LMFDB - Embedded newform 704.2.m.a.641.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [704,2,Mod(257,704)] 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("704.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(704, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.62146830230$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	704.641
Dual form			704.2.m.a.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.118034 + 0.363271i) q^{3} +(2.61803 + 1.90211i) q^{5} +(0.618034 - 1.90211i) q^{7} +(2.30902 - 1.67760i) q^{9} +(0.309017 + 3.30220i) q^{11} +(1.00000 - 0.726543i) q^{13} +(-0.381966 + 1.17557i) q^{15} +(0.500000 + 0.363271i) q^{17} +(-1.80902 - 5.56758i) q^{19} +0.763932 q^{21} -1.23607 q^{23} +(1.69098 + 5.20431i) q^{25} +(1.80902 + 1.31433i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(1.61803 - 1.17557i) q^{31} +(-1.16312 + 0.502029i) q^{33} +(5.23607 - 3.80423i) q^{35} +(1.14590 - 3.52671i) q^{37} +(0.381966 + 0.277515i) q^{39} +(1.73607 + 5.34307i) q^{41} -8.56231 q^{43} +9.23607 q^{45} +(2.00000 + 6.15537i) q^{47} +(2.42705 + 1.76336i) q^{49} +(-0.0729490 + 0.224514i) q^{51} +(-1.23607 + 0.898056i) q^{53} +(-5.47214 + 9.23305i) q^{55} +(1.80902 - 1.31433i) q^{57} +(-2.66312 + 8.19624i) q^{59} +(-2.00000 - 1.45309i) q^{61} +(-1.76393 - 5.42882i) q^{63} +4.00000 q^{65} +11.0902 q^{67} +(-0.145898 - 0.449028i) q^{69} +(-4.23607 - 3.07768i) q^{71} +(3.20820 - 9.87384i) q^{73} +(-1.69098 + 1.22857i) q^{75} +(6.47214 + 1.45309i) q^{77} +(10.8541 - 7.88597i) q^{79} +(2.38197 - 7.33094i) q^{81} +(-7.54508 - 5.48183i) q^{83} +(0.618034 + 1.90211i) q^{85} -1.70820 q^{87} -8.09017 q^{89} +(-0.763932 - 2.35114i) q^{91} +(0.618034 + 0.449028i) q^{93} +(5.85410 - 18.0171i) q^{95} +(-5.78115 + 4.20025i) q^{97} +(6.25329 + 7.10642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{5} - 2 q^{7} + 7 q^{9} - q^{11} + 4 q^{13} - 6 q^{15} + 2 q^{17} - 5 q^{19} + 12 q^{21} + 4 q^{23} + 9 q^{25} + 5 q^{27} - 10 q^{29} + 2 q^{31} + 11 q^{33} + 12 q^{35} + 18 q^{37}+ \cdots - 13 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 6 * q^5 - 2 * q^7 + 7 * q^9 - q^11 + 4 * q^13 - 6 * q^15 + 2 * q^17 - 5 * q^19 + 12 * q^21 + 4 * q^23 + 9 * q^25 + 5 * q^27 - 10 * q^29 + 2 * q^31 + 11 * q^33 + 12 * q^35 + 18 * q^37 + 6 * q^39 - 2 * q^41 + 6 * q^43 + 28 * q^45 + 8 * q^47 + 3 * q^49 - 7 * q^51 + 4 * q^53 - 4 * q^55 + 5 * q^57 + 5 * q^59 - 8 * q^61 - 16 * q^63 + 16 * q^65 + 22 * q^67 - 14 * q^69 - 8 * q^71 - 14 * q^73 - 9 * q^75 + 8 * q^77 + 30 * q^79 + 14 * q^81 - 19 * q^83 - 2 * q^85 + 20 * q^87 - 10 * q^89 - 12 * q^91 - 2 * q^93 + 10 * q^95 - 3 * q^97 - 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	0.979331	−	0.202265i	$-0.0648303\pi$
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	−0.911184	+	0.412000i	$0.864830\pi$
$4$		0			0
$5$	2.61803	+	1.90211i	1.17082	+	0.850651i	0.991107	−	0.133068i	$-0.0424829\pi$
$5$	2.61803	+	1.90211i	1.17082	+	0.850651i	0.179714	+	0.983719i	$0.442483\pi$
$6$		0			0
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	−0.763710	−	0.645560i	$-0.776624\pi$
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	0.997305	−	0.0733714i	$-0.0233759\pi$
$8$		0			0
$9$	2.30902	−	1.67760i	0.769672	−	0.559200i
$10$		0			0
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$12$		0			0
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	−0.440411	−	0.897796i	$-0.645167\pi$
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	0.717761	+	0.696290i	$0.245167\pi$
$14$		0			0
$15$	−0.381966	+	1.17557i	−0.0986232	+	0.303531i
$16$		0			0
$17$	0.500000	+	0.363271i	0.121268	+	0.0881062i	0.646766	−	0.762688i	$-0.276121\pi$
$17$	0.500000	+	0.363271i	0.121268	+	0.0881062i	−0.525498	+	0.850795i	$0.676121\pi$
$18$		0			0
$19$	−1.80902	−	5.56758i	−0.415017	−	1.27729i	−0.912236	−	0.409666i	$-0.865645\pi$
$19$	−1.80902	−	5.56758i	−0.415017	−	1.27729i	0.497219	−	0.867625i	$-0.334355\pi$
$20$		0			0
$21$	0.763932			0.166704
$22$		0			0
$23$	−1.23607			−0.257738			−0.128869	−	0.991662i	$-0.541135\pi$
$23$	−1.23607			−0.257738			−0.128869	+	0.991662i	$0.541135\pi$
$24$		0			0
$25$	1.69098	+	5.20431i	0.338197	+	1.04086i
$26$		0			0
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$		0			0
$29$	−1.38197	+	4.25325i	−0.256625	+	0.789809i	0.736881	+	0.676023i	$0.236298\pi$
$29$	−1.38197	+	4.25325i	−0.256625	+	0.789809i	−0.993505	+	0.113787i	$0.963702\pi$
$30$		0			0
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	−0.432923	−	0.901431i	$-0.642518\pi$
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	0.723531	+	0.690292i	$0.242518\pi$
$32$		0			0
$33$	−1.16312	+	0.502029i	−0.202473	+	0.0873920i
$34$		0			0
$35$	5.23607	−	3.80423i	0.885057	−	0.643032i
$36$		0			0
$37$	1.14590	−	3.52671i	0.188384	−	0.579788i	−0.811606	−	0.584206i	$-0.801406\pi$
$37$	1.14590	−	3.52671i	0.188384	−	0.579788i	0.999990	+	0.00441771i	$0.00140621\pi$
$38$		0			0
$39$	0.381966	+	0.277515i	0.0611635	+	0.0444379i
$40$		0			0
$41$	1.73607	+	5.34307i	0.271128	+	0.834447i	0.990218	+	0.139530i	$0.0445591\pi$
$41$	1.73607	+	5.34307i	0.271128	+	0.834447i	−0.719090	+	0.694917i	$0.755441\pi$
$42$		0			0
$43$	−8.56231			−1.30574			−0.652870	−	0.757470i	$-0.726435\pi$
$43$	−8.56231			−1.30574			−0.652870	+	0.757470i	$0.726435\pi$
$44$		0			0
$45$	9.23607			1.37683
$46$		0			0
$47$	2.00000	+	6.15537i	0.291730	+	0.897853i	0.984300	+	0.176502i	$0.0564783\pi$
$47$	2.00000	+	6.15537i	0.291730	+	0.897853i	−0.692570	+	0.721350i	$0.743522\pi$
$48$		0			0
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$		0			0
$51$	−0.0729490	+	0.224514i	−0.0102149	+	0.0314382i
$52$		0			0
$53$	−1.23607	+	0.898056i	−0.169787	+	0.123357i	−0.669434	−	0.742872i	$-0.733463\pi$
$53$	−1.23607	+	0.898056i	−0.169787	+	0.123357i	0.499647	+	0.866229i	$0.333463\pi$
$54$		0			0
$55$	−5.47214	+	9.23305i	−0.737863	+	1.24498i
$56$		0			0
$57$	1.80902	−	1.31433i	0.239610	−	0.174087i
$58$		0			0
$59$	−2.66312	+	8.19624i	−0.346709	+	1.06706i	0.613954	+	0.789342i	$0.289578\pi$
$59$	−2.66312	+	8.19624i	−0.346709	+	1.06706i	−0.960663	+	0.277718i	$0.910422\pi$
$60$		0			0
$61$	−2.00000	−	1.45309i	−0.256074	−	0.186048i	0.452341	−	0.891845i	$-0.350589\pi$
$61$	−2.00000	−	1.45309i	−0.256074	−	0.186048i	−0.708414	+	0.705797i	$0.750589\pi$
$62$		0			0
$63$	−1.76393	−	5.42882i	−0.222235	−	0.683968i
$64$		0			0
$65$	4.00000			0.496139
$66$		0			0
$67$	11.0902			1.35488			0.677440	−	0.735578i	$-0.263089\pi$
$67$	11.0902			1.35488			0.677440	+	0.735578i	$0.263089\pi$
$68$		0			0
$69$	−0.145898	−	0.449028i	−0.0175641	−	0.0540566i
$70$		0			0
$71$	−4.23607	−	3.07768i	−0.502729	−	0.365254i	0.307330	−	0.951603i	$-0.400565\pi$
$71$	−4.23607	−	3.07768i	−0.502729	−	0.365254i	−0.810058	+	0.586349i	$0.800565\pi$
$72$		0			0
$73$	3.20820	−	9.87384i	0.375492	−	1.15565i	−0.567654	−	0.823267i	$-0.692149\pi$
$73$	3.20820	−	9.87384i	0.375492	−	1.15565i	0.943146	−	0.332378i	$-0.107851\pi$
