LMFDB - Embedded newform 1890.2.bf.e.1259.7

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)

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);

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")

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			1259.7
Character	$\chi$	$=$	1890.1259
Dual form			1890.2.bf.e.629.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00815 + 1.99591i) q^{5} +(-2.45843 + 0.977807i) q^{7} +1.00000 q^{8} +(2.23258 - 0.124872i) q^{10} +(1.44107 - 0.832005i) q^{11} +(-1.04814 + 1.81544i) q^{13} +(2.07602 + 1.64016i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.45463i q^{17} -4.66141i q^{19} +(-1.22443 - 1.87103i) q^{20} +(-1.44107 - 0.832005i) q^{22} +(-2.82486 + 4.89279i) q^{23} +(-2.96728 - 4.02433i) q^{25} +2.09629 q^{26} +(0.382411 - 2.61797i) q^{28} +(4.10738 - 2.37140i) q^{29} +(-1.73402 - 1.00114i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.45590 - 3.72732i) q^{34} +(0.526851 - 5.89257i) q^{35} -4.86789i q^{37} +(-4.03690 + 2.33070i) q^{38} +(-1.00815 + 1.99591i) q^{40} +(-4.07169 + 7.05238i) q^{41} +(2.25274 - 1.30062i) q^{43} +1.66401i q^{44} +5.64971 q^{46} +(8.90154 - 5.13931i) q^{47} +(5.08779 - 4.80775i) q^{49} +(-2.00154 + 4.58191i) q^{50} +(-1.04814 - 1.81544i) q^{52} -13.8374 q^{53} +(0.207788 + 3.71503i) q^{55} +(-2.45843 + 0.977807i) q^{56} +(-4.10738 - 2.37140i) q^{58} +(-0.0862901 + 0.149459i) q^{59} +(-5.17503 + 2.98781i) q^{61} +2.00228i q^{62} +1.00000 q^{64} +(-2.56676 - 3.92222i) q^{65} +(-4.70611 - 2.71707i) q^{67} +(-6.45590 - 3.72732i) q^{68} +(-5.36654 + 2.49002i) q^{70} -12.0450i q^{71} -4.79644 q^{73} +(-4.21571 + 2.43394i) q^{74} +(4.03690 + 2.33070i) q^{76} +(-2.72924 + 3.45452i) q^{77} +(-6.30891 - 10.9273i) q^{79} +(2.23258 - 0.124872i) q^{80} +8.14339 q^{82} +(-2.24015 + 1.29335i) q^{83} +(-14.8787 - 7.51536i) q^{85} +(-2.25274 - 1.30062i) q^{86} +(1.44107 - 0.832005i) q^{88} +11.2248 q^{89} +(0.801642 - 5.48801i) q^{91} +(-2.82486 - 4.89279i) q^{92} +(-8.90154 - 5.13931i) q^{94} +(9.30373 + 4.69938i) q^{95} +(-4.73188 - 8.19586i) q^{97} +(-6.70752 - 2.00228i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 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 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * 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
$5$	−1.00815	+	1.99591i	−0.450857	+	0.892596i
$5$	−1.00815	+	1.99591i	−0.450857	+	0.892596i
$6$		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	−0.973976	−	0.226651i	$-0.927222\pi$
$13$	−1.04814	+	1.81544i	−0.290703	+	0.503512i	0.683273	+	0.730163i	$0.260556\pi$
$14$	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	$0.359388\pi$
$17$			7.45463i			1.80801i	−0.427518	+	0.904007i	$0.640612\pi$
$18$		0			0
$19$		−	4.66141i		−	1.06940i	−0.845042	−	0.534700i	$-0.820425\pi$
$19$		−	4.66141i		−	1.06940i	0.845042	−	0.534700i	$-0.179575\pi$
$20$	−1.22443	−	1.87103i	−0.273791	−	0.418376i
$21$		0			0
$22$	−1.44107	−	0.832005i	−0.307238	−	0.177384i
$23$	−2.82486	+	4.89279i	−0.589023	+	1.02022i	0.405337	+	0.914167i	$0.367154\pi$
$23$	−2.82486	+	4.89279i	−0.589023	+	1.02022i	−0.994361	+	0.106051i	$0.966179\pi$
$24$		0			0
$25$	−2.96728	−	4.02433i	−0.593456	−	0.804867i
$26$	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
$35$	0.526851	−	5.89257i	0.0890541	−	0.996027i
$36$		0			0
$37$		−	4.86789i		−	0.800276i	−0.916455	−	0.400138i	$-0.868962\pi$
$37$		−	4.86789i		−	0.800276i	0.916455	−	0.400138i	$-0.131038\pi$
$38$	−4.03690	+	2.33070i	−0.654871	+	0.378090i
$39$		0			0
$40$	−1.00815	+	1.99591i	−0.159402	+	0.315580i
$41$	−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	−0.318296	−	0.947991i	$-0.603111\pi$
$43$	2.25274	−	1.30062i	0.343540	−	0.198343i	0.661836	+	0.749648i	$0.269777\pi$
$44$			1.66401i			0.250859i
$45$		0			0
$46$	5.64971			0.833005
$47$	8.90154	−	5.13931i	1.29842	−	0.749645i	0.318292	−	0.947993i	$-0.396891\pi$
