LMFDB - Embedded newform 740.2.cc.a.17.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(17,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.cc (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.19
Character	$\chi$	$=$	740.17
Dual form			740.2.cc.a.653.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.52279 - 1.76647i) q^{3} +(2.17830 + 0.504970i) q^{5} +(-0.140686 - 1.60805i) q^{7} +(2.21796 - 6.09379i) q^{9} +(-1.80657 + 1.04302i) q^{11} +(-1.69802 + 0.618029i) q^{13} +(6.38741 - 2.57398i) q^{15} +(0.325312 - 0.893787i) q^{17} +(-0.202887 - 0.289753i) q^{19} +(-3.19550 - 3.80824i) q^{21} +(-0.668708 + 1.15824i) q^{23} +(4.49001 + 2.19996i) q^{25} +(-2.77779 - 10.3669i) q^{27} +(0.409932 - 1.52989i) q^{29} +(-2.13006 + 2.13006i) q^{31} +(-2.71512 + 5.82259i) q^{33} +(0.505559 - 3.57386i) q^{35} +(-0.390265 + 6.07023i) q^{37} +(-3.19201 + 4.55867i) q^{39} +(2.41886 + 6.64576i) q^{41} +7.94783 q^{43} +(7.90857 - 12.1541i) q^{45} +(-11.5088 + 3.08377i) q^{47} +(4.32763 - 0.763078i) q^{49} +(-0.758159 - 2.82949i) q^{51} +(-0.888838 + 10.1595i) q^{53} +(-4.46196 + 1.35976i) q^{55} +(-1.02368 - 0.372590i) q^{57} +(-0.173318 + 1.98104i) q^{59} +(6.43041 - 13.7901i) q^{61} +(-10.1111 - 2.70927i) q^{63} +(-4.01089 + 0.488805i) q^{65} +(-8.77728 + 0.767912i) q^{67} +(0.358987 + 4.10324i) q^{69} +(0.779820 - 4.42258i) q^{71} +(-0.726701 - 0.726701i) q^{73} +(15.2135 - 2.38147i) q^{75} +(1.93139 + 2.75831i) q^{77} +(-6.95588 + 0.608561i) q^{79} +(-10.4174 - 8.74128i) q^{81} +(4.84469 - 2.25912i) q^{83} +(1.15996 - 1.78267i) q^{85} +(-1.66833 - 4.58371i) q^{87} +(1.35807 + 0.118816i) q^{89} +(1.23271 + 2.64355i) q^{91} +(-1.61099 + 9.13638i) q^{93} +(-0.295633 - 0.733622i) q^{95} +(-11.8848 - 6.86169i) q^{97} +(2.34907 + 13.3223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) $ 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.52279	−	1.76647i	1.45653	−	1.01987i	0.465674	−	0.884956i	$-0.345812\pi$
$3$	2.52279	−	1.76647i	1.45653	−	1.01987i	0.990857	−	0.134918i	$-0.0430771\pi$
$4$		0			0
$5$	2.17830	+	0.504970i	0.974167	+	0.225829i
$5$	2.17830	+	0.504970i	0.974167	+	0.225829i
$6$		0			0
$7$	−0.140686	−	1.60805i	−0.0531743	−	0.607785i	−0.975298	−	0.220891i	$-0.929103\pi$
$7$	−0.140686	−	1.60805i	−0.0531743	−	0.607785i	0.922124	−	0.386894i	$-0.126452\pi$
$8$		0			0
$9$	2.21796	−	6.09379i	0.739320	−	2.03126i
$10$		0			0
$11$	−1.80657	+	1.04302i	−0.544702	+	0.314484i	−0.746982	−	0.664844i	$-0.768498\pi$
$11$	−1.80657	+	1.04302i	−0.544702	+	0.314484i	0.202281	+	0.979328i	$0.435165\pi$
$12$		0			0
$13$	−1.69802	+	0.618029i	−0.470946	+	0.171410i	−0.566581	−	0.824006i	$-0.691734\pi$
$13$	−1.69802	+	0.618029i	−0.470946	+	0.171410i	0.0956346	+	0.995417i	$0.469512\pi$
$14$		0			0
$15$	6.38741	−	2.57398i	1.64922	−	0.664600i
$16$		0			0
$17$	0.325312	−	0.893787i	0.0788997	−	0.216775i	−0.893971	−	0.448125i	$-0.852092\pi$
$17$	0.325312	−	0.893787i	0.0788997	−	0.216775i	0.972871	+	0.231350i	$0.0743142\pi$
$18$		0			0
$19$	−0.202887	−	0.289753i	−0.0465455	−	0.0664739i	0.795205	−	0.606341i	$-0.207363\pi$
$19$	−0.202887	−	0.289753i	−0.0465455	−	0.0664739i	−0.841750	+	0.539867i	$0.818474\pi$
$20$		0			0
$21$	−3.19550	−	3.80824i	−0.697314	−	0.831027i
$22$		0			0
$23$	−0.668708	+	1.15824i	−0.139435	+	0.241509i	−0.927283	−	0.374361i	$-0.877862\pi$
$23$	−0.668708	+	1.15824i	−0.139435	+	0.241509i	0.787848	+	0.615870i	$0.211195\pi$
$24$		0			0
$25$	4.49001	+	2.19996i	0.898002	+	0.439991i
$26$		0			0
$27$	−2.77779	−	10.3669i	−0.534586	−	1.99510i
$28$		0			0
$29$	0.409932	−	1.52989i	0.0761224	−	0.284093i	−0.917363	−	0.398052i	$-0.869687\pi$
$29$	0.409932	−	1.52989i	0.0761224	−	0.284093i	0.993485	+	0.113959i	$0.0363532\pi$
$30$		0			0
$31$	−2.13006	+	2.13006i	−0.382570	+	0.382570i	−0.872027	−	0.489457i	$-0.837195\pi$
$31$	−2.13006	+	2.13006i	−0.382570	+	0.382570i	0.489457	+	0.872027i	$0.337195\pi$
$32$		0			0
$33$	−2.71512	+	5.82259i	−0.472641	+	1.01358i
$34$		0			0
$35$	0.505559	−	3.57386i	0.0854551	−	0.604092i
$36$		0			0
$37$	−0.390265	+	6.07023i	−0.0641591	+	0.997940i
$37$	−0.390265	+	6.07023i	−0.0641591	+	0.997940i
$38$		0			0
$39$	−3.19201	+	4.55867i	−0.511131	+	0.729971i
$40$		0			0
$41$	2.41886	+	6.64576i	0.377762	+	1.03789i	0.972282	+	0.233812i	$0.0751199\pi$
$41$	2.41886	+	6.64576i	0.377762	+	1.03789i	−0.594520	+	0.804081i	$0.702658\pi$
$42$		0			0
$43$	7.94783			1.21203			0.606016	−	0.795452i	$-0.292767\pi$
$43$	7.94783			1.21203			0.606016	+	0.795452i	$0.292767\pi$
$44$		0			0
$45$	7.90857	−	12.1541i	1.17894	−	1.81183i
$46$		0			0
$47$	−11.5088	+	3.08377i	−1.67873	+	0.449814i	−0.967443	−	0.253088i	$-0.918554\pi$
$47$	−11.5088	+	3.08377i	−1.67873	+	0.449814i	−0.711287	+	0.702902i	$0.751887\pi$
$48$		0			0
$49$	4.32763	−	0.763078i	0.618233	−	0.109011i
$50$		0			0
$51$	−0.758159	−	2.82949i	−0.106163	−	0.396208i
$52$		0			0
$53$	−0.888838	+	10.1595i	−0.122091	+	1.39551i	0.649969	+	0.759961i	$0.274782\pi$
$53$	−0.888838	+	10.1595i	−0.122091	+	1.39551i	−0.772060	+	0.635550i	$0.780774\pi$
$54$		0			0
$55$	−4.46196	+	1.35976i	−0.601650	+	0.183350i
$56$		0			0
$57$	−1.02368	−	0.372590i	−0.135590	−	0.0493507i
$58$		0			0
$59$	−0.173318	+	1.98104i	−0.0225641	+	0.257909i	0.976531	+	0.215377i	$0.0690980\pi$
$59$	−0.173318	+	1.98104i	−0.0225641	+	0.257909i	−0.999095	+	0.0425321i	$0.986458\pi$
$60$		0			0
$61$	6.43041	−	13.7901i	0.823330	−	1.76564i	0.206662	−	0.978412i	$-0.433740\pi$
$61$	6.43041	−	13.7901i	0.823330	−	1.76564i	0.616668	−	0.787224i	$-0.288482\pi$
$62$		0			0
$63$	−10.1111	−	2.70927i	−1.27388	−	0.341336i
$64$		0			0
$65$	−4.01089	+	0.488805i	−0.497490	+	0.0606288i
$66$		0			0
$67$	−8.77728	+	0.767912i	−1.07231	+	0.0938154i	−0.609613	−	0.792699i	$-0.708675\pi$
$67$	−8.77728	+	0.767912i	−1.07231	+	0.0938154i	−0.462701	+	0.886514i	$0.653120\pi$
$68$		0			0
$69$	0.358987	+	4.10324i	0.0432169	+	0.493972i
$70$		0			0
$71$	0.779820	−	4.42258i	0.0925477	−	0.524864i	−0.902924	−	0.429801i	$-0.858584\pi$
$71$	0.779820	−	4.42258i	0.0925477	−	0.524864i	0.995471	−	0.0950628i	$-0.0303052\pi$
$72$		0			0
$73$	−0.726701	−	0.726701i	−0.0850539	−	0.0850539i	0.663300	−	0.748354i	$-0.269155\pi$
$73$	−0.726701	−	0.726701i	−0.0850539	−	0.0850539i	−0.748354	+	0.663300i	$0.769155\pi$
$74$		0			0
$75$	15.2135	−	2.38147i	1.75670	−	0.274988i
$76$		0			0
$77$	1.93139	+	2.75831i	0.220103	+	0.314339i
$78$		0			0
$79$	−6.95588	+	0.608561i	−0.782598	+	0.0684684i	−0.471450	−	0.881893i	$-0.656269\pi$
$79$	−6.95588	+	0.608561i	−0.782598	+	0.0684684i	−0.311148	+	0.950361i	$0.600714\pi$
$80$		0			0
$81$	−10.4174	−	8.74128i	−1.15749	−	0.971253i
$82$		0			0
$83$	4.84469	−	2.25912i	0.531774	−	0.247970i	−0.138135	−	0.990413i	$-0.544111\pi$
$83$	4.84469	−	2.25912i	0.531774	−	0.247970i	0.669909	+	0.742443i	$0.266333\pi$
