LMFDB - Embedded newform 1323.2.i.d.521.13

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			521.13
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.13

$q$-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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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			0
$3$		0			0
$4$	−0.203760			−0.101880
$5$	−0.154215	+	0.267109i	−0.0689672	+	0.119455i	−0.898447	−	0.439082i	$-0.855304\pi$
$5$	−0.154215	+	0.267109i	−0.0689672	+	0.119455i	0.829480	+	0.558537i	$0.188637\pi$
$6$		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	−0.852404	−	0.522884i	$-0.824856\pi$
$11$	−2.73879	+	1.58124i	−0.825775	+	0.476761i	0.0266288	+	0.999645i	$0.491523\pi$
$12$		0			0
$13$	−3.00394	+	1.73432i	−0.833143	+	0.481015i	−0.854927	−	0.518748i	$-0.826398\pi$
$13$	−3.00394	+	1.73432i	−0.833143	+	0.481015i	0.0217849	+	0.999763i	$0.493065\pi$
$14$		0			0
$15$		0			0
$16$	−4.36600			−1.09150
$17$	−2.44124	+	4.22836i	−0.592088	+	1.02553i	0.401862	+	0.915700i	$0.368363\pi$
$17$	−2.44124	+	4.22836i	−0.592088	+	1.02553i	−0.993951	+	0.109827i	$0.964970\pi$
$18$		0			0
$19$	−4.62558	+	2.67058i	−1.06118	+	0.612673i	−0.925759	−	0.378115i	$-0.876572\pi$
$19$	−4.62558	+	2.67058i	−1.06118	+	0.612673i	−0.135422	+	0.990788i	$0.543239\pi$
$20$	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	$-0.547305\pi$
$23$	−5.17269	−	2.98645i	−1.07858	−	0.622719i	−0.930513	+	0.366259i	$0.880639\pi$
$24$		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	0.227499	−	0.973778i	$-0.426945\pi$
$29$	−2.70372	−	1.56099i	−0.502069	−	0.289869i	−0.729567	+	0.683909i	$0.760279\pi$
$30$		0			0
$31$		−	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
$33$		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	−0.682626	−	0.730768i	$-0.739162\pi$
$37$	−5.92568	−	10.2636i	−0.974176	−	1.68732i	−0.291550	−	0.956556i	$-0.594171\pi$
$38$	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	0.994247	−	0.107109i	$-0.0341593\pi$
$41$	2.58920	+	4.48462i	0.404365	+	0.700380i	−0.589883	+	0.807489i	$0.700826\pi$
$42$		0			0
$43$	2.75159	−	4.76589i	0.419613	−	0.726792i	−0.576287	−	0.817247i	$-0.695499\pi$
$43$	2.75159	−	4.76589i	0.419613	−	0.726792i	0.995900	+	0.0904557i	$0.0288323\pi$
$44$	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	0.494905	−	0.868947i	$-0.335203\pi$
$53$	−0.0740521	−	0.0427540i	−0.0101718	−	0.00587272i	−0.505077	+	0.863074i	$0.668536\pi$
$54$		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	$0.112938\pi$
$61$			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
$66$		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	$0.152937\pi$
$71$			7.78899i			0.924384i	−0.886780	+	0.462192i	$0.847063\pi$
$72$		0			0
$73$	8.32679	+	4.80748i	0.974577	+	0.562672i	0.900629	−	0.434590i	$-0.143107\pi$
$73$	8.32679	+	4.80748i	0.974577	+	0.562672i	0.0739487	+	0.997262i	$0.476440\pi$
$74$	−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	−0.999864	−	0.0164715i	$-0.994757\pi$
$83$	−4.42464	+	7.66370i	−0.485667	+	0.841201i	0.514197	+	0.857672i	$0.328090\pi$
$84$		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	0.812089	−	0.583533i	$-0.198330\pi$
$89$	−0.936885	−	1.62273i	−0.0993096	−	0.172009i	−0.911399	+	0.411524i	$0.864997\pi$
$90$		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	0.940116	−	0.340855i	$-0.110717\pi$
