LMFDB - Embedded newform 429.2.bb.b.25.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(25,429)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("429.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.b.103.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.386931 + 0.532564i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.484125 - 1.48998i) q^{4} +(0.663105 - 0.912685i) q^{5} +(0.386931 - 0.532564i) q^{6} +(3.82419 + 1.24256i) q^{7} +(2.23297 - 0.725535i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.742639 q^{10} +(-2.15706 - 2.51935i) q^{11} -1.56666 q^{12} +(-2.85740 + 2.19892i) q^{13} +(0.817956 + 2.51741i) q^{14} +(-1.07293 - 0.348615i) q^{15} +(-1.28451 - 0.933253i) q^{16} +(-1.63950 - 1.19117i) q^{17} +(-0.626067 - 0.203421i) q^{18} +(2.02272 - 0.657222i) q^{19} +(-1.03886 - 1.42987i) q^{20} -4.02099i q^{21} +(0.507082 - 2.12358i) q^{22} +2.39350 q^{23} +(-1.38005 - 1.89948i) q^{24} +(1.15180 + 3.54487i) q^{25} +(-2.27668 - 0.670921i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.70277 - 5.09643i) q^{28} +(2.23943 - 6.89227i) q^{29} +(-0.229488 - 0.706291i) q^{30} +(4.11515 + 5.66402i) q^{31} -5.74095i q^{32} +(-1.72947 + 2.83000i) q^{33} -1.33404i q^{34} +(3.66990 - 2.66634i) q^{35} +(0.484125 + 1.48998i) q^{36} +(-0.801277 - 0.260351i) q^{37} +(1.13267 + 0.822930i) q^{38} +(2.97428 + 2.03805i) q^{39} +(0.818506 - 2.51910i) q^{40} +(4.60558 - 1.49644i) q^{41} +(2.14144 - 1.55585i) q^{42} -12.2699 q^{43} +(-4.79807 + 1.99430i) q^{44} +1.12814i q^{45} +(0.926117 + 1.27469i) q^{46} +(-2.18753 + 0.710772i) q^{47} +(-0.490640 + 1.51003i) q^{48} +(7.41739 + 5.38905i) q^{49} +(-1.44221 + 1.98503i) q^{50} +(-0.626235 + 1.92735i) q^{51} +(1.89301 + 5.32203i) q^{52} +(-11.4692 + 8.33286i) q^{53} +0.658286i q^{54} +(-3.72972 + 0.298124i) q^{55} +9.44081 q^{56} +(-1.25011 - 1.72063i) q^{57} +(4.53708 - 1.47419i) q^{58} +(4.96443 + 1.61304i) q^{59} +(-1.03886 + 1.42987i) q^{60} +(-0.578093 - 0.420009i) q^{61} +(-1.42418 + 4.38317i) q^{62} +(-3.82419 + 1.24256i) q^{63} +(0.488400 - 0.354843i) q^{64} +(0.112164 + 4.06602i) q^{65} +(-2.17634 + 0.173959i) q^{66} +5.16940i q^{67} +(-2.56855 + 1.86616i) q^{68} +(-0.739632 - 2.27635i) q^{69} +(2.83999 + 0.922770i) q^{70} +(-7.15036 + 9.84163i) q^{71} +(-1.38005 + 1.89948i) q^{72} +(12.8466 + 4.17412i) q^{73} +(-0.171385 - 0.527469i) q^{74} +(3.01545 - 2.19085i) q^{75} -3.33200i q^{76} +(-5.11857 - 12.3147i) q^{77} +(0.0654495 + 2.37258i) q^{78} +(9.87453 - 7.17427i) q^{79} +(-1.70353 + 0.553511i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.57899 + 1.87375i) q^{82} +(-6.89236 + 9.48652i) q^{83} +(-5.99121 - 1.94666i) q^{84} +(-2.17433 + 0.706481i) q^{85} +(-4.74761 - 6.53453i) q^{86} -7.24696 q^{87} +(-6.64451 - 4.06060i) q^{88} -10.8606i q^{89} +(-0.600807 + 0.436512i) q^{90} +(-13.6595 + 4.85861i) q^{91} +(1.15875 - 3.56627i) q^{92} +(4.11515 - 5.66402i) q^{93} +(-1.22495 - 0.889981i) q^{94} +(0.741439 - 2.28192i) q^{95} +(-5.45997 + 1.77405i) q^{96} +(5.69825 + 7.84297i) q^{97} +6.03542i q^{98} +(3.22593 + 0.770308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36}+ \cdots + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.386931	+	0.532564i	0.273601	+	0.376580i	0.923601	−	0.383354i	$-0.125231\pi$
$2$	0.386931	+	0.532564i	0.273601	+	0.376580i	−0.650000	+	0.759934i	$0.725231\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.484125	−	1.48998i	0.242062	−	0.744991i
$5$	0.663105	−	0.912685i	0.296549	−	0.408165i	−0.634578	−	0.772859i	$-0.718826\pi$
$5$	0.663105	−	0.912685i	0.296549	−	0.408165i	0.931128	+	0.364693i	$0.118826\pi$
$6$	0.386931	−	0.532564i	0.157964	−	0.217418i
$7$	3.82419	+	1.24256i	1.44541	+	0.469642i	0.923579	−	0.383408i	$-0.125250\pi$
$7$	3.82419	+	1.24256i	1.44541	+	0.469642i	0.521830	+	0.853050i	$0.325250\pi$
$8$	2.23297	−	0.725535i	0.789473	−	0.256515i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.742639			0.234843
$11$	−2.15706	−	2.51935i	−0.650377	−	0.759611i
$11$	−2.15706	−	2.51935i	−0.650377	−	0.759611i
$12$	−1.56666			−0.452256
$13$	−2.85740	+	2.19892i	−0.792501	+	0.609871i
$13$	−2.85740	+	2.19892i	−0.792501	+	0.609871i
$14$	0.817956	+	2.51741i	0.218608	+	0.672806i
$15$	−1.07293	−	0.348615i	−0.277028	−	0.0900119i
$16$	−1.28451	−	0.933253i	−0.321128	−	0.233313i
$17$	−1.63950	−	1.19117i	−0.397638	−	0.288901i	0.370940	−	0.928657i	$-0.379036\pi$
$17$	−1.63950	−	1.19117i	−0.397638	−	0.288901i	−0.768578	+	0.639756i	$0.779036\pi$
$18$	−0.626067	−	0.203421i	−0.147565	−	0.0479469i
$19$	2.02272	−	0.657222i	0.464044	−	0.150777i	−0.0676578	−	0.997709i	$-0.521553\pi$
$19$	2.02272	−	0.657222i	0.464044	−	0.150777i	0.531702	+	0.846931i	$0.321553\pi$
$20$	−1.03886	−	1.42987i	−0.232296	−	0.319728i
$21$		−	4.02099i		−	0.877453i
$22$	0.507082	−	2.12358i	0.108110	−	0.452749i
$23$	2.39350			0.499079			0.249539	−	0.968365i	$-0.419721\pi$
$23$	2.39350			0.499079			0.249539	+	0.968365i	$0.419721\pi$
$24$	−1.38005	−	1.89948i	−0.281701	−	0.387729i
$25$	1.15180	+	3.54487i	0.230360	+	0.708974i
$26$	−2.27668	−	0.670921i	−0.446494	−	0.131578i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	3.70277	−	5.09643i	0.699758	−	0.963134i
$29$	2.23943	−	6.89227i	0.415852	−	1.27986i	−0.495634	−	0.868532i	$-0.665064\pi$
$29$	2.23943	−	6.89227i	0.415852	−	1.27986i	0.911486	−	0.411331i	$-0.134936\pi$
$30$	−0.229488	−	0.706291i	−0.0418986	−	0.128951i
$31$	4.11515	+	5.66402i	0.739104	+	1.01729i	0.998670	+	0.0515635i	$0.0164205\pi$
$31$	4.11515	+	5.66402i	0.739104	+	1.01729i	−0.259566	+	0.965725i	$0.583580\pi$
$32$		−	5.74095i		−	1.01487i
$33$	−1.72947	+	2.83000i	−0.301063	+	0.492640i
$34$		−	1.33404i		−	0.228786i
$35$	3.66990	−	2.66634i	0.620327	−	0.450694i
$36$	0.484125	+	1.48998i	0.0806874	+	0.248330i
$37$	−0.801277	−	0.260351i	−0.131729	−	0.0428014i	0.242411	−	0.970174i	$-0.422062\pi$
$37$	−0.801277	−	0.260351i	−0.131729	−	0.0428014i	−0.374140	+	0.927372i	$0.622062\pi$
$38$	1.13267	+	0.822930i	0.183743	+	0.133497i
$39$	2.97428	+	2.03805i	0.476266	+	0.326349i
$40$	0.818506	−	2.51910i	0.129417	−	0.398305i
$41$	4.60558	−	1.49644i	0.719271	−	0.233705i	0.0735639	−	0.997291i	$-0.476563\pi$
$41$	4.60558	−	1.49644i	0.719271	−	0.233705i	0.645707	+	0.763585i	$0.276563\pi$
$42$	2.14144	−	1.55585i	0.330431	−	0.240072i
$43$	−12.2699			−1.87115			−0.935574	−	0.353131i	$-0.885117\pi$
$43$	−12.2699			−1.87115			−0.935574	+	0.353131i	$0.885117\pi$
$44$	−4.79807	+	1.99430i	−0.723336	+	0.300652i
$45$			1.12814i			0.168173i
$46$	0.926117	+	1.27469i	0.136549	+	0.187943i
$47$	−2.18753	+	0.710772i	−0.319084	+	0.103677i	−0.464180	−	0.885741i	$-0.653651\pi$
$47$	−2.18753	+	0.710772i	−0.319084	+	0.103677i	0.145096	+	0.989418i	$0.453651\pi$
$48$	−0.490640	+	1.51003i	−0.0708178	+	0.217955i
$49$	7.41739	+	5.38905i	1.05963	+	0.769864i
$50$	−1.44221	+	1.98503i	−0.203959	+	0.280725i
$51$	−0.626235	+	1.92735i	−0.0876905	+	0.269883i
$52$	1.89301	+	5.32203i	0.262514	+	0.738033i
$53$	−11.4692	+	8.33286i	−1.57542	+	1.14461i	−0.653690	+	0.756762i	$0.726780\pi$
$53$	−11.4692	+	8.33286i	−1.57542	+	1.14461i	−0.921725	+	0.387844i	$0.873220\pi$
$54$			0.658286i			0.0895813i
$55$	−3.72972	+	0.298124i	−0.502916	+	0.0401990i
$56$	9.44081			1.26158
$57$	−1.25011	−	1.72063i	−0.165581	−	0.227903i
$58$	4.53708	−	1.47419i	0.595748	−	0.193570i
$59$	4.96443	+	1.61304i	0.646314	+	0.210000i	0.613788	−	0.789471i	$-0.289645\pi$
$59$	4.96443	+	1.61304i	0.646314	+	0.210000i	0.0325258	+	0.999471i	$0.489645\pi$
$60$	−1.03886	+	1.42987i	−0.134116	+	0.184595i
$61$	−0.578093	−	0.420009i	−0.0740172	−	0.0537767i	0.550161	−	0.835058i	$-0.314566\pi$
$61$	−0.578093	−	0.420009i	−0.0740172	−	0.0537767i	−0.624179	+	0.781282i	$0.714566\pi$
$62$	−1.42418	+	4.38317i	−0.180871	+	0.556663i
$63$	−3.82419	+	1.24256i	−0.481803	+	0.156547i
$64$	0.488400	−	0.354843i	0.0610500	−	0.0443554i
$65$	0.112164	+	4.06602i	0.0139123	+	0.504328i
$66$	−2.17634	+	0.173959i	−0.267890	+	0.0214129i
$67$			5.16940i			0.631543i	0.948835	+	0.315772i	$0.102263\pi$
$67$			5.16940i			0.631543i	−0.948835	+	0.315772i	$0.897737\pi$
$68$	−2.56855	+	1.86616i	−0.311482	+	0.226305i
$69$	−0.739632	−	2.27635i	−0.0890412	−	0.274041i
$70$	2.83999	+	0.922770i	0.339444	+	0.110292i
$71$	−7.15036	+	9.84163i	−0.848592	+	1.16799i	0.135579	+	0.990766i	$0.456710\pi$
$71$	−7.15036	+	9.84163i	−0.848592	+	1.16799i	−0.984171	+	0.177220i	$0.943290\pi$
$72$	−1.38005	+	1.89948i	−0.162640	+	0.223855i
$73$	12.8466	+	4.17412i	1.50358	+	0.488544i	0.941061	−	0.338238i	$-0.109831\pi$
$73$	12.8466	+	4.17412i	1.50358	+	0.488544i	0.562523	+	0.826782i	$0.309831\pi$
$74$	−0.171385	−	0.527469i	−0.0199231	−	0.0613170i
$75$	3.01545	−	2.19085i	0.348194	−	0.252978i
$76$		−	3.33200i		−	0.382206i
$77$	−5.11857	−	12.3147i	−0.583316	−	1.40339i
$78$	0.0654495	+	2.37258i	0.00741069	+	0.268642i
$79$	9.87453	−	7.17427i	1.11097	−	0.807168i	0.128155	−	0.991754i	$-0.459094\pi$
