LMFDB - Embedded newform 372.2.p.a.191.44

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			191.44
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.43

$q$-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} +(0.703924 + 1.58256i) q^{3} +(-0.472843 + 1.94330i) q^{4} +(3.08078 - 1.77869i) q^{5} +(-1.14461 + 2.16561i) q^{6} +(-2.77350 - 1.60128i) q^{7} +(-2.57403 + 1.17234i) q^{8} +(-2.00898 + 2.22800i) q^{9} +(4.66988 + 1.87138i) q^{10} +(3.05678 + 5.29450i) q^{11} +(-3.40823 + 0.619636i) q^{12} +(-0.185643 - 0.321544i) q^{13} +(-0.643031 - 4.48323i) q^{14} +(4.98351 + 3.62345i) q^{15} +(-3.55284 - 1.83775i) q^{16} +(2.57727 + 1.48799i) q^{17} +(-4.23292 - 0.286981i) q^{18} +(-3.49788 - 2.01950i) q^{19} +(1.99980 + 6.82792i) q^{20} +(0.581786 - 5.51641i) q^{21} +(-3.21608 + 8.02546i) q^{22} +2.65226 q^{23} +(-3.66722 - 3.24831i) q^{24} +(3.82746 - 6.62936i) q^{25} +(0.195318 - 0.487400i) q^{26} +(-4.94011 - 1.61098i) q^{27} +(4.42320 - 4.63260i) 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} +(0.597536 + 4.16604i) q^{34} -11.3927 q^{35} +(-3.37975 - 4.95755i) q^{36} +(0.414892 - 0.718613i) q^{37} +(-0.810977 - 5.65415i) q^{38} +(0.378183 - 0.520134i) q^{39} +(-5.84478 + 8.19011i) q^{40} +(3.17691 - 1.83419i) q^{41} +(6.64233 - 4.17349i) q^{42} +(1.72024 + 0.993180i) q^{43} +(-11.7342 + 3.43678i) q^{44} +(-2.22630 + 10.4373i) q^{45} +(2.31762 + 2.94916i) q^{46} -0.401400 q^{47} +(0.407420 - 6.91621i) q^{48} +(1.62821 + 2.82014i) q^{49} +(10.7160 - 1.53700i) q^{50} +(-0.540624 + 5.12612i) q^{51} +(0.712637 - 0.208721i) q^{52} +(-3.45351 + 1.99388i) q^{53} +(-2.52549 - 6.90086i) q^{54} +(18.8345 + 10.8741i) q^{55} +(9.01632 + 0.870260i) q^{56} +(0.733736 - 6.95717i) q^{57} +(10.9435 - 8.60000i) q^{58} +(1.44539 - 2.50350i) q^{59} +(-9.39787 + 7.97114i) q^{60} -4.54137 q^{61} +(7.77025 - 1.27404i) 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} +(-4.11026 + 4.30483i) q^{68} +(1.86699 + 4.19735i) q^{69} +(-9.95531 - 12.6681i) q^{70} +(-2.26297 - 3.91958i) q^{71} +(2.55920 - 8.09015i) q^{72} +(1.93098 + 3.34456i) q^{73} +(1.16160 - 0.166609i) q^{74} +(13.1856 + 1.39061i) q^{75} +(5.57845 - 5.84252i) q^{76} -19.5791i q^{77} +(0.908828 - 0.0339901i) q^{78} +(-4.13036 - 2.38466i) q^{79} +(-14.2143 + 0.657685i) q^{80} +(-0.927992 - 8.95203i) q^{81} +(4.81560 + 1.92978i) q^{82} +(0.118745 + 0.205672i) q^{83} +(10.4450 + 3.73898i) q^{84} +10.5867 q^{85} +(0.398834 + 2.78068i) q^{86} +(15.5751 - 6.92784i) q^{87} +(-14.0752 - 10.0446i) q^{88} +14.4700i q^{89} +(-13.5511 + 6.64493i) 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} +(8.04646 - 5.59056i) q^{96} +11.8456 q^{97} +(-1.71306 + 4.27481i) 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	$0.0405660\pi$
$6$	−1.14461	+	2.16561i	−0.467284	+	0.884107i
$7$	−2.77350	−	1.60128i	−1.04829	−	0.605228i	−0.126117	−	0.992015i	$-0.540251\pi$
$7$	−2.77350	−	1.60128i	−1.04829	−	0.605228i	−0.922169	+	0.386788i	$0.873585\pi$
$8$	−2.57403	+	1.17234i	−0.910056	+	0.414485i
$9$	−2.00898	+	2.22800i	−0.669660	+	0.742668i
$10$	4.66988	+	1.87138i	1.47675	+	0.591784i
$11$	3.05678	+	5.29450i	0.921654	+	1.59635i	0.796856	+	0.604169i	$0.206495\pi$
$11$	3.05678	+	5.29450i	0.921654	+	1.59635i	0.124798	+	0.992182i	$0.460172\pi$
$12$	−3.40823	+	0.619636i	−0.983872	+	0.178873i
$13$	−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	$0.849730\pi$
$14$	−0.643031	−	4.48323i	−0.171857	−	1.19819i
$15$	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	$0.549139\pi$
$18$	−4.23292	−	0.286981i	−0.997710	−	0.0676420i
$19$	−3.49788	−	2.01950i	−0.802468	−	0.463305i	0.0418652	−	0.999123i	$-0.486670\pi$
$19$	−3.49788	−	2.01950i	−0.802468	−	0.463305i	−0.844334	+	0.535818i	$0.820003\pi$
$20$	1.99980	+	6.82792i	0.447169	+	1.52677i
$21$	0.581786	−	5.51641i	0.126956	−	1.20378i
$22$	−3.21608	+	8.02546i	−0.685672	+	1.71103i
$23$	2.65226			0.553034			0.276517	−	0.961009i	$-0.410820\pi$
$23$	2.65226			0.553034			0.276517	+	0.961009i	$0.410820\pi$
$24$	−3.66722	−	3.24831i	−0.748567	−	0.663059i
$25$	3.82746	−	6.62936i	0.765493	−	1.32587i
$26$	0.195318	−	0.487400i	0.0383051	−	0.0955870i
$27$	−4.94011	−	1.61098i	−0.950725	−	0.310034i
$28$	4.42320	−	4.63260i	0.835907	−	0.875478i
$29$		−	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
$34$	0.597536	+	4.16604i	0.102477	+	0.714469i
$35$	−11.3927			−1.92572
$36$	−3.37975	−	4.95755i	−0.563291	−	0.826258i
$37$	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	$0.144939\pi$
$38$	−0.810977	−	5.65415i	−0.131558	−	0.917224i
$39$	0.378183	−	0.520134i	0.0605577	−	0.0832881i
$40$	−5.84478	+	8.19011i	−0.924142	+	1.29497i
$41$	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	$0.240857\pi$
$42$	6.64233	−	4.17349i	1.02493	−	0.643983i
$43$	1.72024	+	0.993180i	0.262334	+	0.151459i	0.625399	−	0.780305i	$-0.284936\pi$
$43$	1.72024	+	0.993180i	0.262334	+	0.151459i	−0.363065	+	0.931764i	$0.618270\pi$
$44$	−11.7342	+	3.43678i	−1.76899	+	0.518114i
$45$	−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	$-0.509320\pi$
$47$	−0.401400			−0.0585503			−0.0292751	+	0.999571i	$0.509320\pi$
$48$	0.407420	−	6.91621i	0.0588060	−	0.998269i
$49$	1.62821	+	2.82014i	0.232601	+	0.402878i
$50$	10.7160	−	1.53700i	1.51548	−	0.217365i
$51$	−0.540624	+	5.12612i	−0.0757026	+	0.717800i
$52$	0.712637	−	0.208721i	0.0988249	−	0.0289444i
$53$	−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	$0.421641\pi$
$54$	−2.52549	−	6.90086i	−0.343676	−	0.939088i
$55$	18.8345	+	10.8741i	2.53965	+	1.46627i
$56$	9.01632	+	0.870260i	1.20486	+	0.116293i
$57$	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	−0.756467	−	0.654032i	$-0.773076\pi$
$59$	1.44539	−	2.50350i	0.188174	−	0.325927i	0.944642	+	0.328104i	$0.106410\pi$
$60$	−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	$0.593899\pi$
$62$	7.77025	−	1.27404i	0.986823	−	0.161803i
$63$	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	$-0.776124\pi$
$67$	−4.77967	+	2.75954i	−0.583930	+	0.337132i	0.178764	+	0.983892i	$0.442790\pi$
$68$	−4.11026	+	4.30483i	−0.498442	+	0.522038i
$69$	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	0.699926	−	0.714215i	$-0.253216\pi$
$71$	−2.26297	−	3.91958i	−0.268565	−	0.465169i	−0.968492	+	0.249047i	$0.919883\pi$
$72$	2.55920	−	8.09015i	0.301604	−	0.953433i
$73$	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	$0.760767\pi$
$74$	1.16160	−	0.166609i	0.135034	−	0.0193679i
$75$	13.1856	+	1.39061i	1.52254	+	0.160574i
$76$	5.57845	−	5.84252i	0.639892	−	0.670184i
$77$		−	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	$-0.419794\pi$
$79$	−4.13036	−	2.38466i	−0.464701	−	0.268296i	−0.714019	+	0.700126i	$0.753127\pi$
