LMFDB - Embedded newform 441.4.e.w.226.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$0.124036 - 0.214837i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.w.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.124036 - 0.214837i) q^{2} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} +3.95388 q^{8} +O(q^{10})$	\(q+(0.124036 - 0.214837i) q^{2} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} +3.95388 q^{8} +(-1.54234 - 2.67141i) q^{10} +(30.1558 + 52.2313i) q^{11} -36.4269 q^{13} +(-31.2634 + 54.1498i) q^{16} +(24.3731 + 42.2154i) q^{17} +(-25.2750 + 43.7776i) q^{19} +98.7116 q^{20} +14.9616 q^{22} +(69.3962 - 120.198i) q^{23} +(-14.8097 - 25.6511i) q^{25} +(-4.51824 + 7.82583i) q^{26} +61.1345 q^{29} +(-0.584676 - 1.01269i) q^{31} +(23.5711 + 40.8264i) q^{32} +12.0925 q^{34} +(-34.7634 + 60.2120i) q^{37} +(6.27001 + 10.8600i) q^{38} +(24.5825 - 42.5781i) q^{40} +308.115 q^{41} +174.443 q^{43} +(-239.390 + 414.636i) q^{44} +(-17.2153 - 29.8177i) q^{46} +(-194.681 + 337.197i) q^{47} -7.34774 q^{50} +(-144.587 - 250.432i) q^{52} +(157.467 + 272.742i) q^{53} +749.950 q^{55} +(7.58287 - 13.1339i) q^{58} +(-422.263 - 731.381i) q^{59} +(-169.269 + 293.182i) q^{61} -0.290084 q^{62} -488.520 q^{64} +(-226.477 + 392.270i) q^{65} +(485.775 + 841.387i) q^{67} +(-193.485 + 335.125i) q^{68} +98.4698 q^{71} +(355.117 + 615.082i) q^{73} +(8.62383 + 14.9369i) q^{74} -401.289 q^{76} +(243.442 - 421.654i) q^{79} +(388.748 + 673.332i) q^{80} +(38.2174 - 66.1944i) q^{82} +605.688 q^{83} +606.139 q^{85} +(21.6372 - 37.4767i) q^{86} +(119.232 + 206.517i) q^{88} +(-109.034 + 188.853i) q^{89} +1101.80 q^{92} +(48.2949 + 83.6491i) q^{94} +(314.284 + 544.357i) q^{95} +782.288 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8}+O(q^{10}) $ 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8	$ 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8} - 55 q^{10} + 35 q^{11} - 124 q^{13} - 241 q^{16} - 48 q^{17} - 202 q^{19} + 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} - 274 q^{26} - 106 q^{29} - 95 q^{31} + 683 q^{32} + 48 q^{34} - 262 q^{37} + 398 q^{38} + 21 q^{40} + 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} + 210 q^{47} + 2756 q^{50} + 324 q^{52} + 393 q^{53} + 2062 q^{55} + 1249 q^{58} - 1143 q^{59} - 70 q^{61} + 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} - 1944 q^{68} - 636 q^{71} + 988 q^{73} + 1002 q^{74} + 4680 q^{76} - 861 q^{79} - 175 q^{80} + 124 q^{82} + 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} - 1766 q^{89} + 1344 q^{92} - 3294 q^{94} - 736 q^{95} - 38 q^{97}+O(q^{100}) $ 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8 - 55 * q^10 + 35 * q^11 - 124 * q^13 - 241 * q^16 - 48 * q^17 - 202 * q^19 + 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 - 274 * q^26 - 106 * q^29 - 95 * q^31 + 683 * q^32 + 48 * q^34 - 262 * q^37 + 398 * q^38 + 21 * q^40 + 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 + 210 * q^47 + 2756 * q^50 + 324 * q^52 + 393 * q^53 + 2062 * q^55 + 1249 * q^58 - 1143 * q^59 - 70 * q^61 + 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 - 1944 * q^68 - 636 * q^71 + 988 * q^73 + 1002 * q^74 + 4680 * q^76 - 861 * q^79 - 175 * q^80 + 124 * q^82 + 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 - 1766 * q^89 + 1344 * q^92 - 3294 * q^94 - 736 * q^95 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.124036	−	0.214837i	0.0438533	−	0.0759562i	−0.843266	−	0.537497i	$-0.819370\pi$
$2$	0.124036	−	0.214837i	0.0438533	−	0.0759562i	0.887119	+	0.461541i	$0.152703\pi$
$3$		0			0
$3$		0			0
$4$	3.96923	+	6.87491i	0.496154	+	0.859364i
$5$	6.21730	−	10.7687i	0.556092	−	0.963180i	−0.441725	−	0.897150i	$-0.645633\pi$
$5$	6.21730	−	10.7687i	0.556092	−	0.963180i	0.997818	−	0.0660299i	$-0.0210333\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	3.95388			0.174739
$9$		0			0
$10$	−1.54234	−	2.67141i	−0.0487730	−	0.0844773i
$11$	30.1558	+	52.2313i	0.826573	+	1.43167i	0.900711	+	0.434419i	$0.143046\pi$
$11$	30.1558	+	52.2313i	0.826573	+	1.43167i	−0.0741379	+	0.997248i	$0.523621\pi$
$12$		0			0
$13$	−36.4269			−0.777154			−0.388577	−	0.921416i	$-0.627033\pi$
$13$	−36.4269			−0.777154			−0.388577	+	0.921416i	$0.627033\pi$
$14$		0			0
$15$		0			0
$16$	−31.2634	+	54.1498i	−0.488491	+	0.846091i
$17$	24.3731	+	42.2154i	0.347726	+	0.602279i	0.985845	−	0.167659i	$-0.0536207\pi$
$17$	24.3731	+	42.2154i	0.347726	+	0.602279i	−0.638119	+	0.769937i	$0.720287\pi$
$18$		0			0
$19$	−25.2750	+	43.7776i	−0.305183	+	0.528593i	−0.977302	−	0.211851i	$-0.932051\pi$
$19$	−25.2750	+	43.7776i	−0.305183	+	0.528593i	0.672119	+	0.740443i	$0.265384\pi$
$20$	98.7116			1.10363
$21$		0			0
$22$	14.9616			0.144992
$23$	69.3962	−	120.198i	0.629135	−	1.08969i	−0.358590	−	0.933495i	$-0.616743\pi$
$23$	69.3962	−	120.198i	0.629135	−	1.08969i	0.987726	−	0.156199i	$-0.0499241\pi$
$24$		0			0
$25$	−14.8097	−	25.6511i	−0.118478	−	0.205209i
$26$	−4.51824	+	7.82583i	−0.0340808	+	0.0590297i
$27$		0			0
$28$		0			0
$29$	61.1345			0.391462			0.195731	−	0.980658i	$-0.437292\pi$
$29$	61.1345			0.391462			0.195731	+	0.980658i	$0.437292\pi$
$30$		0			0
$31$	−0.584676	−	1.01269i	−0.00338745	−	0.00586724i	0.864327	−	0.502931i	$-0.167745\pi$
$31$	−0.584676	−	1.01269i	−0.00338745	−	0.00586724i	−0.867714	+	0.497064i	$0.834412\pi$
$32$	23.5711	+	40.8264i	0.130213	+	0.225536i
$33$		0			0
$34$	12.0925			0.0609957
$35$		0			0
$36$		0			0
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	−0.932863	−	0.360232i	$-0.882698\pi$
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$38$	6.27001	+	10.8600i	0.0267666	+	0.0463611i
$39$		0			0
$40$	24.5825	−	42.5781i	0.0971708	−	0.168305i
$41$	308.115			1.17365			0.586823	−	0.809715i	$-0.300378\pi$
$41$	308.115			1.17365			0.586823	+	0.809715i	$0.300378\pi$
$42$		0			0
$43$	174.443			0.618657			0.309329	−	0.950955i	$-0.399896\pi$
$43$	174.443			0.618657			0.309329	+	0.950955i	$0.399896\pi$
$44$	−239.390	+	414.636i	−0.820215	+	1.42065i
$45$		0			0
$46$	−17.2153	−	29.8177i	−0.0551794	−	0.0955734i
$47$	−194.681	+	337.197i	−0.604194	+	1.04649i	0.387984	+	0.921666i	$0.373172\pi$
$47$	−194.681	+	337.197i	−0.604194	+	1.04649i	−0.992178	+	0.124829i	$0.960162\pi$
$48$		0			0
$49$		0			0
$50$	−7.34774			−0.0207825
$51$		0			0
$52$	−144.587	−	250.432i	−0.385588	−	0.667858i
$53$	157.467	+	272.742i	0.408110	+	0.706867i	0.994678	−	0.103033i	$-0.0328547\pi$
$53$	157.467	+	272.742i	0.408110	+	0.706867i	−0.586568	+	0.809900i	$0.699521\pi$
$54$		0			0
$55$	749.950			1.83860
$56$		0			0
$57$		0			0
$58$	7.58287	−	13.1339i	0.0171669	−	0.0297339i
$59$	−422.263	−	731.381i	−0.931762	−	1.61386i	−0.780308	−	0.625396i	$-0.784938\pi$
$59$	−422.263	−	731.381i	−0.931762	−	1.61386i	−0.151455	−	0.988464i	$-0.548396\pi$
$60$		0			0
$61$	−169.269	+	293.182i	−0.355290	+	0.615380i	−0.987167	−	0.159688i	$-0.948951\pi$
$61$	−169.269	+	293.182i	−0.355290	+	0.615380i	0.631878	+	0.775068i	$0.282284\pi$
