LMFDB - Embedded newform 880.2.bo.k.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.4
Root			$0.856564 - 2.63623i$ of defining polynomial
Character	$\chi$	$=$	880.81
Dual form			880.2.bo.k.641.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.856564 - 2.63623i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(1.40759 + 4.33212i) q^{7} +(-3.78896 - 2.75284i) q^{9} +(3.01954 + 1.37200i) q^{11} +(-2.34636 - 1.70473i) q^{13} +(0.856564 + 2.63623i) q^{15} +(5.73433 - 4.16623i) q^{17} +(2.20745 - 6.79384i) q^{19} +12.6262 q^{21} +1.86699 q^{23} +(0.309017 - 0.951057i) q^{25} +(-3.77509 + 2.74276i) q^{27} +(-0.312324 - 0.961233i) q^{29} +(3.56804 + 2.59234i) q^{31} +(6.20333 - 6.78500i) q^{33} +(-3.68512 - 2.67740i) q^{35} +(-1.66589 - 5.12709i) q^{37} +(-6.50386 + 4.72533i) q^{39} +(-1.38684 + 4.26825i) q^{41} +6.73002 q^{43} +4.68342 q^{45} +(-2.42584 + 7.46596i) q^{47} +(-11.1228 + 8.08120i) q^{49} +(-6.07134 - 18.6857i) q^{51} +(-0.578008 - 0.419948i) q^{53} +(-3.24930 + 0.664870i) q^{55} +(-16.0193 - 11.6387i) q^{57} +(1.17528 + 3.61715i) q^{59} +(-1.71184 + 1.24373i) q^{61} +(6.59234 - 20.2891i) q^{63} +2.90026 q^{65} +12.8384 q^{67} +(1.59920 - 4.92182i) q^{69} +(3.40673 - 2.47513i) q^{71} +(0.422042 + 1.29891i) q^{73} +(-2.24251 - 1.62928i) q^{75} +(-1.69339 + 15.0122i) q^{77} +(-9.90032 - 7.19300i) q^{79} +(-0.344817 - 1.06124i) q^{81} +(-13.2153 + 9.60151i) q^{83} +(-2.19032 + 6.74110i) q^{85} -2.80156 q^{87} -11.8165 q^{89} +(4.08237 - 12.5643i) q^{91} +(9.89025 - 7.18569i) q^{93} +(2.20745 + 6.79384i) q^{95} +(8.78139 + 6.38005i) q^{97} +(-7.66403 - 13.5108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37}+ \cdots + 10 q^{99}+O(q^{100}) $ 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	0.856564	−	2.63623i	0.494537	−	1.52203i	−0.323140	−	0.946351i	$-0.604738\pi$
$3$	0.856564	−	2.63623i	0.494537	−	1.52203i	0.817677	−	0.575678i	$-0.195262\pi$
$4$		0			0
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	1.40759	+	4.33212i	0.532019	+	1.63739i	0.750003	+	0.661434i	$0.230052\pi$
$7$	1.40759	+	4.33212i	0.532019	+	1.63739i	−0.217984	+	0.975952i	$0.569948\pi$
$8$		0			0
$9$	−3.78896	−	2.75284i	−1.26299	−	0.917615i
$10$		0			0
$11$	3.01954	+	1.37200i	0.910425	+	0.413673i
$11$	3.01954	+	1.37200i	0.910425	+	0.413673i
$12$		0			0
$13$	−2.34636	−	1.70473i	−0.650762	−	0.472807i	0.212768	−	0.977103i	$-0.431752\pi$
$13$	−2.34636	−	1.70473i	−0.650762	−	0.472807i	−0.863531	+	0.504296i	$0.831752\pi$
$14$		0			0
$15$	0.856564	+	2.63623i	0.221164	+	0.680672i
$16$		0			0
$17$	5.73433	−	4.16623i	1.39078	−	1.01046i	0.394999	−	0.918682i	$-0.370745\pi$
$17$	5.73433	−	4.16623i	1.39078	−	1.01046i	0.995779	−	0.0917781i	$-0.0292550\pi$
$18$		0			0
$19$	2.20745	−	6.79384i	0.506424	−	1.55861i	−0.291938	−	0.956437i	$-0.594300\pi$
$19$	2.20745	−	6.79384i	0.506424	−	1.55861i	0.798363	−	0.602177i	$-0.205700\pi$
$20$		0			0
$21$	12.6262			2.75525
$22$		0			0
$23$	1.86699			0.389295			0.194647	−	0.980873i	$-0.437644\pi$
$23$	1.86699			0.389295			0.194647	+	0.980873i	$0.437644\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−3.77509	+	2.74276i	−0.726516	+	0.527844i
$28$		0			0
$29$	−0.312324	−	0.961233i	−0.0579970	−	0.178497i	0.917861	−	0.396902i	$-0.129915\pi$
$29$	−0.312324	−	0.961233i	−0.0579970	−	0.178497i	−0.975858	+	0.218405i	$0.929915\pi$
$30$		0			0
$31$	3.56804	+	2.59234i	0.640840	+	0.465597i	0.860139	−	0.510061i	$-0.170377\pi$
$31$	3.56804	+	2.59234i	0.640840	+	0.465597i	−0.219299	+	0.975658i	$0.570377\pi$
$32$		0			0
$33$	6.20333	−	6.78500i	1.07986	−	1.18112i
$34$		0			0
$35$	−3.68512	−	2.67740i	−0.622899	−	0.452563i
$36$		0			0
$37$	−1.66589	−	5.12709i	−0.273871	−	0.842888i	−0.989516	−	0.144424i	$-0.953867\pi$
$37$	−1.66589	−	5.12709i	−0.273871	−	0.842888i	0.715645	−	0.698464i	$-0.246133\pi$
$38$		0			0
$39$	−6.50386	+	4.72533i	−1.04145	+	0.756659i
$40$		0			0
$41$	−1.38684	+	4.26825i	−0.216588	+	0.666588i	0.782450	+	0.622714i	$0.213970\pi$
$41$	−1.38684	+	4.26825i	−0.216588	+	0.666588i	−0.999037	+	0.0438739i	$0.986030\pi$
$42$		0			0
$43$	6.73002			1.02632			0.513159	−	0.858293i	$-0.328475\pi$
$43$	6.73002			1.02632			0.513159	+	0.858293i	$0.328475\pi$
$44$		0			0
$45$	4.68342			0.698163
$46$		0			0
$47$	−2.42584	+	7.46596i	−0.353845	+	1.08902i	0.602832	+	0.797868i	$0.294039\pi$
$47$	−2.42584	+	7.46596i	−0.353845	+	1.08902i	−0.956676	+	0.291154i	$0.905961\pi$
$48$		0			0
$49$	−11.1228	+	8.08120i	−1.58897	+	1.15446i
$50$		0			0
$51$	−6.07134	−	18.6857i	−0.850157	−	2.61651i
$52$		0			0
$53$	−0.578008	−	0.419948i	−0.0793956	−	0.0576843i	0.547379	−	0.836885i	$-0.315625\pi$
$53$	−0.578008	−	0.419948i	−0.0793956	−	0.0576843i	−0.626775	+	0.779200i	$0.715625\pi$
$54$		0			0
$55$	−3.24930	+	0.664870i	−0.438135	+	0.0896511i
$56$		0			0
$57$	−16.0193	−	11.6387i	−2.12181	−	1.54159i
$58$		0			0
$59$	1.17528	+	3.61715i	0.153009	+	0.470913i	0.997954	−	0.0639406i	$-0.0203668\pi$
$59$	1.17528	+	3.61715i	0.153009	+	0.470913i	−0.844945	+	0.534853i	$0.820367\pi$
$60$		0			0
$61$	−1.71184	+	1.24373i	−0.219179	+	0.159243i	−0.691957	−	0.721939i	$-0.743251\pi$
$61$	−1.71184	+	1.24373i	−0.219179	+	0.159243i	0.472778	+	0.881181i	$0.343251\pi$
$62$		0			0
$63$	6.59234	−	20.2891i	0.830556	−	2.55619i
$64$		0			0
$65$	2.90026			0.359733
$66$		0			0
$67$	12.8384			1.56847			0.784233	−	0.620467i	$-0.213057\pi$
$67$	12.8384			1.56847			0.784233	+	0.620467i	$0.213057\pi$
$68$		0			0
$69$	1.59920	−	4.92182i	0.192521	−	0.592518i
$70$		0			0
$71$	3.40673	−	2.47513i	0.404304	−	0.293744i	−0.366988	−	0.930226i	$-0.619611\pi$
$71$	3.40673	−	2.47513i	0.404304	−	0.293744i	0.771292	+	0.636482i	$0.219611\pi$
$72$		0			0
$73$	0.422042	+	1.29891i	0.0493963	+	0.152026i	0.972712	−	0.232015i	$-0.0745319\pi$
$73$	0.422042	+	1.29891i	0.0493963	+	0.152026i	−0.923316	+	0.384042i	$0.874532\pi$
$74$		0			0
$75$	−2.24251	−	1.62928i	−0.258943	−	0.188133i
$76$		0			0
$77$	−1.69339	+	15.0122i	−0.192979	+	1.71080i
$78$		0			0
$79$	−9.90032	−	7.19300i	−1.11387	−	0.809276i	−0.130604	−	0.991435i	$-0.541692\pi$
$79$	−9.90032	−	7.19300i	−1.11387	−	0.809276i	−0.983269	+	0.182159i	$0.941692\pi$
$80$		0			0
$81$	−0.344817	−	1.06124i	−0.0383130	−	0.117915i
$82$		0			0
$83$	−13.2153	+	9.60151i	−1.45057	+	1.05390i	−0.464876	+	0.885376i	$0.653901\pi$
$83$	−13.2153	+	9.60151i	−1.45057	+	1.05390i	−0.985697	+	0.168527i	$0.946099\pi$
$84$		0			0
$85$	−2.19032	+	6.74110i	−0.237573	+	0.731175i
$86$		0			0