$97$	10.9813	+	6.34007i	1.11498	+	0.643736i	0.174868	+	0.984592i	$0.444050\pi$
$98$		0			0
$99$		0			0
$100$	−0.499709	−	0.865522i	−0.0499709	−	0.0865522i
$101$	−3.68322	−	6.37952i	−0.366494	−	0.634786i	0.622521	−	0.782603i	$-0.286109\pi$
$101$	−3.68322	−	6.37952i	−0.366494	−	0.634786i	−0.989015	+	0.147817i	$0.952775\pi$
$102$		0			0
$103$	−6.91120	−	3.99019i	−0.680981	−	0.393165i	0.119244	−	0.992865i	$-0.461953\pi$
$103$	−6.91120	−	3.99019i	−0.680981	−	0.393165i	−0.800225	+	0.599700i	$0.795286\pi$
$104$	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	$-0.365818\pi$
$107$	14.5228	−	8.38472i	1.40397	−	0.810582i	0.994797	+	0.101876i	$0.0324844\pi$
$108$		0			0
$109$	4.43255	−	7.67740i	0.424561	−	0.735361i	−0.571818	−	0.820380i	$-0.693762\pi$
$109$	4.43255	−	7.67740i	0.424561	−	0.735361i	0.996379	+	0.0850190i	$0.0270951\pi$
$110$	−1.44800			−0.138061
$111$		0			0
$112$		0			0
$113$	−13.5621	+	7.83007i	−1.27581	+	0.736591i	−0.976076	−	0.217430i	$-0.930233\pi$
$113$	−13.5621	+	7.83007i	−1.27581	+	0.736591i	−0.299738	+	0.954022i	$0.596899\pi$
$114$		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	−0.0241447	−	0.999708i	$-0.507686\pi$
$131$	9.77105	−	16.9240i	0.853701	−	1.47865i	0.877845	−	0.478944i	$-0.158980\pi$
$132$		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	−0.557615	−	0.830100i	$-0.688283\pi$
$137$	−1.37570	+	0.794262i	−0.117534	+	0.0678584i	0.440080	+	0.897958i	$0.354950\pi$
$138$		0			0
$139$	−3.97274	+	2.29366i	−0.336963	+	0.194546i	−0.658928	−	0.752206i	$-0.728990\pi$
$139$	−3.97274	+	2.29366i	−0.336963	+	0.194546i	0.321965	+	0.946752i	$0.395657\pi$
$140$		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	0.803831	−	0.594858i	$-0.202792\pi$
$149$	8.42966	+	4.86686i	0.690584	+	0.398709i	−0.113247	+	0.993567i	$0.536125\pi$
$150$		0			0
$151$	3.00916	+	5.21203i	0.244882	+	0.424149i	0.962099	−	0.272702i	$-0.0879173\pi$
$151$	3.00916	+	5.21203i	0.244882	+	0.424149i	−0.717216	+	0.696851i	$0.754584\pi$
$152$	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	$-0.773737\pi$
$157$		−	16.3506i		−	1.30492i	0.757823	−	0.652461i	$-0.226263\pi$
$158$		−	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	0.964399	−	0.264452i	$-0.0851910\pi$
$163$	3.23235	+	5.59860i	0.253177	+	0.438516i	−0.711221	+	0.702968i	$0.751858\pi$
$164$	−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	0.913062	−	0.407820i	$-0.133711\pi$
$167$	1.33556	+	2.31325i	0.103348	+	0.179005i	−0.809714	+	0.586825i	$0.800378\pi$
$168$		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	0.996436	−	0.0843484i	$-0.0268809\pi$
$179$	19.0198	+	10.9811i	1.42161	+	0.820765i	0.425170	+	0.905113i	$0.360214\pi$
$180$		0			0
$181$		−	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
$183$		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	$-0.975738\pi$
$191$		−	2.10475i		−	0.152294i	0.997097	−	0.0761470i	$-0.0242618\pi$
$192$		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	$0.0877995\pi$
$197$			7.64511i			0.544692i	−0.962199	+	0.272346i	$0.912200\pi$
$198$		0			0
$199$	−5.93394	−	3.42596i	−0.420646	−	0.242860i	0.274708	−	0.961528i	$-0.411419\pi$
$199$	−5.93394	−	3.42596i	−0.420646	−	0.242860i	−0.695354	+	0.718668i	$0.744752\pi$
$200$	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	0.755804	−	0.654798i	$-0.227246\pi$
