LMFDB - Embedded newform 192.2.s.a.107.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] 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("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.743452 - 1.20303i) q^{2} +(-1.02851 - 1.39362i) q^{3} +(-0.894559 + 1.78879i) q^{4} +(1.69041 + 2.52988i) q^{5} +(-0.911914 + 2.27341i) q^{6} +(-1.66919 + 4.02977i) q^{7} +(2.81703 - 0.253698i) q^{8} +(-0.884335 + 2.86670i) q^{9} +(1.78678 - 3.91447i) q^{10} +(-3.48146 - 0.692506i) q^{11} +(3.41295 - 0.593115i) q^{12} +(3.08756 + 2.06304i) q^{13} +(6.08890 - 0.987862i) q^{14} +(1.78708 - 4.95780i) q^{15} +(-2.39953 - 3.20035i) q^{16} +(-2.62540 - 2.62540i) q^{17} +(4.10618 - 1.06737i) q^{18} +(2.52347 + 1.68613i) q^{19} +(-6.03760 + 0.760665i) q^{20} +(7.33274 - 1.81846i) q^{21} +(1.75519 + 4.70315i) q^{22} +(1.33827 + 3.23086i) q^{23} +(-3.25090 - 3.66492i) q^{24} +(-1.62940 + 3.93371i) q^{25} +(0.186447 - 5.24819i) q^{26} +(4.90462 - 1.71600i) q^{27} +(-5.71523 - 6.59069i) q^{28} +(-0.240184 - 1.20749i) q^{29} +(-7.29299 + 1.53598i) q^{30} -5.17881 q^{31} +(-2.06618 + 5.26601i) q^{32} +(2.61563 + 5.56407i) q^{33} +(-1.20657 + 5.11028i) q^{34} +(-13.0165 + 2.58914i) q^{35} +(-4.33683 - 4.14632i) q^{36} +(2.19976 + 3.29218i) q^{37} +(0.152384 - 4.28937i) q^{38} +(-0.300497 - 6.42473i) q^{39} +(5.40377 + 6.69790i) q^{40} +(-2.03421 + 0.842597i) q^{41} +(-7.63919 - 7.46956i) q^{42} +(10.1438 + 2.01773i) q^{43} +(4.35312 - 5.60811i) q^{44} +(-8.74731 + 2.60864i) q^{45} +(2.89188 - 4.01196i) q^{46} +(3.16961 - 3.16961i) q^{47} +(-1.99212 + 6.63562i) q^{48} +(-8.50315 - 8.50315i) q^{49} +(5.94375 - 0.964313i) q^{50} +(-0.958550 + 6.35904i) q^{51} +(-6.45234 + 3.67748i) q^{52} +(-1.90453 + 9.57473i) q^{53} +(-5.71075 - 4.62464i) q^{54} +(-4.13316 - 9.97832i) q^{55} +(-3.67980 + 11.7755i) q^{56} +(-0.245597 - 5.25095i) q^{57} +(-1.27408 + 1.18666i) q^{58} +(8.20460 - 5.48214i) q^{59} +(7.26981 + 7.63175i) q^{60} +(-1.36061 - 6.84027i) q^{61} +(3.85019 + 6.23026i) q^{62} +(-10.0760 - 8.34872i) q^{63} +(7.87127 - 1.42935i) q^{64} +11.2986i q^{65} +(4.74915 - 7.28330i) q^{66} +(3.78731 - 0.753342i) q^{67} +(7.04485 - 2.34771i) q^{68} +(3.12616 - 5.18800i) q^{69} +(12.7919 + 13.7343i) q^{70} +(-4.21150 - 1.74446i) q^{71} +(-1.76392 + 8.29992i) q^{72} +(-1.11189 + 0.460562i) q^{73} +(2.32517 - 5.09396i) q^{74} +(7.15794 - 1.77511i) q^{75} +(-5.27352 + 3.00562i) q^{76} +(8.60185 - 12.8736i) q^{77} +(-7.50573 + 5.13798i) q^{78} +(2.41654 - 2.41654i) q^{79} +(4.04032 - 11.4805i) q^{80} +(-7.43590 - 5.07024i) q^{81} +(2.52600 + 1.82078i) q^{82} +(-2.81558 + 4.21381i) q^{83} +(-3.30673 + 14.7434i) q^{84} +(2.20394 - 11.0800i) q^{85} +(-5.11404 - 13.7034i) q^{86} +(-1.43574 + 1.57664i) q^{87} +(-9.98306 - 1.06757i) q^{88} +(6.04112 + 2.50231i) q^{89} +(9.64147 + 8.58386i) q^{90} +(-13.4673 + 8.99856i) q^{91} +(-6.97648 - 0.496318i) q^{92} +(5.32645 + 7.21727i) q^{93} +(-6.16959 - 1.45668i) q^{94} +9.23435i q^{95} +(9.46389 - 2.53668i) q^{96} +3.52102i q^{97} +(-3.90785 + 16.5512i) q^{98} +(5.06398 - 9.36789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.743452	−	1.20303i	−0.525700	−	0.850670i
$2$	−0.743452	−	1.20303i	−0.525700	−	0.850670i
$3$	−1.02851	−	1.39362i	−0.593810	−	0.804605i
$3$	−1.02851	−	1.39362i	−0.593810	−	0.804605i
$4$	−0.894559	+	1.78879i	−0.447279	+	0.894394i
$5$	1.69041	+	2.52988i	0.755976	+	1.13140i	0.987353	+	0.158535i	$0.0506769\pi$
$5$	1.69041	+	2.52988i	0.755976	+	1.13140i	−0.231377	+	0.972864i	$0.574323\pi$
$6$	−0.911914	+	2.27341i	−0.372287	+	0.928118i
$7$	−1.66919	+	4.02977i	−0.630894	+	1.52311i	0.207608	+	0.978212i	$0.433432\pi$
$7$	−1.66919	+	4.02977i	−0.630894	+	1.52311i	−0.838501	+	0.544900i	$0.816568\pi$
$8$	2.81703	−	0.253698i	0.995969	−	0.0896959i
$9$	−0.884335	+	2.86670i	−0.294778	+	0.955566i
$10$	1.78678	−	3.91447i	0.565030	−	1.23786i
$11$	−3.48146	−	0.692506i	−1.04970	−	0.208798i	−0.360044	−	0.932935i	$-0.617238\pi$
$11$	−3.48146	−	0.692506i	−1.04970	−	0.208798i	−0.689656	+	0.724137i	$0.742238\pi$
$12$	3.41295	−	0.593115i	0.985233	−	0.171218i
$13$	3.08756	+	2.06304i	0.856334	+	0.572184i	0.904412	−	0.426659i	$-0.140310\pi$
$13$	3.08756	+	2.06304i	0.856334	+	0.572184i	−0.0480780	+	0.998844i	$0.515310\pi$
$14$	6.08890	−	0.987862i	1.62733	−	0.264017i
$15$	1.78708	−	4.95780i	0.461422	−	1.28010i
$16$	−2.39953	−	3.20035i	−0.599882	−	0.800088i
$17$	−2.62540	−	2.62540i	−0.636752	−	0.636752i	0.313001	−	0.949753i	$-0.398666\pi$
$17$	−2.62540	−	2.62540i	−0.636752	−	0.636752i	−0.949753	+	0.313001i	$0.898666\pi$
$18$	4.10618	−	1.06737i	0.967836	−	0.251582i
$19$	2.52347	+	1.68613i	0.578924	+	0.386825i	0.810279	−	0.586045i	$-0.199316\pi$
$19$	2.52347	+	1.68613i	0.578924	+	0.386825i	−0.231354	+	0.972870i	$0.574316\pi$
$20$	−6.03760	+	0.760665i	−1.35005	+	0.170090i
$21$	7.33274	−	1.81846i	1.60013	−	0.396820i
$22$	1.75519	+	4.70315i	0.374209	+	1.00271i
$23$	1.33827	+	3.23086i	0.279048	+	0.673680i	0.999810	−	0.0195019i	$-0.00620805\pi$
$23$	1.33827	+	3.23086i	0.279048	+	0.673680i	−0.720762	+	0.693182i	$0.756208\pi$
$24$	−3.25090	−	3.66492i	−0.663587	−	0.748099i
$25$	−1.62940	+	3.93371i	−0.325879	+	0.786742i
$26$	0.186447	−	5.24819i	0.0365652	−	1.02926i
$27$	4.90462	−	1.71600i	0.943895	−	0.330245i
$28$	−5.71523	−	6.59069i	−1.08008	−	1.24552i
$29$	−0.240184	−	1.20749i	−0.0446011	−	0.224225i	0.952056	−	0.305924i	$-0.0989654\pi$
$29$	−0.240184	−	1.20749i	−0.0446011	−	0.224225i	−0.996657	+	0.0816990i	$0.973965\pi$
$30$	−7.29299	+	1.53598i	−1.33151	+	0.280430i
$31$	−5.17881			−0.930141			−0.465071	−	0.885274i	$-0.653971\pi$
$31$	−5.17881			−0.930141			−0.465071	+	0.885274i	$0.653971\pi$
$32$	−2.06618	+	5.26601i	−0.365253	+	0.930908i
$33$	2.61563	+	5.56407i	0.455323	+	0.968581i
$34$	−1.20657	+	5.11028i	−0.206925	+	0.876406i
$35$	−13.0165	+	2.58914i	−2.20019	+	0.437644i
$36$	−4.33683	−	4.14632i	−0.722804	−	0.691053i
$37$	2.19976	+	3.29218i	0.361639	+	0.541231i	0.967019	−	0.254706i	$-0.0819787\pi$
$37$	2.19976	+	3.29218i	0.361639	+	0.541231i	−0.605380	+	0.795937i	$0.706979\pi$
$38$	0.152384	−	4.28937i	0.0247199	−	0.695827i
$39$	−0.300497	−	6.42473i	−0.0481180	−	1.02878i
$40$	5.40377	+	6.69790i	0.854411	+	1.05903i
$41$	−2.03421	+	0.842597i	−0.317690	+	0.131591i	−0.535830	−	0.844326i	$-0.680001\pi$
$41$	−2.03421	+	0.842597i	−0.317690	+	0.131591i	0.218140	+	0.975918i	$0.430001\pi$
$42$	−7.63919	−	7.46956i	−1.17875	−	1.15258i
$43$	10.1438	+	2.01773i	1.54691	+	0.307700i	0.893417	−	0.449229i	$-0.148301\pi$
$43$	10.1438	+	2.01773i	1.54691	+	0.307700i	0.653497	+	0.756929i	$0.273301\pi$
$44$	4.35312	−	5.60811i	0.656257	−	0.845455i
$45$	−8.74731	+	2.60864i	−1.30397	+	0.388873i
$46$	2.89188	−	4.01196i	0.426385	−	0.591531i
$47$	3.16961	−	3.16961i	0.462335	−	0.462335i	−0.437085	−	0.899420i	$-0.643989\pi$
$47$	3.16961	−	3.16961i	0.462335	−	0.462335i	0.899420	+	0.437085i	$0.143989\pi$
$48$	−1.99212	+	6.63562i	−0.287538	+	0.957769i
$49$	−8.50315	−	8.50315i	−1.21474	−	1.21474i
$50$	5.94375	−	0.964313i	0.840573	−	0.136375i
$51$	−0.958550	+	6.35904i	−0.134224	+	0.890444i
$52$	−6.45234	+	3.67748i	−0.894779	+	0.509974i
$53$	−1.90453	+	9.57473i	−0.261608	+	1.31519i	0.596869	+	0.802339i	$0.296411\pi$
$53$	−1.90453	+	9.57473i	−0.261608	+	1.31519i	−0.858477	+	0.512852i	$0.828589\pi$
$54$	−5.71075	−	4.62464i	−0.777135	−	0.629334i
$55$	−4.13316	−	9.97832i	−0.557315	−	1.34548i
$56$	−3.67980	+	11.7755i	−0.491734	+	1.57356i
$57$	−0.245597	−	5.25095i	−0.0325301	−	0.695506i
$58$	−1.27408	+	1.18666i	−0.167295	+	0.155816i
$59$	8.20460	−	5.48214i	1.06815	−	0.713714i	0.108267	−	0.994122i	$-0.465470\pi$
$59$	8.20460	−	5.48214i	1.06815	−	0.713714i	0.959881	+	0.280408i	$0.0904698\pi$
$60$	7.26981	+	7.63175i	0.938529	+	0.985255i
$61$	−1.36061	−	6.84027i	−0.174209	−	0.875807i	−0.964704	−	0.263338i	$-0.915176\pi$
$61$	−1.36061	−	6.84027i	−0.174209	−	0.875807i	0.790495	−	0.612469i	$-0.209824\pi$
$62$	3.85019	+	6.23026i	0.488975	+	0.791243i
$63$	−10.0760	−	8.34872i	−1.26946	−	1.05184i
$64$	7.87127	−	1.42935i	0.983909	−	0.178669i
$65$			11.2986i			1.40141i
$66$	4.74915	−	7.28330i	0.584580	−	0.896512i
$67$	3.78731	−	0.753342i	0.462693	−	0.0920354i	0.0417612	−	0.999128i	$-0.486703\pi$
$67$	3.78731	−	0.753342i	0.462693	−	0.0920354i	0.420932	+	0.907092i	$0.361703\pi$
$68$	7.04485	−	2.34771i	0.854313	−	0.284701i
$69$	3.12616	−	5.18800i	0.376345	−	0.624562i
$70$	12.7919	+	13.7343i	1.52893	+	1.64156i
$71$	−4.21150	−	1.74446i	−0.499813	−	0.207029i	0.118511	−	0.992953i	$-0.462188\pi$
$71$	−4.21150	−	1.74446i	−0.499813	−	0.207029i	−0.618324	+	0.785923i	$0.712188\pi$
$72$	−1.76392	+	8.29992i	−0.207880	+	0.978154i
$73$	−1.11189	+	0.460562i	−0.130137	+	0.0539047i	−0.446802	−	0.894633i	$-0.647437\pi$
$73$	−1.11189	+	0.460562i	−0.130137	+	0.0539047i	0.316664	+	0.948538i	$0.397437\pi$
$74$	2.32517	−	5.09396i	0.270295	−	0.592161i
$75$	7.15794	−	1.77511i	0.826527	−	0.204972i
$76$	−5.27352	+	3.00562i	−0.604915	+	0.344768i
$77$	8.60185	−	12.8736i	0.980272	−	1.46708i
$78$	−7.50573	+	5.13798i	−0.849857	+	0.581762i
$79$	2.41654	−	2.41654i	0.271882	−	0.271882i	−0.557975	−	0.829857i	$-0.688422\pi$
$79$	2.41654	−	2.41654i	0.271882	−	0.271882i	0.829857	+	0.557975i	$0.188422\pi$
