LMFDB - Embedded newform 400.2.u.a.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(81,400)] 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("400.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-5,0,-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:	$3.19401608085$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	400.81
Dual form			400.2.u.a.321.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80902 + 1.31433i) q^{3} +(-0.690983 + 2.12663i) q^{5} -2.61803 q^{7} +(0.618034 - 1.90211i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(1.04508 - 3.21644i) q^{13} +(-1.54508 - 4.75528i) q^{15} +(-4.23607 - 3.07768i) q^{17} +(6.16312 + 4.47777i) q^{19} +(4.73607 - 3.44095i) q^{21} +(-1.69098 - 5.20431i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(-0.690983 - 2.12663i) q^{27} +(-3.54508 + 2.57565i) q^{29} +(-3.80902 - 2.76741i) q^{31} +(2.23607 + 1.62460i) q^{33} +(1.80902 - 5.56758i) q^{35} +(-2.54508 + 7.83297i) q^{37} +(2.33688 + 7.19218i) q^{39} +(1.76393 - 5.42882i) q^{41} -4.38197 q^{43} +(3.61803 + 2.62866i) q^{45} +(0.118034 - 0.0857567i) q^{47} -0.145898 q^{49} +11.7082 q^{51} +(-6.42705 + 4.66953i) q^{53} +2.76393 q^{55} -17.0344 q^{57} +(-0.736068 + 2.26538i) q^{59} +(-4.07295 - 12.5352i) q^{61} +(-1.61803 + 4.97980i) q^{63} +(6.11803 + 4.44501i) q^{65} +(11.0902 + 8.05748i) q^{67} +(9.89919 + 7.19218i) q^{69} +(-6.97214 + 5.06555i) q^{71} +(3.39919 + 10.4616i) q^{73} +11.1803 q^{75} +(1.00000 + 3.07768i) q^{77} +(-4.30902 + 3.13068i) q^{79} +(8.89919 + 6.46564i) q^{81} +(-3.66312 - 2.66141i) q^{83} +(9.47214 - 6.88191i) q^{85} +(3.02786 - 9.31881i) q^{87} +(1.23607 + 3.80423i) q^{89} +(-2.73607 + 8.42075i) q^{91} +10.5279 q^{93} +(-13.7812 + 10.0126i) q^{95} +(12.3541 - 8.97578i) q^{97} -2.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{3} - 5 q^{5} - 6 q^{7} - 2 q^{9} - 6 q^{11} - 7 q^{13} + 5 q^{15} - 8 q^{17} + 9 q^{19} + 10 q^{21} - 9 q^{23} - 5 q^{25} - 5 q^{27} - 3 q^{29} - 13 q^{31} + 5 q^{35} + q^{37} + 25 q^{39} + 16 q^{41}+ \cdots + 8 q^{99}+O(q^{100}) $ 4 * q - 5 * q^3 - 5 * q^5 - 6 * q^7 - 2 * q^9 - 6 * q^11 - 7 * q^13 + 5 * q^15 - 8 * q^17 + 9 * q^19 + 10 * q^21 - 9 * q^23 - 5 * q^25 - 5 * q^27 - 3 * q^29 - 13 * q^31 + 5 * q^35 + q^37 + 25 * q^39 + 16 * q^41 - 22 * q^43 + 10 * q^45 - 4 * q^47 - 14 * q^49 + 20 * q^51 - 19 * q^53 + 20 * q^55 - 10 * q^57 + 6 * q^59 - 23 * q^61 - 2 * q^63 + 20 * q^65 + 22 * q^67 + 15 * q^69 - 10 * q^71 - 11 * q^73 + 4 * q^77 - 15 * q^79 + 11 * q^81 + q^83 + 20 * q^85 + 30 * q^87 - 4 * q^89 - 2 * q^91 + 60 * q^93 - 35 * q^95 + 36 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.80902	+	1.31433i	−1.04444	+	0.758827i	−0.971147	−	0.238483i	$-0.923350\pi$
$3$	−1.80902	+	1.31433i	−1.04444	+	0.758827i	−0.0732898	+	0.997311i	$0.523350\pi$
$4$		0			0
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$		0			0
$7$	−2.61803			−0.989524			−0.494762	−	0.869029i	$-0.664745\pi$
$7$	−2.61803			−0.989524			−0.494762	+	0.869029i	$0.664745\pi$
$8$		0			0
$9$	0.618034	−	1.90211i	0.206011	−	0.634038i
$10$		0			0
$11$	−0.381966	−	1.17557i	−0.115167	−	0.354448i	0.876815	−	0.480828i	$-0.159664\pi$
$11$	−0.381966	−	1.17557i	−0.115167	−	0.354448i	−0.991982	+	0.126380i	$0.959664\pi$
$12$		0			0
$13$	1.04508	−	3.21644i	0.289854	−	0.892080i	−0.695047	−	0.718964i	$-0.744616\pi$
$13$	1.04508	−	3.21644i	0.289854	−	0.892080i	0.984901	−	0.173116i	$-0.0553835\pi$
$14$		0			0
$15$	−1.54508	−	4.75528i	−0.398939	−	1.22781i
$16$		0			0
$17$	−4.23607	−	3.07768i	−1.02740	−	0.746448i	−0.0596113	−	0.998222i	$-0.518986\pi$
$17$	−4.23607	−	3.07768i	−1.02740	−	0.746448i	−0.967786	+	0.251774i	$0.918986\pi$
$18$		0			0
$19$	6.16312	+	4.47777i	1.41392	+	1.02727i	0.992739	+	0.120292i	$0.0383832\pi$
$19$	6.16312	+	4.47777i	1.41392	+	1.02727i	0.421178	+	0.906978i	$0.361617\pi$
$20$		0			0
$21$	4.73607	−	3.44095i	1.03349	−	0.750878i
$22$		0			0
$23$	−1.69098	−	5.20431i	−0.352594	−	1.08517i	−0.957391	−	0.288794i	$-0.906746\pi$
$23$	−1.69098	−	5.20431i	−0.352594	−	1.08517i	0.604797	−	0.796380i	$-0.293254\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$		0			0
$27$	−0.690983	−	2.12663i	−0.132980	−	0.409270i
$28$		0			0
$29$	−3.54508	+	2.57565i	−0.658306	+	0.478287i	−0.866090	−	0.499887i	$-0.833375\pi$
$29$	−3.54508	+	2.57565i	−0.658306	+	0.478287i	0.207785	+	0.978175i	$0.433375\pi$
$30$		0			0
$31$	−3.80902	−	2.76741i	−0.684120	−	0.497042i	0.190602	−	0.981667i	$-0.438956\pi$
$31$	−3.80902	−	2.76741i	−0.684120	−	0.497042i	−0.874722	+	0.484625i	$0.838956\pi$
$32$		0			0
$33$	2.23607	+	1.62460i	0.389249	+	0.282806i
$34$		0			0
$35$	1.80902	−	5.56758i	0.305780	−	0.941093i
$36$		0			0
$37$	−2.54508	+	7.83297i	−0.418409	+	1.28773i	0.490756	+	0.871297i	$0.336721\pi$
$37$	−2.54508	+	7.83297i	−0.418409	+	1.28773i	−0.909166	+	0.416435i	$0.863279\pi$
$38$		0			0
$39$	2.33688	+	7.19218i	0.374200	+	1.15167i
$40$		0			0
$41$	1.76393	−	5.42882i	0.275480	−	0.847840i	−0.713612	−	0.700541i	$-0.752942\pi$
$41$	1.76393	−	5.42882i	0.275480	−	0.847840i	0.989092	−	0.147299i	$-0.0470579\pi$
$42$		0			0
$43$	−4.38197			−0.668244			−0.334122	−	0.942530i	$-0.608440\pi$
$43$	−4.38197			−0.668244			−0.334122	+	0.942530i	$0.608440\pi$
$44$		0			0
$45$	3.61803	+	2.62866i	0.539345	+	0.391857i
$46$		0			0
$47$	0.118034	−	0.0857567i	0.0172170	−	0.0125089i	−0.579143	−	0.815226i	$-0.696613\pi$
$47$	0.118034	−	0.0857567i	0.0172170	−	0.0125089i	0.596360	+	0.802717i	$0.296613\pi$
$48$		0			0
$49$	−0.145898			−0.0208426
$50$		0			0
$51$	11.7082			1.63948
$52$		0			0
$53$	−6.42705	+	4.66953i	−0.882823	+	0.641409i	−0.933997	−	0.357281i	$-0.883704\pi$
$53$	−6.42705	+	4.66953i	−0.882823	+	0.641409i	0.0511736	+	0.998690i	$0.483704\pi$
$54$		0			0
$55$	2.76393			0.372689
$56$		0			0
$57$	−17.0344			−2.25627
$58$		0			0
$59$	−0.736068	+	2.26538i	−0.0958279	+	0.294928i	−0.987469	−	0.157816i	$-0.949555\pi$
$59$	−0.736068	+	2.26538i	−0.0958279	+	0.294928i	0.891641	+	0.452744i	$0.149555\pi$
$60$		0			0
$61$	−4.07295	−	12.5352i	−0.521488	−	1.60497i	−0.771158	−	0.636643i	$-0.780322\pi$
$61$	−4.07295	−	12.5352i	−0.521488	−	1.60497i	0.249671	−	0.968331i	$-0.419678\pi$
$62$		0			0
$63$	−1.61803	+	4.97980i	−0.203853	+	0.627395i
$64$		0			0
$65$	6.11803	+	4.44501i	0.758849	+	0.551336i
$66$		0			0
$67$	11.0902	+	8.05748i	1.35488	+	0.984378i	0.998752	+	0.0499406i	$0.0159032\pi$
$67$	11.0902	+	8.05748i	1.35488	+	0.984378i	0.356128	+	0.934437i	$0.384097\pi$
$68$		0			0
$69$	9.89919	+	7.19218i	1.19172	+	0.865837i
$70$		0			0
$71$	−6.97214	+	5.06555i	−0.827440	+	0.601171i	−0.918834	−	0.394644i	$-0.870868\pi$
$71$	−6.97214	+	5.06555i	−0.827440	+	0.601171i	0.0913937	+	0.995815i	$0.470868\pi$
$72$		0			0