$84$		0			0
$85$	1.15996	−	1.78267i	0.125816	−	0.193357i
$86$		0			0
$87$	−1.66833	−	4.58371i	−0.178864	−	0.491425i
$88$		0			0
$89$	1.35807	+	0.118816i	0.143955	+	0.0125944i	0.158905	−	0.987294i	$-0.449203\pi$
$89$	1.35807	+	0.118816i	0.143955	+	0.0125944i	−0.0149504	+	0.999888i	$0.504759\pi$
$90$		0			0
$91$	1.23271	+	2.64355i	0.129223	+	0.277120i
$92$		0			0
$93$	−1.61099	+	9.13638i	−0.167052	+	0.947398i
$94$		0			0
$95$	−0.295633	−	0.733622i	−0.0303313	−	0.0752680i
$96$		0			0
$97$	−11.8848	−	6.86169i	−1.20672	−	0.696699i	−0.244678	−	0.969604i	$-0.578682\pi$
$97$	−11.8848	−	6.86169i	−1.20672	−	0.696699i	−0.962041	+	0.272905i	$0.912016\pi$
$98$		0			0
$99$	2.34907	+	13.3223i	0.236091	+	1.33894i
$100$		0			0
$101$	−0.451565	−	0.260711i	−0.0449323	−	0.0259417i	0.477366	−	0.878705i	$-0.341592\pi$
$101$	−0.451565	−	0.260711i	−0.0449323	−	0.0259417i	−0.522298	+	0.852763i	$0.674925\pi$
$102$		0			0
$103$	−3.16449	+	1.82702i	−0.311806	+	0.180021i	−0.647735	−	0.761866i	$-0.724283\pi$
$103$	−3.16449	+	1.82702i	−0.311806	+	0.180021i	0.335928	+	0.941888i	$0.390950\pi$
$104$		0			0
$105$	−5.03771	−	9.90914i	−0.491630	−	0.967033i
$106$		0			0
$107$	−14.6680	−	6.83982i	−1.41801	−	0.661231i	−0.445759	−	0.895153i	$-0.647066\pi$
$107$	−14.6680	−	6.83982i	−1.41801	−	0.661231i	−0.972255	+	0.233923i	$0.924844\pi$
$108$		0			0
$109$	6.38617	+	4.47164i	0.611684	+	0.428306i	0.837940	−	0.545762i	$-0.183760\pi$
$109$	6.38617	+	4.47164i	0.611684	+	0.428306i	−0.226256	+	0.974068i	$0.572649\pi$
$110$		0			0
$111$	9.73835	+	16.0033i	0.924323	+	1.51896i
$112$		0			0
$113$	16.2180	−	2.85968i	1.52566	−	0.269016i	0.653008	−	0.757351i	$-0.273507\pi$
$113$	16.2180	−	2.85968i	1.52566	−	0.269016i	0.872656	+	0.488335i	$0.162395\pi$
$114$		0			0
$115$	−2.04152	+	2.18531i	−0.190373	+	0.203781i
$116$		0			0
$117$			11.7182i			1.08334i
$118$		0			0
$119$	−1.48302	−	0.397374i	−0.135948	−	0.0364272i
$120$		0			0
$121$	−3.32420	+	5.75768i	−0.302200	+	0.523426i
$122$		0			0
$123$	17.8418	+	12.4930i	1.60874	+	1.12645i
$124$		0			0
$125$	8.66969	+	7.05949i	0.775441	+	0.631420i
$126$		0			0
$127$	15.6140	+	1.36605i	1.38552	+	0.121217i	0.755392	−	0.655273i	$-0.227446\pi$
$127$	15.6140	+	1.36605i	1.38552	+	0.121217i	0.630129	+	0.776490i	$0.283002\pi$
$128$		0			0
$129$	20.0507	−	14.0396i	1.76536	−	1.23612i
$130$		0			0
$131$	17.3562	−	8.09333i	1.51642	−	0.707117i	0.526687	−	0.850059i	$-0.323434\pi$
$131$	17.3562	−	8.09333i	1.51642	−	0.707117i	0.989731	+	0.142942i	$0.0456561\pi$
$132$		0			0
$133$	−0.437393	+	0.367017i	−0.0379268	+	0.0318244i
$134$		0			0
$135$	−0.815920	−	23.9849i	−0.0702232	−	2.06429i
$136$		0			0
$137$	−1.76924	+	6.60290i	−0.151156	+	0.564124i	0.848247	+	0.529600i	$0.177658\pi$
$137$	−1.76924	+	6.60290i	−0.151156	+	0.564124i	−0.999404	+	0.0345235i	$0.989009\pi$
$138$		0			0
$139$	−10.6929	−	3.89190i	−0.906960	−	0.330107i	−0.153922	−	0.988083i	$-0.549190\pi$
$139$	−10.6929	−	3.89190i	−0.906960	−	0.330107i	−0.753039	+	0.657976i	$0.771413\pi$
$140$		0			0
$141$	−23.5868	+	28.1097i	−1.98637	+	2.36726i
$142$		0			0
$143$	2.42298	−	2.88759i	0.202620	−	0.241473i
$144$		0			0
$145$	1.66550	−	3.12555i	0.138312	−	0.259563i
$146$		0			0
$147$	9.56972	−	9.56972i	0.789297	−	0.789297i
$148$		0			0
$149$		−	1.43000i		−	0.117151i	−0.998283	−	0.0585753i	$-0.981344\pi$
$149$		−	1.43000i		−	0.117151i	0.998283	−	0.0585753i	$-0.0186558\pi$
$150$		0			0
$151$	2.37268	+	0.418367i	0.193086	+	0.0340462i	0.269355	−	0.963041i	$-0.413190\pi$
$151$	2.37268	+	0.418367i	0.193086	+	0.0340462i	−0.0762690	+	0.997087i	$0.524301\pi$
$152$		0			0
$153$	−4.72502	−	3.96477i	−0.381995	−	0.320532i
$154$		0			0
$155$	−5.71553	+	3.56430i	−0.459083	+	0.286291i
$156$		0			0
$157$	5.66155	+	12.1412i	0.451841	+	0.968976i	0.991861	+	0.127324i	$0.0406388\pi$
$157$	5.66155	+	12.1412i	0.451841	+	0.968976i	−0.540020	+	0.841652i	$0.681583\pi$
$158$		0			0
$159$	15.7041	+	27.2003i	1.24542	+	2.15712i
$160$		0			0
$161$	1.95658	+	0.912367i	0.154200	+	0.0719046i
$162$		0			0
$163$	−12.9203	−	15.3978i	−1.01199	−	1.20605i	−0.978423	−	0.206611i	$-0.933757\pi$
$163$	−12.9203	−	15.3978i	−1.01199	−	1.20605i	−0.0335703	−	0.999436i	$-0.510688\pi$
$164$		0			0
$165$	−8.85458	+	11.3123i	−0.689328	+	0.880662i
$166$		0			0
$167$	−14.7756	−	2.60534i	−1.14337	−	0.201607i	−0.430292	−	0.902690i	$-0.641589\pi$
$167$	−14.7756	−	2.60534i	−1.14337	−	0.201607i	−0.713080	+	0.701082i	$0.752700\pi$
$168$		0			0
$169$	−7.45726	+	6.25739i	−0.573635	+	0.481337i
$170$		0			0
$171$	−2.21569	+	0.593692i	−0.169438	+	0.0454008i
$172$		0			0
$173$	−10.5543	+	15.0731i	−0.802428	+	1.14599i	0.184182	+	0.982892i	$0.441036\pi$
$173$	−10.5543	+	15.0731i	−0.802428	+	1.14599i	−0.986611	+	0.163094i	$0.947853\pi$
$174$		0			0
$175$	2.90595	−	7.52966i	0.219669	−	0.569188i
$176$		0			0
$177$	3.06221	+	5.30390i	0.230170	+	0.398665i
$178$		0			0
$179$	11.7490	+	11.7490i	0.878164	+	0.878164i	0.993345	−	0.115180i	$-0.0367446\pi$
$179$	11.7490	+	11.7490i	0.878164	+	0.878164i	−0.115180	+	0.993345i	$0.536745\pi$
$180$		0			0
$181$	−21.6604	+	7.88375i	−1.61001	+	0.585995i	−0.981442	−	0.191762i	$-0.938580\pi$
$181$	−21.6604	+	7.88375i	−1.61001	+	0.585995i	−0.628566	+	0.777756i	$0.716358\pi$
$182$		0			0
$183$	−8.13723	−	46.1485i	−0.601521	−	3.41140i
$184$		0			0
$185$	−3.91540	+	13.0257i	−0.287866	+	0.957671i
$186$		0			0
$187$	0.344543	+	1.95400i	0.0251954	+	0.142890i
$188$		0			0
$189$	−16.2796	+	5.92530i	−1.18417	+	0.431002i
$190$		0			0
$191$	13.2978	+	13.2978i	0.962197	+	0.962197i	0.999311	−	0.0371142i	$-0.0118165\pi$
$191$	13.2978	+	13.2978i	0.962197	+	0.962197i	−0.0371142	+	0.999311i	$0.511817\pi$
$192$		0			0
$193$	−9.88768	−	17.1260i	−0.711731	−	1.23275i	−0.964207	−	0.265151i	$-0.914578\pi$
$193$	−9.88768	−	17.1260i	−0.711731	−	1.23275i	0.252476	−	0.967603i	$-0.418755\pi$
$194$		0			0
$195$	−9.25516	+	8.31829i	−0.662776	+	0.595685i
$196$		0			0
$197$	−10.7882	+	15.4071i	−0.768624	+	1.09771i	0.223774	+	0.974641i	$0.428162\pi$
$197$	−10.7882	+	15.4071i	−0.768624	+	1.09771i	−0.992398	+	0.123068i	$0.960727\pi$
$198$		0			0
$199$	−6.12678	+	1.64167i	−0.434316	+	0.116375i	−0.469351	−	0.883011i	$-0.655512\pi$
$199$	−6.12678	+	1.64167i	−0.434316	+	0.116375i	0.0350355	+	0.999386i	$0.488846\pi$
$200$		0			0
$201$	−20.7867	+	17.4421i	−1.46618	+	1.23027i
$202$		0			0
$203$	−2.51780	−	0.443957i	−0.176715	−	0.0311596i
$204$		0			0
$205$	1.91310	+	15.6979i	0.133617	+	1.09639i
$206$		0			0
$207$	5.57488	+	6.64389i	0.387481	+	0.461782i
$208$		0			0
$209$	0.668750	+	0.311843i	0.0462584	+	0.0215706i
$210$		0			0
$211$	−10.1656	−	17.6073i	−0.699826	−	1.21213i	−0.968527	−	0.248910i	$-0.919928\pi$
$211$	−10.1656	−	17.6073i	−0.699826	−	1.21213i	0.268701	−	0.963224i	$-0.413406\pi$
