LMFDB - Embedded newform 440.2.y.d.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, 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("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.856564 - 2.63623i$ of defining polynomial
Character	$\chi$	$=$	440.81
Dual form			440.2.y.d.201.1

$q$-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 $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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	$0.395262\pi$
$3$	−0.856564	+	2.63623i	−0.494537	+	1.52203i	−0.817677	+	0.575678i	$0.804738\pi$
$4$		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	$-0.769948\pi$
$7$	−1.40759	−	4.33212i	−0.532019	−	1.63739i	0.217984	−	0.975952i	$-0.430052\pi$
$8$		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	$0.405700\pi$
$19$	−2.20745	+	6.79384i	−0.506424	+	1.55861i	−0.798363	+	0.602177i	$0.794300\pi$
$20$		0			0
$21$	12.6262			2.75525
$22$		0			0
$23$	−1.86699			−0.389295			−0.194647	−	0.980873i	$-0.562356\pi$
$23$	−1.86699			−0.389295			−0.194647	+	0.980873i	$0.562356\pi$
$24$		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	0.219299	−	0.975658i	$-0.429623\pi$
$31$	−3.56804	−	2.59234i	−0.640840	−	0.465597i	−0.860139	+	0.510061i	$0.829623\pi$
$32$		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	$-0.671525\pi$
$43$	−6.73002			−1.02632			−0.513159	+	0.858293i	$0.671525\pi$
$44$		0			0
$45$	4.68342			0.698163
$46$		0			0
$47$	2.42584	−	7.46596i	0.353845	−	1.08902i	−0.602832	−	0.797868i	$-0.705961\pi$
$47$	2.42584	−	7.46596i	0.353845	−	1.08902i	0.956676	−	0.291154i	$-0.0940390\pi$
$48$		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	0.844945	−	0.534853i	$-0.179633\pi$
$59$	−1.17528	−	3.61715i	−0.153009	−	0.470913i	−0.997954	+	0.0639406i	$0.979633\pi$
$60$		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	$-0.786943\pi$
$67$	−12.8384			−1.56847			−0.784233	+	0.620467i	$0.786943\pi$
$68$		0			0
$69$	1.59920	−	4.92182i	0.192521	−	0.592518i
$70$		0			0
$71$	−3.40673	+	2.47513i	−0.404304	+	0.293744i	−0.771292	−	0.636482i	$-0.780389\pi$
$71$	−3.40673	+	2.47513i	−0.404304	+	0.293744i	0.366988	+	0.930226i	$0.380389\pi$
$72$		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	0.983269	−	0.182159i	$-0.0583084\pi$
$79$	9.90032	+	7.19300i	1.11387	+	0.809276i	0.130604	+	0.991435i	$0.458308\pi$
$80$		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	$-0.346099\pi$
$83$	13.2153	−	9.60151i	1.45057	−	1.05390i	0.985697	−	0.168527i	$-0.0539011\pi$
$84$		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	0.811769	−	0.583979i	$-0.198505\pi$
$103$	−1.91023	−	5.87907i	−0.188220	−	0.579282i	−0.999989	+	0.00469684i	$0.998505\pi$
$104$		0			0
$105$	−10.2148	+	7.42147i	−0.996860	+	0.724261i
$106$		0			0
$107$	0.311410	−	0.958421i	0.0301051	−	0.0926541i	−0.934875	−	0.354977i	$-0.884489\pi$
$107$	0.311410	−	0.958421i	0.0301051	−	0.0926541i	0.964980	+	0.262323i	$0.0844886\pi$
$108$		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	−0.999287	−	0.0377597i	$-0.987978\pi$
$127$	−14.3366	+	10.4162i	−1.27217	+	0.924287i	−0.272885	+	0.962047i	$0.587978\pi$
$128$		0			0
$129$	5.76469	−	17.7419i	0.507553	−	1.56209i
$130$		0			0
$131$	14.3999			1.25812			0.629061	−	0.777356i	$-0.283440\pi$
