LMFDB - Embedded newform 5733.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5733,2,Mod(1,5733)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5733, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

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

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

chi := DirichletCharacter("5733.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5733 = 3^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5733.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$45.7782354788$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 637)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.210756$ of defining polynomial
Character	$\chi$	$=$	5733.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.21076 q^{2} -0.534070 q^{4} +2.21076 q^{5} -3.06814 q^{8} +O(q^{10})$	$q+1.21076 q^{2} -0.534070 q^{4} +2.21076 q^{5} -3.06814 q^{8} +2.67669 q^{10} +0.789244 q^{11} +1.00000 q^{13} -2.64663 q^{16} -1.74483 q^{17} -4.32331 q^{19} -1.18070 q^{20} +0.955582 q^{22} +1.11256 q^{23} -0.112558 q^{25} +1.21076 q^{26} +8.48965 q^{29} -5.70041 q^{31} +2.93186 q^{32} -2.11256 q^{34} +2.27890 q^{37} -5.23448 q^{38} -6.78291 q^{40} +12.1363 q^{41} +8.06814 q^{43} -0.421512 q^{44} +1.34704 q^{46} +8.74483 q^{47} -0.136281 q^{50} -0.534070 q^{52} -7.95558 q^{53} +1.74483 q^{55} +10.2789 q^{58} +10.9556 q^{59} +13.0681 q^{61} -6.90180 q^{62} +8.84302 q^{64} +2.21076 q^{65} +6.55779 q^{67} +0.931860 q^{68} -5.85738 q^{71} -8.00936 q^{73} +2.75919 q^{74} +2.30895 q^{76} -6.91116 q^{79} -5.85105 q^{80} +14.6941 q^{82} +3.14262 q^{83} -3.85738 q^{85} +9.76855 q^{86} -2.42151 q^{88} +3.39145 q^{89} -0.594184 q^{92} +10.5878 q^{94} -9.55779 q^{95} +0.0981974 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{8}+O(q^{10}) $ 3 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 6 * q^8	$ 3 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{8} + 14 q^{10} + 4 q^{11} + 3 q^{13} + 4 q^{16} + 4 q^{17} - 7 q^{19} + 16 q^{20} - 8 q^{22} - q^{23} + 4 q^{25} + 2 q^{26} + 7 q^{29} + 3 q^{31} + 24 q^{32} - 2 q^{34} - 10 q^{37} + 12 q^{38} + 22 q^{40} + 6 q^{41} + 9 q^{43} + 2 q^{44} - 28 q^{46} + 17 q^{47} + 30 q^{50} + 6 q^{52} - 13 q^{53} - 4 q^{55} + 14 q^{58} + 22 q^{59} + 24 q^{61} - 18 q^{62} + 20 q^{64} + 5 q^{65} - 14 q^{67} + 18 q^{68} - 4 q^{71} - 5 q^{73} - 8 q^{74} + 8 q^{76} + q^{79} + 40 q^{80} - 20 q^{82} + 23 q^{83} + 2 q^{85} - 6 q^{86} - 4 q^{88} - 11 q^{89} - 30 q^{92} + 16 q^{94} + 5 q^{95} + 3 q^{97}+O(q^{100}) $ 3 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 6 * q^8 + 14 * q^10 + 4 * q^11 + 3 * q^13 + 4 * q^16 + 4 * q^17 - 7 * q^19 + 16 * q^20 - 8 * q^22 - q^23 + 4 * q^25 + 2 * q^26 + 7 * q^29 + 3 * q^31 + 24 * q^32 - 2 * q^34 - 10 * q^37 + 12 * q^38 + 22 * q^40 + 6 * q^41 + 9 * q^43 + 2 * q^44 - 28 * q^46 + 17 * q^47 + 30 * q^50 + 6 * q^52 - 13 * q^53 - 4 * q^55 + 14 * q^58 + 22 * q^59 + 24 * q^61 - 18 * q^62 + 20 * q^64 + 5 * q^65 - 14 * q^67 + 18 * q^68 - 4 * q^71 - 5 * q^73 - 8 * q^74 + 8 * q^76 + q^79 + 40 * q^80 - 20 * q^82 + 23 * q^83 + 2 * q^85 - 6 * q^86 - 4 * q^88 - 11 * q^89 - 30 * q^92 + 16 * q^94 + 5 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.21076	0.856134	0.428067	−	0.903747i	$-0.359195\pi$
$2$	1.21076	0.856134	0.428067	+	0.903747i	$0.359195\pi$
$3$	0	0
$3$	0	0
$4$	−0.534070	−0.267035
$5$	2.21076	0.988680	0.494340	−	0.869269i	$-0.335410\pi$
$5$	2.21076	0.988680	0.494340	+	0.869269i	$0.335410\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−3.06814	−1.08475
$9$	0	0
$10$	2.67669	0.846442
$11$	0.789244	0.237966	0.118983	−	0.992896i	$-0.462037\pi$
$11$	0.789244	0.237966	0.118983	+	0.992896i	$0.462037\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	−2.64663	−0.661657
$17$	−1.74483	−0.423182	−0.211591	−	0.977358i	$-0.567865\pi$
$17$	−1.74483	−0.423182	−0.211591	+	0.977358i	$0.567865\pi$
$18$	0	0
$19$	−4.32331	−0.991836	−0.495918	−	0.868369i	$-0.665168\pi$
$19$	−4.32331	−0.991836	−0.495918	+	0.868369i	$0.665168\pi$
$20$	−1.18070	−0.264012
$21$	0	0
$22$	0.955582	0.203731
$23$	1.11256	0.231984	0.115992	−	0.993250i	$-0.462995\pi$
$23$	1.11256	0.231984	0.115992	+	0.993250i	$0.462995\pi$
$24$	0	0
$25$	−0.112558	−0.0225117
$26$	1.21076	0.237449
$27$	0	0
$28$	0	0
$29$	8.48965	1.57649	0.788244	−	0.615362i	$-0.210990\pi$
$29$	8.48965	1.57649	0.788244	+	0.615362i	$0.210990\pi$
$30$	0	0
$31$	−5.70041	−1.02382	−0.511912	−	0.859038i	$-0.671063\pi$
$31$	−5.70041	−1.02382	−0.511912	+	0.859038i	$0.671063\pi$
$32$	2.93186	0.518284
$33$	0	0
$34$	−2.11256	−0.362301
$35$	0	0
$36$	0	0
$37$	2.27890	0.374648	0.187324	−	0.982298i	$-0.440019\pi$
$37$	2.27890	0.374648	0.187324	+	0.982298i	$0.440019\pi$
$38$	−5.23448	−0.849144
$39$	0	0
$40$	−6.78291	−1.07247
$41$	12.1363	1.89537	0.947684	−	0.319209i	$-0.103417\pi$
$41$	12.1363	1.89537	0.947684	+	0.319209i	$0.103417\pi$
$42$	0	0
$43$	8.06814	1.23038	0.615190	−	0.788379i	$-0.289079\pi$
$43$	8.06814	1.23038	0.615190	+	0.788379i	$0.289079\pi$
$44$	−0.421512	−0.0635453
$45$	0	0
$46$	1.34704	0.198610
