LMFDB - Embedded newform 800.2.u.a.321.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(161,800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("800.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-3,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			321.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	800.321
Dual form			800.2.u.a.481.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30902 - 0.951057i) q^{3} +(-1.80902 - 1.31433i) q^{5} +0.236068 q^{7} +(-0.118034 - 0.363271i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.07295 - 3.30220i) q^{13} +(1.11803 + 3.44095i) q^{15} +(2.30902 - 1.67760i) q^{17} +(-4.11803 + 2.99193i) q^{19} +(-0.309017 - 0.224514i) q^{21} +(-0.309017 + 0.951057i) q^{23} +(1.54508 + 4.75528i) q^{25} +(-1.69098 + 5.20431i) q^{27} +(-2.42705 - 1.76336i) q^{29} +(-4.42705 + 3.21644i) q^{31} +(1.30902 - 0.951057i) q^{33} +(-0.427051 - 0.310271i) q^{35} +(-0.190983 - 0.587785i) q^{37} +(-1.73607 + 5.34307i) q^{39} +(2.92705 + 9.00854i) q^{41} -2.52786 q^{43} +(-0.263932 + 0.812299i) q^{45} +(7.04508 + 5.11855i) q^{47} -6.94427 q^{49} -4.61803 q^{51} +(-2.00000 - 1.45309i) q^{53} +(1.80902 - 1.31433i) q^{55} +8.23607 q^{57} +(3.09017 + 9.51057i) q^{59} +(-0.500000 + 1.53884i) q^{61} +(-0.0278640 - 0.0857567i) q^{63} +(-2.39919 + 7.38394i) q^{65} +(-3.66312 + 2.66141i) q^{67} +(1.30902 - 0.951057i) q^{69} +(-10.6631 - 7.74721i) q^{71} +(-0.854102 + 2.62866i) q^{73} +(2.50000 - 7.69421i) q^{75} +(-0.0729490 + 0.224514i) q^{77} +(-7.85410 - 5.70634i) q^{79} +(6.23607 - 4.53077i) q^{81} +(9.89919 - 7.19218i) q^{83} -6.38197 q^{85} +(1.50000 + 4.61653i) q^{87} +(-2.90983 + 8.95554i) q^{89} +(-0.253289 - 0.779543i) q^{91} +8.85410 q^{93} +11.3820 q^{95} +(0.263932 + 0.191758i) q^{97} +0.381966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} - 5 q^{5} - 8 q^{7} + 4 q^{9} + q^{11} - 11 q^{13} + 7 q^{17} - 12 q^{19} + q^{21} + q^{23} - 5 q^{25} - 9 q^{27} - 3 q^{29} - 11 q^{31} + 3 q^{33} + 5 q^{35} - 3 q^{37} + 2 q^{39} + 5 q^{41}+ \cdots + 6 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 - 5 * q^5 - 8 * q^7 + 4 * q^9 + q^11 - 11 * q^13 + 7 * q^17 - 12 * q^19 + q^21 + q^23 - 5 * q^25 - 9 * q^27 - 3 * q^29 - 11 * q^31 + 3 * q^33 + 5 * q^35 - 3 * q^37 + 2 * q^39 + 5 * q^41 - 28 * q^43 - 10 * q^45 + 17 * q^47 + 8 * q^49 - 14 * q^51 - 8 * q^53 + 5 * q^55 + 24 * q^57 - 10 * q^59 - 2 * q^61 - 18 * q^63 + 15 * q^65 + q^67 + 3 * q^69 - 27 * q^71 + 10 * q^73 + 10 * q^75 - 7 * q^77 - 18 * q^79 + 16 * q^81 + 15 * q^83 - 30 * q^85 + 6 * q^87 - 34 * q^89 + 37 * q^91 + 22 * q^93 + 50 * q^95 + 10 * q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−1.30902	−	0.951057i	−0.755761	−	0.549093i	0.141846	−	0.989889i	$-0.454696\pi$
$3$	−1.30902	−	0.951057i	−0.755761	−	0.549093i	−0.897607	+	0.440796i	$0.854696\pi$
$4$		0			0
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$		0			0
$7$	0.236068			0.0892253			0.0446127	−	0.999004i	$-0.485795\pi$
$7$	0.236068			0.0892253			0.0446127	+	0.999004i	$0.485795\pi$
$8$		0			0
$9$	−0.118034	−	0.363271i	−0.0393447	−	0.121090i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i	−0.986773	−	0.162108i	$-0.948171\pi$
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i	0.893601	+	0.448862i	$0.148171\pi$
$12$		0			0
$13$	−1.07295	−	3.30220i	−0.297583	−	0.915865i	−0.982342	−	0.187095i	$-0.940093\pi$
$13$	−1.07295	−	3.30220i	−0.297583	−	0.915865i	0.684759	−	0.728769i	$-0.259907\pi$
$14$		0			0
$15$	1.11803	+	3.44095i	0.288675	+	0.888451i
$16$		0			0
$17$	2.30902	−	1.67760i	0.560019	−	0.406878i	−0.271447	−	0.962453i	$-0.587502\pi$
$17$	2.30902	−	1.67760i	0.560019	−	0.406878i	0.831466	+	0.555576i	$0.187502\pi$
$18$		0			0
$19$	−4.11803	+	2.99193i	−0.944742	+	0.686395i	−0.949557	−	0.313593i	$-0.898467\pi$
$19$	−4.11803	+	2.99193i	−0.944742	+	0.686395i	0.00481560	+	0.999988i	$0.498467\pi$
$20$		0			0
$21$	−0.309017	−	0.224514i	−0.0674330	−	0.0489930i
$22$		0			0
$23$	−0.309017	+	0.951057i	−0.0644345	+	0.198309i	−0.978091	−	0.208178i	$-0.933247\pi$
$23$	−0.309017	+	0.951057i	−0.0644345	+	0.198309i	0.913656	+	0.406487i	$0.133247\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$		0			0
$27$	−1.69098	+	5.20431i	−0.325430	+	1.00157i
$28$		0			0
$29$	−2.42705	−	1.76336i	−0.450692	−	0.327447i	0.339177	−	0.940723i	$-0.389851\pi$
$29$	−2.42705	−	1.76336i	−0.450692	−	0.327447i	−0.789869	+	0.613276i	$0.789851\pi$
$30$		0			0
$31$	−4.42705	+	3.21644i	−0.795122	+	0.577690i	−0.909479	−	0.415750i	$-0.863519\pi$
$31$	−4.42705	+	3.21644i	−0.795122	+	0.577690i	0.114357	+	0.993440i	$0.463519\pi$
$32$		0			0
$33$	1.30902	−	0.951057i	0.227871	−	0.165558i
$34$		0			0
$35$	−0.427051	−	0.310271i	−0.0721848	−	0.0524453i
$36$		0			0
$37$	−0.190983	−	0.587785i	−0.0313974	−	0.0966313i	0.934130	−	0.356934i	$-0.116178\pi$
$37$	−0.190983	−	0.587785i	−0.0313974	−	0.0966313i	−0.965527	+	0.260302i	$0.916178\pi$
$38$		0			0
$39$	−1.73607	+	5.34307i	−0.277993	+	0.855576i
$40$		0			0
$41$	2.92705	+	9.00854i	0.457129	+	1.40690i	0.868618	+	0.495482i	$0.165009\pi$
$41$	2.92705	+	9.00854i	0.457129	+	1.40690i	−0.411489	+	0.911415i	$0.634991\pi$
$42$		0			0
$43$	−2.52786			−0.385496			−0.192748	−	0.981248i	$-0.561740\pi$
$43$	−2.52786			−0.385496			−0.192748	+	0.981248i	$0.561740\pi$
$44$		0			0
$45$	−0.263932	+	0.812299i	−0.0393447	+	0.121090i
$46$		0			0
$47$	7.04508	+	5.11855i	1.02763	+	0.746618i	0.967833	−	0.251593i	$-0.0809543\pi$
$47$	7.04508	+	5.11855i	1.02763	+	0.746618i	0.0597980	+	0.998210i	$0.480954\pi$
$48$		0			0
$49$	−6.94427			−0.992039
$50$		0			0
$51$	−4.61803			−0.646654
$52$		0			0
$53$	−2.00000	−	1.45309i	−0.274721	−	0.199597i	0.441891	−	0.897069i	$-0.354308\pi$
$53$	−2.00000	−	1.45309i	−0.274721	−	0.199597i	−0.716612	+	0.697472i	$0.754308\pi$
$54$		0			0
$55$	1.80902	−	1.31433i	0.243928	−	0.177224i
$56$		0			0
$57$	8.23607			1.09089
$58$		0			0
$59$	3.09017	+	9.51057i	0.402306	+	1.23817i	0.923124	+	0.384502i	$0.125627\pi$
$59$	3.09017	+	9.51057i	0.402306	+	1.23817i	−0.520818	+	0.853668i	$0.674373\pi$
$60$		0			0
$61$	−0.500000	+	1.53884i	−0.0640184	+	0.197028i	−0.977950	−	0.208840i	$-0.933031\pi$
$61$	−0.500000	+	1.53884i	−0.0640184	+	0.197028i	0.913931	+	0.405869i	$0.133031\pi$
$62$		0			0
$63$	−0.0278640	−	0.0857567i	−0.00351054	−	0.0108043i
$64$		0			0
$65$	−2.39919	+	7.38394i	−0.297583	+	0.915865i
$66$		0			0
$67$	−3.66312	+	2.66141i	−0.447521	+	0.325143i	−0.788616	−	0.614886i	$-0.789202\pi$
$67$	−3.66312	+	2.66141i	−0.447521	+	0.325143i	0.341095	+	0.940029i	$0.389202\pi$
$68$		0			0
$69$	1.30902	−	0.951057i	0.157587	−	0.114494i
$70$		0			0
$71$	−10.6631	−	7.74721i	−1.26548	−	0.919425i	−0.266466	−	0.963844i	$-0.585856\pi$
