LMFDB - Embedded newform 1352.2.o.f.1161.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(361,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1352, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1352.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,0,0,0,6,0,-6,0,-6,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1161.1
Root			$0.560908 - 1.63871i$ of defining polynomial
Character	$\chi$	$=$	1352.1161
Dual form			1352.2.o.f.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13871 + 1.97231i) q^{3} -1.12182i q^{5} +(2.26053 - 1.30512i) q^{7} +(-1.09334 - 1.89372i) q^{9} +(-2.26053 - 1.30512i) q^{11} +(2.21257 + 1.27743i) q^{15} +(-2.77743 - 4.81064i) q^{17} +(-6.88024 + 3.97231i) q^{19} +5.94462i q^{21} +(-1.13871 + 1.97231i) q^{23} +3.74153 q^{25} -1.85229 q^{27} +(-3.89924 + 6.75369i) q^{29} +8.26259i q^{31} +(5.14819 - 2.97231i) q^{33} +(-1.46410 - 2.53590i) q^{35} +(-3.11971 - 1.80117i) q^{37} +(-4.96410 - 2.86603i) q^{41} +(2.01690 + 3.49337i) q^{43} +(-2.12440 + 1.22652i) q^{45} +2.66562i q^{47} +(-0.0933372 + 0.161665i) q^{49} +12.6508 q^{51} -9.54002 q^{53} +(-1.46410 + 2.53590i) q^{55} -18.0933i q^{57} +(-3.31749 + 1.91535i) q^{59} +(-3.84229 - 6.65503i) q^{61} +(-4.94304 - 2.85387i) q^{63} +(1.52690 + 0.881557i) q^{67} +(-2.59334 - 4.49179i) q^{69} +(-0.880242 + 0.508208i) q^{71} +0.323330i q^{73} +(-4.26053 + 7.37945i) q^{75} -6.81333 q^{77} -2.66877 q^{79} +(5.38924 - 9.33444i) q^{81} -2.77953i q^{83} +(-5.39666 + 3.11576i) q^{85} +(-8.88024 - 15.3810i) q^{87} +(9.99531 + 5.77080i) q^{89} +(-16.2964 - 9.40872i) q^{93} +(4.45620 + 7.71837i) q^{95} +(-13.5553 + 7.82618i) q^{97} +5.70773i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{19} + 2 q^{23} - 20 q^{25} - 28 q^{27} - 8 q^{29} - 6 q^{33} + 16 q^{35} + 24 q^{37} - 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49} + 68 q^{51} + 20 q^{53}+ \cdots - 30 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^19 + 2 * q^23 - 20 * q^25 - 28 * q^27 - 8 * q^29 - 6 * q^33 + 16 * q^35 + 24 * q^37 - 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 + 20 * q^53 + 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 42 * q^67 - 18 * q^69 + 54 * q^71 - 22 * q^75 - 60 * q^77 + 16 * q^79 - 20 * q^81 - 6 * q^85 - 10 * q^87 + 18 * q^89 - 36 * q^93 + 16 * q^95 - 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.13871	+	1.97231i	−0.657437	+	1.13871i	0.323840	+	0.946112i	$0.395026\pi$
$3$	−1.13871	+	1.97231i	−0.657437	+	1.13871i	−0.981277	+	0.192602i	$0.938307\pi$
$4$		0			0
$5$		−	1.12182i		−	0.501691i	−0.968027	−	0.250846i	$-0.919291\pi$
$5$		−	1.12182i		−	0.501691i	0.968027	−	0.250846i	$-0.0807087\pi$
$6$		0			0
$7$	2.26053	−	1.30512i	0.854400	−	0.493288i	−0.00773308	−	0.999970i	$-0.502462\pi$
$7$	2.26053	−	1.30512i	0.854400	−	0.493288i	0.862133	+	0.506682i	$0.169128\pi$
$8$		0			0
$9$	−1.09334	−	1.89372i	−0.364446	−	0.631239i
$10$		0			0
$11$	−2.26053	−	1.30512i	−0.681575	−	0.393508i	0.118873	−	0.992909i	$-0.462072\pi$
$11$	−2.26053	−	1.30512i	−0.681575	−	0.393508i	−0.800448	+	0.599402i	$0.795405\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	2.21257	+	1.27743i	0.571283	+	0.329830i
$16$		0			0
$17$	−2.77743	−	4.81064i	−0.673625	−	1.16675i	−0.976869	−	0.213840i	$-0.931403\pi$
$17$	−2.77743	−	4.81064i	−0.673625	−	1.16675i	0.303244	−	0.952913i	$-0.401930\pi$
$18$		0			0
$19$	−6.88024	+	3.97231i	−1.57844	+	0.911310i	−0.583358	+	0.812215i	$0.698261\pi$
$19$	−6.88024	+	3.97231i	−1.57844	+	0.911310i	−0.995078	+	0.0990951i	$0.968405\pi$
$20$		0			0
$21$			5.94462i			1.29722i
$22$		0			0
$23$	−1.13871	+	1.97231i	−0.237438	+	0.411255i	−0.959978	−	0.280074i	$-0.909641\pi$
$23$	−1.13871	+	1.97231i	−0.237438	+	0.411255i	0.722540	+	0.691329i	$0.242974\pi$
$24$		0			0
$25$	3.74153			0.748306
$26$		0			0
$27$	−1.85229			−0.356473
$28$		0			0
$29$	−3.89924	+	6.75369i	−0.724071	+	1.25413i	0.235284	+	0.971927i	$0.424398\pi$
$29$	−3.89924	+	6.75369i	−0.724071	+	1.25413i	−0.959355	+	0.282202i	$0.908935\pi$
$30$		0			0
$31$			8.26259i			1.48400i	0.670397	+	0.742002i	$0.266124\pi$
$31$			8.26259i			1.48400i	−0.670397	+	0.742002i	$0.733876\pi$
$32$		0			0
$33$	5.14819	−	2.97231i	0.896185	−	0.517413i
$34$		0			0
$35$	−1.46410	−	2.53590i	−0.247478	−	0.428645i
$36$		0			0
$37$	−3.11971	−	1.80117i	−0.512878	−	0.296110i	0.221138	−	0.975243i	$-0.429023\pi$
$37$	−3.11971	−	1.80117i	−0.512878	−	0.296110i	−0.734016	+	0.679132i	$0.762356\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.96410	−	2.86603i	−0.775262	−	0.447598i	0.0594862	−	0.998229i	$-0.481054\pi$
$41$	−4.96410	−	2.86603i	−0.775262	−	0.447598i	−0.834749	+	0.550631i	$0.814387\pi$
$42$		0			0
$43$	2.01690	+	3.49337i	0.307574	+	0.532734i	0.977831	−	0.209395i	$-0.0671495\pi$
$43$	2.01690	+	3.49337i	0.307574	+	0.532734i	−0.670257	+	0.742129i	$0.733816\pi$
$44$		0			0
$45$	−2.12440	+	1.22652i	−0.316687	+	0.182839i
$46$		0			0
$47$			2.66562i			0.388820i	0.980920	+	0.194410i	$0.0622792\pi$
$47$			2.66562i			0.388820i	−0.980920	+	0.194410i	$0.937721\pi$
$48$		0			0
$49$	−0.0933372	+	0.161665i	−0.0133339	+	0.0230950i
$50$		0			0
$51$	12.6508			1.77146
$52$		0			0
$53$	−9.54002			−1.31042			−0.655211	−	0.755446i	$-0.727420\pi$
$53$	−9.54002			−1.31042			−0.655211	+	0.755446i	$0.727420\pi$
$54$		0			0
$55$	−1.46410	+	2.53590i	−0.197419	+	0.341940i
$56$		0			0
$57$		−	18.0933i		−	2.39652i
$58$		0			0
$59$	−3.31749	+	1.91535i	−0.431900	+	0.249358i	−0.700156	−	0.713990i	$-0.746886\pi$
$59$	−3.31749	+	1.91535i	−0.431900	+	0.249358i	0.268256	+	0.963348i	$0.413553\pi$
$60$		0			0
$61$	−3.84229	−	6.65503i	−0.491954	−	0.852090i	0.508003	−	0.861355i	$-0.330384\pi$
$61$	−3.84229	−	6.65503i	−0.491954	−	0.852090i	−0.999957	+	0.00926564i	$0.997051\pi$
$62$		0			0
$63$	−4.94304	−	2.85387i	−0.622765	−	0.359553i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.52690	+	0.881557i	0.186541	+	0.107699i	0.590362	−	0.807139i	$-0.298985\pi$
$67$	1.52690	+	0.881557i	0.186541	+	0.107699i	−0.403821	+	0.914838i	$0.632318\pi$
$68$		0			0
$69$	−2.59334	−	4.49179i	−0.312201	−	0.540748i
$70$		0			0
$71$	−0.880242	+	0.508208i	−0.104466	+	0.0603132i	−0.551323	−	0.834292i	$-0.685877\pi$
$71$	−0.880242	+	0.508208i	−0.104466	+	0.0603132i	0.446857	+	0.894605i	$0.352543\pi$
$72$		0			0
$73$			0.323330i			0.0378429i	0.999821	+	0.0189214i	$0.00602324\pi$
$73$			0.323330i			0.0378429i	−0.999821	+	0.0189214i	$0.993977\pi$
$74$		0			0