$74$		0			0
$75$	−1.69098	+	1.22857i	−0.195258	+	0.141863i
$76$		0			0
$77$	6.47214	+	1.45309i	0.737568	+	0.165594i
$78$		0			0
$79$	10.8541	−	7.88597i	1.22118	−	0.887241i	0.224984	−	0.974362i	$-0.427767\pi$
$79$	10.8541	−	7.88597i	1.22118	−	0.887241i	0.996198	+	0.0871218i	$0.0277669\pi$
$80$		0			0
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$		0			0
$83$	−7.54508	−	5.48183i	−0.828181	−	0.601708i	0.0908634	−	0.995863i	$-0.471037\pi$
$83$	−7.54508	−	5.48183i	−0.828181	−	0.601708i	−0.919044	+	0.394155i	$0.871037\pi$
$84$		0			0
$85$	0.618034	+	1.90211i	0.0670352	+	0.206313i
$86$		0			0
$87$	−1.70820			−0.183139
$88$		0			0
$89$	−8.09017			−0.857556			−0.428778	−	0.903410i	$-0.641056\pi$
$89$	−8.09017			−0.857556			−0.428778	+	0.903410i	$0.641056\pi$
$90$		0			0
$91$	−0.763932	−	2.35114i	−0.0800818	−	0.246467i
$92$		0			0
$93$	0.618034	+	0.449028i	0.0640871	+	0.0465620i
$94$		0			0
$95$	5.85410	−	18.0171i	0.600618	−	1.84851i
$96$		0			0
$97$	−5.78115	+	4.20025i	−0.586987	+	0.426471i	−0.841236	−	0.540668i	$-0.818172\pi$
$97$	−5.78115	+	4.20025i	−0.586987	+	0.426471i	0.254249	+	0.967139i	$0.418172\pi$
$98$		0			0
$99$	6.25329	+	7.10642i	0.628479	+	0.714222i
$100$		0			0
$101$	−3.38197	+	2.45714i	−0.336518	+	0.244495i	−0.743191	−	0.669079i	$-0.766689\pi$
$101$	−3.38197	+	2.45714i	−0.336518	+	0.244495i	0.406673	+	0.913574i	$0.366689\pi$
$102$		0			0
$103$	−4.85410	+	14.9394i	−0.478289	+	1.47202i	0.363181	+	0.931718i	$0.381691\pi$
$103$	−4.85410	+	14.9394i	−0.478289	+	1.47202i	−0.841470	+	0.540303i	$0.818309\pi$
$104$		0			0
$105$	2.00000	+	1.45309i	0.195180	+	0.141807i
$106$		0			0
$107$	−0.354102	−	1.08981i	−0.0342323	−	0.105356i	0.932480	−	0.361221i	$-0.117640\pi$
$107$	−0.354102	−	1.08981i	−0.0342323	−	0.105356i	−0.966713	+	0.255864i	$0.917640\pi$
$108$		0			0
$109$	−18.9443			−1.81453			−0.907266	−	0.420557i	$-0.861835\pi$
$109$	−18.9443			−1.81453			−0.907266	+	0.420557i	$0.861835\pi$
$110$		0			0
$111$	1.41641			0.134439
$112$		0			0
$113$	−0.572949	−	1.76336i	−0.0538985	−	0.165883i	0.920484	−	0.390781i	$-0.127795\pi$
$113$	−0.572949	−	1.76336i	−0.0538985	−	0.165883i	−0.974382	+	0.224898i	$0.927795\pi$
$114$		0			0
$115$	−3.23607	−	2.35114i	−0.301765	−	0.219245i
$116$		0			0
$117$	1.09017	−	3.35520i	0.100786	−	0.310188i
$118$		0			0
$119$	1.00000	−	0.726543i	0.0916698	−	0.0666020i
$120$		0			0
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$		0			0
$123$	−1.73607	+	1.26133i	−0.156536	+	0.113730i
$124$		0			0
$125$	−0.472136	+	1.45309i	−0.0422291	+	0.129968i
$126$		0			0
$127$	−8.85410	−	6.43288i	−0.785675	−	0.570826i	0.121002	−	0.992652i	$-0.461389\pi$
$127$	−8.85410	−	6.43288i	−0.785675	−	0.570826i	−0.906677	+	0.421826i	$0.861389\pi$
$128$		0			0
$129$	−1.01064	−	3.11044i	−0.0889822	−	0.273859i
$130$		0			0
$131$	6.79837			0.593977			0.296988	−	0.954881i	$-0.404018\pi$
$131$	6.79837			0.593977			0.296988	+	0.954881i	$0.404018\pi$
$132$		0			0
$133$	−11.7082			−1.01523
$134$		0			0
$135$	2.23607	+	6.88191i	0.192450	+	0.592300i
$136$		0			0
$137$	−13.0172	−	9.45756i	−1.11214	−	0.808014i	−0.129138	−	0.991627i	$-0.541221\pi$
$137$	−13.0172	−	9.45756i	−1.11214	−	0.808014i	−0.982999	+	0.183612i	$0.941221\pi$
$138$		0			0
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$		0			0
$141$	−2.00000	+	1.45309i	−0.168430	+	0.122372i
$142$		0			0
$143$	2.70820	+	3.07768i	0.226471	+	0.257369i
$144$		0			0
$145$	−11.7082	+	8.50651i	−0.972313	+	0.706427i
$146$		0			0
$147$	−0.354102	+	1.08981i	−0.0292058	+	0.0898863i
$148$		0			0
$149$	−5.00000	−	3.63271i	−0.409616	−	0.297603i	0.363830	−	0.931465i	$-0.381469\pi$
$149$	−5.00000	−	3.63271i	−0.409616	−	0.297603i	−0.773446	+	0.633862i	$0.781469\pi$
$150$		0			0
$151$	2.47214	+	7.60845i	0.201180	+	0.619167i	0.999849	+	0.0173966i	$0.00553779\pi$
$151$	2.47214	+	7.60845i	0.201180	+	0.619167i	−0.798669	+	0.601770i	$0.794462\pi$
$152$		0			0
$153$	1.76393			0.142605
$154$		0			0
$155$	6.47214			0.519854
$156$		0			0
$157$	−3.00000	−	9.23305i	−0.239426	−	0.736878i	−0.996503	−	0.0835524i	$-0.973373\pi$
$157$	−3.00000	−	9.23305i	−0.239426	−	0.736878i	0.757077	−	0.653325i	$-0.226627\pi$
$158$		0			0
$159$	−0.472136	−	0.343027i	−0.0374428	−	0.0272038i
$160$		0			0
$161$	−0.763932	+	2.35114i	−0.0602063	+	0.185296i
$162$		0			0
$163$	−0.736068	+	0.534785i	−0.0576533	+	0.0418876i	−0.616239	−	0.787559i	$-0.711344\pi$
$163$	−0.736068	+	0.534785i	−0.0576533	+	0.0418876i	0.558585	+	0.829447i	$0.311344\pi$
$164$		0			0
$165$	−4.00000	−	0.898056i	−0.311400	−	0.0699136i
$166$		0			0
$167$	−11.9443	+	8.67802i	−0.924276	+	0.671525i	−0.944585	−	0.328268i	$-0.893535\pi$
$167$	−11.9443	+	8.67802i	−0.924276	+	0.671525i	0.0203090	+	0.999794i	$0.493535\pi$
$168$		0			0
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$		0			0
$171$	−13.5172	−	9.82084i	−1.03369	−	0.751018i
$172$		0			0
$173$	−6.76393	−	20.8172i	−0.514252	−	1.58271i	−0.784638	−	0.619954i	$-0.787151\pi$
$173$	−6.76393	−	20.8172i	−0.514252	−	1.58271i	0.270386	−	0.962752i	$-0.412849\pi$
$174$		0			0
$175$	10.9443			0.827309
$176$		0			0
$177$	−3.29180			−0.247427
$178$		0			0
$179$	−2.66312	−	8.19624i	−0.199051	−	0.612616i	−0.999905	−	0.0137566i	$-0.995621\pi$
$179$	−2.66312	−	8.19624i	−0.199051	−	0.612616i	0.800855	−	0.598859i	$-0.204379\pi$
$180$		0			0
$181$	−3.38197	−	2.45714i	−0.251380	−	0.182638i	0.454958	−	0.890513i	$-0.349654\pi$
$181$	−3.38197	−	2.45714i	−0.251380	−	0.182638i	−0.706338	+	0.707875i	$0.749654\pi$
$182$		0			0
$183$	0.291796	−	0.898056i	0.0215702	−	0.0663862i
$184$		0			0
$185$	9.70820	−	7.05342i	0.713761	−	0.518578i
$186$		0			0
$187$	−1.04508	+	1.76336i	−0.0764242	+	0.128949i
$188$		0			0
$189$	3.61803	−	2.62866i	0.263173	−	0.191207i
$190$		0			0
$191$	−1.47214	+	4.53077i	−0.106520	+	0.327835i	−0.990084	−	0.140475i	$-0.955137\pi$
$191$	−1.47214	+	4.53077i	−0.106520	+	0.327835i	0.883564	+	0.468310i	$0.155137\pi$
$192$		0			0
$193$	−14.0902	−	10.2371i	−1.01423	−	0.736883i	−0.0491400	−	0.998792i	$-0.515648\pi$
$193$	−14.0902	−	10.2371i	−1.01423	−	0.736883i	−0.965093	+	0.261909i	$0.915648\pi$
$194$		0			0
$195$	0.472136	+	1.45309i	0.0338104	+	0.104058i
$196$		0			0
$197$	20.9443			1.49222			0.746109	−	0.665824i	$-0.231920\pi$
$197$	20.9443			1.49222			0.746109	+	0.665824i	$0.231920\pi$
$198$		0			0
$199$	18.9443			1.34292			0.671462	−	0.741039i	$-0.265667\pi$
$199$	18.9443			1.34292			0.671462	+	0.741039i	$0.265667\pi$
$200$		0			0
$201$	1.30902	+	4.02874i	0.0923309	+	0.284165i
$202$		0			0
$203$	7.23607	+	5.25731i	0.507872	+	0.368991i
$204$		0			0
$205$	−5.61803	+	17.2905i	−0.392381	+	1.20762i
$206$		0			0
$207$	−2.85410	+	2.07363i	−0.198374	+	0.144127i
$208$		0			0
$209$	17.8262	−	7.69421i	1.23307	−	0.532220i
$210$		0			0
$211$	4.92705	−	3.57971i	0.339192	−	0.246438i	−0.405129	−	0.914260i	$-0.632773\pi$
