LMFDB - Embedded newform 405.2.r.a.368.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			368.15
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.45457 + 0.214747i) q^{2} +(4.00918 + 0.706926i) q^{4} +(-1.21103 + 1.87974i) q^{5} +(1.02748 + 0.719449i) q^{7} +(4.92901 + 1.32073i) q^{8} +O(q^{10})$	\(q+(2.45457 + 0.214747i) q^{2} +(4.00918 + 0.706926i) q^{4} +(-1.21103 + 1.87974i) q^{5} +(1.02748 + 0.719449i) q^{7} +(4.92901 + 1.32073i) q^{8} +(-3.37621 + 4.35388i) q^{10} +(-0.955177 + 2.62433i) q^{11} +(-0.519069 - 5.93299i) q^{13} +(2.36752 + 1.98658i) q^{14} +(4.16396 + 1.51556i) q^{16} +(5.37628 - 1.44057i) q^{17} +(-1.75284 + 1.01200i) q^{19} +(-6.18405 + 6.68010i) q^{20} +(-2.90811 + 6.23647i) q^{22} +(-2.67978 - 3.82712i) q^{23} +(-2.06683 - 4.55282i) q^{25} -14.6744i q^{26} +(3.61075 + 3.61075i) q^{28} +(-2.13514 + 1.79159i) q^{29} +(0.860131 - 4.87805i) q^{31} +(0.645681 + 0.301086i) q^{32} +(13.5058 - 2.38144i) q^{34} +(-2.59668 + 1.06012i) q^{35} +(0.354589 + 1.32334i) q^{37} +(-4.51978 + 2.10761i) q^{38} +(-8.45178 + 7.66582i) q^{40} +(0.207426 - 0.247201i) q^{41} +(3.79373 + 8.13568i) q^{43} +(-5.68468 + 9.84615i) q^{44} +(-5.75583 - 9.96940i) q^{46} +(0.213694 - 0.305187i) q^{47} +(-1.85603 - 5.09941i) q^{49} +(-4.09548 - 11.6191i) q^{50} +(2.11314 - 24.1534i) q^{52} +(-7.96878 + 7.96878i) q^{53} +(-3.77630 - 4.97361i) q^{55} +(4.11426 + 4.90319i) q^{56} +(-5.62558 + 3.93908i) q^{58} +(-2.97238 + 1.08186i) q^{59} +(-0.0275256 - 0.156106i) q^{61} +(3.15880 - 11.7888i) q^{62} +(-6.15484 - 3.55350i) q^{64} +(11.7811 + 6.20929i) q^{65} +(8.09208 - 0.707965i) q^{67} +(22.5728 - 1.97487i) q^{68} +(-6.60139 + 2.04451i) q^{70} +(-7.01095 - 4.04777i) q^{71} +(-1.41949 + 5.29760i) q^{73} +(0.586179 + 3.32439i) q^{74} +(-7.74284 + 2.81816i) q^{76} +(-2.86949 + 2.00924i) q^{77} +(10.3148 + 12.2927i) q^{79} +(-7.89151 + 5.99177i) q^{80} +(0.562227 - 0.562227i) q^{82} +(0.151375 - 1.73023i) q^{83} +(-3.80292 + 11.8506i) q^{85} +(7.56486 + 20.7843i) q^{86} +(-8.17410 + 11.6738i) q^{88} +(-6.44892 - 11.1699i) q^{89} +(3.73515 - 6.46947i) q^{91} +(-8.03821 - 17.2380i) q^{92} +(0.590066 - 0.703213i) q^{94} +(0.220434 - 4.52043i) q^{95} +(-3.21455 + 1.49897i) q^{97} +(-3.46068 - 12.9154i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	2.45457	+	0.214747i	1.73564	+	0.151849i	0.910618	−	0.413249i	$-0.135606\pi$
$2$	2.45457	+	0.214747i	1.73564	+	0.151849i	0.825024	+	0.565098i	$0.191162\pi$
$3$		0			0
$3$		0			0
$4$	4.00918	+	0.706926i	2.00459	+	0.353463i
$5$	−1.21103	+	1.87974i	−0.541587	+	0.840645i
$5$	−1.21103	+	1.87974i	−0.541587	+	0.840645i
$6$		0			0
$7$	1.02748	+	0.719449i	0.388351	+	0.271926i	0.751404	−	0.659842i	$-0.229377\pi$
$7$	1.02748	+	0.719449i	0.388351	+	0.271926i	−0.363054	+	0.931768i	$0.618266\pi$
$8$	4.92901	+	1.32073i	1.74267	+	0.466947i
$9$		0			0
$10$	−3.37621	+	4.35388i	−1.06765	+	1.37682i
$11$	−0.955177	+	2.62433i	−0.287997	+	0.791264i	0.708350	+	0.705862i	$0.249440\pi$
$11$	−0.955177	+	2.62433i	−0.287997	+	0.791264i	−0.996347	+	0.0854029i	$0.972782\pi$
$12$		0			0
$13$	−0.519069	−	5.93299i	−0.143964	−	1.64552i	−0.633652	−	0.773618i	$-0.718445\pi$
$13$	−0.519069	−	5.93299i	−0.143964	−	1.64552i	0.489688	−	0.871898i	$-0.337111\pi$
$14$	2.36752	+	1.98658i	0.632746	+	0.530937i
$15$		0			0
$16$	4.16396	+	1.51556i	1.04099	+	0.378889i
$17$	5.37628	−	1.44057i	1.30394	−	0.349390i	0.461001	−	0.887400i	$-0.347490\pi$
$17$	5.37628	−	1.44057i	1.30394	−	0.349390i	0.842938	+	0.538010i	$0.180824\pi$
$18$		0			0
$19$	−1.75284	+	1.01200i	−0.402128	+	0.232169i	−0.687402	−	0.726277i	$-0.741249\pi$
$19$	−1.75284	+	1.01200i	−0.402128	+	0.232169i	0.285274	+	0.958446i	$0.407916\pi$
$20$	−6.18405	+	6.68010i	−1.38280	+	1.49372i
$21$		0			0
$22$	−2.90811	+	6.23647i	−0.620012	+	1.32962i
$23$	−2.67978	−	3.82712i	−0.558772	−	0.798009i	0.436020	−	0.899937i	$-0.356388\pi$
$23$	−2.67978	−	3.82712i	−0.558772	−	0.798009i	−0.994792	+	0.101928i	$0.967499\pi$
$24$		0			0
$25$	−2.06683	−	4.55282i	−0.413367	−	0.910565i
$26$		−	14.6744i		−	2.87789i
$27$		0			0
$28$	3.61075	+	3.61075i	0.682367	+	0.682367i
$29$	−2.13514	+	1.79159i	−0.396485	+	0.332691i	−0.819133	−	0.573603i	$-0.805545\pi$
$29$	−2.13514	+	1.79159i	−0.396485	+	0.332691i	0.422648	+	0.906294i	$0.361101\pi$
$30$		0			0
$31$	0.860131	−	4.87805i	0.154484	−	0.876123i	−0.804772	−	0.593584i	$-0.797712\pi$
$31$	0.860131	−	4.87805i	0.154484	−	0.876123i	0.959256	−	0.282539i	$-0.0911765\pi$
$32$	0.645681	+	0.301086i	0.114141	+	0.0532250i
$33$		0			0
$34$	13.5058	−	2.38144i	2.31623	−	0.408413i
$35$	−2.59668	+	1.06012i	−0.438919	+	0.179193i
$36$		0			0
$37$	0.354589	+	1.32334i	0.0582941	+	0.217556i	0.988928	−	0.148394i	$-0.0474105\pi$
$37$	0.354589	+	1.32334i	0.0582941	+	0.217556i	−0.930634	+	0.365951i	$0.880744\pi$
$38$	−4.51978	+	2.10761i	−0.733206	+	0.341899i
$39$		0			0
$40$	−8.45178	+	7.66582i	−1.33634	+	1.21207i
$41$	0.207426	−	0.247201i	0.0323945	−	0.0386063i	−0.749604	−	0.661887i	$-0.769756\pi$
$41$	0.207426	−	0.247201i	0.0323945	−	0.0386063i	0.781998	+	0.623280i	$0.214200\pi$
$42$		0			0
$43$	3.79373	+	8.13568i	0.578538	+	1.24068i	0.950005	+	0.312234i	$0.101077\pi$
$43$	3.79373	+	8.13568i	0.578538	+	1.24068i	−0.371467	+	0.928446i	$0.621145\pi$
$44$	−5.68468	+	9.84615i	−0.856997	+	1.48436i
$45$		0			0
$46$	−5.75583	−	9.96940i	−0.848652	−	1.46991i
$47$	0.213694	−	0.305187i	0.0311705	−	0.0445161i	−0.803264	−	0.595623i	$-0.796905\pi$
$47$	0.213694	−	0.305187i	0.0311705	−	0.0445161i	0.834435	+	0.551107i	$0.185794\pi$
$48$		0			0
$49$	−1.85603	−	5.09941i	−0.265148	−	0.728487i
$50$	−4.09548	−	11.6191i	−0.579188	−	1.64318i
$51$		0			0
$52$	2.11314	−	24.1534i	0.293040	−	3.34947i
$53$	−7.96878	+	7.96878i	−1.09460	+	1.09460i	−0.0995653	+	0.995031i	$0.531745\pi$
$53$	−7.96878	+	7.96878i	−1.09460	+	1.09460i	−0.995031	+	0.0995653i	$0.968255\pi$
$54$		0			0
$55$	−3.77630	−	4.97361i	−0.509197	−	0.670642i
$56$	4.11426	+	4.90319i	0.549792	+	0.655216i
$57$		0			0
$58$	−5.62558	+	3.93908i	−0.738675	+	0.517226i
$59$	−2.97238	+	1.08186i	−0.386971	+	0.140846i	−0.528177	−	0.849134i	$-0.677124\pi$