$75$	−4.26053	+	7.37945i	−0.491964	+	0.852106i
$76$		0			0
$77$	−6.81333			−0.776451
$78$		0			0
$79$	−2.66877			−0.300260			−0.150130	−	0.988666i	$-0.547969\pi$
$79$	−2.66877			−0.300260			−0.150130	+	0.988666i	$0.547969\pi$
$80$		0			0
$81$	5.38924	−	9.33444i	0.598804	−	1.03716i
$82$		0			0
$83$		−	2.77953i		−	0.305093i	−0.988296	−	0.152547i	$-0.951253\pi$
$83$		−	2.77953i		−	0.305093i	0.988296	−	0.152547i	$-0.0487474\pi$
$84$		0			0
$85$	−5.39666	+	3.11576i	−0.585350	+	0.337952i
$86$		0			0
$87$	−8.88024	−	15.3810i	−0.952062	−	1.64902i
$88$		0			0
$89$	9.99531	+	5.77080i	1.05950	+	0.611703i	0.925294	−	0.379250i	$-0.123818\pi$
$89$	9.99531	+	5.77080i	1.05950	+	0.611703i	0.134207	+	0.990953i	$0.457151\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−16.2964	−	9.40872i	−1.68986	−	0.975639i
$94$		0			0
$95$	4.45620	+	7.71837i	0.457197	+	0.791888i
$96$		0			0
$97$	−13.5553	+	7.82618i	−1.37634	+	0.794628i	−0.991716	−	0.128447i	$-0.959001\pi$
$97$	−13.5553	+	7.82618i	−1.37634	+	0.794628i	−0.384619	+	0.923075i	$0.625667\pi$
$98$		0			0
$99$			5.70773i			0.573649i
$100$		0			0
$101$	8.17667	−	14.1624i	0.813609	−	1.40921i	−0.0967132	−	0.995312i	$-0.530833\pi$
$101$	8.17667	−	14.1624i	0.813609	−	1.40921i	0.910322	−	0.413900i	$-0.135834\pi$
$102$		0			0
$103$	2.24363			0.221072			0.110536	−	0.993872i	$-0.464743\pi$
$103$	2.24363			0.221072			0.110536	+	0.993872i	$0.464743\pi$
$104$		0			0
$105$	6.66877			0.650805
$106$		0			0
$107$	5.41614	−	9.38103i	0.523598	−	0.906898i	−0.476025	−	0.879432i	$-0.657923\pi$
$107$	5.41614	−	9.38103i	0.523598	−	0.906898i	0.999623	−	0.0274665i	$-0.00874397\pi$
$108$		0			0
$109$		−	2.92820i		−	0.280471i	−0.990118	−	0.140236i	$-0.955214\pi$
$109$		−	2.92820i		−	0.280471i	0.990118	−	0.140236i	$-0.0447860\pi$
$110$		0			0
$111$	7.10492	−	4.10203i	0.674369	−	0.389347i
$112$		0			0
$113$	−5.02106	−	8.69673i	−0.472342	−	0.818120i	0.527158	−	0.849768i	$-0.323258\pi$
$113$	−5.02106	−	8.69673i	−0.472342	−	0.818120i	−0.999499	+	0.0316481i	$0.989924\pi$
$114$		0			0
$115$	2.21257	+	1.27743i	0.206323	+	0.119121i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.5569	−	7.24974i	−1.15109	−	0.664582i
$120$		0			0
$121$	−2.09334	−	3.62577i	−0.190303	−	0.329615i
$122$		0			0
$123$	11.3054	−	6.52716i	1.01937	−	0.588535i
$124$		0			0
$125$		−	9.80639i		−	0.877110i
$126$		0			0
$127$	0.195671	−	0.338912i	0.0173630	−	0.0300736i	−0.857213	−	0.514961i	$-0.827806\pi$
$127$	0.195671	−	0.338912i	0.0173630	−	0.0300736i	0.874576	+	0.484888i	$0.161140\pi$
$128$		0			0
$129$	−9.18667			−0.808842
$130$		0			0
$131$	−19.3533			−1.69091			−0.845455	−	0.534047i	$-0.820670\pi$
$131$	−19.3533			−1.69091			−0.845455	+	0.534047i	$0.820670\pi$
$132$		0			0
$133$	−10.3687	+	17.9590i	−0.899077	+	1.55725i
$134$		0			0
$135$			2.07793i			0.178840i
$136$		0			0
$137$	−3.44304	+	1.98784i	−0.294159	+	0.169833i	−0.639816	−	0.768528i	$-0.720989\pi$
$137$	−3.44304	+	1.98784i	−0.294159	+	0.169833i	0.345657	+	0.938361i	$0.387656\pi$
$138$		0			0
$139$	9.48100	+	16.4216i	0.804168	+	1.39286i	0.916851	+	0.399229i	$0.130722\pi$
$139$	9.48100	+	16.4216i	0.804168	+	1.39286i	−0.112684	+	0.993631i	$0.535945\pi$
$140$		0			0
$141$	−5.25742	−	3.03537i	−0.442755	−	0.255624i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	7.57639	+	4.37423i	0.629185	+	0.363260i
$146$		0			0
$147$	−0.212569	−	0.368180i	−0.0175324	−	0.0303670i
$148$		0			0
$149$	1.27259	−	0.734731i	0.104255	−	0.0601915i	−0.446966	−	0.894551i	$-0.647496\pi$
$149$	1.27259	−	0.734731i	0.104255	−	0.0601915i	0.551221	+	0.834359i	$0.314162\pi$
$150$		0			0
$151$		−	5.59382i		−	0.455218i	−0.973753	−	0.227609i	$-0.926909\pi$
$151$		−	5.59382i		−	0.455218i	0.973753	−	0.227609i	$-0.0730909\pi$
$152$		0			0
$153$	−6.07333	+	10.5193i	−0.491000	+	0.850436i
$154$		0			0
$155$	9.26910			0.744512
$156$		0			0
$157$	0.430307			0.0343422			0.0171711	−	0.999853i	$-0.494534\pi$
$157$	0.430307			0.0343422			0.0171711	+	0.999853i	$0.494534\pi$
$158$		0			0
$159$	10.8633	−	18.8159i	0.861519	−	1.49220i
$160$		0			0
$161$			5.94462i			0.468502i
$162$		0			0
$163$	3.18873	−	1.84102i	0.249761	−	0.144199i	−0.369894	−	0.929074i	$-0.620606\pi$
$163$	3.18873	−	1.84102i	0.249761	−	0.144199i	0.619655	+	0.784875i	$0.287273\pi$
$164$		0			0
$165$	−3.33438	−	5.77532i	−0.259582	−	0.449608i
$166$		0			0
$167$	−14.2605	−	8.23332i	−1.10351	−	0.637113i	−0.166371	−	0.986063i	$-0.553205\pi$
$167$	−14.2605	−	8.23332i	−1.10351	−	0.637113i	−0.937141	+	0.348950i	$0.886538\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	15.0449	+	8.68615i	1.15051	+	0.664246i
$172$		0			0
$173$	11.8897	+	20.5936i	0.903959	+	1.56570i	0.822309	+	0.569041i	$0.192686\pi$
$173$	11.8897	+	20.5936i	0.903959	+	1.56570i	0.0816498	+	0.996661i	$0.473981\pi$
$174$		0			0
$175$	8.45784	−	4.88313i	0.639352	−	0.369130i
$176$		0			0
$177$		−	8.72415i		−	0.655747i
$178$		0			0
$179$	2.53796	−	4.39587i	0.189696	−	0.328563i	−0.755453	−	0.655203i	$-0.772583\pi$
$179$	2.53796	−	4.39587i	0.189696	−	0.328563i	0.945149	+	0.326640i	$0.105916\pi$
$180$		0			0
$181$	−9.16667			−0.681353			−0.340676	−	0.940181i	$-0.610656\pi$
$181$	−9.16667			−0.681353			−0.340676	+	0.940181i	$0.610656\pi$
$182$		0			0
$183$	17.5011			1.29371
$184$		0			0
$185$	−2.02058	+	3.49974i	−0.148556	+	0.257306i
$186$		0			0
$187$			14.4995i			1.06031i
$188$		0			0
$189$	−4.18716	+	2.41746i	−0.304571	+	0.175844i
$190$		0			0
$191$	8.49205	+	14.7087i	0.614463	+	1.06428i	0.990478	+	0.137668i	$0.0439608\pi$
$191$	8.49205	+	14.7087i	0.614463	+	1.06428i	−0.376015	+	0.926614i	$0.622706\pi$
$192$		0			0
$193$	17.7426	+	10.2437i	1.27714	+	0.737356i	0.976321	−	0.216325i	$-0.0694072\pi$
$193$	17.7426	+	10.2437i	1.27714	+	0.737356i	0.300817	+	0.953682i	$0.402740\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.4594	+	7.77080i	0.958944	+	0.553646i	0.895848	−	0.444361i	$-0.146569\pi$
$197$	13.4594	+	7.77080i	0.958944	+	0.553646i	0.0630958	+	0.998007i	$0.479903\pi$
$198$		0			0
$199$	−9.67873	−	16.7640i	−0.686107	−	1.18837i	−0.973088	−	0.230436i	$-0.925985\pi$
$199$	−9.67873	−	16.7640i	−0.686107	−	1.18837i	0.286981	−	0.957936i	$-0.407348\pi$
$200$		0			0
$201$	−3.47741	+	2.00768i	−0.245277	+	0.141611i
$202$		0			0
$203$			20.3559i			1.42870i
$204$		0			0
$205$	−3.21515	+	5.56881i	−0.224556	+	0.388942i
$206$		0			0
$207$	4.97999			0.346133
$208$		0			0
$209$	20.7373			1.43443
$210$		0			0
