LMFDB - Embedded newform 900.2.s.d.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(49,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.49"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.1333317747165888577536.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} + 5x^{12} + 15x^{10} + 45x^{8} + 60x^{6} + 80x^{4} + 192x^{2} + 256 $ x^16 + 3x^14 + 5x^12 + 15x^10 + 45x^8 + 60x^6 + 80x^4 + 192*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.7
Root			$1.15347 - 0.818235i$ of defining polynomial
Character	$\chi$	$=$	900.49
Dual form			900.2.s.d.349.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28535 - 1.16098i) q^{3} +(4.32643 - 2.49787i) q^{7} +(0.304233 - 2.98453i) q^{9} +(-1.99787 - 3.46041i) q^{11} +(-1.33642 - 0.771582i) q^{13} +6.99574i q^{17} +2.25667 q^{19} +(2.66098 - 8.23355i) q^{21} +(-6.75116 - 3.89778i) q^{23} +(-3.07395 - 4.18937i) q^{27} +(3.08304 + 5.33998i) q^{29} +(0.271582 - 0.470394i) q^{31} +(-6.58543 - 2.12833i) q^{33} +6.25240i q^{37} +(-2.61356 + 0.559811i) q^{39} +(-0.0979532 + 0.169660i) q^{41} +(-0.0747616 + 0.0431636i) q^{43} +(3.31658 - 1.91483i) q^{47} +(8.97869 - 15.5515i) q^{49} +(8.12194 + 8.99195i) q^{51} +4.19164i q^{53} +(2.90060 - 2.61995i) q^{57} +(3.51278 - 6.08432i) q^{59} +(1.45470 + 2.51962i) q^{61} +(-6.13873 - 13.6723i) q^{63} +(7.76470 + 4.48295i) q^{67} +(-13.2028 + 2.82798i) q^{69} +8.79130 q^{71} -2.28650i q^{73} +(-17.2873 - 9.98082i) q^{77} +(-6.32211 - 10.9502i) q^{79} +(-8.81488 - 1.81599i) q^{81} +(-12.0911 + 6.98082i) q^{83} +(10.1624 + 3.28437i) q^{87} +10.3577 q^{89} -7.70924 q^{91} +(-0.197042 - 0.919921i) q^{93} +(-8.08758 + 4.66936i) q^{97} +(-10.9355 + 4.90993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{9} + 6 q^{11} + 16 q^{19} + 26 q^{21} + 18 q^{29} - 4 q^{31} + 34 q^{39} + 18 q^{41} + 18 q^{49} + 6 q^{51} + 30 q^{59} + 2 q^{61} - 18 q^{69} - 48 q^{71} - 14 q^{79} - 62 q^{81} - 12 q^{89}+ \cdots - 66 q^{99}+O(q^{100}) $ 16 * q - 10 * q^9 + 6 * q^11 + 16 * q^19 + 26 * q^21 + 18 * q^29 - 4 * q^31 + 34 * q^39 + 18 * q^41 + 18 * q^49 + 6 * q^51 + 30 * q^59 + 2 * q^61 - 18 * q^69 - 48 * q^71 - 14 * q^79 - 62 * q^81 - 12 * q^89 - 44 * q^91 - 66 * q^99

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	1.28535	−	1.16098i	0.742095	−	0.670294i
$3$	1.28535	−	1.16098i	0.742095	−	0.670294i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.32643	−	2.49787i	1.63524	−	0.944105i	0.652797	−	0.757533i	$-0.273595\pi$
$7$	4.32643	−	2.49787i	1.63524	−	0.944105i	0.982441	−	0.186573i	$-0.0597379\pi$
$8$		0			0
$9$	0.304233	−	2.98453i	0.101411	−	0.994845i
$10$		0			0
$11$	−1.99787	−	3.46041i	−0.602380	−	1.04335i	−0.992460	−	0.122571i	$-0.960886\pi$
$11$	−1.99787	−	3.46041i	−0.602380	−	1.04335i	0.390080	−	0.920781i	$-0.372447\pi$
$12$		0			0
$13$	−1.33642	−	0.771582i	−0.370656	−	0.213998i	0.303089	−	0.952962i	$-0.401982\pi$
$13$	−1.33642	−	0.771582i	−0.370656	−	0.213998i	−0.673745	+	0.738964i	$0.735315\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			6.99574i			1.69672i	0.529424	+	0.848358i	$0.322408\pi$
$17$			6.99574i			1.69672i	−0.529424	+	0.848358i	$0.677592\pi$
$18$		0			0
$19$	2.25667			0.517715			0.258857	−	0.965916i	$-0.416654\pi$
$19$	2.25667			0.517715			0.258857	+	0.965916i	$0.416654\pi$
$20$		0			0
$21$	2.66098	−	8.23355i	0.580674	−	1.79671i
$22$		0			0
$23$	−6.75116	−	3.89778i	−1.40771	−	0.812744i	−0.412546	−	0.910937i	$-0.635360\pi$
$23$	−6.75116	−	3.89778i	−1.40771	−	0.812744i	−0.995167	+	0.0981929i	$0.968694\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.07395	−	4.18937i	−0.591582	−	0.806245i
$28$		0			0
$29$	3.08304	+	5.33998i	0.572506	+	0.991609i	0.996308	+	0.0858540i	$0.0273619\pi$
$29$	3.08304	+	5.33998i	0.572506	+	0.991609i	−0.423802	+	0.905755i	$0.639305\pi$
$30$		0			0
$31$	0.271582	−	0.470394i	0.0487775	−	0.0844852i	−0.840606	−	0.541647i	$-0.817801\pi$
$31$	0.271582	−	0.470394i	0.0487775	−	0.0844852i	0.889383	+	0.457162i	$0.151134\pi$
$32$		0			0
$33$	−6.58543	−	2.12833i	−1.14638	−	0.370495i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			6.25240i			1.02789i	0.857824	+	0.513944i	$0.171816\pi$
$37$			6.25240i			1.02789i	−0.857824	+	0.513944i	$0.828184\pi$
$38$		0			0
$39$	−2.61356	+	0.559811i	−0.418504	+	0.0896414i
$40$		0			0
$41$	−0.0979532	+	0.169660i	−0.0152977	+	0.0264964i	−0.873573	−	0.486693i	$-0.838203\pi$
$41$	−0.0979532	+	0.169660i	−0.0152977	+	0.0264964i	0.858275	+	0.513190i	$0.171536\pi$
$42$		0			0
$43$	−0.0747616	+	0.0431636i	−0.0114010	+	0.00658239i	−0.505690	−	0.862715i	$-0.668762\pi$
$43$	−0.0747616	+	0.0431636i	−0.0114010	+	0.00658239i	0.494289	+	0.869298i	$0.335429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.31658	−	1.91483i	0.483774	−	0.279307i	−0.238214	−	0.971213i	$-0.576562\pi$
$47$	3.31658	−	1.91483i	0.483774	−	0.279307i	0.721988	+	0.691906i	$0.243229\pi$
$48$		0			0
$49$	8.97869	−	15.5515i	1.28267	−	2.22165i
$50$		0			0
$51$	8.12194	+	8.99195i	1.13730	+	1.25912i
$52$		0			0
$53$			4.19164i			0.575766i	0.957666	+	0.287883i	$0.0929515\pi$
$53$			4.19164i			0.575766i	−0.957666	+	0.287883i	$0.907049\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.90060	−	2.61995i	0.384194	−	0.347021i
$58$		0			0
$59$	3.51278	−	6.08432i	0.457326	−	0.792111i	−0.541493	−	0.840705i	$-0.682141\pi$
$59$	3.51278	−	6.08432i	0.457326	−	0.792111i	0.998819	+	0.0485942i	$0.0154741\pi$
$60$		0			0
$61$	1.45470	+	2.51962i	0.186256	+	0.322604i	0.943999	−	0.329948i	$-0.107031\pi$
$61$	1.45470	+	2.51962i	0.186256	+	0.322604i	−0.757743	+	0.652553i	$0.773698\pi$
$62$		0			0
$63$	−6.13873	−	13.6723i	−0.773407	−	1.72255i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	7.76470	+	4.48295i	0.948609	+	0.547680i	0.892649	−	0.450753i	$-0.148845\pi$
$67$	7.76470	+	4.48295i	0.948609	+	0.547680i	0.0559605	+	0.998433i	$0.482178\pi$
$68$		0			0
$69$	−13.2028	+	2.82798i	−1.58944	+	0.340449i
$70$		0			0
$71$	8.79130			1.04334			0.521668	−	0.853149i	$-0.325310\pi$
$71$	8.79130			1.04334			0.521668	+	0.853149i	$0.325310\pi$
$72$		0			0
$73$		−	2.28650i		−	0.267614i	−0.991007	−	0.133807i	$-0.957280\pi$
$73$		−	2.28650i		−	0.267614i	0.991007	−	0.133807i	$-0.0427203\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−17.2873	−	9.98082i	−1.97007	−	1.13742i
$78$		0			0