$73$	3.39919	+	10.4616i	0.397845	+	1.22444i	0.926724	+	0.375743i	$0.122612\pi$
$73$	3.39919	+	10.4616i	0.397845	+	1.22444i	−0.528879	+	0.848697i	$0.677388\pi$
$74$		0			0
$75$	11.1803			1.29099
$76$		0			0
$77$	1.00000	+	3.07768i	0.113961	+	0.350735i
$78$		0			0
$79$	−4.30902	+	3.13068i	−0.484802	+	0.352229i	−0.803182	−	0.595734i	$-0.796861\pi$
$79$	−4.30902	+	3.13068i	−0.484802	+	0.352229i	0.318380	+	0.947963i	$0.396861\pi$
$80$		0			0
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$		0			0
$83$	−3.66312	−	2.66141i	−0.402080	−	0.292128i	0.368308	−	0.929704i	$-0.379937\pi$
$83$	−3.66312	−	2.66141i	−0.402080	−	0.292128i	−0.770387	+	0.637576i	$0.779937\pi$
$84$		0			0
$85$	9.47214	−	6.88191i	1.02740	−	0.746448i
$86$		0			0
$87$	3.02786	−	9.31881i	0.324621	−	0.999081i
$88$		0			0
$89$	1.23607	+	3.80423i	0.131023	+	0.403247i	0.994950	−	0.100369i	$-0.0320025\pi$
$89$	1.23607	+	3.80423i	0.131023	+	0.403247i	−0.863927	+	0.503617i	$0.832002\pi$
$90$		0			0
$91$	−2.73607	+	8.42075i	−0.286818	+	0.882735i
$92$		0			0
$93$	10.5279			1.09169
$94$		0			0
$95$	−13.7812	+	10.0126i	−1.41392	+	1.02727i
$96$		0			0
$97$	12.3541	−	8.97578i	1.25437	−	0.911352i	0.255902	−	0.966703i	$-0.417628\pi$
$97$	12.3541	−	8.97578i	1.25437	−	0.911352i	0.998467	+	0.0553503i	$0.0176276\pi$
$98$		0			0
$99$	−2.47214			−0.248459
$100$		0			0
$101$	−17.9443			−1.78552			−0.892761	−	0.450531i	$-0.851235\pi$
$101$	−17.9443			−1.78552			−0.892761	+	0.450531i	$0.851235\pi$
$102$		0			0
$103$	−2.54508	+	1.84911i	−0.250775	+	0.182198i	−0.706070	−	0.708142i	$-0.749534\pi$
$103$	−2.54508	+	1.84911i	−0.250775	+	0.182198i	0.455295	+	0.890340i	$0.349534\pi$
$104$		0			0
$105$	4.04508	+	12.4495i	0.394760	+	1.21495i
$106$		0			0
$107$	−16.7082			−1.61524			−0.807622	−	0.589701i	$-0.799246\pi$
$107$	−16.7082			−1.61524			−0.807622	+	0.589701i	$0.799246\pi$
$108$		0			0
$109$	0.909830	−	2.80017i	0.0871459	−	0.268208i	−0.897981	−	0.440033i	$-0.854967\pi$
$109$	0.909830	−	2.80017i	0.0871459	−	0.268208i	0.985127	+	0.171826i	$0.0549666\pi$
$110$		0			0
$111$	−5.69098	−	17.5150i	−0.540164	−	1.66245i
$112$		0			0
$113$	−3.26393	+	10.0453i	−0.307045	+	0.944987i	0.671861	+	0.740677i	$0.265495\pi$
$113$	−3.26393	+	10.0453i	−0.307045	+	0.944987i	−0.978906	+	0.204310i	$0.934505\pi$
$114$		0			0
$115$	12.2361			1.14102
$116$		0			0
$117$	−5.47214	−	3.97574i	−0.505899	−	0.367557i
$118$		0			0
$119$	11.0902	+	8.05748i	1.01663	+	0.738628i
$120$		0			0
$121$	7.66312	−	5.56758i	0.696647	−	0.506144i
$122$		0			0
$123$	3.94427	+	12.1392i	0.355643	+	1.09456i
$124$		0			0
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$		0			0
$127$	−2.32624	−	7.15942i	−0.206420	−	0.635296i	−0.999652	−	0.0263764i	$-0.991603\pi$
$127$	−2.32624	−	7.15942i	−0.206420	−	0.635296i	0.793232	−	0.608920i	$-0.208397\pi$
$128$		0			0
$129$	7.92705	−	5.75934i	0.697938	−	0.507082i
$130$		0			0
$131$	−0.881966	−	0.640786i	−0.0770577	−	0.0559857i	0.548589	−	0.836092i	$-0.315165\pi$
$131$	−0.881966	−	0.640786i	−0.0770577	−	0.0559857i	−0.625647	+	0.780106i	$0.715165\pi$
$132$		0			0
$133$	−16.1353	−	11.7229i	−1.39910	−	1.01651i
$134$		0			0
$135$	5.00000			0.430331
$136$		0			0
$137$	1.54508	−	4.75528i	0.132006	−	0.406271i	−0.863107	−	0.505022i	$-0.831485\pi$
$137$	1.54508	−	4.75528i	0.132006	−	0.406271i	0.995112	+	0.0987504i	$0.0314845\pi$
$138$		0			0
$139$	−3.01722	−	9.28605i	−0.255917	−	0.787633i	−0.993648	−	0.112537i	$-0.964102\pi$
$139$	−3.01722	−	9.28605i	−0.255917	−	0.787633i	0.737730	−	0.675096i	$-0.235898\pi$
$140$		0			0
$141$	−0.100813	+	0.310271i	−0.00848999	+	0.0261295i
$142$		0			0
$143$	−4.18034			−0.349578
$144$		0			0
$145$	−3.02786	−	9.31881i	−0.251450	−	0.773885i
$146$		0			0
$147$	0.263932	−	0.191758i	0.0217687	−	0.0158159i
$148$		0			0
$149$	−18.4164			−1.50873			−0.754365	−	0.656455i	$-0.772055\pi$
$149$	−18.4164			−1.50873			−0.754365	+	0.656455i	$0.772055\pi$
$150$		0			0
$151$	−0.381966			−0.0310840			−0.0155420	−	0.999879i	$-0.504947\pi$
$151$	−0.381966			−0.0310840			−0.0155420	+	0.999879i	$0.504947\pi$
$152$		0			0
$153$	−8.47214	+	6.15537i	−0.684932	+	0.497632i
$154$		0			0
$155$	8.51722	−	6.18812i	0.684120	−	0.497042i
$156$		0			0
$157$	4.23607			0.338075			0.169038	−	0.985610i	$-0.445934\pi$
$157$	4.23607			0.338075			0.169038	+	0.985610i	$0.445934\pi$
$158$		0			0
$159$	5.48936	−	16.8945i	0.435334	−	1.33982i
$160$		0			0
$161$	4.42705	+	13.6251i	0.348900	+	1.07381i
$162$		0			0
$163$	−4.69098	+	14.4374i	−0.367426	+	1.13082i	0.581022	+	0.813888i	$0.302653\pi$
$163$	−4.69098	+	14.4374i	−0.367426	+	1.13082i	−0.948448	+	0.316933i	$0.897347\pi$
$164$		0			0
$165$	−5.00000	+	3.63271i	−0.389249	+	0.282806i
$166$		0			0
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.198190	−	0.980164i	$-0.563506\pi$
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.993435	+	0.114398i	$0.963506\pi$
$168$		0			0
$169$	1.26393	+	0.918300i	0.0972255	+	0.0706385i
$170$		0			0
$171$	12.3262	−	8.95554i	0.942611	−	0.684847i
$172$		0			0
$173$	2.01722	+	6.20837i	0.153366	+	0.472013i	0.997992	−	0.0633445i	$-0.0201767\pi$
$173$	2.01722	+	6.20837i	0.153366	+	0.472013i	−0.844625	+	0.535358i	$0.820177\pi$
$174$		0			0
$175$	10.5902	+	7.69421i	0.800542	+	0.581628i
$176$		0			0
$177$	−1.64590	−	5.06555i	−0.123713	−	0.380750i
$178$		0			0
$179$	2.66312	−	1.93487i	0.199051	−	0.144619i	−0.483795	−	0.875181i	$-0.660742\pi$
$179$	2.66312	−	1.93487i	0.199051	−	0.144619i	0.682846	+	0.730562i	$0.260742\pi$
$180$		0			0
$181$	6.70820	+	4.87380i	0.498617	+	0.362266i	0.808488	−	0.588512i	$-0.200286\pi$
$181$	6.70820	+	4.87380i	0.498617	+	0.362266i	−0.309872	+	0.950778i	$0.600286\pi$
$182$		0			0
$183$	23.8435	+	17.3233i	1.76256	+	1.28057i
$184$		0			0
$185$	−14.8992	−	10.8249i	−1.09541	−	0.795862i
$186$		0			0
$187$	−2.00000	+	6.15537i	−0.146254	+	0.450125i
$188$		0			0
$189$	1.80902	+	5.56758i	0.131587	+	0.404982i
$190$		0			0
$191$	0.0901699	−	0.277515i	0.00652447	−	0.0200802i	−0.947741	−	0.319040i	$-0.896640\pi$
$191$	0.0901699	−	0.277515i	0.00652447	−	0.0200802i	0.954266	+	0.298960i	$0.0966396\pi$
$192$		0			0
$193$	−7.70820			−0.554849			−0.277424	−	0.960747i	$-0.589481\pi$
$193$	−7.70820			−0.554849			−0.277424	+	0.960747i	$0.589481\pi$
$194$		0			0
$195$	−16.9098			−1.21094
$196$		0			0
$197$	11.9443	−	8.67802i	0.850994	−	0.618283i	−0.0744258	−	0.997227i	$-0.523712\pi$
$197$	11.9443	−	8.67802i	0.850994	−	0.618283i	0.925420	+	0.378943i	$0.123712\pi$
$198$		0			0
$199$	−9.38197			−0.665070			−0.332535	−	0.943091i	$-0.607904\pi$
$199$	−9.38197			−0.665070			−0.332535	+	0.943091i	$0.607904\pi$
$200$		0			0
$201$	−30.6525			−2.16206
$202$		0			0
$203$	9.28115	−	6.74315i	0.651409	−	0.473277i
$204$		0			0