$87$	−2.80156			−0.300359
$88$		0			0
$89$	−11.8165			−1.25255			−0.626273	−	0.779604i	$-0.715420\pi$
$89$	−11.8165			−1.25255			−0.626273	+	0.779604i	$0.715420\pi$
$90$		0			0
$91$	4.08237	−	12.5643i	0.427949	−	1.31709i
$92$		0			0
$93$	9.89025	−	7.18569i	1.02557	−	0.745121i
$94$		0			0
$95$	2.20745	+	6.79384i	0.226480	+	0.697034i
$96$		0			0
$97$	8.78139	+	6.38005i	0.891615	+	0.647796i	0.936299	−	0.351205i	$-0.114228\pi$
$97$	8.78139	+	6.38005i	0.891615	+	0.647796i	−0.0446836	+	0.999001i	$0.514228\pi$
$98$		0			0
$99$	−7.66403	−	13.5108i	−0.770264	−	1.35788i
$100$		0			0
$101$	−10.2475	−	7.44521i	−1.01966	−	0.740826i	−0.0534466	−	0.998571i	$-0.517021\pi$
$101$	−10.2475	−	7.44521i	−1.01966	−	0.740826i	−0.966213	+	0.257745i	$0.917021\pi$
$102$		0			0
$103$	1.91023	+	5.87907i	0.188220	+	0.579282i	0.999989	−	0.00469684i	$-0.00149505\pi$
$103$	1.91023	+	5.87907i	0.188220	+	0.579282i	−0.811769	+	0.583979i	$0.801495\pi$
$104$		0			0
$105$	−10.2148	+	7.42147i	−0.996860	+	0.724261i
$106$		0			0
$107$	−0.311410	+	0.958421i	−0.0301051	+	0.0926541i	−0.964980	−	0.262323i	$-0.915511\pi$
$107$	−0.311410	+	0.958421i	−0.0301051	+	0.0926541i	0.934875	+	0.354977i	$0.115511\pi$
$108$		0			0
$109$	6.60399			0.632548			0.316274	−	0.948668i	$-0.397568\pi$
$109$	6.60399			0.632548			0.316274	+	0.948668i	$0.397568\pi$
$110$		0			0
$111$	−14.9431			−1.41834
$112$		0			0
$113$	−3.17084	+	9.75885i	−0.298288	+	0.918035i	0.683810	+	0.729661i	$0.260322\pi$
$113$	−3.17084	+	9.75885i	−0.298288	+	0.918035i	−0.982097	+	0.188375i	$0.939678\pi$
$114$		0			0
$115$	−1.51043	+	1.09739i	−0.140848	+	0.102332i
$116$		0			0
$117$	4.19741	+	12.9183i	0.388051	+	1.19430i
$118$		0			0
$119$	26.1202	+	18.9774i	2.39443	+	1.73966i
$120$		0			0
$121$	7.23524	+	8.28561i	0.657749	+	0.753237i
$122$		0			0
$123$	10.0642	+	7.31205i	0.907456	+	0.659305i
$124$		0			0
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	14.3366	−	10.4162i	1.27217	−	0.924287i	0.272885	−	0.962047i	$-0.412022\pi$
$127$	14.3366	−	10.4162i	1.27217	−	0.924287i	0.999287	+	0.0377597i	$0.0120221\pi$
$128$		0			0
$129$	5.76469	−	17.7419i	0.507553	−	1.56209i
$130$		0			0
$131$	−14.3999			−1.25812			−0.629061	−	0.777356i	$-0.716560\pi$
$131$	−14.3999			−1.25812			−0.629061	+	0.777356i	$0.716560\pi$
$132$		0			0
$133$	32.5389			2.82148
$134$		0			0
$135$	1.44195	−	4.43788i	0.124104	−	0.381952i
$136$		0			0
$137$	−3.61606	+	2.62722i	−0.308941	+	0.224459i	−0.731442	−	0.681904i	$-0.761152\pi$
$137$	−3.61606	+	2.62722i	−0.308941	+	0.224459i	0.422501	+	0.906362i	$0.361152\pi$
$138$		0			0
$139$	−1.49726	−	4.60808i	−0.126996	−	0.390853i	0.867264	−	0.497849i	$-0.165877\pi$
$139$	−1.49726	−	4.60808i	−0.126996	−	0.390853i	−0.994259	+	0.106996i	$0.965877\pi$
$140$		0			0
$141$	17.6041	+	12.7901i	1.48253	+	1.07712i
$142$		0			0
$143$	−4.74603	−	8.36669i	−0.396883	−	0.699658i
$144$		0			0
$145$	0.817674	+	0.594075i	0.0679041	+	0.0493352i
$146$		0			0
$147$	11.7765	+	36.2444i	0.971311	+	2.98939i
$148$		0			0
$149$	8.67777	−	6.30477i	0.710911	−	0.516507i	−0.172557	−	0.985000i	$-0.555203\pi$
$149$	8.67777	−	6.30477i	0.710911	−	0.516507i	0.883467	+	0.468493i	$0.155203\pi$
$150$		0			0
$151$	0.0623641	−	0.191937i	0.00507512	−	0.0156196i	−0.948487	−	0.316816i	$-0.897386\pi$
$151$	0.0623641	−	0.191937i	0.00507512	−	0.0156196i	0.953562	+	0.301197i	$0.0973861\pi$
$152$		0			0
$153$	−33.1961			−2.68375
$154$		0			0
$155$	−4.41034			−0.354247
$156$		0			0
$157$	−0.902942	+	2.77897i	−0.0720626	+	0.221786i	−0.980601	−	0.196016i	$-0.937199\pi$
$157$	−0.902942	+	2.77897i	−0.0720626	+	0.221786i	0.908538	+	0.417802i	$0.137199\pi$
$158$		0			0
$159$	−1.60218	+	1.16405i	−0.127061	+	0.0923153i
$160$		0			0
$161$	2.62796	+	8.08803i	0.207112	+	0.637426i
$162$		0			0
$163$	6.86174	+	4.98535i	0.537453	+	0.390483i	0.823138	−	0.567841i	$-0.192221\pi$
$163$	6.86174	+	4.98535i	0.537453	+	0.390483i	−0.285685	+	0.958324i	$0.592221\pi$
$164$		0			0
$165$	−1.03048	+	9.13541i	−0.0802227	+	0.711191i
$166$		0			0
$167$	−8.14210	−	5.91558i	−0.630055	−	0.457761i	0.226365	−	0.974043i	$-0.427316\pi$
$167$	−8.14210	−	5.91558i	−0.630055	−	0.457761i	−0.856419	+	0.516281i	$0.827316\pi$
$168$		0			0
$169$	−1.41793	−	4.36393i	−0.109071	−	0.335687i
$170$		0			0
$171$	−27.0663	+	19.6649i	−2.06982	+	1.50381i
$172$		0			0
$173$	1.78384	−	5.49008i	0.135623	−	0.417403i	−0.860064	−	0.510187i	$-0.829576\pi$
$173$	1.78384	−	5.49008i	0.135623	−	0.417403i	0.995686	+	0.0927832i	$0.0295764\pi$
$174$		0			0
$175$	4.55506			0.344330
$176$		0			0
$177$	10.5424			0.792412
$178$		0			0
$179$	−5.21222	+	16.0416i	−0.389580	+	1.19900i	0.543524	+	0.839394i	$0.317090\pi$
$179$	−5.21222	+	16.0416i	−0.389580	+	1.19900i	−0.933103	+	0.359609i	$0.882910\pi$
$180$		0			0
$181$	−12.2205	+	8.87872i	−0.908343	+	0.659950i	−0.940595	−	0.339530i	$-0.889732\pi$
$181$	−12.2205	+	8.87872i	−0.908343	+	0.659950i	0.0322522	+	0.999480i	$0.489732\pi$
$182$		0			0
$183$	1.81245	+	5.57814i	0.133980	+	0.412348i
$184$		0			0
$185$	4.36136	+	3.16871i	0.320654	+	0.232968i
$186$		0			0
$187$	23.0311	−	4.71261i	1.68420	−	0.344620i
$188$		0			0
$189$	−17.1957	−	12.4934i	−1.25081	−	0.908764i
$190$		0			0
$191$	−3.22423	−	9.92317i	−0.233297	−	0.718016i	−0.997343	−	0.0728530i	$-0.976790\pi$
$191$	−3.22423	−	9.92317i	−0.233297	−	0.718016i	0.764045	−	0.645163i	$-0.223210\pi$
$192$		0			0
$193$	−11.2656	+	8.18491i	−0.810913	+	0.589163i	−0.914095	−	0.405500i	$-0.867098\pi$
$193$	−11.2656	+	8.18491i	−0.810913	+	0.589163i	0.103182	+	0.994662i	$0.467098\pi$
$194$		0			0
$195$	2.48425	−	7.64575i	0.177901	−	0.547523i
$196$		0			0
$197$	−2.25234			−0.160473			−0.0802363	−	0.996776i	$-0.525567\pi$
$197$	−2.25234			−0.160473			−0.0802363	+	0.996776i	$0.525567\pi$
$198$		0			0
$199$	−22.1246			−1.56837			−0.784184	−	0.620528i	$-0.786918\pi$
$199$	−22.1246			−1.56837			−0.784184	+	0.620528i	$0.786918\pi$
$200$		0			0
$201$	10.9969	−	33.8451i	0.775665	−	2.38725i
$202$		0			0
$203$	3.72455	−	2.70605i	0.261412	−	0.189927i
$204$		0			0
$205$	−1.38684	−	4.26825i	−0.0968609	−	0.298107i
$206$		0			0
$207$	−7.07396	−	5.13953i	−0.491674	−	0.357222i
$208$		0			0
$209$	15.9866	−	17.4857i	1.10582	−	1.20951i
$210$		0			0
$211$	6.28703	+	4.56779i	0.432817	+	0.314460i	0.782774	−	0.622306i	$-0.213804\pi$
$211$	6.28703	+	4.56779i	0.432817	+	0.314460i	−0.349957	+	0.936766i	$0.613804\pi$
$212$		0			0
$213$	−3.60694	−	11.1010i	−0.247144	−	0.760630i
$214$		0			0
