LMFDB - Embedded newform 5733.2.a.bm.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:	$5$
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			1.1
Root			$-1.72525$ 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)

$f(q)$	$=$	$q-2.72525 q^{2} +5.42699 q^{4} +2.18716 q^{5} -9.33940 q^{8} -5.96057 q^{10} +1.04815 q^{11} -1.00000 q^{13} +14.5982 q^{16} -5.29125 q^{17} -0.756906 q^{19} +11.8697 q^{20} -2.85648 q^{22} -0.653584 q^{23} -0.216314 q^{25} +2.72525 q^{26} +3.10408 q^{29} -1.02791 q^{31} -21.1050 q^{32} +14.4200 q^{34} -10.8932 q^{37} +2.06276 q^{38} -20.4268 q^{40} +7.32040 q^{41} +0.887771 q^{43} +5.68833 q^{44} +1.78118 q^{46} +2.33751 q^{47} +0.589510 q^{50} -5.42699 q^{52} -4.88814 q^{53} +2.29249 q^{55} -8.45941 q^{58} -1.04815 q^{59} +12.4998 q^{61} +2.80132 q^{62} +28.3200 q^{64} -2.18716 q^{65} +4.47889 q^{67} -28.7155 q^{68} +6.60274 q^{71} +8.28347 q^{73} +29.6868 q^{74} -4.10772 q^{76} +2.14014 q^{79} +31.9287 q^{80} -19.9499 q^{82} -6.66558 q^{83} -11.5728 q^{85} -2.41940 q^{86} -9.78914 q^{88} -5.76777 q^{89} -3.54699 q^{92} -6.37030 q^{94} -1.65548 q^{95} +2.88777 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$5 q - 4 q^{2} + 8 q^{4} + 2 q^{5} - 9 q^{8} + 5 q^{10} - 11 q^{11} - 5 q^{13} + 10 q^{16} - 5 q^{17} - 9 q^{19} + q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} + 4 q^{26} + 3 q^{29} + 6 q^{31} - 22 q^{32} + 22 q^{34}+ \cdots + 12 q^{97}+O(q^{100})$ 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

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

)

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

$2$	−2.72525	−1.92704	−0.963521	−	0.267631i	$-0.913759\pi$
$2$	−2.72525	−1.92704	−0.963521	+	0.267631i	$0.913759\pi$
$3$	0	0
$3$	0	0
$4$	5.42699	2.71349
$5$	2.18716	0.978129	0.489065	−	0.872247i	$-0.337338\pi$
$5$	2.18716	0.978129	0.489065	+	0.872247i	$0.337338\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−9.33940	−3.30198
$9$	0	0
$10$	−5.96057	−1.88490
$11$	1.04815	0.316031	0.158015	−	0.987437i	$-0.449490\pi$
$11$	1.04815	0.316031	0.158015	+	0.987437i	$0.449490\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	14.5982	3.64956
$17$	−5.29125	−1.28332	−0.641658	−	0.766991i	$-0.721753\pi$
$17$	−5.29125	−1.28332	−0.641658	+	0.766991i	$0.721753\pi$
$18$	0	0
$19$	−0.756906	−0.173646	−0.0868231	−	0.996224i	$-0.527671\pi$
$19$	−0.756906	−0.173646	−0.0868231	+	0.996224i	$0.527671\pi$
$20$	11.8697	2.65415
$21$	0	0
$22$	−2.85648	−0.609005
$23$	−0.653584	−0.136282	−0.0681408	−	0.997676i	$-0.521707\pi$
$23$	−0.653584	−0.136282	−0.0681408	+	0.997676i	$0.521707\pi$
$24$	0	0
$25$	−0.216314	−0.0432628
$26$	2.72525	0.534466
$27$	0	0
$28$	0	0
$29$	3.10408	0.576414	0.288207	−	0.957568i	$-0.406941\pi$
$29$	3.10408	0.576414	0.288207	+	0.957568i	$0.406941\pi$
$30$	0	0
$31$	−1.02791	−0.184618	−0.0923092	−	0.995730i	$-0.529425\pi$
$31$	−1.02791	−0.184618	−0.0923092	+	0.995730i	$0.529425\pi$
$32$	−21.1050	−3.73088
$33$	0	0
$34$	14.4200	2.47301
$35$	0	0
$36$	0	0
$37$	−10.8932	−1.79084	−0.895418	−	0.445227i	$-0.853123\pi$
$37$	−10.8932	−1.79084	−0.895418	+	0.445227i	$0.853123\pi$
$38$	2.06276	0.334624
$39$	0	0
$40$	−20.4268	−3.22976
$41$	7.32040	1.14325	0.571627	−	0.820514i	$-0.306312\pi$
$41$	7.32040	1.14325	0.571627	+	0.820514i	$0.306312\pi$
$42$	0	0
$43$	0.887771	0.135384	0.0676919	−	0.997706i	$-0.478437\pi$
$43$	0.887771	0.135384	0.0676919	+	0.997706i	$0.478437\pi$
$44$	5.68833	0.857547
$45$	0	0
$46$	1.78118	0.262621
$47$	2.33751	0.340961	0.170480	−	0.985361i	$-0.445468\pi$
$47$	2.33751	0.340961	0.170480	+	0.985361i	$0.445468\pi$
$48$	0	0
$49$	0	0
$50$	0.589510	0.0833692
$51$	0	0
$52$	−5.42699	−0.752588
$53$	−4.88814	−0.671438	−0.335719	−	0.941962i	$-0.608979\pi$
$53$	−4.88814	−0.671438	−0.335719	+	0.941962i	$0.608979\pi$
$54$	0	0
$55$	2.29249	0.309119
$56$	0	0
$57$	0	0
$58$	−8.45941	−1.11077
$59$	−1.04815	−0.136458	−0.0682291	−	0.997670i	$-0.521735\pi$
$59$	−1.04815	−0.136458	−0.0682291	+	0.997670i	$0.521735\pi$
$60$	0	0
$61$	12.4998	1.60043	0.800217	−	0.599711i	$-0.204718\pi$
$61$	12.4998	1.60043	0.800217	+	0.599711i	$0.204718\pi$
$62$	2.80132	0.355768
$63$	0	0
$64$	28.3200	3.54000
$65$	−2.18716	−0.271284
$66$	0	0
$67$	4.47889	0.547183	0.273592	−	0.961846i	$-0.411788\pi$
$67$	4.47889	0.547183	0.273592	+	0.961846i	$0.411788\pi$
$68$	−28.7155	−3.48227
$69$	0	0
$70$	0	0
$71$	6.60274	0.783601	0.391801	−	0.920050i	$-0.371852\pi$
$71$	6.60274	0.783601	0.391801	+	0.920050i	$0.371852\pi$
$72$	0	0
$73$	8.28347	0.969507	0.484754	−	0.874651i	$-0.338909\pi$
$73$	8.28347	0.969507	0.484754	+	0.874651i	$0.338909\pi$
