LMFDB - Embedded newform 5733.2.a.bp.1.4

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:	$5$
Coefficient field:	5.5.375116.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 7x^{2} + 2x - 2 $ x^5 - x^4 - 6x^3 + 7x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.32173$ 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)

$f(q)$	$=$	$q+1.78646 q^{2} +1.19144 q^{4} +3.42992 q^{5} -1.44447 q^{8} +O(q^{10})$	$q+1.78646 q^{2} +1.19144 q^{4} +3.42992 q^{5} -1.44447 q^{8} +6.12741 q^{10} -1.59502 q^{11} +1.00000 q^{13} -4.96335 q^{16} +0.0394874 q^{17} +3.64346 q^{19} +4.08653 q^{20} -2.84944 q^{22} +3.42236 q^{23} +6.76436 q^{25} +1.78646 q^{26} +10.0028 q^{29} +6.15479 q^{31} -5.97790 q^{32} +0.0705426 q^{34} -11.1303 q^{37} +6.50890 q^{38} -4.95440 q^{40} -5.08793 q^{41} +2.91631 q^{43} -1.90037 q^{44} +6.11391 q^{46} -4.10864 q^{47} +12.0842 q^{50} +1.19144 q^{52} +10.2912 q^{53} -5.47080 q^{55} +17.8697 q^{58} +9.19324 q^{59} +1.96051 q^{61} +10.9953 q^{62} -0.752565 q^{64} +3.42992 q^{65} +12.0569 q^{67} +0.0470468 q^{68} -1.79825 q^{71} +6.70505 q^{73} -19.8837 q^{74} +4.34095 q^{76} +14.6318 q^{79} -17.0239 q^{80} -9.08937 q^{82} -5.34655 q^{83} +0.135439 q^{85} +5.20986 q^{86} +2.30395 q^{88} -12.4694 q^{89} +4.07753 q^{92} -7.33991 q^{94} +12.4968 q^{95} +12.5010 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) $ 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8	$ 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8} + 2 q^{10} + q^{11} + 5 q^{13} - 13 q^{17} + 7 q^{19} - 13 q^{20} - 19 q^{22} + 4 q^{23} + 16 q^{25} + 12 q^{29} + 6 q^{31} - 21 q^{32} + 7 q^{34} + 11 q^{37} - 14 q^{38} + 11 q^{40} - 10 q^{41} + 10 q^{43} + 29 q^{44} + q^{46} + 4 q^{47} + 29 q^{50} + 6 q^{52} + 9 q^{53} - 12 q^{55} + 34 q^{58} - 7 q^{59} + 23 q^{61} + 24 q^{62} - 13 q^{64} - 3 q^{65} + 25 q^{67} - 20 q^{68} + 27 q^{71} + 18 q^{73} - 15 q^{74} + 2 q^{76} + 8 q^{79} - 41 q^{80} + 26 q^{82} - 12 q^{83} + 10 q^{85} + 19 q^{86} - 36 q^{88} - 29 q^{89} + 50 q^{92} - 2 q^{94} + 33 q^{95} + 13 q^{97}+O(q^{100}) $ 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8 + 2 * q^10 + q^11 + 5 * q^13 - 13 * q^17 + 7 * q^19 - 13 * q^20 - 19 * q^22 + 4 * q^23 + 16 * q^25 + 12 * q^29 + 6 * q^31 - 21 * q^32 + 7 * q^34 + 11 * q^37 - 14 * q^38 + 11 * q^40 - 10 * q^41 + 10 * q^43 + 29 * q^44 + q^46 + 4 * q^47 + 29 * q^50 + 6 * q^52 + 9 * q^53 - 12 * q^55 + 34 * q^58 - 7 * q^59 + 23 * q^61 + 24 * q^62 - 13 * q^64 - 3 * q^65 + 25 * q^67 - 20 * q^68 + 27 * q^71 + 18 * q^73 - 15 * q^74 + 2 * q^76 + 8 * q^79 - 41 * q^80 + 26 * q^82 - 12 * q^83 + 10 * q^85 + 19 * q^86 - 36 * q^88 - 29 * q^89 + 50 * q^92 - 2 * q^94 + 33 * q^95 + 13 * 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 $

$2$	1.78646	1.26322	0.631609	−	0.775287i	$-0.282395\pi$
$2$	1.78646	1.26322	0.631609	+	0.775287i	$0.282395\pi$
$3$	0	0
$3$	0	0
$4$	1.19144	0.595718
$5$	3.42992	1.53391	0.766954	−	0.641703i	$-0.221772\pi$
$5$	3.42992	1.53391	0.766954	+	0.641703i	$0.221772\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.44447	−0.510696
$9$	0	0
$10$	6.12741	1.93766
$11$	−1.59502	−0.480917	−0.240459	−	0.970659i	$-0.577298\pi$
$11$	−1.59502	−0.480917	−0.240459	+	0.970659i	$0.577298\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	−4.96335	−1.24084
$17$	0.0394874	0.00957710	0.00478855	−	0.999989i	$-0.498476\pi$
$17$	0.0394874	0.00957710	0.00478855	+	0.999989i	$0.498476\pi$
$18$	0	0
$19$	3.64346	0.835867	0.417934	−	0.908478i	$-0.362754\pi$
$19$	3.64346	0.835867	0.417934	+	0.908478i	$0.362754\pi$
$20$	4.08653	0.913777
$21$	0	0
$22$	−2.84944	−0.607503
$23$	3.42236	0.713612	0.356806	−	0.934179i	$-0.383866\pi$
$23$	3.42236	0.713612	0.356806	+	0.934179i	$0.383866\pi$
$24$	0	0
$25$	6.76436	1.35287
$26$	1.78646	0.350353
$27$	0	0
$28$	0	0
$29$	10.0028	1.85748	0.928740	−	0.370731i	$-0.120893\pi$
$29$	10.0028	1.85748	0.928740	+	0.370731i	$0.120893\pi$
$30$	0	0
$31$	6.15479	1.10543	0.552716	−	0.833369i	$-0.313591\pi$
$31$	6.15479	1.10543	0.552716	+	0.833369i	$0.313591\pi$
$32$	−5.97790	−1.05675
$33$	0	0
$34$	0.0705426	0.0120980
$35$	0	0
$36$	0	0
$37$	−11.1303	−1.82980	−0.914901	−	0.403678i	$-0.867732\pi$
$37$	−11.1303	−1.82980	−0.914901	+	0.403678i	$0.867732\pi$
$38$	6.50890	1.05588
$39$	0	0
$40$	−4.95440	−0.783359
$41$	−5.08793	−0.794601	−0.397300	−	0.917689i	$-0.630053\pi$
$41$	−5.08793	−0.794601	−0.397300	+	0.917689i	$0.630053\pi$
$42$	0	0
$43$	2.91631	0.444732	0.222366	−	0.974963i	$-0.428622\pi$
$43$	2.91631	0.444732	0.222366	+	0.974963i	$0.428622\pi$
$44$	−1.90037	−0.286491
$45$	0	0
$46$	6.11391	0.901447
$47$	−4.10864	−0.599306	−0.299653	−	0.954048i	$-0.596871\pi$
$47$	−4.10864	−0.599306	−0.299653	+	0.954048i	$0.596871\pi$
$48$	0	0
$49$	0	0
$50$	12.0842	1.70897
$51$	0	0
$52$	1.19144	0.165223
$53$	10.2912	1.41360	0.706799	−	0.707414i	$-0.250138\pi$
$53$	10.2912	1.41360	0.706799	+	0.707414i	$0.250138\pi$
$54$	0	0
$55$	−5.47080	−0.737683
$56$	0	0
$57$	0	0
$58$	17.8697	2.34640
