LMFDB - Embedded newform 63.4.e.d.37.2

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			37.2
Root			$0.799027 + 1.38396i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.4.e.d.46.2

$q$-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	−0.972000	−	0.234983i	$-0.924497\pi$
$2$	−0.799027	+	1.38396i	−0.282499	+	0.489302i	0.689501	+	0.724285i	$0.257830\pi$
$3$		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	$-0.528400\pi$
$5$	9.14584	−	15.8411i	0.818029	−	1.41687i	0.907132	−	0.420846i	$-0.138267\pi$
$6$		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	$0.150586\pi$
$11$	30.6336	+	53.0590i	0.839672	+	1.45435i	−0.0504975	+	0.998724i	$0.516081\pi$
$12$		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	$-0.969660\pi$
$17$	−40.6644	−	70.4329i	−0.580152	−	1.00485i	0.415309	−	0.909680i	$-0.363673\pi$
$18$		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	−0.932292	−	0.361705i	$-0.882195\pi$
$23$	−16.8655	+	29.2119i	−0.152900	+	0.264831i	0.779392	+	0.626536i	$0.215528\pi$
$24$		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	$-0.553265\pi$
$29$	−52.0227			−0.333116			−0.166558	+	0.986032i	$0.553265\pi$
$30$		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	$-0.626475\pi$
$41$	−203.176			−0.773921			−0.386960	+	0.922096i	$0.626475\pi$
$42$		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	−0.991729	−	0.128346i	$-0.959033\pi$
$47$	−123.961	+	214.706i	−0.384713	+	0.666343i	0.607016	+	0.794690i	$0.292366\pi$
$48$		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	0.942728	−	0.333563i	$-0.108251\pi$
$53$	70.4131	+	121.959i	0.182490	+	0.316082i	−0.760238	+	0.649645i	$0.774918\pi$
$54$		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	0.717603	−	0.696453i	$-0.245239\pi$
$59$	−110.734	−	191.797i	−0.244344	−	0.423217i	−0.961947	+	0.273236i	$0.911906\pi$
$60$		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	$-0.704209\pi$
$71$	−716.031			−1.19686			−0.598431	+	0.801174i	$0.704209\pi$
$72$		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	$-0.475634\pi$
$83$	115.652			0.152946			0.0764728	+	0.997072i	$0.475634\pi$
$84$		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	$-0.644367\pi$
$89$	469.682	−	813.513i	0.559395	−	0.968901i	0.997547	−	0.0699997i	$-0.0222998\pi$
$90$		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	$0.0506938\pi$
$101$	640.502	+	1109.38i	0.631013	+	1.09295i	−0.356332	+	0.934359i	$0.615973\pi$
$102$		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	−0.834332	−	0.551262i	$-0.814146\pi$
$107$	66.6758	−	115.486i	0.0602411	−	0.104341i	0.894573	+	0.446922i	$0.147480\pi$
$108$		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	$-0.185450\pi$
$113$	2006.09			1.67006			0.835031	+	0.550204i	$0.185450\pi$
$114$		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	−0.850322	−	0.526263i	$-0.823593\pi$
$131$	45.8755	−	79.4587i	0.0305967	−	0.0529950i	0.880918	+	0.473268i	$0.156926\pi$
$132$		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	$-0.968864\pi$
$137$	−933.564	−	1616.98i	−0.582188	−	1.00838i	0.413032	−	0.910717i	$-0.364470\pi$
$138$		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	$0.497621\pi$
$149$	−1568.27	+	2716.32i	−0.862264	+	1.49348i	−0.869739	+	0.493513i	$0.835713\pi$
$150$		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	$-0.162630\pi$
$167$	3765.03			1.74459			0.872296	+	0.488979i	$0.162630\pi$
$168$		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	$-0.663953\pi$
$173$	1154.49	−	1999.64i	0.507366	−	0.878783i	0.999964	−	0.00852600i	$-0.00271394\pi$
$174$		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	$0.0516705\pi$
$179$	1516.88	+	2627.31i	0.633390	+	1.09706i	−0.353464	+	0.935448i	$0.614996\pi$