$62$	−0.290084			−0.000594204
$63$		0			0
$64$	−488.520			−0.954141
$65$	−226.477	+	392.270i	−0.432169	+	0.748539i
$66$		0			0
$67$	485.775	+	841.387i	0.885774	+	1.53421i	0.844824	+	0.535044i	$0.179705\pi$
$67$	485.775	+	841.387i	0.885774	+	1.53421i	0.0409498	+	0.999161i	$0.486962\pi$
$68$	−193.485	+	335.125i	−0.345051	+	0.597646i
$69$		0			0
$70$		0			0
$71$	98.4698			0.164595			0.0822973	−	0.996608i	$-0.473774\pi$
$71$	98.4698			0.164595			0.0822973	+	0.996608i	$0.473774\pi$
$72$		0			0
$73$	355.117	+	615.082i	0.569361	+	0.986162i	0.996629	+	0.0820374i	$0.0261427\pi$
$73$	355.117	+	615.082i	0.569361	+	0.986162i	−0.427268	+	0.904125i	$0.640524\pi$
$74$	8.62383	+	14.9369i	0.0135473	+	0.0234646i
$75$		0			0
$76$	−401.289			−0.605671
$77$		0			0
$78$		0			0
$79$	243.442	−	421.654i	0.346701	−	0.600504i	−0.638960	−	0.769240i	$-0.720635\pi$
$79$	243.442	−	421.654i	0.346701	−	0.600504i	0.985661	+	0.168736i	$0.0539686\pi$
$80$	388.748	+	673.332i	0.543292	+	0.941010i
$81$		0			0
$82$	38.2174	−	66.1944i	0.0514683	−	0.0891458i
$83$	605.688			0.800999			0.400499	−	0.916297i	$-0.368837\pi$
$83$	605.688			0.800999			0.400499	+	0.916297i	$0.368837\pi$
$84$		0			0
$85$	606.139			0.773470
$86$	21.6372	−	37.4767i	0.0271302	−	0.0469908i
$87$		0			0
$88$	119.232	+	206.517i	0.144434	+	0.250168i
$89$	−109.034	+	188.853i	−0.129861	+	0.224925i	−0.923622	−	0.383303i	$-0.874786\pi$
$89$	−109.034	+	188.853i	−0.129861	+	0.224925i	0.793762	+	0.608229i	$0.208120\pi$
$90$		0			0
$91$		0			0
$92$	1101.80			1.24859
$93$		0			0
$94$	48.2949	+	83.6491i	0.0529919	+	0.0917846i
$95$	314.284	+	544.357i	0.339420	+	0.587893i
$96$		0			0
$97$	782.288			0.818859			0.409429	−	0.912342i	$-0.365728\pi$
$97$	782.288			0.818859			0.409429	+	0.912342i	$0.365728\pi$
$98$		0			0
$99$		0			0
$100$	117.566	−	203.631i	0.117566	−	0.203631i
$101$	155.823	+	269.893i	0.153514	+	0.265895i	0.932517	−	0.361126i	$-0.117608\pi$
$101$	155.823	+	269.893i	0.153514	+	0.265895i	−0.779003	+	0.627021i	$0.784274\pi$
$102$		0			0
$103$	−74.6289	+	129.261i	−0.0713922	+	0.123655i	−0.899512	−	0.436897i	$-0.856078\pi$
$103$	−74.6289	+	129.261i	−0.0713922	+	0.123655i	0.828119	+	0.560552i	$0.189411\pi$
$104$	−144.028			−0.135799
$105$		0			0
$106$	78.1265			0.0715879
$107$	425.760	−	737.437i	0.384670	−	0.666269i	−0.607053	−	0.794661i	$-0.707648\pi$
$107$	425.760	−	737.437i	0.384670	−	0.666269i	0.991723	+	0.128393i	$0.0409818\pi$
$108$		0			0
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	−0.993062	−	0.117592i	$-0.962483\pi$
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	0.394694	−	0.918813i	$-0.370851\pi$
$110$	93.0208	−	161.117i	0.0806289	−	0.139653i
$111$		0			0
$112$		0			0
$113$	−1048.55			−0.872917			−0.436459	−	0.899724i	$-0.643767\pi$
$113$	−1048.55			−0.872917			−0.436459	+	0.899724i	$0.643767\pi$
$114$		0			0
$115$	−862.914	−	1494.61i	−0.699715	−	1.21194i
$116$	242.657	+	420.294i	0.194225	+	0.336408i
$117$		0			0
$118$	−209.503			−0.163444
$119$		0			0
$120$		0			0
$121$	−1153.24	+	1997.47i	−0.866446	+	1.50073i
$122$	41.9909	+	72.7303i	0.0311613	+	0.0539729i
$123$		0			0
$124$	4.64143	−	8.03919i	0.00336139	−	0.00582210i
$125$	1186.02			0.848647
$126$		0			0
$127$	488.408			0.341254			0.170627	−	0.985336i	$-0.445421\pi$
$127$	488.408			0.341254			0.170627	+	0.985336i	$0.445421\pi$
$128$	−249.163	+	431.563i	−0.172056	+	0.298009i
$129$		0			0
$130$	56.1826	+	97.3111i	0.0379041	+	0.0656519i
$131$	927.114	−	1605.81i	0.618338	−	1.07099i	−0.371451	−	0.928453i	$-0.621139\pi$
$131$	927.114	−	1605.81i	0.618338	−	1.07099i	0.989789	−	0.142541i	$-0.0455272\pi$
$132$		0			0
$133$		0			0
$134$	241.014			0.155377
$135$		0			0
$136$	96.3683	+	166.915i	0.0607611	+	0.105241i
$137$	−255.558	−	442.639i	−0.159370	−	0.276038i	0.775271	−	0.631628i	$-0.217613\pi$
$137$	−255.558	−	442.639i	−0.159370	−	0.276038i	−0.934642	+	0.355591i	$0.884280\pi$
$138$		0			0
$139$	−2266.10			−1.38279			−0.691397	−	0.722475i	$-0.743005\pi$
$139$	−2266.10			−1.38279			−0.691397	+	0.722475i	$0.743005\pi$
$140$		0			0
$141$		0			0
$142$	12.2138	−	21.1549i	0.00721802	−	0.0125020i
$143$	−1098.48	−	1902.62i	−0.642375	−	1.11263i
$144$		0			0
$145$	380.091	−	658.338i	0.217689	−	0.377048i
$146$	176.189			0.0998735
$147$		0			0
$148$	−551.936			−0.306546
$149$	753.950	−	1305.88i	0.414537	−	0.717999i	−0.580843	−	0.814016i	$-0.697277\pi$
$149$	753.950	−	1305.88i	0.414537	−	0.717999i	0.995380	+	0.0960168i	$0.0306102\pi$
$150$		0			0
$151$	−795.913	−	1378.56i	−0.428943	−	0.742952i	0.567836	−	0.823142i	$-0.307781\pi$
$151$	−795.913	−	1378.56i	−0.428943	−	0.742952i	−0.996780	+	0.0801897i	$0.974447\pi$
$152$	−99.9344	+	173.091i	−0.0533273	+	0.0923656i
$153$		0			0
$154$		0			0
$155$	−14.5404			−0.00753494
$156$		0			0
$157$	582.080	+	1008.19i	0.295892	+	0.512500i	0.975192	−	0.221361i	$-0.0710498\pi$
$157$	582.080	+	1008.19i	0.295892	+	0.512500i	−0.679300	+	0.733861i	$0.737717\pi$
$158$	−60.3911	−	104.601i	−0.0304080	−	0.0526682i
$159$		0			0
$160$	586.195			0.289642
$161$		0			0
$162$		0			0
$163$	577.940	−	1001.02i	0.277716	−	0.481019i	−0.693101	−	0.720841i	$-0.743756\pi$
$163$	577.940	−	1001.02i	0.277716	−	0.481019i	0.970817	+	0.239822i	$0.0770892\pi$
$164$	1222.98	+	2118.26i	0.582309	+	1.00859i
$165$		0			0
$166$	75.1271	−	130.124i	0.0351265	−	0.0608408i
$167$	−2890.61			−1.33941			−0.669707	−	0.742626i	$-0.733580\pi$
$167$	−2890.61			−1.33941			−0.669707	+	0.742626i	$0.733580\pi$
$168$		0			0
$169$	−870.082			−0.396032
$170$	75.1830	−	130.221i	0.0339193	−	0.0587499i
$171$		0			0
$172$	692.403	+	1199.28i	0.306949	+	0.531651i
$173$	−947.468	+	1641.06i	−0.416385	+	0.721200i	−0.995573	−	0.0939940i	$-0.970037\pi$
$173$	−947.468	+	1641.06i	−0.416385	+	0.721200i	0.579188	+	0.815194i	$0.303370\pi$
$174$		0			0
$175$		0			0
$176$	−3771.09			−1.61509
$177$		0			0
$178$	27.0483	+	46.8491i	0.0113897	+	0.0197275i
$179$	−2144.25	−	3713.94i	−0.895355	−	1.55080i	−0.833365	−	0.552723i	$-0.813589\pi$
$179$	−2144.25	−	3713.94i	−0.895355	−	1.55080i	−0.0619893	−	0.998077i	$-0.519744\pi$
$180$		0			0
$181$	−383.732			−0.157583			−0.0787917	−	0.996891i	$-0.525106\pi$
$181$	−383.732			−0.157583			−0.0787917	+	0.996891i	$0.525106\pi$
$182$		0			0
$183$		0			0
$184$	274.385	−	475.248i	0.109934	−	0.190412i
$185$	432.269	+	748.712i	0.171790	+	0.297548i
$186$		0			0
$187$	−1469.98	+	2546.07i	−0.574841	+	0.995655i
$188$	−3090.93			−1.19909
$189$		0			0
$190$	155.930			0.0595388
$191$	192.655	−	333.689i	0.0729845	−	0.126413i	−0.827224	−	0.561873i	$-0.810081\pi$
$191$	192.655	−	333.689i	0.0729845	−	0.126413i	0.900208	+	0.435460i	$0.143414\pi$
$192$		0			0
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	0.801262	−	0.598314i	$-0.204163\pi$
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	−0.918786	+	0.394756i	$0.870829\pi$
$194$	97.0318	−	168.064i	0.0359097	−	0.0621974i
$195$		0			0
$196$		0			0
$197$	1250.23			0.452158			0.226079	−	0.974109i	$-0.427409\pi$
$197$	1250.23			0.452158			0.226079	+	0.974109i	$0.427409\pi$