$212$		0			0
$213$	−5.84505	−	12.5348i	−0.400496	−	0.858867i
$214$		0			0
$215$	17.3128	+	4.01341i	1.18072	+	0.273712i
$216$		0			0
$217$	3.72491	+	3.12557i	0.252863	+	0.212177i
$218$		0			0
$219$	−3.11701	−	0.549613i	−0.210628	−	0.0371394i
$220$		0			0
$221$			1.71872i			0.115614i
$222$		0			0
$223$	15.4682	−	15.4682i	1.03583	−	1.03583i	0.0364922	−	0.999334i	$-0.488382\pi$
$223$	15.4682	−	15.4682i	1.03583	−	1.03583i	0.999334	−	0.0364922i	$-0.0116184\pi$
$224$		0			0
$225$	23.3647	−	22.4818i	1.55765	−	1.49879i
$226$		0			0
$227$	14.5897	−	17.3873i	0.968352	−	1.15404i	−0.0196826	−	0.999806i	$-0.506266\pi$
$227$	14.5897	−	17.3873i	0.968352	−	1.15404i	0.988035	−	0.154231i	$-0.0492900\pi$
$228$		0			0
$229$	−5.72103	+	6.81806i	−0.378056	+	0.450550i	−0.921200	−	0.389090i	$-0.872789\pi$
$229$	−5.72103	+	6.81806i	−0.378056	+	0.450550i	0.543144	+	0.839640i	$0.317234\pi$
$230$		0			0
$231$	9.74498	+	3.54688i	0.641173	+	0.233368i
$232$		0			0
$233$	3.00810	−	11.2264i	0.197067	−	0.735465i	−0.794655	−	0.607062i	$-0.792348\pi$
$233$	3.00810	−	11.2264i	0.197067	−	0.735465i	0.991722	−	0.128403i	$-0.0409852\pi$
$234$		0			0
$235$	−26.6269	+	0.905795i	−1.73694	+	0.0590876i
$236$		0			0
$237$	−16.4732	+	13.8226i	−1.07005	+	0.897877i
$238$		0			0
$239$	−22.7231	+	10.5960i	−1.46984	+	0.685396i	−0.982232	−	0.187669i	$-0.939907\pi$
$239$	−22.7231	+	10.5960i	−1.46984	+	0.685396i	−0.487604	+	0.873065i	$0.662129\pi$
$240$		0			0
$241$	0.874999	−	0.612681i	0.0563636	−	0.0394662i	−0.545055	−	0.838400i	$-0.683491\pi$
$241$	0.874999	−	0.612681i	0.0563636	−	0.0394662i	0.601419	+	0.798934i	$0.294602\pi$
$242$		0			0
$243$	−9.64706	−	0.844008i	−0.618859	−	0.0541432i
$244$		0			0
$245$	9.81222	+	0.523108i	0.626880	+	0.0334201i
$246$		0			0
$247$	0.523583	+	0.366616i	0.0333148	+	0.0233272i
$248$		0			0
$249$	8.23145	−	14.2573i	0.521647	−	0.903519i
$250$		0			0
$251$	10.4688	+	2.80511i	0.660786	+	0.177057i	0.573601	−	0.819135i	$-0.305546\pi$
$251$	10.4688	+	2.80511i	0.660786	+	0.177057i	0.0871855	+	0.996192i	$0.472213\pi$
$252$		0			0
$253$		−	2.78992i		−	0.175400i
$254$		0			0
$255$	−0.222694	−	6.54633i	−0.0139456	−	0.409947i
$256$		0			0
$257$	−5.44027	+	0.959266i	−0.339354	+	0.0598373i	−0.340729	−	0.940162i	$-0.610674\pi$
$257$	−5.44027	+	0.959266i	−0.339354	+	0.0598373i	0.00137414	+	0.999999i	$0.499563\pi$
$258$		0			0
$259$	9.81613	−	0.226432i	0.609944	−	0.0140698i
$260$		0			0
$261$	−8.41360	−	5.89127i	−0.520789	−	0.364660i
$262$		0			0
$263$	−5.66701	−	2.64257i	−0.349443	−	0.162948i	0.239969	−	0.970781i	$-0.422863\pi$
$263$	−5.66701	−	2.64257i	−0.349443	−	0.162948i	−0.589412	+	0.807833i	$0.700640\pi$
$264$		0			0
$265$	−7.06639	+	21.6816i	−0.434085	+	1.33189i
$266$		0			0
$267$	3.63600	−	2.09925i	0.222520	−	0.128472i
$268$		0			0
$269$	21.8197	+	12.5976i	1.33037	+	0.768090i	0.985356	−	0.170508i	$-0.0545409\pi$
$269$	21.8197	+	12.5976i	1.33037	+	0.768090i	0.345014	+	0.938598i	$0.387874\pi$
$270$		0			0
$271$	2.67072	+	15.1464i	0.162235	+	0.920079i	0.951870	+	0.306502i	$0.0991587\pi$
$271$	2.67072	+	15.1464i	0.162235	+	0.920079i	−0.789635	+	0.613577i	$0.789730\pi$
$272$		0			0
$273$	7.77962	+	4.49157i	0.470844	+	0.271842i
$274$		0			0
$275$	−10.4061	+	0.708814i	−0.627513	+	0.0427431i
$276$		0			0
$277$	3.26427	−	18.5126i	0.196131	−	1.11232i	−0.714667	−	0.699465i	$-0.753422\pi$
$277$	3.26427	−	18.5126i	0.196131	−	1.11232i	0.910799	−	0.412851i	$-0.135467\pi$
$278$		0			0
$279$	8.25576	+	17.7045i	0.494259	+	1.05994i
$280$		0			0
$281$	10.8626	+	0.950353i	0.648007	+	0.0566933i	0.406421	−	0.913686i	$-0.366777\pi$
$281$	10.8626	+	0.950353i	0.648007	+	0.0566933i	0.241586	+	0.970379i	$0.422332\pi$
$282$		0			0
$283$	−2.74403	−	7.53915i	−0.163115	−	0.448156i	0.831027	−	0.556232i	$-0.187753\pi$
$283$	−2.74403	−	7.53915i	−0.163115	−	0.448156i	−0.994143	+	0.108076i	$0.965531\pi$
$284$		0			0
$285$	−2.04174	−	1.32854i	−0.120942	−	0.0786960i
$286$		0			0
$287$	10.3464	−	4.82460i	0.610728	−	0.284787i
$288$		0			0
$289$	12.3297	+	10.3459i	0.725278	+	0.608581i
$290$		0			0
$291$	−42.1038	+	3.68361i	−2.46817	+	0.215937i
$292$		0			0
$293$	6.03350	+	8.61673i	0.352481	+	0.503395i	0.955765	−	0.294131i	$-0.0950304\pi$
$293$	6.03350	+	8.61673i	0.352481	+	0.503395i	−0.603284	+	0.797526i	$0.706141\pi$
$294$		0			0
$295$	−1.37790	+	4.22778i	−0.0802247	+	0.246151i
$296$		0			0
$297$	15.8312	+	15.8312i	0.918618	+	0.918618i
$298$		0			0
$299$	0.419657	−	2.37999i	0.0242694	−	0.137638i
$300$		0			0
$301$	−1.11815	−	12.7805i	−0.0644490	−	0.736655i
$302$		0			0
$303$	−1.59974	+	0.139959i	−0.0919026	+	0.00804044i
$304$		0			0
$305$	20.9709	−	26.7918i	1.20079	−	1.53409i
$306$		0			0
$307$	−23.1873	−	6.21301i	−1.32337	−	0.354595i	−0.473128	−	0.880993i	$-0.656875\pi$
$307$	−23.1873	−	6.21301i	−1.32337	−	0.354595i	−0.850238	+	0.526398i	$0.823542\pi$
$308$		0			0
$309$	−4.75595	+	10.1992i	−0.270556	+	0.580210i
$310$		0			0
$311$	0.388965	−	4.44589i	0.0220562	−	0.252103i	−0.977160	−	0.212507i	$-0.931837\pi$
$311$	0.388965	−	4.44589i	0.0220562	−	0.252103i	0.999216	−	0.0395964i	$-0.0126072\pi$
$312$		0			0
$313$	−16.9677	−	6.17574i	−0.959071	−	0.349073i	−0.185402	−	0.982663i	$-0.559359\pi$
$313$	−16.9677	−	6.17574i	−0.959071	−	0.349073i	−0.773669	+	0.633590i	$0.781581\pi$
$314$		0			0
$315$	−20.6570	−	11.0074i	−1.16389	−	0.620199i
$316$		0			0
$317$	2.15861	−	24.6730i	0.121239	−	1.38577i	−0.655140	−	0.755507i	$-0.727391\pi$
$317$	2.15861	−	24.6730i	0.121239	−	1.38577i	0.776380	−	0.630265i	$-0.217054\pi$
$318$		0			0
$319$	0.855138	+	3.19142i	0.0478785	+	0.178685i
$320$		0			0
$321$	−49.0867	+	8.65531i	−2.73975	+	0.483092i
$322$		0			0
$323$	−0.324979	+	0.0870778i	−0.0180823	+	0.00484514i
$324$		0			0
$325$	−8.98377	−	0.960614i	−0.498330	−	0.0532853i
$326$		0			0
$327$	24.0100			1.32775
$328$		0			0
$329$	6.57798	+	18.0728i	0.362656	+	0.996388i
$330$		0			0
$331$	11.5581	−	16.5067i	0.635292	−	0.907291i	−0.364421	−	0.931234i	$-0.618733\pi$
$331$	11.5581	−	16.5067i	0.635292	−	0.907291i	0.999713	+	0.0239431i	$0.00762204\pi$
$332$		0			0
$333$	36.1251	+	15.8417i	1.97965	+	0.868121i
$334$		0			0
$335$	−19.5073	−	2.75952i	−1.06580	−	0.150768i
$336$		0			0
$337$	12.8433	−	27.5425i	0.699619	−	1.50034i	−0.158758	−	0.987318i	$-0.550749\pi$
$337$	12.8433	−	27.5425i	0.699619	−	1.50034i	0.858377	−	0.513020i	$-0.171473\pi$
$338$		0			0
$339$	35.8631	−	35.8631i	1.94782	−	1.94782i
$340$		0			0
$341$	1.62640	−	6.06981i	0.0880745	−	0.328699i
$342$		0			0
$343$	−4.76038	−	17.7660i	−0.257037	−	0.959274i
$344$		0			0
$345$	−1.29003	+	9.11937i	−0.0694529	+	0.490971i
$346$		0			0
$347$	−14.3704	+	24.8902i	−0.771441	+	1.33618i	0.165332	+	0.986238i	$0.447130\pi$
$347$	−14.3704	+	24.8902i	−0.771441	+	1.33618i	−0.936773	+	0.349937i	$0.886203\pi$