$59$	9.19324	1.19686	0.598429	−	0.801176i	$-0.295792\pi$
$59$	9.19324	1.19686	0.598429	+	0.801176i	$0.295792\pi$
$60$	0	0
$61$	1.96051	0.251018	0.125509	−	0.992092i	$-0.459944\pi$
$61$	1.96051	0.251018	0.125509	+	0.992092i	$0.459944\pi$
$62$	10.9953	1.39640
$63$	0	0
$64$	−0.752565	−0.0940706
$65$	3.42992	0.425429
$66$	0	0
$67$	12.0569	1.47298	0.736491	−	0.676448i	$-0.236482\pi$
$67$	12.0569	1.47298	0.736491	+	0.676448i	$0.236482\pi$
$68$	0.0470468	0.00570526
$69$	0	0
$70$	0	0
$71$	−1.79825	−0.213413	−0.106707	−	0.994291i	$-0.534031\pi$
$71$	−1.79825	−0.213413	−0.106707	+	0.994291i	$0.534031\pi$
$72$	0	0
$73$	6.70505	0.784767	0.392384	−	0.919802i	$-0.371651\pi$
$73$	6.70505	0.784767	0.392384	+	0.919802i	$0.371651\pi$
$74$	−19.8837	−2.31144
$75$	0	0
$76$	4.34095	0.497942
$77$	0	0
$78$	0	0
$79$	14.6318	1.64620	0.823101	−	0.567896i	$-0.192242\pi$
$79$	14.6318	1.64620	0.823101	+	0.567896i	$0.192242\pi$
$80$	−17.0239	−1.90333
$81$	0	0
$82$	−9.08937	−1.00375
$83$	−5.34655	−0.586860	−0.293430	−	0.955981i	$-0.594797\pi$
$83$	−5.34655	−0.586860	−0.293430	+	0.955981i	$0.594797\pi$
$84$	0	0
$85$	0.135439	0.0146904
$86$	5.20986	0.561794
$87$	0	0
$88$	2.30395	0.245602
$89$	−12.4694	−1.32175	−0.660877	−	0.750494i	$-0.729816\pi$
$89$	−12.4694	−1.32175	−0.660877	+	0.750494i	$0.729816\pi$
$90$	0	0
$91$	0	0
$92$	4.07753	0.425112
$93$	0	0
$94$	−7.33991	−0.757054
$95$	12.4968	1.28214
$96$	0	0
$97$	12.5010	1.26929	0.634643	−	0.772806i	$-0.281147\pi$
$97$	12.5010	1.26929	0.634643	+	0.772806i	$0.281147\pi$
$98$	0	0
$99$	0	0
$100$	8.05930	0.805930
$101$	−6.85121	−0.681721	−0.340860	−	0.940114i	$-0.610718\pi$
$101$	−6.85121	−0.681721	−0.340860	+	0.940114i	$0.610718\pi$
$102$	0	0
$103$	−9.14251	−0.900838	−0.450419	−	0.892817i	$-0.648725\pi$
$103$	−9.14251	−0.900838	−0.450419	+	0.892817i	$0.648725\pi$
$104$	−1.44447	−0.141641
$105$	0	0
$106$	18.3847	1.78568
$107$	−13.6772	−1.32222	−0.661112	−	0.750287i	$-0.729915\pi$
$107$	−13.6772	−1.32222	−0.661112	+	0.750287i	$0.729915\pi$
$108$	0	0
$109$	5.64433	0.540629	0.270315	−	0.962772i	$-0.412872\pi$
$109$	5.64433	0.540629	0.270315	+	0.962772i	$0.412872\pi$
$110$	−9.77336	−0.931854
$111$	0	0
$112$	0	0
$113$	3.61852	0.340402	0.170201	−	0.985409i	$-0.445558\pi$
$113$	3.61852	0.340402	0.170201	+	0.985409i	$0.445558\pi$
$114$	0	0
$115$	11.7384	1.09461
$116$	11.9178	1.10654
$117$	0	0
$118$	16.4233	1.51189
$119$	0	0
$120$	0	0
$121$	−8.45590	−0.768719
$122$	3.50238	0.317090
$123$	0	0
$124$	7.33304	0.658527
$125$	6.05160	0.541272
$126$	0	0
$127$	12.6716	1.12442	0.562210	−	0.826995i	$-0.309951\pi$
$127$	12.6716	1.12442	0.562210	+	0.826995i	$0.309951\pi$
$128$	10.6114	0.937921
$129$	0	0
$130$	6.12741	0.537410
$131$	−11.3110	−0.988244	−0.494122	−	0.869393i	$-0.664510\pi$
$131$	−11.3110	−0.988244	−0.494122	+	0.869393i	$0.664510\pi$
$132$	0	0
$133$	0	0
$134$	21.5391	1.86070
$135$	0	0
$136$	−0.0570382	−0.00489098
$137$	0.764677	0.0653308	0.0326654	−	0.999466i	$-0.489600\pi$
$137$	0.764677	0.0653308	0.0326654	+	0.999466i	$0.489600\pi$
$138$	0	0
$139$	0.894171	0.0758426	0.0379213	−	0.999281i	$-0.487926\pi$
$139$	0.894171	0.0758426	0.0379213	+	0.999281i	$0.487926\pi$
$140$	0	0
$141$	0	0
$142$	−3.21250	−0.269587
$143$	−1.59502	−0.133382
$144$	0	0
$145$	34.3089	2.84920
$146$	11.9783	0.991331
$147$	0	0
$148$	−13.2610	−1.09005
$149$	12.5117	1.02500	0.512501	−	0.858687i	$-0.328719\pi$
$149$	12.5117	1.02500	0.512501	+	0.858687i	$0.328719\pi$
$150$	0	0
$151$	−1.83383	−0.149235	−0.0746174	−	0.997212i	$-0.523774\pi$
$151$	−1.83383	−0.149235	−0.0746174	+	0.997212i	$0.523774\pi$
$152$	−5.26285	−0.426874
$153$	0	0
$154$	0	0
$155$	21.1104	1.69563
$156$	0	0
$157$	−18.3249	−1.46248	−0.731241	−	0.682119i	$-0.761059\pi$
$157$	−18.3249	−1.46248	−0.731241	+	0.682119i	$0.761059\pi$
$158$	26.1390	2.07951
$159$	0	0
$160$	−20.5037	−1.62096
$161$	0	0
$162$	0	0
$163$	14.7756	1.15731	0.578657	−	0.815571i	$-0.303577\pi$
$163$	14.7756	1.15731	0.578657	+	0.815571i	$0.303577\pi$
$164$	−6.06194	−0.473358
$165$	0	0
$166$	−9.55139	−0.741332
$167$	−6.61137	−0.511603	−0.255801	−	0.966729i	$-0.582339\pi$
$167$	−6.61137	−0.511603	−0.255801	+	0.966729i	$0.582339\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0.241956	0.0185572
$171$	0	0
$172$	3.47459	0.264935
$173$	−0.725190	−0.0551352	−0.0275676	−	0.999620i	$-0.508776\pi$
$173$	−0.725190	−0.0551352	−0.0275676	+	0.999620i	$0.508776\pi$
$174$	0	0
$175$	0	0
$176$	7.91666	0.596741
$177$	0	0
$178$	−22.2761	−1.66966
$179$	18.7935	1.40469	0.702346	−	0.711836i	$-0.252136\pi$
$179$	18.7935	1.40469	0.702346	+	0.711836i	$0.252136\pi$
$180$	0	0
$181$	7.45429	0.554073	0.277036	−	0.960859i	$-0.410648\pi$
$181$	7.45429	0.554073	0.277036	+	0.960859i	$0.410648\pi$
$182$	0	0
$183$	0	0
$184$	−4.94348	−0.364438
$185$	−38.1759	−2.80675
$186$	0	0
$187$	−0.0629833	−0.00460579
$188$	−4.89518	−0.357018
$189$	0	0
$190$	22.3250	1.61963
$191$	−20.3799	−1.47464	−0.737320	−	0.675544i	$-0.763909\pi$
$191$	−20.3799	−1.47464	−0.737320	+	0.675544i	$0.763909\pi$