$79$	9.87453	−	7.17427i	1.11097	−	0.807168i	0.982816	+	0.184586i	$0.0590943\pi$
$80$	−1.70353	+	0.553511i	−0.190461	+	0.0618844i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.57899	+	1.87375i	0.284802	+	0.206921i
$83$	−6.89236	+	9.48652i	−0.756534	+	1.04128i	0.240960	+	0.970535i	$0.422538\pi$
$83$	−6.89236	+	9.48652i	−0.756534	+	1.04128i	−0.997494	+	0.0707453i	$0.977462\pi$
$84$	−5.99121	−	1.94666i	−0.653695	−	0.212398i
$85$	−2.17433	+	0.706481i	−0.235839	+	0.0766287i
$86$	−4.74761	−	6.53453i	−0.511948	−	0.704636i
$87$	−7.24696			−0.776956
$88$	−6.64451	−	4.06060i	−0.708307	−	0.432861i
$89$		−	10.8606i		−	1.15122i	−0.817725	−	0.575609i	$-0.804765\pi$
$89$		−	10.8606i		−	1.15122i	0.817725	−	0.575609i	$-0.195235\pi$
$90$	−0.600807	+	0.436512i	−0.0633307	+	0.0460124i
$91$	−13.6595	+	4.85861i	−1.43191	+	0.509321i
$92$	1.15875	−	3.56627i	0.120808	−	0.371809i
$93$	4.11515	−	5.66402i	0.426722	−	0.587332i
$94$	−1.22495	−	0.889981i	−0.126344	−	0.0917946i
$95$	0.741439	−	2.28192i	0.0760701	−	0.234120i
$96$	−5.45997	+	1.77405i	−0.557256	+	0.181063i
$97$	5.69825	+	7.84297i	0.578570	+	0.796333i	0.993538	−	0.113503i	$-0.0362071\pi$
$97$	5.69825	+	7.84297i	0.578570	+	0.796333i	−0.414968	+	0.909836i	$0.636207\pi$
$98$			6.03542i			0.609670i
$99$	3.22593	+	0.770308i	0.324218	+	0.0774188i
$100$	5.83941			0.583941
$101$	2.98098	−	2.16581i	0.296619	−	0.215506i	−0.429515	−	0.903060i	$-0.641315\pi$
$101$	2.98098	−	2.16581i	0.296619	−	0.215506i	0.726134	+	0.687554i	$0.241315\pi$
$102$	−1.26875	+	0.412241i	−0.125625	+	0.0408180i
$103$	3.54475	−	10.9096i	0.349274	−	1.07496i	−0.609981	−	0.792416i	$-0.708823\pi$
$103$	3.54475	−	10.9096i	0.349274	−	1.07496i	0.959256	−	0.282540i	$-0.0911770\pi$
$104$	−4.78509	+	6.98326i	−0.469217	+	0.684765i
$105$	−3.66990	−	2.66634i	−0.358146	−	0.260208i
$106$	−8.87556	−	2.88385i	−0.862071	−	0.280104i
$107$	2.93213	+	9.02418i	0.283460	+	0.872400i	0.986856	+	0.161602i	$0.0516661\pi$
$107$	2.93213	+	9.02418i	0.283460	+	0.872400i	−0.703396	+	0.710798i	$0.748334\pi$
$108$	1.26745	−	0.920860i	0.121961	−	0.0886098i
$109$			14.0974i			1.35028i	0.737688	+	0.675142i	$0.235918\pi$
$109$			14.0974i			1.35028i	−0.737688	+	0.675142i	$0.764082\pi$
$110$	−1.60191	−	1.87096i	−0.152737	−	0.178389i
$111$			0.842512i			0.0799677i
$112$	−3.75260	−	5.16502i	−0.354588	−	0.488048i
$113$	4.80092	+	14.7757i	0.451632	+	1.38998i	0.875044	+	0.484044i	$0.160832\pi$
$113$	4.80092	+	14.7757i	0.451632	+	1.38998i	−0.423412	+	0.905937i	$0.639168\pi$
$114$	0.432640	−	1.33153i	0.0405204	−	0.124709i
$115$	1.58714	−	2.18451i	0.148002	−	0.203707i
$116$	−9.18519	−	6.67343i	−0.852824	−	0.619613i
$117$	1.01919	−	3.45850i	0.0942246	−	0.319739i
$118$	1.06184	+	3.26801i	0.0977505	+	0.300845i
$119$	−4.78969	−	6.59244i	−0.439070	−	0.604328i
$120$	−2.64874			−0.241796
$121$	−1.69421	+	10.8687i	−0.154019	+	0.988068i
$122$		−	0.470386i		−	0.0425867i
$123$	−2.84641	−	3.91774i	−0.256652	−	0.353251i
$124$	10.4315	−	3.38941i	0.936780	−	0.304378i
$125$	9.36374	+	3.04246i	0.837519	+	0.272126i
$126$	−2.14144	−	1.55585i	−0.190774	−	0.138606i
$127$	0.0779493	+	0.0566334i	0.00691688	+	0.00502541i	0.591238	−	0.806497i	$-0.298639\pi$
$127$	0.0779493	+	0.0566334i	0.00691688	+	0.00502541i	−0.584321	+	0.811522i	$0.698639\pi$
$128$	−10.5420	−	3.42530i	−0.931788	−	0.302756i
$129$	3.79162	+	11.6694i	0.333833	+	1.02743i
$130$	−2.12202	+	1.63300i	−0.186113	+	0.143224i
$131$	−13.5704			−1.18565			−0.592824	−	0.805332i	$-0.701987\pi$
$131$	−13.5704			−1.18565			−0.592824	+	0.805332i	$0.701987\pi$
$132$	3.37938	+	3.94696i	0.294137	+	0.343539i
$133$	8.55191			0.741545
$134$	−2.75304	+	2.00020i	−0.237826	+	0.172791i
$135$	1.07293	−	0.348615i	0.0923427	−	0.0300040i
$136$	−4.52520	−	1.47033i	−0.388032	−	0.126079i
$137$	−5.31065	+	7.30948i	−0.453719	+	0.624491i	−0.973192	−	0.229996i	$-0.926129\pi$
$137$	−5.31065	+	7.30948i	−0.453719	+	0.624491i	0.519472	+	0.854487i	$0.326129\pi$
$138$	0.926117	−	1.27469i	0.0788363	−	0.108509i
$139$	1.04092	−	3.20362i	0.0882897	−	0.271728i	−0.897157	−	0.441711i	$-0.854371\pi$
$139$	1.04092	−	3.20362i	0.0882897	−	0.271728i	0.985447	+	0.169984i	$0.0543715\pi$
$140$	−2.19611	−	6.75893i	−0.185605	−	0.571234i
$141$	1.35197	+	1.86083i	0.113856	+	0.156710i
$142$	−8.00799			−0.672016
$143$	11.7034	+	2.45559i	0.978689	+	0.205347i
$144$	1.58774			0.132312
$145$	−4.80549	−	6.61419i	−0.399074	−	0.549279i
$146$	2.74776	+	8.45674i	0.227406	+	0.699885i
$147$	2.83319	−	8.71966i	0.233678	−	0.719186i
$148$	−0.775836	+	1.06785i	−0.0637733	+	0.0877764i
$149$	9.88395	−	13.6041i	0.809725	−	1.11449i	−0.181641	−	0.983365i	$-0.558141\pi$
$149$	9.88395	−	13.6041i	0.809725	−	1.11449i	0.991366	−	0.131126i	$-0.0418591\pi$
$150$	2.33354	+	0.758212i	0.190533	+	0.0619078i
$151$	−14.6385	+	4.75634i	−1.19126	+	0.387065i	−0.836540	−	0.547906i	$-0.815425\pi$
$151$	−14.6385	+	4.75634i	−1.19126	+	0.387065i	−0.354724	+	0.934971i	$0.615425\pi$
$152$	4.03983	−	2.93511i	0.327674	−	0.238069i
$153$	2.02654			0.163836
$154$	4.57785	−	7.49091i	0.368894	−	0.603635i
$155$	7.89825			0.634403
$156$	4.47658	−	3.44496i	0.358413	−	0.275818i
$157$	−2.18396	−	6.72152i	−0.174299	−	0.536436i	0.825302	−	0.564691i	$-0.191005\pi$
$157$	−2.18396	−	6.72152i	−0.174299	−	0.536436i	−0.999601	+	0.0282554i	$0.991005\pi$
$158$	7.64152	+	2.48288i	0.607926	+	0.197527i
$159$	11.4692	+	8.33286i	0.909566	+	0.660839i
$160$	−5.23968	−	3.80685i	−0.414233	−	0.300958i
$161$	9.15320	+	2.97405i	0.721373	+	0.234388i
$162$	0.626067	−	0.203421i	0.0491884	−	0.0159823i
$163$	1.77287	+	2.44015i	0.138862	+	0.191127i	0.872784	−	0.488107i	$-0.162312\pi$
$163$	1.77287	+	2.44015i	0.138862	+	0.191127i	−0.733922	+	0.679234i	$0.762312\pi$
$164$		−	7.58670i		−	0.592422i
$165$	1.43608	+	3.45505i	0.111799	+	0.268976i
$166$	−7.71904			−0.599114
$167$	−7.19005	−	9.89626i	−0.556383	−	0.765795i	0.434478	−	0.900682i	$-0.356933\pi$
$167$	−7.19005	−	9.89626i	−0.556383	−	0.765795i	−0.990861	+	0.134887i	$0.956933\pi$
$168$	−2.91737	−	8.97875i	−0.225080	−	0.692725i
$169$	3.32950	−	12.5664i	0.256116	−	0.966646i
$170$	−1.21756	−	0.884609i	−0.0933826	−	0.0678464i
$171$	−1.25011	+	1.72063i	−0.0955984	+	0.131580i
$172$	−5.94018	+	18.2820i	−0.452934	+	1.39399i
$173$	−1.23987	−	3.81592i	−0.0942655	−	0.290119i	0.892796	−	0.450461i	$-0.148740\pi$
$173$	−1.23987	−	3.81592i	−0.0942655	−	0.290119i	−0.987062	+	0.160342i	$0.948740\pi$
$174$	−2.80407	−	3.85947i	−0.212576	−	0.292586i
$175$			14.9874i			1.13294i
$176$	0.419579	+	5.24921i	0.0316270	+	0.395674i
$177$		−	5.21991i		−	0.392353i
$178$	5.78395	−	4.20228i	0.433525	−	0.314974i
$179$	1.77240	+	5.45490i	0.132476	+	0.407718i	0.995189	−	0.0979754i	$-0.0312367\pi$
$179$	1.77240	+	5.45490i	0.132476	+	0.407718i	−0.862713	+	0.505694i	$0.831237\pi$
$180$	1.68091	+	0.546161i	0.125288	+	0.0407084i
$181$	−0.753102	−	0.547161i	−0.0559777	−	0.0406701i	0.559445	−	0.828868i	$-0.311014\pi$
$181$	−0.753102	−	0.547161i	−0.0559777	−	0.0406701i	−0.615422	+	0.788198i	$0.711014\pi$
$182$	−7.87282	−	5.39464i	−0.583572	−	0.399877i
$183$	−0.220812	+	0.679589i	−0.0163229	+	0.0502367i
$184$	5.34460	−	1.73657i	0.394009	−	0.128021i
$185$	−0.768949	+	0.558674i	−0.0565342	+	0.0410745i
$186$	4.60874			0.337929
$187$	0.535536	+	6.69990i	0.0391623	+	0.489945i
$188$			3.60349i			0.262811i
$189$	2.36348	+	3.25305i	0.171918	+	0.236625i
$190$	1.50215	−	0.488079i	0.108978	−	0.0354090i
$191$	−2.14235	+	6.59348i	−0.155015	+	0.477088i	−0.998162	−	0.0605950i	$-0.980700\pi$
$191$	−2.14235	+	6.59348i	−0.155015	+	0.477088i	0.843147	+	0.537683i	$0.180700\pi$
$192$	−0.488400	−	0.354843i	−0.0352472	−	0.0256086i
$193$	16.1082	−	22.1710i	1.15949	−	1.59591i	0.446410	−	0.894829i	$-0.352702\pi$
$193$	16.1082	−	22.1710i	1.15949	−	1.59591i	0.713084	−	0.701078i	$-0.247298\pi$
$194$	−1.97206	+	6.06937i	−0.141586	+	0.435756i
$195$	3.83236	−	1.36315i	0.274441	−	0.0976168i
$196$	11.6205	−	8.44281i	0.830038	−	0.603058i
$197$			2.55033i			0.181704i	0.995864	+	0.0908518i	$0.0289589\pi$
$197$			2.55033i			0.181704i	−0.995864	+	0.0908518i	$0.971041\pi$
$198$	0.837973	+	2.01607i	0.0595521	+	0.143276i
$199$	−13.7970			−0.978046			−0.489023	−	0.872271i	$-0.662647\pi$
$199$	−13.7970			−0.978046			−0.489023	+	0.872271i	$0.662647\pi$
$200$	5.14386	+	7.07991i	0.363726	+	0.500625i
$201$	4.91639	−	1.59743i	0.346776	−	0.112674i
$202$	2.30686	+	0.749546i	0.162310	+	0.0527379i
$203$	17.1281	−	23.5747i	1.20215	−	1.65462i
$204$	2.56855	+	1.86616i	0.179834	+	0.130657i
$205$	1.68820	−	5.19575i	0.117909	−	0.362887i
$206$	7.18164	−	2.33346i	0.500368	−	0.162580i
$207$	−1.93638	+	1.40686i	−0.134588	+	0.0977837i
$208$	5.72252	−	0.157860i	0.396785	−	0.0109456i
$209$	−6.01890	−	3.67827i	−0.416336	−	0.254431i
$210$		−	2.98615i		−	0.206064i
$211$	−8.40158	+	6.10411i	−0.578389	+	0.420224i	−0.838143	−	0.545451i	$-0.816358\pi$
