LMFDB - Embedded newform 372.2.p.a.191.18

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			191.18
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.17

$q$-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} +(-0.703924 - 1.58256i) q^{3} +(-0.472843 - 1.94330i) q^{4} +(3.08078 - 1.77869i) q^{5} +(2.37483 + 0.600161i) q^{6} +(2.77350 + 1.60128i) q^{7} +(2.57403 + 1.17234i) q^{8} +(-2.00898 + 2.22800i) q^{9} +(-0.714273 + 4.97993i) q^{10} +(-3.05678 - 5.29450i) q^{11} +(-2.74254 + 2.11624i) 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} +(-0.721909 - 4.18077i) q^{18} +(3.49788 + 2.01950i) q^{19} +(-4.91325 - 5.14584i) q^{20} +(0.581786 - 5.51641i) q^{21} +(8.55830 + 1.22752i) q^{22} -2.65226 q^{23} +(0.0433739 - 4.89879i) 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} +(8.38382 - 2.37511i) 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} +(5.27961 + 2.85056i) 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} +(5.62556 + 5.46732i) q^{42} +(-1.72024 - 0.993180i) q^{43} +(-8.84343 + 8.44371i) q^{44} +(-2.22630 + 10.4373i) q^{45} +(2.31762 - 2.94916i) q^{46} +0.401400 q^{47} +(5.40928 + 4.32894i) q^{48} +(1.62821 + 2.82014i) q^{49} +(4.02693 + 10.0489i) q^{50} +(0.540624 - 5.12612i) q^{51} +(-0.537076 + 0.512801i) q^{52} +(-3.45351 + 1.99388i) q^{53} +(-6.10814 + 4.08541i) q^{54} +(-18.8345 - 10.8741i) q^{55} +(5.26183 + 7.37323i) q^{56} +(0.733736 - 6.95717i) q^{57} +(10.9435 + 8.60000i) q^{58} +(-1.44539 + 2.50350i) q^{59} +(-4.68503 + 11.3978i) 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} +(-4.08177 - 14.4081i) q^{66} +(4.77967 - 2.75954i) q^{67} +(1.67297 - 5.71201i) q^{68} +(1.86699 + 4.19735i) q^{69} +(-9.95531 + 12.6681i) q^{70} +(2.26297 + 3.91958i) q^{71} +(-7.78315 + 3.37973i) q^{72} +(1.93098 + 3.34456i) q^{73} +(0.436514 + 1.08928i) q^{74} +(-13.1856 - 1.39061i) q^{75} +(2.27055 - 7.75234i) q^{76} -19.5791i q^{77} +(-0.247893 - 0.875027i) q^{78} +(4.13036 + 2.38466i) q^{79} +(-7.67672 + 11.9811i) q^{80} +(-0.927992 - 8.95203i) q^{81} +(-0.736561 + 5.13532i) q^{82} +(-0.118745 - 0.205672i) q^{83} +(-10.9951 + 1.47781i) q^{84} +10.5867 q^{85} +(2.60756 - 1.04494i) q^{86} +(-15.5751 + 6.92784i) q^{87} +(-1.66129 - 17.2118i) q^{88} +14.4700i q^{89} +(-9.66033 - 11.5960i) q^{90} -1.18907i q^{91} +(1.25410 + 5.15414i) q^{92} +(9.60882 + 0.818894i) q^{93} +(-0.350756 + 0.446335i) q^{94} +14.3683 q^{95} +(-9.54033 + 2.23207i) q^{96} +11.8456 q^{97} +(-4.55862 - 0.653845i) q^{98} +(17.9372 + 3.82603i) 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 $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.703924	−	1.58256i	−0.406411	−	0.913690i
$3$	−0.703924	−	1.58256i	−0.406411	−	0.913690i
$4$	−0.472843	−	1.94330i	−0.236421	−	0.971651i
$5$	3.08078	−	1.77869i	1.37777	−	0.795454i	0.385876	−	0.922551i	$-0.373899\pi$
$5$	3.08078	−	1.77869i	1.37777	−	0.795454i	0.991890	+	0.127097i	$0.0405660\pi$
$6$	2.37483	+	0.600161i	0.969519	+	0.245015i
$7$	2.77350	+	1.60128i	1.04829	+	0.605228i	0.922169	−	0.386788i	$-0.126415\pi$
$7$	2.77350	+	1.60128i	1.04829	+	0.605228i	0.126117	+	0.992015i	$0.459749\pi$
$8$	2.57403	+	1.17234i	0.910056	+	0.414485i
$9$	−2.00898	+	2.22800i	−0.669660	+	0.742668i
$10$	−0.714273	+	4.97993i	−0.225873	+	1.57479i
$11$	−3.05678	−	5.29450i	−0.921654	−	1.59635i	−0.796856	−	0.604169i	$-0.793505\pi$
$11$	−3.05678	−	5.29450i	−0.921654	−	1.59635i	−0.124798	−	0.992182i	$-0.539828\pi$
$12$	−2.74254	+	2.11624i	−0.791704	+	0.610905i
$13$	−0.185643	−	0.321544i	−0.0514882	−	0.0891802i	0.839133	−	0.543927i	$-0.183063\pi$
$13$	−0.185643	−	0.321544i	−0.0514882	−	0.0891802i	−0.890621	+	0.454747i	$0.849730\pi$
$14$	−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	$-0.215806\pi$
$17$	2.57727	+	1.48799i	0.625081	+	0.360891i	−0.153764	+	0.988108i	$0.549139\pi$
$18$	−0.721909	−	4.18077i	−0.170156	−	0.985417i
$19$	3.49788	+	2.01950i	0.802468	+	0.463305i	0.844334	−	0.535818i	$-0.179997\pi$
$19$	3.49788	+	2.01950i	0.802468	+	0.463305i	−0.0418652	+	0.999123i	$0.513330\pi$
$20$	−4.91325	−	5.14584i	−1.09864	−	1.15064i
$21$	0.581786	−	5.51641i	0.126956	−	1.20378i
$22$	8.55830	+	1.22752i	1.82463	+	0.261708i
$23$	−2.65226			−0.553034			−0.276517	−	0.961009i	$-0.589180\pi$
$23$	−2.65226			−0.553034			−0.276517	+	0.961009i	$0.589180\pi$
$24$	0.0433739	−	4.89879i	0.00885365	−	0.999961i
$25$	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	$-0.366852\pi$
$30$	8.38382	−	2.37511i	1.53067	−	0.433634i
$31$	−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
$36$	5.27961	+	2.85056i	0.879935	+	0.475093i
$37$	0.414892	−	0.718613i	0.0682078	−	0.118139i	−0.829905	−	0.557905i	$-0.811605\pi$
$37$	0.414892	−	0.718613i	0.0682078	−	0.118139i	0.898112	+	0.439766i	$0.144939\pi$
$38$	−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	$-0.574191\pi$
$41$	3.17691	−	1.83419i	0.496150	−	0.286453i	0.727122	+	0.686508i	$0.240857\pi$
$42$	5.62556	+	5.46732i	0.868043	+	0.843626i
$43$	−1.72024	−	0.993180i	−0.262334	−	0.151459i	0.363065	−	0.931764i	$-0.381730\pi$
$43$	−1.72024	−	0.993180i	−0.262334	−	0.151459i	−0.625399	+	0.780305i	$0.715064\pi$
$44$	−8.84343	+	8.44371i	−1.33320	+	1.27294i
$45$	−2.22630	+	10.4373i	−0.331878	+	1.55591i
$46$	2.31762	−	2.94916i	0.341715	−	0.434831i
$47$	0.401400			0.0585503			0.0292751	−	0.999571i	$-0.490680\pi$
$47$	0.401400			0.0585503			0.0292751	+	0.999571i	$0.490680\pi$
$48$	5.40928	+	4.32894i	0.780762	+	0.624828i
$49$	1.62821	+	2.82014i	0.232601	+	0.402878i
$50$	4.02693	+	10.0489i	0.569494	+	1.42112i
$51$	0.540624	−	5.12612i	0.0757026	−	0.717800i
$52$	−0.537076	+	0.512801i	−0.0744791	+	0.0711127i
$53$	−3.45351	+	1.99388i	−0.474376	+	0.273881i	−0.718070	−	0.695971i	$-0.754974\pi$
$53$	−3.45351	+	1.99388i	−0.474376	+	0.273881i	0.243694	+	0.969852i	$0.421641\pi$
$54$	−6.10814	+	4.08541i	−0.831213	+	0.555954i
$55$	−18.8345	−	10.8741i	−2.53965	−	1.46627i
$56$	5.26183	+	7.37323i	0.703141	+	0.985289i
$57$	0.733736	−	6.95717i	0.0971857	−	0.921500i
$58$	10.9435	+	8.60000i	1.43695	+	1.12924i
$59$	−1.44539	+	2.50350i	−0.188174	+	0.325927i	−0.944642	−	0.328104i	$-0.893590\pi$
$59$	−1.44539	+	2.50350i	−0.188174	+	0.325927i	0.756467	+	0.654032i	$0.226924\pi$
$60$	−4.68503	+	11.3978i	−0.604835	+	1.47145i
$61$	−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
$66$	−4.08177	−	14.4081i	−0.502431	−	1.77351i
$67$	4.77967	−	2.75954i	0.583930	−	0.337132i	−0.178764	−	0.983892i	$-0.557210\pi$
$67$	4.77967	−	2.75954i	0.583930	−	0.337132i	0.762694	+	0.646760i	$0.223876\pi$
$68$	1.67297	−	5.71201i	0.202877	−	0.692682i
$69$	1.86699	+	4.19735i	0.224759	+	0.505302i
$70$	−9.95531	+	12.6681i	−1.18989	+	1.51413i
$71$	2.26297	+	3.91958i	0.268565	+	0.465169i	0.968492	−	0.249047i	$-0.0801172\pi$
$71$	2.26297	+	3.91958i	0.268565	+	0.465169i	−0.699926	+	0.714215i	$0.746784\pi$
$72$	−7.78315	+	3.37973i	−0.917253	+	0.398306i
$73$	1.93098	+	3.34456i	0.226004	+	0.391451i	0.956620	−	0.291338i	$-0.0941003\pi$
$73$	1.93098	+	3.34456i	0.226004	+	0.391451i	−0.730616	+	0.682789i	$0.760767\pi$
$74$	0.436514	+	1.08928i	0.0507437	+	0.126627i
$75$	−13.1856	−	1.39061i	−1.52254	−	0.160574i
$76$	2.27055	−	7.75234i	0.260450	−	0.889254i
$77$		−	19.5791i		−	2.23124i
$78$	−0.247893	−	0.875027i	−0.0280683	−	0.0990773i
$79$	4.13036	+	2.38466i	0.464701	+	0.268296i	0.714019	−	0.700126i	$-0.246873\pi$
