LMFDB - Embedded newform 372.2.p.a.191.17

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			191.17
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.873830 - 1.11194i) q^{2} +(1.72250 - 0.181663i) q^{3} +(-0.472843 + 1.94330i) q^{4} +(-3.08078 + 1.77869i) q^{5} +(-1.70717 - 1.75658i) q^{6} +(-2.77350 - 1.60128i) q^{7} +(2.57403 - 1.17234i) q^{8} +(2.93400 - 0.625827i) q^{9} +(4.66988 + 1.87138i) q^{10} +(-3.05678 - 5.29450i) q^{11} +(-0.461446 + 3.43323i) 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} +(-3.25970 - 2.71558i) q^{18} +(-3.49788 - 2.01950i) q^{19} +(-1.99980 - 6.82792i) q^{20} +(-5.06825 - 2.25436i) q^{21} +(-3.21608 + 8.02546i) q^{22} -2.65226 q^{23} +(4.22079 - 2.48696i) 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} +(8.38382 + 2.37511i) 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} +(-0.171149 + 5.99756i) 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} +(1.92206 + 7.60554i) q^{42} +(1.72024 + 0.993180i) q^{43} +(11.7342 - 3.43678i) q^{44} +(-7.92584 + 7.14670i) q^{45} +(2.31762 + 2.94916i) q^{46} +0.401400 q^{47} +(-6.45361 - 2.52011i) q^{48} +(1.62821 + 2.82014i) q^{49} +(-10.7160 + 1.53700i) q^{50} +(-4.70966 - 2.09486i) q^{51} +(0.712637 - 0.208721i) q^{52} +(3.45351 - 1.99388i) q^{53} +(-6.10814 - 4.08541i) q^{54} +(18.8345 + 10.8741i) q^{55} +(-9.01632 - 0.870260i) q^{56} +(-6.39196 - 2.84315i) q^{57} +(10.9435 - 8.60000i) q^{58} +(-1.44539 + 2.50350i) q^{59} +(-4.68503 - 11.3978i) 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} +(-4.08177 + 14.4081i) q^{66} +(-4.77967 + 2.75954i) q^{67} +(4.11026 - 4.30483i) q^{68} +(-4.56851 + 0.481816i) q^{69} +(-9.95531 - 12.6681i) q^{70} +(2.26297 + 3.91958i) q^{71} +(6.81851 - 5.05054i) q^{72} +(1.93098 + 3.34456i) q^{73} +(-1.16160 + 0.166609i) q^{74} +(5.38849 - 12.1144i) q^{75} +(5.57845 - 5.84252i) q^{76} +19.5791i q^{77} +(-0.247893 + 0.875027i) q^{78} +(-4.13036 - 2.38466i) q^{79} +(14.2143 - 0.657685i) q^{80} +(8.21668 - 3.67235i) q^{81} +(4.81560 + 1.92978i) q^{82} +(-0.118745 - 0.205672i) q^{83} +(6.77739 - 8.78317i) q^{84} +10.5867 q^{85} +(-0.398834 - 2.78068i) q^{86} +(1.78788 + 16.9524i) q^{87} +(-14.0752 - 10.0446i) q^{88} -14.4700i q^{89} +(14.8726 + 2.56810i) q^{90} +1.18907i q^{91} +(1.25410 - 5.15414i) q^{92} +(3.74177 - 8.88815i) q^{93} +(-0.350756 - 0.446335i) q^{94} +14.3683 q^{95} +(2.83714 + 9.37820i) q^{96} +11.8456 q^{97} +(1.71306 - 4.27481i) q^{98} +(-12.2820 - 13.6210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

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

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

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
$3$	1.72250	−	0.181663i	0.994485	−	0.104883i
$3$	1.72250	−	0.181663i	0.994485	−	0.104883i
$4$	−0.472843	+	1.94330i	−0.236421	+	0.971651i
$5$	−3.08078	+	1.77869i	−1.37777	+	0.795454i	−0.991890	−	0.127097i	$-0.959434\pi$
$5$	−3.08078	+	1.77869i	−1.37777	+	0.795454i	−0.385876	+	0.922551i	$0.626101\pi$
$6$	−1.70717	−	1.75658i	−0.696949	−	0.717121i
$7$	−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
$9$	2.93400	−	0.625827i	0.977999	−	0.208609i
$10$	4.66988	+	1.87138i	1.47675	+	0.591784i
$11$	−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	$-0.539828\pi$
$12$	−0.461446	+	3.43323i	−0.133208	+	0.991088i
$13$	−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	0.153764	−	0.988108i	$-0.450861\pi$
$17$	−2.57727	−	1.48799i	−0.625081	−	0.360891i	−0.778844	+	0.627217i	$0.784194\pi$
$18$	−3.25970	−	2.71558i	−0.768319	−	0.640068i
$19$	−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
$21$	−5.06825	−	2.25436i	−1.10598	−	0.491942i
$22$	−3.21608	+	8.02546i	−0.685672	+	1.71103i
$23$	−2.65226			−0.553034			−0.276517	−	0.961009i	$-0.589180\pi$
$23$	−2.65226			−0.553034			−0.276517	+	0.961009i	$0.589180\pi$
$24$	4.22079	−	2.48696i	0.861565	−	0.507648i
$25$	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	$0.366852\pi$
$29$			9.84173i			1.82756i	−0.406205	+	0.913782i	$0.633148\pi$
$30$	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
$34$	0.597536	+	4.16604i	0.102477	+	0.714469i
$35$	11.3927			1.92572
$36$	−0.171149	+	5.99756i	−0.0285249	+	0.999593i
$37$	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	−0.727122	−	0.686508i	$-0.759143\pi$
$41$	−3.17691	+	1.83419i	−0.496150	+	0.286453i	0.230972	+	0.972960i	$0.425809\pi$
$42$	1.92206	+	7.60554i	0.296580	+	1.17356i
$43$	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
$45$	−7.92584	+	7.14670i	−1.18152	+	1.06537i
$46$	2.31762	+	2.94916i	0.341715	+	0.434831i
$47$	0.401400			0.0585503			0.0292751	−	0.999571i	$-0.490680\pi$
$47$	0.401400			0.0585503			0.0292751	+	0.999571i	$0.490680\pi$
$48$	−6.45361	−	2.52011i	−0.931498	−	0.363746i
$49$	1.62821	+	2.82014i	0.232601	+	0.402878i
$50$	−10.7160	+	1.53700i	−1.51548	+	0.217365i
$51$	−4.70966	−	2.09486i	−0.659484	−	0.293340i
$52$	0.712637	−	0.208721i	0.0988249	−	0.0289444i
$53$	3.45351	−	1.99388i	0.474376	−	0.273881i	−0.243694	−	0.969852i	$-0.578359\pi$
$53$	3.45351	−	1.99388i	0.474376	−	0.273881i	0.718070	+	0.695971i	$0.245026\pi$
$54$	−6.10814	−	4.08541i	−0.831213	−	0.555954i
$55$	18.8345	+	10.8741i	2.53965	+	1.46627i
$56$	−9.01632	−	0.870260i	−1.20486	−	0.116293i
$57$	−6.39196	−	2.84315i	−0.846635	−	0.376585i
$58$	10.9435	−	8.60000i	1.43695	−	1.12924i
$59$	−1.44539	+	2.50350i	−0.188174	+	0.325927i	−0.944642	−	0.328104i	$-0.893590\pi$
$59$	−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	$0.593899\pi$
$62$	−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
$66$	−4.08177	+	14.4081i	−0.502431	+	1.77351i
$67$	−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
$69$	−4.56851	+	0.481816i	−0.549984	+	0.0580039i
$70$	−9.95531	−	12.6681i	−1.18989	−	1.51413i
$71$	2.26297	+	3.91958i	0.268565	+	0.465169i	0.968492	−	0.249047i	$-0.0801172\pi$
$71$	2.26297	+	3.91958i	0.268565	+	0.465169i	−0.699926	+	0.714215i	$0.746784\pi$
$72$	6.81851	−	5.05054i	0.803569	−	0.595211i
