LMFDB - Embedded newform 378.3.q.a.197.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(71,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.71"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			197.9
Character	$\chi$	$=$	378.197
Dual form			378.3.q.a.71.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-2.76866 + 1.59849i) q^{5} +(-1.32288 + 2.29129i) q^{7} +2.82843i q^{8} -4.52120 q^{10} +(16.3294 + 9.42781i) q^{11} +(-5.18593 - 8.98229i) q^{13} +(-3.24037 + 1.87083i) q^{14} +(-2.00000 + 3.46410i) q^{16} +24.4251i q^{17} -26.5935 q^{19} +(-5.53732 - 3.19697i) q^{20} +(13.3329 + 23.0933i) q^{22} +(-35.3991 + 20.4377i) q^{23} +(-7.38968 + 12.7993i) q^{25} -14.6680i q^{26} -5.29150 q^{28} +(18.8212 + 10.8664i) q^{29} +(1.37716 + 2.38532i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-17.2712 + 29.9145i) q^{34} -8.45840i q^{35} +45.6422 q^{37} +(-32.5702 - 18.8044i) q^{38} +(-4.52120 - 7.83095i) q^{40} +(12.8400 - 7.41318i) q^{41} +(14.4554 - 25.0374i) q^{43} +37.7112i q^{44} -57.8065 q^{46} +(25.7813 + 14.8849i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-18.1009 + 10.4506i) q^{50} +(10.3719 - 17.9646i) q^{52} -18.1401i q^{53} -60.2809 q^{55} +(-6.48074 - 3.74166i) q^{56} +(15.3674 + 26.6172i) q^{58} +(46.4112 - 26.7955i) q^{59} +(13.9337 - 24.1339i) q^{61} +3.89520i q^{62} -8.00000 q^{64} +(28.7161 + 16.5793i) q^{65} +(46.2776 + 80.1552i) q^{67} +(-42.3056 + 24.4251i) q^{68} +(5.98099 - 10.3594i) q^{70} -81.9005i q^{71} -81.2899 q^{73} +(55.9000 + 32.2739i) q^{74} +(-26.5935 - 46.0612i) q^{76} +(-43.2036 + 24.9436i) q^{77} +(42.3065 - 73.2770i) q^{79} -12.7879i q^{80} +20.9677 q^{82} +(99.9040 + 57.6796i) q^{83} +(-39.0432 - 67.6249i) q^{85} +(35.4083 - 20.4430i) q^{86} +(-26.6659 + 46.1866i) q^{88} -13.7346i q^{89} +27.4413 q^{91} +(-70.7982 - 40.8754i) q^{92} +(21.0504 + 36.4603i) q^{94} +(73.6282 - 42.5093i) q^{95} +(55.7929 - 96.6361i) q^{97} -9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−2.76866	+	1.59849i	−0.553732	+	0.319697i	−0.750626	−	0.660728i	$-0.770248\pi$
$5$	−2.76866	+	1.59849i	−0.553732	+	0.319697i	0.196894	+	0.980425i	$0.436915\pi$
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	−4.52120			−0.452120
$11$	16.3294	+	9.42781i	1.48449	+	0.857073i	0.999844	−	0.0176350i	$-0.00561367\pi$
$11$	16.3294	+	9.42781i	1.48449	+	0.857073i	0.484650	+	0.874708i	$0.338947\pi$
$12$		0			0
$13$	−5.18593	−	8.98229i	−0.398917	−	0.690945i	0.594675	−	0.803966i	$-0.297281\pi$
$13$	−5.18593	−	8.98229i	−0.398917	−	0.690945i	−0.993593	+	0.113021i	$0.963947\pi$
$14$	−3.24037	+	1.87083i	−0.231455	+	0.133631i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			24.4251i			1.43677i	0.695645	+	0.718386i	$0.255119\pi$
$17$			24.4251i			1.43677i	−0.695645	+	0.718386i	$0.744881\pi$
$18$		0			0
$19$	−26.5935			−1.39966			−0.699828	−	0.714312i	$-0.746740\pi$
$19$	−26.5935			−1.39966			−0.699828	+	0.714312i	$0.746740\pi$
$20$	−5.53732	−	3.19697i	−0.276866	−	0.159849i
$21$		0			0
$22$	13.3329	+	23.0933i	0.606042	+	1.04970i
$23$	−35.3991	+	20.4377i	−1.53909	+	0.888595i	−0.540200	+	0.841537i	$0.681651\pi$
$23$	−35.3991	+	20.4377i	−1.53909	+	0.888595i	−0.998892	+	0.0470582i	$0.985015\pi$
$24$		0			0
$25$	−7.38968	+	12.7993i	−0.295587	+	0.511972i
$26$		−	14.6680i		−	0.564154i
$27$		0			0
$28$	−5.29150			−0.188982
$29$	18.8212	+	10.8664i	0.649006	+	0.374704i	0.788075	−	0.615579i	$-0.211078\pi$
$29$	18.8212	+	10.8664i	0.649006	+	0.374704i	−0.139069	+	0.990283i	$0.544411\pi$
$30$		0			0
$31$	1.37716	+	2.38532i	0.0444246	+	0.0769457i	0.887383	−	0.461034i	$-0.152521\pi$
$31$	1.37716	+	2.38532i	0.0444246	+	0.0769457i	−0.842958	+	0.537979i	$0.819188\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−17.2712	+	29.9145i	−0.507976	+	0.879840i
$35$		−	8.45840i		−	0.241668i
$36$		0			0
$37$	45.6422			1.23357			0.616786	−	0.787131i	$-0.288434\pi$
$37$	45.6422			1.23357			0.616786	+	0.787131i	$0.288434\pi$
$38$	−32.5702	−	18.8044i	−0.857111	−	0.494853i
$39$		0			0
$40$	−4.52120	−	7.83095i	−0.113030	−	0.195774i
$41$	12.8400	−	7.41318i	0.313171	−	0.180809i	−0.335174	−	0.942156i	$-0.608795\pi$
$41$	12.8400	−	7.41318i	0.313171	−	0.180809i	0.648345	+	0.761347i	$0.275462\pi$
$42$		0			0
$43$	14.4554	−	25.0374i	0.336171	−	0.582266i	−0.647538	−	0.762033i	$-0.724201\pi$
$43$	14.4554	−	25.0374i	0.336171	−	0.582266i	0.983709	+	0.179767i	$0.0575345\pi$
$44$			37.7112i			0.857073i
$45$		0			0
$46$	−57.8065			−1.25666
$47$	25.7813	+	14.8849i	0.548539	+	0.316699i	0.748533	−	0.663098i	$-0.230759\pi$
$47$	25.7813	+	14.8849i	0.548539	+	0.316699i	−0.199993	+	0.979797i	$0.564092\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	−18.1009	+	10.4506i	−0.362019	+	0.209012i
$51$		0			0
$52$	10.3719	−	17.9646i	0.199459	−	0.345473i
$53$		−	18.1401i		−	0.342266i	−0.985248	−	0.171133i	$-0.945257\pi$
$53$		−	18.1401i		−	0.342266i	0.985248	−	0.171133i	$-0.0547428\pi$
$54$		0			0
$55$	−60.2809			−1.09602
$56$	−6.48074	−	3.74166i	−0.115728	−	0.0668153i
$57$		0			0
$58$	15.3674	+	26.6172i	0.264956	+	0.458917i
$59$	46.4112	−	26.7955i	0.786631	−	0.454162i	−0.0521440	−	0.998640i	$-0.516605\pi$
$59$	46.4112	−	26.7955i	0.786631	−	0.454162i	0.838775	+	0.544478i	$0.183272\pi$
$60$		0			0
$61$	13.9337	−	24.1339i	0.228422	−	0.395638i	−0.728919	−	0.684600i	$-0.759977\pi$
$61$	13.9337	−	24.1339i	0.228422	−	0.395638i	0.957341	+	0.288962i	$0.0933102\pi$
$62$			3.89520i			0.0628259i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	28.7161	+	16.5793i	0.441787	+	0.255066i
$66$		0			0
$67$	46.2776	+	80.1552i	0.690711	+	1.19635i	0.971605	+	0.236607i	$0.0760355\pi$
$67$	46.2776	+	80.1552i	0.690711	+	1.19635i	−0.280895	+	0.959739i	$0.590631\pi$
$68$	−42.3056	+	24.4251i	−0.622141	+	0.359193i
$69$		0			0
$70$	5.98099	−	10.3594i	0.0854427	−	0.147991i
$71$		−	81.9005i		−	1.15353i	−0.816911	−	0.576764i	$-0.804315\pi$
$71$		−	81.9005i		−	1.15353i	0.816911	−	0.576764i	$-0.195685\pi$
$72$		0			0
$73$	−81.2899			−1.11356			−0.556780	−	0.830660i	$-0.687964\pi$
$73$	−81.2899			−1.11356			−0.556780	+	0.830660i	$0.687964\pi$
$74$	55.9000	+	32.2739i	0.755406	+	0.436134i
$75$		0			0
$76$	−26.5935	−	46.0612i	−0.349914	−	0.606069i
$77$	−43.2036	+	24.9436i	−0.561086	+	0.323943i
$78$		0			0
$79$	42.3065	−	73.2770i	0.535525	−	0.927557i	−0.463613	−	0.886038i	$-0.653447\pi$
$79$	42.3065	−	73.2770i	0.535525	−	0.927557i	0.999138	−	0.0415187i	$-0.0132196\pi$
$80$		−	12.7879i		−	0.159849i
$81$		0			0
$82$	20.9677			0.255703
$83$	99.9040	+	57.6796i	1.20366	+	0.694935i	0.961368	−	0.275268i	$-0.0887665\pi$
$83$	99.9040	+	57.6796i	1.20366	+	0.694935i	0.242295	+	0.970203i	$0.422100\pi$
$84$		0			0
$85$	−39.0432	−	67.6249i	−0.459332	−	0.795587i
$86$	35.4083	−	20.4430i	0.411724	−	0.237709i
$87$		0			0
$88$	−26.6659	+	46.1866i	−0.303021	+	0.524848i
$89$		−	13.7346i		−	0.154321i	−0.997019	−	0.0771606i	$-0.975415\pi$