$211$	−2.74784	−	4.75940i	−0.189169	−	0.327651i	−0.944974	+	0.327147i	$0.893913\pi$
$212$	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	−0.223307	−	0.974748i	$-0.571685\pi$
$223$	−17.6080	−	10.1660i	−1.17912	−	0.680764i	−0.955810	+	0.293985i	$0.905019\pi$
$224$		0			0
$225$		0			0
$226$	11.6238	+	20.1330i	0.773204	+	1.33923i
$227$	0.161235	+	0.279268i	0.0107016	+	0.0185356i	0.871327	−	0.490704i	$-0.163260\pi$
$227$	0.161235	+	0.279268i	0.0107016	+	0.0185356i	−0.860625	+	0.509239i	$0.829927\pi$
$228$		0			0
$229$	−2.30171	−	1.32889i	−0.152101	−	0.0878157i	0.422018	−	0.906588i	$-0.361322\pi$
$229$	−2.30171	−	1.32889i	−0.152101	−	0.0878157i	−0.574119	+	0.818772i	$0.694655\pi$
$230$	−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	$-0.390971\pi$
$233$	20.1415	−	11.6287i	1.31952	−	0.761823i	0.983651	+	0.180087i	$0.0576378\pi$
$234$		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	−0.490550	−	0.871413i	$-0.663204\pi$
$239$	0.291265	−	0.168162i	0.0188404	−	0.0108775i	0.509391	+	0.860535i	$0.329871\pi$
$240$		0			0
$241$	−19.1846	+	11.0762i	−1.23579	+	0.713483i	−0.968231	−	0.250059i	$-0.919550\pi$
$241$	−19.1846	+	11.0762i	−1.23579	+	0.713483i	−0.267558	+	0.963542i	$0.586217\pi$
$242$	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	0.387647	+	0.921808i	$0.373288\pi$
$257$	−9.69064	+	16.7847i	−0.604486	+	1.04700i	−0.992133	+	0.125192i	$0.960045\pi$
$258$		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	−0.357909	−	0.933757i	$-0.616510\pi$
$263$	4.40776	−	2.54482i	0.271794	−	0.156920i	0.629703	+	0.776836i	$0.283177\pi$
$264$		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	−0.778609	−	0.627510i	$-0.784074\pi$
$269$	2.52800	−	4.37863i	0.154135	−	0.266970i	0.932744	+	0.360540i	$0.117408\pi$
$270$		0			0
$271$	−27.1767	+	15.6905i	−1.65087	+	0.953128i	−0.674150	+	0.738595i	$0.735490\pi$
$271$	−27.1767	+	15.6905i	−1.65087	+	0.953128i	−0.976717	+	0.214533i	$0.931177\pi$
$272$	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	−0.930322	−	0.366744i	$-0.880473\pi$
$277$	−13.0279	−	22.5650i	−0.782771	−	1.35580i	0.147551	−	0.989054i	$-0.452861\pi$
$278$	3.40496	+	5.89756i	0.204216	+	0.353712i
$279$		0			0
$280$		0			0
$281$	4.14335	+	2.39217i	0.247172	+	0.142705i	0.618469	−	0.785810i	$-0.287753\pi$
$281$	4.14335	+	2.39217i	0.247172	+	0.142705i	−0.371297	+	0.928514i	$0.621087\pi$
$282$		0			0
$283$		−	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
$285$		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	0.823473	−	0.567356i	$-0.192033\pi$
$293$	−1.36267	−	2.36021i	−0.0796079	−	0.137885i	−0.903081	+	0.429471i	$0.858700\pi$
$294$		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	$-0.923763\pi$
$307$		−	8.31294i		−	0.474444i	0.971455	−	0.237222i	$-0.0762369\pi$
$308$		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	$-0.891533\pi$
$313$		−	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			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	0.998236	+	0.0593723i	$0.0189099\pi$
$337$	10.1065	+	17.5050i	0.550536	+	0.953556i	−0.447700	+	0.894184i	$0.647757\pi$
$338$	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	$-0.842592\pi$
$347$		−	17.6817i		−	0.949205i	0.880200	−	0.474602i	$-0.157408\pi$
$348$		0			0
$349$	−3.62628	−	2.09363i	−0.194110	−	0.112070i	0.399795	−	0.916605i	$-0.369081\pi$
