LMFDB - Embedded newform 5733.2.a.bf.1.1

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:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
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			1.1
Root			$2.36865$ 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)

$f(q)$	$=$	$q-2.61050 q^{2} +4.81471 q^{4} -3.81471 q^{5} -7.34780 q^{8} +O(q^{10})$	$q-2.61050 q^{2} +4.81471 q^{4} -3.81471 q^{5} -7.34780 q^{8} +9.95830 q^{10} +4.73730 q^{11} -1.00000 q^{13} +9.55201 q^{16} -5.22100 q^{17} -2.92259 q^{19} -18.3667 q^{20} -12.3667 q^{22} -3.33101 q^{23} +9.55201 q^{25} +2.61050 q^{26} +0.922589 q^{29} +7.51941 q^{31} -10.2399 q^{32} +13.6294 q^{34} +0.154821 q^{37} +7.62942 q^{38} +28.0297 q^{40} +6.36672 q^{41} -6.55201 q^{43} +22.8087 q^{44} +8.69560 q^{46} +9.03571 q^{47} -24.9355 q^{50} -4.81471 q^{52} -8.55201 q^{53} -18.0714 q^{55} -2.40842 q^{58} +3.95830 q^{59} -12.4420 q^{61} -19.6294 q^{62} +7.62729 q^{64} +3.81471 q^{65} -10.6620 q^{67} -25.1376 q^{68} +6.58248 q^{71} +7.73517 q^{73} -0.404161 q^{74} -14.0714 q^{76} +13.3646 q^{79} -36.4381 q^{80} -16.6203 q^{82} -1.40629 q^{83} +19.9166 q^{85} +17.1040 q^{86} -34.8087 q^{88} -1.96953 q^{89} -16.0378 q^{92} -23.5877 q^{94} +11.1488 q^{95} +2.11001 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) $ 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8	$ 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 9 q^{16} - 2 q^{17} - 7 q^{19} - 32 q^{20} - 8 q^{22} - 3 q^{23} + 9 q^{25} + q^{26} - q^{29} - 3 q^{31} - 7 q^{32} + 30 q^{34} + 10 q^{37} + 6 q^{38} + 14 q^{40} - 16 q^{41} + 3 q^{43} + 12 q^{44} - 18 q^{46} + 5 q^{47} - 13 q^{50} - 7 q^{52} - 5 q^{53} - 10 q^{55} - 4 q^{58} - 20 q^{59} - 12 q^{61} - 54 q^{62} + 5 q^{64} + 3 q^{65} - 22 q^{67} - 10 q^{68} + 13 q^{73} + 6 q^{74} + 6 q^{76} + 11 q^{79} - 42 q^{80} - 10 q^{82} + q^{83} + 8 q^{85} + 10 q^{86} - 60 q^{88} - 5 q^{89} - 34 q^{92} - 34 q^{94} - 13 q^{95} + 17 q^{97}+O(q^{100}) $ 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 9 * q^16 - 2 * q^17 - 7 * q^19 - 32 * q^20 - 8 * q^22 - 3 * q^23 + 9 * q^25 + q^26 - q^29 - 3 * q^31 - 7 * q^32 + 30 * q^34 + 10 * q^37 + 6 * q^38 + 14 * q^40 - 16 * q^41 + 3 * q^43 + 12 * q^44 - 18 * q^46 + 5 * q^47 - 13 * q^50 - 7 * q^52 - 5 * q^53 - 10 * q^55 - 4 * q^58 - 20 * q^59 - 12 * q^61 - 54 * q^62 + 5 * q^64 + 3 * q^65 - 22 * q^67 - 10 * q^68 + 13 * q^73 + 6 * q^74 + 6 * q^76 + 11 * q^79 - 42 * q^80 - 10 * q^82 + q^83 + 8 * q^85 + 10 * q^86 - 60 * q^88 - 5 * q^89 - 34 * q^92 - 34 * q^94 - 13 * q^95 + 17 * 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 $

$2$	−2.61050	−1.84590	−0.922951	−	0.384917i	$-0.874230\pi$
$2$	−2.61050	−1.84590	−0.922951	+	0.384917i	$0.874230\pi$
$3$	0	0
$3$	0	0
$4$	4.81471	2.40735
$5$	−3.81471	−1.70599	−0.852995	−	0.521919i	$-0.825216\pi$
$5$	−3.81471	−1.70599	−0.852995	+	0.521919i	$0.825216\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−7.34780	−2.59784
$9$	0	0
$10$	9.95830	3.14909
$11$	4.73730	1.42835	0.714175	−	0.699968i	$-0.246802\pi$
$11$	4.73730	1.42835	0.714175	+	0.699968i	$0.246802\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	9.55201	2.38800
$17$	−5.22100	−1.26628	−0.633139	−	0.774038i	$-0.718234\pi$
$17$	−5.22100	−1.26628	−0.633139	+	0.774038i	$0.718234\pi$
$18$	0	0
$19$	−2.92259	−0.670488	−0.335244	−	0.942131i	$-0.608819\pi$
$19$	−2.92259	−0.670488	−0.335244	+	0.942131i	$0.608819\pi$
$20$	−18.3667	−4.10692
$21$	0	0
$22$	−12.3667	−2.63659
$23$	−3.33101	−0.694563	−0.347282	−	0.937761i	$-0.612895\pi$
$23$	−3.33101	−0.694563	−0.347282	+	0.937761i	$0.612895\pi$
$24$	0	0
$25$	9.55201	1.91040
$26$	2.61050	0.511961
$27$	0	0
$28$	0	0
$29$	0.922589	0.171321	0.0856603	−	0.996324i	$-0.472700\pi$
$29$	0.922589	0.171321	0.0856603	+	0.996324i	$0.472700\pi$
$30$	0	0
$31$	7.51941	1.35053	0.675263	−	0.737577i	$-0.264030\pi$
$31$	7.51941	1.35053	0.675263	+	0.737577i	$0.264030\pi$
$32$	−10.2399	−1.81018
$33$	0	0
$34$	13.6294	2.33743
$35$	0	0
$36$	0	0
$37$	0.154821	0.0254525	0.0127262	−	0.999919i	$-0.495949\pi$
$37$	0.154821	0.0254525	0.0127262	+	0.999919i	$0.495949\pi$
$38$	7.62942	1.23766
$39$	0	0
$40$	28.0297	4.43189
$41$	6.36672	0.994314	0.497157	−	0.867661i	$-0.334377\pi$
$41$	6.36672	0.994314	0.497157	+	0.867661i	$0.334377\pi$
$42$	0	0
$43$	−6.55201	−0.999172	−0.499586	−	0.866264i	$-0.666514\pi$
$43$	−6.55201	−0.999172	−0.499586	+	0.866264i	$0.666514\pi$
$44$	22.8087	3.43854
$45$	0	0
$46$	8.69560	1.28210
$47$	9.03571	1.31799	0.658997	−	0.752146i	$-0.270981\pi$
$47$	9.03571	1.31799	0.658997	+	0.752146i	$0.270981\pi$
$48$	0	0
$49$	0	0
$50$	−24.9355	−3.52641
$51$	0	0
$52$	−4.81471	−0.667680
$53$	−8.55201	−1.17471	−0.587354	−	0.809330i	$-0.699830\pi$
$53$	−8.55201	−1.17471	−0.587354	+	0.809330i	$0.699830\pi$
$54$	0	0
$55$	−18.0714	−2.43675
$56$	0	0
$57$	0	0
$58$	−2.40842	−0.316241
$59$	3.95830	0.515327	0.257663	−	0.966235i	$-0.417047\pi$