$79$	4.13036	+	2.38466i	0.464701	+	0.268296i	−0.249318	+	0.968422i	$0.580206\pi$
$80$	−7.67672	+	11.9811i	−0.858284	+	1.33953i
$81$	−0.927992	−	8.95203i	−0.103110	−	0.994670i
$82$	−0.736561	+	5.13532i	−0.0813396	+	0.567102i
$83$	−0.118745	−	0.205672i	−0.0130339	−	0.0225754i	0.859435	−	0.511245i	$-0.170816\pi$
$83$	−0.118745	−	0.205672i	−0.0130339	−	0.0225754i	−0.872469	+	0.488670i	$0.837482\pi$
$84$	−10.9951	+	1.47781i	−1.19967	+	0.161242i
$85$	10.5867			1.14829
$86$	2.60756	−	1.04494i	0.281180	−	0.112679i
$87$	−15.5751	+	6.92784i	−1.66983	+	0.742742i
$88$	−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	$0.721793\pi$
$90$	−9.66033	−	11.5960i	−1.01829	−	1.22232i
$91$		−	1.18907i		−	0.124648i
$92$	1.25410	+	5.15414i	0.130749	+	0.537356i
$93$	9.60882	+	0.818894i	0.996388	+	0.0849153i
$94$	−0.350756	+	0.446335i	−0.0361777	+	0.0460359i
$95$	14.3683			1.47415
$96$	−9.54033	+	2.23207i	−0.973706	+	0.227810i
$97$	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
$99$	17.9372	+	3.82603i	1.80275	+	0.384531i
$100$	−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	$0.789003\pi$
$102$	5.22755	+	5.08050i	0.517604	+	0.503044i
$103$	−0.753274	+	0.434903i	−0.0742222	+	0.0428522i	−0.536652	−	0.843804i	$-0.680311\pi$
$103$	−0.753274	+	0.434903i	−0.0742222	+	0.0428522i	0.462430	+	0.886656i	$0.346978\pi$
$104$	−0.100893	−	1.04530i	−0.00989337	−	0.102500i
$105$	−8.01962	−	18.0297i	−0.782635	−	1.75951i
$106$	0.800689	−	5.58242i	0.0777698	−	0.542213i
$107$	−0.888203	+	1.53841i	−0.0858658	+	0.148724i	−0.905760	−	0.423791i	$-0.860699\pi$
$107$	−0.888203	+	1.53841i	−0.0858658	+	0.148724i	0.819894	+	0.572515i	$0.194032\pi$
$108$	0.794728	−	10.3619i	0.0764728	−	0.997072i
$109$	−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
$111$	−1.42930	−	0.150741i	−0.135663	−	0.0143077i
$112$	−12.7966	−	0.592088i	−1.20916	−	0.0559470i
$113$	−13.5753	+	7.83770i	−1.27706	+	0.737309i	−0.976306	−	0.216394i	$-0.930570\pi$
$113$	−13.5753	+	7.83770i	−1.27706	+	0.737309i	−0.300750	+	0.953703i	$0.597237\pi$
$114$	7.09483	+	6.89526i	0.664492	+	0.645800i
$115$	−8.17102	+	4.71754i	−0.761951	+	0.439913i
$116$	−19.1255	+	4.65359i	−1.77575	+	0.432075i
$117$	1.08935	+	0.232361i	0.100711	+	0.0214818i
$118$	−1.52072	−	3.79483i	−0.139994	−	0.349342i
$119$	4.76538	+	8.25389i	0.436842	+	0.756633i
$120$	−8.57979	−	15.1692i	−0.783224	−	1.38475i
$121$	−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
$126$	4.69238	−	12.7514i	0.418030	−	1.13598i
$127$	10.5173	+	6.07215i	0.933257	+	0.538816i	0.887840	−	0.460152i	$-0.152205\pi$
$127$	10.5173	+	6.07215i	0.933257	+	0.538816i	0.0454166	+	0.998968i	$0.485538\pi$
$128$	−11.2996	+	0.565294i	−0.998751	+	0.0499654i
$129$	−0.360848	+	3.42150i	−0.0317709	+	0.301246i
$130$	1.73386	−	0.694821i	0.152070	−	0.0609398i
$131$	1.50511	−	2.60693i	0.131502	−	0.227769i	−0.792754	−	0.609542i	$-0.791353\pi$
$131$	1.50511	−	2.60693i	0.131502	−	0.227769i	0.924256	+	0.381774i	$0.124687\pi$
$132$	19.5878	+	8.05151i	1.70490	+	0.700794i
$133$	6.46758	+	11.2022i	0.560811	+	0.971352i
$134$	−1.10816	+	7.72610i	−0.0957302	+	0.667434i
$135$	18.0848	−	3.82384i	1.55649	−	0.329104i
$136$	4.88955	+	6.85157i	0.419275	+	0.587517i
$137$	4.90084	−	2.82950i	0.418707	−	0.241741i	−0.275817	−	0.961210i	$-0.588948\pi$
$137$	4.90084	−	2.82950i	0.418707	−	0.241741i	0.694524	+	0.719470i	$0.255615\pi$
$138$	−6.29865	−	1.59178i	−0.536177	−	0.135502i
$139$			17.8292i			1.51225i	0.654428	+	0.756124i	$0.272910\pi$
$139$			17.8292i			1.51225i	−0.654428	+	0.756124i	$0.727090\pi$
$140$	−5.38697	−	22.1395i	−0.455282	−	1.87113i
$141$	−0.282555	−	0.635239i	−0.0237955	−	0.0534968i
$142$	−6.33581	−	0.908747i	−0.531689	−	0.0762604i
$143$	−1.13494	+	1.96578i	−0.0949086	+	0.164387i
$144$	3.04307	−	11.6077i	0.253589	−	0.967312i
$145$	−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	$-0.0756977\pi$
$149$	15.3042	+	8.83588i	1.25377	+	0.723864i	0.281913	+	0.959440i	$0.409031\pi$
$150$	13.0683	−	13.4465i	1.06702	−	1.09790i
$151$			10.4211i			0.848059i	0.905648	+	0.424030i	$0.139385\pi$
$151$			10.4211i			0.848059i	−0.905648	+	0.424030i	$0.860615\pi$
$152$	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
$156$	1.18960	+	0.488982i	0.0952441	+	0.0391499i
$157$	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
$162$	10.7651	+	6.79067i	0.845784	+	0.533526i
$163$		−	22.9981i		−	1.80135i	−0.434497	−	0.900673i	$-0.643074\pi$
$163$		−	22.9981i		−	1.80135i	0.434497	−	0.900673i	$-0.356926\pi$
$164$	−5.06657	−	5.30641i	−0.395632	−	0.414361i
$165$	−3.95084	+	37.4613i	−0.307573	+	2.91636i
$166$	0.332458	+	0.0476846i	0.0258038	+	0.00370104i
$167$	11.2744	−	19.5278i	0.872440	−	1.51111i	0.0129750	−	0.999916i	$-0.495870\pi$
$167$	11.2744	−	19.5278i	0.872440	−	1.51111i	0.859465	−	0.511195i	$-0.170797\pi$
$168$	7.96464	−	13.5173i	0.614485	−	1.04289i
$169$	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	$-0.759225\pi$
$173$	−6.53145	+	3.77094i	−0.496577	+	0.286699i	0.230722	+	0.973020i	$0.425891\pi$
$174$	5.90663	−	23.3724i	0.447780	−	1.77186i
$175$	21.2310	−	12.2577i	1.60491	−	0.926595i
$176$	20.5902	+	13.1929i	1.55205	+	0.994452i
$177$	4.97938	+	0.525148i	0.374273	+	0.0394726i
$178$	−16.0899	−	12.6444i	−1.20599	−	0.947734i
$179$	−9.76408	+	16.9119i	−0.729802	+	1.26405i	0.227165	+	0.973856i	$0.427054\pi$
$179$	−9.76408	+	16.9119i	−0.729802	+	1.26405i	−0.956967	+	0.290198i	$0.906279\pi$
$180$	21.3356	−	0.608842i	1.59026	−	0.0453804i
$181$	11.2743	+	19.5277i	0.838015	+	1.45148i	0.891552	+	0.452919i	$0.149617\pi$
$181$	11.2743	+	19.5277i	0.838015	+	1.45148i	−0.0535365	+	0.998566i	$0.517049\pi$
$182$	1.32218	+	1.03904i	0.0980065	+	0.0770191i
$183$	3.19678	+	7.18699i	0.236313	+	0.531277i
$184$	−6.82699	−	3.10935i	−0.503292	−	0.229224i
$185$		−	2.95185i		−	0.217024i
$186$	−9.30704	+	9.96890i	−0.682425	+	0.730956i
$187$		−	18.1938i		−	1.33046i
$188$	−0.189799	−	0.780042i	−0.0138425	−	0.0568904i
$189$	11.1218	+	12.3786i	0.808990	+	0.900410i
$190$	−12.5554	+	15.9767i	−0.910865	+	1.15907i
$191$	−6.07250	−	10.5179i	−0.439391	−	0.761047i	0.558252	−	0.829672i	$-0.311472\pi$
$191$	−6.07250	−	10.5179i	−0.439391	−	0.761047i	−0.997643	+	0.0686243i	$0.978139\pi$
$192$	5.85469	−	12.5588i	0.422526	−	0.906351i
$193$	0.160455	−	0.277917i	0.0115498	−	0.0200049i	−0.860193	−	0.509969i	$-0.829657\pi$
$193$	0.160455	−	0.277917i	0.0115498	−	0.0200049i	0.871743	+	0.489964i	$0.162990\pi$
$194$	−10.3510	+	13.1717i	−0.743161	+	0.945670i
$195$	−0.239941	+	2.27509i	−0.0171826	+	0.162922i
$196$	4.71050	−	4.49759i	0.336464	−	0.321256i
$197$	−5.99718	+	3.46247i	−0.427281	+	0.246691i	−0.698188	−	0.715915i	$-0.746010\pi$
$197$	−5.99718	+	3.46247i	−0.427281	+	0.246691i	0.270906	+	0.962606i	$0.412677\pi$
$198$	−19.9284	+	16.6018i	−1.41625	+	1.17984i
$199$	6.67806	−	3.85558i	0.473395	−	0.273315i	−0.244265	−	0.969709i	$-0.578547\pi$
$199$	6.67806	−	3.85558i	0.473395	−	0.273315i	0.717660	+	0.696394i	$0.245213\pi$
$200$	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
$204$	−10.2172	+	1.37325i	−0.715349	+	0.0961469i
$205$	6.52491	−	11.3015i	0.455719	−	0.789329i
$206$	0.174645	−	1.21763i	0.0121681	−	0.0848363i
$207$	5.32833	−	5.90924i	0.370345	−	0.410720i
$208$	1.25048	+	0.801227i	0.0867051	+	0.0555551i
$209$		−	24.6927i		−	1.70803i
