LMFDB - Embedded newform 735.2.p.g.374.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(374,735)] 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("735.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.32
Character	$\chi$	$=$	735.374
Dual form			735.2.p.g.509.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10453 + 1.91310i) q^{2} +(1.38025 - 1.04638i) q^{3} +(-1.43998 + 2.49412i) q^{4} +(0.889228 - 2.05165i) q^{5} +(3.52637 + 1.48480i) q^{6} -1.94389 q^{8} +(0.810168 - 2.88853i) q^{9} +(4.90720 - 0.564929i) q^{10} +(-3.30554 - 1.90846i) q^{11} +(0.622272 + 4.94927i) q^{12} +6.50161 q^{13} +(-0.919457 - 3.76226i) q^{15} +(0.732874 + 1.26937i) q^{16} +(-2.54654 - 1.47025i) q^{17} +(6.42092 - 1.64054i) q^{18} +(-1.76224 + 1.01743i) q^{19} +(3.83659 + 5.17218i) q^{20} -8.43180i q^{22} +(1.50029 + 2.59858i) q^{23} +(-2.68305 + 2.03405i) q^{24} +(-3.41855 - 3.64877i) q^{25} +(7.18123 + 12.4383i) q^{26} +(-1.90428 - 4.83464i) q^{27} +2.25259i q^{29} +(6.18203 - 5.91455i) q^{30} +(5.77216 + 3.33256i) q^{31} +(-3.56285 + 6.17104i) q^{32} +(-6.55944 + 0.824719i) q^{33} -6.49574i q^{34} +(6.03772 + 6.18009i) q^{36} +(-2.91560 + 1.68332i) q^{37} +(-3.89289 - 2.24756i) q^{38} +(8.97383 - 6.80317i) q^{39} +(-1.72856 + 3.98818i) q^{40} -3.51094 q^{41} +7.03729i q^{43} +(9.51983 - 5.49628i) q^{44} +(-5.20584 - 4.23075i) q^{45} +(-3.31424 + 5.74043i) q^{46} +(-4.34120 + 2.50639i) q^{47} +(2.33980 + 0.985185i) q^{48} +(3.20459 - 10.5702i) q^{50} +(-5.05330 + 0.635352i) q^{51} +(-9.36219 + 16.2158i) q^{52} +(0.967113 - 1.67509i) q^{53} +(7.14584 - 8.98309i) q^{54} +(-6.85487 + 5.08477i) q^{55} +(-1.36770 + 3.24827i) q^{57} +(-4.30944 + 2.48806i) q^{58} +(-3.96509 + 6.86774i) q^{59} +(10.7075 + 3.12434i) q^{60} +(11.8342 - 6.83249i) q^{61} +14.7237i q^{62} -12.8096 q^{64} +(5.78141 - 13.3390i) q^{65} +(-8.82289 - 11.6380i) q^{66} +(-9.34121 - 5.39315i) q^{67} +(7.33395 - 4.23426i) q^{68} +(4.78988 + 2.01681i) q^{69} +10.9926i q^{71} +(-1.57488 + 5.61499i) q^{72} +(-1.65449 + 2.86566i) q^{73} +(-6.44074 - 3.71856i) q^{74} +(-8.53645 - 1.45910i) q^{75} -5.86030i q^{76} +(22.9271 + 9.65357i) q^{78} +(2.92489 + 5.06605i) q^{79} +(3.25601 - 0.374839i) q^{80} +(-7.68725 - 4.68040i) q^{81} +(-3.87795 - 6.71680i) q^{82} -2.66330i q^{83} +(-5.28089 + 3.91724i) q^{85} +(-13.4631 + 7.77291i) q^{86} +(2.35707 + 3.10913i) q^{87} +(6.42561 + 3.70983i) q^{88} +(-6.75793 - 11.7051i) q^{89} +(2.34385 - 14.6323i) q^{90} -8.64156 q^{92} +(11.4541 - 1.44013i) q^{93} +(-9.58999 - 5.53678i) q^{94} +(0.520378 + 4.52022i) q^{95} +(1.53965 + 12.2457i) q^{96} +4.46688 q^{97} +(-8.19069 + 8.00200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) $ 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	1.10453	+	1.91310i	0.781022	+	1.35277i	0.931347	+	0.364133i	$0.118635\pi$
$2$	1.10453	+	1.91310i	0.781022	+	1.35277i	−0.150325	+	0.988637i	$0.548032\pi$
$3$	1.38025	−	1.04638i	0.796886	−	0.604129i
$3$	1.38025	−	1.04638i	0.796886	−	0.604129i
$4$	−1.43998	+	2.49412i	−0.719990	+	1.24706i
$5$	0.889228	−	2.05165i	0.397675	−	0.917526i
$5$	0.889228	−	2.05165i	0.397675	−	0.917526i
$6$	3.52637	+	1.48480i	1.43963	+	0.606166i
$7$		0			0
$7$		0			0
$8$	−1.94389			−0.687269
$9$	0.810168	−	2.88853i	0.270056	−	0.962845i
$10$	4.90720	−	0.564929i	1.55179	−	0.178646i
$11$	−3.30554	−	1.90846i	−0.996659	−	0.575421i	−0.0894006	−	0.995996i	$-0.528495\pi$
$11$	−3.30554	−	1.90846i	−0.996659	−	0.575421i	−0.907258	+	0.420575i	$0.861828\pi$
$12$	0.622272	+	4.94927i	0.179635	+	1.42873i
$13$	6.50161			1.80322			0.901611	−	0.432548i	$-0.142385\pi$
$13$	6.50161			1.80322			0.901611	+	0.432548i	$0.142385\pi$
$14$		0			0
$15$	−0.919457	−	3.76226i	−0.237403	−	0.971411i
$16$	0.732874	+	1.26937i	0.183218	+	0.317344i
$17$	−2.54654	−	1.47025i	−0.617628	−	0.356587i	0.158317	−	0.987388i	$-0.449393\pi$
$17$	−2.54654	−	1.47025i	−0.617628	−	0.356587i	−0.775945	+	0.630801i	$0.782726\pi$
$18$	6.42092	−	1.64054i	1.51343	−	0.386679i
$19$	−1.76224	+	1.01743i	−0.404285	+	0.233414i	−0.688331	−	0.725397i	$-0.741656\pi$
$19$	−1.76224	+	1.01743i	−0.404285	+	0.233414i	0.284046	+	0.958811i	$0.408323\pi$
$20$	3.83659	+	5.17218i	0.857888	+	1.15653i
$21$		0			0
$22$		−	8.43180i		−	1.79767i
$23$	1.50029	+	2.59858i	0.312832	+	0.541842i	0.978974	−	0.203983i	$-0.0653888\pi$
$23$	1.50029	+	2.59858i	0.312832	+	0.541842i	−0.666142	+	0.745825i	$0.732056\pi$
$24$	−2.68305	+	2.03405i	−0.547675	+	0.415199i
$25$	−3.41855	−	3.64877i	−0.683710	−	0.729754i
$26$	7.18123	+	12.4383i	1.40836	+	2.43934i
$27$	−1.90428	−	4.83464i	−0.366478	−	0.930427i
$28$		0			0
$29$			2.25259i			0.418296i	0.977884	+	0.209148i	$0.0670690\pi$
$29$			2.25259i			0.418296i	−0.977884	+	0.209148i	$0.932931\pi$
$30$	6.18203	−	5.91455i	1.12868	−	1.07984i
$31$	5.77216	+	3.33256i	1.03671	+	0.598545i	0.918900	−	0.394491i	$-0.129079\pi$
$31$	5.77216	+	3.33256i	1.03671	+	0.598545i	0.117810	+	0.993036i	$0.462413\pi$
$32$	−3.56285	+	6.17104i	−0.629829	+	1.09090i
$33$	−6.55944	+	0.824719i	−1.14185	+	0.143565i
$34$		−	6.49574i		−	1.11401i
$35$		0			0
$36$	6.03772	+	6.18009i	1.00629	+	1.03001i
$37$	−2.91560	+	1.68332i	−0.479321	+	0.276736i	−0.720134	−	0.693835i	$-0.755919\pi$
$37$	−2.91560	+	1.68332i	−0.479321	+	0.276736i	0.240812	+	0.970572i	$0.422586\pi$
$38$	−3.89289	−	2.24756i	−0.631510	−	0.364603i
$39$	8.97383	−	6.80317i	1.43696	−	1.08938i
$40$	−1.72856	+	3.98818i	−0.273309	+	0.630587i
$41$	−3.51094			−0.548317			−0.274158	−	0.961685i	$-0.588399\pi$
$41$	−3.51094			−0.548317			−0.274158	+	0.961685i	$0.588399\pi$
$42$		0			0
$43$			7.03729i			1.07318i	0.843844	+	0.536588i	$0.180287\pi$
$43$			7.03729i			1.07318i	−0.843844	+	0.536588i	$0.819713\pi$
$44$	9.51983	−	5.49628i	1.43517	−	0.828595i
$45$	−5.20584	−	4.23075i	−0.776041	−	0.630683i
$46$	−3.31424	+	5.74043i	−0.488658	+	0.846380i
$47$	−4.34120	+	2.50639i	−0.633229	+	0.365595i	−0.782002	−	0.623276i	$-0.785801\pi$
$47$	−4.34120	+	2.50639i	−0.633229	+	0.365595i	0.148772	+	0.988871i	$0.452468\pi$
$48$	2.33980	+	0.985185i	0.337721	+	0.142199i
$49$		0			0
$50$	3.20459	−	10.5702i	0.453197	−	1.49486i
$51$	−5.05330	+	0.635352i	−0.707604	+	0.0889671i
$52$	−9.36219	+	16.2158i	−1.29830	+	2.24873i
$53$	0.967113	−	1.67509i	0.132843	−	0.230091i	−0.791928	−	0.610614i	$-0.790923\pi$
$53$	0.967113	−	1.67509i	0.132843	−	0.230091i	0.924771	+	0.380523i	$0.124256\pi$
$54$	7.14584	−	8.98309i	0.972425	−	1.22244i
$55$	−6.85487	+	5.08477i	−0.924310	+	0.685630i
$56$		0			0
$57$	−1.36770	+	3.24827i	−0.181157	+	0.430244i
$58$	−4.30944	+	2.48806i	−0.565858	+	0.326698i
$59$	−3.96509	+	6.86774i	−0.516211	+	0.894104i	0.483612	+	0.875283i	$0.339325\pi$
$59$	−3.96509	+	6.86774i	−0.516211	+	0.894104i	−0.999823	+	0.0188214i	$0.994009\pi$
$60$	10.7075	+	3.12434i	1.38234	+	0.403351i
$61$	11.8342	−	6.83249i	1.51522	−	0.874810i	0.515375	−	0.856965i	$-0.327653\pi$
$61$	11.8342	−	6.83249i	1.51522	−	0.874810i	0.999841	−	0.0178455i	$-0.00568070\pi$
$62$			14.7237i			1.86991i
$63$		0			0
$64$	−12.8096			−1.60121
$65$	5.78141	−	13.3390i	0.717096	−	1.65450i
$66$	−8.82289	−	11.6380i	−1.08602	−	1.43254i
$67$	−9.34121	−	5.39315i	−1.14121	−	0.658878i	−0.194480	−	0.980906i	$-0.562302\pi$
$67$	−9.34121	−	5.39315i	−1.14121	−	0.658878i	−0.946730	+	0.322029i	$0.895635\pi$
$68$	7.33395	−	4.23426i	0.889372	−	0.513479i
$69$	4.78988	+	2.01681i	0.576634	+	0.242795i
$70$		0			0
$71$			10.9926i			1.30458i	0.757971	+	0.652288i	$0.226191\pi$
$71$			10.9926i			1.30458i	−0.757971	+	0.652288i	$0.773809\pi$
$72$	−1.57488	+	5.61499i	−0.185601	+	0.661733i
$73$	−1.65449	+	2.86566i	−0.193643	+	0.335400i	−0.946455	−	0.322836i	$-0.895364\pi$
$73$	−1.65449	+	2.86566i	−0.193643	+	0.335400i	0.752812	+	0.658236i	$0.228697\pi$
$74$	−6.44074	−	3.71856i	−0.748721	−	0.432274i
$75$	−8.53645	−	1.45910i	−0.985705	−	0.168482i
$76$		−	5.86030i		−	0.672223i
$77$		0			0
$78$	22.9271	+	9.65357i	2.59598	+	1.09305i
$79$	2.92489	+	5.06605i	0.329075	+	0.569975i	0.982329	−	0.187164i	$-0.0599296\pi$
$79$	2.92489	+	5.06605i	0.329075	+	0.569975i	−0.653253	+	0.757140i	$0.726596\pi$
$80$	3.25601	−	0.374839i	0.364032	−	0.0419082i
$81$	−7.68725	−	4.68040i	−0.854139	−	0.520044i
$82$	−3.87795	−	6.71680i	−0.428248	−	0.741746i
