LMFDB - Embedded newform 693.2.m.k.190.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(64,693)] 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("693.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(693, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.8
Character	$\chi$	$=$	693.190
Dual form			693.2.m.k.631.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.16885 - 1.57576i) q^{2} +(1.60284 - 4.93305i) q^{4} +(-0.946867 - 0.687939i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-2.64012 - 8.12545i) q^{8} -3.13763 q^{10} +(-3.31646 - 0.0332550i) q^{11} +(1.36132 - 0.989057i) q^{13} +(-0.828426 - 2.54963i) q^{14} +(-10.1372 - 7.36509i) q^{16} +(4.52787 + 3.28969i) q^{17} +(1.34551 + 4.14105i) q^{19} +(-4.91131 + 3.56828i) q^{20} +(-7.24529 + 5.15381i) q^{22} -0.119612 q^{23} +(-1.12179 - 3.45251i) q^{25} +(1.39398 - 4.29023i) q^{26} +(-4.19630 - 3.04879i) q^{28} +(-1.35844 + 4.18083i) q^{29} +(5.10728 - 3.71065i) q^{31} -16.5044 q^{32} +15.0040 q^{34} +(-0.946867 + 0.687939i) q^{35} +(1.80904 - 5.56765i) q^{37} +(9.44350 + 6.86111i) q^{38} +(-3.08997 + 9.50996i) q^{40} +(-3.40428 - 10.4773i) q^{41} +5.97227 q^{43} +(-5.47981 + 16.3069i) q^{44} +(-0.259420 + 0.188480i) q^{46} +(3.88781 + 11.9654i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-7.87331 - 5.72029i) q^{50} +(-2.69708 - 8.30076i) q^{52} +(-0.337364 + 0.245109i) q^{53} +(3.11737 + 2.31301i) q^{55} -8.54361 q^{56} +(3.64175 + 11.2082i) q^{58} +(-0.223587 + 0.688131i) q^{59} +(7.16627 + 5.20660i) q^{61} +(5.22980 - 16.0957i) q^{62} +(-15.5211 + 11.2767i) q^{64} -1.96940 q^{65} +8.78741 q^{67} +(23.4857 - 17.0633i) q^{68} +(-0.969582 + 2.98407i) q^{70} +(-2.59926 - 1.88847i) q^{71} +(-4.50828 + 13.8750i) q^{73} +(-4.84975 - 14.9260i) q^{74} +22.5846 q^{76} +(-1.05647 + 3.14386i) q^{77} +(-11.7115 + 8.50887i) q^{79} +(4.53182 + 13.9475i) q^{80} +(-23.8931 - 17.3593i) q^{82} +(2.79864 + 2.03333i) q^{83} +(-2.02418 - 6.22979i) q^{85} +(12.9529 - 9.41086i) q^{86} +(8.48564 + 27.0355i) q^{88} -12.0621 q^{89} +(-0.519978 - 1.60033i) q^{91} +(-0.191720 + 0.590052i) q^{92} +(27.2867 + 19.8250i) q^{94} +(1.57477 - 4.84665i) q^{95} +(4.85066 - 3.52421i) q^{97} -2.68084 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52}+ \cdots - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	2.16885	−	1.57576i	1.53361	−	1.11423i	0.579415	−	0.815033i	$-0.303281\pi$
$2$	2.16885	−	1.57576i	1.53361	−	1.11423i	0.954191	−	0.299197i	$-0.0967188\pi$
$3$		0			0
$3$		0			0
$4$	1.60284	−	4.93305i	0.801422	−	2.46652i
$5$	−0.946867	−	0.687939i	−0.423452	−	0.307656i	0.355573	−	0.934648i	$-0.384286\pi$
$5$	−0.946867	−	0.687939i	−0.423452	−	0.307656i	−0.779025	+	0.626993i	$0.784286\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−2.64012	−	8.12545i	−0.933423	−	2.87278i
$9$		0			0
$10$	−3.13763			−0.992207
$11$	−3.31646	−	0.0332550i	−0.999950	−	0.0100268i
$11$	−3.31646	−	0.0332550i	−0.999950	−	0.0100268i
$12$		0			0
$13$	1.36132	−	0.989057i	0.377562	−	0.274315i	−0.382777	−	0.923841i	$-0.625032\pi$
$13$	1.36132	−	0.989057i	0.377562	−	0.274315i	0.760340	+	0.649525i	$0.225032\pi$
$14$	−0.828426	−	2.54963i	−0.221406	−	0.681418i
$15$		0			0
$16$	−10.1372	−	7.36509i	−2.53429	−	1.84127i
$17$	4.52787	+	3.28969i	1.09817	+	0.797867i	0.980760	−	0.195217i	$-0.0625411\pi$
$17$	4.52787	+	3.28969i	1.09817	+	0.797867i	0.117409	+	0.993084i	$0.462541\pi$
$18$		0			0
$19$	1.34551	+	4.14105i	0.308681	+	0.950022i	0.978278	+	0.207298i	$0.0664669\pi$
$19$	1.34551	+	4.14105i	0.308681	+	0.950022i	−0.669597	+	0.742725i	$0.733533\pi$
$20$	−4.91131	+	3.56828i	−1.09820	+	0.797891i
$21$		0			0
$22$	−7.24529	+	5.15381i	−1.54470	+	1.09880i
$23$	−0.119612			−0.0249408			−0.0124704	−	0.999922i	$-0.503970\pi$
$23$	−0.119612			−0.0249408			−0.0124704	+	0.999922i	$0.503970\pi$
$24$		0			0
$25$	−1.12179	−	3.45251i	−0.224358	−	0.690502i
$26$	1.39398	−	4.29023i	0.273382	−	0.841383i
$27$		0			0
$28$	−4.19630	−	3.04879i	−0.793026	−	0.576167i
$29$	−1.35844	+	4.18083i	−0.252255	+	0.776361i	0.742103	+	0.670286i	$0.233829\pi$
$29$	−1.35844	+	4.18083i	−0.252255	+	0.776361i	−0.994358	+	0.106075i	$0.966171\pi$
$30$		0			0
$31$	5.10728	−	3.71065i	0.917294	−	0.666453i	−0.0255548	−	0.999673i	$-0.508135\pi$
$31$	5.10728	−	3.71065i	0.917294	−	0.666453i	0.942849	+	0.333220i	$0.108135\pi$
$32$	−16.5044			−2.91759
$33$		0			0
$34$	15.0040			2.57317
$35$	−0.946867	+	0.687939i	−0.160050	+	0.116283i
$36$		0			0
$37$	1.80904	−	5.56765i	0.297404	−	0.915317i	−0.684999	−	0.728544i	$-0.740197\pi$
$37$	1.80904	−	5.56765i	0.297404	−	0.915317i	0.982403	−	0.186772i	$-0.0598027\pi$
$38$	9.44350	+	6.86111i	1.53194	+	1.11302i
$39$		0			0
$40$	−3.08997	+	9.50996i	−0.488568	+	1.50366i
$41$	−3.40428	−	10.4773i	−0.531660	−	1.63628i	−0.750757	−	0.660578i	$-0.770311\pi$
$41$	−3.40428	−	10.4773i	−0.531660	−	1.63628i	0.219097	−	0.975703i	$-0.429689\pi$
$42$		0			0
$43$	5.97227			0.910762			0.455381	−	0.890297i	$-0.349503\pi$
$43$	5.97227			0.910762			0.455381	+	0.890297i	$0.349503\pi$
$44$	−5.47981	+	16.3069i	−0.826113	+	2.45836i
$45$		0			0
$46$	−0.259420	+	0.188480i	−0.0382494	+	0.0277898i
$47$	3.88781	+	11.9654i	0.567095	+	1.74534i	0.661642	+	0.749820i	$0.269860\pi$
$47$	3.88781	+	11.9654i	0.567095	+	1.74534i	−0.0945469	+	0.995520i	$0.530140\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−7.87331	−	5.72029i	−1.11345	−	0.808972i
$51$		0			0
$52$	−2.69708	−	8.30076i	−0.374018	−	1.15111i
$53$	−0.337364	+	0.245109i	−0.0463405	+	0.0336683i	−0.610714	−	0.791851i	$-0.709118\pi$
$53$	−0.337364	+	0.245109i	−0.0463405	+	0.0336683i	0.564374	+	0.825519i	$0.309118\pi$
$54$		0			0
$55$	3.11737	+	2.31301i	0.420346	+	0.311886i
$56$	−8.54361			−1.14169
$57$		0			0
$58$	3.64175	+	11.2082i	0.478185	+	1.47170i
$59$	−0.223587	+	0.688131i	−0.0291086	+	0.0895870i	−0.964555	−	0.263881i	$-0.914998\pi$
$59$	−0.223587	+	0.688131i	−0.0291086	+	0.0895870i	0.935447	+	0.353468i	$0.114998\pi$
$60$		0			0
$61$	7.16627	+	5.20660i	0.917546	+	0.666637i	0.942912	−	0.333042i	$-0.108075\pi$
$61$	7.16627	+	5.20660i	0.917546	+	0.666637i	−0.0253656	+	0.999678i	$0.508075\pi$
$62$	5.22980	−	16.0957i	0.664186	−	2.04415i
$63$		0			0
$64$	−15.5211	+	11.2767i	−1.94014	+	1.40959i
$65$	−1.96940			−0.244274
$66$		0			0
$67$	8.78741			1.07355			0.536777	−	0.843724i	$-0.319642\pi$
$67$	8.78741			1.07355			0.536777	+	0.843724i	$0.319642\pi$
$68$	23.4857	−	17.0633i	2.84805	−	2.06923i
$69$		0			0
$70$	−0.969582	+	2.98407i	−0.115887	+	0.356664i
$71$	−2.59926	−	1.88847i	−0.308475	−	0.224120i	0.422767	−	0.906239i	$-0.361059\pi$
$71$	−2.59926	−	1.88847i	−0.308475	−	0.224120i	−0.731242	+	0.682118i	$0.761059\pi$
$72$		0			0
$73$	−4.50828	+	13.8750i	−0.527654	+	1.62395i	0.231354	+	0.972870i	$0.425685\pi$
$73$	−4.50828	+	13.8750i	−0.527654	+	1.62395i	−0.759008	+	0.651082i	$0.774315\pi$
$74$	−4.84975	−	14.9260i	−0.563772	−	1.73511i
$75$		0			0
$76$	22.5846			2.59064
$77$	−1.05647	+	3.14386i	−0.120396	+	0.358276i
$78$		0			0
$79$	−11.7115	+	8.50887i	−1.31764	+	0.957322i	−0.317683	+	0.948197i	$0.602905\pi$
$79$	−11.7115	+	8.50887i	−1.31764	+	0.957322i	−0.999958	+	0.00912524i	$0.997095\pi$
$80$	4.53182	+	13.9475i	0.506673	+	1.55938i
$81$		0			0
