LMFDB - Embedded newform 5733.2.a.bs.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:	$1$
Dimension:	$6$
Coefficient field:	6.6.46162368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 8x^{4} + 17x^{2} - 7 $ x^6 - 8x^4 + 17x^2 - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 819)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.66159$ 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)

$f(q)$	$=$	$q-1.66159 q^{2} +0.760877 q^{4} +2.05891 q^{5} +2.05891 q^{8} +O(q^{10})$	$q-1.66159 q^{2} +0.760877 q^{4} +2.05891 q^{5} +2.05891 q^{8} -3.42107 q^{10} -1.56658 q^{11} -1.00000 q^{13} -4.94282 q^{16} -7.34599 q^{17} +1.47825 q^{19} +1.56658 q^{20} +2.60301 q^{22} -0.492334 q^{23} -0.760877 q^{25} +1.66159 q^{26} +7.32327 q^{29} +10.0676 q^{31} +4.09511 q^{32} +12.2060 q^{34} -7.64652 q^{37} -2.45624 q^{38} +4.23912 q^{40} +4.00010 q^{41} -0.875237 q^{43} -1.19197 q^{44} +0.818057 q^{46} +3.32318 q^{47} +1.26426 q^{50} -0.760877 q^{52} +9.80223 q^{53} -3.22545 q^{55} -12.1683 q^{58} -2.24893 q^{59} -5.55950 q^{61} -16.7282 q^{62} +3.08126 q^{64} -2.05891 q^{65} -8.05718 q^{67} -5.58940 q^{68} -10.8538 q^{71} -13.0241 q^{73} +12.7054 q^{74} +1.12476 q^{76} +10.9097 q^{79} -10.1768 q^{80} -6.64652 q^{82} -13.4773 q^{83} -15.1248 q^{85} +1.45428 q^{86} -3.22545 q^{88} +10.5514 q^{89} -0.374606 q^{92} -5.52175 q^{94} +3.04358 q^{95} -13.3308 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{4}+O(q^{10}) $ 6 * q + 4 * q^4	$ 6 q + 4 q^{4} - 4 q^{10} - 6 q^{13} - 12 q^{16} + 10 q^{19} - 18 q^{22} - 4 q^{25} + 8 q^{31} + 6 q^{34} - 10 q^{37} + 26 q^{40} - 40 q^{43} + 22 q^{46} - 4 q^{52} - 36 q^{58} - 2 q^{61} - 14 q^{64} - 66 q^{67} - 28 q^{73} - 28 q^{76} - 20 q^{79} - 4 q^{82} - 56 q^{85} - 32 q^{94} + 22 q^{97}+O(q^{100}) $ 6 * q + 4 * q^4 - 4 * q^10 - 6 * q^13 - 12 * q^16 + 10 * q^19 - 18 * q^22 - 4 * q^25 + 8 * q^31 + 6 * q^34 - 10 * q^37 + 26 * q^40 - 40 * q^43 + 22 * q^46 - 4 * q^52 - 36 * q^58 - 2 * q^61 - 14 * q^64 - 66 * q^67 - 28 * q^73 - 28 * q^76 - 20 * q^79 - 4 * q^82 - 56 * q^85 - 32 * q^94 + 22 * 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 $

$2$	−1.66159	−1.17492	−0.587460	−	0.809253i	$-0.699872\pi$
$2$	−1.66159	−1.17492	−0.587460	+	0.809253i	$0.699872\pi$
$3$	0	0
$3$	0	0
$4$	0.760877	0.380438
$5$	2.05891	0.920774	0.460387	−	0.887718i	$-0.347711\pi$
$5$	2.05891	0.920774	0.460387	+	0.887718i	$0.347711\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	2.05891	0.727936
$9$	0	0
$10$	−3.42107	−1.08184
$11$	−1.56658	−0.472341	−0.236171	−	0.971712i	$-0.575892\pi$
$11$	−1.56658	−0.472341	−0.236171	+	0.971712i	$0.575892\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−4.94282	−1.23571
$17$	−7.34599	−1.78167	−0.890833	−	0.454332i	$-0.849878\pi$
$17$	−7.34599	−1.78167	−0.890833	+	0.454332i	$0.849878\pi$
$18$	0	0
$19$	1.47825	0.339133	0.169567	−	0.985519i	$-0.445763\pi$
$19$	1.47825	0.339133	0.169567	+	0.985519i	$0.445763\pi$
$20$	1.56658	0.350298
$21$	0	0
$22$	2.60301	0.554964
$23$	−0.492334	−0.102659	−0.0513294	−	0.998682i	$-0.516346\pi$
$23$	−0.492334	−0.102659	−0.0513294	+	0.998682i	$0.516346\pi$
$24$	0	0
$25$	−0.760877	−0.152175
$26$	1.66159	0.325864
$27$	0	0
$28$	0	0
$29$	7.32327	1.35990	0.679949	−	0.733259i	$-0.262002\pi$
$29$	7.32327	1.35990	0.679949	+	0.733259i	$0.262002\pi$
$30$	0	0
$31$	10.0676	1.80819	0.904096	−	0.427330i	$-0.140546\pi$
$31$	10.0676	1.80819	0.904096	+	0.427330i	$0.140546\pi$
$32$	4.09511	0.723920
$33$	0	0
$34$	12.2060	2.09332
$35$	0	0
$36$	0	0
$37$	−7.64652	−1.25708	−0.628540	−	0.777777i	$-0.716347\pi$
$37$	−7.64652	−1.25708	−0.628540	+	0.777777i	$0.716347\pi$
$38$	−2.45624	−0.398454
$39$	0	0
$40$	4.23912	0.670264
$41$	4.00010	0.624710	0.312355	−	0.949965i	$-0.398882\pi$
$41$	4.00010	0.624710	0.312355	+	0.949965i	$0.398882\pi$
$42$	0	0
$43$	−0.875237	−0.133472	−0.0667362	−	0.997771i	$-0.521259\pi$
$43$	−0.875237	−0.133472	−0.0667362	+	0.997771i	$0.521259\pi$
$44$	−1.19197	−0.179697
$45$	0	0
$46$	0.818057	0.120616
$47$	3.32318	0.484735	0.242368	−	0.970184i	$-0.422076\pi$
$47$	3.32318	0.484735	0.242368	+	0.970184i	$0.422076\pi$
$48$	0	0
$49$	0	0
$50$	1.26426	0.178794
$51$	0	0
$52$	−0.760877	−0.105515
$53$	9.80223	1.34644	0.673220	−	0.739442i	$-0.264911\pi$
$53$	9.80223	1.34644	0.673220	+	0.739442i	$0.264911\pi$
$54$	0	0
$55$	−3.22545	−0.434920
$56$	0	0
$57$	0	0
$58$	−12.1683	−1.59777
$59$	−2.24893	−0.292786	−0.146393	−	0.989227i	$-0.546766\pi$
$59$	−2.24893	−0.292786	−0.146393	+	0.989227i	$0.546766\pi$
$60$	0	0
$61$	−5.55950	−0.711821	−0.355911	−	0.934520i	$-0.615829\pi$
$61$	−5.55950	−0.711821	−0.355911	+	0.934520i	$0.615829\pi$
$62$	−16.7282	−2.12448
$63$	0	0
$64$	3.08126	0.385157
$65$	−2.05891	−0.255377
$66$	0	0
$67$	−8.05718	−0.984341	−0.492171	−	0.870499i	$-0.663796\pi$