$47$	8.74483	1.27556	0.637782	−	0.770217i	$-0.279852\pi$
$47$	8.74483	1.27556	0.637782	+	0.770217i	$0.279852\pi$
$48$	0	0
$49$	0	0
$50$	−0.136281	−0.0192730
$51$	0	0
$52$	−0.534070	−0.0740622
$53$	−7.95558	−1.09278	−0.546392	−	0.837530i	$-0.683999\pi$
$53$	−7.95558	−1.09278	−0.546392	+	0.837530i	$0.683999\pi$
$54$	0	0
$55$	1.74483	0.235272
$56$	0	0
$57$	0	0
$58$	10.2789	1.34969
$59$	10.9556	1.42630	0.713148	−	0.701014i	$-0.247269\pi$
$59$	10.9556	1.42630	0.713148	+	0.701014i	$0.247269\pi$
$60$	0	0
$61$	13.0681	1.67320	0.836602	−	0.547811i	$-0.184539\pi$
$61$	13.0681	1.67320	0.836602	+	0.547811i	$0.184539\pi$
$62$	−6.90180	−0.876530
$63$	0	0
$64$	8.84302	1.10538
$65$	2.21076	0.274211
$66$	0	0
$67$	6.55779	0.801162	0.400581	−	0.916261i	$-0.368808\pi$
$67$	6.55779	0.801162	0.400581	+	0.916261i	$0.368808\pi$
$68$	0.931860	0.113005
$69$	0	0
$70$	0	0
$71$	−5.85738	−0.695144	−0.347572	−	0.937653i	$-0.612994\pi$
$71$	−5.85738	−0.695144	−0.347572	+	0.937653i	$0.612994\pi$
$72$	0	0
$73$	−8.00936	−0.937425	−0.468712	−	0.883351i	$-0.655282\pi$
$73$	−8.00936	−0.937425	−0.468712	+	0.883351i	$0.655282\pi$
$74$	2.75919	0.320749
$75$	0	0
$76$	2.30895	0.264855
$77$	0	0
$78$	0	0
$79$	−6.91116	−0.777567	−0.388783	−	0.921329i	$-0.627105\pi$
$79$	−6.91116	−0.777567	−0.388783	+	0.921329i	$0.627105\pi$
$80$	−5.85105	−0.654167
$81$	0	0
$82$	14.6941	1.62269
$83$	3.14262	0.344947	0.172473	−	0.985014i	$-0.444824\pi$
$83$	3.14262	0.344947	0.172473	+	0.985014i	$0.444824\pi$
$84$	0	0
$85$	−3.85738	−0.418392
$86$	9.76855	1.05337
$87$	0	0
$88$	−2.42151	−0.258134
$89$	3.39145	0.359493	0.179747	−	0.983713i	$-0.442472\pi$
$89$	3.39145	0.359493	0.179747	+	0.983713i	$0.442472\pi$
$90$	0	0
$91$	0	0
$92$	−0.594184	−0.0619480
$93$	0	0
$94$	10.5878	1.09205
$95$	−9.55779	−0.980609
$96$	0	0
$97$	0.0981974	0.00997044	0.00498522	−	0.999988i	$-0.498413\pi$
$97$	0.0981974	0.00997044	0.00498522	+	0.999988i	$0.498413\pi$
$98$	0	0
$99$	0	0
$100$	0.0601141	0.00601141
$101$	6.90180	0.686755	0.343378	−	0.939197i	$-0.388429\pi$
$101$	6.90180	0.686755	0.343378	+	0.939197i	$0.388429\pi$
$102$	0	0
$103$	15.8223	1.55902	0.779510	−	0.626390i	$-0.215468\pi$
$103$	15.8223	1.55902	0.779510	+	0.626390i	$0.215468\pi$
$104$	−3.06814	−0.300856
$105$	0	0
$106$	−9.63227	−0.935569
$107$	2.02372	0.195641	0.0978203	−	0.995204i	$-0.468813\pi$
$107$	2.02372	0.195641	0.0978203	+	0.995204i	$0.468813\pi$
$108$	0	0
$109$	−17.3470	−1.66154	−0.830772	−	0.556612i	$-0.812101\pi$
$109$	−17.3470	−1.66154	−0.830772	+	0.556612i	$0.812101\pi$
$110$	2.11256	0.201425
$111$	0	0
$112$	0	0
$113$	−10.1807	−0.957720	−0.478860	−	0.877891i	$-0.658950\pi$
$113$	−10.1807	−0.957720	−0.478860	+	0.877891i	$0.658950\pi$
$114$	0	0
$115$	2.45960	0.229358
$116$	−4.53407	−0.420978
$117$	0	0
$118$	13.2645	1.22110
$119$	0	0
$120$	0	0
$121$	−10.3771	−0.943372
$122$	15.8223	1.43249
$123$	0	0
$124$	3.04442	0.273397
$125$	−11.3026	−1.01094
$126$	0	0
$127$	16.4452	1.45928	0.729639	−	0.683832i	$-0.239688\pi$
$127$	16.4452	1.45928	0.729639	+	0.683832i	$0.239688\pi$
$128$	4.84302	0.428067
$129$	0	0
$130$	2.67669	0.234761
$131$	12.3327	1.07751	0.538755	−	0.842462i	$-0.318895\pi$
$131$	12.3327	1.07751	0.538755	+	0.842462i	$0.318895\pi$
$132$	0	0
$133$	0	0
$134$	7.93989	0.685902
$135$	0	0
$136$	5.35337	0.459048
$137$	3.34704	0.285957	0.142978	−	0.989726i	$-0.454332\pi$
$137$	3.34704	0.285957	0.142978	+	0.989726i	$0.454332\pi$
$138$	0	0
$139$	6.16634	0.523022	0.261511	−	0.965201i	$-0.415779\pi$
$139$	6.16634	0.523022	0.261511	+	0.965201i	$0.415779\pi$
$140$	0	0
$141$	0	0
$142$	−7.09186	−0.595136
$143$	0.789244	0.0659999
$144$	0	0
$145$	18.7685	1.55864
$146$	−9.69738	−0.802561
$147$	0	0
$148$	−1.21709	−0.100044
$149$	−18.8367	−1.54316	−0.771581	−	0.636131i	$-0.780534\pi$
$149$	−18.8367	−1.54316	−0.771581	+	0.636131i	$0.780534\pi$
$150$	0	0
$151$	20.1901	1.64304	0.821522	−	0.570177i	$-0.193125\pi$
$151$	20.1901	1.64304	0.821522	+	0.570177i	$0.193125\pi$
$152$	13.2645	1.07590
$153$	0	0
$154$	0	0
$155$	−12.6022	−1.01223
$156$	0	0
$157$	−13.8811	−1.10783	−0.553916	−	0.832572i	$-0.686867\pi$
$157$	−13.8811	−1.10783	−0.553916	+	0.832572i	$0.686867\pi$
$158$	−8.36773	−0.665701
$159$	0	0
$160$	6.48163	0.512418
$161$	0	0
$162$	0	0
$163$	11.4897	0.899939	0.449970	−	0.893044i	$-0.351435\pi$
$163$	11.4897	0.899939	0.449970	+	0.893044i	$0.351435\pi$
$164$	−6.48163	−0.506130
$165$	0	0
$166$	3.80494	0.295321
$167$	−12.9699	−1.00364	−0.501822	−	0.864971i	$-0.667337\pi$
$167$	−12.9699	−1.00364	−0.501822	+	0.864971i	$0.667337\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−4.67035	−0.358200
$171$	0	0
$172$	−4.30895	−0.328555
$173$	2.48029	0.188573	0.0942865	−	0.995545i	$-0.469943\pi$
$173$	2.48029	0.188573	0.0942865	+	0.995545i	$0.469943\pi$
$174$	0	0
$175$	0	0
$176$	−2.08884	−0.157452
$177$	0	0
$178$	4.10622	0.307774
$179$	8.15698	0.609681	0.304841	−	0.952403i	$-0.401397\pi$
$179$	8.15698	0.609681	0.304841	+	0.952403i	$0.401397\pi$
$180$	0	0
$181$	−3.60855	−0.268221	−0.134111	−	0.990966i	$-0.542818\pi$
$181$	−3.60855	−0.268221	−0.134111	+	0.990966i	$0.542818\pi$