$131$	14.3999			1.25812			0.629061	+	0.777356i	$0.283440\pi$
$132$		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	0.994259	−	0.106996i	$-0.0341234\pi$
$139$	1.49726	+	4.60808i	0.126996	+	0.390853i	−0.867264	+	0.497849i	$0.834123\pi$
$140$		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	−0.953562	−	0.301197i	$-0.902614\pi$
$151$	−0.0623641	+	0.191937i	−0.00507512	+	0.0156196i	0.948487	+	0.316816i	$0.102614\pi$
$152$		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	0.285685	−	0.958324i	$-0.407779\pi$
$163$	−6.86174	−	4.98535i	−0.537453	−	0.390483i	−0.823138	+	0.567841i	$0.807779\pi$
$164$		0			0
$165$	−1.03048	+	9.13541i	−0.0802227	+	0.711191i
$166$		0			0
$167$	8.14210	+	5.91558i	0.630055	+	0.457761i	0.856419	−	0.516281i	$-0.172684\pi$
$167$	8.14210	+	5.91558i	0.630055	+	0.457761i	−0.226365	+	0.974043i	$0.572684\pi$
$168$		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	$-0.682910\pi$
$179$	5.21222	−	16.0416i	0.389580	−	1.19900i	0.933103	−	0.359609i	$-0.117090\pi$
$180$		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	$0.0232104\pi$
$191$	3.22423	+	9.92317i	0.233297	+	0.718016i	−0.764045	+	0.645163i	$0.776790\pi$
$192$		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	$-0.213082\pi$
$199$	22.1246			1.56837			0.784184	+	0.620528i	$0.213082\pi$
$200$		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	0.349957	−	0.936766i	$-0.386196\pi$
$211$	−6.28703	−	4.56779i	−0.432817	−	0.314460i	−0.782774	+	0.622306i	$0.786196\pi$
$212$		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	−0.998954	−	0.0457224i	$-0.985441\pi$
$223$	−2.44767	+	7.53316i	−0.163908	+	0.504458i	0.835046	+	0.550180i	$0.185441\pi$
$224$		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	$-0.865182\pi$
$227$	−6.26291	−	19.2752i	−0.415684	−	1.27934i	0.495954	−	0.868349i	$-0.334818\pi$
$228$		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	$0.215944\pi$
$239$	−3.40378	+	10.4758i	−0.220173	+	0.677621i	−0.998746	+	0.0500677i	$0.984056\pi$
$240$		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	0.894308	−	0.447451i	$-0.147668\pi$
$251$	11.8048	+	8.57671i	0.745114	+	0.541357i	−0.149195	+	0.988808i	$0.547668\pi$
$252$		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	$-0.278715\pi$
$263$	20.7753			1.28106			0.640529	+	0.767934i	$0.278715\pi$
$264$		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	$-0.957219\pi$
$271$	−4.41220	−	13.5794i	−0.268022	−	0.824888i	0.722959	−	0.690891i	$-0.242781\pi$
$272$		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	$-0.539703\pi$
$283$	9.41156	−	28.9658i	0.559459	−	1.72184i	0.683866	−	0.729608i	$-0.260297\pi$
$284$		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	$-0.366614\pi$
$307$	14.2585			0.813777			0.406889	+	0.913478i	$0.366614\pi$
$308$		0			0
$309$	17.1348			0.974766
$310$		0			0
$311$	5.31873	−	16.3694i	0.301598	−	0.928222i	−0.679327	−	0.733835i	$-0.737728\pi$
$311$	5.31873	−	16.3694i	0.301598	−	0.928222i	0.980925	−	0.194387i	$-0.0622717\pi$
$312$		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	$-0.405019\pi$
$331$	10.6971			0.587967			0.293983	+	0.955811i	$0.405019\pi$
$332$		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	−0.578558	−	0.815641i	$-0.696384\pi$
