LMFDB - Embedded newform 441.2.i.d.68.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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([5, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.5
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.48451i q^{2} +(-0.995298 + 1.41753i) q^{3} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +(2.10433 + 1.47753i) q^{6} -2.66653i q^{8} +(-1.01876 - 2.82172i) q^{9} +O(q^{10})$	\(q-1.48451i q^{2} +(-0.995298 + 1.41753i) q^{3} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +(2.10433 + 1.47753i) q^{6} -2.66653i q^{8} +(-1.01876 - 2.82172i) q^{9} +(-0.396525 + 0.228934i) q^{10} +(2.73879 + 1.58124i) q^{11} +(0.202802 - 0.288836i) q^{12} +(3.00394 + 1.73432i) q^{13} +(0.532124 + 0.0472485i) q^{15} -4.36600 q^{16} +(-2.44124 - 4.22836i) q^{17} +(-4.18887 + 1.51236i) q^{18} +(4.62558 + 2.67058i) q^{19} +(0.0314230 + 0.0544262i) q^{20} +(2.34736 - 4.06575i) q^{22} +(5.17269 - 2.98645i) q^{23} +(3.77988 + 2.65399i) q^{24} +(2.45244 - 4.24774i) q^{25} +(2.57462 - 4.45937i) q^{26} +(5.01384 + 1.36433i) q^{27} +(2.70372 - 1.56099i) q^{29} +(0.0701408 - 0.789942i) q^{30} -7.52188i q^{31} +1.14830i q^{32} +(-4.96736 + 2.30850i) q^{33} +(-6.27702 + 3.62404i) q^{34} +(0.207584 + 0.574955i) q^{36} +(-5.92568 + 10.2636i) q^{37} +(3.96450 - 6.86671i) q^{38} +(-5.44827 + 2.53199i) q^{39} +(-0.712254 + 0.411220i) q^{40} +(2.58920 - 4.48462i) q^{41} +(2.75159 + 4.76589i) q^{43} +(-0.558056 - 0.322194i) q^{44} +(-0.596598 + 0.707274i) q^{45} +(-4.43341 - 7.67889i) q^{46} -8.46396 q^{47} +(4.34547 - 6.18892i) q^{48} +(-6.30580 - 3.64066i) q^{50} +(8.42357 + 0.747948i) q^{51} +(-0.612084 - 0.353387i) q^{52} +(0.0740521 - 0.0427540i) q^{53} +(2.02536 - 7.44308i) q^{54} -0.975406i q^{55} +(-8.38945 + 3.89886i) q^{57} +(-2.31731 - 4.01369i) q^{58} +2.08866 q^{59} +(-0.108426 - 0.00962738i) q^{60} +5.42667i q^{61} -11.1663 q^{62} -7.02734 q^{64} -1.06984i q^{65} +(3.42698 + 7.37408i) q^{66} -0.110827 q^{67} +(0.497429 + 0.861572i) q^{68} +(-0.914990 + 10.3048i) q^{69} +7.78899i q^{71} +(-7.52421 + 2.71656i) q^{72} +(-8.32679 + 4.80748i) q^{73} +(15.2364 + 8.79672i) q^{74} +(3.58038 + 7.70416i) q^{75} +(-0.942510 - 0.544159i) q^{76} +(3.75876 + 8.08799i) q^{78} +5.13650 q^{79} +(0.673305 + 1.16620i) q^{80} +(-6.92424 + 5.74934i) q^{81} +(-6.65745 - 3.84368i) q^{82} +(-4.42464 - 7.66370i) q^{83} +(-0.752954 + 1.30416i) q^{85} +(7.07500 - 4.08475i) q^{86} +(-0.478258 + 5.38625i) q^{87} +(4.21642 - 7.30306i) q^{88} +(-0.936885 + 1.62273i) q^{89} +(1.04995 + 0.885654i) q^{90} +(-1.05399 + 0.608521i) q^{92} +(10.6625 + 7.48651i) q^{93} +12.5648i q^{94} -1.64738i q^{95} +(-1.62775 - 1.14290i) q^{96} +(-10.9813 + 6.34007i) q^{97} +(1.67164 - 9.33900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.48451i		−	1.04970i	−0.851193	−	0.524852i	$-0.824121\pi$
$2$		−	1.48451i		−	1.04970i	0.851193	−	0.524852i	$-0.175879\pi$
$3$	−0.995298	+	1.41753i	−0.574636	+	0.818409i
$3$	−0.995298	+	1.41753i	−0.574636	+	0.818409i
$4$	−0.203760			−0.101880
$5$	−0.154215	−	0.267109i	−0.0689672	−	0.119455i	0.829480	−	0.558537i	$-0.188637\pi$
$5$	−0.154215	−	0.267109i	−0.0689672	−	0.119455i	−0.898447	+	0.439082i	$0.855304\pi$
$6$	2.10433	+	1.47753i	0.859088	+	0.603198i
$7$		0			0
$7$		0			0
$8$		−	2.66653i		−	0.942761i
$9$	−1.01876	−	2.82172i	−0.339588	−	0.940574i
$10$	−0.396525	+	0.228934i	−0.125392	+	0.0723952i
$11$	2.73879	+	1.58124i	0.825775	+	0.476761i	0.852404	−	0.522884i	$-0.175144\pi$
$11$	2.73879	+	1.58124i	0.825775	+	0.476761i	−0.0266288	+	0.999645i	$0.508477\pi$
$12$	0.202802	−	0.288836i	0.0585440	−	0.0833797i
$13$	3.00394	+	1.73432i	0.833143	+	0.481015i	0.854927	−	0.518748i	$-0.173602\pi$
$13$	3.00394	+	1.73432i	0.833143	+	0.481015i	−0.0217849	+	0.999763i	$0.506935\pi$
$14$		0			0
$15$	0.532124	+	0.0472485i	0.137394	+	0.0121995i
$16$	−4.36600			−1.09150
$17$	−2.44124	−	4.22836i	−0.592088	−	1.02553i	−0.993951	−	0.109827i	$-0.964970\pi$
$17$	−2.44124	−	4.22836i	−0.592088	−	1.02553i	0.401862	−	0.915700i	$-0.368363\pi$
$18$	−4.18887	+	1.51236i	−0.987325	+	0.356467i
$19$	4.62558	+	2.67058i	1.06118	+	0.612673i	0.925759	−	0.378115i	$-0.123428\pi$
$19$	4.62558	+	2.67058i	1.06118	+	0.612673i	0.135422	+	0.990788i	$0.456761\pi$
$20$	0.0314230	+	0.0544262i	0.00702639	+	0.0121701i
$21$		0			0
$22$	2.34736	−	4.06575i	0.500459	−	0.866820i
$23$	5.17269	−	2.98645i	1.07858	−	0.622719i	0.148067	−	0.988977i	$-0.452695\pi$
$23$	5.17269	−	2.98645i	1.07858	−	0.622719i	0.930513	+	0.366259i	$0.119361\pi$
$24$	3.77988	+	2.65399i	0.771564	+	0.541744i
$25$	2.45244	−	4.24774i	0.490487	−	0.849548i
$26$	2.57462	−	4.45937i	0.504924	−	0.874554i
$27$	5.01384	+	1.36433i	0.964914	+	0.262566i
$28$		0			0
$29$	2.70372	−	1.56099i	0.502069	−	0.289869i	−0.227499	−	0.973778i	$-0.573055\pi$
$29$	2.70372	−	1.56099i	0.502069	−	0.289869i	0.729567	+	0.683909i	$0.239721\pi$
$30$	0.0701408	−	0.789942i	0.0128059	−	0.144223i
$31$		−	7.52188i		−	1.35097i	−0.737374	−	0.675485i	$-0.763934\pi$
$31$		−	7.52188i		−	1.35097i	0.737374	−	0.675485i	$-0.236066\pi$
$32$			1.14830i			0.202993i
$33$	−4.96736	+	2.30850i	−0.864706	+	0.401858i
$34$	−6.27702	+	3.62404i	−1.07650	+	0.621518i
$35$		0			0
$36$	0.207584	+	0.574955i	0.0345973	+	0.0958259i
$37$	−5.92568	+	10.2636i	−0.974176	+	1.68732i	−0.291550	+	0.956556i	$0.594171\pi$
$37$	−5.92568	+	10.2636i	−0.974176	+	1.68732i	−0.682626	+	0.730768i	$0.739162\pi$
$38$	3.96450	−	6.86671i	0.643126	−	1.11393i
$39$	−5.44827	+	2.53199i	−0.872421	+	0.405443i
$40$	−0.712254	+	0.411220i	−0.112617	+	0.0650196i
$41$	2.58920	−	4.48462i	0.404365	−	0.700380i	−0.589883	−	0.807489i	$-0.700826\pi$
$41$	2.58920	−	4.48462i	0.404365	−	0.700380i	0.994247	+	0.107109i	$0.0341593\pi$
$42$		0			0
$43$	2.75159	+	4.76589i	0.419613	+	0.726792i	0.995900	−	0.0904557i	$-0.0288323\pi$
$43$	2.75159	+	4.76589i	0.419613	+	0.726792i	−0.576287	+	0.817247i	$0.695499\pi$
$44$	−0.558056	−	0.322194i	−0.0841301	−	0.0485726i
$45$	−0.596598	+	0.707274i	−0.0889356	+	0.105434i
$46$	−4.43341	−	7.67889i	−0.653671	−	1.13219i
$47$	−8.46396			−1.23460			−0.617298	−	0.786730i	$-0.711773\pi$
$47$	−8.46396			−1.23460			−0.617298	+	0.786730i	$0.711773\pi$
$48$	4.34547	−	6.18892i	0.627215	−	0.893294i
$49$		0			0
$50$	−6.30580	−	3.64066i	−0.891775	−	0.514867i
$51$	8.42357	+	0.747948i	1.17954	+	0.104734i
$52$	−0.612084	−	0.353387i	−0.0848807	−	0.0490059i
$53$	0.0740521	−	0.0427540i	0.0101718	−	0.00587272i	−0.494905	−	0.868947i	$-0.664797\pi$
$53$	0.0740521	−	0.0427540i	0.0101718	−	0.00587272i	0.505077	+	0.863074i	$0.331464\pi$
$54$	2.02536	−	7.44308i	0.275616	−	1.01288i
$55$		−	0.975406i		−	0.131524i
$56$		0			0
$57$	−8.38945	+	3.89886i	−1.11121	+	0.516417i
$58$	−2.31731	−	4.01369i	−0.304277	−	0.527024i
$59$	2.08866			0.271921			0.135960	−	0.990714i	$-0.456588\pi$
$59$	2.08866			0.271921			0.135960	+	0.990714i	$0.456588\pi$
$60$	−0.108426	−	0.00962738i	−0.0139977	−	0.00124289i
$61$			5.42667i			0.694814i	0.937714	+	0.347407i	$0.112938\pi$
$61$			5.42667i			0.694814i	−0.937714	+	0.347407i	$0.887062\pi$
$62$	−11.1663			−1.41812
$63$		0			0
$64$	−7.02734			−0.878418
$65$		−	1.06984i		−	0.132697i
$66$	3.42698	+	7.37408i	0.421832	+	0.907686i
$67$	−0.110827			−0.0135396			−0.00676982	−	0.999977i	$-0.502155\pi$
$67$	−0.110827			−0.0135396			−0.00676982	+	0.999977i	$0.502155\pi$
$68$	0.497429	+	0.861572i	0.0603221	+	0.104481i
$69$	−0.914990	+	10.3048i	−0.110152	+	1.24056i
$70$		0			0
$71$			7.78899i			0.924384i	0.886780	+	0.462192i	$0.152937\pi$
$71$			7.78899i			0.924384i	−0.886780	+	0.462192i	$0.847063\pi$
$72$	−7.52421	+	2.71656i	−0.886737	+	0.320150i
$73$	−8.32679	+	4.80748i	−0.974577	+	0.562672i	−0.900629	−	0.434590i	$-0.856893\pi$
$73$	−8.32679	+	4.80748i	−0.974577	+	0.562672i	−0.0739487	+	0.997262i	$0.523560\pi$
$74$	15.2364	+	8.79672i	1.77119	+	1.02260i
$75$	3.58038	+	7.70416i	0.413427	+	0.889600i
$76$	−0.942510	−	0.544159i	−0.108113	−	0.0624193i
$77$		0			0
$78$	3.75876	+	8.08799i	0.425596	+	0.915784i
$79$	5.13650			0.577901			0.288951	−	0.957344i	$-0.406694\pi$
$79$	5.13650			0.577901			0.288951	+	0.957344i	$0.406694\pi$
$80$	0.673305	+	1.16620i	0.0752778	+	0.130385i
$81$	−6.92424	+	5.74934i	−0.769360	+	0.638815i
$82$	−6.65745	−	3.84368i	−0.735193	−	0.424464i