$211$	4.92705	−	3.57971i	0.339192	−	0.246438i	0.744321	+	0.667822i	$0.232773\pi$
$212$		0			0
$213$	0.618034	−	1.90211i	0.0423470	−	0.130331i
$214$		0			0
$215$	−22.4164	−	16.2865i	−1.52879	−	1.11073i
$216$		0			0
$217$	−1.23607	−	3.80423i	−0.0839098	−	0.258248i
$218$		0			0
$219$	3.96556			0.267968
$220$		0			0
$221$	0.763932			0.0513876
$222$		0			0
$223$	−7.94427	−	24.4500i	−0.531988	−	1.63729i	−0.750069	−	0.661359i	$-0.769980\pi$
$223$	−7.94427	−	24.4500i	−0.531988	−	1.63729i	0.218081	−	0.975931i	$-0.430020\pi$
$224$		0			0
$225$	12.6353	+	9.18005i	0.842350	+	0.612003i
$226$		0			0
$227$	4.48278	−	13.7966i	0.297532	−	0.915711i	−0.684827	−	0.728706i	$-0.740122\pi$
$227$	4.48278	−	13.7966i	0.297532	−	0.915711i	0.982359	−	0.187005i	$-0.0598780\pi$
$228$		0			0
$229$	1.38197	−	1.00406i	0.0913229	−	0.0663500i	−0.541187	−	0.840902i	$-0.682025\pi$
$229$	1.38197	−	1.00406i	0.0913229	−	0.0663500i	0.632510	+	0.774552i	$0.282025\pi$
$230$		0			0
$231$	0.236068	+	2.52265i	0.0155321	+	0.165978i
$232$		0			0
$233$	7.78115	−	5.65334i	0.509760	−	0.370363i	−0.302972	−	0.952999i	$-0.597979\pi$
$233$	7.78115	−	5.65334i	0.509760	−	0.370363i	0.812733	+	0.582637i	$0.197979\pi$
$234$		0			0
$235$	−6.47214	+	19.9192i	−0.422196	+	1.29938i
$236$		0			0
$237$	4.14590	+	3.01217i	0.269305	+	0.195662i
$238$		0			0
$239$	6.70820	+	20.6457i	0.433918	+	1.33546i	0.894192	+	0.447684i	$0.147751\pi$
$239$	6.70820	+	20.6457i	0.433918	+	1.33546i	−0.460274	+	0.887777i	$0.652249\pi$
$240$		0			0
$241$	−11.0902			−0.714381			−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902			−0.714381			−0.357190	+	0.934032i	$0.616265\pi$
$242$		0			0
$243$	9.65248			0.619207
$244$		0			0
$245$	3.00000	+	9.23305i	0.191663	+	0.589878i
$246$		0			0
$247$	−5.85410	−	4.25325i	−0.372488	−	0.270628i
$248$		0			0
$249$	1.10081	−	3.38795i	0.0697612	−	0.214703i
$250$		0			0
$251$	−16.9443	+	12.3107i	−1.06951	+	0.777047i	−0.975825	−	0.218555i	$-0.929866\pi$
$251$	−16.9443	+	12.3107i	−1.06951	+	0.777047i	−0.0936883	+	0.995602i	$0.529866\pi$
$252$		0			0
$253$	−0.381966	−	4.08174i	−0.0240140	−	0.256617i
$254$		0			0
$255$	−0.618034	+	0.449028i	−0.0387028	+	0.0281192i
$256$		0			0
$257$	−1.73607	+	5.34307i	−0.108293	+	0.333291i	−0.990489	−	0.137590i	$-0.956064\pi$
$257$	−1.73607	+	5.34307i	−0.108293	+	0.333291i	0.882196	+	0.470882i	$0.156064\pi$
$258$		0			0
$259$	−6.00000	−	4.35926i	−0.372822	−	0.270871i
$260$		0			0
$261$	3.94427	+	12.1392i	0.244144	+	0.751399i
$262$		0			0
$263$	23.2361			1.43280			0.716399	−	0.697691i	$-0.245789\pi$
$263$	23.2361			1.43280			0.716399	+	0.697691i	$0.245789\pi$
$264$		0			0
$265$	−4.94427			−0.303724
$266$		0			0
$267$	−0.954915	−	2.93893i	−0.0584399	−	0.179859i
$268$		0			0
$269$	5.00000	+	3.63271i	0.304855	+	0.221490i	0.729686	−	0.683783i	$-0.239666\pi$
$269$	5.00000	+	3.63271i	0.304855	+	0.221490i	−0.424830	+	0.905273i	$0.639666\pi$
$270$		0			0
$271$	−0.618034	+	1.90211i	−0.0375429	+	0.115545i	−0.968072	−	0.250674i	$-0.919348\pi$
$271$	−0.618034	+	1.90211i	−0.0375429	+	0.115545i	0.930529	+	0.366219i	$0.119348\pi$
$272$		0			0
$273$	0.763932	−	0.555029i	0.0462353	−	0.0335919i
$274$		0			0
$275$	−16.6631	+	7.19218i	−1.00482	+	0.433705i
$276$		0			0
$277$	−19.1803	+	13.9353i	−1.15243	+	0.837293i	−0.988803	−	0.149228i	$-0.952321\pi$
$277$	−19.1803	+	13.9353i	−1.15243	+	0.837293i	−0.163632	+	0.986521i	$0.552321\pi$
$278$		0			0
$279$	1.76393	−	5.42882i	0.105604	−	0.325015i
$280$		0			0
$281$	13.0172	+	9.45756i	0.776542	+	0.564191i	0.903939	−	0.427661i	$-0.140662\pi$
$281$	13.0172	+	9.45756i	0.776542	+	0.564191i	−0.127397	+	0.991852i	$0.540662\pi$
$282$		0			0
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	0.886961	+	0.461844i	$0.152812\pi$
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	−0.446101	+	0.894982i	$0.647188\pi$
$284$		0			0
$285$	7.23607			0.428628
$286$		0			0
$287$	11.2361			0.663244
$288$		0			0
$289$	−5.13525	−	15.8047i	−0.302074	−	0.929688i
$290$		0			0
$291$	−2.20820	−	1.60435i	−0.129447	−	0.0940489i
$292$		0			0
$293$	8.76393	−	26.9726i	0.511994	−	1.57576i	−0.276691	−	0.960959i	$-0.589238\pi$
$293$	8.76393	−	26.9726i	0.511994	−	1.57576i	0.788685	−	0.614798i	$-0.210762\pi$
$294$		0			0
$295$	−22.5623	+	16.3925i	−1.31363	+	0.954407i
$296$		0			0
$297$	−3.78115	+	6.37988i	−0.219405	+	0.370198i
$298$		0			0
$299$	−1.23607	+	0.898056i	−0.0714837	+	0.0519359i
$300$		0			0
$301$	−5.29180	+	16.2865i	−0.305014	+	0.938737i
$302$		0			0
$303$	−1.29180	−	0.938545i	−0.0742117	−	0.0539180i
$304$		0			0
$305$	−2.47214	−	7.60845i	−0.141554	−	0.435659i
$306$		0			0
$307$	27.7984			1.58654			0.793268	−	0.608872i	$-0.208378\pi$
$307$	27.7984			1.58654			0.793268	+	0.608872i	$0.208378\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$		0			0
$311$	−8.05573	−	24.7930i	−0.456798	−	1.40588i	−0.869011	−	0.494793i	$-0.835244\pi$
$311$	−8.05573	−	24.7930i	−0.456798	−	1.40588i	0.412212	−	0.911088i	$-0.364756\pi$
$312$		0			0
$313$	−3.50000	−	2.54290i	−0.197832	−	0.143733i	0.484459	−	0.874814i	$-0.339016\pi$
$313$	−3.50000	−	2.54290i	−0.197832	−	0.143733i	−0.682291	+	0.731081i	$0.739016\pi$
$314$		0			0
$315$	5.70820	−	17.5680i	0.321621	−	0.989847i
$316$		0			0
$317$	−3.00000	+	2.17963i	−0.168497	+	0.122420i	−0.668838	−	0.743408i	$-0.733208\pi$
$317$	−3.00000	+	2.17963i	−0.168497	+	0.122420i	0.500341	+	0.865828i	$0.333208\pi$
$318$		0			0
$319$	−14.4721	−	3.24920i	−0.810284	−	0.181920i
$320$		0			0
$321$	0.354102	−	0.257270i	0.0197640	−	0.0143594i
$322$		0			0
$323$	1.11803	−	3.44095i	0.0622091	−	0.191460i
$324$		0			0
$325$	5.47214	+	3.97574i	0.303539	+	0.220534i
$326$		0			0
$327$	−2.23607	−	6.88191i	−0.123655	−	0.380570i
$328$		0			0
$329$	12.9443			0.713641
$330$		0			0
$331$	6.27051			0.344658			0.172329	−	0.985039i	$-0.444871\pi$
$331$	6.27051			0.344658			0.172329	+	0.985039i	$0.444871\pi$
$332$		0			0
$333$	−3.27051	−	10.0656i	−0.179223	−	0.551591i
$334$		0			0
$335$	29.0344	+	21.0948i	1.58632	+	1.15253i
$336$		0			0
$337$	−8.28115	+	25.4868i	−0.451103	+	1.38835i	0.424547	+	0.905406i	$0.360433\pi$
$337$	−8.28115	+	25.4868i	−0.451103	+	1.38835i	−0.875650	+	0.482947i	$0.839567\pi$
$338$		0			0
$339$	0.572949	−	0.416272i	0.0311183	−	0.0226088i
$340$		0			0
$341$	4.38197	+	4.97980i	0.237297	+	0.269671i
$342$		0			0
$343$	16.1803	−	11.7557i	0.873656	−	0.634748i
$344$		0			0
$345$	0.472136	−	1.45309i	0.0254189	−	0.0782315i
$346$		0			0
$347$	−13.4443	−	9.76784i	−0.721726	−	0.524365i	0.165209	−	0.986259i	$-0.447170\pi$
$347$	−13.4443	−	9.76784i	−0.721726	−	0.524365i	−0.886935	+	0.461894i	$0.847170\pi$
$348$		0			0
$349$	6.05573	+	18.6376i	0.324156	+	0.997649i	0.971820	+	0.235723i	$0.0757458\pi$
$349$	6.05573	+	18.6376i	0.324156	+	0.997649i	−0.647665	+	0.761926i	$0.724254\pi$
$350$		0			0
$351$	2.76393			0.147528
$352$		0			0
$353$	32.6180			1.73608			0.868041	−	0.496492i	$-0.165379\pi$
$353$	32.6180			1.73608			0.868041	+	0.496492i	$0.165379\pi$
