LMFDB - Embedded newform 900.2.i.e.301.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(301,900)] 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, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.301"); 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.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.142635249.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 $ x^8 - 3x^7 + 3x^6 + 3x^5 - 11x^4 + 6x^3 + 12x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.3
Root			$0.818235 - 1.15347i$ of defining polynomial
Character	$\chi$	$=$	900.301
Dual form			900.2.i.e.601.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16098 + 1.28535i) q^{3} +(-2.49787 - 4.32643i) q^{7} +(-0.304233 + 2.98453i) q^{9} +(-1.99787 - 3.46041i) q^{11} +(0.771582 - 1.33642i) q^{13} +6.99574 q^{17} -2.25667 q^{19} +(2.66098 - 8.23355i) q^{21} +(3.89778 - 6.75116i) q^{23} +(-4.18937 + 3.07395i) q^{27} +(-3.08304 - 5.33998i) q^{29} +(0.271582 - 0.470394i) q^{31} +(2.12833 - 6.58543i) q^{33} +6.25240 q^{37} +(2.61356 - 0.559811i) q^{39} +(-0.0979532 + 0.169660i) q^{41} +(-0.0431636 - 0.0747616i) q^{43} +(-1.91483 - 3.31658i) q^{47} +(-8.97869 + 15.5515i) q^{49} +(8.12194 + 8.99195i) q^{51} -4.19164 q^{53} +(-2.61995 - 2.90060i) q^{57} +(-3.51278 + 6.08432i) q^{59} +(1.45470 + 2.51962i) q^{61} +(13.6723 - 6.13873i) q^{63} +(4.48295 - 7.76470i) q^{67} +(13.2028 - 2.82798i) q^{69} +8.79130 q^{71} +2.28650 q^{73} +(-9.98082 + 17.2873i) q^{77} +(6.32211 + 10.9502i) q^{79} +(-8.81488 - 1.81599i) q^{81} +(-6.98082 - 12.0911i) q^{83} +(3.28437 - 10.1624i) q^{87} -10.3577 q^{89} -7.70924 q^{91} +(0.919921 - 0.197042i) q^{93} +(4.66936 + 8.08758i) q^{97} +(10.9355 - 4.90993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - q^{7} + 5 q^{9} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 8 q^{19} + 13 q^{21} + 3 q^{23} + 16 q^{27} - 9 q^{29} - 2 q^{31} + 12 q^{33} + 2 q^{37} - 17 q^{39} + 9 q^{41} + 8 q^{43} - 12 q^{47}+ \cdots + 33 q^{99}+O(q^{100}) $ 8 * q + q^3 - q^7 + 5 * q^9 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 8 * q^19 + 13 * q^21 + 3 * q^23 + 16 * q^27 - 9 * q^29 - 2 * q^31 + 12 * q^33 + 2 * q^37 - 17 * q^39 + 9 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 + 3 * q^51 + 24 * q^53 - 40 * q^57 - 15 * q^59 + q^61 + 35 * q^63 + 11 * q^67 + 9 * q^69 - 24 * q^71 + 20 * q^73 - 36 * q^77 + 7 * q^79 - 31 * q^81 - 12 * q^83 + 9 * q^87 + 6 * q^89 - 22 * q^91 - 19 * q^93 + 5 * q^97 + 33 * 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
$3$	1.16098	+	1.28535i	0.670294	+	0.742095i
$3$	1.16098	+	1.28535i	0.670294	+	0.742095i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.49787	−	4.32643i	−0.944105	−	1.63524i	−0.757533	−	0.652797i	$-0.773595\pi$
$7$	−2.49787	−	4.32643i	−0.944105	−	1.63524i	−0.186573	−	0.982441i	$-0.559738\pi$
$8$		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
$13$	0.771582	−	1.33642i	0.213998	−	0.370656i	−0.738964	−	0.673745i	$-0.764685\pi$
$13$	0.771582	−	1.33642i	0.213998	−	0.370656i	0.952962	+	0.303089i	$0.0980180\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.99574			1.69672			0.848358	−	0.529424i	$-0.177592\pi$
$17$	6.99574			1.69672			0.848358	+	0.529424i	$0.177592\pi$
$18$		0			0
$19$	−2.25667			−0.517715			−0.258857	−	0.965916i	$-0.583346\pi$
$19$	−2.25667			−0.517715			−0.258857	+	0.965916i	$0.583346\pi$
$20$		0			0
$21$	2.66098	−	8.23355i	0.580674	−	1.79671i
$22$		0			0
$23$	3.89778	−	6.75116i	0.812744	−	1.40771i	−0.0981929	−	0.995167i	$-0.531306\pi$
$23$	3.89778	−	6.75116i	0.812744	−	1.40771i	0.910937	−	0.412546i	$-0.135360\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.18937	+	3.07395i	−0.806245	+	0.591582i
$28$		0			0
$29$	−3.08304	−	5.33998i	−0.572506	−	0.991609i	−0.996308	−	0.0858540i	$-0.972638\pi$
$29$	−3.08304	−	5.33998i	−0.572506	−	0.991609i	0.423802	−	0.905755i	$-0.360695\pi$
$30$		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
$33$	2.12833	−	6.58543i	0.370495	−	1.14638i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.25240			1.02789			0.513944	−	0.857824i	$-0.328184\pi$
$37$	6.25240			1.02789			0.513944	+	0.857824i	$0.328184\pi$
$38$		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
$43$	−0.0431636	−	0.0747616i	−0.00658239	−	0.0114010i	0.862715	−	0.505690i	$-0.168762\pi$
$43$	−0.0431636	−	0.0747616i	−0.00658239	−	0.0114010i	−0.869298	+	0.494289i	$0.835429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.91483	−	3.31658i	−0.279307	−	0.483774i	0.691906	−	0.721988i	$-0.256771\pi$
$47$	−1.91483	−	3.31658i	−0.279307	−	0.483774i	−0.971213	+	0.238214i	$0.923438\pi$
$48$		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
$53$	−4.19164			−0.575766			−0.287883	−	0.957666i	$-0.592951\pi$
$53$	−4.19164			−0.575766			−0.287883	+	0.957666i	$0.592951\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.61995	−	2.90060i	−0.347021	−	0.384194i
$58$		0			0
$59$	−3.51278	+	6.08432i	−0.457326	+	0.792111i	−0.998819	−	0.0485942i	$-0.984526\pi$
$59$	−3.51278	+	6.08432i	−0.457326	+	0.792111i	0.541493	+	0.840705i	$0.317859\pi$
$60$		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