$73$	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
$75$	5.38849	−	12.1144i	0.622209	−	1.39885i
$76$	5.57845	−	5.84252i	0.639892	−	0.670184i
$77$			19.5791i			2.23124i
$78$	−0.247893	+	0.875027i	−0.0280683	+	0.0990773i
$79$	−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
$81$	8.21668	−	3.67235i	0.912965	−	0.408039i
$82$	4.81560	+	1.92978i	0.531794	+	0.213109i
$83$	−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	$0.837482\pi$
$84$	6.77739	−	8.78317i	0.739474	−	0.958322i
$85$	10.5867			1.14829
$86$	−0.398834	−	2.78068i	−0.0430074	−	0.299849i
$87$	1.78788	+	16.9524i	0.191680	+	1.81748i
$88$	−14.0752	−	10.0446i	−1.50042	−	1.07076i
$89$		−	14.4700i		−	1.53382i	−0.641754	−	0.766911i	$-0.721793\pi$
$89$		−	14.4700i		−	1.53382i	0.641754	−	0.766911i	$-0.278207\pi$
$90$	14.8726	+	2.56810i	1.56771	+	0.270702i
$91$			1.18907i			0.124648i
$92$	1.25410	−	5.15414i	0.130749	−	0.537356i
$93$	3.74177	−	8.88815i	0.388003	−	0.921658i
$94$	−0.350756	−	0.446335i	−0.0361777	−	0.0460359i
$95$	14.3683			1.47415
$96$	2.83714	+	9.37820i	0.289564	+	0.957159i
$97$	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
$99$	−12.2820	−	13.6210i	−1.23439	−	1.36896i
$100$	11.0731	+	10.5726i	1.10731	+	1.05726i
$101$		−	12.3690i		−	1.23076i	−0.788231	−	0.615379i	$-0.789003\pi$
$101$		−	12.3690i		−	1.23076i	0.788231	−	0.615379i	$-0.210997\pi$
$102$	1.78607	+	7.06744i	0.176847	+	0.699781i
$103$	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
$105$	19.6239	−	2.06963i	1.91510	−	0.201976i
$106$	−5.23486	−	2.09779i	−0.508455	−	0.203756i
$107$	−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	$0.787843\pi$
$110$	−4.36675	−	30.4451i	−0.416353	−	2.90282i
$111$	0.584105	−	1.31318i	0.0554408	−	0.124642i
$112$	6.91105	+	10.7861i	0.653033	+	1.01919i
$113$	13.5753	−	7.83770i	1.27706	−	0.737309i	0.300750	−	0.953703i	$-0.402763\pi$
$113$	13.5753	−	7.83770i	1.27706	−	0.737309i	0.976306	+	0.216394i	$0.0694296\pi$
$114$	2.42405	+	9.59193i	0.227033	+	0.898367i
$115$	8.17102	−	4.71754i	0.761951	−	0.439913i
$116$	−19.1255	−	4.65359i	−1.77575	−	0.432075i
$117$	−0.745908	−	0.827228i	−0.0689592	−	0.0764773i
$118$	4.04678	−	0.580431i	0.372536	−	0.0534330i
$119$	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
$124$	8.20654	+	7.52680i	0.736969	+	0.675927i
$125$			9.44457i			0.844748i
$126$	4.69238	+	12.7514i	0.418030	+	1.13598i
$127$	−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
$129$	3.14353	+	1.39825i	0.276772	+	0.123109i
$130$	−0.265200	−	1.84898i	−0.0232596	−	0.162166i
$131$	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
$134$	7.24508	+	2.90336i	0.625880	+	0.250812i
$135$	−12.3540	+	13.7500i	−1.06326	+	1.18341i
$136$	−8.37840	−	0.808688i	−0.718442	−	0.0693444i
$137$	−4.90084	+	2.82950i	−0.418707	+	0.241741i	−0.694524	−	0.719470i	$-0.744385\pi$
$137$	−4.90084	+	2.82950i	−0.418707	+	0.241741i	0.275817	+	0.961210i	$0.411052\pi$
$138$	4.52785	+	4.65890i	0.385436	+	0.396592i
$139$		−	17.8292i		−	1.51225i	−0.654428	−	0.756124i	$-0.727090\pi$
$139$		−	17.8292i		−	1.51225i	0.654428	−	0.756124i	$-0.272910\pi$
$140$	−5.38697	+	22.1395i	−0.455282	+	1.87113i
$141$	0.691411	−	0.0729195i	0.0582273	−	0.00614093i
$142$	2.38091	−	5.94134i	0.199801	−	0.498586i
$143$	−1.13494	+	1.96578i	−0.0949086	+	0.164387i
$144$	−11.5741	−	3.16850i	−0.964511	−	0.264041i
$145$	−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	−0.281913	−	0.959440i	$-0.590969\pi$
$149$	−15.3042	−	8.83588i	−1.25377	−	0.723864i	−0.971856	+	0.235576i	$0.924302\pi$
$150$	−18.1791	+	4.59419i	−1.48432	+	0.375114i
$151$		−	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
$156$	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	$0.442389\pi$
$158$	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
$162$	−11.2634	−	5.92749i	−0.884939	−	0.465707i
$163$			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
$165$	34.4178	+	15.3091i	2.67943	+	1.19181i
$166$	−0.124933	+	0.311760i	−0.00969669	+	0.0241972i
$167$	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	$-0.170797\pi$
$168$	−15.6887	+	0.138908i	−1.21041	+	0.0107170i
$169$	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	−0.230722	−	0.973020i	$-0.574109\pi$
$173$	6.53145	−	3.77094i	0.496577	−	0.286699i	0.727299	+	0.686321i	$0.240775\pi$
$174$	17.2878	−	16.8015i	1.31058	−	1.27372i
$175$	−21.2310	+	12.2577i	−1.60491	+	0.926595i
$176$	1.13027	+	24.4281i	0.0851973	+	1.84134i
$177$	−2.03490	+	4.57484i	−0.152952	+	0.343866i
$178$	−16.0899	+	12.6444i	−1.20599	+	0.947734i
$179$	−9.76408	+	16.9119i	−0.729802	+	1.26405i	0.227165	+	0.973856i	$0.427054\pi$
$179$	−9.76408	+	16.9119i	−0.729802	+	1.26405i	−0.956967	+	0.290198i	$0.906279\pi$
$180$	−10.1405	−	18.7816i	−0.755829	−	1.39990i
$181$	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
$183$	−7.82250	+	0.824998i	−0.578256	+	0.0609856i
$184$	−6.82699	+	3.10935i	−0.503292	+	0.229224i
$185$			2.95185i			0.217024i
$186$	−13.1528	+	3.60609i	−0.964410	+	0.264411i
$187$			18.1938i			1.33046i
$188$	−0.189799	+	0.780042i	−0.0138425	+	0.0568904i
$189$	−16.2811	−	3.44245i	−1.18427	−	0.250401i
$190$	−12.5554	−	15.9767i	−0.910865	−	1.15907i
$191$	−6.07250	−	10.5179i	−0.439391	−	0.761047i	0.558252	−	0.829672i	$-0.311472\pi$
$191$	−6.07250	−	10.5179i	−0.439391	−	0.761047i	−0.997643	+	0.0686243i	$0.978139\pi$
$192$	7.94887	−	11.3497i	0.573660	−	0.819093i
$193$	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
$195$	2.09025	+	0.929748i	0.149686	+	0.0665807i
$196$	−6.25028	+	1.83062i	−0.446448	+	0.130758i
$197$	5.99718	−	3.46247i	0.427281	−	0.246691i	−0.270906	−	0.962606i	$-0.587323\pi$
$197$	5.99718	−	3.46247i	0.427281	−	0.246691i	0.698188	+	0.715915i	$0.253990\pi$
$198$	−4.41343	+	25.5594i	−0.313649	+	1.81643i
$199$	−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
$204$	6.29788	−	8.16175i	0.440940	−	0.571437i
$205$	6.52491	−	11.3015i	0.455719	−	0.789329i
$206$	−1.14182	−	0.457568i	−0.0795544	−	0.0318803i