$47$	8.90154	−	5.13931i	1.29842	−	0.749645i	0.980132	+	0.198348i	$0.0635575\pi$
$48$		0			0
$49$	5.08779	−	4.80775i	0.726827	−	0.686821i
$50$	−2.00154	+	4.58191i	−0.283060	+	0.647979i
$51$		0			0
$52$	−1.04814	−	1.81544i	−0.145351	−	0.251756i
$53$	−13.8374			−1.90071			−0.950354	−	0.311170i	$-0.899279\pi$
$53$	−13.8374			−1.90071			−0.950354	+	0.311170i	$0.899279\pi$
$54$		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
$65$	−2.56676	−	3.92222i	−0.318367	−	0.486492i
$66$		0			0
$67$	−4.70611	−	2.71707i	−0.574943	−	0.331943i	0.184178	−	0.982893i	$-0.441038\pi$
$67$	−4.70611	−	2.71707i	−0.574943	−	0.331943i	−0.759121	+	0.650949i	$0.774371\pi$
$68$	−6.45590	−	3.72732i	−0.782893	−	0.452003i
$69$		0			0
$70$	−5.36654	+	2.49002i	−0.641425	+	0.297614i
$71$		−	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	$-0.590563\pi$
$73$	−4.79644			−0.561381			−0.280691	+	0.959798i	$0.590563\pi$
$74$	−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	−0.617880	−	0.786272i	$-0.712008\pi$
$83$	−2.24015	+	1.29335i	−0.245888	+	0.141964i	0.371992	+	0.928236i	$0.378675\pi$
$84$		0			0
$85$	−14.8787	−	7.51536i	−1.61383	−	0.815156i
$86$	−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
$95$	9.30373	+	4.69938i	0.954543	+	0.482147i
$96$		0			0
$97$	−4.73188	−	8.19586i	−0.480450	−	0.832164i	0.519298	−	0.854593i	$-0.326193\pi$
$97$	−4.73188	−	8.19586i	−0.480450	−	0.832164i	−0.999748	+	0.0224290i	$0.992860\pi$
$98$	−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	$0.436940\pi$
$103$	−7.61856	+	13.1957i	−0.750679	+	1.30021i	−0.947494	+	0.319773i	$0.896393\pi$
$104$	−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	$-0.686070\pi$
$107$	−11.4163			−1.10366			−0.551829	+	0.833957i	$0.686070\pi$
$108$		0			0
$109$	−10.6147			−1.01670			−0.508351	−	0.861150i	$-0.669745\pi$
$109$	−10.6147			−1.01670			−0.508351	+	0.861150i	$0.669745\pi$
$110$	3.11342	−	2.03747i	0.296853	−	0.194265i
$111$		0			0
$112$	2.07602	+	1.64016i	0.196166	+	0.154981i
$113$	6.87120	−	11.9013i	0.646388	−	1.11958i	−0.337591	−	0.941293i	$-0.609612\pi$
$113$	6.87120	−	11.9013i	0.646388	−	1.11958i	0.983979	−	0.178284i	$-0.0570546\pi$
$114$		0			0
$115$	−6.91769	−	10.5708i	−0.645078	−	0.985733i
$116$			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	$-0.783138\pi$
$127$		−	14.1949i		−	1.25960i	0.776759	−	0.629798i	$-0.216862\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.11336	+	4.18399i	−0.185354	+	0.366960i
$131$	−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	0.999103	−	0.0423355i	$-0.0134798\pi$
$137$	5.41797	+	9.38419i	0.462888	+	0.801746i	−0.536215	+	0.844081i	$0.680147\pi$
$138$		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	$0.544674\pi$
$140$	4.83969	+	3.40255i	0.409029	+	0.287568i
$141$		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
$155$	3.74633	−	2.45165i	0.300913	−	0.196922i
$156$		0			0
$157$	7.48808	−	12.9697i	0.597614	−	1.03510i	−0.395559	−	0.918441i	$-0.629449\pi$
$157$	7.48808	−	12.9697i	0.597614	−	1.03510i	0.993172	−	0.116657i	$-0.0372177\pi$
$158$	−6.30891	+	10.9273i	−0.501910	+	0.869333i
$159$		0			0
$160$	−1.22443	−	1.87103i	−0.0967998	−	0.147918i
$161$	2.16051	−	14.7908i	0.170272	−	1.16568i
$162$		0			0
$163$		−	8.03539i		−	0.629380i	−0.949194	−	0.314690i	$-0.898099\pi$
$163$		−	8.03539i		−	0.629380i	0.949194	−	0.314690i	$-0.101901\pi$
$164$	−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	0.650890	−	0.759172i	$-0.274396\pi$
$167$	4.12075	+	2.37911i	0.318873	+	0.184101i	−0.332017	+	0.943273i	$0.607729\pi$
$168$		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	−0.945509	−	0.325595i	$-0.894435\pi$
$173$	−14.9456	+	8.62882i	−1.13629	+	0.656037i	−0.190781	+	0.981633i	$0.561102\pi$
$174$		0			0
$175$	11.2299	+	6.99213i	0.848899	+	0.528555i
$176$	−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
$185$	9.71584	+	4.90754i	0.714323	+	0.360810i
