LMFDB - Embedded newform 372.2.p.a.335.44

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(191,372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("372.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.44
Character	$\chi$	$=$	372.335
Dual form			372.2.p.a.191.43

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.873830 + 1.11194i) q^{2} +(-1.72250 - 0.181663i) q^{3} +(-0.472843 + 1.94330i) q^{4} +(-3.08078 - 1.77869i) q^{5} +(-1.30317 - 2.07406i) q^{6} +(2.77350 - 1.60128i) q^{7} +(-2.57403 + 1.17234i) q^{8} +(2.93400 + 0.625827i) q^{9} +(-0.714273 - 4.97993i) q^{10} +(3.05678 - 5.29450i) q^{11} +(1.16750 - 3.26143i) q^{12} +(-0.185643 + 0.321544i) q^{13} +(4.20411 + 1.68473i) q^{14} +(4.98351 + 3.62345i) q^{15} +(-3.55284 - 1.83775i) q^{16} +(-2.57727 + 1.48799i) q^{17} +(1.86793 + 3.80931i) q^{18} +(3.49788 - 2.01950i) q^{19} +(4.91325 - 5.14584i) q^{20} +(-5.06825 + 2.25436i) q^{21} +(8.55830 - 1.22752i) q^{22} +2.65226 q^{23} +(4.64673 - 1.55175i) q^{24} +(3.82746 + 6.62936i) q^{25} +(-0.519760 + 0.0745493i) q^{26} +(-4.94011 - 1.61098i) q^{27} +(1.80034 + 6.14691i) q^{28} -9.84173i q^{29} +(0.325666 + 8.70767i) q^{30} +(-2.68661 - 4.87669i) q^{31} +(-1.06110 - 5.55644i) q^{32} +(-6.22711 + 8.56446i) q^{33} +(-3.90666 - 1.56554i) q^{34} -11.3927 q^{35} +(-2.60349 + 5.40572i) q^{36} +(0.414892 + 0.718613i) q^{37} +(5.30212 + 2.12475i) q^{38} +(0.378183 - 0.520134i) q^{39} +(10.0152 + 0.966676i) q^{40} +(-3.17691 - 1.83419i) q^{41} +(-6.93551 - 3.66568i) q^{42} +(-1.72024 + 0.993180i) q^{43} +(8.84343 + 8.44371i) q^{44} +(-7.92584 - 7.14670i) q^{45} +(2.31762 + 2.94916i) q^{46} -0.401400 q^{47} +(5.78591 + 3.81094i) q^{48} +(1.62821 - 2.82014i) q^{49} +(-4.02693 + 10.0489i) q^{50} +(4.70966 - 2.09486i) q^{51} +(-0.537076 - 0.512801i) q^{52} +(3.45351 + 1.99388i) q^{53} +(-2.52549 - 6.90086i) q^{54} +(-18.8345 + 10.8741i) q^{55} +(-5.26183 + 7.37323i) q^{56} +(-6.39196 + 2.84315i) q^{57} +(10.9435 - 8.60000i) q^{58} +(1.44539 + 2.50350i) q^{59} +(-9.39787 + 7.97114i) q^{60} -4.54137 q^{61} +(3.07497 - 7.24876i) q^{62} +(9.13957 - 2.96243i) q^{63} +(5.25124 - 6.03527i) q^{64} +(1.14385 - 0.660404i) q^{65} +(-14.9646 + 0.559677i) q^{66} +(4.77967 + 2.75954i) q^{67} +(-1.67297 - 5.71201i) q^{68} +(-4.56851 - 0.481816i) q^{69} +(-9.95531 - 12.6681i) q^{70} +(-2.26297 + 3.91958i) q^{71} +(-8.28587 + 1.82874i) q^{72} +(1.93098 - 3.34456i) q^{73} +(-0.436514 + 1.08928i) q^{74} +(-5.38849 - 12.1144i) q^{75} +(2.27055 + 7.75234i) q^{76} -19.5791i q^{77} +(0.908828 - 0.0339901i) q^{78} +(4.13036 - 2.38466i) q^{79} +(7.67672 + 11.9811i) q^{80} +(8.21668 + 3.67235i) q^{81} +(-0.736561 - 5.13532i) q^{82} +(0.118745 - 0.205672i) q^{83} +(-1.98442 - 10.9151i) q^{84} +10.5867 q^{85} +(-2.60756 - 1.04494i) q^{86} +(-1.78788 + 16.9524i) q^{87} +(-1.66129 + 17.2118i) q^{88} +14.4700i q^{89} +(1.02090 - 15.0581i) q^{90} +1.18907i q^{91} +(-1.25410 + 5.15414i) q^{92} +(3.74177 + 8.88815i) q^{93} +(-0.350756 - 0.446335i) q^{94} -14.3683 q^{95} +(0.818339 + 9.76372i) q^{96} +11.8456 q^{97} +(4.55862 - 0.653845i) q^{98} +(12.2820 - 13.6210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.873830	+	1.11194i	0.617891	+	0.786264i
$2$	0.873830	+	1.11194i	0.617891	+	0.786264i
$3$	−1.72250	−	0.181663i	−0.994485	−	0.104883i
$3$	−1.72250	−	0.181663i	−0.994485	−	0.104883i
$4$	−0.472843	+	1.94330i	−0.236421	+	0.971651i
$5$	−3.08078	−	1.77869i	−1.37777	−	0.795454i	−0.385876	−	0.922551i	$-0.626101\pi$
$5$	−3.08078	−	1.77869i	−1.37777	−	0.795454i	−0.991890	+	0.127097i	$0.959434\pi$
$6$	−1.30317	−	2.07406i	−0.532017	−	0.846733i
$7$	2.77350	−	1.60128i	1.04829	−	0.605228i	0.126117	−	0.992015i	$-0.459749\pi$
$7$	2.77350	−	1.60128i	1.04829	−	0.605228i	0.922169	+	0.386788i	$0.126415\pi$
$8$	−2.57403	+	1.17234i	−0.910056	+	0.414485i
$9$	2.93400	+	0.625827i	0.977999	+	0.208609i
$10$	−0.714273	−	4.97993i	−0.225873	−	1.57479i
$11$	3.05678	−	5.29450i	0.921654	−	1.59635i	0.124798	−	0.992182i	$-0.460172\pi$
$11$	3.05678	−	5.29450i	0.921654	−	1.59635i	0.796856	−	0.604169i	$-0.206495\pi$
$12$	1.16750	−	3.26143i	0.337027	−	0.941495i
$13$	−0.185643	+	0.321544i	−0.0514882	+	0.0891802i	−0.890621	−	0.454747i	$-0.849730\pi$
$13$	−0.185643	+	0.321544i	−0.0514882	+	0.0891802i	0.839133	+	0.543927i	$0.183063\pi$
$14$	4.20411	+	1.68473i	1.12359	+	0.450264i
$15$	4.98351	+	3.62345i	1.28674	+	0.935571i
$16$	−3.55284	−	1.83775i	−0.888210	−	0.459438i
$17$	−2.57727	+	1.48799i	−0.625081	+	0.360891i	−0.778844	−	0.627217i	$-0.784194\pi$
$17$	−2.57727	+	1.48799i	−0.625081	+	0.360891i	0.153764	+	0.988108i	$0.450861\pi$
$18$	1.86793	+	3.80931i	0.440275	+	0.897863i
$19$	3.49788	−	2.01950i	0.802468	−	0.463305i	−0.0418652	−	0.999123i	$-0.513330\pi$
$19$	3.49788	−	2.01950i	0.802468	−	0.463305i	0.844334	+	0.535818i	$0.179997\pi$
$20$	4.91325	−	5.14584i	1.09864	−	1.15064i
$21$	−5.06825	+	2.25436i	−1.10598	+	0.491942i
$22$	8.55830	−	1.22752i	1.82463	−	0.261708i
$23$	2.65226			0.553034			0.276517	−	0.961009i	$-0.410820\pi$
$23$	2.65226			0.553034			0.276517	+	0.961009i	$0.410820\pi$
$24$	4.64673	−	1.55175i	0.948509	−	0.316749i
$25$	3.82746	+	6.62936i	0.765493	+	1.32587i
$26$	−0.519760	+	0.0745493i	−0.101933	+	0.0146203i
$27$	−4.94011	−	1.61098i	−0.950725	−	0.310034i
$28$	1.80034	+	6.14691i	0.340233	+	1.16166i
$29$		−	9.84173i		−	1.82756i	−0.406205	−	0.913782i	$-0.633148\pi$
$29$		−	9.84173i		−	1.82756i	0.406205	−	0.913782i	$-0.366852\pi$
$30$	0.325666	+	8.70767i	0.0594583	+	1.58980i
$31$	−2.68661	−	4.87669i	−0.482529	−	0.875880i
$31$	−2.68661	−	4.87669i	−0.482529	−	0.875880i
$32$	−1.06110	−	5.55644i	−0.187577	−	0.982250i
$33$	−6.22711	+	8.56446i	−1.08400	+	1.49088i
$34$	−3.90666	−	1.56554i	−0.669987	−	0.268487i
$35$	−11.3927			−1.92572
$36$	−2.60349	+	5.40572i	−0.433915	+	0.900954i
$37$	0.414892	+	0.718613i	0.0682078	+	0.118139i	0.898112	−	0.439766i	$-0.144939\pi$
$37$	0.414892	+	0.718613i	0.0682078	+	0.118139i	−0.829905	+	0.557905i	$0.811605\pi$
$38$	5.30212	+	2.12475i	0.860118	+	0.344680i
$39$	0.378183	−	0.520134i	0.0605577	−	0.0832881i
$40$	10.0152	+	0.966676i	1.58355	+	0.152845i
$41$	−3.17691	−	1.83419i	−0.496150	−	0.286453i	0.230972	−	0.972960i	$-0.425809\pi$
$41$	−3.17691	−	1.83419i	−0.496150	−	0.286453i	−0.727122	+	0.686508i	$0.759143\pi$
$42$	−6.93551	−	3.66568i	−1.07017	−	0.565627i
$43$	−1.72024	+	0.993180i	−0.262334	+	0.151459i	−0.625399	−	0.780305i	$-0.715064\pi$
$43$	−1.72024	+	0.993180i	−0.262334	+	0.151459i	0.363065	+	0.931764i	$0.381730\pi$
$44$	8.84343	+	8.44371i	1.33320	+	1.27294i
$45$	−7.92584	−	7.14670i	−1.18152	−	1.06537i
$46$	2.31762	+	2.94916i	0.341715	+	0.434831i
$47$	−0.401400			−0.0585503			−0.0292751	−	0.999571i	$-0.509320\pi$
$47$	−0.401400			−0.0585503			−0.0292751	+	0.999571i	$0.509320\pi$
$48$	5.78591	+	3.81094i	0.835124	+	0.550062i
$49$	1.62821	−	2.82014i	0.232601	−	0.402878i
$50$	−4.02693	+	10.0489i	−0.569494	+	1.42112i
$51$	4.70966	−	2.09486i	0.659484	−	0.293340i
$52$	−0.537076	−	0.512801i	−0.0744791	−	0.0711127i
$53$	3.45351	+	1.99388i	0.474376	+	0.273881i	0.718070	−	0.695971i	$-0.245026\pi$
$53$	3.45351	+	1.99388i	0.474376	+	0.273881i	−0.243694	+	0.969852i	$0.578359\pi$
$54$	−2.52549	−	6.90086i	−0.343676	−	0.939088i
$55$	−18.8345	+	10.8741i	−2.53965	+	1.46627i
$56$	−5.26183	+	7.37323i	−0.703141	+	0.985289i
$57$	−6.39196	+	2.84315i	−0.846635	+	0.376585i
$58$	10.9435	−	8.60000i	1.43695	−	1.12924i
$59$	1.44539	+	2.50350i	0.188174	+	0.325927i	0.944642	−	0.328104i	$-0.106410\pi$
$59$	1.44539	+	2.50350i	0.188174	+	0.325927i	−0.756467	+	0.654032i	$0.773076\pi$
$60$	−9.39787	+	7.97114i	−1.21326	+	1.02907i
$61$	−4.54137			−0.581463			−0.290732	−	0.956805i	$-0.593899\pi$
$61$	−4.54137			−0.581463			−0.290732	+	0.956805i	$0.593899\pi$
$62$	3.07497	−	7.24876i	0.390522	−	0.920594i
$63$	9.13957	−	2.96243i	1.15148	−	0.373230i
$64$	5.25124	−	6.03527i	0.656405	−	0.754409i
$65$	1.14385	−	0.660404i	0.141877	−	0.0819130i
$66$	−14.9646	+	0.559677i	−1.84202	+	0.0688914i
$67$	4.77967	+	2.75954i	0.583930	+	0.337132i	0.762694	−	0.646760i	$-0.223876\pi$
$67$	4.77967	+	2.75954i	0.583930	+	0.337132i	−0.178764	+	0.983892i	$0.557210\pi$
$68$	−1.67297	−	5.71201i	−0.202877	−	0.692682i
$69$	−4.56851	−	0.481816i	−0.549984	−	0.0580039i
$70$	−9.95531	−	12.6681i	−1.18989	−	1.51413i
$71$	−2.26297	+	3.91958i	−0.268565	+	0.465169i	−0.968492	−	0.249047i	$-0.919883\pi$
$71$	−2.26297	+	3.91958i	−0.268565	+	0.465169i	0.699926	+	0.714215i	$0.253216\pi$
$72$	−8.28587	+	1.82874i	−0.976500	+	0.215519i
$73$	1.93098	−	3.34456i	0.226004	−	0.391451i	−0.730616	−	0.682789i	$-0.760767\pi$
$73$	1.93098	−	3.34456i	0.226004	−	0.391451i	0.956620	+	0.291338i	$0.0941003\pi$
$74$	−0.436514	+	1.08928i	−0.0507437	+	0.126627i
$75$	−5.38849	−	12.1144i	−0.622209	−	1.39885i
$76$	2.27055	+	7.75234i	0.260450	+	0.889254i
$77$		−	19.5791i		−	2.23124i
$78$	0.908828	−	0.0339901i	0.102905	−	0.00384862i
$79$	4.13036	−	2.38466i	0.464701	−	0.268296i	−0.249318	−	0.968422i	$-0.580206\pi$
