LMFDB - Embedded newform 900.2.o.c.299.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(299,900)] 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("900.299"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.7
Character	$\chi$	$=$	900.299
Dual form			900.2.o.c.599.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.901786 - 1.08940i) q^{2} +(-1.07843 + 1.35535i) q^{3} +(-0.373566 + 1.96480i) q^{4} +(2.44903 - 0.0473955i) q^{6} +(-1.92400 + 3.33246i) q^{7} +(2.47732 - 1.36487i) q^{8} +(-0.673959 - 2.92332i) q^{9} +(-1.40956 + 2.44144i) q^{11} +(-2.26013 - 2.62522i) q^{12} +(-5.01498 + 2.89540i) q^{13} +(5.36540 - 0.909171i) q^{14} +(-3.72090 - 1.46797i) q^{16} -2.42512 q^{17} +(-2.57688 + 3.37041i) q^{18} -4.07233i q^{19} +(-2.44175 - 6.20153i) q^{21} +(3.93081 - 0.666079i) q^{22} +(3.76512 - 2.17379i) q^{23} +(-0.821751 + 4.82957i) q^{24} +(7.67667 + 2.85227i) q^{26} +(4.68894 + 2.23915i) q^{27} +(-5.82889 - 5.02517i) q^{28} +(6.07280 + 3.50613i) q^{29} +(1.94857 - 1.12501i) q^{31} +(1.75626 + 5.37732i) q^{32} +(-1.78888 - 4.54338i) q^{33} +(2.18694 + 2.64192i) q^{34} +(5.99551 - 0.232146i) q^{36} -4.29414i q^{37} +(-4.43638 + 3.67237i) q^{38} +(1.48404 - 9.91956i) q^{39} +(0.0948994 - 0.0547902i) q^{41} +(-4.55399 + 8.25249i) q^{42} +(-0.102997 + 0.178397i) q^{43} +(-4.27038 - 3.68155i) q^{44} +(-5.76345 - 2.14141i) q^{46} +(-9.33217 - 5.38793i) q^{47} +(6.00235 - 3.46002i) q^{48} +(-3.90353 - 6.76112i) q^{49} +(2.61533 - 3.28689i) q^{51} +(-3.81546 - 10.9351i) q^{52} +7.55580 q^{53} +(-1.78910 - 7.12735i) q^{54} +(-0.217988 + 10.8816i) q^{56} +(5.51944 + 4.39174i) q^{57} +(-1.65680 - 9.77747i) q^{58} +(-4.16744 - 7.21822i) q^{59} +(-3.06480 + 5.30839i) q^{61} +(-2.98277 - 1.10825i) q^{62} +(11.0385 + 3.37851i) q^{63} +(4.27426 - 6.76245i) q^{64} +(-3.33635 + 6.04596i) q^{66} +(-2.59211 - 4.48967i) q^{67} +(0.905942 - 4.76488i) q^{68} +(-1.11418 + 7.44736i) q^{69} -5.46464 q^{71} +(-5.65956 - 6.32213i) q^{72} -12.9936i q^{73} +(-4.67802 + 3.87240i) q^{74} +(8.00132 + 1.52128i) q^{76} +(-5.42400 - 9.39464i) q^{77} +(-12.1446 + 7.32861i) q^{78} +(-4.32475 - 2.49689i) q^{79} +(-8.09156 + 3.94039i) q^{81} +(-0.145267 - 0.0539740i) q^{82} +(6.68080 + 3.85716i) q^{83} +(13.0969 - 2.48088i) q^{84} +(0.287226 - 0.0486706i) q^{86} +(-11.3012 + 4.44965i) q^{87} +(-0.159703 + 7.97210i) q^{88} -0.134752i q^{89} -22.2830i q^{91} +(2.86456 + 8.20978i) q^{92} +(-0.576624 + 3.85425i) q^{93} +(2.54603 + 15.0252i) q^{94} +(-9.18217 - 3.41874i) q^{96} +(-11.2555 - 6.49834i) q^{97} +(-3.84538 + 10.3496i) q^{98} +(8.08708 + 2.47517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 12 q^{8} - 4 q^{9} + 28 q^{12} + 30 q^{14} - 18 q^{18} - 4 q^{21} - 42 q^{22} + 28 q^{24} + 12 q^{29} - 48 q^{33} + 6 q^{34} + 42 q^{36} - 6 q^{38} - 60 q^{41} + 16 q^{42} - 12 q^{46} - 74 q^{48}+ \cdots + 84 q^{98}+O(q^{100}) $ 48 * q + 6 * q^6 + 12 * q^8 - 4 * q^9 + 28 * q^12 + 30 * q^14 - 18 * q^18 - 4 * q^21 - 42 * q^22 + 28 * q^24 + 12 * q^29 - 48 * q^33 + 6 * q^34 + 42 * q^36 - 6 * q^38 - 60 * q^41 + 16 * q^42 - 12 * q^46 - 74 * q^48 - 24 * q^49 - 90 * q^52 + 32 * q^54 - 42 * q^56 - 16 * q^57 + 84 * q^58 + 84 * q^62 + 48 * q^64 + 16 * q^66 + 6 * q^68 - 36 * q^69 - 80 * q^72 - 84 * q^74 + 6 * q^76 - 46 * q^78 - 50 * q^84 - 54 * q^86 + 114 * q^88 - 42 * q^92 - 24 * q^93 - 18 * q^94 - 18 * q^96 - 48 * q^97 + 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.901786	−	1.08940i	−0.637659	−	0.770319i
$2$	−0.901786	−	1.08940i	−0.637659	−	0.770319i
$3$	−1.07843	+	1.35535i	−0.622634	+	0.782513i
$3$	−1.07843	+	1.35535i	−0.622634	+	0.782513i
$4$	−0.373566	+	1.96480i	−0.186783	+	0.982401i
$5$		0			0
$5$		0			0
$6$	2.44903	−	0.0473955i	0.999813	−	0.0193492i
$7$	−1.92400	+	3.33246i	−0.727203	+	1.25955i	0.230858	+	0.972987i	$0.425847\pi$
$7$	−1.92400	+	3.33246i	−0.727203	+	1.25955i	−0.958061	+	0.286565i	$0.907487\pi$
$8$	2.47732	−	1.36487i	0.875866	−	0.482554i
$9$	−0.673959	−	2.92332i	−0.224653	−	0.974439i
$10$		0			0
$11$	−1.40956	+	2.44144i	−0.425000	+	0.736121i	−0.996420	−	0.0845363i	$-0.973059\pi$
$11$	−1.40956	+	2.44144i	−0.425000	+	0.736121i	0.571421	+	0.820657i	$0.306392\pi$
$12$	−2.26013	−	2.62522i	−0.652444	−	0.757837i
$13$	−5.01498	+	2.89540i	−1.39091	+	0.803039i	−0.993415	−	0.114567i	$-0.963452\pi$
$13$	−5.01498	+	2.89540i	−1.39091	+	0.803039i	−0.397490	+	0.917607i	$0.630119\pi$
$14$	5.36540	−	0.909171i	1.43396	−	0.242986i
$15$		0			0
$16$	−3.72090	−	1.46797i	−0.930224	−	0.366991i
$17$	−2.42512			−0.588178			−0.294089	−	0.955778i	$-0.595016\pi$
$17$	−2.42512			−0.588178			−0.294089	+	0.955778i	$0.595016\pi$
$18$	−2.57688	+	3.37041i	−0.607377	+	0.794414i
$19$		−	4.07233i		−	0.934256i	−0.884190	−	0.467128i	$-0.845289\pi$
$19$		−	4.07233i		−	0.934256i	0.884190	−	0.467128i	$-0.154711\pi$
$20$		0			0
$21$	−2.44175	−	6.20153i	−0.532834	−	1.35329i
$22$	3.93081	−	0.666079i	0.838053	−	0.142009i
$23$	3.76512	−	2.17379i	0.785082	−	0.453267i	−0.0531462	−	0.998587i	$-0.516925\pi$
$23$	3.76512	−	2.17379i	0.785082	−	0.453267i	0.838228	+	0.545319i	$0.183592\pi$
$24$	−0.821751	+	4.82957i	−0.167739	+	0.985831i
$25$		0			0
$26$	7.67667	+	2.85227i	1.50552	+	0.559376i
$27$	4.68894	+	2.23915i	0.902388	+	0.430925i
$28$	−5.82889	−	5.02517i	−1.10156	−	0.949667i
$29$	6.07280	+	3.50613i	1.12769	+	0.651073i	0.943353	−	0.331790i	$-0.107653\pi$
$29$	6.07280	+	3.50613i	1.12769	+	0.651073i	0.184338	+	0.982863i	$0.440986\pi$
$30$		0			0
$31$	1.94857	−	1.12501i	0.349974	−	0.202058i	−0.314700	−	0.949191i	$-0.601904\pi$
$31$	1.94857	−	1.12501i	0.349974	−	0.202058i	0.664674	+	0.747134i	$0.268571\pi$
$32$	1.75626	+	5.37732i	0.310465	+	0.950585i
$33$	−1.78888	−	4.54338i	−0.311405	−	0.790902i
$34$	2.18694	+	2.64192i	0.375057	+	0.453085i
$35$		0			0
$36$	5.99551	−	0.232146i	0.999251	−	0.0386911i
$37$		−	4.29414i		−	0.705953i	−0.935632	−	0.352976i	$-0.885170\pi$
$37$		−	4.29414i		−	0.705953i	0.935632	−	0.352976i	$-0.114830\pi$
$38$	−4.43638	+	3.67237i	−0.719675	+	0.595737i
$39$	1.48404	−	9.91956i	0.237636	−	1.58840i
$40$		0			0
$41$	0.0948994	−	0.0547902i	0.0148208	−	0.00855679i	−0.492571	−	0.870272i	$-0.663943\pi$
$41$	0.0948994	−	0.0547902i	0.0148208	−	0.00855679i	0.507392	+	0.861715i	$0.330610\pi$
$42$	−4.55399	+	8.25249i	−0.702695	+	1.27339i
$43$	−0.102997	+	0.178397i	−0.0157069	+	0.0272052i	−0.873772	−	0.486336i	$-0.838333\pi$
$43$	−0.102997	+	0.178397i	−0.0157069	+	0.0272052i	0.858065	+	0.513541i	$0.171667\pi$
$44$	−4.27038	−	3.68155i	−0.643783	−	0.555015i
$45$		0			0
$46$	−5.76345	−	2.14141i	−0.849775	−	0.315734i
$47$	−9.33217	−	5.38793i	−1.36124	−	0.785910i	−0.371448	−	0.928454i	$-0.621139\pi$
$47$	−9.33217	−	5.38793i	−1.36124	−	0.785910i	−0.989789	+	0.142543i	$0.954472\pi$
$48$	6.00235	−	3.46002i	0.866365	−	0.499411i
$49$	−3.90353	−	6.76112i	−0.557647	−	0.965874i
$50$		0			0
$51$	2.61533	−	3.28689i	0.366220	−	0.460257i
$52$	−3.81546	−	10.9351i	−0.529110	−	1.51642i
$53$	7.55580			1.03787			0.518934	−	0.854814i	$-0.326329\pi$
$53$	7.55580			1.03787			0.518934	+	0.854814i	$0.326329\pi$
$54$	−1.78910	−	7.12735i	−0.243466	−	0.969910i
$55$		0			0
$56$	−0.217988	+	10.8816i	−0.0291299	+	1.45411i
$57$	5.51944	+	4.39174i	0.731068	+	0.581700i
$58$	−1.65680	−	9.77747i	−0.217548	−	1.28384i
$59$	−4.16744	−	7.21822i	−0.542554	−	0.939732i	−0.998756	−	0.0498554i	$-0.984124\pi$
$59$	−4.16744	−	7.21822i	−0.542554	−	0.939732i	0.456202	−	0.889876i	$-0.349209\pi$
$60$		0			0
$61$	−3.06480	+	5.30839i	−0.392407	+	0.679669i	−0.992767	−	0.120061i	$-0.961691\pi$
$61$	−3.06480	+	5.30839i	−0.392407	+	0.679669i	0.600359	+	0.799730i	$0.295024\pi$
$62$	−2.98277	−	1.10825i	−0.378813	−	0.140748i
$63$	11.0385	+	3.37851i	1.39072	+	0.425652i
$64$	4.27426	−	6.76245i	0.534283	−	0.845306i
$65$		0			0
$66$	−3.33635	+	6.04596i	−0.410677	+	0.744206i
$67$	−2.59211	−	4.48967i	−0.316677	−	0.548500i	0.663116	−	0.748517i	$-0.269234\pi$
$67$	−2.59211	−	4.48967i	−0.316677	−	0.548500i	−0.979792	+	0.200017i	$0.935900\pi$
$68$	0.905942	−	4.76488i	0.109862	−	0.577827i
$69$	−1.11418	+	7.44736i	−0.134131	+	0.896557i
$70$		0			0
$71$	−5.46464			−0.648533			−0.324267	−	0.945966i	$-0.605118\pi$
$71$	−5.46464			−0.648533			−0.324267	+	0.945966i	$0.605118\pi$
$72$	−5.65956	−	6.32213i	−0.666986	−	0.745071i
$73$		−	12.9936i		−	1.52078i	−0.649466	−	0.760390i	$-0.725008\pi$