$63$	13.6723	−	6.13873i	1.72255	−	0.773407i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.48295	−	7.76470i	0.547680	−	0.948609i	−0.450753	−	0.892649i	$-0.648845\pi$
$67$	4.48295	−	7.76470i	0.547680	−	0.948609i	0.998433	−	0.0559605i	$-0.0178221\pi$
$68$		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
$73$	2.28650			0.267614			0.133807	−	0.991007i	$-0.457280\pi$
$73$	2.28650			0.267614			0.133807	+	0.991007i	$0.457280\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.98082	+	17.2873i	−1.13742	+	1.97007i
$78$		0			0
$79$	6.32211	+	10.9502i	0.711293	+	1.23199i	0.964372	+	0.264549i	$0.0852232\pi$
$79$	6.32211	+	10.9502i	0.711293	+	1.23199i	−0.253080	+	0.967445i	$0.581443\pi$
$80$		0			0
$81$	−8.81488	−	1.81599i	−0.979432	−	0.201776i
$82$		0			0
$83$	−6.98082	−	12.0911i	−0.766244	−	1.32717i	−0.939586	−	0.342313i	$-0.888790\pi$
$83$	−6.98082	−	12.0911i	−0.766244	−	1.32717i	0.173342	−	0.984862i	$-0.444544\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.28437	−	10.1624i	0.352121	−	1.08952i
$88$		0			0
$89$	−10.3577			−1.09792			−0.548958	−	0.835850i	$-0.684975\pi$
$89$	−10.3577			−1.09792			−0.548958	+	0.835850i	$0.684975\pi$
$90$		0			0
$91$	−7.70924			−0.808148
$92$		0			0
$93$	0.919921	−	0.197042i	0.0953914	−	0.0204324i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.66936	+	8.08758i	0.474102	+	0.821169i	0.999560	−	0.0296505i	$-0.00943942\pi$
$97$	4.66936	+	8.08758i	0.474102	+	0.821169i	−0.525458	+	0.850819i	$0.676106\pi$
$98$		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
$103$	−8.20711	+	14.2151i	−0.808670	+	1.40066i	0.105115	+	0.994460i	$0.466479\pi$
$103$	−8.20711	+	14.2151i	−0.808670	+	1.40066i	−0.913785	+	0.406198i	$0.866854\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.3662			1.09882			0.549408	−	0.835554i	$-0.314853\pi$
$107$	11.3662			1.09882			0.549408	+	0.835554i	$0.314853\pi$
$108$		0			0
$109$	−2.22683			−0.213292			−0.106646	−	0.994297i	$-0.534011\pi$
$109$	−2.22683			−0.213292			−0.106646	+	0.994297i	$0.534011\pi$
$110$		0			0
$111$	7.25894	+	8.03650i	0.688988	+	0.762791i
$112$		0			0
$113$	−1.41696	+	2.45425i	−0.133297	+	0.230877i	−0.924945	−	0.380100i	$-0.875890\pi$
$113$	−1.41696	+	2.45425i	−0.133297	+	0.230877i	0.791649	+	0.610976i	$0.209223\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.75385	+	2.70939i	0.347043	+	0.250484i
$118$		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
$123$	−0.331794	+	0.0710686i	−0.0299168	+	0.00640804i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.02130			−0.623040			−0.311520	−	0.950240i	$-0.600838\pi$
$127$	−7.02130			−0.623040			−0.311520	+	0.950240i	$0.600838\pi$
$128$		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
$133$	5.63685	+	9.76331i	0.488777	+	0.846587i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.39565	+	2.41734i	0.119238	+	0.206527i	0.919466	−	0.393169i	$-0.128621\pi$
$137$	1.39565	+	2.41734i	0.119238	+	0.206527i	−0.800228	+	0.599696i	$0.795288\pi$
$138$		0			0
$139$	1.95799	−	3.39135i	0.166075	−	0.287650i	−0.770962	−	0.636882i	$-0.780224\pi$
$139$	1.95799	−	3.39135i	0.166075	−	0.287650i	0.937036	+	0.349231i	$0.113557\pi$
$140$		0			0
$141$	2.03987	−	6.31172i	0.171788	−	0.531543i
$142$		0			0
$143$	−6.16607			−0.515633
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−30.4132	+	6.51436i	−2.50844	+	0.537296i
$148$		0			0
$149$	6.37860	−	11.0481i	0.522555	−	0.905093i	−0.477100	−	0.878849i	$-0.658312\pi$
$149$	6.37860	−	11.0481i	0.522555	−	0.905093i	0.999656	−	0.0262436i	$-0.00835456\pi$
$150$		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
$153$	−2.12833	+	20.8790i	−0.172066	+	1.68797i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.04839	−	10.4761i	0.482714	−	0.836086i	−0.517089	−	0.855932i	$-0.672984\pi$
$157$	6.04839	−	10.4761i	0.482714	−	0.836086i	0.999803	+	0.0198461i	$0.00631762\pi$
$158$		0			0
$159$	−4.86643	−	5.38771i	−0.385933	−	0.427273i
$160$		0			0
$161$	−38.9446			−3.06926
$162$		0			0
$163$	−10.8563			−0.850333			−0.425166	−	0.905115i	$-0.639784\pi$
$163$	−10.8563			−0.850333			−0.425166	+	0.905115i	$0.639784\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.59369	−	4.49240i	0.200706	−	0.347632i	−0.748050	−	0.663642i	$-0.769010\pi$
$167$	2.59369	−	4.49240i	0.200706	−	0.347632i	0.948756	+	0.316010i	$0.102343\pi$
$168$		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
$173$	−1.68739	−	2.92264i	−0.128290	−	0.222204i	0.794724	−	0.606970i	$-0.207615\pi$
$173$	−1.68739	−	2.92264i	−0.128290	−	0.222204i	−0.923014	+	0.384766i	$0.874282\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.8987	+	2.54865i	−0.894365	+	0.191568i
$178$		0			0
$179$	19.5997			1.46495			0.732474	−	0.680795i	$-0.238366\pi$
$179$	19.5997			1.46495			0.732474	+	0.680795i	$0.238366\pi$
$180$		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
$183$	−1.54970	+	4.79504i	−0.114557	+	0.354460i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−13.9766	−	24.2081i	−1.02207	−	1.77027i
$188$		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
$193$	−5.17150	+	8.95729i	−0.372252	+	0.644760i	−0.989912	−	0.141686i	$-0.954748\pi$
$193$	−5.17150	+	8.95729i	−0.372252	+	0.644760i	0.617659	+	0.786446i	$0.288081\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.0256			1.14177			0.570887	−	0.821028i	$-0.306599\pi$
