LMFDB - Embedded newform 5733.2.a.bm.1.3

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:	$5$
Coefficient field:	5.5.746052.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 7x^{3} + 8x + 2 $ x^5 - x^4 - 7x^3 + 8x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.265608$ 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)

$f(q)$	$=$	$q-1.26561 q^{2} -0.398235 q^{4} -2.90260 q^{5} +3.03523 q^{8} +O(q^{10})$	$q-1.26561 q^{2} -0.398235 q^{4} -2.90260 q^{5} +3.03523 q^{8} +3.67356 q^{10} -2.03656 q^{11} -1.00000 q^{13} -3.04494 q^{16} +3.99866 q^{17} -6.96210 q^{19} +1.15592 q^{20} +2.57749 q^{22} +0.627280 q^{23} +3.42509 q^{25} +1.26561 q^{26} -1.09606 q^{29} +10.4325 q^{31} -2.21675 q^{32} -5.06074 q^{34} -3.08537 q^{37} +8.81129 q^{38} -8.81005 q^{40} -0.521150 q^{41} +0.329024 q^{43} +0.811031 q^{44} -0.793891 q^{46} +10.5457 q^{47} -4.33482 q^{50} +0.398235 q^{52} -7.11900 q^{53} +5.91133 q^{55} +1.38719 q^{58} +2.03656 q^{59} -2.40081 q^{61} -13.2034 q^{62} +8.89542 q^{64} +2.90260 q^{65} +14.6942 q^{67} -1.59241 q^{68} -3.60141 q^{71} -2.97573 q^{73} +3.90487 q^{74} +2.77255 q^{76} -8.76150 q^{79} +8.83824 q^{80} +0.659572 q^{82} +12.8039 q^{83} -11.6065 q^{85} -0.416416 q^{86} -6.18143 q^{88} -2.68098 q^{89} -0.249805 q^{92} -13.3467 q^{94} +20.2082 q^{95} +2.32902 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} + 8 q^{4} + 2 q^{5} - 9 q^{8}+O(q^{10}) $ 5 * q - 4 * q^2 + 8 * q^4 + 2 * q^5 - 9 * q^8	$ 5 q - 4 q^{2} + 8 q^{4} + 2 q^{5} - 9 q^{8} + 5 q^{10} - 11 q^{11} - 5 q^{13} + 10 q^{16} - 5 q^{17} - 9 q^{19} + q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} + 4 q^{26} + 3 q^{29} + 6 q^{31} - 22 q^{32} + 22 q^{34} + 4 q^{37} - 10 q^{38} - 28 q^{40} + 14 q^{41} + 2 q^{43} + 3 q^{46} + q^{47} - 9 q^{50} - 8 q^{52} - 17 q^{53} - 27 q^{58} + 11 q^{59} + 11 q^{61} - 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} - 32 q^{68} - 15 q^{71} + 33 q^{74} - 8 q^{76} + 2 q^{79} + 55 q^{80} - 34 q^{82} + 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} - 4 q^{89} - 21 q^{92} - 20 q^{94} + 12 q^{95} + 12 q^{97}+O(q^{100}) $ 5 * q - 4 * q^2 + 8 * q^4 + 2 * q^5 - 9 * q^8 + 5 * q^10 - 11 * q^11 - 5 * q^13 + 10 * q^16 - 5 * q^17 - 9 * q^19 + q^20 + 8 * q^22 - 10 * q^23 + 9 * q^25 + 4 * q^26 + 3 * q^29 + 6 * q^31 - 22 * q^32 + 22 * q^34 + 4 * q^37 - 10 * q^38 - 28 * q^40 + 14 * q^41 + 2 * q^43 + 3 * q^46 + q^47 - 9 * q^50 - 8 * q^52 - 17 * q^53 - 27 * q^58 + 11 * q^59 + 11 * q^61 - 23 * q^62 + 9 * q^64 - 2 * q^65 + 13 * q^67 - 32 * q^68 - 15 * q^71 + 33 * q^74 - 8 * q^76 + 2 * q^79 + 55 * q^80 - 34 * q^82 + 6 * q^83 - 22 * q^85 - 28 * q^86 - 3 * q^88 - 4 * q^89 - 21 * q^92 - 20 * q^94 + 12 * q^95 + 12 * 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 $

$2$	−1.26561	−0.894920	−0.447460	−	0.894304i	$-0.647671\pi$
$2$	−1.26561	−0.894920	−0.447460	+	0.894304i	$0.647671\pi$
$3$	0	0
$3$	0	0
$4$	−0.398235	−0.199118
$5$	−2.90260	−1.29808	−0.649041	−	0.760753i	$-0.724830\pi$
$5$	−2.90260	−1.29808	−0.649041	+	0.760753i	$0.724830\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	3.03523	1.07311
$9$	0	0
$10$	3.67356	1.16168
$11$	−2.03656	−0.614047	−0.307024	−	0.951702i	$-0.599333\pi$
$11$	−2.03656	−0.614047	−0.307024	+	0.951702i	$0.599333\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−3.04494	−0.761235
$17$	3.99866	0.969818	0.484909	−	0.874565i	$-0.338853\pi$
$17$	3.99866	0.969818	0.484909	+	0.874565i	$0.338853\pi$
$18$	0	0
$19$	−6.96210	−1.59722	−0.798608	−	0.601852i	$-0.794430\pi$
$19$	−6.96210	−1.59722	−0.798608	+	0.601852i	$0.794430\pi$
$20$	1.15592	0.258471
$21$	0	0
$22$	2.57749	0.549523
$23$	0.627280	0.130797	0.0653985	−	0.997859i	$-0.479168\pi$
$23$	0.627280	0.130797	0.0653985	+	0.997859i	$0.479168\pi$
$24$	0	0
$25$	3.42509	0.685017
$26$	1.26561	0.248206
$27$	0	0
$28$	0	0
$29$	−1.09606	−0.203534	−0.101767	−	0.994808i	$-0.532450\pi$
$29$	−1.09606	−0.203534	−0.101767	+	0.994808i	$0.532450\pi$
$30$	0	0
$31$	10.4325	1.87373	0.936864	−	0.349693i	$-0.113714\pi$
$31$	10.4325	1.87373	0.936864	+	0.349693i	$0.113714\pi$
$32$	−2.21675	−0.391870
$33$	0	0
$34$	−5.06074	−0.867910
$35$	0	0
$36$	0	0
$37$	−3.08537	−0.507232	−0.253616	−	0.967305i	$-0.581620\pi$
$37$	−3.08537	−0.507232	−0.253616	+	0.967305i	$0.581620\pi$
$38$	8.81129	1.42938
$39$	0	0
$40$	−8.81005	−1.39299
$41$	−0.521150	−0.0813900	−0.0406950	−	0.999172i	$-0.512957\pi$
$41$	−0.521150	−0.0813900	−0.0406950	+	0.999172i	$0.512957\pi$
$42$	0	0
$43$	0.329024	0.0501757	0.0250879	−	0.999685i	$-0.492013\pi$
$43$	0.329024	0.0501757	0.0250879	+	0.999685i	$0.492013\pi$
$44$	0.811031	0.122268
$45$	0	0
$46$	−0.793891	−0.117053
$47$	10.5457	1.53825	0.769123	−	0.639101i	$-0.220693\pi$
$47$	10.5457	1.53825	0.769123	+	0.639101i	$0.220693\pi$
$48$	0	0
$49$	0	0
$50$	−4.33482	−0.613036
$51$	0	0
$52$	0.398235	0.0552253
$53$	−7.11900	−0.977870	−0.488935	−	0.872320i	$-0.662614\pi$
$53$	−7.11900	−0.977870	−0.488935	+	0.872320i	$0.662614\pi$
$54$	0	0
$55$	5.91133	0.797084
$56$	0	0
$57$	0	0
$58$	1.38719	0.182147