$211$	−8.40158	+	6.10411i	−0.578389	+	0.420224i	0.259754	+	0.965675i	$0.416358\pi$
$212$	6.86329	+	21.1230i	0.471373	+	1.45074i
$213$	11.5695	+	3.75917i	0.792731	+	0.257574i
$214$	−3.67142	+	5.05328i	−0.250973	+	0.345435i
$215$	−8.13625	+	11.1986i	−0.554888	+	0.763737i
$216$	2.23297	+	0.725535i	0.151934	+	0.0493664i
$217$	8.69928	+	26.7736i	0.590546	+	1.81751i
$218$	−7.50776	+	5.45470i	−0.508489	+	0.369439i
$219$		−	13.5077i		−	0.912768i
$220$	−1.36145	+	5.70155i	−0.0917891	+	0.384399i
$221$	7.30401	−	0.201487i	0.491321	−	0.0135535i
$222$	−0.448692	+	0.325994i	−0.0301142	+	0.0218793i
$223$	−9.29582	+	3.02040i	−0.622494	+	0.202261i	−0.603247	−	0.797554i	$-0.706127\pi$
$223$	−9.29582	+	3.02040i	−0.622494	+	0.202261i	−0.0192469	+	0.999815i	$0.506127\pi$
$224$	7.13345	−	21.9545i	0.476624	−	1.46690i
$225$	−3.01545	−	2.19085i	−0.201030	−	0.146057i
$226$	−6.01139	+	8.27397i	−0.399872	+	0.550376i
$227$	−11.3378	−	3.68387i	−0.752516	−	0.244507i	−0.0924525	−	0.995717i	$-0.529471\pi$
$227$	−11.3378	−	3.68387i	−0.752516	−	0.244507i	−0.660063	+	0.751210i	$0.729471\pi$
$228$	−3.16892	+	1.02964i	−0.209867	+	0.0681898i
$229$	−17.2787	−	23.7821i	−1.14181	−	1.57156i	−0.763401	−	0.645925i	$-0.776472\pi$
$229$	−17.2787	−	23.7821i	−1.14181	−	1.57156i	−0.378407	−	0.925639i	$-0.623528\pi$
$230$	1.77750			0.117205
$231$	−10.1303	+	8.67351i	−0.666523	+	0.570675i
$232$		−	17.0150i		−	1.11709i
$233$	3.38877	−	2.46208i	0.222005	−	0.161296i	−0.471224	−	0.882014i	$-0.656187\pi$
$233$	3.38877	−	2.46208i	0.222005	−	0.161296i	0.693229	+	0.720717i	$0.256187\pi$
$234$	2.23623	−	0.795414i	0.146187	−	0.0519978i
$235$	−0.801851	+	2.46784i	−0.0523070	+	0.160984i
$236$	4.80681	−	6.61600i	0.312896	−	0.430665i
$237$	−9.87453	−	7.17427i	−0.641420	−	0.466019i
$238$	1.65762	−	5.10163i	0.107448	−	0.330690i
$239$	4.37633	−	1.42196i	0.283081	−	0.0919787i	−0.164035	−	0.986455i	$-0.552451\pi$
$239$	4.37633	−	1.42196i	0.283081	−	0.0919787i	0.447116	+	0.894476i	$0.352451\pi$
$240$	1.05284	+	1.44911i	0.0679606	+	0.0935397i
$241$		−	13.7535i		−	0.885939i	−0.896537	−	0.442969i	$-0.853925\pi$
$241$		−	13.7535i		−	0.885939i	0.896537	−	0.442969i	$-0.146075\pi$
$242$	−6.44385	+	3.30317i	−0.414226	+	0.212336i
$243$	−1.00000			−0.0641500
$244$	−0.905675	+	0.658012i	−0.0579799	+	0.0421249i
$245$	9.83701	−	3.19624i	0.628463	−	0.204200i
$246$	0.985088	−	3.03179i	0.0628069	−	0.193300i
$247$	−4.33455	+	6.32575i	−0.275801	+	0.402498i
$248$	13.2985	+	9.66189i	0.844453	+	0.613531i
$249$	11.1521	+	3.62353i	0.706734	+	0.229632i
$250$	2.00281	+	6.16402i	0.126669	+	0.389847i
$251$	−3.50995	+	2.55013i	−0.221546	+	0.160963i	−0.693022	−	0.720916i	$-0.743721\pi$
$251$	−3.50995	+	2.55013i	−0.221546	+	0.160963i	0.471476	+	0.881879i	$0.343721\pi$
$252$			6.29953i			0.396833i
$253$	−5.16291	−	6.03005i	−0.324589	−	0.379106i
$254$			0.0634262i			0.00397971i
$255$	1.34381	+	1.84959i	0.0841525	+	0.115826i
$256$	−2.62793	−	8.08793i	−0.164246	−	0.505496i
$257$	9.20612	−	28.3335i	0.574262	−	1.76740i	−0.0644179	−	0.997923i	$-0.520519\pi$
$257$	9.20612	−	28.3335i	0.574262	−	1.76740i	0.638680	−	0.769473i	$-0.279481\pi$
$258$	−4.74761	+	6.53453i	−0.295573	+	0.406822i
$259$	−2.74074	−	1.99126i	−0.170301	−	0.123731i
$260$	6.11260	+	1.80134i	0.379088	+	0.111714i
$261$	2.23943	+	6.89227i	0.138617	+	0.426621i
$262$	−5.25079	−	7.22709i	−0.324395	−	0.446491i
$263$	−8.38343			−0.516944			−0.258472	−	0.966019i	$-0.583219\pi$
$263$	−8.38343			−0.516944			−0.258472	+	0.966019i	$0.583219\pi$
$264$	−1.80859	+	7.57410i	−0.111311	+	0.466154i
$265$			15.9933i			0.982462i
$266$	3.30900	+	4.55444i	0.202888	+	0.279251i
$267$	−10.3290	+	3.35610i	−0.632125	+	0.205390i
$268$	7.70232	+	2.50264i	0.470494	+	0.152873i
$269$	1.26407	+	0.918397i	0.0770714	+	0.0559957i	0.625654	−	0.780101i	$-0.284832\pi$
$269$	1.26407	+	0.918397i	0.0770714	+	0.0559957i	−0.548582	+	0.836097i	$0.684832\pi$
$270$	0.600807	+	0.436512i	0.0365640	+	0.0265653i
$271$	−8.23966	−	2.67723i	−0.500524	−	0.162630i	0.0478647	−	0.998854i	$-0.484758\pi$
$271$	−8.23966	−	2.67723i	−0.500524	−	0.162630i	−0.548388	+	0.836224i	$0.684758\pi$
$272$	0.994301	+	3.06014i	0.0602884	+	0.185549i
$273$	8.84184	+	11.4896i	0.535133	+	0.695382i
$274$	−5.94762			−0.359309
$275$	6.44626	−	10.5483i	0.388724	−	0.636084i
$276$	−3.74980			−0.225711
$277$	19.5158	−	14.1791i	1.17259	−	0.851939i	0.181276	−	0.983432i	$-0.441977\pi$
$277$	19.5158	−	14.1791i	1.17259	−	0.851939i	0.991317	+	0.131494i	$0.0419773\pi$
$278$	2.10890	−	0.685223i	0.126483	−	0.0410969i
$279$	−6.65846	−	2.16346i	−0.398632	−	0.129523i
$280$	6.26025	−	8.61649i	0.374121	−	0.514934i
$281$	2.11948	−	2.91722i	0.126438	−	0.174027i	−0.741105	−	0.671389i	$-0.765698\pi$
$281$	2.11948	−	2.91722i	0.126438	−	0.174027i	0.867543	+	0.497362i	$0.165698\pi$
$282$	−0.467891	+	1.44002i	−0.0278625	+	0.0857519i
$283$	4.25907	+	13.1081i	0.253176	+	0.779194i	0.994184	+	0.107698i	$0.0343480\pi$
$283$	4.25907	+	13.1081i	0.253176	+	0.779194i	−0.741008	+	0.671496i	$0.765652\pi$
$284$	11.2022	+	15.4185i	0.664728	+	0.914919i
$285$	−2.39935			−0.142125
$286$	3.22065	+	7.18297i	0.190441	+	0.424738i
$287$	19.4720			1.14940
$288$	3.37445	+	4.64453i	0.198841	+	0.273681i
$289$	−3.98420	−	12.2621i	−0.234365	−	0.721300i
$290$	1.66309	−	5.11847i	0.0976600	−	0.300567i
$291$	5.69825	−	7.84297i	0.334038	−	0.459763i
$292$	12.4387	−	17.1204i	0.727922	−	1.00190i
$293$	12.1739	+	3.95555i	0.711208	+	0.231085i	0.642207	−	0.766531i	$-0.278019\pi$
$293$	12.1739	+	3.95555i	0.711208	+	0.231085i	0.0690008	+	0.997617i	$0.478019\pi$
$294$	5.74003	−	1.86505i	0.334765	−	0.108772i
$295$	4.76414	−	3.46135i	0.277379	−	0.201527i
$296$	−1.97812			−0.114976
$297$	−0.264261	−	3.30608i	−0.0153340	−	0.191838i
$298$	11.0695			0.641236
$299$	−6.83919	+	5.26311i	−0.395520	+	0.304374i
$300$	−1.80448	−	5.55361i	−0.104182	−	0.320638i
$301$	−46.9226	−	15.2461i	−2.70457	−	0.878769i
$302$	−8.19714	−	5.95557i	−0.471692	−	0.342705i
$303$	−2.98098	−	2.16581i	−0.171253	−	0.124422i
$304$	−3.21157	−	1.04350i	−0.184196	−	0.0598489i
$305$	−0.766672	+	0.249107i	−0.0438995	+	0.0142638i
$306$	0.784130	+	1.07926i	0.0448257	+	0.0616973i
$307$		−	20.1735i		−	1.15137i	−0.817673	−	0.575683i	$-0.804736\pi$
$307$		−	20.1735i		−	1.15137i	0.817673	−	0.575683i	$-0.195264\pi$
$308$	−20.8268	+	1.66472i	−1.18671	+	0.0948563i
$309$	−11.4710			−0.652565
$310$	3.05607	+	4.20632i	0.173573	+	0.238903i
$311$	−2.88109	−	8.86707i	−0.163371	−	0.502806i	0.835541	−	0.549428i	$-0.185154\pi$
$311$	−2.88109	−	8.86707i	−0.163371	−	0.502806i	−0.998913	+	0.0466223i	$0.985154\pi$
$312$	8.12015	+	2.39295i	0.459713	+	0.135474i
$313$	0.355638	+	0.258386i	0.0201019	+	0.0146049i	0.597791	−	0.801652i	$-0.296045\pi$
$313$	0.355638	+	0.258386i	0.0201019	+	0.0146049i	−0.577689	+	0.816257i	$0.696045\pi$
$314$	2.73460	−	3.76386i	0.154323	−	0.212407i
$315$	−1.40178	+	4.31423i	−0.0789812	+	0.243079i
$316$	−5.90903	−	18.1861i	−0.332409	−	1.02305i
$317$	1.61093	+	2.21725i	0.0904786	+	0.124533i	0.851857	−	0.523775i	$-0.175477\pi$
$317$	1.61093	+	2.21725i	0.0904786	+	0.124533i	−0.761378	+	0.648308i	$0.775477\pi$
$318$			9.33232i			0.523331i
$319$	−22.1946	+	9.22511i	−1.24266	+	0.516507i
$320$		−	0.681054i		−	0.0380721i
$321$	7.67643	−	5.57725i	0.428456	−	0.311292i
$322$	1.95778	+	6.02542i	0.109103	+	0.335783i
$323$	−4.09913	−	1.33189i	−0.228081	−	0.0741082i
$324$	−1.26745	−	0.920860i	−0.0704142	−	0.0511589i
$325$	−11.0860	−	7.59641i	−0.614943	−	0.421373i
$326$	−0.613557	+	1.88833i	−0.0339818	+	0.104585i
$327$	13.4074	−	4.35633i	0.741431	−	0.240905i
$328$	9.19839	−	6.68302i	0.507896	−	0.369008i
$329$	−9.24871			−0.509898
$330$	−1.28437	+	2.10167i	−0.0707025	+	0.115693i
$331$		−	3.04838i		−	0.167554i	−0.996485	−	0.0837770i	$-0.973302\pi$
$331$		−	3.04838i		−	0.167554i	0.996485	−	0.0837770i	$-0.0266983\pi$
$332$	10.7980	+	14.8621i	0.592616	+	0.815666i
$333$	0.801277	−	0.260351i	0.0439097	−	0.0142671i
$334$	2.48834	−	7.65833i	0.136156	−	0.419045i
$335$	4.71804	+	3.42786i	0.257774	+	0.187284i
$336$	−3.75260	+	5.16502i	−0.204721	+	0.281775i
$337$	−4.53967	+	13.9717i	−0.247292	+	0.761086i	0.747959	+	0.663745i	$0.231034\pi$
$337$	−4.53967	+	13.9717i	−0.247292	+	0.761086i	−0.995251	+	0.0973413i	$0.968966\pi$
$338$	7.98070	−	3.08915i	0.434093	−	0.168028i
$339$	12.5690	−	9.13189i	0.682652	−	0.495976i
$340$			3.58173i			0.194247i
$341$	5.39302	−	22.5851i	0.292048	−	1.22305i
$342$	−1.40005			−0.0757061
$343$	5.12496	+	7.05390i	0.276722	+	0.380875i
$344$	−27.3984	+	8.90227i	−1.47722	+	0.479978i
$345$	−2.56805	−	0.834409i	−0.138259	−	0.0449231i
$346$	1.55248	−	2.13681i	0.0834619	−	0.114875i
$347$	−4.42657	−	3.21609i	−0.237631	−	0.172649i	0.462596	−	0.886569i	$-0.346918\pi$
$347$	−4.42657	−	3.21609i	−0.237631	−	0.172649i	−0.700227	+	0.713920i	$0.746918\pi$
$348$	−3.50843	+	10.7978i	−0.188072	+	0.578825i