$197$	16.0256			1.14177			0.570887	+	0.821028i	$0.306599\pi$
$198$		0			0
$199$	−22.2353			−1.57622			−0.788111	−	0.615533i	$-0.788941\pi$
$199$	−22.2353			−1.57622			−0.788111	+	0.615533i	$0.788941\pi$
$200$		0			0
$201$	15.1850	−	3.25254i	1.07106	−	0.229417i
$202$		0			0
$203$	−15.4020	+	26.6771i	−1.08101	+	1.87237i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	18.9632	+	13.6870i	1.31804	+	0.951311i
$208$		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
$213$	10.2066	+	11.2999i	0.699342	+	0.774254i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.71350			−0.184205
$218$		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
$223$	5.62407	+	9.74117i	0.376615	+	0.652317i	0.990567	−	0.137026i	$-0.0437545\pi$
$223$	5.62407	+	9.74117i	0.376615	+	0.652317i	−0.613952	+	0.789343i	$0.710421\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.07451	+	8.78931i	0.336807	+	0.583367i	0.983830	−	0.179103i	$-0.0573197\pi$
$227$	5.07451	+	8.78931i	0.336807	+	0.583367i	−0.647023	+	0.762470i	$0.723986\pi$
$228$		0			0
$229$	1.18428	−	2.05123i	0.0782595	−	0.135549i	−0.824240	−	0.566241i	$-0.808397\pi$
$229$	1.18428	−	2.05123i	0.0782595	−	0.135549i	0.902499	+	0.430692i	$0.141730\pi$
$230$		0			0
$231$	−33.8077	+	7.24145i	−2.22439	+	0.476452i
$232$		0			0
$233$	24.1831			1.58429			0.792144	−	0.610334i	$-0.208965\pi$
$233$	24.1831			1.58429			0.792144	+	0.610334i	$0.208965\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.73495	+	20.8391i	−0.437482	+	1.35365i
$238$		0			0
$239$	0.897782	−	1.55500i	0.0580727	−	0.100585i	−0.835528	−	0.549449i	$-0.814838\pi$
$239$	0.897782	−	1.55500i	0.0580727	−	0.100585i	0.893600	+	0.448864i	$0.148171\pi$
$240$		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
$243$	−7.89977	−	13.4385i	−0.506770	−	0.862081i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.74120	+	3.01585i	−0.110790	+	0.191894i
$248$		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
$253$	−31.1490			−1.95832
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.9979	+	19.0489i	−0.686028	+	1.18824i	0.287084	+	0.957905i	$0.407314\pi$
$257$	−10.9979	+	19.0489i	−0.686028	+	1.18824i	−0.973113	+	0.230330i	$0.926019\pi$
$258$		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
$263$	−7.57664	−	13.1231i	−0.467196	−	0.809207i	0.532102	−	0.846680i	$-0.321402\pi$
$263$	−7.57664	−	13.1231i	−0.467196	−	0.809207i	−0.999298	+	0.0374737i	$0.988069\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−12.0251	−	13.3133i	−0.735927	−	0.814758i
$268$		0			0
$269$	−7.99147			−0.487249			−0.243624	−	0.969870i	$-0.578336\pi$
$269$	−7.99147			−0.487249			−0.243624	+	0.969870i	$0.578336\pi$
$270$		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
$273$	−8.95030	−	9.90904i	−0.541697	−	0.599723i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.10702	+	15.7738i	0.547188	+	0.947757i	0.998466	+	0.0553736i	$0.0176350\pi$
$277$	9.10702	+	15.7738i	0.547188	+	0.947757i	−0.451278	+	0.892383i	$0.649032\pi$
$278$		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
$283$	5.82637	−	10.0916i	0.346342	−	0.599882i	−0.639255	−	0.768995i	$-0.720757\pi$
$283$	5.82637	−	10.0916i	0.346342	−	0.599882i	0.985597	+	0.169113i	$0.0540904\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.978696			0.0577706
$288$		0			0
$289$	31.9403			1.87884
$290$		0			0
$291$	−4.97428	+	15.3913i	−0.291598	+	0.902254i
$292$		0			0
$293$	3.09156	−	5.35473i	0.180611	−	0.312827i	−0.761478	−	0.648191i	$-0.775526\pi$
$293$	3.09156	−	5.35473i	0.180611	−	0.312827i	0.942089	+	0.335364i	$0.108859\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	19.0069	+	8.35559i	1.10289	+	0.484840i
$298$		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
$303$	4.24078	−	13.1217i	0.243626	−	0.753822i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	12.9872			0.741219			0.370610	−	0.928789i	$-0.379149\pi$
$307$	12.9872			0.741219			0.370610	+	0.928789i	$0.379149\pi$
$308$		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
$313$	−8.34609	−	14.4559i	−0.471749	−	0.817093i	0.527729	−	0.849413i	$-0.323044\pi$
$313$	−8.34609	−	14.4559i	−0.471749	−	0.817093i	−0.999478	+	0.0323199i	$0.989710\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.4787	−	28.5419i	−0.925535	−	1.60307i	−0.790698	−	0.612206i	$-0.790282\pi$
$317$	−16.4787	−	28.5419i	−0.925535	−	1.60307i	−0.134837	−	0.990868i	$-0.543051\pi$
$318$		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
$323$	−15.7870			−0.878414
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.58532	−	2.86225i	−0.142968	−	0.158283i
$328$		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
$333$	−1.90219	+	18.6605i	−0.104239	+	1.02259i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−14.9270	+	25.8543i	−0.813125	+	1.40837i	0.0975411	+	0.995231i	$0.468902\pi$
$337$	−14.9270	+	25.8543i	−0.813125	+	1.40837i	−0.910666	+	0.413143i	$0.864431\pi$
$338$		0			0
$339$	−4.79964	+	1.02806i	−0.260680	+	0.0558364i
$340$		0			0
$341$	−2.17034			−0.117530
$342$		0			0
$343$	54.7401			2.95569
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.41910	+	4.19000i	−0.129864	+	0.224931i	−0.923624	−	0.383301i	$-0.874787\pi$
