LMFDB - Embedded newform 63.4.e.d.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(37,63)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 19x^{6} + 319x^{4} + 798x^{2} + 1764 $ x^8 + 19x^6 + 319x^4 + 798*x^2 + 1764
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$-0.799027 - 1.38396i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.4.e.d.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(-9.14584 + 15.8411i) q^{5} +(12.3924 + 13.7633i) q^{7} +21.4878 q^{8} +O(q^{10})$	\(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(-9.14584 + 15.8411i) q^{5} +(12.3924 + 13.7633i) q^{7} +21.4878 q^{8} +(14.6156 + 25.3149i) q^{10} +(-30.6336 - 53.0590i) q^{11} +32.4462 q^{13} +(28.9496 - 6.15337i) q^{14} +(-4.61555 + 7.99438i) q^{16} +(40.6644 + 70.4329i) q^{17} +(10.4542 - 18.1072i) q^{19} -99.6206 q^{20} -97.9084 q^{22} +(16.8655 - 29.2119i) q^{23} +(-104.793 - 181.507i) q^{25} +(25.9254 - 44.9041i) q^{26} +(-31.1693 + 95.9287i) q^{28} +52.0227 q^{29} +(-96.9622 - 167.943i) q^{31} +(93.3271 + 161.647i) q^{32} +129.968 q^{34} +(-331.364 + 70.4329i) q^{35} +(133.578 - 231.363i) q^{37} +(-16.7064 - 28.9364i) q^{38} +(-196.524 + 340.390i) q^{40} +203.176 q^{41} -21.9520 q^{43} +(166.838 - 288.971i) q^{44} +(-26.9520 - 46.6822i) q^{46} +(123.961 - 214.706i) q^{47} +(-35.8547 + 341.121i) q^{49} -334.929 q^{50} +(88.3547 + 153.035i) q^{52} +(-70.4131 - 121.959i) q^{53} +1120.68 q^{55} +(266.286 + 295.742i) q^{56} +(41.5676 - 71.9971i) q^{58} +(110.734 + 191.797i) q^{59} +(-326.263 + 565.104i) q^{61} -309.902 q^{62} +224.435 q^{64} +(-296.748 + 513.983i) q^{65} +(-302.239 - 523.493i) q^{67} +(-221.468 + 383.593i) q^{68} +(-167.293 + 514.871i) q^{70} +716.031 q^{71} +(-194.438 - 336.777i) q^{73} +(-213.465 - 369.731i) q^{74} +113.872 q^{76} +(350.639 - 1079.15i) q^{77} +(144.871 - 250.923i) q^{79} +(-84.4263 - 146.231i) q^{80} +(162.343 - 281.186i) q^{82} -115.652 q^{83} -1487.64 q^{85} +(-17.5403 + 30.3806i) q^{86} +(-658.249 - 1140.12i) q^{88} +(-469.682 + 813.513i) q^{89} +(402.088 + 446.566i) q^{91} +183.707 q^{92} +(-198.096 - 343.112i) q^{94} +(191.225 + 331.212i) q^{95} +120.394 q^{97} +(443.447 + 322.186i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 12 q^{7}+O(q^{10}) $ 8 * q - 6 * q^4 - 12 * q^7	$ 8 q - 6 q^{4} - 12 q^{7} - 22 q^{10} + 204 q^{13} + 102 q^{16} - 222 q^{19} - 172 q^{22} - 366 q^{25} - 166 q^{28} - 220 q^{31} + 2040 q^{34} + 374 q^{37} - 822 q^{40} - 1676 q^{43} - 1716 q^{46} + 380 q^{49} + 40 q^{52} + 5020 q^{55} + 1694 q^{58} - 1332 q^{61} - 1372 q^{64} - 1890 q^{67} - 866 q^{70} - 1750 q^{73} + 4912 q^{76} - 8 q^{79} - 2480 q^{82} - 2232 q^{85} - 2682 q^{88} + 466 q^{91} + 1416 q^{94} + 6020 q^{97}+O(q^{100}) $ 8 * q - 6 * q^4 - 12 * q^7 - 22 * q^10 + 204 * q^13 + 102 * q^16 - 222 * q^19 - 172 * q^22 - 366 * q^25 - 166 * q^28 - 220 * q^31 + 2040 * q^34 + 374 * q^37 - 822 * q^40 - 1676 * q^43 - 1716 * q^46 + 380 * q^49 + 40 * q^52 + 5020 * q^55 + 1694 * q^58 - 1332 * q^61 - 1372 * q^64 - 1890 * q^67 - 866 * q^70 - 1750 * q^73 + 4912 * q^76 - 8 * q^79 - 2480 * q^82 - 2232 * q^85 - 2682 * q^88 + 466 * q^91 + 1416 * q^94 + 6020 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.799027	−	1.38396i	0.282499	−	0.489302i	−0.689501	−	0.724285i	$-0.742170\pi$
$2$	0.799027	−	1.38396i	0.282499	−	0.489302i	0.972000	+	0.234983i	$0.0755034\pi$
$3$		0			0
$3$		0			0
$4$	2.72311	+	4.71657i	0.340389	+	0.589571i
$5$	−9.14584	+	15.8411i	−0.818029	+	1.41687i	0.0891033	+	0.996022i	$0.471600\pi$
$5$	−9.14584	+	15.8411i	−0.818029	+	1.41687i	−0.907132	+	0.420846i	$0.861733\pi$
$6$		0			0
$7$	12.3924	+	13.7633i	0.669129	+	0.743146i
$7$	12.3924	+	13.7633i	0.669129	+	0.743146i
$8$	21.4878			0.949635
$9$		0			0
$10$	14.6156	+	25.3149i	0.462184	+	0.800527i
$11$	−30.6336	−	53.0590i	−0.839672	−	1.45435i	−0.890169	−	0.455630i	$-0.849414\pi$
$11$	−30.6336	−	53.0590i	−0.839672	−	1.45435i	0.0504975	−	0.998724i	$-0.483919\pi$
$12$		0			0
$13$	32.4462			0.692228			0.346114	−	0.938192i	$-0.387501\pi$
$13$	32.4462			0.692228			0.346114	+	0.938192i	$0.387501\pi$
$14$	28.9496	−	6.15337i	0.552651	−	0.117468i
$15$		0			0
$16$	−4.61555	+	7.99438i	−0.0721180	+	0.124912i
$17$	40.6644	+	70.4329i	0.580152	+	1.00485i	0.995461	+	0.0951718i	$0.0303400\pi$
$17$	40.6644	+	70.4329i	0.580152	+	1.00485i	−0.415309	+	0.909680i	$0.636327\pi$
$18$		0			0
$19$	10.4542	−	18.1072i	0.126230	−	0.218636i	−0.795983	−	0.605319i	$-0.793046\pi$
$19$	10.4542	−	18.1072i	0.126230	−	0.218636i	0.922213	+	0.386682i	$0.126379\pi$
$20$	−99.6206			−1.11379
$21$		0			0
$22$	−97.9084			−0.948825
$23$	16.8655	−	29.2119i	0.152900	−	0.264831i	−0.779392	−	0.626536i	$-0.784472\pi$
$23$	16.8655	−	29.2119i	0.152900	−	0.264831i	0.932292	+	0.361705i	$0.117805\pi$
$24$		0			0
$25$	−104.793	−	181.507i	−0.838343	−	1.45205i
$26$	25.9254	−	44.9041i	0.195554	−	0.338709i
$27$		0			0
$28$	−31.1693	+	95.9287i	−0.210373	+	0.647458i
$29$	52.0227			0.333116			0.166558	−	0.986032i	$-0.446735\pi$
$29$	52.0227			0.333116			0.166558	+	0.986032i	$0.446735\pi$
$30$		0			0
$31$	−96.9622	−	167.943i	−0.561772	−	0.973017i	−0.997342	−	0.0728626i	$-0.976787\pi$
$31$	−96.9622	−	167.943i	−0.561772	−	0.973017i	0.435570	−	0.900155i	$-0.356547\pi$
$32$	93.3271	+	161.647i	0.515564	+	0.892983i
$33$		0			0
$34$	129.968			0.655568
$35$	−331.364	+	70.4329i	−1.60031	+	0.340152i
$36$		0			0
$37$	133.578	−	231.363i	0.593515	−	1.02800i	−0.400240	−	0.916410i	$-0.631073\pi$
$37$	133.578	−	231.363i	0.593515	−	1.02800i	0.993755	−	0.111587i	$-0.0355935\pi$
$38$	−16.7064	−	28.9364i	−0.0713194	−	0.123529i
$39$		0			0
$40$	−196.524	+	340.390i	−0.776829	+	1.34551i
$41$	203.176			0.773921			0.386960	−	0.922096i	$-0.373525\pi$
$41$	203.176			0.773921			0.386960	+	0.922096i	$0.373525\pi$
$42$		0			0
$43$	−21.9520			−0.0778523			−0.0389262	−	0.999242i	$-0.512394\pi$
$43$	−21.9520			−0.0778523			−0.0389262	+	0.999242i	$0.512394\pi$
$44$	166.838	−	288.971i	0.571630	−	0.990092i
$45$		0			0
$46$	−26.9520	−	46.6822i	−0.0863882	−	0.149629i
$47$	123.961	−	214.706i	0.384713	−	0.666343i	−0.607016	−	0.794690i	$-0.707634\pi$
$47$	123.961	−	214.706i	0.384713	−	0.666343i	0.991729	+	0.128346i	$0.0409669\pi$
$48$		0			0
$49$	−35.8547	+	341.121i	−0.104533	+	0.994521i
$50$	−334.929			−0.947324
$51$		0			0
$52$	88.3547	+	153.035i	0.235627	+	0.408117i
$53$	−70.4131	−	121.959i	−0.182490	−	0.316082i	0.760238	−	0.649645i	$-0.225082\pi$
$53$	−70.4131	−	121.959i	−0.182490	−	0.316082i	−0.942728	+	0.333563i	$0.891749\pi$
$54$		0			0
$55$	1120.68			2.74750
$56$	266.286	+	295.742i	0.635429	+	0.705718i
$57$		0			0
$58$	41.5676	−	71.9971i	0.0941050	−	0.162995i
$59$	110.734	+	191.797i	0.244344	+	0.423217i	0.961947	−	0.273236i	$-0.0880940\pi$
$59$	110.734	+	191.797i	0.244344	+	0.423217i	−0.717603	+	0.696453i	$0.754761\pi$
$60$		0			0
$61$	−326.263	+	565.104i	−0.684815	+	1.18613i	0.288680	+	0.957426i	$0.406784\pi$
$61$	−326.263	+	565.104i	−0.684815	+	1.18613i	−0.973495	+	0.228709i	$0.926550\pi$
$62$	−309.902			−0.634800
$63$		0			0
$64$	224.435			0.438349
$65$	−296.748	+	513.983i	−0.566263	+	0.980796i
$66$		0			0
$67$	−302.239	−	523.493i	−0.551110	−	0.954551i	−0.998195	−	0.0600592i	$-0.980871\pi$
$67$	−302.239	−	523.493i	−0.551110	−	0.954551i	0.447085	−	0.894492i	$-0.352462\pi$