$59$	3.95830	0.515327	0.257663	+	0.966235i	$0.417047\pi$
$60$	0	0
$61$	−12.4420	−1.59303	−0.796517	−	0.604616i	$-0.793327\pi$
$61$	−12.4420	−1.59303	−0.796517	+	0.604616i	$0.793327\pi$
$62$	−19.6294	−2.49294
$63$	0	0
$64$	7.62729	0.953411
$65$	3.81471	0.473156
$66$	0	0
$67$	−10.6620	−1.30257	−0.651286	−	0.758832i	$-0.725770\pi$
$67$	−10.6620	−1.30257	−0.651286	+	0.758832i	$0.725770\pi$
$68$	−25.1376	−3.04838
$69$	0	0
$70$	0	0
$71$	6.58248	0.781196	0.390598	−	0.920561i	$-0.372268\pi$
$71$	6.58248	0.781196	0.390598	+	0.920561i	$0.372268\pi$
$72$	0	0
$73$	7.73517	0.905333	0.452667	−	0.891680i	$-0.350473\pi$
$73$	7.73517	0.905333	0.452667	+	0.891680i	$0.350473\pi$
$74$	−0.404161	−0.0469828
$75$	0	0
$76$	−14.0714	−1.61410
$77$	0	0
$78$	0	0
$79$	13.3646	1.50363	0.751817	−	0.659372i	$-0.229178\pi$
$79$	13.3646	1.50363	0.751817	+	0.659372i	$0.229178\pi$
$80$	−36.4381	−4.07391
$81$	0	0
$82$	−16.6203	−1.83541
$83$	−1.40629	−0.154360	−0.0771802	−	0.997017i	$-0.524592\pi$
$83$	−1.40629	−0.154360	−0.0771802	+	0.997017i	$0.524592\pi$
$84$	0	0
$85$	19.9166	2.16026
$86$	17.1040	1.84437
$87$	0	0
$88$	−34.8087	−3.71062
$89$	−1.96953	−0.208770	−0.104385	−	0.994537i	$-0.533287\pi$
$89$	−1.96953	−0.208770	−0.104385	+	0.994537i	$0.533287\pi$
$90$	0	0
$91$	0	0
$92$	−16.0378	−1.67206
$93$	0	0
$94$	−23.5877	−2.43289
$95$	11.1488	1.14385
$96$	0	0
$97$	2.11001	0.214239	0.107119	−	0.994246i	$-0.465837\pi$
$97$	2.11001	0.214239	0.107119	+	0.994246i	$0.465837\pi$
$98$	0	0
$99$	0	0
$100$	45.9901	4.59901
$101$	0.850419	0.0846198	0.0423099	−	0.999105i	$-0.486528\pi$
$101$	0.850419	0.0846198	0.0423099	+	0.999105i	$0.486528\pi$
$102$	0	0
$103$	1.47460	0.145296	0.0726482	−	0.997358i	$-0.476855\pi$
$103$	1.47460	0.145296	0.0726482	+	0.997358i	$0.476855\pi$
$104$	7.34780	0.720511
$105$	0	0
$106$	22.3250	2.16840
$107$	−2.62418	−0.253689	−0.126844	−	0.991923i	$-0.540485\pi$
$107$	−2.62418	−0.253689	−0.126844	+	0.991923i	$0.540485\pi$
$108$	0	0
$109$	−17.9166	−1.71610	−0.858049	−	0.513567i	$-0.828324\pi$
$109$	−17.9166	−1.71610	−0.858049	+	0.513567i	$0.828324\pi$
$110$	47.1754	4.49800
$111$	0	0
$112$	0	0
$113$	−0.922589	−0.0867899	−0.0433950	−	0.999058i	$-0.513817\pi$
$113$	−0.922589	−0.0867899	−0.0433950	+	0.999058i	$0.513817\pi$
$114$	0	0
$115$	12.7068	1.18492
$116$	4.44200	0.412429
$117$	0	0
$118$	−10.3331	−0.951242
$119$	0	0
$120$	0	0
$121$	11.4420	1.04018
$122$	32.4798	2.94059
$123$	0	0
$124$	36.2038	3.25119
$125$	−17.3646	−1.55314
$126$	0	0
$127$	17.4746	1.55062	0.775310	−	0.631581i	$-0.217594\pi$
$127$	17.4746	1.55062	0.775310	+	0.631581i	$0.217594\pi$
$128$	0.568798	0.0502751
$129$	0	0
$130$	−9.95830	−0.873401
$131$	0.967402	0.0845223	0.0422611	−	0.999107i	$-0.486544\pi$
$131$	0.967402	0.0845223	0.0422611	+	0.999107i	$0.486544\pi$
$132$	0	0
$133$	0	0
$134$	27.8332	2.40442
$135$	0	0
$136$	38.3629	3.28959
$137$	−3.29628	−0.281620	−0.140810	−	0.990037i	$-0.544971\pi$
$137$	−3.29628	−0.281620	−0.140810	+	0.990037i	$0.544971\pi$
$138$	0	0
$139$	−0.370581	−0.0314323	−0.0157161	−	0.999876i	$-0.505003\pi$
$139$	−0.370581	−0.0314323	−0.0157161	+	0.999876i	$0.505003\pi$
$140$	0	0
$141$	0	0
$142$	−17.1836	−1.44201
$143$	−4.73730	−0.396153
$144$	0	0
$145$	−3.51941	−0.292271
$146$	−20.1927	−1.67116
$147$	0	0
$148$	0.745420	0.0612732
$149$	15.7425	1.28968	0.644840	−	0.764318i	$-0.276924\pi$
$149$	15.7425	1.28968	0.644840	+	0.764318i	$0.276924\pi$
$150$	0	0
$151$	10.2914	0.837505	0.418753	−	0.908100i	$-0.362467\pi$
$151$	10.2914	0.837505	0.418753	+	0.908100i	$0.362467\pi$
$152$	21.4746	1.74182
$153$	0	0
$154$	0	0
$155$	−28.6844	−2.30398
$156$	0	0
$157$	11.4137	0.910909	0.455455	−	0.890259i	$-0.349477\pi$
$157$	11.4137	0.910909	0.455455	+	0.890259i	$0.349477\pi$
$158$	−34.8883	−2.77556
$159$	0	0
$160$	39.0623	3.08815
$161$	0	0
$162$	0	0
$163$	−13.4746	−1.05541	−0.527706	−	0.849427i	$-0.676948\pi$
$163$	−13.4746	−1.05541	−0.527706	+	0.849427i	$0.676948\pi$
$164$	30.6539	2.39367
$165$	0	0
$166$	3.67112	0.284934
$167$	19.1905	1.48501	0.742504	−	0.669842i	$-0.233638\pi$
$167$	19.1905	1.48501	0.742504	+	0.669842i	$0.233638\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−51.9923	−3.98763
$171$	0	0
$172$	−31.5460	−2.40536
$173$	−19.5124	−1.48350	−0.741752	−	0.670675i	$-0.766005\pi$
$173$	−19.5124	−1.48350	−0.741752	+	0.670675i	$0.766005\pi$
$174$	0	0
$175$	0	0
$176$	45.2507	3.41090
$177$	0	0
$178$	5.14146	0.385369
$179$	16.5856	1.23967	0.619833	−	0.784734i	$-0.287201\pi$
$179$	16.5856	1.23967	0.619833	+	0.784734i	$0.287201\pi$
$180$	0	0
$181$	2.81684	0.209374	0.104687	−	0.994505i	$-0.466616\pi$
$181$	2.81684	0.209374	0.104687	+	0.994505i	$0.466616\pi$
$182$	0	0
$183$	0	0
$184$	24.4756	1.80436
$185$	−0.590599	−0.0434217
$186$	0	0
$187$	−24.7334	−1.80869
$188$	43.5043	3.17288
$189$	0	0
$190$	−29.1040	−2.11143
$191$	−15.1601	−1.09694	−0.548472	−	0.836169i	$-0.684790\pi$
$191$	−15.1601	−1.09694	−0.548472	+	0.836169i	$0.684790\pi$
$192$	0	0
