LMFDB - Embedded newform 5733.2.a.bp.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:	$0$
Dimension:	$5$
Coefficient field:	5.5.375116.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 7x^{2} + 2x - 2 $ x^5 - x^4 - 6x^3 + 7x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.562376$ 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)

$f(q)$	$=$	$q-0.0776754 q^{2} -1.99397 q^{4} -2.20243 q^{5} +0.310233 q^{8} +O(q^{10})$	$q-0.0776754 q^{2} -1.99397 q^{4} -2.20243 q^{5} +0.310233 q^{8} +0.171074 q^{10} -2.91629 q^{11} +1.00000 q^{13} +3.96384 q^{16} -0.393942 q^{17} -0.124751 q^{19} +4.39156 q^{20} +0.226524 q^{22} -3.38187 q^{23} -0.149317 q^{25} -0.0776754 q^{26} +0.642223 q^{29} -5.95780 q^{31} -0.928358 q^{32} +0.0305996 q^{34} +4.18670 q^{37} +0.00969009 q^{38} -0.683265 q^{40} +0.434984 q^{41} -6.74934 q^{43} +5.81499 q^{44} +0.262688 q^{46} -9.46321 q^{47} +0.0115983 q^{50} -1.99397 q^{52} -12.4338 q^{53} +6.42292 q^{55} -0.0498849 q^{58} -7.33555 q^{59} +2.39394 q^{61} +0.462775 q^{62} -7.85556 q^{64} -2.20243 q^{65} +6.14047 q^{67} +0.785507 q^{68} +14.0826 q^{71} +7.55295 q^{73} -0.325204 q^{74} +0.248750 q^{76} -2.37472 q^{79} -8.73006 q^{80} -0.0337875 q^{82} -9.78804 q^{83} +0.867628 q^{85} +0.524258 q^{86} -0.904729 q^{88} -6.40363 q^{89} +6.74335 q^{92} +0.735058 q^{94} +0.274755 q^{95} -14.9096 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) $ 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8	$ 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8} + 2 q^{10} + q^{11} + 5 q^{13} - 13 q^{17} + 7 q^{19} - 13 q^{20} - 19 q^{22} + 4 q^{23} + 16 q^{25} + 12 q^{29} + 6 q^{31} - 21 q^{32} + 7 q^{34} + 11 q^{37} - 14 q^{38} + 11 q^{40} - 10 q^{41} + 10 q^{43} + 29 q^{44} + q^{46} + 4 q^{47} + 29 q^{50} + 6 q^{52} + 9 q^{53} - 12 q^{55} + 34 q^{58} - 7 q^{59} + 23 q^{61} + 24 q^{62} - 13 q^{64} - 3 q^{65} + 25 q^{67} - 20 q^{68} + 27 q^{71} + 18 q^{73} - 15 q^{74} + 2 q^{76} + 8 q^{79} - 41 q^{80} + 26 q^{82} - 12 q^{83} + 10 q^{85} + 19 q^{86} - 36 q^{88} - 29 q^{89} + 50 q^{92} - 2 q^{94} + 33 q^{95} + 13 q^{97}+O(q^{100}) $ 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8 + 2 * q^10 + q^11 + 5 * q^13 - 13 * q^17 + 7 * q^19 - 13 * q^20 - 19 * q^22 + 4 * q^23 + 16 * q^25 + 12 * q^29 + 6 * q^31 - 21 * q^32 + 7 * q^34 + 11 * q^37 - 14 * q^38 + 11 * q^40 - 10 * q^41 + 10 * q^43 + 29 * q^44 + q^46 + 4 * q^47 + 29 * q^50 + 6 * q^52 + 9 * q^53 - 12 * q^55 + 34 * q^58 - 7 * q^59 + 23 * q^61 + 24 * q^62 - 13 * q^64 - 3 * q^65 + 25 * q^67 - 20 * q^68 + 27 * q^71 + 18 * q^73 - 15 * q^74 + 2 * q^76 + 8 * q^79 - 41 * q^80 + 26 * q^82 - 12 * q^83 + 10 * q^85 + 19 * q^86 - 36 * q^88 - 29 * q^89 + 50 * q^92 - 2 * q^94 + 33 * q^95 + 13 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0776754	−0.0549248	−0.0274624	−	0.999623i	$-0.508743\pi$
$2$	−0.0776754	−0.0549248	−0.0274624	+	0.999623i	$0.508743\pi$
$3$	0	0
$3$	0	0
$4$	−1.99397	−0.996983
$5$	−2.20243	−0.984955	−0.492478	−	0.870325i	$-0.663909\pi$
$5$	−2.20243	−0.984955	−0.492478	+	0.870325i	$0.663909\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0.310233	0.109684
$9$	0	0
$10$	0.171074	0.0540984
$11$	−2.91629	−0.879295	−0.439647	−	0.898170i	$-0.644897\pi$
$11$	−2.91629	−0.879295	−0.439647	+	0.898170i	$0.644897\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	3.96384	0.990959
$17$	−0.393942	−0.0955449	−0.0477724	−	0.998858i	$-0.515212\pi$
$17$	−0.393942	−0.0955449	−0.0477724	+	0.998858i	$0.515212\pi$
$18$	0	0
$19$	−0.124751	−0.0286199	−0.0143099	−	0.999898i	$-0.504555\pi$
$19$	−0.124751	−0.0286199	−0.0143099	+	0.999898i	$0.504555\pi$
$20$	4.39156	0.981984
$21$	0	0
$22$	0.226524	0.0482951
$23$	−3.38187	−0.705170	−0.352585	−	0.935780i	$-0.614697\pi$
$23$	−3.38187	−0.705170	−0.352585	+	0.935780i	$0.614697\pi$
$24$	0	0
$25$	−0.149317	−0.0298635
$26$	−0.0776754	−0.0152334
$27$	0	0
$28$	0	0
$29$	0.642223	0.119258	0.0596289	−	0.998221i	$-0.481008\pi$
$29$	0.642223	0.119258	0.0596289	+	0.998221i	$0.481008\pi$
$30$	0	0
$31$	−5.95780	−1.07005	−0.535026	−	0.844835i	$-0.679698\pi$
$31$	−5.95780	−1.07005	−0.535026	+	0.844835i	$0.679698\pi$
$32$	−0.928358	−0.164112
$33$	0	0
$34$	0.0305996	0.00524778
$35$	0	0
$36$	0	0
$37$	4.18670	0.688290	0.344145	−	0.938917i	$-0.388169\pi$
$37$	4.18670	0.688290	0.344145	+	0.938917i	$0.388169\pi$
$38$	0.00969009	0.00157194
$39$	0	0
$40$	−0.683265	−0.108034
$41$	0.434984	0.0679331	0.0339665	−	0.999423i	$-0.489186\pi$
$41$	0.434984	0.0679331	0.0339665	+	0.999423i	$0.489186\pi$
$42$	0	0
$43$	−6.74934	−1.02927	−0.514633	−	0.857411i	$-0.672072\pi$
$43$	−6.74934	−1.02927	−0.514633	+	0.857411i	$0.672072\pi$
$44$	5.81499	0.876642
$45$	0	0
$46$	0.262688	0.0387313
$47$	−9.46321	−1.38035	−0.690175	−	0.723642i	$-0.742467\pi$
$47$	−9.46321	−1.38035	−0.690175	+	0.723642i	$0.742467\pi$
$48$	0	0
$49$	0	0
$50$	0.0115983	0.00164024
$51$	0	0
$52$	−1.99397	−0.276513
$53$	−12.4338	−1.70792	−0.853959	−	0.520341i	$-0.825805\pi$
$53$	−12.4338	−1.70792	−0.853959	+	0.520341i	$0.825805\pi$
$54$	0	0
