LMFDB - Embedded newform 784.2.w.f.227.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(19,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.13
Character	$\chi$	$=$	784.227
Dual form			784.2.w.f.411.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31418 + 0.522432i) q^{2} +(2.48480 - 0.665801i) q^{3} +(1.45413 + 1.37314i) q^{4} +(0.837076 - 3.12401i) q^{5} +(3.61331 + 0.423158i) q^{6} +(1.19362 + 2.56423i) q^{8} +(3.13287 - 1.80877i) q^{9} +(2.73215 - 3.66819i) q^{10} +(-1.40398 + 0.376195i) q^{11} +(4.52746 + 2.44381i) q^{12} +(-3.11315 + 3.11315i) q^{13} -8.31987i q^{15} +(0.228992 + 3.99344i) q^{16} +(-2.02443 - 1.16881i) q^{17} +(5.06211 - 0.740329i) q^{18} +(-1.18070 + 4.40643i) q^{19} +(5.50691 - 3.39330i) q^{20} +(-2.04161 - 0.239095i) q^{22} +(-1.15450 - 1.99965i) q^{23} +(4.67317 + 5.57689i) q^{24} +(-4.72861 - 2.73006i) q^{25} +(-5.71764 + 2.46483i) q^{26} +(1.12329 - 1.12329i) q^{27} +(-1.55163 - 1.55163i) q^{29} +(4.34656 - 10.9338i) q^{30} +(3.88952 - 6.73685i) q^{31} +(-1.78536 + 5.36773i) q^{32} +(-3.23814 + 1.86954i) q^{33} +(-2.04984 - 2.59365i) q^{34} +(7.03929 + 1.67168i) q^{36} +(-1.01669 - 0.272421i) q^{37} +(-3.85371 + 5.17400i) q^{38} +(-5.66282 + 9.80830i) q^{39} +(9.00983 - 1.58242i) q^{40} -2.77210 q^{41} +(7.12142 + 7.12142i) q^{43} +(-2.55813 - 1.38082i) q^{44} +(-3.02815 - 11.3012i) q^{45} +(-0.472536 - 3.23104i) q^{46} +(1.42516 + 2.46844i) q^{47} +(3.22783 + 9.77044i) q^{48} +(-4.78797 - 6.05817i) q^{50} +(-5.80851 - 1.55638i) q^{51} +(-8.80171 + 0.252146i) q^{52} +(-2.97221 - 11.0925i) q^{53} +(2.06305 - 0.889362i) q^{54} +4.70094i q^{55} +11.7352i q^{57} +(-1.22850 - 2.84974i) q^{58} +(-1.01120 - 3.77383i) q^{59} +(11.4243 - 12.0982i) q^{60} +(13.9045 + 3.72571i) q^{61} +(8.63107 - 6.82142i) q^{62} +(-5.15056 + 6.12142i) q^{64} +(7.11957 + 12.3315i) q^{65} +(-5.23220 + 0.765203i) q^{66} +(-0.695627 - 2.59612i) q^{67} +(-1.33886 - 4.47942i) q^{68} +(-4.20006 - 4.20006i) q^{69} -7.48345 q^{71} +(8.37754 + 5.87444i) q^{72} +(-5.65210 + 9.78973i) q^{73} +(-1.19379 - 0.889159i) q^{74} +(-13.5673 - 3.63536i) q^{75} +(-7.76752 + 4.78626i) q^{76} +(-12.5661 + 9.93142i) q^{78} +(0.706717 - 0.408024i) q^{79} +(12.6672 + 2.62744i) q^{80} +(-3.38303 + 5.85958i) q^{81} +(-3.64303 - 1.44823i) q^{82} +(2.65285 + 2.65285i) q^{83} +(-5.34597 + 5.34597i) q^{85} +(5.63837 + 13.0793i) q^{86} +(-4.88857 - 2.82241i) q^{87} +(-2.64046 - 3.15109i) q^{88} +(-2.40944 - 4.17328i) q^{89} +(1.92458 - 16.4338i) q^{90} +(1.06700 - 4.49303i) q^{92} +(5.17929 - 19.3294i) q^{93} +(0.583317 + 3.98852i) q^{94} +(12.7774 + 7.37703i) q^{95} +(-0.862438 + 14.5264i) q^{96} +5.86541i q^{97} +(-3.71804 + 3.71804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.31418	+	0.522432i	0.929265	+	0.369415i
$2$	1.31418	+	0.522432i	0.929265	+	0.369415i
$3$	2.48480	−	0.665801i	1.43460	−	0.384400i	0.543962	−	0.839110i	$-0.316924\pi$
$3$	2.48480	−	0.665801i	1.43460	−	0.384400i	0.890640	+	0.454710i	$0.150257\pi$
$4$	1.45413	+	1.37314i	0.727065	+	0.686568i
$5$	0.837076	−	3.12401i	0.374352	−	1.39710i	−0.479938	−	0.877302i	$-0.659341\pi$
$5$	0.837076	−	3.12401i	0.374352	−	1.39710i	0.854290	−	0.519797i	$-0.173992\pi$
$6$	3.61331	+	0.423158i	1.47513	+	0.172753i
$7$		0			0
$7$		0			0
$8$	1.19362	+	2.56423i	0.422007	+	0.906592i
$9$	3.13287	−	1.80877i	1.04429	−	0.602922i
$10$	2.73215	−	3.66819i	0.863981	−	1.15998i
$11$	−1.40398	+	0.376195i	−0.423315	+	0.113427i	−0.464187	−	0.885737i	$-0.653653\pi$
$11$	−1.40398	+	0.376195i	−0.423315	+	0.113427i	0.0408713	+	0.999164i	$0.486987\pi$
$12$	4.52746	+	2.44381i	1.30697	+	0.705468i
$13$	−3.11315	+	3.11315i	−0.863433	+	0.863433i	−0.991735	−	0.128303i	$-0.959047\pi$
$13$	−3.11315	+	3.11315i	−0.863433	+	0.863433i	0.128303	+	0.991735i	$0.459047\pi$
$14$		0			0
$15$		−	8.31987i		−	2.14818i
$16$	0.228992	+	3.99344i	0.0572479	+	0.998360i
$17$	−2.02443	−	1.16881i	−0.490997	−	0.283477i	0.233991	−	0.972239i	$-0.424821\pi$
$17$	−2.02443	−	1.16881i	−0.490997	−	0.283477i	−0.724988	+	0.688761i	$0.758155\pi$
$18$	5.06211	−	0.740329i	1.19315	−	0.174497i
$19$	−1.18070	+	4.40643i	−0.270871	+	1.01090i	0.687687	+	0.726007i	$0.258626\pi$
$19$	−1.18070	+	4.40643i	−0.270871	+	1.01090i	−0.958558	+	0.284897i	$0.908041\pi$
$20$	5.50691	−	3.39330i	1.23138	−	0.758764i
$21$		0			0
$22$	−2.04161	−	0.239095i	−0.435274	−	0.0509753i
$23$	−1.15450	−	1.99965i	−0.240729	−	0.416955i	0.720193	−	0.693774i	$-0.244053\pi$
$23$	−1.15450	−	1.99965i	−0.240729	−	0.416955i	−0.960922	+	0.276819i	$0.910720\pi$
$24$	4.67317	+	5.57689i	0.953907	+	1.13838i
$25$	−4.72861	−	2.73006i	−0.945722	−	0.546013i
$26$	−5.71764	+	2.46483i	−1.12132	+	0.483392i
$27$	1.12329	−	1.12329i	0.216177	−	0.216177i
$28$		0			0
$29$	−1.55163	−	1.55163i	−0.288130	−	0.288130i	0.548210	−	0.836341i	$-0.315309\pi$
$29$	−1.55163	−	1.55163i	−0.288130	−	0.288130i	−0.836341	+	0.548210i	$0.815309\pi$
$30$	4.34656	−	10.9338i	0.793570	−	1.99623i
$31$	3.88952	−	6.73685i	0.698579	−	1.20997i	−0.270380	−	0.962754i	$-0.587149\pi$
$31$	3.88952	−	6.73685i	0.698579	−	1.20997i	0.968959	−	0.247221i	$-0.0795172\pi$
$32$	−1.78536	+	5.36773i	−0.315611	+	0.948889i
$33$	−3.23814	+	1.86954i	−0.563687	+	0.325445i
$34$	−2.04984	−	2.59365i	−0.351545	−	0.444807i
$35$		0			0
$36$	7.03929	+	1.67168i	1.17322	+	0.278614i
$37$	−1.01669	−	0.272421i	−0.167142	−	0.0447857i	0.174277	−	0.984697i	$-0.444241\pi$
$37$	−1.01669	−	0.272421i	−0.167142	−	0.0447857i	−0.341420	+	0.939911i	$0.610908\pi$
$38$	−3.85371	+	5.17400i	−0.625154	+	0.839333i
$39$	−5.66282	+	9.80830i	−0.906778	+	1.57058i
$40$	9.00983	−	1.58242i	1.42458	−	0.250202i
$41$	−2.77210			−0.432929			−0.216464	−	0.976290i	$-0.569453\pi$
$41$	−2.77210			−0.432929			−0.216464	+	0.976290i	$0.569453\pi$
$42$		0			0
$43$	7.12142	+	7.12142i	1.08601	+	1.08601i	0.995935	+	0.0900717i	$0.0287096\pi$
$43$	7.12142	+	7.12142i	1.08601	+	1.08601i	0.0900717	+	0.995935i	$0.471290\pi$
$44$	−2.55813	−	1.38082i	−0.385653	−	0.208166i
$45$	−3.02815	−	11.3012i	−0.451410	−	1.68468i
$46$	−0.472536	−	3.23104i	−0.0696716	−	0.476390i
$47$	1.42516	+	2.46844i	0.207880	+	0.360059i	0.951047	−	0.309047i	$-0.100010\pi$
$47$	1.42516	+	2.46844i	0.207880	+	0.360059i	−0.743166	+	0.669107i	$0.766677\pi$
$48$	3.22783	+	9.77044i	0.465898	+	1.41024i
$49$		0			0
$50$	−4.78797	−	6.05817i	−0.677121	−	0.856754i
$51$	−5.80851	−	1.55638i	−0.813354	−	0.217937i
$52$	−8.80171	+	0.252146i	−1.22058	+	0.0349664i
$53$	−2.97221	−	11.0925i	−0.408265	−	1.52367i	−0.797954	−	0.602719i	$-0.794084\pi$
$53$	−2.97221	−	11.0925i	−0.408265	−	1.52367i	0.389689	−	0.920947i	$-0.372583\pi$
$54$	2.06305	−	0.889362i	0.280745	−	0.121027i
$55$			4.70094i			0.633875i
$56$		0			0
$57$			11.7352i			1.55437i
$58$	−1.22850	−	2.84974i	−0.161310	−	0.374189i
$59$	−1.01120	−	3.77383i	−0.131646	−	0.491311i	0.868343	−	0.495965i	$-0.165185\pi$
$59$	−1.01120	−	3.77383i	−0.131646	−	0.491311i	−0.999989	+	0.00465348i	$0.998519\pi$
$60$	11.4243	−	12.0982i	1.47487	−	1.56187i
$61$	13.9045	+	3.72571i	1.78029	+	0.477028i	0.990637	−	0.136523i	$-0.0435926\pi$
$61$	13.9045	+	3.72571i	1.78029	+	0.477028i	0.789655	+	0.613551i	$0.210259\pi$
$62$	8.63107	−	6.82142i	1.09615	−	0.866321i
$63$		0			0
$64$	−5.15056	+	6.12142i	−0.643819	+	0.765177i
$65$	7.11957	+	12.3315i	0.883074	+	1.52953i
$66$	−5.23220	+	0.765203i	−0.644039	+	0.0941900i
$67$	−0.695627	−	2.59612i	−0.0849844	−	0.317166i	0.910327	−	0.413890i	$-0.135830\pi$
$67$	−0.695627	−	2.59612i	−0.0849844	−	0.317166i	−0.995311	+	0.0967240i	$0.969164\pi$
$68$	−1.33886	−	4.47942i	−0.162360	−	0.543210i
$69$	−4.20006	−	4.20006i	−0.505628	−	0.505628i
$70$		0			0
$71$	−7.48345			−0.888122			−0.444061	−	0.895997i	$-0.646463\pi$
$71$	−7.48345			−0.888122			−0.444061	+	0.895997i	$0.646463\pi$
$72$	8.37754	+	5.87444i	0.987303	+	0.692309i
$73$	−5.65210	+	9.78973i	−0.661529	+	1.14580i	0.318685	+	0.947861i	$0.396759\pi$
$73$	−5.65210	+	9.78973i	−0.661529	+	1.14580i	−0.980214	+	0.197941i	$0.936575\pi$
$74$	−1.19379	−	0.889159i	−0.138775	−	0.103363i
$75$	−13.5673	−	3.63536i	−1.56662	−	0.419775i
$76$	−7.76752	+	4.78626i	−0.890995	+	0.549022i
$77$		0			0
$78$	−12.5661	+	9.93142i	−1.42283	+	1.12451i
$79$	0.706717	−	0.408024i	0.0795119	−	0.0459062i	−0.459717	−	0.888066i	$-0.652049\pi$
$79$	0.706717	−	0.408024i	0.0795119	−	0.0459062i	0.539229	+	0.842159i	$0.318716\pi$
$80$	12.6672	+	2.62744i	1.41624	+	0.293757i
$81$	−3.38303	+	5.85958i	−0.375892	+	0.651065i
$82$	−3.64303	−	1.44823i	−0.402306	−	0.159930i