$71$	−10.6631	−	7.74721i	−1.26548	−	0.919425i	−0.999013	+	0.0444196i	$0.985856\pi$
$72$		0			0
$73$	−0.854102	+	2.62866i	−0.0999651	+	0.307661i	−0.988516	−	0.151118i	$-0.951713\pi$
$73$	−0.854102	+	2.62866i	−0.0999651	+	0.307661i	0.888551	+	0.458778i	$0.151713\pi$
$74$		0			0
$75$	2.50000	−	7.69421i	0.288675	−	0.888451i
$76$		0			0
$77$	−0.0729490	+	0.224514i	−0.00831331	+	0.0255857i
$78$		0			0
$79$	−7.85410	−	5.70634i	−0.883656	−	0.642013i	0.0505605	−	0.998721i	$-0.483899\pi$
$79$	−7.85410	−	5.70634i	−0.883656	−	0.642013i	−0.934216	+	0.356708i	$0.883899\pi$
$80$		0			0
$81$	6.23607	−	4.53077i	0.692896	−	0.503419i
$82$		0			0
$83$	9.89919	−	7.19218i	1.08658	−	0.789444i	0.107759	−	0.994177i	$-0.465633\pi$
$83$	9.89919	−	7.19218i	1.08658	−	0.789444i	0.978818	+	0.204733i	$0.0656325\pi$
$84$		0			0
$85$	−6.38197			−0.692221
$86$		0			0
$87$	1.50000	+	4.61653i	0.160817	+	0.494943i
$88$		0			0
$89$	−2.90983	+	8.95554i	−0.308441	+	0.949285i	0.669929	+	0.742425i	$0.266324\pi$
$89$	−2.90983	+	8.95554i	−0.308441	+	0.949285i	−0.978371	+	0.206860i	$0.933676\pi$
$90$		0			0
$91$	−0.253289	−	0.779543i	−0.0265519	−	0.0817183i
$92$		0			0
$93$	8.85410			0.918128
$94$		0			0
$95$	11.3820			1.16777
$96$		0			0
$97$	0.263932	+	0.191758i	0.0267982	+	0.0194701i	0.601104	−	0.799171i	$-0.294728\pi$
$97$	0.263932	+	0.191758i	0.0267982	+	0.0194701i	−0.574306	+	0.818641i	$0.694728\pi$
$98$		0			0
$99$	0.381966			0.0383890
$100$		0			0
$101$	−4.61803			−0.459512			−0.229756	−	0.973248i	$-0.573793\pi$
$101$	−4.61803			−0.459512			−0.229756	+	0.973248i	$0.573793\pi$
$102$		0			0
$103$	−11.7812	−	8.55951i	−1.16083	−	0.843393i	−0.170949	−	0.985280i	$-0.554683\pi$
$103$	−11.7812	−	8.55951i	−1.16083	−	0.843393i	−0.989883	+	0.141887i	$0.954683\pi$
$104$		0			0
$105$	0.263932	+	0.812299i	0.0257571	+	0.0792723i
$106$		0			0
$107$	7.09017			0.685433			0.342716	−	0.939439i	$-0.388653\pi$
$107$	7.09017			0.685433			0.342716	+	0.939439i	$0.388653\pi$
$108$		0			0
$109$	−3.83688	−	11.8087i	−0.367507	−	1.13107i	−0.948397	−	0.317087i	$-0.897295\pi$
$109$	−3.83688	−	11.8087i	−0.367507	−	1.13107i	0.580890	−	0.813982i	$-0.302705\pi$
$110$		0			0
$111$	−0.309017	+	0.951057i	−0.0293306	+	0.0902703i
$112$		0			0
$113$	−6.07295	−	18.6906i	−0.571295	−	1.75827i	−0.648462	−	0.761247i	$-0.724587\pi$
$113$	−6.07295	−	18.6906i	−0.571295	−	1.75827i	0.0771670	−	0.997018i	$-0.475413\pi$
$114$		0			0
$115$	1.80902	−	1.31433i	0.168692	−	0.122562i
$116$		0			0
$117$	−1.07295	+	0.779543i	−0.0991942	+	0.0720688i
$118$		0			0
$119$	0.545085	−	0.396027i	0.0499679	−	0.0363038i
$120$		0			0
$121$	8.09017	+	5.87785i	0.735470	+	0.534350i
$122$		0			0
$123$	4.73607	−	14.5761i	0.427037	−	1.31428i
$124$		0			0
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$		0			0
$127$	−0.909830	+	2.80017i	−0.0807344	+	0.248475i	−0.983274	−	0.182132i	$-0.941700\pi$
$127$	−0.909830	+	2.80017i	−0.0807344	+	0.248475i	0.902540	+	0.430606i	$0.141700\pi$
$128$		0			0
$129$	3.30902	+	2.40414i	0.291343	+	0.211673i
$130$		0			0
$131$	0.572949	−	0.416272i	0.0500588	−	0.0363698i	−0.562474	−	0.826815i	$-0.690151\pi$
$131$	0.572949	−	0.416272i	0.0500588	−	0.0363698i	0.612533	+	0.790445i	$0.290151\pi$
$132$		0			0
$133$	−0.972136	+	0.706298i	−0.0842949	+	0.0612438i
$134$		0			0
$135$	9.89919	−	7.19218i	0.851986	−	0.619004i
$136$		0			0
$137$	0.336881	+	1.03681i	0.0287817	+	0.0885809i	0.964416	−	0.264391i	$-0.0851710\pi$
$137$	0.336881	+	1.03681i	0.0287817	+	0.0885809i	−0.935634	+	0.352972i	$0.885171\pi$
$138$		0			0
$139$	−5.97214	+	18.3803i	−0.506550	+	1.55900i	0.291599	+	0.956541i	$0.405813\pi$
$139$	−5.97214	+	18.3803i	−0.506550	+	1.55900i	−0.798149	+	0.602460i	$0.794187\pi$
$140$		0			0
$141$	−4.35410	−	13.4005i	−0.366682	−	1.12853i
$142$		0			0
$143$	3.47214			0.290355
$144$		0			0
$145$	2.07295	+	6.37988i	0.172149	+	0.529820i
$146$		0			0
$147$	9.09017	+	6.60440i	0.749745	+	0.544721i
$148$		0			0
$149$	6.70820			0.549557			0.274779	−	0.961507i	$-0.411395\pi$
$149$	6.70820			0.549557			0.274779	+	0.961507i	$0.411395\pi$
$150$		0			0
$151$	−10.6525			−0.866886			−0.433443	−	0.901181i	$-0.642701\pi$
$151$	−10.6525			−0.866886			−0.433443	+	0.901181i	$0.642701\pi$
$152$		0			0
$153$	−0.881966	−	0.640786i	−0.0713027	−	0.0518045i
$154$		0			0
$155$	12.2361			0.982825
$156$		0			0
$157$	−9.14590			−0.729922			−0.364961	−	0.931023i	$-0.618918\pi$
$157$	−9.14590			−0.729922			−0.364961	+	0.931023i	$0.618918\pi$
$158$		0			0
$159$	1.23607	+	3.80423i	0.0980266	+	0.301695i
$160$		0			0
$161$	−0.0729490	+	0.224514i	−0.00574919	+	0.0176942i
$162$		0			0
$163$	−6.13525	−	18.8824i	−0.480550	−	1.47898i	−0.838323	−	0.545173i	$-0.816464\pi$
$163$	−6.13525	−	18.8824i	−0.480550	−	1.47898i	0.357773	−	0.933808i	$-0.383536\pi$
$164$		0			0
$165$	−3.61803			−0.281664
$166$		0			0
$167$	18.2082	−	13.2290i	1.40899	−	1.02369i	0.415525	−	0.909582i	$-0.363598\pi$
$167$	18.2082	−	13.2290i	1.40899	−	1.02369i	0.993468	−	0.114112i	$-0.0364022\pi$
$168$		0			0
$169$	0.763932	−	0.555029i	0.0587640	−	0.0426945i
$170$		0			0
$171$	1.57295	+	1.14281i	0.120286	+	0.0873932i
$172$		0			0
$173$	−3.79837	+	11.6902i	−0.288785	+	0.888789i	0.696454	+	0.717602i	$0.254760\pi$
$173$	−3.79837	+	11.6902i	−0.288785	+	0.888789i	−0.985239	+	0.171187i	$0.945240\pi$
$174$		0			0
$175$	0.364745	+	1.12257i	0.0275721	+	0.0848583i
$176$		0			0
$177$	5.00000	−	15.3884i	0.375823	−	1.15666i
$178$		0			0
$179$	−8.51722	−	6.18812i	−0.636607	−	0.462522i	0.222076	−	0.975029i	$-0.428717\pi$
$179$	−8.51722	−	6.18812i	−0.636607	−	0.462522i	−0.858683	+	0.512507i	$0.828717\pi$
$180$		0			0
$181$	−13.3262	+	9.68208i	−0.990531	+	0.719663i	−0.960037	−	0.279872i	$-0.909708\pi$
$181$	−13.3262	+	9.68208i	−0.990531	+	0.719663i	−0.0304941	+	0.999535i	$0.509708\pi$
$182$		0			0
$183$	2.11803	−	1.53884i	0.156570	−	0.113754i
$184$		0			0
$185$	−0.427051	+	1.31433i	−0.0313974	+	0.0966313i
$186$		0			0
$187$	0.881966	+	2.71441i	0.0644957	+	0.198497i
$188$		0			0
$189$	−0.399187	+	1.22857i	−0.0290366	+	0.0893654i
$190$		0			0
$191$	−5.10739	−	15.7189i	−0.369558	−	1.13738i	−0.947077	−	0.321005i	$-0.895979\pi$
$191$	−5.10739	−	15.7189i	−0.369558	−	1.13738i	0.577520	−	0.816377i	$-0.304021\pi$
$192$		0			0
$193$	9.70820			0.698812			0.349406	−	0.936971i	$-0.386383\pi$
$193$	9.70820			0.698812			0.349406	+	0.936971i	$0.386383\pi$
$194$		0			0
$195$	10.1631	−	7.38394i	0.727796	−	0.528775i
$196$		0			0
$197$	−0.763932	−	0.555029i	−0.0544279	−	0.0395442i	0.560239	−	0.828331i	$-0.310709\pi$
$197$	−0.763932	−	0.555029i	−0.0544279	−	0.0395442i	−0.614667	+	0.788787i	$0.710709\pi$
$198$		0			0