$55$	6.42292	0.866066
$56$	0	0
$57$	0	0
$58$	−0.0498849	−0.00655021
$59$	−7.33555	−0.955007	−0.477504	−	0.878630i	$-0.658458\pi$
$59$	−7.33555	−0.955007	−0.477504	+	0.878630i	$0.658458\pi$
$60$	0	0
$61$	2.39394	0.306513	0.153256	−	0.988186i	$-0.451024\pi$
$61$	2.39394	0.306513	0.153256	+	0.988186i	$0.451024\pi$
$62$	0.462775	0.0587724
$63$	0	0
$64$	−7.85556	−0.981945
$65$	−2.20243	−0.273177
$66$	0	0
$67$	6.14047	0.750178	0.375089	−	0.926989i	$-0.377612\pi$
$67$	6.14047	0.750178	0.375089	+	0.926989i	$0.377612\pi$
$68$	0.785507	0.0952567
$69$	0	0
$70$	0	0
$71$	14.0826	1.67129	0.835646	−	0.549269i	$-0.185094\pi$
$71$	14.0826	1.67129	0.835646	+	0.549269i	$0.185094\pi$
$72$	0	0
$73$	7.55295	0.884006	0.442003	−	0.897014i	$-0.354268\pi$
$73$	7.55295	0.884006	0.442003	+	0.897014i	$0.354268\pi$
$74$	−0.325204	−0.0378042
$75$	0	0
$76$	0.248750	0.0285335
$77$	0	0
$78$	0	0
$79$	−2.37472	−0.267177	−0.133589	−	0.991037i	$-0.542650\pi$
$79$	−2.37472	−0.267177	−0.133589	+	0.991037i	$0.542650\pi$
$80$	−8.73006	−0.976050
$81$	0	0
$82$	−0.0337875	−0.00373121
$83$	−9.78804	−1.07438	−0.537189	−	0.843462i	$-0.680514\pi$
$83$	−9.78804	−1.07438	−0.537189	+	0.843462i	$0.680514\pi$
$84$	0	0
$85$	0.867628	0.0941074
$86$	0.524258	0.0565322
$87$	0	0
$88$	−0.904729	−0.0964445
$89$	−6.40363	−0.678784	−0.339392	−	0.940645i	$-0.610221\pi$
$89$	−6.40363	−0.678784	−0.339392	+	0.940645i	$0.610221\pi$
$90$	0	0
$91$	0	0
$92$	6.74335	0.703042
$93$	0	0
$94$	0.735058	0.0758155
$95$	0.274755	0.0281893
$96$	0	0
$97$	−14.9096	−1.51384	−0.756919	−	0.653509i	$-0.773296\pi$
$97$	−14.9096	−1.51384	−0.756919	+	0.653509i	$0.773296\pi$
$98$	0	0
$99$	0	0
$100$	0.297734	0.0297734
$101$	−19.9821	−1.98829	−0.994145	−	0.108057i	$-0.965537\pi$
$101$	−19.9821	−1.98829	−0.994145	+	0.108057i	$0.965537\pi$
$102$	0	0
$103$	14.6745	1.44592	0.722960	−	0.690890i	$-0.242781\pi$
$103$	14.6745	1.44592	0.722960	+	0.690890i	$0.242781\pi$
$104$	0.310233	0.0304208
$105$	0	0
$106$	0.965802	0.0938070
$107$	5.03973	0.487209	0.243604	−	0.969875i	$-0.421670\pi$
$107$	5.03973	0.487209	0.243604	+	0.969875i	$0.421670\pi$
$108$	0	0
$109$	−0.122682	−0.0117508	−0.00587542	−	0.999983i	$-0.501870\pi$
$109$	−0.122682	−0.0117508	−0.00587542	+	0.999983i	$0.501870\pi$
$110$	−0.498902	−0.0475685
$111$	0	0
$112$	0	0
$113$	4.16138	0.391470	0.195735	−	0.980657i	$-0.437291\pi$
$113$	4.16138	0.391470	0.195735	+	0.980657i	$0.437291\pi$
$114$	0	0
$115$	7.44833	0.694560
$116$	−1.28057	−0.118898
$117$	0	0
$118$	0.569792	0.0524536
$119$	0	0
$120$	0	0
$121$	−2.49525	−0.226841
$122$	−0.185950	−0.0168352
$123$	0	0
$124$	11.8797	1.06682
$125$	11.3410	1.01437
$126$	0	0
$127$	14.9711	1.32847	0.664237	−	0.747522i	$-0.268756\pi$
$127$	14.9711	1.32847	0.664237	+	0.747522i	$0.268756\pi$
$128$	2.46690	0.218045
$129$	0	0
$130$	0.171074	0.0150042
$131$	18.7422	1.63751	0.818755	−	0.574143i	$-0.194665\pi$
$131$	18.7422	1.63751	0.818755	+	0.574143i	$0.194665\pi$
$132$	0	0
$133$	0	0
$134$	−0.476964	−0.0412034
$135$	0	0
$136$	−0.122214	−0.0104797
$137$	13.5905	1.16111	0.580557	−	0.814219i	$-0.302835\pi$
$137$	13.5905	1.16111	0.580557	+	0.814219i	$0.302835\pi$
$138$	0	0
$139$	15.7292	1.33413	0.667066	−	0.744999i	$-0.267550\pi$
$139$	15.7292	1.33413	0.667066	+	0.744999i	$0.267550\pi$
$140$	0	0
$141$	0	0
$142$	−1.09387	−0.0917953
$143$	−2.91629	−0.243873
$144$	0	0
$145$	−1.41445	−0.117464
$146$	−0.586678	−0.0485538
$147$	0	0
$148$	−8.34815	−0.686213
$149$	−3.34809	−0.274286	−0.137143	−	0.990551i	$-0.543792\pi$
$149$	−3.34809	−0.274286	−0.137143	+	0.990551i	$0.543792\pi$
$150$	0	0
$151$	−20.4476	−1.66401	−0.832003	−	0.554771i	$-0.812806\pi$
$151$	−20.4476	−1.66401	−0.832003	+	0.554771i	$0.812806\pi$
$152$	−0.0387019	−0.00313914
$153$	0	0
$154$	0	0
$155$	13.1216	1.05395
$156$	0	0
$157$	−10.2014	−0.814158	−0.407079	−	0.913393i	$-0.633453\pi$
$157$	−10.2014	−0.814158	−0.407079	+	0.913393i	$0.633453\pi$
$158$	0.184457	0.0146746
$159$	0	0
$160$	2.04464	0.161643
$161$	0	0
$162$	0	0
$163$	15.5835	1.22060	0.610299	−	0.792171i	$-0.291049\pi$
$163$	15.5835	1.22060	0.610299	+	0.792171i	$0.291049\pi$
$164$	−0.867344	−0.0677282
$165$	0	0
$166$	0.760290	0.0590099
$167$	1.53310	0.118635	0.0593174	−	0.998239i	$-0.481108\pi$
$167$	1.53310	0.118635	0.0593174	+	0.998239i	$0.481108\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−0.0673933	−0.00516883
$171$	0	0
$172$	13.4580	1.02616
$173$	−13.9844	−1.06322	−0.531609	−	0.846990i	$-0.678412\pi$
$173$	−13.9844	−1.06322	−0.531609	+	0.846990i	$0.678412\pi$
$174$	0	0
$175$	0	0
$176$	−11.5597	−0.871345
$177$	0	0
$178$	0.497404	0.0372820
$179$	21.9304	1.63915	0.819577	−	0.572969i	$-0.194208\pi$
$179$	21.9304	1.63915	0.819577	+	0.572969i	$0.194208\pi$
$180$	0	0
$181$	−0.955265	−0.0710043	−0.0355021	−	0.999370i	$-0.511303\pi$
$181$	−0.955265	−0.0710043	−0.0355021	+	0.999370i	$0.511303\pi$
$182$	0	0
$183$	0	0
$184$	−1.04917	−0.0773457
$185$	−9.22091	−0.677934
$186$	0	0
$187$	1.14885	0.0840121
$188$	18.8693	1.37619
$189$	0	0
$190$	−0.0213417	−0.00154829