$79$	4.13036	−	2.38466i	0.464701	−	0.268296i	0.714019	+	0.700126i	$0.246873\pi$
$80$	7.67672	+	11.9811i	0.858284	+	1.33953i
$81$	8.21668	+	3.67235i	0.912965	+	0.408039i
$82$	−0.736561	−	5.13532i	−0.0813396	−	0.567102i
$83$	0.118745	−	0.205672i	0.0130339	−	0.0225754i	−0.859435	−	0.511245i	$-0.829184\pi$
$83$	0.118745	−	0.205672i	0.0130339	−	0.0225754i	0.872469	+	0.488670i	$0.162518\pi$
$84$	−1.98442	−	10.9151i	−0.216518	−	1.19093i
$85$	10.5867			1.14829
$86$	−2.60756	−	1.04494i	−0.281180	−	0.112679i
$87$	−1.78788	+	16.9524i	−0.191680	+	1.81748i
$88$	−1.66129	+	17.2118i	−0.177094	+	1.83478i
$89$			14.4700i			1.53382i	0.641754	+	0.766911i	$0.278207\pi$
$89$			14.4700i			1.53382i	−0.641754	+	0.766911i	$0.721793\pi$
$90$	1.02090	−	15.0581i	0.107612	−	1.58726i
$91$			1.18907i			0.124648i
$92$	−1.25410	+	5.15414i	−0.130749	+	0.537356i
$93$	3.74177	+	8.88815i	0.388003	+	0.921658i
$94$	−0.350756	−	0.446335i	−0.0361777	−	0.0460359i
$95$	−14.3683			−1.47415
$96$	0.818339	+	9.76372i	0.0835214	+	0.996506i
$97$	11.8456			1.20274			0.601369	−	0.798971i	$-0.294622\pi$
$97$	11.8456			1.20274			0.601369	+	0.798971i	$0.294622\pi$
$98$	4.55862	−	0.653845i	0.460490	−	0.0660483i
$99$	12.2820	−	13.6210i	1.23439	−	1.36896i
$100$	−14.6926	+	4.30327i	−1.46926	+	0.430327i
$101$			12.3690i			1.23076i	0.788231	+	0.615379i	$0.210997\pi$
$101$			12.3690i			1.23076i	−0.788231	+	0.615379i	$0.789003\pi$
$102$	6.44482	+	3.40633i	0.638132	+	0.337277i
$103$	−0.753274	−	0.434903i	−0.0742222	−	0.0428522i	0.462430	−	0.886656i	$-0.346978\pi$
$103$	−0.753274	−	0.434903i	−0.0742222	−	0.0428522i	−0.536652	+	0.843804i	$0.680311\pi$
$104$	0.100893	−	1.04530i	0.00989337	−	0.102500i
$105$	19.6239	+	2.06963i	1.91510	+	0.201976i
$106$	0.800689	+	5.58242i	0.0777698	+	0.542213i
$107$	0.888203	+	1.53841i	0.0858658	+	0.148724i	0.905760	−	0.423791i	$-0.139301\pi$
$107$	0.888203	+	1.53841i	0.0858658	+	0.148724i	−0.819894	+	0.572515i	$0.805968\pi$
$108$	5.46652	−	8.83839i	0.526017	−	0.850474i
$109$	−16.4118			−1.57197			−0.785983	−	0.618247i	$-0.787843\pi$
$109$	−16.4118			−1.57197			−0.785983	+	0.618247i	$0.787843\pi$
$110$	−28.5496	−	11.4408i	−2.72210	−	1.09084i
$111$	−0.584105	−	1.31318i	−0.0554408	−	0.124642i
$112$	−12.7966	+	0.592088i	−1.20916	+	0.0559470i
$113$	13.5753	+	7.83770i	1.27706	+	0.737309i	0.976306	−	0.216394i	$-0.0694296\pi$
$113$	13.5753	+	7.83770i	1.27706	+	0.737309i	0.300750	+	0.953703i	$0.402763\pi$
$114$	−8.74691	−	4.62307i	−0.819223	−	0.432990i
$115$	−8.17102	−	4.71754i	−0.761951	−	0.439913i
$116$	19.1255	+	4.65359i	1.77575	+	0.432075i
$117$	−0.745908	+	0.827228i	−0.0689592	+	0.0764773i
$118$	−1.52072	+	3.79483i	−0.139994	+	0.349342i
$119$	−4.76538	+	8.25389i	−0.436842	+	0.756633i
$120$	−17.0756	−	3.48449i	−1.55878	−	0.318089i
$121$	−13.1878	−	22.8420i	−1.19889	−	2.07654i
$122$	−3.96839	−	5.04976i	−0.359281	−	0.457183i
$123$	5.13902	+	3.73652i	0.463370	+	0.336910i
$124$	10.7472	−	2.91498i	0.965129	−	0.261773i
$125$		−	9.44457i		−	0.844748i
$126$	11.2805	+	7.57405i	1.00495	+	0.674750i
$127$	10.5173	−	6.07215i	0.933257	−	0.538816i	0.0454166	−	0.998968i	$-0.485538\pi$
$127$	10.5173	−	6.07215i	0.933257	−	0.538816i	0.887840	+	0.460152i	$0.152205\pi$
$128$	11.2996	+	0.565294i	0.998751	+	0.0499654i
$129$	3.14353	−	1.39825i	0.276772	−	0.123109i
$130$	1.73386	+	0.694821i	0.152070	+	0.0609398i
$131$	−1.50511	−	2.60693i	−0.131502	−	0.227769i	0.792754	−	0.609542i	$-0.208647\pi$
$131$	−1.50511	−	2.60693i	−0.131502	−	0.227769i	−0.924256	+	0.381774i	$0.875313\pi$
$132$	−13.6989	−	16.1508i	−1.19233	−	1.40575i
$133$	6.46758	−	11.2022i	0.560811	−	0.971352i
$134$	1.10816	+	7.72610i	0.0957302	+	0.667434i
$135$	12.3540	+	13.7500i	1.06326	+	1.18341i
$136$	4.88955	−	6.85157i	0.419275	−	0.587517i
$137$	−4.90084	−	2.82950i	−0.418707	−	0.241741i	0.275817	−	0.961210i	$-0.411052\pi$
$137$	−4.90084	−	2.82950i	−0.418707	−	0.241741i	−0.694524	+	0.719470i	$0.744385\pi$
$138$	−3.45635	−	5.50095i	−0.294224	−	0.468272i
$139$		−	17.8292i		−	1.51225i	−0.654428	−	0.756124i	$-0.727090\pi$
$139$		−	17.8292i		−	1.51225i	0.654428	−	0.756124i	$-0.272910\pi$
$140$	5.38697	−	22.1395i	0.455282	−	1.87113i
$141$	0.691411	+	0.0729195i	0.0582273	+	0.00614093i
$142$	−6.33581	+	0.908747i	−0.531689	+	0.0762604i
$143$	1.13494	+	1.96578i	0.0949086	+	0.164387i
$144$	−9.27391	−	7.61542i	−0.772825	−	0.634619i
$145$	−17.5054	+	30.3202i	−1.45374	+	2.51796i
$146$	5.40631	−	0.775429i	0.447430	−	0.0641750i
$147$	−3.31690	+	4.56191i	−0.273574	+	0.376260i
$148$	−1.59266	+	0.466468i	−0.130916	+	0.0383434i
$149$	−15.3042	+	8.83588i	−1.25377	+	0.723864i	−0.971856	−	0.235576i	$-0.924302\pi$
$149$	−15.3042	+	8.83588i	−1.25377	+	0.723864i	−0.281913	+	0.959440i	$0.590969\pi$
$150$	8.76189	−	16.5776i	0.715405	−	1.35356i
$151$		−	10.4211i		−	0.848059i	−0.905648	−	0.424030i	$-0.860615\pi$
$151$		−	10.4211i		−	0.848059i	0.905648	−	0.424030i	$-0.139385\pi$
$152$	−6.63610	+	9.29895i	−0.538259	+	0.754245i
$153$	−8.49294	+	2.75283i	−0.686613	+	0.222553i
$154$	21.7708	−	17.1088i	1.75435	−	1.37866i
$155$	−0.397265	+	19.8026i	−0.0319091	+	1.59059i
$156$	0.831956	+	0.980865i	0.0666098	+	0.0785321i
$157$	4.51089			0.360008			0.180004	−	0.983666i	$-0.442389\pi$
$157$	4.51089			0.360008			0.180004	+	0.983666i	$0.442389\pi$
$158$	6.26084	+	2.50894i	0.498086	+	0.199601i
$159$	−5.58644	−	4.06183i	−0.443034	−	0.322124i
$160$	−6.61418	+	19.0055i	−0.522897	+	1.50252i
$161$	7.35604	−	4.24701i	0.579737	−	0.334712i
$162$	3.09653	+	12.3455i	0.243286	+	0.969955i
$163$			22.9981i			1.80135i	0.434497	+	0.900673i	$0.356926\pi$
$163$			22.9981i			1.80135i	−0.434497	+	0.900673i	$0.643074\pi$
$164$	5.06657	−	5.30641i	0.395632	−	0.414361i
$165$	34.4178	−	15.3091i	2.67943	−	1.19181i
$166$	0.332458	−	0.0476846i	0.0258038	−	0.00370104i
$167$	−11.2744	−	19.5278i	−0.872440	−	1.51111i	−0.859465	−	0.511195i	$-0.829203\pi$
$167$	−11.2744	−	19.5278i	−0.872440	−	1.51111i	−0.0129750	−	0.999916i	$-0.504130\pi$
$168$	10.4029	−	11.7445i	0.802603	−	0.906108i
$169$	6.43107	+	11.1389i	0.494698	+	0.856842i
$170$	9.25096	+	11.7718i	0.709516	+	0.902856i
$171$	11.5266	−	3.73614i	0.881463	−	0.285710i
$172$	−1.11665	−	3.81256i	−0.0851434	−	0.290705i
$173$	6.53145	+	3.77094i	0.496577	+	0.286699i	0.727299	−	0.686321i	$-0.240775\pi$
$173$	6.53145	+	3.77094i	0.496577	+	0.286699i	−0.230722	+	0.973020i	$0.574109\pi$
$174$	−20.4124	+	12.8255i	−1.54746	+	0.972296i
$175$	21.2310	+	12.2577i	1.60491	+	0.926595i
$176$	−20.5902	+	13.1929i	−1.55205	+	0.994452i
$177$	−2.03490	−	4.57484i	−0.152952	−	0.343866i
$178$	−16.0899	+	12.6444i	−1.20599	+	0.947734i
$179$	9.76408	+	16.9119i	0.729802	+	1.26405i	0.956967	+	0.290198i	$0.0937210\pi$
$179$	9.76408	+	16.9119i	0.729802	+	1.26405i	−0.227165	+	0.973856i	$0.572946\pi$
$180$	17.6359	−	12.0230i	1.31450	−	0.896144i
$181$	11.2743	−	19.5277i	0.838015	−	1.45148i	−0.0535365	−	0.998566i	$-0.517049\pi$
$181$	11.2743	−	19.5277i	0.838015	−	1.45148i	0.891552	−	0.452919i	$-0.149617\pi$
$182$	−1.32218	+	1.03904i	−0.0980065	+	0.0770191i
$183$	7.82250	+	0.824998i	0.578256	+	0.0609856i
$184$	−6.82699	+	3.10935i	−0.503292	+	0.229224i
$185$		−	2.95185i		−	0.217024i
$186$	−6.61346	+	11.9274i	−0.484923	+	0.874557i
$187$			18.1938i			1.33046i
$188$	0.189799	−	0.780042i	0.0138425	−	0.0568904i
$189$	−16.2811	+	3.44245i	−1.18427	+	0.250401i
$190$	−12.5554	−	15.9767i	−0.910865	−	1.15907i
$191$	6.07250	−	10.5179i	0.439391	−	0.761047i	−0.558252	−	0.829672i	$-0.688528\pi$
$191$	6.07250	−	10.5179i	0.439391	−	0.761047i	0.997643	+	0.0686243i	$0.0218610\pi$
$192$	−10.1416	+	9.44178i	−0.731909	+	0.681402i
$193$	0.160455	+	0.277917i	0.0115498	+	0.0200049i	0.871743	−	0.489964i	$-0.162990\pi$
$193$	0.160455	+	0.277917i	0.0115498	+	0.0200049i	−0.860193	+	0.509969i	$0.829657\pi$
$194$	10.3510	+	13.1717i	0.743161	+	0.945670i
$195$	−2.09025	+	0.929748i	−0.149686	+	0.0665807i
$196$	4.71050	+	4.49759i	0.336464	+	0.321256i
$197$	5.99718	+	3.46247i	0.427281	+	0.246691i	0.698188	−	0.715915i	$-0.253990\pi$
$197$	5.99718	+	3.46247i	0.427281	+	0.246691i	−0.270906	+	0.962606i	$0.587323\pi$
$198$	25.8782	+	1.75447i	1.83909	+	0.124685i
$199$	6.67806	+	3.85558i	0.473395	+	0.273315i	0.717660	−	0.696394i	$-0.245213\pi$
$199$	6.67806	+	3.85558i	0.473395	+	0.273315i	−0.244265	+	0.969709i	$0.578547\pi$
$200$	−17.6239	−	12.5771i	−1.24620	−	0.889334i
$201$	−7.73167	−	5.62160i	−0.545350	−	0.396517i
$202$	−13.7536	+	10.8084i	−0.967701	+	0.760475i
$203$	−15.7594	−	27.2961i	−1.10609	−	1.91581i
$204$	1.84402	+	10.1428i	0.129107	+	0.710140i
$205$	6.52491	+	11.3015i	0.455719	+	0.789329i
$206$	−0.174645	−	1.21763i	−0.0121681	−	0.0848363i
$207$	7.78172	+	1.65985i	0.540867	+	0.115368i
$208$	1.25048	−	0.801227i	0.0867051	−	0.0555551i
$209$		−	24.6927i		−	1.70803i
$210$	14.8467	+	23.6293i	1.02452	+	1.63057i
$211$	2.96435	−	1.71147i	0.204074	−	0.117822i	−0.394480	−	0.918904i	$-0.629075\pi$
$211$	2.96435	−	1.71147i	0.204074	−	0.117822i	0.598554	+	0.801082i	$0.295742\pi$