$347$	−2.41910	+	4.19000i	−0.129864	+	0.224931i	0.793760	+	0.608231i	$0.208121\pi$
$348$		0			0
$349$	16.0325	+	27.7691i	0.858200	+	1.48645i	0.873644	+	0.486566i	$0.161751\pi$
$349$	16.0325	+	27.7691i	0.858200	+	1.48645i	−0.0154438	+	0.999881i	$0.504916\pi$
$350$		0			0
$351$	0.875644	+	7.97056i	0.0467384	+	0.425437i
$352$		0			0
$353$	−4.92975	−	8.53857i	−0.262384	−	0.454462i	0.704491	−	0.709713i	$-0.251175\pi$
$353$	−4.92975	−	8.53857i	−0.262384	−	0.454462i	−0.966875	+	0.255251i	$0.917842\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	18.6155	−	57.5997i	0.985239	−	3.04850i
$358$		0			0
$359$	9.93266			0.524226			0.262113	−	0.965037i	$-0.415581\pi$
$359$	9.93266			0.524226			0.262113	+	0.965037i	$0.415581\pi$
$360$		0			0
$361$	−13.9075			−0.731972
$362$		0			0
$363$	−8.41043	+	1.80147i	−0.441433	+	0.0945527i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.51065	+	16.4729i	0.496452	+	0.859880i	0.999992	−	0.00409206i	$-0.00130255\pi$
$367$	9.51065	+	16.4729i	0.496452	+	0.859880i	−0.503540	+	0.863972i	$0.667969\pi$
$368$		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
$373$	−0.939241	+	1.62681i	−0.0486320	+	0.0842332i	−0.889317	−	0.457292i	$-0.848820\pi$
$373$	−0.939241	+	1.62681i	−0.0486320	+	0.0842332i	0.840685	+	0.541525i	$0.182153\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.51526			−0.490061
$378$		0			0
$379$	22.8435			1.17339			0.586697	−	0.809807i	$-0.300428\pi$
$379$	22.8435			1.17339			0.586697	+	0.809807i	$0.300428\pi$
$380$		0			0
$381$	−8.15162	−	9.02481i	−0.417620	−	0.462355i
$382$		0			0
$383$	−2.35133	+	4.07262i	−0.120147	+	0.208101i	−0.919826	−	0.392327i	$-0.871670\pi$
$383$	−2.35133	+	4.07262i	−0.120147	+	0.208101i	0.799678	+	0.600429i	$0.205003\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.236260	−	0.106078i	0.0120098	−	0.00539227i
$388$		0			0
$389$	5.38287	+	9.32340i	0.272922	+	0.472715i	0.969609	−	0.244661i	$-0.0786765\pi$
$389$	5.38287	+	9.32340i	0.272922	+	0.472715i	−0.696687	+	0.717376i	$0.745343\pi$
$390$		0			0
$391$	27.2679	−	47.2293i	1.37899	−	2.38849i
$392$		0			0
$393$	14.1694	−	3.03501i	0.714750	−	0.153096i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.10958			0.407008			0.203504	−	0.979074i	$-0.434767\pi$
$397$	8.10958			0.407008			0.203504	+	0.979074i	$0.434767\pi$
$398$		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
$403$	−0.419095	−	0.725894i	−0.0208766	−	0.0361594i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.4915	−	21.6359i	−0.619179	−	1.07245i
$408$		0			0
$409$	15.7166	−	27.2219i	0.777136	−	1.34604i	−0.156450	−	0.987686i	$-0.550005\pi$
$409$	15.7166	−	27.2219i	0.777136	−	1.34604i	0.933586	−	0.358353i	$-0.116662\pi$
$410$		0			0
$411$	−1.48679	+	4.60038i	−0.0733379	+	0.226920i
$412$		0			0
$413$	35.0979			1.72705
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.63226	−	1.42060i	0.324783	−	0.0695669i
$418$		0			0
$419$	−13.1848	+	22.8368i	−0.644121	+	1.11565i	0.340383	+	0.940287i	$0.389443\pi$
$419$	−13.1848	+	22.8368i	−0.644121	+	1.11565i	−0.984504	+	0.175363i	$0.943890\pi$
$420$		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
$423$	10.4810	−	4.70586i	0.509604	−	0.228807i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	7.26732	−	12.5874i	0.351690	−	0.609145i
$428$		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
$433$	17.9840			0.864258			0.432129	−	0.901812i	$-0.357763\pi$
$433$	17.9840			0.864258			0.432129	+	0.901812i	$0.357763\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.79599	+	15.2351i	−0.420769	+	0.728794i
$438$		0			0
$439$	−11.3577	−	19.6721i	−0.542074	−	0.938900i	−0.998785	−	0.0492847i	$-0.984306\pi$
$439$	−11.3577	−	19.6721i	−0.542074	−	0.938900i	0.456711	−	0.889615i	$-0.349028\pi$
$440$		0			0
$441$	−43.6825	−	31.5285i	−2.08012	−	1.50136i
$442$		0			0
$443$	11.4578	+	19.8455i	0.544377	+	0.942888i	0.998646	+	0.0520235i	$0.0165671\pi$
$443$	11.4578	+	19.8455i	0.544377	+	0.942888i	−0.454269	+	0.890864i	$0.650100\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	21.6060	−	4.62791i	1.02193	−	0.218892i
$448$		0			0
$449$	−5.36966			−0.253410			−0.126705	−	0.991940i	$-0.540440\pi$
$449$	−5.36966			−0.253410			−0.126705	+	0.991940i	$0.540440\pi$
$450$		0			0
$451$	0.782790			0.0368601
$452$		0			0
$453$	−0.200857	+	0.621487i	−0.00943710	+	0.0292000i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.62309	−	16.6677i	−0.450149	−	0.779682i	0.548246	−	0.836317i	$-0.315296\pi$
$457$	−9.62309	−	16.6677i	−0.450149	−	0.779682i	−0.998395	+	0.0566358i	$0.981963\pi$
$458$		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
$463$	8.56075	−	14.8277i	0.397852	−	0.689100i	−0.595609	−	0.803275i	$-0.703089\pi$
$463$	8.56075	−	14.8277i	0.397852	−	0.689100i	0.993461	+	0.114175i	$0.0364225\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.9318			1.19998			0.599990	−	0.800007i	$-0.295171\pi$
$467$	25.9318			1.19998			0.599990	+	0.800007i	$0.295171\pi$
$468$		0			0
$469$	−44.7913			−2.06827
$470$		0			0
$471$	20.4875	−	4.38833i	0.944016	−	0.202203i
$472$		0			0
$473$	−0.172471	+	0.298728i	−0.00793020	+	0.0137355i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.27524	−	12.5101i	0.0583890	−	0.572798i