$83$	2.65285	+	2.65285i	0.291188	+	0.291188i	0.837550	−	0.546361i	$-0.183987\pi$
$83$	2.65285	+	2.65285i	0.291188	+	0.291188i	−0.546361	+	0.837550i	$0.683987\pi$
$84$		0			0
$85$	−5.34597	+	5.34597i	−0.579852	+	0.579852i
$86$	5.63837	+	13.0793i	0.608001	+	1.41038i
$87$	−4.88857	−	2.82241i	−0.524109	−	0.302595i
$88$	−2.64046	−	3.15109i	−0.281474	−	0.335907i
$89$	−2.40944	−	4.17328i	−0.255400	−	0.442367i	0.709604	−	0.704601i	$-0.248874\pi$
$89$	−2.40944	−	4.17328i	−0.255400	−	0.442367i	−0.965004	+	0.262234i	$0.915541\pi$
$90$	1.92458	−	16.4338i	0.202868	−	1.73227i
$91$		0			0
$92$	1.06700	−	4.49303i	0.111242	−	0.468430i
$93$	5.17929	−	19.3294i	0.537068	−	2.00436i
$94$	0.583317	+	3.98852i	0.0601646	+	0.411384i
$95$	12.7774	+	7.37703i	1.31093	+	0.756867i
$96$	−0.862438	+	14.5264i	−0.0880223	+	1.48260i
$97$			5.86541i			0.595542i	0.954637	+	0.297771i	$0.0962432\pi$
$97$			5.86541i			0.595542i	−0.954637	+	0.297771i	$0.903757\pi$
$98$		0			0
$99$	−3.71804	+	3.71804i	−0.373677	+	0.373677i
$100$	−3.12727	−	10.4629i	−0.312727	−	1.04629i
$101$	−1.39442	+	0.373632i	−0.138749	+	0.0371778i	−0.327525	−	0.944842i	$-0.606215\pi$
$101$	−1.39442	+	0.373632i	−0.138749	+	0.0371778i	0.188776	+	0.982020i	$0.439548\pi$
$102$	−6.82031	−	5.07992i	−0.675311	−	0.502987i
$103$	2.10134	−	1.21321i	0.207051	−	0.119541i	−0.392889	−	0.919586i	$-0.628524\pi$
$103$	2.10134	−	1.21321i	0.207051	−	0.119541i	0.599940	+	0.800045i	$0.295191\pi$
$104$	−11.6987	−	4.26692i	−1.14716	−	0.418406i
$105$		0			0
$106$	1.88903	−	16.1302i	0.183479	−	1.56671i
$107$	1.16493	−	4.34758i	0.112618	−	0.420297i	−0.886480	−	0.462768i	$-0.846856\pi$
$107$	1.16493	−	4.34758i	0.112618	−	0.420297i	0.999098	+	0.0424712i	$0.0135231\pi$
$108$	3.17584	−	0.0909797i	0.305595	−	0.00875453i
$109$	−3.14518	+	0.842750i	−0.301254	+	0.0807208i	−0.406280	−	0.913749i	$-0.633174\pi$
$109$	−3.14518	+	0.842750i	−0.301254	+	0.0807208i	0.105026	+	0.994470i	$0.466507\pi$
$110$	−2.45592	+	6.17788i	−0.234163	+	0.589038i
$111$	−2.70765			−0.256998
$112$		0			0
$113$	11.5397			1.08556			0.542781	−	0.839875i	$-0.317372\pi$
$113$	11.5397			1.08556			0.542781	+	0.839875i	$0.317372\pi$
$114$	−6.13084	+	15.4222i	−0.574206	+	1.44442i
$115$	−7.21331	+	1.93280i	−0.672645	+	0.180235i
$116$	−0.125673	−	4.38687i	−0.0116684	−	0.407311i
$117$	−4.12215	+	15.3841i	−0.381093	+	1.42226i
$118$	0.642678	−	5.48777i	0.0591633	−	0.505190i
$119$		0			0
$120$	21.3341	−	9.93074i	1.94752	−	0.906548i
$121$	−7.69665	+	4.44366i	−0.699695	+	0.403969i
$122$	16.3266	+	12.1604i	1.47814	+	1.10095i
$123$	−6.88811	+	1.84566i	−0.621080	+	0.166418i
$124$	14.9065	−	4.45542i	1.33864	−	0.400108i
$125$	−1.05228	+	1.05228i	−0.0941192	+	0.0941192i
$126$		0			0
$127$		−	4.49210i		−	0.398610i	−0.979938	−	0.199305i	$-0.936132\pi$
$127$		−	4.49210i		−	0.398610i	0.979938	−	0.199305i	$-0.0638684\pi$
$128$	−9.96677	+	5.35383i	−0.880946	+	0.473216i
$129$	22.4368	+	12.9539i	1.97545	+	1.14053i
$130$	2.91404	+	19.9252i	0.255579	+	1.74756i
$131$	3.58012	−	13.3612i	0.312796	−	1.16737i	−0.613227	−	0.789907i	$-0.710129\pi$
$131$	3.58012	−	13.3612i	0.312796	−	1.16737i	0.926024	−	0.377465i	$-0.123204\pi$
$132$	−7.27581	−	1.72785i	−0.633278	−	0.150390i
$133$		0			0
$134$	0.442115	−	3.77518i	0.0381929	−	0.326126i
$135$	−2.56889	−	4.44945i	−0.221095	−	0.382947i
$136$	0.580692	−	6.58622i	0.0497939	−	0.564764i
$137$	2.18423	+	1.26106i	0.186611	+	0.107740i	0.590395	−	0.807114i	$-0.298972\pi$
$137$	2.18423	+	1.26106i	0.186611	+	0.107740i	−0.403784	+	0.914854i	$0.632305\pi$
$138$	−3.32538	−	7.71387i	−0.283075	−	0.656648i
$139$	6.00381	−	6.00381i	0.509237	−	0.509237i	−0.405055	−	0.914292i	$-0.632748\pi$
$139$	6.00381	−	6.00381i	0.509237	−	0.509237i	0.914292	+	0.405055i	$0.132748\pi$
$140$		0			0
$141$	5.18472	+	5.18472i	0.436632	+	0.436632i
$142$	−9.83459	−	3.90959i	−0.825300	−	0.328085i
$143$	3.19964	−	5.54195i	0.267568	−	0.463441i
$144$	7.94060	+	12.0968i	0.661717	+	1.00806i
$145$	−6.14613	+	3.54847i	−0.510409	+	0.294685i
$146$	−12.5423	+	9.91262i	−1.03801	+	0.820374i
$147$		0			0
$148$	−1.10433	−	1.79219i	−0.0907750	−	0.147317i
$149$	8.20870	+	2.19951i	0.672483	+	0.180191i	0.578873	−	0.815418i	$-0.303493\pi$
$149$	8.20870	+	2.19951i	0.672483	+	0.180191i	0.0936097	+	0.995609i	$0.470159\pi$
$150$	−15.9307	−	11.8655i	−1.30073	−	0.968815i
$151$	5.11927	−	8.86683i	0.416600	−	0.721572i	−0.578995	−	0.815331i	$-0.696555\pi$
$151$	5.11927	−	8.86683i	0.416600	−	0.721572i	0.995595	+	0.0937588i	$0.0298882\pi$
$152$	−12.7084	+	2.23201i	−1.03079	+	0.181040i
$153$	−8.45639			−0.683659
$154$		0			0
$155$	−17.7902	−	17.7902i	−1.42894	−	1.42894i
$156$	−21.7026	+	6.48672i	−1.73760	+	0.519353i
$157$	−3.79998	−	14.1817i	−0.303272	−	1.13183i	−0.934423	−	0.356166i	$-0.884084\pi$
$157$	−3.79998	−	14.1817i	−0.303272	−	1.13183i	0.631151	−	0.775660i	$-0.282583\pi$
$158$	1.14192	−	0.167004i	0.0908461	−	0.0132861i
$159$	−14.7707	−	25.5836i	−1.17139	−	2.02892i
$160$	15.2743	+	10.0707i	1.20754	+	0.796157i
$161$		0			0
$162$	−7.50714	+	5.93313i	−0.589816	+	0.466151i
$163$	22.2047	+	5.94974i	1.73921	+	0.466019i	0.982271	−	0.187468i	$-0.0600282\pi$
$163$	22.2047	+	5.94974i	1.73921	+	0.466019i	0.756937	+	0.653488i	$0.226695\pi$
$164$	−4.03099	−	3.80647i	−0.314768	−	0.297235i
$165$	3.12989	+	11.6809i	0.243662	+	0.909358i
$166$	2.10039	+	4.87225i	0.163022	+	0.378160i
$167$		−	3.82099i		−	0.295677i	−0.989011	−	0.147839i	$-0.952768\pi$
$167$		−	3.82099i		−	0.295677i	0.989011	−	0.147839i	$-0.0472316\pi$
$168$		0			0
$169$		−	6.38341i		−	0.491032i
$170$	−9.81846	+	4.23265i	−0.753041	+	0.324630i
$171$	4.27121	+	15.9404i	0.326628	+	1.21899i
$172$	0.576792	+	20.1342i	0.0439800	+	1.53522i
$173$	−8.02996	−	2.15162i	−0.610506	−	0.163585i	−0.0596981	−	0.998216i	$-0.519014\pi$
$173$	−8.02996	−	2.15162i	−0.610506	−	0.163585i	−0.550808	+	0.834632i	$0.685680\pi$
$174$	−4.94993	−	6.26310i	−0.375253	−	0.474804i
$175$		0			0
$176$	−1.82381	−	5.52056i	−0.137475	−	0.416128i
$177$	−5.02524	−	8.70397i	−0.377720	−	0.654230i
$178$	−0.986187	−	6.74320i	−0.0739178	−	0.505424i
$179$	−5.00112	−	18.6644i	−0.373801	−	1.39504i	−0.855089	−	0.518482i	$-0.826497\pi$
$179$	−5.00112	−	18.6644i	−0.373801	−	1.39504i	0.481288	−	0.876563i	$-0.340169\pi$
$180$	11.1148	−	20.5915i	0.828446	−	1.53480i
$181$	−6.07189	−	6.07189i	−0.451320	−	0.451320i	0.444472	−	0.895793i	$-0.353391\pi$
$181$	−6.07189	−	6.07189i	−0.451320	−	0.451320i	−0.895793	+	0.444472i	$0.853391\pi$
$182$		0			0
$183$	37.0306			2.73738
$184$	3.74953	−	5.34720i	0.276419	−	0.394201i
$185$	−1.70209	+	2.94810i	−0.125140	+	0.216749i
$186$	16.9048	−	22.6964i	1.23952	−	1.66418i
$187$	3.28196	+	0.879398i	0.240001	+	0.0643080i
$188$	−1.31715	+	5.54637i	−0.0960627	+	0.404511i
$189$		0			0
$190$	12.9378	+	16.3700i	0.938605	+	1.18761i
$191$	−13.1707	+	7.60410i	−0.952997	+	0.550213i	−0.894011	−	0.448046i	$-0.852120\pi$
$191$	−13.1707	+	7.60410i	−0.952997	+	0.550213i	−0.0589865	+	0.998259i	$0.518787\pi$
$192$	−8.72246	+	18.6398i	−0.629490	+	1.34521i
$193$	−11.2397	+	19.4678i	−0.809053	+	1.40132i	0.104468	+	0.994528i	$0.466686\pi$
$193$	−11.2397	+	19.4678i	−0.809053	+	1.40132i	−0.913521	+	0.406792i	$0.866647\pi$
$194$	−3.06428	+	7.70820i	−0.220002	+	0.553416i
$195$	25.9010	+	25.9010i	1.85481	+	1.85481i
$196$		0			0
$197$	−8.31581	+	8.31581i	−0.592477	+	0.592477i	−0.938300	−	0.345823i	$-0.887600\pi$
$197$	−8.31581	+	8.31581i	−0.592477	+	0.592477i	0.345823	+	0.938300i	$0.387600\pi$
$198$	−6.82859	+	2.94375i	−0.485286	+	0.209203i
$199$	−8.85088	−	5.11006i	−0.627422	−	0.362242i	0.152331	−	0.988330i	$-0.451322\pi$
$199$	−8.85088	−	5.11006i	−0.627422	−	0.362242i	−0.779753	+	0.626087i	$0.784655\pi$
$200$	1.35636	−	15.3839i	0.0959093	−	1.08781i
$201$	−3.45699	−	5.98769i	−0.243837	−	0.422339i
$202$	−2.02771	−	0.237467i	−0.142669	−	0.0167081i
$203$		0			0
$204$	−6.30920	−	10.2391i	−0.441732	−	0.716878i
$205$	−2.32046	+	8.66006i	−0.162068	+	0.604845i
$206$	3.39535	−	0.496567i	0.236565	−	0.0345974i
$207$	−7.23378	−	4.17642i	−0.502782	−	0.290282i
$208$	−13.1451	−	11.7193i	−0.911446	−	0.812587i
$209$		−	6.63070i		−	0.458655i
$210$		0			0
$211$	5.73766	−	5.73766i	0.394997	−	0.394997i	−0.481467	−	0.876464i	$-0.659896\pi$
$211$	5.73766	−	5.73766i	0.394997	−	0.394997i	0.876464	+	0.481467i	$0.159896\pi$
$212$	10.9095	−	20.2111i	0.749265	−	1.38811i
$213$	−18.5949	+	4.98248i	−1.27410	+	0.341394i
$214$	3.80224	−	5.10490i	0.259916	−	0.348964i
$215$	28.2086	−	16.2862i	1.92381	−	1.11071i
$216$	4.22115	+	1.53960i	0.287213	+	0.104756i