$59$	2.03656	0.265138	0.132569	−	0.991174i	$-0.457677\pi$
$59$	2.03656	0.265138	0.132569	+	0.991174i	$0.457677\pi$
$60$	0	0
$61$	−2.40081	−0.307393	−0.153696	−	0.988118i	$-0.549118\pi$
$61$	−2.40081	−0.307393	−0.153696	+	0.988118i	$0.549118\pi$
$62$	−13.2034	−1.67684
$63$	0	0
$64$	8.89542	1.11193
$65$	2.90260	0.360023
$66$	0	0
$67$	14.6942	1.79518	0.897589	−	0.440832i	$-0.145317\pi$
$67$	14.6942	1.79518	0.897589	+	0.440832i	$0.145317\pi$
$68$	−1.59241	−0.193108
$69$	0	0
$70$	0	0
$71$	−3.60141	−0.427409	−0.213704	−	0.976898i	$-0.568553\pi$
$71$	−3.60141	−0.427409	−0.213704	+	0.976898i	$0.568553\pi$
$72$	0	0
$73$	−2.97573	−0.348283	−0.174141	−	0.984721i	$-0.555715\pi$
$73$	−2.97573	−0.348283	−0.174141	+	0.984721i	$0.555715\pi$
$74$	3.90487	0.453932
$75$	0	0
$76$	2.77255	0.318034
$77$	0	0
$78$	0	0
$79$	−8.76150	−0.985746	−0.492873	−	0.870101i	$-0.664053\pi$
$79$	−8.76150	−0.985746	−0.492873	+	0.870101i	$0.664053\pi$
$80$	8.83824	0.988145
$81$	0	0
$82$	0.659572	0.0728376
$83$	12.8039	1.40541	0.702703	−	0.711483i	$-0.251976\pi$
$83$	12.8039	1.40541	0.702703	+	0.711483i	$0.251976\pi$
$84$	0	0
$85$	−11.6065	−1.25890
$86$	−0.416416	−0.0449033
$87$	0	0
$88$	−6.18143	−0.658943
$89$	−2.68098	−0.284184	−0.142092	−	0.989853i	$-0.545383\pi$
$89$	−2.68098	−0.284184	−0.142092	+	0.989853i	$0.545383\pi$
$90$	0	0
$91$	0	0
$92$	−0.249805	−0.0260440
$93$	0	0
$94$	−13.3467	−1.37661
$95$	20.2082	2.07332
$96$	0	0
$97$	2.32902	0.236477	0.118238	−	0.992985i	$-0.462275\pi$
$97$	2.32902	0.236477	0.118238	+	0.992985i	$0.462275\pi$
$98$	0	0
$99$	0	0
$100$	−1.36399	−0.136399
$101$	1.45324	0.144603	0.0723014	−	0.997383i	$-0.476966\pi$
$101$	1.45324	0.144603	0.0723014	+	0.997383i	$0.476966\pi$
$102$	0	0
$103$	11.6353	1.14646	0.573230	−	0.819394i	$-0.305690\pi$
$103$	11.6353	1.14646	0.573230	+	0.819394i	$0.305690\pi$
$104$	−3.03523	−0.297628
$105$	0	0
$106$	9.00987	0.875115
$107$	−19.6259	−1.89731	−0.948656	−	0.316310i	$-0.897556\pi$
$107$	−19.6259	−1.89731	−0.948656	+	0.316310i	$0.897556\pi$
$108$	0	0
$109$	−1.10676	−0.106008	−0.0530040	−	0.998594i	$-0.516880\pi$
$109$	−1.10676	−0.106008	−0.0530040	+	0.998594i	$0.516880\pi$
$110$	−7.48143	−0.713326
$111$	0	0
$112$	0	0
$113$	1.09606	0.103109	0.0515545	−	0.998670i	$-0.483582\pi$
$113$	1.09606	0.103109	0.0515545	+	0.998670i	$0.483582\pi$
$114$	0	0
$115$	−1.82074	−0.169785
$116$	0.436491	0.0405272
$117$	0	0
$118$	−2.57749	−0.237277
$119$	0	0
$120$	0	0
$121$	−6.85241	−0.622946
$122$	3.03849	0.275092
$123$	0	0
$124$	−4.15458	−0.373092
$125$	4.57134	0.408873
$126$	0	0
$127$	5.18143	0.459778	0.229889	−	0.973217i	$-0.426164\pi$
$127$	5.18143	0.459778	0.229889	+	0.973217i	$0.426164\pi$
$128$	−6.82461	−0.603216
$129$	0	0
$130$	−3.67356	−0.322192
$131$	10.5667	0.923217	0.461609	−	0.887084i	$-0.347272\pi$
$131$	10.5667	0.923217	0.461609	+	0.887084i	$0.347272\pi$
$132$	0	0
$133$	0	0
$134$	−18.5971	−1.60654
$135$	0	0
$136$	12.1368	1.04073
$137$	5.87177	0.501659	0.250830	−	0.968031i	$-0.419297\pi$
$137$	5.87177	0.501659	0.250830	+	0.968031i	$0.419297\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	0	0
$142$	4.55797	0.382497
$143$	2.03656	0.170306
$144$	0	0
$145$	3.18143	0.264204
$146$	3.76611	0.311685
$147$	0	0
$148$	1.22870	0.100999
$149$	10.1054	0.827868	0.413934	−	0.910307i	$-0.364154\pi$
$149$	10.1054	0.827868	0.413934	+	0.910307i	$0.364154\pi$
$150$	0	0
$151$	−0.187726	−0.0152769	−0.00763847	−	0.999971i	$-0.502431\pi$
$151$	−0.187726	−0.0152769	−0.00763847	+	0.999971i	$0.502431\pi$
$152$	−21.1316	−1.71400
$153$	0	0
$154$	0	0
$155$	−30.2813	−2.43225
$156$	0	0
$157$	12.0718	0.963434	0.481717	−	0.876327i	$-0.340013\pi$
$157$	12.0718	0.963434	0.481717	+	0.876327i	$0.340013\pi$
$158$	11.0886	0.882164
$159$	0	0
$160$	6.43435	0.508680
$161$	0	0
$162$	0	0
$163$	14.9136	1.16812	0.584060	−	0.811711i	$-0.301463\pi$
$163$	14.9136	1.16812	0.584060	+	0.811711i	$0.301463\pi$
$164$	0.207540	0.0162062
$165$	0	0
$166$	−16.2047	−1.25773
$167$	5.05664	0.391294	0.195647	−	0.980674i	$-0.437319\pi$
$167$	5.05664	0.391294	0.195647	+	0.980674i	$0.437319\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	14.6893	1.12662
$171$	0	0
$172$	−0.131029	−0.00999087
$173$	−0.595615	−0.0452837	−0.0226419	−	0.999744i	$-0.507208\pi$
$173$	−0.595615	−0.0452837	−0.0226419	+	0.999744i	$0.507208\pi$
$174$	0	0
$175$	0	0
$176$	6.20121	0.467434
$177$	0	0
$178$	3.39308	0.254322
$179$	−8.07664	−0.603676	−0.301838	−	0.953359i	$-0.597600\pi$
$179$	−8.07664	−0.603676	−0.301838	+	0.953359i	$0.597600\pi$
$180$	0	0
$181$	−1.89324	−0.140724	−0.0703618	−	0.997522i	$-0.522415\pi$
$181$	−1.89324	−0.140724	−0.0703618	+	0.997522i	$0.522415\pi$
$182$	0	0
$183$	0	0
$184$	1.90394	0.140360
$185$	8.95559	0.658428
$186$	0	0
$187$	−8.14353	−0.595514
$188$	−4.19966	−0.306292
$189$	0	0
$190$	−25.5757	−1.85545
$191$	−3.70174	−0.267849	−0.133924	−	0.990992i	$-0.542758\pi$
$191$	−3.70174	−0.267849	−0.133924	+	0.990992i	$0.542758\pi$
$192$	0	0
$193$	13.5875	0.978047	0.489024	−	0.872271i	$-0.337353\pi$
$193$	13.5875	0.978047	0.489024	+	0.872271i	$0.337353\pi$
