LMFDB - Embedded newform 1890.2.bf.f.1259.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(629,1890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1890.629"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bf (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,16,0,-16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1259.4
Character	$\chi$	$=$	1890.1259
Dual form			1890.2.bf.f.629.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22443 + 1.87103i) q^{5} +(2.45843 - 0.977807i) q^{7} -1.00000 q^{8} +(-2.23258 - 0.124872i) q^{10} +(1.44107 - 0.832005i) q^{11} +(1.04814 - 1.81544i) q^{13} +(2.07602 + 1.64016i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.45463i q^{17} -4.66141i q^{19} +(-1.00815 - 1.99591i) q^{20} +(1.44107 + 0.832005i) q^{22} +(2.82486 - 4.89279i) q^{23} +(-2.00154 - 4.58191i) q^{25} +2.09629 q^{26} +(-0.382411 + 2.61797i) q^{28} +(4.10738 - 2.37140i) q^{29} +(-1.73402 - 1.00114i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.45590 - 3.72732i) q^{34} +(-1.18067 + 5.79707i) q^{35} +4.86789i q^{37} +(4.03690 - 2.33070i) q^{38} +(1.22443 - 1.87103i) q^{40} +(-4.07169 + 7.05238i) q^{41} +(-2.25274 + 1.30062i) q^{43} +1.66401i q^{44} +5.64971 q^{46} +(-8.90154 + 5.13931i) q^{47} +(5.08779 - 4.80775i) q^{49} +(2.96728 - 4.02433i) q^{50} +(1.04814 + 1.81544i) q^{52} +13.8374 q^{53} +(-0.207788 + 3.71503i) q^{55} +(-2.45843 + 0.977807i) q^{56} +(4.10738 + 2.37140i) q^{58} +(-0.0862901 + 0.149459i) q^{59} +(-5.17503 + 2.98781i) q^{61} -2.00228i q^{62} +1.00000 q^{64} +(2.11336 + 4.18399i) q^{65} +(4.70611 + 2.71707i) q^{67} +(6.45590 + 3.72732i) q^{68} +(-5.61075 + 1.87604i) q^{70} -12.0450i q^{71} +4.79644 q^{73} +(-4.21571 + 2.43394i) q^{74} +(4.03690 + 2.33070i) q^{76} +(2.72924 - 3.45452i) q^{77} +(-6.30891 - 10.9273i) q^{79} +(2.23258 + 0.124872i) q^{80} -8.14339 q^{82} +(2.24015 - 1.29335i) q^{83} +(13.9479 + 9.12768i) q^{85} +(-2.25274 - 1.30062i) q^{86} +(-1.44107 + 0.832005i) q^{88} +11.2248 q^{89} +(0.801642 - 5.48801i) q^{91} +(2.82486 + 4.89279i) q^{92} +(-8.90154 - 5.13931i) q^{94} +(8.72165 + 5.70757i) q^{95} +(4.73188 + 8.19586i) q^{97} +(6.70752 + 2.00228i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 24 q^{11} - 16 q^{16} + 24 q^{22} + 24 q^{23} - 58 q^{25} + 36 q^{29} + 16 q^{32} + 48 q^{35} - 54 q^{43} + 48 q^{46} + 32 q^{49} - 50 q^{50} + 24 q^{53} + 36 q^{58}+ \cdots + 64 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 24 * q^11 - 16 * q^16 + 24 * q^22 + 24 * q^23 - 58 * q^25 + 36 * q^29 + 16 * q^32 + 48 * q^35 - 54 * q^43 + 48 * q^46 + 32 * q^49 - 50 * q^50 + 24 * q^53 + 36 * q^58 + 32 * q^64 + 90 * q^65 - 66 * q^67 + 36 * q^70 - 12 * q^74 - 18 * q^77 + 34 * q^79 + 4 * q^85 - 54 * q^86 - 24 * q^88 + 16 * q^91 + 24 * q^92 - 12 * q^95 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.22443	+	1.87103i	−0.547582	+	0.836752i
$5$	−1.22443	+	1.87103i	−0.547582	+	0.836752i
$6$		0			0
$7$	2.45843	−	0.977807i	0.929200	−	0.369576i
$7$	2.45843	−	0.977807i	0.929200	−	0.369576i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.23258	−	0.124872i	−0.706003	−	0.0394879i
$11$	1.44107	−	0.832005i	0.434500	−	0.250859i	−0.266762	−	0.963763i	$-0.585954\pi$
$11$	1.44107	−	0.832005i	0.434500	−	0.250859i	0.701262	+	0.712904i	$0.252620\pi$
$12$		0			0
$13$	1.04814	−	1.81544i	0.290703	−	0.503512i	−0.683273	−	0.730163i	$-0.739444\pi$
$13$	1.04814	−	1.81544i	0.290703	−	0.503512i	0.973976	+	0.226651i	$0.0727776\pi$
$14$	2.07602	+	1.64016i	0.554840	+	0.438352i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	7.45463i		−	1.80801i	−0.427518	−	0.904007i	$-0.640612\pi$
$17$		−	7.45463i		−	1.80801i	0.427518	−	0.904007i	$-0.359388\pi$
$18$		0			0
$19$		−	4.66141i		−	1.06940i	−0.845042	−	0.534700i	$-0.820425\pi$
$19$		−	4.66141i		−	1.06940i	0.845042	−	0.534700i	$-0.179575\pi$
$20$	−1.00815	−	1.99591i	−0.225429	−	0.446298i
$21$		0			0
$22$	1.44107	+	0.832005i	0.307238	+	0.177384i
$23$	2.82486	−	4.89279i	0.589023	−	1.02022i	−0.405337	−	0.914167i	$-0.632846\pi$
$23$	2.82486	−	4.89279i	0.589023	−	1.02022i	0.994361	−	0.106051i	$-0.0338207\pi$
$24$		0			0
$25$	−2.00154	−	4.58191i	−0.400307	−	0.916381i
$26$	2.09629			0.411116
$27$		0			0
$28$	−0.382411	+	2.61797i	−0.0722688	+	0.494750i
$29$	4.10738	−	2.37140i	0.762721	−	0.440357i	−0.0675508	−	0.997716i	$-0.521518\pi$
$29$	4.10738	−	2.37140i	0.762721	−	0.440357i	0.830272	+	0.557359i	$0.188185\pi$
$30$		0			0
$31$	−1.73402	−	1.00114i	−0.311440	−	0.179810i	0.336131	−	0.941815i	$-0.390882\pi$
$31$	−1.73402	−	1.00114i	−0.311440	−	0.179810i	−0.647571	+	0.762005i	$0.724215\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	6.45590	−	3.72732i	1.10718	−	0.639229i
$35$	−1.18067	+	5.79707i	−0.199570	+	0.979884i
$36$		0			0
$37$			4.86789i			0.800276i	0.916455	+	0.400138i	$0.131038\pi$
$37$			4.86789i			0.800276i	−0.916455	+	0.400138i	$0.868962\pi$
$38$	4.03690	−	2.33070i	0.654871	−	0.378090i
$39$		0			0
$40$	1.22443	−	1.87103i	0.193600	−	0.295836i
$41$	−4.07169	+	7.05238i	−0.635892	+	1.10140i	0.350434	+	0.936587i	$0.386034\pi$
$41$	−4.07169	+	7.05238i	−0.635892	+	1.10140i	−0.986325	+	0.164809i	$0.947299\pi$
$42$		0			0
$43$	−2.25274	+	1.30062i	−0.343540	+	0.198343i	−0.661836	−	0.749648i	$-0.730223\pi$
$43$	−2.25274	+	1.30062i	−0.343540	+	0.198343i	0.318296	+	0.947991i	$0.396889\pi$
$44$			1.66401i			0.250859i
$45$		0			0
$46$	5.64971			0.833005
$47$	−8.90154	+	5.13931i	−1.29842	+	0.749645i	−0.980132	−	0.198348i	$-0.936442\pi$
$47$	−8.90154	+	5.13931i	−1.29842	+	0.749645i	−0.318292	+	0.947993i	$0.603109\pi$
$48$		0			0
$49$	5.08779	−	4.80775i	0.726827	−	0.686821i
$50$	2.96728	−	4.02433i	0.419637	−	0.569127i
$51$		0			0
$52$	1.04814	+	1.81544i	0.145351	+	0.251756i
$53$	13.8374			1.90071			0.950354	−	0.311170i	$-0.100721\pi$
$53$	13.8374			1.90071			0.950354	+	0.311170i	$0.100721\pi$
$54$		0			0
$55$	−0.207788	+	3.71503i	−0.0280181	+	0.500935i
$56$	−2.45843	+	0.977807i	−0.328522	+	0.130665i
$57$		0			0
$58$	4.10738	+	2.37140i	0.539325	+	0.311380i
$59$	−0.0862901	+	0.149459i	−0.0112340	+	0.0194579i	−0.871588	−	0.490240i	$-0.836909\pi$
$59$	−0.0862901	+	0.149459i	−0.0112340	+	0.0194579i	0.860354	+	0.509697i	$0.170243\pi$
$60$		0			0
$61$	−5.17503	+	2.98781i	−0.662595	+	0.382550i	−0.793265	−	0.608876i	$-0.791621\pi$
$61$	−5.17503	+	2.98781i	−0.662595	+	0.382550i	0.130670	+	0.991426i	$0.458287\pi$
$62$		−	2.00228i		−	0.254290i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.11336	+	4.18399i	0.262131	+	0.518960i
$66$		0			0
$67$	4.70611	+	2.71707i	0.574943	+	0.331943i	0.759121	−	0.650949i	$-0.225629\pi$
$67$	4.70611	+	2.71707i	0.574943	+	0.331943i	−0.184178	+	0.982893i	$0.558962\pi$
$68$	6.45590	+	3.72732i	0.782893	+	0.452003i
$69$		0			0
$70$	−5.61075	+	1.87604i	−0.670612	+	0.224230i
$71$		−	12.0450i		−	1.42947i	−0.699393	−	0.714737i	$-0.746546\pi$
$71$		−	12.0450i		−	1.42947i	0.699393	−	0.714737i	$-0.253454\pi$
$72$		0			0
$73$	4.79644			0.561381			0.280691	−	0.959798i	$-0.409437\pi$
$73$	4.79644			0.561381			0.280691	+	0.959798i	$0.409437\pi$
$74$	−4.21571	+	2.43394i	−0.490067	+	0.282940i
$75$		0			0
$76$	4.03690	+	2.33070i	0.463064	+	0.267350i
$77$	2.72924	−	3.45452i	0.311026	−	0.393679i
$78$		0			0
$79$	−6.30891	−	10.9273i	−0.709807	−	1.22942i	−0.964928	−	0.262513i	$-0.915449\pi$