$349$	19.8348	−	6.44472i	1.06173	−	0.344978i	0.274470	−	0.961596i	$-0.411498\pi$
$349$	19.8348	−	6.44472i	1.06173	−	0.344978i	0.787263	+	0.616618i	$0.211498\pi$
$350$	−7.98178	+	5.79910i	−0.426644	+	0.309975i
$351$	−3.60418	+	0.0994242i	−0.192377	+	0.00530687i
$352$	−14.4634	+	12.3836i	−0.770904	+	0.660046i
$353$			15.6505i			0.832992i	0.909138	+	0.416496i	$0.136742\pi$
$353$			15.6505i			0.832992i	−0.909138	+	0.416496i	$0.863258\pi$
$354$	2.77994	−	2.01974i	0.147752	−	0.107348i
$355$	4.24087	+	13.0521i	0.225082	+	0.692731i
$356$	−16.1820	−	5.25786i	−0.857647	−	0.278666i
$357$	−4.78969	+	6.59244i	−0.253497	+	0.348909i
$358$	−2.21929	+	3.05458i	−0.117293	+	0.161440i
$359$	−4.75791	−	1.54594i	−0.251113	−	0.0815914i	0.180756	−	0.983528i	$-0.442146\pi$
$359$	−4.75791	−	1.54594i	−0.251113	−	0.0815914i	−0.431869	+	0.901937i	$0.642146\pi$
$360$	0.818506	+	2.51910i	0.0431390	+	0.132768i
$361$	−11.7119	+	8.50916i	−0.616414	+	0.447851i
$362$		−	0.612789i		−	0.0322074i
$363$	10.8603	−	1.74734i	0.570020	−	0.0917114i
$364$	0.626326	+	22.7046i	0.0328284	+	1.19005i
$365$	12.3283	−	8.95704i	0.645293	−	0.468833i
$366$	−0.447364	+	0.145357i	−0.0233841	+	0.00759795i
$367$	2.16499	−	6.66316i	0.113012	−	0.347814i	−0.878515	−	0.477714i	$-0.841466\pi$
$367$	2.16499	−	6.66316i	0.113012	−	0.347814i	0.991527	+	0.129900i	$0.0414655\pi$
$368$	−3.07448	−	2.23374i	−0.160268	−	0.116442i
$369$	−2.84641	+	3.91774i	−0.148178	+	0.203949i
$370$	−0.595059	−	0.193346i	−0.0309357	−	0.0100516i
$371$	−54.2145	+	17.6153i	−2.81467	+	0.914543i
$372$	−6.44705	−	8.87360i	−0.334264	−	0.460075i
$373$	−21.4113			−1.10864			−0.554318	−	0.832305i	$-0.687021\pi$
$373$	−21.4113			−1.10864			−0.554318	+	0.832305i	$0.687021\pi$
$374$	−3.36091	+	2.87760i	−0.173789	+	0.148797i
$375$		−	9.84562i		−	0.508426i
$376$	−4.36900	+	3.17426i	−0.225314	+	0.163700i
$377$	8.75658	+	24.6183i	0.450987	+	1.26791i
$378$	−0.817956	+	2.51741i	−0.0420711	+	0.129482i
$379$	−14.7779	+	20.3400i	−0.759090	+	1.04480i	0.238199	+	0.971216i	$0.423443\pi$
$379$	−14.7779	+	20.3400i	−0.759090	+	1.04480i	−0.997289	+	0.0735813i	$0.976557\pi$
$380$	−3.04106	−	2.20946i	−0.156003	−	0.113343i
$381$	0.0297740	−	0.0916348i	0.00152537	−	0.00469460i
$382$	−4.34039	+	1.41028i	−0.222074	+	0.0721562i
$383$	22.1589	+	30.4991i	1.13227	+	1.55843i	0.783690	+	0.621153i	$0.213335\pi$
$383$	22.1589	+	30.4991i	1.13227	+	1.55843i	0.348578	+	0.937280i	$0.386665\pi$
$384$			11.0845i			0.565653i
$385$	−14.6336	−	3.49431i	−0.745798	−	0.178086i
$386$	18.0403			0.918225
$387$	9.92659	−	7.21209i	0.504597	−	0.366611i
$388$	14.4446	−	4.69332i	0.733311	−	0.238267i
$389$	−5.12467	+	15.7721i	−0.259831	+	0.799678i	0.733008	+	0.680220i	$0.238116\pi$
$389$	−5.12467	+	15.7721i	−0.259831	+	0.799678i	−0.992839	+	0.119458i	$0.961884\pi$
$390$	2.20882	+	1.51353i	0.111848	+	0.0766408i
$391$	−3.92415	−	2.85106i	−0.198453	−	0.144184i
$392$	20.4727	+	6.65199i	1.03403	+	0.335976i
$393$	4.19347	+	12.9062i	0.211533	+	0.651031i
$394$	−1.35821	+	0.986801i	−0.0684259	+	0.0497143i
$395$		−	13.7696i		−	0.692825i
$396$	2.70950	−	4.43365i	0.136157	−	0.222800i
$397$			0.339439i			0.0170360i	0.999964	+	0.00851799i	$0.00271139\pi$
$397$			0.339439i			0.0170360i	−0.999964	+	0.00851799i	$0.997289\pi$
$398$	−5.33849	−	7.34781i	−0.267595	−	0.368312i
$399$	−2.64269	−	8.13335i	−0.132300	−	0.407177i
$400$	1.82876	−	5.62835i	0.0914381	−	0.281417i
$401$	14.9459	−	20.5713i	0.746365	−	1.02728i	−0.251862	−	0.967763i	$-0.581043\pi$
$401$	14.9459	−	20.5713i	0.746365	−	1.02728i	0.998227	−	0.0595203i	$-0.0189571\pi$
$402$	2.75304	+	2.00020i	0.137309	+	0.0997609i
$403$	−24.2134	−	7.13551i	−1.20615	−	0.355445i
$404$	−1.78385	−	5.49013i	−0.0887499	−	0.273144i
$405$	−0.663105	−	0.912685i	−0.0329499	−	0.0453517i
$406$	19.1824			0.952008
$407$	1.07249	+	2.58028i	0.0531612	+	0.127900i
$408$			4.75807i			0.235560i
$409$	12.2047	+	16.7983i	0.603481	+	0.830621i	0.996021	−	0.0891142i	$-0.0284036\pi$
$409$	12.2047	+	16.7983i	0.603481	+	0.830621i	−0.392540	+	0.919735i	$0.628404\pi$
$410$	3.42028	−	1.11132i	0.168916	−	0.0548841i
$411$	8.59281	+	2.79197i	0.423852	+	0.137718i
$412$	−14.5390	−	10.5632i	−0.716287	−	0.520413i
$413$	16.9806	+	12.3372i	0.835563	+	0.607072i
$414$	−1.49849	−	0.486889i	−0.0736467	−	0.0239293i
$415$	4.08785	+	12.5811i	0.200665	+	0.617582i
$416$	12.6239	+	16.4042i	0.618937	+	0.804283i
$417$	−3.36849			−0.164956
$418$	−0.369979	−	4.62868i	−0.0180963	−	0.226396i
$419$	9.37534			0.458015			0.229008	−	0.973425i	$-0.426452\pi$
$419$	9.37534			0.458015			0.229008	+	0.973425i	$0.426452\pi$
$420$	−5.74949	+	4.17725i	−0.280546	+	0.203829i
$421$	−15.0533	+	4.89112i	−0.733654	+	0.238379i	−0.651933	−	0.758277i	$-0.726042\pi$
$421$	−15.0533	+	4.89112i	−0.733654	+	0.238379i	−0.0817209	+	0.996655i	$0.526042\pi$
$422$	−6.50166	−	2.11252i	−0.316496	−	0.102836i
$423$	1.35197	−	1.86083i	0.0657350	−	0.0904764i
$424$	−19.5646	+	26.9283i	−0.950139	+	1.30775i
$425$	2.33416	−	7.18382i	0.113224	−	0.348466i
$426$	2.47461	+	7.61605i	0.119895	+	0.368999i
$427$	−1.68885	−	2.32451i	−0.0817294	−	0.112491i
$428$	14.8654			0.718546
$429$	−1.28115	−	11.8894i	−0.0618545	−	0.574027i
$430$	−9.11213			−0.439426
$431$	−15.8374	−	21.7983i	−0.762861	−	1.04999i	−0.996971	−	0.0777784i	$-0.975217\pi$
$431$	−15.8374	−	21.7983i	−0.762861	−	1.04999i	0.234109	−	0.972210i	$-0.424783\pi$
$432$	−0.490640	−	1.51003i	−0.0236059	−	0.0726516i
$433$	5.77784	−	17.7823i	0.277665	−	0.854565i	−0.710837	−	0.703357i	$-0.751684\pi$
$433$	5.77784	−	17.7823i	0.277665	−	0.854565i	0.988502	−	0.151208i	$-0.0483164\pi$
$434$	−10.8927	+	14.9925i	−0.522864	+	0.719661i
$435$	−4.80549	+	6.61419i	−0.230406	+	0.317126i
$436$	21.0048	+	6.82488i	1.00595	+	0.326853i
$437$	4.84138	−	1.57306i	0.231595	−	0.0752497i
$438$	7.19374	−	5.22656i	0.343730	−	0.249734i
$439$	−2.43458			−0.116196			−0.0580981	−	0.998311i	$-0.518504\pi$
$439$	−2.43458			−0.116196			−0.0580981	+	0.998311i	$0.518504\pi$
$440$	−8.11205	+	3.37175i	−0.386727	+	0.160742i
$441$	−9.16840			−0.436590
$442$	2.93345	+	3.81189i	0.139530	+	0.181313i
$443$	2.64704	+	8.14675i	0.125765	+	0.387064i	0.994040	−	0.109020i	$-0.0347711\pi$
$443$	2.64704	+	8.14675i	0.125765	+	0.387064i	−0.868275	+	0.496083i	$0.834771\pi$
$444$	1.25533	+	0.407881i	0.0595753	+	0.0193572i
$445$	−9.91227	−	7.20169i	−0.469887	−	0.341393i
$446$	−5.20539	−	3.78194i	−0.246482	−	0.179080i
$447$	−15.9926	−	5.19630i	−0.756423	−	0.245777i
$448$	2.30865	−	0.750125i	0.109073	−	0.0354401i
$449$	−17.9020	−	24.6401i	−0.844850	−	1.16284i	−0.984974	−	0.172702i	$-0.944750\pi$
$449$	−17.9020	−	24.6401i	−0.844850	−	1.16284i	0.140124	−	0.990134i	$-0.455250\pi$
$450$		−	2.45363i		−	0.115665i
$451$	−13.7046	−	8.37514i	−0.645323	−	0.394370i
$452$	24.3398			1.14485
$453$	9.04709	+	12.4523i	0.425070	+	0.585058i
$454$	−2.42504	−	7.46351i	−0.113813	−	0.350280i
$455$	−4.62332	+	15.6886i	−0.216745	+	0.735494i
$456$	−4.03983	−	2.93511i	−0.189183	−	0.137449i
$457$	−8.36316	+	11.5109i	−0.391212	+	0.538457i	−0.958511	−	0.285055i	$-0.907988\pi$
$457$	−8.36316	+	11.5109i	−0.391212	+	0.538457i	0.567299	+	0.823512i	$0.307988\pi$
$458$	5.97983	−	18.4040i	0.279419	−	0.859964i
$459$	−0.626235	−	1.92735i	−0.0292302	−	0.0899612i
$460$	−2.48651	−	3.42239i	−0.115934	−	0.159570i
$461$			7.93590i			0.369612i	0.982775	+	0.184806i	$0.0591656\pi$
$461$			7.93590i			0.369612i	−0.982775	+	0.184806i	$0.940834\pi$
$462$	−8.53892	−	2.03898i	−0.397266	−	0.0948617i
$463$			19.9380i			0.926599i	0.886202	+	0.463299i	$0.153335\pi$
$463$			19.9380i			0.926599i	−0.886202	+	0.463299i	$0.846665\pi$
$464$	−9.30881	+	6.76325i	−0.432151	+	0.313976i
$465$	−2.44069	−	7.51168i	−0.113184	−	0.348346i
$466$	2.62243	+	0.852080i	0.121482	+	0.0394719i
$467$	−6.58067	−	4.78114i	−0.304517	−	0.221245i	0.425023	−	0.905182i	$-0.360266\pi$
$467$	−6.58067	−	4.78114i	−0.304517	−	0.221245i	−0.729540	+	0.683938i	$0.760266\pi$
$468$	−4.65969	−	3.19293i	−0.215394	−	0.147593i
$469$	−6.42327	+	19.7688i	−0.296599	+	0.912838i
$470$	−1.62455	+	0.527847i	−0.0749347	+	0.0243478i
$471$	−5.71767	+	4.15413i	−0.263456	+	0.191412i
$472$	12.2557			0.564116
$473$	26.4669	+	30.9122i	1.21695	+	1.42135i
$474$		−	8.03477i		−	0.369049i
$475$	4.65954	+	6.41330i	0.213794	+	0.294262i
$476$	−12.1414	+	3.94499i	−0.556501	+	0.180818i
$477$	4.38084	−	13.4828i	0.200585	−	0.617337i
$478$	2.45062	+	1.78048i	0.112089	+	0.0814372i
$479$	−3.05847	+	4.20963i	−0.139745	+	0.192343i	−0.873153	−	0.487446i	$-0.837929\pi$
$479$	−3.05847	+	4.20963i	−0.139745	+	0.192343i	0.733408	+	0.679789i	$0.237929\pi$
$480$	−2.00138	+	6.15961i	−0.0913501	+	0.281147i
$481$	2.86206	−	1.01802i	0.130499	−	0.0464176i
$482$	7.32461	−	5.32164i	0.333627	−	0.242394i
$483$		−	9.62424i		−	0.437918i
$484$	15.3740	+	7.78617i	0.698820	+	0.353917i
$485$	10.9367			0.496610
$486$	−0.386931	−	0.532564i	−0.0175515	−	0.0241576i