$193$	0.0651962	0.00469293	0.00234646	−	0.999997i	$-0.499253\pi$
$193$	0.0651962	0.00469293	0.00234646	+	0.999997i	$0.499253\pi$
$194$	−5.50818	−0.395464
$195$	0	0
$196$	0	0
$197$	17.1415	1.22128	0.610639	−	0.791909i	$-0.290913\pi$
$197$	17.1415	1.22128	0.610639	+	0.791909i	$0.290913\pi$
$198$	0	0
$199$	−6.44200	−0.456661	−0.228331	−	0.973584i	$-0.573327\pi$
$199$	−6.44200	−0.456661	−0.228331	+	0.973584i	$0.573327\pi$
$200$	−70.1862	−4.96292
$201$	0	0
$202$	−2.22002	−0.156200
$203$	0	0
$204$	0	0
$205$	−24.2872	−1.69629
$206$	−3.84944	−0.268203
$207$	0	0
$208$	−9.55201	−0.662313
$209$	−13.8452	−0.957691
$210$	0	0
$211$	−16.0266	−1.10332	−0.551659	−	0.834070i	$-0.686005\pi$
$211$	−16.0266	−1.10332	−0.551659	+	0.834070i	$0.686005\pi$
$212$	−41.1754	−2.82794
$213$	0	0
$214$	6.85042	0.468285
$215$	24.9940	1.70458
$216$	0	0
$217$	0	0
$218$	46.7713	3.16775
$219$	0	0
$220$	−87.0086	−5.86612
$221$	5.22100	0.351202
$222$	0	0
$223$	−20.0266	−1.34108	−0.670540	−	0.741873i	$-0.733938\pi$
$223$	−20.0266	−1.34108	−0.670540	+	0.741873i	$0.733938\pi$
$224$	0	0
$225$	0	0
$226$	2.40842	0.160206
$227$	19.2171	1.27549	0.637743	−	0.770249i	$-0.279868\pi$
$227$	19.2171	1.27549	0.637743	+	0.770249i	$0.279868\pi$
$228$	0	0
$229$	−5.25884	−0.347514	−0.173757	−	0.984789i	$-0.555591\pi$
$229$	−5.25884	−0.347514	−0.173757	+	0.984789i	$0.555591\pi$
$230$	−33.1712	−2.18724
$231$	0	0
$232$	−6.77900	−0.445063
$233$	26.6234	1.74416	0.872079	−	0.489365i	$-0.162771\pi$
$233$	26.6234	1.74416	0.872079	+	0.489365i	$0.162771\pi$
$234$	0	0
$235$	−34.4686	−2.24848
$236$	19.0581	1.24057
$237$	0	0
$238$	0	0
$239$	−4.29104	−0.277564	−0.138782	−	0.990323i	$-0.544319\pi$
$239$	−4.29104	−0.277564	−0.138782	+	0.990323i	$0.544319\pi$
$240$	0	0
$241$	−7.52367	−0.484642	−0.242321	−	0.970196i	$-0.577909\pi$
$241$	−7.52367	−0.484642	−0.242321	+	0.970196i	$0.577909\pi$
$242$	−29.8693	−1.92007
$243$	0	0
$244$	−59.9046	−3.83500
$245$	0	0
$246$	0	0
$247$	2.92259	0.185960
$248$	−55.2511	−3.50845
$249$	0	0
$250$	45.3303	2.86694
$251$	11.3198	0.714498	0.357249	−	0.934009i	$-0.383715\pi$
$251$	11.3198	0.714498	0.357249	+	0.934009i	$0.383715\pi$
$252$	0	0
$253$	−15.7800	−0.992079
$254$	−45.6174	−2.86229
$255$	0	0
$256$	−16.7394	−1.04621
$257$	−24.8504	−1.55013	−0.775063	−	0.631884i	$-0.782282\pi$
$257$	−24.8504	−1.55013	−0.775063	+	0.631884i	$0.782282\pi$
$258$	0	0
$259$	0	0
$260$	18.3667	1.13906
$261$	0	0
$262$	−2.52540	−0.156020
$263$	−17.1762	−1.05913	−0.529565	−	0.848270i	$-0.677645\pi$
$263$	−17.1762	−1.05913	−0.529565	+	0.848270i	$0.677645\pi$
$264$	0	0
$265$	32.6234	2.00404
$266$	0	0
$267$	0	0
$268$	−51.3345	−3.13575
$269$	−7.74640	−0.472306	−0.236153	−	0.971716i	$-0.575887\pi$
$269$	−7.74640	−0.472306	−0.236153	+	0.971716i	$0.575887\pi$
$270$	0	0
$271$	29.7008	1.80420	0.902099	−	0.431530i	$-0.142026\pi$
$271$	29.7008	1.80420	0.902099	+	0.431530i	$0.142026\pi$
$272$	−49.8710	−3.02388
$273$	0	0
$274$	8.60494	0.519844
$275$	45.2507	2.72872
$276$	0	0
$277$	25.1488	1.51105	0.755523	−	0.655122i	$-0.227383\pi$
$277$	25.1488	1.51105	0.755523	+	0.655122i	$0.227383\pi$
$278$	0.967402	0.0580209
$279$	0	0
$280$	0	0
$281$	−8.40030	−0.501120	−0.250560	−	0.968101i	$-0.580615\pi$
$281$	−8.40030	−0.501120	−0.250560	+	0.968101i	$0.580615\pi$
$282$	0	0
$283$	21.3912	1.27157	0.635787	−	0.771864i	$-0.280676\pi$
$283$	21.3912	1.27157	0.635787	+	0.771864i	$0.280676\pi$
$284$	31.6927	1.88062
$285$	0	0
$286$	12.3667	0.731259
$287$	0	0
$288$	0	0
$289$	10.2588	0.603461
$290$	9.18742	0.539504
$291$	0	0
$292$	37.2426	2.17946
$293$	−9.59895	−0.560777	−0.280388	−	0.959887i	$-0.590463\pi$
$293$	−9.59895	−0.560777	−0.280388	+	0.959887i	$0.590463\pi$
$294$	0	0
$295$	−15.0998	−0.879142
$296$	−1.13760	−0.0661215
$297$	0	0
$298$	−41.0959	−2.38062
$299$	3.33101	0.192637
$300$	0	0
$301$	0	0
$302$	−26.8658	−1.54595
$303$	0	0
$304$	−27.9166	−1.60113
$305$	47.4626	2.71770
$306$	0	0
$307$	15.1488	0.864589	0.432295	−	0.901732i	$-0.357704\pi$
$307$	15.1488	0.864589	0.432295	+	0.901732i	$0.357704\pi$
$308$	0	0
$309$	0	0
$310$	74.8805	4.25293
$311$	−4.37058	−0.247833	−0.123916	−	0.992293i	$-0.539545\pi$
$311$	−4.37058	−0.247833	−0.123916	+	0.992293i	$0.539545\pi$
$312$	0	0
$313$	1.49280	0.0843783	0.0421891	−	0.999110i	$-0.486567\pi$
$313$	1.49280	0.0843783	0.0421891	+	0.999110i	$0.486567\pi$
$314$	−29.7954	−1.68145
$315$	0	0
$316$	64.3466	3.61978
$317$	−23.2129	−1.30377	−0.651883	−	0.758320i	$-0.726021\pi$
$317$	−23.2129	−1.30377	−0.651883	+	0.758320i	$0.726021\pi$
$318$	0	0
$319$	4.37058	0.244706
$320$	−29.0959	−1.62651
$321$	0	0
$322$	0	0
$323$	15.2588	0.849024
$324$	0	0
$325$	−9.55201	−0.529850
$326$	35.1754	1.94819
$327$	0	0
$328$	−46.7814	−2.58307
$329$	0	0
$330$	0	0
$331$	1.10402	0.0606822	0.0303411	−	0.999540i	$-0.490341\pi$
$331$	1.10402	0.0606822	0.0303411	+	0.999540i	$0.490341\pi$
$332$	−6.77088	−0.371600
$333$	0	0
$334$	−50.0969	−2.74118
$335$	40.6725	2.22218
$336$	0	0