$348$		0			0
$349$	−3.66171	−	4.36386i	−0.196007	−	0.233592i	0.659085	−	0.752069i	$-0.270944\pi$
$349$	−3.66171	−	4.36386i	−0.196007	−	0.233592i	−0.855092	+	0.518477i	$0.826499\pi$
$350$		0			0
$351$	11.1238	+	15.8864i	0.593743	+	0.847953i
$352$		0			0
$353$	−0.191171	+	0.525238i	−0.0101750	+	0.0279556i	−0.944676	−	0.328004i	$-0.893624\pi$
$353$	−0.191171	+	0.525238i	−0.0101750	+	0.0279556i	0.934501	+	0.355960i	$0.115846\pi$
$354$		0			0
$355$	3.93196	−	9.23994i	0.208687	−	0.490405i
$356$		0			0
$357$	−4.44329	+	1.61723i	−0.235164	+	0.0855926i
$358$		0			0
$359$	9.27102	−	5.35263i	0.489306	−	0.282501i	−0.234981	−	0.972000i	$-0.575503\pi$
$359$	9.27102	−	5.35263i	0.489306	−	0.282501i	0.724286	+	0.689499i	$0.242169\pi$
$360$		0			0
$361$	6.45559	−	17.7366i	0.339768	−	0.933504i
$362$		0			0
$363$	1.78455	+	20.3975i	0.0936647	+	1.07059i
$364$		0			0
$365$	−1.21601	−	1.94994i	−0.0636490	−	0.102064i
$366$		0			0
$367$	−11.6783	+	8.17723i	−0.609602	+	0.426848i	−0.837192	−	0.546909i	$-0.815804\pi$
$367$	−11.6783	+	8.17723i	−0.609602	+	0.426848i	0.227590	+	0.973757i	$0.426915\pi$
$368$		0			0
$369$	45.8628			2.38752
$370$		0			0
$371$	16.4620			0.854663
$372$		0			0
$373$	4.41872	−	3.09402i	0.228792	−	0.160202i	−0.453560	−	0.891226i	$-0.649846\pi$
$373$	4.41872	−	3.09402i	0.228792	−	0.160202i	0.682352	+	0.731024i	$0.260957\pi$
$374$		0			0
$375$	34.3422	+	2.49480i	1.77342	+	0.128831i
$376$		0			0
$377$	0.249442	+	2.85113i	0.0128469	+	0.146841i
$378$		0			0
$379$	2.87793	−	7.90705i	0.147829	−	0.406158i	−0.843572	−	0.537017i	$-0.819551\pi$
$379$	2.87793	−	7.90705i	0.147829	−	0.406158i	0.991401	+	0.130859i	$0.0417735\pi$
$380$		0			0
$381$	41.8040	−	24.1355i	2.14168	−	1.23650i
$382$		0			0
$383$	16.3521	−	5.95167i	0.835553	−	0.304116i	0.111417	−	0.993774i	$-0.464461\pi$
$383$	16.3521	−	5.95167i	0.835553	−	0.304116i	0.724136	+	0.689657i	$0.242239\pi$
$384$		0			0
$385$	2.81429	+	6.98374i	0.143430	+	0.355924i
$386$		0			0
$387$	17.6280	−	48.4324i	0.896079	−	2.46196i
$388$		0			0
$389$	6.08489	+	8.69012i	0.308516	+	0.440607i	0.943230	−	0.332141i	$-0.107771\pi$
$389$	6.08489	+	8.69012i	0.308516	+	0.440607i	−0.634714	+	0.772747i	$0.718882\pi$
$390$		0			0
$391$	0.817678	+	0.974470i	0.0413517	+	0.0492811i
$392$		0			0
$393$	29.4893	−	51.0770i	1.48754	−	2.57649i
$394$		0			0
$395$	−15.4593	−	2.18688i	−0.777843	−	0.110034i
$396$		0			0
$397$	−2.39797	−	8.94933i	−0.120350	−	0.449154i	0.879281	−	0.476303i	$-0.158024\pi$
$397$	−2.39797	−	8.94933i	−0.120350	−	0.449154i	−0.999631	+	0.0271495i	$0.991357\pi$
$398$		0			0
$399$	−0.455125	+	1.69855i	−0.0227847	+	0.0850337i
$400$		0			0
$401$	−10.6994	+	10.6994i	−0.534302	+	0.534302i	−0.921850	−	0.387548i	$-0.873322\pi$
$401$	−10.6994	+	10.6994i	−0.534302	+	0.534302i	0.387548	+	0.921850i	$0.373322\pi$
$402$		0			0
$403$	2.30045	−	4.93333i	0.114593	−	0.245746i
$404$		0			0
$405$	−18.2783	−	24.3017i	−0.908255	−	1.20756i
$406$		0			0
$407$	−5.62636	−	11.3734i	−0.278888	−	0.563756i
$408$		0			0
$409$	4.49990	−	6.42652i	0.222506	−	0.317771i	−0.692343	−	0.721569i	$-0.743421\pi$
$409$	4.49990	−	6.42652i	0.222506	−	0.317771i	0.914848	+	0.403798i	$0.132310\pi$
$410$		0			0
$411$	7.20043	+	19.7830i	0.355171	+	0.975824i
$412$		0			0
$413$	3.20999			0.157953
$414$		0			0
$415$	11.6940	−	2.47462i	0.574036	−	0.121474i
$416$		0			0
$417$	−33.8508	+	9.07031i	−1.65768	+	0.444175i
$418$		0			0
$419$	19.7379	−	3.48032i	0.964259	−	0.170025i	0.330715	−	0.943731i	$-0.392710\pi$
$419$	19.7379	−	3.48032i	0.964259	−	0.170025i	0.633545	+	0.773706i	$0.281599\pi$
$420$		0			0
$421$	−6.96440	−	25.9915i	−0.339424	−	1.26675i	−0.898993	−	0.437963i	$-0.855700\pi$
$421$	−6.96440	−	25.9915i	−0.339424	−	1.26675i	0.559569	−	0.828784i	$-0.310967\pi$
$422$		0			0
$423$	−6.73417	+	76.9719i	−0.327426	+	3.74250i
$424$		0			0
$425$	3.42694	−	3.29744i	0.166231	−	0.159949i
$426$		0			0
$427$	−23.0797	−	8.40034i	−1.11691	−	0.406521i
$428$		0			0
$429$	1.01180	−	11.5649i	0.0488501	−	0.558359i
$430$		0			0
$431$	−1.74486	+	3.74187i	−0.0840470	+	0.180239i	−0.943840	−	0.330404i	$-0.892815\pi$
$431$	−1.74486	+	3.74187i	−0.0840470	+	0.180239i	0.859793	+	0.510643i	$0.170593\pi$
$432$		0			0
$433$	−28.8648	−	7.73429i	−1.38715	−	0.371686i	−0.513438	−	0.858127i	$-0.671628\pi$
$433$	−28.8648	−	7.73429i	−1.38715	−	0.371686i	−0.873714	+	0.486440i	$0.838295\pi$
$434$		0			0
$435$	−1.31950	−	10.8272i	−0.0632653	−	0.519123i
$436$		0			0
$437$	0.471275	−	0.0412312i	0.0225441	−	0.00197236i
$438$		0			0
$439$	−3.50330	−	40.0429i	−0.167203	−	1.91114i	−0.365179	−	0.930937i	$-0.618992\pi$
$439$	−3.50330	−	40.0429i	−0.167203	−	1.91114i	0.197975	−	0.980207i	$-0.436563\pi$
$440$		0			0
$441$	4.94847	−	28.0641i	0.235641	−	1.33639i
$442$		0			0
$443$	9.22004	+	9.22004i	0.438057	+	0.438057i	0.891358	−	0.453300i	$-0.149754\pi$
$443$	9.22004	+	9.22004i	0.438057	+	0.438057i	−0.453300	+	0.891358i	$0.649754\pi$
$444$		0			0
$445$	2.89829	+	0.944601i	0.137392	+	0.0447784i
$446$		0			0
$447$	−2.52607	−	3.60760i	−0.119479	−	0.170633i
$448$		0			0
$449$	4.14354	−	0.362513i	0.195546	−	0.0171080i	0.0110378	−	0.999939i	$-0.496486\pi$
$449$	4.14354	−	0.362513i	0.195546	−	0.0171080i	0.184508	+	0.982831i	$0.440931\pi$
$450$		0			0
$451$	−11.3015	−	9.48310i	−0.532168	−	0.446542i
$452$		0			0
$453$	6.72479	−	3.13582i	0.315958	−	0.147334i
$454$		0			0
$455$	1.35030	+	6.38094i	0.0633030	+	0.299143i
$456$		0			0
$457$	2.92086	+	8.02499i	0.136632	+	0.375393i	0.989072	−	0.147431i	$-0.0471006\pi$
$457$	2.92086	+	8.02499i	0.136632	+	0.375393i	−0.852440	+	0.522824i	$0.824878\pi$
$458$		0			0
$459$	−10.1694	−	0.889708i	−0.474668	−	0.0415280i
$460$		0			0
$461$	−2.68291	−	5.75353i	−0.124956	−	0.267969i	0.833871	−	0.551959i	$-0.186119\pi$
$461$	−2.68291	−	5.75353i	−0.124956	−	0.267969i	−0.958827	+	0.283990i	$0.908342\pi$
$462$		0			0
$463$	−2.52336	+	14.3107i	−0.117271	+	0.665074i	0.868330	+	0.495986i	$0.165193\pi$
$463$	−2.52336	+	14.3107i	−0.117271	+	0.665074i	−0.985601	+	0.169088i	$0.945918\pi$
$464$		0			0
$465$	−8.12282	+	19.0883i	−0.376687	+	0.885199i
$466$		0			0
$467$	11.7582	+	6.78863i	0.544107	+	0.314140i	0.746742	−	0.665114i	$-0.231617\pi$
$467$	11.7582	+	6.78863i	0.544107	+	0.314140i	−0.202635	+	0.979254i	$0.564950\pi$
$468$		0			0
$469$	2.46968	+	14.0062i	0.114039	+	0.646748i
$470$		0			0
$471$	35.7300	+	20.6288i	1.64635	+	0.950523i
$472$		0			0
$473$	−14.3583	+	8.28978i	−0.660196	+	0.381164i
$474$		0			0
$475$	−0.273522	−	1.74734i	−0.0125501	−	0.0801733i
$476$		0			0
$477$	59.9383	+	27.9497i	2.74439	+	1.27973i
$478$		0			0
$479$	−10.6583	−	7.46303i	−0.486991	−	0.340995i	0.304155	−	0.952623i	$-0.401626\pi$
$479$	−10.6583	−	7.46303i	−0.486991	−	0.340995i	−0.791145	+	0.611628i	$0.790515\pi$