$182$	0	0
$183$	0	0
$184$	−3.41349	−0.251645
$185$	5.03808	0.370407
$186$	0	0
$187$	−1.37709	−0.100703
$188$	−4.67035	−0.340620
$189$	0	0
$190$	−11.5722	−0.839532
$191$	−0.337675	−0.0244333	−0.0122167	−	0.999925i	$-0.503889\pi$
$191$	−0.337675	−0.0244333	−0.0122167	+	0.999925i	$0.503889\pi$
$192$	0	0
$193$	8.42151	0.606194	0.303097	−	0.952960i	$-0.401979\pi$
$193$	8.42151	0.606194	0.303097	+	0.952960i	$0.401979\pi$
$194$	0.118893	0.00853603
$195$	0	0
$196$	0	0
$197$	8.51035	0.606337	0.303169	−	0.952937i	$-0.401955\pi$
$197$	8.51035	0.606337	0.303169	+	0.952937i	$0.401955\pi$
$198$	0	0
$199$	14.6166	1.03614	0.518071	−	0.855338i	$-0.326650\pi$
$199$	14.6166	1.03614	0.518071	+	0.855338i	$0.326650\pi$
$200$	0.345345	0.0244196
$201$	0	0
$202$	8.35640	0.587954
$203$	0	0
$204$	0	0
$205$	26.8304	1.87391
$206$	19.1570	1.33473
$207$	0	0
$208$	−2.64663	−0.183511
$209$	−3.41215	−0.236023
$210$	0	0
$211$	−23.8667	−1.64305	−0.821527	−	0.570169i	$-0.806878\pi$
$211$	−23.8667	−1.64305	−0.821527	+	0.570169i	$0.806878\pi$
$212$	4.24884	0.291811
$213$	0	0
$214$	2.45023	0.167495
$215$	17.8367	1.21645
$216$	0	0
$217$	0	0
$218$	−21.0030	−1.42250
$219$	0	0
$220$	−0.931860	−0.0628260
$221$	−1.74483	−0.117370
$222$	0	0
$223$	−1.27890	−0.0856412	−0.0428206	−	0.999083i	$-0.513634\pi$
$223$	−1.27890	−0.0856412	−0.0428206	+	0.999083i	$0.513634\pi$
$224$	0	0
$225$	0	0
$226$	−12.3263	−0.819936
$227$	9.57849	0.635747	0.317873	−	0.948133i	$-0.397031\pi$
$227$	9.57849	0.635747	0.317873	+	0.948133i	$0.397031\pi$
$228$	0	0
$229$	13.5134	0.892989	0.446494	−	0.894786i	$-0.352672\pi$
$229$	13.5134	0.892989	0.446494	+	0.894786i	$0.352672\pi$
$230$	2.97797	0.196361
$231$	0	0
$232$	−26.0474	−1.71010
$233$	−28.9586	−1.89714	−0.948571	−	0.316565i	$-0.897470\pi$
$233$	−28.9586	−1.89714	−0.948571	+	0.316565i	$0.897470\pi$
$234$	0	0
$235$	19.3327	1.26112
$236$	−5.85105	−0.380871
$237$	0	0
$238$	0	0
$239$	24.1363	1.56125	0.780623	−	0.625002i	$-0.214902\pi$
$239$	24.1363	1.56125	0.780623	+	0.625002i	$0.214902\pi$
$240$	0	0
$241$	9.92552	0.639359	0.319680	−	0.947526i	$-0.396425\pi$
$241$	9.92552	0.639359	0.319680	+	0.947526i	$0.396425\pi$
$242$	−12.5641	−0.807653
$243$	0	0
$244$	−6.97930	−0.446804
$245$	0	0
$246$	0	0
$247$	−4.32331	−0.275086
$248$	17.4897	1.11059
$249$	0	0
$250$	−13.6847	−0.865497
$251$	18.4990	1.16765	0.583824	−	0.811880i	$-0.301556\pi$
$251$	18.4990	1.16765	0.583824	+	0.811880i	$0.301556\pi$
$252$	0	0
$253$	0.878080	0.0552044
$254$	19.9112	1.24934
$255$	0	0
$256$	−11.8223	−0.738895
$257$	16.6767	1.04026	0.520132	−	0.854086i	$-0.325883\pi$
$257$	16.6767	1.04026	0.520132	+	0.854086i	$0.325883\pi$
$258$	0	0
$259$	0	0
$260$	−1.18070	−0.0732238
$261$	0	0
$262$	14.9319	0.922493
$263$	13.4690	0.830531	0.415266	−	0.909700i	$-0.363689\pi$
$263$	13.4690	0.830531	0.415266	+	0.909700i	$0.363689\pi$
$264$	0	0
$265$	−17.5878	−1.08041
$266$	0	0
$267$	0	0
$268$	−3.50232	−0.213938
$269$	−30.5578	−1.86314	−0.931571	−	0.363560i	$-0.881561\pi$
$269$	−30.5578	−1.86314	−0.931571	+	0.363560i	$0.881561\pi$
$270$	0	0
$271$	−4.22512	−0.256658	−0.128329	−	0.991732i	$-0.540961\pi$
$271$	−4.22512	−0.256658	−0.128329	+	0.991732i	$0.540961\pi$
$272$	4.61791	0.280002
$273$	0	0
$274$	4.05244	0.244817
$275$	−0.0888361	−0.00535702
$276$	0	0
$277$	−3.00000	−0.180253	−0.0901263	−	0.995930i	$-0.528727\pi$
$277$	−3.00000	−0.180253	−0.0901263	+	0.995930i	$0.528727\pi$
$278$	7.46593	0.447777
$279$	0	0
$280$	0	0
$281$	6.27890	0.374568	0.187284	−	0.982306i	$-0.440032\pi$
$281$	6.27890	0.374568	0.187284	+	0.982306i	$0.440032\pi$
$282$	0	0
$283$	−23.5371	−1.39914	−0.699568	−	0.714566i	$-0.746624\pi$
$283$	−23.5371	−1.39914	−0.699568	+	0.714566i	$0.746624\pi$
$284$	3.12825	0.185628
$285$	0	0
$286$	0.955582	0.0565047
$287$	0	0
$288$	0	0
$289$	−13.9556	−0.820917
$290$	22.7241	1.33441
$291$	0	0
$292$	4.27756	0.250325
$293$	21.6166	1.26285	0.631427	−	0.775435i	$-0.282470\pi$
$293$	21.6166	1.26285	0.631427	+	0.775435i	$0.282470\pi$
$294$	0	0
$295$	24.2201	1.41015
$296$	−6.99197	−0.406400
$297$	0	0
$298$	−22.8066	−1.32115
$299$	1.11256	0.0643409
$300$	0	0
$301$	0	0
$302$	24.4452	1.40667
$303$	0	0
$304$	11.4422	0.656256
$305$	28.8905	1.65426
$306$	0	0
$307$	20.3945	1.16397	0.581987	−	0.813198i	$-0.302275\pi$
$307$	20.3945	1.16397	0.581987	+	0.813198i	$0.302275\pi$
$308$	0	0
$309$	0	0
$310$	−15.2582	−0.866608
$311$	12.9492	0.734284	0.367142	−	0.930165i	$-0.380336\pi$
$311$	12.9492	0.734284	0.367142	+	0.930165i	$0.380336\pi$
$312$	0	0
$313$	33.2345	1.87852	0.939262	−	0.343201i	$-0.111511\pi$
$313$	33.2345	1.87852	0.939262	+	0.343201i	$0.111511\pi$
$314$	−16.8066	−0.948453
$315$	0	0
$316$	3.69105	0.207638
$317$	4.87175	0.273624	0.136812	−	0.990597i	$-0.456314\pi$
$317$	4.87175	0.273624	0.136812	+	0.990597i	$0.456314\pi$
$318$	0	0
$319$	6.70041	0.375151
$320$	19.5498	1.09287
$321$	0	0
$322$	0	0
$323$	7.54343	0.419728
$324$	0	0
$325$	−0.112558	−0.00624362
$326$	13.9112	0.770468
$327$	0	0
$328$	−37.2358	−2.05600
$329$	0	0
$330$	0	0
$331$	6.87175	0.377705	0.188853	−	0.982005i	$-0.439523\pi$