$186$		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	0.272718	−	0.962094i	$-0.412077\pi$
$193$	−5.89207	−	3.40179i	−0.424120	−	0.244866i	−0.696839	+	0.717228i	$0.745411\pi$
$194$	−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	$-0.598963\pi$
$197$	−8.58750			−0.611834			−0.305917	+	0.952058i	$0.598963\pi$
$198$		0			0
$199$		−	5.10064i		−	0.361575i	−0.983522	−	0.180788i	$-0.942135\pi$
$199$		−	5.10064i		−	0.361575i	0.983522	−	0.180788i	$-0.0578646\pi$
$200$	−2.96728	−	4.02433i	−0.209818	−	0.284563i
$201$		0			0
$202$	−5.28548	+	9.15472i	−0.371885	+	0.644124i
$203$	−7.77895	+	9.84614i	−0.545975	+	0.691064i
$204$		0			0
$205$	−9.97102	−	15.2365i	−0.696406	−	1.06417i
$206$	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
$220$	−3.32121	−	1.67757i	−0.223916	−	0.113101i
$221$	−13.5334	−	7.81352i	−0.910356	−	0.525594i
$222$		0			0
$223$	8.87226	+	15.3672i	0.594131	+	1.02906i	0.993669	+	0.112348i	$0.0358372\pi$
$223$	8.87226	+	15.3672i	0.594131	+	1.02906i	−0.399538	+	0.916717i	$0.630829\pi$
$224$	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	−0.513586	−	0.858038i	$-0.671683\pi$
$227$	−0.411273	+	0.237449i	−0.0272972	+	0.0157600i	0.486289	+	0.873798i	$0.338350\pi$
$228$		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	$0.784892\pi$
$230$	−5.69574	+	11.2763i	−0.375566	+	0.743537i
$231$		0			0
$232$	4.10738	−	2.37140i	0.269663	−	0.155690i
$233$	21.4794			1.40716			0.703582	−	0.710614i	$-0.251583\pi$
$233$	21.4794			1.40716			0.703582	+	0.710614i	$0.251583\pi$
$234$		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
$245$	4.46657	+	15.0017i	0.285359	+	0.958421i
$246$		0			0
$247$	8.46249	+	4.88582i	0.538456	+	0.310877i
$248$	−1.73402	−	1.00114i	−0.110111	−	0.0635724i
$249$		0			0
$250$	−7.12721	−	8.61411i	−0.450764	−	0.544804i
$251$	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	0.314285	−	0.949329i	$-0.398235\pi$
$257$	−5.62239	−	3.24609i	−0.350715	−	0.202485i	−0.665000	+	0.746843i	$0.731569\pi$
$258$		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	0.697231	−	0.716846i	$-0.254415\pi$
$263$	−4.41420	−	7.64563i	−0.272192	−	0.471450i	−0.969423	+	0.245397i	$0.921082\pi$
$264$		0			0
$265$	13.9501	−	27.6181i	0.856948	−	1.69657i
$266$	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
$275$	−7.62433	−	3.33057i	−0.459765	−	0.200841i
$276$		0			0
$277$	1.93149	−	1.11514i	0.116052	−	0.0670026i	−0.440850	−	0.897581i	$-0.645323\pi$
$277$	1.93149	−	1.11514i	0.116052	−	0.0670026i	0.556902	+	0.830578i	$0.311990\pi$
$278$		−	8.81729i		−	0.528826i
$279$		0			0
$280$	0.526851	−	5.89257i	0.0314854	−	0.352149i
$281$	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	−0.945971	−	0.324250i	$-0.894888\pi$
$283$	−3.23291	+	5.59957i	−0.192177	+	0.332860i	0.753795	+	0.657110i	$0.228221\pi$
$284$	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
$290$	8.87393	−	5.80722i	0.521095	−	0.341012i
$291$		0			0
$292$	2.39822	−	4.15384i	0.140345	−	0.243085i
$293$	−16.0415	−	9.26155i	−0.937153	−	0.541066i	−0.0480865	−	0.998843i	$-0.515312\pi$
$293$	−16.0415	−	9.26155i	−0.937153	−	0.541066i	−0.889067	+	0.457777i	$0.848646\pi$
$294$		0			0
$295$	−0.211313	−	0.322903i	−0.0123031	−	0.0188002i
$296$		−	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	$-0.468690\pi$
$307$	3.44142			0.196412			0.0982062	+	0.995166i	$0.468690\pi$
$308$	−1.62708	−	4.09086i	−0.0927115	−	0.233098i
$309$		0			0
$310$	−3.99636	−	2.01859i	−0.226978	−	0.114648i
$311$	−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	0.837398	−	0.546593i	$-0.184076\pi$
$313$	−0.967111	−	1.67509i	−0.0546644	−	0.0946815i	−0.892063	+	0.451912i	$0.850742\pi$
$314$	−14.9762			−0.845153
$315$		0			0
$316$	12.6178			0.709807
$317$	5.12038	+	8.86877i	0.287589	+	0.498120i	0.973234	−	0.229817i	$-0.0738128\pi$
$317$	5.12038	+	8.86877i	0.287589	+	0.498120i	−0.685644	+	0.727937i	$0.740479\pi$
$318$		0			0
$319$	3.94603	−	6.83472i	0.220935	−	0.382671i