$74$	29.6868	3.45102
$75$	0	0
$76$	−4.10772	−0.471188
$77$	0	0
$78$	0	0
$79$	2.14014	0.240785	0.120392	−	0.992726i	$-0.461585\pi$
$79$	2.14014	0.240785	0.120392	+	0.992726i	$0.461585\pi$
$80$	31.9287	3.56974
$81$	0	0
$82$	−19.9499	−2.20310
$83$	−6.66558	−0.731642	−0.365821	−	0.930685i	$-0.619212\pi$
$83$	−6.66558	−0.731642	−0.365821	+	0.930685i	$0.619212\pi$
$84$	0	0
$85$	−11.5728	−1.25525
$86$	−2.41940	−0.260890
$87$	0	0
$88$	−9.78914	−1.04353
$89$	−5.76777	−0.611382	−0.305691	−	0.952131i	$-0.598887\pi$
$89$	−5.76777	−0.611382	−0.305691	+	0.952131i	$0.598887\pi$
$90$	0	0
$91$	0	0
$92$	−3.54699	−0.369800
$93$	0	0
$94$	−6.37030	−0.657046
$95$	−1.65548	−0.169848
$96$	0	0
$97$	2.88777	0.293209	0.146604	−	0.989195i	$-0.453166\pi$
$97$	2.88777	0.293209	0.146604	+	0.989195i	$0.453166\pi$
$98$	0	0
$99$	0	0
$100$	−1.17393	−0.117393
$101$	−11.2543	−1.11985	−0.559924	−	0.828544i	$-0.689170\pi$
$101$	−11.2543	−1.11985	−0.559924	+	0.828544i	$0.689170\pi$
$102$	0	0
$103$	−20.2334	−1.99366	−0.996828	−	0.0795900i	$-0.974639\pi$
$103$	−20.2334	−1.99366	−0.996828	+	0.0795900i	$0.974639\pi$
$104$	9.33940	0.915804
$105$	0	0
$106$	13.3214	1.29389
$107$	−9.05517	−0.875396	−0.437698	−	0.899122i	$-0.644206\pi$
$107$	−9.05517	−0.875396	−0.437698	+	0.899122i	$0.644206\pi$
$108$	0	0
$109$	15.1014	1.44645	0.723226	−	0.690612i	$-0.242659\pi$
$109$	15.1014	1.44645	0.723226	+	0.690612i	$0.242659\pi$
$110$	−6.24760	−0.595685
$111$	0	0
$112$	0	0
$113$	−3.10408	−0.292008	−0.146004	−	0.989284i	$-0.546641\pi$
$113$	−3.10408	−0.292008	−0.146004	+	0.989284i	$0.546641\pi$
$114$	0	0
$115$	−1.42950	−0.133301
$116$	16.8458	1.56410
$117$	0	0
$118$	2.85648	0.262961
$119$	0	0
$120$	0	0
$121$	−9.90137	−0.900125
$122$	−34.0651	−3.08410
$123$	0	0
$124$	−5.57847	−0.500961
$125$	−11.4089	−1.02045
$126$	0	0
$127$	8.78914	0.779910	0.389955	−	0.920834i	$-0.372491\pi$
$127$	8.78914	0.779910	0.389955	+	0.920834i	$0.372491\pi$
$128$	−34.9691	−3.09086
$129$	0	0
$130$	5.96057	0.522776
$131$	−10.5145	−0.918653	−0.459327	−	0.888267i	$-0.651909\pi$
$131$	−10.5145	−0.918653	−0.459327	+	0.888267i	$0.651909\pi$
$132$	0	0
$133$	0	0
$134$	−12.2061	−1.05445
$135$	0	0
$136$	49.4171	4.23748
$137$	−8.73165	−0.745995	−0.372998	−	0.927832i	$-0.621670\pi$
$137$	−8.73165	−0.745995	−0.372998	+	0.927832i	$0.621670\pi$
$138$	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
$142$	−17.9941	−1.51003
$143$	−1.04815	−0.0876511
$144$	0	0
$145$	6.78914	0.563808
$146$	−22.5745	−1.86828
$147$	0	0
$148$	−59.1174	−4.85942
$149$	−15.3926	−1.26101	−0.630507	−	0.776183i	$-0.717153\pi$
$149$	−15.3926	−1.26101	−0.630507	+	0.776183i	$0.717153\pi$
$150$	0	0
$151$	−13.6757	−1.11291	−0.556457	−	0.830876i	$-0.687840\pi$
$151$	−13.6757	−1.11291	−0.556457	+	0.830876i	$0.687840\pi$
$152$	7.06905	0.573376
$153$	0	0
$154$	0	0
$155$	−2.24821	−0.180581
$156$	0	0
$157$	−3.38756	−0.270357	−0.135178	−	0.990821i	$-0.543161\pi$
$157$	−3.38756	−0.270357	−0.135178	+	0.990821i	$0.543161\pi$
$158$	−5.83242	−0.464002
$159$	0	0
$160$	−46.1602	−3.64928
$161$	0	0
$162$	0	0
$163$	−13.8100	−1.08169	−0.540843	−	0.841124i	$-0.681895\pi$
$163$	−13.8100	−1.08169	−0.540843	+	0.841124i	$0.681895\pi$
$164$	39.7277	3.10221
$165$	0	0
$166$	18.1654	1.40991
$167$	16.3783	1.26739	0.633695	−	0.773583i	$-0.281538\pi$
$167$	16.3783	1.26739	0.633695	+	0.773583i	$0.281538\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	31.5389	2.41892
$171$	0	0
$172$	4.81792	0.367363
$173$	4.12546	0.313653	0.156826	−	0.987626i	$-0.449874\pi$
$173$	4.12546	0.313653	0.156826	+	0.987626i	$0.449874\pi$
$174$	0	0
$175$	0	0
$176$	15.3012	1.15337
$177$	0	0
$178$	15.7186	1.17816
$179$	−14.4136	−1.07732	−0.538661	−	0.842523i	$-0.681069\pi$
$179$	−14.4136	−1.07732	−0.538661	+	0.842523i	$0.681069\pi$
$180$	0	0
$181$	−18.1014	−1.34547	−0.672733	−	0.739885i	$-0.734880\pi$
$181$	−18.1014	−1.34547	−0.672733	+	0.739885i	$0.734880\pi$
$182$	0	0
$183$	0	0
$184$	6.10408	0.449999
$185$	−23.8253	−1.75167
$186$	0	0
$187$	−5.54605	−0.405567
$188$	12.6856	0.925195
$189$	0	0
$190$	4.51159	0.327305
$191$	−5.54135	−0.400958	−0.200479	−	0.979698i	$-0.564250\pi$
$191$	−5.54135	−0.400958	−0.200479	+	0.979698i	$0.564250\pi$
$192$	0	0
$193$	−8.74088	−0.629182	−0.314591	−	0.949227i	$-0.601867\pi$
$193$	−8.74088	−0.629182	−0.314591	+	0.949227i	$0.601867\pi$
$194$	−7.86990	−0.565026
$195$	0	0
$196$	0	0
$197$	5.46874	0.389632	0.194816	−	0.980840i	$-0.437589\pi$
$197$	5.46874	0.389632	0.194816	+	0.980840i	$0.437589\pi$
$198$	0	0
$199$	−19.5368	−1.38493	−0.692463	−	0.721454i	$-0.743474\pi$
$199$	−19.5368	−1.38493	−0.692463	+	0.721454i	$0.743474\pi$