$79$	−6.32211	−	10.9502i	−0.711293	−	1.23199i	−0.964372	−	0.264549i	$-0.914777\pi$
$79$	−6.32211	−	10.9502i	−0.711293	−	1.23199i	0.253080	−	0.967445i	$-0.418557\pi$
$80$		0			0
$81$	−8.81488	−	1.81599i	−0.979432	−	0.201776i
$82$		0			0
$83$	−12.0911	+	6.98082i	−1.32717	+	0.766244i	−0.984862	−	0.173342i	$-0.944544\pi$
$83$	−12.0911	+	6.98082i	−1.32717	+	0.766244i	−0.342313	+	0.939586i	$0.611210\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.1624	+	3.28437i	1.08952	+	0.352121i
$88$		0			0
$89$	10.3577			1.09792			0.548958	−	0.835850i	$-0.315025\pi$
$89$	10.3577			1.09792			0.548958	+	0.835850i	$0.315025\pi$
$90$		0			0
$91$	−7.70924			−0.808148
$92$		0			0
$93$	−0.197042	−	0.919921i	−0.0204324	−	0.0953914i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.08758	+	4.66936i	−0.821169	+	0.474102i	−0.850819	−	0.525458i	$-0.823894\pi$
$97$	−8.08758	+	4.66936i	−0.821169	+	0.474102i	0.0296505	+	0.999560i	$0.490561\pi$
$98$		0			0
$99$	−10.9355	+	4.90993i	−1.09906	+	0.493467i
$100$		0			0
$101$	−3.98082	−	6.89498i	−0.396106	−	0.686076i	0.597135	−	0.802140i	$-0.296306\pi$
$101$	−3.98082	−	6.89498i	−0.396106	−	0.686076i	−0.993242	+	0.116064i	$0.962972\pi$
$102$		0			0
$103$	14.2151	+	8.20711i	1.40066	+	0.808670i	0.994460	−	0.105115i	$-0.0335211\pi$
$103$	14.2151	+	8.20711i	1.40066	+	0.808670i	0.406198	+	0.913785i	$0.366854\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			11.3662i			1.09882i	0.835554	+	0.549408i	$0.185147\pi$
$107$			11.3662i			1.09882i	−0.835554	+	0.549408i	$0.814853\pi$
$108$		0			0
$109$	2.22683			0.213292			0.106646	−	0.994297i	$-0.465989\pi$
$109$	2.22683			0.213292			0.106646	+	0.994297i	$0.465989\pi$
$110$		0			0
$111$	7.25894	+	8.03650i	0.688988	+	0.762791i
$112$		0			0
$113$	2.45425	+	1.41696i	0.230877	+	0.133297i	0.610976	−	0.791649i	$-0.290777\pi$
$113$	2.45425	+	1.41696i	0.230877	+	0.133297i	−0.380100	+	0.924945i	$0.624110\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.70939	+	3.75385i	−0.250484	+	0.347043i
$118$		0			0
$119$	17.4744	+	30.2666i	1.60188	+	2.77453i
$120$		0			0
$121$	−2.48295	+	4.30060i	−0.225723	+	0.390963i
$122$		0			0
$123$	0.0710686	+	0.331794i	0.00640804	+	0.0299168i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	7.02130i		−	0.623040i	−0.950240	−	0.311520i	$-0.899162\pi$
$127$		−	7.02130i		−	0.623040i	0.950240	−	0.311520i	$-0.100838\pi$
$128$		0			0
$129$	−0.0459823	+	0.142277i	−0.00404852	+	0.0125268i
$130$		0			0
$131$	4.18312	−	7.24538i	0.365481	−	0.633032i	−0.623372	−	0.781925i	$-0.714238\pi$
$131$	4.18312	−	7.24538i	0.365481	−	0.633032i	0.988853	+	0.148893i	$0.0475711\pi$
$132$		0			0
$133$	9.76331	−	5.63685i	0.846587	−	0.488777i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.41734	+	1.39565i	−0.206527	+	0.119238i	−0.599696	−	0.800228i	$-0.704712\pi$
$137$	−2.41734	+	1.39565i	−0.206527	+	0.119238i	0.393169	+	0.919466i	$0.371379\pi$
$138$		0			0
$139$	−1.95799	+	3.39135i	−0.166075	+	0.287650i	−0.937036	−	0.349231i	$-0.886443\pi$
$139$	−1.95799	+	3.39135i	−0.166075	+	0.287650i	0.770962	+	0.636882i	$0.219776\pi$
$140$		0			0
$141$	2.03987	−	6.31172i	0.171788	−	0.531543i
$142$		0			0
$143$			6.16607i			0.515633i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.51436	−	30.4132i	−0.537296	−	2.50844i
$148$		0			0
$149$	−6.37860	+	11.0481i	−0.522555	+	0.905093i	0.477100	+	0.878849i	$0.341688\pi$
$149$	−6.37860	+	11.0481i	−0.522555	+	0.905093i	−0.999656	+	0.0262436i	$0.991645\pi$
$150$		0			0
$151$	0.188545	+	0.326569i	0.0153436	+	0.0265758i	0.873595	−	0.486653i	$-0.161782\pi$
$151$	0.188545	+	0.326569i	0.0153436	+	0.0265758i	−0.858252	+	0.513229i	$0.828449\pi$
$152$		0			0
$153$	20.8790	+	2.12833i	1.68797	+	0.172066i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.4761	+	6.04839i	0.836086	+	0.482714i	0.855932	−	0.517089i	$-0.172984\pi$
$157$	10.4761	+	6.04839i	0.836086	+	0.482714i	−0.0198461	+	0.999803i	$0.506318\pi$
$158$		0			0
$159$	4.86643	+	5.38771i	0.385933	+	0.427273i
$160$		0			0
$161$	−38.9446			−3.06926
$162$		0			0
$163$			10.8563i			0.850333i	0.905115	+	0.425166i	$0.139784\pi$
$163$			10.8563i			0.850333i	−0.905115	+	0.425166i	$0.860216\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.49240	+	2.59369i	0.347632	+	0.200706i	0.663642	−	0.748050i	$-0.269010\pi$
$167$	4.49240	+	2.59369i	0.347632	+	0.200706i	−0.316010	+	0.948756i	$0.602343\pi$
$168$		0			0
$169$	−5.30932	−	9.19602i	−0.408409	−	0.707386i
$170$		0			0
$171$	0.686552	−	6.73509i	0.0525019	−	0.515046i
$172$		0			0
$173$	−2.92264	+	1.68739i	−0.222204	+	0.128290i	−0.606970	−	0.794724i	$-0.707615\pi$
$173$	−2.92264	+	1.68739i	−0.222204	+	0.128290i	0.384766	+	0.923014i	$0.374282\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.54865	−	11.8987i	−0.191568	−	0.894365i
$178$		0			0
$179$	−19.5997			−1.46495			−0.732474	−	0.680795i	$-0.761634\pi$
$179$	−19.5997			−1.46495			−0.732474	+	0.680795i	$0.761634\pi$
$180$		0			0
$181$	5.84865			0.434727			0.217363	−	0.976091i	$-0.430254\pi$
$181$	5.84865			0.434727			0.217363	+	0.976091i	$0.430254\pi$
$182$		0			0
$183$	4.79504	+	1.54970i	0.354460	+	0.114557i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	24.2081	−	13.9766i	1.77027	−	1.02207i
$188$		0			0
$189$	−23.7637	−	10.4467i	−1.72856	−	0.759886i
$190$		0			0
$191$	12.2956	+	21.2965i	0.889676	+	1.54096i	0.840259	+	0.542186i	$0.182403\pi$
$191$	12.2956	+	21.2965i	0.889676	+	1.54096i	0.0494171	+	0.998778i	$0.484264\pi$
$192$		0			0
$193$	8.95729	+	5.17150i	0.644760	+	0.372252i	0.786446	−	0.617659i	$-0.211919\pi$
$193$	8.95729	+	5.17150i	0.644760	+	0.372252i	−0.141686	+	0.989912i	$0.545252\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			16.0256i			1.14177i	0.821028	+	0.570887i	$0.193401\pi$
$197$			16.0256i			1.14177i	−0.821028	+	0.570887i	$0.806599\pi$
$198$		0			0
$199$	22.2353			1.57622			0.788111	−	0.615533i	$-0.211059\pi$
$199$	22.2353			1.57622			0.788111	+	0.615533i	$0.211059\pi$
$200$		0			0
$201$	15.1850	−	3.25254i	1.07106	−	0.229417i
$202$		0			0
$203$	26.6771	+	15.4020i	1.87237	+	1.08101i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−13.6870	+	18.9632i	−0.951311	+	1.31804i
$208$		0			0
$209$	−4.50852	−	7.80899i	−0.311861	−	0.540159i
$210$		0			0
$211$	−12.1779	+	21.0927i	−0.838360	+	1.45208i	0.0529050	+	0.998600i	$0.483152\pi$