$83$	−4.42464	−	7.66370i	−0.485667	−	0.841201i	0.514197	−	0.857672i	$-0.328090\pi$
$83$	−4.42464	−	7.66370i	−0.485667	−	0.841201i	−0.999864	+	0.0164715i	$0.994757\pi$
$84$		0			0
$85$	−0.752954	+	1.30416i	−0.0816694	+	0.141455i
$86$	7.07500	−	4.08475i	0.762917	−	0.440470i
$87$	−0.478258	+	5.38625i	−0.0512746	+	0.577467i
$88$	4.21642	−	7.30306i	0.449472	−	0.778508i
$89$	−0.936885	+	1.62273i	−0.0993096	+	0.172009i	−0.911399	−	0.411524i	$-0.864997\pi$
$89$	−0.936885	+	1.62273i	−0.0993096	+	0.172009i	0.812089	+	0.583533i	$0.198330\pi$
$90$	1.04995	+	0.885654i	0.110675	+	0.0933562i
$91$		0			0
$92$	−1.05399	+	0.608521i	−0.109886	+	0.0634427i
$93$	10.6625	+	7.48651i	1.10565	+	0.776315i
$94$			12.5648i			1.29596i
$95$		−	1.64738i		−	0.169017i
$96$	−1.62775	−	1.14290i	−0.166131	−	0.116647i
$97$	−10.9813	+	6.34007i	−1.11498	+	0.643736i	−0.940116	−	0.340855i	$-0.889283\pi$
$97$	−10.9813	+	6.34007i	−1.11498	+	0.643736i	−0.174868	+	0.984592i	$0.555950\pi$
$98$		0			0
$99$	1.67164	−	9.33900i	0.168006	−	0.938605i
$100$	−0.499709	+	0.865522i	−0.0499709	+	0.0865522i
$101$	−3.68322	+	6.37952i	−0.366494	+	0.634786i	−0.989015	−	0.147817i	$-0.952775\pi$
$101$	−3.68322	+	6.37952i	−0.366494	+	0.634786i	0.622521	+	0.782603i	$0.286109\pi$
$102$	1.11033	−	12.5048i	0.109939	−	1.23816i
$103$	6.91120	−	3.99019i	0.680981	−	0.393165i	−0.119244	−	0.992865i	$-0.538047\pi$
$103$	6.91120	−	3.99019i	0.680981	−	0.393165i	0.800225	+	0.599700i	$0.204714\pi$
$104$	4.62463	−	8.01009i	0.453482	−	0.785454i
$105$		0			0
$106$	−0.0634686	−	0.109931i	−0.00616462	−	0.0106774i
$107$	−14.5228	−	8.38472i	−1.40397	−	0.810582i	−0.409172	−	0.912457i	$-0.634182\pi$
$107$	−14.5228	−	8.38472i	−1.40397	−	0.810582i	−0.994797	+	0.101876i	$0.967516\pi$
$108$	−1.02162	−	0.277997i	−0.0983056	−	0.0267502i
$109$	4.43255	+	7.67740i	0.424561	+	0.735361i	0.996379	−	0.0850190i	$-0.0270951\pi$
$109$	4.43255	+	7.67740i	0.424561	+	0.735361i	−0.571818	+	0.820380i	$0.693762\pi$
$110$	−1.44800			−0.138061
$111$	−8.65108	−	18.6151i	−0.821125	−	1.76687i
$112$		0			0
$113$	13.5621	+	7.83007i	1.27581	+	0.736591i	0.976076	−	0.217430i	$-0.0697674\pi$
$113$	13.5621	+	7.83007i	1.27581	+	0.736591i	0.299738	+	0.954022i	$0.403101\pi$
$114$	5.78789	+	12.4542i	0.542085	+	1.16644i
$115$	−1.59542	−	0.921114i	−0.148773	−	0.0858943i
$116$	−0.550911	+	0.318069i	−0.0511508	+	0.0295320i
$117$	1.83348	−	10.2431i	0.169505	−	0.946979i
$118$		−	3.10063i		−	0.285437i
$119$		0			0
$120$	0.125990	−	1.41893i	0.0115012	−	0.129530i
$121$	−0.499366	−	0.864928i	−0.0453969	−	0.0786298i
$122$	8.05593			0.729350
$123$	3.78005	+	8.13379i	0.340835	+	0.733399i
$124$			1.53266i			0.137637i
$125$	−3.05497			−0.273245
$126$		0			0
$127$	−6.78064			−0.601685			−0.300842	−	0.953674i	$-0.597268\pi$
$127$	−6.78064			−0.601685			−0.300842	+	0.953674i	$0.597268\pi$
$128$			12.7287i			1.12507i
$129$	−9.49443	−	0.843032i	−0.835938	−	0.0742249i
$130$	−1.58818			−0.139293
$131$	9.77105	+	16.9240i	0.853701	+	1.47865i	0.877845	+	0.478944i	$0.158980\pi$
$131$	9.77105	+	16.9240i	0.853701	+	1.47865i	−0.0241447	+	0.999708i	$0.507686\pi$
$132$	1.01215	−	0.470381i	0.0880964	−	0.0409414i
$133$		0			0
$134$			0.164523i			0.0142126i
$135$	−0.408786	−	1.54964i	−0.0351827	−	0.133372i
$136$	−11.2750	+	6.50965i	−0.966826	+	0.558198i
$137$	1.37570	+	0.794262i	0.117534	+	0.0678584i	0.557615	−	0.830100i	$-0.311717\pi$
$137$	1.37570	+	0.794262i	0.117534	+	0.0678584i	−0.440080	+	0.897958i	$0.645050\pi$
$138$	15.2976	+	1.35831i	1.30222	+	0.115627i
$139$	3.97274	+	2.29366i	0.336963	+	0.194546i	0.658928	−	0.752206i	$-0.271010\pi$
$139$	3.97274	+	2.29366i	0.336963	+	0.194546i	−0.321965	+	0.946752i	$0.604343\pi$
$140$		0			0
$141$	8.42416	−	11.9979i	0.709442	−	1.01040i
$142$	11.5628			0.970330
$143$	5.48476	+	9.49989i	0.458659	+	0.794421i
$144$	4.44792	+	12.3196i	0.370660	+	1.02664i
$145$	−0.833911	−	0.481459i	−0.0692525	−	0.0399830i
$146$	7.13673	+	12.3612i	0.590640	+	1.02302i
$147$		0			0
$148$	1.20742	−	2.09131i	0.0992493	−	0.171905i
$149$	−8.42966	+	4.86686i	−0.690584	+	0.398709i	−0.803831	−	0.594858i	$-0.797208\pi$
$149$	−8.42966	+	4.86686i	−0.690584	+	0.398709i	0.113247	+	0.993567i	$0.463875\pi$
$150$	11.4369	−	5.31510i	0.933817	−	0.433976i
$151$	3.00916	−	5.21203i	0.244882	−	0.424149i	−0.717216	−	0.696851i	$-0.754584\pi$
$151$	3.00916	−	5.21203i	0.244882	−	0.424149i	0.962099	+	0.272702i	$0.0879173\pi$
$152$	7.12118	−	12.3343i	0.577604	−	1.00044i
$153$	−9.44420	+	11.1962i	−0.763518	+	0.905160i
$154$		0			0
$155$	−2.00916	+	1.15999i	−0.161380	+	0.0931726i
$156$	1.11014	−	0.515920i	0.0888824	−	0.0413066i
$157$		−	16.3506i		−	1.30492i	−0.757823	−	0.652461i	$-0.773737\pi$
$157$		−	16.3506i		−	1.30492i	0.757823	−	0.652461i	$-0.226263\pi$
$158$		−	7.62517i		−	0.606626i
$159$	−0.0130990	+	0.147524i	−0.00103882	+	0.0116994i
$160$	0.306721	−	0.177086i	0.0242484	−	0.0139998i
$161$		0			0
$162$	8.53493	+	10.2791i	0.670567	+	0.807601i
$163$	3.23235	−	5.59860i	0.253177	−	0.438516i	−0.711221	−	0.702968i	$-0.751858\pi$
$163$	3.23235	−	5.59860i	0.253177	−	0.438516i	0.964399	+	0.264452i	$0.0851910\pi$
$164$	−0.527576	+	0.913788i	−0.0411968	+	0.0713549i
$165$	1.38266	+	0.970819i	0.107640	+	0.0755782i
$166$	−11.3768	+	6.56841i	−0.883012	+	0.509807i
$167$	1.33556	−	2.31325i	0.103348	−	0.179005i	−0.809714	−	0.586825i	$-0.800378\pi$
$167$	1.33556	−	2.31325i	0.103348	−	0.179005i	0.913062	+	0.407820i	$0.133711\pi$
$168$		0			0
$169$	−0.484236	−	0.838722i	−0.0372489	−	0.0645171i
$170$	1.93603	+	1.11777i	0.148487	+	0.0857287i
$171$	2.82327	−	15.7728i	0.215901	−	1.20618i
$172$	−0.560665	−	0.971100i	−0.0427503	−	0.0740457i
$173$	−20.1966			−1.53552			−0.767760	−	0.640737i	$-0.778629\pi$
$173$	−20.1966			−1.53552			−0.767760	+	0.640737i	$0.778629\pi$
$174$	7.99593	+	0.709977i	0.606170	+	0.0538232i
$175$		0			0
$176$	−11.9575	−	6.90369i	−0.901334	−	0.520385i
$177$	−2.07884	+	2.96074i	−0.156255	+	0.222543i
$178$	2.40896	+	1.39081i	0.180559	+	0.104246i
$179$	−19.0198	+	10.9811i	−1.42161	+	0.820765i	−0.996436	−	0.0843484i	$-0.973119\pi$
$179$	−19.0198	+	10.9811i	−1.42161	+	0.820765i	−0.425170	+	0.905113i	$0.639786\pi$
$180$	0.121563	−	0.144114i	0.00906078	−	0.0107417i
$181$		−	2.50569i		−	0.186246i	−0.995655	−	0.0931232i	$-0.970315\pi$
$181$		−	2.50569i		−	0.186246i	0.995655	−	0.0931232i	$-0.0296850\pi$
$182$		0			0
$183$	−7.69245	−	5.40116i	−0.568642	−	0.399265i
$184$	−7.96347	−	13.7931i	−0.587075	−	1.01684i
$185$	3.65533			0.268745
$186$	11.1138	−	15.8285i	0.814902	−	1.16060i
$187$		−	15.4408i		−	1.12914i
$188$	1.72462			0.125781
$189$		0			0
$190$	−2.44554			−0.177418
$191$		−	2.10475i		−	0.152294i	−0.997097	−	0.0761470i	$-0.975738\pi$
$191$		−	2.10475i		−	0.152294i	0.997097	−	0.0761470i	$-0.0242618\pi$
$192$	6.99430	−	9.96145i	0.504770	−	0.718906i
$193$	−5.95460			−0.428621			−0.214311	−	0.976766i	$-0.568750\pi$
$193$	−5.95460			−0.428621			−0.214311	+	0.976766i	$0.568750\pi$
$194$	9.41187	+	16.3018i	0.675733	+	1.17040i
$195$	1.51652	+	1.06481i	0.108601	+	0.0762525i
$196$		0			0
$197$			7.64511i			0.544692i	0.962199	+	0.272346i	$0.0877995\pi$
$197$			7.64511i			0.544692i	−0.962199	+	0.272346i	$0.912200\pi$
$198$	−13.8638	−	2.48157i	−0.985259	−	0.176357i
$199$	5.93394	−	3.42596i	0.420646	−	0.242860i	−0.274708	−	0.961528i	$-0.588581\pi$
$199$	5.93394	−	3.42596i	0.420646	−	0.242860i	0.695354	+	0.718668i	$0.255248\pi$
$200$	−11.3267	−	6.53949i	−0.800921	−	0.462412i
$201$	0.110306	−	0.157100i	0.00778036	−	0.0110810i
$202$	9.47044	+	5.46776i	0.666338	+	0.384710i
$203$		0			0
$204$	−1.71639	−	0.152402i	−0.120171	−	0.0106703i
$205$	−1.59718			−0.111552
$206$	−5.92346	−	10.2597i	−0.412707	−	0.714829i
$207$	−13.6967	−	11.5534i	−0.951986	−	0.803017i
$208$	−13.1152	−	7.57207i	−0.909376	−	0.525028i
$209$	8.44565	+	14.6283i	0.584198	+	1.01186i
$210$		0			0
$211$	−2.74784	+	4.75940i	−0.189169	+	0.327651i	−0.944974	−	0.327147i	$-0.893913\pi$
$211$	−2.74784	+	4.75940i	−0.189169	+	0.327651i	0.755804	+	0.654798i	$0.227246\pi$
$212$	−0.0150889	+	0.00871157i	−0.00103631	+	0.000598313i
$213$	−11.0411	−	7.75237i	−0.756524	−	0.531184i
$214$	−12.4472	+	21.5591i	−0.850872	+	1.47375i
$215$	0.848675	−	1.46995i	0.0578791	−	0.100250i