$207$	−7.78172	+	1.65985i	−0.540867	+	0.115368i
$208$	0.0686432	+	1.48356i	0.00475955	+	0.102866i
$209$			24.6927i			1.70803i
$210$	−19.4493	−	20.0122i	−1.34213	−	1.38098i
$211$	−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
$216$	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
$220$	−30.0375	+	31.4594i	−2.02512	+	2.12099i
$221$			1.10494i			0.0743265i
$222$	−1.97059	+	0.498004i	−0.132257	+	0.0334238i
$223$	−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	$0.0968860\pi$
$227$	11.0974	+	19.2213i	0.736563	+	1.27577i	−0.217471	+	0.976067i	$0.569781\pi$
$228$	8.54749	−	11.0771i	0.566072	−	0.733601i
$229$	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
$231$	3.55679	+	33.7249i	0.234019	+	2.21894i
$232$	11.5379	+	25.3329i	0.757497	+	1.66319i
$233$			9.83948i			0.644606i	0.946637	+	0.322303i	$0.104457\pi$
$233$			9.83948i			0.644606i	−0.946637	+	0.322303i	$0.895543\pi$
$234$	−0.268035	+	1.55227i	−0.0175220	+	0.101475i
$235$	−1.23663	+	0.713966i	−0.0806685	+	0.0465740i
$236$	−4.18160	−	3.99260i	−0.272199	−	0.259896i
$237$	−7.54774	−	3.35724i	−0.490278	−	0.218076i
$238$	5.01373	−	12.5113i	0.324992	−	0.810989i
$239$	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	$0.163198\pi$
$242$	36.9229	−	5.29586i	2.37349	−	0.340431i
$243$	13.4861	−	7.81828i	0.865133	−	0.501543i
$244$	2.14736	−	8.82525i	0.137470	−	0.564979i
$245$	−10.0323	−	5.79216i	−0.640941	−	0.370047i
$246$	8.64543	+	2.44923i	0.551213	+	0.156157i
$247$			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	−0.723562	−	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
$254$	2.43841	+	17.0006i	0.152999	+	1.06672i
$255$	18.2355	−	1.92320i	1.14195	−	0.120436i
$256$	9.24533	+	13.0585i	0.577833	+	0.816155i
$257$	20.8370	−	12.0302i	1.29977	−	0.750425i	0.319409	−	0.947617i	$-0.396516\pi$
$257$	20.8370	−	12.0302i	1.29977	−	0.750425i	0.980365	+	0.197192i	$0.0631823\pi$
$258$	−1.19214	−	4.71726i	−0.0742192	−	0.293684i
$259$	−2.30141	+	1.32872i	−0.143002	+	0.0825625i
$260$	−1.82423	+	1.91058i	−0.113134	+	0.118489i
$261$	6.15922	+	28.8756i	0.381246	+	1.78736i
$262$	−4.21398	+	0.604412i	−0.260340	+	0.0373407i
$263$	−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
$266$	6.80464	−	16.9804i	0.417219	−	1.04113i
$267$	−2.62867	−	24.9246i	−0.160872	−	1.52536i
$268$	−3.10259	−	10.5932i	−0.189521	−	0.647081i
$269$	7.85469	−	4.53491i	0.478909	−	0.276498i	−0.241053	−	0.970512i	$-0.577493\pi$
$269$	7.85469	−	4.53491i	0.478909	−	0.276498i	0.719962	+	0.694014i	$0.244159\pi$
$270$	26.0845	+	1.72176i	1.58745	+	0.104783i
$271$		−	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
$273$	0.216010	+	2.04817i	0.0130735	+	0.123961i
$274$	7.42875	+	2.97696i	0.448787	+	0.179845i
$275$	−46.7989			−2.82208
$276$	1.22387	−	9.10581i	0.0736685	−	0.548105i
$277$	−30.7346			−1.84666			−0.923332	−	0.384003i	$-0.874545\pi$
$277$	−30.7346			−1.84666			−0.923332	+	0.384003i	$0.874545\pi$
$278$	−19.8250	+	15.5796i	−1.18903	+	0.934405i
$279$	4.83054	−	15.9896i	0.289197	−	0.957270i
$280$	29.3252	−	13.3561i	1.75252	−	0.798182i
$281$			20.3178i			1.21206i	0.795442	+	0.606030i	$0.207239\pi$
$281$			20.3178i			1.21206i	−0.795442	+	0.606030i	$0.792761\pi$
$282$	−0.685258	−	0.705092i	−0.0408065	−	0.0419876i
$283$			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
$285$	24.7493	−	2.61018i	1.46602	−	0.154613i
$286$	3.17758	−	0.455762i	0.187894	−	0.0269498i
$287$	11.7482			0.693476
$288$	6.59063	+	15.6385i	0.388357	+	0.921509i
$289$	−4.07177	−	7.05252i	−0.239516	−	0.414854i
$290$	−18.4177	+	45.9597i	−1.08152	+	2.69885i
$291$	20.4040	−	2.15190i	1.19610	−	0.126147i
$292$	−7.41253	+	2.17103i	−0.433786	+	0.127050i
$293$	−4.23382	−	2.44440i	−0.247342	−	0.142803i	0.371204	−	0.928551i	$-0.378945\pi$
$293$	−4.23382	−	2.44440i	−0.247342	−	0.142803i	−0.618547	+	0.785748i	$0.712278\pi$
$294$	2.17418	−	7.67454i	0.126801	−	0.447588i
$295$		−	10.2836i		−	0.598735i
$296$	0.225484	−	2.33612i	0.0131060	−	0.135785i
$297$	−23.6302	−	21.2310i	−1.37116	−	1.23195i
$298$	3.54825	+	24.7385i	0.205545	+	1.43306i
$299$	0.492374	+	0.852817i	0.0284747	+	0.0493197i
$300$	20.9940	+	16.1997i	1.21209	+	0.935287i
$301$	−3.18072	−	5.50918i	−0.183334	−	0.317544i
$302$	−11.5877	+	9.10629i	−0.666798	+	0.524008i
$303$	−2.24698	−	21.3055i	−0.129086	−	1.22397i
$304$	8.71606	+	13.6032i	0.499900	+	0.780197i
$305$	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	0.759850	−	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	$-0.554503\pi$
$311$	−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
$315$	33.4262	−	7.12988i	1.88335	−	0.401723i
$316$	6.58713	−	6.89896i	0.370555	−	0.388097i
$317$	−13.3515	−	7.70849i	−0.749894	−	0.432952i	0.0757614	−	0.997126i	$-0.475861\pi$
$317$	−13.3515	−	7.70849i	−0.749894	−	0.432952i	−0.825656	+	0.564174i	$0.809195\pi$
$318$	−9.39813	−	2.66247i	−0.527021	−	0.149304i
$319$	52.1070	−	30.0840i	2.91743	−	1.68438i
$320$	−5.44305	+	27.9336i	−0.304276	+	1.56154i
$321$	−1.25046	+	2.81127i	−0.0697936	+	0.156910i
$322$	−1.70548	−	11.8907i	−0.0950429	−	0.662642i
$323$	6.00999	+	10.4096i	0.334405	+	0.579207i
$324$	3.25128	+	17.7039i	0.180627	+	0.983552i
$325$	−2.84217			−0.157655
$326$	25.5726	−	20.0964i	1.41633	−	1.11304i
$327$	−28.2693	+	2.98141i	−1.56330	+	0.164873i
$328$	−6.02717	+	8.44568i	−0.332795	+	0.466335i
$329$	−1.11328	−	0.642755i	−0.0613774	−	0.0354362i
$330$	−13.0525	−	51.6483i	−0.718514	−	2.84315i
$331$	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
$336$	13.8637	+	17.3236i	0.756327	+	0.945078i
$337$	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
$342$	5.91792	+	16.0817i	0.320005	+	0.869600i
$343$			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	−0.973784	−	0.227473i	$-0.926954\pi$
$347$	−5.40014	+	9.35333i	−0.289895	+	0.502113i	0.683889	+	0.729586i	$0.260287\pi$
$348$	−33.7889	−	4.54142i	−1.81128	−	0.243446i
$349$	−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
$351$	−1.43510	−	1.28939i	−0.0766001	−	0.0688228i
