LMFDB - Embedded newform 441.4.e.x.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not 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:	$26.0198423125$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$-0.799027 + 1.38396i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.x.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.0755034\pi$
$2$	0.799027	+	1.38396i	0.282499	+	0.489302i	−0.689501	+	0.724285i	$0.742170\pi$
$3$		0			0
$3$		0			0
$4$	2.72311	−	4.71657i	0.340389	−	0.589571i
$5$	9.14584	+	15.8411i	0.818029	+	1.41687i	0.907132	+	0.420846i	$0.138267\pi$
$5$	9.14584	+	15.8411i	0.818029	+	1.41687i	−0.0891033	+	0.996022i	$0.528400\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	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	0.0504975	+	0.998724i	$0.483919\pi$
$11$	−30.6336	+	53.0590i	−0.839672	+	1.45435i	−0.890169	+	0.455630i	$0.849414\pi$
$12$		0			0
$13$	−32.4462			−0.692228			−0.346114	−	0.938192i	$-0.612499\pi$
$13$	−32.4462			−0.692228			−0.346114	+	0.938192i	$0.612499\pi$
$14$		0			0
$15$		0			0
$16$	−4.61555	−	7.99438i	−0.0721180	−	0.124912i
$17$	−40.6644	+	70.4329i	−0.580152	+	1.00485i	0.415309	+	0.909680i	$0.363673\pi$
$17$	−40.6644	+	70.4329i	−0.580152	+	1.00485i	−0.995461	+	0.0951718i	$0.969660\pi$
$18$		0			0
$19$	−10.4542	−	18.1072i	−0.126230	−	0.218636i	0.795983	−	0.605319i	$-0.206954\pi$
$19$	−10.4542	−	18.1072i	−0.126230	−	0.218636i	−0.922213	+	0.386682i	$0.873621\pi$
$20$	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	$-0.117805\pi$
$23$	16.8655	+	29.2119i	0.152900	+	0.264831i	−0.779392	+	0.626536i	$0.784472\pi$
$24$		0			0
$25$	−104.793	+	181.507i	−0.838343	+	1.45205i
$26$	−25.9254	−	44.9041i	−0.195554	−	0.338709i
$27$		0			0
$28$		0			0
$29$	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	−0.435570	−	0.900155i	$-0.643453\pi$
$31$	96.9622	−	167.943i	0.561772	−	0.973017i	0.997342	−	0.0728626i	$-0.0232135\pi$
$32$	93.3271	−	161.647i	0.515564	−	0.892983i
$33$		0			0
$34$	−129.968			−0.655568
$35$		0			0
$36$		0			0
$37$	133.578	+	231.363i	0.593515	+	1.02800i	0.993755	+	0.111587i	$0.0355935\pi$
$37$	133.578	+	231.363i	0.593515	+	1.02800i	−0.400240	+	0.916410i	$0.631073\pi$
$38$	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	0.607016	−	0.794690i	$-0.292366\pi$
$47$	−123.961	−	214.706i	−0.384713	−	0.666343i	−0.991729	+	0.128346i	$0.959033\pi$
$48$		0			0
$49$		0			0
$50$	−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	$-0.891749\pi$
$53$	−70.4131	+	121.959i	−0.182490	+	0.316082i	0.760238	+	0.649645i	$0.225082\pi$
$54$		0			0
$55$	−1120.68			−2.74750
$56$		0			0
$57$		0			0
$58$	41.5676	+	71.9971i	0.0941050	+	0.162995i
$59$	−110.734	+	191.797i	−0.244344	+	0.423217i	−0.961947	−	0.273236i	$-0.911906\pi$
$59$	−110.734	+	191.797i	−0.244344	+	0.423217i	0.717603	+	0.696453i	$0.245239\pi$
$60$		0			0
$61$	326.263	+	565.104i	0.684815	+	1.18613i	0.973495	+	0.228709i	$0.0734503\pi$
$61$	326.263	+	565.104i	0.684815	+	1.18613i	−0.288680	+	0.957426i	$0.593216\pi$
$62$	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	0.447085	+	0.894492i	$0.352462\pi$
$67$	−302.239	+	523.493i	−0.551110	+	0.954551i	−0.998195	+	0.0600592i	$0.980871\pi$
$68$	221.468	+	383.593i	0.394954	+	0.684081i
$69$		0			0
$70$		0			0
$71$	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	$-0.732420\pi$
$73$	194.438	−	336.777i	0.311743	−	0.539956i	0.978740	+	0.205105i	$0.0657537\pi$
$74$	−213.465	+	369.731i	−0.335334	+	0.580816i
$75$		0			0
$76$	−113.872			−0.171869
$77$		0			0
$78$		0			0
$79$	144.871	+	250.923i	0.206319	+	0.357355i	0.950552	−	0.310565i	$-0.100518\pi$
$79$	144.871	+	250.923i	0.206319	+	0.357355i	−0.744233	+	0.667920i	$0.767185\pi$