$198$		0			0
$199$	−546.122	−	945.912i	−0.194541	−	0.336954i	0.752209	−	0.658924i	$-0.228988\pi$
$199$	−546.122	−	945.912i	−0.194541	−	0.336954i	−0.946750	+	0.321970i	$0.895655\pi$
$200$	−58.5558	−	101.422i	−0.0207026	−	0.0358580i
$201$		0			0
$202$	77.3105			0.0269285
$203$		0			0
$204$		0			0
$205$	1915.65	−	3318.00i	0.652656	−	1.13043i
$206$	18.5133	+	32.0660i	0.00626158	+	0.0108454i
$207$		0			0
$208$	1138.83	−	1972.51i	0.379633	−	0.657543i
$209$	−3048.75			−1.00902
$210$		0			0
$211$	−3620.05			−1.18111			−0.590556	−	0.806997i	$-0.701091\pi$
$211$	−3620.05			−1.18111			−0.590556	+	0.806997i	$0.701091\pi$
$212$	−1250.05	+	2165.15i	−0.404970	+	0.701429i
$213$		0			0
$214$	−105.619	−	182.937i	−0.0337382	−	0.0584362i
$215$	1084.56	−	1878.52i	0.344030	−	0.595878i
$216$		0			0
$217$		0			0
$218$	−337.844			−0.104962
$219$		0			0
$220$	2976.72	+	5155.84i	0.912230	+	1.58003i
$221$	−887.835	−	1537.78i	−0.270236	−	0.468063i
$222$		0			0
$223$	183.844			0.0552069			0.0276034	−	0.999619i	$-0.491212\pi$
$223$	183.844			0.0552069			0.0276034	+	0.999619i	$0.491212\pi$
$224$		0			0
$225$		0			0
$226$	−130.058	+	225.268i	−0.0382803	+	0.0663035i
$227$	−1139.76	−	1974.12i	−0.333253	−	0.577211i	0.649895	−	0.760024i	$-0.274813\pi$
$227$	−1139.76	−	1974.12i	−0.333253	−	0.577211i	−0.983148	+	0.182813i	$0.941480\pi$
$228$		0			0
$229$	2706.34	−	4687.51i	0.780960	−	1.35266i	−0.150424	−	0.988622i	$-0.548064\pi$
$229$	2706.34	−	4687.51i	0.780960	−	1.35266i	0.931383	−	0.364040i	$-0.118603\pi$
$230$	−428.130			−0.122739
$231$		0			0
$232$	241.719			0.0684035
$233$	569.184	−	985.856i	0.160036	−	0.277191i	−0.774845	−	0.632151i	$-0.782172\pi$
$233$	569.184	−	985.856i	0.160036	−	0.277191i	0.934882	+	0.354960i	$0.115506\pi$
$234$		0			0
$235$	2420.78	+	4192.91i	0.671975	+	1.16390i
$236$	3352.12	−	5806.04i	0.924595	−	1.60145i
$237$		0			0
$238$		0			0
$239$	6226.36			1.68515			0.842573	−	0.538583i	$-0.181040\pi$
$239$	6226.36			1.68515			0.842573	+	0.538583i	$0.181040\pi$
$240$		0			0
$241$	−1598.10	−	2767.99i	−0.427147	−	0.739841i	0.569471	−	0.822012i	$-0.307148\pi$
$241$	−1598.10	−	2767.99i	−0.427147	−	0.739841i	−0.996618	+	0.0821704i	$0.973815\pi$
$242$	286.086	+	495.516i	0.0759931	+	0.131624i
$243$		0			0
$244$	−2687.47			−0.705113
$245$		0			0
$246$		0			0
$247$	920.689	−	1594.68i	0.237174	−	0.410798i
$248$	−2.31174	−	4.00406i	−0.000591919	−	0.00102523i
$249$		0			0
$250$	147.109	−	254.801i	0.0372160	−	0.0644600i
$251$	239.608			0.0602546			0.0301273	−	0.999546i	$-0.490409\pi$
$251$	239.608			0.0602546			0.0301273	+	0.999546i	$0.490409\pi$
$252$		0			0
$253$	8370.78			2.08010
$254$	60.5802	−	104.928i	0.0149651	−	0.0259203i
$255$		0			0
$256$	−1892.27	−	3277.51i	−0.461980	−	0.800173i
$257$	−349.559	+	605.453i	−0.0848439	+	0.146954i	−0.905325	−	0.424720i	$-0.860372\pi$
$257$	−349.559	+	605.453i	−0.0848439	+	0.146954i	0.820481	+	0.571674i	$0.193706\pi$
$258$		0			0
$259$		0			0
$260$	−3595.76			−0.857690
$261$		0			0
$262$	−229.991	−	398.356i	−0.0542324	−	0.0939333i
$263$	−459.520	−	795.912i	−0.107738	−	0.186609i	0.807115	−	0.590394i	$-0.201028\pi$
$263$	−459.520	−	795.912i	−0.107738	−	0.186609i	−0.914854	+	0.403785i	$0.867694\pi$
$264$		0			0
$265$	3916.09			0.907787
$266$		0			0
$267$		0			0
$268$	−3856.30	+	6679.32i	−0.878960	+	1.52240i
$269$	1389.59	+	2406.84i	0.314961	+	0.545529i	0.979429	−	0.201788i	$-0.0646751\pi$
$269$	1389.59	+	2406.84i	0.314961	+	0.545529i	−0.664468	+	0.747317i	$0.731342\pi$
$270$		0			0
$271$	1113.49	−	1928.62i	0.249593	−	0.432308i	−0.713820	−	0.700329i	$-0.753036\pi$
$271$	1113.49	−	1928.62i	0.249593	−	0.432308i	0.963413	+	0.268021i	$0.0863698\pi$
$272$	−3047.94			−0.679443
$273$		0			0
$274$	−126.793			−0.0279557
$275$	893.195	−	1547.06i	0.195861	−	0.339241i
$276$		0			0
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	−0.924379	−	0.381476i	$-0.875416\pi$
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	0.131821	−	0.991273i	$-0.457917\pi$
$278$	−281.078	+	486.842i	−0.0606402	+	0.105032i
$279$		0			0
$280$		0			0
$281$	−2730.61			−0.579696			−0.289848	−	0.957073i	$-0.593605\pi$
$281$	−2730.61			−0.579696			−0.289848	+	0.957073i	$0.593605\pi$
$282$		0			0
$283$	−884.926	−	1532.74i	−0.185878	−	0.321950i	0.757994	−	0.652261i	$-0.226179\pi$
$283$	−884.926	−	1532.74i	−0.185878	−	0.321950i	−0.943872	+	0.330312i	$0.892846\pi$
$284$	390.849	+	676.971i	0.0816642	+	0.141447i
$285$		0			0
$286$	−545.004			−0.112681
$287$		0			0
$288$		0			0
$289$	1268.41	−	2196.95i	0.258174	−	0.447170i
$290$	−94.2900	−	163.315i	−0.0190928	−	0.0330696i
$291$		0			0
$292$	−2819.09	+	4882.80i	−0.564981	+	0.978576i
$293$	8228.81			1.64072			0.820362	−	0.571844i	$-0.193772\pi$
$293$	8228.81			1.64072			0.820362	+	0.571844i	$0.193772\pi$
$294$		0			0
$295$	−10501.4			−2.07258
$296$	−137.451	+	238.071i	−0.0269904	+	0.0467487i
$297$		0			0
$298$	−187.034	−	323.952i	−0.0363577	−	0.0629733i
$299$	−2527.89	+	4378.43i	−0.488935	+	0.846860i
$300$		0			0
$301$		0			0
$302$	−394.887			−0.0752424
$303$		0			0
$304$	−1580.36	−	2737.27i	−0.298158	−	0.516425i
$305$	2104.79	+	3645.61i	0.395148	+	0.684416i
$306$		0			0
$307$	−6019.62			−1.11908			−0.559541	−	0.828803i	$-0.689023\pi$
$307$	−6019.62			−1.11908			−0.559541	+	0.828803i	$0.689023\pi$
$308$		0			0
$309$		0			0
$310$	−1.80354	+	3.12382i	−0.000330432	+	0.000572326i
$311$	−596.857	−	1033.79i	−0.108825	−	0.188491i	0.806469	−	0.591276i	$-0.201376\pi$
$311$	−596.857	−	1033.79i	−0.108825	−	0.188491i	−0.915295	+	0.402785i	$0.868042\pi$
$312$		0			0
$313$	−4423.02	+	7660.89i	−0.798734	+	1.38345i	0.121707	+	0.992566i	$0.461163\pi$
$313$	−4423.02	+	7660.89i	−0.798734	+	1.38345i	−0.920441	+	0.390882i	$0.872170\pi$
$314$	288.795			0.0519034
$315$		0			0
$316$	3865.11			0.688068
$317$	3040.72	−	5266.68i	0.538750	−	0.933142i	−0.460222	−	0.887804i	$-0.652230\pi$
$317$	3040.72	−	5266.68i	0.538750	−	0.933142i	0.998972	−	0.0453380i	$-0.0144365\pi$
$318$		0			0
$319$	1843.56	+	3193.13i	0.323572	+	0.560442i
$320$	−3037.28	+	5260.72i	−0.530590	+	0.919009i
$321$		0			0
$322$		0			0
$323$	−2464.12			−0.424480
$324$		0			0
$325$	539.471	+	934.391i	0.0920753	+	0.159479i
$326$	−143.371	−	248.325i	−0.0243576	−	0.0421885i
$327$		0			0
$328$	1218.25			0.205082
$329$		0			0
$330$		0			0
$331$	−1526.65	+	2644.23i	−0.253511	+	0.439094i	−0.964490	−	0.264119i	$-0.914919\pi$
$331$	−1526.65	+	2644.23i	−0.253511	+	0.439094i	0.710979	+	0.703213i	$0.248252\pi$
$332$	2404.12	+	4164.05i	0.397419	+	0.688349i
$333$		0			0
$334$	−358.539	+	621.009i	−0.0587377	+	0.101737i
$335$	12080.8			1.97029
$336$		0			0
$337$	3865.80			0.624877			0.312438	−	0.949938i	$-0.398854\pi$
$337$	3865.80			0.624877			0.312438	+	0.949938i	$0.398854\pi$
$338$	−107.921	+	186.925i	−0.0173673	+	0.0300811i
$339$		0			0
$340$	2405.90	+	4167.15i	0.383760	+	0.664692i
$341$	35.2627	−	61.0768i	0.00559995	−	0.00969940i
$342$		0			0
$343$		0			0
$344$	689.726			0.108103