$216$	3.63803	−	13.3696i	0.247537	−	0.909683i
$217$		0			0
$218$	11.3971	−	6.58015i	0.771912	−	0.445664i
$219$	1.47292	−	16.5883i	0.0995304	−	1.12093i
$220$			0.198749i			0.0133997i
$221$		−	16.9356i		−	1.13921i
$222$	−27.6343	+	12.8426i	−1.85469	+	0.861938i
$223$	17.6080	−	10.1660i	1.17912	−	0.680764i	0.223307	−	0.974748i	$-0.428315\pi$
$223$	17.6080	−	10.1660i	1.17912	−	0.680764i	0.955810	+	0.293985i	$0.0949815\pi$
$224$		0			0
$225$	−14.4844	−	2.59265i	−0.965627	−	0.172843i
$226$	11.6238	−	20.1330i	0.773204	−	1.33923i
$227$	0.161235	−	0.279268i	0.0107016	−	0.0185356i	−0.860625	−	0.509239i	$-0.829927\pi$
$227$	0.161235	−	0.279268i	0.0107016	−	0.0185356i	0.871327	+	0.490704i	$0.163260\pi$
$228$	1.70944	−	0.794434i	0.113210	−	0.0526126i
$229$	2.30171	−	1.32889i	0.152101	−	0.0878157i	−0.422018	−	0.906588i	$-0.638678\pi$
$229$	2.30171	−	1.32889i	0.152101	−	0.0878157i	0.574119	+	0.818772i	$0.305345\pi$
$230$	−1.36740	+	2.36841i	−0.0901637	+	0.156168i
$231$		0			0
$232$	−4.16244	−	7.20956i	−0.273278	−	0.473331i
$233$	−20.1415	−	11.6287i	−1.31952	−	0.761823i	−0.335866	−	0.941910i	$-0.609029\pi$
$233$	−20.1415	−	11.6287i	−1.31952	−	0.761823i	−0.983651	+	0.180087i	$0.942362\pi$
$234$	−15.2060	−	2.72181i	−0.994049	−	0.177931i
$235$	1.30527	+	2.26080i	0.0851466	+	0.147478i
$236$	−0.425587			−0.0277033
$237$	−5.11235	+	7.28112i	−0.332083	+	0.472960i
$238$		0			0
$239$	−0.291265	−	0.168162i	−0.0188404	−	0.0108775i	0.490550	−	0.871413i	$-0.336796\pi$
$239$	−0.291265	−	0.168162i	−0.0188404	−	0.0108775i	−0.509391	+	0.860535i	$0.670129\pi$
$240$	−2.32326	−	0.206287i	−0.149966	−	0.0133158i
$241$	19.1846	+	11.0762i	1.23579	+	0.713483i	0.968231	−	0.250059i	$-0.0804500\pi$
$241$	19.1846	+	11.0762i	1.23579	+	0.713483i	0.267558	+	0.963542i	$0.413783\pi$
$242$	−1.28399	+	0.741313i	−0.0825381	+	0.0476534i
$243$	−1.25815	−	15.5376i	−0.0807106	−	0.996738i
$244$		−	1.10574i		−	0.0707878i
$245$		0			0
$246$	12.0747	−	5.61151i	0.769853	−	0.357777i
$247$	9.26331	+	16.0445i	0.589410	+	1.02089i
$248$	−20.0573			−1.27364
$249$	15.2673	+	1.35562i	0.967528	+	0.0859091i
$250$			4.53512i			0.286826i
$251$	13.9800			0.882409			0.441205	−	0.897407i	$-0.354551\pi$
$251$	13.9800			0.882409			0.441205	+	0.897407i	$0.354551\pi$
$252$		0			0
$253$	18.8892			1.18755
$254$			10.0659i			0.631592i
$255$	−1.09926	−	2.36536i	−0.0688384	−	0.148124i
$256$	4.84121			0.302576
$257$	−9.69064	−	16.7847i	−0.604486	−	1.04700i	−0.992133	−	0.125192i	$-0.960045\pi$
$257$	−9.69064	−	16.7847i	−0.604486	−	1.04700i	0.387647	−	0.921808i	$-0.373288\pi$
$258$	−1.25149	+	14.0945i	−0.0779142	+	0.877488i
$259$		0			0
$260$			0.217991i			0.0135192i
$261$	−7.15915	−	6.03887i	−0.443140	−	0.373797i
$262$	25.1237	−	14.5052i	1.55215	−	0.896134i
$263$	−4.40776	−	2.54482i	−0.271794	−	0.156920i	0.357909	−	0.933757i	$-0.383490\pi$
$263$	−4.40776	−	2.54482i	−0.271794	−	0.156920i	−0.629703	+	0.776836i	$0.716823\pi$
$264$	6.15568	+	13.2456i	0.378856	+	0.815211i
$265$	−0.0228400	−	0.0131867i	−0.00140305	−	0.000810050i
$266$		0			0
$267$	−1.36779	−	2.94316i	−0.0837072	−	0.180119i
$268$	0.0225821			0.00137942
$269$	2.52800	+	4.37863i	0.154135	+	0.266970i	0.932744	−	0.360540i	$-0.117408\pi$
$269$	2.52800	+	4.37863i	0.154135	+	0.266970i	−0.778609	+	0.627510i	$0.784074\pi$
$270$	−2.30045	+	0.606846i	−0.140001	+	0.0369315i
$271$	27.1767	+	15.6905i	1.65087	+	0.953128i	0.976717	+	0.214533i	$0.0688231\pi$
$271$	27.1767	+	15.6905i	1.65087	+	0.953128i	0.674150	+	0.738595i	$0.264510\pi$
$272$	10.6585	+	18.4610i	0.646265	+	1.11936i
$273$		0			0
$274$	1.17909	−	2.04224i	0.0712313	−	0.123376i
$275$	13.4334	−	7.75577i	0.810064	−	0.467691i
$276$	0.186439	−	2.09972i	0.0112223	−	0.126388i
$277$	−13.0279	+	22.5650i	−0.782771	+	1.35580i	0.147551	+	0.989054i	$0.452861\pi$
$277$	−13.0279	+	22.5650i	−0.782771	+	1.35580i	−0.930322	+	0.366744i	$0.880473\pi$
$278$	3.40496	−	5.89756i	0.204216	−	0.353712i
$279$	−21.2247	+	7.66301i	−1.27069	+	0.458773i
$280$		0			0
$281$	−4.14335	+	2.39217i	−0.247172	+	0.142705i	−0.618469	−	0.785810i	$-0.712247\pi$
$281$	−4.14335	+	2.39217i	−0.247172	+	0.142705i	0.371297	+	0.928514i	$0.378913\pi$
$282$	−17.8109	−	12.5057i	−1.06063	−	0.744705i
$283$		−	1.07069i		−	0.0636457i	−0.999494	−	0.0318228i	$-0.989869\pi$
$283$		−	1.07069i		−	0.0636457i	0.999494	−	0.0318228i	$-0.0101312\pi$
$284$		−	1.58709i		−	0.0941764i
$285$	2.33520	+	1.63963i	0.138325	+	0.0971235i
$286$	14.1026	−	8.14217i	0.833907	−	0.481457i
$287$		0			0
$288$	3.24019	−	1.16985i	0.190930	−	0.0689339i
$289$	−3.41933	+	5.92245i	−0.201137	+	0.348380i
$290$	−0.714729	+	1.23795i	−0.0419703	+	0.0726947i
$291$	1.94247	−	21.8766i	0.113870	−	1.28243i
$292$	1.69667	−	0.979573i	0.0992901	−	0.0573252i
$293$	−1.36267	+	2.36021i	−0.0796079	+	0.137885i	−0.903081	−	0.429471i	$-0.858700\pi$
$293$	−1.36267	+	2.36021i	−0.0796079	+	0.137885i	0.823473	+	0.567356i	$0.192033\pi$
$294$		0			0
$295$	−0.322104	−	0.557900i	−0.0187536	−	0.0324822i
$296$	27.3682	+	15.8010i	1.59074	+	0.918415i
$297$	11.5745	+	11.6647i	0.671621	+	0.676854i
$298$	7.22489	+	12.5139i	0.418527	+	0.724910i
$299$	20.7179			1.19815
$300$	−0.729540	−	1.56980i	−0.0421200	−	0.0906326i
$301$		0			0
$302$	−7.73729	−	4.46713i	−0.445231	−	0.257054i
$303$	−5.37724	−	11.5706i	−0.308914	−	0.664712i
$304$	−20.1953	−	11.6598i	−1.15828	−	0.668733i
$305$	1.44951	−	0.836876i	0.0829988	−	0.0479194i
$306$	16.6208	+	14.0200i	0.950150	+	0.801469i
$307$		−	8.31294i		−	0.474444i	−0.971455	−	0.237222i	$-0.923763\pi$
$307$		−	8.31294i		−	0.474444i	0.971455	−	0.237222i	$-0.0762369\pi$
$308$		0			0
$309$	−1.22251	+	13.7682i	−0.0695464	+	0.783248i
$310$	1.72201	+	2.98261i	0.0978037	+	0.169401i
$311$	−6.00047			−0.340255			−0.170128	−	0.985422i	$-0.554418\pi$
$311$	−6.00047			−0.340255			−0.170128	+	0.985422i	$0.554418\pi$
$312$	6.75163	+	14.5280i	0.382236	+	0.822484i
$313$		−	11.8253i		−	0.668403i	−0.942502	−	0.334201i	$-0.891533\pi$
$313$		−	11.8253i		−	0.668403i	0.942502	−	0.334201i	$-0.108467\pi$
$314$	−24.2726			−1.36978
$315$		0			0
$316$	−1.04662			−0.0588767
$317$			29.6442i			1.66498i	0.554038	+	0.832491i	$0.313086\pi$
$317$			29.6442i			1.66498i	−0.554038	+	0.832491i	$0.686914\pi$
$318$	0.219000	+	0.0194455i	0.0122809	+	0.00109045i
$319$	9.87322			0.552794
$320$	1.08372	+	1.87707i	0.0605821	+	0.104931i
$321$	26.3400	−	12.2411i	1.47016	−	0.683232i
$322$		0			0
$323$		−	26.0781i		−	1.45103i
$324$	1.41089	−	1.17149i	0.0783826	−	0.0650826i
$325$	14.7339	−	8.50664i	0.817291	−	0.471863i
$326$	−8.31116	−	4.79845i	−0.460313	−	0.265762i
$327$	−15.2946	−	1.35804i	−0.845794	−	0.0751000i
$328$	−11.9584	−	6.90417i	−0.660291	−	0.381219i
$329$		0			0
$330$	1.44119	−	2.05257i	0.0793348	−	0.112990i
$331$	−17.0501			−0.937158			−0.468579	−	0.883422i	$-0.655234\pi$
$331$	−17.0501			−0.937158			−0.468579	+	0.883422i	$0.655234\pi$
$332$	0.901567	+	1.56156i	0.0494799	+	0.0857017i
$333$	34.9979	+	6.26447i	1.91787	+	0.343291i
$334$	−3.43404	−	1.98264i	−0.187902	−	0.108485i
$335$	0.0170912	+	0.0296028i	0.000933791	+	0.00161737i
$336$		0			0
$337$	10.1065	−	17.5050i	0.550536	−	0.953556i	−0.447700	−	0.894184i	$-0.647757\pi$
$337$	10.1065	−	17.5050i	0.550536	−	0.953556i	0.998236	−	0.0593723i	$-0.0189099\pi$
$338$	−1.24509	+	0.718852i	−0.0677239	+	0.0391004i
$339$	−24.5977	+	11.4314i	−1.33596	+	0.620866i
$340$	0.153422	−	0.265735i	0.00832049	−	0.0144115i
$341$	11.8939	−	20.6008i	0.644090	−	1.11560i
$342$	−23.4148	−	4.19116i	−1.26613	−	0.226632i
$343$		0			0
$344$	12.7084	−	7.33719i	0.685191	−	0.395595i
$345$	2.89362	−	1.34476i	0.155787	−	0.0723996i
$346$			29.9820i			1.61184i
$347$		−	17.6817i		−	0.949205i	−0.880200	−	0.474602i	$-0.842592\pi$
$347$		−	17.6817i		−	0.949205i	0.880200	−	0.474602i	$-0.157408\pi$
$348$	0.0974500	−	1.09751i	0.00522387	−	0.0588324i
$349$	3.62628	−	2.09363i	0.194110	−	0.112070i	−0.399795	−	0.916605i	$-0.630919\pi$
$349$	3.62628	−	2.09363i	0.194110	−	0.112070i	0.593905	+	0.804535i	$0.297585\pi$
$350$		0			0
$351$	12.6951	+	12.7940i	0.677613	+	0.682893i
$352$	−1.81574	+	3.14495i	−0.0967791	+	0.167626i
$353$	−15.2477	+	26.4097i	−0.811551	+	1.40565i	0.100227	+	0.994965i	$0.468043\pi$
$353$	−15.2477	+	26.4097i	−0.811551	+	1.40565i	−0.911778	+	0.410684i	$0.865290\pi$
$354$	4.39523	+	3.08606i	0.233604	+	0.164022i