$191$	−19.6834	−1.42424	−0.712121	−	0.702056i	$-0.752265\pi$
$191$	−19.6834	−1.42424	−0.712121	+	0.702056i	$0.752265\pi$
$192$	0	0
$193$	15.0951	1.08657	0.543283	−	0.839550i	$-0.317181\pi$
$193$	15.0951	1.08657	0.543283	+	0.839550i	$0.317181\pi$
$194$	1.15811	0.0831472
$195$	0	0
$196$	0	0
$197$	11.0323	0.786015	0.393008	−	0.919535i	$-0.371435\pi$
$197$	11.0323	0.786015	0.393008	+	0.919535i	$0.371435\pi$
$198$	0	0
$199$	−7.17701	−0.508765	−0.254382	−	0.967104i	$-0.581872\pi$
$199$	−7.17701	−0.508765	−0.254382	+	0.967104i	$0.581872\pi$
$200$	−0.0463231	−0.00327554
$201$	0	0
$202$	1.55211	0.109206
$203$	0	0
$204$	0	0
$205$	−0.958020	−0.0669110
$206$	−1.13985	−0.0794168
$207$	0	0
$208$	3.96384	0.274843
$209$	0.363811	0.0251653
$210$	0	0
$211$	15.7119	1.08165	0.540825	−	0.841135i	$-0.318112\pi$
$211$	15.7119	1.08165	0.540825	+	0.841135i	$0.318112\pi$
$212$	24.7926	1.70277
$213$	0	0
$214$	−0.391463	−0.0267598
$215$	14.8649	1.01378
$216$	0	0
$217$	0	0
$218$	0.00952939	0.000645412 0
$219$	0	0
$220$	−12.8071	−0.863453
$221$	−0.393942	−0.0264994
$222$	0	0
$223$	−6.20889	−0.415778	−0.207889	−	0.978152i	$-0.566659\pi$
$223$	−6.20889	−0.415778	−0.207889	+	0.978152i	$0.566659\pi$
$224$	0	0
$225$	0	0
$226$	−0.323237	−0.0215014
$227$	23.6879	1.57222	0.786111	−	0.618085i	$-0.212091\pi$
$227$	23.6879	1.57222	0.786111	+	0.618085i	$0.212091\pi$
$228$	0	0
$229$	9.04226	0.597530	0.298765	−	0.954327i	$-0.403425\pi$
$229$	9.04226	0.597530	0.298765	+	0.954327i	$0.403425\pi$
$230$	−0.578552	−0.0381486
$231$	0	0
$232$	0.199239	0.0130807
$233$	−5.34449	−0.350129	−0.175065	−	0.984557i	$-0.556013\pi$
$233$	−5.34449	−0.350129	−0.175065	+	0.984557i	$0.556013\pi$
$234$	0	0
$235$	20.8420	1.35958
$236$	14.6268	0.952126
$237$	0	0
$238$	0	0
$239$	27.2548	1.76297	0.881484	−	0.472215i	$-0.156545\pi$
$239$	27.2548	1.76297	0.881484	+	0.472215i	$0.156545\pi$
$240$	0	0
$241$	15.6761	1.00979	0.504894	−	0.863182i	$-0.331532\pi$
$241$	15.6761	1.00979	0.504894	+	0.863182i	$0.331532\pi$
$242$	0.193819	0.0124592
$243$	0	0
$244$	−4.77344	−0.305588
$245$	0	0
$246$	0	0
$247$	−0.124751	−0.00793773
$248$	−1.84831	−0.117368
$249$	0	0
$250$	−0.880916	−0.0557140
$251$	−18.2218	−1.15015	−0.575075	−	0.818101i	$-0.695027\pi$
$251$	−18.2218	−1.15015	−0.575075	+	0.818101i	$0.695027\pi$
$252$	0	0
$253$	9.86253	0.620052
$254$	−1.16289	−0.0729662
$255$	0	0
$256$	15.5195	0.969969
$257$	15.0614	0.939502	0.469751	−	0.882799i	$-0.344344\pi$
$257$	15.0614	0.939502	0.469751	+	0.882799i	$0.344344\pi$
$258$	0	0
$259$	0	0
$260$	4.39156	0.272353
$261$	0	0
$262$	−1.45580	−0.0899399
$263$	27.7916	1.71370	0.856852	−	0.515563i	$-0.172417\pi$
$263$	27.7916	1.71370	0.856852	+	0.515563i	$0.172417\pi$
$264$	0	0
$265$	27.3846	1.68222
$266$	0	0
$267$	0	0
$268$	−12.2439	−0.747915
$269$	−8.00809	−0.488262	−0.244131	−	0.969742i	$-0.578503\pi$
$269$	−8.00809	−0.488262	−0.244131	+	0.969742i	$0.578503\pi$
$270$	0	0
$271$	−20.2645	−1.23098	−0.615490	−	0.788144i	$-0.711042\pi$
$271$	−20.2645	−1.23098	−0.615490	+	0.788144i	$0.711042\pi$
$272$	−1.56152	−0.0946811
$273$	0	0
$274$	−1.05565	−0.0637740
$275$	0.435453	0.0262588
$276$	0	0
$277$	−29.4339	−1.76851	−0.884256	−	0.467003i	$-0.845334\pi$
$277$	−29.4339	−1.76851	−0.884256	+	0.467003i	$0.845334\pi$
$278$	−1.22177	−0.0732769
$279$	0	0
$280$	0	0
$281$	3.76735	0.224741	0.112371	−	0.993666i	$-0.464156\pi$
$281$	3.76735	0.224741	0.112371	+	0.993666i	$0.464156\pi$
$282$	0	0
$283$	−22.4407	−1.33396	−0.666980	−	0.745075i	$-0.732414\pi$
$283$	−22.4407	−1.33396	−0.666980	+	0.745075i	$0.732414\pi$
$284$	−28.0801	−1.66625
$285$	0	0
$286$	0.226524	0.0133946
$287$	0	0
$288$	0	0
$289$	−16.8448	−0.990871
$290$	0.109868	0.00645166
$291$	0	0
$292$	−15.0603	−0.881339
$293$	8.13635	0.475331	0.237665	−	0.971347i	$-0.423618\pi$
$293$	8.13635	0.475331	0.237665	+	0.971347i	$0.423618\pi$
$294$	0	0
$295$	16.1560	0.940639
$296$	1.29885	0.0754943
$297$	0	0
$298$	0.260064	0.0150651
$299$	−3.38187	−0.195579
$300$	0	0
$301$	0	0
$302$	1.58828	0.0913951
$303$	0	0
$304$	−0.494493	−0.0283611
$305$	−5.27248	−0.301901
$306$	0	0
$307$	−18.9247	−1.08009	−0.540046	−	0.841636i	$-0.681593\pi$
$307$	−18.9247	−1.08009	−0.540046	+	0.841636i	$0.681593\pi$
$308$	0	0
$309$	0	0
$310$	−1.01923	−0.0578882
$311$	11.6189	0.658849	0.329425	−	0.944182i	$-0.393145\pi$
$311$	11.6189	0.658849	0.329425	+	0.944182i	$0.393145\pi$
$312$	0	0
$313$	11.7023	0.661455	0.330727	−	0.943726i	$-0.392706\pi$
$313$	11.7023	0.661455	0.330727	+	0.943726i	$0.392706\pi$
$314$	0.792395	0.0447174
$315$	0	0
$316$	4.73512	0.266371
$317$	33.0069	1.85385	0.926926	−	0.375244i	$-0.122441\pi$
$317$	33.0069	1.85385	0.926926	+	0.375244i	$0.122441\pi$
$318$	0	0
$319$	−1.87291	−0.104863
$320$	17.3013	0.967172
$321$	0	0
$322$	0	0
$323$	0.0491447	0.00273448
$324$	0	0
$325$	−0.149317	−0.00828263
$326$	−1.21046	−0.0670411
$327$	0	0
$328$	0.134946	0.00745116
$329$	0	0
$330$	0	0
$331$	14.7746	0.812085	0.406043	−	0.913854i	$-0.366908\pi$
$331$	14.7746	0.812085	0.406043	+	0.913854i	$0.366908\pi$
$332$	19.5170	1.07114
$333$	0	0
$334$	−0.119084	−0.00651599