$478$		0			0
$479$	10.4574	+	18.1127i	0.477810	+	0.827591i	0.999676	−	0.0254364i	$-0.00809754\pi$
$479$	10.4574	+	18.1127i	0.477810	+	0.827591i	−0.521867	+	0.853027i	$0.674764\pi$
$480$		0			0
$481$	4.82424	−	8.35583i	0.219966	−	0.380993i
$482$		0			0
$483$	−45.2140	−	50.0573i	−2.05731	−	2.27769i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−20.2373			−0.917039			−0.458520	−	0.888684i	$-0.651620\pi$
$487$	−20.2373			−0.917039			−0.458520	+	0.888684i	$0.651620\pi$
$488$		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
$493$	−21.5681	−	37.3571i	−0.971379	−	1.68248i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.9595	−	38.0350i	−0.985018	−	1.70610i
$498$		0			0
$499$	14.1384	−	24.4884i	0.632920	−	1.09625i	−0.354032	−	0.935233i	$-0.615189\pi$
$499$	14.1384	−	24.4884i	0.632920	−	1.09625i	0.986952	−	0.161016i	$-0.0514772\pi$
$500$		0			0
$501$	8.78552	−	1.88182i	0.392508	−	0.0840733i
$502$		0			0
$503$	17.4165			0.776565			0.388282	−	0.921540i	$-0.373069\pi$
$503$	17.4165			0.776565			0.388282	+	0.921540i	$0.373069\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−5.65603	+	17.5007i	−0.251193	+	0.777236i
$508$		0			0
$509$	−11.1060	+	19.2362i	−0.492267	+	0.852631i	−0.999960	−	0.00890659i	$-0.997165\pi$
$509$	−11.1060	+	19.2362i	−0.492267	+	0.852631i	0.507694	+	0.861538i	$0.330498\pi$
$510$		0			0
$511$	−5.71137	−	9.89238i	−0.252656	−	0.437613i
$512$		0			0
$513$	9.45401	−	6.93688i	0.417405	−	0.306271i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−7.65116	+	13.2522i	−0.336498	+	0.582831i
$518$		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
$523$	−26.0991			−1.14123			−0.570617	−	0.821216i	$-0.693296\pi$
$523$	−26.0991			−1.14123			−0.570617	+	0.821216i	$0.693296\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.89991	−	3.29075i	0.0827616	−	0.143347i
$528$		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
$533$	0.151158	+	0.261813i	0.00654737	+	0.0113404i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	22.7549	+	25.1924i	0.981946	+	1.08713i
$538$		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
$543$	6.79019	+	7.51754i	0.291395	+	0.322609i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.52825	−	7.84315i	−0.193614	−	0.335349i	0.752831	−	0.658213i	$-0.228688\pi$
$547$	−4.52825	−	7.84315i	−0.193614	−	0.335349i	−0.946445	+	0.322864i	$0.895354\pi$
$548$		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
$553$	31.5836	−	54.7044i	1.34307	−	2.32627i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.8467			1.05279			0.526394	−	0.850241i	$-0.323544\pi$
$557$	24.8467			1.05279			0.526394	+	0.850241i	$0.323544\pi$
$558$		0			0
$559$	−0.133217			−0.00563448
$560$		0			0
$561$	14.8893	−	46.0699i	0.628625	−	1.94507i
$562$		0			0
$563$	11.6767	−	20.2247i	0.492115	−	0.852369i	−0.507843	−	0.861449i	$-0.669557\pi$
$563$	11.6767	−	20.2247i	0.492115	−	0.852369i	0.999959	+	0.00908064i	$0.00289050\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	14.1617	+	42.6731i	0.594734	+	1.79210i
$568$		0			0
$569$	7.54510	+	13.0685i	0.316307	+	0.547860i	0.979714	−	0.200398i	$-0.0642236\pi$
$569$	7.54510	+	13.0685i	0.316307	+	0.547860i	−0.663407	+	0.748258i	$0.730890\pi$
$570$		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
$573$	−13.0985	+	40.5290i	−0.547197	+	1.69312i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.12662			0.338316			0.169158	−	0.985589i	$-0.445895\pi$
$577$	8.12662			0.338316			0.169158	+	0.985589i	$0.445895\pi$
$578$		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
$583$	8.37435	+	14.5048i	0.346830	+	0.600727i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.54937	−	11.3438i	−0.270321	−	0.468210i	0.698623	−	0.715490i	$-0.253797\pi$
$587$	−6.54937	−	11.3438i	−0.270321	−	0.468210i	−0.968944	+	0.247280i	$0.920463\pi$
$588$		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
$593$	8.60478			0.353356			0.176678	−	0.984269i	$-0.443465\pi$
$593$	8.60478			0.353356			0.176678	+	0.984269i	$0.443465\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−25.8149	−	28.5801i	−1.05653	−	1.16971i
$598$		0			0
$599$	−12.1827	+	21.1010i	−0.497771	+	0.862165i	−0.999997	−	0.00257140i	$-0.999181\pi$
$599$	−12.1827	+	21.1010i	−0.497771	+	0.862165i	0.502225	+	0.864737i	$0.332515\pi$
$600$		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
$603$	21.8101	+	15.7418i	0.888178	+	0.641056i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.713502	+	1.23582i	−0.0289602	+	0.0501605i	−0.880142	−	0.474710i	$-0.842553\pi$
$607$	−0.713502	+	1.23582i	−0.0289602	+	0.0501605i	0.851182	+	0.524871i	$0.175886\pi$
$608$		0			0
$609$	−52.1709	+	11.1747i	−2.11407	+	0.452823i
$610$		0			0
$611$	−5.90979			−0.239085
$612$		0			0
$613$	6.92878			0.279851			0.139925	−	0.990162i	$-0.455314\pi$
$613$	6.92878			0.279851			0.139925	+	0.990162i	$0.455314\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.2466	−	22.9437i	0.533286	−	0.923679i	−0.465958	−	0.884807i	$-0.654290\pi$
$617$	13.2466	−	22.9437i	0.533286	−	0.923679i	0.999244	−	0.0388718i	$-0.0123764\pi$
$618$		0			0
$619$	13.4798	+	23.3478i	0.541801	+	0.938426i	0.998801	+	0.0489597i	$0.0155906\pi$
