LMFDB - Embedded newform 648.2.d.j.325.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(325,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.325"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-1,0,1,0,0,-6,-1,0,-8,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.31435290000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{4} - 8x + 16 $ x^8 - x^7 - 2x^4 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			325.6
Root			$-0.295065 + 1.38309i$ of defining polynomial
Character	$\chi$	$=$	648.325
Dual form			648.2.d.j.325.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.295065 + 1.38309i) q^{2} +(-1.82587 + 0.816201i) q^{4} -0.696047i q^{5} -1.59013 q^{7} +(-1.66763 - 2.28452i) q^{8} +(0.962695 - 0.205379i) q^{10} -2.73921i q^{11} -5.50539i q^{13} +(-0.469191 - 2.19929i) q^{14} +(2.66763 - 2.98056i) q^{16} -5.65175 q^{17} +0.963328i q^{19} +(0.568114 + 1.27089i) q^{20} +(3.78857 - 0.808243i) q^{22} -6.57714 q^{23} +4.51552 q^{25} +(7.61444 - 1.62444i) q^{26} +(2.90338 - 1.29787i) q^{28} -3.29178i q^{29} +7.39688 q^{31} +(4.90951 + 2.81011i) q^{32} +(-1.66763 - 7.81687i) q^{34} +1.10680i q^{35} -6.25538i q^{37} +(-1.33237 + 0.284244i) q^{38} +(-1.59013 + 1.16075i) q^{40} +1.86377 q^{41} +3.46223i q^{43} +(2.23574 + 5.00145i) q^{44} +(-1.94068 - 9.09677i) q^{46} -7.71337 q^{47} -4.47149 q^{49} +(1.33237 + 6.24537i) q^{50} +(4.49350 + 10.0521i) q^{52} -2.54179i q^{53} -1.90662 q^{55} +(2.65175 + 3.63267i) q^{56} +(4.55282 - 0.971287i) q^{58} -5.33494i q^{59} -9.16503i q^{61} +(2.18256 + 10.2305i) q^{62} +(-2.43802 + 7.61945i) q^{64} -3.83201 q^{65} +6.87947i q^{67} +(10.3194 - 4.61296i) q^{68} +(-1.53081 + 0.326579i) q^{70} +3.68351 q^{71} +2.83201 q^{73} +(8.65175 - 1.84574i) q^{74} +(-0.786270 - 1.75892i) q^{76} +4.35569i q^{77} -5.75740 q^{79} +(-2.07461 - 1.85680i) q^{80} +(0.549933 + 2.57776i) q^{82} +6.63916i q^{83} +3.93388i q^{85} +(-4.78857 + 1.02158i) q^{86} +(-6.25776 + 4.56798i) q^{88} -2.98701 q^{89} +8.75427i q^{91} +(12.0090 - 5.36827i) q^{92} +(-2.27594 - 10.6683i) q^{94} +0.670522 q^{95} +2.49675 q^{97} +(-1.31938 - 6.18447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{4} - 6 q^{7} - q^{8} - 8 q^{10} - 16 q^{14} + 9 q^{16} - 14 q^{17} + 8 q^{20} - q^{22} + 10 q^{23} - 2 q^{25} + 14 q^{26} + 2 q^{28} + 10 q^{31} - 11 q^{32} - q^{34} - 23 q^{38} - 6 q^{40}+ \cdots + 33 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^4 - 6 * q^7 - q^8 - 8 * q^10 - 16 * q^14 + 9 * q^16 - 14 * q^17 + 8 * q^20 - q^22 + 10 * q^23 - 2 * q^25 + 14 * q^26 + 2 * q^28 + 10 * q^31 - 11 * q^32 - q^34 - 23 * q^38 - 6 * q^40 + 8 * q^41 + 9 * q^44 - 10 * q^46 - 6 * q^47 - 18 * q^49 + 23 * q^50 + 8 * q^52 - 2 * q^55 - 10 * q^56 + 14 * q^58 - 26 * q^62 + 13 * q^64 + 14 * q^65 + 39 * q^68 + 36 * q^71 - 22 * q^73 + 38 * q^74 - 5 * q^76 + 30 * q^79 - 48 * q^80 + 19 * q^82 - 7 * q^86 - 31 * q^88 + 32 * q^89 + 30 * q^92 + 12 * q^94 - 44 * q^95 + 33 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.295065	+	1.38309i	0.208642	+	0.977992i
$2$	0.295065	+	1.38309i	0.208642	+	0.977992i
$3$		0			0
$3$		0			0
$4$	−1.82587	+	0.816201i	−0.912937	+	0.408101i
$5$		−	0.696047i		−	0.311282i	−0.987814	−	0.155641i	$-0.950256\pi$
$5$		−	0.696047i		−	0.311282i	0.987814	−	0.155641i	$-0.0497442\pi$
$6$		0			0
$7$	−1.59013			−0.601012			−0.300506	−	0.953780i	$-0.597156\pi$
$7$	−1.59013			−0.601012			−0.300506	+	0.953780i	$0.597156\pi$
$8$	−1.66763	−	2.28452i	−0.589596	−	0.807698i
$9$		0			0
$10$	0.962695	−	0.205379i	0.304431	−	0.0649464i
$11$		−	2.73921i		−	0.825902i	−0.910753	−	0.412951i	$-0.864498\pi$
$11$		−	2.73921i		−	0.825902i	0.910753	−	0.412951i	$-0.135502\pi$
$12$		0			0
$13$		−	5.50539i		−	1.52692i	−0.645855	−	0.763460i	$-0.723499\pi$
$13$		−	5.50539i		−	1.52692i	0.645855	−	0.763460i	$-0.276501\pi$
$14$	−0.469191	−	2.19929i	−0.125396	−	0.587785i
$15$		0			0
$16$	2.66763	−	2.98056i	0.666908	−	0.745140i
$17$	−5.65175			−1.37075			−0.685375	−	0.728190i	$-0.740362\pi$
$17$	−5.65175			−1.37075			−0.685375	+	0.728190i	$0.740362\pi$
$18$		0			0
$19$			0.963328i			0.221003i	0.993876	+	0.110501i	$0.0352457\pi$
$19$			0.963328i			0.221003i	−0.993876	+	0.110501i	$0.964754\pi$
$20$	0.568114	+	1.27089i	0.127034	+	0.284180i
$21$		0			0
$22$	3.78857	−	0.808243i	0.807726	−	0.172318i
$23$	−6.57714			−1.37143			−0.685714	−	0.727871i	$-0.740510\pi$
$23$	−6.57714			−1.37143			−0.685714	+	0.727871i	$0.740510\pi$
$24$		0			0
$25$	4.51552			0.903104
$26$	7.61444	−	1.62444i	1.49332	−	0.318580i
$27$		0			0
$28$	2.90338	−	1.29787i	0.548686	−	0.245274i
$29$		−	3.29178i		−	0.611268i	−0.952149	−	0.305634i	$-0.901132\pi$
$29$		−	3.29178i		−	0.611268i	0.952149	−	0.305634i	$-0.0988684\pi$
$30$		0			0
$31$	7.39688			1.32852			0.664259	−	0.747502i	$-0.268747\pi$
$31$	7.39688			1.32852			0.664259	+	0.747502i	$0.268747\pi$
$32$	4.90951	+	2.81011i	0.867886	+	0.496763i
$33$		0			0
$34$	−1.66763	−	7.81687i	−0.285996	−	1.34058i
$35$			1.10680i			0.187084i
$36$		0			0
$37$		−	6.25538i		−	1.02838i	−0.857677	−	0.514189i	$-0.828093\pi$
$37$		−	6.25538i		−	1.02838i	0.857677	−	0.514189i	$-0.171907\pi$
$38$	−1.33237	+	0.284244i	−0.216139	+	0.0461105i
$39$		0			0
$40$	−1.59013	+	1.16075i	−0.251421	+	0.183530i
$41$	1.86377			0.291072			0.145536	−	0.989353i	$-0.453509\pi$
$41$	1.86377			0.291072			0.145536	+	0.989353i	$0.453509\pi$
$42$		0			0
$43$			3.46223i			0.527985i	0.964525	+	0.263992i	$0.0850393\pi$
$43$			3.46223i			0.527985i	−0.964525	+	0.263992i	$0.914961\pi$
$44$	2.23574	+	5.00145i	0.337051	+	0.753996i
$45$		0			0
$46$	−1.94068	−	9.09677i	−0.286138	−	1.34125i
$47$	−7.71337			−1.12511			−0.562555	−	0.826760i	$-0.690182\pi$
$47$	−7.71337			−1.12511			−0.562555	+	0.826760i	$0.690182\pi$
$48$		0			0
$49$	−4.47149			−0.638784
$50$	1.33237	+	6.24537i	0.188426	+	0.883228i
$51$		0			0
$52$	4.49350	+	10.0521i	0.623137	+	1.39398i
$53$		−	2.54179i		−	0.349141i	−0.984645	−	0.174571i	$-0.944146\pi$
$53$		−	2.54179i		−	0.349141i	0.984645	−	0.174571i	$-0.0558537\pi$
$54$		0			0
$55$	−1.90662			−0.257088
$56$	2.65175	+	3.63267i	0.354355	+	0.485436i
$57$		0			0
$58$	4.55282	−	0.971287i	0.597815	−	0.127536i
$59$		−	5.33494i		−	0.694550i	−0.937763	−	0.347275i	$-0.887107\pi$
$59$		−	5.33494i		−	0.694550i	0.937763	−	0.347275i	$-0.112893\pi$
$60$		0			0
$61$		−	9.16503i		−	1.17346i	−0.809782	−	0.586731i	$-0.800415\pi$
$61$		−	9.16503i		−	1.17346i	0.809782	−	0.586731i	$-0.199585\pi$
$62$	2.18256	+	10.2305i	0.277185	+	1.29928i
$63$		0			0
$64$	−2.43802	+	7.61945i	−0.304752	+	0.952432i
$65$	−3.83201			−0.475302
$66$		0			0
$67$			6.87947i			0.840461i	0.907417	+	0.420231i	$0.138051\pi$
$67$			6.87947i			0.840461i	−0.907417	+	0.420231i	$0.861949\pi$
$68$	10.3194	−	4.61296i	1.25141	−	0.559404i
