LMFDB - Embedded newform 1323.2.i.d.1097.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.13
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.d.521.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.48451i q^{2} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +2.66653i q^{8} +O(q^{10})$	\(q+1.48451i q^{2} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +2.66653i q^{8} +(0.396525 - 0.228934i) q^{10} +(-2.73879 - 1.58124i) q^{11} +(-3.00394 - 1.73432i) q^{13} -4.36600 q^{16} +(-2.44124 - 4.22836i) q^{17} +(-4.62558 - 2.67058i) q^{19} +(0.0314230 + 0.0544262i) q^{20} +(2.34736 - 4.06575i) q^{22} +(-5.17269 + 2.98645i) q^{23} +(2.45244 - 4.24774i) q^{25} +(2.57462 - 4.45937i) q^{26} +(-2.70372 + 1.56099i) q^{29} +7.52188i q^{31} -1.14830i q^{32} +(6.27702 - 3.62404i) q^{34} +(-5.92568 + 10.2636i) q^{37} +(3.96450 - 6.86671i) q^{38} +(0.712254 - 0.411220i) q^{40} +(2.58920 - 4.48462i) q^{41} +(2.75159 + 4.76589i) q^{43} +(0.558056 + 0.322194i) q^{44} +(-4.43341 - 7.67889i) q^{46} -8.46396 q^{47} +(6.30580 + 3.64066i) q^{50} +(0.612084 + 0.353387i) q^{52} +(-0.0740521 + 0.0427540i) q^{53} +0.975406i q^{55} +(-2.31731 - 4.01369i) q^{58} +2.08866 q^{59} -5.42667i q^{61} -11.1663 q^{62} -7.02734 q^{64} +1.06984i q^{65} -0.110827 q^{67} +(0.497429 + 0.861572i) q^{68} -7.78899i q^{71} +(8.32679 - 4.80748i) q^{73} +(-15.2364 - 8.79672i) q^{74} +(0.942510 + 0.544159i) q^{76} +5.13650 q^{79} +(0.673305 + 1.16620i) q^{80} +(6.65745 + 3.84368i) q^{82} +(-4.42464 - 7.66370i) q^{83} +(-0.752954 + 1.30416i) q^{85} +(-7.07500 + 4.08475i) q^{86} +(4.21642 - 7.30306i) q^{88} +(-0.936885 + 1.62273i) q^{89} +(1.05399 - 0.608521i) q^{92} -12.5648i q^{94} +1.64738i q^{95} +(10.9813 - 6.34007i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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	$0.175879\pi$
$2$			1.48451i			1.04970i	−0.851193	+	0.524852i	$0.824121\pi$
$3$		0			0
$3$		0			0
$4$	−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	$0.855304\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.66653i			0.942761i
$9$		0			0
$10$	0.396525	−	0.228934i	0.125392	−	0.0723952i
$11$	−2.73879	−	1.58124i	−0.825775	−	0.476761i	0.0266288	−	0.999645i	$-0.491523\pi$
$11$	−2.73879	−	1.58124i	−0.825775	−	0.476761i	−0.852404	+	0.522884i	$0.824856\pi$
$12$		0			0
$13$	−3.00394	−	1.73432i	−0.833143	−	0.481015i	0.0217849	−	0.999763i	$-0.493065\pi$
$13$	−3.00394	−	1.73432i	−0.833143	−	0.481015i	−0.854927	+	0.518748i	$0.826398\pi$
$14$		0			0
$15$		0			0
$16$	−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	$-0.368363\pi$
$18$		0			0
$19$	−4.62558	−	2.67058i	−1.06118	−	0.612673i	−0.135422	−	0.990788i	$-0.543239\pi$
$19$	−4.62558	−	2.67058i	−1.06118	−	0.612673i	−0.925759	+	0.378115i	$0.876572\pi$
$20$	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	−0.930513	−	0.366259i	$-0.880639\pi$
$23$	−5.17269	+	2.98645i	−1.07858	+	0.622719i	−0.148067	+	0.988977i	$0.547305\pi$
$24$		0			0
$25$	2.45244	−	4.24774i	0.490487	−	0.849548i
$26$	2.57462	−	4.45937i	0.504924	−	0.874554i
$27$		0			0
$28$		0			0
$29$	−2.70372	+	1.56099i	−0.502069	+	0.289869i	−0.729567	−	0.683909i	$-0.760279\pi$
$29$	−2.70372	+	1.56099i	−0.502069	+	0.289869i	0.227499	+	0.973778i	$0.426945\pi$
$30$		0			0
$31$			7.52188i			1.35097i	0.737374	+	0.675485i	$0.236066\pi$
$31$			7.52188i			1.35097i	−0.737374	+	0.675485i	$0.763934\pi$
$32$		−	1.14830i		−	0.202993i
$33$		0			0
$34$	6.27702	−	3.62404i	1.07650	−	0.621518i
$35$		0			0
$36$		0			0
$37$	−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
$39$		0			0
$40$	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			0
$46$	−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	$0.711773\pi$
$48$		0			0
$49$		0			0
$50$	6.30580	+	3.64066i	0.891775	+	0.514867i
$51$		0			0
$52$	0.612084	+	0.353387i	0.0848807	+	0.0490059i
$53$	−0.0740521	+	0.0427540i	−0.0101718	+	0.00587272i	−0.505077	−	0.863074i	$-0.668536\pi$
$53$	−0.0740521	+	0.0427540i	−0.0101718	+	0.00587272i	0.494905	+	0.868947i	$0.335203\pi$
$54$		0			0
$55$			0.975406i			0.131524i
$56$		0			0
$57$		0			0
$58$	−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			0
$61$		−	5.42667i		−	0.694814i	−0.937714	−	0.347407i	$-0.887062\pi$
$61$		−	5.42667i		−	0.694814i	0.937714	−	0.347407i	$-0.112938\pi$
$62$	−11.1663			−1.41812
$63$		0			0
$64$	−7.02734			−0.878418
$65$			1.06984i			0.132697i
$66$		0			0
$67$	−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			0
$70$		0			0
$71$		−	7.78899i		−	0.924384i	−0.886780	−	0.462192i	$-0.847063\pi$
$71$		−	7.78899i		−	0.924384i	0.886780	−	0.462192i	$-0.152937\pi$