$199$	−2.09017			−0.148168			−0.0740841	−	0.997252i	$-0.523603\pi$
$199$	−2.09017			−0.148168			−0.0740841	+	0.997252i	$0.523603\pi$
$200$		0			0
$201$	7.32624			0.516753
$202$		0			0
$203$	−0.572949	−	0.416272i	−0.0402131	−	0.0292166i
$204$		0			0
$205$	6.54508	−	20.1437i	0.457129	−	1.40690i
$206$		0			0
$207$	0.381966			0.0265485
$208$		0			0
$209$	−1.57295	−	4.84104i	−0.108803	−	0.334862i
$210$		0			0
$211$	4.68034	−	14.4046i	0.322208	−	0.991654i	−0.650477	−	0.759526i	$-0.725431\pi$
$211$	4.68034	−	14.4046i	0.322208	−	0.991654i	0.972685	−	0.232128i	$-0.0745689\pi$
$212$		0			0
$213$	6.59017	+	20.2825i	0.451551	+	1.38973i
$214$		0			0
$215$	4.57295	+	3.32244i	0.311873	+	0.226589i
$216$		0			0
$217$	−1.04508	+	0.759299i	−0.0709450	+	0.0515446i
$218$		0			0
$219$	3.61803	−	2.62866i	0.244484	−	0.177628i
$220$		0			0
$221$	−8.01722	−	5.82485i	−0.539297	−	0.391822i
$222$		0			0
$223$	6.10739	−	18.7966i	0.408981	−	1.25871i	−0.508544	−	0.861036i	$-0.669816\pi$
$223$	6.10739	−	18.7966i	0.408981	−	1.25871i	0.917525	−	0.397678i	$-0.130184\pi$
$224$		0			0
$225$	1.54508	−	1.12257i	0.103006	−	0.0748380i
$226$		0			0
$227$	−4.07295	+	12.5352i	−0.270331	+	0.831994i	0.720086	+	0.693885i	$0.244102\pi$
$227$	−4.07295	+	12.5352i	−0.270331	+	0.831994i	−0.990417	+	0.138109i	$0.955898\pi$
$228$		0			0
$229$	19.6353	+	14.2658i	1.29753	+	0.942714i	0.999928	−	0.0119751i	$-0.00381187\pi$
$229$	19.6353	+	14.2658i	1.29753	+	0.942714i	0.297606	+	0.954689i	$0.403812\pi$
$230$		0			0
$231$	0.309017	−	0.224514i	0.0203318	−	0.0147719i
$232$		0			0
$233$	−22.3262	+	16.2210i	−1.46264	+	1.06267i	−0.479975	+	0.877282i	$0.659354\pi$
$233$	−22.3262	+	16.2210i	−1.46264	+	1.06267i	−0.982665	+	0.185388i	$0.940646\pi$
$234$		0			0
$235$	−6.01722	−	18.5191i	−0.392520	−	1.20805i
$236$		0			0
$237$	4.85410	+	14.9394i	0.315308	+	0.970418i
$238$		0			0
$239$	−3.80902	+	11.7229i	−0.246385	+	0.758295i	0.749021	+	0.662547i	$0.230524\pi$
$239$	−3.80902	+	11.7229i	−0.246385	+	0.758295i	−0.995406	+	0.0957480i	$0.969476\pi$
$240$		0			0
$241$	−2.40983	−	7.41669i	−0.155231	−	0.477751i	0.842953	−	0.537987i	$-0.180815\pi$
$241$	−2.40983	−	7.41669i	−0.155231	−	0.477751i	−0.998184	+	0.0602353i	$0.980815\pi$
$242$		0			0
$243$	3.94427			0.253025
$244$		0			0
$245$	12.5623	+	9.12705i	0.802576	+	0.583106i
$246$		0			0
$247$	14.2984	+	10.3884i	0.909784	+	0.660997i
$248$		0			0
$249$	−19.7984			−1.25467
$250$		0			0
$251$	−19.4721			−1.22907			−0.614535	−	0.788889i	$-0.710656\pi$
$251$	−19.4721			−1.22907			−0.614535	+	0.788889i	$0.710656\pi$
$252$		0			0
$253$	−0.809017	−	0.587785i	−0.0508625	−	0.0369537i
$254$		0			0
$255$	8.35410	+	6.06961i	0.523154	+	0.380094i
$256$		0			0
$257$	−9.09017			−0.567029			−0.283515	−	0.958968i	$-0.591500\pi$
$257$	−9.09017			−0.567029			−0.283515	+	0.958968i	$0.591500\pi$
$258$		0			0
$259$	−0.0450850	−	0.138757i	−0.00280144	−	0.00862196i
$260$		0			0
$261$	−0.354102	+	1.08981i	−0.0219184	+	0.0674578i
$262$		0			0
$263$	−1.19098	−	3.66547i	−0.0734392	−	0.226022i	0.907599	−	0.419839i	$-0.137913\pi$
$263$	−1.19098	−	3.66547i	−0.0734392	−	0.226022i	−0.981038	+	0.193816i	$0.937913\pi$
$264$		0			0
$265$	1.70820	+	5.25731i	0.104934	+	0.322954i
$266$		0			0
$267$	12.3262	−	8.95554i	0.754354	−	0.548070i
$268$		0			0
$269$	21.2533	−	15.4414i	1.29584	−	0.941480i	0.295930	−	0.955210i	$-0.404370\pi$
$269$	21.2533	−	15.4414i	1.29584	−	0.941480i	0.999906	+	0.0137297i	$0.00437043\pi$
$270$		0			0
$271$	−12.2082	−	8.86978i	−0.741596	−	0.538801i	0.151615	−	0.988440i	$-0.451553\pi$
$271$	−12.2082	−	8.86978i	−0.741596	−	0.538801i	−0.893210	+	0.449639i	$0.851553\pi$
$272$		0			0
$273$	−0.409830	+	1.26133i	−0.0248040	+	0.0763390i
$274$		0			0
$275$	−5.00000			−0.301511
$276$		0			0
$277$	−8.85410	+	27.2501i	−0.531991	+	1.63730i	0.218070	+	0.975933i	$0.430024\pi$
$277$	−8.85410	+	27.2501i	−0.531991	+	1.63730i	−0.750061	+	0.661368i	$0.769976\pi$
$278$		0			0
$279$	1.69098	+	1.22857i	0.101237	+	0.0735526i
$280$		0			0
$281$	2.66312	−	1.93487i	0.158868	−	0.115425i	−0.505511	−	0.862820i	$-0.668696\pi$
$281$	2.66312	−	1.93487i	0.158868	−	0.115425i	0.664379	+	0.747396i	$0.268696\pi$
$282$		0			0
$283$	−3.76393	+	2.73466i	−0.223743	+	0.162558i	−0.694010	−	0.719966i	$-0.744158\pi$
$283$	−3.76393	+	2.73466i	−0.223743	+	0.162558i	0.470267	+	0.882524i	$0.344158\pi$
$284$		0			0
$285$	−14.8992	−	10.8249i	−0.882552	−	0.641211i
$286$		0			0
$287$	0.690983	+	2.12663i	0.0407874	+	0.125531i
$288$		0			0
$289$	−2.73607	+	8.42075i	−0.160945	+	0.495338i
$290$		0			0
$291$	−0.163119	−	0.502029i	−0.00956220	−	0.0294294i
$292$		0			0
$293$	31.7984			1.85768			0.928840	−	0.370480i	$-0.120807\pi$
$293$	31.7984			1.85768			0.928840	+	0.370480i	$0.120807\pi$
$294$		0			0
$295$	6.90983	−	21.2663i	0.402306	−	1.23817i
$296$		0			0
$297$	−4.42705	−	3.21644i	−0.256884	−	0.186637i
$298$		0			0
$299$	3.47214			0.200799
$300$		0			0
$301$	−0.596748			−0.0343960
$302$		0			0
$303$	6.04508	+	4.39201i	0.347281	+	0.252314i
$304$		0			0
$305$	2.92705	−	2.12663i	0.167602	−	0.121770i
$306$		0			0
$307$	−27.1246			−1.54808			−0.774042	−	0.633135i	$-0.781768\pi$
$307$	−27.1246			−1.54808			−0.774042	+	0.633135i	$0.781768\pi$
$308$		0			0
$309$	7.28115	+	22.4091i	0.414210	+	1.27481i
$310$		0			0
$311$	−8.79180	+	27.0584i	−0.498537	+	1.53434i	0.312834	+	0.949808i	$0.398722\pi$
$311$	−8.79180	+	27.0584i	−0.498537	+	1.53434i	−0.811371	+	0.584531i	$0.801278\pi$
$312$		0			0
$313$	−7.88197	−	24.2582i	−0.445515	−	1.37115i	−0.881918	−	0.471403i	$-0.843748\pi$
$313$	−7.88197	−	24.2582i	−0.445515	−	1.37115i	0.436403	−	0.899751i	$-0.356252\pi$
$314$		0			0
$315$	−0.0623059	+	0.191758i	−0.00351054	+	0.0108043i
$316$		0			0
$317$	−16.6353	+	12.0862i	−0.934329	+	0.678830i	−0.947049	−	0.321089i	$-0.895951\pi$
$317$	−16.6353	+	12.0862i	−0.934329	+	0.678830i	0.0127199	+	0.999919i	$0.495951\pi$
$318$		0			0
$319$	2.42705	−	1.76336i	0.135889	−	0.0987290i
$320$		0			0
$321$	−9.28115	−	6.74315i	−0.518023	−	0.376366i
$322$		0			0
$323$	−4.48936	+	13.8168i	−0.249794	+	0.768788i
$324$		0			0
$325$	14.0451	−	10.2044i	0.779081	−	0.566036i
$326$		0			0
$327$	−6.20820	+	19.1069i	−0.343314	+	1.05661i
$328$		0			0
$329$	1.66312	+	1.20833i	0.0916907	+	0.0666172i
$330$		0			0
$331$	−15.4443	+	11.2209i	−0.848894	+	0.616758i	−0.924841	−	0.380354i	$-0.875802\pi$
$331$	−15.4443	+	11.2209i	−0.848894	+	0.616758i	0.0759469	+	0.997112i	$0.475802\pi$
$332$		0			0
$333$	−0.190983	+	0.138757i	−0.0104658	+	0.00760385i
$334$		0			0
$335$	10.1246			0.553167
$336$		0			0
$337$	−9.41641	−	28.9807i	−0.512944	−	1.57868i	−0.786991	−	0.616964i	$-0.788362\pi$
$337$	−9.41641	−	28.9807i	−0.512944	−	1.57868i	0.274047	−	0.961716i	$-0.411638\pi$