$352$	26.1750	−	22.6028i	1.39513	−	1.20473i
$353$	−7.25715	−	4.18992i	−0.386259	−	0.223007i	0.294279	−	0.955720i	$-0.404921\pi$
$353$	−7.25715	−	4.18992i	−0.386259	−	0.223007i	−0.680538	+	0.732713i	$0.738254\pi$
$354$	6.86512	−	1.73494i	0.364877	−	0.0922110i
$355$	−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	0.918390	−	0.395677i	$-0.129490\pi$
$359$	2.20791	+	3.82420i	0.116529	+	0.201834i	−0.801861	+	0.597511i	$0.796157\pi$
$360$	−12.0230	+	27.6876i	−0.633667	+	1.45926i
$361$	−1.34323	−	2.32654i	−0.0706963	−	0.122450i
$362$	11.8619	−	29.6004i	0.623448	−	1.55576i
$363$	−18.5664	+	41.7410i	−0.974485	+	2.19083i
$364$	−2.31072	−	0.562243i	−0.121115	−	0.0294696i
$365$	−11.8979	−	6.86923i	−0.622762	−	0.359552i
$366$	7.75289	+	7.97729i	0.405250	+	0.416979i
$367$	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
$369$	−8.17317	+	7.36971i	−0.425478	+	0.383652i
$370$	3.28230	−	2.57942i	0.170638	−	0.134097i
$371$	−12.7711			−0.663041
$372$	15.5031	+	11.4741i	0.803797	+	0.594903i
$373$	20.0003			1.03557			0.517787	−	0.855510i	$-0.326756\pi$
$373$	20.0003			1.03557			0.517787	+	0.855510i	$0.326756\pi$
$374$	20.2305	−	15.8983i	1.04610	−	0.822082i
$375$	1.71573	+	16.2683i	0.0885997	+	0.840089i
$376$	1.03322	−	0.470577i	0.0532840	−	0.0242682i
$377$	3.16455	−	1.82705i	0.162983	−	0.0940980i
$378$	10.3991	+	21.1118i	0.534870	+	1.08587i
$379$	−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
$381$	−19.2191	−	8.54867i	−0.984622	−	0.437961i
$382$	−6.38897	+	15.9431i	−0.326888	+	0.815721i
$383$	−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	$0.941948\pi$
$384$	−19.5662	+	1.07899i	−0.998483	+	0.0550622i
$385$	−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	0.422641	−	0.906297i	$-0.361103\pi$
$389$	−2.97651	−	1.71849i	−0.150915	−	0.0871308i	−0.573556	+	0.819166i	$0.694436\pi$
$390$	−0.792697	−	3.13669i	−0.0401398	−	0.158832i
$391$	6.83559	+	3.94653i	0.345691	+	0.199585i
$392$	7.49722	+	5.35031i	0.378667	+	0.270232i
$393$	2.11897	−	4.76386i	0.106888	−	0.240305i
$394$	−9.09059	−	3.64292i	−0.457977	−	0.183528i
$395$	16.9663			0.853666
$396$	32.2772	−	17.4271i	1.62199	−	0.875743i
$397$	−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	$-0.772521\pi$
$401$		−	26.2467i		−	1.31070i	0.755325	−	0.655350i	$-0.227479\pi$
$402$	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
$406$	−44.1228	+	6.32854i	−2.18978	+	0.314080i
$407$	−5.07293			−0.251456
$408$	−14.5787	+	0.129080i	−0.721753	+	0.00639040i
$409$	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
$414$	8.64556	+	7.20241i	0.424906	+	0.353979i
$415$	0.731652	+	0.422419i	0.0359154	+	0.0207358i
$416$	1.58965	−	1.37271i	0.0779392	−	0.0673025i
$417$	−3.23889	−	30.7107i	−0.158609	−	1.50391i
$418$	27.4569	−	21.5772i	1.34296	−	1.05538i
$419$	−26.1142			−1.27576			−0.637880	−	0.770135i	$-0.720189\pi$
$419$	−26.1142			−1.27576			−0.637880	+	0.770135i	$0.720189\pi$
$420$	−5.25712	+	39.1139i	−0.256521	+	1.90856i
$421$	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
$423$	1.17771	−	0.251207i	0.0572621	−	0.0122141i
$424$	6.55192	−	9.18099i	0.318189	−	0.445868i
$425$	−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
$428$	−2.56962	−	2.45347i	−0.124207	−	0.118593i
$429$	−1.59783	+	3.59222i	−0.0771438	+	0.173434i
$430$	6.17468	+	7.85726i	0.297770	+	0.378911i
$431$	−12.2535	+	21.2237i	−0.590231	+	1.02231i	0.403970	+	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	$0.340176\pi$
$434$	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
$438$	2.57847	−	9.10165i	0.123204	−	0.434894i
$439$	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
$441$	6.54209	+	7.25531i	0.311528	+	0.345491i
$442$	1.22863	−	0.965531i	0.0584402	−	0.0459256i
$443$	−4.02219	−	6.96664i	−0.191100	−	0.330995i	0.754515	−	0.656283i	$-0.227872\pi$
$443$	−4.02219	−	6.96664i	−0.191100	−	0.330995i	−0.945615	+	0.325288i	$0.894539\pi$
$444$	2.27572	+	1.75602i	0.108001	+	0.0833370i
$445$	25.7377	+	44.5790i	1.22008	+	2.11325i
$446$	1.57651	+	10.9914i	0.0746497	+	0.520460i
$447$	−27.9666	−	12.4396i	−1.32277	−	0.588372i
$448$	−24.2285	+	8.33011i	−1.14469	+	0.393561i
$449$			13.0155i			0.614239i	0.951671	+	0.307120i	$0.0993652\pi$
$449$			13.0155i			0.614239i	−0.951671	+	0.307120i	$0.900635\pi$
$450$	−30.4789	+	11.2160i	−1.43679	+	0.528725i
$451$	19.4222	+	11.2134i	0.914558	+	0.528020i
$452$	8.81203	+	30.0869i	0.414483	+	1.41517i
$453$	−1.89313	−	17.9504i	−0.0889470	−	0.843382i
$454$	11.6758	−	29.1359i	0.547972	−	1.36742i
$455$	−2.11499	−	3.66326i	−0.0991520	−	0.171736i
$456$	−19.7862	+	0.175187i	−0.926574	+	0.00820389i
$457$	−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
$459$	−15.1292	−	3.19889i	−0.706169	−	0.149312i
$460$	5.30399	+	18.1094i	0.247300	+	0.844355i
$461$			21.1539i			0.985237i	0.870245	+	0.492619i	$0.163960\pi$
$461$			21.1539i			0.985237i	−0.870245	+	0.492619i	$0.836040\pi$
$462$	34.3922	−	33.4248i	1.60007	−	1.55506i
$463$			4.36207i			0.202722i	0.994850	+	0.101361i	$0.0323198\pi$
$463$			4.36207i			0.202722i	−0.994850	+	0.101361i	$0.967680\pi$
$464$	18.0867	−	34.9661i	0.839653	−	1.62326i
$465$	4.28169	+	34.0379i	0.198559	+	1.57847i
$466$	10.9410	−	8.59803i	0.506830	−	0.398296i
$467$	−1.88534			−0.0872431			−0.0436216	−	0.999048i	$-0.513890\pi$
$467$	−1.88534			−0.0872431			−0.0436216	+	0.999048i	$0.513890\pi$
$468$	1.96025	−	1.05838i	0.0906126	−	0.0489234i
$469$	17.6752			0.816167
$470$	1.87449	+	0.751175i	0.0864638	+	0.0346491i
$471$	7.77000	−	0.819460i	0.358023	−	0.0377587i
$472$	−0.785538	+	8.13856i	−0.0361573	+	0.374608i
$473$		−	12.1437i		−	0.558369i
$474$	2.86236	+	11.3263i	0.131473	+	0.520235i
$475$	−26.7760	+	15.4591i	−1.22857	+	0.709314i
$476$	−18.2931	+	5.35778i	−0.838461	+	0.245574i
$477$	8.88475	−	8.01135i	0.406805	−	0.366814i
$478$	0.181150	−	0.452045i	0.00828562	−	0.0206761i
$479$	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
$482$	−0.473670	+	0.0679387i	−0.0215751	+	0.00309452i