$192$	0	0
$193$	−10.3020	−0.741556	−0.370778	−	0.928722i	$-0.620909\pi$
$193$	−10.3020	−0.741556	−0.370778	+	0.928722i	$0.620909\pi$
$194$	22.3326	1.60338
$195$	0	0
$196$	0	0
$197$	−22.1453	−1.57779	−0.788895	−	0.614528i	$-0.789347\pi$
$197$	−22.1453	−1.57779	−0.788895	+	0.614528i	$0.789347\pi$
$198$	0	0
$199$	14.6391	1.03774	0.518871	−	0.854853i	$-0.326353\pi$
$199$	14.6391	1.03774	0.518871	+	0.854853i	$0.326353\pi$
$200$	−9.77088	−0.690905
$201$	0	0
$202$	−12.2394	−0.861162
$203$	0	0
$204$	0	0
$205$	−17.4512	−1.21884
$206$	−16.3327	−1.13795
$207$	0	0
$208$	−4.96335	−0.344147
$209$	−5.81140	−0.401983
$210$	0	0
$211$	−16.5084	−1.13649	−0.568243	−	0.822861i	$-0.692377\pi$
$211$	−16.5084	−1.13649	−0.568243	+	0.822861i	$0.692377\pi$
$212$	12.2613	0.842107
$213$	0	0
$214$	−24.4337	−1.67026
$215$	10.0027	0.682178
$216$	0	0
$217$	0	0
$218$	10.0834	0.682932
$219$	0	0
$220$	−6.51811	−0.439451
$221$	0.0394874	0.00265621
$222$	0	0
$223$	12.1251	0.811958	0.405979	−	0.913882i	$-0.366931\pi$
$223$	12.1251	0.811958	0.405979	+	0.913882i	$0.366931\pi$
$224$	0	0
$225$	0	0
$226$	6.46434	0.430001
$227$	−14.6634	−0.973242	−0.486621	−	0.873613i	$-0.661771\pi$
$227$	−14.6634	−0.973242	−0.486621	+	0.873613i	$0.661771\pi$
$228$	0	0
$229$	−13.3777	−0.884023	−0.442011	−	0.897010i	$-0.645735\pi$
$229$	−13.3777	−0.884023	−0.442011	+	0.897010i	$0.645735\pi$
$230$	20.9702	1.38274
$231$	0	0
$232$	−14.4488	−0.948607
$233$	−6.94354	−0.454886	−0.227443	−	0.973791i	$-0.573037\pi$
$233$	−6.94354	−0.454886	−0.227443	+	0.973791i	$0.573037\pi$
$234$	0	0
$235$	−14.0923	−0.919280
$236$	10.9532	0.712990
$237$	0	0
$238$	0	0
$239$	−10.1854	−0.658836	−0.329418	−	0.944184i	$-0.606853\pi$
$239$	−10.1854	−0.658836	−0.329418	+	0.944184i	$0.606853\pi$
$240$	0	0
$241$	9.74501	0.627731	0.313865	−	0.949467i	$-0.398376\pi$
$241$	9.74501	0.627731	0.313865	+	0.949467i	$0.398376\pi$
$242$	−15.1061	−0.971059
$243$	0	0
$244$	2.33583	0.149536
$245$	0	0
$246$	0	0
$247$	3.64346	0.231828
$248$	−8.89038	−0.564540
$249$	0	0
$250$	10.8109	0.683744
$251$	−25.5879	−1.61509	−0.807546	−	0.589805i	$-0.799205\pi$
$251$	−25.5879	−1.61509	−0.807546	+	0.589805i	$0.799205\pi$
$252$	0	0
$253$	−5.45874	−0.343188
$254$	22.6372	1.42039
$255$	0	0
$256$	20.4619	1.27887
$257$	11.5666	0.721505	0.360753	−	0.932662i	$-0.382520\pi$
$257$	11.5666	0.721505	0.360753	+	0.932662i	$0.382520\pi$
$258$	0	0
$259$	0	0
$260$	4.08653	0.253436
$261$	0	0
$262$	−20.2066	−1.24837
$263$	−4.29399	−0.264779	−0.132389	−	0.991198i	$-0.542265\pi$
$263$	−4.29399	−0.264779	−0.132389	+	0.991198i	$0.542265\pi$
$264$	0	0
$265$	35.2978	2.16833
$266$	0	0
$267$	0	0
$268$	14.3650	0.877482
$269$	−6.80665	−0.415009	−0.207504	−	0.978234i	$-0.566534\pi$
$269$	−6.80665	−0.415009	−0.207504	+	0.978234i	$0.566534\pi$
$270$	0	0
$271$	10.6765	0.648549	0.324274	−	0.945963i	$-0.394880\pi$
$271$	10.6765	0.648549	0.324274	+	0.945963i	$0.394880\pi$
$272$	−0.195990	−0.0118836
$273$	0	0
$274$	1.36606	0.0825270
$275$	−10.7893	−0.650619
$276$	0	0
$277$	27.8236	1.67176	0.835880	−	0.548912i	$-0.184958\pi$
$277$	27.8236	1.67176	0.835880	+	0.548912i	$0.184958\pi$
$278$	1.59740	0.0958057
$279$	0	0
$280$	0	0
$281$	−27.3000	−1.62858	−0.814291	−	0.580458i	$-0.802874\pi$
$281$	−27.3000	−1.62858	−0.814291	+	0.580458i	$0.802874\pi$
$282$	0	0
$283$	−15.8447	−0.941872	−0.470936	−	0.882167i	$-0.656084\pi$
$283$	−15.8447	−0.941872	−0.470936	+	0.882167i	$0.656084\pi$
$284$	−2.14250	−0.127134
$285$	0	0
$286$	−2.84944	−0.168491
$287$	0	0
$288$	0	0
$289$	−16.9984	−0.999908
$290$	61.2915	3.59916
$291$	0	0
$292$	7.98865	0.467500
$293$	16.4408	0.960481	0.480240	−	0.877137i	$-0.340549\pi$
$293$	16.4408	0.960481	0.480240	+	0.877137i	$0.340549\pi$
$294$	0	0
$295$	31.5321	1.83587
$296$	16.0773	0.934472
$297$	0	0
$298$	22.3517	1.29480
$299$	3.42236	0.197920
$300$	0	0
$301$	0	0
$302$	−3.27606	−0.188516
$303$	0	0
$304$	−18.0838	−1.03718
$305$	6.72440	0.385038
$306$	0	0
$307$	24.0573	1.37302	0.686512	−	0.727119i	$-0.259141\pi$
$307$	24.0573	1.37302	0.686512	+	0.727119i	$0.259141\pi$
$308$	0	0
$309$	0	0
$310$	37.7129	2.14195
$311$	−34.1237	−1.93497	−0.967487	−	0.252919i	$-0.918609\pi$
$311$	−34.1237	−1.93497	−0.967487	+	0.252919i	$0.918609\pi$
$312$	0	0
$313$	−30.5918	−1.72915	−0.864575	−	0.502504i	$-0.832412\pi$
$313$	−30.5918	−1.72915	−0.864575	+	0.502504i	$0.832412\pi$
$314$	−32.7366	−1.84743
$315$	0	0
$316$	17.4328	0.980672
$317$	4.41815	0.248148	0.124074	−	0.992273i	$-0.460404\pi$
$317$	4.41815	0.248148	0.124074	+	0.992273i	$0.460404\pi$
$318$	0	0
$319$	−15.9548	−0.893295
$320$	−2.58124	−0.144296
$321$	0	0
$322$	0	0
$323$	0.143871	0.00800519
$324$	0	0
$325$	6.76436	0.375219
$326$	26.3960	1.46194
$327$	0	0
$328$	7.34933	0.405799
$329$	0	0
$330$	0	0
$331$	24.8674	1.36684	0.683418	−	0.730027i	$-0.260493\pi$
$331$	24.8674	1.36684	0.683418	+	0.730027i	$0.260493\pi$
$332$	−6.37007	−0.349603
$333$	0	0
$334$	−11.8109	−0.646266
$335$	41.3541	2.25942
$336$	0	0
$337$	−10.1490	−0.552851	−0.276426	−	0.961035i	$-0.589150\pi$
