LMFDB - Embedded newform 336.3.bv.a.325.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(61,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 10])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bv (of order $12$, degree $4$, 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:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			325.34
Character	$\chi$	$=$	336.325
Dual form			336.3.bv.a.61.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0723663 + 1.99869i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-3.98953 + 0.289276i) q^{4} +(4.92050 + 1.31844i) q^{5} +(-1.01706 - 3.31143i) q^{6} +(4.79724 + 5.09769i) q^{7} +(-0.866880 - 7.95289i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-2.27908 + 9.92997i) q^{10} +(21.1318 - 5.66224i) q^{11} +(6.54493 - 2.27242i) q^{12} +(-3.69839 - 3.69839i) q^{13} +(-9.84155 + 9.95710i) q^{14} -8.82320 q^{15} +(15.8326 - 2.30815i) q^{16} +(10.5410 + 6.08583i) q^{17} +(3.18605 + 5.08420i) q^{18} +(-2.59084 + 9.66914i) q^{19} +(-20.0119 - 3.83659i) q^{20} +(-10.3112 - 6.37806i) q^{21} +(12.8463 + 41.8261i) q^{22} +(-10.4617 + 6.04009i) q^{23} +(5.01550 + 12.9168i) q^{24} +(0.822383 + 0.474803i) q^{25} +(7.12430 - 7.65958i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-20.6134 - 18.9497i) q^{28} +(-21.8773 + 21.8773i) q^{29} +(-0.638502 - 17.6348i) q^{30} +(28.4858 + 16.4463i) q^{31} +(5.75902 + 31.4775i) q^{32} +(-32.8158 + 18.9462i) q^{33} +(-11.4009 + 21.5085i) q^{34} +(16.8838 + 31.4081i) q^{35} +(-9.93118 + 6.73585i) q^{36} +(8.40958 - 31.3850i) q^{37} +(-19.5131 - 4.47856i) q^{38} +(7.84547 + 4.52959i) q^{39} +(6.21996 - 40.2751i) q^{40} -58.6341 q^{41} +(12.0016 - 21.0704i) q^{42} +(34.1238 + 34.1238i) q^{43} +(-82.6677 + 28.7025i) q^{44} +(14.7615 - 3.95533i) q^{45} +(-12.8293 - 20.4727i) q^{46} +(16.5666 - 9.56471i) q^{47} +(-25.4538 + 10.9592i) q^{48} +(-2.97293 + 48.9097i) q^{49} +(-0.889472 + 1.67805i) q^{50} +(-20.3636 - 5.45641i) q^{51} +(15.8247 + 13.6850i) q^{52} +(-43.3291 + 11.6100i) q^{53} +(-7.60955 - 7.07777i) q^{54} +111.444 q^{55} +(36.3828 - 42.5710i) q^{56} -17.3382i q^{57} +(-45.3091 - 42.1428i) q^{58} +(8.13524 + 30.3611i) q^{59} +(35.2004 - 2.55234i) q^{60} +(10.3192 - 38.5119i) q^{61} +(-30.8096 + 58.1244i) q^{62} +(20.1101 + 6.04833i) q^{63} +(-62.4970 + 13.7884i) q^{64} +(-13.3218 - 23.0741i) q^{65} +(-40.2424 - 64.2176i) q^{66} +(0.332301 + 1.24016i) q^{67} +(-43.8139 - 21.2303i) q^{68} +(14.7951 - 14.7951i) q^{69} +(-61.5532 + 36.0184i) q^{70} -88.3684i q^{71} +(-14.1816 - 19.3619i) q^{72} +(44.3565 - 76.8277i) q^{73} +(63.3374 + 14.5369i) q^{74} +(-1.58872 - 0.425697i) q^{75} +(7.53917 - 39.3247i) q^{76} +(130.238 + 80.5600i) q^{77} +(-8.48549 + 16.0085i) q^{78} +(-67.8864 - 117.583i) q^{79} +(80.9476 + 9.51722i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-4.24313 - 117.191i) q^{82} +(81.6106 + 81.6106i) q^{83} +(42.9817 + 22.4627i) q^{84} +(43.8430 + 43.8430i) q^{85} +(-65.7336 + 70.6724i) q^{86} +(26.7941 - 46.4087i) q^{87} +(-63.3498 - 163.150i) q^{88} +(-20.7865 - 36.0033i) q^{89} +(8.97372 + 29.2174i) q^{90} +(1.11118 - 36.5953i) q^{91} +(39.9901 - 27.1234i) q^{92} +(-55.0303 - 14.7453i) q^{93} +(20.3158 + 32.4193i) q^{94} +(-25.4964 + 44.1611i) q^{95} +(-23.7460 - 50.0812i) q^{96} +37.3983i q^{97} +(-97.9705 - 2.40256i) q^{98} +(46.4085 - 46.4085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) $ 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0723663	+	1.99869i	0.0361832	+	0.999345i
$2$	0.0723663	+	1.99869i	0.0361832	+	0.999345i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$4$	−3.98953	+	0.289276i	−0.997382	+	0.0723189i
$5$	4.92050	+	1.31844i	0.984100	+	0.263689i	0.714770	−	0.699359i	$-0.246531\pi$
$5$	4.92050	+	1.31844i	0.984100	+	0.263689i	0.269330	+	0.963048i	$0.413198\pi$
$6$	−1.01706	−	3.31143i	−0.169510	−	0.551906i
$7$	4.79724	+	5.09769i	0.685320	+	0.728242i
$7$	4.79724	+	5.09769i	0.685320	+	0.728242i
$8$	−0.866880	−	7.95289i	−0.108360	−	0.994112i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	−2.27908	+	9.92997i	−0.227908	+	0.992997i
$11$	21.1318	−	5.66224i	1.92107	−	0.514749i	0.933226	−	0.359290i	$-0.116981\pi$
$11$	21.1318	−	5.66224i	1.92107	−	0.514749i	0.987842	−	0.155458i	$-0.0496854\pi$
$12$	6.54493	−	2.27242i	0.545411	−	0.189369i
$13$	−3.69839	−	3.69839i	−0.284492	−	0.284492i	0.550406	−	0.834897i	$-0.314473\pi$
$13$	−3.69839	−	3.69839i	−0.284492	−	0.284492i	−0.834897	+	0.550406i	$0.814473\pi$
$14$	−9.84155	+	9.95710i	−0.702968	+	0.711222i
$15$	−8.82320			−0.588213
$16$	15.8326	−	2.30815i	0.989540	−	0.144259i
$17$	10.5410	+	6.08583i	0.620057	+	0.357990i	0.776891	−	0.629635i	$-0.216796\pi$
$17$	10.5410	+	6.08583i	0.620057	+	0.357990i	−0.156834	+	0.987625i	$0.550129\pi$
$18$	3.18605	+	5.08420i	0.177003	+	0.282456i
$19$	−2.59084	+	9.66914i	−0.136360	+	0.508902i	0.863629	+	0.504128i	$0.168186\pi$
$19$	−2.59084	+	9.66914i	−0.136360	+	0.508902i	−0.999989	+	0.00477362i	$0.998481\pi$
$20$	−20.0119	−	3.83659i	−1.00059	−	0.191829i
$21$	−10.3112	−	6.37806i	−0.491008	−	0.303717i
$22$	12.8463	+	41.8261i	0.583922	+	1.90119i
$23$	−10.4617	+	6.04009i	−0.454858	+	0.262613i	−0.709880	−	0.704323i	$-0.751251\pi$
$23$	−10.4617	+	6.04009i	−0.454858	+	0.262613i	0.255022	+	0.966935i	$0.417917\pi$
$24$	5.01550	+	12.9168i	0.208979	+	0.538202i
$25$	0.822383	+	0.474803i	0.0328953	+	0.0189921i
$26$	7.12430	−	7.65958i	0.274012	−	0.294599i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−20.6134	−	18.9497i	−0.736192	−	0.676773i
$29$	−21.8773	+	21.8773i	−0.754389	+	0.754389i	−0.975295	−	0.220906i	$-0.929099\pi$
$29$	−21.8773	+	21.8773i	−0.754389	+	0.754389i	0.220906	+	0.975295i	$0.429099\pi$
$30$	−0.638502	−	17.6348i	−0.0212834	−	0.587828i
$31$	28.4858	+	16.4463i	0.918896	+	0.530525i	0.883283	−	0.468841i	$-0.155328\pi$
$31$	28.4858	+	16.4463i	0.918896	+	0.530525i	0.0356133	+	0.999366i	$0.488662\pi$
$32$	5.75902	+	31.4775i	0.179969	+	0.983672i
$33$	−32.8158	+	18.9462i	−0.994418	+	0.574128i
$34$	−11.4009	+	21.5085i	−0.335320	+	0.632604i
$35$	16.8838	+	31.4081i	0.482394	+	0.897374i
$36$	−9.93118	+	6.73585i	−0.275866	+	0.187107i
$37$	8.40958	−	31.3850i	0.227286	−	0.848243i	−0.754190	−	0.656657i	$-0.771970\pi$
$37$	8.40958	−	31.3850i	0.227286	−	0.848243i	0.981476	−	0.191586i	$-0.0613632\pi$
$38$	−19.5131	−	4.47856i	−0.513503	−	0.117857i
$39$	7.84547	+	4.52959i	0.201166	+	0.116143i
$40$	6.21996	−	40.2751i	0.155499	−	1.00688i
$41$	−58.6341			−1.43010			−0.715050	−	0.699073i	$-0.753596\pi$
$41$	−58.6341			−1.43010			−0.715050	+	0.699073i	$0.753596\pi$
$42$	12.0016	−	21.0704i	0.285752	−	0.501676i
$43$	34.1238	+	34.1238i	0.793578	+	0.793578i	0.982074	−	0.188496i	$-0.0603613\pi$
$43$	34.1238	+	34.1238i	0.793578	+	0.793578i	−0.188496	+	0.982074i	$0.560361\pi$
$44$	−82.6677	+	28.7025i	−1.87881	+	0.652330i
$45$	14.7615	−	3.95533i	0.328033	−	0.0878963i
$46$	−12.8293	−	20.4727i	−0.278899	−	0.445058i
$47$	16.5666	−	9.56471i	0.352480	−	0.203504i	−0.313297	−	0.949655i	$-0.601434\pi$
$47$	16.5666	−	9.56471i	0.352480	−	0.203504i	0.665777	+	0.746151i	$0.268100\pi$
$48$	−25.4538	+	10.9592i	−0.530288	+	0.228316i
$49$	−2.97293	+	48.9097i	−0.0606721	+	0.998158i
$50$	−0.889472	+	1.67805i	−0.0177894	+	0.0335610i
$51$	−20.3636	−	5.45641i	−0.399286	−	0.106988i
$52$	15.8247	+	13.6850i	0.304321	+	0.263173i
$53$	−43.3291	+	11.6100i	−0.817531	+	0.219057i	−0.643267	−	0.765642i	$-0.722421\pi$
$53$	−43.3291	+	11.6100i	−0.817531	+	0.219057i	−0.174264	+	0.984699i	$0.555755\pi$
$54$	−7.60955	−	7.07777i	−0.140918	−	0.131070i
$55$	111.444			2.02626
$56$	36.3828	−	42.5710i	0.649692	−	0.760197i
$57$		−	17.3382i		−	0.304179i
$58$	−45.3091	−	42.1428i	−0.781192	−	0.726599i
$59$	8.13524	+	30.3611i	0.137885	+	0.514595i	0.999969	+	0.00782982i	$0.00249234\pi$
$59$	8.13524	+	30.3611i	0.137885	+	0.514595i	−0.862084	+	0.506765i	$0.830841\pi$
$60$	35.2004	−	2.55234i	0.586673	−	0.0425389i
$61$	10.3192	−	38.5119i	0.169168	−	0.631342i	−0.828304	−	0.560279i	$-0.810694\pi$
$61$	10.3192	−	38.5119i	0.169168	−	0.631342i	0.997472	−	0.0710636i	$-0.0226393\pi$
$62$	−30.8096	+	58.1244i	−0.496929	+	0.937490i
$63$	20.1101	+	6.04833i	0.319209	+	0.0960052i
$64$	−62.4970	+	13.7884i	−0.976516	+	0.215444i
$65$	−13.3218	−	23.0741i	−0.204951	−	0.354986i
$66$	−40.2424	−	64.2176i	−0.609733	−	0.972993i
$67$	0.332301	+	1.24016i	0.00495971	+	0.0185099i	0.968361	−	0.249552i	$-0.0802834\pi$
$67$	0.332301	+	1.24016i	0.00495971	+	0.0185099i	−0.963402	+	0.268062i	$0.913617\pi$
$68$	−43.8139	−	21.2303i	−0.644323	−	0.312211i
$69$	14.7951	−	14.7951i	0.214422	−	0.214422i
$70$	−61.5532	+	36.0184i	−0.879332	+	0.514548i
$71$		−	88.3684i		−	1.24463i	−0.782768	−	0.622313i	$-0.786193\pi$
$71$		−	88.3684i		−	1.24463i	0.782768	−	0.622313i	$-0.213807\pi$
$72$	−14.1816	−	19.3619i	−0.196966	−	0.268915i
$73$	44.3565	−	76.8277i	0.607623	−	1.05243i	−0.384007	−	0.923330i	$-0.625456\pi$
$73$	44.3565	−	76.8277i	0.607623	−	1.05243i	0.991631	−	0.129105i	$-0.0412103\pi$
$74$	63.3374	+	14.5369i	0.855911	+	0.196445i
$75$	−1.58872	−	0.425697i	−0.0211830	−	0.00567596i
$76$	7.53917	−	39.3247i	0.0991996	−	0.517431i