$349$	−3.62628	−	2.09363i	−0.194110	−	0.112070i	−0.593905	+	0.804535i	$0.702415\pi$
$350$		0			0
$351$		0			0
$352$	−1.81574	−	3.14495i	−0.0967791	−	0.167626i
$353$	−15.2477	−	26.4097i	−0.811551	−	1.40565i	−0.911778	−	0.410684i	$-0.865290\pi$
$353$	−15.2477	−	26.4097i	−0.811551	−	1.40565i	0.100227	−	0.994965i	$-0.468043\pi$
$354$		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	−0.618124	−	0.786080i	$-0.712107\pi$
$359$	−4.66901	+	2.69565i	−0.246421	+	0.142271i	0.371703	+	0.928352i	$0.378774\pi$
$360$		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	−0.878557	−	0.477638i	$-0.841493\pi$
$367$	−17.3218	+	10.0007i	−0.904188	+	0.522033i	−0.0256317	+	0.999671i	$0.508160\pi$
$368$	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	−0.300730	−	0.953709i	$-0.597230\pi$
$373$	13.0474	−	22.5988i	0.675571	−	1.17012i	0.976302	−	0.216414i	$-0.0694363\pi$
$374$	−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	−0.415280	−	0.909693i	$-0.636317\pi$
$383$	11.3543	−	19.6662i	0.580177	−	1.00490i	0.995458	−	0.0952034i	$-0.0303501\pi$
$384$		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	−0.595392	−	0.803436i	$-0.703003\pi$
$389$	−3.89121	+	2.24659i	−0.197292	+	0.113907i	0.398100	+	0.917342i	$0.369670\pi$
$390$		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	−0.275362	−	0.961341i	$-0.588798\pi$
$397$	8.35854	−	4.82581i	0.419503	−	0.242200i	0.694865	+	0.719140i	$0.255464\pi$
$398$	−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	$-0.498872\pi$
$401$	−17.2356	−	9.95098i	−0.860705	−	0.496928i	−0.864248	+	0.503066i	$0.832205\pi$
$402$		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	$0.0191011\pi$
$409$			2.42571i			0.119944i	−0.998200	+	0.0599718i	$0.980899\pi$
$410$			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	−0.961970	−	0.273155i	$-0.911933\pi$
$419$	−14.6878	−	25.4399i	−0.717544	−	1.24282i	0.244426	−	0.969668i	$-0.421400\pi$
$420$		0			0
$421$	−18.2078	+	31.5368i	−0.887392	+	1.53701i	−0.0444443	+	0.999012i	$0.514152\pi$
$421$	−18.2078	+	31.5368i	−0.887392	+	1.53701i	−0.842948	+	0.537996i	$0.819182\pi$
$422$	−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	0.0360172	−	0.999351i	$-0.488533\pi$
$431$	−16.8459	−	9.72598i	−0.811438	−	0.468484i	−0.847455	+	0.530867i	$0.821866\pi$
$432$		0			0
$433$			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
$435$		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	$0.0563189\pi$
$439$			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	$0.993498\pi$
$444$		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	$0.120395\pi$
$449$			15.6497i			0.738556i	−0.929319	+	0.369278i	$0.879605\pi$
$450$		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	0.471585	+	0.881821i	$0.343682\pi$
$461$	−11.3342	+	19.6314i	−0.527886	+	0.914326i	−0.999472	+	0.0325056i	$0.989651\pi$
$462$		0			0
$463$	−21.0052	−	36.3821i	−0.976194	−	1.69082i	−0.675937	−	0.736960i	$-0.736261\pi$
$463$	−21.0052	−	36.3821i	−0.976194	−	1.69082i	−0.300257	−	0.953858i	$-0.597073\pi$
$464$	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	−0.996162	−	0.0875236i	$-0.972105\pi$
$467$	−12.4016	−	21.4802i	−0.573879	−	0.993987i	0.422284	−	0.906464i	$-0.361229\pi$
$468$		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	0.901186	−	0.433433i	$-0.142698\pi$