$487$	0.390286	−	0.126811i	0.0176855	−	0.00574638i	−0.300161	−	0.953889i	$-0.597040\pi$
$487$	0.390286	−	0.126811i	0.0176855	−	0.00574638i	0.317846	+	0.948142i	$0.397040\pi$
$488$	−1.59559	−	0.518440i	−0.0722292	−	0.0234687i
$489$	1.77287	−	2.44015i	0.0801719	−	0.110347i
$490$	5.50844	+	4.00212i	0.248846	+	0.180797i
$491$	6.28993	−	19.3584i	0.283861	−	0.873634i	−0.702877	−	0.711311i	$-0.748102\pi$
$491$	6.28993	−	19.3584i	0.283861	−	0.873634i	0.986738	−	0.162322i	$-0.0518984\pi$
$492$	−7.21538	+	2.34442i	−0.325295	+	0.105695i
$493$	−11.8814	+	8.63236i	−0.535113	+	0.388782i
$494$	−5.04604	+	0.139199i	−0.227032	+	0.00626286i
$495$	2.84218	−	2.43346i	0.127746	−	0.109376i
$496$		−	11.1160i		−	0.499123i
$497$	−39.5731	+	28.7516i	−1.77510	+	1.28968i
$498$	2.38531	+	7.34124i	0.106889	+	0.328969i
$499$	12.4783	+	4.05444i	0.558605	+	0.181502i	0.574693	−	0.818369i	$-0.305121\pi$
$499$	12.4783	+	4.05444i	0.558605	+	0.181502i	−0.0160883	+	0.999871i	$0.505121\pi$
$500$	9.06644	−	12.4789i	0.405463	−	0.558072i
$501$	−7.19005	+	9.89626i	−0.321228	+	0.442132i
$502$	−2.71622	−	0.882553i	−0.121231	−	0.0393902i
$503$	−13.7312	−	42.2602i	−0.612242	−	1.88429i	−0.436021	−	0.899936i	$-0.643613\pi$
$503$	−13.7312	−	42.2602i	−0.612242	−	1.88429i	−0.176221	−	0.984351i	$-0.556387\pi$
$504$	−7.63778	+	5.54917i	−0.340214	+	0.247180i
$505$		−	4.15685i		−	0.184978i
$506$	1.21370	−	5.08279i	0.0539556	−	0.225958i
$507$	−12.9802	+	0.716685i	−0.576472	+	0.0318291i
$508$	0.122120	−	0.0887254i	0.00541820	−	0.00393655i
$509$	29.3431	−	9.53417i	1.30061	−	0.422595i	0.424818	−	0.905279i	$-0.360338\pi$
$509$	29.3431	−	9.53417i	1.30061	−	0.422595i	0.875794	+	0.482684i	$0.160338\pi$
$510$	−0.465067	+	1.43133i	−0.0205935	+	0.0633802i
$511$	43.9414	+	31.9253i	1.94385	+	1.41229i
$512$	−9.74009	+	13.4061i	−0.430455	+	0.592471i
$513$	2.02272	+	0.657222i	0.0893054	+	0.0290171i
$514$	18.6515	−	6.06025i	0.822684	−	0.267306i
$515$	−7.60650	−	10.4695i	−0.335183	−	0.461339i
$516$	19.2228			0.846237
$517$	6.50931	+	3.97797i	0.286279	+	0.174951i
$518$		−	2.23010i		−	0.0979849i
$519$	−3.24602	+	2.35837i	−0.142484	+	0.103521i
$520$	3.20050	+	8.99792i	0.140351	+	0.394585i
$521$	−9.36242	+	28.8146i	−0.410175	+	1.26239i	0.506321	+	0.862345i	$0.331005\pi$
$521$	−9.36242	+	28.8146i	−0.410175	+	1.26239i	−0.916496	+	0.400044i	$0.868995\pi$
$522$	−2.80407	+	3.85947i	−0.122731	+	0.168924i
$523$	−16.1650	−	11.7446i	−0.706846	−	0.513554i	0.175309	−	0.984514i	$-0.443908\pi$
$523$	−16.1650	−	11.7446i	−0.706846	−	0.513554i	−0.882155	+	0.470960i	$0.843908\pi$
$524$	−6.56975	+	20.2196i	−0.287001	+	0.883298i
$525$	14.2539	−	4.63137i	0.622091	−	0.202130i
$526$	−3.24380	−	4.46471i	−0.141437	−	0.194671i
$527$		−	14.1880i		−	0.618041i
$528$	4.86264	−	2.02114i	0.211619	−	0.0879588i
$529$	−17.2712			−0.750920
$530$	−8.51747	+	6.18830i	−0.369975	+	0.268803i
$531$	−4.96443	+	1.61304i	−0.215438	+	0.0700000i
$532$	4.14019	−	12.7422i	0.179500	−	0.552444i
$533$	−9.86944	+	14.4032i	−0.427493	+	0.623874i
$534$	−5.78395	−	4.20228i	−0.250296	−	0.181851i
$535$	10.1805	+	3.30786i	0.440143	+	0.143011i
$536$	3.75058	+	11.5431i	0.162001	+	0.498586i
$537$	4.64021	−	3.37131i	0.200240	−	0.145483i
$538$			1.02855i			0.0443440i
$539$	−2.42285	−	30.3114i	−0.104360	−	1.30561i
$540$		−	1.76741i		−	0.0760574i
$541$	−9.98135	−	13.7382i	−0.429132	−	0.590649i	0.538622	−	0.842548i	$-0.318945\pi$
$541$	−9.98135	−	13.7382i	−0.429132	−	0.590649i	−0.967754	+	0.251898i	$0.918945\pi$
$542$	−1.76238	−	5.42405i	−0.0757007	−	0.232983i
$543$	−0.287659	+	0.885325i	−0.0123446	+	0.0379929i
$544$	−6.83845	+	9.41232i	−0.293196	+	0.403550i
$545$	12.8665	+	9.34803i	0.551139	+	0.400426i
$546$	−2.69777	+	9.15453i	−0.115454	+	0.391778i
$547$	−2.83660	−	8.73016i	−0.121284	−	0.373275i	0.871921	−	0.489646i	$-0.162874\pi$
$547$	−2.83660	−	8.73016i	−0.121284	−	0.373275i	−0.993206	+	0.116371i	$0.962874\pi$
$548$	8.31998	+	11.4515i	0.355412	+	0.489183i
$549$	0.714562			0.0304968
$550$	8.11189	−	0.648398i	0.345892	−	0.0276478i
$551$		−	15.4129i		−	0.656614i
$552$	−3.30315	−	4.54639i	−0.140591	−	0.193507i
$553$	46.6766	−	15.1661i	1.98489	−	0.644929i
$554$	15.1025	+	4.90711i	0.641646	+	0.208483i
$555$	0.768949	+	0.558674i	0.0326400	+	0.0237144i
$556$	−4.26941	−	3.10191i	−0.181063	−	0.131550i
$557$	−43.0154	−	13.9765i	−1.82262	−	0.592205i	−0.999711	−	0.0240321i	$-0.992350\pi$
$557$	−43.0154	−	13.9765i	−1.82262	−	0.592205i	−0.822909	−	0.568173i	$-0.807650\pi$
$558$	−1.42418	−	4.38317i	−0.0602902	−	0.185554i
$559$	35.0601	−	26.9806i	1.48289	−	1.14116i
$560$	−7.20240			−0.304357
$561$	6.20650	−	2.57971i	0.262038	−	0.108915i
$562$	2.37370			0.100129
$563$	−22.6269	+	16.4394i	−0.953612	+	0.692840i	−0.951658	−	0.307158i	$-0.900622\pi$
$563$	−22.6269	+	16.4394i	−0.953612	+	0.692840i	−0.00195373	+	0.999998i	$0.500622\pi$
$564$	3.42712	−	1.11354i	0.144308	−	0.0468884i
$565$	16.6691	+	5.41611i	0.701273	+	0.227857i
$566$	−5.33293	+	7.34014i	−0.224160	+	0.308529i
$567$	2.36348	−	3.25305i	0.0992569	−	0.136615i
$568$	−8.82608	+	27.1639i	−0.370334	+	1.13977i
$569$	−9.59042	−	29.5163i	−0.402051	−	1.23739i	−0.923332	−	0.384002i	$-0.874546\pi$
$569$	−9.59042	−	29.5163i	−0.402051	−	1.23739i	0.521281	−	0.853385i	$-0.325454\pi$
$570$	−0.928381	−	1.27781i	−0.0388856	−	0.0535214i
$571$	17.6052			0.736756			0.368378	−	0.929676i	$-0.379913\pi$
$571$	17.6052			0.736756			0.368378	+	0.929676i	$0.379913\pi$
$572$	9.32470	−	16.2491i	0.389885	−	0.679408i
$573$	6.93280			0.289622
$574$	7.53433	+	10.3701i	0.314477	+	0.432840i
$575$	2.75683	+	8.48464i	0.114968	+	0.353834i
$576$	−0.186552	+	0.574149i	−0.00777301	+	0.0239229i
$577$	15.8466	−	21.8110i	0.659704	−	0.908005i	−0.339767	−	0.940510i	$-0.610348\pi$
$577$	15.8466	−	21.8110i	0.659704	−	0.908005i	0.999472	+	0.0325045i	$0.0103483\pi$
$578$	4.98875	−	6.86642i	0.207505	−	0.285606i
$579$	−26.0636	−	8.46859i	−1.08317	−	0.351942i
$580$	−12.1815	+	3.95801i	−0.505809	+	0.164347i
$581$	−38.1452	+	27.7141i	−1.58253	+	1.14978i
$582$	6.38172			0.264531
$583$	45.7331	+	10.9204i	1.89407	+	0.452278i
$584$	31.7146			1.31236
$585$	−2.48069	−	3.22355i	−0.102564	−	0.133278i
$586$	2.60388	+	8.01392i	0.107565	+	0.331052i
$587$	−15.8234	−	5.14135i	−0.653104	−	0.212206i	−0.0363215	−	0.999340i	$-0.511564\pi$
$587$	−15.8234	−	5.14135i	−0.653104	−	0.212206i	−0.616782	+	0.787134i	$0.711564\pi$
$588$	−11.6205	−	8.44281i	−0.479222	−	0.348175i
$589$	12.0463	+	8.75218i	0.496361	+	0.360627i
$590$	3.68678	+	1.19791i	0.151782	+	0.0493171i
$591$	2.42551	−	0.788096i	0.0997721	−	0.0324179i
$592$	0.786277	+	1.08222i	0.0323158	+	0.0444789i
$593$			2.17288i			0.0892294i	0.999004	+	0.0446147i	$0.0142060\pi$
$593$			2.17288i			0.0892294i	−0.999004	+	0.0446147i	$0.985794\pi$
$594$	1.65845	−	1.41996i	0.0680470	−	0.0582616i
$595$	−9.19289			−0.376872
$596$	−15.4848	−	21.3130i	−0.634282	−	0.873014i
$597$	4.26352	+	13.1218i	0.174494	+	0.537038i
$598$	−5.44923	−	1.60585i	−0.222836	−	0.0656680i
$599$	−12.9843	−	9.43364i	−0.530524	−	0.385448i	0.290030	−	0.957018i	$-0.406335\pi$
$599$	−12.9843	−	9.43364i	−0.530524	−	0.385448i	−0.820554	+	0.571570i	$0.806335\pi$
$600$	5.14386	−	7.07991i	0.209997	−	0.289036i
$601$	12.1034	−	37.2505i	0.493709	−	1.51948i	−0.325249	−	0.945628i	$-0.605448\pi$
$601$	12.1034	−	37.2505i	0.493709	−	1.51948i	0.818959	−	0.573852i	$-0.194552\pi$
$602$	−10.0363	−	30.8885i	−0.409048	−	1.25892i
$603$	−3.03850	−	4.18214i	−0.123737	−	0.170310i
$604$			24.1138i			0.981176i
$605$	8.79631	+	8.75340i	0.357621	+	0.355876i
$606$		−	2.42558i		−	0.0985325i
$607$	30.6094	−	22.2391i	1.24240	−	0.902656i	0.244643	−	0.969613i	$-0.421329\pi$
$607$	30.6094	−	22.2391i	1.24240	−	0.902656i	0.997756	+	0.0669575i	$0.0213292\pi$
$608$	−3.77308	−	11.6123i	−0.153019	−	0.470943i
$609$	−27.7138	−	9.00475i	−1.12302	−	0.364891i
$610$	−0.429314	−	0.311915i	−0.0173824	−	0.0126291i
$611$	4.68773	−	6.84117i	0.189645	−	0.276764i
$612$	0.981098	−	3.01951i	0.0396585	−	0.122056i
$613$	−16.7274	+	5.43506i	−0.675612	+	0.219520i	−0.626673	−	0.779282i	$-0.715584\pi$
$613$	−16.7274	+	5.43506i	−0.675612	+	0.219520i	−0.0489390	+	0.998802i	$0.515584\pi$
$614$	10.7437	−	7.80576i	0.433581	−	0.315015i
$615$	−5.46313			−0.220295
$616$	−20.3644	−	23.7847i	−0.820504	−	0.958312i
$617$			28.7614i			1.15789i	0.815367	+	0.578945i	$0.196535\pi$
$617$			28.7614i			1.15789i	−0.815367	+	0.578945i	$0.803465\pi$
$618$	−4.43850	−	6.10907i	−0.178543	−	0.245743i
$619$	23.7054	−	7.70235i	0.952800	−	0.309584i	0.208947	−	0.977927i	$-0.432996\pi$
$619$	23.7054	−	7.70235i	0.952800	−	0.309584i	0.743853	+	0.668343i	$0.232996\pi$
$620$	3.82374	−	11.7683i	0.153565	−	0.472624i
$621$	1.93638	+	1.40686i	0.0777043	+	0.0564555i
$622$	3.60751	−	4.96530i	0.144648	−	0.199091i
$623$	13.4948	−	41.5329i	0.540660	−	1.66398i
$624$	−1.91849	−	5.39366i	−0.0768010	−	0.215919i
$625$	−6.09128	+	4.42558i	−0.243651	+	0.177023i
$626$			0.289378i			0.0115659i