$483$	13.4423	+	5.97915i	0.611645	+	0.272061i
$484$	−38.1530	−	36.4285i	−1.73423	−	1.65584i
$485$	−36.4937	+	21.0696i	−1.65709	+	0.956723i
$486$	−20.4780	−	8.16394i	−0.928903	−	0.370324i
$487$	−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
$489$	4.17789	+	39.6141i	0.188931	+	1.79141i
$490$	2.32597	+	16.2167i	0.105077	+	0.732597i
$491$	−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
$496$	−18.5072	+	12.3888i	−0.831000	+	0.556273i
$497$		−	14.4946i		−	0.650172i
$498$	−0.158562	+	0.559701i	−0.00710533	+	0.0250808i
$499$	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
$501$	15.8727	−	35.6848i	0.709138	−	1.59428i
$502$	−10.4683	+	1.50147i	−0.467221	+	0.0670137i
$503$	−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
$506$	8.52989	−	21.2856i	0.379200	−	0.946260i
$507$	9.05398	−	20.3551i	0.402101	−	0.904001i
$508$	16.7730	−	17.5670i	0.744183	−	0.779412i
$509$	27.7984	−	16.0494i	1.23214	−	0.711378i	0.264667	−	0.964340i	$-0.414738\pi$
$509$	27.7984	−	16.0494i	1.23214	−	0.711378i	0.967476	+	0.252962i	$0.0814046\pi$
$510$	−18.0732	−	18.5964i	−0.800297	−	0.823460i
$511$		−	12.3682i		−	0.547136i
$512$	6.44146	−	21.6912i	0.284675	−	0.958624i
$513$	−20.5333	−	4.34154i	−0.906568	−	0.191684i
$514$	−31.5849	−	12.6572i	−1.39315	−	0.558284i
$515$	−1.54711	+	2.67968i	−0.0681739	+	0.118081i
$516$	−4.20361	+	5.44768i	−0.185054	+	0.239821i
$517$	−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	0.725680	−	0.688032i	$-0.241525\pi$
$521$	11.2453	+	6.49249i	0.492667	+	0.284441i	−0.233013	+	0.972474i	$0.574859\pi$
$522$	26.7260	−	32.0811i	1.16976	−	1.40415i
$523$			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
$528$	6.38456	+	41.8720i	0.277852	+	1.82225i
$529$	−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
$534$	−25.4178	+	24.7028i	−1.09994	+	1.06899i
$535$		−	6.31935i		−	0.273209i
$536$	−9.06788	+	12.7065i	−0.391673	+	0.548839i
$537$	−13.7464	+	30.9045i	−0.593199	+	1.33363i
$538$	−11.9062	−	4.77124i	−0.513314	−	0.205703i
$539$	9.95416	−	17.2411i	0.428756	−	0.742627i
$540$	−20.8789	−	30.5091i	−0.898486	−	1.31290i
$541$	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
$546$	2.08870	−	2.02994i	0.0893880	−	0.0868736i
$547$	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
$549$	−13.3244	+	2.84211i	−0.568670	+	0.121298i
$550$	40.8942	+	52.0377i	1.74374	+	2.21890i
$551$	19.8754	−	34.4252i	0.846720	−	1.46656i
$552$	−11.1946	+	6.59605i	−0.476474	+	0.280746i
$553$	7.63704	+	13.2277i	0.324760	+	0.562501i
$554$	26.8568	+	34.1752i	1.14104	+	1.45196i
$555$	0.536241	+	5.08456i	0.0227622	+	0.215827i
$556$	34.6474	+	8.43039i	1.46938	+	0.357528i
$557$			21.6523i			0.917439i	0.888581	+	0.458719i	$0.151692\pi$
$557$			21.6523i			0.917439i	−0.888581	+	0.458719i	$0.848308\pi$
$558$	−22.0006	+	8.60086i	−0.931359	+	0.364103i
$559$		−	0.737509i		−	0.0311933i
$560$	−40.4765	−	20.9370i	−1.71045	−	0.884750i
$561$	3.30514	+	31.3388i	0.139543	+	1.32313i
$562$	22.5923	−	17.7543i	0.952999	−	0.748921i
$563$	−8.47962	−	14.6871i	−0.357373	−	0.618989i	0.630148	−	0.776475i	$-0.282994\pi$
$563$	−8.47962	−	14.6871i	−0.357373	−	0.618989i	−0.987521	+	0.157486i	$0.949661\pi$
$564$	−0.185224	+	1.37810i	−0.00779935	+	0.0580285i
$565$	−27.8816	+	48.2924i	−1.17299	+	2.03168i
$566$	21.2620	−	16.7089i	0.893710	−	0.702329i
$567$	−28.6695	−	2.97195i	−1.20400	−	0.124810i
$568$	10.4200	+	7.43614i	0.437215	+	0.312013i
$569$	15.1144	−	8.72630i	0.633628	−	0.365825i	−0.148528	−	0.988908i	$-0.547453\pi$
$569$	15.1144	−	8.72630i	0.633628	−	0.365825i	0.782156	+	0.623083i	$0.214120\pi$
$570$	−24.5290	−	25.2390i	−1.02741	−	1.05714i
$571$	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
$576$	11.6301	−	20.9938i	0.484587	−	0.874743i
$577$	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
$579$	0.225897	−	0.507860i	0.00938796	−	0.0211060i
$580$	67.1986	−	19.6815i	2.79027	−	0.817231i
$581$			0.760575i			0.0315540i
$582$	−20.2224	−	20.8077i	−0.838247	−	0.862509i
$583$	−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	$-0.469870\pi$
$587$	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
$592$	−2.79468	+	1.79065i	−0.114861	+	0.0735952i
$593$		−	25.8419i		−	1.06120i	−0.847623	−	0.530599i	$-0.821967\pi$
$593$		−	25.8419i		−	1.06120i	0.847623	−	0.530599i	$-0.178033\pi$
$594$	−2.95894	+	44.8278i	−0.121407	+	1.83931i
$595$	−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	$-0.985185\pi$
$599$	−13.2101	−	22.8806i	−0.539751	−	0.934876i	0.459166	−	0.888350i	$-0.348148\pi$
$600$	−0.332024	−	37.4999i	−0.0135548	−	1.53093i
$601$	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
$603$	−12.2965	+	11.0877i	−0.500754	+	0.451528i
$604$	20.2514	+	4.92756i	0.824017	+	0.200499i
$605$		−	93.8280i		−	3.81465i
$606$	−21.7271	+	21.1159i	−0.882603	+	0.857776i
$607$	−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
$609$	22.1868	−	49.8803i	0.899056	−	2.02125i
$610$	−21.2077	−	8.49866i	−0.858673	−	0.344101i
$611$	−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	$-0.0457639\pi$
$614$	−2.34303	−	16.3357i	−0.0945571	−	0.659255i
$615$	9.18609	−	20.6521i	0.370419	−	0.832773i
$616$	22.9533	+	50.3971i	0.924815	+	2.03056i
$617$	−13.6038	−	7.85413i	−0.547666	−	0.316195i	0.200514	−	0.979691i	$-0.435739\pi$
$617$	−13.6038	−	7.85413i	−0.547666	−	0.316195i	−0.748180	+	0.663496i	$0.769072\pi$
$618$	−2.04991	−	0.580733i	−0.0824593	−	0.0233605i
$619$		−	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
$624$	0.387745	+	2.54296i	0.0155222	+	0.101800i
$625$	2.33836	+	4.05017i	0.0935346	+	0.162007i
$626$	−20.9011	+	2.99786i	−0.835378	+	0.119819i
$627$	4.48574	+	42.5331i	0.179143	+	1.69861i
$628$	−2.13294	+	8.76602i	−0.0851136	+	0.349802i
$629$	−2.13858	+	1.23471i	−0.0852707	+	0.0492311i
$630$	−37.1369	−	30.9378i	−1.47957	−	1.23259i
$631$	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
$633$	−5.41699	−	2.40949i	−0.215306	−	0.0957685i
$634$	3.09552	+	21.5820i	0.122939	+	0.857132i
$635$	43.2018			1.71441