$68$	−221.468	+	383.593i	−0.394954	+	0.684081i
$69$		0			0
$70$	−167.293	+	514.871i	−0.285647	+	0.879126i
$71$	716.031			1.19686			0.598431	−	0.801174i	$-0.295791\pi$
$71$	716.031			1.19686			0.598431	+	0.801174i	$0.295791\pi$
$72$		0			0
$73$	−194.438	−	336.777i	−0.311743	−	0.539956i	0.666996	−	0.745061i	$-0.267580\pi$
$73$	−194.438	−	336.777i	−0.311743	−	0.539956i	−0.978740	+	0.205105i	$0.934246\pi$
$74$	−213.465	−	369.731i	−0.335334	−	0.580816i
$75$		0			0
$76$	113.872			0.171869
$77$	350.639	−	1079.15i	0.518949	−	1.59715i
$78$		0			0
$79$	144.871	−	250.923i	0.206319	−	0.357355i	−0.744233	−	0.667920i	$-0.767185\pi$
$79$	144.871	−	250.923i	0.206319	−	0.357355i	0.950552	+	0.310565i	$0.100518\pi$
$80$	−84.4263	−	146.231i	−0.117989	−	0.204363i
$81$		0			0
$82$	162.343	−	281.186i	0.218632	−	0.378681i
$83$	−115.652			−0.152946			−0.0764728	−	0.997072i	$-0.524366\pi$
$83$	−115.652			−0.152946			−0.0764728	+	0.997072i	$0.524366\pi$
$84$		0			0
$85$	−1487.64			−1.89832
$86$	−17.5403	+	30.3806i	−0.0219932	+	0.0380933i
$87$		0			0
$88$	−658.249	−	1140.12i	−0.797382	−	1.38111i
$89$	−469.682	+	813.513i	−0.559395	+	0.968901i	0.438152	+	0.898901i	$0.355633\pi$
$89$	−469.682	+	813.513i	−0.559395	+	0.968901i	−0.997547	+	0.0699997i	$0.977700\pi$
$90$		0			0
$91$	402.088	+	446.566i	0.463190	+	0.514427i
$92$	183.707			0.208182
$93$		0			0
$94$	−198.096	−	343.112i	−0.217362	−	0.376482i
$95$	191.225	+	331.212i	0.206519	+	0.357701i
$96$		0			0
$97$	120.394			0.126022			0.0630110	−	0.998013i	$-0.479930\pi$
$97$	120.394			0.126022			0.0630110	+	0.998013i	$0.479930\pi$
$98$	443.447	+	322.186i	0.457091	+	0.332099i
$99$		0			0
$100$	570.725	−	988.525i	0.570725	−	0.988525i
$101$	−640.502	−	1109.38i	−0.631013	−	1.09295i	−0.987345	−	0.158587i	$-0.949306\pi$
$101$	−640.502	−	1109.38i	−0.631013	−	1.09295i	0.356332	−	0.934359i	$-0.384027\pi$
$102$		0			0
$103$	−265.669	+	460.153i	−0.254147	+	0.440196i	−0.964664	−	0.263485i	$-0.915128\pi$
$103$	−265.669	+	460.153i	−0.254147	+	0.440196i	0.710516	+	0.703681i	$0.248461\pi$
$104$	697.198			0.657364
$105$		0			0
$106$	−225.048			−0.206213
$107$	−66.6758	+	115.486i	−0.0602411	+	0.104341i	−0.894573	−	0.446922i	$-0.852520\pi$
$107$	−66.6758	+	115.486i	−0.0602411	+	0.104341i	0.834332	+	0.551262i	$0.185854\pi$
$108$		0			0
$109$	108.884	+	188.593i	0.0956811	+	0.165725i	0.909893	−	0.414844i	$-0.136164\pi$
$109$	108.884	+	188.593i	0.0956811	+	0.165725i	−0.814212	+	0.580568i	$0.802830\pi$
$110$	895.455	−	1550.97i	0.776166	−	1.34436i
$111$		0			0
$112$	−167.227	+	35.5448i	−0.141084	+	0.0299881i
$113$	−2006.09			−1.67006			−0.835031	−	0.550204i	$-0.814550\pi$
$113$	−2006.09			−1.67006			−0.835031	+	0.550204i	$0.814550\pi$
$114$		0			0
$115$	308.499	+	534.335i	0.250153	+	0.433278i
$116$	141.664	+	245.369i	0.113389	+	0.196396i
$117$		0			0
$118$	353.917			0.276108
$119$	−465.454	+	1432.51i	−0.358556	+	1.10351i
$120$		0			0
$121$	−1211.34	+	2098.10i	−0.910097	+	1.57633i
$122$	521.386	+	903.067i	0.386919	+	0.670163i
$123$		0			0
$124$	528.078	−	914.658i	0.382442	−	0.662409i
$125$	1547.22			1.10710
$126$		0			0
$127$	1638.92			1.14512			0.572562	−	0.819861i	$-0.305950\pi$
$127$	1638.92			1.14512			0.572562	+	0.819861i	$0.305950\pi$
$128$	−567.287	+	982.570i	−0.391731	+	0.678498i
$129$		0			0
$130$	474.220	+	821.372i	0.319937	+	0.554147i
$131$	−45.8755	+	79.4587i	−0.0305967	+	0.0529950i	−0.880918	−	0.473268i	$-0.843074\pi$
$131$	−45.8755	+	79.4587i	−0.0305967	+	0.0529950i	0.850322	+	0.526263i	$0.176407\pi$
$132$		0			0
$133$	378.768	−	80.5088i	0.246943	−	0.0524887i
$134$	−965.989			−0.622752
$135$		0			0
$136$	873.789	+	1513.45i	0.550932	+	0.954243i
$137$	933.564	+	1616.98i	0.582188	+	1.00838i	0.995220	+	0.0976621i	$0.0311364\pi$
$137$	933.564	+	1616.98i	0.582188	+	1.00838i	−0.413032	+	0.910717i	$0.635530\pi$
$138$		0			0
$139$	639.778			0.390397			0.195199	−	0.980764i	$-0.437465\pi$
$139$	639.778			0.390397			0.195199	+	0.980764i	$0.437465\pi$
$140$	−1234.54	−	1371.10i	−0.745271	−	0.827710i
$141$		0			0
$142$	572.128	−	990.955i	0.338112	−	0.585627i
$143$	−993.946	−	1721.56i	−0.581244	−	1.00674i
$144$		0			0
$145$	−475.792	+	824.095i	−0.272499	+	0.471982i
$146$	−621.446			−0.352269
$147$		0			0
$148$	1454.99			0.808103
$149$	1568.27	−	2716.32i	0.862264	−	1.49348i	−0.00747495	−	0.999972i	$-0.502379\pi$
$149$	1568.27	−	2716.32i	0.862264	−	1.49348i	0.869739	−	0.493513i	$-0.164287\pi$
$150$		0			0
$151$	1360.68	+	2356.77i	0.733317	+	1.27014i	0.955458	+	0.295128i	$0.0953623\pi$
$151$	1360.68	+	2356.77i	0.733317	+	1.27014i	−0.222141	+	0.975015i	$0.571304\pi$
$152$	224.638	−	389.085i	0.119872	−	0.207625i
$153$		0			0
$154$	−1213.32	−	1347.54i	−0.634886	−	0.705116i
$155$	3547.20			1.83818
$156$		0			0
$157$	−1439.87	−	2493.93i	−0.731939	−	1.26776i	−0.956053	−	0.293193i	$-0.905282\pi$
$157$	−1439.87	−	2493.93i	−0.731939	−	1.26776i	0.224114	−	0.974563i	$-0.428051\pi$
$158$	−231.511	−	400.989i	−0.116570	−	0.201905i
$159$		0			0
$160$	−3414.22			−1.68699
$161$	611.056	−	129.883i	0.299118	−	0.0635788i
$162$		0			0
$163$	−323.071	+	559.576i	−0.155245	+	0.268892i	−0.933148	−	0.359492i	$-0.882950\pi$
$163$	−323.071	+	559.576i	−0.155245	+	0.268892i	0.777903	+	0.628384i	$0.216283\pi$
$164$	553.271	+	958.293i	0.263434	+	0.456281i
$165$		0			0
$166$	−92.4093	+	160.058i	−0.0432069	+	0.0748366i
$167$	−3765.03			−1.74459			−0.872296	−	0.488979i	$-0.837370\pi$
$167$	−3765.03			−1.74459			−0.872296	+	0.488979i	$0.837370\pi$
$168$		0			0
$169$	−1144.24			−0.520821
$170$	−1188.67	+	2058.83i	−0.536274	+	0.928854i
$171$		0			0
$172$	−59.7777	−	103.538i	−0.0265001	−	0.0458995i
$173$	−1154.49	+	1999.64i	−0.507366	+	0.878783i	0.492598	+	0.870257i	$0.336047\pi$
$173$	−1154.49	+	1999.64i	−0.507366	+	0.878783i	−0.999964	+	0.00852600i	$0.997286\pi$
$174$		0			0
$175$	1199.48	−	3691.60i	0.518128	−	1.59462i
$176$	565.565			0.242222
$177$		0			0
$178$	750.577	+	1300.04i	0.316057	+	0.547427i
$179$	−1516.88	−	2627.31i	−0.633390	−	1.09706i	−0.986854	−	0.161616i	$-0.948329\pi$
$179$	−1516.88	−	2627.31i	−0.633390	−	1.09706i	0.353464	−	0.935448i	$-0.385004\pi$
$180$		0			0
$181$	−4079.71			−1.67537			−0.837686	−	0.546152i	$-0.816092\pi$
$181$	−4079.71			−1.67537			−0.837686	+	0.546152i	$0.816092\pi$
$182$	939.307	−	199.654i	0.382561	−	0.0813149i
$183$		0			0
$184$	362.403	−	627.700i	0.145199	−	0.251493i
$185$	2443.36	+	4232.03i	0.971025	+	1.68186i
$186$		0			0
$187$	2491.40	−	4315.23i	0.974274	−	1.68749i
$188$	1350.24			0.523809
$189$		0			0
$190$	611.177			0.233365
$191$	438.554	−	759.599i	0.166140	−	0.287762i	−0.770920	−	0.636932i	$-0.780203\pi$
$191$	438.554	−	759.599i	0.166140	−	0.287762i	0.937059	+	0.349170i	$0.113536\pi$
$192$		0			0
$193$	729.356	+	1263.28i	0.272022	+	0.471155i	0.969379	−	0.245568i	$-0.0789744\pi$
$193$	729.356	+	1263.28i	0.272022	+	0.471155i	−0.697358	+	0.716723i	$0.745641\pi$
$194$	96.1979	−	166.620i	0.0356011	−	0.0616629i
$195$		0			0
$196$	−1706.56	+	759.799i	−0.621923	+	0.276895i
$197$	−952.250			−0.344391			−0.172195	−	0.985063i	$-0.555086\pi$
$197$	−952.250			−0.344391			−0.172195	+	0.985063i	$0.555086\pi$
$198$		0			0
$199$	−1671.11	−	2894.44i	−0.595285	−	1.03106i	−0.993507	−	0.113774i	$-0.963706\pi$