$215$	−5.44470	+	3.95581i	−0.371326	+	0.269784i
$216$		0			0
$217$	−6.20796	+	19.1061i	−0.421424	+	1.29701i
$218$		0			0
$219$	3.78574			0.255817
$220$		0			0
$221$	−20.5571			−1.38282
$222$		0			0
$223$	2.44767	−	7.53316i	0.163908	−	0.504458i	−0.835046	−	0.550180i	$-0.814559\pi$
$223$	2.44767	−	7.53316i	0.163908	−	0.504458i	0.998954	+	0.0457224i	$0.0145590\pi$
$224$		0			0
$225$	−3.78896	+	2.75284i	−0.252598	+	0.183523i
$226$		0			0
$227$	6.26291	+	19.2752i	0.415684	+	1.27934i	0.911638	+	0.410994i	$0.134818\pi$
$227$	6.26291	+	19.2752i	0.415684	+	1.27934i	−0.495954	+	0.868349i	$0.665182\pi$
$228$		0			0
$229$	−7.99349	−	5.80761i	−0.528225	−	0.383778i	0.291468	−	0.956580i	$-0.405856\pi$
$229$	−7.99349	−	5.80761i	−0.528225	−	0.383778i	−0.819693	+	0.572803i	$0.805856\pi$
$230$		0			0
$231$	38.1252	+	17.3231i	2.50845	+	1.13977i
$232$		0			0
$233$	−7.92728	−	5.75950i	−0.519333	−	0.377318i	0.297019	−	0.954871i	$-0.404007\pi$
$233$	−7.92728	−	5.75950i	−0.519333	−	0.377318i	−0.816353	+	0.577554i	$0.804007\pi$
$234$		0			0
$235$	−2.42584	−	7.46596i	−0.158244	−	0.487025i
$236$		0			0
$237$	−27.4427	+	19.9383i	−1.78259	+	1.29513i
$238$		0			0
$239$	3.40378	−	10.4758i	0.220173	−	0.677621i	−0.778573	−	0.627554i	$-0.784056\pi$
$239$	3.40378	−	10.4758i	0.220173	−	0.677621i	0.998746	−	0.0500677i	$-0.0159437\pi$
$240$		0			0
$241$	−13.3108			−0.857421			−0.428711	−	0.903442i	$-0.641032\pi$
$241$	−13.3108			−0.857421			−0.428711	+	0.903442i	$0.641032\pi$
$242$		0			0
$243$	−17.0918			−1.09644
$244$		0			0
$245$	4.24854	−	13.0757i	0.271429	−	0.835373i
$246$		0			0
$247$	−16.7611	+	12.1777i	−1.06649	+	0.774847i
$248$		0			0
$249$	13.9920	+	43.0630i	0.886709	+	2.72901i
$250$		0			0
$251$	−11.8048	−	8.57671i	−0.745114	−	0.541357i	0.149195	−	0.988808i	$-0.452332\pi$
$251$	−11.8048	−	8.57671i	−0.745114	−	0.541357i	−0.894308	+	0.447451i	$0.852332\pi$
$252$		0			0
$253$	5.63745	+	2.56151i	0.354424	+	0.161041i
$254$		0			0
$255$	15.8950	+	11.5484i	0.995381	+	0.723187i
$256$		0			0
$257$	0.298365	+	0.918272i	0.0186115	+	0.0572802i	0.959931	−	0.280237i	$-0.0904130\pi$
$257$	0.298365	+	0.918272i	0.0186115	+	0.0572802i	−0.941319	+	0.337517i	$0.890413\pi$
$258$		0			0
$259$	19.8662	−	14.4337i	1.23443	−	0.896865i
$260$		0			0
$261$	−1.46274	+	4.50186i	−0.0905414	+	0.278658i
$262$		0			0
$263$	−20.7753			−1.28106			−0.640529	−	0.767934i	$-0.721285\pi$
$263$	−20.7753			−1.28106			−0.640529	+	0.767934i	$0.721285\pi$
$264$		0			0
$265$	0.714458			0.0438888
$266$		0			0
$267$	−10.1216	+	31.1510i	−0.619430	+	1.90641i
$268$		0			0
$269$	3.16639	−	2.30052i	0.193058	−	0.140265i	−0.487057	−	0.873370i	$-0.661930\pi$
$269$	3.16639	−	2.30052i	0.193058	−	0.140265i	0.680115	+	0.733105i	$0.261930\pi$
$270$		0			0
$271$	4.41220	+	13.5794i	0.268022	+	0.824888i	0.990982	+	0.133997i	$0.0427813\pi$
$271$	4.41220	+	13.5794i	0.268022	+	0.824888i	−0.722959	+	0.690891i	$0.757219\pi$
$272$		0			0
$273$	−29.6255	−	21.5242i	−1.79302	−	1.30270i
$274$		0			0
$275$	2.23794	−	2.44778i	0.134953	−	0.147607i
$276$		0			0
$277$	−3.04431	−	2.21182i	−0.182915	−	0.132895i	0.492560	−	0.870279i	$-0.336061\pi$
$277$	−3.04431	−	2.21182i	−0.182915	−	0.132895i	−0.675475	+	0.737383i	$0.736061\pi$
$278$		0			0
$279$	−6.38290	−	19.6445i	−0.382134	−	1.17609i
$280$		0			0
$281$	8.34820	−	6.06532i	0.498012	−	0.361827i	−0.310245	−	0.950657i	$-0.600411\pi$
$281$	8.34820	−	6.06532i	0.498012	−	0.361827i	0.808257	+	0.588830i	$0.200411\pi$
$282$		0			0
$283$	−9.41156	+	28.9658i	−0.559459	+	1.72184i	0.124406	+	0.992231i	$0.460297\pi$
$283$	−9.41156	+	28.9658i	−0.559459	+	1.72184i	−0.683866	+	0.729608i	$0.739703\pi$
$284$		0			0
$285$	19.8010			1.17291
$286$		0			0
$287$	−20.4426			−1.20669
$288$		0			0
$289$	10.2717	−	31.6131i	0.604219	−	1.85959i
$290$		0			0
$291$	24.3411	−	17.6849i	1.42690	−	1.03670i
$292$		0			0
$293$	−2.44293	−	7.51856i	−0.142717	−	0.439239i	0.853993	−	0.520284i	$-0.174174\pi$
$293$	−2.44293	−	7.51856i	−0.142717	−	0.439239i	−0.996710	+	0.0810455i	$0.974174\pi$
$294$		0			0
$295$	−3.07693	−	2.23552i	−0.179146	−	0.130157i
$296$		0			0
$297$	−15.1621	+	3.10246i	−0.879793	+	0.180023i
$298$		0			0
$299$	−4.38063	−	3.18271i	−0.253338	−	0.184061i
$300$		0			0
$301$	9.47311	+	29.1552i	0.546021	+	1.68048i
$302$		0			0
$303$	−28.4049	+	20.6374i	−1.63182	+	1.18559i
$304$		0			0
$305$	0.653865	−	2.01239i	0.0374402	−	0.115229i
$306$		0			0
$307$	−14.2585			−0.813777			−0.406889	−	0.913478i	$-0.633386\pi$
$307$	−14.2585			−0.813777			−0.406889	+	0.913478i	$0.633386\pi$
$308$		0			0
$309$	17.1348			0.974766
$310$		0			0
$311$	−5.31873	+	16.3694i	−0.301598	+	0.928222i	0.679327	+	0.733835i	$0.262272\pi$
$311$	−5.31873	+	16.3694i	−0.301598	+	0.928222i	−0.980925	+	0.194387i	$0.937728\pi$
$312$		0			0
$313$	6.44301	−	4.68112i	0.364181	−	0.264593i	−0.390613	−	0.920555i	$-0.627737\pi$
$313$	6.44301	−	4.68112i	0.364181	−	0.264593i	0.754794	+	0.655962i	$0.227737\pi$
$314$		0			0
$315$	6.59234	+	20.2891i	0.371436	+	1.14316i
$316$		0			0
$317$	11.1083	+	8.07068i	0.623907	+	0.453295i	0.854284	−	0.519807i	$-0.173996\pi$
$317$	11.1083	+	8.07068i	0.623907	+	0.453295i	−0.230377	+	0.973101i	$0.573996\pi$
$318$		0			0
$319$	0.375738	−	3.33099i	0.0210373	−	0.186500i
$320$		0			0
$321$	2.25988	+	1.64190i	0.126134	+	0.0916418i
$322$		0			0
$323$	−15.6465	−	48.1549i	−0.870593	−	2.67941i
$324$		0			0
$325$	−2.34636	+	1.70473i	−0.130152	+	0.0945613i
$326$		0			0
$327$	5.65674	−	17.4097i	0.312819	−	0.962756i
$328$		0			0
$329$	−35.7580			−1.97140
$330$		0			0
$331$	−10.6971			−0.587967			−0.293983	−	0.955811i	$-0.594981\pi$
$331$	−10.6971			−0.587967			−0.293983	+	0.955811i	$0.594981\pi$
$332$		0			0
$333$	−7.80206	+	24.0123i	−0.427550	+	1.31587i
$334$		0			0
$335$	−10.3865	+	7.54625i	−0.567476	+	0.412296i
$336$		0			0
$337$	3.54742	+	10.9178i	0.193240	+	0.594732i	0.999993	+	0.00384240i	$0.00122308\pi$
$337$	3.54742	+	10.9178i	0.193240	+	0.594732i	−0.806753	+	0.590889i	$0.798777\pi$
$338$		0			0
$339$	23.0106	+	16.7181i	1.24976	+	0.908005i
$340$		0			0
$341$	7.21717	+	12.7230i	0.390832	+	0.688990i
$342$		0			0
$343$	−24.8693	−	18.0686i	−1.34281	−	0.975611i
$344$		0			0
$345$	1.59920	+	4.92182i	0.0860978	+	0.264982i
$346$		0			0
$347$	−0.342361	+	0.248740i	−0.0183789	+	0.0133530i	−0.596937	−	0.802288i	$-0.703616\pi$
$347$	−0.342361	+	0.248740i	−0.0183789	+	0.0133530i	0.578558	+	0.815641i	$0.303616\pi$
$348$		0			0
$349$	0.261913	−	0.806085i	0.0140199	−	0.0431488i	−0.943802	−	0.330512i	$-0.892779\pi$