$69$		0			0
$70$	−1.53081	+	0.326579i	−0.182967	+	0.0390336i
$71$	3.68351			0.437153			0.218576	−	0.975820i	$-0.429859\pi$
$71$	3.68351			0.437153			0.218576	+	0.975820i	$0.429859\pi$
$72$		0			0
$73$	2.83201			0.331461			0.165731	−	0.986171i	$-0.447002\pi$
$73$	2.83201			0.331461			0.165731	+	0.986171i	$0.447002\pi$
$74$	8.65175	−	1.84574i	1.00575	−	0.214563i
$75$		0			0
$76$	−0.786270	−	1.75892i	−0.0901914	−	0.201762i
$77$			4.35569i			0.496377i
$78$		0			0
$79$	−5.75740			−0.647758			−0.323879	−	0.946099i	$-0.604987\pi$
$79$	−5.75740			−0.647758			−0.323879	+	0.946099i	$0.604987\pi$
$80$	−2.07461	−	1.85680i	−0.231948	−	0.207596i
$81$		0			0
$82$	0.549933	+	2.57776i	0.0607299	+	0.284666i
$83$			6.63916i			0.728743i	0.931254	+	0.364371i	$0.118716\pi$
$83$			6.63916i			0.728743i	−0.931254	+	0.364371i	$0.881284\pi$
$84$		0			0
$85$			3.93388i			0.426689i
$86$	−4.78857	+	1.02158i	−0.516365	+	0.110160i
$87$		0			0
$88$	−6.25776	+	4.56798i	−0.667079	+	0.486949i
$89$	−2.98701			−0.316622			−0.158311	−	0.987389i	$-0.550605\pi$
$89$	−2.98701			−0.316622			−0.158311	+	0.987389i	$0.550605\pi$
$90$		0			0
$91$			8.75427i			0.917697i
$92$	12.0090	−	5.36827i	1.25203	−	0.559681i
$93$		0			0
$94$	−2.27594	−	10.6683i	−0.234745	−	1.10035i
$95$	0.670522			0.0687941
$96$		0			0
$97$	2.49675			0.253506			0.126753	−	0.991934i	$-0.459544\pi$
$97$	2.49675			0.253506			0.126753	+	0.991934i	$0.459544\pi$
$98$	−1.31938	−	6.18447i	−0.133277	−	0.624726i
$99$		0			0
$100$	−8.24477	+	3.68557i	−0.824477	+	0.368557i
$101$			9.49321i			0.944610i	0.881435	+	0.472305i	$0.156578\pi$
$101$			9.49321i			0.944610i	−0.881435	+	0.472305i	$0.843422\pi$
$102$		0			0
$103$	−14.7444			−1.45281			−0.726405	−	0.687267i	$-0.758810\pi$
$103$	−14.7444			−1.45281			−0.726405	+	0.687267i	$0.758810\pi$
$104$	−12.5771	+	9.18095i	−1.23329	+	0.900266i
$105$		0			0
$106$	3.51552	−	0.749991i	0.341457	−	0.0728456i
$107$		−	7.83384i		−	0.757325i	−0.925535	−	0.378663i	$-0.876384\pi$
$107$		−	7.83384i		−	0.757325i	0.925535	−	0.378663i	$-0.123616\pi$
$108$		0			0
$109$			0.242400i			0.0232177i	0.999933	+	0.0116089i	$0.00369529\pi$
$109$			0.242400i			0.0232177i	−0.999933	+	0.0116089i	$0.996305\pi$
$110$	−0.562575	−	2.63702i	−0.0536394	−	0.251430i
$111$		0			0
$112$	−4.24188	+	4.73948i	−0.400820	+	0.447839i
$113$	−8.69578			−0.818030			−0.409015	−	0.912528i	$-0.634128\pi$
$113$	−8.69578			−0.818030			−0.409015	+	0.912528i	$0.634128\pi$
$114$		0			0
$115$			4.57799i			0.426900i
$116$	2.68675	+	6.01037i	0.249459	+	0.558049i
$117$		0			0
$118$	7.37870	−	1.57415i	0.679264	−	0.144912i
$119$	8.98701			0.823838
$120$		0			0
$121$	3.49675			0.317886
$122$	12.6761	−	2.70428i	1.14764	−	0.244834i
$123$		0			0
$124$	−13.5058	+	6.03734i	−1.21285	+	0.542169i
$125$		−	6.62325i		−	0.592401i
$126$		0			0
$127$	−1.72754			−0.153295			−0.0766473	−	0.997058i	$-0.524422\pi$
$127$	−1.72754			−0.153295			−0.0766473	+	0.997058i	$0.524422\pi$
$128$	−11.2578	−	1.12377i	−0.995055	−	0.0993279i
$129$		0			0
$130$	−1.13069	−	5.30001i	−0.0991680	−	0.464841i
$131$			6.63916i			0.580066i	0.957017	+	0.290033i	$0.0936663\pi$
$131$			6.63916i			0.580066i	−0.957017	+	0.290033i	$0.906334\pi$
$132$		0			0
$133$		−	1.53182i		−	0.132825i
$134$	−9.51493	+	2.02989i	−0.821964	+	0.175356i
$135$		0			0
$136$	9.42503	+	12.9115i	0.808189	+	1.10715i
$137$	−3.62649			−0.309832			−0.154916	−	0.987928i	$-0.549511\pi$
$137$	−3.62649			−0.309832			−0.154916	+	0.987928i	$0.549511\pi$
$138$		0			0
$139$			17.3111i			1.46831i	0.678981	+	0.734155i	$0.262422\pi$
$139$			17.3111i			1.46831i	−0.678981	+	0.734155i	$0.737578\pi$
$140$	−0.903375	−	2.02088i	−0.0763491	−	0.170796i
$141$		0			0
$142$	1.08687	+	5.09463i	0.0912085	+	0.427532i
$143$	−15.0804			−1.26109
$144$		0			0
$145$	−2.29123			−0.190276
$146$	0.835625	+	3.91692i	0.0691568	+	0.324166i
$147$		0			0
$148$	5.10565	+	11.4215i	0.419682	+	0.938844i
$149$		−	21.6218i		−	1.77133i	−0.464324	−	0.885665i	$-0.653703\pi$
$149$		−	21.6218i		−	1.77133i	0.464324	−	0.885665i	$-0.346297\pi$
$150$		0			0
$151$	12.7004			1.03354			0.516771	−	0.856124i	$-0.327134\pi$
$151$	12.7004			1.03354			0.516771	+	0.856124i	$0.327134\pi$
$152$	2.20074	−	1.60648i	0.178503	−	0.130302i
$153$		0			0
$154$	−6.02431	+	1.28521i	−0.485453	+	0.103565i
$155$		−	5.14857i		−	0.413543i
$156$		0			0
$157$		−	17.4689i		−	1.39417i	−0.716990	−	0.697083i	$-0.754481\pi$
$157$		−	17.4689i		−	1.39417i	0.716990	−	0.697083i	$-0.245519\pi$
$158$	−1.69880	−	7.96299i	−0.135150	−	0.633502i
$159$		0			0
$160$	1.95597	−	3.41725i	0.154633	−	0.270157i
$161$	10.4585			0.824245
$162$		0			0
$163$			8.56748i			0.671057i	0.942030	+	0.335528i	$0.108915\pi$
$163$			8.56748i			0.671057i	−0.942030	+	0.335528i	$0.891085\pi$
$164$	−3.40301	+	1.52121i	−0.265731	+	0.118787i
$165$		0			0
$166$	−9.18256	+	1.95898i	−0.712705	+	0.152046i
$167$	11.9506			0.924769			0.462384	−	0.886680i	$-0.346994\pi$
$167$	11.9506			0.924769			0.462384	+	0.886680i	$0.346994\pi$
$168$		0			0
$169$	−17.3093			−1.33148
$170$	−5.44091	+	1.16075i	−0.417299	+	0.0890254i
$171$		0			0
$172$	−2.82587	−	6.32159i	−0.215471	−	0.482017i
$173$		−	13.0450i		−	0.991791i	−0.868382	−	0.495895i	$-0.834840\pi$
$173$		−	13.0450i		−	0.991791i	0.868382	−	0.495895i	$-0.165160\pi$
$174$		0			0
$175$	−7.18026			−0.542777
$176$	−8.16438	−	7.30719i	−0.615413	−	0.550800i
$177$		0			0
$178$	−0.881360	−	4.13130i	−0.0660607	−	0.309654i
$179$			3.31875i			0.248055i	0.992279	+	0.124028i	$0.0395811\pi$
$179$			3.31875i			0.248055i	−0.992279	+	0.124028i	$0.960419\pi$
$180$		0			0
$181$		−	14.9128i		−	1.10846i	−0.832363	−	0.554231i	$-0.813013\pi$
$181$		−	14.9128i		−	1.10846i	0.832363	−	0.554231i	$-0.186987\pi$
$182$	−12.1079	+	2.58308i	−0.897501	+	0.191470i
$183$		0			0
$184$	10.9682	+	15.0256i	0.808589	+	1.10770i
$185$	−4.35403			−0.320115
$186$		0			0
$187$			15.4813i			1.13211i
$188$	14.0836	−	6.29566i	1.02715	−	0.459158i
$189$		0			0
$190$	0.197847	+	0.927391i	0.0143533	+	0.0672800i
$191$	−7.31767			−0.529488			−0.264744	−	0.964319i	$-0.585287\pi$
$191$	−7.31767			−0.529488			−0.264744	+	0.964319i	$0.585287\pi$
$192$		0			0
$193$	20.4708			1.47352			0.736759	−	0.676156i	$-0.236355\pi$
$193$	20.4708			1.47352			0.736759	+	0.676156i	$0.236355\pi$
$194$	0.736701	+	3.45322i	0.0528920	+	0.247927i
$195$		0			0
$196$	8.16438	−	3.64964i	0.583170	−	0.260688i
$197$			20.5437i			1.46368i	0.681479	+	0.731838i	$0.261337\pi$
$197$			20.5437i			1.46368i	−0.681479	+	0.731838i	$0.738663\pi$
$198$		0			0
$199$	1.95597			0.138655			0.0693275	−	0.997594i	$-0.477915\pi$
$199$	1.95597			0.138655			0.0693275	+	0.997594i	$0.477915\pi$
$200$	−7.53022	−	10.3158i	−0.532467	−	0.729435i
$201$		0			0
$202$	−13.1300	+	2.80111i	−0.923821	+	0.197085i