$331$	6.87175	0.377705	0.188853	+	0.982005i	$0.439523\pi$
$332$	−1.67838	−0.0921129
$333$	0	0
$334$	−15.7034	−0.859254
$335$	14.4977	0.792093
$336$	0	0
$337$	11.0712	0.603085	0.301542	−	0.953453i	$-0.402499\pi$
$337$	11.0712	0.603085	0.301542	+	0.953453i	$0.402499\pi$
$338$	1.21076	0.0658564
$339$	0	0
$340$	2.06011	0.111725
$341$	−4.49901	−0.243635
$342$	0	0
$343$	0	0
$344$	−24.7542	−1.33466
$345$	0	0
$346$	3.00303	0.161444
$347$	−5.62593	−0.302016	−0.151008	−	0.988533i	$-0.548252\pi$
$347$	−5.62593	−0.302016	−0.151008	+	0.988533i	$0.548252\pi$
$348$	0	0
$349$	−18.4783	−0.989122	−0.494561	−	0.869143i	$-0.664671\pi$
$349$	−18.4783	−0.989122	−0.494561	+	0.869143i	$0.664671\pi$
$350$	0	0
$351$	0	0
$352$	2.31395	0.123334
$353$	4.67035	0.248578	0.124289	−	0.992246i	$-0.460335\pi$
$353$	4.67035	0.248578	0.124289	+	0.992246i	$0.460335\pi$
$354$	0	0
$355$	−12.9492	−0.687275
$356$	−1.81127	−0.0959974
$357$	0	0
$358$	9.87611	0.521968
$359$	11.7211	0.618616	0.309308	−	0.950962i	$-0.399903\pi$
$359$	11.7211	0.618616	0.309308	+	0.950962i	$0.399903\pi$
$360$	0	0
$361$	−0.308953	−0.0162607
$362$	−4.36907	−0.229633
$363$	0	0
$364$	0	0
$365$	−17.7067	−0.926813
$366$	0	0
$367$	−19.9699	−1.04242	−0.521211	−	0.853428i	$-0.674520\pi$
$367$	−19.9699	−1.04242	−0.521211	+	0.853428i	$0.674520\pi$
$368$	−2.94453	−0.153494
$369$	0	0
$370$	6.09989	0.317118
$371$	0	0
$372$	0	0
$373$	−4.42651	−0.229196	−0.114598	−	0.993412i	$-0.536558\pi$
$373$	−4.42651	−0.229196	−0.114598	+	0.993412i	$0.536558\pi$
$374$	−1.66732	−0.0862153
$375$	0	0
$376$	−26.8304	−1.38367
$377$	8.48965	0.437239
$378$	0	0
$379$	−32.5702	−1.67302	−0.836509	−	0.547953i	$-0.815407\pi$
$379$	−32.5702	−1.67302	−0.836509	+	0.547953i	$0.815407\pi$
$380$	5.10453	0.261857
$381$	0	0
$382$	−0.408842	−0.0209182
$383$	14.1964	0.725402	0.362701	−	0.931906i	$-0.381855\pi$
$383$	14.1964	0.725402	0.362701	+	0.931906i	$0.381855\pi$
$384$	0	0
$385$	0	0
$386$	10.1964	0.518983
$387$	0	0
$388$	−0.0524443	−0.00266246
$389$	−17.3170	−0.878006	−0.439003	−	0.898486i	$-0.644668\pi$
$389$	−17.3170	−0.878006	−0.439003	+	0.898486i	$0.644668\pi$
$390$	0	0
$391$	−1.94122	−0.0981718
$392$	0	0
$393$	0	0
$394$	10.3040	0.519106
$395$	−15.2789	−0.768765
$396$	0	0
$397$	−15.7241	−0.789171	−0.394586	−	0.918859i	$-0.629112\pi$
$397$	−15.7241	−0.789171	−0.394586	+	0.918859i	$0.629112\pi$
$398$	17.6971	0.887075
$399$	0	0
$400$	0.297900	0.0148950
$401$	−3.57849	−0.178701	−0.0893506	−	0.996000i	$-0.528479\pi$
$401$	−3.57849	−0.178701	−0.0893506	+	0.996000i	$0.528479\pi$
$402$	0	0
$403$	−5.70041	−0.283958
$404$	−3.68605	−0.183388
$405$	0	0
$406$	0	0
$407$	1.79861	0.0891536
$408$	0	0
$409$	31.3501	1.55016	0.775080	−	0.631863i	$-0.217709\pi$
$409$	31.3501	1.55016	0.775080	+	0.631863i	$0.217709\pi$
$410$	32.4850	1.60432
$411$	0	0
$412$	−8.45023	−0.416313
$413$	0	0
$414$	0	0
$415$	6.94756	0.341042
$416$	2.93186	0.143746
$417$	0	0
$418$	−4.13128	−0.202068
$419$	−28.7716	−1.40558	−0.702792	−	0.711396i	$-0.748063\pi$
$419$	−28.7716	−1.40558	−0.702792	+	0.711396i	$0.748063\pi$
$420$	0	0
$421$	−0.190060	−0.00926297	−0.00463148	−	0.999989i	$-0.501474\pi$
$421$	−0.190060	−0.00926297	−0.00463148	+	0.999989i	$0.501474\pi$
$422$	−28.8968	−1.40667
$423$	0	0
$424$	24.4088	1.18540
$425$	0.196395	0.00952655
$426$	0	0
$427$	0	0
$428$	−1.08081	−0.0522429
$429$	0	0
$430$	21.5959	1.04145
$431$	−25.6734	−1.23664	−0.618322	−	0.785925i	$-0.712187\pi$
$431$	−25.6734	−1.23664	−0.618322	+	0.785925i	$0.712187\pi$
$432$	0	0
$433$	−1.82233	−0.0875755	−0.0437877	−	0.999041i	$-0.513943\pi$
$433$	−1.82233	−0.0875755	−0.0437877	+	0.999041i	$0.513943\pi$
$434$	0	0
$435$	0	0
$436$	9.26454	0.443691
$437$	−4.80994	−0.230091
$438$	0	0
$439$	−0.735465	−0.0351018	−0.0175509	−	0.999846i	$-0.505587\pi$
$439$	−0.735465	−0.0351018	−0.0175509	+	0.999846i	$0.505587\pi$
$440$	−5.35337	−0.255212
$441$	0	0
$442$	−2.11256	−0.100484
$443$	3.71174	0.176350	0.0881751	−	0.996105i	$-0.471896\pi$
$443$	3.71174	0.176350	0.0881751	+	0.996105i	$0.471896\pi$
$444$	0	0
$445$	7.49768	0.355424
$446$	−1.54843	−0.0733203
$447$	0	0
$448$	0	0
$449$	5.17570	0.244256	0.122128	−	0.992514i	$-0.461028\pi$
$449$	5.17570	0.244256	0.122128	+	0.992514i	$0.461028\pi$
$450$	0	0
$451$	9.57849	0.451033
$452$	5.43721	0.255745
$453$	0	0
$454$	11.5972	0.544284
$455$	0	0
$456$	0	0
$457$	−34.1299	−1.59653	−0.798266	−	0.602305i	$-0.794249\pi$
$457$	−34.1299	−1.59653	−0.798266	+	0.602305i	$0.794249\pi$
$458$	16.3614	0.764518
$459$	0	0
$460$	−1.31360	−0.0612467
$461$	−11.4008	−0.530989	−0.265494	−	0.964112i	$-0.585535\pi$
$461$	−11.4008	−0.530989	−0.265494	+	0.964112i	$0.585535\pi$
$462$	0	0
$463$	−30.0124	−1.39479	−0.697397	−	0.716685i	$-0.745659\pi$
$463$	−30.0124	−1.39479	−0.697397	+	0.716685i	$0.745659\pi$
$464$	−22.4690	−1.04310
$465$	0	0
$466$	−35.0618	−1.62421
$467$	34.1663	1.58103	0.790515	−	0.612443i	$-0.209813\pi$
$467$	34.1663	1.58103	0.790515	+	0.612443i	$0.209813\pi$
$468$	0	0
$469$	0	0
$470$	23.4072	1.07969
$471$	0	0
$472$	−33.6133	−1.54718
$473$	6.36773	0.292789
$474$	0	0
$475$	0.486625	0.0223279