$354$		0			0
$355$	−5.23607	−	16.1150i	−0.277902	−	0.855293i
$356$		0			0
$357$	0.381966	+	0.277515i	0.0202158	+	0.0146876i
$358$		0			0
$359$	−1.58359	+	4.87380i	−0.0835788	+	0.257229i	−0.984109	−	0.177564i	$-0.943178\pi$
$359$	−1.58359	+	4.87380i	−0.0835788	+	0.257229i	0.900531	+	0.434793i	$0.143178\pi$
$360$		0			0
$361$	−12.3541	+	8.97578i	−0.650216	+	0.472409i
$362$		0			0
$363$	−2.01722	−	3.68571i	−0.105877	−	0.193450i
$364$		0			0
$365$	27.1803	−	19.7477i	1.42268	−	1.03364i
$366$		0			0
$367$	−6.09017	+	18.7436i	−0.317904	+	0.978409i	0.656638	+	0.754206i	$0.271978\pi$
$367$	−6.09017	+	18.7436i	−0.317904	+	0.978409i	−0.974542	+	0.224203i	$0.928022\pi$
$368$		0			0
$369$	12.9721	+	9.42481i	0.675302	+	0.490636i
$370$		0			0
$371$	0.944272	+	2.90617i	0.0490242	+	0.150881i
$372$		0			0
$373$	4.29180			0.222221			0.111110	−	0.993808i	$-0.464559\pi$
$373$	4.29180			0.222221			0.111110	+	0.993808i	$0.464559\pi$
$374$		0			0
$375$	−0.583592			−0.0301366
$376$		0			0
$377$	1.70820	+	5.25731i	0.0879770	+	0.270765i
$378$		0			0
$379$	−11.5451	−	8.38800i	−0.593031	−	0.430862i	0.250367	−	0.968151i	$-0.419449\pi$
$379$	−11.5451	−	8.38800i	−0.593031	−	0.430862i	−0.843398	+	0.537289i	$0.819449\pi$
$380$		0			0
$381$	1.29180	−	3.97574i	0.0661807	−	0.203683i
$382$		0			0
$383$	−22.9443	+	16.6700i	−1.17240	+	0.851797i	−0.991294	−	0.131667i	$-0.957967\pi$
$383$	−22.9443	+	16.6700i	−1.17240	+	0.851797i	−0.181104	+	0.983464i	$0.557967\pi$
$384$		0			0
$385$	14.1803	+	16.1150i	0.722697	+	0.821294i
$386$		0			0
$387$	−19.7705	+	14.3641i	−1.00499	+	0.730169i
$388$		0			0
$389$	3.29180	−	10.1311i	0.166901	−	0.513667i	−0.832271	−	0.554370i	$-0.812959\pi$
$389$	3.29180	−	10.1311i	0.166901	−	0.513667i	0.999171	+	0.0407020i	$0.0129594\pi$
$390$		0			0
$391$	−0.618034	−	0.449028i	−0.0312553	−	0.0227083i
$392$		0			0
$393$	0.802439	+	2.46965i	0.0404777	+	0.124578i
$394$		0			0
$395$	43.4164			2.18452
$396$		0			0
$397$	17.1246			0.859460			0.429730	−	0.902958i	$-0.358609\pi$
$397$	17.1246			0.859460			0.429730	+	0.902958i	$0.358609\pi$
$398$		0			0
$399$	−1.38197	−	4.25325i	−0.0691848	−	0.212929i
$400$		0			0
$401$	14.3992	+	10.4616i	0.719061	+	0.522428i	0.886084	−	0.463525i	$-0.153415\pi$
$401$	14.3992	+	10.4616i	0.719061	+	0.522428i	−0.167023	+	0.985953i	$0.553415\pi$
$402$		0			0
$403$	0.763932	−	2.35114i	0.0380542	−	0.117119i
$404$		0			0
$405$	20.1803	−	14.6619i	1.00277	−	0.728554i
$406$		0			0
$407$	12.0000	+	2.69417i	0.594818	+	0.133545i
$408$		0			0
$409$	10.8541	−	7.88597i	0.536701	−	0.389936i	−0.286157	−	0.958183i	$-0.592378\pi$
$409$	10.8541	−	7.88597i	0.536701	−	0.389936i	0.822858	+	0.568247i	$0.192378\pi$
$410$		0			0
$411$	1.89919	−	5.84510i	0.0936800	−	0.288317i
$412$		0			0
$413$	13.9443	+	10.1311i	0.686153	+	0.498519i
$414$		0			0
$415$	−9.32624	−	28.7032i	−0.457807	−	1.40899i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.8541			−0.530258			−0.265129	−	0.964213i	$-0.585414\pi$
$419$	−10.8541			−0.530258			−0.265129	+	0.964213i	$0.585414\pi$
$420$		0			0
$421$	9.70820	+	29.8788i	0.473149	+	1.45620i	0.848438	+	0.529295i	$0.177543\pi$
$421$	9.70820	+	29.8788i	0.473149	+	1.45620i	−0.375289	+	0.926908i	$0.622457\pi$
$422$		0			0
$423$	14.9443	+	10.8576i	0.726615	+	0.527917i
$424$		0			0
$425$	−1.04508	+	3.21644i	−0.0506941	+	0.156020i
$426$		0			0
$427$	−4.00000	+	2.90617i	−0.193574	+	0.140639i
$428$		0			0
$429$	−0.798374	+	1.34708i	−0.0385459	+	0.0650378i
$430$		0			0
$431$	−13.7082	+	9.95959i	−0.660301	+	0.479737i	−0.866765	−	0.498718i	$-0.833804\pi$
$431$	−13.7082	+	9.95959i	−0.660301	+	0.479737i	0.206464	+	0.978454i	$0.433804\pi$
$432$		0			0
$433$	8.57295	−	26.3848i	0.411990	−	1.26797i	−0.502926	−	0.864329i	$-0.667743\pi$
$433$	8.57295	−	26.3848i	0.411990	−	1.26797i	0.914916	−	0.403644i	$-0.132257\pi$
$434$		0			0
$435$	−4.47214	−	3.24920i	−0.214423	−	0.155787i
$436$		0			0
$437$	2.23607	+	6.88191i	0.106966	+	0.329206i
$438$		0			0
$439$	6.58359			0.314218			0.157109	−	0.987581i	$-0.449783\pi$
$439$	6.58359			0.314218			0.157109	+	0.987581i	$0.449783\pi$
$440$		0			0
$441$	8.56231			0.407729
$442$		0			0
$443$	−2.64590	−	8.14324i	−0.125710	−	0.386897i	0.868319	−	0.496005i	$-0.165200\pi$
$443$	−2.64590	−	8.14324i	−0.125710	−	0.386897i	−0.994030	+	0.109109i	$0.965200\pi$
$444$		0			0
$445$	−21.1803	−	15.3884i	−1.00404	−	0.729481i
$446$		0			0
$447$	0.729490	−	2.24514i	0.0345037	−	0.106191i
$448$		0			0
$449$	−7.50000	+	5.44907i	−0.353947	+	0.257157i	−0.750523	−	0.660844i	$-0.770198\pi$
$449$	−7.50000	+	5.44907i	−0.353947	+	0.257157i	0.396576	+	0.918002i	$0.370198\pi$
$450$		0			0
$451$	−17.1074	+	7.38394i	−0.805556	+	0.347696i
$452$		0			0
$453$	−2.47214	+	1.79611i	−0.116151	+	0.0843887i
$454$		0			0
$455$	2.47214	−	7.60845i	0.115896	−	0.356690i
$456$		0			0
$457$	7.63525	+	5.54734i	0.357162	+	0.259493i	0.751867	−	0.659314i	$-0.229153\pi$
$457$	7.63525	+	5.54734i	0.357162	+	0.259493i	−0.394705	+	0.918808i	$0.629153\pi$
$458$		0			0
$459$	0.427051	+	1.31433i	0.0199330	+	0.0613476i
$460$		0			0
$461$	−1.34752			−0.0627605			−0.0313802	−	0.999508i	$-0.509990\pi$
$461$	−1.34752			−0.0627605			−0.0313802	+	0.999508i	$0.509990\pi$
$462$		0			0
$463$	19.4164			0.902357			0.451178	−	0.892434i	$-0.351004\pi$
$463$	19.4164			0.902357			0.451178	+	0.892434i	$0.351004\pi$
$464$		0			0
$465$	0.763932	+	2.35114i	0.0354265	+	0.109032i
$466$		0			0
$467$	26.9443	+	19.5762i	1.24683	+	0.905877i	0.998034	−	0.0626787i	$-0.0199643\pi$
$467$	26.9443	+	19.5762i	1.24683	+	0.905877i	0.248798	+	0.968555i	$0.419964\pi$
$468$		0			0
$469$	6.85410	−	21.0948i	0.316493	−	0.974065i
$470$		0			0
$471$	3.00000	−	2.17963i	0.138233	−	0.100432i
$472$		0			0
$473$	−2.64590	−	28.2744i	−0.121659	−	1.30006i
$474$		0			0
$475$	25.9164	−	18.8294i	1.18913	−	0.863951i
$476$		0			0
$477$	−1.34752	+	4.14725i	−0.0616989	+	0.189890i
$478$		0			0
$479$	−27.8885	−	20.2622i	−1.27426	−	0.925804i	−0.274896	−	0.961474i	$-0.588644\pi$
$479$	−27.8885	−	20.2622i	−1.27426	−	0.925804i	−0.999364	+	0.0356697i	$0.988644\pi$
$480$		0			0
$481$	−1.41641	−	4.35926i	−0.0645826	−	0.198765i
$482$		0			0
$483$	−0.944272			−0.0429659
$484$		0			0
$485$	−23.1246			−1.05003
$486$		0			0
$487$	0.416408	+	1.28157i	0.0188692	+	0.0580736i	0.960048	−	0.279836i	$-0.0902801\pi$
$487$	0.416408	+	1.28157i	0.0188692	+	0.0580736i	−0.941179	+	0.337910i	$0.890280\pi$
$488$		0			0
$489$	−0.281153	−	0.204270i	−0.0127142	−	0.00923739i
$490$		0			0
$491$	7.06231	−	21.7355i	0.318717	−	0.980911i	−0.655480	−	0.755213i	$-0.727534\pi$
$491$	7.06231	−	21.7355i	0.318717	−	0.980911i	0.974197	−	0.225699i	$-0.0724664\pi$
$492$		0			0
$493$	−2.23607	+	1.62460i	−0.100707	+	0.0731682i
$494$		0			0
$495$	2.85410	+	30.4993i	0.128282	+	1.37084i
$496$		0			0
$497$	−8.47214	+	6.15537i	−0.380027	+	0.276106i
$498$		0			0
$499$	−9.53444	+	29.3440i	−0.426820	+	1.31362i	0.474420	+	0.880298i	$0.342658\pi$