$337$	−10.1490	−0.552851	−0.276426	+	0.961035i	$0.589150\pi$
$338$	1.78646	0.0971706
$339$	0	0
$340$	0.161367	0.00875133
$341$	−9.81703	−0.531622
$342$	0	0
$343$	0	0
$344$	−4.21250	−0.227123
$345$	0	0
$346$	−1.29552	−0.0696477
$347$	0.296340	0.0159083	0.00795417	−	0.999968i	$-0.497468\pi$
$347$	0.296340	0.0159083	0.00795417	+	0.999968i	$0.497468\pi$
$348$	0	0
$349$	−28.7148	−1.53707	−0.768534	−	0.639809i	$-0.779013\pi$
$349$	−28.7148	−1.53707	−0.768534	+	0.639809i	$0.779013\pi$
$350$	0	0
$351$	0	0
$352$	9.53488	0.508211
$353$	21.6081	1.15008	0.575042	−	0.818124i	$-0.304986\pi$
$353$	21.6081	1.15008	0.575042	+	0.818124i	$0.304986\pi$
$354$	0	0
$355$	−6.16786	−0.327356
$356$	−14.8565	−0.787394
$357$	0	0
$358$	33.5738	1.77443
$359$	−6.39890	−0.337721	−0.168860	−	0.985640i	$-0.554009\pi$
$359$	−6.39890	−0.337721	−0.168860	+	0.985640i	$0.554009\pi$
$360$	0	0
$361$	−5.72519	−0.301326
$362$	13.3168	0.699915
$363$	0	0
$364$	0	0
$365$	22.9978	1.20376
$366$	0	0
$367$	−0.718923	−0.0375275	−0.0187637	−	0.999824i	$-0.505973\pi$
$367$	−0.718923	−0.0375275	−0.0187637	+	0.999824i	$0.505973\pi$
$368$	−16.9864	−0.885476
$369$	0	0
$370$	−68.1997	−3.54553
$371$	0	0
$372$	0	0
$373$	−9.89739	−0.512468	−0.256234	−	0.966615i	$-0.582482\pi$
$373$	−9.89739	−0.512468	−0.256234	+	0.966615i	$0.582482\pi$
$374$	−0.112517	−0.00581812
$375$	0	0
$376$	5.93478	0.306063
$377$	10.0028	0.515172
$378$	0	0
$379$	3.64783	0.187376	0.0936882	−	0.995602i	$-0.470134\pi$
$379$	3.64783	0.187376	0.0936882	+	0.995602i	$0.470134\pi$
$380$	14.8891	0.763796
$381$	0	0
$382$	−36.4079	−1.86279
$383$	15.7029	0.802378	0.401189	−	0.915995i	$-0.368597\pi$
$383$	15.7029	0.802378	0.401189	+	0.915995i	$0.368597\pi$
$384$	0	0
$385$	0	0
$386$	−18.4041	−0.936746
$387$	0	0
$388$	14.8942	0.756137
$389$	−10.4826	−0.531490	−0.265745	−	0.964043i	$-0.585618\pi$
$389$	−10.4826	−0.531490	−0.265745	+	0.964043i	$0.585618\pi$
$390$	0	0
$391$	0.135140	0.00683433
$392$	0	0
$393$	0	0
$394$	−39.5618	−1.99309
$395$	50.1858	2.52512
$396$	0	0
$397$	−26.2193	−1.31591	−0.657953	−	0.753059i	$-0.728578\pi$
$397$	−26.2193	−1.31591	−0.657953	+	0.753059i	$0.728578\pi$
$398$	26.1522	1.31089
$399$	0	0
$400$	−33.5739	−1.67869
$401$	29.9844	1.49735	0.748676	−	0.662936i	$-0.230690\pi$
$401$	29.9844	1.49735	0.748676	+	0.662936i	$0.230690\pi$
$402$	0	0
$403$	6.15479	0.306592
$404$	−8.16279	−0.406114
$405$	0	0
$406$	0	0
$407$	17.7530	0.879984
$408$	0	0
$409$	−16.1232	−0.797242	−0.398621	−	0.917116i	$-0.630511\pi$
$409$	−16.1232	−0.797242	−0.398621	+	0.917116i	$0.630511\pi$
$410$	−31.1758	−1.53966
$411$	0	0
$412$	−10.8927	−0.536646
$413$	0	0
$414$	0	0
$415$	−18.3382	−0.900188
$416$	−5.97790	−0.293090
$417$	0	0
$418$	−10.3818	−0.507792
$419$	−6.10021	−0.298015	−0.149007	−	0.988836i	$-0.547608\pi$
$419$	−6.10021	−0.298015	−0.149007	+	0.988836i	$0.547608\pi$
$420$	0	0
$421$	11.1161	0.541768	0.270884	−	0.962612i	$-0.412684\pi$
$421$	11.1161	0.541768	0.270884	+	0.962612i	$0.412684\pi$
$422$	−29.4916	−1.43563
$423$	0	0
$424$	−14.8652	−0.721919
$425$	0.267107	0.0129566
$426$	0	0
$427$	0	0
$428$	−16.2955	−0.787673
$429$	0	0
$430$	17.8694	0.861739
$431$	5.86033	0.282282	0.141141	−	0.989989i	$-0.454923\pi$
$431$	5.86033	0.282282	0.141141	+	0.989989i	$0.454923\pi$
$432$	0	0
$433$	32.1012	1.54268	0.771342	−	0.636421i	$-0.219586\pi$
$433$	32.1012	1.54268	0.771342	+	0.636421i	$0.219586\pi$
$434$	0	0
$435$	0	0
$436$	6.72487	0.322063
$437$	12.4692	0.596485
$438$	0	0
$439$	29.1979	1.39354	0.696769	−	0.717295i	$-0.254620\pi$
$439$	29.1979	1.39354	0.696769	+	0.717295i	$0.254620\pi$
$440$	7.90238	0.376731
$441$	0	0
$442$	0.0705426	0.00335537
$443$	28.1516	1.33752	0.668762	−	0.743476i	$-0.266824\pi$
$443$	28.1516	1.33752	0.668762	+	0.743476i	$0.266824\pi$
$444$	0	0
$445$	−42.7691	−2.02745
$446$	21.6610	1.02568
$447$	0	0
$448$	0	0
$449$	−5.39643	−0.254673	−0.127337	−	0.991860i	$-0.540643\pi$
$449$	−5.39643	−0.254673	−0.127337	+	0.991860i	$0.540643\pi$
$450$	0	0
$451$	8.11536	0.382137
$452$	4.31124	0.202784
$453$	0	0
$454$	−26.1955	−1.22942
$455$	0	0
$456$	0	0
$457$	29.5079	1.38032	0.690161	−	0.723656i	$-0.257540\pi$
$457$	29.5079	1.38032	0.690161	+	0.723656i	$0.257540\pi$
$458$	−23.8987	−1.11671
$459$	0	0
$460$	13.9856	0.652082
$461$	−17.6176	−0.820533	−0.410267	−	0.911966i	$-0.634564\pi$
$461$	−17.6176	−0.820533	−0.410267	+	0.911966i	$0.634564\pi$
$462$	0	0
$463$	6.40031	0.297448	0.148724	−	0.988879i	$-0.452483\pi$
$463$	6.40031	0.297448	0.148724	+	0.988879i	$0.452483\pi$
$464$	−49.6476	−2.30483
$465$	0	0
$466$	−12.4043	−0.574620
$467$	−15.4278	−0.713915	−0.356958	−	0.934121i	$-0.616186\pi$
$467$	−15.4278	−0.713915	−0.356958	+	0.934121i	$0.616186\pi$
$468$	0	0
$469$	0	0
$470$	−25.1753	−1.16125
$471$	0	0
$472$	−13.2793	−0.611230
$473$	−4.65157	−0.213880
$474$	0	0
$475$	24.6457	1.13082
$476$	0	0
$477$	0	0
$478$	−18.1957	−0.832253
$479$	23.1297	1.05682	0.528411	−	0.848989i	$-0.322788\pi$
$479$	23.1297	1.05682	0.528411	+	0.848989i	$0.322788\pi$