$67$	−8.05718	−0.984341	−0.492171	+	0.870499i	$0.663796\pi$
$68$	−5.58940	−0.677814
$69$	0	0
$70$	0	0
$71$	−10.8538	−1.28810	−0.644052	−	0.764982i	$-0.722748\pi$
$71$	−10.8538	−1.28810	−0.644052	+	0.764982i	$0.722748\pi$
$72$	0	0
$73$	−13.0241	−1.52435	−0.762176	−	0.647369i	$-0.775869\pi$
$73$	−13.0241	−1.52435	−0.762176	+	0.647369i	$0.775869\pi$
$74$	12.7054	1.47697
$75$	0	0
$76$	1.12476	0.129019
$77$	0	0
$78$	0	0
$79$	10.9097	1.22744	0.613720	−	0.789524i	$-0.289673\pi$
$79$	10.9097	1.22744	0.613720	+	0.789524i	$0.289673\pi$
$80$	−10.1768	−1.13780
$81$	0	0
$82$	−6.64652	−0.733985
$83$	−13.4773	−1.47933	−0.739663	−	0.672978i	$-0.765015\pi$
$83$	−13.4773	−1.47933	−0.739663	+	0.672978i	$0.765015\pi$
$84$	0	0
$85$	−15.1248	−1.64051
$86$	1.45428	0.156819
$87$	0	0
$88$	−3.22545	−0.343834
$89$	10.5514	1.11845	0.559225	−	0.829016i	$-0.311099\pi$
$89$	10.5514	1.11845	0.559225	+	0.829016i	$0.311099\pi$
$90$	0	0
$91$	0	0
$92$	−0.374606	−0.0390553
$93$	0	0
$94$	−5.52175	−0.569525
$95$	3.04358	0.312265
$96$	0	0
$97$	−13.3308	−1.35354	−0.676768	−	0.736196i	$-0.736620\pi$
$97$	−13.3308	−1.35354	−0.676768	+	0.736196i	$0.736620\pi$
$98$	0	0
$99$	0	0
$100$	−0.578933	−0.0578933
$101$	4.39742	0.437560	0.218780	−	0.975774i	$-0.429792\pi$
$101$	4.39742	0.437560	0.218780	+	0.975774i	$0.429792\pi$
$102$	0	0
$103$	−5.36389	−0.528519	−0.264260	−	0.964452i	$-0.585128\pi$
$103$	−5.36389	−0.528519	−0.264260	+	0.964452i	$0.585128\pi$
$104$	−2.05891	−0.201893
$105$	0	0
$106$	−16.2873	−1.58196
$107$	8.53797	0.825396	0.412698	−	0.910868i	$-0.364586\pi$
$107$	8.53797	0.825396	0.412698	+	0.910868i	$0.364586\pi$
$108$	0	0
$109$	−5.94282	−0.569219	−0.284609	−	0.958644i	$-0.591864\pi$
$109$	−5.94282	−0.569219	−0.284609	+	0.958644i	$0.591864\pi$
$110$	5.35937	0.510996
$111$	0	0
$112$	0	0
$113$	0.492334	0.0463149	0.0231574	−	0.999732i	$-0.492628\pi$
$113$	0.492334	0.0463149	0.0231574	+	0.999732i	$0.492628\pi$
$114$	0	0
$115$	−1.01367	−0.0945255
$116$	5.57211	0.517357
$117$	0	0
$118$	3.73680	0.344000
$119$	0	0
$120$	0	0
$121$	−8.54583	−0.776894
$122$	9.23761	0.836334
$123$	0	0
$124$	7.66019	0.687905
$125$	−11.8611	−1.06089
$126$	0	0
$127$	−19.1488	−1.69918	−0.849592	−	0.527440i	$-0.823152\pi$
$127$	−19.1488	−1.69918	−0.849592	+	0.527440i	$0.823152\pi$
$128$	−13.3100	−1.17645
$129$	0	0
$130$	3.42107	0.300047
$131$	10.0645	0.879343	0.439672	−	0.898159i	$-0.355095\pi$
$131$	10.0645	0.879343	0.439672	+	0.898159i	$0.355095\pi$
$132$	0	0
$133$	0	0
$134$	13.3877	1.15652
$135$	0	0
$136$	−15.1248	−1.29694
$137$	20.0514	1.71310	0.856552	−	0.516061i	$-0.172602\pi$
$137$	20.0514	1.71310	0.856552	+	0.516061i	$0.172602\pi$
$138$	0	0
$139$	3.61668	0.306763	0.153382	−	0.988167i	$-0.450984\pi$
$139$	3.61668	0.306763	0.153382	+	0.988167i	$0.450984\pi$
$140$	0	0
$141$	0	0
$142$	18.0345	1.51342
$143$	1.56658	0.131004
$144$	0	0
$145$	15.0780	1.25216
$146$	21.6407	1.79099
$147$	0	0
$148$	−5.81806	−0.478241
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	12.2495	0.996852	0.498426	−	0.866932i	$-0.333911\pi$
$151$	12.2495	0.996852	0.498426	+	0.866932i	$0.333911\pi$
$152$	3.04358	0.246867
$153$	0	0
$154$	0	0
$155$	20.7283	1.66494
$156$	0	0
$157$	−6.33981	−0.505972	−0.252986	−	0.967470i	$-0.581413\pi$
$157$	−6.33981	−0.505972	−0.252986	+	0.967470i	$0.581413\pi$
$158$	−18.1275	−1.44214
$159$	0	0
$160$	8.43147	0.666566
$161$	0	0
$162$	0	0
$163$	−21.8227	−1.70929	−0.854643	−	0.519216i	$-0.826224\pi$
$163$	−21.8227	−1.70929	−0.854643	+	0.519216i	$0.826224\pi$
$164$	3.04358	0.237664
$165$	0	0
$166$	22.3937	1.73809
$167$	−1.38199	−0.106942	−0.0534709	−	0.998569i	$-0.517028\pi$
$167$	−1.38199	−0.106942	−0.0534709	+	0.998569i	$0.517028\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	25.1311	1.92747
$171$	0	0
$172$	−0.665947	−0.0507780
$173$	−7.60287	−0.578036	−0.289018	−	0.957324i	$-0.593329\pi$
$173$	−7.60287	−0.578036	−0.289018	+	0.957324i	$0.593329\pi$
$174$	0	0
$175$	0	0
$176$	7.74332	0.583675
$177$	0	0
$178$	−17.5322	−1.31409
$179$	−10.1996	−0.762351	−0.381175	−	0.924503i	$-0.624481\pi$
$179$	−10.1996	−0.762351	−0.381175	+	0.924503i	$0.624481\pi$
$180$	0	0
$181$	2.10069	0.156143	0.0780714	−	0.996948i	$-0.475124\pi$
$181$	2.10069	0.156143	0.0780714	+	0.996948i	$0.475124\pi$
$182$	0	0
$183$	0	0
$184$	−1.01367	−0.0747290
$185$	−15.7435	−1.15749
$186$	0	0
$187$	11.5081	0.841554
$188$	2.52853	0.184412
$189$	0	0
$190$	−5.05718	−0.366886
$191$	−4.58744	−0.331936	−0.165968	−	0.986131i	$-0.553075\pi$
$191$	−4.58744	−0.331936	−0.165968	+	0.986131i	$0.553075\pi$
$192$	0	0
$193$	0.899313	0.0647340	0.0323670	−	0.999476i	$-0.489695\pi$
$193$	0.899313	0.0647340	0.0323670	+	0.999476i	$0.489695\pi$
$194$	22.1503	1.59030
$195$	0	0
$196$	0	0
$197$	25.1484	1.79175	0.895875	−	0.444305i	$-0.146549\pi$
$197$	25.1484	1.79175	0.895875	+	0.444305i	$0.146549\pi$
$198$	0	0