$205$	10.3262	+	7.50245i	0.721216	+	0.523994i
$206$		0			0
$207$	−10.9443			−0.760679
$208$		0			0
$209$	2.90983	−	8.95554i	0.201277	−	0.619467i
$210$		0			0
$211$	−6.16312	−	18.9681i	−0.424287	−	1.30582i	−0.903676	−	0.428217i	$-0.859142\pi$
$211$	−6.16312	−	18.9681i	−0.424287	−	1.30582i	0.479389	−	0.877602i	$-0.340858\pi$
$212$		0			0
$213$	5.95492	−	18.3273i	0.408024	−	1.25577i
$214$		0			0
$215$	3.02786	−	9.31881i	0.206499	−	0.635537i
$216$		0			0
$217$	9.97214	+	7.24518i	0.676953	+	0.491835i
$218$		0			0
$219$	−19.8992	−	14.4576i	−1.34466	−	0.976954i
$220$		0			0
$221$	−14.3262	+	10.4086i	−0.963687	+	0.700160i
$222$		0			0
$223$	−1.76393	−	5.42882i	−0.118122	−	0.363541i	0.874464	−	0.485091i	$-0.161214\pi$
$223$	−1.76393	−	5.42882i	−0.118122	−	0.363541i	−0.992585	+	0.121550i	$0.961214\pi$
$224$		0			0
$225$	−8.09017	+	5.87785i	−0.539345	+	0.391857i
$226$		0			0
$227$	7.90983	+	24.3440i	0.524994	+	1.61576i	0.764328	+	0.644828i	$0.223071\pi$
$227$	7.90983	+	24.3440i	0.524994	+	1.61576i	−0.239334	+	0.970937i	$0.576929\pi$
$228$		0			0
$229$	−16.3262	+	11.8617i	−1.07887	+	0.783844i	−0.977485	−	0.211004i	$-0.932327\pi$
$229$	−16.3262	+	11.8617i	−1.07887	+	0.783844i	−0.101383	+	0.994847i	$0.532327\pi$
$230$		0			0
$231$	−5.85410	−	4.25325i	−0.385172	−	0.279844i
$232$		0			0
$233$	−4.85410	−	3.52671i	−0.318003	−	0.231043i	0.417320	−	0.908760i	$-0.362969\pi$
$233$	−4.85410	−	3.52671i	−0.318003	−	0.231043i	−0.735323	+	0.677717i	$0.762969\pi$
$234$		0			0
$235$	0.100813	+	0.310271i	0.00657632	+	0.0202398i
$236$		0			0
$237$	3.68034	−	11.3269i	0.239064	−	0.735763i
$238$		0			0
$239$	6.87132	+	21.1478i	0.444469	+	1.36793i	0.883065	+	0.469250i	$0.155476\pi$
$239$	6.87132	+	21.1478i	0.444469	+	1.36793i	−0.438596	+	0.898684i	$0.644524\pi$
$240$		0			0
$241$	3.54508	−	10.9106i	0.228359	−	0.702817i	−0.769574	−	0.638557i	$-0.779532\pi$
$241$	3.54508	−	10.9106i	0.228359	−	0.702817i	0.997933	−	0.0642594i	$-0.0204685\pi$
$242$		0			0
$243$	−17.8885			−1.14755
$244$		0			0
$245$	0.100813	−	0.310271i	0.00644071	−	0.0198225i
$246$		0			0
$247$	20.8435	−	15.1437i	1.32624	−	0.963568i
$248$		0			0
$249$	10.1246			0.641621
$250$		0			0
$251$	8.05573			0.508473			0.254237	−	0.967142i	$-0.418176\pi$
$251$	8.05573			0.508473			0.254237	+	0.967142i	$0.418176\pi$
$252$		0			0
$253$	−5.47214	+	3.97574i	−0.344030	+	0.249953i
$254$		0			0
$255$	−8.09017	+	24.8990i	−0.506626	+	1.55923i
$256$		0			0
$257$	−3.61803			−0.225687			−0.112843	−	0.993613i	$-0.535996\pi$
$257$	−3.61803			−0.225687			−0.112843	+	0.993613i	$0.535996\pi$
$258$		0			0
$259$	6.66312	−	20.5070i	0.414026	−	1.27424i
$260$		0			0
$261$	2.70820	+	8.33499i	0.167634	+	0.515923i
$262$		0			0
$263$	4.28115	−	13.1760i	0.263987	−	0.812469i	−0.727938	−	0.685643i	$-0.759521\pi$
$263$	4.28115	−	13.1760i	0.263987	−	0.812469i	0.991925	−	0.126826i	$-0.0404789\pi$
$264$		0			0
$265$	−5.48936	−	16.8945i	−0.337209	−	1.03782i
$266$		0			0
$267$	−7.23607	−	5.25731i	−0.442840	−	0.321742i
$268$		0			0
$269$	11.5623	+	8.40051i	0.704966	+	0.512188i	0.881546	−	0.472098i	$-0.156503\pi$
$269$	11.5623	+	8.40051i	0.704966	+	0.512188i	−0.176580	+	0.984286i	$0.556503\pi$
$270$		0			0
$271$	10.4721	−	7.60845i	0.636137	−	0.462181i	−0.222384	−	0.974959i	$-0.571384\pi$
$271$	10.4721	−	7.60845i	0.636137	−	0.462181i	0.858521	+	0.512779i	$0.171384\pi$
$272$		0			0
$273$	−6.11803	−	18.8294i	−0.370280	−	1.13961i
$274$		0			0
$275$	−1.90983	+	5.87785i	−0.115167	+	0.354448i
$276$		0			0
$277$	6.54508	+	20.1437i	0.393256	+	1.21032i	0.930311	+	0.366771i	$0.119537\pi$
$277$	6.54508	+	20.1437i	0.393256	+	1.21032i	−0.537055	+	0.843547i	$0.680463\pi$
$278$		0			0
$279$	−7.61803	+	5.53483i	−0.456080	+	0.331361i
$280$		0			0
$281$	−7.39919	−	5.37582i	−0.441398	−	0.320695i	0.344792	−	0.938679i	$-0.387949\pi$
$281$	−7.39919	−	5.37582i	−0.441398	−	0.320695i	−0.786190	+	0.617984i	$0.787949\pi$
$282$		0			0
$283$	−5.88197	−	4.27350i	−0.349647	−	0.254033i	0.399074	−	0.916919i	$-0.369332\pi$
$283$	−5.88197	−	4.27350i	−0.349647	−	0.254033i	−0.748721	+	0.662886i	$0.769332\pi$
$284$		0			0
$285$	11.7705	−	36.2259i	0.697225	−	2.14584i
$286$		0			0
$287$	−4.61803	+	14.2128i	−0.272594	+	0.838958i
$288$		0			0
$289$	3.21885	+	9.90659i	0.189344	+	0.582741i
$290$		0			0
$291$	−10.5517	+	32.4747i	−0.618549	+	1.90370i
$292$		0			0
$293$	0.472136			0.0275825			0.0137912	−	0.999905i	$-0.495610\pi$
$293$	0.472136			0.0275825			0.0137912	+	0.999905i	$0.495610\pi$
$294$		0			0
$295$	−4.30902	−	3.13068i	−0.250881	−	0.182275i
$296$		0			0
$297$	−2.23607	+	1.62460i	−0.129750	+	0.0942688i
$298$		0			0
$299$	−18.5066			−1.07026
$300$		0			0
$301$	11.4721			0.661243
$302$		0			0
$303$	32.4615	−	23.5847i	1.86486	−	1.35490i
$304$		0			0
$305$	29.4721			1.68757
$306$		0			0
$307$	−10.7639			−0.614330			−0.307165	−	0.951656i	$-0.599380\pi$
$307$	−10.7639			−0.614330			−0.307165	+	0.951656i	$0.599380\pi$
$308$		0			0
$309$	2.17376	−	6.69015i	0.123661	−	0.380589i
$310$		0			0
$311$	1.51722	+	4.66953i	0.0860337	+	0.264785i	0.984813	−	0.173616i	$-0.0555452\pi$
$311$	1.51722	+	4.66953i	0.0860337	+	0.264785i	−0.898780	+	0.438401i	$0.855545\pi$
$312$		0			0
$313$	1.76393	−	5.42882i	0.0997033	−	0.306855i	−0.888748	−	0.458397i	$-0.848424\pi$
$313$	1.76393	−	5.42882i	0.0997033	−	0.306855i	0.988451	+	0.151542i	$0.0484238\pi$
$314$		0			0
$315$	−9.47214	−	6.88191i	−0.533694	−	0.387752i
$316$		0			0
$317$	11.5172	+	8.36775i	0.646872	+	0.469980i	0.862204	−	0.506561i	$-0.169084\pi$
$317$	11.5172	+	8.36775i	0.646872	+	0.469980i	−0.215333	+	0.976541i	$0.569084\pi$
$318$		0			0
$319$	4.38197	+	3.18368i	0.245343	+	0.178252i
$320$		0			0
$321$	30.2254	−	21.9601i	1.68702	−	1.22569i
$322$		0			0
$323$	−12.3262	−	37.9363i	−0.685850	−	2.11083i
$324$		0			0
$325$	−13.6803	+	9.93935i	−0.758849	+	0.551336i
$326$		0			0
$327$	2.03444	+	6.26137i	0.112505	+	0.346254i
$328$		0			0
$329$	−0.309017	+	0.224514i	−0.0170367	+	0.0123779i
$330$		0			0
$331$	25.9443	+	18.8496i	1.42603	+	1.03607i	0.990739	+	0.135777i	$0.0433530\pi$
$331$	25.9443	+	18.8496i	1.42603	+	1.03607i	0.435287	+	0.900292i	$0.356647\pi$
$332$		0			0
$333$	13.3262	+	9.68208i	0.730273	+	0.530575i
$334$		0			0
$335$	−24.7984	+	18.0171i	−1.35488	+	0.984378i
$336$		0			0
$337$	−2.80902	+	8.64527i	−0.153017	+	0.470938i	−0.997955	−	0.0639272i	$-0.979637\pi$
$337$	−2.80902	+	8.64527i	−0.153017	+	0.470938i	0.844938	+	0.534865i	$0.179637\pi$
$338$		0			0
$339$	−7.29837	−	22.4621i	−0.396393	−	1.21997i
$340$		0			0
$341$	−1.79837	+	5.53483i	−0.0973874	+	0.299728i
$342$		0			0
$343$	18.7082			1.01015
$344$		0			0
$345$	−22.1353	+	16.0822i	−1.19172	+	0.865837i
$346$		0			0
$347$	5.54508	−	4.02874i	0.297676	−	0.216274i	−0.428915	−	0.903345i	$-0.641104\pi$