$627$	−1.63830	+	6.86096i	−0.0654275	+	0.274000i
$628$	−11.0723			−0.441831
$629$	1.00358	+	1.38130i	0.0400152	+	0.0550762i
$630$	−2.83999	+	0.922770i	−0.113148	+	0.0367640i
$631$	35.0657	+	11.3935i	1.39594	+	0.453570i	0.907877	−	0.419237i	$-0.137702\pi$
$631$	35.0657	+	11.3935i	1.39594	+	0.453570i	0.488067	+	0.872806i	$0.337702\pi$
$632$	16.8443	−	23.1842i	0.670031	−	0.922219i
$633$	8.40158	+	6.10411i	0.333933	+	0.242616i
$634$	−0.557511	+	1.71584i	−0.0221416	+	0.0681448i
$635$	0.103377	−	0.0335892i	0.00410239	−	0.00133295i
$636$	17.9683	−	13.0548i	0.712491	−	0.517655i
$637$	−33.0445	+	0.911560i	−1.30927	+	0.0361173i
$638$	−13.5007	−	8.25057i	−0.534499	−	0.326643i
$639$		−	12.1649i		−	0.481237i
$640$	−10.1167	+	7.35018i	−0.399896	+	0.290541i
$641$	−5.56468	−	17.1263i	−0.219792	−	0.676449i	−0.998779	−	0.0494088i	$-0.984266\pi$
$641$	−5.56468	−	17.1263i	−0.219792	−	0.676449i	0.778987	−	0.627040i	$-0.215734\pi$
$642$	5.94049	+	1.93018i	0.234452	+	0.0761782i
$643$	16.4493	−	22.6405i	0.648696	−	0.892854i	−0.350346	−	0.936621i	$-0.613936\pi$
$643$	16.4493	−	22.6405i	0.648696	−	0.892854i	0.999042	+	0.0437668i	$0.0139359\pi$
$644$	8.86258	−	12.1983i	0.349234	−	0.480680i
$645$	13.1647	+	4.27748i	0.518361	+	0.168426i
$646$	−0.876762	−	2.69839i	−0.0344957	−	0.106167i
$647$	−26.6318	+	19.3491i	−1.04700	+	0.760693i	−0.971640	−	0.236463i	$-0.924012\pi$
$647$	−26.6318	+	19.3491i	−1.04700	+	0.760693i	−0.0753635	+	0.997156i	$0.524012\pi$
$648$		−	2.34788i		−	0.0922335i
$649$	−6.64475	−	15.9865i	−0.260829	−	0.627527i
$650$	−0.243950	−	8.84331i	−0.00956850	−	0.346863i
$651$	22.7750	−	16.5470i	0.892623	−	0.648529i
$652$	4.49406	−	1.46021i	0.176001	−	0.0571862i
$653$	−10.8922	+	33.5227i	−0.426245	+	1.31185i	0.475553	+	0.879687i	$0.342248\pi$
$653$	−10.8922	+	33.5227i	−0.426245	+	1.31185i	−0.901797	+	0.432159i	$0.857752\pi$
$654$	7.50776	+	5.45470i	0.293576	+	0.213296i
$655$	−8.99857	+	12.3855i	−0.351603	+	0.483941i
$656$	−7.31249	−	2.37597i	−0.285505	−	0.0927661i
$657$	−12.8466	+	4.17412i	−0.501194	+	0.162848i
$658$	−3.57861	−	4.92553i	−0.139509	−	0.192017i
$659$	16.3220			0.635815			0.317908	−	0.948122i	$-0.397020\pi$
$659$	16.3220			0.635815			0.317908	+	0.948122i	$0.397020\pi$
$660$	5.84321	−	0.467059i	0.227447	−	0.0181802i
$661$		−	19.2698i		−	0.749507i	−0.927124	−	0.374754i	$-0.877727\pi$
$661$		−	19.2698i		−	0.749507i	0.927124	−	0.374754i	$-0.122273\pi$
$662$	1.62346	−	1.17951i	0.0630974	−	0.0458430i
$663$	−2.44869	−	6.88427i	−0.0950992	−	0.267363i
$664$	−8.50761	+	26.1837i	−0.330159	+	1.01613i
$665$	5.67081	−	7.80520i	0.219905	−	0.302673i
$666$	0.448692	+	0.325994i	0.0173865	+	0.0126320i
$667$	5.36008	−	16.4966i	0.207543	−	0.638752i
$668$	−18.2261	+	5.92203i	−0.705190	+	0.229130i
$669$	5.74513	+	7.90750i	0.222120	+	0.305722i
$670$			3.83900i			0.148313i
$671$	0.188831	+	2.36240i	0.00728974	+	0.0911994i
$672$	−23.0843			−0.890497
$673$	2.35885	−	1.71380i	0.0909269	−	0.0660623i	−0.541393	−	0.840770i	$-0.682103\pi$
$673$	2.35885	−	1.71380i	0.0909269	−	0.0660623i	0.632320	+	0.774707i	$0.282103\pi$
$674$	−9.19736	+	2.98840i	−0.354269	+	0.115109i
$675$	−1.15180	+	3.54487i	−0.0443327	+	0.136442i
$676$	−17.1118	−	11.0446i	−0.658147	−	0.424793i
$677$	24.9841	+	18.1520i	0.960215	+	0.697637i	0.953201	−	0.302338i	$-0.0977672\pi$
$677$	24.9841	+	18.1520i	0.960215	+	0.697637i	0.00701447	+	0.999975i	$0.497767\pi$
$678$	9.72663	+	3.16037i	0.373549	+	0.121373i
$679$	12.0459	+	37.0734i	0.462279	+	1.42275i
$680$	−4.34262	+	3.15510i	−0.166532	+	0.120993i
$681$			11.9213i			0.456824i
$682$	14.1147	−	5.86675i	0.540482	−	0.224649i
$683$		−	27.3094i		−	1.04496i	−0.852650	−	0.522482i	$-0.825006\pi$
$683$		−	27.3094i		−	1.04496i	0.852650	−	0.522482i	$-0.174994\pi$
$684$	1.95850	+	2.69564i	0.0748851	+	0.103070i
$685$	3.14974	+	9.69390i	0.120345	+	0.370385i
$686$	−1.77365	+	5.45874i	−0.0677184	+	0.208416i
$687$	−17.2787	+	23.7821i	−0.659223	+	0.907343i
$688$	15.7609	+	11.4510i	0.600878	+	0.436563i
$689$	14.4488	−	49.0302i	0.550457	−	1.86790i
$690$	−0.549279	−	1.69051i	−0.0209107	−	0.0643565i
$691$	−1.88200	−	2.59035i	−0.0715946	−	0.0985414i	0.771718	−	0.635965i	$-0.219398\pi$
$691$	−1.88200	−	2.59035i	−0.0715946	−	0.0985414i	−0.843313	+	0.537423i	$0.819398\pi$
$692$	−6.28591			−0.238954
$693$	11.3794	+	6.95420i	0.432269	+	0.264168i
$694$		−	3.60184i		−	0.136724i
$695$	−2.23366	−	3.07437i	−0.0847276	−	0.116618i
$696$	−16.1822	+	5.25792i	−0.613386	+	0.199301i
$697$	−9.33339	−	3.03260i	−0.353527	−	0.114868i
$698$	11.1069	+	8.06965i	0.420403	+	0.305441i
$699$	−3.38877	−	2.46208i	−0.128175	−	0.0931245i
$700$	22.3310	+	7.25579i	0.844034	+	0.274243i
$701$	5.30992	+	16.3422i	0.200553	+	0.617238i	0.999867	+	0.0163243i	$0.00519641\pi$
$701$	5.30992	+	16.3422i	0.200553	+	0.617238i	−0.799314	+	0.600914i	$0.794804\pi$
$702$	−1.44752	−	1.88099i	−0.0546330	−	0.0709933i
$703$	−1.79187			−0.0675816
$704$	−1.94748	−	0.465031i	−0.0733984	−	0.0175265i
$705$	2.59484			0.0977275
$706$	−8.33489	+	6.05565i	−0.313688	+	0.227908i
$707$	14.0910	−	4.57844i	0.529946	−	0.172190i
$708$	−7.77758	−	2.52709i	−0.292299	−	0.0949738i
$709$	8.13159	−	11.1922i	0.305388	−	0.420331i	−0.628548	−	0.777771i	$-0.716350\pi$
$709$	8.13159	−	11.1922i	0.305388	−	0.420331i	0.933936	+	0.357440i	$0.116350\pi$
$710$	−5.31014	+	7.30878i	−0.199286	+	0.274293i
$711$	−3.77174	+	11.6082i	−0.141451	+	0.435342i
$712$	−7.87972	−	24.2513i	−0.295305	−	0.908855i
$713$	9.84962	+	13.5568i	0.368871	+	0.507707i
$714$	−5.36417			−0.200749
$715$	10.0018	−	9.05322i	0.374045	−	0.338571i
$716$	8.98576			0.335814
$717$	−2.70472	−	3.72273i	−0.101010	−	0.139028i
$718$	−1.01767	−	3.13206i	−0.0379790	−	0.116887i
$719$	−8.55271	+	26.3225i	−0.318962	+	0.981665i	0.655130	+	0.755516i	$0.272614\pi$
$719$	−8.55271	+	26.3225i	−0.318962	+	0.981665i	−0.974093	+	0.226149i	$0.927386\pi$
$720$	1.05284	−	1.44911i	0.0392371	−	0.0540052i
$721$	27.1116	−	37.3159i	1.00969	−	1.38972i
$722$	−9.06335	−	2.94486i	−0.337303	−	0.109596i
$723$	−13.0803	+	4.25006i	−0.486463	+	0.158061i
$724$	−1.17986	+	0.857215i	−0.0438490	+	0.0318581i
$725$	27.0116			1.00319
$726$	5.13276	+	5.10773i	0.190495	+	0.189565i
$727$	−28.7921			−1.06784			−0.533919	−	0.845535i	$-0.679281\pi$
$727$	−28.7921			−1.06784			−0.533919	+	0.845535i	$0.679281\pi$
$728$	−26.9762	+	20.7596i	−0.999805	+	0.769402i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	9.54040	+	3.09986i	0.353106	+	0.114731i
$731$	20.1166	+	14.6156i	0.744040	+	0.540577i
$732$	0.905675	+	0.658012i	0.0334747	+	0.0243208i
$733$	23.3976	+	7.60233i	0.864209	+	0.280798i	0.707385	−	0.706828i	$-0.249875\pi$
$733$	23.3976	+	7.60233i	0.864209	+	0.280798i	0.156823	+	0.987627i	$0.449875\pi$
$734$	4.38626	−	1.42518i	0.161900	−	0.0526045i
$735$	−6.07961	−	8.36786i	−0.224250	−	0.308653i
$736$		−	13.7410i		−	0.506498i
$737$	13.0235	−	11.1507i	0.479727	−	0.410741i
$738$	−3.18781			−0.117345
$739$	17.9093	+	24.6501i	0.658805	+	0.906767i	0.999441	−	0.0334282i	$-0.0106425\pi$
$739$	17.9093	+	24.6501i	0.658805	+	0.906767i	−0.340636	+	0.940195i	$0.610642\pi$
$740$	0.460147	+	1.41619i	0.0169153	+	0.0520601i
$741$	7.35560	+	2.16764i	0.270215	+	0.0796302i
$742$	−30.3585	−	22.0568i	−1.11450	−	0.809729i
$743$	−4.48167	+	6.16849i	−0.164416	+	0.226300i	−0.883274	−	0.468858i	$-0.844666\pi$
$743$	−4.48167	+	6.16849i	−0.164416	+	0.226300i	0.718857	+	0.695158i	$0.244666\pi$
$744$	5.07956	−	15.6333i	0.186226	−	0.573144i
$745$	−5.86216	−	18.0419i	−0.214773	−	0.661003i
$746$	−8.28469	−	11.4029i	−0.303324	−	0.417490i
$747$		−	11.7260i		−	0.429031i
$748$	10.2420	+	2.44565i	0.374485	+	0.0894218i
$749$			38.1535i			1.39410i
$750$	5.24343	−	3.80957i	0.191463	−	0.139106i
$751$	−9.53925	−	29.3588i	−0.348092	−	1.07132i	−0.959908	−	0.280317i	$-0.909560\pi$
$751$	−9.53925	−	29.3588i	−0.348092	−	1.07132i	0.611815	−	0.791001i	$-0.290440\pi$
$752$	3.47324	+	1.12852i	0.126656	+	0.0411530i
$753$	3.50995	+	2.55013i	0.127910	+	0.0929320i
$754$	−9.72265	+	14.1890i	−0.354078	+	0.516734i
$755$	−5.36582	+	16.5143i	−0.195282	+	0.601017i
$756$	5.99121	−	1.94666i	0.217898	−	0.0707994i
$757$	2.94643	−	2.14071i	0.107090	−	0.0778054i	−0.532951	−	0.846146i	$-0.678917\pi$
$757$	2.94643	−	2.14071i	0.107090	−	0.0778054i	0.640041	+	0.768340i	$0.278917\pi$
$758$	−16.5504			−0.601137
$759$	−4.13949	+	6.77361i	−0.150254	+	0.245866i
$760$		−	5.63338i		−	0.204344i
$761$	6.07366	+	8.35967i	0.220170	+	0.303038i	0.904786	−	0.425866i	$-0.140030\pi$
$761$	6.07366	+	8.35967i	0.220170	+	0.303038i	−0.684617	+	0.728903i	$0.740030\pi$
$762$	0.0603219	−	0.0195998i	0.00218523	−	0.000710025i
$763$	−17.5168	+	53.9111i	−0.634150	+	1.95171i
$764$	8.78701	+	6.38414i	0.317903	+	0.230970i
$765$	1.34381	−	1.84959i	0.0485855	−	0.0668722i
$766$	−7.66878	+	23.6021i	−0.277084	+	0.852778i
$767$	−17.7323	+	6.30728i	−0.640277	+	0.227743i
$768$	−6.88001	+	4.99862i	−0.248261	+	0.180372i