$636$	5.25185	+	12.7768i	0.208250	+	0.506631i
$637$	0.604533	−	1.04708i	0.0239525	−	0.0414869i
$638$	−78.9845	−	31.6519i	−3.12702	−	1.25311i
$639$	9.09253	+	10.0838i	0.359695	+	0.398909i
$640$	35.8170	−	18.3569i	1.41579	−	0.725619i
$641$	−24.3183	+	14.0402i	−0.960514	+	0.554553i	−0.896331	−	0.443385i	$-0.853777\pi$
$641$	−24.3183	+	14.0402i	−0.960514	+	0.554553i	−0.0641831	+	0.997938i	$0.520444\pi$
$642$	4.21866	−	1.06613i	0.166497	−	0.0420768i
$643$			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
$645$	−12.1716	+	1.28367i	−0.479255	+	0.0505445i
$646$	6.32321	−	15.7790i	0.248783	−	0.620817i
$647$	−11.1617			−0.438812			−0.219406	−	0.975634i	$-0.570412\pi$
$647$	−11.1617			−0.438812			−0.219406	+	0.975634i	$0.570412\pi$
$648$	16.8447	−	19.0855i	0.661723	−	0.749748i
$649$	17.6730			0.693726
$650$	2.48358	+	3.16034i	0.0974139	+	0.123959i
$651$	−24.6102	+	18.6597i	−0.964551	+	0.731330i
$652$	−44.6921	−	10.8745i	−1.75028	−	0.425877i
$653$			23.0069i			0.900329i	0.892946	+	0.450165i	$0.148635\pi$
$653$			23.0069i			0.900329i	−0.892946	+	0.450165i	$0.851365\pi$
$654$	28.0177	+	28.8287i	1.09558	+	1.12729i
$655$			10.7085i			0.418416i
$656$	14.6578	−	0.678208i	0.572293	−	0.0264796i
$657$	7.75861	+	8.60446i	0.302692	+	0.335692i
$658$	0.258113	+	1.79957i	0.0100623	+	0.0701545i
$659$	−44.2361			−1.72319			−0.861597	−	0.507592i	$-0.830536\pi$
$659$	−44.2361			−1.72319			−0.861597	+	0.507592i	$0.830536\pi$
$660$	−46.0245	+	59.6454i	−1.79150	+	2.32170i
$661$	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
$663$	0.200727	+	1.90326i	0.00779558	+	0.0739165i
$664$	−0.546769	−	0.390196i	−0.0212188	−	0.0151425i
$665$	−39.8504	−	23.0076i	−1.54533	−	0.892198i
$666$	−3.30387	+	1.21579i	−0.128022	+	0.0471110i
$667$		−	26.1028i		−	1.01070i
$668$	32.6175	+	31.1432i	1.26201	+	1.20497i
$669$	−12.4257	−	5.52697i	−0.480405	−	0.213685i
$670$	−27.4847	+	3.94213i	−1.06182	+	0.152298i
$671$	13.8820	+	24.0443i	0.535908	+	0.928219i
$672$	7.14834	−	30.5535i	0.275753	−	1.17863i
$673$	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
$675$	8.22832	−	38.9158i	0.316708	−	1.49787i
$676$	18.6054	+	17.7645i	0.715594	+	0.683249i
$677$	−7.71546	+	4.45452i	−0.296529	+	0.171201i	−0.640883	−	0.767639i	$-0.721431\pi$
$677$	−7.71546	+	4.45452i	−0.296529	+	0.171201i	0.344354	+	0.938840i	$0.388098\pi$
$678$	−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
$682$	30.4973	+	37.2451i	1.16780	+	1.42619i
$683$	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
$687$	8.89088	−	19.9884i	0.339208	−	0.762606i
$688$	−4.28651	−	6.68998i	−0.163422	−	0.255053i
$689$	−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	−0.891646	−	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
$693$	12.2531	+	57.4449i	0.465457	+	2.18215i
$694$	15.1192	−	2.16855i	0.573917	−	0.0823171i
$695$	31.7125	+	54.9277i	1.20292	+	2.08353i
$696$	24.4760	+	41.5399i	0.927759	+	1.57456i
$697$	10.9170			0.413512
$698$	7.79304	+	9.91661i	0.294971	+	0.375349i
$699$	1.78747	+	16.9485i	0.0676082	+	0.641050i
$700$	−13.7815	−	47.0541i	−0.520891	−	1.77848i
$701$	14.7131	+	8.49461i	0.555706	+	0.320837i	0.751420	−	0.659824i	$-0.229369\pi$
$701$	14.7131	+	8.49461i	0.555706	+	0.320837i	−0.195714	+	0.980661i	$0.562702\pi$
$702$	−0.179701	+	2.72247i	−0.00678239	+	0.102753i
$703$	−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
$708$	−7.92811	−	6.11760i	−0.297956	−	0.229913i
$709$	−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
$714$	6.36330	−	22.4616i	0.238141	−	0.840603i
$715$		−	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	$0.388152\pi$
$719$	−17.1882	+	29.7708i	−0.641012	+	1.11026i	−0.985207	+	0.171367i	$0.945182\pi$
$720$	41.2931	−	10.8253i	1.53890	−	0.403437i
$721$	−2.78561			−0.103741
$722$	−1.41323	+	3.52660i	−0.0525951	+	0.131246i
$723$	0.238182	−	0.535479i	0.00885808	−	0.0199147i
$724$	−43.2793	+	12.6759i	−1.60846	+	0.471096i
$725$	65.2444	+	37.6689i	2.42312	+	1.39899i
$726$	62.6375	−	15.8296i	2.32470	−	0.587493i
$727$	−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
$732$	2.09560	−	15.5916i	0.0774555	−	0.576281i
$733$	−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
$735$	−18.3329	−	8.15448i	−0.676217	−	0.300783i
$736$	−2.81430	−	14.7371i	−0.103737	−	0.543217i
$737$	29.2208	+	16.8706i	1.07636	+	0.621438i
$738$	15.3367	+	2.64824i	0.564551	+	0.0974830i
$739$	−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
$741$	0.272427	+	2.58311i	0.0100078	+	0.0948928i
$742$	11.1597	+	14.2007i	0.409687	+	0.521325i
$743$	14.3976			0.528195			0.264098	−	0.964496i	$-0.414926\pi$
$743$	14.3976			0.528195			0.264098	+	0.964496i	$0.414926\pi$
$744$	−0.788512	−	27.2650i	−0.0289083	−	0.999582i
$745$	62.8651			2.30320
$746$	−17.4768	−	22.2392i	−0.639872	−	0.814234i
$747$	−0.477111	−	0.529127i	−0.0174566	−	0.0193597i
$748$	−35.3561	−	8.60282i	−1.29275	−	0.314550i
$749$	4.92687	−	2.84453i	0.180024	−	0.103937i
$750$	16.5902	−	16.1235i	0.605787	−	0.588746i
$751$	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
$753$	5.26389	−	11.8343i	0.191827	−	0.431264i
$754$	−4.79686	−	1.92227i	−0.174691	−	0.0700050i
$755$	18.5359	+	32.1052i	0.674592	+	1.16843i
$756$	14.3881	−	30.0113i	0.523290	−	1.09150i
$757$	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	$0.0726481\pi$
$761$	45.7116	+	26.3916i	1.65704	+	0.956695i	0.682976	+	0.730440i	$0.260685\pi$
$762$	7.28854	+	28.8406i	0.264036	+	1.04479i
$763$	45.5182	+	26.2800i	1.64787	+	0.951398i
$764$	23.3108	−	6.82740i	0.843354	−	0.247007i
$765$	31.0613	−	6.62543i	1.12302	−	0.239543i
$766$	−6.89036	+	17.1943i	−0.248959	+	0.621255i
$767$	1.07331			0.0387550
$768$	18.2973	+	20.8137i	0.660247	+	0.751049i
$769$	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	$-0.892040\pi$
$773$		−	18.5002i		−	0.665404i	0.943032	−	0.332702i	$-0.107960\pi$
$774$	−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
$778$	0.690098	+	4.81138i	0.0247412	+	0.172496i
$779$	14.8166			0.530860
$780$	−2.79514	+	3.62237i	−0.100082	+	0.129702i