$73$		−	12.9936i		−	1.52078i	0.649466	−	0.760390i	$-0.274992\pi$
$74$	−4.67802	+	3.87240i	−0.543809	+	0.450157i
$75$		0			0
$76$	8.00132	+	1.52128i	0.917814	+	0.174503i
$77$	−5.42400	−	9.39464i	−0.618122	−	1.07062i
$78$	−12.1446	+	7.32861i	−1.37511	+	0.829802i
$79$	−4.32475	−	2.49689i	−0.486572	−	0.280923i	0.236579	−	0.971612i	$-0.423974\pi$
$79$	−4.32475	−	2.49689i	−0.486572	−	0.280923i	−0.723151	+	0.690690i	$0.757307\pi$
$80$		0			0
$81$	−8.09156	+	3.94039i	−0.899062	+	0.437821i
$82$	−0.145267	−	0.0539740i	−0.0160421	−	0.00596043i
$83$	6.68080	+	3.85716i	0.733314	+	0.423379i	0.819633	−	0.572889i	$-0.194177\pi$
$83$	6.68080	+	3.85716i	0.733314	+	0.423379i	−0.0863196	+	0.996267i	$0.527511\pi$
$84$	13.0969	−	2.48088i	1.42899	−	0.270687i
$85$		0			0
$86$	0.287226	−	0.0486706i	0.0309724	−	0.00524829i
$87$	−11.3012	+	4.44965i	−1.21161	+	0.477053i
$88$	−0.159703	+	7.97210i	−0.0170244	+	0.849829i
$89$		−	0.134752i		−	0.0142837i	−0.999974	−	0.00714184i	$-0.997727\pi$
$89$		−	0.134752i		−	0.0142837i	0.999974	−	0.00714184i	$-0.00227334\pi$
$90$		0			0
$91$		−	22.2830i		−	2.33589i
$92$	2.86456	+	8.20978i	0.298651	+	0.855928i
$93$	−0.576624	+	3.85425i	−0.0597931	+	0.399667i
$94$	2.54603	+	15.0252i	0.262603	+	1.54973i
$95$		0			0
$96$	−9.18217	−	3.41874i	−0.937151	−	0.348924i
$97$	−11.2555	−	6.49834i	−1.14282	−	0.659806i	−0.195691	−	0.980666i	$-0.562695\pi$
$97$	−11.2555	−	6.49834i	−1.14282	−	0.659806i	−0.947127	+	0.320859i	$0.896028\pi$
$98$	−3.84538	+	10.3496i	−0.388442	+	1.04546i
$99$	8.08708	+	2.47517i	0.812782	+	0.248764i
$100$		0			0
$101$	2.90860	+	1.67928i	0.289417	+	0.167095i	0.637679	−	0.770302i	$-0.279895\pi$
$101$	2.90860	+	1.67928i	0.289417	+	0.167095i	−0.348262	+	0.937397i	$0.613228\pi$
$102$	−5.93920	+	0.114940i	−0.588068	+	0.0113807i
$103$	1.91884	+	3.32353i	0.189069	+	0.327477i	0.944940	−	0.327244i	$-0.106120\pi$
$103$	1.91884	+	3.32353i	0.189069	+	0.327477i	−0.755871	+	0.654720i	$0.772786\pi$
$104$	−8.47188	+	14.0176i	−0.830736	+	1.37454i
$105$		0			0
$106$	−6.81371	−	8.23125i	−0.661806	−	0.799490i
$107$			0.556704i			0.0538186i	0.999638	+	0.0269093i	$0.00856653\pi$
$107$			0.556704i			0.0538186i	−0.999638	+	0.0269093i	$0.991433\pi$
$108$	−6.15112	+	8.37638i	−0.591892	+	0.806017i
$109$	−15.5306			−1.48756			−0.743779	−	0.668425i	$-0.766969\pi$
$109$	−15.5306			−1.48756			−0.743779	+	0.668425i	$0.766969\pi$
$110$		0			0
$111$	5.82008	+	4.63095i	0.552417	+	0.439551i
$112$	12.0509	−	9.57538i	1.13871	−	0.904789i
$113$	−3.79280	−	6.56932i	−0.356796	−	0.617989i	0.630627	−	0.776086i	$-0.282798\pi$
$113$	−3.79280	−	6.56932i	−0.356796	−	0.617989i	−0.987424	+	0.158096i	$0.949464\pi$
$114$	−0.193010	−	9.97326i	−0.0180771	−	0.934081i
$115$		0			0
$116$	−9.15745	+	10.6221i	−0.850248	+	0.986236i
$117$	11.8441	+	12.7090i	1.09498	+	1.17495i
$118$	−4.10536	+	11.0493i	−0.377929	+	1.01717i
$119$	4.66593	−	8.08162i	0.427725	−	0.740841i
$120$		0			0
$121$	1.52626	+	2.64356i	0.138751	+	0.240323i
$122$	8.54673	−	1.44825i	0.773784	−	0.131118i
$123$	−0.0280827	+	0.187710i	−0.00253213	+	0.0169252i
$124$	1.48250	+	4.24883i	0.133132	+	0.381556i
$125$		0			0
$126$	−6.27386	−	15.0720i	−0.558920	−	1.34272i
$127$	18.5602			1.64695			0.823476	−	0.567352i	$-0.192032\pi$
$127$	18.5602			1.64695			0.823476	+	0.567352i	$0.192032\pi$
$128$	−11.2214	+	1.44192i	−0.991845	+	0.127449i
$129$	−0.130714	−	0.331987i	−0.0115088	−	0.0292298i
$130$		0			0
$131$	4.75330	+	8.23296i	0.415298	+	0.719317i	0.995460	−	0.0951841i	$-0.0303440\pi$
$131$	4.75330	+	8.23296i	0.415298	+	0.719317i	−0.580162	+	0.814501i	$0.697011\pi$
$132$	9.59512	−	1.81755i	0.835148	−	0.158198i
$133$	13.5709	+	7.83515i	1.17674	+	0.679394i
$134$	−2.55350	+	6.87255i	−0.220588	+	0.593698i
$135$		0			0
$136$	−6.00781	+	3.30997i	−0.515165	+	0.283828i
$137$	0.400425	−	0.693556i	0.0342106	−	0.0592545i	−0.848413	−	0.529335i	$-0.822442\pi$
$137$	0.400425	−	0.693556i	0.0342106	−	0.0592545i	0.882624	+	0.470080i	$0.155775\pi$
$138$	9.11787	−	5.50214i	0.776165	−	0.468373i
$139$	−6.32423	+	3.65130i	−0.536415	+	0.309699i	−0.743625	−	0.668597i	$-0.766895\pi$
$139$	−6.32423	+	3.65130i	−0.536415	+	0.309699i	0.207210	+	0.978296i	$0.433562\pi$
$140$		0			0
$141$	17.3667	−	6.83785i	1.46254	−	0.575851i
$142$	4.92793	+	5.95316i	0.413543	+	0.499578i
$143$		−	16.3250i		−	1.36517i
$144$	−1.78359	+	11.8667i	−0.148633	+	0.988892i
$145$		0			0
$146$	−14.1551	+	11.7174i	−1.17149	+	0.969739i
$147$	13.3734	+	2.00076i	1.10302	+	0.165020i
$148$	8.43715	+	1.60414i	0.693529	+	0.131860i
$149$	−0.0985697	+	0.0569092i	−0.00807514	+	0.00466219i	−0.504032	−	0.863685i	$-0.668151\pi$
$149$	−0.0985697	+	0.0569092i	−0.00807514	+	0.00466219i	0.495957	+	0.868347i	$0.334817\pi$
$150$		0			0
$151$	−1.46894	−	0.848093i	−0.119541	−	0.0690169i	0.439037	−	0.898469i	$-0.355320\pi$
$151$	−1.46894	−	0.848093i	−0.119541	−	0.0690169i	−0.558578	+	0.829452i	$0.688653\pi$
$152$	−5.55820	−	10.0885i	−0.450829	−	0.818283i
$153$	1.63443	+	7.08940i	0.132136	+	0.573144i
$154$	−5.34319	+	14.3808i	−0.430567	+	1.15884i
$155$		0			0
$156$	18.9356	+	6.62145i	1.51606	+	0.530140i
$157$	−19.4804	+	11.2470i	−1.55471	+	0.897612i	−0.556961	+	0.830539i	$0.688033\pi$
$157$	−19.4804	+	11.2470i	−1.55471	+	0.897612i	−0.997748	+	0.0670730i	$0.978634\pi$
$158$	1.17989	+	6.96302i	0.0938669	+	0.553948i
$159$	−8.14843	+	10.2408i	−0.646213	+	0.812146i
$160$		0			0
$161$			16.7295i			1.31847i
$162$	11.5895	+	5.26152i	0.910557	+	0.413384i
$163$	1.64377			0.128750			0.0643749	−	0.997926i	$-0.479495\pi$
$163$	1.64377			0.128750			0.0643749	+	0.997926i	$0.479495\pi$
$164$	0.0722007	+	0.206926i	0.00563793	+	0.0161582i
$165$		0			0
$166$	−1.82268	−	10.7564i	−0.141467	−	0.834857i
$167$	2.11198	−	1.21935i	0.163430	−	0.0943561i	−0.416054	−	0.909340i	$-0.636587\pi$
$167$	2.11198	−	1.21935i	0.163430	−	0.0943561i	0.579484	+	0.814984i	$0.303254\pi$
$168$	−14.5133	−	12.0305i	−1.11973	−	0.928175i
$169$	10.2667	−	17.7824i	0.789745	−	1.36788i
$170$		0			0
$171$	−11.9047	+	2.74458i	−0.910376	+	0.209884i
$172$	−0.312038	−	0.269012i	−0.0237927	−	0.0205120i
$173$	5.27925	−	9.14392i	0.401374	−	0.695200i	−0.592518	−	0.805557i	$-0.701866\pi$
$173$	5.27925	−	9.14392i	0.401374	−	0.695200i	0.993892	+	0.110357i	$0.0351995\pi$
$174$	15.0387	+	8.29881i	1.14008	+	0.629131i
$175$		0			0
$176$	8.82879	−	7.01514i	0.665495	−	0.528786i
$177$	14.2775	+	2.13602i	1.07317	+	0.160553i
$178$	−0.146798	+	0.121517i	−0.0110030	+	0.00910812i
$179$	3.01061			0.225023			0.112512	−	0.993650i	$-0.464110\pi$
$179$	3.01061			0.225023			0.112512	+	0.993650i	$0.464110\pi$
$180$		0			0
$181$	−19.5270			−1.45143			−0.725715	−	0.687996i	$-0.758491\pi$
$181$	−19.5270			−1.45143			−0.725715	+	0.687996i	$0.758491\pi$
$182$	−24.2750	+	20.0945i	−1.79938	+	1.48950i
$183$	−3.88955	−	9.87863i	−0.287524	−	0.730249i
$184$	6.36048	−	10.5241i	0.468901	−	0.775846i
$185$		0			0
$186$	4.71879	−	2.84754i	0.345999	−	0.208791i
$187$	3.41836	−	5.92078i	0.249975	−	0.432970i
$188$	14.0724	−	16.3231i	1.02633	−	1.19049i
$189$	−16.4834	+	11.3176i	−1.19899	+	0.823234i
$190$		0			0
$191$	0.482086	−	0.834997i	0.0348825	−	0.0604183i	−0.848057	−	0.529905i	$-0.822228\pi$
$191$	0.482086	−	0.834997i	0.0348825	−	0.0604183i	0.882940	+	0.469487i	$0.155561\pi$
$192$	4.55599	+	13.0860i	0.328800	+	0.944400i
$193$	−13.8507	+	7.99670i	−0.996995	+	0.575615i	−0.907358	−	0.420359i	$-0.861904\pi$
$193$	−13.8507	+	7.99670i	−0.996995	+	0.575615i	−0.0896373	+	0.995974i	$0.528571\pi$
$194$	3.07074	+	18.1217i	0.220466	+	1.30107i
$195$		0			0
$196$	14.7425	−	5.14395i	1.05303	−	0.367425i
$197$	26.0766			1.85788			0.928939	−	0.370233i	$-0.120722\pi$
$197$	26.0766			1.85788			0.928939	+	0.370233i	$0.120722\pi$
$198$	−4.59637	−	11.0421i	−0.326650	−	0.784728i
$199$		−	16.6714i		−	1.18181i	−0.806743	−	0.590903i	$-0.798772\pi$
$199$		−	16.6714i		−	1.18181i	0.806743	−	0.590903i	$-0.201228\pi$
$200$		0			0
$201$	8.88050	+	1.32859i	0.626382	+	0.0937113i
$202$	−0.793533	−	4.68297i	−0.0558328	−	0.329493i
$203$	−23.3681	+	13.4916i	−1.64012	+	0.946924i
$204$	5.48110	+	6.36648i	0.383753	+	0.445743i
$205$		0			0
$206$	1.89025	−	5.08748i	0.131700	−	0.354462i
$207$	−8.89223	−	9.54159i	−0.618052	−	0.663187i
$208$	22.9106	−	3.41167i	1.58856	−	0.236557i
$209$	9.94233	+	5.74021i	0.687726	+	0.397059i
$210$		0			0
$211$	−18.9378	+	10.9337i	−1.30373	+	0.752709i	−0.981042	−	0.193796i	$-0.937920\pi$