$200$	2.02024	0.142853
$201$	0	0
$202$	30.6708	2.15799
$203$	0	0
$204$	0	0
$205$	16.0109	1.11825
$206$	55.1411	3.84186
$207$	0	0
$208$	−14.5982	−1.01221
$209$	−0.793355	−0.0548775
$210$	0	0
$211$	16.6905	1.14902	0.574511	−	0.818497i	$-0.305192\pi$
$211$	16.6905	1.14902	0.574511	+	0.818497i	$0.305192\pi$
$212$	−26.5279	−1.82194
$213$	0	0
$214$	24.6776	1.68693
$215$	1.94170	0.132423
$216$	0	0
$217$	0	0
$218$	−41.1551	−2.78737
$219$	0	0
$220$	12.4413	0.838792
$221$	5.29125	0.355928
$222$	0	0
$223$	5.34217	0.357738	0.178869	−	0.983873i	$-0.442756\pi$
$223$	5.34217	0.357738	0.178869	+	0.983873i	$0.442756\pi$
$224$	0	0
$225$	0	0
$226$	8.45941	0.562711
$227$	20.1215	1.33551	0.667757	−	0.744380i	$-0.267255\pi$
$227$	20.1215	1.33551	0.667757	+	0.744380i	$0.267255\pi$
$228$	0	0
$229$	−25.2497	−1.66855	−0.834275	−	0.551349i	$-0.814113\pi$
$229$	−25.2497	−1.66855	−0.834275	+	0.551349i	$0.814113\pi$
$230$	3.89573	0.256877
$231$	0	0
$232$	−28.9903	−1.90331
$233$	0.793355	0.0519744	0.0259872	−	0.999662i	$-0.491727\pi$
$233$	0.793355	0.0519744	0.0259872	+	0.999662i	$0.491727\pi$
$234$	0	0
$235$	5.11252	0.333504
$236$	−5.68833	−0.370278
$237$	0	0
$238$	0	0
$239$	−20.0488	−1.29685	−0.648425	−	0.761279i	$-0.724572\pi$
$239$	−20.0488	−1.29685	−0.648425	+	0.761279i	$0.724572\pi$
$240$	0	0
$241$	−13.8120	−0.889712	−0.444856	−	0.895602i	$-0.646745\pi$
$241$	−13.8120	−0.889712	−0.444856	+	0.895602i	$0.646745\pi$
$242$	26.9837	1.73458
$243$	0	0
$244$	67.8362	4.34277
$245$	0	0
$246$	0	0
$247$	0.756906	0.0481608
$248$	9.60008	0.609606
$249$	0	0
$250$	31.0922	1.96644
$251$	−26.1095	−1.64802	−0.824010	−	0.566576i	$-0.808268\pi$
$251$	−26.1095	−1.64802	−0.824010	+	0.566576i	$0.808268\pi$
$252$	0	0
$253$	−0.685057	−0.0430692
$254$	−23.9526	−1.50292
$255$	0	0
$256$	38.6595	2.41622
$257$	10.6198	0.662444	0.331222	−	0.943553i	$-0.392539\pi$
$257$	10.6198	0.662444	0.331222	+	0.943553i	$0.392539\pi$
$258$	0	0
$259$	0	0
$260$	−11.8697	−0.736128
$261$	0	0
$262$	28.6546	1.77028
$263$	−10.3578	−0.638686	−0.319343	−	0.947639i	$-0.603462\pi$
$263$	−10.3578	−0.638686	−0.319343	+	0.947639i	$0.603462\pi$
$264$	0	0
$265$	−10.6912	−0.656753
$266$	0	0
$267$	0	0
$268$	24.3069	1.48478
$269$	11.9701	0.729827	0.364914	−	0.931041i	$-0.381099\pi$
$269$	11.9701	0.729827	0.364914	+	0.931041i	$0.381099\pi$
$270$	0	0
$271$	2.75691	0.167470	0.0837351	−	0.996488i	$-0.473315\pi$
$271$	2.75691	0.167470	0.0837351	+	0.996488i	$0.473315\pi$
$272$	−77.2429	−4.68354
$273$	0	0
$274$	23.7959	1.43757
$275$	−0.226731	−0.0136724
$276$	0	0
$277$	−23.9275	−1.43766	−0.718831	−	0.695185i	$-0.755322\pi$
$277$	−23.9275	−1.43766	−0.718831	+	0.695185i	$0.755322\pi$
$278$	−10.9010	−0.653799
$279$	0	0
$280$	0	0
$281$	3.87870	0.231384	0.115692	−	0.993285i	$-0.463091\pi$
$281$	3.87870	0.231384	0.115692	+	0.993285i	$0.463091\pi$
$282$	0	0
$283$	6.20999	0.369146	0.184573	−	0.982819i	$-0.440910\pi$
$283$	6.20999	0.369146	0.184573	+	0.982819i	$0.440910\pi$
$284$	35.8330	2.12630
$285$	0	0
$286$	2.85648	0.168907
$287$	0	0
$288$	0	0
$289$	10.9973	0.646901
$290$	−18.5021	−1.08648
$291$	0	0
$292$	44.9543	2.63075
$293$	16.5754	0.968347	0.484174	−	0.874972i	$-0.339120\pi$
$293$	16.5754	0.968347	0.484174	+	0.874972i	$0.339120\pi$
$294$	0	0
$295$	−2.29249	−0.133474
$296$	101.736	5.91330
$297$	0	0
$298$	41.9488	2.43003
$299$	0.653584	0.0377977
$300$	0	0
$301$	0	0
$302$	37.2698	2.14463
$303$	0	0
$304$	−11.0495	−0.633732
$305$	27.3391	1.56543
$306$	0	0
$307$	7.05788	0.402815	0.201407	−	0.979508i	$-0.435449\pi$
$307$	7.05788	0.402815	0.201407	+	0.979508i	$0.435449\pi$
$308$	0	0
$309$	0	0
$310$	6.12694	0.347987
$311$	21.1102	1.19705	0.598525	−	0.801104i	$-0.295754\pi$
$311$	21.1102	1.19705	0.598525	+	0.801104i	$0.295754\pi$
$312$	0	0
$313$	−1.98052	−0.111946	−0.0559728	−	0.998432i	$-0.517826\pi$
$313$	−1.98052	−0.111946	−0.0559728	+	0.998432i	$0.517826\pi$
$314$	9.23194	0.520989
$315$	0	0
$316$	11.6145	0.653368
$317$	18.0459	1.01356	0.506781	−	0.862075i	$-0.330835\pi$
$317$	18.0459	1.01356	0.506781	+	0.862075i	$0.330835\pi$
$318$	0	0
$319$	3.25356	0.182164
$320$	61.9406	3.46258
$321$	0	0
$322$	0	0
$323$	4.00498	0.222843
$324$	0	0
$325$	0.216314	0.0119989
$326$	37.6358	2.08446
$327$	0	0
$328$	−68.3682	−3.77500
$329$	0	0
$330$	0	0
$331$	−14.6738	−0.806544	−0.403272	−	0.915080i	$-0.632127\pi$
$331$	−14.6738	−0.806544	−0.403272	+	0.915080i	$0.632127\pi$
$332$	−36.1740	−1.98531
$333$	0	0
$334$	−44.6349	−2.44231
$335$	9.79606	0.535216
$336$	0	0
$337$	12.8080	0.697698	0.348849	−	0.937179i	$-0.386573\pi$