$338$		0			0
$339$	−9.82624	+	30.2421i	−0.533688	+	1.64252i
$340$		0			0
$341$	−1.69098	−	5.20431i	−0.0915719	−	0.281829i
$342$		0			0
$343$	−3.29180			−0.177740
$344$		0			0
$345$	−3.61803			−0.194788
$346$		0			0
$347$	14.4443	+	10.4944i	0.775409	+	0.563368i	0.903598	−	0.428382i	$-0.140916\pi$
$347$	14.4443	+	10.4944i	0.775409	+	0.563368i	−0.128189	+	0.991750i	$0.540916\pi$
$348$		0			0
$349$	14.7082			0.787312			0.393656	−	0.919258i	$-0.371210\pi$
$349$	14.7082			0.787312			0.393656	+	0.919258i	$0.371210\pi$
$350$		0			0
$351$	19.0000			1.01414
$352$		0			0
$353$	−6.70820	−	4.87380i	−0.357042	−	0.259406i	0.394775	−	0.918778i	$-0.370822\pi$
$353$	−6.70820	−	4.87380i	−0.357042	−	0.259406i	−0.751817	+	0.659372i	$0.770822\pi$
$354$		0			0
$355$	9.10739	+	28.0297i	0.483370	+	1.48766i
$356$		0			0
$357$	−1.09017			−0.0576979
$358$		0			0
$359$	1.29837	+	3.99598i	0.0685256	+	0.210900i	0.979455	−	0.201662i	$-0.0646341\pi$
$359$	1.29837	+	3.99598i	0.0685256	+	0.210900i	−0.910930	+	0.412562i	$0.864634\pi$
$360$		0			0
$361$	2.13525	−	6.57164i	0.112382	−	0.345876i
$362$		0			0
$363$	−5.00000	−	15.3884i	−0.262432	−	0.807682i
$364$		0			0
$365$	5.00000	−	3.63271i	0.261712	−	0.190145i
$366$		0			0
$367$	−15.6631	+	11.3799i	−0.817608	+	0.594027i	−0.916026	−	0.401118i	$-0.868622\pi$
$367$	−15.6631	+	11.3799i	−0.817608	+	0.594027i	0.0984182	+	0.995145i	$0.468622\pi$
$368$		0			0
$369$	2.92705	−	2.12663i	0.152376	−	0.110708i
$370$		0			0
$371$	−0.472136	−	0.343027i	−0.0245121	−	0.0178091i
$372$		0			0
$373$	−9.30902	+	28.6502i	−0.482003	+	1.48345i	0.354273	+	0.935142i	$0.384728\pi$
$373$	−9.30902	+	28.6502i	−0.482003	+	1.48345i	−0.836276	+	0.548309i	$0.815272\pi$
$374$		0			0
$375$	−14.6353	+	10.6331i	−0.755761	+	0.549093i
$376$		0			0
$377$	−3.21885	+	9.90659i	−0.165779	+	0.510215i
$378$		0			0
$379$	−21.1353	−	15.3557i	−1.08565	−	0.788767i	−0.106987	−	0.994260i	$-0.534120\pi$
$379$	−21.1353	−	15.3557i	−1.08565	−	0.788767i	−0.978659	+	0.205493i	$0.934120\pi$
$380$		0			0
$381$	3.85410	−	2.80017i	0.197452	−	0.143457i
$382$		0			0
$383$	−14.1631	+	10.2901i	−0.723702	+	0.525800i	−0.887565	−	0.460683i	$-0.847604\pi$
$383$	−14.1631	+	10.2901i	−0.723702	+	0.525800i	0.163863	+	0.986483i	$0.447604\pi$
$384$		0			0
$385$	0.427051	−	0.310271i	0.0217645	−	0.0158129i
$386$		0			0
$387$	0.298374	+	0.918300i	0.0151672	+	0.0466798i
$388$		0			0
$389$	4.19098	−	12.8985i	0.212491	−	0.653981i	−0.786831	−	0.617169i	$-0.788280\pi$
$389$	4.19098	−	12.8985i	0.212491	−	0.653981i	0.999322	−	0.0368123i	$-0.0117204\pi$
$390$		0			0
$391$	0.881966	+	2.71441i	0.0446029	+	0.137274i
$392$		0			0
$393$	−1.14590			−0.0578029
$394$		0			0
$395$	6.70820	+	20.6457i	0.337526	+	1.03880i
$396$		0			0
$397$	2.19098	+	1.59184i	0.109962	+	0.0798923i	0.641407	−	0.767200i	$-0.278351\pi$
$397$	2.19098	+	1.59184i	0.109962	+	0.0798923i	−0.531445	+	0.847093i	$0.678351\pi$
$398$		0			0
$399$	1.94427			0.0973353
$400$		0			0
$401$	3.12461			0.156036			0.0780178	−	0.996952i	$-0.475141\pi$
$401$	3.12461			0.156036			0.0780178	+	0.996952i	$0.475141\pi$
$402$		0			0
$403$	15.3713	+	11.1679i	0.765700	+	0.556314i
$404$		0			0
$405$	−17.2361			−0.856467
$406$		0			0
$407$	0.618034			0.0306348
$408$		0			0
$409$	−8.72542	−	26.8541i	−0.431444	−	1.32785i	−0.896687	−	0.442666i	$-0.854033\pi$
$409$	−8.72542	−	26.8541i	−0.431444	−	1.32785i	0.465242	−	0.885184i	$-0.345967\pi$
$410$		0			0
$411$	0.545085	−	1.67760i	0.0268871	−	0.0827499i
$412$		0			0
$413$	0.729490	+	2.24514i	0.0358959	+	0.110476i
$414$		0			0
$415$	−27.3607			−1.34308
$416$		0			0
$417$	25.2984	−	18.3803i	1.23887	−	0.900089i
$418$		0			0
$419$	21.1803	−	15.3884i	1.03473	−	0.751773i	0.0654780	−	0.997854i	$-0.479143\pi$
$419$	21.1803	−	15.3884i	1.03473	−	0.751773i	0.969249	+	0.246081i	$0.0791428\pi$
$420$		0			0
$421$	−6.97214	−	5.06555i	−0.339801	−	0.246880i	0.404777	−	0.914416i	$-0.367349\pi$
$421$	−6.97214	−	5.06555i	−0.339801	−	0.246880i	−0.744578	+	0.667536i	$0.767349\pi$
$422$		0			0
$423$	1.02786	−	3.16344i	0.0499765	−	0.153812i
$424$		0			0
$425$	11.5451	+	8.38800i	0.560019	+	0.406878i
$426$		0			0
$427$	−0.118034	+	0.363271i	−0.00571207	+	0.0175799i
$428$		0			0
$429$	−4.54508	−	3.30220i	−0.219439	−	0.159432i
$430$		0			0
$431$	3.09017	−	2.24514i	0.148848	−	0.108145i	−0.510869	−	0.859659i	$-0.670676\pi$
$431$	3.09017	−	2.24514i	0.148848	−	0.108145i	0.659717	+	0.751514i	$0.270676\pi$
$432$		0			0
$433$	−1.19098	+	0.865300i	−0.0572350	+	0.0415837i	−0.616035	−	0.787719i	$-0.711262\pi$
$433$	−1.19098	+	0.865300i	−0.0572350	+	0.0415837i	0.558800	+	0.829303i	$0.311262\pi$
$434$		0			0
$435$	3.35410	−	10.3229i	0.160817	−	0.494943i
$436$		0			0
$437$	−1.57295	−	4.84104i	−0.0752444	−	0.231578i
$438$		0			0
$439$	−12.7812	+	39.3363i	−0.610011	+	1.87742i	−0.152261	+	0.988340i	$0.548655\pi$
$439$	−12.7812	+	39.3363i	−0.610011	+	1.87742i	−0.457750	+	0.889081i	$0.651345\pi$
$440$		0			0
$441$	0.819660	+	2.52265i	0.0390314	+	0.120126i
$442$		0			0
$443$	−22.4721			−1.06768			−0.533842	−	0.845584i	$-0.679252\pi$
$443$	−22.4721			−1.06768			−0.533842	+	0.845584i	$0.679252\pi$
$444$		0			0
$445$	17.0344	−	12.3762i	0.807510	−	0.586690i
$446$		0			0
$447$	−8.78115	−	6.37988i	−0.415334	−	0.301758i
$448$		0			0
$449$	−23.0000			−1.08544			−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000			−1.08544			−0.542719	+	0.839915i	$0.682605\pi$
$450$		0			0
$451$	−9.47214			−0.446025
$452$		0			0
$453$	13.9443	+	10.1311i	0.655159	+	0.476001i
$454$		0			0
$455$	−0.566371	+	1.74311i	−0.0265519	+	0.0817183i
$456$		0			0
$457$	9.74265			0.455742			0.227871	−	0.973691i	$-0.426824\pi$
$457$	9.74265			0.455742			0.227871	+	0.973691i	$0.426824\pi$
$458$		0			0
$459$	4.82624	+	14.8536i	0.225269	+	0.693308i
$460$		0			0
$461$	2.38197	−	7.33094i	0.110939	−	0.341436i	−0.880139	−	0.474716i	$-0.842551\pi$
$461$	2.38197	−	7.33094i	0.110939	−	0.341436i	0.991078	+	0.133280i	$0.0425509\pi$
$462$		0			0
$463$	0.392609	+	1.20833i	0.0182461	+	0.0561557i	0.959765	−	0.280804i	$-0.0906012\pi$
$463$	0.392609	+	1.20833i	0.0182461	+	0.0561557i	−0.941519	+	0.336960i	$0.890601\pi$
$464$		0			0
$465$	−16.0172	−	11.6372i	−0.742781	−	0.539662i
$466$		0			0
$467$	19.7533	−	14.3516i	0.914073	−	0.664113i	−0.0279685	−	0.999609i	$-0.508904\pi$
$467$	19.7533	−	14.3516i	0.914073	−	0.664113i	0.942042	+	0.335496i	$0.108904\pi$
$468$		0			0
$469$	−0.864745	+	0.628274i	−0.0399302	+	0.0290110i
$470$		0			0
$471$	11.9721	+	8.69827i	0.551647	+	0.400795i
$472$		0			0
$473$	0.781153	−	2.40414i	0.0359175	−	0.110543i
$474$		0			0
$475$	−20.5902	−	14.9596i	−0.944742	−	0.686395i
$476$		0			0