$769$			31.2861i			1.12821i	0.825704	+	0.564103i	$0.190778\pi$
$769$			31.2861i			1.12821i	−0.825704	+	0.564103i	$0.809222\pi$
$770$	−3.80125	−	9.14540i	−0.136988	−	0.329577i
$771$	−29.7916			−1.07292
$772$	−25.2361	−	34.7345i	−0.908267	−	1.25012i
$773$	32.1206	−	10.4366i	1.15530	−	0.375379i	0.332161	−	0.943223i	$-0.392222\pi$
$773$	32.1206	−	10.4366i	1.15530	−	0.375379i	0.823136	+	0.567844i	$0.192222\pi$
$774$	7.68180	+	2.49597i	0.276117	+	0.0897157i
$775$	−15.3384	+	21.1115i	−0.550972	+	0.758348i
$776$	18.4144	+	13.3788i	0.661037	+	0.480272i
$777$	−1.04687	+	3.22193i	−0.0375562	+	0.115586i
$778$	−10.3826	+	3.37350i	−0.372233	+	0.120946i
$779$	8.33231	−	6.05378i	0.298536	−	0.216899i
$780$	−0.175724	−	6.37008i	−0.00629191	−	0.228085i
$781$	40.2182	−	3.21472i	1.43912	−	0.115032i
$782$		−	3.19303i		−	0.114182i
$783$	5.86291	−	4.25966i	0.209523	−	0.152228i
$784$	−4.49838	−	13.8446i	−0.160656	−	0.494450i
$785$	−7.58283	−	2.46381i	−0.270643	−	0.0879371i
$786$	−5.25079	+	7.22709i	−0.187289	+	0.257782i
$787$	18.7238	−	25.7711i	0.667432	−	0.918641i	−0.332267	−	0.943185i	$-0.607813\pi$
$787$	18.7238	−	25.7711i	0.667432	−	0.918641i	0.999699	+	0.0245442i	$0.00781344\pi$
$788$	3.79995	+	1.23468i	0.135368	+	0.0439836i
$789$	2.59062	+	7.97311i	0.0922286	+	0.283850i
$790$	7.33321	−	5.32789i	0.260904	−	0.189558i
$791$			62.4705i			2.22120i
$792$	7.76228	−	0.620454i	0.275821	−	0.0220469i
$793$	2.57541	−	0.0710448i	0.0914555	−	0.00252287i
$794$	−0.180773	+	0.131339i	−0.00641540	+	0.00466106i
$795$	15.2106	−	4.94221i	0.539463	−	0.175282i
$796$	−6.67948	+	20.5573i	−0.236748	+	0.728636i
$797$	35.6431	+	25.8962i	1.26254	+	0.917291i	0.998880	−	0.0473232i	$-0.0150691\pi$
$797$	35.6431	+	25.8962i	1.26254	+	0.917291i	0.263664	+	0.964615i	$0.415069\pi$
$798$	3.30900	−	4.55444i	0.117137	−	0.161226i
$799$	4.43312	+	1.44041i	0.156832	+	0.0509579i
$800$	20.3509	−	6.61242i	0.719514	−	0.233784i
$801$	6.38368	+	8.78638i	0.225556	+	0.310451i
$802$	16.7386			0.591060
$803$	−17.1948	−	41.3689i	−0.606793	−	1.45988i
$804$		−	8.09870i		−	0.285619i
$805$	8.78390	−	6.38188i	0.309592	−	0.224932i
$806$	−5.56879	−	15.6561i	−0.196152	−	0.551464i
$807$	0.482830	−	1.48600i	0.0169964	−	0.0523096i
$808$	5.08506	−	6.99899i	0.178892	−	0.246224i
$809$	2.57404	+	1.87015i	0.0904985	+	0.0657510i	0.632114	−	0.774875i	$-0.282187\pi$
$809$	2.57404	+	1.87015i	0.0904985	+	0.0657510i	−0.541616	+	0.840626i	$0.682187\pi$
$810$	0.229488	−	0.706291i	0.00806339	−	0.0248166i
$811$	15.9175	−	5.17190i	0.558938	−	0.181610i	−0.0159052	−	0.999874i	$-0.505063\pi$
$811$	15.9175	−	5.17190i	0.558938	−	0.181610i	0.574843	+	0.818264i	$0.305063\pi$
$812$	−26.8338	−	36.9336i	−0.941683	−	1.29612i
$813$			8.66369i			0.303849i
$814$	−0.959190	+	1.56956i	−0.0336196	+	0.0550130i
$815$	3.40268			0.119191
$816$	2.60311	−	1.89127i	0.0911272	−	0.0662078i
$817$	−24.8187	+	8.06407i	−0.868295	+	0.282126i
$818$	−4.22380	+	12.9995i	−0.147682	+	0.454518i
$819$	8.19498	−	11.9596i	0.286356	−	0.417901i
$820$	−6.92427	−	5.03078i	−0.241806	−	0.175682i
$821$	−10.8649	−	3.53023i	−0.379188	−	0.123206i	0.113220	−	0.993570i	$-0.463883\pi$
$821$	−10.8649	−	3.53023i	−0.379188	−	0.123206i	−0.492409	+	0.870364i	$0.663883\pi$
$822$	1.83792	+	5.65652i	0.0641047	+	0.197294i
$823$	−26.1641	+	19.0093i	−0.912023	+	0.662623i	−0.941526	−	0.336941i	$-0.890608\pi$
$823$	−26.1641	+	19.0093i	−0.912023	+	0.662623i	0.0295027	+	0.999565i	$0.490608\pi$
$824$		−	26.9326i		−	0.938243i
$825$	−12.0240	−	2.87117i	−0.418622	−	0.0999612i
$826$			13.8169i			0.480752i
$827$	17.1587	+	23.6170i	0.596668	+	0.821243i	0.995398	−	0.0958252i	$-0.0305490\pi$
$827$	17.1587	+	23.6170i	0.596668	+	0.821243i	−0.398730	+	0.917068i	$0.630549\pi$
$828$	1.15875	+	3.56627i	0.0402694	+	0.123936i
$829$	−2.16417	+	6.66064i	−0.0751648	+	0.231334i	−0.981579	−	0.191056i	$-0.938809\pi$
$829$	−2.16417	+	6.66064i	−0.0751648	+	0.231334i	0.906414	+	0.422390i	$0.138809\pi$
$830$	−5.11853	+	7.04505i	−0.177667	+	0.244537i
$831$	−19.5158	−	14.1791i	−0.676997	−	0.491867i
$832$	−0.615283	+	2.08788i	−0.0213311	+	0.0723843i
$833$	−5.74157	−	17.6707i	−0.198934	−	0.612255i
$834$	−1.30337	−	1.79394i	−0.0451321	−	0.0621189i
$835$	−13.7999			−0.477566
$836$	−8.39445	+	7.18731i	−0.290328	+	0.248578i
$837$			7.00112i			0.241994i
$838$	3.62760	+	4.99297i	0.125314	+	0.172479i
$839$	−38.3309	+	12.4545i	−1.32333	+	0.429976i	−0.883637	−	0.468173i	$-0.844913\pi$
$839$	−38.3309	+	12.4545i	−1.32333	+	0.429976i	−0.439692	+	0.898148i	$0.644913\pi$
$840$	−10.1293	−	3.29121i	−0.349494	−	0.113557i
$841$	−19.0268	−	13.8238i	−0.656097	−	0.476683i
$842$	−8.42942	−	6.12433i	−0.290497	−	0.211058i
$843$	−3.42940	−	1.11428i	−0.118115	−	0.0383778i
$844$	5.02760	+	15.4734i	0.173057	+	0.532615i
$845$	−9.26136	−	11.3716i	−0.318600	−	0.391196i
$846$	1.51413			0.0520567
$847$	−19.9840	+	39.4590i	−0.686659	+	1.35583i
$848$	22.5090			0.772962
$849$	11.1504	−	8.10123i	0.382681	−	0.278034i
$850$	4.72901	−	1.53655i	0.162204	−	0.0527031i
$851$	−1.91785	−	0.623149i	−0.0657432	−	0.0213613i
$852$	11.2022	−	15.4185i	0.383781	−	0.528229i
$853$	−11.4725	+	15.7906i	−0.392813	+	0.540660i	−0.958922	−	0.283670i	$-0.908448\pi$
$853$	−11.4725	+	15.7906i	−0.392813	+	0.540660i	0.566109	+	0.824330i	$0.308448\pi$
$854$	0.584481	−	1.79885i	0.0200005	−	0.0615553i
$855$	0.741439	+	2.28192i	0.0253567	+	0.0780399i
$856$	13.0947	+	18.0233i	0.447568	+	0.616025i
$857$	−3.39761			−0.116060			−0.0580300	−	0.998315i	$-0.518482\pi$
$857$	−3.39761			−0.116060			−0.0580300	+	0.998315i	$0.518482\pi$
$858$	5.83617	−	5.28268i	0.199244	−	0.180348i
$859$	7.52693			0.256816			0.128408	−	0.991721i	$-0.459013\pi$
$859$	7.52693			0.256816			0.128408	+	0.991721i	$0.459013\pi$
$860$	12.7467	+	17.5444i	0.434660	+	0.598258i
$861$	−6.01719	−	18.5190i	−0.205065	−	0.631126i
$862$	5.48103	−	16.8689i	0.186685	−	0.574556i
$863$	−12.1335	+	16.7003i	−0.413029	+	0.568485i	−0.963954	−	0.266069i	$-0.914275\pi$
$863$	−12.1335	+	16.7003i	−0.413029	+	0.568485i	0.550925	+	0.834555i	$0.314275\pi$
$864$	3.37445	−	4.64453i	0.114801	−	0.158010i
$865$	−4.30490	−	1.39875i	−0.146371	−	0.0475588i
$866$	11.7059	−	3.80347i	0.397781	−	0.129247i
$867$	−10.4308	+	7.57840i	−0.354247	+	0.257376i
$868$	44.1038			1.49698
$869$	−39.3744	−	9.40206i	−1.33569	−	0.318943i
$870$	−5.38187			−0.182463
$871$	−11.3671	−	14.7711i	−0.385160	−	0.500499i
$872$	10.2281	+	31.4790i	0.346368	+	1.06601i
$873$	−9.21997	−	2.99575i	−0.312049	−	0.101391i
$874$	2.71103	+	1.96968i	0.0917021	+	0.0666255i
$875$	32.0283	+	23.2699i	1.08276	+	0.786668i
$876$	−20.1263	−	6.53943i	−0.680004	−	0.220947i
$877$	−6.52474	+	2.12002i	−0.220325	+	0.0715879i	−0.417099	−	0.908861i	$-0.636953\pi$
$877$	−6.52474	+	2.12002i	−0.220325	+	0.0715879i	0.196774	+	0.980449i	$0.436953\pi$
$878$	−0.942014	−	1.29657i	−0.0317914	−	0.0437571i
$879$		−	12.8004i		−	0.431747i
$880$	5.06910	+	3.09783i	0.170879	+	0.104428i
$881$	−52.4884			−1.76838			−0.884189	−	0.467130i	$-0.845288\pi$
$881$	−52.4884			−1.76838			−0.884189	+	0.467130i	$0.845288\pi$
$882$	−3.54753	−	4.88276i	−0.119452	−	0.164411i
$883$	−4.46924	−	13.7549i	−0.150402	−	0.462889i	0.847264	−	0.531172i	$-0.178248\pi$
$883$	−4.46924	−	13.7549i	−0.150402	−	0.462889i	−0.997666	+	0.0682824i	$0.978248\pi$
$884$	3.23584	−	10.9804i	0.108833	−	0.369311i
$885$	−4.76414	−	3.46135i	−0.160145	−	0.116352i
$886$	−3.31444	+	4.56194i	−0.111351	+	0.153261i
$887$	−12.8395	+	39.5160i	−0.431109	+	1.32682i	0.465913	+	0.884831i	$0.345726\pi$
$887$	−12.8395	+	39.5160i	−0.431109	+	1.32682i	−0.897022	+	0.441986i	$0.854274\pi$
$888$	0.611272	+	1.88130i	0.0205130	+	0.0631324i
$889$	0.227723	+	0.313434i	0.00763758	+	0.0105122i
$890$		−	8.06547i		−	0.270355i
$891$	−3.06261	+	1.27296i	−0.102601	+	0.0426458i
$892$			15.3129i			0.512712i
$893$	−3.95763	+	2.87539i	−0.132437	+	0.0962212i
$894$	−3.42065	−	10.5277i	−0.114404	−	0.352098i
$895$	6.15389	+	1.99952i	0.205702	+	0.0668366i
$896$	−36.0585	−	26.1980i	−1.20463	−	0.875214i
$897$	7.11894	+	4.87806i	0.237695	+	0.162874i
$898$	6.19556	−	19.0680i	0.206749	−	0.636307i
$899$	48.2536	−	15.6785i	1.60935	−	0.522909i
$900$	−4.72418	+	3.43232i	−0.157473	+	0.114411i
$901$	28.7297			0.957124
$902$	−0.842415	−	10.5392i	−0.0280493	−	0.350916i
$903$			49.3373i			1.64184i
$904$	21.4406	+	29.5104i	0.713103	+	0.981502i
$905$	−0.998771	+	0.324520i	−0.0332003	+	0.0107874i
$906$	−3.13103	+	9.63632i	−0.104021	+	0.320145i
$907$	17.0430	+	12.3825i	0.565905	+	0.411154i	0.833615	−	0.552346i	$-0.186267\pi$
$907$	17.0430	+	12.3825i	0.565905	+	0.411154i	−0.267711	+	0.963499i	$0.586267\pi$
$908$	−10.9778	+	15.1097i	−0.364312	+	0.501432i
$909$	−1.13863	+	3.50435i	−0.0377661	+	0.116232i
$910$	−10.1441	+	3.60819i	−0.336274	+	0.119610i
$911$	30.7439	−	22.3367i	1.01859	−	0.740049i	0.0525972	−	0.998616i	$-0.483250\pi$