$80$	−14.2143	+	0.657685i	−1.58921	+	0.0735314i
$81$	−0.927992	−	8.95203i	−0.103110	−	0.994670i
$82$	4.81560	+	1.92978i	0.531794	+	0.213109i
$83$	0.118745	+	0.205672i	0.0130339	+	0.0225754i	0.872469	−	0.488670i	$-0.162518\pi$
$83$	0.118745	+	0.205672i	0.0130339	+	0.0225754i	−0.859435	+	0.511245i	$0.829184\pi$
$84$	10.4450	+	3.73898i	1.13964	+	0.407956i
$85$	10.5867			1.14829
$86$	0.398834	+	2.78068i	0.0430074	+	0.299849i
$87$	15.5751	−	6.92784i	1.66983	−	0.742742i
$88$	−14.0752	−	10.0446i	−1.50042	−	1.07076i
$89$			14.4700i			1.53382i	0.641754	+	0.766911i	$0.278207\pi$
$89$			14.4700i			1.53382i	−0.641754	+	0.766911i	$0.721793\pi$
$90$	−13.5511	+	6.64493i	−1.42842	+	0.700437i
$91$			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
$96$	8.04646	−	5.59056i	0.821239	−	0.570585i
$97$	11.8456			1.20274			0.601369	−	0.798971i	$-0.294622\pi$
$97$	11.8456			1.20274			0.601369	+	0.798971i	$0.294622\pi$
$98$	−1.71306	+	4.27481i	−0.173046	+	0.431821i
$99$	−17.9372	−	3.82603i	−1.80275	−	0.384531i
$100$	11.0731	+	10.5726i	1.10731	+	1.05726i
$101$			12.3690i			1.23076i	0.788231	+	0.615379i	$0.210997\pi$
$101$			12.3690i			1.23076i	−0.788231	+	0.615379i	$0.789003\pi$
$102$	−6.17238	+	3.87821i	−0.611156	+	0.384000i
$103$	0.753274	−	0.434903i	0.0742222	−	0.0428522i	−0.462430	−	0.886656i	$-0.653022\pi$
$103$	0.753274	−	0.434903i	0.0742222	−	0.0428522i	0.536652	+	0.843804i	$0.319689\pi$
$104$	0.854810	+	0.610026i	0.0838210	+	0.0598180i
$105$	−8.01962	−	18.0297i	−0.782635	−	1.75951i
$106$	−5.23486	−	2.09779i	−0.508455	−	0.203756i
$107$	0.888203	−	1.53841i	0.0858658	−	0.148724i	−0.819894	−	0.572515i	$-0.805968\pi$
$107$	0.888203	−	1.53841i	0.0858658	−	0.148724i	0.905760	+	0.423791i	$0.139301\pi$
$108$	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	$0.787843\pi$
$110$	4.36675	+	30.4451i	0.416353	+	2.90282i
$111$	1.42930	+	0.150741i	0.135663	+	0.0143077i
$112$	6.91105	+	10.7861i	0.653033	+	1.01919i
$113$	−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	$0.597237\pi$
$114$	8.37715	−	5.26351i	0.784592	−	0.492973i
$115$	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
$118$	4.04678	−	0.580431i	0.372536	−	0.0534330i
$119$	−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
$124$	8.20654	+	7.52680i	0.736969	+	0.675927i
$125$		−	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	$-0.514462\pi$
$127$	−10.5173	−	6.07215i	−0.933257	−	0.538816i	−0.887840	+	0.460152i	$0.847795\pi$
$128$	11.2996	+	0.565294i	0.998751	+	0.0499654i
$129$	−0.360848	+	3.42150i	−0.0317709	+	0.301246i
$130$	−0.265200	−	1.84898i	−0.0232596	−	0.162166i
$131$	−1.50511	+	2.60693i	−0.131502	+	0.227769i	−0.924256	−	0.381774i	$-0.875313\pi$
$131$	−1.50511	+	2.60693i	−0.131502	+	0.227769i	0.792754	+	0.609542i	$0.208647\pi$
$132$	−13.6989	−	16.1508i	−1.19233	−	1.40575i
$133$	6.46758	+	11.2022i	0.560811	+	0.971352i
$134$	−7.24508	−	2.90336i	−0.625880	−	0.250812i
$135$	−18.0848	+	3.82384i	−1.55649	+	0.329104i
$136$	−8.37840	−	0.808688i	−0.718442	−	0.0693444i
$137$	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	$0.255615\pi$
$138$	−3.03579	+	5.74376i	−0.258424	+	0.488941i
$139$		−	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
$141$	−0.282555	−	0.635239i	−0.0237955	−	0.0534968i
$142$	2.38091	−	5.94134i	0.199801	−	0.498586i
$143$	1.13494	−	1.96578i	0.0949086	−	0.164387i
$144$	11.2321	−	4.22373i	0.936009	−	0.351977i
$145$	−17.5054	−	30.3202i	−1.45374	−	2.51796i
$146$	−2.03161	+	5.06972i	−0.168138	+	0.419573i
$147$	−3.31690	+	4.56191i	−0.273574	+	0.376260i
$148$	1.20030	+	1.14605i	0.0986644	+	0.0942048i
$149$	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	$0.409031\pi$
$150$	9.97568	+	15.8768i	0.814511	+	1.29634i
$151$		−	10.4211i		−	0.848059i	−0.905648	−	0.424030i	$-0.860615\pi$
$151$		−	10.4211i		−	0.848059i	0.905648	−	0.424030i	$-0.139385\pi$
$152$	11.3712	+	1.09755i	0.922324	+	0.0890233i
$153$	−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	$0.442389\pi$
$158$	−0.957616	−	6.67652i	−0.0761838	−	0.531155i
$159$	−5.58644	−	4.06183i	−0.443034	−	0.322124i
$160$	−13.1522	−	15.2308i	−1.03977	−	1.20410i
$161$	−7.35604	−	4.24701i	−0.579737	−	0.334712i
$162$	9.14326	−	8.85443i	0.718362	−	0.695669i
$163$			22.9981i			1.80135i	0.434497	+	0.900673i	$0.356926\pi$
$163$			22.9981i			1.80135i	−0.434497	+	0.900673i	$0.643074\pi$
$164$	2.06221	+	7.04098i	0.161031	+	0.549808i
$165$	−3.95084	+	37.4613i	−0.307573	+	2.91636i
$166$	−0.124933	+	0.311760i	−0.00969669	+	0.0241972i
$167$	−11.2744	+	19.5278i	−0.872440	+	1.51111i	−0.0129750	+	0.999916i	$0.504130\pi$
$167$	−11.2744	+	19.5278i	−0.872440	+	1.51111i	−0.859465	+	0.511195i	$0.829203\pi$
$168$	4.96957	+	14.8814i	0.383411	+	1.14813i
$169$	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
$172$	−2.74345	+	2.87332i	−0.209186	+	0.219089i
$173$	−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	$0.425891\pi$
$174$	21.3134	+	11.2649i	1.61576	+	0.853991i
$175$	−21.2310	+	12.2577i	−1.60491	+	0.926595i
$176$	−1.13027	−	24.4281i	−0.0851973	−	1.84134i
$177$	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	$-0.572946\pi$
$179$	9.76408	−	16.9119i	0.729802	−	1.26405i	0.956967	−	0.290198i	$-0.0937210\pi$
$180$	−19.2302	−	9.26160i	−1.43333	−	0.690319i
$181$	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
$186$	7.48591	+	11.4001i	0.548893	+	0.835892i
$187$			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	0.997643	−	0.0686243i	$-0.0218610\pi$
$191$	6.07250	+	10.5179i	0.439391	+	0.761047i	−0.558252	+	0.829672i	$0.688528\pi$
$192$	13.2476	+	4.06202i	0.956066	+	0.293151i
$193$	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
$196$	−6.25028	+	1.83062i	−0.446448	+	0.130758i
$197$	−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	$0.412677\pi$
$198$	−11.4197	−	23.2884i	−0.811563	−	1.65504i
$199$	−6.67806	+	3.85558i	−0.473395	+	0.273315i	−0.717660	−	0.696394i	$-0.754787\pi$
$199$	−6.67806	+	3.85558i	−0.473395	+	0.273315i	0.244265	+	0.969709i	$0.421453\pi$
$200$	−2.08014	+	21.5512i	−0.147088	+	1.52390i
$201$	−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
$204$	−9.70596	−	3.47444i	−0.679553	−	0.243260i
$205$	6.52491	−	11.3015i	0.455719	−	0.789329i
$206$	1.14182	+	0.457568i	0.0795544	+	0.0318803i
$207$	−5.32833	+	5.90924i	−0.370345	+	0.410720i
$208$	0.0686432	+	1.48356i	0.00475955	+	0.102866i
$209$		−	24.6927i		−	1.70803i
$210$	13.0402	−	24.6722i	0.899859	−	1.70255i
$211$	−2.96435	−	1.71147i	−0.204074	−	0.117822i	0.394480	−	0.918904i	$-0.370925\pi$
$211$	−2.96435	−	1.71147i	−0.204074	−	0.117822i	−0.598554	+	0.801082i	$0.704258\pi$
$212$	−2.24175	−	7.65400i	−0.153964	−	0.525679i
$213$	4.61000	−	6.34037i	0.315872	−	0.434435i