$89$		−	13.7346i		−	0.154321i	0.997019	−	0.0771606i	$-0.0245854\pi$
$90$		0			0
$91$	27.4413			0.301553
$92$	−70.7982	−	40.8754i	−0.769546	−	0.444298i
$93$		0			0
$94$	21.0504	+	36.4603i	0.223940	+	0.387876i
$95$	73.6282	−	42.5093i	0.775034	−	0.447466i
$96$		0			0
$97$	55.7929	−	96.6361i	0.575184	−	0.996248i	−0.420837	−	0.907136i	$-0.638264\pi$
$97$	55.7929	−	96.6361i	0.575184	−	0.996248i	0.996022	−	0.0891122i	$-0.0284030\pi$
$98$		−	9.89949i		−	0.101015i
$99$		0			0
$100$	−29.5587			−0.295587
$101$	−125.514	−	72.4658i	−1.24272	−	0.717483i	−0.273071	−	0.961994i	$-0.588039\pi$
$101$	−125.514	−	72.4658i	−1.24272	−	0.717483i	−0.969647	+	0.244510i	$0.921373\pi$
$102$		0			0
$103$	22.4051	+	38.8068i	0.217525	+	0.376765i	0.954051	−	0.299645i	$-0.0968681\pi$
$103$	22.4051	+	38.8068i	0.217525	+	0.376765i	−0.736525	+	0.676410i	$0.763535\pi$
$104$	25.4057	−	14.6680i	0.244286	−	0.141039i
$105$		0			0
$106$	12.8270	−	22.2170i	0.121009	−	0.209594i
$107$			100.220i			0.936634i	0.883560	+	0.468317i	$0.155139\pi$
$107$			100.220i			0.936634i	−0.883560	+	0.468317i	$0.844861\pi$
$108$		0			0
$109$	−60.7449			−0.557292			−0.278646	−	0.960394i	$-0.589886\pi$
$109$	−60.7449			−0.557292			−0.278646	+	0.960394i	$0.589886\pi$
$110$	−73.8287	−	42.6250i	−0.671170	−	0.387500i
$111$		0			0
$112$	−5.29150	−	9.16515i	−0.0472456	−	0.0818317i
$113$	−12.6128	+	7.28199i	−0.111617	+	0.0644424i	−0.554769	−	0.832004i	$-0.687194\pi$
$113$	−12.6128	+	7.28199i	−0.111617	+	0.0644424i	0.443152	+	0.896446i	$0.353860\pi$
$114$		0			0
$115$	65.3387	−	113.170i	0.568163	−	0.984087i
$116$			43.4656i			0.374704i
$117$		0			0
$118$	75.7892			0.642282
$119$	−55.9650	−	32.3114i	−0.470294	−	0.271524i
$120$		0			0
$121$	117.267	+	203.112i	0.969149	+	1.67862i
$122$	34.1305	−	19.7053i	0.279758	−	0.161519i
$123$		0			0
$124$	−2.75433	+	4.77063i	−0.0222123	+	0.0384728i
$125$		−	127.174i		−	1.01739i
$126$		0			0
$127$	221.852			1.74687			0.873433	−	0.486944i	$-0.161888\pi$
$127$	221.852			1.74687			0.873433	+	0.486944i	$0.161888\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	23.4466	+	40.6107i	0.180359	+	0.312390i
$131$	−2.93262	+	1.69315i	−0.0223864	+	0.0129248i	−0.511151	−	0.859491i	$-0.670781\pi$
$131$	−2.93262	+	1.69315i	−0.0223864	+	0.0129248i	0.488765	+	0.872415i	$0.337448\pi$
$132$		0			0
$133$	35.1798	−	60.9333i	0.264510	−	0.458145i
$134$			130.893i			0.976812i
$135$		0			0
$136$	−69.0847			−0.507976
$137$	18.6956	+	10.7939i	0.136464	+	0.0787877i	0.566678	−	0.823939i	$-0.308228\pi$
$137$	18.6956	+	10.7939i	0.136464	+	0.0787877i	−0.430214	+	0.902727i	$0.641562\pi$
$138$		0			0
$139$	30.1614	+	52.2410i	0.216988	+	0.375835i	0.953886	−	0.300170i	$-0.0970433\pi$
$139$	30.1614	+	52.2410i	0.216988	+	0.375835i	−0.736897	+	0.676005i	$0.763710\pi$
$140$	14.6504	−	8.45840i	0.104646	−	0.0604171i
$141$		0			0
$142$	57.9124	−	100.307i	0.407834	−	0.706389i
$143$		−	195.568i		−	1.36761i
$144$		0			0
$145$	−69.4792			−0.479167
$146$	−99.5594	−	57.4807i	−0.681914	−	0.393703i
$147$		0			0
$148$	45.6422	+	79.0546i	0.308393	+	0.534153i
$149$	−13.4563	+	7.76899i	−0.0903107	+	0.0521409i	−0.544475	−	0.838777i	$-0.683271\pi$
$149$	−13.4563	+	7.76899i	−0.0903107	+	0.0521409i	0.454165	+	0.890918i	$0.349938\pi$
$150$		0			0
$151$	−13.4117	+	23.2297i	−0.0888192	+	0.153839i	−0.907012	−	0.421104i	$-0.861643\pi$
$151$	−13.4117	+	23.2297i	−0.0888192	+	0.153839i	0.818193	+	0.574944i	$0.194976\pi$
$152$		−	75.2177i		−	0.494853i
$153$		0			0
$154$	−70.5512			−0.458125
$155$	−7.62579	−	4.40275i	−0.0491987	−	0.0284049i
$156$		0			0
$157$	−53.0669	−	91.9146i	−0.338006	−	0.585444i	0.646052	−	0.763294i	$-0.276419\pi$
$157$	−53.0669	−	91.9146i	−0.338006	−	0.585444i	−0.984058	+	0.177850i	$0.943086\pi$
$158$	103.629	−	59.8304i	0.655882	−	0.378673i
$159$		0			0
$160$	9.04241	−	15.6619i	0.0565150	−	0.0978869i
$161$		−	108.146i		−	0.671715i
$162$		0			0
$163$	11.8953			0.0729774			0.0364887	−	0.999334i	$-0.488383\pi$
$163$	11.8953			0.0729774			0.0364887	+	0.999334i	$0.488383\pi$
$164$	25.6800	+	14.8264i	0.156586	+	0.0904047i
$165$		0			0
$166$	81.5713	+	141.286i	0.491393	+	0.851118i
$167$	−120.719	+	69.6971i	−0.722868	+	0.417348i	−0.815807	−	0.578324i	$-0.803707\pi$
$167$	−120.719	+	69.6971i	−0.722868	+	0.417348i	0.0929395	+	0.995672i	$0.470374\pi$
$168$		0			0
$169$	30.7123	−	53.1953i	0.181730	−	0.314765i
$170$		−	110.431i		−	0.649594i
$171$		0			0
$172$	57.8215			0.336171
$173$	198.663	+	114.698i	1.14834	+	0.662994i	0.948482	−	0.316830i	$-0.102619\pi$
$173$	198.663	+	114.698i	1.14834	+	0.662994i	0.199858	+	0.979825i	$0.435952\pi$
$174$		0			0
$175$	−19.5513	−	33.8638i	−0.111721	−	0.193507i
$176$	−65.3178	+	37.7112i	−0.371124	+	0.214268i
$177$		0			0
$178$	9.71182	−	16.8214i	0.0545608	−	0.0945021i
$179$			202.541i			1.13152i	0.824571	+	0.565758i	$0.191416\pi$
$179$			202.541i			1.13152i	−0.824571	+	0.565758i	$0.808584\pi$
$180$		0			0
$181$	4.20404			0.0232267			0.0116134	−	0.999933i	$-0.496303\pi$
$181$	4.20404			0.0232267			0.0116134	+	0.999933i	$0.496303\pi$
$182$	33.6086	+	19.4040i	0.184663	+	0.106615i
$183$		0			0
$184$	−57.8065	−	100.124i	−0.314166	−	0.544151i
$185$	−126.368	+	72.9584i	−0.683069	+	0.394370i
$186$		0			0
$187$	−230.275	+	398.849i	−1.23142	+	2.13288i
$188$			59.5395i			0.316699i
$189$		0			0
$190$	120.234			0.632813
$191$	235.481	+	135.955i	1.23288	+	0.711806i	0.967630	−	0.252372i	$-0.0812106\pi$
$191$	235.481	+	135.955i	1.23288	+	0.711806i	0.265255	+	0.964178i	$0.414544\pi$
$192$		0			0
$193$	72.2766	+	125.187i	0.374490	+	0.648636i	0.990251	−	0.139297i	$-0.0444843\pi$
$193$	72.2766	+	125.187i	0.374490	+	0.648636i	−0.615760	+	0.787934i	$0.711151\pi$
$194$	136.664	−	78.9030i	0.704454	−	0.406717i
$195$		0			0
$196$	7.00000	−	12.1244i	0.0357143	−	0.0618590i
$197$			53.0627i			0.269354i	0.990890	+	0.134677i	$0.0429996\pi$
$197$			53.0627i			0.269354i	−0.990890	+	0.134677i	$0.957000\pi$
$198$		0			0
$199$	−114.808			−0.576923			−0.288461	−	0.957491i	$-0.593144\pi$
$199$	−114.808			−0.576923			−0.288461	+	0.957491i	$0.593144\pi$
$200$	−36.2019	−	20.9012i	−0.181009	−	0.104506i
$201$		0			0
$202$	−102.482	−	177.504i	−0.507337	−	0.878734i
$203$	−49.7962	+	28.7498i	−0.245301	+	0.141625i
$204$		0			0
$205$	−23.6997	+	41.0492i	−0.115609	+	0.200240i
$206$			63.3713i			0.307628i
$207$		0			0
$208$	41.4874			0.199459
$209$	−434.256	−	250.718i	−2.07778	−	1.19961i
$210$		0			0
$211$	−180.480	−	312.600i	−0.855353	−	1.48152i	−0.876317	−	0.481735i	$-0.840007\pi$
$211$	−180.480	−	312.600i	−0.855353	−	1.48152i	0.0209634	−	0.999780i	$-0.493327\pi$
$212$	31.4196	−	18.1401i	0.148206	−	0.0855665i
$213$		0			0
$214$	−70.8661	+	122.744i	−0.331150	+	0.573569i
$215$			92.4269i			0.429892i
$216$		0			0
$217$	−7.28726			−0.0335818
$218$	−74.3970	−	42.9531i	−0.341271	−	0.197033i
$219$		0			0