$480$		0			0
$481$	−3.08890	−	10.5486i	−0.140842	−	0.480974i
$482$		0			0
$483$	6.54770	−	1.15454i	0.297931	−	0.0525332i
$484$		0			0
$485$	−22.4238	−	20.9483i	−1.01821	−	0.951214i
$486$		0			0
$487$		−	22.7681i		−	1.03172i	−0.856672	−	0.515862i	$-0.827472\pi$
$487$		−	22.7681i		−	1.03172i	0.856672	−	0.515862i	$-0.172528\pi$
$488$		0			0
$489$	−59.7948	−	16.0220i	−2.70402	−	0.724539i
$490$		0			0
$491$	15.8890	−	27.5206i	0.717061	−	1.24199i	−0.245098	−	0.969498i	$-0.578820\pi$
$491$	15.8890	−	27.5206i	0.717061	−	1.24199i	0.962159	−	0.272488i	$-0.0878465\pi$
$492$		0			0
$493$	−1.23404	−	0.864082i	−0.0555782	−	0.0389163i
$494$		0			0
$495$	−1.61035	+	30.2061i	−0.0723796	+	1.35766i
$496$		0			0
$497$	−7.22143	−	0.631794i	−0.323926	−	0.0283398i
$498$		0			0
$499$	−10.4524	+	7.31881i	−0.467911	+	0.327635i	−0.783641	−	0.621214i	$-0.786640\pi$
$499$	−10.4524	+	7.31881i	−0.467911	+	0.327635i	0.315729	+	0.948849i	$0.397751\pi$
$500$		0			0
$501$	−41.8780	+	19.5280i	−1.87097	+	0.872448i
$502$		0			0
$503$	−12.9832	+	10.8942i	−0.578894	+	0.485750i	−0.884584	−	0.466381i	$-0.845557\pi$
$503$	−12.9832	+	10.8942i	−0.578894	+	0.485750i	0.305690	+	0.952131i	$0.401113\pi$
$504$		0			0
$505$	−0.851993	−	0.795934i	−0.0379132	−	0.0354186i
$506$		0			0
$507$	−7.75957	+	28.9591i	−0.344614	+	1.28612i
$508$		0			0
$509$	−38.3473	−	13.9573i	−1.69972	−	0.618646i	−0.703923	−	0.710277i	$-0.748570\pi$
$509$	−38.3473	−	13.9573i	−1.69972	−	0.618646i	−0.995793	+	0.0916305i	$0.970792\pi$
$510$		0			0
$511$	−1.06633	+	1.27081i	−0.0471718	+	0.0562172i
$512$		0			0
$513$	−2.44025	+	2.90818i	−0.107740	+	0.128399i
$514$		0			0
$515$	−7.81581	+	2.38183i	−0.344406	+	0.104956i
$516$		0			0
$517$	17.5750	−	17.5750i	0.772948	−	0.772948i
$518$		0			0
$519$			56.6701i			2.48754i
$520$		0			0
$521$	−13.6202	−	2.40160i	−0.596710	−	0.105216i	−0.132867	−	0.991134i	$-0.542418\pi$
$521$	−13.6202	−	2.40160i	−0.596710	−	0.105216i	−0.463842	+	0.885918i	$0.653530\pi$
$522$		0			0
$523$	−5.27861	−	4.42928i	−0.230818	−	0.193679i	0.520042	−	0.854141i	$-0.325916\pi$
$523$	−5.27861	−	4.42928i	−0.230818	−	0.193679i	−0.750860	+	0.660462i	$0.770361\pi$
$524$		0			0
$525$	−5.96984	−	24.1290i	−0.260545	−	1.05308i
$526$		0			0
$527$	1.21089	+	2.59675i	0.0527470	+	0.113116i
$528$		0			0
$529$	10.6057	+	18.3695i	0.461116	+	0.798676i
$530$		0			0
$531$	11.6876	+	5.45003i	0.507200	+	0.236511i
$532$		0			0
$533$	−8.21454	−	9.78971i	−0.355811	−	0.424039i
$534$		0			0
$535$	−28.4976	−	22.3061i	−1.23206	−	0.964378i
$536$		0			0
$537$	50.3947	+	8.88594i	2.17469	+	0.383457i
$538$		0			0
$539$	−7.02226	+	5.89238i	−0.302470	+	0.253803i
$540$		0			0
$541$	12.3211	−	3.30143i	0.529725	−	0.141939i	0.0159639	−	0.999873i	$-0.494918\pi$
$541$	12.3211	−	3.30143i	0.529725	−	0.141939i	0.513761	+	0.857933i	$0.328252\pi$
$542$		0			0
$543$	−40.7182	+	58.1516i	−1.74739	+	2.49552i
$544$		0			0
$545$	11.6530	+	12.9654i	0.499158	+	0.555377i
$546$		0			0
$547$	−1.42213	−	2.46320i	−0.0608058	−	0.105319i	0.834020	−	0.551734i	$-0.186034\pi$
$547$	−1.42213	−	2.46320i	−0.0608058	−	0.105319i	−0.894826	+	0.446415i	$0.852700\pi$
$548$		0			0
$549$	−69.7714	−	69.7714i	−2.97777	−	2.97777i
$550$		0			0
$551$	−0.526459	+	0.191615i	−0.0224279	+	0.00816309i
$552$		0			0
$553$	1.95719	+	11.0998i	0.0832282	+	0.472010i
$554$		0			0
$555$	13.1319	+	39.7776i	0.557418	+	1.68846i
$556$		0			0
$557$	−5.39443	−	30.5933i	−0.228569	−	1.29628i	−0.855743	−	0.517401i	$-0.826899\pi$
$557$	−5.39443	−	30.5933i	−0.228569	−	1.29628i	0.627174	−	0.778879i	$-0.284212\pi$
$558$		0			0
$559$	−13.4956	+	4.91199i	−0.570802	+	0.207755i
$560$		0			0
$561$	4.32089	+	4.32089i	0.182428	+	0.182428i
$562$		0			0
$563$	−7.33529	−	12.7051i	−0.309146	−	0.535456i	0.669030	−	0.743235i	$-0.266710\pi$
$563$	−7.33529	−	12.7051i	−0.309146	−	0.535456i	−0.978176	+	0.207779i	$0.933376\pi$
$564$		0			0
$565$	36.7719	+	1.96038i	1.54700	+	0.0824737i
$566$		0			0
$567$	−12.5908	+	17.9815i	−0.528764	+	0.755153i
$568$		0			0
$569$	31.5806	−	8.46199i	1.32393	−	0.354745i	0.473479	−	0.880805i	$-0.342998\pi$
$569$	31.5806	−	8.46199i	1.32393	−	0.354745i	0.850447	+	0.526060i	$0.176331\pi$
$570$		0			0
$571$	−21.0828	+	17.6906i	−0.882288	+	0.740328i	−0.966648	−	0.256108i	$-0.917560\pi$
$571$	−21.0828	+	17.6906i	−0.882288	+	0.740328i	0.0843600	+	0.996435i	$0.473115\pi$
$572$		0			0
$573$	57.0378	+	10.0573i	2.38279	+	0.420150i
$574$		0			0
$575$	−5.55057	+	3.72937i	−0.231475	+	0.155525i
$576$		0			0
$577$	22.5523	+	26.8768i	0.938865	+	1.11890i	0.992732	+	0.120347i	$0.0384009\pi$
$577$	22.5523	+	26.8768i	0.938865	+	1.11890i	−0.0538670	+	0.998548i	$0.517155\pi$
$578$		0			0
$579$	−55.1971	−	25.7388i	−2.29391	−	1.06967i
$580$		0			0
$581$	−4.31435	−	7.47267i	−0.178989	−	0.310019i
$582$		0			0
$583$	−8.99082	−	19.2809i	−0.372362	−	0.798533i
$584$		0			0
$585$	−5.91732	+	25.5257i	−0.244651	+	1.05536i
$586$		0			0
$587$	−6.93499	−	5.81915i	−0.286238	−	0.240182i	0.488351	−	0.872647i	$-0.337599\pi$
$587$	−6.93499	−	5.81915i	−0.286238	−	0.240182i	−0.774589	+	0.632465i	$0.782043\pi$
$588$		0			0
$589$	1.04935	+	0.185029i	0.0432378	+	0.00762400i
$590$		0			0
$591$			57.9258i			2.38275i
$592$		0			0
$593$	−1.55756	+	1.55756i	−0.0639612	+	0.0639612i	−0.738364	−	0.674403i	$-0.764401\pi$
$593$	−1.55756	+	1.55756i	−0.0639612	+	0.0639612i	0.674403	+	0.738364i	$0.264401\pi$
$594$		0			0
$595$	−3.02980	−	1.61448i	−0.124210	−	0.0661872i
$596$		0			0
$597$	−12.5566	+	14.9644i	−0.513907	+	0.612451i
$598$		0			0
$599$	−7.19881	+	8.57920i	−0.294135	+	0.350537i	−0.892792	−	0.450469i	$-0.851257\pi$
$599$	−7.19881	+	8.57920i	−0.294135	+	0.350537i	0.598657	+	0.801006i	$0.295701\pi$
$600$		0			0
$601$	42.8196	+	15.5851i	1.74665	+	0.635728i	0.999579	−	0.0290197i	$-0.00923854\pi$
$601$	42.8196	+	15.5851i	1.74665	+	0.635728i	0.747068	+	0.664747i	$0.231461\pi$
$602$		0			0
$603$	−14.7881	+	55.1901i	−0.602220	+	2.24751i
$604$		0			0
$605$	−10.1486	+	10.8634i	−0.412598	+	0.441658i
$606$		0			0
$607$	−28.8679	+	24.2230i	−1.17171	+	0.983182i	−0.999998	−	0.00196467i	$-0.999375\pi$
$607$	−28.8679	+	24.2230i	−1.17171	+	0.983182i	−0.171713	+	0.985147i	$0.554930\pi$
$608$		0			0
$609$	−7.13612	+	3.32763i	−0.289170	+	0.134842i
$610$		0			0
$611$	17.6363	−	12.3491i	0.713489	−	0.499590i
$612$		0			0
$613$	15.0486	+	1.31658i	0.607808	+	0.0531763i	0.386905	−	0.922120i	$-0.373544\pi$
$613$	15.0486	+	1.31658i	0.607808	+	0.0531763i	0.220903	+	0.975296i	$0.429100\pi$
$614$		0			0
$615$	32.5563	+	36.2231i	1.31280	+	1.46065i
$616$		0			0
$617$	−17.7928	−	12.4586i	−0.716311	−	0.501566i	0.157691	−	0.987488i	$-0.449595\pi$
$617$	−17.7928	−	12.4586i	−0.716311	−	0.501566i	−0.874002	+	0.485922i	$0.838484\pi$
$618$		0			0
