LMFDB - Embedded newform 1323.2.o.e.440.11

Newspace parameters

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

Newform invariants

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			440.11
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.11

$q$-expansion

$f(q)$	$=$	$q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +O(q^{10})$	\(q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +0.0647728i q^{10} +(3.64120 + 2.10225i) q^{11} +(1.74714 - 1.00871i) q^{13} +(-1.95521 + 3.38652i) q^{16} +4.38762 q^{17} -5.24685i q^{19} +(-0.525467 + 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(-5.43444 + 3.13757i) q^{23} +(2.35985 - 4.08738i) q^{25} -0.246821 q^{26} +(7.27689 + 4.20131i) q^{29} +(-1.03204 + 0.595849i) q^{31} +(1.25878 - 0.726755i) q^{32} +(-0.464883 - 0.268400i) q^{34} -3.23252 q^{37} +(-0.320962 + 0.555922i) q^{38} +(0.223540 - 0.129061i) q^{40} +(-0.0994958 - 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} -8.34605i q^{44} +0.767730 q^{46} +(4.98595 - 8.63591i) q^{47} +(-0.500069 + 0.288715i) q^{50} +(-3.46814 - 2.00233i) q^{52} +4.21753i q^{53} -2.22598i q^{55} +(-0.514008 - 0.890287i) q^{58} +(-6.71960 - 11.6387i) q^{59} +(-11.3564 - 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(-0.924990 - 0.534043i) q^{65} +(3.29001 + 5.69847i) q^{67} +(-4.35478 - 7.54270i) q^{68} -8.50587i q^{71} -5.61202i q^{73} +(0.342497 + 0.197741i) q^{74} +(-9.01980 + 5.20758i) q^{76} +(-0.286342 + 0.495959i) q^{79} +2.07029 q^{80} +0.0243455i q^{82} +(5.42692 - 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(-0.839806 + 0.484862i) q^{86} +(-1.02494 + 1.77525i) q^{88} +12.8738 q^{89} +(10.7875 + 6.22819i) q^{92} +(-1.05656 + 0.610003i) q^{94} +(-2.40568 + 1.38892i) q^{95} +(-0.493773 - 0.285080i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48q + 24q^{4} + O(q^{10}) $	$ 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.105953	−	0.0611722i	−0.0749204	−	0.0432553i	0.462072	−	0.886842i	$-0.347106\pi$
$2$	−0.105953	−	0.0611722i	−0.0749204	−	0.0432553i	−0.536992	+	0.843587i	$0.680440\pi$
$3$		0			0
$3$		0			0
$4$	−0.992516	−	1.71909i	−0.496258	−	0.859544i
$5$	−0.264715	−	0.458500i	−0.118384	−	0.205047i	0.800743	−	0.599008i	$-0.204438\pi$
$5$	−0.264715	−	0.458500i	−0.118384	−	0.205047i	−0.919127	+	0.393960i	$0.871105\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.487547i			0.172374i
$9$		0			0
$10$			0.0647728i			0.0204830i
$11$	3.64120	+	2.10225i	1.09786	+	0.633851i	0.935659	−	0.352906i	$-0.114807\pi$
$11$	3.64120	+	2.10225i	1.09786	+	0.633851i	0.162204	+	0.986757i	$0.448140\pi$
$12$		0			0
$13$	1.74714	−	1.00871i	0.484570	−	0.279767i	−0.237749	−	0.971327i	$-0.576410\pi$
$13$	1.74714	−	1.00871i	0.484570	−	0.279767i	0.722319	+	0.691560i	$0.243076\pi$
$14$		0			0
$15$		0			0
$16$	−1.95521	+	3.38652i	−0.488802	+	0.846630i
$17$	4.38762			1.06415			0.532077	−	0.846696i	$-0.321412\pi$
$17$	4.38762			1.06415			0.532077	+	0.846696i	$0.321412\pi$
$18$		0			0
$19$		−	5.24685i		−	1.20371i	−0.798605	−	0.601855i	$-0.794428\pi$
$19$		−	5.24685i		−	1.20371i	0.798605	−	0.601855i	$-0.205572\pi$
$20$	−0.525467	+	0.910136i	−0.117498	+	0.203513i
$21$		0			0
$22$	−0.257198	−	0.445480i	−0.0548348	−	0.0949767i
$23$	−5.43444	+	3.13757i	−1.13316	+	0.654230i	−0.944727	−	0.327857i	$-0.893674\pi$
$23$	−5.43444	+	3.13757i	−1.13316	+	0.654230i	−0.188431	+	0.982086i	$0.560340\pi$
$24$		0			0
$25$	2.35985	−	4.08738i	0.471970	−	0.817477i
$26$	−0.246821			−0.0484056
$27$		0			0
$28$		0			0
$29$	7.27689	+	4.20131i	1.35128	+	0.780164i	0.988429	−	0.151681i	$-0.0484687\pi$
$29$	7.27689	+	4.20131i	1.35128	+	0.780164i	0.362855	+	0.931846i	$0.381802\pi$
$30$		0			0
$31$	−1.03204	+	0.595849i	−0.185360	+	0.107018i	−0.589809	−	0.807543i	$-0.700797\pi$
$31$	−1.03204	+	0.595849i	−0.185360	+	0.107018i	0.404449	+	0.914561i	$0.367463\pi$
$32$	1.25878	−	0.726755i	0.222522	−	0.128473i
$33$		0			0
$34$	−0.464883	−	0.268400i	−0.0797268	−	0.0460303i
$35$		0			0
$36$		0			0
$37$	−3.23252			−0.531424			−0.265712	−	0.964053i	$-0.585607\pi$
$37$	−3.23252			−0.531424			−0.265712	+	0.964053i	$0.585607\pi$
$38$	−0.320962	+	0.555922i	−0.0520668	+	0.0901824i
$39$		0			0
$40$	0.223540	−	0.129061i	0.0353448	−	0.0204063i
$41$	−0.0994958	−	0.172332i	−0.0155386	−	0.0269137i	0.858152	−	0.513396i	$-0.171613\pi$
$41$	−0.0994958	−	0.172332i	−0.0155386	−	0.0269137i	−0.873690	+	0.486483i	$0.838280\pi$
$42$		0			0
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	−0.387786	−	0.921750i	$-0.626760\pi$
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	0.992151	−	0.125042i	$-0.0399067\pi$
$44$		−	8.34605i		−	1.25821i
$45$		0			0
$46$	0.767730			0.113196
$47$	4.98595	−	8.63591i	0.727275	−	1.25968i	−0.230756	−	0.973012i	$-0.574120\pi$
$47$	4.98595	−	8.63591i	0.727275	−	1.25968i	0.958031	−	0.286665i	$-0.0925468\pi$
$48$		0			0
$49$		0			0
$50$	−0.500069	+	0.288715i	−0.0707204	+	0.0408304i
$51$		0			0
$52$	−3.46814	−	2.00233i	−0.480944	−	0.277673i
$53$			4.21753i			0.579323i	0.957129	+	0.289661i	$0.0935427\pi$
$53$			4.21753i			0.579323i	−0.957129	+	0.289661i	$0.906457\pi$
$54$		0			0
$55$		−	2.22598i		−	0.300152i
$56$		0			0
$57$		0			0
$58$	−0.514008	−	0.890287i	−0.0674925	−	0.116900i
$59$	−6.71960	−	11.6387i	−0.874817	−	1.51523i	−0.856958	−	0.515387i	$-0.827648\pi$
$59$	−6.71960	−	11.6387i	−0.874817	−	1.51523i	−0.0178590	−	0.999841i	$-0.505685\pi$