$82$	−23.8931	−	17.3593i	−2.63855	−	1.91702i
$83$	2.79864	+	2.03333i	0.307191	+	0.223187i	0.730690	−	0.682709i	$-0.239198\pi$
$83$	2.79864	+	2.03333i	0.307191	+	0.223187i	−0.423499	+	0.905896i	$0.639198\pi$
$84$		0			0
$85$	−2.02418	−	6.22979i	−0.219553	−	0.675716i
$86$	12.9529	−	9.41086i	1.39675	−	1.01480i
$87$		0			0
$88$	8.48564	+	27.0355i	0.904572	+	2.88200i
$89$	−12.0621			−1.27858			−0.639292	−	0.768964i	$-0.720772\pi$
$89$	−12.0621			−1.27858			−0.639292	+	0.768964i	$0.720772\pi$
$90$		0			0
$91$	−0.519978	−	1.60033i	−0.0545085	−	0.167760i
$92$	−0.191720	+	0.590052i	−0.0199881	+	0.0615172i
$93$		0			0
$94$	27.2867	+	19.8250i	2.81441	+	2.04479i
$95$	1.57477	−	4.84665i	0.161568	−	0.497256i
$96$		0			0
$97$	4.85066	−	3.52421i	0.492510	−	0.357830i	−0.313639	−	0.949542i	$-0.601548\pi$
$97$	4.85066	−	3.52421i	0.492510	−	0.357830i	0.806149	+	0.591713i	$0.201548\pi$
$98$	−2.68084			−0.270806
$99$		0			0
$100$	−18.8294			−1.88294
$101$	−0.0822061	+	0.0597262i	−0.00817981	+	0.00594298i	−0.591868	−	0.806035i	$-0.701609\pi$
$101$	−0.0822061	+	0.0597262i	−0.00817981	+	0.00594298i	0.583688	+	0.811978i	$0.301609\pi$
$102$		0			0
$103$	−0.537659	+	1.65474i	−0.0529771	+	0.163047i	−0.974045	−	0.226356i	$-0.927319\pi$
$103$	−0.537659	+	1.65474i	−0.0529771	+	0.163047i	0.921067	+	0.389403i	$0.127319\pi$
$104$	−11.6306	−	8.45012i	−1.14047	−	0.828602i
$105$		0			0
$106$	−0.345457	+	1.06321i	−0.0335538	+	0.103268i
$107$	3.40019	+	10.4647i	0.328708	+	1.01166i	0.969739	+	0.244145i	$0.0785073\pi$
$107$	3.40019	+	10.4647i	0.328708	+	1.01166i	−0.641030	+	0.767516i	$0.721493\pi$
$108$		0			0
$109$	16.5040			1.58080			0.790400	−	0.612592i	$-0.209873\pi$
$109$	16.5040			1.58080			0.790400	+	0.612592i	$0.209873\pi$
$110$	10.4058	+	0.104342i	0.992157	+	0.00994863i
$111$		0			0
$112$	−10.1372	+	7.36509i	−0.957873	+	0.695935i
$113$	−1.94096	−	5.97366i	−0.182590	−	0.561955i	0.817308	−	0.576201i	$-0.195465\pi$
$113$	−1.94096	−	5.97366i	−0.182590	−	0.561955i	−0.999899	+	0.0142456i	$0.995465\pi$
$114$		0			0
$115$	0.113257	+	0.0822858i	0.0105612	+	0.00767319i
$116$	18.4469	+	13.4024i	1.71275	+	1.24439i
$117$		0			0
$118$	0.599402	+	1.84477i	0.0551795	+	0.169825i
$119$	4.52787	−	3.28969i	0.415069	−	0.301565i
$120$		0			0
$121$	10.9978	+	0.220578i	0.999799	+	0.0200525i
$122$	23.7469			2.14994
$123$		0			0
$124$	−10.1187	−	31.1420i	−0.908683	−	2.79664i
$125$	−3.12129	+	9.60633i	−0.279176	+	0.859216i
$126$		0			0
$127$	−13.9458	−	10.1322i	−1.23749	−	0.899087i	−0.240058	−	0.970758i	$-0.577167\pi$
$127$	−13.9458	−	10.1322i	−1.23749	−	0.899087i	−0.997428	+	0.0716717i	$0.977167\pi$
$128$	−5.69318	+	17.5218i	−0.503211	+	1.54872i
$129$		0			0
$130$	−4.27133	+	3.10330i	−0.374620	+	0.272177i
$131$	−0.324063			−0.0283135			−0.0141567	−	0.999900i	$-0.504506\pi$
$131$	−0.324063			−0.0283135			−0.0141567	+	0.999900i	$0.504506\pi$
$132$		0			0
$133$	4.35416			0.377553
$134$	19.0586	−	13.8468i	1.64641	−	1.19619i
$135$		0			0
$136$	14.7761	−	45.4762i	1.26704	−	3.89955i
$137$	−8.39158	−	6.09684i	−0.716941	−	0.520888i	0.168464	−	0.985708i	$-0.446119\pi$
$137$	−8.39158	−	6.09684i	−0.716941	−	0.520888i	−0.885406	+	0.464819i	$0.846119\pi$
$138$		0			0
$139$	4.13390	−	12.7228i	0.350633	−	1.07914i	−0.607866	−	0.794040i	$-0.707974\pi$
$139$	4.13390	−	12.7228i	0.350633	−	1.07914i	0.958499	−	0.285097i	$-0.0920260\pi$
$140$	1.87596	+	5.77360i	0.158547	+	0.487958i
$141$		0			0
$142$	−8.61317			−0.722801
$143$	−4.54765	+	3.23490i	−0.380294	+	0.270516i
$144$		0			0
$145$	4.16242	−	3.02417i	0.345670	−	0.251144i
$146$	12.0860	+	37.1968i	1.00024	+	3.07843i
$147$		0			0
$148$	−24.5659	−	17.8482i	−2.01930	−	1.46711i
$149$	−7.82310	−	5.68381i	−0.640893	−	0.465636i	0.219264	−	0.975666i	$-0.429635\pi$
$149$	−7.82310	−	5.68381i	−0.640893	−	0.465636i	−0.860157	+	0.510029i	$0.829635\pi$
$150$		0			0
$151$	0.791336	+	2.43548i	0.0643980	+	0.198197i	0.978078	−	0.208237i	$-0.0667724\pi$
$151$	0.791336	+	2.43548i	0.0643980	+	0.198197i	−0.913680	+	0.406433i	$0.866772\pi$
$152$	30.0956	−	21.8657i	2.44108	−	1.77355i
$153$		0			0
$154$	2.66265	+	8.48330i	0.214563	+	0.683604i
$155$	−7.38862			−0.593468
$156$		0			0
$157$	5.71965	+	17.6033i	0.456478	+	1.40489i	0.869391	+	0.494124i	$0.164511\pi$
$157$	5.71965	+	17.6033i	0.456478	+	1.40489i	−0.412914	+	0.910770i	$0.635489\pi$
$158$	−11.9924	+	36.9089i	−0.954065	+	2.93631i
$159$		0			0
$160$	15.6274	+	11.3540i	1.23546	+	0.897612i
$161$	−0.0369622	+	0.113758i	−0.00291303	+	0.00896538i
$162$		0			0
$163$	−5.24100	+	3.80781i	−0.410507	+	0.298251i	−0.773807	−	0.633421i	$-0.781650\pi$
$163$	−5.24100	+	3.80781i	−0.410507	+	0.298251i	0.363300	+	0.931672i	$0.381650\pi$
$164$	−57.1416			−4.46201
$165$		0			0
$166$	9.27386			0.719791
$167$	−20.4331	+	14.8455i	−1.58116	+	1.14878i	−0.665814	+	0.746118i	$0.731916\pi$
$167$	−20.4331	+	14.8455i	−1.58116	+	1.14878i	−0.915348	+	0.402664i	$0.868084\pi$
$168$		0			0
$169$	−3.14226	+	9.67089i	−0.241712	+	0.743914i
$170$	−14.2068	−	10.3218i	−1.08961	−	0.791649i
$171$		0			0
$172$	9.57262	−	29.4615i	0.729905	−	2.24642i
$173$	2.86398	+	8.81443i	0.217745	+	0.670149i	0.998947	+	0.0458716i	$0.0146065\pi$
$173$	2.86398	+	8.81443i	0.217745	+	0.670149i	−0.781203	+	0.624277i	$0.785394\pi$
$174$		0			0
$175$	−3.63018			−0.274416
$176$	33.3746	+	24.7631i	2.51570	+	1.86659i
$177$		0			0
$178$	−26.1609	+	19.0070i	−1.96084	+	1.42464i
$179$	4.77239	+	14.6879i	0.356705	+	1.09783i	0.955014	+	0.296560i	$0.0958395\pi$
$179$	4.77239	+	14.6879i	0.356705	+	1.09783i	−0.598309	+	0.801265i	$0.704160\pi$
$180$		0			0
$181$	−8.52043	−	6.19045i	−0.633318	−	0.460133i	0.224230	−	0.974536i	$-0.428013\pi$
$181$	−8.52043	−	6.19045i	−0.633318	−	0.460133i	−0.857548	+	0.514404i	$0.828013\pi$
$182$	−3.64948	−	2.65151i	−0.270518	−	0.196543i
$183$		0			0
$184$	0.315790	+	0.971903i	0.0232804	+	0.0716496i
$185$	−5.54313	+	4.02732i	−0.407539	+	0.296094i
$186$		0			0
$187$	−14.9071	−	11.0607i	−1.09011	−	0.808838i
$188$	65.2577			4.75940
$189$		0			0
$190$	−4.22172	−	12.9931i	−0.306276	−	0.942619i
$191$	2.12090	−	6.52745i	0.153463	−	0.472309i	−0.844539	−	0.535494i	$-0.820126\pi$
$191$	2.12090	−	6.52745i	0.153463	−	0.472309i	0.998002	+	0.0631843i	$0.0201256\pi$
$192$		0			0
$193$	−18.0651	−	13.1251i	−1.30035	−	0.944763i	−0.300395	−	0.953815i	$-0.597119\pi$
$193$	−18.0651	−	13.1251i	−1.30035	−	0.944763i	−0.999959	+	0.00905222i	$0.997119\pi$
$194$	4.96703	−	15.2870i	0.356612	−	1.09754i
$195$		0			0
$196$	−4.19630	+	3.04879i	−0.299736	+	0.217771i
$197$	−4.45203			−0.317194			−0.158597	−	0.987343i	$-0.550697\pi$
$197$	−4.45203			−0.317194			−0.158597	+	0.987343i	$0.550697\pi$
$198$		0			0
$199$	−15.0993			−1.07036			−0.535180	−	0.844738i	$-0.679756\pi$
$199$	−15.0993			−1.07036			−0.535180	+	0.844738i	$0.679756\pi$
$200$	−25.0916	+	18.2301i	−1.77424	+	1.28906i
$201$		0			0
$202$	−0.0841782	+	0.259074i	−0.00592276	+	0.0182284i
$203$	3.55643	+	2.58390i	0.249612	+	0.181354i
$204$		0			0
$205$	−3.98435	+	12.2626i	−0.278279	+	0.856454i
$206$	1.44138	+	4.43611i	0.100426	+	0.309078i
$207$		0			0
$208$	−21.0844			−1.46194
$209$	−4.32461	−	13.7784i	−0.299140	−	0.953070i
$210$		0			0
$211$	18.4849	−	13.4300i	1.27255	−	0.924563i	0.273250	−	0.961943i	$-0.411901\pi$