$911$	30.7439	−	22.3367i	1.01859	−	0.740049i	0.965993	+	0.258566i	$0.0832501\pi$
$912$			3.37684i			0.111818i
$913$	38.7670	−	3.09872i	1.28300	−	0.102553i
$914$	−9.36625			−0.309808
$915$	0.473830	+	0.652170i	0.0156643	+	0.0215601i
$916$	−43.7999	+	14.2315i	−1.44719	+	0.470221i
$917$	−51.8957	−	16.8619i	−1.71375	−	0.556830i
$918$	0.784130	−	1.07926i	0.0258801	−	0.0356210i
$919$	18.1496	+	13.1865i	0.598700	+	0.434981i	0.845417	−	0.534106i	$-0.179352\pi$
$919$	18.1496	+	13.1865i	0.598700	+	0.434981i	−0.246717	+	0.969088i	$0.579352\pi$
$920$	1.95909	−	6.02947i	0.0645893	−	0.198786i
$921$	−19.1862	+	6.23397i	−0.632206	+	0.205416i
$922$	−4.22638	+	3.07064i	−0.139188	+	0.101126i
$923$	−1.20949	−	43.8446i	−0.0398108	−	1.44316i
$924$	8.01907	+	19.2930i	0.263808	+	0.634693i
$925$		−	3.14029i		−	0.103252i
$926$	−10.6183	+	7.71463i	−0.348938	+	0.253518i
$927$	3.54475	+	10.9096i	0.116425	+	0.358319i
$928$	−39.5682	−	12.8565i	−1.29889	−	0.422035i
$929$	−29.5226	+	40.6344i	−0.968605	+	1.33317i	−0.0258564	+	0.999666i	$0.508231\pi$
$929$	−29.5226	+	40.6344i	−0.968605	+	1.33317i	−0.942748	+	0.333505i	$0.891769\pi$
$930$	3.05607	−	4.20632i	0.100213	−	0.137931i
$931$	18.5451	+	6.02567i	0.607792	+	0.197483i
$932$	−2.02787	−	6.24116i	−0.0664252	−	0.204436i
$933$	−7.54278	+	5.48015i	−0.246940	+	0.179412i
$934$		−	5.35460i		−	0.175208i
$935$	6.47002	+	3.95396i	0.211592	+	0.129308i
$936$	−0.233436	−	8.46219i	−0.00763010	−	0.276595i
$937$	16.1285	−	11.7180i	0.526895	−	0.382812i	−0.292300	−	0.956327i	$-0.594421\pi$
$937$	16.1285	−	11.7180i	0.526895	−	0.382812i	0.819195	+	0.573515i	$0.194421\pi$
$938$	−13.0135	+	4.22835i	−0.424906	+	0.138060i
$939$	0.135842	−	0.418078i	0.00443303	−	0.0136435i
$940$	3.28885	+	2.38949i	0.107270	+	0.0779365i
$941$	20.6497	−	28.4219i	0.673161	−	0.926526i	−0.326666	−	0.945140i	$-0.605925\pi$
$941$	20.6497	−	28.4219i	0.673161	−	0.926526i	0.999827	+	0.0186135i	$0.00592520\pi$
$942$	−4.42468	−	1.43767i	−0.144164	−	0.0468417i
$943$	11.0235	−	3.58174i	0.358973	−	0.116637i
$944$	−4.87150	−	6.70504i	−0.158554	−	0.218231i
$945$	4.53625			0.147564
$946$	−6.22187	+	26.0562i	−0.202290	+	0.847161i
$947$			20.9549i			0.680944i	0.940255	+	0.340472i	$0.110587\pi$
$947$			20.9549i			0.680944i	−0.940255	+	0.340472i	$0.889413\pi$
$948$	−15.4700	+	11.2396i	−0.502444	+	0.365047i
$949$	−45.8865	+	16.3215i	−1.48954	+	0.529820i
$950$	−1.61258	+	4.96300i	−0.0523189	+	0.161021i
$951$	1.61093	−	2.21725i	0.0522378	−	0.0718992i
$952$	−15.4783	−	11.2456i	−0.501653	−	0.364472i
$953$	14.5536	−	44.7913i	0.471436	−	1.45093i	−0.379268	−	0.925287i	$-0.623824\pi$
$953$	14.5536	−	44.7913i	0.471436	−	1.45093i	0.850704	−	0.525645i	$-0.176176\pi$
$954$	8.87556	−	2.88385i	0.287357	−	0.0933680i
$955$	4.59717	+	6.32746i	0.148761	+	0.204752i
$956$		−	7.20906i		−	0.233158i
$957$	15.6321	+	18.2576i	0.505314	+	0.590185i
$958$	−3.42531			−0.110667
$959$	−29.3914	+	21.3541i	−0.949097	+	0.689560i
$960$	−0.647720	+	0.210457i	−0.0209051	+	0.00679247i
$961$	−5.56715	+	17.1339i	−0.179585	+	0.552707i
$962$	1.64958	+	1.13033i	0.0531845	+	0.0364433i
$963$	−7.67643	−	5.57725i	−0.247369	−	0.179724i
$964$	−20.4924	−	6.65839i	−0.660017	−	0.214452i
$965$	−9.55376	−	29.4034i	−0.307546	−	0.946530i
$966$	5.12553	−	3.72391i	0.164911	−	0.119815i
$967$			17.0942i			0.549711i	0.961486	+	0.274856i	$0.0886301\pi$
$967$			17.0942i			0.549711i	−0.961486	+	0.274856i	$0.911370\pi$
$968$	4.10254	+	25.4988i	0.131861	+	0.819561i
$969$			4.31008i			0.138460i
$970$	4.23174	+	5.82450i	0.135873	+	0.187013i
$971$	−11.0660	−	34.0575i	−0.355124	−	1.09296i	−0.955938	−	0.293569i	$-0.905157\pi$
$971$	−11.0660	−	34.0575i	−0.355124	−	1.09296i	0.600814	−	0.799389i	$-0.294843\pi$
$972$	−0.484125	+	1.48998i	−0.0155283	+	0.0477912i
$973$	7.96136	−	10.9579i	0.255230	−	0.351293i
$974$	0.218549	+	0.158785i	0.00700275	+	0.00508780i
$975$	−3.79884	+	12.8909i	−0.121660	+	0.412838i
$976$	0.350593	+	1.07901i	0.0112222	+	0.0345384i
$977$	12.4711	+	17.1650i	0.398986	+	0.549157i	0.960489	−	0.278317i	$-0.0897767\pi$
$977$	12.4711	+	17.1650i	0.398986	+	0.549157i	−0.561503	+	0.827475i	$0.689777\pi$
$978$	1.98551			0.0634896
$979$	−27.3615	+	23.4268i	−0.874478	+	0.748725i
$980$		−	16.2043i		−	0.517629i
$981$	−8.28623	−	11.4050i	−0.264559	−	0.364134i
$982$	12.7434	−	4.14057i	0.406657	−	0.132131i
$983$	57.6906	+	18.7448i	1.84004	+	0.597867i	0.998319	+	0.0579603i	$0.0184597\pi$
$983$	57.6906	+	18.7448i	1.84004	+	0.597867i	0.841725	+	0.539906i	$0.181540\pi$
$984$	−9.19839	−	6.68302i	−0.293234	−	0.213047i
$985$	2.32765	+	1.69114i	0.0741651	+	0.0538841i
$986$	−9.19457	−	2.98750i	−0.292815	−	0.0951413i
$987$	2.85801	+	8.79605i	0.0909715	+	0.279981i
$988$	7.32679	+	9.52086i	0.233096	+	0.302899i
$989$	−29.3681			−0.933850
$990$	2.39570	+	0.572060i	0.0761404	+	0.0181813i
$991$	−40.3005			−1.28019			−0.640094	−	0.768297i	$-0.721105\pi$
$991$	−40.3005			−1.28019			−0.640094	+	0.768297i	$0.721105\pi$
$992$	32.5169	−	23.6249i	1.03241	−	0.750091i
$993$	−2.89918	+	0.942001i	−0.0920027	+	0.0298935i
$994$	−30.6241	−	9.95038i	−0.971338	−	0.315607i
$995$	−9.14888	+	12.5923i	−0.290039	+	0.399204i
$996$	10.7980	−	14.8621i	0.342147	−	0.470925i
$997$	3.30194	−	10.1623i	0.104574	−	0.321844i	−0.885057	−	0.465483i	$-0.845880\pi$
$997$	3.30194	−	10.1623i	0.104574	−	0.321844i	0.989630	+	0.143639i	$0.0458805\pi$
$998$	2.66898	+	8.21428i	0.0844851	+	0.260018i
$999$	−0.495216	−	0.681607i	−0.0156680	−	0.0215651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.25.9	yes	56
11.4	even	5	inner	429.2.bb.b.103.6	yes	56
13.12	even	2	inner	429.2.bb.b.25.6	✓	56
143.103	even	10	inner	429.2.bb.b.103.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.25.6	✓	56	13.12	even	2	inner
429.2.bb.b.25.9	yes	56	1.1	even	1	trivial
429.2.bb.b.103.6	yes	56	11.4	even	5	inner
429.2.bb.b.103.9	yes	56	143.103	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.386931 + 0.532564i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.484125 - 1.48998i) q^{4} +(0.663105 - 0.912685i) q^{5} +(0.386931 - 0.532564i) q^{6} +(3.82419 + 1.24256i) q^{7} +(2.23297 - 0.725535i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.742639 q^{10} +(-2.15706 - 2.51935i) q^{11} -1.56666 q^{12} +(-2.85740 + 2.19892i) q^{13} +(0.817956 + 2.51741i) q^{14} +(-1.07293 - 0.348615i) q^{15} +(-1.28451 - 0.933253i) q^{16} +(-1.63950 - 1.19117i) q^{17} +(-0.626067 - 0.203421i) q^{18} +(2.02272 - 0.657222i) q^{19} +(-1.03886 - 1.42987i) q^{20} -4.02099i q^{21} +(0.507082 - 2.12358i) q^{22} +2.39350 q^{23} +(-1.38005 - 1.89948i) q^{24} +(1.15180 + 3.54487i) q^{25} +(-2.27668 - 0.670921i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.70277 - 5.09643i) q^{28} +(2.23943 - 6.89227i) q^{29} +(-0.229488 - 0.706291i) q^{30} +(4.11515 + 5.66402i) q^{31} -5.74095i q^{32} +(-1.72947 + 2.83000i) q^{33} -1.33404i q^{34} +(3.66990 - 2.66634i) q^{35} +(0.484125 + 1.48998i) q^{36} +(-0.801277 - 0.260351i) q^{37} +(1.13267 + 0.822930i) q^{38} +(2.97428 + 2.03805i) q^{39} +(0.818506 - 2.51910i) q^{40} +(4.60558 - 1.49644i) q^{41} +(2.14144 - 1.55585i) q^{42} -12.2699 q^{43} +(-4.79807 + 1.99430i) q^{44} +1.12814i q^{45} +(0.926117 + 1.27469i) q^{46} +(-2.18753 + 0.710772i) q^{47} +(-0.490640 + 1.51003i) q^{48} +(7.41739 + 5.38905i) q^{49} +(-1.44221 + 1.98503i) q^{50} +(-0.626235 + 1.92735i) q^{51} +(1.89301 + 5.32203i) q^{52} +(-11.4692 + 8.33286i) q^{53} +0.658286i q^{54} +(-3.72972 + 0.298124i) q^{55} +9.44081 q^{56} +(-1.25011 - 1.72063i) q^{57} +(4.53708 - 1.47419i) q^{58} +(4.96443 + 1.61304i) q^{59} +(-1.03886 + 1.42987i) q^{60} +(-0.578093 - 0.420009i) q^{61} +(-1.42418 + 4.38317i) q^{62} +(-3.82419 + 1.24256i) q^{63} +(0.488400 - 0.354843i) q^{64} +(0.112164 + 4.06602i) q^{65} +(-2.17634 + 0.173959i) q^{66} +5.16940i q^{67} +(-2.56855 + 1.86616i) q^{68} +(-0.739632 - 2.27635i) q^{69} +(2.83999 + 0.922770i) q^{70} +(-7.15036 + 9.84163i) q^{71} +(-1.38005 + 1.89948i) q^{72} +(12.8466 + 4.17412i) q^{73} +(-0.171385 - 0.527469i) q^{74} +(3.01545 - 2.19085i) q^{75} -3.33200i q^{76} +(-5.11857 - 12.3147i) q^{77} +(0.0654495 + 2.37258i) q^{78} +(9.87453 - 7.17427i) q^{79} +(-1.70353 + 0.553511i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.57899 + 1.87375i) q^{82} +(-6.89236 + 9.48652i) q^{83} +(-5.99121 - 1.94666i) q^{84} +(-2.17433 + 0.706481i) q^{85} +(-4.74761 - 6.53453i) q^{86} -7.24696 q^{87} +(-6.64451 - 4.06060i) q^{88} -10.8606i q^{89} +(-0.600807 + 0.436512i) q^{90} +(-13.6595 + 4.85861i) q^{91} +(1.15875 - 3.56627i) q^{92} +(4.11515 - 5.66402i) q^{93} +(-1.22495 - 0.889981i) q^{94} +(0.741439 - 2.28192i) q^{95} +(-5.45997 + 1.77405i) q^{96} +(5.69825 + 7.84297i) q^{97} +6.03542i q^{98} +(3.22593 + 0.770308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36}+ \cdots + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Introduction

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