$83$		−	2.66330i		−	0.292336i	−0.989260	−	0.146168i	$-0.953306\pi$
$83$		−	2.66330i		−	0.292336i	0.989260	−	0.146168i	$-0.0466939\pi$
$84$		0			0
$85$	−5.28089	+	3.91724i	−0.572793	+	0.424884i
$86$	−13.4631	+	7.77291i	−1.45176	+	0.838175i
$87$	2.35707	+	3.10913i	0.252705	+	0.333334i
$88$	6.42561	+	3.70983i	0.684972	+	0.395469i
$89$	−6.75793	−	11.7051i	−0.716339	−	1.24074i	−0.962441	−	0.271492i	$-0.912483\pi$
$89$	−6.75793	−	11.7051i	−0.716339	−	1.24074i	0.246101	−	0.969244i	$-0.420850\pi$
$90$	2.34385	−	14.6323i	0.247063	−	1.54238i
$91$		0			0
$92$	−8.64156			−0.900945
$93$	11.4541	−	1.44013i	1.18774	−	0.149334i
$94$	−9.58999	−	5.53678i	−0.989132	−	0.571075i
$95$	0.520378	+	4.52022i	0.0533896	+	0.463765i
$96$	1.53965	+	12.2457i	0.157140	+	1.24982i
$97$	4.46688			0.453543			0.226771	−	0.973948i	$-0.427183\pi$
$97$	4.46688			0.453543			0.226771	+	0.973948i	$0.427183\pi$
$98$		0			0
$99$	−8.19069	+	8.00200i	−0.823195	+	0.804231i
$100$	14.0231	−	3.27211i	1.40231	−	0.327211i
$101$	4.43523	−	7.68205i	0.441322	−	0.764392i	−0.556466	−	0.830871i	$-0.687843\pi$
$101$	4.43523	−	7.68205i	0.441322	−	0.764392i	0.997788	+	0.0664781i	$0.0211763\pi$
$102$	−6.79703	−	8.96573i	−0.673006	−	0.887740i
$103$	−0.661216	−	1.14526i	−0.0651516	−	0.112846i	0.831610	−	0.555361i	$-0.187420\pi$
$103$	−0.661216	−	1.14526i	−0.0651516	−	0.112846i	−0.896761	+	0.442515i	$0.854086\pi$
$104$	−12.6384			−1.23930
$105$		0			0
$106$	4.27283			0.415014
$107$	−1.66222	−	2.87905i	−0.160693	−	0.278328i	0.774425	−	0.632666i	$-0.218040\pi$
$107$	−1.66222	−	2.87905i	−0.160693	−	0.278328i	−0.935117	+	0.354338i	$0.884706\pi$
$108$	14.8003	+	2.21229i	1.42416	+	0.212878i
$109$	−6.14927	+	10.6509i	−0.588994	+	1.02017i	0.405371	+	0.914152i	$0.367142\pi$
$109$	−6.14927	+	10.6509i	−0.588994	+	1.02017i	−0.994365	+	0.106015i	$0.966191\pi$
$110$	−17.2991	−	7.49779i	−1.64941	−	0.714886i
$111$	−2.26285	+	5.37423i	−0.214780	+	0.510099i
$112$		0			0
$113$	−20.4591			−1.92463			−0.962314	−	0.271941i	$-0.912334\pi$
$113$	−20.4591			−1.92463			−0.962314	+	0.271941i	$0.912334\pi$
$114$	−7.72496	+	0.971260i	−0.723509	+	0.0909668i
$115$	6.66548	−	0.767346i	0.621560	−	0.0715553i
$116$	−5.61823	−	3.24369i	−0.521640	−	0.301169i
$117$	5.26740	−	18.7801i	0.486971	−	1.73622i
$118$	−17.5183			−1.61269
$119$		0			0
$120$	1.78732	+	7.31342i	0.163160	+	0.667620i
$121$	1.78441	+	3.09068i	0.162219	+	0.280971i
$122$	26.1425	+	15.0934i	2.36683	+	1.36649i
$123$	−4.84597	+	3.67379i	−0.436946	+	0.331254i
$124$	−16.6236	+	9.59763i	−1.49284	+	0.861893i
$125$	−10.5259	+	3.76908i	−0.941463	+	0.337117i
$126$		0			0
$127$			0.597329i			0.0530044i	0.999649	+	0.0265022i	$0.00843689\pi$
$127$			0.597329i			0.0530044i	−0.999649	+	0.0265022i	$0.991563\pi$
$128$	−7.02295	−	12.1641i	−0.620747	−	1.07517i
$129$	7.36370	+	9.71321i	0.648337	+	0.855200i
$130$	31.9047	−	3.67294i	2.79823	−	0.322139i
$131$	2.90591	+	5.03319i	0.253891	+	0.439752i	0.964594	−	0.263741i	$-0.0849563\pi$
$131$	2.90591	+	5.03319i	0.253891	+	0.439752i	−0.710703	+	0.703492i	$0.751623\pi$
$132$	7.38852	−	17.5476i	0.643088	−	1.52732i
$133$		0			0
$134$		−	23.8276i		−	2.05839i
$135$	−11.6123	−	0.392180i	−0.999430	−	0.0337535i
$136$	4.95020	+	2.85800i	0.424476	+	0.245071i
$137$	−0.546844	+	0.947161i	−0.0467200	+	0.0809215i	−0.888440	−	0.458993i	$-0.848210\pi$
$137$	−0.546844	+	0.947161i	−0.0467200	+	0.0809215i	0.841720	+	0.539915i	$0.181544\pi$
$138$	1.43221	+	11.3912i	0.121918	+	0.969681i
$139$		−	7.35968i		−	0.624240i	−0.950043	−	0.312120i	$-0.898961\pi$
$139$		−	7.35968i		−	0.624240i	0.950043	−	0.312120i	$-0.101039\pi$
$140$		0			0
$141$	−3.36929	+	8.00200i	−0.283745	+	0.673890i
$142$	−21.0299	+	12.1416i	−1.76479	+	1.01890i
$143$	−21.4913	−	12.4080i	−1.79720	−	1.03761i
$144$	4.26038	−	1.08852i	0.355032	−	0.0907103i
$145$	4.62153	+	2.00307i	0.383797	+	0.166346i
$146$	−7.30973			−0.604958
$147$		0			0
$148$		−	9.69579i		−	0.796989i
$149$	−9.36993	+	5.40973i	−0.767615	+	0.443183i	−0.832023	−	0.554741i	$-0.812817\pi$
$149$	−9.36993	+	5.40973i	−0.767615	+	0.443183i	0.0644082	+	0.997924i	$0.479484\pi$
$150$	−6.63737	−	17.9428i	−0.541939	−	1.46502i
$151$	4.14799	−	7.18453i	0.337559	−	0.584669i	−0.646414	−	0.762987i	$-0.723732\pi$
$151$	4.14799	−	7.18453i	0.337559	−	0.584669i	0.983973	+	0.178318i	$0.0570655\pi$
$152$	3.42559	−	1.97777i	0.277852	−	0.160418i
$153$	−6.30999	+	6.16463i	−0.510132	+	0.498381i
$154$		0			0
$155$	11.9700	−	8.87905i	0.961454	−	0.713183i
$156$	4.04577	+	32.1782i	0.323921	+	2.57632i
$157$	2.70593	−	4.68680i	0.215957	−	0.374048i	−0.737612	−	0.675225i	$-0.764046\pi$
$157$	2.70593	−	4.68680i	0.215957	−	0.374048i	0.953568	+	0.301178i	$0.0973797\pi$
$158$	−6.46126	+	11.1912i	−0.514030	+	0.890326i
$159$	−0.417928	−	3.32401i	−0.0331438	−	0.263611i
$160$	9.49264	+	12.7972i	0.750459	+	1.01171i
$161$		0			0
$162$	0.463276	−	19.8762i	0.0363984	−	1.56162i
$163$	14.8583	−	8.57846i	1.16379	−	0.671917i	0.211584	−	0.977360i	$-0.432138\pi$
$163$	14.8583	−	8.57846i	1.16379	−	0.671917i	0.952210	+	0.305443i	$0.0988046\pi$
$164$	5.05569	−	8.75671i	0.394783	−	0.683784i
$165$	−4.14080	+	14.1911i	−0.322361	+	1.10477i
$166$	5.09518	−	2.94170i	0.395463	−	0.228320i
$167$		−	9.60588i		−	0.743325i	−0.928368	−	0.371663i	$-0.878788\pi$
$167$		−	9.60588i		−	0.743325i	0.928368	−	0.371663i	$-0.121212\pi$
$168$		0			0
$169$	29.2709			2.25161
$170$	−13.3270	−	5.77619i	−1.02213	−	0.443014i
$171$	1.51117	+	5.91457i	0.115562	+	0.452298i
$172$	−17.5518	−	10.1336i	−1.33832	−	0.772677i
$173$	8.80967	−	5.08627i	0.669787	−	0.386702i	−0.126209	−	0.992004i	$-0.540281\pi$
$173$	8.80967	−	5.08627i	0.669787	−	0.386702i	0.795996	+	0.605302i	$0.206948\pi$
$174$	−3.34464	+	7.94346i	−0.253556	+	0.602192i
$175$		0			0
$176$		−	5.59463i		−	0.421711i
$177$	1.71347	+	13.6282i	0.128793	+	1.02436i
$178$	14.9287	−	25.8573i	1.11895	−	1.93808i
$179$	20.4854	+	11.8273i	1.53115	+	0.884011i	0.999309	+	0.0371678i	$0.0118336\pi$
$179$	20.4854	+	11.8273i	1.53115	+	0.884011i	0.531843	+	0.846843i	$0.321500\pi$
$180$	18.0483	−	6.89180i	1.34524	−	0.513684i
$181$			15.6330i			1.16199i	0.813906	+	0.580997i	$0.197337\pi$
$181$			15.6330i			1.16199i	−0.813906	+	0.580997i	$0.802663\pi$
$182$		0			0
$183$	9.18476	−	21.8136i	0.678957	−	1.61251i
$184$	−2.91640	−	5.05135i	−0.215000	−	0.372391i
$185$	0.860958	+	7.47864i	0.0632989	+	0.549841i
$186$	15.4066	+	20.3223i	1.12966	+	1.49010i
$187$	5.61181	+	9.71993i	0.410376	+	0.710792i
$188$		−	14.4366i		−	1.05290i
$189$		0			0
$190$	−8.07288	+	5.98826i	−0.585668	+	0.434434i
$191$	9.33503	−	5.38958i	0.675459	−	0.389976i	−0.122683	−	0.992446i	$-0.539150\pi$
$191$	9.33503	−	5.38958i	0.675459	−	0.389976i	0.798142	+	0.602470i	$0.205817\pi$
$192$	−17.6805	+	13.4038i	−1.27598	+	0.967335i
$193$	1.59886	+	0.923104i	0.115089	+	0.0664465i	0.556439	−	0.830888i	$-0.312167\pi$
$193$	1.59886	+	0.923104i	0.115089	+	0.0664465i	−0.441351	+	0.897335i	$0.645500\pi$
$194$	4.93381	+	8.54561i	0.354227	+	0.613539i
$195$	−5.97795	−	24.4607i	−0.428090	−	1.75167i
$196$		0			0
$197$	8.09941			0.577059			0.288530	−	0.957471i	$-0.406834\pi$
$197$	8.09941			0.577059			0.288530	+	0.957471i	$0.406834\pi$
$198$	−24.3555	−	6.83118i	−1.73087	−	0.485471i
$199$	−8.74922	−	5.05137i	−0.620216	−	0.358082i	0.156737	−	0.987640i	$-0.449902\pi$
$199$	−8.74922	−	5.05137i	−0.620216	−	0.358082i	−0.776953	+	0.629559i	$0.783236\pi$
$200$	6.64528	+	7.09281i	0.469892	+	0.501537i
$201$	−18.5365	+	2.33059i	−1.30746	+	0.164387i
$202$	19.5954			1.37873
$203$		0			0
$204$	5.69201	−	13.5184i	0.398521	−	0.946480i
$205$	−3.12203	+	7.20323i	−0.218052	+	0.503095i
$206$	1.46067	−	2.52995i	0.101770	−	0.176270i
$207$	8.72158	−	2.22835i	0.606192	−	0.154881i
$208$	4.76486	+	8.25298i	0.330383	+	0.572241i
$209$	7.76686			0.537245
$210$		0			0
$211$	10.6818			0.735367			0.367684	−	0.929951i	$-0.380151\pi$
$211$	10.6818			0.735367			0.367684	+	0.929951i	$0.380151\pi$
$212$	2.78525	+	4.82419i	0.191292	+	0.331327i
$213$	11.5024	+	15.1725i	0.788133	+	1.03960i
$214$	3.67195	−	6.36000i	0.251009	−	0.434761i
$215$	14.4381	+	6.25775i	0.984668	+	0.426775i
$216$	3.70170	+	9.39800i	0.251869	+	0.639453i
$217$		0			0
$218$	−27.1683			−1.84007
$219$	0.714969	+	5.68654i	0.0483131	+	0.384261i