$199$	−1671.11	−	2894.44i	−0.595285	−	1.03106i	0.398222	−	0.917289i	$-0.369627\pi$
$200$	−2251.77	−	3900.18i	−0.796120	−	1.37892i
$201$		0			0
$202$	−2047.11			−0.713041
$203$	644.689	+	716.002i	0.222898	+	0.247554i
$204$		0			0
$205$	−1858.22	+	3218.52i	−0.633090	+	1.09654i
$206$	424.554	+	735.349i	0.143593	+	0.248710i
$207$		0			0
$208$	−149.757	+	259.387i	−0.0499221	+	0.0864677i
$209$	−1281.00			−0.423966
$210$		0			0
$211$	1439.27			0.469589			0.234794	−	0.972045i	$-0.424558\pi$
$211$	1439.27			0.469589			0.234794	+	0.972045i	$0.424558\pi$
$212$	383.485	−	664.216i	0.124235	−	0.215182i
$213$		0			0
$214$	106.552	+	184.553i	0.0340361	+	0.0589522i
$215$	200.770	−	347.743i	0.0636855	−	0.110306i
$216$		0			0
$217$	1109.85	−	3415.75i	0.347196	−	1.06855i
$218$	348.007			0.108119
$219$		0			0
$220$	3051.74	+	5285.77i	0.935220	+	1.61985i
$221$	1319.41	+	2285.28i	0.401597	+	0.695587i
$222$		0			0
$223$	1009.86			0.303253			0.151626	−	0.988438i	$-0.451549\pi$
$223$	1009.86			0.303253			0.151626	+	0.988438i	$0.451549\pi$
$224$	−1068.24	+	3287.69i	−0.318638	+	0.980661i
$225$		0			0
$226$	−1602.92	+	2776.34i	−0.471790	+	0.817165i
$227$	−1474.30	−	2553.57i	−0.431070	−	0.746635i	0.565896	−	0.824477i	$-0.308530\pi$
$227$	−1474.30	−	2553.57i	−0.431070	−	0.746635i	−0.996966	+	0.0778419i	$0.975197\pi$
$228$		0			0
$229$	2019.42	−	3497.74i	0.582739	−	1.00933i	−0.412414	−	0.910997i	$-0.635314\pi$
$229$	2019.42	−	3497.74i	0.582739	−	1.00933i	0.995153	−	0.0983374i	$-0.0313524\pi$
$230$	985.995			0.282672
$231$		0			0
$232$	1117.85			0.316339
$233$	1497.90	−	2594.44i	0.421162	−	0.729473i	−0.574892	−	0.818230i	$-0.694956\pi$
$233$	1497.90	−	2594.44i	0.421162	−	0.729473i	0.996053	+	0.0887561i	$0.0282892\pi$
$234$		0			0
$235$	2267.45	+	3927.34i	0.629413	+	1.09018i
$236$	−603.081	+	1044.57i	−0.166344	+	0.288117i
$237$		0			0
$238$	1610.62	+	1788.78i	0.438660	+	0.487183i
$239$	1810.28			0.489948			0.244974	−	0.969530i	$-0.421221\pi$
$239$	1810.28			0.489948			0.244974	+	0.969530i	$0.421221\pi$
$240$		0			0
$241$	1874.71	+	3247.10i	0.501083	+	0.867900i	0.999999	+	0.00125048i	$0.000398042\pi$
$241$	1874.71	+	3247.10i	0.501083	+	0.867900i	−0.498917	+	0.866650i	$0.666269\pi$
$242$	1935.79	+	3352.88i	0.514203	+	0.890625i
$243$		0			0
$244$	−3553.80			−0.932414
$245$	−5075.80	−	3687.81i	−1.32359	−	0.961656i
$246$		0			0
$247$	339.200	−	587.512i	0.0873797	−	0.151346i
$248$	−2083.50	−	3608.74i	−0.533478	−	0.924012i
$249$		0			0
$250$	1236.27	−	2141.28i	0.312754	−	0.541706i
$251$	2706.96			0.680724			0.340362	−	0.940295i	$-0.389450\pi$
$251$	2706.96			0.680724			0.340362	+	0.940295i	$0.389450\pi$
$252$		0			0
$253$	−2066.61			−0.513544
$254$	1309.54	−	2268.20i	0.323496	−	0.560312i
$255$		0			0
$256$	1804.29	+	3125.13i	0.440502	+	0.762971i
$257$	2687.64	−	4655.13i	0.652337	−	1.12988i	−0.330218	−	0.943905i	$-0.607122\pi$
$257$	2687.64	−	4655.13i	0.652337	−	1.12988i	0.982554	−	0.185975i	$-0.0595445\pi$
$258$		0			0
$259$	4839.67	−	1028.69i	1.16109	−	0.246795i
$260$	−3232.31			−0.770998
$261$		0			0
$262$	73.3116	+	126.979i	0.0172870	+	0.0299420i
$263$	2623.28	+	4543.66i	0.615051	+	1.06530i	0.990376	+	0.138406i	$0.0441979\pi$
$263$	2623.28	+	4543.66i	0.615051	+	1.06530i	−0.375324	+	0.926893i	$0.622469\pi$
$264$		0			0
$265$	2575.95			0.597129
$266$	191.225	−	588.527i	0.0440781	−	0.135658i
$267$		0			0
$268$	1646.06	−	2851.06i	0.375184	−	0.649837i
$269$	1506.66	+	2609.61i	0.341496	+	0.591489i	0.984711	−	0.174197i	$-0.0557329\pi$
$269$	1506.66	+	2609.61i	0.341496	+	0.591489i	−0.643214	+	0.765686i	$0.722400\pi$
$270$		0			0
$271$	−3448.62	+	5973.19i	−0.773022	+	1.33891i	0.162877	+	0.986646i	$0.447923\pi$
$271$	−3448.62	+	5973.19i	−0.773022	+	1.33891i	−0.935899	+	0.352267i	$0.885411\pi$
$272$	−750.756			−0.167358
$273$		0			0
$274$	2983.77			0.657869
$275$	−6420.37	+	11120.4i	−1.40787	+	2.43850i
$276$		0			0
$277$	−1659.30	−	2874.00i	−0.359920	−	0.623400i	0.628027	−	0.778191i	$-0.283863\pi$
$277$	−1659.30	−	2874.00i	−0.359920	−	0.623400i	−0.987947	+	0.154792i	$0.950529\pi$
$278$	511.200	−	885.424i	0.110287	−	0.191022i
$279$		0			0
$280$	−7120.28	+	1513.45i	−1.51971	+	0.323021i
$281$	−6274.14			−1.33197			−0.665986	−	0.745964i	$-0.731989\pi$
$281$	−6274.14			−1.33197			−0.665986	+	0.745964i	$0.731989\pi$
$282$		0			0
$283$	−3886.24	−	6731.16i	−0.816300	−	1.41387i	−0.908391	−	0.418122i	$-0.862689\pi$
$283$	−3886.24	−	6731.16i	−0.816300	−	1.41387i	0.0920914	−	0.995751i	$-0.470645\pi$
$284$	1949.83	+	3377.21i	0.407399	+	0.705635i
$285$		0			0
$286$	−3176.76			−0.656803
$287$	2517.85	+	2796.36i	0.517853	+	0.575136i
$288$		0			0
$289$	−850.695	+	1473.45i	−0.173152	+	0.299908i
$290$	760.341	+	1316.95i	0.153961	+	0.266669i
$291$		0			0
$292$	1058.95	−	1834.16i	0.212228	−	0.367590i
$293$	854.897			0.170456			0.0852280	−	0.996361i	$-0.472838\pi$
$293$	854.897			0.170456			0.0852280	+	0.996361i	$0.472838\pi$
$294$		0			0
$295$	−4051.02			−0.799523
$296$	2870.29	−	4971.49i	0.563623	−	0.976223i
$297$		0			0
$298$	−2506.17	−	4340.82i	−0.487177	−	0.843815i
$299$	547.222	−	947.817i	0.105842	−	0.183323i
$300$		0			0
$301$	−272.039	−	302.131i	−0.0520932	−	0.0578557i
$302$	4348.89			0.828645
$303$		0			0
$304$	96.5041	+	167.150i	0.0182069	+	0.0315352i
$305$	−5967.90	−	10336.7i	−1.12040	−	1.94058i
$306$		0			0
$307$	2550.68			0.474185			0.237092	−	0.971487i	$-0.423806\pi$
$307$	2550.68			0.474185			0.237092	+	0.971487i	$0.423806\pi$
$308$	6044.71	−	1284.83i	1.11828	−	0.237695i
$309$		0			0
$310$	2834.31	−	4909.17i	0.519284	−	0.899427i
$311$	−3740.25	−	6478.31i	−0.681962	−	1.18119i	−0.974381	−	0.224903i	$-0.927794\pi$
$311$	−3740.25	−	6478.31i	−0.681962	−	1.18119i	0.292419	−	0.956290i	$-0.405540\pi$
$312$		0			0
$313$	−3.12392	+	5.41079i	−0.000564135	+	0.000977111i	−0.866307	−	0.499511i	$-0.833513\pi$
$313$	−3.12392	+	5.41079i	−0.000564135	+	0.000977111i	0.865743	+	0.500488i	$0.166846\pi$
$314$	−4601.99			−0.827088
$315$		0			0
$316$	1578.00			0.280915
$317$	−482.902	+	836.410i	−0.0855598	+	0.148194i	−0.905630	−	0.424070i	$-0.860601\pi$
$317$	−482.902	+	836.410i	−0.0855598	+	0.148194i	0.820070	+	0.572263i	$0.193935\pi$
$318$		0			0
$319$	−1593.64	−	2760.27i	−0.279708	−	0.484469i
$320$	−2052.64	+	3555.28i	−0.358582	+	0.621083i
$321$		0			0
$322$	308.499	−	949.455i	0.0533912	−	0.164320i
$323$	1700.46			0.292929
$324$		0			0
$325$	−3400.13	−	5889.20i	−0.580324	−	1.00515i
$326$	516.285	+	894.232i	0.0877129	+	0.151923i
$327$		0			0
$328$	4365.80			0.734942
$329$	4491.23	−	954.632i	0.752613	−	0.159971i
$330$		0			0
$331$	−3355.10	+	5811.20i	−0.557139	+	0.964992i	0.440595	+	0.897706i	$0.354767\pi$
$331$	−3355.10	+	5811.20i	−0.557139	+	0.964992i	−0.997734	+	0.0672865i	$0.978566\pi$
$332$	−314.934	−	545.482i	−0.0520610	−	0.0901723i
$333$		0			0
$334$	−3008.36	+	5210.64i	−0.492845	+	0.853633i
$335$	11056.9			1.80330
$336$		0			0
$337$	−605.546			−0.0978819			−0.0489409	−	0.998802i	$-0.515585\pi$
$337$	−605.546			−0.0978819			−0.0489409	+	0.998802i	$0.515585\pi$
$338$	−914.281	+	1583.58i	−0.147131	+	0.254839i
$339$		0			0
$340$	−4051.02	−	7016.57i	−0.646168	−	1.11920i
$341$	−5940.61	+	10289.4i	−0.943408	+	1.63403i
$342$		0			0
$343$	−5139.26	+	3733.84i	−0.809021	+	0.587780i
$344$	−471.700			−0.0739313