$72$		0			0
$73$	8.32679	−	4.80748i	0.974577	−	0.562672i	0.0739487	−	0.997262i	$-0.476440\pi$
$73$	8.32679	−	4.80748i	0.974577	−	0.562672i	0.900629	+	0.434590i	$0.143107\pi$
$74$	−15.2364	−	8.79672i	−1.77119	−	1.02260i
$75$		0			0
$76$	0.942510	+	0.544159i	0.108113	+	0.0624193i
$77$		0			0
$78$		0			0
$79$	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
$81$		0			0
$82$	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			0
$88$	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	$0.198330\pi$
$90$		0			0
$91$		0			0
$92$	1.05399	−	0.608521i	0.109886	−	0.0634427i
$93$		0			0
$94$		−	12.5648i		−	1.29596i
$95$			1.64738i			0.169017i
$96$		0			0
$97$	10.9813	−	6.34007i	1.11498	−	0.643736i	0.174868	−	0.984592i	$-0.444050\pi$
$97$	10.9813	−	6.34007i	1.11498	−	0.643736i	0.940116	+	0.340855i	$0.110717\pi$
$98$		0			0
$99$		0			0
$100$	−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	$0.286109\pi$
$102$		0			0
$103$	−6.91120	+	3.99019i	−0.680981	+	0.393165i	−0.800225	−	0.599700i	$-0.795286\pi$
$103$	−6.91120	+	3.99019i	−0.680981	+	0.393165i	0.119244	+	0.992865i	$0.461953\pi$
$104$	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	0.994797	−	0.101876i	$-0.0324844\pi$
$107$	14.5228	+	8.38472i	1.40397	+	0.810582i	0.409172	+	0.912457i	$0.365818\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$		0			0
$113$	−13.5621	−	7.83007i	−1.27581	−	0.736591i	−0.299738	−	0.954022i	$-0.596899\pi$
$113$	−13.5621	−	7.83007i	−1.27581	−	0.736591i	−0.976076	+	0.217430i	$0.930233\pi$
$114$		0			0
$115$	1.59542	+	0.921114i	0.148773	+	0.0858943i
$116$	0.550911	−	0.318069i	0.0511508	−	0.0295320i
$117$		0			0
$118$			3.10063i			0.285437i
$119$		0			0
$120$		0			0
$121$	−0.499366	−	0.864928i	−0.0453969	−	0.0786298i
$122$	8.05593			0.729350
$123$		0			0
$124$		−	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
$129$		0			0
$130$	−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	$0.507686\pi$
$132$		0			0
$133$		0			0
$134$		−	0.164523i		−	0.0142126i
$135$		0			0
$136$	11.2750	−	6.50965i	0.966826	−	0.558198i
$137$	−1.37570	−	0.794262i	−0.117534	−	0.0678584i	0.440080	−	0.897958i	$-0.354950\pi$
$137$	−1.37570	−	0.794262i	−0.117534	−	0.0678584i	−0.557615	+	0.830100i	$0.688283\pi$
$138$		0			0
$139$	−3.97274	−	2.29366i	−0.336963	−	0.194546i	0.321965	−	0.946752i	$-0.395657\pi$
$139$	−3.97274	−	2.29366i	−0.336963	−	0.194546i	−0.658928	+	0.752206i	$0.728990\pi$
$140$		0			0
$141$		0			0
$142$	11.5628			0.970330
$143$	5.48476	+	9.49989i	0.458659	+	0.794421i
$144$		0			0
$145$	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	−0.113247	−	0.993567i	$-0.536125\pi$
$149$	8.42966	−	4.86686i	0.690584	−	0.398709i	0.803831	+	0.594858i	$0.202792\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$		0			0
$155$	2.00916	−	1.15999i	0.161380	−	0.0931726i
$156$		0			0
$157$			16.3506i			1.30492i	0.757823	+	0.652461i	$0.226263\pi$
$157$			16.3506i			1.30492i	−0.757823	+	0.652461i	$0.773737\pi$
$158$			7.62517i			0.606626i
$159$		0			0
$160$	−0.306721	+	0.177086i	−0.0242484	+	0.0139998i
$161$		0			0
$162$		0			0
$163$	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
$165$		0			0
$166$	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
$171$		0			0
$172$	−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	$0.778629\pi$
$174$		0			0
$175$		0			0
$176$	11.9575	+	6.90369i	0.901334	+	0.520385i
$177$		0			0
$178$	−2.40896	−	1.39081i	−0.180559	−	0.104246i
$179$	19.0198	−	10.9811i	1.42161	−	0.820765i	0.425170	−	0.905113i	$-0.360214\pi$
$179$	19.0198	−	10.9811i	1.42161	−	0.820765i	0.996436	+	0.0843484i	$0.0268809\pi$
$180$		0			0
$181$			2.50569i			0.186246i	0.995655	+	0.0931232i	$0.0296850\pi$
$181$			2.50569i			0.186246i	−0.995655	+	0.0931232i	$0.970315\pi$
$182$		0			0
$183$		0			0
$184$	−7.96347	−	13.7931i	−0.587075	−	1.01684i
$185$	3.65533			0.268745
$186$		0			0
$187$			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	$0.0242618\pi$
$191$			2.10475i			0.152294i	−0.997097	+	0.0761470i	$0.975738\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$		0			0
$197$		−	7.64511i		−	0.544692i	−0.962199	−	0.272346i	$-0.912200\pi$
$197$		−	7.64511i		−	0.544692i	0.962199	−	0.272346i	$-0.0877995\pi$
$198$		0			0
$199$	−5.93394	+	3.42596i	−0.420646	+	0.242860i	−0.695354	−	0.718668i	$-0.744752\pi$
$199$	−5.93394	+	3.42596i	−0.420646	+	0.242860i	0.274708	+	0.961528i	$0.411419\pi$
$200$	11.3267	+	6.53949i	0.800921	+	0.462412i
$201$		0			0
$202$	−9.47044	−	5.46776i	−0.666338	−	0.384710i
$203$		0			0
$204$		0			0
$205$	−1.59718			−0.111552