$220$	−2.81115	−	24.4188i	−0.189528	−	1.64632i
$221$	−16.5566	−	9.55898i	−1.11372	−	0.643006i
$222$	−12.7809	+	1.60694i	−0.857795	+	0.107851i
$223$	−4.13183			−0.276688			−0.138344	−	0.990384i	$-0.544178\pi$
$223$	−4.13183			−0.276688			−0.138344	+	0.990384i	$0.544178\pi$
$224$		0			0
$225$	−13.3092	+	6.91848i	−0.887280	+	0.461232i
$226$	−22.5977	−	39.1404i	−1.50318	−	2.60358i
$227$	−6.21430	−	3.58783i	−0.412458	−	0.238132i	0.279388	−	0.960178i	$-0.409869\pi$
$227$	−6.21430	−	3.58783i	−0.412458	−	0.238132i	−0.691845	+	0.722046i	$0.743202\pi$
$228$	−6.13212	−	8.08867i	−0.406109	−	0.535685i
$229$	−9.05093	+	5.22556i	−0.598102	+	0.345315i	−0.768295	−	0.640096i	$-0.778894\pi$
$229$	−9.05093	+	5.22556i	−0.598102	+	0.345315i	0.170192	+	0.985411i	$0.445561\pi$
$230$	8.83025	+	11.9042i	0.582250	+	0.784941i
$231$		0			0
$232$		−	4.37879i		−	0.287481i
$233$	−1.95072	−	3.37875i	−0.127796	−	0.221349i	0.795026	−	0.606575i	$-0.207457\pi$
$233$	−1.95072	−	3.37875i	−0.127796	−	0.221349i	−0.922822	+	0.385226i	$0.874124\pi$
$234$	41.7463	−	10.6661i	2.72904	−	0.697268i
$235$	1.28193	+	11.1354i	0.0836240	+	0.726393i
$236$	−11.4193	−	19.7788i	−0.743334	−	1.28749i
$237$	9.33810	+	3.93186i	0.606574	+	0.255402i
$238$		0			0
$239$			23.7873i			1.53867i	0.638844	+	0.769336i	$0.279413\pi$
$239$			23.7873i			1.53867i	−0.638844	+	0.769336i	$0.720587\pi$
$240$	4.10187	−	3.92440i	0.264775	−	0.253319i
$241$	−11.5030	−	6.64126i	−0.740974	−	0.427801i	0.0814495	−	0.996677i	$-0.474045\pi$
$241$	−11.5030	−	6.64126i	−0.740974	−	0.427801i	−0.822423	+	0.568876i	$0.807378\pi$
$242$	−3.94187	+	6.82752i	−0.253393	+	0.438889i
$243$	−15.5078	+	1.58370i	−0.994826	+	0.101594i
$244$			39.3546i			2.51942i
$245$		0			0
$246$	−12.3809	−	5.21303i	−0.789375	−	0.332371i
$247$	−11.4574	+	6.61492i	−0.729015	+	0.420897i
$248$	−11.2204	−	6.47812i	−0.712498	−	0.411361i
$249$	−2.78683	−	3.67602i	−0.176608	−	0.232958i
$250$	−18.8368	−	15.9740i	−1.19134	−	1.01029i
$251$	−9.12747			−0.576121			−0.288060	−	0.957612i	$-0.593010\pi$
$251$	−9.12747			−0.576121			−0.288060	+	0.957612i	$0.593010\pi$
$252$		0			0
$253$		−	11.4530i		−	0.720041i
$254$	−1.14275	+	0.659769i	−0.0717027	+	0.0413976i
$255$	−3.19001	+	10.9326i	−0.199766	+	0.684625i
$256$	2.70450	−	4.68433i	0.169031	−	0.292770i
$257$	5.79051	−	3.34315i	0.361202	−	0.208540i	−0.308406	−	0.951255i	$-0.599795\pi$
$257$	5.79051	−	3.34315i	0.361202	−	0.208540i	0.669608	+	0.742715i	$0.266462\pi$
$258$	−10.4489	+	24.8161i	−0.650523	+	1.54498i
$259$		0			0
$260$	24.9440	+	33.6275i	1.54696	+	2.08549i
$261$	6.50669	+	1.82498i	0.402754	+	0.112963i
$262$	−6.41935	+	11.1186i	−0.396588	+	0.686911i
$263$	12.0642	−	20.8958i	0.743908	−	1.28849i	−0.206795	−	0.978384i	$-0.566303\pi$
$263$	12.0642	−	20.8958i	0.743908	−	1.28849i	0.950703	−	0.310103i	$-0.100363\pi$
$264$	12.7508	−	1.60316i	0.784759	−	0.0986678i
$265$	−2.57672	−	3.47371i	−0.158286	−	0.213389i
$266$		0			0
$267$	−21.5756	−	9.08453i	−1.32041	−	0.555964i
$268$	26.9023	−	15.5321i	1.64332	−	0.948771i
$269$	9.50393	−	16.4613i	0.579465	−	1.00366i	−0.416076	−	0.909330i	$-0.636595\pi$
$269$	9.50393	−	16.4613i	0.579465	−	1.00366i	0.995541	−	0.0943328i	$-0.0300718\pi$
$270$	−12.0759	−	22.6488i	−0.734916	−	1.37836i
$271$	10.2612	−	5.92429i	0.623321	−	0.359875i	−0.154840	−	0.987940i	$-0.549486\pi$
$271$	10.2612	−	5.92429i	0.623321	−	0.359875i	0.778161	+	0.628065i	$0.216153\pi$
$272$		−	4.31002i		−	0.261334i
$273$		0			0
$274$	−2.41603			−0.145957
$275$	4.33664	+	18.5853i	0.261509	+	1.12074i
$276$	−11.9275	+	9.04238i	−0.717951	+	0.544287i
$277$	14.3051	+	8.25906i	0.859511	+	0.496239i	0.863848	−	0.503752i	$-0.168047\pi$
$277$	14.3051	+	8.25906i	0.859511	+	0.496239i	−0.00433762	+	0.999991i	$0.501381\pi$
$278$	14.0798	−	8.12900i	0.844452	−	0.487545i
$279$	14.3026	−	13.9731i	0.856275	−	0.836550i
$280$		0			0
$281$		−	10.1076i		−	0.602968i	−0.953471	−	0.301484i	$-0.902518\pi$
$281$		−	10.1076i		−	0.602968i	0.953471	−	0.301484i	$-0.0974820\pi$
$282$	−19.0302	+	2.39266i	−1.13323	+	0.142481i
$283$	−3.00101	+	5.19791i	−0.178392	+	0.308984i	−0.941330	−	0.337488i	$-0.890423\pi$
$283$	−3.00101	+	5.19791i	−0.178392	+	0.308984i	0.762938	+	0.646472i	$0.223756\pi$
$284$	−27.4167	−	15.8291i	−1.62688	−	0.939282i
$285$	5.44813	+	5.69451i	0.322719	+	0.337314i
$286$		−	54.8203i		−	3.24159i
$287$		0			0
$288$	14.9388	+	15.2910i	0.880275	+	0.901031i
$289$	−4.17674	−	7.23433i	−0.245691	−	0.425549i
$290$	1.27255	+	11.0539i	0.0747269	+	0.649109i
$291$	6.16540	−	4.67406i	0.361422	−	0.273998i
$292$	−4.76486	−	8.25298i	−0.278842	−	0.482969i
$293$			3.55369i			0.207609i	0.994598	+	0.103805i	$0.0331016\pi$
$293$			3.55369i			0.207609i	−0.994598	+	0.103805i	$0.966898\pi$
$294$		0			0
$295$	10.5643	+	14.2420i	0.615080	+	0.829200i
$296$	5.66760	−	3.27219i	0.329422	−	0.190192i
$297$	−2.93202	+	19.6153i	−0.170133	+	1.13820i
$298$	−20.6988	−	11.9504i	−1.19905	−	0.692271i
$299$	9.75431	+	16.8950i	0.564106	+	0.977061i
$300$	15.9315	−	19.1899i	0.919805	−	1.10793i
$301$		0			0
$302$	18.3264			1.05456
$303$	−1.91664	−	15.2441i	−0.110108	−	0.875750i
$304$	−2.58299	−	1.49129i	−0.148145	−	0.0855314i
$305$	−3.49457	−	30.3553i	−0.200099	−	1.73814i
$306$	−18.7632	−	5.26264i	−1.07262	−	0.300845i
$307$	−29.0345			−1.65709			−0.828544	−	0.559923i	$-0.810831\pi$
$307$	−29.0345			−1.65709			−0.828544	+	0.559923i	$0.810831\pi$
$308$		0			0
$309$	−2.11102	−	0.888858i	−0.120092	−	0.0505654i
$310$	30.2078	+	13.0927i	1.71569	+	0.743614i
$311$	−4.32216	+	7.48620i	−0.245087	+	0.424503i	−0.962156	−	0.272499i	$-0.912150\pi$
$311$	−4.32216	+	7.48620i	−0.245087	+	0.424503i	0.717069	+	0.697002i	$0.245483\pi$
$312$	−17.4441	+	13.2246i	−0.987580	+	0.748696i
$313$	−5.42607	−	9.39824i	−0.306700	−	0.531220i	0.670938	−	0.741513i	$-0.265891\pi$
$313$	−5.42607	−	9.39824i	−0.306700	−	0.531220i	−0.977638	+	0.210293i	$0.932558\pi$
$314$	11.9551			0.674667
$315$		0			0
$316$	−16.8471			−0.947724
$317$	−4.67046	−	8.08947i	−0.262319	−	0.454350i	0.704539	−	0.709665i	$-0.251154\pi$
$317$	−4.67046	−	8.08947i	−0.262319	−	0.454350i	−0.966858	+	0.255316i	$0.917821\pi$
$318$	5.89756	−	4.47101i	0.330719	−	0.250722i
$319$	4.29897	−	7.44604i	0.240696	−	0.416898i
$320$	−11.3907	+	26.2809i	−0.636759	+	1.46915i
$321$	−5.30686	−	2.23448i	−0.296200	−	0.124717i
$322$		0			0
$323$	5.98348			0.332930
$324$	22.7430	−	12.4332i	1.26350	−	0.690736i
$325$	−22.2261	−	23.7229i	−1.23288	−	1.31591i
$326$	32.8230	+	18.9504i	1.81790	+	1.04956i
$327$	2.65734	+	21.1353i	0.146951	+	1.16879i
$328$	6.82488			0.376841
$329$		0			0
$330$	−31.7226	+	7.75268i	−1.74627	+	0.426771i
$331$	−1.45459	−	2.51942i	−0.0799515	−	0.138480i	0.823277	−	0.567639i	$-0.192143\pi$
$331$	−1.45459	−	2.51942i	−0.0799515	−	0.138480i	−0.903229	+	0.429159i	$0.858810\pi$
$332$	6.64260	+	3.83511i	0.364560	+	0.210479i
$333$	2.50020	+	9.78557i	0.137010	+	0.536246i
$334$	18.3771	−	10.6100i	1.00555	−	0.580553i
$335$	−19.3713	+	14.3692i	−1.05837	+	0.785071i
$336$		0			0
$337$			15.2910i			0.832954i	0.909146	+	0.416477i	$0.136735\pi$
$337$			15.2910i			0.832954i	−0.909146	+	0.416477i	$0.863265\pi$
$338$	32.3307	+	55.9983i	1.75856	+	3.04591i
$339$	−28.2386	+	21.4080i	−1.53371	+	1.16272i
$340$	−2.16567	−	18.8119i	−0.117450	−	1.02022i
$341$	−12.7201	−	22.0318i	−0.688830	−	1.19309i
$342$	−9.64606	+	9.42384i	−0.521599	+	0.509583i
$343$		0			0
$344$		−	13.6797i		−	0.737561i
$345$	8.39708	−	8.03377i	0.452084	−	0.432524i
$346$	19.4611	+	11.2359i	1.04624	+	0.604045i
$347$	−15.7892	+	27.3477i	−0.847609	+	1.46810i	0.0357279	+	0.999362i	$0.488625\pi$
$347$	−15.7892	+	27.3477i	−0.847609	+	1.46810i	−0.883336	+	0.468739i	$0.844708\pi$
$348$	−11.1487	+	1.40172i	−0.597632	+	0.0751403i
$349$		−	8.25024i		−	0.441625i	−0.975316	−	0.220813i	$-0.929129\pi$
$349$		−	8.25024i		−	0.441625i	0.975316	−	0.220813i	$-0.0708709\pi$
$350$		0			0
$351$	−12.3809	−	31.4329i	−0.660842	−	1.67777i
$352$	23.5543	−	13.5991i	1.25545	−	0.724834i
$353$	3.71360	+	2.14405i	0.197655	+	0.114116i	0.595561	−	0.803310i	$-0.296930\pi$
$353$	3.71360	+	2.14405i	0.197655	+	0.114116i	−0.397906	+	0.917426i	$0.630263\pi$
$354$	−24.1796	+	18.3308i	−1.28513	+	0.974272i
$355$	22.5529	+	9.77488i	1.19698	+	0.518797i