$349$	0.261913	−	0.806085i	0.0140199	−	0.0431488i	0.957822	+	0.287363i	$0.0927786\pi$
$350$		0			0
$351$	13.5334			0.722357
$352$		0			0
$353$	9.79855			0.521524			0.260762	−	0.965403i	$-0.416026\pi$
$353$	9.79855			0.521524			0.260762	+	0.965403i	$0.416026\pi$
$354$		0			0
$355$	−1.30125	+	4.00485i	−0.0690634	+	0.212555i
$356$		0			0
$357$	72.4025	−	52.6035i	3.83195	−	2.78407i
$358$		0			0
$359$	−2.35059	−	7.23438i	−0.124060	−	0.381816i	0.869669	−	0.493635i	$-0.164332\pi$
$359$	−2.35059	−	7.23438i	−0.124060	−	0.381816i	−0.993729	+	0.111819i	$0.964332\pi$
$360$		0			0
$361$	−25.9121	−	18.8263i	−1.36380	−	0.990856i
$362$		0			0
$363$	28.0402	−	11.9766i	1.47173	−	0.628609i
$364$		0			0
$365$	−1.10492	−	0.802772i	−0.0578342	−	0.0420190i
$366$		0			0
$367$	0.577181	+	1.77638i	0.0301286	+	0.0927263i	0.964990	−	0.262286i	$-0.0844765\pi$
$367$	0.577181	+	1.77638i	0.0301286	+	0.0927263i	−0.934861	+	0.355013i	$0.884477\pi$
$368$		0			0
$369$	17.0045	−	12.3545i	0.885218	−	0.643149i
$370$		0			0
$371$	1.00566	−	3.09512i	0.0522115	−	0.160690i
$372$		0			0
$373$	20.0214			1.03667			0.518335	−	0.855178i	$-0.326552\pi$
$373$	20.0214			1.03667			0.518335	+	0.855178i	$0.326552\pi$
$374$		0			0
$375$	2.77190			0.143140
$376$		0			0
$377$	−0.905819	+	2.78782i	−0.0466520	+	0.143580i
$378$		0			0
$379$	19.4206	−	14.1099i	0.997571	−	0.724778i	0.0360048	−	0.999352i	$-0.488537\pi$
$379$	19.4206	−	14.1099i	0.997571	−	0.724778i	0.961566	+	0.274574i	$0.0885368\pi$
$380$		0			0
$381$	−15.1792	−	46.7168i	−0.777655	−	2.39338i
$382$		0			0
$383$	15.9188	+	11.5657i	0.813411	+	0.590978i	0.914818	−	0.403867i	$-0.132334\pi$
$383$	15.9188	+	11.5657i	0.813411	+	0.590978i	−0.101407	+	0.994845i	$0.532334\pi$
$384$		0			0
$385$	−7.45398	−	13.1405i	−0.379890	−	0.669701i
$386$		0			0
$387$	−25.4998	−	18.5267i	−1.29623	−	0.941765i
$388$		0			0
$389$	7.72700	+	23.7812i	0.391774	+	1.20576i	0.931445	+	0.363881i	$0.118549\pi$
$389$	7.72700	+	23.7812i	0.391774	+	1.20576i	−0.539671	+	0.841876i	$0.681451\pi$
$390$		0			0
$391$	10.7059	−	7.77832i	0.541422	−	0.393366i
$392$		0			0
$393$	−12.3344	+	37.9614i	−0.622188	+	1.91490i
$394$		0			0
$395$	12.2375			0.615734
$396$		0			0
$397$	−19.3120			−0.969240			−0.484620	−	0.874725i	$-0.661042\pi$
$397$	−19.3120			−0.969240			−0.484620	+	0.874725i	$0.661042\pi$
$398$		0			0
$399$	27.8717	−	85.7801i	1.39533	−	4.29438i
$400$		0			0
$401$	−18.8072	+	13.6642i	−0.939185	+	0.682358i	−0.948224	−	0.317601i	$-0.897123\pi$
$401$	−18.8072	+	13.6642i	−0.939185	+	0.682358i	0.00903949	+	0.999959i	$0.497123\pi$
$402$		0			0
$403$	−3.95268	−	12.1651i	−0.196897	−	0.605986i
$404$		0			0
$405$	0.902742	+	0.655880i	0.0448576	+	0.0325910i
$406$		0			0
$407$	2.00413	−	17.7670i	0.0993412	−	0.880679i
$408$		0			0
$409$	4.79143	+	3.48118i	0.236921	+	0.172133i	0.699911	−	0.714231i	$-0.253223\pi$
$409$	4.79143	+	3.48118i	0.236921	+	0.172133i	−0.462989	+	0.886364i	$0.653223\pi$
$410$		0			0
$411$	3.82858	+	11.7832i	0.188850	+	0.581220i
$412$		0			0
$413$	−14.0156	+	10.1829i	−0.689663	+	0.501069i
$414$		0			0
$415$	5.04781	−	15.5356i	0.247787	−	0.762611i
$416$		0			0
$417$	−13.4305			−0.657693
$418$		0			0
$419$	1.11739			0.0545881			0.0272940	−	0.999627i	$-0.491311\pi$
$419$	1.11739			0.0545881			0.0272940	+	0.999627i	$0.491311\pi$
$420$		0			0
$421$	5.32574	−	16.3909i	0.259561	−	0.798845i	−0.733336	−	0.679866i	$-0.762038\pi$
$421$	5.32574	−	16.3909i	0.259561	−	0.798845i	0.992897	−	0.118979i	$-0.0379621\pi$
$422$		0			0
$423$	29.7440	−	21.6103i	1.44620	−	1.05073i
$424$		0			0
$425$	−2.19032	−	6.74110i	−0.106246	−	0.326992i
$426$		0			0
$427$	−7.79753	−	5.66524i	−0.377349	−	0.274160i
$428$		0			0
$429$	−26.1218	+	5.34504i	−1.26117	+	0.258061i
$430$		0			0
$431$	6.26903	+	4.55472i	0.301969	+	0.219393i	0.728443	−	0.685107i	$-0.240244\pi$
$431$	6.26903	+	4.55472i	0.301969	+	0.219393i	−0.426474	+	0.904500i	$0.640244\pi$
$432$		0			0
$433$	1.21711	+	3.74587i	0.0584904	+	0.180015i	0.976033	−	0.217623i	$-0.0698302\pi$
$433$	1.21711	+	3.74587i	0.0584904	+	0.180015i	−0.917543	+	0.397637i	$0.869830\pi$
$434$		0			0
$435$	2.26651	−	1.64671i	0.108671	−	0.0789539i
$436$		0			0
$437$	4.12130	−	12.6840i	0.197148	−	0.606760i
$438$		0			0
$439$	34.7505			1.65855			0.829275	−	0.558841i	$-0.188754\pi$
$439$	34.7505			1.65855			0.829275	+	0.558841i	$0.188754\pi$
$440$		0			0
$441$	64.3903			3.06620
$442$		0			0
$443$	−7.51612	+	23.1322i	−0.357102	+	1.09905i	0.597679	+	0.801735i	$0.296090\pi$
$443$	−7.51612	+	23.1322i	−0.357102	+	1.09905i	−0.954781	+	0.297310i	$0.903910\pi$
$444$		0			0
$445$	9.55974	−	6.94556i	0.453175	−	0.329251i
$446$		0			0
$447$	−9.18777	−	28.2770i	−0.434567	−	1.33746i
$448$		0			0
$449$	15.3095	+	11.1230i	0.722498	+	0.524925i	0.887181	−	0.461421i	$-0.152660\pi$
$449$	15.3095	+	11.1230i	0.722498	+	0.524925i	−0.164683	+	0.986346i	$0.552660\pi$
$450$		0			0
$451$	−10.0436	+	10.9854i	−0.472936	+	0.517282i
$452$		0			0
$453$	−0.452572	−	0.328812i	−0.0212637	−	0.0154490i
$454$		0			0
$455$	4.08237	+	12.5643i	0.191385	+	0.589021i
$456$		0			0
$457$	13.1231	−	9.53447i	0.613871	−	0.446004i	−0.236904	−	0.971533i	$-0.576133\pi$
$457$	13.1231	−	9.53447i	0.613871	−	0.446004i	0.850775	+	0.525529i	$0.176133\pi$
$458$		0			0
$459$	−10.2206	+	31.4558i	−0.477057	+	1.46823i
$460$		0			0
$461$	−11.3851			−0.530258			−0.265129	−	0.964213i	$-0.585415\pi$
$461$	−11.3851			−0.530258			−0.265129	+	0.964213i	$0.585415\pi$
$462$		0			0
$463$	36.4523			1.69408			0.847040	−	0.531529i	$-0.178382\pi$
$463$	36.4523			1.69408			0.847040	+	0.531529i	$0.178382\pi$
$464$		0			0
$465$	−3.77774	+	11.6267i	−0.175189	+	0.539175i
$466$		0			0
$467$	22.6893	−	16.4847i	1.04993	−	0.762822i	0.0777339	−	0.996974i	$-0.475232\pi$
$467$	22.6893	−	16.4847i	1.04993	−	0.762822i	0.972200	+	0.234153i	$0.0752316\pi$
$468$		0			0
$469$	18.0713	+	55.6177i	0.834454	+	2.56819i
$470$		0			0
$471$	6.55258	+	4.76073i	0.301927	+	0.219363i
$472$		0			0
$473$	20.3216	+	9.23358i	0.934386	+	0.424561i
$474$		0			0
$475$	−5.77919	−	4.19883i	−0.265167	−	0.192655i
$476$		0			0
$477$	1.03400	+	3.18233i	0.0473437	+	0.145709i
$478$		0			0
$479$	−29.4024	+	21.3621i	−1.34343	+	0.976058i	−0.344118	+	0.938926i	$0.611822\pi$
$479$	−29.4024	+	21.3621i	−1.34343	+	0.976058i	−0.999310	+	0.0371313i	$0.988178\pi$
$480$		0			0
$481$	−4.83151	+	14.8699i	−0.220298	+	0.678008i
$482$		0			0
$483$	23.5729			1.07261
$484$		0			0