$220$	−60.2809	−	104.410i	−0.274004	−	0.474589i
$221$	219.393	−	126.667i	0.992731	−	0.573153i
$222$		0			0
$223$	103.429	−	179.144i	0.463805	−	0.803334i	−0.535342	−	0.844636i	$-0.679817\pi$
$223$	103.429	−	179.144i	0.463805	−	0.803334i	0.999147	+	0.0413015i	$0.0131504\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−20.5966			−0.0911353
$227$	−114.004	−	65.8205i	−0.502222	−	0.289958i	0.227409	−	0.973799i	$-0.426975\pi$
$227$	−114.004	−	65.8205i	−0.502222	−	0.289958i	−0.729631	+	0.683841i	$0.760308\pi$
$228$		0			0
$229$	−118.264	−	204.839i	−0.516436	−	0.894494i	−0.999818	−	0.0190842i	$-0.993925\pi$
$229$	−118.264	−	204.839i	−0.516436	−	0.894494i	0.483381	−	0.875410i	$-0.339408\pi$
$230$	160.047	−	92.4029i	0.695855	−	0.401752i
$231$		0			0
$232$	−30.7349	+	53.2343i	−0.132478	+	0.229458i
$233$		−	155.574i		−	0.667699i	−0.942626	−	0.333849i	$-0.891652\pi$
$233$		−	155.574i		−	0.667699i	0.942626	−	0.333849i	$-0.108348\pi$
$234$		0			0
$235$	−95.1730			−0.404992
$236$	92.8225	+	53.5911i	0.393316	+	0.227081i
$237$		0			0
$238$	−45.6952	−	79.1465i	−0.191997	−	0.332548i
$239$	51.6119	−	29.7981i	0.215949	−	0.124678i	−0.388124	−	0.921607i	$-0.626877\pi$
$239$	51.6119	−	29.7981i	0.215949	−	0.124678i	0.604073	+	0.796929i	$0.293543\pi$
$240$		0			0
$241$	59.7453	−	103.482i	0.247906	−	0.429385i	−0.715039	−	0.699085i	$-0.753591\pi$
$241$	59.7453	−	103.482i	0.247906	−	0.429385i	0.962945	+	0.269699i	$0.0869243\pi$
$242$			331.681i			1.37058i
$243$		0			0
$244$	55.7349			0.228422
$245$	19.3806	+	11.1894i	0.0791046	+	0.0456710i
$246$		0			0
$247$	137.912	+	238.870i	0.558347	+	0.967085i
$248$	−6.74669	+	3.89520i	−0.0272044	+	0.0157065i
$249$		0			0
$250$	89.9253	−	155.755i	0.359701	−	0.623021i
$251$			483.177i			1.92501i	0.271267	+	0.962504i	$0.412557\pi$
$251$			483.177i			1.92501i	−0.271267	+	0.962504i	$0.587443\pi$
$252$		0			0
$253$	−770.730			−3.04636
$254$	271.712	+	156.873i	1.06973	+	0.617611i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−136.833	+	79.0003i	−0.532422	+	0.307394i	−0.742002	−	0.670397i	$-0.766124\pi$
$257$	−136.833	+	79.0003i	−0.532422	+	0.307394i	0.209580	+	0.977792i	$0.432790\pi$
$258$		0			0
$259$	−60.3789	+	104.579i	−0.233123	+	0.403781i
$260$			66.3171i			0.255066i
$261$		0			0
$262$	−4.78895			−0.0182784
$263$	244.980	+	141.439i	0.931483	+	0.537792i	0.887280	−	0.461231i	$-0.152592\pi$
$263$	244.980	+	141.439i	0.931483	+	0.537792i	0.0442024	+	0.999023i	$0.485925\pi$
$264$		0			0
$265$	28.9967	+	50.2238i	0.109422	+	0.189524i
$266$	86.1726	−	49.7518i	0.323957	−	0.187037i
$267$		0			0
$268$	−92.5552	+	160.310i	−0.345355	+	0.598173i
$269$		−	125.436i		−	0.466303i	−0.972440	−	0.233152i	$-0.925096\pi$
$269$		−	125.436i		−	0.466303i	0.972440	−	0.233152i	$-0.0749039\pi$
$270$		0			0
$271$	418.065			1.54268			0.771338	−	0.636426i	$-0.219588\pi$
$271$	418.065			1.54268			0.771338	+	0.636426i	$0.219588\pi$
$272$	−84.6111	−	48.8502i	−0.311070	−	0.179597i
$273$		0			0
$274$	15.2649	+	26.4396i	0.0557113	+	0.0964948i
$275$	−241.339	+	139.337i	−0.877595	+	0.506680i
$276$		0			0
$277$	−228.356	+	395.524i	−0.824389	+	1.42788i	0.0779971	+	0.996954i	$0.475148\pi$
$277$	−228.356	+	395.524i	−0.824389	+	1.42788i	−0.902386	+	0.430929i	$0.858186\pi$
$278$			85.3093i			0.306868i
$279$		0			0
$280$	23.9240			0.0854427
$281$	−221.123	−	127.665i	−0.786913	−	0.454324i	0.0519617	−	0.998649i	$-0.483453\pi$
$281$	−221.123	−	127.665i	−0.786913	−	0.454324i	−0.838875	+	0.544325i	$0.816786\pi$
$282$		0			0
$283$	−4.11688	−	7.13065i	−0.0145473	−	0.0251966i	0.858660	−	0.512545i	$-0.171297\pi$
$283$	−4.11688	−	7.13065i	−0.0145473	−	0.0251966i	−0.873207	+	0.487349i	$0.837964\pi$
$284$	141.856	−	81.9005i	0.499492	−	0.288382i
$285$		0			0
$286$	138.287	−	239.520i	0.483522	−	0.837484i
$287$			39.2269i			0.136679i
$288$		0			0
$289$	−307.587			−1.06431
$290$	−85.0944	−	49.1292i	−0.293429	−	0.169411i
$291$		0			0
$292$	−81.2899	−	140.798i	−0.278390	−	0.482186i
$293$	−92.6650	+	53.5002i	−0.316263	+	0.182594i	−0.649726	−	0.760169i	$-0.725116\pi$
$293$	−92.6650	+	53.5002i	−0.316263	+	0.182594i	0.333463	+	0.942763i	$0.391783\pi$
$294$		0			0
$295$	−85.6646	+	148.375i	−0.290389	+	0.502968i
$296$			129.096i			0.436134i
$297$		0			0
$298$	−21.9740			−0.0737384
$299$	367.154	+	211.977i	1.22794	+	0.708952i
$300$		0			0
$301$	38.2453	+	66.2428i	0.127061	+	0.220076i
$302$	−32.8518	+	18.9670i	−0.108781	+	0.0628046i
$303$		0			0
$304$	53.1869	−	92.1224i	0.174957	−	0.303034i
$305$			89.0915i			0.292103i
$306$		0			0
$307$	540.799			1.76156			0.880780	−	0.473526i	$-0.157019\pi$
$307$	540.799			1.76156			0.880780	+	0.473526i	$0.157019\pi$
$308$	−86.4073	−	49.8873i	−0.280543	−	0.161972i
$309$		0			0
$310$	−6.22643	−	10.7845i	−0.0200853	−	0.0347887i
$311$	−226.920	+	131.012i	−0.729646	+	0.421261i	−0.818293	−	0.574802i	$-0.805079\pi$
$311$	−226.920	+	131.012i	−0.729646	+	0.421261i	0.0886465	+	0.996063i	$0.471746\pi$
$312$		0			0
$313$	−302.440	+	523.842i	−0.966262	+	1.67362i	−0.260077	+	0.965588i	$0.583748\pi$
$313$	−302.440	+	523.842i	−0.966262	+	1.67362i	−0.706185	+	0.708027i	$0.749585\pi$
$314$		−	150.096i		−	0.478013i
$315$		0			0
$316$	169.226			0.535525
$317$	−75.7622	−	43.7413i	−0.238997	−	0.137985i	0.375718	−	0.926734i	$-0.377396\pi$
$317$	−75.7622	−	43.7413i	−0.238997	−	0.137985i	−0.614716	+	0.788749i	$0.710729\pi$
$318$		0			0
$319$	204.893	+	354.885i	0.642297	+	1.11249i
$320$	22.1493	−	12.7879i	0.0692165	−	0.0399622i
$321$		0			0
$322$	76.4708	−	132.451i	0.237487	−	0.411340i
$323$		−	649.549i		−	2.01099i
$324$		0			0
$325$	153.289			0.471660
$326$	14.5687	+	8.41126i	0.0446894	+	0.0258014i
$327$		0			0
$328$	20.9677	+	36.3170i	0.0639258	+	0.110723i
$329$	−68.2110	+	39.3816i	−0.207328	+	0.119701i
$330$		0			0
$331$	−68.1379	+	118.018i	−0.205855	+	0.356551i	−0.950405	−	0.311016i	$-0.899331\pi$
$331$	−68.1379	+	118.018i	−0.205855	+	0.356551i	0.744550	+	0.667567i	$0.232664\pi$
$332$			230.718i			0.694935i
$333$		0			0
$334$	−197.133			−0.590219
$335$	−256.254	−	147.948i	−0.764937	−	0.441637i
$336$		0			0
$337$	−121.241	−	209.996i	−0.359767	−	0.623135i	0.628155	−	0.778088i	$-0.283810\pi$
$337$	−121.241	−	209.996i	−0.359767	−	0.623135i	−0.987922	+	0.154954i	$0.950477\pi$
$338$	75.2296	−	43.4338i	0.222573	−	0.128502i
$339$		0			0
$340$	78.0865	−	135.250i	0.229666	−	0.397793i
$341$			51.9345i			0.152301i
$342$		0			0
$343$	18.5203			0.0539949
$344$	70.8166	+	40.8860i	0.205862	+	0.118855i
$345$		0			0
$346$	162.208	+	280.952i	0.468808	+	0.811999i
$347$	−558.304	+	322.337i	−1.60894	+	0.928924i	−0.619338	+	0.785125i	$0.712599\pi$
$347$	−558.304	+	322.337i	−1.60894	+	0.928924i	−0.989607	+	0.143800i	$0.954068\pi$
$348$		0			0
$349$	−302.915	+	524.665i	−0.867952	+	1.50334i	−0.00386633	+	0.999993i	$0.501231\pi$
$349$	−302.915	+	524.665i	−0.867952	+	1.50334i	−0.864086	+	0.503345i	$0.832103\pi$