$337$	12.8080	0.697698	0.348849	+	0.937179i	$0.386573\pi$
$338$	−2.72525	−0.148234
$339$	0	0
$340$	−62.8056	−3.40611
$341$	−1.07741	−0.0583451
$342$	0	0
$343$	0	0
$344$	−8.29125	−0.447034
$345$	0	0
$346$	−11.2429	−0.604423
$347$	−20.2054	−1.08468	−0.542342	−	0.840158i	$-0.682462\pi$
$347$	−20.2054	−1.08468	−0.542342	+	0.840158i	$0.682462\pi$
$348$	0	0
$349$	18.4434	0.987252	0.493626	−	0.869674i	$-0.335671\pi$
$349$	18.4434	0.987252	0.493626	+	0.869674i	$0.335671\pi$
$350$	0	0
$351$	0	0
$352$	−22.1213	−1.17907
$353$	−8.14436	−0.433480	−0.216740	−	0.976229i	$-0.569542\pi$
$353$	−8.14436	−0.433480	−0.216740	+	0.976229i	$0.569542\pi$
$354$	0	0
$355$	14.4413	0.766463
$356$	−31.3016	−1.65898
$357$	0	0
$358$	39.2806	2.07604
$359$	32.6100	1.72109	0.860545	−	0.509375i	$-0.170123\pi$
$359$	32.6100	1.72109	0.860545	+	0.509375i	$0.170123\pi$
$360$	0	0
$361$	−18.4271	−0.969847
$362$	49.3308	2.59277
$363$	0	0
$364$	0	0
$365$	18.1173	0.948304
$366$	0	0
$367$	3.16012	0.164957	0.0824786	−	0.996593i	$-0.473716\pi$
$367$	3.16012	0.164957	0.0824786	+	0.996593i	$0.473716\pi$
$368$	−9.54117	−0.497368
$369$	0	0
$370$	64.9298	3.37554
$371$	0	0
$372$	0	0
$373$	−1.47770	−0.0765123	−0.0382561	−	0.999268i	$-0.512180\pi$
$373$	−1.47770	−0.0765123	−0.0382561	+	0.999268i	$0.512180\pi$
$374$	15.1144	0.781545
$375$	0	0
$376$	−21.8309	−1.12584
$377$	−3.10408	−0.159868
$378$	0	0
$379$	10.7254	0.550927	0.275463	−	0.961312i	$-0.411169\pi$
$379$	10.7254	0.550927	0.275463	+	0.961312i	$0.411169\pi$
$380$	−8.98426	−0.460883
$381$	0	0
$382$	15.1016	0.772664
$383$	−21.4109	−1.09405	−0.547023	−	0.837118i	$-0.684239\pi$
$383$	−21.4109	−1.09405	−0.547023	+	0.837118i	$0.684239\pi$
$384$	0	0
$385$	0	0
$386$	23.8211	1.21246
$387$	0	0
$388$	15.6719	0.795620
$389$	−34.7819	−1.76351	−0.881755	−	0.471707i	$-0.843638\pi$
$389$	−34.7819	−1.76351	−0.881755	+	0.471707i	$0.843638\pi$
$390$	0	0
$391$	3.45828	0.174893
$392$	0	0
$393$	0	0
$394$	−14.9037	−0.750837
$395$	4.68084	0.235519
$396$	0	0
$397$	−4.45211	−0.223445	−0.111722	−	0.993739i	$-0.535637\pi$
$397$	−4.45211	−0.223445	−0.111722	+	0.993739i	$0.535637\pi$
$398$	53.2426	2.66881
$399$	0	0
$400$	−3.15780	−0.157890
$401$	13.7537	0.686829	0.343415	−	0.939184i	$-0.388416\pi$
$401$	13.7537	0.686829	0.343415	+	0.939184i	$0.388416\pi$
$402$	0	0
$403$	1.02791	0.0512039
$404$	−61.0771	−3.03870
$405$	0	0
$406$	0	0
$407$	−11.4178	−0.565959
$408$	0	0
$409$	3.49207	0.172672	0.0863358	−	0.996266i	$-0.472484\pi$
$409$	3.49207	0.172672	0.0863358	+	0.996266i	$0.472484\pi$
$410$	−43.6337	−2.15492
$411$	0	0
$412$	−109.806	−5.40977
$413$	0	0
$414$	0	0
$415$	−14.5787	−0.715641
$416$	21.1050	1.03476
$417$	0	0
$418$	2.16209	0.105751
$419$	−3.56737	−0.174278	−0.0871388	−	0.996196i	$-0.527772\pi$
$419$	−3.56737	−0.174278	−0.0871388	+	0.996196i	$0.527772\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−45.4858	−2.21422
$423$	0	0
$424$	45.6523	2.21707
$425$	1.14457	0.0555198
$426$	0	0
$427$	0	0
$428$	−49.1423	−2.37538
$429$	0	0
$430$	−5.29162	−0.255185
$431$	11.3642	0.547396	0.273698	−	0.961816i	$-0.411753\pi$
$431$	11.3642	0.547396	0.273698	+	0.961816i	$0.411753\pi$
$432$	0	0
$433$	21.2136	1.01946	0.509731	−	0.860334i	$-0.329745\pi$
$433$	21.2136	1.01946	0.509731	+	0.860334i	$0.329745\pi$
$434$	0	0
$435$	0	0
$436$	81.9551	3.92494
$437$	0.494702	0.0236648
$438$	0	0
$439$	24.5007	1.16935	0.584676	−	0.811267i	$-0.301222\pi$
$439$	24.5007	1.16935	0.584676	+	0.811267i	$0.301222\pi$
$440$	−21.4105	−1.02070
$441$	0	0
$442$	−14.4200	−0.685888
$443$	−40.4688	−1.92273	−0.961366	−	0.275274i	$-0.911231\pi$
$443$	−40.4688	−1.92273	−0.961366	+	0.275274i	$0.911231\pi$
$444$	0	0
$445$	−12.6151	−0.598011
$446$	−14.5587	−0.689376
$447$	0	0
$448$	0	0
$449$	27.7638	1.31025	0.655127	−	0.755519i	$-0.272615\pi$
$449$	27.7638	1.31025	0.655127	+	0.755519i	$0.272615\pi$
$450$	0	0
$451$	7.67291	0.361303
$452$	−16.8458	−0.792361
$453$	0	0
$454$	−54.8362	−2.57359
$455$	0	0
$456$	0	0
$457$	−11.1939	−0.523629	−0.261815	−	0.965118i	$-0.584321\pi$
$457$	−11.1939	−0.523629	−0.261815	+	0.965118i	$0.584321\pi$
$458$	68.8119	3.21537
$459$	0	0
$460$	−7.75786	−0.361712
$461$	−9.29773	−0.433038	−0.216519	−	0.976278i	$-0.569470\pi$
$461$	−9.29773	−0.433038	−0.216519	+	0.976278i	$0.569470\pi$
$462$	0	0
$463$	28.2439	1.31260	0.656302	−	0.754499i	$-0.272120\pi$
$463$	28.2439	1.31260	0.656302	+	0.754499i	$0.272120\pi$
$464$	45.3142	2.10366
$465$	0	0
$466$	−2.16209	−0.100157
$467$	22.2606	1.03010	0.515050	−	0.857160i	$-0.327773\pi$
$467$	22.2606	1.03010	0.515050	+	0.857160i	$0.327773\pi$
$468$	0	0
$469$	0	0
$470$	−13.9329	−0.642676
$471$	0	0