$199$	12.8285	0.909385	0.454693	−	0.890648i	$-0.349749\pi$
$199$	12.8285	0.909385	0.454693	+	0.890648i	$0.349749\pi$
$200$	−1.56658	−0.110774
$201$	0	0
$202$	−7.30671	−0.514098
$203$	0	0
$204$	0	0
$205$	8.23585	0.575217
$206$	8.91257	0.620968
$207$	0	0
$208$	4.94282	0.342723
$209$	−2.31579	−0.160187
$210$	0	0
$211$	−19.3365	−1.33118	−0.665591	−	0.746317i	$-0.731821\pi$
$211$	−19.3365	−1.33118	−0.665591	+	0.746317i	$0.731821\pi$
$212$	7.45829	0.512237
$213$	0	0
$214$	−14.1866	−0.969775
$215$	−1.80204	−0.122898
$216$	0	0
$217$	0	0
$218$	9.87452	0.668787
$219$	0	0
$220$	−2.45417	−0.165460
$221$	7.34599	0.494145
$222$	0	0
$223$	−16.9097	−1.13236	−0.566179	−	0.824282i	$-0.691579\pi$
$223$	−16.9097	−1.13236	−0.566179	+	0.824282i	$0.691579\pi$
$224$	0	0
$225$	0	0
$226$	−0.818057	−0.0544163
$227$	20.7337	1.37614	0.688072	−	0.725642i	$-0.258457\pi$
$227$	20.7337	1.37614	0.688072	+	0.725642i	$0.258457\pi$
$228$	0	0
$229$	−11.8148	−0.780743	−0.390372	−	0.920657i	$-0.627653\pi$
$229$	−11.8148	−0.780743	−0.390372	+	0.920657i	$0.627653\pi$
$230$	1.68431	0.111060
$231$	0	0
$232$	15.0780	0.989918
$233$	−8.28522	−0.542783	−0.271392	−	0.962469i	$-0.587484\pi$
$233$	−8.28522	−0.542783	−0.271392	+	0.962469i	$0.587484\pi$
$234$	0	0
$235$	6.84213	0.446332
$236$	−1.71116	−0.111387
$237$	0	0
$238$	0	0
$239$	−29.4790	−1.90684	−0.953419	−	0.301651i	$-0.902462\pi$
$239$	−29.4790	−1.90684	−0.953419	+	0.301651i	$0.902462\pi$
$240$	0	0
$241$	−12.7907	−0.823922	−0.411961	−	0.911201i	$-0.635156\pi$
$241$	−12.7907	−0.823922	−0.411961	+	0.911201i	$0.635156\pi$
$242$	14.1997	0.912788
$243$	0	0
$244$	−4.23010	−0.270804
$245$	0	0
$246$	0	0
$247$	−1.47825	−0.0940586
$248$	20.7283	1.31625
$249$	0	0
$250$	19.7083	1.24647
$251$	5.79670	0.365885	0.182942	−	0.983124i	$-0.441438\pi$
$251$	5.79670	0.365885	0.182942	+	0.983124i	$0.441438\pi$
$252$	0	0
$253$	0.771280	0.0484900
$254$	31.8175	1.99641
$255$	0	0
$256$	15.9532	0.997076
$257$	0.564625	0.0352203	0.0176102	−	0.999845i	$-0.494394\pi$
$257$	0.564625	0.0352203	0.0176102	+	0.999845i	$0.494394\pi$
$258$	0	0
$259$	0	0
$260$	−1.56658	−0.0971551
$261$	0	0
$262$	−16.7231	−1.03316
$263$	−5.80213	−0.357775	−0.178887	−	0.983870i	$-0.557250\pi$
$263$	−5.80213	−0.357775	−0.178887	+	0.983870i	$0.557250\pi$
$264$	0	0
$265$	20.1819	1.23977
$266$	0	0
$267$	0	0
$268$	−6.13052	−0.374481
$269$	−23.6541	−1.44222	−0.721109	−	0.692822i	$-0.756367\pi$
$269$	−23.6541	−1.44222	−0.721109	+	0.692822i	$0.756367\pi$
$270$	0	0
$271$	−2.71410	−0.164870	−0.0824349	−	0.996596i	$-0.526270\pi$
$271$	−2.71410	−0.164870	−0.0824349	+	0.996596i	$0.526270\pi$
$272$	36.3099	2.20161
$273$	0	0
$274$	−33.3171	−2.01276
$275$	1.19197	0.0718787
$276$	0	0
$277$	−18.3581	−1.10303	−0.551517	−	0.834164i	$-0.685951\pi$
$277$	−18.3581	−1.10303	−0.551517	+	0.834164i	$0.685951\pi$
$278$	−6.00944	−0.360422
$279$	0	0
$280$	0	0
$281$	−15.7435	−0.939179	−0.469590	−	0.882885i	$-0.655598\pi$
$281$	−15.7435	−0.939179	−0.469590	+	0.882885i	$0.655598\pi$
$282$	0	0
$283$	8.78495	0.522211	0.261106	−	0.965310i	$-0.415913\pi$
$283$	8.78495	0.522211	0.261106	+	0.965310i	$0.415913\pi$
$284$	−8.25837	−0.490044
$285$	0	0
$286$	−2.60301	−0.153919
$287$	0	0
$288$	0	0
$289$	36.9636	2.17433
$290$	−25.0534	−1.47119
$291$	0	0
$292$	−9.90972	−0.579922
$293$	−18.2775	−1.06778	−0.533891	−	0.845553i	$-0.679271\pi$
$293$	−18.2775	−1.06778	−0.533891	+	0.845553i	$0.679271\pi$
$294$	0	0
$295$	−4.63036	−0.269590
$296$	−15.7435	−0.915073
$297$	0	0
$298$	0	0
$299$	0.492334	0.0284724
$300$	0	0
$301$	0	0
$302$	−20.3537	−1.17122
$303$	0	0
$304$	−7.30671	−0.419068
$305$	−11.4465	−0.655427
$306$	0	0
$307$	24.3743	1.39111	0.695557	−	0.718471i	$-0.255158\pi$
$307$	24.3743	1.39111	0.695557	+	0.718471i	$0.255158\pi$
$308$	0	0
$309$	0	0
$310$	−34.4419	−1.95617
$311$	−4.49243	−0.254742	−0.127371	−	0.991855i	$-0.540654\pi$
$311$	−4.49243	−0.254742	−0.127371	+	0.991855i	$0.540654\pi$
$312$	0	0
$313$	13.1729	0.744577	0.372289	−	0.928117i	$-0.378573\pi$
$313$	13.1729	0.744577	0.372289	+	0.928117i	$0.378573\pi$
$314$	10.5342	0.594477
$315$	0	0
$316$	8.30095	0.466965
$317$	−20.3041	−1.14039	−0.570196	−	0.821509i	$-0.693133\pi$
$317$	−20.3041	−1.14039	−0.570196	+	0.821509i	$0.693133\pi$
$318$	0	0
$319$	−11.4725	−0.642336
$320$	6.34404	0.354643
$321$	0	0
$322$	0	0
$323$	−10.8592	−0.604222
$324$	0	0
$325$	0.760877	0.0422058
$326$	36.2604	2.00828
$327$	0	0
$328$	8.23585	0.454749
$329$	0	0
$330$	0	0
$331$	−21.0618	−1.15766	−0.578831	−	0.815447i	$-0.696491\pi$
$331$	−21.0618	−1.15766	−0.578831	+	0.815447i	$0.696491\pi$
$332$	−10.2546	−0.562792
$333$	0	0
$334$	2.29630	0.125648
$335$	−16.5890	−0.906356
$336$	0	0
$337$	−20.3880	−1.11060	−0.555302	−	0.831649i	$-0.687397\pi$
$337$	−20.3880	−1.11060	−0.555302	+	0.831649i	$0.687397\pi$
$338$	−1.66159	−0.0903785
$339$	0	0