$211$	−18.9378	+	10.9337i	−1.30373	+	0.752709i	−0.322689	+	0.946505i	$0.604587\pi$
$212$	−2.82259	+	14.8457i	−0.193856	+	1.01960i
$213$	5.89326	−	7.40651i	0.403799	−	0.507486i
$214$	0.606471	−	0.502027i	0.0414575	−	0.0343179i
$215$		0			0
$216$	14.6722	−	0.852694i	0.998316	−	0.0580185i
$217$			8.65806i			0.587747i
$218$	14.0052	+	16.9189i	0.948555	+	1.14589i
$219$	17.6108	+	14.0127i	1.19003	+	0.946890i
$220$		0			0
$221$	12.1619	−	7.02169i	0.818100	−	0.472330i
$222$	−0.203523	−	10.5165i	−0.0136596	−	0.705821i
$223$	1.23432	−	2.13791i	0.0826563	−	0.143165i	−0.821734	−	0.569871i	$-0.806993\pi$
$223$	1.23432	−	2.13791i	0.0826563	−	0.143165i	0.904390	+	0.426707i	$0.140326\pi$
$224$	−21.2987	−	4.49329i	−1.42308	−	0.300221i
$225$		0			0
$226$	−3.73630	+	10.0560i	−0.248535	+	0.668913i
$227$	−7.81598	−	4.51256i	−0.518765	−	0.299509i	0.217664	−	0.976024i	$-0.430156\pi$
$227$	−7.81598	−	4.51256i	−0.518765	−	0.299509i	−0.736429	+	0.676515i	$0.763490\pi$
$228$	−10.6908	+	9.20401i	−0.708014	+	0.609550i
$229$	6.05048	+	10.4797i	0.399827	+	0.692521i	0.993704	−	0.112035i	$-0.0357368\pi$
$229$	6.05048	+	10.4797i	0.399827	+	0.692521i	−0.593877	+	0.804556i	$0.702403\pi$
$230$		0			0
$231$	18.5825	+	2.78007i	1.22264	+	0.182915i
$232$	19.8297	+	0.397244i	1.30188	+	0.0260803i
$233$	−12.9280			−0.846943			−0.423471	−	0.905909i	$-0.639189\pi$
$233$	−12.9280			−0.846943			−0.423471	+	0.905909i	$0.639189\pi$
$234$	3.16431	−	24.3637i	0.206858	−	1.59270i
$235$		0			0
$236$	15.7392	−	5.49172i	1.02453	−	0.357480i
$237$	8.04813	−	3.16882i	0.522782	−	0.205837i
$238$	−13.0117	+	2.20485i	−0.843426	+	0.142919i
$239$	4.58101	+	7.93455i	0.296321	+	0.513243i	0.975291	−	0.220923i	$-0.0709068\pi$
$239$	4.58101	+	7.93455i	0.296321	+	0.513243i	−0.678970	+	0.734166i	$0.737573\pi$
$240$		0			0
$241$	5.29982	−	9.17956i	0.341391	−	0.591307i	−0.643300	−	0.765614i	$-0.722435\pi$
$241$	5.29982	−	9.17956i	0.341391	−	0.591307i	0.984691	+	0.174307i	$0.0557685\pi$
$242$	1.50352	−	4.04662i	0.0966500	−	0.260127i
$243$	3.38559	−	15.2164i	0.217186	−	0.976130i
$244$	−9.28503	−	8.00476i	−0.594413	−	0.512452i
$245$		0			0
$246$	0.229815	−	0.138681i	0.0146524	−	0.00884195i
$247$	11.7910	+	20.4226i	0.750245	+	1.29946i
$248$	3.29175	−	5.44656i	0.209027	−	0.345857i
$249$	−12.4326	+	4.89515i	−0.787886	+	0.310217i
$250$		0			0
$251$	10.2219			0.645198			0.322599	−	0.946536i	$-0.395443\pi$
$251$	10.2219			0.645198			0.322599	+	0.946536i	$0.395443\pi$
$252$	−10.7617	+	20.4264i	−0.677925	+	1.28675i
$253$			12.2564i			0.770554i
$254$	−16.7373	−	20.2194i	−1.05019	−	1.26868i
$255$		0			0
$256$	11.6902	+	10.9243i	0.730635	+	0.682769i
$257$	−3.22348	−	5.58322i	−0.201075	−	0.348272i	0.747800	−	0.663924i	$-0.231110\pi$
$257$	−3.22348	−	5.58322i	−0.201075	−	0.348272i	−0.948875	+	0.315652i	$0.897777\pi$
$258$	−0.243788	+	0.441780i	−0.0151776	+	0.0275040i
$259$	14.3101	+	8.26192i	0.889184	+	0.513371i
$260$		0			0
$261$	6.15672	−	20.1157i	0.381091	−	1.24513i
$262$	4.68249	−	12.6026i	0.289285	−	0.778591i
$263$	15.7050	+	9.06727i	0.968410	+	0.559112i	0.898751	−	0.438459i	$-0.144476\pi$
$263$	15.7050	+	9.06727i	0.968410	+	0.559112i	0.0696586	+	0.997571i	$0.477809\pi$
$264$	−10.6328	−	8.81384i	−0.654402	−	0.542454i
$265$		0			0
$266$	−3.70244	−	21.8497i	−0.227011	−	1.33969i
$267$	0.182636	+	0.145321i	0.0111772	+	0.00889351i
$268$	9.78963	−	3.41580i	0.597997	−	0.208653i
$269$			3.40907i			0.207854i	0.994585	+	0.103927i	$0.0331409\pi$
$269$			3.40907i			0.207854i	−0.994585	+	0.103927i	$0.966859\pi$
$270$		0			0
$271$			8.61740i			0.523470i	0.965140	+	0.261735i	$0.0842946\pi$
$271$			8.61740i			0.523470i	−0.965140	+	0.261735i	$0.915705\pi$
$272$	9.02363	+	3.55999i	0.547138	+	0.215856i
$273$	30.2013	+	24.0307i	1.82786	+	1.45440i
$274$	−1.11665	+	0.189218i	−0.0674596	+	0.0114311i
$275$		0			0
$276$	−14.2164	−	4.97122i	−0.855725	−	0.299232i
$277$	6.25343	+	3.61042i	0.375732	+	0.216929i	0.675960	−	0.736938i	$-0.263729\pi$
$277$	6.25343	+	3.61042i	0.375732	+	0.216929i	−0.300228	+	0.953868i	$0.597063\pi$
$278$	9.68081	+	3.59691i	0.580617	+	0.215728i
$279$	−4.60202	−	4.93808i	−0.275515	−	0.295635i
$280$		0			0
$281$	−23.6911	−	13.6781i	−1.41329	−	0.815964i	−0.417595	−	0.908633i	$-0.637127\pi$
$281$	−23.6911	−	13.6781i	−1.41329	−	0.815964i	−0.995697	+	0.0926691i	$0.970460\pi$
$282$	−23.1101	−	12.7529i	−1.37619	−	0.759424i
$283$	2.69628	+	4.67010i	0.160277	+	0.277609i	0.934968	−	0.354732i	$-0.115428\pi$
$283$	2.69628	+	4.67010i	0.160277	+	0.277609i	−0.774691	+	0.632340i	$0.782094\pi$
$284$	2.04140	−	10.7369i	0.121135	−	0.637120i
$285$		0			0
$286$	−17.7844	+	14.7217i	−1.05161	+	0.870510i
$287$			0.421665i			0.0248901i
$288$	14.5360	−	8.75819i	0.856540	−	0.516081i
$289$	−11.1188			−0.654046
$290$		0			0
$291$	20.9458	−	8.24707i	1.22786	−	0.483452i
$292$	25.5298	+	4.85395i	1.49402	+	0.284056i
$293$	−8.93355	−	15.4734i	−0.521904	−	0.903964i	−0.999675	−	0.0254795i	$-0.991889\pi$
$293$	−8.93355	−	15.4734i	−0.521904	−	0.903964i	0.477772	−	0.878484i	$-0.341445\pi$
$294$	−9.88032	−	16.3732i	−0.576232	−	0.954903i
$295$		0			0
$296$	−5.86095	−	10.6380i	−0.340661	−	0.618320i
$297$	−12.0761	+	8.29153i	−0.700727	+	0.481123i
$298$	0.150885	+	0.0560615i	0.00874056	+	0.00324755i
$299$	−12.5880	+	21.8031i	−0.727983	+	1.26090i
$300$		0			0
$301$	−0.396333	−	0.686469i	−0.0228443	−	0.0395674i
$302$	0.400760	+	2.36506i	0.0230612	+	0.136094i
$303$	−5.41276	+	2.13119i	−0.310955	+	0.122433i
$304$	−5.97804	+	15.1527i	−0.342864	+	0.869068i
$305$		0			0
$306$	6.24925	−	8.17366i	0.357246	−	0.467257i
$307$	−5.37209			−0.306601			−0.153301	−	0.988180i	$-0.548990\pi$
$307$	−5.37209			−0.306601			−0.153301	+	0.988180i	$0.548990\pi$
$308$	20.4848	−	7.14757i	1.16723	−	0.407270i
$309$	−6.57389	−	0.983502i	−0.373976	−	0.0559495i
$310$		0			0
$311$	−15.1587	−	26.2557i	−0.859572	−	1.48882i	−0.872338	−	0.488903i	$-0.837397\pi$
$311$	−15.1587	−	26.2557i	−0.859572	−	1.48882i	0.0127664	−	0.999919i	$-0.495936\pi$
$312$	−9.86246	−	26.5995i	−0.558352	−	1.50590i
$313$	−21.4061	−	12.3588i	−1.20994	−	0.698561i	−0.247196	−	0.968965i	$-0.579509\pi$
$313$	−21.4061	−	12.3588i	−1.20994	−	0.698561i	−0.962747	+	0.270404i	$0.912843\pi$
$314$	29.8197	+	11.0795i	1.68282	+	0.625252i
$315$		0			0
$316$	6.52148	−	7.56452i	0.366862	−	0.425537i
$317$	12.1999	−	21.1308i	0.685215	−	1.18683i	−0.288155	−	0.957584i	$-0.593042\pi$
$317$	12.1999	−	21.1308i	0.685215	−	1.18683i	0.973369	−	0.229243i	$-0.0736249\pi$
$318$	18.5044	−	0.358111i	1.03767	−	0.0200819i
$319$	−17.1200	+	9.88424i	−0.958537	+	0.553411i
$320$		0			0
$321$	−0.754530	−	0.600368i	−0.0421137	−	0.0335093i
$322$	18.2250	−	15.0864i	1.01564	−	0.840733i
$323$			9.87589i			0.549509i
$324$	−4.71937	−	17.3703i	−0.262187	−	0.965017i
$325$		0			0
$326$	−1.48233	−	1.79071i	−0.0820985	−	0.0991785i
$327$	16.7487	−	21.0494i	0.926205	−	1.16403i
$328$	0.160315	−	0.265258i	0.00885191	−	0.0146464i
$329$	35.9101	−	20.7327i	1.97979	−	1.14303i
$330$		0			0
$331$	24.4351	+	14.1076i	1.34308	+	0.775426i	0.987258	−	0.159129i	$-0.0508685\pi$
$331$	24.4351	+	14.1076i	1.34308	+	0.775426i	0.355819	+	0.934555i	$0.384202\pi$
$332$	−10.0743	+	11.6856i	−0.552898	+	0.641328i
$333$	−12.5531	+	2.89408i	−0.687908	+	0.158595i
$334$	−3.23290	−	1.20119i	−0.176897	−	0.0657259i
$335$		0			0
$336$	−0.0181210	+	26.6597i	−0.000988584	+	1.45440i
$337$	−24.8043	+	14.3208i	−1.35118	+	0.780101i	−0.988414	−	0.151781i	$-0.951499\pi$
$337$	−24.8043	+	14.3208i	−1.35118	+	0.780101i	−0.362761	+	0.931882i	$0.618166\pi$
$338$	−28.6304	+	4.85145i	−1.55729	+	0.263884i
$339$	12.9940	+	1.94400i	0.705738	+	0.105584i
$340$		0			0
$341$			6.34309i			0.343498i
$342$	13.7254	+	10.4939i	0.742186	+	0.567446i
$343$	3.10557			0.167685
$344$	−0.0116696	+	0.582524i	−0.000629180	+	0.0314076i
$345$		0			0
$346$	−14.7221	+	2.49467i	−0.791465	+	0.134114i
$347$	−18.0974	+	10.4485i	−0.971520	+	0.560907i	−0.899699	−	0.436510i	$-0.856214\pi$
$347$	−18.0974	+	10.4485i	−0.971520	+	0.560907i	−0.0718207	+	0.997418i	$0.522881\pi$
$348$	−4.52096	−	23.8668i	−0.242349	−	1.27939i
$349$	6.50620	−	11.2691i	0.348269	−	0.603219i	−0.637673	−	0.770307i	$-0.720103\pi$
$349$	6.50620	−	11.2691i	0.348269	−	0.603219i	0.985942	+	0.167088i	$0.0534363\pi$
$350$		0			0
$351$	−29.9982	+	2.34707i	−1.60119	+	0.125277i
$352$	−15.6039	−	3.29189i	−0.831693	−	0.175458i