$211$	−9.93720	+	17.2117i	−0.684105	+	1.18490i	0.289612	+	0.957144i	$0.406474\pi$
$211$	−9.93720	+	17.2117i	−0.684105	+	1.18490i	−0.973717	+	0.227761i	$0.926860\pi$
$212$		0			0
$213$		−	2.31481i		−	0.158608i
$214$		0			0
$215$	3.91892	−	2.26259i	0.267268	−	0.154307i
$216$		0			0
$217$	10.7836	+	18.6778i	0.732042	+	1.26793i
$218$		0			0
$219$	−0.637706	−	0.368180i	−0.0430922	−	0.0248793i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	14.9613	+	8.63792i	1.00188	+	0.578438i	0.908805	−	0.417220i	$-0.136996\pi$
$223$	14.9613	+	8.63792i	1.00188	+	0.578438i	0.0930791	+	0.995659i	$0.470329\pi$
$224$		0			0
$225$	−4.09075	−	7.08539i	−0.272717	−	0.472359i
$226$		0			0
$227$	6.97616	−	4.02769i	0.463024	−	0.267327i	−0.250291	−	0.968171i	$-0.580526\pi$
$227$	6.97616	−	4.02769i	0.463024	−	0.267327i	0.713315	+	0.700844i	$0.247193\pi$
$228$		0			0
$229$			10.9282i			0.722156i	0.932536	+	0.361078i	$0.117591\pi$
$229$			10.9282i			0.722156i	−0.932536	+	0.361078i	$0.882409\pi$
$230$		0			0
$231$	7.75843	−	13.4380i	0.510467	−	0.884155i
$232$		0			0
$233$	4.66877			0.305861			0.152931	−	0.988237i	$-0.451129\pi$
$233$	4.66877			0.305861			0.152931	+	0.988237i	$0.451129\pi$
$234$		0			0
$235$	2.99033			0.195068
$236$		0			0
$237$	3.03896	−	5.26364i	0.197402	−	0.341910i
$238$		0			0
$239$			17.4862i			1.13109i	0.824718	+	0.565545i	$0.191334\pi$
$239$			17.4862i			1.13109i	−0.824718	+	0.565545i	$0.808666\pi$
$240$		0			0
$241$	12.2184	−	7.05428i	0.787054	−	0.454406i	−0.0518703	−	0.998654i	$-0.516518\pi$
$241$	12.2184	−	7.05428i	0.787054	−	0.454406i	0.838924	+	0.544248i	$0.183185\pi$
$242$		0			0
$243$	9.49516	+	16.4461i	0.609115	+	1.05502i
$244$		0			0
$245$	0.181358	+	0.104707i	0.0115865	+	0.00668950i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	5.48210	+	3.16509i	0.347414	+	0.200579i
$250$		0			0
$251$	−9.28642	−	16.0846i	−0.586154	−	1.01525i	−0.994731	−	0.102524i	$-0.967308\pi$
$251$	−9.28642	−	16.0846i	−0.586154	−	1.01525i	0.408577	−	0.912724i	$-0.366025\pi$
$252$		0			0
$253$	5.14819	−	2.97231i	0.323664	−	0.186868i
$254$		0			0
$255$		−	14.1918i		−	0.888728i
$256$		0			0
$257$	−2.16562	+	3.75096i	−0.135087	+	0.233978i	−0.925631	−	0.378428i	$-0.876465\pi$
$257$	−2.16562	+	3.75096i	−0.135087	+	0.233978i	0.790543	+	0.612406i	$0.209798\pi$
$258$		0			0
$259$	−9.40294			−0.584270
$260$		0			0
$261$	17.0528			1.05554
$262$		0			0
$263$	2.11282	−	3.65951i	0.130282	−	0.225655i	−0.793503	−	0.608566i	$-0.791745\pi$
$263$	2.11282	−	3.65951i	0.130282	−	0.225655i	0.923785	+	0.382911i	$0.125078\pi$
$264$		0			0
$265$			10.7021i			0.657427i
$266$		0			0
$267$	−22.7636	+	13.1426i	−1.39311	+	0.804312i
$268$		0			0
$269$	4.11440	+	7.12634i	0.250859	+	0.434501i	0.963763	−	0.266761i	$-0.0859536\pi$
$269$	4.11440	+	7.12634i	0.250859	+	0.434501i	−0.712903	+	0.701262i	$0.752620\pi$
$270$		0			0
$271$	−6.68567	−	3.85997i	−0.406125	−	0.234477i	0.282998	−	0.959120i	$-0.408671\pi$
$271$	−6.68567	−	3.85997i	−0.406125	−	0.234477i	−0.689124	+	0.724644i	$0.742004\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.45784	−	4.88313i	−0.510027	−	0.294464i
$276$		0			0
$277$	−4.75153	−	8.22990i	−0.285492	−	0.494487i	0.687236	−	0.726434i	$-0.258824\pi$
$277$	−4.75153	−	8.22990i	−0.285492	−	0.494487i	−0.972728	+	0.231947i	$0.925490\pi$
$278$		0			0
$279$	15.6470	−	9.03380i	0.936761	−	0.540839i
$280$		0			0
$281$		−	23.0300i		−	1.37386i	−0.726726	−	0.686928i	$-0.758959\pi$
$281$		−	23.0300i		−	1.37386i	0.726726	−	0.686928i	$-0.241041\pi$
$282$		0			0
$283$	−6.68567	+	11.5799i	−0.397422	+	0.688355i	−0.993407	−	0.114641i	$-0.963428\pi$
$283$	−6.68567	+	11.5799i	−0.397422	+	0.688355i	0.595985	+	0.802995i	$0.296762\pi$
$284$		0			0
$285$	−20.2973			−1.20231
$286$		0			0
$287$	−14.9620			−0.883179
$288$		0			0
$289$	−6.92820	+	12.0000i	−0.407541	+	0.705882i
$290$		0			0
$291$		−	35.6471i		−	2.08967i
$292$		0			0
$293$	−15.0659	+	8.69831i	−0.880160	+	0.508161i	−0.870711	−	0.491795i	$-0.836341\pi$
$293$	−15.0659	+	8.69831i	−0.880160	+	0.508161i	−0.00944872	+	0.999955i	$0.503008\pi$
$294$		0			0
$295$	2.14867	+	3.72161i	0.125101	+	0.216681i
$296$		0			0
$297$	4.18716	+	2.41746i	0.242963	+	0.140275i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	9.11851	+	5.26458i	0.525582	+	0.303445i
$302$		0			0
$303$	18.6218	+	32.2539i	1.06979	+	1.85294i
$304$		0			0
$305$	−7.46572	+	4.31034i	−0.427486	+	0.246809i
$306$		0			0
$307$		−	4.00315i		−	0.228472i	−0.993454	−	0.114236i	$-0.963558\pi$
$307$		−	4.00315i		−	0.228472i	0.993454	−	0.114236i	$-0.0364420\pi$
$308$		0			0
$309$	−2.55485	+	4.42514i	−0.145341	+	0.251737i
$310$		0			0
$311$	−28.4630			−1.61399			−0.806996	−	0.590557i	$-0.798908\pi$
$311$	−28.4630			−1.61399			−0.806996	+	0.590557i	$0.798908\pi$
$312$		0			0
$313$	−3.55906			−0.201170			−0.100585	−	0.994928i	$-0.532071\pi$
$313$	−3.55906			−0.201170			−0.100585	+	0.994928i	$0.532071\pi$
$314$		0			0
$315$	−3.20151	+	5.54518i	−0.180385	+	0.312436i
$316$		0			0
$317$			1.38125i			0.0775787i	0.999247	+	0.0387894i	$0.0123501\pi$
$317$			1.38125i			0.0775787i	−0.999247	+	0.0387894i	$0.987650\pi$
$318$		0			0
$319$	17.6287	−	10.1779i	0.987018	−	0.569855i
$320$		0			0
$321$	12.3349	+	21.3646i	0.688465	+	1.19246i
$322$		0			0
$323$	38.2187	+	22.0656i	2.12655	+	1.22776i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.77532	+	3.33438i	0.319376	+	0.184392i
$328$		0			0
$329$	3.47894	+	6.02570i	0.191800	+	0.332208i
$330$		0			0
$331$	−8.16461	+	4.71384i	−0.448767	+	0.259096i	−0.707310	−	0.706904i	$-0.750091\pi$
$331$	−8.16461	+	4.71384i	−0.448767	+	0.259096i	0.258542	+	0.966000i	$0.416758\pi$
$332$		0			0
$333$			7.87713i			0.431664i
$334$		0			0
$335$	0.988945	−	1.71290i	0.0540318	−	0.0935859i
$336$		0			0
$337$	1.21215			0.0660298			0.0330149	−	0.999455i	$-0.489489\pi$
$337$	1.21215			0.0660298			0.0330149	+	0.999455i	$0.489489\pi$
$338$		0			0
$339$	22.8702			1.24214
$340$		0			0
$341$	10.7836	−	18.6778i	0.583967	−	1.01146i
$342$		0			0
$343$			18.7589i			1.01289i
$344$		0			0
$345$	−5.03896	+	2.90925i	−0.271289	+	0.156629i
$346$		0			0
$347$	7.13871	+	12.3646i	0.383226	+	0.663767i	0.991521	−	0.129944i	$-0.0414796\pi$
$347$	7.13871	+	12.3646i	0.383226	+	0.663767i	−0.608295	+	0.793711i	$0.708146\pi$
$348$		0			0
$349$	−20.2862	−	11.7123i	−1.08590	−	0.626943i	−0.153416	−	0.988162i	$-0.549027\pi$
$349$	−20.2862	−	11.7123i	−1.08590	−	0.626943i	−0.932481	+	0.361219i	$0.882361\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.02421	−	4.05543i	−0.373861	−	0.215849i	0.301283	−	0.953535i	$-0.402585\pi$