$345$		0			0
$346$	1844.94	+	3195.53i	0.286660	+	0.496510i
$347$	−3469.08	−	6008.62i	−0.536686	−	0.929567i	−0.999080	−	0.0428923i	$-0.986343\pi$
$347$	−3469.08	−	6008.62i	−0.536686	−	0.929567i	0.462394	−	0.886675i	$-0.346991\pi$
$348$		0			0
$349$	10368.9			1.59035			0.795176	−	0.606378i	$-0.207378\pi$
$349$	10368.9			1.59035			0.795176	+	0.606378i	$0.207378\pi$
$350$	−4150.59	−	4609.72i	−0.633882	−	0.704000i
$351$		0			0
$352$	5717.90	−	9903.69i	0.865809	−	1.49963i
$353$	2940.88	+	5093.75i	0.443420	+	0.768026i	0.997941	−	0.0641440i	$-0.0204317\pi$
$353$	2940.88	+	5093.75i	0.443420	+	0.768026i	−0.554521	+	0.832170i	$0.687098\pi$
$354$		0			0
$355$	−6548.70	+	11342.7i	−0.979068	+	1.69580i
$356$	−5115.98			−0.761647
$357$		0			0
$358$	−4848.11			−0.715728
$359$	−294.634	+	510.322i	−0.0433153	+	0.0750244i	−0.886870	−	0.462019i	$-0.847125\pi$
$359$	−294.634	+	510.322i	−0.0433153	+	0.0750244i	0.843555	+	0.537043i	$0.180459\pi$
$360$		0			0
$361$	3210.92	+	5561.47i	0.468132	+	0.810829i
$362$	−3259.80	+	5646.14i	−0.473291	+	0.819763i
$363$		0			0
$364$	−1011.33	+	3112.52i	−0.145626	+	0.448188i
$365$	7113.21			1.02006
$366$		0			0
$367$	1774.36	+	3073.28i	0.252373	+	0.437122i	0.964179	−	0.265254i	$-0.0854558\pi$
$367$	1774.36	+	3073.28i	0.252373	+	0.437122i	−0.711806	+	0.702376i	$0.752122\pi$
$368$	155.687	+	269.658i	0.0220537	+	0.0381982i
$369$		0			0
$370$	7809.25			1.09725
$371$	805.964	−	2480.49i	0.112786	−	0.347117i
$372$		0			0
$373$	790.667	−	1369.47i	0.109756	−	0.190104i	−0.805915	−	0.592031i	$-0.798326\pi$
$373$	790.667	−	1369.47i	0.109756	−	0.190104i	0.915672	+	0.401927i	$0.131660\pi$
$374$	−3981.39	−	6895.97i	−0.550462	−	0.953429i
$375$		0			0
$376$	2663.64	−	4613.56i	0.365337	−	0.632783i
$377$	1687.94			0.230592
$378$		0			0
$379$	3057.01			0.414322			0.207161	−	0.978307i	$-0.433578\pi$
$379$	3057.01			0.414322			0.207161	+	0.978307i	$0.433578\pi$
$380$	−1041.46	+	1803.85i	−0.140594	+	0.243515i
$381$		0			0
$382$	−700.834	−	1213.88i	−0.0938685	−	0.162585i
$383$	5289.87	−	9162.33i	0.705744	−	1.22238i	−0.260678	−	0.965426i	$-0.583946\pi$
$383$	5289.87	−	9162.33i	0.705744	−	1.22238i	0.966422	−	0.256959i	$-0.0827204\pi$
$384$		0			0
$385$	13888.0	+	15424.2i	1.83843	+	2.04180i
$386$	2331.10			0.307383
$387$		0			0
$388$	327.846	+	567.845i	0.0428965	+	0.0742989i
$389$	3696.65	+	6402.78i	0.481819	+	0.834534i	0.999782	−	0.0208684i	$-0.00664310\pi$
$389$	3696.65	+	6402.78i	0.481819	+	0.834534i	−0.517964	+	0.855403i	$0.673310\pi$
$390$		0			0
$391$	2743.31			0.354821
$392$	−770.438	+	7329.94i	−0.0992678	+	0.944433i
$393$		0			0
$394$	−760.874	+	1317.87i	−0.0972900	+	0.168511i
$395$	2649.93	+	4589.81i	0.337550	+	0.584654i
$396$		0			0
$397$	−889.086	+	1539.94i	−0.112398	+	0.194679i	−0.916737	−	0.399492i	$-0.869186\pi$
$397$	−889.086	+	1539.94i	−0.112398	+	0.194679i	0.804339	+	0.594171i	$0.202520\pi$
$398$	−5341.04			−0.672669
$399$		0			0
$400$	1934.71			0.241839
$401$	73.8031	−	127.831i	0.00919090	−	0.0159191i	−0.861393	−	0.507938i	$-0.830408\pi$
$401$	73.8031	−	127.831i	0.00919090	−	0.0159191i	0.870584	+	0.492019i	$0.163741\pi$
$402$		0			0
$403$	−3146.06	−	5449.13i	−0.388874	−	0.673550i
$404$	3488.31	−	6041.94i	0.429579	−	0.744053i
$405$		0			0
$406$	1506.04	−	320.115i	0.184097	−	0.0391307i
$407$	−16367.9			−1.99343
$408$		0			0
$409$	1080.03	+	1870.66i	0.130572	+	0.226157i	0.923897	−	0.382641i	$-0.124985\pi$
$409$	1080.03	+	1870.66i	0.130572	+	0.226157i	−0.793325	+	0.608798i	$0.791652\pi$
$410$	2969.53	+	5143.37i	0.357694	+	0.619544i
$411$		0			0
$412$	−2893.79			−0.346036
$413$	−1267.48	+	3900.89i	−0.151014	+	0.464770i
$414$		0			0
$415$	1057.74	−	1832.05i	0.125114	−	0.216704i
$416$	3028.11	+	5244.84i	0.356888	+	0.618148i
$417$		0			0
$418$	−1023.56	+	1772.85i	−0.119770	+	0.207447i
$419$	−13491.0			−1.57298			−0.786488	−	0.617605i	$-0.788103\pi$
$419$	−13491.0			−1.57298			−0.786488	+	0.617605i	$0.788103\pi$
$420$		0			0
$421$	−14146.7			−1.63769			−0.818847	−	0.574012i	$-0.805386\pi$
$421$	−14146.7			−1.63769			−0.818847	+	0.574012i	$0.805386\pi$
$422$	1150.01	−	1991.88i	0.132658	−	0.229771i
$423$		0			0
$424$	−1513.02	−	2620.63i	−0.173299	−	0.300163i
$425$	8522.69	−	14761.7i	0.972732	−	1.68482i
$426$		0			0
$427$	−11820.9	+	2512.58i	−1.33970	+	0.284759i
$428$	−726.262			−0.0820215
$429$		0			0
$430$	−320.841	−	555.712i	−0.0359821	−	0.0623229i
$431$	4544.26	+	7870.89i	0.507864	+	0.879646i	0.999959	+	0.00910411i	$0.00289797\pi$
$431$	4544.26	+	7870.89i	0.507864	+	0.879646i	−0.492095	+	0.870542i	$0.663769\pi$
$432$		0			0
$433$	15461.2			1.71597			0.857986	−	0.513673i	$-0.171716\pi$
$433$	15461.2			1.71597			0.857986	+	0.513673i	$0.171716\pi$
$434$	−3840.44	−	4265.26i	−0.424763	−	0.471749i
$435$		0			0
$436$	−593.009	+	1027.12i	−0.0651376	+	0.112822i
$437$	−352.632	−	610.776i	−0.0386010	−	0.0668590i
$438$		0			0
$439$	891.091	−	1543.41i	0.0968780	−	0.167798i	−0.813513	−	0.581547i	$-0.802448\pi$
$439$	891.091	−	1543.41i	0.0968780	−	0.167798i	0.910391	+	0.413749i	$0.135781\pi$
$440$	24081.0			2.60913
$441$		0			0
$442$	4216.97			0.453803
$443$	6712.36	−	11626.1i	0.719896	−	1.24690i	−0.241145	−	0.970489i	$-0.577523\pi$
$443$	6712.36	−	11626.1i	0.719896	−	1.24690i	0.961041	−	0.276407i	$-0.0891437\pi$
$444$		0			0
$445$	−8591.27	−	14880.5i	−0.915203	−	1.58518i
$446$	806.907	−	1397.60i	0.0856685	−	0.148382i
$447$		0			0
$448$	2781.29	+	3088.95i	0.293312	+	0.325757i
$449$	−418.639			−0.0440018			−0.0220009	−	0.999758i	$-0.507004\pi$
$449$	−418.639			−0.0440018			−0.0220009	+	0.999758i	$0.507004\pi$
$450$		0			0
$451$	−6224.02	−	10780.3i	−0.649839	−	1.12555i
$452$	−5462.80	−	9461.85i	−0.568470	−	0.984619i
$453$		0			0
$454$	−4712.03			−0.487107
$455$	−10751.5	+	2285.28i	−1.10778	+	0.235463i
$456$		0			0
$457$	354.205	−	613.501i	0.0362560	−	0.0627973i	−0.847328	−	0.531070i	$-0.821790\pi$
$457$	354.205	−	613.501i	0.0362560	−	0.0627973i	0.883584	+	0.468273i	$0.155123\pi$
$458$	−3227.15	−	5589.59i	−0.329246	−	0.570271i
$459$		0			0
$460$	−1680.15	+	2910.11i	−0.170299	+	0.294966i
$461$	−8223.97			−0.830865			−0.415432	−	0.909624i	$-0.636370\pi$
$461$	−8223.97			−0.830865			−0.415432	+	0.909624i	$0.636370\pi$
$462$		0			0
$463$	−9414.17			−0.944954			−0.472477	−	0.881343i	$-0.656640\pi$
$463$	−9414.17			−0.944954			−0.472477	+	0.881343i	$0.656640\pi$
$464$	−240.114	+	415.889i	−0.0240237	+	0.0416103i
$465$		0			0
$466$	−2393.73	−	4146.05i	−0.237955	−	0.412151i
$467$	−5410.76	+	9371.72i	−0.536146	+	0.928632i	0.462961	+	0.886379i	$0.346787\pi$
$467$	−5410.76	+	9371.72i	−0.536146	+	0.928632i	−0.999107	+	0.0422535i	$0.986546\pi$
$468$		0			0
$469$	3459.50	−	10647.2i	0.340607	−	1.04827i
$470$	7247.02			0.711234
$471$		0			0
$472$	2379.43	+	4121.29i	0.232038	+	0.401902i
$473$	672.470	+	1164.75i	0.0653704	+	0.113225i
$474$		0			0
$475$	−4382.11			−0.423295
$476$	−8024.02	+	1705.54i	−0.772648	+	0.164230i
$477$		0			0
$478$	1446.47	−	2505.35i	0.138410	−	0.239733i
$479$	4092.75	+	7088.85i	0.390402	+	0.676196i	0.992503	−	0.122224i	$-0.0390026\pi$
$479$	4092.75	+	7088.85i	0.390402	+	0.676196i	−0.602100	+	0.798420i	$0.705669\pi$
$480$		0			0
$481$	4334.09	−	7506.87i	0.410848	−	0.711609i
$482$	5991.79			0.566221
$483$		0			0