$477$	−0.291796	+	0.898056i	−0.0133604	+	0.0411192i
$478$		0			0
$479$	−33.8607	−	24.6012i	−1.54713	−	1.12406i	−0.945656	−	0.325169i	$-0.894579\pi$
$479$	−33.8607	−	24.6012i	−1.54713	−	1.12406i	−0.601478	−	0.798889i	$-0.705421\pi$
$480$		0			0
$481$	−1.73607	+	1.26133i	−0.0791579	+	0.0575116i
$482$		0			0
$483$	0.309017	−	0.224514i	0.0140608	−	0.0102157i
$484$		0			0
$485$	−0.225425	−	0.693786i	−0.0102360	−	0.0315032i
$486$		0			0
$487$	−9.39919	−	28.9277i	−0.425918	−	1.31084i	−0.902113	−	0.431500i	$-0.857984\pi$
$487$	−9.39919	−	28.9277i	−0.425918	−	1.31084i	0.476195	−	0.879340i	$-0.342016\pi$
$488$		0			0
$489$	−9.92705	+	30.5523i	−0.448917	+	1.38162i
$490$		0			0
$491$	3.29180	+	10.1311i	0.148557	+	0.457210i	0.997451	−	0.0713518i	$-0.0227313\pi$
$491$	3.29180	+	10.1311i	0.148557	+	0.457210i	−0.848895	+	0.528562i	$0.822731\pi$
$492$		0			0
$493$	−8.56231			−0.385627
$494$		0			0
$495$	−0.690983	−	0.502029i	−0.0310574	−	0.0225645i
$496$		0			0
$497$	−2.51722	−	1.82887i	−0.112913	−	0.0820359i
$498$		0			0
$499$	−0.729490			−0.0326565			−0.0163282	−	0.999867i	$-0.505198\pi$
$499$	−0.729490			−0.0326565			−0.0163282	+	0.999867i	$0.505198\pi$
$500$		0			0
$501$	−36.4164			−1.62697
$502$		0			0
$503$	−9.59017	−	6.96767i	−0.427605	−	0.310673i	0.353086	−	0.935591i	$-0.385132\pi$
$503$	−9.59017	−	6.96767i	−0.427605	−	0.310673i	−0.780690	+	0.624918i	$0.785132\pi$
$504$		0			0
$505$	8.35410	+	6.06961i	0.371753	+	0.270094i
$506$		0			0
$507$	−1.52786			−0.0678548
$508$		0			0
$509$	−0.826238	−	2.54290i	−0.0366224	−	0.112712i	0.931074	−	0.364830i	$-0.118873\pi$
$509$	−0.826238	−	2.54290i	−0.0366224	−	0.112712i	−0.967697	+	0.252118i	$0.918873\pi$
$510$		0			0
$511$	−0.201626	+	0.620541i	−0.00891941	+	0.0274511i
$512$		0			0
$513$	−8.60739	−	26.4908i	−0.380026	−	1.16960i
$514$		0			0
$515$	10.0623	+	30.9686i	0.443398	+	1.36464i
$516$		0			0
$517$	−7.04508	+	5.11855i	−0.309842	+	0.225114i
$518$		0			0
$519$	16.0902	−	11.6902i	0.706280	−	0.513143i
$520$		0			0
$521$	24.3885	+	17.7193i	1.06848	+	0.776297i	0.975639	−	0.219384i	$-0.0704046\pi$
$521$	24.3885	+	17.7193i	1.06848	+	0.776297i	0.0928428	+	0.995681i	$0.470405\pi$
$522$		0			0
$523$	−6.09017	+	18.7436i	−0.266305	+	0.819601i	0.725085	+	0.688659i	$0.241800\pi$
$523$	−6.09017	+	18.7436i	−0.266305	+	0.819601i	−0.991390	+	0.130942i	$0.958200\pi$
$524$		0			0
$525$	0.590170	−	1.81636i	0.0257571	−	0.0792723i
$526$		0			0
$527$	−4.82624	+	14.8536i	−0.210234	+	0.647034i
$528$		0			0
$529$	17.7984	+	12.9313i	0.773842	+	0.562229i
$530$		0			0
$531$	3.09017	−	2.24514i	0.134102	−	0.0974308i
$532$		0			0
$533$	26.6074	−	19.3314i	1.15249	−	0.837336i
$534$		0			0
$535$	−12.8262	−	9.31881i	−0.554527	−	0.402887i
$536$		0			0
$537$	5.26393	+	16.2007i	0.227155	+	0.699113i
$538$		0			0
$539$	2.14590	−	6.60440i	0.0924304	−	0.284471i
$540$		0			0
$541$	11.3435	+	34.9116i	0.487693	+	1.50097i	0.828042	+	0.560666i	$0.189455\pi$
$541$	11.3435	+	34.9116i	0.487693	+	1.50097i	−0.340348	+	0.940299i	$0.610545\pi$
$542$		0			0
$543$	26.6525			1.14377
$544$		0			0
$545$	−8.57953	+	26.4051i	−0.367507	+	1.13107i
$546$		0			0
$547$	5.30902	+	3.85723i	0.226997	+	0.164923i	0.695471	−	0.718554i	$-0.255196\pi$
$547$	5.30902	+	3.85723i	0.226997	+	0.164923i	−0.468474	+	0.883478i	$0.655196\pi$
$548$		0			0
$549$	0.618034			0.0263770
$550$		0			0
$551$	15.2705			0.650546
$552$		0			0
$553$	−1.85410	−	1.34708i	−0.0788444	−	0.0572838i
$554$		0			0
$555$	1.80902	−	1.31433i	0.0767885	−	0.0557901i
$556$		0			0
$557$	6.52786			0.276594			0.138297	−	0.990391i	$-0.455837\pi$
$557$	6.52786			0.276594			0.138297	+	0.990391i	$0.455837\pi$
$558$		0			0
$559$	2.71227	+	8.34751i	0.114717	+	0.353062i
$560$		0			0
$561$	1.42705	−	4.39201i	0.0602501	−	0.185431i
$562$		0			0
$563$	12.6631	+	38.9731i	0.533687	+	1.64252i	0.746470	+	0.665420i	$0.231747\pi$
$563$	12.6631	+	38.9731i	0.533687	+	1.64252i	−0.212783	+	0.977100i	$0.568253\pi$
$564$		0			0
$565$	−13.5795	+	41.7935i	−0.571295	+	1.75827i
$566$		0			0
$567$	1.47214	−	1.06957i	0.0618239	−	0.0449177i
$568$		0			0
$569$	−3.42705	+	2.48990i	−0.143669	+	0.104382i	−0.657298	−	0.753631i	$-0.728301\pi$
$569$	−3.42705	+	2.48990i	−0.143669	+	0.104382i	0.513629	+	0.858012i	$0.328301\pi$
$570$		0			0
$571$	12.5451	+	9.11454i	0.524995	+	0.381432i	0.818482	−	0.574532i	$-0.194816\pi$
$571$	12.5451	+	9.11454i	0.524995	+	0.381432i	−0.293487	+	0.955963i	$0.594816\pi$
$572$		0			0
$573$	−8.26393	+	25.4338i	−0.345231	+	1.06251i
$574$		0			0
$575$	−5.00000			−0.208514
$576$		0			0
$577$	8.89261	−	27.3686i	0.370204	−	1.13937i	−0.576453	−	0.817130i	$-0.695564\pi$
$577$	8.89261	−	27.3686i	0.370204	−	1.13937i	0.946658	−	0.322241i	$-0.104436\pi$
$578$		0			0
$579$	−12.7082	−	9.23305i	−0.528135	−	0.383712i
$580$		0			0
$581$	2.33688	−	1.69784i	0.0969502	−	0.0704384i
$582$		0			0
$583$	2.00000	−	1.45309i	0.0828315	−	0.0601806i
$584$		0			0
$585$	2.96556			0.122611
$586$		0			0
$587$	−8.74265	−	26.9071i	−0.360848	−	1.11057i	−0.952541	−	0.304411i	$-0.901540\pi$
$587$	−8.74265	−	26.9071i	−0.360848	−	1.11057i	0.591693	−	0.806163i	$-0.298460\pi$
$588$		0			0
$589$	8.60739	−	26.4908i	0.354661	−	1.09154i
$590$		0			0
$591$	0.472136	+	1.45309i	0.0194211	+	0.0597719i
$592$		0			0
$593$	3.70820			0.152278			0.0761388	−	0.997097i	$-0.475741\pi$
$593$	3.70820			0.152278			0.0761388	+	0.997097i	$0.475741\pi$
$594$		0			0
$595$	−1.50658			−0.0617637
$596$		0			0
$597$	2.73607	+	1.98787i	0.111980	+	0.0813581i
$598$		0			0
$599$	32.9443			1.34607			0.673033	−	0.739612i	$-0.264991\pi$
$599$	32.9443			1.34607			0.673033	+	0.739612i	$0.264991\pi$
$600$		0			0
$601$	24.0000			0.978980			0.489490	−	0.872009i	$-0.337183\pi$
$601$	24.0000			0.978980			0.489490	+	0.872009i	$0.337183\pi$
$602$		0			0
$603$	1.39919	+	1.01657i	0.0569793	+	0.0413979i
$604$		0			0
$605$	−6.90983	−	21.2663i	−0.280925	−	0.864597i
$606$		0			0
$607$	−36.7984			−1.49360			−0.746800	−	0.665049i	$-0.768411\pi$
$607$	−36.7984			−1.49360			−0.746800	+	0.665049i	$0.768411\pi$
$608$		0			0
$609$	0.354102	+	1.08981i	0.0143489	+	0.0441615i
$610$		0			0
$611$	9.34346	−	28.7562i	0.377996	−	1.16335i
$612$		0			0
$613$	−3.91641	−	12.0535i	−0.158182	−	0.486835i	0.840287	−	0.542142i	$-0.182386\pi$
$613$	−3.91641	−	12.0535i	−0.158182	−	0.486835i	−0.998469	+	0.0553067i	$0.982386\pi$
$614$		0			0
$615$	−27.7254	+	20.1437i	−1.11800	+	0.812272i
$616$		0			0
$617$	−10.8541	+	7.88597i	−0.436970	+	0.317477i	−0.784430	−	0.620218i	$-0.787044\pi$
$617$	−10.8541	+	7.88597i	−0.436970	+	0.317477i	0.347460	+	0.937695i	$0.387044\pi$
$618$		0			0
$619$	28.6074	−	20.7845i	1.14983	−	0.835399i	0.161370	−	0.986894i	$-0.448409\pi$
