LMFDB - Embedded newform 504.2.p.g.307.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(307,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-2,0,2,0,0,0,10,0,0,8,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.20457921756784916168704.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 - 4x^12 - 4x^10 + 16x^8 - 16x^6 - 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.9
Root			$-1.40199 + 0.185533i$ of defining polynomial
Character	$\chi$	$=$	504.307
Dual form			504.2.p.g.307.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.185533 - 1.40199i) q^{2} +(-1.93115 - 0.520231i) q^{4} -3.84444 q^{5} +(1.62140 + 2.09071i) q^{7} +(-1.08765 + 2.61094i) q^{8} +(-0.713272 + 5.38987i) q^{10} +4.54637 q^{11} -1.81625 q^{13} +(3.23198 - 1.88529i) q^{14} +(3.45872 + 2.00929i) q^{16} +3.49124i q^{17} +1.68700i q^{19} +(7.42422 + 2.00000i) q^{20} +(0.843502 - 6.37397i) q^{22} +5.00632i q^{23} +9.77975 q^{25} +(-0.336975 + 2.54637i) q^{26} +(-2.04352 - 4.88099i) q^{28} -1.81625i q^{29} +5.34329 q^{31} +(3.45872 - 4.47630i) q^{32} +(4.89469 + 0.647741i) q^{34} +(-6.23338 - 8.03761i) q^{35} +1.42654i q^{37} +(2.36516 + 0.312995i) q^{38} +(4.18142 - 10.0376i) q^{40} +8.97551i q^{41} -8.03761 q^{43} +(-8.77975 - 2.36516i) q^{44} +(7.01881 + 0.928837i) q^{46} -4.83580 q^{47} +(-1.74213 + 6.77975i) q^{49} +(1.81447 - 13.7111i) q^{50} +(3.50747 + 0.944872i) q^{52} +5.87263i q^{53} -17.4783 q^{55} +(-7.22224 + 1.95941i) q^{56} +(-2.54637 - 0.336975i) q^{58} +8.46675i q^{59} +3.01955 q^{61} +(0.991357 - 7.49124i) q^{62} +(-5.63402 - 5.67959i) q^{64} +6.98249 q^{65} -4.42914 q^{67} +(1.81625 - 6.74213i) q^{68} +(-12.4252 + 7.24789i) q^{70} +1.47928i q^{71} -6.98249i q^{73} +(2.00000 + 0.264671i) q^{74} +(0.877633 - 3.25787i) q^{76} +(7.37148 + 9.50514i) q^{77} +2.97813i q^{79} +(-13.2968 - 7.72462i) q^{80} +(12.5836 + 1.66525i) q^{82} -10.5770i q^{83} -13.4219i q^{85} +(-1.49124 + 11.2687i) q^{86} +(-4.94487 + 11.8703i) q^{88} -15.9580i q^{89} +(-2.94487 - 3.79726i) q^{91} +(2.60444 - 9.66797i) q^{92} +(-0.897201 + 6.77975i) q^{94} -6.48559i q^{95} +11.6085i q^{97} +(9.18192 + 3.70032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64}+ \cdots - 66 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.185533	−	1.40199i	0.131192	−	0.991357i
$2$	0.185533	−	1.40199i	0.131192	−	0.991357i
$3$		0			0
$3$		0			0
$4$	−1.93115	−	0.520231i	−0.965577	−	0.260116i
$5$	−3.84444			−1.71929			−0.859644	−	0.510894i	$-0.829314\pi$
$5$	−3.84444			−1.71929			−0.859644	+	0.510894i	$0.829314\pi$
$6$		0			0
$7$	1.62140	+	2.09071i	0.612831	+	0.790214i
$7$	1.62140	+	2.09071i	0.612831	+	0.790214i
$8$	−1.08765	+	2.61094i	−0.384543	+	0.923107i
$9$		0			0
$10$	−0.713272	+	5.38987i	−0.225556	+	1.70443i
$11$	4.54637			1.37078			0.685391	−	0.728175i	$-0.259631\pi$
$11$	4.54637			1.37078			0.685391	+	0.728175i	$0.259631\pi$
$12$		0			0
$13$	−1.81625			−0.503738			−0.251869	−	0.967761i	$-0.581045\pi$
$13$	−1.81625			−0.503738			−0.251869	+	0.967761i	$0.581045\pi$
$14$	3.23198	−	1.88529i	0.863782	−	0.503865i
$15$		0			0
$16$	3.45872	+	2.00929i	0.864680	+	0.502324i
$17$			3.49124i			0.846751i	0.905954	+	0.423375i	$0.139155\pi$
$17$			3.49124i			0.846751i	−0.905954	+	0.423375i	$0.860845\pi$
$18$		0			0
$19$			1.68700i			0.387025i	0.981098	+	0.193513i	$0.0619881\pi$
$19$			1.68700i			0.387025i	−0.981098	+	0.193513i	$0.938012\pi$
$20$	7.42422	+	2.00000i	1.66011	+	0.447214i
$21$		0			0
$22$	0.843502	−	6.37397i	0.179835	−	1.35893i
$23$			5.00632i			1.04389i	0.852979	+	0.521945i	$0.174793\pi$
$23$			5.00632i			1.04389i	−0.852979	+	0.521945i	$0.825207\pi$
$24$		0			0
$25$	9.77975			1.95595
$26$	−0.336975	+	2.54637i	−0.0660863	+	0.499384i
$27$		0			0
$28$	−2.04352	−	4.88099i	−0.386189	−	0.922420i
$29$		−	1.81625i		−	0.337270i	−0.985679	−	0.168635i	$-0.946064\pi$
$29$		−	1.81625i		−	0.337270i	0.985679	−	0.168635i	$-0.0539359\pi$
$30$		0			0
$31$	5.34329			0.959683			0.479842	−	0.877355i	$-0.340694\pi$
$31$	5.34329			0.959683			0.479842	+	0.877355i	$0.340694\pi$
$32$	3.45872	−	4.47630i	0.611421	−	0.791306i
$33$		0			0
$34$	4.89469	+	0.647741i	0.839433	+	0.111087i
$35$	−6.23338	−	8.03761i	−1.05363	−	1.35860i
$36$		0			0
$37$			1.42654i			0.234522i	0.993101	+	0.117261i	$0.0374114\pi$
$37$			1.42654i			0.234522i	−0.993101	+	0.117261i	$0.962589\pi$
$38$	2.36516	+	0.312995i	0.383680	+	0.0507745i
$39$		0			0
$40$	4.18142	−	10.0376i	0.661140	−	1.58709i
$41$			8.97551i			1.40174i	0.713290	+	0.700869i	$0.247204\pi$
$41$			8.97551i			1.40174i	−0.713290	+	0.700869i	$0.752796\pi$
$42$		0			0
$43$	−8.03761			−1.22572			−0.612862	−	0.790190i	$-0.709982\pi$
$43$	−8.03761			−1.22572			−0.612862	+	0.790190i	$0.709982\pi$
$44$	−8.77975	−	2.36516i	−1.32360	−	0.356562i
$45$		0			0
$46$	7.01881	+	0.928837i	1.03487	+	0.136950i
$47$	−4.83580			−0.705374			−0.352687	−	0.935741i	$-0.614732\pi$
$47$	−4.83580			−0.705374			−0.352687	+	0.935741i	$0.614732\pi$
$48$		0			0
$49$	−1.74213	+	6.77975i	−0.248876	+	0.968535i
$50$	1.81447	−	13.7111i	0.256604	−	1.93904i
$51$		0			0
$52$	3.50747	+	0.944872i	0.486398	+	0.131030i
$53$			5.87263i			0.806668i	0.915053	+	0.403334i	$0.132149\pi$
$53$			5.87263i			0.806668i	−0.915053	+	0.403334i	$0.867851\pi$
$54$		0			0
$55$	−17.4783			−2.35677
$56$	−7.22224	+	1.95941i	−0.965112	+	0.261837i
$57$		0			0
$58$	−2.54637	−	0.336975i	−0.334355	−	0.0442470i
$59$			8.46675i			1.10228i	0.834414	+	0.551139i	$0.185806\pi$
$59$			8.46675i			1.10228i	−0.834414	+	0.551139i	$0.814194\pi$
$60$		0			0
$61$	3.01955			0.386613			0.193307	−	0.981138i	$-0.438079\pi$
$61$	3.01955			0.386613			0.193307	+	0.981138i	$0.438079\pi$
$62$	0.991357	−	7.49124i	0.125903	−	0.951389i
$63$		0			0
$64$	−5.63402	−	5.67959i	−0.704253	−	0.709949i
$65$	6.98249			0.866071
$66$		0			0
$67$	−4.42914			−0.541105			−0.270553	−	0.962705i	$-0.587206\pi$
$67$	−4.42914			−0.541105			−0.270553	+	0.962705i	$0.587206\pi$
$68$	1.81625	−	6.74213i	0.220253	−	0.817604i
$69$		0			0
$70$	−12.4252	+	7.24789i	−1.48509	+	0.866289i
$71$			1.47928i			0.175558i	0.996140	+	0.0877791i	$0.0279769\pi$
$71$			1.47928i			0.175558i	−0.996140	+	0.0877791i	$0.972023\pi$
$72$		0			0
$73$		−	6.98249i		−	0.817238i	−0.912705	−	0.408619i	$-0.866010\pi$
$73$		−	6.98249i		−	0.817238i	0.912705	−	0.408619i	$-0.133990\pi$
$74$	2.00000	+	0.264671i	0.232495	+	0.0307674i
$75$		0			0
$76$	0.877633	−	3.25787i	0.100671	−	0.373703i
$77$	7.37148	+	9.50514i	0.840058	+	1.08321i
$78$		0			0
$79$			2.97813i			0.335065i	0.985867	+	0.167533i	$0.0535800\pi$
$79$			2.97813i			0.335065i	−0.985867	+	0.167533i	$0.946420\pi$