$206$	−5.92346	−	10.2597i	−0.412707	−	0.714829i
$207$		0			0
$208$	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
$213$		0			0
$214$	−12.4472	+	21.5591i	−0.850872	+	1.47375i
$215$	0.848675	−	1.46995i	0.0578791	−	0.100250i
$216$		0			0
$217$		0			0
$218$	−11.3971	+	6.58015i	−0.771912	+	0.445664i
$219$		0			0
$220$		−	0.198749i		−	0.0133997i
$221$			16.9356i			1.13921i
$222$		0			0
$223$	−17.6080	+	10.1660i	−1.17912	+	0.680764i	−0.955810	−	0.293985i	$-0.905019\pi$
$223$	−17.6080	+	10.1660i	−1.17912	+	0.680764i	−0.223307	+	0.974748i	$0.571685\pi$
$224$		0			0
$225$		0			0
$226$	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	$0.163260\pi$
$228$		0			0
$229$	−2.30171	+	1.32889i	−0.152101	+	0.0878157i	−0.574119	−	0.818772i	$-0.694655\pi$
$229$	−2.30171	+	1.32889i	−0.152101	+	0.0878157i	0.422018	+	0.906588i	$0.361322\pi$
$230$	−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	0.983651	−	0.180087i	$-0.0576378\pi$
$233$	20.1415	+	11.6287i	1.31952	+	0.761823i	0.335866	+	0.941910i	$0.390971\pi$
$234$		0			0
$235$	1.30527	+	2.26080i	0.0851466	+	0.147478i
$236$	−0.425587			−0.0277033
$237$		0			0
$238$		0			0
$239$	0.291265	+	0.168162i	0.0188404	+	0.0108775i	0.509391	−	0.860535i	$-0.329871\pi$
$239$	0.291265	+	0.168162i	0.0188404	+	0.0108775i	−0.490550	+	0.871413i	$0.663204\pi$
$240$		0			0
$241$	−19.1846	−	11.0762i	−1.23579	−	0.713483i	−0.267558	−	0.963542i	$-0.586217\pi$
$241$	−19.1846	−	11.0762i	−1.23579	−	0.713483i	−0.968231	+	0.250059i	$0.919550\pi$
$242$	1.28399	−	0.741313i	0.0825381	−	0.0476534i
$243$		0			0
$244$			1.10574i			0.0707878i
$245$		0			0
$246$		0			0
$247$	9.26331	+	16.0445i	0.589410	+	1.02089i
$248$	−20.0573			−1.27364
$249$		0			0
$250$		−	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
$255$		0			0
$256$	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	$-0.373288\pi$
$258$		0			0
$259$		0			0
$260$		−	0.217991i		−	0.0135192i
$261$		0			0
$262$	−25.1237	+	14.5052i	−1.55215	+	0.896134i
$263$	4.40776	+	2.54482i	0.271794	+	0.156920i	0.629703	−	0.776836i	$-0.283177\pi$
$263$	4.40776	+	2.54482i	0.271794	+	0.156920i	−0.357909	+	0.933757i	$0.616510\pi$
$264$		0			0
$265$	0.0228400	+	0.0131867i	0.00140305	+	0.000810050i
$266$		0			0
$267$		0			0
$268$	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	$0.784074\pi$
$270$		0			0
$271$	−27.1767	−	15.6905i	−1.65087	−	0.953128i	−0.976717	−	0.214533i	$-0.931177\pi$
$271$	−27.1767	−	15.6905i	−1.65087	−	0.953128i	−0.674150	−	0.738595i	$-0.735490\pi$
$272$	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			0
$277$	−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
$279$		0			0
$280$		0			0
$281$	4.14335	−	2.39217i	0.247172	−	0.142705i	−0.371297	−	0.928514i	$-0.621087\pi$
$281$	4.14335	−	2.39217i	0.247172	−	0.142705i	0.618469	+	0.785810i	$0.287753\pi$
$282$		0			0
$283$			1.07069i			0.0636457i	0.999494	+	0.0318228i	$0.0101312\pi$
$283$			1.07069i			0.0636457i	−0.999494	+	0.0318228i	$0.989869\pi$
$284$			1.58709i			0.0941764i
$285$		0			0
$286$	−14.1026	+	8.14217i	−0.833907	+	0.481457i
$287$		0			0
$288$		0			0
$289$	−3.41933	+	5.92245i	−0.201137	+	0.348380i
$290$	−0.714729	+	1.23795i	−0.0419703	+	0.0726947i
$291$		0			0
$292$	−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
$297$		0			0
$298$	7.22489	+	12.5139i	0.418527	+	0.724910i
$299$	20.7179			1.19815
$300$		0			0
$301$		0			0
$302$	7.73729	+	4.46713i	0.445231	+	0.257054i
$303$		0			0
$304$	20.1953	+	11.6598i	1.15828	+	0.668733i
$305$	−1.44951	+	0.836876i	−0.0829988	+	0.0479194i
$306$		0			0
$307$			8.31294i			0.474444i	0.971455	+	0.237222i	$0.0762369\pi$
$307$			8.31294i			0.474444i	−0.971455	+	0.237222i	$0.923763\pi$
$308$		0			0
$309$		0			0
$310$	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	$0.554418\pi$
$312$		0			0
$313$			11.8253i			0.668403i	0.942502	+	0.334201i	$0.108467\pi$
$313$			11.8253i			0.668403i	−0.942502	+	0.334201i	$0.891533\pi$
$314$	−24.2726			−1.36978
$315$		0			0
$316$	−1.04662			−0.0588767
$317$		−	29.6442i		−	1.66498i	−0.554038	−	0.832491i	$-0.686914\pi$
$317$		−	29.6442i		−	1.66498i	0.554038	−	0.832491i	$-0.313086\pi$
$318$		0			0
$319$	9.87322			0.552794
$320$	1.08372	+	1.87707i	0.0605821	+	0.104931i
$321$		0			0
$322$		0			0
$323$			26.0781i			1.45103i
$324$		0			0
$325$	−14.7339	+	8.50664i	−0.817291	+	0.471863i
$326$	8.31116	+	4.79845i	0.460313	+	0.265762i
$327$		0			0
$328$	11.9584	+	6.90417i	0.660291	+	0.381219i
$329$		0			0
$330$		0			0
$331$	−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
$333$		0			0
$334$	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
