LMFDB - Embedded newform 552.2.u.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(17,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 11, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.u (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63887 + 0.560462i) q^{3} +(0.535830 - 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(2.37176 - 1.83704i) q^{9} +O(q^{10})$	\(q+(-1.63887 + 0.560462i) q^{3} +(0.535830 - 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(2.37176 - 1.83704i) q^{9} +(-0.0428413 - 0.0938095i) q^{11} +(0.657474 + 4.57283i) q^{13} +(-0.685154 + 0.864667i) q^{15} +(-1.03008 + 1.18877i) q^{17} +(-2.88216 + 2.49740i) q^{19} +(3.47713 - 0.656879i) q^{21} +(-4.75668 - 0.611543i) q^{23} +(-1.90854 + 4.17913i) q^{25} +(-2.85741 + 4.33995i) q^{27} +(-3.84300 - 3.32998i) q^{29} +(-1.22648 + 0.360126i) q^{31} +(0.122788 + 0.129730i) q^{33} +(-1.18370 + 0.540576i) q^{35} +(-1.41013 + 2.19421i) q^{37} +(-3.64041 - 7.12577i) q^{39} +(-2.08672 - 3.24700i) q^{41} +(-2.23913 + 7.62577i) q^{43} +(0.638263 - 1.80108i) q^{45} +5.18450i q^{47} +(-2.71156 - 0.796185i) q^{49} +(1.02190 - 2.52556i) q^{51} +(-0.0372918 + 0.259370i) q^{53} +(-0.0552596 - 0.0355132i) q^{55} +(3.32377 - 5.70825i) q^{57} +(7.30521 - 1.05033i) q^{59} +(3.48865 + 11.8813i) q^{61} +(-5.33039 + 3.02533i) q^{63} +(1.92698 + 2.22385i) q^{65} +(3.71843 + 1.69815i) q^{67} +(8.13831 - 1.66370i) q^{69} +(-6.95935 - 3.17823i) q^{71} +(-2.38975 - 2.75792i) q^{73} +(0.785606 - 7.91870i) q^{75} +(0.0593598 + 0.202161i) q^{77} +(-10.2666 + 1.47612i) q^{79} +(2.25054 - 8.71407i) q^{81} +(4.49498 + 2.88875i) q^{83} +(-0.142584 + 0.991693i) q^{85} +(8.16450 + 3.30354i) q^{87} +(7.99786 + 2.34838i) q^{89} -9.43850i q^{91} +(1.80819 - 1.27759i) q^{93} +(-0.684348 + 2.33067i) q^{95} +(-3.52007 - 5.47733i) q^{97} +(-0.273942 - 0.143793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^9	$ 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) $ 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$	$1$	$1$

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
$3$	−1.63887	+	0.560462i	−0.946200	+	0.323583i
$3$	−1.63887	+	0.560462i	−0.946200	+	0.323583i
$4$		0			0
$5$	0.535830	−	0.344357i	0.239630	−	0.154001i	−0.415314	−	0.909678i	$-0.636328\pi$
$5$	0.535830	−	0.344357i	0.239630	−	0.154001i	0.654944	+	0.755677i	$0.272692\pi$
$6$		0			0
$7$	−2.02223	−	0.290753i	−0.764333	−	0.109894i	−0.250887	−	0.968016i	$-0.580722\pi$
$7$	−2.02223	−	0.290753i	−0.764333	−	0.109894i	−0.513446	+	0.858122i	$0.671631\pi$
$8$		0			0
$9$	2.37176	−	1.83704i	0.790588	−	0.612348i
$10$		0			0
$11$	−0.0428413	−	0.0938095i	−0.0129172	−	0.0282846i	0.903063	−	0.429507i	$-0.141313\pi$
$11$	−0.0428413	−	0.0938095i	−0.0129172	−	0.0282846i	−0.915981	+	0.401222i	$0.868585\pi$
$12$		0			0
$13$	0.657474	+	4.57283i	0.182350	+	1.26827i	0.851186	+	0.524864i	$0.175884\pi$
$13$	0.657474	+	4.57283i	0.182350	+	1.26827i	−0.668835	+	0.743411i	$0.733207\pi$
$14$		0			0
$15$	−0.685154	+	0.864667i	−0.176906	+	0.223256i
$16$		0			0
$17$	−1.03008	+	1.18877i	−0.249830	+	0.288320i	−0.866788	−	0.498677i	$-0.833819\pi$
$17$	−1.03008	+	1.18877i	−0.249830	+	0.288320i	0.616958	+	0.786996i	$0.288365\pi$
$18$		0			0
$19$	−2.88216	+	2.49740i	−0.661212	+	0.572944i	−0.919483	−	0.393129i	$-0.871393\pi$
$19$	−2.88216	+	2.49740i	−0.661212	+	0.572944i	0.258271	+	0.966073i	$0.416847\pi$
$20$		0			0
$21$	3.47713	−	0.656879i	0.758771	−	0.143343i
$22$		0			0
$23$	−4.75668	−	0.611543i	−0.991837	−	0.127515i
$23$	−4.75668	−	0.611543i	−0.991837	−	0.127515i
$24$		0			0
$25$	−1.90854	+	4.17913i	−0.381709	+	0.835825i
$26$		0			0
$27$	−2.85741	+	4.33995i	−0.549909	+	0.835224i
$28$		0			0
$29$	−3.84300	−	3.32998i	−0.713628	−	0.618362i	0.220464	−	0.975395i	$-0.429243\pi$
$29$	−3.84300	−	3.32998i	−0.713628	−	0.618362i	−0.934092	+	0.357033i	$0.883788\pi$
$30$		0			0
$31$	−1.22648	+	0.360126i	−0.220281	+	0.0646805i	−0.390011	−	0.920810i	$-0.627529\pi$
$31$	−1.22648	+	0.360126i	−0.220281	+	0.0646805i	0.169729	+	0.985491i	$0.445711\pi$
$32$		0			0
$33$	0.122788	+	0.129730i	0.0213746	+	0.0225831i
$34$		0			0
$35$	−1.18370	+	0.540576i	−0.200081	+	0.0913740i
$36$		0			0
$37$	−1.41013	+	2.19421i	−0.231825	+	0.360726i	−0.937604	−	0.347706i	$-0.886961\pi$
$37$	−1.41013	+	2.19421i	−0.231825	+	0.360726i	0.705779	+	0.708432i	$0.250597\pi$
$38$		0			0
$39$	−3.64041	−	7.12577i	−0.582932	−	1.14104i
$40$		0			0
$41$	−2.08672	−	3.24700i	−0.325891	−	0.507096i	0.639190	−	0.769049i	$-0.279270\pi$
$41$	−2.08672	−	3.24700i	−0.325891	−	0.507096i	−0.965081	+	0.261953i	$0.915633\pi$
$42$		0			0
$43$	−2.23913	+	7.62577i	−0.341464	+	1.16292i	0.592505	+	0.805566i	$0.298139\pi$
$43$	−2.23913	+	7.62577i	−0.341464	+	1.16292i	−0.933969	+	0.357353i	$0.883679\pi$
$44$		0			0
$45$	0.638263	−	1.80108i	0.0951467	−	0.268489i
$46$		0			0
$47$			5.18450i			0.756237i	0.925757	+	0.378119i	$0.123429\pi$
$47$			5.18450i			0.756237i	−0.925757	+	0.378119i	$0.876571\pi$
$48$		0			0
$49$	−2.71156	−	0.796185i	−0.387365	−	0.113741i
$50$		0			0
$51$	1.02190	−	2.52556i	0.143094	−	0.353649i
$52$		0			0
$53$	−0.0372918	+	0.259370i	−0.00512242	+	0.0356272i	−0.992222	−	0.124478i	$-0.960274\pi$
$53$	−0.0372918	+	0.259370i	−0.00512242	+	0.0356272i	0.987100	+	0.160105i	$0.0511834\pi$
$54$		0			0
$55$	−0.0552596	−	0.0355132i	−0.00745120	−	0.00478860i
$56$		0			0
$57$	3.32377	−	5.70825i	0.440244	−	0.756076i
$58$		0			0
$59$	7.30521	−	1.05033i	0.951057	−	0.136741i	0.350713	−	0.936483i	$-0.385939\pi$
$59$	7.30521	−	1.05033i	0.951057	−	0.136741i	0.600344	+	0.799742i	$0.295030\pi$
$60$		0			0
$61$	3.48865	+	11.8813i	0.446676	+	1.52124i	0.808219	+	0.588883i	$0.200432\pi$
$61$	3.48865	+	11.8813i	0.446676	+	1.52124i	−0.361543	+	0.932356i	$0.617750\pi$
$62$		0			0
$63$	−5.33039	+	3.02533i	−0.671566	+	0.381156i
$64$		0			0
$65$	1.92698	+	2.22385i	0.239012	+	0.275835i
$66$		0			0
$67$	3.71843	+	1.69815i	0.454279	+	0.207462i	0.629395	−	0.777086i	$-0.283303\pi$
$67$	3.71843	+	1.69815i	0.454279	+	0.207462i	−0.175116	+	0.984548i	$0.556030\pi$
$68$		0			0
$69$	8.13831	−	1.66370i	0.979737	−	0.200286i
$70$		0			0
$71$	−6.95935	−	3.17823i	−0.825923	−	0.377186i	−0.0428232	−	0.999083i	$-0.513635\pi$
$71$	−6.95935	−	3.17823i	−0.825923	−	0.377186i	−0.783100	+	0.621896i	$0.786362\pi$
$72$		0			0
$73$	−2.38975	−	2.75792i	−0.279699	−	0.322790i	0.598466	−	0.801148i	$-0.295777\pi$
$73$	−2.38975	−	2.75792i	−0.279699	−	0.322790i	−0.878164	+	0.478359i	$0.841232\pi$
$74$		0			0
$75$	0.785606	−	7.91870i	0.0907139	−	0.914372i
$76$		0			0
$77$	0.0593598	+	0.202161i	0.00676468	+	0.0230384i
$78$		0			0
$79$	−10.2666	+	1.47612i	−1.15509	+	0.166076i	−0.693120	−	0.720822i	$-0.743765\pi$
$79$	−10.2666	+	1.47612i	−1.15509	+	0.166076i	−0.461965	+	0.886898i	$0.652856\pi$