$214$	2.48677	−	0.356678i	0.169992	−	0.0243820i
$215$	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
$220$	−30.0375	+	31.4594i	−2.02512	+	2.12099i
$221$		−	1.10494i		−	0.0743265i
$222$	1.08135	+	1.72102i	0.0725754	+	0.115508i
$223$	−6.79973	−	3.92583i	−0.455344	−	0.262893i	0.254741	−	0.967009i	$-0.418010\pi$
$223$	−6.79973	−	3.92583i	−0.455344	−	0.262893i	−0.710084	+	0.704117i	$0.751343\pi$
$224$	−5.95448	+	17.1099i	−0.397850	+	1.14321i
$225$	7.08093	+	21.8459i	0.472062	+	1.45639i
$226$	−20.5776	−	8.24616i	−1.36880	−	0.548527i
$227$	−11.0974	−	19.2213i	−0.736563	−	1.27577i	−0.954034	−	0.299698i	$-0.903114\pi$
$227$	−11.0974	−	19.2213i	−0.736563	−	1.27577i	0.217471	−	0.976067i	$-0.430219\pi$
$228$	13.1729	+	4.71552i	0.872399	+	0.312293i
$229$	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	$0.0296355\pi$
$230$	12.3857	+	4.96339i	0.816690	+	0.327277i
$231$	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	$-0.104457\pi$
$234$	0.693538	+	1.41435i	0.0453380	+	0.0924587i
$235$	−1.23663	+	0.713966i	−0.0806685	+	0.0465740i
$236$	4.18160	+	3.99260i	0.272199	+	0.259896i
$237$	0.866408	−	8.21515i	0.0562793	−	0.533632i
$238$	5.01373	−	12.5113i	0.324992	−	0.810989i
$239$	−0.172177	−	0.298220i	−0.0111372	−	0.0192902i	0.860403	−	0.509614i	$-0.170212\pi$
$239$	−0.172177	−	0.298220i	−0.0111372	−	0.0192902i	−0.871540	+	0.490324i	$0.836878\pi$
$240$	−11.0466	−	22.0320i	−0.713056	−	1.42216i
$241$	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	$0.163198\pi$
$242$	−36.9229	+	5.29586i	−2.37349	+	0.340431i
$243$	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
$246$	0.335829	+	8.97939i	0.0214116	+	0.572505i
$247$			1.49963i			0.0954191i
$248$	−1.19827	+	15.7024i	−0.0760903	+	0.997101i
$249$	−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	−0.959563	−	0.281493i	$-0.909170\pi$
$251$	−3.73896	+	6.47607i	−0.236001	+	0.408766i	0.723562	+	0.690259i	$0.242504\pi$
$252$	1.43530	+	19.1617i	0.0904155	+	1.20707i
$253$	8.10737	+	14.0424i	0.509706	+	0.882836i
$254$	−2.43841	−	17.0006i	−0.152999	−	1.06672i
$255$	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	$0.603484\pi$
$258$	−4.11984	+	2.58857i	−0.256490	+	0.161157i
$259$	−2.30141	+	1.32872i	−0.143002	+	0.0825625i
$260$	1.82423	−	1.91058i	0.113134	−	0.118489i
$261$	21.9274	+	19.7719i	1.35727	+	1.22385i
$262$	−4.21398	+	0.604412i	−0.260340	+	0.0373407i
$263$	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
$266$	−6.80464	+	16.9804i	−0.417219	+	1.04113i
$267$	−22.8997	+	10.1858i	−1.40144	+	0.623362i
$268$	−3.10259	−	10.5932i	−0.189521	−	0.647081i
$269$	−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	$0.422507\pi$
$270$	−20.0550	−	16.7680i	−1.22051	−	1.02047i
$271$		−	17.0366i		−	1.03490i	−0.855714	−	0.517449i	$-0.826882\pi$
$271$		−	17.0366i		−	1.03490i	0.855714	−	0.517449i	$-0.173118\pi$
$272$	−6.42208	−	10.0230i	−0.389396	−	0.607732i
$273$	−1.88177	+	0.837016i	−0.113890	+	0.0506585i
$274$	7.42875	+	2.97696i	0.448787	+	0.179845i
$275$	46.7989			2.82208
$276$	−9.03951	+	1.64343i	−0.544115	+	0.0989231i
$277$	−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	$-0.207239\pi$
$282$	0.459446	−	0.869277i	0.0273596	−	0.0517647i
$283$			19.1215i			1.13665i	0.822803	+	0.568327i	$0.192409\pi$
$283$			19.1215i			1.13665i	−0.822803	+	0.568327i	$0.807591\pi$
$284$	8.68695	−	2.54429i	0.515476	−	0.150976i
$285$	−10.1142	−	22.7386i	−0.599111	−	1.34692i
$286$	3.17758	−	0.455762i	0.187894	−	0.0269498i
$287$	−11.7482			−0.693476
$288$	14.5115	+	8.79866i	0.855098	+	0.518466i
$289$	−4.07177	−	7.05252i	−0.239516	−	0.414854i
$290$	18.4177	−	45.9597i	1.08152	−	2.69885i
$291$	8.33841	+	18.7464i	0.488806	+	1.09893i
$292$	−7.41253	+	2.17103i	−0.433786	+	0.127050i
$293$	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	$0.621055\pi$
$294$	−7.97100	+	0.298115i	−0.464878	+	0.0173864i
$295$		−	10.2836i		−	0.598735i
$296$	−0.225484	+	2.33612i	−0.0131060	+	0.135785i
$297$	−6.57149	−	31.0799i	−0.381317	−	1.80344i
$298$	3.54825	+	24.7385i	0.205545	+	1.43306i
$299$	−0.492374	−	0.852817i	−0.0284747	−	0.0493197i
$300$	−8.93710	+	24.9660i	−0.515984	+	1.44141i
$301$	−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
$304$	8.71606	+	13.6032i	0.499900	+	0.780197i
$305$	−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	$-0.225272\pi$
$307$	10.1059	+	5.83464i	0.576774	+	0.333001i	−0.183076	+	0.983099i	$0.558606\pi$
$308$	38.0480	+	9.25783i	2.16799	+	0.527514i
$309$	1.21851	+	0.885961i	0.0693184	+	0.0504005i
$310$	21.6723	−	17.7459i	1.23090	−	1.00790i
$311$	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	−0.574168	−	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
$316$	6.58713	−	6.89896i	0.370555	−	0.388097i
$317$	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	$0.524139\pi$
$318$	−0.365067	−	9.76117i	−0.0204719	−	0.547379i
$319$	52.1070	−	30.0840i	2.91743	−	1.68438i
$320$	5.44305	−	27.9336i	0.304276	−	1.56154i
$321$	3.05986	+	0.322707i	0.170785	+	0.0180117i
$322$	−1.70548	−	11.8907i	−0.0950429	−	0.662642i
$323$	−6.00999	−	10.4096i	−0.334405	−	0.579207i
$324$	17.8353	+	2.42954i	0.990849	+	0.134974i
$325$	−2.84217			−0.157655
$326$	−25.5726	+	20.0964i	−1.41633	+	1.11304i
$327$	−11.5527	−	25.9727i	−0.638865	−	1.43629i
$328$	−6.02717	+	8.44568i	−0.332795	+	0.466335i
$329$	1.11328	+	0.642755i	0.0613774	+	0.0354362i
$330$	−45.1073	+	28.3417i	−2.48307	+	1.56016i
$331$	3.78430	−	2.18487i	0.208004	−	0.120091i	−0.392380	−	0.919803i	$-0.628348\pi$
$331$	3.78430	−	2.18487i	0.208004	−	0.120091i	0.600383	+	0.799712i	$0.295015\pi$
$332$	−0.455830	+	0.133506i	−0.0250169	+	0.00732710i
$333$	0.767563	+	2.36806i	0.0420622	+	0.129769i
$334$	−31.5658	+	4.52750i	−1.72720	+	0.247734i
$335$	−9.81674	+	17.0031i	−0.536346	+	0.928978i
$336$	−12.2048	+	18.5297i	−0.665826	+	1.01088i
$337$	2.68650			0.146343			0.0731714	−	0.997319i	$-0.476688\pi$
$337$	2.68650			0.146343			0.0731714	+	0.997319i	$0.476688\pi$
$338$	18.0056	−	2.58254i	0.979373	−	0.140472i
$339$	−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
$344$	−5.59229	−	0.539771i	−0.301516	−	0.0291025i
$345$	13.2176	+	9.61032i	0.711609	+	0.517402i
$346$	−9.90045	−	3.96746i	−0.532252	−	0.213292i
$347$	5.40014	−	9.35333i	0.289895	−	0.502113i	−0.683889	−	0.729586i	$-0.739713\pi$
$347$	5.40014	−	9.35333i	0.289895	−	0.502113i	0.973784	+	0.227473i	$0.0730463\pi$
$348$	6.09829	+	33.5429i	0.326903	+	1.79809i
$349$	−8.91825			−0.477383			−0.238692	−	0.971095i	$-0.576719\pi$
$349$	−8.91825			−0.477383			−0.238692	+	0.971095i	$0.576719\pi$
$350$	−32.1821	−	12.8965i	−1.72021	−	0.689348i
$351$	0.399098	+	1.88753i	0.0213023	+	0.100749i
$352$	26.1750	−	22.6028i	1.39513	−	1.20473i