$619$	13.4798	+	23.3478i	0.541801	+	0.938426i	−0.457000	+	0.889467i	$0.651076\pi$
$620$		0			0
$621$	4.42347	+	40.2647i	0.177508	+	1.61577i
$622$		0			0
$623$	25.8722	+	44.8120i	1.03655	+	1.79535i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−4.80294	+	14.8611i	−0.191811	+	0.593496i
$628$		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
$633$	−41.2498	+	8.83550i	−1.63953	+	0.351179i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	13.8556	+	23.9986i	0.548978	+	0.950858i
$638$		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
$643$	−3.53154	+	6.11680i	−0.139270	+	0.241223i	−0.927221	−	0.374516i	$-0.877809\pi$
$643$	−3.53154	+	6.11680i	−0.139270	+	0.241223i	0.787950	+	0.615739i	$0.211142\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.4037			1.03804			0.519019	−	0.854763i	$-0.326297\pi$
$647$	26.4037			1.03804			0.519019	+	0.854763i	$0.326297\pi$
$648$		0			0
$649$	28.0723			1.10193
$650$		0			0
$651$	−3.15033	−	3.48779i	−0.123471	−	0.136697i
$652$		0			0
$653$	3.85985	−	6.68545i	0.151048	−	0.261622i	−0.780565	−	0.625074i	$-0.785069\pi$
$653$	3.85985	−	6.68545i	0.151048	−	0.261622i	0.931613	+	0.363452i	$0.118402\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.695628	+	6.82413i	−0.0271390	+	0.266235i
$658$		0			0
$659$	11.1426	+	19.2996i	0.434055	+	0.751806i	0.997218	−	0.0745403i	$-0.0237489\pi$
$659$	11.1426	+	19.2996i	0.434055	+	0.751806i	−0.563163	+	0.826346i	$0.690416\pi$
$660$		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
$663$	18.2837	−	3.91629i	0.710082	−	0.152096i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−48.0680			−1.86120
$668$		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
$673$	−3.91580	−	6.78237i	−0.150943	−	0.261441i	0.780631	−	0.624992i	$-0.214898\pi$
$673$	−3.91580	−	6.78237i	−0.150943	−	0.261441i	−0.931574	+	0.363551i	$0.881564\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.00171	−	15.5914i	−0.345964	−	0.599227i	0.639565	−	0.768737i	$-0.279115\pi$
$677$	−9.00171	−	15.5914i	−0.345964	−	0.599227i	−0.985528	+	0.169511i	$0.945781\pi$
$678$		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
$683$	−30.3356			−1.16076			−0.580379	−	0.814347i	$-0.697096\pi$
$683$	−30.3356			−1.16076			−0.580379	+	0.814347i	$0.697096\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.01148	−	0.859238i	0.153047	−	0.0327820i
$688$		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
$693$	−48.5580	−	35.0475i	−1.84457	−	1.33134i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.685255	+	1.18690i	−0.0259559	+	0.0449569i
$698$		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
$703$	−14.1096			−0.532153
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.8871	+	34.4455i	−0.747932	+	1.29546i
$708$		0			0
$709$	−15.4500	−	26.7602i	−0.580237	−	1.00500i	−0.995451	−	0.0952767i	$-0.969626\pi$
$709$	−15.4500	−	26.7602i	−0.580237	−	1.00500i	0.415213	−	0.909724i	$-0.363707\pi$
$710$		0			0
$711$	−34.6047	+	15.5371i	−1.29778	+	0.582688i
$712$		0			0
$713$	−2.11713	−	3.66698i	−0.0792873	−	0.137330i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.04103	−	0.651374i	0.113569	−	0.0243260i
$718$		0			0
$719$	−21.2462			−0.792349			−0.396175	−	0.918175i	$-0.629662\pi$
$719$	−21.2462			−0.792349			−0.396175	+	0.918175i	$0.629662\pi$
$720$		0			0
$721$	82.0011			3.05388
$722$		0			0
$723$	−7.91881	+	24.5022i	−0.294504	+	0.911245i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	12.4910	+	21.6351i	0.463267	+	0.802402i	0.999121	−	0.0419082i	$-0.0133437\pi$
$727$	12.4910	+	21.6351i	0.463267	+	0.802402i	−0.535854	+	0.844310i	$0.680010\pi$
$728$		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
$733$	−5.23384	+	9.06528i	−0.193316	+	0.334834i	−0.946347	−	0.323151i	$-0.895258\pi$
$733$	−5.23384	+	9.06528i	−0.193316	+	0.334834i	0.753031	+	0.657985i	$0.228591\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−35.8254			−1.31964
$738$		0			0
$739$	35.6244			1.31046			0.655232	−	0.755428i	$-0.272571\pi$
$739$	35.6244			1.31046			0.655232	+	0.755428i	$0.272571\pi$
$740$		0			0
$741$	−5.89792	+	1.26331i	−0.216666	+	0.0464087i
$742$		0			0
$743$	5.02770	−	8.70823i	0.184448	−	0.319474i	−0.758942	−	0.651158i	$-0.774283\pi$
$743$	5.02770	−	8.70823i	0.184448	−	0.319474i	0.943391	+	0.331684i	$0.107617\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	38.2102	−	17.1560i	1.39804	−	0.627704i
$748$		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
$753$	−18.3780	−	20.3466i	−0.669731	−	0.741472i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	6.42042			0.233354			0.116677	−	0.993170i	$-0.462776\pi$
$757$	6.42042			0.233354			0.116677	+	0.993170i	$0.462776\pi$
$758$		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
$763$	5.56234	+	9.63425i	0.201370	+	0.348783i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.42080	+	9.38910i	0.195734	+	0.339021i
$768$		0			0
$769$	7.40088	−	12.8187i	0.266883	−	0.462254i	−0.701173	−	0.712992i	$-0.747340\pi$
$769$	7.40088	−	12.8187i	0.266883	−	0.462254i	0.968055	+	0.250737i	$0.0806731\pi$
$770$		0			0
$771$	−37.2527	+	7.97935i	−1.34162	+	0.287369i
$772$		0			0
$773$	−7.48046			−0.269053			−0.134527	−	0.990910i	$-0.542951\pi$