$80$	4.04032	−	11.4805i	0.451722	−	1.28355i
$81$	−7.43590	−	5.07024i	−0.826212	−	0.563360i
$82$	2.52600	+	1.82078i	0.278951	+	0.201072i
$83$	−2.81558	+	4.21381i	−0.309050	+	0.462525i	−0.953186	−	0.302385i	$-0.902217\pi$
$83$	−2.81558	+	4.21381i	−0.309050	+	0.462525i	0.644136	+	0.764911i	$0.277217\pi$
$84$	−3.30673	+	14.7434i	−0.360794	+	1.60864i
$85$	2.20394	−	11.0800i	0.239051	−	1.20179i
$86$	−5.11404	−	13.7034i	−0.551461	−	1.47767i
$87$	−1.43574	+	1.57664i	−0.153928	+	0.169033i
$88$	−9.98306	−	1.06757i	−1.06420	−	0.113803i
$89$	6.04112	+	2.50231i	0.640358	+	0.265245i	0.679147	−	0.734003i	$-0.262350\pi$
$89$	6.04112	+	2.50231i	0.640358	+	0.265245i	−0.0387891	+	0.999247i	$0.512350\pi$
$90$	9.64147	+	8.58386i	1.01630	+	0.904819i
$91$	−13.4673	+	8.99856i	−1.41176	+	0.943306i
$92$	−6.97648	−	0.496318i	−0.727348	−	0.0517447i
$93$	5.32645	+	7.21727i	0.552328	+	0.748396i
$94$	−6.16959	−	1.45668i	−0.636344	−	0.150245i
$95$			9.23435i			0.947425i
$96$	9.46389	−	2.53668i	0.965904	−	0.258899i
$97$			3.52102i			0.357506i	0.983894	+	0.178753i	$0.0572062\pi$
$97$			3.52102i			0.357506i	−0.983894	+	0.178753i	$0.942794\pi$
$98$	−3.90785	+	16.5512i	−0.394753	+	1.67193i
$99$	5.06398	−	9.36789i	0.508949	−	0.941508i
$100$	−5.57899	−	6.43358i	−0.557899	−	0.643358i
$101$	3.93751	−	2.63096i	0.391797	−	0.261790i	−0.344032	−	0.938958i	$-0.611793\pi$
$101$	3.93751	−	2.63096i	0.391797	−	0.261790i	0.735829	+	0.677168i	$0.236793\pi$
$102$	8.36275	−	3.57448i	0.828035	−	0.353926i
$103$	−0.856014	−	0.354572i	−0.0843455	−	0.0349371i	0.340112	−	0.940385i	$-0.389535\pi$
$103$	−0.856014	−	0.354572i	−0.0843455	−	0.0349371i	−0.424457	+	0.905448i	$0.639535\pi$
$104$	9.22112	+	5.02833i	0.904205	+	0.493068i
$105$	16.9959	+	15.4770i	1.65863	+	1.51040i
$106$	12.9346	−	4.82715i	1.25632	−	0.468854i
$107$	1.02997	−	5.17800i	0.0995708	−	0.500576i	−0.898527	−	0.438919i	$-0.855361\pi$
$107$	1.02997	−	5.17800i	0.0995708	−	0.500576i	0.998097	−	0.0616572i	$-0.0196386\pi$
$108$	−1.31791	+	10.3084i	−0.126816	+	0.991926i
$109$	10.9383	−	16.3703i	1.04770	−	1.56799i	0.246909	−	0.969039i	$-0.420585\pi$
$109$	10.9383	−	16.3703i	1.04770	−	1.56799i	0.800787	−	0.598949i	$-0.204415\pi$
$110$	−8.93141	+	12.3907i	−0.851576	+	1.18141i
$111$	2.32556	−	6.45167i	0.220732	−	0.612365i
$112$	16.9020	−	4.32758i	1.59709	−	0.408918i
$113$	−3.88801	+	3.88801i	−0.365754	+	0.365754i	−0.865926	−	0.500172i	$-0.833270\pi$
$113$	−3.88801	+	3.88801i	−0.365754	+	0.365754i	0.500172	+	0.865926i	$0.333270\pi$
$114$	−6.13446	+	4.19929i	−0.574545	+	0.393300i
$115$	−5.91147	+	8.84715i	−0.551248	+	0.825001i
$116$	2.37480	+	0.650530i	0.220495	+	0.0604002i
$117$	−8.64455	+	7.02667i	−0.799189	+	0.649616i
$118$	−12.6949	−	5.79467i	−1.16866	−	0.533442i
$119$	14.9620	−	6.19748i	1.37157	−	0.568122i
$120$	3.77647	−	14.4196i	0.344743	−	1.31633i
$121$	1.47834	+	0.612348i	0.134394	+	0.0556680i
$122$	−7.21750	+	6.72227i	−0.653441	+	0.608606i
$123$	3.26646	+	1.96829i	0.294527	+	0.177475i
$124$	4.63275	−	9.26379i	0.416033	−	0.831913i
$125$	2.21482	−	0.440555i	0.198100	−	0.0394044i
$126$	−2.55272	+	18.3286i	−0.227415	+	1.63284i
$127$			16.7719i			1.48826i	0.668034	+	0.744131i	$0.267136\pi$
$127$			16.7719i			1.48826i	−0.668034	+	0.744131i	$0.732864\pi$
$128$	−7.57146	−	8.40672i	−0.669229	−	0.743056i
$129$	−7.62105	−	16.2118i	−0.670996	−	1.42737i
$130$	13.5925	−	8.39993i	1.19214	−	0.736723i
$131$	3.43669	+	17.2774i	0.300265	+	1.50953i	0.776444	+	0.630186i	$0.217021\pi$
$131$	3.43669	+	17.2774i	0.300265	+	1.50953i	−0.476179	+	0.879348i	$0.657979\pi$
$132$	−12.2928	−	0.298579i	−1.06995	−	0.0259880i
$133$	−11.0069	+	7.35456i	−0.954417	+	0.637721i
$134$	−3.72197	−	3.99617i	−0.321529	−	0.345216i
$135$	12.6321	+	9.50738i	1.08720	+	0.818265i
$136$	−8.06187	−	6.72975i	−0.691299	−	0.577071i
$137$	−5.32136	−	12.8469i	−0.454634	−	1.09758i	−0.970540	−	0.240939i	$-0.922545\pi$
$137$	−5.32136	−	12.8469i	−0.454634	−	1.09758i	0.515906	−	0.856645i	$-0.327455\pi$
$138$	−8.56546	+	0.0961669i	−0.729140	+	0.00818627i
$139$	−1.41013	+	7.08920i	−0.119606	+	0.601298i	0.873765	+	0.486347i	$0.161671\pi$
$139$	−1.41013	+	7.08920i	−0.119606	+	0.601298i	−0.993371	+	0.114951i	$0.963329\pi$
$140$	7.01258	−	25.5999i	0.592671	−	2.16358i
$141$	−7.67720	−	1.15725i	−0.646537	−	0.0974577i
$142$	1.03241	+	6.36348i	0.0866380	+	0.534012i
$143$	−9.32055	−	9.32055i	−0.779423	−	0.779423i
$144$	11.2964	−	4.04854i	0.941369	−	0.337379i
$145$	2.64880	−	2.64880i	0.219971	−	0.219971i
$146$	1.38071	+	0.995236i	0.114268	+	0.0823663i
$147$	−3.10456	+	20.5957i	−0.256060	+	1.69871i
$148$	−7.85683	+	0.989866i	−0.645828	+	0.0813665i
$149$	−9.04104	−	1.79837i	−0.740671	−	0.147329i	−0.189687	−	0.981845i	$-0.560747\pi$
$149$	−9.04104	−	1.79837i	−0.740671	−	0.147329i	−0.550984	+	0.834516i	$0.685747\pi$
$150$	−7.45709	−	7.29150i	−0.608869	−	0.595348i
$151$	10.2347	−	4.23934i	0.832885	−	0.344992i	0.0748410	−	0.997195i	$-0.476155\pi$
$151$	10.2347	−	4.23934i	0.832885	−	0.344992i	0.758044	+	0.652203i	$0.226155\pi$
$152$	7.53646	+	4.10967i	0.611287	+	0.333338i
$153$	9.84794	−	5.20448i	0.796159	−	0.420758i
$154$	−21.8824	−	0.777391i	−1.76333	−	0.0626440i
$155$	−8.75433	−	13.1018i	−0.703165	−	1.05236i
$156$	11.7613	+	5.20977i	0.941657	+	0.417116i
$157$	16.8912	−	3.35987i	1.34807	−	0.268147i	0.532314	−	0.846547i	$-0.321323\pi$
$157$	16.8912	−	3.35987i	1.34807	−	0.268147i	0.815753	+	0.578400i	$0.196323\pi$
$158$	−4.70375	−	1.11059i	−0.374210	−	0.0883536i
$159$	15.3023	−	7.19352i	1.21355	−	0.570483i
$160$	−16.8151	+	3.67454i	−1.32935	+	0.290498i
$161$	−15.2534			−1.20214
$162$	−0.571410	+	12.7151i	−0.0448942	+	0.998992i
$163$	−3.34769	−	16.8300i	−0.262211	−	1.31823i	−0.857405	−	0.514643i	$-0.827925\pi$
$163$	−3.34769	−	16.8300i	−0.262211	−	1.31823i	0.595193	−	0.803582i	$-0.297075\pi$
$164$	0.312491	−	4.39252i	0.0244015	−	0.342998i
$165$	−9.65496	+	16.0228i	−0.751638	+	1.24738i
$166$	7.16258	+	0.254457i	0.555924	+	0.0197497i
$167$	−1.22144	+	2.94883i	−0.0945182	+	0.228187i	−0.964067	−	0.265661i	$-0.914410\pi$
$167$	−1.22144	+	2.94883i	−0.0945182	+	0.228187i	0.869548	+	0.493848i	$0.164410\pi$
$168$	20.1952	−	6.98294i	1.55809	−	0.538746i
$169$	0.301994	+	0.729078i	0.0232303	+	0.0560829i
$170$	−14.9680	+	5.58601i	−1.14800	+	0.428427i
$171$	−7.06522	+	5.74293i	−0.540291	+	0.439173i
$172$	−12.6835	+	16.3401i	−0.967108	+	1.24592i
$173$	−7.18488	−	4.80078i	−0.546256	−	0.364997i	0.251613	−	0.967828i	$-0.419039\pi$
$173$	−7.18488	−	4.80078i	−0.546256	−	0.364997i	−0.797869	+	0.602831i	$0.794039\pi$
$174$	2.96415	+	0.555087i	0.224712	+	0.0420810i
$175$	−13.1322	−	13.1322i	−0.992701	−	0.992701i
$176$	6.13761	+	12.8036i	0.462640	+	0.965107i
$177$	−16.0785	−	5.79563i	−1.20853	−	0.435627i
$178$	−1.48093	−	9.12800i	−0.111000	−	0.684172i
$179$	−7.38237	−	4.93275i	−0.551785	−	0.368691i	0.248202	−	0.968708i	$-0.420160\pi$
$179$	−7.38237	−	4.93275i	−0.551785	−	0.368691i	−0.799987	+	0.600018i	$0.795160\pi$
$180$	3.15867	−	17.9807i	0.235433	−	1.34020i
$181$	−19.3001	−	3.83904i	−1.43457	−	0.285353i	−0.584229	−	0.811589i	$-0.698603\pi$
$181$	−19.3001	−	3.83904i	−1.43457	−	0.285353i	−0.850339	+	0.526235i	$0.823603\pi$
$182$	20.8378	+	9.51156i	1.54460	+	0.705043i
$183$	−8.13331	+	8.93146i	−0.601232	+	0.660233i
$184$	4.58959	+	8.76190i	0.338349	+	0.645936i
$185$	−4.61032	+	11.1303i	−0.338958	+	0.818316i
$186$	4.72263	−	11.7736i	0.346280	−	0.863280i
$187$	7.32211	+	10.9583i	0.535446	+	0.801351i
$188$	2.83436	+	8.50517i	0.206717	+	0.620303i
$189$	−1.27163	+	22.6289i	−0.0924977	+	1.64601i
$190$	11.1092	−	6.86530i	0.805946	−	0.498061i
$191$	9.13099			0.660695			0.330348	−	0.943859i	$-0.392834\pi$
$191$	9.13099			0.660695			0.330348	+	0.943859i	$0.392834\pi$
$192$	−10.0876	−	9.49944i	−0.728013	−	0.685563i
$193$	23.6494			1.70232			0.851160	−	0.524906i	$-0.175900\pi$
$193$	23.6494			1.70232			0.851160	+	0.524906i	$0.175900\pi$
$194$	4.23589	−	2.61771i	0.304119	−	0.187941i
$195$	15.7459	−	11.6207i	1.12758	−	0.832174i
$196$	22.8169	−	7.60377i	1.62978	−	0.543127i
$197$	6.24273	+	9.34291i	0.444776	+	0.665655i	0.984338	−	0.176291i	$-0.0564101\pi$
$197$	6.24273	+	9.34291i	0.444776	+	0.665655i	−0.539562	+	0.841946i	$0.681410\pi$
$198$	−15.0347	+	0.872456i	−1.06847	+	0.0620028i
$199$	−7.52440	+	18.1655i	−0.533391	+	1.28772i	0.395874	+	0.918305i	$0.370442\pi$
$199$	−7.52440	+	18.1655i	−0.533391	+	1.28772i	−0.929265	+	0.369414i	$0.879558\pi$
$200$	−3.59208	+	11.4947i	−0.253998	+	0.812801i
$201$	−4.94515	−	4.50323i	−0.348804	−	0.317634i
$202$	−6.09247	−	2.78095i	−0.428665	−	0.195667i
$203$	5.26682	+	1.04764i	0.369658	+	0.0735296i
$204$	−10.5175	−	7.40318i	−0.736372	−	0.518326i
$205$	−5.57033	−	3.72197i	−0.389049	−	0.259954i
$206$	0.209844	+	1.29342i	0.0146205	+	0.0901166i
$207$	−10.4454	+	0.979240i	−0.726003	+	0.0680619i
$208$	−0.806232	−	14.8316i	−0.0559021	−	1.02839i
$209$	−7.61772	−	7.61772i	−0.526929	−	0.526929i
$210$	5.98373	−	31.9529i	0.412916	−	2.20496i
$211$	−12.5441	−	8.38171i	−0.863572	−	0.577021i	0.0429981	−	0.999075i	$-0.486309\pi$
$211$	−12.5441	−	8.38171i	−0.863572	−	0.577021i	−0.906570	+	0.422055i	$0.861309\pi$
$212$	−15.4235	−	11.9720i	−1.05929	−	0.822238i