$60$		0			0
$61$	−11.3564	−	6.55662i	−1.45404	−	0.839489i	−0.455330	−	0.890323i	$-0.650479\pi$
$61$	−11.3564	−	6.55662i	−1.45404	−	0.839489i	−0.998707	+	0.0508335i	$0.983812\pi$
$62$	0.145798			0.0185163
$63$		0			0
$64$	7.64300			0.955375
$65$	−0.924990	−	0.534043i	−0.114731	−	0.0662399i
$66$		0			0
$67$	3.29001	+	5.69847i	0.401939	+	0.696179i	0.993960	−	0.109744i	$-0.0350030\pi$
$67$	3.29001	+	5.69847i	0.401939	+	0.696179i	−0.592021	+	0.805923i	$0.701670\pi$
$68$	−4.35478	−	7.54270i	−0.528095	−	0.914687i
$69$		0			0
$70$		0			0
$71$		−	8.50587i		−	1.00946i	−0.863277	−	0.504730i	$-0.831592\pi$
$71$		−	8.50587i		−	1.00946i	0.863277	−	0.504730i	$-0.168408\pi$
$72$		0			0
$73$		−	5.61202i		−	0.656837i	−0.944532	−	0.328419i	$-0.893484\pi$
$73$		−	5.61202i		−	0.656837i	0.944532	−	0.328419i	$-0.106516\pi$
$74$	0.342497	+	0.197741i	0.0398145	+	0.0229869i
$75$		0			0
$76$	−9.01980	+	5.20758i	−1.03464	+	0.597351i
$77$		0			0
$78$		0			0
$79$	−0.286342	+	0.495959i	−0.0322160	+	0.0557997i	−0.881684	−	0.471841i	$-0.843590\pi$
$79$	−0.286342	+	0.495959i	−0.0322160	+	0.0557997i	0.849468	+	0.527640i	$0.176923\pi$
$80$	2.07029			0.231465
$81$		0			0
$82$			0.0243455i			0.00268851i
$83$	5.42692	−	9.39971i	0.595682	−	1.03175i	−0.397768	−	0.917486i	$-0.630215\pi$
$83$	5.42692	−	9.39971i	0.595682	−	1.03175i	0.993450	−	0.114266i	$-0.0364516\pi$
$84$		0			0
$85$	−1.16147	−	2.01172i	−0.125979	−	0.218202i
$86$	−0.839806	+	0.484862i	−0.0905586	+	0.0522840i
$87$		0			0
$88$	−1.02494	+	1.77525i	−0.109259	+	0.189243i
$89$	12.8738			1.36461			0.682307	−	0.731065i	$-0.260977\pi$
$89$	12.8738			1.36461			0.682307	+	0.731065i	$0.260977\pi$
$90$		0			0
$91$		0			0
$92$	10.7875	+	6.22819i	1.12468	+	0.649333i
$93$		0			0
$94$	−1.05656	+	0.610003i	−0.108975	+	0.0629170i
$95$	−2.40568	+	1.38892i	−0.246817	+	0.142500i
$96$		0			0
$97$	−0.493773	−	0.285080i	−0.0501351	−	0.0289455i	0.474723	−	0.880135i	$-0.342548\pi$
$97$	−0.493773	−	0.285080i	−0.0501351	−	0.0289455i	−0.524858	+	0.851190i	$0.675882\pi$
$98$		0			0
$99$		0			0
$100$	−9.36876			−0.936876
$101$	−5.81552	+	10.0728i	−0.578666	+	1.00228i	0.416966	+	0.908922i	$0.363093\pi$
$101$	−5.81552	+	10.0728i	−0.578666	+	1.00228i	−0.995633	+	0.0933576i	$0.970240\pi$
$102$		0			0
$103$	−5.54001	+	3.19853i	−0.545874	+	0.315160i	−0.747456	−	0.664311i	$-0.768725\pi$
$103$	−5.54001	+	3.19853i	−0.545874	+	0.315160i	0.201582	+	0.979472i	$0.435392\pi$
$104$	0.491795	+	0.851814i	0.0482245	+	0.0835272i
$105$		0			0
$106$	0.257996	−	0.446862i	0.0250588	−	0.0434031i
$107$		−	0.253263i		−	0.0244839i	−0.999925	−	0.0122419i	$-0.996103\pi$
$107$		−	0.253263i		−	0.0244839i	0.999925	−	0.0122419i	$-0.00389683\pi$
$108$		0			0
$109$	11.9720			1.14671			0.573357	−	0.819306i	$-0.305641\pi$
$109$	11.9720			1.14671			0.573357	+	0.819306i	$0.305641\pi$
$110$	−0.136168	+	0.235851i	−0.0129831	+	0.0224875i
$111$		0			0
$112$		0			0
$113$	−4.28636	+	2.47473i	−0.403227	+	0.232803i	−0.687875	−	0.725829i	$-0.741456\pi$
$113$	−4.28636	+	2.47473i	−0.403227	+	0.232803i	0.284648	+	0.958632i	$0.408123\pi$
$114$		0			0
$115$	2.87715	+	1.66113i	0.268296	+	0.154901i
$116$		−	16.6795i		−	1.54865i
$117$		0			0
$118$			1.64421i			0.151362i
$119$		0			0
$120$		0			0
$121$	3.33888	+	5.78311i	0.303535	+	0.525737i
$122$	0.802166	+	1.38939i	0.0726247	+	0.125790i
$123$		0			0
$124$	2.04863	+	1.18278i	0.183973	+	0.106217i
$125$	−5.14590			−0.460263
$126$		0			0
$127$	−3.68446			−0.326943			−0.163472	−	0.986548i	$-0.552269\pi$
$127$	−3.68446			−0.326943			−0.163472	+	0.986548i	$0.552269\pi$
$128$	−3.32736	−	1.92105i	−0.294100	−	0.169798i
$129$		0			0
$130$	0.0653372	+	0.113167i	0.00573045	+	0.00992543i
$131$	−2.72837	−	4.72567i	−0.238379	−	0.412884i	0.721871	−	0.692028i	$-0.243283\pi$
$131$	−2.72837	−	4.72567i	−0.238379	−	0.412884i	−0.960249	+	0.279144i	$0.909949\pi$
$132$		0			0
$133$		0			0
$134$		−	0.805030i		−	0.0695440i
$135$		0			0
$136$			2.13917i			0.183432i
$137$	1.39996	+	0.808270i	0.119607	+	0.0690551i	0.558610	−	0.829431i	$-0.311335\pi$
$137$	1.39996	+	0.808270i	0.119607	+	0.0690551i	−0.439003	+	0.898486i	$0.644668\pi$
$138$		0			0
$139$	9.79085	−	5.65275i	0.830449	−	0.479460i	−0.0235572	−	0.999722i	$-0.507499\pi$
$139$	9.79085	−	5.65275i	0.830449	−	0.479460i	0.854006	+	0.520262i	$0.174166\pi$
$140$		0			0
$141$		0			0
$142$	−0.520323	+	0.901226i	−0.0436645	+	0.0756292i
$143$	8.48226			0.709322
$144$		0			0
$145$		−	4.44860i		−	0.369436i
$146$	−0.343300	+	0.594613i	−0.0284117	+	0.0492105i
$147$		0			0
$148$	3.20833	+	5.55699i	0.263723	+	0.456782i
$149$	−4.61426	+	2.66404i	−0.378015	+	0.218247i	−0.676954	−	0.736025i	$-0.736700\pi$
$149$	−4.61426	+	2.66404i	−0.378015	+	0.218247i	0.298939	+	0.954272i	$0.403367\pi$
$150$		0			0
$151$	1.32132	−	2.28859i	0.107527	−	0.186243i	−0.807241	−	0.590222i	$-0.799040\pi$
$151$	1.32132	−	2.28859i	0.107527	−	0.186243i	0.914768	+	0.403980i	$0.132373\pi$
$152$	2.55808			0.207488
$153$		0			0
$154$		0			0
$155$	0.546393	+	0.315460i	0.0438873	+	0.0253384i
$156$		0			0
$157$	11.3181	−	6.53448i	0.903279	−	0.521508i	0.0250163	−	0.999687i	$-0.492036\pi$
$157$	11.3181	−	6.53448i	0.903279	−	0.521508i	0.878263	+	0.478179i	$0.158703\pi$
$158$	0.0606778	−	0.0350324i	0.00482727	−	0.00278703i
$159$		0			0
$160$	−0.666434	−	0.384766i	−0.0526862	−	0.0304184i
$161$		0			0
$162$		0			0