$80$	−13.2968	−	7.72462i	−1.48663	−	0.863639i
$81$		0			0
$82$	12.5836	+	1.66525i	1.38962	+	0.183897i
$83$		−	10.5770i		−	1.16098i	−0.814268	−	0.580489i	$-0.802862\pi$
$83$		−	10.5770i		−	1.16098i	0.814268	−	0.580489i	$-0.197138\pi$
$84$		0			0
$85$		−	13.4219i		−	1.45581i
$86$	−1.49124	+	11.2687i	−0.160805	+	1.21513i
$87$		0			0
$88$	−4.94487	+	11.8703i	−0.527125	+	1.26538i
$89$		−	15.9580i		−	1.69154i	−0.533544	−	0.845772i	$-0.679140\pi$
$89$		−	15.9580i		−	1.69154i	0.533544	−	0.845772i	$-0.320860\pi$
$90$		0			0
$91$	−2.94487	−	3.79726i	−0.308707	−	0.398061i
$92$	2.60444	−	9.66797i	0.271532	−	1.00796i
$93$		0			0
$94$	−0.897201	+	6.77975i	−0.0925392	+	0.699278i
$95$		−	6.48559i		−	0.665408i
$96$		0			0
$97$			11.6085i			1.17866i	0.807892	+	0.589331i	$0.200609\pi$
$97$			11.6085i			1.17866i	−0.807892	+	0.589331i	$0.799391\pi$
$98$	9.18192	+	3.70032i	0.927514	+	0.373789i
$99$		0			0
$100$	−18.8862	−	5.08773i	−1.88862	−	0.508773i
$101$	11.5333			1.14761			0.573805	−	0.818992i	$-0.305467\pi$
$101$	11.5333			1.14761			0.573805	+	0.818992i	$0.305467\pi$
$102$		0			0
$103$	1.14230			0.112555			0.0562773	−	0.998415i	$-0.482077\pi$
$103$	1.14230			0.112555			0.0562773	+	0.998415i	$0.482077\pi$
$104$	1.97545	−	4.74213i	0.193709	−	0.465004i
$105$		0			0
$106$	8.23338	+	1.08957i	0.799696	+	0.105828i
$107$	−0.0796192			−0.00769707			−0.00384854	−	0.999993i	$-0.501225\pi$
$107$	−0.0796192			−0.00769707			−0.00384854	+	0.999993i	$0.501225\pi$
$108$		0			0
$109$			20.1081i			1.92601i	0.269489	+	0.963004i	$0.413145\pi$
$109$			20.1081i			1.92601i	−0.269489	+	0.963004i	$0.586855\pi$
$110$	−3.24280	+	24.5044i	−0.309189	+	2.33640i
$111$		0			0
$112$	1.40711	+	10.4890i	0.132959	+	0.991121i
$113$	−4.98249			−0.468713			−0.234356	−	0.972151i	$-0.575298\pi$
$113$	−4.98249			−0.468713			−0.234356	+	0.972151i	$0.575298\pi$
$114$		0			0
$115$		−	19.2465i		−	1.79475i
$116$	−0.944872	+	3.50747i	−0.0877292	+	0.325660i
$117$		0			0
$118$	11.8703	+	1.57086i	1.09275	+	0.144610i
$119$	−7.29918	+	5.66070i	−0.669114	+	0.518915i
$120$		0			0
$121$	9.66949			0.879045
$122$	0.560226	−	4.23338i	0.0507205	−	0.383272i
$123$		0			0
$124$	−10.3187	−	2.77975i	−0.926649	−	0.249629i
$125$	−18.3755			−1.64355
$126$		0			0
$127$		−	5.38471i		−	0.477816i	−0.971042	−	0.238908i	$-0.923211\pi$
$127$		−	5.38471i		−	0.477816i	0.971042	−	0.238908i	$-0.0767894\pi$
$128$	−9.00803	+	6.84510i	−0.796205	+	0.605027i
$129$		0			0
$130$	1.29548	−	9.78938i	0.113621	−	0.858586i
$131$			13.0927i			1.14392i	0.820282	+	0.571959i	$0.193816\pi$
$131$			13.0927i			1.14392i	−0.820282	+	0.571959i	$0.806184\pi$
$132$		0			0
$133$	−3.52704	+	2.73531i	−0.305833	+	0.237181i
$134$	−0.821752	+	6.20961i	−0.0709885	+	0.536428i
$135$		0			0
$136$	−9.11543	−	3.79726i	−0.781642	−	0.325612i
$137$	19.5595			1.67108			0.835540	−	0.549429i	$-0.185155\pi$
$137$	19.5595			1.67108			0.835540	+	0.549429i	$0.185155\pi$
$138$		0			0
$139$		−	14.5910i		−	1.23759i	−0.785553	−	0.618795i	$-0.787621\pi$
$139$		−	14.5910i		−	1.23759i	0.785553	−	0.618795i	$-0.212379\pi$
$140$	7.85620	+	18.7647i	0.663970	+	1.58590i
$141$		0			0
$142$	2.07394	+	0.274455i	0.174041	+	0.0230318i
$143$	−8.25737			−0.690516
$144$		0			0
$145$			6.98249i			0.579864i
$146$	−9.78938	−	1.29548i	−0.810175	−	0.107215i
$147$		0			0
$148$	0.742132	−	2.75488i	0.0610029	−	0.226449i
$149$		−	18.3973i		−	1.50717i	−0.657352	−	0.753584i	$-0.728324\pi$
$149$		−	18.3973i		−	1.50717i	0.657352	−	0.753584i	$-0.271676\pi$
$150$		0			0
$151$		−	9.88759i		−	0.804641i	−0.915499	−	0.402320i	$-0.868204\pi$
$151$		−	9.88759i		−	0.804641i	0.915499	−	0.402320i	$-0.131796\pi$
$152$	−4.40467	−	1.83488i	−0.357266	−	0.148828i
$153$		0			0
$154$	14.6938	−	8.57123i	1.18406	−	0.690689i
$155$	−20.5420			−1.64997
$156$		0			0
$157$	−12.3582			−0.986294			−0.493147	−	0.869946i	$-0.664154\pi$
$157$	−12.3582			−0.986294			−0.493147	+	0.869946i	$0.664154\pi$
$158$	4.17531	+	0.552541i	0.332169	+	0.0439578i
$159$		0			0
$160$	−13.2968	+	17.2089i	−1.05121	+	1.36048i
$161$	−10.4668	+	8.11723i	−0.824896	+	0.639728i
$162$		0			0
$163$	−3.57086			−0.279692			−0.139846	−	0.990173i	$-0.544661\pi$
$163$	−3.57086			−0.279692			−0.139846	+	0.990173i	$0.544661\pi$
$164$	4.66934	−	17.3331i	0.364614	−	1.35349i
$165$		0			0
$166$	−14.8289	−	1.96239i	−1.15094	−	0.152311i
$167$	19.5788			1.51505			0.757525	−	0.652806i	$-0.226408\pi$
$167$	19.5788			1.51505			0.757525	+	0.652806i	$0.226408\pi$
$168$		0			0
$169$	−9.70122			−0.746248
$170$	−18.8174	−	2.49020i	−1.44323	−	0.190990i
$171$		0			0
$172$	15.5219	+	4.18142i	1.18353	+	0.318830i
$173$	−5.49424			−0.417719			−0.208860	−	0.977946i	$-0.566975\pi$
$173$	−5.49424			−0.417719			−0.208860	+	0.977946i	$0.566975\pi$
$174$		0			0
$175$	15.8569	+	20.4466i	1.19867	+	1.54562i
$176$	15.7246	+	9.13500i	1.18529	+	0.688576i
$177$		0			0
$178$	−22.3730	−	2.96074i	−1.67692	−	0.221917i
$179$	−10.0306			−0.749725			−0.374862	−	0.927080i	$-0.622310\pi$
$179$	−10.0306			−0.749725			−0.374862	+	0.927080i	$0.622310\pi$
$180$		0			0
$181$	24.2481			1.80235			0.901174	−	0.433458i	$-0.142707\pi$
$181$	24.2481			1.80235			0.901174	+	0.433458i	$0.142707\pi$
$182$	−5.87009	+	3.42417i	−0.435120	+	0.253816i
$183$		0			0
$184$	−13.0712	−	5.44513i	−0.963621	−	0.401420i
$185$		−	5.48426i		−	0.403211i
$186$		0			0
$187$			15.8725i			1.16071i
$188$	9.33868	+	2.51574i	0.681093	+	0.183479i
$189$		0			0
$190$	−9.09274	−	1.20329i	−0.659657	−	0.0872960i
$191$		−	8.49422i		−	0.614620i	−0.951609	−	0.307310i	$-0.900571\pi$
$191$		−	8.49422i		−	0.614620i	0.951609	−	0.307310i	$-0.0994288\pi$
$192$		0			0
$193$	−11.2955			−0.813067			−0.406533	−	0.913636i	$-0.633262\pi$
$193$	−11.2955			−0.813067			−0.406533	+	0.913636i	$0.633262\pi$
$194$	16.2750	+	2.15376i	1.16848	+	0.154631i
$195$		0			0
$196$	6.89136	−	12.1864i	0.492240	−	0.870459i
$197$		−	2.38473i		−	0.169905i	−0.996385	−	0.0849526i	$-0.972926\pi$
$197$		−	2.38473i		−	0.169905i	0.996385	−	0.0849526i	$-0.0270739\pi$
$198$		0			0
$199$	2.46338			0.174624			0.0873120	−	0.996181i	$-0.472172\pi$
$199$	2.46338			0.174624			0.0873120	+	0.996181i	$0.472172\pi$
$200$	−10.6370	+	25.5343i	−0.752147	+	1.80555i
$201$		0			0
$202$	2.13981	−	16.1696i	0.150557	−	1.13769i
$203$	3.79726	−	2.94487i	0.266515	−	0.206690i
$204$		0			0
$205$		−	34.5058i		−	2.40999i
$206$	0.211935	−	1.60150i	0.0147662	−	0.111582i
$207$		0			0
$208$	−6.28191	−	3.64939i	−0.435572	−	0.253040i
$209$			7.66975i			0.530528i
$210$		0			0
$211$	−0.0376150			−0.00258952			−0.00129476	−	0.999999i	$-0.500412\pi$
$211$	−0.0376150			−0.00258952			−0.00129476	+	0.999999i	$0.500412\pi$