$347$	0.342361	−	0.248740i	0.0183789	−	0.0133530i	0.596937	+	0.802288i	$0.296384\pi$
$348$		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	0.993729	−	0.111819i	$-0.0356677\pi$
$359$	2.35059	+	7.23438i	0.124060	+	0.381816i	−0.869669	+	0.493635i	$0.835668\pi$
$360$		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	0.934861	−	0.355013i	$-0.115523\pi$
$367$	−0.577181	−	1.77638i	−0.0301286	−	0.0927263i	−0.964990	+	0.262286i	$0.915523\pi$
$368$		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	−0.961566	−	0.274574i	$-0.911463\pi$
$379$	−19.4206	+	14.1099i	−0.997571	+	0.724778i	−0.0360048	+	0.999352i	$0.511463\pi$
$380$		0			0
$381$	−15.1792	−	46.7168i	−0.777655	−	2.39338i
$382$		0			0
$383$	−15.9188	−	11.5657i	−0.813411	−	0.590978i	0.101407	−	0.994845i	$-0.467666\pi$
$383$	−15.9188	−	11.5657i	−0.813411	−	0.590978i	−0.914818	+	0.403867i	$0.867666\pi$
$384$		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	$-0.508689\pi$
$419$	−1.11739			−0.0545881			−0.0272940	+	0.999627i	$0.508689\pi$
$420$		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	0.426474	−	0.904500i	$-0.359756\pi$
$431$	−6.26903	−	4.55472i	−0.301969	−	0.219393i	−0.728443	+	0.685107i	$0.759756\pi$
$432$		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	$-0.811246\pi$
$439$	−34.7505			−1.65855			−0.829275	+	0.558841i	$0.811246\pi$
$440$		0			0
$441$	64.3903			3.06620
$442$		0			0
$443$	7.51612	−	23.1322i	0.357102	−	1.09905i	−0.597679	−	0.801735i	$-0.703910\pi$
$443$	7.51612	−	23.1322i	0.357102	−	1.09905i	0.954781	−	0.297310i	$-0.0960896\pi$
$444$		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	$-0.821618\pi$
$463$	−36.4523			−1.69408			−0.847040	+	0.531529i	$0.821618\pi$
$464$		0			0
$465$	−3.77774	+	11.6267i	−0.175189	+	0.539175i
$466$		0			0
$467$	−22.6893	+	16.4847i	−1.04993	+	0.762822i	−0.972200	−	0.234153i	$-0.924768\pi$
$467$	−22.6893	+	16.4847i	−1.04993	+	0.762822i	−0.0777339	+	0.996974i	$0.524768\pi$
$468$		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	$-0.388178\pi$
$479$	29.4024	−	21.3621i	1.34343	−	0.976058i	0.999310	−	0.0371313i	$-0.0118220\pi$
$480$		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	$-0.503732\pi$
$487$	12.9210	−	39.7667i	0.585506	−	1.80200i	0.597230	−	0.802070i	$-0.296268\pi$
$488$		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	$0.0438708\pi$
$491$	5.98118	+	18.4082i	0.269927	+	0.830749i	−0.720590	+	0.693361i	$0.756129\pi$
$492$		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	0.999943	−	0.0106764i	$-0.00339846\pi$
$499$	4.12581	+	12.6979i	0.184697	+	0.568438i	−0.815246	+	0.579114i	$0.803398\pi$
$500$		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	$-0.604780\pi$
$503$	11.0902	−	34.1322i	0.494489	−	1.52188i	0.817751	−	0.575572i	$-0.195220\pi$
$504$		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	−0.994615	−	0.103641i	$-0.966951\pi$
$523$	−27.5208	+	19.9950i	−1.20340	+	0.874321i	−0.208785	+	0.977962i	$0.566951\pi$
$524$		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	$0.266046\pi$
$547$	−7.20288	+	22.1682i	−0.307973	+	0.947843i	−0.978551	+	0.206004i	$0.933954\pi$
$548$		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	0.717727	−	0.696324i	$-0.245182\pi$
$563$	6.57905	+	4.77996i	0.277274	+	0.201451i	−0.440454	+	0.897775i	$0.645182\pi$