$203$			5.23435i			0.367379i
$204$		0			0
$205$		−	1.29727i		−	0.0906054i
$206$	−4.35055	−	20.3928i	−0.303117	−	1.42084i
$207$		0			0
$208$	−16.4091	−	14.6863i	−1.13777	−	1.01831i
$209$	2.63876			0.182527
$210$		0			0
$211$		−	10.5191i		−	0.724165i	−0.932146	−	0.362082i	$-0.882066\pi$
$211$		−	10.5191i		−	0.724165i	0.932146	−	0.362082i	$-0.117934\pi$
$212$	2.07461	+	4.64098i	0.142485	+	0.318744i
$213$		0			0
$214$	10.8349	−	2.31149i	0.740658	−	0.158010i
$215$	2.40987			0.164352
$216$		0			0
$217$	−11.7620			−0.798456
$218$	−0.335261	+	0.0715236i	−0.0227067	+	0.00484419i
$219$		0			0
$220$	3.48124	−	1.55618i	0.234705	−	0.104918i
$221$			31.1151i			2.09303i
$222$		0			0
$223$	−3.86259			−0.258658			−0.129329	−	0.991602i	$-0.541282\pi$
$223$	−3.86259			−0.258658			−0.129329	+	0.991602i	$0.541282\pi$
$224$	−7.80675	−	4.46844i	−0.521610	−	0.298560i
$225$		0			0
$226$	−2.56582	−	12.0270i	−0.170676	−	0.800027i
$227$		−	16.0715i		−	1.06670i	−0.845894	−	0.533351i	$-0.820933\pi$
$227$		−	16.0715i		−	1.06670i	0.845894	−	0.533351i	$-0.179067\pi$
$228$		0			0
$229$			8.61775i			0.569477i	0.958605	+	0.284739i	$0.0919068\pi$
$229$			8.61775i			0.569477i	−0.958605	+	0.284739i	$0.908093\pi$
$230$	−6.33178	+	1.35080i	−0.417505	+	0.0890694i
$231$		0			0
$232$	−7.52012	+	5.48947i	−0.493720	+	0.360401i
$233$	24.1535			1.58235			0.791176	−	0.611589i	$-0.209469\pi$
$233$	24.1535			1.58235			0.791176	+	0.611589i	$0.209469\pi$
$234$		0			0
$235$			5.36886i			0.350226i
$236$	4.35438	+	9.74092i	0.283446	+	0.634080i
$237$		0			0
$238$	2.65175	+	12.4298i	0.171887	+	0.805707i
$239$	4.02985			0.260670			0.130335	−	0.991470i	$-0.458395\pi$
$239$	4.02985			0.260670			0.130335	+	0.991470i	$0.458395\pi$
$240$		0			0
$241$	−5.63297			−0.362852			−0.181426	−	0.983405i	$-0.558071\pi$
$241$	−5.63297			−0.362852			−0.181426	+	0.983405i	$0.558071\pi$
$242$	1.03177	+	4.83631i	0.0663244	+	0.310890i
$243$		0			0
$244$	7.48051	+	16.7342i	0.478891	+	1.07130i
$245$			3.11237i			0.198842i
$246$		0			0
$247$	5.30350			0.337453
$248$	−12.3353	−	16.8983i	−0.783290	−	1.07304i
$249$		0			0
$250$	9.16054	−	1.95428i	0.579364	−	0.123600i
$251$			13.8828i			0.876276i	0.898908	+	0.438138i	$0.144362\pi$
$251$			13.8828i			0.876276i	−0.898908	+	0.438138i	$0.855638\pi$
$252$		0			0
$253$			18.0161i			1.13267i
$254$	−0.509737	−	2.38935i	−0.0319837	−	0.149921i
$255$		0			0
$256$	−1.76750	−	15.9021i	−0.110469	−	0.993880i
$257$	10.8508			0.676853			0.338427	−	0.940993i	$-0.390105\pi$
$257$	10.8508			0.676853			0.338427	+	0.940993i	$0.390105\pi$
$258$		0			0
$259$			9.94686i			0.618068i
$260$	6.99676	−	3.12769i	0.433921	−	0.193971i
$261$		0			0
$262$	−9.18256	+	1.95898i	−0.567300	+	0.121026i
$263$	23.2101			1.43120			0.715598	−	0.698512i	$-0.246154\pi$
$263$	23.2101			1.43120			0.715598	+	0.698512i	$0.246154\pi$
$264$		0			0
$265$	−1.76920			−0.108681
$266$	2.11864	−	0.451985i	0.129902	−	0.0277130i
$267$		0			0
$268$	−5.61504	−	12.5610i	−0.342993	−	0.767288i
$269$			4.01966i			0.245083i	0.992463	+	0.122541i	$0.0391044\pi$
$269$			4.01966i			0.245083i	−0.992463	+	0.122541i	$0.960896\pi$
$270$		0			0
$271$	−6.75621			−0.410411			−0.205205	−	0.978719i	$-0.565786\pi$
$271$	−6.75621			−0.410411			−0.205205	+	0.978719i	$0.565786\pi$
$272$	−15.0768	+	16.8454i	−0.914164	+	1.02140i
$273$		0			0
$274$	−1.07005	−	5.01576i	−0.0646440	−	0.303013i
$275$		−	12.3689i		−	0.745875i
$276$		0			0
$277$		−	2.11997i		−	0.127377i	−0.997970	−	0.0636885i	$-0.979714\pi$
$277$		−	2.11997i		−	0.127377i	0.997970	−	0.0636885i	$-0.0202864\pi$
$278$	−23.9428	+	5.10790i	−1.43600	+	0.306352i
$279$		0			0
$280$	2.52851	−	1.84574i	0.151107	−	0.110304i
$281$	26.1160			1.55795			0.778976	−	0.627054i	$-0.215739\pi$
$281$	26.1160			1.55795			0.778976	+	0.627054i	$0.215739\pi$
$282$		0			0
$283$		−	19.0960i		−	1.13514i	−0.823326	−	0.567569i	$-0.807884\pi$
$283$		−	19.0960i		−	1.13514i	0.823326	−	0.567569i	$-0.192116\pi$
$284$	−6.72563	+	3.00649i	−0.399093	+	0.178402i
$285$		0			0
$286$	−4.44969	−	20.8575i	−0.263116	−	1.23333i
$287$	−2.96364			−0.174938
$288$		0			0
$289$	14.9423			0.878956
$290$	−0.676061	−	3.16898i	−0.0396997	−	0.186089i
$291$		0			0
$292$	−5.17089	+	2.31149i	−0.302603	+	0.135270i
$293$		−	5.85568i		−	0.342092i	−0.985263	−	0.171046i	$-0.945285\pi$
$293$		−	5.85568i		−	0.342092i	0.985263	−	0.171046i	$-0.0547147\pi$
$294$		0			0
$295$	−3.71337			−0.216201
$296$	−14.2905	+	10.4317i	−0.830619	+	0.606328i
$297$		0			0
$298$	29.9049	−	6.37984i	1.73235	−	0.369574i
$299$			36.2097i			2.09406i
$300$		0			0
$301$		−	5.50539i		−	0.317325i
$302$	3.74743	+	17.5658i	0.215640	+	1.01080i
$303$		0			0
$304$	2.87126	+	2.56980i	0.164678	+	0.147388i
$305$	−6.37929			−0.365277
$306$		0			0
$307$		−	13.7071i		−	0.782305i	−0.920326	−	0.391152i	$-0.872077\pi$
$307$		−	13.7071i		−	0.782305i	0.920326	−	0.391152i	$-0.127923\pi$
$308$	−3.55512	−	7.95295i	−0.202572	−	0.453161i
$309$		0			0
$310$	7.12094	−	1.51916i	0.404442	−	0.0862826i
$311$	19.1596			1.08644			0.543221	−	0.839590i	$-0.317205\pi$
$311$	19.1596			1.08644			0.543221	+	0.839590i	$0.317205\pi$
$312$		0			0
$313$	25.2205			1.42555			0.712773	−	0.701395i	$-0.247439\pi$
$313$	25.2205			1.42555			0.712773	+	0.701395i	$0.247439\pi$
$314$	24.1610	−	5.15444i	1.36348	−	0.290882i
$315$		0			0
$316$	10.5123	−	4.69919i	0.591362	−	0.264350i
$317$		−	2.47026i		−	0.138744i	−0.997591	−	0.0693719i	$-0.977900\pi$
$317$		−	2.47026i		−	0.138744i	0.997591	−	0.0693719i	$-0.0220995\pi$
$318$		0			0
$319$	−9.01686			−0.504847
$320$	5.30350	+	1.69697i	0.296474	+	0.0948637i
$321$		0			0
$322$	3.08593	+	14.4650i	0.171972	+	0.806105i
$323$		−	5.44449i		−	0.302939i
$324$		0			0
$325$		−	24.8597i		−	1.37897i
$326$	−11.8496	+	2.52796i	−0.656288	+	0.140011i
$327$		0			0
$328$	−3.10808	−	4.25781i	−0.171615	−	0.235098i
$329$	12.2652			0.676205
$330$		0			0
$331$		−	28.2213i		−	1.55118i	−0.631235	−	0.775592i	$-0.717452\pi$
$331$		−	28.2213i		−	1.55118i	0.631235	−	0.775592i	$-0.282548\pi$
$332$	−5.41889	−	12.1223i	−0.297400	−	0.665296i
$333$		0			0
$334$	3.52621	+	16.5288i	0.192946	+	0.904416i
$335$	4.78843			0.261620
$336$		0			0
$337$	−11.2113			−0.610718			−0.305359	−	0.952237i	$-0.598777\pi$
$337$	−11.2113			−0.610718			−0.305359	+	0.952237i	$0.598777\pi$
$338$	−5.10735	−	23.9403i	−0.277803	−	1.30218i
$339$		0			0
$340$	−3.21084	−	7.18277i	−0.174132	−	0.389540i
$341$		−	20.2616i		−	1.09723i
$342$		0			0
$343$	18.2411			0.984929
$344$	7.90951	−	5.77371i	0.426452	−	0.311298i
$345$		0			0
$346$	18.0424	−	3.84911i	0.969963	−	0.206929i
$347$			20.5887i			1.10526i	0.833428	+	0.552628i	$0.186375\pi$
$347$			20.5887i			1.10526i	−0.833428	+	0.552628i	$0.813625\pi$
$348$		0			0