$77$	130.238	+	80.5600i	1.69141	+	1.04623i
$78$	−8.48549	+	16.0085i	−0.108788	+	0.205237i
$79$	−67.8864	−	117.583i	−0.859322	−	1.48839i	−0.872577	−	0.488477i	$-0.837553\pi$
$79$	−67.8864	−	117.583i	−0.859322	−	1.48839i	0.0132552	−	0.999912i	$-0.495781\pi$
$80$	80.9476	+	9.51722i	1.01185	+	0.118965i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	−4.24313	−	117.191i	−0.0517455	−	1.42916i
$83$	81.6106	+	81.6106i	0.983260	+	0.983260i	0.999862	−	0.0166022i	$-0.00528489\pi$
$83$	81.6106	+	81.6106i	0.983260	+	0.983260i	−0.0166022	+	0.999862i	$0.505285\pi$
$84$	42.9817	+	22.4627i	0.511687	+	0.267413i
$85$	43.8430	+	43.8430i	0.515800	+	0.515800i
$86$	−65.7336	+	70.6724i	−0.764344	+	0.821772i
$87$	26.7941	−	46.4087i	0.307978	−	0.533434i
$88$	−63.3498	−	163.150i	−0.719885	−	1.85398i
$89$	−20.7865	−	36.0033i	−0.233556	−	0.404531i	0.725296	−	0.688437i	$-0.241703\pi$
$89$	−20.7865	−	36.0033i	−0.233556	−	0.404531i	−0.958852	+	0.283906i	$0.908370\pi$
$90$	8.97372	+	29.2174i	0.0997080	+	0.324638i
$91$	1.11118	−	36.5953i	0.0122108	−	0.402147i
$92$	39.9901	−	27.1234i	0.434675	−	0.294820i
$93$	−55.0303	−	14.7453i	−0.591724	−	0.158552i
$94$	20.3158	+	32.4193i	0.216125	+	0.344886i
$95$	−25.4964	+	44.1611i	−0.268383	+	0.464854i
$96$	−23.7460	−	50.0812i	−0.247354	−	0.521679i
$97$			37.3983i			0.385550i	0.981243	+	0.192775i	$0.0617487\pi$
$97$			37.3983i			0.385550i	−0.981243	+	0.192775i	$0.938251\pi$
$98$	−97.9705	−	2.40256i	−0.999699	−	0.0245159i
$99$	46.4085	−	46.4085i	0.468773	−	0.468773i
$100$	−3.41827	−	1.65634i	−0.0341827	−	0.0165634i
$101$	35.3171	+	131.805i	0.349675	+	1.30500i	0.887055	+	0.461663i	$0.152747\pi$
$101$	35.3171	+	131.805i	0.349675	+	1.30500i	−0.537381	+	0.843340i	$0.680586\pi$
$102$	9.43203	−	41.0954i	0.0924709	−	0.402896i
$103$	87.5223	+	151.593i	0.849731	+	1.47178i	0.881448	+	0.472281i	$0.156569\pi$
$103$	87.5223	+	151.593i	0.849731	+	1.47178i	−0.0317166	+	0.999497i	$0.510097\pi$
$104$	−26.2069	+	32.6190i	−0.251989	+	0.313644i
$105$	−42.3270	−	44.9779i	−0.403114	−	0.428361i
$106$	−26.3404	−	85.7613i	−0.248494	−	0.809069i
$107$	−14.6441	+	54.6525i	−0.136861	+	0.510771i	0.863123	+	0.504994i	$0.168505\pi$
$107$	−14.6441	+	54.6525i	−0.136861	+	0.510771i	−0.999983	+	0.00577672i	$0.998161\pi$
$108$	13.5956	−	15.7213i	0.125885	−	0.145568i
$109$	5.25344	+	19.6061i	0.0481967	+	0.179872i	0.985828	−	0.167758i	$-0.0536529\pi$
$109$	5.25344	+	19.6061i	0.0481967	+	0.179872i	−0.937631	+	0.347631i	$0.886986\pi$
$110$	8.06480	+	222.742i	0.0733163	+	2.02493i
$111$			56.2780i			0.507009i
$112$	87.7192	+	69.6372i	0.783207	+	0.621761i
$113$	32.9492			0.291586			0.145793	−	0.989315i	$-0.453427\pi$
$113$	32.9492			0.291586			0.145793	+	0.989315i	$0.453427\pi$
$114$	34.6537	−	1.25470i	0.303980	−	0.0110062i
$115$	−59.4405	+	15.9270i	−0.516874	+	0.138496i
$116$	80.9515	−	93.6086i	0.697857	−	0.806971i
$117$	−15.1563	−	4.06112i	−0.129541	−	0.0347104i
$118$	−60.0938	+	18.4569i	−0.509269	+	0.156415i
$119$	19.5439	+	82.9298i	0.164234	+	0.696889i
$120$	7.64865	+	70.1700i	0.0637388	+	0.584750i
$121$	309.701	−	178.806i	2.55951	−	1.47773i
$122$	77.7201	+	17.8380i	0.637050	+	0.146213i
$123$	98.0967	−	26.2849i	0.797534	−	0.213699i
$124$	−118.402	−	57.3726i	−0.954857	−	0.462682i
$125$	−86.6309	−	86.6309i	−0.693047	−	0.693047i
$126$	−10.6334	+	40.6316i	−0.0843924	+	0.322473i
$127$	30.1302			0.237245			0.118623	−	0.992939i	$-0.462152\pi$
$127$	30.1302			0.237245			0.118623	+	0.992939i	$0.462152\pi$
$128$	−32.0814	−	123.914i	−0.250636	−	0.968081i
$129$	−72.3876	−	41.7930i	−0.561144	−	0.323977i
$130$	45.1538	−	28.2960i	0.347337	−	0.217661i
$131$	12.1545	−	45.3612i	0.0927825	−	0.346269i	−0.903891	−	0.427762i	$-0.859302\pi$
$131$	12.1545	−	45.3612i	0.0927825	−	0.346269i	0.996674	+	0.0814930i	$0.0259688\pi$
$132$	125.439	−	85.0792i	0.950294	−	0.644539i
$133$	−61.7192	+	33.1779i	−0.464054	+	0.249458i
$134$	−2.45466	+	0.753913i	−0.0183183	+	0.00562621i
$135$	−22.9233	+	13.2348i	−0.169803	+	0.0980355i
$136$	39.2622	−	89.1069i	0.288693	−	0.655198i
$137$	−185.470	−	107.081i	−1.35380	−	0.781615i	−0.365017	−	0.931001i	$-0.618937\pi$
$137$	−185.470	−	107.081i	−1.35380	−	0.781615i	−0.988779	+	0.149386i	$0.952270\pi$
$138$	30.6416	+	28.5002i	0.222040	+	0.206523i
$139$	104.469	−	104.469i	0.751575	−	0.751575i	−0.223198	−	0.974773i	$-0.571650\pi$
$139$	104.469	−	104.469i	0.751575	−	0.751575i	0.974773	+	0.223198i	$0.0716497\pi$
$140$	−76.4440	−	120.419i	−0.546028	−	0.860138i
$141$	−23.4287	+	23.4287i	−0.166161	+	0.166161i
$142$	176.621	−	6.39490i	1.24381	−	0.0450345i
$143$	−99.0947	−	57.2123i	−0.692970	−	0.400086i
$144$	37.6722	−	29.7457i	0.261612	−	0.206567i
$145$	−136.491	+	78.8032i	−0.941318	+	0.543470i
$146$	156.765	+	83.0952i	1.07373	+	0.569145i
$147$	−16.9518	−	83.1603i	−0.115318	−	0.565716i
$148$	−24.4713	+	127.644i	−0.165347	+	0.862459i
$149$	11.7572	−	43.8783i	0.0789071	−	0.294485i	−0.915184	−	0.403037i	$-0.867955\pi$
$149$	11.7572	−	43.8783i	0.0789071	−	0.294485i	0.994091	+	0.108552i	$0.0346213\pi$
$150$	0.735866	−	3.20617i	0.00490578	−	0.0213745i
$151$	−125.014	−	72.1769i	−0.827908	−	0.477993i	0.0252280	−	0.999682i	$-0.491969\pi$
$151$	−125.014	−	72.1769i	−0.827908	−	0.477993i	−0.853136	+	0.521689i	$0.825302\pi$
$152$	79.1436	+	12.2227i	0.520681	+	0.0804123i
$153$	36.5150			0.238660
$154$	−151.590	+	266.136i	−0.984349	+	1.72816i
$155$	118.481	+	118.481i	0.764392	+	0.764392i
$156$	−32.6100	−	15.8014i	−0.209039	−	0.101291i
$157$	−233.747	+	62.6324i	−1.48884	+	0.398932i	−0.909344	−	0.416045i	$-0.863416\pi$
$157$	−233.747	+	62.6324i	−1.48884	+	0.398932i	−0.579492	+	0.814978i	$0.696749\pi$
$158$	230.099	−	144.193i	1.45632	−	0.912614i
$159$	67.2864	−	38.8478i	0.423185	−	0.244326i
$160$	−13.1641	+	162.478i	−0.0822755	+	1.01549i
$161$	−80.9780	−	24.3550i	−0.502969	−	0.151273i
$162$	15.9039	+	8.43007i	0.0981722	+	0.0520375i
$163$	118.535	+	31.7615i	0.727211	+	0.194856i	0.603387	−	0.797449i	$-0.293817\pi$
$163$	118.535	+	31.7615i	0.727211	+	0.194856i	0.123824	+	0.992304i	$0.460484\pi$
$164$	233.922	−	16.9614i	1.42636	−	0.103423i
$165$	−186.450	+	49.9590i	−1.13000	+	0.302782i
$166$	−157.208	+	169.020i	−0.947039	+	1.01819i
$167$	−303.161			−1.81533			−0.907666	−	0.419693i	$-0.862138\pi$
$167$	−303.161			−1.81533			−0.907666	+	0.419693i	$0.862138\pi$
$168$	−41.7855	+	87.5327i	−0.248723	+	0.521028i
$169$		−	141.644i		−	0.838129i
$170$	−84.4558	+	90.8013i	−0.496799	+	0.534125i
$171$	7.77251	+	29.0074i	0.0454533	+	0.169634i
$172$	−146.009	−	126.267i	−0.848891	−	0.734109i
$173$	13.4124	−	50.0556i	0.0775281	−	0.289339i	−0.916267	−	0.400569i	$-0.868812\pi$
$173$	13.4124	−	50.0556i	0.0775281	−	0.289339i	0.993795	+	0.111230i	$0.0354791\pi$
$174$	94.6957	+	50.1947i	0.544228	+	0.288475i
$175$	1.52477	+	6.47000i	0.00871298	+	0.0369715i
$176$	321.502	−	138.423i	1.82672	−	0.786496i
$177$	−27.2210	−	47.1482i	−0.153791	−	0.266374i
$178$	70.4551	−	44.1512i	0.395815	−	0.248040i
$179$	−32.7672	−	122.289i	−0.183057	−	0.683177i	−0.995038	−	0.0994939i	$-0.968278\pi$
$179$	−32.7672	−	122.289i	−0.183057	−	0.683177i	0.811981	−	0.583683i	$-0.198389\pi$
$180$	−57.7472	+	20.0500i	−0.320818	+	0.111389i
$181$	−112.597	+	112.597i	−0.622083	+	0.622083i	−0.946064	−	0.323981i	$-0.894979\pi$
$181$	−112.597	+	112.597i	−0.622083	+	0.622083i	0.323981	+	0.946064i	$0.394979\pi$
$182$	73.2232	−	0.427361i	0.402325	−	0.00234814i
$183$			69.0576i			0.377364i
$184$	57.1052	+	77.9651i	0.310355	+	0.423723i
$185$	82.7587	−	143.342i	0.447344	−	0.774823i
$186$	25.4890	−	111.056i	0.137038	−	0.597073i
$187$	257.208	+	68.9188i	1.37545	+	0.368550i
$188$	−63.3259	+	42.9510i	−0.336840	+	0.228463i
$189$	−36.3563	−	1.10392i	−0.192361	−	0.00584087i
$190$	−90.1095	−	47.7637i	−0.474260	−	0.251388i
$191$	−169.430	−	293.462i	−0.887070	−	1.53645i	−0.843322	−	0.537408i	$-0.819403\pi$
$191$	−169.430	−	293.462i	−0.887070	−	1.53645i	−0.0437481	−	0.999043i	$-0.513930\pi$
$192$	98.3784	−	51.0851i	0.512388	−	0.266068i
$193$	78.3235	−	135.660i	0.405821	−	0.702903i	−0.588596	−	0.808428i	$-0.700319\pi$
$193$	78.3235	−	135.660i	0.405821	−	0.702903i	0.994417	+	0.105525i	$0.0336522\pi$
$194$	−74.7477	+	2.70638i	−0.385297	+	0.0139504i
$195$	32.6316	+	32.6316i	0.167342	+	0.167342i
$196$	−2.28780	−	195.987i	−0.0116724	−	0.999932i
$197$	80.2306	+	80.2306i	0.407262	+	0.407262i	0.880783	−	0.473521i	$-0.157017\pi$
$197$	80.2306	+	80.2306i	0.407262	+	0.407262i	−0.473521	+	0.880783i	$0.657017\pi$
$198$	96.1147	+	89.3979i	0.485428	+	0.451505i
$199$	−46.2412	+	80.0921i	−0.232368	+	0.402473i	−0.958504	−	0.285078i	$-0.907981\pi$
$199$	−46.2412	+	80.0921i	−0.232368	+	0.402473i	0.726137	+	0.687550i	$0.241314\pi$
$200$	3.06315	−	6.95193i	0.0153158	−	0.0347596i
$201$	−1.11190	−	1.92587i	−0.00553184	−	0.00958143i
$202$	−260.882	+	80.1263i	−1.29150	+	0.396665i
$203$	−216.474	−	6.57303i	−1.06638	−	0.0323795i
$204$	82.8195	+	15.8778i	0.405978	+	0.0778323i
$205$	−288.509	−	77.3057i	−1.40736	−	0.377101i
$206$	−296.654	+	185.900i	−1.44007	+	0.902429i
$207$	−18.1203	+	31.3852i	−0.0875375	+	0.151619i
$208$	−67.0917	−	50.0189i	−0.322556	−	0.240475i
$209$			218.996i			1.04783i