$484$	−13194.4			−1.23915
$485$	−1101.10	+	1907.17i	−0.103090	+	0.178557i
$486$		0			0
$487$	2001.58	+	3466.83i	0.186242	+	0.322581i	0.943994	−	0.329961i	$-0.107036\pi$
$487$	2001.58	+	3466.83i	0.186242	+	0.322581i	−0.757752	+	0.652543i	$0.773702\pi$
$488$	−7010.67	+	12142.8i	−0.650324	+	1.12639i
$489$		0			0
$490$	−9159.47	+	4078.01i	−0.844455	+	0.375971i
$491$	11180.8			1.02766			0.513831	−	0.857891i	$-0.328226\pi$
$491$	11180.8			1.02766			0.513831	+	0.857891i	$0.328226\pi$
$492$		0			0
$493$	2115.47	+	3664.11i	0.193258	+	0.334733i
$494$	−542.060	−	938.876i	−0.0493693	−	0.0855101i
$495$		0			0
$496$	1790.14			0.162056
$497$	8873.37	+	9854.92i	0.800855	+	0.889443i
$498$		0			0
$499$	1885.54	−	3265.85i	0.169155	−	0.292985i	−0.768968	−	0.639287i	$-0.779229\pi$
$499$	1885.54	−	3265.85i	0.169155	−	0.292985i	0.938123	+	0.346302i	$0.112563\pi$
$500$	4213.24	+	7297.55i	0.376844	+	0.652713i
$501$		0			0
$502$	2162.93	−	3746.31i	0.192304	−	0.333080i
$503$	−13597.2			−1.20531			−0.602654	−	0.798003i	$-0.705890\pi$
$503$	−13597.2			−1.20531			−0.602654	+	0.798003i	$0.705890\pi$
$504$		0			0
$505$	23431.7			2.06475
$506$	−1651.28	+	2860.09i	−0.145075	+	0.251278i
$507$		0			0
$508$	4462.97	+	7730.08i	0.389788	+	0.675132i
$509$	−3680.38	+	6374.60i	−0.320491	+	0.555106i	−0.980589	−	0.196073i	$-0.937181\pi$
$509$	−3680.38	+	6374.60i	−0.320491	+	0.555106i	0.660099	+	0.751179i	$0.270515\pi$
$510$		0			0
$511$	2225.58	−	6849.59i	0.192669	−	0.592971i
$512$	−3309.87			−0.285698
$513$		0			0
$514$	−4295.00	−	7439.16i	−0.368569	−	0.638380i
$515$	−4859.54	−	8416.97i	−0.415800	−	0.720186i
$516$		0			0
$517$	−15189.5			−1.29213
$518$	2443.36	−	7519.84i	0.207249	−	0.637844i
$519$		0			0
$520$	−6376.46	+	11044.4i	−0.537743	+	0.931398i
$521$	−6899.40	−	11950.1i	−0.580169	−	1.00488i	−0.995459	−	0.0951930i	$-0.969653\pi$
$521$	−6899.40	−	11950.1i	−0.580169	−	1.00488i	0.415290	−	0.909689i	$-0.363680\pi$
$522$		0			0
$523$	−9423.58	+	16322.1i	−0.787886	+	1.36466i	0.139373	+	0.990240i	$0.455491\pi$
$523$	−9423.58	+	16322.1i	−0.787886	+	1.36466i	−0.927260	+	0.374419i	$0.877842\pi$
$524$	−499.697			−0.0416591
$525$		0			0
$526$	8384.29			0.695005
$527$	7885.83	−	13658.7i	0.651826	−	1.12900i
$528$		0			0
$529$	5514.61	+	9551.58i	0.453243	+	0.785040i
$530$	2058.25	−	3565.00i	0.168688	−	0.292177i
$531$		0			0
$532$	1411.15	+	1567.25i	0.115002	+	0.127724i
$533$	6592.29			0.535730
$534$		0			0
$535$	−1219.61	−	2112.43i	−0.0985579	−	0.170707i
$536$	−6494.45	−	11248.7i	−0.523354	−	0.906475i
$537$		0			0
$538$	4815.44			0.385889
$539$	19197.9	−	8547.36i	1.53416	−	0.683044i
$540$		0			0
$541$	7234.77	−	12531.0i	0.574948	−	0.995839i	−0.421099	−	0.907015i	$-0.638356\pi$
$541$	7234.77	−	12531.0i	0.574948	−	0.995839i	0.996047	−	0.0888248i	$-0.0283111\pi$
$542$	5511.09	+	9545.49i	0.436756	+	0.756483i
$543$		0			0
$544$	−7590.19	+	13146.6i	−0.598211	+	1.03613i
$545$	−3983.36			−0.313080
$546$		0			0
$547$	5749.63			0.449427			0.224713	−	0.974425i	$-0.427855\pi$
$547$	5749.63			0.449427			0.224713	+	0.974425i	$0.427855\pi$
$548$	−5084.39	+	8806.43i	−0.396340	+	0.686482i
$549$		0			0
$550$	10260.1	+	17771.0i	0.795441	+	1.37774i
$551$	543.857	−	941.988i	0.0420492	−	0.0728313i
$552$		0			0
$553$	5248.82	−	1115.66i	0.403622	−	0.0857916i
$554$	−5303.31			−0.406708
$555$		0			0
$556$	1742.19	+	3017.55i	0.132887	+	0.230167i
$557$	−2715.39	−	4703.19i	−0.206561	−	0.357775i	0.744068	−	0.668104i	$-0.232894\pi$
$557$	−2715.39	−	4703.19i	−0.206561	−	0.357775i	−0.950629	+	0.310330i	$0.899561\pi$
$558$		0			0
$559$	−712.260			−0.0538915
$560$	966.362	−	2974.14i	0.0729219	−	0.224429i
$561$		0			0
$562$	−5013.21	+	8683.14i	−0.376280	+	0.651737i
$563$	12065.3	+	20897.8i	0.903185	+	1.56436i	0.823335	+	0.567556i	$0.192111\pi$
$563$	12065.3	+	20897.8i	0.903185	+	1.56436i	0.0798500	+	0.996807i	$0.474556\pi$
$564$		0			0
$565$	18347.4	−	31778.6i	1.36616	−	2.36626i
$566$	−12420.8			−0.922415
$567$		0			0
$568$	15385.9			1.13658
$569$	−9024.27	+	15630.5i	−0.664880	+	1.15161i	0.314437	+	0.949278i	$0.398184\pi$
$569$	−9024.27	+	15630.5i	−0.664880	+	1.15161i	−0.979318	+	0.202328i	$0.935149\pi$
$570$		0			0
$571$	5637.42	+	9764.30i	0.413168	+	0.715628i	0.995234	−	0.0975136i	$-0.0310889\pi$
$571$	5637.42	+	9764.30i	0.413168	+	0.715628i	−0.582066	+	0.813141i	$0.697756\pi$
$572$	5413.25	−	9376.02i	0.395698	−	0.685369i
$573$		0			0
$574$	5881.87	−	1250.22i	0.427708	−	0.0909113i
$575$	−7069.54			−0.512731
$576$		0			0
$577$	12047.5	+	20866.8i	0.869225	+	1.50554i	0.862790	+	0.505562i	$0.168715\pi$
$577$	12047.5	+	20866.8i	0.869225	+	1.50554i	0.00643457	+	0.999979i	$0.497952\pi$
$578$	1359.46	+	2354.65i	0.0978303	+	0.169447i
$579$		0			0
$580$	−5182.53			−0.371022
$581$	−1433.21	−	1591.75i	−0.102340	−	0.113661i
$582$		0			0
$583$	−4314.02	+	7472.10i	−0.306464	+	0.530811i
$584$	−4178.05	−	7236.59i	−0.296043	−	0.512761i
$585$		0			0
$586$	683.086	−	1183.14i	0.0481536	−	0.0834045i
$587$	11438.9			0.804315			0.402157	−	0.915571i	$-0.368260\pi$
$587$	11438.9			0.804315			0.402157	+	0.915571i	$0.368260\pi$
$588$		0			0
$589$	−4054.66			−0.283649
$590$	−3236.87	+	5606.43i	−0.225864	+	0.391208i
$591$		0			0
$592$	1233.07	+	2135.74i	0.0856063	+	0.148274i
$593$	2087.22	−	3615.17i	0.144539	−	0.250349i	−0.784662	−	0.619924i	$-0.787163\pi$
$593$	2087.22	−	3615.17i	0.144539	−	0.250349i	0.929201	+	0.369575i	$0.120497\pi$
$594$		0			0
$595$	−18435.5	−	20474.8i	−1.27022	−	1.41073i
$596$	17082.2			1.17402
$597$		0			0
$598$	−874.491	−	1514.66i	−0.0598003	−	0.103577i
$599$	5727.77	+	9920.79i	0.390702	+	0.676715i	0.992542	−	0.121901i	$-0.0388991\pi$
$599$	5727.77	+	9920.79i	0.390702	+	0.676715i	−0.601841	+	0.798616i	$0.705566\pi$
$600$		0			0
$601$	−17539.2			−1.19042			−0.595208	−	0.803572i	$-0.702930\pi$
$601$	−17539.2			−1.19042			−0.595208	+	0.803572i	$0.702930\pi$
$602$	−635.503	+	135.079i	−0.0430252	+	0.00914519i
$603$		0			0
$604$	−7410.59	+	12835.5i	−0.499226	+	0.864685i
$605$	−22157.4	−	38377.8i	−1.48897	−	2.57898i
$606$		0			0
$607$	−1692.86	+	2932.12i	−0.113198	+	0.196064i	−0.917058	−	0.398754i	$-0.869443\pi$
$607$	−1692.86	+	2932.12i	−0.113198	+	0.196064i	0.803860	+	0.594818i	$0.202776\pi$
$608$	3902.65			0.260318
$609$		0			0
$610$	−19074.1			−1.26604
$611$	4022.06	−	6966.41i	0.266309	−	0.461261i
$612$		0			0
$613$	−2135.94	−	3699.56i	−0.140734	−	0.243758i	0.787039	−	0.616903i	$-0.211613\pi$
$613$	−2135.94	−	3699.56i	−0.140734	−	0.243758i	−0.927773	+	0.373145i	$0.878279\pi$
$614$	2038.06	−	3530.02i	0.133957	−	0.232020i
$615$		0			0
$616$	7534.47	−	23188.5i	0.492812	−	1.51671i
$617$	−13123.9			−0.856321			−0.428160	−	0.903703i	$-0.640838\pi$
$617$	−13123.9			−0.856321			−0.428160	+	0.903703i	$0.640838\pi$
$618$		0			0
$619$	946.969	+	1640.20i	0.0614893	+	0.106503i	0.895131	−	0.445803i	$-0.147082\pi$
$619$	946.969	+	1640.20i	0.0614893	+	0.106503i	−0.833642	+	0.552305i	$0.813748\pi$
$620$	9659.43	+	16730.6i	0.625697	+	1.08374i
$621$		0			0
$622$	−11954.3			−0.770614
$623$	−17017.1	+	3617.06i	−1.09434	+	0.232607i
$624$		0			0
$625$	−1051.49	+	1821.23i	−0.0672952	+	0.116559i
$626$	4.99219	+	8.64673i	0.000318735	+	0.000552066i
$627$		0			0
$628$	7841.87	−	13582.5i	0.498288	−	0.863060i
$629$	21727.5			1.37731
$630$		0			0