$79$	−6.30891	−	10.9273i	−0.709807	−	1.22942i	0.255121	−	0.966909i	$-0.417885\pi$
$80$	2.23258	+	0.124872i	0.249610	+	0.0139611i
$81$		0			0
$82$	−8.14339			−0.899286
$83$	2.24015	−	1.29335i	0.245888	−	0.141964i	−0.371992	−	0.928236i	$-0.621325\pi$
$83$	2.24015	−	1.29335i	0.245888	−	0.141964i	0.617880	+	0.786272i	$0.287992\pi$
$84$		0			0
$85$	13.9479	+	9.12768i	1.51286	+	0.990036i
$86$	−2.25274	−	1.30062i	−0.242919	−	0.140250i
$87$		0			0
$88$	−1.44107	+	0.832005i	−0.153619	+	0.0886920i
$89$	11.2248			1.18982			0.594912	−	0.803791i	$-0.297187\pi$
$89$	11.2248			1.18982			0.594912	+	0.803791i	$0.297187\pi$
$90$		0			0
$91$	0.801642	−	5.48801i	0.0840350	−	0.575300i
$92$	2.82486	+	4.89279i	0.294512	+	0.510109i
$93$		0			0
$94$	−8.90154	−	5.13931i	−0.918124	−	0.530079i
$95$	8.72165	+	5.70757i	0.894823	+	0.585585i
$96$		0			0
$97$	4.73188	+	8.19586i	0.480450	+	0.832164i	0.999748	−	0.0224290i	$-0.00713998\pi$
$97$	4.73188	+	8.19586i	0.480450	+	0.832164i	−0.519298	+	0.854593i	$0.673807\pi$
$98$	6.70752	+	2.00228i	0.677562	+	0.202261i
$99$		0			0
$100$	4.96881	+	0.557572i	0.496881	+	0.0557572i
$101$	−5.28548	−	9.15472i	−0.525925	−	0.910928i	−0.999544	−	0.0301987i	$-0.990386\pi$
$101$	−5.28548	−	9.15472i	−0.525925	−	0.910928i	0.473619	−	0.880730i	$-0.342947\pi$
$102$		0			0
$103$	7.61856	−	13.1957i	0.750679	−	1.30021i	−0.196816	−	0.980441i	$-0.563060\pi$
$103$	7.61856	−	13.1957i	0.750679	−	1.30021i	0.947494	−	0.319773i	$-0.103607\pi$
$104$	−1.04814	+	1.81544i	−0.102779	+	0.178018i
$105$		0			0
$106$	6.91868	+	11.9835i	0.672002	+	1.16394i
$107$	11.4163			1.10366			0.551829	−	0.833957i	$-0.313930\pi$
$107$	11.4163			1.10366			0.551829	+	0.833957i	$0.313930\pi$
$108$		0			0
$109$	−10.6147			−1.01670			−0.508351	−	0.861150i	$-0.669745\pi$
$109$	−10.6147			−1.01670			−0.508351	+	0.861150i	$0.669745\pi$
$110$	−3.32121	+	1.67757i	−0.316664	+	0.159950i
$111$		0			0
$112$	−2.07602	−	1.64016i	−0.196166	−	0.154981i
$113$	−6.87120	+	11.9013i	−0.646388	+	1.11958i	0.337591	+	0.941293i	$0.390388\pi$
$113$	−6.87120	+	11.9013i	−0.646388	+	1.11958i	−0.983979	+	0.178284i	$0.942945\pi$
$114$		0			0
$115$	5.69574	+	11.2763i	0.531131	+	1.05152i
$116$			4.74279i			0.440357i
$117$		0			0
$118$	−0.172580			−0.0158873
$119$	−7.28919	−	18.3267i	−0.668199	−	1.68001i
$120$		0			0
$121$	−4.11554	+	7.12832i	−0.374140	+	0.648029i
$122$	−5.17503	−	2.98781i	−0.468526	−	0.270503i
$123$		0			0
$124$	1.73402	−	1.00114i	0.155720	−	0.0899050i
$125$	11.0236	+	1.86529i	0.985985	+	0.166837i
$126$		0			0
$127$			14.1949i			1.25960i	0.776759	+	0.629798i	$0.216862\pi$
$127$			14.1949i			1.25960i	−0.776759	+	0.629798i	$0.783138\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.56676	+	3.92222i	−0.225120	+	0.344002i
$131$	−1.14681	+	1.98633i	−0.100197	+	0.173547i	−0.911766	−	0.410710i	$-0.865281\pi$
$131$	−1.14681	+	1.98633i	−0.100197	+	0.173547i	0.811569	+	0.584257i	$0.198614\pi$
$132$		0			0
$133$	−4.55796	−	11.4598i	−0.395225	−	0.993687i
$134$			5.43415i			0.469439i
$135$		0			0
$136$			7.45463i			0.639229i
$137$	−5.41797	−	9.38419i	−0.462888	−	0.801746i	0.536215	−	0.844081i	$-0.319853\pi$
$137$	−5.41797	−	9.38419i	−0.462888	−	0.801746i	−0.999103	+	0.0423355i	$0.986520\pi$
$138$		0			0
$139$	7.63600	+	4.40865i	0.647677	+	0.373936i	0.787566	−	0.616231i	$-0.211341\pi$
$139$	7.63600	+	4.40865i	0.647677	+	0.373936i	−0.139889	+	0.990167i	$0.544674\pi$
$140$	−4.43007	−	3.92103i	−0.374409	−	0.331387i
$141$		0			0
$142$	10.4312	−	6.02248i	0.875371	−	0.505396i
$143$		−	3.48824i		−	0.291701i
$144$		0			0
$145$	−0.592241	+	10.5887i	−0.0491830	+	0.879340i
$146$	2.39822	+	4.15384i	0.198478	+	0.343774i
$147$		0			0
$148$	−4.21571	−	2.43394i	−0.346529	−	0.200069i
$149$	−12.4184	−	7.16974i	−1.01735	−	0.587368i	−0.104016	−	0.994576i	$-0.533169\pi$
$149$	−12.4184	−	7.16974i	−1.01735	−	0.587368i	−0.913336	+	0.407207i	$0.866503\pi$
$150$		0			0
$151$	3.45207	+	5.97917i	0.280926	+	0.486578i	0.971613	−	0.236576i	$-0.0760252\pi$
$151$	3.45207	+	5.97917i	0.280926	+	0.486578i	−0.690687	+	0.723154i	$0.742692\pi$
$152$			4.66141i			0.378090i
$153$		0			0
$154$	4.35632	+	0.636335i	0.351043	+	0.0512773i
$155$	3.99636	−	2.01859i	0.320995	−	0.162137i
$156$		0			0
$157$	−7.48808	+	12.9697i	−0.597614	+	1.03510i	0.395559	+	0.918441i	$0.370551\pi$
$157$	−7.48808	+	12.9697i	−0.597614	+	1.03510i	−0.993172	+	0.116657i	$0.962782\pi$
$158$	6.30891	−	10.9273i	0.501910	−	0.869333i
$159$		0			0
$160$	1.00815	+	1.99591i	0.0797010	+	0.157790i
$161$	2.16051	−	14.7908i	0.170272	−	1.16568i
$162$		0			0
$163$			8.03539i			0.629380i	0.949194	+	0.314690i	$0.101901\pi$
$163$			8.03539i			0.629380i	−0.949194	+	0.314690i	$0.898099\pi$
$164$	−4.07169	−	7.05238i	−0.317946	−	0.550698i
$165$		0			0
$166$	2.24015	+	1.29335i	0.173869	+	0.100384i
$167$	−4.12075	−	2.37911i	−0.318873	−	0.184101i	0.332017	−	0.943273i	$-0.392271\pi$
$167$	−4.12075	−	2.37911i	−0.318873	−	0.184101i	−0.650890	+	0.759172i	$0.725604\pi$
$168$		0			0
$169$	4.30279	+	7.45265i	0.330984	+	0.573281i
$170$	−0.930873	+	16.6430i	−0.0713947	+	1.27646i
$171$		0			0
$172$		−	2.60124i		−	0.198343i
$173$	14.9456	−	8.62882i	1.13629	−	0.656037i	0.190781	−	0.981633i	$-0.438898\pi$
$173$	14.9456	−	8.62882i	1.13629	−	0.656037i	0.945509	+	0.325595i	$0.105565\pi$
$174$		0			0
$175$	−9.40086	−	9.30719i	−0.710638	−	0.703558i
$176$	−1.44107	−	0.832005i	−0.108625	−	0.0627147i
$177$		0			0
$178$	5.61239	+	9.72094i	0.420666	+	0.728616i
$179$		−	0.602635i		−	0.0450430i	−0.999746	−	0.0225215i	$-0.992831\pi$
$179$		−	0.602635i		−	0.0450430i	0.999746	−	0.0225215i	$-0.00716943\pi$
$180$		0			0
$181$			12.7778i			0.949769i	0.880048	+	0.474885i	$0.157510\pi$
$181$			12.7778i			0.949769i	−0.880048	+	0.474885i	$0.842490\pi$
$182$	5.15358	−	2.04976i	0.382009	−	0.151939i
$183$		0			0
$184$	−2.82486	+	4.89279i	−0.208251	+	0.360702i
$185$	−9.10798	−	5.96039i	−0.669632	−	0.438217i
$186$		0			0
$187$	−6.20229	−	10.7427i	−0.453556	−	0.785582i
$188$		−	10.2786i		−	0.749645i
$189$		0			0
$190$	−0.582079	+	10.4070i	−0.0422284	+	0.755000i
$191$	−16.3178	+	9.42111i	−1.18072	+	0.681687i	−0.956180	−	0.292778i	$-0.905420\pi$
$191$	−16.3178	+	9.42111i	−1.18072	+	0.681687i	−0.224537	+	0.974466i	$0.572087\pi$
$192$		0			0
$193$	5.89207	+	3.40179i	0.424120	+	0.244866i	0.696839	−	0.717228i	$-0.254589\pi$
$193$	5.89207	+	3.40179i	0.424120	+	0.244866i	−0.272718	+	0.962094i	$0.587923\pi$
$194$	−4.73188	+	8.19586i	−0.339730	+	0.588429i
$195$		0			0
$196$	1.61974	+	6.81003i	0.115696	+	0.486430i
$197$	8.58750			0.611834			0.305917	−	0.952058i	$-0.401037\pi$
$197$	8.58750			0.611834			0.305917	+	0.952058i	$0.401037\pi$
$198$		0			0
$199$		−	5.10064i		−	0.361575i	−0.983522	−	0.180788i	$-0.942135\pi$
$199$		−	5.10064i		−	0.361575i	0.983522	−	0.180788i	$-0.0578646\pi$
$200$	2.00154	+	4.58191i	0.141530	+	0.323990i
$201$		0			0
$202$	5.28548	−	9.15472i	0.371885	−	0.644124i
$203$	7.77895	−	9.84614i	0.545975	−	0.691064i
$204$		0			0
$205$	−8.20973	−	16.2534i	−0.573392	−	1.13519i
$206$	15.2371			1.06162
$207$		0			0
$208$	−2.09629			−0.145351
$209$	−3.87831	−	6.71743i	−0.268268	−	0.464655i
$210$		0			0
$211$	5.01715	−	8.68995i	0.345395	−	0.598241i	−0.640031	−	0.768349i	$-0.721078\pi$
$211$	5.01715	−	8.68995i	0.345395	−	0.598241i	0.985425	+	0.170108i	$0.0544118\pi$
$212$	−6.91868	+	11.9835i	−0.475177	+	0.823031i