$59$	−2.97238	+	1.08186i	−0.386971	+	0.140846i	0.141206	+	0.989980i	$0.454902\pi$
$60$		0			0
$61$	−0.0275256	−	0.156106i	−0.00352429	−	0.0199873i	0.982995	−	0.183633i	$-0.0587858\pi$
$61$	−0.0275256	−	0.156106i	−0.00352429	−	0.0199873i	−0.986519	+	0.163646i	$0.947675\pi$
$62$	3.15880	−	11.7888i	0.401168	−	1.49718i
$63$		0			0
$64$	−6.15484	−	3.55350i	−0.769355	−	0.444187i
$65$	11.7811	+	6.20929i	1.46126	+	0.770168i
$66$		0			0
$67$	8.09208	−	0.707965i	0.988605	−	0.0864917i	0.418633	−	0.908156i	$-0.362509\pi$
$67$	8.09208	−	0.707965i	0.988605	−	0.0864917i	0.569972	+	0.821664i	$0.306954\pi$
$68$	22.5728	−	1.97487i	2.73736	−	0.239488i
$69$		0			0
$70$	−6.60139	+	2.04451i	−0.789017	+	0.244366i
$71$	−7.01095	−	4.04777i	−0.832046	−	0.480382i	0.0225065	−	0.999747i	$-0.492835\pi$
$71$	−7.01095	−	4.04777i	−0.832046	−	0.480382i	−0.854553	+	0.519365i	$0.826169\pi$
$72$		0			0
$73$	−1.41949	+	5.29760i	−0.166139	+	0.620037i	0.831754	+	0.555145i	$0.187337\pi$
$73$	−1.41949	+	5.29760i	−0.166139	+	0.620037i	−0.997892	+	0.0648926i	$0.979330\pi$
$74$	0.586179	+	3.32439i	0.0681419	+	0.386452i
$75$		0			0
$76$	−7.74284	+	2.81816i	−0.888165	+	0.323266i
$77$	−2.86949	+	2.00924i	−0.327009	+	0.228974i
$78$		0			0
$79$	10.3148	+	12.2927i	1.16051	+	1.38304i	0.909838	+	0.414964i	$0.136206\pi$
$79$	10.3148	+	12.2927i	1.16051	+	1.38304i	0.250668	+	0.968073i	$0.419350\pi$
$80$	−7.89151	+	5.99177i	−0.882298	+	0.669900i
$81$		0			0
$82$	0.562227	−	0.562227i	0.0620876	−	0.0620876i
$83$	0.151375	−	1.73023i	0.0166156	−	0.189917i	−0.983351	−	0.181718i	$-0.941834\pi$
$83$	0.151375	−	1.73023i	0.0166156	−	0.189917i	0.999966	−	0.00819974i	$-0.00261009\pi$
$84$		0			0
$85$	−3.80292	+	11.8506i	−0.412485	+	1.28537i
$86$	7.56486	+	20.7843i	0.815740	+	2.24123i
$87$		0			0
$88$	−8.17410	+	11.6738i	−0.871361	+	1.24443i
$89$	−6.44892	−	11.1699i	−0.683584	−	1.18400i	−0.973879	−	0.227066i	$-0.927087\pi$
$89$	−6.44892	−	11.1699i	−0.683584	−	1.18400i	0.290295	−	0.956937i	$-0.406247\pi$
$90$		0			0
$91$	3.73515	−	6.46947i	0.391550	−	0.678185i
$92$	−8.03821	−	17.2380i	−0.838041	−	1.79719i
$93$		0			0
$94$	0.590066	−	0.703213i	0.0608606	−	0.0725309i
$95$	0.220434	−	4.52043i	0.0226161	−	0.463787i
$96$		0			0
$97$	−3.21455	+	1.49897i	−0.326388	+	0.152197i	−0.578904	−	0.815395i	$-0.696520\pi$
$97$	−3.21455	+	1.49897i	−0.326388	+	0.152197i	0.252517	+	0.967593i	$0.418742\pi$
$98$	−3.46068	−	12.9154i	−0.349581	−	1.30466i
$99$		0			0
$100$	−5.06779	−	19.7142i	−0.506779	−	1.97142i
$101$	9.18834	−	1.62015i	0.914274	−	0.161211i	0.303330	−	0.952885i	$-0.401901\pi$
$101$	9.18834	−	1.62015i	0.914274	−	0.161211i	0.610943	+	0.791674i	$0.290790\pi$
$102$		0			0
$103$	−0.625323	−	0.291593i	−0.0616149	−	0.0287315i	0.391567	−	0.920150i	$-0.371933\pi$
$103$	−0.625323	−	0.291593i	−0.0616149	−	0.0287315i	−0.453181	+	0.891418i	$0.649711\pi$
$104$	5.27735	−	29.9293i	0.517487	−	2.93481i
$105$		0			0
$106$	−21.2712	+	17.8487i	−2.06604	+	1.73361i
$107$	7.01111	+	7.01111i	0.677790	+	0.677790i	0.959500	−	0.281710i	$-0.0909016\pi$
$107$	7.01111	+	7.01111i	0.677790	+	0.677790i	−0.281710	+	0.959500i	$0.590902\pi$
$108$		0			0
$109$			3.98129i			0.381339i	0.981654	+	0.190669i	$0.0610658\pi$
$109$			3.98129i			0.381339i	−0.981654	+	0.190669i	$0.938934\pi$
$110$	−8.20113	−	13.0190i	−0.781947	−	1.24131i
$111$		0			0
$112$	3.18801	+	4.55296i	0.301239	+	0.430214i
$113$	−5.38280	+	11.5434i	−0.506371	+	1.08592i	0.472480	+	0.881341i	$0.343359\pi$
$113$	−5.38280	+	11.5434i	−0.506371	+	1.08592i	−0.978851	+	0.204575i	$0.934419\pi$
$114$		0			0
$115$	10.4393	−	0.402540i	0.973466	−	0.0375371i
$116$	−9.82667	+	5.67343i	−0.912383	+	0.526765i
$117$		0			0
$118$	−7.52823	+	2.01718i	−0.693030	+	0.185697i
$119$	6.56043	+	2.38780i	0.601394	+	0.218889i
$120$		0			0
$121$	2.45176	+	2.05727i	0.222887	+	0.187024i
$122$	−0.0340403	−	0.389083i	−0.00308187	−	0.0352259i
$123$		0			0
$124$	6.89684	−	18.9489i	0.619354	−	1.70166i
$125$	11.0611	+	1.62848i	0.989335	+	0.145656i
$126$		0			0
$127$	−1.43624	−	0.384839i	−0.127445	−	0.0341489i	0.194532	−	0.980896i	$-0.437681\pi$
$127$	−1.43624	−	0.384839i	−0.127445	−	0.0341489i	−0.321978	+	0.946747i	$0.604348\pi$
$128$	−15.5115	−	10.8613i	−1.37104	−	0.960012i
$129$		0			0
$130$	27.5840	+	17.7711i	2.41928	+	1.55863i
$131$	4.86082	+	0.857093i	0.424691	+	0.0748846i	0.381909	−	0.924200i	$-0.375267\pi$
$131$	4.86082	+	0.857093i	0.424691	+	0.0748846i	0.0427823	+	0.999084i	$0.486378\pi$
$132$		0			0
$133$	−2.52909	−	0.221266i	−0.219300	−	0.0191862i
$134$	20.0146			1.72900
$135$		0			0
$136$	28.4024			2.43548
$137$	−9.23718	−	0.808148i	−0.789185	−	0.0690448i	−0.314566	−	0.949236i	$-0.601859\pi$
$137$	−9.23718	−	0.808148i	−0.789185	−	0.0690448i	−0.474620	+	0.880191i	$0.657414\pi$
$138$		0			0
$139$	0.653880	+	0.115297i	0.0554614	+	0.00977934i	0.201310	−	0.979528i	$-0.435480\pi$
$139$	0.653880	+	0.115297i	0.0554614	+	0.00977934i	−0.145849	+	0.989307i	$0.546591\pi$
$140$	−11.1600	+	2.41455i	−0.943190	+	0.204067i
$141$		0			0
$142$	−16.3396	−	11.4411i	−1.37119	−	0.960117i
$143$	16.0659	+	4.30485i	1.34350	+	0.359990i
$144$		0			0
$145$	−0.782020	−	6.18317i	−0.0649432	−	0.513484i
$146$	−4.62188	+	12.6985i	−0.382509	+	1.05094i
$147$		0			0
$148$	0.486104	+	5.55619i	0.0399575	+	0.456716i
$149$	−3.98025	−	3.33983i	−0.326075	−	0.273610i	0.465023	−	0.885298i	$-0.346046\pi$
$149$	−3.98025	−	3.33983i	−0.326075	−	0.273610i	−0.791098	+	0.611689i	$0.790490\pi$
$150$		0			0
$151$	3.92942	+	1.43019i	0.319772	+	0.116387i	0.496919	−	0.867797i	$-0.334465\pi$
$151$	3.92942	+	1.43019i	0.319772	+	0.116387i	−0.177147	+	0.984184i	$0.556687\pi$
$152$	−9.97633	+	2.67315i	−0.809187	+	0.216821i
$153$		0			0
$154$	−7.47485	+	4.31561i	−0.602340	+	0.347761i
$155$	8.12781	+	7.52426i	0.652841	+	0.604363i
$156$		0			0
$157$	5.80347	−	12.4456i	0.463168	−	0.993266i	−0.526538	−	0.850151i	$-0.676510\pi$
$157$	5.80347	−	12.4456i	0.463168	−	0.993266i	0.989706	−	0.143115i	$-0.0457119\pi$
$158$	22.6786	+	32.3884i	1.80421	+	2.57668i
$159$		0			0