$339$		0			0
$340$	0.153422	−	0.265735i	0.00832049	−	0.0144115i
$341$	11.8939	−	20.6008i	0.644090	−	1.11560i
$342$		0			0
$343$		0			0
$344$	−12.7084	+	7.33719i	−0.685191	+	0.395595i
$345$		0			0
$346$		−	29.9820i		−	1.61184i
$347$			17.6817i			0.949205i	0.880200	+	0.474602i	$0.157408\pi$
$347$			17.6817i			0.949205i	−0.880200	+	0.474602i	$0.842592\pi$
$348$		0			0
$349$	−3.62628	+	2.09363i	−0.194110	+	0.112070i	−0.593905	−	0.804535i	$-0.702415\pi$
$349$	−3.62628	+	2.09363i	−0.194110	+	0.112070i	0.399795	+	0.916605i	$0.369081\pi$
$350$		0			0
$351$		0			0
$352$	−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	$0.865290\pi$
$354$		0			0
$355$	−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	0.371703	−	0.928352i	$-0.378774\pi$
$359$	−4.66901	−	2.69565i	−0.246421	−	0.142271i	−0.618124	+	0.786080i	$0.712107\pi$
$360$		0			0
$361$	4.76400	+	8.25150i	0.250737	+	0.434289i
$362$	−3.71971			−0.195504
$363$		0			0
$364$		0			0
$365$	−2.56824	−	1.48277i	−0.134428	−	0.0776119i
$366$		0			0
$367$	−17.3218	−	10.0007i	−0.904188	−	0.522033i	−0.0256317	−	0.999671i	$-0.508160\pi$
$367$	−17.3218	−	10.0007i	−0.904188	−	0.522033i	−0.878557	+	0.477638i	$0.841493\pi$
$368$	22.5840	−	13.0389i	1.17727	−	0.679698i
$369$		0			0
$370$			5.42636i			0.282103i
$371$		0			0
$372$		0			0
$373$	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
$375$		0			0
$376$		−	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
$381$		0			0
$382$	−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	$0.636317\pi$
$384$		0			0
$385$		0			0
$386$		−	8.83964i		−	0.449926i
$387$		0			0
$388$	−2.23756	+	1.29185i	−0.113595	+	0.0655840i
$389$	−3.89121	−	2.24659i	−0.197292	−	0.113907i	0.398100	−	0.917342i	$-0.369670\pi$
$389$	−3.89121	−	2.24659i	−0.197292	−	0.113907i	−0.595392	+	0.803436i	$0.703003\pi$
$390$		0			0
$391$	25.2556	+	14.5813i	1.27723	+	0.737409i
$392$		0			0
$393$		0			0
$394$	11.3492			0.571766
$395$	−0.792127	−	1.37200i	−0.0398562	−	0.0690330i
$396$		0			0
$397$	8.35854	+	4.82581i	0.419503	+	0.242200i	0.694865	−	0.719140i	$-0.255464\pi$
$397$	8.35854	+	4.82581i	0.419503	+	0.242200i	−0.275362	+	0.961341i	$0.588798\pi$
$398$	−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	−0.864248	−	0.503066i	$-0.832205\pi$
$401$	−17.2356	+	9.95098i	−0.860705	+	0.496928i	0.00354346	+	0.999994i	$0.498872\pi$
$402$		0			0
$403$	13.0454	−	22.5953i	0.649837	−	1.12555i
$404$	0.750494	−	1.29989i	0.0373385	−	0.0646721i
$405$		0			0
$406$		0			0
$407$	32.4584	−	18.7398i	1.60890	−	0.928900i
$408$		0			0
$409$		−	2.42571i		−	0.119944i	−0.998200	−	0.0599718i	$-0.980899\pi$
$409$		−	2.42571i		−	0.119944i	0.998200	−	0.0599718i	$-0.0191011\pi$
$410$		−	2.37102i		−	0.117096i
$411$		0			0
$412$	1.40823	−	0.813042i	0.0693785	−	0.0400557i
$413$		0			0
$414$		0			0
$415$	−1.36470	+	2.36372i	−0.0669903	+	0.116031i
$416$	−1.99153	+	3.44942i	−0.0976426	+	0.169122i
$417$		0			0
$418$	−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
$423$		0			0
$424$	−0.114005	−	0.197462i	−0.00553656	−	0.00958961i
$425$	−23.9480			−1.16165
$426$		0			0
$427$		0			0
$428$	−2.95916	−	1.70847i	−0.143037	−	0.0825822i
$429$		0			0
$430$	2.18215	+	1.25986i	0.105232	+	0.0607560i
$431$	−16.8459	+	9.72598i	−0.811438	+	0.468484i	−0.847455	−	0.530867i	$-0.821866\pi$
$431$	−16.8459	+	9.72598i	−0.811438	+	0.468484i	0.0360172	+	0.999351i	$0.488533\pi$
$432$		0			0
$433$		−	9.94623i		−	0.477985i	−0.971021	−	0.238993i	$-0.923183\pi$
$433$		−	9.94623i		−	0.477985i	0.971021	−	0.238993i	$-0.0768172\pi$
$434$		0			0
$435$		0			0
$436$	−0.903178	−	1.56435i	−0.0432544	−	0.0749188i
$437$	31.9023			1.52609
$438$		0			0
$439$		−	7.37561i		−	0.352019i	−0.984389	−	0.176009i	$-0.943681\pi$
$439$		−	7.37561i		−	0.352019i	0.984389	−	0.176009i	$-0.0563189\pi$
$440$	−2.60095			−0.123995
$441$		0			0
$442$	−25.1411			−1.19584
$443$		−	0.859823i		−	0.0408514i	−0.999791	−	0.0204257i	$-0.993498\pi$
$443$		−	0.859823i		−	0.0408514i	0.999791	−	0.0204257i	$-0.00650216\pi$
$444$		0			0
$445$	0.577929			0.0273964
$446$	−15.0914	−	26.1392i	−0.714601	−	1.23772i
$447$		0			0
$448$		0			0
$449$		−	15.6497i		−	0.738556i	−0.929319	−	0.369278i	$-0.879605\pi$
$449$		−	15.6497i		−	0.738556i	0.929319	−	0.369278i	$-0.120395\pi$
$450$		0			0
$451$	−14.1825	+	8.18828i	−0.667829	+	0.385571i
$452$	2.76342	+	1.59546i	0.129980	+	0.0750441i
$453$		0			0
$454$	0.414575	+	0.239355i	0.0194570	+	0.0112335i
$455$		0			0
$456$		0			0
$457$	−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
$459$		0			0
$460$	−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			0