$564$		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	$-0.255543\pi$
$571$	33.1999			1.38937			0.694687	+	0.719312i	$0.255543\pi$
$572$		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	$-0.726189\pi$
$587$	−13.8125	−	42.5104i	−0.570102	−	1.75459i	0.0821818	−	0.996617i	$-0.473811\pi$
$588$		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	−0.216314	−	0.976324i	$-0.569403\pi$
$599$	15.7954	−	11.4760i	0.645381	−	0.468897i	0.861695	+	0.507427i	$0.169403\pi$
$600$		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	0.887504	−	0.460800i	$-0.152437\pi$
$607$	17.8254	+	12.9509i	0.723511	+	0.525662i	−0.163993	+	0.986461i	$0.552437\pi$
$608$		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	$0.278138\pi$
$619$	−8.16306	+	25.1233i	−0.328101	+	1.00979i	−0.970021	+	0.243020i	$0.921862\pi$
$620$		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	$-0.821139\pi$
$631$	−11.9266	−	36.7063i	−0.474790	−	1.46125i	0.371451	−	0.928453i	$-0.378861\pi$
$632$		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	−0.743164	−	0.669109i	$-0.766676\pi$
$643$	−8.53160	+	6.19857i	−0.336453	+	0.244448i	0.406711	+	0.913557i	$0.366676\pi$
$644$		0			0
$645$	5.76469	+	17.7419i	0.226984	+	0.698586i
$646$		0			0
$647$	−13.6858	−	9.94328i	−0.538042	−	0.390911i	0.285315	−	0.958434i	$-0.407902\pi$
$647$	−13.6858	−	9.94328i	−0.538042	−	0.390911i	−0.823358	+	0.567523i	$0.807902\pi$
$648$		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	$-0.537084\pi$
$659$	−5.96793			−0.232477			−0.116239	+	0.993221i	$0.537084\pi$
$660$		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	$-0.582889\pi$
$683$	−13.4576			−0.514940			−0.257470	+	0.966286i	$0.582889\pi$
$684$		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	0.940340	−	0.340237i	$-0.110507\pi$
$691$	23.8510	+	17.3288i	0.907337	+	0.659219i	−0.0330033	+	0.999455i	$0.510507\pi$
$692$		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	$-0.737404\pi$
$719$	−15.0519	−	46.3250i	−0.561341	−	1.72763i	0.117239	−	0.993104i	$-0.462596\pi$
$720$		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	$-0.889281\pi$
$727$	−50.6964			−1.88023			−0.940113	+	0.340864i	$0.889281\pi$
$728$		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	0.283864	−	0.958865i	$-0.408384\pi$
$739$	−14.6892	−	10.6724i	−0.540352	−	0.392589i	−0.824216	+	0.566276i	$0.808384\pi$
$740$		0			0
$741$	17.7462	+	54.6172i	0.651923	+	2.00641i
$742$		0			0
$743$	3.02269	−	2.19611i	0.110892	−	0.0805676i	−0.530957	−	0.847399i	$-0.678168\pi$
$743$	3.02269	−	2.19611i	0.110892	−	0.0805676i	0.641849	+	0.766831i	$0.278168\pi$
$744$		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	$0.269616\pi$
$751$	−8.60395	+	26.4802i	−0.313963	+	0.966277i	−0.976179	+	0.216965i	$0.930384\pi$
$752$		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	−0.623830	−	0.781560i	$-0.714424\pi$
$787$	−2.05619	+	1.49391i	−0.0732954	+	0.0532523i	0.550534	+	0.834813i	$0.314424\pi$
$788$		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	$-0.789266\pi$
$811$	6.00008	−	18.4663i	0.210691	−	0.648441i	0.999432	−	0.0337144i	$-0.0107337\pi$
$812$		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	0.0478087	−	0.998857i	$-0.484776\pi$
$823$	−25.4573	−	18.4958i	−0.887387	−	0.644724i	−0.935195	+	0.354132i	$0.884776\pi$