$485$	−10.8544			−0.492873
$486$		0			0
$487$	−12.9210	+	39.7667i	−0.585506	+	1.80200i	0.0117243	+	0.999931i	$0.496268\pi$
$487$	−12.9210	+	39.7667i	−0.585506	+	1.80200i	−0.597230	+	0.802070i	$0.703732\pi$
$488$		0			0
$489$	19.0201	−	13.8189i	0.860116	−	0.624911i
$490$		0			0
$491$	−5.98118	−	18.4082i	−0.269927	−	0.830749i	−0.990517	−	0.137388i	$-0.956129\pi$
$491$	−5.98118	−	18.4082i	−0.269927	−	0.830749i	0.720590	−	0.693361i	$-0.243871\pi$
$492$		0			0
$493$	−5.79569	−	4.21081i	−0.261025	−	0.189645i
$494$		0			0
$495$	14.1418	+	6.42565i	0.635625	+	0.288811i
$496$		0			0
$497$	15.5178	+	11.2744i	0.696070	+	0.505725i
$498$		0			0
$499$	−4.12581	−	12.6979i	−0.184697	−	0.568438i	0.815246	−	0.579114i	$-0.196602\pi$
$499$	−4.12581	−	12.6979i	−0.184697	−	0.568438i	−0.999943	+	0.0106764i	$0.996602\pi$
$500$		0			0
$501$	−22.5691	+	16.3974i	−1.00831	+	0.732581i
$502$		0			0
$503$	−11.0902	+	34.1322i	−0.494489	+	1.52188i	0.323262	+	0.946309i	$0.395220\pi$
$503$	−11.0902	+	34.1322i	−0.494489	+	1.52188i	−0.817751	+	0.575572i	$0.804780\pi$
$504$		0			0
$505$	12.6665			0.563654
$506$		0			0
$507$	−12.7189			−0.564865
$508$		0			0
$509$	5.53612	−	17.0384i	0.245384	−	0.755215i	−0.750189	−	0.661224i	$-0.770037\pi$
$509$	5.53612	−	17.0384i	0.245384	−	0.755215i	0.995573	−	0.0939914i	$-0.0299626\pi$
$510$		0			0
$511$	−5.03298	+	3.65667i	−0.222646	+	0.161762i
$512$		0			0
$513$	10.3006	+	31.7019i	0.454781	+	1.39967i
$514$		0			0
$515$	−5.00104	−	3.63347i	−0.220372	−	0.160110i
$516$		0			0
$517$	−17.5682	+	19.2155i	−0.772648	+	0.845097i
$518$		0			0
$519$	−12.9452	−	9.40521i	−0.568230	−	0.412843i
$520$		0			0
$521$	2.24328	+	6.90411i	0.0982799	+	0.302474i	0.988095	−	0.153848i	$-0.0491665\pi$
$521$	2.24328	+	6.90411i	0.0982799	+	0.302474i	−0.889815	+	0.456322i	$0.849167\pi$
$522$		0			0
$523$	27.5208	−	19.9950i	1.20340	−	0.874321i	0.208785	−	0.977962i	$-0.433049\pi$
$523$	27.5208	−	19.9950i	1.20340	−	0.874321i	0.994615	+	0.103641i	$0.0330492\pi$
$524$		0			0
$525$	3.90170	−	12.0082i	0.170284	−	0.524080i
$526$		0			0
$527$	31.2606			1.36173
$528$		0			0
$529$	−19.5143			−0.848450
$530$		0			0
$531$	5.50434	−	16.9406i	0.238868	−	0.735161i
$532$		0			0
$533$	10.5302	−	7.65065i	0.456114	−	0.331386i
$534$		0			0
$535$	−0.311410	−	0.958421i	−0.0134634	−	0.0414362i
$536$		0			0
$537$	37.8247	+	27.4812i	1.63226	+	1.18590i
$538$		0			0
$539$	−44.6732	+	9.14101i	−1.92421	+	0.393731i
$540$		0			0
$541$	−15.4421	−	11.2194i	−0.663910	−	0.482359i	0.204071	−	0.978956i	$-0.434583\pi$
$541$	−15.4421	−	11.2194i	−0.663910	−	0.482359i	−0.867981	+	0.496597i	$0.834583\pi$
$542$		0			0
$543$	12.9387	+	39.8213i	0.555253	+	1.70889i
$544$		0			0
$545$	−5.34274	+	3.88173i	−0.228858	+	0.166275i
$546$		0			0
$547$	7.20288	−	22.1682i	0.307973	−	0.947843i	−0.670578	−	0.741839i	$-0.733954\pi$
$547$	7.20288	−	22.1682i	0.307973	−	0.947843i	0.978551	−	0.206004i	$-0.0660460\pi$
$548$		0			0
$549$	9.90988			0.422944
$550$		0			0
$551$	−7.21991			−0.307578
$552$		0			0
$553$	17.2253	−	53.0142i	0.732496	−	2.25439i
$554$		0			0
$555$	12.0892	−	8.78335i	0.513160	−	0.372832i
$556$		0			0
$557$	−8.77107	−	26.9946i	−0.371642	−	1.14380i	−0.945716	−	0.324993i	$-0.894638\pi$
$557$	−8.77107	−	26.9946i	−0.371642	−	1.14380i	0.574074	−	0.818803i	$-0.305362\pi$
$558$		0			0
$559$	−15.7910	−	11.4729i	−0.667889	−	0.485250i
$560$		0			0
$561$	7.30406	−	64.7519i	0.308378	−	2.73383i
$562$		0			0
$563$	−6.57905	−	4.77996i	−0.277274	−	0.201451i	0.440454	−	0.897775i	$-0.354818\pi$
$563$	−6.57905	−	4.77996i	−0.277274	−	0.201451i	−0.717727	+	0.696324i	$0.754818\pi$
$564$		0			0
$565$	−3.17084	−	9.75885i	−0.133398	−	0.410558i
$566$		0			0
$567$	4.11204	−	2.98757i	0.172690	−	0.125466i
$568$		0			0
$569$	5.04977	−	15.5416i	0.211697	−	0.651538i	−0.787674	−	0.616092i	$-0.788715\pi$
$569$	5.04977	−	15.5416i	0.211697	−	0.651538i	0.999372	−	0.0354457i	$-0.0112851\pi$
$570$		0			0
$571$	−33.1999			−1.38937			−0.694687	−	0.719312i	$-0.744457\pi$
$571$	−33.1999			−1.38937			−0.694687	+	0.719312i	$0.744457\pi$
$572$		0			0
$573$	−28.9215			−1.20822
$574$		0			0
$575$	0.576932	−	1.77561i	0.0240597	−	0.0740482i
$576$		0			0
$577$	36.4288	−	26.4671i	1.51655	−	1.10184i	0.553388	−	0.832923i	$-0.313335\pi$
$577$	36.4288	−	26.4671i	1.51655	−	1.10184i	0.963164	−	0.268916i	$-0.0866654\pi$
$578$		0			0
$579$	11.9276	+	36.7095i	0.495696	+	1.52560i
$580$		0			0
$581$	−60.1967	−	43.7355i	−2.49738	−	1.81445i
$582$		0			0
$583$	−1.16915	−	2.06108i	−0.0484213	−	0.0853610i
$584$		0			0
$585$	−10.9890	−	7.98395i	−0.454338	−	0.330096i
$586$		0			0
$587$	13.8125	+	42.5104i	0.570102	+	1.75459i	0.652283	+	0.757975i	$0.273811\pi$
$587$	13.8125	+	42.5104i	0.570102	+	1.75459i	−0.0821818	+	0.996617i	$0.526189\pi$
$588$		0			0
$589$	25.4882	−	18.5183i	1.05022	−	0.763032i
$590$		0			0
$591$	−1.92927	+	5.93769i	−0.0793597	+	0.244244i
$592$		0			0
$593$	−18.7395			−0.769538			−0.384769	−	0.923013i	$-0.625719\pi$
$593$	−18.7395			−0.769538			−0.384769	+	0.923013i	$0.625719\pi$
$594$		0			0
$595$	−32.2863			−1.32361
$596$		0			0
$597$	−18.9511	+	58.3255i	−0.775617	+	2.38710i
$598$		0			0
$599$	−15.7954	+	11.4760i	−0.645381	+	0.468897i	−0.861695	−	0.507427i	$-0.830597\pi$
$599$	−15.7954	+	11.4760i	−0.645381	+	0.468897i	0.216314	+	0.976324i	$0.430597\pi$
$600$		0			0
$601$	−9.67674	−	29.7819i	−0.394722	−	1.21483i	−0.929177	−	0.369634i	$-0.879483\pi$
$601$	−9.67674	−	29.7819i	−0.394722	−	1.21483i	0.534455	−	0.845197i	$-0.320517\pi$
$602$		0			0
$603$	−48.6444	−	35.3422i	−1.98095	−	1.43925i
$604$		0			0
$605$	−10.7236	−	2.45043i	−0.435976	−	0.0996243i
$606$		0			0
$607$	−17.8254	−	12.9509i	−0.723511	−	0.525662i	0.163993	−	0.986461i	$-0.447563\pi$
$607$	−17.8254	−	12.9509i	−0.723511	−	0.525662i	−0.887504	+	0.460800i	$0.847563\pi$
$608$		0			0
$609$	−3.94345	−	12.1367i	−0.159797	−	0.491803i
$610$		0			0
$611$	18.4193	−	13.3824i	0.745166	−	0.541394i
$612$		0			0
$613$	11.7098	−	36.0390i	0.472954	−	1.45560i	−0.375743	−	0.926724i	$-0.622612\pi$
$613$	11.7098	−	36.0390i	0.472954	−	1.45560i	0.848697	−	0.528879i	$-0.177388\pi$
$614$		0			0
$615$	−12.4400			−0.501629
$616$		0			0
$617$	−34.0287			−1.36995			−0.684973	−	0.728569i	$-0.740186\pi$
$617$	−34.0287			−1.36995			−0.684973	+	0.728569i	$0.740186\pi$
$618$		0			0
$619$	8.16306	−	25.1233i	0.328101	−	1.00979i	−0.641921	−	0.766771i	$-0.721862\pi$
$619$	8.16306	−	25.1233i	0.328101	−	1.00979i	0.970021	−	0.243020i	$-0.0781379\pi$