$466$	−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			0
$469$		0			0
$470$	−3.35617	+	1.93769i	−0.154809	+	0.0893788i
$471$		0			0
$472$			5.56948i			0.256356i
$473$		−	17.4037i		−	0.800222i
$474$		0			0
$475$	−22.6879	+	13.0989i	−1.04099	+	0.601017i
$476$		0			0
$477$		0			0
$478$	−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			0
$481$	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
$486$		0			0
$487$	−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
$489$		0			0
$490$		0			0
$491$	26.2797	+	15.1726i	1.18599	+	0.684731i	0.957392	−	0.288791i	$-0.0932532\pi$
$491$	26.2797	+	15.1726i	1.18599	+	0.684731i	0.228596	+	0.973521i	$0.426587\pi$
$492$		0			0
$493$	13.2009	+	7.62153i	0.594538	+	0.343257i
$494$	−23.8182	+	13.7514i	−1.07163	+	0.618707i
$495$		0			0
$496$		−	32.8405i		−	1.47458i
$497$		0			0
$498$		0			0
$499$	−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
$501$		0			0
$502$			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
$507$		0			0
$508$	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	$0.836732\pi$
$510$		0			0
$511$		0			0
$512$		−	18.2707i		−	0.807457i
$513$		0			0
$514$	24.9170	−	14.3858i	1.09904	−	0.634532i
$515$	2.13163	+	1.23070i	0.0939307	+	0.0542309i
$516$		0			0
$517$	23.1810	+	13.3835i	1.01950	+	0.588607i
$518$		0			0
$519$		0			0
$520$	−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	$0.935598\pi$
$522$		0			0
$523$	5.90591	+	3.40978i	0.258247	+	0.149099i	0.623535	−	0.781796i	$-0.285696\pi$
$523$	5.90591	+	3.40978i	0.258247	+	0.149099i	−0.365287	+	0.930895i	$0.619029\pi$
$524$	−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
$528$		0			0
$529$	6.33781	−	10.9774i	0.275557	−	0.477278i
$530$	−0.0195757	+	0.0339061i	−0.000850313	+	0.00147279i
$531$		0			0
$532$		0			0
$533$	−15.5556	+	8.98102i	−0.673787	+	0.389011i
$534$		0			0
$535$		−	5.17221i		−	0.223614i
$536$		−	0.295523i		−	0.0127646i
$537$		0			0
$538$	−6.50011	+	3.75284i	−0.280240	+	0.161796i
$539$		0			0
$540$		0			0
$541$	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
$543$		0			0
$544$	−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
$549$		0			0
$550$	−11.5135	−	19.9420i	−0.490937	−	0.850328i
$551$	16.6750			0.710381
$552$		0			0
$553$		0			0
$554$	−33.4979	−	19.3400i	−1.42319	−	0.821678i
$555$		0			0
$556$	0.809487	+	0.467357i	0.0343299	+	0.0198204i
$557$	6.24761	−	3.60706i	0.264720	−	0.152836i	−0.361766	−	0.932269i	$-0.617826\pi$
$557$	6.24761	−	3.60706i	0.264720	−	0.152836i	0.626486	+	0.779433i	$0.284493\pi$
$558$		0			0
$559$		−	19.0886i		−	0.807361i
$560$		0			0
$561$		0			0
$562$	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	$0.338216\pi$
$564$		0			0
$565$			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	$0.184268\pi$
$569$			26.1007i			1.09420i	−0.837067	+	0.547100i	$0.815732\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$		0			0
$575$			29.2963i			1.22174i
$576$		0			0
$577$	16.7403	−	9.66501i	0.696907	−	0.402360i	−0.109287	−	0.994010i	$-0.534857\pi$
$577$	16.7403	−	9.66501i	0.696907	−	0.402360i	0.806194	+	0.591651i	$0.201523\pi$
$578$	−8.79192	−	5.07602i	−0.365696	−	0.211135i
$579$		0			0
$580$	−0.169918	−	0.0981022i	−0.00705546	−	0.00407347i
$581$		0			0
$582$		0			0
$583$	0.270417			0.0111995
$584$	12.8193	+	22.2036i	0.530465	+	0.918793i
$585$		0			0
$586$	−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
$591$		0			0
$592$	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	$0.868468\pi$
$594$		0			0
$595$		0			0
$596$	−1.71763	+	0.991674i	−0.0703569	+	0.0406206i
$597$		0			0
$598$			30.7559i			1.25770i
$599$		−	34.3077i		−	1.40177i	−0.713272	−	0.700887i	$-0.752788\pi$
$599$		−	34.3077i		−	1.40177i	0.713272	−	0.700887i	$-0.247212\pi$
$600$		0			0
$601$	24.0139	−	13.8644i	0.979547	−	0.565541i	0.0774133	−	0.996999i	$-0.475334\pi$
$601$	24.0139	−	13.8644i	0.979547	−	0.565541i	0.902133	+	0.431458i	$0.142001\pi$
$602$		0			0
$603$		0			0
$604$	−0.613149	+	1.06200i	−0.0249487	+	0.0432123i
$605$	−0.154020	+	0.266770i	−0.00626180	+	0.0108458i
$606$		0			0
$607$	−13.0526	+	7.53592i	−0.529788	+	0.305873i	−0.740930	−	0.671582i	$-0.765615\pi$
$607$	−13.0526	+	7.53592i	−0.529788	+	0.305873i	0.211142	+	0.977455i	$0.432282\pi$
$608$	−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
$612$		0			0
$613$	−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
$615$		0			0
$616$		0			0
$617$	−15.9761	−	9.22381i	−0.643174	−	0.371337i	0.142662	−	0.989771i	$-0.454434\pi$
$617$	−15.9761	−	9.22381i	−0.643174	−	0.371337i	−0.785836	+	0.618435i	$0.787767\pi$