$824$		0			0
$825$	−4.53598	−	7.99640i	−0.157923	−	0.278399i
$826$		0			0
$827$	5.23796	+	3.80560i	0.182142	+	0.132334i	0.675120	−	0.737708i	$-0.264092\pi$
$827$	5.23796	+	3.80560i	0.182142	+	0.132334i	−0.492978	+	0.870042i	$0.664092\pi$
$828$		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	−0.882849	−	0.469657i	$-0.844378\pi$
$839$	3.11229	−	9.57863i	0.107448	−	0.330691i	0.990297	+	0.138965i	$0.0443777\pi$
$840$		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	$-0.346593\pi$
$859$	27.1693			0.927004			0.463502	+	0.886096i	$0.346593\pi$
$860$		0			0
$861$	−17.5104	+	53.8915i	−0.596754	+	1.83662i
$862$		0			0
$863$	−27.1023	+	19.6910i	−0.922574	+	0.670289i	−0.944163	−	0.329478i	$-0.893127\pi$
$863$	−27.1023	+	19.6910i	−0.922574	+	0.670289i	0.0215894	+	0.999767i	$0.493127\pi$
$864$		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	$0.248274\pi$
$883$	−8.24871	+	25.3869i	−0.277591	+	0.854337i	−0.988522	+	0.151076i	$0.951726\pi$
$884$		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	$0.231455\pi$
$887$	15.8860	+	48.8922i	0.533401	+	1.64164i	−0.213679	+	0.976904i	$0.568545\pi$
$888$		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	−0.493373	−	0.869818i	$-0.664236\pi$
$907$	5.46347	−	3.96944i	0.181412	−	0.131803i	0.674785	+	0.738014i	$0.264236\pi$
$908$		0			0
$909$	18.3317	+	56.4193i	0.608025	+	1.87131i
$910$		0			0
$911$	10.5901	+	7.69413i	0.350864	+	0.254918i	0.749231	−	0.662308i	$-0.230423\pi$
$911$	10.5901	+	7.69413i	0.350864	+	0.254918i	−0.398367	+	0.917226i	$0.630423\pi$
$912$		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	−0.594882	−	0.803813i	$-0.702801\pi$
$919$	−0.431662	+	0.313621i	−0.0142392	+	0.0103454i	0.580643	+	0.814158i	$0.302801\pi$
$920$		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	$-0.420852\pi$
$947$	15.1463			0.492190			0.246095	+	0.969246i	$0.420852\pi$
$948$		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	$-0.396226\pi$
$967$	19.9187			0.640544			0.320272	+	0.947326i	$0.396226\pi$
$968$		0			0
$969$	−140.350			−4.50868
$970$		0			0
$971$	−4.43889	+	13.6615i	−0.142451	+	0.438418i	−0.996674	−	0.0814874i	$-0.974033\pi$
$971$	−4.43889	+	13.6615i	−0.142451	+	0.438418i	0.854224	+	0.519906i	$0.174033\pi$
$972$		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	0.988248	−	0.152862i	$-0.0488489\pi$
$983$	3.10044	+	9.54216i	0.0988886	+	0.304348i	−0.889359	+	0.457210i	$0.848849\pi$
$984$		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	$-0.522513\pi$
$991$	−4.44920			−0.141333			−0.0706667	+	0.997500i	$0.522513\pi$
$992$		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	440.2.y.d.81.1	✓	16
4.3	odd	2		880.2.bo.k.81.4		16
11.3	even	5	inner	440.2.y.d.201.1	yes	16
11.5	even	5		4840.2.a.bg.1.2		8
11.6	odd	10		4840.2.a.bh.1.2		8
44.3	odd	10		880.2.bo.k.641.4		16
44.27	odd	10		9680.2.a.df.1.7		8
44.39	even	10		9680.2.a.de.1.7		8

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

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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), 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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Groups

Database

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