$472$	9.78914	0.450582
$473$	0.930521	0.0427854
$474$	0	0
$475$	0.163729	0.00751242
$476$	0	0
$477$	0	0
$478$	54.6380	2.49909
$479$	−32.8764	−1.50216	−0.751081	−	0.660210i	$-0.770467\pi$
$479$	−32.8764	−1.50216	−0.751081	+	0.660210i	$0.770467\pi$
$480$	0	0
$481$	10.8932	0.496688
$482$	37.6413	1.71451
$483$	0	0
$484$	−53.7346	−2.44248
$485$	6.31603	0.286796
$486$	0	0
$487$	−27.8924	−1.26392	−0.631962	−	0.774999i	$-0.717750\pi$
$487$	−27.8924	−1.26392	−0.631962	+	0.774999i	$0.717750\pi$
$488$	−116.741	−5.28460
$489$	0	0
$490$	0	0
$491$	−10.6571	−0.480948	−0.240474	−	0.970656i	$-0.577303\pi$
$491$	−10.6571	−0.480948	−0.240474	+	0.970656i	$0.577303\pi$
$492$	0	0
$493$	−16.4245	−0.739722
$494$	−2.06276	−0.0928079
$495$	0	0
$496$	−15.0057	−0.673776
$497$	0	0
$498$	0	0
$499$	−24.5114	−1.09728	−0.548641	−	0.836058i	$-0.684854\pi$
$499$	−24.5114	−1.09728	−0.548641	+	0.836058i	$0.684854\pi$
$500$	−61.9162	−2.76897
$501$	0	0
$502$	71.1550	3.17580
$503$	−38.0054	−1.69458	−0.847288	−	0.531134i	$-0.821766\pi$
$503$	−38.0054	−1.69458	−0.847288	+	0.531134i	$0.821766\pi$
$504$	0	0
$505$	−24.6151	−1.09536
$506$	1.86695	0.0829962
$507$	0	0
$508$	47.6986	2.11628
$509$	39.8501	1.76632	0.883161	−	0.469070i	$-0.155411\pi$
$509$	39.8501	1.76632	0.883161	+	0.469070i	$0.155411\pi$
$510$	0	0
$511$	0	0
$512$	−35.4186	−1.56530
$513$	0	0
$514$	−28.9416	−1.27656
$515$	−44.2537	−1.95005
$516$	0	0
$517$	2.45007	0.107754
$518$	0	0
$519$	0	0
$520$	20.4268	0.895775
$521$	−19.6334	−0.860155	−0.430077	−	0.902792i	$-0.641514\pi$
$521$	−19.6334	−0.860155	−0.430077	+	0.902792i	$0.641514\pi$
$522$	0	0
$523$	−22.8324	−0.998391	−0.499195	−	0.866489i	$-0.666371\pi$
$523$	−22.8324	−0.998391	−0.499195	+	0.866489i	$0.666371\pi$
$524$	−57.0619	−2.49276
$525$	0	0
$526$	28.2275	1.23078
$527$	5.43894	0.236924
$528$	0	0
$529$	−22.5728	−0.981427
$530$	29.1361	1.26559
$531$	0	0
$532$	0	0
$533$	−7.32040	−0.317082
$534$	0	0
$535$	−19.8051	−0.856251
$536$	−41.8301	−1.80679
$537$	0	0
$538$	−32.6214	−1.40641
$539$	0	0
$540$	0	0
$541$	−9.64668	−0.414743	−0.207372	−	0.978262i	$-0.566491\pi$
$541$	−9.64668	−0.414743	−0.207372	+	0.978262i	$0.566491\pi$
$542$	−7.51326	−0.322722
$543$	0	0
$544$	111.672	4.78790
$545$	33.0292	1.41482
$546$	0	0
$547$	−43.8570	−1.87519	−0.937596	−	0.347728i	$-0.886953\pi$
$547$	−43.8570	−1.87519	−0.937596	+	0.347728i	$0.886953\pi$
$548$	−47.3866	−2.02425
$549$	0	0
$550$	0.617897	0.0263472
$551$	−2.34950	−0.100092
$552$	0	0
$553$	0	0
$554$	65.2083	2.77044
$555$	0	0
$556$	21.7080	0.920622
$557$	−14.9195	−0.632161	−0.316080	−	0.948732i	$-0.602367\pi$
$557$	−14.9195	−0.632161	−0.316080	+	0.948732i	$0.602367\pi$
$558$	0	0
$559$	−0.887771	−0.0375487
$560$	0	0
$561$	0	0
$562$	−10.5704	−0.445886
$563$	−17.2697	−0.727832	−0.363916	−	0.931432i	$-0.618560\pi$
$563$	−17.2697	−0.727832	−0.363916	+	0.931432i	$0.618560\pi$
$564$	0	0
$565$	−6.78914	−0.285621
$566$	−16.9238	−0.711359
$567$	0	0
$568$	−61.6657	−2.58743
$569$	−26.5324	−1.11230	−0.556148	−	0.831083i	$-0.687721\pi$
$569$	−26.5324	−1.11230	−0.556148	+	0.831083i	$0.687721\pi$
$570$	0	0
$571$	−1.98569	−0.0830985	−0.0415492	−	0.999136i	$-0.513229\pi$
$571$	−1.98569	−0.0830985	−0.0415492	+	0.999136i	$0.513229\pi$
$572$	−5.68833	−0.237841
$573$	0	0
$574$	0	0
$575$	0.141379	0.00589593
$576$	0	0
$577$	−11.8983	−0.495333	−0.247666	−	0.968845i	$-0.579664\pi$
$577$	−11.8983	−0.495333	−0.247666	+	0.968845i	$0.579664\pi$
$578$	−29.9704	−1.24661
$579$	0	0
$580$	36.8446	1.52989
$581$	0	0
$582$	0	0
$583$	−5.12353	−0.212195
$584$	−77.3627	−3.20129
$585$	0	0
$586$	−45.1722	−1.86605
$587$	33.5122	1.38320	0.691598	−	0.722283i	$-0.256907\pi$
$587$	33.5122	1.38320	0.691598	+	0.722283i	$0.256907\pi$
$588$	0	0
$589$	0.778033	0.0320583
$590$	6.24760	0.257210
$591$	0	0
$592$	−159.022	−6.53576
$593$	35.2815	1.44884	0.724419	−	0.689360i	$-0.242108\pi$
$593$	35.2815	1.44884	0.724419	+	0.689360i	$0.242108\pi$
$594$	0	0
$595$	0	0
$596$	−83.5357	−3.42176
$597$	0	0
$598$	−1.78118	−0.0728379
$599$	25.0068	1.02175	0.510876	−	0.859655i	$-0.329321\pi$
$599$	25.0068	1.02175	0.510876	+	0.859655i	$0.329321\pi$
$600$	0	0
$601$	28.4688	1.16127	0.580634	−	0.814165i	$-0.302805\pi$
$601$	28.4688	1.16127	0.580634	+	0.814165i	$0.302805\pi$
$602$	0	0
$603$	0	0
$604$	−74.2180	−3.01989
$605$	−21.6559	−0.880438
$606$	0	0
$607$	−36.0469	−1.46310	−0.731549	−	0.681789i	$-0.761202\pi$
$607$	−36.0469	−1.46310	−0.731549	+	0.681789i	$0.761202\pi$
$608$	15.9745	0.647853
$609$	0	0
$610$	−74.5058	−3.01665
$611$	−2.33751	−0.0945655
$612$	0	0
$613$	18.3253	0.740151	0.370075	−	0.929002i	$-0.379332\pi$