$353$	−7.02421	−	4.05543i	−0.373861	−	0.215849i	−0.675144	+	0.737686i	$0.735919\pi$
$354$		0			0
$355$	0.570116	+	0.987470i	0.0302586	+	0.0524095i
$356$		0			0
$357$	28.5975	−	16.5107i	1.51354	−	0.873841i
$358$		0			0
$359$		−	26.3302i		−	1.38965i	−0.719177	−	0.694827i	$-0.755481\pi$
$359$		−	26.3302i		−	1.38965i	0.719177	−	0.694827i	$-0.244519\pi$
$360$		0			0
$361$	22.0585	−	38.2064i	1.16097	−	2.01086i
$362$		0			0
$363$	9.53485			0.500450
$364$		0			0
$365$	0.362716			0.0189854
$366$		0			0
$367$	5.04279	−	8.73437i	0.263232	−	0.455930i	−0.703867	−	0.710332i	$-0.748545\pi$
$367$	5.04279	−	8.73437i	0.263232	−	0.455930i	0.967099	+	0.254401i	$0.0818783\pi$
$368$		0			0
$369$			12.5341i			0.652501i
$370$		0			0
$371$	−21.5655	+	12.4508i	−1.11962	+	0.646415i
$372$		0			0
$373$	−0.305425	−	0.529011i	−0.0158143	−	0.0273912i	0.858010	−	0.513633i	$-0.171701\pi$
$373$	−0.305425	−	0.529011i	−0.0158143	−	0.0273912i	−0.873824	+	0.486242i	$0.838367\pi$
$374$		0			0
$375$	19.3412	+	11.1667i	0.998777	+	0.576644i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−3.12291	−	1.80301i	−0.160413	−	0.0926146i	0.417644	−	0.908611i	$-0.362856\pi$
$379$	−3.12291	−	1.80301i	−0.160413	−	0.0926146i	−0.578058	+	0.815996i	$0.696189\pi$
$380$		0			0
$381$	0.445627	+	0.771848i	0.0228302	+	0.0395430i
$382$		0			0
$383$	10.3744	−	5.98969i	0.530109	−	0.306059i	−0.210952	−	0.977497i	$-0.567656\pi$
$383$	10.3744	−	5.98969i	0.530109	−	0.306059i	0.741061	+	0.671438i	$0.234323\pi$
$384$		0			0
$385$			7.64330i			0.389539i
$386$		0			0
$387$	4.41030	−	7.63886i	0.224188	−	0.388305i
$388$		0			0
$389$	10.1245			0.513335			0.256667	−	0.966500i	$-0.417375\pi$
$389$	10.1245			0.513335			0.256667	+	0.966500i	$0.417375\pi$
$390$		0			0
$391$	12.6508			0.639777
$392$		0			0
$393$	22.0379	−	38.1708i	1.11167	−	1.92546i
$394$		0			0
$395$			2.99387i			0.150638i
$396$		0			0
$397$	9.98985	−	5.76764i	0.501376	−	0.289470i	−0.227906	−	0.973683i	$-0.573188\pi$
$397$	9.98985	−	5.76764i	0.501376	−	0.289470i	0.729282	+	0.684214i	$0.239854\pi$
$398$		0			0
$399$	−23.6139	−	40.9004i	−1.18217	−	2.04758i
$400$		0			0
$401$	−4.40408	−	2.54270i	−0.219929	−	0.126976i	0.385988	−	0.922504i	$-0.373861\pi$
$401$	−4.40408	−	2.54270i	−0.219929	−	0.126976i	−0.605917	+	0.795528i	$0.707194\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−10.4715	−	6.04573i	−0.520334	−	0.300415i
$406$		0			0
$407$	4.70147	+	8.14318i	0.233043	+	0.403643i
$408$		0			0
$409$	33.6287	−	19.4155i	1.66283	−	0.960036i	0.691476	−	0.722399i	$-0.256961\pi$
$409$	33.6287	−	19.4155i	1.66283	−	0.960036i	0.971354	−	0.237636i	$-0.0763727\pi$
$410$		0			0
$411$		−	9.05433i		−	0.446617i
$412$		0			0
$413$	−4.99952	+	8.65942i	−0.246010	+	0.426102i
$414$		0			0
$415$	−3.11812			−0.153063
$416$		0			0
$417$	−43.1846			−2.11476
$418$		0			0
$419$	9.36751	−	16.2250i	0.457633	−	0.792643i	−0.541203	−	0.840892i	$-0.682031\pi$
$419$	9.36751	−	16.2250i	0.457633	−	0.792643i	0.998835	+	0.0482492i	$0.0153642\pi$
$420$		0			0
$421$		−	7.50063i		−	0.365558i	−0.983154	−	0.182779i	$-0.941491\pi$
$421$		−	7.50063i		−	0.365558i	0.983154	−	0.182779i	$-0.0585093\pi$
$422$		0			0
$423$	5.04792	−	2.91442i	0.245438	−	0.141704i
$424$		0			0
$425$	−10.3918	−	17.9992i	−0.504077	−	0.873088i
$426$		0			0
$427$	−17.3712	−	10.0293i	−0.840651	−	0.485350i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.41341	−	5.43483i	−0.453428	−	0.261787i	0.255849	−	0.966717i	$-0.417645\pi$
$431$	−9.41341	−	5.43483i	−0.453428	−	0.261787i	−0.709277	+	0.704930i	$0.750978\pi$
$432$		0			0
$433$	0.0780169	+	0.135129i	0.00374925	+	0.00649389i	0.867894	−	0.496750i	$-0.165473\pi$
$433$	0.0780169	+	0.135129i	0.00374925	+	0.00649389i	−0.864145	+	0.503243i	$0.832140\pi$
$434$		0			0
$435$	−17.2547	+	9.96200i	−0.827299	+	0.477641i
$436$		0			0
$437$		−	18.0933i		−	0.865520i
$438$		0			0
$439$	−3.85435	+	6.67593i	−0.183958	+	0.318625i	−0.943225	−	0.332155i	$-0.892224\pi$
$439$	−3.85435	+	6.67593i	−0.183958	+	0.318625i	0.759267	+	0.650779i	$0.225558\pi$
$440$		0			0
$441$	0.408196			0.0194379
$442$		0			0
$443$	−5.59697			−0.265920			−0.132960	−	0.991121i	$-0.542448\pi$
$443$	−5.59697			−0.265920			−0.132960	+	0.991121i	$0.542448\pi$
$444$		0			0
$445$	6.47377	−	11.2129i	0.306886	−	0.531543i
$446$		0			0
$447$			3.34659i			0.158288i
$448$		0			0
$449$	−16.3728	+	9.45283i	−0.772679	+	0.446107i	−0.833830	−	0.552022i	$-0.813856\pi$
$449$	−16.3728	+	9.45283i	−0.772679	+	0.446107i	0.0611504	+	0.998129i	$0.480523\pi$
$450$		0			0
$451$	7.48100	+	12.9575i	0.352266	+	0.610143i
$452$		0			0
$453$	11.0327	+	6.36976i	0.518363	+	0.299277i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.11698	+	5.26369i	0.426474	+	0.246225i	0.697844	−	0.716250i	$-0.254143\pi$
$457$	9.11698	+	5.26369i	0.426474	+	0.246225i	−0.271369	+	0.962475i	$0.587476\pi$
$458$		0			0
$459$	5.14460	+	8.91071i	0.240129	+	0.415916i
$460$		0			0
$461$	−1.45515	+	0.840131i	−0.0677731	+	0.0391288i	−0.533504	−	0.845798i	$-0.679125\pi$
$461$	−1.45515	+	0.840131i	−0.0677731	+	0.0391288i	0.465731	+	0.884927i	$0.345792\pi$
$462$		0			0
$463$			18.7795i			0.872759i	0.899763	+	0.436379i	$0.143739\pi$
$463$			18.7795i			0.872759i	−0.899763	+	0.436379i	$0.856261\pi$
$464$		0			0
$465$	−10.5549	+	18.2815i	−0.489470	+	0.847786i
$466$		0			0
$467$	−16.6604			−0.770949			−0.385475	−	0.922718i	$-0.625962\pi$
$467$	−16.6604			−0.770949			−0.385475	+	0.922718i	$0.625962\pi$
$468$		0			0
$469$	4.60214			0.212507
$470$		0			0
$471$	−0.489996	+	0.848698i	−0.0225778	+	0.0391059i
$472$		0			0
$473$		−	10.5292i		−	0.484131i
$474$		0			0
$475$	−25.7426	+	14.8625i	−1.18115	+	0.681939i
$476$		0			0
$477$	10.4305	+	18.0661i	0.477578	+	0.827189i
$478$		0			0
$479$	−10.6704	−	6.16056i	−0.487543	−	0.281483i	0.236011	−	0.971750i	$-0.424160\pi$
$479$	−10.6704	−	6.16056i	−0.487543	−	0.281483i	−0.723555	+	0.690267i	$0.757493\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−11.7246	−	6.76922i	−0.533489	−	0.308010i
$484$		0			0
$485$	8.77953	+	15.2066i	0.398658	+	0.690496i
$486$		0			0
$487$	−32.2215	+	18.6031i	−1.46009	+	0.842986i	−0.999015	−	0.0443730i	$-0.985871\pi$
$487$	−32.2215	+	18.6031i	−1.46009	+	0.842986i	−0.461079	+	0.887359i	$0.652538\pi$
$488$		0			0
$489$			8.38556i			0.379208i
$490$		0			0
$491$	−7.36708	+	12.7602i	−0.332472	+	0.575858i	−0.982996	−	0.183628i	$-0.941216\pi$