$337$	−4.24237	−0.231096	−0.115548	−	0.993302i	$-0.536862\pi$
$337$	−4.24237	−0.231096	−0.115548	+	0.993302i	$0.536862\pi$
$338$	−2.61050	−0.141992
$339$	0	0
$340$	95.8926	5.20051
$341$	35.6217	1.92902
$342$	0	0
$343$	0	0
$344$	48.1428	2.59569
$345$	0	0
$346$	50.9372	2.73840
$347$	−14.0336	−0.753362	−0.376681	−	0.926343i	$-0.622935\pi$
$347$	−14.0336	−0.753362	−0.376681	+	0.926343i	$0.622935\pi$
$348$	0	0
$349$	−4.10575	−0.219776	−0.109888	−	0.993944i	$-0.535049\pi$
$349$	−4.10575	−0.219776	−0.109888	+	0.993944i	$0.535049\pi$
$350$	0	0
$351$	0	0
$352$	−48.5096	−2.58557
$353$	−16.0753	−0.855601	−0.427800	−	0.903873i	$-0.640711\pi$
$353$	−16.0753	−0.855601	−0.427800	+	0.903873i	$0.640711\pi$
$354$	0	0
$355$	−25.1102	−1.33271
$356$	−9.48272	−0.502583
$357$	0	0
$358$	−43.2967	−2.28830
$359$	18.1510	0.957971	0.478985	−	0.877823i	$-0.341005\pi$
$359$	18.1510	0.957971	0.478985	+	0.877823i	$0.341005\pi$
$360$	0	0
$361$	−10.4585	−0.550446
$362$	−7.35336	−0.386484
$363$	0	0
$364$	0	0
$365$	−29.5074	−1.54449
$366$	0	0
$367$	23.3955	1.22123	0.610616	−	0.791927i	$-0.290922\pi$
$367$	23.3955	1.22123	0.610616	+	0.791927i	$0.290922\pi$
$368$	−31.8178	−1.65862
$369$	0	0
$370$	1.54176	0.0801522
$371$	0	0
$372$	0	0
$373$	−4.75164	−0.246031	−0.123015	−	0.992405i	$-0.539256\pi$
$373$	−4.75164	−0.246031	−0.123015	+	0.992405i	$0.539256\pi$
$374$	64.5666	3.33866
$375$	0	0
$376$	−66.3926	−3.42394
$377$	−0.922589	−0.0475158
$378$	0	0
$379$	−6.81258	−0.349939	−0.174969	−	0.984574i	$-0.555983\pi$
$379$	−6.81258	−0.349939	−0.174969	+	0.984574i	$0.555983\pi$
$380$	53.6784	2.75364
$381$	0	0
$382$	39.5753	2.02485
$383$	2.25746	0.115351	0.0576754	−	0.998335i	$-0.481631\pi$
$383$	2.25746	0.115351	0.0576754	+	0.998335i	$0.481631\pi$
$384$	0	0
$385$	0	0
$386$	−0.170195	−0.00866268
$387$	0	0
$388$	10.1591	0.515749
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	17.3912	0.879511
$392$	0	0
$393$	0	0
$394$	−44.7478	−2.25436
$395$	−50.9820	−2.56518
$396$	0	0
$397$	−24.9897	−1.25420	−0.627100	−	0.778939i	$-0.715758\pi$
$397$	−24.9897	−1.25420	−0.627100	+	0.778939i	$0.715758\pi$
$398$	16.8168	0.842952
$399$	0	0
$400$	91.2409	4.56204
$401$	−27.6529	−1.38092	−0.690460	−	0.723370i	$-0.742592\pi$
$401$	−27.6529	−1.38092	−0.690460	+	0.723370i	$0.742592\pi$
$402$	0	0
$403$	−7.51941	−0.374568
$404$	4.09452	0.203710
$405$	0	0
$406$	0	0
$407$	0.733435	0.0363550
$408$	0	0
$409$	−13.1488	−0.650168	−0.325084	−	0.945685i	$-0.605393\pi$
$409$	−13.1488	−0.650168	−0.325084	+	0.945685i	$0.605393\pi$
$410$	63.4017	3.13119
$411$	0	0
$412$	7.09976	0.349780
$413$	0	0
$414$	0	0
$415$	5.36459	0.263337
$416$	10.2399	0.502053
$417$	0	0
$418$	36.1428	1.76780
$419$	−5.69462	−0.278200	−0.139100	−	0.990278i	$-0.544421\pi$
$419$	−5.69462	−0.278200	−0.139100	+	0.990278i	$0.544421\pi$
$420$	0	0
$421$	−23.0206	−1.12196	−0.560978	−	0.827831i	$-0.689575\pi$
$421$	−23.0206	−1.12196	−0.560978	+	0.827831i	$0.689575\pi$
$422$	41.8375	2.03662
$423$	0	0
$424$	62.8384	3.05170
$425$	−49.8710	−2.41910
$426$	0	0
$427$	0	0
$428$	−12.6347	−0.610719
$429$	0	0
$430$	−65.2469	−3.14648
$431$	−20.8045	−1.00212	−0.501058	−	0.865414i	$-0.667056\pi$
$431$	−20.8045	−1.00212	−0.501058	+	0.865414i	$0.667056\pi$
$432$	0	0
$433$	−31.4808	−1.51287	−0.756436	−	0.654068i	$-0.773061\pi$
$433$	−31.4808	−1.51287	−0.756436	+	0.654068i	$0.773061\pi$
$434$	0	0
$435$	0	0
$436$	−86.2632	−4.13126
$437$	9.73517	0.465696
$438$	0	0
$439$	−22.3811	−1.06819	−0.534095	−	0.845425i	$-0.679347\pi$
$439$	−22.3811	−1.06819	−0.534095	+	0.845425i	$0.679347\pi$
$440$	132.785	6.33028
$441$	0	0
$442$	−13.6294	−0.648285
$443$	−8.52465	−0.405018	−0.202509	−	0.979280i	$-0.564910\pi$
$443$	−8.52465	−0.405018	−0.202509	+	0.979280i	$0.564910\pi$
$444$	0	0
$445$	7.51319	0.356159
$446$	52.2795	2.47550
$447$	0	0
$448$	0	0
$449$	−18.7142	−0.883178	−0.441589	−	0.897218i	$-0.645585\pi$
$449$	−18.7142	−0.883178	−0.441589	+	0.897218i	$0.645585\pi$
$450$	0	0
$451$	30.1610	1.42023
$452$	−4.44200	−0.208934
$453$	0	0
$454$	−50.1663	−2.35442
$455$	0	0
$456$	0	0
$457$	−14.1366	−0.661283	−0.330641	−	0.943756i	$-0.607265\pi$
$457$	−14.1366	−0.661283	−0.330641	+	0.943756i	$0.607265\pi$
$458$	13.7282	0.641476
$459$	0	0
$460$	61.1797	2.85252
$461$	−2.67636	−0.124651	−0.0623253	−	0.998056i	$-0.519852\pi$
$461$	−2.67636	−0.124651	−0.0623253	+	0.998056i	$0.519852\pi$
$462$	0	0
$463$	−2.53162	−0.117655	−0.0588273	−	0.998268i	$-0.518736\pi$
$463$	−2.53162	−0.117655	−0.0588273	+	0.998268i	$0.518736\pi$
$464$	8.81258	0.409114
$465$	0	0
$466$	−69.5005	−3.21955
$467$	2.00426	0.0927460	0.0463730	−	0.998924i	$-0.485234\pi$
$467$	2.00426	0.0927460	0.0463730	+	0.998924i	$0.485234\pi$
$468$	0	0
$469$	0	0
$470$	89.9803	4.15048
$471$	0	0
$472$	−29.0848	−1.33874
$473$	−31.0388	−1.42717
$474$	0	0
$475$	−27.9166	−1.28090
$476$	0	0
$477$	0	0
$478$	11.2018	0.512357
$479$	−14.6609	−0.669872	−0.334936	−	0.942241i	$-0.608715\pi$