$613$	18.3253	0.740151	0.370075	+	0.929002i	$0.379332\pi$
$614$	−19.2345	−0.776241
$615$	0	0
$616$	0	0
$617$	−44.3782	−1.78660	−0.893299	−	0.449463i	$-0.851615\pi$
$617$	−44.3782	−1.78660	−0.893299	+	0.449463i	$0.851615\pi$
$618$	0	0
$619$	25.0085	1.00518	0.502588	−	0.864526i	$-0.332381\pi$
$619$	25.0085	1.00518	0.502588	+	0.864526i	$0.332381\pi$
$620$	−12.2010	−0.490005
$621$	0	0
$622$	−57.5306	−2.30677
$623$	0	0
$624$	0	0
$625$	−23.8716	−0.954866
$626$	5.39741	0.215724
$627$	0	0
$628$	−18.3842	−0.733611
$629$	57.6388	2.29821
$630$	0	0
$631$	−18.4638	−0.735032	−0.367516	−	0.930017i	$-0.619792\pi$
$631$	−18.4638	−0.735032	−0.367516	+	0.930017i	$0.619792\pi$
$632$	−19.9876	−0.795066
$633$	0	0
$634$	−49.1797	−1.95318
$635$	19.2233	0.762853
$636$	0	0
$637$	0	0
$638$	−8.86677	−0.351039
$639$	0	0
$640$	−76.4832	−3.02326
$641$	21.2567	0.839589	0.419795	−	0.907619i	$-0.362102\pi$
$641$	21.2567	0.839589	0.419795	+	0.907619i	$0.362102\pi$
$642$	0	0
$643$	36.0554	1.42188	0.710942	−	0.703251i	$-0.248269\pi$
$643$	36.0554	1.42188	0.710942	+	0.703251i	$0.248269\pi$
$644$	0	0
$645$	0	0
$646$	−10.9146	−0.429428
$647$	39.8234	1.56562	0.782809	−	0.622262i	$-0.213786\pi$
$647$	39.8234	1.56562	0.782809	+	0.622262i	$0.213786\pi$
$648$	0	0
$649$	−1.09863	−0.0431250
$650$	−0.589510	−0.0231225
$651$	0	0
$652$	−74.9469	−2.93515
$653$	32.4669	1.27053	0.635265	−	0.772295i	$-0.280891\pi$
$653$	32.4669	1.27053	0.635265	+	0.772295i	$0.280891\pi$
$654$	0	0
$655$	−22.9969	−0.898562
$656$	106.865	4.17237
$657$	0	0
$658$	0	0
$659$	−23.5230	−0.916327	−0.458164	−	0.888868i	$-0.651493\pi$
$659$	−23.5230	−0.916327	−0.458164	+	0.888868i	$0.651493\pi$
$660$	0	0
$661$	−14.0389	−0.546049	−0.273025	−	0.962007i	$-0.588024\pi$
$661$	−14.0389	−0.546049	−0.273025	+	0.962007i	$0.588024\pi$
$662$	39.9897	1.55424
$663$	0	0
$664$	62.2525	2.41587
$665$	0	0
$666$	0	0
$667$	−2.02878	−0.0785547
$668$	88.8848	3.43905
$669$	0	0
$670$	−26.6967	−1.03138
$671$	13.1017	0.505786
$672$	0	0
$673$	−47.1937	−1.81918	−0.909592	−	0.415502i	$-0.863606\pi$
$673$	−47.1937	−1.81918	−0.909592	+	0.415502i	$0.863606\pi$
$674$	−34.9051	−1.34449
$675$	0	0
$676$	5.42699	0.208730
$677$	−9.58876	−0.368526	−0.184263	−	0.982877i	$-0.558990\pi$
$677$	−9.58876	−0.368526	−0.184263	+	0.982877i	$0.558990\pi$
$678$	0	0
$679$	0	0
$680$	108.083	4.14481
$681$	0	0
$682$	2.93621	0.112433
$683$	−47.3161	−1.81050	−0.905250	−	0.424879i	$-0.860317\pi$
$683$	−47.3161	−1.81050	−0.905250	+	0.424879i	$0.860317\pi$
$684$	0	0
$685$	−19.0976	−0.729680
$686$	0	0
$687$	0	0
$688$	12.9599	0.494091
$689$	4.88814	0.186223
$690$	0	0
$691$	27.1119	1.03138	0.515692	−	0.856774i	$-0.327535\pi$
$691$	27.1119	1.03138	0.515692	+	0.856774i	$0.327535\pi$
$692$	22.3888	0.851095
$693$	0	0
$694$	55.0648	2.09023
$695$	8.74866	0.331855
$696$	0	0
$697$	−38.7340	−1.46716
$698$	−50.2628	−1.90248
$699$	0	0
$700$	0	0
$701$	1.79821	0.0679176	0.0339588	−	0.999423i	$-0.489189\pi$
$701$	1.79821	0.0679176	0.0339588	+	0.999423i	$0.489189\pi$
$702$	0	0
$703$	8.24515	0.310972
$704$	29.6838	1.11875
$705$	0	0
$706$	22.1954	0.835336
$707$	0	0
$708$	0	0
$709$	−28.3230	−1.06369	−0.531846	−	0.846841i	$-0.678502\pi$
$709$	−28.3230	−1.06369	−0.531846	+	0.846841i	$0.678502\pi$
$710$	−39.3561	−1.47701
$711$	0	0
$712$	53.8675	2.01877
$713$	0.671827	0.0251601
$714$	0	0
$715$	−2.29249	−0.0857341
$716$	−78.2223	−2.92331
$717$	0	0
$718$	−88.8704	−3.31661
$719$	−41.8971	−1.56250	−0.781249	−	0.624220i	$-0.785417\pi$
$719$	−41.8971	−1.56250	−0.781249	+	0.624220i	$0.785417\pi$
$720$	0	0
$721$	0	0
$722$	50.2184	1.86894
$723$	0	0
$724$	−98.2361	−3.65092
$725$	−0.671457	−0.0249373
$726$	0	0
$727$	−19.5123	−0.723670	−0.361835	−	0.932242i	$-0.617850\pi$
$727$	−19.5123	−0.723670	−0.361835	+	0.932242i	$0.617850\pi$
$728$	0	0
$729$	0	0
$730$	−49.3742	−1.82742
$731$	−4.69742	−0.173740
$732$	0	0
$733$	−17.7540	−0.655757	−0.327879	−	0.944720i	$-0.606334\pi$
$733$	−17.7540	−0.655757	−0.327879	+	0.944720i	$0.606334\pi$
$734$	−8.61213	−0.317880
$735$	0	0
$736$	13.7939	0.508450
$737$	4.69457	0.172927
$738$	0	0
$739$	44.3142	1.63012	0.815061	−	0.579375i	$-0.196703\pi$
$739$	44.3142	1.63012	0.815061	+	0.579375i	$0.196703\pi$
$740$	−129.299	−4.75314
$741$	0	0
$742$	0	0
$743$	7.16727	0.262941	0.131471	−	0.991320i	$-0.458030\pi$
$743$	7.16727	0.262941	0.131471	+	0.991320i	$0.458030\pi$
$744$	0	0
$745$	−33.6662	−1.23344
$746$	4.02710	0.147442
$747$	0	0
$748$	−30.0983	−1.10050
$749$	0	0
$750$	0	0
$751$	−33.9065	−1.23726	−0.618632	−	0.785681i	$-0.712313\pi$
$751$	−33.9065	−1.23726	−0.618632	+	0.785681i	$0.712313\pi$
$752$	34.1235	1.24436