$353$	−14.2274	+	24.6426i	−0.757249	+	1.31159i	0.186999	+	0.982360i	$0.440124\pi$
$353$	−14.2274	+	24.6426i	−0.757249	+	1.31159i	−0.944248	+	0.329234i	$0.893210\pi$
$354$	−10.5483	−	17.4801i	−0.560636	−	0.929058i
$355$		0			0
$356$	0.264761	+	0.0503387i	0.0140323	+	0.00266795i
$357$	5.92155	+	15.0395i	0.313402	+	0.795973i
$358$	−2.71492	−	3.27974i	−0.143488	−	0.173340i
$359$	−5.90878			−0.311854			−0.155927	−	0.987769i	$-0.549836\pi$
$359$	−5.90878			−0.311854			−0.155927	+	0.987769i	$0.549836\pi$
$360$		0			0
$361$	2.41614			0.127165
$362$	17.6092	+	21.2726i	0.925517	+	1.11806i
$363$	−5.22892	−	0.782284i	−0.274447	−	0.0410593i
$364$	43.7816	+	8.32415i	2.29478	+	0.436304i
$365$		0			0
$366$	−7.25419	+	13.1457i	−0.379183	+	0.687135i
$367$	−12.1136	+	20.9815i	−0.632327	+	1.09522i	0.354747	+	0.934962i	$0.384567\pi$
$367$	−12.1136	+	20.9815i	−0.632327	+	1.09522i	−0.987075	+	0.160261i	$0.948766\pi$
$368$	−17.2007	+	2.56140i	−0.896648	+	0.133522i
$369$	−0.224127	−	0.240495i	−0.0116676	−	0.0125196i
$370$		0			0
$371$	−14.5373	+	25.1794i	−0.754741	+	1.30725i
$372$	−7.35743	−	2.57277i	−0.381465	−	0.133392i
$373$	6.56430	−	3.78990i	0.339887	−	0.196234i	−0.320335	−	0.947304i	$-0.603796\pi$
$373$	6.56430	−	3.78990i	0.339887	−	0.196234i	0.660222	+	0.751071i	$0.270462\pi$
$374$	−9.53270	+	1.61532i	−0.492924	+	0.0835264i
$375$		0			0
$376$	−30.4726	−	0.610451i	−1.57151	−	0.0314816i
$377$	−40.6066			−2.09135
$378$	27.1938	+	7.75090i	1.39870	+	0.398663i
$379$			27.0962i			1.39184i	0.718120	+	0.695919i	$0.245003\pi$
$379$			27.0962i			1.39184i	−0.718120	+	0.695919i	$0.754997\pi$
$380$		0			0
$381$	−20.0160	+	25.1556i	−1.02545	+	1.28876i
$382$	−1.34438	+	0.227806i	−0.0687845	+	0.0116556i
$383$	−22.8862	+	13.2134i	−1.16943	+	0.675171i	−0.953546	−	0.301247i	$-0.902597\pi$
$383$	−22.8862	+	13.2134i	−1.16943	+	0.675171i	−0.215885	+	0.976419i	$0.569264\pi$
$384$	10.1473	−	16.7640i	0.517827	−	0.855486i
$385$		0			0
$386$	21.2019	+	7.87758i	1.07915	+	0.400958i
$387$	0.590926	+	0.180862i	0.0300384	+	0.00919372i
$388$	16.9726	−	19.6872i	0.861653	−	0.999465i
$389$	17.7208	+	10.2311i	0.898482	+	0.518739i	0.876707	−	0.481024i	$-0.159735\pi$
$389$	17.7208	+	10.2311i	0.898482	+	0.518739i	0.0217745	+	0.999763i	$0.493068\pi$
$390$		0			0
$391$	−9.13087	+	5.27171i	−0.461768	+	0.266602i
$392$	−18.8984	−	11.4217i	−0.954511	−	0.576881i
$393$	−16.2847	−	2.43631i	−0.821454	−	0.122895i
$394$	−23.5155	−	28.4077i	−1.18469	−	1.43116i
$395$		0			0
$396$	−7.88428	+	14.9649i	−0.396200	+	0.752013i
$397$			0.127520i			0.00640003i	0.999995	+	0.00320001i	$0.00101860\pi$
$397$			0.127520i			0.00640003i	−0.999995	+	0.00320001i	$0.998981\pi$
$398$	−18.1618	+	15.0340i	−0.910367	+	0.753588i
$399$	−25.2547	+	9.94362i	−1.26432	+	0.497804i
$400$		0			0
$401$	12.8500	−	7.41894i	0.641698	−	0.370484i	−0.143571	−	0.989640i	$-0.545858\pi$
$401$	12.8500	−	7.41894i	0.641698	−	0.370484i	0.785268	+	0.619156i	$0.212525\pi$
$402$	−6.56095	−	10.8725i	−0.327230	−	0.542270i
$403$	−6.51470	+	11.2838i	−0.324520	+	0.562086i
$404$	−4.38601	+	5.08751i	−0.218212	+	0.253113i
$405$		0			0
$406$	35.7707	+	13.2906i	1.77527	+	0.659602i
$407$	10.4839	+	6.05287i	0.519667	+	0.300030i
$408$	1.99285	−	11.7123i	0.0986605	−	0.579844i
$409$	−7.36570	−	12.7578i	−0.364210	−	0.630831i	0.624439	−	0.781074i	$-0.285328\pi$
$409$	−7.36570	−	12.7578i	−0.364210	−	0.630831i	−0.988649	+	0.150243i	$0.951994\pi$
$410$		0			0
$411$	0.508181	+	1.29067i	0.0250667	+	0.0636641i
$412$	−7.24688	+	2.52858i	−0.357028	+	0.124574i
$413$	32.0726			1.57819
$414$	−2.37569	+	18.2916i	−0.116759	+	0.898984i
$415$		0			0
$416$	−24.3771	−	21.8821i	−1.19518	−	1.07286i
$417$	1.87148	−	12.5093i	0.0916465	−	0.612581i
$418$	−2.71249	−	16.0076i	−0.132672	−	0.782956i
$419$	−5.63765	−	9.76469i	−0.275417	−	0.477037i	0.694823	−	0.719181i	$-0.255483\pi$
$419$	−5.63765	−	9.76469i	−0.275417	−	0.477037i	−0.970240	+	0.242144i	$0.922149\pi$
$420$		0			0
$421$	0.0177583	−	0.0307583i	0.000865488	−	0.00149907i	−0.865592	−	0.500749i	$-0.833058\pi$
$421$	0.0177583	−	0.0307583i	0.000865488	−	0.00149907i	0.866458	+	0.499250i	$0.166391\pi$
$422$	28.9890	+	10.7709i	1.41116	+	0.524317i
$423$	−9.46112	+	30.9121i	−0.460016	+	1.50300i
$424$	18.7182	−	10.3127i	0.909034	−	0.500828i
$425$		0			0
$426$	−13.3831	+	0.259000i	−0.648412	+	0.0125486i
$427$	−11.7933	−	20.4266i	−0.570719	−	0.988515i
$428$	−1.09381	−	0.207965i	−0.0528715	−	0.0100524i
$429$	22.1261	+	17.6054i	1.06826	+	0.849999i
$430$		0			0
$431$	−17.3085			−0.833722			−0.416861	−	0.908970i	$-0.636870\pi$
$431$	−17.3085			−0.833722			−0.416861	+	0.908970i	$0.636870\pi$
$432$	−14.1601	−	15.2149i	−0.681277	−	0.732025i
$433$			16.3482i			0.785642i	0.919615	+	0.392821i	$0.128501\pi$
$433$			16.3482i			0.785642i	−0.919615	+	0.392821i	$0.871499\pi$
$434$	9.43205	−	7.80771i	0.452753	−	0.374782i
$435$		0			0
$436$	5.80169	−	30.5145i	0.277850	−	1.46138i
$437$	−8.85240	−	15.3328i	−0.423468	−	0.733468i
$438$	−0.615837	−	31.8216i	−0.0294258	−	1.52050i
$439$	9.80512	+	5.66099i	0.467973	+	0.270184i	0.715391	−	0.698725i	$-0.246249\pi$
$439$	9.80512	+	5.66099i	0.467973	+	0.270184i	−0.247418	+	0.968909i	$0.579582\pi$
$440$		0			0
$441$	−17.1341	+	15.9680i	−0.815907	+	0.760380i
$442$	−18.6169	−	6.91709i	−0.885514	−	0.329013i
$443$	−31.1828	−	18.0034i	−1.48154	−	0.855368i	−0.481760	−	0.876303i	$-0.660002\pi$
$443$	−31.1828	−	18.0034i	−1.48154	−	0.855368i	−0.999781	+	0.0209350i	$0.993336\pi$
$444$	−11.2731	+	9.70534i	−0.534997	+	0.460595i
$445$		0			0
$446$	−3.44212	+	0.583270i	−0.162989	+	0.0276186i
$447$	0.0291689	−	0.194970i	0.00137964	−	0.00922174i
$448$	14.3119	+	27.2547i	0.676175	+	1.28767i
$449$		−	0.577403i		−	0.0272493i	−0.999907	−	0.0136247i	$-0.995663\pi$
$449$		−	0.577403i		−	0.0272493i	0.999907	−	0.0136247i	$-0.00433700\pi$
$450$		0			0
$451$			0.308921i			0.0145465i
$452$	14.3243	−	4.99803i	0.673757	−	0.235087i
$453$	2.73362	−	1.07632i	0.128437	−	0.0505699i
$454$	2.13238	+	12.5841i	0.100077	+	0.590599i
$455$		0			0
$456$	19.6676	+	3.34644i	0.921019	+	0.156711i
$457$	−20.1532	−	11.6355i	−0.942727	−	0.544283i	−0.0519127	−	0.998652i	$-0.516532\pi$
$457$	−20.1532	−	11.6355i	−0.942727	−	0.544283i	−0.890814	+	0.454368i	$0.849865\pi$
$458$	5.96035	−	16.0419i	0.278509	−	0.749587i
$459$	−11.3713	−	5.43021i	−0.530765	−	0.253461i
$460$		0			0
$461$	6.87023	+	3.96653i	0.319979	+	0.184740i	0.651383	−	0.758749i	$-0.274189\pi$
$461$	6.87023	+	3.96653i	0.319979	+	0.184740i	−0.331404	+	0.943489i	$0.607522\pi$
$462$	−13.7288	−	22.7507i	−0.638721	−	1.05846i
$463$	−15.5833	−	26.9910i	−0.724216	−	1.25438i	−0.959296	−	0.282403i	$-0.908868\pi$
$463$	−15.5833	−	26.9910i	−0.724216	−	1.25438i	0.235079	−	0.971976i	$-0.424465\pi$
$464$	−17.4494	−	21.9606i	−0.810068	−	1.01950i
$465$		0			0
$466$	11.6583	+	14.0837i	0.540060	+	0.652416i
$467$		−	28.3340i		−	1.31114i	−0.755133	−	0.655571i	$-0.772428\pi$
$467$		−	28.3340i		−	1.31114i	0.755133	−	0.655571i	$-0.227572\pi$
$468$	−29.3952	+	18.5236i	−1.35879	+	0.856254i
$469$	19.9488			0.921152
$470$		0			0
$471$	5.76468	−	38.5321i	0.265622	−	1.77546i
$472$	−20.1760	−	12.1938i	−0.928676	−	0.561267i
$473$	−0.290363	−	0.502923i	−0.0133509	−	0.0231244i
$474$	−10.7098	−	5.91000i	−0.491917	−	0.271455i
$475$		0			0
$476$	14.1358	+	12.1866i	0.647911	+	0.558574i
$477$	−5.09230	−	22.0880i	−0.233160	−	1.01134i
$478$	4.51277	−	12.1458i	0.206409	−	0.555536i
$479$	12.2322	−	21.1868i	0.558904	−	0.968049i	−0.438685	−	0.898641i	$-0.644556\pi$
$479$	12.2322	−	21.1868i	0.558904	−	0.968049i	0.997588	−	0.0694084i	$-0.0221112\pi$
$480$		0			0
$481$	12.4333	+	21.5350i	0.566908	+	0.981914i
$482$	−14.7795	+	2.50439i	−0.673186	+	0.114072i
$483$	−22.6744	−	18.0417i	−1.03172	−	0.820924i
$484$	−5.76422	+	2.01125i	−0.262010	+	0.0914206i
$485$		0			0
$486$	−19.6297	+	10.0336i	−0.890422	+	0.455136i
$487$	4.05853			0.183909			0.0919547	−	0.995763i	$-0.470688\pi$
$487$	4.05853			0.183909			0.0919547	+	0.995763i	$0.470688\pi$
$488$	−0.347241	+	17.3336i	−0.0157188	+	0.784657i
$489$	−1.77270	+	2.22788i	−0.0801641	+	0.100748i
$490$		0			0
$491$	8.28040	+	14.3421i	0.373689	+	0.647249i	0.990130	−	0.140153i	$-0.0447593\pi$
$491$	8.28040	+	14.3421i	0.373689	+	0.647249i	−0.616441	+	0.787401i	$0.711426\pi$
$492$	−0.358322	−	0.125299i	−0.0161544	−	0.00564891i
$493$	−14.7273	−	8.50280i	−0.663283	−	0.382947i