$194$	−2.94763	−0.211628
$195$	0	0
$196$	0	0
$197$	9.70258	0.691280	0.345640	−	0.938367i	$-0.387662\pi$
$197$	9.70258	0.691280	0.345640	+	0.938367i	$0.387662\pi$
$198$	0	0
$199$	−26.2720	−1.86237	−0.931185	−	0.364547i	$-0.881224\pi$
$199$	−26.2720	−1.86237	−0.931185	+	0.364547i	$0.881224\pi$
$200$	10.3959	0.735102
$201$	0	0
$202$	−1.83923	−0.129408
$203$	0	0
$204$	0	0
$205$	1.51269	0.105651
$206$	−14.7257	−1.02599
$207$	0	0
$208$	3.04494	0.211128
$209$	14.1788	0.980765
$210$	0	0
$211$	10.0338	0.690758	0.345379	−	0.938463i	$-0.387750\pi$
$211$	10.0338	0.690758	0.345379	+	0.938463i	$0.387750\pi$
$212$	2.83504	0.194711
$213$	0	0
$214$	24.8388	1.69794
$215$	−0.955026	−0.0651322
$216$	0	0
$217$	0	0
$218$	1.40072	0.0948688
$219$	0	0
$220$	−2.35410	−0.158713
$221$	−3.99866	−0.268979
$222$	0	0
$223$	−17.4961	−1.17163	−0.585813	−	0.810446i	$-0.699225\pi$
$223$	−17.4961	−1.17163	−0.585813	+	0.810446i	$0.699225\pi$
$224$	0	0
$225$	0	0
$226$	−1.38719	−0.0922743
$227$	−9.51630	−0.631619	−0.315810	−	0.948823i	$-0.602276\pi$
$227$	−9.51630	−0.631619	−0.315810	+	0.948823i	$0.602276\pi$
$228$	0	0
$229$	−21.1170	−1.39545	−0.697725	−	0.716366i	$-0.745804\pi$
$229$	−21.1170	−1.39545	−0.697725	+	0.716366i	$0.745804\pi$
$230$	2.30435	0.151944
$231$	0	0
$232$	−3.32680	−0.218415
$233$	−14.1788	−0.928881	−0.464441	−	0.885604i	$-0.653745\pi$
$233$	−14.1788	−0.928881	−0.464441	+	0.885604i	$0.653745\pi$
$234$	0	0
$235$	−30.6099	−1.99677
$236$	−0.811031	−0.0527936
$237$	0	0
$238$	0	0
$239$	16.5275	1.06907	0.534536	−	0.845145i	$-0.320486\pi$
$239$	16.5275	1.06907	0.534536	+	0.845145i	$0.320486\pi$
$240$	0	0
$241$	13.6890	0.881786	0.440893	−	0.897560i	$-0.354662\pi$
$241$	13.6890	0.881786	0.440893	+	0.897560i	$0.354662\pi$
$242$	8.67247	0.557487
$243$	0	0
$244$	0.956089	0.0612073
$245$	0	0
$246$	0	0
$247$	6.96210	0.442988
$248$	31.6649	2.01073
$249$	0	0
$250$	−5.78553	−0.365909
$251$	−14.6603	−0.925349	−0.462674	−	0.886528i	$-0.653110\pi$
$251$	−14.6603	−0.925349	−0.462674	+	0.886528i	$0.653110\pi$
$252$	0	0
$253$	−1.27750	−0.0803155
$254$	−6.55767	−0.411464
$255$	0	0
$256$	−9.15355	−0.572097
$257$	−1.75277	−0.109335	−0.0546675	−	0.998505i	$-0.517410\pi$
$257$	−1.75277	−0.109335	−0.0546675	+	0.998505i	$0.517410\pi$
$258$	0	0
$259$	0	0
$260$	−1.15592	−0.0716870
$261$	0	0
$262$	−13.3733	−0.826206
$263$	−26.9416	−1.66129	−0.830645	−	0.556802i	$-0.812028\pi$
$263$	−26.9416	−1.66129	−0.830645	+	0.556802i	$0.812028\pi$
$264$	0	0
$265$	20.6636	1.26936
$266$	0	0
$267$	0	0
$268$	−5.85174	−0.357452
$269$	−22.0691	−1.34558	−0.672789	−	0.739835i	$-0.734904\pi$
$269$	−22.0691	−1.34558	−0.672789	+	0.739835i	$0.734904\pi$
$270$	0	0
$271$	8.96210	0.544409	0.272204	−	0.962239i	$-0.412247\pi$
$271$	8.96210	0.544409	0.272204	+	0.962239i	$0.412247\pi$
$272$	−12.1757	−0.738259
$273$	0	0
$274$	−7.43137	−0.448945
$275$	−6.97541	−0.420633
$276$	0	0
$277$	−7.52925	−0.452389	−0.226194	−	0.974082i	$-0.572628\pi$
$277$	−7.52925	−0.452389	−0.226194	+	0.974082i	$0.572628\pi$
$278$	−5.06243	−0.303625
$279$	0	0
$280$	0	0
$281$	−29.7762	−1.77630	−0.888151	−	0.459553i	$-0.848010\pi$
$281$	−29.7762	−1.77630	−0.888151	+	0.459553i	$0.848010\pi$
$282$	0	0
$283$	−0.301451	−0.0179194	−0.00895970	−	0.999960i	$-0.502852\pi$
$283$	−0.301451	−0.0179194	−0.00895970	+	0.999960i	$0.502852\pi$
$284$	1.43421	0.0851046
$285$	0	0
$286$	−2.57749	−0.152410
$287$	0	0
$288$	0	0
$289$	−1.01069	−0.0594526
$290$	−4.02645	−0.236441
$291$	0	0
$292$	1.18504	0.0693492
$293$	−19.2471	−1.12443	−0.562214	−	0.826992i	$-0.690050\pi$
$293$	−19.2471	−1.12443	−0.562214	+	0.826992i	$0.690050\pi$
$294$	0	0
$295$	−5.91133	−0.344171
$296$	−9.36480	−0.544318
$297$	0	0
$298$	−12.7895	−0.740876
$299$	−0.627280	−0.0362765
$300$	0	0
$301$	0	0
$302$	0.237588	0.0136716
$303$	0	0
$304$	21.1992	1.21586
$305$	6.96860	0.399021
$306$	0	0
$307$	3.57779	0.204195	0.102098	−	0.994774i	$-0.467445\pi$
$307$	3.57779	0.204195	0.102098	+	0.994774i	$0.467445\pi$
$308$	0	0
$309$	0	0
$310$	38.3243	2.17667
$311$	−23.8306	−1.35131	−0.675655	−	0.737218i	$-0.736139\pi$
$311$	−23.8306	−1.35131	−0.675655	+	0.737218i	$0.736139\pi$
$312$	0	0
$313$	18.0814	1.02202	0.511009	−	0.859575i	$-0.329272\pi$
$313$	18.0814	1.02202	0.511009	+	0.859575i	$0.329272\pi$
$314$	−15.2782	−0.862196
$315$	0	0
$316$	3.48914	0.196279
$317$	27.5482	1.54726	0.773630	−	0.633638i	$-0.218439\pi$
$317$	27.5482	1.54726	0.773630	+	0.633638i	$0.218439\pi$
$318$	0	0
$319$	2.23220	0.124979
$320$	−25.8198	−1.44337
$321$	0	0
$322$	0	0
$323$	−27.8391	−1.54901
$324$	0	0
$325$	−3.42509	−0.189990
$326$	−18.8747	−1.04537
$327$	0	0
$328$	−1.58181	−0.0873408
$329$	0	0
$330$	0	0
$331$	−18.1814	−0.999339	−0.499669	−	0.866216i	$-0.666545\pi$
$331$	−18.1814	−0.999339	−0.499669	+	0.866216i	$0.666545\pi$
$332$	−5.09895	−0.279841
$333$	0	0
$334$	−6.39972	−0.350177
$335$	−42.6513	−2.33029
$336$	0	0
$337$	−17.1381	−0.933572	−0.466786	−	0.884370i	$-0.654588\pi$
$337$	−17.1381	−0.933572	−0.466786	+	0.884370i	$0.654588\pi$
$338$	−1.26561	−0.0688400
$339$	0	0
$340$	4.62212	0.250670