$80$	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	0.997547	+	0.0699997i	$0.0222998\pi$
$89$	469.682	+	813.513i	0.559395	+	0.968901i	−0.438152	+	0.898901i	$0.644367\pi$
$90$		0			0
$91$		0			0
$92$	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	$-0.520070\pi$
$97$	−120.394			−0.126022			−0.0630110	+	0.998013i	$0.520070\pi$
$98$		0			0
$99$		0			0
$100$	570.725	+	988.525i	0.570725	+	0.988525i
$101$	640.502	−	1109.38i	0.631013	−	1.09295i	−0.356332	−	0.934359i	$-0.615973\pi$
$101$	640.502	−	1109.38i	0.631013	−	1.09295i	0.987345	−	0.158587i	$-0.0506938\pi$
$102$		0			0
$103$	265.669	+	460.153i	0.254147	+	0.440196i	0.964664	−	0.263485i	$-0.0848718\pi$
$103$	265.669	+	460.153i	0.254147	+	0.440196i	−0.710516	+	0.703681i	$0.751539\pi$
$104$	−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	$-0.185854\pi$
$107$	−66.6758	−	115.486i	−0.0602411	−	0.104341i	−0.894573	+	0.446922i	$0.852520\pi$
$108$		0			0
$109$	108.884	−	188.593i	0.0956811	−	0.165725i	−0.814212	−	0.580568i	$-0.802830\pi$
$109$	108.884	−	188.593i	0.0956811	−	0.165725i	0.909893	+	0.414844i	$0.136164\pi$
$110$	−895.455	−	1550.97i	−0.776166	−	1.34436i
$111$		0			0
$112$		0			0
$113$	−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
$119$		0			0
$120$		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	$-0.156926\pi$
$131$	45.8755	+	79.4587i	0.0305967	+	0.0529950i	−0.850322	+	0.526263i	$0.823593\pi$
$132$		0			0
$133$		0			0
$134$	−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	−0.413032	−	0.910717i	$-0.635530\pi$
$137$	933.564	−	1616.98i	0.582188	−	1.00838i	0.995220	−	0.0976621i	$-0.0311364\pi$
$138$		0			0
$139$	−639.778			−0.390397			−0.195199	−	0.980764i	$-0.562535\pi$
$139$	−639.778			−0.390397			−0.195199	+	0.980764i	$0.562535\pi$
$140$		0			0
$141$		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	0.869739	+	0.493513i	$0.164287\pi$
$149$	1568.27	+	2716.32i	0.862264	+	1.49348i	−0.00747495	+	0.999972i	$0.502379\pi$
$150$		0			0
$151$	1360.68	−	2356.77i	0.733317	−	1.27014i	−0.222141	−	0.975015i	$-0.571304\pi$
$151$	1360.68	−	2356.77i	0.733317	−	1.27014i	0.955458	−	0.295128i	$-0.0953623\pi$
$152$	−224.638	−	389.085i	−0.119872	−	0.207625i
$153$		0			0
$154$		0			0
$155$	3547.20			1.83818
$156$		0			0
$157$	1439.87	−	2493.93i	0.731939	−	1.26776i	−0.224114	−	0.974563i	$-0.571949\pi$
$157$	1439.87	−	2493.93i	0.731939	−	1.26776i	0.956053	−	0.293193i	$-0.0947178\pi$
$158$	−231.511	+	400.989i	−0.116570	+	0.201905i
$159$		0			0
$160$	3414.22			1.68699
$161$		0			0
$162$		0			0
$163$	−323.071	−	559.576i	−0.155245	−	0.268892i	0.777903	−	0.628384i	$-0.216283\pi$
$163$	−323.071	−	559.576i	−0.155245	−	0.268892i	−0.933148	+	0.359492i	$0.882950\pi$
$164$	−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	0.999964	+	0.00852600i	$0.00271394\pi$
$173$	1154.49	+	1999.64i	0.507366	+	0.878783i	−0.492598	+	0.870257i	$0.663953\pi$
$174$		0			0
$175$		0			0
$176$	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	0.353464	+	0.935448i	$0.385004\pi$
$179$	−1516.88	+	2627.31i	−0.633390	+	1.09706i	−0.986854	+	0.161616i	$0.948329\pi$
$180$		0			0
$181$	4079.71			1.67537			0.837686	−	0.546152i	$-0.183908\pi$
$181$	4079.71			1.67537			0.837686	+	0.546152i	$0.183908\pi$
$182$		0			0
$183$		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	$-0.113536\pi$
$191$	438.554	+	759.599i	0.166140	+	0.287762i	−0.770920	+	0.636932i	$0.780203\pi$
$192$		0			0
$193$	729.356	−	1263.28i	0.272022	−	0.471155i	−0.697358	−	0.716723i	$-0.745641\pi$
$193$	729.356	−	1263.28i	0.272022	−	0.471155i	0.969379	+	0.245568i	$0.0789744\pi$
$194$	−96.1979	−	166.620i	−0.0356011	−	0.0616629i
$195$		0			0
$196$		0			0
$197$	−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	−0.398222	−	0.917289i	$-0.630373\pi$