$210$	27.0558	+	6.83748i	1.86703	+	0.471831i
$211$	2.96435	+	1.71147i	0.204074	+	0.117822i	0.598554	−	0.801082i	$-0.295742\pi$
$211$	2.96435	+	1.71147i	0.204074	+	0.117822i	−0.394480	+	0.918904i	$0.629075\pi$
$212$	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
$216$	10.8274	+	9.93821i	0.736710	+	0.676209i
$217$	−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
$222$	1.41658	−	1.45758i	0.0950746	−	0.0978264i
$223$	6.79973	+	3.92583i	0.455344	+	0.262893i	0.710084	−	0.704117i	$-0.248657\pi$
$223$	6.79973	+	3.92583i	0.455344	+	0.262893i	−0.254741	+	0.967009i	$0.581990\pi$
$224$	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	0.954034	+	0.299698i	$0.0968860\pi$
$227$	11.0974	+	19.2213i	0.736563	+	1.27577i	−0.217471	+	0.976067i	$0.569781\pi$
$228$	−13.8668	+	1.86378i	−0.918353	+	0.123432i
$229$	6.31522	−	10.9383i	0.417322	−	0.722822i	−0.578347	−	0.815791i	$-0.696302\pi$
$229$	6.31522	−	10.9383i	0.417322	−	0.722822i	0.995669	+	0.0929683i	$0.0296355\pi$
$230$	1.89444	−	13.2080i	0.124915	−	0.870913i
$231$	−30.9850	+	13.7822i	−2.03866	+	0.906801i
$232$	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	$-0.104457\pi$
$234$	−1.21028	+	1.00826i	−0.0791187	+	0.0659119i
$235$	1.23663	−	0.713966i	0.0806685	−	0.0465740i
$236$	5.54849	+	1.62508i	0.361176	+	0.105783i
$237$	0.866408	−	8.21515i	0.0562793	−	0.533632i
$238$	−13.3420	−	1.91365i	−0.864834	−	0.124043i
$239$	0.172177	+	0.298220i	0.0111372	+	0.0192902i	0.871540	−	0.490324i	$-0.163122\pi$
$239$	0.172177	+	0.298220i	0.0111372	+	0.0192902i	−0.860403	+	0.509614i	$0.829788\pi$
$240$	24.3646	+	3.71507i	1.57273	+	0.239807i
$241$	0.169181	−	0.293031i	0.0108979	−	0.0188758i	−0.860525	−	0.509408i	$-0.829864\pi$
$241$	0.169181	−	0.293031i	0.0108979	−	0.0188758i	0.871423	+	0.490532i	$0.163198\pi$
$242$	−13.8751	−	34.6241i	−0.891925	−	2.22572i
$243$	−13.5139	+	7.77015i	−0.866915	+	0.498456i
$244$	2.14736	+	8.82525i	0.137470	+	0.564979i
$245$	10.0323	+	5.79216i	0.640941	+	0.370047i
$246$	8.64543	−	2.44923i	0.551213	−	0.156157i
$247$		−	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	$-0.757496\pi$
$251$	3.73896	−	6.47607i	0.236001	−	0.408766i	0.959563	+	0.281493i	$0.0908297\pi$
$252$	10.0785	+	16.3602i	0.634884	+	1.03059i
$253$	8.10737	+	14.0424i	0.509706	+	0.882836i
$254$	−15.9422	+	6.38860i	−1.00030	+	0.400856i
$255$	−7.45222	−	16.7540i	−0.466676	−	1.04918i
$256$	9.24533	−	13.0585i	0.577833	−	0.816155i
$257$	−20.8370	+	12.0302i	−1.29977	+	0.750425i	−0.980365	−	0.197192i	$-0.936818\pi$
$257$	−20.8370	+	12.0302i	−1.29977	+	0.750425i	−0.319409	+	0.947617i	$0.603484\pi$
$258$	−3.48920	−	3.39105i	−0.217228	−	0.211118i
$259$	2.30141	−	1.32872i	0.143002	−	0.0825625i
$260$	−0.742500	+	2.53512i	−0.0460479	+	0.157221i
$261$	21.9274	+	19.7719i	1.35727	+	1.22385i
$262$	1.58355	+	3.95162i	0.0978322	+	0.244132i
$263$	−8.57162			−0.528549			−0.264274	−	0.964448i	$-0.585132\pi$
$263$	−8.57162			−0.528549			−0.264274	+	0.964448i	$0.585132\pi$
$264$	−26.0692	+	14.7449i	−1.60445	+	0.907484i
$265$	−7.09299	+	12.2854i	−0.435719	+	0.754688i
$266$	−18.1078	−	2.59721i	−1.11026	−	0.159245i
$267$	22.8997	−	10.1858i	1.40144	−	0.623362i
$268$	−7.62266	−	7.98351i	−0.465628	−	0.487670i
$269$	−7.85469	+	4.53491i	−0.478909	+	0.276498i	−0.719962	−	0.694014i	$-0.755841\pi$
$269$	−7.85469	+	4.53491i	−0.478909	+	0.276498i	0.241053	+	0.970512i	$0.422507\pi$
$270$	−11.5512	+	23.4507i	−0.702982	+	1.42717i
$271$			17.0366i			1.03490i	0.855714	+	0.517449i	$0.173118\pi$
$271$			17.0366i			1.03490i	−0.855714	+	0.517449i	$0.826882\pi$
$272$	−11.8912	−	0.550197i	−0.721010	−	0.0333606i
$273$	−1.88177	+	0.837016i	−0.113890	+	0.0506585i
$274$	−1.13625	+	7.92197i	−0.0686434	+	0.478584i
$275$	−46.7989			−2.82208
$276$	7.27393	−	5.61281i	0.437839	−	0.337851i
$277$	−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
$279$	−5.46794	−	15.7830i	−0.327357	−	0.944901i
$280$	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	$-0.207239\pi$
$282$	0.953257	+	0.240905i	0.0567656	+	0.0143457i
$283$		−	19.1215i		−	1.13665i	−0.822803	−	0.568327i	$-0.807591\pi$
$283$		−	19.1215i		−	1.13665i	0.822803	−	0.568327i	$-0.192409\pi$
$284$	6.54689	−	6.25098i	0.388487	−	0.370927i
$285$	−10.1142	−	22.7386i	−0.599111	−	1.34692i
$286$	−1.19409	−	2.97975i	−0.0706080	−	0.176196i
$287$	11.7482			0.693476
$288$	10.2480	+	13.5269i	0.603872	+	0.797081i
$289$	−4.07177	−	7.05252i	−0.239516	−	0.414854i
$290$	49.0111	+	7.02968i	2.87803	+	0.412797i
$291$	−8.33841	−	18.7464i	−0.488806	−	1.09893i
$292$	5.58643	−	5.33393i	0.326921	−	0.312145i
$293$	4.23382	+	2.44440i	0.247342	+	0.142803i	0.618547	−	0.785748i	$-0.287722\pi$
$293$	4.23382	+	2.44440i	0.247342	+	0.142803i	−0.371204	+	0.928551i	$0.621055\pi$
$294$	2.17418	+	7.67454i	0.126801	+	0.447588i
$295$			10.2836i			0.598735i
$296$	1.91040	−	1.36334i	0.111040	−	0.0792424i
$297$	−6.57149	−	31.0799i	−0.381317	−	1.80344i
$298$	−23.1983	+	9.29637i	−1.34384	+	0.538524i
$299$	0.492374	+	0.852817i	0.0284747	+	0.0493197i
$300$	3.53233	+	26.2811i	0.203939	+	1.51734i
$301$	−3.18072	−	5.50918i	−0.183334	−	0.317544i
$302$	−11.5877	−	9.10629i	−0.666798	−	0.524008i
$303$	19.5746	−	8.70682i	1.12453	−	0.500194i
$304$	−16.1387	−	0.746728i	−0.925620	−	0.0428278i
$305$	−13.9910	+	8.07768i	−0.801120	+	0.462527i
$306$	4.36039	−	11.8492i	0.249267	−	0.677373i
$307$	−10.1059	−	5.83464i	−0.576774	−	0.333001i	0.183076	−	0.983099i	$-0.441394\pi$
$307$	−10.1059	−	5.83464i	−0.576774	−	0.333001i	−0.759850	+	0.650098i	$0.774728\pi$
$308$	−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	$-0.554503\pi$
$311$	−6.00978			−0.340783			−0.170392	+	0.985376i	$0.554503\pi$
$312$	−1.58323	+	0.895481i	−0.0896326	+	0.0506966i
$313$	7.46529	−	12.9303i	0.421963	−	0.730862i	−0.574168	−	0.818737i	$-0.694674\pi$
$313$	7.46529	−	12.9303i	0.421963	−	0.730862i	0.996131	+	0.0878754i	$0.0280077\pi$
$314$	−3.94175	+	5.01586i	−0.222446	+	0.283061i
$315$	−22.8878	+	25.3830i	−1.28958	+	1.43017i
$316$	2.68111	−	9.15410i	0.150824	−	0.514958i
$317$	13.3515	+	7.70849i	0.749894	+	0.432952i	0.825656	−	0.564174i	$-0.190805\pi$
$317$	13.3515	+	7.70849i	0.749894	+	0.432952i	−0.0757614	+	0.997126i	$0.524139\pi$
$318$	−9.39813	+	2.66247i	−0.527021	+	0.149304i
$319$	−52.1070	+	30.0840i	−2.91743	+	1.68438i
$320$	26.9128	+	9.25300i	1.50447	+	0.517259i
$321$	3.05986	+	0.322707i	0.170785	+	0.0180117i
$322$	11.1504	−	4.46835i	0.621386	−	0.249011i
$323$	6.00999	+	10.4096i	0.334405	+	0.579207i
$324$	−16.9577	+	6.03627i	−0.942094	+	0.335348i
$325$	−2.84217			−0.157655
$326$	25.5726	+	20.0964i	1.41633	+	1.11304i
$327$	11.5527	+	25.9727i	0.638865	+	1.43629i
$328$	10.3278	−	0.996841i	0.570255	−	0.0550413i
$329$	1.11328	+	0.642755i	0.0613774	+	0.0354362i
$330$	−38.2025	−	37.1279i	−2.10298	−	2.04382i
$331$	−3.78430	+	2.18487i	−0.208004	+	0.120091i	−0.600383	−	0.799712i	$-0.704985\pi$
$331$	−3.78430	+	2.18487i	−0.208004	+	0.120091i	0.392380	+	0.919803i	$0.371652\pi$
$332$	−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
$336$	8.07080	+	20.6681i	0.440298	+	1.12754i
$337$	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
$342$	5.91792	−	16.0817i	0.320005	−	0.869600i
$343$		−	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	$-0.926954\pi$
$347$	−5.40014	+	9.35333i	−0.289895	+	0.502113i	0.683889	+	0.729586i	$0.260287\pi$