$80$		0			0
$81$	2.25054	−	8.71407i	0.250060	−	0.968230i
$82$		0			0
$83$	4.49498	+	2.88875i	0.493389	+	0.317082i	0.763567	−	0.645729i	$-0.223446\pi$
$83$	4.49498	+	2.88875i	0.493389	+	0.317082i	−0.270178	+	0.962810i	$0.587083\pi$
$84$		0			0
$85$	−0.142584	+	0.991693i	−0.0154654	+	0.107564i
$86$		0			0
$87$	8.16450	+	3.30354i	0.875326	+	0.354176i
$88$		0			0
$89$	7.99786	+	2.34838i	0.847771	+	0.248928i	0.676634	−	0.736319i	$-0.263438\pi$
$89$	7.99786	+	2.34838i	0.847771	+	0.248928i	0.171137	+	0.985247i	$0.445256\pi$
$90$		0			0
$91$		−	9.43850i		−	0.989423i
$92$		0			0
$93$	1.80819	−	1.27759i	0.187501	−	0.132480i
$94$		0			0
$95$	−0.684348	+	2.33067i	−0.0702126	+	0.239122i
$96$		0			0
$97$	−3.52007	−	5.47733i	−0.357409	−	0.556139i	0.615263	−	0.788322i	$-0.289050\pi$
$97$	−3.52007	−	5.47733i	−0.357409	−	0.556139i	−0.972672	+	0.232183i	$0.925413\pi$
$98$		0			0
$99$	−0.273942	−	0.143793i	−0.0275322	−	0.0144517i
$100$		0			0
$101$	6.50458	−	10.1213i	0.647230	−	1.00711i	−0.350284	−	0.936644i	$-0.613915\pi$
$101$	6.50458	−	10.1213i	0.647230	−	1.00711i	0.997514	−	0.0704663i	$-0.0224487\pi$
$102$		0			0
$103$	13.5741	−	6.19907i	1.33749	−	0.610812i	0.387149	−	0.922017i	$-0.373460\pi$
$103$	13.5741	−	6.19907i	1.33749	−	0.610812i	0.950343	+	0.311205i	$0.100733\pi$
$104$		0			0
$105$	1.63695	−	1.54935i	0.159750	−	0.151201i
$106$		0			0
$107$	19.0201	−	5.58479i	1.83874	−	0.539902i	0.838749	−	0.544518i	$-0.183288\pi$
$107$	19.0201	−	5.58479i	1.83874	−	0.539902i	0.999989	+	0.00461618i	$0.00146938\pi$
$108$		0			0
$109$	−5.89119	−	5.10475i	−0.564274	−	0.488946i	0.325379	−	0.945584i	$-0.394508\pi$
$109$	−5.89119	−	5.10475i	−0.564274	−	0.488946i	−0.889653	+	0.456638i	$0.849054\pi$
$110$		0			0
$111$	1.08125	−	4.38635i	0.102628	−	0.416333i
$112$		0			0
$113$	−4.45999	+	9.76602i	−0.419561	+	0.918710i	0.575346	+	0.817910i	$0.304867\pi$
$113$	−4.45999	+	9.76602i	−0.419561	+	0.918710i	−0.994907	+	0.100800i	$0.967860\pi$
$114$		0			0
$115$	−2.75936	+	1.31031i	−0.257312	+	0.122187i
$116$		0			0
$117$	9.95986	+	9.63787i	0.920790	+	0.891021i
$118$		0			0
$119$	2.42870	−	2.10448i	0.222638	−	0.192917i
$120$		0			0
$121$	7.19650	−	8.30521i	0.654228	−	0.755019i
$122$		0			0
$123$	5.23967	+	4.15187i	0.472445	+	0.374361i
$124$		0			0
$125$	0.869688	+	6.04881i	0.0777873	+	0.541022i
$126$		0			0
$127$	1.04473	+	2.28764i	0.0927049	+	0.202995i	0.950304	−	0.311323i	$-0.100772\pi$
$127$	1.04473	+	2.28764i	0.0927049	+	0.202995i	−0.857599	+	0.514319i	$0.828045\pi$
$128$		0			0
$129$	−0.604322	−	13.7526i	−0.0532076	−	1.21085i
$130$		0			0
$131$	8.01824	+	1.15285i	0.700557	+	0.100725i	0.483384	−	0.875408i	$-0.339407\pi$
$131$	8.01824	+	1.15285i	0.700557	+	0.100725i	0.217173	+	0.976133i	$0.430317\pi$
$132$		0			0
$133$	6.55453	−	4.21234i	0.568350	−	0.365256i
$134$		0			0
$135$	−0.0365938	+	3.30945i	−0.00314949	+	0.284832i
$136$		0			0
$137$	−13.1713			−1.12530			−0.562651	−	0.826695i	$-0.690218\pi$
$137$	−13.1713			−1.12530			−0.562651	+	0.826695i	$0.690218\pi$
$138$		0			0
$139$	−6.71985			−0.569971			−0.284985	−	0.958532i	$-0.591989\pi$
$139$	−6.71985			−0.569971			−0.284985	+	0.958532i	$0.591989\pi$
$140$		0			0
$141$	−2.90571	−	8.49670i	−0.244705	−	0.715551i
$142$		0			0
$143$	0.400808	−	0.257583i	0.0335172	−	0.0215402i
$144$		0			0
$145$	−3.20590	−	0.460938i	−0.266235	−	0.0382789i
$146$		0			0
$147$	4.89011	−	0.214884i	0.403329	−	0.0177233i
$148$		0			0
$149$	3.28266	+	7.18802i	0.268926	+	0.588865i	0.995125	−	0.0986186i	$-0.0314424\pi$
$149$	3.28266	+	7.18802i	0.268926	+	0.588865i	−0.726199	+	0.687484i	$0.758715\pi$
$150$		0			0
$151$	−1.25005	−	8.69428i	−0.101728	−	0.707531i	−0.975308	−	0.220850i	$-0.929117\pi$
$151$	−1.25005	−	8.69428i	−0.101728	−	0.707531i	0.873580	−	0.486680i	$-0.161792\pi$
$152$		0			0
$153$	−0.259274	+	4.71178i	−0.0209610	+	0.380925i
$154$		0			0
$155$	−0.533170	+	0.615311i	−0.0428253	+	0.0494230i
$156$		0			0
$157$	6.79208	−	5.88538i	0.542067	−	0.469704i	−0.340266	−	0.940329i	$-0.610517\pi$
$157$	6.79208	−	5.88538i	0.542067	−	0.469704i	0.882333	+	0.470625i	$0.155972\pi$
$158$		0			0
$159$	−0.0842507	−	0.445973i	−0.00668152	−	0.0353680i
$160$		0			0
$161$	9.44132	+	2.61970i	0.744080	+	0.206462i
$162$		0			0
$163$	−6.47411	+	14.1763i	−0.507091	+	1.11037i	0.467008	+	0.884253i	$0.345332\pi$
$163$	−6.47411	+	14.1763i	−0.507091	+	1.11037i	−0.974099	+	0.226121i	$0.927395\pi$
$164$		0			0
$165$	0.110467	+	0.0272305i	0.00859983	+	0.00211989i
$166$		0			0
$167$	−15.3783	−	13.3254i	−1.19001	−	1.03115i	−0.998769	−	0.0496079i	$-0.984203\pi$
$167$	−15.3783	−	13.3254i	−1.19001	−	1.03115i	−0.191243	−	0.981543i	$-0.561252\pi$
$168$		0			0
$169$	−8.00510	+	2.35051i	−0.615777	+	0.180808i
$170$		0			0
$171$	−2.24796	+	11.2179i	−0.171906	+	0.857855i
$172$		0			0
$173$	−18.6268	+	8.50657i	−1.41617	+	0.646742i	−0.968854	−	0.247635i	$-0.920347\pi$
$173$	−18.6268	+	8.50657i	−1.41617	+	0.646742i	−0.447314	+	0.894377i	$0.647619\pi$
$174$		0			0
$175$	5.07462	−	7.89626i	0.383605	−	0.596901i
$176$		0			0
$177$	−11.3836	+	5.81564i	−0.855643	+	0.437131i
$178$		0			0
$179$	−4.38531	−	6.82368i	−0.327774	−	0.510026i	0.637784	−	0.770215i	$-0.279851\pi$
$179$	−4.38531	−	6.82368i	−0.327774	−	0.510026i	−0.965558	+	0.260190i	$0.916215\pi$
$180$		0			0
$181$	−4.72462	+	16.0906i	−0.351179	+	1.19600i	0.574757	+	0.818324i	$0.305096\pi$
$181$	−4.72462	+	16.0906i	−0.351179	+	1.19600i	−0.925936	+	0.377681i	$0.876722\pi$
$182$		0			0
$183$	−12.3764	−	17.5165i	−0.914891	−	1.29486i
$184$		0			0
$185$			1.66131i			0.122142i
$186$		0			0
$187$	0.155648	+	0.0457024i	0.0113821	+	0.00334209i
$188$		0			0
$189$	7.04021	−	7.94560i	0.512100	−	0.577957i
$190$		0			0
$191$	1.08550	−	7.54981i	0.0785439	−	0.546285i	−0.912116	−	0.409931i	$-0.865553\pi$
$191$	1.08550	−	7.54981i	0.0785439	−	0.546285i	0.990660	−	0.136354i	$-0.0435383\pi$
$192$		0			0
$193$	14.3450	+	9.21897i	1.03258	+	0.663596i	0.943140	−	0.332397i	$-0.107857\pi$
$193$	14.3450	+	9.21897i	1.03258	+	0.663596i	0.0894354	+	0.995993i	$0.471494\pi$
$194$		0			0
$195$	−4.40445	−	2.56460i	−0.315409	−	0.183655i
$196$		0			0
$197$	−23.3210	+	3.35305i	−1.66155	+	0.238895i	−0.908144	−	0.418657i	$-0.862501\pi$
$197$	−23.3210	+	3.35305i	−1.66155	+	0.238895i	−0.753409	+	0.657553i	$0.771592\pi$
$198$		0			0
$199$	0.0199279	+	0.0678681i	0.00141265	+	0.00481104i	0.960196	−	0.279326i	$-0.0901111\pi$
$199$	0.0199279	+	0.0678681i	0.00141265	+	0.00481104i	−0.958784	+	0.284137i	$0.908293\pi$
$200$		0			0
$201$	−7.04576	−	0.699003i	−0.496970	−	0.0493039i
$202$		0			0
$203$	6.80325	+	7.85137i	0.477495	+	0.551058i
$204$		0			0
$205$	−2.23625	−	1.02126i	−0.156187	−	0.0713280i
$206$		0			0
$207$	−12.4052	+	7.28780i	−0.862218	+	0.506537i
$208$		0			0
$209$	0.357756	+	0.163382i	0.0247465	+	0.0113013i