$212$	3.05513	−	11.3410i	0.209827	−	0.778901i
$213$		0			0
$214$	−0.0147720	+	0.111625i	−0.00100979	+	0.00763055i
$215$	30.9002			2.10737
$216$		0			0
$217$	8.66361	+	11.1713i	0.588124	+	0.758355i
$218$	28.1914	+	3.73072i	1.90936	+	0.252676i
$219$		0			0
$220$	33.7532	+	9.09274i	2.27564	+	0.613033i
$221$		−	6.34099i		−	0.426541i
$222$		0			0
$223$	12.9144			0.864812			0.432406	−	0.901679i	$-0.357665\pi$
$223$	12.9144			0.864812			0.432406	+	0.901679i	$0.357665\pi$
$224$	14.9666	−	0.0266914i	0.999998	−	0.00178340i
$225$		0			0
$226$	−0.924416	+	6.98540i	−0.0614913	+	0.464662i
$227$			1.48426i			0.0985141i	0.998786	+	0.0492571i	$0.0156854\pi$
$227$			1.48426i			0.0985141i	−0.998786	+	0.0492571i	$0.984315\pi$
$228$		0			0
$229$	4.66934			0.308559			0.154279	−	0.988027i	$-0.450694\pi$
$229$	4.66934			0.308559			0.154279	+	0.988027i	$0.450694\pi$
$230$	−26.9834	−	3.57086i	−1.77923	−	0.235456i
$231$		0			0
$232$	4.74213	+	1.97545i	0.311336	+	0.129695i
$233$	8.35650			0.547452			0.273726	−	0.961808i	$-0.411744\pi$
$233$	8.35650			0.547452			0.273726	+	0.961808i	$0.411744\pi$
$234$		0			0
$235$	18.5910			1.21274
$236$	4.40467	−	16.3506i	0.286720	−	1.06433i
$237$		0			0
$238$	6.58201	+	11.2836i	0.426648	+	0.731409i
$239$		−	19.8547i		−	1.28430i	−0.766580	−	0.642148i	$-0.778043\pi$
$239$		−	19.8547i		−	1.28430i	0.766580	−	0.642148i	$-0.221957\pi$
$240$		0			0
$241$			6.57701i			0.423662i	0.977306	+	0.211831i	$0.0679427\pi$
$241$			6.57701i			0.423662i	−0.977306	+	0.211831i	$0.932057\pi$
$242$	1.79401	−	13.5565i	0.115323	−	0.871447i
$243$		0			0
$244$	−5.83121	−	1.57086i	−0.373305	−	0.100564i
$245$	6.69753	−	26.0644i	0.427889	−	1.66519i
$246$		0			0
$247$		−	3.06403i		−	0.194960i
$248$	−5.81164	+	13.9510i	−0.369040	+	0.885890i
$249$		0			0
$250$	−3.40926	+	25.7622i	−0.215620	+	1.62935i
$251$		−	4.85827i		−	0.306652i	−0.988176	−	0.153326i	$-0.951002\pi$
$251$		−	4.85827i		−	0.306652i	0.988176	−	0.153326i	$-0.0489984\pi$
$252$		0			0
$253$			22.7606i			1.43094i
$254$	−7.54931	−	0.999042i	−0.473686	−	0.0626855i
$255$		0			0
$256$	7.92547	+	13.8992i	0.495342	+	0.868698i
$257$		−	9.20998i		−	0.574503i	−0.957855	−	0.287251i	$-0.907259\pi$
$257$		−	9.20998i		−	0.574503i	0.957855	−	0.287251i	$-0.0927415\pi$
$258$		0			0
$259$	−2.98249	+	2.31300i	−0.185323	+	0.143723i
$260$	−13.4843	−	3.63251i	−0.836259	−	0.225279i
$261$		0			0
$262$	18.3559	+	2.42914i	1.13403	+	0.150073i
$263$			3.90849i			0.241008i	0.992713	+	0.120504i	$0.0384511\pi$
$263$			3.90849i			0.241008i	−0.992713	+	0.120504i	$0.961549\pi$
$264$		0			0
$265$		−	22.5770i		−	1.38689i
$266$	3.18049	+	5.45236i	0.195009	+	0.334306i
$267$		0			0
$268$	8.55335	+	2.30418i	0.522479	+	0.140750i
$269$	9.24872			0.563905			0.281952	−	0.959428i	$-0.409018\pi$
$269$	9.24872			0.563905			0.281952	+	0.959428i	$0.409018\pi$
$270$		0			0
$271$	−16.5201			−1.00352			−0.501762	−	0.865006i	$-0.667315\pi$
$271$	−16.5201			−1.00352			−0.501762	+	0.865006i	$0.667315\pi$
$272$	−7.01494	+	12.0752i	−0.425343	+	0.732168i
$273$		0			0
$274$	3.62893	−	27.4222i	0.219232	−	1.65664i
$275$	44.4624			2.68118
$276$		0			0
$277$		−	3.26465i		−	0.196154i	−0.995179	−	0.0980769i	$-0.968731\pi$
$277$		−	3.26465i		−	0.196154i	0.995179	−	0.0980769i	$-0.0312691\pi$
$278$	−20.4564	−	2.70711i	−1.22689	−	0.162361i
$279$		0			0
$280$	27.7655	−	7.53284i	1.65931	−	0.450174i
$281$	−19.1680			−1.14347			−0.571733	−	0.820440i	$-0.693729\pi$
$281$	−19.1680			−1.14347			−0.571733	+	0.820440i	$0.693729\pi$
$282$		0			0
$283$			20.2780i			1.20540i	0.797968	+	0.602700i	$0.205908\pi$
$283$			20.2780i			1.20540i	−0.797968	+	0.602700i	$0.794092\pi$
$284$	0.769567	−	2.85672i	0.0456654	−	0.169515i
$285$		0			0
$286$	−1.53201	+	11.5767i	−0.0905899	+	0.684548i
$287$	−18.7652	+	14.5529i	−1.10767	+	0.859029i
$288$		0			0
$289$	4.81122			0.283013
$290$	9.78938	+	1.29548i	0.574852	+	0.0760734i
$291$		0			0
$292$	−3.63251	+	13.4843i	−0.212576	+	0.789107i
$293$	5.07037			0.296214			0.148107	−	0.988971i	$-0.452682\pi$
$293$	5.07037			0.296214			0.148107	+	0.988971i	$0.452682\pi$
$294$		0			0
$295$		−	32.5500i		−	1.89513i
$296$	−3.72462	−	1.55158i	−0.216489	−	0.0901839i
$297$		0			0
$298$	−25.7929	−	3.41331i	−1.49414	−	0.197728i
$299$		−	9.09274i		−	0.525847i
$300$		0			0
$301$	−13.0322	−	16.8043i	−0.751162	−	0.968585i
$302$	−13.8623	−	1.83448i	−0.797686	−	0.105562i
$303$		0			0
$304$	−3.38969	+	5.83488i	−0.194412	+	0.334653i
$305$	−11.6085			−0.664700
$306$		0			0
$307$			15.2465i			0.870164i	0.900391	+	0.435082i	$0.143281\pi$
$307$			15.2465i			0.870164i	−0.900391	+	0.435082i	$0.856719\pi$
$308$	−9.29060	−	22.1908i	−0.529381	−	1.26444i
$309$		0			0
$310$	−3.81122	+	28.7997i	−0.216463	+	1.63571i
$311$	−8.91481			−0.505513			−0.252756	−	0.967530i	$-0.581337\pi$
$311$	−8.91481			−0.505513			−0.252756	+	0.967530i	$0.581337\pi$
$312$		0			0
$313$		−	24.9335i		−	1.40932i	−0.709543	−	0.704662i	$-0.751098\pi$
$313$		−	24.9335i		−	1.40932i	0.709543	−	0.704662i	$-0.248902\pi$
$314$	−2.29286	+	17.3261i	−0.129394	+	0.977769i
$315$		0			0
$316$	1.54931	−	5.75122i	0.0871558	−	0.323532i
$317$			16.1127i			0.904980i	0.891769	+	0.452490i	$0.149464\pi$
$317$			16.1127i			0.904980i	−0.891769	+	0.452490i	$0.850536\pi$
$318$		0			0
$319$		−	8.25737i		−	0.462324i
$320$	21.6597	+	21.8349i	1.21081	+	1.22061i
$321$		0			0
$322$	9.43836	+	16.1803i	0.525979	+	0.901693i
$323$	−5.88974			−0.327714
$324$		0			0
$325$	−17.7625			−0.985287
$326$	−0.662513	+	5.00632i	−0.0366932	+	0.277274i
$327$		0			0
$328$	−23.4345	−	9.76223i	−1.29395	−	0.539029i
$329$	−7.84076	−	10.1103i	−0.432275	−	0.557396i
$330$		0			0
$331$	22.3802			1.23012			0.615062	−	0.788479i	$-0.289131\pi$
$331$	22.3802			1.23012			0.615062	+	0.788479i	$0.289131\pi$
$332$	−5.50249	+	20.4258i	−0.301988	+	1.12101i
$333$		0			0
$334$	3.63251	−	27.4492i	0.198762	−	1.50196i
$335$	17.0276			0.930315
$336$		0			0
$337$	2.22051			0.120959			0.0604795	−	0.998169i	$-0.480737\pi$
$337$	2.22051			0.120959			0.0604795	+	0.998169i	$0.480737\pi$
$338$	−1.79990	+	13.6010i	−0.0979015	+	0.739798i
$339$		0			0
$340$	−6.98249	+	25.9197i	−0.378679	+	1.40570i
$341$	24.2926			1.31552
$342$		0			0
$343$	−16.9992	+	7.35038i	−0.917869	+	0.396883i
$344$	8.74213	−	20.9857i	0.471344	−	1.13148i
$345$		0			0
$346$	−1.01936	+	7.70287i	−0.0548013	+	0.414109i
$347$	17.4186			0.935080			0.467540	−	0.883972i	$-0.345140\pi$
$347$	17.4186			0.935080			0.467540	+	0.883972i	$0.345140\pi$
$348$		0			0
$349$	29.0839			1.55683			0.778413	−	0.627753i	$-0.216025\pi$
$349$	29.0839			1.55683			0.778413	+	0.627753i	$0.216025\pi$