$494$	11.6154	−	31.2619i	0.522600	−	1.40654i
$495$		0			0
$496$	−8.90191	+	1.32561i	−0.399708	+	0.0595215i
$497$	10.5140	−	18.2107i	0.471615	−	0.816862i
$498$	16.5443	+	9.12968i	0.741368	+	0.409111i
$499$	−17.4221	+	10.0586i	−0.779919	+	0.450287i	−0.836402	−	0.548117i	$-0.815345\pi$
$499$	−17.4221	+	10.0586i	−0.779919	+	0.450287i	0.0564823	+	0.998404i	$0.482012\pi$
$500$		0			0
$501$	−0.624979	+	4.17746i	−0.0279220	+	0.186635i
$502$	−9.21793	−	11.1357i	−0.411416	−	0.497009i
$503$		−	21.9942i		−	0.980674i	−0.871533	−	0.490337i	$-0.836874\pi$
$503$		−	21.9942i		−	0.980674i	0.871533	−	0.490337i	$-0.163126\pi$
$504$	31.9572	−	6.69650i	1.42349	−	0.298286i
$505$		0			0
$506$	13.3521	−	11.0527i	0.593572	−	0.491350i
$507$	13.0295	+	33.0921i	0.578660	+	1.46967i
$508$	−6.93345	+	36.4671i	−0.307622	+	1.61797i
$509$	−19.2701	+	11.1256i	−0.854134	+	0.493134i	−0.862044	−	0.506834i	$-0.830816\pi$
$509$	−19.2701	+	11.1256i	−0.854134	+	0.493134i	0.00790954	+	0.999969i	$0.497482\pi$
$510$		0			0
$511$	43.3005	+	24.9996i	1.91550	+	1.10592i
$512$	1.35887	−	22.5866i	0.0600541	−	0.998195i
$513$	9.11856	−	19.0949i	0.402594	−	0.843061i
$514$	−3.17546	+	8.54651i	−0.140063	+	0.376970i
$515$		0			0
$516$	0.701118	−	0.132809i	0.0308650	−	0.00584660i
$517$	26.3086	−	15.1893i	1.15705	−	0.668023i
$518$	−3.90411	−	23.0398i	−0.171537	−	1.01231i
$519$	6.69992	+	17.0164i	0.294094	+	0.746935i
$520$		0			0
$521$		−	18.5073i		−	0.810820i	−0.914135	−	0.405410i	$-0.867129\pi$
$521$		−	18.5073i		−	0.810820i	0.914135	−	0.405410i	$-0.132871\pi$
$522$	−27.4660	+	11.4330i	−1.20215	+	0.500407i
$523$	−0.982630			−0.0429674			−0.0214837	−	0.999769i	$-0.506839\pi$
$523$	−0.982630			−0.0429674			−0.0214837	+	0.999769i	$0.506839\pi$
$524$	−17.9518	+	6.26375i	−0.784229	+	0.273633i
$525$		0			0
$526$	−4.28467	−	25.2856i	−0.186821	−	1.10251i
$527$	−4.72552	+	2.72828i	−0.205847	+	0.118846i
$528$	−0.0132759	+	19.5315i	−0.000577759	+	0.849999i
$529$	−2.04924	+	3.54939i	−0.0890973	+	0.154321i
$530$		0			0
$531$	−18.2924	+	17.0475i	−0.793824	+	0.739800i
$532$	−20.4641	+	23.7371i	−0.887233	+	1.02914i
$533$	−0.317279	+	0.549543i	−0.0137429	+	0.0238034i
$534$	−0.00638665	−	0.330012i	−0.000276377	−	0.0142810i
$535$		0			0
$536$	−12.5493	−	7.58446i	−0.542047	−	0.327599i
$537$	−3.24674	+	4.08043i	−0.140107	+	0.176084i
$538$	3.71382	−	3.07425i	0.160114	−	0.132540i
$539$	22.0091			0.948000
$540$		0			0
$541$	27.5892			1.18615			0.593077	−	0.805146i	$-0.297913\pi$
$541$	27.5892			1.18615			0.593077	+	0.805146i	$0.297913\pi$
$542$	9.38776	−	7.77104i	0.403239	−	0.333795i
$543$	21.0586	−	26.4659i	0.903710	−	1.13576i
$544$	−4.25913	−	13.0406i	−0.182609	−	0.559113i
$545$		0			0
$546$	−1.05611	−	54.5717i	−0.0451975	−	2.33545i
$547$	−23.0955	+	40.0026i	−0.987492	+	1.71039i	−0.357198	+	0.934029i	$0.616268\pi$
$547$	−23.0955	+	40.0026i	−0.987492	+	1.71039i	−0.630293	+	0.776357i	$0.717065\pi$
$548$	1.21312	+	1.04584i	0.0518218	+	0.0446763i
$549$	17.5836	+	5.38174i	0.750452	+	0.229687i
$550$		0			0
$551$	14.2781	−	24.7305i	0.608269	−	1.05355i
$552$	7.40449	+	19.9702i	0.315156	+	0.849989i
$553$	16.6416	−	9.60803i	0.707673	−	0.408575i
$554$	−1.70608	−	10.0683i	−0.0724843	−	0.427760i
$555$		0			0
$556$	−4.81156	−	13.7899i	−0.204056	−	0.584821i
$557$	44.3389			1.87870			0.939350	−	0.342960i	$-0.111429\pi$
$557$	44.3389			1.87870			0.939350	+	0.342960i	$0.111429\pi$
$558$	−1.22950	+	9.46651i	−0.0520487	+	0.400749i
$559$		−	1.19287i		−	0.0504532i
$560$		0			0
$561$	4.33826	+	11.0183i	0.183162	+	0.465191i
$562$	6.46347	+	38.1436i	0.272645	+	1.60899i
$563$	24.4824	−	14.1349i	1.03181	−	0.595717i	0.114309	−	0.993445i	$-0.463535\pi$
$563$	24.4824	−	14.1349i	1.03181	−	0.595717i	0.917503	+	0.397728i	$0.130201\pi$
$564$	6.94743	+	36.6765i	0.292539	+	1.54436i
$565$		0			0
$566$	2.65612	−	7.14875i	0.111645	−	0.300484i
$567$	2.43693	−	34.5461i	0.102341	−	1.45080i
$568$	−13.5377	+	7.45852i	−0.568028	+	0.312953i
$569$	−22.8891	−	13.2150i	−0.959561	−	0.554003i	−0.0635229	−	0.997980i	$-0.520234\pi$
$569$	−22.8891	−	13.2150i	−0.959561	−	0.554003i	−0.896038	+	0.443978i	$0.853567\pi$
$570$		0			0
$571$	−14.6651	+	8.46690i	−0.613715	+	0.354329i	−0.774418	−	0.632674i	$-0.781957\pi$
$571$	−14.6651	+	8.46690i	−0.613715	+	0.354329i	0.160703	+	0.987003i	$0.448624\pi$
$572$	32.0754	+	6.09846i	1.34114	+	0.254989i
$573$	0.611817	+	1.55389i	0.0255590	+	0.0649145i
$574$	0.459360	−	0.380251i	0.0191733	−	0.0158714i
$575$		0			0
$576$	−22.6495	−	7.93740i	−0.943727	−	0.330725i
$577$		−	7.68326i		−	0.319858i	−0.987129	−	0.159929i	$-0.948873\pi$
$577$		−	7.68326i		−	0.319858i	0.987129	−	0.159929i	$-0.0511265\pi$
$578$	10.0268	+	12.1128i	0.417058	+	0.503824i
$579$	4.09872	−	27.3965i	0.170337	−	1.13856i
$580$		0			0
$581$	−25.7077	+	14.8423i	−1.06654	+	0.615764i
$582$	−27.8729	−	15.3812i	−1.15537	−	0.637570i
$583$	−10.6504	+	18.4470i	−0.441094	+	0.763997i
$584$	−17.7345	−	32.1892i	−0.733859	−	1.33200i
$585$		0			0
$586$	−8.80047	+	23.6858i	−0.363544	+	0.978452i
$587$	31.5153	+	18.1954i	1.30078	+	0.751003i	0.980537	−	0.196334i	$-0.0629036\pi$
$587$	31.5153	+	18.1954i	1.30078	+	0.751003i	0.320239	+	0.947337i	$0.396237\pi$
$588$	−8.92693	+	25.5287i	−0.368141	+	1.05278i
$589$	−4.58141	−	7.93523i	−0.188774	−	0.326965i
$590$		0			0
$591$	−28.1219	+	35.3429i	−1.15678	+	1.45381i
$592$	−6.30366	+	15.9781i	−0.259079	+	0.656695i
$593$	21.9804			0.902628			0.451314	−	0.892365i	$-0.350955\pi$
$593$	21.9804			0.902628			0.451314	+	0.892365i	$0.350955\pi$
$594$	19.9228	+	5.67848i	0.817443	+	0.232991i
$595$		0			0
$596$	−0.0749932	−	0.214929i	−0.00307184	−	0.00880385i
$597$	22.5956	+	17.9790i	0.924778	+	0.735833i
$598$	35.1038	−	5.94837i	1.43550	−	0.243247i
$599$	6.71878	+	11.6373i	0.274522	+	0.475486i	0.970014	−	0.243048i	$-0.0781471\pi$
$599$	6.71878	+	11.6373i	0.274522	+	0.475486i	−0.695493	+	0.718533i	$0.744814\pi$
$600$		0			0
$601$	18.6923	−	32.3760i	0.762475	−	1.32064i	−0.179097	−	0.983831i	$-0.557317\pi$
$601$	18.6923	−	32.3760i	0.762475	−	1.32064i	0.941571	−	0.336813i	$-0.109349\pi$
$602$	−0.390429	+	1.05081i	−0.0159127	+	0.0428279i
$603$	−11.3777	+	10.6034i	−0.463337	+	0.431804i
$604$	2.21508	−	2.56936i	0.0901304	−	0.104546i
$605$		0			0
$606$	7.20285	+	3.97476i	0.292596	+	0.161464i
$607$	−23.8250	−	41.2660i	−0.967025	−	1.67494i	−0.704072	−	0.710128i	$-0.748637\pi$
$607$	−23.8250	−	41.2660i	−0.967025	−	1.67494i	−0.262953	−	0.964809i	$-0.584696\pi$
$608$	21.8982	−	7.15205i	0.888090	−	0.290054i
$609$	6.91512	−	46.2218i	0.280215	−	1.87300i
$610$		0			0
$611$	62.4008			2.52447
$612$	−14.5398	+	0.562983i	−0.587738	+	0.0227572i
$613$			23.4840i			0.948509i	0.880388	+	0.474254i	$0.157282\pi$
$613$			23.4840i			0.948509i	−0.880388	+	0.474254i	$0.842718\pi$
$614$	4.84447	+	5.85233i	0.195507	+	0.236181i
$615$		0			0
$616$	−26.2594	−	15.8705i	−1.05802	−	0.639441i
$617$	−11.4664	−	19.8603i	−0.461619	−	0.799547i	0.537423	−	0.843313i	$-0.319398\pi$
$617$	−11.4664	−	19.8603i	−0.461619	−	0.799547i	−0.999042	+	0.0437658i	$0.986064\pi$
$618$	4.85682	+	8.04848i	0.195370	+	0.323757i
$619$	−22.6185	−	13.0588i	−0.909116	−	0.524878i	−0.0289695	−	0.999580i	$-0.509223\pi$
$619$	−22.6185	−	13.0588i	−0.909116	−	0.524878i	−0.880147	+	0.474702i	$0.842556\pi$
$620$		0			0
$621$	22.5219	−	1.76212i	0.903773	−	0.0707114i
$622$	−14.9329	+	40.1908i	−0.598754	+	1.61150i
$623$	0.449056	+	0.259263i	0.0179910	+	0.0103871i
$624$	−20.0835	+	34.7312i	−0.803985	+	1.39036i
$625$		0			0
$626$	5.84006	+	34.4647i	0.233416	+	1.37749i
$627$	−18.5022	+	7.28493i	−0.738905	+	0.290932i
$628$	−14.8210	−	42.4767i	−0.591422	−	1.69501i
$629$			10.4138i			0.415226i
$630$		0			0
$631$		−	16.5066i		−	0.657117i	−0.944484	−	0.328558i	$-0.893437\pi$
$631$		−	16.5066i		−	0.657117i	0.944484	−	0.328558i	$-0.106563\pi$
$632$	−14.1217	−	0.282897i	−0.561732	−	0.0112530i
$633$	5.60409	−	37.4587i	0.222743	−	1.48885i
$634$	−34.0215	+	5.76497i	−1.35117	+	0.228956i
$635$		0			0
$636$	−17.0771	−	19.8357i	−0.677152	−	0.786535i
$637$	39.1523	+	22.6046i	1.55127	+	0.895626i
$638$	26.2064	+	9.73700i	1.03752	+	0.385491i
$639$	3.68295	+	15.9749i	0.145695	+	0.631956i
$640$		0			0
$641$	−9.94563	−	5.74211i	−0.392829	−	0.226800i	0.290556	−	0.956858i	$-0.406160\pi$
$641$	−9.94563	−	5.74211i	−0.392829	−	0.226800i	−0.683385	+	0.730058i	$0.739493\pi$