$213$		0			0
$214$	5.70816	+	9.88683i	0.390202	+	0.675850i
$215$	0.324822	−	5.80748i	0.0221527	−	0.396067i
$216$		0			0
$217$	−5.24190	−	0.765693i	−0.355844	−	0.0519786i
$218$	−5.30734	−	9.19258i	−0.359458	−	0.622600i
$219$		0			0
$220$	−3.11342	−	2.03747i	−0.209907	−	0.137366i
$221$	−13.5334	−	7.81352i	−0.910356	−	0.525594i
$222$		0			0
$223$	−8.87226	−	15.3672i	−0.594131	−	1.02906i	−0.993669	−	0.112348i	$-0.964163\pi$
$223$	−8.87226	−	15.3672i	−0.594131	−	1.02906i	0.399538	−	0.916717i	$-0.369171\pi$
$224$	0.382411	−	2.61797i	0.0255509	−	0.174920i
$225$		0			0
$226$	−13.7424			−0.914131
$227$	0.411273	−	0.237449i	0.0272972	−	0.0157600i	−0.486289	−	0.873798i	$-0.661650\pi$
$227$	0.411273	−	0.237449i	0.0272972	−	0.0157600i	0.513586	+	0.858038i	$0.328317\pi$
$228$		0			0
$229$	−9.51279	−	5.49221i	−0.628623	−	0.362936i	0.151596	−	0.988443i	$-0.451559\pi$
$229$	−9.51279	−	5.49221i	−0.628623	−	0.362936i	−0.780219	+	0.625507i	$0.784892\pi$
$230$	−6.91769	+	10.5708i	−0.456139	+	0.697018i
$231$		0			0
$232$	−4.10738	+	2.37140i	−0.269663	+	0.155690i
$233$	−21.4794			−1.40716			−0.703582	−	0.710614i	$-0.748417\pi$
$233$	−21.4794			−1.40716			−0.703582	+	0.710614i	$0.748417\pi$
$234$		0			0
$235$	1.28351	−	22.9478i	0.0837269	−	1.49695i
$236$	−0.0862901	−	0.149459i	−0.00561701	−	0.00972894i
$237$		0			0
$238$	12.2268	−	15.4760i	0.792546	−	1.00316i
$239$	14.6228	+	8.44250i	0.945873	+	0.546100i	0.891797	−	0.452437i	$-0.149445\pi$
$239$	14.6228	+	8.44250i	0.945873	+	0.546100i	0.0540768	+	0.998537i	$0.482778\pi$
$240$		0			0
$241$	8.00911	−	4.62406i	0.515912	−	0.297862i	−0.219348	−	0.975647i	$-0.570393\pi$
$241$	8.00911	−	4.62406i	0.515912	−	0.297862i	0.735261	+	0.677784i	$0.237060\pi$
$242$	−8.23107			−0.529113
$243$		0			0
$244$		−	5.97562i		−	0.382550i
$245$	2.76581	+	15.4062i	0.176701	+	0.984265i
$246$		0			0
$247$	−8.46249	−	4.88582i	−0.538456	−	0.310877i
$248$	1.73402	+	1.00114i	0.110111	+	0.0635724i
$249$		0			0
$250$	3.89643	+	10.4794i	0.246432	+	0.662775i
$251$	9.36996			0.591426			0.295713	−	0.955277i	$-0.404443\pi$
$251$	9.36996			0.591426			0.295713	+	0.955277i	$0.404443\pi$
$252$		0			0
$253$		−	9.40117i		−	0.591047i
$254$	−12.2932	+	7.09746i	−0.771342	+	0.445334i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.62239	+	3.24609i	0.350715	+	0.202485i	0.665000	−	0.746843i	$-0.268431\pi$
$257$	5.62239	+	3.24609i	0.350715	+	0.202485i	−0.314285	+	0.949329i	$0.601765\pi$
$258$		0			0
$259$	4.75985	+	11.9674i	0.295763	+	0.743616i
$260$	−4.68012	−	0.261767i	−0.290249	−	0.0162341i
$261$		0			0
$262$	−2.29362			−0.141700
$263$	4.41420	+	7.64563i	0.272192	+	0.471450i	0.969423	−	0.245397i	$-0.0789182\pi$
$263$	4.41420	+	7.64563i	0.272192	+	0.471450i	−0.697231	+	0.716846i	$0.745585\pi$
$264$		0			0
$265$	−16.9429	+	25.8902i	−1.04079	+	1.59042i
$266$	7.64546	−	9.67719i	0.468773	−	0.593346i
$267$		0			0
$268$	−4.70611	+	2.71707i	−0.287471	+	0.165972i
$269$	−11.6257			−0.708833			−0.354416	−	0.935088i	$-0.615320\pi$
$269$	−11.6257			−0.708833			−0.354416	+	0.935088i	$0.615320\pi$
$270$		0			0
$271$		−	16.8123i		−	1.02128i	−0.859796	−	0.510638i	$-0.829409\pi$
$271$		−	16.8123i		−	1.02128i	0.859796	−	0.510638i	$-0.170591\pi$
$272$	−6.45590	+	3.72732i	−0.391446	+	0.226002i
$273$		0			0
$274$	5.41797	−	9.38419i	0.327311	−	0.566920i
$275$	−6.69653	−	4.93758i	−0.403816	−	0.297747i
$276$		0			0
$277$	−1.93149	+	1.11514i	−0.116052	+	0.0670026i	−0.556902	−	0.830578i	$-0.688010\pi$
$277$	−1.93149	+	1.11514i	−0.116052	+	0.0670026i	0.440850	+	0.897581i	$0.354677\pi$
$278$			8.81729i			0.528826i
$279$		0			0
$280$	1.18067	−	5.79707i	0.0705587	−	0.346441i
$281$	2.79869	−	1.61582i	0.166956	−	0.0963919i	−0.414194	−	0.910189i	$-0.635936\pi$
$281$	2.79869	−	1.61582i	0.166956	−	0.0963919i	0.581150	+	0.813797i	$0.302603\pi$
$282$		0			0
$283$	3.23291	−	5.59957i	0.192177	−	0.332860i	−0.753795	−	0.657110i	$-0.771779\pi$
$283$	3.23291	−	5.59957i	0.192177	−	0.332860i	0.945971	+	0.324250i	$0.105112\pi$
$284$	10.4312	+	6.02248i	0.618981	+	0.357369i
$285$		0			0
$286$	3.02090	−	1.74412i	0.178630	−	0.103132i
$287$	−3.11412	+	21.3191i	−0.183821	+	1.25843i
$288$		0			0
$289$	−38.5715			−2.26891
$290$	−9.46617	+	4.78143i	−0.555872	+	0.280775i
$291$		0			0
$292$	−2.39822	+	4.15384i	−0.140345	+	0.243085i
$293$	16.0415	+	9.26155i	0.937153	+	0.541066i	0.889067	−	0.457777i	$-0.151354\pi$
$293$	16.0415	+	9.26155i	0.937153	+	0.541066i	0.0480865	+	0.998843i	$0.484688\pi$
$294$		0			0
$295$	−0.173986	−	0.344454i	−0.0101299	−	0.0200549i
$296$		−	4.86789i		−	0.282940i
$297$		0			0
$298$		−	14.3395i		−	0.830664i
$299$	−5.92171	−	10.2567i	−0.342461	−	0.593160i
$300$		0			0
$301$	−4.26646	+	5.40024i	−0.245915	+	0.311264i
$302$	−3.45207	+	5.97917i	−0.198645	+	0.344062i
$303$		0			0
$304$	−4.03690	+	2.33070i	−0.231532	+	0.133675i
$305$	0.746186	−	13.3410i	0.0427265	−	0.763905i
$306$		0			0
$307$	−3.44142			−0.196412			−0.0982062	−	0.995166i	$-0.531310\pi$
$307$	−3.44142			−0.196412			−0.0982062	+	0.995166i	$0.531310\pi$
$308$	1.62708	+	4.09086i	0.0927115	+	0.233098i
$309$		0			0
$310$	3.74633	+	2.45165i	0.212777	+	0.139245i
$311$	−16.6186	+	28.7842i	−0.942352	+	1.63220i	−0.181385	+	0.983412i	$0.558058\pi$
$311$	−16.6186	+	28.7842i	−0.942352	+	1.63220i	−0.760967	+	0.648790i	$0.775275\pi$
$312$		0			0
$313$	0.967111	+	1.67509i	0.0546644	+	0.0946815i	0.892063	−	0.451912i	$-0.149258\pi$
$313$	0.967111	+	1.67509i	0.0546644	+	0.0946815i	−0.837398	+	0.546593i	$0.815924\pi$
$314$	−14.9762			−0.845153
$315$		0			0
$316$	12.6178			0.709807
$317$	−5.12038	−	8.86877i	−0.287589	−	0.498120i	0.685644	−	0.727937i	$-0.259521\pi$
$317$	−5.12038	−	8.86877i	−0.287589	−	0.498120i	−0.973234	+	0.229817i	$0.926187\pi$
$318$		0			0
$319$	3.94603	−	6.83472i	0.220935	−	0.382671i
$320$	−1.22443	+	1.87103i	−0.0684478	+	0.104594i
$321$		0			0
$322$	13.8894	−	5.52433i	0.774028	−	0.307859i
$323$	−34.7491			−1.93349
$324$		0			0
$325$	−10.4161	−	1.16883i	−0.577779	−	0.0648351i
$326$	−6.95885	+	4.01770i	−0.385415	+	0.222520i
$327$		0			0
$328$	4.07169	−	7.05238i	0.224822	−	0.389402i
$329$	−16.8586	+	21.3386i	−0.929444	+	1.17644i
$330$		0			0
$331$	−2.81788	−	4.88070i	−0.154884	−	0.268268i	0.778133	−	0.628100i	$-0.216167\pi$
$331$	−2.81788	−	4.88070i	−0.154884	−	0.268268i	−0.933017	+	0.359832i	$0.882834\pi$
$332$			2.58670i			0.141964i
$333$		0			0
$334$		−	4.75823i		−	0.260359i
$335$	−10.8460	+	5.47842i	−0.592583	+	0.299318i
$336$		0			0
$337$	−11.8563	−	6.84524i	−0.645854	−	0.372884i	0.141012	−	0.990008i	$-0.454964\pi$
$337$	−11.8563	−	6.84524i	−0.645854	−	0.372884i	−0.786866	+	0.617124i	$0.788298\pi$
$338$	−4.30279	+	7.45265i	−0.234041	+	0.405371i
$339$		0			0
$340$	−14.8787	+	7.51536i	−0.806913	+	0.407578i
$341$	−3.33181			−0.180428
$342$		0			0
$343$	7.80693	−	16.7944i	0.421535	−	0.906812i
$344$	2.25274	−	1.30062i	0.121460	−	0.0701248i
$345$		0			0
$346$	14.9456	+	8.62882i	0.803478	+	0.463888i
$347$	−4.89520	+	8.47874i	−0.262788	+	0.455163i	−0.966982	−	0.254845i	$-0.917975\pi$
$347$	−4.89520	+	8.47874i	−0.262788	+	0.455163i	0.704193	+	0.710008i	$0.251309\pi$
$348$		0			0
$349$	14.0539	−	8.11400i	0.752286	−	0.434332i	−0.0742335	−	0.997241i	$-0.523651\pi$
$349$	14.0539	−	8.11400i	0.752286	−	0.434332i	0.826519	+	0.562909i	$0.190318\pi$