$180$		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	−0.937059	−	0.349170i	$-0.886464\pi$
$191$	−438.554	+	759.599i	−0.166140	+	0.287762i	0.770920	+	0.636932i	$0.219797\pi$
$192$		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	$-0.444914\pi$
$197$	952.250			0.344391			0.172195	+	0.985063i	$0.444914\pi$
$198$		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	0.996966	−	0.0778419i	$-0.0248029\pi$
$227$	1474.30	+	2553.57i	0.431070	+	0.746635i	−0.565896	+	0.824477i	$0.691470\pi$
$228$		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	−0.996053	−	0.0887561i	$-0.971711\pi$
$233$	−1497.90	+	2594.44i	−0.421162	+	0.729473i	0.574892	+	0.818230i	$0.305044\pi$
$234$		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	$-0.578779\pi$
$239$	−1810.28			−0.489948			−0.244974	+	0.969530i	$0.578779\pi$
$240$		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	$-0.610550\pi$
$251$	−2706.96			−0.680724			−0.340362	+	0.940295i	$0.610550\pi$
$252$		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	$0.392878\pi$
$257$	−2687.64	+	4655.13i	−0.652337	+	1.12988i	−0.982554	+	0.185975i	$0.940456\pi$
$258$		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	$-0.955802\pi$
$263$	−2623.28	−	4543.66i	−0.615051	−	1.06530i	0.375324	−	0.926893i	$-0.377531\pi$
$264$		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	0.643214	−	0.765686i	$-0.277600\pi$
$269$	−1506.66	−	2609.61i	−0.341496	−	0.591489i	−0.984711	+	0.174197i	$0.944267\pi$
$270$		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	$-0.268011\pi$
$281$	6274.14			1.33197			0.665986	+	0.745964i	$0.268011\pi$
$282$		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	$-0.527162\pi$
$293$	−854.897			−0.170456			−0.0852280	+	0.996361i	$0.527162\pi$
$294$		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	$0.0722064\pi$
$311$	3740.25	+	6478.31i	0.681962	+	1.18119i	−0.292419	+	0.956290i	$0.594460\pi$
$312$		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	−0.820070	−	0.572263i	$-0.806065\pi$
$317$	482.902	−	836.410i	0.0855598	−	0.148194i	0.905630	+	0.424070i	$0.139399\pi$
$318$		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	$0.0136572\pi$
$347$	3469.08	+	6008.62i	0.536686	+	0.929567i	−0.462394	+	0.886675i	$0.653009\pi$
$348$		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	0.554521	−	0.832170i	$-0.312902\pi$
$353$	−2940.88	−	5093.75i	−0.443420	−	0.768026i	−0.997941	+	0.0641440i	$0.979568\pi$
$354$		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	−0.843555	−	0.537043i	$-0.819541\pi$
$359$	294.634	−	510.322i	0.0433153	−	0.0750244i	0.886870	+	0.462019i	$0.152875\pi$
$360$		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	$0.416054\pi$
$383$	−5289.87	+	9162.33i	−0.705744	+	1.22238i	−0.966422	+	0.256959i	$0.917280\pi$
$384$		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	0.517964	−	0.855403i	$-0.326690\pi$
$389$	−3696.65	−	6402.78i	−0.481819	−	0.834534i	−0.999782	+	0.0208684i	$0.993357\pi$
$390$		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	−0.870584	−	0.492019i	$-0.836259\pi$
$401$	−73.8031	+	127.831i	−0.00919090	+	0.0159191i	0.861393	+	0.507938i	$0.169592\pi$
$402$		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	$-0.211897\pi$
$419$	13491.0			1.57298			0.786488	+	0.617605i	$0.211897\pi$
$420$		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	$-0.997102\pi$
$431$	−4544.26	−	7870.89i	−0.507864	−	0.879646i	0.492095	−	0.870542i	$-0.336231\pi$
$432$		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	$0.422477\pi$
$443$	−6712.36	+	11626.1i	−0.719896	+	1.24690i	−0.961041	+	0.276407i	$0.910856\pi$