$773$	−7.48046			−0.269053			−0.134527	+	0.990910i	$0.542951\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	16.6375	−	51.4794i	0.596868	−	1.84681i
$778$		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
$783$	29.3308	+	12.8940i	1.04820	+	0.460795i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−26.1587	+	45.3082i	−0.932457	+	1.61506i	−0.153350	+	0.988172i	$0.549006\pi$
$787$	−26.1587	+	45.3082i	−0.932457	+	1.61506i	−0.779107	+	0.626891i	$0.784327\pi$
$788$		0			0
$789$	8.07141	−	24.9743i	0.287350	−	0.889110i
$790$		0			0
$791$	14.1575			0.503384
$792$		0			0
$793$	4.48969			0.159434
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.8679	+	46.5366i	−0.951711	+	1.64841i	−0.209991	+	0.977703i	$0.567343\pi$
$797$	−26.8679	+	46.5366i	−0.951711	+	1.64841i	−0.741721	+	0.670709i	$0.765990\pi$
$798$		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
$803$	−4.56812	−	7.91222i	−0.161205	−	0.279216i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.27797	−	10.2718i	−0.326600	−	0.361585i
$808$		0			0
$809$	−26.1908			−0.920819			−0.460410	−	0.887707i	$-0.652297\pi$
$809$	−26.1908			−0.920819			−0.460410	+	0.887707i	$0.652297\pi$
$810$		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
$813$	4.61199	+	5.10602i	0.161750	+	0.179076i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.0974059	+	0.168712i	0.00340780	+	0.00590249i
$818$		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
$823$	0.588886	−	1.01998i	0.0205273	−	0.0355543i	−0.855579	−	0.517672i	$-0.826799\pi$
$823$	0.588886	−	1.01998i	0.0205273	−	0.0355543i	0.876107	+	0.482117i	$0.160132\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.7188			−1.13775			−0.568873	−	0.822426i	$-0.692620\pi$
$827$	−32.7188			−1.13775			−0.568873	+	0.822426i	$0.692620\pi$
$828$		0			0
$829$	−5.99342			−0.208160			−0.104080	−	0.994569i	$-0.533190\pi$
$829$	−5.99342			−0.208160			−0.104080	+	0.994569i	$0.533190\pi$
$830$		0			0
$831$	−9.70173	+	30.0188i	−0.336549	+	1.04134i
$832$		0			0
$833$	−62.8125	+	108.794i	−2.17632	+	3.76951i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.308210	+	2.80548i	0.0106533	+	0.0969716i
$838$		0			0
$839$	19.1933	+	33.2439i	0.662628	+	1.14771i	0.979923	+	0.199378i	$0.0638922\pi$
$839$	19.1933	+	33.2439i	0.662628	+	1.14771i	−0.317295	+	0.948327i	$0.602774\pi$
$840$		0			0
$841$	−4.51023	+	7.81195i	−0.155525	+	0.269378i
$842$		0			0
$843$	−11.8295	+	36.6025i	−0.407429	+	1.26066i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	24.8083			0.852425
$848$		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
$853$	10.8595	+	18.8092i	0.371822	+	0.644015i	0.989846	−	0.142145i	$-0.0453998\pi$
$853$	10.8595	+	18.8092i	0.371822	+	0.644015i	−0.618024	+	0.786159i	$0.712067\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.29983	−	3.98342i	−0.0785607	−	0.136071i	0.824068	−	0.566490i	$-0.191699\pi$
$857$	−2.29983	−	3.98342i	−0.0785607	−	0.136071i	−0.902629	+	0.430419i	$0.858366\pi$
$858$		0			0
$859$	−7.45896	+	12.9193i	−0.254496	+	0.440801i	−0.964759	−	0.263137i	$-0.915243\pi$
$859$	−7.45896	+	12.9193i	−0.254496	+	0.440801i	0.710262	+	0.703937i	$0.248576\pi$
$860$		0			0
$861$	1.13625	+	1.25796i	0.0387233	+	0.0428713i
$862$		0			0
$863$	−11.4089			−0.388362			−0.194181	−	0.980966i	$-0.562205\pi$
$863$	−11.4089			−0.388362			−0.194181	+	0.980966i	$0.562205\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	37.0822	+	41.0544i	1.25938	+	1.39428i
$868$		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
$873$	−25.5582	+	11.4754i	−0.865015	+	0.388382i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	13.9642	−	24.1867i	0.471537	−	0.816727i	−0.527932	−	0.849286i	$-0.677033\pi$
$877$	13.9642	−	24.1867i	0.471537	−	0.816727i	0.999470	+	0.0325596i	$0.0103659\pi$
$878$		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
$883$	20.3895			0.686161			0.343081	−	0.939306i	$-0.388530\pi$
$883$	20.3895			0.686161			0.343081	+	0.939306i	$0.388530\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.7725	−	34.2471i	0.663897	−	1.14990i	−0.315686	−	0.948864i	$-0.602235\pi$
$887$	19.7725	−	34.2471i	0.663897	−	1.14990i	0.979583	−	0.201040i	$-0.0644321\pi$
$888$		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
$893$	4.32113	+	7.48442i	0.144601	+	0.250457i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.40770	−	19.8265i	0.213947	−	0.661989i
$898$		0			0
$899$	−3.34919			−0.111702
$900$		0			0
$901$	−29.3236			−0.976911
$902$		0			0
$903$	−0.730411	+	0.156450i	−0.0243066	+	0.00520634i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	18.4798	+	32.0080i	0.613613	+	1.06281i	0.990626	+	0.136601i	$0.0436179\pi$
$907$	18.4798	+	32.0080i	0.613613	+	1.06281i	−0.377013	+	0.926208i	$0.623049\pi$
$908$		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
$913$	−27.8935	+	48.3130i	−0.923140	+	1.59893i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−41.7955			−1.38021
$918$		0			0
$919$	−8.42079			−0.277776			−0.138888	−	0.990308i	$-0.544353\pi$
$919$	−8.42079			−0.277776			−0.138888	+	0.990308i	$0.544353\pi$
$920$		0			0
$921$	15.0779	+	16.6931i	0.496835	+	0.550055i
$922$		0			0
$923$	6.78321	−	11.7489i	0.223272	−	0.386718i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−39.9286	−	28.8191i	−1.31143	−	0.946543i