$491$	−7.36708	+	12.7602i	−0.332472	+	0.575858i	0.650524	+	0.759486i	$0.274549\pi$
$492$		0			0
$493$	43.3195			1.95101
$494$		0			0
$495$	6.40303			0.287795
$496$		0			0
$497$	−1.32654	+	2.29764i	−0.0595036	+	0.103063i
$498$		0			0
$499$		−	19.2287i		−	0.860795i	−0.902639	−	0.430397i	$-0.858373\pi$
$499$		−	19.2287i		−	0.860795i	0.902639	−	0.430397i	$-0.141627\pi$
$500$		0			0
$501$	32.4773	−	18.7508i	1.45098	−	0.837723i
$502$		0			0
$503$	−17.4040	−	30.1447i	−0.776007	−	1.34408i	−0.934226	−	0.356680i	$-0.883909\pi$
$503$	−17.4040	−	30.1447i	−0.776007	−	1.34408i	0.158219	−	0.987404i	$-0.449425\pi$
$504$		0			0
$505$	−15.8876	−	9.17272i	−0.706990	−	0.408181i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.52370	−	2.61176i	−0.200510	−	0.115764i	0.396384	−	0.918085i	$-0.370265\pi$
$509$	−4.52370	−	2.61176i	−0.200510	−	0.115764i	−0.596893	+	0.802321i	$0.703598\pi$
$510$		0			0
$511$	0.421983	+	0.730896i	0.0186674	+	0.0323329i
$512$		0			0
$513$	12.7442	−	7.35787i	0.562670	−	0.324858i
$514$		0			0
$515$		−	2.51694i		−	0.110910i
$516$		0			0
$517$	3.47894	−	6.02570i	0.153004	−	0.265010i
$518$		0			0
$519$	−54.1559			−2.37718
$520$		0			0
$521$	−7.92917			−0.347383			−0.173692	−	0.984800i	$-0.555570\pi$
$521$	−7.92917			−0.347383			−0.173692	+	0.984800i	$0.555570\pi$
$522$		0			0
$523$	−15.9683	+	27.6578i	−0.698243	+	1.20939i	0.270832	+	0.962627i	$0.412701\pi$
$523$	−15.9683	+	27.6578i	−0.698243	+	1.20939i	−0.969075	+	0.246766i	$0.920632\pi$
$524$		0			0
$525$			22.2420i			0.970719i
$526$		0			0
$527$	39.7484	−	22.9487i	1.73147	−	0.999663i
$528$		0			0
$529$	8.90666	+	15.4268i	0.387246	+	0.670730i
$530$		0			0
$531$	7.25426	+	4.18825i	0.314808	+	0.181755i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−10.5238	−	6.07591i	−0.454983	−	0.262685i
$536$		0			0
$537$	5.78001	+	10.0113i	0.249426	+	0.432018i
$538$		0			0
$539$	0.421983	−	0.243632i	0.0181761	−	0.0104940i
$540$		0			0
$541$			17.1534i			0.737483i	0.929532	+	0.368742i	$0.120211\pi$
$541$			17.1534i			0.737483i	−0.929532	+	0.368742i	$0.879789\pi$
$542$		0			0
$543$	10.4382	−	18.0795i	0.447946	−	0.775866i
$544$		0			0
$545$	−3.28491			−0.140710
$546$		0			0
$547$	15.4885			0.662241			0.331121	−	0.943588i	$-0.392573\pi$
$547$	15.4885			0.662241			0.331121	+	0.943588i	$0.392573\pi$
$548$		0			0
$549$	−8.40183	+	14.5524i	−0.358581	+	0.621081i
$550$		0			0
$551$		−	61.9560i		−	2.63941i
$552$		0			0
$553$	−6.03283	+	3.48306i	−0.256542	+	0.148115i
$554$		0			0
$555$	−4.60172	−	7.97041i	−0.195332	−	0.338325i
$556$		0			0
$557$	27.4972	+	15.8755i	1.16509	+	0.672667i	0.952519	−	0.304478i	$-0.0984821\pi$
$557$	27.4972	+	15.8755i	1.16509	+	0.672667i	0.212574	+	0.977145i	$0.431815\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−28.5975	−	16.5107i	−1.20739	−	0.697084i
$562$		0			0
$563$	−17.0739	−	29.5728i	−0.719577	−	1.24634i	−0.961167	−	0.275966i	$-0.911002\pi$
$563$	−17.0739	−	29.5728i	−0.719577	−	1.24634i	0.241590	−	0.970378i	$-0.422331\pi$
$564$		0			0
$565$	−9.75613	+	5.63270i	−0.410444	+	0.236970i
$566$		0			0
$567$		−	28.1344i		−	1.18153i
$568$		0			0
$569$	1.13987	−	1.97431i	0.0477858	−	0.0827674i	−0.841143	−	0.540812i	$-0.818117\pi$
$569$	1.13987	−	1.97431i	0.0477858	−	0.0827674i	0.888929	+	0.458045i	$0.151450\pi$
$570$		0			0
$571$	24.5631			1.02793			0.513967	−	0.857810i	$-0.328176\pi$
$571$	24.5631			1.02793			0.513967	+	0.857810i	$0.328176\pi$
$572$		0			0
$573$	−38.6801			−1.61588
$574$		0			0
$575$	−4.26053	+	7.37945i	−0.177676	+	0.307744i
$576$		0			0
$577$			10.6670i			0.444073i	0.975038	+	0.222037i	$0.0712704\pi$
$577$			10.6670i			0.444073i	−0.975038	+	0.222037i	$0.928730\pi$
$578$		0			0
$579$	−40.4074	+	23.3292i	−1.67928	+	0.969530i
$580$		0			0
$581$	−3.62761	−	6.28321i	−0.150499	−	0.260672i
$582$		0			0
$583$	21.5655	+	12.4508i	0.893151	+	0.515661i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.74262	+	1.00610i	0.0719258	+	0.0415264i	0.535532	−	0.844515i	$-0.320111\pi$
$587$	1.74262	+	1.00610i	0.0719258	+	0.0415264i	−0.463606	+	0.886042i	$0.653445\pi$
$588$		0			0
$589$	−32.8216	−	56.8486i	−1.35239	−	2.34241i
$590$		0			0
$591$	−30.6528	+	17.6974i	−1.26089	+	0.727975i
$592$		0			0
$593$			38.9058i			1.59767i	0.601552	+	0.798834i	$0.294549\pi$
$593$			38.9058i			1.59767i	−0.601552	+	0.798834i	$0.705451\pi$
$594$		0			0
$595$	−8.13287	+	14.0865i	−0.333415	+	0.577492i
$596$		0			0
$597$	44.0852			1.80429
$598$		0			0
$599$	14.2815			0.583528			0.291764	−	0.956490i	$-0.405758\pi$
$599$	14.2815			0.583528			0.291764	+	0.956490i	$0.405758\pi$
$600$		0			0
$601$	−17.0590	+	29.5470i	−0.695850	+	1.20525i	0.274043	+	0.961717i	$0.411639\pi$
$601$	−17.0590	+	29.5470i	−0.695850	+	1.20525i	−0.969893	+	0.243530i	$0.921695\pi$
$602$		0			0
$603$		−	3.85536i		−	0.157002i
$604$		0			0
$605$	−4.06744	+	2.34834i	−0.165365	+	0.0954736i
$606$		0			0
$607$	−3.28327	−	5.68679i	−0.133264	−	0.230820i	0.791669	−	0.610950i	$-0.209212\pi$
$607$	−3.28327	−	5.68679i	−0.133264	−	0.230820i	−0.924933	+	0.380130i	$0.875879\pi$
$608$		0			0
$609$	−40.1481	−	23.1795i	−1.62688	−	0.939281i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	40.0955	+	23.1491i	1.61944	+	0.934985i	0.987064	+	0.160325i	$0.0512542\pi$
$613$	40.0955	+	23.1491i	1.61944	+	0.934985i	0.632378	+	0.774660i	$0.282079\pi$
$614$		0			0
$615$	−7.32228	−	12.6826i	−0.295263	−	0.511410i
$616$		0			0
$617$	−17.1021	+	9.87393i	−0.688506	+	0.397509i	−0.803052	−	0.595909i	$-0.796792\pi$
$617$	−17.1021	+	9.87393i	−0.688506	+	0.397509i	0.114546	+	0.993418i	$0.463459\pi$
$618$		0			0
$619$			6.07074i			0.244004i	0.992530	+	0.122002i	$0.0389314\pi$
$619$			6.07074i			0.244004i	−0.992530	+	0.122002i	$0.961069\pi$
$620$		0			0
$621$	2.10923	−	3.65329i	0.0846404	−	0.146601i
$622$		0			0
$623$	30.1263			1.20698
$624$		0			0
$625$	7.70668			0.308267
$626$		0			0
$627$	−23.6139	+	40.9004i	−0.943047	+	1.63341i
$628$		0			0
$629$			20.0104i			0.797869i
$630$		0			0
$631$	20.9641	−	12.1036i	0.834566	−	0.481837i	−0.0208475	−	0.999783i	$-0.506636\pi$
$631$	20.9641	−	12.1036i	0.834566	−	0.481837i	0.855413	+	0.517946i	$0.173303\pi$
$632$		0			0
$633$	−22.6312	−	39.1985i	−0.899511	−	1.55800i
$634$		0			0
$635$	−0.380197	−	0.219507i	−0.0150877	−	0.00871087i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.92480	+	1.11129i	0.0761440	+	0.0439618i
$640$		0			0
$641$	16.8871	+	29.2494i	0.667002	+	1.15528i	0.978738	+	0.205112i	$0.0657560\pi$