$217$		0			0
$218$	−4.57361	−	0.535620i	−0.309764	−	0.0362768i
$219$	−7.52635	+	28.0887i	−0.508583	+	1.89806i
$220$	−6.45504	+	6.83579i	−0.435199	+	0.460869i
$221$	9.94104	−	2.66369i	0.668706	−	0.179179i
$222$	−3.55833	−	1.41456i	−0.238819	−	0.0949390i
$223$	17.4929			1.17141			0.585705	−	0.810524i	$-0.300818\pi$
$223$	17.4929			1.17141			0.585705	+	0.810524i	$0.300818\pi$
$224$		0			0
$225$	−19.7522			−1.31681
$226$	15.1652	+	6.02869i	1.00877	+	0.401022i
$227$	16.9291	−	4.53614i	1.12362	−	0.301074i	0.351275	−	0.936272i	$-0.385748\pi$
$227$	16.9291	−	4.53614i	1.12362	−	0.301074i	0.772349	+	0.635198i	$0.219081\pi$
$228$	−16.1140	+	17.0645i	−1.06718	+	1.13013i
$229$	−1.80926	+	6.75227i	−0.119560	+	0.446202i	−0.999588	−	0.0287195i	$-0.990857\pi$
$229$	−1.80926	+	6.75227i	−0.119560	+	0.446202i	0.880028	+	0.474922i	$0.157524\pi$
$230$	−10.4893	−	1.22842i	−0.691646	−	0.0809993i
$231$		0			0
$232$	2.12668	−	5.83078i	0.139624	−	0.382810i
$233$	−25.0933	+	14.4876i	−1.64392	+	0.949116i	−0.664495	+	0.747293i	$0.731353\pi$
$233$	−25.0933	+	14.4876i	−1.64392	+	0.949116i	−0.979422	+	0.201823i	$0.935313\pi$
$234$	−13.4544	+	18.0639i	−0.879539	+	1.18087i
$235$	8.90440	−	2.38593i	0.580859	−	0.155641i
$236$	3.71158	−	6.87615i	0.241603	−	0.447599i
$237$	1.48439	−	1.48439i	0.0964215	−	0.0964215i
$238$		0			0
$239$		−	13.3587i		−	0.864105i	−0.901848	−	0.432053i	$-0.857789\pi$
$239$		−	13.3587i		−	0.864105i	0.901848	−	0.432053i	$-0.142211\pi$
$240$	33.2249	−	1.90518i	2.14466	−	0.122979i
$241$	−10.5510	−	6.09164i	−0.679651	−	0.392397i	0.120072	−	0.992765i	$-0.461687\pi$
$241$	−10.5510	−	6.09164i	−0.679651	−	0.392397i	−0.799724	+	0.600368i	$0.795021\pi$
$242$	−12.4363	+	1.81879i	−0.799434	+	0.116916i
$243$	−5.73831	+	21.4157i	−0.368113	+	1.37381i
$244$	15.1031	+	24.5105i	0.966877	+	1.56912i
$245$		0			0
$246$	−10.0164	−	1.17304i	−0.638625	−	0.0747900i
$247$	−10.0422	−	17.3936i	−0.638969	−	1.10673i
$248$	21.9174	+	1.93241i	1.39176	+	0.122708i
$249$	8.35808	+	4.82554i	0.529672	+	0.305806i
$250$	−1.93264	+	0.833143i	−0.122231	+	0.0526926i
$251$	−6.68926	+	6.68926i	−0.422223	+	0.422223i	−0.885968	−	0.463746i	$-0.846505\pi$
$251$	−6.68926	+	6.68926i	−0.422223	+	0.422223i	0.463746	+	0.885968i	$0.346505\pi$
$252$		0			0
$253$	2.37314	+	2.37314i	0.149198	+	0.149198i
$254$	2.34682	−	5.90343i	0.147252	−	0.370414i
$255$	−9.72432	+	16.8430i	−0.608961	+	1.05475i
$256$	−15.8951	+	1.82893i	−0.993445	+	0.114308i
$257$	−3.32837	+	1.92163i	−0.207618	+	0.119868i	−0.600204	−	0.799847i	$-0.704914\pi$
$257$	−3.32837	+	1.92163i	−0.207618	+	0.119868i	0.392586	+	0.919715i	$0.371581\pi$
$258$	22.7184	+	28.7454i	1.41439	+	1.78961i
$259$		0			0
$260$	−6.57999	+	27.7077i	−0.408074	+	1.71836i
$261$	−7.66759	−	2.05452i	−0.474612	−	0.127172i
$262$	11.6852	−	15.6886i	0.721915	−	0.969246i
$263$	3.15784	−	5.46953i	0.194720	−	0.337266i	−0.752088	−	0.659062i	$-0.770953\pi$
$263$	3.15784	−	5.46953i	0.194720	−	0.337266i	0.946809	+	0.321797i	$0.104287\pi$
$264$	−8.65903	−	6.07181i	−0.532926	−	0.373694i
$265$	−37.1409			−2.28155
$266$		0			0
$267$	−8.76556	−	8.76556i	−0.536444	−	0.536444i
$268$	2.55329	−	4.73028i	0.155967	−	0.288948i
$269$	6.24090	+	23.2914i	0.380514	+	1.42010i	0.845118	+	0.534580i	$0.179530\pi$
$269$	6.24090	+	23.2914i	0.380514	+	1.42010i	−0.464603	+	0.885519i	$0.653803\pi$
$270$	−1.05145	−	7.18944i	−0.0639891	−	0.437535i
$271$	−4.73315	−	8.19805i	−0.287518	−	0.497996i	0.685699	−	0.727886i	$-0.259497\pi$
$271$	−4.73315	−	8.19805i	−0.287518	−	0.497996i	−0.973217	+	0.229890i	$0.926163\pi$
$272$	4.20398	−	8.35210i	0.254904	−	0.506420i
$273$		0			0
$274$	2.21165	+	2.79837i	0.133610	+	0.169056i
$275$	7.66590	+	2.05407i	0.462271	+	0.123865i
$276$	−0.340179	−	11.8747i	−0.0204764	−	0.714772i
$277$	−3.03526	−	11.3278i	−0.182371	−	0.680619i	−0.995178	−	0.0980853i	$-0.968728\pi$
$277$	−3.03526	−	11.3278i	−0.182371	−	0.680619i	0.812807	−	0.582533i	$-0.197938\pi$
$278$	11.0267	−	4.75350i	0.661335	−	0.285096i
$279$		−	28.1409i		−	1.68475i
$280$		0			0
$281$			5.59517i			0.333780i	0.985976	+	0.166890i	$0.0533724\pi$
$281$			5.59517i			0.333780i	−0.985976	+	0.166890i	$0.946628\pi$
$282$	4.10499	+	9.52231i	0.244448	+	0.567045i
$283$	−0.992910	−	3.70559i	−0.0590224	−	0.220275i	0.930115	−	0.367268i	$-0.119707\pi$
$283$	−0.992910	−	3.70559i	−0.0590224	−	0.220275i	−0.989137	+	0.146994i	$0.953040\pi$
$284$	−10.8819	−	10.2758i	−0.645723	−	0.609756i
$285$	36.6609	+	9.82326i	2.17160	+	0.581880i
$286$	7.10019	−	5.61151i	0.419843	−	0.331816i
$287$		0			0
$288$	4.11564	+	20.0457i	0.242516	+	1.18120i
$289$	−5.76778	−	9.99009i	−0.339281	−	0.587652i
$290$	−9.93095	+	1.45239i	−0.583165	+	0.0852874i
$291$	3.90519	+	14.5744i	0.228927	+	0.854365i
$292$	−21.6615	+	6.47444i	−1.26765	+	0.378888i
$293$	9.74731	+	9.74731i	0.569444	+	0.569444i	0.931973	−	0.362529i	$-0.118087\pi$
$293$	9.74731	+	9.74731i	0.569444	+	0.569444i	−0.362529	+	0.931973i	$0.618087\pi$
$294$		0			0
$295$	−12.6359			−0.735692
$296$	−0.514987	−	2.93219i	−0.0299330	−	0.170430i
$297$	−1.15450	+	1.99965i	−0.0669908	+	0.116031i
$298$	9.63860	+	7.17904i	0.558349	+	0.415870i
$299$	9.81932	+	2.63108i	0.567866	+	0.152159i
$300$	−14.7368	−	23.9161i	−0.850832	−	1.38080i
$301$		0			0
$302$	11.3599	−	8.97813i	0.653691	−	0.516633i
$303$	−3.21608	+	1.85681i	−0.184759	+	0.106671i
$304$	−17.8672	−	3.70601i	−1.02475	−	0.212555i
$305$	23.2783	−	40.3192i	1.33291	−	2.30867i
$306$	−11.1132	−	4.41789i	−0.635300	−	0.252554i
$307$	−20.5735	−	20.5735i	−1.17419	−	1.17419i	−0.981201	−	0.192988i	$-0.938182\pi$
$307$	−20.5735	−	20.5735i	−1.17419	−	1.17419i	−0.192988	−	0.981201i	$-0.561818\pi$
$308$		0			0
$309$	4.41365	−	4.41365i	0.251084	−	0.251084i
$310$	−14.0853	−	32.6736i	−0.799992	−	1.85574i
$311$	−0.495271	−	0.285945i	−0.0280843	−	0.0162145i	0.485892	−	0.874019i	$-0.338495\pi$
$311$	−0.495271	−	0.285945i	−0.0280843	−	0.0162145i	−0.513976	+	0.857804i	$0.671828\pi$
$312$	−31.9100	−	2.81343i	−1.80655	−	0.159279i
$313$	0.707287	+	1.22506i	0.0399782	+	0.0692443i	0.885322	−	0.464978i	$-0.153938\pi$
$313$	0.707287	+	1.22506i	0.0399782	+	0.0692443i	−0.845344	+	0.534222i	$0.820604\pi$
$314$	2.41513	−	20.6226i	0.136294	−	1.16380i
$315$		0			0
$316$	1.58793	+	0.377100i	0.0893281	+	0.0212135i
$317$	6.77681	−	25.2914i	0.380624	−	1.42051i	−0.464328	−	0.885663i	$-0.653704\pi$
$317$	6.77681	−	25.2914i	0.380624	−	1.42051i	0.844951	−	0.534843i	$-0.179629\pi$
$318$	−6.04567	−	41.3382i	−0.339024	−	2.31813i
$319$	2.76217	+	1.59474i	0.154652	+	0.0892882i
$320$	14.8120	+	21.2145i	0.828014	+	1.18593i
$321$		−	11.5785i		−	0.646248i
$322$		0			0
$323$	7.54051	−	7.54051i	0.419565	−	0.419565i
$324$	−12.9654	+	3.87523i	−0.720299	+	0.215291i
$325$	23.2200	−	6.22177i	1.28801	−	0.345122i
$326$	26.0726	+	19.4195i	1.44403	+	1.07554i
$327$	−7.25406	+	4.18813i	−0.401150	+	0.231604i
$328$	−3.30882	−	7.10830i	−0.182699	−	0.392490i
$329$		0			0
$330$	−1.98924	+	16.9860i	−0.109504	+	0.935046i
$331$	−0.727156	+	2.71378i	−0.0399681	+	0.149163i	−0.983026	−	0.183465i	$-0.941269\pi$
$331$	−0.727156	+	2.71378i	−0.0399681	+	0.149163i	0.943058	+	0.332628i	$0.107935\pi$
$332$	0.214865	+	7.50032i	0.0117922	+	0.411633i
$333$	−3.67790	+	0.985490i	−0.201548	+	0.0540045i
$334$	1.99621	−	5.02147i	0.109228	−	0.274763i
$335$	−8.69259			−0.474927
$336$		0			0
$337$	−23.9205			−1.30303			−0.651517	−	0.758634i	$-0.725867\pi$
$337$	−23.9205			−1.30303			−0.651517	+	0.758634i	$0.725867\pi$
$338$	3.33490	−	8.38894i	0.181394	−	0.456298i
$339$	28.6738	−	7.68312i	1.55735	−	0.417290i
$340$	−15.1145	+	0.432991i	−0.819698	+	0.0234822i
$341$	−2.92644	+	10.9216i	−0.158475	+	0.591438i
$342$	−2.71462	+	23.1799i	−0.146790	+	1.25343i
$343$		0			0
$344$	−9.76072	+	26.7612i	−0.526263	+	1.44287i
$345$	−16.6368	+	9.60525i	−0.895695	+	0.517130i
$346$	−9.42872	−	7.02272i	−0.506891	−	0.377544i
$347$	12.0814	−	3.23720i	0.648563	−	0.173782i	0.0804837	−	0.996756i	$-0.474353\pi$
$347$	12.0814	−	3.23720i	0.648563	−	0.173782i	0.568079	+	0.822974i	$0.307687\pi$
$348$	−3.23305	−	10.8168i	−0.173310	−	0.579843i
$349$	21.9157	−	21.9157i	1.17312	−	1.17312i	0.191662	−	0.981461i	$-0.438612\pi$
$349$	21.9157	−	21.9157i	1.17312	−	1.17312i	0.981461	−	0.191662i	$-0.0613878\pi$
$350$		0			0
$351$			6.99394i			0.373309i
$352$	0.487300	−	8.20781i	0.0259732	−	0.437478i
$353$	18.1984	+	10.5069i	0.968604	+	0.559224i	0.898810	−	0.438337i	$-0.144433\pi$
$353$	18.1984	+	10.5069i	0.968604	+	0.559224i	0.0697939	+	0.997561i	$0.477766\pi$
$354$	−2.05683	−	14.0639i	−0.109319	−	0.747489i