$212$	−5.50768	+	5.76841i	−0.378269	+	0.396176i
$213$	4.61000	−	6.34037i	0.315872	−	0.434435i
$214$	−0.934492	+	2.33194i	−0.0638806	+	0.159408i
$215$	7.06623			0.481913
$216$	14.6046	−	1.64477i	0.993718	−	0.111913i
$217$	−15.2603	−	9.22350i	−1.03594	−	0.626132i
$218$	−14.3411	−	18.2490i	−0.971304	−	1.23598i
$219$	−3.93369	+	5.41021i	−0.265814	+	0.365588i
$220$	−12.2259	−	41.7429i	−0.824271	−	2.81431i
$221$		−	1.10494i		−	0.0743265i
$222$	0.949776	−	1.79699i	0.0637448	−	0.120606i
$223$	6.79973	−	3.92583i	0.455344	−	0.262893i	−0.254741	−	0.967009i	$-0.581990\pi$
$223$	6.79973	−	3.92583i	0.455344	−	0.262893i	0.710084	+	0.704117i	$0.248657\pi$
$224$	−11.8404	−	13.7117i	−0.791119	−	0.916151i
$225$	7.08093	+	21.8459i	0.472062	+	1.45639i
$226$	3.14741	+	21.9438i	0.209362	+	1.45968i
$227$	−11.0974	+	19.2213i	−0.736563	+	1.27577i	0.217471	+	0.976067i	$0.430219\pi$
$227$	−11.0974	+	19.2213i	−0.736563	+	1.27577i	−0.954034	+	0.299698i	$0.903114\pi$
$228$	−2.50271	−	13.7659i	−0.165746	−	0.911666i
$229$	6.31522	+	10.9383i	0.417322	+	0.722822i	0.995669	−	0.0929683i	$-0.0296355\pi$
$229$	6.31522	+	10.9383i	0.417322	+	0.722822i	−0.578347	+	0.815791i	$0.696302\pi$
$230$	−1.89444	−	13.2080i	−0.124915	−	0.870913i
$231$	−3.55679	+	33.7249i	−0.234019	+	2.21894i
$232$	11.5379	+	25.3329i	0.757497	+	1.66319i
$233$		−	9.83948i		−	0.644606i	−0.946637	−	0.322303i	$-0.895543\pi$
$233$		−	9.83948i		−	0.644606i	0.946637	−	0.322303i	$-0.104457\pi$
$234$	−1.57163	−	0.106552i	−0.102741	−	0.00696554i
$235$	1.23663	+	0.713966i	0.0806685	+	0.0465740i
$236$	−5.54849	+	1.62508i	−0.361176	+	0.105783i
$237$	−7.54774	+	3.35724i	−0.490278	+	0.218076i
$238$	−13.3420	+	1.91365i	−0.864834	+	0.124043i
$239$	−0.172177	+	0.298220i	−0.0111372	+	0.0192902i	−0.871540	−	0.490324i	$-0.836878\pi$
$239$	−0.172177	+	0.298220i	−0.0111372	+	0.0192902i	0.860403	+	0.509614i	$0.170212\pi$
$240$	−11.0466	−	22.0320i	−0.713056	−	1.42216i
$241$	0.169181	+	0.293031i	0.0108979	+	0.0188758i	0.871423	−	0.490532i	$-0.163198\pi$
$241$	0.169181	+	0.293031i	0.0108979	+	0.0188758i	−0.860525	+	0.509408i	$0.829864\pi$
$242$	13.8751	−	34.6241i	0.891925	−	2.22572i
$243$	−13.4861	−	7.81828i	−0.865133	−	0.501543i
$244$	2.14736	−	8.82525i	0.137470	−	0.564979i
$245$	−10.0323	+	5.79216i	−0.640941	+	0.370047i
$246$	0.335829	+	8.97939i	0.0214116	+	0.572505i
$247$			1.49963i			0.0954191i
$248$	12.6325	+	9.40312i	0.802168	+	0.597099i
$249$	−0.241900	+	0.332698i	−0.0153298	+	0.0210839i
$250$	10.5018	−	8.25295i	0.664195	−	0.521962i
$251$	−3.73896	−	6.47607i	−0.236001	−	0.408766i	0.723562	−	0.690259i	$-0.242504\pi$
$251$	−3.73896	−	6.47607i	−0.236001	−	0.408766i	−0.959563	+	0.281493i	$0.909170\pi$
$252$	1.43530	+	19.1617i	0.0904155	+	1.20707i
$253$	8.10737	−	14.0424i	0.509706	−	0.882836i
$254$	15.9422	+	6.38860i	1.00030	+	0.400856i
$255$	−18.2355	−	1.92320i	−1.14195	−	0.120436i
$256$	9.24533	+	13.0585i	0.577833	+	0.816155i
$257$	20.8370	+	12.0302i	1.29977	+	0.750425i	0.980365	−	0.197192i	$-0.0631823\pi$
$257$	20.8370	+	12.0302i	1.29977	+	0.750425i	0.319409	+	0.947617i	$0.396516\pi$
$258$	4.30169	+	2.27360i	0.267811	+	0.141548i
$259$	2.30141	+	1.32872i	0.143002	+	0.0825625i
$260$	0.742500	+	2.53512i	0.0460479	+	0.157221i
$261$	6.15922	−	28.8756i	0.381246	−	1.78736i
$262$	1.58355	−	3.95162i	0.0978322	−	0.244132i
$263$	8.57162			0.528549			0.264274	−	0.964448i	$-0.414868\pi$
$263$	8.57162			0.528549			0.264274	+	0.964448i	$0.414868\pi$
$264$	5.98830	−	29.3454i	0.368555	−	1.80609i
$265$	−7.09299	−	12.2854i	−0.435719	−	0.754688i
$266$	18.1078	−	2.59721i	1.11026	−	0.159245i
$267$	2.62867	−	24.9246i	0.160872	−	1.52536i
$268$	−7.62266	+	7.98351i	−0.465628	+	0.487670i
$269$	7.85469	+	4.53491i	0.478909	+	0.276498i	0.719962	−	0.694014i	$-0.244159\pi$
$269$	7.85469	+	4.53491i	0.478909	+	0.276498i	−0.241053	+	0.970512i	$0.577493\pi$
$270$	−4.49399	+	25.7521i	−0.273496	+	1.56722i
$271$		−	17.0366i		−	1.03490i	−0.855714	−	0.517449i	$-0.826882\pi$
$271$		−	17.0366i		−	1.03490i	0.855714	−	0.517449i	$-0.173118\pi$
$272$	11.8912	−	0.550197i	0.721010	−	0.0333606i
$273$	0.216010	−	2.04817i	0.0130735	−	0.123961i
$274$	−1.13625	−	7.92197i	−0.0686434	−	0.478584i
$275$	46.7989			2.82208
$276$	3.09650	−	8.65016i	0.186387	−	0.520679i
$277$	−30.7346			−1.84666			−0.923332	−	0.384003i	$-0.874545\pi$
$277$	−30.7346			−1.84666			−0.923332	+	0.384003i	$0.874545\pi$
$278$	19.8250	−	15.5796i	1.18903	−	0.934405i
$279$	−4.83054	−	15.9896i	−0.289197	−	0.957270i
$280$	29.3252	−	13.3561i	1.75252	−	0.798182i
$281$		−	20.3178i		−	1.21206i	−0.795442	−	0.606030i	$-0.792761\pi$
$281$		−	20.3178i		−	1.21206i	0.795442	−	0.606030i	$-0.207239\pi$
$282$	0.523093	+	0.832530i	0.0311498	+	0.0495765i
$283$			19.1215i			1.13665i	0.822803	+	0.568327i	$0.192409\pi$
$283$			19.1215i			1.13665i	−0.822803	+	0.568327i	$0.807591\pi$
$284$	−6.54689	−	6.25098i	−0.388487	−	0.370927i
$285$	24.7493	+	2.61018i	1.46602	+	0.154613i
$286$	−1.19409	+	2.97975i	−0.0706080	+	0.176196i
$287$	−11.7482			−0.693476
$288$	0.364117	−	16.9667i	0.0214558	−	0.999770i
$289$	−4.07177	+	7.05252i	−0.239516	+	0.414854i
$290$	−49.0111	+	7.02968i	−2.87803	+	0.412797i
$291$	−20.4040	−	2.15190i	−1.19610	−	0.126147i
$292$	5.58643	+	5.33393i	0.326921	+	0.312145i
$293$	−4.23382	+	2.44440i	−0.247342	+	0.142803i	−0.618547	−	0.785748i	$-0.712278\pi$
$293$	−4.23382	+	2.44440i	−0.247342	+	0.142803i	0.371204	+	0.928551i	$0.378945\pi$
$294$	−7.97100	+	0.298115i	−0.464878	+	0.0173864i
$295$		−	10.2836i		−	0.598735i
$296$	−1.91040	−	1.36334i	−0.111040	−	0.0792424i
$297$	−23.6302	+	21.2310i	−1.37116	+	1.23195i
$298$	−23.1983	−	9.29637i	−1.34384	−	0.538524i
$299$	−0.492374	+	0.852817i	−0.0284747	+	0.0493197i
$300$	26.0898	−	4.74327i	1.50629	−	0.273853i
$301$	−3.18072	+	5.50918i	−0.183334	+	0.317544i
$302$	11.5877	−	9.10629i	0.666798	−	0.524008i
$303$	2.24698	−	21.3055i	0.129086	−	1.22397i
$304$	−16.1387	+	0.746728i	−0.925620	+	0.0428278i
$305$	13.9910	+	8.07768i	0.801120	+	0.462527i
$306$	−10.4824	−	7.03818i	−0.599238	−	0.402346i
$307$	−10.1059	+	5.83464i	−0.576774	+	0.333001i	−0.759850	−	0.650098i	$-0.774728\pi$
$307$	−10.1059	+	5.83464i	−0.576774	+	0.333001i	0.183076	+	0.983099i	$0.441394\pi$
$308$	38.0480	+	9.25783i	2.16799	+	0.527514i
$309$	1.21851	+	0.885961i	0.0693184	+	0.0504005i
$310$	−22.3666	+	16.8624i	−1.27034	+	0.957720i
$311$	6.00978			0.340783			0.170392	−	0.985376i	$-0.445497\pi$
$311$	6.00978			0.340783			0.170392	+	0.985376i	$0.445497\pi$
$312$	−0.363680	+	1.78220i	−0.0205893	+	0.100897i
$313$	7.46529	+	12.9303i	0.421963	+	0.730862i	0.996131	−	0.0878754i	$-0.0280077\pi$
$313$	7.46529	+	12.9303i	0.421963	+	0.730862i	−0.574168	+	0.818737i	$0.694674\pi$
$314$	3.94175	+	5.01586i	0.222446	+	0.283061i
$315$	−33.4262	−	7.12988i	−1.88335	−	0.401723i
$316$	2.68111	+	9.15410i	0.150824	+	0.514958i
$317$	−13.3515	+	7.70849i	−0.749894	+	0.432952i	−0.825656	−	0.564174i	$-0.809195\pi$
$317$	−13.3515	+	7.70849i	−0.749894	+	0.432952i	0.0757614	+	0.997126i	$0.475861\pi$
$318$	−0.365067	−	9.76117i	−0.0204719	−	0.547379i
$319$	−52.1070	−	30.0840i	−2.91743	−	1.68438i
$320$	−26.9128	+	9.25300i	−1.50447	+	0.517259i
$321$	−1.25046	−	2.81127i	−0.0697936	−	0.156910i
$322$	11.1504	+	4.46835i	0.621386	+	0.249011i
$323$	−6.00999	+	10.4096i	−0.334405	+	0.579207i
$324$	−11.0217	+	14.2310i	−0.612316	+	0.790613i
$325$	−2.84217			−0.157655
$326$	−25.5726	+	20.0964i	−1.41633	+	1.11304i
$327$	28.2693	+	2.98141i	1.56330	+	0.164873i
$328$	10.3278	+	0.996841i	0.570255	+	0.0550413i
$329$	−1.11328	+	0.642755i	−0.0613774	+	0.0354362i
$330$	47.0982	+	24.8932i	2.59267	+	1.37033i
$331$	−3.78430	−	2.18487i	−0.208004	−	0.120091i	0.392380	−	0.919803i	$-0.371652\pi$
$331$	−3.78430	−	2.18487i	−0.208004	−	0.120091i	−0.600383	+	0.799712i	$0.704985\pi$
$332$	0.343535	+	0.328007i	0.0188539	+	0.0180017i
$333$	0.767563	+	2.36806i	0.0420622	+	0.129769i
$334$	11.8620	−	29.6005i	0.649059	−	1.61967i
$335$	−9.81674	−	17.0031i	−0.536346	−	0.928978i
$336$	22.1496	+	1.30479i	1.20836	+	0.0711821i
$337$	2.68650			0.146343			0.0731714	−	0.997319i	$-0.476688\pi$
$337$	2.68650			0.146343			0.0731714	+	0.997319i	$0.476688\pi$
$338$	−6.76623	+	16.8845i	−0.368034	+	0.918398i
$339$	−21.9596	−	15.9665i	−1.19268	−	0.867184i
$340$	−5.00584	+	20.5731i	−0.271480	+	1.11573i
$341$	−34.0320	−	0.682724i	−1.84294	−	0.0369716i
$342$	14.2267	+	9.55222i	0.769292	+	0.516525i
$343$			11.9891i			0.647348i
$344$	3.26360	−	4.57318i	0.175961	−	0.246569i
$345$	13.2176	+	9.61032i	0.711609	+	0.517402i
$346$	1.51431	+	10.5578i	0.0814096	+	0.567589i
$347$	5.40014	+	9.35333i	0.289895	+	0.502113i	0.973784	−	0.227473i	$-0.0730463\pi$
$347$	5.40014	+	9.35333i	0.289895	+	0.502113i	−0.683889	+	0.729586i	$0.739713\pi$
$348$	−32.0982	−	11.4902i	−1.72064	−	0.615939i
$349$	−8.91825			−0.477383			−0.238692	−	0.971095i	$-0.576719\pi$
$349$	−8.91825			−0.477383			−0.238692	+	0.971095i	$0.576719\pi$
$350$	4.92236	+	34.3188i	0.263111	+	1.83442i