$160$	−1.34790	+	0.849088i	−0.106561	+	0.0671263i
$161$		−	5.86025i		−	0.461852i
$162$		0			0
$163$	14.8723	+	14.8723i	1.16489	+	1.16489i	0.983391	+	0.181498i	$0.0580947\pi$
$163$	14.8723	+	14.8723i	1.16489	+	1.16489i	0.181498	+	0.983391i	$0.441905\pi$
$164$	1.00636	−	0.844437i	0.0785835	−	0.0659394i
$165$		0			0
$166$	0.743123	−	4.21446i	0.0576775	−	0.327105i
$167$	3.30546	+	1.54136i	0.255784	+	0.119274i	0.546281	−	0.837602i	$-0.316043\pi$
$167$	3.30546	+	1.54136i	0.255784	+	0.119274i	−0.290497	+	0.956876i	$0.593821\pi$
$168$		0			0
$169$	−22.1284	+	3.90184i	−1.70219	+	0.300142i
$170$	−11.8794	+	28.2714i	−0.911109	+	2.16831i
$171$		0			0
$172$	9.45841	+	35.2993i	0.721197	+	2.69154i
$173$	7.42544	−	3.46254i	0.564546	−	0.263252i	−0.119325	−	0.992855i	$-0.538073\pi$
$173$	7.42544	−	3.46254i	0.564546	−	0.263252i	0.683871	+	0.729603i	$0.260295\pi$
$174$		0			0
$175$	1.15190	−	6.16491i	0.0870751	−	0.466024i
$176$	−7.95463	+	9.47996i	−0.599603	+	0.714579i
$177$		0			0
$178$	−13.4306	−	28.8021i	−1.00667	−	2.15881i
$179$	−3.07632	+	5.32834i	−0.229935	+	0.398259i	−0.957789	−	0.287474i	$-0.907185\pi$
$179$	−3.07632	+	5.32834i	−0.229935	+	0.398259i	0.727854	+	0.685732i	$0.240518\pi$
$180$		0			0
$181$	−4.75332	−	8.23298i	−0.353311	−	0.611953i	0.633516	−	0.773729i	$-0.281611\pi$
$181$	−4.75332	−	8.23298i	−0.353311	−	0.611953i	−0.986827	+	0.161777i	$0.948278\pi$
$182$	10.5575	−	15.0776i	0.782573	−	1.11763i
$183$		0			0
$184$	−8.15408	−	22.4032i	−0.601127	−	1.65158i
$185$	−2.91696	−	0.936070i	−0.214459	−	0.0688212i
$186$		0			0
$187$	−1.35477	+	15.4851i	−0.0990708	+	1.13238i
$188$	1.07248	−	1.07248i	0.0782189	−	0.0782189i
$189$		0			0
$190$	1.51182	−	11.0484i	0.109679	−	0.801534i
$191$	−8.71630	−	10.3877i	−0.630690	−	0.751627i	0.352179	−	0.935933i	$-0.385441\pi$
$191$	−8.71630	−	10.3877i	−0.630690	−	0.751627i	−0.982869	+	0.184306i	$0.940996\pi$
$192$		0			0
$193$	14.3226	−	10.0288i	1.03096	−	0.721888i	0.0697136	−	0.997567i	$-0.477791\pi$
$193$	14.3226	−	10.0288i	1.03096	−	0.721888i	0.961250	+	0.275679i	$0.0889026\pi$
$194$	−8.21222	+	2.98900i	−0.589603	+	0.214598i
$195$		0			0
$196$	−3.83626	−	21.7565i	−0.274019	−	1.55404i
$197$	0.482608	−	1.80112i	0.0343844	−	0.128324i	−0.946600	−	0.322410i	$-0.895507\pi$
$197$	0.482608	−	1.80112i	0.0343844	−	0.128324i	0.980985	+	0.194085i	$0.0621739\pi$
$198$		0			0
$199$	−6.71379	−	3.87621i	−0.475928	−	0.274777i	0.242790	−	0.970079i	$-0.421937\pi$
$199$	−6.71379	−	3.87621i	−0.475928	−	0.274777i	−0.718718	+	0.695302i	$0.755271\pi$
$200$	−4.17442	−	25.1706i	−0.295176	−	1.77983i
$201$		0			0
$202$	22.9013	−	2.00361i	1.61133	−	0.140973i
$203$	−3.48277	+	0.304703i	−0.244443	+	0.0213859i
$204$		0			0
$205$	0.213474	+	0.689273i	0.0149097	+	0.0481409i
$206$	−1.47228	−	0.850021i	−0.102579	−	0.0592237i
$207$		0			0
$208$	6.83040	−	25.4914i	0.473603	−	1.76751i
$209$	−0.981552	−	5.56666i	−0.0678954	−	0.385054i
$210$		0			0
$211$	−20.1076	+	7.31857i	−1.38426	+	0.503831i	−0.923468	−	0.383675i	$-0.874658\pi$
$211$	−20.1076	+	7.31857i	−1.38426	+	0.503831i	−0.460796	+	0.887506i	$0.652436\pi$
$212$	−37.5816	+	26.3149i	−2.58111	+	1.80732i
$213$		0			0
$214$	15.7036	+	18.7149i	1.07348	+	1.27932i
$215$	−19.8873	−	2.72130i	−1.35630	−	0.185591i
$216$		0			0
$217$	4.39327	−	4.39327i	0.298235	−	0.298235i
$218$	−0.854971	+	9.77236i	−0.0579059	+	0.661868i
$219$		0			0
$220$	−11.6239	−	22.6097i	−0.783683	−	1.52434i
$221$	−11.3376	−	31.1497i	−0.762646	−	2.09535i
$222$		0			0
$223$	−13.2104	+	18.8664i	−0.884633	+	1.26339i	0.0791939	+	0.996859i	$0.474765\pi$
$223$	−13.2104	+	18.8664i	−0.884633	+	1.26339i	−0.963827	+	0.266528i	$0.914124\pi$
$224$	0.446808	+	0.773894i	0.0298536	+	0.0517079i
$225$		0			0
$226$	−15.6914	+	27.1782i	−1.04377	+	1.80787i
$227$	10.0438	+	21.5391i	0.666633	+	1.42960i	0.890502	+	0.454979i	$0.150353\pi$
$227$	10.0438	+	21.5391i	0.666633	+	1.42960i	−0.223869	+	0.974619i	$0.571869\pi$
$228$		0			0
$229$	−9.86052	+	11.7513i	−0.651602	+	0.776549i	−0.986155	−	0.165828i	$-0.946970\pi$
$229$	−9.86052	+	11.7513i	−0.651602	+	0.776549i	0.334553	+	0.942377i	$0.391415\pi$
$230$	25.7103	+	1.25374i	1.69529	+	0.0826689i
$231$		0			0
$232$	−12.8903	+	6.01086i	−0.846291	+	0.394632i
$233$	−3.29342	−	12.2912i	−0.215759	−	0.805223i	−0.985898	−	0.167347i	$-0.946480\pi$
$233$	−3.29342	−	12.2912i	−0.215759	−	0.805223i	0.770139	−	0.637876i	$-0.220187\pi$
$234$		0			0
$235$	0.314883	+	0.771279i	0.0205407	+	0.0503127i
$236$	−12.6816	+	2.23611i	−0.825501	+	0.145558i
$237$		0			0
$238$	15.5903	+	7.26986i	1.01057	+	0.471235i
$239$	0.944310	−	5.35545i	0.0610824	−	0.346415i	−0.938915	−	0.344149i	$-0.888167\pi$
$239$	0.944310	−	5.35545i	0.0610824	−	0.346415i	0.999997	−	0.00226637i	$-0.000721408\pi$
$240$		0			0
$241$	5.71656	−	4.79676i	0.368236	−	0.308987i	−0.439827	−	0.898082i	$-0.644960\pi$
$241$	5.71656	−	4.79676i	0.368236	−	0.308987i	0.808063	+	0.589096i	$0.200516\pi$
$242$	5.57622	+	5.57622i	0.358453	+	0.358453i
$243$		0			0
$244$		−	0.645313i		−	0.0413119i
$245$	11.8333	+	2.68666i	0.755999	+	0.171644i
$246$		0			0
$247$	6.91404	+	9.87427i	0.439930	+	0.628285i
$248$	10.6822	−	22.9080i	0.678318	−	1.45466i
$249$		0			0
$250$	26.8005	+	6.37256i	1.69501	+	0.403036i
$251$	−4.37402	+	2.52534i	−0.276086	+	0.159398i	−0.631650	−	0.775254i	$-0.717622\pi$
$251$	−4.37402	+	2.52534i	−0.276086	+	0.159398i	0.355564	+	0.934652i	$0.384289\pi$
$252$		0			0
$253$	12.6033	−	3.37704i	0.792361	−	0.212312i
$254$	−3.44270	−	1.25304i	−0.216014	−	0.0786228i
$255$		0			0
$256$	−24.8532	−	20.8543i	−1.55332	−	1.30339i
$257$	2.32628	+	26.5895i	0.145109	+	1.65861i	0.624514	+	0.781013i	$0.285297\pi$
$257$	2.32628	+	26.5895i	0.145109	+	1.65861i	−0.479405	+	0.877594i	$0.659147\pi$
$258$		0			0
$259$	−0.587745	+	1.61482i	−0.0365207	+	0.100340i
$260$	42.8429	+	33.2225i	2.65700	+	2.06037i
$261$		0			0
$262$	11.7471	+	3.14764i	0.725741	+	0.194462i
$263$	21.4619	+	15.0278i	1.32340	+	0.926654i	0.999809	−	0.0195432i	$-0.00622118\pi$
$263$	21.4619	+	15.0278i	1.32340	+	0.926654i	0.323590	+	0.946197i	$0.395110\pi$
$264$		0			0
$265$	−5.32882	−	24.6296i	−0.327347	−	1.51299i