$355$	−6.26421	+	23.3784i	−0.332470	+	1.24079i
$356$	2.22684	−	9.37699i	0.118022	−	0.496979i
$357$		0			0
$358$	3.17852	−	27.1411i	0.167990	−	1.43445i
$359$	4.78310	+	8.28458i	0.252443	+	0.437243i	0.964198	−	0.265184i	$-0.0854328\pi$
$359$	4.78310	+	8.28458i	0.252443	+	0.437243i	−0.711755	+	0.702428i	$0.752099\pi$
$360$	25.3644	−	21.2542i	1.33682	−	1.12019i
$361$	−1.56807	−	0.905328i	−0.0825302	−	0.0476488i
$362$	−4.80740	−	11.1517i	−0.252671	−	0.586120i
$363$	−16.1661	+	16.1661i	−0.848498	+	0.848498i
$364$		0			0
$365$	25.8520	+	25.8520i	1.35315	+	1.35315i
$366$	48.6648	+	19.3459i	2.54375	+	1.01123i
$367$	−3.06305	+	5.30536i	−0.159890	+	0.276938i	−0.934829	−	0.355099i	$-0.884447\pi$
$367$	−3.06305	+	5.30536i	−0.159890	+	0.276938i	0.774939	+	0.632036i	$0.217781\pi$
$368$	7.72109	−	5.06831i	0.402490	−	0.264204i
$369$	−8.68463	+	5.01408i	−0.452104	+	0.261022i
$370$	−3.77703	+	2.98511i	−0.196359	+	0.155189i
$371$		0			0
$372$	34.0733	−	20.9956i	1.76662	−	1.08857i
$373$	15.8673	+	4.25162i	0.821575	+	0.220140i	0.645035	−	0.764153i	$-0.276843\pi$
$373$	15.8673	+	4.25162i	0.821575	+	0.220140i	0.176540	+	0.984293i	$0.443509\pi$
$374$	3.85365	+	2.87028i	0.199268	+	0.148419i
$375$	−1.91411	+	3.31533i	−0.0988440	+	0.171203i
$376$	−4.62856	+	6.60080i	−0.238700	+	0.340410i
$377$	9.66091			0.497562
$378$		0			0
$379$	6.05253	+	6.05253i	0.310897	+	0.310897i	0.845257	−	0.534360i	$-0.179447\pi$
$379$	6.05253	+	6.05253i	0.310897	+	0.310897i	−0.534360	+	0.845257i	$0.679447\pi$
$380$	8.45032	+	28.2723i	0.433492	+	1.45034i
$381$	−2.99085	−	11.1620i	−0.153226	−	0.571846i
$382$	−21.2813	+	3.11236i	−1.08884	+	0.159242i
$383$	9.64030	+	16.6975i	0.492596	+	0.853202i	0.999964	−	0.00852805i	$-0.00271459\pi$
$383$	9.64030	+	16.6975i	0.492596	+	0.853202i	−0.507367	+	0.861730i	$0.669381\pi$
$384$	−21.2009	+	19.9391i	−1.08190	+	1.01751i
$385$		0			0
$386$	−24.9416	+	19.7121i	−1.26949	+	1.00332i
$387$	35.1915	+	9.42954i	1.78889	+	0.479330i
$388$	−8.05401	+	8.52907i	−0.408880	+	0.432998i
$389$	7.40814	+	27.6476i	0.375608	+	1.40179i	0.852455	+	0.522801i	$0.175113\pi$
$389$	7.40814	+	27.6476i	0.375608	+	1.40179i	−0.476847	+	0.878986i	$0.658221\pi$
$390$	20.5070	+	47.5700i	1.03841	+	2.40880i
$391$			5.39753i			0.272965i
$392$		0			0
$393$		−	35.5835i		−	1.79495i
$394$	−15.2729	+	6.58402i	−0.769438	+	0.331698i
$395$	−0.683093	−	2.54934i	−0.0343701	−	0.128271i
$396$	−10.5119	+	0.301139i	−0.528242	+	0.0151328i
$397$	8.95799	+	2.40028i	0.449588	+	0.120467i	0.476507	−	0.879171i	$-0.341903\pi$
$397$	8.95799	+	2.40028i	0.449588	+	0.120467i	−0.0269184	+	0.999638i	$0.508569\pi$
$398$	−8.96198	−	11.3395i	−0.449223	−	0.568398i
$399$		0			0
$400$	9.81954	−	19.5086i	0.490977	−	0.975429i
$401$	17.5281	+	30.3596i	0.875312	+	1.51609i	0.856430	+	0.516264i	$0.172678\pi$
$401$	17.5281	+	30.3596i	0.875312	+	1.51609i	0.0188827	+	0.999822i	$0.493989\pi$
$402$	−1.41495	−	9.67493i	−0.0705713	−	0.482542i
$403$	8.86416	+	33.0815i	0.441555	+	1.64791i
$404$	−2.54071	−	1.37141i	−0.126405	−	0.0682303i
$405$	15.4735	+	15.4735i	0.768886	+	0.768886i
$406$		0			0
$407$	1.52989			0.0758338
$408$	−2.94221	−	16.7521i	−0.145661	−	0.829352i
$409$	−17.4392	+	30.2056i	−0.862314	+	1.49357i	0.00737621	+	0.999973i	$0.497652\pi$
$409$	−17.4392	+	30.2056i	−0.862314	+	1.49357i	−0.869690	+	0.493598i	$0.835681\pi$
$410$	−7.57378	+	10.1686i	−0.374042	+	0.502191i
$411$	6.26699	+	1.67923i	0.309128	+	0.0828306i
$412$	4.72152	+	1.12126i	0.232613	+	0.0552406i
$413$		0			0
$414$	−7.32458	−	9.26772i	−0.359984	−	0.455484i
$415$	10.5082	−	6.06689i	0.515826	−	0.297812i
$416$	−11.1524	−	22.2686i	−0.546793	−	1.09181i
$417$	10.9209	−	18.9156i	0.534801	−	0.926302i
$418$	3.46409	−	8.71392i	0.169434	−	0.426212i
$419$	8.57828	+	8.57828i	0.419076	+	0.419076i	0.884885	−	0.465809i	$-0.154237\pi$
$419$	8.57828	+	8.57828i	0.419076	+	0.419076i	−0.465809	+	0.884885i	$0.654237\pi$
$420$		0			0
$421$	−7.41183	+	7.41183i	−0.361230	+	0.361230i	−0.864266	−	0.503035i	$-0.832217\pi$
$421$	−7.41183	+	7.41183i	−0.361230	+	0.361230i	0.503035	+	0.864266i	$0.332217\pi$
$422$	10.5379	−	4.54278i	0.512975	−	0.221139i
$423$	8.92967	+	5.15555i	0.434175	+	0.250671i
$424$	24.8959	−	20.8616i	1.20905	−	1.01313i
$425$	6.38184	+	11.0537i	0.309565	+	0.536182i
$426$	−27.0400	−	3.16668i	−1.31009	−	0.153426i
$427$		0			0
$428$	7.66379	−	4.72234i	0.370443	−	0.228263i
$429$	4.26065	−	15.9010i	0.205706	−	0.767706i
$430$	45.5795	−	6.66596i	2.19804	−	0.321461i
$431$	1.39637	+	0.806195i	0.0672608	+	0.0388331i	0.533253	−	0.845956i	$-0.320969\pi$
$431$	1.39637	+	0.806195i	0.0672608	+	0.0388331i	−0.465992	+	0.884789i	$0.654303\pi$
$432$	4.74302	+	4.22857i	0.228198	+	0.203447i
$433$			13.0869i			0.628917i	0.949271	+	0.314458i	$0.101823\pi$
$433$			13.0869i			0.628917i	−0.949271	+	0.314458i	$0.898177\pi$
$434$		0			0
$435$	−12.9093	+	12.9093i	−0.618956	+	0.618956i
$436$	−5.73072	−	3.09330i	−0.274452	−	0.148142i
$437$	10.1744	−	2.72622i	0.486708	−	0.130413i
$438$	−24.5654	+	32.9816i	−1.17378	+	1.57592i
$439$	−1.71358	+	0.989334i	−0.0817846	+	0.0472184i	−0.540335	−	0.841450i	$-0.681702\pi$
$439$	−1.71358	+	0.989334i	−0.0817846	+	0.0472184i	0.458550	+	0.888669i	$0.348369\pi$
$440$	−12.0543	+	5.61113i	−0.574666	+	0.267500i
$441$		0			0
$442$	14.4559	+	1.69294i	0.687597	+	0.0805251i
$443$	8.98048	−	33.5156i	0.426675	−	1.59237i	−0.333562	−	0.942728i	$-0.608251\pi$
$443$	8.98048	−	33.5156i	0.426675	−	1.59237i	0.760237	−	0.649646i	$-0.225083\pi$
$444$	−3.93727	−	3.71797i	−0.186855	−	0.176447i
$445$	−15.0542	+	4.03377i	−0.713640	+	0.191219i
$446$	22.9888	+	9.13884i	1.08855	+	0.432736i
$447$	21.8614			1.03401
$448$		0			0
$449$	20.0460			0.946031			0.473015	−	0.881054i	$-0.343166\pi$
$449$	20.0460			0.946031			0.473015	+	0.881054i	$0.343166\pi$
$450$	−25.9579	−	10.3192i	−1.22367	−	0.486450i
$451$	3.89196	−	1.04285i	0.183265	−	0.0491058i
$452$	16.7802	+	15.8455i	0.789274	+	0.745312i
$453$	6.81682	−	25.4407i	0.320282	−	1.19531i
$454$	24.6177	+	2.88300i	1.15537	+	0.135306i
$455$		0			0
$456$	−30.0918	+	14.0074i	−1.40918	+	0.655954i
$457$	25.9859	−	15.0030i	1.21557	−	0.701810i	0.251603	−	0.967830i	$-0.419042\pi$
$457$	25.9859	−	15.0030i	1.21557	−	0.701810i	0.963967	+	0.266020i	$0.0857088\pi$
$458$	−5.90529	+	7.92847i	−0.275936	+	0.370473i
$459$	−3.58693	+	0.961116i	−0.167424	+	0.0448611i
$460$	−13.1431	−	7.09432i	−0.612800	−	0.330774i
$461$	18.2334	−	18.2334i	0.849213	−	0.849213i	−0.140822	−	0.990035i	$-0.544974\pi$
$461$	18.2334	−	18.2334i	0.849213	−	0.849213i	0.990035	+	0.140822i	$0.0449744\pi$
$462$		0			0
$463$			31.3804i			1.45837i	0.684316	+	0.729186i	$0.260101\pi$
$463$			31.3804i			1.45837i	−0.684316	+	0.729186i	$0.739899\pi$
$464$	5.84103	−	6.55165i	0.271163	−	0.304153i
$465$	−56.0497	−	32.3603i	−2.59924	−	1.50067i
$466$	−40.5459	+	5.92979i	−1.87825	+	0.274692i
$467$	6.17115	−	23.0310i	0.285567	−	1.06575i	−0.662858	−	0.748745i	$-0.730657\pi$
$467$	6.17115	−	23.0310i	0.285567	−	1.06575i	0.948424	−	0.317004i	$-0.102677\pi$
$468$	−27.1186	+	16.7102i	−1.25356	+	0.772428i
$469$		0			0
$470$	12.9485	+	1.51641i	0.597268	+	0.0699466i
$471$	−18.8844	−	32.7088i	−0.870148	−	1.50714i
$472$	8.46999	−	7.09745i	0.389863	−	0.326687i
$473$	−12.6774	−	7.31928i	−0.582906	−	0.336541i
$474$	2.72625	−	1.17526i	0.125221	−	0.0539816i
$475$	17.6129	−	17.6129i	0.808135	−	0.808135i
$476$		0			0
$477$	−29.3752	−	29.3752i	−1.34500	−	1.34500i
$478$	6.97903	−	17.5558i	0.319213	−	0.802982i
$479$	−17.6784	+	30.6199i	−0.807747	+	1.39906i	0.106674	+	0.994294i	$0.465980\pi$
$479$	−17.6784	+	30.6199i	−0.807747	+	1.39906i	−0.914421	+	0.404764i	$0.867354\pi$
$480$	44.6588	+	14.8540i	2.03838	+	0.677989i
$481$	4.01319	−	2.31701i	0.182986	−	0.105647i
$482$	−10.6835	−	13.5177i	−0.486619	−	0.615714i
$483$		0			0
$484$	−17.2937	−	4.10688i	−0.786077	−	0.186677i
$485$	18.3236	+	4.90979i	0.832032	+	0.222942i
$486$	−18.7294	+	25.1461i	−0.849582	+	1.14065i
$487$	5.31153	−	9.19984i	0.240688	−	0.416884i	−0.720222	−	0.693743i	$-0.755960\pi$
$487$	5.31153	−	9.19984i	0.240688	−	0.416884i	0.960911	+	0.276859i	$0.0892935\pi$
$488$	7.04312	+	40.1015i	0.318827	+	1.81531i
$489$	59.1357			2.67421
$490$		0			0
$491$	26.9088	+	26.9088i	1.21438	+	1.21438i	0.969572	+	0.244806i	$0.0787243\pi$
$491$	26.9088	+	26.9088i	1.21438	+	1.21438i	0.244806	+	0.969572i	$0.421276\pi$
$492$	−12.5506	−	6.77448i	−0.565823	−	0.305417i
$493$	1.32761	+	4.95472i	0.0597927	+	0.223149i
$494$	−4.11027	−	28.1046i	−0.184930	−	1.26449i