$163$	17.0269			1.33365			0.666825	−	0.745214i	$-0.267653\pi$
$163$	17.0269			1.33365			0.666825	+	0.745214i	$0.267653\pi$
$164$	−0.197502	+	0.342084i	−0.0154223	+	0.0267123i
$165$		0			0
$166$	−1.15000	+	0.663954i	−0.0892575	+	0.0515328i
$167$	10.6605	+	18.4645i	0.824932	+	1.42882i	0.901971	+	0.431796i	$0.142120\pi$
$167$	10.6605	+	18.4645i	0.824932	+	1.42882i	−0.0770396	+	0.997028i	$0.524547\pi$
$168$		0			0
$169$	−4.46499	+	7.73360i	−0.343461	+	0.594892i
$170$			0.284198i			0.0217970i
$171$		0			0
$172$	−15.7337			−1.19968
$173$	−10.2433	+	17.7418i	−0.778781	+	1.34889i	0.153864	+	0.988092i	$0.450828\pi$
$173$	−10.2433	+	17.7418i	−0.778781	+	1.34889i	−0.932645	+	0.360796i	$0.882505\pi$
$174$		0			0
$175$		0			0
$176$	−14.2386	+	8.22066i	−1.07327	+	0.619655i
$177$		0			0
$178$	−1.36402	−	0.787516i	−0.102237	−	0.0590268i
$179$			14.4071i			1.07684i	0.842676	+	0.538420i	$0.180979\pi$
$179$			14.4071i			1.07684i	−0.842676	+	0.538420i	$0.819021\pi$
$180$		0			0
$181$		−	6.97309i		−	0.518306i	−0.965836	−	0.259153i	$-0.916557\pi$
$181$		−	6.97309i		−	0.518306i	0.965836	−	0.259153i	$-0.0834434\pi$
$182$		0			0
$183$		0			0
$184$	−1.52971	−	2.64954i	−0.112772	−	0.195327i
$185$	0.855697	+	1.48211i	0.0629121	+	0.108967i
$186$		0			0
$187$	15.9762	+	9.22386i	1.16829	+	0.674515i
$188$	−19.7945			−1.44366
$189$		0			0
$190$	0.339853			0.0246555
$191$	9.38310	+	5.41734i	0.678937	+	0.391985i	0.799455	−	0.600727i	$-0.205122\pi$
$191$	9.38310	+	5.41734i	0.678937	+	0.391985i	−0.120517	+	0.992711i	$0.538455\pi$
$192$		0			0
$193$	−5.26223	−	9.11444i	−0.378783	−	0.656072i	0.612102	−	0.790779i	$-0.290324\pi$
$193$	−5.26223	−	9.11444i	−0.378783	−	0.656072i	−0.990886	+	0.134707i	$0.956991\pi$
$194$	0.0348780	+	0.0604104i	0.00250409	+	0.00433722i
$195$		0			0
$196$		0			0
$197$		−	15.5156i		−	1.10544i	−0.833366	−	0.552721i	$-0.813590\pi$
$197$		−	15.5156i		−	1.10544i	0.833366	−	0.552721i	$-0.186410\pi$
$198$		0			0
$199$			12.5479i			0.889495i	0.895656	+	0.444748i	$0.146707\pi$
$199$			12.5479i			0.889495i	−0.895656	+	0.444748i	$0.853293\pi$
$200$	1.99279	+	1.15054i	0.140912	+	0.0813553i
$201$		0			0
$202$	1.23235	−	0.711497i	0.0867078	−	0.0500608i
$203$		0			0
$204$		0			0
$205$	−0.0526760	+	0.0912375i	−0.00367905	+	0.00637231i
$206$	0.782644			0.0545294
$207$		0			0
$208$			7.88898i			0.547002i
$209$	11.0302	−	19.1048i	0.762973	−	1.32151i
$210$		0			0
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	0.821852	−	0.569701i	$-0.192941\pi$
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	−0.904302	+	0.426894i	$0.859608\pi$
$212$	7.25031	−	4.18597i	0.497953	−	0.287493i
$213$		0			0
$214$	−0.0154927	+	0.0268341i	−0.00105906	+	0.00183434i
$215$	−4.19636			−0.286189
$216$		0			0
$217$		0			0
$218$	−1.26848	−	0.732357i	−0.0859123	−	0.0496015i
$219$		0			0
$220$	−3.82666	+	2.20932i	−0.257993	+	0.148953i
$221$	7.66580	−	4.42585i	0.515657	−	0.297715i
$222$		0			0
$223$	2.42193	+	1.39830i	0.162184	+	0.0936370i	0.578895	−	0.815402i	$-0.303484\pi$
$223$	2.42193	+	1.39830i	0.162184	+	0.0936370i	−0.416711	+	0.909039i	$0.636817\pi$
$224$		0			0
$225$		0			0
$226$	0.605540			0.0402799
$227$	−1.42300	+	2.46471i	−0.0944480	+	0.163589i	−0.909378	−	0.415970i	$-0.863442\pi$
$227$	−1.42300	+	2.46471i	−0.0944480	+	0.163589i	0.814930	+	0.579559i	$0.196775\pi$
$228$		0			0
$229$	20.5460	−	11.8623i	1.35772	−	0.783880i	0.368404	−	0.929666i	$-0.379904\pi$
$229$	20.5460	−	11.8623i	1.35772	−	0.783880i	0.989316	+	0.145786i	$0.0465711\pi$
$230$	−0.203229	−	0.352004i	−0.0134006	−	0.0232104i
$231$		0			0
$232$	−2.04834	+	3.54782i	−0.134480	+	0.232926i
$233$			18.7298i			1.22703i	0.789684	+	0.613514i	$0.210245\pi$
$233$			18.7298i			1.22703i	−0.789684	+	0.613514i	$0.789755\pi$
$234$		0			0
$235$	−5.27942			−0.344391
$236$	−13.3386	+	23.1032i	−0.868270	+	1.50389i
$237$		0			0
$238$		0			0
$239$	−11.1421	+	6.43288i	−0.720721	+	0.416109i	−0.815018	−	0.579436i	$-0.803273\pi$
$239$	−11.1421	+	6.43288i	−0.720721	+	0.416109i	0.0942969	+	0.995544i	$0.469940\pi$
$240$		0			0
$241$	−3.64082	−	2.10203i	−0.234526	−	0.135403i	0.378132	−	0.925752i	$-0.376566\pi$
$241$	−3.64082	−	2.10203i	−0.234526	−	0.135403i	−0.612658	+	0.790348i	$0.709900\pi$
$242$		−	0.816987i		−	0.0525179i
$243$		0			0
$244$			26.0302i			1.66641i
$245$		0			0
$246$		0			0
$247$	−5.29257	−	9.16700i	−0.336758	−	0.583282i
$248$	−0.290504	−	0.503168i	−0.0184470	−	0.0319512i
$249$		0			0
$250$	0.545226	+	0.314786i	0.0344831	+	0.0199088i
$251$	−7.50592			−0.473770			−0.236885	−	0.971538i	$-0.576126\pi$
$251$	−7.50592			−0.473770			−0.236885	+	0.971538i	$0.576126\pi$
$252$		0			0
$253$	−26.3838			−1.65874
$254$	0.390381	+	0.225387i	0.0244947	+	0.0141420i
$255$		0			0
$256$	−7.40797	−	12.8310i	−0.462998	−	0.801936i
$257$	2.51960	+	4.36408i	0.157169	+	0.272224i	0.933847	−	0.357674i	$-0.116430\pi$
$257$	2.51960	+	4.36408i	0.157169	+	0.272224i	−0.776678	+	0.629898i	$0.783097\pi$
$258$		0			0
$259$		0			0
$260$			2.12018i			0.131488i
$261$		0			0
$262$			0.667601i			0.0412445i
$263$	−12.2494	−	7.07220i	−0.755331	−	0.436091i	0.0722856	−	0.997384i	$-0.476971\pi$
$263$	−12.2494	−	7.07220i	−0.755331	−	0.436091i	−0.827617	+	0.561293i	$0.810304\pi$
$264$		0			0
$265$	1.93374	−	1.11644i	0.118789	−	0.0685826i
$266$		0			0
$267$		0			0
$268$	6.53078	−	11.3116i	0.398931	−	0.690969i
$269$	15.7771			0.961948			0.480974	−	0.876735i	$-0.340283\pi$