$211$	18.4849	−	13.4300i	1.27255	−	0.924563i	0.999301	+	0.0373803i	$0.0119013\pi$
$212$	0.668393	+	2.05710i	0.0459054	+	0.141282i
$213$		0			0
$214$	23.8643	+	17.3385i	1.63133	+	1.18523i
$215$	−5.65494	−	4.10856i	−0.385664	−	0.280201i
$216$		0			0
$217$	−1.95081	−	6.00397i	−0.132429	−	0.407576i
$218$	35.7947	−	26.0064i	2.42432	−	1.76137i
$219$		0			0
$220$	16.4068	−	11.6707i	1.10615	−	0.786840i
$221$	9.41757			0.633494
$222$		0			0
$223$	3.00076	+	9.23540i	0.200946	+	0.618448i	0.999856	+	0.0169970i	$0.00541058\pi$
$223$	3.00076	+	9.23540i	0.200946	+	0.618448i	−0.798910	+	0.601451i	$0.794589\pi$
$224$	−5.10013	+	15.6966i	−0.340767	+	1.04877i
$225$		0			0
$226$	−13.6227	−	9.89747i	−0.906169	−	0.658370i
$227$	5.75308	−	17.7062i	0.381845	−	1.17520i	−0.556898	−	0.830581i	$-0.688009\pi$
$227$	5.75308	−	17.7062i	0.381845	−	1.17520i	0.938743	−	0.344618i	$-0.111991\pi$
$228$		0			0
$229$	−7.31573	+	5.31519i	−0.483437	+	0.351237i	−0.802655	−	0.596444i	$-0.796580\pi$
$229$	−7.31573	+	5.31519i	−0.483437	+	0.351237i	0.319218	+	0.947681i	$0.396580\pi$
$230$	0.375299			0.0247465
$231$		0			0
$232$	37.5576			2.46578
$233$	6.97631	−	5.06859i	0.457033	−	0.332054i	−0.335333	−	0.942100i	$-0.608849\pi$
$233$	6.97631	−	5.06859i	0.457033	−	0.332054i	0.792366	+	0.610045i	$0.208849\pi$
$234$		0			0
$235$	4.55026	−	14.0043i	0.296826	−	0.913537i
$236$	3.03621	+	2.20593i	0.197640	+	0.143594i
$237$		0			0
$238$	4.63649	−	14.2697i	0.300539	−	0.924965i
$239$	6.39265	+	19.6745i	0.413506	+	1.27264i	0.913581	+	0.406658i	$0.133306\pi$
$239$	6.39265	+	19.6745i	0.413506	+	1.27264i	−0.500075	+	0.865982i	$0.666694\pi$
$240$		0			0
$241$	−24.8415			−1.60018			−0.800090	−	0.599880i	$-0.795215\pi$
$241$	−24.8415			−1.60018			−0.800090	+	0.599880i	$0.795215\pi$
$242$	24.2001	−	16.8515i	1.55564	−	1.08325i
$243$		0			0
$244$	37.1708	−	27.0062i	2.37962	−	1.72889i
$245$	0.361671	+	1.11311i	0.0231063	+	0.0711139i
$246$		0			0
$247$	5.92741	+	4.30651i	0.377152	+	0.274017i
$248$	−43.6346	−	31.7024i	−2.77080	−	2.01310i
$249$		0			0
$250$	8.36767	+	25.7531i	0.529218	+	1.62877i
$251$	8.50085	−	6.17623i	0.536569	−	0.389840i	−0.286240	−	0.958158i	$-0.592405\pi$
$251$	8.50085	−	6.17623i	0.536569	−	0.389840i	0.822809	+	0.568318i	$0.192405\pi$
$252$		0			0
$253$	0.396689	+	0.00397770i	0.0249396	+	0.000250076i
$254$	−46.2121			−2.89961
$255$		0			0
$256$	3.40547	+	10.4810i	0.212842	+	0.655060i
$257$	1.13747	−	3.50077i	0.0709534	−	0.218372i	−0.909291	−	0.416160i	$-0.863376\pi$
$257$	1.13747	−	3.50077i	0.0709534	−	0.218372i	0.980245	+	0.197788i	$0.0633757\pi$
$258$		0			0
$259$	−4.73613	−	3.44100i	−0.294289	−	0.213813i
$260$	−3.15664	+	9.71514i	−0.195767	+	0.602508i
$261$		0			0
$262$	−0.702842	+	0.510645i	−0.0434217	+	0.0315477i
$263$	10.1816			0.627824			0.313912	−	0.949452i	$-0.398360\pi$
$263$	10.1816			0.627824			0.313912	+	0.949452i	$0.398360\pi$
$264$		0			0
$265$	0.488059			0.0299812
$266$	9.44350	−	6.86111i	0.579018	−	0.420681i
$267$		0			0
$268$	14.0849	−	43.3487i	0.860369	−	2.64794i
$269$	−25.9044	−	18.8207i	−1.57942	−	1.14752i	−0.917355	−	0.398070i	$-0.869680\pi$
$269$	−25.9044	−	18.8207i	−1.57942	−	1.14752i	−0.662065	−	0.749446i	$-0.730320\pi$
$270$		0			0
$271$	−6.41141	+	19.7323i	−0.389466	+	1.19865i	0.543723	+	0.839265i	$0.317014\pi$
$271$	−6.41141	+	19.7323i	−0.389466	+	1.19865i	−0.933189	+	0.359387i	$0.882986\pi$
$272$	−21.6709	−	66.6963i	−1.31399	−	4.04406i
$273$		0			0
$274$	−27.8072			−1.67990
$275$	3.60555	+	11.4874i	0.217423	+	0.692717i
$276$		0			0
$277$	−12.2537	+	8.90281i	−0.736251	+	0.534918i	−0.891535	−	0.452952i	$-0.850371\pi$
$277$	−12.2537	+	8.90281i	−0.736251	+	0.534918i	0.155283	+	0.987870i	$0.450371\pi$
$278$	−11.0823	−	34.1079i	−0.664674	−	2.04566i
$279$		0			0
$280$	8.08966	+	5.87748i	0.483450	+	0.351247i
$281$	20.8126	+	15.1212i	1.24157	+	0.902056i	0.997702	−	0.0677516i	$-0.0215825\pi$
$281$	20.8126	+	15.1212i	1.24157	+	0.902056i	0.243871	+	0.969808i	$0.421583\pi$
$282$		0			0
$283$	5.56058	+	17.1137i	0.330542	+	1.01730i	0.968876	+	0.247545i	$0.0796237\pi$
$283$	5.56058	+	17.1137i	0.330542	+	1.01730i	−0.638334	+	0.769759i	$0.720376\pi$
$284$	−13.4821	+	9.79534i	−0.800017	+	0.581247i
$285$		0			0
$286$	−4.76574	+	14.1820i	−0.281804	+	0.838599i
$287$	−11.0165			−0.650283
$288$		0			0
$289$	4.42625	+	13.6226i	0.260368	+	0.801329i
$290$	4.26227	−	13.1179i	0.250289	−	0.770311i
$291$		0			0
$292$	61.2202	+	44.4791i	3.58264	+	2.60294i
$293$	9.56714	−	29.4446i	0.558918	−	1.72017i	−0.126446	−	0.991974i	$-0.540357\pi$
$293$	9.56714	−	29.4446i	0.558918	−	1.72017i	0.685364	−	0.728201i	$-0.259643\pi$
$294$		0			0
$295$	0.685100	−	0.497754i	0.0398880	−	0.0289804i
$296$	−50.0158			−2.90711
$297$		0			0
$298$	−25.9234			−1.50170
$299$	−0.162830	+	0.118303i	−0.00941672	+	0.00684165i
$300$		0			0
$301$	1.84553	−	5.67996i	0.106375	−	0.327388i
$302$	5.55402	+	4.03523i	0.319598	+	0.232201i
$303$		0			0
$304$	16.8595	−	51.8883i	0.966961	−	2.97600i
$305$	−3.20368	−	9.85991i	−0.183442	−	0.564577i
$306$		0			0
$307$	−10.0193			−0.571830			−0.285915	−	0.958255i	$-0.592298\pi$
$307$	−10.0193			−0.571830			−0.285915	+	0.958255i	$0.592298\pi$
$308$	13.8155	+	10.2507i	0.787209	+	0.584090i
$309$		0			0
$310$	−16.0248	+	11.6427i	−0.910146	+	0.661260i
$311$	5.04762	+	15.5350i	0.286224	+	0.880907i	0.986029	+	0.166573i	$0.0532702\pi$
$311$	5.04762	+	15.5350i	0.286224	+	0.880907i	−0.699805	+	0.714334i	$0.746730\pi$
$312$		0			0
$313$	−3.61677	−	2.62774i	−0.204432	−	0.148529i	0.480859	−	0.876798i	$-0.340325\pi$
$313$	−3.61677	−	2.62774i	−0.204432	−	0.148529i	−0.685291	+	0.728269i	$0.740325\pi$
$314$	40.1436	+	29.1660i	2.26543	+	1.64593i
$315$		0			0
$316$	23.2030	+	71.4115i	1.30527	+	4.01721i
$317$	9.69060	−	7.04063i	0.544278	−	0.395441i	−0.281393	−	0.959593i	$-0.590797\pi$
$317$	9.69060	−	7.04063i	0.544278	−	0.395441i	0.825671	+	0.564151i	$0.190797\pi$
$318$		0			0
$319$	4.64423	−	13.8204i	0.260027	−	0.773793i
$320$	22.4541			1.25522
$321$		0			0
$322$	0.0990897	+	0.304967i	0.00552206	+	0.0169951i
$323$	−7.53048	+	23.1764i	−0.419007	+	1.28957i
$324$		0			0
$325$	−4.94184	−	3.59046i	−0.274124	−	0.199163i
$326$	−5.36674	+	16.5171i	−0.297236	+	0.914798i
$327$		0			0
$328$	−76.1452	+	55.3227i	−4.20441	+	3.05469i
$329$	12.5812			0.693625
$330$		0			0
$331$	−18.0873			−0.994168			−0.497084	−	0.867702i	$-0.665596\pi$
$331$	−18.0873			−0.994168			−0.497084	+	0.867702i	$0.665596\pi$
$332$	14.5163	−	10.5467i	0.796686	−	0.578826i
$333$		0			0
$334$	−20.9233	+	64.3953i	−1.14487	+	3.52356i
$335$	−8.32051	−	6.04520i	−0.454598	−	0.330285i
$336$		0			0
$337$	5.89785	−	18.1517i	0.321276	−	0.988787i	−0.651817	−	0.758376i	$-0.725993\pi$
$337$	5.89785	−	18.1517i	0.321276	−	0.988787i	0.973093	−	0.230411i	$-0.0740070\pi$
$338$	8.42391	+	25.9261i	0.458200	+	1.41019i
$339$		0			0
$340$	−33.9763			−1.84262
$341$	−17.0615	+	12.1364i	−0.923931	+	0.657222i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−15.7675	−	48.5274i	−0.850127	−	2.61642i
$345$		0			0
$346$	20.1010	+	14.6042i	1.08063	+	0.785127i
$347$	−4.30208	−	3.12564i	−0.230948	−	0.167793i	0.466293	−	0.884630i	$-0.345589\pi$
$347$	−4.30208	−	3.12564i	−0.230948	−	0.167793i	−0.697241	+	0.716837i	$0.745589\pi$
$348$		0			0