$213$	1.90046	+	7.66341i	0.130217	+	0.525088i
$214$	−6.99502	+	2.61051i	−0.478170	+	0.178451i
$215$	12.0426	+	29.0734i	0.821299	+	1.98279i
$216$	13.3811	−	6.07832i	0.910469	−	0.413577i
$217$	8.64440	−	20.8694i	0.586820	−	1.41671i
$218$	−27.8260	−	0.988544i	−1.88461	−	0.0669526i
$219$	1.78544	+	1.07586i	0.120649	+	0.0727001i
$220$	21.5465	+	1.53285i	1.45266	+	0.103345i
$221$	−2.68976	−	13.5224i	−0.180933	−	0.909612i
$222$	−9.49048	+	1.99879i	−0.636960	+	0.134150i
$223$	9.59727			0.642681			0.321341	−	0.946964i	$-0.395867\pi$
$223$	9.59727			0.642681			0.321341	+	0.946964i	$0.395867\pi$
$224$	−17.7720	−	17.1162i	−1.18744	−	1.14362i
$225$	−9.83583	−	8.14970i	−0.655722	−	0.543314i
$226$	7.56794	+	1.78684i	0.503412	+	0.118859i
$227$	22.3302	−	4.44175i	1.48210	−	0.294809i	0.613255	−	0.789885i	$-0.289860\pi$
$227$	22.3302	−	4.44175i	1.48210	−	0.294809i	0.868850	+	0.495076i	$0.164860\pi$
$228$	9.61255	+	4.25797i	0.636607	+	0.281991i
$229$	14.5272	+	21.7414i	0.959982	+	1.43671i	0.898685	+	0.438595i	$0.144524\pi$
$229$	14.5272	+	21.7414i	0.959982	+	1.43671i	0.0612967	+	0.998120i	$0.480476\pi$
$230$	15.0383	+	0.534248i	0.991594	+	0.0352273i
$231$	−26.7879	+	1.25292i	−1.76252	+	0.0824362i
$232$	−0.982944	−	3.34059i	−0.0645334	−	0.219321i
$233$	10.1318	−	4.19674i	0.663759	−	0.274938i	−0.0252606	−	0.999681i	$-0.508042\pi$
$233$	10.1318	−	4.19674i	0.663759	−	0.274938i	0.689019	+	0.724743i	$0.258042\pi$
$234$	14.8801	+	5.17565i	0.972742	+	0.338343i
$235$	13.3767	+	2.66079i	0.872600	+	0.173571i
$236$	2.46689	+	19.5804i	0.160581	+	1.27457i
$237$	−5.85317	−	0.882295i	−0.380204	−	0.0573112i
$238$	−18.5793	−	13.3922i	−1.20432	−	0.868090i
$239$	−0.934652	+	0.934652i	−0.0604576	+	0.0604576i	−0.736689	−	0.676232i	$-0.763612\pi$
$239$	−0.934652	+	0.934652i	−0.0604576	+	0.0604576i	0.676232	+	0.736689i	$0.263612\pi$
$240$	−20.1549	+	6.17710i	−1.30099	+	0.398730i
$241$	13.7023	+	13.7023i	0.882643	+	0.882643i	0.993803	−	0.111160i	$-0.0354565\pi$
$241$	13.7023	+	13.7023i	0.882643	+	0.882643i	−0.111160	+	0.993803i	$0.535456\pi$
$242$	−0.362401	−	2.23373i	−0.0232960	−	0.143590i
$243$	0.581929	+	15.5776i	0.0373308	+	0.999303i
$244$	13.4530	+	3.68517i	0.861237	+	0.235919i
$245$	7.13814	−	35.8858i	0.456039	−	2.29266i
$246$	−0.0605484	−	5.39297i	−0.00386043	−	0.343843i
$247$	4.31281	+	10.4120i	0.274418	+	0.662503i
$248$	−14.5888	+	1.31385i	−0.926392	+	0.0834298i
$249$	8.76828	−	0.410109i	0.555667	−	0.0259896i
$250$	−2.17661	−	2.33696i	−0.137661	−	0.147802i
$251$	−4.12402	+	2.75558i	−0.260306	+	0.173931i	−0.678874	−	0.734254i	$-0.737532\pi$
$251$	−4.12402	+	2.75558i	−0.260306	+	0.173931i	0.418569	+	0.908185i	$0.362532\pi$
$252$	23.9477	−	10.5555i	1.50856	−	0.664931i
$253$	−2.42173	−	12.1749i	−0.152253	−	0.765427i
$254$	20.1770	−	12.4691i	1.26602	−	0.782379i
$255$	−17.7080	+	8.32440i	−1.10892	+	0.521294i
$256$	−4.48451	+	15.3587i	−0.280282	+	0.959918i
$257$			22.8107i			1.42289i	0.702740	+	0.711447i	$0.251960\pi$
$257$			22.8107i			1.42289i	−0.702740	+	0.711447i	$0.748040\pi$
$258$	−13.8374	+	21.2210i	−0.861478	+	1.32116i
$259$	−16.9386	+	3.36929i	−1.05251	+	0.209357i
$260$	−20.2107	−	10.1072i	−1.25342	−	0.626823i
$261$	3.67391	+	0.379288i	0.227409	+	0.0234774i
$262$	18.2302	−	16.9794i	1.12627	−	1.04899i
$263$	22.8303	+	9.45661i	1.40778	+	0.583120i	0.951758	−	0.306851i	$-0.0992754\pi$
$263$	22.8303	+	9.45661i	1.40778	+	0.583120i	0.456018	+	0.889971i	$0.349275\pi$
$264$	8.77989	+	15.0106i	0.540365	+	0.923836i
$265$	−27.4424	+	11.3670i	−1.68577	+	0.698271i
$266$	17.0308	+	7.77383i	1.04423	+	0.476644i
$267$	−2.72609	−	10.9927i	−0.166834	−	0.672740i
$268$	−2.04040	+	7.44860i	−0.124637	+	0.454996i
$269$	1.02799	−	1.53850i	0.0626779	−	0.0938042i	−0.798807	−	0.601588i	$-0.794535\pi$
$269$	1.02799	−	1.53850i	0.0626779	−	0.0938042i	0.861485	+	0.507784i	$0.169535\pi$
$270$	2.04627	−	22.2651i	0.124532	−	1.35501i
$271$	0.0319023	−	0.0319023i	0.00193792	−	0.00193792i	−0.706137	−	0.708075i	$-0.749564\pi$
$271$	0.0319023	−	0.0319023i	0.00193792	−	0.00193792i	0.708075	+	0.706137i	$0.249564\pi$
$272$	−2.10248	+	14.7019i	−0.127481	+	0.891434i
$273$	26.3918	+	9.51314i	1.59730	+	0.575762i
$274$	−11.4990	+	15.9528i	−0.694681	+	0.963744i
$275$	8.39680	−	12.5667i	0.506346	−	0.757800i
$276$	6.48370	+	10.2330i	0.390273	+	0.615954i
$277$	0.626270	−	3.14847i	0.0376289	−	0.189173i	−0.957399	−	0.288768i	$-0.906754\pi$
$277$	0.626270	−	3.14847i	0.0376289	−	0.189173i	0.995028	+	0.0995943i	$0.0317545\pi$
$278$	9.57688	−	3.57405i	0.574383	−	0.214357i
$279$	4.57980	−	14.8461i	0.274185	−	0.888811i
$280$	−36.0109	+	10.5959i	−2.15206	+	0.633228i
$281$	10.5921	+	4.38740i	0.631872	+	0.261730i	0.675548	−	0.737316i	$-0.263907\pi$
$281$	10.5921	+	4.38740i	0.631872	+	0.261730i	−0.0436760	+	0.999046i	$0.513907\pi$
$282$	4.31543	+	10.0963i	0.256980	+	0.601223i
$283$	3.92232	−	2.62081i	0.233158	−	0.155791i	−0.433504	−	0.901152i	$-0.642723\pi$
$283$	3.92232	−	2.62081i	0.233158	−	0.155791i	0.666661	+	0.745361i	$0.267723\pi$
$284$	6.88791	−	5.97296i	0.408722	−	0.354430i
$285$	12.8691	−	9.49762i	0.762303	−	0.562591i
$286$	−4.28351	+	18.1423i	−0.253289	+	1.07277i
$287$		−	9.60385i		−	0.566898i
$288$	−13.2689	−	10.5800i	−0.781875	−	0.623435i
$289$		−	3.21460i		−	0.189094i
$290$	−5.15583	−	1.21733i	−0.302761	−	0.0714839i
$291$	4.90696	−	3.62141i	0.287651	−	0.212291i
$292$	0.170807	−	2.40094i	0.00999573	−	0.140505i
$293$	−0.574936	+	0.384160i	−0.0335881	+	0.0224428i	−0.572251	−	0.820079i	$-0.693930\pi$
$293$	−0.574936	+	0.384160i	−0.0335881	+	0.0224428i	0.538663	+	0.842521i	$0.318930\pi$
$294$	27.0853	−	11.5770i	1.57965	−	0.675187i
$295$	27.7384	+	11.4896i	1.61499	+	0.668951i
$296$	7.03201	+	8.71608i	0.408727	+	0.506612i
$297$	−18.2636	+	2.57772i	−1.05976	+	0.149574i
$298$	4.55808	+	12.2136i	0.264043	+	0.707517i
$299$	−2.53342	+	12.7364i	−0.146511	+	0.736562i
$300$	−3.22790	+	14.3920i	−0.186363	+	0.830921i
$301$	−25.0629	+	37.5092i	−1.44460	+	2.16200i
$302$	−12.7090	−	9.16086i	−0.731322	−	0.527148i
$303$	−7.71632	−	2.78141i	−0.443291	−	0.159788i
$304$	−0.658936	−	12.1219i	−0.0377926	−	0.695240i
$305$	15.0051	−	15.0051i	0.859189	−	0.859189i
$306$	−13.5826	−	7.97808i	−0.776467	−	0.456076i
$307$	6.16137	−	9.22115i	0.351648	−	0.526279i	−0.612909	−	0.790154i	$-0.710001\pi$
$307$	6.16137	−	9.22115i	0.351648	−	0.526279i	0.964557	+	0.263875i	$0.0850007\pi$
$308$	15.3333	+	26.9031i	0.873694	+	1.53295i
$309$	0.386280	+	1.55764i	0.0219747	+	0.0886108i
$310$	−9.25340	+	20.2723i	−0.525558	+	1.15139i
$311$	−15.3264	+	6.34839i	−0.869078	+	0.359984i	−0.772251	−	0.635317i	$-0.780869\pi$
$311$	−15.3264	+	6.34839i	−0.869078	+	0.359984i	−0.0968270	+	0.995301i	$0.530869\pi$
$312$	−2.47645	−	18.0224i	−0.140201	−	1.02032i
$313$	−18.6363	−	7.71943i	−1.05339	−	0.436328i	−0.212288	−	0.977207i	$-0.568092\pi$
$313$	−18.6363	−	7.71943i	−1.05339	−	0.436328i	−0.841100	+	0.540879i	$0.818092\pi$
$314$	−16.5998	−	17.8227i	−0.936783	−	1.00580i
$315$	4.08865	−	39.6040i	0.230369	−	2.23143i
$316$	2.16094	+	6.48442i	0.121563	+	0.364777i
$317$	7.16716	−	1.42564i	0.402548	−	0.0800718i	0.0103359	−	0.999947i	$-0.496710\pi$
$317$	7.16716	−	1.42564i	0.402548	−	0.0800718i	0.392212	+	0.919875i	$0.371710\pi$
$318$	−20.0306	−	13.0611i	−1.12326	−	0.732432i
$319$			4.37016i			0.244682i
$320$	16.9218	+	17.4972i	0.945958	+	0.978124i
$321$	−8.27548	+	3.89025i	−0.461892	+	0.217132i
$322$	11.3402	+	18.3503i	0.631965	+	1.02262i
$323$	−2.19835	−	11.0519i	−0.122320	−	0.614943i
$324$	15.7214	−	8.76563i	0.873413	−	0.486980i
$325$	−13.1463	+	8.78405i	−0.729223	+	0.487251i
$326$	−17.7581	+	16.5396i	−0.983530	+	0.916046i
$327$	−34.0640	+	1.59324i	−1.88374	+	0.0881062i
$328$	−5.51665	+	2.88969i	−0.304606	+	0.159557i
$329$	7.48214	+	18.0635i	0.412504	+	0.995873i
$330$	26.4539	−	0.297006i	1.45624	−	0.0163496i
$331$	0.424003	−	2.13161i	0.0233053	−	0.117164i	−0.967382	−	0.253324i	$-0.918476\pi$
$331$	0.424003	−	2.13161i	0.0233053	−	0.117164i	0.990687	+	0.136160i	$0.0434762\pi$
$332$	−5.01891	−	8.80597i	−0.275449	−	0.483290i
$333$	−11.3830	+	3.39467i	−0.623785	+	0.186027i
$334$	4.45561	−	0.722878i	0.243800	−	0.0395541i
$335$	8.30799	+	8.30799i	0.453914	+	0.453914i
$336$	−23.4148	−	19.1039i	−1.27738	−	1.04220i
$337$	−16.0483	+	16.0483i	−0.874208	+	0.874208i	−0.992928	−	0.118719i	$-0.962121\pi$
$337$	−16.0483	+	16.0483i	−0.874208	+	0.874208i	0.118719	+	0.992928i	$0.462121\pi$
$338$	0.652584	−	0.905341i	0.0354959	−	0.0492441i
$339$	9.41726	+	1.41954i	0.511475	+	0.0770988i
$340$	17.8481	+	13.8541i	0.967952	+	0.751341i
$341$	18.0298	+	3.58635i	0.976369	+	0.194212i
$342$	12.1616	+	4.23008i	0.657622	+	0.228736i
$343$	20.2507	−	8.38812i	1.09344	−	0.452916i
$344$	29.0872	+	3.11052i	1.56828	+	0.167708i
$345$	18.4095	−	0.861048i	0.991136	−	0.0463573i
$346$	−0.433870	+	12.2128i	−0.0233250	+	0.656562i
$347$	−14.7999	−	22.1497i	−0.794502	−	1.18906i	−0.978524	−	0.206134i	$-0.933912\pi$
$347$	−14.7999	−	22.1497i	−0.794502	−	1.18906i	0.184022	−	0.982922i	$-0.441088\pi$
$348$	−1.53592	−	3.97864i	−0.0823338	−	0.213277i
$349$	−0.786555	+	0.156456i	−0.0421033	+	0.00837487i	−0.216097	−	0.976372i	$-0.569333\pi$
$349$	−0.786555	+	0.156456i	−0.0421033	+	0.00837487i	0.173994	+	0.984747i	$0.444333\pi$