$355$	2.08051	−	1.20118i	0.110422	−	0.0637522i
$356$	0.190900	−	0.330649i	0.0101177	−	0.0175243i
$357$		0			0
$358$	16.3015	+	28.2350i	0.861561	+	1.49227i
$359$	4.66901	+	2.69565i	0.246421	+	0.142271i	0.618124	−	0.786080i	$-0.287893\pi$
$359$	4.66901	+	2.69565i	0.246421	+	0.142271i	−0.371703	+	0.928352i	$0.621226\pi$
$360$	1.88597	+	1.59085i	0.0993992	+	0.0838450i
$361$	4.76400	+	8.25150i	0.250737	+	0.434289i
$362$	−3.71971			−0.195504
$363$	1.72308	+	0.152996i	0.0904381	+	0.00803021i
$364$		0			0
$365$	2.56824	+	1.48277i	0.134428	+	0.0776119i
$366$	−8.01805	+	11.4195i	−0.419110	+	0.596907i
$367$	17.3218	+	10.0007i	0.904188	+	0.522033i	0.878557	−	0.477638i	$-0.158507\pi$
$367$	17.3218	+	10.0007i	0.904188	+	0.522033i	0.0256317	+	0.999671i	$0.491840\pi$
$368$	−22.5840	+	13.0389i	−1.17727	+	0.679698i
$369$	−15.2921	−	2.73723i	−0.796077	−	0.142494i
$370$		−	5.42636i		−	0.282103i
$371$		0			0
$372$	−2.17259	−	1.52545i	−0.112643	−	0.0790911i
$373$	13.0474	+	22.5988i	0.675571	+	1.17012i	0.976302	+	0.216414i	$0.0694363\pi$
$373$	13.0474	+	22.5988i	0.675571	+	1.17012i	−0.300730	+	0.953709i	$0.597230\pi$
$374$	−22.9219			−1.18526
$375$	3.04060	−	4.33050i	0.157016	−	0.223626i
$376$			22.5694i			1.16393i
$377$	10.8291			0.557726
$378$		0			0
$379$	30.5222			1.56782			0.783910	−	0.620875i	$-0.213222\pi$
$379$	30.5222			1.56782			0.783910	+	0.620875i	$0.213222\pi$
$380$			0.335671i			0.0172195i
$381$	6.74876	−	9.61174i	0.345750	−	0.492425i
$382$	−3.12451			−0.159864
$383$	11.3543	+	19.6662i	0.580177	+	1.00490i	0.995458	+	0.0952034i	$0.0303501\pi$
$383$	11.3543	+	19.6662i	0.580177	+	1.00490i	−0.415280	+	0.909693i	$0.636317\pi$
$384$	−18.0433	−	12.6689i	−0.920770	−	0.646507i
$385$		0			0
$386$			8.83964i			0.449926i
$387$	10.6448	−	12.6195i	0.541106	−	0.641487i
$388$	2.23756	−	1.29185i	0.113595	−	0.0655840i
$389$	3.89121	+	2.24659i	0.197292	+	0.113907i	0.595392	−	0.803436i	$-0.296997\pi$
$389$	3.89121	+	2.24659i	0.197292	+	0.113907i	−0.398100	+	0.917342i	$0.630330\pi$
$390$	1.58071	−	2.25129i	0.0800426	−	0.113999i
$391$	−25.2556	−	14.5813i	−1.27723	−	0.737409i
$392$		0			0
$393$	−33.7153	−	2.99366i	−1.70071	−	0.151010i
$394$	11.3492			0.571766
$395$	−0.792127	−	1.37200i	−0.0398562	−	0.0690330i
$396$	−0.340615	+	1.90292i	−0.0171165	+	0.0956253i
$397$	−8.35854	−	4.82581i	−0.419503	−	0.242200i	0.275362	−	0.961341i	$-0.411202\pi$
$397$	−8.35854	−	4.82581i	−0.419503	−	0.242200i	−0.694865	+	0.719140i	$0.744536\pi$
$398$	−5.08587	−	8.80898i	−0.254931	−	0.441554i
$399$		0			0
$400$	−10.7073	+	18.5457i	−0.535367	+	0.927283i
$401$	17.2356	−	9.95098i	0.860705	−	0.496928i	−0.00354346	−	0.999994i	$-0.501128\pi$
$401$	17.2356	−	9.95098i	0.860705	−	0.496928i	0.864248	+	0.503066i	$0.167795\pi$
$402$	−0.233216	−	0.163749i	−0.0116317	−	0.00816708i
$403$	13.0454	−	22.5953i	0.649837	−	1.12555i
$404$	0.750494	−	1.29989i	0.0373385	−	0.0646721i
$405$	2.60352	+	0.962890i	0.129370	+	0.0478464i
$406$		0			0
$407$	−32.4584	+	18.7398i	−1.60890	+	0.928900i
$408$	1.99443	−	22.4617i	0.0987388	−	1.11202i
$409$			2.42571i			0.119944i	0.998200	+	0.0599718i	$0.0191011\pi$
$409$			2.42571i			0.119944i	−0.998200	+	0.0599718i	$0.980899\pi$
$410$			2.37102i			0.117096i
$411$	−2.49512	+	1.15957i	−0.123075	+	0.0571972i
$412$	−1.40823	+	0.813042i	−0.0693785	+	0.0400557i
$413$		0			0
$414$	−17.1511	+	20.3328i	−0.842931	+	0.999304i
$415$	−1.36470	+	2.36372i	−0.0669903	+	0.116031i
$416$	−1.99153	+	3.44942i	−0.0976426	+	0.169122i
$417$	−7.20538	+	3.34859i	−0.352849	+	0.163981i
$418$	21.7158	−	12.5376i	1.06216	−	0.613236i
$419$	−14.6878	+	25.4399i	−0.717544	+	1.24282i	0.244426	+	0.969668i	$0.421400\pi$
$419$	−14.6878	+	25.4399i	−0.717544	+	1.24282i	−0.961970	+	0.273155i	$0.911933\pi$
$420$		0			0
$421$	−18.2078	−	31.5368i	−0.887392	−	1.53701i	−0.842948	−	0.537996i	$-0.819182\pi$
$421$	−18.2078	−	31.5368i	−0.887392	−	1.53701i	−0.0444443	−	0.999012i	$-0.514152\pi$
$422$	7.06537	+	4.07919i	0.343937	+	0.198572i
$423$	8.62277	+	23.8829i	0.419254	+	1.16123i
$424$	−0.114005	−	0.197462i	−0.00553656	−	0.00958961i
$425$	−23.9480			−1.16165
$426$	−11.5084	+	16.3906i	−0.557586	+	0.794127i
$427$		0			0
$428$	2.95916	+	1.70847i	0.143037	+	0.0825822i
$429$	−18.9253	−	1.68042i	−0.913723	−	0.0811316i
$430$	−2.18215	−	1.25986i	−0.105232	−	0.0607560i
$431$	16.8459	−	9.72598i	0.811438	−	0.468484i	−0.0360172	−	0.999351i	$-0.511467\pi$
$431$	16.8459	−	9.72598i	0.811438	−	0.468484i	0.847455	+	0.530867i	$0.178134\pi$
$432$	−21.8904	−	5.95667i	−1.05320	−	0.286591i
$433$			9.94623i			0.477985i	0.971021	+	0.238993i	$0.0768172\pi$
$433$			9.94623i			0.477985i	−0.971021	+	0.238993i	$0.923183\pi$
$434$		0			0
$435$	1.51247	−	0.702896i	0.0725174	−	0.0337013i
$436$	−0.903178	−	1.56435i	−0.0432544	−	0.0749188i
$437$	31.9023			1.52609
$438$	−24.6255	−	2.18655i	−1.17665	−	0.104478i
$439$			7.37561i			0.352019i	0.984389	+	0.176009i	$0.0563189\pi$
$439$			7.37561i			0.352019i	−0.984389	+	0.176009i	$0.943681\pi$
$440$	−2.60095			−0.123995
$441$		0			0
$442$	−25.1411			−1.19584
$443$			0.859823i			0.0408514i	0.999791	+	0.0204257i	$0.00650216\pi$
$443$			0.859823i			0.0408514i	−0.999791	+	0.0204257i	$0.993498\pi$
$444$	1.76275	+	3.79303i	0.0836563	+	0.180009i
$445$	0.577929			0.0273964
$446$	−15.0914	−	26.1392i	−0.714601	−	1.23772i
$447$	1.49111	−	16.7932i	0.0705271	−	0.794293i
$448$		0			0
$449$			15.6497i			0.738556i	0.929319	+	0.369278i	$0.120395\pi$
$449$			15.6497i			0.738556i	−0.929319	+	0.369278i	$0.879605\pi$
$450$	−3.84880	+	21.5022i	−0.181434	+	1.01362i
$451$	14.1825	−	8.18828i	0.667829	−	0.385571i
$452$	−2.76342	−	1.59546i	−0.129980	−	0.0750441i
$453$	4.39317	+	9.45309i	0.206409	+	0.444145i
$454$	−0.414575	−	0.239355i	−0.0194570	−	0.0112335i
$455$		0			0
$456$	10.3964	+	22.3707i	0.486857	+	1.04761i
$457$	−5.63119			−0.263416			−0.131708	−	0.991289i	$-0.542046\pi$
$457$	−5.63119			−0.263416			−0.131708	+	0.991289i	$0.542046\pi$
$458$	−1.97275	−	3.41690i	−0.0921806	−	0.159661i
$459$	−6.47112	−	24.5310i	−0.302046	−	1.14501i
$460$	0.325083	+	0.187687i	0.0151571	+	0.00875093i
$461$	−11.3342	−	19.6314i	−0.527886	−	0.914326i	−0.999472	−	0.0325056i	$-0.989651\pi$
$461$	−11.3342	−	19.6314i	−0.527886	−	0.914326i	0.471585	−	0.881821i	$-0.343682\pi$
$462$		0			0
$463$	−21.0052	+	36.3821i	−0.976194	+	1.69082i	−0.300257	+	0.953858i	$0.597073\pi$
$463$	−21.0052	+	36.3821i	−0.976194	+	1.69082i	−0.675937	+	0.736960i	$0.736261\pi$
$464$	−11.8045	+	6.81531i	−0.548008	+	0.316393i
$465$	0.355398	−	4.00257i	0.0164812	−	0.185615i
$466$	−17.2629	+	29.9003i	−0.799690	+	1.38510i
$467$	−12.4016	+	21.4802i	−0.573879	+	0.993987i	0.422284	+	0.906464i	$0.361229\pi$
$467$	−12.4016	+	21.4802i	−0.573879	+	0.993987i	−0.996162	+	0.0875236i	$0.972105\pi$
$468$	−0.373591	+	2.08715i	−0.0172692	+	0.0964785i
$469$		0			0
$470$	3.35617	−	1.93769i	0.154809	−	0.0893788i
$471$	23.1774	+	16.2737i	1.06796	+	0.749854i
$472$		−	5.56948i		−	0.256356i
$473$			17.4037i			0.800222i
$474$	10.8089	+	7.58931i	0.496468	+	0.348589i
$475$	22.6879	−	13.0989i	1.04099	−	0.601017i
$476$		0			0
$477$	−0.196082	−	0.165398i	−0.00897796	−	0.00757307i
$478$	−0.249637	+	0.432385i	−0.0114181	+	0.0197768i
$479$	1.64647	−	2.85177i	0.0752291	−	0.130301i	−0.825957	−	0.563733i	$-0.809365\pi$
$479$	1.64647	−	2.85177i	0.0752291	−	0.130301i	0.901186	+	0.433433i	$0.142698\pi$
$480$	−0.0542555	+	0.611039i	−0.00247641	+	0.0278900i
$481$	−35.6008	+	20.5541i	−1.62326	+	0.937187i
$482$	16.4427	−	28.4797i	0.748946	−	1.29721i
$483$		0			0
$484$	0.101751	+	0.176238i	0.00462505	+	0.00801082i
$485$	3.38698	+	1.95547i	0.153795	+	0.0887934i
$486$	−23.0657	+	1.86774i	−1.04628	+	0.0847223i
$487$	−5.22240	−	9.04546i	−0.236650	−	0.409889i	0.723101	−	0.690742i	$-0.242716\pi$
$487$	−5.22240	−	9.04546i	−0.236650	−	0.409889i	−0.959751	+	0.280853i	$0.909383\pi$
$488$	14.4704			0.655043
$489$	4.71901	+	10.1542i	0.213401	+	0.459190i
$490$		0			0
$491$	−26.2797	−	15.1726i	−1.18599	−	0.684731i	−0.228596	−	0.973521i	$-0.573413\pi$
$491$	−26.2797	−	15.1726i	−1.18599	−	0.684731i	−0.957392	+	0.288791i	$0.906747\pi$
$492$	−0.770224	−	1.65734i	−0.0347244	−	0.0747189i
$493$	−13.2009	−	7.62153i	−0.594538	−	0.343257i
$494$	23.8182	−	13.7514i	1.07163	−	0.618707i