$641$	16.8871	+	29.2494i	0.667002	+	1.15528i	−0.311737	+	0.950169i	$0.600911\pi$
$642$		0			0
$643$	−28.4102	+	16.4026i	−1.12039	+	0.646856i	−0.941500	−	0.337013i	$-0.890583\pi$
$643$	−28.4102	+	16.4026i	−1.12039	+	0.646856i	−0.178888	+	0.983869i	$0.557250\pi$
$644$		0			0
$645$			10.3058i			0.405789i
$646$		0			0
$647$	19.0100	−	32.9262i	0.747359	−	1.29446i	−0.201726	−	0.979442i	$-0.564655\pi$
$647$	19.0100	−	32.9262i	0.747359	−	1.29446i	0.949085	−	0.315021i	$-0.102012\pi$
$648$		0			0
$649$	9.99904			0.392497
$650$		0			0
$651$	−49.1179			−1.92508
$652$		0			0
$653$	10.0005	−	17.3213i	0.391349	−	0.677836i	−0.601279	−	0.799039i	$-0.705342\pi$
$653$	10.0005	−	17.3213i	0.391349	−	0.677836i	0.992628	+	0.121203i	$0.0386752\pi$
$654$		0			0
$655$			21.7109i			0.848315i
$656$		0			0
$657$	0.612294	−	0.353508i	0.0238879	−	0.0137917i
$658$		0			0
$659$	−5.59588	−	9.69234i	−0.217984	−	0.377560i	0.736207	−	0.676756i	$-0.236615\pi$
$659$	−5.59588	−	9.69234i	−0.217984	−	0.377560i	−0.954192	+	0.299196i	$0.903282\pi$
$660$		0			0
$661$	−22.5870	−	13.0406i	−0.878531	−	0.507220i	−0.00835740	−	0.999965i	$-0.502660\pi$
$661$	−22.5870	−	13.0406i	−0.878531	−	0.507220i	−0.870174	+	0.492745i	$0.835994\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	20.1467	+	11.6317i	0.781257	+	0.451059i
$666$		0			0
$667$	−8.88024	−	15.3810i	−0.343844	−	0.595556i
$668$		0			0
$669$	−34.0733	+	19.6722i	−1.31735	+	0.760573i
$670$		0			0
$671$			20.0585i			0.774351i
$672$		0			0
$673$	−22.6667	+	39.2598i	−0.873736	+	1.51335i	−0.0156324	+	0.999878i	$0.504976\pi$
$673$	−22.6667	+	39.2598i	−0.873736	+	1.51335i	−0.858103	+	0.513477i	$0.828357\pi$
$674$		0			0
$675$	−6.93040			−0.266751
$676$		0			0
$677$	23.6942			0.910644			0.455322	−	0.890327i	$-0.349524\pi$
$677$	23.6942			0.910644			0.455322	+	0.890327i	$0.349524\pi$
$678$		0			0
$679$	−20.4282	+	35.3826i	−0.783961	+	1.35786i
$680$		0			0
$681$			18.3455i			0.703003i
$682$		0			0
$683$	37.1501	−	21.4486i	1.42151	−	0.820709i	0.425081	−	0.905155i	$-0.360246\pi$
$683$	37.1501	−	21.4486i	1.42151	−	0.820709i	0.996428	+	0.0844466i	$0.0269122\pi$
$684$		0			0
$685$	2.22999	+	3.86246i	0.0852036	+	0.147577i
$686$		0			0
$687$	−21.5538	−	12.4441i	−0.822329	−	0.474772i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	41.6801	+	24.0640i	1.58559	+	0.915439i	0.994022	+	0.109181i	$0.0348228\pi$
$691$	41.6801	+	24.0640i	1.58559	+	0.915439i	0.591564	+	0.806258i	$0.298511\pi$
$692$		0			0
$693$	7.44926	+	12.9025i	0.282974	+	0.490125i
$694$		0			0
$695$	18.4220	−	10.6359i	0.698786	−	0.403444i
$696$		0			0
$697$			31.8407i			1.20605i
$698$		0			0
$699$	−5.31639	+	9.20826i	−0.201084	+	0.348288i
$700$		0			0
$701$	−21.6433			−0.817456			−0.408728	−	0.912656i	$-0.634028\pi$
$701$	−21.6433			−0.817456			−0.408728	+	0.912656i	$0.634028\pi$
$702$		0			0
$703$	28.6192			1.07939
$704$		0			0
$705$	−3.40513	+	5.89786i	−0.128245	+	0.222126i
$706$		0			0
$707$		−	42.6861i		−	1.60537i
$708$		0			0
$709$	10.5449	−	6.08807i	0.396020	−	0.228642i	−0.288745	−	0.957406i	$-0.593238\pi$
$709$	10.5449	−	6.08807i	0.396020	−	0.228642i	0.684765	+	0.728764i	$0.259905\pi$
$710$		0			0
$711$	2.91787	+	5.05389i	0.109428	+	0.189536i
$712$		0			0
$713$	−16.2964	−	9.40872i	−0.610304	−	0.352359i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−34.4882	−	19.9118i	−1.28799	−	0.743619i
$718$		0			0
$719$	−8.66767	−	15.0129i	−0.323250	−	0.559885i	0.657907	−	0.753099i	$-0.271442\pi$
$719$	−8.66767	−	15.0129i	−0.323250	−	0.559885i	−0.981157	+	0.193214i	$0.938109\pi$
$720$		0			0
$721$	5.07180	−	2.92820i	0.188884	−	0.109052i
$722$		0			0
$723$			32.1312i			1.19497i
$724$		0			0
$725$	−14.5891	+	25.2691i	−0.541827	+	0.938471i
$726$		0			0
$727$	−21.9600			−0.814451			−0.407225	−	0.913328i	$-0.633504\pi$
$727$	−21.9600			−0.814451			−0.407225	+	0.913328i	$0.633504\pi$
$728$		0			0
$729$	−10.9137			−0.404210
$730$		0			0
$731$	11.2036	−	19.4052i	0.414379	−	0.717726i
$732$		0			0
$733$			4.24733i			0.156879i	0.996919	+	0.0784393i	$0.0249937\pi$
$733$			4.24733i			0.156879i	−0.996919	+	0.0784393i	$0.975006\pi$
$734$		0			0
$735$	−0.413030	+	0.238463i	−0.0152348	+	0.00879584i
$736$		0			0
$737$	−2.30107	−	3.98557i	−0.0847610	−	0.146810i
$738$		0			0
$739$	−12.1138	−	6.99390i	−0.445613	−	0.257275i	0.260363	−	0.965511i	$-0.416158\pi$
$739$	−12.1138	−	6.99390i	−0.445613	−	0.257275i	−0.705976	+	0.708236i	$0.749491\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−41.8143	−	24.1415i	−1.53402	−	0.885666i	−0.999171	−	0.0407183i	$-0.987035\pi$
$743$	−41.8143	−	24.1415i	−1.53402	−	0.885666i	−0.534848	−	0.844948i	$-0.679631\pi$
$744$		0			0
$745$	−0.824233	−	1.42761i	−0.0301976	−	0.0523037i
$746$		0			0
$747$	−5.26364	+	3.03896i	−0.192587	+	0.111190i
$748$		0			0
$749$		−	28.2748i		−	1.03314i
$750$		0			0
$751$	−7.90298	+	13.6884i	−0.288384	+	0.499496i	−0.973424	−	0.229010i	$-0.926451\pi$
$751$	−7.90298	+	13.6884i	−0.288384	+	0.499496i	0.685040	+	0.728505i	$0.259785\pi$
$752$		0			0
$753$	42.2983			1.54144
$754$		0			0
$755$	−6.27524			−0.228379
$756$		0			0
$757$	−5.30107	+	9.18172i	−0.192671	+	0.333715i	−0.946134	−	0.323774i	$-0.895048\pi$
$757$	−5.30107	+	9.18172i	−0.192671	+	0.333715i	0.753464	+	0.657489i	$0.228382\pi$
$758$		0			0
$759$			13.5384i			0.491414i
$760$		0			0
$761$	30.8970	−	17.8384i	1.12002	−	0.646641i	0.178610	−	0.983920i	$-0.442840\pi$
$761$	30.8970	−	17.8384i	1.12002	−	0.646641i	0.941405	+	0.337279i	$0.109507\pi$
$762$		0			0
$763$	−3.82165	−	6.61929i	−0.138353	−	0.239634i
$764$		0			0
$765$	11.8007	+	6.81316i	0.426656	+	0.246330i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−2.96572	−	1.71226i	−0.106947	−	0.0617457i	0.445573	−	0.895246i	$-0.353000\pi$
$769$	−2.96572	−	1.71226i	−0.106947	−	0.0617457i	−0.552519	+	0.833500i	$0.686333\pi$
$770$		0			0
$771$	−4.93203	−	8.54253i	−0.177623	−	0.307652i
$772$		0			0
$773$	−25.8369	+	14.9169i	−0.929288	+	0.536525i	−0.886586	−	0.462563i	$-0.846930\pi$
$773$	−25.8369	+	14.9169i	−0.929288	+	0.536525i	−0.0427017	+	0.999088i	$0.513596\pi$
$774$		0			0
$775$			30.9147i			1.11049i
$776$		0			0
$777$	10.7073	−	18.5455i	0.384121	−	0.665316i
$778$		0			0
$779$	45.5390			1.63160
$780$		0			0
$781$	2.65309			0.0949349
$782$		0			0
$783$	7.22253	−	12.5098i	0.258112	−	0.447063i
$784$		0			0
$785$		−	0.482725i		−	0.0172292i
$786$		0			0
$787$	25.0330	−	14.4528i	0.892331	−	0.515188i	0.0176269	−	0.999845i	$-0.494389\pi$