$753$	0	0
$754$	8.45941	0.308073
$755$	−29.9110	−1.08857
$756$	0	0
$757$	−0.906670	−0.0329535	−0.0164767	−	0.999864i	$-0.505245\pi$
$757$	−0.906670	−0.0329535	−0.0164767	+	0.999864i	$0.505245\pi$
$758$	−29.2294	−1.06166
$759$	0	0
$760$	15.4612	0.560836
$761$	20.2494	0.734039	0.367020	−	0.930213i	$-0.380378\pi$
$761$	20.2494	0.734039	0.367020	+	0.930213i	$0.380378\pi$
$762$	0	0
$763$	0	0
$764$	−30.0729	−1.08800
$765$	0	0
$766$	58.3500	2.10827
$767$	1.04815	0.0378467
$768$	0	0
$769$	36.9094	1.33099	0.665494	−	0.746403i	$-0.268221\pi$
$769$	36.9094	1.33099	0.665494	+	0.746403i	$0.268221\pi$
$770$	0	0
$771$	0	0
$772$	−47.4367	−1.70728
$773$	−9.88037	−0.355372	−0.177686	−	0.984087i	$-0.556861\pi$
$773$	−9.88037	−0.355372	−0.177686	+	0.984087i	$0.556861\pi$
$774$	0	0
$775$	0.222352	0.00798711
$776$	−26.9701	−0.968169
$777$	0	0
$778$	94.7893	3.39836
$779$	−5.54086	−0.198522
$780$	0	0
$781$	6.92069	0.247642
$782$	−9.42467	−0.337025
$783$	0	0
$784$	0	0
$785$	−7.40915	−0.264444
$786$	0	0
$787$	−37.6821	−1.34322	−0.671611	−	0.740904i	$-0.734397\pi$
$787$	−37.6821	−1.34322	−0.671611	+	0.740904i	$0.734397\pi$
$788$	29.6788	1.05726
$789$	0	0
$790$	−12.7565	−0.453854
$791$	0	0
$792$	0	0
$793$	−12.4998	−0.443880
$794$	12.1331	0.430588
$795$	0	0
$796$	−106.026	−3.75799
$797$	28.3837	1.00540	0.502701	−	0.864460i	$-0.332340\pi$
$797$	28.3837	1.00540	0.502701	+	0.864460i	$0.332340\pi$
$798$	0	0
$799$	−12.3683	−0.437560
$800$	4.56531	0.161408
$801$	0	0
$802$	−37.4824	−1.32355
$803$	8.68236	0.306394
$804$	0	0
$805$	0	0
$806$	−2.80132	−0.0986722
$807$	0	0
$808$	105.109	3.69771
$809$	11.7465	0.412987	0.206493	−	0.978448i	$-0.433795\pi$
$809$	11.7465	0.412987	0.206493	+	0.978448i	$0.433795\pi$
$810$	0	0
$811$	−2.01940	−0.0709108	−0.0354554	−	0.999371i	$-0.511288\pi$
$811$	−2.01940	−0.0709108	−0.0354554	+	0.999371i	$0.511288\pi$
$812$	0	0
$813$	0	0
$814$	31.1163	1.09063
$815$	−30.2048	−1.05803
$816$	0	0
$817$	−0.671959	−0.0235089
$818$	−9.51676	−0.332746
$819$	0	0
$820$	86.8910	3.03437
$821$	15.0842	0.526441	0.263220	−	0.964736i	$-0.415215\pi$
$821$	15.0842	0.526441	0.263220	+	0.964736i	$0.415215\pi$
$822$	0	0
$823$	−14.7766	−0.515079	−0.257539	−	0.966268i	$-0.582912\pi$
$823$	−14.7766	−0.515079	−0.257539	+	0.966268i	$0.582912\pi$
$824$	188.968	6.58301
$825$	0	0
$826$	0	0
$827$	−13.0407	−0.453471	−0.226736	−	0.973956i	$-0.572805\pi$
$827$	−13.0407	−0.453471	−0.226736	+	0.973956i	$0.572805\pi$
$828$	0	0
$829$	25.4581	0.884198	0.442099	−	0.896966i	$-0.354234\pi$
$829$	25.4581	0.884198	0.442099	+	0.896966i	$0.354234\pi$
$830$	39.7306	1.37907
$831$	0	0
$832$	−28.3200	−0.981820
$833$	0	0
$834$	0	0
$835$	35.8220	1.23967
$836$	−4.30553	−0.148910
$837$	0	0
$838$	9.72198	0.335840
$839$	32.1703	1.11064	0.555321	−	0.831636i	$-0.312596\pi$
$839$	32.1703	1.11064	0.555321	+	0.831636i	$0.312596\pi$
$840$	0	0
$841$	−19.3647	−0.667747
$842$	27.2525	0.939183
$843$	0	0
$844$	90.5792	3.11787
$845$	2.18716	0.0752407
$846$	0	0
$847$	0	0
$848$	−71.3582	−2.45045
$849$	0	0
$850$	−3.11924	−0.106989
$851$	7.11964	0.244058
$852$	0	0
$853$	19.3910	0.663934	0.331967	−	0.943291i	$-0.392288\pi$
$853$	19.3910	0.663934	0.331967	+	0.943291i	$0.392288\pi$
$854$	0	0
$855$	0	0
$856$	84.5699	2.89054
$857$	17.4242	0.595199	0.297600	−	0.954691i	$-0.403814\pi$
$857$	17.4242	0.595199	0.297600	+	0.954691i	$0.403814\pi$
$858$	0	0
$859$	35.4917	1.21096	0.605481	−	0.795860i	$-0.292981\pi$
$859$	35.4917	1.21096	0.605481	+	0.795860i	$0.292981\pi$
$860$	10.5376	0.359329
$861$	0	0
$862$	−30.9704	−1.05486
$863$	−56.0019	−1.90633	−0.953164	−	0.302455i	$-0.902194\pi$
$863$	−56.0019	−1.90633	−0.953164	+	0.302455i	$0.902194\pi$
$864$	0	0
$865$	9.02306	0.306793
$866$	−57.8124	−1.96455
$867$	0	0
$868$	0	0
$869$	2.24320	0.0760953
$870$	0	0
$871$	−4.47889	−0.151761
$872$	−141.038	−4.77615
$873$	0	0
$874$	−1.34819	−0.0456031
$875$	0	0
$876$	0	0
$877$	25.2062	0.851153	0.425577	−	0.904922i	$-0.360071\pi$
$877$	25.2062	0.851153	0.425577	+	0.904922i	$0.360071\pi$
$878$	−66.7704	−2.25339
$879$	0	0
$880$	33.4663	1.12815
$881$	−18.6082	−0.626925	−0.313463	−	0.949601i	$-0.601489\pi$
$881$	−18.6082	−0.626925	−0.313463	+	0.949601i	$0.601489\pi$
$882$	0	0
$883$	−11.2552	−0.378768	−0.189384	−	0.981903i	$-0.560649\pi$
$883$	−11.2552	−0.378768	−0.189384	+	0.981903i	$0.560649\pi$
$884$	28.7155	0.965808
$885$	0	0
$886$	110.288	3.70519
$887$	−39.2112	−1.31658	−0.658292	−	0.752762i	$-0.728721\pi$
$887$	−39.2112	−1.31658	−0.658292	+	0.752762i	$0.728721\pi$
$888$	0	0
$889$	0	0
$890$	34.3792	1.15239
$891$	0	0
$892$	28.9919	0.970720
$893$	−1.76928	−0.0592066