$350$	3.35984	−	12.7950i	0.179591	−	0.683920i
$351$		0			0
$352$		−	1.66401i		−	0.0886920i
$353$	20.9960	−	12.1220i	1.11750	−	0.645191i	0.176741	−	0.984257i	$-0.443444\pi$
$353$	20.9960	−	12.1220i	1.11750	−	0.645191i	0.940762	+	0.339066i	$0.110111\pi$
$354$		0			0
$355$	22.5365	+	14.7482i	1.19612	+	0.782755i
$356$	−5.61239	+	9.72094i	−0.297456	+	0.515209i
$357$		0			0
$358$	0.521897	−	0.301317i	0.0275831	−	0.0159251i
$359$			31.3617i			1.65521i	0.561313	+	0.827604i	$0.310296\pi$
$359$			31.3617i			1.65521i	−0.561313	+	0.827604i	$0.689704\pi$
$360$		0			0
$361$	−2.72872			−0.143617
$362$	−11.0659	+	6.38892i	−0.581612	+	0.335794i
$363$		0			0
$364$	4.35194	+	3.43825i	0.228103	+	0.180213i
$365$	−5.87292	+	8.97431i	−0.307402	+	0.469737i
$366$		0			0
$367$	0.616195	+	1.06728i	0.0321651	+	0.0557116i	0.881660	−	0.471885i	$-0.156426\pi$
$367$	0.616195	+	1.06728i	0.0321651	+	0.0557116i	−0.849495	+	0.527597i	$0.823093\pi$
$368$	−5.64971			−0.294512
$369$		0			0
$370$	0.607862	−	10.8679i	0.0316012	−	0.564997i
$371$	34.0182	−	13.5303i	1.76614	−	0.702457i
$372$		0			0
$373$	−23.9159	−	13.8079i	−1.23832	−	0.714944i	−0.269569	−	0.962981i	$-0.586881\pi$
$373$	−23.9159	−	13.8079i	−1.23832	−	0.714944i	−0.968751	+	0.248037i	$0.920214\pi$
$374$	6.20229	−	10.7427i	0.320713	−	0.555491i
$375$		0			0
$376$	8.90154	−	5.13931i	0.459062	−	0.265040i
$377$		−	9.94225i		−	0.512052i
$378$		0			0
$379$	23.2265			1.19307			0.596533	−	0.802589i	$-0.296545\pi$
$379$	23.2265			1.19307			0.596533	+	0.802589i	$0.296545\pi$
$380$	−9.30373	+	4.69938i	−0.477271	+	0.241073i
$381$		0			0
$382$	−16.3178	−	9.42111i	−0.834893	−	0.482026i
$383$	20.6052	+	11.8964i	1.05288	+	0.607880i	0.923454	−	0.383709i	$-0.125354\pi$
$383$	20.6052	+	11.8964i	1.05288	+	0.607880i	0.129425	+	0.991589i	$0.458687\pi$
$384$		0			0
$385$	3.12175	+	9.33633i	0.159099	+	0.475824i
$386$			6.80357i			0.346293i
$387$		0			0
$388$	−9.46377			−0.480450
$389$	8.18328	−	4.72462i	0.414909	−	0.239548i	−0.277988	−	0.960585i	$-0.589668\pi$
$389$	8.18328	−	4.72462i	0.414909	−	0.239548i	0.692897	+	0.721037i	$0.256334\pi$
$390$		0			0
$391$	−36.4740	−	21.0583i	−1.84457	−	1.06496i
$392$	−5.08779	+	4.80775i	−0.256972	+	0.242828i
$393$		0			0
$394$	4.29375	+	7.43699i	0.216316	+	0.374670i
$395$	28.1703	+	1.57561i	1.41740	+	0.0792775i
$396$		0			0
$397$	21.7234			1.09026			0.545132	−	0.838350i	$-0.316479\pi$
$397$	21.7234			1.09026			0.545132	+	0.838350i	$0.316479\pi$
$398$	4.41729	−	2.55032i	0.221419	−	0.127836i
$399$		0			0
$400$	−2.96728	+	4.02433i	−0.148364	+	0.201217i
$401$	10.6544	+	6.15134i	0.532057	+	0.307183i	0.741854	−	0.670562i	$-0.233947\pi$
$401$	10.6544	+	6.15134i	0.532057	+	0.307183i	−0.209797	+	0.977745i	$0.567280\pi$
$402$		0			0
$403$	−3.63501	+	2.09867i	−0.181073	+	0.104542i
$404$	10.5710			0.525925
$405$		0			0
$406$	12.4165	+	1.81369i	0.616220	+	0.0900122i
$407$	4.05010	+	7.01498i	0.200756	+	0.347720i
$408$		0			0
$409$	−2.50285	−	1.44502i	−0.123758	−	0.0714517i	0.436843	−	0.899538i	$-0.356097\pi$
$409$	−2.50285	−	1.44502i	−0.123758	−	0.0714517i	−0.560601	+	0.828086i	$0.689430\pi$
$410$	9.97102	−	15.2365i	0.492433	−	0.752480i
$411$		0			0
$412$	7.61856	+	13.1957i	0.375339	+	0.650107i
$413$	−0.0659965	+	0.451810i	−0.00324748	+	0.0222321i
$414$		0			0
$415$	−0.323006	+	5.77502i	−0.0158558	+	0.283484i
$416$	−1.04814	−	1.81544i	−0.0513894	−	0.0890091i
$417$		0			0
$418$	3.87831	−	6.71743i	0.189694	−	0.328560i
$419$	12.7397	−	22.0658i	0.622374	−	1.07798i	−0.366668	−	0.930352i	$-0.619501\pi$
$419$	12.7397	−	22.0658i	0.622374	−	1.07798i	0.989042	−	0.147632i	$-0.0471652\pi$
$420$		0			0
$421$	−2.96965	−	5.14359i	−0.144732	−	0.250683i	0.784541	−	0.620077i	$-0.212899\pi$
$421$	−2.96965	−	5.14359i	−0.144732	−	0.250683i	−0.929273	+	0.369394i	$0.879565\pi$
$422$	10.0343			0.488462
$423$		0			0
$424$	−13.8374			−0.672002
$425$	−34.1564	+	14.9207i	−1.65683	+	0.723761i
$426$		0			0
$427$	−9.80098	+	12.4055i	−0.474303	+	0.600345i
$428$	−5.70816	+	9.88683i	−0.275914	+	0.477898i
$429$		0			0
$430$	5.19183	−	2.62243i	0.250372	−	0.126465i
$431$			29.4344i			1.41781i	0.705306	+	0.708903i	$0.250810\pi$
$431$			29.4344i			1.41781i	−0.705306	+	0.708903i	$0.749190\pi$
$432$		0			0
$433$	14.2559			0.685093			0.342546	−	0.939501i	$-0.388711\pi$
$433$	14.2559			0.685093			0.342546	+	0.939501i	$0.388711\pi$
$434$	−1.95784	−	4.92247i	−0.0939795	−	0.236286i
$435$		0			0
$436$	5.30734	−	9.19258i	0.254176	−	0.440245i
$437$	−22.8073	−	13.1678i	−1.09102	−	0.629902i
$438$		0			0
$439$	−9.41191	+	5.43397i	−0.449206	+	0.259349i	−0.707495	−	0.706719i	$-0.750175\pi$
$439$	−9.41191	+	5.43397i	−0.449206	+	0.259349i	0.258289	+	0.966068i	$0.416841\pi$
$440$	0.207788	−	3.71503i	0.00990590	−	0.177107i
$441$		0			0
$442$		−	15.6270i		−	0.743303i
$443$	−5.24859	−	9.09083i	−0.249368	−	0.431918i	0.713983	−	0.700164i	$-0.246890\pi$
$443$	−5.24859	−	9.09083i	−0.249368	−	0.431918i	−0.963351	+	0.268245i	$0.913556\pi$
$444$		0			0
$445$	−13.7440	+	21.0019i	−0.651527	+	0.995587i
$446$	8.87226	−	15.3672i	0.420114	−	0.727659i
$447$		0			0
$448$	2.45843	−	0.977807i	0.116150	−	0.0461970i
$449$		−	37.0684i		−	1.74937i	−0.484695	−	0.874683i	$-0.661070\pi$
$449$		−	37.0684i		−	1.74937i	0.484695	−	0.874683i	$-0.338930\pi$
$450$		0			0
$451$			13.5507i			0.638076i
$452$	−6.87120	−	11.9013i	−0.323194	−	0.559789i
$453$		0			0
$454$	0.411273	+	0.237449i	0.0193020	+	0.0111440i
$455$	9.28670	+	8.21960i	0.435367	+	0.385341i
$456$		0			0
$457$	−17.5211	+	10.1158i	−0.819601	+	0.473197i	−0.850279	−	0.526333i	$-0.823567\pi$
$457$	−17.5211	+	10.1158i	−0.819601	+	0.473197i	0.0306780	+	0.999529i	$0.490233\pi$
$458$		−	10.9844i		−	0.513269i
$459$		0			0
$460$	−12.6134	−	0.705490i	−0.588104	−	0.0328936i
$461$	−6.80701	−	11.7901i	−0.317034	−	0.549119i	0.662834	−	0.748766i	$-0.269354\pi$
$461$	−6.80701	−	11.7901i	−0.317034	−	0.549119i	−0.979868	+	0.199648i	$0.936020\pi$
$462$		0			0
$463$	19.8188	+	11.4424i	0.921057	+	0.531773i	0.883972	−	0.467539i	$-0.154859\pi$
$463$	19.8188	+	11.4424i	0.921057	+	0.531773i	0.0370852	+	0.999312i	$0.488193\pi$
$464$	−4.10738	−	2.37140i	−0.190680	−	0.110089i
$465$		0			0
$466$	−10.7397	−	18.6017i	−0.497507	−	0.861708i
$467$		−	3.34545i		−	0.154809i	−0.997000	−	0.0774044i	$-0.975337\pi$
$467$		−	3.34545i		−	0.154809i	0.997000	−	0.0774044i	$-0.0246633\pi$
$468$		0			0
$469$	14.2264	+	2.07808i	0.656916	+	0.0959567i
$470$	20.5151	−	10.3624i	0.946293	−	0.477980i
$471$		0			0
$472$	0.0862901	−	0.149459i	0.00397182	−	0.00687940i
$473$	−2.16425	+	3.74858i	−0.0995121	+	0.172360i
$474$		0			0
$475$	−21.3581	+	9.32997i	−0.979978	+	0.428088i
$476$	19.5160	+	2.85073i	0.894514	+	0.130663i
$477$		0			0
$478$			16.8850i			0.772302i
$479$	8.15257	+	14.1207i	0.372500	+	0.645189i	0.989949	−	0.141421i	$-0.0451673\pi$
$479$	8.15257	+	14.1207i	0.372500	+	0.645189i	−0.617449	+	0.786611i	$0.711834\pi$
$480$		0			0
$481$	8.83734	+	5.10224i	0.402948	+	0.232642i
$482$	8.00911	+	4.62406i	0.364805	+	0.210620i
$483$		0			0
$484$	−4.11554	−	7.12832i	−0.187070	−	0.324014i
$485$	−21.1286	−	1.18176i	−0.959401	−	0.0536609i
$486$		0			0
$487$		−	5.20248i		−	0.235747i	−0.993029	−	0.117873i	$-0.962392\pi$
$487$		−	5.20248i		−	0.235747i	0.993029	−	0.117873i	$-0.0376077\pi$
$488$	5.17503	−	2.98781i	0.234263	−	0.135252i
$489$		0			0