$340$	−11.5081	−0.624113
$341$	−15.7717	−0.854084
$342$	0	0
$343$	0	0
$344$	−1.80204	−0.0971593
$345$	0	0
$346$	12.6328	0.679146
$347$	−8.96214	−0.481113	−0.240557	−	0.970635i	$-0.577330\pi$
$347$	−8.96214	−0.481113	−0.240557	+	0.970635i	$0.577330\pi$
$348$	0	0
$349$	25.0345	1.34006	0.670032	−	0.742332i	$-0.266280\pi$
$349$	25.0345	1.34006	0.670032	+	0.742332i	$0.266280\pi$
$350$	0	0
$351$	0	0
$352$	−6.41531	−0.341937
$353$	33.7187	1.79466	0.897332	−	0.441356i	$-0.145502\pi$
$353$	33.7187	1.79466	0.897332	+	0.441356i	$0.145502\pi$
$354$	0	0
$355$	−22.3469	−1.18605
$356$	8.02835	0.425502
$357$	0	0
$358$	16.9475	0.895701
$359$	14.7147	0.776613	0.388306	−	0.921530i	$-0.373060\pi$
$359$	14.7147	0.776613	0.388306	+	0.921530i	$0.373060\pi$
$360$	0	0
$361$	−16.8148	−0.884989
$362$	−3.49048	−0.183455
$363$	0	0
$364$	0	0
$365$	−26.8154	−1.40358
$366$	0	0
$367$	−11.8616	−0.619169	−0.309584	−	0.950872i	$-0.600190\pi$
$367$	−11.8616	−0.619169	−0.309584	+	0.950872i	$0.600190\pi$
$368$	2.43352	0.126856
$369$	0	0
$370$	26.1592	1.35995
$371$	0	0
$372$	0	0
$373$	3.64076	0.188511	0.0942557	−	0.995548i	$-0.469953\pi$
$373$	3.64076	0.188511	0.0942557	+	0.995548i	$0.469953\pi$
$374$	−19.1217	−0.988759
$375$	0	0
$376$	6.84213	0.352856
$377$	−7.32327	−0.377168
$378$	0	0
$379$	12.9669	0.666065	0.333032	−	0.942915i	$-0.391928\pi$
$379$	12.9669	0.666065	0.333032	+	0.942915i	$0.391928\pi$
$380$	2.31579	0.118798
$381$	0	0
$382$	7.62244	0.389998
$383$	−30.2455	−1.54547	−0.772736	−	0.634728i	$-0.781112\pi$
$383$	−30.2455	−1.54547	−0.772736	+	0.634728i	$0.781112\pi$
$384$	0	0
$385$	0	0
$386$	−1.49429	−0.0760573
$387$	0	0
$388$	−10.1431	−0.514937
$389$	−15.6258	−0.792259	−0.396129	−	0.918195i	$-0.629647\pi$
$389$	−15.6258	−0.792259	−0.396129	+	0.918195i	$0.629647\pi$
$390$	0	0
$391$	3.61668	0.182904
$392$	0	0
$393$	0	0
$394$	−41.7863	−2.10516
$395$	22.4622	1.13019
$396$	0	0
$397$	−18.3125	−0.919076	−0.459538	−	0.888158i	$-0.651985\pi$
$397$	−18.3125	−0.919076	−0.459538	+	0.888158i	$0.651985\pi$
$398$	−21.3156	−1.06846
$399$	0	0
$400$	3.76088	0.188044
$401$	−7.08912	−0.354014	−0.177007	−	0.984210i	$-0.556641\pi$
$401$	−7.08912	−0.354014	−0.177007	+	0.984210i	$0.556641\pi$
$402$	0	0
$403$	−10.0676	−0.501502
$404$	3.34590	0.166465
$405$	0	0
$406$	0	0
$407$	11.9789	0.593771
$408$	0	0
$409$	12.1683	0.601682	0.300841	−	0.953674i	$-0.402733\pi$
$409$	12.1683	0.601682	0.300841	+	0.953674i	$0.402733\pi$
$410$	−13.6846	−0.675834
$411$	0	0
$412$	−4.08126	−0.201069
$413$	0	0
$414$	0	0
$415$	−27.7486	−1.36212
$416$	−4.09511	−0.200779
$417$	0	0
$418$	3.84789	0.188206
$419$	−7.41285	−0.362142	−0.181071	−	0.983470i	$-0.557956\pi$
$419$	−7.41285	−0.362142	−0.181071	+	0.983470i	$0.557956\pi$
$420$	0	0
$421$	−21.6408	−1.05471	−0.527353	−	0.849646i	$-0.676815\pi$
$421$	−21.6408	−1.05471	−0.527353	+	0.849646i	$0.676815\pi$
$422$	32.1294	1.56403
$423$	0	0
$424$	20.1819	0.980122
$425$	5.58940	0.271126
$426$	0	0
$427$	0	0
$428$	6.49634	0.314012
$429$	0	0
$430$	2.99424	0.144395
$431$	−10.0873	−0.485886	−0.242943	−	0.970041i	$-0.578113\pi$
$431$	−10.0873	−0.485886	−0.242943	+	0.970041i	$0.578113\pi$
$432$	0	0
$433$	18.3034	0.879607	0.439804	−	0.898094i	$-0.355048\pi$
$433$	18.3034	0.879607	0.439804	+	0.898094i	$0.355048\pi$
$434$	0	0
$435$	0	0
$436$	−4.52175	−0.216553
$437$	−0.727791	−0.0348150
$438$	0	0
$439$	6.91547	0.330058	0.165029	−	0.986289i	$-0.447228\pi$
$439$	6.91547	0.330058	0.165029	+	0.986289i	$0.447228\pi$
$440$	−6.64092	−0.316594
$441$	0	0
$442$	−12.2060	−0.580581
$443$	13.6673	0.649354	0.324677	−	0.945825i	$-0.394744\pi$
$443$	13.6673	0.649354	0.324677	+	0.945825i	$0.394744\pi$
$444$	0	0
$445$	21.7245	1.02984
$446$	28.0970	1.33043
$447$	0	0
$448$	0	0
$449$	−8.61026	−0.406343	−0.203172	−	0.979143i	$-0.565125\pi$
$449$	−8.61026	−0.406343	−0.203172	+	0.979143i	$0.565125\pi$
$450$	0	0
$451$	−6.26647	−0.295077
$452$	0.374606	0.0176200
$453$	0	0
$454$	−34.4509	−1.61686
$455$	0	0
$456$	0	0
$457$	11.6328	0.544161	0.272081	−	0.962274i	$-0.412288\pi$
$457$	11.6328	0.544161	0.272081	+	0.962274i	$0.412288\pi$
$458$	19.6313	0.917311
$459$	0	0
$460$	−0.771280	−0.0359611
$461$	22.7431	1.05925	0.529625	−	0.848232i	$-0.322333\pi$
$461$	22.7431	1.05925	0.529625	+	0.848232i	$0.322333\pi$
$462$	0	0
$463$	32.1937	1.49617	0.748085	−	0.663603i	$-0.230974\pi$
$463$	32.1937	1.49617	0.748085	+	0.663603i	$0.230974\pi$
$464$	−36.1976	−1.68043
$465$	0	0
$466$	13.7666	0.637727
$467$	−6.88051	−0.318392	−0.159196	−	0.987247i	$-0.550890\pi$
$467$	−6.88051	−0.318392	−0.159196	+	0.987247i	$0.550890\pi$
$468$	0	0
$469$	0	0
$470$	−11.3688	−0.524404
$471$	0	0
$472$	−4.63036	−0.213129
$473$	1.37113	0.0630445
$474$	0	0
$475$	−1.12476	−0.0516077
$476$	0	0
$477$	0	0
$478$	48.9819	2.24038
$479$	13.9923	0.639327	0.319663	−	0.947531i	$-0.396430\pi$