$345$		0			0
$346$	235.040	+	407.101i	0.0365198	+	0.0632541i
$347$	−49.7965	−	86.2501i	−0.00770380	−	0.0133434i	0.862148	−	0.506657i	$-0.169119\pi$
$347$	−49.7965	−	86.2501i	−0.00770380	−	0.0133434i	−0.869852	+	0.493313i	$0.835786\pi$
$348$		0			0
$349$	3607.34			0.553285			0.276643	−	0.960973i	$-0.410778\pi$
$349$	3607.34			0.553285			0.276643	+	0.960973i	$0.410778\pi$
$350$		0			0
$351$		0			0
$352$	−1421.61	+	2462.30i	−0.215262	+	0.372844i
$353$	−3565.37	−	6175.40i	−0.537579	−	0.931114i	−0.999034	−	0.0439501i	$-0.986006\pi$
$353$	−3565.37	−	6175.40i	−0.537579	−	0.931114i	0.461455	−	0.887164i	$-0.347328\pi$
$354$		0			0
$355$	612.216	−	1060.39i	0.0915298	−	0.158534i
$356$	−1731.13			−0.257724
$357$		0			0
$358$	−1063.85			−0.157057
$359$	−3250.14	+	5629.41i	−0.477816	+	0.827602i	−0.999677	−	0.0254289i	$-0.991905\pi$
$359$	−3250.14	+	5629.41i	−0.477816	+	0.827602i	0.521860	+	0.853031i	$0.325238\pi$
$360$		0			0
$361$	2151.85	+	3727.11i	0.313727	+	0.543390i
$362$	−47.5966	+	82.4398i	−0.00691056	+	0.0119694i
$363$		0			0
$364$		0			0
$365$	8831.49			1.26647
$366$		0			0
$367$	412.443	+	714.372i	0.0586631	+	0.101607i	0.893866	−	0.448335i	$-0.147983\pi$
$367$	412.443	+	714.372i	0.0586631	+	0.101607i	−0.835202	+	0.549943i	$0.814650\pi$
$368$	4339.12	+	7515.58i	0.614654	+	1.06461i
$369$		0			0
$370$	214.468			0.0301342
$371$		0			0
$372$		0			0
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	−0.908596	−	0.417677i	$-0.862845\pi$
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	0.816016	+	0.578029i	$0.196178\pi$
$374$	364.660	+	631.610i	0.0504174	+	0.0873255i
$375$		0			0
$376$	−769.746	+	1333.24i	−0.105576	+	0.182863i
$377$	−2226.94			−0.304226
$378$		0			0
$379$	−1338.29			−0.181380			−0.0906902	−	0.995879i	$-0.528907\pi$
$379$	−1338.29			−0.181380			−0.0906902	+	0.995879i	$0.528907\pi$
$380$	−2494.93	+	4321.35i	−0.336809	+	0.583370i
$381$		0			0
$382$	−47.7924	−	82.7788i	−0.00640123	−	0.0110873i
$383$	−176.688	+	306.032i	−0.0235727	+	0.0408290i	−0.877571	−	0.479447i	$-0.840837\pi$
$383$	−176.688	+	306.032i	−0.0235727	+	0.0408290i	0.853998	+	0.520276i	$0.174171\pi$
$384$		0			0
$385$		0			0
$386$	−156.341			−0.0206154
$387$		0			0
$388$	3105.08	+	5378.16i	0.406280	+	0.703697i
$389$	5868.59	+	10164.7i	0.764908	+	1.32486i	0.940295	+	0.340360i	$0.110549\pi$
$389$	5868.59	+	10164.7i	0.764908	+	1.32486i	−0.175387	+	0.984500i	$0.556118\pi$
$390$		0			0
$391$	6765.59			0.875066
$392$		0			0
$393$		0			0
$394$	155.073	−	268.595i	0.0198286	−	0.0343442i
$395$	−3027.11	−	5243.10i	−0.385595	−	0.667871i
$396$		0			0
$397$	6640.71	−	11502.1i	0.839516	−	1.45408i	−0.0507841	−	0.998710i	$-0.516172\pi$
$397$	6640.71	−	11502.1i	0.839516	−	1.45408i	0.890300	−	0.455374i	$-0.150495\pi$
$398$	−270.955			−0.0341250
$399$		0			0
$400$	1852.01			0.231501
$401$	−3741.18	+	6479.91i	−0.465899	+	0.806961i	−0.999242	−	0.0389385i	$-0.987602\pi$
$401$	−3741.18	+	6479.91i	−0.465899	+	0.806961i	0.533343	+	0.845899i	$0.320936\pi$
$402$		0			0
$403$	21.2979	+	36.8891i	0.00263257	+	0.00455975i
$404$	−1236.99	+	2142.54i	−0.152333	+	0.263849i
$405$		0			0
$406$		0			0
$407$	−4193.27			−0.510694
$408$		0			0
$409$	−6898.30	−	11948.2i	−0.833983	−	1.44450i	−0.894856	−	0.446355i	$-0.852722\pi$
$409$	−6898.30	−	11948.2i	−0.833983	−	1.44450i	0.0608735	−	0.998145i	$-0.480611\pi$
$410$	−475.218	−	823.102i	−0.0572423	−	0.0991466i
$411$		0			0
$412$	−1184.88			−0.141686
$413$		0			0
$414$		0			0
$415$	3765.75	−	6522.46i	0.445429	−	0.771506i
$416$	−858.622	−	1487.18i	−0.101196	−	0.175276i
$417$		0			0
$418$	−378.154	+	654.982i	−0.0442491	+	0.0766417i
$419$	9497.56			1.10737			0.553683	−	0.832728i	$-0.313222\pi$
$419$	9497.56			1.10737			0.553683	+	0.832728i	$0.313222\pi$
$420$		0			0
$421$	624.367			0.0722797			0.0361399	−	0.999347i	$-0.488494\pi$
$421$	624.367			0.0722797			0.0361399	+	0.999347i	$0.488494\pi$
$422$	−449.016	+	777.719i	−0.0517957	+	0.0897127i
$423$		0			0
$424$	622.608	+	1078.39i	0.0713126	+	0.123517i
$425$	721.915	−	1250.39i	0.0823954	−	0.142713i
$426$		0			0
$427$		0			0
$428$	6759.75			0.763423
$429$		0			0
$430$	−269.050	−	466.007i	−0.0301738	−	0.0522625i
$431$	−6698.64	−	11602.4i	−0.748636	−	1.29668i	−0.948476	−	0.316848i	$-0.897376\pi$
$431$	−6698.64	−	11602.4i	−0.748636	−	1.29668i	0.199840	−	0.979829i	$-0.435958\pi$
$432$		0			0
$433$	14057.3			1.56016			0.780079	−	0.625681i	$-0.215179\pi$
$433$	14057.3			1.56016			0.780079	+	0.625681i	$0.215179\pi$
$434$		0			0
$435$		0			0
$436$	5405.61	−	9362.79i	0.593766	−	1.02843i
$437$	3507.98	+	6075.99i	0.384003	+	0.665112i
$438$		0			0
$439$	−8184.42	+	14175.8i	−0.889798	+	1.54117i	−0.0496832	+	0.998765i	$0.515821\pi$
$439$	−8184.42	+	14175.8i	−0.889798	+	1.54117i	−0.840114	+	0.542409i	$0.817512\pi$
$440$	2965.22			0.321275
$441$		0			0
$442$	−440.494			−0.0474031
$443$	−589.354	+	1020.79i	−0.0632078	+	0.109479i	−0.895898	−	0.444261i	$-0.853466\pi$
$443$	−589.354	+	1020.79i	−0.0632078	+	0.109479i	0.832690	+	0.553740i	$0.186800\pi$
$444$		0			0
$445$	1355.80	+	2348.31i	0.144429	+	0.250159i
$446$	22.8033	−	39.4965i	0.00242101	−	0.00419331i
$447$		0			0
$448$		0			0
$449$	12400.9			1.30342			0.651709	−	0.758469i	$-0.274052\pi$
$449$	12400.9			1.30342			0.651709	+	0.758469i	$0.274052\pi$
$450$		0			0
$451$	9291.45	+	16093.3i	0.970105	+	1.68027i
$452$	−4161.95	−	7208.71i	−0.433101	−	0.750153i
$453$		0			0
$454$	−565.484			−0.0584570
$455$		0			0
$456$		0			0
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	0.491971	+	0.870611i	$0.336277\pi$
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	−0.999957	+	0.00924618i	$0.997057\pi$
$458$	−671.366	−	1162.84i	−0.0684954	−	0.118637i
$459$		0			0
$460$	6850.21	−	11864.9i	0.694332	−	1.20262i
$461$	−16010.3			−1.61751			−0.808755	−	0.588146i	$-0.799858\pi$
$461$	−16010.3			−1.61751			−0.808755	+	0.588146i	$0.799858\pi$
$462$		0			0
$463$	17372.4			1.74377			0.871883	−	0.489714i	$-0.162899\pi$
$463$	17372.4			1.74377			0.871883	+	0.489714i	$0.162899\pi$
$464$	−1911.27	+	3310.42i	−0.191225	+	0.331212i
$465$		0			0
$466$	−141.199	−	244.563i	−0.0140363	−	0.0243115i
$467$	−1054.03	+	1825.64i	−0.104443	+	0.180900i	−0.913510	−	0.406815i	$-0.866639\pi$
$467$	−1054.03	+	1825.64i	−0.104443	+	0.180900i	0.809068	+	0.587716i	$0.199973\pi$
$468$		0			0
$469$		0			0
$470$	1201.05			0.117873
$471$		0			0
$472$	−1669.58	−	2891.80i	−0.162815	−	0.282004i
$473$	5260.45	+	9111.37i	0.511365	+	0.885711i
$474$		0			0
$475$	1497.26			0.144629
$476$		0			0
$477$		0			0
$478$	772.293	−	1337.65i	0.0738992	−	0.127997i
$479$	1225.02	+	2121.80i	0.116853	+	0.202395i	0.918519	−	0.395377i	$-0.129386\pi$
$479$	1225.02	+	2121.80i	0.116853	+	0.202395i	−0.801666	+	0.597772i	$0.796053\pi$
$480$		0			0
$481$	1266.32	−	2193.34i	0.120040	−	0.207916i
$482$	−792.887			−0.0749274
$483$		0			0
$484$	−18309.9			−1.71956
$485$	4863.72	−	8424.21i	0.455361	−	0.788709i
$486$		0			0
$487$	−322.618	−	558.791i	−0.0300189	−	0.0519943i	0.850626	−	0.525772i	$-0.176223\pi$