$499$	−9.53444	+	29.3440i	−0.426820	+	1.31362i	−0.901241	+	0.433319i	$0.857342\pi$
$500$		0			0
$501$	−4.56231	−	3.31471i	−0.203829	−	0.148090i
$502$		0			0
$503$	1.00000	+	3.07768i	0.0445878	+	0.137227i	0.970872	−	0.239598i	$-0.0770157\pi$
$503$	1.00000	+	3.07768i	0.0445878	+	0.137227i	−0.926284	+	0.376825i	$0.877016\pi$
$504$		0			0
$505$	−13.5279			−0.601982
$506$		0			0
$507$	−4.38197			−0.194610
$508$		0			0
$509$	2.56231	+	7.88597i	0.113572	+	0.349539i	0.991647	−	0.128985i	$-0.0411719\pi$
$509$	2.56231	+	7.88597i	0.113572	+	0.349539i	−0.878074	+	0.478524i	$0.841172\pi$
$510$		0			0
$511$	−16.7984	−	12.2047i	−0.743116	−	0.539906i
$512$		0			0
$513$	4.04508	−	12.4495i	0.178595	−	0.549658i
$514$		0			0
$515$	−41.1246	+	29.8788i	−1.81217	+	1.31662i
$516$		0			0
$517$	−19.7082	+	8.50651i	−0.866766	+	0.374116i
$518$		0			0
$519$	6.76393	−	4.91428i	0.296904	−	0.215713i
$520$		0			0
$521$	−6.19098	+	19.0539i	−0.271232	+	0.834766i	0.718960	+	0.695052i	$0.244618\pi$
$521$	−6.19098	+	19.0539i	−0.271232	+	0.834766i	−0.990192	+	0.139714i	$0.955382\pi$
$522$		0			0
$523$	−7.44427	−	5.40858i	−0.325515	−	0.236501i	0.413010	−	0.910726i	$-0.364477\pi$
$523$	−7.44427	−	5.40858i	−0.325515	−	0.236501i	−0.738525	+	0.674226i	$0.764477\pi$
$524$		0			0
$525$	1.29180	+	3.97574i	0.0563786	+	0.173515i
$526$		0			0
$527$	1.23607			0.0538440
$528$		0			0
$529$	−21.4721			−0.933571
$530$		0			0
$531$	7.60081	+	23.3929i	0.329847	+	1.01517i
$532$		0			0
$533$	5.61803	+	4.08174i	0.243344	+	0.176800i
$534$		0			0
$535$	1.14590	−	3.52671i	0.0495415	−	0.152473i
$536$		0			0
$537$	2.66312	−	1.93487i	0.114922	−	0.0834958i
$538$		0			0
$539$	−5.07295	+	8.55951i	−0.218507	+	0.368684i
$540$		0			0
$541$	−2.52786	+	1.83660i	−0.108681	+	0.0789616i	−0.640798	−	0.767709i	$-0.721397\pi$
$541$	−2.52786	+	1.83660i	−0.108681	+	0.0789616i	0.532117	+	0.846671i	$0.321397\pi$
$542$		0			0
$543$	0.493422	−	1.51860i	0.0211748	−	0.0651693i
$544$		0			0
$545$	−49.5967	−	36.0341i	−2.12449	−	1.54353i
$546$		0			0
$547$	2.57295	+	7.91872i	0.110011	+	0.338580i	0.990874	−	0.134792i	$-0.0430366\pi$
$547$	2.57295	+	7.91872i	0.110011	+	0.338580i	−0.880863	+	0.473372i	$0.843037\pi$
$548$		0			0
$549$	−7.05573			−0.301131
$550$		0			0
$551$	26.1803			1.11532
$552$		0			0
$553$	−8.29180	−	25.5195i	−0.352603	−	1.08520i
$554$		0			0
$555$	3.70820	+	2.69417i	0.157404	+	0.114361i
$556$		0			0
$557$	−10.8885	+	33.5115i	−0.461362	+	1.41993i	0.402138	+	0.915579i	$0.368267\pi$
$557$	−10.8885	+	33.5115i	−0.461362	+	1.41993i	−0.863500	+	0.504348i	$0.831733\pi$
$558$		0			0
$559$	−8.56231	+	6.22088i	−0.362147	+	0.263115i
$560$		0			0
$561$	−0.763932	−	0.171513i	−0.0322532	−	0.00724130i
$562$		0			0
$563$	−0.309017	+	0.224514i	−0.0130235	+	0.00946214i	−0.594278	−	0.804260i	$-0.702562\pi$
$563$	−0.309017	+	0.224514i	−0.0130235	+	0.00946214i	0.581254	+	0.813722i	$0.302562\pi$
$564$		0			0
$565$	1.85410	−	5.70634i	0.0780027	−	0.240067i
$566$		0			0
$567$	−12.4721	−	9.06154i	−0.523780	−	0.380549i
$568$		0			0
$569$	11.8090	+	36.3444i	0.495060	+	1.52364i	0.816864	+	0.576831i	$0.195711\pi$
$569$	11.8090	+	36.3444i	0.495060	+	1.52364i	−0.321804	+	0.946806i	$0.604289\pi$
$570$		0			0
$571$	−2.47214			−0.103456			−0.0517278	−	0.998661i	$-0.516473\pi$
$571$	−2.47214			−0.103456			−0.0517278	+	0.998661i	$0.516473\pi$
$572$		0			0
$573$	−1.81966			−0.0760174
$574$		0			0
$575$	−2.09017	−	6.43288i	−0.0871661	−	0.268270i
$576$		0			0
$577$	5.50000	+	3.99598i	0.228968	+	0.166355i	0.696354	−	0.717698i	$-0.254804\pi$
$577$	5.50000	+	3.99598i	0.228968	+	0.166355i	−0.467386	+	0.884053i	$0.654804\pi$
$578$		0			0
$579$	2.05573	−	6.32688i	0.0854331	−	0.262936i
$580$		0			0
$581$	−15.0902	+	10.9637i	−0.626046	+	0.454849i
$582$		0			0
$583$	−3.34752	−	3.80423i	−0.138640	−	0.157555i
$584$		0			0
$585$	9.23607	−	6.71040i	0.381864	−	0.277441i
$586$		0			0
$587$	6.84346	−	21.0620i	0.282460	−	0.869322i	−0.704689	−	0.709517i	$-0.748913\pi$
$587$	6.84346	−	21.0620i	0.282460	−	0.869322i	0.987149	−	0.159805i	$-0.0510866\pi$
$588$		0			0
$589$	−9.47214	−	6.88191i	−0.390293	−	0.283564i
$590$		0			0
$591$	2.47214	+	7.60845i	0.101690	+	0.312970i
$592$		0			0
$593$	−28.6869			−1.17803			−0.589015	−	0.808122i	$-0.700484\pi$
$593$	−28.6869			−1.17803			−0.589015	+	0.808122i	$0.700484\pi$
$594$		0			0
$595$	4.00000			0.163984
$596$		0			0
$597$	2.23607	+	6.88191i	0.0915162	+	0.281658i
$598$		0			0
$599$	−10.8541	−	7.88597i	−0.443487	−	0.322212i	0.343532	−	0.939141i	$-0.388377\pi$
$599$	−10.8541	−	7.88597i	−0.443487	−	0.322212i	−0.787019	+	0.616929i	$0.788377\pi$
$600$		0			0
$601$	−8.38854	+	25.8173i	−0.342176	+	1.05311i	0.620903	+	0.783888i	$0.286766\pi$
$601$	−8.38854	+	25.8173i	−0.342176	+	1.05311i	−0.963078	+	0.269221i	$0.913234\pi$
$602$		0			0
$603$	25.6074	−	18.6049i	1.04281	−	0.757648i
$604$		0			0
$605$	−32.1803	−	15.2169i	−1.30832	−	0.618655i
$606$		0			0
$607$	18.7082	−	13.5923i	0.759343	−	0.551695i	−0.139366	−	0.990241i	$-0.544506\pi$
$607$	18.7082	−	13.5923i	0.759343	−	0.551695i	0.898709	+	0.438546i	$0.144506\pi$
$608$		0			0
$609$	−1.05573	+	3.24920i	−0.0427803	+	0.131664i
$610$		0			0
$611$	6.47214	+	4.70228i	0.261835	+	0.190234i
$612$		0			0
$613$	−11.0344	−	33.9605i	−0.445677	−	1.37165i	−0.881740	−	0.471736i	$-0.843627\pi$
$613$	−11.0344	−	33.9605i	−0.445677	−	1.37165i	0.436063	−	0.899916i	$-0.356373\pi$
$614$		0			0
$615$	−6.94427			−0.280020
$616$		0			0
$617$	23.4508			0.944096			0.472048	−	0.881573i	$-0.343515\pi$
$617$	23.4508			0.944096			0.472048	+	0.881573i	$0.343515\pi$
$618$		0			0
$619$	1.60739	+	4.94704i	0.0646065	+	0.198838i	0.978149	−	0.207905i	$-0.0666644\pi$
$619$	1.60739	+	4.94704i	0.0646065	+	0.198838i	−0.913543	+	0.406743i	$0.866664\pi$
$620$		0			0
$621$	−2.23607	−	1.62460i	−0.0897303	−	0.0651929i
$622$		0			0
$623$	−5.00000	+	15.3884i	−0.200321	+	0.616524i
$624$		0			0
$625$	18.1353	−	13.1760i	0.725410	−	0.527041i
$626$		0			0
$627$	4.89919	+	5.56758i	0.195655	+	0.222348i
$628$		0			0
$629$	1.85410	−	1.34708i	0.0739279	−	0.0537118i
$630$		0			0
$631$	−7.32624	+	22.5478i	−0.291653	+	0.897615i	0.692672	+	0.721252i	$0.256433\pi$
$631$	−7.32624	+	22.5478i	−0.291653	+	0.897615i	−0.984325	+	0.176363i	$0.943567\pi$
$632$		0			0
$633$	1.88197	+	1.36733i	0.0748014	+	0.0543464i
$634$		0			0
$635$	−10.9443	−	33.6830i	−0.434310	−	1.33667i
$636$		0			0
$637$	3.70820			0.146924
$638$		0			0
$639$	−14.9443			−0.591186
$640$		0			0
$641$	5.15248	+	15.8577i	0.203511	+	0.626341i	0.999771	+	0.0213875i	$0.00680836\pi$
$641$	5.15248	+	15.8577i	0.203511	+	0.626341i	−0.796261	+	0.604954i	$0.793192\pi$
$642$		0			0
$643$	−32.3435	−	23.4989i	−1.27550	−	0.926706i	−0.276094	−	0.961131i	$-0.589040\pi$
$643$	−32.3435	−	23.4989i	−1.27550	−	0.926706i	−0.999407	+	0.0344245i	$0.989040\pi$
$644$		0			0
$645$	3.27051	−	10.0656i	0.128776	−	0.396332i