$356$	38.9252			2.06303
$357$		0			0
$358$			52.2543i			2.76173i
$359$	−6.17938	+	3.56767i	−0.326135	+	0.188294i	−0.654124	−	0.756387i	$-0.726963\pi$
$359$	−6.17938	+	3.56767i	−0.326135	+	0.188294i	0.327989	+	0.944682i	$0.393629\pi$
$360$	10.1196	+	8.22410i	0.533349	+	0.433448i
$361$	−7.42968	+	12.8686i	−0.391036	+	0.677294i
$362$	−29.9076	+	17.2672i	−1.57191	+	0.907542i
$363$	5.69696	+	2.39874i	0.299013	+	0.125901i
$364$		0			0
$365$	4.40811	+	5.94265i	0.230731	+	0.311053i
$366$	51.8766	−	6.52245i	2.71163	−	0.340934i
$367$	−12.1957	+	21.1235i	−0.636609	+	1.10264i	0.349563	+	0.936913i	$0.386330\pi$
$367$	−12.1957	+	21.1235i	−0.636609	+	1.10264i	−0.986172	+	0.165726i	$0.947003\pi$
$368$	−2.19905	+	3.80886i	−0.114633	+	0.198551i
$369$	−2.84445	+	10.1415i	−0.148076	+	0.527944i
$370$	−13.3565	+	9.90750i	−0.694370	+	0.515067i
$371$		0			0
$372$	−12.9019	+	30.6417i	−0.668931	+	1.58870i
$373$	−19.0999	+	11.0273i	−0.988956	+	0.570974i	−0.904962	−	0.425492i	$-0.860101\pi$
$373$	−19.0999	+	11.0273i	−0.988956	+	0.570974i	−0.0839940	+	0.996466i	$0.526768\pi$
$374$	−12.3968	+	21.4719i	−0.641025	+	1.11029i
$375$	−10.5844	+	16.2164i	−0.546577	+	0.837409i
$376$	8.43881	−	4.87215i	0.435199	−	0.251262i
$377$			14.6455i			0.754280i
$378$		0			0
$379$	1.15801			0.0594828			0.0297414	−	0.999558i	$-0.490532\pi$
$379$	1.15801			0.0594828			0.0297414	+	0.999558i	$0.490532\pi$
$380$	−12.0233	−	5.21114i	−0.616782	−	0.267326i
$381$	0.625034	+	0.824462i	0.0320215	+	0.0422385i
$382$	20.6217	+	11.9059i	1.05510	+	0.609160i
$383$	1.84403	−	1.06465i	0.0942255	−	0.0544011i	−0.452147	−	0.891944i	$-0.649342\pi$
$383$	1.84403	−	1.06465i	0.0942255	−	0.0544011i	0.546372	+	0.837542i	$0.316008\pi$
$384$	−22.4217	−	9.44079i	−1.14420	−	0.481773i
$385$		0			0
$386$			4.07839i			0.207585i
$387$	20.3275	+	5.70139i	1.03330	+	0.289818i
$388$	−6.43222	+	11.1409i	−0.326546	+	0.565595i
$389$	20.9207	+	12.0785i	1.06072	+	0.612406i	0.925631	−	0.378427i	$-0.123535\pi$
$389$	20.9207	+	12.0785i	1.06072	+	0.612406i	0.135088	+	0.990834i	$0.456868\pi$
$390$	40.1931	−	38.4541i	2.03526	−	1.94720i
$391$		−	8.82320i		−	0.446208i
$392$		0			0
$393$	9.27752	+	3.90635i	0.467989	+	0.197049i
$394$	8.94606	+	15.4950i	0.450696	+	0.780628i
$395$	12.9947	−	1.49598i	0.653832	−	0.0752707i
$396$	−8.16352	−	31.9513i	−0.410232	−	1.60561i
$397$	6.00792	+	10.4060i	0.301529	+	0.522263i	0.976482	−	0.215597i	$-0.0691697\pi$
$397$	6.00792	+	10.4060i	0.301529	+	0.522263i	−0.674954	+	0.737860i	$0.735836\pi$
$398$		−	22.3176i		−	1.11868i
$399$		0			0
$400$	2.12629	−	7.01351i	0.106315	−	0.350675i
$401$	26.6997	−	15.4151i	1.33332	−	0.769792i	0.347513	−	0.937675i	$-0.387026\pi$
$401$	26.6997	−	15.4151i	1.33332	−	0.769792i	0.985807	+	0.167883i	$0.0536930\pi$
$402$	−24.9328	−	32.8880i	−1.24353	−	1.64030i
$403$	37.5283	+	21.6670i	1.86942	+	1.07931i
$404$	12.7733	+	22.1240i	0.635495	+	1.10071i
$405$	−16.4383	+	11.6096i	−0.816824	+	0.576887i
$406$		0			0
$407$	12.8502			0.636959
$408$	9.82306	−	1.23505i	0.486314	−	0.0611443i
$409$	13.5699	+	7.83456i	0.670986	+	0.387394i	0.796450	−	0.604704i	$-0.206709\pi$
$409$	13.5699	+	7.83456i	0.670986	+	0.387394i	−0.125464	+	0.992098i	$0.540042\pi$
$410$	−17.2289	+	1.98343i	−0.850875	+	0.0979547i
$411$	0.236313	+	1.87953i	0.0116564	+	0.0927101i
$412$	3.80855			0.187634
$413$		0			0
$414$	13.8963	+	14.2240i	0.682968	+	0.699072i
$415$	−5.46417	−	2.36828i	−0.268226	−	0.116254i
$416$	−23.1643	+	40.1217i	−1.13572	+	1.96713i
$417$	−7.70103	−	10.1582i	−0.377121	−	0.497448i
$418$	8.57874	+	14.8588i	0.419600	+	0.726769i
$419$	19.5975			0.957399			0.478699	−	0.877979i	$-0.341108\pi$
$419$	19.5975			0.957399			0.478699	+	0.877979i	$0.341108\pi$
$420$		0			0
$421$	−32.5791			−1.58781			−0.793903	−	0.608044i	$-0.791954\pi$
$421$	−32.5791			−1.58781			−0.793903	+	0.608044i	$0.791954\pi$
$422$	11.7984	+	20.4355i	0.574338	+	0.994782i
$423$	3.72270	+	14.5703i	0.181004	+	0.708433i
$424$	−1.87996	+	3.25619i	−0.0912990	+	0.158134i
$425$	3.34089	+	14.3179i	0.162057	+	0.694518i
$426$	−16.3217	+	38.7638i	−0.790789	+	1.87811i
$427$		0			0
$428$	9.57425			0.462789
$429$	−42.6469	+	5.36200i	−2.05901	+	0.258880i
$430$	3.97557	+	34.5334i	0.191719	+	1.66535i
$431$	24.1528	+	13.9447i	1.16340	+	0.671690i	0.952117	−	0.305734i	$-0.0989019\pi$
$431$	24.1528	+	13.9447i	1.16340	+	0.671690i	0.211285	+	0.977425i	$0.432235\pi$
$432$	4.74137	−	5.96042i	0.228119	−	0.286771i
$433$	3.47350			0.166926			0.0834629	−	0.996511i	$-0.473402\pi$
$433$	3.47350			0.166926			0.0834629	+	0.996511i	$0.473402\pi$
$434$		0			0
$435$	8.47483	−	2.07116i	0.406337	−	0.0993046i
$436$	−17.7097	−	30.6740i	−0.848139	−	1.46902i
$437$	−5.28774	−	3.05288i	−0.252947	−	0.146039i
$438$	−10.0892	+	7.64878i	−0.482083	+	0.365473i
$439$	−3.41910	+	1.97402i	−0.163185	+	0.0942147i	−0.579368	−	0.815066i	$-0.696701\pi$
$439$	−3.41910	+	1.97402i	−0.163185	+	0.0942147i	0.416184	+	0.909281i	$0.363367\pi$
$440$	13.3251	−	9.88423i	0.635249	−	0.471212i
$441$		0			0
$442$		−	42.2328i		−	2.00881i
$443$	−8.01539	−	13.8831i	−0.380823	−	0.659604i	0.610357	−	0.792126i	$-0.291026\pi$
$443$	−8.01539	−	13.8831i	−0.380823	−	0.659604i	−0.991180	+	0.132522i	$0.957693\pi$
$444$	−10.1455	−	13.3826i	−0.481484	−	0.635110i
$445$	−30.0241	+	3.45644i	−1.42328	+	0.163851i
$446$	−4.56373	−	7.90462i	−0.216099	−	0.374295i
$447$	−7.27218	+	17.2713i	−0.343962	+	0.816905i
$448$		0			0
$449$			21.1001i			0.995777i	0.867241	+	0.497889i	$0.165891\pi$
$449$			21.1001i			0.995777i	−0.867241	+	0.497889i	$0.834109\pi$
$450$	−27.9362	−	17.8202i	−1.31692	−	0.840053i
$451$	11.6056	+	6.70048i	0.546485	+	0.315513i
$452$	29.4607	−	51.0274i	1.38571	−	2.40013i
$453$	−1.79251	−	14.2568i	−0.0842195	−	0.669844i
$454$		−	15.8515i		−	0.743947i
$455$		0			0
$456$	2.65867	−	6.31429i	0.124503	−	0.295694i
$457$	8.31969	−	4.80338i	0.389179	−	0.224692i	−0.292625	−	0.956227i	$-0.594529\pi$
$457$	8.31969	−	4.80338i	0.389179	−	0.224692i	0.681804	+	0.731535i	$0.261196\pi$
$458$	−19.9941	−	11.5436i	−0.934262	−	0.539397i
$459$	−2.25879	+	15.1114i	−0.105431	+	0.705339i
$460$	−7.68432	+	17.7295i	−0.358283	+	0.826641i
$461$	24.5367			1.14279			0.571393	−	0.820676i	$-0.306403\pi$
$461$	24.5367			1.14279			0.571393	+	0.820676i	$0.306403\pi$
$462$		0			0
$463$		−	14.5875i		−	0.677937i	−0.940798	−	0.338968i	$-0.889922\pi$
$463$		−	14.5875i		−	0.677937i	0.940798	−	0.338968i	$-0.110078\pi$
$464$	−2.85938	+	1.65086i	−0.132743	+	0.0766395i
$465$	7.23069	−	24.7805i	0.335315	−	1.14917i
$466$	4.30927	−	7.46387i	0.199623	−	0.345757i
$467$	−15.5179	+	8.95926i	−0.718083	+	0.414585i	−0.814047	−	0.580800i	$-0.802740\pi$
$467$	−15.5179	+	8.95926i	−0.718083	+	0.414585i	0.0959639	+	0.995385i	$0.469407\pi$
$468$	39.2549	+	40.1805i	1.81456	+	1.85735i
$469$		0			0
$470$	−19.8872	+	14.7519i	−0.917330	+	0.680452i
$471$	−1.16934	−	9.30039i	−0.0538802	−	0.428539i
$472$	7.70770	−	13.3501i	0.354776	−	0.614490i
$473$	13.4304	−	23.2621i	0.617529	−	1.06959i
$474$	2.79216	+	22.2076i	0.128248	+	1.02003i
$475$	9.73665	+	2.95187i	0.446748	+	0.135441i
$476$		0			0
$477$	−4.05503	−	4.15064i	−0.185667	−	0.190045i
$478$	−45.5076	+	26.2738i	−2.08147	+	1.20174i
$479$	−1.48248	+	2.56774i	−0.0677364	+	0.117323i	−0.897905	−	0.440190i	$-0.854911\pi$
$479$	−1.48248	+	2.56774i	−0.0677364	+	0.117323i	0.830168	+	0.557513i	$0.188244\pi$
$480$	26.4930	+	7.73037i	1.20923	+	0.352841i
$481$	−18.9561	+	10.9443i	−0.864322	+	0.499017i
$482$		−	29.3419i		−	1.33649i
$483$		0			0
$484$	−10.2780			−0.467184
$485$	3.97207	−	9.16448i	0.180362	−	0.416138i
$486$	−20.1586	−	27.9188i	−0.914414	−	1.26642i
$487$	−28.8004	−	16.6279i	−1.30507	−	0.753482i	−0.323800	−	0.946125i	$-0.604961\pi$
$487$	−28.8004	−	16.6279i	−1.30507	−	0.753482i	−0.981269	+	0.192644i	$0.938294\pi$
$488$	−23.0044	+	13.2816i	−1.04136	+	0.601230i
$489$	11.5318	−	27.3879i	0.521487	−	1.23852i
$490$		0			0
$491$		−	25.4892i		−	1.15031i	−0.818043	−	0.575157i	$-0.804941\pi$
$491$		−	25.4892i		−	1.15031i	0.818043	−	0.575157i	$-0.195059\pi$
$492$	−2.18476	−	17.3766i	−0.0984966	−	0.783398i
$493$	3.31187	−	5.73632i	0.149159	−	0.258351i
$494$	−25.3101	−	14.6128i	−1.13875	−	0.657460i
$495$	9.13393	+	23.9200i	0.410540	+	1.07513i