$350$		−	55.2993i		−	0.157998i
$351$		0			0
$352$	−106.663			−0.303021
$353$	−141.198	−	81.5210i	−0.399996	−	0.230938i	0.286487	−	0.958084i	$-0.407513\pi$
$353$	−141.198	−	81.5210i	−0.399996	−	0.230938i	−0.686482	+	0.727147i	$0.740846\pi$
$354$		0			0
$355$	130.917	+	226.755i	0.368780	+	0.638745i
$356$	23.7890	−	13.7346i	0.0668231	−	0.0385803i
$357$		0			0
$358$	−143.218	+	248.062i	−0.400051	+	0.692909i
$359$		−	227.325i		−	0.633217i	−0.948556	−	0.316608i	$-0.897456\pi$
$359$		−	227.325i		−	0.633217i	0.948556	−	0.316608i	$-0.102544\pi$
$360$		0			0
$361$	346.212			0.959036
$362$	5.14888	+	2.97270i	0.0142234	+	0.00821189i
$363$		0			0
$364$	27.4413	+	47.5298i	0.0753883	+	0.130576i
$365$	225.064	−	129.941i	0.616614	−	0.356002i
$366$		0			0
$367$	337.753	−	585.006i	0.920308	−	1.59402i	0.121370	−	0.992607i	$-0.461271\pi$
$367$	337.753	−	585.006i	0.920308	−	1.59402i	0.798938	−	0.601413i	$-0.205395\pi$
$368$		−	163.501i		−	0.444298i
$369$		0			0
$370$	−206.358			−0.557723
$371$	41.5642	+	23.9971i	0.112033	+	0.0646822i
$372$		0			0
$373$	−222.392	−	385.194i	−0.596225	−	1.03269i	−0.993373	−	0.114937i	$-0.963333\pi$
$373$	−222.392	−	385.194i	−0.596225	−	1.03269i	0.397148	−	0.917755i	$-0.370000\pi$
$374$	−564.057	+	325.658i	−1.50817	+	0.870745i
$375$		0			0
$376$	−42.1007	+	72.9206i	−0.111970	+	0.193938i
$377$		−	225.410i		−	0.597903i
$378$		0			0
$379$	586.241			1.54681			0.773405	−	0.633912i	$-0.218552\pi$
$379$	586.241			1.54681			0.773405	+	0.633912i	$0.218552\pi$
$380$	147.256	+	85.0186i	0.387517	+	0.223733i
$381$		0			0
$382$	192.269	+	333.020i	0.503323	+	0.871781i
$383$	130.125	−	75.1280i	0.339753	−	0.196157i	−0.320410	−	0.947279i	$-0.603821\pi$
$383$	130.125	−	75.1280i	0.339753	−	0.196157i	0.660163	+	0.751122i	$0.270487\pi$
$384$		0			0
$385$	79.7441	−	138.121i	0.207128	−	0.358755i
$386$			204.429i			0.529609i
$387$		0			0
$388$	223.171			0.575184
$389$	467.627	+	269.985i	1.20213	+	0.694048i	0.961028	−	0.276452i	$-0.0891587\pi$
$389$	467.627	+	269.985i	1.20213	+	0.694048i	0.241099	+	0.970500i	$0.422492\pi$
$390$		0			0
$391$	−499.193	−	864.628i	−1.27671	−	2.21132i
$392$	17.1464	−	9.89949i	0.0437409	−	0.0252538i
$393$		0			0
$394$	−37.5210	+	64.9882i	−0.0952309	+	0.164945i
$395$			270.505i			0.684824i
$396$		0			0
$397$	491.223			1.23734			0.618669	−	0.785652i	$-0.287672\pi$
$397$	491.223			1.23734			0.618669	+	0.785652i	$0.287672\pi$
$398$	−140.610	−	81.1813i	−0.353292	−	0.203973i
$399$		0			0
$400$	−29.5587	−	51.1972i	−0.0738968	−	0.127993i
$401$	187.085	−	108.014i	0.466546	−	0.269361i	−0.248247	−	0.968697i	$-0.579854\pi$
$401$	187.085	−	108.014i	0.466546	−	0.269361i	0.714793	+	0.699336i	$0.246521\pi$
$402$		0			0
$403$	14.2837	−	24.7401i	0.0354435	−	0.0613899i
$404$		−	289.863i		−	0.717483i
$405$		0			0
$406$	−81.3168			−0.200288
$407$	745.311	+	430.306i	1.83123	+	1.05726i
$408$		0			0
$409$	−52.8761	−	91.5842i	−0.129282	−	0.223922i	0.794117	−	0.607765i	$-0.207934\pi$
$409$	−52.8761	−	91.5842i	−0.129282	−	0.223922i	−0.923398	+	0.383843i	$0.874600\pi$
$410$	−58.0523	+	33.5165i	−0.141591	+	0.0817476i
$411$		0			0
$412$	−44.8103	+	77.6136i	−0.108763	+	0.188383i
$413$			141.789i			0.343314i
$414$		0			0
$415$	−368.800			−0.888675
$416$	50.8115	+	29.3360i	0.122143	+	0.0705193i
$417$		0			0
$418$	−354.569	−	614.131i	−0.848251	−	1.46921i
$419$	−11.5619	+	6.67526i	−0.0275940	+	0.0159314i	−0.513734	−	0.857950i	$-0.671738\pi$
$419$	−11.5619	+	6.67526i	−0.0275940	+	0.0159314i	0.486140	+	0.873881i	$0.338405\pi$
$420$		0			0
$421$	237.620	−	411.570i	0.564419	−	0.977602i	−0.432685	−	0.901545i	$-0.642434\pi$
$421$	237.620	−	411.570i	0.564419	−	0.977602i	0.997104	−	0.0760565i	$-0.0242329\pi$
$422$		−	510.473i		−	1.20965i
$423$		0			0
$424$	51.3080			0.121009
$425$	−312.625	−	180.494i	−0.735587	−	0.424692i
$426$		0			0
$427$	36.8652	+	63.8523i	0.0863353	+	0.149537i
$428$	−173.586	+	100.220i	−0.405574	+	0.234159i
$429$		0			0
$430$	−65.3557	+	113.199i	−0.151990	+	0.263254i
$431$		−	235.192i		−	0.545690i	−0.962058	−	0.272845i	$-0.912035\pi$
$431$		−	235.192i		−	0.545690i	0.962058	−	0.272845i	$-0.0879646\pi$
$432$		0			0
$433$	−21.0400			−0.0485913			−0.0242957	−	0.999705i	$-0.507734\pi$
$433$	−21.0400			−0.0485913			−0.0242957	+	0.999705i	$0.507734\pi$
$434$	−8.92504	−	5.15287i	−0.0205646	−	0.0118730i
$435$		0			0
$436$	−60.7449	−	105.213i	−0.139323	−	0.241315i
$437$	941.385	−	543.509i	2.15420	−	1.24373i
$438$		0			0
$439$	124.576	−	215.771i	0.283772	−	0.491507i	−0.688539	−	0.725199i	$-0.741748\pi$
$439$	124.576	−	215.771i	0.283772	−	0.491507i	0.972311	+	0.233693i	$0.0750809\pi$
$440$		−	170.500i		−	0.387500i
$441$		0			0
$442$	358.268			0.810561
$443$	−282.967	−	163.371i	−0.638751	−	0.368783i	0.145382	−	0.989376i	$-0.453559\pi$
$443$	−282.967	−	163.371i	−0.638751	−	0.368783i	−0.784133	+	0.620592i	$0.786892\pi$
$444$		0			0
$445$	21.9546	+	38.0264i	0.0493361	+	0.0854526i
$446$	253.347	−	146.270i	0.568043	−	0.327960i
$447$		0			0
$448$	10.5830	−	18.3303i	0.0236228	−	0.0409159i
$449$		−	510.632i		−	1.13727i	−0.822592	−	0.568633i	$-0.807473\pi$
$449$		−	510.632i		−	1.13727i	0.822592	−	0.568633i	$-0.192527\pi$
$450$		0			0
$451$	279.560			0.619868
$452$	−25.2255	−	14.5640i	−0.0558087	−	0.0322212i
$453$		0			0
$454$	−93.0842	−	161.227i	−0.205031	−	0.355125i
$455$	−75.9757	+	43.8646i	−0.166980	+	0.0964057i
$456$		0			0
$457$	90.5487	−	156.835i	0.198137	−	0.343184i	−0.749787	−	0.661679i	$-0.769844\pi$
$457$	90.5487	−	156.835i	0.198137	−	0.343184i	0.947924	+	0.318495i	$0.103178\pi$
$458$		−	334.501i		−	0.730351i
$459$		0			0
$460$	261.355			0.568163
$461$	−256.511	−	148.097i	−0.556423	−	0.321251i	0.195286	−	0.980746i	$-0.437437\pi$
$461$	−256.511	−	148.097i	−0.556423	−	0.321251i	−0.751709	+	0.659495i	$0.770770\pi$
$462$		0			0
$463$	−268.155	−	464.458i	−0.579169	−	1.00315i	−0.995575	−	0.0939712i	$-0.970044\pi$
$463$	−268.155	−	464.458i	−0.579169	−	1.00315i	0.416406	−	0.909179i	$-0.363289\pi$
$464$	−75.2847	+	43.4656i	−0.162252	+	0.0936760i
$465$		0			0
$466$	110.007	−	190.538i	0.236067	−	0.408880i
$467$			87.9169i			0.188259i	0.995560	+	0.0941294i	$0.0300068\pi$
$467$			87.9169i			0.188259i	−0.995560	+	0.0941294i	$0.969993\pi$
$468$		0			0
$469$	−244.878			−0.522128
$470$	−116.563	−	67.2975i	−0.248006	−	0.143186i
$471$		0			0
$472$	75.7892	+	131.271i	0.160570	+	0.278116i
$473$	472.096	−	272.565i	0.998089	−	0.576247i
$474$		0			0
$475$	196.517	−	340.378i	0.413720	−	0.716585i
$476$		−	129.246i		−	0.271524i
$477$		0			0
$478$	84.2818			0.176322
$479$	257.970	+	148.939i	0.538559	+	0.310937i	0.744495	−	0.667628i	$-0.232691\pi$
$479$	257.970	+	148.939i	0.538559	+	0.310937i	−0.205936	+	0.978565i	$0.566024\pi$
$480$		0			0
$481$	−236.697	−	409.971i	−0.492094	−	0.852331i
$482$	146.345	−	84.4926i	0.303621	−	0.175296i
$483$		0			0
$484$	−234.534	+	406.225i	−0.484575	+	0.839308i