$479$	−14.6609	−0.669872	−0.334936	+	0.942241i	$0.608715\pi$
$480$	0	0
$481$	−0.154821	−0.00705925
$482$	19.6405	0.894602
$483$	0	0
$484$	55.0899	2.50409
$485$	−8.04907	−0.365489
$486$	0	0
$487$	38.2143	1.73165	0.865827	−	0.500344i	$-0.166793\pi$
$487$	38.2143	1.73165	0.865827	+	0.500344i	$0.166793\pi$
$488$	91.4213	4.13845
$489$	0	0
$490$	0	0
$491$	−21.3758	−0.964677	−0.482339	−	0.875985i	$-0.660213\pi$
$491$	−21.3758	−0.964677	−0.482339	+	0.875985i	$0.660213\pi$
$492$	0	0
$493$	−4.81684	−0.216939
$494$	−7.62942	−0.343264
$495$	0	0
$496$	71.8255	3.22506
$497$	0	0
$498$	0	0
$499$	27.0920	1.21281	0.606403	−	0.795158i	$-0.292612\pi$
$499$	27.0920	1.21281	0.606403	+	0.795158i	$0.292612\pi$
$500$	−83.6054	−3.73895
$501$	0	0
$502$	−29.5503	−1.31889
$503$	24.8778	1.10925	0.554623	−	0.832102i	$-0.312863\pi$
$503$	24.8778	1.10925	0.554623	+	0.832102i	$0.312863\pi$
$504$	0	0
$505$	−3.24410	−0.144361
$506$	41.1936	1.83128
$507$	0	0
$508$	84.1351	3.73289
$509$	2.70297	0.119807	0.0599034	−	0.998204i	$-0.480921\pi$
$509$	2.70297	0.119807	0.0599034	+	0.998204i	$0.480921\pi$
$510$	0	0
$511$	0	0
$512$	42.5607	1.88093
$513$	0	0
$514$	64.8720	2.86138
$515$	−5.62516	−0.247874
$516$	0	0
$517$	42.8049	1.88256
$518$	0	0
$519$	0	0
$520$	−28.0297	−1.22918
$521$	−33.4472	−1.46535	−0.732675	−	0.680579i	$-0.761728\pi$
$521$	−33.4472	−1.46535	−0.732675	+	0.680579i	$0.761728\pi$
$522$	0	0
$523$	−19.3198	−0.844795	−0.422397	−	0.906411i	$-0.638811\pi$
$523$	−19.3198	−0.844795	−0.422397	+	0.906411i	$0.638811\pi$
$524$	4.65776	0.203475
$525$	0	0
$526$	44.8384	1.95505
$527$	−39.2588	−1.71014
$528$	0	0
$529$	−11.9044	−0.517582
$530$	−85.1634	−3.69926
$531$	0	0
$532$	0	0
$533$	−6.36672	−0.275773
$534$	0	0
$535$	10.0105	0.432791
$536$	78.3424	3.38387
$537$	0	0
$538$	20.2220	0.871832
$539$	0	0
$540$	0	0
$541$	−24.9554	−1.07292	−0.536459	−	0.843927i	$-0.680238\pi$
$541$	−24.9554	−1.07292	−0.536459	+	0.843927i	$0.680238\pi$
$542$	−77.5340	−3.33037
$543$	0	0
$544$	53.4626	2.29219
$545$	68.3466	2.92765
$546$	0	0
$547$	3.80037	0.162492	0.0812460	−	0.996694i	$-0.474110\pi$
$547$	3.80037	0.162492	0.0812460	+	0.996694i	$0.474110\pi$
$548$	−15.8706	−0.677960
$549$	0	0
$550$	−118.127	−5.03695
$551$	−2.69635	−0.114868
$552$	0	0
$553$	0	0
$554$	−65.6510	−2.78924
$555$	0	0
$556$	−1.78424	−0.0756686
$557$	−43.8792	−1.85922	−0.929610	−	0.368546i	$-0.879856\pi$
$557$	−43.8792	−1.85922	−0.929610	+	0.368546i	$0.879856\pi$
$558$	0	0
$559$	6.55201	0.277120
$560$	0	0
$561$	0	0
$562$	21.9290	0.925018
$563$	12.3768	0.521620	0.260810	−	0.965390i	$-0.416010\pi$
$563$	12.3768	0.521620	0.260810	+	0.965390i	$0.416010\pi$
$564$	0	0
$565$	3.51941	0.148063
$566$	−55.8417	−2.34720
$567$	0	0
$568$	−48.3667	−2.02942
$569$	26.6234	1.11611	0.558056	−	0.829803i	$-0.311547\pi$
$569$	26.6234	1.11611	0.558056	+	0.829803i	$0.311547\pi$
$570$	0	0
$571$	10.9983	0.460263	0.230132	−	0.973160i	$-0.426084\pi$
$571$	10.9983	0.460263	0.230132	+	0.973160i	$0.426084\pi$
$572$	−22.8087	−0.953680
$573$	0	0
$574$	0	0
$575$	−31.8178	−1.32689
$576$	0	0
$577$	−30.4238	−1.26656	−0.633280	−	0.773923i	$-0.718292\pi$
$577$	−30.4238	−1.26656	−0.633280	+	0.773923i	$0.718292\pi$
$578$	−26.7807	−1.11393
$579$	0	0
$580$	−16.9449	−0.703600
$581$	0	0
$582$	0	0
$583$	−40.5134	−1.67789
$584$	−56.8365	−2.35191
$585$	0	0
$586$	25.0581	1.03514
$587$	3.84207	0.158579	0.0792895	−	0.996852i	$-0.474735\pi$
$587$	3.84207	0.158579	0.0792895	+	0.996852i	$0.474735\pi$
$588$	0	0
$589$	−21.9761	−0.905511
$590$	39.4179	1.62281
$591$	0	0
$592$	1.47886	0.0607806
$593$	−23.8904	−0.981061	−0.490530	−	0.871424i	$-0.663197\pi$
$593$	−23.8904	−0.981061	−0.490530	+	0.871424i	$0.663197\pi$
$594$	0	0
$595$	0	0
$596$	75.7958	3.10471
$597$	0	0
$598$	−8.69560	−0.355589
$599$	15.4206	0.630070	0.315035	−	0.949080i	$-0.397984\pi$
$599$	15.4206	0.630070	0.315035	+	0.949080i	$0.397984\pi$
$600$	0	0
$601$	1.49280	0.0608928	0.0304464	−	0.999536i	$-0.490307\pi$
$601$	1.49280	0.0608928	0.0304464	+	0.999536i	$0.490307\pi$
$602$	0	0
$603$	0	0
$604$	49.5503	2.01617
$605$	−43.6479	−1.77454
$606$	0	0
$607$	4.44626	0.180468	0.0902340	−	0.995921i	$-0.471239\pi$
$607$	4.44626	0.180468	0.0902340	+	0.995921i	$0.471239\pi$
$608$	29.9271	1.21370
$609$	0	0
$610$	−123.901	−5.01661
$611$	−9.03571	−0.365546
$612$	0	0
$613$	26.6640	1.07695	0.538474	−	0.842642i	$-0.319001\pi$
$613$	26.6640	1.07695	0.538474	+	0.842642i	$0.319001\pi$
$614$	−39.5460	−1.59595
$615$	0	0
$616$	0	0
$617$	−27.3495	−1.10105	−0.550525	−	0.834819i	$-0.685572\pi$
$617$	−27.3495	−1.10105	−0.550525	+	0.834819i	$0.685572\pi$
$618$	0	0
$619$	9.24836	0.371723	0.185861	−	0.982576i	$-0.440492\pi$
$619$	9.24836	0.371723	0.185861	+	0.982576i	$0.440492\pi$
$620$	−138.107	−5.54651
$621$	0	0
$622$	11.4094	0.457475
$623$	0	0
$624$	0	0
$625$	18.4808	0.739233
$626$	−3.89697	−0.155754
$627$	0	0
$628$	54.9535	2.19288
$629$	−0.808323	−0.0322299
$630$	0	0
$631$	24.5134	0.975864	0.487932	−	0.872882i	$-0.337751\pi$