$210$		0			0
$211$	12.6387	+	14.5858i	0.870084	+	1.00413i	0.999921	+	0.0125950i	$0.00400922\pi$
$211$	12.6387	+	14.5858i	0.870084	+	1.00413i	−0.129837	+	0.991535i	$0.541445\pi$
$212$		0			0
$213$	13.1867	+	1.30824i	0.903539	+	0.0896392i
$214$		0			0
$215$	1.42619	+	4.85717i	0.0972657	+	0.331257i
$216$		0			0
$217$	2.58493	−	0.371657i	0.175476	−	0.0252297i
$218$		0			0
$219$	5.46218	+	3.18049i	0.369100	+	0.214918i
$220$		0			0
$221$	−6.11330	−	3.92878i	−0.411225	−	0.264278i
$222$		0			0
$223$	−0.574581	+	3.99630i	−0.0384768	+	0.267612i	−0.999974	−	0.00720241i	$-0.997707\pi$
$223$	−0.574581	+	3.99630i	−0.0384768	+	0.267612i	0.961497	+	0.274815i	$0.0886165\pi$
$224$		0			0
$225$	3.15062	+	13.4180i	0.210042	+	0.894532i
$226$		0			0
$227$	22.2143	+	6.52272i	1.47442	+	0.432928i	0.917532	−	0.397662i	$-0.130178\pi$
$227$	22.2143	+	6.52272i	1.47442	+	0.432928i	0.556885	+	0.830590i	$0.311997\pi$
$228$		0			0
$229$		−	19.9260i		−	1.31675i	−0.752691	−	0.658374i	$-0.771244\pi$
$229$		−	19.9260i		−	1.31675i	0.752691	−	0.658374i	$-0.228756\pi$
$230$		0			0
$231$	−0.210586	−	0.298046i	−0.0138556	−	0.0196100i
$232$		0			0
$233$	0.478602	−	1.62997i	0.0313542	−	0.106783i	−0.942329	−	0.334687i	$-0.891369\pi$
$233$	0.478602	−	1.62997i	0.0313542	−	0.106783i	0.973683	+	0.227905i	$0.0731875\pi$
$234$		0			0
$235$	1.78532	+	2.77801i	0.116461	+	0.181217i
$236$		0			0
$237$	15.9983	−	8.17321i	1.03920	−	0.530907i
$238$		0			0
$239$	8.00221	−	12.4517i	0.517620	−	0.805432i	−0.479788	−	0.877384i	$-0.659287\pi$
$239$	8.00221	−	12.4517i	0.517620	−	0.805432i	0.997408	+	0.0719523i	$0.0229229\pi$
$240$		0			0
$241$	−13.4146	+	6.12624i	−0.864110	+	0.394626i	−0.797619	−	0.603161i	$-0.793908\pi$
$241$	−13.4146	+	6.12624i	−0.864110	+	0.394626i	−0.0664908	+	0.997787i	$0.521180\pi$
$242$		0			0
$243$	1.19557	+	15.5425i	0.0766962	+	0.997055i
$244$		0			0
$245$	−1.72710	+	0.507123i	−0.110341	+	0.0323989i
$246$		0			0
$247$	−13.3152	−	11.5376i	−0.847223	−	0.734123i
$248$		0			0
$249$	−8.98571	−	2.21501i	−0.569446	−	0.140370i
$250$		0			0
$251$	3.53646	−	7.74377i	0.223220	−	0.488783i	−0.764577	−	0.644532i	$-0.777052\pi$
$251$	3.53646	−	7.74377i	0.223220	−	0.488783i	0.987797	+	0.155750i	$0.0497794\pi$
$252$		0			0
$253$	0.146414	+	0.472421i	0.00920498	+	0.0297009i
$254$		0			0
$255$	−0.322130	−	1.70517i	−0.0201726	−	0.106782i
$256$		0			0
$257$	17.8354	−	15.4544i	1.11254	−	0.964021i	0.112977	−	0.993598i	$-0.463961\pi$
$257$	17.8354	−	15.4544i	1.11254	−	0.964021i	0.999563	+	0.0295765i	$0.00941586\pi$
$258$		0			0
$259$	3.48960	−	4.02721i	0.216833	−	0.250239i
$260$		0			0
$261$	−15.2320	−	0.838167i	−0.942839	−	0.0518812i
$262$		0			0
$263$	0.165744	+	1.15277i	0.0102202	+	0.0710831i	0.994293	−	0.106682i	$-0.0340225\pi$
$263$	0.165744	+	1.15277i	0.0102202	+	0.0710831i	−0.984073	+	0.177765i	$0.943113\pi$
$264$		0			0
$265$	0.0693337	+	0.151820i	0.00425914	+	0.00932621i
$266$		0			0
$267$	−14.4236	+	0.633809i	−0.882710	+	0.0387885i
$268$		0			0
$269$	−10.6408	−	1.52992i	−0.648783	−	0.0932808i	−0.189936	−	0.981796i	$-0.560828\pi$
$269$	−10.6408	−	1.52992i	−0.648783	−	0.0932808i	−0.458846	+	0.888516i	$0.651737\pi$
$270$		0			0
$271$	−6.05670	+	3.89240i	−0.367918	+	0.236447i	−0.711515	−	0.702670i	$-0.751991\pi$
$271$	−6.05670	+	3.89240i	−0.367918	+	0.236447i	0.343597	+	0.939117i	$0.388354\pi$
$272$		0			0
$273$	5.28992	+	15.4684i	0.320160	+	0.936192i
$274$		0			0
$275$	0.473806			0.0285716
$276$		0			0
$277$	−15.3419			−0.921808			−0.460904	−	0.887450i	$-0.652475\pi$
$277$	−15.3419			−0.921808			−0.460904	+	0.887450i	$0.652475\pi$
$278$		0			0
$279$	−2.24734	+	3.10722i	−0.134545	+	0.186025i
$280$		0			0
$281$	−14.9645	+	9.61709i	−0.892706	+	0.573707i	−0.904619	−	0.426222i	$-0.859844\pi$
$281$	−14.9645	+	9.61709i	−0.892706	+	0.573707i	0.0119127	+	0.999929i	$0.496208\pi$
$282$		0			0
$283$	29.3820	+	4.22449i	1.74658	+	0.251120i	0.940283	−	0.340395i	$-0.110561\pi$
$283$	29.3820	+	4.22449i	1.74658	+	0.251120i	0.806294	+	0.591515i	$0.201470\pi$
$284$		0			0
$285$	−0.184700	−	4.20321i	−0.0109407	−	0.248977i
$286$		0			0
$287$	3.27576	+	7.17291i	0.193362	+	0.423403i
$288$		0			0
$289$	2.06723	+	14.3779i	0.121602	+	0.845760i
$290$		0			0
$291$	8.83876	+	7.00375i	0.518137	+	0.410567i
$292$		0			0
$293$	−21.8593	+	25.2270i	−1.27703	+	1.47377i	−0.470724	+	0.882281i	$0.656007\pi$
$293$	−21.8593	+	25.2270i	−1.27703	+	1.47377i	−0.806309	+	0.591494i	$0.798538\pi$
$294$		0			0
$295$	3.55266	−	3.07840i	0.206844	−	0.179231i
$296$		0			0
$297$	0.529544	+	0.0821229i	0.0307273	+	0.00476525i
$298$		0			0
$299$	−0.330912	−	22.1536i	−0.0191371	−	1.28117i
$300$		0			0
$301$	6.74526	−	14.7701i	0.388790	−	0.851332i
$302$		0			0
$303$	−4.98752	+	20.2331i	−0.286526	+	1.16236i
$304$		0			0
$305$	5.96071	+	5.16499i	0.341309	+	0.295746i
$306$		0			0
$307$	−14.9314	+	4.38425i	−0.852180	+	0.250223i	−0.678519	−	0.734583i	$-0.737378\pi$
$307$	−14.9314	+	4.38425i	−0.852180	+	0.250223i	−0.173661	+	0.984806i	$0.555560\pi$
$308$		0			0
$309$	−18.7717	+	17.7672i	−1.06789	+	1.01074i
$310$		0			0
$311$	−2.96642	+	1.35472i	−0.168210	+	0.0768190i	−0.497741	−	0.867326i	$-0.665837\pi$
$311$	−2.96642	+	1.35472i	−0.168210	+	0.0768190i	0.329530	+	0.944145i	$0.393110\pi$
$312$		0			0
$313$	12.0448	−	18.7421i	0.680815	−	1.05937i	−0.313154	−	0.949702i	$-0.601386\pi$
$313$	12.0448	−	18.7421i	0.680815	−	1.05937i	0.993968	−	0.109666i	$-0.0349781\pi$
$314$		0			0
$315$	−1.81439	+	3.45662i	−0.102229	+	0.194759i
$316$		0			0
$317$	−3.53877	−	5.50643i	−0.198757	−	0.309272i	0.727541	−	0.686065i	$-0.240663\pi$
$317$	−3.53877	−	5.50643i	−0.198757	−	0.309272i	−0.926298	+	0.376793i	$0.877027\pi$
$318$		0			0
$319$	−0.147744	+	0.503171i	−0.00827210	+	0.0281722i
$320$		0			0
$321$	−28.0413	+	19.8127i	−1.56511	+	1.10584i
$322$		0			0
$323$		−	5.99875i		−	0.333779i
$324$		0			0
$325$	−20.3653	−	5.97978i	−1.12966	−	0.331698i
$326$		0			0
$327$	12.5159	+	5.06421i	0.692131	+	0.280051i
$328$		0			0
$329$	1.50741	−	10.4843i	0.0831063	−	0.578017i
$330$		0			0
$331$	16.8908	+	10.8550i	0.928401	+	0.596647i	0.915084	−	0.403264i	$-0.132124\pi$
$331$	16.8908	+	10.8550i	0.928401	+	0.596647i	0.0133177	+	0.999911i	$0.495761\pi$
$332$		0			0
$333$	0.686356	+	7.79463i	0.0376121	+	0.427143i
$334$		0			0
$335$	2.57722	−	0.370548i	0.140808	−	0.0202452i
$336$		0			0
$337$	0.882914	+	3.00693i	0.0480954	+	0.163798i	0.980039	−	0.198805i	$-0.0637062\pi$
$337$	0.882914	+	3.00693i	0.0480954	+	0.163798i	−0.931944	+	0.362603i	$0.881888\pi$
$338$		0			0
$339$	1.83585	−	18.5049i	0.0997096	−	1.00505i
$340$		0			0
$341$	0.0863270	+	0.0996267i	0.00467487	+	0.00539509i
$342$		0			0
$343$	18.2607	+	8.33940i	0.985988	+	0.450285i
$344$		0			0
$345$	3.78784	−	3.69394i	0.203931	−	0.198875i
$346$		0			0