$485$			356.737i			0.735539i
$486$		0			0
$487$	−441.814			−0.907215			−0.453608	−	0.891202i	$-0.649863\pi$
$487$	−441.814			−0.907215			−0.453608	+	0.891202i	$0.649863\pi$
$488$	68.2610	+	39.4105i	0.139879	+	0.0807593i
$489$		0			0
$490$	15.8242	+	27.4083i	0.0322943	+	0.0559354i
$491$	−288.654	+	166.655i	−0.587891	+	0.339419i	−0.764263	−	0.644905i	$-0.776897\pi$
$491$	−288.654	+	166.655i	−0.587891	+	0.339419i	0.176372	+	0.984324i	$0.443564\pi$
$492$		0			0
$493$	−265.413	+	459.710i	−0.538364	+	0.932474i
$494$			390.073i			0.789622i
$495$		0			0
$496$	−11.0173			−0.0222123
$497$	187.658	+	108.344i	0.377581	+	0.217996i
$498$		0			0
$499$	422.243	+	731.347i	0.846179	+	1.46563i	0.884593	+	0.466363i	$0.154436\pi$
$499$	422.243	+	731.347i	0.846179	+	1.46563i	−0.0384141	+	0.999262i	$0.512231\pi$
$500$	220.271	−	127.174i	0.440542	−	0.254347i
$501$		0			0
$502$	−341.658	+	591.769i	−0.680593	+	1.17882i
$503$		−	60.3243i		−	0.119929i	−0.998201	−	0.0599645i	$-0.980901\pi$
$503$		−	60.3243i		−	0.119929i	0.998201	−	0.0599645i	$-0.0190987\pi$
$504$		0			0
$505$	463.343			0.917510
$506$	−943.948	−	544.989i	−1.86551	−	1.07705i
$507$		0			0
$508$	221.852	+	384.259i	0.436717	+	0.756415i
$509$	−339.888	+	196.234i	−0.667756	+	0.385529i	−0.795226	−	0.606313i	$-0.792648\pi$
$509$	−339.888	+	196.234i	−0.667756	+	0.385529i	0.127470	+	0.991842i	$0.459314\pi$
$510$		0			0
$511$	107.536	−	186.259i	0.210443	−	0.364498i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−223.447			−0.434721
$515$	−124.064	−	71.6286i	−0.240902	−	0.139085i
$516$		0			0
$517$	280.663	+	486.123i	0.542869	+	0.940276i
$518$	−147.898	+	85.3887i	−0.285517	+	0.164843i
$519$		0			0
$520$	−46.8932	+	81.2215i	−0.0901793	+	0.156195i
$521$			45.5654i			0.0874577i	0.999043	+	0.0437288i	$0.0139238\pi$
$521$			45.5654i			0.0874577i	−0.999043	+	0.0437288i	$0.986076\pi$
$522$		0			0
$523$	445.063			0.850980			0.425490	−	0.904963i	$-0.360102\pi$
$523$	445.063			0.850980			0.425490	+	0.904963i	$0.360102\pi$
$524$	−5.86524	−	3.38630i	−0.0111932	−	0.00646240i
$525$		0			0
$526$	200.025	+	346.454i	0.380276	+	0.658658i
$527$	−58.2616	+	33.6374i	−0.110553	+	0.0638280i
$528$		0			0
$529$	570.898	−	988.825i	1.07920	−	1.86923i
$530$			82.0151i			0.154745i
$531$		0			0
$532$	140.719			0.264510
$533$	−133.175	−	76.8884i	−0.249859	−	0.144256i
$534$		0			0
$535$	−160.200	−	277.475i	−0.299439	−	0.518644i
$536$	−226.713	+	130.893i	−0.422972	+	0.244203i
$537$		0			0
$538$	88.6964	−	153.627i	0.164863	−	0.285551i
$539$		−	131.989i		−	0.244878i
$540$		0			0
$541$	302.399			0.558964			0.279482	−	0.960151i	$-0.409837\pi$
$541$	302.399			0.558964			0.279482	+	0.960151i	$0.409837\pi$
$542$	512.023	+	295.617i	0.944692	+	0.545418i
$543$		0			0
$544$	−69.0847	−	119.658i	−0.126994	−	0.219960i
$545$	168.182	−	97.0999i	0.308591	−	0.178165i
$546$		0			0
$547$	−169.176	+	293.021i	−0.309279	+	0.535688i	−0.978205	−	0.207642i	$-0.933421\pi$
$547$	−169.176	+	293.021i	−0.309279	+	0.535688i	0.668926	+	0.743329i	$0.266754\pi$
$548$			43.1756i			0.0787877i
$549$		0			0
$550$	−394.104			−0.716554
$551$	−500.520	−	288.975i	−0.908385	−	0.524456i
$552$		0			0
$553$	111.932	+	193.873i	0.202409	+	0.350583i
$554$	−559.355	+	322.944i	−1.00967	+	0.582931i
$555$		0			0
$556$	−60.3228	+	104.482i	−0.108494	+	0.187917i
$557$		−	250.404i		−	0.449559i	−0.974410	−	0.224780i	$-0.927834\pi$
$557$		−	250.404i		−	0.449559i	0.974410	−	0.224780i	$-0.0721662\pi$
$558$		0			0
$559$	−299.858			−0.536418
$560$	29.3007	+	16.9168i	0.0523228	+	0.0302086i
$561$		0			0
$562$	−180.546	−	312.714i	−0.321256	−	0.556431i
$563$	721.716	−	416.683i	1.28191	−	0.740112i	0.304713	−	0.952444i	$-0.401439\pi$
$563$	721.716	−	416.683i	1.28191	−	0.740112i	0.977197	+	0.212332i	$0.0681060\pi$
$564$		0			0
$565$	23.2803	−	40.3227i	0.0412041	−	0.0713676i
$566$		−	11.6443i		−	0.0205730i
$567$		0			0
$568$	231.650			0.407834
$569$	205.714	+	118.769i	0.361536	+	0.208733i	0.669754	−	0.742583i	$-0.266399\pi$
$569$	205.714	+	118.769i	0.361536	+	0.208733i	−0.308218	+	0.951316i	$0.599733\pi$
$570$		0			0
$571$	−396.747	−	687.186i	−0.694829	−	1.20348i	−0.970238	−	0.242152i	$-0.922147\pi$
$571$	−396.747	−	687.186i	−0.694829	−	1.20348i	0.275410	−	0.961327i	$-0.411186\pi$
$572$	338.733	−	195.568i	0.592191	−	0.341901i
$573$		0			0
$574$	−27.7376	+	48.0429i	−0.0483233	+	0.0836985i
$575$		−	604.112i		−	1.05063i
$576$		0			0
$577$	−164.298			−0.284745			−0.142372	−	0.989813i	$-0.545473\pi$
$577$	−164.298			−0.284745			−0.142372	+	0.989813i	$0.545473\pi$
$578$	−376.715	−	217.497i	−0.651757	−	0.376292i
$579$		0			0
$580$	−69.4792	−	120.342i	−0.119792	−	0.207485i
$581$	−264.321	+	152.606i	−0.454942	+	0.262661i
$582$		0			0
$583$	171.021	−	296.218i	0.293347	−	0.508092i
$584$		−	229.923i		−	0.393703i
$585$		0			0
$586$	−151.321			−0.258227
$587$	796.533	+	459.879i	1.35696	+	0.783439i	0.989212	−	0.146488i	$-0.0467969\pi$
$587$	796.533	+	459.879i	1.35696	+	0.783439i	0.367744	+	0.929927i	$0.380130\pi$
$588$		0			0
$589$	−36.6235	−	63.4338i	−0.0621792	−	0.107697i
$590$	−209.835	+	121.148i	−0.355652	+	0.205336i
$591$		0			0
$592$	−91.2844	+	158.109i	−0.154197	+	0.267076i
$593$			1156.90i			1.95092i	0.220178	+	0.975460i	$0.429336\pi$
$593$			1156.90i			1.95092i	−0.220178	+	0.975460i	$0.570664\pi$
$594$		0			0
$595$	206.597			0.347222
$596$	−26.9126	−	15.5380i	−0.0451553	−	0.0260704i
$597$		0			0
$598$	299.780	+	519.235i	0.501305	+	0.868285i
$599$	784.703	−	453.049i	1.31002	−	0.756342i	0.327923	−	0.944705i	$-0.393651\pi$
$599$	784.703	−	453.049i	1.31002	−	0.756342i	0.982100	+	0.188363i	$0.0603181\pi$
$600$		0			0
$601$	−529.218	+	916.632i	−0.880562	+	1.52518i	−0.0298440	+	0.999555i	$0.509501\pi$
$601$	−529.218	+	916.632i	−0.880562	+	1.52518i	−0.850718	+	0.525623i	$0.823832\pi$
$602$			108.174i			0.179691i
$603$		0			0
$604$	−53.6468			−0.0888192
$605$	−649.345	−	374.900i	−1.07330	−	0.619669i
$606$		0			0
$607$	461.576	+	799.472i	0.760421	+	1.31709i	0.942634	+	0.333829i	$0.108341\pi$
$607$	461.576	+	799.472i	0.760421	+	1.31709i	−0.182213	+	0.983259i	$0.558326\pi$
$608$	130.281	−	75.2177i	0.214278	−	0.123713i
$609$		0			0
$610$	−62.9972	+	109.114i	−0.103274	+	0.178876i
$611$		−	308.767i		−	0.505347i
$612$		0			0
$613$	−613.947			−1.00154			−0.500772	−	0.865579i	$-0.666951\pi$
$613$	−613.947			−1.00154			−0.500772	+	0.865579i	$0.666951\pi$
$614$	662.341	+	382.403i	1.07873	+	0.622805i
$615$		0			0
$616$	−70.5512	−	122.198i	−0.114531	−	0.198374i
$617$	−460.026	+	265.596i	−0.745585	+	0.430464i	−0.824096	−	0.566450i	$-0.808317\pi$
$617$	−460.026	+	265.596i	−0.745585	+	0.430464i	0.0785114	+	0.996913i	$0.474983\pi$
$618$		0			0
$619$	−210.891	+	365.273i	−0.340695	+	0.590102i	−0.984562	−	0.175036i	$-0.943996\pi$
$619$	−210.891	+	365.273i	−0.340695	+	0.590102i	0.643867	+	0.765138i	$0.277329\pi$