$349$	−6.37385	−	19.6167i	−0.341184	−	1.05006i	−0.963595	−	0.267366i	$-0.913847\pi$
$349$	−6.37385	−	19.6167i	−0.341184	−	1.05006i	0.622411	−	0.782691i	$-0.286153\pi$
$350$	−7.87331	+	5.72029i	−0.420846	+	0.305763i
$351$		0			0
$352$	54.7360	+	0.548853i	2.91744	+	0.0292540i
$353$	−7.31745			−0.389468			−0.194734	−	0.980856i	$-0.562384\pi$
$353$	−7.31745			−0.389468			−0.194734	+	0.980856i	$0.562384\pi$
$354$		0			0
$355$	1.16200	+	3.57626i	0.0616725	+	0.189808i
$356$	−19.3337	+	59.5030i	−1.02468	+	3.15365i
$357$		0			0
$358$	33.4952	+	24.3357i	1.77028	+	1.28618i
$359$	−7.48717	+	23.0431i	−0.395157	+	1.21617i	0.533681	+	0.845686i	$0.320808\pi$
$359$	−7.48717	+	23.0431i	−0.395157	+	1.21617i	−0.928839	+	0.370484i	$0.879192\pi$
$360$		0			0
$361$	0.0334113	−	0.0242747i	0.00175849	−	0.00127762i
$362$	−28.2342			−1.48395
$363$		0			0
$364$	−8.72794			−0.457468
$365$	13.8139	−	10.0364i	0.723054	−	0.525329i
$366$		0			0
$367$	−6.95470	+	21.4044i	−0.363032	+	1.11730i	0.588172	+	0.808736i	$0.299848\pi$
$367$	−6.95470	+	21.4044i	−0.363032	+	1.11730i	−0.951204	+	0.308562i	$0.900152\pi$
$368$	1.21253	+	0.880954i	0.0632074	+	0.0459229i
$369$		0			0
$370$	−5.67611	+	17.4693i	−0.295087	+	0.908184i
$371$	0.128861	+	0.396595i	0.00669015	+	0.0205902i
$372$		0			0
$373$	6.25290			0.323763			0.161881	−	0.986810i	$-0.448244\pi$
$373$	6.25290			0.323763			0.161881	+	0.986810i	$0.448244\pi$
$374$	−49.7602	−	0.498959i	−2.57304	−	0.0258005i
$375$		0			0
$376$	86.9604	−	63.1804i	4.48464	−	3.25828i
$377$	2.28582	+	7.03502i	0.117726	+	0.362322i
$378$		0			0
$379$	−10.3710	−	7.53496i	−0.532722	−	0.387045i	0.288653	−	0.957434i	$-0.406793\pi$
$379$	−10.3710	−	7.53496i	−0.532722	−	0.387045i	−0.821375	+	0.570389i	$0.806793\pi$
$380$	−21.3846	−	15.5369i	−1.09701	−	0.797024i
$381$		0			0
$382$	−5.68579	−	17.4990i	−0.290910	−	0.895329i
$383$	5.23220	−	3.80142i	0.267353	−	0.194243i	−0.446029	−	0.895018i	$-0.647162\pi$
$383$	5.23220	−	3.80142i	0.267353	−	0.194243i	0.713382	+	0.700775i	$0.247162\pi$
$384$		0			0
$385$	3.16312	−	2.25003i	0.161208	−	0.114672i
$386$	−59.8624			−3.04691
$387$		0			0
$388$	−9.61025	−	29.5773i	−0.487887	−	1.50156i
$389$	4.60335	−	14.1676i	0.233399	−	0.718328i	−0.763931	−	0.645298i	$-0.776733\pi$
$389$	4.60335	−	14.1676i	0.233399	−	0.718328i	0.997330	−	0.0730300i	$-0.0232669\pi$
$390$		0			0
$391$	−0.541588	−	0.393487i	−0.0273893	−	0.0198995i
$392$	−2.64012	+	8.12545i	−0.133346	+	0.410397i
$393$		0			0
$394$	−9.65577	+	7.01533i	−0.486451	+	0.353427i
$395$	16.9428			0.852483
$396$		0			0
$397$	1.85862			0.0932813			0.0466407	−	0.998912i	$-0.485148\pi$
$397$	1.85862			0.0932813			0.0466407	+	0.998912i	$0.485148\pi$
$398$	−32.7480	+	23.7928i	−1.64151	+	1.19263i
$399$		0			0
$400$	−14.0563	+	43.2608i	−0.702814	+	2.16304i
$401$	−7.07282	−	5.13871i	−0.353200	−	0.256615i	0.397010	−	0.917814i	$-0.370048\pi$
$401$	−7.07282	−	5.13871i	−0.353200	−	0.256615i	−0.750210	+	0.661199i	$0.770048\pi$
$402$		0			0
$403$	3.28259	−	10.1028i	0.163518	−	0.503255i
$404$	0.162869	+	0.501258i	0.00810302	+	0.0249385i
$405$		0			0
$406$	11.7849			0.584877
$407$	−6.18476	+	18.4047i	−0.306567	+	0.912289i
$408$		0			0
$409$	−10.2905	+	7.47649i	−0.508833	+	0.369689i	−0.812381	−	0.583128i	$-0.801829\pi$
$409$	−10.2905	+	7.47649i	−0.508833	+	0.369689i	0.303548	+	0.952816i	$0.401829\pi$
$410$	10.6814	+	32.8740i	0.527517	+	1.62353i
$411$		0			0
$412$	7.30115	+	5.30460i	0.359702	+	0.261339i
$413$	0.585359	+	0.425288i	0.0288036	+	0.0209271i
$414$		0			0
$415$	−1.25113	−	3.85059i	−0.0614157	−	0.189018i
$416$	−22.4677	+	16.3238i	−1.10157	+	0.800338i
$417$		0			0
$418$	−31.0908	−	23.0686i	−1.52070	−	1.12832i
$419$	8.09885			0.395655			0.197827	−	0.980237i	$-0.436611\pi$
$419$	8.09885			0.395655			0.197827	+	0.980237i	$0.436611\pi$
$420$		0			0
$421$	−8.18233	−	25.1826i	−0.398782	−	1.22733i	−0.925977	−	0.377581i	$-0.876756\pi$
$421$	−8.18233	−	25.1826i	−0.398782	−	1.22733i	0.527194	−	0.849745i	$-0.323244\pi$
$422$	18.9283	−	58.2554i	0.921417	−	2.83583i
$423$		0			0
$424$	2.88230	+	2.09412i	0.139977	+	0.101699i
$425$	6.27837	−	19.3228i	0.304546	−	0.937295i
$426$		0			0
$427$	7.16627	−	5.20660i	0.346800	−	0.251965i
$428$	57.0728			2.75872
$429$		0			0
$430$	−18.7388			−0.903665
$431$	−0.288371	+	0.209514i	−0.0138903	+	0.0100919i	−0.594709	−	0.803941i	$-0.702733\pi$
$431$	−0.288371	+	0.209514i	−0.0138903	+	0.0100919i	0.580818	+	0.814033i	$0.302733\pi$
$432$		0			0
$433$	−5.65144	+	17.3933i	−0.271591	+	0.835871i	0.718510	+	0.695516i	$0.244824\pi$
$433$	−5.65144	+	17.3933i	−0.271591	+	0.835871i	−0.990101	+	0.140355i	$0.955176\pi$
$434$	−13.6918	−	9.94768i	−0.657228	−	0.477504i
$435$		0			0
$436$	26.4534	−	81.4151i	1.26689	−	3.89908i
$437$	−0.160939	−	0.495320i	−0.00769876	−	0.0236944i
$438$		0			0
$439$	6.67633			0.318644			0.159322	−	0.987227i	$-0.449069\pi$
$439$	6.67633			0.318644			0.159322	+	0.987227i	$0.449069\pi$
$440$	10.5640	−	31.4366i	0.503620	−	1.49868i
$441$		0			0
$442$	20.4253	−	14.8398i	0.971531	−	0.705858i
$443$	6.31639	+	19.4398i	0.300101	+	0.923615i	0.981460	+	0.191666i	$0.0613890\pi$
$443$	6.31639	+	19.4398i	0.300101	+	0.923615i	−0.681360	+	0.731949i	$0.738611\pi$
$444$		0			0
$445$	11.4212	+	8.29801i	0.541418	+	0.393363i
$446$	21.0610	+	15.3017i	0.997266	+	0.724556i
$447$		0			0
$448$	5.92853	+	18.2461i	0.280097	+	0.862048i
$449$	4.46116	−	3.24122i	0.210535	−	0.152963i	−0.477521	−	0.878620i	$-0.658464\pi$
$449$	4.46116	−	3.24122i	0.210535	−	0.152963i	0.688056	+	0.725658i	$0.258464\pi$
$450$		0			0
$451$	10.9417	+	34.8608i	0.515227	+	1.64153i
$452$	−32.5794			−1.53241
$453$		0			0
$454$	−15.4231	−	47.4674i	−0.723842	−	2.22776i
$455$	−0.608578	+	1.87301i	−0.0285306	+	0.0878081i
$456$		0			0
$457$	−1.62026	−	1.17719i	−0.0757926	−	0.0550666i	0.549244	−	0.835662i	$-0.314916\pi$
$457$	−1.62026	−	1.17719i	−0.0757926	−	0.0550666i	−0.625036	+	0.780596i	$0.714916\pi$
$458$	−7.49123	+	23.0556i	−0.350042	+	1.07732i
$459$		0			0
$460$	0.587453	−	0.426809i	0.0273901	−	0.0199001i
$461$	8.17436			0.380718			0.190359	−	0.981715i	$-0.439035\pi$
$461$	8.17436			0.380718			0.190359	+	0.981715i	$0.439035\pi$
$462$		0			0
$463$	−4.26686			−0.198298			−0.0991488	−	0.995073i	$-0.531612\pi$
$463$	−4.26686			−0.198298			−0.0991488	+	0.995073i	$0.531612\pi$
$464$	44.5629	−	32.3768i	2.06878	−	1.50306i
$465$		0			0
$466$	7.14368	−	21.9860i	0.330924	−	1.01848i
$467$	32.7764	+	23.8134i	1.51671	+	1.10195i	0.963089	+	0.269184i	$0.0867541\pi$
$467$	32.7764	+	23.8134i	1.51671	+	1.10195i	0.553620	+	0.832769i	$0.313246\pi$
$468$		0			0
$469$	2.71546	−	8.35733i	0.125388	−	0.385905i
$470$	−12.1985	−	37.5432i	−0.562676	−	1.73174i
$471$		0			0
$472$	6.18168			0.284535
$473$	−19.8068	−	0.198608i	−0.910717	−	0.00913200i
$474$		0			0
$475$	12.7876	−	9.29077i	0.586737	−	0.426290i
$476$	−8.97072	−	27.6090i	−0.411172	−	1.26546i
$477$		0			0
$478$	44.8670	+	32.5978i	2.05217	+	1.49099i
$479$	6.66697	+	4.84384i	0.304622	+	0.221321i	0.729585	−	0.683890i	$-0.239713\pi$
$479$	6.66697	+	4.84384i	0.304622	+	0.221321i	−0.424964	+	0.905210i	$0.639713\pi$
$480$		0			0
$481$	−3.04404	−	9.36860i	−0.138796	−	0.427172i
$482$	−53.8773	+	39.1442i	−2.45405	+	1.78297i
$483$		0			0