$631$	20443.8			1.28979			0.644894	−	0.764272i	$-0.276902\pi$
$631$	20443.8			1.28979			0.644894	+	0.764272i	$0.276902\pi$
$632$	3112.95	−	5391.79i	0.195928	−	0.339357i
$633$		0			0
$634$	771.703	+	1336.63i	0.0483411	+	0.0837292i
$635$	−14989.3	+	25962.3i	−0.936745	+	1.62249i
$636$		0			0
$637$	−1163.35	+	11068.1i	−0.0723603	+	0.688436i
$638$	−5093.46			−0.316069
$639$		0			0
$640$	−10376.6	−	17972.9i	−0.640895	−	1.11006i
$641$	9614.27	+	16652.4i	0.592419	+	1.02610i	0.993906	+	0.110235i	$0.0351604\pi$
$641$	9614.27	+	16652.4i	0.592419	+	1.02610i	−0.401486	+	0.915865i	$0.631506\pi$
$642$		0			0
$643$	−18525.1			−1.13617			−0.568087	−	0.822969i	$-0.692316\pi$
$643$	−18525.1			−1.13617			−0.568087	+	0.822969i	$0.692316\pi$
$644$	2276.57	+	2528.40i	0.139301	+	0.154710i
$645$		0			0
$646$	1358.71	−	2353.36i	0.0827522	−	0.143331i
$647$	4011.20	+	6947.60i	0.243735	+	0.422161i	0.961775	−	0.273840i	$-0.0882940\pi$
$647$	4011.20	+	6947.60i	0.243735	+	0.422161i	−0.718040	+	0.696001i	$0.754961\pi$
$648$		0			0
$649$	6784.36	−	11750.9i	0.410338	−	0.710726i
$650$	−10867.2			−0.655764
$651$		0			0
$652$	−3519.03			−0.211374
$653$	1025.85	−	1776.82i	0.0614769	−	0.106481i	−0.833649	−	0.552295i	$-0.813752\pi$
$653$	1025.85	−	1776.82i	0.0614769	−	0.106481i	0.895126	+	0.445814i	$0.147086\pi$
$654$		0			0
$655$	−839.141	−	1453.43i	−0.0500579	−	0.0867029i
$656$	−937.770	+	1624.26i	−0.0558136	+	0.0966721i
$657$		0			0
$658$	2267.45	−	6978.45i	0.134338	−	0.413447i
$659$	−14765.2			−0.872792			−0.436396	−	0.899755i	$-0.643745\pi$
$659$	−14765.2			−0.872792			−0.436396	+	0.899755i	$0.643745\pi$
$660$		0			0
$661$	−323.532	−	560.374i	−0.0190377	−	0.0329743i	0.856350	−	0.516397i	$-0.172727\pi$
$661$	−323.532	−	560.374i	−0.0190377	−	0.0329743i	−0.875387	+	0.483422i	$0.839394\pi$
$662$	5361.63	+	9286.62i	0.314782	+	0.545218i
$663$		0			0
$664$	−2485.11			−0.145243
$665$	−2188.81	+	6736.41i	−0.127637	+	0.392822i
$666$		0			0
$667$	877.390	−	1519.68i	0.0509335	−	0.0882195i
$668$	−10252.6	−	17758.0i	−0.593840	−	1.02856i
$669$		0			0
$670$	8834.78	−	15302.3i	0.509429	−	0.882357i
$671$	39978.5			2.30008
$672$		0			0
$673$	−22596.6			−1.29426			−0.647130	−	0.762380i	$-0.724031\pi$
$673$	−22596.6			−1.29426			−0.647130	+	0.762380i	$0.724031\pi$
$674$	−483.848	+	838.049i	−0.0276515	+	0.0478938i
$675$		0			0
$676$	−3115.90	−	5396.90i	−0.177282	−	0.307061i
$677$	12602.1	−	21827.5i	0.715420	−	1.23914i	−0.247377	−	0.968919i	$-0.579569\pi$
$677$	12602.1	−	21827.5i	0.715420	−	1.23914i	0.962797	−	0.270225i	$-0.0870980\pi$
$678$		0			0
$679$	1491.97	+	1657.01i	0.0843250	+	0.0936528i
$680$	−31966.2			−1.80272
$681$		0			0
$682$	9493.42	+	16443.1i	0.533023	+	0.923223i
$683$	−8510.27	−	14740.2i	−0.476774	−	0.825796i	0.522872	−	0.852411i	$-0.324860\pi$
$683$	−8510.27	−	14740.2i	−0.476774	−	0.825796i	−0.999646	+	0.0266151i	$0.991527\pi$
$684$		0			0
$685$	−34152.9			−1.90499
$686$	1061.06	+	10096.0i	0.0590549	+	0.561903i
$687$		0			0
$688$	101.321	−	175.493i	0.00561456	−	0.00972470i
$689$	−2284.64	−	3957.11i	−0.126325	−	0.218801i
$690$		0			0
$691$	9645.26	−	16706.1i	0.531003	−	0.919724i	−0.468342	−	0.883547i	$-0.655149\pi$
$691$	9645.26	−	16706.1i	0.531003	−	0.919724i	0.999345	−	0.0361772i	$-0.0115181\pi$
$692$	−12575.2			−0.690806
$693$		0			0
$694$	−11087.6			−0.606452
$695$	−5851.31	+	10134.8i	−0.319356	+	0.553142i
$696$		0			0
$697$	8262.04	+	14310.3i	0.448991	+	0.777676i
$698$	8285.01	−	14350.1i	0.449273	−	0.778163i
$699$		0			0
$700$	20678.0	−	4395.20i	1.11651	−	0.237319i
$701$	28511.4			1.53618			0.768088	−	0.640345i	$-0.221208\pi$
$701$	28511.4			1.53618			0.768088	+	0.640345i	$0.221208\pi$
$702$		0			0
$703$	−2792.90	−	4837.45i	−0.149838	−	0.259528i
$704$	−6875.25	−	11908.3i	−0.368069	−	0.637515i
$705$		0			0
$706$	9399.37			0.501062
$707$	7331.32	−	22563.3i	0.389990	−	1.20026i
$708$		0			0
$709$	−14213.3	+	24618.1i	−0.752877	+	1.30402i	0.193546	+	0.981091i	$0.438001\pi$
$709$	−14213.3	+	24618.1i	−0.752877	+	1.30402i	−0.946423	+	0.322930i	$0.895332\pi$
$710$	10465.2	+	18126.2i	0.553171	+	0.958120i
$711$		0			0
$712$	−10092.4	+	17480.6i	−0.531221	+	0.920102i
$713$	−6541.27			−0.343580
$714$		0			0
$715$	36361.9			1.90190
$716$	8261.26	−	14308.9i	0.431198	−	0.746857i
$717$		0			0
$718$	470.842	+	815.522i	0.0244731	+	0.0423886i
$719$	10881.7	−	18847.6i	0.564420	−	0.977603i	−0.432684	−	0.901546i	$-0.642433\pi$
$719$	10881.7	−	18847.6i	0.564420	−	0.977603i	0.997103	−	0.0760577i	$-0.0242333\pi$
$720$		0			0
$721$	−9625.49	+	2045.94i	−0.497187	+	0.105679i
$722$	10262.4			0.528987
$723$		0			0
$724$	−11109.5	−	19242.2i	−0.570278	−	0.987750i
$725$	−5451.61	−	9442.47i	−0.279266	−	0.483703i
$726$		0			0
$727$	−13422.8			−0.684763			−0.342382	−	0.939561i	$-0.611234\pi$
$727$	−13422.8			−0.684763			−0.342382	+	0.939561i	$0.611234\pi$
$728$	8639.98	+	9595.71i	0.439861	+	0.488518i
$729$		0			0
$730$	5683.65	−	9844.36i	0.288166	−	0.499118i
$731$	−892.666	−	1546.14i	−0.0451661	−	0.0782301i
$732$		0			0
$733$	−2279.76	+	3948.66i	−0.114877	+	0.198973i	−0.917731	−	0.397204i	$-0.869981\pi$
$733$	−2279.76	+	3948.66i	−0.114877	+	0.198973i	0.802854	+	0.596176i	$0.203314\pi$
$734$	5671.04			0.285180
$735$		0			0
$736$	6296.04			0.315319
$737$	−18517.4	+	32073.0i	−0.925503	+	1.60302i
$738$		0			0
$739$	18332.7	+	31753.2i	0.912557	+	1.58059i	0.810439	+	0.585823i	$0.199228\pi$
$739$	18332.7	+	31753.2i	0.912557	+	1.58059i	0.102118	+	0.994772i	$0.467438\pi$
$740$	−13307.1	+	23048.6i	−0.661052	+	1.14498i
$741$		0			0
$742$	−2788.89	−	3097.39i	−0.137983	−	0.153247i
$743$	−10321.3			−0.509625			−0.254813	−	0.966990i	$-0.582014\pi$
$743$	−10321.3			−0.509625			−0.254813	+	0.966990i	$0.582014\pi$
$744$		0			0
$745$	28686.2	+	49686.0i	1.41071	+	2.44343i
$746$	−1263.53	−	2188.50i	−0.0620121	−	0.107408i
$747$		0			0
$748$	27137.4			1.32653
$749$	−2415.74	+	513.476i	−0.117849	+	0.0250494i
$750$		0			0
$751$	13339.0	−	23103.9i	0.648134	−	1.12260i	−0.335434	−	0.942064i	$-0.608883\pi$
$751$	13339.0	−	23103.9i	0.648134	−	1.12260i	0.983568	−	0.180537i	$-0.0577836\pi$
$752$	1144.30	+	1981.98i	0.0554896	+	0.0961107i
$753$		0			0
$754$	1348.71	−	2336.03i	0.0651421	−	0.112829i
$755$	−49778.4			−2.39950
$756$		0			0
$757$	−11630.8			−0.558425			−0.279212	−	0.960229i	$-0.590073\pi$
$757$	−11630.8			−0.558425			−0.279212	+	0.960229i	$0.590073\pi$
$758$	2442.63	−	4230.77i	0.117045	−	0.202729i
$759$		0			0
$760$	4109.01	+	7117.02i	0.196118	+	0.339686i
$761$	−18045.8	+	31256.3i	−0.859607	+	1.48888i	0.0126976	+	0.999919i	$0.495958\pi$
$761$	−18045.8	+	31256.3i	−0.859607	+	1.48888i	−0.872304	+	0.488963i	$0.837375\pi$
$762$		0			0
$763$	−1246.32	+	3835.74i	−0.0591345	+	0.181996i
$764$	4776.93			0.226208
$765$		0			0
$766$	−8453.51	−	14641.9i	−0.398744	−	0.690644i
$767$	3592.89	+	6223.07i	0.169142	+	0.292962i
$768$		0			0
$769$	33089.3			1.55167			0.775833	−	0.630938i	$-0.217330\pi$
$769$	33089.3			1.55167			0.775833	+	0.630938i	$0.217330\pi$
$770$	32443.3	−	6895.97i	1.51841	−	0.322745i
$771$		0			0
$772$	−3972.23	+	6880.11i	−0.185186	+	0.320752i
$773$	15495.4	+	26838.8i	0.720997	+	1.24880i	0.960601	+	0.277933i	$0.0896493\pi$
$773$	15495.4	+	26838.8i	0.720997	+	1.24880i	−0.239603	+	0.970871i	$0.577017\pi$
$774$		0			0