$631$	24.5134	0.975864	0.487932	+	0.872882i	$0.337751\pi$
$632$	−98.2003	−3.90620
$633$	0	0
$634$	60.5972	2.40662
$635$	−66.6605	−2.64534
$636$	0	0
$637$	0	0
$638$	−11.4094	−0.451703
$639$	0	0
$640$	−2.16980	−0.0857689
$641$	−34.3972	−1.35861	−0.679304	−	0.733857i	$-0.737718\pi$
$641$	−34.3972	−1.35861	−0.679304	+	0.733857i	$0.737718\pi$
$642$	0	0
$643$	7.69036	0.303278	0.151639	−	0.988436i	$-0.451545\pi$
$643$	7.69036	0.303278	0.151639	+	0.988436i	$0.451545\pi$
$644$	0	0
$645$	0	0
$646$	−39.8332	−1.56722
$647$	41.9123	1.64774	0.823872	−	0.566776i	$-0.191809\pi$
$647$	41.9123	1.64774	0.823872	+	0.566776i	$0.191809\pi$
$648$	0	0
$649$	18.7516	0.736066
$650$	24.9355	0.978051
$651$	0	0
$652$	−64.8763	−2.54075
$653$	−34.2262	−1.33938	−0.669688	−	0.742642i	$-0.733572\pi$
$653$	−34.2262	−1.33938	−0.669688	+	0.742642i	$0.733572\pi$
$654$	0	0
$655$	−3.69036	−0.144194
$656$	60.8149	2.37442
$657$	0	0
$658$	0	0
$659$	−45.1685	−1.75951	−0.879757	−	0.475424i	$-0.842295\pi$
$659$	−45.1685	−1.75951	−0.879757	+	0.475424i	$0.842295\pi$
$660$	0	0
$661$	−11.9839	−0.466119	−0.233059	−	0.972463i	$-0.574874\pi$
$661$	−11.9839	−0.466119	−0.233059	+	0.972463i	$0.574874\pi$
$662$	−2.88203	−0.112013
$663$	0	0
$664$	10.3331	0.401004
$665$	0	0
$666$	0	0
$667$	−3.07315	−0.118993
$668$	92.3968	3.57494
$669$	0	0
$670$	−106.176	−4.10192
$671$	−58.9415	−2.27541
$672$	0	0
$673$	−29.5117	−1.13759	−0.568796	−	0.822479i	$-0.692591\pi$
$673$	−29.5117	−1.13759	−0.568796	+	0.822479i	$0.692591\pi$
$674$	11.0747	0.426581
$675$	0	0
$676$	4.81471	0.185181
$677$	−31.0662	−1.19397	−0.596985	−	0.802252i	$-0.703635\pi$
$677$	−31.0662	−1.19397	−0.596985	+	0.802252i	$0.703635\pi$
$678$	0	0
$679$	0	0
$680$	−146.343	−5.61200
$681$	0	0
$682$	−92.9904	−3.56079
$683$	−5.79433	−0.221714	−0.110857	−	0.993836i	$-0.535360\pi$
$683$	−5.79433	−0.221714	−0.110857	+	0.993836i	$0.535360\pi$
$684$	0	0
$685$	12.5744	0.480441
$686$	0	0
$687$	0	0
$688$	−62.5848	−2.38602
$689$	8.55201	0.325806
$690$	0	0
$691$	−18.8617	−0.717531	−0.358766	−	0.933428i	$-0.616802\pi$
$691$	−18.8617	−0.717531	−0.358766	+	0.933428i	$0.616802\pi$
$692$	−93.9467	−3.57132
$693$	0	0
$694$	36.6347	1.39063
$695$	1.41366	0.0536232
$696$	0	0
$697$	−33.2406	−1.25908
$698$	10.7181	0.405685
$699$	0	0
$700$	0	0
$701$	32.3180	1.22064	0.610318	−	0.792157i	$-0.291042\pi$
$701$	32.3180	1.22064	0.610318	+	0.792157i	$0.291042\pi$
$702$	0	0
$703$	−0.452479	−0.0170656
$704$	36.1328	1.36180
$705$	0	0
$706$	41.9645	1.57936
$707$	0	0
$708$	0	0
$709$	4.72296	0.177374	0.0886872	−	0.996060i	$-0.471733\pi$
$709$	4.72296	0.177374	0.0886872	+	0.996060i	$0.471733\pi$
$710$	65.5503	2.46006
$711$	0	0
$712$	14.4717	0.542350
$713$	−25.0472	−0.938026
$714$	0	0
$715$	18.0714	0.675833
$716$	79.8548	2.98431
$717$	0	0
$718$	−47.3831	−1.76832
$719$	−40.8902	−1.52495	−0.762474	−	0.647019i	$-0.776015\pi$
$719$	−40.8902	−1.52495	−0.762474	+	0.647019i	$0.776015\pi$
$720$	0	0
$721$	0	0
$722$	27.3018	1.01607
$723$	0	0
$724$	13.5623	0.504037
$725$	8.81258	0.327291
$726$	0	0
$727$	−18.7292	−0.694627	−0.347313	−	0.937749i	$-0.612906\pi$
$727$	−18.7292	−0.694627	−0.347313	+	0.937749i	$0.612906\pi$
$728$	0	0
$729$	0	0
$730$	77.0291	2.85098
$731$	34.2080	1.26523
$732$	0	0
$733$	14.1100	0.521165	0.260583	−	0.965452i	$-0.416085\pi$
$733$	14.1100	0.521165	0.260583	+	0.965452i	$0.416085\pi$
$734$	−61.0738	−2.25428
$735$	0	0
$736$	34.1093	1.25728
$737$	−50.5092	−1.86053
$738$	0	0
$739$	−49.9209	−1.83637	−0.918184	−	0.396154i	$-0.870345\pi$
$739$	−49.9209	−1.83637	−0.918184	+	0.396154i	$0.870345\pi$
$740$	−2.84356	−0.104531
$741$	0	0
$742$	0	0
$743$	−2.15868	−0.0791945	−0.0395972	−	0.999216i	$-0.512607\pi$
$743$	−2.15868	−0.0791945	−0.0395972	+	0.999216i	$0.512607\pi$
$744$	0	0
$745$	−60.0532	−2.20018
$746$	12.4042	0.454149
$747$	0	0
$748$	−119.084	−4.35415
$749$	0	0
$750$	0	0
$751$	16.8372	0.614399	0.307199	−	0.951645i	$-0.400608\pi$
$751$	16.8372	0.614399	0.307199	+	0.951645i	$0.400608\pi$
$752$	86.3092	3.14737
$753$	0	0
$754$	2.40842	0.0877095
$755$	−39.2588	−1.42878
$756$	0	0
$757$	−17.6028	−0.639785	−0.319893	−	0.947454i	$-0.603647\pi$
$757$	−17.6028	−0.639785	−0.319893	+	0.947454i	$0.603647\pi$
$758$	17.7842	0.645953
$759$	0	0
$760$	−81.9193	−2.97153
$761$	19.2179	0.696648	0.348324	−	0.937374i	$-0.386751\pi$
$761$	19.2179	0.696648	0.348324	+	0.937374i	$0.386751\pi$
$762$	0	0
$763$	0	0
$764$	−72.9913	−2.64073
$765$	0	0
$766$	−5.89310	−0.212926
$767$	−3.95830	−0.142926
$768$	0	0
$769$	14.0406	0.506315	0.253158	−	0.967425i	$-0.418531\pi$
$769$	14.0406	0.506315	0.253158	+	0.967425i	$0.418531\pi$
$770$	0	0
$771$	0	0
$772$	0.313901	0.0112975
$773$	22.4339	0.806891	0.403445	−	0.915004i	$-0.367813\pi$
$773$	22.4339	0.806891	0.403445	+	0.915004i	$0.367813\pi$
$774$	0	0
$775$	71.8255	2.58005
$776$	−15.5039	−0.556558
$777$	0	0
$778$	15.6630	0.561546
$779$	−18.6073	−0.666676
$780$	0	0
$781$	31.1832	1.11582