$479$	13.9923	0.639327	0.319663	+	0.947531i	$0.396430\pi$
$480$	0	0
$481$	7.64652	0.348651
$482$	21.2529	0.968043
$483$	0	0
$484$	−6.50232	−0.295560
$485$	−27.4469	−1.24630
$486$	0	0
$487$	29.6616	1.34409	0.672047	−	0.740509i	$-0.265415\pi$
$487$	29.6616	1.34409	0.672047	+	0.740509i	$0.265415\pi$
$488$	−11.4465	−0.518160
$489$	0	0
$490$	0	0
$491$	0.610063	0.0275317	0.0137659	−	0.999905i	$-0.495618\pi$
$491$	0.610063	0.0275317	0.0137659	+	0.999905i	$0.495618\pi$
$492$	0	0
$493$	−53.7967	−2.42288
$494$	2.45624	0.110511
$495$	0	0
$496$	−49.7623	−2.23439
$497$	0	0
$498$	0	0
$499$	−20.3639	−0.911613	−0.455806	−	0.890079i	$-0.650649\pi$
$499$	−20.3639	−0.911613	−0.455806	+	0.890079i	$0.650649\pi$
$500$	−9.02487	−0.403604
$501$	0	0
$502$	−9.63173	−0.429885
$503$	−11.8439	−0.528092	−0.264046	−	0.964510i	$-0.585057\pi$
$503$	−11.8439	−0.528092	−0.264046	+	0.964510i	$0.585057\pi$
$504$	0	0
$505$	9.05391	0.402894
$506$	−1.28155	−0.0569719
$507$	0	0
$508$	−14.5699	−0.646435
$509$	12.4699	0.552719	0.276359	−	0.961054i	$-0.410872\pi$
$509$	12.4699	0.552719	0.276359	+	0.961054i	$0.410872\pi$
$510$	0	0
$511$	0	0
$512$	0.112296	0.00496282
$513$	0	0
$514$	−0.938174	−0.0413811
$515$	−11.0438	−0.486647
$516$	0	0
$517$	−5.20602	−0.228960
$518$	0	0
$519$	0	0
$520$	−4.23912	−0.185898
$521$	18.6802	0.818396	0.409198	−	0.912446i	$-0.365809\pi$
$521$	18.6802	0.818396	0.409198	+	0.912446i	$0.365809\pi$
$522$	0	0
$523$	−42.6134	−1.86335	−0.931677	−	0.363287i	$-0.881654\pi$
$523$	−42.6134	−1.86335	−0.931677	+	0.363287i	$0.881654\pi$
$524$	7.65788	0.334536
$525$	0	0
$526$	9.64076	0.420357
$527$	−73.9564	−3.22159
$528$	0	0
$529$	−22.7576	−0.989461
$530$	−33.5341	−1.45663
$531$	0	0
$532$	0	0
$533$	−4.00010	−0.173263
$534$	0	0
$535$	17.5789	0.760004
$536$	−16.5890	−0.716537
$537$	0	0
$538$	39.3034	1.69449
$539$	0	0
$540$	0	0
$541$	−4.13052	−0.177585	−0.0887925	−	0.996050i	$-0.528301\pi$
$541$	−4.13052	−0.177585	−0.0887925	+	0.996050i	$0.528301\pi$
$542$	4.50972	0.193709
$543$	0	0
$544$	−30.0826	−1.28978
$545$	−12.2358	−0.524122
$546$	0	0
$547$	−22.0298	−0.941928	−0.470964	−	0.882153i	$-0.656094\pi$
$547$	−22.0298	−0.941928	−0.470964	+	0.882153i	$0.656094\pi$
$548$	15.2566	0.651730
$549$	0	0
$550$	−1.98057	−0.0844518
$551$	10.8256	0.461186
$552$	0	0
$553$	0	0
$554$	30.5037	1.29598
$555$	0	0
$556$	2.75185	0.116704
$557$	−31.2797	−1.32536	−0.662682	−	0.748901i	$-0.730582\pi$
$557$	−31.2797	−1.32536	−0.662682	+	0.748901i	$0.730582\pi$
$558$	0	0
$559$	0.875237	0.0370186
$560$	0	0
$561$	0	0
$562$	26.1592	1.10346
$563$	−4.87247	−0.205350	−0.102675	−	0.994715i	$-0.532740\pi$
$563$	−4.87247	−0.205350	−0.102675	+	0.994715i	$0.532740\pi$
$564$	0	0
$565$	1.01367	0.0426455
$566$	−14.5970	−0.613557
$567$	0	0
$568$	−22.3469	−0.937657
$569$	−8.29066	−0.347562	−0.173781	−	0.984784i	$-0.555599\pi$
$569$	−8.29066	−0.347562	−0.173781	+	0.984784i	$0.555599\pi$
$570$	0	0
$571$	−21.8616	−0.914878	−0.457439	−	0.889241i	$-0.651233\pi$
$571$	−21.8616	−0.914878	−0.457439	+	0.889241i	$0.651233\pi$
$572$	1.19197	0.0498389
$573$	0	0
$574$	0	0
$575$	0.374606	0.0156221
$576$	0	0
$577$	1.70945	0.0711655	0.0355828	−	0.999367i	$-0.488671\pi$
$577$	1.70945	0.0711655	0.0355828	+	0.999367i	$0.488671\pi$
$578$	−61.4183	−2.55467
$579$	0	0
$580$	11.4725	0.476369
$581$	0	0
$582$	0	0
$583$	−15.3560	−0.635979
$584$	−26.8154	−1.10963
$585$	0	0
$586$	30.3696	1.25456
$587$	8.81756	0.363940	0.181970	−	0.983304i	$-0.441753\pi$
$587$	8.81756	0.363940	0.181970	+	0.983304i	$0.441753\pi$
$588$	0	0
$589$	14.8824	0.613217
$590$	7.69375	0.316747
$591$	0	0
$592$	37.7954	1.55338
$593$	6.59135	0.270674	0.135337	−	0.990800i	$-0.456788\pi$
$593$	6.59135	0.270674	0.135337	+	0.990800i	$0.456788\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	−0.818057	−0.0334528
$599$	−34.5133	−1.41018	−0.705088	−	0.709120i	$-0.749093\pi$
$599$	−34.5133	−1.41018	−0.705088	+	0.709120i	$0.749093\pi$
$600$	0	0
$601$	−19.4282	−0.792493	−0.396246	−	0.918144i	$-0.629687\pi$
$601$	−19.4282	−0.792493	−0.396246	+	0.918144i	$0.629687\pi$
$602$	0	0
$603$	0	0
$604$	9.32038	0.379241
$605$	−17.5951	−0.715343
$606$	0	0
$607$	7.65116	0.310551	0.155276	−	0.987871i	$-0.450373\pi$
$607$	7.65116	0.310551	0.155276	+	0.987871i	$0.450373\pi$
$608$	6.05358	0.245505
$609$	0	0
$610$	19.0194	0.770074
$611$	−3.32318	−0.134441
$612$	0	0
$613$	−29.9396	−1.20925	−0.604624	−	0.796511i	$-0.706676\pi$
$613$	−29.9396	−1.20925	−0.604624	+	0.796511i	$0.706676\pi$
$614$	−40.5000	−1.63445
$615$	0	0
$616$	0	0
$617$	−22.7753	−0.916901	−0.458450	−	0.888720i	$-0.651595\pi$
$617$	−22.7753	−0.916901	−0.458450	+	0.888720i	$0.651595\pi$
$618$	0	0
$619$	17.2255	0.692349	0.346175	−	0.938170i	$-0.387480\pi$
$619$	17.2255	0.692349	0.346175	+	0.938170i	$0.387480\pi$
$620$	15.7717	0.633405
$621$	0	0
$622$	7.46457	0.299302
$623$	0	0