$894$	0	0
$895$	−31.5249	−1.05376
$896$	0	0
$897$	0	0
$898$	−75.6633	−2.52492
$899$	−3.19073	−0.106417
$900$	0	0
$901$	25.8644	0.861667
$902$	−20.9106	−0.696247
$903$	0	0
$904$	28.9903	0.964203
$905$	−39.5907	−1.31604
$906$	0	0
$907$	21.5970	0.717116	0.358558	−	0.933508i	$-0.383269\pi$
$907$	21.5970	0.717116	0.358558	+	0.933508i	$0.383269\pi$
$908$	109.199	3.62391
$909$	0	0
$910$	0	0
$911$	32.4434	1.07490	0.537449	−	0.843297i	$-0.319388\pi$
$911$	32.4434	1.07490	0.537449	+	0.843297i	$0.319388\pi$
$912$	0	0
$913$	−6.98656	−0.231221
$914$	30.5062	1.00906
$915$	0	0
$916$	−137.030	−4.52760
$917$	0	0
$918$	0	0
$919$	35.7372	1.17886	0.589430	−	0.807819i	$-0.299352\pi$
$919$	35.7372	1.17886	0.589430	+	0.807819i	$0.299352\pi$
$920$	13.3506	0.440157
$921$	0	0
$922$	25.3386	0.834483
$923$	−6.60274	−0.217332
$924$	0	0
$925$	2.35636	0.0774765
$926$	−76.9716	−2.52944
$927$	0	0
$928$	−65.5118	−2.15053
$929$	11.7769	0.386389	0.193194	−	0.981161i	$-0.438115\pi$
$929$	11.7769	0.386389	0.193194	+	0.981161i	$0.438115\pi$
$930$	0	0
$931$	0	0
$932$	4.30553	0.141032
$933$	0	0
$934$	−60.6658	−1.98505
$935$	−12.1301	−0.396697
$936$	0	0
$937$	−18.9937	−0.620497	−0.310248	−	0.950655i	$-0.600412\pi$
$937$	−18.9937	−0.620497	−0.310248	+	0.950655i	$0.600412\pi$
$938$	0	0
$939$	0	0
$940$	27.7456	0.904961
$941$	6.81864	0.222281	0.111141	−	0.993805i	$-0.464550\pi$
$941$	6.81864	0.222281	0.111141	+	0.993805i	$0.464550\pi$
$942$	0	0
$943$	−4.78450	−0.155805
$944$	−15.3012	−0.498012
$945$	0	0
$946$	−2.53590	−0.0824493
$947$	−1.05992	−0.0344426	−0.0172213	−	0.999852i	$-0.505482\pi$
$947$	−1.05992	−0.0344426	−0.0172213	+	0.999852i	$0.505482\pi$
$948$	0	0
$949$	−8.28347	−0.268893
$950$	−0.446204	−0.0144768
$951$	0	0
$952$	0	0
$953$	40.4127	1.30910	0.654548	−	0.756020i	$-0.272859\pi$
$953$	40.4127	1.30910	0.654548	+	0.756020i	$0.272859\pi$
$954$	0	0
$955$	−12.1199	−0.392189
$956$	−108.805	−3.51899
$957$	0	0
$958$	89.5964	2.89473
$959$	0	0
$960$	0	0
$961$	−29.9434	−0.965916
$962$	−29.6868	−0.957140
$963$	0	0
$964$	−74.9578	−2.41423
$965$	−19.1177	−0.615422
$966$	0	0
$967$	−36.2949	−1.16717	−0.583583	−	0.812053i	$-0.698350\pi$
$967$	−36.2949	−1.16717	−0.583583	+	0.812053i	$0.698350\pi$
$968$	92.4729	2.97219
$969$	0	0
$970$	−17.2128	−0.552668
$971$	−21.4437	−0.688160	−0.344080	−	0.938940i	$-0.611809\pi$
$971$	−21.4437	−0.688160	−0.344080	+	0.938940i	$0.611809\pi$
$972$	0	0
$973$	0	0
$974$	76.0137	2.43564
$975$	0	0
$976$	182.475	5.84088
$977$	39.8277	1.27420	0.637100	−	0.770781i	$-0.280134\pi$
$977$	39.8277	1.27420	0.637100	+	0.770781i	$0.280134\pi$
$978$	0	0
$979$	−6.04551	−0.193215
$980$	0	0
$981$	0	0
$982$	29.0432	0.926807
$983$	15.8814	0.506538	0.253269	−	0.967396i	$-0.418494\pi$
$983$	15.8814	0.506538	0.253269	+	0.967396i	$0.418494\pi$
$984$	0	0
$985$	11.9610	0.381110
$986$	44.7608	1.42548
$987$	0	0
$988$	4.10772	0.130684
$989$	−0.580233	−0.0184503
$990$	0	0
$991$	−17.6687	−0.561265	−0.280633	−	0.959815i	$-0.590544\pi$
$991$	−17.6687	−0.561265	−0.280633	+	0.959815i	$0.590544\pi$
$992$	21.6941	0.688789
$993$	0	0
$994$	0	0
$995$	−42.7301	−1.35464
$996$	0	0
$997$	24.8608	0.787350	0.393675	−	0.919250i	$-0.371203\pi$
$997$	24.8608	0.787350	0.393675	+	0.919250i	$0.371203\pi$
$998$	66.7997	2.11451
$999$	0	0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bm.1.1		5
3.2	odd	2		637.2.a.k.1.5		5
7.3	odd	6		819.2.j.h.352.5		10
7.5	odd	6		819.2.j.h.235.5		10
7.6	odd	2		5733.2.a.bl.1.1		5
21.2	odd	6		637.2.e.m.508.1		10
21.5	even	6		91.2.e.c.53.1	✓	10
21.11	odd	6		637.2.e.m.79.1		10
21.17	even	6		91.2.e.c.79.1	yes	10
21.20	even	2		637.2.a.l.1.5		5
39.38	odd	2		8281.2.a.bx.1.1		5
84.47	odd	6		1456.2.r.p.417.2		10
84.59	odd	6		1456.2.r.p.625.2		10
273.38	even	6		1183.2.e.f.170.5		10
273.194	even	6		1183.2.e.f.508.5		10
273.272	even	2		8281.2.a.bw.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.1	✓	10	21.5	even	6
91.2.e.c.79.1	yes	10	21.17	even	6
637.2.a.k.1.5		5	3.2	odd	2
637.2.a.l.1.5		5	21.20	even	2
637.2.e.m.79.1		10	21.11	odd	6
637.2.e.m.508.1		10	21.2	odd	6
819.2.j.h.235.5		10	7.5	odd	6
819.2.j.h.352.5		10	7.3	odd	6
1183.2.e.f.170.5		10	273.38	even	6
1183.2.e.f.508.5		10	273.194	even	6
1456.2.r.p.417.2		10	84.47	odd	6
1456.2.r.p.625.2		10	84.59	odd	6
5733.2.a.bl.1.1		5	7.6	odd	2
5733.2.a.bm.1.1		5	1.1	even	1	trivial
8281.2.a.bw.1.1		5	273.272	even	2
8281.2.a.bx.1.1		5	39.38	odd	2

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	5733.2.a.bm.1.1

Level	$5733$
Weight	$2$
Character	5733.1
Self dual	yes
Analytic conductor	$45.778$
Analytic rank	$1$
Dimension	$5$
CM	no
Inner twists	$1$