$496$			9.76937i			0.438658i
$497$		0			0
$498$	3.95447	−	9.39179i	0.177204	−	0.420856i
$499$	16.8358	+	29.1604i	0.753673	+	1.30540i	0.946031	+	0.324076i	$0.105053\pi$
$499$	16.8358	+	29.1604i	0.753673	+	1.30540i	−0.192358	+	0.981325i	$0.561613\pi$
$500$	5.75651	−	31.6802i	0.257439	−	1.41678i
$501$	−10.0514	−	13.2585i	−0.449064	−	0.592346i
$502$	−10.0816	−	17.4618i	−0.449963	−	0.779358i
$503$		−	35.2418i		−	1.57135i	−0.618637	−	0.785677i	$-0.712315\pi$
$503$		−	35.2418i		−	1.57135i	0.618637	−	0.785677i	$-0.287685\pi$
$504$		0			0
$505$	−11.8170	−	15.9306i	−0.525848	−	0.708904i
$506$	21.9107	−	12.6502i	0.974050	−	0.562368i
$507$	40.4011	−	30.6286i	1.79428	−	1.36026i
$508$	−1.48981	−	0.860142i	−0.0660996	−	0.0381626i
$509$	−11.5914	−	20.0770i	−0.513782	−	0.889896i	−0.999872	−	0.0159875i	$-0.994911\pi$
$509$	−11.5914	−	20.0770i	−0.513782	−	0.889896i	0.486090	−	0.873908i	$-0.338423\pi$
$510$	−24.4387	+	5.97256i	−1.08216	+	0.264469i
$511$		0			0
$512$	−16.1430			−0.713426
$513$	8.27468	+	6.58231i	0.365336	+	0.290616i
$514$	12.7916	+	7.38523i	0.564213	+	0.325749i
$515$	−2.93765	+	0.338189i	−0.129448	+	0.0149024i
$516$	−34.8295	+	4.37911i	−1.53328	+	0.192780i
$517$	19.1334			0.841484
$518$		0			0
$519$	6.83735	−	16.2386i	0.300126	−	0.712795i
$520$	−11.2384	+	25.9296i	−0.492837	+	1.13709i
$521$	7.18762	−	12.4493i	0.314895	−	0.545415i	−0.664520	−	0.747271i	$-0.731364\pi$
$521$	7.18762	−	12.4493i	0.314895	−	0.545415i	0.979415	+	0.201856i	$0.0646972\pi$
$522$	3.69547	+	14.4637i	0.161746	+	0.633060i
$523$	−12.6242	−	21.8658i	−0.552018	−	0.956124i	−0.998129	−	0.0611461i	$-0.980524\pi$
$523$	−12.6242	−	21.8658i	−0.552018	−	0.956124i	0.446110	−	0.894978i	$-0.352809\pi$
$524$	−16.7378			−0.731195
$525$		0			0
$526$	53.3010			2.32403
$527$	−9.79936	−	16.9730i	−0.426867	−	0.739355i
$528$	−5.85412	−	7.72197i	−0.254768	−	0.336056i
$529$	6.99825	−	12.1213i	0.304272	−	0.527014i
$530$	3.79952	−	8.76636i	0.165040	−	0.380786i
$531$	16.6253	+	17.0173i	0.721477	+	0.738489i
$532$		0			0
$533$	−22.8268			−0.988737
$534$	−6.45128	−	51.3106i	−0.279174	−	2.22042i
$535$	−7.38490	+	0.850166i	−0.319277	+	0.0367559i
$536$	18.1583	+	10.4837i	0.784318	+	0.452826i
$537$	40.6508	−	5.11102i	1.75421	−	0.220557i
$538$	41.9896			1.81030
$539$		0			0
$540$	17.6997	−	28.3978i	0.761673	−	1.22205i
$541$	−7.88973	−	13.6654i	−0.339206	−	0.587522i	0.645078	−	0.764117i	$-0.276825\pi$
$541$	−7.88973	−	13.6654i	−0.339206	−	0.587522i	−0.984284	+	0.176595i	$0.943492\pi$
$542$	22.6676	+	13.0871i	0.973655	+	0.562140i
$543$	16.3581	+	21.5774i	0.701994	+	0.925977i
$544$	18.1459	−	10.4766i	0.778000	−	0.449179i
$545$	16.3837	+	22.0872i	0.701802	+	0.946112i
$546$		0			0
$547$		−	8.23195i		−	0.351973i	−0.984393	−	0.175986i	$-0.943689\pi$
$547$		−	8.23195i		−	0.351973i	0.984393	−	0.175986i	$-0.0563115\pi$
$548$	−1.57489	−	2.72779i	−0.0672759	−	0.116525i
$549$	−10.1482	−	39.7190i	−0.433113	−	1.69517i
$550$	−30.7657	+	28.8245i	−1.31185	+	1.22908i
$551$	−2.29185	−	3.96960i	−0.0976360	−	0.169111i
$552$	−9.31100	−	3.92045i	−0.396303	−	0.166865i
$553$		0			0
$554$			36.4896i			1.55029i
$555$	9.01386	+	9.42149i	0.382617	+	0.399920i
$556$	18.3559	+	10.5978i	0.778464	+	0.449446i
$557$	14.4676	−	25.0586i	0.613011	−	1.06177i	−0.377719	−	0.925920i	$-0.623292\pi$
$557$	14.4676	−	25.0586i	0.613011	−	1.06177i	0.990730	−	0.135845i	$-0.0433750\pi$
$558$	42.5298	+	11.9286i	1.80043	+	0.504980i
$559$			45.7537i			1.93518i
$560$		0			0
$561$	17.9164	+	7.54382i	0.756433	+	0.318500i
$562$	19.3369	−	11.1641i	0.815677	−	0.470931i
$563$	5.39368	+	3.11404i	0.227316	+	0.131241i	0.609333	−	0.792914i	$-0.291437\pi$
$563$	5.39368	+	3.11404i	0.227316	+	0.131241i	−0.382017	+	0.924155i	$0.624770\pi$
$564$	−15.1062	−	19.9261i	−0.636087	−	0.839041i
$565$	−18.1928	+	41.9749i	−0.765376	+	1.76590i
$566$	−13.2589			−0.557312
$567$		0			0
$568$		−	21.3683i		−	0.896594i
$569$	8.56862	−	4.94710i	0.359215	−	0.207393i	−0.309521	−	0.950893i	$-0.600169\pi$
$569$	8.56862	−	4.94710i	0.359215	−	0.207393i	0.668736	+	0.743500i	$0.266835\pi$
$570$	−4.87656	+	16.7126i	−0.204257	+	0.700014i
$571$	−9.60472	+	16.6359i	−0.401945	+	0.696189i	−0.993961	−	0.109737i	$-0.964999\pi$
$571$	−9.60472	+	16.6359i	−0.401945	+	0.696189i	0.592015	+	0.805927i	$0.298332\pi$
$572$	61.8942	−	35.7347i	2.58793	−	1.49414i
$573$	7.24509	−	17.2070i	0.302668	−	0.718831i
$574$		0			0
$575$	4.35281	−	14.3576i	0.181525	−	0.598753i
$576$	−10.3780	+	37.0011i	−0.432415	+	1.54171i
$577$	19.0377	−	32.9742i	0.792549	−	1.37273i	−0.131835	−	0.991272i	$-0.542087\pi$
$577$	19.0377	−	32.9742i	0.792549	−	1.37273i	0.924384	−	0.381463i	$-0.124580\pi$
$578$	9.22669	−	15.9811i	0.383780	−	0.664726i
$579$	3.17275	−	0.398910i	0.131855	−	0.0165781i
$580$	−11.6508	+	8.64228i	−0.483773	+	0.358851i
$581$		0			0
$582$	15.7519	+	6.63241i	0.652935	+	0.274922i
$583$	−6.39367	+	3.69139i	−0.264799	+	0.152882i
$584$	3.21614	−	5.57052i	0.133085	−	0.230510i
$585$	−33.8463	−	27.5067i	−1.39937	−	1.13726i
$586$	−6.79859	+	3.92517i	−0.280847	+	0.162147i
$587$			11.9232i			0.492124i	0.969254	+	0.246062i	$0.0791367\pi$
$587$			11.9232i			0.492124i	−0.969254	+	0.246062i	$0.920863\pi$
$588$		0			0
$589$	−13.5625			−0.558835
$590$	−15.5777	+	35.9414i	−0.641326	+	1.47968i
$591$	11.1792	−	8.47508i	0.459851	−	0.348618i
$592$	−4.27353	−	2.46732i	−0.175641	−	0.101406i
$593$	−14.5994	+	8.42896i	−0.599525	+	0.346136i	−0.768855	−	0.639424i	$-0.779173\pi$
$593$	−14.5994	+	8.42896i	−0.599525	+	0.346136i	0.169330	+	0.985559i	$0.445840\pi$
$594$	−40.7647	+	16.0565i	−1.67260	+	0.658806i
$595$		0			0
$596$		−	31.1596i		−	1.27635i
$597$	−17.3618	+	2.18289i	−0.710569	+	0.0893399i
$598$	−21.5479	+	37.3220i	−0.881159	+	1.52621i
$599$	11.7736	+	6.79751i	0.481058	+	0.277739i	0.720857	−	0.693084i	$-0.243748\pi$
$599$	11.7736	+	6.79751i	0.481058	+	0.277739i	−0.239800	+	0.970822i	$0.577082\pi$
$600$	16.5939	+	2.83633i	0.677444	+	0.115793i
$601$		−	46.2155i		−	1.88517i	−0.333966	−	0.942585i	$-0.608387\pi$
$601$		−	46.2155i		−	1.88517i	0.333966	−	0.942585i	$-0.391613\pi$
$602$		0			0
$603$	−23.1462	+	22.6130i	−0.942588	+	0.920874i
$604$	11.9461	+	20.6912i	0.486078	+	0.841912i
$605$	7.92775	−	0.912661i	0.322309	−	0.0371049i
$606$	27.0465	−	20.5043i	1.09869	−	0.832930i
$607$	−4.37164	−	7.57190i	−0.177439	−	0.307334i	0.763563	−	0.645733i	$-0.223448\pi$
$607$	−4.37164	−	7.57190i	−0.177439	−	0.307334i	−0.941003	+	0.338399i	$0.890115\pi$
$608$		−	14.4998i		−	0.588044i
$609$		0			0
$610$	54.2130	−	40.2139i	2.19502	−	1.62821i
$611$	−28.2248	+	16.2956i	−1.14185	+	0.659249i
$612$	−6.28906	−	24.6148i	−0.254220	−	0.994995i
$613$	−21.0938	−	12.1785i	−0.851970	−	0.491885i	0.00934480	−	0.999956i	$-0.497025\pi$
$613$	−21.0938	−	12.1785i	−0.851970	−	0.491885i	−0.861315	+	0.508071i	$0.830359\pi$
$614$	−32.0696	−	55.5461i	−1.29422	−	2.24166i
$615$	3.22816	+	13.2091i	0.130172	+	0.532641i
$616$		0			0
$617$	25.3125			1.01904			0.509522	−	0.860458i	$-0.329822\pi$
$617$	25.3125			1.01904			0.509522	+	0.860458i	$0.329822\pi$
$618$	−0.631212	−	5.02038i	−0.0253911	−	0.201949i
$619$	26.2018	+	15.1276i	1.05314	+	0.608029i	0.923526	−	0.383535i	$-0.125294\pi$
$619$	26.2018	+	15.1276i	1.05314	+	0.608029i	0.129612	+	0.991565i	$0.458627\pi$
$620$	4.90885	+	42.6403i	0.197144	+	1.71247i
$621$	9.70623	−	12.2018i	0.389498	−	0.489641i
$622$	−19.0958			−0.765673
$623$		0			0
$624$	15.2125	+	6.40529i	0.608986	+	0.256417i
$625$	−1.62705	+	24.9470i	−0.0650820	+	0.997880i
$626$	11.9865	−	20.7613i	0.479079	−	0.829788i
$627$	10.7202	−	8.12711i	0.428123	−	0.324565i
$628$	7.79296	+	13.4978i	0.310973	+	0.538621i
$629$	9.89959			0.394723
$630$		0			0
$631$	−5.90652			−0.235135			−0.117568	−	0.993065i	$-0.537510\pi$
$631$	−5.90652			−0.235135			−0.117568	+	0.993065i	$0.537510\pi$
$632$	−5.68566	−	9.84784i	−0.226163	−	0.391726i
$633$	14.7436	−	11.1773i	0.586004	−	0.444257i
$634$	10.3173	−	17.8701i	0.409754	−	0.709714i
$635$	1.22551	+	0.531161i	0.0486329	+	0.0210785i
$636$	8.89228	+	3.74415i	0.352602	+	0.148465i
$637$		0			0
$638$	18.9934			0.751956
$639$	31.7524	+	8.90582i	1.25610	+	0.352309i
$640$	−31.2015	+	3.59199i	−1.23335	+	0.141986i
$641$	−0.111457	−	0.0643495i	−0.00440227	−	0.00254165i	0.497797	−	0.867293i	$-0.334142\pi$