$646$		0			0
$647$	23.5066	−	17.0785i	0.924139	−	0.671426i	−0.0204118	−	0.999792i	$-0.506498\pi$
$647$	23.5066	−	17.0785i	0.924139	−	0.671426i	0.944551	+	0.328365i	$0.106498\pi$
$648$		0			0
$649$	−27.8885	−	6.26137i	−1.09472	−	0.245780i
$650$		0			0
$651$	1.23607	−	0.898056i	0.0484453	−	0.0351976i
$652$		0			0
$653$	4.74265	−	14.5964i	0.185594	−	0.571200i	−0.814364	−	0.580354i	$-0.802914\pi$
$653$	4.74265	−	14.5964i	0.185594	−	0.571200i	0.999958	+	0.00915459i	$0.00291404\pi$
$654$		0			0
$655$	17.7984	+	12.9313i	0.695440	+	0.505267i
$656$		0			0
$657$	−9.15654	−	28.1809i	−0.357231	−	1.09944i
$658$		0			0
$659$	−16.9098			−0.658713			−0.329357	−	0.944206i	$-0.606832\pi$
$659$	−16.9098			−0.658713			−0.329357	+	0.944206i	$0.606832\pi$
$660$		0			0
$661$	3.52786			0.137218			0.0686090	−	0.997644i	$-0.478144\pi$
$661$	3.52786			0.137218			0.0686090	+	0.997644i	$0.478144\pi$
$662$		0			0
$663$	0.0901699	+	0.277515i	0.00350191	+	0.0107778i
$664$		0			0
$665$	−30.6525	−	22.2703i	−1.18865	−	0.863606i
$666$		0			0
$667$	1.70820	−	5.25731i	0.0661419	−	0.203564i
$668$		0			0
$669$	7.94427	−	5.77185i	0.307143	−	0.223153i
$670$		0			0
$671$	4.18034	−	7.05342i	0.161380	−	0.272294i
$672$		0			0
$673$	−7.97214	+	5.79210i	−0.307303	+	0.223269i	−0.730738	−	0.682657i	$-0.760824\pi$
$673$	−7.97214	+	5.79210i	−0.307303	+	0.223269i	0.423435	+	0.905926i	$0.360824\pi$
$674$		0			0
$675$	−3.78115	+	11.6372i	−0.145537	+	0.447916i
$676$		0			0
$677$	−11.6180	−	8.44100i	−0.446517	−	0.324414i	0.341702	−	0.939808i	$-0.388997\pi$
$677$	−11.6180	−	8.44100i	−0.446517	−	0.324414i	−0.788219	+	0.615395i	$0.788997\pi$
$678$		0			0
$679$	4.41641	+	13.5923i	0.169486	+	0.521625i
$680$		0			0
$681$	5.54102			0.212332
$682$		0			0
$683$	18.4721			0.706817			0.353408	−	0.935469i	$-0.385023\pi$
$683$	18.4721			0.706817			0.353408	+	0.935469i	$0.385023\pi$
$684$		0			0
$685$	−16.0902	−	49.5205i	−0.614774	−	1.89208i
$686$		0			0
$687$	0.527864	+	0.383516i	0.0201393	+	0.0146320i
$688$		0			0
$689$	−0.583592	+	1.79611i	−0.0222331	+	0.0684264i
$690$		0			0
$691$	21.2082	−	15.4087i	0.806798	−	0.586173i	−0.106102	−	0.994355i	$-0.533837\pi$
$691$	21.2082	−	15.4087i	0.806798	−	0.586173i	0.912901	+	0.408182i	$0.133837\pi$
$692$		0			0
$693$	17.3820	−	7.50245i	0.660286	−	0.284995i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.07295	+	3.30220i	−0.0406408	+	0.125080i
$698$		0			0
$699$	2.97214	+	2.15938i	0.112417	+	0.0816754i
$700$		0			0
$701$	4.58359	+	14.1068i	0.173120	+	0.532808i	0.999543	−	0.0302419i	$-0.00962778\pi$
$701$	4.58359	+	14.1068i	0.173120	+	0.532808i	−0.826423	+	0.563050i	$0.809628\pi$
$702$		0			0
$703$	−21.7082			−0.818740
$704$		0			0
$705$	−8.00000			−0.301297
$706$		0			0
$707$	2.58359	+	7.95148i	0.0971660	+	0.299046i
$708$		0			0
$709$	19.7984	+	14.3844i	0.743544	+	0.540216i	0.893819	−	0.448428i	$-0.148016\pi$
$709$	19.7984	+	14.3844i	0.743544	+	0.540216i	−0.150275	+	0.988644i	$0.548016\pi$
$710$		0			0
$711$	11.8328	−	36.4177i	0.443765	−	1.36577i
$712$		0			0
$713$	−2.00000	+	1.45309i	−0.0749006	+	0.0544185i
$714$		0			0
$715$	1.23607	+	13.2088i	0.0462263	+	0.493981i
$716$		0			0
$717$	−6.70820	+	4.87380i	−0.250522	+	0.182015i
$718$		0			0
$719$	−8.29180	+	25.5195i	−0.309232	+	0.951718i	0.668832	+	0.743413i	$0.266794\pi$
$719$	−8.29180	+	25.5195i	−0.309232	+	0.951718i	−0.978064	+	0.208304i	$0.933206\pi$
$720$		0			0
$721$	25.4164	+	18.4661i	0.946556	+	0.687714i
$722$		0			0
$723$	−1.30902	−	4.02874i	−0.0486829	−	0.149830i
$724$		0			0
$725$	−24.4721			−0.908872
$726$		0			0
$727$	−2.87539			−0.106642			−0.0533211	−	0.998577i	$-0.516981\pi$
$727$	−2.87539			−0.106642			−0.0533211	+	0.998577i	$0.516981\pi$
$728$		0			0
$729$	−6.00658	−	18.4863i	−0.222466	−	0.684679i
$730$		0			0
$731$	−4.28115	−	3.11044i	−0.158344	−	0.115044i
$732$		0			0
$733$	2.90983	−	8.95554i	0.107477	−	0.330780i	−0.882827	−	0.469699i	$-0.844363\pi$
$733$	2.90983	−	8.95554i	0.107477	−	0.330780i	0.990304	+	0.138918i	$0.0443626\pi$
$734$		0			0
$735$	−3.00000	+	2.17963i	−0.110657	+	0.0803968i
$736$		0			0
$737$	3.42705	+	36.6219i	0.126237	+	1.34899i
$738$		0			0
$739$	30.3885	−	22.0786i	1.11786	−	0.812173i	0.133977	−	0.990984i	$-0.457225\pi$
$739$	30.3885	−	22.0786i	1.11786	−	0.812173i	0.983883	+	0.178811i	$0.0572251\pi$
$740$		0			0
$741$	0.854102	−	2.62866i	0.0313762	−	0.0965661i
$742$		0			0
$743$	−7.09017	−	5.15131i	−0.260113	−	0.188983i	0.450084	−	0.892986i	$-0.351394\pi$
$743$	−7.09017	−	5.15131i	−0.260113	−	0.188983i	−0.710197	+	0.704003i	$0.751394\pi$
$744$		0			0
$745$	−6.18034	−	19.0211i	−0.226430	−	0.696880i
$746$		0			0
$747$	−26.6180			−0.973903
$748$		0			0
$749$	−2.29180			−0.0837404
$750$		0			0
$751$	10.4377	+	32.1239i	0.380877	+	1.17222i	0.939427	+	0.342748i	$0.111358\pi$
$751$	10.4377	+	32.1239i	0.380877	+	1.17222i	−0.558551	+	0.829470i	$0.688642\pi$
$752$		0			0
$753$	−6.47214	−	4.70228i	−0.235858	−	0.171361i
$754$		0			0
$755$	−8.00000	+	24.6215i	−0.291150	+	0.896067i
$756$		0			0
$757$	−2.14590	+	1.55909i	−0.0779940	+	0.0566660i	−0.626099	−	0.779744i	$-0.715349\pi$
$757$	−2.14590	+	1.55909i	−0.0779940	+	0.0566660i	0.548105	+	0.836410i	$0.315349\pi$
$758$		0			0
$759$	1.43769	−	0.620541i	0.0521850	−	0.0225242i
$760$		0			0
$761$	3.44427	−	2.50241i	0.124855	−	0.0907123i	−0.523605	−	0.851961i	$-0.675413\pi$
$761$	3.44427	−	2.50241i	0.124855	−	0.0907123i	0.648460	+	0.761249i	$0.275413\pi$
$762$		0			0
$763$	−11.7082	+	36.0341i	−0.423865	+	1.30452i
$764$		0			0
$765$	4.61803	+	3.35520i	0.166965	+	0.121307i
$766$		0			0
$767$	3.29180	+	10.1311i	0.118860	+	0.365813i
$768$		0			0
$769$	13.4164			0.483808			0.241904	−	0.970300i	$-0.422228\pi$
$769$	13.4164			0.483808			0.241904	+	0.970300i	$0.422228\pi$
$770$		0			0
$771$	−2.14590			−0.0772826
$772$		0			0
$773$	1.20163	+	3.69822i	0.0432195	+	0.133016i	0.970338	−	0.241753i	$-0.0777222\pi$
$773$	1.20163	+	3.69822i	0.0432195	+	0.133016i	−0.927118	+	0.374768i	$0.877722\pi$
$774$		0			0
$775$	8.85410	+	6.43288i	0.318049	+	0.231076i
$776$		0			0
$777$	0.875388	−	2.69417i	0.0314044	−	0.0966527i
$778$		0			0
$779$	26.6074	−	19.3314i	0.953309	−	0.692619i
$780$		0			0
$781$	8.85410	−	14.9394i	0.316825	−	0.534573i
$782$		0			0
$783$	−8.09017	+	5.87785i	−0.289119	+	0.210057i
$784$		0			0
$785$	9.70820	−	29.8788i	0.346501	−	1.06642i
$786$		0			0
$787$	−21.2082	−	15.4087i	−0.755991	−	0.549259i	0.141687	−	0.989911i	$-0.454747\pi$
$787$	−21.2082	−	15.4087i	−0.755991	−	0.549259i	−0.897678	+	0.440652i	$0.854747\pi$
$788$		0			0
$789$	2.74265	+	8.44100i	0.0976408	+	0.300507i
$790$		0			0
$791$	−3.70820			−0.131849
$792$		0			0
$793$	−3.05573			−0.108512
$794$		0			0
$795$	−0.583592	−	1.79611i	−0.0206979	−	0.0637015i
$796$		0			0
$797$	−20.0344	−	14.5559i	−0.709656	−	0.515596i	0.173406	−	0.984850i	$-0.444523\pi$
$797$	−20.0344	−	14.5559i	−0.709656	−	0.515596i	−0.883063	+	0.469255i	$0.844523\pi$