$353$	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	$0.595079\pi$
$354$	3.76719	+	5.99568i	0.200224	+	0.318667i
$355$	−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
$358$	27.3372	−	3.92099i	1.44482	−	0.207231i
$359$	−2.20791	−	3.82420i	−0.116529	−	0.201834i	0.801861	−	0.597511i	$-0.203843\pi$
$359$	−2.20791	−	3.82420i	−0.116529	−	0.201834i	−0.918390	+	0.395677i	$0.870510\pi$
$360$	−6.50553	−	29.4760i	−0.342872	−	1.55352i
$361$	−1.34323	−	2.32654i	−0.0706963	−	0.122450i
$362$	−11.8619	+	29.6004i	−0.623448	+	1.55576i
$363$	−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
$366$	5.19809	−	9.83485i	0.271708	−	0.514076i
$367$	8.33445	−	4.81190i	0.435055	−	0.251179i	−0.266443	−	0.963851i	$-0.585848\pi$
$367$	8.33445	−	4.81190i	0.435055	−	0.251179i	0.701498	+	0.712672i	$0.252515\pi$
$368$	−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
$372$	−6.13482	+	18.2856i	−0.318076	+	0.948065i
$373$	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
$378$	−4.04576	+	23.1836i	−0.208092	+	1.19243i
$379$	−20.3811	−	11.7671i	−1.04691	−	0.604433i	−0.125127	−	0.992141i	$-0.539934\pi$
$379$	−20.3811	−	11.7671i	−1.04691	−	0.604433i	−0.921782	+	0.387708i	$0.873267\pi$
$380$	6.79393	−	27.9218i	0.348521	−	1.43236i
$381$	2.20617	−	20.9185i	0.113025	−	1.07169i
$382$	−6.38897	+	15.9431i	−0.326888	+	0.815721i
$383$	6.54906	+	11.3433i	0.334641	+	0.579616i	0.983416	−	0.181365i	$-0.0580516\pi$
$383$	6.54906	+	11.3433i	0.334641	+	0.579616i	−0.648775	+	0.760981i	$0.724718\pi$
$384$	7.05944	+	18.2802i	0.360250	+	0.932856i
$385$	−34.8251	−	60.3188i	−1.77485	−	3.07413i
$386$	0.449239	−	0.0644345i	0.0228657	−	0.00327963i
$387$	−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	$0.638897\pi$
$390$	2.73944	−	1.72124i	0.138717	−	0.0871583i
$391$	6.83559	+	3.94653i	0.345691	+	0.199585i
$392$	−7.49722	−	5.35031i	−0.378667	−	0.270232i
$393$	−5.18511	−	0.546846i	−0.261554	−	0.0275847i
$394$	−9.09059	−	3.64292i	−0.457977	−	0.183528i
$395$	−16.9663			−0.853666
$396$	15.9166	−	33.0482i	0.799839	−	1.66074i
$397$	−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	$0.886986\pi$
$398$	−10.1227	−	4.05652i	−0.507404	−	0.203335i
$399$	−13.1754	+	18.1208i	−0.659596	+	0.907175i
$400$	−25.7815	+	16.5191i	−1.28907	+	0.825956i
$401$			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
$406$	−44.1228	+	6.32854i	−2.18978	+	0.314080i
$407$	5.07293			0.251456
$408$	−4.61797	−	13.8286i	−0.228623	−	0.684616i
$409$	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	$-0.0376768\pi$
$410$	18.2683	−	2.62023i	0.902206	−	0.129404i
$411$	7.92767	+	5.76411i	0.391043	+	0.284323i
$412$	0.488967	+	1.66948i	0.0240897	+	0.0822493i
$413$	−8.01761	+	4.62897i	−0.394521	+	0.227777i
$414$	−11.2268	−	0.761147i	−0.551767	−	0.0374083i
$415$	0.731652	+	0.422419i	0.0359154	+	0.0207358i
$416$	−1.58965	+	1.37271i	−0.0779392	+	0.0673025i
$417$	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	$-0.279811\pi$
$419$	26.1142			1.27576			0.637880	+	0.770135i	$0.279811\pi$
$420$	38.8291	−	7.05934i	1.89466	−	0.344461i
$421$	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	$0.817230\pi$
$422$	−0.687279	−	4.79172i	−0.0334562	−	0.233257i
$423$	0.806406	−	0.894321i	0.0392088	−	0.0434834i
$424$	6.55192	−	9.18099i	0.318189	−	0.445868i
$425$	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
$428$	2.56962	+	2.45347i	0.124207	+	0.118593i
$429$	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	$-0.632370\pi$
$431$	12.2535	−	21.2237i	0.590231	−	1.02231i	0.994201	−	0.107538i	$-0.0342967\pi$
$432$	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	$0.340176\pi$
$434$	−23.5909	−	8.90882i	−1.13240	−	0.427637i
$435$	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	$-0.569565\pi$
$439$	10.8997	−	6.29294i	0.520214	−	0.300346i	0.737022	+	0.675869i	$0.236231\pi$
$440$	−61.2287	−	5.90983i	−2.91897	−	0.281740i
$441$	−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	0.945615	−	0.325288i	$-0.105461\pi$
$443$	4.02219	+	6.96664i	0.191100	+	0.330995i	−0.754515	+	0.656283i	$0.772128\pi$
$444$	−0.968769	+	2.70628i	−0.0459757	+	0.128435i
$445$	25.7377	+	44.5790i	1.22008	+	2.11325i
$446$	−1.57651	−	10.9914i	−0.0746497	−	0.520460i
$447$	−3.21030	+	30.4396i	−0.151842	+	1.43974i
$448$	−24.2285	+	8.33011i	−1.14469	+	0.393561i
$449$		−	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
$452$	−8.81203	−	30.0869i	−0.414483	−	1.41517i
$453$	16.4920	−	7.33569i	0.774864	−	0.344661i
$454$	11.6758	−	29.1359i	0.547972	−	1.36742i
$455$	2.11499	+	3.66326i	0.0991520	+	0.171736i
$456$	6.26751	+	18.7681i	0.293503	+	0.878899i
$457$	−27.0822			−1.26685			−0.633426	−	0.773803i	$-0.718352\pi$
$457$	−27.0822			−1.26685			−0.633426	+	0.773803i	$0.718352\pi$
$458$	17.6812	−	2.53602i	0.826188	−	0.118500i
$459$	−10.3349	−	11.5028i	−0.482392	−	0.536904i
$460$	5.30399	+	18.1094i	0.247300	+	0.844355i
$461$		−	21.1539i		−	0.985237i	−0.870245	−	0.492619i	$-0.836040\pi$
$461$		−	21.1539i		−	0.985237i	0.870245	−	0.492619i	$-0.163960\pi$
$462$	42.4007	+	22.4104i	1.97266	+	1.04262i
$463$			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
$465$	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	$-0.486110\pi$
$467$	1.88534			0.0872431			0.0436216	+	0.999048i	$0.486110\pi$
$468$	−0.966642	+	2.00707i	−0.0446830	+	0.0927770i
$469$	17.6752			0.816167
$470$	−1.87449	−	0.751175i	−0.0864638	−	0.0346491i
$471$	3.17532	+	7.13874i	0.146311	+	0.328936i
$472$	−0.785538	+	8.13856i	−0.0361573	+	0.374608i
$473$			12.1437i			0.558369i
$474$	9.89189	−	6.21525i	0.454350	−	0.285476i
$475$	−26.7760	+	15.4591i	−1.22857	+	0.709314i
$476$	18.2931	−	5.35778i	0.838461	−	0.245574i
$477$	2.49565	−	11.7001i	0.114268	−	0.535711i
$478$	0.181150	−	0.452045i	0.00828562	−	0.0206761i
$479$	−13.9198	+	24.1097i	−0.636010	+	1.10160i	0.350290	+	0.936641i	$0.386083\pi$
$479$	−13.9198	+	24.1097i	−0.636010	+	1.10160i	−0.986300	+	0.164960i	$0.947250\pi$
$480$	14.8455	−	31.5354i	0.677601	−	1.43939i
$481$	−0.308088			−0.0140476
$482$	0.473670	−	0.0679387i	0.0215751	−	0.00309452i
$483$	1.54305	−	14.6309i	0.0702111	−	0.665731i
$484$	−38.1530	−	36.4285i	−1.73423	−	1.65584i
$485$	36.4937	−	21.0696i	1.65709	−	0.956723i
$486$	20.4488	+	8.23689i	0.927577	+	0.373633i
$487$	−13.1436	+	7.58848i	−0.595595	+	0.343867i	−0.767307	−	0.641280i	$-0.778404\pi$
$487$	−13.1436	+	7.58848i	−0.595595	+	0.343867i	0.171712	+	0.985147i	$0.445070\pi$
$488$	11.6896	−	5.32403i	0.529164	−	0.241007i
$489$	−36.3958	+	16.1889i	−1.64587	+	0.732087i
$490$	2.32597	+	16.2167i	0.105077	+	0.732597i
$491$	15.8753	+	27.4968i	0.716440	+	1.24091i	0.962401	+	0.271632i	$0.0875632\pi$