$335$	−13.5239	−0.738892
$336$	0	0
$337$	−13.0713	−0.712041	−0.356020	−	0.934478i	$-0.615867\pi$
$337$	−13.0713	−0.712041	−0.356020	+	0.934478i	$0.615867\pi$
$338$	−0.0776754	−0.00422498
$339$	0	0
$340$	−1.73002	−0.0938235
$341$	17.3747	0.940892
$342$	0	0
$343$	0	0
$344$	−2.09387	−0.112894
$345$	0	0
$346$	1.08625	0.0583970
$347$	−6.37950	−0.342469	−0.171235	−	0.985230i	$-0.554776\pi$
$347$	−6.37950	−0.342469	−0.171235	+	0.985230i	$0.554776\pi$
$348$	0	0
$349$	10.3287	0.552881	0.276441	−	0.961031i	$-0.410845\pi$
$349$	10.3287	0.552881	0.276441	+	0.961031i	$0.410845\pi$
$350$	0	0
$351$	0	0
$352$	2.70736	0.144303
$353$	−30.1517	−1.60481	−0.802407	−	0.596777i	$-0.796448\pi$
$353$	−30.1517	−1.60481	−0.802407	+	0.596777i	$0.796448\pi$
$354$	0	0
$355$	−31.0158	−1.64615
$356$	12.7686	0.676736
$357$	0	0
$358$	−1.70345	−0.0900302
$359$	29.1771	1.53991	0.769955	−	0.638098i	$-0.220279\pi$
$359$	29.1771	1.53991	0.769955	+	0.638098i	$0.220279\pi$
$360$	0	0
$361$	−18.9844	−0.999181
$362$	0.0742005	0.00389989
$363$	0	0
$364$	0	0
$365$	−16.6348	−0.870706
$366$	0	0
$367$	4.48431	0.234079	0.117040	−	0.993127i	$-0.462660\pi$
$367$	4.48431	0.234079	0.117040	+	0.993127i	$0.462660\pi$
$368$	−13.4052	−0.698794
$369$	0	0
$370$	0.716237	0.0372354
$371$	0	0
$372$	0	0
$373$	23.9891	1.24211	0.621055	−	0.783767i	$-0.286704\pi$
$373$	23.9891	1.24211	0.621055	+	0.783767i	$0.286704\pi$
$374$	−0.0892372	−0.00461435
$375$	0	0
$376$	−2.93580	−0.151402
$377$	0.642223	0.0330762
$378$	0	0
$379$	20.2228	1.03878	0.519389	−	0.854538i	$-0.326160\pi$
$379$	20.2228	1.03878	0.519389	+	0.854538i	$0.326160\pi$
$380$	−0.547853	−0.0281043
$381$	0	0
$382$	1.52892	0.0782262
$383$	−23.0819	−1.17943	−0.589714	−	0.807612i	$-0.700760\pi$
$383$	−23.0819	−1.17943	−0.589714	+	0.807612i	$0.700760\pi$
$384$	0	0
$385$	0	0
$386$	−1.17251	−0.0596794
$387$	0	0
$388$	29.7292	1.50927
$389$	33.3369	1.69025	0.845124	−	0.534570i	$-0.179526\pi$
$389$	33.3369	1.69025	0.845124	+	0.534570i	$0.179526\pi$
$390$	0	0
$391$	1.33226	0.0673754
$392$	0	0
$393$	0	0
$394$	−0.856934	−0.0431717
$395$	5.23015	0.263157
$396$	0	0
$397$	20.1880	1.01321	0.506605	−	0.862179i	$-0.330900\pi$
$397$	20.1880	1.01321	0.506605	+	0.862179i	$0.330900\pi$
$398$	0.557477	0.0279438
$399$	0	0
$400$	−0.591869	−0.0295935
$401$	4.21487	0.210481	0.105240	−	0.994447i	$-0.466439\pi$
$401$	4.21487	0.210481	0.105240	+	0.994447i	$0.466439\pi$
$402$	0	0
$403$	−5.95780	−0.296779
$404$	39.8436	1.98229
$405$	0	0
$406$	0	0
$407$	−12.2096	−0.605210
$408$	0	0
$409$	−7.44627	−0.368195	−0.184097	−	0.982908i	$-0.558936\pi$
$409$	−7.44627	−0.368195	−0.184097	+	0.982908i	$0.558936\pi$
$410$	0.0744146	0.00367507
$411$	0	0
$412$	−29.2604	−1.44156
$413$	0	0
$414$	0	0
$415$	21.5574	1.05821
$416$	−0.928358	−0.0455165
$417$	0	0
$418$	−0.0282591	−0.00138220
$419$	−12.2817	−0.600000	−0.300000	−	0.953939i	$-0.596987\pi$
$419$	−12.2817	−0.600000	−0.300000	+	0.953939i	$0.596987\pi$
$420$	0	0
$421$	26.9884	1.31533	0.657667	−	0.753309i	$-0.271544\pi$
$421$	26.9884	1.31533	0.657667	+	0.753309i	$0.271544\pi$
$422$	−1.22042	−0.0594093
$423$	0	0
$424$	−3.85738	−0.187331
$425$	0.0588223	0.00285330
$426$	0	0
$427$	0	0
$428$	−10.0490	−0.485739
$429$	0	0
$430$	−1.15464	−0.0556816
$431$	20.3167	0.978621	0.489310	−	0.872110i	$-0.337248\pi$
$431$	20.3167	0.978621	0.489310	+	0.872110i	$0.337248\pi$
$432$	0	0
$433$	9.02891	0.433902	0.216951	−	0.976183i	$-0.430389\pi$
$433$	9.02891	0.433902	0.216951	+	0.976183i	$0.430389\pi$
$434$	0	0
$435$	0	0
$436$	0.244624	0.0117154
$437$	0.421893	0.0201819
$438$	0	0
$439$	−10.0349	−0.478940	−0.239470	−	0.970904i	$-0.576974\pi$
$439$	−10.0349	−0.478940	−0.239470	+	0.970904i	$0.576974\pi$
$440$	1.99260	0.0949935
$441$	0	0
$442$	0.0305996	0.00145547
$443$	33.6409	1.59833	0.799165	−	0.601112i	$-0.205275\pi$
$443$	33.6409	1.59833	0.799165	+	0.601112i	$0.205275\pi$
$444$	0	0
$445$	14.1035	0.668571
$446$	0.482278	0.0228365
$447$	0	0
$448$	0	0
$449$	−1.21577	−0.0573759	−0.0286879	−	0.999588i	$-0.509133\pi$
$449$	−1.21577	−0.0573759	−0.0286879	+	0.999588i	$0.509133\pi$
$450$	0	0
$451$	−1.26854	−0.0597332
$452$	−8.29766	−0.390289
$453$	0	0
$454$	−1.83997	−0.0863540
$455$	0	0
$456$	0	0
$457$	−28.4334	−1.33006	−0.665029	−	0.746817i	$-0.731581\pi$
$457$	−28.4334	−1.33006	−0.665029	+	0.746817i	$0.731581\pi$
$458$	−0.702361	−0.0328192
$459$	0	0
$460$	−14.8517	−0.692465
$461$	30.9864	1.44318	0.721590	−	0.692320i	$-0.243412\pi$
$461$	30.9864	1.44318	0.721590	+	0.692320i	$0.243412\pi$
$462$	0	0
$463$	−14.7992	−0.687779	−0.343889	−	0.939010i	$-0.611745\pi$
$463$	−14.7992	−0.687779	−0.343889	+	0.939010i	$0.611745\pi$
$464$	2.54567	0.118180
$465$	0	0
$466$	0.415135	0.0192308
$467$	−1.82996	−0.0846804	−0.0423402	−	0.999103i	$-0.513481\pi$
$467$	−1.82996	−0.0846804	−0.0423402	+	0.999103i	$0.513481\pi$
$468$	0	0
$469$	0	0
$470$	−1.61891	−0.0746748
$471$	0	0
$472$	−2.27573	−0.104749
$473$	19.6830	0.905027
$474$	0	0
$475$	0.0186275	0.000854689 0
$476$	0	0
$477$	0	0
$478$	−2.11703	−0.0968306