$798$		0			0
$799$	−1.23607	+	3.80423i	−0.0437289	+	0.134584i
$800$		0			0
$801$	−18.6803	+	13.5721i	−0.660037	+	0.479545i
$802$		0			0
$803$	33.5967	+	7.54294i	1.18560	+	0.266185i
$804$		0			0
$805$	−6.47214	+	4.70228i	−0.228113	+	0.165734i
$806$		0			0
$807$	−0.729490	+	2.24514i	−0.0256793	+	0.0790327i
$808$		0			0
$809$	−13.6803	−	9.93935i	−0.480975	−	0.349449i	0.320728	−	0.947171i	$-0.396072\pi$
$809$	−13.6803	−	9.93935i	−0.480975	−	0.349449i	−0.801703	+	0.597722i	$0.796072\pi$
$810$		0			0
$811$	2.59017	+	7.97172i	0.0909532	+	0.279925i	0.986178	−	0.165690i	$-0.0529851\pi$
$811$	2.59017	+	7.97172i	0.0909532	+	0.279925i	−0.895225	+	0.445615i	$0.852985\pi$
$812$		0			0
$813$	−0.763932			−0.0267923
$814$		0			0
$815$	−2.94427			−0.103133
$816$		0			0
$817$	15.4894	+	47.6713i	0.541904	+	1.66781i
$818$		0			0
$819$	−5.70820	−	4.14725i	−0.199461	−	0.144917i
$820$		0			0
$821$	−9.43769	+	29.0462i	−0.329378	+	1.01372i	0.640048	+	0.768335i	$0.278915\pi$
$821$	−9.43769	+	29.0462i	−0.329378	+	1.01372i	−0.969426	+	0.245386i	$0.921085\pi$
$822$		0			0
$823$	19.0902	−	13.8698i	0.665441	−	0.483472i	−0.203055	−	0.979167i	$-0.565087\pi$
$823$	19.0902	−	13.8698i	0.665441	−	0.483472i	0.868496	+	0.495696i	$0.165087\pi$
$824$		0			0
$825$	−4.57953	−	5.20431i	−0.159439	−	0.181191i
$826$		0			0
$827$	−31.8607	+	23.1481i	−1.10790	+	0.804940i	−0.982332	−	0.187145i	$-0.940077\pi$
$827$	−31.8607	+	23.1481i	−1.10790	+	0.804940i	−0.125572	+	0.992085i	$0.540077\pi$
$828$		0			0
$829$	−9.59675	+	29.5358i	−0.333309	+	1.02582i	0.634240	+	0.773136i	$0.281313\pi$
$829$	−9.59675	+	29.5358i	−0.333309	+	1.02582i	−0.967549	+	0.252683i	$0.918687\pi$
$830$		0			0
$831$	−7.32624	−	5.32282i	−0.254144	−	0.184647i
$832$		0			0
$833$	0.572949	+	1.76336i	0.0198515	+	0.0610967i
$834$		0			0
$835$	−47.7771			−1.65339
$836$		0			0
$837$	4.47214			0.154580
$838$		0			0
$839$	−3.74265	−	11.5187i	−0.129210	−	0.397669i	0.865434	−	0.501023i	$-0.167043\pi$
$839$	−3.74265	−	11.5187i	−0.129210	−	0.397669i	−0.994645	+	0.103354i	$0.967043\pi$
$840$		0			0
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$		0			0
$843$	−1.89919	+	5.84510i	−0.0654115	+	0.201316i
$844$		0			0
$845$	−30.0344	+	21.8213i	−1.03322	+	0.750676i
$846$		0			0
$847$	−2.79837	+	21.8213i	−0.0961533	+	0.749789i
$848$		0			0
$849$	−7.41641	+	5.38834i	−0.254530	+	0.184927i
$850$		0			0
$851$	−1.41641	+	4.35926i	−0.0485538	+	0.149433i
$852$		0			0
$853$	−24.6525	−	17.9111i	−0.844085	−	0.613263i	0.0794240	−	0.996841i	$-0.474692\pi$
$853$	−24.6525	−	17.9111i	−0.844085	−	0.613263i	−0.923509	+	0.383577i	$0.874692\pi$
$854$		0			0
$855$	−16.7082	−	51.4226i	−0.571409	−	1.75861i
$856$		0			0
$857$	−10.7426			−0.366962			−0.183481	−	0.983023i	$-0.558737\pi$
$857$	−10.7426			−0.366962			−0.183481	+	0.983023i	$0.558737\pi$
$858$		0			0
$859$	46.5066			1.58678			0.793392	−	0.608711i	$-0.208313\pi$
$859$	46.5066			1.58678			0.793392	+	0.608711i	$0.208313\pi$
$860$		0			0
$861$	1.32624	+	4.08174i	0.0451981	+	0.139105i
$862$		0			0
$863$	−26.8885	−	19.5357i	−0.915297	−	0.665002i	0.0270522	−	0.999634i	$-0.491388\pi$
$863$	−26.8885	−	19.5357i	−0.915297	−	0.665002i	−0.942349	+	0.334632i	$0.891388\pi$
$864$		0			0
$865$	21.8885	−	67.3660i	0.744233	−	2.29051i
$866$		0			0
$867$	5.13525	−	3.73098i	0.174402	−	0.126711i
$868$		0			0
$869$	29.3951	+	33.4055i	0.997161	+	1.13320i
$870$		0			0
$871$	11.0902	−	8.05748i	0.375776	−	0.273017i
$872$		0			0
$873$	−6.30244	+	19.3969i	−0.213305	+	0.656486i
$874$		0			0
$875$	2.47214	+	1.79611i	0.0835734	+	0.0607197i
$876$		0			0
$877$	8.70820	+	26.8011i	0.294055	+	0.905009i	0.983537	+	0.180706i	$0.0578382\pi$
$877$	8.70820	+	26.8011i	0.294055	+	0.905009i	−0.689482	+	0.724303i	$0.742162\pi$
$878$		0			0
$879$	10.8328			0.365382
$880$		0			0
$881$	−46.3394			−1.56121			−0.780607	−	0.625022i	$-0.785090\pi$
$881$	−46.3394			−1.56121			−0.780607	+	0.625022i	$0.785090\pi$
$882$		0			0
$883$	−1.06231	−	3.26944i	−0.0357494	−	0.110025i	0.931589	−	0.363512i	$-0.118423\pi$
$883$	−1.06231	−	3.26944i	−0.0357494	−	0.110025i	−0.967339	+	0.253487i	$0.918423\pi$
$884$		0			0
$885$	−8.61803	−	6.26137i	−0.289692	−	0.210474i
$886$		0			0
$887$	11.6738	−	35.9281i	0.391967	−	1.20635i	−0.539332	−	0.842093i	$-0.681323\pi$
$887$	11.6738	−	35.9281i	0.391967	−	1.20635i	0.931299	−	0.364256i	$-0.118677\pi$
$888$		0			0
$889$	−17.7082	+	12.8658i	−0.593914	+	0.431504i
$890$		0			0
$891$	24.9443	+	5.60034i	0.835665	+	0.187618i
$892$		0			0
$893$	30.6525	−	22.2703i	1.02575	−	0.745248i
$894$		0			0
$895$	8.61803	−	26.5236i	0.288069	−	0.886586i
$896$		0			0
$897$	−0.472136	−	0.343027i	−0.0157642	−	0.0114533i
$898$		0			0
$899$	2.76393	+	8.50651i	0.0921823	+	0.283708i
$900$		0			0
$901$	−0.944272			−0.0314583
$902$		0			0
$903$	−6.54102			−0.217672
$904$		0			0
$905$	−4.18034	−	12.8658i	−0.138959	−	0.427672i
$906$		0			0
$907$	−8.44427	−	6.13512i	−0.280387	−	0.203713i	0.438699	−	0.898634i	$-0.355439\pi$
$907$	−8.44427	−	6.13512i	−0.280387	−	0.203713i	−0.719086	+	0.694921i	$0.755439\pi$
$908$		0			0
$909$	−3.68692	+	11.3472i	−0.122287	+	0.376362i
$910$		0			0
$911$	14.7082	−	10.6861i	0.487305	−	0.354047i	−0.316842	−	0.948478i	$-0.602623\pi$
$911$	14.7082	−	10.6861i	0.487305	−	0.354047i	0.804147	+	0.594431i	$0.202623\pi$
$912$		0			0
$913$	15.7705	−	26.6093i	0.521928	−	0.880641i
$914$		0			0
$915$	2.47214	−	1.79611i	0.0817263	−	0.0593776i
$916$		0			0
$917$	4.20163	−	12.9313i	0.138750	−	0.427028i
$918$		0			0
$919$	35.1246	+	25.5195i	1.15865	+	0.841811i	0.989607	−	0.143797i	$-0.0459311\pi$
$919$	35.1246	+	25.5195i	1.15865	+	0.841811i	0.169047	+	0.985608i	$0.445931\pi$
$920$		0			0
$921$	3.28115	+	10.0984i	0.108118	+	0.332752i
$922$		0			0
$923$	−6.47214			−0.213033
$924$		0			0
$925$	20.2918			0.667190
$926$		0			0
$927$	13.8541	+	42.6385i	0.455028	+	1.40043i
$928$		0			0
$929$	13.1525	+	9.55583i	0.431519	+	0.313517i	0.782256	−	0.622957i	$-0.214069\pi$
$929$	13.1525	+	9.55583i	0.431519	+	0.313517i	−0.350737	+	0.936474i	$0.614069\pi$
$930$		0			0
$931$	5.42705	−	16.7027i	0.177864	−	0.547410i
$932$		0			0
$933$	8.05573	−	5.85283i	0.263733	−	0.191613i
$934$		0			0
$935$	−6.09017	+	2.62866i	−0.199170	+	0.0859662i
$936$		0			0
$937$	30.6246	−	22.2501i	1.00046	−	0.726879i	0.0382752	−	0.999267i	$-0.487814\pi$
$937$	30.6246	−	22.2501i	1.00046	−	0.726879i	0.962187	+	0.272389i	$0.0878137\pi$
$938$		0			0
$939$	0.510643	−	1.57160i	0.0166642	−	0.0512872i
$940$		0			0
$941$	38.9787	+	28.3197i	1.27067	+	0.923196i	0.999229	−	0.0392595i	$-0.0124999\pi$
$941$	38.9787	+	28.3197i	1.27067	+	0.923196i	0.271441	+	0.962455i	$0.412500\pi$
$942$		0			0
$943$	−2.14590	−	6.60440i	−0.0698801	−	0.215069i
$944$		0			0
$945$	14.4721			0.470779
$946$		0			0
$947$	−30.2148			−0.981848			−0.490924	−	0.871202i	$-0.663341\pi$
$947$	−30.2148			−0.981848			−0.490924	+	0.871202i	$0.663341\pi$
$948$		0			0