$351$	1.43510	−	1.28939i	0.0766001	−	0.0688228i
$352$	−32.6621	−	11.3669i	−1.74090	−	0.605855i
$353$	−7.25715	+	4.18992i	−0.386259	+	0.223007i	−0.680538	−	0.732713i	$-0.738254\pi$
$353$	−7.25715	+	4.18992i	−0.386259	+	0.223007i	0.294279	+	0.955720i	$0.404921\pi$
$354$	3.30882	−	6.26032i	0.175862	−	0.332732i
$355$	13.9434	−	8.05024i	0.740040	−	0.427262i
$356$	−28.1196	−	6.84206i	−1.49034	−	0.362628i
$357$	9.70779	−	13.3516i	0.513791	−	0.706642i
$358$	−10.2729	+	25.6352i	−0.542942	+	1.35486i
$359$	−2.20791	+	3.82420i	−0.116529	+	0.201834i	−0.918390	−	0.395677i	$-0.870510\pi$
$359$	−2.20791	+	3.82420i	−0.116529	+	0.201834i	0.801861	+	0.597511i	$0.203843\pi$
$360$	28.7797	+	9.10403i	1.51682	+	0.479825i
$361$	−1.34323	+	2.32654i	−0.0706963	+	0.122450i
$362$	31.5656	−	4.52747i	1.65905	−	0.237958i
$363$	18.5664	+	41.7410i	0.974485	+	2.19083i
$364$	−2.31072	−	0.562243i	−0.121115	−	0.0294696i
$365$	−11.8979	+	6.86923i	−0.622762	+	0.359552i
$366$	5.91818	+	9.41910i	0.309348	+	0.492344i
$367$	−8.33445	−	4.81190i	−0.435055	−	0.251179i	0.266443	−	0.963851i	$-0.414152\pi$
$367$	−8.33445	−	4.81190i	−0.435055	−	0.251179i	−0.701498	+	0.712672i	$0.747485\pi$
$368$	−9.42304	−	4.87419i	−0.491210	−	0.254085i
$369$	−8.17317	−	7.36971i	−0.425478	−	0.383652i
$370$	3.28230	−	2.57942i	0.170638	−	0.134097i
$371$	12.7711			0.663041
$372$	−19.0416	+	3.06868i	−0.987262	+	0.159104i
$373$	20.0003			1.03557			0.517787	−	0.855510i	$-0.326756\pi$
$373$	20.0003			1.03557			0.517787	+	0.855510i	$0.326756\pi$
$374$	−20.2305	+	15.8983i	−1.04610	+	0.822082i
$375$	−1.71573	+	16.2683i	−0.0885997	+	0.840089i
$376$	1.03322	−	0.470577i	0.0532840	−	0.0242682i
$377$	3.16455	+	1.82705i	0.162983	+	0.0940980i
$378$	−18.0547	−	15.0955i	−0.928633	−	0.776430i
$379$	20.3811	−	11.7671i	1.04691	−	0.604433i	0.125127	−	0.992141i	$-0.460066\pi$
$379$	20.3811	−	11.7671i	1.04691	−	0.604433i	0.921782	+	0.387708i	$0.126733\pi$
$380$	6.79393	−	27.9218i	0.348521	−	1.43236i
$381$	−19.2191	+	8.54867i	−0.984622	+	0.437961i
$382$	17.0016	−	2.43855i	0.869880	−	0.124767i
$383$	6.54906	−	11.3433i	0.334641	−	0.579616i	−0.648775	−	0.760981i	$-0.724718\pi$
$383$	6.54906	−	11.3433i	0.334641	−	0.579616i	0.983416	+	0.181365i	$0.0580516\pi$
$384$	−19.3608	−	3.02643i	−0.988002	−	0.154442i
$385$	−34.8251	+	60.3188i	−1.77485	+	3.07413i
$386$	−0.168818	+	0.421270i	−0.00859259	+	0.0214421i
$387$	−5.66873	+	1.83742i	−0.288158	+	0.0934011i
$388$	−5.60111	+	23.0196i	−0.284353	+	1.16864i
$389$	−2.97651	+	1.71849i	−0.150915	+	0.0871308i	−0.573556	−	0.819166i	$-0.694436\pi$
$389$	−2.97651	+	1.71849i	−0.150915	+	0.0871308i	0.422641	+	0.906297i	$0.361103\pi$
$390$	−2.86036	−	1.51181i	−0.144840	−	0.0765533i
$391$	−6.83559	+	3.94653i	−0.345691	+	0.199585i
$392$	−0.884895	+	9.16794i	−0.0446939	+	0.463051i
$393$	2.11897	+	4.76386i	0.106888	+	0.240305i
$394$	1.39043	+	9.69415i	0.0700491	+	0.488384i
$395$	−16.9663			−0.853666
$396$	20.6623	+	30.3083i	1.03832	+	1.52305i
$397$	−15.3396	−	26.5690i	−0.769872	−	1.33346i	−0.937632	−	0.347630i	$-0.886986\pi$
$397$	−15.3396	−	26.5690i	−0.769872	−	1.33346i	0.167759	−	0.985828i	$-0.446347\pi$
$398$	1.54830	+	10.7948i	0.0776091	+	0.541093i
$399$	−13.1754	+	18.1208i	−0.659596	+	0.907175i
$400$	−1.41524	−	30.5870i	−0.0707619	−	1.52935i
$401$			26.2467i			1.31070i	0.755325	+	0.655350i	$0.227479\pi$
$401$			26.2467i			1.31070i	−0.755325	+	0.655350i	$0.772521\pi$
$402$	−0.505255	−	13.5095i	−0.0251998	−	0.673793i
$403$	2.06682	+	0.0414630i	0.102956	+	0.00206542i
$404$	−24.0366	−	5.84858i	−1.19587	−	0.290978i
$405$	−18.7818	−	25.9286i	−0.933275	−	1.28840i
$406$	16.5807	−	41.3757i	0.822886	−	2.05344i
$407$	5.07293			0.251456
$408$	−9.66691	+	10.9136i	−0.478583	+	0.540302i
$409$	12.1094	+	20.9740i	0.598769	+	1.03710i	0.993003	+	0.118089i	$0.0376768\pi$
$409$	12.1094	+	20.9740i	0.598769	+	1.03710i	−0.394234	+	0.919010i	$0.628990\pi$
$410$	−6.86496	+	17.1309i	−0.339036	+	0.846035i
$411$	7.92767	+	5.76411i	0.391043	+	0.284323i
$412$	1.20133	−	1.25820i	0.0591851	−	0.0619869i
$413$	8.01761	+	4.62897i	0.394521	+	0.227777i
$414$	4.95423	+	10.1033i	0.243487	+	0.496549i
$415$	−0.731652	+	0.422419i	−0.0359154	+	0.0207358i
$416$	1.98363	+	0.690328i	0.0972553	+	0.0338461i
$417$	−3.23889	+	30.7107i	−0.158609	+	1.50391i
$418$	27.4569	−	21.5772i	1.34296	−	1.05538i
$419$	26.1142			1.27576			0.637880	−	0.770135i	$-0.279811\pi$
$419$	26.1142			1.27576			0.637880	+	0.770135i	$0.279811\pi$
$420$	−13.3010	+	37.1566i	−0.649021	+	1.81306i
$421$	1.03761	−	1.79719i	0.0505700	−	0.0875898i	−0.839632	−	0.543155i	$-0.817230\pi$
$421$	1.03761	−	1.79719i	0.0505700	−	0.0875898i	0.890202	+	0.455565i	$0.150563\pi$
$422$	4.49339	+	1.80066i	0.218735	+	0.0876548i
$423$	−1.17771	−	0.251207i	−0.0572621	−	0.0122141i
$424$	−11.2269	−	1.08363i	−0.545228	−	0.0526257i
$425$	−19.7288	−	11.3905i	−0.956990	−	0.552518i
$426$	11.0785	−	0.414335i	0.536755	−	0.0200746i
$427$	−12.5955	+	7.27202i	−0.609539	+	0.351918i
$428$	−3.40958	+	0.998619i	−0.164808	+	0.0482701i
$429$	−1.59783	−	3.59222i	−0.0771438	−	0.173434i
$430$	6.17468	+	7.85726i	0.297770	+	0.378911i
$431$	12.2535	+	21.2237i	0.590231	+	1.02231i	0.994201	+	0.107538i	$0.0342967\pi$
$431$	12.2535	+	21.2237i	0.590231	+	1.02231i	−0.403970	+	0.914772i	$0.632370\pi$
$432$	14.5908	+	14.8023i	0.702002	+	0.712175i
$433$	20.0291			0.962538			0.481269	−	0.876573i	$-0.340176\pi$
$433$	20.0291			0.962538			0.481269	+	0.876573i	$0.340176\pi$
$434$	−3.07887	−	25.0284i	−0.147790	−	1.20140i
$435$	35.6610	−	49.0464i	1.70982	−	2.35160i
$436$	7.76021	−	31.8931i	0.371647	−	1.52740i
$437$	9.27727	−	5.35624i	0.443792	−	0.256224i
$438$	−9.45323	+	0.353550i	−0.451693	+	0.0168933i
$439$	−10.8997	−	6.29294i	−0.520214	−	0.300346i	0.216808	−	0.976214i	$-0.430435\pi$
$439$	−10.8997	−	6.29294i	−0.520214	−	0.300346i	−0.737022	+	0.675869i	$0.763769\pi$
$440$	35.7324	−	50.0707i	1.70348	−	2.38703i
$441$	6.54209	−	7.25531i	0.311528	−	0.345491i
$442$	1.22863	−	0.965531i	0.0584402	−	0.0459256i
$443$	4.02219	−	6.96664i	0.191100	−	0.330995i	−0.754515	−	0.656283i	$-0.772128\pi$
$443$	4.02219	−	6.96664i	0.191100	−	0.330995i	0.945615	+	0.325288i	$0.105461\pi$
$444$	2.82809	−	0.514163i	0.134215	−	0.0244011i
$445$	25.7377	−	44.5790i	1.22008	−	2.11325i
$446$	10.3071	+	4.13042i	0.488056	+	0.195581i
$447$	27.9666	−	12.4396i	1.32277	−	0.588372i
$448$	4.90016	−	25.1476i	0.231511	−	1.18811i
$449$		−	13.0155i		−	0.614239i	−0.951671	−	0.307120i	$-0.900635\pi$
$449$		−	13.0155i		−	0.614239i	0.951671	−	0.307120i	$-0.0993652\pi$
$450$	−18.1039	+	26.9632i	−0.853424	+	1.27106i
$451$	−19.4222	+	11.2134i	−0.914558	+	0.528020i
$452$	−21.6500	+	22.6749i	−1.01833	+	1.06654i
$453$	−1.89313	+	17.9504i	−0.0889470	+	0.843382i
$454$	−31.0703	+	4.45643i	−1.45820	+	0.209151i
$455$	2.11499	−	3.66326i	0.0991520	−	0.171736i
$456$	13.1199	−	14.8119i	0.614397	−	0.693631i
$457$	−27.0822			−1.26685			−0.633426	−	0.773803i	$-0.718352\pi$
$457$	−27.0822			−1.26685			−0.633426	+	0.773803i	$0.718352\pi$
$458$	−6.64434	+	16.5804i	−0.310470	+	0.774750i
$459$	15.1292	−	3.19889i	0.706169	−	0.149312i
$460$	13.0312	−	13.6481i	0.607583	−	0.636346i
$461$		−	21.1539i		−	0.985237i	−0.870245	−	0.492619i	$-0.836040\pi$
$461$		−	21.1539i		−	0.985237i	0.870245	−	0.492619i	$-0.163960\pi$
$462$	−40.6083	+	25.5149i	−1.88927	+	1.18706i
$463$			4.36207i			0.202722i	0.994850	+	0.101361i	$0.0323198\pi$
$463$			4.36207i			0.202722i	−0.994850	+	0.101361i	$0.967680\pi$
$464$	−18.0867	+	34.9661i	−0.839653	+	1.62326i
$465$	4.28169	−	34.0379i	0.198559	−	1.57847i
$466$	10.9410	−	8.59803i	0.506830	−	0.398296i
$467$	1.88534			0.0872431			0.0436216	−	0.999048i	$-0.486110\pi$
$467$	1.88534			0.0872431			0.0436216	+	0.999048i	$0.486110\pi$
$468$	−1.25486	−	1.84067i	−0.0580057	−	0.0850852i
$469$	17.6752			0.816167
$470$	0.286709	+	1.99894i	0.0132249	+	0.0922044i
$471$	−7.77000	−	0.819460i	−0.358023	−	0.0377587i
$472$	−6.65543	−	4.74958i	−0.306341	−	0.218617i
$473$			12.1437i			0.558369i
$474$	−10.3285	−	5.45901i	−0.474404	−	0.250740i
$475$	26.7760	+	15.4591i	1.22857	+	0.709314i
$476$	−13.7865	−	13.1634i	−0.631904	−	0.603342i
$477$	8.88475	+	8.01135i	0.406805	+	0.366814i
$478$	−0.482058	+	0.0691417i	−0.0220488	+	0.00316247i
$479$	−13.9198	−	24.1097i	−0.636010	−	1.10160i	−0.986300	−	0.164960i	$-0.947250\pi$
$479$	−13.9198	−	24.1097i	−0.636010	−	1.10160i	0.350290	−	0.936641i	$-0.386083\pi$
$480$	14.8455	−	31.5354i	0.677601	−	1.43939i
$481$	−0.308088			−0.0140476
$482$	−0.177998	+	0.444180i	−0.00810760	+	0.0202318i
$483$	−13.4423	+	5.97915i	−0.611645	+	0.272061i
$484$	50.6246	−	14.8272i	2.30112	−	0.673965i
$485$	−36.4937	−	21.0696i	−1.65709	−	0.956723i
$486$	−3.09105	−	21.8276i	−0.140213	−	0.990121i
$487$	13.1436	+	7.58848i	0.595595	+	0.343867i	0.767307	−	0.641280i	$-0.221596\pi$
$487$	13.1436	+	7.58848i	0.595595	+	0.343867i	−0.171712	+	0.985147i	$0.554930\pi$
$488$	11.6896	−	5.32403i	0.529164	−	0.241007i
$489$	4.17789	−	39.6141i	0.188931	−	1.79141i