$341$	−21.2464	−1.15056
$342$	0	0
$343$	0	0
$344$	0.998663	0.0538443
$345$	0	0
$346$	0.753815	0.0405253
$347$	−22.2688	−1.19545	−0.597725	−	0.801701i	$-0.703929\pi$
$347$	−22.2688	−1.19545	−0.597725	+	0.801701i	$0.703929\pi$
$348$	0	0
$349$	−19.9368	−1.06719	−0.533595	−	0.845740i	$-0.679159\pi$
$349$	−19.9368	−1.06719	−0.533595	+	0.845740i	$0.679159\pi$
$350$	0	0
$351$	0	0
$352$	4.51456	0.240627
$353$	22.9152	1.21965	0.609825	−	0.792536i	$-0.291240\pi$
$353$	22.9152	1.21965	0.609825	+	0.792536i	$0.291240\pi$
$354$	0	0
$355$	10.4535	0.554812
$356$	1.06766	0.0565860
$357$	0	0
$358$	10.2219	0.540242
$359$	−27.2314	−1.43722	−0.718610	−	0.695413i	$-0.755221\pi$
$359$	−27.2314	−1.43722	−0.718610	+	0.695413i	$0.755221\pi$
$360$	0	0
$361$	29.4708	1.55110
$362$	2.39611	0.125936
$363$	0	0
$364$	0	0
$365$	8.63735	0.452099
$366$	0	0
$367$	10.8564	0.566702	0.283351	−	0.959016i	$-0.408554\pi$
$367$	10.8564	0.566702	0.283351	+	0.959016i	$0.408554\pi$
$368$	−1.91003	−0.0995671
$369$	0	0
$370$	−11.3343	−0.589241
$371$	0	0
$372$	0	0
$373$	−2.37144	−0.122789	−0.0613943	−	0.998114i	$-0.519555\pi$
$373$	−2.37144	−0.122789	−0.0613943	+	0.998114i	$0.519555\pi$
$374$	10.3065	0.532938
$375$	0	0
$376$	32.0085	1.65071
$377$	1.09606	0.0564501
$378$	0	0
$379$	−29.2197	−1.50092	−0.750458	−	0.660918i	$-0.770167\pi$
$379$	−29.2197	−1.50092	−0.750458	+	0.660918i	$0.770167\pi$
$380$	−8.04761	−0.412834
$381$	0	0
$382$	4.68496	0.239703
$383$	−3.06595	−0.156663	−0.0783313	−	0.996927i	$-0.524959\pi$
$383$	−3.06595	−0.156663	−0.0783313	+	0.996927i	$0.524959\pi$
$384$	0	0
$385$	0	0
$386$	−17.1964	−0.875274
$387$	0	0
$388$	−0.927499	−0.0470866
$389$	−27.7410	−1.40652	−0.703261	−	0.710932i	$-0.748274\pi$
$389$	−27.7410	−1.40652	−0.703261	+	0.710932i	$0.748274\pi$
$390$	0	0
$391$	2.50828	0.126849
$392$	0	0
$393$	0	0
$394$	−12.2797	−0.618641
$395$	25.4311	1.27958
$396$	0	0
$397$	−17.2312	−0.864808	−0.432404	−	0.901680i	$-0.642335\pi$
$397$	−17.2312	−0.864808	−0.432404	+	0.901680i	$0.642335\pi$
$398$	33.2500	1.66667
$399$	0	0
$400$	−10.4292	−0.521459
$401$	−16.6440	−0.831163	−0.415582	−	0.909556i	$-0.636422\pi$
$401$	−16.6440	−0.831163	−0.415582	+	0.909556i	$0.636422\pi$
$402$	0	0
$403$	−10.4325	−0.519679
$404$	−0.578731	−0.0287930
$405$	0	0
$406$	0	0
$407$	6.28355	0.311464
$408$	0	0
$409$	13.6338	0.674147	0.337073	−	0.941478i	$-0.390563\pi$
$409$	13.6338	0.674147	0.337073	+	0.941478i	$0.390563\pi$
$410$	−1.91447	−0.0945491
$411$	0	0
$412$	−4.63359	−0.228280
$413$	0	0
$414$	0	0
$415$	−37.1645	−1.82433
$416$	2.21675	0.108685
$417$	0	0
$418$	−17.9448	−0.877707
$419$	−10.8502	−0.530066	−0.265033	−	0.964239i	$-0.585383\pi$
$419$	−10.8502	−0.530066	−0.265033	+	0.964239i	$0.585383\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−12.6989	−0.618173
$423$	0	0
$424$	−21.6078	−1.04937
$425$	13.6958	0.664342
$426$	0	0
$427$	0	0
$428$	7.81574	0.377788
$429$	0	0
$430$	1.20869	0.0582881
$431$	−1.20953	−0.0582609	−0.0291304	−	0.999576i	$-0.509274\pi$
$431$	−1.20953	−0.0582609	−0.0291304	+	0.999576i	$0.509274\pi$
$432$	0	0
$433$	5.56422	0.267399	0.133700	−	0.991022i	$-0.457314\pi$
$433$	5.56422	0.267399	0.133700	+	0.991022i	$0.457314\pi$
$434$	0	0
$435$	0	0
$436$	0.440749	0.0211081
$437$	−4.36719	−0.208911
$438$	0	0
$439$	19.7192	0.941146	0.470573	−	0.882361i	$-0.344047\pi$
$439$	19.7192	0.941146	0.470573	+	0.882361i	$0.344047\pi$
$440$	17.9422	0.855362
$441$	0	0
$442$	5.06074	0.240715
$443$	−22.2310	−1.05623	−0.528113	−	0.849174i	$-0.677100\pi$
$443$	−22.2310	−1.05623	−0.528113	+	0.849174i	$0.677100\pi$
$444$	0	0
$445$	7.78182	0.368894
$446$	22.1432	1.04851
$447$	0	0
$448$	0	0
$449$	−18.4579	−0.871082	−0.435541	−	0.900169i	$-0.643443\pi$
$449$	−18.4579	−0.871082	−0.435541	+	0.900169i	$0.643443\pi$
$450$	0	0
$451$	1.06136	0.0499773
$452$	−0.436491	−0.0205308
$453$	0	0
$454$	12.0439	0.565249
$455$	0	0
$456$	0	0
$457$	−29.9819	−1.40250	−0.701248	−	0.712917i	$-0.747373\pi$
$457$	−29.9819	−1.40250	−0.701248	+	0.712917i	$0.747373\pi$
$458$	26.7258	1.24882
$459$	0	0
$460$	0.725084	0.0338072
$461$	29.1498	1.35764	0.678821	−	0.734304i	$-0.262491\pi$
$461$	29.1498	1.35764	0.678821	+	0.734304i	$0.262491\pi$
$462$	0	0
$463$	1.55900	0.0724530	0.0362265	−	0.999344i	$-0.488466\pi$
$463$	1.55900	0.0724530	0.0362265	+	0.999344i	$0.488466\pi$
$464$	3.33744	0.154937
$465$	0	0
$466$	17.9448	0.831275
$467$	12.4231	0.574874	0.287437	−	0.957800i	$-0.407197\pi$
$467$	12.4231	0.574874	0.287437	+	0.957800i	$0.407197\pi$
$468$	0	0
$469$	0	0
$470$	38.7402	1.78695
$471$	0	0
$472$	6.18143	0.284523
$473$	−0.670079	−0.0308103
$474$	0	0
$475$	−23.8458	−1.09412
$476$	0	0
$477$	0	0
$478$	−20.9173	−0.956735
$479$	36.0558	1.64743	0.823716	−	0.567003i	$-0.191897\pi$
$479$	36.0558	1.64743	0.823716	+	0.567003i	$0.191897\pi$
$480$	0	0
$481$	3.08537	0.140681
$482$	−17.3249	−0.789128
$483$	0	0
$484$	2.72887	0.124040
$485$	−6.76023	−0.306966
$486$	0	0
$487$	7.30004	0.330796	0.165398	−	0.986227i	$-0.447109\pi$
$487$	7.30004	0.330796	0.165398	+	0.986227i	$0.447109\pi$
$488$	−7.28702	−0.329868