$620$		−	17.6110i		−	0.0284049i
$621$		0			0
$622$	−370.559			−0.595754
$623$	31.4699	+	18.1692i	0.0505135	+	0.0291640i
$624$		0			0
$625$	18.5432	+	32.1177i	0.0296691	+	0.0513883i
$626$	−740.824	+	427.715i	−1.18342	+	0.683250i
$627$		0			0
$628$	106.134	−	183.829i	0.169003	−	0.292722i
$629$			1114.82i			1.77236i
$630$		0			0
$631$	−552.102			−0.874964			−0.437482	−	0.899227i	$-0.644130\pi$
$631$	−552.102			−0.874964			−0.437482	+	0.899227i	$0.644130\pi$
$632$	207.259	+	119.661i	0.327941	+	0.189337i
$633$		0			0
$634$	−61.8595	−	107.144i	−0.0975703	−	0.168997i
$635$	−614.233	+	354.628i	−0.967296	+	0.558469i
$636$		0			0
$637$	−36.3015	+	62.8760i	−0.0569882	+	0.0987064i
$638$			579.524i			0.908346i
$639$		0			0
$640$	36.1696			0.0565150
$641$	−391.148	−	225.829i	−0.610215	−	0.352308i	0.162834	−	0.986653i	$-0.447936\pi$
$641$	−391.148	−	225.829i	−0.610215	−	0.352308i	−0.773050	+	0.634345i	$0.781270\pi$
$642$		0			0
$643$	409.507	+	709.287i	0.636869	+	1.10309i	0.986116	+	0.166059i	$0.0531041\pi$
$643$	409.507	+	709.287i	0.636869	+	1.10309i	−0.349247	+	0.937031i	$0.613563\pi$
$644$	187.314	−	108.146i	0.290861	−	0.167929i
$645$		0			0
$646$	459.300	−	795.531i	0.710991	−	1.23147i
$647$			908.400i			1.40402i	0.712168	+	0.702009i	$0.247714\pi$
$647$			908.400i			1.40402i	−0.712168	+	0.702009i	$0.752286\pi$
$648$		0			0
$649$	1010.49			1.55700
$650$	187.740	+	108.392i	0.288831	+	0.166757i
$651$		0			0
$652$	11.8953	+	20.6033i	0.0182444	+	0.0316002i
$653$	199.877	−	115.399i	0.306090	−	0.176721i	−0.339085	−	0.940756i	$-0.610118\pi$
$653$	199.877	−	115.399i	0.306090	−	0.176721i	0.645176	+	0.764034i	$0.276784\pi$
$654$		0			0
$655$	5.41295	−	9.37551i	0.00826405	−	0.0143137i
$656$			59.3055i			0.0904047i
$657$		0			0
$658$	−111.388			−0.169283
$659$	39.7641	+	22.9578i	0.0603400	+	0.0348373i	0.529867	−	0.848081i	$-0.322242\pi$
$659$	39.7641	+	22.9578i	0.0603400	+	0.0348373i	−0.469526	+	0.882918i	$0.655575\pi$
$660$		0			0
$661$	−169.751	−	294.018i	−0.256810	−	0.444808i	0.708576	−	0.705635i	$-0.249338\pi$
$661$	−169.751	−	294.018i	−0.256810	−	0.444808i	−0.965386	+	0.260827i	$0.916005\pi$
$662$	−166.903	+	96.3615i	−0.252119	+	0.145561i
$663$		0			0
$664$	−163.143	+	282.571i	−0.245697	+	0.425559i
$665$			224.938i			0.338253i
$666$		0			0
$667$	−888.337			−1.33184
$668$	−241.438	−	139.394i	−0.361434	−	0.208674i
$669$		0			0
$670$	−209.230	−	362.398i	−0.312284	−	0.540892i
$671$	455.060	−	262.729i	0.678181	−	0.391548i
$672$		0			0
$673$	263.886	−	457.063i	0.392104	−	0.679143i	−0.600623	−	0.799532i	$-0.705081\pi$
$673$	263.886	−	457.063i	0.392104	−	0.679143i	0.992727	+	0.120389i	$0.0384142\pi$
$674$		−	342.923i		−	0.508787i
$675$		0			0
$676$	122.849			0.181730
$677$	−162.175	−	93.6317i	−0.239549	−	0.138304i	0.375420	−	0.926855i	$-0.377498\pi$
$677$	−162.175	−	93.6317i	−0.239549	−	0.138304i	−0.614970	+	0.788551i	$0.710832\pi$
$678$		0			0
$679$	147.614	+	255.675i	0.217399	+	0.376546i
$680$	191.272	−	110.431i	0.281282	−	0.162398i
$681$		0			0
$682$	−36.7232	+	63.6065i	−0.0538464	+	0.0932647i
$683$			575.317i			0.842338i	0.906982	+	0.421169i	$0.138380\pi$
$683$			575.317i			0.842338i	−0.906982	+	0.421169i	$0.861620\pi$
$684$		0			0
$685$	−69.0157			−0.100753
$686$	22.6826	+	13.0958i	0.0330650	+	0.0190901i
$687$		0			0
$688$	57.8215	+	100.150i	0.0840428	+	0.145566i
$689$	−162.940	+	94.0733i	−0.236487	+	0.136536i
$690$		0			0
$691$	−269.115	+	466.122i	−0.389458	+	0.674561i	−0.992377	−	0.123242i	$-0.960671\pi$
$691$	−269.115	+	466.122i	−0.389458	+	0.674561i	0.602919	+	0.797803i	$0.294004\pi$
$692$			458.792i			0.662994i
$693$		0			0
$694$	−911.706			−1.31370
$695$	−167.013	−	96.4251i	−0.240307	−	0.138741i
$696$		0			0
$697$	181.068	+	313.619i	0.259782	+	0.449955i
$698$	−741.988	+	428.387i	−1.06302	+	0.613735i
$699$		0			0
$700$	39.1025	−	67.7276i	0.0558607	−	0.0967536i
$701$			356.636i			0.508753i	0.967105	+	0.254376i	$0.0818702\pi$
$701$			356.636i			0.508753i	−0.967105	+	0.254376i	$0.918130\pi$
$702$		0			0
$703$	−1213.78			−1.72658
$704$	−130.636	−	75.4224i	−0.185562	−	0.107134i
$705$		0			0
$706$	−115.288	−	199.685i	−0.163298	−	0.282840i
$707$	332.080	−	191.727i	0.469703	−	0.271183i
$708$		0			0
$709$	200.807	−	347.809i	0.283226	−	0.490562i	−0.688951	−	0.724808i	$-0.741929\pi$
$709$	200.807	−	347.809i	0.283226	−	0.490562i	0.972177	+	0.234245i	$0.0752619\pi$
$710$			370.289i			0.521533i
$711$		0			0
$712$	38.8473			0.0545608
$713$	−97.5007	−	56.2920i	−0.136747	−	0.0789510i
$714$		0			0
$715$	312.612	+	541.460i	0.437220	+	0.757287i
$716$	−350.812	+	202.541i	−0.489961	+	0.282879i
$717$		0			0
$718$	160.743	−	278.415i	0.223876	−	0.387764i
$719$		−	916.413i		−	1.27457i	−0.770630	−	0.637283i	$-0.780058\pi$
$719$		−	916.413i		−	1.27457i	0.770630	−	0.637283i	$-0.219942\pi$
$720$		0			0
$721$	−118.557			−0.164434
$722$	424.021	+	244.809i	0.587287	+	0.339070i
$723$		0			0
$724$	4.20404	+	7.28161i	0.00580668	+	0.0100575i
$725$	−278.165	+	160.599i	−0.383676	+	0.221515i
$726$		0			0
$727$	−354.343	+	613.739i	−0.487404	+	0.844208i	−0.999895	−	0.0144843i	$-0.995389\pi$
$727$	−354.343	+	613.739i	−0.487404	+	0.844208i	0.512491	+	0.858692i	$0.328723\pi$
$728$			77.6158i			0.106615i
$729$		0			0
$730$	367.528			0.503463
$731$	611.542	+	353.074i	0.836583	+	0.483002i
$732$		0			0
$733$	−640.861	−	1110.00i	−0.874298	−	1.51433i	−0.857508	−	0.514470i	$-0.827989\pi$
$733$	−640.861	−	1110.00i	−0.874298	−	1.51433i	−0.0167898	−	0.999859i	$-0.505345\pi$
$734$	827.323	−	477.655i	1.12714	−	0.650756i
$735$		0			0
$736$	115.613	−	200.248i	0.157083	−	0.272076i
$737$			1745.19i			2.36796i
$738$		0			0
$739$	−1077.96			−1.45867			−0.729336	−	0.684155i	$-0.760171\pi$
$739$	−1077.96			−1.45867			−0.729336	+	0.684155i	$0.760171\pi$
$740$	−252.735	−	145.917i	−0.341534	−	0.197185i
$741$		0			0
$742$	33.9370	+	58.7807i	0.0457372	+	0.0792192i
$743$	229.237	−	132.350i	0.308529	−	0.178130i	−0.337739	−	0.941240i	$-0.609662\pi$
$743$	229.237	−	132.350i	0.308529	−	0.178130i	0.646268	+	0.763110i	$0.276329\pi$
$744$		0			0
$745$	24.8373	−	43.0194i	0.0333386	−	0.0577442i
$746$		−	629.019i		−	0.843189i
$747$		0			0
$748$	−921.101			−1.23142
$749$	−229.633	−	132.578i	−0.306585	−	0.177007i
$750$		0			0
$751$	18.2733	+	31.6504i	0.0243320	+	0.0421443i	0.877935	−	0.478780i	$-0.158921\pi$
$751$	18.2733	+	31.6504i	0.0243320	+	0.0421443i	−0.853603	+	0.520924i	$0.825587\pi$
$752$	−103.125	+	59.5395i	−0.137135	+	0.0791748i
$753$		0			0
$754$	159.389	−	276.069i	0.211391	−	0.366140i
$755$		−	85.7536i		−	0.113581i
$756$		0			0
$757$	299.469			0.395600			0.197800	−	0.980242i	$-0.436620\pi$
$757$	299.469			0.395600			0.197800	+	0.980242i	$0.436620\pi$
$758$	717.996	+	414.535i	0.947224	+	0.546880i
$759$		0			0
$760$	120.234	+	208.252i	0.158203	+	0.274016i
$761$	437.315	−	252.484i	0.574658	−	0.331779i	−0.184350	−	0.982861i	$-0.559018\pi$