$320$	−1.00815	+	1.99591i	−0.0563571	+	0.111575i
$321$		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
$335$	10.1675	−	6.65374i	0.555508	−	0.363533i
$336$		0			0
$337$	11.8563	+	6.84524i	0.645854	+	0.372884i	0.786866	−	0.617124i	$-0.211702\pi$
$337$	11.8563	+	6.84524i	0.645854	+	0.372884i	−0.141012	+	0.990008i	$0.545036\pi$
$338$	4.30279	−	7.45265i	0.234041	−	0.405371i
$339$		0			0
$340$	13.9479	−	9.12768i	0.756429	−	0.495018i
$341$	−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	−0.704193	−	0.710008i	$-0.748691\pi$
$347$	4.89520	−	8.47874i	0.262788	−	0.455163i	0.966982	+	0.254845i	$0.0820246\pi$
$348$		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	$0.190318\pi$
$350$	0.440421	−	13.2214i	0.0235415	−	0.706715i
$351$		0			0
$352$			1.66401i			0.0886920i
$353$	−20.9960	+	12.1220i	−1.11750	+	0.645191i	−0.940762	−	0.339066i	$-0.889889\pi$
$353$	−20.9960	+	12.1220i	−1.11750	+	0.645191i	−0.176741	+	0.984257i	$0.556556\pi$
$354$		0			0
$355$	24.0406	+	12.1431i	1.27594	+	0.644489i
$356$	−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
$365$	4.83552	−	9.57325i	0.253103	−	0.501087i
$366$		0			0
$367$	−0.616195	−	1.06728i	−0.0321651	−	0.0557116i	0.849495	−	0.527597i	$-0.176907\pi$
$367$	−0.616195	−	1.06728i	−0.0321651	−	0.0557116i	−0.881660	+	0.471885i	$0.843574\pi$
$368$	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	0.968751	−	0.248037i	$-0.0797855\pi$
$373$	23.9159	+	13.8079i	1.23832	+	0.714944i	0.269569	+	0.962981i	$0.413119\pi$
$374$	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	$0.296545\pi$
$380$	−8.72165	+	5.70757i	−0.447411	+	0.292792i
$381$		0			0
$382$	16.3178	+	9.42111i	0.834893	+	0.482026i
$383$	−20.6052	−	11.8964i	−1.05288	−	0.607880i	−0.129425	−	0.991589i	$-0.541313\pi$
$383$	−20.6052	−	11.8964i	−1.05288	−	0.607880i	−0.923454	+	0.383709i	$0.874646\pi$
$384$		0			0
$385$	−4.14342	−	8.92998i	−0.211168	−	0.455114i
$386$			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	$-0.683521\pi$
$397$	−21.7234			−1.09026			−0.545132	+	0.838350i	$0.683521\pi$
$398$	−4.41729	+	2.55032i	−0.221419	+	0.127836i
$399$		0			0
$400$	−2.00154	+	4.58191i	−0.100077	+	0.229095i
$401$	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	$0.689430\pi$
$410$	−8.20973	+	16.2534i	−0.405450	+	0.802700i
$411$		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
$425$	29.9999	−	22.1200i	1.45521	−	1.07298i
$426$		0			0
$427$	9.80098	−	12.4055i	0.474303	−	0.600345i
$428$	5.70816	−	9.88683i	0.275914	−	0.477898i
$429$		0			0
$430$	4.86701	−	3.18504i	0.234708	−	0.153596i
$431$			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	$-0.611289\pi$
$433$	−14.2559			−0.685093			−0.342546	+	0.939501i	$0.611289\pi$
$434$	−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	0.963351	−	0.268245i	$-0.0864438\pi$
$443$	5.24859	+	9.09083i	0.249368	+	0.431918i	−0.713983	+	0.700164i	$0.753110\pi$
$444$		0			0
$445$	−11.3162	+	22.4036i	−0.536441	+	1.06203i
$446$	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
$455$	10.1454	+	7.13273i	0.475623	+	0.334387i
$456$		0			0
$457$	17.5211	−	10.1158i	0.819601	−	0.473197i	−0.0306780	−	0.999529i	$-0.509767\pi$
$457$	17.5211	−	10.1158i	0.819601	−	0.473197i	0.850279	+	0.526333i	$0.176433\pi$
$458$			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	−0.0370852	−	0.999312i	$-0.511807\pi$
$463$	−19.8188	−	11.4424i	−0.921057	−	0.531773i	−0.883972	+	0.467539i	$0.845141\pi$
$464$	−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	$0.0246633\pi$
$467$			3.34545i			0.154809i	−0.997000	+	0.0774044i	$0.975337\pi$
$468$		0			0
$469$	14.2264	+	2.07808i	0.656916	+	0.0959567i
$470$	19.2316	−	12.5855i	0.887089	−	0.580524i
$471$		0			0
$472$	−0.0862901	+	0.149459i	−0.00397182	+	0.00687940i
$473$	2.16425	−	3.74858i	0.0995121	−	0.172360i
$474$		0			0
$475$	−18.7591	+	13.8317i	−0.860725	+	0.634642i
$476$	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	$0.0376077\pi$