$347$	5.54508	−	4.02874i	0.297676	−	0.216274i	0.726590	+	0.687071i	$0.241104\pi$
$348$		0			0
$349$	25.1246			1.34489			0.672445	−	0.740147i	$-0.265244\pi$
$349$	25.1246			1.34489			0.672445	+	0.740147i	$0.265244\pi$
$350$		0			0
$351$	−7.56231			−0.403646
$352$		0			0
$353$	23.9164	−	17.3763i	1.27294	−	0.924846i	0.273626	−	0.961836i	$-0.411777\pi$
$353$	23.9164	−	17.3763i	1.27294	−	0.924846i	0.999316	+	0.0369896i	$0.0117768\pi$
$354$		0			0
$355$	−5.95492	−	18.3273i	−0.316054	−	0.972714i
$356$		0			0
$357$	−30.6525			−1.62230
$358$		0			0
$359$	−7.80902	+	24.0337i	−0.412144	+	1.26845i	0.502636	+	0.864498i	$0.332363\pi$
$359$	−7.80902	+	24.0337i	−0.412144	+	1.26845i	−0.914780	+	0.403951i	$0.867637\pi$
$360$		0			0
$361$	12.0623	+	37.1240i	0.634858	+	1.95389i
$362$		0			0
$363$	−6.54508	+	20.1437i	−0.343528	+	1.05727i
$364$		0			0
$365$	−24.5967			−1.28745
$366$		0			0
$367$	15.5902	+	11.3269i	0.813800	+	0.591260i	0.914930	−	0.403613i	$-0.132246\pi$
$367$	15.5902	+	11.3269i	0.813800	+	0.591260i	−0.101130	+	0.994873i	$0.532246\pi$
$368$		0			0
$369$	−9.23607	−	6.71040i	−0.480810	−	0.349329i
$370$		0			0
$371$	16.8262	−	12.2250i	0.873575	−	0.634689i
$372$		0			0
$373$	4.97214	+	15.3027i	0.257447	+	0.792342i	0.993338	+	0.115241i	$0.0367640\pi$
$373$	4.97214	+	15.3027i	0.257447	+	0.792342i	−0.735890	+	0.677101i	$0.763236\pi$
$374$		0			0
$375$	−7.72542	+	23.7764i	−0.398939	+	1.22781i
$376$		0			0
$377$	4.57953	+	14.0943i	0.235858	+	0.725895i
$378$		0			0
$379$	−4.04508	+	2.93893i	−0.207782	+	0.150963i	−0.686810	−	0.726837i	$-0.740989\pi$
$379$	−4.04508	+	2.93893i	−0.207782	+	0.150963i	0.479028	+	0.877800i	$0.340989\pi$
$380$		0			0
$381$	13.6180	+	9.89408i	0.697673	+	0.506889i
$382$		0			0
$383$	11.1353	+	8.09024i	0.568985	+	0.413392i	0.834736	−	0.550650i	$-0.185620\pi$
$383$	11.1353	+	8.09024i	0.568985	+	0.413392i	−0.265751	+	0.964042i	$0.585620\pi$
$384$		0			0
$385$	−7.23607			−0.368784
$386$		0			0
$387$	−2.70820	+	8.33499i	−0.137666	+	0.423692i
$388$		0			0
$389$	−3.83688	−	11.8087i	−0.194538	−	0.598725i	−0.999982	−	0.00605338i	$-0.998073\pi$
$389$	−3.83688	−	11.8087i	−0.194538	−	0.598725i	0.805444	−	0.592672i	$-0.201927\pi$
$390$		0			0
$391$	−8.85410	+	27.2501i	−0.447771	+	1.37810i
$392$		0			0
$393$	2.43769			0.122965
$394$		0			0
$395$	−3.68034	−	11.3269i	−0.185178	−	0.569919i
$396$		0			0
$397$	−16.2533	+	11.8087i	−0.815729	+	0.592662i	−0.915486	−	0.402350i	$-0.868194\pi$
$397$	−16.2533	+	11.8087i	−0.815729	+	0.592662i	0.0997568	+	0.995012i	$0.468194\pi$
$398$		0			0
$399$	44.5967			2.23263
$400$		0			0
$401$	−36.5967			−1.82755			−0.913777	−	0.406216i	$-0.866848\pi$
$401$	−36.5967			−1.82755			−0.913777	+	0.406216i	$0.866848\pi$
$402$		0			0
$403$	−12.8820	+	9.35930i	−0.641696	+	0.466220i
$404$		0			0
$405$	−19.8992	+	14.4576i	−0.988799	+	0.718404i
$406$		0			0
$407$	10.1803			0.504621
$408$		0			0
$409$	−6.34346	+	19.5232i	−0.313664	+	0.965358i	0.662637	+	0.748941i	$0.269437\pi$
$409$	−6.34346	+	19.5232i	−0.313664	+	0.965358i	−0.976301	+	0.216417i	$0.930563\pi$
$410$		0			0
$411$	3.45492	+	10.6331i	0.170418	+	0.524494i
$412$		0			0
$413$	1.92705	−	5.93085i	0.0948240	−	0.291838i
$414$		0			0
$415$	8.19098	−	5.95110i	0.402080	−	0.292128i
$416$		0			0
$417$	17.6631	+	12.8330i	0.864967	+	0.628435i
$418$		0			0
$419$	21.1353	+	15.3557i	1.03252	+	0.750173i	0.968812	−	0.247795i	$-0.0797060\pi$
$419$	21.1353	+	15.3557i	1.03252	+	0.750173i	0.0637123	+	0.997968i	$0.479706\pi$
$420$		0			0
$421$	−4.00000	+	2.90617i	−0.194948	+	0.141638i	−0.680977	−	0.732304i	$-0.738445\pi$
$421$	−4.00000	+	2.90617i	−0.194948	+	0.141638i	0.486029	+	0.873943i	$0.338445\pi$
$422$		0			0
$423$	−0.0901699	−	0.277515i	−0.00438421	−	0.0134932i
$424$		0			0
$425$	8.09017	+	24.8990i	0.392431	+	1.20778i
$426$		0			0
$427$	10.6631	+	32.8177i	0.516024	+	1.58816i
$428$		0			0
$429$	7.56231	−	5.49434i	0.365112	−	0.265269i
$430$		0			0
$431$	2.66312	+	1.93487i	0.128278	+	0.0931994i	0.650074	−	0.759871i	$-0.274738\pi$
$431$	2.66312	+	1.93487i	0.128278	+	0.0931994i	−0.521796	+	0.853070i	$0.674738\pi$
$432$		0			0
$433$	−1.83688	−	1.33457i	−0.0882749	−	0.0641354i	0.542772	−	0.839880i	$-0.317375\pi$
$433$	−1.83688	−	1.33457i	−0.0882749	−	0.0641354i	−0.631047	+	0.775744i	$0.717375\pi$
$434$		0			0
$435$	17.7254	+	12.8783i	0.849869	+	0.617466i
$436$		0			0
$437$	12.8820	−	39.6466i	0.616228	−	1.89655i
$438$		0			0
$439$	−5.19098	−	15.9762i	−0.247752	−	0.762503i	−0.995172	−	0.0981502i	$-0.968707\pi$
$439$	−5.19098	−	15.9762i	−0.247752	−	0.762503i	0.747420	−	0.664352i	$-0.231293\pi$
$440$		0			0
$441$	−0.0901699	+	0.277515i	−0.00429381	+	0.0132150i
$442$		0			0
$443$	8.34752			0.396603			0.198301	−	0.980141i	$-0.436458\pi$
$443$	8.34752			0.396603			0.198301	+	0.980141i	$0.436458\pi$
$444$		0			0
$445$	−8.94427			−0.423999
$446$		0			0
$447$	33.3156	−	24.2052i	1.57577	−	1.14487i
$448$		0			0
$449$	−23.9098			−1.12837			−0.564187	−	0.825647i	$-0.690810\pi$
$449$	−23.9098			−1.12837			−0.564187	+	0.825647i	$0.690810\pi$
$450$		0			0
$451$	−7.05573			−0.332241
$452$		0			0
$453$	0.690983	−	0.502029i	0.0324652	−	0.0235874i
$454$		0			0
$455$	−16.0172	−	11.6372i	−0.750899	−	0.545560i
$456$		0			0
$457$	−4.47214			−0.209198			−0.104599	−	0.994514i	$-0.533356\pi$
$457$	−4.47214			−0.209198			−0.104599	+	0.994514i	$0.533356\pi$
$458$		0			0
$459$	−3.61803	+	11.1352i	−0.168875	+	0.519745i
$460$		0			0
$461$	−6.57953	−	20.2497i	−0.306439	−	0.943123i	−0.979136	−	0.203205i	$-0.934864\pi$
$461$	−6.57953	−	20.2497i	−0.306439	−	0.943123i	0.672697	−	0.739918i	$-0.265136\pi$
$462$		0			0
$463$	4.92705	−	15.1639i	0.228979	−	0.704726i	−0.768884	−	0.639389i	$-0.779188\pi$
$463$	4.92705	−	15.1639i	0.228979	−	0.704726i	0.997863	−	0.0653377i	$-0.0208125\pi$
$464$		0			0
$465$	−7.27458	+	22.3888i	−0.337350	+	1.03826i
$466$		0			0
$467$	−5.88197	−	4.27350i	−0.272185	−	0.197754i	0.443317	−	0.896365i	$-0.353802\pi$
$467$	−5.88197	−	4.27350i	−0.272185	−	0.197754i	−0.715502	+	0.698611i	$0.753802\pi$
$468$		0			0
$469$	−29.0344	−	21.0948i	−1.34069	−	0.974065i
$470$		0			0
$471$	−7.66312	+	5.56758i	−0.353098	+	0.256541i
$472$		0			0
$473$	1.67376	+	5.15131i	0.0769597	+	0.236857i
$474$		0			0
$475$	−11.7705	−	36.2259i	−0.540068	−	1.66216i
$476$		0			0
$477$	4.90983	+	15.1109i	0.224806	+	0.691881i
$478$		0			0
$479$	18.1074	−	13.1558i	0.827348	−	0.601103i	−0.0914599	−	0.995809i	$-0.529153\pi$
$479$	18.1074	−	13.1558i	0.827348	−	0.601103i	0.918808	+	0.394705i	$0.129153\pi$
$480$		0			0
$481$	22.5344	+	16.3722i	1.02748	+	0.746509i
$482$		0			0
$483$	−25.9164	−	18.8294i	−1.17924	−	0.856766i
$484$		0			0
$485$	10.5517	+	32.4747i	0.479126	+	1.47460i
$486$		0			0