$490$	−11.9592	+	10.0984i	−0.540263	+	0.456197i
$491$	20.6633	+	11.9299i	0.932521	+	0.538391i	0.887608	−	0.460600i	$-0.152366\pi$
$491$	20.6633	+	11.9299i	0.932521	+	0.538391i	0.0449127	+	0.998991i	$0.485699\pi$
$492$		0			0
$493$	−17.6779	−	30.6190i	−0.796172	−	1.37901i
$494$		−	9.77165i		−	0.439647i
$495$		0			0
$496$			2.00228i			0.0899050i
$497$	−11.7777	−	29.6117i	−0.528300	−	1.32827i
$498$		0			0
$499$	16.1660	−	28.0003i	0.723688	−	1.25346i	−0.235824	−	0.971796i	$-0.575779\pi$
$499$	16.1660	−	28.0003i	0.723688	−	1.25346i	0.959512	−	0.281668i	$-0.0908877\pi$
$500$	−7.12721	+	8.61411i	−0.318738	+	0.385235i
$501$		0			0
$502$	4.68498	+	8.11462i	0.209101	+	0.362173i
$503$		−	10.0768i		−	0.449301i	−0.974439	−	0.224651i	$-0.927876\pi$
$503$		−	10.0768i		−	0.449301i	0.974439	−	0.224651i	$-0.0721241\pi$
$504$		0			0
$505$	23.6005	+	1.32001i	1.05021	+	0.0587399i
$506$	8.14166	−	4.70059i	0.361941	−	0.208967i
$507$		0			0
$508$	−12.2932	−	7.09746i	−0.545421	−	0.314899i
$509$	−10.5573	+	18.2858i	−0.467944	+	0.810503i	−0.999329	−	0.0366275i	$-0.988338\pi$
$509$	−10.5573	+	18.2858i	−0.467944	+	0.810503i	0.531385	+	0.847131i	$0.321672\pi$
$510$		0			0
$511$	11.7917	−	4.69000i	0.521636	−	0.207473i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			6.49218i			0.286358i
$515$	15.3612	+	30.4118i	0.676898	+	1.34011i
$516$		0			0
$517$	−8.55186	+	14.8122i	−0.376110	+	0.651442i
$518$	−7.98412	+	10.1058i	−0.350802	+	0.444025i
$519$		0			0
$520$	−2.11336	−	4.18399i	−0.0926772	−	0.183480i
$521$	−21.9402			−0.961216			−0.480608	−	0.876936i	$-0.659584\pi$
$521$	−21.9402			−0.961216			−0.480608	+	0.876936i	$0.659584\pi$
$522$		0			0
$523$	7.10550			0.310702			0.155351	−	0.987859i	$-0.450349\pi$
$523$	7.10550			0.310702			0.155351	+	0.987859i	$0.450349\pi$
$524$	−1.14681	−	1.98633i	−0.0500986	−	0.0867733i
$525$		0			0
$526$	−4.41420	+	7.64563i	−0.192468	+	0.333365i
$527$	−7.46313	+	12.9265i	−0.325099	+	0.563088i
$528$		0			0
$529$	−4.45963	−	7.72430i	−0.193897	−	0.335839i
$530$	−30.8930	−	1.72790i	−1.34191	−	0.0750551i
$531$		0			0
$532$	12.2034	+	1.78257i	0.529085	+	0.0772843i
$533$	8.53543	+	14.7838i	0.369711	+	0.640358i
$534$		0			0
$535$	−13.9785	+	21.3603i	−0.604344	+	0.923488i
$536$	−4.70611	−	2.71707i	−0.203273	−	0.117360i
$537$		0			0
$538$	−5.81286	−	10.0682i	−0.250610	−	0.434070i
$539$	3.33181	−	11.1614i	0.143511	−	0.480755i
$540$		0			0
$541$	−36.7965			−1.58200			−0.791002	−	0.611813i	$-0.790441\pi$
$541$	−36.7965			−1.58200			−0.791002	+	0.611813i	$0.790441\pi$
$542$	14.5599	−	8.40617i	0.625402	−	0.361076i
$543$		0			0
$544$	−6.45590	−	3.72732i	−0.276794	−	0.159807i
$545$	12.9970	−	19.8604i	0.556728	−	0.850727i
$546$		0			0
$547$	−14.6902	+	8.48140i	−0.628108	+	0.362638i	−0.780019	−	0.625756i	$-0.784791\pi$
$547$	−14.6902	+	8.48140i	−0.628108	+	0.362638i	0.151911	+	0.988394i	$0.451457\pi$
$548$	10.8359			0.462888
$549$		0			0
$550$	0.927806	−	8.26815i	0.0395618	−	0.352555i
$551$	−11.0540	−	19.1462i	−0.470918	−	0.815654i
$552$		0			0
$553$	−26.1949	−	20.6953i	−1.11392	−	0.880052i
$554$	−1.93149	−	1.11514i	−0.0820610	−	0.0473780i
$555$		0			0
$556$	−7.63600	+	4.40865i	−0.323839	+	0.186968i
$557$	−2.63451			−0.111628			−0.0558139	−	0.998441i	$-0.517775\pi$
$557$	−2.63451			−0.111628			−0.0558139	+	0.998441i	$0.517775\pi$
$558$		0			0
$559$			5.45295i			0.230635i
$560$	5.61075	−	1.87604i	0.237097	−	0.0792772i
$561$		0			0
$562$	2.79869	+	1.61582i	0.118055	+	0.0681594i
$563$	20.7641	+	11.9882i	0.875104	+	0.505242i	0.869041	−	0.494740i	$-0.164737\pi$
$563$	20.7641	+	11.9882i	0.875104	+	0.505242i	0.00606320	+	0.999982i	$0.498070\pi$
$564$		0			0
$565$	−13.8544	−	27.4285i	−0.582857	−	1.15393i
$566$	6.46583			0.271779
$567$		0			0
$568$			12.0450i			0.505396i
$569$	−36.5400	+	21.0964i	−1.53184	+	0.884407i	−0.532560	+	0.846392i	$0.678770\pi$
$569$	−36.5400	+	21.0964i	−1.53184	+	0.884407i	−0.999277	+	0.0380144i	$0.987897\pi$
$570$		0			0
$571$	12.7469	−	22.0783i	0.533441	−	0.923947i	−0.465796	−	0.884892i	$-0.654232\pi$
$571$	12.7469	−	22.0783i	0.533441	−	0.923947i	0.999237	−	0.0390547i	$-0.0124347\pi$
$572$	3.02090	+	1.74412i	0.126310	+	0.0729253i
$573$		0			0
$574$	−20.0200	+	7.96266i	−0.835617	+	0.332355i
$575$	−28.0724	−	3.15012i	−1.17070	−	0.131369i
$576$		0			0
$577$	32.7696			1.36422			0.682108	−	0.731251i	$-0.261063\pi$
$577$	32.7696			1.36422			0.682108	+	0.731251i	$0.261063\pi$
$578$	−19.2858	−	33.4039i	−0.802182	−	1.38942i
$579$		0			0
$580$	−8.87393	−	5.80722i	−0.368470	−	0.241132i
$581$	4.24261	−	5.37005i	0.176013	−	0.222787i
$582$		0			0
$583$	19.9407	−	11.5128i	0.825858	−	0.476810i
$584$	−4.79644			−0.198478
$585$		0			0
$586$			18.5231i			0.765182i
$587$	−19.1726	+	11.0693i	−0.791337	+	0.456879i	−0.840433	−	0.541915i	$-0.817699\pi$
$587$	−19.1726	+	11.0693i	−0.791337	+	0.456879i	0.0490959	+	0.998794i	$0.484366\pi$
$588$		0			0
$589$	−4.66672	+	8.08300i	−0.192289	+	0.333054i
$590$	0.211313	−	0.322903i	0.00869960	−	0.0132937i
$591$		0			0
$592$	4.21571	−	2.43394i	0.173265	−	0.100034i
$593$		−	26.0392i		−	1.06930i	−0.845073	−	0.534650i	$-0.820443\pi$
$593$		−	26.0392i		−	1.06930i	0.845073	−	0.534650i	$-0.179557\pi$
$594$		0			0
$595$	43.2150	+	8.80148i	1.77164	+	0.360825i
$596$	12.4184	−	7.16974i	0.508676	−	0.293684i
$597$		0			0
$598$	5.92171	−	10.2567i	0.242157	−	0.419428i
$599$	−18.1227	−	10.4631i	−0.740472	−	0.427512i	0.0817689	−	0.996651i	$-0.473943\pi$
$599$	−18.1227	−	10.4631i	−0.740472	−	0.427512i	−0.822241	+	0.569140i	$0.807276\pi$
$600$		0			0
$601$	−25.4768	+	14.7091i	−1.03922	+	0.599995i	−0.919613	−	0.392826i	$-0.871497\pi$
$601$	−25.4768	+	14.7091i	−1.03922	+	0.599995i	−0.119609	+	0.992821i	$0.538164\pi$
$602$	−6.80997	−	0.994743i	−0.277554	−	0.0405427i
$603$		0			0
$604$	−6.90415			−0.280926
$605$	−8.29813	−	16.4284i	−0.337367	−	0.667911i
$606$		0			0
$607$	−6.62507	+	11.4750i	−0.268903	+	0.465754i	−0.968579	−	0.248707i	$-0.919994\pi$
$607$	−6.62507	+	11.4750i	−0.268903	+	0.465754i	0.699676	+	0.714461i	$0.253328\pi$
$608$	−4.03690	−	2.33070i	−0.163718	−	0.0945225i
$609$		0			0
$610$	11.9268	−	6.02430i	0.482901	−	0.243917i
$611$			21.5469i			0.871695i
$612$		0			0
$613$		−	17.3252i		−	0.699759i	−0.936795	−	0.349880i	$-0.886222\pi$
$613$		−	17.3252i		−	0.699759i	0.936795	−	0.349880i	$-0.113778\pi$
$614$	−1.72071	−	2.98036i	−0.0694423	−	0.120278i
$615$		0			0
$616$	−2.72924	+	3.45452i	−0.109964	+	0.139187i
$617$	−9.93911	+	17.2150i	−0.400133	+	0.693052i	−0.993742	−	0.111703i	$-0.964370\pi$
$617$	−9.93911	+	17.2150i	−0.400133	+	0.693052i	0.593608	+	0.804754i	$0.297703\pi$
$618$		0			0
$619$	30.8618	−	17.8181i	1.24044	−	0.716168i	0.271256	−	0.962507i	$-0.412561\pi$
$619$	30.8618	−	17.8181i	1.24044	−	0.716168i	0.969184	+	0.246339i	$0.0792276\pi$
$620$	−0.250028	+	4.47025i	−0.0100414	+	0.179529i
$621$		0			0
$622$	−33.2371			−1.33269
$623$	27.5954	−	10.9757i	1.10559	−	0.439731i
$624$		0			0
$625$	−16.9877	+	18.3417i	−0.679509	+	0.733668i
$626$	−0.967111	+	1.67509i	−0.0386535	+	0.0669499i
$627$		0			0
$628$	−7.48808	−	12.9697i	−0.298807	−	0.517549i
$629$	36.2883			1.44691
$630$		0			0
$631$	28.1609			1.12107			0.560533	−	0.828132i	$-0.310596\pi$
$631$	28.1609			1.12107			0.560533	+	0.828132i	$0.310596\pi$
$632$	6.30891	+	10.9273i	0.250955	+	0.434666i
$633$		0			0
$634$	5.12038	−	8.86877i	0.203356	−	0.352224i