$781$	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
$786$	−7.14877	+	1.80662i	−0.254988	+	0.0644401i
$787$	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
$789$	−14.7646	+	1.55714i	−0.525634	+	0.0554358i
$790$	−14.8256	−	18.8656i	−0.527473	−	0.671207i
$791$	−50.2015			−1.78496
$792$	−47.5827	−	20.6622i	−1.69078	−	0.734200i
$793$	0.843076	+	1.46025i	0.0299385	+	0.0518550i
$794$	42.9474	−	6.15996i	1.52415	−	0.218609i
$795$	−9.98586	+	22.4501i	−0.354162	+	0.796225i
$796$	−4.33488	−	14.8006i	−0.153646	−	0.524592i
$797$	33.3991	−	19.2830i	1.18306	−	0.683039i	0.226338	−	0.974049i	$-0.427325\pi$
$797$	33.3991	−	19.2830i	1.18306	−	0.683039i	0.956720	+	0.291010i	$0.0939913\pi$
$798$	8.63628	−	30.4848i	0.305721	−	1.07915i
$799$	−1.03452	−	0.597280i	−0.0365986	−	0.0211302i
$800$	40.8970	+	14.2327i	1.44593	+	0.503202i
$801$	−9.05574	−	42.4551i	−0.319969	−	1.50008i
$802$	−29.1849	+	22.9352i	−1.03056	+	0.809870i
$803$	11.8052	−	20.4472i	0.416595	−	0.721564i
$804$	−7.26859	−	17.6831i	−0.256343	−	0.623634i
$805$	−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	−0.288422	−	0.957504i	$-0.593130\pi$
$809$	−35.8908	−	20.7216i	−1.26185	−	0.728532i	−0.973433	+	0.228971i	$0.926464\pi$
$810$	45.2433	−	1.77286i	1.58969	−	0.0622919i
$811$	−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
$813$	−3.09491	−	29.3454i	−0.108543	−	1.02919i
$814$	4.43288	+	5.64082i	0.155372	+	0.197711i
$815$	−40.9064	−	70.8519i	−1.43289	−	2.48183i
$816$	12.8828	+	16.0979i	0.450989	+	0.563540i
$817$	−4.01146	−	6.94805i	−0.140343	−	0.243081i
$818$	−33.9035	+	4.86279i	−1.18541	+	0.170023i
$819$	0.744152	+	3.48873i	0.0260028	+	0.121906i
$820$	18.8769	+	18.0237i	0.659210	+	0.629414i
$821$			12.0693i			0.421222i	0.977570	+	0.210611i	$0.0675454\pi$
$821$			12.0693i			0.421222i	−0.977570	+	0.210611i	$0.932455\pi$
$822$	13.3368	+	3.77828i	0.465175	+	0.131783i
$823$	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
$825$	−80.6109	+	8.50161i	−2.80651	+	0.295988i
$826$	−12.1532	−	4.87021i	−0.422863	−	0.169456i
$827$	−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	$0.854679\pi$
$828$	0.453932	−	15.9071i	0.0157752	−	0.552809i
$829$	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
$831$	−52.9403	+	5.58333i	−1.83648	+	0.193684i
$832$	−2.91546	−	0.568096i	−0.101075	−	0.0196952i
$833$		−	9.69104i		−	0.335775i
$834$	−31.3183	+	30.4374i	−1.08447	+	1.05396i
$835$			80.2146i			2.77594i
$836$	−47.9853	−	11.6758i	−1.65961	−	0.403815i
$837$	5.41589	−	28.4195i	0.187201	−	0.982322i
$838$	22.8193	+	29.0375i	0.788281	+	1.00308i
$839$	39.4541			1.36211			0.681053	−	0.732234i	$-0.261522\pi$
$839$	39.4541			1.36211			0.681053	+	0.732234i	$0.261522\pi$
$840$	48.0863	−	28.3332i	1.65913	−	0.977589i
$841$	−67.8597			−2.33999
$842$	1.09168	−	2.72420i	0.0376219	−	0.0938823i
$843$	3.69099	+	34.9974i	0.127124	+	1.20537i
$844$	4.72757	−	4.95137i	0.162730	−	0.170433i
$845$			45.7555i			1.57404i
$846$	−1.30844	−	1.09003i	−0.0449852	−	0.0374761i
$847$	73.1528	−	42.2348i	2.51356	−	1.45121i
$848$	−15.9340	+	0.737255i	−0.547176	+	0.0253174i
$849$	3.47366	+	32.9367i	0.119216	+	1.13039i
$850$	29.9052	+	11.9841i	1.02574	+	0.411050i
$851$	−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	$0.704233\pi$
$854$	−2.92024	−	20.3600i	−0.0999287	−	0.696705i
$855$	42.1564	−	8.99204i	1.44172	−	0.307521i
$856$	−0.482718	+	5.00119i	−0.0164990	+	0.170937i
$857$	25.8746	−	14.9387i	0.883861	−	0.510297i	0.0119313	−	0.999929i	$-0.496202\pi$
$857$	25.8746	−	14.9387i	0.883861	−	0.510297i	0.871929	+	0.489632i	$0.162869\pi$
$858$	5.39058	−	1.36230i	0.184032	−	0.0465081i
$859$	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
$861$	20.2363	−	2.13422i	0.689651	−	0.0727339i
$862$	34.3071	−	4.92068i	1.16850	−	0.167599i
$863$	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
$868$	−10.7083	−	34.0166i	−0.363464	−	1.15460i
$869$			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
$873$	34.7550	−	7.41330i	1.17628	−	0.250902i
$874$	−2.15092	−	14.9963i	−0.0727559	−	0.507256i
$875$	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	$-0.480194\pi$
$878$	−16.5219	−	6.62090i	−0.557586	−	0.223444i
$879$	−7.73680	−	3.44134i	−0.260956	−	0.116074i
$880$	−46.9321	−	73.2472i	−1.58208	−	2.46916i
$881$	−25.8554	+	14.9276i	−0.871091	+	0.502925i	−0.867711	−	0.497070i	$-0.834409\pi$
$881$	−25.8554	+	14.9276i	−0.871091	+	0.502925i	−0.00338024	+	0.999994i	$0.501076\pi$
$882$	2.35084	−	13.6143i	0.0791569	−	0.458419i
$883$			15.9306i			0.536107i	0.963404	+	0.268054i	$0.0863804\pi$
$883$			15.9306i			0.536107i	−0.963404	+	0.268054i	$0.913620\pi$
$884$	−2.14724	−	0.522464i	−0.0722193	−	0.0175724i
$885$	−1.86815	−	17.7135i	−0.0627972	−	0.595433i
$886$	−4.23181	+	10.5601i	−0.142170	+	0.354774i
$887$	−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	$0.243322\pi$
$888$	−0.0359909	−	4.06493i	−0.00120778	−	0.136410i
$889$	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
$894$	10.6059	+	41.9674i	0.354715	+	1.40360i
$895$		−	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
$900$	39.1049	+	24.0900i	1.30350	+	0.803002i
$901$	−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
$906$	−18.3056	+	17.7906i	−0.608161	+	0.591054i
$907$		−	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
$909$	−7.74084	−	36.2905i	−0.256747	−	1.20368i
$910$	−2.22521	+	5.55281i	−0.0737649	+	0.184074i
$911$	−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	$0.926133\pi$
$912$	17.4846	+	21.8481i	0.578972	+	0.723463i
$913$	−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
$918$	9.66331	+	19.6181i	0.318937	+	0.647493i
$919$	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
$921$	18.4673	+	8.21429i	0.608519	+	0.270670i
$922$	23.5220	−	18.4849i	0.774657	−	0.608769i
$923$	0.840211	−	1.45529i	0.0276559	−	0.0479014i
$924$	−67.2195	−	9.03468i	−2.21136	−	0.297219i
$925$	−3.17597	−	5.50093i	−0.104425	−	0.180870i
$926$	4.85038	−	3.81170i	0.159393	−	0.125260i