$479$	1.64647	+	2.85177i	0.0752291	+	0.130301i	−0.825957	+	0.563733i	$0.809365\pi$
$480$		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	−0.959751	−	0.280853i	$-0.909383\pi$
$487$	−5.22240	+	9.04546i	−0.236650	+	0.409889i	0.723101	+	0.690742i	$0.242716\pi$
$488$	14.4704			0.655043
$489$		0			0
$490$		0			0
$491$	26.2797	−	15.1726i	1.18599	−	0.684731i	0.228596	−	0.973521i	$-0.426587\pi$
$491$	26.2797	−	15.1726i	1.18599	−	0.684731i	0.957392	+	0.288791i	$0.0932532\pi$
$492$		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	−0.887225	−	0.461336i	$-0.847370\pi$
$499$	−0.984757	+	1.70565i	−0.0440838	+	0.0763554i	0.843142	+	0.537692i	$0.180704\pi$
$500$	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	−0.871315	−	0.490725i	$-0.836732\pi$
$509$	−0.240892	+	0.417237i	−0.0106774	+	0.0184937i	0.860637	+	0.509218i	$0.170065\pi$
$510$		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	−0.979602	−	0.200948i	$-0.935598\pi$
$521$	−7.20770	+	12.4841i	−0.315775	+	0.546939i	0.663827	+	0.747886i	$0.268931\pi$
$522$		0			0
$523$	5.90591	−	3.40978i	0.258247	−	0.149099i	−0.365287	−	0.930895i	$-0.619029\pi$
$523$	5.90591	−	3.40978i	0.258247	−	0.149099i	0.623535	+	0.781796i	$0.285696\pi$
$524$	−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	0.991507	−	0.130051i	$-0.0415142\pi$
$541$	8.91128	+	15.4348i	0.383126	+	0.663594i	−0.608381	+	0.793645i	$0.708181\pi$
$542$	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	−0.973918	−	0.226900i	$-0.927141\pi$
$547$	−6.79325	+	11.7663i	−0.290458	+	0.503089i	0.683460	+	0.729988i	$0.260474\pi$
$548$	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	0.626486	−	0.779433i	$-0.284493\pi$
$557$	6.24761	+	3.60706i	0.264720	+	0.152836i	−0.361766	+	0.932269i	$0.617826\pi$
$558$		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	$-0.815732\pi$
$569$		−	26.1007i		−	1.09420i	0.837067	−	0.547100i	$-0.184268\pi$
$570$		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	0.806194	−	0.591651i	$-0.201523\pi$
$577$	16.7403	+	9.66501i	0.696907	+	0.402360i	−0.109287	+	0.994010i	$0.534857\pi$
$578$	−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	−0.663622	−	0.748068i	$-0.730982\pi$
$587$	7.65692	−	13.2622i	0.316035	−	0.547389i	0.979657	+	0.200679i	$0.0643150\pi$
$588$		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	−0.915833	−	0.401560i	$-0.868468\pi$
$593$	−19.6195	−	33.9820i	−0.805678	−	1.39547i	0.110155	−	0.993914i	$-0.464865\pi$
$594$		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	$0.247212\pi$
$599$			34.3077i			1.40177i	−0.713272	+	0.700887i	$0.752788\pi$
$600$		0			0
$601$	24.0139	+	13.8644i	0.979547	+	0.565541i	0.902133	−	0.431458i	$-0.142001\pi$
$601$	24.0139	+	13.8644i	0.979547	+	0.565541i	0.0774133	+	0.996999i	$0.475334\pi$
$602$		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	0.211142	−	0.977455i	$-0.432282\pi$
$607$	−13.0526	−	7.53592i	−0.529788	−	0.305873i	−0.740930	+	0.671582i	$0.765615\pi$
$608$	−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	−0.946920	−	0.321469i	$-0.895823\pi$
$613$	−4.82944	+	8.36484i	−0.195059	+	0.337853i	0.751861	+	0.659322i	$0.229157\pi$
$614$	−12.3406			−0.498027
$615$		0			0
$616$		0			0
$617$	−15.9761	+	9.22381i	−0.643174	+	0.371337i	−0.785836	−	0.618435i	$-0.787767\pi$