$487$	−322.618	−	558.791i	−0.0300189	−	0.0519943i	−0.880645	+	0.473778i	$0.842890\pi$
$488$	−669.270	+	1159.21i	−0.0620828	+	0.107531i
$489$		0			0
$490$		0			0
$491$	−11766.1			−1.08146			−0.540731	−	0.841196i	$-0.681852\pi$
$491$	−11766.1			−1.08146			−0.540731	+	0.841196i	$0.681852\pi$
$492$		0			0
$493$	1490.03	+	2580.81i	0.136121	+	0.235769i
$494$	−228.397	−	395.595i	−0.0208018	−	0.0360297i
$495$		0			0
$496$	73.1159			0.00661896
$497$		0			0
$498$		0			0
$499$	22.0104	−	38.1232i	0.00197459	−	0.00342010i	−0.865036	−	0.501709i	$-0.832705\pi$
$499$	22.0104	−	38.1232i	0.00197459	−	0.00342010i	0.867011	+	0.498289i	$0.166038\pi$
$500$	4707.59	+	8153.78i	0.421059	+	0.729296i
$501$		0			0
$502$	29.7200	−	51.4765i	0.00264236	−	0.00457671i
$503$	8290.27			0.734880			0.367440	−	0.930047i	$-0.380234\pi$
$503$	8290.27			0.734880			0.367440	+	0.930047i	$0.380234\pi$
$504$		0			0
$505$	3875.19			0.341473
$506$	1038.28	−	1798.35i	0.0912195	−	0.157997i
$507$		0			0
$508$	1938.60	+	3357.76i	0.169314	+	0.293261i
$509$	−3457.52	+	5988.60i	−0.301084	+	0.521493i	−0.976382	−	0.216052i	$-0.930682\pi$
$509$	−3457.52	+	5988.60i	−0.301084	+	0.521493i	0.675298	+	0.737545i	$0.264015\pi$
$510$		0			0
$511$		0			0
$512$	−4925.45			−0.425148
$513$		0			0
$514$	86.7157	+	150.196i	0.00744137	+	0.0128888i
$515$	927.980	+	1607.31i	0.0794014	+	0.137527i
$516$		0			0
$517$	−23483.0			−1.99764
$518$		0			0
$519$		0			0
$520$	−895.464	+	1550.99i	−0.0755167	+	0.130799i
$521$	−6699.64	−	11604.1i	−0.563371	−	0.975788i	−0.997199	−	0.0747919i	$-0.976171\pi$
$521$	−6699.64	−	11604.1i	−0.563371	−	0.975788i	0.433828	−	0.900996i	$-0.357163\pi$
$522$		0			0
$523$	−4968.50	+	8605.69i	−0.415406	+	0.719504i	−0.995471	−	0.0950662i	$-0.969694\pi$
$523$	−4968.50	+	8605.69i	−0.415406	+	0.719504i	0.580065	+	0.814570i	$0.303027\pi$
$524$	14719.7			1.22716
$525$		0			0
$526$	−227.988			−0.0188988
$527$	28.5007	−	49.3647i	0.00235581	−	0.00408038i
$528$		0			0
$529$	−3548.17	−	6145.60i	−0.291622	−	0.505104i
$530$	485.736	−	841.320i	0.0398095	−	0.0689521i
$531$		0			0
$532$		0			0
$533$	−11223.7			−0.912104
$534$		0			0
$535$	−5294.15	−	9169.74i	−0.427825	−	0.741014i
$536$	1920.70	+	3326.75i	0.154779	+	0.268085i
$537$		0			0
$538$	689.435			0.0552484
$539$		0			0
$540$		0			0
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	−0.989407	−	0.145166i	$-0.953628\pi$
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	0.620421	+	0.784269i	$0.286962\pi$
$542$	−276.226	−	478.437i	−0.0218910	−	0.0379163i
$543$		0			0
$544$	−1149.00	+	1990.13i	−0.0905570	+	0.156849i
$545$	−16934.4			−1.33099
$546$		0			0
$547$	−16821.6			−1.31488			−0.657438	−	0.753508i	$-0.728360\pi$
$547$	−16821.6			−1.31488			−0.657438	+	0.753508i	$0.728360\pi$
$548$	2028.73	−	3513.87i	0.158144	−	0.273914i
$549$		0			0
$550$	−221.577	−	383.782i	−0.0171783	−	0.0297537i
$551$	−1545.17	+	2676.32i	−0.119467	+	0.206924i
$552$		0			0
$553$		0			0
$554$	−1812.83			−0.139025
$555$		0			0
$556$	−8994.69	−	15579.3i	−0.686079	−	1.18832i
$557$	902.972	+	1563.99i	0.0686897	+	0.118974i	0.898325	−	0.439332i	$-0.144785\pi$
$557$	902.972	+	1563.99i	0.0686897	+	0.118974i	−0.829635	+	0.558306i	$0.811451\pi$
$558$		0			0
$559$	−6354.40			−0.480792
$560$		0			0
$561$		0			0
$562$	−338.694	+	586.635i	−0.0254216	+	0.0440315i
$563$	−6107.45	−	10578.4i	−0.457190	−	0.791877i	0.541621	−	0.840623i	$-0.317811\pi$
$563$	−6107.45	−	10578.4i	−0.457190	−	0.791877i	−0.998811	+	0.0487460i	$0.984478\pi$
$564$		0			0
$565$	−6519.17	+	11291.5i	−0.485423	+	0.840776i
$566$	−439.050			−0.0326054
$567$		0			0
$568$	389.338			0.0287610
$569$	2141.89	−	3709.86i	0.157808	−	0.273331i	−0.776270	−	0.630400i	$-0.782891\pi$
$569$	2141.89	−	3709.86i	0.157808	−	0.273331i	0.934078	+	0.357070i	$0.116224\pi$
$570$		0			0
$571$	−3179.97	−	5507.87i	−0.233060	−	0.403673i	0.725647	−	0.688067i	$-0.241541\pi$
$571$	−3179.97	−	5507.87i	−0.233060	−	0.403673i	−0.958707	+	0.284395i	$0.908207\pi$
$572$	8720.25	−	15103.9i	0.637433	−	1.10407i
$573$		0			0
$574$		0			0
$575$	−4110.95			−0.298153
$576$		0			0
$577$	7234.36	+	12530.3i	0.521959	+	0.904059i	0.999674	+	0.0255444i	$0.00813192\pi$
$577$	7234.36	+	12530.3i	0.521959	+	0.904059i	−0.477715	+	0.878515i	$0.658535\pi$
$578$	−314.656	−	545.001i	−0.0226436	−	0.0392198i
$579$		0			0
$580$	6034.68			0.432028
$581$		0			0
$582$		0			0
$583$	−9497.10	+	16449.5i	−0.674665	+	1.16855i
$584$	1404.09	+	2431.96i	0.0994894	+	0.172321i
$585$		0			0
$586$	1020.67	−	1767.85i	0.0719513	−	0.124623i
$587$	−11132.6			−0.782777			−0.391388	−	0.920226i	$-0.628005\pi$
$587$	−11132.6			−0.782777			−0.391388	+	0.920226i	$0.628005\pi$
$588$		0			0
$589$	59.1108			0.00413517
$590$	−1302.55	+	2256.07i	−0.0908897	+	0.157426i
$591$		0			0
$592$	−2173.65	−	3764.87i	−0.150906	−	0.261377i
$593$	9887.81	−	17126.2i	0.684728	−	1.18598i	−0.288794	−	0.957391i	$-0.593254\pi$
$593$	9887.81	−	17126.2i	0.684728	−	1.18598i	0.973522	−	0.228592i	$-0.0734123\pi$
$594$		0			0
$595$		0			0
$596$	11970.4			0.822696
$597$		0			0
$598$	627.098	+	1086.17i	0.0428829	+	0.0742753i
$599$	−11945.5	−	20690.2i	−0.814825	−	1.41132i	−0.909453	−	0.415806i	$-0.863500\pi$
$599$	−11945.5	−	20690.2i	−0.814825	−	1.41132i	0.0946282	−	0.995513i	$-0.469834\pi$
$600$		0			0
$601$	−19395.5			−1.31641			−0.658204	−	0.752840i	$-0.728683\pi$
$601$	−19395.5			−1.31641			−0.658204	+	0.752840i	$0.728683\pi$
$602$		0			0
$603$		0			0
$604$	6318.32	−	10943.7i	0.425644	−	0.737237i
$605$	14340.1	+	24837.8i	0.963648	+	1.66909i
$606$		0			0
$607$	7298.36	−	12641.1i	0.488025	−	0.845285i	−0.511880	−	0.859057i	$-0.671051\pi$
$607$	7298.36	−	12641.1i	0.488025	−	0.845285i	0.999905	+	0.0137724i	$0.00438402\pi$
$608$	−2383.04			−0.158956
$609$		0			0
$610$	1044.28			0.0693142
$611$	7091.62	−	12283.0i	0.469552	−	0.813288i
$612$		0			0
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	0.831570	−	0.555420i	$-0.187442\pi$
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	−0.896793	+	0.442451i	$0.854109\pi$
$614$	−746.650	+	1293.24i	−0.0490755	+	0.0850012i
$615$		0			0
$616$		0			0
$617$	−16262.4			−1.06110			−0.530551	−	0.847653i	$-0.678015\pi$
$617$	−16262.4			−1.06110			−0.530551	+	0.847653i	$0.678015\pi$
$618$		0			0
$619$	−6010.49	−	10410.5i	−0.390278	−	0.675981i	0.602208	−	0.798339i	$-0.294288\pi$
$619$	−6010.49	−	10410.5i	−0.390278	−	0.675981i	−0.992486	+	0.122358i	$0.960954\pi$
$620$	−57.7143	−	99.9642i	−0.00373849	−	0.00647526i
$621$		0			0
$622$	−296.127			−0.0190894
$623$		0			0
$624$		0			0
$625$	9225.06	−	15978.3i	0.590404	−	1.02261i
$626$	1097.23	+	1900.45i	0.0700543	+	0.121338i
$627$		0			0
$628$	−4620.82	+	8003.49i	−0.293616	+	0.508557i
$629$	−3389.16			−0.214841
$630$		0			0
$631$	25347.6			1.59916			0.799582	−	0.600557i	$-0.205055\pi$
$631$	25347.6			1.59916			0.799582	+	0.600557i	$0.205055\pi$
$632$	962.542	−	1667.17i	0.0605821	−	0.104931i
$633$		0			0
$634$	−754.317	−	1306.51i	−0.0472519	−	0.0818428i