$350$	−6.03526	+	25.5616i	−0.322598	+	1.36632i
$351$	18.6835	+	4.82018i	0.997251	+	0.257282i
$352$	10.8401	−	16.9026i	0.577778	−	0.900911i
$353$	−15.2832			−0.813444			−0.406722	−	0.913552i	$-0.633328\pi$
$353$	−15.2832			−0.813444			−0.406722	+	0.913552i	$0.633328\pi$
$354$	4.98128	+	23.6517i	0.264752	+	1.25707i
$355$	−2.70590	−	13.6035i	−0.143614	−	0.721998i
$356$	−9.88025	+	8.56782i	−0.523652	+	0.454094i
$357$	−24.0255	−	14.4772i	−1.27156	−	0.766213i
$358$	−0.445796	+	12.5485i	−0.0235611	+	0.663207i
$359$	6.76376	−	16.3292i	0.356977	−	0.861820i	−0.638745	−	0.769419i	$-0.720546\pi$
$359$	6.76376	−	16.3292i	0.356977	−	0.861820i	0.995722	−	0.0924007i	$-0.0294541\pi$
$360$	−23.9796	+	9.56779i	−1.26383	+	0.504267i
$361$	−3.74611	−	9.04390i	−0.197164	−	0.475995i
$362$	9.73025	+	26.0728i	0.511411	+	1.37035i
$363$	−0.667107	−	2.69004i	−0.0350141	−	0.141191i
$364$	−4.04924	−	32.1399i	−0.212238	−	1.68459i
$365$	−3.04473	−	2.03442i	−0.159369	−	0.106487i
$366$	16.7915	+	3.14450i	0.877708	+	0.164366i
$367$	−13.6752	−	13.6752i	−0.713838	−	0.713838i	0.253498	−	0.967336i	$-0.418419\pi$
$367$	−13.6752	−	13.6752i	−0.713838	−	0.713838i	−0.967336	+	0.253498i	$0.918419\pi$
$368$	7.12868	−	12.0355i	0.371608	−	0.627392i
$369$	−0.616548	−	6.57660i	−0.0320962	−	0.342364i
$370$	16.8176	−	2.72849i	0.874307	−	0.141847i
$371$	−35.4050	−	23.6569i	−1.83814	−	1.22820i
$372$	−17.6750	+	3.07163i	−0.916406	+	0.159257i
$373$	20.1495	+	4.00798i	1.04330	+	0.207526i	0.686858	−	0.726791i	$-0.258989\pi$
$373$	20.1495	+	4.00798i	1.04330	+	0.207526i	0.356443	+	0.934317i	$0.383989\pi$
$374$	7.73954	−	16.9557i	0.400202	−	0.876758i
$375$	−2.89193	−	2.63350i	−0.149339	−	0.135993i
$376$	8.12475	−	9.73300i	0.419002	−	0.501941i
$377$	1.74951	−	4.22370i	0.0901046	−	0.217532i
$378$	28.1686	−	15.2937i	1.44884	−	0.786621i
$379$	−15.2098	−	22.7630i	−0.781274	−	1.16926i	−0.981865	−	0.189584i	$-0.939286\pi$
$379$	−15.2098	−	22.7630i	−0.781274	−	1.16926i	0.200591	−	0.979675i	$-0.435714\pi$
$380$	−16.5183	−	8.26067i	−0.847371	−	0.423763i
$381$	23.3735	−	17.2500i	1.19746	−	0.883745i
$382$	−6.78845	−	10.9848i	−0.347327	−	0.562034i
$383$	0.731898			0.0373982			0.0186991	−	0.999825i	$-0.494048\pi$
$383$	0.731898			0.0373982			0.0186991	+	0.999825i	$0.494048\pi$
$384$	−3.92842	+	19.1981i	−0.200471	+	0.979700i
$385$	47.1094			2.40092
$386$	−17.5822	−	28.4509i	−0.894910	−	1.44811i
$387$	−14.7547	+	27.2948i	−0.750024	+	1.38747i
$388$	−6.29836	−	3.14976i	−0.319751	−	0.159905i
$389$	1.45175	+	2.17270i	0.0736067	+	0.110160i	0.866447	−	0.499270i	$-0.166398\pi$
$389$	1.45175	+	2.17270i	0.0736067	+	0.110160i	−0.792840	+	0.609430i	$0.791398\pi$
$390$	−25.6863	−	10.3033i	−1.30068	−	0.521729i
$391$	4.96880	−	11.9958i	0.251283	−	0.606651i
$392$	−26.1108	−	21.7964i	−1.31880	−	1.10088i
$393$	20.5434	−	22.5594i	1.03628	−	1.13797i
$394$	6.59862	−	14.4562i	0.332434	−	0.728292i
$395$	10.1985	+	2.02861i	0.513143	+	0.102071i
$396$	12.2271	+	17.4385i	0.614437	+	0.876319i
$397$	−8.79283	−	5.87518i	−0.441299	−	0.294867i	0.315001	−	0.949091i	$-0.397995\pi$
$397$	−8.79283	−	5.87518i	−0.441299	−	0.294867i	−0.756300	+	0.654224i	$0.772995\pi$
$398$	27.4477	−	4.45311i	1.37583	−	0.223214i
$399$	21.5701	+	7.77513i	1.07986	+	0.389243i
$400$	16.4990	−	4.22441i	0.824952	−	0.211221i
$401$	8.20199	+	8.20199i	0.409588	+	0.409588i	0.881595	−	0.472007i	$-0.156470\pi$
$401$	8.20199	+	8.20199i	0.409588	+	0.409588i	−0.472007	+	0.881595i	$0.656470\pi$
$402$	−1.74104	+	9.29710i	−0.0868351	+	0.463697i
$403$	−15.9899	−	10.6841i	−0.796512	−	0.532212i
$404$	1.18390	+	9.39692i	0.0589011	+	0.467514i
$405$	0.257361	−	27.3828i	0.0127884	−	1.36066i
$406$	−2.65529	−	7.11501i	−0.131780	−	0.353112i
$407$	−5.37854	−	12.9849i	−0.266604	−	0.643640i
$408$	−1.08698	+	18.1568i	−0.0538137	+	0.898894i
$409$	3.08042	−	7.43679i	0.152317	−	0.367725i	−0.829241	−	0.558891i	$-0.811227\pi$
$409$	3.08042	−	7.43679i	0.152317	−	0.367725i	0.981558	+	0.191166i	$0.0612269\pi$
$410$	−0.336373	+	9.46838i	−0.0166123	+	0.467610i
$411$	−12.4306	+	20.6291i	−0.613155	+	1.01756i
$412$	1.40001	−	1.21404i	0.0689735	−	0.0598115i
$413$	8.39677	+	42.2134i	0.413178	+	2.07719i
$414$	8.94368	+	11.8381i	0.439558	+	0.581809i
$415$	−15.4199			−0.756935
$416$	−17.2435	+	11.9965i	−0.845430	+	0.588177i
$417$	11.3300	−	5.32613i	0.554831	−	0.260822i
$418$	−3.50093	+	14.8277i	−0.171236	+	0.725249i
$419$	−17.0535	+	3.39216i	−0.833120	+	0.165718i	−0.593180	−	0.805070i	$-0.702128\pi$
$419$	−17.0535	+	3.39216i	−0.833120	+	0.165718i	−0.239940	+	0.970788i	$0.577128\pi$
$420$	−42.8889	+	16.5569i	−2.09277	+	0.807893i
$421$	−3.54586	−	5.30676i	−0.172815	−	0.258635i	0.734944	−	0.678127i	$-0.237208\pi$
$421$	−3.54586	−	5.30676i	−0.172815	−	0.258635i	−0.907759	+	0.419492i	$0.862208\pi$
$422$	−0.757495	+	21.3223i	−0.0368743	+	1.03795i
$423$	6.28332	+	11.8893i	0.305505	+	0.578078i
$424$	−2.93603	+	27.4555i	−0.142586	+	1.33335i
$425$	14.6054	−	6.04974i	0.708464	−	0.293455i
$426$	7.80641	−	7.98369i	0.378222	−	0.386811i
$427$	29.8359	+	5.93473i	1.44386	+	0.287202i
$428$	8.34099	+	6.47442i	0.403177	+	0.312953i
$429$	−3.40300	+	22.5755i	−0.164298	+	1.08996i
$430$	26.0231	−	36.1023i	1.25494	−	1.74101i
$431$	−17.4015	+	17.4015i	−0.838202	+	0.838202i	−0.988622	−	0.150420i	$-0.951937\pi$
$431$	−17.4015	+	17.4015i	−0.838202	+	0.838202i	0.150420	+	0.988622i	$0.451937\pi$
$432$	−17.2606	−	11.5789i	−0.830451	−	0.557091i
$433$	−24.4164	−	24.4164i	−1.17338	−	1.17338i	−0.981399	−	0.191978i	$-0.938510\pi$
$433$	−24.4164	−	24.4164i	−1.17338	−	1.17338i	−0.191978	−	0.981399i	$-0.561490\pi$
$434$	−31.5332	+	5.11595i	−1.51364	+	0.245573i
$435$	−6.41572	−	0.967093i	−0.307610	−	0.0463686i
$436$	19.4980	+	34.2104i	0.933787	+	1.63838i
$437$	−2.07057	+	10.4095i	−0.0990489	+	0.497952i
$438$	−0.0330957	−	2.94779i	−0.00158137	−	0.140851i
$439$	−0.156658	−	0.378206i	−0.00747688	−	0.0180508i	0.920097	−	0.391691i	$-0.128110\pi$
$439$	−0.156658	−	0.378206i	−0.00747688	−	0.0180508i	−0.927574	+	0.373640i	$0.878110\pi$
$440$	−14.1747	−	27.0606i	−0.675752	−	1.29006i
$441$	31.8956	−	16.8563i	1.51884	−	0.802682i
$442$	−14.2681	+	13.2891i	−0.678663	+	0.632097i
$443$	−14.5934	+	9.75098i	−0.693352	+	0.463283i	−0.851652	−	0.524108i	$-0.824399\pi$
$443$	−14.5934	+	9.75098i	−0.693352	+	0.463283i	0.158300	+	0.987391i	$0.449399\pi$
$444$	9.46032	+	9.93132i	0.448967	+	0.471320i
$445$	3.88143	+	19.5133i	0.183998	+	0.925019i
$446$	−7.13511	−	11.5458i	−0.337857	−	0.546710i
$447$	6.79255	+	14.4494i	0.321277	+	0.683433i
$448$	−7.37868	+	34.1053i	−0.348610	+	1.61132i
$449$			3.54753i			0.167418i	0.996490	+	0.0837092i	$0.0266767\pi$
$449$			3.54753i			0.167418i	−0.996490	+	0.0837092i	$0.973323\pi$
$450$	−2.49187	+	17.8917i	−0.117468	+	0.843423i
$451$	7.66552	−	1.52477i	0.360955	−	0.0717985i
$452$	−3.47678	−	10.4329i	−0.163534	−	0.490722i
$453$	−16.4345	−	9.90300i	−0.772159	−	0.465284i
$454$	−21.9450	−	23.5616i	−1.02993	−	1.10580i
$455$	−45.5306	−	18.8594i	−2.13451	−	0.884143i
$456$	−2.02401	−	14.7298i	−0.0947830	−	0.689785i
$457$	10.7014	−	4.43266i	0.500590	−	0.207351i	−0.118077	−	0.993004i	$-0.537673\pi$
$457$	10.7014	−	4.43266i	0.500590	−	0.207351i	0.618667	+	0.785653i	$0.287673\pi$
$458$	15.3553	−	33.6403i	0.717508	−	1.57191i
$459$	−17.3818	−	8.37139i	−0.811311	−	0.390743i
$460$	−10.5375	−	18.4887i	−0.491314	−	0.862039i
$461$	4.16318	−	6.23064i	0.193899	−	0.290190i	−0.721763	−	0.692141i	$-0.756668\pi$
$461$	4.16318	−	6.23064i	0.193899	−	0.290190i	0.915661	+	0.401951i	$0.131668\pi$
$462$	21.4228	+	31.2952i	0.996681	+	1.45598i
$463$	−3.41234	+	3.41234i	−0.158585	+	0.158585i	−0.781939	−	0.623354i	$-0.785769\pi$
$463$	−3.41234	+	3.41234i	−0.158585	+	0.158585i	0.623354	+	0.781939i	$0.285769\pi$
$464$	−3.28806	+	3.66608i	−0.152644	+	0.170194i
$465$	−9.25495	+	25.6755i	−0.429188	+	1.19067i
$466$	−12.5813	−	9.06882i	−0.582819	−	0.420105i
$467$	−0.812779	+	1.21641i	−0.0376109	+	0.0562887i	−0.849799	−	0.527108i	$-0.823277\pi$
$467$	−0.812779	+	1.21641i	−0.0376109	+	0.0562887i	0.812188	+	0.583396i	$0.198277\pi$
$468$	−4.83618	−	21.7490i	−0.223553	−	1.00535i
$469$	−3.28593	+	16.5195i	−0.151730	+	0.762798i
$470$	−6.74393	−	18.0707i	−0.311074	−	0.833541i
$471$	−22.0552	−	20.0842i	−1.01625	−	0.925433i
$472$	21.7218	−	17.5248i	0.999825	−	0.806645i
$473$	−33.9179	−	14.0493i	−1.55955	−	0.645986i
$474$	3.29012	+	7.69747i	0.151120	+	0.353557i
$475$	−10.7445	+	7.17924i	−0.492991	+	0.329406i
$476$	−2.29844	+	32.3079i	−0.105349	+	1.48083i
$477$	−25.7636	−	13.9270i	−1.17963	−	0.637673i
$478$	1.81928	+	0.429545i	0.0832120	+	0.0196469i
$479$		−	22.7501i		−	1.03948i	−0.854324	−	0.519740i	$-0.826029\pi$
$479$		−	22.7501i		−	1.03948i	0.854324	−	0.519740i	$-0.173971\pi$
$480$	22.4154	+	19.6545i	1.02312	+	0.897102i
$481$			14.7030i			0.670399i
$482$	6.29727	−	26.6713i	0.286833	−	1.21484i
$483$	15.6883	+	21.2575i	0.713843	+	0.967248i
$484$	−2.41782	+	2.09665i	−0.109901	+	0.0953024i
$485$	−8.90778	+	5.95199i	−0.404481	+	0.270266i
$486$	18.3077	−	12.2813i	0.830452	−	0.557090i
$487$	−32.7878	−	13.5812i	−1.48576	−	0.615422i	−0.515370	−	0.856968i	$-0.672345\pi$
$487$	−32.7878	−	13.5812i	−1.48576	−	0.615422i	−0.970389	+	0.241546i	$0.922345\pi$