$491$	15.8753	+	27.4968i	0.716440	+	1.24091i	−0.245961	+	0.969280i	$0.579103\pi$
$492$	−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
$496$	−18.5072	+	12.3888i	−0.831000	+	0.556273i
$497$			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	$-0.0792115\pi$
$499$	27.7107	+	15.9988i	1.24050	+	0.716204i	0.271305	+	0.962493i	$0.412545\pi$
$500$	18.3537	+	4.46580i	0.820800	+	0.199717i
$501$	−38.8403	−	4.09628i	−1.73526	−	0.183008i
$502$	−10.4683	+	1.50147i	−0.467221	+	0.0670137i
$503$	4.57160	−	7.91825i	0.203838	−	0.353057i	−0.745924	−	0.666031i	$-0.767992\pi$
$503$	4.57160	−	7.91825i	0.203838	−	0.353057i	0.949762	+	0.312974i	$0.101325\pi$
$504$	−20.0526	+	18.3400i	−0.893212	+	0.816931i
$505$	22.0005	+	38.1061i	0.979011	+	1.69570i
$506$	−8.52989	+	21.2856i	−0.379200	+	0.946260i
$507$	22.1550	+	2.33657i	0.983939	+	0.103771i
$508$	16.7730	−	17.5670i	0.744183	−	0.779412i
$509$	−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	$0.585262\pi$
$510$	−12.1176	+	22.9266i	−0.536576	+	1.01521i
$511$		−	12.3682i		−	0.547136i
$512$	−6.44146	+	21.6912i	−0.284675	+	0.958624i
$513$	14.0265	+	15.6116i	0.619287	+	0.689269i
$514$	−31.5849	−	12.6572i	−1.39315	−	0.558284i
$515$	1.54711	−	2.67968i	0.0681739	−	0.118081i
$516$	−6.47838	−	2.31907i	−0.285195	−	0.102091i
$517$	−1.22699	−	2.12521i	−0.0539631	−	0.0934668i
$518$	−3.48850	−	1.39796i	−0.153276	−	0.0614230i
$519$	−10.5654	−	7.68195i	−0.463769	−	0.337200i
$520$	3.71853	+	0.358914i	0.163068	+	0.0157394i
$521$	−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	$0.758475\pi$
$522$	−2.82439	+	41.6593i	−0.123620	+	1.82338i
$523$			9.02722i			0.394733i	0.980330	+	0.197366i	$0.0632389\pi$
$523$			9.02722i			0.394733i	−0.980330	+	0.197366i	$0.936761\pi$
$524$	−4.35437	−	4.15756i	−0.190222	−	0.181624i
$525$	−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
$530$	−19.8588	+	2.84835i	−0.862610	+	0.123725i
$531$	2.67403	+	8.24982i	0.116043	+	0.358012i
$532$	−24.8274	+	7.27159i	−1.07640	+	0.315263i
$533$	−1.17955	−	0.681011i	−0.0510918	−	0.0294979i
$534$	−31.3365	−	16.5625i	−1.35606	−	0.716730i
$535$		−	6.31935i		−	0.273209i
$536$	9.06788	−	12.7065i	0.391673	−	0.548839i
$537$	33.6372	+	3.54754i	1.45155	+	0.153088i
$538$	−11.9062	−	4.77124i	−0.513314	−	0.205703i
$539$	−9.95416	+	17.2411i	−0.428756	+	0.742627i
$540$	1.12041	−	36.9524i	0.0482149	−	1.59018i
$541$	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
$544$	5.53319	−	15.8994i	0.237234	−	0.681680i
$545$	−50.5612	+	29.1915i	−2.16580	+	1.25043i
$546$	−2.57506	−	1.36102i	−0.110203	−	0.0582462i
$547$	7.05376	−	4.07249i	0.301597	−	0.174127i	−0.341563	−	0.939859i	$-0.610956\pi$
$547$	7.05376	−	4.07249i	0.301597	−	0.174127i	0.643160	+	0.765732i	$0.277623\pi$
$548$	3.18125	+	10.8617i	0.135896	+	0.463990i
$549$	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
$552$	−9.72640	−	8.61536i	−0.413983	−	0.366694i
$553$	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	$-0.151692\pi$
$558$	−12.7717	+	19.8717i	−0.540671	+	0.841234i
$559$		−	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	0.987521	−	0.157486i	$-0.0503390\pi$
$563$	8.47962	+	14.6871i	0.357373	+	0.618989i	−0.630148	+	0.776475i	$0.717006\pi$
$564$	1.36807	−	0.248722i	0.0576060	−	0.0104731i
$565$	−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
$568$	10.4200	+	7.43614i	0.437215	+	0.312013i
$569$	−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	$0.452547\pi$
$570$	16.4460	−	31.1161i	0.688847	−	1.30331i
$571$	6.07695	−	3.50853i	0.254312	−	0.146827i	−0.367425	−	0.930053i	$-0.619760\pi$
$571$	6.07695	−	3.50853i	0.254312	−	0.146827i	0.621737	+	0.783226i	$0.286427\pi$
$572$	3.28345	+	3.13504i	0.137288	+	0.131083i
$573$	−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
$576$	2.89695	+	23.8245i	0.120706	+	0.992688i
$577$	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	$0.140734\pi$
$578$	4.28397	−	10.6903i	0.178190	−	0.444657i
$579$	0.552768	+	0.0582975i	0.0229723	+	0.00242276i
$580$	67.1986	−	19.6815i	2.79027	−	0.817231i
$581$		−	0.760575i		−	0.0315540i
$582$	−13.5586	+	25.6530i	−0.562020	+	1.06335i
$583$	−21.1132	−	12.1897i	−0.874420	−	0.504847i
$584$	−8.89136	−	6.34522i	−0.367927	−	0.262567i
$585$	3.76936	−	1.22177i	0.155844	−	0.0505139i
$586$	0.981603	+	6.84376i	0.0405496	+	0.282713i
$587$	−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
$592$	−2.79468	+	1.79065i	−0.114861	+	0.0735952i
$593$			25.8419i			1.06120i	0.847623	+	0.530599i	$0.178033\pi$
$593$			25.8419i			1.06120i	−0.847623	+	0.530599i	$0.821967\pi$
$594$	28.8167	−	34.4656i	1.18236	−	1.41414i
$595$	−29.3622	−	16.9523i	−1.20373	−	0.694975i
$596$	−24.4073	+	25.5627i	−0.999761	+	1.04709i
$597$	−10.8025	−	7.85439i	−0.442118	−	0.321459i
$598$	0.518034	−	1.29271i	0.0211840	−	0.0528628i
$599$	13.2101	+	22.8806i	0.539751	+	0.934876i	0.998917	+	0.0465254i	$0.0148148\pi$
$599$	13.2101	+	22.8806i	0.539751	+	0.934876i	−0.459166	+	0.888350i	$0.651852\pi$
$600$	−35.5704	+	11.8785i	−1.45215	+	0.484938i
$601$	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	$0.0366928\pi$
$602$	3.34649	−	8.35087i	0.136393	−	0.340356i
$603$	3.45400	−	16.1930i	0.140658	−	0.659430i
$604$	20.2514	+	4.92756i	0.824017	+	0.200499i
$605$			93.8280i			3.81465i
$606$	−26.7864	−	14.1576i	−1.08812	−	0.575114i
$607$	−38.5090	+	22.2332i	−1.56303	+	0.902417i	−0.566084	+	0.824348i	$0.691542\pi$
$607$	−38.5090	+	22.2332i	−1.56303	+	0.902417i	−0.996948	+	0.0780688i	$0.975125\pi$
$608$	−7.50966	+	21.5787i	−0.304557	+	0.875130i
$609$	−54.2910	−	5.72579i	−2.19998	−	0.232021i
$610$	−21.2077	−	8.49866i	−0.858673	−	0.344101i
$611$	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	−0.370760	−	0.928729i	$-0.620903\pi$
$613$	15.3238	−	26.5416i	0.618923	−	1.07201i	0.989683	−	0.143277i	$-0.0457639\pi$
$614$	2.34303	+	16.3357i	0.0945571	+	0.659255i
$615$	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	$0.564261\pi$
$618$	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	$-0.0668968\pi$
$620$	38.6704	+	8.59154i	1.55304	+	0.345044i
$621$	−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
$626$	20.9011	−	2.99786i	0.835378	−	0.119819i
$627$	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
$630$	48.2245	+	3.26950i	1.92131	+	0.130260i
$631$	22.1769	−	12.8038i	0.882847	−	0.509712i	0.0112513	−	0.999937i	$-0.496419\pi$
$631$	22.1769	−	12.8038i	0.882847	−	0.509712i	0.871596	+	0.490224i	$0.163085\pi$
$632$	13.4273	+	1.29601i	0.534109	+	0.0515525i
$633$	0.621819	−	5.89600i	0.0247151	−	0.234345i
$634$	3.09552	+	21.5820i	0.122939	+	0.857132i
$635$	−43.2018			−1.71441
$636$	10.5349	−	8.93553i	0.417735	−	0.354317i
$637$	0.604533	−	1.04708i	0.0239525	−	0.0414869i