$349$		−	3.39445i		−	0.181701i	−0.995865	−	0.0908505i	$-0.971041\pi$
$349$		−	3.39445i		−	0.181701i	0.995865	−	0.0908505i	$-0.0289585\pi$
$350$	−2.11864	−	9.93094i	−0.113246	−	0.530831i
$351$		0			0
$352$	7.69748	−	13.4482i	0.410277	−	0.716789i
$353$	1.00648			0.0535696			0.0267848	−	0.999641i	$-0.491473\pi$
$353$	1.00648			0.0535696			0.0267848	+	0.999641i	$0.491473\pi$
$354$		0			0
$355$		−	2.56390i		−	0.136078i
$356$	5.45390	−	2.43800i	0.289056	−	0.129214i
$357$		0			0
$358$	−4.59013	+	0.979246i	−0.242596	+	0.0517547i
$359$	31.4772			1.66131			0.830653	−	0.556791i	$-0.187968\pi$
$359$	31.4772			1.66131			0.830653	+	0.556791i	$0.187968\pi$
$360$		0			0
$361$	18.0720			0.951158
$362$	20.6258	−	4.40024i	1.08407	−	0.231272i
$363$		0			0
$364$	−7.14525	−	15.9842i	−0.374513	−	0.837800i
$365$		−	1.97121i		−	0.103178i
$366$		0			0
$367$	17.3333			0.904793			0.452397	−	0.891817i	$-0.350569\pi$
$367$	17.3333			0.904793			0.452397	+	0.891817i	$0.350569\pi$
$368$	−17.5454	+	19.6036i	−0.914616	+	1.02191i
$369$		0			0
$370$	−1.28472	−	6.02202i	−0.0667895	−	0.313070i
$371$			4.04177i			0.209838i
$372$		0			0
$373$			13.0183i			0.674064i	0.941493	+	0.337032i	$0.109423\pi$
$373$			13.0183i			0.674064i	−0.941493	+	0.337032i	$0.890577\pi$
$374$	−21.4120	+	4.56798i	−1.10719	+	0.236205i
$375$		0			0
$376$	12.8630	+	17.6213i	0.663361	+	0.908749i
$377$	−18.1225			−0.933357
$378$		0			0
$379$		−	22.8643i		−	1.17446i	−0.809421	−	0.587229i	$-0.800219\pi$
$379$		−	22.8643i		−	1.17446i	0.809421	−	0.587229i	$-0.199781\pi$
$380$	−1.22429	+	0.547281i	−0.0628046	+	0.0280749i
$381$		0			0
$382$	−2.15919	−	10.1210i	−0.110474	−	0.517835i
$383$	−30.0234			−1.53412			−0.767061	−	0.641574i	$-0.778282\pi$
$383$	−30.0234			−1.53412			−0.767061	+	0.641574i	$0.778282\pi$
$384$		0			0
$385$	3.03177			0.154513
$386$	6.04020	+	28.3129i	0.307438	+	1.44109i
$387$		0			0
$388$	−4.55874	+	2.03785i	−0.231435	+	0.103456i
$389$			38.0444i			1.92893i	0.264218	+	0.964463i	$0.414886\pi$
$389$			38.0444i			1.92893i	−0.264218	+	0.964463i	$0.585114\pi$
$390$		0			0
$391$	37.1723			1.87989
$392$	7.45679	+	10.2152i	0.376625	+	0.515945i
$393$		0			0
$394$	−28.4137	+	6.06171i	−1.43146	+	0.305385i
$395$			4.00742i			0.201635i
$396$		0			0
$397$			37.4510i			1.87961i	0.341709	+	0.939806i	$0.388994\pi$
$397$			37.4510i			1.87961i	−0.341709	+	0.939806i	$0.611006\pi$
$398$	0.577138	+	2.70528i	0.0289293	+	0.135604i
$399$		0			0
$400$	12.0457	−	13.4588i	0.602287	−	0.672939i
$401$	4.70804			0.235108			0.117554	−	0.993066i	$-0.462495\pi$
$401$	4.70804			0.235108			0.117554	+	0.993066i	$0.462495\pi$
$402$		0			0
$403$		−	40.7227i		−	2.02854i
$404$	−7.74837	−	17.3334i	−0.385496	−	0.862369i
$405$		0			0
$406$	−7.23958	+	1.54447i	−0.359294	+	0.0766508i
$407$	−17.1348			−0.849339
$408$		0			0
$409$	−10.7275			−0.530443			−0.265221	−	0.964188i	$-0.585445\pi$
$409$	−10.7275			−0.530443			−0.265221	+	0.964188i	$0.585445\pi$
$410$	1.79424	−	0.382779i	0.0886114	−	0.0189041i
$411$		0			0
$412$	26.9214	−	12.0344i	1.32632	−	0.592893i
$413$			8.48324i			0.417433i
$414$		0			0
$415$	4.62117			0.226844
$416$	15.4708	−	27.0287i	0.758517	−	1.32519i
$417$		0			0
$418$	0.778603	+	3.64964i	0.0380827	+	0.178510i
$419$		−	4.12921i		−	0.201725i	−0.994900	−	0.100863i	$-0.967840\pi$
$419$		−	4.12921i		−	0.201725i	0.994900	−	0.100863i	$-0.0321602\pi$
$420$		0			0
$421$			15.8565i			0.772797i	0.922332	+	0.386399i	$0.126281\pi$
$421$			15.8565i			0.772797i	−0.922332	+	0.386399i	$0.873719\pi$
$422$	14.5489	−	3.10381i	0.708227	−	0.151091i
$423$		0			0
$424$	−5.80675	+	4.23876i	−0.282001	+	0.205852i
$425$	−25.5206			−1.23793
$426$		0			0
$427$			14.5736i			0.705265i
$428$	6.39399	+	14.3036i	0.309065	+	0.691390i
$429$		0			0
$430$	0.711067	+	3.33307i	0.0342907	+	0.160735i
$431$	16.1853			0.779619			0.389810	−	0.920895i	$-0.372541\pi$
$431$	16.1853			0.779619			0.389810	+	0.920895i	$0.372541\pi$
$432$		0			0
$433$	−32.8306			−1.57774			−0.788868	−	0.614563i	$-0.789332\pi$
$433$	−32.8306			−1.57774			−0.788868	+	0.614563i	$0.789332\pi$
$434$	−3.47055	−	16.2679i	−0.166592	−	0.780884i
$435$		0			0
$436$	−0.197847	−	0.442592i	−0.00947516	−	0.0211963i
$437$		−	6.33594i		−	0.303089i
$438$		0			0
$439$	−21.8546			−1.04307			−0.521533	−	0.853231i	$-0.674640\pi$
$439$	−21.8546			−1.04307			−0.521533	+	0.853231i	$0.674640\pi$
$440$	3.17953	+	4.35569i	0.151578	+	0.207650i
$441$		0			0
$442$	−43.0349	+	9.18095i	−2.04696	+	0.436693i
$443$		−	35.1606i		−	1.67053i	−0.549848	−	0.835265i	$-0.685314\pi$
$443$		−	35.1606i		−	1.67053i	0.549848	−	0.835265i	$-0.314686\pi$
$444$		0			0
$445$			2.07910i			0.0985587i
$446$	−1.13971	−	5.34230i	−0.0539669	−	0.252965i
$447$		0			0
$448$	3.87676	−	12.1159i	0.183160	−	0.572423i
$449$	3.21851			0.151891			0.0759453	−	0.997112i	$-0.475803\pi$
$449$	3.21851			0.151891			0.0759453	+	0.997112i	$0.475803\pi$
$450$		0			0
$451$		−	5.10526i		−	0.240397i
$452$	15.8774	−	7.09751i	0.746810	−	0.333839i
$453$		0			0
$454$	22.2283	−	4.74212i	1.04323	−	0.222559i
$455$	6.09338			0.285662
$456$		0			0
$457$	−8.11025			−0.379381			−0.189691	−	0.981844i	$-0.560749\pi$
$457$	−8.11025			−0.379381			−0.189691	+	0.981844i	$0.560749\pi$
$458$	−11.9191	+	2.54279i	−0.556944	+	0.118817i
$459$		0			0
$460$	−3.73657	−	8.35884i	−0.174218	−	0.389733i
$461$		−	20.9940i		−	0.977788i	−0.872343	−	0.488894i	$-0.837401\pi$
$461$		−	20.9940i		−	0.977788i	0.872343	−	0.488894i	$-0.162599\pi$
$462$		0			0
$463$	8.90011			0.413623			0.206812	−	0.978381i	$-0.433691\pi$
$463$	8.90011			0.413623			0.206812	+	0.978381i	$0.433691\pi$
$464$	−9.81135	−	8.78125i	−0.455480	−	0.407659i
$465$		0			0
$466$	7.12686	+	33.4065i	0.330145	+	1.54753i
$467$		−	26.0527i		−	1.20557i	−0.797902	−	0.602787i	$-0.794057\pi$
$467$		−	26.0527i		−	1.20557i	0.797902	−	0.602787i	$-0.205943\pi$
$468$		0			0
$469$		−	10.9392i		−	0.505128i
$470$	−7.42562	+	1.58416i	−0.342518	+	0.0730719i
$471$		0			0
$472$	−12.1877	+	8.89671i	−0.560987	+	0.409504i
$473$	9.48375			0.436063
$474$		0			0
$475$			4.34993i			0.199588i
$476$	−16.4091	+	7.33521i	−0.752112	+	0.336209i
$477$		0			0
$478$	1.18907	+	5.57365i	0.0543866	+	0.254933i
$479$	−17.4229			−0.796071			−0.398035	−	0.917370i	$-0.630308\pi$
$479$	−17.4229			−0.796071			−0.398035	+	0.917370i	$0.630308\pi$
$480$		0			0
$481$	−34.4383			−1.57025
$482$	−1.66209	−	7.79091i	−0.0757062	−	0.354866i
$483$		0			0
$484$	−6.38462	+	2.85405i	−0.290210	+	0.129729i
$485$		−	1.73785i		−	0.0789118i
$486$		0			0
$487$	−29.7367			−1.34750			−0.673750	−	0.738959i	$-0.735318\pi$
$487$	−29.7367			−1.34750			−0.673750	+	0.738959i	$0.735318\pi$
$488$	−20.9377	+	15.2839i	−0.947803	+	0.691869i
$489$		0			0
$490$	−4.30468	+	0.918349i	−0.194466	+	0.0414868i
$491$		−	23.8268i		−	1.07529i	−0.843171	−	0.537645i	$-0.819314\pi$