$348$	20.8275	+	26.9914i	1.11647	+	1.44689i
$349$	−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
$351$	−0.399098	−	1.88753i	−0.0213023	−	0.100749i
$352$	−32.6621	+	11.3669i	−1.74090	+	0.605855i
$353$	7.25715	+	4.18992i	0.386259	+	0.223007i	0.680538	−	0.732713i	$-0.261746\pi$
$353$	7.25715	+	4.18992i	0.386259	+	0.223007i	−0.294279	+	0.955720i	$0.595079\pi$
$354$	−4.93506	+	5.07790i	−0.262296	+	0.269887i
$355$	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	$-0.129490\pi$
$359$	2.20791	+	3.82420i	0.116529	+	0.201834i	−0.801861	+	0.597511i	$0.796157\pi$
$360$	−17.9667	+	24.2560i	−0.946926	+	1.27840i
$361$	−1.34323	−	2.32654i	−0.0706963	−	0.122450i
$362$	−31.5656	−	4.52747i	−1.65905	−	0.237958i
$363$	45.4319	+	4.79147i	2.38456	+	0.251487i
$364$	−2.31072	+	0.562243i	−0.121115	+	0.0294696i
$365$	11.8979	+	6.86923i	0.622762	+	0.359552i
$366$	−10.7850	−	2.72556i	−0.563740	−	0.142467i
$367$	−8.33445	+	4.81190i	−0.435055	+	0.251179i	−0.701498	−	0.712672i	$-0.747485\pi$
$367$	−8.33445	+	4.81190i	−0.435055	+	0.251179i	0.266443	+	0.963851i	$0.414152\pi$
$368$	9.42304	−	4.87419i	0.491210	−	0.254085i
$369$	−2.29577	+	10.7630i	−0.119513	+	0.560301i
$370$	3.28230	+	2.57942i	0.170638	+	0.134097i
$371$	−12.7711			−0.663041
$372$	−2.95210	−	19.0600i	−0.153060	−	0.988217i
$373$	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
$375$	−14.9466	+	6.64827i	−0.771839	+	0.343315i
$376$	1.03322	+	0.470577i	0.0532840	+	0.0242682i
$377$	−3.16455	+	1.82705i	−0.162983	+	0.0940980i
$378$	−23.4828	+	1.55003i	−1.20783	+	0.0797249i
$379$	20.3811	+	11.7671i	1.04691	+	0.604433i	0.921782	−	0.387708i	$-0.126733\pi$
$379$	20.3811	+	11.7671i	1.04691	+	0.604433i	0.125127	+	0.992141i	$0.460066\pi$
$380$	−6.79393	−	27.9218i	−0.348521	−	1.43236i
$381$	2.20617	−	20.9185i	0.113025	−	1.07169i
$382$	17.0016	+	2.43855i	0.869880	+	0.124767i
$383$	−6.54906	−	11.3433i	−0.334641	−	0.579616i	0.648775	−	0.760981i	$-0.275282\pi$
$383$	−6.54906	−	11.3433i	−0.334641	−	0.579616i	−0.983416	+	0.181365i	$0.941948\pi$
$384$	8.84866	+	17.4843i	0.451556	+	0.892243i
$385$	−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	$-0.305564\pi$
$389$	2.97651	+	1.71849i	0.150915	+	0.0871308i	−0.422641	+	0.906297i	$0.638897\pi$
$390$	−2.32010	−	2.25484i	−0.117483	−	0.114178i
$391$	−6.83559	−	3.94653i	−0.345691	−	0.199585i
$392$	0.884895	+	9.16794i	0.0446939	+	0.463051i
$393$	−5.18511	−	0.546846i	−0.261554	−	0.0275847i
$394$	1.39043	−	9.69415i	0.0700491	−	0.488384i
$395$	16.9663			0.853666
$396$	−1.04633	−	36.6664i	−0.0525801	−	1.84256i
$397$	−15.3396	+	26.5690i	−0.769872	+	1.33346i	0.167759	+	0.985828i	$0.446347\pi$
$397$	−15.3396	+	26.5690i	−0.769872	+	1.33346i	−0.937632	+	0.347630i	$0.886986\pi$
$398$	−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	$0.772521\pi$
$402$	13.0071	−	3.68487i	0.648733	−	0.183785i
$403$	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
$408$	7.40113	−	12.5610i	0.366411	−	0.621861i
$409$	12.1094	−	20.9740i	0.598769	−	1.03710i	−0.394234	−	0.919010i	$-0.628990\pi$
$409$	12.1094	−	20.9740i	0.598769	−	1.03710i	0.993003	−	0.118089i	$-0.0376768\pi$
$410$	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
$414$	1.91469	+	11.0885i	0.0941018	+	0.544969i
$415$	−0.731652	−	0.422419i	−0.0359154	−	0.0207358i
$416$	−1.98363	+	0.690328i	−0.0972553	+	0.0338461i
$417$	28.2157	−	12.5504i	1.38173	−	0.614595i
$418$	27.4569	+	21.5772i	1.34296	+	1.05538i
$419$	−26.1142			−1.27576			−0.637880	−	0.770135i	$-0.720189\pi$
$419$	−26.1142			−1.27576			−0.637880	+	0.770135i	$0.720189\pi$
$420$	−31.2450	+	24.1097i	−1.52460	+	1.17643i
$421$	1.03761	+	1.79719i	0.0505700	+	0.0875898i	0.890202	−	0.455565i	$-0.150563\pi$
$421$	1.03761	+	1.79719i	0.0505700	+	0.0875898i	−0.839632	+	0.543155i	$0.817230\pi$
$422$	−4.49339	+	1.80066i	−0.218735	+	0.0876548i
$423$	−0.806406	+	0.894321i	−0.0392088	+	0.0434834i
$424$	−11.2269	+	1.08363i	−0.545228	+	0.0526257i
$425$	19.7288	−	11.3905i	0.956990	−	0.552518i
$426$	3.02178	+	10.6665i	0.146406	+	0.516792i
$427$	−12.5955	−	7.27202i	−0.609539	−	0.351918i
$428$	3.40958	+	0.998619i	0.164808	+	0.0482701i
$429$	3.90987	+	0.412353i	0.188770	+	0.0199086i
$430$	6.17468	−	7.85726i	0.297770	−	0.378911i
$431$	−12.2535	+	21.2237i	−0.590231	+	1.02231i	0.403970	+	0.914772i	$0.367630\pi$
$431$	−12.2535	+	21.2237i	−0.590231	+	1.02231i	−0.994201	+	0.107538i	$0.965703\pi$
$432$	−20.5120	+	3.35514i	−0.986885	+	0.161424i
$433$	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
$438$	2.57847	+	9.10165i	0.123204	+	0.434894i
$439$	−10.8997	+	6.29294i	−0.520214	+	0.300346i	−0.737022	−	0.675869i	$-0.763769\pi$
$439$	−10.8997	+	6.29294i	−0.520214	+	0.300346i	0.216808	+	0.976214i	$0.430435\pi$
$440$	−35.7324	−	50.0707i	−1.70348	−	2.38703i
$441$	−9.55433	−	2.03796i	−0.454968	−	0.0970455i
$442$	1.22863	+	0.965531i	0.0584402	+	0.0459256i
$443$	−4.02219	−	6.96664i	−0.191100	−	0.330995i	0.754515	−	0.656283i	$-0.227872\pi$
$443$	−4.02219	−	6.96664i	−0.191100	−	0.330995i	−0.945615	+	0.325288i	$0.894539\pi$
$444$	0.382900	+	2.84884i	0.0181716	+	0.135200i
$445$	25.7377	+	44.5790i	1.22008	+	2.11325i
$446$	−10.3071	+	4.13042i	−0.488056	+	0.195581i
$447$	3.21030	−	30.4396i	0.151842	−	1.43974i
$448$	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	$-0.0993652\pi$
$450$	−30.4789	−	11.2160i	−1.43679	−	0.528725i
$451$	−19.4222	−	11.2134i	−0.914558	−	0.528020i
$452$	21.6500	+	22.6749i	1.01833	+	1.06654i
$453$	16.4920	−	7.33569i	0.774864	−	0.344661i
$454$	−31.0703	−	4.45643i	−1.45820	−	0.209151i
$455$	−2.11499	−	3.66326i	−0.0991520	−	0.171736i
$456$	10.0448	−	17.0478i	0.470392	−	0.798335i
$457$	−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
$459$	10.3349	+	11.5028i	0.482392	+	0.536904i
$460$	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	$-0.163960\pi$
$462$	11.7506	−	46.4969i	0.546688	−	2.16323i
$463$		−	4.36207i		−	0.202722i	−0.994850	−	0.101361i	$-0.967680\pi$
$463$		−	4.36207i		−	0.202722i	0.994850	−	0.101361i	$-0.0323198\pi$
$464$	18.0867	+	34.9661i	0.839653	+	1.62326i
$465$	31.0592	−	14.5683i	1.44034	−	0.675587i
$466$	10.9410	+	8.59803i	0.506830	+	0.398296i
$467$	−1.88534			−0.0872431			−0.0436216	−	0.999048i	$-0.513890\pi$
$467$	−1.88534			−0.0872431			−0.0436216	+	0.999048i	$0.513890\pi$
$468$	−0.0635455	−	2.22681i	−0.00293739	−	0.102935i
$469$	17.6752			0.816167
$470$	−0.286709	+	1.99894i	−0.0132249	+	0.0922044i
$471$	−3.17532	−	7.13874i	−0.146311	−	0.328936i
$472$	−6.65543	+	4.74958i	−0.306341	+	0.218617i
$473$			12.1437i			0.558369i
$474$	8.37770	+	8.14204i	0.384801	+	0.373976i
$475$	26.7760	−	15.4591i	1.22857	−	0.709314i
$476$	13.7865	−	13.1634i	0.631904	−	0.603342i
$477$	2.49565	−	11.7001i	0.114268	−	0.535711i
$478$	−0.482058	−	0.0691417i	−0.0220488	−	0.00316247i
$479$	13.9198	−	24.1097i	0.636010	−	1.10160i	−0.350290	−	0.936641i	$-0.613917\pi$
$479$	13.9198	−	24.1097i	0.636010	−	1.10160i	0.986300	−	0.164960i	$-0.0527496\pi$
$480$	−25.4215	+	23.8458i	−1.16033	+	1.08841i
$481$	−0.308088			−0.0140476
$482$	0.177998	+	0.444180i	0.00810760	+	0.0202318i
$483$	−1.54305	+	14.6309i	−0.0702111	+	0.665731i
$484$	50.6246	+	14.8272i	2.30112	+	0.673965i
$485$	36.4937	−	21.0696i	1.65709	−	0.956723i
$486$	3.16884	−	21.8165i	0.143742	−	0.989615i
$487$	13.1436	−	7.58848i	0.595595	−	0.343867i	−0.171712	−	0.985147i	$-0.554930\pi$