$487$	8.25329	−	25.4010i	0.373992	−	1.15103i	−0.570164	−	0.821531i	$-0.693120\pi$
$487$	8.25329	−	25.4010i	0.373992	−	1.15103i	0.944156	−	0.329499i	$-0.106880\pi$
$488$		0			0
$489$	−10.4894	−	32.2829i	−0.474345	−	1.45988i
$490$		0			0
$491$	−1.16312	+	3.57971i	−0.0524908	+	0.161550i	−0.973866	−	0.227125i	$-0.927067\pi$
$491$	−1.16312	+	3.57971i	−0.0524908	+	0.161550i	0.921375	+	0.388676i	$0.127067\pi$
$492$		0			0
$493$	22.9443			1.03336
$494$		0			0
$495$	1.70820	−	5.25731i	0.0767781	−	0.236299i
$496$		0			0
$497$	18.2533	−	13.2618i	0.818772	−	0.594873i
$498$		0			0
$499$	−29.5623			−1.32339			−0.661695	−	0.749773i	$-0.730163\pi$
$499$	−29.5623			−1.32339			−0.661695	+	0.749773i	$0.730163\pi$
$500$		0			0
$501$	42.5623			1.90154
$502$		0			0
$503$	−12.8541	+	9.33905i	−0.573136	+	0.416408i	−0.836243	−	0.548359i	$-0.815253\pi$
$503$	−12.8541	+	9.33905i	−0.573136	+	0.416408i	0.263107	+	0.964767i	$0.415253\pi$
$504$		0			0
$505$	12.3992	−	38.1608i	0.551757	−	1.69813i
$506$		0			0
$507$	−3.49342			−0.155148
$508$		0			0
$509$	9.60739	−	29.5685i	0.425840	−	1.31060i	−0.476347	−	0.879257i	$-0.658040\pi$
$509$	9.60739	−	29.5685i	0.425840	−	1.31060i	0.902188	−	0.431344i	$-0.141960\pi$
$510$		0			0
$511$	−8.89919	−	27.3889i	−0.393677	−	1.21161i
$512$		0			0
$513$	5.26393	−	16.2007i	0.232408	−	0.715279i
$514$		0			0
$515$	−2.17376	−	6.69015i	−0.0957874	−	0.294803i
$516$		0			0
$517$	−0.145898	−	0.106001i	−0.00641659	−	0.00466192i
$518$		0			0
$519$	−11.8090	−	8.57975i	−0.518358	−	0.376609i
$520$		0			0
$521$	−6.80902	+	4.94704i	−0.298308	+	0.216734i	−0.726864	−	0.686782i	$-0.759023\pi$
$521$	−6.80902	+	4.94704i	−0.298308	+	0.216734i	0.428555	+	0.903516i	$0.359023\pi$
$522$		0			0
$523$	5.68034	+	17.4823i	0.248384	+	0.764447i	0.995061	+	0.0992609i	$0.0316478\pi$
$523$	5.68034	+	17.4823i	0.248384	+	0.764447i	−0.746678	+	0.665186i	$0.768352\pi$
$524$		0			0
$525$	−29.2705			−1.27747
$526$		0			0
$527$	7.61803	+	23.4459i	0.331847	+	1.02132i
$528$		0			0
$529$	−5.61803	+	4.08174i	−0.244262	+	0.177467i
$530$		0			0
$531$	3.85410	+	2.80017i	0.167254	+	0.121517i
$532$		0			0
$533$	−15.6180	−	11.3472i	−0.676492	−	0.491500i
$534$		0			0
$535$	11.5451	−	35.5321i	0.499138	−	1.53619i
$536$		0			0
$537$	−2.27458	+	7.00042i	−0.0981552	+	0.302091i
$538$		0			0
$539$	0.0557281	+	0.171513i	0.00240038	+	0.00738761i
$540$		0			0
$541$	2.67376	−	8.22899i	0.114954	−	0.353792i	−0.876983	−	0.480521i	$-0.840448\pi$
$541$	2.67376	−	8.22899i	0.114954	−	0.353792i	0.991937	+	0.126729i	$0.0404477\pi$
$542$		0			0
$543$	−18.5410			−0.795671
$544$		0			0
$545$	5.32624	+	3.86974i	0.228151	+	0.165761i
$546$		0			0
$547$	7.57295	−	5.50207i	0.323796	−	0.235252i	−0.413998	−	0.910278i	$-0.635868\pi$
$547$	7.57295	−	5.50207i	0.323796	−	0.235252i	0.737794	+	0.675026i	$0.235868\pi$
$548$		0			0
$549$	−26.3607			−1.12505
$550$		0			0
$551$	−33.3820			−1.42212
$552$		0			0
$553$	11.2812	−	8.19624i	0.479723	−	0.348539i
$554$		0			0
$555$	41.1803			1.74801
$556$		0			0
$557$	−7.81966			−0.331330			−0.165665	−	0.986182i	$-0.552977\pi$
$557$	−7.81966			−0.331330			−0.165665	+	0.986182i	$0.552977\pi$
$558$		0			0
$559$	−4.57953	+	14.0943i	−0.193693	+	0.596127i
$560$		0			0
$561$	−4.47214	−	13.7638i	−0.188814	−	0.581109i
$562$		0			0
$563$	−0.607391	+	1.86936i	−0.0255985	+	0.0787840i	−0.963040	−	0.269360i	$-0.913188\pi$
$563$	−0.607391	+	1.86936i	−0.0255985	+	0.0787840i	0.937441	+	0.348144i	$0.113188\pi$
$564$		0			0
$565$	−19.1074	−	13.8823i	−0.803854	−	0.584034i
$566$		0			0
$567$	−23.2984	−	16.9273i	−0.978440	−	0.710878i
$568$		0			0
$569$	−14.1353	−	10.2699i	−0.592581	−	0.430535i	0.250657	−	0.968076i	$-0.419353\pi$
$569$	−14.1353	−	10.2699i	−0.592581	−	0.430535i	−0.843238	+	0.537541i	$0.819353\pi$
$570$		0			0
$571$	−26.1353	+	18.9884i	−1.09373	+	0.794639i	−0.980025	−	0.198876i	$-0.936271\pi$
$571$	−26.1353	+	18.9884i	−1.09373	+	0.794639i	−0.113702	+	0.993515i	$0.536271\pi$
$572$		0			0
$573$	0.201626	+	0.620541i	0.00842305	+	0.0259235i
$574$		0			0
$575$	−8.45492	+	26.0216i	−0.352594	+	1.08517i
$576$		0			0
$577$	4.90983	+	15.1109i	0.204399	+	0.629075i	0.999738	+	0.0229098i	$0.00729304\pi$
$577$	4.90983	+	15.1109i	0.204399	+	0.629075i	−0.795339	+	0.606165i	$0.792707\pi$
$578$		0			0
$579$	13.9443	−	10.1311i	0.579504	−	0.421034i
$580$		0			0
$581$	9.59017	+	6.96767i	0.397867	+	0.289068i
$582$		0			0
$583$	7.94427	+	5.77185i	0.329018	+	0.239046i
$584$		0			0
$585$	12.2361	−	8.89002i	0.505899	−	0.367557i
$586$		0			0
$587$	9.72542	−	29.9318i	0.401411	−	1.23542i	−0.522444	−	0.852674i	$-0.674979\pi$
$587$	9.72542	−	29.9318i	0.401411	−	1.23542i	0.923855	−	0.382743i	$-0.125021\pi$
$588$		0			0
$589$	−11.0836	−	34.1118i	−0.456691	−	1.40555i
$590$		0			0
$591$	−10.2016	+	31.3974i	−0.419639	+	1.29152i
$592$		0			0
$593$	19.5623			0.803328			0.401664	−	0.915787i	$-0.368432\pi$
$593$	19.5623			0.803328			0.401664	+	0.915787i	$0.368432\pi$
$594$		0			0
$595$	−24.7984	+	18.0171i	−1.01663	+	0.738628i
$596$		0			0
$597$	16.9721	−	12.3310i	0.694623	−	0.504673i
$598$		0			0
$599$	15.1803			0.620252			0.310126	−	0.950695i	$-0.399629\pi$
$599$	15.1803			0.620252			0.310126	+	0.950695i	$0.399629\pi$
$600$		0			0
$601$	−22.4377			−0.915253			−0.457626	−	0.889145i	$-0.651300\pi$
$601$	−22.4377			−0.915253			−0.457626	+	0.889145i	$0.651300\pi$
$602$		0			0
$603$	22.1803	−	16.1150i	0.903253	−	0.656252i
$604$		0			0
$605$	6.54508	+	20.1437i	0.266096	+	0.818958i
$606$		0			0
$607$	−1.27051			−0.0515684			−0.0257842	−	0.999668i	$-0.508208\pi$
$607$	−1.27051			−0.0515684			−0.0257842	+	0.999668i	$0.508208\pi$
$608$		0			0
$609$	−7.92705	+	24.3970i	−0.321220	+	0.988614i
$610$		0			0
$611$	−0.152476	−	0.469272i	−0.00616851	−	0.0189847i
$612$		0			0
$613$	−3.10081	+	9.54332i	−0.125241	+	0.385451i	−0.993945	−	0.109880i	$-0.964953\pi$
$613$	−3.10081	+	9.54332i	−0.125241	+	0.385451i	0.868704	+	0.495331i	$0.164953\pi$
$614$		0			0
$615$	−28.5410			−1.15088
$616$		0			0
$617$	−24.7533	−	17.9843i	−0.996530	−	0.724021i	−0.0351885	−	0.999381i	$-0.511203\pi$
$617$	−24.7533	−	17.9843i	−0.996530	−	0.724021i	−0.961341	+	0.275359i	$0.911203\pi$
$618$		0			0
$619$	−32.9336	−	23.9277i	−1.32371	−	0.961735i	−0.999878	−	0.0156216i	$-0.995027\pi$
$619$	−32.9336	−	23.9277i	−1.32371	−	0.961735i	−0.323836	−	0.946113i	$-0.604973\pi$
$620$		0			0
$621$	−9.89919	+	7.19218i	−0.397241	+	0.288612i
$622$		0			0
$623$	−3.23607	−	9.95959i	−0.129650	−	0.399023i
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$	6.50658	+	20.0252i	0.259848	+	0.799729i
$628$		0			0
$629$	34.8885	−	25.3480i	1.39110	−	1.01069i
$630$		0			0
$631$	6.33688	+	4.60401i	0.252267	+	0.183283i	0.706731	−	0.707482i	$-0.250169\pi$