$489$	0	0
$490$	0	0
$491$	−4.49178	−0.202711	−0.101356	−	0.994850i	$-0.532318\pi$
$491$	−4.49178	−0.202711	−0.101356	+	0.994850i	$0.532318\pi$
$492$	0	0
$493$	−4.38279	−0.197391
$494$	−8.81129	−0.396439
$495$	0	0
$496$	−31.7663	−1.42635
$497$	0	0
$498$	0	0
$499$	11.3674	0.508873	0.254437	−	0.967089i	$-0.418110\pi$
$499$	11.3674	0.508873	0.254437	+	0.967089i	$0.418110\pi$
$500$	−1.82047	−0.0814139
$501$	0	0
$502$	18.5542	0.828113
$503$	17.1080	0.762806	0.381403	−	0.924409i	$-0.375441\pi$
$503$	17.1080	0.762806	0.381403	+	0.924409i	$0.375441\pi$
$504$	0	0
$505$	−4.21818	−0.187706
$506$	1.61681	0.0718759
$507$	0	0
$508$	−2.06343	−0.0915498
$509$	3.28284	0.145509	0.0727547	−	0.997350i	$-0.476821\pi$
$509$	3.28284	0.145509	0.0727547	+	0.997350i	$0.476821\pi$
$510$	0	0
$511$	0	0
$512$	25.2340	1.11520
$513$	0	0
$514$	2.21833	0.0978462
$515$	−33.7726	−1.48820
$516$	0	0
$517$	−21.4770	−0.944555
$518$	0	0
$519$	0	0
$520$	8.81005	0.386346
$521$	−4.77061	−0.209004	−0.104502	−	0.994525i	$-0.533325\pi$
$521$	−4.77061	−0.209004	−0.104502	+	0.994525i	$0.533325\pi$
$522$	0	0
$523$	−25.5124	−1.11558	−0.557789	−	0.829983i	$-0.688350\pi$
$523$	−25.5124	−1.11558	−0.557789	+	0.829983i	$0.688350\pi$
$524$	−4.20803	−0.183829
$525$	0	0
$526$	34.0975	1.48672
$527$	41.7160	1.81718
$528$	0	0
$529$	−22.6065	−0.982892
$530$	−26.1520	−1.13597
$531$	0	0
$532$	0	0
$533$	0.521150	0.0225735
$534$	0	0
$535$	56.9663	2.46287
$536$	44.6001	1.92643
$537$	0	0
$538$	27.9309	1.20418
$539$	0	0
$540$	0	0
$541$	−16.5157	−0.710064	−0.355032	−	0.934854i	$-0.615530\pi$
$541$	−16.5157	−0.710064	−0.355032	+	0.934854i	$0.615530\pi$
$542$	−11.3425	−0.487202
$543$	0	0
$544$	−8.86405	−0.380043
$545$	3.21247	0.137607
$546$	0	0
$547$	23.3317	0.997591	0.498796	−	0.866720i	$-0.333776\pi$
$547$	23.3317	0.997591	0.498796	+	0.866720i	$0.333776\pi$
$548$	−2.33835	−0.0998892
$549$	0	0
$550$	8.82814	0.376433
$551$	7.63090	0.325087
$552$	0	0
$553$	0	0
$554$	9.52909	0.404852
$555$	0	0
$556$	−1.59294	−0.0675557
$557$	20.0471	0.849422	0.424711	−	0.905329i	$-0.360376\pi$
$557$	20.0471	0.849422	0.424711	+	0.905329i	$0.360376\pi$
$558$	0	0
$559$	−0.329024	−0.0139162
$560$	0	0
$561$	0	0
$562$	37.6851	1.58965
$563$	−40.5284	−1.70807	−0.854034	−	0.520218i	$-0.825851\pi$
$563$	−40.5284	−1.70807	−0.854034	+	0.520218i	$0.825851\pi$
$564$	0	0
$565$	−3.18143	−0.133844
$566$	0.381519	0.0160364
$567$	0	0
$568$	−10.9311	−0.458659
$569$	21.4504	0.899246	0.449623	−	0.893219i	$-0.351558\pi$
$569$	21.4504	0.899246	0.449623	+	0.893219i	$0.351558\pi$
$570$	0	0
$571$	−10.9559	−0.458489	−0.229244	−	0.973369i	$-0.573625\pi$
$571$	−10.9559	−0.458489	−0.229244	+	0.973369i	$0.573625\pi$
$572$	−0.811031	−0.0339109
$573$	0	0
$574$	0	0
$575$	2.14849	0.0895982
$576$	0	0
$577$	−34.7415	−1.44631	−0.723154	−	0.690687i	$-0.757308\pi$
$577$	−34.7415	−1.44631	−0.723154	+	0.690687i	$0.757308\pi$
$578$	1.27914	0.0532053
$579$	0	0
$580$	−1.26696	−0.0526076
$581$	0	0
$582$	0	0
$583$	14.4983	0.600458
$584$	−9.03201	−0.373747
$585$	0	0
$586$	24.3593	1.00627
$587$	−22.8463	−0.942967	−0.471483	−	0.881875i	$-0.656281\pi$
$587$	−22.8463	−0.942967	−0.471483	+	0.881875i	$0.656281\pi$
$588$	0	0
$589$	−72.6320	−2.99275
$590$	7.48143	0.308006
$591$	0	0
$592$	9.39476	0.386122
$593$	17.5935	0.722480	0.361240	−	0.932473i	$-0.382354\pi$
$593$	17.5935	0.722480	0.361240	+	0.932473i	$0.382354\pi$
$594$	0	0
$595$	0	0
$596$	−4.02433	−0.164843
$597$	0	0
$598$	0.793891	0.0324646
$599$	−31.0073	−1.26692	−0.633461	−	0.773774i	$-0.718366\pi$
$599$	−31.0073	−1.26692	−0.633461	+	0.773774i	$0.718366\pi$
$600$	0	0
$601$	1.43754	0.0586385	0.0293193	−	0.999570i	$-0.490666\pi$
$601$	1.43754	0.0586385	0.0293193	+	0.999570i	$0.490666\pi$
$602$	0	0
$603$	0	0
$604$	0.0747591	0.00304191
$605$	19.8898	0.808635
$606$	0	0
$607$	33.0171	1.34012	0.670061	−	0.742306i	$-0.266268\pi$
$607$	33.0171	1.34012	0.670061	+	0.742306i	$0.266268\pi$
$608$	15.4333	0.625901
$609$	0	0
$610$	−8.81953	−0.357092
$611$	−10.5457	−0.426633
$612$	0	0
$613$	−43.1657	−1.74345	−0.871723	−	0.489999i	$-0.836997\pi$
$613$	−43.1657	−1.74345	−0.871723	+	0.489999i	$0.836997\pi$
$614$	−4.52808	−0.182738
$615$	0	0
$616$	0	0
$617$	−2.45772	−0.0989441	−0.0494721	−	0.998776i	$-0.515754\pi$
$617$	−2.45772	−0.0989441	−0.0494721	+	0.998776i	$0.515754\pi$
$618$	0	0
$619$	−37.7789	−1.51846	−0.759231	−	0.650822i	$-0.774425\pi$
$619$	−37.7789	−1.51846	−0.759231	+	0.650822i	$0.774425\pi$
$620$	12.0591	0.484305
$621$	0	0
$622$	30.1602	1.20932
$623$	0	0
$624$	0	0
$625$	−30.3942	−1.21577
$626$	−22.8839	−0.914625
$627$	0	0
$628$	−4.80741	−0.191837
$629$	−12.3374	−0.491922
$630$	0	0
$631$	−28.4828	−1.13388	−0.566942	−	0.823758i	$-0.691874\pi$
$631$	−28.4828	−1.13388	−0.566942	+	0.823758i	$0.691874\pi$
$632$	−26.5932	−1.05782
$633$	0	0
$634$	−34.8652	−1.38467
$635$	−15.0396	−0.596829
$636$	0	0
$637$	0	0
$638$	−2.82509	−0.111847
$639$	0	0
$640$	19.8091	0.783024
$641$	27.1922	1.07403	0.537014	−	0.843573i	$-0.319552\pi$
$641$	27.1922	1.07403	0.537014	+	0.843573i	$0.319552\pi$
$642$	0	0