$266$	−6.16030	−	1.08623i	−0.377712	−	0.0666009i
$267$		0			0
$268$	32.9431	+	2.88214i	2.01232	+	0.176055i
$269$	2.30251			0.140387			0.0701934	−	0.997533i	$-0.477638\pi$
$269$	2.30251			0.140387			0.0701934	+	0.997533i	$0.477638\pi$
$270$		0			0
$271$	6.12068			0.371805			0.185902	−	0.982568i	$-0.440479\pi$
$271$	6.12068			0.371805			0.185902	+	0.982568i	$0.440479\pi$
$272$	24.5699	+	2.14958i	1.48977	+	0.130338i
$273$		0			0
$274$	−22.4997	−	3.96731i	−1.35926	−	0.239674i
$275$	13.9223	−	1.07529i	0.839546	−	0.0648426i
$276$		0			0
$277$	8.67336	+	6.07315i	0.521132	+	0.364901i	0.804351	−	0.594155i	$-0.202513\pi$
$277$	8.67336	+	6.07315i	0.521132	+	0.364901i	−0.283219	+	0.959055i	$0.591402\pi$
$278$	1.58023	+	0.423423i	0.0947762	+	0.0253952i
$279$		0			0
$280$	−14.1992	+	1.79585i	−0.848564	+	0.107323i
$281$	2.07965	−	5.71378i	0.124061	−	0.340856i	−0.862078	−	0.506776i	$-0.830837\pi$
$281$	2.07965	−	5.71378i	0.124061	−	0.340856i	0.986139	+	0.165920i	$0.0530594\pi$
$282$		0			0
$283$	0.312211	+	3.56859i	0.0185590	+	0.212131i	0.999812	+	0.0194049i	$0.00617717\pi$
$283$	0.312211	+	3.56859i	0.0185590	+	0.212131i	−0.981253	+	0.192726i	$0.938267\pi$
$284$	−25.2466	−	21.1845i	−1.49811	−	1.25707i
$285$		0			0
$286$	38.5104	+	14.0167i	2.27717	+	0.828822i
$287$	0.390974	−	0.104761i	0.0230785	−	0.00618386i
$288$		0			0
$289$	12.1067	−	6.98981i	0.712160	−	0.411166i
$290$	−0.591705	−	15.3449i	−0.0347461	−	0.901086i
$291$		0			0
$292$	−9.43599	+	20.2355i	−0.552200	+	1.18420i
$293$	−15.2979	−	21.8477i	−0.893714	−	1.27636i	−0.960412	−	0.278582i	$-0.910135\pi$
$293$	−15.2979	−	21.8477i	−0.893714	−	1.27636i	0.0666984	−	0.997773i	$-0.478753\pi$
$294$		0			0
$295$	1.56602	−	6.89745i	0.0911771	−	0.401585i
$296$			6.99110i			0.406349i
$297$		0			0
$298$	−9.05259	−	9.05259i	−0.524403	−	0.524403i
$299$	−21.3153	+	17.8856i	−1.23269	+	1.03435i
$300$		0			0
$301$	−1.95523	+	11.0886i	−0.112697	+	0.639138i
$302$	9.33791	+	4.35434i	0.537336	+	0.250564i
$303$		0			0
$304$	−8.83248	+	1.55741i	−0.506578	+	0.0893233i
$305$	0.326772	+	0.137307i	0.0187109	+	0.00786217i
$306$		0			0
$307$	3.38428	+	12.6303i	0.193151	+	0.720850i	0.992738	+	0.120299i	$0.0383854\pi$
$307$	3.38428	+	12.6303i	0.193151	+	0.720850i	−0.799586	+	0.600551i	$0.794948\pi$
$308$	−12.9247	+	6.02688i	−0.736453	+	0.343413i
$309$		0			0
$310$	18.3345	+	20.2142i	1.04133	+	1.14809i
$311$	7.01743	−	8.36305i	0.397922	−	0.474225i	−0.529463	−	0.848333i	$-0.677607\pi$
$311$	7.01743	−	8.36305i	0.397922	−	0.474225i	0.927385	+	0.374108i	$0.122051\pi$
$312$		0			0
$313$	−2.03021	−	4.35380i	−0.114754	−	0.246091i	0.840539	−	0.541751i	$-0.182238\pi$
$313$	−2.03021	−	4.35380i	−0.114754	−	0.246091i	−0.955293	+	0.295660i	$0.904461\pi$
$314$	16.9177	−	29.3023i	0.954720	−	1.65362i
$315$		0			0
$316$	32.6638	+	56.5754i	1.83748	+	3.18262i
$317$	18.1287	−	25.8905i	1.01821	−	1.45415i	0.131787	−	0.991278i	$-0.457929\pi$
$317$	18.1287	−	25.8905i	1.01821	−	1.45415i	0.886423	−	0.462876i	$-0.153182\pi$
$318$		0			0
$319$	−2.66229	−	7.31459i	−0.149060	−	0.409538i
$320$	14.1333	−	7.26611i	0.790076	−	0.406188i
$321$		0			0
$322$	1.25847	−	14.3844i	0.0701318	−	0.801610i
$323$	−7.96588	+	7.96588i	−0.443234	+	0.443234i
$324$		0			0
$325$	−25.9390	+	14.6257i	−1.43884	+	0.811290i
$326$	33.3113	+	39.6989i	1.84494	+	2.19872i
$327$		0			0
$328$	1.34889	−	0.944503i	0.0744800	−	0.0521515i
$329$	0.439133	−	0.159831i	0.0242102	−	0.00881179i
$330$		0			0
$331$	−4.86664	−	27.6001i	−0.267495	−	1.51704i	−0.761835	−	0.647771i	$-0.775701\pi$
$331$	−4.86664	−	27.6001i	−0.267495	−	1.51704i	0.494340	−	0.869268i	$-0.335410\pi$
$332$	1.83003	−	6.82978i	0.100436	−	0.374833i
$333$		0			0
$334$	7.78247	+	4.49321i	0.425838	+	0.245858i
$335$	−8.46893	+	16.0684i	−0.462707	+	0.877908i
$336$		0			0
$337$	−35.9100	+	3.14172i	−1.95614	+	0.171140i	−0.994620	−	0.103586i	$-0.966968\pi$
$337$	−35.9100	+	3.14172i	−1.95614	+	0.171140i	−0.961522	+	0.274727i	$0.911413\pi$
$338$	−55.1537	+	4.82532i	−2.99997	+	0.262463i
$339$		0			0
$340$	−23.6240	+	44.8226i	−1.28119	+	2.43085i
$341$	11.9800	+	6.91666i	0.648754	+	0.374558i
$342$		0			0
$343$	4.03422	−	15.0559i	0.217828	−	0.812944i
$344$	7.95435	+	45.1114i	0.428870	+	2.43224i
$345$		0			0
$346$	18.9698	−	6.90445i	1.01982	−	0.371186i
$347$	−13.1696	+	9.22149i	−0.706984	+	0.495035i	−0.870913	−	0.491437i	$-0.836472\pi$
$347$	−13.1696	+	9.22149i	−0.706984	+	0.495035i	0.163930	+	0.986472i	$0.447583\pi$
$348$		0			0
$349$	−3.65928	−	4.36096i	−0.195877	−	0.233437i	0.659162	−	0.752001i	$-0.270911\pi$
$349$	−3.65928	−	4.36096i	−0.195877	−	0.233437i	−0.855039	+	0.518564i	$0.826467\pi$
$350$	4.15130	−	14.8848i	0.221896	−	0.795628i
$351$		0			0
$352$	−1.40689	+	1.40689i	−0.0749873	+	0.0749873i
$353$	1.22287	−	13.9775i	0.0650869	−	0.743946i	−0.891599	−	0.452825i	$-0.850416\pi$
$353$	1.22287	−	13.9775i	0.0650869	−	0.743946i	0.956686	−	0.291121i	$-0.0940282\pi$
$354$		0			0
$355$	16.0992	−	8.27679i	0.854456	−	0.439286i
$356$	−17.9586	−	49.3408i	−0.951804	−	2.61506i
$357$		0			0
$358$	−8.69528	+	12.4181i	−0.459560	+	0.656319i
$359$	3.44870	+	5.97333i	0.182016	+	0.315260i	0.942567	−	0.334018i	$-0.108405\pi$
$359$	3.44870	+	5.97333i	0.182016	+	0.315260i	−0.760551	+	0.649278i	$0.775071\pi$
$360$		0			0
$361$	−7.45171	+	12.9067i	−0.392195	+	0.679302i
$362$	−9.89933	−	21.2292i	−0.520297	−	1.11578i
$363$		0			0
$364$	19.5483	−	23.2968i	1.02461	−	1.22108i
$365$	−8.23907	−	9.08380i	−0.431253	−	0.475468i
$366$		0			0
$367$	−3.23085	+	1.50657i	−0.168649	+	0.0786424i	−0.505110	−	0.863055i	$-0.668548\pi$
$367$	−3.23085	+	1.50657i	−0.168649	+	0.0786424i	0.336460	+	0.941698i	$0.390770\pi$
$368$	−5.35826	−	19.9973i	−0.279319	−	1.04243i
$369$		0			0
$370$	−6.95886	−	2.92406i	−0.361774	−	0.152014i
$371$	−13.9209	+	2.45463i	−0.722736	+	0.127438i
$372$		0			0
$373$	−11.1529	−	5.20069i	−0.577476	−	0.269282i	0.111859	−	0.993724i	$-0.464319\pi$
$373$	−11.1529	−	5.20069i	−0.577476	−	0.269282i	−0.689335	+	0.724443i	$0.742097\pi$
$374$	−6.65076	+	37.7184i	−0.343903	+	1.95037i
$375$		0			0