$631$	6.33688	+	4.60401i	0.252267	+	0.183283i	−0.454464	+	0.890765i	$0.650169\pi$
$632$		0			0
$633$	36.0795	+	26.2133i	1.43403	+	1.04189i
$634$		0			0
$635$	16.8328			0.667990
$636$		0			0
$637$	−0.152476	+	0.469272i	−0.00604131	+	0.0185932i
$638$		0			0
$639$	5.32624	+	16.3925i	0.210703	+	0.648476i
$640$		0			0
$641$	−5.39261	+	16.5967i	−0.212995	+	0.655532i	0.786295	+	0.617852i	$0.211997\pi$
$641$	−5.39261	+	16.5967i	−0.212995	+	0.655532i	−0.999290	+	0.0376802i	$0.988003\pi$
$642$		0			0
$643$	−19.0557			−0.751485			−0.375742	−	0.926724i	$-0.622612\pi$
$643$	−19.0557			−0.751485			−0.375742	+	0.926724i	$0.622612\pi$
$644$		0			0
$645$	6.77051	+	20.8375i	0.266589	+	0.820475i
$646$		0			0
$647$	−18.3262	+	13.3148i	−0.720479	+	0.523458i	−0.886537	−	0.462657i	$-0.846896\pi$
$647$	−18.3262	+	13.3148i	−0.720479	+	0.523458i	0.166058	+	0.986116i	$0.446896\pi$
$648$		0			0
$649$	2.94427			0.115573
$650$		0			0
$651$	−27.5623			−1.08025
$652$		0			0
$653$	−24.6803	+	17.9313i	−0.965816	+	0.701707i	−0.954494	−	0.298229i	$-0.903604\pi$
$653$	−24.6803	+	17.9313i	−0.965816	+	0.701707i	−0.0113221	+	0.999936i	$0.503604\pi$
$654$		0			0
$655$	1.97214	−	1.43284i	0.0770577	−	0.0559857i
$656$		0			0
$657$	22.0000			0.858302
$658$		0			0
$659$	−0.0344419	+	0.106001i	−0.00134166	+	0.00412922i	−0.951725	−	0.306952i	$-0.900691\pi$
$659$	−0.0344419	+	0.106001i	−0.00134166	+	0.00412922i	0.950383	+	0.311081i	$0.100691\pi$
$660$		0			0
$661$	−10.6803	−	32.8707i	−0.415417	−	1.27852i	−0.911877	−	0.410463i	$-0.865367\pi$
$661$	−10.6803	−	32.8707i	−0.415417	−	1.27852i	0.496460	−	0.868059i	$-0.334633\pi$
$662$		0			0
$663$	12.2361	−	37.6587i	0.475210	−	1.46254i
$664$		0			0
$665$	36.0795	−	26.2133i	1.39910	−	1.01651i
$666$		0			0
$667$	19.3992	+	14.0943i	0.751140	+	0.545735i
$668$		0			0
$669$	10.3262	+	7.50245i	0.399235	+	0.290062i
$670$		0			0
$671$	−13.1803	+	9.57608i	−0.508821	+	0.369680i
$672$		0			0
$673$	−10.2361	−	31.5034i	−0.394571	−	1.21437i	−0.929295	−	0.369339i	$-0.879584\pi$
$673$	−10.2361	−	31.5034i	−0.394571	−	1.21437i	0.534723	−	0.845027i	$-0.320416\pi$
$674$		0			0
$675$	−3.45492	+	10.6331i	−0.132980	+	0.409270i
$676$		0			0
$677$	−2.42705	−	7.46969i	−0.0932791	−	0.287084i	0.893522	−	0.449019i	$-0.148226\pi$
$677$	−2.42705	−	7.46969i	−0.0932791	−	0.287084i	−0.986801	+	0.161935i	$0.948226\pi$
$678$		0			0
$679$	−32.3435	+	23.4989i	−1.24123	+	0.901805i
$680$		0			0
$681$	−46.3050	−	33.6425i	−1.77441	−	1.28918i
$682$		0			0
$683$	−16.7533	−	12.1720i	−0.641047	−	0.465748i	0.219163	−	0.975688i	$-0.429667\pi$
$683$	−16.7533	−	12.1720i	−0.641047	−	0.465748i	−0.860210	+	0.509941i	$0.829667\pi$
$684$		0			0
$685$	9.04508	+	6.57164i	0.345595	+	0.251089i
$686$		0			0
$687$	13.9443	−	42.9161i	0.532007	−	1.63735i
$688$		0			0
$689$	8.30244	+	25.5523i	0.316298	+	0.973464i
$690$		0			0
$691$	14.4787	−	44.5609i	0.550796	−	1.69518i	−0.155998	−	0.987757i	$-0.549859\pi$
$691$	14.4787	−	44.5609i	0.550796	−	1.69518i	0.706794	−	0.707419i	$-0.250141\pi$
$692$		0			0
$693$	6.47214			0.245856
$694$		0			0
$695$	21.8328			0.828166
$696$		0			0
$697$	−24.1803	+	17.5680i	−0.915896	+	0.665437i
$698$		0			0
$699$	13.4164			0.507455
$700$		0			0
$701$	2.18034			0.0823503			0.0411752	−	0.999152i	$-0.486890\pi$
$701$	2.18034			0.0823503			0.0411752	+	0.999152i	$0.486890\pi$
$702$		0			0
$703$	−50.7599	+	36.8792i	−1.91444	+	1.39093i
$704$		0			0
$705$	−0.590170	−	0.428784i	−0.0222271	−	0.0161489i
$706$		0			0
$707$	46.9787			1.76682
$708$		0			0
$709$	−11.3090	+	34.8056i	−0.424719	+	1.30715i	0.478544	+	0.878064i	$0.341165\pi$
$709$	−11.3090	+	34.8056i	−0.424719	+	1.30715i	−0.903263	+	0.429087i	$0.858835\pi$
$710$		0			0
$711$	3.29180	+	10.1311i	0.123452	+	0.379946i
$712$		0			0
$713$	−7.96149	+	24.5030i	−0.298160	+	0.917643i
$714$		0			0
$715$	2.88854	−	8.89002i	0.108025	−	0.332468i
$716$		0			0
$717$	−40.2254	−	29.2255i	−1.50225	−	1.09145i
$718$		0			0
$719$	−30.9894	−	22.5151i	−1.15571	−	0.839671i	−0.166479	−	0.986045i	$-0.553240\pi$
$719$	−30.9894	−	22.5151i	−1.15571	−	0.839671i	−0.989229	+	0.146374i	$0.953240\pi$
$720$		0			0
$721$	6.66312	−	4.84104i	0.248148	−	0.180290i
$722$		0			0
$723$	7.92705	+	24.3970i	0.294810	+	0.907332i
$724$		0			0
$725$	21.9098			0.813711
$726$		0			0
$727$	−3.50000	−	10.7719i	−0.129808	−	0.399507i	0.864939	−	0.501878i	$-0.167357\pi$
$727$	−3.50000	−	10.7719i	−0.129808	−	0.399507i	−0.994746	+	0.102370i	$0.967357\pi$
$728$		0			0
$729$	5.66312	−	4.11450i	0.209745	−	0.152389i
$730$		0			0
$731$	18.5623	+	13.4863i	0.686552	+	0.498809i
$732$		0			0
$733$	−8.78115	−	6.37988i	−0.324339	−	0.235646i	0.413686	−	0.910420i	$-0.364241\pi$
$733$	−8.78115	−	6.37988i	−0.324339	−	0.235646i	−0.738025	+	0.674774i	$0.764241\pi$
$734$		0			0
$735$	0.225425	+	0.693786i	0.00831492	+	0.0255907i
$736$		0			0
$737$	5.23607	−	16.1150i	0.192873	−	0.593602i
$738$		0			0
$739$	−3.50000	−	10.7719i	−0.128750	−	0.396250i	0.865816	−	0.500363i	$-0.166800\pi$
$739$	−3.50000	−	10.7719i	−0.128750	−	0.396250i	−0.994566	+	0.104112i	$0.966800\pi$
$740$		0			0
$741$	−17.8024	+	54.7903i	−0.653989	+	2.01277i
$742$		0			0
$743$	46.2492			1.69672			0.848360	−	0.529420i	$-0.177591\pi$
$743$	46.2492			1.69672			0.848360	+	0.529420i	$0.177591\pi$
$744$		0			0
$745$	12.7254	−	39.1648i	0.466223	−	1.43489i
$746$		0			0
$747$	−7.32624	+	5.32282i	−0.268053	+	0.194752i
$748$		0			0
$749$	43.7426			1.59832
$750$		0			0
$751$	31.7639			1.15908			0.579541	−	0.814943i	$-0.303232\pi$
$751$	31.7639			1.15908			0.579541	+	0.814943i	$0.303232\pi$
$752$		0			0
$753$	−14.5729	+	10.5879i	−0.531068	+	0.385843i
$754$		0			0
$755$	0.263932	−	0.812299i	0.00960547	−	0.0295626i
$756$		0			0
$757$	15.0000			0.545184			0.272592	−	0.962130i	$-0.412119\pi$
$757$	15.0000			0.545184			0.272592	+	0.962130i	$0.412119\pi$
$758$		0			0
$759$	4.67376	−	14.3844i	0.169647	−	0.522119i
$760$		0			0
$761$	−7.77051	−	23.9152i	−0.281681	−	0.866924i	−0.987374	−	0.158407i	$-0.949364\pi$
$761$	−7.77051	−	23.9152i	−0.281681	−	0.866924i	0.705693	−	0.708518i	$-0.250636\pi$
$762$		0			0
$763$	−2.38197	+	7.33094i	−0.0862330	+	0.265398i
$764$		0			0
$765$	−7.23607	−	22.2703i	−0.261621	−	0.805185i
$766$		0			0
$767$	6.51722	+	4.73504i	0.235323	+	0.170972i
$768$		0			0
$769$	−31.9787	−	23.2339i	−1.15318	−	0.837836i	−0.164281	−	0.986414i	$-0.552530\pi$
$769$	−31.9787	−	23.2339i	−1.15318	−	0.837836i	−0.988901	+	0.148578i	$0.952530\pi$
$770$		0			0
$771$	6.54508	−	4.75528i	0.235715	−	0.171257i
$772$		0			0
$773$	8.24265	+	25.3683i	0.296467	+	0.912433i	0.982725	+	0.185074i	$0.0592524\pi$
$773$	8.24265	+	25.3683i	0.296467	+	0.912433i	−0.686257	+	0.727359i	$0.740748\pi$
$774$		0			0
$775$	7.27458	+	22.3888i	0.261310	+	0.804231i