$618$		0			0
$619$	29.3519	+	16.9463i	1.17975	+	0.681130i	0.955957	−	0.293506i	$-0.0948220\pi$
$619$	29.3519	+	16.9463i	1.17975	+	0.681130i	0.223795	+	0.974636i	$0.428155\pi$
$620$	−0.409387	+	0.236360i	−0.0164414	+	0.00949244i
$621$		0			0
$622$		−	8.90774i		−	0.357168i
$623$		0			0
$624$		0			0
$625$	−11.7911	−	20.4227i	−0.471642	−	0.816908i
$626$	−17.5547			−0.701626
$627$		0			0
$628$		−	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
$633$		0			0
$634$	44.0070			1.74774
$635$	1.04568	+	1.81117i	0.0414965	+	0.0718741i
$636$		0			0
$637$		0			0
$638$			14.6569i			0.580271i
$639$		0			0
$640$	−3.39996	+	1.96297i	−0.134395	+	0.0775931i
$641$	−34.7673	−	20.0729i	−1.37323	−	0.792833i	−0.381894	−	0.924206i	$-0.624728\pi$
$641$	−34.7673	−	20.0729i	−1.37323	−	0.792833i	−0.991333	+	0.131373i	$0.958061\pi$
$642$		0			0
$643$	−30.0552	−	17.3524i	−1.18526	−	0.684311i	−0.228036	−	0.973653i	$-0.573230\pi$
$643$	−30.0552	−	17.3524i	−1.18526	−	0.684311i	−0.957226	+	0.289342i	$0.906564\pi$
$644$		0			0
$645$		0			0
$646$	−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	$0.742184\pi$
$648$		0			0
$649$	−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	−0.518888	−	0.854843i	$-0.673654\pi$
$653$	−0.971455	+	0.560870i	−0.0380160	+	0.0219485i	0.480872	+	0.876791i	$0.340320\pi$
$654$		0			0
$655$	3.01369	−	5.21987i	0.117755	−	0.203957i
$656$	−11.3044	+	19.5799i	−0.441364	+	0.764466i
$657$		0			0
$658$		0			0
$659$	5.45240	−	3.14795i	0.212395	−	0.122627i	−0.390029	−	0.920803i	$-0.627535\pi$
$659$	5.45240	−	3.14795i	0.212395	−	0.122627i	0.602424	+	0.798176i	$0.294202\pi$
$660$		0			0
$661$		−	43.5222i		−	1.69282i	−0.532533	−	0.846409i	$-0.678760\pi$
$661$		−	43.5222i		−	1.69282i	0.532533	−	0.846409i	$-0.321240\pi$
$662$		−	25.3110i		−	0.983739i
$663$		0			0
$664$	20.4355	−	11.7984i	0.793051	−	0.457868i
$665$		0			0
$666$		0			0
$667$	9.32368	−	16.1491i	0.361014	−	0.625295i
$668$	−0.272134	+	0.471349i	−0.0105292	+	0.0182370i
$669$		0			0
$670$	−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
$675$		0			0
$676$	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	$0.159480\pi$
$678$		0			0
$679$		0			0
$680$	−3.47757	−	2.00778i	−0.133359	−	0.0769947i
$681$		0			0
$682$	30.5821	+	17.6566i	1.17105	+	0.676104i
$683$	−3.81262	+	2.20122i	−0.145886	+	0.0842272i	−0.571166	−	0.820834i	$-0.693509\pi$
$683$	−3.81262	+	2.20122i	−0.145886	+	0.0842272i	0.425280	+	0.905062i	$0.360175\pi$
$684$		0			0
$685$			0.489950i			0.0187200i
$686$		0			0
$687$		0			0
$688$	−12.0134	−	20.8079i	−0.458008	−	0.793294i
$689$	0.296597			0.0112995
$690$		0			0
$691$		−	9.33079i		−	0.354960i	−0.984124	−	0.177480i	$-0.943206\pi$
$691$		−	9.33079i		−	0.354960i	0.984124	−	0.177480i	$-0.0567945\pi$
$692$	4.11527			0.156439
$693$		0			0
$694$	−26.2486			−0.996385
$695$			1.41487i			0.0536691i
$696$		0			0
$697$	−25.2834			−0.957679
$698$	−3.10802	−	5.38324i	−0.117640	−	0.203759i
$699$		0			0
$700$		0			0
$701$		−	22.9051i		−	0.865116i	−0.901606	−	0.432558i	$-0.857611\pi$
$701$		−	22.9051i		−	0.865116i	0.901606	−	0.432558i	$-0.142389\pi$
$702$		0			0
$703$	54.8195	−	31.6500i	2.06756	−	1.19370i
$704$	19.2464	+	11.1119i	0.725376	+	0.418796i
$705$		0			0
$706$	−39.2054	−	22.6353i	−1.47552	−	0.851889i
$707$		0			0
$708$		0			0
$709$	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
$711$		0			0
$712$	−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			0
$718$	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	$0.0450318\pi$
$720$		0			0
$721$		0			0
$722$	−12.2494	+	7.07220i	−0.455876	+	0.263200i
$723$		0			0
$724$		−	0.510560i		−	0.0189748i
$725$			15.3130i			0.568709i
$726$		0			0
$727$	25.0380	−	14.4557i	0.928610	−	0.536133i	0.0422381	−	0.999108i	$-0.486551\pi$
$727$	25.0380	−	14.4557i	0.928610	−	0.536133i	0.886372	+	0.462975i	$0.153218\pi$
$728$		0			0
$729$		0			0
$730$	2.20119	−	3.81257i	0.0814696	−	0.141109i
$731$	13.4346	−	23.2694i	0.496896	−	0.860650i
$732$		0			0
$733$	27.5498	−	15.9059i	1.01757	−	0.587496i	0.104173	−	0.994559i	$-0.466780\pi$
$733$	27.5498	−	15.9059i	1.01757	−	0.587496i	0.913400	+	0.407063i	$0.133447\pi$
$734$	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
$738$		0			0
$739$	−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
$741$		0			0
$742$		0			0
$743$	−11.8554	−	6.84471i	−0.434932	−	0.251108i	0.266513	−	0.963831i	$-0.414128\pi$
$743$	−11.8554	−	6.84471i	−0.434932	−	0.251108i	−0.701446	+	0.712723i	$0.747462\pi$
$744$		0			0
$745$	−2.59997	−	1.50109i	−0.0952554	−	0.0549957i
$746$	−33.5481	+	19.3690i	−1.22828	+	0.709150i