$635$	3036.58	−	5259.51i	0.189769	−	0.328689i
$636$		0			0
$637$		0			0
$638$	914.669			0.0567588
$639$		0			0
$640$	3098.24	+	5366.31i	0.191358	+	0.331441i
$641$	−2555.80	−	4426.78i	−0.157485	−	0.272772i	0.776476	−	0.630147i	$-0.217005\pi$
$641$	−2555.80	−	4426.78i	−0.157485	−	0.272772i	−0.933961	+	0.357374i	$0.883672\pi$
$642$		0			0
$643$	10931.3			0.670435			0.335217	−	0.942141i	$-0.391190\pi$
$643$	10931.3			0.670435			0.335217	+	0.942141i	$0.391190\pi$
$644$		0			0
$645$		0			0
$646$	−305.639	+	529.382i	−0.0186149	+	0.0322419i
$647$	9203.06	+	15940.2i	0.559211	+	0.968582i	0.997563	+	0.0697783i	$0.0222292\pi$
$647$	9203.06	+	15940.2i	0.559211	+	0.968582i	−0.438352	+	0.898804i	$0.644437\pi$
$648$		0			0
$649$	25467.3	−	44110.7i	1.54034	−	2.66795i
$650$	267.655			0.0161512
$651$		0			0
$652$	9175.91			0.551160
$653$	9960.71	−	17252.5i	0.596926	−	1.03391i	−0.396346	−	0.918101i	$-0.629722\pi$
$653$	9960.71	−	17252.5i	0.596926	−	1.03391i	0.993272	−	0.115805i	$-0.0369447\pi$
$654$		0			0
$655$	−11528.3	−	19967.6i	−0.687707	−	1.19114i
$656$	−9632.74	+	16684.4i	−0.573316	+	0.993012i
$657$		0			0
$658$		0			0
$659$	18858.8			1.11477			0.557385	−	0.830254i	$-0.311805\pi$
$659$	18858.8			1.11477			0.557385	+	0.830254i	$0.311805\pi$
$660$		0			0
$661$	12916.0	+	22371.2i	0.760023	+	1.31640i	0.942838	+	0.333251i	$0.108146\pi$
$661$	12916.0	+	22371.2i	0.760023	+	1.31640i	−0.182815	+	0.983147i	$0.558521\pi$
$662$	378.718	+	655.960i	0.0222346	+	0.0385115i
$663$		0			0
$664$	2394.82			0.139965
$665$		0			0
$666$		0			0
$667$	4242.50	−	7348.22i	0.246282	−	0.426573i
$668$	−11473.5	−	19872.7i	−0.664555	−	1.15104i
$669$		0			0
$670$	1498.46	−	2595.41i	0.0864037	−	0.149656i
$671$	−20417.7			−1.17469
$672$		0			0
$673$	−16275.0			−0.932178			−0.466089	−	0.884738i	$-0.654337\pi$
$673$	−16275.0			−0.932178			−0.466089	+	0.884738i	$0.654337\pi$
$674$	479.498	−	830.515i	0.0274029	−	0.0474633i
$675$		0			0
$676$	−3453.55	−	5981.73i	−0.196493	−	0.340335i
$677$	13135.9	−	22752.0i	0.745720	−	1.29163i	−0.204137	−	0.978942i	$-0.565439\pi$
$677$	13135.9	−	22752.0i	0.745720	−	1.29163i	0.949857	−	0.312683i	$-0.101228\pi$
$678$		0			0
$679$		0			0
$680$	2396.60			0.135155
$681$		0			0
$682$	−8.74769	−	15.1514i	−0.000491153	−	0.000850702i
$683$	−4036.14	−	6990.81i	−0.226118	−	0.391648i	0.730536	−	0.682874i	$-0.239270\pi$
$683$	−4036.14	−	6990.81i	−0.226118	−	0.391648i	−0.956654	+	0.291226i	$0.905937\pi$
$684$		0			0
$685$	−6355.51			−0.354499
$686$		0			0
$687$		0			0
$688$	−5453.67	+	9446.04i	−0.302208	+	0.523440i
$689$	−5736.05	−	9935.13i	−0.317164	−	0.549344i
$690$		0			0
$691$	−12242.6	+	21204.9i	−0.673997	+	1.16740i	0.302763	+	0.953066i	$0.402091\pi$
$691$	−12242.6	+	21204.9i	−0.673997	+	1.16740i	−0.976761	+	0.214332i	$0.931243\pi$
$692$	−15042.9			−0.826364
$693$		0			0
$694$	−24.7062			−0.00135135
$695$	−14089.1	+	24403.0i	−0.768962	+	1.33188i
$696$		0			0
$697$	7509.71	+	13007.2i	0.408107	+	0.706862i
$698$	447.440	−	774.989i	0.0242634	−	0.0420254i
$699$		0			0
$700$		0			0
$701$	−778.448			−0.0419423			−0.0209712	−	0.999780i	$-0.506676\pi$
$701$	−778.448			−0.0419423			−0.0209712	+	0.999780i	$0.506676\pi$
$702$		0			0
$703$	−1757.29	−	3043.72i	−0.0942780	−	0.163294i
$704$	−14731.7	−	25516.0i	−0.788667	−	1.36601i
$705$		0			0
$706$	−1768.93			−0.0942985
$707$		0			0
$708$		0			0
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	0.985389	−	0.170322i	$-0.0544806\pi$
$710$	−151.874	−	263.053i	−0.00802777	−	0.0139045i
$711$		0			0
$712$	−431.109	+	746.703i	−0.0226917	+	0.0393032i
$713$	−162.297			−0.00852466
$714$		0			0
$715$	−27318.3			−1.42888
$716$	17022.0	−	29483.0i	0.888467	−	1.53887i
$717$		0			0
$718$	806.269	+	1396.50i	0.0419077	+	0.0725862i
$719$	40.9418	−	70.9132i	0.00212360	−	0.00367819i	−0.864962	−	0.501838i	$-0.832657\pi$
$719$	40.9418	−	70.9132i	0.00212360	−	0.00367819i	0.867085	+	0.498160i	$0.165991\pi$
$720$		0			0
$721$		0			0
$722$	1067.63			0.0550318
$723$		0			0
$724$	−1523.12	−	2638.13i	−0.0781856	−	0.135421i
$725$	−905.382	−	1568.17i	−0.0463794	−	0.0803315i
$726$		0			0
$727$	32542.9			1.66018			0.830088	−	0.557632i	$-0.188290\pi$
$727$	32542.9			1.66018			0.830088	+	0.557632i	$0.188290\pi$
$728$		0			0
$729$		0			0
$730$	1095.42	−	1897.33i	0.0555389	−	0.0961962i
$731$	4251.70	+	7364.16i	0.215123	+	0.372604i
$732$		0			0
$733$	−2534.47	+	4389.83i	−0.127712	+	0.221203i	−0.922790	−	0.385304i	$-0.874097\pi$
$733$	−2534.47	+	4389.83i	−0.127712	+	0.221203i	0.795078	+	0.606507i	$0.207430\pi$
$734$	204.631			0.0102903
$735$		0			0
$736$	6542.98			0.327687
$737$	−29297.8	+	50745.3i	−1.46431	+	2.53627i
$738$		0			0
$739$	19214.2	+	33280.0i	0.956437	+	1.65660i	0.731045	+	0.682329i	$0.239033\pi$
$739$	19214.2	+	33280.0i	0.956437	+	1.65660i	0.225392	+	0.974268i	$0.427634\pi$
$740$	−3431.55	+	5943.62i	−0.170468	+	0.295259i
$741$		0			0
$742$		0			0
$743$	−21592.9			−1.06617			−0.533086	−	0.846061i	$-0.678968\pi$
$743$	−21592.9			−1.06617			−0.533086	+	0.846061i	$0.678968\pi$
$744$		0			0
$745$	−9375.07	−	16238.1i	−0.461042	−	0.798548i
$746$	165.445	+	286.560i	0.00811982	+	0.0140639i
$747$		0			0
$748$	−23338.7			−1.14084
$749$		0			0
$750$		0			0
$751$	−4056.30	+	7025.72i	−0.197093	+	0.341374i	−0.947585	−	0.319505i	$-0.896483\pi$
$751$	−4056.30	+	7025.72i	−0.197093	+	0.341374i	0.750492	+	0.660880i	$0.229817\pi$
$752$	−12172.8	−	21083.9i	−0.590287	−	1.02241i
$753$		0			0
$754$	−276.220	+	478.428i	−0.0133413	+	0.0231078i
$755$	−19793.7			−0.954129
$756$		0			0
$757$	3108.01			0.149224			0.0746120	−	0.997213i	$-0.476228\pi$
$757$	3108.01			0.149224			0.0746120	+	0.997213i	$0.476228\pi$
$758$	−165.996	+	287.513i	−0.00795414	+	0.0137770i
$759$		0			0
$760$	1242.64	+	2152.32i	0.0593098	+	0.102728i
$761$	3605.96	−	6245.71i	0.171769	−	0.297512i	−0.767269	−	0.641325i	$-0.778385\pi$
$761$	3605.96	−	6245.71i	0.171769	−	0.297512i	0.939038	+	0.343812i	$0.111718\pi$
$762$		0			0
$763$		0			0
$764$	3058.77			0.144846
$765$		0			0
$766$	43.8313	+	75.9181i	0.00206748	+	0.00358098i
$767$	15381.7	+	26641.9i	0.724123	+	1.25422i
$768$		0			0
$769$	7533.07			0.353250			0.176625	−	0.984278i	$-0.443482\pi$
$769$	7533.07			0.353250			0.176625	+	0.984278i	$0.443482\pi$
$770$		0			0
$771$		0			0
$772$	2501.50	−	4332.73i	0.116621	−	0.201993i
$773$	12416.3	+	21505.7i	0.577728	+	1.00065i	0.995739	+	0.0922122i	$0.0293938\pi$
$773$	12416.3	+	21505.7i	0.577728	+	1.00065i	−0.418012	+	0.908442i	$0.637273\pi$
$774$		0			0
$775$	−17.3178	+	29.9952i	−0.000802674	+	0.00139027i
$776$	3093.08			0.143086
$777$		0			0
$778$	2911.66			0.134175
$779$	−7787.61	+	13488.5i	−0.358177	+	0.620381i
$780$		0			0
$781$	2969.43	+	5143.20i	0.136049	+	0.235644i
$782$	839.177	−	1453.50i	0.0383746	−	0.0664667i
$783$		0			0
$784$		0			0
$785$	14475.9			0.658173
$786$		0			0
$787$	18156.6	+	31448.1i	0.822378	+	1.42440i	0.903907	+	0.427730i	$0.140686\pi$
$787$	18156.6	+	31448.1i	0.822378	+	1.42440i	−0.0815287	+	0.996671i	$0.525980\pi$