$638$	78.9845	+	31.6519i	3.12702	+	1.25311i
$639$	13.2791	+	2.83246i	0.525313	+	0.112050i
$640$	35.8170	−	18.3569i	1.41579	−	0.725619i
$641$	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	$0.146223\pi$
$642$	2.31496	+	3.68438i	0.0913642	+	0.145411i
$643$			18.9282i			0.746454i	0.927740	+	0.373227i	$0.121749\pi$
$643$			18.9282i			0.746454i	−0.927740	+	0.373227i	$0.878251\pi$
$644$	11.7315	−	12.2868i	0.462285	−	0.484169i
$645$	4.97409	+	11.1827i	0.195855	+	0.440319i
$646$	6.32321	−	15.7790i	0.248783	−	0.620817i
$647$	11.1617			0.438812			0.219406	−	0.975634i	$-0.429588\pi$
$647$	11.1617			0.438812			0.219406	+	0.975634i	$0.429588\pi$
$648$	12.8835	+	21.9549i	0.506111	+	0.862468i
$649$	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	$-0.148635\pi$
$654$	18.7851	−	35.5416i	0.734555	−	1.38979i
$655$			10.7085i			0.418416i
$656$	−14.6578	+	0.678208i	−0.572293	+	0.0264796i
$657$	−11.3310	−	2.41692i	−0.442064	−	0.0942931i
$658$	0.258113	+	1.79957i	0.0100623	+	0.0701545i
$659$	44.2361			1.72319			0.861597	−	0.507592i	$-0.169464\pi$
$659$	44.2361			1.72319			0.861597	+	0.507592i	$0.169464\pi$
$660$	−70.9304	−	25.3910i	−2.76096	−	0.988343i
$661$	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	$0.606894\pi$
$662$	5.73628	+	2.29873i	0.222947	+	0.0893427i
$663$	1.74864	−	0.777796i	0.0679114	−	0.0302071i
$664$	−0.546769	−	0.390196i	−0.0212188	−	0.0151425i
$665$	39.8504	+	23.0076i	1.54533	+	0.892198i
$666$	−1.96243	+	2.92277i	−0.0760427	+	0.113255i
$667$		−	26.1028i		−	1.01070i
$668$	−32.6175	−	31.1432i	−1.26201	−	1.20497i
$669$	1.42635	−	13.5245i	0.0551460	−	0.522886i
$670$	−27.4847	+	3.94213i	−1.06182	+	0.152298i
$671$	−13.8820	−	24.0443i	−0.535908	−	0.928219i
$672$	−31.2690	+	2.62078i	−1.20623	+	0.101099i
$673$	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
$676$	18.6054	+	17.7645i	0.715594	+	0.683249i
$677$	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	$0.278569\pi$
$678$	−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
$682$	30.4973	+	37.2451i	1.16780	+	1.42619i
$683$	−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
$687$	21.7559	+	2.29448i	0.830040	+	0.0875399i
$688$	−4.28651	−	6.68998i	−0.163422	−	0.255053i
$689$	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	$-0.850449\pi$
$691$	−24.8514	+	14.3480i	−0.945391	+	0.545822i	−0.0537452	+	0.998555i	$0.517116\pi$
$692$	−4.23971	−	14.4756i	−0.161170	−	0.550281i
$693$	43.6222	+	39.3340i	1.65707	+	1.49417i
$694$	15.1192	−	2.16855i	0.573917	−	0.0823171i
$695$	−31.7125	−	54.9277i	−1.20292	−	2.08353i
$696$	−31.9690	+	36.0918i	−1.21178	+	1.36805i
$697$	10.9170			0.413512
$698$	−7.79304	−	9.91661i	−0.294971	−	0.375349i
$699$	15.5715	−	6.92625i	0.588970	−	0.261975i
$700$	−13.7815	−	47.0541i	−0.520891	−	1.77848i
$701$	−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	$0.770631\pi$
$702$	−1.75009	+	2.09316i	−0.0660528	+	0.0790011i
$703$	−2.90248	+	1.67575i	−0.109469	+	0.0632020i
$704$	48.0056	+	9.35420i	1.80928	+	0.352550i
$705$	−2.00038	−	1.45445i	−0.0753388	−	0.0547779i
$706$	1.68256	+	11.7308i	0.0633239	+	0.441496i
$707$	19.8062	−	34.3054i	0.744889	−	1.29019i
$708$	−3.37498	+	9.42811i	−0.126840	+	0.354330i
$709$	−6.66115			−0.250165			−0.125082	−	0.992146i	$-0.539920\pi$
$709$	−6.66115			−0.250165			−0.125082	+	0.992146i	$0.539920\pi$
$710$	−3.23276	−	22.5389i	−0.121323	−	0.845868i
$711$	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
$716$	28.2480	+	26.9712i	1.05568	+	1.00796i
$717$	0.350750	−	0.482405i	0.0130990	−	0.0180157i
$718$	2.32297	−	5.79677i	0.0866925	−	0.216334i
$719$	17.1882	−	29.7708i	0.641012	−	1.11026i	−0.344196	−	0.938898i	$-0.611848\pi$
$719$	17.1882	−	29.7708i	0.641012	−	1.11026i	0.985207	−	0.171367i	$-0.0548183\pi$
$720$	27.0909	−	32.9908i	1.00962	−	1.22949i
$721$	−2.78561			−0.103741
$722$	1.41323	−	3.52660i	0.0525951	−	0.131246i
$723$	0.582829	+	0.0614679i	0.0216757	+	0.00228602i
$724$	−43.2793	+	12.6759i	−1.60846	+	0.471096i
$725$	−65.2444	−	37.6689i	−2.42312	−	1.39899i
$726$	−34.3719	−	54.7047i	−1.27566	−	2.03028i
$727$	−22.4845	−	12.9814i	−0.833902	−	0.481454i	0.0212845	−	0.999773i	$-0.493224\pi$
$727$	−22.4845	−	12.9814i	−0.833902	−	0.481454i	−0.855187	+	0.518320i	$0.826558\pi$
$728$	−1.39399	−	3.06070i	−0.0516648	−	0.113437i
$729$	21.8095	+	15.9169i	0.807758	+	0.589514i
$730$	2.75849	+	19.2323i	0.102096	+	0.711819i
$731$	2.95568	+	5.11939i	0.109320	+	0.189348i
$732$	15.4781	−	2.81400i	0.572085	−	0.104008i
$733$	−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	$0.981087\pi$
$734$	12.6335	+	5.06267i	0.466310	+	0.186867i
$735$	−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
$738$	−13.9740	+	6.85228i	−0.514390	+	0.252236i
$739$	−8.30220	+	4.79328i	−0.305401	+	0.176324i	−0.644867	−	0.764295i	$-0.723087\pi$
$739$	−8.30220	+	4.79328i	−0.305401	+	0.176324i	0.339465	+	0.940619i	$0.389754\pi$
$740$	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	$-0.585074\pi$
$743$	−14.3976			−0.528195			−0.264098	+	0.964496i	$0.585074\pi$
$744$	−25.6934	+	9.15694i	−0.941965	+	0.335710i
$745$	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
$750$	20.4533	+	10.8103i	0.746848	+	0.394737i
$751$	1.29107	+	0.745397i	0.0471117	+	0.0271999i	0.523371	−	0.852105i	$-0.324674\pi$
$751$	1.29107	+	0.745397i	0.0471117	+	0.0271999i	−0.476259	+	0.879305i	$0.658008\pi$
$752$	1.42611	+	0.737674i	0.0520049	+	0.0269002i
$753$	−12.8807	−	1.35846i	−0.469399	−	0.0495050i
$754$	−4.79686	−	1.92227i	−0.174691	−	0.0700050i
$755$	−18.5359	−	32.1052i	−0.674592	−	1.16843i
$756$	−29.3142	+	15.7598i	−1.06615	+	0.573180i
$757$	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	$0.701164\pi$
$758$	−4.72533	−	32.9451i	−0.171632	−	1.19662i
$759$	−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	$-0.739315\pi$
$762$	25.1881	−	15.8261i	0.912467	−	0.573319i
$763$	45.5182	+	26.2800i	1.64787	+	0.951398i
$764$	−23.3108	+	6.82740i	−0.843354	+	0.247007i
$765$	−21.2684	+	23.5872i	−0.768962	+	0.852795i
$766$	−6.89036	+	17.1943i	−0.248959	+	0.621255i
$767$	−1.07331			−0.0387550
$768$	−14.1578	+	23.8235i	−0.510875	+	0.859655i
$769$	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	$0.0144899\pi$
$770$	36.6400	−	91.4319i	1.32041	−	3.29498i
$771$	−33.7062	−	24.5073i	−1.21390	−	0.882610i
$772$	0.464206	+	0.443224i	0.0167071	+	0.0159520i
$773$			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
$778$	0.690098	+	4.81138i	0.0247412	+	0.172496i
$779$	−14.8166			−0.530860
$780$	4.30773	+	1.54204i	0.154241	+	0.0552138i
$781$	13.8348	−	23.9626i	0.495048	−	0.857449i
$782$	1.58482	+	11.0494i	0.0566730	+	0.395126i
$783$	−15.8549	+	48.6193i	−0.566607	+	1.73751i
$784$	−0.602045	−	13.0118i	−0.0215016	−	0.464706i