$479$	9.34659	0.427057	0.213528	−	0.976937i	$-0.431504\pi$
$479$	9.34659	0.427057	0.213528	+	0.976937i	$0.431504\pi$
$480$	0	0
$481$	4.18670	0.190897
$482$	−1.21765	−0.0554623
$483$	0	0
$484$	4.97544	0.226156
$485$	32.8372	1.49106
$486$	0	0
$487$	23.3739	1.05917	0.529587	−	0.848256i	$-0.322347\pi$
$487$	23.3739	1.05917	0.529587	+	0.848256i	$0.322347\pi$
$488$	0.742679	0.0336195
$489$	0	0
$490$	0	0
$491$	21.4726	0.969044	0.484522	−	0.874779i	$-0.338993\pi$
$491$	21.4726	0.969044	0.484522	+	0.874779i	$0.338993\pi$
$492$	0	0
$493$	−0.252998	−0.0113945
$494$	0.00969009	0.000435978 0
$495$	0	0
$496$	−23.6157	−1.06038
$497$	0	0
$498$	0	0
$499$	−22.1915	−0.993427	−0.496714	−	0.867915i	$-0.665460\pi$
$499$	−22.1915	−0.993427	−0.496714	+	0.867915i	$0.665460\pi$
$500$	−22.6136	−1.01131
$501$	0	0
$502$	1.41539	0.0631718
$503$	17.3231	0.772399	0.386200	−	0.922415i	$-0.373788\pi$
$503$	17.3231	0.772399	0.386200	+	0.922415i	$0.373788\pi$
$504$	0	0
$505$	44.0090	1.95838
$506$	−0.766076	−0.0340562
$507$	0	0
$508$	−29.8520	−1.32447
$509$	−26.8613	−1.19061	−0.595303	−	0.803502i	$-0.702968\pi$
$509$	−26.8613	−1.19061	−0.595303	+	0.803502i	$0.702968\pi$
$510$	0	0
$511$	0	0
$512$	−6.13928	−0.271321
$513$	0	0
$514$	−1.16990	−0.0516019
$515$	−32.3195	−1.42417
$516$	0	0
$517$	27.5975	1.21374
$518$	0	0
$519$	0	0
$520$	−0.683265	−0.0299632
$521$	−10.2029	−0.446998	−0.223499	−	0.974704i	$-0.571748\pi$
$521$	−10.2029	−0.446998	−0.223499	+	0.974704i	$0.571748\pi$
$522$	0	0
$523$	−11.9147	−0.520992	−0.260496	−	0.965475i	$-0.583886\pi$
$523$	−11.9147	−0.520992	−0.260496	+	0.965475i	$0.583886\pi$
$524$	−37.3712	−1.63257
$525$	0	0
$526$	−2.15872	−0.0941248
$527$	2.34703	0.102238
$528$	0	0
$529$	−11.5629	−0.502736
$530$	−2.12711	−0.0923957
$531$	0	0
$532$	0	0
$533$	0.434984	0.0188412
$534$	0	0
$535$	−11.0996	−0.479879
$536$	1.90498	0.0822825
$537$	0	0
$538$	0.622031	0.0268177
$539$	0	0
$540$	0	0
$541$	19.9687	0.858520	0.429260	−	0.903181i	$-0.358774\pi$
$541$	19.9687	0.858520	0.429260	+	0.903181i	$0.358774\pi$
$542$	1.57405	0.0676114
$543$	0	0
$544$	0.365719	0.0156801
$545$	0.270199	0.0115740
$546$	0	0
$547$	−16.7640	−0.716778	−0.358389	−	0.933572i	$-0.616674\pi$
$547$	−16.7640	−0.716778	−0.358389	+	0.933572i	$0.616674\pi$
$548$	−27.0990	−1.15761
$549$	0	0
$550$	−0.0338239	−0.00144226
$551$	−0.0801180	−0.00341314
$552$	0	0
$553$	0	0
$554$	2.28629	0.0971351
$555$	0	0
$556$	−31.3635	−1.33011
$557$	−23.3797	−0.990628	−0.495314	−	0.868714i	$-0.664947\pi$
$557$	−23.3797	−0.990628	−0.495314	+	0.868714i	$0.664947\pi$
$558$	0	0
$559$	−6.74934	−0.285467
$560$	0	0
$561$	0	0
$562$	−0.292630	−0.0123439
$563$	42.0038	1.77025	0.885124	−	0.465355i	$-0.154073\pi$
$563$	42.0038	1.77025	0.885124	+	0.465355i	$0.154073\pi$
$564$	0	0
$565$	−9.16514	−0.385580
$566$	1.74309	0.0732675
$567$	0	0
$568$	4.36887	0.183314
$569$	−12.5796	−0.527366	−0.263683	−	0.964609i	$-0.584937\pi$
$569$	−12.5796	−0.527366	−0.263683	+	0.964609i	$0.584937\pi$
$570$	0	0
$571$	−8.79876	−0.368217	−0.184108	−	0.982906i	$-0.558940\pi$
$571$	−8.79876	−0.368217	−0.184108	+	0.982906i	$0.558940\pi$
$572$	5.81499	0.243137
$573$	0	0
$574$	0	0
$575$	0.504972	0.0210588
$576$	0	0
$577$	−1.41370	−0.0588531	−0.0294266	−	0.999567i	$-0.509368\pi$
$577$	−1.41370	−0.0588531	−0.0294266	+	0.999567i	$0.509368\pi$
$578$	1.30843	0.0544234
$579$	0	0
$580$	2.82036	0.117109
$581$	0	0
$582$	0	0
$583$	36.2607	1.50176
$584$	2.34317	0.0969612
$585$	0	0
$586$	−0.631994	−0.0261074
$587$	−24.3046	−1.00316	−0.501580	−	0.865111i	$-0.667248\pi$
$587$	−24.3046	−1.00316	−0.501580	+	0.865111i	$0.667248\pi$
$588$	0	0
$589$	0.743243	0.0306248
$590$	−1.25492	−0.0516644
$591$	0	0
$592$	16.5954	0.682067
$593$	−26.7063	−1.09670	−0.548348	−	0.836250i	$-0.684743\pi$
$593$	−26.7063	−1.09670	−0.548348	+	0.836250i	$0.684743\pi$
$594$	0	0
$595$	0	0
$596$	6.67597	0.273459
$597$	0	0
$598$	0.262688	0.0107421
$599$	33.6537	1.37505	0.687526	−	0.726160i	$-0.258697\pi$
$599$	33.6537	1.37505	0.687526	+	0.726160i	$0.258697\pi$
$600$	0	0
$601$	12.5737	0.512890	0.256445	−	0.966559i	$-0.417449\pi$
$601$	12.5737	0.512890	0.256445	+	0.966559i	$0.417449\pi$
$602$	0	0
$603$	0	0
$604$	40.7719	1.65899
$605$	5.49560	0.223428
$606$	0	0
$607$	−21.4417	−0.870292	−0.435146	−	0.900360i	$-0.643303\pi$
$607$	−21.4417	−0.870292	−0.435146	+	0.900360i	$0.643303\pi$
$608$	0.115814	0.00469687
$609$	0	0
$610$	0.409542	0.0165819
$611$	−9.46321	−0.382840
$612$	0	0
$613$	30.7261	1.24102	0.620509	−	0.784200i	$-0.286926\pi$
$613$	30.7261	1.24102	0.620509	+	0.784200i	$0.286926\pi$
$614$	1.46999	0.0593238
$615$	0	0
$616$	0	0
$617$	−0.216739	−0.00872559	−0.00436279	−	0.999990i	$-0.501389\pi$
$617$	−0.216739	−0.00872559	−0.00436279	+	0.999990i	$0.501389\pi$
$618$	0	0
$619$	−30.4980	−1.22582	−0.612909	−	0.790153i	$-0.710001\pi$
$619$	−30.4980	−1.22582	−0.612909	+	0.790153i	$0.710001\pi$
$620$	−26.1641	−1.05077
$621$	0	0
$622$	−0.902505	−0.0361871
$623$	0	0
$624$	0	0
$625$	−24.2311	−0.969245
$626$	−0.908983	−0.0363303
$627$	0	0
$628$	20.3412	0.811702
$629$	−1.64932	−0.0657626
$630$	0	0