$788$	4962.45	+	8595.21i	0.224340	+	0.388568i
$789$		0			0
$790$	−1501.88			−0.0676386
$791$		0			0
$792$		0			0
$793$	6165.94	−	10679.7i	0.276115	−	0.478245i
$794$	−1647.37	−	2853.34i	−0.0736311	−	0.127533i
$795$		0			0
$796$	4335.37	−	7509.08i	0.193044	−	0.334362i
$797$	31665.7			1.40735			0.703675	−	0.710522i	$-0.251541\pi$
$797$	31665.7			1.40735			0.703675	+	0.710522i	$0.251541\pi$
$798$		0			0
$799$	−18979.9			−0.840375
$800$	698.162	−	1209.25i	0.0308547	−	0.0534419i
$801$		0			0
$802$	928.081	+	1607.48i	0.0408625	+	0.0707759i
$803$	−21417.7	+	37096.5i	−0.941237	+	1.63027i
$804$		0			0
$805$		0			0
$806$	10.5668			0.000461788
$807$		0			0
$808$	616.105	+	1067.13i	0.0268249	+	0.0464621i
$809$	6192.30	+	10725.4i	0.269110	+	0.466111i	0.968632	−	0.248499i	$-0.0799373\pi$
$809$	6192.30	+	10725.4i	0.269110	+	0.466111i	−0.699523	+	0.714610i	$0.746604\pi$
$810$		0			0
$811$	−16742.4			−0.724914			−0.362457	−	0.932000i	$-0.618062\pi$
$811$	−16742.4			−0.724914			−0.362457	+	0.932000i	$0.618062\pi$
$812$		0			0
$813$		0			0
$814$	−520.116	+	900.868i	−0.0223957	+	0.0387904i
$815$	−7186.45	−	12447.3i	−0.308872	−	0.534982i
$816$		0			0
$817$	−4409.04	+	7636.67i	−0.188804	+	0.327018i
$818$	−3422.55			−0.146292
$819$		0			0
$820$	30414.6			1.29527
$821$	13228.2	−	22911.9i	0.562322	−	0.973970i	−0.434971	−	0.900444i	$-0.643241\pi$
$821$	13228.2	−	22911.9i	0.562322	−	0.973970i	0.997293	−	0.0735259i	$-0.0234252\pi$
$822$		0			0
$823$	−11549.3	−	20003.9i	−0.489164	−	0.847257i	0.510758	−	0.859724i	$-0.329365\pi$
$823$	−11549.3	−	20003.9i	−0.489164	−	0.847257i	−0.999922	+	0.0124673i	$0.996031\pi$
$824$	−295.074	+	511.083i	−0.0124750	+	0.0216073i
$825$		0			0
$826$		0			0
$827$	−20647.6			−0.868183			−0.434092	−	0.900869i	$-0.642931\pi$
$827$	−20647.6			−0.868183			−0.434092	+	0.900869i	$0.642931\pi$
$828$		0			0
$829$	−11684.3	−	20237.7i	−0.489519	−	0.847871i	0.510409	−	0.859932i	$-0.329494\pi$
$829$	−11684.3	−	20237.7i	−0.489519	−	0.847871i	−0.999927	+	0.0120609i	$0.996161\pi$
$830$	−934.176	−	1618.04i	−0.0390671	−	0.0676662i
$831$		0			0
$832$	17795.3			0.741514
$833$		0			0
$834$		0			0
$835$	−17971.8	+	31128.0i	−0.744838	+	1.29010i
$836$	−12101.2	−	20959.8i	−0.500631	−	0.867119i
$837$		0			0
$838$	1178.04	−	2040.42i	0.0485617	−	0.0841113i
$839$	16735.5			0.688645			0.344322	−	0.938851i	$-0.388109\pi$
$839$	16735.5			0.688645			0.344322	+	0.938851i	$0.388109\pi$
$840$		0			0
$841$	−20651.6			−0.846758
$842$	77.4439	−	134.137i	0.00316971	−	0.00549009i
$843$		0			0
$844$	−14368.8	−	24887.5i	−0.586013	−	1.01500i
$845$	−5409.56	+	9369.63i	−0.220230	+	0.381450i
$846$		0			0
$847$		0			0
$848$	−19691.9			−0.797432
$849$		0			0
$850$	−179.087	−	310.188i	−0.00722662	−	0.0125169i
$851$	4824.90	+	8356.97i	0.194354	+	0.336631i
$852$		0			0
$853$	10294.5			0.413219			0.206609	−	0.978424i	$-0.433757\pi$
$853$	10294.5			0.413219			0.206609	+	0.978424i	$0.433757\pi$
$854$		0			0
$855$		0			0
$856$	1683.40	−	2915.74i	0.0672168	−	0.116423i
$857$	16394.3	+	28395.7i	0.653463	+	1.13183i	0.982277	+	0.187437i	$0.0600180\pi$
$857$	16394.3	+	28395.7i	0.653463	+	1.13183i	−0.328813	+	0.944395i	$0.606649\pi$
$858$		0			0
$859$	−2454.88	+	4251.98i	−0.0975081	+	0.168889i	−0.910653	−	0.413173i	$-0.864421\pi$
$859$	−2454.88	+	4251.98i	−0.0975081	+	0.168889i	0.813145	+	0.582062i	$0.197754\pi$
$860$	17219.5			0.682768
$861$		0			0
$862$	−3323.49			−0.131321
$863$	8897.48	−	15410.9i	0.350954	−	0.607871i	−0.635463	−	0.772132i	$-0.719191\pi$
$863$	8897.48	−	15410.9i	0.350954	−	0.607871i	0.986417	+	0.164261i	$0.0525239\pi$
$864$		0			0
$865$	11781.4	+	20406.0i	0.463097	+	0.802108i
$866$	1743.60	−	3020.01i	0.0684181	−	0.118504i
$867$		0			0
$868$		0			0
$869$	29364.7			1.14629
$870$		0			0
$871$	−17695.3	−	30649.1i	−0.688383	−	1.19231i
$872$	−2692.36	−	4663.30i	−0.104558	−	0.181100i
$873$		0			0
$874$	1740.46			0.0673592
$875$		0			0
$876$		0			0
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	0.311099	+	0.950377i	$0.399303\pi$
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	−0.978601	+	0.205769i	$0.934030\pi$
$878$	2030.33	+	3516.63i	0.0780412	+	0.135171i
$879$		0			0
$880$	−23446.0	+	40609.7i	−0.898141	+	1.55563i
$881$	40848.2			1.56210			0.781051	−	0.624467i	$-0.214684\pi$
$881$	40848.2			1.56210			0.781051	+	0.624467i	$0.214684\pi$
$882$		0			0
$883$	30035.1			1.14469			0.572345	−	0.820013i	$-0.306034\pi$
$883$	30035.1			1.14469			0.572345	+	0.820013i	$0.306034\pi$
$884$	7048.04	−	12207.6i	0.268158	−	0.464463i
$885$		0			0
$886$	146.202	+	253.230i	0.00554375	+	0.00960205i
$887$	−16605.4	+	28761.3i	−0.628583	+	1.08874i	0.359253	+	0.933240i	$0.383032\pi$
$887$	−16605.4	+	28761.3i	−0.628583	+	1.08874i	−0.987836	+	0.155498i	$0.950302\pi$
$888$		0			0
$889$		0			0
$890$	672.671			0.0253348
$891$		0			0
$892$	729.721	+	1263.91i	0.0273911	+	0.0474428i
$893$	−9841.11	−	17045.3i	−0.368780	−	0.638745i
$894$		0			0
$895$	−53325.7			−1.99160
$896$		0			0
$897$		0			0
$898$	1538.16	−	2664.17i	0.0571592	−	0.0990027i
$899$	−35.7439	−	61.9102i	−0.00132606	−	0.00229680i
$900$		0			0
$901$	−7675.93	+	13295.1i	−0.283820	+	0.491591i
$902$	4609.90			0.170169
$903$		0			0
$904$	−4145.86			−0.152532
$905$	−2385.78	+	4132.29i	−0.0876310	+	0.151781i
$906$		0			0
$907$	−1248.92	−	2163.18i	−0.0457217	−	0.0791923i	0.842259	−	0.539073i	$-0.181225\pi$
$907$	−1248.92	−	2163.18i	−0.0457217	−	0.0791923i	−0.887981	+	0.459881i	$0.847892\pi$
$908$	9047.93	−	15671.5i	0.330690	−	0.572771i
$909$		0			0
$910$		0			0
$911$	1895.00			0.0689180			0.0344590	−	0.999406i	$-0.489029\pi$
$911$	1895.00			0.0689180			0.0344590	+	0.999406i	$0.489029\pi$
$912$		0			0
$913$	18265.0	+	31635.9i	0.662084	+	1.14676i
$914$	1231.13	+	2132.38i	0.0445538	+	0.0771694i
$915$		0			0
$916$	42968.3			1.54990
$917$		0			0
$918$		0			0
$919$	−3135.36	+	5430.59i	−0.112542	+	0.194928i	−0.916794	−	0.399360i	$-0.869233\pi$
$919$	−3135.36	+	5430.59i	−0.112542	+	0.194928i	0.804253	+	0.594287i	$0.202566\pi$
$920$	−3411.86	−	5909.52i	−0.122267	−	0.211773i
$921$		0			0
$922$	−1985.85	+	3439.59i	−0.0709332	+	0.122860i
$923$	−3586.95			−0.127915
$924$		0			0
$925$	2059.34			0.0732008
$926$	2154.80	−	3732.23i	0.0764700	−	0.132450i
$927$		0			0
$928$	1441.01	+	2495.90i	0.0509735	+	0.0882887i
$929$	15776.3	−	27325.3i	0.557161	−	0.965032i	−0.440570	−	0.897718i	$-0.645224\pi$
$929$	15776.3	−	27325.3i	0.557161	−	0.965032i	0.997732	−	0.0673138i	$-0.0214429\pi$
$930$		0			0
$931$		0			0
$932$	9036.89			0.317611
$933$		0			0
$934$	261.476	+	452.889i	0.00916033	+	0.0158662i
$935$	18278.6	+	31659.4i	0.639330	+	1.10735i
$936$		0			0
$937$	22030.2			0.768084			0.384042	−	0.923316i	$-0.374532\pi$
$937$	22030.2			0.768084			0.384042	+	0.923316i	$0.374532\pi$
$938$		0			0
$939$		0			0
$940$	−19217.3	+	33285.3i	−0.666806	+	1.15494i
$941$	16269.3	+	28179.3i	0.563618	+	0.976214i	0.997177	+	0.0750892i	$0.0239242\pi$