$619$	28.6074	−	20.7845i	1.14983	−	0.835399i	0.988458	+	0.151495i	$0.0484087\pi$
$620$		0			0
$621$	−4.42705	−	3.21644i	−0.177651	−	0.129071i
$622$		0			0
$623$	−0.686918	+	2.11412i	−0.0275208	+	0.0847002i
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$	−2.54508	+	7.83297i	−0.101641	+	0.312819i
$628$		0			0
$629$	−1.42705	−	1.03681i	−0.0569002	−	0.0413405i
$630$		0			0
$631$	9.32624	−	6.77591i	0.371272	−	0.269745i	−0.386466	−	0.922303i	$-0.626304\pi$
$631$	9.32624	−	6.77591i	0.371272	−	0.269745i	0.757738	+	0.652559i	$0.226304\pi$
$632$		0			0
$633$	−19.8262	+	14.4046i	−0.788022	+	0.572532i
$634$		0			0
$635$	5.32624	−	3.86974i	0.211365	−	0.153566i
$636$		0			0
$637$	7.45085	+	22.9314i	0.295213	+	0.908573i
$638$		0			0
$639$	−1.55573	+	4.78804i	−0.0615437	+	0.189412i
$640$		0			0
$641$	7.85410	+	24.1724i	0.310218	+	0.954754i	0.977678	+	0.210108i	$0.0673816\pi$
$641$	7.85410	+	24.1724i	0.310218	+	0.954754i	−0.667460	+	0.744646i	$0.732618\pi$
$642$		0			0
$643$	−5.00000			−0.197181			−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000			−0.197181			−0.0985904	+	0.995128i	$0.531433\pi$
$644$		0			0
$645$	−2.82624	−	8.69827i	−0.111283	−	0.342494i
$646$		0			0
$647$	12.0451	+	8.75127i	0.473541	+	0.344048i	0.798820	−	0.601570i	$-0.205458\pi$
$647$	12.0451	+	8.75127i	0.473541	+	0.344048i	−0.325279	+	0.945618i	$0.605458\pi$
$648$		0			0
$649$	−10.0000			−0.392534
$650$		0			0
$651$	2.09017			0.0819202
$652$		0			0
$653$	−21.6074	−	15.6987i	−0.845563	−	0.614337i	0.0783564	−	0.996925i	$-0.475033\pi$
$653$	−21.6074	−	15.6987i	−0.845563	−	0.614337i	−0.923919	+	0.382588i	$0.875033\pi$
$654$		0			0
$655$	−1.58359			−0.0618761
$656$		0			0
$657$	1.05573			0.0411879
$658$		0			0
$659$	−15.1418	−	46.6018i	−0.589842	−	1.81535i	−0.578888	−	0.815407i	$-0.696513\pi$
$659$	−15.1418	−	46.6018i	−0.589842	−	1.81535i	−0.0109542	−	0.999940i	$-0.503487\pi$
$660$		0			0
$661$	−5.10081	+	15.6987i	−0.198399	+	0.610608i	0.801521	+	0.597966i	$0.204024\pi$
$661$	−5.10081	+	15.6987i	−0.198399	+	0.610608i	−0.999920	+	0.0126422i	$0.995976\pi$
$662$		0			0
$663$	4.95492	+	15.2497i	0.192433	+	0.592248i
$664$		0			0
$665$	2.68692			0.104194
$666$		0			0
$667$	2.42705	−	1.76336i	0.0939758	−	0.0682774i
$668$		0			0
$669$	−25.8713	+	18.7966i	−1.00024	+	0.726719i
$670$		0			0
$671$	−1.30902	−	0.951057i	−0.0505340	−	0.0367151i
$672$		0			0
$673$	12.8885	−	39.6669i	0.496817	−	1.52905i	−0.317289	−	0.948329i	$-0.602773\pi$
$673$	12.8885	−	39.6669i	0.496817	−	1.52905i	0.814106	−	0.580716i	$-0.197227\pi$
$674$		0			0
$675$	−27.3607			−1.05311
$676$		0			0
$677$	11.2984	−	34.7728i	0.434232	−	1.33643i	−0.459640	−	0.888105i	$-0.652022\pi$
$677$	11.2984	−	34.7728i	0.434232	−	1.33643i	0.893872	−	0.448323i	$-0.147978\pi$
$678$		0			0
$679$	0.0623059	+	0.0452679i	0.00239108	+	0.00173722i
$680$		0			0
$681$	17.2533	−	12.5352i	0.661147	−	0.480352i
$682$		0			0
$683$	−3.04508	+	2.21238i	−0.116517	+	0.0846545i	−0.644518	−	0.764589i	$-0.722942\pi$
$683$	−3.04508	+	2.21238i	−0.116517	+	0.0846545i	0.528001	+	0.849244i	$0.322942\pi$
$684$		0			0
$685$	0.753289	−	2.31838i	0.0287817	−	0.0885809i
$686$		0			0
$687$	−12.1353	−	37.3485i	−0.462989	−	1.42493i
$688$		0			0
$689$	−2.65248	+	8.16348i	−0.101051	+	0.311004i
$690$		0			0
$691$	5.70163	+	17.5478i	0.216900	+	0.667550i	0.999013	+	0.0444134i	$0.0141419\pi$
$691$	5.70163	+	17.5478i	0.216900	+	0.667550i	−0.782113	+	0.623136i	$0.785858\pi$
$692$		0			0
$693$	0.0901699			0.00342527
$694$		0			0
$695$	34.9615	−	25.4010i	1.32617	−	0.963515i
$696$		0			0
$697$	21.8713	+	15.8904i	0.828435	+	0.601894i
$698$		0			0
$699$	44.6525			1.68891
$700$		0			0
$701$	16.2918			0.615333			0.307666	−	0.951494i	$-0.400452\pi$
$701$	16.2918			0.615333			0.307666	+	0.951494i	$0.400452\pi$
$702$		0			0
$703$	2.54508	+	1.84911i	0.0959897	+	0.0697406i
$704$		0			0
$705$	−9.73607	+	29.9645i	−0.366682	+	1.12853i
$706$		0			0
$707$	−1.09017			−0.0410001
$708$		0			0
$709$	−1.01722	−	3.13068i	−0.0382025	−	0.117575i	0.930137	−	0.367214i	$-0.119688\pi$
$709$	−1.01722	−	3.13068i	−0.0382025	−	0.117575i	−0.968339	+	0.249638i	$0.919688\pi$
$710$		0			0
$711$	−1.14590	+	3.52671i	−0.0429745	+	0.132262i
$712$		0			0
$713$	−1.69098	−	5.20431i	−0.0633278	−	0.194903i
$714$		0			0
$715$	−6.28115	−	4.56352i	−0.234902	−	0.170666i
$716$		0			0
$717$	16.1353	−	11.7229i	0.602582	−	0.437802i
$718$		0			0
$719$	36.3435	−	26.4051i	1.35538	−	0.984743i	0.356659	−	0.934235i	$-0.383916\pi$
$719$	36.3435	−	26.4051i	1.35538	−	0.984743i	0.998724	−	0.0505081i	$-0.0160841\pi$
$720$		0			0
$721$	−2.78115	−	2.02063i	−0.103576	−	0.0752520i
$722$		0			0
$723$	−3.89919	+	12.0005i	−0.145012	+	0.446302i
$724$		0			0
$725$	4.63525	−	14.2658i	0.172149	−	0.529820i
$726$		0			0
$727$	−0.416408	+	1.28157i	−0.0154437	+	0.0475309i	−0.958481	−	0.285155i	$-0.907955\pi$
$727$	−0.416408	+	1.28157i	−0.0154437	+	0.0475309i	0.943038	+	0.332686i	$0.107955\pi$
$728$		0			0
$729$	−23.8713	−	17.3435i	−0.884123	−	0.642353i
$730$		0			0
$731$	−5.83688	+	4.24074i	−0.215885	+	0.156850i
$732$		0			0
$733$	12.1803	−	8.84953i	0.449891	−	0.326865i	−0.339662	−	0.940548i	$-0.610313\pi$
$733$	12.1803	−	8.84953i	0.449891	−	0.326865i	0.789553	+	0.613683i	$0.210313\pi$
$734$		0			0
$735$	−7.76393	−	23.8949i	−0.286377	−	0.881378i
$736$		0			0
$737$	−1.39919	−	4.30625i	−0.0515397	−	0.158623i
$738$		0			0
$739$	8.79837	−	27.0786i	0.323653	−	0.996103i	−0.648391	−	0.761307i	$-0.724558\pi$
$739$	8.79837	−	27.0786i	0.323653	−	0.996103i	0.972045	−	0.234796i	$-0.0754421\pi$
$740$		0			0
$741$	−8.83688	−	27.1971i	−0.324631	−	0.999111i
$742$		0			0
$743$	8.90983			0.326870			0.163435	−	0.986554i	$-0.447743\pi$
$743$	8.90983			0.326870			0.163435	+	0.986554i	$0.447743\pi$
$744$		0			0
$745$	−12.1353	−	8.81678i	−0.444601	−	0.323022i
$746$		0			0
$747$	−3.78115	−	2.74717i	−0.138345	−	0.100514i
$748$		0			0
$749$	1.67376			0.0611579
$750$		0			0
$751$	46.5755			1.69956			0.849781	−	0.527135i	$-0.176734\pi$
$751$	46.5755			1.69956			0.849781	+	0.527135i	$0.176734\pi$
$752$		0			0
$753$	25.4894	+	18.5191i	0.928884	+	0.674874i
$754$		0			0
$755$	19.2705	+	14.0008i	0.701326	+	0.509543i
$756$		0			0
$757$	−12.8885			−0.468442			−0.234221	−	0.972183i	$-0.575254\pi$
$757$	−12.8885			−0.468442			−0.234221	+	0.972183i	$0.575254\pi$
$758$		0			0
$759$	0.500000	+	1.53884i	0.0181489	+	0.0558564i
$760$		0			0
$761$	−8.15248	+	25.0907i	−0.295527	+	0.909539i	0.687517	+	0.726168i	$0.258701\pi$
$761$	−8.15248	+	25.0907i	−0.295527	+	0.909539i	−0.983044	+	0.183370i	$0.941299\pi$
$762$		0			0
$763$	−0.905765	−	2.78766i	−0.0327909	−	0.100920i
$764$		0			0
$765$	0.753289	+	2.31838i	0.0272352	+	0.0838214i
$766$		0			0