$484$	18.7159	−	53.8991i	0.850721	−	2.44996i
$485$	−7.01738			−0.318643
$486$		0			0
$487$	−0.298165	−	0.917658i	−0.0135111	−	0.0415830i	0.944074	−	0.329735i	$-0.106959\pi$
$487$	−0.298165	−	0.917658i	−0.0135111	−	0.0415830i	−0.957585	+	0.288152i	$0.906959\pi$
$488$	23.3862	−	71.9752i	1.05864	−	3.25816i
$489$		0			0
$490$	2.53840	+	1.84426i	0.114673	+	0.0833150i
$491$	9.40289	−	28.9391i	0.424346	−	1.30600i	−0.479272	−	0.877666i	$-0.659099\pi$
$491$	9.40289	−	28.9391i	0.424346	−	1.30600i	0.903619	−	0.428338i	$-0.140901\pi$
$492$		0			0
$493$	−19.9045	+	14.4614i	−0.896452	+	0.651310i
$494$	19.6417			0.883720
$495$		0			0
$496$	−79.1027			−3.55181
$497$	−2.59926	+	1.88847i	−0.116593	+	0.0847096i
$498$		0			0
$499$	−11.6064	+	35.7208i	−0.519573	+	1.59908i	0.255231	+	0.966880i	$0.417848\pi$
$499$	−11.6064	+	35.7208i	−0.519573	+	1.59908i	−0.774804	+	0.632201i	$0.782152\pi$
$500$	42.3855	+	30.7949i	1.89554	+	1.37719i
$501$		0			0
$502$	8.70479	−	26.7906i	0.388514	−	1.19572i
$503$	−7.10421	−	21.8645i	−0.316761	−	0.974890i	−0.975023	−	0.222102i	$-0.928708\pi$
$503$	−7.10421	−	21.8645i	−0.316761	−	0.974890i	0.658262	−	0.752789i	$-0.271292\pi$
$504$		0			0
$505$	0.118926			0.00529214
$506$	0.866624	−	0.616459i	0.0385262	−	0.0274049i
$507$		0			0
$508$	−72.3355	+	52.5548i	−3.20937	+	2.33174i
$509$	−1.29651	−	3.99024i	−0.0574667	−	0.176864i	0.918203	−	0.396110i	$-0.129640\pi$
$509$	−1.29651	−	3.99024i	−0.0574667	−	0.176864i	−0.975670	+	0.219246i	$0.929640\pi$
$510$		0			0
$511$	11.8028	+	8.57525i	0.522126	+	0.379347i
$512$	−5.90848	−	4.29276i	−0.261120	−	0.189715i
$513$		0			0
$514$	−3.04937	−	9.38501i	−0.134502	−	0.413955i
$515$	1.64746	−	1.19695i	0.0725955	−	0.0527438i
$516$		0			0
$517$	−12.4958	−	39.8122i	−0.549567	−	1.75094i
$518$	−15.6941			−0.689560
$519$		0			0
$520$	5.19945	+	16.0023i	0.228011	+	0.701746i
$521$	11.4156	−	35.1338i	0.500129	−	1.53924i	−0.308680	−	0.951166i	$-0.599887\pi$
$521$	11.4156	−	35.1338i	0.500129	−	1.53924i	0.808809	−	0.588072i	$-0.200113\pi$
$522$		0			0
$523$	1.49381	+	1.08531i	0.0653196	+	0.0474575i	0.619966	−	0.784629i	$-0.287146\pi$
$523$	1.49381	+	1.08531i	0.0653196	+	0.0474575i	−0.554646	+	0.832086i	$0.687146\pi$
$524$	−0.519422	+	1.59862i	−0.0226910	+	0.0698359i
$525$		0			0
$526$	22.0823	−	16.0438i	0.962835	−	0.699541i
$527$	35.3320			1.53909
$528$		0			0
$529$	−22.9857			−0.999378
$530$	1.05852	−	0.769063i	0.0459793	−	0.0334060i
$531$		0			0
$532$	6.97904	−	21.4793i	0.302580	−	0.931244i
$533$	−14.9970	−	10.8959i	−0.649591	−	0.471956i
$534$		0			0
$535$	3.97955	−	12.2478i	0.172051	−	0.529518i
$536$	−23.1998	−	71.4017i	−1.00208	−	3.08408i
$537$		0			0
$538$	−85.8395			−3.70081
$539$	2.66352	+	1.97627i	0.114726	+	0.0851239i
$540$		0			0
$541$	7.87615	−	5.72236i	0.338622	−	0.246023i	−0.405458	−	0.914114i	$-0.632888\pi$
$541$	7.87615	−	5.72236i	0.338622	−	0.246023i	0.744080	+	0.668090i	$0.232888\pi$
$542$	17.1880	+	52.8992i	0.738287	+	2.27221i
$543$		0			0
$544$	−74.7296	−	54.2942i	−3.20400	−	2.32785i
$545$	−15.6271	−	11.3538i	−0.669392	−	0.486342i
$546$		0			0
$547$	−0.394754	−	1.21493i	−0.0168785	−	0.0519466i	0.942263	−	0.334875i	$-0.108694\pi$
$547$	−0.394754	−	1.21493i	−0.0168785	−	0.0519466i	−0.959141	+	0.282928i	$0.908694\pi$
$548$	−43.5264	+	31.6238i	−1.85936	+	1.35090i
$549$		0			0
$550$	25.9213	+	19.2329i	1.10529	+	0.820096i
$551$	−19.1408			−0.815427
$552$		0			0
$553$	4.47338	+	13.7676i	0.190227	+	0.585459i
$554$	−12.5476	+	38.6177i	−0.533098	+	1.64071i
$555$		0			0
$556$	−56.1364	−	40.7855i	−2.38071	−	1.72969i
$557$	11.3679	−	34.9869i	0.481675	−	1.48244i	−0.355065	−	0.934842i	$-0.615541\pi$
$557$	11.3679	−	34.9869i	0.481675	−	1.48244i	0.836740	−	0.547601i	$-0.184459\pi$
$558$		0			0
$559$	8.13017	−	5.90691i	0.343870	−	0.249836i
$560$	14.6653			0.619721
$561$		0			0
$562$	68.9667			2.90918
$563$	11.8603	−	8.61698i	0.499850	−	0.363162i	−0.309110	−	0.951026i	$-0.600031\pi$
$563$	11.8603	−	8.61698i	0.499850	−	0.363162i	0.808960	+	0.587864i	$0.200031\pi$
$564$		0			0
$565$	−2.27168	+	6.99153i	−0.0955705	+	0.294136i
$566$	39.0271	+	28.3549i	1.64043	+	1.19184i
$567$		0			0
$568$	−8.48234	+	26.1060i	−0.355911	+	1.09538i
$569$	8.60433	+	26.4814i	0.360712	+	1.11016i	0.952623	+	0.304155i	$0.0983740\pi$
$569$	8.60433	+	26.4814i	0.360712	+	1.11016i	−0.591910	+	0.806004i	$0.701626\pi$
$570$		0			0
$571$	14.5879			0.610485			0.305243	−	0.952275i	$-0.401262\pi$
$571$	14.5879			0.610485			0.305243	+	0.952275i	$0.401262\pi$
$572$	8.66871	+	27.6188i	0.362457	+	1.15480i
$573$		0			0
$574$	−23.8931	+	17.3593i	−0.997278	+	0.724565i
$575$	0.134179	+	0.412962i	0.00559567	+	0.0172217i
$576$		0			0
$577$	21.1272	+	15.3498i	0.879537	+	0.639021i	0.933129	−	0.359542i	$-0.117067\pi$
$577$	21.1272	+	15.3498i	0.879537	+	0.639021i	−0.0535917	+	0.998563i	$0.517067\pi$
$578$	31.0658	+	22.5706i	1.29217	+	0.938814i
$579$		0			0
$580$	−8.24668	−	25.3807i	−0.342425	−	1.05387i
$581$	2.79864	−	2.03333i	0.116107	−	0.0843568i
$582$		0			0
$583$	1.12700	−	0.801675i	0.0466757	−	0.0332020i
$584$	124.643			5.15778
$585$		0			0
$586$	−25.6480	−	78.9364i	−1.05951	−	3.26083i
$587$	4.53123	−	13.9457i	0.187024	−	0.575600i	−0.812954	−	0.582329i	$-0.802142\pi$
$587$	4.53123	−	13.9457i	0.187024	−	0.575600i	0.999977	+	0.00672835i	$0.00214172\pi$
$588$		0			0
$589$	22.2379	+	16.1568i	0.916297	+	0.665729i
$590$	0.701535	−	2.15910i	0.0288818	−	0.0888889i
$591$		0			0
$592$	−59.3448	+	43.1165i	−2.43906	+	1.77208i
$593$	17.7060			0.727100			0.363550	−	0.931575i	$-0.381565\pi$
$593$	17.7060			0.727100			0.363550	+	0.931575i	$0.381565\pi$
$594$		0			0
$595$	−6.55039			−0.268540
$596$	−40.5777	+	29.4814i	−1.66213	+	1.20761i
$597$		0			0
$598$	−0.166737	+	0.513163i	−0.00681837	+	0.0209848i
$599$	−16.4173	−	11.9279i	−0.670795	−	0.487361i	0.199496	−	0.979899i	$-0.436069\pi$
$599$	−16.4173	−	11.9279i	−0.670795	−	0.487361i	−0.870291	+	0.492538i	$0.836069\pi$
$600$		0			0
$601$	−3.38302	+	10.4119i	−0.137996	+	0.424709i	−0.996044	−	0.0888608i	$-0.971677\pi$
$601$	−3.38302	+	10.4119i	−0.137996	+	0.424709i	0.858048	+	0.513570i	$0.171677\pi$
$602$	−4.94758	−	15.2271i	−0.201648	−	0.620610i
$603$		0			0
$604$	13.2827			0.540467
$605$	−10.2617	−	7.77466i	−0.417197	−	0.316085i
$606$		0			0
$607$	27.4651	−	19.9545i	1.11477	−	0.809929i	0.131364	−	0.991334i	$-0.458064\pi$
$607$	27.4651	−	19.9545i	1.11477	−	0.809929i	0.983409	+	0.181405i	$0.0580644\pi$
$608$	−22.2068	−	68.3454i	−0.900603	−	2.77177i
$609$		0			0
$610$	−22.4851	−	16.3364i	−0.910396	−	0.661442i
$611$	17.1271	+	12.4435i	0.692887	+	0.503412i
$612$		0			0
$613$	2.30828	+	7.10415i	0.0932305	+	0.286934i	0.986788	−	0.162014i	$-0.0517989\pi$
$613$	2.30828	+	7.10415i	0.0932305	+	0.286934i	−0.893558	+	0.448948i	$0.851799\pi$
$614$	−21.7303	+	15.7880i	−0.876962	+	0.637150i
$615$		0			0
$616$	28.3345	+	0.284118i	1.14163	+	0.0114474i
$617$	−29.3727			−1.18250			−0.591250	−	0.806489i	$-0.701365\pi$
$617$	−29.3727			−1.18250			−0.591250	+	0.806489i	$0.701365\pi$
$618$		0			0
$619$	11.1661	+	34.3658i	0.448805	+	1.38128i	0.878257	+	0.478189i	$0.158707\pi$
$619$	11.1661	+	34.3658i	0.448805	+	1.38128i	−0.429452	+	0.903090i	$0.641293\pi$
$620$	−11.8428	+	36.4484i	−0.475618	+	1.46380i
$621$		0			0