$480$	0	0
$481$	−11.1303	−0.507496
$482$	17.4091	0.792961
$483$	0	0
$484$	−10.0747	−0.457940
$485$	42.8775	1.94697
$486$	0	0
$487$	7.81085	0.353943	0.176972	−	0.984216i	$-0.443370\pi$
$487$	7.81085	0.353943	0.176972	+	0.984216i	$0.443370\pi$
$488$	−2.83189	−0.128194
$489$	0	0
$490$	0	0
$491$	24.7444	1.11670	0.558350	−	0.829605i	$-0.311435\pi$
$491$	24.7444	1.11670	0.558350	+	0.829605i	$0.311435\pi$
$492$	0	0
$493$	0.394986	0.0177893
$494$	6.50890	0.292849
$495$	0	0
$496$	−30.5484	−1.37166
$497$	0	0
$498$	0	0
$499$	−17.2052	−0.770209	−0.385104	−	0.922873i	$-0.625835\pi$
$499$	−17.2052	−0.770209	−0.385104	+	0.922873i	$0.625835\pi$
$500$	7.21010	0.322445
$501$	0	0
$502$	−45.7117	−2.04021
$503$	31.0833	1.38593	0.692967	−	0.720969i	$-0.256303\pi$
$503$	31.0833	1.38593	0.692967	+	0.720969i	$0.256303\pi$
$504$	0	0
$505$	−23.4991	−1.04570
$506$	−9.75182	−0.433521
$507$	0	0
$508$	15.0974	0.669838
$509$	−18.6852	−0.828209	−0.414104	−	0.910229i	$-0.635905\pi$
$509$	−18.6852	−0.828209	−0.414104	+	0.910229i	$0.635905\pi$
$510$	0	0
$511$	0	0
$512$	15.3316	0.677569
$513$	0	0
$514$	20.6633	0.911418
$515$	−31.3581	−1.38180
$516$	0	0
$517$	6.55337	0.288217
$518$	0	0
$519$	0	0
$520$	−4.95440	−0.217265
$521$	−5.25437	−0.230198	−0.115099	−	0.993354i	$-0.536719\pi$
$521$	−5.25437	−0.230198	−0.115099	+	0.993354i	$0.536719\pi$
$522$	0	0
$523$	0.906833	0.0396530	0.0198265	−	0.999803i	$-0.493689\pi$
$523$	0.906833	0.0396530	0.0198265	+	0.999803i	$0.493689\pi$
$524$	−13.4763	−0.588715
$525$	0	0
$526$	−7.67104	−0.334473
$527$	0.243037	0.0105868
$528$	0	0
$529$	−11.2874	−0.490758
$530$	63.0582	2.73907
$531$	0	0
$532$	0	0
$533$	−5.08793	−0.220383
$534$	0	0
$535$	−46.9117	−2.02817
$536$	−17.4157	−0.752245
$537$	0	0
$538$	−12.1598	−0.524246
$539$	0	0
$540$	0	0
$541$	−13.1604	−0.565810	−0.282905	−	0.959148i	$-0.591298\pi$
$541$	−13.1604	−0.565810	−0.282905	+	0.959148i	$0.591298\pi$
$542$	19.0731	0.819258
$543$	0	0
$544$	−0.236052	−0.0101206
$545$	19.3596	0.829275
$546$	0	0
$547$	2.77123	0.118489	0.0592446	−	0.998243i	$-0.481131\pi$
$547$	2.77123	0.118489	0.0592446	+	0.998243i	$0.481131\pi$
$548$	0.911065	0.0389187
$549$	0	0
$550$	−19.2746	−0.821874
$551$	36.4450	1.55261
$552$	0	0
$553$	0	0
$554$	49.7058	2.11180
$555$	0	0
$556$	1.06535	0.0451808
$557$	−13.1292	−0.556301	−0.278151	−	0.960537i	$-0.589721\pi$
$557$	−13.1292	−0.556301	−0.278151	+	0.960537i	$0.589721\pi$
$558$	0	0
$559$	2.91631	0.123347
$560$	0	0
$561$	0	0
$562$	−48.7703	−2.05725
$563$	−23.7475	−1.00084	−0.500419	−	0.865783i	$-0.666821\pi$
$563$	−23.7475	−1.00084	−0.500419	+	0.865783i	$0.666821\pi$
$564$	0	0
$565$	12.4112	0.522144
$566$	−28.3060	−1.18979
$567$	0	0
$568$	2.59751	0.108989
$569$	−31.3578	−1.31459	−0.657293	−	0.753635i	$-0.728299\pi$
$569$	−31.3578	−1.31459	−0.657293	+	0.753635i	$0.728299\pi$
$570$	0	0
$571$	13.0846	0.547573	0.273787	−	0.961790i	$-0.411724\pi$
$571$	13.0846	0.547573	0.273787	+	0.961790i	$0.411724\pi$
$572$	−1.90037	−0.0794584
$573$	0	0
$574$	0	0
$575$	23.1501	0.965425
$576$	0	0
$577$	−39.0098	−1.62400	−0.812000	−	0.583658i	$-0.801621\pi$
$577$	−39.0098	−1.62400	−0.812000	+	0.583658i	$0.801621\pi$
$578$	−30.3670	−1.26310
$579$	0	0
$580$	40.8769	1.69732
$581$	0	0
$582$	0	0
$583$	−16.4146	−0.679824
$584$	−9.68521	−0.400777
$585$	0	0
$586$	29.3708	1.21330
$587$	−9.86312	−0.407094	−0.203547	−	0.979065i	$-0.565247\pi$
$587$	−9.86312	−0.407094	−0.203547	+	0.979065i	$0.565247\pi$
$588$	0	0
$589$	22.4247	0.923995
$590$	56.3308	2.31910
$591$	0	0
$592$	55.2434	2.27049
$593$	−47.2896	−1.94195	−0.970977	−	0.239175i	$-0.923123\pi$
$593$	−47.2896	−1.94195	−0.970977	+	0.239175i	$0.923123\pi$
$594$	0	0
$595$	0	0
$596$	14.9069	0.610612
$597$	0	0
$598$	6.11391	0.250016
$599$	−14.4370	−0.589881	−0.294940	−	0.955516i	$-0.595300\pi$
$599$	−14.4370	−0.589881	−0.294940	+	0.955516i	$0.595300\pi$
$600$	0	0
$601$	−16.9536	−0.691552	−0.345776	−	0.938317i	$-0.612384\pi$
$601$	−16.9536	−0.691552	−0.345776	+	0.938317i	$0.612384\pi$
$602$	0	0
$603$	0	0
$604$	−2.18489	−0.0889019
$605$	−29.0031	−1.17914
$606$	0	0
$607$	31.0905	1.26192	0.630962	−	0.775814i	$-0.282660\pi$
$607$	31.0905	1.26192	0.630962	+	0.775814i	$0.282660\pi$
$608$	−21.7802	−0.883305
$609$	0	0
$610$	12.0129	0.486387
$611$	−4.10864	−0.166218
$612$	0	0
$613$	−3.08480	−0.124594	−0.0622969	−	0.998058i	$-0.519843\pi$
$613$	−3.08480	−0.124594	−0.0622969	+	0.998058i	$0.519843\pi$
$614$	42.9774	1.73443
$615$	0	0
$616$	0	0
$617$	40.3163	1.62307	0.811537	−	0.584301i	$-0.198631\pi$
$617$	40.3163	1.62307	0.811537	+	0.584301i	$0.198631\pi$
$618$	0	0
$619$	5.35155	0.215097	0.107548	−	0.994200i	$-0.465700\pi$
$619$	5.35155	0.215097	0.107548	+	0.994200i	$0.465700\pi$
$620$	25.1518	1.01012
$621$	0	0
$622$	−60.9605	−2.44429
$623$	0	0
$624$	0	0
$625$	−13.0653	−0.522611
$626$	−54.6510	−2.18429
$627$	0	0
$628$	−21.8329	−0.871228
$629$	−0.439505	−0.0175242
$630$	0	0
$631$	−8.84966	−0.352300	−0.176150	−	0.984363i	$-0.556364\pi$