$487$	13.1436	−	7.58848i	0.595595	−	0.343867i	0.767307	+	0.641280i	$0.221596\pi$
$488$	−11.6896	−	5.32403i	−0.529164	−	0.241007i
$489$	−36.3958	+	16.1889i	−1.64587	+	0.732087i
$490$	−15.2071	+	6.09402i	−0.686986	+	0.275300i
$491$	−15.8753	−	27.4968i	−0.716440	−	1.24091i	−0.962401	−	0.271632i	$-0.912437\pi$
$491$	−15.8753	−	27.4968i	−0.716440	−	1.24091i	0.245961	−	0.969280i	$-0.420897\pi$
$492$	−4.83123	+	11.7535i	−0.217809	+	0.529887i
$493$	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
$498$	−0.158562	−	0.559701i	−0.00710533	−	0.0250808i
$499$	−27.7107	−	15.9988i	−1.24050	−	0.716204i	−0.271305	−	0.962493i	$-0.587455\pi$
$499$	−27.7107	−	15.9988i	−1.24050	−	0.716204i	−0.969196	+	0.246290i	$0.920788\pi$
$500$	−18.3537	+	4.46580i	−0.820800	+	0.199717i
$501$	−38.8403	−	4.09628i	−1.73526	−	0.183008i
$502$	3.93382	+	9.81651i	0.175575	+	0.438132i
$503$	−4.57160	+	7.91825i	−0.203838	+	0.353057i	−0.949762	−	0.312974i	$-0.898675\pi$
$503$	−4.57160	+	7.91825i	−0.203838	+	0.353057i	0.745924	+	0.666031i	$0.232008\pi$
$504$	−26.9985	−	3.08932i	−1.20261	−	0.137609i
$505$	22.0005	+	38.1061i	0.979011	+	1.69570i
$506$	−22.6988	−	3.25570i	−1.00908	−	0.144733i
$507$	−22.1550	−	2.33657i	−0.983939	−	0.103771i
$508$	6.82700	−	23.3094i	0.302899	−	1.03419i
$509$	−27.7984	+	16.0494i	−1.23214	+	0.711378i	−0.967476	−	0.252962i	$-0.918595\pi$
$509$	−27.7984	+	16.0494i	−1.23214	+	0.711378i	−0.264667	+	0.964340i	$0.585262\pi$
$510$	25.1415	+	6.35372i	1.11329	+	0.281347i
$511$			12.3682i			0.547136i
$512$	6.44146	+	21.6912i	0.284675	+	0.958624i
$513$	14.0265	+	15.6116i	0.619287	+	0.689269i
$514$	4.83101	−	33.6819i	0.213087	−	1.48565i
$515$	−1.54711	+	2.67968i	−0.0681739	+	0.118081i
$516$	6.81963	−	0.916597i	0.300218	−	0.0403509i
$517$	−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	$-0.425141\pi$
$521$	−11.2453	−	6.49249i	−0.492667	−	0.284441i	−0.725680	+	0.688032i	$0.758475\pi$
$522$	−41.1460	+	7.10483i	−1.80091	+	0.310970i
$523$		−	9.02722i		−	0.394733i	−0.980330	−	0.197366i	$-0.936761\pi$
$523$		−	9.02722i		−	0.394733i	0.980330	−	0.197366i	$-0.0632389\pi$
$524$	−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
$528$	6.38456	−	41.8720i	0.277852	−	1.82225i
$529$	−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
$534$	−8.68436	+	34.3639i	−0.375809	+	1.48707i
$535$			6.31935i			0.273209i
$536$	15.5381	−	1.49975i	0.671145	−	0.0647793i
$537$	33.6372	+	3.54754i	1.45155	+	0.153088i
$538$	1.82109	−	12.6967i	0.0785130	−	0.547394i
$539$	9.95416	−	17.2411i	0.428756	−	0.742627i
$540$	−15.9822	−	33.3362i	−0.687763	−	1.43456i
$541$	11.5758	−	20.0498i	0.497682	−	0.862010i	−0.502315	−	0.864685i	$-0.667518\pi$
$541$	11.5758	−	20.0498i	0.497682	−	0.862010i	0.999996	+	0.00267499i	$0.000851475\pi$
$542$	−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
$546$	0.713634	−	2.82384i	0.0305407	−	0.120849i
$547$	−7.05376	+	4.07249i	−0.301597	+	0.174127i	−0.643160	−	0.765732i	$-0.722377\pi$
$547$	−7.05376	+	4.07249i	−0.301597	+	0.174127i	0.341563	+	0.939859i	$0.389044\pi$
$548$	−7.81590	−	8.18590i	−0.333879	−	0.349684i
$549$	9.12353	−	10.1182i	0.389383	−	0.431834i
$550$	40.8942	−	52.0377i	1.74374	−	2.21890i
$551$	19.8754	−	34.4252i	0.846720	−	1.46656i
$552$	−0.115039	+	12.9928i	−0.00489637	+	0.553012i
$553$	7.63704	+	13.2277i	0.324760	+	0.562501i
$554$	26.8568	−	34.1752i	1.14104	−	1.45196i
$555$	−4.67148	+	2.07788i	−0.198293	+	0.0882011i
$556$	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	$-0.151692\pi$
$558$	22.3278	+	7.71157i	0.945212	+	0.326457i
$559$			0.737509i			0.0311933i
$560$	−40.4765	+	20.9370i	−1.71045	+	0.884750i
$561$	−28.7928	+	12.8071i	−1.21563	+	0.540715i
$562$	22.5923	+	17.7543i	0.952999	+	0.748921i
$563$	−8.47962	−	14.6871i	−0.357373	−	0.618989i	0.630148	−	0.776475i	$-0.282994\pi$
$563$	−8.47962	−	14.6871i	−0.357373	−	0.618989i	−0.987521	+	0.157486i	$0.949661\pi$
$564$	−1.10086	+	0.849459i	−0.0463544	+	0.0357687i
$565$	−27.8816	+	48.2924i	−1.17299	+	2.03168i
$566$	21.2620	+	16.7089i	0.893710	+	0.702329i
$567$	11.7609	−	26.3145i	0.493913	−	1.10510i
$568$	1.22987	+	12.7421i	0.0516043	+	0.534646i
$569$	−15.1144	+	8.72630i	−0.633628	+	0.365825i	−0.782156	−	0.623083i	$-0.785880\pi$
$569$	−15.1144	+	8.72630i	−0.633628	+	0.365825i	0.148528	+	0.988908i	$0.452547\pi$
$570$	34.1221	+	8.62327i	1.42922	+	0.361189i
$571$	−6.07695	+	3.50853i	−0.254312	+	0.146827i	−0.621737	−	0.783226i	$-0.713573\pi$
$571$	−6.07695	+	3.50853i	−0.254312	+	0.146827i	0.367425	+	0.930053i	$0.380240\pi$
$572$	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
$576$	−23.9962	−	0.424959i	−0.999843	−	0.0177066i
$577$	1.95480	−	3.38581i	0.0813792	−	0.140953i	−0.822463	−	0.568818i	$-0.807401\pi$
$577$	1.95480	−	3.38581i	0.0813792	−	0.140953i	0.903843	+	0.427865i	$0.140734\pi$
$578$	11.4000	+	1.63511i	0.474179	+	0.0680117i
$579$	−0.552768	−	0.0582975i	−0.0229723	−	0.00242276i
$580$	−50.6440	+	48.3549i	−2.10288	+	2.00783i
$581$		−	0.760575i		−	0.0315540i
$582$	28.1313	+	7.10927i	1.16608	+	0.294689i
$583$	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	$-0.469870\pi$
$587$	4.57982			0.189030			0.0945148	+	0.995523i	$0.469870\pi$
$588$	−10.4335	−	4.28868i	−0.430272	−	0.176862i
$589$	−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	$0.821967\pi$
$594$	40.3014	+	19.8514i	1.65359	+	0.814511i
$595$	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	−0.998917	−	0.0465254i	$-0.985185\pi$
$599$	−13.2101	−	22.8806i	−0.539751	−	0.934876i	0.459166	−	0.888350i	$-0.348148\pi$
$600$	−32.3098	−	19.0375i	−1.31904	−	0.777202i
$601$	9.73435	−	16.8604i	0.397073	−	0.687750i	−0.596291	−	0.802768i	$-0.703359\pi$
$601$	9.73435	−	16.8604i	0.397073	−	0.687750i	0.993363	+	0.115019i	$0.0366928\pi$
$602$	8.90531	+	1.27729i	0.362953	+	0.0520585i
$603$	−3.45400	+	16.1930i	−0.140658	+	0.659430i
$604$	20.2514	−	4.92756i	0.824017	−	0.200499i
$605$			93.8280i			3.81465i
$606$	−7.42338	+	29.3742i	−0.301554	+	1.19324i
$607$	38.5090	−	22.2332i	1.56303	−	0.902417i	0.566084	−	0.824348i	$-0.308458\pi$
$607$	38.5090	−	22.2332i	1.56303	−	0.902417i	0.996948	−	0.0780688i	$-0.0248754\pi$
$608$	14.9328	−	17.2929i	0.605606	−	0.701319i
$609$	−54.2910	−	5.72579i	−2.19998	−	0.232021i
$610$	3.24378	−	22.6157i	0.131337	−	0.915683i
$611$	−0.0745173	−	0.129068i	−0.00301465	−	0.00522152i
$612$	9.36540	+	15.2027i	0.378574	+	0.614532i
$613$	15.3238	−	26.5416i	0.618923	−	1.07201i	−0.370760	−	0.928729i	$-0.620903\pi$
$613$	15.3238	−	26.5416i	0.618923	−	1.07201i	0.989683	−	0.143277i	$-0.0457639\pi$
$614$	15.3186	−	6.13872i	0.618210	−	0.247738i
$615$	−22.4783	−	2.37066i	−0.906412	−	0.0955944i
$616$	22.9533	−	50.3971i	0.924815	−	2.03056i
$617$	13.6038	+	7.85413i	0.547666	+	0.316195i	0.748180	−	0.663496i	$-0.230928\pi$
$617$	13.6038	+	7.85413i	0.547666	+	0.316195i	−0.200514	+	0.979691i	$0.564261\pi$
$618$	−2.04991	+	0.580733i	−0.0824593	+	0.0233605i
$619$			10.3808i			0.417238i	0.977997	+	0.208619i	$0.0668968\pi$
$619$			10.3808i			0.417238i	−0.977997	+	0.208619i	$0.933103\pi$
$620$	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
$624$	0.387745	−	2.54296i	0.0155222	−	0.101800i
$625$	2.33836	+	4.05017i	0.0935346	+	0.162007i
$626$	7.85435	+	19.5999i	0.313923	+	0.783368i
$627$	−39.0776	+	17.3818i	−1.56061	+	0.694162i
$628$	−2.13294	−	8.76602i	−0.0851136	−	0.349802i