$767$	28.0902	−	20.4087i	1.01428	−	0.736916i
$768$		0			0
$769$	2.76393	−	2.00811i	0.0996699	−	0.0724144i	−0.536834	−	0.843688i	$-0.680380\pi$
$769$	2.76393	−	2.00811i	0.0996699	−	0.0724144i	0.636504	+	0.771273i	$0.280380\pi$
$770$		0			0
$771$	11.8992	+	8.64527i	0.428539	+	0.311352i
$772$		0			0
$773$	11.3156	−	34.8258i	0.406994	−	1.25260i	−0.512225	−	0.858851i	$-0.671179\pi$
$773$	11.3156	−	34.8258i	0.406994	−	1.25260i	0.919219	−	0.393747i	$-0.128821\pi$
$774$		0			0
$775$	−22.1353	−	16.0822i	−0.795122	−	0.577690i
$776$		0			0
$777$	−0.0729490	+	0.224514i	−0.00261703	+	0.00805439i
$778$		0			0
$779$	−39.0066	−	28.3399i	−1.39756	−	1.01538i
$780$		0			0
$781$	10.6631	−	7.74721i	0.381556	−	0.277217i
$782$		0			0
$783$	13.2812	−	9.64932i	0.474630	−	0.344839i
$784$		0			0
$785$	16.5451	+	12.0207i	0.590519	+	0.429037i
$786$		0			0
$787$	−14.0000	−	43.0876i	−0.499046	−	1.53591i	−0.810555	−	0.585663i	$-0.800834\pi$
$787$	−14.0000	−	43.0876i	−0.499046	−	1.53591i	0.311509	−	0.950243i	$-0.399166\pi$
$788$		0			0
$789$	−1.92705	+	5.93085i	−0.0686048	+	0.211144i
$790$		0			0
$791$	−1.43363	−	4.41226i	−0.0509740	−	0.156882i
$792$		0			0
$793$	5.61803			0.199502
$794$		0			0
$795$	2.76393	−	8.50651i	0.0980266	−	0.301695i
$796$		0			0
$797$	1.01722	+	0.739054i	0.0360318	+	0.0261786i	0.605655	−	0.795727i	$-0.292911\pi$
$797$	1.01722	+	0.739054i	0.0360318	+	0.0261786i	−0.569624	+	0.821906i	$0.692911\pi$
$798$		0			0
$799$	24.8541			0.879275
$800$		0			0
$801$	3.59675			0.127085
$802$		0			0
$803$	−2.23607	−	1.62460i	−0.0789091	−	0.0573308i
$804$		0			0
$805$	0.427051	−	0.310271i	0.0150516	−	0.0109356i
$806$		0			0
$807$	−42.5066			−1.49630
$808$		0			0
$809$	−7.34346	−	22.6008i	−0.258182	−	0.794603i	−0.993186	−	0.116540i	$-0.962820\pi$
$809$	−7.34346	−	22.6008i	−0.258182	−	0.794603i	0.735004	−	0.678063i	$-0.237180\pi$
$810$		0			0
$811$	8.94427	−	27.5276i	0.314076	−	0.966626i	−0.662057	−	0.749453i	$-0.730316\pi$
$811$	8.94427	−	27.5276i	0.314076	−	0.966626i	0.976133	−	0.217173i	$-0.0696835\pi$
$812$		0			0
$813$	7.54508	+	23.2214i	0.264618	+	0.814409i
$814$		0			0
$815$	−13.7188	+	42.2223i	−0.480550	+	1.47898i
$816$		0			0
$817$	10.4098	−	7.56318i	0.364194	−	0.264602i
$818$		0			0
$819$	−0.253289	+	0.184025i	−0.00885063	+	0.00643036i
$820$		0			0
$821$	−9.44427	−	6.86167i	−0.329607	−	0.239474i	0.410657	−	0.911790i	$-0.365299\pi$
$821$	−9.44427	−	6.86167i	−0.329607	−	0.239474i	−0.740264	+	0.672316i	$0.765299\pi$
$822$		0			0
$823$	−0.145898	+	0.449028i	−0.00508569	+	0.0156521i	−0.953567	−	0.301180i	$-0.902619\pi$
$823$	−0.145898	+	0.449028i	−0.00508569	+	0.0156521i	0.948481	+	0.316833i	$0.102619\pi$
$824$		0			0
$825$	6.54508	+	4.75528i	0.227871	+	0.165558i
$826$		0			0
$827$	8.88197	−	27.3359i	0.308856	−	0.950562i	−0.669354	−	0.742944i	$-0.733429\pi$
$827$	8.88197	−	27.3359i	0.308856	−	0.950562i	0.978210	−	0.207618i	$-0.0665711\pi$
$828$		0			0
$829$	−42.2705	−	30.7113i	−1.46812	−	1.06665i	−0.981155	−	0.193225i	$-0.938105\pi$
$829$	−42.2705	−	30.7113i	−1.46812	−	1.06665i	−0.486961	−	0.873424i	$-0.661895\pi$
$830$		0			0
$831$	37.5066	−	27.2501i	1.30109	−	0.945296i
$832$		0			0
$833$	−16.0344	+	11.6497i	−0.555560	+	0.403638i
$834$		0			0
$835$	−50.3262			−1.74161
$836$		0			0
$837$	−9.25329	−	28.4787i	−0.319840	−	0.984368i
$838$		0			0
$839$	7.74671	−	23.8419i	0.267446	−	0.823115i	−0.723674	−	0.690142i	$-0.757548\pi$
$839$	7.74671	−	23.8419i	0.267446	−	0.823115i	0.991120	−	0.132972i	$-0.0424521\pi$
$840$		0			0
$841$	−6.18034	−	19.0211i	−0.213115	−	0.655901i
$842$		0			0
$843$	−5.32624			−0.183445
$844$		0			0
$845$	−2.11146			−0.0726363
$846$		0			0
$847$	1.90983	+	1.38757i	0.0656225	+	0.0476776i
$848$		0			0
$849$	7.52786			0.258356
$850$		0			0
$851$	0.618034			0.0211859
$852$		0			0
$853$	−30.3885	−	22.0786i	−1.04048	−	0.755956i	−0.0701040	−	0.997540i	$-0.522333\pi$
$853$	−30.3885	−	22.0786i	−1.04048	−	0.755956i	−0.970380	+	0.241584i	$0.922333\pi$
$854$		0			0
$855$	−1.34346	−	4.13474i	−0.0459453	−	0.141405i
$856$		0			0
$857$	20.7426			0.708555			0.354278	−	0.935140i	$-0.384727\pi$
$857$	20.7426			0.708555			0.354278	+	0.935140i	$0.384727\pi$
$858$		0			0
$859$	6.75329	+	20.7845i	0.230419	+	0.709158i	0.997696	+	0.0678415i	$0.0216112\pi$
$859$	6.75329	+	20.7845i	0.230419	+	0.709158i	−0.767277	+	0.641316i	$0.778389\pi$
$860$		0			0
$861$	1.11803	−	3.44095i	0.0381025	−	0.117267i
$862$		0			0
$863$	12.8197	+	39.4549i	0.436386	+	1.34306i	0.891659	+	0.452707i	$0.149542\pi$
$863$	12.8197	+	39.4549i	0.436386	+	1.34306i	−0.455273	+	0.890352i	$0.650458\pi$
$864$		0			0
$865$	22.2361	−	16.1554i	0.756049	−	0.549302i
$866$		0			0
$867$	11.5902	−	8.42075i	0.393623	−	0.285984i
$868$		0			0
$869$	7.85410	−	5.70634i	0.266432	−	0.193574i
$870$		0			0
$871$	12.7188	+	9.24078i	0.430962	+	0.313112i
$872$		0			0
$873$	0.0385072	−	0.118513i	0.00130327	−	0.00401105i
$874$		0			0
$875$	0.815595	−	2.51014i	0.0275721	−	0.0848583i
$876$		0			0
$877$	−7.66312	+	23.5847i	−0.258765	+	0.796397i	0.734299	+	0.678826i	$0.237511\pi$
$877$	−7.66312	+	23.5847i	−0.258765	+	0.796397i	−0.993064	+	0.117571i	$0.962489\pi$
$878$		0			0
$879$	−41.6246	−	30.2421i	−1.40396	−	1.02004i
$880$		0			0
$881$	−34.4164	+	25.0050i	−1.15952	+	0.842439i	−0.989717	−	0.143039i	$-0.954313\pi$
$881$	−34.4164	+	25.0050i	−1.15952	+	0.842439i	−0.169801	+	0.985478i	$0.554313\pi$
$882$		0			0
$883$	29.3435	−	21.3193i	0.987486	−	0.717451i	0.0281169	−	0.999605i	$-0.491049\pi$
$883$	29.3435	−	21.3193i	0.987486	−	0.717451i	0.959369	+	0.282154i	$0.0910489\pi$
$884$		0			0
$885$	−29.2705	+	21.2663i	−0.983917	+	0.714858i
$886$		0			0
$887$	−6.63525	−	20.4212i	−0.222790	−	0.685677i	−0.998508	−	0.0545980i	$-0.982612\pi$
$887$	−6.63525	−	20.4212i	−0.222790	−	0.685677i	0.775718	−	0.631079i	$-0.217388\pi$
$888$		0			0
$889$	−0.214782	+	0.661030i	−0.00720355	+	0.0221702i
$890$		0			0
$891$	2.38197	+	7.33094i	0.0797989	+	0.245596i
$892$		0			0
$893$	−44.3262			−1.48332
$894$		0			0
$895$	7.27458	+	22.3888i	0.243162	+	0.748376i
$896$		0			0
$897$	−4.54508	−	3.30220i	−0.151756	−	0.110257i
$898$		0			0
$899$	16.4164			0.547518
$900$		0			0
$901$	−7.05573			−0.235060
$902$		0			0
$903$	0.781153	+	0.567541i	0.0259951	+	0.0188866i
$904$		0			0
$905$	36.8328			1.22436
$906$		0			0
$907$	−18.8541			−0.626040			−0.313020	−	0.949747i	$-0.601341\pi$
$907$	−18.8541			−0.626040			−0.313020	+	0.949747i	$0.601341\pi$
$908$		0			0
$909$	0.545085	+	1.67760i	0.0180793	+	0.0556424i
$910$		0			0
$911$	−5.12868	+	15.7844i	−0.169921	+	0.522962i	−0.999365	−	0.0356271i	$-0.988657\pi$
$911$	−5.12868	+	15.7844i	−0.169921	+	0.522962i	0.829444	+	0.558589i	$0.188657\pi$
$912$		0			0