$617$	−15.9761	+	9.22381i	−0.643174	+	0.371337i	0.142662	+	0.989771i	$0.454434\pi$
$618$		0			0
$619$	29.3519	−	16.9463i	1.17975	−	0.681130i	0.223795	−	0.974636i	$-0.428155\pi$
$619$	29.3519	−	16.9463i	1.17975	−	0.681130i	0.955957	+	0.293506i	$0.0948220\pi$
$620$	−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	−0.991333	−	0.131373i	$-0.958061\pi$
$641$	−34.7673	+	20.0729i	−1.37323	+	0.792833i	−0.381894	+	0.924206i	$0.624728\pi$
$642$		0			0
$643$	−30.0552	+	17.3524i	−1.18526	+	0.684311i	−0.957226	−	0.289342i	$-0.906564\pi$
$643$	−30.0552	+	17.3524i	−1.18526	+	0.684311i	−0.228036	+	0.973653i	$0.573230\pi$
$644$		0			0
$645$		0			0
$646$	−38.7132			−1.52315
$647$	7.18466	−	12.4442i	0.282458	−	0.489232i	−0.689532	−	0.724256i	$-0.742184\pi$
$647$	7.18466	−	12.4442i	0.282458	−	0.489232i	0.971990	+	0.235024i	$0.0755169\pi$
$648$		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	0.480872	−	0.876791i	$-0.340320\pi$
$653$	−0.971455	−	0.560870i	−0.0380160	−	0.0219485i	−0.518888	+	0.854843i	$0.673654\pi$
$654$		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	0.602424	−	0.798176i	$-0.294202\pi$
$659$	5.45240	+	3.14795i	0.212395	+	0.122627i	−0.390029	+	0.920803i	$0.627535\pi$
$660$		0			0
$661$			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
$663$		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	−0.998212	−	0.0597668i	$-0.980964\pi$
$673$	−11.6052	+	20.1008i	−0.447347	+	0.774827i	0.550866	+	0.834594i	$0.314298\pi$
$674$	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	0.425280	−	0.905062i	$-0.360175\pi$
$683$	−3.81262	−	2.20122i	−0.145886	−	0.0842272i	−0.571166	+	0.820834i	$0.693509\pi$
$684$		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	$0.0567945\pi$
$691$			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
$696$		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	$0.142389\pi$
$701$			22.9051i			0.865116i	−0.901606	+	0.432558i	$0.857611\pi$
$702$		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	0.990010	−	0.141000i	$-0.0450318\pi$
$719$	9.99888	+	17.3186i	0.372895	+	0.645873i	−0.617114	+	0.786873i	$0.711698\pi$
$720$		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	0.886372	−	0.462975i	$-0.153218\pi$
$727$	25.0380	+	14.4557i	0.928610	+	0.536133i	0.0422381	+	0.999108i	$0.486551\pi$
$728$		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	0.913400	−	0.407063i	$-0.133447\pi$
$733$	27.5498	+	15.9059i	1.01757	+	0.587496i	0.104173	+	0.994559i	$0.466780\pi$
$734$	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	−0.995851	−	0.0909988i	$-0.970994\pi$
$739$	−11.3935	+	19.7342i	−0.419118	+	0.725934i	0.576733	+	0.816933i	$0.304327\pi$
$740$	−0.744811			−0.0273798
$741$		0			0
$742$		0			0
$743$	−11.8554	+	6.84471i	−0.434932	+	0.251108i	−0.701446	−	0.712723i	$-0.747462\pi$
$743$	−11.8554	+	6.84471i	−0.434932	+	0.251108i	0.266513	+	0.963831i	$0.414128\pi$
$744$		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	−0.989921	−	0.141622i	$-0.954768\pi$
$751$	−10.2030	+	17.6721i	−0.372312	+	0.644864i	0.617608	+	0.786486i	$0.288102\pi$
$752$	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	0.0639453	+	0.997953i	$0.479632\pi$
$761$	−22.9595	+	39.7670i	−0.832280	+	1.44155i	−0.896226	+	0.443598i	$0.853702\pi$
$762$		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	−0.402731	−	0.915318i	$-0.631939\pi$