$631$	−8.84966	−0.352300	−0.176150	+	0.984363i	$0.556364\pi$
$632$	−21.1351	−0.840708
$633$	0	0
$634$	7.89285	0.313465
$635$	43.4625	1.72476
$636$	0	0
$637$	0	0
$638$	−28.5025	−1.12843
$639$	0	0
$640$	36.3961	1.43868
$641$	19.7426	0.779787	0.389893	−	0.920860i	$-0.372512\pi$
$641$	19.7426	0.779787	0.389893	+	0.920860i	$0.372512\pi$
$642$	0	0
$643$	−17.4196	−0.686962	−0.343481	−	0.939160i	$-0.611606\pi$
$643$	−17.4196	−0.686962	−0.343481	+	0.939160i	$0.611606\pi$
$644$	0	0
$645$	0	0
$646$	0.257019	0.0101123
$647$	42.4616	1.66934	0.834669	−	0.550753i	$-0.185659\pi$
$647$	42.4616	1.66934	0.834669	+	0.550753i	$0.185659\pi$
$648$	0	0
$649$	−14.6634	−0.575589
$650$	12.0842	0.473983
$651$	0	0
$652$	17.6042	0.689433
$653$	−5.29008	−0.207017	−0.103508	−	0.994629i	$-0.533007\pi$
$653$	−5.29008	−0.207017	−0.103508	+	0.994629i	$0.533007\pi$
$654$	0	0
$655$	−38.7957	−1.51587
$656$	25.2532	0.985971
$657$	0	0
$658$	0	0
$659$	−44.9462	−1.75086	−0.875428	−	0.483348i	$-0.839421\pi$
$659$	−44.9462	−1.75086	−0.875428	+	0.483348i	$0.839421\pi$
$660$	0	0
$661$	30.1770	1.17375	0.586874	−	0.809678i	$-0.300358\pi$
$661$	30.1770	1.17375	0.586874	+	0.809678i	$0.300358\pi$
$662$	44.4246	1.72661
$663$	0	0
$664$	7.72290	0.299707
$665$	0	0
$666$	0	0
$667$	34.2333	1.32552
$668$	−7.87703	−0.304771
$669$	0	0
$670$	73.8774	2.85413
$671$	−3.12706	−0.120719
$672$	0	0
$673$	−32.0501	−1.23544	−0.617720	−	0.786398i	$-0.711944\pi$
$673$	−32.0501	−1.23544	−0.617720	+	0.786398i	$0.711944\pi$
$674$	−18.1308	−0.698371
$675$	0	0
$676$	1.19144	0.0458245
$677$	15.4436	0.593548	0.296774	−	0.954948i	$-0.404089\pi$
$677$	15.4436	0.593548	0.296774	+	0.954948i	$0.404089\pi$
$678$	0	0
$679$	0	0
$680$	−0.195636	−0.00750231
$681$	0	0
$682$	−17.5377	−0.671554
$683$	16.9780	0.649644	0.324822	−	0.945775i	$-0.394696\pi$
$683$	16.9780	0.649644	0.324822	+	0.945775i	$0.394696\pi$
$684$	0	0
$685$	2.62278	0.100211
$686$	0	0
$687$	0	0
$688$	−14.4746	−0.551841
$689$	10.2912	0.392062
$690$	0	0
$691$	−19.5864	−0.745100	−0.372550	−	0.928012i	$-0.621516\pi$
$691$	−19.5864	−0.745100	−0.372550	+	0.928012i	$0.621516\pi$
$692$	−0.864018	−0.0328450
$693$	0	0
$694$	0.529399	0.0200957
$695$	3.06693	0.116335
$696$	0	0
$697$	−0.200909	−0.00760997
$698$	−51.2978	−1.94165
$699$	0	0
$700$	0	0
$701$	−6.84859	−0.258668	−0.129334	−	0.991601i	$-0.541284\pi$
$701$	−6.84859	−0.258668	−0.129334	+	0.991601i	$0.541284\pi$
$702$	0	0
$703$	−40.5526	−1.52947
$704$	1.20036	0.0452402
$705$	0	0
$706$	38.6020	1.45281
$707$	0	0
$708$	0	0
$709$	−22.4005	−0.841269	−0.420634	−	0.907230i	$-0.638192\pi$
$709$	−22.4005	−0.841269	−0.420634	+	0.907230i	$0.638192\pi$
$710$	−11.0186	−0.413522
$711$	0	0
$712$	18.0116	0.675014
$713$	21.0639	0.788850
$714$	0	0
$715$	−5.47080	−0.204596
$716$	22.3913	0.836801
$717$	0	0
$718$	−11.4314	−0.426615
$719$	−52.5124	−1.95838	−0.979191	−	0.202943i	$-0.934949\pi$
$719$	−52.5124	−1.95838	−0.979191	+	0.202943i	$0.934949\pi$
$720$	0	0
$721$	0	0
$722$	−10.2278	−0.380640
$723$	0	0
$724$	8.88132	0.330071
$725$	67.6628	2.51293
$726$	0	0
$727$	−22.4202	−0.831519	−0.415760	−	0.909475i	$-0.636484\pi$
$727$	−22.4202	−0.831519	−0.415760	+	0.909475i	$0.636484\pi$
$728$	0	0
$729$	0	0
$730$	41.0846	1.52061
$731$	0.115157	0.00425925
$732$	0	0
$733$	19.4700	0.719140	0.359570	−	0.933118i	$-0.382923\pi$
$733$	19.4700	0.719140	0.359570	+	0.933118i	$0.382923\pi$
$734$	−1.28433	−0.0474054
$735$	0	0
$736$	−20.4585	−0.754111
$737$	−19.2310	−0.708382
$738$	0	0
$739$	6.10823	0.224695	0.112347	−	0.993669i	$-0.464163\pi$
$739$	6.10823	0.224695	0.112347	+	0.993669i	$0.464163\pi$
$740$	−45.4842	−1.67203
$741$	0	0
$742$	0	0
$743$	−11.8031	−0.433015	−0.216507	−	0.976281i	$-0.569467\pi$
$743$	−11.8031	−0.433015	−0.216507	+	0.976281i	$0.569467\pi$
$744$	0	0
$745$	42.9143	1.57226
$746$	−17.6813	−0.647358
$747$	0	0
$748$	−0.0750406	−0.00274376
$749$	0	0
$750$	0	0
$751$	0.480357	0.0175285	0.00876423	−	0.999962i	$-0.497210\pi$
$751$	0.480357	0.0175285	0.00876423	+	0.999962i	$0.497210\pi$
$752$	20.3926	0.743642
$753$	0	0
$754$	17.8697	0.650775
$755$	−6.28988	−0.228912
$756$	0	0
$757$	−30.1679	−1.09647	−0.548235	−	0.836324i	$-0.684700\pi$
$757$	−30.1679	−1.09647	−0.548235	+	0.836324i	$0.684700\pi$
$758$	6.51670	0.236697
$759$	0	0
$760$	−18.0512	−0.654785
$761$	−34.6292	−1.25531	−0.627654	−	0.778492i	$-0.715985\pi$
$761$	−34.6292	−1.25531	−0.627654	+	0.778492i	$0.715985\pi$
$762$	0	0
$763$	0	0
$764$	−24.2814	−0.878470
$765$	0	0
$766$	28.0525	1.01358
$767$	9.19324	0.331949
$768$	0	0
$769$	−4.33487	−0.156320	−0.0781598	−	0.996941i	$-0.524904\pi$
$769$	−4.33487	−0.156320	−0.0781598	+	0.996941i	$0.524904\pi$
$770$	0	0
$771$	0	0
$772$	−12.2742	−0.441758
$773$	−3.11423	−0.112011	−0.0560055	−	0.998430i	$-0.517836\pi$
$773$	−3.11423	−0.112011	−0.0560055	+	0.998430i	$0.517836\pi$
$774$	0	0
$775$	41.6332	1.49551
$776$	−18.0573	−0.648219
$777$	0	0
$778$	−18.7268	−0.671388
$779$	−18.5377	−0.664181
$780$	0	0
$781$	2.86825	0.102634
$782$	0.241422	0.00863325
$783$	0	0
$784$	0	0