$347$	−14.9892	−	6.84533i	−0.804662	−	0.367477i	−0.0297590	−	0.999557i	$-0.509474\pi$
$347$	−14.9892	−	6.84533i	−0.804662	−	0.367477i	−0.774903	+	0.632080i	$0.782201\pi$
$348$		0			0
$349$	−6.54214	−	7.55003i	−0.350193	−	0.404144i	0.553137	−	0.833090i	$-0.313430\pi$
$349$	−6.54214	−	7.55003i	−0.350193	−	0.404144i	−0.903330	+	0.428946i	$0.858885\pi$
$350$		0			0
$351$	−21.7245	−	10.2131i	−1.15957	−	0.545133i
$352$		0			0
$353$	9.09448	+	30.9729i	0.484050	+	1.64852i	0.733166	+	0.680050i	$0.238042\pi$
$353$	9.09448	+	30.9729i	0.484050	+	1.64852i	−0.249116	+	0.968474i	$0.580140\pi$
$354$		0			0
$355$	−4.82347	+	0.693510i	−0.256003	+	0.0368077i
$356$		0			0
$357$	−2.80083	+	4.81015i	−0.148236	+	0.254580i
$358$		0			0
$359$	−10.4213	−	6.69735i	−0.550014	−	0.353472i	0.235930	−	0.971770i	$-0.424186\pi$
$359$	−10.4213	−	6.69735i	−0.550014	−	0.353472i	−0.785944	+	0.618298i	$0.787823\pi$
$360$		0			0
$361$	−0.634174	+	4.41078i	−0.0333776	+	0.232146i
$362$		0			0
$363$	−7.13935	+	17.6445i	−0.374719	+	0.926096i
$364$		0			0
$365$	−2.23020	−	0.654847i	−0.116734	−	0.0342763i
$366$		0			0
$367$		−	15.6903i		−	0.819025i	−0.912305	−	0.409512i	$-0.865699\pi$
$367$		−	15.6903i		−	0.819025i	0.912305	−	0.409512i	$-0.134301\pi$
$368$		0			0
$369$	−10.9141	−	3.86772i	−0.568164	−	0.201345i
$370$		0			0
$371$	0.150825	−	0.513664i	0.00783046	−	0.0266681i
$372$		0			0
$373$	3.64388	+	5.66999i	0.188673	+	0.293581i	0.922684	−	0.385556i	$-0.125990\pi$
$373$	3.64388	+	5.66999i	0.188673	+	0.293581i	−0.734011	+	0.679137i	$0.762354\pi$
$374$		0			0
$375$	−4.81543	−	9.42577i	−0.248668	−	0.486745i
$376$		0			0
$377$	12.7008	−	19.7628i	0.654123	−	1.01784i
$378$		0			0
$379$	1.33432	−	0.609364i	0.0685395	−	0.0313009i	−0.380850	−	0.924637i	$-0.624369\pi$
$379$	1.33432	−	0.609364i	0.0685395	−	0.0313009i	0.449390	+	0.893336i	$0.351641\pi$
$380$		0			0
$381$	−2.99431	−	3.16361i	−0.153403	−	0.162077i
$382$		0			0
$383$	5.63794	−	1.65545i	0.288085	−	0.0845894i	−0.134497	−	0.990914i	$-0.542942\pi$
$383$	5.63794	−	1.65545i	0.288085	−	0.0845894i	0.422582	+	0.906325i	$0.361124\pi$
$384$		0			0
$385$	0.101422	+	0.0878829i	0.00516896	+	0.00447893i
$386$		0			0
$387$	8.69819	+	22.1999i	0.442154	+	1.12849i
$388$		0			0
$389$	3.64207	−	7.97502i	0.184660	−	0.404350i	−0.794550	−	0.607199i	$-0.792293\pi$
$389$	3.64207	−	7.97502i	0.184660	−	0.404350i	0.979210	+	0.202850i	$0.0650202\pi$
$390$		0			0
$391$	5.62673	−	5.02467i	0.284556	−	0.254109i
$392$		0			0
$393$	−13.7869	+	2.60455i	−0.695460	+	0.131382i
$394$		0			0
$395$	−4.99285	+	4.32633i	−0.251218	+	0.217681i
$396$		0			0
$397$	19.1402	−	22.0890i	0.960618	−	1.10861i	−0.0334046	−	0.999442i	$-0.510635\pi$
$397$	19.1402	−	22.0890i	0.960618	−	1.10861i	0.994023	−	0.109171i	$-0.0348195\pi$
$398$		0			0
$399$	−8.38114	+	10.5770i	−0.419582	+	0.529514i
$400$		0			0
$401$	2.64569	+	18.4012i	0.132119	+	0.918911i	0.942785	+	0.333402i	$0.108196\pi$
$401$	2.64569	+	18.4012i	0.132119	+	0.918911i	−0.810665	+	0.585510i	$0.800894\pi$
$402$		0			0
$403$	−2.45317	−	5.37169i	−0.122201	−	0.267583i
$404$		0			0
$405$	−1.79485	−	5.44425i	−0.0891866	−	0.270527i
$406$		0			0
$407$	0.266250	+	0.0382809i	0.0131975	+	0.00189752i
$408$		0			0
$409$	14.8692	−	9.55583i	0.735233	−	0.472505i	−0.118673	−	0.992933i	$-0.537864\pi$
$409$	14.8692	−	9.55583i	0.735233	−	0.472505i	0.853905	+	0.520428i	$0.174228\pi$
$410$		0			0
$411$	21.5860	−	7.38202i	1.06476	−	0.364128i
$412$		0			0
$413$	−15.0782			−0.741951
$414$		0			0
$415$	3.40331			0.167062
$416$		0			0
$417$	11.0129	−	3.76622i	0.539306	−	0.184433i
$418$		0			0
$419$	−0.0318643	+	0.0204779i	−0.00155667	+	0.00100041i	−0.541419	−	0.840753i	$-0.682113\pi$
$419$	−0.0318643	+	0.0204779i	−0.00155667	+	0.00100041i	0.539862	+	0.841753i	$0.318476\pi$
$420$		0			0
$421$	17.6185	+	2.53316i	0.858673	+	0.123459i	0.557567	−	0.830132i	$-0.311735\pi$
$421$	17.6185	+	2.53316i	0.858673	+	0.123459i	0.301106	+	0.953591i	$0.402644\pi$
$422$		0			0
$423$	9.52416	+	12.2964i	0.463080	+	0.597872i
$424$		0			0
$425$	−3.00208	−	6.57364i	−0.145622	−	0.318869i
$426$		0			0
$427$	−3.60035	−	25.0410i	−0.174233	−	1.21182i
$428$		0			0
$429$	−0.512505	+	0.646782i	−0.0247440	+	0.0312269i
$430$		0			0
$431$	−25.8650	+	29.8498i	−1.24587	+	1.43782i	−0.389853	+	0.920877i	$0.627474\pi$
$431$	−25.8650	+	29.8498i	−1.24587	+	1.43782i	−0.856022	+	0.516939i	$0.827071\pi$
$432$		0			0
$433$	−21.6667	+	18.7743i	−1.04124	+	0.902237i	−0.995313	−	0.0967083i	$-0.969169\pi$
$433$	−21.6667	+	18.7743i	−1.04124	+	0.902237i	−0.0459238	+	0.998945i	$0.514623\pi$
$434$		0			0
$435$	5.51238	−	1.04137i	0.264298	−	0.0499297i
$436$		0			0
$437$	15.2368	−	10.1168i	0.728874	−	0.483952i
$438$		0			0
$439$	1.21471	−	2.65985i	0.0579752	−	0.126948i	−0.878427	−	0.477876i	$-0.841407\pi$
$439$	1.21471	−	2.65985i	0.0579752	−	0.126948i	0.936402	+	0.350928i	$0.114134\pi$
$440$		0			0
$441$	−7.89380	+	3.09289i	−0.375895	+	0.147280i
$442$		0			0
$443$	−20.2053	−	17.5080i	−0.959982	−	0.831829i	0.0258330	−	0.999666i	$-0.491776\pi$
$443$	−20.2053	−	17.5080i	−0.959982	−	0.831829i	−0.985815	+	0.167837i	$0.946322\pi$
$444$		0			0
$445$	5.09417	−	1.49578i	0.241487	−	0.0709069i
$446$		0			0
$447$	−9.40845	−	9.94040i	−0.445004	−	0.470165i
$448$		0			0
$449$	24.4965	−	11.1872i	1.15606	−	0.527956i	0.257274	−	0.966338i	$-0.417176\pi$
$449$	24.4965	−	11.1872i	1.15606	−	0.527956i	0.898789	+	0.438382i	$0.144448\pi$
$450$		0			0
$451$	−0.215201	+	0.334860i	−0.0101334	+	0.0157679i
$452$		0			0
$453$	6.92148	+	13.5482i	0.325199	+	0.636548i
$454$		0			0
$455$	−3.25021	−	5.05743i	−0.152372	−	0.237096i
$456$		0			0
$457$	−0.423692	+	1.44296i	−0.0198195	+	0.0674989i	−0.968809	−	0.247809i	$-0.920290\pi$
$457$	−0.423692	+	1.44296i	−0.0198195	+	0.0674989i	0.948990	+	0.315308i	$0.102108\pi$
$458$		0			0
$459$	−2.21586	−	7.86730i	−0.103428	−	0.367214i
$460$		0			0
$461$		−	17.2006i		−	0.801112i	−0.916272	−	0.400556i	$-0.868817\pi$
$461$		−	17.2006i		−	0.801112i	0.916272	−	0.400556i	$-0.131183\pi$
$462$		0			0
$463$	23.2816	+	6.83609i	1.08199	+	0.317700i	0.773673	−	0.633585i	$-0.218417\pi$
$463$	23.2816	+	6.83609i	1.08199	+	0.317700i	0.308313	+	0.951285i	$0.400236\pi$
$464$		0			0
$465$	0.528936	−	1.30723i	0.0245288	−	0.0606215i
$466$		0			0
$467$	−5.39977	+	37.5562i	−0.249872	+	1.73789i	0.349065	+	0.937098i	$0.386499\pi$
$467$	−5.39977	+	37.5562i	−0.249872	+	1.73789i	−0.598937	+	0.800796i	$0.704410\pi$
$468$		0			0
$469$	−7.02580	−	4.51521i	−0.324421	−	0.208493i
$470$		0			0
$471$	−7.83279	+	13.4520i	−0.360916	+	0.619838i
$472$		0			0
$473$	0.811297	−	0.116647i	0.0373035	−	0.00536343i
$474$		0			0
$475$	−4.93625	−	16.8113i	−0.226490	−	0.771356i
$476$		0			0
$477$	0.388027	+	0.683671i	0.0177665	+	0.0313031i
$478$		0			0