$269$	15.7771			0.961948			0.480974	+	0.876735i	$0.340283\pi$
$270$		0			0
$271$			16.8078i			1.02100i	0.859877	+	0.510501i	$0.170540\pi$
$271$			16.8078i			1.02100i	−0.859877	+	0.510501i	$0.829460\pi$
$272$	−8.57871	+	14.8588i	−0.520160	+	0.900944i
$273$		0			0
$274$	−0.0988873	−	0.171278i	−0.00597400	−	0.0103473i
$275$	17.1854	−	9.92198i	1.03632	−	0.598318i
$276$		0			0
$277$	−8.91066	+	15.4337i	−0.535390	+	0.927322i	0.463755	+	0.885964i	$0.346502\pi$
$277$	−8.91066	+	15.4337i	−0.535390	+	0.927322i	−0.999144	+	0.0413586i	$0.986831\pi$
$278$	−1.38317			−0.0829568
$279$		0			0
$280$		0			0
$281$	−7.59774	−	4.38656i	−0.453243	−	0.261680i	0.255956	−	0.966688i	$-0.417610\pi$
$281$	−7.59774	−	4.38656i	−0.453243	−	0.261680i	−0.709199	+	0.705008i	$0.750943\pi$
$282$		0			0
$283$	−18.7047	+	10.7991i	−1.11188	+	0.641942i	−0.939315	−	0.343056i	$-0.888538\pi$
$283$	−18.7047	+	10.7991i	−1.11188	+	0.641942i	−0.172562	+	0.984999i	$0.555204\pi$
$284$	−14.6223	+	8.44221i	−0.867676	+	0.500953i
$285$		0			0
$286$	−0.898724	−	0.518879i	−0.0531427	−	0.0306819i
$287$		0			0
$288$		0			0
$289$	2.25120			0.132424
$290$	−0.272131	+	0.471344i	−0.0159801	+	0.0276783i
$291$		0			0
$292$	−9.64756	+	5.57002i	−0.564581	+	0.325961i
$293$	9.79756	+	16.9699i	0.572379	+	0.991390i	0.996321	+	0.0857006i	$0.0273128\pi$
$293$	9.79756	+	16.9699i	0.572379	+	0.991390i	−0.423942	+	0.905690i	$0.639354\pi$
$294$		0			0
$295$	−3.55755	+	6.16186i	−0.207129	+	0.358758i
$296$		−	1.57601i		−	0.0916035i
$297$		0			0
$298$	0.651862			0.0377613
$299$	−6.32983	+	10.9636i	−0.366063	+	0.634040i
$300$		0			0
$301$		0			0
$302$	−0.279996	+	0.161656i	−0.0161120	+	0.00930224i
$303$		0			0
$304$	17.7686	+	10.2587i	1.01910	+	0.588376i
$305$			6.94254i			0.397529i
$306$		0			0
$307$		−	27.7677i		−	1.58478i	−0.610012	−	0.792392i	$-0.708835\pi$
$307$		−	27.7677i		−	1.58478i	0.610012	−	0.792392i	$-0.291165\pi$
$308$		0			0
$309$		0			0
$310$	−0.0385948	−	0.0668482i	−0.00219204	−	0.00379672i
$311$	−10.0080	−	17.3344i	−0.567501	−	0.982941i	−0.996812	−	0.0797841i	$-0.974577\pi$
$311$	−10.0080	−	17.3344i	−0.567501	−	0.982941i	0.429311	−	0.903157i	$-0.358756\pi$
$312$		0			0
$313$	15.9654	+	9.21765i	0.902420	+	0.521012i	0.877984	−	0.478689i	$-0.158888\pi$
$313$	15.9654	+	9.21765i	0.902420	+	0.521012i	0.0244352	+	0.999701i	$0.492221\pi$
$314$	−1.59891			−0.0902320
$315$		0			0
$316$	1.13680			0.0639498
$317$	12.5992	+	7.27416i	0.707642	+	0.408558i	0.810187	−	0.586171i	$-0.199365\pi$
$317$	12.5992	+	7.27416i	0.707642	+	0.408558i	−0.102545	+	0.994728i	$0.532699\pi$
$318$		0			0
$319$	17.6644	+	30.5956i	0.989016	+	1.71303i
$320$	−2.02322	−	3.50431i	−0.113101	−	0.195897i
$321$		0			0
$322$		0			0
$323$		−	23.0212i		−	1.28093i
$324$		0			0
$325$		−	9.52166i		−	0.528167i
$326$	−1.80406	−	1.04157i	−0.0999176	−	0.0576874i
$327$		0			0
$328$	0.0840197	−	0.0485088i	0.00463921	−	0.00267845i
$329$		0			0
$330$		0			0
$331$	14.8446	−	25.7115i	0.815930	−	1.41323i	−0.0927274	−	0.995692i	$-0.529559\pi$
$331$	14.8446	−	25.7115i	0.815930	−	1.41323i	0.908658	−	0.417541i	$-0.137108\pi$
$332$	−21.5452			−1.18245
$333$		0			0
$334$		−	2.60850i		−	0.142731i
$335$	1.74183	−	3.01694i	0.0951664	−	0.164833i
$336$		0			0
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	0.712868	−	0.701298i	$-0.247396\pi$
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	−0.963776	+	0.266713i	$0.914063\pi$
$338$	0.946163	−	0.546267i	0.0514645	−	0.0297130i
$339$		0			0
$340$	−2.30555	+	3.99333i	−0.125036	+	0.216569i
$341$	−5.01049			−0.271333
$342$		0			0
$343$		0			0
$344$	3.34665	+	1.93219i	0.180439	+	0.104177i
$345$		0			0
$346$	2.17062	−	1.25321i	0.116693	−	0.0673728i
$347$	−15.7313	+	9.08247i	−0.844501	+	0.487573i	−0.858791	−	0.512325i	$-0.828784\pi$
$347$	−15.7313	+	9.08247i	−0.844501	+	0.487573i	0.0142910	+	0.999898i	$0.495451\pi$
$348$		0			0
$349$	5.70494	+	3.29375i	0.305378	+	0.176310i	0.644856	−	0.764304i	$-0.276917\pi$
$349$	5.70494	+	3.29375i	0.305378	+	0.176310i	−0.339478	+	0.940614i	$0.610250\pi$
$350$		0			0
$351$		0			0
$352$	6.11128			0.325732
$353$	−10.4692	+	18.1332i	−0.557221	+	0.965135i	0.440506	+	0.897750i	$0.354799\pi$
$353$	−10.4692	+	18.1332i	−0.557221	+	0.965135i	−0.997727	+	0.0673857i	$0.978534\pi$
$354$		0			0
$355$	−3.89994	+	2.25163i	−0.206987	+	0.119504i
$356$	−12.7774	−	22.1311i	−0.677201	−	1.17295i
$357$		0			0
$358$	0.881317	−	1.52649i	0.0465791	−	0.0806773i
$359$		−	14.2265i		−	0.750845i	−0.926854	−	0.375422i	$-0.877498\pi$
$359$		−	14.2265i		−	0.750845i	0.926854	−	0.375422i	$-0.122502\pi$
$360$		0			0
$361$	−8.52944			−0.448918
$362$	−0.426560	+	0.738823i	−0.0224195	+	0.0388317i
$363$		0			0
$364$		0			0
$365$	−2.57311	+	1.48559i	−0.134683	+	0.0777591i
$366$		0			0
$367$	−10.7237	−	6.19136i	−0.559775	−	0.323186i	0.193280	−	0.981144i	$-0.438087\pi$
$367$	−10.7237	−	6.19136i	−0.559775	−	0.323186i	−0.753055	+	0.657957i	$0.771421\pi$
$368$		−	24.5384i		−	1.27915i
$369$		0			0
$370$		−	0.209380i		−	0.0108851i
$371$		0			0
$372$		0			0
$373$	10.6559	+	18.4565i	0.551740	+	0.955642i	0.998149	+	0.0608130i	$0.0193693\pi$
$373$	10.6559	+	18.4565i	0.551740	+	0.955642i	−0.446409	+	0.894829i	$0.647297\pi$
$374$	−1.12849	−	1.95460i	−0.0583527	−	0.101070i
$375$		0			0
$376$	4.21041	+	2.43088i	0.217135	+	0.125363i
$377$	16.9517			0.873057
$378$		0			0