$941$	16269.3	+	28179.3i	0.563618	+	0.976214i	−0.433559	+	0.901125i	$0.642742\pi$
$942$		0			0
$943$	21382.0	−	37034.8i	0.738383	−	1.27892i
$944$	52805.6			1.82063
$945$		0			0
$946$	2609.94			0.0897003
$947$	−20355.5	+	35256.8i	−0.698485	+	1.20981i	0.270507	+	0.962718i	$0.412809\pi$
$947$	−20355.5	+	35256.8i	−0.698485	+	1.20981i	−0.968992	+	0.247093i	$0.920525\pi$
$948$		0			0
$949$	−12935.8	−	22405.5i	−0.442481	−	0.766400i
$950$	185.714	−	321.666i	0.00634248	−	0.0109855i
$951$		0			0
$952$		0			0
$953$	52516.4			1.78507			0.892536	−	0.450976i	$-0.148924\pi$
$953$	52516.4			1.78507			0.892536	+	0.450976i	$0.148924\pi$
$954$		0			0
$955$	−2395.59	−	4149.29i	−0.0811723	−	0.140595i
$956$	24713.9	+	42805.7i	0.836091	+	1.44815i
$957$		0			0
$958$	607.786			0.0204976
$959$		0			0
$960$		0			0
$961$	14894.8	−	25798.6i	0.499977	−	0.865986i
$962$	−314.139	−	544.105i	−0.0105283	−	0.0182356i
$963$		0			0
$964$	12686.4	−	21973.6i	0.423862	−	0.734150i
$965$	−7836.58			−0.261418
$966$		0			0
$967$	14721.6			0.489570			0.244785	−	0.969577i	$-0.421283\pi$
$967$	14721.6			0.489570			0.244785	+	0.969577i	$0.421283\pi$
$968$	−4559.78	+	7897.77i	−0.151402	+	0.262235i
$969$		0			0
$970$	−1206.55	−	2089.81i	−0.0399382	−	0.0691750i
$971$	−6886.25	+	11927.3i	−0.227590	+	0.394198i	−0.957093	−	0.289779i	$-0.906418\pi$
$971$	−6886.25	+	11927.3i	−0.227590	+	0.394198i	0.729503	+	0.683978i	$0.239751\pi$
$972$		0			0
$973$		0			0
$974$	−160.065			−0.00526572
$975$		0			0
$976$	−10583.8	−	18331.8i	−0.347111	−	0.601215i
$977$	12391.0	+	21461.9i	0.405757	+	0.702791i	0.994409	−	0.105595i	$-0.0336748\pi$
$977$	12391.0	+	21461.9i	0.405757	+	0.702791i	−0.588653	+	0.808386i	$0.700341\pi$
$978$		0			0
$979$	−13152.0			−0.429358
$980$		0			0
$981$		0			0
$982$	−1459.42	+	2527.79i	−0.0474257	+	0.0821437i
$983$	−21402.4	−	37070.0i	−0.694435	−	1.20280i	−0.970371	−	0.241620i	$-0.922321\pi$
$983$	−21402.4	−	37070.0i	−0.694435	−	1.20280i	0.275936	−	0.961176i	$-0.411012\pi$
$984$		0			0
$985$	7773.05	−	13463.3i	0.251442	−	0.435510i
$986$	739.271			0.0238775
$987$		0			0
$988$	14617.7			0.470700
$989$	12105.7	−	20967.6i	0.389219	−	0.674147i
$990$		0			0
$991$	−224.931	−	389.592i	−0.00721006	−	0.0124882i	0.862398	−	0.506231i	$-0.168962\pi$
$991$	−224.931	−	389.592i	−0.00721006	−	0.0124882i	−0.869608	+	0.493743i	$0.835628\pi$
$992$	27.5630	−	47.7404i	0.000882182	−	0.00152798i
$993$		0			0
$994$		0			0
$995$	−13581.6			−0.432730
$996$		0			0
$997$	−10736.9	−	18596.8i	−0.341063	−	0.590739i	0.643567	−	0.765390i	$-0.277454\pi$
$997$	−10736.9	−	18596.8i	−0.341063	−	0.590739i	−0.984630	+	0.174651i	$0.944120\pi$
$998$	−5.46017	−	9.45729i	−0.000173185	−	0.000299965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.w.226.2		6
3.2	odd	2		147.4.e.n.79.2		6
7.2	even	3		441.4.a.t.1.2		3
7.3	odd	6		63.4.e.c.46.2		6
7.4	even	3	inner	441.4.e.w.361.2		6
7.5	odd	6		441.4.a.s.1.2		3
7.6	odd	2		63.4.e.c.37.2		6
21.2	odd	6		147.4.a.m.1.2		3
21.5	even	6		147.4.a.l.1.2		3
21.11	odd	6		147.4.e.n.67.2		6
21.17	even	6		21.4.e.b.4.2	✓	6
21.20	even	2		21.4.e.b.16.2	yes	6
84.23	even	6		2352.4.a.cg.1.3		3
84.47	odd	6		2352.4.a.ci.1.1		3
84.59	odd	6		336.4.q.k.193.3		6
84.83	odd	2		336.4.q.k.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.2	✓	6	21.17	even	6
21.4.e.b.16.2	yes	6	21.20	even	2
63.4.e.c.37.2		6	7.6	odd	2
63.4.e.c.46.2		6	7.3	odd	6
147.4.a.l.1.2		3	21.5	even	6
147.4.a.m.1.2		3	21.2	odd	6
147.4.e.n.67.2		6	21.11	odd	6
147.4.e.n.79.2		6	3.2	odd	2
336.4.q.k.193.3		6	84.59	odd	6
336.4.q.k.289.3		6	84.83	odd	2
441.4.a.s.1.2		3	7.5	odd	6
441.4.a.t.1.2		3	7.2	even	3
441.4.e.w.226.2		6	1.1	even	1	trivial
441.4.e.w.361.2		6	7.4	even	3	inner
2352.4.a.cg.1.3		3	84.23	even	6
2352.4.a.ci.1.1		3	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.124036 - 0.214837i) q^{2} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} +3.95388 q^{8} +O(q^{10})\)	\(q+(0.124036 - 0.214837i) q^{2} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} +3.95388 q^{8} +(-1.54234 - 2.67141i) q^{10} +(30.1558 + 52.2313i) q^{11} -36.4269 q^{13} +(-31.2634 + 54.1498i) q^{16} +(24.3731 + 42.2154i) q^{17} +(-25.2750 + 43.7776i) q^{19} +98.7116 q^{20} +14.9616 q^{22} +(69.3962 - 120.198i) q^{23} +(-14.8097 - 25.6511i) q^{25} +(-4.51824 + 7.82583i) q^{26} +61.1345 q^{29} +(-0.584676 - 1.01269i) q^{31} +(23.5711 + 40.8264i) q^{32} +12.0925 q^{34} +(-34.7634 + 60.2120i) q^{37} +(6.27001 + 10.8600i) q^{38} +(24.5825 - 42.5781i) q^{40} +308.115 q^{41} +174.443 q^{43} +(-239.390 + 414.636i) q^{44} +(-17.2153 - 29.8177i) q^{46} +(-194.681 + 337.197i) q^{47} -7.34774 q^{50} +(-144.587 - 250.432i) q^{52} +(157.467 + 272.742i) q^{53} +749.950 q^{55} +(7.58287 - 13.1339i) q^{58} +(-422.263 - 731.381i) q^{59} +(-169.269 + 293.182i) q^{61} -0.290084 q^{62} -488.520 q^{64} +(-226.477 + 392.270i) q^{65} +(485.775 + 841.387i) q^{67} +(-193.485 + 335.125i) q^{68} +98.4698 q^{71} +(355.117 + 615.082i) q^{73} +(8.62383 + 14.9369i) q^{74} -401.289 q^{76} +(243.442 - 421.654i) q^{79} +(388.748 + 673.332i) q^{80} +(38.2174 - 66.1944i) q^{82} +605.688 q^{83} +606.139 q^{85} +(21.6372 - 37.4767i) q^{86} +(119.232 + 206.517i) q^{88} +(-109.034 + 188.853i) q^{89} +1101.80 q^{92} +(48.2949 + 83.6491i) q^{94} +(314.284 + 544.357i) q^{95} +782.288 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8}+O(q^{10}) \) 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8	\( 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8} - 55 q^{10} + 35 q^{11} - 124 q^{13} - 241 q^{16} - 48 q^{17} - 202 q^{19} + 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} - 274 q^{26} - 106 q^{29} - 95 q^{31} + 683 q^{32} + 48 q^{34} - 262 q^{37} + 398 q^{38} + 21 q^{40} + 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} + 210 q^{47} + 2756 q^{50} + 324 q^{52} + 393 q^{53} + 2062 q^{55} + 1249 q^{58} - 1143 q^{59} - 70 q^{61} + 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} - 1944 q^{68} - 636 q^{71} + 988 q^{73} + 1002 q^{74} + 4680 q^{76} - 861 q^{79} - 175 q^{80} + 124 q^{82} + 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} - 1766 q^{89} + 1344 q^{92} - 3294 q^{94} - 736 q^{95} - 38 q^{97}+O(q^{100}) \) 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8 - 55 * q^10 + 35 * q^11 - 124 * q^13 - 241 * q^16 - 48 * q^17 - 202 * q^19 + 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 - 274 * q^26 - 106 * q^29 - 95 * q^31 + 683 * q^32 + 48 * q^34 - 262 * q^37 + 398 * q^38 + 21 * q^40 + 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 + 210 * q^47 + 2756 * q^50 + 324 * q^52 + 393 * q^53 + 2062 * q^55 + 1249 * q^58 - 1143 * q^59 - 70 * q^61 + 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 - 1944 * q^68 - 636 * q^71 + 988 * q^73 + 1002 * q^74 + 4680 * q^76 - 861 * q^79 - 175 * q^80 + 124 * q^82 + 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 - 1766 * q^89 + 1344 * q^92 - 3294 * q^94 - 736 * q^95 - 38 * q^97

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