$479$	23.5632	+	27.1934i	1.07663	+	1.24250i	0.968672	+	0.248342i	$0.0798858\pi$
$479$	23.5632	+	27.1934i	1.07663	+	1.24250i	0.107958	+	0.994155i	$0.465569\pi$
$480$		0			0
$481$	−10.9609	−	5.00567i	−0.499773	−	0.228239i
$482$		0			0
$483$	−16.9413	+	0.998153i	−0.770856	+	0.0454175i
$484$		0			0
$485$	−3.77231	−	1.72276i	−0.171292	−	0.0782264i
$486$		0			0
$487$	−10.2030	−	11.7749i	−0.462342	−	0.533571i	0.475924	−	0.879486i	$-0.342114\pi$
$487$	−10.2030	−	11.7749i	−0.462342	−	0.533571i	−0.938266	+	0.345916i	$0.887568\pi$
$488$		0			0
$489$	2.66491	−	26.8616i	0.120511	−	1.21472i
$490$		0			0
$491$	7.99551	+	27.2302i	0.360832	+	1.22888i	0.917362	+	0.398054i	$0.130314\pi$
$491$	7.99551	+	27.2302i	0.360832	+	1.22888i	−0.556530	+	0.830828i	$0.687868\pi$
$492$		0			0
$493$	7.91718	−	1.13832i	0.356572	−	0.0512673i
$494$		0			0
$495$	−0.196302	+	0.0172854i	−0.00882312	+	0.000776920i
$496$		0			0
$497$	13.1494	+	8.45058i	0.589829	+	0.379060i
$498$		0			0
$499$	2.71046	−	18.8516i	0.121337	−	0.843915i	−0.834708	−	0.550693i	$-0.814363\pi$
$499$	2.71046	−	18.8516i	0.121337	−	0.843915i	0.956044	−	0.293222i	$-0.0947275\pi$
$500$		0			0
$501$	32.6714	+	13.2196i	1.45965	+	0.590607i
$502$		0			0
$503$	−12.4263	−	3.64870i	−0.554062	−	0.162687i	−0.00729702	−	0.999973i	$-0.502323\pi$
$503$	−12.4263	−	3.64870i	−0.554062	−	0.162687i	−0.546765	+	0.837286i	$0.684141\pi$
$504$		0			0
$505$		−	7.66320i		−	0.341008i
$506$		0			0
$507$	11.8019	−	8.33872i	0.524141	−	0.370336i
$508$		0			0
$509$	6.41159	−	21.8359i	0.284189	−	0.967858i	−0.686422	−	0.727203i	$-0.740820\pi$
$509$	6.41159	−	21.8359i	0.284189	−	0.967858i	0.970611	−	0.240655i	$-0.0773621\pi$
$510$		0			0
$511$	4.03076	+	6.27198i	0.178310	+	0.277456i
$512$		0			0
$513$	−2.60310	−	19.6445i	−0.114930	−	0.867328i
$514$		0			0
$515$	5.13869	−	7.99597i	0.226438	−	0.352344i
$516$		0			0
$517$	0.486355	−	0.222111i	0.0213899	−	0.00976843i
$518$		0			0
$519$	25.7592	−	24.3807i	1.13070	−	1.07019i
$520$		0			0
$521$	38.8350	−	11.4030i	1.70139	−	0.499574i	0.720389	−	0.693570i	$-0.243963\pi$
$521$	38.8350	−	11.4030i	1.70139	−	0.499574i	0.981002	+	0.193997i	$0.0621451\pi$
$522$		0			0
$523$	−30.1923	−	26.1617i	−1.32022	−	1.14397i	−0.978971	−	0.203999i	$-0.934606\pi$
$523$	−30.1923	−	26.1617i	−1.32022	−	1.14397i	−0.341245	−	0.939975i	$-0.610848\pi$
$524$		0			0
$525$	−3.89107	+	15.7850i	−0.169820	+	0.688916i
$526$		0			0
$527$	0.835256	−	1.82896i	0.0363843	−	0.0796706i
$528$		0			0
$529$	22.2520	+	5.81783i	0.967480	+	0.252949i
$530$		0			0
$531$	15.3967	−	15.9111i	0.668162	−	0.690484i
$532$		0			0
$533$	13.4760	−	11.6770i	0.583711	−	0.505788i
$534$		0			0
$535$	8.26835	−	9.54218i	0.357472	−	0.412545i
$536$		0			0
$537$	11.0113	+	8.72529i	0.475175	+	0.376524i
$538$		0			0
$539$	0.0414771	+	0.288479i	0.00178654	+	0.0124257i
$540$		0			0
$541$	−0.192769	−	0.422104i	−0.00828777	−	0.0181477i	0.905443	−	0.424468i	$-0.139539\pi$
$541$	−0.192769	−	0.422104i	−0.00828777	−	0.0181477i	−0.913731	+	0.406321i	$0.866812\pi$
$542$		0			0
$543$	−1.27514	−	29.0183i	−0.0547214	−	1.24529i
$544$		0			0
$545$	−4.91453	−	0.706603i	−0.210515	−	0.0302675i
$546$		0			0
$547$	−30.8167	+	19.8047i	−1.31763	+	0.846787i	−0.995013	−	0.0997433i	$-0.968198\pi$
$547$	−30.8167	+	19.8047i	−1.31763	+	0.846787i	−0.322614	+	0.946531i	$0.604561\pi$
$548$		0			0
$549$	30.1006	+	21.7707i	1.28466	+	0.929152i
$550$		0			0
$551$	19.3925			0.826146
$552$		0			0
$553$	21.1907			0.901121
$554$		0			0
$555$	−0.931102	−	2.72267i	−0.0395231	−	0.115571i
$556$		0			0
$557$	22.8872	−	14.7087i	0.969762	−	0.623228i	0.0430789	−	0.999072i	$-0.486283\pi$
$557$	22.8872	−	14.7087i	0.969762	−	0.623228i	0.926683	+	0.375843i	$0.122647\pi$
$558$		0			0
$559$	−36.3435	−	5.22541i	−1.53717	−	0.221011i
$560$		0			0
$561$	−0.280701	+	0.0123347i	−0.0118512	+	0.000520771i
$562$		0			0
$563$	7.51512	+	16.4558i	0.316725	+	0.693530i	0.999305	−	0.0372806i	$-0.0118695\pi$
$563$	7.51512	+	16.4558i	0.316725	+	0.693530i	−0.682580	+	0.730811i	$0.739142\pi$
$564$		0			0
$565$	0.973200	+	6.76875i	0.0409428	+	0.284764i
$566$		0			0
$567$	−7.08476	+	16.9675i	−0.297532	+	0.712570i
$568$		0			0
$569$	−5.13183	+	5.92245i	−0.215138	+	0.248282i	−0.853053	−	0.521825i	$-0.825252\pi$
$569$	−5.13183	+	5.92245i	−0.215138	+	0.248282i	0.637915	+	0.770107i	$0.279797\pi$
$570$		0			0
$571$	11.2944	−	9.78668i	0.472657	−	0.409560i	−0.385690	−	0.922628i	$-0.626037\pi$
$571$	11.2944	−	9.78668i	0.472657	−	0.409560i	0.858348	+	0.513068i	$0.171491\pi$
$572$		0			0
$573$	2.45239	+	12.9815i	0.102450	+	0.542310i
$574$		0			0
$575$	11.6340	−	18.7116i	0.485173	−	0.780328i
$576$		0			0
$577$	15.2558	−	33.4056i	0.635109	−	1.39070i	−0.268894	−	0.963170i	$-0.586658\pi$
$577$	15.2558	−	33.4056i	0.635109	−	1.39070i	0.904003	−	0.427525i	$-0.140615\pi$
$578$		0			0
$579$	−28.6764	−	7.06883i	−1.19175	−	0.293771i
$580$		0			0
$581$	−8.25000	−	7.14866i	−0.342267	−	0.296576i
$582$		0			0
$583$	0.0259290	−	0.00761343i	0.00107387	−	0.000315316i
$584$		0			0
$585$	8.65566	+	1.73451i	0.357867	+	0.0717132i
$586$		0			0
$587$	−16.7069	+	7.62980i	−0.689569	+	0.314916i	−0.729202	−	0.684299i	$-0.760108\pi$
$587$	−16.7069	+	7.62980i	−0.689569	+	0.314916i	0.0396328	+	0.999214i	$0.487381\pi$
$588$		0			0
$589$	2.63552	−	4.10094i	0.108595	−	0.168976i
$590$		0			0
$591$	36.3408	−	18.5657i	1.49486	−	0.763693i
$592$		0			0
$593$	22.1174	+	34.4153i	0.908251	+	1.41327i	0.910609	+	0.413269i	$0.135613\pi$
$593$	22.1174	+	34.4153i	0.908251	+	1.41327i	−0.00235753	+	0.999997i	$0.500750\pi$
$594$		0			0
$595$	0.576676	−	1.96398i	0.0236414	−	0.0805153i
$596$		0			0
$597$	−0.0706966	−	0.100058i	−0.00289342	−	0.00409510i
$598$		0			0
$599$			45.1686i			1.84554i	0.385355	+	0.922769i	$0.374079\pi$
$599$			45.1686i			1.84554i	−0.385355	+	0.922769i	$0.625921\pi$
$600$		0			0
$601$	20.1974	+	5.93050i	0.823871	+	0.241910i	0.666382	−	0.745611i	$-0.267842\pi$
$601$	20.1974	+	5.93050i	0.823871	+	0.241910i	0.157489	+	0.987521i	$0.449660\pi$
$602$		0			0
$603$	11.9388	−	2.80331i	0.486187	−	0.114160i
$604$		0			0
$605$	0.996145	−	6.92834i	0.0404991	−	0.281677i
$606$		0			0
$607$	11.3581	+	7.29944i	0.461013	+	0.296275i	0.750456	−	0.660920i	$-0.229834\pi$
$607$	11.3581	+	7.29944i	0.461013	+	0.296275i	−0.289443	+	0.957195i	$0.593470\pi$
$608$		0			0
$609$	−15.5500	−	9.05438i	−0.630118	−	0.366902i
$610$		0			0
$611$	−23.7078	+	3.40867i	−0.959117	+	0.137900i
$612$		0			0
$613$	11.2844	+	38.4311i	0.455773	+	1.55222i	0.792050	+	0.610456i	$0.209014\pi$
$613$	11.2844	+	38.4311i	0.455773	+	1.55222i	−0.336277	+	0.941763i	$0.609168\pi$
$614$		0			0
$615$	4.23729	+	0.420378i	0.170864	+	0.0169513i
$616$		0			0
$617$	−18.0484	−	20.8290i	−0.726603	−	0.838545i	0.265481	−	0.964116i	$-0.414469\pi$