$619$	1.46187	−	2.53203i	0.0587575	−	0.101771i	−0.835150	−	0.550022i	$-0.814619\pi$
$619$	1.46187	−	2.53203i	0.0587575	−	0.101771i	0.893908	+	0.448251i	$0.147953\pi$
$620$		0			0
$621$	13.8648	+	3.71506i	0.556376	+	0.149080i
$622$		0			0
$623$		−	2.20056i		−	0.0881634i
$624$		0			0
$625$	15.3204	+	19.7556i	0.612816	+	0.790226i
$626$		0			0
$627$	2.23797	−	0.394615i	0.0893761	−	0.0157594i
$628$		0			0
$629$	5.29853	+	2.32353i	0.211266	+	0.0926452i
$630$		0			0
$631$	−13.9908	−	9.79649i	−0.556966	−	0.389992i	0.260930	−	0.965358i	$-0.415971\pi$
$631$	−13.9908	−	9.79649i	−0.556966	−	0.389992i	−0.817896	+	0.575366i	$0.804860\pi$
$632$		0			0
$633$	−56.7483	−	26.4622i	−2.25554	−	1.05178i
$634$		0			0
$635$	33.3223	+	10.8603i	1.32235	+	0.430978i
$636$		0			0
$637$	−6.87680	+	3.97032i	−0.272469	+	0.157310i
$638$		0			0
$639$	−25.2207	−	14.5612i	−0.997715	−	0.576031i
$640$		0			0
$641$	−5.35783	−	30.3857i	−0.211621	−	1.20016i	−0.886674	−	0.462395i	$-0.846990\pi$
$641$	−5.35783	−	30.3857i	−0.211621	−	1.20016i	0.675052	−	0.737770i	$-0.264121\pi$
$642$		0			0
$643$	15.1327	+	8.73687i	0.596776	+	0.344549i	0.767772	−	0.640723i	$-0.221365\pi$
$643$	15.1327	+	8.73687i	0.596776	+	0.344549i	−0.170996	+	0.985272i	$0.554699\pi$
$644$		0			0
$645$	50.7660	−	20.4576i	1.99891	−	0.805516i
$646$		0			0
$647$	−1.33702	+	7.58262i	−0.0525637	+	0.298104i	−0.999745	−	0.0225960i	$-0.992807\pi$
$647$	−1.33702	+	7.58262i	−0.0525637	+	0.298104i	0.947181	+	0.320700i	$0.103918\pi$
$648$		0			0
$649$	−1.75316	−	3.75966i	−0.0688175	−	0.147580i
$650$		0			0
$651$	14.9184	+	1.30519i	0.584697	+	0.0511544i
$652$		0			0
$653$	10.5728	+	29.0485i	0.413746	+	1.13676i	0.955183	+	0.296016i	$0.0956580\pi$
$653$	10.5728	+	29.0485i	0.413746	+	1.13676i	−0.541438	+	0.840741i	$0.682120\pi$
$654$		0			0
$655$	41.8940	−	8.86537i	1.63693	−	0.346399i
$656$		0			0
$657$	−6.04016	+	2.81657i	−0.235649	+	0.109885i
$658$		0			0
$659$	−13.6018	−	11.4133i	−0.529851	−	0.444598i	0.338199	−	0.941075i	$-0.390182\pi$
$659$	−13.6018	−	11.4133i	−0.529851	−	0.444598i	−0.868050	+	0.496477i	$0.834627\pi$
$660$		0			0
$661$	−23.5508	+	2.06043i	−0.916021	+	0.0801414i	−0.535408	−	0.844593i	$-0.679842\pi$
$661$	−23.5508	+	2.06043i	−0.916021	+	0.0801414i	−0.380612	+	0.924735i	$0.624287\pi$
$662$		0			0
$663$	3.03608	+	4.33597i	0.117911	+	0.168395i
$664$		0			0
$665$	−1.13811	+	0.578603i	−0.0441339	+	0.0224373i
$666$		0			0
$667$	1.49785	+	1.49785i	0.0579968	+	0.0579968i
$668$		0			0
$669$	11.6988	−	66.3471i	0.452301	−	2.56513i
$670$		0			0
$671$	2.76637	+	31.6198i	0.106795	+	1.22067i
$672$		0			0
$673$	−2.05379	+	0.179683i	−0.0791678	+	0.00692629i	−0.126671	−	0.991945i	$-0.540429\pi$
$673$	−2.05379	+	0.179683i	−0.0791678	+	0.00692629i	0.0475030	+	0.998871i	$0.484874\pi$
$674$		0			0
$675$	10.3343	−	52.6583i	0.397768	−	2.02682i
$676$		0			0
$677$	−16.7579	−	4.49026i	−0.644058	−	0.172575i	−0.0780172	−	0.996952i	$-0.524859\pi$
$677$	−16.7579	−	4.49026i	−0.644058	−	0.172575i	−0.566041	+	0.824377i	$0.691526\pi$
$678$		0			0
$679$	−9.36191	+	20.0767i	−0.359277	+	0.770472i
$680$		0			0
$681$	6.09243	−	69.6368i	0.233463	−	2.66849i
$682$		0			0
$683$	6.22686	+	2.26639i	0.238264	+	0.0867210i	0.458392	−	0.888750i	$-0.348425\pi$
$683$	6.22686	+	2.26639i	0.238264	+	0.0867210i	−0.220128	+	0.975471i	$0.570648\pi$
$684$		0			0
$685$	−7.18821	+	13.4897i	−0.274647	+	0.515415i
$686$		0			0
$687$	−2.38901	+	27.3065i	−0.0911465	+	1.04181i
$688$		0			0
$689$	−4.76958	−	17.8003i	−0.181707	−	0.678138i
$690$		0			0
$691$	1.70897	−	0.301337i	0.0650122	−	0.0114634i	−0.141047	−	0.990003i	$-0.545047\pi$
$691$	1.70897	−	0.301337i	0.0650122	−	0.0114634i	0.206060	+	0.978539i	$0.433936\pi$
$692$		0			0
$693$	21.0923	−	5.65168i	0.801232	−	0.214689i
$694$		0			0
$695$	−21.3271	−	13.8773i	−0.808983	−	0.526397i
$696$		0			0
$697$	6.72677			0.254795
$698$		0			0
$699$	−12.2423	−	33.6355i	−0.463047	−	1.27221i
$700$		0			0
$701$	26.8972	−	38.4132i	1.01589	−	1.45085i	0.127458	−	0.991844i	$-0.459318\pi$
$701$	26.8972	−	38.4132i	1.01589	−	1.45085i	0.888435	−	0.459002i	$-0.151793\pi$
$702$		0			0
$703$	1.83805	−	1.11849i	0.0693232	−	0.0421847i
$704$		0			0
$705$	−65.5738	+	49.3208i	−2.46965	+	1.85753i
$706$		0			0
$707$	−0.355707	+	0.762816i	−0.0133777	+	0.0286886i
$708$		0			0
$709$	12.9812	−	12.9812i	0.487518	−	0.487518i	−0.420004	−	0.907522i	$-0.637971\pi$
$709$	12.9812	−	12.9812i	0.487518	−	0.487518i	0.907522	+	0.420004i	$0.137971\pi$
$710$		0			0
$711$	−11.7194	+	43.7375i	−0.439512	+	1.64028i
$712$		0			0
$713$	−1.04272	−	3.89150i	−0.0390503	−	0.145738i
$714$		0			0
$715$	6.73613	−	5.06652i	0.251917	−	0.189477i
$716$		0			0
$717$	−38.6081	+	66.8712i	−1.44185	+	2.49735i
$718$		0			0
$719$	24.2454	+	28.8946i	0.904201	+	1.07759i	0.996643	+	0.0818671i	$0.0260883\pi$
$719$	24.2454	+	28.8946i	0.904201	+	1.07759i	−0.0924419	+	0.995718i	$0.529467\pi$
$720$		0			0
$721$	3.38313	+	4.83161i	0.125994	+	0.179939i
$722$		0			0
$723$	1.12515	−	3.09132i	0.0418448	−	0.114968i
$724$		0			0
$725$	5.20628	−	5.96738i	0.193356	−	0.221623i
$726$		0			0
$727$	−5.28634	+	1.92407i	−0.196059	+	0.0713598i	−0.438184	−	0.898885i	$-0.644378\pi$
$727$	−5.28634	+	1.92407i	−0.196059	+	0.0713598i	0.242124	+	0.970245i	$0.422156\pi$
$728$		0			0
$729$	9.50289	−	5.48650i	0.351959	−	0.203204i
$730$		0			0
$731$	2.58552	−	7.10366i	0.0956290	−	0.262738i
$732$		0			0
$733$	−0.434567	−	4.96712i	−0.0160511	−	0.183465i	−0.999988	−	0.00494697i	$-0.998425\pi$
$733$	−0.434567	−	4.96712i	−0.0160511	−	0.183465i	0.983937	−	0.178518i	$-0.0571302\pi$
$734$		0			0
$735$	25.6782	−	16.0133i	0.947154	−	0.590661i
$736$		0			0
$737$	15.0558	−	10.5422i	0.554588	−	0.388327i
$738$		0			0
$739$	−32.9859			−1.21341			−0.606703	−	0.794929i	$-0.707508\pi$
$739$	−32.9859			−1.21341			−0.606703	+	0.794929i	$0.707508\pi$
$740$		0			0
$741$	1.96851			0.0723148
$742$		0			0
$743$	−32.7804	+	22.9531i	−1.20260	+	0.842066i	−0.990811	−	0.135250i	$-0.956816\pi$
$743$	−32.7804	+	22.9531i	−1.20260	+	0.842066i	−0.211784	+	0.977316i	$0.567927\pi$
$744$		0			0
$745$	0.722109	−	3.11498i	0.0264560	−	0.114124i
$746$		0			0
$747$	−3.02126	−	34.5332i	−0.110542	−	1.26350i
$748$		0			0
$749$	−8.93518	+	24.5492i	−0.326484	+	0.897008i
$750$		0			0
$751$	37.1442	−	21.4452i	1.35541	−	0.782547i	0.366410	−	0.930454i	$-0.380587\pi$
$751$	37.1442	−	21.4452i	1.35541	−	0.782547i	0.989001	+	0.147907i	$0.0472536\pi$
$752$		0			0
$753$	31.3658	−	11.4162i	1.14303	−	0.416030i
$754$		0			0
$755$	4.95714	+	2.10946i	0.180409	+	0.0767711i
$756$		0			0
$757$	−0.0514548	+	0.141371i	−0.00187016	+	0.00513821i	−0.940624	−	0.339450i	$-0.889759\pi$
$757$	−0.0514548	+	0.141371i	−0.00187016	+	0.00513821i	0.938754	+	0.344588i	$0.111981\pi$
$758$		0			0
$759$	−4.92831	−	7.03836i	−0.178886	−	0.255476i