$350$	31.6079	−	18.4377i	1.68951	−	0.985534i
$351$		0			0
$352$	15.7246	−	20.3509i	0.838125	−	1.08471i
$353$			7.02449i			0.373876i	0.982372	+	0.186938i	$0.0598563\pi$
$353$			7.02449i			0.373876i	−0.982372	+	0.186938i	$0.940144\pi$
$354$		0			0
$355$		−	5.68700i		−	0.301835i
$356$	−8.30185	+	30.8174i	−0.439997	+	1.63332i
$357$		0			0
$358$	−1.86102	+	14.0629i	−0.0983577	+	0.743245i
$359$		−	11.1509i		−	0.588521i	−0.955725	−	0.294260i	$-0.904927\pi$
$359$		−	11.1509i		−	0.588521i	0.955725	−	0.294260i	$-0.0950733\pi$
$360$		0			0
$361$	16.1540			0.850211
$362$	4.49883	−	33.9956i	0.236453	−	1.78677i
$363$		0			0
$364$	3.71155	+	8.86511i	0.194538	+	0.464658i
$365$			26.8438i			1.40507i
$366$		0			0
$367$	6.42880			0.335581			0.167790	−	0.985823i	$-0.446337\pi$
$367$	6.42880			0.335581			0.167790	+	0.985823i	$0.446337\pi$
$368$	−10.0592	+	17.3154i	−0.524370	+	0.902630i
$369$		0			0
$370$	−7.68889	−	1.01751i	−0.399726	−	0.0528980i
$371$	−12.2780	+	9.52188i	−0.637440	+	0.494351i
$372$		0			0
$373$			1.75527i			0.0908842i	0.998967	+	0.0454421i	$0.0144697\pi$
$373$			1.75527i			0.0908842i	−0.998967	+	0.0454421i	$0.985530\pi$
$374$	22.2531	+	2.94487i	1.15068	+	0.152276i
$375$		0			0
$376$	5.25967	−	12.6260i	0.271247	−	0.651136i
$377$			3.29878i			0.169896i
$378$		0			0
$379$	−19.0061			−0.976280			−0.488140	−	0.872765i	$-0.662324\pi$
$379$	−19.0061			−0.976280			−0.488140	+	0.872765i	$0.662324\pi$
$380$	−3.37401	+	12.5247i	−0.173083	+	0.642503i
$381$		0			0
$382$	−11.9088	−	1.57596i	−0.609308	−	0.0806330i
$383$	−28.4936			−1.45595			−0.727977	−	0.685602i	$-0.759539\pi$
$383$	−28.4936			−1.45595			−0.727977	+	0.685602i	$0.759539\pi$
$384$		0			0
$385$	−28.3392	−	36.5420i	−1.44430	−	1.86235i
$386$	−2.09569	+	15.8362i	−0.106668	+	0.806039i
$387$		0			0
$388$	6.03909	−	22.4178i	0.306589	−	1.13809i
$389$			29.3858i			1.48992i	0.667110	+	0.744960i	$0.267531\pi$
$389$			29.3858i			1.48992i	−0.667110	+	0.744960i	$0.732469\pi$
$390$		0			0
$391$	−17.4783			−0.883914
$392$	−15.8067	−	11.9226i	−0.798358	−	0.602183i
$393$		0			0
$394$	−3.34337	−	0.442447i	−0.168437	−	0.0222902i
$395$		−	11.4492i		−	0.576074i
$396$		0			0
$397$	−15.5442			−0.780143			−0.390071	−	0.920785i	$-0.627550\pi$
$397$	−15.5442			−0.780143			−0.390071	+	0.920785i	$0.627550\pi$
$398$	0.457038	−	3.45363i	0.0229092	−	0.173115i
$399$		0			0
$400$	33.8254	+	19.6504i	1.69127	+	0.982520i
$401$	15.5595			0.777004			0.388502	−	0.921448i	$-0.372993\pi$
$401$	15.5595			0.777004			0.388502	+	0.921448i	$0.372993\pi$
$402$		0			0
$403$	−9.70478			−0.483429
$404$	−22.2726	−	6.00000i	−1.10811	−	0.298511i
$405$		0			0
$406$	−3.42417	−	5.87009i	−0.169938	−	0.291328i
$407$			6.48559i			0.321479i
$408$		0			0
$409$			18.3565i			0.907670i	0.891086	+	0.453835i	$0.149945\pi$
$409$			18.3565i			0.907670i	−0.891086	+	0.453835i	$0.850055\pi$
$410$	−48.3769	−	6.40198i	−2.38916	−	0.316171i
$411$		0			0
$412$	−2.20597	−	0.594262i	−0.108680	−	0.0292772i
$413$	−17.7015	+	13.7280i	−0.871035	+	0.675510i
$414$		0			0
$415$			40.6627i			1.99605i
$416$	−6.28191	+	8.13010i	−0.307996	+	0.398611i
$417$		0			0
$418$	10.7529	+	1.42299i	0.525942	+	0.0696008i
$419$			21.1680i			1.03412i	0.855948	+	0.517062i	$0.172974\pi$
$419$			21.1680i			1.03412i	−0.855948	+	0.517062i	$0.827026\pi$
$420$		0			0
$421$			2.20597i			0.107512i	0.998554	+	0.0537561i	$0.0171193\pi$
$421$			2.20597i			0.107512i	−0.998554	+	0.0537561i	$0.982881\pi$
$422$	−0.00697882	+	0.0527358i	−0.000339724	+	0.00256714i
$423$		0			0
$424$	−15.3331	−	6.38738i	−0.744641	−	0.310199i
$425$			34.1435i			1.65620i
$426$		0			0
$427$	4.89589	+	6.31300i	0.236929	+	0.305507i
$428$	0.153757	+	0.0414204i	0.00743212	+	0.00200213i
$429$		0			0
$430$	5.73300	−	43.3217i	0.276470	−	2.08916i
$431$		−	17.4255i		−	0.839358i	−0.907673	−	0.419679i	$-0.862143\pi$
$431$		−	17.4255i		−	0.839358i	0.907673	−	0.419679i	$-0.137857\pi$
$432$		0			0
$433$		−	2.18549i		−	0.105028i	−0.998620	−	0.0525139i	$-0.983277\pi$
$433$		−	2.18549i		−	0.105028i	0.998620	−	0.0525139i	$-0.0167234\pi$
$434$	17.2694	−	10.0737i	0.828958	−	0.483551i
$435$		0			0
$436$	10.4609	−	38.8319i	0.500985	−	1.85971i
$437$	−8.44568			−0.404012
$438$		0			0
$439$	27.5128			1.31311			0.656556	−	0.754277i	$-0.272013\pi$
$439$	27.5128			1.31311			0.656556	+	0.754277i	$0.272013\pi$
$440$	19.0103	−	45.6347i	0.906280	−	2.17555i
$441$		0			0
$442$	−8.89000	−	1.17646i	−0.422854	−	0.0559586i
$443$	−3.37840			−0.160513			−0.0802563	−	0.996774i	$-0.525574\pi$
$443$	−3.37840			−0.160513			−0.0802563	+	0.996774i	$0.525574\pi$
$444$		0			0
$445$			61.3496i			2.90825i
$446$	2.39605	−	18.1059i	0.113456	−	0.857338i
$447$		0			0
$448$	2.73938	−	20.9880i	0.129424	−	0.991589i
$449$	−1.76553			−0.0833206			−0.0416603	−	0.999132i	$-0.513265\pi$
$449$	−1.76553			−0.0833206			−0.0416603	+	0.999132i	$0.513265\pi$
$450$		0			0
$451$			40.8060i			1.92148i
$452$	9.62195	+	2.59205i	0.452579	+	0.121920i
$453$		0			0
$454$	2.08093	+	0.275380i	0.0976627	+	0.0129242i
$455$	11.3214	+	14.5984i	0.530755	+	0.684381i
$456$		0			0
$457$	−24.4178			−1.14222			−0.571108	−	0.820875i	$-0.693486\pi$
$457$	−24.4178			−1.14222			−0.571108	+	0.820875i	$0.693486\pi$
$458$	0.866317	−	6.54637i	0.0404803	−	0.305892i
$459$		0			0
$460$	−10.0126	+	37.1680i	−0.466841	+	1.73297i
$461$	−7.77884			−0.362297			−0.181148	−	0.983456i	$-0.557981\pi$
$461$	−7.77884			−0.362297			−0.181148	+	0.983456i	$0.557981\pi$
$462$		0			0
$463$			16.5615i			0.769678i	0.922984	+	0.384839i	$0.125743\pi$
$463$			16.5615i			0.769678i	−0.922984	+	0.384839i	$0.874257\pi$
$464$	3.64939	−	6.28191i	0.169419	−	0.291630i
$465$		0			0
$466$	1.55041	−	11.7157i	0.0718212	−	0.542721i
$467$		−	14.1103i		−	0.652945i	−0.945207	−	0.326472i	$-0.894140\pi$
$467$		−	14.1103i		−	0.652945i	0.945207	−	0.326472i	$-0.105860\pi$
$468$		0			0
$469$	−7.18140	−	9.26004i	−0.331606	−	0.427589i
$470$	3.44924	−	26.0644i	0.159102	−	1.20226i
$471$		0			0
$472$	−22.1062	−	9.20888i	−1.01752	−	0.423873i
$473$	−36.5420			−1.68020
$474$		0			0
$475$			16.4985i			0.757002i
$476$	17.0407	−	7.13442i	0.781060	−	0.327006i
$477$		0			0
$478$	−27.8362	−	3.68371i	−1.27320	−	0.168489i
$479$	−8.74757			−0.399687			−0.199843	−	0.979828i	$-0.564043\pi$
$479$	−8.74757			−0.399687			−0.199843	+	0.979828i	$0.564043\pi$
$480$		0			0
$481$		−	2.59097i		−	0.118138i
$482$	9.22090	+	1.22025i	0.420001	+	0.0555810i
$483$		0			0
$484$	−18.6733	−	5.03037i	−0.848786	−	0.228653i
$485$		−	44.6281i		−	2.02646i
$486$		0			0
$487$		−	31.0252i		−	1.40589i	−0.711246	−	0.702943i	$-0.751869\pi$
$487$		−	31.0252i		−	1.40589i	0.711246	−	0.702943i	$-0.248131\pi$