$787$	25.0330	−	14.4528i	0.892331	−	0.515188i	0.874704	+	0.484657i	$0.161056\pi$
$788$		0			0
$789$	4.81179	+	8.33427i	0.171304	+	0.296708i
$790$		0			0
$791$	−22.7005	−	13.1061i	−0.807137	−	0.466001i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−21.1079	−	12.1867i	−0.748621	−	0.432217i
$796$		0			0
$797$	0.225157	+	0.389984i	0.00797548	+	0.0138139i	0.869986	−	0.493077i	$-0.164128\pi$
$797$	0.225157	+	0.389984i	0.00797548	+	0.0138139i	−0.862010	+	0.506891i	$0.830795\pi$
$798$		0			0
$799$	12.8233	−	7.40355i	0.453657	−	0.261919i
$800$		0			0
$801$		−	25.2377i		−	0.891730i
$802$		0			0
$803$	0.421983	−	0.730896i	0.0148915	−	0.0257928i
$804$		0			0
$805$	6.66877			0.235043
$806$		0			0
$807$	−18.7405			−0.659696
$808$		0			0
$809$	−16.2605	+	28.1640i	−0.571688	+	0.990193i	0.424705	+	0.905332i	$0.360378\pi$
$809$	−16.2605	+	28.1640i	−0.571688	+	0.990193i	−0.996393	+	0.0848610i	$0.972955\pi$
$810$		0			0
$811$		−	0.00315434i		−	0.000110764i	−1.00000		5.53819e-5i	$-0.999982\pi$
$811$		−	0.00315434i		−	0.000110764i	1.00000		5.53819e-5i	$-1.76286e-5\pi$
$812$		0			0
$813$	15.2261	−	8.79080i	0.534003	−	0.308307i
$814$		0			0
$815$	−2.06528	−	3.57717i	−0.0723436	−	0.125303i
$816$		0			0
$817$	−27.7535	−	16.0235i	−0.970972	−	0.560591i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	37.4594	+	21.6272i	1.30734	+	0.754795i	0.981652	−	0.190682i	$-0.0610699\pi$
$821$	37.4594	+	21.6272i	1.30734	+	0.754795i	0.325691	+	0.945476i	$0.394403\pi$
$822$		0			0
$823$	20.3934	+	35.3224i	0.710869	+	1.23126i	0.964531	+	0.263969i	$0.0850316\pi$
$823$	20.3934	+	35.3224i	0.710869	+	1.23126i	−0.253662	+	0.967293i	$0.581635\pi$
$824$		0			0
$825$	19.2621	−	11.1210i	0.670620	−	0.387183i
$826$		0			0
$827$			15.0453i			0.523175i	0.965180	+	0.261588i	$0.0842461\pi$
$827$			15.0453i			0.523175i	−0.965180	+	0.261588i	$0.915754\pi$
$828$		0			0
$829$	−17.0196	+	29.4788i	−0.591115	+	1.02384i	0.402968	+	0.915214i	$0.367979\pi$
$829$	−17.0196	+	29.4788i	−0.591115	+	1.02384i	−0.994083	+	0.108626i	$0.965355\pi$
$830$		0			0
$831$	21.6425			0.750771
$832$		0			0
$833$	1.03695			0.0359282
$834$		0			0
$835$	−9.23627	+	15.9977i	−0.319634	+	0.553623i
$836$		0			0
$837$		−	15.3047i		−	0.529008i
$838$		0			0
$839$	−38.2873	+	22.1052i	−1.32182	+	0.763156i	−0.984020	−	0.178061i	$-0.943018\pi$
$839$	−38.2873	+	22.1052i	−1.32182	+	0.763156i	−0.337805	+	0.941216i	$0.609684\pi$
$840$		0			0
$841$	−15.9082	−	27.5538i	−0.548558	−	0.950131i
$842$		0			0
$843$	45.4223	+	26.2246i	1.56443	+	0.903223i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−9.46410	−	5.46410i	−0.325190	−	0.187749i
$848$		0			0
$849$	−15.2261	−	26.3724i	−0.522559	−	0.905099i
$850$		0			0
$851$	7.10492	−	4.10203i	0.243553	−	0.140616i
$852$		0			0
$853$		−	47.0540i		−	1.61110i	−0.592528	−	0.805550i	$-0.701870\pi$
$853$		−	47.0540i		−	1.61110i	0.592528	−	0.805550i	$-0.298130\pi$
$854$		0			0
$855$	9.74426	−	16.8776i	0.333247	−	0.577200i
$856$		0			0
$857$	−7.26478			−0.248160			−0.124080	−	0.992272i	$-0.539598\pi$
$857$	−7.26478			−0.248160			−0.124080	+	0.992272i	$0.539598\pi$
$858$		0			0
$859$	−18.3788			−0.627077			−0.313538	−	0.949575i	$-0.601514\pi$
$859$	−18.3788			−0.627077			−0.313538	+	0.949575i	$0.601514\pi$
$860$		0			0
$861$	17.0374	−	29.5097i	0.580634	−	1.00569i
$862$		0			0
$863$			15.0390i			0.511932i	0.966686	+	0.255966i	$0.0823936\pi$
$863$			15.0390i			0.511932i	−0.966686	+	0.255966i	$0.917606\pi$
$864$		0			0
$865$	23.1022	−	13.3381i	0.785499	−	0.453508i
$866$		0			0
$867$	−15.7785	−	27.3291i	−0.535865	−	0.928146i
$868$		0			0
$869$	6.03283	+	3.48306i	0.204650	+	0.118155i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	29.6411	+	17.1133i	1.00320	+	0.579197i
$874$		0			0
$875$	−12.7985	−	22.1676i	−0.432668	−	0.749403i
$876$		0			0
$877$	−22.7305	+	13.1234i	−0.767554	+	0.443147i	−0.832001	−	0.554774i	$-0.812805\pi$
$877$	−22.7305	+	13.1234i	−0.767554	+	0.443147i	0.0644477	+	0.997921i	$0.479471\pi$
$878$		0			0
$879$		−	39.6195i		−	1.33633i
$880$		0			0
$881$	7.20353	−	12.4769i	0.242693	−	0.420357i	−0.718787	−	0.695230i	$-0.755303\pi$
$881$	7.20353	−	12.4769i	0.242693	−	0.420357i	0.961480	+	0.274873i	$0.0886359\pi$
$882$		0			0
$883$	−36.9503			−1.24348			−0.621739	−	0.783225i	$-0.713573\pi$
$883$	−36.9503			−1.24348			−0.621739	+	0.783225i	$0.713573\pi$
$884$		0			0
$885$	−9.78689			−0.328983
$886$		0			0
$887$	23.9103	−	41.4138i	0.802828	−	1.39054i	−0.114920	−	0.993375i	$-0.536661\pi$
$887$	23.9103	−	41.4138i	0.802828	−	1.39054i	0.917748	−	0.397164i	$-0.130005\pi$
$888$		0			0
$889$		−	1.02150i		−	0.0342599i
$890$		0			0
$891$	−24.3651	+	14.0672i	−0.816261	+	0.471268i
$892$		0			0
$893$	−10.5886	−	18.3401i	−0.354336	−	0.613727i
$894$		0			0
$895$	−4.93136	−	2.84712i	−0.164837	−	0.0951687i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−55.8029	−	32.2178i	−1.86113	−	1.07453i
$900$		0			0
$901$	26.4967	+	45.8936i	0.882733	+	1.52894i
$902$		0			0
$903$	−20.7667	+	11.9897i	−0.691074	+	0.398992i
$904$		0			0
$905$			10.2833i			0.341829i
$906$		0			0
$907$	10.7353	−	18.5940i	0.356459	−	0.617404i	−0.630908	−	0.775858i	$-0.717317\pi$
$907$	10.7353	−	18.5940i	0.356459	−	0.617404i	0.987366	+	0.158453i	$0.0506508\pi$
$908$		0			0
$909$	−35.7594			−1.18607
$910$		0			0
$911$	−28.2594			−0.936277			−0.468138	−	0.883655i	$-0.655075\pi$
$911$	−28.2594			−0.936277			−0.468138	+	0.883655i	$0.655075\pi$
$912$		0			0
$913$	−3.62761	+	6.28321i	−0.120056	+	0.207944i
$914$		0			0
$915$		−	19.6330i		−	0.649046i
$916$		0			0
$917$	−43.7488	+	25.2584i	−1.44471	+	0.834105i
$918$		0			0
$919$	−22.7232	−	39.3577i	−0.749568	−	1.29829i	−0.948030	−	0.318181i	$-0.896928\pi$
$919$	−22.7232	−	39.3577i	−0.749568	−	1.29829i	0.198462	−	0.980109i	$-0.436405\pi$
$920$		0			0
$921$	7.89546	+	4.55845i	0.260164	+	0.150206i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−11.6725	−	6.73912i	−0.383789	−	0.221581i
$926$		0			0
$927$	−2.45305	−	4.24880i	−0.0805686	−	0.139549i
$928$		0			0
$929$	−15.1077	+	8.72243i	−0.495667	+	0.286174i	−0.726923	−	0.686719i	$-0.759050\pi$
$929$	−15.1077	+	8.72243i	−0.495667	+	0.286174i	0.231255	+	0.972893i	$0.425717\pi$
$930$		0			0
$931$		−	1.48306i		−	0.0486052i
$932$		0			0
$933$	32.4113	−	56.1380i	1.06110	−	1.83787i
$934$		0			0
$935$	16.2657			0.531947
$936$		0			0
$937$	44.7794			1.46288			0.731440	−	0.681906i	$-0.238848\pi$
$937$	44.7794			1.46288			0.731440	+	0.681906i	$0.238848\pi$