$476$	0	0
$477$	0	0
$478$	29.2231	1.33664
$479$	−12.8761	−0.588324	−0.294162	−	0.955756i	$-0.595041\pi$
$479$	−12.8761	−0.588324	−0.294162	+	0.955756i	$0.595041\pi$
$480$	0	0
$481$	2.27890	0.103909
$482$	12.0174	0.547377
$483$	0	0
$484$	5.54210	0.251913
$485$	0.217091	0.00985758
$486$	0	0
$487$	−21.9399	−0.994191	−0.497096	−	0.867696i	$-0.665600\pi$
$487$	−21.9399	−0.994191	−0.497096	+	0.867696i	$0.665600\pi$
$488$	−40.0949	−1.81501
$489$	0	0
$490$	0	0
$491$	−4.11256	−0.185597	−0.0927986	−	0.995685i	$-0.529581\pi$
$491$	−4.11256	−0.185597	−0.0927986	+	0.995685i	$0.529581\pi$
$492$	0	0
$493$	−14.8130	−0.667142
$494$	−5.23448	−0.235510
$495$	0	0
$496$	15.0869	0.677420
$497$	0	0
$498$	0	0
$499$	19.0331	0.852038	0.426019	−	0.904714i	$-0.359916\pi$
$499$	19.0331	0.852038	0.426019	+	0.904714i	$0.359916\pi$
$500$	6.03639	0.269956
$501$	0	0
$502$	22.3978	0.999662
$503$	−35.8698	−1.59935	−0.799677	−	0.600430i	$-0.794996\pi$
$503$	−35.8698	−1.59935	−0.799677	+	0.600430i	$0.794996\pi$
$504$	0	0
$505$	15.2582	0.678981
$506$	1.06314	0.0472624
$507$	0	0
$508$	−8.78291	−0.389679
$509$	17.5465	0.777733	0.388867	−	0.921294i	$-0.372867\pi$
$509$	17.5465	0.777733	0.388867	+	0.921294i	$0.372867\pi$
$510$	0	0
$511$	0	0
$512$	−24.0000	−1.06066
$513$	0	0
$514$	20.1914	0.890604
$515$	34.9793	1.54137
$516$	0	0
$517$	6.90180	0.303541
$518$	0	0
$519$	0	0
$520$	−6.78291	−0.297450
$521$	−8.84302	−0.387420	−0.193710	−	0.981059i	$-0.562052\pi$
$521$	−8.84302	−0.387420	−0.193710	+	0.981059i	$0.562052\pi$
$522$	0	0
$523$	−21.9112	−0.958108	−0.479054	−	0.877785i	$-0.659020\pi$
$523$	−21.9112	−0.958108	−0.479054	+	0.877785i	$0.659020\pi$
$524$	−6.58651	−0.287733
$525$	0	0
$526$	16.3076	0.711046
$527$	9.94622	0.433264
$528$	0	0
$529$	−21.7622	−0.946183
$530$	−21.2946	−0.924978
$531$	0	0
$532$	0	0
$533$	12.1363	0.525681
$534$	0	0
$535$	4.47396	0.193426
$536$	−20.1202	−0.869061
$537$	0	0
$538$	−36.9980	−1.59510
$539$	0	0
$540$	0	0
$541$	22.8654	0.983061	0.491530	−	0.870860i	$-0.336438\pi$
$541$	22.8654	0.983061	0.491530	+	0.870860i	$0.336438\pi$
$542$	−5.11559	−0.219733
$543$	0	0
$544$	−5.11559	−0.219329
$545$	−38.3501	−1.64274
$546$	0	0
$547$	−35.2676	−1.50793	−0.753966	−	0.656913i	$-0.771862\pi$
$547$	−35.2676	−1.50793	−0.753966	+	0.656913i	$0.771862\pi$
$548$	−1.78755	−0.0763605
$549$	0	0
$550$	−0.107559	−0.00458632
$551$	−36.7034	−1.56362
$552$	0	0
$553$	0	0
$554$	−3.63227	−0.154320
$555$	0	0
$556$	−3.29326	−0.139665
$557$	−39.8698	−1.68934	−0.844668	−	0.535290i	$-0.820202\pi$
$557$	−39.8698	−1.68934	−0.844668	+	0.535290i	$0.820202\pi$
$558$	0	0
$559$	8.06814	0.341246
$560$	0	0
$561$	0	0
$562$	7.60221	0.320680
$563$	25.5972	1.07879	0.539397	−	0.842052i	$-0.318652\pi$
$563$	25.5972	1.07879	0.539397	+	0.842052i	$0.318652\pi$
$564$	0	0
$565$	−22.5070	−0.946878
$566$	−28.4977	−1.19785
$567$	0	0
$568$	17.9713	0.754058
$569$	25.0949	1.05203	0.526016	−	0.850475i	$-0.323685\pi$
$569$	25.0949	1.05203	0.526016	+	0.850475i	$0.323685\pi$
$570$	0	0
$571$	−31.2488	−1.30772	−0.653862	−	0.756614i	$-0.726852\pi$
$571$	−31.2488	−1.30772	−0.653862	+	0.756614i	$0.726852\pi$
$572$	−0.421512	−0.0176243
$573$	0	0
$574$	0	0
$575$	−0.125228	−0.00522236
$576$	0	0
$577$	12.8717	0.535858	0.267929	−	0.963439i	$-0.413661\pi$
$577$	12.8717	0.535858	0.267929	+	0.963439i	$0.413661\pi$
$578$	−16.8968	−0.702814
$579$	0	0
$580$	−10.0237	−0.416212
$581$	0	0
$582$	0	0
$583$	−6.27890	−0.260045
$584$	24.5738	1.01687
$585$	0	0
$586$	26.1724	1.08117
$587$	9.96692	0.411379	0.205689	−	0.978617i	$-0.434056\pi$
$587$	9.96692	0.411379	0.205689	+	0.978617i	$0.434056\pi$
$588$	0	0
$589$	24.6447	1.01547
$590$	29.3246	1.20728
$591$	0	0
$592$	−6.03139	−0.247889
$593$	−20.5909	−0.845566	−0.422783	−	0.906231i	$-0.638947\pi$
$593$	−20.5909	−0.845566	−0.422783	+	0.906231i	$0.638947\pi$
$594$	0	0
$595$	0	0
$596$	10.0601	0.412078
$597$	0	0
$598$	1.34704	0.0550844
$599$	12.5371	0.512252	0.256126	−	0.966643i	$-0.417554\pi$
$599$	12.5371	0.512252	0.256126	+	0.966643i	$0.417554\pi$
$600$	0	0
$601$	−1.82233	−0.0743343	−0.0371672	−	0.999309i	$-0.511833\pi$
$601$	−1.82233	−0.0743343	−0.0371672	+	0.999309i	$0.511833\pi$
$602$	0	0
$603$	0	0
$604$	−10.7829	−0.438750
$605$	−22.9412	−0.932693
$606$	0	0
$607$	30.9780	1.25736	0.628678	−	0.777665i	$-0.283596\pi$
$607$	30.9780	1.25736	0.628678	+	0.777665i	$0.283596\pi$
$608$	−12.6754	−0.514053
$609$	0	0
$610$	34.9793	1.41627
$611$	8.74483	0.353778
$612$	0	0
$613$	12.4502	0.502860	0.251430	−	0.967875i	$-0.419099\pi$
$613$	12.4502	0.502860	0.251430	+	0.967875i	$0.419099\pi$
$614$	24.6927	0.996518
$615$	0	0
$616$	0	0
$617$	−31.7809	−1.27945	−0.639726	−	0.768603i	$-0.720952\pi$
$617$	−31.7809	−1.27945	−0.639726	+	0.768603i	$0.720952\pi$
$618$	0	0
$619$	4.22512	0.169822	0.0849109	−	0.996389i	$-0.472939\pi$
$619$	4.22512	0.169822	0.0849109	+	0.996389i	$0.472939\pi$
$620$	6.73047	0.270302
$621$	0	0
$622$	15.6784	0.628646
$623$	0	0
$624$	0	0
$625$	−24.4245	−0.976982
$626$	40.2388	1.60827
$627$	0	0
$628$	7.41349	0.295830
$629$	−3.97628	−0.158545
$630$	0	0