$211$	−12.1779	+	21.0927i	−0.838360	+	1.45208i	−0.891265	+	0.453483i	$0.850181\pi$
$212$		0			0
$213$	11.2999	−	10.2066i	0.774254	−	0.699342i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	2.71350i		−	0.184205i
$218$		0			0
$219$	−2.65459	−	2.93894i	−0.179380	−	0.198595i
$220$		0			0
$221$	5.39778	−	9.34923i	0.363094	−	0.628897i
$222$		0			0
$223$	9.74117	−	5.62407i	0.652317	−	0.376615i	−0.137026	−	0.990567i	$-0.543754\pi$
$223$	9.74117	−	5.62407i	0.652317	−	0.376615i	0.789343	+	0.613952i	$0.210421\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.78931	+	5.07451i	−0.583367	+	0.336807i	−0.762470	−	0.647023i	$-0.776014\pi$
$227$	−8.78931	+	5.07451i	−0.583367	+	0.336807i	0.179103	+	0.983830i	$0.442680\pi$
$228$		0			0
$229$	−1.18428	+	2.05123i	−0.0782595	+	0.135549i	−0.902499	−	0.430692i	$-0.858270\pi$
$229$	−1.18428	+	2.05123i	−0.0782595	+	0.135549i	0.824240	+	0.566241i	$0.191603\pi$
$230$		0			0
$231$	−33.8077	+	7.24145i	−2.22439	+	0.476452i
$232$		0			0
$233$		−	24.1831i		−	1.58429i	−0.610334	−	0.792144i	$-0.708965\pi$
$233$		−	24.1831i		−	1.58429i	0.610334	−	0.792144i	$-0.291035\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−20.8391	−	6.73495i	−1.35365	−	0.437482i
$238$		0			0
$239$	−0.897782	+	1.55500i	−0.0580727	+	0.100585i	−0.893600	−	0.448864i	$-0.851829\pi$
$239$	−0.897782	+	1.55500i	−0.0580727	+	0.100585i	0.835528	+	0.549449i	$0.185162\pi$
$240$		0			0
$241$	7.43339	+	12.8750i	0.478827	+	0.829352i	0.999705	−	0.0242785i	$-0.00772884\pi$
$241$	7.43339	+	12.8750i	0.478827	+	0.829352i	−0.520878	+	0.853631i	$0.674396\pi$
$242$		0			0
$243$	−13.4385	+	7.89977i	−0.862081	+	0.506770i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.01585	−	1.74120i	−0.191894	−	0.110790i
$248$		0			0
$249$	−7.43668	+	23.0104i	−0.471281	+	1.45822i
$250$		0			0
$251$	−15.8297			−0.999159			−0.499580	−	0.866268i	$-0.666512\pi$
$251$	−15.8297			−0.999159			−0.499580	+	0.866268i	$0.666512\pi$
$252$		0			0
$253$			31.1490i			1.95832i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−19.0489	−	10.9979i	−1.18824	−	0.686028i	−0.230330	−	0.973113i	$-0.573981\pi$
$257$	−19.0489	−	10.9979i	−1.18824	−	0.686028i	−0.957905	+	0.287084i	$0.907314\pi$
$258$		0			0
$259$	15.6177	+	27.0506i	0.970435	+	1.68084i
$260$		0			0
$261$	16.8753	−	7.57683i	1.04456	−	0.468994i
$262$		0			0
$263$	−13.1231	+	7.57664i	−0.809207	+	0.467196i	−0.846680	−	0.532102i	$-0.821402\pi$
$263$	−13.1231	+	7.57664i	−0.809207	+	0.467196i	0.0374737	+	0.999298i	$0.488069\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	13.3133	−	12.0251i	0.814758	−	0.735927i
$268$		0			0
$269$	7.99147			0.487249			0.243624	−	0.969870i	$-0.421664\pi$
$269$	7.99147			0.487249			0.243624	+	0.969870i	$0.421664\pi$
$270$		0			0
$271$	3.97248			0.241311			0.120656	−	0.992694i	$-0.461500\pi$
$271$	3.97248			0.241311			0.120656	+	0.992694i	$0.461500\pi$
$272$		0			0
$273$	−9.90904	+	8.95030i	−0.599723	+	0.541697i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.7738	+	9.10702i	−0.947757	+	0.547188i	−0.892383	−	0.451278i	$-0.850968\pi$
$277$	−15.7738	+	9.10702i	−0.947757	+	0.547188i	−0.0553736	+	0.998466i	$0.517635\pi$
$278$		0			0
$279$	−1.32128	−	0.953654i	−0.0791030	−	0.0570938i
$280$		0			0
$281$	11.1043	+	19.2333i	0.662429	+	1.14736i	0.979975	+	0.199119i	$0.0638079\pi$
$281$	11.1043	+	19.2333i	0.662429	+	1.14736i	−0.317546	+	0.948243i	$0.602859\pi$
$282$		0			0
$283$	−10.0916	−	5.82637i	−0.599882	−	0.346342i	0.169113	−	0.985597i	$-0.445910\pi$
$283$	−10.0916	−	5.82637i	−0.599882	−	0.346342i	−0.768995	+	0.639255i	$0.779243\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			0.978696i			0.0577706i
$288$		0			0
$289$	−31.9403			−1.87884
$290$		0			0
$291$	−4.97428	+	15.3913i	−0.291598	+	0.902254i
$292$		0			0
$293$	−5.35473	−	3.09156i	−0.312827	−	0.180611i	0.335364	−	0.942089i	$-0.391141\pi$
$293$	−5.35473	−	3.09156i	−0.312827	−	0.180611i	−0.648191	+	0.761478i	$0.724474\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8.35559	+	19.0069i	−0.484840	+	1.10289i
$298$		0			0
$299$	6.01492	+	10.4181i	0.347852	+	0.602497i
$300$		0			0
$301$	−0.215634	+	0.373489i	−0.0124289	+	0.0215276i
$302$		0			0
$303$	−13.1217	−	4.24078i	−0.753822	−	0.243626i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			12.9872i			0.741219i	0.928789	+	0.370610i	$0.120851\pi$
$307$			12.9872i			0.741219i	−0.928789	+	0.370610i	$0.879149\pi$
$308$		0			0
$309$	27.7997	−	5.95455i	1.58147	−	0.338743i
$310$		0			0
$311$	11.0958	−	19.2185i	0.629186	−	1.08978i	−0.358529	−	0.933519i	$-0.616722\pi$
$311$	11.0958	−	19.2185i	0.629186	−	1.08978i	0.987715	−	0.156264i	$-0.0499451\pi$
$312$		0			0
$313$	−14.4559	+	8.34609i	−0.817093	+	0.471749i	−0.849413	−	0.527729i	$-0.823044\pi$
$313$	−14.4559	+	8.34609i	−0.817093	+	0.471749i	0.0323199	+	0.999478i	$0.489710\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	28.5419	−	16.4787i	1.60307	−	0.925535i	0.612206	−	0.790698i	$-0.290282\pi$
$317$	28.5419	−	16.4787i	1.60307	−	0.925535i	0.990868	−	0.134837i	$-0.0430512\pi$
$318$		0			0
$319$	12.3190	−	21.3371i	0.689732	−	1.19465i
$320$		0			0
$321$	13.1960	+	14.6096i	0.736530	+	0.815426i
$322$		0			0
$323$			15.7870i			0.878414i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.86225	−	2.58532i	0.158283	−	0.142968i
$328$		0			0
$329$	9.56599	−	16.5688i	0.527390	−	0.913466i
$330$		0			0
$331$	−14.3333	−	24.8260i	−0.787830	−	1.36456i	−0.927294	−	0.374334i	$-0.877871\pi$
$331$	−14.3333	−	24.8260i	−0.787830	−	1.36456i	0.139464	−	0.990227i	$-0.455462\pi$
$332$		0			0
$333$	18.6605	+	1.90219i	1.02259	+	0.104239i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−25.8543	−	14.9270i	−1.40837	−	0.813125i	−0.413143	−	0.910666i	$-0.635569\pi$
$337$	−25.8543	−	14.9270i	−1.40837	−	0.813125i	−0.995231	+	0.0975411i	$0.968902\pi$
$338$		0			0
$339$	4.79964	−	1.02806i	0.260680	−	0.0558364i
$340$		0			0
$341$	−2.17034			−0.117530
$342$		0			0
$343$		−	54.7401i		−	2.95569i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.19000	−	2.41910i	−0.224931	−	0.129864i	0.383301	−	0.923624i	$-0.374787\pi$
$347$	−4.19000	−	2.41910i	−0.224931	−	0.129864i	−0.608231	+	0.793760i	$0.708121\pi$
$348$		0			0
$349$	−16.0325	−	27.7691i	−0.858200	−	1.48645i	−0.873644	−	0.486566i	$-0.838249\pi$