$490$	−15.2071	−	6.09402i	−0.686986	−	0.275300i
$491$	15.8753	−	27.4968i	0.716440	−	1.24091i	−0.245961	−	0.969280i	$-0.579103\pi$
$491$	15.8753	−	27.4968i	0.716440	−	1.24091i	0.962401	−	0.271632i	$-0.0875632\pi$
$492$	−9.69113	+	8.21988i	−0.436910	+	0.370581i
$493$	14.6444	+	25.3648i	0.659551	+	1.14238i
$494$	−1.66750	+	1.31042i	−0.0750246	+	0.0589586i
$495$	−62.0658	+	20.1175i	−2.78965	+	0.904213i
$496$	0.582940	+	22.2634i	0.0261748	+	0.999657i
$497$			14.4946i			0.650172i
$498$	−0.581321	+	0.0217414i	−0.0260496	+	0.000974254i
$499$	−27.7107	+	15.9988i	−1.24050	+	0.716204i	−0.969196	−	0.246290i	$-0.920788\pi$
$499$	−27.7107	+	15.9988i	−1.24050	+	0.716204i	−0.271305	+	0.962493i	$0.587455\pi$
$500$	18.3537	+	4.46580i	0.820800	+	0.199717i
$501$	15.8727	+	35.6848i	0.709138	+	1.59428i
$502$	3.93382	−	9.81651i	0.175575	−	0.438132i
$503$	4.57160	+	7.91825i	0.203838	+	0.353057i	0.949762	−	0.312974i	$-0.101325\pi$
$503$	4.57160	+	7.91825i	0.203838	+	0.353057i	−0.745924	+	0.666031i	$0.767992\pi$
$504$	−20.0526	+	18.3400i	−0.893212	+	0.816931i
$505$	22.0005	−	38.1061i	0.979011	−	1.69570i
$506$	22.6988	−	3.25570i	1.00908	−	0.144733i
$507$	−9.05398	−	20.3551i	−0.402101	−	0.904001i
$508$	6.82700	+	23.3094i	0.302899	+	1.03419i
$509$	27.7984	+	16.0494i	1.23214	+	0.711378i	0.967476	−	0.252962i	$-0.0814046\pi$
$509$	27.7984	+	16.0494i	1.23214	+	0.711378i	0.264667	+	0.964340i	$0.414738\pi$
$510$	−13.7963	−	21.9575i	−0.610908	−	0.972293i
$511$		−	12.3682i		−	0.547136i
$512$	−6.44146	+	21.6912i	−0.284675	+	0.958624i
$513$	−20.5333	+	4.34154i	−0.906568	+	0.191684i
$514$	4.83101	+	33.6819i	0.213087	+	1.48565i
$515$	1.54711	+	2.67968i	0.0681739	+	0.118081i
$516$	1.23082	+	6.76998i	0.0541838	+	0.298032i
$517$	−1.22699	+	2.12521i	−0.0539631	+	0.0934668i
$518$	0.533577	+	3.72011i	0.0234440	+	0.163452i
$519$	−10.5654	−	7.68195i	−0.463769	−	0.337200i
$520$	−2.17009	+	3.04088i	−0.0951648	+	0.133351i
$521$	11.2453	−	6.49249i	0.492667	−	0.284441i	−0.233013	−	0.972474i	$-0.574859\pi$
$521$	11.2453	−	6.49249i	0.492667	−	0.284441i	0.725680	+	0.688032i	$0.241525\pi$
$522$	37.4902	−	18.3837i	1.64090	−	0.804631i
$523$			9.02722i			0.394733i	0.980330	+	0.197366i	$0.0632389\pi$
$523$			9.02722i			0.394733i	−0.980330	+	0.197366i	$0.936761\pi$
$524$	5.77774	−	1.69222i	0.252402	−	0.0739249i
$525$	−34.3435	−	24.9707i	−1.49887	−	1.08981i
$526$	7.49014	+	9.53117i	0.326586	+	0.415579i
$527$	14.1806	+	8.57092i	0.617717	+	0.373355i
$528$	37.8633	−	18.9843i	1.64779	−	0.826184i
$529$	−15.9655			−0.694153
$530$	7.46265	−	18.6224i	0.324157	−	0.808905i
$531$	2.67403	+	8.24982i	0.116043	+	0.358012i
$532$	18.7111	+	17.8653i	0.811228	+	0.774560i
$533$	1.17955	−	0.681011i	0.0510918	−	0.0294979i
$534$	30.0118	−	18.8569i	1.29874	−	0.816020i
$535$		−	6.31935i		−	0.273209i
$536$	−15.5381	−	1.49975i	−0.671145	−	0.0647793i
$537$	−13.7464	−	30.9045i	−0.593199	−	1.33363i
$538$	1.82109	+	12.6967i	0.0785130	+	0.547394i
$539$	−9.95416	−	17.2411i	−0.428756	−	0.742627i
$540$	−32.5619	+	17.5059i	−1.40124	+	0.753333i
$541$	11.5758	+	20.0498i	0.497682	+	0.862010i	0.999996	−	0.00267499i	$-0.000851475\pi$
$541$	11.5758	+	20.0498i	0.497682	+	0.862010i	−0.502315	+	0.864685i	$0.667518\pi$
$542$	18.9437	−	14.8871i	0.813702	−	0.639454i
$543$	−22.9675	+	31.5883i	−0.985629	+	1.35559i
$544$	11.0027	+	12.7416i	0.471736	+	0.546291i
$545$	50.5612	+	29.1915i	2.16580	+	1.25043i
$546$	2.46621	−	1.54956i	0.105544	−	0.0663151i
$547$	−7.05376	−	4.07249i	−0.301597	−	0.174127i	0.341563	−	0.939859i	$-0.389044\pi$
$547$	−7.05376	−	4.07249i	−0.301597	−	0.174127i	−0.643160	+	0.765732i	$0.722377\pi$
$548$	7.81590	−	8.18590i	0.333879	−	0.349684i
$549$	−13.3244	−	2.84211i	−0.568670	−	0.121298i
$550$	40.8942	+	52.0377i	1.74374	+	2.21890i
$551$	−19.8754	−	34.4252i	−0.846720	−	1.46656i
$552$	12.3243	−	4.11563i	0.524558	−	0.175173i
$553$	7.63704	−	13.2277i	0.324760	−	0.562501i
$554$	−26.8568	−	34.1752i	−1.14104	−	1.45196i
$555$	−0.536241	+	5.08456i	−0.0227622	+	0.215827i
$556$	34.6474	+	8.43039i	1.46938	+	0.357528i
$557$		−	21.6523i		−	0.917439i	−0.888581	−	0.458719i	$-0.848308\pi$
$557$		−	21.6523i		−	0.917439i	0.888581	−	0.458719i	$-0.151692\pi$
$558$	13.5584	−	19.3434i	0.573974	−	0.818873i
$559$		−	0.737509i		−	0.0311933i
$560$	40.4765	+	20.9370i	1.71045	+	0.884750i
$561$	3.30514	−	31.3388i	0.139543	−	1.32313i
$562$	22.5923	−	17.7543i	0.952999	−	0.748921i
$563$	8.47962	−	14.6871i	0.357373	−	0.618989i	−0.630148	−	0.776475i	$-0.717006\pi$
$563$	8.47962	−	14.6871i	0.357373	−	0.618989i	0.987521	+	0.157486i	$0.0503390\pi$
$564$	−0.468633	+	1.30914i	−0.0197330	+	0.0551248i
$565$	−27.8816	−	48.2924i	−1.17299	−	2.03168i
$566$	−21.2620	+	16.7089i	−0.893710	+	0.702329i
$567$	28.6695	−	2.97195i	1.20400	−	0.124810i
$568$	1.22987	−	12.7421i	0.0516043	−	0.534646i
$569$	15.1144	+	8.72630i	0.633628	+	0.365825i	0.782156	−	0.623083i	$-0.214120\pi$
$569$	15.1144	+	8.72630i	0.633628	+	0.365825i	−0.148528	+	0.988908i	$0.547453\pi$
$570$	18.7243	+	29.8007i	0.784274	+	1.24821i
$571$	−6.07695	−	3.50853i	−0.254312	−	0.146827i	0.367425	−	0.930053i	$-0.380240\pi$
$571$	−6.07695	−	3.50853i	−0.254312	−	0.146827i	−0.621737	+	0.783226i	$0.713573\pi$
$572$	−4.35675	+	1.27603i	−0.182165	+	0.0533535i
$573$	−12.3706	+	17.0139i	−0.516788	+	0.710765i
$574$	−10.2660	−	13.0634i	−0.428493	−	0.545255i
$575$	10.1514	+	17.5828i	0.423343	+	0.733252i
$576$	19.1842	−	14.4211i	0.799340	−	0.600879i
$577$	1.95480	+	3.38581i	0.0813792	+	0.140953i	0.903843	−	0.427865i	$-0.140734\pi$
$577$	1.95480	+	3.38581i	0.0813792	+	0.140953i	−0.822463	+	0.568818i	$0.807401\pi$
$578$	−11.4000	+	1.63511i	−0.474179	+	0.0680117i
$579$	−0.225897	−	0.507860i	−0.00938796	−	0.0211060i
$580$	−50.6440	−	48.3549i	−2.10288	−	2.00783i
$581$		−	0.760575i		−	0.0315540i
$582$	−15.4368	−	24.5685i	−0.639878	−	1.01840i
$583$	21.1132	−	12.1897i	0.874420	−	0.504847i
$584$	−1.04944	+	10.8728i	−0.0434263	+	0.449918i
$585$	3.76936	−	1.22177i	0.155844	−	0.0505139i
$586$	−6.41767	−	2.57179i	−0.265112	−	0.106240i
$587$	−4.57982			−0.189030			−0.0945148	−	0.995523i	$-0.530130\pi$
$587$	−4.57982			−0.189030			−0.0945148	+	0.995523i	$0.530130\pi$
$588$	−7.29678	−	8.60281i	−0.300914	−	0.354774i
$589$	−19.2459	−	11.6325i	−0.793014	−	0.479307i
$590$	11.4348	−	8.98613i	0.470764	−	0.369953i
$591$	−9.70113	−	7.05357i	−0.399051	−	0.290145i
$592$	−0.153410	−	3.31559i	−0.00630510	−	0.136270i
$593$			25.8419i			1.06120i	0.847623	+	0.530599i	$0.178033\pi$
$593$			25.8419i			1.06120i	−0.847623	+	0.530599i	$0.821967\pi$
$594$	−44.2565	−	7.72319i	−1.81587	−	0.316886i
$595$	29.3622	−	16.9523i	1.20373	−	0.694975i
$596$	−9.93430	−	33.9187i	−0.406925	−	1.38936i
$597$	−10.8025	−	7.85439i	−0.442118	−	0.321459i
$598$	−1.37854	+	0.197724i	−0.0563726	+	0.00808554i
$599$	13.2101	−	22.8806i	0.539751	−	0.934876i	−0.459166	−	0.888350i	$-0.651852\pi$
$599$	13.2101	−	22.8806i	0.539751	−	0.934876i	0.998917	−	0.0465254i	$-0.0148148\pi$
$600$	28.0723	+	24.8656i	1.14605	+	1.01513i
$601$	9.73435	+	16.8604i	0.397073	+	0.687750i	0.993363	−	0.115019i	$-0.0366928\pi$
$601$	9.73435	+	16.8604i	0.397073	+	0.687750i	−0.596291	+	0.802768i	$0.703359\pi$
$602$	−8.90531	+	1.27729i	−0.362953	+	0.0520585i
$603$	12.2965	+	11.0877i	0.500754	+	0.451528i
$604$	20.2514	+	4.92756i	0.824017	+	0.200499i
$605$			93.8280i			3.81465i
$606$	25.6540	−	16.1189i	1.04212	−	0.654785i
$607$	38.5090	+	22.2332i	1.56303	+	0.902417i	0.996948	+	0.0780688i	$0.0248754\pi$
$607$	38.5090	+	22.2332i	1.56303	+	0.902417i	0.566084	+	0.824348i	$0.308458\pi$
$608$	−14.9328	−	17.2929i	−0.605606	−	0.701319i
$609$	22.1868	+	49.8803i	0.899056	+	2.02125i
$610$	3.24378	+	22.6157i	0.131337	+	0.915683i
$611$	0.0745173	−	0.129068i	0.00301465	−	0.00522152i
$612$	−1.33375	−	17.8060i	−0.0539137	−	0.719765i
$613$	15.3238	+	26.5416i	0.618923	+	1.07201i	0.989683	+	0.143277i	$0.0457639\pi$
$613$	15.3238	+	26.5416i	0.618923	+	1.07201i	−0.370760	+	0.928729i	$0.620903\pi$
$614$	−15.3186	−	6.13872i	−0.618210	−	0.247738i
$615$	−9.18609	−	20.6521i	−0.370419	−	0.832773i
$616$	22.9533	+	50.3971i	0.924815	+	2.03056i
$617$	−13.6038	+	7.85413i	−0.547666	+	0.316195i	−0.748180	−	0.663496i	$-0.769072\pi$
$617$	−13.6038	+	7.85413i	−0.547666	+	0.316195i	0.200514	+	0.979691i	$0.435739\pi$
$618$	0.0796279	+	2.12909i	0.00320310	+	0.0856446i
$619$		−	10.3808i		−	0.417238i	−0.977997	−	0.208619i	$-0.933103\pi$
$619$		−	10.3808i		−	0.417238i	0.977997	−	0.208619i	$-0.0668968\pi$
$620$	−38.2947	−	10.1355i	−1.53795	−	0.407053i
$621$	−13.1025	−	4.27274i	−0.525783	−	0.171459i
$622$	5.25152	+	6.68254i	0.210567	+	0.267945i
$623$	23.1706	+	40.1327i	0.928311	+	1.60788i
$624$	−2.29950	+	1.15295i	−0.0920537	+	0.0461548i
$625$	2.33836	−	4.05017i	0.0935346	−	0.162007i
$626$	−7.85435	+	19.5999i	−0.313923	+	0.783368i
$627$	−4.48574	+	42.5331i	−0.179143	+	1.69861i
$628$	−2.13294	+	8.76602i	−0.0851136	+	0.349802i
$629$	−2.13858	−	1.23471i	−0.0852707	−	0.0492311i