$629$	2.13858	−	1.23471i	0.0852707	−	0.0492311i
$630$	−8.22451	−	47.6304i	−0.327672	−	1.89764i
$631$	−22.1769	+	12.8038i	−0.882847	+	0.509712i	−0.871596	−	0.490224i	$-0.836915\pi$
$631$	−22.1769	+	12.8038i	−0.882847	+	0.509712i	−0.0112513	+	0.999937i	$0.503581\pi$
$632$	7.83602	+	10.9804i	0.311700	+	0.436776i
$633$	0.621819	−	5.89600i	0.0247151	−	0.234345i
$634$	−20.2383	+	8.11021i	−0.803767	+	0.322098i
$635$	43.2018			1.71441
$636$	5.25185	−	12.7768i	0.208250	−	0.506631i
$637$	0.604533	−	1.04708i	0.0239525	−	0.0414869i
$638$	12.0809	−	84.2285i	0.478288	−	3.33464i
$639$	−13.2791	−	2.83246i	−0.525313	−	0.112050i
$640$	−33.8060	+	21.8400i	−1.33630	+	0.863301i
$641$	24.3183	−	14.0402i	0.960514	−	0.554553i	0.0641831	−	0.997938i	$-0.479556\pi$
$641$	24.3183	−	14.0402i	0.960514	−	0.554553i	0.896331	+	0.443385i	$0.146223\pi$
$642$	−3.03263	+	3.12040i	−0.119688	+	0.123152i
$643$		−	18.9282i		−	0.746454i	−0.927740	−	0.373227i	$-0.878251\pi$
$643$		−	18.9282i		−	0.746454i	0.927740	−	0.373227i	$-0.121749\pi$
$644$	−4.77497	+	16.3032i	−0.188160	+	0.642435i
$645$	4.97409	+	11.1827i	0.195855	+	0.440319i
$646$	−16.8266	−	2.41345i	−0.662035	−	0.0949559i
$647$	−11.1617			−0.438812			−0.219406	−	0.975634i	$-0.570412\pi$
$647$	−11.1617			−0.438812			−0.219406	+	0.975634i	$0.570412\pi$
$648$	8.10614	−	24.1307i	0.318439	−	0.947943i
$649$	17.6730			0.693726
$650$	2.48358	−	3.16034i	0.0974139	−	0.123959i
$651$	25.3388	+	17.6576i	0.993106	+	0.692057i
$652$	−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	$-0.148635\pi$
$654$	−38.9752	−	9.84974i	−1.52405	−	0.385155i
$655$		−	10.7085i		−	0.418416i
$656$	−7.91627	+	12.3550i	−0.309078	+	0.482380i
$657$	−11.3310	−	2.41692i	−0.442064	−	0.0942931i
$658$	−1.68753	+	0.676253i	−0.0657868	+	0.0263631i
$659$	−44.2361			−1.72319			−0.861597	−	0.507592i	$-0.830536\pi$
$659$	−44.2361			−1.72319			−0.861597	+	0.507592i	$0.830536\pi$
$660$	74.6667	−	10.0356i	2.90640	−	0.390636i
$661$	16.7855	+	29.0733i	0.652879	+	1.13082i	0.982421	+	0.186679i	$0.0597725\pi$
$661$	16.7855	+	29.0733i	0.652879	+	1.13082i	−0.329542	+	0.944141i	$0.606894\pi$
$662$	0.877382	−	6.11713i	0.0341004	−	0.237749i
$663$	−1.74864	+	0.777796i	−0.0679114	+	0.0302071i
$664$	−0.0645350	−	0.668614i	−0.00250444	−	0.0259473i
$665$	39.8504	+	23.0076i	1.54533	+	0.892198i
$666$	−3.30387	−	1.21579i	−0.128022	−	0.0471110i
$667$			26.1028i			1.01070i
$668$	−43.2795	−	12.6760i	−1.67453	−	0.490448i
$669$	1.42635	−	13.5245i	0.0551460	−	0.522886i
$670$	10.3283	+	25.7735i	0.399019	+	0.995716i
$671$	13.8820	+	24.0443i	0.535908	+	0.928219i
$672$	−30.0343	−	9.08611i	−1.15860	−	0.350504i
$673$	8.11001	+	14.0469i	0.312618	+	0.541470i	0.978928	−	0.204204i	$-0.0654607\pi$
$673$	8.11001	+	14.0469i	0.312618	+	0.541470i	−0.666310	+	0.745675i	$0.732127\pi$
$674$	−2.34754	+	2.98724i	−0.0904239	+	0.115064i
$675$	29.5879	−	26.5838i	1.13884	−	1.02321i
$676$	−24.6872	−	7.23054i	−0.949508	−	0.278098i
$677$	7.71546	−	4.45452i	0.296529	−	0.171201i	−0.344354	−	0.938840i	$-0.611902\pi$
$677$	7.71546	−	4.45452i	0.296529	−	0.171201i	0.640883	+	0.767639i	$0.278569\pi$
$678$	−36.9429	+	10.4658i	−1.41878	+	0.401937i
$679$	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	$-0.194093\pi$
$683$	42.8490			1.63957			0.819785	+	0.572671i	$0.194093\pi$
$684$	12.7107	+	20.6331i	0.486007	+	0.788926i
$685$	10.0656	−	17.4341i	0.384587	−	0.666124i
$686$	13.3312	+	10.4764i	0.508986	+	0.399991i
$687$	−21.7559	−	2.29448i	−0.830040	−	0.0875399i
$688$	7.93695	+	0.367237i	0.302593	+	0.0140008i
$689$	1.28224	+	0.740303i	0.0488495	+	0.0282033i
$690$	−22.2360	+	6.29941i	−0.846512	+	0.239815i
$691$	24.8514	−	14.3480i	0.945391	−	0.545822i	0.0537452	−	0.998555i	$-0.482884\pi$
$691$	24.8514	−	14.3480i	0.945391	−	0.545822i	0.891646	+	0.452733i	$0.149551\pi$
$692$	10.4164	+	10.9095i	0.395973	+	0.414718i
$693$	43.6222	+	39.3340i	1.65707	+	1.49417i
$694$	−5.68157	−	14.1779i	−0.215670	−	0.538185i
$695$	31.7125	+	54.9277i	1.20292	+	2.08353i
$696$	−48.2126	−	0.426874i	−1.82749	−	0.0161806i
$697$	10.9170			0.413512
$698$	7.79304	−	9.91661i	0.294971	−	0.375349i
$699$	−15.5715	+	6.92625i	−0.588970	+	0.261975i
$700$	−33.8593	−	35.4622i	−1.27976	−	1.34034i
$701$	−14.7131	−	8.49461i	−0.555706	−	0.320837i	0.195714	−	0.980661i	$-0.437298\pi$
$701$	−14.7131	−	8.49461i	−0.555706	−	0.320837i	−0.751420	+	0.659824i	$0.770631\pi$
$702$	2.44758	+	1.20561i	0.0923778	+	0.0455027i
$703$	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
$708$	−1.33394	−	9.92474i	−0.0501326	−	0.372995i
$709$	−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
$714$	6.36330	+	22.4616i	0.238141	+	0.840603i
$715$			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	0.344196	+	0.938898i	$0.388152\pi$
$719$	−17.1882	+	29.7708i	−0.641012	+	1.11026i	−0.985207	+	0.171367i	$0.945182\pi$
$720$	−11.2715	−	41.1736i	−0.420065	−	1.53445i
$721$	−2.78561			−0.103741
$722$	3.76074	+	0.539405i	0.139960	+	0.0200746i
$723$	−0.582829	−	0.0614679i	−0.0216757	−	0.00228602i
$724$	32.6173	−	31.1430i	1.21221	−	1.15742i
$725$	−65.2444	−	37.6689i	−2.42312	−	1.39899i
$726$	−45.0276	+	46.3309i	−1.67113	+	1.71950i
$727$	22.4845	+	12.9814i	0.833902	+	0.481454i	0.855187	−	0.518320i	$-0.173442\pi$
$727$	22.4845	+	12.9814i	0.833902	+	0.481454i	−0.0212845	+	0.999773i	$0.506776\pi$
$728$	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
$732$	12.4549	−	9.61063i	0.460346	−	0.355219i
$733$	−12.1208	−	20.9938i	−0.447690	−	0.775422i	0.550545	−	0.834805i	$-0.314420\pi$
$733$	−12.1208	−	20.9938i	−0.447690	−	0.775422i	−0.998235	+	0.0593832i	$0.981087\pi$
$734$	1.93233	−	13.4722i	0.0713235	−	0.497269i
$735$	2.10444	−	19.9540i	0.0776233	−	0.736013i
$736$	−2.81430	+	14.7371i	−0.103737	+	0.543217i
$737$	−29.2208	−	16.8706i	−1.07636	−	0.621438i
$738$	−9.96178	−	11.9578i	−0.366698	−	0.440174i
$739$	8.30220	−	4.79328i	0.305401	−	0.176324i	−0.339465	−	0.940619i	$-0.610246\pi$
$739$	8.30220	−	4.79328i	0.305401	−	0.176324i	0.644867	+	0.764295i	$0.276913\pi$
$740$	−5.73634	+	1.39576i	−0.210872	+	0.0513092i
$741$	−2.37325	+	1.05563i	−0.0871835	+	0.0387794i
$742$	11.1597	−	14.2007i	0.409687	−	0.521325i
$743$	14.3976			0.528195			0.264098	−	0.964496i	$-0.414926\pi$
$743$	14.3976			0.528195			0.264098	+	0.964496i	$0.414926\pi$
$744$	23.7734	+	13.3727i	0.871573	+	0.490265i
$745$	62.8651			2.30320
$746$	−17.4768	+	22.2392i	−0.639872	+	0.814234i
$747$	0.696793	+	0.148627i	0.0254943	+	0.00543799i
$748$	−35.3561	+	8.60282i	−1.29275	+	0.314550i
$749$	−4.92687	+	2.84453i	−0.180024	+	0.103937i
$750$	5.66827	−	22.4292i	0.206976	−	0.819000i
$751$	−1.29107	−	0.745397i	−0.0471117	−	0.0271999i	0.476259	−	0.879305i	$-0.341992\pi$
$751$	−1.29107	−	0.745397i	−0.0471117	−	0.0271999i	−0.523371	+	0.852105i	$0.675326\pi$
$752$	−1.42611	+	0.737674i	−0.0520049	+	0.0269002i
$753$	−12.8807	−	1.35846i	−0.469399	−	0.0495050i
$754$	0.733695	−	5.11534i	0.0267196	−	0.186290i
$755$	18.5359	+	32.1052i	0.674592	+	1.16843i
$756$	18.7965	−	27.4661i	0.683621	−	0.998932i
$757$	11.0988	+	19.2237i	0.403393	+	0.698698i	0.994133	−	0.108164i	$-0.0344973\pi$
$757$	11.0988	+	19.2237i	0.403393	+	0.698698i	−0.590740	+	0.806862i	$0.701164\pi$
$758$	−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	−0.974068	−	0.226255i	$-0.927352\pi$
$761$	−45.7116	−	26.3916i	−1.65704	−	0.956695i	−0.682976	−	0.730440i	$-0.739315\pi$