$444$		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	$-0.492996\pi$
$449$	418.639			0.0440018			0.0220009	+	0.999758i	$0.492996\pi$
$450$		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	$-0.363630\pi$
$461$	8223.97			0.830865			0.415432	+	0.909624i	$0.363630\pi$
$462$		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	$-0.653213\pi$
$467$	5410.76	−	9371.72i	0.536146	−	0.928632i	0.999107	−	0.0422535i	$-0.0134537\pi$
$468$		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	0.602100	−	0.798420i	$-0.294331\pi$
$479$	−4092.75	−	7088.85i	−0.390402	−	0.676196i	−0.992503	+	0.122224i	$0.960997\pi$
$480$		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	$-0.671774\pi$
$491$	−11180.8			−1.02766			−0.513831	+	0.857891i	$0.671774\pi$
$492$		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	$-0.294110\pi$
$503$	13597.2			1.20531			0.602654	+	0.798003i	$0.294110\pi$
$504$		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	−0.660099	−	0.751179i	$-0.729485\pi$
$509$	3680.38	−	6374.60i	0.320491	−	0.555106i	0.980589	+	0.196073i	$0.0628188\pi$
$510$		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	$0.0303468\pi$
$521$	6899.40	+	11950.1i	0.580169	+	1.00488i	−0.415290	+	0.909689i	$0.636320\pi$
$522$		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	0.950629	−	0.310330i	$-0.100439\pi$
$557$	2715.39	+	4703.19i	0.206561	+	0.357775i	−0.744068	+	0.668104i	$0.767106\pi$
$558$		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	$-0.807889\pi$
$563$	−12065.3	−	20897.8i	−0.903185	−	1.56436i	−0.0798500	−	0.996807i	$-0.525444\pi$
$564$		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	$-0.601816\pi$
$569$	9024.27	−	15630.5i	0.664880	−	1.15161i	0.979318	−	0.202328i	$-0.0648509\pi$
$570$		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	$-0.631740\pi$
$587$	−11438.9			−0.804315			−0.402157	+	0.915571i	$0.631740\pi$
$588$		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	−0.929201	−	0.369575i	$-0.879503\pi$
$593$	−2087.22	+	3615.17i	−0.144539	+	0.250349i	0.784662	+	0.619924i	$0.212837\pi$
$594$		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	0.601841	−	0.798616i	$-0.294434\pi$
$599$	−5727.77	−	9920.79i	−0.390702	−	0.676715i	−0.992542	+	0.121901i	$0.961101\pi$
$600$		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	$-0.359162\pi$
$617$	13123.9			0.856321			0.428160	+	0.903703i	$0.359162\pi$
$618$		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	$-0.964840\pi$
$641$	−9614.27	−	16652.4i	−0.592419	−	1.02610i	0.401486	−	0.915865i	$-0.368494\pi$
$642$		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	0.718040	−	0.696001i	$-0.245039\pi$
$647$	−4011.20	−	6947.60i	−0.243735	−	0.422161i	−0.961775	+	0.273840i	$0.911706\pi$
$648$		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	−0.895126	−	0.445814i	$-0.852914\pi$
$653$	−1025.85	+	1776.82i	−0.0614769	+	0.106481i	0.833649	+	0.552295i	$0.186248\pi$
$654$		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	$-0.356255\pi$
$659$	14765.2			0.872792			0.436396	+	0.899755i	$0.356255\pi$
$660$		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	$0.420431\pi$
$677$	−12602.1	+	21827.5i	−0.715420	+	1.23914i	−0.962797	+	0.270225i	$0.912902\pi$
$678$		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	0.999646	−	0.0266151i	$-0.00847285\pi$
$683$	8510.27	+	14740.2i	0.476774	+	0.825796i	−0.522872	+	0.852411i	$0.675140\pi$
$684$		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	$-0.778792\pi$
$701$	−28511.4			−1.53618			−0.768088	+	0.640345i	$0.778792\pi$
$702$		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	$0.357567\pi$
$719$	−10881.7	+	18847.6i	−0.564420	+	0.977603i	−0.997103	+	0.0760577i	$0.975767\pi$