$491$		−	23.8268i		−	1.07529i	0.843171	−	0.537645i	$-0.180686\pi$
$492$		0			0
$493$			18.6043i			0.837895i
$494$	1.56487	+	7.33521i	0.0704070	+	0.330027i
$495$		0			0
$496$	19.7321	−	22.0469i	0.885999	−	0.989933i
$497$	−5.85726			−0.262734
$498$		0			0
$499$			19.4708i			0.871632i	0.900036	+	0.435816i	$0.143540\pi$
$499$			19.4708i			0.871632i	−0.900036	+	0.435816i	$0.856460\pi$
$500$	5.40590	+	12.0932i	0.241759	+	0.540825i
$501$		0			0
$502$	−19.2012	+	4.09633i	−0.856991	+	0.182828i
$503$	1.23494			0.0550631			0.0275316	−	0.999621i	$-0.491235\pi$
$503$	1.23494			0.0550631			0.0275316	+	0.999621i	$0.491235\pi$
$504$		0			0
$505$	6.60772			0.294040
$506$	−24.9179	+	5.31592i	−1.10774	+	0.236322i
$507$		0			0
$508$	3.15428	−	1.41002i	0.139948	−	0.0625596i
$509$		−	0.453647i		−	0.0201075i	−0.999949	−	0.0100538i	$-0.996800\pi$
$509$		−	0.453647i		−	0.0201075i	0.999949	−	0.0100538i	$-0.00320027\pi$
$510$		0			0
$511$	−4.50325			−0.199212
$512$	21.4725	−	7.13674i	0.948958	−	0.315403i
$513$		0			0
$514$	3.20168	+	15.0076i	0.141220	+	0.661957i
$515$			10.2628i			0.452233i
$516$		0			0
$517$			21.1285i			0.929231i
$518$	−13.7574	+	2.93497i	−0.604465	+	0.128955i
$519$		0			0
$520$	6.39037	+	8.75427i	0.280236	+	0.383900i
$521$	−29.0873			−1.27434			−0.637170	−	0.770724i	$-0.719895\pi$
$521$	−29.0873			−1.27434			−0.637170	+	0.770724i	$0.719895\pi$
$522$		0			0
$523$		−	2.95874i		−	0.129377i	−0.997906	−	0.0646883i	$-0.979395\pi$
$523$		−	2.95874i		−	0.129377i	0.997906	−	0.0646883i	$-0.0206053\pi$
$524$	−5.41889	−	12.1223i	−0.236725	−	0.529564i
$525$		0			0
$526$	6.84848	+	32.1017i	0.298608	+	1.39970i
$527$	−41.8053			−1.82107
$528$		0			0
$529$	20.2587			0.880815
$530$	−0.522029	−	2.44697i	−0.0226755	−	0.106289i
$531$		0			0
$532$	1.25027	+	2.79690i	0.0542061	+	0.121261i
$533$		−	10.2608i		−	0.444444i
$534$		0			0
$535$	−5.45272			−0.235741
$536$	15.7163	−	11.4724i	0.678839	−	0.495533i
$537$		0			0
$538$	−5.55955	+	1.18606i	−0.239689	+	0.0511346i
$539$			12.2483i			0.527573i
$540$		0			0
$541$			14.9753i			0.643838i	0.946767	+	0.321919i	$0.104328\pi$
$541$			14.9753i			0.643838i	−0.946767	+	0.321919i	$0.895672\pi$
$542$	−1.99352	−	9.34444i	−0.0856289	−	0.401378i
$543$		0			0
$544$	−27.7473	−	15.8821i	−1.18966	−	0.680937i
$545$	0.168722			0.00722724
$546$		0			0
$547$			18.2132i			0.778741i	0.921081	+	0.389370i	$0.127307\pi$
$547$			18.2132i			0.778741i	−0.921081	+	0.389370i	$0.872693\pi$
$548$	6.62152	−	2.95995i	0.282857	−	0.126443i
$549$		0			0
$550$	17.1074	−	3.64964i	0.729460	−	0.155621i
$551$	3.17106			0.135092
$552$		0			0
$553$	9.15500			0.389310
$554$	2.93211	−	0.625529i	0.124574	−	0.0265762i
$555$		0			0
$556$	−14.1294	−	31.6079i	−0.599219	−	1.34048i
$557$		−	35.7359i		−	1.51418i	−0.653310	−	0.757090i	$-0.726620\pi$
$557$		−	35.7359i		−	1.51418i	0.653310	−	0.757090i	$-0.273380\pi$
$558$		0			0
$559$	19.0609			0.806190
$560$	3.29890	+	2.95254i	0.139404	+	0.124768i
$561$		0			0
$562$	7.70591	+	36.1208i	0.325054	+	1.52366i
$563$			9.28675i			0.391390i	0.980665	+	0.195695i	$0.0626962\pi$
$563$			9.28675i			0.391390i	−0.980665	+	0.195695i	$0.937304\pi$
$564$		0			0
$565$			6.05267i			0.254638i
$566$	26.4114	−	5.63454i	1.11016	−	0.236838i
$567$		0			0
$568$	−6.14274	−	8.41504i	−0.257744	−	0.353087i
$569$	11.3345			0.475168			0.237584	−	0.971367i	$-0.423644\pi$
$569$	11.3345			0.475168			0.237584	+	0.971367i	$0.423644\pi$
$570$		0			0
$571$		−	43.6296i		−	1.82584i	−0.408138	−	0.912920i	$-0.633822\pi$
$571$		−	43.6296i		−	1.82584i	0.408138	−	0.912920i	$-0.366178\pi$
$572$	27.5349	−	12.3086i	1.15129	−	0.514650i
$573$		0			0
$574$	−0.874464	−	4.09898i	−0.0364994	−	0.171088i
$575$	−29.6992			−1.23854
$576$		0			0
$577$	6.98123			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$577$	6.98123			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$578$	4.40893	+	20.6665i	0.183387	+	0.859612i
$579$		0			0
$580$	4.18350	−	1.87011i	0.173710	−	0.0776519i
$581$		−	10.5571i		−	0.437983i
$582$		0			0
$583$	−6.96248			−0.288356
$584$	−4.72274	−	6.46976i	−0.195428	−	0.267721i
$585$		0			0
$586$	8.09892	−	1.72780i	0.334563	−	0.0713749i
$587$			8.48213i			0.350095i	0.984560	+	0.175048i	$0.0560079\pi$
$587$			8.48213i			0.350095i	−0.984560	+	0.175048i	$0.943992\pi$
$588$		0			0
$589$			7.12562i			0.293606i
$590$	−1.09568	−	5.13592i	−0.0451085	−	0.211442i
$591$		0			0
$592$	−18.6445	−	16.6870i	−0.766286	−	0.685833i
$593$	−9.40869			−0.386368			−0.193184	−	0.981163i	$-0.561881\pi$
$593$	−9.40869			−0.386368			−0.193184	+	0.981163i	$0.561881\pi$
$594$		0			0
$595$		−	6.25538i		−	0.256445i
$596$	17.6478	+	39.4788i	0.722881	+	1.61711i
$597$		0			0
$598$	−50.0812	+	10.6842i	−2.04797	+	0.436909i
$599$	29.9247			1.22269			0.611344	−	0.791365i	$-0.290629\pi$
$599$	29.9247			1.22269			0.611344	+	0.791365i	$0.290629\pi$
$600$		0			0
$601$	−3.63946			−0.148456			−0.0742282	−	0.997241i	$-0.523649\pi$
$601$	−3.63946			−0.148456			−0.0742282	+	0.997241i	$0.523649\pi$
$602$	7.61444	−	1.62444i	0.310342	−	0.0662074i
$603$		0			0
$604$	−23.1893	+	10.3661i	−0.943558	+	0.421789i
$605$		−	2.43390i		−	0.0989520i
$606$		0			0
$607$	−7.26716			−0.294965			−0.147482	−	0.989065i	$-0.547117\pi$
$607$	−7.26716			−0.294965			−0.147482	+	0.989065i	$0.547117\pi$
$608$	−2.70706	+	4.72947i	−0.109786	+	0.191805i
$609$		0			0
$610$	−1.88230	−	8.82313i	−0.0762122	−	0.357238i
$611$			42.4651i			1.71795i
$612$		0			0
$613$			32.6469i			1.31859i	0.751882	+	0.659297i	$0.229146\pi$
$613$			32.6469i			1.31859i	−0.751882	+	0.659297i	$0.770854\pi$
$614$	18.9581	−	4.04448i	0.765088	−	0.163222i
$615$		0			0
$616$	9.95065	−	7.26369i	0.400923	−	0.292662i
$617$	−31.3502			−1.26211			−0.631056	−	0.775737i	$-0.717378\pi$
$617$	−31.3502			−1.26211			−0.631056	+	0.775737i	$0.717378\pi$
$618$		0			0
$619$			1.99289i			0.0801010i	0.999198	+	0.0400505i	$0.0127519\pi$
$619$			1.99289i			0.0801010i	−0.999198	+	0.0400505i	$0.987248\pi$
$620$	4.20227	+	9.40065i	0.168767	+	0.377539i
$621$		0			0
$622$	5.65332	+	26.4994i	0.226677	+	1.06253i
$623$	4.74973			0.190294
$624$		0			0
$625$	17.9675			0.718700
$626$	7.44167	+	34.8822i	0.297429	+	1.39417i
$627$		0			0
$628$	14.2581	+	31.8959i	0.568960	+	1.27279i
$629$			35.3538i			1.40965i
$630$		0			0
$631$	−15.4643			−0.615623			−0.307812	−	0.951447i	$-0.599597\pi$
$631$	−15.4643			−0.615623			−0.307812	+	0.951447i	$0.599597\pi$
$632$	9.60121	+	13.1529i	0.381916	+	0.523193i
$633$		0			0
$634$	3.41660	−	0.728887i	0.135690	−	0.0289478i
$635$			1.20245i			0.0477178i
$636$		0			0
$637$			24.6173i			0.975372i
$638$	−2.66056	−	12.4711i	−0.105332	−	0.493737i
$639$		0			0
$640$	−0.782194	+	7.83593i	−0.0309189	+	0.309742i
$641$	24.7275			0.976679			0.488340	−	0.872654i	$-0.337603\pi$