$210$	86.8339	−	87.8535i	0.413495	−	0.418350i
$211$	157.603	−	157.603i	0.746935	−	0.746935i	−0.226968	−	0.973902i	$-0.572881\pi$
$211$	157.603	−	157.603i	0.746935	−	0.746935i	0.973902	+	0.226968i	$0.0728812\pi$
$212$	169.504	−	58.8525i	0.799548	−	0.277606i
$213$	39.6145	+	147.843i	0.185984	+	0.694100i
$214$	−110.293	−	25.3140i	−0.515389	−	0.118290i
$215$	122.916	+	212.897i	0.571702	+	0.990217i
$216$	32.4059	+	26.0357i	0.150027	+	0.120536i
$217$	52.8151	+	224.108i	0.243388	+	1.03276i
$218$	−38.8063	+	11.9188i	−0.178011	+	0.0546735i
$219$	−39.7690	+	148.420i	−0.181593	+	0.677716i
$220$	−444.609	+	32.2381i	−2.02095	+	0.146537i
$221$	−16.4768	−	61.4924i	−0.0745558	−	0.278246i
$222$	−112.482	+	4.07263i	−0.506677	+	0.0183452i
$223$			15.8266i			0.0709712i	0.999370	+	0.0354856i	$0.0112978\pi$
$223$			15.8266i			0.0709712i	−0.999370	+	0.0354856i	$0.988702\pi$
$224$	−132.835	+	180.363i	−0.593015	+	0.805192i
$225$	2.84882			0.0126614
$226$	2.38441	+	65.8552i	0.0105505	+	0.291395i
$227$	54.5476	−	14.6160i	0.240298	−	0.0643876i	−0.136660	−	0.990618i	$-0.543637\pi$
$227$	54.5476	−	14.6160i	0.240298	−	0.0643876i	0.376958	+	0.926230i	$0.376970\pi$
$228$	5.01553	+	69.1713i	0.0219979	+	0.303383i
$229$	77.6637	+	20.8099i	0.339143	+	0.0908730i	0.424371	−	0.905488i	$-0.360495\pi$
$229$	77.6637	+	20.8099i	0.339143	+	0.0908730i	−0.0852282	+	0.996361i	$0.527162\pi$
$230$	−36.1347	−	117.651i	−0.157107	−	0.511524i
$231$	−254.007	−	76.3953i	−1.09960	−	0.330716i
$232$	192.953	+	155.023i	0.831693	+	0.668202i
$233$	−95.4149	+	55.0878i	−0.409506	+	0.236428i	−0.690577	−	0.723259i	$-0.742644\pi$
$233$	−95.4149	+	55.0878i	−0.409506	+	0.236428i	0.281072	+	0.959687i	$0.409310\pi$
$234$	7.02011	−	30.5866i	0.0300005	−	0.130712i
$235$	94.1263	−	25.2211i	0.400537	−	0.107324i
$236$	−41.2385	−	118.773i	−0.174739	−	0.503276i
$237$	166.287	+	166.287i	0.701633	+	0.701633i
$238$	−164.337	+	45.0635i	−0.690490	+	0.189342i
$239$	−452.832			−1.89470			−0.947348	−	0.320205i	$-0.896248\pi$
$239$	−452.832			−1.89470			−0.947348	+	0.320205i	$0.896248\pi$
$240$	−139.695	+	20.3652i	−0.582060	+	0.0848551i
$241$	−241.806	−	139.607i	−1.00334	−	0.579281i	−0.0941085	−	0.995562i	$-0.530000\pi$
$241$	−241.806	−	139.607i	−1.00334	−	0.579281i	−0.909236	+	0.416281i	$0.863333\pi$
$242$	379.790	+	606.057i	1.56938	+	2.50437i
$243$	−4.03459	+	15.0573i	−0.0166032	+	0.0619642i
$244$	−30.0283	+	156.629i	−0.123067	+	0.641923i
$245$	−79.1130	+	236.741i	−0.322910	+	0.966288i
$246$	59.6344	+	194.163i	0.242416	+	0.789280i
$247$	45.3422	−	26.1783i	0.183572	−	0.105985i
$248$	106.102	−	240.801i	0.427829	−	0.970973i
$249$	−173.122	−	99.9521i	−0.695270	−	0.401414i
$250$	166.879	−	179.417i	0.667516	−	0.717670i
$251$	−270.827	+	270.827i	−1.07899	+	1.07899i	−0.0823917	+	0.996600i	$0.526256\pi$
$251$	−270.827	+	270.827i	−1.07899	+	1.07899i	−0.996600	+	0.0823917i	$0.973744\pi$
$252$	−81.9796	−	18.3126i	−0.325316	−	0.0726690i
$253$	−186.874	+	186.874i	−0.738634	+	0.738634i
$254$	2.18041	+	60.2209i	0.00858428	+	0.237090i
$255$	−93.0050	−	53.6965i	−0.364726	−	0.210574i
$256$	245.345	−	73.0881i	0.958379	−	0.285500i
$257$	279.282	−	161.244i	1.08670	−	0.627408i	0.154006	−	0.988070i	$-0.450783\pi$
$257$	279.282	−	161.244i	1.08670	−	0.627408i	0.932697	+	0.360662i	$0.117449\pi$
$258$	78.2929	−	147.705i	0.303461	−	0.572499i
$259$	200.334	−	107.692i	0.773490	−	0.415799i
$260$	59.8225	+	88.2009i	0.230086	+	0.339234i
$261$	−24.0229	+	89.6548i	−0.0920419	+	0.343505i
$262$	91.5426	+	21.0105i	0.349399	+	0.0801926i
$263$	274.153	+	158.282i	1.04241	+	0.601833i	0.920514	−	0.390710i	$-0.127771\pi$
$263$	274.153	+	158.282i	1.04241	+	0.601833i	0.121892	+	0.992543i	$0.461104\pi$
$264$	179.125	+	244.556i	0.678502	+	0.926350i
$265$	−228.508			−0.862295
$266$	−70.7787	−	120.957i	−0.266085	−	0.454724i
$267$	50.9163	+	50.9163i	0.190698	+	0.190698i
$268$	−1.68447	−	4.85154i	−0.00628534	−	0.0181028i
$269$	188.322	−	50.4607i	0.700081	−	0.187586i	0.108814	−	0.994062i	$-0.465295\pi$
$269$	188.322	−	50.4607i	0.700081	−	0.187586i	0.591267	+	0.806476i	$0.298628\pi$
$270$	−28.1111	−	44.8589i	−0.104115	−	0.166144i
$271$	313.057	−	180.744i	1.15519	−	0.666951i	0.205045	−	0.978752i	$-0.434266\pi$
$271$	313.057	−	180.744i	1.15519	−	0.666951i	0.950147	+	0.311802i	$0.100932\pi$
$272$	180.938	+	72.0247i	0.665214	+	0.264797i
$273$	14.5462	+	61.7233i	0.0532828	+	0.226093i
$274$	200.600	−	378.446i	0.732118	−	1.38119i
$275$	20.0669	+	5.37690i	0.0729704	+	0.0195524i
$276$	−54.7457	+	63.3054i	−0.198354	+	0.229368i
$277$	101.864	−	27.2943i	0.367740	−	0.0985355i	−0.0702168	−	0.997532i	$-0.522369\pi$
$277$	101.864	−	27.2943i	0.367740	−	0.0985355i	0.437956	+	0.898996i	$0.355702\pi$
$278$	216.361	+	201.241i	0.778277	+	0.723889i
$279$	98.6776			0.353683
$280$	235.149	−	161.502i	0.839818	−	0.576793i
$281$		−	16.9851i		−	0.0604452i	−0.999543	−	0.0302226i	$-0.990378\pi$
$281$		−	16.9851i		−	0.0604452i	0.999543	−	0.0302226i	$-0.00962162\pi$
$282$	−48.5221	−	45.1312i	−0.172064	−	0.160040i
$283$	97.8174	+	365.060i	0.345645	+	1.28996i	0.891857	+	0.452317i	$0.149402\pi$
$283$	97.8174	+	365.060i	0.345645	+	1.28996i	−0.546213	+	0.837646i	$0.683931\pi$
$284$	25.5628	+	352.548i	0.0900100	+	1.24137i
$285$	22.8595	−	85.3127i	0.0802087	−	0.299343i
$286$	107.179	−	202.200i	0.374750	−	0.706992i
$287$	−281.282	−	298.899i	−0.980076	−	1.04146i
$288$	62.1786	+	73.1424i	0.215898	+	0.253967i
$289$	−70.4254	−	121.980i	−0.243686	−	0.422077i
$290$	−167.381	−	267.101i	−0.577174	−	0.921038i
$291$	−16.7652	−	62.5686i	−0.0576124	−	0.215012i
$292$	−154.737	+	319.338i	−0.529922	+	1.09362i
$293$	323.812	−	323.812i	1.10516	−	1.10516i	0.111382	−	0.993778i	$-0.464472\pi$
$293$	323.812	−	323.812i	1.10516	−	1.10516i	0.993778	−	0.111382i	$-0.0355278\pi$
$294$	164.985	−	39.8994i	0.561173	−	0.135712i
$295$			160.118i			0.542772i
$296$	−256.892	−	39.6735i	−0.867877	−	0.134032i
$297$	−56.8386	+	98.4474i	−0.191376	+	0.331473i
$298$	88.5499	+	20.3236i	0.297147	+	0.0682000i
$299$	61.0302	+	16.3530i	0.204114	+	0.0546923i
$300$	6.46140	+	1.23875i	0.0215380	+	0.00412917i
$301$	−10.2525	+	337.653i	−0.0340615	+	1.12177i
$302$	135.212	−	255.088i	0.447723	−	0.844661i
$303$	−118.173	−	204.682i	−0.390011	−	0.675519i
$304$	−18.7020	+	159.068i	−0.0615198	+	0.523250i
$305$	101.552	−	175.892i	0.332956	−	0.576696i
$306$	2.64245	+	72.9821i	0.00863547	+	0.238504i
$307$	225.697	+	225.697i	0.735170	+	0.735170i	0.971639	−	0.236469i	$-0.0759901\pi$
$307$	225.697	+	225.697i	0.735170	+	0.735170i	−0.236469	+	0.971639i	$0.575990\pi$
$308$	−542.894	−	283.722i	−1.76264	−	0.921174i
$309$	−214.385	−	214.385i	−0.693803	−	0.693803i
$310$	−228.232	+	245.380i	−0.736233	+	0.791550i
$311$	252.796	−	437.856i	0.812850	−	1.40790i	−0.0980110	−	0.995185i	$-0.531248\pi$
$311$	252.796	−	437.856i	0.812850	−	1.40790i	0.910861	−	0.412713i	$-0.135419\pi$
$312$	29.2222	−	66.3208i	0.0936610	−	0.212567i
$313$	−121.482	−	210.413i	−0.388122	−	0.672247i	0.604075	−	0.796927i	$-0.293543\pi$
$313$	−121.482	−	210.413i	−0.388122	−	0.672247i	−0.992197	+	0.124681i	$0.960209\pi$
$314$	−142.098	−	462.656i	−0.452542	−	1.47343i
$315$	90.9775	+	56.2749i	0.288818	+	0.178650i
$316$	304.848	+	449.461i	0.964710	+	1.42235i
$317$	−320.549	−	85.8907i	−1.01119	−	0.270949i	−0.285066	−	0.958508i	$-0.592016\pi$
$317$	−320.549	−	85.8907i	−1.01119	−	0.270949i	−0.726128	+	0.687559i	$0.758682\pi$
$318$	82.5141	+	131.673i	0.259478	+	0.414067i
$319$	−338.431	+	586.180i	−1.06091	+	1.83755i
$320$	−325.696	−	14.5530i	−1.01780	−	0.0454781i
$321$		−	98.0002i		−	0.305297i
$322$	42.8179	−	163.612i	0.132975	−	0.508113i
$323$	−86.1547	+	86.1547i	−0.266733	+	0.266733i
$324$	−15.6982	+	32.3970i	−0.0484512	+	0.0999908i
$325$	−1.28549	−	4.79751i	−0.00395535	−	0.0147616i
$326$	−54.9034	+	239.214i	−0.168415	+	0.733785i
$327$	−17.5783	−	30.4466i	−0.0537564	−	0.0931088i
$328$	50.8287	+	466.311i	0.154966	+	1.42168i
$329$	128.232	+	38.5670i	0.389762	+	0.117225i
$330$	−113.345	−	369.040i	−0.343471	−	1.11830i
$331$	101.731	−	379.665i	0.307344	−	1.14702i	−0.623565	−	0.781772i	$-0.714316\pi$
$331$	101.731	−	379.665i	0.307344	−	1.14702i	0.930909	−	0.365252i	$-0.119017\pi$
$332$	−349.195	−	301.980i	−1.05179	−	0.909577i
$333$	−25.2287	−	94.1550i	−0.0757620	−	0.282748i
$334$	−21.9386	−	605.924i	−0.0656844	−	1.81414i
$335$			6.54034i			0.0195234i
$336$	−177.975	−	77.1818i	−0.529686	−	0.229708i
$337$	331.157			0.982663			0.491331	−	0.870973i	$-0.336510\pi$
$337$	331.157			0.982663			0.491331	+	0.870973i	$0.336510\pi$
$338$	283.102	−	10.2502i	0.837580	−	0.0303261i
$339$	−55.1251	+	14.7707i	−0.162611	+	0.0435714i
$340$	−187.595	−	162.230i	−0.551751	−	0.477147i
$341$	695.077	+	186.245i	2.03835	+	0.546174i
$342$	−57.4144	+	17.6340i	−0.167878	+	0.0515614i
$343$	−263.589	+	219.477i	−0.768480	+	0.639874i
$344$	241.802	−	300.965i	0.702913	−	0.874897i
$345$	92.3060	−	53.2929i	0.267554	−	0.154472i
$346$	101.016	+	23.1848i	0.291955	+	0.0670082i
$347$	−431.876	+	115.721i	−1.24460	+	0.333489i	−0.820248	−	0.572008i	$-0.806164\pi$
$347$	−431.876	+	115.721i	−1.24460	+	0.333489i	−0.424351	+	0.905498i	$0.639498\pi$