$785$	13.8970	−	8.02346i	0.496007	−	0.286370i
$786$	−3.92284	−	6.24341i	−0.139923	−	0.222695i
$787$	17.3884	+	10.0392i	0.619829	+	0.357858i	0.776802	−	0.629745i	$-0.216840\pi$
$787$	17.3884	+	10.0392i	0.619829	+	0.357858i	−0.156974	+	0.987603i	$0.550174\pi$
$788$	−3.89290	−	13.2915i	−0.138679	−	0.473491i
$789$	6.03377	+	13.5651i	0.214808	+	0.482930i
$790$	−14.8256	−	18.8656i	−0.527473	−	0.671207i
$791$	50.2015			1.78496
$792$	50.6562	−	11.1801i	1.79999	−	0.397269i
$793$	0.843076	+	1.46025i	0.0299385	+	0.0518550i
$794$	−42.9474	+	6.15996i	−1.52415	+	0.218609i
$795$	−24.4353	−	2.57706i	−0.866632	−	0.0913990i
$796$	−4.33488	−	14.8006i	−0.153646	−	0.524592i
$797$	−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	$0.572675\pi$
$798$	−31.6624	+	1.18417i	−1.12084	+	0.0419193i
$799$	−1.03452	−	0.597280i	−0.0365986	−	0.0211302i
$800$	−40.8970	−	14.2327i	−1.44593	−	0.503202i
$801$	−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
$804$	14.5803	−	12.3668i	0.514208	−	0.436144i
$805$	−30.2164			−1.06499
$806$	−1.85216	−	2.26196i	−0.0652394	−	0.0796742i
$807$	−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	$0.406870\pi$
$810$	12.4191	−	43.5415i	0.436362	−	1.52989i
$811$	−22.0053	+	12.7048i	−0.772712	+	0.446126i	−0.833841	−	0.552004i	$-0.813863\pi$
$811$	−22.0053	+	12.7048i	−0.772712	+	0.446126i	0.0611290	+	0.998130i	$0.480530\pi$
$812$	−45.5928	−	43.5320i	−1.59999	−	1.52767i
$813$	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
$816$	11.3413	−	17.2187i	0.397025	−	0.602776i
$817$	−4.01146	−	6.94805i	−0.140343	−	0.243081i
$818$	33.9035	−	4.86279i	1.18541	−	0.170023i
$819$	−2.64925	−	2.38882i	−0.0925723	−	0.0834721i
$820$	18.8769	+	18.0237i	0.659210	+	0.629414i
$821$		−	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	$-0.217738\pi$
$823$	17.6508	+	10.1907i	0.615267	+	0.355225i	−0.159757	+	0.987156i	$0.551071\pi$
$824$	−1.42909	+	2.00254i	−0.0497848	+	0.0697619i
$825$	32.9429	+	74.0619i	1.14692	+	2.57850i
$826$	−12.1532	−	4.87021i	−0.422863	−	0.169456i
$827$	1.92701	+	3.33768i	0.0670087	+	0.116062i	0.897583	−	0.440845i	$-0.145321\pi$
$827$	1.92701	+	3.33768i	0.0670087	+	0.116062i	−0.830575	+	0.556907i	$0.811988\pi$
$828$	−8.96396	−	13.1487i	−0.311519	−	0.456949i
$829$	31.4599			1.09265			0.546323	−	0.837574i	$-0.316027\pi$
$829$	31.4599			1.09265			0.546323	+	0.837574i	$0.316027\pi$
$830$	0.169632	+	1.18268i	0.00588802	+	0.0410514i
$831$	−21.6348	−	48.6393i	−0.750504	−	1.68728i
$832$	−2.91546	−	0.568096i	−0.101075	−	0.0196952i
$833$			9.69104i			0.335775i
$834$	38.6110	+	20.4074i	1.33699	+	0.706650i
$835$			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	$-0.738478\pi$
$839$	−39.4541			−1.36211			−0.681053	+	0.732234i	$0.738478\pi$
$840$	41.7796	+	37.0071i	1.44153	+	1.27687i
$841$	−67.8597			−2.33999
$842$	−1.09168	+	2.72420i	−0.0376219	+	0.0938823i
$843$	32.1541	−	14.3022i	1.10745	−	0.492594i
$844$	4.72757	−	4.95137i	0.162730	−	0.170433i
$845$		−	45.7555i		−	1.57404i
$846$	1.69910	+	0.115194i	0.0584162	+	0.00396046i
$847$	73.1528	−	42.2348i	2.51356	−	1.45121i
$848$	15.9340	−	0.737255i	0.547176	−	0.0253174i
$849$	−30.2609	+	13.4601i	−1.03855	+	0.461949i
$850$	29.9052	+	11.9841i	1.02574	+	0.411050i
$851$	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	$0.704233\pi$
$854$	2.92024	+	20.3600i	0.0999287	+	0.696705i
$855$	28.8655	−	32.0125i	0.987181	−	1.09480i
$856$	−0.482718	+	5.00119i	−0.0164990	+	0.170937i
$857$	−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	$0.503798\pi$
$858$	2.95805	+	4.70789i	0.100986	+	0.160725i
$859$	8.94147	−	5.16236i	0.305079	−	0.176138i	−0.339643	−	0.940554i	$-0.610306\pi$
$859$	8.94147	−	5.16236i	0.305079	−	0.176138i	0.644722	+	0.764417i	$0.276973\pi$
$860$	−3.34122	+	13.7318i	−0.113935	+	0.468251i
$861$	−8.26987	−	18.5923i	−0.281836	−	0.633623i
$862$	34.3071	−	4.92068i	1.16850	−	0.167599i
$863$	−6.01828	−	10.4240i	−0.204865	−	0.354836i	0.745225	−	0.666813i	$-0.232342\pi$
$863$	−6.01828	−	10.4240i	−0.204865	−	0.354836i	−0.950090	+	0.311977i	$0.899009\pi$
$864$	−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
$868$	−10.7083	−	34.0166i	−0.363464	−	1.15460i
$869$		−	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
$873$	−23.7976	+	26.3920i	−0.805426	+	0.893235i
$874$	−2.15092	−	14.9963i	−0.0727559	−	0.507256i
$875$	−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	−0.895440	−	0.445182i	$-0.853139\pi$
$877$	−24.6763	−	42.7406i	−0.833259	−	1.44325i	0.0621815	−	0.998065i	$-0.480194\pi$
$878$	16.5219	+	6.62090i	0.557586	+	0.223444i
$879$	−0.888111	+	8.42093i	−0.0299552	+	0.284031i
$880$	−46.9321	−	73.2472i	−1.58208	−	2.46916i
$881$	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	$0.165591\pi$
$882$	−6.08276	−	12.4047i	−0.204817	−	0.417688i
$883$			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
$885$	16.2744	−	7.23889i	0.547059	−	0.243333i
$886$	−4.23181	+	10.5601i	−0.142170	+	0.354774i
$887$	7.10309	−	12.3029i	0.238498	−	0.413091i	−0.721785	−	0.692117i	$-0.756678\pi$
$887$	7.10309	−	12.3029i	0.238498	−	0.413091i	0.960284	+	0.279026i	$0.0900115\pi$
$888$	−3.85578	+	1.28761i	−0.129391	+	0.0432095i
$889$	19.4464	+	33.6822i	0.652213	+	1.12967i
$890$	−27.0790	+	67.5733i	−0.907691	+	2.26506i
$891$	44.5598	−	32.2776i	1.49281	−	1.08134i
$892$	10.8443	−	11.3576i	0.363093	−	0.380282i
$893$	1.40405	+	0.810628i	0.0469847	+	0.0271266i
$894$	−36.6524	+	23.0293i	−1.22584	+	0.770216i
$895$		−	69.4690i		−	2.32209i
$896$	−30.4342	−	19.6617i	−1.01674	−	0.656850i
$897$	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
$902$	4.50301	+	31.3951i	0.149934	+	1.04534i
$903$	6.47960	−	8.91172i	0.215628	−	0.296564i
$904$	25.7547	−	36.0893i	0.856590	−	1.20031i
$905$	69.4675	+	40.1071i	2.30918	+	1.33320i
$906$	22.5681	+	11.9281i	0.749775	+	0.396285i
$907$		−	49.7055i		−	1.65044i	−0.564808	−	0.825222i	$-0.691050\pi$
$907$		−	49.7055i		−	1.65044i	0.564808	−	0.825222i	$-0.308950\pi$
$908$	42.6002	−	12.4770i	1.41374	−	0.414064i
$909$	−27.5581	−	24.8490i	−0.914044	−	0.824190i
$910$	−2.22521	+	5.55281i	−0.0737649	+	0.184074i
$911$	20.6984	−	35.8507i	0.685769	−	1.18779i	−0.287425	−	0.957803i	$-0.592799\pi$
$911$	20.6984	−	35.8507i	0.685769	−	1.18779i	0.973194	−	0.229984i	$-0.0738673\pi$
$912$	−15.3924	+	23.3693i	−0.509694	+	0.773835i
$913$	−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
$916$	18.2703	+	17.4445i	0.603667	+	0.576382i
$917$	8.34887	−	4.82022i	0.275704	−	0.159178i
$918$	3.75952	−	21.5433i	0.124083	−	0.711035i
$919$	31.9151	−	18.4262i	1.05278	−	0.607825i	0.129356	−	0.991598i	$-0.458709\pi$
$919$	31.9151	−	18.4262i	1.05278	−	0.607825i	0.923427	+	0.383774i	$0.125376\pi$