$643$	37.1664	1.46570	0.732849	−	0.680391i	$-0.238190\pi$
$643$	37.1664	1.46570	0.732849	+	0.680391i	$0.238190\pi$
$644$	0	0
$645$	0	0
$646$	35.2334	1.38624
$647$	18.8319	0.740357	0.370178	−	0.928961i	$-0.379297\pi$
$647$	18.8319	0.740357	0.370178	+	0.928961i	$0.379297\pi$
$648$	0	0
$649$	−4.14759	−0.162807
$650$	4.33482	0.170026
$651$	0	0
$652$	−5.93910	−0.232593
$653$	26.0185	1.01818	0.509090	−	0.860713i	$-0.329982\pi$
$653$	26.0185	1.01818	0.509090	+	0.860713i	$0.329982\pi$
$654$	0	0
$655$	−30.6709	−1.19841
$656$	1.58687	0.0619569
$657$	0	0
$658$	0	0
$659$	33.3339	1.29851	0.649253	−	0.760573i	$-0.275082\pi$
$659$	33.3339	1.29851	0.649253	+	0.760573i	$0.275082\pi$
$660$	0	0
$661$	−6.29841	−0.244980	−0.122490	−	0.992470i	$-0.539088\pi$
$661$	−6.29841	−0.244980	−0.122490	+	0.992470i	$0.539088\pi$
$662$	23.0105	0.894329
$663$	0	0
$664$	38.8626	1.50816
$665$	0	0
$666$	0	0
$667$	−0.687538	−0.0266216
$668$	−2.01373	−0.0779136
$669$	0	0
$670$	53.9799	2.08542
$671$	4.88941	0.188754
$672$	0	0
$673$	18.3188	0.706137	0.353068	−	0.935598i	$-0.385138\pi$
$673$	18.3188	0.706137	0.353068	+	0.935598i	$0.385138\pi$
$674$	21.6901	0.835473
$675$	0	0
$676$	−0.398235	−0.0153167
$677$	24.3392	0.935430	0.467715	−	0.883879i	$-0.345077\pi$
$677$	24.3392	0.935430	0.467715	+	0.883879i	$0.345077\pi$
$678$	0	0
$679$	0	0
$680$	−35.2284	−1.35095
$681$	0	0
$682$	26.8896	1.02966
$683$	−11.7682	−0.450297	−0.225149	−	0.974324i	$-0.572287\pi$
$683$	−11.7682	−0.450297	−0.225149	+	0.974324i	$0.572287\pi$
$684$	0	0
$685$	−17.0434	−0.651195
$686$	0	0
$687$	0	0
$688$	−1.00186	−0.0381955
$689$	7.11900	0.271212
$690$	0	0
$691$	−1.17785	−0.0448074	−0.0224037	−	0.999749i	$-0.507132\pi$
$691$	−1.17785	−0.0448074	−0.0224037	+	0.999749i	$0.507132\pi$
$692$	0.237195	0.00901679
$693$	0	0
$694$	28.1835	1.06983
$695$	−11.6104	−0.440408
$696$	0	0
$697$	−2.08390	−0.0789335
$698$	25.2321	0.955050
$699$	0	0
$700$	0	0
$701$	31.2867	1.18168	0.590841	−	0.806788i	$-0.298796\pi$
$701$	31.2867	1.18168	0.590841	+	0.806788i	$0.298796\pi$
$702$	0	0
$703$	21.4806	0.810158
$704$	−18.1161	−0.682776
$705$	0	0
$706$	−29.0016	−1.09149
$707$	0	0
$708$	0	0
$709$	15.3748	0.577411	0.288706	−	0.957418i	$-0.406775\pi$
$709$	15.3748	0.577411	0.288706	+	0.957418i	$0.406775\pi$
$710$	−13.2300	−0.496512
$711$	0	0
$712$	−8.13739	−0.304962
$713$	6.54409	0.245078
$714$	0	0
$715$	−5.91133	−0.221071
$716$	3.21640	0.120203
$717$	0	0
$718$	34.4643	1.28620
$719$	−11.1417	−0.415517	−0.207759	−	0.978180i	$-0.566617\pi$
$719$	−11.1417	−0.415517	−0.207759	+	0.978180i	$0.566617\pi$
$720$	0	0
$721$	0	0
$722$	−37.2985	−1.38811
$723$	0	0
$724$	0.753956	0.0280206
$725$	−3.75411	−0.139424
$726$	0	0
$727$	6.24735	0.231702	0.115851	−	0.993267i	$-0.463041\pi$
$727$	6.24735	0.231702	0.115851	+	0.993267i	$0.463041\pi$
$728$	0	0
$729$	0	0
$730$	−10.9315	−0.404593
$731$	1.31566	0.0486613
$732$	0	0
$733$	−30.9669	−1.14379	−0.571894	−	0.820327i	$-0.693791\pi$
$733$	−30.9669	−1.14379	−0.571894	+	0.820327i	$0.693791\pi$
$734$	−13.7400	−0.507153
$735$	0	0
$736$	−1.39053	−0.0512554
$737$	−29.9256	−1.10232
$738$	0	0
$739$	2.33744	0.0859843	0.0429921	−	0.999075i	$-0.486311\pi$
$739$	2.33744	0.0859843	0.0429921	+	0.999075i	$0.486311\pi$
$740$	−3.56643	−0.131105
$741$	0	0
$742$	0	0
$743$	−24.3612	−0.893726	−0.446863	−	0.894603i	$-0.647459\pi$
$743$	−24.3612	−0.893726	−0.446863	+	0.894603i	$0.647459\pi$
$744$	0	0
$745$	−29.3320	−1.07464
$746$	3.00132	0.109886
$747$	0	0
$748$	3.24304	0.118577
$749$	0	0
$750$	0	0
$751$	−12.0253	−0.438810	−0.219405	−	0.975634i	$-0.570412\pi$
$751$	−12.0253	−0.438810	−0.219405	+	0.975634i	$0.570412\pi$
$752$	−32.1110	−1.17097
$753$	0	0
$754$	−1.38719	−0.0505184
$755$	0.544894	0.0198307
$756$	0	0
$757$	25.9905	0.944641	0.472321	−	0.881427i	$-0.343416\pi$
$757$	25.9905	0.944641	0.472321	+	0.881427i	$0.343416\pi$
$758$	36.9807	1.34320
$759$	0	0
$760$	61.3364	2.22491
$761$	13.3270	0.483103	0.241552	−	0.970388i	$-0.422344\pi$
$761$	13.3270	0.483103	0.241552	+	0.970388i	$0.422344\pi$
$762$	0	0
$763$	0	0
$764$	1.47416	0.0533334
$765$	0	0
$766$	3.88029	0.140200
$767$	−2.03656	−0.0735361
$768$	0	0
$769$	−9.24486	−0.333378	−0.166689	−	0.986010i	$-0.553308\pi$
$769$	−9.24486	−0.333378	−0.166689	+	0.986010i	$0.553308\pi$
$770$	0	0
$771$	0	0
$772$	−5.41101	−0.194746
$773$	−10.1419	−0.364780	−0.182390	−	0.983226i	$-0.558383\pi$
$773$	−10.1419	−0.364780	−0.182390	+	0.983226i	$0.558383\pi$
$774$	0	0
$775$	35.7322	1.28354
$776$	7.06912	0.253766
$777$	0	0
$778$	35.1092	1.25873
$779$	3.62830	0.129997
$780$	0	0
$781$	7.33450	0.262449
$782$	−3.17450	−0.113520
$783$	0	0
$784$	0	0
$785$	−35.0396	−1.25062
$786$	0	0
$787$	−45.2823	−1.61414	−0.807070	−	0.590456i	$-0.798948\pi$
$787$	−45.2823	−1.61414	−0.807070	+	0.590456i	$0.798948\pi$
$788$	−3.86391	−0.137646
$789$	0	0
$790$	−32.1859	−1.14512
$791$	0	0
$792$	0	0
$793$	2.40081	0.0852554
$794$	21.8079	0.773935
$795$	0	0
$796$	10.4624	0.370831
$797$	27.0784	0.959165	0.479583	−	0.877497i	$-0.340788\pi$
$797$	27.0784	0.959165	0.479583	+	0.877497i	$0.340788\pi$