$635$	−26.5592	−	17.3807i	−1.05397	−	0.689732i
$636$		0			0
$637$	−3.39543	−	14.2758i	−0.134532	−	0.565626i
$638$	7.89205			0.312449
$639$		0			0
$640$	−2.23258	−	0.124872i	−0.0882504	−	0.00493599i
$641$	−25.4170	+	14.6745i	−1.00391	+	0.579608i	−0.909403	−	0.415916i	$-0.863461\pi$
$641$	−25.4170	+	14.6745i	−1.00391	+	0.579608i	−0.0945076	+	0.995524i	$0.530128\pi$
$642$		0			0
$643$	16.7337	−	28.9836i	0.659912	−	1.14300i	−0.320726	−	0.947172i	$-0.603927\pi$
$643$	16.7337	−	28.9836i	0.659912	−	1.14300i	0.980638	−	0.195830i	$-0.0627400\pi$
$644$	11.7289	+	9.26644i	0.462185	+	0.365149i
$645$		0			0
$646$	−17.3745	−	30.0936i	−0.683592	−	1.18402i
$647$			19.6226i			0.771445i	0.922615	+	0.385723i	$0.126048\pi$
$647$			19.6226i			0.771445i	−0.922615	+	0.385723i	$0.873952\pi$
$648$		0			0
$649$			0.287175i			0.0112726i
$650$	−4.19579	−	9.60499i	−0.164572	−	0.376739i
$651$		0			0
$652$	−6.95885	−	4.01770i	−0.272530	−	0.157345i
$653$	9.70880	−	16.8161i	0.379935	−	0.658066i	−0.611118	−	0.791540i	$-0.709280\pi$
$653$	9.70880	−	16.8161i	0.379935	−	0.658066i	0.991052	+	0.133474i	$0.0426131\pi$
$654$		0			0
$655$	−2.31231	−	4.57785i	−0.0903492	−	0.178871i
$656$	8.14339			0.317946
$657$		0			0
$658$	−26.9091	−	3.93065i	−1.04903	−	0.153233i
$659$	10.8291	−	6.25219i	0.421842	−	0.243551i	−0.274023	−	0.961723i	$-0.588354\pi$
$659$	10.8291	−	6.25219i	0.421842	−	0.243551i	0.695865	+	0.718172i	$0.255021\pi$
$660$		0			0
$661$	3.75358	+	2.16713i	0.145997	+	0.0842916i	0.571219	−	0.820798i	$-0.306471\pi$
$661$	3.75358	+	2.16713i	0.145997	+	0.0842916i	−0.425222	+	0.905089i	$0.639804\pi$
$662$	2.81788	−	4.88070i	0.109520	−	0.189694i
$663$		0			0
$664$	−2.24015	+	1.29335i	−0.0869347	+	0.0501918i
$665$	27.0225	+	5.50360i	1.04789	+	0.213420i
$666$		0			0
$667$		−	26.7954i		−	1.03752i
$668$	4.12075	−	2.37911i	0.159436	−	0.0920507i
$669$		0			0
$670$	−10.1675	−	6.65374i	−0.392804	−	0.257056i
$671$	−4.97174	+	8.61131i	−0.191932	+	0.332436i
$672$		0			0
$673$	−1.47592	+	0.852124i	−0.0568926	+	0.0328470i	−0.528177	−	0.849135i	$-0.677124\pi$
$673$	−1.47592	+	0.852124i	−0.0568926	+	0.0328470i	0.471284	+	0.881982i	$0.343791\pi$
$674$		−	13.6905i		−	0.527338i
$675$		0			0
$676$	−8.60558			−0.330984
$677$	−5.08519	+	2.93594i	−0.195440	+	0.112837i	−0.594527	−	0.804076i	$-0.702661\pi$
$677$	−5.08519	+	2.93594i	−0.195440	+	0.112837i	0.399087	+	0.916913i	$0.369327\pi$
$678$		0			0
$679$	19.6470	+	15.5221i	0.753983	+	0.595684i
$680$	−13.9479	−	9.12768i	−0.534876	−	0.350031i
$681$		0			0
$682$	−1.66591	−	2.88543i	−0.0637908	−	0.110489i
$683$	−10.9483			−0.418926			−0.209463	−	0.977817i	$-0.567172\pi$
$683$	−10.9483			−0.418926			−0.209463	+	0.977817i	$0.567172\pi$
$684$		0			0
$685$	24.1921	+	1.35310i	0.924332	+	0.0516994i
$686$	18.4478	−	1.63620i	0.704342	−	0.0624702i
$687$		0			0
$688$	2.25274	+	1.30062i	0.0858850	+	0.0495857i
$689$	14.5035	−	25.1209i	0.552541	−	0.957029i
$690$		0			0
$691$	−34.4759	+	19.9047i	−1.31153	+	0.757210i	−0.982349	−	0.187058i	$-0.940105\pi$
$691$	−34.4759	+	19.9047i	−1.31153	+	0.757210i	−0.329177	+	0.944268i	$0.606771\pi$
$692$			17.2576i			0.656037i
$693$		0			0
$694$	−9.79041			−0.371639
$695$	−17.5985	+	8.88913i	−0.667549	+	0.337184i
$696$		0			0
$697$	52.5729	+	30.3530i	1.99134	+	1.14970i
$698$	14.0539	+	8.11400i	0.531946	+	0.307119i
$699$		0			0
$700$	12.7607	−	3.48779i	0.482309	−	0.131826i
$701$		−	7.84396i		−	0.296262i	−0.988968	−	0.148131i	$-0.952674\pi$
$701$		−	7.84396i		−	0.296262i	0.988968	−	0.148131i	$-0.0473258\pi$
$702$		0			0
$703$	22.6912			0.855815
$704$	1.44107	−	0.832005i	0.0543125	−	0.0313574i
$705$		0			0
$706$	20.9960	+	12.1220i	0.790194	+	0.456219i
$707$	−21.9455	−	17.3381i	−0.825347	−	0.652066i
$708$		0			0
$709$	10.3461	+	17.9200i	0.388557	+	0.673001i	0.992256	−	0.124212i	$-0.0396402\pi$
$709$	10.3461	+	17.9200i	0.388557	+	0.673001i	−0.603698	+	0.797213i	$0.706307\pi$
$710$	−1.50408	+	26.8913i	−0.0564470	+	1.00921i
$711$		0			0
$712$	−11.2248			−0.420666
$713$	−9.79674	+	5.65615i	−0.366891	+	0.211825i
$714$		0			0
$715$	6.52661	+	4.27111i	0.244082	+	0.159730i
$716$	0.521897	+	0.301317i	0.0195042	+	0.0112608i
$717$		0			0
$718$	−27.1600	+	15.6809i	−1.01360	+	0.585204i
$719$	21.2881			0.793910			0.396955	−	0.917838i	$-0.370067\pi$
$719$	21.2881			0.793910			0.396955	+	0.917838i	$0.370067\pi$
$720$		0			0
$721$	5.82684	−	39.8903i	0.217003	−	1.48559i
$722$	−1.36436	−	2.36314i	−0.0507763	−	0.0879471i
$723$		0			0
$724$	−11.0659	−	6.38892i	−0.411262	−	0.237442i
$725$	−19.0866	−	14.0732i	−0.708858	−	0.522665i
$726$		0			0
$727$	4.79802	+	8.31041i	0.177949	+	0.308216i	0.941178	−	0.337912i	$-0.109721\pi$
$727$	4.79802	+	8.31041i	0.177949	+	0.308216i	−0.763229	+	0.646128i	$0.776387\pi$
$728$	−0.801642	+	5.48801i	−0.0297108	+	0.203399i
$729$		0			0
$730$	−10.7084	−	0.598941i	−0.396337	−	0.0221678i
$731$	9.69565	+	16.7934i	0.358607	+	0.621125i
$732$		0			0
$733$	−22.1972	+	38.4466i	−0.819871	+	1.42006i	0.0859066	+	0.996303i	$0.472621\pi$
$733$	−22.1972	+	38.4466i	−0.819871	+	1.42006i	−0.905777	+	0.423754i	$0.860712\pi$
$734$	−0.616195	+	1.06728i	−0.0227442	+	0.0393941i
$735$		0			0
$736$	−2.82486	−	4.89279i	−0.104126	−	0.180351i
$737$	9.04247			0.333084
$738$		0			0
$739$	−17.8223			−0.655603			−0.327801	−	0.944747i	$-0.606308\pi$
$739$	−17.8223			−0.655603			−0.327801	+	0.944747i	$0.606308\pi$
$740$	9.71584	−	4.90754i	0.357161	−	0.180405i
$741$		0			0
$742$	28.7267	+	22.6955i	1.05459	+	0.833179i
$743$	25.2903	−	43.8041i	0.927811	−	1.60702i	0.140835	−	0.990033i	$-0.455021\pi$
$743$	25.2903	−	43.8041i	0.927811	−	1.60702i	0.786976	−	0.616983i	$-0.211645\pi$
$744$		0			0
$745$	28.6203	−	14.4563i	1.04857	−	0.529638i
$746$		−	27.6157i		−	1.01108i
$747$		0			0
$748$	12.4046			0.453556
$749$	28.0663	−	11.1630i	1.02552	−	0.407886i
$750$		0			0
$751$	−22.2173	+	38.4816i	−0.810722	+	1.40421i	0.101637	+	0.994822i	$0.467592\pi$
$751$	−22.2173	+	38.4816i	−0.810722	+	1.40421i	−0.912359	+	0.409390i	$0.865741\pi$
$752$	8.90154	+	5.13931i	0.324606	+	0.187411i
$753$		0			0
$754$	8.61024	−	4.97113i	0.313567	−	0.181038i
$755$	−15.4140	−	0.862134i	−0.560975	−	0.0313763i
$756$		0			0
$757$		−	26.2968i		−	0.955774i	−0.878421	−	0.477887i	$-0.841403\pi$
$757$		−	26.2968i		−	0.955774i	0.878421	−	0.477887i	$-0.158597\pi$
$758$	11.6133	+	20.1148i	0.421812	+	0.730601i
$759$		0			0
$760$	−8.72165	−	5.70757i	−0.316368	−	0.207035i
$761$	11.6947	−	20.2558i	0.423932	−	0.734272i	−0.572388	−	0.819983i	$-0.693983\pi$
$761$	11.6947	−	20.2558i	0.423932	−	0.734272i	0.996320	+	0.0857107i	$0.0273161\pi$
$762$		0			0
$763$	−26.0955	+	10.3791i	−0.944720	+	0.375749i
$764$		−	18.8422i		−	0.681687i
$765$		0			0
$766$			23.7929i			0.859672i
$767$	0.180889	+	0.313309i	0.00653152	+	0.0113129i
$768$		0			0
$769$	−21.6845	−	12.5196i	−0.781963	−	0.451467i	0.0551625	−	0.998477i	$-0.482432\pi$
$769$	−21.6845	−	12.5196i	−0.781963	−	0.451467i	−0.837126	+	0.547011i	$0.815766\pi$
$770$	−6.52462	+	7.37168i	−0.235131	+	0.265657i
$771$		0			0
$772$	−5.89207	+	3.40179i	−0.212060	+	0.122433i
$773$			55.5416i			1.99769i	0.0480317	+	0.998846i	$0.484705\pi$
$773$			55.5416i			1.99769i	−0.0480317	+	0.998846i	$0.515295\pi$
$774$		0			0
$775$	−1.11642	+	9.94895i	−0.0401028	+	0.357377i
$776$	−4.73188	−	8.19586i	−0.169865	−	0.294214i
$777$		0			0