$620$		0			0
$621$	−7.04805	+	5.12071i	−0.282829	+	0.205487i
$622$		0			0
$623$	−16.6328	−	51.1904i	−0.666378	−	2.05090i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−32.4027	−	57.1220i	−1.29404	−	2.28123i
$628$		0			0
$629$	−30.9134	−	22.4599i	−1.23260	−	0.895535i
$630$		0			0
$631$	11.9266	+	36.7063i	0.474790	+	1.46125i	0.846241	+	0.532801i	$0.178861\pi$
$631$	11.9266	+	36.7063i	0.474790	+	1.46125i	−0.371451	+	0.928453i	$0.621139\pi$
$632$		0			0
$633$	17.4270	−	12.6615i	0.692661	−	0.503248i
$634$		0			0
$635$	−5.47611	+	16.8537i	−0.217313	+	0.668820i
$636$		0			0
$637$	39.8744			1.57988
$638$		0			0
$639$	−19.7216			−0.780175
$640$		0			0
$641$	−5.63182	+	17.3330i	−0.222444	+	0.684611i	0.776097	+	0.630613i	$0.217196\pi$
$641$	−5.63182	+	17.3330i	−0.222444	+	0.684611i	−0.998541	+	0.0539980i	$0.982804\pi$
$642$		0			0
$643$	8.53160	−	6.19857i	0.336453	−	0.244448i	−0.406711	−	0.913557i	$-0.633324\pi$
$643$	8.53160	−	6.19857i	0.336453	−	0.244448i	0.743164	+	0.669109i	$0.233324\pi$
$644$		0			0
$645$	5.76469	+	17.7419i	0.226984	+	0.698586i
$646$		0			0
$647$	13.6858	+	9.94328i	0.538042	+	0.390911i	0.823358	−	0.567523i	$-0.192098\pi$
$647$	13.6858	+	9.94328i	0.538042	+	0.390911i	−0.285315	+	0.958434i	$0.592098\pi$
$648$		0			0
$649$	−1.41391	+	12.5346i	−0.0555009	+	0.492027i
$650$		0			0
$651$	45.0507	+	32.7312i	1.76568	+	1.28284i
$652$		0			0
$653$	14.8138	+	45.5921i	0.579707	+	1.78416i	0.619559	+	0.784950i	$0.287311\pi$
$653$	14.8138	+	45.5921i	0.579707	+	1.78416i	−0.0398519	+	0.999206i	$0.512689\pi$
$654$		0			0
$655$	11.6497	−	8.46403i	0.455193	−	0.330717i
$656$		0			0
$657$	1.97660	−	6.08335i	0.0771145	−	0.237334i
$658$		0			0
$659$	5.96793			0.232477			0.116239	−	0.993221i	$-0.462916\pi$
$659$	5.96793			0.232477			0.116239	+	0.993221i	$0.462916\pi$
$660$		0			0
$661$	−22.5701			−0.877875			−0.438937	−	0.898518i	$-0.644645\pi$
$661$	−22.5701			−0.877875			−0.438937	+	0.898518i	$0.644645\pi$
$662$		0			0
$663$	−17.6084	+	54.1932i	−0.683855	+	2.10469i
$664$		0			0
$665$	−26.3245	+	19.1259i	−1.02082	+	0.741670i
$666$		0			0
$667$	−0.583105	−	1.79461i	−0.0225779	−	0.0694877i
$668$		0			0
$669$	−17.7626	−	12.9053i	−0.686741	−	0.498946i
$670$		0			0
$671$	−6.87536	+	1.40683i	−0.265420	+	0.0543102i
$672$		0			0
$673$	−5.41980	−	3.93772i	−0.208918	−	0.151788i	0.478406	−	0.878139i	$-0.341215\pi$
$673$	−5.41980	−	3.93772i	−0.208918	−	0.151788i	−0.687324	+	0.726351i	$0.741215\pi$
$674$		0			0
$675$	1.44195	+	4.43788i	0.0555009	+	0.170814i
$676$		0			0
$677$	−33.5903	+	24.4048i	−1.29098	+	0.937952i	−0.999825	−	0.0187237i	$-0.994040\pi$
$677$	−33.5903	+	24.4048i	−1.29098	+	0.937952i	−0.291156	+	0.956676i	$0.594040\pi$
$678$		0			0
$679$	−15.2785	+	47.0225i	−0.586337	+	1.80456i
$680$		0			0
$681$	56.1786			2.15277
$682$		0			0
$683$	13.4576			0.514940			0.257470	−	0.966286i	$-0.417111\pi$
$683$	13.4576			0.514940			0.257470	+	0.966286i	$0.417111\pi$
$684$		0			0
$685$	1.38121	−	4.25093i	0.0527734	−	0.162420i
$686$		0			0
$687$	−22.1571	+	16.0981i	−0.845348	+	0.614181i
$688$		0			0
$689$	0.640317	+	1.97069i	0.0243942	+	0.0750775i
$690$		0			0
$691$	−23.8510	−	17.3288i	−0.907337	−	0.659219i	0.0330033	−	0.999455i	$-0.489493\pi$
$691$	−23.8510	−	17.3288i	−0.907337	−	0.659219i	−0.940340	+	0.340237i	$0.889493\pi$
$692$		0			0
$693$	47.7425	−	52.2191i	1.81359	−	1.98364i
$694$		0			0
$695$	3.91987	+	2.84795i	0.148689	+	0.108029i
$696$		0			0
$697$	9.82992	+	30.2534i	0.372335	+	1.14593i
$698$		0			0
$699$	−21.9736	+	15.9648i	−0.831118	+	0.603843i
$700$		0			0
$701$	−2.79053	+	8.58837i	−0.105397	+	0.324378i	−0.989823	−	0.142301i	$-0.954550\pi$
$701$	−2.79053	+	8.58837i	−0.105397	+	0.324378i	0.884427	+	0.466679i	$0.154550\pi$
$702$		0			0
$703$	−38.5100			−1.45243
$704$		0			0
$705$	−21.7599			−0.819524
$706$		0			0
$707$	17.8293	−	54.8730i	0.670540	−	2.06371i
$708$		0			0
$709$	−39.7093	+	28.8505i	−1.49131	+	1.08350i	−0.517628	+	0.855606i	$0.673185\pi$
$709$	−39.7093	+	28.8505i	−1.49131	+	1.08350i	−0.973685	+	0.227897i	$0.926815\pi$
$710$		0			0
$711$	17.7107	+	54.5081i	0.664205	+	2.04421i
$712$		0			0
$713$	6.66151	+	4.83987i	0.249475	+	0.181254i
$714$		0			0
$715$	8.75744	+	3.97915i	0.327510	+	0.148812i
$716$		0			0
$717$	−24.7010	−	17.9463i	−0.922476	−	0.670218i
$718$		0			0
$719$	15.0519	+	46.3250i	0.561341	+	1.72763i	0.678580	+	0.734526i	$0.262596\pi$
$719$	15.0519	+	46.3250i	0.561341	+	1.72763i	−0.117239	+	0.993104i	$0.537404\pi$
$720$		0			0
$721$	−22.7800	+	16.5507i	−0.848372	+	0.616378i
$722$		0			0
$723$	−11.4015	+	35.0902i	−0.424027	+	1.30502i
$724$		0			0
$725$	−1.01070			−0.0375365
$726$		0			0
$727$	50.6964			1.88023			0.940113	−	0.340864i	$-0.110719\pi$
$727$	50.6964			1.88023			0.940113	+	0.340864i	$0.110719\pi$
$728$		0			0
$729$	−13.6058	+	41.8743i	−0.503917	+	1.55090i
$730$		0			0
$731$	38.5921	−	28.0388i	1.42738	−	1.03705i
$732$		0			0
$733$	−14.5728	−	44.8504i	−0.538258	−	1.65659i	−0.736502	−	0.676435i	$-0.763524\pi$
$733$	−14.5728	−	44.8504i	−0.538258	−	1.65659i	0.198244	−	0.980153i	$-0.436476\pi$
$734$		0			0
$735$	−30.8313	−	22.4003i	−1.13723	−	0.826246i
$736$		0			0
$737$	38.7662	+	17.6143i	1.42797	+	0.648832i
$738$		0			0
$739$	14.6892	+	10.6724i	0.540352	+	0.392589i	0.824216	−	0.566276i	$-0.191616\pi$
$739$	14.6892	+	10.6724i	0.540352	+	0.392589i	−0.283864	+	0.958865i	$0.591616\pi$
$740$		0			0
$741$	17.7462	+	54.6172i	0.651923	+	2.00641i
$742$		0			0
$743$	−3.02269	+	2.19611i	−0.110892	+	0.0805676i	−0.641849	−	0.766831i	$-0.721832\pi$
$743$	−3.02269	+	2.19611i	−0.110892	+	0.0805676i	0.530957	+	0.847399i	$0.321832\pi$
$744$		0			0
$745$	−3.31461	+	10.2013i	−0.121438	+	0.373748i
$746$		0			0
$747$	76.5040			2.79913
$748$		0			0
$749$	−4.59033			−0.167727
$750$		0			0
$751$	8.60395	−	26.4802i	0.313963	−	0.966277i	−0.662217	−	0.749312i	$-0.730384\pi$
$751$	8.60395	−	26.4802i	0.313963	−	0.966277i	0.976179	−	0.216965i	$-0.0696158\pi$
$752$		0			0
$753$	−32.7218	+	23.7738i	−1.19245	+	0.866364i
$754$		0			0
$755$	0.0623641	+	0.191937i	0.00226966	+	0.00698530i
$756$		0			0
$757$	−36.4311	−	26.4688i	−1.32411	−	0.962023i	−0.999871	−	0.0160486i	$-0.994891\pi$
$757$	−36.4311	−	26.4688i	−1.32411	−	0.962023i	−0.324240	−	0.945975i	$-0.605109\pi$
$758$		0			0
$759$	11.5816	−	12.6675i	0.420384	−	0.459802i
$760$		0			0
$761$	15.1341	+	10.9956i	0.548610	+	0.398589i	0.827273	−	0.561800i	$-0.189891\pi$
$761$	15.1341	+	10.9956i	0.548610	+	0.398589i	−0.278663	+	0.960389i	$0.589891\pi$