$782$	−45.3997	−1.62349
$783$	0	0
$784$	0	0
$785$	−43.5398	−1.55400
$786$	0	0
$787$	0.926847	0.0330385	0.0165193	−	0.999864i	$-0.494742\pi$
$787$	0.926847	0.0330385	0.0165193	+	0.999864i	$0.494742\pi$
$788$	82.5311	2.94005
$789$	0	0
$790$	133.089	4.73508
$791$	0	0
$792$	0	0
$793$	12.4420	0.441828
$794$	65.2357	2.31513
$795$	0	0
$796$	−31.0164	−1.09935
$797$	−26.0154	−0.921512	−0.460756	−	0.887527i	$-0.652422\pi$
$797$	−26.0154	−0.921512	−0.460756	+	0.887527i	$0.652422\pi$
$798$	0	0
$799$	−47.1754	−1.66895
$800$	−97.8118	−3.45817
$801$	0	0
$802$	72.1879	2.54904
$803$	36.6438	1.29313
$804$	0	0
$805$	0	0
$806$	19.6294	0.691417
$807$	0	0
$808$	−6.24870	−0.219829
$809$	44.8539	1.57698	0.788490	−	0.615048i	$-0.210863\pi$
$809$	44.8539	1.57698	0.788490	+	0.615048i	$0.210863\pi$
$810$	0	0
$811$	−27.2511	−0.956916	−0.478458	−	0.878110i	$-0.658804\pi$
$811$	−27.2511	−0.956916	−0.478458	+	0.878110i	$0.658804\pi$
$812$	0	0
$813$	0	0
$814$	−1.91463	−0.0671078
$815$	51.4017	1.80052
$816$	0	0
$817$	19.1488	0.669933
$818$	34.3250	1.20015
$819$	0	0
$820$	−116.936	−4.08357
$821$	−20.4003	−0.711975	−0.355988	−	0.934491i	$-0.615855\pi$
$821$	−20.4003	−0.711975	−0.355988	+	0.934491i	$0.615855\pi$
$822$	0	0
$823$	54.3509	1.89455	0.947276	−	0.320418i	$-0.103824\pi$
$823$	54.3509	1.89455	0.947276	+	0.320418i	$0.103824\pi$
$824$	−10.8350	−0.377457
$825$	0	0
$826$	0	0
$827$	−3.48272	−0.121106	−0.0605530	−	0.998165i	$-0.519286\pi$
$827$	−3.48272	−0.121106	−0.0605530	+	0.998165i	$0.519286\pi$
$828$	0	0
$829$	29.8417	1.03645	0.518223	−	0.855246i	$-0.326594\pi$
$829$	29.8417	1.03645	0.518223	+	0.855246i	$0.326594\pi$
$830$	−14.0043	−0.486095
$831$	0	0
$832$	−7.62729	−0.264429
$833$	0	0
$834$	0	0
$835$	−73.2063	−2.53341
$836$	−66.6605	−2.30550
$837$	0	0
$838$	14.8658	0.513530
$839$	−43.0033	−1.48464	−0.742320	−	0.670045i	$-0.766275\pi$
$839$	−43.0033	−1.48464	−0.742320	+	0.670045i	$0.766275\pi$
$840$	0	0
$841$	−28.1488	−0.970649
$842$	60.0953	2.07102
$843$	0	0
$844$	−77.1634	−2.65608
$845$	−3.81471	−0.131230
$846$	0	0
$847$	0	0
$848$	−81.6889	−2.80521
$849$	0	0
$850$	130.188	4.46542
$851$	−0.515711	−0.0176784
$852$	0	0
$853$	−34.1023	−1.16764	−0.583820	−	0.811883i	$-0.698443\pi$
$853$	−34.1023	−1.16764	−0.583820	+	0.811883i	$0.698443\pi$
$854$	0	0
$855$	0	0
$856$	19.2819	0.659043
$857$	−45.7344	−1.56226	−0.781129	−	0.624370i	$-0.785356\pi$
$857$	−45.7344	−1.56226	−0.781129	+	0.624370i	$0.785356\pi$
$858$	0	0
$859$	−15.9861	−0.545437	−0.272719	−	0.962094i	$-0.587923\pi$
$859$	−15.9861	−0.545437	−0.272719	+	0.962094i	$0.587923\pi$
$860$	120.339	4.10352
$861$	0	0
$862$	54.3100	1.84981
$863$	24.5096	0.834315	0.417157	−	0.908834i	$-0.363026\pi$
$863$	24.5096	0.834315	0.417157	+	0.908834i	$0.363026\pi$
$864$	0	0
$865$	74.4343	2.53084
$866$	82.1807	2.79261
$867$	0	0
$868$	0	0
$869$	63.3120	2.14771
$870$	0	0
$871$	10.6620	0.361269
$872$	131.648	4.45815
$873$	0	0
$874$	−25.4137	−0.859630
$875$	0	0
$876$	0	0
$877$	53.4913	1.80627	0.903136	−	0.429354i	$-0.141259\pi$
$877$	53.4913	1.80627	0.903136	+	0.429354i	$0.141259\pi$
$878$	58.4258	1.97177
$879$	0	0
$880$	−172.618	−5.81896
$881$	26.1745	0.881840	0.440920	−	0.897546i	$-0.354652\pi$
$881$	26.1745	0.881840	0.440920	+	0.897546i	$0.354652\pi$
$882$	0	0
$883$	23.1840	0.780202	0.390101	−	0.920772i	$-0.372440\pi$
$883$	23.1840	0.780202	0.390101	+	0.920772i	$0.372440\pi$
$884$	25.1376	0.845469
$885$	0	0
$886$	22.2536	0.747624
$887$	−13.7008	−0.460029	−0.230015	−	0.973187i	$-0.573877\pi$
$887$	−13.7008	−0.460029	−0.230015	+	0.973187i	$0.573877\pi$
$888$	0	0
$889$	0	0
$890$	−19.6132	−0.657435
$891$	0	0
$892$	−96.4223	−3.22846
$893$	−26.4077	−0.883699
$894$	0	0
$895$	−63.2692	−2.11486
$896$	0	0
$897$	0	0
$898$	48.8534	1.63026
$899$	6.93733	0.231373
$900$	0	0
$901$	44.6500	1.48751
$902$	−78.7354	−2.62160
$903$	0	0
$904$	6.77900	0.225466
$905$	−10.7454	−0.357190
$906$	0	0
$907$	25.5621	0.848777	0.424388	−	0.905480i	$-0.360489\pi$
$907$	25.5621	0.848777	0.424388	+	0.905480i	$0.360489\pi$
$908$	92.5249	3.07055
$909$	0	0
$910$	0	0
$911$	−2.07643	−0.0687951	−0.0343976	−	0.999408i	$-0.510951\pi$
$911$	−2.07643	−0.0687951	−0.0343976	+	0.999408i	$0.510951\pi$
$912$	0	0
$913$	−6.66202	−0.220481
$914$	36.9036	1.22066
$915$	0	0
$916$	−25.3198	−0.836589
$917$	0	0
$918$	0	0
$919$	17.8514	0.588863	0.294432	−	0.955673i	$-0.404870\pi$
$919$	17.8514	0.588863	0.294432	+	0.955673i	$0.404870\pi$
$920$	−93.3672	−3.07823
$921$	0	0
$922$	6.98664	0.230093
$923$	−6.58248	−0.216665
$924$	0	0
$925$	1.47886	0.0486245
$926$	6.60881	0.217179
$927$	0	0
$928$	−9.44724	−0.310121
$929$	−37.0553	−1.21575	−0.607873	−	0.794034i	$-0.707977\pi$
$929$	−37.0553	−1.21575	−0.607873	+	0.794034i	$0.707977\pi$
$930$	0	0
$931$	0	0
$932$	128.184	4.19881
$933$	0	0
$934$	−5.23212	−0.171200
$935$	94.3509	3.08560
$936$	0	0
$937$	−39.7540	−1.29871	−0.649354	−	0.760486i	$-0.724961\pi$
$937$	−39.7540	−1.29871	−0.649354	+	0.760486i	$0.724961\pi$