$349$	−16.0325	−	27.7691i	−0.858200	−	1.48645i	0.0154438	−	0.999881i	$-0.495084\pi$
$350$		0			0
$351$	0.875644	+	7.97056i	0.0467384	+	0.425437i
$352$		0			0
$353$	−8.53857	+	4.92975i	−0.454462	+	0.262384i	−0.709713	−	0.704491i	$-0.751175\pi$
$353$	−8.53857	+	4.92975i	−0.454462	+	0.262384i	0.255251	+	0.966875i	$0.417842\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	57.5997	+	18.6155i	3.04850	+	0.985239i
$358$		0			0
$359$	−9.93266			−0.524226			−0.262113	−	0.965037i	$-0.584419\pi$
$359$	−9.93266			−0.524226			−0.262113	+	0.965037i	$0.584419\pi$
$360$		0			0
$361$	−13.9075			−0.731972
$362$		0			0
$363$	1.80147	+	8.41043i	0.0945527	+	0.441433i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.4729	+	9.51065i	−0.859880	+	0.496452i	−0.863972	−	0.503540i	$-0.832031\pi$
$367$	−16.4729	+	9.51065i	−0.859880	+	0.496452i	0.00409206	+	0.999992i	$0.498697\pi$
$368$		0			0
$369$	0.476555	+	0.343961i	0.0248085	+	0.0179059i
$370$		0			0
$371$	10.4702	+	18.1349i	0.543584	+	0.941515i
$372$		0			0
$373$	1.62681	+	0.939241i	0.0842332	+	0.0486320i	0.541525	−	0.840685i	$-0.317847\pi$
$373$	1.62681	+	0.939241i	0.0842332	+	0.0486320i	−0.457292	+	0.889317i	$0.651180\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	9.51526i		−	0.490061i
$378$		0			0
$379$	−22.8435			−1.17339			−0.586697	−	0.809807i	$-0.699572\pi$
$379$	−22.8435			−1.17339			−0.586697	+	0.809807i	$0.699572\pi$
$380$		0			0
$381$	−8.15162	−	9.02481i	−0.417620	−	0.462355i
$382$		0			0
$383$	4.07262	+	2.35133i	0.208101	+	0.120147i	0.600429	−	0.799678i	$-0.294997\pi$
$383$	4.07262	+	2.35133i	0.208101	+	0.120147i	−0.392327	+	0.919826i	$0.628330\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.106078	+	0.236260i	0.00539227	+	0.0120098i
$388$		0			0
$389$	−5.38287	−	9.32340i	−0.272922	−	0.472715i	0.696687	−	0.717376i	$-0.254657\pi$
$389$	−5.38287	−	9.32340i	−0.272922	−	0.472715i	−0.969609	+	0.244661i	$0.921323\pi$
$390$		0			0
$391$	27.2679	−	47.2293i	1.37899	−	2.38849i
$392$		0			0
$393$	−3.03501	−	14.1694i	−0.153096	−	0.714750i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			8.10958i			0.407008i	0.979074	+	0.203504i	$0.0652330\pi$
$397$			8.10958i			0.407008i	−0.979074	+	0.203504i	$0.934767\pi$
$398$		0			0
$399$	6.00495	−	18.5804i	0.300624	−	0.930182i
$400$		0			0
$401$	6.22744	−	10.7862i	0.310984	−	0.538640i	−0.667592	−	0.744527i	$-0.732675\pi$
$401$	6.22744	−	10.7862i	0.310984	−	0.538640i	0.978576	+	0.205888i	$0.0660082\pi$
$402$		0			0
$403$	−0.725894	+	0.419095i	−0.0361594	+	0.0208766i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.6359	−	12.4915i	1.07245	−	0.619179i
$408$		0			0
$409$	−15.7166	+	27.2219i	−0.777136	+	1.34604i	0.156450	+	0.987686i	$0.449995\pi$
$409$	−15.7166	+	27.2219i	−0.777136	+	1.34604i	−0.933586	+	0.358353i	$0.883338\pi$
$410$		0			0
$411$	−1.48679	+	4.60038i	−0.0733379	+	0.226920i
$412$		0			0
$413$		−	35.0979i		−	1.72705i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.42060	+	6.63226i	0.0695669	+	0.324783i
$418$		0			0
$419$	13.1848	−	22.8368i	0.644121	−	1.11565i	−0.340383	−	0.940287i	$-0.610557\pi$
$419$	13.1848	−	22.8368i	0.644121	−	1.11565i	0.984504	−	0.175363i	$-0.0561100\pi$
$420$		0			0
$421$	6.61555	+	11.4585i	0.322422	+	0.558451i	0.980987	−	0.194072i	$-0.0621696\pi$
$421$	6.61555	+	11.4585i	0.322422	+	0.558451i	−0.658565	+	0.752524i	$0.728836\pi$
$422$		0			0
$423$	−4.70586	−	10.4810i	−0.228807	−	0.509604i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.5874	+	7.26732i	0.609145	+	0.351690i
$428$		0			0
$429$	7.15871	+	7.92554i	0.345626	+	0.382649i
$430$		0			0
$431$	24.2895			1.16999			0.584993	−	0.811039i	$-0.301097\pi$
$431$	24.2895			1.16999			0.584993	+	0.811039i	$0.301097\pi$
$432$		0			0
$433$		−	17.9840i		−	0.864258i	−0.901812	−	0.432129i	$-0.857763\pi$
$433$		−	17.9840i		−	0.864258i	0.901812	−	0.432129i	$-0.142237\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.2351	−	8.79599i	−0.728794	−	0.420769i
$438$		0			0
$439$	11.3577	+	19.6721i	0.542074	+	0.938900i	0.998785	+	0.0492847i	$0.0156942\pi$
$439$	11.3577	+	19.6721i	0.542074	+	0.938900i	−0.456711	+	0.889615i	$0.650972\pi$
$440$		0			0
$441$	−43.6825	−	31.5285i	−2.08012	−	1.50136i
$442$		0			0
$443$	19.8455	−	11.4578i	0.942888	−	0.544377i	0.0520235	−	0.998646i	$-0.483433\pi$
$443$	19.8455	−	11.4578i	0.942888	−	0.544377i	0.890864	+	0.454269i	$0.150100\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.62791	+	21.6060i	0.218892	+	1.02193i
$448$		0			0
$449$	5.36966			0.253410			0.126705	−	0.991940i	$-0.459560\pi$
$449$	5.36966			0.253410			0.126705	+	0.991940i	$0.459560\pi$
$450$		0			0
$451$	0.782790			0.0368601
$452$		0			0
$453$	0.621487	+	0.200857i	0.0292000	+	0.00943710i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.6677	−	9.62309i	0.779682	−	0.450149i	−0.0566358	−	0.998395i	$-0.518037\pi$
$457$	16.6677	−	9.62309i	0.779682	−	0.450149i	0.836317	+	0.548246i	$0.184704\pi$
$458$		0			0
$459$	29.3077	−	21.5045i	1.36797	−	1.00375i
$460$		0			0
$461$	−17.6870	−	30.6347i	−0.823763	−	1.42680i	−0.902861	−	0.429933i	$-0.858537\pi$
$461$	−17.6870	−	30.6347i	−0.823763	−	1.42680i	0.0790973	−	0.996867i	$-0.474796\pi$
$462$		0			0
$463$	−14.8277	−	8.56075i	−0.689100	−	0.397852i	0.114175	−	0.993461i	$-0.463578\pi$
$463$	−14.8277	−	8.56075i	−0.689100	−	0.397852i	−0.803275	+	0.595609i	$0.796911\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			25.9318i			1.19998i	0.800007	+	0.599990i	$0.204829\pi$
$467$			25.9318i			1.19998i	−0.800007	+	0.599990i	$0.795171\pi$
$468$		0			0
$469$	44.7913			2.06827
$470$		0			0
$471$	20.4875	−	4.38833i	0.944016	−	0.202203i
$472$		0			0
$473$	0.298728	+	0.172471i	0.0137355	+	0.00793020i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	12.5101	+	1.27524i	0.572798	+	0.0583890i
$478$		0			0
$479$	−10.4574	−	18.1127i	−0.477810	−	0.827591i	0.521867	−	0.853027i	$-0.325236\pi$
$479$	−10.4574	−	18.1127i	−0.477810	−	0.827591i	−0.999676	+	0.0254364i	$0.991902\pi$
$480$		0			0
$481$	4.82424	−	8.35583i	0.219966	−	0.380993i
$482$		0			0
$483$	−50.0573	+	45.2140i	−2.27769	+	2.05731i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	20.2373i		−	0.917039i	−0.888684	−	0.458520i	$-0.848380\pi$
$487$		−	20.2373i		−	0.917039i	0.888684	−	0.458520i	$-0.151620\pi$
$488$		0			0
$489$	12.6040	+	13.9541i	0.569973	+	0.631028i