$761$	437.315	−	252.484i	0.574658	−	0.331779i	0.759008	+	0.651082i	$0.225685\pi$
$762$		0			0
$763$	80.3579	−	139.184i	0.105318	−	0.182417i
$764$			543.820i			0.711806i
$765$		0			0
$766$	212.494			0.277407
$767$	−481.371	−	277.919i	−0.627602	−	0.362346i
$768$		0			0
$769$	376.324	+	651.812i	0.489368	+	0.847610i	0.999925	−	0.0122340i	$-0.00389431\pi$
$769$	376.324	+	651.812i	0.489368	+	0.847610i	−0.510558	+	0.859844i	$0.670561\pi$
$770$	195.332	−	112.775i	0.253678	−	0.146461i
$771$		0			0
$772$	−144.553	+	250.374i	−0.187245	+	0.324318i
$773$		−	4.76817i		−	0.00616840i	−0.999995	−	0.00308420i	$-0.999018\pi$
$773$		−	4.76817i		−	0.00616840i	0.999995	−	0.00308420i	$-0.000981732\pi$
$774$		0			0
$775$	−40.7072			−0.0525254
$776$	273.328	+	157.806i	0.352227	+	0.203358i
$777$		0			0
$778$	381.816	+	661.325i	0.490766	+	0.850032i
$779$	−341.460	+	197.142i	−0.438332	+	0.253071i
$780$		0			0
$781$	772.142	−	1337.39i	0.988658	−	1.71241i
$782$		−	1411.93i		−	1.80554i
$783$		0			0
$784$	28.0000			0.0357143
$785$	293.849	+	169.654i	0.374329	+	0.216119i
$786$		0			0
$787$	424.871	+	735.899i	0.539862	+	0.935068i	0.998911	+	0.0466572i	$0.0148569\pi$
$787$	424.871	+	735.899i	0.539862	+	0.935068i	−0.459049	+	0.888411i	$0.651810\pi$
$788$	−91.9072	+	53.0627i	−0.116634	+	0.0673384i
$789$		0			0
$790$	−191.276	+	331.300i	−0.242122	+	0.419367i
$791$		−	38.5327i		−	0.0487139i
$792$		0			0
$793$	−289.037			−0.364485
$794$	601.623	+	347.347i	0.757711	+	0.437465i
$795$		0			0
$796$	−114.808	−	198.853i	−0.144231	−	0.249815i
$797$	166.295	−	96.0104i	0.208651	−	0.120465i	−0.392033	−	0.919951i	$-0.628228\pi$
$797$	166.295	−	96.0104i	0.208651	−	0.120465i	0.600684	+	0.799486i	$0.294895\pi$
$798$		0			0
$799$	−363.565	+	629.712i	−0.455025	+	0.788126i
$800$		−	83.6047i		−	0.104506i
$801$		0			0
$802$	305.508			0.380933
$803$	−1327.42	−	766.386i	−1.65307	−	0.954403i
$804$		0			0
$805$	172.870	+	299.420i	0.214745	+	0.371950i
$806$	34.9878	−	20.2002i	0.0434092	−	0.0250623i
$807$		0			0
$808$	204.964	−	355.009i	0.253669	−	0.439367i
$809$		−	1015.55i		−	1.25532i	−0.778488	−	0.627660i	$-0.784013\pi$
$809$		−	1015.55i		−	1.25532i	0.778488	−	0.627660i	$-0.215987\pi$
$810$		0			0
$811$	481.576			0.593805			0.296902	−	0.954908i	$-0.404046\pi$
$811$	481.576			0.593805			0.296902	+	0.954908i	$0.404046\pi$
$812$	−99.5923	−	57.4996i	−0.122651	−	0.0708124i
$813$		0			0
$814$	608.544	+	1054.03i	0.747597	+	1.29488i
$815$	−32.9341	+	19.0145i	−0.0404099	+	0.0233307i
$816$		0			0
$817$	−384.418	+	665.832i	−0.470524	+	0.814972i
$818$		−	149.556i		−	0.182832i
$819$		0			0
$820$	−94.7990			−0.115609
$821$	−415.980	−	240.166i	−0.506675	−	0.292529i	0.224791	−	0.974407i	$-0.427830\pi$
$821$	−415.980	−	240.166i	−0.506675	−	0.292529i	−0.731466	+	0.681878i	$0.761164\pi$
$822$		0			0
$823$	−294.402	−	509.919i	−0.357718	−	0.619586i	0.629861	−	0.776708i	$-0.283112\pi$
$823$	−294.402	−	509.919i	−0.357718	−	0.619586i	−0.987579	+	0.157122i	$0.949779\pi$
$824$	−109.762	+	63.3713i	−0.133207	+	0.0769069i
$825$		0			0
$826$	−100.260	+	173.655i	−0.121380	+	0.210236i
$827$			280.409i			0.339068i	0.985524	+	0.169534i	$0.0542262\pi$
$827$			280.409i			0.339068i	−0.985524	+	0.169534i	$0.945774\pi$
$828$		0			0
$829$	190.758			0.230106			0.115053	−	0.993359i	$-0.463296\pi$
$829$	190.758			0.230106			0.115053	+	0.993359i	$0.463296\pi$
$830$	−451.686	−	260.781i	−0.544200	−	0.314194i
$831$		0			0
$832$	41.4874	+	71.8583i	0.0498647	+	0.0863681i
$833$	148.069	−	85.4879i	0.177754	−	0.102627i
$834$		0			0
$835$	222.820	−	385.935i	0.266850	−	0.462198i
$836$		−	1002.87i		−	1.19961i
$837$		0			0
$838$	−18.8805			−0.0225304
$839$	929.306	+	536.535i	1.10763	+	0.639493i	0.938216	−	0.346051i	$-0.112478\pi$
$839$	929.306	+	536.535i	1.10763	+	0.639493i	0.169419	+	0.985544i	$0.445811\pi$
$840$		0			0
$841$	−184.342	−	319.290i	−0.219194	−	0.379655i
$842$	582.048	−	336.046i	0.691269	−	0.399104i
$843$		0			0
$844$	360.959	−	625.200i	0.427677	−	0.740758i
$845$			196.373i			0.232394i
$846$		0			0
$847$	−620.519			−0.732608
$848$	62.8392	+	36.2802i	0.0741028	+	0.0427833i
$849$		0			0
$850$	−255.257	−	442.118i	−0.300302	−	0.520139i
$851$	−1615.69	+	932.821i	−1.89858	+	1.09615i
$852$		0			0
$853$	504.339	−	873.540i	0.591253	−	1.02408i	−0.402811	−	0.915283i	$-0.631967\pi$
$853$	504.339	−	873.540i	0.591253	−	1.02408i	0.994064	−	0.108797i	$-0.0346998\pi$
$854$			104.270i			0.122097i
$855$		0			0
$856$	−283.465			−0.331150
$857$	261.331	+	150.880i	0.304937	+	0.176055i	0.644659	−	0.764471i	$-0.277000\pi$
$857$	261.331	+	150.880i	0.304937	+	0.176055i	−0.339722	+	0.940526i	$0.610333\pi$
$858$		0			0
$859$	−544.251	−	942.670i	−0.633587	−	1.09740i	−0.986813	−	0.161866i	$-0.948249\pi$
$859$	−544.251	−	942.670i	−0.633587	−	1.09740i	0.353226	−	0.935538i	$-0.385085\pi$
$860$	−160.088	+	92.4269i	−0.186149	+	0.107473i
$861$		0			0
$862$	166.306	−	288.051i	0.192930	−	0.334165i
$863$		−	1120.50i		−	1.29838i	−0.760627	−	0.649189i	$-0.775108\pi$
$863$		−	1120.50i		−	1.29838i	0.760627	−	0.649189i	$-0.224892\pi$
$864$		0			0
$865$	−733.373			−0.847830
$866$	−25.7687	−	14.8776i	−0.0297560	−	0.0171796i
$867$		0			0
$868$	−7.28726	−	12.6219i	−0.00839546	−	0.0145414i
$869$	1381.68	−	797.715i	1.58997	−	0.917969i
$870$		0			0
$871$	479.985	−	831.358i	0.551073	−	0.954486i
$872$		−	171.812i		−	0.197033i
$873$		0			0
$874$	1537.27			1.75890
$875$	291.391	+	168.235i	0.333019	+	0.192268i
$876$		0			0
$877$	−22.9814	−	39.8049i	−0.0262046	−	0.0453876i	0.852626	−	0.522522i	$-0.175009\pi$
$877$	−22.9814	−	39.8049i	−0.0262046	−	0.0453876i	−0.878830	+	0.477134i	$0.841675\pi$
$878$	305.147	−	176.177i	0.347548	−	0.200657i
$879$		0			0
$880$	120.562	−	208.819i	0.137002	−	0.237294i
$881$		−	881.775i		−	1.00088i	−0.865771	−	0.500440i	$-0.833172\pi$
$881$		−	881.775i		−	1.00088i	0.865771	−	0.500440i	$-0.166828\pi$
$882$		0			0
$883$	216.488			0.245174			0.122587	−	0.992458i	$-0.460881\pi$
$883$	216.488			0.245174			0.122587	+	0.992458i	$0.460881\pi$
$884$	438.787	+	253.334i	0.496365	+	0.286577i
$885$		0			0
$886$	−231.041	−	400.175i	−0.260769	−	0.451665i
$887$	−123.029	+	71.0306i	−0.138702	+	0.0800796i	−0.567745	−	0.823204i	$-0.692184\pi$
$887$	−123.029	+	71.0306i	−0.138702	+	0.0800796i	0.429043	+	0.903284i	$0.358851\pi$
$888$		0			0
$889$	−293.483	+	508.327i	−0.330127	+	0.571796i
$890$			62.0969i			0.0697718i
$891$		0			0
$892$	413.714			0.463805
$893$	−685.615	−	395.840i	−0.767766	−	0.443270i
$894$		0			0
$895$	−323.760	−	560.768i	−0.361743	−	0.626557i
$896$	25.9230	−	14.9666i	0.0289319	−	0.0167038i
$897$		0			0
$898$	361.071	−	625.394i	0.402084	−	0.696430i
$899$			59.8593i			0.0665843i
$900$		0			0
$901$	443.074			0.491758
$902$	342.390	+	197.679i	0.379590	+	0.219156i
$903$		0			0
$904$	−20.5966	−	35.6743i	−0.0227838	−	0.0394627i