$617$	−18.0484	−	20.8290i	−0.726603	−	0.838545i	−0.992085	+	0.125571i	$0.959924\pi$
$618$		0			0
$619$	−10.1156	−	4.61963i	−0.406579	−	0.185679i	0.201618	−	0.979464i	$-0.435380\pi$
$619$	−10.1156	−	4.61963i	−0.406579	−	0.185679i	−0.608198	+	0.793786i	$0.708107\pi$
$620$		0			0
$621$	16.2459	−	18.8963i	0.651924	−	0.758284i
$622$		0			0
$623$	−15.4907	−	7.07438i	−0.620623	−	0.283429i
$624$		0			0
$625$	−12.4942	−	14.4191i	−0.499768	−	0.576763i
$626$		0			0
$627$	−0.677883	−	0.0672521i	−0.0270720	−	0.00268579i
$628$		0			0
$629$	−1.15587	−	3.93653i	−0.0460876	−	0.156960i
$630$		0			0
$631$	−23.6718	+	3.40350i	−0.942361	+	0.135491i	−0.596337	−	0.802734i	$-0.703378\pi$
$631$	−23.6718	+	3.40350i	−0.942361	+	0.135491i	−0.346024	+	0.938226i	$0.612469\pi$
$632$		0			0
$633$	−28.8879	−	16.8207i	−1.14819	−	0.668564i
$634$		0			0
$635$	1.34756	+	0.866026i	0.0534764	+	0.0343672i
$636$		0			0
$637$	1.85804	−	12.9230i	0.0736183	−	0.512026i
$638$		0			0
$639$	−22.3445	+	5.24662i	−0.883934	+	0.207553i
$640$		0			0
$641$	1.60949	+	0.472588i	0.0635709	+	0.0186661i	0.313363	−	0.949633i	$-0.398544\pi$
$641$	1.60949	+	0.472588i	0.0635709	+	0.0186661i	−0.249792	+	0.968299i	$0.580362\pi$
$642$		0			0
$643$		−	3.01298i		−	0.118820i	−0.998234	−	0.0594101i	$-0.981078\pi$
$643$		−	3.01298i		−	0.118820i	0.998234	−	0.0594101i	$-0.0189220\pi$
$644$		0			0
$645$	−5.05960	−	7.16093i	−0.199222	−	0.281961i
$646$		0			0
$647$	1.60800	−	5.47636i	0.0632171	−	0.215298i	−0.921827	−	0.387603i	$-0.873303\pi$
$647$	1.60800	−	5.47636i	0.0632171	−	0.215298i	0.985044	+	0.172305i	$0.0551214\pi$
$648$		0			0
$649$	−0.411496	−	0.640300i	−0.0161526	−	0.0251340i
$650$		0			0
$651$	−4.02805	+	2.05785i	−0.157872	+	0.0806535i
$652$		0			0
$653$	14.0872	−	21.9201i	0.551274	−	0.857799i	−0.448071	−	0.893998i	$-0.647889\pi$
$653$	14.0872	−	21.9201i	0.551274	−	0.857799i	0.999345	+	0.0361994i	$0.0115251\pi$
$654$		0			0
$655$	4.69340	−	2.14340i	0.183386	−	0.0837498i
$656$		0			0
$657$	−10.7343	−	2.15106i	−0.418786	−	0.0839207i
$658$		0			0
$659$	6.81122	−	1.99996i	0.265328	−	0.0779072i	−0.146363	−	0.989231i	$-0.546757\pi$
$659$	6.81122	−	1.99996i	0.265328	−	0.0779072i	0.411690	+	0.911324i	$0.364939\pi$
$660$		0			0
$661$	24.4317	+	21.1702i	0.950284	+	0.823426i	0.984391	−	0.175993i	$-0.0563135\pi$
$661$	24.4317	+	21.1702i	0.950284	+	0.823426i	−0.0341077	+	0.999418i	$0.510859\pi$
$662$		0			0
$663$	12.2208	+	3.01247i	0.474617	+	0.116995i
$664$		0			0
$665$	2.06156	−	4.51419i	0.0799440	−	0.175053i
$666$		0			0
$667$	16.2435	+	18.1898i	0.628952	+	0.704313i
$668$		0			0
$669$	−1.29811	−	6.87144i	−0.0501879	−	0.265665i
$670$		0			0
$671$	0.965115	−	0.836277i	0.0372579	−	0.0322841i
$672$		0			0
$673$	−15.0009	+	17.3120i	−0.578243	+	0.667328i	−0.967226	−	0.253917i	$-0.918281\pi$
$673$	−15.0009	+	17.3120i	−0.578243	+	0.667328i	0.388983	+	0.921245i	$0.372827\pi$
$674$		0			0
$675$	−12.6837	−	20.2245i	−0.488197	−	0.778440i
$676$		0			0
$677$	4.88397	+	33.9688i	0.187706	+	1.30553i	0.837928	+	0.545781i	$0.183767\pi$
$677$	4.88397	+	33.9688i	0.187706	+	1.30553i	−0.650221	+	0.759745i	$0.725324\pi$
$678$		0			0
$679$	5.52585	+	12.0999i	0.212063	+	0.464352i
$680$		0			0
$681$	−40.0620	+	1.76043i	−1.53518	+	0.0674597i
$682$		0			0
$683$	−44.7456	−	6.43345i	−1.71214	−	0.246169i	−0.784631	−	0.619963i	$-0.787148\pi$
$683$	−44.7456	−	6.43345i	−1.71214	−	0.246169i	−0.927512	+	0.373794i	$0.878057\pi$
$684$		0			0
$685$	−7.05758	+	4.53563i	−0.269656	+	0.173298i
$686$		0			0
$687$	11.1678	+	32.6561i	0.426077	+	1.24591i
$688$		0			0
$689$	−1.21057			−0.0461191
$690$		0			0
$691$	13.3631			0.508355			0.254177	−	0.967158i	$-0.418195\pi$
$691$	13.3631			0.508355			0.254177	+	0.967158i	$0.418195\pi$
$692$		0			0
$693$	0.512166	+	0.370432i	0.0194556	+	0.0140715i
$694$		0			0
$695$	−3.60070	+	2.31403i	−0.136582	+	0.0877761i
$696$		0			0
$697$	6.00942	+	0.864024i	0.227623	+	0.0327272i
$698$		0			0
$699$	0.129171	+	2.93954i	0.00488568	+	0.111184i
$700$		0			0
$701$	−2.53732	−	5.55595i	−0.0958332	−	0.209845i	0.855644	−	0.517565i	$-0.173161\pi$
$701$	−2.53732	−	5.55595i	−0.0958332	−	0.209845i	−0.951477	+	0.307720i	$0.900434\pi$
$702$		0			0
$703$	−1.41560	−	9.84574i	−0.0533905	−	0.371339i
$704$		0			0
$705$	−4.48287	−	3.55218i	−0.168834	−	0.133783i
$706$		0			0
$707$	−16.0966	+	18.5765i	−0.605375	+	0.698640i
$708$		0			0
$709$	−32.2847	+	27.9749i	−1.21248	+	1.05062i	−0.215223	+	0.976565i	$0.569048\pi$
$709$	−32.2847	+	27.9749i	−1.21248	+	1.05062i	−0.997254	+	0.0740529i	$0.976407\pi$
$710$		0			0
$711$	−21.6383	+	22.3613i	−0.811501	+	0.838612i
$712$		0			0
$713$	6.05418	−	0.962961i	0.226731	−	0.0360632i
$714$		0			0
$715$	0.126064	−	0.276042i	0.00471453	−	0.0103234i
$716$		0			0
$717$	−6.13586	+	24.8916i	−0.229148	+	0.929592i
$718$		0			0
$719$	−32.2772	−	27.9683i	−1.20374	−	1.04304i	−0.997921	−	0.0644522i	$-0.979470\pi$
$719$	−32.2772	−	27.9683i	−1.20374	−	1.04304i	−0.205815	−	0.978591i	$-0.565985\pi$
$720$		0			0
$721$	−29.2523	+	8.58926i	−1.08941	+	0.319881i
$722$		0			0
$723$	18.5512	−	17.5585i	0.689927	−	0.653006i
$724$		0			0
$725$	21.2510	−	9.70499i	0.789241	−	0.360434i
$726$		0			0
$727$	−23.5028	+	36.5711i	−0.871671	+	1.35635i	0.0619481	+	0.998079i	$0.480269\pi$
$727$	−23.5028	+	36.5711i	−0.871671	+	1.35635i	−0.933619	+	0.358267i	$0.883368\pi$
$728$		0			0
$729$	−10.6704	−	24.8021i	−0.395200	−	0.918595i
$730$		0			0
$731$	−6.75883	−	10.5169i	−0.249984	−	0.388983i
$732$		0			0
$733$	−5.70778	+	19.4389i	−0.210822	+	0.717992i	0.784392	+	0.620266i	$0.212975\pi$
$733$	−5.70778	+	19.4389i	−0.210822	+	0.717992i	−0.995213	+	0.0977265i	$0.968843\pi$
$734$		0			0
$735$	2.54627	−	1.79908i	0.0939205	−	0.0663602i
$736$		0			0
$737$		−	0.421575i		−	0.0155289i
$738$		0			0
$739$	8.38621	+	2.46241i	0.308492	+	0.0905814i	0.432314	−	0.901723i	$-0.357697\pi$
$739$	8.38621	+	2.46241i	0.308492	+	0.0905814i	−0.123822	+	0.992304i	$0.539515\pi$
$740$		0			0
$741$	28.2882	+	11.4460i	1.03919	+	0.420480i
$742$		0			0
$743$	4.58372	−	31.8805i	0.168161	−	1.16958i	−0.714522	−	0.699613i	$-0.753356\pi$
$743$	4.58372	−	31.8805i	0.168161	−	1.16958i	0.882683	−	0.469969i	$-0.155735\pi$
$744$		0			0
$745$	4.23419	+	2.72115i	0.155129	+	0.0996951i
$746$		0			0
$747$	15.9678	−	1.40605i	0.584231	−	0.0514445i
$748$		0			0
$749$	−40.0868	+	5.76361i	−1.46474	+	0.210598i
$750$		0			0
$751$	3.57950	+	12.1907i	0.130618	+	0.444843i	0.998666	−	0.0516367i	$-0.0164438\pi$
$751$	3.57950	+	12.1907i	0.130618	+	0.444843i	−0.868048	+	0.496480i	$0.834626\pi$
$752$		0			0
$753$	−1.45570	+	14.6731i	−0.0530486	+	0.534716i
$754$		0			0
$755$	−3.66375	−	4.22819i	−0.133337	−	0.153880i
$756$		0			0
$757$	−26.7615	−	12.2216i	−0.972664	−	0.444201i	−0.135275	−	0.990808i	$-0.543192\pi$
$757$	−26.7615	−	12.2216i	−0.972664	−	0.444201i	−0.837389	+	0.546608i	$0.815919\pi$