$495$	8.50291	+	14.7275i	0.382177	+	0.661950i
$496$	27.7939	+	13.9899i	1.24798	+	0.628165i
$497$		0			0
$498$	8.46299	+	10.7081i	0.379236	+	0.479843i
$499$	−12.2441	−	3.28081i	−0.548123	−	0.146869i	−0.0258790	−	0.999665i	$-0.508238\pi$
$499$	−12.2441	−	3.28081i	−0.548123	−	0.146869i	−0.522244	+	0.852796i	$0.674905\pi$
$500$	−2.97509	+	0.0852287i	−0.133050	+	0.00381154i
$501$	−2.54402	−	9.49441i	−0.113658	−	0.424179i
$502$	−12.2856	+	5.29621i	−0.548332	+	0.236381i
$503$		−	13.7074i		−	0.611183i	−0.952163	−	0.305591i	$-0.901146\pi$
$503$		−	13.7074i		−	0.611183i	0.952163	−	0.305591i	$-0.0988542\pi$
$504$		0			0
$505$			4.66892i			0.207764i
$506$	1.87893	+	4.35854i	0.0835286	+	0.193761i
$507$	−4.25008	−	15.8615i	−0.188753	−	0.704434i
$508$	6.16827	−	6.53211i	0.273673	−	0.289815i
$509$	−23.0168	−	6.16734i	−1.02020	−	0.273363i	−0.290317	−	0.956931i	$-0.593761\pi$
$509$	−23.0168	−	6.16734i	−1.02020	−	0.273363i	−0.729887	+	0.683568i	$0.760427\pi$
$510$	−21.5788	+	17.0544i	−0.955526	+	0.755183i
$511$		0			0
$512$	−21.8445	−	5.90058i	−0.965401	−	0.260771i
$513$	3.62343	+	6.27596i	0.159978	+	0.277091i
$514$	−5.37799	+	0.786525i	−0.237213	+	0.0346922i
$515$	−2.03109	−	7.58014i	−0.0895007	−	0.334021i
$516$	14.8386	+	49.6454i	0.653231	+	2.18552i
$517$	−2.92950	−	2.92950i	−0.128839	−	0.128839i
$518$		0			0
$519$	−21.3854			−0.938715
$520$	−23.1226	+	32.9752i	−1.01400	+	1.44606i
$521$	11.8589	−	20.5402i	0.519548	−	0.899884i	−0.480194	−	0.877163i	$-0.659434\pi$
$521$	11.8589	−	20.5402i	0.519548	−	0.899884i	0.999742	−	0.0227214i	$-0.00723308\pi$
$522$	−9.00323	−	6.70580i	−0.394061	−	0.293505i
$523$	−18.1369	−	4.85978i	−0.793073	−	0.212503i	−0.160532	−	0.987031i	$-0.551321\pi$
$523$	−18.1369	−	4.85978i	−0.793073	−	0.212503i	−0.632540	+	0.774527i	$0.717988\pi$
$524$	23.5527	−	14.5129i	1.02890	−	0.634000i
$525$		0			0
$526$	7.00742	−	5.53819i	0.305538	−	0.241476i
$527$	−15.7482	+	9.09220i	−0.686000	+	0.396063i
$528$	−8.20740	−	12.5032i	−0.357181	−	0.544132i
$529$	8.83428	−	15.3014i	0.384099	−	0.665279i
$530$	−48.8098	−	19.4036i	−2.12016	−	0.842837i
$531$	−9.99392	−	9.99392i	−0.433699	−	0.433699i
$532$		0			0
$533$	8.62996	−	8.62996i	0.373805	−	0.373805i
$534$	−6.94011	−	16.0989i	−0.300328	−	0.696668i
$535$	−12.6067	−	7.27851i	−0.545037	−	0.314677i
$536$	5.82673	−	4.88252i	0.251676	−	0.210893i
$537$	−24.8536	−	43.0476i	−1.07251	−	1.85764i
$538$	−3.96648	+	33.8694i	−0.171007	+	1.46022i
$539$		0			0
$540$	2.37420	−	9.99751i	0.102169	−	0.430224i
$541$	−6.76561	+	25.2496i	−0.290876	+	1.08556i	0.653561	+	0.756874i	$0.273274\pi$
$541$	−6.76561	+	25.2496i	−0.290876	+	1.08556i	−0.944437	+	0.328691i	$0.893392\pi$
$542$	−1.93728	−	13.2464i	−0.0832133	−	0.568984i
$543$	−19.1301	−	11.0448i	−0.820952	−	0.473977i
$544$	9.88818	−	8.77986i	0.423952	−	0.376433i
$545$			10.5310i			0.451100i
$546$		0			0
$547$	−23.8532	+	23.8532i	−1.01989	+	1.01989i	−0.0200929	+	0.999798i	$0.506396\pi$
$547$	−23.8532	+	23.8532i	−1.01989	+	1.01989i	−0.999798	+	0.0200929i	$0.993604\pi$
$548$	1.44454	+	4.83299i	0.0617076	+	0.206455i
$549$	50.3001	−	13.4779i	2.14675	−	0.575221i
$550$	9.00125	+	6.70433i	0.383815	+	0.285873i
$551$	8.66915	−	5.00513i	0.369318	−	0.213226i
$552$	5.75665	−	15.7832i	0.245020	−	0.671777i
$553$		0			0
$554$	1.92910	−	16.4724i	0.0819595	−	0.699845i
$555$	−2.26650	+	8.45871i	−0.0962077	+	0.359052i
$556$	16.9744	−	0.486273i	0.719874	−	0.0206225i
$557$	−41.6206	+	11.1522i	−1.76352	+	0.472534i	−0.987426	−	0.158083i	$-0.949468\pi$
$557$	−41.6206	+	11.1522i	−1.76352	+	0.472534i	−0.776094	+	0.630617i	$0.782802\pi$
$558$	14.7017	−	36.9822i	0.622373	−	1.56558i
$559$	−44.3401			−1.87539
$560$		0			0
$561$	8.74052			0.369025
$562$	−2.92309	+	7.35305i	−0.123303	+	0.310170i
$563$	8.61735	−	2.30901i	0.363178	−	0.0973133i	−0.0726153	−	0.997360i	$-0.523135\pi$
$563$	8.61735	−	2.30901i	0.363178	−	0.0973133i	0.435793	+	0.900047i	$0.356468\pi$
$564$	0.419931	+	14.6586i	0.0176823	+	0.617238i
$565$	9.65958	−	36.0500i	0.406382	−	1.51664i
$566$	0.631056	−	5.38854i	0.0265253	−	0.226497i
$567$		0			0
$568$	−8.93237	−	19.1893i	−0.374794	−	0.805164i
$569$	5.49552	−	3.17284i	0.230384	−	0.133012i	−0.380365	−	0.924836i	$-0.624202\pi$
$569$	5.49552	−	3.17284i	0.230384	−	0.133012i	0.610749	+	0.791824i	$0.290868\pi$
$570$	43.0470	+	32.0623i	1.80304	+	1.34294i
$571$	36.2565	−	9.71490i	1.51729	−	0.406556i	0.598439	−	0.801168i	$-0.295788\pi$
$571$	36.2565	−	9.71490i	1.51729	−	0.406556i	0.918848	+	0.394612i	$0.129121\pi$
$572$	12.2625	−	3.66516i	0.512723	−	0.153248i
$573$	−27.6637	+	27.6637i	−1.15567	+	1.15567i
$574$		0			0
$575$			12.6074i			0.525765i
$576$	−5.06383	+	28.4938i	−0.210993	+	1.18724i
$577$	1.63907	+	0.946316i	0.0682353	+	0.0393957i	0.533729	−	0.845655i	$-0.320790\pi$
$577$	1.63907	+	0.946316i	0.0682353	+	0.0393957i	−0.465494	+	0.885051i	$0.654123\pi$
$578$	−2.36076	−	16.1420i	−0.0981945	−	0.671420i
$579$	−14.9668	+	55.8569i	−0.622000	+	2.32134i
$580$	−13.8098	−	3.27954i	−0.573421	−	0.136175i
$581$		0			0
$582$	−2.48199	+	21.1935i	−0.102882	+	0.878500i
$583$	8.34585	+	14.4554i	0.345650	+	0.598683i
$584$	−31.8496	−	2.80810i	−1.31794	−	0.116200i
$585$	44.6094	+	25.7553i	1.84437	+	1.06485i
$586$	7.71740	+	17.9020i	0.318803	+	0.739525i
$587$	26.8519	−	26.8519i	1.10830	−	1.10830i	0.114923	−	0.993374i	$-0.463338\pi$
$587$	26.8519	−	26.8519i	1.10830	−	1.10830i	0.993374	−	0.114923i	$-0.0366621\pi$
$588$		0			0
$589$	25.0931	+	25.0931i	1.03394	+	1.03394i
$590$	−16.6059	−	6.60141i	−0.683653	−	0.271776i
$591$	−15.1265	+	26.1998i	−0.622220	+	1.07772i
$592$	0.855082	−	4.12246i	0.0351437	−	0.169432i
$593$	23.8885	−	13.7920i	0.980984	−	0.566372i	0.0784171	−	0.996921i	$-0.475013\pi$
$593$	23.8885	−	13.7920i	0.980984	−	0.566372i	0.902567	+	0.430549i	$0.141680\pi$
$594$	−2.56190	+	2.02475i	−0.105116	+	0.0830765i
$595$		0			0
$596$	8.91628	+	14.4700i	0.365225	+	0.592716i
$597$	−25.3950	−	6.80456i	−1.03935	−	0.278492i
$598$	11.5298	+	8.58763i	0.471488	+	0.351174i
$599$	−11.8101	+	20.4557i	−0.482548	+	0.835797i	−0.999799	−	0.0200365i	$-0.993622\pi$
$599$	−11.8101	+	20.4557i	−0.482548	+	0.835797i	0.517252	+	0.855833i	$0.326955\pi$
$600$	−6.87232	−	39.1290i	−0.280561	−	1.59744i
$601$	5.61717			0.229129			0.114565	−	0.993416i	$-0.463453\pi$
$601$	5.61717			0.229129			0.114565	+	0.993416i	$0.463453\pi$
$602$		0			0
$603$	−6.87508	−	6.87508i	−0.279975	−	0.279975i
$604$	19.6195	−	5.86408i	0.798304	−	0.238606i
$605$	7.43936	+	27.7641i	0.302453	+	1.12877i
$606$	−5.19656	+	0.759991i	−0.211096	+	0.0308725i
$607$	−2.43281	−	4.21375i	−0.0987446	−	0.171031i	0.812421	−	0.583072i	$-0.198149\pi$
$607$	−2.43281	−	4.21375i	−0.0987446	−	0.171031i	−0.911165	+	0.412041i	$0.864816\pi$
$608$	−21.5445	−	14.2047i	−0.873746	−	0.576078i
$609$		0			0
$610$	51.6558	−	40.8253i	2.09148	−	1.65297i
$611$	−12.1214	−	3.24791i	−0.490378	−	0.131396i
$612$	−12.2967	−	11.6118i	−0.497065	−	0.469378i
$613$	−1.06941	−	3.99109i	−0.0431931	−	0.161199i	0.940961	−	0.338516i	$-0.109925\pi$
$613$	−1.06941	−	3.99109i	−0.0431931	−	0.161199i	−0.984154	+	0.177317i	$0.943258\pi$
$614$	−16.2890	−	37.7854i	−0.657369	−	1.52490i
$615$			23.0635i			0.930010i
$616$		0			0
$617$		−	25.3025i		−	1.01864i	−0.860578	−	0.509319i	$-0.829897\pi$
$617$		−	25.3025i		−	1.01864i	0.860578	−	0.509319i	$-0.170103\pi$
$618$	8.10616	−	3.49450i	0.326078	−	0.140569i
$619$	4.75356	+	17.7405i	0.191062	+	0.713051i	0.993251	+	0.115982i	$0.0370015\pi$
$619$	4.75356	+	17.7405i	0.191062	+	0.713051i	−0.802190	+	0.597069i	$0.796332\pi$
$620$	−1.44090	−	50.2975i	−0.0578678	−	2.02000i
$621$	−3.54302	−	0.949348i	−0.142176	−	0.0380960i
$622$	−0.501488	−	0.634528i	−0.0201078	−	0.0254423i
$623$		0			0
$624$	−40.4656	−	20.3681i	−1.61992	−	0.815378i
$625$	−11.2438	−	19.4749i	−0.449753	−	0.778995i
$626$	0.289493	+	1.97945i	0.0115705	+	0.0791148i
$627$	−4.41472	−	16.4760i	−0.176307	−	0.657987i
$628$	13.9478	−	25.8400i	0.556577	−	1.03113i
$629$	1.73981	+	1.73981i	0.0693707	+	0.0693707i
$630$		0			0
$631$	−41.4293			−1.64928			−0.824638	−	0.565661i	$-0.808621\pi$
$631$	−41.4293			−1.64928			−0.824638	+	0.565661i	$0.808621\pi$
$632$	1.88982	+	1.32516i	0.0751729	+	0.0527121i
$633$	10.4368	−	18.0771i	0.414826	−	0.718500i
$634$	22.1190	−	29.6970i	0.878456	−	1.17942i
$635$	−14.0334	−	3.76023i	−0.556897	−	0.149220i
$636$	13.6513	−	57.4842i	0.541308	−	2.27940i
$637$		0			0
$638$	2.79684	+	3.53881i	0.110728	+	0.140103i
$639$	−23.4447	+	13.5358i	−0.927458	+	0.535468i
$640$	8.38246	+	35.6178i	0.331346	+	1.40792i