$622$	35.4269	+	25.7391i	1.42049	+	1.03204i
$623$	−3.72740	+	11.4718i	−0.149335	+	0.459607i
$624$		0			0
$625$	−5.12039	+	3.72018i	−0.204816	+	0.148807i
$626$	−11.9849			−0.479014
$627$		0			0
$628$	96.0055			3.83104
$629$	26.5069	−	19.2584i	1.05690	−	0.767884i
$630$		0			0
$631$	12.0937	−	37.2206i	0.481442	−	1.48173i	−0.355626	−	0.934628i	$-0.615732\pi$
$631$	12.0937	−	37.2206i	0.481442	−	1.48173i	0.837068	−	0.547099i	$-0.184268\pi$
$632$	100.058	+	72.6964i	3.98010	+	2.89171i
$633$		0			0
$634$	9.92308	−	30.5401i	0.394096	−	1.21290i
$635$	6.23445	+	19.1877i	0.247407	+	0.761440i
$636$		0			0
$637$	−1.68268			−0.0666704
$638$	−11.7050	−	37.2925i	−0.463405	−	1.47642i
$639$		0			0
$640$	17.4446	−	12.6743i	0.689559	−	0.500994i
$641$	−8.60878	−	26.4951i	−0.340026	−	1.04649i	−0.964193	−	0.265202i	$-0.914561\pi$
$641$	−8.60878	−	26.4951i	−0.340026	−	1.04649i	0.624167	−	0.781291i	$-0.285439\pi$
$642$		0			0
$643$	−10.6319	−	7.72449i	−0.419279	−	0.304624i	0.358068	−	0.933695i	$-0.383435\pi$
$643$	−10.6319	−	7.72449i	−0.419279	−	0.304624i	−0.777348	+	0.629071i	$0.783435\pi$
$644$	0.501928	+	0.364672i	0.0197787	+	0.0143701i
$645$		0			0
$646$	20.1880	+	62.1324i	0.794287	+	2.44457i
$647$	2.72318	−	1.97851i	0.107059	−	0.0777831i	−0.532968	−	0.846136i	$-0.678923\pi$
$647$	2.72318	−	1.97851i	0.107059	−	0.0777831i	0.640027	+	0.768353i	$0.278923\pi$
$648$		0			0
$649$	0.764402	−	2.27472i	0.0300054	−	0.0892907i
$650$	−16.3758			−0.642312
$651$		0			0
$652$	10.3836	+	31.9574i	0.406653	+	1.25155i
$653$	−7.68828	+	23.6621i	−0.300866	+	0.925970i	0.680322	+	0.732913i	$0.261840\pi$
$653$	−7.68828	+	23.6621i	−0.300866	+	0.925970i	−0.981188	+	0.193056i	$0.938160\pi$
$654$		0			0
$655$	0.306844	+	0.222935i	0.0119894	+	0.00871080i
$656$	−42.6565	+	131.283i	−1.66546	+	5.12575i
$657$		0			0
$658$	27.2867	−	19.8250i	1.06375	−	0.772858i
$659$	30.5058			1.18834			0.594169	−	0.804340i	$-0.297481\pi$
$659$	30.5058			1.18834			0.594169	+	0.804340i	$0.297481\pi$
$660$		0			0
$661$	10.2042			0.396899			0.198449	−	0.980111i	$-0.436409\pi$
$661$	10.2042			0.396899			0.198449	+	0.980111i	$0.436409\pi$
$662$	−39.2286	+	28.5012i	−1.52466	+	1.10773i
$663$		0			0
$664$	9.13299	−	28.1085i	0.354429	−	1.09082i
$665$	−4.12281	−	2.99540i	−0.159876	−	0.116156i
$666$		0			0
$667$	0.162485	−	0.500078i	0.00629146	−	0.0193631i
$668$	40.4826	+	124.593i	1.56632	+	4.82063i
$669$		0			0
$670$	−27.5717			−1.06519
$671$	−23.5935	−	17.5058i	−0.910816	−	0.675803i
$672$		0			0
$673$	39.4150	−	28.6367i	1.51934	−	1.10386i	0.557520	−	0.830163i	$-0.311753\pi$
$673$	39.4150	−	28.6367i	1.51934	−	1.10386i	0.961815	−	0.273699i	$-0.0882471\pi$
$674$	−15.8112	−	48.6619i	−0.609025	−	1.87439i
$675$		0			0
$676$	42.6704	+	31.0018i	1.64117	+	1.19238i
$677$	−12.9476	−	9.40696i	−0.497616	−	0.361539i	0.310490	−	0.950577i	$-0.399507\pi$
$677$	−12.9476	−	9.40696i	−0.497616	−	0.361539i	−0.808106	+	0.589038i	$0.799507\pi$
$678$		0			0
$679$	−1.85279	−	5.70230i	−0.0711035	−	0.218834i
$680$	−45.2758	+	32.8948i	−1.73625	+	1.26146i
$681$		0			0
$682$	−17.8797	+	53.2067i	−0.684649	+	2.03739i
$683$	−26.6991			−1.02161			−0.510805	−	0.859696i	$-0.670653\pi$
$683$	−26.6991			−1.02161			−0.510805	+	0.859696i	$0.670653\pi$
$684$		0			0
$685$	3.75146	+	11.5458i	0.143336	+	0.441142i
$686$	−0.828426	+	2.54963i	−0.0316294	+	0.0973454i
$687$		0			0
$688$	−60.5419	−	43.9863i	−2.30814	−	1.67696i
$689$	−0.216833	+	0.667344i	−0.00826069	+	0.0254238i
$690$		0			0
$691$	−12.7417	+	9.25738i	−0.484717	+	0.352167i	−0.803149	−	0.595778i	$-0.796844\pi$
$691$	−12.7417	+	9.25738i	−0.484717	+	0.352167i	0.318432	+	0.947946i	$0.396844\pi$
$692$	48.0725			1.82744
$693$		0			0
$694$	−14.2558			−0.541143
$695$	−12.6668	+	9.20296i	−0.480479	+	0.349088i
$696$		0			0
$697$	19.0529	−	58.6389i	0.721682	−	2.22111i
$698$	−44.7351	−	32.5019i	−1.69325	−	1.23022i
$699$		0			0
$700$	−5.81862	+	17.9079i	−0.219923	+	0.676854i
$701$	9.94164	+	30.5972i	0.375491	+	1.15564i	0.943147	+	0.332376i	$0.107850\pi$
$701$	9.94164	+	30.5972i	0.375491	+	1.15564i	−0.567656	+	0.823266i	$0.692150\pi$
$702$		0			0
$703$	25.4900			0.961374
$704$	51.8500	−	36.8826i	1.95417	−	1.39007i
$705$		0			0
$706$	−15.8704	+	11.5305i	−0.597291	+	0.433957i
$707$	0.0313999	+	0.0966390i	0.00118092	+	0.00363448i
$708$		0			0
$709$	2.85455	+	2.07396i	0.107205	+	0.0778890i	0.640096	−	0.768295i	$-0.278894\pi$
$709$	2.85455	+	2.07396i	0.107205	+	0.0778890i	−0.532891	+	0.846184i	$0.678894\pi$
$710$	8.15553	+	5.92534i	0.306072	+	0.222374i
$711$		0			0
$712$	31.8455	+	98.0103i	1.19346	+	3.67309i
$713$	−0.610892	+	0.443839i	−0.0228781	+	0.0166219i
$714$		0			0
$715$	6.53143	+	0.0654924i	0.244262	+	0.00244928i
$716$	80.1055			2.99368
$717$		0			0
$718$	20.0719	+	61.7750i	0.749077	+	2.30542i
$719$	−11.4690	+	35.2980i	−0.427722	+	1.31639i	0.472641	+	0.881255i	$0.343301\pi$
$719$	−11.4690	+	35.2980i	−0.427722	+	1.31639i	−0.900363	+	0.435139i	$0.856699\pi$
$720$		0			0
$721$	1.40761	+	1.02269i	0.0524221	+	0.0380869i
$722$	0.0342128	−	0.105296i	0.00127327	−	0.00391872i
$723$		0			0
$724$	−44.1947	+	32.1093i	−1.64248	+	1.19333i
$725$	15.9582			0.592674
$726$		0			0
$727$	−7.85215			−0.291220			−0.145610	−	0.989342i	$-0.546514\pi$
$727$	−7.85215			−0.291220			−0.145610	+	0.989342i	$0.546514\pi$
$728$	−11.6306	+	8.45012i	−0.431058	+	0.313182i
$729$		0			0
$730$	14.1453	−	43.5348i	0.523542	−	1.61130i
$731$	27.0416	+	19.6469i	1.00017	+	0.726667i
$732$		0			0
$733$	−8.99114	+	27.6719i	−0.332096	+	1.02208i	0.636040	+	0.771656i	$0.280571\pi$
$733$	−8.99114	+	27.6719i	−0.332096	+	1.02208i	−0.968135	+	0.250428i	$0.919429\pi$
$734$	18.6444	+	57.3817i	0.688179	+	2.11800i
$735$		0			0
$736$	1.97412			0.0727671
$737$	−29.1431	−	0.292226i	−1.07350	−	0.0107643i
$738$		0			0
$739$	5.81344	−	4.22371i	0.213851	−	0.155372i	−0.475704	−	0.879606i	$-0.657806\pi$
$739$	5.81344	−	4.22371i	0.213851	−	0.155372i	0.689554	+	0.724234i	$0.257806\pi$
$740$	10.9822	+	33.7997i	0.403713	+	1.24250i
$741$		0			0
$742$	0.904419	+	0.657099i	0.0332023	+	0.0241228i
$743$	8.59339	+	6.24346i	0.315261	+	0.229050i	0.734151	−	0.678987i	$-0.237581\pi$
$743$	8.59339	+	6.24346i	0.315261	+	0.229050i	−0.418890	+	0.908037i	$0.637581\pi$
$744$		0			0
$745$	3.49732	+	10.7636i	0.128132	+	0.394349i
$746$	13.5616	−	9.85307i	0.496525	−	0.360746i
$747$		0			0
$748$	−78.4566	+	55.8088i	−2.86866	+	2.04057i
$749$	11.0032			0.402049
$750$		0			0
$751$	4.94567	+	15.2212i	0.180470	+	0.555430i	0.999841	−	0.0178338i	$-0.00567699\pi$
$751$	4.94567	+	15.2212i	0.180470	+	0.555430i	−0.819371	+	0.573264i	$0.805677\pi$
$752$	48.7152	−	149.930i	1.77646	−	5.46738i
$753$		0			0
$754$	16.0431	+	11.6560i	0.584255	+	0.424486i
$755$	0.926173	−	2.85047i	0.0337069	−	0.103739i
$756$		0			0
$757$	6.96721	−	5.06197i	0.253228	−	0.183981i	−0.453928	−	0.891038i	$-0.649978\pi$
$757$	6.96721	−	5.06197i	0.253228	−	0.183981i	0.707156	+	0.707058i	$0.249978\pi$
$758$	−34.3664			−1.24824
$759$		0			0
$760$	−43.5388			−1.57932
$761$	12.5649	−	9.12892i	0.455477	−	0.330923i	−0.336278	−	0.941763i	$-0.609168\pi$
$761$	12.5649	−	9.12892i	0.455477	−	0.330923i	0.791754	+	0.610840i	$0.209168\pi$
$762$		0			0
$763$	5.10002	−	15.6963i	0.184633	−	0.568243i
$764$	−28.8007	−	20.9250i	−1.04197	−	0.757038i