$758$		0			0
$759$	−0.504727	−	0.692175i	−0.0183204	−	0.0251244i
$760$		0			0
$761$	−20.8926	−	9.54134i	−0.757357	−	0.345873i	−0.000971515	−	1.00000i	$-0.500309\pi$
$761$	−20.8926	−	9.54134i	−0.757357	−	0.345873i	−0.756385	+	0.654126i	$0.773037\pi$
$762$		0			0
$763$	10.4292	+	12.0359i	0.377561	+	0.435728i
$764$		0			0
$765$	1.48361	+	2.61400i	0.0536400	+	0.0945092i
$766$		0			0
$767$	9.60597	+	32.7149i	0.346851	+	1.18127i
$768$		0			0
$769$	21.4432	−	3.08306i	0.773261	−	0.111178i	0.255621	−	0.966777i	$-0.417720\pi$
$769$	21.4432	−	3.08306i	0.773261	−	0.111178i	0.517639	+	0.855599i	$0.326811\pi$
$770$		0			0
$771$	−20.5682	+	35.3238i	−0.740744	+	1.27216i
$772$		0			0
$773$	37.7994	+	24.2922i	1.35955	+	0.873729i	0.998274	−	0.0587296i	$-0.0187050\pi$
$773$	37.7994	+	24.2922i	1.35955	+	0.873729i	0.361276	+	0.932459i	$0.382341\pi$
$774$		0			0
$775$	0.835770	−	5.81291i	0.0300218	−	0.208806i
$776$		0			0
$777$	−3.46188	+	8.55584i	−0.124194	+	0.306939i
$778$		0			0
$779$	14.1233	+	4.14698i	0.506020	+	0.148581i
$780$		0			0
$781$			0.789012i			0.0282331i
$782$		0			0
$783$	25.4330	−	7.16333i	0.908902	−	0.255996i
$784$		0			0
$785$	1.61273	−	5.49246i	0.0575609	−	0.196034i
$786$		0			0
$787$	7.16576	+	11.1501i	0.255432	+	0.397460i	0.945159	−	0.326609i	$-0.105906\pi$
$787$	7.16576	+	11.1501i	0.255432	+	0.397460i	−0.689728	+	0.724069i	$0.742270\pi$
$788$		0			0
$789$	−0.917718	−	1.79635i	−0.0326716	−	0.0639517i
$790$		0			0
$791$	11.8587	−	18.4524i	0.421645	−	0.656093i
$792$		0			0
$793$	−52.0372	+	23.7646i	−1.84790	+	0.843906i
$794$		0			0
$795$	−0.198718	−	0.209953i	−0.00704780	−	0.00744628i
$796$		0			0
$797$	−40.8373	+	11.9909i	−1.44653	+	0.424740i	−0.908394	−	0.418116i	$-0.862691\pi$
$797$	−40.8373	+	11.9909i	−1.44653	+	0.424740i	−0.538139	+	0.842856i	$0.680872\pi$
$798$		0			0
$799$	−6.16319	−	5.34043i	−0.218038	−	0.188931i
$800$		0			0
$801$	23.2831	−	9.12260i	0.822669	−	0.322331i
$802$		0			0
$803$	−0.156339	+	0.342334i	−0.00551707	+	0.0120807i
$804$		0			0
$805$	5.96105	−	1.84747i	0.210099	−	0.0651146i
$806$		0			0
$807$	18.2963	−	3.45644i	0.644062	−	0.121673i
$808$		0			0
$809$	37.9129	−	32.8517i	1.33295	−	1.15501i	0.357713	−	0.933832i	$-0.383557\pi$
$809$	37.9129	−	32.8517i	1.33295	−	1.15501i	0.975234	−	0.221174i	$-0.0709888\pi$
$810$		0			0
$811$	−22.6744	+	26.1676i	−0.796206	+	0.918870i	−0.998167	−	0.0605233i	$-0.980723\pi$
$811$	−22.6744	+	26.1676i	−0.796206	+	0.918870i	0.201961	+	0.979394i	$0.435269\pi$
$812$		0			0
$813$	7.74457	−	9.77368i	0.271614	−	0.342778i
$814$		0			0
$815$	1.41269	+	9.82549i	0.0494845	+	0.344172i
$816$		0			0
$817$	−12.5911	−	27.5707i	−0.440507	−	0.964576i
$818$		0			0
$819$	−17.3389	−	22.3859i	−0.605871	−	0.782227i
$820$		0			0
$821$	−33.7191	−	4.84808i	−1.17681	−	0.169199i	−0.473963	−	0.880545i	$-0.657177\pi$
$821$	−33.7191	−	4.84808i	−1.17681	−	0.169199i	−0.702842	+	0.711346i	$0.748086\pi$
$822$		0			0
$823$	−8.31892	+	5.34625i	−0.289979	+	0.186358i	−0.677540	−	0.735486i	$-0.736954\pi$
$823$	−8.31892	+	5.34625i	−0.289979	+	0.186358i	0.387561	+	0.921844i	$0.373318\pi$
$824$		0			0
$825$	−0.776505	+	0.265550i	−0.0270344	+	0.00924528i
$826$		0			0
$827$	−35.6621			−1.24009			−0.620046	−	0.784565i	$-0.712886\pi$
$827$	−35.6621			−1.24009			−0.620046	+	0.784565i	$0.712886\pi$
$828$		0			0
$829$	−22.8738			−0.794439			−0.397220	−	0.917724i	$-0.630025\pi$
$829$	−22.8738			−0.794439			−0.397220	+	0.917724i	$0.630025\pi$
$830$		0			0
$831$	25.1434	−	8.59857i	0.872214	−	0.298281i
$832$		0			0
$833$	3.73959	−	2.40329i	0.129569	−	0.0832691i
$834$		0			0
$835$	−12.8289	−	1.84451i	−0.443961	−	0.0638320i
$836$		0			0
$837$	1.94162	−	6.35187i	0.0671121	−	0.219553i
$838$		0			0
$839$	8.20754	+	17.9720i	0.283356	+	0.620463i	0.996773	−	0.0802772i	$-0.0255806\pi$
$839$	8.20754	+	17.9720i	0.283356	+	0.620463i	−0.713417	+	0.700740i	$0.752853\pi$
$840$		0			0
$841$	−0.447230	−	3.11055i	−0.0154217	−	0.107260i
$842$		0			0
$843$	19.1348	−	24.1481i	0.659036	−	0.831706i
$844$		0			0
$845$	−3.47996	+	4.01608i	−0.119714	+	0.138157i
$846$		0			0
$847$	−16.9678	+	14.7027i	−0.583020	+	0.505190i
$848$		0			0
$849$	−50.5208	+	9.54410i	−1.73387	+	0.327553i
$850$		0			0
$851$	8.04941	−	9.57481i	0.275930	−	0.328220i
$852$		0			0
$853$	−14.3247	+	31.3667i	−0.490469	+	1.07398i	0.488982	+	0.872294i	$0.337368\pi$
$853$	−14.3247	+	31.3667i	−0.490469	+	1.07398i	−0.979451	+	0.201683i	$0.935359\pi$
$854$		0			0
$855$	2.65844	+	6.78499i	0.0909167	+	0.232042i
$856$		0			0
$857$	−6.61888	−	5.73529i	−0.226097	−	0.195914i	0.534445	−	0.845204i	$-0.320521\pi$
$857$	−6.61888	−	5.73529i	−0.226097	−	0.195914i	−0.760541	+	0.649290i	$0.775066\pi$
$858$		0			0
$859$	30.8330	−	9.05337i	1.05201	−	0.308897i	0.290379	−	0.956912i	$-0.406219\pi$
$859$	30.8330	−	9.05337i	1.05201	−	0.308897i	0.761628	+	0.648015i	$0.224400\pi$
$860$		0			0
$861$	−9.38867	−	9.91950i	−0.319965	−	0.338056i
$862$		0			0
$863$	−38.7548	+	17.6987i	−1.31923	+	0.602471i	−0.945668	−	0.325135i	$-0.894590\pi$
$863$	−38.7548	+	17.6987i	−1.31923	+	0.602471i	−0.373560	+	0.927606i	$0.621863\pi$
$864$		0			0
$865$	−7.05149	+	10.9723i	−0.239758	+	0.373070i
$866$		0			0
$867$	−11.4462	−	22.4049i	−0.388733	−	0.760909i
$868$		0			0
$869$	0.578310	+	0.899868i	0.0196178	+	0.0305259i
$870$		0			0
$871$	−5.32059	+	18.1203i	−0.180281	+	0.613981i
$872$		0			0
$873$	−18.4109	−	6.52443i	−0.623114	−	0.220818i
$874$		0			0
$875$		−	12.4850i		−	0.422069i
$876$		0			0
$877$	29.8035	+	8.75111i	1.00639	+	0.295504i	0.743077	−	0.669206i	$-0.233365\pi$
$877$	29.8035	+	8.75111i	1.00639	+	0.295504i	0.263317	+	0.964709i	$0.415184\pi$
$878$		0			0
$879$	21.6857	−	53.5949i	0.731440	−	1.80771i
$880$		0			0
$881$	−5.02807	+	34.9710i	−0.169400	+	1.17820i	0.710729	+	0.703466i	$0.248365\pi$
$881$	−5.02807	+	34.9710i	−0.169400	+	1.17820i	−0.880128	+	0.474736i	$0.842544\pi$
$882$		0			0
$883$	39.0268	+	25.0810i	1.31336	+	0.844042i	0.994599	−	0.103795i	$-0.0330984\pi$
$883$	39.0268	+	25.0810i	1.31336	+	0.844042i	0.318756	+	0.947837i	$0.396735\pi$
$884$		0			0
$885$	−4.09701	+	7.03621i	−0.137719	+	0.236520i
$886$		0			0
$887$	31.6407	−	4.54925i	1.06239	−	0.152749i	0.411111	−	0.911585i	$-0.365141\pi$
$887$	31.6407	−	4.54925i	1.06239	−	0.152749i	0.651281	+	0.758837i	$0.274232\pi$
$888$		0			0
$889$	−1.44755	−	4.92991i	−0.0485493	−	0.165344i
$890$		0			0
$891$	−0.913879	+	0.162201i	−0.0306161	+	0.00543393i
$892$		0			0
$893$	−12.9478	−	14.9426i	−0.433281	−	0.500033i
$894$		0			0
$895$	−4.69956	−	2.14622i	−0.157089	−	0.0717401i
$896$		0			0
$897$	12.9586	+	36.1213i	0.432673	+	1.20605i
$898$		0			0
$899$	5.91256	+	2.70018i	0.197195	+	0.0900559i
$900$		0			0
$901$	−0.269918	−	0.311502i	−0.00899228	−	0.0103776i
$902$		0			0