$488$	−3.28422	+	7.88386i	−0.148670	+	0.356885i
$489$		0			0
$490$	−35.2994	−	14.2257i	−1.59466	−	0.642650i
$491$	22.0446			0.994859			0.497429	−	0.867505i	$-0.334277\pi$
$491$	22.0446			0.994859			0.497429	+	0.867505i	$0.334277\pi$
$492$		0			0
$493$	6.34099			0.285584
$494$	−4.29574	−	0.568479i	−0.193275	−	0.0255771i
$495$		0			0
$496$	18.4809	+	10.7362i	0.829819	+	0.482072i
$497$	−3.09274	+	2.39850i	−0.138728	+	0.107587i
$498$		0			0
$499$	40.6409			1.81934			0.909668	−	0.415337i	$-0.136336\pi$
$499$	40.6409			1.81934			0.909668	+	0.415337i	$0.136336\pi$
$500$	35.4859	+	9.55949i	1.58698	+	0.427514i
$501$		0			0
$502$	−6.81125	−	0.901371i	−0.304001	−	0.0402301i
$503$	−33.1848			−1.47964			−0.739818	−	0.672807i	$-0.765088\pi$
$503$	−33.1848			−1.47964			−0.739818	+	0.672807i	$0.765088\pi$
$504$		0			0
$505$	−44.3392			−1.97307
$506$	31.9101	+	4.22284i	1.41858	+	0.187728i
$507$		0			0
$508$	−2.80130	+	10.3987i	−0.124287	+	0.461368i
$509$	−35.5240			−1.57457			−0.787287	−	0.616586i	$-0.788515\pi$
$509$	−35.5240			−1.57457			−0.787287	+	0.616586i	$0.788515\pi$
$510$		0			0
$511$	14.5984	−	11.3214i	0.645793	−	0.500829i
$512$	20.9569	−	8.53268i	0.926175	−	0.377095i
$513$		0			0
$514$	−12.9123	−	1.70876i	−0.569537	−	0.0753700i
$515$	−4.39152			−0.193514
$516$		0			0
$517$	−21.9853			−0.966914
$518$	2.68945	+	4.61056i	0.118168	+	0.202576i
$519$		0			0
$520$	−7.59452	+	18.2309i	−0.333042	+	0.799476i
$521$		−	26.4737i		−	1.15984i	−0.814675	−	0.579918i	$-0.803085\pi$
$521$		−	26.4737i		−	1.15984i	0.814675	−	0.579918i	$-0.196915\pi$
$522$		0			0
$523$		−	41.7100i		−	1.82385i	−0.410358	−	0.911924i	$-0.634596\pi$
$523$		−	41.7100i		−	1.82385i	0.410358	−	0.911924i	$-0.365404\pi$
$524$	6.81125	−	25.2841i	0.297551	−	1.10454i
$525$		0			0
$526$	5.47967	+	0.725155i	0.238925	+	0.0316183i
$527$			18.6547i			0.812613i
$528$		0			0
$529$	−2.06320			−0.0897043
$530$	−31.6528	−	4.18878i	−1.37491	−	0.181949i
$531$		0			0
$532$	8.23425	−	3.44743i	0.357000	−	0.149465i
$533$		−	16.3018i		−	0.706110i
$534$		0			0
$535$	0.306091			0.0132335
$536$	4.81736	−	11.5642i	0.208078	−	0.499498i
$537$		0			0
$538$	1.71594	−	12.9666i	0.0739796	−	0.559031i
$539$	−7.92038	+	30.8232i	−0.341155	+	1.32765i
$540$		0			0
$541$		−	10.3187i		−	0.443637i	−0.975088	−	0.221818i	$-0.928801\pi$
$541$		−	10.3187i		−	0.443637i	0.975088	−	0.221818i	$-0.0711992\pi$
$542$	−3.06502	+	23.1610i	−0.131654	+	0.994850i
$543$		0			0
$544$	15.6279	+	12.0752i	0.670039	+	0.517721i
$545$		−	77.3045i		−	3.31136i
$546$		0			0
$547$	19.6461			0.840006			0.420003	−	0.907523i	$-0.362029\pi$
$547$	19.6461			0.840006			0.420003	+	0.907523i	$0.362029\pi$
$548$	−37.7724	−	10.1755i	−1.61356	−	0.434674i
$549$		0			0
$550$	8.24924	−	62.3358i	0.351749	−	2.65801i
$551$	3.06403			0.130532
$552$		0			0
$553$	−6.22640	+	4.82873i	−0.264773	+	0.205339i
$554$	−4.57701	−	0.605701i	−0.194458	−	0.0257337i
$555$		0			0
$556$	−7.59068	+	28.1774i	−0.321916	+	1.19499i
$557$			30.0989i			1.27533i	0.770314	+	0.637665i	$0.220100\pi$
$557$			30.0989i			1.27533i	−0.770314	+	0.637665i	$0.779900\pi$
$558$		0			0
$559$	14.5984			0.617445
$560$	−5.40956	−	40.3245i	−0.228596	−	1.70402i
$561$		0			0
$562$	−3.55629	+	26.8733i	−0.150013	+	1.13358i
$563$		−	6.35650i		−	0.267894i	−0.990988	−	0.133947i	$-0.957235\pi$
$563$		−	6.35650i		−	0.267894i	0.990988	−	0.133947i	$-0.0427653\pi$
$564$		0			0
$565$	19.1549			0.805852
$566$	28.4295	+	3.76223i	1.19498	+	0.158139i
$567$		0			0
$568$	−3.86231	−	1.60894i	−0.162059	−	0.0675097i
$569$	37.7589			1.58294			0.791469	−	0.611210i	$-0.209317\pi$
$569$	37.7589			1.58294			0.791469	+	0.611210i	$0.209317\pi$
$570$		0			0
$571$	−29.0324			−1.21497			−0.607484	−	0.794332i	$-0.707821\pi$
$571$	−29.0324			−1.21497			−0.607484	+	0.794332i	$0.707821\pi$
$572$	15.9463	+	4.29574i	0.666746	+	0.179614i
$573$		0			0
$574$	16.9214	+	29.0086i	0.706287	+	1.21080i
$575$			48.9605i			2.04179i
$576$		0			0
$577$		−	38.4060i		−	1.59886i	−0.600758	−	0.799431i	$-0.705134\pi$
$577$		−	38.4060i		−	1.59886i	0.600758	−	0.799431i	$-0.294866\pi$
$578$	0.892640	−	6.74528i	0.0371289	−	0.280567i
$579$		0			0
$580$	3.63251	−	13.4843i	0.150832	−	0.559904i
$581$	22.1134	−	17.1495i	0.917420	−	0.711483i
$582$		0			0
$583$			26.6992i			1.10577i
$584$	18.2309	+	7.59452i	0.754398	+	0.314263i
$585$		0			0
$586$	0.940721	−	7.10861i	0.0388608	−	0.293654i
$587$			0.157054i			0.00648231i	0.999995	+	0.00324116i	$0.00103169\pi$
$587$			0.157054i			0.00648231i	−0.999995	+	0.00324116i	$0.998968\pi$
$588$		0			0
$589$			9.01416i			0.371422i
$590$	−45.6347	−	6.03909i	−1.87875	−	0.248626i
$591$		0			0
$592$	−2.86635	+	4.93401i	−0.117806	+	0.202787i
$593$			37.5927i			1.54375i	0.635776	+	0.771874i	$0.280680\pi$
$593$			37.5927i			1.54375i	−0.635776	+	0.771874i	$0.719320\pi$
$594$		0			0
$595$	28.0613	−	21.7622i	1.15040	−	0.892165i
$596$	−9.57086	+	35.5281i	−0.392038	+	1.45529i
$597$		0			0
$598$	−12.7479	−	1.68700i	−0.521302	−	0.0689868i
$599$		−	18.7569i		−	0.766387i	−0.923668	−	0.383194i	$-0.874824\pi$
$599$		−	18.7569i		−	0.766387i	0.923668	−	0.383194i	$-0.125176\pi$
$600$		0			0
$601$		−	2.44051i		−	0.0995503i	−0.998760	−	0.0497751i	$-0.984150\pi$
$601$		−	2.44051i		−	0.0995503i	0.998760	−	0.0497751i	$-0.0158505\pi$
$602$	−25.9774	+	15.1532i	−1.05876	+	0.617600i
$603$		0			0
$604$	−5.14383	+	19.0945i	−0.209300	+	0.776943i
$605$	−37.1738			−1.51133
$606$		0			0
$607$	−40.4839			−1.64319			−0.821596	−	0.570070i	$-0.806916\pi$
$607$	−40.4839			−1.64319			−0.821596	+	0.570070i	$0.806916\pi$
$608$	7.55154	+	5.83488i	0.306255	+	0.236635i
$609$		0			0
$610$	−2.15376	+	16.2750i	−0.0872031	+	0.658955i
$611$	8.78304			0.355324
$612$		0			0
$613$		−	8.57378i		−	0.346292i	−0.984896	−	0.173146i	$-0.944607\pi$
$613$		−	8.57378i		−	0.346292i	0.984896	−	0.173146i	$-0.0553932\pi$
$614$	21.3754	+	2.82873i	0.862643	+	0.114158i
$615$		0			0
$616$	−32.8350	+	8.90821i	−1.32296	+	0.358922i
$617$	−31.3390			−1.26166			−0.630830	−	0.775921i	$-0.717285\pi$
$617$	−31.3390			−1.26166			−0.630830	+	0.775921i	$0.717285\pi$
$618$		0			0
$619$		−	41.5595i		−	1.67042i	−0.549933	−	0.835209i	$-0.685347\pi$
$619$		−	41.5595i		−	1.67042i	0.549933	−	0.835209i	$-0.314653\pi$
$620$	39.6698	+	10.6866i	1.59318	+	0.429183i
$621$		0			0
$622$	−1.65399	+	12.4985i	−0.0663191	+	0.501143i
$623$	33.3635	−	25.8743i	1.33668	−	1.03663i
$624$		0			0
$625$	21.7447			0.869789
$626$	−34.9565	−	4.62599i	−1.39714	−	0.184892i
$627$		0			0
$628$	23.8657	+	6.42914i	0.952343	+	0.256551i
$629$	−4.98041			−0.198582
$630$		0			0
$631$			48.0528i			1.91295i	0.291814	+	0.956475i	$0.405741\pi$