$720$		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	$-0.417986\pi$
$743$	10321.3			0.509625			0.254813	+	0.966990i	$0.417986\pi$
$744$		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	$-0.504042\pi$
$761$	18045.8	−	31256.3i	0.859607	−	1.48888i	0.872304	−	0.488963i	$-0.162625\pi$
$762$		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	$-0.910351\pi$
$773$	−15495.4	−	26838.8i	−0.720997	−	1.24880i	0.239603	−	0.970871i	$-0.422983\pi$
$774$		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	$-0.351162\pi$
$797$	20283.3			0.901470			0.450735	+	0.892658i	$0.351162\pi$
$798$		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	0.987465	−	0.157836i	$-0.0504517\pi$
$809$	8215.67	+	14230.0i	0.357043	+	0.618416i	−0.630423	+	0.776252i	$0.717118\pi$
$810$		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	−0.916192	−	0.400740i	$-0.868753\pi$
$821$	−2612.24	+	4524.54i	−0.111045	+	0.192335i	0.805147	+	0.593075i	$0.202086\pi$
$822$		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	$-0.568812\pi$
$827$	−10202.6			−0.428996			−0.214498	+	0.976724i	$0.568812\pi$
$828$		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	$-0.721637\pi$
$839$	−31173.6			−1.28275			−0.641377	+	0.767226i	$0.721637\pi$
$840$		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	$-0.982708\pi$
$857$	−13705.4	−	23738.4i	−0.546285	−	0.946194i	0.452240	−	0.891896i	$-0.350625\pi$
$858$		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	−0.927866	−	0.372913i	$-0.878359\pi$
$863$	−3574.18	+	6190.66i	−0.140981	+	0.244186i	0.786885	+	0.617099i	$0.211692\pi$
$864$		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	$-0.545384\pi$
$881$	−7431.50			−0.284192			−0.142096	+	0.989853i	$0.545384\pi$
$882$		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	$0.458903\pi$
$887$	−20986.8	+	36350.3i	−0.794441	+	1.37601i	−0.923194	+	0.384335i	$0.874431\pi$
$888$		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	$-0.240136\pi$
$911$	40072.0			1.45735			0.728675	+	0.684860i	$0.240136\pi$
$912$		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	−0.740689	−	0.671848i	$-0.765501\pi$
$929$	5988.52	−	10372.4i	0.211493	−	0.366317i	0.952182	+	0.305532i	$0.0988341\pi$
$930$		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	0.799489	−	0.600681i	$-0.205104\pi$
$941$	−3477.20	−	6022.69i	−0.120461	−	0.208644i	−0.919949	+	0.392037i	$0.871771\pi$
$942$		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	−0.772313	−	0.635242i	$-0.780900\pi$
$947$	4778.75	−	8277.03i	0.163979	−	0.284020i	0.936292	+	0.351222i	$0.114234\pi$
$948$		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	$-0.454198\pi$
$953$	8437.24			0.286788			0.143394	+	0.989666i	$0.454198\pi$
$954$		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	$-0.624043\pi$
$971$	18491.5	−	32028.2i	0.611143	−	1.05853i	0.991048	−	0.133506i	$-0.0426234\pi$
$972$		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	0.974432	−	0.224683i	$-0.0721346\pi$
$977$	8936.51	+	15478.5i	0.292635	+	0.506859i	−0.681797	+	0.731541i	$0.738801\pi$
$978$		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	$0.0177311\pi$
$983$	16872.0	+	29223.2i	0.547440	+	0.948195i	−0.451009	+	0.892520i	$0.648936\pi$
$984$		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.37.2	✓	8
3.2	odd	2	inner	63.4.e.d.37.3	yes	8
7.2	even	3		441.4.a.w.1.3		4
7.3	odd	6		441.4.e.x.361.2		8
7.4	even	3	inner	63.4.e.d.46.2	yes	8
7.5	odd	6		441.4.a.v.1.3		4
7.6	odd	2		441.4.e.x.226.2		8
21.2	odd	6		441.4.a.w.1.2		4
21.5	even	6		441.4.a.v.1.2		4
21.11	odd	6	inner	63.4.e.d.46.3	yes	8
21.17	even	6		441.4.e.x.361.3		8
21.20	even	2		441.4.e.x.226.3		8

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