$760$		0			0
$761$	31.6586	+	37.7292i	1.14762	+	1.36768i	0.919042	+	0.394159i	$0.128964\pi$
$761$	31.6586	+	37.7292i	1.14762	+	1.36768i	0.228581	+	0.973525i	$0.426592\pi$
$762$		0			0
$763$	6.29217	−	10.8984i	0.227792	−	0.394547i
$764$		0			0
$765$	−8.29045	−	11.0225i	−0.299742	−	0.398518i
$766$		0			0
$767$	−0.930041	−	3.47096i	−0.0335818	−	0.125329i
$768$		0			0
$769$	0.927474	−	3.46138i	0.0334456	−	0.124821i	−0.947185	−	0.320689i	$-0.896086\pi$
$769$	0.927474	−	3.46138i	0.0334456	−	0.124821i	0.980630	+	0.195868i	$0.0627524\pi$
$770$		0			0
$771$	−12.0301	+	12.0301i	−0.433254	+	0.433254i
$772$		0			0
$773$	−3.90102	+	8.36577i	−0.140310	+	0.300896i	−0.963888	−	0.266307i	$-0.914197\pi$
$773$	−3.90102	+	8.36577i	−0.140310	+	0.300896i	0.823578	+	0.567203i	$0.191974\pi$
$774$		0			0
$775$	−14.2500	+	4.87795i	−0.511876	+	0.175221i
$776$		0			0
$777$	24.3640	−	17.9112i	0.874054	−	0.642560i
$778$		0			0
$779$	1.43487	−	2.04921i	0.0514096	−	0.0734205i
$780$		0			0
$781$	3.20406	+	8.80308i	0.114650	+	0.314999i
$782$		0			0
$783$	−16.9988			−0.607489
$784$		0			0
$785$	6.20161	+	29.3062i	0.221345	+	1.04598i
$786$		0			0
$787$	−3.32403	+	0.890671i	−0.118489	+	0.0317490i	−0.317576	−	0.948233i	$-0.602869\pi$
$787$	−3.32403	+	0.890671i	−0.118489	+	0.0317490i	0.199087	+	0.979982i	$0.436202\pi$
$788$		0			0
$789$	−18.9647	+	3.34399i	−0.675161	+	0.119049i
$790$		0			0
$791$	−6.88015	−	25.6771i	−0.244630	−	0.912972i
$792$		0			0
$793$	−2.39631	+	27.3900i	−0.0850956	+	0.972647i
$794$		0			0
$795$	20.4729	+	67.1805i	0.726100	+	2.38265i
$796$		0			0
$797$	−37.6585	−	13.7066i	−1.33393	−	0.485511i	−0.426035	−	0.904707i	$-0.640090\pi$
$797$	−37.6585	−	13.7066i	−1.33393	−	0.485511i	−0.907896	+	0.419195i	$0.862312\pi$
$798$		0			0
$799$	−0.987711	+	11.2896i	−0.0349427	+	0.399397i
$800$		0			0
$801$	3.73618	−	8.01226i	0.132011	−	0.283099i
$802$		0			0
$803$	2.07080	+	0.554870i	0.0730771	+	0.0195809i
$804$		0			0
$805$	3.80130	+	2.97543i	0.133978	+	0.104870i
$806$		0			0
$807$	77.2998	−	6.76285i	2.72108	−	0.238064i
$808$		0			0
$809$	−0.363464	−	4.15441i	−0.0127787	−	0.146061i	0.987125	−	0.159952i	$-0.0511339\pi$
$809$	−0.363464	−	4.15441i	−0.0127787	−	0.146061i	−0.999904	+	0.0138906i	$0.995578\pi$
$810$		0			0
$811$	0.660558	−	3.74621i	0.0231953	−	0.131547i	−0.971011	−	0.239034i	$-0.923169\pi$
$811$	0.660558	−	3.74621i	0.0231953	−	0.131547i	0.994207	+	0.107487i	$0.0342803\pi$
$812$		0			0
$813$	33.4934	+	33.4934i	1.17466	+	1.17466i
$814$		0			0
$815$	−20.3688	−	40.0654i	−0.713490	−	1.40343i
$816$		0			0
$817$	−1.61251	−	2.30291i	−0.0564146	−	0.0805685i
$818$		0			0
$819$	18.8434	−	1.64858i	0.658440	−	0.0576060i
$820$		0			0
$821$	21.7574	+	18.2566i	0.759337	+	0.637160i	0.937954	−	0.346759i	$-0.112718\pi$
$821$	21.7574	+	18.2566i	0.759337	+	0.637160i	−0.178617	+	0.983919i	$0.557162\pi$
$822$		0			0
$823$	11.2695	−	5.25505i	0.392830	−	0.183179i	−0.216159	−	0.976358i	$-0.569353\pi$
$823$	11.2695	−	5.25505i	0.392830	−	0.183179i	0.608989	+	0.793179i	$0.291575\pi$
$824$		0			0
$825$	−25.0003	+	20.1703i	−0.870400	+	0.702241i
$826$		0			0
$827$	−16.2098	−	44.5360i	−0.563669	−	1.54867i	−0.814215	−	0.580564i	$-0.802832\pi$
$827$	−16.2098	−	44.5360i	−0.563669	−	1.54867i	0.250546	−	0.968105i	$-0.419390\pi$
$828$		0			0
$829$	−18.3107	−	1.60198i	−0.635956	−	0.0556389i	−0.235381	−	0.971903i	$-0.575634\pi$
$829$	−18.3107	−	1.60198i	−0.635956	−	0.0556389i	−0.400575	+	0.916264i	$0.631189\pi$
$830$		0			0
$831$	−24.4670	−	52.4696i	−0.848751	−	1.82015i
$832$		0			0
$833$	0.725800	−	4.11622i	0.0251475	−	0.142618i
$834$		0			0
$835$	−30.8702	−	13.1365i	−1.06831	−	0.454606i
$836$		0			0
$837$	27.9989	+	16.1652i	0.967783	+	0.558750i
$838$		0			0
$839$	−0.313988	−	1.78072i	−0.0108401	−	0.0614772i	0.978908	−	0.204302i	$-0.0654925\pi$
$839$	−0.313988	−	1.78072i	−0.0108401	−	0.0614772i	−0.989748	+	0.142825i	$0.954381\pi$
$840$		0			0
$841$	22.9422	+	13.2457i	0.791111	+	0.456748i
$842$		0			0
$843$	29.0827	−	16.7909i	1.00166	−	0.578310i
$844$		0			0
$845$	−19.4040	+	9.86479i	−0.667517	+	0.339359i
$846$		0			0
$847$	9.72630	+	4.53545i	0.334200	+	0.155840i
$848$		0			0
$849$	−20.2403	−	14.1724i	−0.694645	−	0.486396i
$850$		0			0
$851$	−6.76979	−	4.51123i	−0.232065	−	0.154643i
$852$		0			0
$853$	31.1626	−	5.49481i	1.06699	−	0.188139i	0.387532	−	0.921856i	$-0.373328\pi$
$853$	31.1626	−	5.49481i	1.06699	−	0.188139i	0.679455	+	0.733718i	$0.262216\pi$
$854$		0			0
$855$	−5.12624	+	0.174385i	−0.175314	+	0.00596384i
$856$		0			0
$857$			55.8312i			1.90716i	0.301143	+	0.953579i	$0.402632\pi$
$857$			55.8312i			1.90716i	−0.301143	+	0.953579i	$0.597368\pi$
$858$		0			0
$859$	−9.07967	−	2.43289i	−0.309794	−	0.0830092i	0.100572	−	0.994930i	$-0.467933\pi$
$859$	−9.07967	−	2.43289i	−0.309794	−	0.0830092i	−0.410367	+	0.911921i	$0.634599\pi$
$860$		0			0
$861$	17.5792	−	30.4481i	0.599098	−	1.03767i
$862$		0			0
$863$	21.6858	+	15.1846i	0.738195	+	0.516889i	0.881148	−	0.472840i	$-0.156771\pi$
$863$	21.6858	+	15.1846i	0.738195	+	0.516889i	−0.142954	+	0.989729i	$0.545660\pi$
$864$		0			0
$865$	−30.6019	+	27.5042i	−1.04050	+	0.935170i
$866$		0			0
$867$	49.3810	+	4.32028i	1.67707	+	0.146724i
$868$		0			0
$869$	11.9315	−	8.35456i	0.404750	−	0.283409i
$870$		0			0
$871$	14.4294	−	6.72854i	0.488922	−	0.227988i
$872$		0			0
$873$	−68.1737	+	57.2046i	−2.30733	+	1.93608i
$874$		0			0
$875$	10.1323	−	14.9345i	0.342534	−	0.504877i
$876$		0			0
$877$	−0.705650	+	2.63352i	−0.0238281	+	0.0889277i	−0.976816	−	0.214081i	$-0.931324\pi$
$877$	−0.705650	+	2.63352i	−0.0238281	+	0.0889277i	0.952988	+	0.303009i	$0.0979911\pi$
$878$		0			0
$879$	30.4425	+	11.0802i	1.02680	+	0.373724i
$880$		0			0
$881$	6.38997	−	7.61528i	0.215284	−	0.256565i	−0.647585	−	0.761993i	$-0.724221\pi$
$881$	6.38997	−	7.61528i	0.215284	−	0.256565i	0.862869	+	0.505428i	$0.168665\pi$
$882$		0			0
$883$	−1.19206	+	1.42064i	−0.0401159	+	0.0478083i	−0.785729	−	0.618570i	$-0.787712\pi$
$883$	−1.19206	+	1.42064i	−0.0401159	+	0.0478083i	0.745613	+	0.666379i	$0.232157\pi$
$884$		0			0
$885$	3.99211	+	13.0998i	0.134193	+	0.440346i
$886$		0			0
$887$	−22.8201	+	22.8201i	−0.766225	+	0.766225i	−0.977440	−	0.211215i	$-0.932258\pi$
$887$	−22.8201	+	22.8201i	−0.766225	+	0.766225i	0.211215	+	0.977440i	$0.432258\pi$
$888$		0			0
$889$		−	25.3003i		−	0.848545i
$890$		0			0
$891$	27.9372	+	4.92609i	0.935932	+	0.165030i
$892$		0			0
$893$	3.22852	+	2.70905i	0.108038	+	0.0906549i
$894$		0			0
$895$	19.6601	+	31.5259i	0.657163	+	1.05379i
$896$		0			0
$897$	−3.14549	−	6.74552i	−0.105025	−	0.225226i
$898$		0			0
$899$	2.38557	+	4.13193i	0.0795632	+	0.137808i
$900$		0			0
$901$	8.79125	+	4.09943i	0.292879	+	0.136572i
$902$		0			0
$903$	−25.3972	−	30.2672i	−0.845167	−	1.00723i
$904$		0			0