$642$	0.0263853	+	1.36339i	0.00104134	+	0.0538085i
$643$	19.6527	+	34.0395i	0.775027	+	1.34239i	0.934779	+	0.355229i	$0.115597\pi$
$643$	19.6527	+	34.0395i	0.775027	+	1.34239i	−0.159752	+	0.987157i	$0.551070\pi$
$644$	−32.8702	−	6.24956i	−1.29527	−	0.246267i
$645$		0			0
$646$	10.7587	−	8.90593i	0.423297	−	0.350399i
$647$			25.1943i			0.990489i	0.868754	+	0.495244i	$0.164921\pi$
$647$			25.1943i			0.990489i	−0.868754	+	0.495244i	$0.835079\pi$
$648$	−14.6673	+	20.8055i	−0.576185	+	0.817319i
$649$	23.4971			0.922341
$650$		0			0
$651$	−11.7347	−	9.33715i	−0.459920	−	0.365952i
$652$	−0.614055	+	3.22968i	−0.0240483	+	0.126484i
$653$	−6.89358	−	11.9400i	−0.269766	−	0.467249i	0.699035	−	0.715087i	$-0.253613\pi$
$653$	−6.89358	−	11.9400i	−0.269766	−	0.467249i	−0.968801	+	0.247838i	$0.920280\pi$
$654$	−38.0348	+	0.736080i	−1.48728	+	0.0287830i
$655$		0			0
$656$	−0.433541	+	0.0645596i	−0.0169269	+	0.00252063i
$657$	−37.9843	+	8.75713i	−1.48191	+	0.341648i
$658$	−54.9694	−	20.4239i	−2.14293	−	0.796205i
$659$	2.25898	−	3.91266i	0.0879972	−	0.152416i	−0.818667	−	0.574268i	$-0.805287\pi$
$659$	2.25898	−	3.91266i	0.0879972	−	0.152416i	0.906664	+	0.421853i	$0.138620\pi$
$660$		0			0
$661$	8.35512	+	14.4715i	0.324977	+	0.562876i	0.981508	−	0.191423i	$-0.0613102\pi$
$661$	8.35512	+	14.4715i	0.324977	+	0.562876i	−0.656531	+	0.754299i	$0.727977\pi$
$662$	−6.66646	−	39.3416i	−0.259099	−	1.52905i
$663$	−3.59897	+	24.0561i	−0.139773	+	0.934263i
$664$	21.8150	+	0.437015i	0.846588	+	0.0169595i
$665$		0			0
$666$	14.4730	+	11.0655i	0.560819	+	0.428779i
$667$	30.4865			1.18044
$668$	1.60682	+	4.60512i	0.0621697	+	0.178178i
$669$	1.56648	+	3.97853i	0.0605637	+	0.153819i
$670$		0			0
$671$	−8.64006	−	14.9650i	−0.333546	−	0.577718i
$672$	29.0593	−	24.0216i	1.12099	−	0.926652i
$673$	8.89270	+	5.13420i	0.342789	+	0.197909i	0.661504	−	0.749941i	$-0.269918\pi$
$673$	8.89270	+	5.13420i	0.342789	+	0.197909i	−0.318716	+	0.947850i	$0.603252\pi$
$674$	37.9691	+	14.1074i	1.46252	+	0.543398i
$675$		0			0
$676$	31.1036	+	26.8149i	1.19629	+	1.03134i
$677$	−21.1841	+	36.6920i	−0.814172	+	1.41019i	0.0957490	+	0.995406i	$0.469475\pi$
$677$	−21.1841	+	36.6920i	−0.814172	+	1.41019i	−0.909921	+	0.414782i	$0.863858\pi$
$678$	−9.60003	−	15.9087i	−0.368687	−	0.610970i
$679$	43.3109	−	25.0056i	1.66212	−	0.959626i
$680$		0			0
$681$	14.5451	−	5.72691i	0.557371	−	0.219456i
$682$	6.91013	−	5.72011i	0.264603	−	0.219034i
$683$			7.70020i			0.294640i	0.989089	+	0.147320i	$0.0470647\pi$
$683$			7.70020i			0.294640i	−0.989089	+	0.147320i	$0.952935\pi$
$684$	−0.945376	−	24.4157i	−0.0361474	−	0.933557i
$685$		0			0
$686$	−2.80056	−	3.38320i	−0.106926	−	0.129171i
$687$	−20.7288	−	3.10118i	−0.790853	−	0.118317i
$688$	0.645122	−	0.512599i	0.0245951	−	0.0195426i
$689$	−37.8922	+	21.8771i	−1.44358	+	0.833450i
$690$		0			0
$691$	−35.8315	−	20.6873i	−1.36309	−	0.786983i	−0.373060	−	0.927807i	$-0.621691\pi$
$691$	−35.8315	−	20.6873i	−1.36309	−	0.786983i	−0.990035	+	0.140824i	$0.955025\pi$
$692$	15.9939	+	13.7885i	0.607995	+	0.524161i
$693$	−23.8079	+	22.1877i	−0.904389	+	0.842839i
$694$	27.7026	+	10.2929i	1.05158	+	0.390713i
$695$		0			0
$696$	−21.9234	+	26.4478i	−0.831006	+	1.00250i
$697$	−0.230142	+	0.132873i	−0.00871726	+	0.00503292i
$698$	−18.1437	+	3.07446i	−0.686748	+	0.116370i
$699$	13.9420	−	17.5220i	0.527336	−	0.662744i
$700$		0			0
$701$		−	12.5415i		−	0.473685i	−0.971548	−	0.236842i	$-0.923887\pi$
$701$		−	12.5415i		−	0.473685i	0.971548	−	0.236842i	$-0.0761125\pi$
$702$	29.6088	+	30.5634i	1.11751	+	1.15354i
$703$	−17.4872			−0.659541
$704$	10.4852	+	19.9674i	0.395177	+	0.752551i
$705$		0			0
$706$	39.6756	−	6.72306i	1.49321	−	0.253026i
$707$	−11.1923	+	6.46187i	−0.420929	+	0.243024i
$708$	−9.53046	+	27.2546i	−0.358177	+	1.02429i
$709$	0.973370	−	1.68593i	0.0365557	−	0.0633163i	−0.847169	−	0.531324i	$-0.821695\pi$
$709$	0.973370	−	1.68593i	0.0365557	−	0.0633163i	0.883724	+	0.468008i	$0.155028\pi$
$710$		0			0
$711$	−4.38451	+	14.3254i	−0.164432	+	0.537245i
$712$	−0.183919	−	0.333824i	−0.00689265	−	0.0125106i
$713$	4.89108	−	8.47159i	0.183172	−	0.317264i
$714$	11.0440	−	20.0133i	0.413310	−	0.748978i
$715$		0			0
$716$	−1.12466	+	5.91525i	−0.0420305	+	0.221063i
$717$	−15.6944	−	2.34800i	−0.586119	−	0.0876877i
$718$	5.32846	+	6.43700i	0.198856	+	0.240227i
$719$	−25.7606			−0.960708			−0.480354	−	0.877075i	$-0.659492\pi$
$719$	−25.7606			−0.960708			−0.480354	+	0.877075i	$0.659492\pi$
$720$		0			0
$721$	−14.7674			−0.549965
$722$	−2.17884	−	2.63213i	−0.0810880	−	0.0979578i
$723$	6.72603	+	17.0827i	0.250144	+	0.635311i
$724$	7.29461	−	38.3667i	0.271102	−	1.42589i
$725$		0			0
$726$	3.86315	+	6.40181i	0.143375	+	0.237594i
$727$	−4.10126	+	7.10360i	−0.152107	+	0.263458i	−0.932002	−	0.362453i	$-0.881939\pi$
$727$	−4.10126	+	7.10360i	−0.152107	+	0.263458i	0.779895	+	0.625911i	$0.215273\pi$
$728$	−30.4133	−	55.2021i	−1.12719	−	2.04593i
$729$	16.9724	+	20.9985i	0.628607	+	0.777723i
$730$		0			0
$731$	0.249781	−	0.432633i	0.00923848	−	0.0160015i
$732$	20.8626	−	3.95188i	0.771102	−	0.146066i
$733$	18.3119	−	10.5724i	0.676364	−	0.390499i	−0.122120	−	0.992515i	$-0.538969\pi$
$733$	18.3119	−	10.5724i	0.676364	−	0.390499i	0.798484	+	0.602017i	$0.205636\pi$
$734$	33.7810	−	5.72422i	1.24688	−	0.211285i
$735$		0			0
$736$	18.3017	+	16.4285i	0.674610	+	0.605563i
$737$	14.6150			0.538350
$738$	−0.0598789	+	0.461038i	−0.00220417	+	0.0169710i
$739$		−	0.668371i		−	0.0245864i	−0.999924	−	0.0122932i	$-0.996087\pi$
$739$		−	0.668371i		−	0.0245864i	0.999924	−	0.0122932i	$-0.00391315\pi$
$740$		0			0
$741$	−40.3957	−	6.04349i	−1.48397	−	0.222013i
$742$	40.5399	−	6.86951i	1.48827	−	0.252188i
$743$	29.3436	−	16.9416i	1.07651	−	0.621526i	0.146560	−	0.989202i	$-0.453180\pi$
$743$	29.3436	−	16.9416i	1.07651	−	0.621526i	0.929954	+	0.367676i	$0.119847\pi$
$744$	3.83207	+	10.3352i	0.140490	+	0.378908i
$745$		0			0
$746$	−10.0483	−	3.73344i	−0.367894	−	0.136691i
$747$	6.77312	−	22.1297i	0.247816	−	0.809683i
$748$	10.3562	+	8.92821i	0.378659	+	0.326448i
$749$	−1.85519	−	1.07110i	−0.0677873	−	0.0391370i
$750$		0			0
$751$	9.22222	−	5.32445i	0.336524	−	0.194292i	−0.322210	−	0.946668i	$-0.604426\pi$
$751$	9.22222	−	5.32445i	0.336524	−	0.194292i	0.658734	+	0.752376i	$0.271092\pi$
$752$	26.8147	+	33.7472i	0.977833	+	1.23064i
$753$	−11.0236	+	13.8542i	−0.401723	+	0.504876i
$754$	36.6185	+	44.2367i	1.33357	+	1.61101i
$755$		0			0
$756$	−16.0792	−	36.6145i	−0.584796	−	1.33166i
$757$			11.8276i			0.429880i	0.976627	+	0.214940i	$0.0689557\pi$
$757$			11.8276i			0.429880i	−0.976627	+	0.214940i	$0.931044\pi$
$758$	29.5185	−	24.4350i	1.07216	−	0.887518i
$759$	−16.6118	−	13.2177i	−0.602968	−	0.479773i
$760$		0			0
$761$	0.0449006	−	0.0259234i	0.00162765	−	0.000939722i	−0.499186	−	0.866495i	$-0.666368\pi$
$761$	0.0449006	−	0.0259234i	0.00162765	−	0.000939722i	0.500814	+	0.865555i	$0.333034\pi$
$762$	45.4545	−	0.879671i	1.64664	−	0.0318671i
$763$	29.8808	−	51.7550i	1.08176	−	1.87366i
$764$	1.46051	+	1.25913i	0.0528395	+	0.0455537i
$765$		0			0
$766$	35.0330	+	13.0165i	1.26580	+	0.470306i
$767$	41.7992	+	24.1328i	1.50928	+	0.871385i
$768$	−27.4133	+	4.06314i	−0.989193	+	0.146616i
$769$	−13.0480	−	22.5999i	−0.470524	−	0.814972i	0.528907	−	0.848680i	$-0.322602\pi$
$769$	−13.0480	−	22.5999i	−0.470524	−	0.814972i	−0.999432	+	0.0337073i	$0.989269\pi$
$770$		0			0
$771$	11.0435	+	1.65219i	0.397723	+	0.0595023i
$772$	−10.5378	−	30.2012i	−0.379264	−	1.08696i
$773$	−11.4187			−0.410702			−0.205351	−	0.978688i	$-0.565834\pi$
$773$	−11.4187			−0.410702			−0.205351	+	0.978688i	$0.565834\pi$
$774$	−0.335858	−	0.806850i	−0.0120722	−	0.0290016i
$775$		0			0
$776$	−36.7528	−	0.736259i	−1.31935	−	0.0264302i
$777$	−26.6303	+	10.4852i	−0.955356	+	0.376156i
$778$	−4.83464	−	28.5313i	−0.173330	−	1.02290i
$779$	−0.223124	−	0.386461i	−0.00799423	−	0.0138464i
$780$		0			0
$781$	7.70276	−	13.3416i	0.275626	−	0.477399i
$782$	13.9771	+	5.19318i	0.499819	+	0.185708i
$783$	20.6243	+	30.0380i	0.737051	+	1.07347i
$784$	4.59956	+	30.8877i	0.164270	+	1.10313i
$785$		0			0
$786$	12.0312	+	19.9375i	0.429138	+	0.711147i
$787$	−15.4071	−	26.6858i	−0.549202	−	0.951246i	−0.998329	−	0.0577782i	$-0.981598\pi$
$787$	−15.4071	−	26.6858i	−0.549202	−	0.951246i	0.449127	−	0.893468i	$-0.351735\pi$
$788$	−9.74131	+	51.2353i	−0.347020	+	1.82518i