$488$	−5.56825	−	18.9240i	−0.252063	−	0.856651i
$489$	−20.0114	+	21.9752i	−0.904947	+	0.993752i
$490$	−48.4786	+	18.0920i	−2.19004	+	0.817314i
$491$	1.10976	−	5.57913i	0.0500827	−	0.251783i	−0.947631	−	0.319368i	$-0.896529\pi$
$491$	1.10976	−	5.57913i	0.0500827	−	0.251783i	0.997714	+	0.0675851i	$0.0215294\pi$
$492$	−6.44289	+	4.08226i	−0.290468	+	0.184042i
$493$	−2.53956	+	3.80071i	−0.114376	+	0.171176i
$494$	9.31963	−	12.9293i	0.419310	−	0.581717i
$495$	32.2599	−	3.02433i	1.44998	−	0.135933i
$496$	12.4267	+	16.5740i	0.557975	+	0.744195i
$497$	14.0596	−	14.0596i	0.630658	−	0.630658i
$498$	−7.01217	−	10.2436i	−0.314223	−	0.459027i
$499$	14.8120	−	22.1677i	0.663076	−	0.992364i	−0.335654	−	0.941985i	$-0.608957\pi$
$499$	14.8120	−	22.1677i	0.663076	−	0.992364i	0.998730	−	0.0503786i	$-0.0160428\pi$
$500$	−1.19323	+	4.35595i	−0.0533627	+	0.194804i
$501$	5.36581	−	1.33067i	0.239726	−	0.0594501i
$502$	6.38105	+	2.91267i	0.284800	+	0.129999i
$503$	21.9742	−	9.10199i	0.979779	−	0.405838i	0.165435	−	0.986221i	$-0.447097\pi$
$503$	21.9742	−	9.10199i	0.979779	−	0.405838i	0.814344	+	0.580383i	$0.197097\pi$
$504$	−30.5025	−	20.9623i	−1.35869	−	0.933735i
$505$	13.3120	+	5.51403i	0.592378	+	0.245371i
$506$	−12.8463	+	11.9648i	−0.571087	+	0.531902i
$507$	0.705451	−	1.17073i	0.0313302	−	0.0519938i
$508$	−30.0013	−	15.0034i	−1.33109	−	0.665669i
$509$	−30.7288	+	6.11234i	−1.36203	+	0.270925i	−0.821409	−	0.570340i	$-0.806811\pi$
$509$	−30.7288	+	6.11234i	−1.36203	+	0.270925i	−0.540623	+	0.841265i	$0.681811\pi$
$510$	23.1795	+	15.1144i	1.02641	+	0.669278i
$511$		−	5.24945i		−	0.232222i
$512$	21.8110	−	6.02344i	0.963918	−	0.266201i
$513$	15.2701	+	3.93955i	0.674191	+	0.173935i
$514$	27.4420	−	16.9587i	1.21041	−	0.748015i
$515$	−0.549991	−	2.76499i	−0.0242355	−	0.121840i
$516$	35.8170	+	0.869957i	1.57675	+	0.0382977i
$517$	−13.2299	+	8.83991i	−0.581848	+	0.388779i
$518$	16.6464	+	17.8727i	0.731399	+	0.785280i
$519$	0.699268	+	14.9506i	0.0306945	+	0.656259i
$520$	2.86642	+	31.8283i	0.125701	+	1.39576i
$521$	14.3239	+	34.5809i	0.627540	+	1.51502i	0.842670	+	0.538430i	$0.180982\pi$
$521$	14.3239	+	34.5809i	0.627540	+	1.51502i	−0.215130	+	0.976585i	$0.569018\pi$
$522$	−2.27508	−	4.70180i	−0.0995775	−	0.205792i
$523$	−4.16622	+	20.9450i	−0.182176	+	0.915862i	0.776229	+	0.630451i	$0.217130\pi$
$523$	−4.16622	+	20.9450i	−0.182176	+	0.915862i	−0.958405	+	0.285411i	$0.907870\pi$
$524$	−33.9800	−	9.30814i	−1.48442	−	0.406628i
$525$	−4.79466	+	31.8079i	−0.209256	+	1.38821i
$526$	−5.59663	−	34.4960i	−0.244025	−	1.50410i
$527$	13.5964	+	13.5964i	0.592269	+	0.592269i
$528$	11.5307	−	21.7221i	0.501810	−	0.945333i
$529$	7.61597	−	7.61597i	0.331129	−	0.331129i
$530$	34.0770	+	24.5632i	1.48021	+	1.06696i
$531$	8.46002	+	28.3681i	0.367133	+	1.23107i
$532$	−3.30946	−	26.2681i	−0.143483	−	1.13886i
$533$	−8.01905	−	1.59509i	−0.347343	−	0.0690909i
$534$	−11.1978	+	11.4521i	−0.484575	+	0.495580i
$535$	14.8408	−	6.14727i	0.641625	−	0.265770i
$536$	10.4778	−	3.08302i	0.452573	−	0.133166i
$537$	0.718490	+	15.3616i	0.0310051	+	0.662901i
$538$	−2.61513	−	0.0929048i	−0.112746	−	0.00400541i
$539$	23.7149	+	35.4919i	1.02147	+	1.52874i
$540$	−28.3069	+	14.0913i	−1.21813	+	0.606394i
$541$	25.8204	−	5.13599i	1.11010	−	0.220814i	0.394209	−	0.919021i	$-0.371019\pi$
$541$	25.8204	−	5.13599i	1.11010	−	0.220814i	0.715896	+	0.698207i	$0.246019\pi$
$542$	−0.0620971	−	0.0146616i	−0.00266730	−	0.000629768i
$543$	14.5002	+	30.8455i	0.622265	+	1.32371i
$544$	19.2499	−	8.40082i	0.825333	−	0.360182i
$545$	59.9051			2.56605
$546$	−8.17644	−	38.8227i	−0.349919	−	1.66146i
$547$	−1.99831	−	10.0462i	−0.0854414	−	0.429543i	−0.999702	−	0.0244161i	$-0.992227\pi$
$547$	−1.99831	−	10.0462i	−0.0854414	−	0.429543i	0.914260	−	0.405127i	$-0.132773\pi$
$548$	27.7406	+	1.97351i	1.18502	+	0.0843044i
$549$	20.8122	+	2.14862i	0.888244	+	0.0917009i
$550$	−21.3607	−	0.758859i	−0.910824	−	0.0323579i
$551$	1.42988	−	3.45205i	0.0609151	−	0.147062i
$552$	7.49028	−	15.4078i	0.318808	−	0.655801i
$553$	5.70445	+	13.7718i	0.242578	+	0.585635i
$554$	−4.25331	+	1.58732i	−0.180706	+	0.0674386i
$555$	20.2531	−	5.02260i	0.859697	−	0.213198i
$556$	−11.4196	−	8.86413i	−0.484301	−	0.375923i
$557$	1.16495	+	0.778397i	0.0493606	+	0.0329817i	0.580006	−	0.814612i	$-0.303050\pi$
$557$	1.16495	+	0.778397i	0.0493606	+	0.0329817i	−0.530645	+	0.847594i	$0.678050\pi$
$558$	−21.2651	+	5.52771i	−0.900224	+	0.234006i
$559$	27.1569	+	27.1569i	1.14861	+	1.14861i
$560$	39.5196	+	35.4446i	1.67001	+	1.49781i
$561$	7.74083	−	21.4750i	0.326818	−	0.906673i
$562$	−2.59656	−	16.0044i	−0.109529	−	0.675106i
$563$	25.4602	+	17.0119i	1.07302	+	0.716968i	0.960947	−	0.276732i	$-0.0892515\pi$
$563$	25.4602	+	17.0119i	1.07302	+	0.716968i	0.112071	+	0.993700i	$0.464251\pi$
$564$	8.93777	−	12.6977i	0.376348	−	0.534668i
$565$	−16.4086	−	3.26387i	−0.690314	−	0.137312i
$566$	−6.06896	−	2.77022i	−0.255098	−	0.116441i
$567$	32.8438	−	21.5018i	1.37931	−	0.902992i
$568$	−12.3065	−	3.84574i	−0.516368	−	0.161364i
$569$	−13.6572	+	32.9714i	−0.572539	+	1.38223i	0.326847	+	0.945077i	$0.394014\pi$
$569$	−13.6572	+	32.9714i	−0.572539	+	1.38223i	−0.899386	+	0.437155i	$0.855986\pi$
$570$	−20.9935	−	8.42094i	−0.879321	−	0.352714i
$571$	−17.2468	−	25.8117i	−0.721757	−	1.08019i	−0.993050	−	0.117689i	$-0.962451\pi$
$571$	−17.2468	−	25.8117i	−0.721757	−	1.08019i	0.271293	−	0.962497i	$-0.412549\pi$
$572$	25.0103	−	8.33471i	1.04573	−	0.348492i
$573$	−9.39131	−	12.7251i	−0.392328	−	0.531599i
$574$	−11.5537	+	7.14000i	−0.482243	+	0.298018i
$575$	−14.8898			−0.620949
$576$	−2.86333	+	23.8286i	−0.119305	+	0.992858i
$577$	−36.8843			−1.53551			−0.767757	−	0.640741i	$-0.778627\pi$
$577$	−36.8843			−1.53551			−0.767757	+	0.640741i	$0.778627\pi$
$578$	−3.86725	+	2.38990i	−0.160857	+	0.0994067i
$579$	−24.3236	−	32.9582i	−1.01086	−	1.36970i
$580$	2.36863	+	7.10764i	0.0983521	+	0.295129i
$581$	−12.2810	−	18.3798i	−0.509501	−	0.762521i
$582$	−8.00474	−	3.21087i	−0.331807	−	0.133095i
$583$	13.2611	−	32.0152i	0.549219	−	1.32593i
$584$	−3.01539	+	1.57950i	−0.124778	+	0.0653602i
$585$	−32.3895	−	9.99171i	−1.33914	−	0.413106i
$586$	0.889592	+	0.406060i	0.0367487	+	0.0167742i
$587$	37.9234	+	7.54343i	1.56527	+	0.311351i	0.900214	−	0.435447i	$-0.143410\pi$
$587$	37.9234	+	7.54343i	1.56527	+	0.311351i	0.665051	+	0.746798i	$0.268410\pi$
$588$	−34.0642	−	23.9775i	−1.40478	−	0.988814i
$589$	−13.0686	−	8.73214i	−0.538481	−	0.359802i
$590$	−6.79980	−	41.9120i	−0.279944	−	1.72549i
$591$	6.59972	−	18.3093i	0.271476	−	0.753142i
$592$	5.25774	−	14.9397i	0.216092	−	0.614018i
$593$	−31.9188	−	31.9188i	−1.31075	−	1.31075i	−0.920862	−	0.389888i	$-0.872514\pi$
$593$	−31.9188	−	31.9188i	−1.31075	−	1.31075i	−0.389888	−	0.920862i	$-0.627486\pi$
$594$	16.6792	+	20.0552i	0.684355	+	0.822876i
$595$	40.9709	+	27.3759i	1.67964	+	1.12230i
$596$	11.3047	−	14.5638i	0.463057	−	0.596555i
$597$	33.0547	−	8.19728i	1.35284	−	0.335492i
$598$	17.2057	−	6.42109i	0.703593	−	0.262578i
$599$	16.5939	+	40.0613i	0.678009	+	1.63686i	0.767638	+	0.640884i	$0.221432\pi$
$599$	16.5939	+	40.0613i	0.678009	+	1.63686i	−0.0896284	+	0.995975i	$0.528568\pi$
$600$	19.7138	−	6.81648i	0.804811	−	0.278282i
$601$	−6.78725	+	16.3859i	−0.276858	+	0.668394i	−0.999745	−	0.0225721i	$-0.992814\pi$
$601$	−6.78725	+	16.3859i	−0.276858	+	0.668394i	0.722888	+	0.690966i	$0.242814\pi$
$602$	63.7577	+	2.26505i	2.59857	+	0.0923166i
$603$	−1.18964	+	11.5233i	−0.0484460	+	0.469264i
$604$	−1.57223	+	22.1000i	−0.0639731	+	0.899236i
$605$	0.949836	+	4.77515i	0.0386163	+	0.194137i
$606$	2.39059	+	11.3508i	0.0971112	+	0.461095i
$607$	23.8735			0.968997			0.484499	−	0.874792i	$-0.339002\pi$
$607$	23.8735			0.968997			0.484499	+	0.874792i	$0.339002\pi$
$608$	−14.0931	+	9.80478i	−0.571552	+	0.397637i
$609$	−3.95697	−	8.41743i	−0.160345	−	0.341092i
$610$	−29.2071	−	6.89600i	−1.18256	−	0.279211i
$611$	16.3254	−	3.24732i	0.660455	−	0.131373i
$612$	0.500162	+	22.2716i	0.0202179	+	0.900276i
$613$	16.5222	+	24.7272i	0.667326	+	0.998724i	0.998478	+	0.0551466i	$0.0175626\pi$
$613$	16.5222	+	24.7272i	0.667326	+	0.998724i	−0.331152	+	0.943577i	$0.607437\pi$
$614$	−15.6740	−	0.556833i	−0.632551	−	0.0224720i
$615$	0.542132	+	11.5910i	0.0218609	+	0.467394i
$616$	20.9656	−	38.4475i	0.844730	−	1.54909i
$617$	−38.2873	+	15.8591i	−1.54139	+	0.638464i	−0.981733	−	0.190263i	$-0.939066\pi$
$617$	−38.2873	+	15.8591i	−1.54139	+	0.638464i	−0.559654	+	0.828726i	$0.689066\pi$
$618$	1.58670	−	1.62273i	0.0638265	−	0.0652759i
$619$	−24.1015	−	4.79409i	−0.968721	−	0.192691i	−0.314720	−	0.949184i	$-0.601911\pi$
$619$	−24.1015	−	4.79409i	−0.968721	−	0.192691i	−0.654001	+	0.756494i	$0.726911\pi$
$620$	31.2676	−	3.93934i	1.25574	−	0.158208i
$621$	12.1078	+	13.5497i	0.485871	+	0.543730i
$622$	19.0317	+	13.7183i	0.763102	+	0.550055i
$623$	−20.1675	+	20.1675i	−0.807995	+	0.807995i
$624$	−19.8403	+	16.3780i	−0.794250	+	0.655646i
$625$	19.9122	+	19.9122i	0.796487	+	0.796487i
$626$	4.56853	+	28.1591i	0.182595	+	1.12546i
$627$	−2.78128	+	18.4511i	−0.111074	+	0.736865i
$628$	−9.10009	+	33.2204i	−0.363133	+	1.32564i
$629$	2.86802	−	14.4185i	0.114356	−	0.574904i