$641$	−0.111457	−	0.0643495i	−0.00440227	−	0.00254165i	−0.502200	+	0.864752i	$0.667476\pi$
$642$	−1.58679	−	12.6206i	−0.0626257	−	0.498097i
$643$	0.150563			0.00593763			0.00296881	−	0.999996i	$-0.499055\pi$
$643$	0.150563			0.00593763			0.00296881	+	0.999996i	$0.499055\pi$
$644$		0			0
$645$	26.4761	−	6.47049i	1.04250	−	0.254775i
$646$	6.60894	+	11.4470i	0.260025	+	0.450377i
$647$	−35.8147	−	20.6776i	−1.40802	−	0.812920i	−0.412822	−	0.910812i	$-0.635457\pi$
$647$	−35.8147	−	20.6776i	−1.40802	−	0.812920i	−0.995197	+	0.0978912i	$0.968790\pi$
$648$	14.9432	+	9.09817i	0.587023	+	0.357410i
$649$	26.2136	−	15.1344i	1.02897	−	0.594078i
$650$	20.8350	−	68.7235i	0.817214	−	2.69556i
$651$		0			0
$652$			49.4113i			1.93509i
$653$	−14.7304	−	25.5138i	−0.576446	−	0.998433i	−0.995883	−	0.0906487i	$-0.971106\pi$
$653$	−14.7304	−	25.5138i	−0.576446	−	0.998433i	0.419437	−	0.907784i	$-0.362227\pi$
$654$	−37.4990	+	28.4284i	−1.46633	+	1.11164i
$655$	12.9104	−	1.48627i	0.504450	−	0.0580734i
$656$	−2.57308	−	4.45670i	−0.100462	−	0.174005i
$657$	6.93713	+	7.10071i	0.270643	+	0.277025i
$658$		0			0
$659$		−	22.4678i		−	0.875220i	−0.899165	−	0.437610i	$-0.855825\pi$
$659$		−	22.4678i		−	0.875220i	0.899165	−	0.437610i	$-0.144175\pi$
$660$	−29.4315	−	30.7625i	−1.14562	−	1.19743i
$661$	20.3164	+	11.7297i	0.790218	+	0.456233i	0.840039	−	0.542526i	$-0.182532\pi$
$661$	20.3164	+	11.7297i	0.790218	+	0.456233i	−0.0498213	+	0.998758i	$0.515865\pi$
$662$	3.21328	−	5.56557i	0.124888	−	0.216312i
$663$	−32.8546	+	4.13081i	−1.27597	+	0.160427i
$664$			5.17717i			0.200913i
$665$		0			0
$666$	−15.9593	+	15.5916i	−0.618409	+	0.604163i
$667$	−5.85354	+	3.37954i	−0.226650	+	0.130856i
$668$	23.9582	+	13.8323i	0.926971	+	0.535187i
$669$	−5.70294	+	4.32347i	−0.220489	+	0.167155i
$670$	−48.8860	−	21.1882i	−1.88863	−	0.818570i
$671$	−52.1580			−2.01354
$672$		0			0
$673$		−	44.5504i		−	1.71729i	−0.512570	−	0.858645i	$-0.671307\pi$
$673$		−	44.5504i		−	1.71729i	0.512570	−	0.858645i	$-0.328693\pi$
$674$	−29.2533	+	16.8894i	−1.12680	+	0.650555i
$675$	−11.1306	+	23.4757i	−0.428418	+	0.903581i
$676$	−42.1496	+	73.0052i	−1.62114	+	2.80789i
$677$	−39.5783	+	22.8505i	−1.52112	+	0.878217i	−0.521427	+	0.853296i	$0.674600\pi$
$677$	−39.5783	+	22.8505i	−1.52112	+	0.878217i	−0.999689	+	0.0249214i	$0.992066\pi$
$678$	−72.1462	−	30.3776i	−2.77076	−	1.16664i
$679$		0			0
$680$	10.2655	−	7.61467i	0.393663	−	0.292009i
$681$	−12.3315	+	1.55044i	−0.472545	+	0.0594130i
$682$	28.0994	−	48.6697i	1.07598	−	1.86366i
$683$	−19.3444	+	33.5055i	−0.740192	+	1.28205i	0.212215	+	0.977223i	$0.431932\pi$
$683$	−19.3444	+	33.5055i	−0.740192	+	1.28205i	−0.952407	+	0.304828i	$0.901401\pi$
$684$	−16.9277	−	4.74783i	−0.647246	−	0.181538i
$685$	1.45698	+	1.96418i	0.0556682	+	0.0750473i
$686$		0			0
$687$	−7.02460	+	16.6833i	−0.268005	+	0.636508i
$688$	−8.93296	+	5.15745i	−0.340566	+	0.196626i
$689$	6.28779	−	10.8908i	0.239546	−	0.414905i
$690$	24.6443	+	7.19095i	0.938192	+	0.273755i
$691$	16.6768	−	9.62834i	0.634415	−	0.366279i	−0.148045	−	0.988981i	$-0.547298\pi$
$691$	16.6768	−	9.62834i	0.634415	−	0.366279i	0.782460	+	0.622701i	$0.213965\pi$
$692$			29.2965i			1.11369i
$693$		0			0
$694$	−69.7587			−2.64800
$695$	−15.0995	−	6.54443i	−0.572756	−	0.248244i
$696$	−4.58189	−	6.04381i	−0.173676	−	0.229090i
$697$	8.94077	+	5.16195i	0.338656	+	0.195523i
$698$	15.7836	−	9.11265i	0.597417	−	0.344919i
$699$	−6.22794	−	2.62231i	−0.235562	−	0.0991849i
$700$		0			0
$701$		−	6.75777i		−	0.255238i	−0.991823	−	0.127619i	$-0.959267\pi$
$701$		−	6.75777i		−	0.255238i	0.991823	−	0.127619i	$-0.0407334\pi$
$702$	46.4594	−	58.4046i	1.75350	−	2.20434i
$703$	3.42531	−	5.93282i	0.129188	−	0.223760i
$704$	42.3428	+	24.4466i	1.59586	+	0.921367i
$705$	13.4213	+	14.0282i	0.505474	+	0.528333i
$706$			9.47268i			0.356509i
$707$		0			0
$708$	−36.4577	−	15.3507i	−1.37016	−	0.576916i
$709$	−2.44586	−	4.23635i	−0.0918561	−	0.159099i	0.816436	−	0.577436i	$-0.195947\pi$
$709$	−2.44586	−	4.23635i	−0.0918561	−	0.159099i	−0.908292	+	0.418336i	$0.862613\pi$
$710$	6.21001	+	53.9427i	0.233057	+	2.02443i
$711$	17.0031	−	4.34428i	0.637667	−	0.162923i
$712$	13.1367	+	22.7534i	0.492318	+	0.852719i
$713$			19.9992i			0.748977i
$714$		0			0
$715$	−44.5677	+	33.0592i	−1.66674	+	1.23634i
$716$	−58.9972	+	34.0620i	−2.20483	+	1.27296i
$717$	24.8906	+	32.8324i	0.929557	+	1.22615i
$718$	−13.6506	−	7.88121i	−0.509438	−	0.294124i
$719$	19.0108	+	32.9277i	0.708985	+	1.22800i	0.965234	+	0.261387i	$0.0841798\pi$
$719$	19.0108	+	32.9277i	0.708985	+	1.22800i	−0.256249	+	0.966611i	$0.582487\pi$
$720$	1.55518	−	9.70876i	0.0579581	−	0.361824i
$721$		0			0
$722$	−32.8253			−1.22163
$723$	−22.8263	+	2.86995i	−0.848919	+	0.106735i
$724$	−38.9906	−	22.5112i	−1.44907	−	0.836624i
$725$	8.21919	−	7.70059i	0.305253	−	0.285993i
$726$	1.70344	+	13.5484i	0.0632205	+	0.502827i
$727$	18.6502			0.691699			0.345849	−	0.938290i	$-0.387591\pi$
$727$	18.6502			0.691699			0.345849	+	0.938290i	$0.387591\pi$
$728$		0			0
$729$	−19.7475	+	18.4130i	−0.731387	+	0.681962i
$730$	−6.50002	+	14.9970i	−0.240576	+	0.555065i
$731$	10.3466	−	17.9208i	0.382681	−	0.662824i
$732$	41.1799	+	54.3191i	1.52205	+	2.00769i
$733$	−18.7967	−	32.5568i	−0.694271	−	1.20251i	−0.970426	−	0.241399i	$-0.922394\pi$
$733$	−18.7967	−	32.5568i	−0.694271	−	1.20251i	0.276155	−	0.961113i	$-0.410940\pi$
$734$	−53.8821			−1.98882
$735$		0			0
$736$	−21.3813			−0.788124
$737$	20.5852	+	35.6546i	0.758264	+	1.31335i
$738$	−22.5435	+	5.75984i	−0.829837	+	0.212023i
$739$	24.7189	−	42.8144i	0.909300	−	1.57495i	0.0942603	−	0.995548i	$-0.469951\pi$
$739$	24.7189	−	42.8144i	0.909300	−	1.57495i	0.815039	−	0.579406i	$-0.196715\pi$
$740$	−19.8924	−	8.62177i	−0.731259	−	0.316942i
$741$	−8.89228	+	21.1190i	−0.326666	+	0.775826i
$742$		0			0
$743$	42.7477			1.56826			0.784131	−	0.620596i	$-0.213109\pi$
$743$	42.7477			1.56826			0.784131	+	0.620596i	$0.213109\pi$
$744$	−22.2656	+	2.79945i	−0.816295	+	0.102633i
$745$	2.76689	+	24.0343i	0.101371	+	0.880550i
$746$	−42.1929	−	24.3601i	−1.54479	−	0.891886i
$747$	−7.69304	−	2.15772i	−0.281474	−	0.0789470i
$748$	−32.3236			−1.18187
$749$		0			0
$750$	−42.7144	−	2.33761i	−1.55971	−	0.0853575i
$751$	−2.79526	−	4.84152i	−0.102000	−	0.176670i	0.810508	−	0.585727i	$-0.199191\pi$
$751$	−2.79526	−	4.84152i	−0.102000	−	0.176670i	−0.912509	+	0.409057i	$0.865858\pi$
$752$	−6.36310	−	3.67374i	−0.232039	−	0.133968i
$753$	−12.5982	+	9.55082i	−0.459103	+	0.348051i
$754$	−28.0183	+	16.1764i	−1.02037	+	0.589109i
$755$	−11.0517	−	14.8989i	−0.402211	−	0.542227i
$756$		0			0
$757$			42.9931i			1.56261i	0.624150	+	0.781305i	$0.285445\pi$
$757$			42.9931i			1.56261i	−0.624150	+	0.781305i	$0.714555\pi$
$758$	1.27906	+	2.21539i	0.0464574	+	0.0804666i
$759$	−11.9842	−	15.8079i	−0.434998	−	0.573791i
$760$	−1.01156	−	8.78681i	−0.0366930	−	0.318731i
$761$	24.5715	+	42.5591i	0.890716	+	1.54277i	0.839019	+	0.544102i	$0.183130\pi$
$761$	24.5715	+	42.5591i	0.890716	+	1.54277i	0.0516970	+	0.998663i	$0.483537\pi$
$762$	−0.886912	+	2.10640i	−0.0321294	+	0.0763068i
$763$		0			0
$764$			31.0436i			1.12312i
$765$	7.03665	+	18.4277i	0.254411	+	0.666253i
$766$	4.07358	+	2.35188i	0.147184	+	0.0849769i
$767$	−25.7795	+	44.6514i	−0.930843	+	1.61227i
$768$	−1.16872	−	9.29547i	−0.0421725	−	0.335421i
$769$		−	27.0203i		−	0.974376i	−0.873297	−	0.487188i	$-0.838023\pi$
$769$		−	27.0203i		−	0.974376i	0.873297	−	0.487188i	$-0.161977\pi$
$770$		0			0
$771$	4.49412	−	10.6735i	0.161852	−	0.384395i
$772$	−4.60466	+	2.65850i	−0.165725	+	0.0956816i
$773$	45.8267	+	26.4581i	1.64827	+	0.951631i	0.977758	+	0.209735i	$0.0672601\pi$
$773$	45.8267	+	26.4581i	1.64827	+	0.951631i	0.670515	+	0.741896i	$0.266073\pi$
$774$	11.5450	+	45.1859i	0.414975	+	1.62417i
$775$	−7.57267	−	32.4538i	−0.272018	−	1.16577i
$776$	−8.68312			−0.311706
$777$		0			0
$778$			53.3645i			1.91321i
$779$	6.18711	−	3.57213i	0.221676	−	0.127985i
$780$	69.6161	+	20.3133i	2.49266	+	0.727331i
$781$	20.9788	−	36.3364i	0.750681	−	1.30022i
$782$	16.8797	−	9.74550i	0.603617	−	0.348499i
$783$	10.8905	−	4.28956i	0.389193	−	0.153296i
$784$		0			0
$785$	−7.20950	−	9.71926i	−0.257318	−	0.346895i