$348$	−93.4708	+	192.900i	−0.268594	+	0.554310i
$349$	60.1357	+	60.1357i	0.172309	+	0.172309i	0.787993	−	0.615684i	$-0.211120\pi$
$349$	60.1357	+	60.1357i	0.172309	+	0.172309i	−0.615684	+	0.787993i	$0.711120\pi$
$350$	−12.8212	+	3.51576i	−0.0366320	+	0.0100450i
$351$	27.1775			0.0774288
$352$	299.931	+	632.566i	0.852077	+	1.79706i
$353$	528.536	+	305.150i	1.49727	+	0.864448i	0.999995	−	0.00314540i	$-0.00100121\pi$
$353$	528.536	+	305.150i	1.49727	+	0.864448i	0.497274	+	0.867594i	$0.334335\pi$
$354$	92.2648	−	57.8184i	0.260635	−	0.163329i
$355$	116.509	−	434.817i	0.328194	−	1.22484i
$356$	93.3431	+	137.623i	0.262200	+	0.386581i
$357$	−69.8740	−	129.983i	−0.195725	−	0.364098i
$358$	242.046	−	74.3410i	0.676106	−	0.207656i
$359$	−42.9209	+	24.7804i	−0.119557	+	0.0690261i	−0.558586	−	0.829447i	$-0.688656\pi$
$359$	−42.9209	+	24.7804i	−0.119557	+	0.0690261i	0.439029	+	0.898473i	$0.355323\pi$
$360$	−44.2528	−	113.968i	−0.122924	−	0.316577i
$361$	225.855	+	130.398i	0.625638	+	0.361212i
$362$	−233.195	−	216.898i	−0.644185	−	0.599167i
$363$	−437.983	+	437.983i	−1.20657	+	1.20657i
$364$	6.15305	+	146.320i	0.0169040	+	0.401977i
$365$	319.549	−	319.549i	0.875477	−	0.875477i
$366$	−138.025	+	4.99745i	−0.377117	+	0.0136542i
$367$	−156.295	−	90.2368i	−0.425871	−	0.245877i	0.271715	−	0.962378i	$-0.412409\pi$
$367$	−156.295	−	90.2368i	−0.425871	−	0.245877i	−0.697586	+	0.716501i	$0.745743\pi$
$368$	−151.696	+	119.778i	−0.412216	+	0.325483i
$369$	−152.336	+	87.9511i	−0.412834	+	0.238350i
$370$	292.486	+	155.036i	0.790502	+	0.419016i
$371$	−267.045	−	165.183i	−0.719797	−	0.445236i
$372$	223.810	+	42.9079i	0.601641	+	0.115344i
$373$	20.6149	−	76.9358i	0.0552678	−	0.206262i	−0.932771	−	0.360471i	$-0.882616\pi$
$373$	20.6149	−	76.9358i	0.0552678	−	0.206262i	0.988038	+	0.154208i	$0.0492827\pi$
$374$	−119.134	+	519.067i	−0.318540	+	1.38788i
$375$	183.772	+	106.101i	0.490058	+	0.282935i
$376$	−90.4283	−	123.461i	−0.240501	−	0.328353i
$377$	161.822			0.429235
$378$	−0.424570	−	72.7449i	−0.00112320	−	0.192447i
$379$	−323.919	−	323.919i	−0.854666	−	0.854666i	0.136037	−	0.990704i	$-0.456563\pi$
$379$	−323.919	−	323.919i	−0.854666	−	0.854666i	−0.990704	+	0.136037i	$0.956563\pi$
$380$	88.9439	−	183.557i	0.234063	−	0.483046i
$381$	−50.4087	+	13.5070i	−0.132306	+	0.0354514i
$382$	574.279	−	359.876i	1.50335	−	0.942083i
$383$	−266.664	+	153.959i	−0.696252	+	0.401981i	−0.805950	−	0.591984i	$-0.798345\pi$
$383$	−266.664	+	153.959i	−0.696252	+	0.401981i	0.109698	+	0.993965i	$0.465012\pi$
$384$	109.223	+	192.931i	0.284434	+	0.502425i
$385$	534.624	+	568.108i	1.38863	+	1.47560i
$386$	276.811	+	146.727i	0.717126	+	0.380122i
$387$	139.842	+	37.4706i	0.361349	+	0.0968232i
$388$	−10.8184	−	149.202i	−0.0278825	−	0.384540i
$389$	−447.157	+	119.815i	−1.14950	+	0.308008i	−0.782766	−	0.622316i	$-0.786192\pi$
$389$	−447.157	+	119.815i	−1.14950	+	0.308008i	−0.366737	+	0.930325i	$0.619525\pi$
$390$	−62.8591	+	67.5820i	−0.161177	+	0.173287i
$391$	−147.036			−0.376051
$392$	391.551	−	18.7554i	0.998855	−	0.0478455i
$393$			81.3395i			0.206971i
$394$	−154.550	+	166.162i	−0.392259	+	0.421731i
$395$	−179.009	−	668.070i	−0.453187	−	1.69132i
$396$	−171.723	+	198.573i	−0.433645	+	0.501447i
$397$	10.0439	−	37.4842i	0.0252994	−	0.0944187i	−0.952122	−	0.305719i	$-0.901103\pi$
$397$	10.0439	−	37.4842i	0.0252994	−	0.0944187i	0.977421	+	0.211300i	$0.0677698\pi$
$398$	−163.426	−	86.6258i	−0.410617	−	0.217653i
$399$	88.3849	−	83.1757i	0.221516	−	0.208460i
$400$	14.1164	+	5.61921i	0.0352910	+	0.0140480i
$401$	−287.386	−	497.767i	−0.716673	−	1.24131i	−0.962311	−	0.271952i	$-0.912331\pi$
$401$	−287.386	−	497.767i	−0.716673	−	1.24131i	0.245638	−	0.969362i	$-0.421002\pi$
$402$	3.76875	−	2.36171i	0.00937500	−	0.00587491i
$403$	−44.5268	−	166.176i	−0.110488	−	0.412348i
$404$	−179.027	−	515.624i	−0.443135	−	1.27630i
$405$	32.4185	−	32.4185i	0.0800457	−	0.0800457i
$406$	−2.52799	−	433.141i	−0.00622658	−	1.06685i
$407$		−	710.837i		−	1.74653i
$408$	−25.7414	+	166.679i	−0.0630918	+	0.408528i
$409$	257.359	−	445.759i	0.629240	−	1.08988i	−0.358464	−	0.933543i	$-0.616699\pi$
$409$	257.359	−	445.759i	0.629240	−	1.08988i	0.987704	−	0.156333i	$-0.0499672\pi$
$410$	133.632	−	582.234i	0.325932	−	1.42008i
$411$	358.301	+	96.0064i	0.871778	+	0.233592i
$412$	−393.025	−	579.467i	−0.953944	−	1.40647i
$413$	−115.745	+	187.121i	−0.280254	+	0.453077i
$414$	−64.0406	−	33.9456i	−0.154688	−	0.0819941i
$415$	293.966	+	509.164i	0.708351	+	1.22690i
$416$	95.1171	−	137.715i	0.228647	−	0.331046i
$417$	−127.948	+	221.612i	−0.306829	+	0.531444i
$418$	−437.705	+	15.8479i	−1.04714	+	0.0379137i
$419$	415.309	+	415.309i	0.991191	+	0.991191i	0.999962	−	0.00877005i	$-0.00279163\pi$
$419$	415.309	+	415.309i	0.991191	+	0.991191i	−0.00877005	+	0.999962i	$0.502792\pi$
$420$	181.876	+	167.197i	0.433038	+	0.398087i
$421$	114.205	+	114.205i	0.271270	+	0.271270i	0.829611	−	0.558341i	$-0.188562\pi$
$421$	114.205	+	114.205i	0.271270	+	0.271270i	−0.558341	+	0.829611i	$0.688562\pi$
$422$	326.405	+	303.595i	0.773472	+	0.719419i
$423$	28.6941	−	49.6997i	0.0678348	−	0.117493i
$424$	129.894	+	334.527i	0.306354	+	0.788980i
$425$	5.77914	+	10.0098i	0.0135980	+	0.0235524i
$426$	−292.626	+	89.8760i	−0.686916	+	0.210976i
$427$	245.826	−	132.147i	0.575704	−	0.309477i
$428$	42.6134	−	222.274i	0.0995639	−	0.519331i
$429$	191.436	+	51.2952i	0.446238	+	0.119569i
$430$	−416.620	+	261.078i	−0.968883	+	0.607157i
$431$	−389.230	+	674.167i	−0.903087	+	1.56419i	−0.0796217	+	0.996825i	$0.525371\pi$
$431$	−389.230	+	674.167i	−0.903087	+	1.56419i	−0.823465	+	0.567367i	$0.807962\pi$
$432$	−49.6922	+	66.6535i	−0.115028	+	0.154291i
$433$			113.384i			0.261857i	0.991392	+	0.130929i	$0.0417959\pi$
$433$			113.384i			0.261857i	−0.991392	+	0.130929i	$0.958204\pi$
$434$	−444.101	+	121.779i	−1.02328	+	0.280597i
$435$	193.028	−	193.028i	0.443742	−	0.443742i
$436$	−26.6303	−	76.6994i	−0.0610787	−	0.175916i
$437$	−31.2978	−	116.805i	−0.0716196	−	0.267288i
$438$	−299.523	−	68.7453i	−0.683843	−	0.156953i
$439$	−280.557	−	485.938i	−0.639081	−	1.10692i	−0.985635	−	0.168891i	$-0.945982\pi$
$439$	−280.557	−	485.938i	−0.639081	−	1.10692i	0.346554	−	0.938030i	$-0.387352\pi$
$440$	−96.6086	−	886.303i	−0.219565	−	2.01433i
$441$	65.6407	+	131.531i	0.148845	+	0.298255i
$442$	121.712	−	37.3821i	0.275366	−	0.0845749i
$443$	202.915	−	757.288i	0.458046	−	1.70945i	−0.220927	−	0.975290i	$-0.570908\pi$
$443$	202.915	−	757.288i	0.458046	−	1.70945i	0.678974	−	0.734162i	$-0.262425\pi$
$444$	−16.2799	−	224.523i	−0.0366664	−	0.505682i
$445$	−54.8116	−	204.560i	−0.123172	−	0.459685i
$446$	−31.6324	+	1.14531i	−0.0709247	+	0.00256796i
$447$			78.6804i			0.176019i
$448$	−370.102	−	252.444i	−0.826122	−	0.563492i
$449$	−538.648			−1.19966			−0.599831	−	0.800127i	$-0.704765\pi$
$449$	−538.648			−1.19966			−0.599831	+	0.800127i	$0.704765\pi$
$450$	0.206159	+	5.69391i	0.000458130	+	0.0126531i
$451$	−1239.04	+	332.000i	−2.74732	+	0.736142i
$452$	−131.452	+	9.53140i	−0.290822	+	0.0210872i
$453$	241.509	+	64.7121i	0.533132	+	0.142852i
$454$	33.1602	+	107.966i	0.0730402	+	0.237811i
$455$	53.7165	−	178.602i	0.118058	−	0.392533i
$456$	−137.889	+	15.0302i	−0.302388	+	0.0329609i
$457$	639.626	−	369.288i	1.39962	−	0.808070i	0.405266	−	0.914199i	$-0.367179\pi$
$457$	639.626	−	369.288i	1.39962	−	0.808070i	0.994352	+	0.106129i	$0.0338456\pi$
$458$	−35.9724	+	156.732i	−0.0785423	+	0.342209i
$459$	−61.0907	+	16.3692i	−0.133095	+	0.0356628i
$460$	232.532	−	80.7360i	0.505505	−	0.175513i
$461$	−29.7853	−	29.7853i	−0.0646102	−	0.0646102i	0.674063	−	0.738674i	$-0.264547\pi$
$461$	−29.7853	−	29.7853i	−0.0646102	−	0.0646102i	−0.738674	+	0.674063i	$0.764547\pi$
$462$	134.309	−	513.210i	0.290712	−	1.11084i
$463$	210.143			0.453872			0.226936	−	0.973910i	$-0.427129\pi$
$463$	210.143			0.453872			0.226936	+	0.973910i	$0.427129\pi$
$464$	−295.879	+	396.871i	−0.637671	+	0.855326i
$465$	−251.336	−	145.109i	−0.540507	−	0.312062i
$466$	−117.008	−	186.718i	−0.251091	−	0.400683i
$467$	207.026	−	772.630i	0.443310	−	1.65445i	−0.277052	−	0.960855i	$-0.589357\pi$
$467$	207.026	−	772.630i	0.443310	−	1.65445i	0.720362	−	0.693599i	$-0.243976\pi$
$468$	61.6412	+	11.8176i	0.131712	+	0.0252512i
$469$	−4.72785	+	7.64333i	−0.0100807	+	0.0162971i
$470$	57.2207	+	186.304i	0.121746	+	0.396392i
$471$	362.990	−	209.572i	0.770678	−	0.444951i
$472$	234.407	−	91.0181i	0.496624	−	0.192835i
$473$	914.314	+	527.879i	1.93301	+	1.11602i
$474$	−320.323	+	344.390i	−0.675787	+	0.726561i
$475$	−6.72160	+	6.72160i	−0.0141507	+	0.0141507i
$476$	−101.960	−	325.197i	−0.214203	−	0.683187i
$477$	−95.1574	+	95.1574i	−0.199491	+	0.199491i
$478$	−32.7698	−	905.072i	−0.0685561	−	1.89346i
$479$	81.6942	+	47.1662i	0.170552	+	0.0984680i	0.582846	−	0.812583i	$-0.301939\pi$
$479$	81.6942	+	47.1662i	0.170552	+	0.0984680i	−0.412294	+	0.911051i	$0.635272\pi$
$480$	−50.8130	−	277.732i	−0.105860	−	0.578609i
$481$	−147.176	+	84.9721i	−0.305979	+	0.176657i
$482$	261.532	−	493.398i	0.542598	−	1.02365i
$483$	146.397	+	4.44520i	0.303099	+	0.00920331i
$484$	−1183.84	+	802.940i	−2.44594	+	1.65897i