$920$	−15.5019	+	21.7223i	−0.511082	+	0.716162i
$921$	−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
$924$	12.1319	+	66.7300i	0.399110	+	2.19526i
$925$	−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	$0.999353\pi$
$930$	43.3396	+	21.8059i	1.42116	+	0.715045i
$931$		−	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
$936$	−3.07644	+	0.678988i	−0.100556	+	0.0221934i
$937$	−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
$940$	−0.802721	−	2.74073i	−0.0261819	−	0.0893927i
$941$	−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	$0.373127\pi$
$942$	−5.16320	+	9.76883i	−0.168226	+	0.318286i
$943$	8.42599	−	4.86475i	0.274388	−	0.158418i
$944$	−9.73606	+	6.23824i	−0.316882	+	0.203037i
$945$	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	−0.998826	−	0.0484463i	$-0.984573\pi$
$947$	−14.0775	+	24.3829i	−0.457457	+	0.792339i	0.541369	+	0.840785i	$0.317906\pi$
$948$	15.5548	+	5.56817i	0.505198	+	0.180846i
$949$	0.716948	−	1.24179i	0.0232731	−	0.0403102i
$950$	−40.5874	−	16.2648i	−1.31683	−	0.527699i
$951$	−2.80069	+	26.5557i	−0.0908185	+	0.861127i
$952$	21.9426	+	15.6591i	0.711163	+	0.507514i
$953$		−	6.04922i		−	0.195953i	−0.995189	−	0.0979767i	$-0.968763\pi$
$953$		−	6.04922i		−	0.195953i	0.995189	−	0.0979767i	$-0.0312370\pi$
$954$	15.1906	−	7.44886i	0.491815	−	0.241166i
$955$	37.4161	+	21.6022i	1.21076	+	0.699030i
$956$	0.660944	−	0.193581i	0.0213764	−	0.00626086i
$957$	84.2891	+	61.2856i	2.72468	+	1.98108i
$958$	−38.9722	+	5.58979i	−1.25913	+	0.180598i
$959$	−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
$964$	0.489451	+	0.467328i	0.0157642	+	0.0150516i
$965$		−	1.14160i		−	0.0367494i
$966$	17.6172	−	11.0692i	0.566823	−	0.356145i
$967$	25.9726	+	14.9953i	0.835222	+	0.482216i	0.855637	−	0.517576i	$-0.173166\pi$
$967$	25.9726	+	14.9953i	0.835222	+	0.482216i	−0.0204153	+	0.999792i	$0.506499\pi$
$968$	7.16727	−	74.2564i	0.230365	−	2.38669i
$969$	12.2432	−	16.8387i	0.393310	−	0.540939i
$970$	55.3175	+	22.1677i	1.77614	+	0.711761i
$971$	23.9852	+	41.5436i	0.769723	+	1.33320i	0.937713	+	0.347410i	$0.112939\pi$
$971$	23.9852	+	41.5436i	0.769723	+	1.33320i	−0.167991	+	0.985789i	$0.553728\pi$
$972$	8.70981	+	29.9356i	0.279367	+	0.960184i
$973$	−28.5495	+	49.4492i	−0.915255	+	1.58527i
$974$	−19.9233	−	7.98395i	−0.638383	−	0.255822i
$975$	−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	$-0.400074\pi$
$978$	−49.8048	−	26.3237i	−1.59258	−	0.841740i
$979$	−76.6116	+	44.2317i	−2.44852	+	1.41365i
$980$	−15.9996	+	16.7570i	−0.511089	+	0.535283i
$981$	32.9710	−	36.5656i	1.05268	−	1.16745i
$982$	−16.7026	+	41.6799i	−0.533001	+	1.33006i
$983$	−27.7308	−	48.0311i	−0.884475	−	1.53196i	−0.846314	−	0.532684i	$-0.821184\pi$
$983$	−27.7308	−	48.0311i	−0.884475	−	1.53196i	−0.0381603	−	0.999272i	$-0.512150\pi$
$984$	−17.6085	−	3.59322i	−0.561337	−	0.114548i
$985$	−12.3173	+	21.3342i	−0.392462	+	0.679765i
$986$	41.0010	−	5.88079i	1.30574	−	0.187283i
$987$	−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
$990$	−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	$0.961402\pi$
$992$	−29.9478	−	9.75335i	−0.950844	−	0.309669i
$993$	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	0.987847	−	0.155428i	$-0.0496755\pi$
$997$	11.3456	+	19.6512i	0.359319	+	0.622359i	−0.628528	+	0.777787i	$0.716342\pi$
$998$	6.42467	+	44.7930i	0.203369	+	1.41790i
$999$	−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.191.44	yes	120
3.2	odd	2	inner	372.2.p.a.191.17	✓	120
4.3	odd	2	inner	372.2.p.a.191.18	yes	120
12.11	even	2	inner	372.2.p.a.191.43	yes	120
31.25	even	3	inner	372.2.p.a.335.44	yes	120
93.56	odd	6	inner	372.2.p.a.335.17	yes	120
124.87	odd	6	inner	372.2.p.a.335.18	yes	120
372.335	even	6	inner	372.2.p.a.335.43	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.17	✓	120	3.2	odd	2	inner
372.2.p.a.191.18	yes	120	4.3	odd	2	inner
372.2.p.a.191.43	yes	120	12.11	even	2	inner
372.2.p.a.191.44	yes	120	1.1	even	1	trivial
372.2.p.a.335.17	yes	120	93.56	odd	6	inner
372.2.p.a.335.18	yes	120	124.87	odd	6	inner
372.2.p.a.335.43	yes	120	372.335	even	6	inner
372.2.p.a.335.44	yes	120	31.25	even	3	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} +(-1.14461 + 2.16561i) q^{6} +(-2.77350 - 1.60128i) q^{7} +(-2.57403 + 1.17234i) q^{8} +(-2.00898 + 2.22800i) q^{9} +(4.66988 + 1.87138i) q^{10} +(3.05678 + 5.29450i) q^{11} +(-3.40823 + 0.619636i) q^{12} +(-0.185643 - 0.321544i) q^{13} +(-0.643031 - 4.48323i) q^{14} +(4.98351 + 3.62345i) q^{15} +(-3.55284 - 1.83775i) q^{16} +(2.57727 + 1.48799i) q^{17} +(-4.23292 - 0.286981i) q^{18} +(-3.49788 - 2.01950i) q^{19} +(1.99980 + 6.82792i) q^{20} +(0.581786 - 5.51641i) q^{21} +(-3.21608 + 8.02546i) q^{22} +2.65226 q^{23} +(-3.66722 - 3.24831i) q^{24} +(3.82746 - 6.62936i) q^{25} +(0.195318 - 0.487400i) q^{26} +(-4.94011 - 1.61098i) q^{27} +(4.42320 - 4.63260i) 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} +(0.597536 + 4.16604i) q^{34} -11.3927 q^{35} +(-3.37975 - 4.95755i) q^{36} +(0.414892 - 0.718613i) q^{37} +(-0.810977 - 5.65415i) q^{38} +(0.378183 - 0.520134i) q^{39} +(-5.84478 + 8.19011i) q^{40} +(3.17691 - 1.83419i) q^{41} +(6.64233 - 4.17349i) q^{42} +(1.72024 + 0.993180i) q^{43} +(-11.7342 + 3.43678i) q^{44} +(-2.22630 + 10.4373i) q^{45} +(2.31762 + 2.94916i) q^{46} -0.401400 q^{47} +(0.407420 - 6.91621i) q^{48} +(1.62821 + 2.82014i) q^{49} +(10.7160 - 1.53700i) q^{50} +(-0.540624 + 5.12612i) q^{51} +(0.712637 - 0.208721i) q^{52} +(-3.45351 + 1.99388i) q^{53} +(-2.52549 - 6.90086i) q^{54} +(18.8345 + 10.8741i) q^{55} +(9.01632 + 0.870260i) q^{56} +(0.733736 - 6.95717i) q^{57} +(10.9435 - 8.60000i) q^{58} +(1.44539 - 2.50350i) q^{59} +(-9.39787 + 7.97114i) q^{60} -4.54137 q^{61} +(7.77025 - 1.27404i) 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} +(-4.11026 + 4.30483i) q^{68} +(1.86699 + 4.19735i) q^{69} +(-9.95531 - 12.6681i) q^{70} +(-2.26297 - 3.91958i) q^{71} +(2.55920 - 8.09015i) q^{72} +(1.93098 + 3.34456i) q^{73} +(1.16160 - 0.166609i) q^{74} +(13.1856 + 1.39061i) q^{75} +(5.57845 - 5.84252i) q^{76} -19.5791i q^{77} +(0.908828 - 0.0339901i) q^{78} +(-4.13036 - 2.38466i) q^{79} +(-14.2143 + 0.657685i) q^{80} +(-0.927992 - 8.95203i) q^{81} +(4.81560 + 1.92978i) q^{82} +(0.118745 + 0.205672i) q^{83} +(10.4450 + 3.73898i) q^{84} +10.5867 q^{85} +(0.398834 + 2.78068i) q^{86} +(15.5751 - 6.92784i) q^{87} +(-14.0752 - 10.0446i) q^{88} +14.4700i q^{89} +(-13.5511 + 6.64493i) 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} +(8.04646 - 5.59056i) q^{96} +11.8456 q^{97} +(-1.71306 + 4.27481i) 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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