$905$	−11.6396	+	6.72010i	−0.0128614	+	0.00742552i
$906$		0			0
$907$	225.530	−	390.629i	0.248655	−	0.430683i	−0.714498	−	0.699637i	$-0.753345\pi$
$907$	225.530	−	390.629i	0.248655	−	0.430683i	0.963153	+	0.268955i	$0.0866782\pi$
$908$		−	263.282i		−	0.289958i
$909$		0			0
$910$	−124.068			−0.136338
$911$	−856.971	−	494.772i	−0.940692	−	0.543109i	−0.0505152	−	0.998723i	$-0.516086\pi$
$911$	−856.971	−	494.772i	−0.940692	−	0.543109i	−0.890177	+	0.455614i	$0.849420\pi$
$912$		0			0
$913$	1087.58	+	1883.75i	1.19122	+	2.06325i
$914$	221.798	−	128.055i	0.242667	−	0.140104i
$915$		0			0
$916$	236.528	−	409.678i	0.258218	−	0.447247i
$917$		−	8.95930i		−	0.00977023i
$918$		0			0
$919$	942.500			1.02557			0.512786	−	0.858517i	$-0.328614\pi$
$919$	942.500			1.02557			0.512786	+	0.858517i	$0.328614\pi$
$920$	320.093	+	184.806i	0.347927	+	0.200876i
$921$		0			0
$922$	−209.440	−	362.761i	−0.227159	−	0.393451i
$923$	−735.654	+	424.730i	−0.797025	+	0.460162i
$924$		0			0
$925$	−337.281	+	584.188i	−0.364628	+	0.631555i
$926$		−	758.457i		−	0.819068i
$927$		0			0
$928$	−122.939			−0.132478
$929$	545.923	+	315.189i	0.587646	+	0.339278i	0.764166	−	0.645019i	$-0.223151\pi$
$929$	545.923	+	315.189i	0.587646	+	0.339278i	−0.176520	+	0.984297i	$0.556484\pi$
$930$		0			0
$931$	93.0771	+	161.214i	0.0999754	+	0.173162i
$932$	269.462	−	155.574i	0.289122	−	0.166925i
$933$		0			0
$934$	−62.1666	+	107.676i	−0.0665596	+	0.115285i
$935$		−	1472.37i		−	1.57473i
$936$		0			0
$937$	236.083			0.251956			0.125978	−	0.992033i	$-0.459793\pi$
$937$	236.083			0.251956			0.125978	+	0.992033i	$0.459793\pi$
$938$	−299.913	−	173.155i	−0.319737	−	0.184600i
$939$		0			0
$940$	−95.1730	−	164.844i	−0.101248	−	0.175366i
$941$	−721.947	+	416.816i	−0.767213	+	0.442950i	−0.831879	−	0.554956i	$-0.812735\pi$
$941$	−721.947	+	416.816i	−0.767213	+	0.442950i	0.0646667	+	0.997907i	$0.479402\pi$
$942$		0			0
$943$	−303.017	+	524.840i	−0.321333	+	0.556564i
$944$			214.364i			0.227081i
$945$		0			0
$946$	770.930			0.814936
$947$	−680.541	−	392.911i	−0.718628	−	0.414900i	0.0956192	−	0.995418i	$-0.469517\pi$
$947$	−680.541	−	392.911i	−0.718628	−	0.414900i	−0.814248	+	0.580518i	$0.802850\pi$
$948$		0			0
$949$	421.564	+	730.170i	0.444219	+	0.769409i
$950$	481.367	−	277.917i	0.506702	−	0.292544i
$951$		0			0
$952$	91.3904	−	158.293i	0.0959984	−	0.166274i
$953$			1096.70i			1.15079i	0.817875	+	0.575396i	$0.195152\pi$
$953$			1096.70i			1.15079i	−0.817875	+	0.575396i	$0.804848\pi$
$954$		0			0
$955$	−869.289			−0.910250
$956$	103.224	+	59.5962i	0.107975	+	0.0623392i
$957$		0			0
$958$	210.631	+	364.824i	0.219866	+	0.380818i
$959$	−49.4639	+	28.5580i	−0.0515786	+	0.0297789i
$960$		0			0
$961$	476.707	−	825.680i	0.496053	−	0.859189i
$962$		−	669.480i		−	0.695925i
$963$		0			0
$964$	238.981			0.247906
$965$	−400.219	−	231.066i	−0.414735	−	0.239447i
$966$		0			0
$967$	−647.975	−	1122.33i	−0.670088	−	1.16063i	−0.977879	−	0.209172i	$-0.932923\pi$
$967$	−647.975	−	1122.33i	−0.670088	−	1.16063i	0.307791	−	0.951454i	$-0.400410\pi$
$968$	−574.489	+	331.681i	−0.593480	+	0.342646i
$969$		0			0
$970$	−252.251	+	436.911i	−0.260052	+	0.450424i
$971$		−	830.704i		−	0.855514i	−0.903894	−	0.427757i	$-0.859304\pi$
$971$		−	830.704i		−	0.855514i	0.903894	−	0.427757i	$-0.140696\pi$
$972$		0			0
$973$	−159.599			−0.164028
$974$	−541.109	−	312.410i	−0.555554	−	0.320749i
$975$		0			0
$976$	55.7349	+	96.5357i	0.0571054	+	0.0989095i
$977$	444.638	−	256.712i	0.455105	−	0.262755i	−0.254879	−	0.966973i	$-0.582036\pi$
$977$	444.638	−	256.712i	0.455105	−	0.262755i	0.709984	+	0.704218i	$0.248702\pi$
$978$		0			0
$979$	129.487	−	224.278i	0.132265	−	0.229089i
$980$			44.7576i			0.0456710i
$981$		0			0
$982$	−471.371			−0.480011
$983$	−765.485	−	441.953i	−0.778723	−	0.449596i	0.0572543	−	0.998360i	$-0.481765\pi$
$983$	−765.485	−	441.953i	−0.778723	−	0.449596i	−0.835978	+	0.548764i	$0.815099\pi$
$984$		0			0
$985$	−84.8199	−	146.912i	−0.0861116	−	0.149150i
$986$	−650.128	+	375.351i	−0.659359	+	0.380681i
$987$		0			0
$988$	−275.823	+	477.740i	−0.279173	+	0.483543i
$989$			1181.74i			1.19488i
$990$		0			0
$991$	1014.86			1.02407			0.512036	−	0.858964i	$-0.328891\pi$
$991$	1014.86			1.02407			0.512036	+	0.858964i	$0.328891\pi$
$992$	−13.4934	−	7.79041i	−0.0136022	−	0.00785324i
$993$		0			0
$994$	153.222	+	265.388i	0.154147	+	0.266990i
$995$	317.863	−	183.519i	0.319461	−	0.184441i
$996$		0			0
$997$	−617.454	+	1069.46i	−0.619312	+	1.07268i	0.370299	+	0.928913i	$0.379255\pi$
$997$	−617.454	+	1069.46i	−0.619312	+	1.07268i	−0.989611	+	0.143768i	$0.954078\pi$
$998$			1194.28i			1.19668i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.q.a.197.9		24
3.2	odd	2		126.3.q.a.29.1	✓	24
9.2	odd	6		1134.3.b.c.323.20		24
9.4	even	3		126.3.q.a.113.1	yes	24
9.5	odd	6	inner	378.3.q.a.71.9		24
9.7	even	3		1134.3.b.c.323.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.1	✓	24	3.2	odd	2
126.3.q.a.113.1	yes	24	9.4	even	3
378.3.q.a.71.9		24	9.5	odd	6	inner
378.3.q.a.197.9		24	1.1	even	1	trivial
1134.3.b.c.323.5		24	9.7	even	3
1134.3.b.c.323.20		24	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-2.76866 + 1.59849i) q^{5} +(-1.32288 + 2.29129i) q^{7} +2.82843i q^{8} -4.52120 q^{10} +(16.3294 + 9.42781i) q^{11} +(-5.18593 - 8.98229i) q^{13} +(-3.24037 + 1.87083i) q^{14} +(-2.00000 + 3.46410i) q^{16} +24.4251i q^{17} -26.5935 q^{19} +(-5.53732 - 3.19697i) q^{20} +(13.3329 + 23.0933i) q^{22} +(-35.3991 + 20.4377i) q^{23} +(-7.38968 + 12.7993i) q^{25} -14.6680i q^{26} -5.29150 q^{28} +(18.8212 + 10.8664i) q^{29} +(1.37716 + 2.38532i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-17.2712 + 29.9145i) q^{34} -8.45840i q^{35} +45.6422 q^{37} +(-32.5702 - 18.8044i) q^{38} +(-4.52120 - 7.83095i) q^{40} +(12.8400 - 7.41318i) q^{41} +(14.4554 - 25.0374i) q^{43} +37.7112i q^{44} -57.8065 q^{46} +(25.7813 + 14.8849i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-18.1009 + 10.4506i) q^{50} +(10.3719 - 17.9646i) q^{52} -18.1401i q^{53} -60.2809 q^{55} +(-6.48074 - 3.74166i) q^{56} +(15.3674 + 26.6172i) q^{58} +(46.4112 - 26.7955i) q^{59} +(13.9337 - 24.1339i) q^{61} +3.89520i q^{62} -8.00000 q^{64} +(28.7161 + 16.5793i) q^{65} +(46.2776 + 80.1552i) q^{67} +(-42.3056 + 24.4251i) q^{68} +(5.98099 - 10.3594i) q^{70} -81.9005i q^{71} -81.2899 q^{73} +(55.9000 + 32.2739i) q^{74} +(-26.5935 - 46.0612i) q^{76} +(-43.2036 + 24.9436i) q^{77} +(42.3065 - 73.2770i) q^{79} -12.7879i q^{80} +20.9677 q^{82} +(99.9040 + 57.6796i) q^{83} +(-39.0432 - 67.6249i) q^{85} +(35.4083 - 20.4430i) q^{86} +(-26.6659 + 46.1866i) q^{88} -13.7346i q^{89} +27.4413 q^{91} +(-70.7982 - 40.8754i) q^{92} +(21.0504 + 36.4603i) q^{94} +(73.6282 - 42.5093i) q^{95} +(55.7929 - 96.6361i) q^{97} -9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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