$485$	−49.3076	+	184.018i	−0.101665	+	0.379420i
$486$	−30.3868	−	6.97425i	−0.0625244	−	0.0143503i
$487$	290.002	+	167.433i	0.595486	+	0.343804i	0.767264	−	0.641332i	$-0.221618\pi$
$487$	290.002	+	167.433i	0.595486	+	0.343804i	−0.171778	+	0.985136i	$0.554951\pi$
$488$	−315.227	−	48.6826i	−0.645956	−	0.0997593i
$489$	−212.552			−0.434666
$490$	−478.896	−	140.990i	−0.977339	−	0.287736i
$491$	110.348	+	110.348i	0.224742	+	0.224742i	0.810492	−	0.585750i	$-0.199200\pi$
$491$	110.348	+	110.348i	0.224742	+	0.224742i	−0.585750	+	0.810492i	$0.699200\pi$
$492$	−383.756	+	133.241i	−0.779992	+	0.270816i
$493$	−363.749	+	97.4663i	−0.737828	+	0.197700i
$494$	55.6036	+	88.7306i	0.112558	+	0.179617i
$495$	289.540	−	167.166i	0.584930	−	0.337709i
$496$	488.965	+	194.639i	0.985817	+	0.392416i
$497$	450.475	−	423.925i	0.906389	−	0.852968i
$498$	187.245	−	353.251i	0.375994	−	0.709339i
$499$	340.835	+	91.3264i	0.683035	+	0.183019i	0.583620	−	0.812027i	$-0.301636\pi$
$499$	340.835	+	91.3264i	0.683035	+	0.183019i	0.0994157	+	0.995046i	$0.468303\pi$
$500$	370.676	+	320.556i	0.741352	+	0.641112i
$501$	507.197	−	135.903i	1.01237	−	0.271264i
$502$	−560.898	−	521.700i	−1.11733	−	1.03924i
$503$	−297.223			−0.590901			−0.295450	−	0.955358i	$-0.595470\pi$
$503$	−297.223			−0.590901			−0.295450	+	0.955358i	$0.595470\pi$
$504$	30.6687	−	165.177i	0.0608505	−	0.327732i
$505$			695.112i			1.37646i
$506$	−387.028	−	359.981i	−0.764877	−	0.711424i
$507$	63.4972	+	236.975i	0.125241	+	0.467406i
$508$	−120.205	+	8.71592i	−0.236624	+	0.0171573i
$509$	−246.393	+	919.550i	−0.484072	+	1.80658i	0.100133	+	0.994974i	$0.468073\pi$
$509$	−246.393	+	919.550i	−0.484072	+	1.80658i	−0.584204	+	0.811607i	$0.698593\pi$
$510$	100.592	−	189.774i	0.197240	−	0.372106i
$511$	604.433	−	142.445i	1.18284	−	0.278758i
$512$	163.835	+	485.079i	0.319991	+	0.947421i
$513$	−26.0073	−	45.0460i	−0.0506966	−	0.0878090i
$514$	342.487	+	546.531i	0.666317	+	1.06329i
$515$	230.787	+	861.307i	0.448129	+	1.67244i
$516$	300.882	+	145.794i	0.583105	+	0.282547i
$517$	295.923	−	295.923i	0.572385	−	0.572385i
$518$	229.740	+	392.612i	0.443514	+	0.757938i
$519$			89.7573i			0.172943i
$520$	−171.957	+	125.949i	−0.330687	+	0.242210i
$521$	225.744	−	391.001i	0.433290	−	0.750481i	−0.563864	−	0.825868i	$-0.690686\pi$
$521$	225.744	−	391.001i	0.433290	−	0.750481i	0.997154	+	0.0753867i	$0.0240191\pi$
$522$	−180.931	−	41.5264i	−0.346610	−	0.0795525i
$523$	−112.729	−	30.2055i	−0.215542	−	0.0577544i	0.149432	−	0.988772i	$-0.452256\pi$
$523$	−112.729	−	30.2055i	−0.215542	−	0.0577544i	−0.364974	+	0.931018i	$0.618922\pi$
$524$	−35.3688	+	184.486i	−0.0674977	+	0.352072i
$525$	−5.45142	−	10.1410i	−0.0103836	−	0.0193162i
$526$	−296.517	+	559.400i	−0.563721	+	1.06350i
$527$	200.178	+	346.719i	0.379845	+	0.657911i
$528$	−475.830	+	375.712i	−0.901193	+	0.711576i
$529$	−191.535	+	331.748i	−0.362069	+	0.627122i
$530$	−16.5363	−	456.717i	−0.0312005	−	0.861730i
$531$	66.6777	+	66.6777i	0.125570	+	0.125570i
$532$	236.633	−	150.218i	0.444798	−	0.282365i
$533$	216.852	+	216.852i	0.406851	+	0.406851i
$534$	−98.0813	+	105.451i	−0.183673	+	0.197473i
$535$	−144.113	+	249.610i	−0.269369	+	0.466561i
$536$	9.57483	−	3.71783i	0.0178635	−	0.00693624i
$537$	109.641	+	189.904i	0.204173	+	0.353639i
$538$	114.483	+	372.745i	0.212794	+	0.692835i
$539$	214.115	+	1050.38i	0.397245	+	1.94876i
$540$	87.6248	−	59.4317i	0.162268	−	0.110059i
$541$	−41.0239	−	10.9923i	−0.0758298	−	0.0203185i	0.220705	−	0.975341i	$-0.429164\pi$
$541$	−41.0239	−	10.9923i	−0.0758298	−	0.0203185i	−0.296534	+	0.955022i	$0.595831\pi$
$542$	383.905	+	612.625i	0.708313	+	1.13030i
$543$	137.903	−	238.854i	0.253964	−	0.439879i
$544$	−130.861	+	366.852i	−0.240554	+	0.674360i
$545$			103.398i			0.189721i
$546$	−122.313	+	33.5400i	−0.224017	+	0.0614287i
$547$	690.910	−	690.910i	1.26309	−	1.26309i	0.313503	−	0.949587i	$-0.398497\pi$
$547$	690.910	−	690.910i	1.26309	−	1.26309i	0.949587	−	0.313503i	$-0.101503\pi$
$548$	770.914	+	373.551i	1.40678	+	0.681663i
$549$	−30.9577	−	115.536i	−0.0563892	−	0.210447i
$550$	−9.29459	+	40.4965i	−0.0168992	+	0.0736300i
$551$	−154.854	−	268.215i	−0.281042	−	0.486779i
$552$	−130.490	−	104.839i	−0.236394	−	0.189925i
$553$	273.733	−	910.137i	0.494996	−	1.64582i
$554$	61.9244	+	201.619i	0.111777	+	0.363933i
$555$	−74.1994	+	276.916i	−0.133693	+	0.498948i
$556$	−386.561	+	447.002i	−0.695254	+	0.803960i
$557$	−23.3340	−	87.0836i	−0.0418922	−	0.156344i	0.941811	−	0.336142i	$-0.109122\pi$
$557$	−23.3340	−	87.0836i	−0.0418922	−	0.156344i	−0.983704	+	0.179798i	$0.942456\pi$
$558$	7.14094	+	197.226i	0.0127974	+	0.353452i
$559$		−	252.407i		−	0.451533i
$560$	339.810	+	458.303i	0.606803	+	0.818397i
$561$	−461.214			−0.822128
$562$	33.9480	−	1.22915i	0.0604057	−	0.00218710i
$563$	−570.719	+	152.924i	−1.01371	+	0.271623i	−0.727179	−	0.686448i	$-0.759169\pi$
$563$	−570.719	+	152.924i	−1.01371	+	0.271623i	−0.286531	+	0.958071i	$0.592502\pi$
$564$	86.6919	−	100.247i	0.153709	−	0.177742i
$565$	162.126	+	43.4416i	0.286949	+	0.0768879i
$566$	−722.562	+	221.925i	−1.27661	+	0.392093i
$567$	61.3202	−	14.4512i	0.108148	−	0.0254871i
$568$	−702.785	+	76.6048i	−1.23730	+	0.134868i
$569$	−541.597	+	312.691i	−0.951839	+	0.549545i	−0.893652	−	0.448761i	$-0.851865\pi$
$569$	−541.597	+	312.691i	−0.951839	+	0.549545i	−0.0581875	+	0.998306i	$0.518532\pi$
$570$	172.168	+	39.5152i	0.302049	+	0.0693250i
$571$	−951.162	+	254.863i	−1.66578	+	0.446345i	−0.963969	−	0.266015i	$-0.914293\pi$
$571$	−951.162	+	254.863i	−1.66578	+	0.446345i	−0.701814	+	0.712360i	$0.747626\pi$
$572$	411.891	+	199.584i	0.720089	+	0.348924i
$573$	415.018	+	415.018i	0.724290	+	0.724290i
$574$	577.050	−	583.826i	1.00531	−	1.01712i
$575$	−11.4714			−0.0199503
$576$	−141.689	+	129.569i	−0.245989	+	0.224946i
$577$	310.590	+	179.319i	0.538284	+	0.310778i	0.744383	−	0.667753i	$-0.232744\pi$
$577$	310.590	+	179.319i	0.538284	+	0.310778i	−0.206099	+	0.978531i	$0.566077\pi$
$578$	238.704	−	149.586i	0.412983	−	0.258799i
$579$	−70.2229	+	262.075i	−0.121283	+	0.452635i
$580$	521.739	−	353.871i	0.899550	−	0.610123i
$581$	−24.5199	+	807.531i	−0.0422029	+	1.38990i
$582$	123.842	−	38.0363i	0.212787	−	0.0653545i
$583$	−849.882	+	490.679i	−1.45777	+	0.841646i
$584$	−649.455	−	286.162i	−1.11208	−	0.490004i
$585$	−69.2222	−	39.9654i	−0.118329	−	0.0683170i
$586$	670.633	+	623.767i	1.14442	+	1.06445i
$587$	−74.6541	+	74.6541i	−0.127179	+	0.127179i	−0.767831	−	0.640652i	$-0.778664\pi$
$587$	−74.6541	+	74.6541i	−0.127179	+	0.127179i	0.640652	+	0.767831i	$0.278664\pi$
$588$	91.6860	+	326.866i	0.155929	+	0.555895i
$589$	−232.823	+	232.823i	−0.395286	+	0.395286i
$590$	−320.026	+	11.5871i	−0.542417	+	0.0196392i
$591$	−170.195	−	98.2620i	−0.287978	−	0.166264i
$592$	60.7047	−	516.318i	0.102542	−	0.872158i
$593$	317.971	−	183.581i	0.536208	−	0.309580i	−0.207333	−	0.978270i	$-0.566478\pi$
$593$	317.971	−	183.581i	0.536208	−	0.309580i	0.743541	+	0.668691i	$0.233145\pi$
$594$	−200.879	−	106.479i	−0.338180	−	0.179257i
$595$	−13.1726	+	433.824i	−0.0221389	+	0.729115i
$596$	−34.2125	+	178.455i	−0.0574036	+	0.299421i
$597$	41.4587	−	154.726i	0.0694451	−	0.259172i
$598$	−28.2681	+	123.164i	−0.0472710	+	0.205960i
$599$	61.0204	+	35.2302i	0.101870	+	0.0588150i	0.550070	−	0.835119i	$-0.314601\pi$
$599$	61.0204	+	35.2302i	0.101870	+	0.0588150i	−0.448199	+	0.893934i	$0.647934\pi$
$600$	−2.00829	+	13.0040i	−0.00334715	+	0.0216733i
$601$	−1097.30			−1.82579			−0.912895	−	0.408194i	$-0.866159\pi$
$601$	−1097.30			−1.82579			−0.912895	+	0.408194i	$0.866159\pi$
$602$	−675.606	+	3.94312i	−1.12227	+	0.00655003i
$603$	2.72359	+	2.72359i	0.00451673	+	0.00451673i
$604$	519.626	+	251.788i	0.860308	+	0.416868i
$605$	1759.63	−	471.491i	2.90848	−	0.779324i
$606$	400.545	−	251.004i	0.660965	−	0.414198i
$607$	−706.019	+	407.621i	−1.16313	+	0.671533i	−0.952052	−	0.305936i	$-0.901031\pi$
$607$	−706.019	+	407.621i	−1.16313	+	0.671533i	−0.211077	+	0.977469i	$0.567697\pi$
$608$	−319.281	−	25.8684i	−0.525133	−	0.0425467i
$609$	365.115	−	86.0459i	0.599532	−	0.141290i
$610$	358.903	+	190.241i	0.588366	+	0.311871i
$611$	−96.6437	−	25.8956i	−0.158173	−	0.0423823i
$612$	−145.677	+	10.5629i	−0.238035	+	0.0172596i
$613$	−681.574	+	182.627i	−1.11187	+	0.297923i	−0.767587	−	0.640944i	$-0.778543\pi$
$613$	−681.574	+	182.627i	−1.11187	+	0.297923i	−0.344278	+	0.938868i	$0.611876\pi$
$614$	−434.766	+	467.432i	−0.708088	+	0.761290i
$615$	517.340			0.841203
$616$	527.784	−	1105.61i	0.856793	−	1.79482i
$617$			895.421i			1.45125i	0.688091	+	0.725625i	$0.258449\pi$
$617$			895.421i			1.45125i	−0.688091	+	0.725625i	$0.741551\pi$
$618$	412.975	−	444.004i	0.668245	−	0.718452i
$619$	−229.704	−	857.267i	−0.371089	−	1.38492i	−0.858976	−	0.512016i	$-0.828899\pi$
$619$	−229.704	−	857.267i	−0.371089	−	1.38492i	0.487887	−	0.872907i	$-0.337768\pi$
$620$	−506.956	−	438.409i	−0.817671	−	0.707110i
$621$	16.2462	−	60.6316i	0.0261613	−	0.0976354i
$622$	893.433	+	473.576i	1.43639	+	0.761376i
$623$	83.8157	−	278.679i	0.134536	−	0.447319i
$624$	134.670	+	53.6068i	0.215817	+	0.0859084i
$625$	−323.919	−	561.045i	−0.518271	−	0.897671i