$786$	2.77405	+	22.0636i	0.0989471	+	0.786981i
$787$	−8.37879	+	14.5125i	−0.298672	+	0.517315i	−0.975832	−	0.218521i	$-0.929877\pi$
$787$	−8.37879	+	14.5125i	−0.298672	+	0.517315i	0.677161	+	0.735835i	$0.263210\pi$
$788$	−11.6630	+	20.2009i	−0.415477	+	0.719627i
$789$	−5.21340	−	41.4650i	−0.185602	−	1.47619i
$790$	17.2150	+	23.2078i	0.612481	+	0.825697i
$791$		0			0
$792$	15.9218	−	15.5550i	0.565756	−	0.552723i
$793$	76.9414	−	44.4222i	2.73227	−	1.57748i
$794$	−13.2719	+	22.9876i	−0.471001	+	0.815798i
$795$	−7.19134	−	2.09836i	−0.255051	−	0.0744211i
$796$	25.1974	−	14.5477i	0.893099	−	0.515631i
$797$		−	55.9724i		−	1.98264i	−0.131462	−	0.991321i	$-0.541967\pi$
$797$		−	55.9724i		−	1.98264i	0.131462	−	0.991321i	$-0.458033\pi$
$798$		0			0
$799$	14.7401			0.521466
$800$	34.6965	−	8.09598i	1.22671	−	0.286236i
$801$	−39.2856	+	10.0374i	−1.38809	+	0.354655i
$802$	58.9813	+	34.0529i	2.08270	+	1.20245i
$803$	10.9380	−	6.31503i	0.385992	−	0.222853i
$804$	20.8794	−	49.5882i	0.736359	−	1.74884i
$805$		0			0
$806$			95.7274i			3.37186i
$807$	−4.10702	−	32.6654i	−0.144574	−	1.14988i
$808$	−8.62160	+	14.9331i	−0.303307	+	0.525343i
$809$	−36.4604	−	21.0504i	−1.28188	−	0.740094i	−0.304689	−	0.952452i	$-0.598553\pi$
$809$	−36.4604	−	21.0504i	−1.28188	−	0.740094i	−0.977192	+	0.212358i	$0.931886\pi$
$810$	−40.3670	−	18.6249i	−1.41835	−	0.654413i
$811$		−	1.35051i		−	0.0474227i	−0.999719	−	0.0237113i	$-0.992452\pi$
$811$		−	1.35051i		−	0.0474227i	0.999719	−	0.0237113i	$-0.00754826\pi$
$812$		0			0
$813$	7.96388	−	18.9141i	0.279306	−	0.663346i
$814$	14.1934	+	24.5837i	0.497479	+	0.861659i
$815$	−4.38758	−	38.1123i	−0.153690	−	1.33502i
$816$	−4.50993	−	5.94890i	−0.157879	−	0.208253i
$817$	−7.15993	−	12.4014i	−0.250494	−	0.433869i
$818$			34.6141i			1.21025i
$819$		0			0
$820$	−13.4701	−	18.1592i	−0.470395	−	0.634147i
$821$	−9.82457	+	5.67222i	−0.342880	+	0.197962i	−0.661545	−	0.749906i	$-0.730099\pi$
$821$	−9.82457	+	5.67222i	−0.342880	+	0.197962i	0.318665	+	0.947867i	$0.396765\pi$
$822$	−3.33471	+	2.52809i	−0.116312	+	0.0881771i
$823$	−26.1348	−	15.0889i	−0.911002	−	0.525967i	−0.0302488	−	0.999542i	$-0.509630\pi$
$823$	−26.1348	−	15.0889i	−0.911002	−	0.525967i	−0.880754	+	0.473575i	$0.842963\pi$
$824$	1.28533	+	2.22626i	0.0447766	+	0.0775554i
$825$	25.4330	+	21.1146i	0.885463	+	0.735114i
$826$		0			0
$827$	34.7911			1.20981			0.604903	−	0.796299i	$-0.293212\pi$
$827$	34.7911			1.20981			0.604903	+	0.796299i	$0.293212\pi$
$828$	−7.00112	+	24.9614i	−0.243306	+	0.867470i
$829$	3.50678	+	2.02464i	0.121796	+	0.0703187i	0.559660	−	0.828722i	$-0.310932\pi$
$829$	3.50678	+	2.02464i	0.121796	+	0.0703187i	−0.437864	+	0.899041i	$0.644265\pi$
$830$	−1.50458	−	13.0694i	−0.0522246	−	0.453645i
$831$	28.3867	−	3.56906i	0.984725	−	0.123809i
$832$	−83.2833			−2.88733
$833$		0			0
$834$	10.9276	−	25.9529i	0.378393	−	0.898676i
$835$	−19.7079	−	8.54181i	−0.682021	−	0.295602i
$836$	−11.1841	+	19.3715i	−0.386811	+	0.669977i
$837$	5.11992	−	34.2524i	0.176970	−	1.18394i
$838$	21.6460	+	37.4920i	0.747749	+	1.29514i
$839$	25.8653			0.892969			0.446485	−	0.894791i	$-0.352676\pi$
$839$	25.8653			0.892969			0.446485	+	0.894791i	$0.352676\pi$
$840$		0			0
$841$	23.9258			0.825029
$842$	−35.9846	−	62.3272i	−1.24011	−	2.14794i
$843$	−10.5764	−	13.9510i	−0.364271	−	0.480497i
$844$	−15.3816	+	26.6417i	−0.529457	+	0.917047i
$845$	26.0285	−	60.0537i	0.895408	−	2.06591i
$846$	−23.7627	+	23.2153i	−0.816978	+	0.798158i
$847$		0			0
$848$	2.83509			0.0973573
$849$	1.29686	+	10.3146i	0.0445080	+	0.353997i
$850$	−23.7015	+	22.2060i	−0.812953	+	0.761660i
$851$	−8.74849	−	5.05094i	−0.299894	−	0.173144i
$852$	−54.4052	+	6.84036i	−1.86389	+	0.234347i
$853$	−37.5709			−1.28640			−0.643201	−	0.765697i	$-0.722394\pi$
$853$	−37.5709			−1.28640			−0.643201	+	0.765697i	$0.722394\pi$
$854$		0			0
$855$	13.4784	+	2.15901i	0.460952	+	0.0738366i
$856$	3.23117	+	5.59655i	0.110439	+	0.191286i
$857$	−19.8563	−	11.4640i	−0.678278	−	0.391604i	0.120928	−	0.992661i	$-0.461413\pi$
$857$	−19.8563	−	11.4640i	−0.678278	−	0.391604i	−0.799206	+	0.601057i	$0.794746\pi$
$858$	−57.3630	−	75.6656i	−1.95834	−	2.58318i
$859$	−16.2512	+	9.38264i	−0.554484	+	0.320132i	−0.750929	−	0.660383i	$-0.770394\pi$
$859$	−16.2512	+	9.38264i	−0.554484	+	0.320132i	0.196444	+	0.980515i	$0.437060\pi$
$860$	−36.3981	+	26.9992i	−1.24117	+	0.920666i
$861$		0			0
$862$			61.6092i			2.09842i
$863$	4.23086	+	7.32807i	0.144020	+	0.249450i	0.929007	−	0.370062i	$-0.120664\pi$
$863$	4.23086	+	7.32807i	0.144020	+	0.249450i	−0.784987	+	0.619512i	$0.787330\pi$
$864$	36.6194	+	5.47373i	1.24582	+	0.186220i
$865$	−2.60144	−	22.5972i	−0.0884517	−	0.768329i
$866$	3.83659	+	6.64517i	0.130373	+	0.225812i
$867$	−13.3348	−	5.61470i	−0.452874	−	0.190685i
$868$		0			0
$869$		−	22.3281i		−	0.757428i
$870$	13.3231	+	13.9256i	0.451694	+	0.472121i
$871$	−60.7329	−	35.0641i	−2.05785	−	1.18810i
$872$	11.9535	−	20.7041i	0.404797	−	0.701129i
$873$	3.61892	−	12.9027i	0.122482	−	0.436691i
$874$		−	13.4880i		−	0.456238i
$875$		0			0
$876$	−15.2125	−	6.40529i	−0.513981	−	0.216415i
$877$	3.27867	−	1.89294i	0.110713	−	0.0639201i	−0.443621	−	0.896214i	$-0.646306\pi$
$877$	3.27867	−	1.89294i	0.110713	−	0.0639201i	0.554334	+	0.832294i	$0.312973\pi$
$878$	−7.55301	−	4.36073i	−0.254902	−	0.147168i
$879$	3.71852	+	4.90498i	0.125423	+	0.165441i
$880$	−11.4782	−	4.97490i	−0.386931	−	0.167704i
$881$	54.6531			1.84131			0.920654	−	0.390379i	$-0.127656\pi$
$881$	54.6531			1.84131			0.920654	+	0.390379i	$0.127656\pi$
$882$		0			0
$883$		−	28.1492i		−	0.947295i	−0.880715	−	0.473647i	$-0.842937\pi$
$883$		−	28.1492i		−	0.947295i	0.880715	−	0.473647i	$-0.157063\pi$
$884$	47.6824	−	27.5295i	1.60373	−	0.925916i
$885$	29.4840	+	8.60311i	0.991093	+	0.289191i
$886$	17.7065	−	30.6686i	0.594862	−	1.03033i
$887$	26.0011	−	15.0117i	0.873032	−	0.504045i	0.00467726	−	0.999989i	$-0.498511\pi$
$887$	26.0011	−	15.0117i	0.873032	−	0.504045i	0.868355	+	0.495944i	$0.165178\pi$
$888$	4.39873	−	10.4469i	0.147612	−	0.350575i
$889$		0			0
$890$	−39.7751	−	53.6215i	−1.33326	−	1.79740i
$891$	16.4782	+	30.1420i	0.552041	+	1.00980i
$892$	5.94975	−	10.3053i	0.199212	−	0.345046i
$893$	5.10015	−	8.83371i	0.170670	−	0.295609i
$894$	−41.0742	+	5.16426i	−1.37373	+	0.172719i
$895$	42.4816	−	31.5118i	1.42000	−	1.05332i
$896$		0			0
$897$	31.1420	+	13.1125i	1.03980	+	0.437814i
$898$	−40.3668	+	23.3058i	−1.34706	+	0.777724i
$899$	−7.50689	+	13.0023i	−0.250369	+	0.433651i
$900$	1.90948	−	43.1572i	0.0636493	−	1.43857i
$901$	−4.92559	+	2.84379i	−0.164095	+	0.0947404i
$902$			29.6036i			0.985691i
$903$		0			0
$904$	39.7702			1.32274
$905$	32.0735	+	13.9013i	1.06616	+	0.462095i
$906$	25.2949	−	19.1764i	0.840367	−	0.637092i
$907$	16.8295	+	9.71653i	0.558815	+	0.322632i	0.752670	−	0.658398i	$-0.228766\pi$
$907$	16.8295	+	9.71653i	0.558815	+	0.322632i	−0.193855	+	0.981030i	$0.562099\pi$
$908$	17.8969	−	10.3328i	0.593931	−	0.342906i
$909$	−18.5966	−	19.0351i	−0.616809	−	0.631354i
$910$		0			0
$911$			53.2832i			1.76535i	0.469982	+	0.882676i	$0.344261\pi$
$911$			53.2832i			1.76535i	−0.469982	+	0.882676i	$0.655739\pi$
$912$	−5.12563	+	0.644446i	−0.169727	+	0.0213397i
$913$	−5.08280	+	8.80366i	−0.168216	+	0.291359i
$914$	18.3787	+	10.6110i	0.607914	+	0.350979i
$915$	−36.5866	−	38.2412i	−1.20952	−	1.26422i
$916$		−	30.0988i		−	0.994493i
$917$		0			0
$918$	−31.4046	+	12.3697i	−1.03650	+	0.408261i
$919$	−22.5064	−	38.9822i	−0.742416	−	1.28590i	−0.951392	−	0.307982i	$-0.900346\pi$
$919$	−22.5064	−	38.9822i	−0.742416	−	1.28590i	0.208976	−	0.977921i	$-0.432987\pi$
$920$	−12.9570	+	1.49163i	−0.427178	+	0.0491777i
$921$	−40.0749	+	30.3812i	−1.32051	+	1.00110i
$922$	27.1015	+	46.9412i	0.892541	+	1.54593i
$923$			71.4693i			2.35244i
$924$		0			0
$925$	16.1092	+	4.88383i	0.529666	+	0.160579i
$926$	27.9073	−	16.1123i	0.917092	−	0.529483i
$927$	−3.84382	+	0.982092i	−0.126248	+	0.0322561i
$928$	−13.9008	−	8.02565i	−0.456317	−	0.263455i
$929$	−21.3495	−	36.9785i	−0.700455	−	1.21322i	−0.968307	−	0.249764i	$-0.919647\pi$
$929$	−21.3495	−	36.9785i	−0.700455	−	1.21322i	0.267852	−	0.963460i	$-0.413686\pi$
$930$	55.3942	−	13.5378i	1.81645	−	0.443921i
$931$		0			0
$932$	11.2360			0.368048