$630$	−50.6845	+	24.5249i	−2.01932	+	0.977095i
$631$	−5.76863	−	13.9267i	−0.229646	−	0.554413i	0.766489	−	0.642258i	$-0.222002\pi$
$631$	−5.76863	−	13.9267i	−0.229646	−	0.554413i	−0.996134	+	0.0878445i	$0.972002\pi$
$632$	6.19439	−	7.42053i	0.246399	−	0.295173i
$633$	1.22086	+	26.1024i	0.0485247	+	1.03748i
$634$	−7.04353	−	7.56242i	−0.279734	−	0.300342i
$635$	−42.4309	+	28.3514i	−1.68382	+	1.12509i
$636$	−0.821153	+	33.8077i	−0.0325608	+	1.34056i
$637$	−8.71163	−	43.7963i	−0.345167	−	1.73527i
$638$	5.25742	−	3.24900i	0.208143	−	0.128629i
$639$	8.72522	−	10.5304i	0.345164	−	0.416577i
$640$	8.46912	−	33.3658i	0.334771	−	1.31890i
$641$		−	40.5694i		−	1.60240i	−0.598400	−	0.801198i	$-0.704197\pi$
$641$		−	40.5694i		−	1.60240i	0.598400	−	0.801198i	$-0.295803\pi$
$642$	10.8325	+	7.06344i	0.427525	+	0.278772i
$643$	27.2528	−	5.42093i	1.07475	−	0.213781i	0.374172	−	0.927359i	$-0.377927\pi$
$643$	27.2528	−	5.42093i	1.07475	−	0.213781i	0.700575	+	0.713579i	$0.252927\pi$
$644$	13.6451	−	27.2852i	0.537692	−	1.07519i
$645$	28.1313	−	46.6851i	1.10767	−	1.83822i
$646$	−11.6614	+	10.8612i	−0.458810	+	0.427329i
$647$	−36.9873	−	15.3206i	−1.45412	−	0.602317i	−0.490945	−	0.871190i	$-0.663349\pi$
$647$	−36.9873	−	15.3206i	−1.45412	−	0.602317i	−0.963175	+	0.268874i	$0.913349\pi$
$648$	−22.2334	−	12.3965i	−0.873412	−	0.486981i
$649$	−32.3604	+	13.4041i	−1.27026	+	0.526158i
$650$	20.3411	+	9.28482i	0.797843	+	0.364180i
$651$	−37.9748	+	9.41743i	−1.48835	+	0.369098i
$652$	33.1000	+	9.06709i	1.29629	+	0.355094i
$653$	15.9518	−	23.8736i	0.624244	−	0.934247i	−0.375728	−	0.926730i	$-0.622607\pi$
$653$	15.9518	−	23.8736i	0.624244	−	0.934247i	0.999972	−	0.00751694i	$-0.00239274\pi$
$654$	27.2417	+	39.7955i	1.06523	+	1.55613i
$655$	−37.9004	+	37.9004i	−1.48089	+	1.48089i
$656$	7.57775	+	4.48835i	0.295861	+	0.175241i
$657$	−0.337004	−	3.59476i	−0.0131478	−	0.140245i
$658$	16.1683	−	22.4306i	0.630306	−	0.874435i
$659$	22.0254	−	32.9634i	0.857988	−	1.28407i	−0.0993356	−	0.995054i	$-0.531672\pi$
$659$	22.0254	−	32.9634i	0.857988	−	1.28407i	0.957324	−	0.289016i	$-0.0933282\pi$
$660$	−20.0245	−	31.6040i	−0.779454	−	1.23019i
$661$	−6.53522	+	32.8548i	−0.254191	+	1.27790i	0.617002	+	0.786961i	$0.288347\pi$
$661$	−6.53522	+	32.8548i	−0.254191	+	1.27790i	−0.871193	+	0.490941i	$0.836653\pi$
$662$	−2.87961	+	1.07466i	−0.111919	+	0.0417678i
$663$	−16.0785	+	17.6564i	−0.624438	+	0.685717i
$664$	−6.86252	+	12.5847i	−0.266317	+	0.488382i
$665$	−37.2124	−	15.4139i	−1.44303	−	0.597724i
$666$	12.5466	+	11.1703i	0.486171	+	0.432841i
$667$	3.57979	−	2.39194i	0.138610	−	0.0926164i
$668$	−4.18218	−	4.82281i	−0.161813	−	0.186600i
$669$	−9.87089	−	13.3749i	−0.381631	−	0.517104i
$670$	3.81816	−	16.1713i	0.147508	−	0.624753i
$671$			24.7564i			0.955710i
$672$	−5.57476	+	42.3715i	−0.215051	+	1.63452i
$673$			24.6322i			0.949502i	0.880120	+	0.474751i	$0.157462\pi$
$673$			24.6322i			0.949502i	−0.880120	+	0.474751i	$0.842538\pi$
$674$	31.2378	+	7.37545i	1.20323	+	0.284092i
$675$	−1.24132	+	22.0894i	−0.0477784	+	0.850222i
$676$	−1.57432	−	0.111999i	−0.0605506	−	0.00430767i
$677$	6.52530	−	4.36006i	0.250788	−	0.167571i	−0.423822	−	0.905745i	$-0.639312\pi$
$677$	6.52530	−	4.36006i	0.250788	−	0.167571i	0.674610	+	0.738174i	$0.264312\pi$
$678$	−5.29353	−	12.3846i	−0.203297	−	0.475628i
$679$	−14.1889	−	5.87725i	−0.544521	−	0.225548i
$680$	3.39759	−	31.7717i	0.130292	−	1.21839i
$681$	−29.1569	−	26.5513i	−1.11729	−	1.01745i
$682$	−9.08981	−	24.3567i	−0.348067	−	0.932665i
$683$	−4.82603	+	24.2621i	−0.184663	+	0.928363i	0.771657	+	0.636039i	$0.219428\pi$
$683$	−4.82603	+	24.2621i	−0.184663	+	0.928363i	−0.956320	+	0.292323i	$0.905572\pi$
$684$	−3.95263	−	17.7756i	−0.151133	−	0.679666i
$685$	23.5059	−	35.1790i	0.898113	−	1.34412i
$686$	−25.1466	−	18.1260i	−0.960101	−	0.692055i
$687$	15.3579	−	42.6066i	0.585940	−	1.62554i
$688$	−17.8829	−	37.3053i	−0.681779	−	1.42225i
$689$	−25.6334	+	25.6334i	−0.976555	+	0.976555i
$690$	−14.7225	−	21.5071i	−0.560475	−	0.818760i
$691$	−18.4404	+	27.5979i	−0.701504	+	1.04988i	0.294060	+	0.955787i	$0.404994\pi$
$691$	−18.4404	+	27.5979i	−0.701504	+	1.04988i	−0.995564	+	0.0940883i	$0.970006\pi$
$692$	15.0149	−	8.55765i	0.570780	−	0.325313i
$693$	29.2977	+	36.0435i	1.11293	+	1.36918i
$694$	−15.6437	+	34.2720i	−0.593825	+	1.30095i
$695$	−20.3186	+	8.41623i	−0.770727	+	0.319246i
$696$	−3.64454	+	4.80568i	−0.138146	+	0.182159i
$697$	7.55275	+	3.12845i	0.286081	+	0.118499i
$698$	0.772986	+	0.829932i	0.0292580	+	0.0314134i
$699$	−16.2693	−	9.80350i	−0.615363	−	0.370803i
$700$	35.2383	−	11.7432i	1.33188	−	0.443852i
$701$	−48.5714	+	9.66146i	−1.83452	+	0.364908i	−0.986329	−	0.164786i	$-0.947307\pi$
$701$	−48.5714	+	9.66146i	−1.83452	+	0.364908i	−0.848189	+	0.529694i	$0.822307\pi$
$702$	−8.09146	−	26.0604i	−0.305392	−	0.983585i
$703$			12.0168i			0.453223i
$704$	−28.3934	−	0.474679i	−1.07012	−	0.0178901i
$705$	−10.0500	−	21.3787i	−0.378503	−	0.805167i
$706$	11.3623	+	18.3862i	0.427627	+	0.691972i
$707$	4.02973	+	20.2588i	0.151554	+	0.761912i
$708$	24.7503	−	23.5765i	0.930175	−	0.886060i
$709$	37.6513	−	25.1578i	1.41402	−	0.944821i	0.414631	−	0.909990i	$-0.363911\pi$
$709$	37.6513	−	25.1578i	1.41402	−	0.944821i	0.999393	−	0.0348310i	$-0.0110893\pi$
$710$	−14.3537	+	13.3688i	−0.538684	+	0.501722i
$711$	4.79046	+	9.06452i	0.179656	+	0.339946i
$712$	17.6528	+	5.51646i	0.661568	+	0.206738i
$713$	−6.93062	−	16.7320i	−0.259554	−	0.626618i
$714$	0.445347	+	39.6665i	0.0166667	+	1.48448i
$715$	7.82432	−	39.3355i	0.292613	−	1.47106i
$716$	15.4276	−	8.79288i	0.576557	−	0.328605i
$717$	2.26385	+	0.341248i	0.0845449	+	0.0127441i
$718$	−24.6730	+	4.00294i	−0.920787	+	0.149388i
$719$	6.05066	+	6.05066i	0.225652	+	0.225652i	0.810873	−	0.585222i	$-0.198992\pi$
$719$	6.05066	+	6.05066i	0.225652	+	0.225652i	−0.585222	+	0.810873i	$0.698992\pi$
$720$	29.3380	+	21.7349i	1.09336	+	0.810014i
$721$	2.85769	−	2.85769i	0.106426	−	0.106426i
$722$	−8.09503	+	11.2304i	−0.301266	+	0.417952i
$723$	5.00280	−	33.1887i	0.186056	−	1.23430i
$724$	24.1323	−	31.0896i	0.896871	−	1.15544i
$725$	5.14127	+	1.02266i	0.190942	+	0.0379807i
$726$	−2.74024	+	2.80247i	−0.101700	+	0.104009i
$727$	−4.65166	+	1.92678i	−0.172521	+	0.0714604i	−0.467272	−	0.884114i	$-0.654763\pi$
$727$	−4.65166	+	1.92678i	−0.172521	+	0.0714604i	0.294751	+	0.955574i	$0.404763\pi$
$728$	−35.6548	+	28.7658i	−1.32146	+	1.06613i
$729$	21.1107	−	16.8327i	0.781877	−	0.623433i
$730$	−0.183861	+	5.17540i	−0.00680499	+	0.191550i
$731$	−21.3341	−	31.9288i	−0.789071	−	1.18093i
$732$	−8.70078	−	22.5385i	−0.321590	−	0.833047i
$733$	2.51322	−	0.499910i	0.0928277	−	0.0184646i	−0.148458	−	0.988919i	$-0.547431\pi$
$733$	2.51322	−	0.499910i	0.0928277	−	0.0184646i	0.241286	+	0.970454i	$0.422431\pi$
$734$	−6.28480	+	26.6185i	−0.231976	+	0.982505i
$735$	−57.3527	+	26.9611i	−2.11549	+	0.994476i
$736$	−19.7788	+	0.371779i	−0.729058	+	0.0137040i
$737$	−13.7071			−0.504906
$738$	−7.45346	+	5.63111i	−0.274366	+	0.207284i
$739$	3.05720	+	15.3696i	0.112461	+	0.565380i	0.995393	+	0.0958789i	$0.0305662\pi$
$739$	3.05720	+	15.3696i	0.112461	+	0.565380i	−0.882932	+	0.469501i	$0.844434\pi$
$740$	−15.7856	−	18.2036i	−0.580288	−	0.669177i
$741$	10.0746	−	16.7193i	0.370101	−	0.614199i
$742$	−2.13798	+	60.1810i	−0.0784879	+	2.20931i
$743$	17.7082	−	42.7513i	0.649649	−	1.56839i	−0.163632	−	0.986521i	$-0.552321\pi$
$743$	17.7082	−	42.7513i	0.649649	−	1.56839i	0.813281	−	0.581871i	$-0.197679\pi$
$744$	16.8358	+	18.9799i	0.617229	+	0.695838i
$745$	−10.7334	−	25.9128i	−0.393242	−	0.949371i
$746$	−10.1585	−	27.2202i	−0.371928	−	0.996602i
$747$	−9.58980	−	11.7978i	−0.350872	−	0.431660i
$748$	−26.1522	+	3.29486i	−0.956218	+	0.120472i
$749$	19.1470	+	12.7936i	0.699615	+	0.467468i
$750$	−1.01816	+	5.43695i	−0.0371780	+	0.198529i
$751$	−31.0947	−	31.0947i	−1.13466	−	1.13466i	−0.989392	−	0.145269i	$-0.953595\pi$
$751$	−31.0947	−	31.0947i	−1.13466	−	1.13466i	−0.145269	−	0.989392i	$-0.546405\pi$
$752$	−17.7495	−	2.53830i	−0.647256	−	0.0925621i
$753$	8.08181	+	2.91316i	0.294518	+	0.106161i
$754$	−6.38192	+	1.03540i	−0.232416	+	0.0377071i
$755$	28.0259	+	18.7263i	1.01997	+	0.681519i
$756$	−39.3407	−	22.5175i	−1.43081	−	0.818954i
$757$	−0.713260	−	0.141876i	−0.0259239	−	0.00515658i	0.182111	−	0.983278i	$-0.441707\pi$
$757$	−0.713260	−	0.141876i	−0.0259239	−	0.00515658i	−0.208035	+	0.978121i	$0.566707\pi$
$758$	−16.0769	+	35.2210i	−0.583938	+	1.27929i
$759$	−14.4763	+	15.8969i	−0.525457	+	0.577022i
$760$	2.34274	+	26.0134i	0.0849801	+	0.943606i
$761$	11.1929	−	27.0222i	0.405744	−	0.979552i	−0.580501	−	0.814260i	$-0.697143\pi$
$761$	11.1929	−	27.0222i	0.405744	−	0.979552i	0.986245	−	0.165293i	$-0.0528569\pi$
$762$	−38.1294	−	15.2945i	−1.38128	−	0.554061i
$763$	47.7105	+	71.4038i	1.72724	+	2.58499i
$764$	−8.16820	+	16.3334i	−0.295515	+	0.590922i
$765$	29.8139	+	16.1164i	1.07792	+	0.582690i
$766$	−0.544131	−	0.880495i	−0.0196603	−	0.0318136i
$767$	36.6420			1.32307
$768$	26.0165	−	9.54687i	0.938789	−	0.344493i
$769$	−44.9314			−1.62027			−0.810134	−	0.586245i	$-0.800606\pi$
$769$	−44.9314			−1.62027			−0.810134	+	0.586245i	$0.800606\pi$