$626$	411.760	−	258.032i	0.657763	−	0.412192i
$627$	−98.1731	−	366.387i	−0.156576	−	0.584349i
$628$	914.423	−	317.491i	1.45609	−	0.505559i
$629$	279.649	−	279.649i	0.444593	−	0.444593i
$630$	−105.892	+	185.908i	−0.168083	+	0.295093i
$631$		−	633.127i		−	1.00337i	−0.865050	−	0.501686i	$-0.832713\pi$
$631$		−	633.127i		−	1.00337i	0.865050	−	0.501686i	$-0.167287\pi$
$632$	−876.274	+	641.824i	−1.38651	+	1.01554i
$633$	−193.024	+	334.327i	−0.304935	+	0.528163i
$634$	148.472	−	646.893i	0.234183	−	1.02034i
$635$	148.255	+	39.7249i	0.233473	+	0.0625589i
$636$	−257.203	+	174.449i	−0.404408	+	0.274291i
$637$	191.882	−	169.892i	0.301228	−	0.266707i
$638$	−1196.08	−	633.999i	−1.87474	−	0.993729i
$639$	−132.553	−	229.588i	−0.207438	−	0.359293i
$640$	5.51753	−	652.018i	0.00862114	−	1.01878i
$641$	275.367	−	476.949i	0.429590	−	0.744071i	−0.567247	−	0.823548i	$-0.691992\pi$
$641$	275.367	−	476.949i	0.429590	−	0.744071i	0.996837	+	0.0794767i	$0.0253249\pi$
$642$	195.872	−	7.09191i	0.305097	−	0.0110466i
$643$	−305.171	−	305.171i	−0.474604	−	0.474604i	0.428797	−	0.903401i	$-0.358938\pi$
$643$	−305.171	−	305.171i	−0.474604	−	0.474604i	−0.903401	+	0.428797i	$0.858938\pi$
$644$	330.109	+	73.7398i	0.512592	+	0.114503i
$645$	−301.081	−	301.081i	−0.466793	−	0.466793i
$646$	−178.431	−	165.962i	−0.276209	−	0.256907i
$647$	−472.338	+	818.113i	−0.730043	+	1.26447i	0.226821	+	0.973936i	$0.427167\pi$
$647$	−472.338	+	818.113i	−0.730043	+	1.26447i	−0.956864	+	0.290535i	$0.906167\pi$
$648$	−65.8876	−	29.0314i	−0.101678	−	0.0448015i
$649$	343.824	+	595.520i	0.529775	+	0.917596i
$650$	9.49570	−	2.91647i	0.0146088	−	0.00448688i
$651$	−188.827	−	351.264i	−0.290056	−	0.539577i
$652$	−482.088	−	92.4238i	−0.739399	−	0.141754i
$653$	372.430	+	99.7922i	0.570336	+	0.152821i	0.532451	−	0.846461i	$-0.321271\pi$
$653$	372.430	+	99.7922i	0.570336	+	0.152821i	0.0378855	+	0.999282i	$0.487938\pi$
$654$	59.5812	−	37.3370i	0.0911028	−	0.0570902i
$655$	119.612	−	207.175i	0.182614	−	0.316297i
$656$	−928.332	+	135.336i	−1.41514	+	0.206305i
$657$		−	266.139i		−	0.405082i
$658$	−67.8039	+	259.087i	−0.103045	+	0.393749i
$659$	−340.024	+	340.024i	−0.515969	+	0.515969i	−0.916349	−	0.400380i	$-0.868878\pi$
$659$	−340.024	+	340.024i	−0.515969	+	0.515969i	0.400380	+	0.916349i	$0.368878\pi$
$660$	729.394	−	253.248i	1.10514	−	0.383709i
$661$	87.2214	+	325.515i	0.131954	+	0.492458i	0.999992	−	0.00403952i	$-0.00128582\pi$
$661$	87.2214	+	325.515i	0.131954	+	0.492458i	−0.868038	+	0.496498i	$0.834619\pi$
$662$	766.194	+	175.854i	1.15739	+	0.265640i
$663$	55.1326	+	95.4924i	0.0831562	+	0.144031i
$664$	578.294	−	719.787i	0.870924	−	1.08402i
$665$	−347.432	+	81.8786i	−0.522455	+	0.123126i
$666$	186.361	−	57.2381i	0.279821	−	0.0859431i
$667$	96.7337	−	361.015i	0.145028	−	0.541252i
$668$	1209.47	−	87.6970i	1.81058	−	0.131283i
$669$	−7.09486	−	26.4784i	−0.0106052	−	0.0395791i
$670$	−13.0721	+	0.473301i	−0.0195106	+	0.000706419i
$671$		−	872.254i		−	1.29993i
$672$	141.383	−	361.302i	0.210392	−	0.537651i
$673$	−71.2791			−0.105912			−0.0529562	−	0.998597i	$-0.516864\pi$
$673$	−71.2791			−0.105912			−0.0529562	+	0.998597i	$0.516864\pi$
$674$	23.9646	+	661.881i	0.0355558	+	0.982019i
$675$	−4.76617	+	1.27709i	−0.00706099	+	0.00189199i
$676$	40.9741	+	565.092i	0.0606126	+	0.835934i
$677$	381.682	+	102.271i	0.563784	+	0.151065i	0.529444	−	0.848345i	$-0.322400\pi$
$677$	381.682	+	102.271i	0.563784	+	0.151065i	0.0343398	+	0.999410i	$0.489067\pi$
$678$	−33.5113	−	109.109i	−0.0494267	−	0.160928i
$679$	−190.645	+	179.409i	−0.280773	+	0.264225i
$680$	310.672	−	386.685i	0.456871	−	0.568655i
$681$	−84.7078	+	48.9061i	−0.124387	+	0.0718151i
$682$	−321.947	+	1402.72i	−0.472062	+	2.05678i
$683$	−273.310	+	73.2333i	−0.400162	+	0.107223i	−0.453286	−	0.891365i	$-0.649749\pi$
$683$	−273.310	+	73.2333i	−0.400162	+	0.107223i	0.0531249	+	0.998588i	$0.483082\pi$
$684$	−39.3998	−	113.477i	−0.0576020	−	0.165903i
$685$	−771.425	−	771.425i	−1.12617	−	1.12617i
$686$	−457.741	−	510.949i	−0.667261	−	0.744824i
$687$	−139.263			−0.202711
$688$	619.033	+	461.508i	0.899758	+	0.670796i
$689$	203.186	+	117.310i	0.294900	+	0.170261i
$690$	113.196	+	180.634i	0.164052	+	0.261789i
$691$	−275.988	+	1030.00i	−0.399403	+	1.49059i	0.414746	+	0.909937i	$0.363870\pi$
$691$	−275.988	+	1030.00i	−0.399403	+	1.49059i	−0.814149	+	0.580655i	$0.802796\pi$
$692$	−39.0291	+	203.578i	−0.0564004	+	0.294188i
$693$	459.210	+	13.9434i	0.662640	+	0.0201204i
$694$	−262.543	−	854.812i	−0.378304	−	1.23172i
$695$	651.776	−	376.303i	0.937807	−	0.541443i
$696$	−392.311	−	172.860i	−0.563665	−	0.248362i
$697$	−618.060	−	356.837i	−0.886743	−	0.511961i
$698$	−115.841	+	124.544i	−0.165961	+	0.178430i
$699$	134.937	−	134.937i	0.193043	−	0.193043i
$700$	−7.95473	−	25.3712i	−0.0113639	−	0.0362445i
$701$	273.691	−	273.691i	0.390429	−	0.390429i	−0.484411	−	0.874840i	$-0.660966\pi$
$701$	273.691	−	273.691i	0.390429	−	0.390429i	0.874840	+	0.484411i	$0.160966\pi$
$702$	1.96674	+	54.3194i	0.00280162	+	0.0773781i
$703$	281.678	+	162.627i	0.400680	+	0.231333i
$704$	−1242.60	+	645.246i	−1.76505	+	0.916543i
$705$	−146.170	+	84.3913i	−0.207333	+	0.119704i
$706$	−571.653	+	1078.46i	−0.809706	+	1.52757i
$707$	−502.478	+	812.338i	−0.710719	+	1.14899i
$708$	122.238	+	180.225i	0.172652	+	0.254555i
$709$	−49.5117	+	184.780i	−0.0698332	+	0.260621i	−0.992012	−	0.126142i	$-0.959740\pi$
$709$	−49.5117	+	184.780i	−0.0698332	+	0.260621i	0.922179	+	0.386763i	$0.126407\pi$
$710$	877.496	+	201.399i	1.23591	+	0.283661i
$711$	−352.748	−	203.659i	−0.496130	−	0.286441i
$712$	−268.311	+	196.523i	−0.376841	+	0.276016i
$713$	−397.348			−0.557290
$714$	254.739	−	149.063i	0.356778	−	0.208771i
$715$	−412.164	−	412.164i	−0.576453	−	0.576453i
$716$	166.101	+	478.395i	0.231984	+	0.668150i
$717$	757.603	−	202.999i	1.05663	−	0.283123i
$718$	−52.6343	−	83.9923i	−0.0733069	−	0.116981i
$719$	48.7959	−	28.1723i	0.0678663	−	0.0391826i	−0.465683	−	0.884952i	$-0.654191\pi$
$719$	48.7959	−	28.1723i	0.0678663	−	0.0391826i	0.533549	+	0.845769i	$0.320858\pi$
$720$	224.584	−	96.6950i	0.311922	−	0.134299i
$721$	−352.909	+	1173.39i	−0.489472	+	1.62745i
$722$	−244.280	+	460.851i	−0.338338	+	0.638298i
$723$	467.133	+	125.168i	0.646104	+	0.173123i
$724$	416.637	−	481.780i	0.575466	−	0.665443i
$725$	−28.3789	+	7.60411i	−0.0391434	+	0.0104884i
$726$	−907.088	−	843.698i	−1.24943	−	1.16212i
$727$	−308.605			−0.424491			−0.212245	−	0.977216i	$-0.568078\pi$
$727$	−308.605			−0.424491			−0.212245	+	0.977216i	$0.568078\pi$
$728$	−292.002	+	22.8867i	−0.401102	+	0.0314377i
$729$		−	27.0000i		−	0.0370370i
$730$	661.805	+	615.555i	0.906582	+	0.843227i
$731$	152.026	+	567.370i	0.207970	+	0.776156i
$732$	−19.9767	−	275.507i	−0.0272906	−	0.376376i
$733$	−150.474	+	561.575i	−0.205285	+	0.766133i	0.784078	+	0.620662i	$0.213136\pi$
$733$	−150.474	+	561.575i	−0.205285	+	0.766133i	−0.989363	+	0.145470i	$0.953530\pi$
$734$	169.045	−	318.915i	0.230306	−	0.434489i
$735$	26.2308	−	431.540i	0.0356881	−	0.587130i
$736$	−250.376	−	294.525i	−0.340185	−	0.400169i
$737$	14.0442	+	24.3253i	0.0190559	+	0.0330058i
$738$	−186.811	−	298.107i	−0.253132	−	0.403940i
$739$	100.090	+	373.541i	0.135440	+	0.505468i	0.999996	+	0.00293126i	$0.000933049\pi$
$739$	100.090	+	373.541i	0.135440	+	0.505468i	−0.864556	+	0.502536i	$0.832400\pi$
$740$	−288.702	+	595.808i	−0.390139	+	0.805146i
$741$	−64.1235	+	64.1235i	−0.0865365	+	0.0865365i
$742$	310.824	−	545.693i	0.418900	−	0.735435i
$743$			423.908i			0.570535i	0.958448	+	0.285268i	$0.0920825\pi$
$743$			423.908i			0.570535i	−0.958448	+	0.285268i	$0.907917\pi$
$744$	−69.5633	+	450.433i	−0.0934991	+	0.605420i
$745$	115.702	−	200.402i	0.155305	−	0.268996i
$746$	155.263	+	35.6352i	0.208127	+	0.0477684i
$747$	334.446	+	89.6146i	0.447719	+	0.119966i
$748$	−1046.08	−	200.549i	−1.39850	−	0.268114i
$749$	−348.853	+	187.530i	−0.465758	+	0.250374i
$750$	−198.764	+	374.981i	−0.265018	+	0.499975i
$751$	221.174	+	383.085i	0.294506	+	0.510099i	0.974870	−	0.222775i	$-0.0715115\pi$
$751$	221.174	+	383.085i	0.294506	+	0.510099i	−0.680364	+	0.732875i	$0.738178\pi$
$752$	240.216	−	189.673i	0.319436	−	0.252224i
$753$	331.694	−	574.511i	0.440497	−	0.762962i
$754$	11.7104	+	323.431i	0.0155311	+	0.428954i
$755$	−519.970	−	519.970i	−0.688703	−	0.688703i
$756$	145.364	−	6.11286i	0.192280	−	0.00808580i
$757$	−834.933	−	834.933i	−1.10295	−	1.10295i	−0.994053	−	0.108897i	$-0.965268\pi$
$757$	−834.933	−	834.933i	−1.10295	−	1.10295i	−0.108897	−	0.994053i	$-0.534732\pi$
$758$	623.972	−	670.854i	0.823182	−	0.885031i
$759$	228.874	−	396.421i	0.301546	−	0.522293i
$760$	373.311	+	164.488i	0.491199	+	0.216432i
$761$	−120.667	−	209.002i	−0.158564	−	0.274642i	0.775787	−	0.630995i	$-0.217353\pi$
$761$	−120.667	−	209.002i	−0.158564	−	0.274642i	−0.934351	+	0.356354i	$0.884020\pi$
$762$	−30.6442	−	99.7740i	−0.0402154	−	0.130937i
$763$	−74.7438	+	120.836i	−0.0979605	+	0.158369i
$764$	760.839	+	1121.76i	0.995862	+	1.46828i
$765$	179.672	+	48.1429i	0.234865	+	0.0629320i
$766$	−327.013	−	521.838i	−0.426910	−	0.681251i
$767$	82.2000	−	142.375i	0.107171	−	0.185625i