$376$	1.45637	−	1.22204i	0.0751066	−	0.0630219i
$377$	11.7378	+	11.7378i	0.604527	+	0.604527i
$378$		0			0
$379$		−	15.9996i		−	0.821843i	−0.911671	−	0.410922i	$-0.865207\pi$
$379$		−	15.9996i		−	0.821843i	0.911671	−	0.410922i	$-0.134793\pi$
$380$	4.07937	−	17.9674i	0.209267	−	0.921708i
$381$		0			0
$382$	−19.1640	−	27.3691i	−0.980518	−	1.40032i
$383$	10.5466	−	22.6172i	0.538904	−	1.15568i	−0.428755	−	0.903421i	$-0.641048\pi$
$383$	10.5466	−	22.6172i	0.538904	−	1.15568i	0.967659	−	0.252262i	$-0.0811746\pi$
$384$		0			0
$385$	−0.301816	−	7.82714i	−0.0153820	−	0.398908i
$386$	37.3095	−	21.5406i	1.89900	−	1.09639i
$387$		0			0
$388$	−13.9473	+	3.73718i	−0.708069	+	0.189726i
$389$	−17.5837	−	6.39994i	−0.891529	−	0.324490i	−0.144676	−	0.989479i	$-0.546214\pi$
$389$	−17.5837	−	6.39994i	−0.891529	−	0.324490i	−0.746853	+	0.664989i	$0.768436\pi$
$390$		0			0
$391$	−19.9205	−	16.7153i	−1.00742	−	0.845327i
$392$	−2.41350	−	27.5864i	−0.121900	−	1.39332i
$393$		0			0
$394$	1.57138	−	4.31732i	0.0791649	−	0.217504i
$395$	−35.5986	+	4.50235i	−1.79116	+	0.226538i
$396$		0			0
$397$	−9.00214	−	2.41212i	−0.451805	−	0.121061i	0.0257391	−	0.999669i	$-0.491806\pi$
$397$	−9.00214	−	2.41212i	−0.451805	−	0.121061i	−0.477544	+	0.878608i	$0.658473\pi$
$398$	−15.6471	−	10.9562i	−0.784316	−	0.549184i
$399$		0			0
$400$	−1.70614	−	22.0902i	−0.0853070	−	1.10451i
$401$	21.8705	+	3.85636i	1.09216	+	0.192578i	0.690588	−	0.723249i	$-0.257352\pi$
$401$	21.8705	+	3.85636i	1.09216	+	0.192578i	0.401575	+	0.915826i	$0.368463\pi$
$402$		0			0
$403$	−29.3879	−	2.57111i	−1.46391	−	0.128076i
$404$	37.9830			1.88972
$405$		0			0
$406$	−8.61413			−0.427512
$407$	−3.81158	−	0.333470i	−0.188933	−	0.0165295i
$408$		0			0
$409$	−2.79062	−	0.492062i	−0.137987	−	0.0243309i	0.104228	−	0.994553i	$-0.466763\pi$
$409$	−2.79062	−	0.492062i	−0.137987	−	0.0243309i	−0.242215	+	0.970223i	$0.577874\pi$
$410$	0.375968	+	1.73771i	0.0185678	+	0.0858195i
$411$		0			0
$412$	−2.30089	−	1.61110i	−0.113357	−	0.0793734i
$413$	−3.83240	−	1.02689i	−0.188580	−	0.0505299i
$414$		0			0
$415$	3.06906	+	2.37990i	0.150654	+	0.116825i
$416$	1.45119	−	3.98710i	0.0711503	−	0.195484i
$417$		0			0
$418$	−1.21386	−	13.8745i	−0.0593720	−	0.678626i
$419$	−3.08697	−	2.59027i	−0.150808	−	0.126543i	0.564262	−	0.825596i	$-0.309161\pi$
$419$	−3.08697	−	2.59027i	−0.150808	−	0.126543i	−0.715070	+	0.699053i	$0.753605\pi$
$420$		0			0
$421$	−4.12343	−	1.50080i	−0.200964	−	0.0731448i	0.239577	−	0.970877i	$-0.422991\pi$
$421$	−4.12343	−	1.50080i	−0.200964	−	0.0731448i	−0.440541	+	0.897733i	$0.645213\pi$
$422$	−50.9271	+	13.6459i	−2.47909	+	0.664271i
$423$		0			0
$424$	−49.8028	+	28.7537i	−2.41864	+	1.39640i
$425$	−17.6705	−	21.4998i	−0.857147	−	1.04290i
$426$		0			0
$427$	0.0840279	−	0.180198i	0.00406640	−	0.00872041i
$428$	23.1524	+	33.0651i	1.11912	+	1.59826i
$429$		0			0
$430$	−48.2302	−	10.9503i	−2.32587	−	0.528073i
$431$		−	14.3108i		−	0.689325i	−0.938727	−	0.344662i	$-0.887993\pi$
$431$		−	14.3108i		−	0.689325i	0.938727	−	0.344662i	$-0.112007\pi$
$432$		0			0
$433$	−10.5706	−	10.5706i	−0.507988	−	0.507988i	0.405920	−	0.913909i	$-0.366951\pi$
$433$	−10.5706	−	10.5706i	−0.507988	−	0.507988i	−0.913909	+	0.405920i	$0.866951\pi$
$434$	11.7270	−	9.84015i	0.562915	−	0.472342i
$435$		0			0
$436$	−2.81448	+	15.9617i	−0.134789	+	0.764427i
$437$	8.57026	+	3.99638i	0.409971	+	0.191173i
$438$		0			0
$439$	23.9432	−	4.22183i	1.14275	−	0.201497i	0.429940	−	0.902857i	$-0.358535\pi$
$439$	23.9432	−	4.22183i	1.14275	−	0.201497i	0.712807	+	0.701360i	$0.247424\pi$
$440$	−12.0447	−	29.5025i	−0.574208	−	1.40647i
$441$		0			0
$442$	−21.1395	−	78.8937i	−1.00550	−	3.75259i
$443$	6.12987	−	2.85840i	0.291239	−	0.135807i	−0.271508	−	0.962436i	$-0.587522\pi$
$443$	6.12987	−	2.85840i	0.291239	−	0.135807i	0.562747	+	0.826629i	$0.309745\pi$
$444$		0			0
$445$	28.8062	+	1.40470i	1.36555	+	0.0665894i
$446$	−36.4773	+	43.4720i	−1.72725	+	2.05846i
$447$		0			0
$448$	−3.76741	−	8.07923i	−0.177993	−	0.381708i
$449$	−1.79424	+	3.10771i	−0.0846753	+	0.146662i	−0.905253	−	0.424873i	$-0.860319\pi$
$449$	−1.79424	+	3.10771i	−0.0846753	+	0.146662i	0.820577	+	0.571535i	$0.193652\pi$
$450$		0			0
$451$	0.450607	+	0.780474i	0.0212183	+	0.0367511i
$452$	−29.7409	+	42.4745i	−1.39890	+	1.99783i
$453$		0			0
$454$	20.0278	+	55.0260i	0.939953	+	2.58250i
$455$	7.63755	+	14.8558i	0.358054	+	0.696451i
$456$		0			0
$457$	2.64330	−	30.2131i	0.123648	−	1.41331i	−0.640347	−	0.768086i	$-0.721209\pi$
$457$	2.64330	−	30.2131i	0.123648	−	1.41331i	0.763995	−	0.645222i	$-0.223235\pi$
$458$	−26.7269	+	26.7269i	−1.24887	+	1.24887i
$459$		0			0
$460$	42.1374	+	5.76593i	1.96467	+	0.268838i
$461$	−25.6308	−	30.5456i	−1.19375	−	1.42265i	−0.881197	−	0.472750i	$-0.843261\pi$
$461$	−25.6308	−	30.5456i	−1.19375	−	1.42265i	−0.312550	−	0.949901i	$-0.601183\pi$
$462$		0			0
$463$	14.0626	−	9.84673i	0.653544	−	0.457616i	−0.199191	−	0.979961i	$-0.563831\pi$
$463$	14.0626	−	9.84673i	0.653544	−	0.457616i	0.852735	+	0.522344i	$0.174942\pi$
$464$	−11.6059	+	4.22420i	−0.538790	+	0.196103i
$465$		0			0
$466$	−5.44442	−	30.8768i	−0.252208	−	1.43034i
$467$	4.75144	−	17.7326i	0.219870	−	0.820568i	−0.764525	−	0.644595i	$-0.777026\pi$
$467$	4.75144	−	17.7326i	0.219870	−	0.820568i	0.984395	−	0.175973i	$-0.0563072\pi$
$468$		0			0
$469$	8.82379	+	5.09442i	0.407445	+	0.235238i
$470$	0.607271	+	1.96078i	0.0280113	+	0.0904439i
$471$		0			0
$472$	−16.0797	+	1.40679i	−0.740129	+	0.0647529i
$473$	−24.9744	+	2.18497i	−1.14832	+	0.100465i
$474$		0			0
$475$	8.23028	+	5.88872i	0.377631	+	0.270193i
$476$	24.6139	+	14.2109i	1.12818	+	0.651354i
$477$		0			0
$478$	3.46794	−	12.9425i	0.158620	−	0.591978i
$479$	−4.07702	−	23.1219i	−0.186284	−	1.05647i	−0.924295	−	0.381679i	$-0.875346\pi$
$479$	−4.07702	−	23.1219i	−0.186284	−	1.05647i	0.738011	−	0.674789i	$-0.235765\pi$
$480$		0			0
$481$	7.66733	−	2.79068i	0.349600	−	0.127244i
$482$	15.0618	−	10.5464i	0.686046	−	0.480374i
$483$		0			0
$484$	8.37519	+	9.98117i	0.380691	+	0.453689i
$485$	1.07523	−	7.85779i	0.0488238	−	0.356804i
$486$		0			0