$631$			48.0528i			1.91295i	−0.291814	+	0.956475i	$0.594259\pi$
$632$	−7.77571	−	3.23917i	−0.309301	−	0.128847i
$633$		0			0
$634$	22.5899	+	2.98944i	0.897158	+	0.118726i
$635$			20.7012i			0.821503i
$636$		0			0
$637$	3.16416	−	12.3137i	0.125368	−	0.487888i
$638$	−11.5767	−	1.53201i	−0.458328	−	0.0606530i
$639$		0			0
$640$	34.6309	−	26.3156i	1.36891	−	1.04021i
$641$	26.9335			1.06381			0.531905	−	0.846804i	$-0.321476\pi$
$641$	26.9335			1.06381			0.531905	+	0.846804i	$0.321476\pi$
$642$		0			0
$643$			20.2780i			0.799685i	0.916584	+	0.399843i	$0.130935\pi$
$643$			20.2780i			0.799685i	−0.916584	+	0.399843i	$0.869065\pi$
$644$	24.4358	−	10.2305i	0.962904	−	0.403138i
$645$		0			0
$646$	−1.09274	+	8.25737i	−0.0429934	+	0.324882i
$647$	16.3928			0.644466			0.322233	−	0.946660i	$-0.395567\pi$
$647$	16.3928			0.644466			0.322233	+	0.946660i	$0.395567\pi$
$648$		0			0
$649$			38.4930i			1.51098i
$650$	−3.29553	+	24.9029i	−0.129261	+	0.976771i
$651$		0			0
$652$	6.89589	+	1.85767i	0.270064	+	0.0727522i
$653$			27.4567i			1.07447i	0.843434	+	0.537233i	$0.180530\pi$
$653$			27.4567i			1.07447i	−0.843434	+	0.537233i	$0.819470\pi$
$654$		0			0
$655$		−	50.3343i		−	1.96672i
$656$	−18.0344	+	31.0438i	−0.704127	+	1.21206i
$657$		0			0
$658$	−15.6292	+	9.11689i	−0.609290	+	0.355413i
$659$	−34.1059			−1.32858			−0.664288	−	0.747477i	$-0.731265\pi$
$659$	−34.1059			−1.32858			−0.664288	+	0.747477i	$0.731265\pi$
$660$		0			0
$661$	42.0551			1.63575			0.817877	−	0.575393i	$-0.195151\pi$
$661$	42.0551			1.63575			0.817877	+	0.575393i	$0.195151\pi$
$662$	4.15226	−	31.3768i	0.161382	−	1.21949i
$663$		0			0
$664$	27.6159	+	11.5041i	1.07171	+	0.446446i
$665$	13.5595	−	10.5157i	0.525815	−	0.407783i
$666$		0			0
$667$	9.09274			0.352072
$668$	−37.8096	−	10.1855i	−1.46290	−	0.394088i
$669$		0			0
$670$	3.15918	−	23.8725i	0.122050	−	0.922275i
$671$	13.7280			0.529963
$672$		0			0
$673$	43.0405			1.65909			0.829544	−	0.558441i	$-0.188600\pi$
$673$	43.0405			1.65909			0.829544	+	0.558441i	$0.188600\pi$
$674$	0.411978	−	3.11313i	0.0158688	−	0.119913i
$675$		0			0
$676$	18.7346	+	5.04688i	0.720560	+	0.194111i
$677$	5.91811			0.227451			0.113726	−	0.993512i	$-0.463722\pi$
$677$	5.91811			0.227451			0.113726	+	0.993512i	$0.463722\pi$
$678$		0			0
$679$	−24.2700	+	18.8220i	−0.931395	+	0.722321i
$680$	35.0438	+	14.5984i	1.34387	+	0.559821i
$681$		0			0
$682$	4.50708	−	34.0580i	0.172585	−	1.30415i
$683$	1.50261			0.0574958			0.0287479	−	0.999587i	$-0.490848\pi$
$683$	1.50261			0.0574958			0.0287479	+	0.999587i	$0.490848\pi$
$684$		0			0
$685$	−75.1954			−2.87307
$686$	7.15126	+	25.1964i	0.273036	+	0.962004i
$687$		0			0
$688$	−27.7998	−	16.1499i	−1.05986	−	0.615711i
$689$		−	10.6662i		−	0.406350i
$690$		0			0
$691$			8.62599i			0.328148i	0.986448	+	0.164074i	$0.0524636\pi$
$691$			8.62599i			0.328148i	−0.986448	+	0.164074i	$0.947536\pi$
$692$	10.6102	+	2.85827i	0.403340	+	0.108655i
$693$		0			0
$694$	3.23173	−	24.4207i	0.122675	−	0.926998i
$695$			56.0941i			2.12777i
$696$		0			0
$697$	−31.3357			−1.18692
$698$	5.39603	−	40.7754i	0.204243	−	1.54337i
$699$		0			0
$700$	−19.9851	−	47.7348i	−0.755366	−	1.80421i
$701$			10.4065i			0.393050i	0.980499	+	0.196525i	$0.0629656\pi$
$701$			10.4065i			0.393050i	−0.980499	+	0.196525i	$0.937034\pi$
$702$		0			0
$703$	−2.40659			−0.0907661
$704$	−25.6144	−	25.8215i	−0.965378	−	0.973186i
$705$		0			0
$706$	9.84827	+	1.30328i	0.370645	+	0.0490494i
$707$	18.7001	+	24.1128i	0.703291	+	0.906857i
$708$		0			0
$709$		−	34.8737i		−	1.30971i	−0.755755	−	0.654855i	$-0.772730\pi$
$709$		−	34.8737i		−	1.30971i	0.755755	−	0.654855i	$-0.227270\pi$
$710$	−7.97313	−	1.05513i	−0.299226	−	0.0395982i
$711$		0			0
$712$	41.6654	+	17.3568i	1.56148	+	0.650472i
$713$			26.7502i			1.00180i
$714$		0			0
$715$	31.7450			1.18719
$716$	19.3707	+	5.21825i	0.723918	+	0.195015i
$717$		0			0
$718$	−15.6334	−	2.06886i	−0.583434	−	0.0772091i
$719$	−8.74757			−0.326229			−0.163115	−	0.986607i	$-0.552154\pi$
$719$	−8.74757			−0.326229			−0.163115	+	0.986607i	$0.552154\pi$
$720$		0			0
$721$	1.85213	+	2.38823i	0.0689769	+	0.0889422i
$722$	2.99710	−	22.6478i	0.111541	−	0.842863i
$723$		0			0
$724$	−46.8268	−	12.6146i	−1.74031	−	0.468819i
$725$		−	17.7625i		−	0.659683i
$726$		0			0
$727$	−23.7851			−0.882140			−0.441070	−	0.897473i	$-0.645401\pi$
$727$	−23.7851			−0.882140			−0.441070	+	0.897473i	$0.645401\pi$
$728$	13.1174	−	3.55879i	0.486164	−	0.131897i
$729$		0			0
$730$	37.6347	+	4.98041i	1.39292	+	0.184333i
$731$		−	28.0613i		−	1.03788i
$732$		0			0
$733$	4.79132			0.176971			0.0884857	−	0.996077i	$-0.471797\pi$
$733$	4.79132			0.176971			0.0884857	+	0.996077i	$0.471797\pi$
$734$	1.19276	−	9.01312i	0.0440254	−	0.332680i
$735$		0			0
$736$	22.4098	+	17.3154i	0.826035	+	0.638256i
$737$	−20.1365			−0.741738
$738$		0			0
$739$	13.7563			0.506035			0.253018	−	0.967462i	$-0.418577\pi$
$739$	13.7563			0.506035			0.253018	+	0.967462i	$0.418577\pi$
$740$	−2.85309	+	10.5910i	−0.104882	+	0.389332i
$741$		0			0
$742$	11.0716	+	18.9802i	0.406452	+	0.696786i
$743$		−	11.5310i		−	0.423033i	−0.977374	−	0.211517i	$-0.932160\pi$
$743$		−	11.5310i		−	0.423033i	0.977374	−	0.211517i	$-0.0678402\pi$
$744$		0			0
$745$			70.7275i			2.59125i
$746$	2.46087	+	0.325660i	0.0900987	+	0.0119233i
$747$		0			0
$748$	8.25737	−	30.6522i	0.301919	−	1.12076i
$749$	−0.129094	−	0.166461i	−0.00471701	−	0.00608234i
$750$		0			0
$751$		−	40.8541i		−	1.49079i	−0.666625	−	0.745393i	$-0.732262\pi$
$751$		−	40.8541i		−	1.49079i	0.666625	−	0.745393i	$-0.267738\pi$
$752$	−16.7257	−	9.71655i	−0.609923	−	0.354326i
$753$		0			0
$754$	4.62486	+	0.612033i	0.168427	+	0.0222889i
$755$			38.0123i			1.38341i
$756$		0			0
$757$			27.8196i			1.01112i	0.862791	+	0.505561i	$0.168714\pi$
$757$			27.8196i			1.01112i	−0.862791	+	0.505561i	$0.831286\pi$
$758$	−3.52627	+	26.6464i	−0.128080	+	0.967842i
$759$		0			0
$760$	16.9335	+	7.05407i	0.614243	+	0.255878i
$761$			26.4737i			0.959672i	0.877358	+	0.479836i	$0.159304\pi$
$761$			26.4737i			0.959672i	−0.877358	+	0.479836i	$0.840696\pi$
$762$		0			0
$763$	−42.0402	+	32.6033i	−1.52196	+	1.18032i
$764$	−4.41896	+	16.4036i	−0.159872	+	0.593463i
$765$		0			0
$766$	−5.28650	+	39.9477i	−0.191009	+	1.44337i
$767$		−	15.3778i		−	0.555259i
$768$		0			0
$769$			31.5945i			1.13933i	0.821878	+	0.569664i	$0.192927\pi$
$769$			31.5945i			1.13933i	−0.821878	+	0.569664i	$0.807073\pi$
$770$	−56.4894	+	32.9516i	−2.03574	+	1.18749i
$771$		0			0
$772$	21.8133	+	5.87626i	0.785079	+	0.211491i
$773$	33.5413			1.20640			0.603199	−	0.797591i	$-0.293893\pi$