$624$	0	0
$625$	−20.6167	−0.824667
$626$	−21.8880	−0.874819
$627$	0	0
$628$	−4.82381	−0.192491
$629$	56.1713	2.23970
$630$	0	0
$631$	−42.6673	−1.69856	−0.849280	−	0.527943i	$-0.822963\pi$
$631$	−42.6673	−1.69856	−0.849280	+	0.527943i	$0.822963\pi$
$632$	22.4622	0.893497
$633$	0	0
$634$	33.7371	1.33987
$635$	−39.4258	−1.56457
$636$	0	0
$637$	0	0
$638$	19.0626	0.754694
$639$	0	0
$640$	−27.4041	−1.08324
$641$	46.5095	1.83701	0.918507	−	0.395405i	$-0.129396\pi$
$641$	46.5095	1.83701	0.918507	+	0.395405i	$0.129396\pi$
$642$	0	0
$643$	11.6947	0.461193	0.230596	−	0.973049i	$-0.425932\pi$
$643$	11.6947	0.461193	0.230596	+	0.973049i	$0.425932\pi$
$644$	0	0
$645$	0	0
$646$	18.0435	0.709912
$647$	−33.9887	−1.33623	−0.668117	−	0.744056i	$-0.732899\pi$
$647$	−33.9887	−1.33623	−0.668117	+	0.744056i	$0.732899\pi$
$648$	0	0
$649$	3.52313	0.138295
$650$	−1.26426	−0.0495885
$651$	0	0
$652$	−16.6044	−0.650278
$653$	−25.9085	−1.01388	−0.506939	−	0.861982i	$-0.669223\pi$
$653$	−25.9085	−1.01388	−0.506939	+	0.861982i	$0.669223\pi$
$654$	0	0
$655$	20.7220	0.809676
$656$	−19.7718	−0.771958
$657$	0	0
$658$	0	0
$659$	39.6881	1.54603	0.773015	−	0.634388i	$-0.218748\pi$
$659$	39.6881	1.54603	0.773015	+	0.634388i	$0.218748\pi$
$660$	0	0
$661$	20.5264	0.798384	0.399192	−	0.916867i	$-0.369291\pi$
$661$	20.5264	0.798384	0.399192	+	0.916867i	$0.369291\pi$
$662$	34.9961	1.36016
$663$	0	0
$664$	−27.7486	−1.07685
$665$	0	0
$666$	0	0
$667$	−3.60550	−0.139605
$668$	−1.05153	−0.0406848
$669$	0	0
$670$	27.5641	1.06490
$671$	8.70940	0.336223
$672$	0	0
$673$	4.92450	0.189826	0.0949128	−	0.995486i	$-0.469743\pi$
$673$	4.92450	0.189826	0.0949128	+	0.995486i	$0.469743\pi$
$674$	33.8764	1.30487
$675$	0	0
$676$	0.760877	0.0292645
$677$	45.0834	1.73269	0.866347	−	0.499443i	$-0.166462\pi$
$677$	45.0834	1.73269	0.866347	+	0.499443i	$0.166462\pi$
$678$	0	0
$679$	0	0
$680$	−31.1406	−1.19419
$681$	0	0
$682$	26.2060	1.00348
$683$	−29.1098	−1.11386	−0.556928	−	0.830561i	$-0.688020\pi$
$683$	−29.1098	−1.11386	−0.556928	+	0.830561i	$0.688020\pi$
$684$	0	0
$685$	41.2840	1.57738
$686$	0	0
$687$	0	0
$688$	4.32614	0.164932
$689$	−9.80223	−0.373435
$690$	0	0
$691$	8.97841	0.341555	0.170777	−	0.985310i	$-0.445372\pi$
$691$	8.97841	0.341555	0.170777	+	0.985310i	$0.445372\pi$
$692$	−5.78485	−0.219907
$693$	0	0
$694$	14.8914	0.565270
$695$	7.44644	0.282459
$696$	0	0
$697$	−29.3847	−1.11302
$698$	−41.5970	−1.57447
$699$	0	0
$700$	0	0
$701$	−2.14849	−0.0811473	−0.0405737	−	0.999177i	$-0.512919\pi$
$701$	−2.14849	−0.0811473	−0.0405737	+	0.999177i	$0.512919\pi$
$702$	0	0
$703$	−11.3034	−0.426317
$704$	−4.82703	−0.181926
$705$	0	0
$706$	−56.0266	−2.10859
$707$	0	0
$708$	0	0
$709$	26.7954	1.00632	0.503160	−	0.864193i	$-0.332171\pi$
$709$	26.7954	1.00632	0.503160	+	0.864193i	$0.332171\pi$
$710$	37.1314	1.39352
$711$	0	0
$712$	21.7245	0.814160
$713$	−4.95661	−0.185627
$714$	0	0
$715$	3.22545	0.120625
$716$	−7.76060	−0.290027
$717$	0	0
$718$	−24.4498	−0.912458
$719$	−38.2738	−1.42737	−0.713686	−	0.700465i	$-0.752976\pi$
$719$	−38.2738	−1.42737	−0.713686	+	0.700465i	$0.752976\pi$
$720$	0	0
$721$	0	0
$722$	27.9393	1.03979
$723$	0	0
$724$	1.59836	0.0594027
$725$	−5.57211	−0.206943
$726$	0	0
$727$	5.70834	0.211711	0.105855	−	0.994382i	$-0.466242\pi$
$727$	5.70834	0.211711	0.105855	+	0.994382i	$0.466242\pi$
$728$	0	0
$729$	0	0
$730$	44.5562	1.64910
$731$	6.42948	0.237803
$732$	0	0
$733$	25.8148	0.953491	0.476745	−	0.879041i	$-0.341816\pi$
$733$	25.8148	0.953491	0.476745	+	0.879041i	$0.341816\pi$
$734$	19.7090	0.727474
$735$	0	0
$736$	−2.01616	−0.0743167
$737$	12.6222	0.464945
$738$	0	0
$739$	−27.4588	−1.01009	−0.505044	−	0.863093i	$-0.668524\pi$
$739$	−27.4588	−1.01009	−0.505044	+	0.863093i	$0.668524\pi$
$740$	−11.9789	−0.440352
$741$	0	0
$742$	0	0
$743$	−47.5933	−1.74603	−0.873014	−	0.487695i	$-0.837838\pi$
$743$	−47.5933	−1.74603	−0.873014	+	0.487695i	$0.837838\pi$
$744$	0	0
$745$	0	0
$746$	−6.04944	−0.221486
$747$	0	0
$748$	8.75623	0.320159
$749$	0	0
$750$	0	0
$751$	−34.2060	−1.24820	−0.624098	−	0.781346i	$-0.714533\pi$
$751$	−34.2060	−1.24820	−0.624098	+	0.781346i	$0.714533\pi$
$752$	−16.4259	−0.598990
$753$	0	0
$754$	12.1683	0.443142
$755$	25.2207	0.917876
$756$	0	0
$757$	2.66811	0.0969740	0.0484870	−	0.998824i	$-0.484560\pi$
$757$	2.66811	0.0969740	0.0484870	+	0.998824i	$0.484560\pi$
$758$	−21.5456	−0.782573
$759$	0	0
$760$	6.26647	0.227309
$761$	−11.1829	−0.405381	−0.202690	−	0.979243i	$-0.564968\pi$
$761$	−11.1829	−0.405381	−0.202690	+	0.979243i	$0.564968\pi$
$762$	0	0
$763$	0	0
$764$	−3.49048	−0.126281
$765$	0	0
$766$	50.2555	1.81581
$767$	2.24893	0.0812042
$768$	0	0
$769$	−19.7929	−0.713749	−0.356875	−	0.934152i	$-0.616158\pi$
$769$	−19.7929	−0.713749	−0.356875	+	0.934152i	$0.616158\pi$
$770$	0	0
$771$	0	0
$772$	0.684266	0.0246273