$630$	−21.2808	−	43.3984i	−0.847848	−	1.72903i
$631$	−22.1769	−	12.8038i	−0.882847	−	0.509712i	−0.0112513	−	0.999937i	$-0.503581\pi$
$631$	−22.1769	−	12.8038i	−0.882847	−	0.509712i	−0.871596	+	0.490224i	$0.836915\pi$
$632$	−7.83602	+	10.9804i	−0.311700	+	0.436776i
$633$	−5.41699	+	2.40949i	−0.215306	+	0.0957685i
$634$	−20.2383	−	8.11021i	−0.803767	−	0.322098i
$635$	−43.2018			−1.71441
$636$	10.5349	−	8.93553i	0.417735	−	0.354317i
$637$	0.604533	+	1.04708i	0.0239525	+	0.0414869i
$638$	−12.0809	−	84.2285i	−0.478288	−	3.33464i
$639$	−9.09253	+	10.0838i	−0.359695	+	0.398909i
$640$	−33.8060	−	21.8400i	−1.33630	−	0.863301i
$641$	−24.3183	−	14.0402i	−0.960514	−	0.554553i	−0.0641831	−	0.997938i	$-0.520444\pi$
$641$	−24.3183	−	14.0402i	−0.960514	−	0.554553i	−0.896331	+	0.443385i	$0.853777\pi$
$642$	2.03329	−	3.84701i	0.0802475	−	0.151829i
$643$			18.9282i			0.746454i	0.927740	+	0.373227i	$0.121749\pi$
$643$			18.9282i			0.746454i	−0.927740	+	0.373227i	$0.878251\pi$
$644$	4.77497	+	16.3032i	0.188160	+	0.642435i
$645$	−12.1716	−	1.28367i	−0.479255	−	0.0505445i
$646$	−16.8266	+	2.41345i	−0.662035	+	0.0949559i
$647$	11.1617			0.438812			0.219406	−	0.975634i	$-0.429588\pi$
$647$	11.1617			0.438812			0.219406	+	0.975634i	$0.429588\pi$
$648$	−25.4552	+	0.180004i	−0.999975	+	0.00707124i
$649$	17.6730			0.693726
$650$	−2.48358	−	3.16034i	−0.0974139	−	0.123959i
$651$	24.6102	+	18.6597i	0.964551	+	0.731330i
$652$	−44.6921	−	10.8745i	−1.75028	−	0.425877i
$653$		−	23.0069i		−	0.900329i	−0.892946	−	0.450165i	$-0.851365\pi$
$653$		−	23.0069i		−	0.900329i	0.892946	−	0.450165i	$-0.148635\pi$
$654$	21.3874	+	34.0392i	0.836314	+	1.33104i
$655$			10.7085i			0.418416i
$656$	7.91627	+	12.3550i	0.309078	+	0.482380i
$657$	7.75861	−	8.60446i	0.302692	−	0.335692i
$658$	−1.68753	−	0.676253i	−0.0657868	−	0.0263631i
$659$	44.2361			1.72319			0.861597	−	0.507592i	$-0.169464\pi$
$659$	44.2361			1.72319			0.861597	+	0.507592i	$0.169464\pi$
$660$	13.4760	+	74.1230i	0.524552	+	2.88524i
$661$	16.7855	−	29.0733i	0.652879	−	1.13082i	−0.329542	−	0.944141i	$-0.606894\pi$
$661$	16.7855	−	29.0733i	0.652879	−	1.13082i	0.982421	−	0.186679i	$-0.0597725\pi$
$662$	−0.877382	−	6.11713i	−0.0341004	−	0.237749i
$663$	−0.200727	+	1.90326i	−0.00779558	+	0.0739165i
$664$	−0.0645350	+	0.668614i	−0.00250444	+	0.0259473i
$665$	−39.8504	+	23.0076i	−1.54533	+	0.892198i
$666$	−1.96243	+	2.92277i	−0.0760427	+	0.113255i
$667$		−	26.1028i		−	1.01070i
$668$	43.2795	−	12.6760i	1.67453	−	0.490448i
$669$	−12.4257	+	5.52697i	−0.480405	+	0.213685i
$670$	10.3283	−	25.7735i	0.399019	−	0.995716i
$671$	−13.8820	+	24.0443i	−0.535908	+	0.928219i
$672$	17.9041	+	25.7693i	0.690667	+	0.994073i
$673$	8.11001	−	14.0469i	0.312618	−	0.541470i	−0.666310	−	0.745675i	$-0.732127\pi$
$673$	8.11001	−	14.0469i	0.312618	−	0.541470i	0.978928	+	0.204204i	$0.0654607\pi$
$674$	2.34754	+	2.98724i	0.0904239	+	0.115064i
$675$	−8.22832	−	38.9158i	−0.316708	−	1.49787i
$676$	−24.6872	+	7.23054i	−0.949508	+	0.278098i
$677$	−7.71546	−	4.45452i	−0.296529	−	0.171201i	0.344354	−	0.938840i	$-0.388098\pi$
$677$	−7.71546	−	4.45452i	−0.296529	−	0.171201i	−0.640883	+	0.767639i	$0.721431\pi$
$678$	−1.43503	−	38.3699i	−0.0551121	−	1.47359i
$679$	32.8538	−	18.9682i	1.26081	−	0.727931i
$680$	−27.2504	+	12.4112i	−1.04501	+	0.475947i
$681$	22.6071	−	31.0927i	0.866307	−	1.19148i
$682$	−28.9790	−	38.4383i	−1.10966	−	1.47188i
$683$	−42.8490			−1.63957			−0.819785	−	0.572671i	$-0.805907\pi$
$683$	−42.8490			−1.63957			−0.819785	+	0.572671i	$0.805907\pi$
$684$	1.81017	+	24.1663i	0.0692136	+	0.924022i
$685$	10.0656	+	17.4341i	0.384587	+	0.666124i
$686$	−13.3312	+	10.4764i	−0.508986	+	0.399991i
$687$	−8.89088	−	19.9884i	−0.339208	−	0.762606i
$688$	7.93695	−	0.367237i	0.302593	−	0.0140008i
$689$	−1.28224	+	0.740303i	−0.0488495	+	0.0282033i
$690$	0.863751	+	23.0950i	0.0328824	+	0.879211i
$691$	24.8514	+	14.3480i	0.945391	+	0.545822i	0.891646	−	0.452733i	$-0.149551\pi$
$691$	24.8514	+	14.3480i	0.945391	+	0.545822i	0.0537452	+	0.998555i	$0.482884\pi$
$692$	−10.4164	+	10.9095i	−0.395973	+	0.414718i
$693$	12.2531	−	57.4449i	0.465457	−	2.18215i
$694$	−5.68157	+	14.1779i	−0.215670	+	0.538185i
$695$	−31.7125	+	54.9277i	−1.20292	+	2.08353i
$696$	−15.2719	−	45.7319i	−0.578879	−	1.73346i
$697$	10.9170			0.413512
$698$	−7.79304	−	9.91661i	−0.294971	−	0.375349i
$699$	−1.78747	+	16.9485i	−0.0676082	+	0.641050i
$700$	−33.8593	+	35.4622i	−1.27976	+	1.34034i
$701$	14.7131	−	8.49461i	0.555706	−	0.320837i	−0.195714	−	0.980661i	$-0.562702\pi$
$701$	14.7131	−	8.49461i	0.555706	−	0.320837i	0.751420	+	0.659824i	$0.229369\pi$
$702$	2.68777	+	0.469042i	0.101443	+	0.0177029i
$703$	2.90248	+	1.67575i	0.109469	+	0.0632020i
$704$	−15.9018	−	46.2512i	−0.599323	−	1.74316i
$705$	−2.00038	−	1.45445i	−0.0753388	−	0.0547779i
$706$	−11.0005	−	4.40828i	−0.414008	−	0.165908i
$707$	19.8062	+	34.3054i	0.744889	+	1.29019i
$708$	9.85248	−	1.79124i	0.370279	−	0.0673187i
$709$	−6.66115			−0.250165			−0.125082	−	0.992146i	$-0.539920\pi$
$709$	−6.66115			−0.250165			−0.125082	+	0.992146i	$0.539920\pi$
$710$	21.1356	+	8.46978i	0.793205	+	0.317865i
$711$	13.6108	−	4.41170i	0.510446	−	0.165452i
$712$	−16.9638	−	37.2463i	−0.635745	−	1.39586i
$713$	−7.12558	−	12.9342i	−0.266855	−	0.484391i
$714$	23.3292	−	0.872511i	0.873074	−	0.0326529i
$715$		−	8.07483i		−	0.301982i
$716$	−37.4818	+	10.9779i	−1.40076	+	0.410263i
$717$	0.350750	−	0.482405i	0.0130990	−	0.0180157i
$718$	−6.18164	+	0.886635i	−0.230697	+	0.0330889i
$719$	17.1882	+	29.7708i	0.641012	+	1.11026i	0.985207	+	0.171367i	$0.0548183\pi$
$719$	17.1882	+	29.7708i	0.641012	+	1.11026i	−0.344196	+	0.938898i	$0.611848\pi$
$720$	15.0254	+	39.9568i	0.559963	+	1.48910i
$721$	−2.78561			−0.103741
$722$	−3.76074	+	0.539405i	−0.139960	+	0.0200746i
$723$	−0.238182	−	0.535479i	−0.00885808	−	0.0199147i
$724$	32.6173	+	31.1430i	1.21221	+	1.15742i
$725$	65.2444	−	37.6689i	2.42312	−	1.39899i
$726$	−30.1897	+	57.1193i	−1.12045	+	2.11990i
$727$	22.4845	−	12.9814i	0.833902	−	0.481454i	−0.0212845	−	0.999773i	$-0.506776\pi$
$727$	22.4845	−	12.9814i	0.833902	−	0.481454i	0.855187	+	0.518320i	$0.173442\pi$
$728$	−1.39399	−	3.06070i	−0.0516648	−	0.113437i
$729$	21.8095	+	15.9169i	0.807758	+	0.589514i
$730$	−18.0349	−	7.22722i	−0.667502	−	0.267491i
$731$	2.95568	−	5.11939i	0.109320	−	0.189348i
$732$	−5.30203	+	14.8114i	−0.195969	+	0.547445i
$733$	−12.1208	+	20.9938i	−0.447690	+	0.775422i	−0.998235	−	0.0593832i	$-0.981087\pi$
$733$	−12.1208	+	20.9938i	−0.447690	+	0.775422i	0.550545	+	0.834805i	$0.314420\pi$
$734$	−1.93233	−	13.4722i	−0.0713235	−	0.497269i
$735$	18.3329	−	8.15448i	0.676217	−	0.300783i
$736$	−2.81430	−	14.7371i	−0.103737	−	0.543217i
$737$	29.2208	−	16.8706i	1.07636	−	0.621438i
$738$	1.05276	−	15.5280i	0.0387525	−	0.571593i
$739$	8.30220	+	4.79328i	0.305401	+	0.176324i	0.644867	−	0.764295i	$-0.276913\pi$
$739$	8.30220	+	4.79328i	0.305401	+	0.176324i	−0.339465	+	0.940619i	$0.610246\pi$
$740$	5.73634	+	1.39576i	0.210872	+	0.0513092i
$741$	0.272427	−	2.58311i	0.0100078	−	0.0948928i
$742$	11.1597	+	14.2007i	0.409687	+	0.521325i
$743$	−14.3976			−0.528195			−0.264098	−	0.964496i	$-0.585074\pi$
$743$	−14.3976			−0.528195			−0.264098	+	0.964496i	$0.585074\pi$
$744$	−20.0513	−	18.4917i	−0.735118	−	0.677939i
$745$	62.8651			2.30320
$746$	17.4768	+	22.2392i	0.639872	+	0.814234i
$747$	0.477111	−	0.529127i	0.0174566	−	0.0193597i
$748$	−35.3561	−	8.60282i	−1.29275	−	0.314550i
$749$	4.92687	+	2.84453i	0.180024	+	0.103937i
$750$	−19.5887	+	12.3079i	−0.715277	+	0.449421i
$751$	−1.29107	+	0.745397i	−0.0471117	+	0.0271999i	−0.523371	−	0.852105i	$-0.675326\pi$
$751$	−1.29107	+	0.745397i	−0.0471117	+	0.0271999i	0.476259	+	0.879305i	$0.341992\pi$
$752$	1.42611	+	0.737674i	0.0520049	+	0.0269002i
$753$	5.26389	+	11.8343i	0.191827	+	0.431264i
$754$	0.733695	+	5.11534i	0.0267196	+	0.186290i
$755$	−18.5359	+	32.1052i	−0.674592	+	1.16843i
$756$	1.00866	−	33.2667i	0.0366848	−	1.20990i
$757$	11.0988	−	19.2237i	0.403393	−	0.698698i	−0.590740	−	0.806862i	$-0.701164\pi$
$757$	11.0988	−	19.2237i	0.403393	−	0.698698i	0.994133	+	0.108164i	$0.0344973\pi$
$758$	30.8940	+	12.3803i	1.12212	+	0.449673i
$759$	−16.5159	+	22.7152i	−0.599489	+	0.824508i
$760$	36.9843	−	16.8445i	1.34156	−	0.611013i
$761$	45.7116	−	26.3916i	1.65704	−	0.956695i	0.682976	−	0.730440i	$-0.260685\pi$
$761$	45.7116	−	26.3916i	1.65704	−	0.956695i	0.974068	−	0.226255i	$-0.0726481\pi$
$762$	−26.2998	−	13.9005i	−0.952742	−	0.503560i
$763$	−45.5182	+	26.2800i	−1.64787	+	0.951398i
$764$	17.5681	+	16.7740i	0.635591	+	0.606862i
$765$	31.0613	+	6.62543i	1.12302	+	0.239543i
$766$	18.3359	−	2.62992i	0.662503	−	0.0950230i
$767$	−1.07331			−0.0387550
$768$	−13.5528	−	24.1727i	−0.489045	−	0.872258i
$769$	12.7582	+	22.0979i	0.460073	+	0.796870i	0.998964	−	0.0455057i	$-0.0144899\pi$
$769$	12.7582	+	22.0979i	0.460073	+	0.796870i	−0.538891	+	0.842375i	$0.681157\pi$
$770$	−97.5023	+	13.9848i	−3.51374	+	0.503977i