$933$	1.86777	+	14.8554i	0.0611482	+	0.486345i
$934$	−34.2800	−	19.7916i	−1.12168	−	0.647600i
$935$	24.9321	−	2.87024i	0.815366	−	0.0938668i
$936$	−10.2392	+	36.5065i	−0.334680	+	1.19325i
$937$	26.4685			0.864688			0.432344	−	0.901709i	$-0.357687\pi$
$937$	26.4685			0.864688			0.432344	+	0.901709i	$0.357687\pi$
$938$		0			0
$939$	−17.3235	−	7.29415i	−0.565330	−	0.238036i
$940$	−29.6189	−	12.8375i	−0.966063	−	0.418711i
$941$	15.8545	−	27.4609i	0.516843	−	0.895199i	−0.482965	−	0.875640i	$-0.660440\pi$
$941$	15.8545	−	27.4609i	0.516843	−	0.895199i	0.999809	−	0.0195596i	$-0.00622642\pi$
$942$	16.5010	−	12.5096i	0.537633	−	0.407586i
$943$	−5.26744	−	9.12347i	−0.171531	−	0.297101i
$944$	−11.6237			−0.378318
$945$		0			0
$946$	59.3370			1.92921
$947$	5.97276	+	10.3451i	0.194089	+	0.336171i	0.946601	−	0.322406i	$-0.104492\pi$
$947$	5.97276	+	10.3451i	0.194089	+	0.336171i	−0.752513	+	0.658578i	$0.771158\pi$
$948$	−23.2532	+	17.6285i	−0.755229	+	0.572548i
$949$	−10.7568	+	18.6314i	−0.349181	+	0.604800i
$950$	5.10720	+	21.8877i	0.165699	+	0.710130i
$951$	−14.9111	−	6.27839i	−0.483524	−	0.203591i
$952$		0			0
$953$	1.76384			0.0571364			0.0285682	−	0.999592i	$-0.490905\pi$
$953$	1.76384			0.0571364			0.0285682	+	0.999592i	$0.490905\pi$
$954$	3.46171	−	12.3422i	0.112077	−	0.399594i
$955$	−2.75658	−	23.9448i	−0.0892008	−	0.774835i
$956$	−59.3284	−	34.2532i	−1.91882	−	1.10783i
$957$	−1.85775	−	14.7757i	−0.0600527	−	0.477632i
$958$	−6.54980			−0.211614
$959$		0			0
$960$	11.7779	+	48.1932i	0.380131	+	1.55543i
$961$	6.71186	+	11.6253i	0.216511	+	0.375009i
$962$	−41.8752	−	24.1766i	−1.35011	−	0.779486i
$963$	−9.66291	+	2.46886i	−0.311383	+	0.0795580i
$964$	33.1282	−	19.1266i	1.06699	−	0.616026i
$965$	3.31564	−	2.45946i	0.106734	−	0.0791728i
$966$		0			0
$967$		−	53.4014i		−	1.71727i	−0.512584	−	0.858637i	$-0.671312\pi$
$967$		−	53.4014i		−	1.71727i	0.512584	−	0.858637i	$-0.328688\pi$
$968$	−3.46869	−	6.00795i	−0.111488	−	0.193103i
$969$	8.25869	−	6.26101i	0.265307	−	0.201133i
$970$	21.9199	−	2.52347i	0.703805	−	0.0810236i
$971$	23.9577	+	41.4959i	0.768838	+	1.33167i	0.938193	+	0.346111i	$0.112498\pi$
$971$	23.9577	+	41.4959i	0.768838	+	1.33167i	−0.169356	+	0.985555i	$0.554169\pi$
$972$	18.3810	−	40.9588i	0.589571	−	1.31375i
$973$		0			0
$974$		−	73.4642i		−	2.35394i
$975$	−55.5007	−	9.48649i	−1.77744	−	0.303811i
$976$	17.3460	+	10.0147i	0.555231	+	0.320563i
$977$	−4.07411	+	7.05657i	−0.130342	+	0.225760i	−0.923809	−	0.382855i	$-0.874941\pi$
$977$	−4.07411	+	7.05657i	−0.130342	+	0.225760i	0.793466	+	0.608614i	$0.208274\pi$
$978$	65.1332	−	8.18920i	2.08273	−	0.261862i
$979$			51.5889i			1.64879i
$980$		0			0
$981$	25.7834	+	26.3914i	0.823201	+	0.842612i
$982$	48.7636	−	28.1537i	1.55611	−	0.898420i
$983$	12.6460	+	7.30116i	0.403344	+	0.232871i	0.687926	−	0.725781i	$-0.258521\pi$
$983$	12.6460	+	7.30116i	0.403344	+	0.232871i	−0.284582	+	0.958652i	$0.591855\pi$
$984$	9.42003	−	7.14143i	0.300300	−	0.227661i
$985$	7.20222	−	16.6172i	0.229482	−	0.529467i
$986$	14.6322			0.465986
$987$		0			0
$988$		−	38.1014i		−	1.21217i
$989$	−18.2870	+	10.5580i	−0.581492	+	0.335725i
$990$	−35.6728	+	43.8946i	−1.13376	+	1.39506i
$991$	−7.84118	+	13.5813i	−0.249083	+	0.431425i	−0.963272	−	0.268529i	$-0.913463\pi$
$991$	−7.84118	+	13.5813i	−0.249083	+	0.431425i	0.714188	+	0.699953i	$0.246796\pi$
$992$	−41.1307	+	23.7468i	−1.30590	+	0.753962i
$993$	−4.64398	−	1.95537i	−0.147372	−	0.0620519i
$994$		0			0
$995$	−18.1437	+	13.4585i	−0.575194	+	0.426664i
$996$	13.1814	−	1.65730i	0.417669	−	0.0525136i
$997$	13.5211	−	23.4192i	0.428218	−	0.741695i	−0.568497	−	0.822685i	$-0.692475\pi$
$997$	13.5211	−	23.4192i	0.428218	−	0.741695i	0.996715	+	0.0809903i	$0.0258083\pi$
$998$	−37.1913	+	64.4173i	−1.17727	+	2.03909i
$999$	13.6904	+	10.8903i	0.433144	+	0.344555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.g.374.32		64
3.2	odd	2	inner	735.2.p.g.374.3		64
5.4	even	2	inner	735.2.p.g.374.1		64
7.2	even	3	inner	735.2.p.g.509.31		64
7.3	odd	6		735.2.g.c.734.4	yes	32
7.4	even	3		735.2.g.c.734.1	✓	32
7.5	odd	6	inner	735.2.p.g.509.30		64
7.6	odd	2	inner	735.2.p.g.374.29		64
15.14	odd	2	inner	735.2.p.g.374.30		64
21.2	odd	6	inner	735.2.p.g.509.4		64
21.5	even	6	inner	735.2.p.g.509.1		64
21.11	odd	6		735.2.g.c.734.30	yes	32
21.17	even	6		735.2.g.c.734.31	yes	32
21.20	even	2	inner	735.2.p.g.374.2		64
35.4	even	6		735.2.g.c.734.32	yes	32
35.9	even	6	inner	735.2.p.g.509.2		64
35.19	odd	6	inner	735.2.p.g.509.3		64
35.24	odd	6		735.2.g.c.734.29	yes	32
35.34	odd	2	inner	735.2.p.g.374.4		64
105.44	odd	6	inner	735.2.p.g.509.29		64
105.59	even	6		735.2.g.c.734.2	yes	32
105.74	odd	6		735.2.g.c.734.3	yes	32
105.89	even	6	inner	735.2.p.g.509.32		64
105.104	even	2	inner	735.2.p.g.374.31		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.1	✓	32	7.4	even	3
735.2.g.c.734.2	yes	32	105.59	even	6
735.2.g.c.734.3	yes	32	105.74	odd	6
735.2.g.c.734.4	yes	32	7.3	odd	6
735.2.g.c.734.29	yes	32	35.24	odd	6
735.2.g.c.734.30	yes	32	21.11	odd	6
735.2.g.c.734.31	yes	32	21.17	even	6
735.2.g.c.734.32	yes	32	35.4	even	6
735.2.p.g.374.1		64	5.4	even	2	inner
735.2.p.g.374.2		64	21.20	even	2	inner
735.2.p.g.374.3		64	3.2	odd	2	inner
735.2.p.g.374.4		64	35.34	odd	2	inner
735.2.p.g.374.29		64	7.6	odd	2	inner
735.2.p.g.374.30		64	15.14	odd	2	inner
735.2.p.g.374.31		64	105.104	even	2	inner
735.2.p.g.374.32		64	1.1	even	1	trivial
735.2.p.g.509.1		64	21.5	even	6	inner
735.2.p.g.509.2		64	35.9	even	6	inner
735.2.p.g.509.3		64	35.19	odd	6	inner
735.2.p.g.509.4		64	21.2	odd	6	inner
735.2.p.g.509.29		64	105.44	odd	6	inner
735.2.p.g.509.30		64	7.5	odd	6	inner
735.2.p.g.509.31		64	7.2	even	3	inner
735.2.p.g.509.32		64	105.89	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10453 + 1.91310i) q^{2} +(1.38025 - 1.04638i) q^{3} +(-1.43998 + 2.49412i) q^{4} +(0.889228 - 2.05165i) q^{5} +(3.52637 + 1.48480i) q^{6} -1.94389 q^{8} +(0.810168 - 2.88853i) q^{9} +(4.90720 - 0.564929i) q^{10} +(-3.30554 - 1.90846i) q^{11} +(0.622272 + 4.94927i) q^{12} +6.50161 q^{13} +(-0.919457 - 3.76226i) q^{15} +(0.732874 + 1.26937i) q^{16} +(-2.54654 - 1.47025i) q^{17} +(6.42092 - 1.64054i) q^{18} +(-1.76224 + 1.01743i) q^{19} +(3.83659 + 5.17218i) q^{20} -8.43180i q^{22} +(1.50029 + 2.59858i) q^{23} +(-2.68305 + 2.03405i) q^{24} +(-3.41855 - 3.64877i) q^{25} +(7.18123 + 12.4383i) q^{26} +(-1.90428 - 4.83464i) q^{27} +2.25259i q^{29} +(6.18203 - 5.91455i) q^{30} +(5.77216 + 3.33256i) q^{31} +(-3.56285 + 6.17104i) q^{32} +(-6.55944 + 0.824719i) q^{33} -6.49574i q^{34} +(6.03772 + 6.18009i) q^{36} +(-2.91560 + 1.68332i) q^{37} +(-3.89289 - 2.24756i) q^{38} +(8.97383 - 6.80317i) q^{39} +(-1.72856 + 3.98818i) q^{40} -3.51094 q^{41} +7.03729i q^{43} +(9.51983 - 5.49628i) q^{44} +(-5.20584 - 4.23075i) q^{45} +(-3.31424 + 5.74043i) q^{46} +(-4.34120 + 2.50639i) q^{47} +(2.33980 + 0.985185i) q^{48} +(3.20459 - 10.5702i) q^{50} +(-5.05330 + 0.635352i) q^{51} +(-9.36219 + 16.2158i) q^{52} +(0.967113 - 1.67509i) q^{53} +(7.14584 - 8.98309i) q^{54} +(-6.85487 + 5.08477i) q^{55} +(-1.36770 + 3.24827i) q^{57} +(-4.30944 + 2.48806i) q^{58} +(-3.96509 + 6.86774i) q^{59} +(10.7075 + 3.12434i) q^{60} +(11.8342 - 6.83249i) q^{61} +14.7237i q^{62} -12.8096 q^{64} +(5.78141 - 13.3390i) q^{65} +(-8.82289 - 11.6380i) q^{66} +(-9.34121 - 5.39315i) q^{67} +(7.33395 - 4.23426i) q^{68} +(4.78988 + 2.01681i) q^{69} +10.9926i q^{71} +(-1.57488 + 5.61499i) q^{72} +(-1.65449 + 2.86566i) q^{73} +(-6.44074 - 3.71856i) q^{74} +(-8.53645 - 1.45910i) q^{75} -5.86030i q^{76} +(22.9271 + 9.65357i) q^{78} +(2.92489 + 5.06605i) q^{79} +(3.25601 - 0.374839i) q^{80} +(-7.68725 - 4.68040i) q^{81} +(-3.87795 - 6.71680i) q^{82} -2.66330i q^{83} +(-5.28089 + 3.91724i) q^{85} +(-13.4631 + 7.77291i) q^{86} +(2.35707 + 3.10913i) q^{87} +(6.42561 + 3.70983i) q^{88} +(-6.75793 - 11.7051i) q^{89} +(2.34385 - 14.6323i) q^{90} -8.64156 q^{92} +(11.4541 - 1.44013i) q^{93} +(-9.58999 - 5.53678i) q^{94} +(0.520378 + 4.52022i) q^{95} +(1.53965 + 12.2457i) q^{96} +4.46688 q^{97} +(-8.19069 + 8.00200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) \) 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more