$778$	8.18328	+	4.72462i	0.293385	+	0.169386i
$779$	32.8740	+	18.9798i	1.17783	+	0.680023i
$780$		0			0
$781$	−10.0215	−	17.3577i	−0.358596	−	0.621107i
$782$		−	42.1165i		−	1.50608i
$783$		0			0
$784$	−6.70752	−	2.00228i	−0.239554	−	0.0715100i
$785$	−15.0982	−	29.8910i	−0.538877	−	1.06686i
$786$		0			0
$787$	7.49527	−	12.9822i	0.267177	−	0.462765i	−0.700954	−	0.713206i	$-0.747242\pi$
$787$	7.49527	−	12.9822i	0.267177	−	0.462765i	0.968132	+	0.250441i	$0.0805757\pi$
$788$	−4.29375	+	7.43699i	−0.152959	+	0.264932i
$789$		0			0
$790$	12.7206	+	25.1840i	0.452579	+	0.896005i
$791$	−5.25524	+	35.9772i	−0.186855	+	1.27920i
$792$		0			0
$793$			12.5266i			0.444833i
$794$	10.8617	+	18.8130i	0.385467	+	0.667648i
$795$		0			0
$796$	4.41729	+	2.55032i	0.156567	+	0.0903938i
$797$	43.9990	+	25.4028i	1.55852	+	0.899814i	0.997399	+	0.0720822i	$0.0229644\pi$
$797$	43.9990	+	25.4028i	1.55852	+	0.899814i	0.561124	+	0.827732i	$0.310369\pi$
$798$		0			0
$799$	38.3116	+	66.3577i	1.35537	+	2.34757i
$800$	−4.96881	−	0.557572i	−0.175674	−	0.0197132i
$801$		0			0
$802$			12.3027i			0.434423i
$803$	6.91203	−	3.99066i	0.243920	−	0.140827i
$804$		0			0
$805$	25.0286	+	22.1527i	0.882144	+	0.780779i
$806$	−3.63501	−	2.09867i	−0.128038	−	0.0739227i
$807$		0			0
$808$	5.28548	+	9.15472i	0.185942	+	0.322062i
$809$			38.3573i			1.34857i	0.738471	+	0.674285i	$0.235548\pi$
$809$			38.3573i			1.34857i	−0.738471	+	0.674285i	$0.764452\pi$
$810$		0			0
$811$			0.237330i			0.00833379i	0.999991	+	0.00416689i	$0.00132637\pi$
$811$			0.237330i			0.00833379i	−0.999991	+	0.00416689i	$0.998674\pi$
$812$	4.63754	+	11.6598i	0.162746	+	0.409180i
$813$		0			0
$814$	−4.05010	+	7.01498i	−0.141956	+	0.245875i
$815$	−15.0345	−	9.83878i	−0.526635	−	0.344638i
$816$		0			0
$817$	6.06273	+	10.5009i	0.212108	+	0.367382i
$818$		−	2.89004i		−	0.101048i
$819$		0			0
$820$	18.1807	+	1.01688i	0.634899	+	0.0355110i
$821$	−34.0959	+	19.6853i	−1.18995	+	0.687020i	−0.958296	−	0.285777i	$-0.907748\pi$
$821$	−34.0959	+	19.6853i	−1.18995	+	0.687020i	−0.231658	+	0.972797i	$0.574415\pi$
$822$		0			0
$823$	12.0228	+	6.94134i	0.419087	+	0.241960i	0.694687	−	0.719312i	$-0.255543\pi$
$823$	12.0228	+	6.94134i	0.419087	+	0.241960i	−0.275600	+	0.961273i	$0.588876\pi$
$824$	−7.61856	+	13.1957i	−0.265405	+	0.459695i
$825$		0			0
$826$	−0.424277	+	0.168750i	−0.0147625	+	0.00587157i
$827$	53.7207			1.86805			0.934027	−	0.357204i	$-0.116270\pi$
$827$	53.7207			1.86805			0.934027	+	0.357204i	$0.116270\pi$
$828$		0			0
$829$			40.2685i			1.39858i	0.714836	+	0.699292i	$0.246501\pi$
$829$			40.2685i			1.39858i	−0.714836	+	0.699292i	$0.753499\pi$
$830$	−5.16281	+	2.60778i	−0.179204	+	0.0905172i
$831$		0			0
$832$	1.04814	−	1.81544i	0.0363378	−	0.0629390i
$833$	−35.8400	−	37.9276i	−1.24178	−	1.31411i
$834$		0			0
$835$	9.49697	−	4.79699i	0.328656	−	0.166007i
$836$	7.75663			0.268268
$837$		0			0
$838$	25.4794			0.880170
$839$	12.6898	+	21.9794i	0.438100	+	0.758812i	0.997543	−	0.0700572i	$-0.0223182\pi$
$839$	12.6898	+	21.9794i	0.438100	+	0.758812i	−0.559443	+	0.828869i	$0.688985\pi$
$840$		0			0
$841$	−3.25296	+	5.63429i	−0.112171	+	0.194286i
$842$	2.96965	−	5.14359i	0.102341	−	0.177260i
$843$		0			0
$844$	5.01715	+	8.68995i	0.172697	+	0.299120i
$845$	−19.2126	−	1.07460i	−0.660935	−	0.0369672i
$846$		0			0
$847$	−3.14765	+	21.5487i	−0.108155	+	0.740422i
$848$	−6.91868	−	11.9835i	−0.237589	−	0.411516i
$849$		0			0
$850$	−29.9999	−	22.1200i	−1.02899	−	0.758709i
$851$	23.8176	+	13.7511i	0.816456	+	0.471381i
$852$		0			0
$853$	−17.2962	−	29.9580i	−0.592212	−	1.02574i	−0.993934	−	0.109979i	$-0.964921\pi$
$853$	−17.2962	−	29.9580i	−0.592212	−	1.02574i	0.401722	−	0.915762i	$-0.368412\pi$
$854$	−15.6440	−	2.28514i	−0.535326	−	0.0781959i
$855$		0			0
$856$	−11.4163			−0.390202
$857$	−16.9137	+	9.76512i	−0.577761	+	0.333570i	−0.760243	−	0.649639i	$-0.774920\pi$
$857$	−16.9137	+	9.76512i	−0.577761	+	0.333570i	0.182482	+	0.983209i	$0.441587\pi$
$858$		0			0
$859$	43.4126	+	25.0643i	1.48122	+	0.855182i	0.999773	−	0.0212940i	$-0.00677859\pi$
$859$	43.4126	+	25.0643i	1.48122	+	0.855182i	0.481446	+	0.876476i	$0.340112\pi$
$860$	4.86701	+	3.18504i	0.165964	+	0.108609i
$861$		0			0
$862$	−25.4910	+	14.7172i	−0.868225	+	0.501270i
$863$	17.7867			0.605465			0.302733	−	0.953076i	$-0.402101\pi$
$863$	17.7867			0.605465			0.302733	+	0.953076i	$0.402101\pi$
$864$		0			0
$865$	−2.15499	+	38.5290i	−0.0732720	+	1.31003i
$866$	7.12793	+	12.3459i	0.242217	+	0.419532i
$867$		0			0
$868$	3.28406	−	4.15678i	0.111468	−	0.141090i
$869$	−18.1832	−	10.4981i	−0.616823	−	0.356123i
$870$		0			0
$871$	9.86535	−	5.69576i	0.334275	−	0.192994i
$872$	10.6147			0.359458
$873$		0			0
$874$		−	26.3356i		−	0.890815i
$875$	28.9248	−	6.19331i	0.977836	−	0.209372i
$876$		0			0
$877$	18.1879	+	10.5008i	0.614163	+	0.354587i	0.774593	−	0.632460i	$-0.217955\pi$
$877$	18.1879	+	10.5008i	0.614163	+	0.354587i	−0.160430	+	0.987047i	$0.551288\pi$
$878$	−9.41191	−	5.43397i	−0.317637	−	0.183388i
$879$		0			0
$880$	3.32121	−	1.67757i	0.111958	−	0.0565507i
$881$	−57.9674			−1.95297			−0.976486	−	0.215580i	$-0.930836\pi$
$881$	−57.9674			−1.95297			−0.976486	+	0.215580i	$0.930836\pi$
$882$		0			0
$883$			42.6213i			1.43432i	0.696908	+	0.717161i	$0.254559\pi$
$883$			42.6213i			1.43432i	−0.696908	+	0.717161i	$0.745441\pi$
$884$	13.5334	−	7.81352i	0.455178	−	0.262797i
$885$		0			0
$886$	5.24859	−	9.09083i	0.176330	−	0.305412i
$887$	−3.27263	−	1.88945i	−0.109884	−	0.0634416i	0.444051	−	0.896002i	$-0.353541\pi$
$887$	−3.27263	−	1.88945i	−0.109884	−	0.0634416i	−0.553935	+	0.832560i	$0.686874\pi$
$888$		0			0
$889$	13.8799	+	34.8973i	0.465517	+	1.17042i
$890$	−25.0602	−	1.40166i	−0.840020	−	0.0469837i
$891$		0			0
$892$	17.7445			0.594131
$893$	23.9564	+	41.4937i	0.801671	+	1.38853i
$894$		0			0
$895$	1.12755	+	0.737885i	0.0376898	+	0.0246648i
$896$	2.07602	+	1.64016i	0.0693550	+	0.0547940i
$897$		0			0
$898$	32.1022	−	18.5342i	1.07126	−	0.618494i
$899$	−9.49639			−0.316722
$900$		0			0
$901$		−	103.152i		−	3.43651i
$902$	−11.7352	+	6.77533i	−0.390740	+	0.225594i
$903$		0			0
$904$	6.87120	−	11.9013i	0.228533	−	0.395830i
$905$	−23.9078	−	15.6456i	−0.794721	−	0.520077i
$906$		0			0
$907$	43.9682	−	25.3850i	1.45994	−	0.842896i	0.460932	−	0.887436i	$-0.347515\pi$
$907$	43.9682	−	25.3850i	1.45994	−	0.842896i	0.999008	+	0.0445394i	$0.0141820\pi$
$908$			0.474897i			0.0157600i
$909$		0			0
$910$	−2.47503	+	12.1523i	−0.0820464	+	0.402845i
$911$	6.59422	−	3.80717i	0.218476	−	0.126137i	−0.386768	−	0.922177i	$-0.626409\pi$
$911$	6.59422	−	3.80717i	0.218476	−	0.126137i	0.605244	+	0.796040i	$0.293075\pi$
$912$		0			0
$913$	2.15215	−	3.72763i	0.0712257	−	0.123367i
$914$	−17.5211	−	10.1158i	−0.579545	−	0.334601i
$915$		0			0
$916$	9.51279	−	5.49221i	0.314312	−	0.181468i
$917$	−0.877104	+	6.00462i	−0.0289645	+	0.198290i
$918$		0			0
$919$	−10.4157			−0.343581			−0.171791	−	0.985133i	$-0.554955\pi$
$919$	−10.4157			−0.343581			−0.171791	+	0.985133i	$0.554955\pi$
$920$	−5.69574	−	11.2763i	−0.187783	−	0.371768i
$921$		0			0
$922$	6.80701	−	11.7901i	0.224177	−	0.388286i
$923$	−21.8669	−	12.6249i	−0.719757	−	0.415552i
$924$		0			0
$925$	22.3042	−	9.74324i	0.733357	−	0.320356i
$926$			22.8848i			0.752040i
$927$		0			0
$928$		−	4.74279i		−	0.155690i