$798$	0	0
$799$	42.1686	1.49182
$800$	−7.59257	−0.268438
$801$	0	0
$802$	21.0648	0.743825
$803$	6.06026	0.213862
$804$	0	0
$805$	0	0
$806$	13.2034	0.465071
$807$	0	0
$808$	4.41091	0.155175
$809$	25.7798	0.906370	0.453185	−	0.891417i	$-0.350288\pi$
$809$	25.7798	0.906370	0.453185	+	0.891417i	$0.350288\pi$
$810$	0	0
$811$	25.7829	0.905362	0.452681	−	0.891673i	$-0.350468\pi$
$811$	25.7829	0.905362	0.452681	+	0.891673i	$0.350468\pi$
$812$	0	0
$813$	0	0
$814$	−7.95252	−0.278736
$815$	−43.2881	−1.51632
$816$	0	0
$817$	−2.29070	−0.0801414
$818$	−17.2550	−0.603308
$819$	0	0
$820$	−0.602407	−0.0210370
$821$	1.71073	0.0597050	0.0298525	−	0.999554i	$-0.490496\pi$
$821$	1.71073	0.0597050	0.0298525	+	0.999554i	$0.490496\pi$
$822$	0	0
$823$	−40.3773	−1.40747	−0.703733	−	0.710465i	$-0.748485\pi$
$823$	−40.3773	−1.40747	−0.703733	+	0.710465i	$0.748485\pi$
$824$	35.3158	1.23028
$825$	0	0
$826$	0	0
$827$	−19.5698	−0.680509	−0.340254	−	0.940333i	$-0.610513\pi$
$827$	−19.5698	−0.680509	−0.340254	+	0.940333i	$0.610513\pi$
$828$	0	0
$829$	−41.5742	−1.44393	−0.721966	−	0.691928i	$-0.756761\pi$
$829$	−41.5742	−1.44393	−0.721966	+	0.691928i	$0.756761\pi$
$830$	47.0357	1.63263
$831$	0	0
$832$	−8.89542	−0.308393
$833$	0	0
$834$	0	0
$835$	−14.6774	−0.507932
$836$	−5.64648	−0.195288
$837$	0	0
$838$	13.7321	0.474367
$839$	45.8480	1.58285	0.791425	−	0.611266i	$-0.209340\pi$
$839$	45.8480	1.58285	0.791425	+	0.611266i	$0.209340\pi$
$840$	0	0
$841$	−27.7986	−0.958574
$842$	12.6561	0.436157
$843$	0	0
$844$	−3.99583	−0.137542
$845$	−2.90260	−0.0998525
$846$	0	0
$847$	0	0
$848$	21.6769	0.744388
$849$	0	0
$850$	−17.3335	−0.594534
$851$	−1.93539	−0.0663443
$852$	0	0
$853$	−40.0236	−1.37038	−0.685191	−	0.728364i	$-0.740281\pi$
$853$	−40.0236	−1.37038	−0.685191	+	0.728364i	$0.740281\pi$
$854$	0	0
$855$	0	0
$856$	−59.5692	−2.03603
$857$	32.8702	1.12282	0.561412	−	0.827536i	$-0.310258\pi$
$857$	32.8702	1.12282	0.561412	+	0.827536i	$0.310258\pi$
$858$	0	0
$859$	34.0503	1.16178	0.580891	−	0.813981i	$-0.302704\pi$
$859$	34.0503	1.16178	0.580891	+	0.813981i	$0.302704\pi$
$860$	0.380325	0.0129690
$861$	0	0
$862$	1.53079	0.0521388
$863$	14.0642	0.478749	0.239375	−	0.970927i	$-0.423058\pi$
$863$	14.0642	0.478749	0.239375	+	0.970927i	$0.423058\pi$
$864$	0	0
$865$	1.72883	0.0587820
$866$	−7.04212	−0.239301
$867$	0	0
$868$	0	0
$869$	17.8434	0.605295
$870$	0	0
$871$	−14.6942	−0.497893
$872$	−3.35926	−0.113759
$873$	0	0
$874$	5.52715	0.186959
$875$	0	0
$876$	0	0
$877$	51.0669	1.72441	0.862204	−	0.506562i	$-0.169084\pi$
$877$	51.0669	1.72441	0.862204	+	0.506562i	$0.169084\pi$
$878$	−24.9568	−0.842251
$879$	0	0
$880$	−17.9996	−0.606768
$881$	−18.4203	−0.620597	−0.310298	−	0.950639i	$-0.600429\pi$
$881$	−18.4203	−0.620597	−0.310298	+	0.950639i	$0.600429\pi$
$882$	0	0
$883$	0.126678	0.00426305	0.00213153	−	0.999998i	$-0.499322\pi$
$883$	0.126678	0.00426305	0.00213153	+	0.999998i	$0.499322\pi$
$884$	1.59241	0.0535585
$885$	0	0
$886$	28.1357	0.945239
$887$	3.87470	0.130100	0.0650498	−	0.997882i	$-0.479279\pi$
$887$	3.87470	0.130100	0.0650498	+	0.997882i	$0.479279\pi$
$888$	0	0
$889$	0	0
$890$	−9.84874	−0.330131
$891$	0	0
$892$	6.96757	0.233291
$893$	−73.4201	−2.45691
$894$	0	0
$895$	23.4433	0.783622
$896$	0	0
$897$	0	0
$898$	23.3605	0.779549
$899$	−11.4347	−0.381367
$900$	0	0
$901$	−28.4665	−0.948356
$902$	−1.34326	−0.0447257
$903$	0	0
$904$	3.32680	0.110648
$905$	5.49533	0.182671
$906$	0	0
$907$	−46.7741	−1.55311	−0.776555	−	0.630050i	$-0.783035\pi$
$907$	−46.7741	−1.55311	−0.776555	+	0.630050i	$0.783035\pi$
$908$	3.78973	0.125766
$909$	0	0
$910$	0	0
$911$	−5.93675	−0.196693	−0.0983467	−	0.995152i	$-0.531355\pi$
$911$	−5.93675	−0.196693	−0.0983467	+	0.995152i	$0.531355\pi$
$912$	0	0
$913$	−26.0759	−0.862986
$914$	37.9454	1.25512
$915$	0	0
$916$	8.40952	0.277858
$917$	0	0
$918$	0	0
$919$	−8.58701	−0.283259	−0.141630	−	0.989920i	$-0.545234\pi$
$919$	−8.58701	−0.283259	−0.141630	+	0.989920i	$0.545234\pi$
$920$	−5.52637	−0.182199
$921$	0	0
$922$	−36.8922	−1.21498
$923$	3.60141	0.118542
$924$	0	0
$925$	−10.5677	−0.347463
$926$	−1.97309	−0.0648396
$927$	0	0
$928$	2.42970	0.0797589
$929$	−8.45945	−0.277546	−0.138773	−	0.990324i	$-0.544316\pi$
$929$	−8.45945	−0.277546	−0.138773	+	0.990324i	$0.544316\pi$
$930$	0	0
$931$	0	0
$932$	5.64648	0.184957
$933$	0	0
$934$	−15.7228	−0.514466
$935$	23.6374	0.773026
$936$	0	0
$937$	33.3596	1.08981	0.544905	−	0.838498i	$-0.316566\pi$
$937$	33.3596	1.08981	0.544905	+	0.838498i	$0.316566\pi$
$938$	0	0
$939$	0	0
$940$	12.1899	0.397592
$941$	−13.4037	−0.436949	−0.218475	−	0.975843i	$-0.570108\pi$
$941$	−13.4037	−0.436949	−0.218475	+	0.975843i	$0.570108\pi$
$942$	0	0
$943$	−0.326907	−0.0106456
$944$	−6.20121	−0.201832
$945$	0	0
$946$	0.848057	0.0275727
$947$	−43.0794	−1.39989	−0.699946	−	0.714196i	$-0.746793\pi$
$947$	−43.0794	−1.39989	−0.699946	+	0.714196i	$0.746793\pi$
$948$	0	0
$949$	2.97573	0.0965962
$950$	30.1794	0.979150
$951$	0	0
$952$	0	0
$953$	−16.7332	−0.542040	−0.271020	−	0.962574i	$-0.587361\pi$