$770$	−35.0236	−	56.6740i	−1.26216	−	2.04239i
$771$	31.7894	−	23.4611i	1.14487	−	0.844929i
$772$	−21.1558	+	42.3038i	−0.761413	+	1.52255i
$773$	0.302362	+	0.452517i	0.0108752	+	0.0162759i	0.836867	−	0.547406i	$-0.184385\pi$
$773$	0.302362	+	0.452517i	0.0108752	+	0.0162759i	−0.825992	+	0.563682i	$0.809385\pi$
$774$	43.8059	−	2.54204i	1.57457	−	0.0913717i
$775$	8.43833	−	20.3719i	0.303114	−	0.731781i
$776$	0.893277	+	9.91881i	0.0320668	+	0.356065i
$777$	22.1170	+	20.1405i	0.793442	+	0.722537i
$778$	1.53451	−	3.36179i	0.0550149	−	0.120526i
$779$	−6.55400	−	1.30367i	−0.234821	−	0.0467089i
$780$	6.70135	+	38.5614i	0.239947	+	1.38072i
$781$	13.4541	+	8.98976i	0.481427	+	0.321679i
$782$	−18.1253	+	2.94065i	−0.648160	+	0.105157i
$783$	−3.25007	−	5.51012i	−0.116148	−	0.196916i
$784$	−6.80951	+	47.6166i	−0.243197	+	1.70059i
$785$	37.0533	+	37.0533i	1.32249	+	1.32249i
$786$	−42.4127	−	7.94249i	−1.51281	−	0.283299i
$787$	7.94267	+	5.30712i	0.283126	+	0.189179i	0.689022	−	0.724741i	$-0.258040\pi$
$787$	7.94267	+	5.30712i	0.283126	+	0.189179i	−0.405896	+	0.913919i	$0.633040\pi$
$788$	−22.2970	+	2.80915i	−0.794297	+	0.100072i
$789$	−10.3023	−	41.5429i	−0.366771	−	1.47897i
$790$	−5.14163	−	13.7773i	−0.182931	−	0.490174i
$791$	−9.17799	−	22.1576i	−0.326332	−	0.787835i
$792$	11.8888	−	27.6743i	0.422449	−	0.983364i
$793$	9.91078	−	23.9267i	0.351942	−	0.849664i
$794$	−0.530968	+	14.9459i	−0.0188434	+	0.530412i
$795$	44.0661	+	26.5531i	1.56286	+	0.941742i
$796$	−25.7632	−	29.7097i	−0.913154	−	1.05303i
$797$	8.50151	+	42.7400i	0.301139	+	1.51393i	0.774224	+	0.632911i	$0.218140\pi$
$797$	8.50151	+	42.7400i	0.301139	+	1.51393i	−0.473085	+	0.881017i	$0.656860\pi$
$798$	−6.68264	−	31.7299i	−0.236563	−	1.12323i
$799$	−16.6430			−0.588786
$800$	−17.3483	−	16.7082i	−0.613357	−	0.590724i
$801$	−12.5158	+	15.1052i	−0.442222	+	0.533715i
$802$	3.76945	−	15.9650i	0.133104	−	0.563745i
$803$	4.18996	−	0.833435i	0.147861	−	0.0294113i
$804$	12.4791	−	4.81743i	0.440103	−	0.169898i
$805$	−25.7846	−	38.5895i	−0.908789	−	1.36010i
$806$	−0.965572	+	27.1794i	−0.0340108	+	0.957353i
$807$	−3.20139	+	0.149735i	−0.112694	+	0.00527091i
$808$	10.4246	−	8.41042i	0.366736	−	0.295878i
$809$	19.7935	−	8.19872i	0.695901	−	0.288252i	−0.00655504	−	0.999979i	$-0.502087\pi$
$809$	19.7935	−	8.19872i	0.695901	−	0.288252i	0.702456	+	0.711727i	$0.252087\pi$
$810$	−33.1336	+	20.0482i	−1.16420	+	0.704421i
$811$	−28.6993	−	5.70864i	−1.00777	−	0.200458i	−0.336509	−	0.941680i	$-0.609246\pi$
$811$	−28.6993	−	5.70864i	−1.00777	−	0.200458i	−0.671259	+	0.741223i	$0.734246\pi$
$812$	−6.58548	+	8.48406i	−0.231105	+	0.297732i
$813$	−0.0772713	−	0.0116477i	−0.00271002	−	0.000408504i
$814$	−11.6226	+	16.1242i	−0.407371	+	0.565154i
$815$	36.9189	−	36.9189i	1.29321	−	1.29321i
$816$	22.6512	−	12.1910i	0.792952	−	0.426771i
$817$	22.1954	+	22.1954i	0.776520	+	0.776520i
$818$	−11.2368	+	1.82306i	−0.392886	+	0.0637418i
$819$	−13.8865	−	46.5644i	−0.485235	−	1.62709i
$820$	11.6408	−	6.63462i	0.406515	−	0.231691i
$821$	5.81656	−	29.2418i	0.202999	−	1.02055i	−0.736093	−	0.676881i	$-0.763331\pi$
$821$	5.81656	−	29.2418i	0.202999	−	1.02055i	0.939092	−	0.343666i	$-0.111669\pi$
$822$	34.0589	−	0.382389i	1.18794	−	0.0133374i
$823$	3.36694	+	8.12850i	0.117364	+	0.283342i	0.971635	−	0.236487i	$-0.0759959\pi$
$823$	3.36694	+	8.12850i	0.117364	+	0.283342i	−0.854271	+	0.519828i	$0.825996\pi$
$824$	−2.50137	−	0.781671i	−0.0871393	−	0.0272308i
$825$	−26.1494	+	1.22305i	−0.910404	+	0.0425813i
$826$	44.5414	−	41.4852i	1.54979	−	1.44345i
$827$	3.30216	−	2.20644i	0.114827	−	0.0767253i	−0.496830	−	0.867848i	$-0.665503\pi$
$827$	3.30216	−	2.20644i	0.114827	−	0.0767253i	0.611658	+	0.791122i	$0.290503\pi$
$828$	7.59234	−	19.5605i	0.263852	−	0.679776i
$829$	5.93252	+	29.8248i	0.206045	+	1.03586i	0.935902	+	0.352259i	$0.114586\pi$
$829$	5.93252	+	29.8248i	0.206045	+	1.03586i	−0.729857	+	0.683599i	$0.760414\pi$
$830$	11.4640	+	18.5506i	0.397921	+	0.643902i
$831$	−5.03189	+	2.36545i	−0.174554	+	0.0820567i
$832$	27.2518	+	11.8256i	0.944787	+	0.409977i
$833$			44.6483i			1.54697i
$834$	−14.8308	−	9.67055i	−0.513548	−	0.334864i
$835$	−9.52494	+	1.89463i	−0.329624	+	0.0655664i
$836$	20.4410	−	6.81199i	0.706966	−	0.235598i
$837$	−25.4001	+	8.88684i	−0.877956	+	0.307174i
$838$	16.7594	+	17.9940i	0.578942	+	0.621593i
$839$	16.4356	+	6.80783i	0.567418	+	0.235032i	0.647902	−	0.761724i	$-0.275647\pi$
$839$	16.4356	+	6.80783i	0.567418	+	0.235032i	−0.0804839	+	0.996756i	$0.525647\pi$
$840$	51.8043	+	39.2874i	1.78742	+	1.35554i
$841$	25.3922	−	10.5178i	0.875592	−	0.362682i
$842$	−3.74801	+	8.21109i	−0.129165	+	0.282973i
$843$	−4.77974	−	19.2738i	−0.164623	−	0.663826i
$844$	26.2145	−	14.9408i	0.902342	−	0.514285i
$845$	−1.33399	+	1.99645i	−0.0458906	+	0.0686801i
$846$	9.63185	−	16.3981i	0.331150	−	0.563780i
$847$	−4.93525	+	4.93525i	−0.169577	+	0.169577i
$848$	35.2125	−	16.8797i	1.20920	−	0.579651i
$849$	−7.68655	−	2.77068i	−0.263802	−	0.0950895i
$850$	−18.1364	−	13.0730i	−0.622073	−	0.448400i
$851$	−7.69270	+	11.5129i	−0.263702	+	0.394658i
$852$	−15.4083	−	3.45585i	−0.527880	−	0.118395i
$853$	−2.31293	+	11.6279i	−0.0791932	+	0.398131i	0.920775	+	0.390095i	$0.127558\pi$
$853$	−2.31293	+	11.6279i	−0.0791932	+	0.398131i	−0.999968	+	0.00803589i	$0.997442\pi$
$854$	−15.0419	−	40.3056i	−0.514723	−	1.37923i
$855$	−26.4721	−	8.16626i	−0.905326	−	0.279280i
$856$	1.58780	−	14.8479i	0.0542699	−	0.507490i
$857$	−15.6390	−	6.47787i	−0.534217	−	0.221280i	0.0992322	−	0.995064i	$-0.468361\pi$
$857$	−15.6390	−	6.47787i	−0.534217	−	0.221280i	−0.633449	+	0.773784i	$0.718361\pi$
$858$	29.6890	−	12.6899i	1.01357	−	0.433227i
$859$	−1.83427	+	1.22562i	−0.0625845	+	0.0418176i	−0.586469	−	0.809972i	$-0.699482\pi$
$859$	−1.83427	+	1.22562i	−0.0625845	+	0.0418176i	0.523884	+	0.851789i	$0.324482\pi$
$860$	−62.7790	−	4.46620i	−2.14075	−	0.152296i
$861$	−13.3841	+	9.87766i	−0.456129	+	0.336630i
$862$	33.8717	+	7.99734i	1.15368	+	0.272391i
$863$		−	9.53930i		−	0.324722i	−0.986731	−	0.162361i	$-0.948089\pi$
$863$		−	9.53930i		−	0.324722i	0.986731	−	0.162361i	$-0.0519109\pi$
$864$	−1.09736	+	29.3734i	−0.0373329	+	0.999303i
$865$		−	26.2922i		−	0.893962i
$866$	−11.2212	+	47.5260i	−0.381313	+	1.61500i
$867$	−4.47992	+	3.30625i	−0.152146	+	0.112286i
$868$	29.5981	+	34.1319i	1.00462	+	1.15851i
$869$	−10.0866	+	6.73963i	−0.342163	+	0.228626i
$870$	3.60634	+	8.43729i	0.122266	+	0.286051i
$871$	13.2477	+	5.48738i	0.448881	+	0.185933i
$872$	26.6603	−	48.8905i	0.902831	−	1.65564i
$873$	−10.0937	−	3.11376i	−0.341620	−	0.105385i
$874$	14.0623	−	5.24798i	0.475663	−	0.177516i
$875$	−1.92161	+	9.66060i	−0.0649623	+	0.326588i
$876$	−3.52167	+	2.23136i	−0.118986	+	0.0753905i
$877$	10.3855	−	15.5430i	0.350693	−	0.524849i	−0.613624	−	0.789598i	$-0.710289\pi$
$877$	10.3855	−	15.5430i	0.350693	−	0.524849i	0.964317	+	0.264749i	$0.0852890\pi$
$878$	−0.338525	+	0.469642i	−0.0114247	+	0.0158496i
$879$	1.12670	+	0.406128i	0.0380026	+	0.0136984i
$880$	−22.0165	+	37.1708i	−0.742176	+	1.25303i
$881$	29.2953	−	29.2953i	0.986983	−	0.986983i	−0.0129335	−	0.999916i	$-0.504117\pi$
$881$	29.2953	−	29.2953i	0.986983	−	0.986983i	0.999916	+	0.0129335i	$0.00411698\pi$
$882$	−43.9915	−	25.8395i	−1.48127	−	0.870060i
$883$	−6.11706	+	9.15483i	−0.205855	+	0.308084i	−0.920003	−	0.391910i	$-0.871814\pi$
$883$	−6.11706	+	9.15483i	−0.205855	+	0.308084i	0.714148	+	0.699995i	$0.246814\pi$
$884$	26.5948	+	7.28512i	0.894480	+	0.245025i
$885$	−12.5171	−	50.4738i	−0.420757	−	1.69666i
$886$	22.5802	+	10.3069i	0.758596	+	0.346266i
$887$	−23.2123	+	9.61487i	−0.779394	+	0.322836i	−0.736671	−	0.676251i	$-0.763603\pi$
$887$	−23.2123	+	9.61487i	−0.779394	+	0.322836i	−0.0427233	+	0.999087i	$0.513603\pi$
$888$	4.91438	−	18.7645i	0.164916	−	0.629696i
$889$	−67.5868	−	27.9954i	−2.26679	−	0.938935i
$890$	20.5894	−	19.1767i	0.690158	−	0.642803i
$891$	22.3766	+	22.8013i	0.749646	+	0.763871i
$892$	−8.58532	+	17.1675i	−0.287458	+	0.574810i
$893$	13.3428	−	2.65405i	0.446500	−	0.0888144i
$894$	12.3331	−	18.9141i	0.412481	−	0.632581i
$895$		−	27.0149i		−	0.903010i
$896$	46.5154	−	16.4789i	1.55397	−	0.550521i
$897$	20.3552	−	9.56885i	0.679642	−	0.319495i
$898$	4.26779	−	2.63742i	0.142418	−	0.0880119i
$899$	1.24387	+	6.25335i	0.0414854	+	0.208561i
$900$	23.3768	−	10.3038i	0.779227	−	0.343461i
$901$	30.1376	−	20.1373i	1.00403	−	0.670871i
$902$	−7.53329	−	8.08826i	−0.250831	−	0.269309i
$903$	78.0509	−	3.65059i	2.59737	−	0.121484i
$904$	−9.96625	+	11.9390i	−0.331473	+	0.397086i
$905$	−22.9129	−	55.3167i	−0.761651	−	1.83879i
$906$	0.304636	+	27.1335i	0.0101209	+	0.901452i
$907$	−3.33864	+	16.7845i	−0.110858	+	0.557320i	0.884937	+	0.465710i	$0.154201\pi$
$907$	−3.33864	+	16.7845i	−0.110858	+	0.557320i	−0.995795	+	0.0916094i	$0.970799\pi$
$908$	−12.0303	+	43.9173i	−0.399239	+	1.45745i
$909$	4.06009	+	13.6143i	0.134665	+	0.451558i
$910$	11.1614	+	68.7958i	0.369998	+	2.28056i
$911$	0.607325	+	0.607325i	0.0201216	+	0.0201216i	0.717096	−	0.696974i	$-0.245471\pi$
$911$	0.607325	+	0.607325i	0.0201216	+	0.0201216i	−0.696974	+	0.717096i	$0.745471\pi$
$912$	−16.2156	+	13.3858i	−0.536952	+	0.443249i
$913$	12.7204	−	12.7204i	0.420984	−	0.420984i