$949$	−3.96556	−	12.2047i	−0.128727	−	0.396182i
$950$		0			0
$951$	−1.14590	−	0.832544i	−0.0371583	−	0.0269971i
$952$		0			0
$953$	−3.50000	+	10.7719i	−0.113376	+	0.348936i	−0.991605	−	0.129305i	$-0.958725\pi$
$953$	−3.50000	+	10.7719i	−0.113376	+	0.348936i	0.878229	+	0.478241i	$0.158725\pi$
$954$		0			0
$955$	−12.4721	+	9.06154i	−0.403589	+	0.293224i
$956$		0			0
$957$	−0.527864	−	5.64083i	−0.0170634	−	0.182342i
$958$		0			0
$959$	−26.0344	+	18.9151i	−0.840696	+	0.610801i
$960$		0			0
$961$	−8.34346	+	25.6785i	−0.269144	+	0.828340i
$962$		0			0
$963$	−2.64590	−	1.92236i	−0.0852629	−	0.0619471i
$964$		0			0
$965$	−17.4164	−	53.6022i	−0.560654	−	1.72552i
$966$		0			0
$967$	−38.0000			−1.22200			−0.610999	−	0.791632i	$-0.709232\pi$
$967$	−38.0000			−1.22200			−0.610999	+	0.791632i	$0.709232\pi$
$968$		0			0
$969$	1.38197			0.0443951
$970$		0			0
$971$	−3.12461	−	9.61657i	−0.100274	−	0.308610i	0.888319	−	0.459228i	$-0.151874\pi$
$971$	−3.12461	−	9.61657i	−0.100274	−	0.308610i	−0.988592	+	0.150617i	$0.951874\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.798374	+	2.45714i	−0.0255684	+	0.0786915i
$976$		0			0
$977$	35.0344	−	25.4540i	1.12085	−	0.814346i	0.136513	−	0.990638i	$-0.456410\pi$
$977$	35.0344	−	25.4540i	1.12085	−	0.814346i	0.984338	+	0.176292i	$0.0564104\pi$
$978$		0			0
$979$	−2.50000	−	26.7153i	−0.0799003	−	0.853826i
$980$		0			0
$981$	−43.7426	+	31.7809i	−1.39660	+	1.01469i
$982$		0			0
$983$	1.85410	−	5.70634i	0.0591367	−	0.182004i	−0.917124	−	0.398601i	$-0.869496\pi$
$983$	1.85410	−	5.70634i	0.0591367	−	0.182004i	0.976261	+	0.216597i	$0.0694958\pi$
$984$		0			0
$985$	54.8328	+	39.8384i	1.74712	+	1.26936i
$986$		0			0
$987$	1.52786	+	4.70228i	0.0486324	+	0.149675i
$988$		0			0
$989$	10.5836			0.336539
$990$		0			0
$991$	−30.5410			−0.970167			−0.485084	−	0.874468i	$-0.661211\pi$
$991$	−30.5410			−0.970167			−0.485084	+	0.874468i	$0.661211\pi$
$992$		0			0
$993$	0.740133	+	2.27790i	0.0234874	+	0.0722868i
$994$		0			0
$995$	49.5967	+	36.0341i	1.57232	+	1.14236i
$996$		0			0
$997$	−2.67376	+	8.22899i	−0.0846789	+	0.260615i	−0.984427	−	0.175795i	$-0.943750\pi$
$997$	−2.67376	+	8.22899i	−0.0846789	+	0.260615i	0.899748	+	0.436410i	$0.143750\pi$
$998$		0			0
$999$	6.70820	−	4.87380i	0.212238	−	0.154200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.m.a.641.1		4
4.3	odd	2		704.2.m.h.641.1		4
8.3	odd	2		22.2.c.a.3.1	✓	4
8.5	even	2		176.2.m.c.113.1		4
11.2	odd	10		7744.2.a.cy.1.1		2
11.4	even	5	inner	704.2.m.a.257.1		4
11.9	even	5		7744.2.a.cz.1.1		2
24.11	even	2		198.2.f.e.91.1		4
40.3	even	4		550.2.ba.c.399.2		8
40.19	odd	2		550.2.h.h.201.1		4
40.27	even	4		550.2.ba.c.399.1		8
44.15	odd	10		704.2.m.h.257.1		4
44.31	odd	10		7744.2.a.bm.1.2		2
44.35	even	10		7744.2.a.bn.1.2		2
88.3	odd	10		242.2.c.a.27.1		4
88.13	odd	10		1936.2.a.n.1.2		2
88.19	even	10		242.2.c.d.27.1		4
88.27	odd	10		242.2.c.a.9.1		4
88.35	even	10		242.2.a.d.1.1		2
88.37	even	10		176.2.m.c.81.1		4
88.43	even	2		242.2.c.c.3.1		4
88.51	even	10		242.2.c.c.81.1		4
88.53	even	10		1936.2.a.o.1.2		2
88.59	odd	10		22.2.c.a.15.1	yes	4
88.75	odd	10		242.2.a.f.1.1		2
88.83	even	10		242.2.c.d.9.1		4
264.35	odd	10		2178.2.a.x.1.1		2
264.59	even	10		198.2.f.e.37.1		4
264.251	even	10		2178.2.a.p.1.1		2
440.59	odd	10		550.2.h.h.301.1		4
440.147	even	20		550.2.ba.c.499.2		8
440.299	even	10		6050.2.a.ci.1.2		2
440.323	even	20		550.2.ba.c.499.1		8
440.339	odd	10		6050.2.a.bs.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.3.1	✓	4	8.3	odd	2
22.2.c.a.15.1	yes	4	88.59	odd	10
176.2.m.c.81.1		4	88.37	even	10
176.2.m.c.113.1		4	8.5	even	2
198.2.f.e.37.1		4	264.59	even	10
198.2.f.e.91.1		4	24.11	even	2
242.2.a.d.1.1		2	88.35	even	10
242.2.a.f.1.1		2	88.75	odd	10
242.2.c.a.9.1		4	88.27	odd	10
242.2.c.a.27.1		4	88.3	odd	10
242.2.c.c.3.1		4	88.43	even	2
242.2.c.c.81.1		4	88.51	even	10
242.2.c.d.9.1		4	88.83	even	10
242.2.c.d.27.1		4	88.19	even	10
550.2.h.h.201.1		4	40.19	odd	2
550.2.h.h.301.1		4	440.59	odd	10
550.2.ba.c.399.1		8	40.27	even	4
550.2.ba.c.399.2		8	40.3	even	4
550.2.ba.c.499.1		8	440.323	even	20
550.2.ba.c.499.2		8	440.147	even	20
704.2.m.a.257.1		4	11.4	even	5	inner
704.2.m.a.641.1		4	1.1	even	1	trivial
704.2.m.h.257.1		4	44.15	odd	10
704.2.m.h.641.1		4	4.3	odd	2
1936.2.a.n.1.2		2	88.13	odd	10
1936.2.a.o.1.2		2	88.53	even	10
2178.2.a.p.1.1		2	264.251	even	10
2178.2.a.x.1.1		2	264.35	odd	10
6050.2.a.bs.1.2		2	440.339	odd	10
6050.2.a.ci.1.2		2	440.299	even	10
7744.2.a.bm.1.2		2	44.31	odd	10
7744.2.a.bn.1.2		2	44.35	even	10
7744.2.a.cy.1.1		2	11.2	odd	10
7744.2.a.cz.1.1		2	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.118034 + 0.363271i) q^{3} +(2.61803 + 1.90211i) q^{5} +(0.618034 - 1.90211i) q^{7} +(2.30902 - 1.67760i) q^{9} +(0.309017 + 3.30220i) q^{11} +(1.00000 - 0.726543i) q^{13} +(-0.381966 + 1.17557i) q^{15} +(0.500000 + 0.363271i) q^{17} +(-1.80902 - 5.56758i) q^{19} +0.763932 q^{21} -1.23607 q^{23} +(1.69098 + 5.20431i) q^{25} +(1.80902 + 1.31433i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(1.61803 - 1.17557i) q^{31} +(-1.16312 + 0.502029i) q^{33} +(5.23607 - 3.80423i) q^{35} +(1.14590 - 3.52671i) q^{37} +(0.381966 + 0.277515i) q^{39} +(1.73607 + 5.34307i) q^{41} -8.56231 q^{43} +9.23607 q^{45} +(2.00000 + 6.15537i) q^{47} +(2.42705 + 1.76336i) q^{49} +(-0.0729490 + 0.224514i) q^{51} +(-1.23607 + 0.898056i) q^{53} +(-5.47214 + 9.23305i) q^{55} +(1.80902 - 1.31433i) q^{57} +(-2.66312 + 8.19624i) q^{59} +(-2.00000 - 1.45309i) q^{61} +(-1.76393 - 5.42882i) q^{63} +4.00000 q^{65} +11.0902 q^{67} +(-0.145898 - 0.449028i) q^{69} +(-4.23607 - 3.07768i) q^{71} +(3.20820 - 9.87384i) q^{73} +(-1.69098 + 1.22857i) q^{75} +(6.47214 + 1.45309i) q^{77} +(10.8541 - 7.88597i) q^{79} +(2.38197 - 7.33094i) q^{81} +(-7.54508 - 5.48183i) q^{83} +(0.618034 + 1.90211i) q^{85} -1.70820 q^{87} -8.09017 q^{89} +(-0.763932 - 2.35114i) q^{91} +(0.618034 + 0.449028i) q^{93} +(5.85410 - 18.0171i) q^{95} +(-5.78115 + 4.20025i) q^{97} +(6.25329 + 7.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{5} - 2 q^{7} + 7 q^{9} - q^{11} + 4 q^{13} - 6 q^{15} + 2 q^{17} - 5 q^{19} + 12 q^{21} + 4 q^{23} + 9 q^{25} + 5 q^{27} - 10 q^{29} + 2 q^{31} + 11 q^{33} + 12 q^{35} + 18 q^{37}+ \cdots - 13 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^5 - 2 * q^7 + 7 * q^9 - q^11 + 4 * q^13 - 6 * q^15 + 2 * q^17 - 5 * q^19 + 12 * q^21 + 4 * q^23 + 9 * q^25 + 5 * q^27 - 10 * q^29 + 2 * q^31 + 11 * q^33 + 12 * q^35 + 18 * q^37 + 6 * q^39 - 2 * q^41 + 6 * q^43 + 28 * q^45 + 8 * q^47 + 3 * q^49 - 7 * q^51 + 4 * q^53 - 4 * q^55 + 5 * q^57 + 5 * q^59 - 8 * q^61 - 16 * q^63 + 16 * q^65 + 22 * q^67 - 14 * q^69 - 8 * q^71 - 14 * q^73 - 9 * q^75 + 8 * q^77 + 30 * q^79 + 14 * q^81 - 19 * q^83 - 2 * q^85 + 20 * q^87 - 10 * q^89 - 12 * q^91 - 2 * q^93 + 10 * q^95 - 3 * q^97 - 13 * q^99

Introduction

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