$773$	53.7486	1.93320	0.966602	−	0.256284i	$-0.0824981\pi$
$773$	53.7486	1.93320	0.966602	+	0.256284i	$0.0824981\pi$
$774$	0	0
$775$	−7.66019	−0.275162
$776$	−27.4469	−0.985287
$777$	0	0
$778$	25.9636	0.930841
$779$	5.91313	0.211860
$780$	0	0
$781$	17.0033	0.608425
$782$	−6.00944	−0.214897
$783$	0	0
$784$	0	0
$785$	−13.0531	−0.465886
$786$	0	0
$787$	19.7174	0.702848	0.351424	−	0.936216i	$-0.385698\pi$
$787$	19.7174	0.702848	0.351424	+	0.936216i	$0.385698\pi$
$788$	19.1348	0.681651
$789$	0	0
$790$	−37.3229	−1.32789
$791$	0	0
$792$	0	0
$793$	5.55950	0.197424
$794$	30.4278	1.07984
$795$	0	0
$796$	9.76088	0.345965
$797$	−46.0667	−1.63177	−0.815883	−	0.578216i	$-0.803749\pi$
$797$	−46.0667	−1.63177	−0.815883	+	0.578216i	$0.803749\pi$
$798$	0	0
$799$	−24.4120	−0.863636
$800$	−3.11587	−0.110163
$801$	0	0
$802$	11.7792	0.415938
$803$	20.4032	0.720015
$804$	0	0
$805$	0	0
$806$	16.7282	0.589225
$807$	0	0
$808$	9.05391	0.318515
$809$	−50.9846	−1.79252	−0.896262	−	0.443525i	$-0.853728\pi$
$809$	−50.9846	−1.79252	−0.896262	+	0.443525i	$0.853728\pi$
$810$	0	0
$811$	−26.8928	−0.944333	−0.472167	−	0.881509i	$-0.656528\pi$
$811$	−26.8928	−0.944333	−0.472167	+	0.881509i	$0.656528\pi$
$812$	0	0
$813$	0	0
$814$	−19.9040	−0.697633
$815$	−44.9310	−1.57387
$816$	0	0
$817$	−1.29382	−0.0452649
$818$	−20.2187	−0.706929
$819$	0	0
$820$	6.26647	0.218835
$821$	38.4293	1.34119	0.670595	−	0.741823i	$-0.266039\pi$
$821$	38.4293	1.34119	0.670595	+	0.741823i	$0.266039\pi$
$822$	0	0
$823$	−25.6739	−0.894935	−0.447467	−	0.894300i	$-0.647674\pi$
$823$	−25.6739	−0.894935	−0.447467	+	0.894300i	$0.647674\pi$
$824$	−11.0438	−0.384728
$825$	0	0
$826$	0	0
$827$	10.9488	0.380726	0.190363	−	0.981714i	$-0.439034\pi$
$827$	10.9488	0.380726	0.190363	+	0.981714i	$0.439034\pi$
$828$	0	0
$829$	−12.3549	−0.429102	−0.214551	−	0.976713i	$-0.568829\pi$
$829$	−12.3549	−0.429102	−0.214551	+	0.976713i	$0.568829\pi$
$830$	46.1067	1.60039
$831$	0	0
$832$	−3.08126	−0.106823
$833$	0	0
$834$	0	0
$835$	−2.84540	−0.0984692
$836$	−1.76203	−0.0609411
$837$	0	0
$838$	12.3171	0.425488
$839$	−38.9389	−1.34432	−0.672160	−	0.740406i	$-0.734633\pi$
$839$	−38.9389	−1.34432	−0.672160	+	0.740406i	$0.734633\pi$
$840$	0	0
$841$	24.6304	0.849323
$842$	35.9580	1.23920
$843$	0	0
$844$	−14.7127	−0.506433
$845$	2.05891	0.0708288
$846$	0	0
$847$	0	0
$848$	−48.4507	−1.66380
$849$	0	0
$850$	−9.28728	−0.318551
$851$	3.76464	0.129050
$852$	0	0
$853$	14.1111	0.483155	0.241577	−	0.970382i	$-0.422335\pi$
$853$	14.1111	0.483155	0.241577	+	0.970382i	$0.422335\pi$
$854$	0	0
$855$	0	0
$856$	17.5789	0.600836
$857$	54.3024	1.85493	0.927467	−	0.373905i	$-0.121982\pi$
$857$	54.3024	1.85493	0.927467	+	0.373905i	$0.121982\pi$
$858$	0	0
$859$	−19.0460	−0.649841	−0.324920	−	0.945741i	$-0.605338\pi$
$859$	−19.0460	−0.649841	−0.324920	+	0.945741i	$0.605338\pi$
$860$	−1.37113	−0.0467551
$861$	0	0
$862$	16.7609	0.570878
$863$	−21.5111	−0.732246	−0.366123	−	0.930567i	$-0.619315\pi$
$863$	−21.5111	−0.732246	−0.366123	+	0.930567i	$0.619315\pi$
$864$	0	0
$865$	−15.6537	−0.532240
$866$	−30.4128	−1.03347
$867$	0	0
$868$	0	0
$869$	−17.0909	−0.579770
$870$	0	0
$871$	8.05718	0.273007
$872$	−12.2358	−0.414355
$873$	0	0
$874$	1.20929	0.0409048
$875$	0	0
$876$	0	0
$877$	3.96552	0.133906	0.0669530	−	0.997756i	$-0.478672\pi$
$877$	3.96552	0.133906	0.0669530	+	0.997756i	$0.478672\pi$
$878$	−11.4907	−0.387791
$879$	0	0
$880$	15.9428	0.537432
$881$	7.97878	0.268812	0.134406	−	0.990926i	$-0.457087\pi$
$881$	7.97878	0.268812	0.134406	+	0.990926i	$0.457087\pi$
$882$	0	0
$883$	−1.30206	−0.0438178	−0.0219089	−	0.999760i	$-0.506974\pi$
$883$	−1.30206	−0.0438178	−0.0219089	+	0.999760i	$0.506974\pi$
$884$	5.58940	0.187992
$885$	0	0
$886$	−22.7095	−0.762939
$887$	14.9261	0.501171	0.250585	−	0.968094i	$-0.419377\pi$
$887$	14.9261	0.501171	0.250585	+	0.968094i	$0.419377\pi$
$888$	0	0
$889$	0	0
$890$	−36.0972	−1.20998
$891$	0	0
$892$	−12.8662	−0.430793
$893$	4.91248	0.164390
$894$	0	0
$895$	−21.0000	−0.701953
$896$	0	0
$897$	0	0
$898$	14.3067	0.477421
$899$	73.7277	2.45896
$900$	0	0
$901$	−72.0071	−2.39891
$902$	10.4123	0.346691
$903$	0	0
$904$	1.01367	0.0337143
$905$	4.32513	0.143772
$906$	0	0
$907$	−30.9507	−1.02770	−0.513851	−	0.857879i	$-0.671782\pi$
$907$	−30.9507	−1.02770	−0.513851	+	0.857879i	$0.671782\pi$
$908$	15.7758	0.523538
$909$	0	0
$910$	0	0
$911$	−0.0895769	−0.00296782	−0.00148391	−	0.999999i	$-0.500472\pi$
$911$	−0.0895769	−0.00296782	−0.00148391	+	0.999999i	$0.500472\pi$
$912$	0	0
$913$	21.1132	0.698747
$914$	−19.3290	−0.639347
$915$	0	0
$916$	−8.98960	−0.297025
$917$	0	0
$918$	0	0
$919$	10.7037	0.353082	0.176541	−	0.984293i	$-0.443509\pi$
$919$	10.7037	0.353082	0.176541	+	0.984293i	$0.443509\pi$
$920$	−2.08706	−0.0688085
$921$	0	0
$922$	−37.7896	−1.24453
$923$	10.8538	0.357256
$924$	0	0