$631$	−14.0505	−0.559343	−0.279671	−	0.960096i	$-0.590226\pi$
$631$	−14.0505	−0.559343	−0.279671	+	0.960096i	$0.590226\pi$
$632$	−0.736717	−0.0293050
$633$	0	0
$634$	−2.56382	−0.101822
$635$	−32.9729	−1.30849
$636$	0	0
$637$	0	0
$638$	0.145479	0.00575956
$639$	0	0
$640$	−5.43317	−0.214765
$641$	18.1731	0.717796	0.358898	−	0.933377i	$-0.383153\pi$
$641$	18.1731	0.717796	0.358898	+	0.933377i	$0.383153\pi$
$642$	0	0
$643$	7.27895	0.287054	0.143527	−	0.989646i	$-0.454156\pi$
$643$	7.27895	0.287054	0.143527	+	0.989646i	$0.454156\pi$
$644$	0	0
$645$	0	0
$646$	−0.00381733	−0.000150191 0
$647$	17.7797	0.698992	0.349496	−	0.936938i	$-0.386353\pi$
$647$	17.7797	0.698992	0.349496	+	0.936938i	$0.386353\pi$
$648$	0	0
$649$	21.3926	0.839733
$650$	0.0115983	0.000454922 0
$651$	0	0
$652$	−31.0731	−1.21692
$653$	−8.13253	−0.318251	−0.159125	−	0.987258i	$-0.550867\pi$
$653$	−8.13253	−0.318251	−0.159125	+	0.987258i	$0.550867\pi$
$654$	0	0
$655$	−41.2782	−1.61287
$656$	1.72421	0.0673189
$657$	0	0
$658$	0	0
$659$	−10.0958	−0.393278	−0.196639	−	0.980476i	$-0.563003\pi$
$659$	−10.0958	−0.393278	−0.196639	+	0.980476i	$0.563003\pi$
$660$	0	0
$661$	−24.3455	−0.946928	−0.473464	−	0.880813i	$-0.656997\pi$
$661$	−24.3455	−0.946928	−0.473464	+	0.880813i	$0.656997\pi$
$662$	−1.14762	−0.0446036
$663$	0	0
$664$	−3.03657	−0.117842
$665$	0	0
$666$	0	0
$667$	−2.17192	−0.0840970
$668$	−3.05695	−0.118277
$669$	0	0
$670$	1.05048	0.0405835
$671$	−6.98143	−0.269515
$672$	0	0
$673$	−39.4811	−1.52189	−0.760943	−	0.648819i	$-0.775263\pi$
$673$	−39.4811	−1.52189	−0.760943	+	0.648819i	$0.775263\pi$
$674$	1.01532	0.0391087
$675$	0	0
$676$	−1.99397	−0.0766910
$677$	17.9830	0.691144	0.345572	−	0.938392i	$-0.387685\pi$
$677$	17.9830	0.691144	0.345572	+	0.938392i	$0.387685\pi$
$678$	0	0
$679$	0	0
$680$	0.269167	0.0103221
$681$	0	0
$682$	−1.34959	−0.0516783
$683$	−15.3265	−0.586452	−0.293226	−	0.956043i	$-0.594729\pi$
$683$	−15.3265	−0.586452	−0.293226	+	0.956043i	$0.594729\pi$
$684$	0	0
$685$	−29.9321	−1.14365
$686$	0	0
$687$	0	0
$688$	−26.7533	−1.01996
$689$	−12.4338	−0.473691
$690$	0	0
$691$	25.2599	0.960931	0.480466	−	0.877014i	$-0.340468\pi$
$691$	25.2599	0.960931	0.480466	+	0.877014i	$0.340468\pi$
$692$	27.8845	1.06001
$693$	0	0
$694$	0.495530	0.0188101
$695$	−34.6424	−1.31406
$696$	0	0
$697$	−0.171358	−0.00649066
$698$	−0.802283	−0.0303669
$699$	0	0
$700$	0	0
$701$	−37.6169	−1.42077	−0.710385	−	0.703813i	$-0.751479\pi$
$701$	−37.6169	−1.42077	−0.710385	+	0.703813i	$0.751479\pi$
$702$	0	0
$703$	−0.522296	−0.0196988
$704$	22.9091	0.863419
$705$	0	0
$706$	2.34205	0.0881441
$707$	0	0
$708$	0	0
$709$	10.7266	0.402847	0.201423	−	0.979504i	$-0.435443\pi$
$709$	10.7266	0.402847	0.201423	+	0.979504i	$0.435443\pi$
$710$	2.40916	0.0904143
$711$	0	0
$712$	−1.98662	−0.0744516
$713$	20.1485	0.754569
$714$	0	0
$715$	6.42292	0.240203
$716$	−43.7285	−1.63421
$717$	0	0
$718$	−2.26635	−0.0845792
$719$	12.3407	0.460230	0.230115	−	0.973163i	$-0.426090\pi$
$719$	12.3407	0.460230	0.230115	+	0.973163i	$0.426090\pi$
$720$	0	0
$721$	0	0
$722$	1.47462	0.0548798
$723$	0	0
$724$	1.90477	0.0707901
$725$	−0.0958949	−0.00356145
$726$	0	0
$727$	−46.5464	−1.72631	−0.863155	−	0.504939i	$-0.831515\pi$
$727$	−46.5464	−1.72631	−0.863155	+	0.504939i	$0.831515\pi$
$728$	0	0
$729$	0	0
$730$	1.29212	0.0478233
$731$	2.65885	0.0983410
$732$	0	0
$733$	−37.8843	−1.39929	−0.699644	−	0.714492i	$-0.746658\pi$
$733$	−37.8843	−1.39929	−0.699644	+	0.714492i	$0.746658\pi$
$734$	−0.348321	−0.0128568
$735$	0	0
$736$	3.13959	0.115727
$737$	−17.9074	−0.659628
$738$	0	0
$739$	18.9782	0.698126	0.349063	−	0.937099i	$-0.386500\pi$
$739$	18.9782	0.698126	0.349063	+	0.937099i	$0.386500\pi$
$740$	18.3862	0.675889
$741$	0	0
$742$	0	0
$743$	−20.2127	−0.741534	−0.370767	−	0.928726i	$-0.620905\pi$
$743$	−20.2127	−0.741534	−0.370767	+	0.928726i	$0.620905\pi$
$744$	0	0
$745$	7.37392	0.270159
$746$	−1.86336	−0.0682226
$747$	0	0
$748$	−2.29077	−0.0837587
$749$	0	0
$750$	0	0
$751$	−47.1535	−1.72066	−0.860328	−	0.509742i	$-0.829741\pi$
$751$	−47.1535	−1.72066	−0.860328	+	0.509742i	$0.829741\pi$
$752$	−37.5106	−1.36787
$753$	0	0
$754$	−0.0498849	−0.00181670
$755$	45.0344	1.63897
$756$	0	0
$757$	−14.7288	−0.535327	−0.267664	−	0.963512i	$-0.586252\pi$
$757$	−14.7288	−0.535327	−0.267664	+	0.963512i	$0.586252\pi$
$758$	−1.57082	−0.0570546
$759$	0	0
$760$	0.0852381	0.00309191
$761$	41.7494	1.51341	0.756706	−	0.653755i	$-0.226807\pi$
$761$	41.7494	1.51341	0.756706	+	0.653755i	$0.226807\pi$
$762$	0	0
$763$	0	0
$764$	39.2481	1.41995
$765$	0	0
$766$	1.79289	0.0647798
$767$	−7.33555	−0.264871
$768$	0	0
$769$	34.0121	1.22651	0.613254	−	0.789886i	$-0.289860\pi$
$769$	34.0121	1.22651	0.613254	+	0.789886i	$0.289860\pi$
$770$	0	0
$771$	0	0
$772$	−30.0990	−1.08329
$773$	−17.0025	−0.611537	−0.305769	−	0.952106i	$-0.598913\pi$
$773$	−17.0025	−0.611537	−0.305769	+	0.952106i	$0.598913\pi$
$774$	0	0
$775$	0.889603	0.0319555
$776$	−4.62544	−0.166044
$777$	0	0
$778$	−2.58946	−0.0928366
$779$	−0.0542648	−0.00194424
$780$	0	0