$641$	24.7275			0.976679			0.488340	+	0.872654i	$0.337603\pi$
$642$		0			0
$643$		−	46.2084i		−	1.82228i	−0.412096	−	0.911141i	$-0.635203\pi$
$643$		−	46.2084i		−	1.82228i	0.412096	−	0.911141i	$-0.364797\pi$
$644$	−19.0959	+	8.53624i	−0.752484	+	0.336375i
$645$		0			0
$646$	7.53022	−	1.60648i	0.296272	−	0.0632059i
$647$	−6.36971			−0.250419			−0.125210	−	0.992130i	$-0.539960\pi$
$647$	−6.36971			−0.250419			−0.125210	+	0.992130i	$0.539960\pi$
$648$		0			0
$649$	−14.6135			−0.573630
$650$	34.3832	−	7.33521i	1.34862	−	0.287711i
$651$		0			0
$652$	−6.99279	−	15.6431i	−0.273859	−	0.612633i
$653$			36.8174i			1.44078i	0.693571	+	0.720389i	$0.256037\pi$
$653$			36.8174i			1.44078i	−0.693571	+	0.720389i	$0.743963\pi$
$654$		0			0
$655$	4.62117			0.180564
$656$	4.97185	−	5.55509i	0.194118	−	0.216890i
$657$		0			0
$658$	3.61904	+	16.9639i	0.141085	+	0.661323i
$659$		−	7.46589i		−	0.290830i	−0.989371	−	0.145415i	$-0.953548\pi$
$659$		−	7.46589i		−	0.290830i	0.989371	−	0.145415i	$-0.0464517\pi$
$660$		0			0
$661$			2.90965i			0.113172i	0.998398	+	0.0565862i	$0.0180216\pi$
$661$			2.90965i			0.113172i	−0.998398	+	0.0565862i	$0.981978\pi$
$662$	39.0326	−	8.32711i	1.51705	−	0.323642i
$663$		0			0
$664$	15.1673	−	11.0717i	0.588604	−	0.429664i
$665$	−1.06622			−0.0413461
$666$		0			0
$667$			21.6505i			0.838310i
$668$	−21.8204	+	9.75413i	−0.844255	+	0.377399i
$669$		0			0
$670$	1.41290	+	6.62283i	0.0545850	+	0.255862i
$671$	−25.1049			−0.969165
$672$		0			0
$673$	−42.1054			−1.62304			−0.811522	−	0.584323i	$-0.801360\pi$
$673$	−42.1054			−1.62304			−0.811522	+	0.584323i	$0.801360\pi$
$674$	−3.30806	−	15.5062i	−0.127422	−	0.597278i
$675$		0			0
$676$	31.6046	−	14.1279i	1.21556	−	0.543379i
$677$		−	38.0983i		−	1.46424i	−0.681177	−	0.732119i	$-0.738532\pi$
$677$		−	38.0983i		−	1.46424i	0.681177	−	0.732119i	$-0.261468\pi$
$678$		0			0
$679$	−3.97015			−0.152360
$680$	8.98701	−	6.56026i	0.344636	−	0.251574i
$681$		0			0
$682$	28.0236	−	5.97848i	1.07308	−	0.228928i
$683$		−	47.0728i		−	1.80119i	−0.434659	−	0.900595i	$-0.643131\pi$
$683$		−	47.0728i		−	1.80119i	0.434659	−	0.900595i	$-0.356869\pi$
$684$		0			0
$685$			2.52421i			0.0964450i
$686$	5.38232	+	25.2291i	0.205498	+	0.963253i
$687$		0			0
$688$	10.3194	+	9.23594i	0.393423	+	0.352117i
$689$	−13.9935			−0.533111
$690$		0			0
$691$		−	3.90892i		−	0.148702i	−0.997232	−	0.0743512i	$-0.976311\pi$
$691$		−	3.90892i		−	0.148702i	0.997232	−	0.0743512i	$-0.0236886\pi$
$692$	10.6473	+	23.8185i	0.404750	+	0.905442i
$693$		0			0
$694$	−28.4760	+	6.07498i	−1.08093	+	0.230603i
$695$	12.0494			0.457058
$696$		0			0
$697$	−10.5336			−0.398987
$698$	4.69484	−	1.00158i	0.177702	−	0.0379105i
$699$		0			0
$700$	13.1102	−	5.86054i	0.495521	−	0.221507i
$701$			16.4480i			0.621231i	0.950536	+	0.310615i	$0.100535\pi$
$701$			16.4480i			0.621231i	−0.950536	+	0.310615i	$0.899465\pi$
$702$		0			0
$703$	6.02598			0.227274
$704$	20.8713	+	6.67824i	0.786615	+	0.251695i
$705$		0			0
$706$	0.296977	+	1.39205i	0.0111769	+	0.0523907i
$707$		−	15.0954i		−	0.567722i
$708$		0			0
$709$			7.90745i			0.296971i	0.988915	+	0.148485i	$0.0474398\pi$
$709$			7.90745i			0.296971i	−0.988915	+	0.148485i	$0.952560\pi$
$710$	3.54610	−	0.756515i	0.133083	−	0.0283915i
$711$		0			0
$712$	4.98123	+	6.82387i	0.186679	+	0.255735i
$713$	−48.6503			−1.82197
$714$		0			0
$715$			10.4967i			0.392553i
$716$	−2.70877	−	6.05962i	−0.101231	−	0.226459i
$717$		0			0
$718$	9.28782	+	43.5358i	0.346618	+	1.62474i
$719$	−37.0556			−1.38194			−0.690970	−	0.722884i	$-0.742816\pi$
$719$	−37.0556			−1.38194			−0.690970	+	0.722884i	$0.742816\pi$
$720$		0			0
$721$	23.4455			0.873156
$722$	5.33241	+	24.9952i	0.198452	+	0.930225i
$723$		0			0
$724$	12.1719	+	27.2289i	0.452364	+	1.01196i
$725$		−	14.8641i		−	0.552038i
$726$		0			0
$727$	−5.66934			−0.210264			−0.105132	−	0.994458i	$-0.533527\pi$
$727$	−5.66934			−0.210264			−0.105132	+	0.994458i	$0.533527\pi$
$728$	19.9993	−	14.5989i	0.741222	−	0.541071i
$729$		0			0
$730$	2.72636	−	0.581634i	0.100907	−	0.0215272i
$731$		−	19.5676i		−	0.723735i
$732$		0			0
$733$			12.5335i			0.462937i	0.972842	+	0.231469i	$0.0743530\pi$
$733$			12.5335i			0.462937i	−0.972842	+	0.231469i	$0.925647\pi$
$734$	5.11446	+	23.9736i	0.188778	+	0.884881i
$735$		0			0
$736$	−32.2905	−	18.4825i	−1.19024	−	0.681274i
$737$	18.8443			0.694139
$738$		0			0
$739$			1.83358i			0.0674492i	0.999431	+	0.0337246i	$0.0107369\pi$
$739$			1.83358i			0.0674492i	−0.999431	+	0.0337246i	$0.989263\pi$
$740$	7.94992	−	3.55377i	0.292245	−	0.130639i
$741$		0			0
$742$	−5.59013	+	1.19258i	−0.205220	+	0.0437811i
$743$	31.3177			1.14893			0.574467	−	0.818528i	$-0.305209\pi$
$743$	31.3177			1.14893			0.574467	+	0.818528i	$0.305209\pi$
$744$		0			0
$745$	−15.0498			−0.551382
$746$	−18.0055	+	3.84125i	−0.659230	+	0.140638i
$747$		0			0
$748$	−12.6359	−	28.2669i	−0.462013	−	1.03354i
$749$			12.4568i			0.455162i
$750$		0			0
$751$	−7.28932			−0.265991			−0.132996	−	0.991117i	$-0.542460\pi$
$751$	−7.28932			−0.265991			−0.132996	+	0.991117i	$0.542460\pi$
$752$	−20.5764	+	22.9902i	−0.750344	+	0.838365i
$753$		0			0
$754$	−5.34731	−	25.0651i	−0.194738	−	0.912815i
$755$		−	8.84005i		−	0.321722i
$756$		0			0
$757$			12.8156i			0.465792i	0.972502	+	0.232896i	$0.0748202\pi$
$757$			12.8156i			0.465792i	−0.972502	+	0.232896i	$0.925180\pi$
$758$	31.6233	−	6.74643i	1.14861	−	0.245042i
$759$		0			0
$760$	−1.11818	−	1.53182i	−0.0405607	−	0.0555648i
$761$	−25.1600			−0.912050			−0.456025	−	0.889967i	$-0.650727\pi$
$761$	−25.1600			−0.912050			−0.456025	+	0.889967i	$0.650727\pi$
$762$		0			0
$763$		−	0.385447i		−	0.0139541i
$764$	13.3611	−	5.97269i	0.483389	−	0.216084i
$765$		0			0
$766$	−8.85883	−	41.5250i	−0.320083	−	1.50036i
$767$	−29.3709			−1.06052
$768$		0			0
$769$	21.4636			0.773996			0.386998	−	0.922081i	$-0.373512\pi$
$769$	21.4636			0.773996			0.386998	+	0.922081i	$0.373512\pi$
$770$	0.894567	+	4.19320i	0.0322379	+	0.151113i
$771$		0			0
$772$	−37.3770	+	16.7083i	−1.34523	+	0.601344i
$773$		−	20.2122i		−	0.726981i	−0.931598	−	0.363491i	$-0.881585\pi$
$773$		−	20.2122i		−	0.726981i	0.931598	−	0.363491i	$-0.118415\pi$
$774$		0			0
$775$	33.4007			1.19979
$776$	−4.16365	−	5.70385i	−0.149466	−	0.204756i
$777$		0			0
$778$	−52.6188	+	11.2255i	−1.88647	+	0.402455i
$779$			1.79542i			0.0643277i
$780$		0			0
$781$		−	10.0899i		−	0.361045i
$782$	10.9682	+	51.4127i	0.392223	+	1.83851i
$783$		0			0
$784$	−11.9283	+	13.3276i	−0.426010	+	0.475984i
$785$	−12.1591			−0.433978
$786$		0			0
$787$			20.2911i			0.723299i	0.932314	+	0.361649i	$0.117786\pi$
$787$			20.2911i			0.723299i	−0.932314	+	0.361649i	$0.882214\pi$
$788$	−16.7678	−	37.5102i	−0.597327	−	1.33624i