$495$	−2.75232	+	0.993708i	−0.123708	+	0.0446638i
$496$			32.8405i			1.47458i
$497$		0			0
$498$	2.01243	−	22.6645i	0.0901792	−	1.01562i
$499$	−0.984757	−	1.70565i	−0.0440838	−	0.0763554i	0.843142	−	0.537692i	$-0.180704\pi$
$499$	−0.984757	−	1.70565i	−0.0440838	−	0.0763554i	−0.887225	+	0.461336i	$0.847370\pi$
$500$	0.622481			0.0278382
$501$	1.94982	+	4.19556i	0.0871115	+	0.187444i
$502$		−	20.7534i		−	0.926269i
$503$	−17.3024			−0.771477			−0.385739	−	0.922608i	$-0.626053\pi$
$503$	−17.3024			−0.771477			−0.385739	+	0.922608i	$0.626053\pi$
$504$		0			0
$505$	2.27203			0.101104
$506$		−	28.0411i		−	1.24658i
$507$	1.67087	+	0.148360i	0.0742059	+	0.00658892i
$508$	1.38163			0.0612998
$509$	−0.240892	−	0.417237i	−0.0106774	−	0.0184937i	0.860637	−	0.509218i	$-0.170065\pi$
$509$	−0.240892	−	0.417237i	−0.0106774	−	0.0184937i	−0.871315	+	0.490725i	$0.836732\pi$
$510$	−3.51139	+	1.63186i	−0.155487	+	0.0722600i
$511$		0			0
$512$			18.2707i			0.807457i
$513$	19.5484	+	19.7007i	0.863082	+	0.869807i
$514$	−24.9170	+	14.3858i	−1.09904	+	0.634532i
$515$	−2.13163	−	1.23070i	−0.0939307	−	0.0542309i
$516$	1.93459	+	0.171777i	0.0851655	+	0.00756204i
$517$	−23.1810	−	13.3835i	−1.01950	−	0.588607i
$518$		0			0
$519$	20.1017	−	28.6292i	0.882365	−	1.25668i
$520$	−2.85276			−0.125102
$521$	−7.20770	−	12.4841i	−0.315775	−	0.546939i	0.663827	−	0.747886i	$-0.268931\pi$
$521$	−7.20770	−	12.4841i	−0.315775	−	0.546939i	−0.979602	+	0.200948i	$0.935598\pi$
$522$	−8.96474	+	10.6278i	−0.392376	+	0.465166i
$523$	−5.90591	−	3.40978i	−0.258247	−	0.149099i	0.365287	−	0.930895i	$-0.380971\pi$
$523$	−5.90591	−	3.40978i	−0.258247	−	0.149099i	−0.623535	+	0.781796i	$0.714304\pi$
$524$	−1.99095	−	3.44843i	−0.0869752	−	0.150645i
$525$		0			0
$526$	−3.77780	+	6.54334i	−0.164720	+	0.285303i
$527$	−31.8052	+	18.3627i	−1.38546	+	0.799893i
$528$	21.6875	−	10.0789i	0.943827	−	0.438628i
$529$	6.33781	−	10.9774i	0.275557	−	0.477278i
$530$	−0.0195757	+	0.0339061i	−0.000850313	+	0.00147279i
$531$	−2.12785	−	5.89363i	−0.0923410	−	0.255762i
$532$		0			0
$533$	15.5556	−	8.98102i	0.673787	−	0.389011i
$534$	−4.36915	+	2.03049i	−0.189071	+	0.0878679i
$535$			5.17221i			0.223614i
$536$			0.295523i			0.0127646i
$537$	3.36439	−	37.8905i	0.145184	−	1.63510i
$538$	6.50011	−	3.75284i	0.280240	−	0.161796i
$539$		0			0
$540$	0.0832945	+	0.315756i	0.00358442	+	0.0135880i
$541$	8.91128	−	15.4348i	0.383126	−	0.663594i	−0.608381	−	0.793645i	$-0.708181\pi$
$541$	8.91128	−	15.4348i	0.383126	−	0.663594i	0.991507	+	0.130051i	$0.0415142\pi$
$542$	23.2926	−	40.3440i	1.00050	−	1.73292i
$543$	3.55188	+	2.49391i	0.152426	+	0.107024i
$544$	4.85542	−	2.80328i	0.208175	−	0.120190i
$545$	1.36713	−	2.36795i	0.0585616	−	0.101432i
$546$		0			0
$547$	−6.79325	−	11.7663i	−0.290458	−	0.503089i	0.683460	−	0.729988i	$-0.260474\pi$
$547$	−6.79325	−	11.7663i	−0.290458	−	0.503089i	−0.973918	+	0.226900i	$0.927141\pi$
$548$	−0.280314	−	0.161839i	−0.0119744	−	0.00691342i
$549$	15.3126	−	5.52850i	0.653524	−	0.235950i
$550$	−11.5135	−	19.9420i	−0.490937	−	0.850328i
$551$	16.6750			0.710381
$552$	27.4782	+	2.43985i	1.16955	+	0.103847i
$553$		0			0
$554$	33.4979	+	19.3400i	1.42319	+	0.821678i
$555$	−3.63814	+	5.18152i	−0.154430	+	0.219943i
$556$	−0.809487	−	0.467357i	−0.0343299	−	0.0198204i
$557$	−6.24761	+	3.60706i	−0.264720	+	0.152836i	−0.626486	−	0.779433i	$-0.715507\pi$
$557$	−6.24761	+	3.60706i	−0.264720	+	0.152836i	0.361766	+	0.932269i	$0.382174\pi$
$558$	11.3758	+	31.5081i	0.481576	+	1.33385i
$559$			19.0886i			0.807361i
$560$		0			0
$561$	21.8877	+	15.3681i	0.924098	+	0.648844i
$562$	3.55119	+	6.15084i	0.149798	+	0.259457i
$563$	23.0944			0.973314			0.486657	−	0.873593i	$-0.338216\pi$
$563$	23.0944			0.973314			0.486657	+	0.873593i	$0.338216\pi$
$564$	−1.71651	+	2.44469i	−0.0722781	+	0.102940i
$565$		−	4.83007i		−	0.203203i
$566$	−1.58944			−0.0668092
$567$		0			0
$568$	20.7696			0.871473
$569$		−	26.1007i		−	1.09420i	−0.837067	−	0.547100i	$-0.815732\pi$
$569$		−	26.1007i		−	1.09420i	0.837067	−	0.547100i	$-0.184268\pi$
$570$	2.43405	−	3.46662i	0.101951	−	0.145201i
$571$	−24.6637			−1.03214			−0.516071	−	0.856546i	$-0.672606\pi$
$571$	−24.6637			−1.03214			−0.516071	+	0.856546i	$0.672606\pi$
$572$	−1.11758	−	1.93570i	−0.0467283	−	0.0809357i
$573$	2.98353	+	2.09485i	0.124639	+	0.0875136i
$574$		0			0
$575$		−	29.2963i		−	1.22174i
$576$	7.15920	+	19.8292i	0.298300	+	0.826218i
$577$	−16.7403	+	9.66501i	−0.696907	+	0.402360i	−0.806194	−	0.591651i	$-0.798477\pi$
$577$	−16.7403	+	9.66501i	−0.696907	+	0.402360i	0.109287	+	0.994010i	$0.465143\pi$
$578$	8.79192	+	5.07602i	0.365696	+	0.211135i
$579$	5.92660	−	8.44080i	0.246301	−	0.350788i
$580$	0.169918	+	0.0981022i	0.00705546	+	0.00407347i
$581$		0			0
$582$	−32.4759	−	2.88361i	−1.34617	−	0.119530i
$583$	0.270417			0.0111995
$584$	12.8193	+	22.2036i	0.530465	+	0.918793i
$585$	−3.01879	+	1.08991i	−0.124811	+	0.0450623i
$586$	3.50375	+	2.02289i	0.144738	+	0.0835648i
$587$	7.65692	+	13.2622i	0.316035	+	0.547389i	0.979657	−	0.200679i	$-0.0643150\pi$
$587$	7.65692	+	13.2622i	0.316035	+	0.547389i	−0.663622	+	0.748068i	$0.730982\pi$
$588$		0			0
$589$	20.0878	−	34.7931i	0.827703	−	1.43362i
$590$	−0.828207	+	0.478166i	−0.0340967	+	0.0196858i
$591$	−10.8372	−	7.60917i	−0.445781	−	0.312999i
$592$	25.8716	−	44.8108i	1.06331	−	1.84171i
$593$	−19.6195	+	33.9820i	−0.805678	+	1.39547i	0.110155	+	0.993914i	$0.464865\pi$
$593$	−19.6195	+	33.9820i	−0.805678	+	1.39547i	−0.915833	+	0.401560i	$0.868468\pi$
$594$	17.3163	−	17.1824i	0.710497	−	0.705004i
$595$		0			0
$596$	1.71763	−	0.991674i	0.0703569	−	0.0406206i
$597$	−1.04965	+	11.8214i	−0.0429592	+	0.483817i
$598$		−	30.7559i		−	1.25770i
$599$			34.3077i			1.40177i	0.713272	+	0.700887i	$0.247212\pi$
$599$			34.3077i			1.40177i	−0.713272	+	0.700887i	$0.752788\pi$
$600$	20.5434	−	9.54720i	0.838680	−	0.389763i
$601$	−24.0139	+	13.8644i	−0.979547	+	0.565541i	−0.902133	−	0.431458i	$-0.857999\pi$
$601$	−24.0139	+	13.8644i	−0.979547	+	0.565541i	−0.0774133	+	0.996999i	$0.524666\pi$
$602$		0			0
$603$	0.112906	+	0.312722i	0.00459790	+	0.0127350i
$604$	−0.613149	+	1.06200i	−0.0249487	+	0.0432123i
$605$	−0.154020	+	0.266770i	−0.00626180	+	0.0108458i
$606$	−17.1766	+	7.98255i	−0.697752	+	0.324269i
$607$	13.0526	−	7.53592i	0.529788	−	0.305873i	−0.211142	−	0.977455i	$-0.567718\pi$
$607$	13.0526	−	7.53592i	0.529788	−	0.305873i	0.740930	+	0.671582i	$0.234385\pi$
$608$	−3.06663	+	5.31156i	−0.124368	+	0.215412i
$609$		0			0
$610$	−1.24235	−	2.15181i	−0.0503012	−	0.0871243i
$611$	−25.4252	−	14.6793i	−1.02859	−	0.593859i
$612$	1.92435	−	2.28134i	0.0777874	−	0.0922178i
$613$	−4.82944	−	8.36484i	−0.195059	−	0.337853i	0.751861	−	0.659322i	$-0.229157\pi$
$613$	−4.82944	−	8.36484i	−0.195059	−	0.337853i	−0.946920	+	0.321469i	$0.895823\pi$
$614$	−12.3406			−0.498027
$615$	1.58967	−	2.26404i	0.0641016	−	0.0912949i
$616$		0			0
$617$	15.9761	+	9.22381i	0.643174	+	0.371337i	0.785836	−	0.618435i	$-0.212233\pi$
$617$	15.9761	+	9.22381i	0.643174	+	0.371337i	−0.142662	+	0.989771i	$0.545566\pi$
$618$	20.4390	+	1.81483i	0.822179	+	0.0730032i
$619$	−29.3519	−	16.9463i	−1.17975	−	0.681130i	−0.223795	−	0.974636i	$-0.571845\pi$
$619$	−29.3519	−	16.9463i	−1.17975	−	0.681130i	−0.955957	+	0.293506i	$0.905178\pi$
$620$	0.409387	−	0.236360i	0.0164414	−	0.00949244i
$621$	30.0096	−	7.91634i	1.20424	−	0.317672i
$622$			8.90774i			0.357168i
$623$		0			0
$624$	23.7871	−	11.0547i	0.952248	−	0.442542i
$625$	−11.7911	−	20.4227i	−0.471642	−	0.816908i
$626$	−17.5547			−0.701626
$627$	−29.1419	−	2.58758i	−1.16382	−	0.103338i
$628$			3.33161i			0.132946i
$629$	57.8641			2.30719
$630$		0			0
$631$	−10.0134			−0.398629			−0.199314	−	0.979936i	$-0.563871\pi$
$631$	−10.0134			−0.398629			−0.199314	+	0.979936i	$0.563871\pi$
$632$		−	13.6966i		−	0.544823i
$633$	−4.01166	−	8.63217i	−0.159449	−	0.343098i
$634$	44.0070			1.74774
$635$	1.04568	+	1.81117i	0.0414965	+	0.0718741i
$636$	0.00266905	−	0.0300595i	0.000105835	−	0.00119194i
$637$		0			0
$638$		−	14.6569i		−	0.580271i
$639$	21.9784	−	7.93514i	0.869451	−	0.313909i
$640$	3.39996	−	1.96297i	0.134395	−	0.0775931i
$641$	34.7673	+	20.0729i	1.37323	+	0.792833i	0.991333	−	0.131373i	$-0.0419387\pi$