$905$	−51.1641	+	6.23534i	−1.70075	+	0.207270i
$906$		0			0
$907$	−27.6389	−	4.87349i	−0.917736	−	0.161822i	−0.305222	−	0.952281i	$-0.598731\pi$
$907$	−27.6389	−	4.87349i	−0.917736	−	0.161822i	−0.612514	+	0.790460i	$0.709842\pi$
$908$		0			0
$909$	−2.59027	+	2.17349i	−0.0859138	+	0.0720903i
$910$		0			0
$911$	18.1126	−	4.85325i	0.600096	−	0.160795i	0.0540329	−	0.998539i	$-0.482792\pi$
$911$	18.1126	−	4.85325i	0.600096	−	0.160795i	0.546063	+	0.837744i	$0.316126\pi$
$912$		0			0
$913$	−6.39597	+	9.13439i	−0.211676	+	0.302304i
$914$		0			0
$915$	5.57826	−	104.635i	0.184412	−	3.45911i
$916$		0			0
$917$	−15.4562	−	26.7710i	−0.510410	−	0.884056i
$918$		0			0
$919$	29.4650	+	29.4650i	0.971962	+	0.971962i	0.999618	−	0.0276554i	$-0.00880410\pi$
$919$	29.4650	+	29.4650i	0.971962	+	0.971962i	−0.0276554	+	0.999618i	$0.508804\pi$
$920$		0			0
$921$	−69.4716	+	25.2856i	−2.28917	+	0.833189i
$922$		0			0
$923$	1.40913	+	7.99159i	0.0463822	+	0.263046i
$924$		0			0
$925$	−15.1065	+	26.3968i	−0.496700	+	0.867923i
$926$		0			0
$927$	4.11476	+	23.3360i	0.135147	+	0.766454i
$928$		0			0
$929$	−5.87042	+	2.13666i	−0.192602	+	0.0701015i	−0.436521	−	0.899694i	$-0.643789\pi$
$929$	−5.87042	+	2.13666i	−0.192602	+	0.0701015i	0.243918	+	0.969796i	$0.421567\pi$
$930$		0			0
$931$	−1.09912	−	1.09912i	−0.0360223	−	0.0360223i
$932$		0			0
$933$	−6.87227	−	11.9031i	−0.224988	−	0.389691i
$934$		0			0
$935$	−0.236192	+	4.43038i	−0.00772431	+	0.144889i
$936$		0			0
$937$	−0.164153	+	0.234434i	−0.00536264	+	0.00765864i	−0.821824	−	0.569741i	$-0.807044\pi$
$937$	−0.164153	+	0.234434i	−0.00536264	+	0.00765864i	0.816462	+	0.577399i	$0.195932\pi$
$938$		0			0
$939$	−53.7151	+	14.3929i	−1.75293	+	0.469696i
$940$		0			0
$941$	9.44490	−	7.92521i	0.307895	−	0.258354i	−0.475726	−	0.879593i	$-0.657815\pi$
$941$	9.44490	−	7.92521i	0.307895	−	0.258354i	0.783621	+	0.621239i	$0.213370\pi$
$942$		0			0
$943$	−9.31486	−	1.64246i	−0.303334	−	0.0534859i
$944$		0			0
$945$	−38.4540	+	4.68637i	−1.25091	+	0.152448i
$946$		0			0
$947$	24.7848	+	29.5374i	0.805399	+	0.959837i	0.999778	−	0.0210898i	$-0.00671359\pi$
$947$	24.7848	+	29.5374i	0.805399	+	0.959837i	−0.194379	+	0.980927i	$0.562269\pi$
$948$		0			0
$949$	1.68308	+	0.784831i	0.0546350	+	0.0254767i
$950$		0			0
$951$	−38.1385	−	66.0578i	−1.23672	−	2.14207i
$952$		0			0
$953$	−7.06417	−	15.1492i	−0.228831	−	0.490730i	0.758046	−	0.652201i	$-0.226154\pi$
$953$	−7.06417	−	15.1492i	−0.228831	−	0.490730i	−0.986877	+	0.161471i	$0.948376\pi$
$954$		0			0
$955$	22.2517	+	35.6817i	0.720048	+	1.15463i
$956$		0			0
$957$	7.79489	+	6.54069i	0.251973	+	0.211430i
$958$		0			0
$959$	10.8667	+	1.91609i	0.350904	+	0.0618738i
$960$		0			0
$961$			21.9257i			0.707280i
$962$		0			0
$963$	−74.2136	+	74.2136i	−2.39150	+	2.39150i
$964$		0			0
$965$	−12.8903	−	42.2985i	−0.414952	−	1.36164i
$966$		0			0
$967$	10.9972	−	13.1059i	0.353645	−	0.421457i	−0.559668	−	0.828717i	$-0.689071\pi$
$967$	10.9972	−	13.1059i	0.353645	−	0.421457i	0.913312	+	0.407260i	$0.133516\pi$
$968$		0			0
$969$	−0.666032	+	0.793746i	−0.0213960	+	0.0254988i
$970$		0			0
$971$	−8.78252	−	3.19658i	−0.281844	−	0.102583i	0.197230	−	0.980357i	$-0.436805\pi$
$971$	−8.78252	−	3.19658i	−0.281844	−	0.102583i	−0.479075	+	0.877774i	$0.659028\pi$
$972$		0			0
$973$	−4.75402	+	17.7422i	−0.152407	+	0.568790i
$974$		0			0
$975$	−24.3610	+	13.4462i	−0.780177	+	0.430622i
$976$		0			0
$977$	−23.7990	+	19.9697i	−0.761398	+	0.638889i	−0.938490	−	0.345306i	$-0.887775\pi$
$977$	−23.7990	+	19.9697i	−0.761398	+	0.638889i	0.177093	+	0.984194i	$0.443331\pi$
$978$		0			0
$979$	−2.57738	+	1.20185i	−0.0823733	+	0.0384113i
$980$		0			0
$981$	41.4135	−	28.9981i	1.32223	−	0.925837i
$982$		0			0
$983$	−4.44667	−	0.389033i	−0.141827	−	0.0124082i	0.0160213	−	0.999872i	$-0.494900\pi$
$983$	−4.44667	−	0.389033i	−0.141827	−	0.0124082i	−0.157848	+	0.987463i	$0.550456\pi$
$984$		0			0
$985$	−31.2800	+	28.1136i	−0.996663	+	0.895774i
$986$		0			0
$987$	48.5200	+	33.9741i	1.54441	+	1.08141i
$988$		0			0
$989$	−5.31477	+	9.20546i	−0.169000	+	0.292717i
$990$		0			0
$991$	−48.9903	−	13.1269i	−1.55623	−	0.416990i	−0.624760	−	0.780817i	$-0.714803\pi$
$991$	−48.9903	−	13.1269i	−1.55623	−	0.416990i	−0.931467	+	0.363827i	$0.881470\pi$
$992$		0			0
$993$		−	62.0600i		−	1.96942i
$994$		0			0
$995$	−14.1750	+	0.482206i	−0.449377	+	0.0152870i
$996$		0			0
$997$	−25.7618	+	4.54250i	−0.815885	+	0.143862i	−0.565992	−	0.824411i	$-0.691507\pi$
$997$	−25.7618	+	4.54250i	−0.815885	+	0.143862i	−0.249893	+	0.968273i	$0.580395\pi$
$998$		0			0
$999$	64.0133	−	12.8160i	2.02529	−	0.405481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.cc.a.17.19	✓	228
5.3	odd	4		740.2.ch.a.313.19	yes	228
37.24	odd	36		740.2.ch.a.357.19	yes	228
185.98	even	36	inner	740.2.cc.a.653.19	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.cc.a.17.19	✓	228	1.1	even	1	trivial
740.2.cc.a.653.19	yes	228	185.98	even	36	inner
740.2.ch.a.313.19	yes	228	5.3	odd	4
740.2.ch.a.357.19	yes	228	37.24	odd	36

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.cc (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.52279 - 1.76647i) q^{3} +(2.17830 + 0.504970i) q^{5} +(-0.140686 - 1.60805i) q^{7} +(2.21796 - 6.09379i) q^{9} +(-1.80657 + 1.04302i) q^{11} +(-1.69802 + 0.618029i) q^{13} +(6.38741 - 2.57398i) q^{15} +(0.325312 - 0.893787i) q^{17} +(-0.202887 - 0.289753i) q^{19} +(-3.19550 - 3.80824i) q^{21} +(-0.668708 + 1.15824i) q^{23} +(4.49001 + 2.19996i) q^{25} +(-2.77779 - 10.3669i) q^{27} +(0.409932 - 1.52989i) q^{29} +(-2.13006 + 2.13006i) q^{31} +(-2.71512 + 5.82259i) q^{33} +(0.505559 - 3.57386i) q^{35} +(-0.390265 + 6.07023i) q^{37} +(-3.19201 + 4.55867i) q^{39} +(2.41886 + 6.64576i) q^{41} +7.94783 q^{43} +(7.90857 - 12.1541i) q^{45} +(-11.5088 + 3.08377i) q^{47} +(4.32763 - 0.763078i) q^{49} +(-0.758159 - 2.82949i) q^{51} +(-0.888838 + 10.1595i) q^{53} +(-4.46196 + 1.35976i) q^{55} +(-1.02368 - 0.372590i) q^{57} +(-0.173318 + 1.98104i) q^{59} +(6.43041 - 13.7901i) q^{61} +(-10.1111 - 2.70927i) q^{63} +(-4.01089 + 0.488805i) q^{65} +(-8.77728 + 0.767912i) q^{67} +(0.358987 + 4.10324i) q^{69} +(0.779820 - 4.42258i) q^{71} +(-0.726701 - 0.726701i) q^{73} +(15.2135 - 2.38147i) q^{75} +(1.93139 + 2.75831i) q^{77} +(-6.95588 + 0.608561i) q^{79} +(-10.4174 - 8.74128i) q^{81} +(4.84469 - 2.25912i) q^{83} +(1.15996 - 1.78267i) q^{85} +(-1.66833 - 4.58371i) q^{87} +(1.35807 + 0.118816i) q^{89} +(1.23271 + 2.64355i) q^{91} +(-1.61099 + 9.13638i) q^{93} +(-0.295633 - 0.733622i) q^{95} +(-11.8848 - 6.86169i) q^{97} +(2.34907 + 13.3223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) \) 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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