$487$			5.20248i			0.235747i	−0.993029	+	0.117873i	$0.962392\pi$
$488$	−5.17503	+	2.98781i	−0.234263	+	0.135252i
$489$		0			0
$490$	10.7585	−	11.3690i	0.486021	−	0.513599i
$491$	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	$-0.0908877\pi$
$500$	−3.89643	+	10.4794i	−0.174254	+	0.468653i
$501$		0			0
$502$	−4.68498	−	8.11462i	−0.209101	−	0.362173i
$503$			10.0768i			0.449301i	0.974439	+	0.224651i	$0.0721241\pi$
$503$			10.0768i			0.449301i	−0.974439	+	0.224651i	$0.927876\pi$
$504$		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
$515$	−18.6568	−	28.5092i	−0.822117	−	1.25626i
$516$		0			0
$517$	8.55186	−	14.8122i	0.376110	−	0.651442i
$518$	7.98412	−	10.1058i	0.350802	−	0.444025i
$519$		0			0
$520$	−2.56676	−	3.92222i	−0.112560	−	0.172001i
$521$	−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	$-0.549651\pi$
$523$	−7.10550			−0.310702			−0.155351	+	0.987859i	$0.549651\pi$
$524$	−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
$535$	11.5093	−	22.7859i	0.497592	−	0.985121i
$536$	−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
$545$	10.7012	−	21.1859i	0.458387	−	0.907504i
$546$		0			0
$547$	14.6902	−	8.48140i	0.628108	−	0.362638i	−0.151911	−	0.988394i	$-0.548543\pi$
$547$	14.6902	−	8.48140i	0.628108	−	0.362638i	0.780019	+	0.625756i	$0.215209\pi$
$548$	−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	$-0.482225\pi$
$557$	2.63451			0.111628			0.0558139	+	0.998441i	$0.482225\pi$
$558$		0			0
$559$			5.45295i			0.230635i
$560$	−5.36654	+	2.49002i	−0.226778	+	0.105223i
$561$		0			0
$562$	−2.79869	−	1.61582i	−0.118055	−	0.0681594i
$563$	−20.7641	−	11.9882i	−0.875104	−	0.505242i	−0.00606320	−	0.999982i	$-0.501930\pi$
$563$	−20.7641	−	11.9882i	−0.875104	−	0.505242i	−0.869041	+	0.494740i	$0.835263\pi$
$564$		0			0
$565$	16.8266	+	25.7125i	0.707902	+	1.08173i
$566$	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	$-0.738937\pi$
$577$	−32.7696			−1.36422			−0.682108	+	0.731251i	$0.738937\pi$
$578$	19.2858	+	33.4039i	0.802182	+	1.38942i
$579$		0			0
$580$	−9.46617	−	4.78143i	−0.393061	−	0.198538i
$581$	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	−0.0490959	−	0.998794i	$-0.515634\pi$
$587$	19.1726	−	11.0693i	0.791337	−	0.456879i	0.840433	+	0.541915i	$0.182301\pi$
$588$		0			0
$589$	−4.66672	+	8.08300i	−0.192289	+	0.333054i
$590$	−0.173986	+	0.344454i	−0.00716290	+	0.0141809i
$591$		0			0
$592$	−4.21571	+	2.43394i	−0.173265	+	0.100034i
$593$			26.0392i			1.06930i	0.845073	+	0.534650i	$0.179557\pi$
$593$			26.0392i			1.06930i	−0.845073	+	0.534650i	$0.820443\pi$
$594$		0			0
$595$	43.9270	+	3.92748i	1.80083	+	0.161011i
$596$	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
$605$	−10.0784	−	15.4006i	−0.409745	−	0.626124i
$606$		0			0
$607$	6.62507	−	11.4750i	0.268903	−	0.465754i	−0.699676	−	0.714461i	$-0.746672\pi$
$607$	6.62507	−	11.4750i	0.268903	−	0.465754i	0.968579	+	0.248707i	$0.0800055\pi$
$608$	4.03690	+	2.33070i	0.163718	+	0.0945225i
$609$		0			0
$610$	−11.1806	+	7.31673i	−0.452688	+	0.296246i
$611$			21.5469i			0.871695i
$612$		0			0
$613$			17.3252i			0.699759i	0.936795	+	0.349880i	$0.113778\pi$
$613$			17.3252i			0.699759i	−0.936795	+	0.349880i	$0.886222\pi$
$614$	−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	−0.593608	−	0.804754i	$-0.702297\pi$
$617$	9.93911	−	17.2150i	0.400133	−	0.693052i	0.993742	+	0.111703i	$0.0356304\pi$
$618$		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
$625$	−7.39051	+	23.8826i	−0.295620	+	0.955305i
$626$	−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
$635$	28.3317	+	14.3106i	1.12431	+	0.567898i
$636$		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	$0.396073\pi$
$643$	−16.7337	+	28.9836i	−0.659912	+	1.14300i	−0.980638	+	0.195830i	$0.937260\pi$
$644$	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	$-0.873952\pi$
$647$		−	19.6226i		−	0.771445i	0.922615	−	0.385723i	$-0.126048\pi$