$769$	5.22983	−	3.01944i	0.188592	−	0.108884i	0.591323	+	0.806434i	$0.298606\pi$
$770$		0			0
$771$		0			0
$772$	1.21331			0.0436680
$773$	−19.1157	+	33.1094i	−0.687545	+	1.19086i	0.285085	+	0.958502i	$0.407978\pi$
$773$	−19.1157	+	33.1094i	−0.687545	+	1.19086i	−0.972630	+	0.232360i	$0.925355\pi$
$774$		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	$-0.670463\pi$
$787$		−	48.2521i		−	1.72000i	0.510293	−	0.860001i	$-0.329537\pi$
$788$		−	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	0.550121	−	0.835085i	$-0.314582\pi$
$797$	−12.6517	−	21.9133i	−0.448145	−	0.776209i	−0.998265	+	0.0588759i	$0.981248\pi$
$798$		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	0.320485	−	0.947254i	$-0.396154\pi$
$809$	−9.65975	−	5.57706i	−0.339619	−	0.196079i	−0.660103	+	0.751175i	$0.729488\pi$
$810$		0			0
$811$			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
$813$		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	$-0.943261\pi$
$821$		−	10.1608i		−	0.354616i	0.984155	−	0.177308i	$-0.0567389\pi$
$822$		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	$-0.923215\pi$
$827$		−	13.7400i		−	0.477787i	0.971046	−	0.238894i	$-0.0767847\pi$
$828$		0			0
$829$	−15.5086	−	8.95388i	−0.538635	−	0.310981i	0.205891	−	0.978575i	$-0.433991\pi$
$829$	−15.5086	−	8.95388i	−0.538635	−	0.310981i	−0.744526	+	0.667594i	$0.767324\pi$
$830$	−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	−0.209261	+	0.977860i	$0.567106\pi$
$839$	−27.5601	+	47.7356i	−0.951482	+	1.64802i	−0.742221	+	0.670155i	$0.766227\pi$
$840$		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	0.535090	−	0.844795i	$-0.320278\pi$
$853$	2.07425	+	1.19757i	0.0710209	+	0.0410039i	−0.464069	+	0.885799i	$0.653611\pi$
$854$		0			0
$855$		0			0
$856$	−22.3581	−	38.7254i	−0.764185	−	1.32361i
$857$	15.2461	+	26.4070i	0.520796	+	0.902046i	0.999708	+	0.0241822i	$0.00769820\pi$
$857$	15.2461	+	26.4070i	0.520796	+	0.902046i	−0.478911	+	0.877863i	$0.658968\pi$
$858$		0			0
$859$	−38.9437	−	22.4841i	−1.32874	−	0.767149i	−0.343636	−	0.939103i	$-0.611659\pi$
$859$	−38.9437	−	22.4841i	−1.32874	−	0.767149i	−0.985105	+	0.171954i	$0.944992\pi$
$860$	−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	−0.550002	+	0.835163i	$0.685373\pi$
$863$	−45.4835	+	26.2599i	−1.54828	+	0.893897i	−0.998274	+	0.0587340i	$0.981294\pi$
$864$		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	−0.877341	−	0.479868i	$-0.840685\pi$
$877$	−0.683876	+	1.18451i	−0.0230929	+	0.0399980i	0.854248	+	0.519866i	$0.174018\pi$
$878$	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	−0.209943	−	0.977714i	$-0.567328\pi$
$887$	22.0913	−	38.2633i	0.741754	−	1.28475i	0.951696	−	0.307041i	$-0.0993390\pi$
$888$		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	0.960265	−	0.279091i	$-0.0900330\pi$
$907$	7.18075	+	12.4374i	0.238433	+	0.412978i	−0.721832	+	0.692068i	$0.756700\pi$
$908$	−0.0328534	−	0.0569037i	−0.00109028	−	0.00188841i
$909$		0			0
$910$		0			0
$911$	41.6920	+	24.0709i	1.38132	+	0.797505i	0.992316	−	0.123732i	$-0.0394863\pi$
$911$	41.6920	+	24.0709i	1.38132	+	0.797505i	0.389003	+	0.921237i	$0.372820\pi$
$912$		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	0.610713	−	0.791852i	$-0.290883\pi$
$919$	−11.5321	−	19.9741i	−0.380408	−	0.658886i	−0.991121	+	0.132966i	$0.957550\pi$