$765$		0			0
$766$	5.35773	−	16.4894i	0.193583	−	0.595786i
$767$	0.376227	+	1.15791i	0.0135848	+	0.0418096i
$768$		0			0
$769$	51.4797			1.85640			0.928202	−	0.372076i	$-0.121354\pi$
$769$	51.4797			1.85640			0.928202	+	0.372076i	$0.121354\pi$
$770$	3.31481	−	9.86429i	0.119458	−	0.355484i
$771$		0			0
$772$	−93.7021	+	68.0785i	−3.37241	+	2.45020i
$773$	6.24454	+	19.2187i	0.224601	+	0.691249i	0.998332	+	0.0577356i	$0.0183880\pi$
$773$	6.24454	+	19.2187i	0.224601	+	0.691249i	−0.773731	+	0.633514i	$0.781612\pi$
$774$		0			0
$775$	−18.5404	−	13.4704i	−0.665989	−	0.483870i
$776$	−41.4422	−	30.1095i	−1.48769	−	1.08087i
$777$		0			0
$778$	−12.3408	−	37.9812i	−0.442441	−	1.36169i
$779$	38.8066	−	28.1946i	1.39039	−	1.01018i
$780$		0			0
$781$	8.55753	+	6.34948i	0.306213	+	0.227202i
$782$	−1.79466			−0.0641769
$783$		0			0
$784$	3.87206	+	11.9170i	0.138288	+	0.425606i
$785$	6.69423	−	20.6027i	0.238927	−	0.735343i
$786$		0			0
$787$	−40.0730	−	29.1148i	−1.42845	−	1.03783i	−0.990303	−	0.138926i	$-0.955635\pi$
$787$	−40.0730	−	29.1148i	−1.42845	−	1.03783i	−0.438147	−	0.898903i	$-0.644365\pi$
$788$	−7.13591	+	21.9621i	−0.254206	+	0.782366i
$789$		0			0
$790$	36.7463	−	26.6977i	1.30737	−	0.949862i
$791$	−6.28108			−0.223330
$792$		0			0
$793$	14.9052			0.529299
$794$	4.03106	−	2.92873i	0.143057	−	0.103937i
$795$		0			0
$796$	−24.2018	+	74.4855i	−0.857810	+	2.64007i
$797$	−21.5700	−	15.6715i	−0.764047	−	0.555113i	0.136102	−	0.990695i	$-0.456543\pi$
$797$	−21.5700	−	15.6715i	−0.764047	−	0.555113i	−0.900149	+	0.435582i	$0.856543\pi$
$798$		0			0
$799$	−21.7591	+	66.9677i	−0.769782	+	2.36915i
$800$	18.5144	+	56.9815i	0.654583	+	2.01460i
$801$		0			0
$802$	−23.4372			−0.827597
$803$	15.4129	−	45.8661i	0.543910	−	1.61858i
$804$		0			0
$805$	0.113257	−	0.0822858i	0.00399178	−	0.00290019i
$806$	−8.80011	−	27.0840i	−0.309971	−	0.953992i
$807$		0			0
$808$	0.702336	+	0.510277i	0.0247081	+	0.0179515i
$809$	41.4858	+	30.1412i	1.45856	+	1.05971i	0.983734	+	0.179631i	$0.0574904\pi$
$809$	41.4858	+	30.1412i	1.45856	+	1.05971i	0.474830	+	0.880078i	$0.342510\pi$
$810$		0			0
$811$	8.32308	+	25.6158i	0.292263	+	0.899493i	0.984127	+	0.177465i	$0.0567896\pi$
$811$	8.32308	+	25.6158i	0.292263	+	0.899493i	−0.691864	+	0.722028i	$0.743210\pi$
$812$	18.4469	−	13.4024i	0.647359	−	0.470334i
$813$		0			0
$814$	15.5876	+	49.6627i	0.546346	+	1.74068i
$815$	7.58207			0.265588
$816$		0			0
$817$	8.03574	+	24.7315i	0.281135	+	0.865245i
$818$	−10.5374	+	32.4307i	−0.368431	+	1.13391i
$819$		0			0
$820$	54.1055	+	39.3099i	1.88945	+	1.37276i
$821$	11.2244	−	34.5451i	0.391734	−	1.20563i	−0.539742	−	0.841831i	$-0.681478\pi$
$821$	11.2244	−	34.5451i	0.391734	−	1.20563i	0.931476	−	0.363803i	$-0.118522\pi$
$822$		0			0
$823$	9.26651	−	6.73251i	0.323010	−	0.234681i	−0.414449	−	0.910073i	$-0.636026\pi$
$823$	9.26651	−	6.73251i	0.323010	−	0.234681i	0.737459	+	0.675392i	$0.236026\pi$
$824$	14.8650			0.517848
$825$		0			0
$826$	1.93971			0.0674910
$827$	−15.2696	+	11.0940i	−0.530978	+	0.385778i	−0.820723	−	0.571326i	$-0.806429\pi$
$827$	−15.2696	+	11.0940i	−0.530978	+	0.385778i	0.289746	+	0.957104i	$0.406429\pi$
$828$		0			0
$829$	−3.71313	+	11.4278i	−0.128962	+	0.396906i	−0.994602	−	0.103762i	$-0.966912\pi$
$829$	−3.71313	+	11.4278i	−0.128962	+	0.396906i	0.865640	+	0.500667i	$0.166912\pi$
$830$	−8.78111	−	6.37985i	−0.304797	−	0.221448i
$831$		0			0
$832$	−9.97584	+	30.7025i	−0.345850	+	1.06442i
$833$	−1.72949	−	5.32283i	−0.0599233	−	0.184425i
$834$		0			0
$835$	29.5603			1.02297
$836$	−74.9010	−	0.751053i	−2.59051	−	0.0259757i
$837$		0			0
$838$	17.5652	−	12.7618i	0.606778	−	0.440850i
$839$	−1.65108	−	5.08151i	−0.0570017	−	0.175433i	0.918502	−	0.395416i	$-0.129400\pi$
$839$	−1.65108	−	5.08151i	−0.0570017	−	0.175433i	−0.975504	+	0.219983i	$0.929400\pi$
$840$		0			0
$841$	7.82747	+	5.68699i	0.269913	+	0.196103i
$842$	−57.4280	−	41.7239i	−1.97910	−	1.43790i
$843$		0			0
$844$	−36.6227	−	112.713i	−1.26060	−	3.87974i
$845$	9.62828	−	6.99536i	0.331223	−	0.240648i
$846$		0			0
$847$	3.60829	−	10.3914i	0.123982	−	0.357051i
$848$	5.22516			0.179433
$849$		0			0
$850$	−16.8313	−	51.8015i	−0.577310	−	1.77678i
$851$	−0.216383	+	0.665959i	−0.00741752	+	0.0228288i
$852$		0			0
$853$	−0.849803	−	0.617418i	−0.0290967	−	0.0211400i	0.573142	−	0.819456i	$-0.305724\pi$
$853$	−0.849803	−	0.617418i	−0.0290967	−	0.0211400i	−0.602239	+	0.798316i	$0.705724\pi$
$854$	7.33819	−	22.5846i	0.251108	−	0.772830i
$855$		0			0
$856$	76.0535	−	55.2561i	2.59946	−	1.88862i
$857$	−13.9506			−0.476542			−0.238271	−	0.971199i	$-0.576581\pi$
$857$	−13.9506			−0.476542			−0.238271	+	0.971199i	$0.576581\pi$
$858$		0			0
$859$	51.5493			1.75884			0.879419	−	0.476048i	$-0.157931\pi$
$859$	51.5493			1.75884			0.879419	+	0.476048i	$0.157931\pi$
$860$	−29.3317	+	21.3107i	−1.00020	+	0.726690i
$861$		0			0
$862$	−0.295289	+	0.908807i	−0.0100576	+	0.0309541i
$863$	−26.8508	−	19.5082i	−0.914012	−	0.664068i	0.0280145	−	0.999608i	$-0.491082\pi$
$863$	−26.8508	−	19.5082i	−0.914012	−	0.664068i	−0.942026	+	0.335539i	$0.891082\pi$
$864$		0			0
$865$	3.35198	−	10.3163i	0.113971	−	0.350766i
$866$	15.1506	+	46.6288i	0.514839	+	1.58451i
$867$		0			0
$868$	−32.7447			−1.11143
$869$	39.1235	−	27.8298i	1.32717	−	0.944063i
$870$		0			0
$871$	11.9625	−	8.69125i	0.405333	−	0.294492i
$872$	−43.5726	−	134.103i	−1.47555	−	4.54129i
$873$		0			0
$874$	−1.12956	−	0.820671i	−0.0382078	−	0.0277596i
$875$	8.17163	+	5.93704i	0.276252	+	0.200709i
$876$		0			0
$877$	−15.5244	−	47.7792i	−0.524221	−	1.61339i	−0.765850	−	0.643019i	$-0.777682\pi$
$877$	−15.5244	−	47.7792i	−0.524221	−	1.61339i	0.241629	−	0.970369i	$-0.422318\pi$
$878$	14.4799	−	10.5203i	0.488674	−	0.355042i
$879$		0			0
$880$	−14.5658	−	46.4070i	−0.491012	−	1.56438i
$881$	−38.9209			−1.31128			−0.655639	−	0.755074i	$-0.727601\pi$
$881$	−38.9209			−1.31128			−0.655639	+	0.755074i	$0.727601\pi$
$882$		0			0
$883$	−3.19938	−	9.84668i	−0.107668	−	0.331367i	0.882680	−	0.469975i	$-0.155737\pi$
$883$	−3.19938	−	9.84668i	−0.107668	−	0.331367i	−0.990347	+	0.138608i	$0.955737\pi$
$884$	15.0949	−	46.4573i	0.507696	−	1.56253i
$885$		0			0
$886$	44.3318	+	32.2089i	1.48936	+	1.08208i
$887$	7.61512	−	23.4369i	0.255691	−	0.786935i	−0.738002	−	0.674798i	$-0.764231\pi$
$887$	7.61512	−	23.4369i	0.255691	−	0.786935i	0.993693	−	0.112136i	$-0.0357694\pi$
$888$		0			0
$889$	−13.9458	+	10.1322i	−0.467726	+	0.339823i
$890$	37.8466			1.26862
$891$		0			0
$892$	50.3684			1.68646
$893$	−44.3185	+	32.1992i	−1.48306	+	1.07751i
$894$		0			0
$895$	5.58557	−	17.1906i	0.186705	−	0.574618i
$896$	14.9049	+	10.8291i	0.497939	+	0.361774i
$897$		0			0
$898$	4.56818	−	14.0594i	0.152442	−	0.469169i
$899$	8.57572	+	26.3934i	0.286016	+	0.880268i
$900$		0			0
$901$	−2.33387			−0.0777525
$902$	78.6631	+	58.3661i	2.61920	+	1.94338i
$903$		0			0
$904$	−43.4144	+	31.5424i	−1.44394	+	1.04908i
$905$	3.80906	+	11.7231i	0.126617	+	0.389688i
$906$		0			0
$907$	−34.8450	−	25.3164i	−1.15701	−	0.840617i	−0.167613	−	0.985853i	$-0.553606\pi$
$907$	−34.8450	−	25.3164i	−1.15701	−	0.840617i	−0.989397	+	0.145236i	$0.953606\pi$
$908$	−78.1240	−	56.7604i	−2.59264	−	1.88366i
$909$		0			0