$199$	1671.11	−	2894.44i	0.595285	−	1.03106i	0.993507	−	0.113774i	$-0.0362941\pi$
$200$	−2251.77	+	3900.18i	−0.796120	+	1.37892i
$201$		0			0
$202$	2047.11			0.713041
$203$		0			0
$204$		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
$217$		0			0
$218$	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	$-0.548451\pi$
$223$	−1009.86			−0.303253			−0.151626	+	0.988438i	$0.548451\pi$
$224$		0			0
$225$		0			0
$226$	−1602.92	−	2776.34i	−0.471790	−	0.817165i
$227$	1474.30	−	2553.57i	0.431070	−	0.746635i	−0.565896	−	0.824477i	$-0.691470\pi$
$227$	1474.30	−	2553.57i	0.431070	−	0.746635i	0.996966	+	0.0778419i	$0.0248029\pi$
$228$		0			0
$229$	−2019.42	−	3497.74i	−0.582739	−	1.00933i	−0.995153	−	0.0983374i	$-0.968648\pi$
$229$	−2019.42	−	3497.74i	−0.582739	−	1.00933i	0.412414	−	0.910997i	$-0.364686\pi$
$230$	−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	$-0.0282892\pi$
$233$	1497.90	+	2594.44i	0.421162	+	0.729473i	−0.574892	+	0.818230i	$0.694956\pi$
$234$		0			0
$235$	2267.45	−	3927.34i	0.629413	−	1.09018i
$236$	603.081	+	1044.57i	0.166344	+	0.288117i
$237$		0			0
$238$		0			0
$239$	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	0.498917	+	0.866650i	$0.333731\pi$
$241$	−1874.71	+	3247.10i	−0.501083	+	0.867900i	−0.999999	+	0.00125048i	$0.999602\pi$
$242$	1935.79	−	3352.88i	0.514203	−	0.890625i
$243$		0			0
$244$	3553.80			0.932414
$245$		0			0
$246$		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	−0.982554	−	0.185975i	$-0.940456\pi$
$257$	−2687.64	−	4655.13i	−0.652337	−	1.12988i	0.330218	−	0.943905i	$-0.392878\pi$
$258$		0			0
$259$		0			0
$260$	−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	−0.375324	−	0.926893i	$-0.622469\pi$
$263$	2623.28	−	4543.66i	0.615051	−	1.06530i	0.990376	−	0.138406i	$-0.0441979\pi$
$264$		0			0
$265$	−2575.95			−0.597129
$266$		0			0
$267$		0			0
$268$	1646.06	+	2851.06i	0.375184	+	0.649837i
$269$	−1506.66	+	2609.61i	−0.341496	+	0.591489i	−0.984711	−	0.174197i	$-0.944267\pi$
$269$	−1506.66	+	2609.61i	−0.341496	+	0.591489i	0.643214	+	0.765686i	$0.277600\pi$
$270$		0			0
$271$	3448.62	+	5973.19i	0.773022	+	1.33891i	0.935899	+	0.352267i	$0.114589\pi$
$271$	3448.62	+	5973.19i	0.773022	+	1.33891i	−0.162877	+	0.986646i	$0.552077\pi$
$272$	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	−0.987947	−	0.154792i	$-0.950529\pi$
$277$	−1659.30	+	2874.00i	−0.359920	+	0.623400i	0.628027	+	0.778191i	$0.283863\pi$
$278$	−511.200	−	885.424i	−0.110287	−	0.191022i
$279$		0			0
$280$		0			0
$281$	−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	−0.0920914	−	0.995751i	$-0.529355\pi$
$283$	3886.24	−	6731.16i	0.816300	−	1.41387i	0.908391	−	0.418122i	$-0.137311\pi$
$284$	1949.83	−	3377.21i	0.407399	−	0.705635i
$285$		0			0
$286$	3176.76			0.656803
$287$		0			0
$288$		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
$301$		0			0
$302$	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	$-0.576194\pi$
$307$	−2550.68			−0.474185			−0.237092	+	0.971487i	$0.576194\pi$
$308$		0			0
$309$		0			0
$310$	2834.31	+	4909.17i	0.519284	+	0.899427i
$311$	3740.25	−	6478.31i	0.681962	−	1.18119i	−0.292419	−	0.956290i	$-0.594460\pi$
$311$	3740.25	−	6478.31i	0.681962	−	1.18119i	0.974381	−	0.224903i	$-0.0722064\pi$
$312$		0			0
$313$	3.12392	+	5.41079i	0.000564135	+	0.000977111i	0.866307	−	0.499511i	$-0.166487\pi$
$313$	3.12392	+	5.41079i	0.000564135	+	0.000977111i	−0.865743	+	0.500488i	$0.833154\pi$
$314$	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	$-0.193935\pi$
$317$	−482.902	−	836.410i	−0.0855598	−	0.148194i	−0.905630	+	0.424070i	$0.860601\pi$
$318$		0			0
$319$	−1593.64	+	2760.27i	−0.279708	+	0.484469i
$320$	2052.64	+	3555.28i	0.358582	+	0.621083i