$487$	7.21511	−	7.21511i	0.326948	−	0.326948i	−0.524477	−	0.851425i	$-0.675739\pi$
$487$	7.21511	−	7.21511i	0.326948	−	0.326948i	0.851425	+	0.524477i	$0.175739\pi$
$488$	0.0704984	−	0.805800i	0.00319131	−	0.0364768i
$489$		0			0
$490$	28.4686	+	9.13575i	1.28608	+	0.412711i
$491$	11.3506	+	31.1854i	0.512243	+	1.40738i	0.878893	+	0.477018i	$0.158282\pi$
$491$	11.3506	+	31.1854i	0.512243	+	1.40738i	−0.366650	+	0.930359i	$0.619495\pi$
$492$		0			0
$493$	−8.89818	+	12.7079i	−0.400754	+	0.572336i
$494$	14.8505	+	25.7218i	0.668156	+	1.15728i
$495$		0			0
$496$	10.9745	−	19.0084i	0.492770	−	0.853502i
$497$	−4.29144	−	9.20302i	−0.192497	−	0.412812i
$498$		0			0
$499$	−15.7113	+	18.7240i	−0.703333	+	0.838200i	−0.992899	−	0.118958i	$-0.962044\pi$
$499$	−15.7113	+	18.7240i	−0.703333	+	0.838200i	0.289566	+	0.957158i	$0.406489\pi$
$500$	43.1947	+	14.3483i	1.93173	+	0.641674i
$501$		0			0
$502$	−11.2786	+	5.25932i	−0.503391	+	0.234735i
$503$	9.98672	+	37.2709i	0.445286	+	1.66183i	0.715181	+	0.698939i	$0.246344\pi$
$503$	9.98672	+	37.2709i	0.445286	+	1.66183i	−0.269896	+	0.962890i	$0.586989\pi$
$504$		0			0
$505$	−8.08185	+	19.2337i	−0.359638	+	0.855889i
$506$	31.6608	−	5.58265i	1.40749	−	0.248179i
$507$		0			0
$508$	−5.48608	−	2.55820i	−0.243405	−	0.113502i
$509$	−0.294649	+	1.67104i	−0.0130601	+	0.0740674i	−0.990641	−	0.136492i	$-0.956417\pi$
$509$	−0.294649	+	1.67104i	−0.0130601	+	0.0740674i	0.977581	+	0.210559i	$0.0675284\pi$
$510$		0			0
$511$	−5.26985	+	4.42193i	−0.233124	+	0.195615i
$512$	−29.7458	−	29.7458i	−1.31459	−	1.31459i
$513$		0			0
$514$			65.7653i			2.90078i
$515$	1.30540	−	0.822317i	0.0575228	−	0.0362356i
$516$		0			0
$517$	0.596795	+	0.852312i	0.0262470	+	0.0374846i
$518$	−1.78944	+	3.83746i	−0.0786234	+	0.168608i
$519$		0			0
$520$	49.8683	+	46.1652i	2.18687	+	2.02448i
$521$	−22.9824	+	13.2689i	−1.00688	+	0.581322i	−0.910276	−	0.414001i	$-0.864131\pi$
$521$	−22.9824	+	13.2689i	−1.00688	+	0.581322i	−0.0966024	+	0.995323i	$0.530798\pi$
$522$		0			0
$523$	14.6802	−	3.93354i	0.641920	−	0.172002i	0.0768469	−	0.997043i	$-0.475515\pi$
$523$	14.6802	−	3.93354i	0.641920	−	0.172002i	0.565073	+	0.825041i	$0.308848\pi$
$524$	18.8820	+	6.87247i	0.824863	+	0.300225i
$525$		0			0
$526$	49.4526	+	41.4957i	2.15624	+	1.80930i
$527$	−2.40286	−	27.4648i	−0.104670	−	1.19639i
$528$		0			0
$529$	0.400836	−	1.10129i	0.0174277	−	0.0478821i
$530$	−7.79083	−	61.5995i	−0.338412	−	2.67571i
$531$		0			0
$532$	−9.98314	−	2.67497i	−0.432824	−	0.115975i
$533$	−1.57431	−	1.10234i	−0.0681909	−	0.0477478i
$534$		0			0
$535$	−21.6697	+	4.68842i	−0.936862	+	0.202698i
$536$	40.8210	+	7.19784i	1.76320	+	0.310900i
$537$		0			0
$538$	5.65168	+	0.494458i	0.243661	+	0.0213176i
$539$	15.1554			0.652788
$540$		0			0
$541$	6.56072			0.282068			0.141034	−	0.990005i	$-0.454957\pi$
$541$	6.56072			0.282068			0.141034	+	0.990005i	$0.454957\pi$
$542$	15.0236	+	1.31440i	0.645320	+	0.0564582i
$543$		0			0
$544$	3.90510	+	0.688574i	0.167430	+	0.0295224i
$545$	−7.48379	−	4.82145i	−0.320570	−	0.206528i
$546$		0			0
$547$	29.4654	+	20.6319i	1.25985	+	0.882156i	0.996585	−	0.0825680i	$-0.0263122\pi$
$547$	29.4654	+	20.6319i	1.25985	+	0.882156i	0.263264	+	0.964724i	$0.415201\pi$
$548$	−36.4622	−	9.77001i	−1.55759	−	0.417354i
$549$		0			0
$550$	34.4041	+	0.350390i	1.46700	+	0.0149407i
$551$	1.92945	−	5.30113i	0.0821975	−	0.225836i
$552$		0			0
$553$	1.75428	+	20.0515i	0.0745994	+	0.852675i
$554$	19.9852	+	16.7696i	0.849089	+	0.712470i
$555$		0			0
$556$	2.54002	+	0.924490i	0.107721	+	0.0392071i
$557$	4.37675	−	1.17275i	0.185449	−	0.0496908i	−0.164899	−	0.986310i	$-0.552730\pi$
$557$	4.37675	−	1.17275i	0.185449	−	0.0496908i	0.350348	+	0.936620i	$0.386063\pi$
$558$		0			0
$559$	46.2997	−	26.7312i	1.95827	−	1.13061i
$560$	−12.4191	+	0.478885i	−0.524804	+	0.0202366i
$561$		0			0
$562$	6.33165	−	13.5783i	0.267085	−	0.572765i
$563$	−1.52340	−	2.17564i	−0.0642037	−	0.0916924i	0.785766	−	0.618524i	$-0.212269\pi$
$563$	−1.52340	−	2.17564i	−0.0642037	−	0.0916924i	−0.849970	+	0.526831i	$0.823380\pi$
$564$		0			0
$565$	−15.1800	−	24.0977i	−0.638625	−	1.01380i
$566$			8.82639i			0.371001i
$567$		0			0
$568$	−29.2111	−	29.2111i	−1.22567	−	1.22567i
$569$	−22.4581	+	18.8446i	−0.941494	+	0.790007i	−0.977845	−	0.209332i	$-0.932871\pi$
$569$	−22.4581	+	18.8446i	−0.941494	+	0.790007i	0.0363507	+	0.999339i	$0.488427\pi$
$570$		0			0
$571$	−2.73020	+	15.4837i	−0.114255	+	0.647973i	0.872861	+	0.487969i	$0.162262\pi$
$571$	−2.73020	+	15.4837i	−0.114255	+	0.647973i	−0.987116	+	0.160004i	$0.948849\pi$
$572$	61.3679	+	28.6163i	2.56592	+	1.19651i
$573$		0			0
$574$	0.982170	−	0.173183i	0.0409950	−	0.00722852i
$575$	−11.8855	+	20.1106i	−0.495661	+	0.838668i
$576$		0			0
$577$	7.02870	+	26.2315i	0.292609	+	1.09203i	0.943098	+	0.332515i	$0.107897\pi$
$577$	7.02870	+	26.2315i	0.292609	+	1.09203i	−0.650489	+	0.759515i	$0.725436\pi$
$578$	31.2178	−	14.5571i	1.29849	−	0.605496i
$579$		0			0
$580$	1.23579	−	25.3422i	0.0513133	−	1.05228i
$581$	1.40035	−	1.66887i	0.0580961	−	0.0692363i
$582$		0			0
$583$	−13.3011	−	28.5243i	−0.550875	−	1.18136i
$584$	−13.9934	+	24.2372i	−0.579049	+	1.00294i
$585$		0			0
$586$	−32.8581	−	56.9118i	−1.35735	−	2.35101i
$587$	−0.208890	+	0.298326i	−0.00862180	+	0.0123132i	−0.823440	−	0.567404i	$-0.807948\pi$
$587$	−0.208890	+	0.298326i	−0.00862180	+	0.0123132i	0.814818	+	0.579717i	$0.196837\pi$
$588$		0			0
$589$	3.42892	+	9.42087i	0.141286	+	0.388180i
$590$	5.32511	−	16.5940i	0.219231	−	0.683163i
$591$		0			0
$592$	−0.529109	+	6.04775i	−0.0217463	+	0.248561i
$593$	5.77411	−	5.77411i	0.237114	−	0.237114i	−0.578540	−	0.815654i	$-0.696377\pi$
$593$	5.77411	−	5.77411i	0.237114	−	0.237114i	0.815654	+	0.578540i	$0.196377\pi$
$594$		0			0
$595$	−12.4333	+	9.44021i	−0.509715	+	0.387011i
$596$	−13.5965	−	16.2037i	−0.556936	−	0.663730i
$597$		0			0
$598$	−56.1607	+	39.3241i	−2.29658	+	1.60808i
$599$	22.4110	−	8.15692i	0.915687	−	0.333283i	0.159166	−	0.987252i	$-0.449120\pi$
$599$	22.4110	−	8.15692i	0.915687	−	0.333283i	0.756521	+	0.653969i	$0.226897\pi$