$927$	1.93793	−	1.74742i	0.0636499	−	0.0573929i
$928$	−54.6850	+	10.4430i	−1.79512	+	0.342809i
$929$		−	0.123923i		−	0.00406578i	−0.999998	−	0.00203289i	$-0.999353\pi$
$929$		−	0.123923i		−	0.00406578i	0.999998	−	0.00203289i	$-0.000647090\pi$
$930$	34.1067	−	34.5043i	1.11840	−	1.13144i
$931$		−	13.1527i		−	0.431062i
$932$	−19.1211	−	4.65253i	−0.626331	−	0.152399i
$933$	−10.3518	+	1.09175i	−0.338904	+	0.0357424i
$934$	1.64747	+	2.09639i	0.0539067	+	0.0685961i
$935$	−32.3612	−	56.0512i	−1.05832	−	1.83307i
$936$	−2.88978	−	1.25485i	−0.0944554	−	0.0410161i
$937$	−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
$939$	10.5100	−	23.6285i	0.342981	−	0.771088i
$940$	−0.802721	−	2.74073i	−0.0261819	−	0.0893927i
$941$	6.62501	−	3.82495i	0.215969	−	0.124690i	−0.388113	−	0.921612i	$-0.626873\pi$
$941$	6.62501	−	3.82495i	0.215969	−	0.124690i	0.604082	+	0.796922i	$0.293540\pi$
$942$	−7.70085	−	7.92374i	−0.250907	−	0.258169i
$943$	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	−0.541369	−	0.840785i	$-0.682094\pi$
$947$	14.0775	−	24.3829i	0.457457	−	0.792339i	0.998826	+	0.0484463i	$0.0154270\pi$
$948$	10.0930	−	13.0801i	0.327806	−	0.424821i
$949$	0.716948	−	1.24179i	0.0232731	−	0.0403102i
$950$	40.5874	+	16.2648i	1.31683	+	0.527699i
$951$	−24.3983	−	10.8524i	−0.791168	−	0.351913i
$952$	21.9426	+	15.6591i	0.711163	+	0.507514i
$953$			6.04922i			0.195953i	0.995189	+	0.0979767i	$0.0312370\pi$
$953$			6.04922i			0.195953i	−0.995189	+	0.0979767i	$0.968763\pi$
$954$	−16.6719	−	2.87880i	−0.539774	−	0.0932047i
$955$	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
$960$	−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
$964$	0.489451	+	0.467328i	0.0157642	+	0.0150516i
$965$			1.14160i			0.0367494i
$966$	−5.09779	−	20.1718i	−0.164019	−	0.649019i
$967$	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	$-0.887061\pi$
$971$	−23.9852	−	41.5436i	−0.769723	−	1.33320i	0.167991	−	0.985789i	$-0.446272\pi$
$972$	8.81647	+	29.9043i	0.282788	+	0.959182i
$973$	−28.5495	+	49.4492i	−0.915255	+	1.58527i
$974$	19.9233	+	7.98395i	0.638383	+	0.255822i
$975$	−4.89564	+	0.516317i	−0.156786	+	0.0165354i
$976$	16.1348	+	8.34592i	0.516461	+	0.267146i
$977$			59.4588i			1.90226i	0.308796	+	0.951128i	$0.400074\pi$
$977$			59.4588i			1.90226i	−0.308796	+	0.951128i	$0.599926\pi$
$978$	40.3979	−	39.2616i	1.29178	−	1.25545i
$979$	−76.6116	+	44.2317i	−2.44852	+	1.41365i
$980$	15.9996	−	16.7570i	0.511089	−	0.535283i
$981$	−48.1522	+	10.2710i	−1.53738	+	0.327927i
$982$	−16.7026	+	41.6799i	−0.533001	+	1.33006i
$983$	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
$986$	−41.0010	+	5.88079i	−1.30574	+	0.187283i
$987$	−2.03440	−	0.904902i	−0.0647555	−	0.0288034i
$988$	−2.91423	−	0.709089i	−0.0927140	−	0.0225591i
$989$	−4.56252	−	2.63417i	−0.145080	−	0.0837617i
$990$	−31.8654	−	86.5930i	−1.01275	−	2.75210i
$991$			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
$996$	0.760913	−	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	$0.716342\pi$
$998$	−6.42467	−	44.7930i	−0.203369	−	1.41790i
$999$	0.891938	−	4.21842i	0.0282197	−	0.133465i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.17	✓	120	1.1	even	1	trivial
372.2.p.a.191.18	yes	120	12.11	even	2	inner
372.2.p.a.191.43	yes	120	4.3	odd	2	inner
372.2.p.a.191.44	yes	120	3.2	odd	2	inner
372.2.p.a.335.17	yes	120	31.25	even	3	inner
372.2.p.a.335.18	yes	120	372.335	even	6	inner
372.2.p.a.335.43	yes	120	124.87	odd	6	inner
372.2.p.a.335.44	yes	120	93.56	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} +(1.72250 - 0.181663i) q^{3} +(-0.472843 + 1.94330i) q^{4} +(-3.08078 + 1.77869i) q^{5} +(-1.70717 - 1.75658i) q^{6} +(-2.77350 - 1.60128i) q^{7} +(2.57403 - 1.17234i) q^{8} +(2.93400 - 0.625827i) q^{9} +(4.66988 + 1.87138i) q^{10} +(-3.05678 - 5.29450i) q^{11} +(-0.461446 + 3.43323i) 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} +(-3.25970 - 2.71558i) q^{18} +(-3.49788 - 2.01950i) q^{19} +(-1.99980 - 6.82792i) q^{20} +(-5.06825 - 2.25436i) q^{21} +(-3.21608 + 8.02546i) q^{22} -2.65226 q^{23} +(4.22079 - 2.48696i) 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} +(8.38382 + 2.37511i) 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} +(-0.171149 + 5.99756i) 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} +(1.92206 + 7.60554i) q^{42} +(1.72024 + 0.993180i) q^{43} +(11.7342 - 3.43678i) q^{44} +(-7.92584 + 7.14670i) q^{45} +(2.31762 + 2.94916i) q^{46} +0.401400 q^{47} +(-6.45361 - 2.52011i) q^{48} +(1.62821 + 2.82014i) q^{49} +(-10.7160 + 1.53700i) q^{50} +(-4.70966 - 2.09486i) q^{51} +(0.712637 - 0.208721i) q^{52} +(3.45351 - 1.99388i) q^{53} +(-6.10814 - 4.08541i) q^{54} +(18.8345 + 10.8741i) q^{55} +(-9.01632 - 0.870260i) q^{56} +(-6.39196 - 2.84315i) q^{57} +(10.9435 - 8.60000i) q^{58} +(-1.44539 + 2.50350i) q^{59} +(-4.68503 - 11.3978i) 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} +(-4.08177 + 14.4081i) q^{66} +(-4.77967 + 2.75954i) q^{67} +(4.11026 - 4.30483i) q^{68} +(-4.56851 + 0.481816i) q^{69} +(-9.95531 - 12.6681i) q^{70} +(2.26297 + 3.91958i) q^{71} +(6.81851 - 5.05054i) q^{72} +(1.93098 + 3.34456i) q^{73} +(-1.16160 + 0.166609i) q^{74} +(5.38849 - 12.1144i) q^{75} +(5.57845 - 5.84252i) q^{76} +19.5791i q^{77} +(-0.247893 + 0.875027i) q^{78} +(-4.13036 - 2.38466i) q^{79} +(14.2143 - 0.657685i) q^{80} +(8.21668 - 3.67235i) q^{81} +(4.81560 + 1.92978i) q^{82} +(-0.118745 - 0.205672i) q^{83} +(6.77739 - 8.78317i) q^{84} +10.5867 q^{85} +(-0.398834 - 2.78068i) q^{86} +(1.78788 + 16.9524i) q^{87} +(-14.0752 - 10.0446i) q^{88} -14.4700i q^{89} +(14.8726 + 2.56810i) q^{90} +1.18907i q^{91} +(1.25410 - 5.15414i) q^{92} +(3.74177 - 8.88815i) q^{93} +(-0.350756 - 0.446335i) q^{94} +14.3683 q^{95} +(2.83714 + 9.37820i) q^{96} +11.8456 q^{97} +(1.71306 - 4.27481i) q^{98} +(-12.2820 - 13.6210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Introduction

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