$379$	10.6001			0.544489			0.272244	−	0.962228i	$-0.412234\pi$
$379$	10.6001			0.544489			0.272244	+	0.962228i	$0.412234\pi$
$380$	4.77535	+	2.75705i	0.244970	+	0.141434i
$381$		0			0
$382$	−0.662781	−	1.14797i	−0.0339108	−	0.0587353i
$383$	6.32174	+	10.9496i	0.323026	+	0.559497i	0.981111	−	0.193446i	$-0.0619666\pi$
$383$	6.32174	+	10.9496i	0.323026	+	0.559497i	−0.658085	+	0.752944i	$0.728633\pi$
$384$		0			0
$385$		0			0
$386$			1.28761i			0.0655375i
$387$		0			0
$388$			1.13179i			0.0574578i
$389$	−11.4538	−	6.61286i	−0.580732	−	0.335286i	0.180692	−	0.983540i	$-0.442166\pi$
$389$	−11.4538	−	6.61286i	−0.580732	−	0.335286i	−0.761424	+	0.648254i	$0.775499\pi$
$390$		0			0
$391$	−23.8442	+	13.7665i	−1.20586	+	0.696201i
$392$		0			0
$393$		0			0
$394$	−0.949125	+	1.64393i	−0.0478162	+	0.0828201i
$395$	0.303196			0.0152554
$396$		0			0
$397$			24.7882i			1.24409i	0.782983	+	0.622043i	$0.213697\pi$
$397$			24.7882i			1.24409i	−0.782983	+	0.622043i	$0.786303\pi$
$398$	0.767582	−	1.32949i	0.0384754	−	0.0666413i
$399$		0			0
$400$	9.22800	+	15.9834i	0.461400	+	0.799168i
$401$	−3.19615	+	1.84530i	−0.159608	+	0.0921499i	−0.577677	−	0.816266i	$-0.696041\pi$
$401$	−3.19615	+	1.84530i	−0.159608	+	0.0921499i	0.418068	+	0.908416i	$0.362707\pi$
$402$		0			0
$403$	−1.20208	+	2.08207i	−0.0598800	+	0.103715i
$404$	23.0880			1.14867
$405$		0			0
$406$		0			0
$407$	−11.7703	−	6.79556i	−0.583430	−	0.336843i
$408$		0			0
$409$	16.0535	−	9.26852i	0.793797	−	0.458299i	−0.0475008	−	0.998871i	$-0.515126\pi$
$409$	16.0535	−	9.26852i	0.793797	−	0.458299i	0.841297	+	0.540573i	$0.181792\pi$
$410$	0.0111624	−	0.00644462i	0.000551272	−	0.000318277i
$411$		0			0
$412$	10.9971	+	6.34918i	0.541788	+	0.312802i
$413$		0			0
$414$		0			0
$415$	−5.74635			−0.282077
$416$	1.46618	−	2.53949i	0.0718852	−	0.124509i
$417$		0			0
$418$	−2.33737	+	1.34948i	−0.114324	+	0.0660053i
$419$	1.46994	+	2.54600i	0.0718111	+	0.124380i	0.899695	−	0.436519i	$-0.143789\pi$
$419$	1.46994	+	2.54600i	0.0718111	+	0.124380i	−0.827884	+	0.560899i	$0.810455\pi$
$420$		0			0
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	0.285031	+	0.958518i	$0.407996\pi$
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	−0.972617	+	0.232415i	$0.925337\pi$
$422$			0.293051i			0.0142655i
$423$		0			0
$424$	−2.05624			−0.0998600
$425$	10.3541	−	17.9339i	0.502249	−	0.869921i
$426$		0			0
$427$		0			0
$428$	−0.435382	+	0.251368i	−0.0210450	+	0.0121503i
$429$		0			0
$430$	0.444618	+	0.256700i	0.0214414	+	0.0123792i
$431$		−	6.76465i		−	0.325842i	−0.986639	−	0.162921i	$-0.947908\pi$
$431$		−	6.76465i		−	0.325842i	0.986639	−	0.162921i	$-0.0520915\pi$
$432$		0			0
$433$			28.3475i			1.36229i	0.732146	+	0.681147i	$0.238519\pi$
$433$			28.3475i			1.36229i	−0.732146	+	0.681147i	$0.761481\pi$
$434$		0			0
$435$		0			0
$436$	−11.8824	−	20.5810i	−0.569066	−	0.985651i
$437$	16.4624	+	28.5137i	0.787503	+	1.36399i
$438$		0			0
$439$	−22.8208	−	13.1756i	−1.08918	−	0.628837i	−0.155821	−	0.987785i	$-0.549802\pi$
$439$	−22.8208	−	13.1756i	−1.08918	−	0.628837i	−0.933358	+	0.358948i	$0.883136\pi$
$440$	1.08527			0.0517382
$441$		0			0
$442$	−1.08296			−0.0515110
$443$	4.75958	+	2.74795i	0.226135	+	0.130559i	0.608788	−	0.793333i	$-0.291656\pi$
$443$	4.75958	+	2.74795i	0.226135	+	0.130559i	−0.382653	+	0.923892i	$0.624989\pi$
$444$		0			0
$445$	−3.40787	−	5.90261i	−0.161549	−	0.279810i
$446$	−0.171074	−	0.296309i	−0.00810060	−	0.0140306i
$447$		0			0
$448$		0			0
$449$			7.38342i			0.348445i	0.984706	+	0.174223i	$0.0557412\pi$
$449$			7.38342i			0.348445i	−0.984706	+	0.174223i	$0.944259\pi$
$450$		0			0
$451$		−	0.836659i		−	0.0393967i
$452$	8.50857	+	4.91242i	0.400209	+	0.231061i
$453$		0			0
$454$	0.301544	−	0.174097i	0.0141522	−	0.00817076i
$455$		0			0
$456$		0			0
$457$	−20.7109	+	35.8724i	−0.968817	+	1.67804i	−0.269826	+	0.962909i	$0.586966\pi$
$457$	−20.7109	+	35.8724i	−0.968817	+	1.67804i	−0.698991	+	0.715130i	$0.746367\pi$
$458$	−2.90256			−0.135628
$459$		0			0
$460$		−	6.59477i		−	0.307483i
$461$	5.44638	−	9.43341i	0.253663	−	0.439357i	−0.710868	−	0.703325i	$-0.751698\pi$
$461$	5.44638	−	9.43341i	0.253663	−	0.439357i	0.964532	+	0.263968i	$0.0850312\pi$
$462$		0			0
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	0.791316	−	0.611407i	$-0.209396\pi$
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	−0.925152	+	0.379597i	$0.876063\pi$
$464$	−28.4557	+	16.4289i	−1.32102	+	0.762692i
$465$		0			0
$466$	1.14574	−	1.98448i	0.0530755	−	0.0919294i
$467$	−23.8882			−1.10541			−0.552707	−	0.833376i	$-0.686405\pi$
$467$	−23.8882			−1.10541			−0.552707	+	0.833376i	$0.686405\pi$
$468$		0			0
$469$		0			0
$470$	0.559372	+	0.322954i	0.0258019	+	0.0148967i
$471$		0			0
$472$	5.67440	−	3.27612i	0.261185	−	0.150795i
$473$	28.8608	−	16.6628i	1.32702	−	0.766156i
$474$		0			0
$475$	−21.4459	−	12.3818i	−0.984005	−	0.568116i
$476$		0			0
$477$		0			0
$478$	1.57406			0.0719956
$479$	0.947645	−	1.64137i	0.0432990	−	0.0749961i	−0.843564	−	0.537029i	$-0.819547\pi$
$479$	0.947645	−	1.64137i	0.0432990	−	0.0749961i	0.886863	+	0.462033i	$0.152880\pi$
$480$		0			0
$481$	−5.64768	+	3.26069i	−0.257512	+	0.148675i
$482$	0.257171	+	0.445434i	0.0117138	+	0.0202890i
$483$		0			0
$484$	6.62778	−	11.4797i	0.301263	−	0.521803i
$485$			0.301860i			0.0137067i
$486$		0			0
$487$	28.2248			1.27899			0.639494	−	0.768796i	$-0.279144\pi$