$929$	21.5567	+	37.3374i	0.707253	+	1.22500i	0.965872	+	0.259019i	$0.0833994\pi$
$929$	21.5567	+	37.3374i	0.707253	+	1.22500i	−0.258619	+	0.965980i	$0.583267\pi$
$930$		0			0
$931$	−22.4109	−	23.7162i	−0.734487	−	0.777269i
$932$	10.7397	−	18.6017i	0.351791	−	0.609320i
$933$		0			0
$934$	2.89724	−	1.67272i	0.0948006	−	0.0547332i
$935$	27.6942	+	1.54898i	0.905697	+	0.0506571i
$936$		0			0
$937$	16.2891			0.532140			0.266070	−	0.963954i	$-0.414275\pi$
$937$	16.2891			0.532140			0.266070	+	0.963954i	$0.414275\pi$
$938$	5.31355	+	13.3595i	0.173494	+	0.436203i
$939$		0			0
$940$	19.2316	+	12.5855i	0.627267	+	0.410492i
$941$	−14.8611	+	25.7402i	−0.484458	+	0.839106i	−0.999841	−	0.0178543i	$-0.994316\pi$
$941$	−14.8611	+	25.7402i	−0.484458	+	0.839106i	0.515383	+	0.856960i	$0.327650\pi$
$942$		0			0
$943$	23.0039	+	39.8439i	0.749110	+	1.29750i
$944$	0.172580			0.00561701
$945$		0			0
$946$	−4.32849			−0.140731
$947$	−12.6233	−	21.8642i	−0.410202	−	0.710490i	0.584710	−	0.811243i	$-0.301208\pi$
$947$	−12.6233	−	21.8642i	−0.410202	−	0.710490i	−0.994912	+	0.100752i	$0.967875\pi$
$948$		0			0
$949$	5.02736	−	8.70764i	0.163195	−	0.282662i
$950$	−18.7591	−	13.8317i	−0.608624	−	0.448760i
$951$		0			0
$952$	7.28919	+	18.3267i	0.236244	+	0.593972i
$953$	46.4580			1.50492			0.752461	−	0.658636i	$-0.228866\pi$
$953$	46.4580			1.50492			0.752461	+	0.658636i	$0.228866\pi$
$954$		0			0
$955$	2.35286	−	42.0667i	0.0761368	−	1.36125i
$956$	−14.6228	+	8.44250i	−0.472937	+	0.273050i
$957$		0			0
$958$	−8.15257	+	14.1207i	−0.263397	+	0.456218i
$959$	−22.4956	−	17.7727i	−0.726422	−	0.573910i
$960$		0			0
$961$	−13.4954	−	23.3748i	−0.435337	−	0.754025i
$962$			10.2045i			0.329006i
$963$		0			0
$964$			9.24813i			0.297862i
$965$	−13.5793	+	6.85900i	−0.437133	+	0.220799i
$966$		0			0
$967$	−38.7680	−	22.3827i	−1.24670	−	0.719780i	−0.276246	−	0.961087i	$-0.589091\pi$
$967$	−38.7680	−	22.3827i	−1.24670	−	0.719780i	−0.970449	+	0.241307i	$0.922424\pi$
$968$	4.11554	−	7.12832i	0.132278	−	0.229113i
$969$		0			0
$970$	−9.54087	−	18.8888i	−0.306339	−	0.606483i
$971$	−5.45198			−0.174962			−0.0874812	−	0.996166i	$-0.527882\pi$
$971$	−5.45198			−0.174962			−0.0874812	+	0.996166i	$0.527882\pi$
$972$		0			0
$973$	23.0834	+	3.37183i	0.740020	+	0.108096i
$974$	4.50548	−	2.60124i	0.144365	−	0.0833491i
$975$		0			0
$976$	5.17503	+	2.98781i	0.165649	+	0.0956374i
$977$	−9.53359	+	16.5127i	−0.305007	+	0.528287i	−0.977263	−	0.212032i	$-0.931992\pi$
$977$	−9.53359	+	16.5127i	−0.305007	+	0.528287i	0.672256	+	0.740319i	$0.265325\pi$
$978$		0			0
$979$	16.1757	−	9.33907i	0.516979	−	0.298478i
$980$	−14.7250	−	5.30783i	−0.470374	−	0.169552i
$981$		0			0
$982$			23.8599i			0.761400i
$983$	26.7964	−	15.4709i	0.854674	−	0.493446i	−0.00755133	−	0.999971i	$-0.502404\pi$
$983$	26.7964	−	15.4709i	0.854674	−	0.493446i	0.862225	+	0.506525i	$0.169070\pi$
$984$		0			0
$985$	−10.5148	+	16.0675i	−0.335030	+	0.511953i
$986$	17.6779	−	30.6190i	0.562979	−	0.975107i
$987$		0			0
$988$	8.46249	−	4.88582i	0.269228	−	0.155439i
$989$			14.6963i			0.467314i
$990$		0			0
$991$	21.5926			0.685912			0.342956	−	0.939351i	$-0.388572\pi$
$991$	21.5926			0.685912			0.342956	+	0.939351i	$0.388572\pi$
$992$	−1.73402	+	1.00114i	−0.0550553	+	0.0317862i
$993$		0			0
$994$	19.7557	−	25.0056i	0.626613	−	0.793130i
$995$	9.54348	+	6.24539i	0.302549	+	0.197992i
$996$		0			0
$997$	−26.8955	−	46.5843i	−0.851788	−	1.47534i	−0.879593	−	0.475726i	$-0.842185\pi$
$997$	−26.8955	−	46.5843i	−0.851788	−	1.47534i	0.0278059	−	0.999613i	$-0.491148\pi$
$998$	32.3319			1.02345
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bf.f.1259.4		32
3.2	odd	2		630.2.bf.e.419.16	yes	32
5.4	even	2		1890.2.bf.e.1259.7		32
7.6	odd	2	inner	1890.2.bf.f.1259.13		32
9.2	odd	6		1890.2.bf.e.629.10		32
9.7	even	3		630.2.bf.f.209.16	yes	32
15.14	odd	2		630.2.bf.f.419.1	yes	32
21.20	even	2		630.2.bf.e.419.1	yes	32
35.34	odd	2		1890.2.bf.e.1259.10		32
45.29	odd	6	inner	1890.2.bf.f.629.13		32
45.34	even	6		630.2.bf.e.209.1	✓	32
63.20	even	6		1890.2.bf.e.629.7		32
63.34	odd	6		630.2.bf.f.209.1	yes	32
105.104	even	2		630.2.bf.f.419.16	yes	32
315.34	odd	6		630.2.bf.e.209.16	yes	32
315.209	even	6	inner	1890.2.bf.f.629.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.1	✓	32	45.34	even	6
630.2.bf.e.209.16	yes	32	315.34	odd	6
630.2.bf.e.419.1	yes	32	21.20	even	2
630.2.bf.e.419.16	yes	32	3.2	odd	2
630.2.bf.f.209.1	yes	32	63.34	odd	6
630.2.bf.f.209.16	yes	32	9.7	even	3
630.2.bf.f.419.1	yes	32	15.14	odd	2
630.2.bf.f.419.16	yes	32	105.104	even	2
1890.2.bf.e.629.7		32	63.20	even	6
1890.2.bf.e.629.10		32	9.2	odd	6
1890.2.bf.e.1259.7		32	5.4	even	2
1890.2.bf.e.1259.10		32	35.34	odd	2
1890.2.bf.f.629.4		32	315.209	even	6	inner
1890.2.bf.f.629.13		32	45.29	odd	6	inner
1890.2.bf.f.1259.4		32	1.1	even	1	trivial
1890.2.bf.f.1259.13		32	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22443 + 1.87103i) q^{5} +(2.45843 - 0.977807i) q^{7} -1.00000 q^{8} +(-2.23258 - 0.124872i) q^{10} +(1.44107 - 0.832005i) q^{11} +(1.04814 - 1.81544i) q^{13} +(2.07602 + 1.64016i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.45463i q^{17} -4.66141i q^{19} +(-1.00815 - 1.99591i) q^{20} +(1.44107 + 0.832005i) q^{22} +(2.82486 - 4.89279i) q^{23} +(-2.00154 - 4.58191i) q^{25} +2.09629 q^{26} +(-0.382411 + 2.61797i) q^{28} +(4.10738 - 2.37140i) q^{29} +(-1.73402 - 1.00114i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.45590 - 3.72732i) q^{34} +(-1.18067 + 5.79707i) q^{35} +4.86789i q^{37} +(4.03690 - 2.33070i) q^{38} +(1.22443 - 1.87103i) q^{40} +(-4.07169 + 7.05238i) q^{41} +(-2.25274 + 1.30062i) q^{43} +1.66401i q^{44} +5.64971 q^{46} +(-8.90154 + 5.13931i) q^{47} +(5.08779 - 4.80775i) q^{49} +(2.96728 - 4.02433i) q^{50} +(1.04814 + 1.81544i) q^{52} +13.8374 q^{53} +(-0.207788 + 3.71503i) q^{55} +(-2.45843 + 0.977807i) q^{56} +(4.10738 + 2.37140i) q^{58} +(-0.0862901 + 0.149459i) q^{59} +(-5.17503 + 2.98781i) q^{61} -2.00228i q^{62} +1.00000 q^{64} +(2.11336 + 4.18399i) q^{65} +(4.70611 + 2.71707i) q^{67} +(6.45590 + 3.72732i) q^{68} +(-5.61075 + 1.87604i) q^{70} -12.0450i q^{71} +4.79644 q^{73} +(-4.21571 + 2.43394i) q^{74} +(4.03690 + 2.33070i) q^{76} +(2.72924 - 3.45452i) q^{77} +(-6.30891 - 10.9273i) q^{79} +(2.23258 + 0.124872i) q^{80} -8.14339 q^{82} +(2.24015 - 1.29335i) q^{83} +(13.9479 + 9.12768i) q^{85} +(-2.25274 - 1.30062i) q^{86} +(-1.44107 + 0.832005i) q^{88} +11.2248 q^{89} +(0.801642 - 5.48801i) q^{91} +(2.82486 + 4.89279i) q^{92} +(-8.90154 - 5.13931i) q^{94} +(8.72165 + 5.70757i) q^{95} +(4.73188 + 8.19586i) q^{97} +(6.70752 + 2.00228i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 24 q^{11} - 16 q^{16} + 24 q^{22} + 24 q^{23} - 58 q^{25} + 36 q^{29} + 16 q^{32} + 48 q^{35} - 54 q^{43} + 48 q^{46} + 32 q^{49} - 50 q^{50} + 24 q^{53} + 36 q^{58}+ \cdots + 64 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 24 * q^11 - 16 * q^16 + 24 * q^22 + 24 * q^23 - 58 * q^25 + 36 * q^29 + 16 * q^32 + 48 * q^35 - 54 * q^43 + 48 * q^46 + 32 * q^49 - 50 * q^50 + 24 * q^53 + 36 * q^58 + 32 * q^64 + 90 * q^65 - 66 * q^67 + 36 * q^70 - 12 * q^74 - 18 * q^77 + 34 * q^79 + 4 * q^85 - 54 * q^86 - 24 * q^88 + 16 * q^91 + 24 * q^92 - 12 * q^95 + 64 * q^98

Introduction

L-functions

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