$928$		0			0
$929$	14.1938	+	24.5843i	0.465683	+	0.806586i	0.999232	−	0.0391829i	$-0.0124755\pi$
$929$	14.1938	+	24.5843i	0.465683	+	0.806586i	−0.533549	+	0.845769i	$0.679142\pi$
$930$		0			0
$931$	20.2619	−	35.0946i	0.664057	−	1.15018i
$932$		0			0
$933$	37.5845	−	8.05042i	1.23046	−	0.263559i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.69342			0.153327			0.0766637	−	0.997057i	$-0.475573\pi$
$937$	4.69342			0.153327			0.0766637	+	0.997057i	$0.475573\pi$
$938$		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
$943$	0.763600	+	1.32259i	0.0248662	+	0.0430696i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.40843	−	11.0997i	−0.208246	−	0.360693i	0.742916	−	0.669385i	$-0.233442\pi$
$947$	−6.40843	−	11.0997i	−0.208246	−	0.360693i	−0.951162	+	0.308692i	$0.900109\pi$
$948$		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
$953$	45.9701			1.48912			0.744560	−	0.667556i	$-0.232660\pi$
$953$	45.9701			1.48912			0.744560	+	0.667556i	$0.232660\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−41.7278	+	8.93788i	−1.34887	+	0.288921i
$958$		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
$963$	−3.45799	+	33.9229i	−0.111432	+	1.09315i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.57354	−	4.45751i	0.0827596	−	0.143344i	−0.821675	−	0.569957i	$-0.806960\pi$
$967$	2.57354	−	4.45751i	0.0827596	−	0.143344i	0.904434	+	0.426613i	$0.140293\pi$
$968$		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
$973$	−19.5632			−0.627169
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.7811	−	34.2618i	0.632852	−	1.09613i	−0.354113	−	0.935202i	$-0.615217\pi$
$977$	19.7811	−	34.2618i	0.632852	−	1.09613i	0.986966	−	0.160930i	$-0.0514493\pi$
$978$		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
$983$	10.2360	+	17.7292i	0.326477	+	0.565474i	0.981810	−	0.189865i	$-0.0608052\pi$
$983$	10.2360	+	17.7292i	0.326477	+	0.565474i	−0.655333	+	0.755340i	$0.727472\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−32.4026	+	6.94047i	−1.03139	+	0.220918i
$988$		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
$993$	15.2693	−	47.2459i	0.484557	−	1.49930i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−11.6193	−	20.1251i	−0.367986	−	0.637370i	0.621265	−	0.783601i	$-0.286619\pi$
$997$	−11.6193	−	20.1251i	−0.367986	−	0.637370i	−0.989250	+	0.146231i	$0.953286\pi$
$998$		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.i.e.301.3	yes	8
3.2	odd	2		2700.2.i.d.901.1		8
5.2	odd	4		900.2.s.d.49.7		16
5.3	odd	4		900.2.s.d.49.2		16
5.4	even	2		900.2.i.d.301.2	✓	8
9.2	odd	6		2700.2.i.d.1801.1		8
9.4	even	3		8100.2.a.z.1.4		4
9.5	odd	6		8100.2.a.ba.1.4		4
9.7	even	3	inner	900.2.i.e.601.3	yes	8
15.2	even	4		2700.2.s.d.1549.8		16
15.8	even	4		2700.2.s.d.1549.1		16
15.14	odd	2		2700.2.i.e.901.4		8
45.2	even	12		2700.2.s.d.2449.1		16
45.4	even	6		8100.2.a.x.1.1		4
45.7	odd	12		900.2.s.d.349.2		16
45.13	odd	12		8100.2.d.q.649.1		8
45.14	odd	6		8100.2.a.y.1.1		4
45.22	odd	12		8100.2.d.q.649.8		8
45.23	even	12		8100.2.d.s.649.1		8
45.29	odd	6		2700.2.i.e.1801.4		8
45.32	even	12		8100.2.d.s.649.8		8
45.34	even	6		900.2.i.d.601.2	yes	8
45.38	even	12		2700.2.s.d.2449.8		16
45.43	odd	12		900.2.s.d.349.7		16

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

\(f(q)\)	\(=\)	\(q+(1.16098 + 1.28535i) q^{3} +(-2.49787 - 4.32643i) q^{7} +(-0.304233 + 2.98453i) q^{9} +(-1.99787 - 3.46041i) q^{11} +(0.771582 - 1.33642i) q^{13} +6.99574 q^{17} -2.25667 q^{19} +(2.66098 - 8.23355i) q^{21} +(3.89778 - 6.75116i) q^{23} +(-4.18937 + 3.07395i) q^{27} +(-3.08304 - 5.33998i) q^{29} +(0.271582 - 0.470394i) q^{31} +(2.12833 - 6.58543i) q^{33} +6.25240 q^{37} +(2.61356 - 0.559811i) q^{39} +(-0.0979532 + 0.169660i) q^{41} +(-0.0431636 - 0.0747616i) q^{43} +(-1.91483 - 3.31658i) q^{47} +(-8.97869 + 15.5515i) q^{49} +(8.12194 + 8.99195i) q^{51} -4.19164 q^{53} +(-2.61995 - 2.90060i) q^{57} +(-3.51278 + 6.08432i) q^{59} +(1.45470 + 2.51962i) q^{61} +(13.6723 - 6.13873i) q^{63} +(4.48295 - 7.76470i) q^{67} +(13.2028 - 2.82798i) q^{69} +8.79130 q^{71} +2.28650 q^{73} +(-9.98082 + 17.2873i) q^{77} +(6.32211 + 10.9502i) q^{79} +(-8.81488 - 1.81599i) q^{81} +(-6.98082 - 12.0911i) q^{83} +(3.28437 - 10.1624i) q^{87} -10.3577 q^{89} -7.70924 q^{91} +(0.919921 - 0.197042i) q^{93} +(4.66936 + 8.08758i) q^{97} +(10.9355 - 4.90993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - q^{7} + 5 q^{9} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 8 q^{19} + 13 q^{21} + 3 q^{23} + 16 q^{27} - 9 q^{29} - 2 q^{31} + 12 q^{33} + 2 q^{37} - 17 q^{39} + 9 q^{41} + 8 q^{43} - 12 q^{47}+ \cdots + 33 q^{99}+O(q^{100}) \) 8 * q + q^3 - q^7 + 5 * q^9 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 8 * q^19 + 13 * q^21 + 3 * q^23 + 16 * q^27 - 9 * q^29 - 2 * q^31 + 12 * q^33 + 2 * q^37 - 17 * q^39 + 9 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 + 3 * q^51 + 24 * q^53 - 40 * q^57 - 15 * q^59 + q^61 + 35 * q^63 + 11 * q^67 + 9 * q^69 - 24 * q^71 + 20 * q^73 - 36 * q^77 + 7 * q^79 - 31 * q^81 - 12 * q^83 + 9 * q^87 + 6 * q^89 - 22 * q^91 - 19 * q^93 + 5 * q^97 + 33 * q^99

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