$600$		0			0
$601$	−0.792095	−	4.49219i	−0.0323102	−	0.183240i	0.964381	−	0.264515i	$-0.0852120\pi$
$601$	−0.792095	−	4.49219i	−0.0323102	−	0.183240i	−0.996692	+	0.0812748i	$0.974101\pi$
$602$	−7.18049	+	26.7979i	−0.292655	+	1.09220i
$603$		0			0
$604$	14.7427	+	8.51171i	0.599872	+	0.346336i
$605$	−6.83627	+	2.11726i	−0.277934	+	0.0860788i
$606$		0			0
$607$	−40.4825	+	3.54176i	−1.64313	+	0.143756i	−0.870859	−	0.491533i	$-0.836437\pi$
$607$	−40.4825	+	3.54176i	−1.64313	+	0.143756i	−0.772275	+	0.635289i	$0.780881\pi$
$608$	−1.43647	+	0.125675i	−0.0582566	+	0.00509680i
$609$		0			0
$610$	0.772598	+	0.407202i	0.0312816	+	0.0164871i
$611$	−1.92160	−	1.10943i	−0.0777394	−	0.0448829i
$612$		0			0
$613$	−5.74347	+	21.4349i	−0.231977	+	0.865749i	0.747512	+	0.664249i	$0.231248\pi$
$613$	−5.74347	+	21.4349i	−0.231977	+	0.865749i	−0.979488	+	0.201500i	$0.935418\pi$
$614$	5.59463	+	31.7288i	0.225781	+	1.28047i
$615$		0			0
$616$	−16.7974	+	6.11376i	−0.676788	+	0.246331i
$617$	10.6418	−	7.45148i	0.428423	−	0.299985i	−0.339406	−	0.940640i	$-0.610226\pi$
$617$	10.6418	−	7.45148i	0.428423	−	0.299985i	0.767829	+	0.640655i	$0.221337\pi$
$618$		0			0
$619$	−7.80404	−	9.30049i	−0.313671	−	0.373818i	0.586057	−	0.810270i	$-0.300679\pi$
$619$	−7.80404	−	9.30049i	−0.313671	−	0.373818i	−0.899728	+	0.436452i	$0.856235\pi$
$620$	27.2667	+	35.9119i	1.09506	+	1.44225i
$621$		0			0
$622$	19.0207	−	19.0207i	0.762661	−	0.762661i
$623$	1.41001	−	16.1165i	0.0564908	−	0.645693i
$624$		0			0
$625$	−16.4564	+	18.8198i	−0.658256	+	0.752794i
$626$	−4.04832	−	11.1227i	−0.161804	−	0.444552i
$627$		0			0
$628$	32.0653	−	45.7939i	1.27954	−	1.82738i
$629$	3.81274	+	6.60386i	0.152024	+	0.263313i
$630$		0			0
$631$	11.6365	−	20.1551i	0.463243	−	0.802360i	−0.535877	−	0.844296i	$-0.680019\pi$
$631$	11.6365	−	20.1551i	0.463243	−	0.802360i	0.999120	+	0.0419354i	$0.0133524\pi$
$632$	34.6065	+	74.2139i	1.37657	+	2.95207i
$633$		0			0
$634$	50.0581	−	59.6569i	1.98806	−	2.36928i
$635$	2.46272	−	2.23370i	0.0977299	−	0.0886417i
$636$		0			0
$637$	−29.2913	+	13.6588i	−1.16057	+	0.541181i
$638$	−4.96400	−	18.5259i	−0.196526	−	0.733447i
$639$		0			0
$640$	39.2013	−	16.0043i	1.54957	−	0.632627i
$641$	36.8613	−	6.49963i	1.45593	−	0.256720i	0.611016	−	0.791618i	$-0.290761\pi$
$641$	36.8613	−	6.49963i	1.45593	−	0.256720i	0.844916	+	0.534898i	$0.179650\pi$
$642$		0			0
$643$	29.5339	+	13.7719i	1.16470	+	0.543110i	0.906179	−	0.422895i	$-0.138986\pi$
$643$	29.5339	+	13.7719i	1.16470	+	0.543110i	0.258524	+	0.966005i	$0.416764\pi$
$644$	4.14276	−	23.4948i	0.163248	−	0.925823i
$645$		0			0
$646$	−21.2635	+	17.8422i	−0.836600	+	0.701991i
$647$	−25.9188	−	25.9188i	−1.01897	−	1.01897i	−0.999816	−	0.0191583i	$-0.993901\pi$
$647$	−25.9188	−	25.9188i	−1.01897	−	1.01897i	−0.0191583	−	0.999816i	$-0.506099\pi$
$648$		0			0
$649$		−	8.83386i		−	0.346759i
$650$	−66.8100	+	30.3295i	−2.62050	+	1.18962i
$651$		0			0
$652$	49.1121	+	70.1394i	1.92338	+	2.74687i
$653$	14.6418	−	31.3994i	0.572978	−	1.22875i	−0.379795	−	0.925071i	$-0.624006\pi$
$653$	14.6418	−	31.3994i	0.572978	−	1.22875i	0.952773	−	0.303684i	$-0.0982167\pi$
$654$		0			0
$655$	−7.49768	+	8.09910i	−0.292959	+	0.316458i
$656$	1.23836	−	0.714967i	0.0483498	−	0.0279148i
$657$		0			0
$658$	1.11221	−	0.298015i	0.0433583	−	0.0116178i
$659$	14.1890	+	5.16436i	0.552723	+	0.201175i	0.603256	−	0.797548i	$-0.293870\pi$
$659$	14.1890	+	5.16436i	0.552723	+	0.201175i	−0.0505327	+	0.998722i	$0.516092\pi$
$660$		0			0
$661$	26.1426	+	21.9363i	1.01683	+	0.853222i	0.989226	−	0.146397i	$-0.0467677\pi$
$661$	26.1426	+	21.9363i	1.01683	+	0.853222i	0.0276043	+	0.999619i	$0.491212\pi$
$662$	−6.01847	−	68.7915i	−0.233915	−	2.67366i
$663$		0			0
$664$	3.03129	−	8.32839i	0.117637	−	0.323204i
$665$	3.47871	−	4.48606i	0.134899	−	0.173962i
$666$		0			0
$667$	12.5783	+	3.37035i	0.487035	+	0.130501i
$668$	12.1625	+	8.51630i	0.470582	+	0.329505i
$669$		0			0
$670$	−24.2382	+	37.6222i	−0.936404	+	1.45347i
$671$	0.435964	+	0.0768722i	0.0168302	+	0.00296762i
$672$		0			0
$673$	44.9802	+	3.93526i	1.73386	+	0.151693i	0.909865	−	0.414905i	$-0.136185\pi$
$673$	44.9802	+	3.93526i	1.73386	+	0.151693i	0.823995	+	0.566598i	$0.191741\pi$
$674$	−88.8183			−3.42115
$675$		0			0
$676$	−91.4752			−3.51828
$677$	−15.7890	−	1.38136i	−0.606822	−	0.0530900i	−0.220396	−	0.975411i	$-0.570735\pi$
$677$	−15.7890	−	1.38136i	−0.606822	−	0.0530900i	−0.386426	+	0.922321i	$0.626290\pi$
$678$		0			0
$679$	−4.38131	−	0.772543i	−0.168139	−	0.0296475i
$680$	−34.3960	+	53.3890i	−1.31903	+	2.04737i
$681$		0			0
$682$	27.9204	+	19.5501i	1.06913	+	0.748612i
$683$	7.02767	+	1.88306i	0.268906	+	0.0720532i	0.390753	−	0.920496i	$-0.372215\pi$
$683$	7.02767	+	1.88306i	0.268906	+	0.0720532i	−0.121846	+	0.992549i	$0.538881\pi$
$684$		0			0
$685$	12.7056	−	16.3848i	0.485455	−	0.626030i
$686$	13.1355	−	36.0895i	0.501515	−	1.37790i
$687$		0			0
$688$	3.46685	+	39.6262i	0.132172	+	1.51074i
$689$	51.4151	+	43.1424i	1.95876	+	1.64359i
$690$		0			0
$691$	42.1583	+	15.3444i	1.60378	+	0.583728i	0.980196	−	0.198030i	$-0.0634544\pi$
$691$	42.1583	+	15.3444i	1.60378	+	0.583728i	0.623582	+	0.781758i	$0.285677\pi$
$692$	32.2177	−	8.63269i	1.22473	−	0.328166i
$693$		0			0
$694$	−34.3061	+	19.8066i	−1.30224	+	0.751849i
$695$	−1.00859	+	1.08950i	−0.0382581	+	0.0413270i
$696$		0			0
$697$	0.759071	−	1.62783i	0.0287519	−	0.0616585i
$698$	−8.04544	−	11.4901i	−0.304525	−	0.434906i
$699$		0			0
$700$	8.97629	−	23.9019i	0.339272	−	0.903407i
$701$			23.7146i			0.895688i	0.894112	+	0.447844i	$0.147808\pi$
$701$			23.7146i			0.895688i	−0.894112	+	0.447844i	$0.852192\pi$
$702$		0			0
$703$	−1.96076	−	1.96076i	−0.0739516	−	0.0739516i
$704$	15.2045	−	12.7581i	0.573041	−	0.480839i
$705$		0			0
$706$	6.00324	−	34.0461i	0.225935	−	1.28134i
$707$	10.6064	+	4.94586i	0.398896	+	0.186008i
$708$		0			0
$709$	−35.6845	+	6.29214i	−1.34016	+	0.236306i	−0.797334	−	0.603539i	$-0.793757\pi$
$709$	−35.6845	+	6.29214i	−1.34016	+	0.236306i	−0.542826	+	0.839845i	$0.682646\pi$
$710$	41.2940	−	16.8587i	1.54974	−	0.632696i