$648$		0			0
$649$			0.287175i			0.0112726i
$650$	−6.22027	−	8.43615i	−0.243979	−	0.330893i
$651$		0			0
$652$	6.95885	+	4.01770i	0.272530	+	0.157345i
$653$	−9.70880	+	16.8161i	−0.379935	+	0.658066i	−0.991052	−	0.133474i	$-0.957387\pi$
$653$	−9.70880	+	16.8161i	−0.379935	+	0.658066i	0.611118	+	0.791540i	$0.290720\pi$
$654$		0			0
$655$	−2.80838	−	4.29144i	−0.109732	−	0.167680i
$656$	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
$665$	−27.4677	−	2.45587i	−1.06515	−	0.0952345i
$666$		0			0
$667$			26.7954i			1.03752i
$668$	−4.12075	+	2.37911i	−0.159436	+	0.0920507i
$669$		0			0
$670$	−10.8460	−	5.47842i	−0.419019	−	0.211650i
$671$	−4.97174	+	8.61131i	−0.191932	+	0.332436i
$672$		0			0
$673$	1.47592	−	0.852124i	0.0568926	−	0.0328470i	−0.471284	−	0.881982i	$-0.656209\pi$
$673$	1.47592	−	0.852124i	0.0568926	−	0.0328470i	0.528177	+	0.849135i	$0.322876\pi$
$674$		−	13.6905i		−	0.527338i
$675$		0			0
$676$	−8.60558			−0.330984
$677$	5.08519	−	2.93594i	0.195440	−	0.112837i	−0.399087	−	0.916913i	$-0.630673\pi$
$677$	5.08519	−	2.93594i	0.195440	−	0.112837i	0.594527	+	0.804076i	$0.297339\pi$
$678$		0			0
$679$	19.6470	+	15.5221i	0.753983	+	0.595684i
$680$	−14.8787	−	7.51536i	−0.570574	−	0.288201i
$681$		0			0
$682$	1.66591	+	2.88543i	0.0637908	+	0.110489i
$683$	10.9483			0.418926			0.209463	−	0.977817i	$-0.432828\pi$
$683$	10.9483			0.418926			0.209463	+	0.977817i	$0.432828\pi$
$684$		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
$695$	−16.4975	+	10.7962i	−0.625784	+	0.409522i
$696$		0			0
$697$	−52.5729	−	30.3530i	−1.99134	−	1.14970i
$698$	−14.0539	−	8.11400i	−0.531946	−	0.307119i
$699$		0			0
$700$	−11.6703	+	6.22930i	−0.441096	+	0.235445i
$701$		−	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
$715$	−6.96220	−	3.51666i	−0.260371	−	0.131516i
$716$	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
$725$	−21.7310	−	9.49287i	−0.807070	−	0.352556i
$726$		0			0
$727$	−4.79802	−	8.31041i	−0.177949	−	0.308216i	0.763229	−	0.646128i	$-0.223613\pi$
$727$	−4.79802	−	8.31041i	−0.177949	−	0.308216i	−0.941178	+	0.337912i	$0.890279\pi$
$728$	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	$-0.527379\pi$
$733$	22.1972	−	38.4466i	0.819871	−	1.42006i	0.905777	−	0.423754i	$-0.139288\pi$
$734$	−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	$0.606308\pi$
$740$	−9.10798	+	5.96039i	−0.334816	+	0.219108i
$741$		0			0
$742$	−28.7267	−	22.6955i	−1.05459	−	0.833179i
$743$	−25.2903	+	43.8041i	−0.927811	+	1.60702i	−0.140835	+	0.990033i	$0.544979\pi$
$743$	−25.2903	+	43.8041i	−0.927811	+	1.60702i	−0.786976	+	0.616983i	$0.788355\pi$
$744$		0			0
$745$	26.8297	−	17.5577i	0.982963	−	0.643265i
$746$		−	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	$0.158597\pi$
$757$			26.2968i			0.955774i	−0.878421	+	0.477887i	$0.841403\pi$
$758$	−11.6133	−	20.1148i	−0.421812	−	0.730601i
$759$		0			0
$760$	9.30373	+	4.69938i	0.337482	+	0.170465i
$761$	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	$0.815766\pi$
$770$	−5.66188	+	8.05329i	−0.204040	+	0.290221i
$771$		0			0
$772$	5.89207	−	3.40179i	0.212060	−	0.122433i
$773$		−	55.5416i		−	1.99769i	−0.0480317	−	0.998846i	$-0.515295\pi$
$773$		−	55.5416i		−	1.99769i	0.0480317	−	0.998846i	$-0.484705\pi$
$774$		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
$785$	18.3373	+	28.0209i	0.654485	+	1.00011i
$786$		0			0
$787$	−7.49527	+	12.9822i	−0.267177	+	0.462765i	−0.968132	−	0.250441i	$-0.919424\pi$
$787$	−7.49527	+	12.9822i	−0.267177	+	0.462765i	0.700954	+	0.713206i	$0.252758\pi$
$788$	4.29375	−	7.43699i	0.152959	−	0.264932i
$789$		0			0
$790$	−15.4496	−	23.6084i	−0.549674	−	0.839947i
$791$	−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	$-0.977036\pi$
$797$	−43.9990	−	25.4028i	−1.55852	−	0.899814i	−0.561124	−	0.827732i	$-0.689631\pi$
$798$		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
$805$	27.3429	+	19.2235i	0.963710	+	0.677538i