$789$	−29.2261	+	11.5073i	−1.04048	+	0.409671i
$790$		0			0
$791$	29.1893			1.03785
$792$	23.4126	−	4.90601i	0.831931	−	0.174327i
$793$		−	35.4953i		−	1.26047i
$794$	0.138919	−	0.114995i	0.00493006	−	0.00408103i
$795$		0			0
$796$	32.7560	+	6.22787i	1.16101	+	0.220741i
$797$	24.9885	+	43.2814i	0.885139	+	1.53311i	0.845554	+	0.533890i	$0.179270\pi$
$797$	24.9885	+	43.2814i	0.885139	+	1.53311i	0.0395849	+	0.999216i	$0.487396\pi$
$798$	33.6069	+	18.5453i	1.18967	+	0.656497i
$799$	22.6316	+	13.0664i	0.800650	+	0.462255i
$800$		0			0
$801$	−0.393923	+	0.0908174i	−0.0139186	+	0.00320887i
$802$	−19.6701	−	7.30842i	−0.694575	−	0.258069i
$803$	31.7229	+	18.3153i	1.11948	+	0.646331i
$804$	−5.92786	+	16.9521i	−0.209060	+	0.597855i
$805$		0			0
$806$	18.1674	−	3.07848i	0.639919	−	0.108435i
$807$	−4.62049	−	3.67645i	−0.162649	−	0.129417i
$808$	9.49756	+	0.190262i	0.334123	+	0.00669340i
$809$		−	31.1937i		−	1.09671i	−0.836245	−	0.548356i	$-0.815254\pi$
$809$		−	31.1937i		−	1.09671i	0.836245	−	0.548356i	$-0.184746\pi$
$810$		0			0
$811$		−	47.9220i		−	1.68277i	−0.540436	−	0.841385i	$-0.681741\pi$
$811$		−	47.9220i		−	1.68277i	0.540436	−	0.841385i	$-0.318259\pi$
$812$	−17.7788	−	50.9537i	−0.623913	−	1.78813i
$813$	−11.6796	−	9.29330i	−0.409622	−	0.325930i
$814$	−2.86024	−	16.8795i	−0.100251	−	0.591626i
$815$		0			0
$816$	−14.5564	+	8.39097i	−0.509577	+	0.293743i
$817$	0.726489	+	0.419439i	0.0254166	+	0.0146743i
$818$	−7.25597	+	19.5289i	−0.253699	+	0.682813i
$819$	−65.1402	+	15.0178i	−2.27618	+	0.524765i
$820$		0			0
$821$	−31.0074	−	17.9021i	−1.08216	−	0.624788i	−0.150685	−	0.988582i	$-0.548148\pi$
$821$	−31.0074	−	17.9021i	−1.08216	−	0.624788i	−0.931480	+	0.363794i	$0.881481\pi$
$822$	0.947782	−	1.71752i	0.0330577	−	0.0599054i
$823$	−12.5300	−	21.7026i	−0.436768	−	0.756504i	0.560670	−	0.828039i	$-0.310543\pi$
$823$	−12.5300	−	21.7026i	−0.436768	−	0.756504i	−0.997438	+	0.0715352i	$0.977210\pi$
$824$	9.28976	+	5.61448i	0.323624	+	0.195590i
$825$		0			0
$826$	−28.9226	−	34.9397i	−1.00635	−	1.21571i
$827$		−	0.111136i		−	0.00386458i	−0.999998	−	0.00193229i	$-0.999385\pi$
$827$		−	0.111136i		−	0.00386458i	0.999998	−	0.00193229i	$-0.000615068\pi$
$828$	22.0692	−	13.9071i	0.766957	−	0.483304i
$829$	−35.8024			−1.24347			−0.621735	−	0.783228i	$-0.713572\pi$
$829$	−35.8024			−1.24347			−0.621735	+	0.783228i	$0.713572\pi$
$830$		0			0
$831$	−11.6373	+	4.58200i	−0.403694	+	0.158948i
$832$	−1.85535	+	46.2892i	−0.0643226	+	1.60479i
$833$	9.46654	+	16.3965i	0.327996	+	0.568106i
$834$	−15.3152	+	9.24188i	−0.530322	+	0.320020i
$835$		0			0
$836$	−14.9925	+	17.3904i	−0.518526	+	0.601459i
$837$	11.6558	−	0.911954i	0.402884	−	0.0315217i
$838$	−5.55366	+	14.9473i	−0.191848	+	0.516346i
$839$	−1.71872	+	2.97691i	−0.0593367	+	0.102774i	−0.894168	−	0.447732i	$-0.852232\pi$
$839$	−1.71872	+	2.97691i	−0.0593367	+	0.102774i	0.834831	+	0.550506i	$0.185565\pi$
$840$		0			0
$841$	10.0860	+	17.4694i	0.347792	+	0.602393i
$842$	−0.0495222	+	0.00839157i	−0.00170665	+	0.000289193i
$843$	44.0879	−	17.3589i	1.51847	−	0.597872i
$844$	−14.4081	−	41.2935i	−0.495948	−	1.42138i
$845$		0			0
$846$	42.2074	−	17.5692i	1.45112	−	0.604042i
$847$	−11.7461			−0.403600
$848$	−28.1144	−	11.0917i	−0.965451	−	0.380889i
$849$	−9.23740	−	1.38198i	−0.317027	−	0.0474295i
$850$		0			0
$851$	−9.33459	−	16.1680i	−0.319985	−	0.554231i
$852$	12.3508	+	14.3459i	0.423132	+	0.491482i
$853$	−11.3788	−	6.56957i	−0.389604	−	0.224938i	0.292385	−	0.956301i	$-0.405551\pi$
$853$	−11.3788	−	6.56957i	−0.389604	−	0.224938i	−0.681988	+	0.731363i	$0.738885\pi$
$854$	−11.6176	+	31.2681i	−0.397548	+	1.06997i
$855$		0			0
$856$	0.759828	+	1.37914i	0.0259704	+	0.0471379i
$857$	−10.4833	+	18.1576i	−0.358103	+	0.620253i	−0.987644	−	0.156715i	$-0.949910\pi$
$857$	−10.4833	+	18.1576i	−0.358103	+	0.620253i	0.629541	+	0.776967i	$0.283243\pi$
$858$	−0.773733	−	39.9804i	−0.0264148	−	1.36491i
$859$	−22.1231	+	12.7728i	−0.754829	+	0.435801i	−0.827436	−	0.561560i	$-0.810201\pi$
$859$	−22.1231	+	12.7728i	−0.754829	+	0.435801i	0.0726072	+	0.997361i	$0.476868\pi$
$860$		0			0
$861$	−0.571504	−	0.454737i	−0.0194768	−	0.0154974i
$862$	15.6086	+	18.8558i	0.531630	+	0.642232i
$863$			12.4343i			0.423267i	0.977349	+	0.211633i	$0.0678783\pi$
$863$			12.4343i			0.423267i	−0.977349	+	0.211633i	$0.932122\pi$
$864$	−3.80565	+	29.1465i	−0.129471	+	0.991583i
$865$		0			0
$866$	17.8096	−	14.7425i	0.605195	−	0.500972i
$867$	11.9909	−	15.0699i	0.407232	−	0.511800i
$868$	−17.0114	−	3.23435i	−0.577404	−	0.109781i
$869$	12.1920	−	7.03906i	0.413586	−	0.238784i
$870$		0			0
$871$	25.9988	+	15.0104i	0.880934	+	0.508608i
$872$	−38.4742	+	21.1972i	−1.30290	+	0.717828i
$873$	−11.4110	+	37.2829i	−0.386203	+	1.26183i
$874$	−8.72053	+	23.4707i	−0.294976	+	0.793908i
$875$		0			0
$876$	−34.1110	+	29.3672i	−1.15250	+	0.992225i
$877$	5.92561	−	3.42115i	0.200094	−	0.115524i	−0.396605	−	0.917989i	$-0.629812\pi$
$877$	5.92561	−	3.42115i	0.200094	−	0.115524i	0.596699	+	0.802465i	$0.296479\pi$
$878$	−2.67506	−	15.7867i	−0.0902789	−	0.532774i
$879$	30.6061	+	4.57890i	1.03232	+	0.154442i
$880$		0			0
$881$		−	11.7126i		−	0.394606i	−0.980343	−	0.197303i	$-0.936782\pi$
$881$		−	11.7126i		−	0.394606i	0.980343	−	0.197303i	$-0.0632183\pi$
$882$	32.8467	+	4.26608i	1.10601	+	0.143646i
$883$	−15.1968			−0.511413			−0.255707	−	0.966754i	$-0.582308\pi$
$883$	−15.1968			−0.511413			−0.255707	+	0.966754i	$0.582308\pi$
$884$	9.25296	+	26.5189i	0.311211	+	0.891926i
$885$		0			0
$886$	8.50738	+	50.2057i	0.285811	+	1.68669i
$887$	29.2394	−	16.8814i	0.981762	−	0.566820i	0.0789600	−	0.996878i	$-0.474840\pi$
$887$	29.2394	−	16.8814i	0.981762	−	0.566820i	0.902802	+	0.430057i	$0.141507\pi$
$888$	20.7389	+	3.52872i	0.695951	+	0.118416i
$889$	−35.7098	+	61.8511i	−1.19767	+	2.07442i
$890$		0			0
$891$	1.78535	−	25.3093i	0.0598115	−	0.847892i
$892$	3.73947	+	3.22385i	0.125207	+	0.107942i
$893$	−21.9414	+	38.0037i	−0.734242	+	1.27174i
$894$	−0.238703	+	0.144044i	−0.00798342	+	0.00481756i
$895$		0			0
$896$	16.7849	−	40.1693i	0.560744	−	1.34196i
$897$	−15.9755	−	40.5744i	−0.533406	−	1.35474i
$898$	−0.629020	+	0.520693i	−0.0209907	+	0.0173758i
$899$	15.7777			0.526217
$900$		0			0
$901$	−18.3237			−0.610452
$902$	0.336537	−	0.278581i	0.0112055	−	0.00927572i
$903$	1.35783	+	0.203141i	0.0451856	+	0.00676010i
$904$	−18.3622	−	11.0976i	−0.610719	−	0.369102i
$905$		0			0
$906$	−3.63768	−	2.00739i	−0.120854	−	0.0666909i
$907$	17.1431	−	29.6927i	0.569228	−	0.985931i	−0.427415	−	0.904056i	$-0.640576\pi$
$907$	17.1431	−	29.6927i	0.569228	−	0.985931i	0.996643	−	0.0818757i	$-0.0260910\pi$
$908$	11.7861	−	13.6711i	0.391135	−	0.453692i
$909$	2.94880	−	9.63454i	0.0978054	−	0.319557i
$910$		0			0
$911$	3.24141	−	5.61428i	0.107393	−	0.186010i	−0.807321	−	0.590113i	$-0.799083\pi$
$911$	3.24141	−	5.61428i	0.107393	−	0.186010i	0.914713	+	0.404104i	$0.132416\pi$
$912$	−14.0903	−	24.4436i	−0.466578	−	0.809407i
$913$	−18.8340	+	10.8738i	−0.623316	+	0.359872i
$914$	5.49825	+	32.4475i	0.181866	+	1.07327i
$915$		0			0
$916$	−22.8509	+	7.97313i	−0.755015	+	0.263440i
$917$	−36.5814			−1.20802
$918$	4.33878	+	17.2847i	0.143201	+	0.570480i
$919$		−	18.1763i		−	0.599580i	−0.954005	−	0.299790i	$-0.903083\pi$
$919$		−	18.1763i		−	0.599580i	0.954005	−	0.299790i	$-0.0969166\pi$
$920$		0			0
$921$	5.79345	−	7.28107i	0.190901	−	0.239920i
$922$	−1.87436	−	11.0614i	−0.0617286	−	0.364287i
$923$	27.4051	−	15.8223i	0.902048	−	0.520798i
$924$	−12.4041	+	35.4723i	−0.408064	+	1.16695i
$925$		0			0
$926$	−15.3511	+	41.3165i	−0.504470	+	1.35774i
$927$	8.42250	−	7.84929i	0.276631	−	0.257805i
$928$	−8.18821	+	38.8131i	−0.268791	+	1.27410i
$929$	−20.6179	−	11.9038i	−0.676452	−	0.390550i	0.122065	−	0.992522i	$-0.461048\pi$
$929$	−20.6179	−	11.9038i	−0.676452	−	0.390550i	−0.798517	+	0.601972i	$0.794382\pi$
$930$		0			0
$931$	−27.5335	+	15.8965i	−0.902373	+	0.520986i
$932$	4.82946	−	25.4010i	0.158194	−	0.832038i
$933$	51.9333	+	7.76961i	1.70022	+	0.254365i
$934$	−30.8670	+	25.5512i	−1.01000	+	0.836062i
$935$		0			0
$936$	46.6877	+	15.3187i	1.52603	+	0.500707i
$937$		−	16.4490i		−	0.537366i	−0.963229	−	0.268683i	$-0.913412\pi$
$937$		−	16.4490i		−	0.537366i	0.963229	−	0.268683i	$-0.0865884\pi$
$938$	−17.9896	−	21.7322i	−0.587381	−	0.709581i
$939$	39.8356	−	15.6846i	1.29999	−	0.511848i
$940$		0			0