$487$	28.2248			1.27899			0.639494	+	0.768796i	$0.279144\pi$
$488$	3.19666	−	5.53677i	0.144706	−	0.250638i
$489$		0			0
$490$		0			0
$491$	2.30250	−	1.32935i	0.103910	−	0.0599927i	−0.447144	−	0.894462i	$-0.647559\pi$
$491$	2.30250	−	1.32935i	0.103910	−	0.0599927i	0.551055	+	0.834469i	$0.314226\pi$
$492$		0			0
$493$	31.9282	+	18.4338i	1.43797	+	0.830215i
$494$			1.29503i			0.0582663i
$495$		0			0
$496$		−	4.66003i		−	0.209242i
$497$		0			0
$498$		0			0
$499$	6.27844	+	10.8746i	0.281062	+	0.486813i	0.971646	−	0.236438i	$-0.0759801\pi$
$499$	6.27844	+	10.8746i	0.281062	+	0.486813i	−0.690585	+	0.723251i	$0.742647\pi$
$500$	5.10739	+	8.84625i	0.228409	+	0.395617i
$501$		0			0
$502$	0.795278	+	0.459154i	0.0354950	+	0.0204930i
$503$	18.1502			0.809278			0.404639	−	0.914476i	$-0.367397\pi$
$503$	18.1502			0.809278			0.404639	+	0.914476i	$0.367397\pi$
$504$		0			0
$505$	6.15782			0.274020
$506$	2.79546	+	1.61396i	0.124273	+	0.0717491i
$507$		0			0
$508$	3.65689	+	6.33391i	0.162248	+	0.281022i
$509$	9.33827	+	16.1744i	0.413912	+	0.716916i	0.995314	−	0.0967005i	$-0.0308289\pi$
$509$	9.33827	+	16.1744i	0.413912	+	0.716916i	−0.581402	+	0.813617i	$0.697496\pi$
$510$		0			0
$511$		0			0
$512$			9.49685i			0.419705i
$513$		0			0
$514$		−	0.616519i		−	0.0271935i
$515$	2.93305	+	1.69340i	0.129245	+	0.0746199i
$516$		0			0
$517$	36.3096	−	20.9634i	1.59690	−	0.921968i
$518$		0			0
$519$		0			0
$520$	0.260371	−	0.450975i	0.0114180	−	0.0197766i
$521$	18.0665			0.791508			0.395754	−	0.918357i	$-0.370483\pi$
$521$	18.0665			0.791508			0.395754	+	0.918357i	$0.370483\pi$
$522$		0			0
$523$		−	21.1338i		−	0.924116i	−0.886850	−	0.462058i	$-0.847111\pi$
$523$		−	21.1338i		−	0.924116i	0.886850	−	0.462058i	$-0.152889\pi$
$524$	−5.41590	+	9.38061i	−0.236595	+	0.409794i
$525$		0			0
$526$	0.865245	+	1.49865i	0.0377265	+	0.0653442i
$527$	−4.52820	+	2.61436i	−0.197252	+	0.113883i
$528$		0			0
$529$	8.18875	−	14.1833i	0.356033	−	0.616666i
$530$	−0.273181			−0.0118662
$531$		0			0
$532$		0			0
$533$	−0.347667	−	0.200725i	−0.0150591	−	0.00869439i
$534$		0			0
$535$	−0.116121	+	0.0670425i	−0.00502035	+	0.00289850i
$536$	−2.77827	+	1.60403i	−0.120003	+	0.0692837i
$537$		0			0
$538$	−1.67164	−	0.965122i	−0.0720695	−	0.0416093i
$539$		0			0
$540$		0			0
$541$	17.7732			0.764131			0.382065	−	0.924135i	$-0.375213\pi$
$541$	17.7732			0.764131			0.382065	+	0.924135i	$0.375213\pi$
$542$	1.02817	−	1.78084i	0.0441637	−	0.0764938i
$543$		0			0
$544$	5.52304	−	3.18873i	0.236798	−	0.136715i
$545$	−3.16918	−	5.48918i	−0.135753	−	0.235131i
$546$		0			0
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	−0.386741	−	0.922188i	$-0.626399\pi$
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	0.992009	−	0.126166i	$-0.0402673\pi$
$548$		−	3.20888i		−	0.137077i
$549$		0			0
$550$	−2.42780			−0.103522
$551$	22.0437	−	38.1808i	0.939092	−	1.62655i
$552$		0			0
$553$		0			0
$554$	1.88823	−	1.09017i	0.0802232	−	0.0463169i
$555$		0			0
$556$	−19.4352	−	11.2209i	−0.824234	−	0.475872i
$557$			11.7214i			0.496651i	0.968677	+	0.248326i	$0.0798803\pi$
$557$			11.7214i			0.496651i	−0.968677	+	0.248326i	$0.920120\pi$
$558$		0			0
$559$		−	15.9905i		−	0.676326i
$560$		0			0
$561$		0			0
$562$	0.536671	+	0.929541i	0.0226381	+	0.0392103i
$563$	−18.3014	−	31.6990i	−0.771314	−	1.33595i	−0.936843	−	0.349750i	$-0.886267\pi$
$563$	−18.3014	−	31.6990i	−0.771314	−	1.33595i	0.165529	−	0.986205i	$-0.447067\pi$
$564$		0			0
$565$	2.26933	+	1.31020i	0.0954713	+	0.0551204i
$566$	2.64243			0.111070
$567$		0			0
$568$	4.14701			0.174005
$569$	−32.6468	−	18.8486i	−1.36862	−	0.790176i	−0.377872	−	0.925858i	$-0.623344\pi$
$569$	−32.6468	−	18.8486i	−1.36862	−	0.790176i	−0.990752	+	0.135682i	$0.956677\pi$
$570$		0			0
$571$	−14.1123	−	24.4432i	−0.590581	−	1.02292i	−0.994154	−	0.107968i	$-0.965565\pi$
$571$	−14.1123	−	24.4432i	−0.590581	−	1.02292i	0.403574	−	0.914947i	$-0.367768\pi$
$572$	−8.41878	−	14.5817i	−0.352007	−	0.609694i
$573$		0			0
$574$		0			0
$575$			29.6168i			1.23511i
$576$		0			0
$577$		−	9.38512i		−	0.390708i	−0.980733	−	0.195354i	$-0.937414\pi$
$577$		−	9.38512i		−	0.390708i	0.980733	−	0.195354i	$-0.0625855\pi$
$578$	−0.238523	−	0.137711i	−0.00992123	−	0.00572802i
$579$		0			0
$580$	−7.64754	+	4.41531i	−0.317547	+	0.183336i
$581$		0			0
$582$		0			0
$583$	−8.86629	+	15.3569i	−0.367204	+	0.636017i
$584$	2.73612			0.113222
$585$		0			0
$586$		−	2.39735i		−	0.0990338i
$587$	−23.1819	+	40.1523i	−0.956821	+	1.65726i	−0.226675	+	0.973971i	$0.572785\pi$
$587$	−23.1819	+	40.1523i	−0.956821	+	1.65726i	−0.730146	+	0.683291i	$0.760548\pi$
$588$		0			0
$589$	3.12633	+	5.41496i	0.128818	+	0.223120i
$590$	0.753870	−	0.435247i	0.0310363	−	0.0179188i
$591$		0			0
$592$	6.32025	−	10.9470i	0.259761	−	0.449919i
$593$	−18.1416			−0.744986			−0.372493	−	0.928035i	$-0.621497\pi$
$593$	−18.1416			−0.744986			−0.372493	+	0.928035i	$0.621497\pi$
$594$		0			0
$595$		0			0
$596$	9.15945	+	5.28821i	0.375186	+	0.216613i
$597$		0			0
$598$	1.34133	−	0.774419i	0.0548512	−	0.0316684i
$599$	−6.02771	+	3.48010i	−0.246286	+	0.142193i	−0.618062	−	0.786129i	$-0.712082\pi$
$599$	−6.02771	+	3.48010i	−0.246286	+	0.142193i	0.371777	+	0.928322i	$0.378749\pi$
$600$		0			0
$601$	−2.08865	−	1.20588i	−0.0851976	−	0.0491889i	0.456796	−	0.889572i	$-0.348997\pi$
$601$	−2.08865	−	1.20588i	−0.0851976	−	0.0491889i	−0.541994	+	0.840383i	$0.682330\pi$