$953$	−16.7332	−0.542040	−0.271020	+	0.962574i	$0.587361\pi$
$954$	0	0
$955$	10.7447	0.347690
$956$	−6.58182	−0.212871
$957$	0	0
$958$	−45.6325	−1.47432
$959$	0	0
$960$	0	0
$961$	77.8366	2.51086
$962$	−3.90487	−0.125898
$963$	0	0
$964$	−5.45144	−0.175579
$965$	−39.4390	−1.26959
$966$	0	0
$967$	44.7594	1.43937	0.719683	−	0.694303i	$-0.244287\pi$
$967$	44.7594	1.43937	0.719683	+	0.694303i	$0.244287\pi$
$968$	−20.7986	−0.668493
$969$	0	0
$970$	8.55580	0.274710
$971$	−4.20259	−0.134867	−0.0674337	−	0.997724i	$-0.521481\pi$
$971$	−4.20259	−0.134867	−0.0674337	+	0.997724i	$0.521481\pi$
$972$	0	0
$973$	0	0
$974$	−9.23899	−0.296036
$975$	0	0
$976$	7.31033	0.233998
$977$	25.6899	0.821892	0.410946	−	0.911660i	$-0.365199\pi$
$977$	25.6899	0.821892	0.410946	+	0.911660i	$0.365199\pi$
$978$	0	0
$979$	5.45999	0.174502
$980$	0	0
$981$	0	0
$982$	5.68483	0.181410
$983$	−31.8244	−1.01504	−0.507520	−	0.861640i	$-0.669438\pi$
$983$	−31.8244	−1.01504	−0.507520	+	0.861640i	$0.669438\pi$
$984$	0	0
$985$	−28.1627	−0.897339
$986$	5.54689	0.176649
$987$	0	0
$988$	−2.77255	−0.0882067
$989$	0.206390	0.00656283
$990$	0	0
$991$	9.47478	0.300976	0.150488	−	0.988612i	$-0.451915\pi$
$991$	9.47478	0.300976	0.150488	+	0.988612i	$0.451915\pi$
$992$	−23.1262	−0.734259
$993$	0	0
$994$	0	0
$995$	76.2570	2.41751
$996$	0	0
$997$	−21.9511	−0.695198	−0.347599	−	0.937643i	$-0.613003\pi$
$997$	−21.9511	−0.695198	−0.347599	+	0.937643i	$0.613003\pi$
$998$	−14.3866	−0.455401
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bm.1.3		5
3.2	odd	2		637.2.a.k.1.3		5
7.3	odd	6		819.2.j.h.352.3		10
7.5	odd	6		819.2.j.h.235.3		10
7.6	odd	2		5733.2.a.bl.1.3		5
21.2	odd	6		637.2.e.m.508.3		10
21.5	even	6		91.2.e.c.53.3	✓	10
21.11	odd	6		637.2.e.m.79.3		10
21.17	even	6		91.2.e.c.79.3	yes	10
21.20	even	2		637.2.a.l.1.3		5
39.38	odd	2		8281.2.a.bx.1.3		5
84.47	odd	6		1456.2.r.p.417.1		10
84.59	odd	6		1456.2.r.p.625.1		10
273.38	even	6		1183.2.e.f.170.3		10
273.194	even	6		1183.2.e.f.508.3		10
273.272	even	2		8281.2.a.bw.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.3	✓	10	21.5	even	6
91.2.e.c.79.3	yes	10	21.17	even	6
637.2.a.k.1.3		5	3.2	odd	2
637.2.a.l.1.3		5	21.20	even	2
637.2.e.m.79.3		10	21.11	odd	6
637.2.e.m.508.3		10	21.2	odd	6
819.2.j.h.235.3		10	7.5	odd	6
819.2.j.h.352.3		10	7.3	odd	6
1183.2.e.f.170.3		10	273.38	even	6
1183.2.e.f.508.3		10	273.194	even	6
1456.2.r.p.417.1		10	84.47	odd	6
1456.2.r.p.625.1		10	84.59	odd	6
5733.2.a.bl.1.3		5	7.6	odd	2
5733.2.a.bm.1.3		5	1.1	even	1	trivial
8281.2.a.bw.1.3		5	273.272	even	2
8281.2.a.bx.1.3		5	39.38	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)

\(f(q)\)	\(=\)	\(q-1.26561 q^{2} -0.398235 q^{4} -2.90260 q^{5} +3.03523 q^{8} +O(q^{10})\)	\(q-1.26561 q^{2} -0.398235 q^{4} -2.90260 q^{5} +3.03523 q^{8} +3.67356 q^{10} -2.03656 q^{11} -1.00000 q^{13} -3.04494 q^{16} +3.99866 q^{17} -6.96210 q^{19} +1.15592 q^{20} +2.57749 q^{22} +0.627280 q^{23} +3.42509 q^{25} +1.26561 q^{26} -1.09606 q^{29} +10.4325 q^{31} -2.21675 q^{32} -5.06074 q^{34} -3.08537 q^{37} +8.81129 q^{38} -8.81005 q^{40} -0.521150 q^{41} +0.329024 q^{43} +0.811031 q^{44} -0.793891 q^{46} +10.5457 q^{47} -4.33482 q^{50} +0.398235 q^{52} -7.11900 q^{53} +5.91133 q^{55} +1.38719 q^{58} +2.03656 q^{59} -2.40081 q^{61} -13.2034 q^{62} +8.89542 q^{64} +2.90260 q^{65} +14.6942 q^{67} -1.59241 q^{68} -3.60141 q^{71} -2.97573 q^{73} +3.90487 q^{74} +2.77255 q^{76} -8.76150 q^{79} +8.83824 q^{80} +0.659572 q^{82} +12.8039 q^{83} -11.6065 q^{85} -0.416416 q^{86} -6.18143 q^{88} -2.68098 q^{89} -0.249805 q^{92} -13.3467 q^{94} +20.2082 q^{95} +2.32902 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} + 8 q^{4} + 2 q^{5} - 9 q^{8}+O(q^{10}) \) 5 * q - 4 * q^2 + 8 * q^4 + 2 * q^5 - 9 * q^8	\( 5 q - 4 q^{2} + 8 q^{4} + 2 q^{5} - 9 q^{8} + 5 q^{10} - 11 q^{11} - 5 q^{13} + 10 q^{16} - 5 q^{17} - 9 q^{19} + q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} + 4 q^{26} + 3 q^{29} + 6 q^{31} - 22 q^{32} + 22 q^{34} + 4 q^{37} - 10 q^{38} - 28 q^{40} + 14 q^{41} + 2 q^{43} + 3 q^{46} + q^{47} - 9 q^{50} - 8 q^{52} - 17 q^{53} - 27 q^{58} + 11 q^{59} + 11 q^{61} - 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} - 32 q^{68} - 15 q^{71} + 33 q^{74} - 8 q^{76} + 2 q^{79} + 55 q^{80} - 34 q^{82} + 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} - 4 q^{89} - 21 q^{92} - 20 q^{94} + 12 q^{95} + 12 q^{97}+O(q^{100}) \) 5 * q - 4 * q^2 + 8 * q^4 + 2 * q^5 - 9 * q^8 + 5 * q^10 - 11 * q^11 - 5 * q^13 + 10 * q^16 - 5 * q^17 - 9 * q^19 + q^20 + 8 * q^22 - 10 * q^23 + 9 * q^25 + 4 * q^26 + 3 * q^29 + 6 * q^31 - 22 * q^32 + 22 * q^34 + 4 * q^37 - 10 * q^38 - 28 * q^40 + 14 * q^41 + 2 * q^43 + 3 * q^46 + q^47 - 9 * q^50 - 8 * q^52 - 17 * q^53 - 27 * q^58 + 11 * q^59 + 11 * q^61 - 23 * q^62 + 9 * q^64 - 2 * q^65 + 13 * q^67 - 32 * q^68 - 15 * q^71 + 33 * q^74 - 8 * q^76 + 2 * q^79 + 55 * q^80 - 34 * q^82 + 6 * q^83 - 22 * q^85 - 28 * q^86 - 3 * q^88 - 4 * q^89 - 21 * q^92 - 20 * q^94 + 12 * q^95 + 12 * q^97

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