$631$	7.31198	0.291085	0.145543	−	0.989352i	$-0.453507\pi$
$631$	7.31198	0.291085	0.145543	+	0.989352i	$0.453507\pi$
$632$	21.2044	0.843467
$633$	0	0
$634$	5.89849	0.234259
$635$	36.3564	1.44276
$636$	0	0
$637$	0	0
$638$	8.11256	0.321179
$639$	0	0
$640$	10.7067	0.423221
$641$	23.0474	0.910319	0.455160	−	0.890410i	$-0.349582\pi$
$641$	23.0474	0.910319	0.455160	+	0.890410i	$0.349582\pi$
$642$	0	0
$643$	−48.9379	−1.92992	−0.964961	−	0.262392i	$-0.915489\pi$
$643$	−48.9379	−1.92992	−0.964961	+	0.262392i	$0.915489\pi$
$644$	0	0
$645$	0	0
$646$	9.13325	0.359343
$647$	33.4309	1.31430	0.657152	−	0.753758i	$-0.271761\pi$
$647$	33.4309	1.31430	0.657152	+	0.753758i	$0.271761\pi$
$648$	0	0
$649$	8.64663	0.339410
$650$	−0.136281	−0.00534537
$651$	0	0
$652$	−6.13628	−0.240315
$653$	10.4629	0.409445	0.204723	−	0.978820i	$-0.434371\pi$
$653$	10.4629	0.409445	0.204723	+	0.978820i	$0.434371\pi$
$654$	0	0
$655$	27.2645	1.06531
$656$	−32.1202	−1.25408
$657$	0	0
$658$	0	0
$659$	8.73849	0.340403	0.170202	−	0.985409i	$-0.445558\pi$
$659$	8.73849	0.340403	0.170202	+	0.985409i	$0.445558\pi$
$660$	0	0
$661$	−4.61354	−0.179446	−0.0897230	−	0.995967i	$-0.528598\pi$
$661$	−4.61354	−0.179446	−0.0897230	+	0.995967i	$0.528598\pi$
$662$	8.32001	0.323366
$663$	0	0
$664$	−9.64199	−0.374182
$665$	0	0
$666$	0	0
$667$	9.44523	0.365721
$668$	6.92686	0.268008
$669$	0	0
$670$	17.5531	0.678137
$671$	10.3140	0.398166
$672$	0	0
$673$	9.83802	0.379228	0.189614	−	0.981859i	$-0.439276\pi$
$673$	9.83802	0.379228	0.189614	+	0.981859i	$0.439276\pi$
$674$	13.4045	0.516321
$675$	0	0
$676$	−0.534070	−0.0205412
$677$	−4.69541	−0.180459	−0.0902296	−	0.995921i	$-0.528760\pi$
$677$	−4.69541	−0.180459	−0.0902296	+	0.995921i	$0.528760\pi$
$678$	0	0
$679$	0	0
$680$	11.8350	0.453851
$681$	0	0
$682$	−5.44721	−0.208584
$683$	−11.0207	−0.421695	−0.210848	−	0.977519i	$-0.567622\pi$
$683$	−11.0207	−0.421695	−0.210848	+	0.977519i	$0.567622\pi$
$684$	0	0
$685$	7.39948	0.282720
$686$	0	0
$687$	0	0
$688$	−21.3534	−0.814090
$689$	−7.95558	−0.303084
$690$	0	0
$691$	−38.7635	−1.47463	−0.737317	−	0.675546i	$-0.763908\pi$
$691$	−38.7635	−1.47463	−0.737317	+	0.675546i	$0.763908\pi$
$692$	−1.32465	−0.0503556
$693$	0	0
$694$	−6.81163	−0.258566
$695$	13.6323	0.517101
$696$	0	0
$697$	−21.1757	−0.802087
$698$	−22.3727	−0.846820
$699$	0	0
$700$	0	0
$701$	32.0681	1.21120	0.605598	−	0.795770i	$-0.292934\pi$
$701$	32.0681	1.21120	0.605598	+	0.795770i	$0.292934\pi$
$702$	0	0
$703$	−9.85238	−0.371590
$704$	6.97930	0.263042
$705$	0	0
$706$	5.65465	0.212816
$707$	0	0
$708$	0	0
$709$	38.3451	1.44008	0.720040	−	0.693933i	$-0.244124\pi$
$709$	38.3451	1.44008	0.720040	+	0.693933i	$0.244124\pi$
$710$	−15.6784	−0.588399
$711$	0	0
$712$	−10.4055	−0.389961
$713$	−6.34204	−0.237511
$714$	0	0
$715$	1.74483	0.0652528
$716$	−4.35640	−0.162806
$717$	0	0
$718$	14.1914	0.529618
$719$	8.72413	0.325355	0.162678	−	0.986679i	$-0.447987\pi$
$719$	8.72413	0.325355	0.162678	+	0.986679i	$0.447987\pi$
$720$	0	0
$721$	0	0
$722$	−0.374067	−0.0139213
$723$	0	0
$724$	1.92722	0.0716244
$725$	−0.955582	−0.0354894
$726$	0	0
$727$	26.6754	0.989334	0.494667	−	0.869083i	$-0.335290\pi$
$727$	26.6754	0.989334	0.494667	+	0.869083i	$0.335290\pi$
$728$	0	0
$729$	0	0
$730$	−21.4385	−0.793476
$731$	−14.0775	−0.520675
$732$	0	0
$733$	26.7211	0.986966	0.493483	−	0.869755i	$-0.335723\pi$
$733$	26.7211	0.986966	0.493483	+	0.869755i	$0.335723\pi$
$734$	−24.1787	−0.892453
$735$	0	0
$736$	3.26187	0.120234
$737$	5.17570	0.190649
$738$	0	0
$739$	36.0538	1.32626	0.663130	−	0.748504i	$-0.269228\pi$
$739$	36.0538	1.32626	0.663130	+	0.748504i	$0.269228\pi$
$740$	−2.69069	−0.0989117
$741$	0	0
$742$	0	0
$743$	2.96058	0.108613	0.0543066	−	0.998524i	$-0.482705\pi$
$743$	2.96058	0.108613	0.0543066	+	0.998524i	$0.482705\pi$
$744$	0	0
$745$	−41.6433	−1.52569
$746$	−5.35942	−0.196222
$747$	0	0
$748$	0.735465	0.0268913
$749$	0	0
$750$	0	0
$751$	43.1550	1.57475	0.787374	−	0.616475i	$-0.211440\pi$
$751$	43.1550	1.57475	0.787374	+	0.616475i	$0.211440\pi$
$752$	−23.1443	−0.843986
$753$	0	0
$754$	10.2789	0.374335
$755$	44.6353	1.62444
$756$	0	0
$757$	18.7335	0.680880	0.340440	−	0.940266i	$-0.389424\pi$
$757$	18.7335	0.680880	0.340440	+	0.940266i	$0.389424\pi$
$758$	−39.4345	−1.43233
$759$	0	0
$760$	29.3246	1.06372
$761$	4.22948	0.153318	0.0766592	−	0.997057i	$-0.475575\pi$
$761$	4.22948	0.153318	0.0766592	+	0.997057i	$0.475575\pi$
$762$	0	0
$763$	0	0
$764$	0.180342	0.00652456
$765$	0	0
$766$	17.1884	0.621041
$767$	10.9556	0.395583
$768$	0	0
$769$	−21.1299	−0.761965	−0.380983	−	0.924582i	$-0.624414\pi$
$769$	−21.1299	−0.761965	−0.380983	+	0.924582i	$0.624414\pi$
$770$	0	0
$771$	0	0
$772$	−4.49768	−0.161875
$773$	−33.0742	−1.18960	−0.594798	−	0.803875i	$-0.702768\pi$
$773$	−33.0742	−1.18960	−0.594798	+	0.803875i	$0.702768\pi$
$774$	0	0
$775$	0.641629	0.0230480
$776$	−0.301284	−0.0108154
$777$	0	0
$778$	−20.9666	−0.751690
$779$	−52.4690	−1.87990
$780$	0	0
$781$	−4.62291	−0.165421
$782$	−2.35034	−0.0840482
$783$	0	0
$784$	0	0
$785$	−30.6877	−1.09529
$786$	0	0
$787$	6.23948	0.222413	0.111207	−	0.993797i	$-0.464528\pi$