$762$	21.3324	+	20.7324i	0.772792	+	0.751054i
$763$	−45.5182	−	26.2800i	−1.64787	−	0.951398i
$764$	−17.5681	+	16.7740i	−0.635591	+	0.606862i
$765$	−21.2684	+	23.5872i	−0.768962	+	0.852795i
$766$	18.3359	+	2.62992i	0.662503	+	0.0950230i
$767$	1.07331			0.0387550
$768$	−27.1738	−	5.43909i	−0.980551	−	0.196266i
$769$	12.7582	−	22.0979i	0.460073	−	0.796870i	−0.538891	−	0.842375i	$-0.681157\pi$
$769$	12.7582	−	22.0979i	0.460073	−	0.796870i	0.998964	+	0.0455057i	$0.0144899\pi$
$770$	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	$0.892040\pi$
$774$	−2.91040	+	7.90891i	−0.104612	+	0.284280i
$775$	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
$780$	4.53463	−	0.609481i	0.162366	−	0.0218229i
$781$	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
$786$	5.13897	−	5.28771i	0.183301	−	0.188606i
$787$	−17.3884	−	10.0392i	−0.619829	−	0.357858i	0.156974	−	0.987603i	$-0.449826\pi$
$787$	−17.3884	−	10.0392i	−0.619829	−	0.357858i	−0.776802	+	0.629745i	$0.783160\pi$
$788$	9.56435	+	10.0171i	0.340716	+	0.356845i
$789$	6.03377	+	13.5651i	0.214808	+	0.482930i
$790$	−14.8256	+	18.8656i	−0.527473	+	0.671207i
$791$	−50.2015			−1.78496
$792$	41.6854	+	30.8768i	1.48123	+	1.09716i
$793$	0.843076	+	1.46025i	0.0299385	+	0.0518550i
$794$	−16.1390	−	40.2735i	−0.572753	−	1.42925i
$795$	24.4353	+	2.57706i	0.866632	+	0.0913990i
$796$	−10.6502	−	11.1544i	−0.377487	−	0.395357i
$797$	−33.3991	+	19.2830i	−1.18306	+	0.683039i	−0.956720	−	0.291010i	$-0.906009\pi$
$797$	−33.3991	+	19.2830i	−1.18306	+	0.683039i	−0.226338	+	0.974049i	$0.572675\pi$
$798$	8.63628	+	30.4848i	0.305721	+	1.07915i
$799$	1.03452	+	0.597280i	0.0365986	+	0.0211302i
$800$	−32.7744	−	28.3015i	−1.15875	−	1.00061i
$801$	−32.2393	−	29.0700i	−1.13912	−	1.02714i
$802$	−29.1849	−	22.9352i	−1.03056	−	0.809870i
$803$	11.8052	−	20.4472i	0.416595	−	0.721564i
$804$	−7.26859	+	17.6831i	−0.256343	+	0.623634i
$805$	−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	$-0.0735362\pi$
$809$	35.8908	+	20.7216i	1.26185	+	0.728532i	0.288422	+	0.957504i	$0.406870\pi$
$810$	45.2433	+	1.77286i	1.58969	+	0.0622919i
$811$	22.0053	−	12.7048i	0.772712	−	0.446126i	−0.0611290	−	0.998130i	$-0.519470\pi$
$811$	22.0053	−	12.7048i	0.772712	−	0.446126i	0.833841	+	0.552004i	$0.186137\pi$
$812$	−60.4962	−	17.7185i	−2.12300	−	0.621797i
$813$	26.9614	−	11.9925i	0.945576	−	0.420594i
$814$	4.43288	−	5.64082i	0.155372	−	0.197711i
$815$	−40.9064	−	70.8519i	−1.43289	−	2.48183i
$816$	7.49979	+	19.2058i	0.262545	+	0.672338i
$817$	−4.01146	−	6.94805i	−0.140343	−	0.243081i
$818$	12.7404	+	31.7927i	0.445459	+	1.11161i
$819$	2.64925	+	2.38882i	0.0925723	+	0.0834721i
$820$	−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	$-0.0675454\pi$
$822$	13.3368	−	3.77828i	0.465175	−	0.131783i
$823$	−17.6508	−	10.1907i	−0.615267	−	0.355225i	0.159757	−	0.987156i	$-0.448929\pi$
$823$	−17.6508	−	10.1907i	−0.615267	−	0.355225i	−0.775024	+	0.631932i	$0.782262\pi$
$824$	−2.44880	+	0.236360i	−0.0853080	+	0.00823398i
$825$	32.9429	+	74.0619i	1.14692	+	2.57850i
$826$	1.85887	−	12.9601i	0.0646783	−	0.450938i
$827$	−1.92701	−	3.33768i	−0.0670087	−	0.116062i	0.830575	−	0.556907i	$-0.188012\pi$
$827$	−1.92701	−	3.33768i	−0.0670087	−	0.116062i	−0.897583	+	0.440845i	$0.854679\pi$
$828$	−14.0029	−	7.56042i	−0.486634	−	0.262743i
$829$	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
$831$	21.6348	+	48.6393i	0.750504	+	1.68728i
$832$	0.965745	−	2.80891i	0.0334812	−	0.0973815i
$833$			9.69104i			0.335775i
$834$	−10.7004	+	42.3412i	−0.370523	+	1.46615i
$835$		−	80.2146i		−	2.77594i
$836$	−47.9853	+	11.6758i	−1.65961	+	0.403815i
$837$	−21.1284	+	19.7633i	−0.730305	+	0.683121i
$838$	22.8193	−	29.0375i	0.788281	−	1.00308i
$839$	39.4541			1.36211			0.681053	−	0.732234i	$-0.261522\pi$
$839$	39.4541			1.36211			0.681053	+	0.732234i	$0.261522\pi$
$840$	0.494147	−	55.8106i	0.0170497	−	1.92565i
$841$	−67.8597			−2.33999
$842$	−2.90507	−	0.416676i	−0.100115	−	0.0143596i
$843$	−32.1541	+	14.3022i	−1.10745	+	0.492594i
$844$	1.92423	−	6.56988i	0.0662346	−	0.226144i
$845$		−	45.7555i		−	1.57404i
$846$	−0.289774	−	1.67816i	−0.00996265	−	0.0576964i
$847$	−73.1528	+	42.2348i	−2.51356	+	1.45121i
$848$	8.60549	−	13.4306i	0.295514	−	0.461210i
$849$	−30.2609	+	13.4601i	−1.03855	+	0.461949i
$850$	−4.57410	+	31.8907i	−0.156890	+	1.09384i
$851$	−1.10040	+	1.90595i	−0.0377212	+	0.0653350i
$852$	−14.5011	−	5.96062i	−0.496798	−	0.204208i
$853$	−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
$855$	−28.8655	+	32.0125i	−0.987181	+	1.09480i
$856$	−4.08980	+	2.91864i	−0.139787	+	0.0997572i
$857$	−25.8746	+	14.9387i	−0.883861	+	0.510297i	−0.871929	−	0.489632i	$-0.837131\pi$
$857$	−25.8746	+	14.9387i	−0.883861	+	0.510297i	−0.0119313	+	0.999929i	$0.503798\pi$
$858$	−3.87508	+	3.98723i	−0.132293	+	0.136122i
$859$	−8.94147	+	5.16236i	−0.305079	+	0.176138i	−0.644722	−	0.764417i	$-0.723027\pi$
$859$	−8.94147	+	5.16236i	−0.305079	+	0.176138i	0.339643	+	0.940554i	$0.389694\pi$
$860$	3.34122	+	13.7318i	0.113935	+	0.468251i
$861$	−8.26987	−	18.5923i	−0.281836	−	0.633623i
$862$	−12.8921	−	32.1711i	−0.439107	−	1.09575i
$863$	6.01828	+	10.4240i	0.204865	+	0.354836i	0.950090	−	0.311977i	$-0.100991\pi$
$863$	6.01828	+	10.4240i	0.204865	+	0.354836i	−0.745225	+	0.666813i	$0.767658\pi$
$864$	14.1933	−	25.7401i	0.482865	−	0.875695i
$865$	−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
$870$	−23.3752	−	82.5113i	−0.792495	−	2.79740i
$871$	−1.77463	−	1.02458i	−0.0601310	−	0.0347167i
$872$	−42.2445	−	19.2402i	−1.43058	−	0.651556i
$873$	−23.7976	+	26.3920i	−0.805426	+	0.893235i
$874$	14.0626	−	5.63538i	0.475675	−	0.190620i
$875$	15.1234	−	26.1945i	0.511265	−	0.885537i
$876$	−12.3737	−	5.08617i	−0.418068	−	0.171846i
$877$	−24.6763	−	42.7406i	−0.833259	−	1.44325i	−0.895440	−	0.445182i	$-0.853139\pi$
$877$	−24.6763	−	42.7406i	−0.833259	−	1.44325i	0.0621815	−	0.998065i	$-0.480194\pi$
$878$	2.52707	−	17.6188i	0.0852845	−	0.594606i
$879$	0.888111	−	8.42093i	0.0299552	−	0.284031i
$880$	86.9000	+	4.02080i	2.92940	+	0.135541i
$881$	25.8554	−	14.9276i	0.871091	−	0.502925i	0.00338024	−	0.999994i	$-0.498924\pi$
$881$	25.8554	−	14.9276i	0.871091	−	0.502925i	0.867711	+	0.497070i	$0.165591\pi$
$882$	10.6150	−	8.84306i	0.357424	−	0.297761i
$883$		−	15.9306i		−	0.536107i	−0.963404	−	0.268054i	$-0.913620\pi$
$883$		−	15.9306i		−	0.536107i	0.963404	−	0.268054i	$-0.0863804\pi$
$884$	−2.14724	+	0.522464i	−0.0722193	+	0.0175724i
$885$	16.2744	−	7.23889i	0.547059	−	0.243333i
$886$	11.2612	+	1.61520i	0.378328	+	0.0542638i
$887$	−7.10309	+	12.3029i	−0.238498	+	0.413091i	−0.960284	−	0.279026i	$-0.909989\pi$
$887$	−7.10309	+	12.3029i	−0.238498	+	0.413091i	0.721785	+	0.692117i	$0.243322\pi$
$888$	−3.50234	−	2.06364i	−0.117531	−	0.0692511i
$889$	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
$894$	31.0419	+	30.1687i	1.03820	+	1.00899i
$895$			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
$900$	39.1049	−	24.0900i	1.30350	−	0.803002i
$901$	−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
$906$	−6.25436	+	24.7484i	−0.207787	+	0.822210i
$907$			49.7055i			1.65044i	0.564808	+	0.825222i	$0.308950\pi$
$907$			49.7055i			1.65044i	−0.564808	+	0.825222i	$0.691050\pi$
$908$	32.1055	−	30.6544i	1.06546	−	1.01730i