$789$		0			0
$790$	−5.54262	+	1.18245i	−0.197197	+	0.0420696i
$791$	13.8274			0.491646
$792$		0			0
$793$	−50.4570			−1.79178
$794$	−51.7981	+	11.0505i	−1.83825	+	0.392166i
$795$		0			0
$796$	−3.57136	+	1.59647i	−0.126583	+	0.0565852i
$797$		−	33.3429i		−	1.18107i	−0.807013	−	0.590533i	$-0.798917\pi$
$797$		−	33.3429i		−	1.18107i	0.807013	−	0.590533i	$-0.201083\pi$
$798$		0			0
$799$	43.5940			1.54224
$800$	22.1690	+	12.6891i	0.783792	+	0.448628i
$801$		0			0
$802$	1.38918	+	6.51164i	0.0490535	+	0.229934i
$803$		−	7.75745i		−	0.273754i
$804$		0			0
$805$		−	7.27960i		−	0.256572i
$806$	56.3231	−	12.0158i	1.98390	−	0.423239i
$807$		0			0
$808$	21.6874	−	15.8312i	0.762959	−	0.556939i
$809$	30.6920			1.07907			0.539536	−	0.841962i	$-0.318600\pi$
$809$	30.6920			1.07907			0.539536	+	0.841962i	$0.318600\pi$
$810$		0			0
$811$		−	49.5457i		−	1.73978i	−0.493241	−	0.869892i	$-0.664188\pi$
$811$		−	49.5457i		−	1.73978i	0.493241	−	0.869892i	$-0.335812\pi$
$812$	−4.27229	−	9.55727i	−0.149928	−	0.335394i
$813$		0			0
$814$	−5.05586	−	23.6989i	−0.177208	−	0.830647i
$815$	5.96337			0.208888
$816$		0			0
$817$	−3.33526			−0.116686
$818$	−3.16532	−	14.8372i	−0.110673	−	0.518769i
$819$		0			0
$820$	1.05884	+	2.36865i	0.0369761	+	0.0827170i
$821$			38.0750i			1.32883i	0.747365	+	0.664414i	$0.231319\pi$
$821$			38.0750i			1.32883i	−0.747365	+	0.664414i	$0.768681\pi$
$822$		0			0
$823$	−22.5252			−0.785178			−0.392589	−	0.919714i	$-0.628421\pi$
$823$	−22.5252			−0.785178			−0.392589	+	0.919714i	$0.628421\pi$
$824$	24.5882	+	33.6838i	0.856571	+	1.17343i
$825$		0			0
$826$	−11.7331	+	2.50310i	−0.408246	+	0.0870941i
$827$			33.5317i			1.16601i	0.812468	+	0.583006i	$0.198124\pi$
$827$			33.5317i			1.16601i	−0.812468	+	0.583006i	$0.801876\pi$
$828$		0			0
$829$		−	37.7559i		−	1.31132i	−0.755058	−	0.655658i	$-0.772391\pi$
$829$		−	37.7559i		−	1.31132i	0.755058	−	0.655658i	$-0.227609\pi$
$830$	1.36354	+	6.39149i	0.0473293	+	0.221852i
$831$		0			0
$832$	41.9480	+	13.4222i	1.45429	+	0.465332i
$833$	25.2717			0.875614
$834$		0			0
$835$		−	8.31821i		−	0.287863i
$836$	−4.81804	+	2.15376i	−0.166635	+	0.0744892i
$837$		0			0
$838$	5.71107	−	1.21838i	0.197286	−	0.0420884i
$839$	19.8121			0.683989			0.341994	−	0.939702i	$-0.388898\pi$
$839$	19.8121			0.683989			0.341994	+	0.939702i	$0.388898\pi$
$840$		0			0
$841$	18.1642			0.626352
$842$	−21.9309	+	4.67868i	−0.755790	+	0.161238i
$843$		0			0
$844$	8.58570	+	19.2065i	0.295532	+	0.661117i
$845$			12.0481i			0.414466i
$846$		0			0
$847$	−5.56028			−0.191053
$848$	−7.57595	−	6.78055i	−0.260159	−	0.232845i
$849$		0			0
$850$	−7.53022	−	35.2972i	−0.258284	−	1.21069i
$851$			41.1425i			1.41035i
$852$		0			0
$853$			6.87537i			0.235408i	0.993049	+	0.117704i	$0.0375534\pi$
$853$			6.87537i			0.235408i	−0.993049	+	0.117704i	$0.962447\pi$
$854$	−20.1566	+	4.30015i	−0.689744	+	0.147148i
$855$		0			0
$856$	−17.8965	+	13.0639i	−0.611690	+	0.446516i
$857$	7.74632			0.264609			0.132305	−	0.991209i	$-0.457762\pi$
$857$	7.74632			0.264609			0.132305	+	0.991209i	$0.457762\pi$
$858$		0			0
$859$			0.686576i			0.0234257i	0.999931	+	0.0117128i	$0.00372839\pi$
$859$			0.686576i			0.0234257i	−0.999931	+	0.0117128i	$0.996272\pi$
$860$	−4.40012	+	1.96694i	−0.150043	+	0.0670721i
$861$		0			0
$862$	4.77571	+	22.3857i	0.162661	+	0.762461i
$863$	−42.9194			−1.46099			−0.730496	−	0.682917i	$-0.760711\pi$
$863$	−42.9194			−1.46099			−0.730496	+	0.682917i	$0.760711\pi$
$864$		0			0
$865$	−9.07991			−0.308726
$866$	−9.68713	−	45.4076i	−0.329182	−	1.54301i
$867$		0			0
$868$	21.4759	−	9.60016i	0.728940	−	0.325851i
$869$			15.7707i			0.534984i
$870$		0			0
$871$	37.8742			1.28332
$872$	0.553766	−	0.404233i	0.0187529	−	0.0136891i
$873$		0			0
$874$	8.76318	−	1.86951i	0.296419	−	0.0632372i
$875$			10.5318i			0.356040i
$876$		0			0
$877$			17.0328i			0.575157i	0.957757	+	0.287578i	$0.0928501\pi$
$877$			17.0328i			0.575157i	−0.957757	+	0.287578i	$0.907150\pi$
$878$	−6.44853	−	30.2269i	−0.217627	−	1.02011i
$879$		0			0
$880$	−5.08615	+	5.68279i	−0.171454	+	0.191567i
$881$	−7.90546			−0.266342			−0.133171	−	0.991093i	$-0.542516\pi$
$881$	−7.90546			−0.266342			−0.133171	+	0.991093i	$0.542516\pi$
$882$		0			0
$883$		−	7.53298i		−	0.253505i	−0.991934	−	0.126752i	$-0.959545\pi$
$883$		−	7.53298i		−	0.253505i	0.991934	−	0.126752i	$-0.0404554\pi$
$884$	−25.3962	−	56.8122i	−0.854165	−	1.91080i
$885$		0			0
$886$	48.6302	−	10.3746i	1.63376	−	0.348543i
$887$	−14.0544			−0.471900			−0.235950	−	0.971765i	$-0.575820\pi$
$887$	−14.0544			−0.471900			−0.235950	+	0.971765i	$0.575820\pi$
$888$		0			0
$889$	2.74702			0.0921320
$890$	−2.87558	+	0.613468i	−0.0963896	+	0.0205635i
$891$		0			0
$892$	7.05260	−	3.15265i	0.236138	−	0.105558i
$893$		−	7.43051i		−	0.248652i
$894$		0			0
$895$	2.31001			0.0772150
$896$	17.9013	+	1.78693i	0.598040	+	0.0596973i
$897$		0			0
$898$	0.949667	+	4.45148i	0.0316908	+	0.148548i
$899$		−	24.3489i		−	0.812081i
$900$		0			0
$901$			14.3655i			0.478585i
$902$	7.06103	−	1.50638i	0.235106	−	0.0501570i
$903$		0			0
$904$	14.5013	+	19.8656i	0.482307	+	0.660721i
$905$	−10.3800			−0.345043
$906$		0			0
$907$		−	45.9522i		−	1.52582i	−0.646505	−	0.762910i	$-0.723770\pi$
$907$		−	45.9522i		−	1.52582i	0.646505	−	0.762910i	$-0.276230\pi$
$908$	13.1176	+	29.3445i	0.435322	+	0.973831i
$909$		0			0
$910$	1.79794	+	8.42770i	0.0596012	+	0.279375i
$911$	−51.5822			−1.70899			−0.854497	−	0.519456i	$-0.826135\pi$
$911$	−51.5822			−1.70899			−0.854497	+	0.519456i	$0.826135\pi$
$912$		0			0
$913$	18.1860			0.601870
$914$	−2.39305	−	11.2172i	−0.0791549	−	0.371032i
$915$		0			0
$916$	−7.03382	−	15.7349i	−0.232404	−	0.519897i
$917$		−	10.5571i		−	0.348627i
$918$		0			0
$919$	−21.2048			−0.699481			−0.349741	−	0.936847i	$-0.613730\pi$
$919$	−21.2048			−0.699481			−0.349741	+	0.936847i	$0.613730\pi$
$920$	10.4585	−	7.63440i	0.344806	−	0.251699i
$921$		0			0
$922$	29.0366	−	6.19458i	0.956269	−	0.204008i
$923$		−	20.2792i		−	0.667497i
$924$		0			0
$925$		−	28.2463i		−	0.928732i
$926$	2.62611	+	12.3096i	0.0862992	+	0.404520i
$927$		0			0
$928$	9.25027	−	16.1610i	0.303655	−	0.530511i
$929$	−3.41033			−0.111889			−0.0559446	−	0.998434i	$-0.517817\pi$
$929$	−3.41033			−0.111889			−0.0559446	+	0.998434i	$0.517817\pi$
$930$		0			0
$931$		−	4.30751i		−	0.141173i
$932$	−44.1013	+	19.7142i	−1.44459	+	0.645759i
$933$		0			0
$934$	36.0332	−	7.68722i	1.17904	−	0.251534i
$935$	10.7757			0.352403
$936$		0			0
$937$	29.4448			0.961919			0.480959	−	0.876743i	$-0.340288\pi$
$937$	29.4448			0.961919			0.480959	+	0.876743i	$0.340288\pi$
$938$	15.1300	−	3.22778i	0.494011	−	0.105391i
$939$		0			0
$940$	−4.38207	−	9.80287i	−0.142927	−	0.319734i
$941$		−	46.8670i		−	1.52782i	−0.645323	−	0.763910i	$-0.723277\pi$