$781$	−41.0688	−1.46956
$782$	−0.103484	−0.00370058
$783$	0	0
$784$	0	0
$785$	22.4678	0.801909
$786$	0	0
$787$	31.1294	1.10964	0.554822	−	0.831969i	$-0.312786\pi$
$787$	31.1294	1.10964	0.554822	+	0.831969i	$0.312786\pi$
$788$	−21.9979	−0.783644
$789$	0	0
$790$	−0.406254	−0.0144539
$791$	0	0
$792$	0	0
$793$	2.39394	0.0850114
$794$	−1.56811	−0.0556503
$795$	0	0
$796$	14.3107	0.507230
$797$	10.5797	0.374752	0.187376	−	0.982288i	$-0.440002\pi$
$797$	10.5797	0.374752	0.187376	+	0.982288i	$0.440002\pi$
$798$	0	0
$799$	3.72795	0.131885
$800$	0.138620	0.00490095
$801$	0	0
$802$	−0.327392	−0.0115606
$803$	−22.0266	−0.777302
$804$	0	0
$805$	0	0
$806$	0.462775	0.0163005
$807$	0	0
$808$	−6.19909	−0.218083
$809$	19.0261	0.668924	0.334462	−	0.942409i	$-0.391445\pi$
$809$	19.0261	0.668924	0.334462	+	0.942409i	$0.391445\pi$
$810$	0	0
$811$	24.9894	0.877497	0.438748	−	0.898610i	$-0.355422\pi$
$811$	24.9894	0.877497	0.438748	+	0.898610i	$0.355422\pi$
$812$	0	0
$813$	0	0
$814$	0.948389	0.0332410
$815$	−34.3216	−1.20223
$816$	0	0
$817$	0.841988	0.0294574
$818$	0.578392	0.0202230
$819$	0	0
$820$	1.91026	0.0667092
$821$	−45.7000	−1.59494	−0.797471	−	0.603358i	$-0.793829\pi$
$821$	−45.7000	−1.59494	−0.797471	+	0.603358i	$0.793829\pi$
$822$	0	0
$823$	−10.3799	−0.361822	−0.180911	−	0.983499i	$-0.557905\pi$
$823$	−10.3799	−0.361822	−0.180911	+	0.983499i	$0.557905\pi$
$824$	4.55250	0.158594
$825$	0	0
$826$	0	0
$827$	9.56239	0.332517	0.166258	−	0.986082i	$-0.446831\pi$
$827$	9.56239	0.332517	0.166258	+	0.986082i	$0.446831\pi$
$828$	0	0
$829$	17.8736	0.620777	0.310388	−	0.950610i	$-0.399541\pi$
$829$	17.8736	0.620777	0.310388	+	0.950610i	$0.399541\pi$
$830$	−1.67448	−0.0581221
$831$	0	0
$832$	−7.85556	−0.272343
$833$	0	0
$834$	0	0
$835$	−3.37654	−0.116850
$836$	−0.725426	−0.0250894
$837$	0	0
$838$	0.953985	0.0329549
$839$	33.6620	1.16214	0.581071	−	0.813853i	$-0.302634\pi$
$839$	33.6620	1.16214	0.581071	+	0.813853i	$0.302634\pi$
$840$	0	0
$841$	−28.5876	−0.985778
$842$	−2.09633	−0.0722444
$843$	0	0
$844$	−31.3289	−1.07839
$845$	−2.20243	−0.0757658
$846$	0	0
$847$	0	0
$848$	−49.2857	−1.69248
$849$	0	0
$850$	−0.00456904	−0.000156717 0
$851$	−14.1589	−0.485361
$852$	0	0
$853$	45.2796	1.55035	0.775173	−	0.631749i	$-0.217663\pi$
$853$	45.2796	1.55035	0.775173	+	0.631749i	$0.217663\pi$
$854$	0	0
$855$	0	0
$856$	1.56349	0.0534389
$857$	−44.5722	−1.52256	−0.761278	−	0.648425i	$-0.775428\pi$
$857$	−44.5722	−1.52256	−0.761278	+	0.648425i	$0.775428\pi$
$858$	0	0
$859$	39.9009	1.36140	0.680701	−	0.732561i	$-0.261675\pi$
$859$	39.9009	1.36140	0.680701	+	0.732561i	$0.261675\pi$
$860$	−29.6402	−1.01072
$861$	0	0
$862$	−1.57811	−0.0537505
$863$	3.11045	0.105881	0.0529406	−	0.998598i	$-0.483141\pi$
$863$	3.11045	0.105881	0.0529406	+	0.998598i	$0.483141\pi$
$864$	0	0
$865$	30.7997	1.04722
$866$	−0.701324	−0.0238320
$867$	0	0
$868$	0	0
$869$	6.92538	0.234927
$870$	0	0
$871$	6.14047	0.208062
$872$	−0.0380601	−0.00128888
$873$	0	0
$874$	−0.0327707	−0.00110848
$875$	0	0
$876$	0	0
$877$	−4.64274	−0.156774	−0.0783872	−	0.996923i	$-0.524977\pi$
$877$	−4.64274	−0.156774	−0.0783872	+	0.996923i	$0.524977\pi$
$878$	0.779466	0.0263057
$879$	0	0
$880$	25.4594	0.858236
$881$	−42.8058	−1.44216	−0.721082	−	0.692850i	$-0.756355\pi$
$881$	−42.8058	−1.44216	−0.721082	+	0.692850i	$0.756355\pi$
$882$	0	0
$883$	−9.60368	−0.323190	−0.161595	−	0.986857i	$-0.551664\pi$
$883$	−9.60368	−0.323190	−0.161595	+	0.986857i	$0.551664\pi$
$884$	0.785507	0.0264194
$885$	0	0
$886$	−2.61307	−0.0877879
$887$	−10.4937	−0.352346	−0.176173	−	0.984359i	$-0.556372\pi$
$887$	−10.4937	−0.352346	−0.176173	+	0.984359i	$0.556372\pi$
$888$	0	0
$889$	0	0
$890$	−1.09550	−0.0367211
$891$	0	0
$892$	12.3803	0.414524
$893$	1.18055	0.0395055
$894$	0	0
$895$	−48.3001	−1.61449
$896$	0	0
$897$	0	0
$898$	0.0944356	0.00315136
$899$	−3.82624	−0.127612
$900$	0	0
$901$	4.89820	0.163183
$902$	0.0985343	0.00328083
$903$	0	0
$904$	1.29100	0.0429380
$905$	2.10390	0.0699360
$906$	0	0
$907$	54.3480	1.80460	0.902298	−	0.431113i	$-0.141879\pi$
$907$	54.3480	1.80460	0.902298	+	0.431113i	$0.141879\pi$
$908$	−47.2329	−1.56748
$909$	0	0
$910$	0	0
$911$	−29.9548	−0.992445	−0.496223	−	0.868195i	$-0.665280\pi$
$911$	−29.9548	−0.992445	−0.496223	+	0.868195i	$0.665280\pi$
$912$	0	0
$913$	28.5448	0.944695
$914$	2.20858	0.0730532
$915$	0	0
$916$	−18.0300	−0.595727
$917$	0	0
$918$	0	0
$919$	30.8093	1.01631	0.508153	−	0.861267i	$-0.330329\pi$
$919$	30.8093	1.01631	0.508153	+	0.861267i	$0.330329\pi$
$920$	2.31072	0.0761821
$921$	0	0
$922$	−2.40688	−0.0792664
$923$	14.0826	0.463533
$924$	0	0
$925$	−0.625147	−0.0205547
$926$	1.14954	0.0377761
$927$	0	0
$928$	−0.596213	−0.0195716
$929$	−19.8880	−0.652503	−0.326252	−	0.945283i	$-0.605786\pi$
$929$	−19.8880	−0.652503	−0.326252	+	0.945283i	$0.605786\pi$
$930$	0	0
$931$	0	0
$932$	10.6567	0.349073
$933$	0	0
$934$	0.142143	0.00465105
$935$	−2.53025	−0.0827482
$936$	0	0
$937$	50.6240	1.65382	0.826908	−	0.562338i	$-0.190098\pi$
$937$	50.6240	1.65382	0.826908	+	0.562338i	$0.190098\pi$