$321$		0			0
$322$		0			0
$323$	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
$329$		0			0
$330$		0			0
$331$	−3355.10	−	5811.20i	−0.557139	−	0.964992i	−0.997734	−	0.0672865i	$-0.978566\pi$
$331$	−3355.10	−	5811.20i	−0.557139	−	0.964992i	0.440595	−	0.897706i	$-0.354767\pi$
$332$	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
$343$		0			0
$344$	−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	0.462394	+	0.886675i	$0.346991\pi$
$347$	−3469.08	+	6008.62i	−0.536686	+	0.929567i	−0.999080	+	0.0428923i	$0.986343\pi$
$348$		0			0
$349$	−10368.9			−1.59035			−0.795176	−	0.606378i	$-0.792622\pi$
$349$	−10368.9			−1.59035			−0.795176	+	0.606378i	$0.792622\pi$
$350$		0			0
$351$		0			0
$352$	5717.90	+	9903.69i	0.865809	+	1.49963i
$353$	−2940.88	+	5093.75i	−0.443420	+	0.768026i	−0.997941	−	0.0641440i	$-0.979568\pi$
$353$	−2940.88	+	5093.75i	−0.443420	+	0.768026i	0.554521	+	0.832170i	$0.312902\pi$
$354$		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	$-0.180459\pi$
$359$	−294.634	−	510.322i	−0.0433153	−	0.0750244i	−0.886870	+	0.462019i	$0.847125\pi$
$360$		0			0
$361$	3210.92	−	5561.47i	0.468132	−	0.810829i
$362$	3259.80	+	5646.14i	0.473291	+	0.819763i
$363$		0			0
$364$		0			0
$365$	7113.21			1.02006
$366$		0			0
$367$	−1774.36	+	3073.28i	−0.252373	+	0.437122i	−0.964179	−	0.265254i	$-0.914544\pi$
$367$	−1774.36	+	3073.28i	−0.252373	+	0.437122i	0.711806	+	0.702376i	$0.247878\pi$
$368$	155.687	−	269.658i	0.0220537	−	0.0381982i
$369$		0			0
$370$	−7809.25			−1.09725
$371$		0			0
$372$		0			0
$373$	790.667	+	1369.47i	0.109756	+	0.190104i	0.915672	−	0.401927i	$-0.131660\pi$
$373$	790.667	+	1369.47i	0.109756	+	0.190104i	−0.805915	+	0.592031i	$0.798326\pi$
$374$	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	−0.966422	−	0.256959i	$-0.917280\pi$
$383$	−5289.87	−	9162.33i	−0.705744	−	1.22238i	0.260678	−	0.965426i	$-0.416054\pi$
$384$		0			0
$385$		0			0
$386$	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	$-0.673310\pi$
$389$	3696.65	−	6402.78i	0.481819	−	0.834534i	0.999782	+	0.0208684i	$0.00664310\pi$
$390$		0			0
$391$	−2743.31			−0.354821
$392$		0			0
$393$		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	$-0.130814\pi$
$397$	889.086	+	1539.94i	0.112398	+	0.194679i	−0.804339	+	0.594171i	$0.797480\pi$
$398$	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	$-0.163741\pi$
$401$	73.8031	+	127.831i	0.00919090	+	0.0159191i	−0.861393	+	0.507938i	$0.830408\pi$
$402$		0			0
$403$	−3146.06	+	5449.13i	−0.388874	+	0.673550i
$404$	−3488.31	−	6041.94i	−0.429579	−	0.744053i
$405$		0			0
$406$		0			0
$407$	−16367.9			−1.99343
$408$		0			0
$409$	−1080.03	+	1870.66i	−0.130572	+	0.226157i	−0.923897	−	0.382641i	$-0.875015\pi$
$409$	−1080.03	+	1870.66i	−0.130572	+	0.226157i	0.793325	+	0.608798i	$0.208348\pi$
$410$	2969.53	−	5143.37i	0.357694	−	0.619544i
$411$		0			0
$412$	2893.79			0.346036
$413$		0			0
$414$		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
$427$		0			0
$428$	−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	−0.492095	−	0.870542i	$-0.663769\pi$
$431$	4544.26	−	7870.89i	0.507864	−	0.879646i	0.999959	−	0.00910411i	$-0.00289797\pi$
$432$		0			0
$433$	−15461.2			−1.71597			−0.857986	−	0.513673i	$-0.828284\pi$
$433$	−15461.2			−1.71597			−0.857986	+	0.513673i	$0.828284\pi$
$434$		0			0
$435$		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	$-0.197552\pi$
$439$	−891.091	−	1543.41i	−0.0968780	−	0.167798i	−0.910391	+	0.413749i	$0.864219\pi$
$440$	−24081.0			−2.60913
$441$		0			0
$442$	4216.97			0.453803
$443$	6712.36	+	11626.1i	0.719896	+	1.24690i	0.961041	+	0.276407i	$0.0891437\pi$
$443$	6712.36	+	11626.1i	0.719896	+	1.24690i	−0.241145	+	0.970489i	$0.577523\pi$