$773$	33.5413			1.20640			0.603199	+	0.797591i	$0.293893\pi$
$774$		0			0
$775$	52.2560			1.87709
$776$	−30.3090	−	12.6260i	−1.08803	−	0.453247i
$777$		0			0
$778$	41.1986	+	5.45204i	1.47704	+	0.195465i
$779$	−15.1417			−0.542509
$780$		0			0
$781$			6.72535i			0.240652i
$782$	−3.24280	+	24.5044i	−0.115962	+	0.876274i
$783$		0			0
$784$	−19.6481	+	19.9488i	−0.701716	+	0.712457i
$785$	47.5105			1.69572
$786$		0			0
$787$		−	1.03147i		−	0.0367679i	−0.999831	−	0.0183840i	$-0.994148\pi$
$787$		−	1.03147i		−	0.0367679i	0.999831	−	0.0183840i	$-0.00585213\pi$
$788$	−1.24061	+	4.60529i	−0.0441950	+	0.164057i
$789$		0			0
$790$	−16.0517	−	2.12421i	−0.571095	−	0.0755761i
$791$	−8.07860	−	10.4169i	−0.287242	−	0.370384i
$792$		0			0
$793$	−5.48426			−0.194752
$794$	−2.88397	+	21.7929i	−0.102348	+	0.773400i
$795$		0			0
$796$	−4.75716	−	1.28152i	−0.168613	−	0.0454224i
$797$	22.2199			0.787070			0.393535	−	0.919310i	$-0.371252\pi$
$797$	22.2199			0.787070			0.393535	+	0.919310i	$0.371252\pi$
$798$		0			0
$799$		−	16.8830i		−	0.597276i
$800$	33.8254	−	43.7771i	1.19591	−	1.54775i
$801$		0			0
$802$	2.88680	−	21.8143i	0.101937	−	0.770288i
$803$		−	31.7450i		−	1.12026i
$804$		0			0
$805$	40.2388	−	31.2062i	1.41823	−	1.09988i
$806$	−1.80056	+	13.6060i	−0.0634219	+	0.479251i
$807$		0			0
$808$	−12.5443	+	30.1128i	−0.441305	+	1.05937i
$809$	52.4790			1.84506			0.922532	−	0.385920i	$-0.126116\pi$
$809$	52.4790			1.84506			0.922532	+	0.385920i	$0.126116\pi$
$810$		0			0
$811$			4.40548i			0.154697i	0.997004	+	0.0773487i	$0.0246455\pi$
$811$			4.40548i			0.154697i	−0.997004	+	0.0773487i	$0.975355\pi$
$812$	−8.86511	+	3.71155i	−0.311104	+	0.130250i
$813$		0			0
$814$	9.09274	+	1.20329i	0.318700	+	0.0421754i
$815$	13.7280			0.480870
$816$		0			0
$817$		−	13.5595i		−	0.474387i
$818$	25.7356	+	3.40574i	0.899825	+	0.119079i
$819$		0			0
$820$	−17.9510	+	66.6361i	−0.626877	+	2.32703i
$821$		−	21.2067i		−	0.740119i	−0.929008	−	0.370060i	$-0.879337\pi$
$821$		−	21.2067i		−	0.740119i	0.929008	−	0.370060i	$-0.120663\pi$
$822$		0			0
$823$		−	29.3609i		−	1.02346i	−0.859148	−	0.511728i	$-0.829006\pi$
$823$		−	29.3609i		−	1.02346i	0.859148	−	0.511728i	$-0.170994\pi$
$824$	−1.24243	+	2.98249i	−0.0432821	+	0.103900i
$825$		0			0
$826$	15.9623	+	27.3644i	0.555399	+	0.952128i
$827$	28.2161			0.981171			0.490585	−	0.871393i	$-0.336783\pi$
$827$	28.2161			0.981171			0.490585	+	0.871393i	$0.336783\pi$
$828$		0			0
$829$	9.77173			0.339386			0.169693	−	0.985497i	$-0.445722\pi$
$829$	9.77173			0.339386			0.169693	+	0.985497i	$0.445722\pi$
$830$	57.0087	+	7.54428i	1.97880	+	0.261866i
$831$		0			0
$832$	10.2328	+	10.3156i	0.354759	+	0.357629i
$833$	−23.6698	−	6.08221i	−0.820108	−	0.210736i
$834$		0			0
$835$	−75.2694			−2.60481
$836$	3.99004	−	14.8115i	0.137999	−	0.512266i
$837$		0			0
$838$	29.6773	+	3.92736i	1.02519	+	0.135668i
$839$	−35.0785			−1.21104			−0.605522	−	0.795828i	$-0.707036\pi$
$839$	−35.0785			−1.21104			−0.605522	+	0.795828i	$0.707036\pi$
$840$		0			0
$841$	25.7012			0.886249
$842$	3.09274	+	0.409280i	0.106583	+	0.0141047i
$843$		0			0
$844$	0.0726403	+	0.0195685i	0.00250038	+	0.000673575i
$845$	37.2958			1.28301
$846$		0			0
$847$	15.6781	+	20.2161i	0.538706	+	0.694633i
$848$	−11.7998	+	20.3118i	−0.405209	+	0.697510i
$849$		0			0
$850$	47.8688	+	6.33475i	1.64189	+	0.217280i
$851$	−7.14173			−0.244815
$852$		0			0
$853$	−18.3536			−0.628416			−0.314208	−	0.949354i	$-0.601739\pi$
$853$	−18.3536			−0.628416			−0.314208	+	0.949354i	$0.601739\pi$
$854$	9.75911	−	5.69272i	0.333950	−	0.194801i
$855$		0			0
$856$	0.0865980	−	0.207881i	0.00295986	−	0.00710522i
$857$			7.62775i			0.260559i	0.991477	+	0.130279i	$0.0415874\pi$
$857$			7.62775i			0.260559i	−0.991477	+	0.130279i	$0.958413\pi$
$858$		0			0
$859$		−	13.9075i		−	0.474518i	−0.971446	−	0.237259i	$-0.923751\pi$
$859$		−	13.9075i		−	0.474518i	0.971446	−	0.237259i	$-0.0762491\pi$
$860$	−59.6730	−	16.0752i	−2.03483	−	0.548161i
$861$		0			0
$862$	−24.4304	−	3.23301i	−0.832104	−	0.110117i
$863$		−	13.3074i		−	0.452989i	−0.974012	−	0.226494i	$-0.927274\pi$
$863$		−	13.3074i		−	0.452989i	0.974012	−	0.226494i	$-0.0727265\pi$
$864$		0			0
$865$	21.1223			0.718179
$866$	−3.06403	−	0.405480i	−0.104120	−	0.0137788i
$867$		0			0
$868$	−10.9191	−	26.0805i	−0.370619	−	0.885231i
$869$			13.5397i			0.459302i
$870$		0			0
$871$	8.04444			0.272575
$872$	−52.5011	−	21.8706i	−1.77791	−	0.740633i
$873$		0			0
$874$	−1.56695	+	11.8408i	−0.0530030	+	0.400520i
$875$	−29.7940	−	38.4178i	−1.00722	−	1.29876i
$876$		0			0
$877$			25.0885i			0.847179i	0.905854	+	0.423589i	$0.139230\pi$
$877$			25.0885i			0.847179i	−0.905854	+	0.423589i	$0.860770\pi$
$878$	5.10453	−	38.5726i	0.172269	−	1.30176i
$879$		0			0
$880$	−60.4524	−	35.1190i	−2.03785	−	1.18386i
$881$		−	5.29180i		−	0.178285i	−0.996019	−	0.0891426i	$-0.971587\pi$
$881$		−	5.29180i		−	0.178285i	0.996019	−	0.0891426i	$-0.0284127\pi$
$882$		0			0
$883$	−21.5219			−0.724269			−0.362134	−	0.932126i	$-0.617952\pi$
$883$	−21.5219			−0.724269			−0.362134	+	0.932126i	$0.617952\pi$
$884$	−3.29878	+	12.2454i	−0.110950	+	0.411858i
$885$		0			0
$886$	−0.626805	+	4.73648i	−0.0210579	+	0.159125i
$887$	−14.7656			−0.495780			−0.247890	−	0.968788i	$-0.579737\pi$
$887$	−14.7656			−0.495780			−0.247890	+	0.968788i	$0.579737\pi$
$888$		0			0
$889$	11.2579	−	8.73076i	0.377577	−	0.292820i
$890$	86.0116	+	11.3824i	2.88311	+	0.381538i
$891$		0			0
$892$	−24.9397	−	6.71848i	−0.835043	−	0.224951i
$893$		−	8.15802i		−	0.272998i
$894$		0			0
$895$	38.5622			1.28899
$896$	−28.9167	−	7.73455i	−0.966040	−	0.258393i
$897$		0			0
$898$	−0.327565	+	2.47526i	−0.0109310	+	0.0826005i
$899$		−	9.70478i		−	0.323672i
$900$		0			0
$901$	−20.5028			−0.683047
$902$	57.2096	+	7.57086i	1.90487	+	0.252082i
$903$		0			0
$904$	5.41922	−	13.0090i	0.180240	−	0.432672i
$905$	−93.2205			−3.09875
$906$		0			0
$907$	46.8609			1.55599			0.777995	−	0.628271i	$-0.216237\pi$
$907$	46.8609			1.55599			0.777995	+	0.628271i	$0.216237\pi$
$908$	0.772161	−	2.86635i	0.0256251	−	0.0951230i
$909$		0			0
$910$	22.5672	−	13.1640i	0.748097	−	0.436383i
$911$		−	54.6440i		−	1.81044i	−0.424945	−	0.905219i	$-0.639707\pi$
$911$		−	54.6440i		−	1.81044i	0.424945	−	0.905219i	$-0.360293\pi$
$912$		0			0
$913$		−	48.0870i		−	1.59145i
$914$	−4.53030	+	34.2335i	−0.149849	+	1.13234i
$915$		0			0
$916$	−9.01722	−	2.42914i	−0.297937	−	0.0802610i
$917$	−27.3731	+	21.2286i	−0.903940	+	0.701029i
$918$		0			0
$919$			28.6186i			0.944041i	0.881588	+	0.472020i	$0.156475\pi$
$919$			28.6186i			0.944041i	−0.881588	+	0.472020i	$0.843525\pi$