$925$	5.81806	0.191297
$926$	−53.4927	−1.75788
$927$	0	0
$928$	29.9896	0.984457
$929$	31.0897	1.02002	0.510010	−	0.860168i	$-0.329642\pi$
$929$	31.0897	1.02002	0.510010	+	0.860168i	$0.329642\pi$
$930$	0	0
$931$	0	0
$932$	−6.30403	−0.206496
$933$	0	0
$934$	11.4326	0.374085
$935$	23.6941	0.774881
$936$	0	0
$937$	42.5023	1.38849	0.694245	−	0.719739i	$-0.255738\pi$
$937$	42.5023	1.38849	0.694245	+	0.719739i	$0.255738\pi$
$938$	0	0
$939$	0	0
$940$	5.20602	0.169802
$941$	−40.5269	−1.32114	−0.660570	−	0.750765i	$-0.729685\pi$
$941$	−40.5269	−1.32114	−0.660570	+	0.750765i	$0.729685\pi$
$942$	0	0
$943$	−1.96938	−0.0641320
$944$	11.1161	0.361797
$945$	0	0
$946$	−2.27825	−0.0740723
$947$	30.7660	0.999760	0.499880	−	0.866095i	$-0.333378\pi$
$947$	30.7660	0.999760	0.499880	+	0.866095i	$0.333378\pi$
$948$	0	0
$949$	13.0241	0.422779
$950$	1.86889	0.0606349
$951$	0	0
$952$	0	0
$953$	32.1371	1.04102	0.520511	−	0.853855i	$-0.325741\pi$
$953$	32.1371	1.04102	0.520511	+	0.853855i	$0.325741\pi$
$954$	0	0
$955$	−9.44514	−0.305638
$956$	−22.4299	−0.725434
$957$	0	0
$958$	−23.2495	−0.751158
$959$	0	0
$960$	0	0
$961$	70.3562	2.26956
$962$	−12.7054	−0.409637
$963$	0	0
$964$	−9.73215	−0.313452
$965$	1.85161	0.0596054
$966$	0	0
$967$	42.1237	1.35461	0.677303	−	0.735704i	$-0.263149\pi$
$967$	42.1237	1.35461	0.677303	+	0.735704i	$0.263149\pi$
$968$	−17.5951	−0.565529
$969$	0	0
$970$	45.6055	1.46430
$971$	40.9601	1.31447	0.657236	−	0.753685i	$-0.271726\pi$
$971$	40.9601	1.31447	0.657236	+	0.753685i	$0.271726\pi$
$972$	0	0
$973$	0	0
$974$	−49.2853	−1.57920
$975$	0	0
$976$	27.4796	0.879601
$977$	24.4165	0.781153	0.390576	−	0.920570i	$-0.372276\pi$
$977$	24.4165	0.781153	0.390576	+	0.920570i	$0.372276\pi$
$978$	0	0
$979$	−16.5297	−0.528291
$980$	0	0
$981$	0	0
$982$	−1.01367	−0.0323476
$983$	−43.3427	−1.38242	−0.691209	−	0.722655i	$-0.742922\pi$
$983$	−43.3427	−1.38242	−0.691209	+	0.722655i	$0.742922\pi$
$984$	0	0
$985$	51.7784	1.64980
$986$	89.3880	2.84670
$987$	0	0
$988$	−1.12476	−0.0357835
$989$	0.430909	0.0137021
$990$	0	0
$991$	−20.2495	−0.643247	−0.321624	−	0.946868i	$-0.604229\pi$
$991$	−20.2495	−0.643247	−0.321624	+	0.946868i	$0.604229\pi$
$992$	41.2278	1.30899
$993$	0	0
$994$	0	0
$995$	26.4127	0.837338
$996$	0	0
$997$	32.4635	1.02813	0.514064	−	0.857752i	$-0.328139\pi$
$997$	32.4635	1.02813	0.514064	+	0.857752i	$0.328139\pi$
$998$	33.8364	1.07107
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bs.1.2		6
3.2	odd	2	inner	5733.2.a.bs.1.5		6
7.2	even	3		819.2.j.i.235.5	yes	12
7.4	even	3		819.2.j.i.352.5	yes	12
7.6	odd	2		5733.2.a.bt.1.2		6
21.2	odd	6		819.2.j.i.235.2	✓	12
21.11	odd	6		819.2.j.i.352.2	yes	12
21.20	even	2		5733.2.a.bt.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.j.i.235.2	✓	12	21.2	odd	6
819.2.j.i.235.5	yes	12	7.2	even	3
819.2.j.i.352.2	yes	12	21.11	odd	6
819.2.j.i.352.5	yes	12	7.4	even	3
5733.2.a.bs.1.2		6	1.1	even	1	trivial
5733.2.a.bs.1.5		6	3.2	odd	2	inner
5733.2.a.bt.1.2		6	7.6	odd	2
5733.2.a.bt.1.5		6	21.20	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)

\(f(q)\)	\(=\)	\(q-1.66159 q^{2} +0.760877 q^{4} +2.05891 q^{5} +2.05891 q^{8} +O(q^{10})\)	\(q-1.66159 q^{2} +0.760877 q^{4} +2.05891 q^{5} +2.05891 q^{8} -3.42107 q^{10} -1.56658 q^{11} -1.00000 q^{13} -4.94282 q^{16} -7.34599 q^{17} +1.47825 q^{19} +1.56658 q^{20} +2.60301 q^{22} -0.492334 q^{23} -0.760877 q^{25} +1.66159 q^{26} +7.32327 q^{29} +10.0676 q^{31} +4.09511 q^{32} +12.2060 q^{34} -7.64652 q^{37} -2.45624 q^{38} +4.23912 q^{40} +4.00010 q^{41} -0.875237 q^{43} -1.19197 q^{44} +0.818057 q^{46} +3.32318 q^{47} +1.26426 q^{50} -0.760877 q^{52} +9.80223 q^{53} -3.22545 q^{55} -12.1683 q^{58} -2.24893 q^{59} -5.55950 q^{61} -16.7282 q^{62} +3.08126 q^{64} -2.05891 q^{65} -8.05718 q^{67} -5.58940 q^{68} -10.8538 q^{71} -13.0241 q^{73} +12.7054 q^{74} +1.12476 q^{76} +10.9097 q^{79} -10.1768 q^{80} -6.64652 q^{82} -13.4773 q^{83} -15.1248 q^{85} +1.45428 q^{86} -3.22545 q^{88} +10.5514 q^{89} -0.374606 q^{92} -5.52175 q^{94} +3.04358 q^{95} -13.3308 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{4}+O(q^{10}) \) 6 * q + 4 * q^4	\( 6 q + 4 q^{4} - 4 q^{10} - 6 q^{13} - 12 q^{16} + 10 q^{19} - 18 q^{22} - 4 q^{25} + 8 q^{31} + 6 q^{34} - 10 q^{37} + 26 q^{40} - 40 q^{43} + 22 q^{46} - 4 q^{52} - 36 q^{58} - 2 q^{61} - 14 q^{64} - 66 q^{67} - 28 q^{73} - 28 q^{76} - 20 q^{79} - 4 q^{82} - 56 q^{85} - 32 q^{94} + 22 q^{97}+O(q^{100}) \) 6 * q + 4 * q^4 - 4 * q^10 - 6 * q^13 - 12 * q^16 + 10 * q^19 - 18 * q^22 - 4 * q^25 + 8 * q^31 + 6 * q^34 - 10 * q^37 + 26 * q^40 - 40 * q^43 + 22 * q^46 - 4 * q^52 - 36 * q^58 - 2 * q^61 - 14 * q^64 - 66 * q^67 - 28 * q^73 - 28 * q^76 - 20 * q^79 - 4 * q^82 - 56 * q^85 - 32 * q^94 + 22 * q^97

Introduction

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