$938$	0	0
$939$	0	0
$940$	−41.5583	−1.35548
$941$	21.1170	0.688394	0.344197	−	0.938897i	$-0.388151\pi$
$941$	21.1170	0.688394	0.344197	+	0.938897i	$0.388151\pi$
$942$	0	0
$943$	−1.47106	−0.0479044
$944$	−29.0769	−0.946373
$945$	0	0
$946$	−1.52889	−0.0497084
$947$	−33.0962	−1.07548	−0.537741	−	0.843110i	$-0.680722\pi$
$947$	−33.0962	−1.07548	−0.537741	+	0.843110i	$0.680722\pi$
$948$	0	0
$949$	7.55295	0.245179
$950$	−0.00144690	−4.69436e−5 0
$951$	0	0
$952$	0	0
$953$	3.06989	0.0994436	0.0497218	−	0.998763i	$-0.484167\pi$
$953$	3.06989	0.0994436	0.0497218	+	0.998763i	$0.484167\pi$
$954$	0	0
$955$	43.3513	1.40282
$956$	−54.3452	−1.75765
$957$	0	0
$958$	−0.726000	−0.0234560
$959$	0	0
$960$	0	0
$961$	4.49541	0.145013
$962$	−0.325204	−0.0104850
$963$	0	0
$964$	−31.2576	−1.00674
$965$	−33.2457	−1.07022
$966$	0	0
$967$	10.0334	0.322651	0.161325	−	0.986901i	$-0.448423\pi$
$967$	10.0334	0.322651	0.161325	+	0.986901i	$0.448423\pi$
$968$	−0.774107	−0.0248807
$969$	0	0
$970$	−2.55064	−0.0818963
$971$	−19.4697	−0.624812	−0.312406	−	0.949949i	$-0.601135\pi$
$971$	−19.4697	−0.624812	−0.312406	+	0.949949i	$0.601135\pi$
$972$	0	0
$973$	0	0
$974$	−1.81558	−0.0581749
$975$	0	0
$976$	9.48919	0.303742
$977$	−1.86853	−0.0597795	−0.0298898	−	0.999553i	$-0.509516\pi$
$977$	−1.86853	−0.0597795	−0.0298898	+	0.999553i	$0.509516\pi$
$978$	0	0
$979$	18.6749	0.596851
$980$	0	0
$981$	0	0
$982$	−1.66789	−0.0532246
$983$	32.2863	1.02977	0.514886	−	0.857258i	$-0.327834\pi$
$983$	32.2863	1.02977	0.514886	+	0.857258i	$0.327834\pi$
$984$	0	0
$985$	−24.2977	−0.774190
$986$	0.0196517	0.000625839 0
$987$	0	0
$988$	0.248750	0.00791378
$989$	22.8254	0.725806
$990$	0	0
$991$	56.8365	1.80547	0.902736	−	0.430195i	$-0.141555\pi$
$991$	56.8365	1.80547	0.902736	+	0.430195i	$0.141555\pi$
$992$	5.53097	0.175609
$993$	0	0
$994$	0	0
$995$	15.8068	0.501111
$996$	0	0
$997$	24.1136	0.763685	0.381843	−	0.924227i	$-0.375290\pi$
$997$	24.1136	0.763685	0.381843	+	0.924227i	$0.375290\pi$
$998$	1.72373	0.0545638
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bp.1.3		5
3.2	odd	2		1911.2.a.u.1.3		5
7.3	odd	6		819.2.j.g.352.3		10
7.5	odd	6		819.2.j.g.235.3		10
7.6	odd	2		5733.2.a.bq.1.3		5
21.5	even	6		273.2.i.e.235.3	yes	10
21.17	even	6		273.2.i.e.79.3	✓	10
21.20	even	2		1911.2.a.t.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.3	✓	10	21.17	even	6
273.2.i.e.235.3	yes	10	21.5	even	6
819.2.j.g.235.3		10	7.5	odd	6
819.2.j.g.352.3		10	7.3	odd	6
1911.2.a.t.1.3		5	21.20	even	2
1911.2.a.u.1.3		5	3.2	odd	2
5733.2.a.bp.1.3		5	1.1	even	1	trivial
5733.2.a.bq.1.3		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.0776754 q^{2} -1.99397 q^{4} -2.20243 q^{5} +0.310233 q^{8} +O(q^{10})\)	\(q-0.0776754 q^{2} -1.99397 q^{4} -2.20243 q^{5} +0.310233 q^{8} +0.171074 q^{10} -2.91629 q^{11} +1.00000 q^{13} +3.96384 q^{16} -0.393942 q^{17} -0.124751 q^{19} +4.39156 q^{20} +0.226524 q^{22} -3.38187 q^{23} -0.149317 q^{25} -0.0776754 q^{26} +0.642223 q^{29} -5.95780 q^{31} -0.928358 q^{32} +0.0305996 q^{34} +4.18670 q^{37} +0.00969009 q^{38} -0.683265 q^{40} +0.434984 q^{41} -6.74934 q^{43} +5.81499 q^{44} +0.262688 q^{46} -9.46321 q^{47} +0.0115983 q^{50} -1.99397 q^{52} -12.4338 q^{53} +6.42292 q^{55} -0.0498849 q^{58} -7.33555 q^{59} +2.39394 q^{61} +0.462775 q^{62} -7.85556 q^{64} -2.20243 q^{65} +6.14047 q^{67} +0.785507 q^{68} +14.0826 q^{71} +7.55295 q^{73} -0.325204 q^{74} +0.248750 q^{76} -2.37472 q^{79} -8.73006 q^{80} -0.0337875 q^{82} -9.78804 q^{83} +0.867628 q^{85} +0.524258 q^{86} -0.904729 q^{88} -6.40363 q^{89} +6.74335 q^{92} +0.735058 q^{94} +0.274755 q^{95} -14.9096 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) \) 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8	\( 5 q + 6 q^{4} - 3 q^{5} - 3 q^{8} + 2 q^{10} + q^{11} + 5 q^{13} - 13 q^{17} + 7 q^{19} - 13 q^{20} - 19 q^{22} + 4 q^{23} + 16 q^{25} + 12 q^{29} + 6 q^{31} - 21 q^{32} + 7 q^{34} + 11 q^{37} - 14 q^{38} + 11 q^{40} - 10 q^{41} + 10 q^{43} + 29 q^{44} + q^{46} + 4 q^{47} + 29 q^{50} + 6 q^{52} + 9 q^{53} - 12 q^{55} + 34 q^{58} - 7 q^{59} + 23 q^{61} + 24 q^{62} - 13 q^{64} - 3 q^{65} + 25 q^{67} - 20 q^{68} + 27 q^{71} + 18 q^{73} - 15 q^{74} + 2 q^{76} + 8 q^{79} - 41 q^{80} + 26 q^{82} - 12 q^{83} + 10 q^{85} + 19 q^{86} - 36 q^{88} - 29 q^{89} + 50 q^{92} - 2 q^{94} + 33 q^{95} + 13 q^{97}+O(q^{100}) \) 5 * q + 6 * q^4 - 3 * q^5 - 3 * q^8 + 2 * q^10 + q^11 + 5 * q^13 - 13 * q^17 + 7 * q^19 - 13 * q^20 - 19 * q^22 + 4 * q^23 + 16 * q^25 + 12 * q^29 + 6 * q^31 - 21 * q^32 + 7 * q^34 + 11 * q^37 - 14 * q^38 + 11 * q^40 - 10 * q^41 + 10 * q^43 + 29 * q^44 + q^46 + 4 * q^47 + 29 * q^50 + 6 * q^52 + 9 * q^53 - 12 * q^55 + 34 * q^58 - 7 * q^59 + 23 * q^61 + 24 * q^62 - 13 * q^64 - 3 * q^65 + 25 * q^67 - 20 * q^68 + 27 * q^71 + 18 * q^73 - 15 * q^74 + 2 * q^76 + 8 * q^79 - 41 * q^80 + 26 * q^82 - 12 * q^83 + 10 * q^85 + 19 * q^86 - 36 * q^88 - 29 * q^89 + 50 * q^92 - 2 * q^94 + 33 * q^95 + 13 * q^97

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