$903$	−2.77652	+	27.9866i	−0.0923970	+	0.931336i
$904$		0			0
$905$	3.00931	+	10.2488i	0.100033	+	0.340681i
$906$		0			0
$907$	−49.5014	+	7.11722i	−1.64367	+	0.236323i	−0.901151	−	0.433506i	$-0.857276\pi$
$907$	−49.5014	+	7.11722i	−1.64367	+	0.236323i	−0.742515	+	0.669829i	$0.766367\pi$
$908$		0			0
$909$	−3.16598	−	35.9546i	−0.105009	−	1.19254i
$910$		0			0
$911$	20.3195	+	13.0586i	0.673216	+	0.432650i	0.832084	−	0.554650i	$-0.187148\pi$
$911$	20.3195	+	13.0586i	0.673216	+	0.432650i	−0.158867	+	0.987300i	$0.550784\pi$
$912$		0			0
$913$	0.0784210	−	0.545430i	0.00259536	−	0.0180511i
$914$		0			0
$915$	−12.6636	−	5.12397i	−0.418645	−	0.169393i
$916$		0			0
$917$	−15.8796	−	4.66266i	−0.524389	−	0.153975i
$918$		0			0
$919$			57.5731i			1.89916i	0.313524	+	0.949580i	$0.398490\pi$
$919$			57.5731i			1.89916i	−0.313524	+	0.949580i	$0.601510\pi$
$920$		0			0
$921$	22.0134	−	15.5537i	0.725365	−	0.512511i
$922$		0			0
$923$	9.95791	−	33.9135i	0.327769	−	1.11628i
$924$		0			0
$925$	−6.47859	−	10.0809i	−0.213015	−	0.331457i
$926$		0			0
$927$	20.8065	−	39.6389i	0.683376	−	1.30191i
$928$		0			0
$929$	24.6215	−	38.3117i	0.807804	−	1.25697i	−0.155308	−	0.987866i	$-0.549637\pi$
$929$	24.6215	−	38.3117i	0.807804	−	1.25697i	0.963112	−	0.269101i	$-0.0867267\pi$
$930$		0			0
$931$	9.80353	−	4.47712i	0.321298	−	0.146732i
$932$		0			0
$933$	4.10229	−	3.88277i	0.134303	−	0.127116i
$934$		0			0
$935$	0.0991387	−	0.0291097i	0.00324218	−	0.000951991i
$936$		0			0
$937$	27.8898	+	24.1667i	0.911121	+	0.789491i	0.978072	−	0.208265i	$-0.0667817\pi$
$937$	27.8898	+	24.1667i	0.911121	+	0.789491i	−0.0669512	+	0.997756i	$0.521327\pi$
$938$		0			0
$939$	−9.23563	+	37.4665i	−0.301393	+	1.22267i
$940$		0			0
$941$	−10.1644	+	22.2569i	−0.331350	+	0.725555i	−0.999835	−	0.0181708i	$-0.994216\pi$
$941$	−10.1644	+	22.2569i	−0.331350	+	0.725555i	0.668485	+	0.743725i	$0.266943\pi$
$942$		0			0
$943$	7.94018	+	16.7210i	0.258568	+	0.544512i
$944$		0			0
$945$	1.03623	−	6.68183i	0.0337087	−	0.217360i
$946$		0			0
$947$	−3.37175	+	2.92164i	−0.109567	+	0.0949405i	−0.707922	−	0.706291i	$-0.750367\pi$
$947$	−3.37175	+	2.92164i	−0.109567	+	0.0949405i	0.598354	+	0.801232i	$0.295822\pi$
$948$		0			0
$949$	11.0403	−	12.7412i	0.358383	−	0.413596i
$950$		0			0
$951$	8.88572	+	7.04096i	0.288139	+	0.228319i
$952$		0			0
$953$	3.90979	+	27.1932i	0.126650	+	0.880873i	0.949758	+	0.312987i	$0.101329\pi$
$953$	3.90979	+	27.1932i	0.126650	+	0.880873i	−0.823107	+	0.567886i	$0.807761\pi$
$954$		0			0
$955$	−2.01819	−	4.41921i	−0.0653070	−	0.143002i
$956$		0			0
$957$	−0.0398750	−	0.907435i	−0.00128897	−	0.0293332i
$958$		0			0
$959$	26.6355	+	3.82960i	0.860105	+	0.123664i
$960$		0			0
$961$	−24.7043	+	15.8765i	−0.796913	+	0.512145i
$962$		0			0
$963$	34.8516	−	48.1865i	1.12308	−	1.55279i
$964$		0			0
$965$	10.8611			0.349631
$966$		0			0
$967$	31.9290			1.02677			0.513384	−	0.858159i	$-0.328392\pi$
$967$	31.9290			1.02677			0.513384	+	0.858159i	$0.328392\pi$
$968$		0			0
$969$	3.36207	+	9.83114i	0.108005	+	0.315822i
$970$		0			0
$971$	−43.9483	+	28.2438i	−1.41037	+	0.906388i	−0.999985	−	0.00552624i	$-0.998241\pi$
$971$	−43.9483	+	28.2438i	−1.41037	+	0.906388i	−0.410382	+	0.911914i	$0.634605\pi$
$972$		0			0
$973$	13.5891	+	1.95382i	0.435647	+	0.0626366i
$974$		0			0
$975$	36.7274	−	1.61389i	1.17622	−	0.0516859i
$976$		0			0
$977$	7.86500	+	17.2219i	0.251624	+	0.550979i	0.992724	−	0.120416i	$-0.0384228\pi$
$977$	7.86500	+	17.2219i	0.251624	+	0.550979i	−0.741100	+	0.671395i	$0.765696\pi$
$978$		0			0
$979$	−0.122338	−	0.850883i	−0.00390995	−	0.0271943i
$980$		0			0
$981$	−23.3502	−	1.28488i	−0.745514	−	0.0410231i
$982$		0			0
$983$	34.4214	−	39.7244i	1.09787	−	1.26701i	0.136836	−	0.990594i	$-0.456307\pi$
$983$	34.4214	−	39.7244i	1.09787	−	1.26701i	0.961037	−	0.276419i	$-0.0891478\pi$
$984$		0			0
$985$	−11.3414	+	9.82741i	−0.361368	+	0.313127i
$986$		0			0
$987$	3.40559	+	18.0272i	0.108401	+	0.573811i
$988$		0			0
$989$	15.3143	−	34.9040i	0.486967	−	1.10988i
$990$		0			0
$991$	1.61549	−	3.53743i	0.0513177	−	0.112370i	−0.882236	−	0.470807i	$-0.843963\pi$
$991$	1.61549	−	3.53743i	0.0513177	−	0.112370i	0.933554	+	0.358437i	$0.116690\pi$
$992$		0			0
$993$	−33.7656	−	8.32333i	−1.07152	−	0.264133i
$994$		0			0
$995$	0.0340488	+	0.0295034i	0.00107942	+	0.000935322i
$996$		0			0
$997$	−26.7271	+	7.84778i	−0.846455	+	0.248542i	−0.676071	−	0.736836i	$-0.736319\pi$
$997$	−26.7271	+	7.84778i	−0.846455	+	0.248542i	−0.170384	+	0.985378i	$0.554501\pi$
$998$		0			0
$999$	−5.49344	−	12.3897i	−0.173805	−	0.391992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.u.a.17.2	✓	240
3.2	odd	2	inner	552.2.u.a.17.7	yes	240
23.19	odd	22	inner	552.2.u.a.65.7	yes	240
69.65	even	22	inner	552.2.u.a.65.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.u.a.17.2	✓	240	1.1	even	1	trivial
552.2.u.a.17.7	yes	240	3.2	odd	2	inner
552.2.u.a.65.2	yes	240	69.65	even	22	inner
552.2.u.a.65.7	yes	240	23.19	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63887 + 0.560462i) q^{3} +(0.535830 - 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(2.37176 - 1.83704i) q^{9} +O(q^{10})\)	\(q+(-1.63887 + 0.560462i) q^{3} +(0.535830 - 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(2.37176 - 1.83704i) q^{9} +(-0.0428413 - 0.0938095i) q^{11} +(0.657474 + 4.57283i) q^{13} +(-0.685154 + 0.864667i) q^{15} +(-1.03008 + 1.18877i) q^{17} +(-2.88216 + 2.49740i) q^{19} +(3.47713 - 0.656879i) q^{21} +(-4.75668 - 0.611543i) q^{23} +(-1.90854 + 4.17913i) q^{25} +(-2.85741 + 4.33995i) q^{27} +(-3.84300 - 3.32998i) q^{29} +(-1.22648 + 0.360126i) q^{31} +(0.122788 + 0.129730i) q^{33} +(-1.18370 + 0.540576i) q^{35} +(-1.41013 + 2.19421i) q^{37} +(-3.64041 - 7.12577i) q^{39} +(-2.08672 - 3.24700i) q^{41} +(-2.23913 + 7.62577i) q^{43} +(0.638263 - 1.80108i) q^{45} +5.18450i q^{47} +(-2.71156 - 0.796185i) q^{49} +(1.02190 - 2.52556i) q^{51} +(-0.0372918 + 0.259370i) q^{53} +(-0.0552596 - 0.0355132i) q^{55} +(3.32377 - 5.70825i) q^{57} +(7.30521 - 1.05033i) q^{59} +(3.48865 + 11.8813i) q^{61} +(-5.33039 + 3.02533i) q^{63} +(1.92698 + 2.22385i) q^{65} +(3.71843 + 1.69815i) q^{67} +(8.13831 - 1.66370i) q^{69} +(-6.95935 - 3.17823i) q^{71} +(-2.38975 - 2.75792i) q^{73} +(0.785606 - 7.91870i) q^{75} +(0.0593598 + 0.202161i) q^{77} +(-10.2666 + 1.47612i) q^{79} +(2.25054 - 8.71407i) q^{81} +(4.49498 + 2.88875i) q^{83} +(-0.142584 + 0.991693i) q^{85} +(8.16450 + 3.30354i) q^{87} +(7.99786 + 2.34838i) q^{89} -9.43850i q^{91} +(1.80819 - 1.27759i) q^{93} +(-0.684348 + 2.33067i) q^{95} +(-3.52007 - 5.47733i) q^{97} +(-0.273942 - 0.143793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^9	\( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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