$785$	−62.8528	−2.24331
$786$	0	0
$787$	−15.2612	−0.544004	−0.272002	−	0.962297i	$-0.587686\pi$
$787$	−15.2612	−0.544004	−0.272002	+	0.962297i	$0.587686\pi$
$788$	−26.3848	−0.939919
$789$	0	0
$790$	89.6548	3.18978
$791$	0	0
$792$	0	0
$793$	1.96051	0.0696198
$794$	−46.8396	−1.66228
$795$	0	0
$796$	17.4416	0.618202
$797$	−15.7622	−0.558325	−0.279162	−	0.960244i	$-0.590057\pi$
$797$	−15.7622	−0.558325	−0.279162	+	0.960244i	$0.590057\pi$
$798$	0	0
$799$	−0.162239	−0.00573962
$800$	−40.4366	−1.42965
$801$	0	0
$802$	53.5660	1.89148
$803$	−10.6947	−0.377408
$804$	0	0
$805$	0	0
$806$	10.9953	0.387292
$807$	0	0
$808$	9.89633	0.348152
$809$	19.7817	0.695489	0.347744	−	0.937589i	$-0.386948\pi$
$809$	19.7817	0.695489	0.347744	+	0.937589i	$0.386948\pi$
$810$	0	0
$811$	−14.8239	−0.520537	−0.260269	−	0.965536i	$-0.583811\pi$
$811$	−14.8239	−0.520537	−0.260269	+	0.965536i	$0.583811\pi$
$812$	0	0
$813$	0	0
$814$	31.7150	1.11161
$815$	50.6791	1.77521
$816$	0	0
$817$	10.6254	0.371737
$818$	−28.8035	−1.00709
$819$	0	0
$820$	−20.7920	−0.726088
$821$	−24.3070	−0.848319	−0.424160	−	0.905587i	$-0.639430\pi$
$821$	−24.3070	−0.848319	−0.424160	+	0.905587i	$0.639430\pi$
$822$	0	0
$823$	−49.1057	−1.71172	−0.855858	−	0.517210i	$-0.826971\pi$
$823$	−49.1057	−1.71172	−0.855858	+	0.517210i	$0.826971\pi$
$824$	13.2060	0.460054
$825$	0	0
$826$	0	0
$827$	49.5213	1.72202	0.861012	−	0.508585i	$-0.169831\pi$
$827$	49.5213	1.72202	0.861012	+	0.508585i	$0.169831\pi$
$828$	0	0
$829$	10.1416	0.352233	0.176116	−	0.984369i	$-0.443647\pi$
$829$	10.1416	0.352233	0.176116	+	0.984369i	$0.443647\pi$
$830$	−32.7605	−1.13713
$831$	0	0
$832$	−0.752565	−0.0260905
$833$	0	0
$834$	0	0
$835$	−22.6765	−0.784751
$836$	−6.92392	−0.239469
$837$	0	0
$838$	−10.8978	−0.376457
$839$	29.9487	1.03394	0.516972	−	0.856002i	$-0.327059\pi$
$839$	29.9487	1.03394	0.516972	+	0.856002i	$0.327059\pi$
$840$	0	0
$841$	71.0568	2.45023
$842$	19.8585	0.684370
$843$	0	0
$844$	−19.6687	−0.677025
$845$	3.42992	0.117993
$846$	0	0
$847$	0	0
$848$	−51.0786	−1.75405
$849$	0	0
$850$	0.477176	0.0163670
$851$	−38.0917	−1.30577
$852$	0	0
$853$	−23.2279	−0.795309	−0.397655	−	0.917535i	$-0.630176\pi$
$853$	−23.2279	−0.795309	−0.397655	+	0.917535i	$0.630176\pi$
$854$	0	0
$855$	0	0
$856$	19.7562	0.675254
$857$	6.41561	0.219153	0.109576	−	0.993978i	$-0.465051\pi$
$857$	6.41561	0.219153	0.109576	+	0.993978i	$0.465051\pi$
$858$	0	0
$859$	−19.1724	−0.654154	−0.327077	−	0.944998i	$-0.606064\pi$
$859$	−19.1724	−0.654154	−0.327077	+	0.944998i	$0.606064\pi$
$860$	11.9176	0.406386
$861$	0	0
$862$	10.4692	0.356584
$863$	−5.45273	−0.185613	−0.0928065	−	0.995684i	$-0.529584\pi$
$863$	−5.45273	−0.185613	−0.0928065	+	0.995684i	$0.529584\pi$
$864$	0	0
$865$	−2.48734	−0.0845722
$866$	57.3474	1.94874
$867$	0	0
$868$	0	0
$869$	−23.3380	−0.791687
$870$	0	0
$871$	12.0569	0.408531
$872$	−8.15304	−0.276097
$873$	0	0
$874$	22.2758	0.753490
$875$	0	0
$876$	0	0
$877$	32.6167	1.10139	0.550693	−	0.834708i	$-0.314363\pi$
$877$	32.6167	1.10139	0.550693	+	0.834708i	$0.314363\pi$
$878$	52.1608	1.76034
$879$	0	0
$880$	27.1535	0.915345
$881$	−33.4768	−1.12786	−0.563931	−	0.825822i	$-0.690712\pi$
$881$	−33.4768	−1.12786	−0.563931	+	0.825822i	$0.690712\pi$
$882$	0	0
$883$	−10.1655	−0.342097	−0.171048	−	0.985263i	$-0.554715\pi$
$883$	−10.1655	−0.342097	−0.171048	+	0.985263i	$0.554715\pi$
$884$	0.0470468	0.00158235
$885$	0	0
$886$	50.2918	1.68958
$887$	15.5935	0.523580	0.261790	−	0.965125i	$-0.415687\pi$
$887$	15.5935	0.523580	0.261790	+	0.965125i	$0.415687\pi$
$888$	0	0
$889$	0	0
$890$	−76.4052	−2.56111
$891$	0	0
$892$	14.4463	0.483699
$893$	−14.9697	−0.500941
$894$	0	0
$895$	64.4602	2.15467
$896$	0	0
$897$	0	0
$898$	−9.64051	−0.321708
$899$	61.5654	2.05332
$900$	0	0
$901$	0.406371	0.0135382
$902$	14.4978	0.482722
$903$	0	0
$904$	−5.22682	−0.173842
$905$	25.5676	0.849896
$906$	0	0
$907$	−59.1827	−1.96513	−0.982564	−	0.185925i	$-0.940472\pi$
$907$	−59.1827	−1.96513	−0.982564	+	0.185925i	$0.940472\pi$
$908$	−17.4705	−0.579778
$909$	0	0
$910$	0	0
$911$	−1.45229	−0.0481166	−0.0240583	−	0.999711i	$-0.507659\pi$
$911$	−1.45229	−0.0481166	−0.0240583	+	0.999711i	$0.507659\pi$
$912$	0	0
$913$	8.52786	0.282231
$914$	52.7147	1.74365
$915$	0	0
$916$	−15.9387	−0.526629
$917$	0	0
$918$	0	0
$919$	38.5540	1.27178	0.635890	−	0.771780i	$-0.280633\pi$
$919$	38.5540	1.27178	0.635890	+	0.771780i	$0.280633\pi$
$920$	−16.9557	−0.559014
$921$	0	0
$922$	−31.4731	−1.03651
$923$	−1.79825	−0.0591901
$924$	0	0
$925$	−75.2890	−2.47549
$926$	11.4339	0.375741
$927$	0	0
$928$	−59.7959	−1.96290
$929$	−42.7457	−1.40244	−0.701220	−	0.712945i	$-0.747361\pi$
$929$	−42.7457	−1.40244	−0.701220	+	0.712945i	$0.747361\pi$
$930$	0	0
$931$	0	0
$932$	−8.27279	−0.270984
$933$	0	0
$934$	−27.5612	−0.901830
$935$	−0.216028	−0.00706486
$936$	0	0
$937$	−47.2424	−1.54334	−0.771671	−	0.636022i	$-0.780579\pi$
$937$	−47.2424	−1.54334	−0.771671	+	0.636022i	$0.780579\pi$
$938$	0	0
$939$	0	0
$940$	−16.7901	−0.547632