$747$		0			0
$748$		−	3.14621i		−	0.115037i
$749$		0			0
$750$		0			0
$751$	−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
$753$		0			0
$754$			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
$759$		0			0
$760$	−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	$-0.479632\pi$
$762$		0			0
$763$		0			0
$764$		−	0.428864i		−	0.0155157i
$765$		0			0
$766$	−29.1946	+	16.8555i	−1.05485	+	0.609015i
$767$	−6.27422	−	3.62242i	−0.226549	−	0.130798i
$768$		0			0
$769$	5.22983	+	3.01944i	0.188592	+	0.108884i	0.591323	−	0.806434i	$-0.298606\pi$
$769$	5.22983	+	3.01944i	0.188592	+	0.108884i	−0.402731	+	0.915318i	$0.631939\pi$
$770$		0			0
$771$		0			0
$772$	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	$-0.407978\pi$
$774$		0			0
$775$	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			0
$781$	−12.3163	+	21.3324i	−0.440711	+	0.763333i
$782$	−21.6461	+	37.4921i	−0.774061	+	1.34071i
$783$		0			0
$784$		0			0
$785$	4.36739	−	2.52152i	0.155879	−	0.0899968i
$786$		0			0
$787$			48.2521i			1.72000i	0.510293	+	0.860001i	$0.329537\pi$
$787$			48.2521i			1.72000i	−0.510293	+	0.860001i	$0.670463\pi$
$788$			1.55777i			0.0554933i
$789$		0			0
$790$	2.03675	−	1.17592i	0.0724643	−	0.0418373i
$791$		0			0
$792$		0			0
$793$	−9.41161	+	16.3014i	−0.334216	+	0.578879i
$794$	−7.16394	+	12.4083i	−0.254239	+	0.440354i
$795$		0			0
$796$	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
$801$		0			0
$802$	−14.7723	−	25.5864i	−0.521628	−	0.903486i
$803$	−30.4071			−1.07304
$804$		0			0
$805$		0			0
$806$	33.5428	+	19.3660i	1.18150	+	0.682137i
$807$		0			0
$808$	−17.0112	−	9.82141i	−0.598451	−	0.345516i
$809$	−9.65975	+	5.57706i	−0.339619	+	0.196079i	−0.660103	−	0.751175i	$-0.729488\pi$
$809$	−9.65975	+	5.57706i	−0.339619	+	0.196079i	0.320485	+	0.947254i	$0.396154\pi$
$810$		0			0
$811$		−	1.90097i		−	0.0667520i	−0.999443	−	0.0333760i	$-0.989374\pi$
$811$		−	1.90097i		−	0.0667520i	0.999443	−	0.0333760i	$-0.0106259\pi$
$812$		0			0
$813$		0			0
$814$	27.8194	+	48.1847i	0.975070	+	1.68887i
$815$	−1.99391			−0.0698438
$816$		0			0
$817$		−	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	$0.0567389\pi$
$821$			10.1608i			0.354616i	−0.984155	+	0.177308i	$0.943261\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$		0			0
$827$			13.7400i			0.477787i	0.971046	+	0.238894i	$0.0767847\pi$
$827$			13.7400i			0.477787i	−0.971046	+	0.238894i	$0.923215\pi$
$828$		0			0
$829$	−15.5086	+	8.95388i	−0.538635	+	0.310981i	−0.744526	−	0.667594i	$-0.767324\pi$
$829$	−15.5086	+	8.95388i	−0.538635	+	0.310981i	0.205891	+	0.978575i	$0.433991\pi$
$830$	−3.50896	−	2.02590i	−0.121798	−	0.0703200i
$831$		0			0
$832$	21.1097	+	12.1877i	0.731848	+	0.422532i
$833$		0			0
$834$		0			0
$835$	−0.823854			−0.0285106
$836$	−1.72089	−	2.98067i	−0.0595182	−	0.103089i
$837$		0			0
$838$	−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			0
$844$	0.559902	−	0.969778i	0.0192726	−	0.0333811i
$845$	−0.149353	+	0.258688i	−0.00513791	+	0.00889912i
$846$		0			0
$847$		0			0
$848$	0.323312	−	0.186664i	0.0111026	−	0.00641007i
$849$		0			0
$850$		−	35.5509i		−	1.21939i
$851$		−	70.7871i		−	2.42655i
$852$		0			0
$853$	2.07425	−	1.19757i	0.0710209	−	0.0410039i	−0.464069	−	0.885799i	$-0.653611\pi$
$853$	2.07425	−	1.19757i	0.0710209	−	0.0410039i	0.535090	+	0.844795i	$0.320278\pi$
$854$		0			0
$855$		0			0
$856$	−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	$-0.00769820\pi$
$858$		0			0
$859$	−38.9437	+	22.4841i	−1.32874	+	0.767149i	−0.985105	−	0.171954i	$-0.944992\pi$
$859$	−38.9437	+	22.4841i	−1.32874	+	0.767149i	−0.343636	+	0.939103i	$0.611659\pi$
$860$	−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	$-0.981294\pi$
$863$	−45.4835	−	26.2599i	−1.54828	−	0.893897i	−0.550002	−	0.835163i	$-0.685373\pi$
$864$		0			0
$865$	3.11463	+	5.39470i	0.105901	+	0.183425i
$866$	14.7652			0.501744
$867$		0			0
$868$		0			0
$869$	−14.0678	−	8.12203i	−0.477217	−	0.275521i
$870$		0			0
$871$	0.332917	+	0.192209i	0.0112804	+	0.00651277i
$872$	−20.4720	+	11.8195i	−0.693270	+	0.400259i
$873$		0			0
$874$			47.3591i			1.60195i
$875$		0			0
$876$		0			0
$877$	−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
$879$		0			0
$880$		−	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
$885$		0			0
$886$	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	$0.567328\pi$
$888$		0			0
$889$		0			0
$890$			0.857939i			0.0287582i
$891$		0			0
$892$	3.58781	−	2.07142i	0.120129	−	0.0693563i
$893$	39.1507	+	22.6037i	1.31013	+	0.756404i
$894$		0			0
$895$	−5.86629	−	3.38691i	−0.196089	−	0.113212i