$920$	−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	$-0.899862\pi$
$937$		−	18.9436i		−	0.618859i	0.950922	−	0.309430i	$-0.100138\pi$
$938$		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	$0.0989501\pi$
$947$			18.8258i			0.611757i	−0.952071	+	0.305878i	$0.901050\pi$
$948$		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	$-0.808095\pi$
$953$		−	35.0089i		−	1.13405i	0.823701	−	0.567024i	$-0.191905\pi$
$954$		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	0.720557	−	0.693395i	$-0.243886\pi$
$967$	−7.47001	−	12.9384i	−0.240219	−	0.416072i	−0.960777	+	0.277323i	$0.910553\pi$
$968$	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	0.999890	−	0.0148426i	$-0.00472472\pi$
$971$	15.1782	+	26.2894i	0.487091	+	0.843666i	−0.512799	+	0.858509i	$0.671391\pi$
$972$		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	$-0.663761\pi$
$977$		−	54.4218i		−	1.74111i	0.492074	−	0.870554i	$-0.336239\pi$
$978$		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	0.576911	−	0.816807i	$-0.304258\pi$
$983$	−13.1343	−	22.7493i	−0.418920	−	0.725590i	−0.995831	+	0.0912165i	$0.970924\pi$
$984$		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	−0.483720	−	0.875223i	$-0.660715\pi$
$991$	16.2471	−	28.1408i	0.516106	−	0.893921i	0.999825	−	0.0186981i	$-0.00595214\pi$
$992$	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	−0.910988	−	0.412433i	$-0.864679\pi$
$997$	−31.8691	+	18.3996i	−1.00931	+	0.582723i	−0.0983170	+	0.995155i	$0.531346\pi$
$998$	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.521.13		48
3.2	odd	2		441.2.i.d.227.20		48
7.2	even	3		1323.2.s.d.656.5		48
7.3	odd	6		1323.2.o.e.440.20		48
7.4	even	3		1323.2.o.e.440.19		48
7.5	odd	6		1323.2.s.d.656.6		48
7.6	odd	2	inner	1323.2.i.d.521.5		48
9.4	even	3		441.2.s.d.374.20		48
9.5	odd	6		1323.2.s.d.962.6		48
21.2	odd	6		441.2.s.d.362.19		48
21.5	even	6		441.2.s.d.362.20		48
21.11	odd	6		441.2.o.e.146.6	yes	48
21.17	even	6		441.2.o.e.146.5	✓	48
21.20	even	2		441.2.i.d.227.19		48
63.4	even	3		441.2.o.e.293.5	yes	48
63.5	even	6	inner	1323.2.i.d.1097.13		48
63.13	odd	6		441.2.s.d.374.19		48
63.23	odd	6	inner	1323.2.i.d.1097.5		48
63.31	odd	6		441.2.o.e.293.6	yes	48
63.32	odd	6		1323.2.o.e.881.20		48
63.40	odd	6		441.2.i.d.68.6		48
63.41	even	6		1323.2.s.d.962.5		48
63.58	even	3		441.2.i.d.68.5		48
63.59	even	6		1323.2.o.e.881.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.5		48	63.58	even	3
441.2.i.d.68.6		48	63.40	odd	6
441.2.i.d.227.19		48	21.20	even	2
441.2.i.d.227.20		48	3.2	odd	2
441.2.o.e.146.5	✓	48	21.17	even	6
441.2.o.e.146.6	yes	48	21.11	odd	6
441.2.o.e.293.5	yes	48	63.4	even	3
441.2.o.e.293.6	yes	48	63.31	odd	6
441.2.s.d.362.19		48	21.2	odd	6
441.2.s.d.362.20		48	21.5	even	6
441.2.s.d.374.19		48	63.13	odd	6
441.2.s.d.374.20		48	9.4	even	3
1323.2.i.d.521.5		48	7.6	odd	2	inner
1323.2.i.d.521.13		48	1.1	even	1	trivial
1323.2.i.d.1097.5		48	63.23	odd	6	inner
1323.2.i.d.1097.13		48	63.5	even	6	inner
1323.2.o.e.440.19		48	7.4	even	3
1323.2.o.e.440.20		48	7.3	odd	6
1323.2.o.e.881.19		48	63.59	even	6
1323.2.o.e.881.20		48	63.32	odd	6
1323.2.s.d.656.5		48	7.2	even	3
1323.2.s.d.656.6		48	7.5	odd	6
1323.2.s.d.962.5		48	63.41	even	6
1323.2.s.d.962.6		48	9.5	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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