$444$		0			0
$445$	−8591.27	+	14880.5i	−0.915203	+	1.58518i
$446$	−806.907	−	1397.60i	−0.0856685	−	0.148382i
$447$		0			0
$448$		0			0
$449$	−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
$455$		0			0
$456$		0			0
$457$	354.205	+	613.501i	0.0362560	+	0.0627973i	0.883584	−	0.468273i	$-0.155123\pi$
$457$	354.205	+	613.501i	0.0362560	+	0.0627973i	−0.847328	+	0.531070i	$0.821790\pi$
$458$	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	0.999107	+	0.0422535i	$0.0134537\pi$
$467$	5410.76	+	9371.72i	0.536146	+	0.928632i	−0.462961	+	0.886379i	$0.653213\pi$
$468$		0			0
$469$		0			0
$470$	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
$476$		0			0
$477$		0			0
$478$	1446.47	+	2505.35i	0.138410	+	0.239733i
$479$	−4092.75	+	7088.85i	−0.390402	+	0.676196i	−0.992503	−	0.122224i	$-0.960997\pi$
$479$	−4092.75	+	7088.85i	−0.390402	+	0.676196i	0.602100	+	0.798420i	$0.294331\pi$
$480$		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	−0.757752	−	0.652543i	$-0.773702\pi$
$487$	2001.58	−	3466.83i	0.186242	−	0.322581i	0.943994	+	0.329961i	$0.107036\pi$
$488$	7010.67	+	12142.8i	0.650324	+	1.12639i
$489$		0			0
$490$		0			0
$491$	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
$497$		0			0
$498$		0			0
$499$	1885.54	+	3265.85i	0.169155	+	0.292985i	0.938123	−	0.346302i	$-0.112563\pi$
$499$	1885.54	+	3265.85i	0.169155	+	0.292985i	−0.768968	+	0.639287i	$0.779229\pi$
$500$	−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	0.980589	−	0.196073i	$-0.0628188\pi$
$509$	3680.38	+	6374.60i	0.320491	+	0.555106i	−0.660099	+	0.751179i	$0.729485\pi$
$510$		0			0
$511$		0			0
$512$	−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
$518$		0			0
$519$		0			0
$520$	−6376.46	−	11044.4i	−0.537743	−	0.931398i
$521$	6899.40	−	11950.1i	0.580169	−	1.00488i	−0.415290	−	0.909689i	$-0.636320\pi$
$521$	6899.40	−	11950.1i	0.580169	−	1.00488i	0.995459	−	0.0951930i	$-0.0303468\pi$
$522$		0			0
$523$	9423.58	+	16322.1i	0.787886	+	1.36466i	0.927260	+	0.374419i	$0.122158\pi$
$523$	9423.58	+	16322.1i	0.787886	+	1.36466i	−0.139373	+	0.990240i	$0.544509\pi$
$524$	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
$532$		0			0
$533$	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
$539$		0			0
$540$		0			0
$541$	7234.77	+	12531.0i	0.574948	+	0.995839i	0.996047	+	0.0888248i	$0.0283111\pi$
$541$	7234.77	+	12531.0i	0.574948	+	0.995839i	−0.421099	+	0.907015i	$0.638356\pi$
$542$	−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
$553$		0			0
$554$	−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	$-0.899561\pi$
$557$	−2715.39	+	4703.19i	−0.206561	+	0.357775i	0.744068	+	0.668104i	$0.232894\pi$
$558$		0			0
$559$	712.260			0.0538915
$560$		0			0
$561$		0			0
$562$	−5013.21	−	8683.14i	−0.376280	−	0.651737i
$563$	−12065.3	+	20897.8i	−0.903185	+	1.56436i	−0.0798500	+	0.996807i	$0.525444\pi$
$563$	−12065.3	+	20897.8i	−0.903185	+	1.56436i	−0.823335	+	0.567556i	$0.807889\pi$
$564$		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	−0.979318	−	0.202328i	$-0.935149\pi$
$569$	−9024.27	−	15630.5i	−0.664880	−	1.15161i	0.314437	−	0.949278i	$-0.398184\pi$
$570$		0			0
$571$	5637.42	−	9764.30i	0.413168	−	0.715628i	−0.582066	−	0.813141i	$-0.697756\pi$
$571$	5637.42	−	9764.30i	0.413168	−	0.715628i	0.995234	+	0.0975136i	$0.0310889\pi$
$572$	−5413.25	−	9376.02i	−0.395698	−	0.685369i
$573$		0			0
$574$		0			0
$575$	−7069.54			−0.512731
$576$		0			0
$577$	−12047.5	+	20866.8i	−0.869225	+	1.50554i	−0.00643457	+	0.999979i	$0.502048\pi$
$577$	−12047.5	+	20866.8i	−0.869225	+	1.50554i	−0.862790	+	0.505562i	$0.831285\pi$
$578$	1359.46	−	2354.65i	0.0978303	−	0.169447i
$579$		0			0
$580$	5182.53			0.371022
$581$		0			0