$762$		0			0
$763$	9.29572	+	28.6093i	0.336528	+	1.03573i
$764$		0			0
$765$	26.8562	−	19.5122i	0.970990	−	0.705465i
$766$		0			0
$767$	3.40862	−	10.4907i	0.123078	−	0.378796i
$768$		0			0
$769$	−13.5701			−0.489351			−0.244675	−	0.969605i	$-0.578681\pi$
$769$	−13.5701			−0.489351			−0.244675	+	0.969605i	$0.578681\pi$
$770$		0			0
$771$	2.67635			0.0963862
$772$		0			0
$773$	−1.01293	+	3.11746i	−0.0364324	+	0.112127i	−0.967619	−	0.252416i	$-0.918775\pi$
$773$	−1.01293	+	3.11746i	−0.0364324	+	0.112127i	0.931186	+	0.364543i	$0.118775\pi$
$774$		0			0
$775$	3.56804	−	2.59234i	0.128168	−	0.0931194i
$776$		0			0
$777$	−21.0338	−	64.7354i	−0.754584	−	2.32237i
$778$		0			0
$779$	25.9364	+	18.8439i	0.929268	+	0.675153i
$780$		0			0
$781$	13.6826	−	2.79973i	0.489603	−	0.100182i
$782$		0			0
$783$	3.81548	+	2.77211i	0.136354	+	0.0990671i
$784$		0			0
$785$	−0.902942	−	2.77897i	−0.0322274	−	0.0991857i
$786$		0			0
$787$	2.05619	−	1.49391i	0.0732954	−	0.0532523i	−0.550534	−	0.834813i	$-0.685576\pi$
$787$	2.05619	−	1.49391i	0.0732954	−	0.0532523i	0.623830	+	0.781560i	$0.285576\pi$
$788$		0			0
$789$	−17.7954	+	54.7685i	−0.633531	+	1.94981i
$790$		0			0
$791$	−46.7397			−1.66187
$792$		0			0
$793$	6.13680			0.217924
$794$		0			0
$795$	0.611978	−	1.88348i	0.0217046	−	0.0668000i
$796$		0			0
$797$	−21.2702	+	15.4537i	−0.753429	+	0.547398i	−0.896888	−	0.442258i	$-0.854178\pi$
$797$	−21.2702	+	15.4537i	−0.753429	+	0.547398i	0.143459	+	0.989656i	$0.454178\pi$
$798$		0			0
$799$	17.1944	+	52.9188i	0.608293	+	1.87213i
$800$		0			0
$801$	44.7723	+	32.5290i	1.58195	+	1.14935i
$802$		0			0
$803$	−0.507734	+	4.50116i	−0.0179175	+	0.158842i
$804$		0			0
$805$	−6.88009	−	4.99868i	−0.242491	−	0.176180i
$806$		0			0
$807$	−3.35248	−	10.3179i	−0.118013	−	0.363206i
$808$		0			0
$809$	6.42589	−	4.66868i	0.225922	−	0.164142i	−0.469066	−	0.883163i	$-0.655409\pi$
$809$	6.42589	−	4.66868i	0.225922	−	0.164142i	0.694989	+	0.719021i	$0.255409\pi$
$810$		0			0
$811$	−6.00008	+	18.4663i	−0.210691	+	0.648441i	0.788740	+	0.614727i	$0.210734\pi$
$811$	−6.00008	+	18.4663i	−0.210691	+	0.648441i	−0.999432	+	0.0337144i	$0.989266\pi$
$812$		0			0
$813$	39.5777			1.38805
$814$		0			0
$815$	−8.48158			−0.297097
$816$		0			0
$817$	14.8562	−	45.7227i	0.519753	−	1.59963i
$818$		0			0
$819$	−50.0554	+	36.3674i	−1.74908	+	1.27078i
$820$		0			0
$821$	−4.04253	−	12.4416i	−0.141085	−	0.434216i	0.855402	−	0.517965i	$-0.173310\pi$
$821$	−4.04253	−	12.4416i	−0.141085	−	0.434216i	−0.996487	+	0.0837498i	$0.973310\pi$
$822$		0			0
$823$	25.4573	+	18.4958i	0.887387	+	0.644724i	0.935195	−	0.354132i	$-0.115224\pi$
$823$	25.4573	+	18.4958i	0.887387	+	0.644724i	−0.0478087	+	0.998857i	$0.515224\pi$
$824$		0			0
$825$	−4.53598	−	7.99640i	−0.157923	−	0.278399i
$826$		0			0
$827$	−5.23796	−	3.80560i	−0.182142	−	0.132334i	0.492978	−	0.870042i	$-0.335908\pi$
$827$	−5.23796	−	3.80560i	−0.182142	−	0.132334i	−0.675120	+	0.737708i	$0.735908\pi$
$828$		0			0
$829$	−15.4639	−	47.5929i	−0.537082	−	1.65297i	−0.739106	−	0.673589i	$-0.764752\pi$
$829$	−15.4639	−	47.5929i	−0.537082	−	1.65297i	0.202023	−	0.979381i	$-0.435248\pi$
$830$		0			0
$831$	−8.43852	+	6.13094i	−0.292729	+	0.212680i
$832$		0			0
$833$	−30.1137	+	92.6805i	−1.04338	+	3.21119i
$834$		0			0
$835$	10.0642			0.348286
$836$		0			0
$837$	−20.5798			−0.711343
$838$		0			0
$839$	−3.11229	+	9.57863i	−0.107448	+	0.330691i	−0.990297	−	0.138965i	$-0.955622\pi$
$839$	−3.11229	+	9.57863i	−0.107448	+	0.330691i	0.882849	+	0.469657i	$0.155622\pi$
$840$		0			0
$841$	22.6351	−	16.4453i	0.780520	−	0.567081i
$842$		0			0
$843$	−8.83883	−	27.2031i	−0.304425	−	0.936925i
$844$		0			0
$845$	3.71218	+	2.69706i	0.127703	+	0.0927816i
$846$		0			0
$847$	−25.7100	+	43.0067i	−0.883406	+	1.47773i
$848$		0			0
$849$	68.2990	+	49.6221i	2.34402	+	1.70303i
$850$		0			0
$851$	−3.11020	−	9.57222i	−0.106616	−	0.328132i
$852$		0			0
$853$	19.6433	−	14.2717i	0.672575	−	0.488654i	−0.198311	−	0.980139i	$-0.563546\pi$
$853$	19.6433	−	14.2717i	0.672575	−	0.488654i	0.870886	+	0.491485i	$0.163546\pi$
$854$		0			0
$855$	10.3384	−	31.8184i	0.353567	−	1.08817i
$856$		0			0
$857$	23.8353			0.814200			0.407100	−	0.913384i	$-0.366540\pi$
$857$	23.8353			0.814200			0.407100	+	0.913384i	$0.366540\pi$
$858$		0			0
$859$	−27.1693			−0.927004			−0.463502	−	0.886096i	$-0.653407\pi$
$859$	−27.1693			−0.927004			−0.463502	+	0.886096i	$0.653407\pi$
$860$		0			0
$861$	−17.5104	+	53.8915i	−0.596754	+	1.83662i
$862$		0			0
$863$	27.1023	−	19.6910i	0.922574	−	0.670289i	−0.0215894	−	0.999767i	$-0.506873\pi$
$863$	27.1023	−	19.6910i	0.922574	−	0.670289i	0.944163	+	0.329478i	$0.106873\pi$
$864$		0			0
$865$	1.78384	+	5.49008i	0.0606523	+	0.186668i
$866$		0			0
$867$	−74.5411	−	54.1573i	−2.53155	−	1.83928i
$868$		0			0
$869$	−20.0256	−	35.3028i	−0.679322	−	1.19757i
$870$		0			0
$871$	−30.1236	−	21.8861i	−1.02070	−	0.741581i
$872$		0			0
$873$	−15.7091	−	48.3476i	−0.531672	−	1.63632i
$874$		0			0
$875$	−3.68512	+	2.67740i	−0.124580	+	0.0905125i
$876$		0			0
$877$	−1.26705	+	3.89958i	−0.0427853	+	0.131680i	−0.970167	−	0.242436i	$-0.922054\pi$
$877$	−1.26705	+	3.89958i	−0.0427853	+	0.131680i	0.927382	+	0.374115i	$0.122054\pi$
$878$		0			0
$879$	−21.9132			−0.739113
$880$		0			0
$881$	34.8285			1.17340			0.586701	−	0.809804i	$-0.300426\pi$
$881$	34.8285			1.17340			0.586701	+	0.809804i	$0.300426\pi$
$882$		0			0
$883$	8.24871	−	25.3869i	0.277591	−	0.854337i	−0.710931	−	0.703262i	$-0.751726\pi$
$883$	8.24871	−	25.3869i	0.277591	−	0.854337i	0.988522	−	0.151076i	$-0.0482738\pi$
$884$		0			0
$885$	−8.52894	+	6.19664i	−0.286697	+	0.208298i
$886$		0			0
$887$	−15.8860	−	48.8922i	−0.533401	−	1.64164i	−0.747080	−	0.664734i	$-0.768545\pi$
$887$	−15.8860	−	48.8922i	−0.533401	−	1.64164i	0.213679	−	0.976904i	$-0.431455\pi$
$888$		0			0
$889$	65.3043	+	47.4463i	2.19024	+	1.59130i
$890$		0			0
$891$	0.414828	−	3.67753i	0.0138973	−	0.123202i
$892$		0			0
$893$	45.3676	+	32.9615i	1.51817	+	1.10301i
$894$		0			0
$895$	−5.21222	−	16.0416i	−0.174225	−	0.536210i
$896$		0			0
$897$	−12.1427	+	8.82215i	−0.405431	+	0.294563i
$898$		0			0
$899$	1.37745	−	4.23937i	0.0459407	−	0.141391i
$900$		0			0
$901$	−5.06409			−0.168709
$902$		0			0
$903$	84.9743			2.82777
$904$		0			0
$905$	4.66782	−	14.3661i	0.155164	−	0.477544i
$906$		0			0
$907$	−5.46347	+	3.96944i	−0.181412	+	0.131803i	−0.674785	−	0.738014i	$-0.735764\pi$