$806$	−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
$815$	16.0379	+	8.10086i	0.561782	+	0.283761i
$816$		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	0.275600	−	0.961273i	$-0.411124\pi$
$823$	−12.0228	−	6.94134i	−0.419087	−	0.241960i	−0.694687	+	0.719312i	$0.744457\pi$
$824$	−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	$-0.883730\pi$
$827$	−53.7207			−1.86805			−0.934027	+	0.357204i	$0.883730\pi$
$828$		0			0
$829$			40.2685i			1.39858i	0.714836	+	0.699292i	$0.246501\pi$
$829$			40.2685i			1.39858i	−0.714836	+	0.699292i	$0.753499\pi$
$830$	−4.83981	+	3.16724i	−0.167992	+	0.109936i
$831$		0			0
$832$	−1.04814	+	1.81544i	−0.0363378	+	0.0629390i
$833$	35.8400	+	37.9276i	1.24178	+	1.31411i
$834$		0			0
$835$	−8.90281	+	5.82612i	−0.308094	+	0.201621i
$836$	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
$850$	−34.1564	−	14.9207i	−1.17156	−	0.511776i
$851$	23.8176	+	13.7511i	0.816456	+	0.471381i
$852$		0			0
$853$	17.2962	+	29.9580i	0.592212	+	1.02574i	0.993934	+	0.109979i	$0.0350785\pi$
$853$	17.2962	+	29.9580i	0.592212	+	1.02574i	−0.401722	+	0.915762i	$0.631588\pi$
$854$	−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	−0.182482	−	0.983209i	$-0.558413\pi$
$857$	16.9137	−	9.76512i	0.577761	−	0.333570i	0.760243	+	0.649639i	$0.225080\pi$
$858$		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	$0.340112\pi$
$860$	−5.19183	−	2.62243i	−0.177040	−	0.0894243i
$861$		0			0
$862$	25.4910	−	14.7172i	0.868225	−	0.501270i
$863$	−17.7867			−0.605465			−0.302733	−	0.953076i	$-0.597899\pi$
$863$	−17.7867			−0.605465			−0.302733	+	0.953076i	$0.597899\pi$
$864$		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
$875$	−25.2770	+	15.3647i	−0.854518	+	0.519421i
$876$		0			0
$877$	−18.1879	−	10.5008i	−0.614163	−	0.354587i	0.160430	−	0.987047i	$-0.448712\pi$
$877$	−18.1879	−	10.5008i	−0.614163	−	0.354587i	−0.774593	+	0.632460i	$0.782045\pi$
$878$	9.41191	+	5.43397i	0.317637	+	0.183388i
$879$		0			0
$880$	3.11342	−	2.03747i	0.104953	−	0.0686829i
$881$	−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	$-0.745441\pi$
$883$		−	42.6213i		−	1.43432i	0.696908	−	0.717161i	$-0.254559\pi$
$884$	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	0.553935	−	0.832560i	$-0.313126\pi$
$887$	3.27263	+	1.88945i	0.109884	+	0.0634416i	−0.444051	+	0.896002i	$0.646459\pi$
$888$		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
$895$	1.20280	+	0.607544i	0.0402052	+	0.0203080i
$896$	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
$905$	−25.5034	−	12.8819i	−0.847760	−	0.428210i
$906$		0			0
$907$	−43.9682	+	25.3850i	−1.45994	+	0.842896i	−0.999008	−	0.0445394i	$-0.985818\pi$
$907$	−43.9682	+	25.3850i	−1.45994	+	0.842896i	−0.460932	+	0.887436i	$0.652485\pi$
$908$		−	0.474897i		−	0.0157600i
$909$		0			0
$910$	1.10443	−	12.3525i	0.0366115	−	0.409482i
$911$	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	$0.554955\pi$
$920$	−6.91769	−	10.5708i	−0.228069	−	0.348509i
$921$		0			0
$922$	−6.80701	+	11.7901i	−0.224177	+	0.388286i
$923$	21.8669	+	12.6249i	0.719757	+	0.415552i
$924$		0			0
$925$	−19.5900	+	14.4444i	−0.644115	+	0.474928i
$926$			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	$-0.585725\pi$
$937$	−16.2891			−0.532140			−0.266070	+	0.963954i	$0.585725\pi$
$938$	−5.31355	−	13.3595i	−0.173494	−	0.436203i
$939$		0			0
$940$	−20.5151	−	10.3624i	−0.669130	−	0.337983i
$941$	−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	0.994912	−	0.100752i	$-0.0321249\pi$
$947$	12.6233	+	21.8642i	0.410202	+	0.710490i	−0.584710	+	0.811243i	$0.698792\pi$
$948$		0			0
$949$	5.02736	−	8.70764i	0.163195	−	0.282662i
$950$	21.3581	+	9.32997i	0.692949	+	0.302704i
$951$		0			0
$952$	−7.28919	−	18.3267i	−0.236244	−	0.593972i
$953$	−46.4580			−1.50492			−0.752461	−	0.658636i	$-0.771134\pi$
$953$	−46.4580			−1.50492			−0.752461	+	0.658636i	$0.771134\pi$