$941$	−50.2899	−1.63940	−0.819702	−	0.572790i	$-0.805861\pi$
$941$	−50.2899	−1.63940	−0.819702	+	0.572790i	$0.805861\pi$
$942$	0	0
$943$	−17.4127	−0.567036
$944$	−45.6293	−1.48511
$945$	0	0
$946$	−8.30984	−0.270176
$947$	−21.1016	−0.685710	−0.342855	−	0.939388i	$-0.611394\pi$
$947$	−21.1016	−0.685710	−0.342855	+	0.939388i	$0.611394\pi$
$948$	0	0
$949$	6.70505	0.217655
$950$	44.0285	1.42847
$951$	0	0
$952$	0	0
$953$	0.279996	0.00906996	0.00453498	−	0.999990i	$-0.498556\pi$
$953$	0.279996	0.00906996	0.00453498	+	0.999990i	$0.498556\pi$
$954$	0	0
$955$	−69.9015	−2.26196
$956$	−12.1352	−0.392481
$957$	0	0
$958$	41.3202	1.33500
$959$	0	0
$960$	0	0
$961$	6.88143	0.221981
$962$	−19.8837	−0.641078
$963$	0	0
$964$	11.6106	0.373951
$965$	−35.3351	−1.13748
$966$	0	0
$967$	23.5683	0.757905	0.378953	−	0.925416i	$-0.376284\pi$
$967$	23.5683	0.757905	0.378953	+	0.925416i	$0.376284\pi$
$968$	12.2143	0.392581
$969$	0	0
$970$	76.5989	2.45944
$971$	−1.41343	−0.0453592	−0.0226796	−	0.999743i	$-0.507220\pi$
$971$	−1.41343	−0.0453592	−0.0226796	+	0.999743i	$0.507220\pi$
$972$	0	0
$973$	0	0
$974$	13.9538	0.447108
$975$	0	0
$976$	−9.73071	−0.311473
$977$	20.4526	0.654336	0.327168	−	0.944966i	$-0.393906\pi$
$977$	20.4526	0.654336	0.327168	+	0.944966i	$0.393906\pi$
$978$	0	0
$979$	19.8890	0.635655
$980$	0	0
$981$	0	0
$982$	44.2049	1.41064
$983$	24.4006	0.778258	0.389129	−	0.921183i	$-0.372776\pi$
$983$	24.4006	0.778258	0.389129	+	0.921183i	$0.372776\pi$
$984$	0	0
$985$	−75.9568	−2.42018
$986$	0.705627	0.0224717
$987$	0	0
$988$	4.34095	0.138104
$989$	9.98065	0.317366
$990$	0	0
$991$	−15.1319	−0.480682	−0.240341	−	0.970689i	$-0.577259\pi$
$991$	−15.1319	−0.480682	−0.240341	+	0.970689i	$0.577259\pi$
$992$	−36.7927	−1.16817
$993$	0	0
$994$	0	0
$995$	50.2111	1.59180
$996$	0	0
$997$	54.0765	1.71262	0.856310	−	0.516462i	$-0.172751\pi$
$997$	54.0765	1.71262	0.856310	+	0.516462i	$0.172751\pi$
$998$	−30.7363	−0.972941
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bp.1.4		5
3.2	odd	2		1911.2.a.u.1.2		5
7.3	odd	6		819.2.j.g.352.2		10
7.5	odd	6		819.2.j.g.235.2		10
7.6	odd	2		5733.2.a.bq.1.4		5
21.5	even	6		273.2.i.e.235.4	yes	10
21.17	even	6		273.2.i.e.79.4	✓	10
21.20	even	2		1911.2.a.t.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.4	✓	10	21.17	even	6
273.2.i.e.235.4	yes	10	21.5	even	6
819.2.j.g.235.2		10	7.5	odd	6
819.2.j.g.352.2		10	7.3	odd	6
1911.2.a.t.1.2		5	21.20	even	2
1911.2.a.u.1.2		5	3.2	odd	2
5733.2.a.bp.1.4		5	1.1	even	1	trivial
5733.2.a.bq.1.4		5	7.6	odd	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)

\(f(q)\)	\(=\)	\(q+1.78646 q^{2} +1.19144 q^{4} +3.42992 q^{5} -1.44447 q^{8} +O(q^{10})\)	\(q+1.78646 q^{2} +1.19144 q^{4} +3.42992 q^{5} -1.44447 q^{8} +6.12741 q^{10} -1.59502 q^{11} +1.00000 q^{13} -4.96335 q^{16} +0.0394874 q^{17} +3.64346 q^{19} +4.08653 q^{20} -2.84944 q^{22} +3.42236 q^{23} +6.76436 q^{25} +1.78646 q^{26} +10.0028 q^{29} +6.15479 q^{31} -5.97790 q^{32} +0.0705426 q^{34} -11.1303 q^{37} +6.50890 q^{38} -4.95440 q^{40} -5.08793 q^{41} +2.91631 q^{43} -1.90037 q^{44} +6.11391 q^{46} -4.10864 q^{47} +12.0842 q^{50} +1.19144 q^{52} +10.2912 q^{53} -5.47080 q^{55} +17.8697 q^{58} +9.19324 q^{59} +1.96051 q^{61} +10.9953 q^{62} -0.752565 q^{64} +3.42992 q^{65} +12.0569 q^{67} +0.0470468 q^{68} -1.79825 q^{71} +6.70505 q^{73} -19.8837 q^{74} +4.34095 q^{76} +14.6318 q^{79} -17.0239 q^{80} -9.08937 q^{82} -5.34655 q^{83} +0.135439 q^{85} +5.20986 q^{86} +2.30395 q^{88} -12.4694 q^{89} +4.07753 q^{92} -7.33991 q^{94} +12.4968 q^{95} +12.5010 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) \) 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8	\( 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8} + 2 q^{10} + q^{11} + 5 q^{13} - 13 q^{17} + 7 q^{19} - 13 q^{20} - 19 q^{22} + 4 q^{23} + 16 q^{25} + 12 q^{29} + 6 q^{31} - 21 q^{32} + 7 q^{34} + 11 q^{37} - 14 q^{38} + 11 q^{40} - 10 q^{41} + 10 q^{43} + 29 q^{44} + q^{46} + 4 q^{47} + 29 q^{50} + 6 q^{52} + 9 q^{53} - 12 q^{55} + 34 q^{58} - 7 q^{59} + 23 q^{61} + 24 q^{62} - 13 q^{64} - 3 q^{65} + 25 q^{67} - 20 q^{68} + 27 q^{71} + 18 q^{73} - 15 q^{74} + 2 q^{76} + 8 q^{79} - 41 q^{80} + 26 q^{82} - 12 q^{83} + 10 q^{85} + 19 q^{86} - 36 q^{88} - 29 q^{89} + 50 q^{92} - 2 q^{94} + 33 q^{95} + 13 q^{97}+O(q^{100}) \) 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8 + 2 * q^10 + q^11 + 5 * q^13 - 13 * q^17 + 7 * q^19 - 13 * q^20 - 19 * q^22 + 4 * q^23 + 16 * q^25 + 12 * q^29 + 6 * q^31 - 21 * q^32 + 7 * q^34 + 11 * q^37 - 14 * q^38 + 11 * q^40 - 10 * q^41 + 10 * q^43 + 29 * q^44 + q^46 + 4 * q^47 + 29 * q^50 + 6 * q^52 + 9 * q^53 - 12 * q^55 + 34 * q^58 - 7 * q^59 + 23 * q^61 + 24 * q^62 - 13 * q^64 - 3 * q^65 + 25 * q^67 - 20 * q^68 + 27 * q^71 + 18 * q^73 - 15 * q^74 + 2 * q^76 + 8 * q^79 - 41 * q^80 + 26 * q^82 - 12 * q^83 + 10 * q^85 + 19 * q^86 - 36 * q^88 - 29 * q^89 + 50 * q^92 - 2 * q^94 + 33 * q^95 + 13 * q^97

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