$896$		0			0
$897$		0			0
$898$	23.2321			0.775266
$899$	−11.7416	−	20.3371i	−0.391605	−	0.678279i
$900$		0			0
$901$	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
$906$		0			0
$907$	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
$909$		0			0
$910$		0			0
$911$	41.6920	−	24.0709i	1.38132	−	0.797505i	0.389003	−	0.921237i	$-0.372820\pi$
$911$	41.6920	−	24.0709i	1.38132	−	0.797505i	0.992316	+	0.123732i	$0.0394863\pi$
$912$		0			0
$913$			27.9857i			0.926190i
$914$		−	8.35954i		−	0.276509i
$915$		0			0
$916$	0.468997	−	0.270776i	0.0154961	−	0.00894668i
$917$		0			0
$918$		0			0
$919$	−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
$921$		0			0
$922$	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
$927$		0			0
$928$	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	$0.288685\pi$
$930$		0			0
$931$		0			0
$932$	−4.10405	−	2.36947i	−0.134433	−	0.0776147i
$933$		0			0
$934$	−31.8876	−	18.4103i	−1.04339	−	0.602403i
$935$	4.12436	−	2.38120i	0.134881	−	0.0778736i
$936$		0			0
$937$			18.9436i			0.618859i	0.950922	+	0.309430i	$0.100138\pi$
$937$			18.9436i			0.618859i	−0.950922	+	0.309430i	$0.899862\pi$
$938$		0			0
$939$		0			0
$940$	−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	$0.859973\pi$
$942$		0			0
$943$			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	$-0.901050\pi$
$947$		−	18.8258i		−	0.611757i	0.952071	−	0.305878i	$-0.0989501\pi$
$948$		0			0
$949$	−33.3509			−1.08262
$950$	−19.4453	−	33.6803i	−0.630890	−	1.09273i
$951$		0			0
$952$		0			0
$953$			35.0089i			1.13405i	0.823701	+	0.567024i	$0.191905\pi$
$953$			35.0089i			1.13405i	−0.823701	+	0.567024i	$0.808095\pi$
$954$		0			0
$955$	0.562196	−	0.324584i	0.0181922	−	0.0105033i
$956$	−0.0593482	−	0.0342647i	−0.00191946	−	0.00110820i
$957$		0			0
$958$	4.23347	+	2.44420i	0.136777	+	0.0789684i
$959$		0			0
$960$		0			0
$961$	−25.5786			−0.825118
$962$	30.5127	+	52.8496i	0.983770	+	1.70394i
$963$		0			0
$964$	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
$969$		0			0
$970$	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			0
$973$		0			0
$974$	13.4280	−	7.75269i	0.430262	−	0.248412i
$975$		0			0
$976$			23.6929i			0.758390i
$977$			54.4218i			1.74111i	0.492074	+	0.870554i	$0.336239\pi$
$977$			54.4218i			1.74111i	−0.492074	+	0.870554i	$0.663761\pi$
$978$		0			0
$979$	5.13186	−	2.96288i	0.164015	−	0.0946940i
$980$		0			0
$981$		0			0
$982$	−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	$0.304258\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	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
$993$		0			0
$994$		0			0
$995$	1.83021	+	1.05667i	0.0580216	+	0.0334988i
$996$		0			0
$997$	−31.8691	−	18.3996i	−1.00931	−	0.582723i	−0.0983170	−	0.995155i	$-0.531346\pi$
$997$	−31.8691	−	18.3996i	−1.00931	−	0.582723i	−0.910988	+	0.412433i	$0.864679\pi$
$998$	2.53205	−	1.46188i	0.0801506	−	0.0462750i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.48451i q^{2} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +2.66653i q^{8} +O(q^{10})\)	\(q+1.48451i q^{2} -0.203760 q^{4} +(-0.154215 - 0.267109i) q^{5} +2.66653i q^{8} +(0.396525 - 0.228934i) q^{10} +(-2.73879 - 1.58124i) q^{11} +(-3.00394 - 1.73432i) q^{13} -4.36600 q^{16} +(-2.44124 - 4.22836i) q^{17} +(-4.62558 - 2.67058i) q^{19} +(0.0314230 + 0.0544262i) q^{20} +(2.34736 - 4.06575i) q^{22} +(-5.17269 + 2.98645i) q^{23} +(2.45244 - 4.24774i) q^{25} +(2.57462 - 4.45937i) q^{26} +(-2.70372 + 1.56099i) q^{29} +7.52188i q^{31} -1.14830i q^{32} +(6.27702 - 3.62404i) q^{34} +(-5.92568 + 10.2636i) q^{37} +(3.96450 - 6.86671i) q^{38} +(0.712254 - 0.411220i) q^{40} +(2.58920 - 4.48462i) q^{41} +(2.75159 + 4.76589i) q^{43} +(0.558056 + 0.322194i) q^{44} +(-4.43341 - 7.67889i) q^{46} -8.46396 q^{47} +(6.30580 + 3.64066i) q^{50} +(0.612084 + 0.353387i) q^{52} +(-0.0740521 + 0.0427540i) q^{53} +0.975406i q^{55} +(-2.31731 - 4.01369i) q^{58} +2.08866 q^{59} -5.42667i q^{61} -11.1663 q^{62} -7.02734 q^{64} +1.06984i q^{65} -0.110827 q^{67} +(0.497429 + 0.861572i) q^{68} -7.78899i q^{71} +(8.32679 - 4.80748i) q^{73} +(-15.2364 - 8.79672i) q^{74} +(0.942510 + 0.544159i) q^{76} +5.13650 q^{79} +(0.673305 + 1.16620i) q^{80} +(6.65745 + 3.84368i) q^{82} +(-4.42464 - 7.66370i) q^{83} +(-0.752954 + 1.30416i) q^{85} +(-7.07500 + 4.08475i) q^{86} +(4.21642 - 7.30306i) q^{88} +(-0.936885 + 1.62273i) q^{89} +(1.05399 - 0.608521i) q^{92} -12.5648i q^{94} +1.64738i q^{95} +(10.9813 - 6.34007i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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