$490$		0			0
$491$	7.10009	−	12.2977i	0.320422	−	0.554988i	−0.660153	−	0.751131i	$-0.729509\pi$
$491$	7.10009	−	12.2977i	0.320422	−	0.554988i	0.980575	+	0.196143i	$0.0628418\pi$
$492$		0			0
$493$	−37.3571	+	21.5681i	−1.68248	+	0.971379i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	38.0350	−	21.9595i	1.70610	−	0.985018i
$498$		0			0
$499$	−14.1384	+	24.4884i	−0.632920	+	1.09625i	0.354032	+	0.935233i	$0.384811\pi$
$499$	−14.1384	+	24.4884i	−0.632920	+	1.09625i	−0.986952	+	0.161016i	$0.948523\pi$
$500$		0			0
$501$	8.78552	−	1.88182i	0.392508	−	0.0840733i
$502$		0			0
$503$		−	17.4165i		−	0.776565i	−0.921540	−	0.388282i	$-0.873069\pi$
$503$		−	17.4165i		−	0.776565i	0.921540	−	0.388282i	$-0.126931\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−17.5007	−	5.65603i	−0.777236	−	0.251193i
$508$		0			0
$509$	11.1060	−	19.2362i	0.492267	−	0.852631i	−0.507694	−	0.861538i	$-0.669502\pi$
$509$	11.1060	−	19.2362i	0.492267	−	0.852631i	0.999960	+	0.00890659i	$0.00283509\pi$
$510$		0			0
$511$	−5.71137	−	9.89238i	−0.252656	−	0.437613i
$512$		0			0
$513$	−6.93688	−	9.45401i	−0.306271	−	0.417405i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−13.2522	−	7.65116i	−0.582831	−	0.336498i
$518$		0			0
$519$	−1.79758	+	5.56201i	−0.0789049	+	0.244145i
$520$		0			0
$521$	5.48898			0.240477			0.120238	−	0.992745i	$-0.461634\pi$
$521$	5.48898			0.240477			0.120238	+	0.992745i	$0.461634\pi$
$522$		0			0
$523$			26.0991i			1.14123i	0.821216	+	0.570617i	$0.193296\pi$
$523$			26.0991i			1.14123i	−0.821216	+	0.570617i	$0.806704\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.29075	+	1.89991i	0.143347	+	0.0827616i
$528$		0			0
$529$	18.8854	+	32.7105i	0.821105	+	1.42220i
$530$		0			0
$531$	−17.0902	−	12.3351i	−0.741650	−	0.535297i
$532$		0			0
$533$	0.261813	−	0.151158i	0.0113404	−	0.00654737i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−25.1924	+	22.7549i	−1.08713	+	0.981946i
$538$		0			0
$539$	−71.7529			−3.09062
$540$		0			0
$541$	18.7828			0.807534			0.403767	−	0.914862i	$-0.367701\pi$
$541$	18.7828			0.807534			0.403767	+	0.914862i	$0.367701\pi$
$542$		0			0
$543$	7.51754	−	6.79019i	0.322609	−	0.291395i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.84315	−	4.52825i	0.335349	−	0.193614i	−0.322864	−	0.946445i	$-0.604646\pi$
$547$	7.84315	−	4.52825i	0.335349	−	0.193614i	0.658213	+	0.752831i	$0.271312\pi$
$548$		0			0
$549$	7.96246	−	3.57506i	0.339830	−	0.152580i
$550$		0			0
$551$	6.95738	+	12.0505i	0.296395	+	0.513370i
$552$		0			0
$553$	−54.7044	−	31.5836i	−2.32627	−	1.34307i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			24.8467i			1.05279i	0.850241	+	0.526394i	$0.176456\pi$
$557$			24.8467i			1.05279i	−0.850241	+	0.526394i	$0.823544\pi$
$558$		0			0
$559$	0.133217			0.00563448
$560$		0			0
$561$	14.8893	−	46.0699i	0.628625	−	1.94507i
$562$		0			0
$563$	−20.2247	−	11.6767i	−0.852369	−	0.492115i	0.00908064	−	0.999959i	$-0.497110\pi$
$563$	−20.2247	−	11.6767i	−0.852369	−	0.492115i	−0.861449	+	0.507843i	$0.830443\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−42.6731	+	14.1617i	−1.79210	+	0.594734i
$568$		0			0
$569$	−7.54510	−	13.0685i	−0.316307	−	0.547860i	0.663407	−	0.748258i	$-0.269110\pi$
$569$	−7.54510	−	13.0685i	−0.316307	−	0.547860i	−0.979714	+	0.200398i	$0.935776\pi$
$570$		0			0
$571$	3.26786	−	5.66011i	0.136756	−	0.236868i	−0.789511	−	0.613736i	$-0.789666\pi$
$571$	3.26786	−	5.66011i	0.136756	−	0.236868i	0.926267	+	0.376868i	$0.122999\pi$
$572$		0			0
$573$	40.5290	+	13.0985i	1.69312	+	0.547197i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			8.12662i			0.338316i	0.985589	+	0.169158i	$0.0541047\pi$
$577$			8.12662i			0.338316i	−0.985589	+	0.169158i	$0.945895\pi$
$578$		0			0
$579$	17.5173	−	3.75211i	0.727992	−	0.155932i
$580$		0			0
$581$	−34.8743	+	60.4041i	−1.44683	+	2.50598i
$582$		0			0
$583$	14.5048	−	8.37435i	0.600727	−	0.346830i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.3438	−	6.54937i	0.468210	−	0.270321i	−0.247280	−	0.968944i	$-0.579537\pi$
$587$	11.3438	−	6.54937i	0.468210	−	0.270321i	0.715490	+	0.698623i	$0.246203\pi$
$588$		0			0
$589$	0.612869	−	1.06152i	0.0252528	−	0.0437392i
$590$		0			0
$591$	18.6054	+	20.5984i	0.765325	+	0.847305i
$592$		0			0
$593$		−	8.60478i		−	0.353356i	−0.984269	−	0.176678i	$-0.943465\pi$
$593$		−	8.60478i		−	0.353356i	0.984269	−	0.176678i	$-0.0565351\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	28.5801	−	25.8149i	1.16971	−	1.05653i
$598$		0			0
$599$	12.1827	−	21.1010i	0.497771	−	0.862165i	−0.502225	−	0.864737i	$-0.667485\pi$
$599$	12.1827	−	21.1010i	0.497771	−	0.862165i	0.999997	+	0.00257140i	$0.000818504\pi$
$600$		0			0
$601$	12.0900	+	20.9404i	0.493160	+	0.854179i	0.999969	−	0.00787996i	$-0.00250829\pi$
$601$	12.0900	+	20.9404i	0.493160	+	0.854179i	−0.506809	+	0.862059i	$0.669175\pi$
$602$		0			0
$603$	15.7418	−	21.8101i	0.641056	−	0.888178i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.23582	−	0.713502i	−0.0501605	−	0.0289602i	0.474710	−	0.880142i	$-0.342553\pi$
$607$	−1.23582	−	0.713502i	−0.0501605	−	0.0289602i	−0.524871	+	0.851182i	$0.675886\pi$
$608$		0			0
$609$	52.1709	−	11.1747i	2.11407	−	0.452823i
$610$		0			0
$611$	−5.90979			−0.239085
$612$		0			0
$613$		−	6.92878i		−	0.279851i	−0.990162	−	0.139925i	$-0.955314\pi$
$613$		−	6.92878i		−	0.279851i	0.990162	−	0.139925i	$-0.0446863\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.9437	+	13.2466i	0.923679	+	0.533286i	0.884807	−	0.465958i	$-0.154290\pi$
$617$	22.9437	+	13.2466i	0.923679	+	0.533286i	0.0388718	+	0.999244i	$0.487624\pi$
$618$		0			0
$619$	−13.4798	−	23.3478i	−0.541801	−	0.938426i	−0.998801	−	0.0489597i	$-0.984409\pi$
$619$	−13.4798	−	23.3478i	−0.541801	−	0.938426i	0.457000	−	0.889467i	$-0.348924\pi$
$620$		0			0
$621$	4.42347	+	40.2647i	0.177508	+	1.61577i
$622$		0			0
$623$	44.8120	−	25.8722i	1.79535	−	1.03655i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−14.8611	−	4.80294i	−0.593496	−	0.191811i
$628$		0			0
$629$	−43.7401			−1.74403
$630$		0			0
$631$	−15.9350			−0.634361			−0.317181	−	0.948365i	$-0.602736\pi$
$631$	−15.9350			−0.634361			−0.317181	+	0.948365i	$0.602736\pi$
$632$		0			0
$633$	8.83550	+	41.2498i	0.351179	+	1.63953i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−23.9986	+	13.8556i	−0.950858	+	0.548978i