$582$		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	0.784662	−	0.619924i	$-0.212837\pi$
$593$	−2087.22	−	3615.17i	−0.144539	−	0.250349i	−0.929201	+	0.369575i	$0.879503\pi$
$594$		0			0
$595$		0			0
$596$	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	$-0.705566\pi$
$599$	5727.77	−	9920.79i	0.390702	−	0.676715i	0.992542	+	0.121901i	$0.0388991\pi$
$600$		0			0
$601$	17539.2			1.19042			0.595208	−	0.803572i	$-0.297070\pi$
$601$	17539.2			1.19042			0.595208	+	0.803572i	$0.297070\pi$
$602$		0			0
$603$		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	$-0.130557\pi$
$607$	1692.86	+	2932.12i	0.113198	+	0.196064i	−0.803860	+	0.594818i	$0.797224\pi$
$608$	−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	−0.927773	−	0.373145i	$-0.878279\pi$
$613$	−2135.94	+	3699.56i	−0.140734	+	0.243758i	0.787039	+	0.616903i	$0.211613\pi$
$614$	−2038.06	−	3530.02i	−0.133957	−	0.232020i
$615$		0			0
$616$		0			0
$617$	−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	$-0.852918\pi$
$619$	−946.969	+	1640.20i	−0.0614893	+	0.106503i	0.833642	+	0.552305i	$0.186252\pi$
$620$	9659.43	−	16730.6i	0.625697	−	1.08374i
$621$		0			0
$622$	11954.3			0.770614
$623$		0			0
$624$		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
$637$		0			0
$638$	−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	−0.401486	−	0.915865i	$-0.631506\pi$
$641$	9614.27	−	16652.4i	0.592419	−	1.02610i	0.993906	−	0.110235i	$-0.0351604\pi$
$642$		0			0
$643$	18525.1			1.13617			0.568087	−	0.822969i	$-0.307684\pi$
$643$	18525.1			1.13617			0.568087	+	0.822969i	$0.307684\pi$
$644$		0			0
$645$		0			0
$646$	1358.71	+	2353.36i	0.0827522	+	0.143331i
$647$	−4011.20	+	6947.60i	−0.243735	+	0.422161i	−0.961775	−	0.273840i	$-0.911706\pi$
$647$	−4011.20	+	6947.60i	−0.243735	+	0.422161i	0.718040	+	0.696001i	$0.245039\pi$
$648$		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	$-0.147086\pi$
$653$	1025.85	+	1776.82i	0.0614769	+	0.106481i	−0.833649	+	0.552295i	$0.813752\pi$
$654$		0			0
$655$	−839.141	+	1453.43i	−0.0500579	+	0.0867029i
$656$	937.770	+	1624.26i	0.0558136	+	0.0966721i
$657$		0			0
$658$		0			0
$659$	−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	$-0.827273\pi$
$661$	323.532	−	560.374i	0.0190377	−	0.0329743i	0.875387	+	0.483422i	$0.160606\pi$
$662$	5361.63	−	9286.62i	0.314782	−	0.545218i
$663$		0			0
$664$	2485.11			0.145243
$665$		0			0
$666$		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	−0.962797	−	0.270225i	$-0.912902\pi$
$677$	−12602.1	−	21827.5i	−0.715420	−	1.23914i	0.247377	−	0.968919i	$-0.420431\pi$
$678$		0			0
$679$		0			0
$680$	−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	$-0.991527\pi$
$683$	−8510.27	+	14740.2i	−0.476774	+	0.825796i	0.522872	+	0.852411i	$0.324860\pi$
$684$		0			0
$685$	34152.9			1.90499
$686$		0			0
$687$		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	−0.999345	−	0.0361772i	$-0.988482\pi$
$691$	−9645.26	−	16706.1i	−0.531003	−	0.919724i	0.468342	−	0.883547i	$-0.344851\pi$
$692$	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
$700$		0			0
$701$	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
$707$		0			0
$708$		0			0
$709$	−14213.3	−	24618.1i	−0.752877	−	1.30402i	−0.946423	−	0.322930i	$-0.895332\pi$
$709$	−14213.3	−	24618.1i	−0.752877	−	1.30402i	0.193546	−	0.981091i	$-0.438001\pi$
$710$	−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	−0.997103	−	0.0760577i	$-0.975767\pi$
$719$	−10881.7	−	18847.6i	−0.564420	−	0.977603i	0.432684	−	0.901546i	$-0.357567\pi$
$720$		0			0
$721$		0			0
$722$	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	$-0.388766\pi$
$727$	13422.8			0.684763			0.342382	+	0.939561i	$0.388766\pi$
$728$		0			0