$909$	−27.5581	−	24.8490i	−0.914044	−	0.824190i
$910$	5.92148	+	0.849320i	0.196295	+	0.0281547i
$911$	−20.6984	+	35.8507i	−0.685769	+	1.18779i	0.287425	+	0.957803i	$0.407201\pi$
$911$	−20.6984	+	35.8507i	−0.685769	+	1.18779i	−0.973194	+	0.229984i	$0.926133\pi$
$912$	10.1787	+	26.0661i	0.337051	+	0.863136i
$913$	−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
$918$	−21.8214	+	1.44036i	−0.720214	+	0.0475391i
$919$	−31.9151	+	18.4262i	−1.05278	+	0.607825i	−0.923427	−	0.383774i	$-0.874624\pi$
$919$	−31.9151	+	18.4262i	−1.05278	+	0.607825i	−0.129356	+	0.991598i	$0.541291\pi$
$920$	−26.5630	+	2.56387i	−0.875756	+	0.0845284i
$921$	−2.11987	+	20.1003i	−0.0698522	+	0.662328i
$922$	23.5220	+	18.4849i	0.774657	+	0.608769i
$923$	0.840211	−	1.45529i	0.0276559	−	0.0479014i
$924$	41.4340	+	53.6964i	1.36308	+	1.76648i
$925$	−3.17597	−	5.50093i	−0.104425	−	0.180870i
$926$	4.85038	+	3.81170i	0.159393	+	0.125260i
$927$	0.544348	−	2.55201i	0.0178787	−	0.0838189i
$928$	−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	$0.999353\pi$
$930$	−10.9413	+	47.2663i	−0.358781	+	1.54992i
$931$			13.1527i			0.431062i
$932$	−19.1211	+	4.65253i	−0.626331	+	0.152399i
$933$	4.23043	+	9.51082i	0.138498	+	0.311370i
$934$	1.64747	−	2.09639i	0.0539067	−	0.0685961i
$935$	−32.3612	−	56.0512i	−1.05832	−	1.83307i
$936$	2.53162	+	1.87520i	0.0827487	+	0.0612928i
$937$	−19.2989	+	33.4267i	−0.630469	+	1.09200i	0.356987	+	0.934109i	$0.383804\pi$
$937$	−19.2989	+	33.4267i	−0.630469	+	1.09200i	−0.987456	+	0.157895i	$0.949529\pi$
$938$	−15.4451	+	19.6539i	−0.504302	+	0.641722i
$939$	−25.7179	−	2.71233i	−0.839272	−	0.0885136i
$940$	−1.97218	−	2.06554i	−0.0643254	−	0.0673705i
$941$	−6.62501	+	3.82495i	−0.215969	+	0.124690i	−0.604082	−	0.796922i	$-0.706460\pi$
$941$	−6.62501	+	3.82495i	−0.215969	+	0.124690i	0.388113	+	0.921612i	$0.373127\pi$
$942$	10.7126	+	2.70726i	0.349035	+	0.0882073i
$943$	−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	$-0.682094\pi$
$947$	14.0775	−	24.3829i	0.457457	−	0.792339i	0.998826	+	0.0484463i	$0.0154270\pi$
$948$	−16.3742	+	2.20078i	−0.531809	+	0.0714781i
$949$	0.716948	−	1.24179i	0.0232731	−	0.0403102i
$950$	−6.20797	+	43.2821i	−0.201413	+	1.40426i
$951$	2.80069	−	26.5557i	0.0908185	−	0.861127i
$952$	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	$-0.0312370\pi$
$954$	10.8291	+	12.9989i	0.350605	+	0.420856i
$955$	−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
$960$	−4.30114	−	49.1044i	−0.138819	−	1.58484i
$961$	−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
$966$	−14.9204	−	14.5007i	−0.480057	−	0.466554i
$967$	−25.9726	−	14.9953i	−0.835222	−	0.482216i	0.0204153	−	0.999792i	$-0.493501\pi$
$967$	−25.9726	−	14.9953i	−0.835222	−	0.482216i	−0.855637	+	0.517576i	$0.826834\pi$
$968$	−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	−0.937713	−	0.347410i	$-0.887061\pi$
$971$	−23.9852	−	41.5436i	−0.769723	−	1.33320i	0.167991	−	0.985789i	$-0.446272\pi$
$972$	21.4897	+	22.5875i	0.689282	+	0.724493i
$973$	−28.5495	+	49.4492i	−0.915255	+	1.58527i
$974$	−3.04733	+	21.2460i	−0.0976426	+	0.680767i
$975$	2.00068	+	4.49791i	0.0640729	+	0.144048i
$976$	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	$-0.400074\pi$
$978$	13.8025	−	54.6164i	0.441357	−	1.74644i
$979$	76.6116	−	44.2317i	2.44852	−	1.41365i
$980$	6.51220	−	22.2346i	0.208025	−	0.710258i
$981$	32.9710	−	36.5656i	1.05268	−	1.16745i
$982$	44.4472	+	6.37507i	1.41837	+	0.203437i
$983$	27.7308	+	48.0311i	0.884475	+	1.53196i	0.846314	+	0.532684i	$0.178816\pi$
$983$	27.7308	+	48.0311i	0.884475	+	1.53196i	0.0381603	+	0.999272i	$0.487850\pi$
$984$	−8.84752	−	15.6426i	−0.282049	−	0.498667i
$985$	−12.3173	+	21.3342i	−0.392462	+	0.679765i
$986$	15.4076	+	38.4483i	0.490678	+	1.22444i
$987$	0.233529	−	2.21429i	0.00743332	−	0.0704816i
$988$	−2.91423	+	0.709089i	−0.0927140	+	0.0225591i
$989$	4.56252	+	2.63417i	0.145080	+	0.0837617i
$990$	−31.8654	+	86.5930i	−1.01275	+	2.75210i
$991$		−	7.61583i		−	0.241925i	−0.992657	−	0.120962i	$-0.961402\pi$
$991$		−	7.61583i		−	0.241925i	0.992657	−	0.120962i	$-0.0385980\pi$
$992$	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
$996$	0.760913	+	0.312771i	0.0241104	+	0.00991054i
$997$	11.3456	+	19.6512i	0.359319	+	0.622359i	0.987847	−	0.155428i	$-0.0496755\pi$
$997$	11.3456	+	19.6512i	0.359319	+	0.622359i	−0.628528	+	0.777787i	$0.716342\pi$
$998$	42.0042	−	16.8326i	1.32962	−	0.532825i
$999$	3.20729	−	2.88165i	0.101474	−	0.0911713i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.17	✓	120	12.11	even	2	inner
372.2.p.a.191.18	yes	120	1.1	even	1	trivial
372.2.p.a.191.43	yes	120	3.2	odd	2	inner
372.2.p.a.191.44	yes	120	4.3	odd	2	inner
372.2.p.a.335.17	yes	120	372.335	even	6	inner
372.2.p.a.335.18	yes	120	31.25	even	3	inner
372.2.p.a.335.43	yes	120	93.56	odd	6	inner
372.2.p.a.335.44	yes	120	124.87	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-0.703924 - 1.58256i) q^{3} +(-0.472843 - 1.94330i) q^{4} +(3.08078 - 1.77869i) q^{5} +(2.37483 + 0.600161i) q^{6} +(2.77350 + 1.60128i) q^{7} +(2.57403 + 1.17234i) q^{8} +(-2.00898 + 2.22800i) q^{9} +(-0.714273 + 4.97993i) q^{10} +(-3.05678 - 5.29450i) q^{11} +(-2.74254 + 2.11624i) 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} +(-0.721909 - 4.18077i) q^{18} +(3.49788 + 2.01950i) q^{19} +(-4.91325 - 5.14584i) q^{20} +(0.581786 - 5.51641i) q^{21} +(8.55830 + 1.22752i) q^{22} -2.65226 q^{23} +(0.0433739 - 4.89879i) 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} +(8.38382 - 2.37511i) 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} +(5.27961 + 2.85056i) 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} +(5.62556 + 5.46732i) q^{42} +(-1.72024 - 0.993180i) q^{43} +(-8.84343 + 8.44371i) q^{44} +(-2.22630 + 10.4373i) q^{45} +(2.31762 - 2.94916i) q^{46} +0.401400 q^{47} +(5.40928 + 4.32894i) q^{48} +(1.62821 + 2.82014i) q^{49} +(4.02693 + 10.0489i) q^{50} +(0.540624 - 5.12612i) q^{51} +(-0.537076 + 0.512801i) q^{52} +(-3.45351 + 1.99388i) q^{53} +(-6.10814 + 4.08541i) q^{54} +(-18.8345 - 10.8741i) q^{55} +(5.26183 + 7.37323i) q^{56} +(0.733736 - 6.95717i) q^{57} +(10.9435 + 8.60000i) q^{58} +(-1.44539 + 2.50350i) q^{59} +(-4.68503 + 11.3978i) 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} +(-4.08177 - 14.4081i) q^{66} +(4.77967 - 2.75954i) q^{67} +(1.67297 - 5.71201i) q^{68} +(1.86699 + 4.19735i) q^{69} +(-9.95531 + 12.6681i) q^{70} +(2.26297 + 3.91958i) q^{71} +(-7.78315 + 3.37973i) q^{72} +(1.93098 + 3.34456i) q^{73} +(0.436514 + 1.08928i) q^{74} +(-13.1856 - 1.39061i) q^{75} +(2.27055 - 7.75234i) q^{76} -19.5791i q^{77} +(-0.247893 - 0.875027i) q^{78} +(4.13036 + 2.38466i) q^{79} +(-7.67672 + 11.9811i) q^{80} +(-0.927992 - 8.95203i) q^{81} +(-0.736561 + 5.13532i) q^{82} +(-0.118745 - 0.205672i) q^{83} +(-10.9951 + 1.47781i) q^{84} +10.5867 q^{85} +(2.60756 - 1.04494i) q^{86} +(-15.5751 + 6.92784i) q^{87} +(-1.66129 - 17.2118i) q^{88} +14.4700i q^{89} +(-9.66033 - 11.5960i) q^{90} -1.18907i q^{91} +(1.25410 + 5.15414i) q^{92} +(9.60882 + 0.818894i) q^{93} +(-0.350756 + 0.446335i) q^{94} +14.3683 q^{95} +(-9.54033 + 2.23207i) q^{96} +11.8456 q^{97} +(-4.55862 - 0.653845i) q^{98} +(17.9372 + 3.82603i) 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

Introduction

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