$602$		0			0
$603$		0			0
$604$	−5.24571			−0.213445
$605$	1.76770	−	3.06175i	0.0718673	−	0.124478i
$606$		0			0
$607$	11.0306	−	6.36850i	0.447717	−	0.258489i	−0.259149	−	0.965837i	$-0.583442\pi$
$607$	11.0306	−	6.36850i	0.447717	−	0.258489i	0.706865	+	0.707348i	$0.250109\pi$
$608$	−3.81318	−	6.60462i	−0.154645	−	0.267853i
$609$		0			0
$610$	0.424690	−	0.735585i	0.0171952	−	0.0297830i
$611$		−	20.1176i		−	0.813870i
$612$		0			0
$613$	−10.3352			−0.417436			−0.208718	−	0.977976i	$-0.566929\pi$
$613$	−10.3352			−0.417436			−0.208718	+	0.977976i	$0.566929\pi$
$614$	−1.69861	+	2.94208i	−0.0685503	+	0.118733i
$615$		0			0
$616$		0			0
$617$	41.3741	−	23.8873i	1.66566	−	0.961668i	0.695721	−	0.718313i	$-0.255085\pi$
$617$	41.3741	−	23.8873i	1.66566	−	0.961668i	0.969937	−	0.243355i	$-0.0782481\pi$
$618$		0			0
$619$	−35.2626	−	20.3588i	−1.41732	−	0.818291i	−0.421259	−	0.906940i	$-0.638412\pi$
$619$	−35.2626	−	20.3588i	−1.41732	−	0.818291i	−0.996063	+	0.0886491i	$0.971745\pi$
$620$		−	1.25240i		−	0.0502975i
$621$		0			0
$622$			2.44884i			0.0981897i
$623$		0			0
$624$		0			0
$625$	−10.4371	−	18.0775i	−0.417483	−	0.723101i
$626$	−1.12773	−	1.95328i	−0.0450731	−	0.0780689i
$627$		0			0
$628$	−22.4667	−	12.9711i	−0.896519	−	0.517605i
$629$	−14.1831			−0.565517
$630$		0			0
$631$	11.4782			0.456942			0.228471	−	0.973551i	$-0.426627\pi$
$631$	11.4782			0.456942			0.228471	+	0.973551i	$0.426627\pi$
$632$	−0.241803	−	0.139605i	−0.00961841	−	0.00555319i
$633$		0			0
$634$	−0.889953	−	1.54144i	−0.0353446	−	0.0612186i
$635$	0.975332	+	1.68932i	0.0387049	+	0.0670388i
$636$		0			0
$637$		0			0
$638$		−	4.32228i		−	0.171121i
$639$		0			0
$640$			2.03412i			0.0804057i
$641$	30.5823	+	17.6567i	1.20793	+	0.697398i	0.962306	−	0.271968i	$-0.0876744\pi$
$641$	30.5823	+	17.6567i	1.20793	+	0.697398i	0.245622	+	0.969366i	$0.421008\pi$
$642$		0			0
$643$	−6.09416	+	3.51846i	−0.240330	+	0.138755i	−0.615328	−	0.788271i	$-0.710977\pi$
$643$	−6.09416	+	3.51846i	−0.240330	+	0.138755i	0.374998	+	0.927025i	$0.377643\pi$
$644$		0			0
$645$		0			0
$646$	−1.40826	+	2.43917i	−0.0554071	+	0.0959680i
$647$	−14.9942			−0.589482			−0.294741	−	0.955577i	$-0.595233\pi$
$647$	−14.9942			−0.589482			−0.294741	+	0.955577i	$0.595233\pi$
$648$		0			0
$649$		−	56.5050i		−	2.21801i
$650$	−0.582461	+	1.00885i	−0.0228460	+	0.0395704i
$651$		0			0
$652$	−16.8995	−	29.2708i	−0.661835	−	1.14633i
$653$	−4.15597	+	2.39945i	−0.162636	+	0.0938977i	−0.579109	−	0.815250i	$-0.696599\pi$
$653$	−4.15597	+	2.39945i	−0.162636	+	0.0938977i	0.416473	+	0.909148i	$0.363266\pi$
$654$		0			0
$655$	−1.44448	+	2.50191i	−0.0564405	+	0.0977577i
$656$	0.778140			0.0303812
$657$		0			0
$658$		0			0
$659$	13.4562	+	7.76893i	0.524179	+	0.302635i	0.738643	−	0.674097i	$-0.235467\pi$
$659$	13.4562	+	7.76893i	0.524179	+	0.302635i	−0.214464	+	0.976732i	$0.568800\pi$
$660$		0			0
$661$	−18.2131	+	10.5154i	−0.708409	+	0.409000i	−0.810472	−	0.585778i	$-0.800789\pi$
$661$	−18.2131	+	10.5154i	−0.708409	+	0.409000i	0.102062	+	0.994778i	$0.467456\pi$
$662$	−3.14566	+	1.81615i	−0.122260	+	0.0705866i
$663$		0			0
$664$	4.58280	+	2.64588i	0.177847	+	0.102680i
$665$		0			0
$666$		0			0
$667$	−52.7277			−2.04163
$668$	21.1614	−	36.6526i	0.818758	−	1.41813i
$669$		0			0
$670$	−0.369106	+	0.213103i	−0.0142598	+	0.00823290i
$671$	−27.5673	−	47.7479i	−1.06422	−	1.84329i
$672$		0			0
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	−0.582036	−	0.813163i	$-0.697744\pi$
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	0.995238	+	0.0974770i	$0.0310772\pi$
$674$			1.12705i			0.0434124i
$675$		0			0
$676$	17.7263			0.681781
$677$	9.03150	−	15.6430i	0.347109	−	0.601210i	−0.638626	−	0.769517i	$-0.720497\pi$
$677$	9.03150	−	15.6430i	0.347109	−	0.601210i	0.985735	+	0.168308i	$0.0538302\pi$
$678$		0			0
$679$		0			0
$680$	0.980808	−	0.566270i	0.0376123	−	0.0217155i
$681$		0			0
$682$	0.530878	+	0.306503i	0.0203284	+	0.0117366i
$683$			45.5647i			1.74349i	0.489963	+	0.871743i	$0.337010\pi$
$683$			45.5647i			1.74349i	−0.489963	+	0.871743i	$0.662990\pi$
$684$		0			0
$685$		−	0.855844i		−	0.0327001i
$686$		0			0
$687$		0			0
$688$	15.4973	+	26.8422i	0.590830	+	1.02335i
$689$	4.25428	+	7.36863i	0.162075	+	0.280723i
$690$		0			0
$691$	−3.33627	−	1.92620i	−0.126918	−	0.0732760i	0.435197	−	0.900335i	$-0.356679\pi$
$691$	−3.33627	−	1.92620i	−0.126918	−	0.0732760i	−0.562115	+	0.827059i	$0.690012\pi$
$692$	40.6664			1.54590
$693$		0			0
$694$	2.22238			0.0843604
$695$	−5.18357	−	2.99273i	−0.196624	−	0.113521i
$696$		0			0
$697$	−0.436550	−	0.756126i	−0.0165355	−	0.0286403i
$698$	−0.402972	−	0.697967i	−0.0152527	−	0.0264185i
$699$		0			0
$700$		0			0
$701$			46.5216i			1.75710i	0.477653	+	0.878549i	$0.341488\pi$
$701$			46.5216i			1.75710i	−0.477653	+	0.878549i	$0.658512\pi$
$702$		0			0
$703$			16.9606i			0.639680i
$704$	27.8297	+	16.0675i	1.04887	+	0.605566i
$705$		0			0
$706$	2.21850	−	1.28085i	0.0834944	−	0.0482055i
$707$		0			0
$708$		0			0
$709$	14.6187	−	25.3203i	0.549017	−	0.950925i	−0.449326	−	0.893368i	$-0.648336\pi$
$709$	14.6187	−	25.3203i	0.549017	−	0.950925i	0.998342	−	0.0575566i	$-0.0183310\pi$
$710$	0.550949			0.0206767
$711$		0			0
$712$			6.27655i			0.235224i
$713$	3.73904	−	6.47621i	0.140028	−	0.242536i
$714$		0			0
$715$	−2.24538	−	3.88911i	−0.0839724	−	0.145445i
$716$	24.7672	−	14.2993i	0.925592	−	0.534391i