$941$	6.86226	−	3.96193i	0.223703	−	0.129155i	−0.383961	−	0.923349i	$-0.625440\pi$
$941$	6.86226	−	3.96193i	0.223703	−	0.129155i	0.607664	+	0.794194i	$0.292107\pi$
$942$	−47.1752	+	28.4676i	−1.53705	+	0.927526i
$943$	0.238205	−	0.412583i	0.00775703	−	0.0134356i
$944$	4.91052	+	32.9759i	0.159824	+	1.07327i
$945$		0			0
$946$	−0.286037	+	0.769848i	−0.00929987	+	0.0250299i
$947$	−43.5441	−	25.1402i	−1.41499	−	0.816947i	−0.419141	−	0.907921i	$-0.637669\pi$
$947$	−43.5441	−	25.1402i	−1.41499	−	0.816947i	−0.995853	+	0.0909742i	$0.971002\pi$
$948$	3.21960	+	16.9967i	0.104568	+	0.552028i
$949$	37.6215	+	65.1624i	1.22125	+	2.11526i
$950$		0			0
$951$	15.4829	+	39.3234i	0.502069	+	1.27515i
$952$	0.528648	−	26.3892i	0.0171336	−	0.855278i
$953$	−32.4601			−1.05149			−0.525743	−	0.850644i	$-0.676213\pi$
$953$	−32.4601			−1.05149			−0.525743	+	0.850644i	$0.676213\pi$
$954$	−19.4704	+	25.4662i	−0.630377	+	0.824497i
$955$		0			0
$956$	−17.3011	+	6.03671i	−0.559558	+	0.195241i
$957$	5.06618	−	33.8632i	0.163766	−	1.09464i
$958$	−34.1116	+	5.78024i	−1.10210	+	0.186751i
$959$	1.54083	+	2.66880i	0.0497561	+	0.0861801i
$960$		0			0
$961$	−12.9687	+	22.4625i	−0.418345	+	0.724596i
$962$	12.2480	−	32.9647i	0.394893	−	1.06283i
$963$	1.62742	−	0.375196i	0.0524429	−	0.0120905i
$964$	16.0562	+	13.8423i	0.517135	+	0.445829i
$965$		0			0
$966$	0.792904	+	40.9711i	0.0255113	+	1.31822i
$967$	12.7403	+	22.0669i	0.409701	+	0.709623i	0.994856	−	0.101299i	$-0.0322997\pi$
$967$	12.7403	+	22.0669i	0.409701	+	0.709623i	−0.585155	+	0.810921i	$0.698966\pi$
$968$	7.38914	+	4.46580i	0.237496	+	0.143536i
$969$	−13.3853	−	10.6505i	−0.429998	−	0.342143i
$970$		0			0
$971$	−40.6423			−1.30427			−0.652137	−	0.758101i	$-0.726127\pi$
$971$	−40.6423			−1.30427			−0.652137	+	0.758101i	$0.726127\pi$
$972$	28.6324	+	12.3363i	0.918385	+	0.395688i
$973$		−	28.1004i		−	0.900856i
$974$	−3.65992	−	4.42134i	−0.117271	−	0.141669i
$975$		0			0
$976$	19.1963	−	15.2529i	0.614460	−	0.488235i
$977$	28.3180	+	49.0482i	0.905973	+	1.56919i	0.819605	+	0.572929i	$0.194193\pi$
$977$	28.3180	+	49.0482i	0.905973	+	1.56919i	0.0863680	+	0.996263i	$0.472474\pi$
$978$	4.02564	−	0.0779073i	0.128726	−	0.00249120i
$979$	0.328989	+	0.189942i	0.0105145	+	0.00607056i
$980$		0			0
$981$	10.4670	+	45.4008i	0.334185	+	1.44953i
$982$	8.15705	−	21.9541i	0.260302	−	0.700584i
$983$	9.10425	+	5.25634i	0.290380	+	0.167651i	0.638113	−	0.769942i	$-0.279715\pi$
$983$	9.10425	+	5.25634i	0.290380	+	0.167651i	−0.347733	+	0.937594i	$0.613048\pi$
$984$	0.186629	+	0.503347i	0.00594952	+	0.0160461i
$985$		0			0
$986$	4.01794	+	23.7115i	0.127957	+	0.755129i
$987$	−10.6266	+	71.0298i	−0.338248	+	2.26090i
$988$	−44.5312	+	15.5378i	−1.41673	+	0.494324i
$989$			0.895580i			0.0284778i
$990$		0			0
$991$			31.2300i			0.992053i	0.868307	+	0.496027i	$0.165208\pi$
$991$			31.2300i			0.992053i	−0.868307	+	0.496027i	$0.834792\pi$
$992$	9.47173	+	8.50229i	0.300728	+	0.269948i
$993$	−45.4725	+	17.9041i	−1.44303	+	0.568168i
$994$	−29.3200	+	4.96829i	−0.929974	+	0.157585i
$995$		0			0
$996$	−4.97359	−	26.2563i	−0.157594	−	0.831963i
$997$	46.6230	+	26.9178i	1.47657	+	0.852495i	0.999650	−	0.0264537i	$-0.00842145\pi$
$997$	46.6230	+	26.9178i	1.47657	+	0.852495i	0.476915	+	0.878949i	$0.341755\pi$
$998$	26.6688	+	9.90880i	0.844187	+	0.313658i
$999$	9.61524	−	20.1350i	0.304213	−	0.637043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.o.c.299.7		48
4.3	odd	2	inner	900.2.o.c.299.24		48
5.2	odd	4		180.2.q.a.11.19	yes	48
5.3	odd	4		900.2.r.f.551.6		48
5.4	even	2		900.2.o.b.299.18		48
9.5	odd	6		900.2.o.b.599.1		48
15.2	even	4		540.2.q.a.251.6		48
20.3	even	4		900.2.r.f.551.14		48
20.7	even	4		180.2.q.a.11.11	✓	48
20.19	odd	2		900.2.o.b.299.1		48
36.23	even	6		900.2.o.b.599.18		48
45.2	even	12		1620.2.e.b.971.44		48
45.7	odd	12		1620.2.e.b.971.5		48
45.14	odd	6	inner	900.2.o.c.599.24		48
45.22	odd	12		540.2.q.a.71.14		48
45.23	even	12		900.2.r.f.851.14		48
45.32	even	12		180.2.q.a.131.11	yes	48
60.47	odd	4		540.2.q.a.251.14		48
180.7	even	12		1620.2.e.b.971.43		48
180.23	odd	12		900.2.r.f.851.6		48
180.47	odd	12		1620.2.e.b.971.6		48
180.59	even	6	inner	900.2.o.c.599.7		48
180.67	even	12		540.2.q.a.71.6		48
180.167	odd	12		180.2.q.a.131.19	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.11	✓	48	20.7	even	4
180.2.q.a.11.19	yes	48	5.2	odd	4
180.2.q.a.131.11	yes	48	45.32	even	12
180.2.q.a.131.19	yes	48	180.167	odd	12
540.2.q.a.71.6		48	180.67	even	12
540.2.q.a.71.14		48	45.22	odd	12
540.2.q.a.251.6		48	15.2	even	4
540.2.q.a.251.14		48	60.47	odd	4
900.2.o.b.299.1		48	20.19	odd	2
900.2.o.b.299.18		48	5.4	even	2
900.2.o.b.599.1		48	9.5	odd	6
900.2.o.b.599.18		48	36.23	even	6
900.2.o.c.299.7		48	1.1	even	1	trivial
900.2.o.c.299.24		48	4.3	odd	2	inner
900.2.o.c.599.7		48	180.59	even	6	inner
900.2.o.c.599.24		48	45.14	odd	6	inner
900.2.r.f.551.6		48	5.3	odd	4
900.2.r.f.551.14		48	20.3	even	4
900.2.r.f.851.6		48	180.23	odd	12
900.2.r.f.851.14		48	45.23	even	12
1620.2.e.b.971.5		48	45.7	odd	12
1620.2.e.b.971.6		48	180.47	odd	12
1620.2.e.b.971.43		48	180.7	even	12
1620.2.e.b.971.44		48	45.2	even	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.901786 - 1.08940i) q^{2} +(-1.07843 + 1.35535i) q^{3} +(-0.373566 + 1.96480i) q^{4} +(2.44903 - 0.0473955i) q^{6} +(-1.92400 + 3.33246i) q^{7} +(2.47732 - 1.36487i) q^{8} +(-0.673959 - 2.92332i) q^{9} +(-1.40956 + 2.44144i) q^{11} +(-2.26013 - 2.62522i) q^{12} +(-5.01498 + 2.89540i) q^{13} +(5.36540 - 0.909171i) q^{14} +(-3.72090 - 1.46797i) q^{16} -2.42512 q^{17} +(-2.57688 + 3.37041i) q^{18} -4.07233i q^{19} +(-2.44175 - 6.20153i) q^{21} +(3.93081 - 0.666079i) q^{22} +(3.76512 - 2.17379i) q^{23} +(-0.821751 + 4.82957i) q^{24} +(7.67667 + 2.85227i) q^{26} +(4.68894 + 2.23915i) q^{27} +(-5.82889 - 5.02517i) q^{28} +(6.07280 + 3.50613i) q^{29} +(1.94857 - 1.12501i) q^{31} +(1.75626 + 5.37732i) q^{32} +(-1.78888 - 4.54338i) q^{33} +(2.18694 + 2.64192i) q^{34} +(5.99551 - 0.232146i) q^{36} -4.29414i q^{37} +(-4.43638 + 3.67237i) q^{38} +(1.48404 - 9.91956i) q^{39} +(0.0948994 - 0.0547902i) q^{41} +(-4.55399 + 8.25249i) q^{42} +(-0.102997 + 0.178397i) q^{43} +(-4.27038 - 3.68155i) q^{44} +(-5.76345 - 2.14141i) q^{46} +(-9.33217 - 5.38793i) q^{47} +(6.00235 - 3.46002i) q^{48} +(-3.90353 - 6.76112i) q^{49} +(2.61533 - 3.28689i) q^{51} +(-3.81546 - 10.9351i) q^{52} +7.55580 q^{53} +(-1.78910 - 7.12735i) q^{54} +(-0.217988 + 10.8816i) q^{56} +(5.51944 + 4.39174i) q^{57} +(-1.65680 - 9.77747i) q^{58} +(-4.16744 - 7.21822i) q^{59} +(-3.06480 + 5.30839i) q^{61} +(-2.98277 - 1.10825i) q^{62} +(11.0385 + 3.37851i) q^{63} +(4.27426 - 6.76245i) q^{64} +(-3.33635 + 6.04596i) q^{66} +(-2.59211 - 4.48967i) q^{67} +(0.905942 - 4.76488i) q^{68} +(-1.11418 + 7.44736i) q^{69} -5.46464 q^{71} +(-5.65956 - 6.32213i) q^{72} -12.9936i q^{73} +(-4.67802 + 3.87240i) q^{74} +(8.00132 + 1.52128i) q^{76} +(-5.42400 - 9.39464i) q^{77} +(-12.1446 + 7.32861i) q^{78} +(-4.32475 - 2.49689i) q^{79} +(-8.09156 + 3.94039i) q^{81} +(-0.145267 - 0.0539740i) q^{82} +(6.68080 + 3.85716i) q^{83} +(13.0969 - 2.48088i) q^{84} +(0.287226 - 0.0486706i) q^{86} +(-11.3012 + 4.44965i) q^{87} +(-0.159703 + 7.97210i) q^{88} -0.134752i q^{89} -22.2830i q^{91} +(2.86456 + 8.20978i) q^{92} +(-0.576624 + 3.85425i) q^{93} +(2.54603 + 15.0252i) q^{94} +(-9.18217 - 3.41874i) q^{96} +(-11.2555 - 6.49834i) q^{97} +(-3.84538 + 10.3496i) q^{98} +(8.08708 + 2.47517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 12 q^{8} - 4 q^{9} + 28 q^{12} + 30 q^{14} - 18 q^{18} - 4 q^{21} - 42 q^{22} + 28 q^{24} + 12 q^{29} - 48 q^{33} + 6 q^{34} + 42 q^{36} - 6 q^{38} - 60 q^{41} + 16 q^{42} - 12 q^{46} - 74 q^{48}+ \cdots + 84 q^{98}+O(q^{100}) \) 48 * q + 6 * q^6 + 12 * q^8 - 4 * q^9 + 28 * q^12 + 30 * q^14 - 18 * q^18 - 4 * q^21 - 42 * q^22 + 28 * q^24 + 12 * q^29 - 48 * q^33 + 6 * q^34 + 42 * q^36 - 6 * q^38 - 60 * q^41 + 16 * q^42 - 12 * q^46 - 74 * q^48 - 24 * q^49 - 90 * q^52 + 32 * q^54 - 42 * q^56 - 16 * q^57 + 84 * q^58 + 84 * q^62 + 48 * q^64 + 16 * q^66 + 6 * q^68 - 36 * q^69 - 80 * q^72 - 84 * q^74 + 6 * q^76 - 46 * q^78 - 50 * q^84 - 54 * q^86 + 114 * q^88 - 42 * q^92 - 24 * q^93 - 18 * q^94 - 18 * q^96 - 48 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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