$638$		0			0
$639$	2.67460	−	26.2379i	0.105806	−	1.03796i
$640$		0			0
$641$	3.58090	+	6.20231i	0.141437	+	0.244976i	0.928038	−	0.372485i	$-0.121494\pi$
$641$	3.58090	+	6.20231i	0.141437	+	0.244976i	−0.786601	+	0.617462i	$0.788161\pi$
$642$		0			0
$643$	6.11680	+	3.53154i	0.241223	+	0.139270i	0.615739	−	0.787950i	$-0.288858\pi$
$643$	6.11680	+	3.53154i	0.241223	+	0.139270i	−0.374516	+	0.927221i	$0.622191\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			26.4037i			1.03804i	0.854763	+	0.519019i	$0.173703\pi$
$647$			26.4037i			1.03804i	−0.854763	+	0.519019i	$0.826297\pi$
$648$		0			0
$649$	−28.0723			−1.10193
$650$		0			0
$651$	−3.15033	−	3.48779i	−0.123471	−	0.136697i
$652$		0			0
$653$	−6.68545	−	3.85985i	−0.261622	−	0.151048i	0.363452	−	0.931613i	$-0.381598\pi$
$653$	−6.68545	−	3.85985i	−0.261622	−	0.151048i	−0.625074	+	0.780565i	$0.714931\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−6.82413	−	0.695628i	−0.266235	−	0.0271390i
$658$		0			0
$659$	−11.1426	−	19.2996i	−0.434055	−	0.751806i	0.563163	−	0.826346i	$-0.309584\pi$
$659$	−11.1426	−	19.2996i	−0.434055	−	0.751806i	−0.997218	+	0.0745403i	$0.976251\pi$
$660$		0			0
$661$	−16.0544	+	27.8070i	−0.624442	+	1.08157i	0.364207	+	0.931318i	$0.381340\pi$
$661$	−16.0544	+	27.8070i	−0.624442	+	1.08157i	−0.988648	+	0.150247i	$0.951993\pi$
$662$		0			0
$663$	−3.91629	−	18.2837i	−0.152096	−	0.710082i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	48.0680i		−	1.86120i
$668$		0			0
$669$	5.99133	−	18.5382i	0.231638	−	0.716729i
$670$		0			0
$671$	5.81261	−	10.0677i	0.224393	−	0.388661i
$672$		0			0
$673$	−6.78237	+	3.91580i	−0.261441	+	0.150943i	−0.624992	−	0.780631i	$-0.714898\pi$
$673$	−6.78237	+	3.91580i	−0.261441	+	0.150943i	0.363551	+	0.931574i	$0.381564\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.5914	−	9.00171i	0.599227	−	0.345964i	−0.169511	−	0.985528i	$-0.554219\pi$
$677$	15.5914	−	9.00171i	0.599227	−	0.345964i	0.768737	+	0.639565i	$0.220885\pi$
$678$		0			0
$679$	−23.3269	+	40.4034i	−0.895205	+	1.55054i
$680$		0			0
$681$	−5.40588	+	16.7267i	−0.207154	+	0.640970i
$682$		0			0
$683$			30.3356i			1.16076i	0.814347	+	0.580379i	$0.197096\pi$
$683$			30.3356i			1.16076i	−0.814347	+	0.580379i	$0.802904\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	0.859238	+	4.01148i	0.0327820	+	0.153047i
$688$		0			0
$689$	3.23419	−	5.60179i	0.123213	−	0.213411i
$690$		0			0
$691$	−14.0575	−	24.3482i	−0.534771	−	0.926251i	−0.999174	−	0.0406267i	$-0.987065\pi$
$691$	−14.0575	−	24.3482i	−0.534771	−	0.926251i	0.464403	−	0.885624i	$-0.346269\pi$
$692$		0			0
$693$	−35.0475	+	48.5580i	−1.33134	+	1.84457i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.18690	−	0.685255i	−0.0449569	−	0.0259559i
$698$		0			0
$699$	−28.0762	−	31.0837i	−1.06194	−	1.17569i
$700$		0			0
$701$	28.4378			1.07408			0.537041	−	0.843556i	$-0.319542\pi$
$701$	28.4378			1.07408			0.537041	+	0.843556i	$0.319542\pi$
$702$		0			0
$703$			14.1096i			0.532153i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−34.4455	−	19.8871i	−1.29546	−	0.747932i
$708$		0			0
$709$	15.4500	+	26.7602i	0.580237	+	1.00500i	0.995451	+	0.0952767i	$0.0303736\pi$
$709$	15.4500	+	26.7602i	0.580237	+	1.00500i	−0.415213	+	0.909724i	$0.636293\pi$
$710$		0			0
$711$	−34.6047	+	15.5371i	−1.29778	+	0.582688i
$712$		0			0
$713$	−3.66698	+	2.11713i	−0.137330	+	0.0792873i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.651374	+	3.04103i	0.0243260	+	0.113569i
$718$		0			0
$719$	21.2462			0.792349			0.396175	−	0.918175i	$-0.370338\pi$
$719$	21.2462			0.792349			0.396175	+	0.918175i	$0.370338\pi$
$720$		0			0
$721$	82.0011			3.05388
$722$		0			0
$723$	24.5022	+	7.91881i	0.911245	+	0.294504i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−21.6351	+	12.4910i	−0.802402	+	0.463267i	−0.844310	−	0.535854i	$-0.819990\pi$
$727$	−21.6351	+	12.4910i	−0.802402	+	0.463267i	0.0419082	+	0.999121i	$0.486656\pi$
$728$		0			0
$729$	−8.10165	+	25.7558i	−0.300061	+	0.953920i
$730$		0			0
$731$	−0.301961	−	0.523013i	−0.0111684	−	0.0193443i
$732$		0			0
$733$	9.06528	+	5.23384i	0.334834	+	0.193316i	0.657985	−	0.753031i	$-0.271409\pi$
$733$	9.06528	+	5.23384i	0.334834	+	0.193316i	−0.323151	+	0.946347i	$0.604742\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	35.8254i		−	1.31964i
$738$		0			0
$739$	−35.6244			−1.31046			−0.655232	−	0.755428i	$-0.727429\pi$
$739$	−35.6244			−1.31046			−0.655232	+	0.755428i	$0.727429\pi$
$740$		0			0
$741$	−5.89792	+	1.26331i	−0.216666	+	0.0464087i
$742$		0			0
$743$	−8.70823	−	5.02770i	−0.319474	−	0.184448i	0.331684	−	0.943391i	$-0.392383\pi$
$743$	−8.70823	−	5.02770i	−0.319474	−	0.184448i	−0.651158	+	0.758942i	$0.725717\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	17.1560	+	38.2102i	0.627704	+	1.39804i
$748$		0			0
$749$	28.3914	+	49.1753i	1.03740	+	1.79683i
$750$		0			0
$751$	−8.86740	+	15.3588i	−0.323576	+	0.560450i	−0.981223	−	0.192876i	$-0.938219\pi$
$751$	−8.86740	+	15.3588i	−0.323576	+	0.560450i	0.657647	+	0.753326i	$0.271552\pi$
$752$		0			0
$753$	−20.3466	+	18.3780i	−0.741472	+	0.669731i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			6.42042i			0.233354i	0.993170	+	0.116677i	$0.0372243\pi$
$757$			6.42042i			0.233354i	−0.993170	+	0.116677i	$0.962776\pi$
$758$		0			0
$759$	36.1635	+	40.0373i	1.31265	+	1.45326i
$760$		0			0
$761$	−12.6955	+	21.9892i	−0.460211	+	0.797108i	−0.998971	−	0.0453506i	$-0.985559\pi$
$761$	−12.6955	+	21.9892i	−0.460211	+	0.797108i	0.538760	+	0.842459i	$0.318893\pi$
$762$		0			0
$763$	9.63425	−	5.56234i	0.348783	−	0.201370i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.38910	+	5.42080i	−0.339021	+	0.195734i
$768$		0			0
$769$	−7.40088	+	12.8187i	−0.266883	+	0.462254i	−0.968055	−	0.250737i	$-0.919327\pi$
$769$	−7.40088	+	12.8187i	−0.266883	+	0.462254i	0.701173	+	0.712992i	$0.252660\pi$
$770$		0			0
$771$	−37.2527	+	7.97935i	−1.34162	+	0.287369i
$772$		0			0
$773$			7.48046i			0.269053i	0.990910	+	0.134527i	$0.0429514\pi$
$773$			7.48046i			0.269053i	−0.990910	+	0.134527i	$0.957049\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	51.4794	+	16.6375i	1.84681	+	0.596868i
$778$		0			0
$779$	−0.221048	+	0.382866i	−0.00791985	+	0.0137176i
$780$		0			0