$914$	−13.2886	−	9.57862i	−0.439548	−	0.316833i
$915$	−36.3442	−	5.47846i	−1.20150	−	0.181112i
$916$	−51.8862	+	6.53704i	−1.71437	+	0.215990i
$917$	−75.3606	−	14.9901i	−2.48862	−	0.495018i
$918$	2.85147	+	27.1345i	0.0941127	+	0.895572i
$919$	3.06068	−	1.26778i	0.100963	−	0.0418201i	−0.331630	−	0.943409i	$-0.607599\pi$
$919$	3.06068	−	1.26778i	0.100963	−	0.0418201i	0.432593	+	0.901589i	$0.357599\pi$
$920$	−14.4083	+	26.4224i	−0.475027	+	0.871120i
$921$	−19.1878	+	0.897448i	−0.632259	+	0.0295719i
$922$	−10.5908	−	0.376246i	−0.348788	−	0.0123910i
$923$	−9.40436	−	14.0746i	−0.309548	−	0.463272i
$924$	21.7222	−	49.0388i	0.714607	−	1.61326i
$925$	−16.5348	+	3.28897i	−0.543660	+	0.108141i
$926$	6.64206	+	1.56824i	0.218272	+	0.0515354i
$927$	1.77345	−	2.14037i	0.0582479	−	0.0702990i
$928$	6.85492	+	1.23008i	0.225024	+	0.0403793i
$929$	15.7346			0.516234			0.258117	−	0.966114i	$-0.416898\pi$
$929$	15.7346			0.516234			0.258117	+	0.966114i	$0.416898\pi$
$930$	37.7690	−	7.95452i	1.23849	−	0.260839i
$931$	−7.12004	−	35.7949i	−0.233350	−	1.17313i
$932$	−1.55643	+	21.8779i	−0.0509827	+	0.716636i
$933$	24.6105	+	14.8297i	0.805713	+	0.485502i
$934$	2.06764	+	0.0734547i	0.0676552	+	0.00240351i
$935$	−15.3459	+	37.0482i	−0.501864	+	1.21161i
$936$	−22.5693	+	21.9874i	−0.737699	+	0.718682i
$937$	22.2317	+	53.6720i	0.726277	+	1.75339i	0.654619	+	0.755959i	$0.272829\pi$
$937$	22.2317	+	53.6720i	0.726277	+	1.75339i	0.0716577	+	0.997429i	$0.477171\pi$
$938$	22.3163	−	8.32836i	0.728654	−	0.271931i
$939$	8.40974	+	33.9114i	0.274442	+	1.10666i
$940$	−16.7258	+	21.5479i	−0.545537	+	0.702814i
$941$	12.3025	+	8.22025i	0.401049	+	0.267972i	0.739696	−	0.672941i	$-0.234969\pi$
$941$	12.3025	+	8.22025i	0.401049	+	0.267972i	−0.338647	+	0.940913i	$0.609969\pi$
$942$	−7.76496	+	41.4647i	−0.252996	+	1.35099i
$943$	−5.44462	−	5.44462i	−0.177301	−	0.177301i
$944$	−37.2320	−	13.1031i	−1.21180	−	0.426468i
$945$	−59.3980	+	35.0351i	−1.93222	+	1.13969i
$946$	8.31467	+	51.2492i	0.270333	+	1.66626i
$947$	−1.11411	−	0.744422i	−0.0362036	−	0.0241905i	0.537337	−	0.843368i	$-0.319430\pi$
$947$	−1.11411	−	0.744422i	−0.0362036	−	0.0241905i	−0.573540	+	0.819177i	$0.694430\pi$
$948$	6.81424	−	9.68081i	0.221316	−	0.314418i
$949$	−4.38320	−	0.871872i	−0.142285	−	0.0283022i
$950$	16.6248	+	7.58851i	0.539381	+	0.246204i
$951$	−9.35829	−	8.52200i	−0.303463	−	0.276345i
$952$	40.5761	−	21.2543i	1.31508	−	0.688856i
$953$	21.1646	−	51.0959i	0.685589	−	1.65516i	−0.0678965	−	0.997692i	$-0.521629\pi$
$953$	21.1646	−	51.0959i	0.685589	−	1.65516i	0.753485	−	0.657465i	$-0.228371\pi$
$954$	2.39943	+	41.3484i	0.0776845	+	1.33870i
$955$	15.4352	+	23.1003i	0.499470	+	0.747510i
$956$	−0.835794	−	2.50800i	−0.0270315	−	0.0811144i
$957$	6.09032	−	4.49475i	0.196872	−	0.145295i
$958$	−27.3691	+	16.9136i	−0.884255	+	0.546455i
$959$	60.6524			1.95857
$960$	6.98017	−	41.5786i	0.225284	−	1.34194i
$961$	−4.17996			−0.134837
$962$	17.6881	−	10.9310i	0.570288	−	0.352429i
$963$	13.9329	+	7.53170i	0.448982	+	0.242706i
$964$	−36.7680	+	12.2530i	−1.18422	+	0.394643i
$965$	39.9773	+	59.8302i	1.28691	+	1.92600i
$966$	13.9098	−	34.6774i	0.447541	−	1.11573i
$967$	−6.66628	+	16.0938i	−0.214373	+	0.517542i	−0.994086	−	0.108595i	$-0.965365\pi$
$967$	−6.66628	+	16.0938i	−0.214373	+	0.517542i	0.779713	+	0.626137i	$0.215365\pi$
$968$	4.31987	+	1.34995i	0.138846	+	0.0433890i
$969$	−13.1410	+	14.4306i	−0.422151	+	0.463578i
$970$	13.7829	+	6.29130i	0.442543	+	0.202002i
$971$	21.6876	+	4.31393i	0.695988	+	0.138441i	0.530391	−	0.847753i	$-0.322045\pi$
$971$	21.6876	+	4.31393i	0.695988	+	0.138441i	0.165597	+	0.986194i	$0.447045\pi$
$972$	−28.3856	−	12.8941i	−0.910468	−	0.413579i
$973$	−26.2141	−	17.5157i	−0.840386	−	0.561528i
$974$	8.03764	+	49.5417i	0.257543	+	1.58742i
$975$	25.7627	+	9.28637i	0.825065	+	0.297402i
$976$	−18.6264	+	20.7679i	−0.596218	+	0.664764i
$977$	−31.3340	−	31.3340i	−1.00246	−	1.00246i	−0.999997	−	0.00246723i	$-0.999215\pi$
$977$	−31.3340	−	31.3340i	−1.00246	−	1.00246i	−0.00246723	−	0.999997i	$-0.500785\pi$
$978$	41.3143	+	7.73680i	1.32109	+	0.247396i
$979$	−19.2991	−	12.8952i	−0.616801	−	0.412133i
$980$	57.8067	+	44.8706i	1.84657	+	1.43334i
$981$	37.2555	+	45.8335i	1.18948	+	1.46335i
$982$	−7.53691	+	2.81275i	−0.240513	+	0.0897583i
$983$	−18.5082	−	44.6826i	−0.590319	−	1.42515i	−0.883196	−	0.469005i	$-0.844613\pi$
$983$	−18.5082	−	44.6826i	−0.590319	−	1.42515i	0.292877	−	0.956150i	$-0.405387\pi$
$984$	9.70106	+	4.71602i	0.309258	+	0.150341i
$985$	−13.0837	+	31.5868i	−0.416881	+	1.00644i
$986$	6.46041	+	0.229512i	0.205741	+	0.00730915i
$987$	17.4781	−	29.0057i	0.556335	−	0.923262i
$988$	−22.4830	−	1.59948i	−0.715280	−	0.0508862i
$989$	7.05610	+	35.4734i	0.224371	+	1.12799i
$990$	−27.6220	−	36.5612i	−0.877886	−	1.16199i
$991$	−26.0054			−0.826089			−0.413044	−	0.910711i	$-0.635535\pi$
$991$	−26.0054			−0.826089			−0.413044	+	0.910711i	$0.635535\pi$
$992$	10.7004	−	27.2717i	0.339737	−	0.865876i
$993$	−3.40674	+	1.60148i	−0.108110	+	0.0508215i
$994$	−27.3667	−	6.46146i	−0.868019	−	0.204945i
$995$	−58.6760	+	11.6714i	−1.86015	+	0.370008i
$996$	−7.11014	+	16.0515i	−0.225293	+	0.508610i
$997$	−13.6836	−	20.4790i	−0.433365	−	0.648577i	0.548940	−	0.835862i	$-0.315031\pi$
$997$	−13.6836	−	20.4790i	−0.433365	−	0.648577i	−0.982306	+	0.187284i	$0.940031\pi$
$998$	−37.6804	−	1.33863i	−1.19275	−	0.0423737i
$999$	16.4384	+	12.3721i	0.520088	+	0.391436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.107.10	✓	240
3.2	odd	2	inner	192.2.s.a.107.21	yes	240
4.3	odd	2		768.2.s.a.335.22		240
12.11	even	2		768.2.s.a.335.17		240
64.3	odd	16	inner	192.2.s.a.131.21	yes	240
64.61	even	16		768.2.s.a.431.17		240
192.125	odd	16		768.2.s.a.431.22		240
192.131	even	16	inner	192.2.s.a.131.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.10	✓	240	1.1	even	1	trivial
192.2.s.a.107.21	yes	240	3.2	odd	2	inner
192.2.s.a.131.10	yes	240	192.131	even	16	inner
192.2.s.a.131.21	yes	240	64.3	odd	16	inner
768.2.s.a.335.17		240	12.11	even	2
768.2.s.a.335.22		240	4.3	odd	2
768.2.s.a.431.17		240	64.61	even	16
768.2.s.a.431.22		240	192.125	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743452 - 1.20303i) q^{2} +(-1.02851 - 1.39362i) q^{3} +(-0.894559 + 1.78879i) q^{4} +(1.69041 + 2.52988i) q^{5} +(-0.911914 + 2.27341i) q^{6} +(-1.66919 + 4.02977i) q^{7} +(2.81703 - 0.253698i) q^{8} +(-0.884335 + 2.86670i) q^{9} +(1.78678 - 3.91447i) q^{10} +(-3.48146 - 0.692506i) q^{11} +(3.41295 - 0.593115i) q^{12} +(3.08756 + 2.06304i) q^{13} +(6.08890 - 0.987862i) q^{14} +(1.78708 - 4.95780i) q^{15} +(-2.39953 - 3.20035i) q^{16} +(-2.62540 - 2.62540i) q^{17} +(4.10618 - 1.06737i) q^{18} +(2.52347 + 1.68613i) q^{19} +(-6.03760 + 0.760665i) q^{20} +(7.33274 - 1.81846i) q^{21} +(1.75519 + 4.70315i) q^{22} +(1.33827 + 3.23086i) q^{23} +(-3.25090 - 3.66492i) q^{24} +(-1.62940 + 3.93371i) q^{25} +(0.186447 - 5.24819i) q^{26} +(4.90462 - 1.71600i) q^{27} +(-5.71523 - 6.59069i) q^{28} +(-0.240184 - 1.20749i) q^{29} +(-7.29299 + 1.53598i) q^{30} -5.17881 q^{31} +(-2.06618 + 5.26601i) q^{32} +(2.61563 + 5.56407i) q^{33} +(-1.20657 + 5.11028i) q^{34} +(-13.0165 + 2.58914i) q^{35} +(-4.33683 - 4.14632i) q^{36} +(2.19976 + 3.29218i) q^{37} +(0.152384 - 4.28937i) q^{38} +(-0.300497 - 6.42473i) q^{39} +(5.40377 + 6.69790i) q^{40} +(-2.03421 + 0.842597i) q^{41} +(-7.63919 - 7.46956i) q^{42} +(10.1438 + 2.01773i) q^{43} +(4.35312 - 5.60811i) q^{44} +(-8.74731 + 2.60864i) q^{45} +(2.89188 - 4.01196i) q^{46} +(3.16961 - 3.16961i) q^{47} +(-1.99212 + 6.63562i) q^{48} +(-8.50315 - 8.50315i) q^{49} +(5.94375 - 0.964313i) q^{50} +(-0.958550 + 6.35904i) q^{51} +(-6.45234 + 3.67748i) q^{52} +(-1.90453 + 9.57473i) q^{53} +(-5.71075 - 4.62464i) q^{54} +(-4.13316 - 9.97832i) q^{55} +(-3.67980 + 11.7755i) q^{56} +(-0.245597 - 5.25095i) q^{57} +(-1.27408 + 1.18666i) q^{58} +(8.20460 - 5.48214i) q^{59} +(7.26981 + 7.63175i) q^{60} +(-1.36061 - 6.84027i) q^{61} +(3.85019 + 6.23026i) q^{62} +(-10.0760 - 8.34872i) q^{63} +(7.87127 - 1.42935i) q^{64} +11.2986i q^{65} +(4.74915 - 7.28330i) q^{66} +(3.78731 - 0.753342i) q^{67} +(7.04485 - 2.34771i) q^{68} +(3.12616 - 5.18800i) q^{69} +(12.7919 + 13.7343i) q^{70} +(-4.21150 - 1.74446i) q^{71} +(-1.76392 + 8.29992i) q^{72} +(-1.11189 + 0.460562i) q^{73} +(2.32517 - 5.09396i) q^{74} +(7.15794 - 1.77511i) q^{75} +(-5.27352 + 3.00562i) q^{76} +(8.60185 - 12.8736i) q^{77} +(-7.50573 + 5.13798i) q^{78} +(2.41654 - 2.41654i) q^{79} +(4.04032 - 11.4805i) q^{80} +(-7.43590 - 5.07024i) q^{81} +(2.52600 + 1.82078i) q^{82} +(-2.81558 + 4.21381i) q^{83} +(-3.30673 + 14.7434i) q^{84} +(2.20394 - 11.0800i) q^{85} +(-5.11404 - 13.7034i) q^{86} +(-1.43574 + 1.57664i) q^{87} +(-9.98306 - 1.06757i) q^{88} +(6.04112 + 2.50231i) q^{89} +(9.64147 + 8.58386i) q^{90} +(-13.4673 + 8.99856i) q^{91} +(-6.97648 - 0.496318i) q^{92} +(5.32645 + 7.21727i) q^{93} +(-6.16959 - 1.45668i) q^{94} +9.23435i q^{95} +(9.46389 - 2.53668i) q^{96} +3.52102i q^{97} +(-3.90785 + 16.5512i) q^{98} +(5.06398 - 9.36789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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