$920$	50.2515	+	20.9335i	1.65674	+	0.690157i
$921$		0			0
$922$	−1.44323	+	10.9059i	−0.0475304	+	0.359166i
$923$		−	2.68675i		−	0.0884353i
$924$		0			0
$925$			13.9512i			0.458714i
$926$	23.2191	+	3.07271i	0.763026	+	0.100975i
$927$		0			0
$928$	−8.13010	−	6.28191i	−0.266884	−	0.206214i
$929$		−	29.6885i		−	0.974048i	−0.873389	−	0.487024i	$-0.838082\pi$
$929$		−	29.6885i		−	0.974048i	0.873389	−	0.487024i	$-0.161918\pi$
$930$		0			0
$931$	−11.4375	−	2.93899i	−0.374848	−	0.0963214i
$932$	−16.1377	−	4.34731i	−0.528608	−	0.142401i
$933$		0			0
$934$	−19.7824	−	2.61792i	−0.647301	−	0.0856609i
$935$		−	61.0209i		−	1.99560i
$936$		0			0
$937$		−	32.4055i		−	1.05864i	−0.848422	−	0.529320i	$-0.822447\pi$
$937$		−	32.4055i		−	1.05864i	0.848422	−	0.529320i	$-0.177553\pi$
$938$	−14.3149	+	8.35021i	−0.467397	+	0.272644i
$939$		0			0
$940$	−35.9020	−	9.67160i	−1.17100	−	0.315453i
$941$	−10.5656			−0.344429			−0.172214	−	0.985060i	$-0.555092\pi$
$941$	−10.5656			−0.344429			−0.172214	+	0.985060i	$0.555092\pi$
$942$		0			0
$943$	−44.9342			−1.46326
$944$	−17.0122	+	29.2841i	−0.553700	+	0.953117i
$945$		0			0
$946$	−6.77975	+	51.2315i	−0.220429	+	1.66568i
$947$	3.44186			0.111845			0.0559226	−	0.998435i	$-0.482190\pi$
$947$	3.44186			0.111845			0.0559226	+	0.998435i	$0.482190\pi$
$948$		0			0
$949$			12.6820i			0.411674i
$950$	23.1307	+	3.06101i	0.750459	+	0.0993124i
$951$		0			0
$952$	−6.84078	−	25.2146i	−0.221711	−	0.817210i
$953$	38.5559			1.24895			0.624475	−	0.781045i	$-0.285313\pi$
$953$	38.5559			1.24895			0.624475	+	0.781045i	$0.285313\pi$
$954$		0			0
$955$			32.6555i			1.05671i
$956$	−10.3291	+	38.3426i	−0.334066	+	1.24009i
$957$		0			0
$958$	−1.62296	+	12.2640i	−0.0524356	+	0.396232i
$959$	31.7137	+	40.8932i	1.02409	+	1.32051i
$960$		0			0
$961$	−2.44924			−0.0790077
$962$	−3.63251	−	0.480710i	−0.117117	−	0.0154987i
$963$		0			0
$964$	3.42157	−	12.7012i	0.110201	−	0.409079i
$965$	43.4248			1.39790
$966$		0			0
$967$		−	10.0322i		−	0.322614i	−0.986904	−	0.161307i	$-0.948429\pi$
$967$		−	10.0322i		−	0.322614i	0.986904	−	0.161307i	$-0.0515709\pi$
$968$	−10.5170	+	25.2465i	−0.338031	+	0.811452i
$969$		0			0
$970$	−62.5682	−	8.28000i	−2.00894	−	0.265855i
$971$		−	28.4807i		−	0.913989i	−0.889469	−	0.456995i	$-0.848926\pi$
$971$		−	28.4807i		−	0.913989i	0.889469	−	0.456995i	$-0.151074\pi$
$972$		0			0
$973$	30.5055	−	23.6578i	0.977960	−	0.758433i
$974$	−43.4970	−	5.75620i	−1.39373	−	0.184441i
$975$		0			0
$976$	10.4438	+	6.06716i	0.334297	+	0.194205i
$977$	−8.98249			−0.287375			−0.143688	−	0.989623i	$-0.545896\pi$
$977$	−8.98249			−0.287375			−0.143688	+	0.989623i	$0.545896\pi$
$978$		0			0
$979$		−	72.5510i		−	2.31874i
$980$	−26.4935	+	46.8500i	−0.846303	+	1.49657i
$981$		0			0
$982$	4.09000	−	30.9063i	0.130517	−	0.986260i
$983$	11.1768			0.356484			0.178242	−	0.983987i	$-0.442959\pi$
$983$	11.1768			0.356484			0.178242	+	0.983987i	$0.442959\pi$
$984$		0			0
$985$			9.16797i			0.292116i
$986$	1.17646	−	8.89000i	0.0374662	−	0.283115i
$987$		0			0
$988$	−1.59400	+	5.91712i	−0.0507120	+	0.188249i
$989$		−	40.2388i		−	1.27952i
$990$		0			0
$991$		−	21.5500i		−	0.684559i	−0.939598	−	0.342279i	$-0.888801\pi$
$991$		−	21.5500i		−	0.684559i	0.939598	−	0.342279i	$-0.111199\pi$
$992$	18.4809	−	23.9182i	0.586770	−	0.759403i
$993$		0			0
$994$	2.78887	+	4.78100i	0.0884576	+	0.151644i
$995$	−9.47031			−0.300229
$996$		0			0
$997$	38.2116			1.21017			0.605087	−	0.796159i	$-0.293138\pi$
$997$	38.2116			1.21017			0.605087	+	0.796159i	$0.293138\pi$
$998$	7.54023	−	56.9781i	0.238682	−	1.80361i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.p.g.307.9		16
3.2	odd	2		168.2.p.a.139.8	yes	16
4.3	odd	2		2016.2.p.g.559.1		16
7.6	odd	2	inner	504.2.p.g.307.10		16
8.3	odd	2	inner	504.2.p.g.307.12		16
8.5	even	2		2016.2.p.g.559.16		16
12.11	even	2		672.2.p.a.559.8		16
21.20	even	2		168.2.p.a.139.7	yes	16
24.5	odd	2		672.2.p.a.559.1		16
24.11	even	2		168.2.p.a.139.6	yes	16
28.27	even	2		2016.2.p.g.559.15		16
56.13	odd	2		2016.2.p.g.559.2		16
56.27	even	2	inner	504.2.p.g.307.11		16
84.83	odd	2		672.2.p.a.559.9		16
168.83	odd	2		168.2.p.a.139.5	✓	16
168.125	even	2		672.2.p.a.559.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.p.a.139.5	✓	16	168.83	odd	2
168.2.p.a.139.6	yes	16	24.11	even	2
168.2.p.a.139.7	yes	16	21.20	even	2
168.2.p.a.139.8	yes	16	3.2	odd	2
504.2.p.g.307.9		16	1.1	even	1	trivial
504.2.p.g.307.10		16	7.6	odd	2	inner
504.2.p.g.307.11		16	56.27	even	2	inner
504.2.p.g.307.12		16	8.3	odd	2	inner
672.2.p.a.559.1		16	24.5	odd	2
672.2.p.a.559.8		16	12.11	even	2
672.2.p.a.559.9		16	84.83	odd	2
672.2.p.a.559.16		16	168.125	even	2
2016.2.p.g.559.1		16	4.3	odd	2
2016.2.p.g.559.2		16	56.13	odd	2
2016.2.p.g.559.15		16	28.27	even	2
2016.2.p.g.559.16		16	8.5	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.185533 - 1.40199i) q^{2} +(-1.93115 - 0.520231i) q^{4} -3.84444 q^{5} +(1.62140 + 2.09071i) q^{7} +(-1.08765 + 2.61094i) q^{8} +(-0.713272 + 5.38987i) q^{10} +4.54637 q^{11} -1.81625 q^{13} +(3.23198 - 1.88529i) q^{14} +(3.45872 + 2.00929i) q^{16} +3.49124i q^{17} +1.68700i q^{19} +(7.42422 + 2.00000i) q^{20} +(0.843502 - 6.37397i) q^{22} +5.00632i q^{23} +9.77975 q^{25} +(-0.336975 + 2.54637i) q^{26} +(-2.04352 - 4.88099i) q^{28} -1.81625i q^{29} +5.34329 q^{31} +(3.45872 - 4.47630i) q^{32} +(4.89469 + 0.647741i) q^{34} +(-6.23338 - 8.03761i) q^{35} +1.42654i q^{37} +(2.36516 + 0.312995i) q^{38} +(4.18142 - 10.0376i) q^{40} +8.97551i q^{41} -8.03761 q^{43} +(-8.77975 - 2.36516i) q^{44} +(7.01881 + 0.928837i) q^{46} -4.83580 q^{47} +(-1.74213 + 6.77975i) q^{49} +(1.81447 - 13.7111i) q^{50} +(3.50747 + 0.944872i) q^{52} +5.87263i q^{53} -17.4783 q^{55} +(-7.22224 + 1.95941i) q^{56} +(-2.54637 - 0.336975i) q^{58} +8.46675i q^{59} +3.01955 q^{61} +(0.991357 - 7.49124i) q^{62} +(-5.63402 - 5.67959i) q^{64} +6.98249 q^{65} -4.42914 q^{67} +(1.81625 - 6.74213i) q^{68} +(-12.4252 + 7.24789i) q^{70} +1.47928i q^{71} -6.98249i q^{73} +(2.00000 + 0.264671i) q^{74} +(0.877633 - 3.25787i) q^{76} +(7.37148 + 9.50514i) q^{77} +2.97813i q^{79} +(-13.2968 - 7.72462i) q^{80} +(12.5836 + 1.66525i) q^{82} -10.5770i q^{83} -13.4219i q^{85} +(-1.49124 + 11.2687i) q^{86} +(-4.94487 + 11.8703i) q^{88} -15.9580i q^{89} +(-2.94487 - 3.79726i) q^{91} +(2.60444 - 9.66797i) q^{92} +(-0.897201 + 6.77975i) q^{94} -6.48559i q^{95} +11.6085i q^{97} +(9.18192 + 3.70032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64}+ \cdots - 66 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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