$729$		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	$-0.130019\pi$
$733$	2279.76	+	3948.66i	0.114877	+	0.198973i	−0.802854	+	0.596176i	$0.796686\pi$
$734$	−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	0.102118	−	0.994772i	$-0.467438\pi$
$739$	18332.7	−	31753.2i	0.912557	−	1.58059i	0.810439	−	0.585823i	$-0.199228\pi$
$740$	13307.1	+	23048.6i	0.661052	+	1.14498i
$741$		0			0
$742$		0			0
$743$	−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
$749$		0			0
$750$		0			0
$751$	13339.0	+	23103.9i	0.648134	+	1.12260i	0.983568	+	0.180537i	$0.0577836\pi$
$751$	13339.0	+	23103.9i	0.648134	+	1.12260i	−0.335434	+	0.942064i	$0.608883\pi$
$752$	−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	0.872304	+	0.488963i	$0.162625\pi$
$761$	18045.8	+	31256.3i	0.859607	+	1.48888i	−0.0126976	+	0.999919i	$0.504042\pi$
$762$		0			0
$763$		0			0
$764$	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	$-0.782670\pi$
$769$	−33089.3			−1.55167			−0.775833	+	0.630938i	$0.782670\pi$
$770$		0			0
$771$		0			0
$772$	−3972.23	−	6880.11i	−0.185186	−	0.320752i
$773$	−15495.4	+	26838.8i	−0.720997	+	1.24880i	0.239603	+	0.970871i	$0.422983\pi$
$773$	−15495.4	+	26838.8i	−0.720997	+	1.24880i	−0.960601	+	0.277933i	$0.910351\pi$
$774$		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
$784$		0			0
$785$	52675.4			2.39499
$786$		0			0
$787$	−12710.6	+	22015.4i	−0.575711	+	0.997161i	0.420253	+	0.907407i	$0.361941\pi$
$787$	−12710.6	+	22015.4i	−0.575711	+	0.997161i	−0.995964	+	0.0897537i	$0.971392\pi$
$788$	−2593.08	+	4491.35i	−0.117227	+	0.203043i
$789$		0			0
$790$	−8469.46			−0.381430
$791$		0			0
$792$		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
$805$		0			0
$806$	−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	$-0.949548\pi$
$809$	−8215.67	+	14230.0i	−0.357043	+	0.618416i	0.630423	+	0.776252i	$0.282882\pi$
$810$		0			0
$811$	−6371.81			−0.275887			−0.137944	−	0.990440i	$-0.544049\pi$
$811$	−6371.81			−0.275887			−0.137944	+	0.990440i	$0.544049\pi$
$812$		0			0
$813$		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	$-0.131247\pi$
$821$	2612.24	+	4524.54i	0.111045	+	0.192335i	−0.805147	+	0.593075i	$0.797914\pi$
$822$		0			0
$823$	−1856.55	+	3215.64i	−0.0786333	+	0.136197i	−0.902660	−	0.430353i	$-0.858389\pi$
$823$	−1856.55	+	3215.64i	−0.0786333	+	0.136197i	0.824027	+	0.566550i	$0.191722\pi$
$824$	5708.65	+	9887.67i	0.241347	+	0.418026i
$825$		0			0
$826$		0			0
$827$	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	−0.476029	−	0.879430i	$-0.657924\pi$
$829$	12497.6	−	21646.5i	0.523594	−	0.906891i	0.999623	−	0.0274616i	$-0.00874239\pi$
$830$	−1690.32	+	2927.72i	−0.0706891	+	0.122437i
$831$		0			0
$832$	−7282.06			−0.303437
$833$		0			0
$834$		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
$847$		0			0
$848$	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	$-0.330613\pi$
$853$	25280.7			1.01477			0.507383	+	0.861721i	$0.330613\pi$
$854$		0			0
$855$		0			0
$856$	−1432.72	−	2481.54i	−0.0572070	−	0.0990855i
$857$	−13705.4	+	23738.4i	−0.546285	+	0.946194i	0.452240	+	0.891896i	$0.350625\pi$
$857$	−13705.4	+	23738.4i	−0.546285	+	0.946194i	−0.998525	+	0.0542972i	$0.982708\pi$
$858$		0			0
$859$	12279.4	+	21268.6i	0.487740	+	0.844790i	0.999901	−	0.0140994i	$-0.00448813\pi$
$859$	12279.4	+	21268.6i	0.487740	+	0.844790i	−0.512161	+	0.858890i	$0.671155\pi$
$860$	−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	$-0.121641\pi$
$863$	3574.18	+	6190.66i	0.140981	+	0.244186i	−0.786885	+	0.617099i	$0.788308\pi$
$864$		0			0
$865$	−21117.6	+	36576.7i	−0.830080	+	1.43774i
$866$	−12353.9	−	21397.6i	−0.484760	−	0.839629i
$867$		0			0
$868$		0			0
$869$	−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