$781$	−17.5639	−	30.4215i	−0.628484	−	1.08857i
$782$		0			0
$783$	12.8940	−	29.3308i	0.460795	−	1.04820i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−45.3082	−	26.1587i	−1.61506	−	0.932457i	−0.988172	−	0.153350i	$-0.950994\pi$
$787$	−45.3082	−	26.1587i	−1.61506	−	0.932457i	−0.626891	−	0.779107i	$-0.715673\pi$
$788$		0			0
$789$	−8.07141	+	24.9743i	−0.287350	+	0.889110i
$790$		0			0
$791$	14.1575			0.503384
$792$		0			0
$793$		−	4.48969i		−	0.159434i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−46.5366	−	26.8679i	−1.64841	−	0.951711i	−0.977703	−	0.209991i	$-0.932657\pi$
$797$	−46.5366	−	26.8679i	−1.64841	−	0.951711i	−0.670709	−	0.741721i	$-0.734010\pi$
$798$		0			0
$799$	13.3957	+	23.2019i	0.473904	+	0.820826i
$800$		0			0
$801$	3.15116	−	30.9130i	0.111341	−	1.09226i
$802$		0			0
$803$	−7.91222	+	4.56812i	−0.279216	+	0.161205i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.2718	−	9.27797i	0.361585	−	0.326600i
$808$		0			0
$809$	26.1908			0.920819			0.460410	−	0.887707i	$-0.347703\pi$
$809$	26.1908			0.920819			0.460410	+	0.887707i	$0.347703\pi$
$810$		0			0
$811$	−52.3506			−1.83828			−0.919140	−	0.393931i	$-0.871115\pi$
$811$	−52.3506			−1.83828			−0.919140	+	0.393931i	$0.871115\pi$
$812$		0			0
$813$	5.10602	−	4.61199i	0.179076	−	0.161750i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.168712	+	0.0974059i	−0.00590249	+	0.00340780i
$818$		0			0
$819$	−2.34540	+	23.0085i	−0.0819550	+	0.803981i
$820$		0			0
$821$	2.42932	+	4.20771i	0.0847839	+	0.146850i	0.905299	−	0.424775i	$-0.139647\pi$
$821$	2.42932	+	4.20771i	0.0847839	+	0.146850i	−0.820515	+	0.571625i	$0.806313\pi$
$822$		0			0
$823$	−1.01998	−	0.588886i	−0.0355543	−	0.0205273i	0.482117	−	0.876107i	$-0.339868\pi$
$823$	−1.01998	−	0.588886i	−0.0355543	−	0.0205273i	−0.517672	+	0.855579i	$0.673201\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	32.7188i		−	1.13775i	−0.822426	−	0.568873i	$-0.807380\pi$
$827$		−	32.7188i		−	1.13775i	0.822426	−	0.568873i	$-0.192620\pi$
$828$		0			0
$829$	5.99342			0.208160			0.104080	−	0.994569i	$-0.466810\pi$
$829$	5.99342			0.208160			0.104080	+	0.994569i	$0.466810\pi$
$830$		0			0
$831$	−9.70173	+	30.0188i	−0.336549	+	1.04134i
$832$		0			0
$833$	108.794	+	62.8125i	3.76951	+	2.17632i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.80548	+	0.308210i	−0.0969716	+	0.0106533i
$838$		0			0
$839$	−19.1933	−	33.2439i	−0.662628	−	1.14771i	−0.979923	−	0.199378i	$-0.936108\pi$
$839$	−19.1933	−	33.2439i	−0.662628	−	1.14771i	0.317295	−	0.948327i	$-0.397226\pi$
$840$		0			0
$841$	−4.51023	+	7.81195i	−0.155525	+	0.269378i
$842$		0			0
$843$	36.6025	+	11.8295i	1.26066	+	0.407429i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			24.8083i			0.852425i
$848$		0			0
$849$	−19.7355	+	4.22724i	−0.677320	+	0.145079i
$850$		0			0
$851$	24.3705	−	42.2109i	0.835410	−	1.44697i
$852$		0			0
$853$	18.8092	−	10.8595i	0.644015	−	0.371822i	−0.142145	−	0.989846i	$-0.545400\pi$
$853$	18.8092	−	10.8595i	0.644015	−	0.371822i	0.786159	+	0.618024i	$0.212067\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.98342	−	2.29983i	0.136071	−	0.0785607i	−0.430419	−	0.902629i	$-0.641634\pi$
$857$	3.98342	−	2.29983i	0.136071	−	0.0785607i	0.566490	+	0.824068i	$0.308301\pi$
$858$		0			0
$859$	7.45896	−	12.9193i	0.254496	−	0.440801i	−0.710262	−	0.703937i	$-0.751424\pi$
$859$	7.45896	−	12.9193i	0.254496	−	0.440801i	0.964759	+	0.263137i	$0.0847570\pi$
$860$		0			0
$861$	1.13625	+	1.25796i	0.0387233	+	0.0428713i
$862$		0			0
$863$			11.4089i			0.388362i	0.980966	+	0.194181i	$0.0622050\pi$
$863$			11.4089i			0.388362i	−0.980966	+	0.194181i	$0.937795\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−41.0544	+	37.0822i	−1.39428	+	1.25938i
$868$		0			0
$869$	−25.2615	+	43.7541i	−0.856937	+	1.48426i
$870$		0			0
$871$	−6.91793	−	11.9822i	−0.234405	−	0.406001i
$872$		0			0
$873$	11.4754	+	25.5582i	0.388382	+	0.865015i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	24.1867	+	13.9642i	0.816727	+	0.471537i	0.849286	−	0.527932i	$-0.177033\pi$
$877$	24.1867	+	13.9642i	0.816727	+	0.471537i	−0.0325596	+	0.999470i	$0.510366\pi$
$878$		0			0
$879$	−10.4719	+	2.24304i	−0.353210	+	0.0756557i
$880$		0			0
$881$	−42.3270			−1.42603			−0.713017	−	0.701147i	$-0.752672\pi$
$881$	−42.3270			−1.42603			−0.713017	+	0.701147i	$0.752672\pi$
$882$		0			0
$883$		−	20.3895i		−	0.686161i	−0.939306	−	0.343081i	$-0.888530\pi$
$883$		−	20.3895i		−	0.686161i	0.939306	−	0.343081i	$-0.111470\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	34.2471	+	19.7725i	1.14990	+	0.663897i	0.948864	−	0.315686i	$-0.102235\pi$
$887$	34.2471	+	19.7725i	1.14990	+	0.663897i	0.201040	+	0.979583i	$0.435568\pi$
$888$		0			0
$889$	−17.5383	−	30.3772i	−0.588215	−	1.01882i
$890$		0			0
$891$	11.3269	+	34.1312i	0.379466	+	1.14344i
$892$		0			0
$893$	7.48442	−	4.32113i	0.250457	−	0.144601i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	19.8265	+	6.40770i	0.661989	+	0.213947i
$898$		0			0
$899$	3.34919			0.111702
$900$		0			0
$901$	−29.3236			−0.976911
$902$		0			0
$903$	0.156450	+	0.730411i	0.00520634	+	0.0243066i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−32.0080	+	18.4798i	−1.06281	+	0.613613i	−0.926208	−	0.377013i	$-0.876951\pi$
$907$	−32.0080	+	18.4798i	−1.06281	+	0.613613i	−0.136601	+	0.990626i	$0.543618\pi$
$908$		0			0
$909$	−21.7894	+	9.78321i	−0.722709	+	0.324489i
$910$		0			0
$911$	4.92335	+	8.52749i	0.163118	+	0.282528i	0.935985	−	0.352039i	$-0.114512\pi$
$911$	4.92335	+	8.52749i	0.163118	+	0.282528i	−0.772867	+	0.634568i	$0.781178\pi$
$912$		0			0
$913$	48.3130	+	27.8935i	1.59893	+	0.923140i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	41.7955i		−	1.38021i
$918$		0			0
$919$	8.42079			0.277776			0.138888	−	0.990308i	$-0.455647\pi$
$919$	8.42079			0.277776			0.138888	+	0.990308i	$0.455647\pi$
$920$		0			0
$921$	15.0779	+	16.6931i	0.496835	+	0.550055i
$922$		0			0
$923$	−11.7489	−	6.78321i	−0.386718	−	0.223272i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	28.8191	−	39.9286i	0.946543	−	1.31143i
$928$		0			0
$929$	−14.1938	−	24.5843i	−0.465683	−	0.806586i	0.533549	−	0.845769i	$-0.320858\pi$
$929$	−14.1938	−	24.5843i	−0.465683	−	0.806586i	−0.999232	+	0.0391829i	$0.987524\pi$
$930$		0			0
$931$	20.2619	−	35.0946i	0.664057	−	1.15018i
$932$		0			0