$717$		0			0
$718$	−0.870265	+	1.50734i	−0.0324780	+	0.0562536i
$719$	3.37122			0.125725			0.0628627	−	0.998022i	$-0.479977\pi$
$719$	3.37122			0.125725			0.0628627	+	0.998022i	$0.479977\pi$
$720$		0			0
$721$		0			0
$722$	0.903723	+	0.521765i	0.0336331	+	0.0194181i
$723$		0			0
$724$	−11.9874	+	6.92091i	−0.445507	+	0.257214i
$725$	34.3448	−	19.8290i	1.27553	−	0.736429i
$726$		0			0
$727$	4.34397	+	2.50799i	0.161109	+	0.0930164i	0.578387	−	0.815763i	$-0.303682\pi$
$727$	4.34397	+	2.50799i	0.161109	+	0.0930164i	−0.417278	+	0.908779i	$0.637016\pi$
$728$		0			0
$729$		0			0
$730$	0.363506			0.0134540
$731$	17.3885	−	30.1178i	0.643138	−	1.11395i
$732$		0			0
$733$	−19.6875	+	11.3666i	−0.727175	+	0.419835i	−0.817388	−	0.576088i	$-0.804579\pi$
$733$	−19.6875	+	11.3666i	−0.727175	+	0.419835i	0.0902126	+	0.995923i	$0.471245\pi$
$734$	0.757478	+	1.31199i	0.0279590	+	0.0484265i
$735$		0			0
$736$	−4.56050	+	7.89901i	−0.168102	+	0.291162i
$737$			27.6657i			1.01908i
$738$		0			0
$739$	−2.39022			−0.0879256			−0.0439628	−	0.999033i	$-0.513998\pi$
$739$	−2.39022			−0.0879256			−0.0439628	+	0.999033i	$0.513998\pi$
$740$	1.69859	−	2.94204i	0.0624413	−	0.108151i
$741$		0			0
$742$		0			0
$743$	36.1039	−	20.8446i	1.32453	−	0.764715i	0.340078	−	0.940397i	$-0.389546\pi$
$743$	36.1039	−	20.8446i	1.32453	−	0.764715i	0.984447	+	0.175682i	$0.0562131\pi$
$744$		0			0
$745$	2.44292	+	1.41042i	0.0895018	+	0.0516739i
$746$		−	2.60737i		−	0.0954627i
$747$		0			0
$748$		−	36.6193i		−	1.33893i
$749$		0			0
$750$		0			0
$751$	−13.2710	−	22.9861i	−0.484267	−	0.838775i	0.515570	−	0.856848i	$-0.327580\pi$
$751$	−13.2710	−	22.9861i	−0.484267	−	0.838775i	−0.999837	+	0.0180728i	$0.994247\pi$
$752$	19.4971	+	33.7700i	0.710987	+	1.23147i
$753$		0			0
$754$	−1.79609	−	1.03697i	−0.0654097	−	0.0377643i
$755$	−1.39909			−0.0509180
$756$		0			0
$757$	20.3580			0.739923			0.369961	−	0.929047i	$-0.379371\pi$
$757$	20.3580			0.739923			0.369961	+	0.929047i	$0.379371\pi$
$758$	−1.12311	−	0.648430i	−0.0407933	−	0.0235520i
$759$		0			0
$760$	−0.677163	−	1.17288i	−0.0245633	−	0.0425448i
$761$	−12.9578	−	22.4436i	−0.469720	−	0.813578i	0.529681	−	0.848197i	$-0.322312\pi$
$761$	−12.9578	−	22.4436i	−0.469720	−	0.813578i	−0.999401	+	0.0346186i	$0.988978\pi$
$762$		0			0
$763$		0			0
$764$		−	21.5072i		−	0.778102i
$765$		0			0
$766$		−	1.54686i		−	0.0558903i
$767$	−23.4802	−	13.5563i	−0.847821	−	0.489489i
$768$		0			0
$769$	−18.8269	+	10.8697i	−0.678914	+	0.391971i	−0.799446	−	0.600738i	$-0.794873\pi$
$769$	−18.8269	+	10.8697i	−0.678914	+	0.391971i	0.120532	+	0.992709i	$0.461540\pi$
$770$		0			0
$771$		0			0
$772$	−10.4457	+	18.0925i	−0.375948	+	0.651162i
$773$	−20.3213			−0.730905			−0.365453	−	0.930830i	$-0.619086\pi$
$773$	−20.3213			−0.730905			−0.365453	+	0.930830i	$0.619086\pi$
$774$		0			0
$775$			5.62446i			0.202037i
$776$	0.138990	−	0.240738i	0.00498945	−	0.00864197i
$777$		0			0
$778$	0.809047	+	1.40131i	0.0290058	+	0.0502394i
$779$	−0.904199	+	0.522039i	−0.0323963	+	0.0187040i
$780$		0			0
$781$	17.8814	−	30.9715i	0.639848	−	1.10825i
$782$	3.36851			0.120458
$783$		0			0
$784$		0			0
$785$	−5.99211	−	3.45955i	−0.213868	−	0.123477i
$786$		0			0
$787$	−16.4065	+	9.47232i	−0.584830	+	0.337652i	−0.763051	−	0.646339i	$-0.776299\pi$
$787$	−16.4065	+	9.47232i	−0.584830	+	0.337652i	0.178221	+	0.983991i	$0.442966\pi$
$788$	−26.6727	+	15.3995i	−0.950176	+	0.548584i
$789$		0			0
$790$	−0.0321246	−	0.0185472i	−0.00114294	−	0.000659879i
$791$		0			0
$792$		0			0
$793$	−26.4550			−0.939445
$794$	1.51635	−	2.62640i	0.0538133	−	0.0932074i
$795$		0			0
$796$	21.5709	−	12.4540i

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +O(q^{10})\)	\(q+(-0.105953 - 0.0611722i) q^{2} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +0.487547i q^{8} +0.0647728i q^{10} +(3.64120 + 2.10225i) q^{11} +(1.74714 - 1.00871i) q^{13} +(-1.95521 + 3.38652i) q^{16} +4.38762 q^{17} -5.24685i q^{19} +(-0.525467 + 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(-5.43444 + 3.13757i) q^{23} +(2.35985 - 4.08738i) q^{25} -0.246821 q^{26} +(7.27689 + 4.20131i) q^{29} +(-1.03204 + 0.595849i) q^{31} +(1.25878 - 0.726755i) q^{32} +(-0.464883 - 0.268400i) q^{34} -3.23252 q^{37} +(-0.320962 + 0.555922i) q^{38} +(0.223540 - 0.129061i) q^{40} +(-0.0994958 - 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} -8.34605i q^{44} +0.767730 q^{46} +(4.98595 - 8.63591i) q^{47} +(-0.500069 + 0.288715i) q^{50} +(-3.46814 - 2.00233i) q^{52} +4.21753i q^{53} -2.22598i q^{55} +(-0.514008 - 0.890287i) q^{58} +(-6.71960 - 11.6387i) q^{59} +(-11.3564 - 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(-0.924990 - 0.534043i) q^{65} +(3.29001 + 5.69847i) q^{67} +(-4.35478 - 7.54270i) q^{68} -8.50587i q^{71} -5.61202i q^{73} +(0.342497 + 0.197741i) q^{74} +(-9.01980 + 5.20758i) q^{76} +(-0.286342 + 0.495959i) q^{79} +2.07029 q^{80} +0.0243455i q^{82} +(5.42692 - 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(-0.839806 + 0.484862i) q^{86} +(-1.02494 + 1.77525i) q^{88} +12.8738 q^{89} +(10.7875 + 6.22819i) q^{92} +(-1.05656 + 0.610003i) q^{94} +(-2.40568 + 1.38892i) q^{95} +(-0.493773 - 0.285080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48q + 24q^{4} + O(q^{10}) \)	\( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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