$641$	34.7673	+	20.0729i	1.37323	+	0.792833i	0.381894	+	0.924206i	$0.375272\pi$
$642$	−18.1720	−	39.1020i	−0.717192	−	1.54323i
$643$	30.0552	+	17.3524i	1.18526	+	0.684311i	0.957226	−	0.289342i	$-0.0934364\pi$
$643$	30.0552	+	17.3524i	1.18526	+	0.684311i	0.228036	+	0.973653i	$0.426770\pi$
$644$		0			0
$645$	1.23901	+	2.66605i	0.0487858	+	0.104976i
$646$	−38.7132			−1.52315
$647$	7.18466	+	12.4442i	0.282458	+	0.489232i	0.971990	−	0.235024i	$-0.0755169\pi$
$647$	7.18466	+	12.4442i	0.282458	+	0.489232i	−0.689532	+	0.724256i	$0.742184\pi$
$648$	15.3308	+	18.4637i	0.602250	+	0.725323i
$649$	5.72040	+	3.30268i	0.224545	+	0.129641i
$650$	−12.6282	−	21.8726i	−0.495317	−	0.857915i
$651$		0			0
$652$	−0.658626	+	1.14077i	−0.0257938	+	0.0446761i
$653$	0.971455	−	0.560870i	0.0380160	−	0.0219485i	−0.480872	−	0.876791i	$-0.659680\pi$
$653$	0.971455	−	0.560870i	0.0380160	−	0.0219485i	0.518888	+	0.854843i	$0.326346\pi$
$654$	−2.01603	+	22.7050i	−0.0788329	+	0.887834i
$655$	3.01369	−	5.21987i	0.117755	−	0.203957i
$656$	−11.3044	+	19.5799i	−0.441364	+	0.764466i
$657$	22.0484	+	18.5982i	0.860190	+	0.725586i
$658$		0			0
$659$	−5.45240	+	3.14795i	−0.212395	+	0.122627i	−0.602424	−	0.798176i	$-0.705798\pi$
$659$	−5.45240	+	3.14795i	−0.212395	+	0.122627i	0.390029	+	0.920803i	$0.372465\pi$
$660$	−0.281732	−	0.197815i	−0.0109664	−	0.00769992i
$661$			43.5222i			1.69282i	0.532533	+	0.846409i	$0.321240\pi$
$661$			43.5222i			1.69282i	−0.532533	+	0.846409i	$0.678760\pi$
$662$			25.3110i			0.983739i
$663$	24.0067	+	16.8560i	0.932343	+	0.654633i
$664$	−20.4355	+	11.7984i	−0.793051	+	0.457868i
$665$		0			0
$666$	9.29965	−	51.9546i	0.360354	−	2.01320i
$667$	9.32368	−	16.1491i	0.361014	−	0.625295i
$668$	−0.272134	+	0.471349i	−0.0105292	+	0.0182370i
$669$	−3.11465	+	35.0779i	−0.120419	+	1.35619i
$670$	0.0439456	−	0.0253720i	0.00169776	−	0.000980205i
$671$	−8.58086	+	14.8625i	−0.331261	+	0.573760i
$672$		0			0
$673$	−11.6052	−	20.1008i	−0.447347	−	0.774827i	0.550866	−	0.834594i	$-0.314298\pi$
$673$	−11.6052	−	20.1008i	−0.447347	−	0.774827i	−0.998212	+	0.0597668i	$0.980964\pi$
$674$	−25.9862	−	15.0032i	−1.00095	−	0.577900i
$675$	18.0914	−	17.9516i	0.696340	−	0.690956i
$676$	0.0986682	+	0.170898i	0.00379493	+	0.00657301i
$677$	45.6425			1.75419			0.877093	−	0.480321i	$-0.159480\pi$
$677$	45.6425			1.75419			0.877093	+	0.480321i	$0.159480\pi$
$678$	16.9699	+	36.5154i	0.651726	+	1.40237i
$679$		0			0
$680$	3.47757	+	2.00778i	0.133359	+	0.0769947i
$681$	0.235392	+	0.506510i	0.00902025	+	0.0194095i
$682$	−30.5821	−	17.6566i	−1.17105	−	0.676104i
$683$	3.81262	−	2.20122i	0.145886	−	0.0842272i	−0.425280	−	0.905062i	$-0.639825\pi$
$683$	3.81262	−	2.20122i	0.145886	−	0.0842272i	0.571166	+	0.820834i	$0.306491\pi$
$684$	−0.575270	+	3.21387i	−0.0219960	+	0.122885i
$685$		−	0.489950i		−	0.0187200i
$686$		0			0
$687$	−0.407146	+	4.58538i	−0.0155336	+	0.174943i
$688$	−12.0134	−	20.8079i	−0.458008	−	0.793294i
$689$	0.296597			0.0112995
$690$	−1.99631	−	4.29560i	−0.0759982	−	0.163531i
$691$			9.33079i			0.354960i	0.984124	+	0.177480i	$0.0567945\pi$
$691$			9.33079i			0.354960i	−0.984124	+	0.177480i	$0.943206\pi$
$692$	4.11527			0.156439
$693$		0			0
$694$	−26.2486			−0.996385
$695$		−	1.41487i		−	0.0536691i
$696$	14.3626	+	1.27529i	0.544413	+	0.0483397i
$697$	−25.2834			−0.957679
$698$	−3.10802	−	5.38324i	−0.117640	−	0.203759i
$699$	36.5309	−	16.9771i	1.38172	−	0.642134i
$700$		0			0
$701$			22.9051i			0.865116i	0.901606	+	0.432558i	$0.142389\pi$
$701$			22.9051i			0.865116i	−0.901606	+	0.432558i	$0.857611\pi$
$702$	18.9928	−	18.8459i	0.716836	−	0.711294i
$703$	−54.8195	+	31.6500i	−2.06756	+	1.19370i
$704$	−19.2464	−	11.1119i	−0.725376	−	0.418796i
$705$	−4.50388	−	0.399910i	−0.169626	−	0.0150615i
$706$	39.2054	+	22.6353i	1.47552	+	0.851889i
$707$		0			0
$708$	0.423586	−	0.603281i	0.0159193	−	0.0226727i
$709$	5.56360			0.208946			0.104473	−	0.994528i	$-0.466684\pi$
$709$	5.56360			0.208946			0.104473	+	0.994528i	$0.466684\pi$
$710$	−1.78316	−	3.08853i	−0.0669210	−	0.115910i
$711$	−5.23288	−	14.4938i	−0.196248	−	0.543559i
$712$	4.32707	+	2.49823i	0.162164	+	0.0936252i
$713$	−22.4637	−	38.9083i	−0.841274	−	1.45713i
$714$		0			0
$715$	1.69167	−	2.93006i	0.0632649	−	0.109578i
$716$	3.87548	−	2.23751i	0.144834	−	0.0836197i
$717$	0.528269	−	0.245504i	0.0197286	−	0.00916853i
$718$	4.00172	−	6.93118i	0.149343	−	0.258669i
$719$	9.99888	−	17.3186i	0.372895	−	0.645873i	−0.617114	−	0.786873i	$-0.711698\pi$
$719$	9.99888	−	17.3186i	0.372895	−	0.645873i	0.990010	+	0.141000i	$0.0450318\pi$
$720$	2.60475	−	3.08796i	0.0970733	−	0.115081i
$721$		0			0
$722$	12.2494	−	7.07220i	0.455876	−	0.263200i
$723$	−34.7952	+	16.1705i	−1.29405	+	0.601388i
$724$			0.510560i			0.0189748i
$725$		−	15.3130i		−	0.568709i
$726$	0.227124	−	2.55792i	0.00842935	−	0.0949333i
$727$	−25.0380	+	14.4557i	−0.928610	+	0.536133i	−0.886372	−	0.462975i	$-0.846782\pi$
$727$	−25.0380	+	14.4557i	−0.928610	+	0.536133i	−0.0422381	+	0.999108i	$0.513449\pi$
$728$		0			0
$729$	23.2772	+	13.6811i	0.862119	+	0.506707i
$730$	2.20119	−	3.81257i	0.0814696	−	0.141109i
$731$	13.4346	−	23.2694i	0.496896	−	0.860650i
$732$	1.56742	+	1.10054i	0.0579334	+	0.0406772i
$733$	−27.5498	+	15.9059i	−1.01757	+	0.587496i	−0.913400	−	0.407063i	$-0.866553\pi$
$733$	−27.5498	+	15.9059i	−1.01757	+	0.587496i	−0.104173	+	0.994559i	$0.533220\pi$
$734$	14.8461	−	25.7143i	0.547981	−	0.949131i
$735$		0			0
$736$	3.42935	+	5.93980i	0.126407	+	0.218944i
$737$	−0.303531	−	0.175244i	−0.0111807	−	0.00645518i
$738$	−4.06344	+	22.7013i	−0.149577	+	0.835646i
$739$	−11.3935	−	19.7342i	−0.419118	−	0.725934i	0.576733	−	0.816933i	$-0.304327\pi$
$739$	−11.3935	−	19.7342i	−0.419118	−	0.725934i	−0.995851	+	0.0909988i	$0.970994\pi$
$740$	−0.744811			−0.0273798
$741$	−31.9633	−	2.83809i	−1.17420	−	0.104260i
$742$		0			0
$743$	11.8554	+	6.84471i	0.434932	+	0.251108i	0.701446	−	0.712723i	$-0.252538\pi$
$743$	11.8554	+	6.84471i	0.434932	+	0.251108i	−0.266513	+	0.963831i	$0.585872\pi$
$744$	19.9630	−	28.4318i	0.731879	−	1.04236i
$745$	2.59997	+	1.50109i	0.0952554	+	0.0549957i
$746$	33.5481	−	19.3690i	1.22828	−	0.709150i
$747$	−17.1172	+	20.2926i	−0.626285	+	0.742468i
$748$			3.14621i			0.115037i
$749$		0			0
$750$	−6.42865	−	4.51380i	−0.234741	−	0.164820i
$751$	−10.2030	−	17.6721i	−0.372312	−	0.644864i	0.617608	−	0.786486i	$-0.288102\pi$
$751$	−10.2030	−	17.6721i	−0.372312	−	0.644864i	−0.989921	+	0.141622i	$0.954768\pi$
$752$	36.9537			1.34756
$753$	−13.9143	+	19.8170i	−0.507064	+	0.722172i
$754$		−	16.0759i		−	0.585448i
$755$	−1.85624			−0.0675554
$756$		0			0
$757$	−4.02306			−0.146221			−0.0731104	−	0.997324i	$-0.523293\pi$
$757$	−4.02306			−0.146221			−0.0731104	+	0.997324i	$0.523293\pi$
$758$		−	45.3104i		−	1.64575i
$759$	−18.8004	+	26.7759i	−0.682410	+	0.971904i
$760$	−4.39278			−0.159343
$761$	−22.9595	−	39.7670i	−0.832280	−	1.44155i	−0.896226	−	0.443598i	$-0.853702\pi$
$761$	−22.9595	−	39.7670i	−0.832280	−	1.44155i	0.0639453	−	0.997953i	$-0.479632\pi$
$762$	−14.2687	−	10.0186i	−0.516900	−	0.362935i
$763$		0			0
$764$			0.428864i			0.0155157i
$765$	4.44705	+	0.796003i	0.160783	+	0.0287795i
$766$	29.1946	−	16.8555i	1.05485	−	0.609015i
$767$	6.27422	+	3.62242i	0.226549	+	0.130798i
$768$	−4.81845	+	6.86255i	−0.173871	+	0.247631i
$769$	−5.22983	−	3.01944i	−0.188592	−	0.108884i	0.402731	−	0.915318i	$-0.368061\pi$
$769$	−5.22983	−	3.01944i	−0.188592	−	0.108884i	−0.591323	+	0.806434i	$0.701394\pi$
$770$		0			0
$771$	33.4378	+	2.96902i	1.20423	+	0.106927i
$772$	1.21331			0.0436680
$773$	−19.1157	−	33.1094i	−0.687545	−	1.19086i	−0.972630	−	0.232360i	$-0.925355\pi$
$773$	−19.1157	−	33.1094i	−0.687545	−	1.19086i	0.285085	−	0.958502i	$-0.407978\pi$
$774$	−18.7338	−	15.8023i	−0.673372	−	0.568002i
$775$	−31.9510	−	18.4469i	−1.14771	−	0.662633i
$776$	16.9060	+	29.2820i	0.606889	+	1.05116i
$777$		0			0
$778$	3.33508	−	5.77653i	0.119568	−	0.207098i
$779$	23.9531	−	13.8293i	0.858209	−	0.495487i
$780$	−0.309008	−	0.216966i	−0.0110642	−	0.00776862i
$781$	−12.3163	+	21.3324i	−0.440711	+	0.763333i
$782$	−21.6461	+	37.4921i	−0.774061	+	1.34071i
$783$	15.6857	−	4.13781i	0.560563	−	0.147873i
$784$		0			0
$785$	−4.36739	+	2.52152i	−0.155879	+	0.0899968i