$768$	−377.706	+	232.264i	−0.491804	+	0.302427i
$769$		−	410.481i		−	0.533785i	−0.963726	−	0.266893i	$-0.914003\pi$
$769$		−	410.481i		−	0.533785i	0.963726	−	0.266893i	$-0.0859969\pi$
$770$	−1096.78	+	1109.66i	−1.42439	+	1.44112i
$771$	−394.965	+	394.965i	−0.512276	+	0.512276i
$772$	−273.230	+	563.877i	−0.353925	+	0.730411i
$773$	−75.4417	−	281.552i	−0.0975961	−	0.364233i	0.899804	−	0.436294i	$-0.143709\pi$
$773$	−75.4417	−	281.552i	−0.0975961	−	0.364233i	−0.997400	+	0.0720605i	$0.977043\pi$
$774$	−64.7722	+	282.213i	−0.0836851	+	0.364616i
$775$	15.6175	+	27.0503i	0.0201516	+	0.0349036i
$776$	297.425	−	32.4199i	0.383280	−	0.0417782i
$777$	−286.888	+	269.979i	−0.369225	+	0.347464i
$778$	−271.833	−	885.057i	−0.349399	−	1.13761i
$779$	151.911	−	566.941i	0.195008	−	0.727781i
$780$	−139.624	−	120.745i	−0.179006	−	0.154802i
$781$	−500.363	−	1867.38i	−0.640670	−	2.39101i
$782$	−10.6404	−	293.879i	−0.0136067	−	0.375804i
$783$		−	160.765i		−	0.205319i
$784$	65.8214	+	781.232i	0.0839559	+	0.996469i
$785$	−1232.73			−1.57036
$786$	−162.573	+	5.88624i	−0.206835	+	0.00748886i
$787$	177.946	−	47.6805i	0.226107	−	0.0605851i	−0.143987	−	0.989580i	$-0.545992\pi$
$787$	177.946	−	47.6805i	0.226107	−	0.0605851i	0.370094	+	0.928994i	$0.379326\pi$
$788$	−343.291	−	296.873i	−0.435648	−	0.376743i
$789$	−529.622	−	141.912i	−0.671258	−	0.179863i
$790$	1322.31	−	406.129i	1.67381	−	0.514087i
$791$	158.065	+	167.965i	0.199830	+	0.212345i
$792$	−409.313	−	328.852i	−0.516809	−	0.415217i
$793$	−180.597	+	104.268i	−0.227738	+	0.131485i
$794$	75.6462	+	17.3620i	0.0952723	+	0.0218665i
$795$	382.301	−	102.437i	0.480882	−	0.128852i
$796$	161.312	−	332.906i	0.202653	−	0.418223i
$797$	−553.410	−	553.410i	−0.694366	−	0.694366i	0.268823	−	0.963190i	$-0.413365\pi$
$797$	−553.410	−	553.410i	−0.694366	−	0.694366i	−0.963190	+	0.268823i	$0.913365\pi$
$798$	172.638	+	170.635i	0.216339	+	0.213828i
$799$	232.837			0.291410
$800$	−10.2095	+	28.6210i	−0.0127619	+	0.0357762i
$801$	−108.010	−	62.3595i	−0.134844	−	0.0778520i
$802$	974.084	−	610.417i	1.21457	−	0.761118i
$803$	502.314	−	1874.66i	0.625547	−	2.33457i
$804$	4.99306	+	7.36166i	0.00621028	+	0.00915629i
$805$	−366.342	−	226.604i	−0.455083	−	0.281495i
$806$	328.913	−	101.021i	0.408080	−	0.125336i
$807$	−292.448	+	168.845i	−0.362389	+	0.209225i
$808$	1017.62	−	395.133i	1.25943	−	0.489026i
$809$	−553.615	−	319.630i	−0.684320	−	0.395093i	0.117160	−	0.993113i	$-0.462621\pi$
$809$	−553.615	−	319.630i	−0.684320	−	0.395093i	−0.801481	+	0.598020i	$0.795954\pi$
$810$	67.1405	+	62.4485i	0.0828896	+	0.0770970i
$811$	423.363	−	423.363i	0.522026	−	0.522026i	−0.396157	−	0.918183i	$-0.629656\pi$
$811$	423.363	−	423.363i	0.522026	−	0.522026i	0.918183	+	0.396157i	$0.129656\pi$
$812$	865.532	−	36.3975i	1.06593	−	0.0448245i
$813$	−442.730	+	442.730i	−0.544563	+	0.544563i
$814$	1420.74	−	51.4406i	1.74538	−	0.0631949i
$815$	541.378	+	312.565i	0.664267	+	0.383515i
$816$	−335.003	−	39.3872i	−0.410543	−	0.0482686i
$817$	−418.358	+	241.539i	−0.512066	+	0.295641i
$818$	909.559	+	482.124i	1.11193	+	0.589393i
$819$	−52.0061	−	96.7443i	−0.0634995	−	0.118125i
$820$	1173.38	+	224.955i	1.43095	+	0.274335i
$821$	−14.1956	+	52.9786i	−0.0172906	+	0.0645293i	−0.974032	−	0.226410i	$-0.927301\pi$
$821$	−14.1956	+	52.9786i	−0.0172906	+	0.0645293i	0.956742	+	0.290939i	$0.0939678\pi$
$822$	−165.958	+	723.080i	−0.201896	+	0.879659i
$823$	−53.0936	−	30.6536i	−0.0645123	−	0.0372462i	0.467397	−	0.884048i	$-0.345192\pi$
$823$	−53.0936	−	30.6536i	−0.0645123	−	0.0372462i	−0.531909	+	0.846801i	$0.678525\pi$
$824$	1129.73	−	827.469i	1.37103	−	1.00421i
$825$	−35.9829			−0.0436156
$826$	−382.372	−	217.797i	−0.462920	−	0.263677i
$827$	371.470	+	371.470i	0.449178	+	0.449178i	0.895081	−	0.445903i	$-0.147117\pi$
$827$	371.470	+	371.470i	0.449178	+	0.449178i	−0.445903	+	0.895081i	$0.647117\pi$
$828$	63.2123	−	130.454i	0.0763433	−	0.157553i
$829$	−410.662	+	110.036i	−0.495370	+	0.132734i	−0.497850	−	0.867263i	$-0.665877\pi$
$829$	−410.662	+	110.036i	−0.495370	+	0.132734i	0.00248039	+	0.999997i	$0.499210\pi$
$830$	−996.387	+	624.393i	−1.20047	+	0.752281i
$831$	−158.186	+	91.3286i	−0.190356	+	0.109902i
$832$	282.133	+	180.144i	0.339103	+	0.216519i
$833$	−328.994	+	497.463i	−0.394951	+	0.597195i
$834$	−452.193	−	239.691i	−0.542198	−	0.287399i
$835$	−1491.70	−	399.700i	−1.78647	−	0.478683i
$836$	−63.3501	−	873.689i	−0.0757777	−	1.04508i
$837$	−165.091	+	44.2360i	−0.197241	+	0.0528506i
$838$	−800.020	+	860.129i	−0.954678	+	1.02641i
$839$	407.044			0.485154			0.242577	−	0.970132i	$-0.422007\pi$
$839$	407.044			0.485154			0.242577	+	0.970132i	$0.422007\pi$
$840$	−321.012	+	375.613i	−0.382158	+	0.447158i
$841$		−	116.232i		−	0.138206i
$842$	−219.995	+	236.524i	−0.261277	+	0.280908i
$843$	7.61422	+	28.4166i	0.00903229	+	0.0337089i
$844$	−583.171	+	674.353i	−0.690961	+	0.798996i
$845$	186.749	−	696.958i	0.221005	−	0.824803i
$846$	101.411	+	53.7541i	0.119871	+	0.0635391i
$847$	2397.21	+	720.985i	2.83023	+	0.851222i
$848$	−659.217	+	283.827i	−0.777378	+	0.334702i
$849$	−327.303	−	566.906i	−0.385516	−	0.667734i
$850$	−19.5882	+	12.2751i	−0.0230450	+	0.0144413i
$851$	101.589	+	379.136i	0.119376	+	0.445518i
$852$	−200.811	−	578.365i	−0.235693	−	0.678832i
$853$	28.5534	−	28.5534i	0.0334741	−	0.0334741i	−0.690172	−	0.723646i	$-0.742465\pi$
$853$	28.5534	−	28.5534i	0.0334741	−	0.0334741i	0.723646	+	0.690172i	$0.242465\pi$
$854$	281.910	+	481.766i	0.330105	+	0.564129i
$855$			152.979i			0.178922i
$856$	447.340	+	69.0858i	0.522594	+	0.0807077i
$857$	−33.9498	+	58.8028i	−0.0396148	+	0.0686148i	−0.885153	−	0.465300i	$-0.845946\pi$
$857$	−33.9498	+	58.8028i	−0.0396148	+	0.0686148i	0.845538	+	0.533915i	$0.179280\pi$
$858$	−88.6696	+	386.334i	−0.103345	+	0.450272i
$859$	2.99302	+	0.801976i	0.00348430	+	0.000933616i	0.260561	−	0.965457i	$-0.416093\pi$
$859$	2.99302	+	0.801976i	0.00348430	+	0.000933616i	−0.257076	+	0.966391i	$0.582759\pi$
$860$	−551.962	−	813.801i	−0.641817	−	0.946280i
$861$	604.586	+	373.972i	0.702191	+	0.434346i
$862$	−1375.62	−	729.164i	−1.59584	−	0.845898i
$863$	826.151	+	1430.94i	0.957301	+	1.65809i	0.729012	+	0.684500i	$0.239980\pi$
$863$	826.151	+	1430.94i	0.957301	+	1.65809i	0.228289	+	0.973594i	$0.426687\pi$
$864$	−136.816	−	94.4958i	−0.158352	−	0.109370i
$865$	131.991	−	228.615i	0.152591	−	0.264295i
$866$	−226.620	+	8.20519i	−0.261686	+	0.00947482i
$867$	172.506	+	172.506i	0.198969	+	0.198969i
$868$	−275.537	−	878.809i	−0.317438	−	1.01245i
$869$	−2100.34	−	2100.34i	−2.41696	−	2.41696i
$870$	399.771	+	371.834i	0.459507	+	0.427395i
$871$	3.35763	−	5.81559i	0.00385492	−	0.00667691i
$872$	151.371	−	58.7762i	0.173591	−	0.0674039i
$873$	56.0975	+	97.1637i	0.0642583	+	0.111299i
$874$	231.192	−	71.0073i	0.264522	−	0.0812440i
$875$	26.0282	−	857.207i	0.0297466	−	0.979665i
$876$	115.725	−	603.629i	0.132106	−	0.689074i
$877$	−992.886	−	266.043i	−1.13214	−	0.303356i	−0.356353	−	0.934351i	$-0.615980\pi$
$877$	−992.886	−	266.043i	−1.13214	−	0.303356i	−0.775787	+	0.630995i	$0.782647\pi$
$878$	950.937	−	595.911i	1.08307	−	0.678714i
$879$	−396.587	+	686.909i	−0.451180	+	0.781466i
$880$	1764.45	−	257.229i	2.00506	−	0.292306i
$881$			434.124i			0.492763i	0.969173	+	0.246382i	$0.0792416\pi$
$881$			434.124i			0.492763i	−0.969173	+	0.246382i	$0.920758\pi$
$882$	−258.139	+	140.714i	−0.292674	+	0.159539i
$883$	406.829	−	406.829i	0.460735	−	0.460735i	−0.438161	−	0.898896i	$-0.644370\pi$
$883$	406.829	−	406.829i	0.460735	−	0.460735i	0.898896	+	0.438161i	$0.144370\pi$
$884$	83.5231	+	240.559i	0.0944831	+	0.272126i
$885$	−71.7788	−	267.882i	−0.0811060	−	0.302692i
$886$	1528.27	+	350.761i	1.72491	+	0.395893i
$887$	42.8256	+	74.1762i	0.0482814	+	0.0836259i	0.889156	−	0.457604i	$-0.151292\pi$
$887$	42.8256	+	74.1762i	0.0482814	+	0.0836259i	−0.840875	+	0.541230i	$0.817959\pi$
$888$	447.573	−	48.7863i	0.504024	−	0.0549395i
$889$	144.542	+	153.594i	0.162589	+	0.172772i
$890$	404.885	−	124.355i	0.454927	−	0.139724i
$891$	50.9601	−	190.186i	0.0571943	−	0.213452i
$892$	−4.57824	−	63.1406i	−0.00513256	−	0.0707854i
$893$	49.5612	+	184.965i	0.0554997	+	0.207128i
$894$	−157.258	+	5.69381i	−0.175904	+	0.00636891i
$895$		−	644.923i		−	0.720585i
$896$	477.775	−	757.989i	0.533231	−	0.845970i
$897$	−109.436			−0.122003
$898$	−38.9800	−	1076.59i	−0.0434075	−	1.19888i
$899$	−982.991	+	263.392i	−1.09343	+	0.292983i
$900$	−11.3654	+	0.824094i	−0.0126283	+	0.000915660i
$901$	−527.387	−	141.313i	−0.585336	−	0.156840i
$902$	−753.230	−	2452.43i	−0.835067	−	2.71888i
$903$	−134.213	−	569.501i	−0.148630	−	0.630677i
$904$	−28.5630	−	262.041i	−0.0315962	−	0.289869i
$905$	−702.487	+	405.581i	−0.776228	+	0.448156i
$906$	−111.862	+	487.384i	−0.123468	+	0.537951i
$907$	1596.53	−	427.790i	1.76023	−	0.471653i	0.773472	−	0.633830i	$-0.218518\pi$
$907$	1596.53	−	427.790i	1.76023	−	0.471653i	0.986762	+	0.162177i	$0.0518515\pi$
$908$	−213.391	+	74.0902i	−0.235012	+	0.0815971i
$909$	289.465	+	289.465i	0.318443	+	0.318443i
$910$	360.858	+	94.4378i	0.396547	+	0.103778i
$911$	1101.79			1.20943			0.604715	−	0.796442i	$-0.293287\pi$