$641$	−17.0933	+	29.6065i	−0.675146	+	1.16939i	0.301280	+	0.953536i	$0.402586\pi$
$641$	−17.0933	+	29.6065i	−0.675146	+	1.16939i	−0.976426	+	0.215852i	$0.930747\pi$
$642$	6.04897	−	15.2162i	0.238734	−	0.600536i
$643$	−3.46526	−	3.46526i	−0.136657	−	0.136657i	0.635469	−	0.772126i	$-0.280807\pi$
$643$	−3.46526	−	3.46526i	−0.136657	−	0.136657i	−0.772126	+	0.635469i	$0.780807\pi$
$644$		0			0
$645$	59.2493	−	59.2493i	2.33294	−	2.33294i
$646$	13.8490	−	5.97018i	0.544881	−	0.234893i
$647$	−27.2890	−	15.7553i	−1.07284	−	0.619406i	−0.143886	−	0.989594i	$-0.545960\pi$
$647$	−27.2890	−	15.7553i	−1.07284	−	0.619406i	−0.928957	+	0.370188i	$0.879293\pi$
$648$	−19.0634	−	1.68077i	−0.748880	−	0.0660270i
$649$	2.83939	+	4.91797i	0.111456	+	0.193047i
$650$	33.7656	+	3.95433i	1.32440	+	0.155101i
$651$		0			0
$652$	24.1188	+	39.1418i	0.944563	+	1.53291i
$653$	−5.18880	+	19.3649i	−0.203053	+	0.757805i	0.786981	+	0.616977i	$0.211643\pi$
$653$	−5.18880	+	19.3649i	−0.203053	+	0.757805i	−0.990034	+	0.140828i	$0.955024\pi$
$654$	−11.7211	+	1.71420i	−0.458333	+	0.0670307i
$655$	−38.7436	−	22.3686i	−1.51384	−	0.874015i
$656$	−0.634787	−	11.0702i	−0.0247843	−	0.432219i
$657$			40.8933i			1.59540i
$658$		0			0
$659$	29.3969	−	29.3969i	1.14514	−	1.14514i	0.157643	−	0.987496i	$-0.449610\pi$
$659$	29.3969	−	29.3969i	1.14514	−	1.14514i	0.987496	−	0.157643i	$-0.0503896\pi$
$660$	−11.4882	+	21.2833i	−0.447178	+	0.828453i
$661$	−46.8440	+	12.5518i	−1.82202	+	0.488208i	−0.997035	−	0.0769483i	$-0.975482\pi$
$661$	−46.8440	+	12.5518i	−1.82202	+	0.488208i	−0.824984	+	0.565157i	$0.808816\pi$
$662$	−2.37338	+	3.18651i	−0.0922440	+	0.123847i
$663$	22.9280	−	13.2375i	0.890450	−	0.514102i
$664$	−3.63603	+	9.96901i	−0.141105	+	0.386873i
$665$		0			0
$666$	−5.34827	−	0.626340i	−0.207241	−	0.0242702i
$667$	−1.31136	+	4.89406i	−0.0507760	+	0.189499i
$668$	5.24675	−	5.55622i	0.203003	−	0.214977i
$669$	43.4664	−	11.6468i	1.68051	−	0.450290i
$670$	−11.4236	−	4.54128i	−0.441333	−	0.175445i
$671$	−20.9232			−0.807733
$672$		0			0
$673$	11.6457			0.448909			0.224454	−	0.974485i	$-0.427940\pi$
$673$	11.6457			0.448909			0.224454	+	0.974485i	$0.427940\pi$
$674$	−31.4359	−	12.4968i	−1.21086	−	0.481360i
$675$	−8.37826	+	2.24495i	−0.322479	+	0.0864080i
$676$	8.76530	−	9.28231i	0.337127	−	0.357012i
$677$	−8.74138	+	32.6233i	−0.335959	+	1.25381i	0.566868	+	0.823809i	$0.308155\pi$
$677$	−8.74138	+	32.6233i	−0.335959	+	1.25381i	−0.902826	+	0.430006i	$0.858512\pi$
$678$	41.6964	+	4.88310i	1.60134	+	0.187534i
$679$		0			0
$680$	−20.0893	−	7.32725i	−0.770391	−	0.280987i
$681$	39.0453	−	22.5428i	1.49622	−	0.863843i
$682$	−9.55165	+	12.8241i	−0.365752	+	0.491060i
$683$	−6.57460	+	1.76166i	−0.251570	+	0.0674080i	−0.382400	−	0.923997i	$-0.624902\pi$
$683$	−6.57460	+	1.76166i	−0.251570	+	0.0674080i	0.130830	+	0.991405i	$0.458236\pi$
$684$	−15.6774	+	29.0444i	−0.599441	+	1.11054i
$685$	5.76794	−	5.76794i	0.220382	−	0.220382i
$686$		0			0
$687$			17.9827i			0.686081i
$688$	−26.8082	+	30.0697i	−1.02205	+	1.14640i
$689$	43.7854	+	25.2795i	1.66809	+	0.963073i
$690$	−26.8818	+	3.93144i	−1.02337	+	0.149667i
$691$	−7.97267	+	29.7544i	−0.303295	+	1.13191i	0.631108	+	0.775695i	$0.282600\pi$
$691$	−7.97267	+	29.7544i	−0.303295	+	1.13191i	−0.934403	+	0.356217i	$0.884066\pi$
$692$	−8.72214	−	14.1550i	−0.331566	−	0.538091i
$693$		0			0
$694$	17.5683	+	2.05744i	0.666884	+	0.0780994i
$695$	−13.7303	−	23.7816i	−0.520821	−	0.902088i
$696$	1.40224	−	15.9043i	0.0531519	−	0.602851i
$697$	5.61193	+	3.24005i	0.212567	+	0.122726i
$698$	40.2507	−	17.3517i	1.52351	−	0.656773i
$699$	−52.7060	+	52.7060i	−1.99352	+	1.99352i
$700$		0			0
$701$	−28.2191	−	28.2191i	−1.06582	−	1.06582i	−0.997675	−	0.0681440i	$-0.978292\pi$
$701$	−28.2191	−	28.2191i	−1.06582	−	1.06582i	−0.0681440	−	0.997675i	$-0.521708\pi$
$702$	−3.65386	+	9.19129i	−0.137906	+	0.346903i
$703$	2.40080	−	4.15831i	0.0905480	−	0.156834i
$704$	4.92842	−	10.5320i	0.185747	−	0.396938i
$705$	20.5371	−	11.8571i	0.773473	−	0.446565i
$706$	18.4269	+	23.3153i	0.693504	+	0.877484i
$707$		0			0
$708$	4.64439	−	19.5571i	0.174547	−	0.734999i
$709$	18.5805	+	4.97862i	0.697804	+	0.186976i	0.590247	−	0.807223i	$-0.299030\pi$
$709$	18.5805	+	4.97862i	0.697804	+	0.186976i	0.107557	+	0.994199i	$0.465697\pi$
$710$	−20.4459	+	27.4507i	−0.767320	+	1.03021i
$711$	1.47604	−	2.55657i	0.0553557	−	0.0958790i
$712$	7.82529	−	11.1597i	0.293265	−	0.418226i
$713$	−17.9618			−0.672673
$714$		0			0
$715$	−14.6347	−	14.6347i	−0.547308	−	0.547308i
$716$	18.3565	−	34.0077i	0.686016	−	1.27093i
$717$	−8.89426	−	33.1938i	−0.332162	−	1.23965i
$718$	1.95773	+	13.3863i	0.0730617	+	0.499571i
$719$	11.9289	+	20.6615i	0.444873	+	0.770543i	0.998043	−	0.0625253i	$-0.0199154\pi$
$719$	11.9289	+	20.6615i	0.444873	+	0.770543i	−0.553170	+	0.833068i	$0.686582\pi$
$720$	44.4372	−	14.6806i	1.65608	−	0.547114i
$721$		0			0
$722$	−1.58776	−	2.00897i	−0.0590902	−	0.0747662i
$723$	−30.2730	−	8.11163i	−1.12587	−	0.301675i
$724$	−0.491786	−	17.1669i	−0.0182771	−	0.638001i
$725$	3.10100	+	11.5731i	0.115168	+	0.429814i
$726$	−29.6907	+	12.7994i	−1.10193	+	0.475031i
$727$			28.5645i			1.05940i	0.848185	+	0.529700i	$0.177695\pi$
$727$			28.5645i			1.05940i	−0.848185	+	0.529700i	$0.822305\pi$
$728$		0			0
$729$			36.7360i			1.36059i
$730$	20.4682	+	47.4800i	0.757563	+	1.75731i
$731$	−6.09328	−	22.7404i	−0.225368	−	0.841085i
$732$	53.8473	+	50.8480i	1.99025	+	1.87940i
$733$	−22.5582	−	6.04445i	−0.833206	−	0.223257i	−0.183094	−	0.983095i	$-0.558611\pi$
$733$	−22.5582	−	6.04445i	−0.833206	−	0.223257i	−0.650112	+	0.759839i	$0.725278\pi$
$734$	−6.79708	+	5.37196i	−0.250885	+	0.198283i
$735$		0			0
$736$	12.7947	−	2.62692i	0.471620	−	0.0968297i
$737$	1.95329	+	3.38320i	0.0719504	+	0.124622i
$738$	−14.0327	+	2.05226i	−0.516550	+	0.0755449i
$739$	−0.460947	−	1.72028i	−0.0169562	−	0.0632814i	0.956929	−	0.290321i	$-0.0937620\pi$
$739$	−0.460947	−	1.72028i	−0.0169562	−	0.0632814i	−0.973886	+	0.227039i	$0.927095\pi$
$740$	−6.52321	+	1.94973i	−0.239798	+	0.0716734i
$741$	−36.5335	−	36.5335i	−1.34209	−	1.34209i
$742$		0			0
$743$	16.7041			0.612815			0.306407	−	0.951900i	$-0.400873\pi$
$743$	16.7041			0.612815			0.306407	+	0.951900i	$0.400873\pi$
$744$	55.7471	−	9.79099i	2.04379	−	0.358955i
$745$	13.7426	−	23.8029i	0.503490	−	0.872070i
$746$	18.6312	+	13.8769i	0.682138	+	0.508071i
$747$	13.1094	+	3.51266i	0.479649	+	0.128522i
$748$	3.56486	+	5.78534i	0.130344	+	0.211533i
$749$		0			0
$750$	−4.24751	+	3.35695i	−0.155097	+	0.122578i
$751$	−1.51512	+	0.874754i	−0.0552874	+	0.0319202i	−0.527389	−	0.849624i	$-0.676829\pi$
$751$	−1.51512	+	0.874754i	−0.0552874	+	0.0319202i	0.472101	+	0.881544i	$0.343496\pi$
$752$	−9.53123	+	6.25653i	−0.347568	+	0.228152i
$753$	−12.1678	+	21.0752i	−0.443419	+	0.768024i
$754$	12.6962	+	5.04716i	0.462367	+	0.183807i
$755$	−23.4148	−	23.4148i	−0.852153	−	0.852153i
$756$		0			0
$757$	−15.6771	+	15.6771i	−0.569792	+	0.569792i	−0.932070	−	0.362278i	$-0.881999\pi$
$757$	−15.6771	+	15.6771i	−0.569792	+	0.569792i	0.362278	+	0.932070i	$0.381999\pi$
$758$	4.79207	+	11.1161i	0.174056	+	0.403756i
$759$	7.47683	+	4.31675i	0.271392	+	0.156688i
$760$	−3.66509	+	41.5695i	−0.132947	+	1.50788i
$761$	−25.9814	−	45.0012i	−0.941826	−	1.63129i	−0.761984	−	0.647596i	$-0.775775\pi$
$761$	−25.9814	−	45.0012i	−0.941826	−	1.63129i	−0.179842	−	0.983695i	$-0.557559\pi$
$762$	1.90087	−	16.2314i	0.0688612	−	0.588000i
$763$		0			0
$764$	−29.5934	−	7.02780i	−1.07065	−	0.254257i
$765$	−7.07864	+	26.4178i	−0.255929	+	0.955139i
$766$	3.94578	+	26.9799i	0.142567	+	0.974823i
$767$	14.8965	+	8.60050i	0.537882	+	0.310546i
$768$	−38.2785	+	15.1275i	−1.38126	+	0.545867i
$769$		−	34.9699i		−	1.26105i	−0.776170	−	0.630524i	$-0.782840\pi$
$769$		−	34.9699i		−	1.26105i	0.776170	−	0.630524i	$-0.217160\pi$
$770$		0			0
$771$	−6.99090	+	6.99090i	−0.251771	+	0.251771i
$772$	−43.0759	+	12.8750i	−1.55034	+	0.463381i
$773$	13.2793	−	3.55817i	0.477622	−	0.127978i	−0.0119731	−	0.999928i	$-0.503811\pi$
$773$	13.2793	−	3.55817i	0.477622	−	0.127978i	0.489595	+	0.871950i	$0.337145\pi$
$774$	41.3216	+	30.7773i	1.48528	+	1.10627i
$775$	−36.7841	+	21.2373i	−1.32132	+	0.762866i
$776$	−15.0403	+	7.00106i	−0.539914	+	0.251323i
$777$		0			0
$778$	−4.70834	+	40.2041i	−0.168802	+	1.44139i
$779$	3.27301	−	12.2150i	0.117268	−	0.437650i
$780$	2.09783	+	73.2291i	0.0751142	+	2.62202i
$781$	10.5066	−	2.81523i	0.375956	−	0.100737i
$782$	−2.81984	+	7.09332i	−0.100837	+	0.253657i