$913$	3.78115	+	11.6372i	0.125138	+	0.385135i
$914$		0			0
$915$	−5.85410			−0.193531
$916$		0			0
$917$	0.135255	−	0.0982684i	0.00446651	−	0.00324511i
$918$		0			0
$919$	13.3713	−	9.71483i	0.441079	−	0.320463i	−0.344984	−	0.938608i	$-0.612116\pi$
$919$	13.3713	−	9.71483i	0.441079	−	0.320463i	0.786064	+	0.618146i	$0.212116\pi$
$920$		0			0
$921$	35.5066	+	25.7970i	1.16998	+	0.850041i
$922$		0			0
$923$	−14.1418	+	43.5241i	−0.465484	+	1.43261i
$924$		0			0
$925$	2.50000	−	1.81636i	0.0821995	−	0.0597214i
$926$		0			0
$927$	−1.71885	+	5.29007i	−0.0564543	+	0.173749i
$928$		0			0
$929$	28.1353	+	20.4415i	0.923088	+	0.670663i	0.944291	−	0.329113i	$-0.106750\pi$
$929$	28.1353	+	20.4415i	0.923088	+	0.670663i	−0.0212029	+	0.999775i	$0.506750\pi$
$930$		0			0
$931$	28.5967	−	20.7768i	0.937221	−	0.680931i
$932$		0			0
$933$	37.2426	−	27.0584i	1.21927	−	0.885851i
$934$		0			0
$935$	1.97214	−	6.06961i	0.0644957	−	0.198497i
$936$		0			0
$937$	−0.933629	−	2.87341i	−0.0305003	−	0.0938703i	0.934648	−	0.355576i	$-0.115715\pi$
$937$	−0.933629	−	2.87341i	−0.0305003	−	0.0938703i	−0.965148	+	0.261705i	$0.915715\pi$
$938$		0			0
$939$	−12.7533	+	39.2506i	−0.416188	+	1.28089i
$940$		0			0
$941$	3.30244	+	10.1639i	0.107656	+	0.331332i	0.990345	−	0.138626i	$-0.0442687\pi$
$941$	3.30244	+	10.1639i	0.107656	+	0.331332i	−0.882688	+	0.469959i	$0.844269\pi$
$942$		0			0
$943$	−9.47214			−0.308455
$944$		0			0
$945$	2.33688	−	1.69784i	0.0760187	−	0.0552309i
$946$		0			0
$947$	−12.5344	−	9.10681i	−0.407315	−	0.295931i	0.365199	−	0.930929i	$-0.381001\pi$
$947$	−12.5344	−	9.10681i	−0.407315	−	0.295931i	−0.772514	+	0.634998i	$0.781001\pi$
$948$		0			0
$949$	9.59675			0.311524
$950$		0			0
$951$	33.2705			1.07887
$952$		0			0
$953$	11.2082	+	8.14324i	0.363069	+	0.263785i	0.754331	−	0.656494i	$-0.227961\pi$
$953$	11.2082	+	8.14324i	0.363069	+	0.263785i	−0.391262	+	0.920279i	$0.627961\pi$
$954$		0			0
$955$	−11.4205	+	35.1486i	−0.369558	+	1.13738i
$956$		0			0
$957$	−4.85410			−0.156911
$958$		0			0
$959$	0.0795268	+	0.244758i	0.00256806	+	0.00790366i
$960$		0			0
$961$	−0.326238	+	1.00406i	−0.0105238	+	0.0323889i
$962$		0			0
$963$	−0.836881	−	2.57565i	−0.0269681	−	0.0829993i
$964$		0			0
$965$	−17.5623	−	12.7598i	−0.565351	−	0.410751i
$966$		0			0
$967$	21.2705	−	15.4539i	0.684013	−	0.496965i	−0.190673	−	0.981654i	$-0.561067\pi$
$967$	21.2705	−	15.4539i	0.684013	−	0.496965i	0.874687	+	0.484689i	$0.161067\pi$
$968$		0			0
$969$	19.0172	−	13.8168i	0.610921	−	0.443860i
$970$		0			0
$971$	11.5623	+	8.40051i	0.371052	+	0.269585i	0.757647	−	0.652664i	$-0.226349\pi$
$971$	11.5623	+	8.40051i	0.371052	+	0.269585i	−0.386595	+	0.922250i	$0.626349\pi$
$972$		0			0
$973$	−1.40983	+	4.33901i	−0.0451971	+	0.139102i
$974$		0			0
$975$	−28.0902			−0.899605
$976$		0			0
$977$	−10.2533	+	31.5564i	−0.328032	+	1.00958i	0.642022	+	0.766686i	$0.278096\pi$
$977$	−10.2533	+	31.5564i	−0.328032	+	1.00958i	−0.970053	+	0.242892i	$0.921904\pi$
$978$		0			0
$979$	−7.61803	−	5.53483i	−0.243473	−	0.176894i
$980$		0			0
$981$	−3.83688	+	2.78766i	−0.122502	+	0.0890030i
$982$		0			0
$983$	−43.4615	+	31.5766i	−1.38621	+	1.00714i	−0.389937	+	0.920842i	$0.627503\pi$
$983$	−43.4615	+	31.5766i	−1.38621	+	1.00714i	−0.996270	+	0.0862962i	$0.972497\pi$
$984$		0			0
$985$	0.652476	+	2.00811i	0.0207896	+	0.0639838i
$986$		0			0
$987$	−1.02786	−	3.16344i	−0.0327173	−	0.100693i
$988$		0			0
$989$	0.781153	−	2.40414i	0.0248392	−	0.0764473i
$990$		0			0
$991$	8.24671	+	25.3808i	0.261965	+	0.806247i	0.992377	+	0.123239i	$0.0393283\pi$
$991$	8.24671	+	25.3808i	0.261965	+	0.806247i	−0.730412	+	0.683007i	$0.760672\pi$
$992$		0			0
$993$	30.8885			0.980218
$994$		0			0
$995$	3.78115	+	2.74717i	0.119871	+	0.0870911i
$996$		0			0
$997$	−12.8992	−	9.37181i	−0.408521	−	0.296808i	0.364482	−	0.931211i	$-0.381246\pi$
$997$	−12.8992	−	9.37181i	−0.408521	−	0.296808i	−0.773003	+	0.634402i	$0.781246\pi$
$998$		0			0
$999$	3.38197			0.107001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.u.a.321.1	✓	4
4.3	odd	2		800.2.u.b.321.1	yes	4
25.6	even	5	inner	800.2.u.a.481.1	yes	4
100.31	odd	10		800.2.u.b.481.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.u.a.321.1	✓	4	1.1	even	1	trivial
800.2.u.a.481.1	yes	4	25.6	even	5	inner
800.2.u.b.321.1	yes	4	4.3	odd	2
800.2.u.b.481.1	yes	4	100.31	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{3} +(-1.80902 - 1.31433i) q^{5} +0.236068 q^{7} +(-0.118034 - 0.363271i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.07295 - 3.30220i) q^{13} +(1.11803 + 3.44095i) q^{15} +(2.30902 - 1.67760i) q^{17} +(-4.11803 + 2.99193i) q^{19} +(-0.309017 - 0.224514i) q^{21} +(-0.309017 + 0.951057i) q^{23} +(1.54508 + 4.75528i) q^{25} +(-1.69098 + 5.20431i) q^{27} +(-2.42705 - 1.76336i) q^{29} +(-4.42705 + 3.21644i) q^{31} +(1.30902 - 0.951057i) q^{33} +(-0.427051 - 0.310271i) q^{35} +(-0.190983 - 0.587785i) q^{37} +(-1.73607 + 5.34307i) q^{39} +(2.92705 + 9.00854i) q^{41} -2.52786 q^{43} +(-0.263932 + 0.812299i) q^{45} +(7.04508 + 5.11855i) q^{47} -6.94427 q^{49} -4.61803 q^{51} +(-2.00000 - 1.45309i) q^{53} +(1.80902 - 1.31433i) q^{55} +8.23607 q^{57} +(3.09017 + 9.51057i) q^{59} +(-0.500000 + 1.53884i) q^{61} +(-0.0278640 - 0.0857567i) q^{63} +(-2.39919 + 7.38394i) q^{65} +(-3.66312 + 2.66141i) q^{67} +(1.30902 - 0.951057i) q^{69} +(-10.6631 - 7.74721i) q^{71} +(-0.854102 + 2.62866i) q^{73} +(2.50000 - 7.69421i) q^{75} +(-0.0729490 + 0.224514i) q^{77} +(-7.85410 - 5.70634i) q^{79} +(6.23607 - 4.53077i) q^{81} +(9.89919 - 7.19218i) q^{83} -6.38197 q^{85} +(1.50000 + 4.61653i) q^{87} +(-2.90983 + 8.95554i) q^{89} +(-0.253289 - 0.779543i) q^{91} +8.85410 q^{93} +11.3820 q^{95} +(0.263932 + 0.191758i) q^{97} +0.381966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} - 5 q^{5} - 8 q^{7} + 4 q^{9} + q^{11} - 11 q^{13} + 7 q^{17} - 12 q^{19} + q^{21} + q^{23} - 5 q^{25} - 9 q^{27} - 3 q^{29} - 11 q^{31} + 3 q^{33} + 5 q^{35} - 3 q^{37} + 2 q^{39} + 5 q^{41}+ \cdots + 6 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 - 5 * q^5 - 8 * q^7 + 4 * q^9 + q^11 - 11 * q^13 + 7 * q^17 - 12 * q^19 + q^21 + q^23 - 5 * q^25 - 9 * q^27 - 3 * q^29 - 11 * q^31 + 3 * q^33 + 5 * q^35 - 3 * q^37 + 2 * q^39 + 5 * q^41 - 28 * q^43 - 10 * q^45 + 17 * q^47 + 8 * q^49 - 14 * q^51 - 8 * q^53 + 5 * q^55 + 24 * q^57 - 10 * q^59 - 2 * q^61 - 18 * q^63 + 15 * q^65 + q^67 + 3 * q^69 - 27 * q^71 + 10 * q^73 + 10 * q^75 - 7 * q^77 - 18 * q^79 + 16 * q^81 + 15 * q^83 - 30 * q^85 + 6 * q^87 - 34 * q^89 + 37 * q^91 + 22 * q^93 + 50 * q^95 + 10 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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