$771$	−33.7062	−	24.5073i	−1.21390	−	0.882610i
$772$	−0.615947	+	0.180402i	−0.0221684	+	0.00649282i
$773$			18.5002i			0.665404i	0.943032	+	0.332702i	$0.107960\pi$
$773$			18.5002i			0.665404i	−0.943032	+	0.332702i	$0.892040\pi$
$774$	−6.99661	−	4.69773i	−0.251488	−	0.168856i
$775$	22.0465	−	36.4759i	0.791932	−	1.31025i
$776$	−30.4909	+	13.8871i	−1.09456	+	0.498516i
$777$	−3.72279	−	2.70679i	−0.133554	−	0.0971056i
$778$	−4.51183	−	1.80805i	−0.161757	−	0.0648217i
$779$	−14.8166			−0.530860
$780$	−0.818419	−	4.50162i	−0.0293041	−	0.161184i
$781$	13.8348	+	23.9626i	0.495048	+	0.857449i
$782$	−10.3615	−	4.15221i	−0.370525	−	0.148483i
$783$	−15.8549	+	48.6193i	−0.566607	+	1.73751i
$784$	−10.9675	+	7.02727i	−0.391696	+	0.250974i
$785$	−13.8970	−	8.02346i	−0.496007	−	0.286370i
$786$	−3.44553	+	6.51898i	−0.122898	+	0.232524i
$787$	−17.3884	+	10.0392i	−0.619829	+	0.357858i	−0.776802	−	0.629745i	$-0.783160\pi$
$787$	−17.3884	+	10.0392i	−0.619829	+	0.357858i	0.156974	+	0.987603i	$0.449826\pi$
$788$	−9.56435	+	10.0171i	−0.340716	+	0.356845i
$789$	−14.7646	−	1.55714i	−0.525634	−	0.0554358i
$790$	−14.8256	−	18.8656i	−0.527473	−	0.671207i
$791$	50.2015			1.78496
$792$	−15.6458	+	49.4596i	−0.555950	+	1.75747i
$793$	0.843076	−	1.46025i	0.0299385	−	0.0518550i
$794$	16.1390	−	40.2735i	0.572753	−	1.42925i
$795$	9.98586	+	22.4501i	0.354162	+	0.796225i
$796$	−10.6502	+	11.1544i	−0.377487	+	0.395357i
$797$	33.3991	+	19.2830i	1.18306	+	0.683039i	0.956720	−	0.291010i	$-0.0939913\pi$
$797$	33.3991	+	19.2830i	1.18306	+	0.683039i	0.226338	+	0.974049i	$0.427325\pi$
$798$	−31.6624	+	1.18417i	−1.12084	+	0.0419193i
$799$	1.03452	−	0.597280i	0.0365986	−	0.0211302i
$800$	32.7744	−	28.3015i	1.15875	−	1.00061i
$801$	−9.05574	+	42.4551i	−0.319969	+	1.50008i
$802$	−29.1849	+	22.9352i	−1.03056	+	0.809870i
$803$	−11.8052	−	20.4472i	−0.416595	−	0.721564i
$804$	14.5803	−	12.3668i	0.514208	−	0.436144i
$805$	−30.2164			−1.06499
$806$	1.75995	+	2.33442i	0.0619915	+	0.0822266i
$807$	−12.7059	−	9.23827i	−0.447268	−	0.325203i
$808$	−14.5006	−	31.8381i	−0.510130	−	1.12006i
$809$	−35.8908	+	20.7216i	−1.26185	+	0.728532i	−0.973433	−	0.228971i	$-0.926464\pi$
$809$	−35.8908	+	20.7216i	−1.26185	+	0.728532i	−0.288422	+	0.957504i	$0.593130\pi$
$810$	12.4191	−	43.5415i	0.436362	−	1.52989i
$811$	22.0053	+	12.7048i	0.772712	+	0.446126i	0.833841	−	0.552004i	$-0.186137\pi$
$811$	22.0053	+	12.7048i	0.772712	+	0.446126i	−0.0611290	+	0.998130i	$0.519470\pi$
$812$	60.4962	−	17.7185i	2.12300	−	0.621797i
$813$	−3.09491	+	29.3454i	−0.108543	+	1.02919i
$814$	4.43288	+	5.64082i	0.155372	+	0.197711i
$815$	40.9064	−	70.8519i	1.43289	−	2.48183i
$816$	−20.5825	−	1.21247i	−0.720532	−	0.0424451i
$817$	−4.01146	+	6.94805i	−0.140343	+	0.243081i
$818$	−12.7404	+	31.7927i	−0.445459	+	1.11161i
$819$	−0.744152	+	3.48873i	−0.0260028	+	0.121906i
$820$	−25.0474	+	7.33604i	−0.874694	+	0.256186i
$821$		−	12.0693i		−	0.421222i	−0.977570	−	0.210611i	$-0.932455\pi$
$821$		−	12.0693i		−	0.421222i	0.977570	−	0.210611i	$-0.0675454\pi$
$822$	0.518063	+	13.8520i	0.0180695	+	0.483143i
$823$	−17.6508	+	10.1907i	−0.615267	+	0.355225i	−0.775024	−	0.631932i	$-0.782262\pi$
$823$	−17.6508	+	10.1907i	−0.615267	+	0.355225i	0.159757	+	0.987156i	$0.448929\pi$
$824$	2.44880	+	0.236360i	0.0853080	+	0.00823398i
$825$	−80.6109	−	8.50161i	−2.80651	−	0.295988i
$826$	1.85887	+	12.9601i	0.0646783	+	0.450938i
$827$	1.92701	−	3.33768i	0.0670087	−	0.116062i	−0.830575	−	0.556907i	$-0.811988\pi$
$827$	1.92701	−	3.33768i	0.0670087	−	0.116062i	0.897583	+	0.440845i	$0.145321\pi$
$828$	−6.90513	+	14.3374i	−0.239970	+	0.498258i
$829$	31.4599			1.09265			0.546323	−	0.837574i	$-0.316027\pi$
$829$	31.4599			1.09265			0.546323	+	0.837574i	$0.316027\pi$
$830$	−1.10905	−	0.444434i	−0.0384956	−	0.0154265i
$831$	52.9403	+	5.58333i	1.83648	+	0.193684i
$832$	0.965745	+	2.80891i	0.0334812	+	0.0973815i
$833$			9.69104i			0.335775i
$834$	−36.9788	+	23.2344i	−1.28047	+	0.804543i
$835$			80.2146i			2.77594i
$836$	47.9853	+	11.6758i	1.65961	+	0.403815i
$837$	5.41589	+	28.4195i	0.187201	+	0.982322i
$838$	22.8193	+	29.0375i	0.788281	+	1.00308i
$839$	−39.4541			−1.36211			−0.681053	−	0.732234i	$-0.738478\pi$
$839$	−39.4541			−1.36211			−0.681053	+	0.732234i	$0.738478\pi$
$840$	−52.9389	+	17.6786i	−1.82657	+	0.609971i
$841$	−67.8597			−2.33999
$842$	2.90507	−	0.416676i	0.100115	−	0.0143596i
$843$	−3.69099	+	34.9974i	−0.127124	+	1.20537i
$844$	1.92423	+	6.56988i	0.0662346	+	0.226144i
$845$		−	45.7555i		−	1.57404i
$846$	−0.749787	−	1.52906i	−0.0257782	−	0.0525701i
$847$	−73.1528	−	42.2348i	−2.51356	−	1.45121i
$848$	−8.60549	−	13.4306i	−0.295514	−	0.461210i
$849$	3.47366	−	32.9367i	0.119216	−	1.13039i
$850$	−4.57410	−	31.8907i	−0.156890	−	1.09384i
$851$	1.10040	+	1.90595i	0.0377212	+	0.0653350i
$852$	10.1414	+	11.9566i	0.347440	+	0.409627i
$853$	−34.9592			−1.19698			−0.598491	−	0.801130i	$-0.704233\pi$
$853$	−34.9592			−1.19698			−0.598491	+	0.801130i	$0.704233\pi$
$854$	−19.0924	−	7.65100i	−0.653329	−	0.261812i
$855$	−42.1564	−	8.99204i	−1.44172	−	0.307521i
$856$	−4.08980	−	2.91864i	−0.139787	−	0.0997572i
$857$	25.8746	+	14.9387i	0.883861	+	0.510297i	0.871929	−	0.489632i	$-0.162869\pi$
$857$	25.8746	+	14.9387i	0.883861	+	0.510297i	0.0119313	+	0.999929i	$0.496202\pi$
$858$	2.59813	−	4.91569i	0.0886986	−	0.167819i
$859$	−8.94147	−	5.16236i	−0.305079	−	0.176138i	0.339643	−	0.940554i	$-0.389694\pi$
$859$	−8.94147	−	5.16236i	−0.305079	−	0.176138i	−0.644722	+	0.764417i	$0.723027\pi$
$860$	−3.34122	+	13.7318i	−0.113935	+	0.468251i
$861$	20.2363	+	2.13422i	0.689651	+	0.0727339i
$862$	−12.8921	+	32.1711i	−0.439107	+	1.09575i
$863$	−6.01828	+	10.4240i	−0.204865	+	0.354836i	−0.950090	−	0.311977i	$-0.899009\pi$
$863$	−6.01828	+	10.4240i	−0.204865	+	0.354836i	0.745225	+	0.666813i	$0.232342\pi$
$864$	−3.70940	+	29.1589i	−0.126196	+	0.992005i
$865$	−13.4146	−	23.2348i	−0.456111	−	0.790008i
$866$	17.5020	+	22.2713i	0.594744	+	0.756809i
$867$	8.29480	−	11.4083i	0.281706	−	0.387445i
$868$	25.1397	−	25.2941i	0.853299	−	0.858536i
$869$		−	29.1576i		−	0.989102i
$870$	85.6986	−	3.20512i	2.90545	−	0.108664i
$871$	−1.77463	+	1.02458i	−0.0601310	+	0.0347167i
$872$	42.2445	−	19.2402i	1.43058	−	0.651556i
$873$	34.7550	+	7.41330i	1.17628	+	0.250902i
$874$	14.0626	+	5.63538i	0.475675	+	0.190620i
$875$	−15.1234	−	26.1945i	−0.511265	−	0.885537i
$876$	−8.65364	−	10.2025i	−0.292379	−	0.344711i
$877$	−24.6763	+	42.7406i	−0.833259	+	1.44325i	0.0621815	+	0.998065i	$0.480194\pi$
$877$	−24.6763	+	42.7406i	−0.833259	+	1.44325i	−0.895440	+	0.445182i	$0.853139\pi$
$878$	−2.52707	−	17.6188i	−0.0852845	−	0.594606i
$879$	7.73680	−	3.44134i	0.260956	−	0.116074i
$880$	86.9000	−	4.02080i	2.92940	−	0.135541i
$881$	−25.8554	−	14.9276i	−0.871091	−	0.502925i	−0.00338024	−	0.999994i	$-0.501076\pi$
$881$	−25.8554	−	14.9276i	−0.871091	−	0.502925i	−0.867711	+	0.497070i	$0.834409\pi$
$882$	13.7842	+	0.934530i	0.464137	+	0.0314673i
$883$			15.9306i			0.536107i	0.963404	+	0.268054i	$0.0863804\pi$
$883$			15.9306i			0.536107i	−0.963404	+	0.268054i	$0.913620\pi$
$884$	2.14724	+	0.522464i	0.0722193	+	0.0175724i
$885$	−1.86815	+	17.7135i	−0.0627972	+	0.595433i
$886$	11.2612	−	1.61520i	0.378328	−	0.0542638i
$887$	7.10309	+	12.3029i	0.238498	+	0.413091i	0.960284	−	0.279026i	$-0.0900115\pi$
$887$	7.10309	+	12.3029i	0.238498	+	0.413091i	−0.721785	+	0.692117i	$0.756678\pi$
$888$	3.04299	+	2.69539i	0.102116	+	0.0904515i
$889$	19.4464	−	33.6822i	0.652213	−	1.12967i
$890$	72.0597	−	10.3356i	2.41545	−	0.346449i
$891$	44.5598	−	32.2776i	1.49281	−	1.08134i
$892$	4.41386	+	15.0702i	0.147787	+	0.504589i
$893$	−1.40405	+	0.810628i	−0.0469847	+	0.0271266i
$894$	38.2702	+	20.2272i	1.27995	+	0.676500i
$895$		−	69.4690i		−	2.32209i
$896$	32.2446	−	16.5260i	1.07722	−	0.552094i
$897$	1.00304	−	1.37953i	0.0334905	−	0.0460612i
$898$	14.4725	−	11.3733i	0.482954	−	0.379533i
$899$	−47.9951	+	26.4409i	−1.60073	+	0.881853i
$900$	−45.8013	+	3.43073i	−1.52671	+	0.114358i
$901$	−11.8675			−0.395364
$902$	−29.4405	−	11.7978i	−0.980260	−	0.392825i
$903$	6.47960	−	8.91172i	0.215628	−	0.296564i
$904$	−44.1316	−	4.25961i	−1.46780	−	0.141673i
$905$	−69.4675	+	40.1071i	−2.30918	+	1.33320i
$906$	−21.6141	+	13.5805i	−0.718080	+	0.451182i
$907$		−	49.7055i		−	1.65044i	−0.564808	−	0.825222i	$-0.691050\pi$
$907$		−	49.7055i		−	1.65044i	0.564808	−	0.825222i	$-0.308950\pi$
$908$	−32.1055	−	30.6544i	−1.06546	−	1.01730i
$909$	−7.74084	+	36.2905i	−0.256747	+	1.20368i
$910$	5.92148	−	0.849320i	0.196295	−	0.0281547i
$911$	20.6984	+	35.8507i	0.685769	+	1.18779i	0.973194	+	0.229984i	$0.0738673\pi$
$911$	20.6984	+	35.8507i	0.685769	+	1.18779i	−0.287425	+	0.957803i	$0.592799\pi$
$912$	27.9346	+	1.64557i	0.925007	+	0.0544903i
$913$	−0.725953	−	1.25739i	−0.0240255	−	0.0416134i
$914$	−23.6653	−	30.1139i	−0.782777	−	0.996081i
$915$	−22.6320	−	16.4554i	−0.748190	−	0.544000i
$916$	−24.2425	+	7.10029i	−0.800995	+	0.234600i