$938$		0			0
$939$	4.05275	−	7.01957i	0.132257	−	0.229075i
$940$		0			0
$941$			0.525176i			0.0171202i	0.999963	+	0.00856012i	$0.00272481\pi$
$941$			0.525176i			0.0171202i	−0.999963	+	0.00856012i	$0.997275\pi$
$942$		0			0
$943$	11.3054	−	6.52716i	0.368154	−	0.212554i
$944$		0			0
$945$	2.71194	+	4.69722i	0.0882194	+	0.152801i
$946$		0			0
$947$	21.0744	+	12.1673i	0.684826	+	0.395384i	0.801671	−	0.597766i	$-0.203945\pi$
$947$	21.0744	+	12.1673i	0.684826	+	0.395384i	−0.116845	+	0.993150i	$0.537278\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−2.72425	−	1.57285i	−0.0883399	−	0.0510031i
$952$		0			0
$953$	26.5257	+	45.9438i	0.859250	+	1.48827i	0.872645	+	0.488355i	$0.162403\pi$
$953$	26.5257	+	45.9438i	0.859250	+	1.48827i	−0.0133948	+	0.999910i	$0.504264\pi$
$954$		0			0
$955$	16.5004	−	9.52652i	0.533941	−	0.308271i
$956$		0			0
$957$			46.3590i			1.49857i
$958$		0			0
$959$	−5.18873	+	8.98715i	−0.167553	+	0.290210i
$960$		0			0
$961$	−37.2704			−1.20227
$962$		0			0
$963$	−23.6867			−0.763292
$964$		0			0
$965$	11.4915	−	19.9039i	0.369925	−	0.640730i
$966$		0			0
$967$		−	26.5793i		−	0.854732i	−0.904079	−	0.427366i	$-0.859442\pi$
$967$		−	26.5793i		−	0.854732i	0.904079	−	0.427366i	$-0.140558\pi$
$968$		0			0
$969$	−87.0404	+	50.2528i	−2.79614	+	1.61435i
$970$		0			0
$971$	27.5500	+	47.7180i	0.884121	+	1.53134i	0.846718	+	0.532042i	$0.178575\pi$
$971$	27.5500	+	47.7180i	0.884121	+	1.53134i	0.0374027	+	0.999300i	$0.488092\pi$
$972$		0			0
$973$	42.8642	+	24.7476i	1.37416	+	0.793373i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.5834	−	17.0800i	−0.946457	−	0.546437i	−0.0544782	−	0.998515i	$-0.517350\pi$
$977$	−29.5834	−	17.0800i	−0.946457	−	0.546437i	−0.891978	+	0.452078i	$0.850683\pi$
$978$		0			0
$979$	−15.0631	−	26.0901i	−0.481420	−	0.833844i
$980$		0			0
$981$	−5.54518	+	3.20151i	−0.177044	+	0.102216i
$982$		0			0
$983$			13.8912i			0.443059i	0.975154	+	0.221530i	$0.0711050\pi$
$983$			13.8912i			0.443059i	−0.975154	+	0.221530i	$0.928895\pi$
$984$		0			0
$985$	8.71740	−	15.0990i	0.277760	−	0.481094i
$986$		0			0
$987$	−15.8461			−0.504386
$988$		0			0
$989$	−9.18667			−0.292119
$990$		0			0
$991$	8.62081	−	14.9317i	0.273849	−	0.474320i	−0.695995	−	0.718047i	$-0.745036\pi$
$991$	8.62081	−	14.9317i	0.273849	−	0.474320i	0.969844	+	0.243726i	$0.0783698\pi$
$992$		0			0
$993$		−	21.4708i		−	0.681357i
$994$		0			0
$995$	−18.8062	+	10.8578i	−0.596196	+	0.344214i
$996$		0			0
$997$	0.728370	+	1.26157i	0.0230677	+	0.0399545i	0.877329	−	0.479890i	$-0.159323\pi$
$997$	0.728370	+	1.26157i	0.0230677	+	0.0399545i	−0.854261	+	0.519844i	$0.825990\pi$
$998$		0			0
$999$	5.77861	+	3.33628i	0.182827	+	0.105555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.f.1161.1		8
13.2	odd	12		1352.2.i.k.1329.1		8
13.3	even	3		104.2.o.a.49.1	yes	8
13.4	even	6		1352.2.f.f.337.8		8
13.5	odd	4		1352.2.i.k.529.1		8
13.6	odd	12		1352.2.a.k.1.4		4
13.7	odd	12		1352.2.a.l.1.4		4
13.8	odd	4		1352.2.i.l.529.1		8
13.9	even	3		1352.2.f.f.337.7		8
13.10	even	6	inner	1352.2.o.f.361.1		8
13.11	odd	12		1352.2.i.l.1329.1		8
13.12	even	2		104.2.o.a.17.1	✓	8
39.29	odd	6		936.2.bi.b.361.2		8
39.38	odd	2		936.2.bi.b.433.3		8
52.3	odd	6		208.2.w.c.49.4		8
52.7	even	12		2704.2.a.be.1.1		4
52.19	even	12		2704.2.a.bd.1.1		4
52.35	odd	6		2704.2.f.q.337.1		8
52.43	odd	6		2704.2.f.q.337.2		8
52.51	odd	2		208.2.w.c.17.4		8
104.3	odd	6		832.2.w.i.257.1		8
104.29	even	6		832.2.w.g.257.4		8
104.51	odd	2		832.2.w.i.641.1		8
104.77	even	2		832.2.w.g.641.4		8
156.107	even	6		1872.2.by.n.1297.2		8
156.155	even	2		1872.2.by.n.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.1	✓	8	13.12	even	2
104.2.o.a.49.1	yes	8	13.3	even	3
208.2.w.c.17.4		8	52.51	odd	2
208.2.w.c.49.4		8	52.3	odd	6
832.2.w.g.257.4		8	104.29	even	6
832.2.w.g.641.4		8	104.77	even	2
832.2.w.i.257.1		8	104.3	odd	6
832.2.w.i.641.1		8	104.51	odd	2
936.2.bi.b.361.2		8	39.29	odd	6
936.2.bi.b.433.3		8	39.38	odd	2
1352.2.a.k.1.4		4	13.6	odd	12
1352.2.a.l.1.4		4	13.7	odd	12
1352.2.f.f.337.7		8	13.9	even	3
1352.2.f.f.337.8		8	13.4	even	6
1352.2.i.k.529.1		8	13.5	odd	4
1352.2.i.k.1329.1		8	13.2	odd	12
1352.2.i.l.529.1		8	13.8	odd	4
1352.2.i.l.1329.1		8	13.11	odd	12
1352.2.o.f.361.1		8	13.10	even	6	inner
1352.2.o.f.1161.1		8	1.1	even	1	trivial
1872.2.by.n.433.3		8	156.155	even	2
1872.2.by.n.1297.2		8	156.107	even	6
2704.2.a.bd.1.1		4	52.19	even	12
2704.2.a.be.1.1		4	52.7	even	12
2704.2.f.q.337.1		8	52.35	odd	6
2704.2.f.q.337.2		8	52.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13871 + 1.97231i) q^{3} -1.12182i q^{5} +(2.26053 - 1.30512i) q^{7} +(-1.09334 - 1.89372i) q^{9} +(-2.26053 - 1.30512i) q^{11} +(2.21257 + 1.27743i) q^{15} +(-2.77743 - 4.81064i) q^{17} +(-6.88024 + 3.97231i) q^{19} +5.94462i q^{21} +(-1.13871 + 1.97231i) q^{23} +3.74153 q^{25} -1.85229 q^{27} +(-3.89924 + 6.75369i) q^{29} +8.26259i q^{31} +(5.14819 - 2.97231i) q^{33} +(-1.46410 - 2.53590i) q^{35} +(-3.11971 - 1.80117i) q^{37} +(-4.96410 - 2.86603i) q^{41} +(2.01690 + 3.49337i) q^{43} +(-2.12440 + 1.22652i) q^{45} +2.66562i q^{47} +(-0.0933372 + 0.161665i) q^{49} +12.6508 q^{51} -9.54002 q^{53} +(-1.46410 + 2.53590i) q^{55} -18.0933i q^{57} +(-3.31749 + 1.91535i) q^{59} +(-3.84229 - 6.65503i) q^{61} +(-4.94304 - 2.85387i) q^{63} +(1.52690 + 0.881557i) q^{67} +(-2.59334 - 4.49179i) q^{69} +(-0.880242 + 0.508208i) q^{71} +0.323330i q^{73} +(-4.26053 + 7.37945i) q^{75} -6.81333 q^{77} -2.66877 q^{79} +(5.38924 - 9.33444i) q^{81} -2.77953i q^{83} +(-5.39666 + 3.11576i) q^{85} +(-8.88024 - 15.3810i) q^{87} +(9.99531 + 5.77080i) q^{89} +(-16.2964 - 9.40872i) q^{93} +(4.45620 + 7.71837i) q^{95} +(-13.5553 + 7.82618i) q^{97} +5.70773i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{19} + 2 q^{23} - 20 q^{25} - 28 q^{27} - 8 q^{29} - 6 q^{33} + 16 q^{35} + 24 q^{37} - 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49} + 68 q^{51} + 20 q^{53}+ \cdots - 30 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^19 + 2 * q^23 - 20 * q^25 - 28 * q^27 - 8 * q^29 - 6 * q^33 + 16 * q^35 + 24 * q^37 - 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 + 20 * q^53 + 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 42 * q^67 - 18 * q^69 + 54 * q^71 - 22 * q^75 - 60 * q^77 + 16 * q^79 - 20 * q^81 - 6 * q^85 - 10 * q^87 + 18 * q^89 - 36 * q^93 + 16 * q^95 - 30 * q^97

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