$787$	6.23948	0.222413	0.111207	+	0.993797i	$0.464528\pi$
$788$	−4.54512	−0.161913
$789$	0	0
$790$	−18.4990	−0.658165
$791$	0	0
$792$	0	0
$793$	13.0681	0.464063
$794$	−19.0381	−0.675636
$795$	0	0
$796$	−7.80628	−0.276686
$797$	32.1837	1.14001	0.570003	−	0.821643i	$-0.306942\pi$
$797$	32.1837	1.14001	0.570003	+	0.821643i	$0.306942\pi$
$798$	0	0
$799$	−15.2582	−0.539796
$800$	−0.330006	−0.0116675
$801$	0	0
$802$	−4.33268	−0.152992
$803$	−6.32134	−0.223075
$804$	0	0
$805$	0	0
$806$	−6.90180	−0.243106
$807$	0	0
$808$	−21.1757	−0.744958
$809$	−47.8016	−1.68062	−0.840308	−	0.542109i	$-0.817626\pi$
$809$	−47.8016	−1.68062	−0.840308	+	0.542109i	$0.817626\pi$
$810$	0	0
$811$	−37.4957	−1.31665	−0.658326	−	0.752733i	$-0.728735\pi$
$811$	−37.4957	−1.31665	−0.658326	+	0.752733i	$0.728735\pi$
$812$	0	0
$813$	0	0
$814$	2.17767	0.0763274
$815$	25.4008	0.889752
$816$	0	0
$817$	−34.8811	−1.22034
$818$	37.9573	1.32714
$819$	0	0
$820$	−14.3293	−0.500401
$821$	−39.6447	−1.38361	−0.691804	−	0.722085i	$-0.743184\pi$
$821$	−39.6447	−1.38361	−0.691804	+	0.722085i	$0.743184\pi$
$822$	0	0
$823$	−17.4659	−0.608824	−0.304412	−	0.952540i	$-0.598460\pi$
$823$	−17.4659	−0.608824	−0.304412	+	0.952540i	$0.598460\pi$
$824$	−48.5451	−1.69115
$825$	0	0
$826$	0	0
$827$	1.53104	0.0532396	0.0266198	−	0.999646i	$-0.491526\pi$
$827$	1.53104	0.0532396	0.0266198	+	0.999646i	$0.491526\pi$
$828$	0	0
$829$	37.2218	1.29277	0.646383	−	0.763013i	$-0.276281\pi$
$829$	37.2218	1.29277	0.646383	+	0.763013i	$0.276281\pi$
$830$	8.41179	0.291978
$831$	0	0
$832$	8.84302	0.306577
$833$	0	0
$834$	0	0
$835$	−28.6734	−0.992283
$836$	1.82233	0.0630265
$837$	0	0
$838$	−34.8354	−1.20337
$839$	−7.37209	−0.254513	−0.127256	−	0.991870i	$-0.540617\pi$
$839$	−7.37209	−0.254513	−0.127256	+	0.991870i	$0.540617\pi$
$840$	0	0
$841$	43.0742	1.48532
$842$	−0.230116	−0.00793034
$843$	0	0
$844$	12.7465	0.438753
$845$	2.21076	0.0760523
$846$	0	0
$847$	0	0
$848$	21.0555	0.723048
$849$	0	0
$850$	0.237786	0.00815600
$851$	2.53541	0.0869126
$852$	0	0
$853$	−4.57215	−0.156548	−0.0782738	−	0.996932i	$-0.524941\pi$
$853$	−4.57215	−0.156548	−0.0782738	+	0.996932i	$0.524941\pi$
$854$	0	0
$855$	0	0
$856$	−6.20906	−0.212221
$857$	−52.0348	−1.77747	−0.888737	−	0.458417i	$-0.848416\pi$
$857$	−52.0348	−1.77747	−0.888737	+	0.458417i	$0.848416\pi$
$858$	0	0
$859$	−42.8905	−1.46340	−0.731702	−	0.681625i	$-0.761274\pi$
$859$	−42.8905	−1.46340	−0.731702	+	0.681625i	$0.761274\pi$
$860$	−9.52604	−0.324835
$861$	0	0
$862$	−31.0842	−1.05873
$863$	7.82233	0.266275	0.133138	−	0.991098i	$-0.457495\pi$
$863$	7.82233	0.266275	0.133138	+	0.991098i	$0.457495\pi$
$864$	0	0
$865$	5.48332	0.186438
$866$	−2.20639	−0.0749763
$867$	0	0
$868$	0	0
$869$	−5.45460	−0.185034
$870$	0	0
$871$	6.55779	0.222202
$872$	53.2231	1.80236
$873$	0	0
$874$	−5.82366	−0.196988
$875$	0	0
$876$	0	0
$877$	−34.7191	−1.17238	−0.586191	−	0.810173i	$-0.699373\pi$
$877$	−34.7191	−1.17238	−0.586191	+	0.810173i	$0.699373\pi$
$878$	−0.890468	−0.0300518
$879$	0	0
$880$	−4.61791	−0.155670
$881$	11.4422	0.385498	0.192749	−	0.981248i	$-0.438260\pi$
$881$	11.4422	0.385498	0.192749	+	0.981248i	$0.438260\pi$
$882$	0	0
$883$	−31.0217	−1.04396	−0.521982	−	0.852956i	$-0.674807\pi$
$883$	−31.0217	−1.04396	−0.521982	+	0.852956i	$0.674807\pi$
$884$	0.931860	0.0313418
$885$	0	0
$886$	4.49401	0.150979
$887$	12.8304	0.430801	0.215401	−	0.976526i	$-0.430894\pi$
$887$	12.8304	0.430801	0.215401	+	0.976526i	$0.430894\pi$
$888$	0	0
$889$	0	0
$890$	9.07786	0.304291
$891$	0	0
$892$	0.683020	0.0228692
$893$	−37.8066	−1.26515
$894$	0	0
$895$	18.0331	0.602780
$896$	0	0
$897$	0	0
$898$	6.26651	0.209116
$899$	−48.3945	−1.61405
$900$	0	0
$901$	13.8811	0.462447
$902$	11.5972	0.386145
$903$	0	0
$904$	31.2358	1.03889
$905$	−7.97761	−0.265185
$906$	0	0
$907$	10.1620	0.337423	0.168711	−	0.985665i	$-0.446039\pi$
$907$	10.1620	0.337423	0.168711	+	0.985665i	$0.446039\pi$
$908$	−5.11559	−0.169767
$909$	0	0
$910$	0	0
$911$	−34.4008	−1.13975	−0.569875	−	0.821731i	$-0.693008\pi$
$911$	−34.4008	−1.13975	−0.569875	+	0.821731i	$0.693008\pi$
$912$	0	0
$913$	2.48029	0.0820856
$914$	−41.3230	−1.36684
$915$	0	0
$916$	−7.21709	−0.238459
$917$	0	0
$918$	0	0
$919$	8.15500	0.269009	0.134504	−	0.990913i	$-0.457056\pi$
$919$	8.15500	0.269009	0.134504	+	0.990913i	$0.457056\pi$
$920$	−7.54638	−0.248797
$921$	0	0
$922$	−13.8036	−0.454598
$923$	−5.85738	−0.192798
$924$	0	0
$925$	−0.256509	−0.00843396
$926$	−36.3377	−1.19413
$927$	0	0
$928$	24.8905	0.817070
$929$	4.80994	0.157809	0.0789045	−	0.996882i	$-0.474858\pi$
$929$	4.80994	0.157809	0.0789045	+	0.996882i	$0.474858\pi$
$930$	0	0
$931$	0	0
$932$	15.4659	0.506603
$933$	0	0
$934$	41.3671	1.35357
$935$	−3.04442	−0.0995631
$936$	0	0
$937$	47.1931	1.54173	0.770865	−	0.636998i	$-0.219824\pi$
$937$	47.1931	1.54173	0.770865	+	0.636998i	$0.219824\pi$
$938$	0	0
$939$	0	0
$940$	−10.3250	−0.336765
$941$	27.5702	0.898762	0.449381	−	0.893340i	$-0.351645\pi$
$941$	27.5702	0.898762	0.449381	+	0.893340i	$0.351645\pi$
$942$	0	0
$943$	13.5023	0.439696