$954$		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
$965$	12.7297	−	8.33051i	0.409784	−	0.268169i
$966$		0			0
$967$	38.7680	+	22.3827i	1.24670	+	0.719780i	0.970449	−	0.241307i	$-0.0775761\pi$
$967$	38.7680	+	22.3827i	1.24670	+	0.719780i	0.276246	+	0.961087i	$0.410909\pi$
$968$	−4.11554	+	7.12832i	−0.132278	+	0.229113i
$969$		0			0
$970$	−11.5877	−	17.7070i	−0.372060	−	0.568539i
$971$	−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	−0.672256	−	0.740319i	$-0.734675\pi$
$977$	9.53359	−	16.5127i	0.305007	−	0.528287i	0.977263	+	0.212032i	$0.0680080\pi$
$978$		0			0
$979$	16.1757	−	9.33907i	0.516979	−	0.298478i
$980$	−15.2251	−	3.63266i	−0.486348	−	0.116041i
$981$		0			0
$982$		−	23.8599i		−	0.761400i
$983$	−26.7964	+	15.4709i	−0.854674	+	0.493446i	−0.862225	−	0.506525i	$-0.830930\pi$
$983$	−26.7964	+	15.4709i	−0.854674	+	0.493446i	0.00755133	+	0.999971i	$0.497596\pi$
$984$		0			0
$985$	8.65746	−	17.1398i	0.275850	−	0.546121i
$986$	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
$995$	10.1804	+	5.14220i	0.322741	+	0.163019i
$996$		0			0
$997$	26.8955	+	46.5843i	0.851788	+	1.47534i	0.879593	+	0.475726i	$0.157815\pi$
$997$	26.8955	+	46.5843i	0.851788	+	1.47534i	−0.0278059	+	0.999613i	$0.508852\pi$
$998$	−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.e.1259.7		32
3.2	odd	2		630.2.bf.f.419.1	yes	32
5.4	even	2		1890.2.bf.f.1259.4		32
7.6	odd	2	inner	1890.2.bf.e.1259.10		32
9.2	odd	6		1890.2.bf.f.629.13		32
9.7	even	3		630.2.bf.e.209.1	✓	32
15.14	odd	2		630.2.bf.e.419.16	yes	32
21.20	even	2		630.2.bf.f.419.16	yes	32
35.34	odd	2		1890.2.bf.f.1259.13		32
45.29	odd	6	inner	1890.2.bf.e.629.10		32
45.34	even	6		630.2.bf.f.209.16	yes	32
63.20	even	6		1890.2.bf.f.629.4		32
63.34	odd	6		630.2.bf.e.209.16	yes	32
105.104	even	2		630.2.bf.e.419.1	yes	32
315.34	odd	6		630.2.bf.f.209.1	yes	32
315.209	even	6	inner	1890.2.bf.e.629.7		32

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

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00815 + 1.99591i) q^{5} +(-2.45843 + 0.977807i) q^{7} +1.00000 q^{8} +(2.23258 - 0.124872i) q^{10} +(1.44107 - 0.832005i) q^{11} +(-1.04814 + 1.81544i) q^{13} +(2.07602 + 1.64016i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.45463i q^{17} -4.66141i q^{19} +(-1.22443 - 1.87103i) q^{20} +(-1.44107 - 0.832005i) q^{22} +(-2.82486 + 4.89279i) q^{23} +(-2.96728 - 4.02433i) q^{25} +2.09629 q^{26} +(0.382411 - 2.61797i) q^{28} +(4.10738 - 2.37140i) q^{29} +(-1.73402 - 1.00114i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.45590 - 3.72732i) q^{34} +(0.526851 - 5.89257i) q^{35} -4.86789i q^{37} +(-4.03690 + 2.33070i) q^{38} +(-1.00815 + 1.99591i) q^{40} +(-4.07169 + 7.05238i) q^{41} +(2.25274 - 1.30062i) q^{43} +1.66401i q^{44} +5.64971 q^{46} +(8.90154 - 5.13931i) q^{47} +(5.08779 - 4.80775i) q^{49} +(-2.00154 + 4.58191i) q^{50} +(-1.04814 - 1.81544i) q^{52} -13.8374 q^{53} +(0.207788 + 3.71503i) q^{55} +(-2.45843 + 0.977807i) q^{56} +(-4.10738 - 2.37140i) q^{58} +(-0.0862901 + 0.149459i) q^{59} +(-5.17503 + 2.98781i) q^{61} +2.00228i q^{62} +1.00000 q^{64} +(-2.56676 - 3.92222i) q^{65} +(-4.70611 - 2.71707i) q^{67} +(-6.45590 - 3.72732i) q^{68} +(-5.36654 + 2.49002i) q^{70} -12.0450i q^{71} -4.79644 q^{73} +(-4.21571 + 2.43394i) q^{74} +(4.03690 + 2.33070i) q^{76} +(-2.72924 + 3.45452i) q^{77} +(-6.30891 - 10.9273i) q^{79} +(2.23258 - 0.124872i) q^{80} +8.14339 q^{82} +(-2.24015 + 1.29335i) q^{83} +(-14.8787 - 7.51536i) q^{85} +(-2.25274 - 1.30062i) q^{86} +(1.44107 - 0.832005i) q^{88} +11.2248 q^{89} +(0.801642 - 5.48801i) q^{91} +(-2.82486 - 4.89279i) q^{92} +(-8.90154 - 5.13931i) q^{94} +(9.30373 + 4.69938i) q^{95} +(-4.73188 - 8.19586i) q^{97} +(-6.70752 - 2.00228i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58}+ \cdots - 64 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

Introduction

L-functions

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