$941$		−	46.8670i		−	1.52782i	0.645323	−	0.763910i	$-0.276723\pi$
$942$		0			0
$943$	−12.2583			−0.399185
$944$	−15.9011	−	14.2316i	−0.517537	−	0.463201i
$945$		0			0
$946$	2.79832	+	13.1169i	0.0909812	+	0.426467i
$947$			36.4679i			1.18505i	0.805553	+	0.592524i	$0.201869\pi$
$947$			36.4679i			1.18505i	−0.805553	+	0.592524i	$0.798131\pi$
$948$		0			0
$949$		−	15.5913i		−	0.506115i
$950$	−6.01634	+	1.28351i	−0.195196	+	0.0416425i
$951$		0			0
$952$	−14.9870	−	20.5310i	−0.485732	−	0.665412i
$953$	38.0590			1.23285			0.616426	−	0.787413i	$-0.288580\pi$
$953$	38.0590			1.23285			0.616426	+	0.787413i	$0.288580\pi$
$954$		0			0
$955$			5.09344i			0.164820i
$956$	−7.35800	+	3.28917i	−0.237975	+	0.106379i
$957$		0			0
$958$	−5.14087	−	24.0974i	−0.166094	−	0.778551i
$959$	5.76659			0.186213
$960$		0			0
$961$	23.7138			0.764962
$962$	−10.1615	−	47.6312i	−0.327620	−	1.53569i
$963$		0			0
$964$	10.2851	−	4.59764i	0.331261	−	0.148080i
$965$		−	14.2486i		−	0.458679i
$966$		0			0
$967$	−22.9728			−0.738756			−0.369378	−	0.929279i	$-0.620429\pi$
$967$	−22.9728			−0.738756			−0.369378	+	0.929279i	$0.620429\pi$
$968$	−5.83128	−	7.98837i	−0.187424	−	0.256756i
$969$		0			0
$970$	2.40360	−	0.512778i	0.0771751	−	0.0164643i
$971$		−	53.8829i		−	1.72919i	−0.502474	−	0.864593i	$-0.667577\pi$
$971$		−	53.8829i		−	1.72919i	0.502474	−	0.864593i	$-0.332423\pi$
$972$		0			0
$973$		−	27.5269i		−	0.882473i
$974$	−8.77426	−	41.1286i	−0.281145	−	1.31784i
$975$		0			0
$976$	−27.3169	−	24.4489i	−0.874394	−	0.782591i
$977$	−38.2048			−1.22228			−0.611140	−	0.791523i	$-0.709289\pi$
$977$	−38.2048			−1.22228			−0.611140	+	0.791523i	$0.709289\pi$
$978$		0			0
$979$			8.18203i			0.261499i
$980$	−2.54032	−	5.68279i	−0.0811475	−	0.181530i
$981$		0			0
$982$	32.9547	−	7.03045i	1.05163	−	0.224351i
$983$	48.6614			1.55206			0.776028	−	0.630698i	$-0.217231\pi$
$983$	48.6614			1.55206			0.776028	+	0.630698i	$0.217231\pi$
$984$		0			0
$985$	14.2994			0.455615
$986$	−25.7314	+	5.48947i	−0.819455	+	0.174820i
$987$		0			0
$988$	−9.68351	+	4.32872i	−0.308074	+	0.137715i
$989$		−	22.7715i		−	0.724093i
$990$		0			0
$991$	−12.7822			−0.406040			−0.203020	−	0.979175i	$-0.565076\pi$
$991$	−12.7822			−0.406040			−0.203020	+	0.979175i	$0.565076\pi$
$992$	36.3150	+	20.7861i	1.15300	+	0.659958i
$993$		0			0
$994$	−1.72827	−	8.10112i	−0.0548174	−	0.256952i
$995$		−	1.36145i		−	0.0431608i
$996$		0			0
$997$		−	24.3827i		−	0.772209i	−0.922455	−	0.386104i	$-0.873820\pi$
$997$		−	24.3827i		−	0.772209i	0.922455	−	0.386104i	$-0.126180\pi$
$998$	−26.9299	+	5.74514i	−0.852450	+	0.181859i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.d.j.325.6		8
3.2	odd	2		648.2.d.k.325.3		8
4.3	odd	2		2592.2.d.j.1297.4		8
8.3	odd	2		2592.2.d.j.1297.5		8
8.5	even	2	inner	648.2.d.j.325.5		8
9.2	odd	6		216.2.n.b.37.2		16
9.4	even	3		72.2.n.b.61.1	yes	16
9.5	odd	6		216.2.n.b.181.8		16
9.7	even	3		72.2.n.b.13.7	yes	16
12.11	even	2		2592.2.d.k.1297.5		8
24.5	odd	2		648.2.d.k.325.4		8
24.11	even	2		2592.2.d.k.1297.4		8
36.7	odd	6		288.2.r.b.49.7		16
36.11	even	6		864.2.r.b.145.4		16
36.23	even	6		864.2.r.b.721.5		16
36.31	odd	6		288.2.r.b.241.2		16
72.5	odd	6		216.2.n.b.181.2		16
72.11	even	6		864.2.r.b.145.5		16
72.13	even	6		72.2.n.b.61.7	yes	16
72.29	odd	6		216.2.n.b.37.8		16
72.43	odd	6		288.2.r.b.49.2		16
72.59	even	6		864.2.r.b.721.4		16
72.61	even	6		72.2.n.b.13.1	✓	16
72.67	odd	6		288.2.r.b.241.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.1	✓	16	72.61	even	6
72.2.n.b.13.7	yes	16	9.7	even	3
72.2.n.b.61.1	yes	16	9.4	even	3
72.2.n.b.61.7	yes	16	72.13	even	6
216.2.n.b.37.2		16	9.2	odd	6
216.2.n.b.37.8		16	72.29	odd	6
216.2.n.b.181.2		16	72.5	odd	6
216.2.n.b.181.8		16	9.5	odd	6
288.2.r.b.49.2		16	72.43	odd	6
288.2.r.b.49.7		16	36.7	odd	6
288.2.r.b.241.2		16	36.31	odd	6
288.2.r.b.241.7		16	72.67	odd	6
648.2.d.j.325.5		8	8.5	even	2	inner
648.2.d.j.325.6		8	1.1	even	1	trivial
648.2.d.k.325.3		8	3.2	odd	2
648.2.d.k.325.4		8	24.5	odd	2
864.2.r.b.145.4		16	36.11	even	6
864.2.r.b.145.5		16	72.11	even	6
864.2.r.b.721.4		16	72.59	even	6
864.2.r.b.721.5		16	36.23	even	6
2592.2.d.j.1297.4		8	4.3	odd	2
2592.2.d.j.1297.5		8	8.3	odd	2
2592.2.d.k.1297.4		8	24.11	even	2
2592.2.d.k.1297.5		8	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.295065 + 1.38309i) q^{2} +(-1.82587 + 0.816201i) q^{4} -0.696047i q^{5} -1.59013 q^{7} +(-1.66763 - 2.28452i) q^{8} +(0.962695 - 0.205379i) q^{10} -2.73921i q^{11} -5.50539i q^{13} +(-0.469191 - 2.19929i) q^{14} +(2.66763 - 2.98056i) q^{16} -5.65175 q^{17} +0.963328i q^{19} +(0.568114 + 1.27089i) q^{20} +(3.78857 - 0.808243i) q^{22} -6.57714 q^{23} +4.51552 q^{25} +(7.61444 - 1.62444i) q^{26} +(2.90338 - 1.29787i) q^{28} -3.29178i q^{29} +7.39688 q^{31} +(4.90951 + 2.81011i) q^{32} +(-1.66763 - 7.81687i) q^{34} +1.10680i q^{35} -6.25538i q^{37} +(-1.33237 + 0.284244i) q^{38} +(-1.59013 + 1.16075i) q^{40} +1.86377 q^{41} +3.46223i q^{43} +(2.23574 + 5.00145i) q^{44} +(-1.94068 - 9.09677i) q^{46} -7.71337 q^{47} -4.47149 q^{49} +(1.33237 + 6.24537i) q^{50} +(4.49350 + 10.0521i) q^{52} -2.54179i q^{53} -1.90662 q^{55} +(2.65175 + 3.63267i) q^{56} +(4.55282 - 0.971287i) q^{58} -5.33494i q^{59} -9.16503i q^{61} +(2.18256 + 10.2305i) q^{62} +(-2.43802 + 7.61945i) q^{64} -3.83201 q^{65} +6.87947i q^{67} +(10.3194 - 4.61296i) q^{68} +(-1.53081 + 0.326579i) q^{70} +3.68351 q^{71} +2.83201 q^{73} +(8.65175 - 1.84574i) q^{74} +(-0.786270 - 1.75892i) q^{76} +4.35569i q^{77} -5.75740 q^{79} +(-2.07461 - 1.85680i) q^{80} +(0.549933 + 2.57776i) q^{82} +6.63916i q^{83} +3.93388i q^{85} +(-4.78857 + 1.02158i) q^{86} +(-6.25776 + 4.56798i) q^{88} -2.98701 q^{89} +8.75427i q^{91} +(12.0090 - 5.36827i) q^{92} +(-2.27594 - 10.6683i) q^{94} +0.670522 q^{95} +2.49675 q^{97} +(-1.31938 - 6.18447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{4} - 6 q^{7} - q^{8} - 8 q^{10} - 16 q^{14} + 9 q^{16} - 14 q^{17} + 8 q^{20} - q^{22} + 10 q^{23} - 2 q^{25} + 14 q^{26} + 2 q^{28} + 10 q^{31} - 11 q^{32} - q^{34} - 23 q^{38} - 6 q^{40}+ \cdots + 33 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^4 - 6 * q^7 - q^8 - 8 * q^10 - 16 * q^14 + 9 * q^16 - 14 * q^17 + 8 * q^20 - q^22 + 10 * q^23 - 2 * q^25 + 14 * q^26 + 2 * q^28 + 10 * q^31 - 11 * q^32 - q^34 - 23 * q^38 - 6 * q^40 + 8 * q^41 + 9 * q^44 - 10 * q^46 - 6 * q^47 - 18 * q^49 + 23 * q^50 + 8 * q^52 - 2 * q^55 - 10 * q^56 + 14 * q^58 - 26 * q^62 + 13 * q^64 + 14 * q^65 + 39 * q^68 + 36 * q^71 - 22 * q^73 + 38 * q^74 - 5 * q^76 + 30 * q^79 - 48 * q^80 + 19 * q^82 - 7 * q^86 - 31 * q^88 + 32 * q^89 + 30 * q^92 + 12 * q^94 - 44 * q^95 + 33 * q^98

Introduction

L-functions

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