$783$	−3.48586			−0.124574
$784$		0			0
$785$	−47.4847			−1.69480
$786$	18.5900	−	46.7631i	0.663082	−	1.66799i
$787$	−23.9812	+	6.42575i	−0.854838	+	0.229053i	−0.659520	−	0.751687i	$-0.729240\pi$
$787$	−23.9812	+	6.42575i	−0.854838	+	0.229053i	−0.195318	+	0.980740i	$0.562574\pi$
$788$	−23.5110	+	0.673530i	−0.837545	+	0.0239935i
$789$	4.20498	−	15.6932i	0.149701	−	0.558692i
$790$	0.434148	−	3.70716i	0.0154463	−	0.131895i
$791$		0			0
$792$	−13.9718	−	5.09599i	−0.496467	−	0.181078i
$793$	−54.8856	+	31.6882i	−1.94904	+	1.12528i
$794$	10.5184	+	7.83434i	0.373284	+	0.278030i
$795$	−92.2878	+	24.7284i	−3.27311	+	0.877027i
$796$	−5.85352	−	19.5842i	−0.207473	−	0.694142i
$797$	−13.3302	+	13.3302i	−0.472179	+	0.472179i	−0.902619	−	0.430440i	$-0.858358\pi$
$797$	−13.3302	+	13.3302i	−0.472179	+	0.472179i	0.430440	+	0.902619i	$0.358358\pi$
$798$		0			0
$799$		−	6.66293i		−	0.235717i
$800$	23.0965	−	20.5077i	0.816585	−	0.725058i
$801$	−15.0970	−	8.71624i	−0.533425	−	0.307973i
$802$	7.17427	+	49.0552i	0.253332	+	1.73220i
$803$	4.25258	−	15.8709i	0.150070	−	0.560070i
$804$	3.19499	−	13.4538i	0.112679	−	0.474479i
$805$		0			0
$806$	−5.63373	+	48.1059i	−0.198440	+	1.69446i
$807$	31.0148	+	53.7192i	1.09177	+	1.89101i
$808$	−2.62248	−	3.12963i	−0.0922584	−	0.110100i
$809$	−18.7601	−	10.8311i	−0.659569	−	0.380803i	0.132544	−	0.991177i	$-0.457686\pi$
$809$	−18.7601	−	10.8311i	−0.659569	−	0.380803i	−0.792113	+	0.610375i	$0.791019\pi$
$810$	12.2511	+	28.4188i	0.430461	+	0.998536i
$811$	−1.51326	+	1.51326i	−0.0531379	+	0.0531379i	−0.733176	−	0.680039i	$-0.761963\pi$
$811$	−1.51326	+	1.51326i	−0.0531379	+	0.0531379i	0.680039	+	0.733176i	$0.261963\pi$
$812$		0			0
$813$	−17.2192	−	17.2192i	−0.603904	−	0.603904i
$814$	2.01055	+	0.799263i	0.0704697	+	0.0280142i
$815$	37.1741	−	64.3874i	1.30215	−	2.25539i
$816$	4.88523	−	23.5523i	0.171017	−	0.824496i
$817$	−39.7883	+	22.9718i	−1.39202	+	0.803681i
$818$	−38.6986	+	30.5848i	−1.35307	+	1.06937i
$819$		0			0
$820$	−15.2657	+	9.40655i	−0.533101	+	0.328491i
$821$	−46.3574	−	12.4214i	−1.61788	−	0.433511i	−0.667506	−	0.744605i	$-0.732638\pi$
$821$	−46.3574	−	12.4214i	−1.61788	−	0.433511i	−0.950379	+	0.311094i	$0.899305\pi$
$822$	7.35866	+	5.48089i	0.256663	+	0.191168i
$823$	−15.0408	+	26.0514i	−0.524290	+	0.908096i	0.475310	+	0.879818i	$0.342336\pi$
$823$	−15.0408	+	26.0514i	−0.524290	+	0.908096i	−0.999600	+	0.0282782i	$0.990998\pi$
$824$	5.61914	+	3.94021i	0.195752	+	0.137264i
$825$	20.4158			0.710789
$826$		0			0
$827$	22.5866	+	22.5866i	0.785414	+	0.785414i	0.980739	−	0.195325i	$-0.0625760\pi$
$827$	22.5866	+	22.5866i	0.785414	+	0.785414i	−0.195325	+	0.980739i	$0.562576\pi$
$828$	−4.78406	−	16.0060i	−0.166258	−	0.556248i
$829$	−8.56747	−	31.9742i	−0.297561	−	1.11051i	−0.939162	−	0.343473i	$-0.888397\pi$
$829$	−8.56747	−	31.9742i	−0.297561	−	1.11051i	0.641602	−	0.767038i	$-0.278270\pi$
$830$	16.9791	−	2.48318i	0.589355	−	0.0861925i
$831$	−15.0840	−	26.1263i	−0.523260	−	0.906313i
$832$	−3.02245	−	35.0914i	−0.104785	−	1.21657i
$833$		0			0
$834$	24.2342	−	19.1531i	0.839161	−	0.663216i
$835$	−11.9368	−	3.19846i	−0.413091	−	0.110687i
$836$	9.10486	−	9.64190i	0.314898	−	0.333472i
$837$	−3.19838	−	11.9365i	−0.110552	−	0.412586i
$838$	6.79183	+	15.7550i	0.234620	+	0.544246i
$839$			35.7894i			1.23559i	0.786340	+	0.617794i	$0.211973\pi$
$839$			35.7894i			1.23559i	−0.786340	+	0.617794i	$0.788027\pi$
$840$		0			0
$841$		−	24.1849i		−	0.833962i
$842$	−13.6126	+	5.86829i	−0.469123	+	0.202235i
$843$	3.72527	+	13.9029i	0.128305	+	0.478841i
$844$	16.2219	−	0.464716i	0.558381	−	0.0159962i
$845$	−19.9418	−	5.34340i	−0.686020	−	0.183818i
$846$	9.04176	+	11.4404i	0.310862	+	0.393331i
$847$		0			0
$848$	43.6164	−	14.4094i	1.49779	−	0.494822i
$849$	−4.93437	−	8.54658i	−0.169347	−	0.293318i
$850$	2.61209	+	17.8606i	0.0895939	+	0.612612i
$851$	0.629017	+	2.34752i	0.0215624	+	0.0804721i
$852$	−33.8810	−	18.2881i	−1.16074	−	0.626541i
$853$	1.27195	+	1.27195i	0.0435507	+	0.0435507i	0.728547	−	0.684996i	$-0.240196\pi$
$853$	1.27195	+	1.27195i	0.0435507	+	0.0435507i	−0.684996	+	0.728547i	$0.740196\pi$
$854$		0			0
$855$	53.3733			1.82533
$856$	12.5387	−	2.20220i	0.428563	−	0.0752696i
$857$	−17.1377	+	29.6834i	−0.585412	+	1.01396i	0.409411	+	0.912350i	$0.365734\pi$
$857$	−17.1377	+	29.6834i	−0.585412	+	1.01396i	−0.994824	+	0.101614i	$0.967599\pi$
$858$	13.9064	−	18.6708i	0.474757	−	0.637411i
$859$	43.1714	+	11.5677i	1.47299	+	0.394686i	0.903955	−	0.427628i	$-0.140651\pi$
$859$	43.1714	+	11.5677i	1.47299	+	0.394686i	0.569034	+	0.822314i	$0.307317\pi$
$860$	63.3821	+	15.0519i	2.16131	+	0.513266i
$861$		0			0
$862$	1.41390	+	1.78899i	0.0481576	+	0.0609333i
$863$	32.5858	−	18.8134i	1.10923	−	0.640416i	0.170602	−	0.985340i	$-0.445429\pi$
$863$	32.5858	−	18.8134i	1.10923	−	0.640416i	0.938631	+	0.344924i	$0.112095\pi$
$864$	4.02403	+	8.03499i	0.136900	+	0.273356i
$865$	−13.4434	+	23.2846i	−0.457088	+	0.791700i
$866$	−6.83701	+	17.1985i	−0.232331	+	0.584430i
$867$	−20.9832	−	20.9832i	−0.712627	−	0.712627i
$868$		0			0
$869$	−0.838719	+	0.838719i	−0.0284516	+	0.0284516i
$870$	−23.7094	+	10.2209i	−0.803825	+	0.346522i
$871$	10.2477	+	5.91651i	0.347230	+	0.200473i
$872$	−5.91515	−	7.05906i	−0.200312	−	0.239050i
$873$	10.6092	+	18.3756i	0.359065	+	0.621920i
$874$	14.7952	+	1.73269i	0.500457	+	0.0586090i
$875$		0			0
$876$	−49.5139	+	30.5100i	−1.67292	+	1.03084i
$877$	5.49616	−	20.5119i	0.185592	−	0.692639i	−0.808911	−	0.587931i	$-0.799943\pi$
$877$	5.49616	−	20.5119i	0.185592	−	0.692639i	0.994503	−	0.104708i	$-0.0333907\pi$
$878$	−2.76881	+	0.404935i	−0.0934427	+	0.0136659i
$879$	30.7099	+	17.7304i	1.03582	+	0.598031i
$880$	−18.7729	+	1.07648i	−0.632836	+	0.0362880i
$881$		−	3.13017i		−	0.105458i	−0.998609	−	0.0527291i	$-0.983208\pi$
$881$		−	3.13017i		−	0.105458i	0.998609	−	0.0527291i	$-0.0167920\pi$
$882$		0			0
$883$	5.90657	−	5.90657i	0.198772	−	0.198772i	−0.600702	−	0.799473i	$-0.705112\pi$
$883$	5.90657	−	5.90657i	0.198772	−	0.198772i	0.799473	+	0.600702i	$0.205112\pi$
$884$	18.1132	+	9.77704i	0.609212	+	0.328838i
$885$	−31.3978	+	8.41301i	−1.05543	+	0.282800i
$886$	29.3116	−	39.3538i	0.984741	−	1.32212i
$887$	−41.9702	+	24.2315i	−1.40922	+	0.813615i	−0.995313	−	0.0967040i	$-0.969170\pi$
$887$	−41.9702	+	24.2315i	−1.40922	+	0.813615i	−0.413908	+	0.910318i	$0.635837\pi$
$888$	−3.23189	−	6.94303i	−0.108455	−	0.232993i
$889$		0			0
$890$	−21.8913	−	2.56371i	−0.733799	−	0.0859359i
$891$	2.54536	−	9.49940i	0.0852727	−	0.318242i
$892$	25.4369	+	24.0201i	0.851692	+	0.804253i
$893$	−12.5597	+	3.36536i	−0.420294	+	0.112617i
$894$	28.7298	+	11.4211i	0.960869	+	0.381979i
$895$	−62.4941			−2.08895
$896$		0			0
$897$	26.1508			0.873151
$898$	26.3441	+	10.4727i	0.879113	+	0.349478i
$899$	−16.4882	+	4.41800i	−0.549912	+	0.147348i
$900$	−28.7223	−	27.1225i	−0.957409	−	0.904082i
$901$	−6.94789	+	25.9299i	−0.231468	+	0.863849i
$902$	5.65955	+	0.662796i	0.188443	+	0.0220687i
$903$		0			0
$904$	13.7740	+	29.5904i	0.458115	+	0.984161i
$905$	−24.0513	+	13.8860i	−0.799491	+	0.461587i
$906$	22.2496	−	29.8723i	0.739192	−	0.992442i
$907$	36.1999	−	9.69974i	1.20200	−	0.322075i	0.398381	−	0.917220i	$-0.369572\pi$
$907$	36.1999	−	9.69974i	1.20200	−	0.322075i	0.803618	+	0.595146i	$0.202906\pi$
$908$	30.8459	+	16.6498i	1.02366	+	0.552544i
$909$	−3.69271	+	3.69271i	−0.122480	+	0.122480i
$910$		0			0
$911$		−	12.0871i		−	0.400463i	−0.979749	−	0.200231i	$-0.935831\pi$
$911$		−	12.0871i		−	0.400463i	0.979749	−	0.200231i	$-0.0641694\pi$
$912$	−46.8639	+	2.68726i	−1.55182	+	0.0889842i
$913$	−4.72253	−	2.72656i	−0.156293	−	0.0902358i
$914$	41.9882	−	6.14073i	1.38885	−	0.203117i
$915$	30.9974	−	115.684i	1.02474	−	3.82439i
$916$	−11.9027	+	7.33431i	−0.393276	+	0.242332i
$917$		0			0
$918$	−5.21599	−	0.610849i	−0.172153	−	0.0201610i
$919$	27.6308	+	47.8579i	0.911455	+	1.57869i	0.812010	+	0.583643i	$0.198373\pi$
$919$	27.6308	+	47.8579i	0.911455	+	1.57869i	0.0994447	+	0.995043i	$0.468293\pi$
$920$	−13.5661	−	16.1896i	−0.447260	−	0.533754i
$921$	−64.8188	−	37.4231i	−2.13585	−	1.23313i
$922$	33.4876	−	14.4362i	1.10286	−	0.475432i
$923$	23.2971	−	23.2971i	0.766833	−	0.766833i
$924$		0			0
$925$	4.06379	+	4.06379i	0.133617	+	0.133617i
$926$	−16.3941	+	41.2395i	−0.538744	+	1.35521i
$927$	4.38882	−	7.60165i	0.144148	−	0.249671i
$928$	11.0989	−	5.55850i	0.364340	−	0.182467i
$929$	−8.64695	+	4.99232i	−0.283697	+	0.163793i	−0.635096	−	0.772433i	$-0.719039\pi$