$933$	−8.05042	−	37.5845i	−0.263559	−	1.23046i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			4.69342i			0.153327i	0.997057	+	0.0766637i	$0.0244268\pi$
$937$			4.69342i			0.153327i	−0.997057	+	0.0766637i	$0.975573\pi$
$938$		0			0
$939$	−8.89111	+	27.5106i	−0.290150	+	0.897776i
$940$		0			0
$941$	−9.51278	+	16.4766i	−0.310108	+	0.537123i	−0.978385	−	0.206789i	$-0.933699\pi$
$941$	−9.51278	+	16.4766i	−0.310108	+	0.537123i	0.668278	+	0.743912i	$0.267032\pi$
$942$		0			0
$943$	1.32259	−	0.763600i	0.0430696	−	0.0248662i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.0997	−	6.40843i	0.360693	−	0.208246i	−0.308692	−	0.951162i	$-0.599891\pi$
$947$	11.0997	−	6.40843i	0.360693	−	0.208246i	0.669385	+	0.742916i	$0.266558\pi$
$948$		0			0
$949$	−1.76422	+	3.05572i	−0.0572690	+	0.0991928i
$950$		0			0
$951$	17.5548	−	54.3175i	0.569253	−	1.76137i
$952$		0			0
$953$		−	45.9701i		−	1.48912i	−0.667556	−	0.744560i	$-0.732660\pi$
$953$		−	45.9701i		−	1.48912i	0.667556	−	0.744560i	$-0.267340\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−8.93788	−	41.7278i	−0.288921	−	1.34887i
$958$		0			0
$959$	−6.97230	+	12.0764i	−0.225147	+	0.389967i
$960$		0			0
$961$	15.3525	+	26.5913i	0.495242	+	0.857783i
$962$		0			0
$963$	33.9229	+	3.45799i	1.09315	+	0.111432i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	4.45751	+	2.57354i	0.143344	+	0.0827596i	0.569957	−	0.821675i	$-0.306960\pi$
$967$	4.45751	+	2.57354i	0.143344	+	0.0827596i	−0.426613	+	0.904434i	$0.640293\pi$
$968$		0			0
$969$	18.3285	+	20.2918i	0.588796	+	0.651867i
$970$		0			0
$971$	−10.3875			−0.333352			−0.166676	−	0.986012i	$-0.553303\pi$
$971$	−10.3875			−0.333352			−0.166676	+	0.986012i	$0.553303\pi$
$972$		0			0
$973$			19.5632i			0.627169i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	34.2618	+	19.7811i	1.09613	+	0.632852i	0.935202	−	0.354113i	$-0.115217\pi$
$977$	34.2618	+	19.7811i	1.09613	+	0.632852i	0.160930	+	0.986966i	$0.448551\pi$
$978$		0			0
$979$	−20.6933	−	35.8419i	−0.661362	−	1.14551i
$980$		0			0
$981$	0.677476	−	6.64606i	0.0216301	−	0.212192i
$982$		0			0
$983$	17.7292	−	10.2360i	0.565474	−	0.326477i	−0.189865	−	0.981810i	$-0.560805\pi$
$983$	17.7292	−	10.2360i	0.565474	−	0.326477i	0.755340	+	0.655333i	$0.227472\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.94047	−	32.4026i	−0.220918	−	1.03139i
$988$		0			0
$989$	0.672970			0.0213992
$990$		0			0
$991$	−19.2415			−0.611228			−0.305614	−	0.952156i	$-0.598862\pi$
$991$	−19.2415			−0.611228			−0.305614	+	0.952156i	$0.598862\pi$
$992$		0			0
$993$	−47.2459	−	15.2693i	−1.49930	−	0.484557i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	20.1251	−	11.6193i	0.637370	−	0.367986i	−0.146231	−	0.989250i	$-0.546714\pi$
$997$	20.1251	−	11.6193i	0.637370	−	0.367986i	0.783601	+	0.621265i	$0.213381\pi$
$998$		0			0
$999$	26.1936	−	19.2196i	0.828730	−	0.608080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.s.d.49.7		16
3.2	odd	2		2700.2.s.d.1549.8		16
5.2	odd	4		900.2.i.d.301.2	✓	8
5.3	odd	4		900.2.i.e.301.3	yes	8
5.4	even	2	inner	900.2.s.d.49.2		16
9.2	odd	6		2700.2.s.d.2449.1		16
9.4	even	3		8100.2.d.q.649.8		8
9.5	odd	6		8100.2.d.s.649.8		8
9.7	even	3	inner	900.2.s.d.349.2		16
15.2	even	4		2700.2.i.e.901.4		8
15.8	even	4		2700.2.i.d.901.1		8
15.14	odd	2		2700.2.s.d.1549.1		16
45.2	even	12		2700.2.i.e.1801.4		8
45.4	even	6		8100.2.d.q.649.1		8
45.7	odd	12		900.2.i.d.601.2	yes	8
45.13	odd	12		8100.2.a.z.1.4		4
45.14	odd	6		8100.2.d.s.649.1		8
45.22	odd	12		8100.2.a.x.1.1		4
45.23	even	12		8100.2.a.ba.1.4		4
45.29	odd	6		2700.2.s.d.2449.8		16
45.32	even	12		8100.2.a.y.1.1		4
45.34	even	6	inner	900.2.s.d.349.7		16
45.38	even	12		2700.2.i.d.1801.1		8
45.43	odd	12		900.2.i.e.601.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.i.d.301.2	✓	8	5.2	odd	4
900.2.i.d.601.2	yes	8	45.7	odd	12
900.2.i.e.301.3	yes	8	5.3	odd	4
900.2.i.e.601.3	yes	8	45.43	odd	12
900.2.s.d.49.2		16	5.4	even	2	inner
900.2.s.d.49.7		16	1.1	even	1	trivial
900.2.s.d.349.2		16	9.7	even	3	inner
900.2.s.d.349.7		16	45.34	even	6	inner
2700.2.i.d.901.1		8	15.8	even	4
2700.2.i.d.1801.1		8	45.38	even	12
2700.2.i.e.901.4		8	15.2	even	4
2700.2.i.e.1801.4		8	45.2	even	12
2700.2.s.d.1549.1		16	15.14	odd	2
2700.2.s.d.1549.8		16	3.2	odd	2
2700.2.s.d.2449.1		16	9.2	odd	6
2700.2.s.d.2449.8		16	45.29	odd	6
8100.2.a.x.1.1		4	45.22	odd	12
8100.2.a.y.1.1		4	45.32	even	12
8100.2.a.z.1.4		4	45.13	odd	12
8100.2.a.ba.1.4		4	45.23	even	12
8100.2.d.q.649.1		8	45.4	even	6
8100.2.d.q.649.8		8	9.4	even	3
8100.2.d.s.649.1		8	45.14	odd	6
8100.2.d.s.649.8		8	9.5	odd	6

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28535 - 1.16098i) q^{3} +(4.32643 - 2.49787i) q^{7} +(0.304233 - 2.98453i) q^{9} +(-1.99787 - 3.46041i) q^{11} +(-1.33642 - 0.771582i) q^{13} +6.99574i q^{17} +2.25667 q^{19} +(2.66098 - 8.23355i) q^{21} +(-6.75116 - 3.89778i) q^{23} +(-3.07395 - 4.18937i) q^{27} +(3.08304 + 5.33998i) q^{29} +(0.271582 - 0.470394i) q^{31} +(-6.58543 - 2.12833i) q^{33} +6.25240i q^{37} +(-2.61356 + 0.559811i) q^{39} +(-0.0979532 + 0.169660i) q^{41} +(-0.0747616 + 0.0431636i) q^{43} +(3.31658 - 1.91483i) q^{47} +(8.97869 - 15.5515i) q^{49} +(8.12194 + 8.99195i) q^{51} +4.19164i q^{53} +(2.90060 - 2.61995i) q^{57} +(3.51278 - 6.08432i) q^{59} +(1.45470 + 2.51962i) q^{61} +(-6.13873 - 13.6723i) q^{63} +(7.76470 + 4.48295i) q^{67} +(-13.2028 + 2.82798i) q^{69} +8.79130 q^{71} -2.28650i q^{73} +(-17.2873 - 9.98082i) q^{77} +(-6.32211 - 10.9502i) q^{79} +(-8.81488 - 1.81599i) q^{81} +(-12.0911 + 6.98082i) q^{83} +(10.1624 + 3.28437i) q^{87} +10.3577 q^{89} -7.70924 q^{91} +(-0.197042 - 0.919921i) q^{93} +(-8.08758 + 4.66936i) q^{97} +(-10.9355 + 4.90993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{9} + 6 q^{11} + 16 q^{19} + 26 q^{21} + 18 q^{29} - 4 q^{31} + 34 q^{39} + 18 q^{41} + 18 q^{49} + 6 q^{51} + 30 q^{59} + 2 q^{61} - 18 q^{69} - 48 q^{71} - 14 q^{79} - 62 q^{81} - 12 q^{89}+ \cdots - 66 q^{99}+O(q^{100}) \) 16 * q - 10 * q^9 + 6 * q^11 + 16 * q^19 + 26 * q^21 + 18 * q^29 - 4 * q^31 + 34 * q^39 + 18 * q^41 + 18 * q^49 + 6 * q^51 + 30 * q^59 + 2 * q^61 - 18 * q^69 - 48 * q^71 - 14 * q^79 - 62 * q^81 - 12 * q^89 - 44 * q^91 - 66 * q^99

Introduction

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