$776$		0			0
$777$	14.8992	+	45.8550i	0.534505	+	1.64504i
$778$		0			0
$779$	35.1803	−	25.5600i	1.26047	−	0.915783i
$780$		0			0
$781$	8.61803	+	6.26137i	0.308378	+	0.224049i
$782$		0			0
$783$	7.92705	+	5.75934i	0.283290	+	0.205822i
$784$		0			0
$785$	−2.92705	+	9.00854i	−0.104471	+	0.321528i
$786$		0			0
$787$	−9.36068	+	28.8092i	−0.333672	+	1.02694i	0.633700	+	0.773579i	$0.281535\pi$
$787$	−9.36068	+	28.8092i	−0.333672	+	1.02694i	−0.967372	+	0.253359i	$0.918465\pi$
$788$		0			0
$789$	9.57295	+	29.4625i	0.340806	+	1.04889i
$790$		0			0
$791$	8.54508	−	26.2991i	0.303828	−	0.935087i
$792$		0			0
$793$	−44.5755			−1.58292
$794$		0			0
$795$	32.1353	+	23.3476i	1.13972	+	0.828055i
$796$		0			0
$797$	4.28115	−	3.11044i	0.151646	−	0.110177i	−0.509375	−	0.860545i	$-0.670123\pi$
$797$	4.28115	−	3.11044i	0.151646	−	0.110177i	0.661021	+	0.750367i	$0.270123\pi$
$798$		0			0
$799$	−0.763932			−0.0270260
$800$		0			0
$801$	8.00000			0.282666
$802$		0			0
$803$	11.0000	−	7.99197i	0.388182	−	0.282030i
$804$		0			0
$805$	−32.0344			−1.12907
$806$		0			0
$807$	−31.9574			−1.12495
$808$		0			0
$809$	2.22542	−	6.84915i	0.0782418	−	0.240803i	−0.904284	−	0.426932i	$-0.859594\pi$
$809$	2.22542	−	6.84915i	0.0782418	−	0.240803i	0.982525	+	0.186129i	$0.0595942\pi$
$810$		0			0
$811$	14.0172	+	43.1406i	0.492211	+	1.51487i	0.821258	+	0.570557i	$0.193273\pi$
$811$	14.0172	+	43.1406i	0.492211	+	1.51487i	−0.329047	+	0.944314i	$0.606727\pi$
$812$		0			0
$813$	−8.94427	+	27.5276i	−0.313689	+	0.965436i
$814$		0			0
$815$	−27.4615	−	19.9519i	−0.961934	−	0.698886i
$816$		0			0
$817$	−27.0066	−	19.6214i	−0.944841	−	0.686467i
$818$		0			0
$819$	14.3262	+	10.4086i	0.500599	+	0.363707i
$820$		0			0
$821$	11.2082	−	8.14324i	0.391169	−	0.284201i	−0.374765	−	0.927120i	$-0.622277\pi$
$821$	11.2082	−	8.14324i	0.391169	−	0.284201i	0.765934	+	0.642919i	$0.222277\pi$
$822$		0			0
$823$	4.20163	+	12.9313i	0.146459	+	0.450756i	0.997196	−	0.0748368i	$-0.0238436\pi$
$823$	4.20163	+	12.9313i	0.146459	+	0.450756i	−0.850736	+	0.525593i	$0.823844\pi$
$824$		0			0
$825$	−4.27051	−	13.1433i	−0.148680	−	0.457590i
$826$		0			0
$827$	−10.1525	−	31.2461i	−0.353036	−	1.08653i	−0.957139	−	0.289628i	$-0.906469\pi$
$827$	−10.1525	−	31.2461i	−0.353036	−	1.08653i	0.604103	−	0.796906i	$-0.293531\pi$
$828$		0			0
$829$	3.59017	−	2.60841i	0.124692	−	0.0905939i	−0.523691	−	0.851908i	$-0.675446\pi$
$829$	3.59017	−	2.60841i	0.124692	−	0.0905939i	0.648383	+	0.761314i	$0.275446\pi$
$830$		0			0
$831$	−38.3156	−	27.8379i	−1.32915	−	0.965686i
$832$		0			0
$833$	0.618034	+	0.449028i	0.0214136	+	0.0155579i
$834$		0			0
$835$	34.4336	−	25.0175i	1.19162	−	0.865766i
$836$		0			0
$837$	−3.25329	+	10.0126i	−0.112450	+	0.346086i
$838$		0			0
$839$	3.02786	+	9.31881i	0.104533	+	0.321721i	0.989621	−	0.143704i	$-0.0459014\pi$
$839$	3.02786	+	9.31881i	0.104533	+	0.321721i	−0.885087	+	0.465425i	$0.845901\pi$
$840$		0			0
$841$	−3.02786	+	9.31881i	−0.104409	+	0.321338i
$842$		0			0
$843$	20.4508			0.704365
$844$		0			0
$845$	−2.82624	+	2.05338i	−0.0972255	+	0.0706385i
$846$		0			0
$847$	−20.0623	+	14.5761i	−0.689349	+	0.500841i
$848$		0			0
$849$	16.2574			0.557951
$850$		0			0
$851$	45.0689			1.54494
$852$		0			0
$853$	−4.38197	+	3.18368i	−0.150036	+	0.109007i	−0.660271	−	0.751028i	$-0.729558\pi$
$853$	−4.38197	+	3.18368i	−0.150036	+	0.109007i	0.510235	+	0.860035i	$0.329558\pi$
$854$		0			0
$855$	10.5279	+	32.4014i	0.360045	+	1.10811i
$856$		0			0
$857$	−3.14590			−0.107462			−0.0537309	−	0.998555i	$-0.517111\pi$
$857$	−3.14590			−0.107462			−0.0537309	+	0.998555i	$0.517111\pi$
$858$		0			0
$859$	−9.45492	+	29.0992i	−0.322598	+	0.992853i	0.649916	+	0.760006i	$0.274804\pi$
$859$	−9.45492	+	29.0992i	−0.322598	+	0.992853i	−0.972513	+	0.232847i	$0.925196\pi$
$860$		0			0
$861$	−10.3262	−	31.7809i	−0.351917	−	1.08309i
$862$		0			0
$863$	4.17376	−	12.8455i	0.142077	−	0.437267i	−0.854547	−	0.519374i	$-0.826165\pi$
$863$	4.17376	−	12.8455i	0.142077	−	0.437267i	0.996623	+	0.0821076i	$0.0261651\pi$
$864$		0			0
$865$	−14.5967			−0.496304
$866$		0			0
$867$	−18.8435	−	13.6906i	−0.639957	−	0.464956i
$868$		0			0
$869$	5.32624	+	3.86974i	0.180680	+	0.131272i
$870$		0			0
$871$	37.5066	−	27.2501i	1.27086	−	0.923335i
$872$		0			0
$873$	−9.43769	−	29.0462i	−0.319418	−	0.983066i
$874$		0			0
$875$	−23.6803	+	17.2048i	−0.800542	+	0.581628i
$876$		0			0
$877$	10.7082	+	32.9565i	0.361590	+	1.11286i	0.952089	+	0.305822i	$0.0989312\pi$
$877$	10.7082	+	32.9565i	0.361590	+	1.11286i	−0.590498	+	0.807039i	$0.701069\pi$
$878$		0			0
$879$	−0.854102	+	0.620541i	−0.0288081	+	0.0209303i
$880$		0			0
$881$	35.1246	+	25.5195i	1.18338	+	0.859775i	0.992549	−	0.121849i	$-0.0388822\pi$
$881$	35.1246	+	25.5195i	1.18338	+	0.859775i	0.190830	+	0.981623i	$0.438882\pi$
$882$		0			0
$883$	24.6525	+	17.9111i	0.829622	+	0.602756i	0.919452	−	0.393202i	$-0.128633\pi$
$883$	24.6525	+	17.9111i	0.829622	+	0.602756i	−0.0898305	+	0.995957i	$0.528633\pi$
$884$		0			0
$885$	11.9098			0.400345
$886$		0			0
$887$	0.652476	−	2.00811i	0.0219080	−	0.0674259i	−0.939505	−	0.342536i	$-0.888714\pi$
$887$	0.652476	−	2.00811i	0.0219080	−	0.0674259i	0.961413	+	0.275110i	$0.0887142\pi$
$888$		0			0
$889$	6.09017	+	18.7436i	0.204258	+	0.628641i
$890$		0			0
$891$	4.20163	−	12.9313i	0.140760	−	0.433214i
$892$		0			0
$893$	1.11146			0.0371935
$894$		0			0
$895$	2.27458	+	7.00042i	0.0760307	+	0.233998i
$896$		0			0
$897$	33.4787	−	24.3237i	1.11782	−	0.812145i
$898$		0			0
$899$	20.6312			0.688089
$900$		0			0
$901$	41.5967			1.38579
$902$		0			0
$903$	−20.7533	+	15.0781i	−0.690626	+	0.501769i
$904$		0			0
$905$	−15.0000	+	10.8981i	−0.498617	+	0.362266i
$906$		0			0
$907$	−33.1803			−1.10174			−0.550868	−	0.834593i	$-0.685703\pi$
$907$	−33.1803			−1.10174			−0.550868	+	0.834593i	$0.685703\pi$
$908$		0			0
$909$	−11.0902	+	34.1320i	−0.367838	+	1.13209i
$910$		0			0
$911$	−8.45492	−	26.0216i	−0.280124	−	0.862133i	−0.987818	−	0.155614i	$-0.950265\pi$
$911$	−8.45492	−	26.0216i	−0.280124	−	0.862133i	0.707694	−	0.706519i	$-0.249735\pi$
$912$		0			0
$913$	−1.72949	+	5.32282i	−0.0572378	+	0.176160i
$914$		0			0
$915$	−53.3156	+	38.7360i	−1.76256	+	1.28057i
$916$		0			0
$917$	2.30902	+	1.67760i	0.0762505	+	0.0553992i
$918$		0			0
$919$	−3.69098	−	2.68166i	−0.121754	−	0.0884597i	0.525242	−	0.850953i	$-0.323975\pi$
$919$	−3.69098	−	2.68166i	−0.121754	−	0.0884597i	−0.646996	+	0.762493i	$0.723975\pi$
$920$		0			0
$921$	19.4721	−	14.1473i	0.641629	−	0.466171i
$922$		0			0
$923$	9.00658	+	27.7194i	0.296455	+	0.912395i
$924$		0			0
$925$	33.3156	−	24.2052i	1.09541	−	0.795862i
$926$		0			0
$927$	1.94427	+	5.98385i	0.0638583	+	0.196536i
$928$		0			0