$917$	−8.34887	−	4.82022i	−0.275704	−	0.159178i
$918$	16.7773	+	14.0275i	0.553733	+	0.462976i
$919$	−31.9151	−	18.4262i	−1.05278	−	0.607825i	−0.129356	−	0.991598i	$-0.541291\pi$
$919$	−31.9151	−	18.4262i	−1.05278	−	0.607825i	−0.923427	+	0.383774i	$0.874624\pi$
$920$	26.5630	+	2.56387i	0.875756	+	0.0845284i
$921$	18.4673	−	8.21429i	0.608519	−	0.270670i
$922$	23.5220	−	18.4849i	0.774657	−	0.608769i
$923$	−0.840211	−	1.45529i	−0.0276559	−	0.0479014i
$924$	−63.8559	−	22.8585i	−2.10070	−	0.751989i
$925$	−3.17597	+	5.50093i	−0.104425	+	0.180870i
$926$	−4.85038	+	3.81170i	−0.159393	+	0.125260i
$927$	−1.93793	−	1.74742i	−0.0636499	−	0.0573929i
$928$	−54.6850	+	10.4430i	−1.79512	+	0.342809i
$929$			0.123923i			0.00406578i	0.999998	+	0.00203289i	$0.000647090\pi$
$929$			0.123923i			0.00406578i	−0.999998	+	0.00203289i	$0.999353\pi$
$930$	41.5897	−	24.9823i	1.36378	−	0.819201i
$931$		−	13.1527i		−	0.431062i
$932$	19.1211	+	4.65253i	0.626331	+	0.152399i
$933$	−10.3518	−	1.09175i	−0.338904	−	0.0357424i
$934$	1.64747	+	2.09639i	0.0539067	+	0.0685961i
$935$	32.3612	−	56.0512i	1.05832	−	1.83307i
$936$	0.950197	−	3.00377i	0.0310582	−	0.0981812i
$937$	−19.2989	−	33.4267i	−0.630469	−	1.09200i	−0.987456	−	0.157895i	$-0.949529\pi$
$937$	−19.2989	−	33.4267i	−0.630469	−	1.09200i	0.356987	−	0.934109i	$-0.383804\pi$
$938$	15.4451	+	19.6539i	0.504302	+	0.641722i
$939$	−10.5100	−	23.6285i	−0.342981	−	0.771088i
$940$	−1.97218	+	2.06554i	−0.0643254	+	0.0673705i
$941$	6.62501	+	3.82495i	0.215969	+	0.124690i	0.604082	−	0.796922i	$-0.293540\pi$
$941$	6.62501	+	3.82495i	0.215969	+	0.124690i	−0.388113	+	0.921612i	$0.626873\pi$
$942$	−5.87846	−	9.35588i	−0.191531	−	0.304831i
$943$	−8.42599	−	4.86475i	−0.274388	−	0.158418i
$944$	−0.534447	−	11.5508i	−0.0173948	−	0.375946i
$945$	56.2814	+	18.3535i	1.83083	+	0.597039i
$946$	−13.5032	+	10.6116i	−0.439026	+	0.345011i
$947$	−14.0775	−	24.3829i	−0.457457	−	0.792339i	0.541369	−	0.840785i	$-0.317906\pi$
$947$	−14.0775	−	24.3829i	−0.457457	−	0.792339i	−0.998826	+	0.0484463i	$0.984573\pi$
$948$	−2.95524	−	16.2550i	−0.0959819	−	0.527937i
$949$	0.716948	+	1.24179i	0.0232731	+	0.0403102i
$950$	6.20797	+	43.2821i	0.201413	+	1.40426i
$951$	24.3983	−	10.8524i	0.791168	−	0.351913i
$952$	2.58988	−	26.8324i	0.0839384	−	0.869643i
$953$		−	6.04922i		−	0.195953i	−0.995189	−	0.0979767i	$-0.968763\pi$
$953$		−	6.04922i		−	0.195953i	0.995189	−	0.0979767i	$-0.0312370\pi$
$954$	−1.14441	+	16.8799i	−0.0370517	+	0.546507i
$955$	−37.4161	+	21.6022i	−1.21076	+	0.699030i
$956$	−0.498118	−	0.475603i	−0.0161103	−	0.0153821i
$957$	84.2891	+	61.2856i	2.72468	+	1.98108i
$958$	14.6452	−	36.5458i	0.473165	−	1.18074i
$959$	−18.1233			−0.585233
$960$	48.0381	−	11.0492i	1.55042	−	0.356612i
$961$	−16.5643	+	26.2035i	−0.534331	+	0.845275i
$962$	−0.269216	−	0.342576i	−0.00867988	−	0.0110451i
$963$	1.64321	+	5.06956i	0.0529516	+	0.163364i
$964$	−0.649444	+	0.190213i	−0.0209172	+	0.00612635i
$965$		−	1.14160i		−	0.0367494i
$966$	−18.3948	−	9.72233i	−0.591842	−	0.312811i
$967$	−25.9726	+	14.9953i	−0.835222	+	0.482216i	−0.855637	−	0.517576i	$-0.826834\pi$
$967$	−25.9726	+	14.9953i	−0.835222	+	0.482216i	0.0204153	+	0.999792i	$0.493501\pi$
$968$	60.7243	+	43.3352i	1.95175	+	1.39285i
$969$	12.2432	−	16.8387i	0.393310	−	0.540939i
$970$	−8.46099	−	58.9902i	−0.271666	−	1.89406i
$971$	23.9852	−	41.5436i	0.769723	−	1.33320i	−0.167991	−	0.985789i	$-0.553728\pi$
$971$	23.9852	−	41.5436i	0.769723	−	1.33320i	0.937713	−	0.347410i	$-0.112939\pi$
$972$	21.5701	−	22.5107i	0.691860	−	0.722031i
$973$	−28.5495	−	49.4492i	−0.915255	−	1.58527i
$974$	3.04733	+	21.2460i	0.0976426	+	0.680767i
$975$	4.89564	+	0.516317i	0.156786	+	0.0165354i
$976$	16.1348	+	8.34592i	0.516461	+	0.267146i
$977$		−	59.4588i		−	1.90226i	−0.308796	−	0.951128i	$-0.599926\pi$
$977$		−	59.4588i		−	1.90226i	0.308796	−	0.951128i	$-0.400074\pi$
$978$	47.6995	−	29.9704i	1.52526	−	0.958348i
$979$	76.6116	+	44.2317i	2.44852	+	1.41365i
$980$	−6.51220	−	22.2346i	−0.208025	−	0.710258i
$981$	−48.1522	−	10.2710i	−1.53738	−	0.327927i
$982$	44.4472	−	6.37507i	1.41837	−	0.203437i
$983$	−27.7308	+	48.0311i	−0.884475	+	1.53196i	−0.0381603	+	0.999272i	$0.512150\pi$
$983$	−27.7308	+	48.0311i	−0.884475	+	1.53196i	−0.846314	+	0.532684i	$0.821184\pi$
$984$	−17.6085	−	3.59322i	−0.561337	−	0.114548i
$985$	−12.3173	−	21.3342i	−0.392462	−	0.679765i
$986$	−15.4076	+	38.4483i	−0.490678	+	1.22444i
$987$	2.03440	−	0.904902i	0.0647555	−	0.0288034i
$988$	−2.91423	−	0.709089i	−0.0927140	−	0.0225591i
$989$	−4.56252	+	2.63417i	−0.145080	+	0.0837617i
$990$	−76.6044	−	51.4345i	−2.43465	−	1.63469i
$991$			7.61583i			0.241925i	0.992657	+	0.120962i	$0.0385980\pi$
$991$			7.61583i			0.241925i	−0.992657	+	0.120962i	$0.961402\pi$
$992$	−24.2463	+	20.1026i	−0.769821	+	0.638260i
$993$	6.12154	+	4.45089i	0.194261	+	0.141245i
$994$	−16.1172	+	12.6658i	−0.511207	+	0.401736i
$995$	−13.7158	−	23.7564i	−0.434819	−	0.753128i
$996$	−0.532151	−	0.627399i	−0.0168619	−	0.0198799i
$997$	11.3456	−	19.6512i	0.359319	−	0.622359i	−0.628528	−	0.777787i	$-0.716342\pi$
$997$	11.3456	−	19.6512i	0.359319	−	0.622359i	0.987847	+	0.155428i	$0.0496755\pi$
$998$	−42.0042	−	16.8326i	−1.32962	−	0.532825i
$999$	−0.891938	−	4.21842i	−0.0282197	−	0.133465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.p.a.335.44	yes	120
3.2	odd	2	inner	372.2.p.a.335.17	yes	120
4.3	odd	2	inner	372.2.p.a.335.18	yes	120
12.11	even	2	inner	372.2.p.a.335.43	yes	120
31.5	even	3	inner	372.2.p.a.191.44	yes	120
93.5	odd	6	inner	372.2.p.a.191.17	✓	120
124.67	odd	6	inner	372.2.p.a.191.18	yes	120
372.191	even	6	inner	372.2.p.a.191.43	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.17	✓	120	93.5	odd	6	inner
372.2.p.a.191.18	yes	120	124.67	odd	6	inner
372.2.p.a.191.43	yes	120	372.191	even	6	inner
372.2.p.a.191.44	yes	120	31.5	even	3	inner
372.2.p.a.335.17	yes	120	3.2	odd	2	inner
372.2.p.a.335.18	yes	120	4.3	odd	2	inner
372.2.p.a.335.43	yes	120	12.11	even	2	inner
372.2.p.a.335.44	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873830 + 1.11194i) q^{2} +(-1.72250 - 0.181663i) q^{3} +(-0.472843 + 1.94330i) q^{4} +(-3.08078 - 1.77869i) q^{5} +(-1.30317 - 2.07406i) q^{6} +(2.77350 - 1.60128i) q^{7} +(-2.57403 + 1.17234i) q^{8} +(2.93400 + 0.625827i) q^{9} +(-0.714273 - 4.97993i) q^{10} +(3.05678 - 5.29450i) q^{11} +(1.16750 - 3.26143i) q^{12} +(-0.185643 + 0.321544i) q^{13} +(4.20411 + 1.68473i) q^{14} +(4.98351 + 3.62345i) q^{15} +(-3.55284 - 1.83775i) q^{16} +(-2.57727 + 1.48799i) q^{17} +(1.86793 + 3.80931i) q^{18} +(3.49788 - 2.01950i) q^{19} +(4.91325 - 5.14584i) q^{20} +(-5.06825 + 2.25436i) q^{21} +(8.55830 - 1.22752i) q^{22} +2.65226 q^{23} +(4.64673 - 1.55175i) q^{24} +(3.82746 + 6.62936i) q^{25} +(-0.519760 + 0.0745493i) q^{26} +(-4.94011 - 1.61098i) q^{27} +(1.80034 + 6.14691i) q^{28} -9.84173i q^{29} +(0.325666 + 8.70767i) q^{30} +(-2.68661 - 4.87669i) q^{31} +(-1.06110 - 5.55644i) q^{32} +(-6.22711 + 8.56446i) q^{33} +(-3.90666 - 1.56554i) q^{34} -11.3927 q^{35} +(-2.60349 + 5.40572i) q^{36} +(0.414892 + 0.718613i) q^{37} +(5.30212 + 2.12475i) q^{38} +(0.378183 - 0.520134i) q^{39} +(10.0152 + 0.966676i) q^{40} +(-3.17691 - 1.83419i) q^{41} +(-6.93551 - 3.66568i) q^{42} +(-1.72024 + 0.993180i) q^{43} +(8.84343 + 8.44371i) q^{44} +(-7.92584 - 7.14670i) q^{45} +(2.31762 + 2.94916i) q^{46} -0.401400 q^{47} +(5.78591 + 3.81094i) q^{48} +(1.62821 - 2.82014i) q^{49} +(-4.02693 + 10.0489i) q^{50} +(4.70966 - 2.09486i) q^{51} +(-0.537076 - 0.512801i) q^{52} +(3.45351 + 1.99388i) q^{53} +(-2.52549 - 6.90086i) q^{54} +(-18.8345 + 10.8741i) q^{55} +(-5.26183 + 7.37323i) q^{56} +(-6.39196 + 2.84315i) q^{57} +(10.9435 - 8.60000i) q^{58} +(1.44539 + 2.50350i) q^{59} +(-9.39787 + 7.97114i) q^{60} -4.54137 q^{61} +(3.07497 - 7.24876i) q^{62} +(9.13957 - 2.96243i) q^{63} +(5.25124 - 6.03527i) q^{64} +(1.14385 - 0.660404i) q^{65} +(-14.9646 + 0.559677i) q^{66} +(4.77967 + 2.75954i) q^{67} +(-1.67297 - 5.71201i) q^{68} +(-4.56851 - 0.481816i) q^{69} +(-9.95531 - 12.6681i) q^{70} +(-2.26297 + 3.91958i) q^{71} +(-8.28587 + 1.82874i) q^{72} +(1.93098 - 3.34456i) q^{73} +(-0.436514 + 1.08928i) q^{74} +(-5.38849 - 12.1144i) q^{75} +(2.27055 + 7.75234i) q^{76} -19.5791i q^{77} +(0.908828 - 0.0339901i) q^{78} +(4.13036 - 2.38466i) q^{79} +(7.67672 + 11.9811i) q^{80} +(8.21668 + 3.67235i) q^{81} +(-0.736561 - 5.13532i) q^{82} +(0.118745 - 0.205672i) q^{83} +(-1.98442 - 10.9151i) q^{84} +10.5867 q^{85} +(-2.60756 - 1.04494i) q^{86} +(-1.78788 + 16.9524i) q^{87} +(-1.66129 + 17.2118i) q^{88} +14.4700i q^{89} +(1.02090 - 15.0581i) q^{90} +1.18907i q^{91} +(-1.25410 + 5.15414i) q^{92} +(3.74177 + 8.88815i) q^{93} +(-0.350756 - 0.446335i) q^{94} -14.3683 q^{95} +(0.818339 + 9.76372i) q^{96} +11.8456 q^{97} +(4.55862 - 0.653845i) q^{98} +(12.2820 - 13.6210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

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