$786$	−4.44410	+	50.0505i	−0.158516	+	1.78524i
$787$		−	48.2521i		−	1.72000i	−0.510293	−	0.860001i	$-0.670463\pi$
$787$		−	48.2521i		−	1.72000i	0.510293	−	0.860001i	$-0.329537\pi$
$788$		−	1.55777i		−	0.0554933i
$789$	7.99438	−	3.71526i	0.284607	−	0.132267i
$790$	−2.03675	+	1.17592i	−0.0724643	+	0.0418373i
$791$		0			0
$792$	−24.9027	−	4.45749i	−0.884880	−	0.158390i
$793$	−9.41161	+	16.3014i	−0.334216	+	0.578879i
$794$	−7.16394	+	12.4083i	−0.254239	+	0.440354i
$795$	0.0414250	−	0.0192516i	0.00146919	−	0.000682784i
$796$	−1.20910	+	0.698076i	−0.0428555	+	0.0247426i
$797$	−12.6517	+	21.9133i	−0.448145	+	0.776209i	−0.998265	−	0.0588759i	$-0.981248\pi$
$797$	−12.6517	+	21.9133i	−0.448145	+	0.776209i	0.550121	+	0.835085i	$0.314582\pi$
$798$		0			0
$799$	20.6626	+	35.7886i	0.730989	+	1.26611i
$800$	4.87769	+	2.81613i	0.172452	+	0.0995653i
$801$	5.53337	+	0.990450i	0.195512	+	0.0349958i
$802$	−14.7723	−	25.5864i	−0.521628	−	0.903486i
$803$	−30.4071			−1.07304
$804$	−0.0224759	+	0.0320107i	−0.000792664	+	0.00112893i
$805$		0			0
$806$	−33.5428	−	19.3660i	−1.18150	−	0.682137i
$807$	−8.72294	−	0.774530i	−0.307062	−	0.0272648i
$808$	17.0112	+	9.82141i	0.598451	+	0.345516i
$809$	9.65975	−	5.57706i	0.339619	−	0.196079i	−0.320485	−	0.947254i	$-0.603846\pi$
$809$	9.65975	−	5.57706i	0.339619	−	0.196079i	0.660103	+	0.751175i	$0.270512\pi$
$810$	1.42942	−	3.86495i	0.0502246	−	0.135800i
$811$			1.90097i			0.0667520i	0.999443	+	0.0333760i	$0.0106259\pi$
$811$			1.90097i			0.0667520i	−0.999443	+	0.0333760i	$0.989374\pi$
$812$		0			0
$813$	−49.2906	+	22.9070i	−1.72870	+	0.803383i
$814$	27.8194	+	48.1847i	0.975070	+	1.68887i
$815$	−1.99391			−0.0698438
$816$	−36.7773	−	3.26554i	−1.28746	−	0.114317i
$817$			29.3934i			1.02834i
$818$	3.60098			0.125905
$819$		0			0
$820$	0.325441			0.0113649
$821$		−	10.1608i		−	0.354616i	−0.984155	−	0.177308i	$-0.943261\pi$
$821$		−	10.1608i		−	0.354616i	0.984155	−	0.177308i	$-0.0567389\pi$
$822$	1.72138	+	3.70402i	0.0600402	+	0.129193i
$823$	31.9526			1.11380			0.556898	−	0.830581i	$-0.311991\pi$
$823$	31.9526			1.11380			0.556898	+	0.830581i	$0.311991\pi$
$824$	−10.6399	−	18.4289i	−0.370660	−	0.642002i
$825$	−2.37621	+	26.7615i	−0.0827292	+	0.931716i
$826$		0			0
$827$		−	13.7400i		−	0.477787i	−0.971046	−	0.238894i	$-0.923215\pi$
$827$		−	13.7400i		−	0.477787i	0.971046	−	0.238894i	$-0.0767847\pi$
$828$	2.79084	+	2.35413i	0.0969885	+	0.0818116i
$829$	15.5086	−	8.95388i	0.538635	−	0.310981i	−0.205891	−	0.978575i	$-0.566009\pi$
$829$	15.5086	−	8.95388i	0.538635	−	0.310981i	0.744526	+	0.667594i	$0.232676\pi$
$830$	3.50896	+	2.02590i	0.121798	+	0.0703200i
$831$	−19.0198	−	40.9263i	−0.659790	−	1.41972i
$832$	−21.1097	−	12.1877i	−0.731848	−	0.422532i
$833$		0			0
$834$	4.97100	+	10.6964i	0.172132	+	0.370388i
$835$	−0.823854			−0.0285106
$836$	−1.72089	−	2.98067i	−0.0595182	−	0.103089i
$837$	10.2623	−	37.7135i	0.354718	−	1.30357i
$838$	37.7658	+	21.8041i	1.30460	+	0.753209i
$839$	−27.5601	−	47.7356i	−0.951482	−	1.64802i	−0.742221	−	0.670155i	$-0.766227\pi$
$839$	−27.5601	−	47.7356i	−0.951482	−	1.64802i	−0.209261	−	0.977860i	$-0.567106\pi$
$840$		0			0
$841$	−9.62659	+	16.6737i	−0.331951	+	0.574957i
$842$	−46.8165	+	27.0295i	−1.61340	+	0.931499i
$843$	0.732912	−	8.25423i	0.0252428	−	0.284291i
$844$	0.559902	−	0.969778i	0.0192726	−	0.0333811i
$845$	−0.149353	+	0.258688i	−0.00513791	+	0.00889912i
$846$	35.4544	−	12.8006i	1.21895	−	0.440092i
$847$		0			0
$848$	−0.323312	+	0.186664i	−0.0111026	+	0.00641007i
$849$	1.51773	+	1.06565i	0.0520882	+	0.0365731i
$850$			35.5509i			1.21939i
$851$			70.7871i			2.42655i
$852$	2.24974	+	1.57963i	0.0770748	+	0.0541171i
$853$	−2.07425	+	1.19757i	−0.0710209	+	0.0410039i	−0.535090	−	0.844795i	$-0.679722\pi$
$853$	−2.07425	+	1.19757i	−0.0710209	+	0.0410039i	0.464069	+	0.885799i	$0.346389\pi$
$854$		0			0
$855$	−4.64845	+	1.67829i	−0.158974	+	0.0573963i
$856$	−22.3581	+	38.7254i	−0.764185	+	1.32361i
$857$	15.2461	−	26.4070i	0.520796	−	0.902046i	−0.478911	−	0.877863i	$-0.658968\pi$
$857$	15.2461	−	26.4070i	0.520796	−	0.902046i	0.999708	−	0.0241822i	$-0.00769820\pi$
$858$	−2.49460	+	28.0948i	−0.0851642	+	0.959140i
$859$	38.9437	−	22.4841i	1.32874	−	0.767149i	0.343636	−	0.939103i	$-0.388341\pi$
$859$	38.9437	−	22.4841i	1.32874	−	0.767149i	0.985105	+	0.171954i	$0.0550079\pi$
$860$	−0.172926	+	0.299517i	−0.00589674	+	0.0102134i
$861$		0			0
$862$	−14.4383	−	25.0078i	−0.491770	−	0.851770i
$863$	45.4835	+	26.2599i	1.54828	+	0.893897i	0.998274	+	0.0587340i	$0.0187064\pi$
$863$	45.4835	+	26.2599i	1.54828	+	0.893897i	0.550002	+	0.835163i	$0.314627\pi$
$864$	−1.56666	+	5.75740i	−0.0532989	+	0.195871i
$865$	3.11463	+	5.39470i	0.105901	+	0.183425i
$866$	14.7652			0.501744
$867$	−4.99198	−	10.7416i	−0.169537	−	0.364804i
$868$		0			0
$869$	14.0678	+	8.12203i	0.477217	+	0.275521i
$870$	−1.04345	−	2.24527i	−0.0353764	−	0.0761219i
$871$	−0.332917	−	0.192209i	−0.0112804	−	0.00651277i
$872$	20.4720	−	11.8195i	0.693270	−	0.400259i
$873$	29.0773	+	24.5272i	0.984117	+	0.830120i
$874$		−	47.3591i		−	1.60195i
$875$		0			0
$876$	−0.300122	+	3.38004i	−0.0101402	+	0.114201i
$877$	−0.683876	−	1.18451i	−0.0230929	−	0.0399980i	0.854248	−	0.519866i	$-0.174018\pi$
$877$	−0.683876	−	1.18451i	−0.0230929	−	0.0399980i	−0.877341	+	0.479868i	$0.840685\pi$
$878$	10.9491			0.369516
$879$	−1.98940	−	4.28073i	−0.0671008	−	0.144385i
$880$			4.25862i			0.143558i
$881$	−20.7141			−0.697876			−0.348938	−	0.937146i	$-0.613458\pi$
$881$	−20.7141			−0.697876			−0.348938	+	0.937146i	$0.613458\pi$
$882$		0			0
$883$	−14.3561			−0.483120			−0.241560	−	0.970386i	$-0.577659\pi$
$883$	−14.3561			−0.483120			−0.241560	+	0.970386i	$0.577659\pi$
$884$			3.45081i			0.116063i
$885$	1.11143	+	0.0986863i	0.0373603	+	0.00331730i
$886$	1.27641			0.0428819
$887$	22.0913	+	38.2633i	0.741754	+	1.28475i	0.951696	+	0.307041i	$0.0993390\pi$
$887$	22.0913	+	38.2633i	0.741754	+	1.28475i	−0.209943	+	0.977714i	$0.567328\pi$
$888$	−49.6378	+	23.0684i	−1.66574	+	0.774124i
$889$		0			0
$890$		−	0.857939i		−	0.0287582i
$891$	−28.0551	+	4.79732i	−0.939881	+	0.160716i
$892$	−3.58781	+	2.07142i	−0.120129	+	0.0693563i
$893$	−39.1507	−	22.6037i	−1.31013	−	0.756404i
$894$	−24.9297	−	2.21356i	−0.833773	−	0.0740327i
$895$	5.86629	+	3.38691i	0.196089	+	0.113212i
$896$		0			0
$897$	−20.6205	+	29.3682i	−0.688499	+	0.980576i
$898$	23.2321			0.775266
$899$	−11.7416	−	20.3371i	−0.391605	−	0.678279i
$900$	2.95135	+	0.528279i	0.0983783	+	0.0176093i
$901$	−0.361558	−	0.208746i	−0.0120453	−	0.00695433i
$902$	−12.1556	−	21.0540i	−0.404736	−	0.701023i
$903$		0			0
$904$	20.8791	−	36.1637i	0.694429	−	1.20279i
$905$	−0.669292	+	0.386416i	−0.0222480	+	0.0128449i
$906$	14.0332	−	6.52169i	0.466221	−	0.216669i
$907$	7.18075	−	12.4374i	0.238433	−	0.412978i	−0.721832	−	0.692068i	$-0.756700\pi$
$907$	7.18075	−	12.4374i	0.238433	−	0.412978i	0.960265	+	0.279091i	$0.0900330\pi$
$908$	−0.0328534	+	0.0569037i	−0.00109028	+	0.00188841i
$909$	21.7536	+	3.89380i	0.721520	+	0.129149i
$910$		0			0
$911$	−41.6920	+	24.0709i	−1.38132	+	0.797505i	−0.992316	−	0.123732i	$-0.960514\pi$
$911$	−41.6920	+	24.0709i	−1.38132	+	0.797505i	−0.389003	+	0.921237i	$0.627180\pi$
$912$	36.6284	−	17.0224i	1.21289	−	0.563669i
$913$		−	27.9857i		−	0.926190i
$914$			8.35954i			0.276509i
$915$	−0.256402	+	2.88766i	−0.00847640	+	0.0954632i
$916$	−0.468997	+	0.270776i	−0.0154961	+	0.00894668i
$917$		0			0
$918$	−36.4164	+	9.60643i	−1.20192	+	0.317059i
$919$	−11.5321	+	19.9741i	−0.380408	+	0.658886i	−0.991121	−	0.132966i	$-0.957550\pi$
$919$	−11.5321	+	19.9741i	−0.380408	+	0.658886i	0.610713	+	0.791852i	$0.290883\pi$
$920$	−2.45618	+	4.25423i	−0.0809778	+	0.140258i
$921$	11.7838	+	8.27385i	0.388290	+	0.272633i
$922$	−29.1430	+	16.8257i	−0.959773	+	0.554125i
$923$	−13.5086	+	23.3977i	−0.444642	+	0.770143i
$924$		0			0
$925$	29.0647	+	50.3416i	0.955642	+	1.65522i
$926$	54.0094	+	31.1824i	1.77486	+	1.02472i
$927$	−18.3001	−	15.4364i	−0.601053	−	0.506999i
$928$	1.79249	+	3.10469i	0.0588414	+	0.101916i
$929$	37.5608			1.23233			0.616165	−	0.787617i	$-0.288685\pi$
$929$	37.5608			1.23233			0.616165	+	0.787617i	$0.288685\pi$
$930$	−5.94185	−	0.527590i	−0.194841	−	0.0173004i
$931$		0			0
$932$	4.10405	+	2.36947i	0.134433	+	0.0776147i