$929$	−8.64695	+	4.99232i	−0.283697	+	0.163793i	0.351399	+	0.936226i	$0.385706\pi$
$930$	−56.7533	−	71.8094i	−1.86101	−	2.35472i
$931$		0			0
$932$	−56.3824	−	13.3896i	−1.84687	−	0.438592i
$933$	−1.42103	−	0.380765i	−0.0465226	−	0.0124657i
$934$	20.1421	−	27.0429i	0.659071	−	0.884871i
$935$	5.49450	−	9.51675i	0.179689	−	0.311231i
$936$	−44.3686	+	7.79255i	−1.45023	+	0.254708i
$937$	−7.92416			−0.258871			−0.129436	−	0.991588i	$-0.541317\pi$
$937$	−7.92416			−0.258871			−0.129436	+	0.991588i	$0.541317\pi$
$938$		0			0
$939$	2.57311	+	2.57311i	0.0839703	+	0.0839703i
$940$	16.2244	+	8.75751i	0.529180	+	0.285638i
$941$	−1.63637	−	6.10702i	−0.0533441	−	0.199083i	0.934111	−	0.356983i	$-0.116194\pi$
$941$	−1.63637	−	6.10702i	−0.0533441	−	0.199083i	−0.987455	+	0.157900i	$0.949528\pi$
$942$	−7.72940	−	52.8510i	−0.251838	−	1.72198i
$943$	3.20038	+	5.54321i	0.104219	+	0.180512i
$944$	14.8390	−	4.90232i	0.482969	−	0.159557i
$945$		0			0
$946$	−12.8365	−	16.2419i	−0.417351	−	0.528070i
$947$	10.9891	+	2.94453i	0.357098	+	0.0956843i	0.432908	−	0.901438i	$-0.357487\pi$
$947$	10.9891	+	2.94453i	0.357098	+	0.0956843i	−0.0758096	+	0.997122i	$0.524154\pi$
$948$	4.19677	−	0.120227i	0.136305	−	0.00390478i
$949$	−12.8811	−	48.0727i	−0.418137	−	1.56051i
$950$	32.3480	−	13.9450i	1.04951	−	0.452434i
$951$		−	67.3561i		−	2.18417i
$952$		0			0
$953$		−	12.7329i		−	0.412460i	−0.978504	−	0.206230i	$-0.933880\pi$
$953$		−	12.7329i		−	0.412460i	0.978504	−	0.206230i	$-0.0661195\pi$
$954$	−23.2577	−	53.9508i	−0.752997	−	1.74672i
$955$	12.7304	+	47.5105i	0.411946	+	1.53741i
$956$	18.3434	−	19.4254i	0.593267	−	0.628261i
$957$	7.92522	+	2.12356i	0.256186	+	0.0686448i
$958$	−39.2294	+	31.0042i	−1.26744	+	1.00170i
$959$		0			0
$960$	50.9294	+	42.8519i	1.64374	+	1.38304i
$961$	−14.7568	−	25.5595i	−0.476025	−	0.824500i
$962$	6.48453	−	0.948356i	0.209070	−	0.0305762i
$963$	−4.21417	−	15.7275i	−0.135800	−	0.506812i
$964$	−6.97792	−	23.3460i	−0.224744	−	0.751925i
$965$	51.4090	+	51.4090i	1.65491	+	1.65491i
$966$		0			0
$967$	−10.6644			−0.342944			−0.171472	−	0.985189i	$-0.554852\pi$
$967$	−10.6644			−0.342944			−0.171472	+	0.985189i	$0.554852\pi$
$968$	−20.5814	−	14.4319i	−0.661512	−	0.463860i
$969$	13.7162	−	23.7571i	0.440628	−	0.763190i
$970$	21.5154	+	16.0252i	0.690819	+	0.514537i
$971$	−2.22623	−	0.596517i	−0.0714431	−	0.0191431i	0.222920	−	0.974837i	$-0.428441\pi$
$971$	−2.22623	−	0.596517i	−0.0714431	−	0.0191431i	−0.294364	+	0.955694i	$0.595108\pi$
$972$	−37.7509	+	23.2617i	−1.21086	+	0.746119i
$973$		0			0
$974$	11.7866	−	9.31532i	0.377666	−	0.298482i
$975$	53.5546	−	30.9198i	1.71512	−	0.990225i
$976$	−11.6944	+	56.3801i	−0.374328	+	1.80468i
$977$	7.66274	−	13.2723i	0.245153	−	0.424617i	−0.717022	−	0.697051i	$-0.754495\pi$
$977$	7.66274	−	13.2723i	0.245153	−	0.424617i	0.962175	+	0.272434i	$0.0878286\pi$
$978$	77.7148	+	30.8943i	2.48505	+	0.987892i
$979$	4.95277	+	4.95277i	0.158291	+	0.158291i
$980$		0			0
$981$	−8.32913	+	8.32913i	−0.265929	+	0.265929i
$982$	21.3050	+	49.4210i	0.679869	+	1.57709i
$983$	−16.1184	−	9.30595i	−0.514097	−	0.296814i	0.220419	−	0.975405i	$-0.429257\pi$
$983$	−16.1184	−	9.30595i	−0.514097	−	0.296814i	−0.734516	+	0.678591i	$0.762591\pi$
$984$	−12.9545	−	15.4597i	−0.412974	−	0.492837i
$985$	19.0177	+	32.9396i	0.605954	+	1.04954i
$986$	−0.843782	+	7.20498i	−0.0268715	+	0.229453i
$987$		0			0
$988$	9.28110	−	39.0818i	0.295271	−	1.24336i
$989$	6.01867	−	22.4620i	0.191383	−	0.714249i
$990$	3.48024	+	23.7967i	0.110609	+	0.756309i
$991$	−23.7555	−	13.7153i	−0.754619	−	0.435680i	0.0727413	−	0.997351i	$-0.476825\pi$
$991$	−23.7555	−	13.7153i	−0.754619	−	0.435680i	−0.827361	+	0.561671i	$0.810159\pi$
$992$	29.2174	+	32.9056i	0.927652	+	1.04475i
$993$			7.22736i			0.229353i
$994$		0			0
$995$	−23.3727	+	23.3727i	−0.740965	+	0.740965i
$996$	5.52761	+	18.4937i	0.175149	+	0.585997i
$997$	−18.7595	+	5.02660i	−0.594120	+	0.159194i	−0.543335	−	0.839516i	$-0.682839\pi$
$997$	−18.7595	+	5.02660i	−0.594120	+	0.159194i	−0.0507843	+	0.998710i	$0.516172\pi$
$998$	−14.3770	−	10.7083i	−0.455096	−	0.338965i
$999$	−1.44804	+	0.836028i	−0.0458140	+	0.0264507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.f.227.13		56
7.2	even	3		112.2.v.a.19.7	yes	56
7.3	odd	6		784.2.j.a.195.6		56
7.4	even	3		784.2.j.a.195.5		56
7.5	odd	6	inner	784.2.w.f.19.7		56
7.6	odd	2		112.2.v.a.3.13	✓	56
16.11	odd	4	inner	784.2.w.f.619.7		56
28.23	odd	6		448.2.z.a.47.12		56
28.27	even	2		448.2.z.a.367.12		56
56.13	odd	2		896.2.z.b.479.12		56
56.27	even	2		896.2.z.a.479.3		56
56.37	even	6		896.2.z.b.607.12		56
56.51	odd	6		896.2.z.a.607.3		56
112.11	odd	12		784.2.j.a.587.6		56
112.13	odd	4		896.2.z.a.31.3		56
112.27	even	4		112.2.v.a.59.7	yes	56
112.37	even	12		448.2.z.a.271.12		56
112.51	odd	12		896.2.z.b.159.12		56
112.59	even	12		784.2.j.a.587.5		56
112.69	odd	4		448.2.z.a.143.12		56
112.75	even	12	inner	784.2.w.f.411.13		56
112.83	even	4		896.2.z.b.31.12		56
112.93	even	12		896.2.z.a.159.3		56
112.107	odd	12		112.2.v.a.75.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.13	✓	56	7.6	odd	2
112.2.v.a.19.7	yes	56	7.2	even	3
112.2.v.a.59.7	yes	56	112.27	even	4
112.2.v.a.75.13	yes	56	112.107	odd	12
448.2.z.a.47.12		56	28.23	odd	6
448.2.z.a.143.12		56	112.69	odd	4
448.2.z.a.271.12		56	112.37	even	12
448.2.z.a.367.12		56	28.27	even	2
784.2.j.a.195.5		56	7.4	even	3
784.2.j.a.195.6		56	7.3	odd	6
784.2.j.a.587.5		56	112.59	even	12
784.2.j.a.587.6		56	112.11	odd	12
784.2.w.f.19.7		56	7.5	odd	6	inner
784.2.w.f.227.13		56	1.1	even	1	trivial
784.2.w.f.411.13		56	112.75	even	12	inner
784.2.w.f.619.7		56	16.11	odd	4	inner
896.2.z.a.31.3		56	112.13	odd	4
896.2.z.a.159.3		56	112.93	even	12
896.2.z.a.479.3		56	56.27	even	2
896.2.z.a.607.3		56	56.51	odd	6
896.2.z.b.31.12		56	112.83	even	4
896.2.z.b.159.12		56	112.51	odd	12
896.2.z.b.479.12		56	56.13	odd	2
896.2.z.b.607.12		56	56.37	even	6

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31418 + 0.522432i) q^{2} +(2.48480 - 0.665801i) q^{3} +(1.45413 + 1.37314i) q^{4} +(0.837076 - 3.12401i) q^{5} +(3.61331 + 0.423158i) q^{6} +(1.19362 + 2.56423i) q^{8} +(3.13287 - 1.80877i) q^{9} +(2.73215 - 3.66819i) q^{10} +(-1.40398 + 0.376195i) q^{11} +(4.52746 + 2.44381i) q^{12} +(-3.11315 + 3.11315i) q^{13} -8.31987i q^{15} +(0.228992 + 3.99344i) q^{16} +(-2.02443 - 1.16881i) q^{17} +(5.06211 - 0.740329i) q^{18} +(-1.18070 + 4.40643i) q^{19} +(5.50691 - 3.39330i) q^{20} +(-2.04161 - 0.239095i) q^{22} +(-1.15450 - 1.99965i) q^{23} +(4.67317 + 5.57689i) q^{24} +(-4.72861 - 2.73006i) q^{25} +(-5.71764 + 2.46483i) q^{26} +(1.12329 - 1.12329i) q^{27} +(-1.55163 - 1.55163i) q^{29} +(4.34656 - 10.9338i) q^{30} +(3.88952 - 6.73685i) q^{31} +(-1.78536 + 5.36773i) q^{32} +(-3.23814 + 1.86954i) q^{33} +(-2.04984 - 2.59365i) q^{34} +(7.03929 + 1.67168i) q^{36} +(-1.01669 - 0.272421i) q^{37} +(-3.85371 + 5.17400i) q^{38} +(-5.66282 + 9.80830i) q^{39} +(9.00983 - 1.58242i) q^{40} -2.77210 q^{41} +(7.12142 + 7.12142i) q^{43} +(-2.55813 - 1.38082i) q^{44} +(-3.02815 - 11.3012i) q^{45} +(-0.472536 - 3.23104i) q^{46} +(1.42516 + 2.46844i) q^{47} +(3.22783 + 9.77044i) q^{48} +(-4.78797 - 6.05817i) q^{50} +(-5.80851 - 1.55638i) q^{51} +(-8.80171 + 0.252146i) q^{52} +(-2.97221 - 11.0925i) q^{53} +(2.06305 - 0.889362i) q^{54} +4.70094i q^{55} +11.7352i q^{57} +(-1.22850 - 2.84974i) q^{58} +(-1.01120 - 3.77383i) q^{59} +(11.4243 - 12.0982i) q^{60} +(13.9045 + 3.72571i) q^{61} +(8.63107 - 6.82142i) q^{62} +(-5.15056 + 6.12142i) q^{64} +(7.11957 + 12.3315i) q^{65} +(-5.23220 + 0.765203i) q^{66} +(-0.695627 - 2.59612i) q^{67} +(-1.33886 - 4.47942i) q^{68} +(-4.20006 - 4.20006i) q^{69} -7.48345 q^{71} +(8.37754 + 5.87444i) q^{72} +(-5.65210 + 9.78973i) q^{73} +(-1.19379 - 0.889159i) q^{74} +(-13.5673 - 3.63536i) q^{75} +(-7.76752 + 4.78626i) q^{76} +(-12.5661 + 9.93142i) q^{78} +(0.706717 - 0.408024i) q^{79} +(12.6672 + 2.62744i) q^{80} +(-3.38303 + 5.85958i) q^{81} +(-3.64303 - 1.44823i) q^{82} +(2.65285 + 2.65285i) q^{83} +(-5.34597 + 5.34597i) q^{85} +(5.63837 + 13.0793i) q^{86} +(-4.88857 - 2.82241i) q^{87} +(-2.64046 - 3.15109i) q^{88} +(-2.40944 - 4.17328i) q^{89} +(1.92458 - 16.4338i) q^{90} +(1.06700 - 4.49303i) q^{92} +(5.17929 - 19.3294i) q^{93} +(0.583317 + 3.98852i) q^{94} +(12.7774 + 7.37703i) q^{95} +(-0.862438 + 14.5264i) q^{96} +5.86541i q^{97} +(-3.71804 + 3.71804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Introduction

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