$938$	0	0
$939$	0	0
$940$	−165.956	−5.41290
$941$	−47.3530	−1.54366	−0.771832	−	0.635827i	$-0.780659\pi$
$941$	−47.3530	−1.54366	−0.771832	+	0.635827i	$0.780659\pi$
$942$	0	0
$943$	−21.2076	−0.690614
$944$	37.8097	1.23060
$945$	0	0
$946$	81.0268	2.63441
$947$	−8.80446	−0.286106	−0.143053	−	0.989715i	$-0.545692\pi$
$947$	−8.80446	−0.286106	−0.143053	+	0.989715i	$0.545692\pi$
$948$	0	0
$949$	−7.73517	−0.251094
$950$	72.8763	2.36442
$951$	0	0
$952$	0	0
$953$	−7.72895	−0.250365	−0.125183	−	0.992134i	$-0.539952\pi$
$953$	−7.72895	−0.250365	−0.125183	+	0.992134i	$0.539952\pi$
$954$	0	0
$955$	57.8312	1.87137
$956$	−20.6601	−0.668196
$957$	0	0
$958$	38.2722	1.23652
$959$	0	0
$960$	0	0
$961$	25.5415	0.823920
$962$	0.404161	0.0130307
$963$	0	0
$964$	−36.2243	−1.16671
$965$	−0.248705	−0.00800608
$966$	0	0
$967$	14.3054	0.460030	0.230015	−	0.973187i	$-0.426122\pi$
$967$	14.3054	0.460030	0.230015	+	0.973187i	$0.426122\pi$
$968$	−84.0735	−2.70222
$969$	0	0
$970$	21.0121	0.674658
$971$	−15.1692	−0.486803	−0.243402	−	0.969926i	$-0.578263\pi$
$971$	−15.1692	−0.486803	−0.243402	+	0.969926i	$0.578263\pi$
$972$	0	0
$973$	0	0
$974$	−99.7583	−3.19646
$975$	0	0
$976$	−118.846	−3.80417
$977$	8.25746	0.264180	0.132090	−	0.991238i	$-0.457831\pi$
$977$	8.25746	0.264180	0.132090	+	0.991238i	$0.457831\pi$
$978$	0	0
$979$	−9.33026	−0.298196
$980$	0	0
$981$	0	0
$982$	55.8016	1.78070
$983$	−25.8525	−0.824568	−0.412284	−	0.911055i	$-0.635269\pi$
$983$	−25.8525	−0.824568	−0.412284	+	0.911055i	$0.635269\pi$
$984$	0	0
$985$	−65.3897	−2.08349
$986$	12.5744	0.400449
$987$	0	0
$988$	14.0714	0.447671
$989$	21.8248	0.693988
$990$	0	0
$991$	−56.2100	−1.78557	−0.892785	−	0.450484i	$-0.851252\pi$
$991$	−56.2100	−1.78557	−0.892785	+	0.450484i	$0.851252\pi$
$992$	−76.9981	−2.44469
$993$	0	0
$994$	0	0
$995$	24.5744	0.779059
$996$	0	0
$997$	−37.4789	−1.18697	−0.593484	−	0.804846i	$-0.702248\pi$
$997$	−37.4789	−1.18697	−0.593484	+	0.804846i	$0.702248\pi$
$998$	−70.7237	−2.23872
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bf.1.1		4
3.2	odd	2		1911.2.a.s.1.4		4
7.6	odd	2		819.2.a.k.1.1		4
21.20	even	2		273.2.a.e.1.4	✓	4
84.83	odd	2		4368.2.a.br.1.1		4
105.104	even	2		6825.2.a.bg.1.1		4
273.272	even	2		3549.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.e.1.4	✓	4	21.20	even	2
819.2.a.k.1.1		4	7.6	odd	2
1911.2.a.s.1.4		4	3.2	odd	2
3549.2.a.w.1.1		4	273.272	even	2
4368.2.a.br.1.1		4	84.83	odd	2
5733.2.a.bf.1.1		4	1.1	even	1	trivial
6825.2.a.bg.1.1		4	105.104	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)

\(f(q)\)	\(=\)	\(q-2.61050 q^{2} +4.81471 q^{4} -3.81471 q^{5} -7.34780 q^{8} +O(q^{10})\)	\(q-2.61050 q^{2} +4.81471 q^{4} -3.81471 q^{5} -7.34780 q^{8} +9.95830 q^{10} +4.73730 q^{11} -1.00000 q^{13} +9.55201 q^{16} -5.22100 q^{17} -2.92259 q^{19} -18.3667 q^{20} -12.3667 q^{22} -3.33101 q^{23} +9.55201 q^{25} +2.61050 q^{26} +0.922589 q^{29} +7.51941 q^{31} -10.2399 q^{32} +13.6294 q^{34} +0.154821 q^{37} +7.62942 q^{38} +28.0297 q^{40} +6.36672 q^{41} -6.55201 q^{43} +22.8087 q^{44} +8.69560 q^{46} +9.03571 q^{47} -24.9355 q^{50} -4.81471 q^{52} -8.55201 q^{53} -18.0714 q^{55} -2.40842 q^{58} +3.95830 q^{59} -12.4420 q^{61} -19.6294 q^{62} +7.62729 q^{64} +3.81471 q^{65} -10.6620 q^{67} -25.1376 q^{68} +6.58248 q^{71} +7.73517 q^{73} -0.404161 q^{74} -14.0714 q^{76} +13.3646 q^{79} -36.4381 q^{80} -16.6203 q^{82} -1.40629 q^{83} +19.9166 q^{85} +17.1040 q^{86} -34.8087 q^{88} -1.96953 q^{89} -16.0378 q^{92} -23.5877 q^{94} +11.1488 q^{95} +2.11001 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) \) 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8	\( 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 9 q^{16} - 2 q^{17} - 7 q^{19} - 32 q^{20} - 8 q^{22} - 3 q^{23} + 9 q^{25} + q^{26} - q^{29} - 3 q^{31} - 7 q^{32} + 30 q^{34} + 10 q^{37} + 6 q^{38} + 14 q^{40} - 16 q^{41} + 3 q^{43} + 12 q^{44} - 18 q^{46} + 5 q^{47} - 13 q^{50} - 7 q^{52} - 5 q^{53} - 10 q^{55} - 4 q^{58} - 20 q^{59} - 12 q^{61} - 54 q^{62} + 5 q^{64} + 3 q^{65} - 22 q^{67} - 10 q^{68} + 13 q^{73} + 6 q^{74} + 6 q^{76} + 11 q^{79} - 42 q^{80} - 10 q^{82} + q^{83} + 8 q^{85} + 10 q^{86} - 60 q^{88} - 5 q^{89} - 34 q^{92} - 34 q^{94} - 13 q^{95} + 17 q^{97}+O(q^{100}) \) 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 9 * q^16 - 2 * q^17 - 7 * q^19 - 32 * q^20 - 8 * q^22 - 3 * q^23 + 9 * q^25 + q^26 - q^29 - 3 * q^31 - 7 * q^32 + 30 * q^34 + 10 * q^37 + 6 * q^38 + 14 * q^40 - 16 * q^41 + 3 * q^43 + 12 * q^44 - 18 * q^46 + 5 * q^47 - 13 * q^50 - 7 * q^52 - 5 * q^53 - 10 * q^55 - 4 * q^58 - 20 * q^59 - 12 * q^61 - 54 * q^62 + 5 * q^64 + 3 * q^65 - 22 * q^67 - 10 * q^68 + 13 * q^73 + 6 * q^74 + 6 * q^76 + 11 * q^79 - 42 * q^80 - 10 * q^82 + q^83 + 8 * q^85 + 10 * q^86 - 60 * q^88 - 5 * q^89 - 34 * q^92 - 34 * q^94 - 13 * q^95 + 17 * q^97

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