$929$	−31.0967	+	22.5931i	−1.02025	+	0.741256i	−0.966334	−	0.257290i	$-0.917171\pi$
$929$	−31.0967	+	22.5931i	−1.02025	+	0.741256i	−0.0539168	+	0.998545i	$0.517171\pi$
$930$		0			0
$931$	−0.899187	−	0.653298i	−0.0294697	−	0.0214110i
$932$		0			0
$933$	−8.88197	−	6.45313i	−0.290783	−	0.211266i
$934$		0			0
$935$	−11.7082	−	8.50651i	−0.382899	−	0.278193i
$936$		0			0
$937$	6.35410	−	19.5559i	0.207579	−	0.638864i	−0.792018	−	0.610498i	$-0.790970\pi$
$937$	6.35410	−	19.5559i	0.207579	−	0.638864i	0.999598	−	0.0283663i	$-0.00903049\pi$
$938$		0			0
$939$	3.94427	+	12.1392i	0.128716	+	0.396148i
$940$		0			0
$941$	−14.8156	+	45.5977i	−0.482975	+	1.48644i	0.351918	+	0.936031i	$0.385529\pi$
$941$	−14.8156	+	45.5977i	−0.482975	+	1.48644i	−0.834893	+	0.550412i	$0.814471\pi$
$942$		0			0
$943$	−31.2361			−1.01719
$944$		0			0
$945$	−13.0902			−0.425823
$946$		0			0
$947$	−44.5066	+	32.3359i	−1.44627	+	1.05078i	−0.459584	+	0.888134i	$0.652002\pi$
$947$	−44.5066	+	32.3359i	−1.44627	+	1.05078i	−0.986685	+	0.162642i	$0.947998\pi$
$948$		0			0
$949$	37.2016			1.20762
$950$		0			0
$951$	−31.8328			−1.03225
$952$		0			0
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.124229	−	0.992254i	$-0.460354\pi$
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.982078	+	0.188474i	$0.0603542\pi$
$954$		0			0
$955$	0.527864	+	0.383516i	0.0170813	+	0.0124103i
$956$		0			0
$957$	−12.1115			−0.391508
$958$		0			0
$959$	−4.04508	+	12.4495i	−0.130623	+	0.402015i
$960$		0			0
$961$	−2.72949	−	8.40051i	−0.0880481	−	0.270984i
$962$		0			0
$963$	−10.3262	+	31.7809i	−0.332758	+	1.02412i
$964$		0			0
$965$	5.32624	−	16.3925i	0.171458	−	0.527692i
$966$		0			0
$967$	0.381966	+	0.277515i	0.0122832	+	0.00892427i	0.593910	−	0.804532i	$-0.297584\pi$
$967$	0.381966	+	0.277515i	0.0122832	+	0.00892427i	−0.581627	+	0.813456i	$0.697584\pi$
$968$		0			0
$969$	72.1591	+	52.4266i	2.31808	+	1.68419i
$970$		0			0
$971$	22.1976	−	16.1275i	0.712354	−	0.517555i	−0.171578	−	0.985170i	$-0.554887\pi$
$971$	22.1976	−	16.1275i	0.712354	−	0.517555i	0.883932	+	0.467615i	$0.154887\pi$
$972$		0			0
$973$	7.89919	+	24.3112i	0.253236	+	0.779381i
$974$		0			0
$975$	11.6844	−	35.9609i	0.374200	−	1.15167i
$976$		0			0
$977$	−5.78115	−	17.7926i	−0.184955	−	0.569234i	0.814992	−	0.579472i	$-0.196741\pi$
$977$	−5.78115	−	17.7926i	−0.184955	−	0.569234i	−0.999948	+	0.0102376i	$0.996741\pi$
$978$		0			0
$979$	4.00000	−	2.90617i	0.127841	−	0.0928816i
$980$		0			0
$981$	−4.76393	−	3.46120i	−0.152101	−	0.110508i
$982$		0			0
$983$	3.07295	+	2.23263i	0.0980119	+	0.0712098i	0.635712	−	0.771926i	$-0.280707\pi$
$983$	3.07295	+	2.23263i	0.0980119	+	0.0712098i	−0.537700	+	0.843136i	$0.680707\pi$
$984$		0			0
$985$	10.2016	+	31.3974i	0.325051	+	1.00040i
$986$		0			0
$987$	0.263932	−	0.812299i	0.00840105	−	0.0258558i
$988$		0			0
$989$	7.40983	+	22.8051i	0.235619	+	0.725160i
$990$		0			0
$991$	15.8156	−	48.6754i	0.502399	−	1.54622i	−0.302701	−	0.953086i	$-0.597888\pi$
$991$	15.8156	−	48.6754i	0.502399	−	1.54622i	0.805100	−	0.593139i	$-0.202112\pi$
$992$		0			0
$993$	−71.7082			−2.27559
$994$		0			0
$995$	6.48278	−	19.9519i	0.205518	−	0.632519i
$996$		0			0
$997$	31.1697	−	22.6461i	0.987154	−	0.717210i	0.0278582	−	0.999612i	$-0.491131\pi$
$997$	31.1697	−	22.6461i	0.987154	−	0.717210i	0.959296	+	0.282402i	$0.0911313\pi$
$998$		0			0
$999$	18.4164			0.582669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.a.81.1		4
4.3	odd	2		200.2.m.a.81.1	✓	4
20.3	even	4		1000.2.q.a.849.2		8
20.7	even	4		1000.2.q.a.849.1		8
20.19	odd	2		1000.2.m.a.401.1		4
25.11	even	5		10000.2.a.g.1.2		2
25.14	even	10		10000.2.a.i.1.1		2
25.21	even	5	inner	400.2.u.a.321.1		4
100.3	even	20		1000.2.q.a.649.1		8
100.11	odd	10		5000.2.a.c.1.1		2
100.39	odd	10		5000.2.a.a.1.2		2
100.47	even	20		1000.2.q.a.649.2		8
100.71	odd	10		200.2.m.a.121.1	yes	4
100.79	odd	10		1000.2.m.a.601.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.a.81.1	✓	4	4.3	odd	2
200.2.m.a.121.1	yes	4	100.71	odd	10
400.2.u.a.81.1		4	1.1	even	1	trivial
400.2.u.a.321.1		4	25.21	even	5	inner
1000.2.m.a.401.1		4	20.19	odd	2
1000.2.m.a.601.1		4	100.79	odd	10
1000.2.q.a.649.1		8	100.3	even	20
1000.2.q.a.649.2		8	100.47	even	20
1000.2.q.a.849.1		8	20.7	even	4
1000.2.q.a.849.2		8	20.3	even	4
5000.2.a.a.1.2		2	100.39	odd	10
5000.2.a.c.1.1		2	100.11	odd	10
10000.2.a.g.1.2		2	25.11	even	5
10000.2.a.i.1.1		2	25.14	even	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80902 + 1.31433i) q^{3} +(-0.690983 + 2.12663i) q^{5} -2.61803 q^{7} +(0.618034 - 1.90211i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(1.04508 - 3.21644i) q^{13} +(-1.54508 - 4.75528i) q^{15} +(-4.23607 - 3.07768i) q^{17} +(6.16312 + 4.47777i) q^{19} +(4.73607 - 3.44095i) q^{21} +(-1.69098 - 5.20431i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(-0.690983 - 2.12663i) q^{27} +(-3.54508 + 2.57565i) q^{29} +(-3.80902 - 2.76741i) q^{31} +(2.23607 + 1.62460i) q^{33} +(1.80902 - 5.56758i) q^{35} +(-2.54508 + 7.83297i) q^{37} +(2.33688 + 7.19218i) q^{39} +(1.76393 - 5.42882i) q^{41} -4.38197 q^{43} +(3.61803 + 2.62866i) q^{45} +(0.118034 - 0.0857567i) q^{47} -0.145898 q^{49} +11.7082 q^{51} +(-6.42705 + 4.66953i) q^{53} +2.76393 q^{55} -17.0344 q^{57} +(-0.736068 + 2.26538i) q^{59} +(-4.07295 - 12.5352i) q^{61} +(-1.61803 + 4.97980i) q^{63} +(6.11803 + 4.44501i) q^{65} +(11.0902 + 8.05748i) q^{67} +(9.89919 + 7.19218i) q^{69} +(-6.97214 + 5.06555i) q^{71} +(3.39919 + 10.4616i) q^{73} +11.1803 q^{75} +(1.00000 + 3.07768i) q^{77} +(-4.30902 + 3.13068i) q^{79} +(8.89919 + 6.46564i) q^{81} +(-3.66312 - 2.66141i) q^{83} +(9.47214 - 6.88191i) q^{85} +(3.02786 - 9.31881i) q^{87} +(1.23607 + 3.80423i) q^{89} +(-2.73607 + 8.42075i) q^{91} +10.5279 q^{93} +(-13.7812 + 10.0126i) q^{95} +(12.3541 - 8.97578i) q^{97} -2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{3} - 5 q^{5} - 6 q^{7} - 2 q^{9} - 6 q^{11} - 7 q^{13} + 5 q^{15} - 8 q^{17} + 9 q^{19} + 10 q^{21} - 9 q^{23} - 5 q^{25} - 5 q^{27} - 3 q^{29} - 13 q^{31} + 5 q^{35} + q^{37} + 25 q^{39} + 16 q^{41}+ \cdots + 8 q^{99}+O(q^{100}) \) 4 * q - 5 * q^3 - 5 * q^5 - 6 * q^7 - 2 * q^9 - 6 * q^11 - 7 * q^13 + 5 * q^15 - 8 * q^17 + 9 * q^19 + 10 * q^21 - 9 * q^23 - 5 * q^25 - 5 * q^27 - 3 * q^29 - 13 * q^31 + 5 * q^35 + q^37 + 25 * q^39 + 16 * q^41 - 22 * q^43 + 10 * q^45 - 4 * q^47 - 14 * q^49 + 20 * q^51 - 19 * q^53 + 20 * q^55 - 10 * q^57 + 6 * q^59 - 23 * q^61 - 2 * q^63 + 20 * q^65 + 22 * q^67 + 15 * q^69 - 10 * q^71 - 11 * q^73 + 4 * q^77 - 15 * q^79 + 11 * q^81 + q^83 + 20 * q^85 + 30 * q^87 - 4 * q^89 - 2 * q^91 + 60 * q^93 - 35 * q^95 + 36 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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