$907$	−5.46347	+	3.96944i	−0.181412	+	0.131803i	0.493373	+	0.869818i	$0.335764\pi$
$908$		0			0
$909$	18.3317	+	56.4193i	0.608025	+	1.87131i
$910$		0			0
$911$	−10.5901	−	7.69413i	−0.350864	−	0.254918i	0.398367	−	0.917226i	$-0.369577\pi$
$911$	−10.5901	−	7.69413i	−0.350864	−	0.254918i	−0.749231	+	0.662308i	$0.769577\pi$
$912$		0			0
$913$	−53.0775	+	10.8607i	−1.75661	+	0.359437i
$914$		0			0
$915$	−4.74505	−	3.44748i	−0.156866	−	0.113970i
$916$		0			0
$917$	−20.2691	−	62.3819i	−0.669345	−	2.06003i
$918$		0			0
$919$	0.431662	−	0.313621i	0.0142392	−	0.0103454i	−0.580643	−	0.814158i	$-0.697199\pi$
$919$	0.431662	−	0.313621i	0.0142392	−	0.0103454i	0.594882	+	0.803813i	$0.297199\pi$
$920$		0			0
$921$	−12.2133	+	37.5888i	−0.402443	+	1.23859i
$922$		0			0
$923$	−12.2128			−0.401990
$924$		0			0
$925$	−5.39094			−0.177253
$926$		0			0
$927$	8.94639	−	27.5341i	0.293838	−	0.904340i
$928$		0			0
$929$	8.02666	−	5.83171i	0.263346	−	0.191332i	−0.448275	−	0.893896i	$-0.647961\pi$
$929$	8.02666	−	5.83171i	0.263346	−	0.191332i	0.711621	+	0.702564i	$0.247961\pi$
$930$		0			0
$931$	30.3493	+	93.4056i	0.994658	+	3.06124i
$932$		0			0
$933$	38.5976	+	28.0428i	1.26363	+	0.918081i
$934$		0			0
$935$	−15.8625	+	17.3499i	−0.518761	+	0.567403i
$936$		0			0
$937$	2.88820	+	2.09840i	0.0943535	+	0.0685518i	0.633962	−	0.773364i	$-0.281428\pi$
$937$	2.88820	+	2.09840i	0.0943535	+	0.0685518i	−0.539608	+	0.841916i	$0.681428\pi$
$938$		0			0
$939$	−6.82167	−	20.9950i	−0.222617	−	0.685144i
$940$		0			0
$941$	39.4995	−	28.6980i	1.28765	−	0.935529i	0.287890	−	0.957663i	$-0.407046\pi$
$941$	39.4995	−	28.6980i	1.28765	−	0.935529i	0.999755	+	0.0221343i	$0.00704613\pi$
$942$		0			0
$943$	−2.58921	+	7.96878i	−0.0843164	+	0.259499i
$944$		0			0
$945$	21.2551			0.691428
$946$		0			0
$947$	−15.1463			−0.492190			−0.246095	−	0.969246i	$-0.579148\pi$
$947$	−15.1463			−0.492190			−0.246095	+	0.969246i	$0.579148\pi$
$948$		0			0
$949$	1.22403	−	3.76718i	0.0397337	−	0.122288i
$950$		0			0
$951$	30.7912	−	22.3711i	0.998473	−	0.725433i
$952$		0			0
$953$	7.91352	+	24.3553i	0.256344	+	0.788946i	0.993562	+	0.113291i	$0.0361391\pi$
$953$	7.91352	+	24.3553i	0.256344	+	0.788946i	−0.737218	+	0.675655i	$0.763861\pi$
$954$		0			0
$955$	8.44116	+	6.13286i	0.273149	+	0.198455i
$956$		0			0
$957$	−8.45942	−	3.84374i	−0.273454	−	0.124250i
$958$		0			0
$959$	−16.4714	−	11.9671i	−0.531888	−	0.386439i
$960$		0			0
$961$	−3.56879	−	10.9836i	−0.115122	−	0.354310i
$962$		0			0
$963$	3.81831	−	2.77416i	0.123043	−	0.0893961i
$964$		0			0
$965$	4.30306	−	13.2435i	0.138520	−	0.426322i
$966$		0			0
$967$	−19.9187			−0.640544			−0.320272	−	0.947326i	$-0.603774\pi$
$967$	−19.9187			−0.640544			−0.320272	+	0.947326i	$0.603774\pi$
$968$		0			0
$969$	−140.350			−4.50868
$970$		0			0
$971$	4.43889	−	13.6615i	0.142451	−	0.438418i	−0.854224	−	0.519906i	$-0.825967\pi$
$971$	4.43889	−	13.6615i	0.142451	−	0.438418i	0.996674	+	0.0814874i	$0.0259670\pi$
$972$		0			0
$973$	17.8552	−	12.9726i	0.572413	−	0.415882i
$974$		0			0
$975$	2.48425	+	7.64575i	0.0795598	+	0.244860i
$976$		0			0
$977$	−39.1921	−	28.4748i	−1.25387	−	0.910988i	−0.255428	−	0.966828i	$-0.582216\pi$
$977$	−39.1921	−	28.4748i	−1.25387	−	0.910988i	−0.998440	+	0.0558400i	$0.982216\pi$
$978$		0			0
$979$	−35.6804	−	16.2122i	−1.14035	−	0.518145i
$980$		0			0
$981$	−25.0223	−	18.1798i	−0.798901	−	0.580435i
$982$		0			0
$983$	−3.10044	−	9.54216i	−0.0988886	−	0.304348i	0.889359	−	0.457210i	$-0.151151\pi$
$983$	−3.10044	−	9.54216i	−0.0988886	−	0.304348i	−0.988248	+	0.152862i	$0.951151\pi$
$984$		0			0
$985$	1.82218	−	1.32389i	0.0580595	−	0.0421827i
$986$		0			0
$987$	−30.6290	+	94.2664i	−0.974932	+	3.00053i
$988$		0			0
$989$	12.5649			0.399540
$990$		0			0
$991$	4.44920			0.141333			0.0706667	−	0.997500i	$-0.477487\pi$
$991$	4.44920			0.141333			0.0706667	+	0.997500i	$0.477487\pi$
$992$		0			0
$993$	−9.16276	+	28.2001i	−0.290771	+	0.894903i
$994$		0			0
$995$	17.8991	−	13.0045i	0.567441	−	0.412270i
$996$		0			0
$997$	13.1142	+	40.3612i	0.415330	+	1.27825i	0.911956	+	0.410289i	$0.134572\pi$
$997$	13.1142	+	40.3612i	0.415330	+	1.27825i	−0.496626	+	0.867965i	$0.665428\pi$
$998$		0			0
$999$	20.3512	+	14.7860i	0.643885	+	0.467810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.k.81.4		16
4.3	odd	2		440.2.y.d.81.1	✓	16
11.3	even	5	inner	880.2.bo.k.641.4		16
11.5	even	5		9680.2.a.df.1.7		8
11.6	odd	10		9680.2.a.de.1.7		8
44.3	odd	10		440.2.y.d.201.1	yes	16
44.27	odd	10		4840.2.a.bg.1.2		8
44.39	even	10		4840.2.a.bh.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.81.1	✓	16	4.3	odd	2
440.2.y.d.201.1	yes	16	44.3	odd	10
880.2.bo.k.81.4		16	1.1	even	1	trivial
880.2.bo.k.641.4		16	11.3	even	5	inner
4840.2.a.bg.1.2		8	44.27	odd	10
4840.2.a.bh.1.2		8	44.39	even	10
9680.2.a.de.1.7		8	11.6	odd	10
9680.2.a.df.1.7		8	11.5	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.856564 - 2.63623i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(1.40759 + 4.33212i) q^{7} +(-3.78896 - 2.75284i) q^{9} +(3.01954 + 1.37200i) q^{11} +(-2.34636 - 1.70473i) q^{13} +(0.856564 + 2.63623i) q^{15} +(5.73433 - 4.16623i) q^{17} +(2.20745 - 6.79384i) q^{19} +12.6262 q^{21} +1.86699 q^{23} +(0.309017 - 0.951057i) q^{25} +(-3.77509 + 2.74276i) q^{27} +(-0.312324 - 0.961233i) q^{29} +(3.56804 + 2.59234i) q^{31} +(6.20333 - 6.78500i) q^{33} +(-3.68512 - 2.67740i) q^{35} +(-1.66589 - 5.12709i) q^{37} +(-6.50386 + 4.72533i) q^{39} +(-1.38684 + 4.26825i) q^{41} +6.73002 q^{43} +4.68342 q^{45} +(-2.42584 + 7.46596i) q^{47} +(-11.1228 + 8.08120i) q^{49} +(-6.07134 - 18.6857i) q^{51} +(-0.578008 - 0.419948i) q^{53} +(-3.24930 + 0.664870i) q^{55} +(-16.0193 - 11.6387i) q^{57} +(1.17528 + 3.61715i) q^{59} +(-1.71184 + 1.24373i) q^{61} +(6.59234 - 20.2891i) q^{63} +2.90026 q^{65} +12.8384 q^{67} +(1.59920 - 4.92182i) q^{69} +(3.40673 - 2.47513i) q^{71} +(0.422042 + 1.29891i) q^{73} +(-2.24251 - 1.62928i) q^{75} +(-1.69339 + 15.0122i) q^{77} +(-9.90032 - 7.19300i) q^{79} +(-0.344817 - 1.06124i) q^{81} +(-13.2153 + 9.60151i) q^{83} +(-2.19032 + 6.74110i) q^{85} -2.80156 q^{87} -11.8165 q^{89} +(4.08237 - 12.5643i) q^{91} +(9.89025 - 7.18569i) q^{93} +(2.20745 + 6.79384i) q^{95} +(8.78139 + 6.38005i) q^{97} +(-7.66403 - 13.5108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37}+ \cdots + 10 q^{99}+O(q^{100}) \) 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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