$875$		0			0
$876$		0			0
$877$	14109.2	+	24437.9i	0.543256	+	0.940946i	0.998714	+	0.0506895i	$0.0161419\pi$
$877$	14109.2	+	24437.9i	0.543256	+	0.940946i	−0.455459	+	0.890257i	$0.650525\pi$
$878$	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	−0.923194	−	0.384335i	$-0.874431\pi$
$887$	−20986.8	−	36350.3i	−0.794441	−	1.37601i	0.128753	−	0.991677i	$-0.458903\pi$
$888$		0			0
$889$		0			0
$890$	−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
$896$		0			0
$897$		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	0.185489	+	0.982646i	$0.440613\pi$
$907$	−20712.1	+	35874.4i	−0.758252	+	1.31333i	−0.943741	+	0.330685i	$0.892720\pi$
$908$	−8029.37	−	13907.3i	−0.293463	−	0.508292i
$909$		0			0
$910$		0			0
$911$	−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
$917$		0			0
$918$		0			0
$919$	10908.7	+	18894.5i	0.391562	+	0.678206i	0.992656	−	0.120973i	$-0.0386015\pi$
$919$	10908.7	+	18894.5i	0.391562	+	0.678206i	−0.601094	+	0.799179i	$0.705268\pi$
$920$	−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	$-0.0988341\pi$
$929$	5988.52	+	10372.4i	0.211493	+	0.366317i	−0.740689	+	0.671848i	$0.765501\pi$
$930$		0			0
$931$		0			0
$932$	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	$-0.414894\pi$
$937$	15155.2			0.528389			0.264194	+	0.964469i	$0.414894\pi$
$938$		0			0
$939$		0			0
$940$	−12349.0	−	21389.2i	−0.428491	−	0.742168i
$941$	−3477.20	+	6022.69i	−0.120461	+	0.208644i	−0.919949	−	0.392037i	$-0.871771\pi$
$941$	−3477.20	+	6022.69i	−0.120461	+	0.208644i	0.799489	+	0.600681i	$0.205104\pi$
$942$		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	$-0.219100\pi$
$947$	−4778.75	−	8277.03i	−0.163979	−	0.284020i	−0.936292	+	0.351222i	$0.885766\pi$
$948$		0			0
$949$	−6308.79	+	10927.1i	−0.215798	+	0.373772i
$950$	3501.43	+	6064.65i	0.119580	+	0.207119i
$951$		0			0
$952$		0			0
$953$	−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
$959$		0			0
$960$		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	0.991048	+	0.133506i	$0.0426234\pi$
$971$	18491.5	+	32028.2i	0.611143	+	1.05853i	−0.379905	+	0.925026i	$0.624043\pi$
$972$		0			0
$973$		0			0
$974$	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	$-0.927865\pi$
$977$	−8936.51	+	15478.5i	−0.292635	+	0.506859i	0.681797	+	0.731541i	$0.261199\pi$
$978$		0			0
$979$	−57552.2			−1.87883
$980$		0			0
$981$		0			0
$982$	8933.76	+	15473.7i	0.290313	+	0.502838i
$983$	16872.0	−	29223.2i	0.547440	−	0.948195i	−0.451009	−	0.892520i	$-0.648936\pi$
$983$	16872.0	−	29223.2i	0.547440	−	0.948195i	0.998449	−	0.0556750i	$-0.0177311\pi$
$984$		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	−0.726044	−	0.687649i	$-0.758643\pi$
$991$	7253.24	−	12563.0i	0.232499	−	0.402701i	0.958543	+	0.284948i	$0.0919763\pi$
$992$	−18098.4	−	31347.4i	−0.579259	−	1.00331i
$993$		0			0
$994$		0			0
$995$	61134.7			1.94784
$996$		0			0
$997$	−21184.4	+	36692.5i	−0.672936	+	1.16556i	0.304132	+	0.952630i	$0.401634\pi$
$997$	−21184.4	+	36692.5i	−0.672936	+	1.16556i	−0.977068	+	0.212929i	$0.931700\pi$
$998$	−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	441.4.e.x.361.3		8
3.2	odd	2	inner	441.4.e.x.361.2		8
7.2	even	3	inner	441.4.e.x.226.3		8
7.3	odd	6		441.4.a.w.1.2		4
7.4	even	3		441.4.a.v.1.2		4
7.5	odd	6		63.4.e.d.37.3	yes	8
7.6	odd	2		63.4.e.d.46.3	yes	8
21.2	odd	6	inner	441.4.e.x.226.2		8
21.5	even	6		63.4.e.d.37.2	✓	8
21.11	odd	6		441.4.a.v.1.3		4
21.17	even	6		441.4.a.w.1.3		4
21.20	even	2		63.4.e.d.46.2	yes	8

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

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

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

Introduction

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