$910$	1.63150	+	5.02125i	0.0540837	+	0.166453i
$911$	−36.7533	+	26.7028i	−1.21769	+	0.884704i	−0.995906	−	0.0903919i	$-0.971188\pi$
$911$	−36.7533	+	26.7028i	−1.21769	+	0.884704i	−0.221784	+	0.975096i	$0.571188\pi$
$912$		0			0
$913$	−9.21396	−	6.83653i	−0.304937	−	0.226256i
$914$	−5.36907			−0.177593
$915$		0			0
$916$	14.4941	+	44.6082i	0.478898	+	1.47390i
$917$	−0.100141	+	0.308202i	−0.00330694	+	0.0101777i
$918$		0			0
$919$	−13.5629	−	9.85403i	−0.447399	−	0.325054i	0.341169	−	0.940002i	$-0.389177\pi$
$919$	−13.5629	−	9.85403i	−0.447399	−	0.325054i	−0.788568	+	0.614948i	$0.789177\pi$
$920$	0.369598	−	1.13751i	0.0121853	−	0.0375025i
$921$		0			0
$922$	17.7289	−	12.8808i	0.583871	−	0.424207i
$923$	−5.40623			−0.177948
$924$		0			0
$925$	−21.2517			−0.698753
$926$	−9.25416	+	6.72354i	−0.304110	+	0.220949i
$927$		0			0
$928$	22.4201	−	69.0020i	0.735976	−	2.26510i
$929$	18.2505	+	13.2597i	0.598778	+	0.435038i	0.845445	−	0.534063i	$-0.179335\pi$
$929$	18.2505	+	13.2597i	0.598778	+	0.435038i	−0.246667	+	0.969100i	$0.579335\pi$
$930$		0			0
$931$	1.34551	−	4.14105i	0.0440973	−	0.135717i
$932$	−13.8216	−	42.5386i	−0.452743	−	1.39340i
$933$		0			0
$934$	108.611			3.55386
$935$	6.50595	+	20.7282i	0.212767	+	0.677883i
$936$		0			0
$937$	−6.11987	+	4.44635i	−0.199928	+	0.145256i	−0.683245	−	0.730189i	$-0.739432\pi$
$937$	−6.11987	+	4.44635i	−0.199928	+	0.145256i	0.483317	+	0.875445i	$0.339432\pi$
$938$	−7.27972	−	22.4047i	−0.237691	−	0.731538i
$939$		0			0
$940$	−61.7903	−	44.8933i	−2.01538	−	1.46426i
$941$	−39.4471	−	28.6600i	−1.28594	−	0.934289i	−0.286223	−	0.958163i	$-0.592400\pi$
$941$	−39.4471	−	28.6600i	−1.28594	−	0.934289i	−0.999715	+	0.0238740i	$0.992400\pi$
$942$		0			0
$943$	0.407194	+	1.25321i	0.0132600	+	0.0408102i
$944$	7.33469	−	5.32896i	0.238724	−	0.173443i
$945$		0			0
$946$	−43.2708	+	30.7800i	−1.40686	+	1.00074i
$947$	14.4056			0.468119			0.234060	−	0.972222i	$-0.424799\pi$
$947$	14.4056			0.468119			0.234060	+	0.972222i	$0.424799\pi$
$948$		0			0
$949$	7.58601	+	23.3473i	0.246252	+	0.757886i
$950$	13.0944	−	40.3005i	0.424839	−	1.30752i
$951$		0			0
$952$	−38.6843	−	28.1058i	−1.25377	−	0.910915i
$953$	9.72527	−	29.9313i	0.315032	−	0.969570i	−0.660709	−	0.750642i	$-0.729744\pi$
$953$	9.72527	−	29.9313i	0.315032	−	0.969570i	0.975741	−	0.218927i	$-0.0702558\pi$
$954$		0			0
$955$	−6.49869	+	4.72157i	−0.210293	+	0.152787i
$956$	107.302			3.47039
$957$		0			0
$958$	22.0924			0.713772
$959$	−8.39158	+	6.09684i	−0.270978	+	0.196877i
$960$		0			0
$961$	2.73581	−	8.41994i	0.0882518	−	0.271611i
$962$	−21.3647	−	15.5224i	−0.688827	−	0.500462i
$963$		0			0
$964$	−39.8170	+	122.544i	−1.28242	+	3.94688i
$965$	8.07600	+	24.8554i	0.259976	+	0.800123i
$966$		0			0
$967$	19.1109			0.614566			0.307283	−	0.951618i	$-0.400580\pi$
$967$	19.1109			0.614566			0.307283	+	0.951618i	$0.400580\pi$
$968$	−27.2432	−	89.9444i	−0.875629	−	2.89092i
$969$		0			0
$970$	−15.2196	+	11.0577i	−0.488672	+	0.355041i
$971$	13.2200	+	40.6871i	0.424251	+	1.30571i	0.903709	+	0.428146i	$0.140833\pi$
$971$	13.2200	+	40.6871i	0.424251	+	1.30571i	−0.479458	+	0.877565i	$0.659167\pi$
$972$		0			0
$973$	−10.8227	−	7.86315i	−0.346960	−	0.252081i
$974$	−2.09268	−	1.52042i	−0.0670539	−	0.0487175i
$975$		0			0
$976$	−34.2986	−	105.560i	−1.09787	−	3.37890i
$977$	32.5446	−	23.6450i	1.04119	−	0.756471i	0.0706755	−	0.997499i	$-0.477485\pi$
$977$	32.5446	−	23.6450i	1.04119	−	0.756471i	0.970518	+	0.241028i	$0.0774845\pi$
$978$		0			0
$979$	40.0035	+	0.401126i	1.27852	+	0.0128201i
$980$	6.07072			0.193922
$981$		0			0
$982$	−25.2077	−	77.5812i	−0.804409	−	2.47572i
$983$	7.40278	−	22.7834i	0.236112	−	0.726678i	−0.760860	−	0.648916i	$-0.775223\pi$
$983$	7.40278	−	22.7834i	0.236112	−	0.726678i	0.996972	−	0.0777617i	$-0.0247773\pi$
$984$		0			0
$985$	4.21548	+	3.06272i	0.134316	+	0.0975865i
$986$	−20.3820	+	62.7293i	−0.649094	+	1.99771i
$987$		0			0
$988$	30.7449	−	22.3375i	0.978127	−	0.710651i
$989$	−0.714356			−0.0227152
$990$		0			0
$991$	−19.7275			−0.626665			−0.313332	−	0.949644i	$-0.601445\pi$
$991$	−19.7275			−0.626665			−0.313332	+	0.949644i	$0.601445\pi$
$992$	−84.2924	+	61.2420i	−2.67629	+	1.94444i
$993$		0			0
$994$	−2.66162	+	8.19161i	−0.0844214	+	0.259822i
$995$	14.2970	+	10.3874i	0.453246	+	0.329302i
$996$		0			0
$997$	0.589757	−	1.81509i	0.0186778	−	0.0574843i	−0.941283	−	0.337618i	$-0.890379\pi$
$997$	0.589757	−	1.81509i	0.0186778	−	0.0574843i	0.959961	+	0.280134i	$0.0903788\pi$
$998$	31.1149	+	95.7617i	0.984924	+	3.03128i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.190.8	yes	32
3.2	odd	2	inner	693.2.m.k.190.1	✓	32
11.2	odd	10		7623.2.a.db.1.16		16
11.4	even	5	inner	693.2.m.k.631.8	yes	32
11.9	even	5		7623.2.a.dc.1.1		16
33.2	even	10		7623.2.a.db.1.1		16
33.20	odd	10		7623.2.a.dc.1.16		16
33.26	odd	10	inner	693.2.m.k.631.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.190.1	✓	32	3.2	odd	2	inner
693.2.m.k.190.8	yes	32	1.1	even	1	trivial
693.2.m.k.631.1	yes	32	33.26	odd	10	inner
693.2.m.k.631.8	yes	32	11.4	even	5	inner
7623.2.a.db.1.1		16	33.2	even	10
7623.2.a.db.1.16		16	11.2	odd	10
7623.2.a.dc.1.1		16	11.9	even	5
7623.2.a.dc.1.16		16	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16885 - 1.57576i) q^{2} +(1.60284 - 4.93305i) q^{4} +(-0.946867 - 0.687939i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-2.64012 - 8.12545i) q^{8} -3.13763 q^{10} +(-3.31646 - 0.0332550i) q^{11} +(1.36132 - 0.989057i) q^{13} +(-0.828426 - 2.54963i) q^{14} +(-10.1372 - 7.36509i) q^{16} +(4.52787 + 3.28969i) q^{17} +(1.34551 + 4.14105i) q^{19} +(-4.91131 + 3.56828i) q^{20} +(-7.24529 + 5.15381i) q^{22} -0.119612 q^{23} +(-1.12179 - 3.45251i) q^{25} +(1.39398 - 4.29023i) q^{26} +(-4.19630 - 3.04879i) q^{28} +(-1.35844 + 4.18083i) q^{29} +(5.10728 - 3.71065i) q^{31} -16.5044 q^{32} +15.0040 q^{34} +(-0.946867 + 0.687939i) q^{35} +(1.80904 - 5.56765i) q^{37} +(9.44350 + 6.86111i) q^{38} +(-3.08997 + 9.50996i) q^{40} +(-3.40428 - 10.4773i) q^{41} +5.97227 q^{43} +(-5.47981 + 16.3069i) q^{44} +(-0.259420 + 0.188480i) q^{46} +(3.88781 + 11.9654i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-7.87331 - 5.72029i) q^{50} +(-2.69708 - 8.30076i) q^{52} +(-0.337364 + 0.245109i) q^{53} +(3.11737 + 2.31301i) q^{55} -8.54361 q^{56} +(3.64175 + 11.2082i) q^{58} +(-0.223587 + 0.688131i) q^{59} +(7.16627 + 5.20660i) q^{61} +(5.22980 - 16.0957i) q^{62} +(-15.5211 + 11.2767i) q^{64} -1.96940 q^{65} +8.78741 q^{67} +(23.4857 - 17.0633i) q^{68} +(-0.969582 + 2.98407i) q^{70} +(-2.59926 - 1.88847i) q^{71} +(-4.50828 + 13.8750i) q^{73} +(-4.84975 - 14.9260i) q^{74} +22.5846 q^{76} +(-1.05647 + 3.14386i) q^{77} +(-11.7115 + 8.50887i) q^{79} +(4.53182 + 13.9475i) q^{80} +(-23.8931 - 17.3593i) q^{82} +(2.79864 + 2.03333i) q^{83} +(-2.02418 - 6.22979i) q^{85} +(12.9529 - 9.41086i) q^{86} +(8.48564 + 27.0355i) q^{88} -12.0621 q^{89} +(-0.519978 - 1.60033i) q^{91} +(-0.191720 + 0.590052i) q^{92} +(27.2867 + 19.8250i) q^{94} +(1.57477 - 4.84665i) q^{95} +(4.85066 - 3.52421i) q^{97} -2.68084 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52}+ \cdots - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Introduction

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