$944$	−28.9954	−0.943718
$945$	0	0
$946$	7.70977	0.250666
$947$	27.8698	0.905646	0.452823	−	0.891600i	$-0.350417\pi$
$947$	27.8698	0.905646	0.452823	+	0.891600i	$0.350417\pi$
$948$	0	0
$949$	−8.00936	−0.259995
$950$	0.589185	0.0191157
$951$	0	0
$952$	0	0
$953$	27.1076	0.878100	0.439050	−	0.898463i	$-0.355315\pi$
$953$	27.1076	0.878100	0.439050	+	0.898463i	$0.355315\pi$
$954$	0	0
$955$	−0.746518	−0.0241567
$956$	−12.8905	−0.416908
$957$	0	0
$958$	−15.5898	−0.503684
$959$	0	0
$960$	0	0
$961$	1.49465	0.0482146
$962$	2.75919	0.0889598
$963$	0	0
$964$	−5.30093	−0.170731
$965$	18.6179	0.599332
$966$	0	0
$967$	−4.45657	−0.143314	−0.0716568	−	0.997429i	$-0.522829\pi$
$967$	−4.45657	−0.143314	−0.0716568	+	0.997429i	$0.522829\pi$
$968$	31.8384	1.02332
$969$	0	0
$970$	0.262844	0.00843940
$971$	−18.9192	−0.607146	−0.303573	−	0.952808i	$-0.598180\pi$
$971$	−18.9192	−0.607146	−0.303573	+	0.952808i	$0.598180\pi$
$972$	0	0
$973$	0	0
$974$	−26.5638	−0.851161
$975$	0	0
$976$	−34.5865	−1.10709
$977$	−17.4359	−0.557823	−0.278911	−	0.960317i	$-0.589974\pi$
$977$	−17.4359	−0.557823	−0.278911	+	0.960317i	$0.589974\pi$
$978$	0	0
$979$	2.67669	0.0855472
$980$	0	0
$981$	0	0
$982$	−4.97930	−0.158896
$983$	−15.3815	−0.490592	−0.245296	−	0.969448i	$-0.578885\pi$
$983$	−15.3815	−0.490592	−0.245296	+	0.969448i	$0.578885\pi$
$984$	0	0
$985$	18.8143	0.599473
$986$	−17.9349	−0.571163
$987$	0	0
$988$	2.30895	0.0734576
$989$	8.97628	0.285429
$990$	0	0
$991$	2.42651	0.0770807	0.0385403	−	0.999257i	$-0.487729\pi$
$991$	2.42651	0.0770807	0.0385403	+	0.999257i	$0.487729\pi$
$992$	−16.7128	−0.530632
$993$	0	0
$994$	0	0
$995$	32.3137	1.02441
$996$	0	0
$997$	15.0869	0.477806	0.238903	−	0.971043i	$-0.423212\pi$
$997$	15.0869	0.477806	0.238903	+	0.971043i	$0.423212\pi$
$998$	23.0444	0.729458
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.be.1.2		3
3.2	odd	2		637.2.a.h.1.2	✓	3
7.6	odd	2		5733.2.a.bd.1.2		3
21.2	odd	6		637.2.e.l.508.2		6
21.5	even	6		637.2.e.k.508.2		6
21.11	odd	6		637.2.e.l.79.2		6
21.17	even	6		637.2.e.k.79.2		6
21.20	even	2		637.2.a.i.1.2	yes	3
39.38	odd	2		8281.2.a.bh.1.2		3
273.272	even	2		8281.2.a.bk.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.h.1.2	✓	3	3.2	odd	2
637.2.a.i.1.2	yes	3	21.20	even	2
637.2.e.k.79.2		6	21.17	even	6
637.2.e.k.508.2		6	21.5	even	6
637.2.e.l.79.2		6	21.11	odd	6
637.2.e.l.508.2		6	21.2	odd	6
5733.2.a.bd.1.2		3	7.6	odd	2
5733.2.a.be.1.2		3	1.1	even	1	trivial
8281.2.a.bh.1.2		3	39.38	odd	2
8281.2.a.bk.1.2		3	273.272	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5733.a (trivial)

\(f(q)\)	\(=\)	\(q+1.21076 q^{2} -0.534070 q^{4} +2.21076 q^{5} -3.06814 q^{8} +O(q^{10})\)	\(q+1.21076 q^{2} -0.534070 q^{4} +2.21076 q^{5} -3.06814 q^{8} +2.67669 q^{10} +0.789244 q^{11} +1.00000 q^{13} -2.64663 q^{16} -1.74483 q^{17} -4.32331 q^{19} -1.18070 q^{20} +0.955582 q^{22} +1.11256 q^{23} -0.112558 q^{25} +1.21076 q^{26} +8.48965 q^{29} -5.70041 q^{31} +2.93186 q^{32} -2.11256 q^{34} +2.27890 q^{37} -5.23448 q^{38} -6.78291 q^{40} +12.1363 q^{41} +8.06814 q^{43} -0.421512 q^{44} +1.34704 q^{46} +8.74483 q^{47} -0.136281 q^{50} -0.534070 q^{52} -7.95558 q^{53} +1.74483 q^{55} +10.2789 q^{58} +10.9556 q^{59} +13.0681 q^{61} -6.90180 q^{62} +8.84302 q^{64} +2.21076 q^{65} +6.55779 q^{67} +0.931860 q^{68} -5.85738 q^{71} -8.00936 q^{73} +2.75919 q^{74} +2.30895 q^{76} -6.91116 q^{79} -5.85105 q^{80} +14.6941 q^{82} +3.14262 q^{83} -3.85738 q^{85} +9.76855 q^{86} -2.42151 q^{88} +3.39145 q^{89} -0.594184 q^{92} +10.5878 q^{94} -9.55779 q^{95} +0.0981974 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{8}+O(q^{10}) \) 3 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 6 * q^8	\( 3 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{8} + 14 q^{10} + 4 q^{11} + 3 q^{13} + 4 q^{16} + 4 q^{17} - 7 q^{19} + 16 q^{20} - 8 q^{22} - q^{23} + 4 q^{25} + 2 q^{26} + 7 q^{29} + 3 q^{31} + 24 q^{32} - 2 q^{34} - 10 q^{37} + 12 q^{38} + 22 q^{40} + 6 q^{41} + 9 q^{43} + 2 q^{44} - 28 q^{46} + 17 q^{47} + 30 q^{50} + 6 q^{52} - 13 q^{53} - 4 q^{55} + 14 q^{58} + 22 q^{59} + 24 q^{61} - 18 q^{62} + 20 q^{64} + 5 q^{65} - 14 q^{67} + 18 q^{68} - 4 q^{71} - 5 q^{73} - 8 q^{74} + 8 q^{76} + q^{79} + 40 q^{80} - 20 q^{82} + 23 q^{83} + 2 q^{85} - 6 q^{86} - 4 q^{88} - 11 q^{89} - 30 q^{92} + 16 q^{94} + 5 q^{95} + 3 q^{97}+O(q^{100}) \) 3 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 6 * q^8 + 14 * q^10 + 4 * q^11 + 3 * q^13 + 4 * q^16 + 4 * q^17 - 7 * q^19 + 16 * q^20 - 8 * q^22 - q^23 + 4 * q^25 + 2 * q^26 + 7 * q^29 + 3 * q^31 + 24 * q^32 - 2 * q^34 - 10 * q^37 + 12 * q^38 + 22 * q^40 + 6 * q^41 + 9 * q^43 + 2 * q^44 - 28 * q^46 + 17 * q^47 + 30 * q^50 + 6 * q^52 - 13 * q^53 - 4 * q^55 + 14 * q^58 + 22 * q^59 + 24 * q^61 - 18 * q^62 + 20 * q^64 + 5 * q^65 - 14 * q^67 + 18 * q^68 - 4 * q^71 - 5 * q^73 - 8 * q^74 + 8 * q^76 + q^79 + 40 * q^80 - 20 * q^82 + 23 * q^83 + 2 * q^85 - 6 * q^86 - 4 * q^88 - 11 * q^89 - 30 * q^92 + 16 * q^94 + 5 * q^95 + 3 * q^97

Introduction

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