$911$	1101.79			1.20943			0.604715	+	0.796442i	$0.293287\pi$
$912$	−40.0191	−	274.510i	−0.0438806	−	0.300998i
$913$	2186.67	+	1262.48i	2.39504	+	1.38278i
$914$	784.380	+	1251.69i	0.858183	+	1.36946i
$915$	−91.0486	+	339.798i	−0.0995067	+	0.371364i
$916$	−315.861	−	60.5555i	−0.344827	−	0.0661087i
$917$	289.546	−	155.649i	0.315753	−	0.169737i
$918$	−37.1379	−	120.917i	−0.0404552	−	0.131718i
$919$	245.577	−	141.784i	0.267222	−	0.154281i	−0.360403	−	0.932797i	$-0.617361\pi$
$919$	245.577	−	141.784i	0.267222	−	0.154281i	0.627624	+	0.778516i	$0.284027\pi$
$920$	178.194	+	458.917i	0.193689	+	0.498823i
$921$	−478.776	−	276.422i	−0.519844	−	0.300132i
$922$	57.3761	−	61.6870i	0.0622301	−	0.0669057i
$923$	−326.821	+	326.821i	−0.354086	+	0.354086i
$924$	1035.47	+	231.303i	1.12064	+	0.250328i
$925$	21.8176	−	21.8176i	0.0235866	−	0.0235866i
$926$	15.2072	+	420.010i	0.0164225	+	0.453575i
$927$	454.779	+	262.567i	0.490593	+	0.283244i
$928$	−814.634	−	562.651i	−0.877839	−	0.606305i
$929$	−313.453	+	180.972i	−0.337409	+	0.194803i	−0.659126	−	0.752033i	$-0.729073\pi$
$929$	−313.453	+	180.972i	−0.337409	+	0.194803i	0.321717	+	0.946836i	$0.395740\pi$
$930$	271.839	−	512.843i	0.292300	−	0.551444i
$931$	−465.213	−	155.463i	−0.499691	−	0.166985i
$932$	364.725	−	247.375i	0.391335	−	0.265424i
$933$	−226.651	+	845.873i	−0.242927	+	0.906617i
$934$	1559.23	+	357.868i	1.66941	+	0.383156i
$935$	1174.73	+	678.230i	1.25639	+	0.725380i
$936$	−19.1589	+	124.057i	−0.0204690	+	0.132539i
$937$	560.337			0.598012			0.299006	−	0.954251i	$-0.403345\pi$
$937$	560.337			0.598012			0.299006	+	0.954251i	$0.403345\pi$
$938$	−15.6188	−	8.89638i	−0.0166512	−	0.00948441i
$939$	297.569	+	297.569i	0.316900	+	0.316900i
$940$	−368.223	+	127.849i	−0.391727	+	0.136009i
$941$	242.068	−	64.8619i	0.257245	−	0.0689287i	−0.127892	−	0.991788i	$-0.540821\pi$
$941$	242.068	−	64.8619i	0.257245	−	0.0689287i	0.385137	+	0.922859i	$0.374154\pi$
$942$	445.138	+	710.338i	0.472546	+	0.754074i
$943$	613.415	−	354.155i	0.650493	−	0.375562i
$944$	198.880	+	461.919i	0.210678	+	0.489321i
$945$	−177.436	−	53.3656i	−0.187763	−	0.0564715i
$946$	−988.902	+	1865.63i	−1.04535	+	1.97213i
$947$	636.072	+	170.435i	0.671670	+	0.179974i	0.578507	−	0.815677i	$-0.303636\pi$
$947$	636.072	+	170.435i	0.671670	+	0.179974i	0.0931632	+	0.995651i	$0.470302\pi$
$948$	−711.509	−	615.304i	−0.750537	−	0.649055i
$949$	−448.187	+	120.091i	−0.472273	+	0.126545i
$950$	−13.9208	−	12.9480i	−0.0146535	−	0.0136295i
$951$	574.792			0.604408
$952$	642.590	−	227.321i	0.674989	−	0.238782i
$953$			1482.31i			1.55541i	0.628628	+	0.777706i	$0.283617\pi$
$953$			1482.31i			1.55541i	−0.628628	+	0.777706i	$0.716383\pi$
$954$	−197.076	−	183.304i	−0.206579	−	0.192142i
$955$	−446.769	−	1667.36i	−0.467821	−	1.74593i
$956$	1806.59	−	130.993i	1.88974	−	0.137022i
$957$	303.429	−	1132.41i	0.317063	−	1.18329i
$958$	−88.3586	+	166.695i	−0.0922324	+	0.174003i
$959$	−343.878	−	1459.16i	−0.358580	−	1.52155i
$960$	551.424	−	121.658i	0.574400	−	0.126727i
$961$	60.4597	+	104.719i	0.0629133	+	0.108969i
$962$	−180.483	−	288.010i	−0.187613	−	0.299387i
$963$	43.9323	+	163.958i	0.0456202	+	0.170257i
$964$	1005.08	+	487.016i	1.04261	+	0.505204i
$965$	564.251	−	564.251i	0.584716	−	0.584716i
$966$	1.70963	+	292.924i	0.00176980	+	0.303234i
$967$			593.933i			0.614202i	0.951677	+	0.307101i	$0.0993589\pi$
$967$			593.933i			0.614202i	−0.951677	+	0.307101i	$0.900641\pi$
$968$	−1690.50	−	2308.02i	−1.74638	−	2.38431i
$969$	105.517	−	182.762i	0.108893	−	0.188608i
$970$	−371.364	−	85.2339i	−0.382850	−	0.0878700i
$971$	−257.810	−	69.0799i	−0.265510	−	0.0711431i	0.123608	−	0.992331i	$-0.460553\pi$
$971$	−257.810	−	69.0799i	−0.265510	−	0.0711431i	−0.389118	+	0.921188i	$0.627220\pi$
$972$	11.7404	−	61.2386i	0.0120786	−	0.0630027i
$973$	1033.71	+	31.3877i	1.06240	+	0.0322587i
$974$	−313.660	+	591.740i	−0.322032	+	0.607536i
$975$	4.30133	+	7.45011i	0.00441162	+	0.00764114i
$976$	74.4896	−	633.563i	0.0763213	−	0.649143i
$977$	−262.599	+	454.835i	−0.268781	+	0.465543i	−0.968547	−	0.248829i	$-0.919954\pi$
$977$	−262.599	+	454.835i	−0.268781	+	0.465543i	0.699766	+	0.714372i	$0.253287\pi$
$978$	−15.3816	−	424.825i	−0.0157276	−	0.434382i
$979$	−643.114	−	643.114i	−0.656909	−	0.656909i
$980$	247.140	−	967.368i	0.252184	−	0.987111i
$981$	43.0580	+	43.0580i	0.0438919	+	0.0438919i
$982$	−212.566	+	228.537i	−0.216463	+	0.232727i
$983$	−341.693	+	591.829i	−0.347602	+	0.602064i	−0.985823	−	0.167789i	$-0.946337\pi$
$983$	−341.693	+	591.829i	−0.347602	+	0.602064i	0.638221	+	0.769853i	$0.279671\pi$
$984$	−294.079	−	757.367i	−0.298861	−	0.769682i
$985$	288.995	+	500.554i	0.293396	+	0.508177i
$986$	−221.128	−	719.969i	−0.224268	−	0.730192i
$987$	−231.825	−	7.03914i	−0.234878	−	0.00713186i
$988$	−173.321	+	117.556i	−0.175426	+	0.118983i
$989$	−563.106	−	150.884i	−0.569369	−	0.152562i
$990$	355.066	+	566.604i	0.358653	+	0.572327i
$991$	−799.020	+	1383.94i	−0.806277	+	1.39651i	0.109149	+	0.994025i	$0.465187\pi$
$991$	−799.020	+	1383.94i	−0.806277	+	1.39651i	−0.915426	+	0.402487i	$0.868146\pi$
$992$	−353.638	+	991.376i	−0.356489	+	0.999371i
$993$			680.796i			0.685595i
$994$	879.894	+	869.682i	0.885205	+	0.874932i
$995$	−333.127	+	333.127i	−0.334801	+	0.334801i
$996$	719.589	+	348.682i	0.722479	+	0.350082i
$997$	−235.560	−	879.121i	−0.236269	−	0.881767i	−0.977573	−	0.210598i	$-0.932459\pi$
$997$	−235.560	−	879.121i	−0.236269	−	0.881767i	0.741304	−	0.671169i	$-0.234208\pi$
$998$	−157.868	+	687.832i	−0.158185	+	0.689210i
$999$	84.4170	+	146.215i	0.0845015	+	0.146361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bv.a.325.34	yes	256
7.5	odd	6	inner	336.3.bv.a.229.54	yes	256
16.13	even	4	inner	336.3.bv.a.157.54	yes	256
112.61	odd	12	inner	336.3.bv.a.61.34	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.bv.a.61.34	✓	256	112.61	odd	12	inner
336.3.bv.a.157.54	yes	256	16.13	even	4	inner
336.3.bv.a.229.54	yes	256	7.5	odd	6	inner
336.3.bv.a.325.34	yes	256	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0723663 + 1.99869i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-3.98953 + 0.289276i) q^{4} +(4.92050 + 1.31844i) q^{5} +(-1.01706 - 3.31143i) q^{6} +(4.79724 + 5.09769i) q^{7} +(-0.866880 - 7.95289i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-2.27908 + 9.92997i) q^{10} +(21.1318 - 5.66224i) q^{11} +(6.54493 - 2.27242i) q^{12} +(-3.69839 - 3.69839i) q^{13} +(-9.84155 + 9.95710i) q^{14} -8.82320 q^{15} +(15.8326 - 2.30815i) q^{16} +(10.5410 + 6.08583i) q^{17} +(3.18605 + 5.08420i) q^{18} +(-2.59084 + 9.66914i) q^{19} +(-20.0119 - 3.83659i) q^{20} +(-10.3112 - 6.37806i) q^{21} +(12.8463 + 41.8261i) q^{22} +(-10.4617 + 6.04009i) q^{23} +(5.01550 + 12.9168i) q^{24} +(0.822383 + 0.474803i) q^{25} +(7.12430 - 7.65958i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-20.6134 - 18.9497i) q^{28} +(-21.8773 + 21.8773i) q^{29} +(-0.638502 - 17.6348i) q^{30} +(28.4858 + 16.4463i) q^{31} +(5.75902 + 31.4775i) q^{32} +(-32.8158 + 18.9462i) q^{33} +(-11.4009 + 21.5085i) q^{34} +(16.8838 + 31.4081i) q^{35} +(-9.93118 + 6.73585i) q^{36} +(8.40958 - 31.3850i) q^{37} +(-19.5131 - 4.47856i) q^{38} +(7.84547 + 4.52959i) q^{39} +(6.21996 - 40.2751i) q^{40} -58.6341 q^{41} +(12.0016 - 21.0704i) q^{42} +(34.1238 + 34.1238i) q^{43} +(-82.6677 + 28.7025i) q^{44} +(14.7615 - 3.95533i) q^{45} +(-12.8293 - 20.4727i) q^{46} +(16.5666 - 9.56471i) q^{47} +(-25.4538 + 10.9592i) q^{48} +(-2.97293 + 48.9097i) q^{49} +(-0.889472 + 1.67805i) q^{50} +(-20.3636 - 5.45641i) q^{51} +(15.8247 + 13.6850i) q^{52} +(-43.3291 + 11.6100i) q^{53} +(-7.60955 - 7.07777i) q^{54} +111.444 q^{55} +(36.3828 - 42.5710i) q^{56} -17.3382i q^{57} +(-45.3091 - 42.1428i) q^{58} +(8.13524 + 30.3611i) q^{59} +(35.2004 - 2.55234i) q^{60} +(10.3192 - 38.5119i) q^{61} +(-30.8096 + 58.1244i) q^{62} +(20.1101 + 6.04833i) q^{63} +(-62.4970 + 13.7884i) q^{64} +(-13.3218 - 23.0741i) q^{65} +(-40.2424 - 64.2176i) q^{66} +(0.332301 + 1.24016i) q^{67} +(-43.8139 - 21.2303i) q^{68} +(14.7951 - 14.7951i) q^{69} +(-61.5532 + 36.0184i) q^{70} -88.3684i q^{71} +(-14.1816 - 19.3619i) q^{72} +(44.3565 - 76.8277i) q^{73} +(63.3374 + 14.5369i) q^{74} +(-1.58872 - 0.425697i) q^{75} +(7.53917 - 39.3247i) q^{76} +(130.238 + 80.5600i) q^{77} +(-8.48549 + 16.0085i) q^{78} +(-67.8864 - 117.583i) q^{79} +(80.9476 + 9.51722i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-4.24313 - 117.191i) q^{82} +(81.6106 + 81.6106i) q^{83} +(42.9817 + 22.4627i) q^{84} +(43.8430 + 43.8430i) q^{85} +(-65.7336 + 70.6724i) q^{86} +(26.7941 - 46.4087i) q^{87} +(-63.3498 - 163.150i) q^{88} +(-20.7865 - 36.0033i) q^{89} +(8.97372 + 29.2174i) q^{90} +(1.11118 - 36.5953i) q^{91} +(39.9901 - 27.1234i) q^{92} +(-55.0303 - 14.7453i) q^{93} +(20.3158 + 32.4193i) q^{94} +(-25.4964 + 44.1611i) q^{95} +(-23.7460 - 50.0812i) q^{96} +37.3983i q^{97} +(-97.9705 - 2.40256i) q^{98} +(46.4085 - 46.4085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) \) 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Introduction

L-functions

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