$775$	−20321.9	+	35198.6i	−0.941915	+	1.63144i
$776$	2587.00			0.119675
$777$		0			0
$778$	11814.9			0.544453
$779$	2124.05	−	3678.96i	0.0976917	−	0.169207i
$780$		0			0
$781$	−21934.6	−	37991.9i	−1.00497	−	1.74066i
$782$	2191.98	−	3796.62i	0.100236	−	0.173615i
$783$		0			0
$784$	−2561.56	−	1861.10i	−0.116689	−	0.0847803i
$785$	52675.4			2.39499
$786$		0			0
$787$	12710.6	+	22015.4i	0.575711	+	0.997161i	0.995964	+	0.0897537i	$0.0286080\pi$
$787$	12710.6	+	22015.4i	0.575711	+	0.997161i	−0.420253	+	0.907407i	$0.638059\pi$
$788$	−2593.08	−	4491.35i	−0.117227	−	0.203043i
$789$		0			0
$790$	8469.46			0.381430
$791$	−24860.3	−	27610.3i	−1.11749	−	1.24110i
$792$		0			0
$793$	−10586.0	+	18335.5i	−0.474048	+	0.821075i
$794$	1420.81	+	2460.91i	0.0635045	+	0.109993i
$795$		0			0
$796$	9101.22	−	15763.8i	0.405257	−	0.701925i
$797$	−20283.3			−0.901470			−0.450735	−	0.892658i	$-0.648838\pi$
$797$	−20283.3			−0.901470			−0.450735	+	0.892658i	$0.648838\pi$
$798$		0			0
$799$	20163.2			0.892768
$800$	19560.0	−	33879.0i	0.864439	−	1.49725i
$801$		0			0
$802$	−117.941	−	204.281i	−0.00519284	−	0.00899426i
$803$	−11912.7	+	20633.4i	−0.523524	+	0.906771i
$804$		0			0
$805$	−3531.14	+	10867.7i	−0.154604	+	0.475820i
$806$	−10055.1			−0.439426
$807$		0			0
$808$	−13763.0	−	23838.2i	−0.599232	−	1.03790i
$809$	−8215.67	−	14230.0i	−0.357043	−	0.618416i	0.630423	−	0.776252i	$-0.282882\pi$
$809$	−8215.67	−	14230.0i	−0.357043	−	0.618416i	−0.987465	+	0.157836i	$0.949548\pi$
$810$		0			0
$811$	6371.81			0.275887			0.137944	−	0.990440i	$-0.455951\pi$
$811$	6371.81			0.275887			0.137944	+	0.990440i	$0.455951\pi$
$812$	−1621.51	+	4990.47i	−0.0700788	+	0.215679i
$813$		0			0
$814$	−13078.4	+	22652.4i	−0.563142	+	0.975390i
$815$	−5909.52	−	10235.6i	−0.253989	−	0.439922i
$816$		0			0
$817$	−229.491	+	397.490i	−0.00982727	+	0.0170213i
$818$	3451.88			0.147545
$819$		0			0
$820$	−20240.5			−0.861987
$821$	2612.24	−	4524.54i	0.111045	−	0.192335i	−0.805147	−	0.593075i	$-0.797914\pi$
$821$	2612.24	−	4524.54i	0.111045	−	0.192335i	0.916192	+	0.400740i	$0.131247\pi$
$822$		0			0
$823$	−1856.55	−	3215.64i	−0.0786333	−	0.136197i	0.824027	−	0.566550i	$-0.191722\pi$
$823$	−1856.55	−	3215.64i	−0.0786333	−	0.136197i	−0.902660	+	0.430353i	$0.858389\pi$
$824$	−5708.65	+	9887.67i	−0.241347	+	0.418026i
$825$		0			0
$826$	4385.90	+	4871.06i	0.184752	+	0.205189i
$827$	10202.6			0.428996			0.214498	−	0.976724i	$-0.431188\pi$
$827$	10202.6			0.428996			0.214498	+	0.976724i	$0.431188\pi$
$828$		0			0
$829$	−12497.6	−	21646.5i	−0.523594	−	0.906891i	−0.999623	−	0.0274616i	$-0.991258\pi$
$829$	−12497.6	−	21646.5i	−0.523594	−	0.906891i	0.476029	−	0.879430i	$-0.342076\pi$
$830$	−1690.32	−	2927.72i	−0.0706891	−	0.122437i
$831$		0			0
$832$	7282.06			0.303437
$833$	−25484.1	+	11346.1i	−1.05999	+	0.471933i
$834$		0			0
$835$	34434.4	−	59642.1i	1.42713	−	2.47186i
$836$	−3488.31	−	6041.94i	−0.144313	−	0.249958i
$837$		0			0
$838$	−10779.7	+	18670.9i	−0.444364	+	0.769661i
$839$	31173.6			1.28275			0.641377	−	0.767226i	$-0.278363\pi$
$839$	31173.6			1.28275			0.641377	+	0.767226i	$0.278363\pi$
$840$		0			0
$841$	−21682.6			−0.889033
$842$	−11303.6	+	19578.4i	−0.462646	+	0.801327i
$843$		0			0
$844$	3919.29	+	6788.40i	0.159843	+	0.276856i
$845$	10465.1	−	18126.0i	0.426046	−	0.737934i
$846$		0			0
$847$	−43888.2	+	9328.63i	−1.78042	+	0.378436i
$848$	1299.98			0.0526434
$849$		0			0
$850$	−13619.7	−	23590.1i	−0.549591	−	0.951920i
$851$	−4505.72	−	7804.13i	−0.181497	−	0.314362i
$852$		0			0
$853$	−25280.7			−1.01477			−0.507383	−	0.861721i	$-0.669387\pi$
$853$	−25280.7			−1.01477			−0.507383	+	0.861721i	$0.669387\pi$
$854$	−5967.90	+	18367.2i	−0.239130	+	0.735963i
$855$		0			0
$856$	−1432.72	+	2481.54i	−0.0572070	+	0.0990855i
$857$	13705.4	+	23738.4i	0.546285	+	0.946194i	0.998525	+	0.0542972i	$0.0172918\pi$
$857$	13705.4	+	23738.4i	0.546285	+	0.946194i	−0.452240	+	0.891896i	$0.649375\pi$
$858$		0			0
$859$	−12279.4	+	21268.6i	−0.487740	+	0.844790i	−0.999901	−	0.0140994i	$-0.995512\pi$
$859$	−12279.4	+	21268.6i	−0.487740	+	0.844790i	0.512161	+	0.858890i	$0.328845\pi$
$860$	2186.87			0.0867113
$861$		0			0
$862$	14523.9			0.573883
$863$	3574.18	−	6190.66i	0.140981	−	0.244186i	−0.786885	−	0.617099i	$-0.788308\pi$
$863$	3574.18	−	6190.66i	0.140981	−	0.244186i	0.927866	+	0.372913i	$0.121641\pi$
$864$		0			0
$865$	−21117.6	−	36576.7i	−0.830080	−	1.43774i
$866$	12353.9	−	21397.6i	0.484760	−	0.839629i
$867$		0			0
$868$	19132.8	−	4066.77i	0.748169	−	0.159027i
$869$	−17751.7			−0.692962
$870$		0			0
$871$	−9806.52	−	16985.4i	−0.381494	−	0.660767i
$872$	2339.69	+	4052.46i	0.0908621	+	0.157378i
$873$		0			0
$874$	−1127.05			−0.0436190
$875$	19173.8	+	21294.7i	0.740791	+	0.822736i
$876$		0			0
$877$	14109.2	−	24437.9i	0.543256	−	0.940946i	−0.455459	−	0.890257i	$-0.650525\pi$
$877$	14109.2	−	24437.9i	0.543256	−	0.940946i	0.998714	−	0.0506895i	$-0.0161419\pi$
$878$	−1424.01	−	2466.46i	−0.0547359	−	0.0948053i
$879$		0			0
$880$	−5172.57	+	8959.15i	−0.198145	+	0.343197i
$881$	7431.50			0.284192			0.142096	−	0.989853i	$-0.454616\pi$
$881$	7431.50			0.284192			0.142096	+	0.989853i	$0.454616\pi$
$882$		0			0
$883$	4937.77			0.188187			0.0940936	−	0.995563i	$-0.470005\pi$
$883$	4937.77			0.188187			0.0940936	+	0.995563i	$0.470005\pi$
$884$	−7185.79	+	12446.1i	−0.273398	+	0.473540i
$885$		0			0
$886$	−10726.7	−	18579.2i	−0.406739	−	0.704493i
$887$	20986.8	−	36350.3i	0.794441	−	1.37601i	−0.128753	−	0.991677i	$-0.541097\pi$
$887$	20986.8	−	36350.3i	0.794441	−	1.37601i	0.923194	−	0.384335i	$-0.125569\pi$
$888$		0			0
$889$	20310.2	+	22556.9i	0.766236	+	0.850995i
$890$	−27458.6			−1.03417
$891$		0			0
$892$	2749.97	+	4763.08i	0.103224	+	0.178789i
$893$	−2591.83	−	4489.17i	−0.0971245	−	0.168224i
$894$		0			0
$895$	55492.5			2.07253
$896$	−20553.4	+	4368.73i	−0.766342	+	0.162889i
$897$		0			0
$898$	−334.504	+	579.378i	−0.0124305	+	0.0215302i
$899$	−5044.24	−	8736.88i	−0.187135	−	0.324128i
$900$		0			0
$901$	5726.62	−	9918.80i	0.211744	−	0.366751i
$902$	−19892.6			−0.734315
$903$		0			0
$904$	−43106.4			−1.58595
$905$	37312.4	−	64626.9i	1.37050	−	2.37378i
$906$		0			0
$907$	−20712.1	−	35874.4i	−0.758252	−	1.31333i	−0.943741	−	0.330685i	$-0.892720\pi$
$907$	−20712.1	−	35874.4i	−0.758252	−	1.31333i	0.185489	−	0.982646i	$-0.440613\pi$
$908$	8029.37	−	13907.3i	0.293463	−	0.508292i
$909$		0			0
$910$	−5428.02	+	16705.6i	−0.197733	+	0.608556i
$911$	−40072.0			−1.45735			−0.728675	−	0.684860i	$-0.759864\pi$
$911$	−40072.0			−1.45735			−0.728675	+	0.684860i	$0.759864\pi$
$912$		0			0
$913$	3542.85	+	6136.40i	0.128424	+	0.222437i
$914$	−566.039	−	980.408i	−0.0204846	−	0.0354803i
$915$		0			0
$916$	21996.5			0.793432
$917$	−1662.12	+	353.291i	−0.0598561	+	0.0127227i
$918$		0			0
$919$	10908.7	−	18894.5i	0.391562	−	0.678206i	−0.601094	−	0.799179i	$-0.705268\pi$
$919$	10908.7	−	18894.5i	0.391562	−	0.678206i	0.992656	+	0.120973i	$0.0386015\pi$
$920$	6628.96	+	11481.7i	0.237555	+	0.411457i
$921$		0			0
$922$	−6571.18	+	11381.6i	−0.234718	+	0.406544i
$923$	23232.5			0.828501
$924$		0			0
$925$	−55992.0			−1.99028
$926$	−7522.18	+	13028.8i	−0.266948	+	0.462368i
$927$		0			0
$928$	4855.13	+	8409.33i	0.171743	+	0.297467i
