391i
$988$	11.7815	+	26.8617i	0.374820	+	0.854585i
$989$	2.24319			0.0713293
$990$	−3.27063	+	19.5746i	−0.103948	+	0.622120i
$991$	−27.3304	+	47.3376i	−0.868179	+	1.50373i	−0.00432276	+	0.999991i	$0.501376\pi$
$991$	−27.3304	+	47.3376i	−0.868179	+	1.50373i	−0.863856	+	0.503739i	$0.831957\pi$
$992$	7.79565	+	13.5025i	0.247512	+	0.428704i
$993$	24.5768	+	5.67951i	0.779923	+	0.180234i
$994$	3.59569	+	6.22793i	0.114049	+	0.197538i
$995$	−10.8363	+	6.25636i	−0.343535	+	0.198340i
$996$	−3.25078	−	0.751228i	−0.103005	−	0.0238036i
$997$	−32.2485	+	18.6187i	−1.02132	+	0.589660i	−0.914486	−	0.404617i	$-0.867405\pi$
$997$	−32.2485	+	18.6187i	−1.02132	+	0.589660i	−0.106834	+	0.994277i	$0.534071\pi$
$998$	2.81093	−	4.86868i	0.0889785	−	0.154115i
$999$	37.0054	−	14.1780i	1.17080	−	0.448573i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.p.b.230.19	✓	96
3.2	odd	2	inner	429.2.p.b.230.30	yes	96
11.10	odd	2	inner	429.2.p.b.230.29	yes	96
13.3	even	3	inner	429.2.p.b.263.20	yes	96
33.32	even	2	inner	429.2.p.b.230.20	yes	96
39.29	odd	6	inner	429.2.p.b.263.29	yes	96
143.120	odd	6	inner	429.2.p.b.263.30	yes	96
429.263	even	6	inner	429.2.p.b.263.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.p.b.230.19	✓	96	1.1	even	1	trivial
429.2.p.b.230.20	yes	96	33.32	even	2	inner
429.2.p.b.230.29	yes	96	11.10	odd	2	inner
429.2.p.b.230.30	yes	96	3.2	odd	2	inner
429.2.p.b.263.19	yes	96	429.263	even	6	inner
429.2.p.b.263.20	yes	96	13.3	even	3	inner
429.2.p.b.263.29	yes	96	39.29	odd	6	inner
429.2.p.b.263.30	yes	96	143.120	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400235 + 0.693228i) q^{2} +(-1.18152 + 1.26649i) q^{3} +(0.679624 + 1.17714i) q^{4} -2.49177i q^{5} +(-0.405079 - 1.32596i) q^{6} +(-0.533256 + 0.307876i) q^{7} -2.68898 q^{8} +(-0.207999 - 2.99278i) q^{9} +O(q^{10})\)	\(q+(-0.400235 + 0.693228i) q^{2} +(-1.18152 + 1.26649i) q^{3} +(0.679624 + 1.17714i) q^{4} -2.49177i q^{5} +(-0.405079 - 1.32596i) q^{6} +(-0.533256 + 0.307876i) q^{7} -2.68898 q^{8} +(-0.207999 - 2.99278i) q^{9} +(1.72737 + 0.997295i) q^{10} +(-3.17941 + 0.944117i) q^{11} +(-2.29383 - 0.530086i) q^{12} +(-2.90515 - 2.13544i) q^{13} -0.492891i q^{14} +(3.15581 + 2.94409i) q^{15} +(-0.283023 + 0.490211i) q^{16} +(-2.03186 - 3.51928i) q^{17} +(2.15793 + 1.05363i) q^{18} +(-5.18322 + 2.99253i) q^{19} +(2.93317 - 1.69347i) q^{20} +(0.240134 - 1.03913i) q^{21} +(0.618024 - 2.58192i) q^{22} +(0.318813 + 0.184067i) q^{23} +(3.17709 - 3.40557i) q^{24} -1.20893 q^{25} +(2.64309 - 1.15925i) q^{26} +(4.03609 + 3.27262i) q^{27} +(-0.724827 - 0.418479i) q^{28} +(1.24579 - 2.15778i) q^{29} +(-3.30399 + 1.00936i) q^{30} -2.67384 q^{31} +(-2.91553 - 5.04985i) q^{32} +(2.56084 - 5.14219i) q^{33} +3.25288 q^{34} +(0.767156 + 1.32875i) q^{35} +(3.38157 - 2.27881i) q^{36} +(3.81325 - 6.60475i) q^{37} -4.79087i q^{38} +(6.13702 - 1.15628i) q^{39} +6.70032i q^{40} +(-4.02997 + 6.98010i) q^{41} +(0.624241 + 0.582362i) q^{42} +(5.27705 - 3.04671i) q^{43} +(-3.27216 - 3.10097i) q^{44} +(-7.45733 + 0.518286i) q^{45} +(-0.255200 + 0.147340i) q^{46} -0.492431i q^{47} +(-0.286448 - 0.937642i) q^{48} +(-3.31043 + 5.73382i) q^{49} +(0.483855 - 0.838061i) q^{50} +(6.85782 + 1.58479i) q^{51} +(0.539306 - 4.87107i) q^{52} -7.11354i q^{53} +(-3.88405 + 1.48811i) q^{54} +(2.35252 + 7.92236i) q^{55} +(1.43391 - 0.827871i) q^{56} +(2.33409 - 10.1003i) q^{57} +(0.997221 + 1.72724i) q^{58} +(-8.67632 + 5.00927i) q^{59} +(-1.32085 + 5.71571i) q^{60} +(2.96548 - 1.71212i) q^{61} +(1.07016 - 1.85358i) q^{62} +(1.03232 + 1.53188i) q^{63} +3.53550 q^{64} +(-5.32102 + 7.23897i) q^{65} +(2.53977 + 3.83333i) q^{66} +(-1.28542 + 2.22641i) q^{67} +(2.76179 - 4.78357i) q^{68} +(-0.609804 + 0.186294i) q^{69} -1.22817 q^{70} +(-12.6355 + 7.29512i) q^{71} +(0.559304 + 8.04752i) q^{72} +15.9862i q^{73} +(3.05240 + 5.28691i) q^{74} +(1.42838 - 1.53109i) q^{75} +(-7.04528 - 4.06759i) q^{76} +(1.40477 - 1.48232i) q^{77} +(-1.65469 + 4.71714i) q^{78} -8.77299i q^{79} +(1.22149 + 0.705229i) q^{80} +(-8.91347 + 1.24499i) q^{81} +(-3.22587 - 5.58737i) q^{82} +1.41718 q^{83} +(1.38640 - 0.423543i) q^{84} +(-8.76923 + 5.06292i) q^{85} +4.87760i q^{86} +(1.26087 + 4.12725i) q^{87} +(8.54936 - 2.53871i) q^{88} +(-0.846297 - 0.488610i) q^{89} +(2.62539 - 5.37706i) q^{90} +(2.20664 + 0.244310i) q^{91} +0.500384i q^{92} +(3.15920 - 3.38639i) q^{93} +(0.341367 + 0.197088i) q^{94} +(7.45671 + 12.9154i) q^{95} +(9.84035 + 2.27403i) q^{96} +(5.19256 + 8.99377i) q^{97} +(-2.64990 - 4.58976i) q^{98} +(3.48685 + 9.31890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9}+O(q^{10}) \) 96 * q + 2 * q^3 - 60 * q^4 - 2 * q^9	\( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9} + 28 q^{12} - 8 q^{15} - 44 q^{16} + 16 q^{22} - 56 q^{25} + 44 q^{27} - 40 q^{31} - 16 q^{33} - 56 q^{34} + 40 q^{36} + 28 q^{37} - 22 q^{42} - 10 q^{45} + 24 q^{48} - 8 q^{49} - 12 q^{55} - 16 q^{58} - 76 q^{60} + 104 q^{64} + 68 q^{66} - 24 q^{67} + 30 q^{69} + 88 q^{70} - 66 q^{75} - 28 q^{78} - 66 q^{81} + 32 q^{82} - 8 q^{88} - 80 q^{91} + 30 q^{93} - 80 q^{97} - 68 q^{99}+O(q^{100}) \) 96 * q + 2 * q^3 - 60 * q^4 - 2 * q^9 + 28 * q^12 - 8 * q^15 - 44 * q^16 + 16 * q^22 - 56 * q^25 + 44 * q^27 - 40 * q^31 - 16 * q^33 - 56 * q^34 + 40 * q^36 + 28 * q^37 - 22 * q^42 - 10 * q^45 + 24 * q^48 - 8 * q^49 - 12 * q^55 - 16 * q^58 - 76 * q^60 + 104 * q^64 + 68 * q^66 - 24 * q^67 + 30 * q^69 + 88 * q^70 - 66 * q^75 - 28 * q^78 - 66 * q^81 + 32 * q^82 - 8 * q^88 - 80 * q^91 + 30 * q^93 - 80 * q^97 - 68 * q^99

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