$711$		0			0
$712$	−17.0345	−	63.5736i	−0.638395	−	2.38252i
$713$	−20.9738	+	9.78025i	−0.785476	+	0.366273i
$714$		0			0
$715$	−27.5482	+	24.9864i	−1.03025	+	0.934439i
$716$	−16.1002	+	19.1875i	−0.601694	+	0.717071i
$717$		0			0
$718$	7.18233	+	15.4026i	0.268042	+	0.574818i
$719$	3.82026	−	6.61689i	0.142472	−	0.246768i	−0.785955	−	0.618284i	$-0.787828\pi$
$719$	3.82026	−	6.61689i	0.142472	−	0.246768i	0.928427	+	0.371515i	$0.121162\pi$
$720$		0			0
$721$	−0.432720	−	0.749493i	−0.0161153	−	0.0279126i
$722$	−21.0624	+	30.0802i	−0.783862	+	1.11947i
$723$		0			0
$724$	−13.2368	−	36.3677i	−0.491941	−	1.35160i
$725$	12.5698	+	6.01798i	0.466830	+	0.223502i
$726$		0			0
$727$	−4.09954	+	46.8579i	−0.152043	+	1.73786i	0.411175	+	0.911557i	$0.365119\pi$
$727$	−4.09954	+	46.8579i	−0.152043	+	1.73786i	−0.563218	+	0.826308i	$0.690437\pi$
$728$	26.9550	−	26.9550i	0.999018	−	0.999018i
$729$		0			0
$730$	−18.2726	−	24.0661i	−0.676301	−	0.890727i
$731$	32.1162	+	38.2746i	1.18786	+	1.41564i
$732$		0			0
$733$	38.5374	−	26.9842i	1.42341	−	0.996682i	0.427723	−	0.903910i	$-0.359316\pi$
$733$	38.5374	−	26.9842i	1.42341	−	0.996682i	0.995687	−	0.0927724i	$-0.0295729\pi$
$734$	−8.25389	+	3.00417i	−0.304657	+	0.110886i
$735$		0			0
$736$	−0.577989	−	3.27794i	−0.0213050	−	0.120826i
$737$	−5.87144	+	21.9125i	−0.216277	+	0.807157i
$738$		0			0
$739$	−40.7581	−	23.5317i	−1.49931	−	0.865628i	−0.499311	−	0.866423i	$-0.666414\pi$
$739$	−40.7581	−	23.5317i	−1.49931	−	0.865628i	−1.00000		0.000795196i	$0.999747\pi$
$740$	−11.0329	−	5.81494i	−0.405576	−	0.213761i
$741$		0			0
$742$	−34.6969	+	3.03559i	−1.27376	+	0.111440i
$743$	5.97266	−	0.522540i	0.219115	−	0.0191701i	0.0229307	−	0.999737i	$-0.492700\pi$
$743$	5.97266	−	0.522540i	0.219115	−	0.0191701i	0.196185	+	0.980567i	$0.437145\pi$
$744$		0			0
$745$	11.0982	−	3.43722i	0.406607	−	0.125930i
$746$	−26.2588	−	15.1605i	−0.961402	−	0.555066i
$747$		0			0
$748$	−16.3784	+	61.1248i	−0.598852	+	2.23495i
$749$	2.15964	+	12.2479i	0.0789114	+	0.447529i
$750$		0			0
$751$	30.7152	−	11.1794i	1.12081	−	0.407943i	0.285865	−	0.958270i	$-0.407719\pi$
$751$	30.7152	−	11.1794i	1.12081	−	0.407943i	0.834949	+	0.550327i	$0.185497\pi$
$752$	1.35234	−	0.946921i	0.0493149	−	0.0345306i
$753$		0			0
$754$	26.2906	+	31.3319i	0.957446	+	1.14104i
$755$	−7.44702	+	5.65429i	−0.271025	+	0.205781i
$756$		0			0
$757$	−6.11549	+	6.11549i	−0.222271	+	0.222271i	−0.809454	−	0.587183i	$-0.800237\pi$
$757$	−6.11549	+	6.11549i	−0.222271	+	0.222271i	0.587183	+	0.809454i	$0.300237\pi$
$758$	3.43586	−	39.2721i	0.124796	−	1.42643i
$759$		0			0
$760$	7.05677	−	21.9901i	0.255976	−	0.797667i
$761$	8.81390	+	24.2160i	0.319503	+	0.877829i	0.990641	+	0.136495i	$0.0435839\pi$
$761$	8.81390	+	24.2160i	0.319503	+	0.877829i	−0.671137	+	0.741333i	$0.734194\pi$
$762$		0			0
$763$	−2.86434	+	4.09070i	−0.103696	+	0.148093i
$764$	−27.6019	−	47.8078i	−0.998601	−	1.72963i
$765$		0			0
$766$	30.7442	−	53.2505i	1.11083	−	1.92402i
$767$	7.96152	+	17.0735i	0.287474	+	0.616490i
$768$		0			0
$769$	17.3950	−	20.7306i	0.627281	−	0.747565i	−0.355023	−	0.934858i	$-0.615527\pi$
$769$	17.3950	−	20.7306i	0.627281	−	0.747565i	0.982304	+	0.187293i	$0.0599713\pi$
$770$	0.940025	−	19.2771i	0.0338762	−	0.694697i
$771$		0			0
$772$	64.5115	−	30.0822i	2.32182	−	1.08268i
$773$	11.1567	+	41.6374i	0.401279	+	1.49759i	0.810817	+	0.585299i	$0.199023\pi$
$773$	11.1567	+	41.6374i	0.401279	+	1.49759i	−0.409539	+	0.912293i	$0.634310\pi$
$774$		0			0
$775$	−23.9866	+	6.16608i	−0.861625	+	0.221492i
$776$	−17.8243	+	3.14290i	−0.639854	+	0.112823i
$777$		0			0
$778$	−41.7860	−	19.4851i	−1.49810	−	0.698576i
$779$	−0.113417	+	0.643218i	−0.00406357	+	0.0230457i
$780$		0			0
$781$	17.3194	−	14.5327i	0.619736	−	0.520020i
$782$	−45.3066	−	45.3066i	−1.62016	−	1.62016i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.45457 + 0.214747i) q^{2} +(4.00918 + 0.706926i) q^{4} +(-1.21103 + 1.87974i) q^{5} +(1.02748 + 0.719449i) q^{7} +(4.92901 + 1.32073i) q^{8} +O(q^{10})\)	\(q+(2.45457 + 0.214747i) q^{2} +(4.00918 + 0.706926i) q^{4} +(-1.21103 + 1.87974i) q^{5} +(1.02748 + 0.719449i) q^{7} +(4.92901 + 1.32073i) q^{8} +(-3.37621 + 4.35388i) q^{10} +(-0.955177 + 2.62433i) q^{11} +(-0.519069 - 5.93299i) q^{13} +(2.36752 + 1.98658i) q^{14} +(4.16396 + 1.51556i) q^{16} +(5.37628 - 1.44057i) q^{17} +(-1.75284 + 1.01200i) q^{19} +(-6.18405 + 6.68010i) q^{20} +(-2.90811 + 6.23647i) q^{22} +(-2.67978 - 3.82712i) q^{23} +(-2.06683 - 4.55282i) q^{25} -14.6744i q^{26} +(3.61075 + 3.61075i) q^{28} +(-2.13514 + 1.79159i) q^{29} +(0.860131 - 4.87805i) q^{31} +(0.645681 + 0.301086i) q^{32} +(13.5058 - 2.38144i) q^{34} +(-2.59668 + 1.06012i) q^{35} +(0.354589 + 1.32334i) q^{37} +(-4.51978 + 2.10761i) q^{38} +(-8.45178 + 7.66582i) q^{40} +(0.207426 - 0.247201i) q^{41} +(3.79373 + 8.13568i) q^{43} +(-5.68468 + 9.84615i) q^{44} +(-5.75583 - 9.96940i) q^{46} +(0.213694 - 0.305187i) q^{47} +(-1.85603 - 5.09941i) q^{49} +(-4.09548 - 11.6191i) q^{50} +(2.11314 - 24.1534i) q^{52} +(-7.96878 + 7.96878i) q^{53} +(-3.77630 - 4.97361i) q^{55} +(4.11426 + 4.90319i) q^{56} +(-5.62558 + 3.93908i) q^{58} +(-2.97238 + 1.08186i) q^{59} +(-0.0275256 - 0.156106i) q^{61} +(3.15880 - 11.7888i) q^{62} +(-6.15484 - 3.55350i) q^{64} +(11.7811 + 6.20929i) q^{65} +(8.09208 - 0.707965i) q^{67} +(22.5728 - 1.97487i) q^{68} +(-6.60139 + 2.04451i) q^{70} +(-7.01095 - 4.04777i) q^{71} +(-1.41949 + 5.29760i) q^{73} +(0.586179 + 3.32439i) q^{74} +(-7.74284 + 2.81816i) q^{76} +(-2.86949 + 2.00924i) q^{77} +(10.3148 + 12.2927i) q^{79} +(-7.89151 + 5.99177i) q^{80} +(0.562227 - 0.562227i) q^{82} +(0.151375 - 1.73023i) q^{83} +(-3.80292 + 11.8506i) q^{85} +(7.56486 + 20.7843i) q^{86} +(-8.17410 + 11.6738i) q^{88} +(-6.44892 - 11.1699i) q^{89} +(3.73515 - 6.46947i) q^{91} +(-8.03821 - 17.2380i) q^{92} +(0.590066 - 0.703213i) q^{94} +(0.220434 - 4.52043i) q^{95} +(-3.21455 + 1.49897i) q^{97} +(-3.46068 - 12.9154i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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