$933$	5.97226	−	8.50583i	0.195523	−	0.278468i
$934$	31.8876	+	18.4103i	1.04339	+	0.602403i
$935$	−4.12436	+	2.38120i	−0.134881	+	0.0778736i
$936$	−27.3137	−	4.88903i	−0.892775	−	0.159803i
$937$		−	18.9436i		−	0.618859i	−0.950922	−	0.309430i	$-0.899862\pi$
$937$		−	18.9436i		−	0.618859i	0.950922	−	0.309430i	$-0.100138\pi$
$938$		0			0
$939$	16.7626	+	11.7697i	0.547027	+	0.384088i
$940$	−0.265963	−	0.460661i	−0.00867475	−	0.0150251i
$941$	−55.5103			−1.80958			−0.904792	−	0.425855i	$-0.859973\pi$
$941$	−55.5103			−1.80958			−0.904792	+	0.425855i	$0.859973\pi$
$942$	24.1585	−	34.4071i	0.787126	−	1.12104i
$943$		−	30.9301i		−	1.00722i
$944$	−9.11911			−0.296802
$945$		0			0
$946$	25.8359			0.839997
$947$			18.8258i			0.611757i	0.952071	+	0.305878i	$0.0989501\pi$
$947$			18.8258i			0.611757i	−0.952071	+	0.305878i	$0.901050\pi$
$948$	1.04169	−	1.48360i	0.0338326	−	0.0481852i
$949$	−33.3509			−1.08262
$950$	−19.4453	−	33.6803i	−0.630890	−	1.09273i
$951$	−42.0214	−	29.5048i	−1.36264	−	0.956758i
$952$		0			0
$953$		−	35.0089i		−	1.13405i	−0.823701	−	0.567024i	$-0.808095\pi$
$953$		−	35.0089i		−	1.13405i	0.823701	−	0.567024i	$-0.191905\pi$
$954$	−0.245535	+	0.291084i	−0.00794949	+	0.00942421i
$955$	−0.562196	+	0.324584i	−0.0181922	+	0.0105033i
$956$	0.0593482	+	0.0342647i	0.00191946	+	0.00110820i
$957$	−9.82680	+	13.9956i	−0.317655	+	0.452412i
$958$	−4.23347	−	2.44420i	−0.136777	−	0.0789684i
$959$		0			0
$960$	−3.73942	−	0.332032i	−0.120689	−	0.0107163i
$961$	−25.5786			−0.825118
$962$	30.5127	+	52.8496i	0.983770	+	1.70394i
$963$	−8.86410	+	49.5213i	−0.285642	+	1.59580i
$964$	−3.90906	−	2.25690i	−0.125902	−	0.0726898i
$965$	0.918291	+	1.59053i	0.0295608	+	0.0512008i
$966$		0			0
$967$	−7.47001	+	12.9384i	−0.240219	+	0.416072i	−0.960777	−	0.277323i	$-0.910553\pi$
$967$	−7.47001	+	12.9384i	−0.240219	+	0.416072i	0.720557	+	0.693395i	$0.243886\pi$
$968$	−2.30636	+	1.33158i	−0.0741291	+	0.0427985i
$969$	36.9665	+	25.9555i	1.18753	+	0.833812i
$970$	2.90291	−	5.02799i	0.0932069	−	0.161439i
$971$	15.1782	−	26.2894i	0.487091	−	0.843666i	−0.512799	−	0.858509i	$-0.671391\pi$
$971$	15.1782	−	26.2894i	0.487091	−	0.843666i	0.999890	+	0.0148426i	$0.00472472\pi$
$972$	0.256362	+	3.16595i	0.00822281	+	0.101548i
$973$		0			0
$974$	−13.4280	+	7.75269i	−0.430262	+	0.248412i
$975$	−2.60627	+	29.3524i	−0.0834673	+	0.940028i
$976$		−	23.6929i		−	0.758390i
$977$		−	54.4218i		−	1.74111i	−0.492074	−	0.870554i	$-0.663761\pi$
$977$		−	54.4218i		−	1.74111i	0.492074	−	0.870554i	$-0.336239\pi$
$978$	15.0740	−	7.00540i	0.482014	−	0.224008i
$979$	−5.13186	+	2.96288i	−0.164015	+	0.0946940i
$980$		0			0
$981$	17.1478	−	20.3289i	0.547486	−	0.649051i
$982$	−22.5239	+	39.0125i	−0.718765	+	1.24494i
$983$	−13.1343	+	22.7493i	−0.418920	+	0.725590i	−0.995831	−	0.0912165i	$-0.970924\pi$
$983$	−13.1343	+	22.7493i	−0.418920	+	0.725590i	0.576911	+	0.816807i	$0.304258\pi$
$984$	21.6890	−	10.0796i	0.691420	−	0.321326i
$985$	2.04208	−	1.17899i	0.0650660	−	0.0375659i
$986$	−11.3142	+	19.5968i	−0.360318	+	0.624089i
$987$		0			0
$988$	−1.88750	−	3.26924i	−0.0600492	−	0.104008i
$989$	28.4662	+	16.4350i	0.905173	+	0.522602i
$990$	1.47517	+	4.08584i	0.0468838	+	0.129857i
$991$	16.2471	+	28.1408i	0.516106	+	0.893921i	0.999825	+	0.0186981i	$0.00595214\pi$
$991$	16.2471	+	28.1408i	0.516106	+	0.893921i	−0.483720	+	0.875223i	$0.660715\pi$
$992$	8.63738			0.274237
$993$	16.9699	−	24.1690i	0.538524	−	0.766979i
$994$		0			0
$995$	−1.83021	−	1.05667i	−0.0580216	−	0.0334988i
$996$	−3.11088	−	0.276222i	−0.0985720	−	0.00875243i
$997$	31.8691	+	18.3996i	1.00931	+	0.582723i	0.910988	−	0.412433i	$-0.135321\pi$
$997$	31.8691	+	18.3996i	1.00931	+	0.582723i	0.0983170	+	0.995155i	$0.468654\pi$
$998$	−2.53205	+	1.46188i	−0.0801506	+	0.0462750i
$999$	−43.7134	+	43.3754i	−1.38303	+	1.37234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.5		48
3.2	odd	2		1323.2.i.d.1097.5		48
7.2	even	3		441.2.o.e.293.5	yes	48
7.3	odd	6		441.2.s.d.374.19		48
7.4	even	3		441.2.s.d.374.20		48
7.5	odd	6		441.2.o.e.293.6	yes	48
7.6	odd	2	inner	441.2.i.d.68.6		48
9.2	odd	6		441.2.s.d.362.19		48
9.7	even	3		1323.2.s.d.656.5		48
21.2	odd	6		1323.2.o.e.881.20		48
21.5	even	6		1323.2.o.e.881.19		48
21.11	odd	6		1323.2.s.d.962.6		48
21.17	even	6		1323.2.s.d.962.5		48
21.20	even	2		1323.2.i.d.1097.13		48
63.2	odd	6		441.2.o.e.146.6	yes	48
63.11	odd	6	inner	441.2.i.d.227.20		48
63.16	even	3		1323.2.o.e.440.19		48
63.20	even	6		441.2.s.d.362.20		48
63.25	even	3		1323.2.i.d.521.13		48
63.34	odd	6		1323.2.s.d.656.6		48
63.38	even	6	inner	441.2.i.d.227.19		48
63.47	even	6		441.2.o.e.146.5	✓	48
63.52	odd	6		1323.2.i.d.521.5		48
63.61	odd	6		1323.2.o.e.440.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.5		48	1.1	even	1	trivial
441.2.i.d.68.6		48	7.6	odd	2	inner
441.2.i.d.227.19		48	63.38	even	6	inner
441.2.i.d.227.20		48	63.11	odd	6	inner
441.2.o.e.146.5	✓	48	63.47	even	6
441.2.o.e.146.6	yes	48	63.2	odd	6
441.2.o.e.293.5	yes	48	7.2	even	3
441.2.o.e.293.6	yes	48	7.5	odd	6
441.2.s.d.362.19		48	9.2	odd	6
441.2.s.d.362.20		48	63.20	even	6
441.2.s.d.374.19		48	7.3	odd	6
441.2.s.d.374.20		48	7.4	even	3
1323.2.i.d.521.5		48	63.52	odd	6
1323.2.i.d.521.13		48	63.25	even	3
1323.2.i.d.1097.5		48	3.2	odd	2
1323.2.i.d.1097.13		48	21.20	even	2
1323.2.o.e.440.19		48	63.16	even	3
1323.2.o.e.440.20		48	63.61	odd	6
1323.2.o.e.881.19		48	21.5	even	6
1323.2.o.e.881.20		48	21.2	odd	6
1323.2.s.d.656.5		48	9.7	even	3
1323.2.s.d.656.6		48	63.34	odd	6
1323.2.s.d.962.5		48	21.17	even	6
1323.2.s.d.962.6		48	21.11	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.48451i q^{2} +(-0.995298 + 1.41753i) q^{3} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +(2.10433 + 1.47753i) q^{6} -2.66653i q^{8} +(-1.01876 - 2.82172i) q^{9} +O(q^{10})\)	\(q-1.48451i q^{2} +(-0.995298 + 1.41753i) q^{3} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +(2.10433 + 1.47753i) q^{6} -2.66653i q^{8} +(-1.01876 - 2.82172i) q^{9} +(-0.396525 + 0.228934i) q^{10} +(2.73879 + 1.58124i) q^{11} +(0.202802 - 0.288836i) q^{12} +(3.00394 + 1.73432i) q^{13} +(0.532124 + 0.0472485i) q^{15} -4.36600 q^{16} +(-2.44124 - 4.22836i) q^{17} +(-4.18887 + 1.51236i) q^{18} +(4.62558 + 2.67058i) q^{19} +(0.0314230 + 0.0544262i) q^{20} +(2.34736 - 4.06575i) q^{22} +(5.17269 - 2.98645i) q^{23} +(3.77988 + 2.65399i) q^{24} +(2.45244 - 4.24774i) q^{25} +(2.57462 - 4.45937i) q^{26} +(5.01384 + 1.36433i) q^{27} +(2.70372 - 1.56099i) q^{29} +(0.0701408 - 0.789942i) q^{30} -7.52188i q^{31} +1.14830i q^{32} +(-4.96736 + 2.30850i) q^{33} +(-6.27702 + 3.62404i) q^{34} +(0.207584 + 0.574955i) q^{36} +(-5.92568 + 10.2636i) q^{37} +(3.96450 - 6.86671i) q^{38} +(-5.44827 + 2.53199i) q^{39} +(-0.712254 + 0.411220i) q^{40} +(2.58920 - 4.48462i) q^{41} +(2.75159 + 4.76589i) q^{43} +(-0.558056 - 0.322194i) q^{44} +(-0.596598 + 0.707274i) q^{45} +(-4.43341 - 7.67889i) q^{46} -8.46396 q^{47} +(4.34547 - 6.18892i) q^{48} +(-6.30580 - 3.64066i) q^{50} +(8.42357 + 0.747948i) q^{51} +(-0.612084 - 0.353387i) q^{52} +(0.0740521 - 0.0427540i) q^{53} +(2.02536 - 7.44308i) q^{54} -0.975406i q^{55} +(-8.38945 + 3.89886i) q^{57} +(-2.31731 - 4.01369i) q^{58} +2.08866 q^{59} +(-0.108426 - 0.00962738i) q^{60} +5.42667i q^{61} -11.1663 q^{62} -7.02734 q^{64} -1.06984i q^{65} +(3.42698 + 7.37408i) q^{66} -0.110827 q^{67} +(0.497429 + 0.861572i) q^{68} +(-0.914990 + 10.3048i) q^{69} +7.78899i q^{71} +(-7.52421 + 2.71656i) q^{72} +(-8.32679 + 4.80748i) q^{73} +(15.2364 + 8.79672i) q^{74} +(3.58038 + 7.70416i) q^{75} +(-0.942510 - 0.544159i) q^{76} +(3.75876 + 8.08799i) q^{78} +5.13650 q^{79} +(0.673305 + 1.16620i) q^{80} +(-6.92424 + 5.74934i) q^{81} +(-6.65745 - 3.84368i) q^{82} +(-4.42464 - 7.66370i) q^{83} +(-0.752954 + 1.30416i) q^{85} +(7.07500 - 4.08475i) q^{86} +(-0.478258 + 5.38625i) q^{87} +(4.21642 - 7.30306i) q^{88} +(-0.936885 + 1.62273i) q^{89} +(1.04995 + 0.885654i) q^{90} +(-1.05399 + 0.608521i) q^{92} +(10.6625 + 7.48651i) q^{93} +12.5648i q^{94} -1.64738i q^{95} +(-1.62775 - 1.14290i) q^{96} +(-10.9813 + 6.34007i) q^{97} +(1.67164 - 9.33900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

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