$929$	−5988.52	+	10372.4i	−0.211493	+	0.366317i	−0.952182	−	0.305532i	$-0.901166\pi$
$929$	−5988.52	+	10372.4i	−0.211493	+	0.366317i	0.740689	+	0.671848i	$0.234499\pi$
$930$		0			0
$931$	5801.93	+	4215.38i	0.204243	+	0.148393i
$932$	16315.8			0.573435
$933$		0			0
$934$	8646.69	+	14976.5i	0.302921	+	0.524675i
$935$	45571.9	+	78932.9i	1.59397	+	2.76083i
$936$		0			0
$937$	−15155.2			−0.528389			−0.264194	−	0.964469i	$-0.585106\pi$
$937$	−15155.2			−0.528389			−0.264194	+	0.964469i	$0.585106\pi$
$938$	−11971.0	−	13295.2i	−0.416701	−	0.462796i
$939$		0			0
$940$	−12349.0	+	21389.2i	−0.428491	+	0.742168i
$941$	3477.20	+	6022.69i	0.120461	+	0.208644i	0.919949	−	0.392037i	$-0.128229\pi$
$941$	3477.20	+	6022.69i	0.120461	+	0.208644i	−0.799489	+	0.600681i	$0.794896\pi$
$942$		0			0
$943$	3426.67	−	5935.16i	0.118333	−	0.204958i
$944$	−2044.39			−0.0704865
$945$		0			0
$946$	2149.29			0.0738682
$947$	−4778.75	+	8277.03i	−0.163979	+	0.284020i	−0.936292	−	0.351222i	$-0.885766\pi$
$947$	−4778.75	+	8277.03i	−0.163979	+	0.284020i	0.772313	+	0.635242i	$0.219100\pi$
$948$		0			0
$949$	−6308.79	−	10927.1i	−0.215798	−	0.373772i
$950$	−3501.43	+	6064.65i	−0.119580	+	0.207119i
$951$		0			0
$952$	−10001.6	+	30781.5i	−0.340497	+	1.04794i
$953$	−8437.24			−0.286788			−0.143394	−	0.989666i	$-0.545802\pi$
$953$	−8437.24			−0.286788			−0.143394	+	0.989666i	$0.545802\pi$
$954$		0			0
$955$	8021.90	+	13894.3i	0.271814	+	0.470796i
$956$	4929.61	+	8538.33i	0.166773	+	0.288859i
$957$		0			0
$958$	13080.9			0.441153
$959$	−10685.8	+	32887.2i	−0.359814	+	1.10739i
$960$		0			0
$961$	−3907.84	+	6768.58i	−0.131175	+	0.227202i
$962$	−6926.12	−	11996.4i	−0.232128	−	0.402057i
$963$		0			0
$964$	−10210.1	+	17684.4i	−0.341126	+	0.590847i
$965$	−26682.3			−0.890087
$966$		0			0
$967$	52344.7			1.74074			0.870369	−	0.492401i	$-0.163881\pi$
$967$	52344.7			1.74074			0.870369	+	0.492401i	$0.163881\pi$
$968$	−26029.0	+	45083.6i	−0.864261	+	1.49694i
$969$		0			0
$970$	1759.62	+	3047.76i	0.0582454	+	0.100884i
$971$	−18491.5	+	32028.2i	−0.611143	+	1.05853i	0.379905	+	0.925026i	$0.375957\pi$
$971$	−18491.5	+	32028.2i	−0.611143	+	1.05853i	−0.991048	+	0.133506i	$0.957377\pi$
$972$		0			0
$973$	7928.41	+	8805.43i	0.261226	+	0.290122i
$974$	6397.25			0.210453
$975$		0			0
$976$	−3011.77	−	5216.54i	−0.0987750	−	0.171083i
$977$	−8936.51	−	15478.5i	−0.292635	−	0.506859i	0.681797	−	0.731541i	$-0.261199\pi$
$977$	−8936.51	−	15478.5i	−0.292635	−	0.506859i	−0.974432	+	0.224683i	$0.927865\pi$
$978$		0			0
$979$	57552.2			1.87883
$980$	3571.86	−	33982.7i	0.116428	−	1.10769i
$981$		0			0
$982$	8933.76	−	15473.7i	0.290313	−	0.502838i
$983$	−16872.0	−	29223.2i	−0.547440	−	0.948195i	−0.998449	−	0.0556750i	$-0.982269\pi$
$983$	−16872.0	−	29223.2i	−0.547440	−	0.948195i	0.451009	−	0.892520i	$-0.351064\pi$
$984$		0			0
$985$	8709.13	−	15084.7i	0.281722	−	0.487956i
$986$	6761.29			0.218381
$987$		0			0
$988$	3694.72			0.118972
$989$	−370.232	+	641.260i	−0.0119036	+	0.0206177i
$990$		0			0
$991$	7253.24	+	12563.0i	0.232499	+	0.402701i	0.958543	−	0.284948i	$-0.0919763\pi$
$991$	7253.24	+	12563.0i	0.232499	+	0.402701i	−0.726044	+	0.687649i	$0.758643\pi$
$992$	18098.4	−	31347.4i	0.579259	−	1.00331i
$993$		0			0
$994$	20728.8	−	4406.00i	0.661447	−	0.140594i
$995$	61134.7			1.94784
$996$		0			0
$997$	21184.4	+	36692.5i	0.672936	+	1.16556i	0.977068	+	0.212929i	$0.0683003\pi$
$997$	21184.4	+	36692.5i	0.672936	+	1.16556i	−0.304132	+	0.952630i	$0.598366\pi$
$998$	−3013.20	−	5219.01i	−0.0955723	−	0.165536i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.e.d.37.3	yes	8
3.2	odd	2	inner	63.4.e.d.37.2	✓	8
7.2	even	3		441.4.a.w.1.2		4
7.3	odd	6		441.4.e.x.361.3		8
7.4	even	3	inner	63.4.e.d.46.3	yes	8
7.5	odd	6		441.4.a.v.1.2		4
7.6	odd	2		441.4.e.x.226.3		8
21.2	odd	6		441.4.a.w.1.3		4
21.5	even	6		441.4.a.v.1.3		4
21.11	odd	6	inner	63.4.e.d.46.2	yes	8
21.17	even	6		441.4.e.x.361.2		8
21.20	even	2		441.4.e.x.226.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.e.d.37.2	✓	8	3.2	odd	2	inner
63.4.e.d.37.3	yes	8	1.1	even	1	trivial
63.4.e.d.46.2	yes	8	21.11	odd	6	inner
63.4.e.d.46.3	yes	8	7.4	even	3	inner
441.4.a.v.1.2		4	7.5	odd	6
441.4.a.v.1.3		4	21.5	even	6
441.4.a.w.1.2		4	7.2	even	3
441.4.a.w.1.3		4	21.2	odd	6
441.4.e.x.226.2		8	21.20	even	2
441.4.e.x.226.3		8	7.6	odd	2
441.4.e.x.361.2		8	21.17	even	6
441.4.e.x.361.3		8	7.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(-9.14584 + 15.8411i) q^{5} +(12.3924 + 13.7633i) q^{7} +21.4878 q^{8} +O(q^{10})\)	\(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(-9.14584 + 15.8411i) q^{5} +(12.3924 + 13.7633i) q^{7} +21.4878 q^{8} +(14.6156 + 25.3149i) q^{10} +(-30.6336 - 53.0590i) q^{11} +32.4462 q^{13} +(28.9496 - 6.15337i) q^{14} +(-4.61555 + 7.99438i) q^{16} +(40.6644 + 70.4329i) q^{17} +(10.4542 - 18.1072i) q^{19} -99.6206 q^{20} -97.9084 q^{22} +(16.8655 - 29.2119i) q^{23} +(-104.793 - 181.507i) q^{25} +(25.9254 - 44.9041i) q^{26} +(-31.1693 + 95.9287i) q^{28} +52.0227 q^{29} +(-96.9622 - 167.943i) q^{31} +(93.3271 + 161.647i) q^{32} +129.968 q^{34} +(-331.364 + 70.4329i) q^{35} +(133.578 - 231.363i) q^{37} +(-16.7064 - 28.9364i) q^{38} +(-196.524 + 340.390i) q^{40} +203.176 q^{41} -21.9520 q^{43} +(166.838 - 288.971i) q^{44} +(-26.9520 - 46.6822i) q^{46} +(123.961 - 214.706i) q^{47} +(-35.8547 + 341.121i) q^{49} -334.929 q^{50} +(88.3547 + 153.035i) q^{52} +(-70.4131 - 121.959i) q^{53} +1120.68 q^{55} +(266.286 + 295.742i) q^{56} +(41.5676 - 71.9971i) q^{58} +(110.734 + 191.797i) q^{59} +(-326.263 + 565.104i) q^{61} -309.902 q^{62} +224.435 q^{64} +(-296.748 + 513.983i) q^{65} +(-302.239 - 523.493i) q^{67} +(-221.468 + 383.593i) q^{68} +(-167.293 + 514.871i) q^{70} +716.031 q^{71} +(-194.438 - 336.777i) q^{73} +(-213.465 - 369.731i) q^{74} +113.872 q^{76} +(350.639 - 1079.15i) q^{77} +(144.871 - 250.923i) q^{79} +(-84.4263 - 146.231i) q^{80} +(162.343 - 281.186i) q^{82} -115.652 q^{83} -1487.64 q^{85} +(-17.5403 + 30.3806i) q^{86} +(-658.249 - 1140.12i) q^{88} +(-469.682 + 813.513i) q^{89} +(402.088 + 446.566i) q^{91} +183.707 q^{92} +(-198.096 - 343.112i) q^{94} +(191.225 + 331.212i) q^{95} +120.394 q^{97} +(443.447 + 322.186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 12 q^{7}+O(q^{10}) \) 8 * q - 6 * q^4 - 12 * q^7	\( 8 q - 6 q^{4} - 12 q^{7} - 22 q^{10} + 204 q^{13} + 102 q^{16} - 222 q^{19} - 172 q^{22} - 366 q^{25} - 166 q^{28} - 220 q^{31} + 2040 q^{34} + 374 q^{37} - 822 q^{40} - 1676 q^{43} - 1716 q^{46} + 380 q^{49} + 40 q^{52} + 5020 q^{55} + 1694 q^{58} - 1332 q^{61} - 1372 q^{64} - 1890 q^{67} - 866 q^{70} - 1750 q^{73} + 4912 q^{76} - 8 q^{79} - 2480 q^{82} - 2232 q^{85} - 2682 q^{88} + 466 q^{91} + 1416 q^{94} + 6020 q^{97}+O(q^{100}) \) 8 * q - 6 * q^4 - 12 * q^7 - 22 * q^10 + 204 * q^13 + 102 * q^16 - 222 * q^19 - 172 * q^22 - 366 * q^25 - 166 * q^28 - 220 * q^31 + 2040 * q^34 + 374 * q^37 - 822 * q^40 - 1676 * q^43 - 1716 * q^46 + 380 * q^49 + 40 * q^52 + 5020 * q^55 + 1694 * q^58 - 1332 * q^61 - 1372 * q^64 - 1890 * q^67 - 866 * q^70 - 1750 * q^73 + 4912 * q^76 - 8 * q^79 - 2480 * q^82 - 2232 * q^85 - 2682 * q^88 + 466 * q^91 + 1416 * q^94 + 6020 * q^97

Introduction

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