LMFDB - Embedded newform 5733.2.a.bx.1.8

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 $ x^10 - 4x^9 - 10x^8 + 52x^7 + 16x^6 - 212x^5 + 64x^4 + 300x^3 - 159x^2 - 80*x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1911)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.56844$ of defining polynomial
Character	$\chi$	$=$	5733.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56844 q^{2} +0.460010 q^{4} +4.07203 q^{5} -2.41539 q^{8} +O(q^{10})$	$q+1.56844 q^{2} +0.460010 q^{4} +4.07203 q^{5} -2.41539 q^{8} +6.38674 q^{10} +4.60112 q^{11} -1.00000 q^{13} -4.70841 q^{16} +3.53841 q^{17} -5.76389 q^{19} +1.87317 q^{20} +7.21659 q^{22} +4.38609 q^{23} +11.5814 q^{25} -1.56844 q^{26} -4.06860 q^{29} +3.28375 q^{31} -2.55410 q^{32} +5.54979 q^{34} +8.96014 q^{37} -9.04033 q^{38} -9.83552 q^{40} +1.14388 q^{41} -7.33023 q^{43} +2.11656 q^{44} +6.87933 q^{46} +7.46654 q^{47} +18.1648 q^{50} -0.460010 q^{52} -4.15199 q^{53} +18.7359 q^{55} -6.38137 q^{58} +5.96858 q^{59} +0.567843 q^{61} +5.15036 q^{62} +5.41087 q^{64} -4.07203 q^{65} -9.76134 q^{67} +1.62770 q^{68} +11.7872 q^{71} +1.93497 q^{73} +14.0535 q^{74} -2.65144 q^{76} +3.44078 q^{79} -19.1728 q^{80} +1.79411 q^{82} +8.69728 q^{83} +14.4085 q^{85} -11.4970 q^{86} -11.1135 q^{88} -14.5467 q^{89} +2.01764 q^{92} +11.7108 q^{94} -23.4707 q^{95} +13.4353 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8	$ 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8} + 8 q^{10} - 12 q^{11} - 10 q^{13} + 24 q^{16} + 10 q^{19} + 16 q^{20} + 8 q^{22} - 14 q^{23} + 32 q^{25} + 4 q^{26} - 18 q^{29} + 14 q^{31} - 28 q^{32} + 4 q^{34} + 24 q^{37} + 4 q^{38} + 16 q^{40} + 24 q^{41} + 2 q^{43} - 48 q^{44} + 20 q^{46} + 18 q^{47} + 28 q^{50} - 16 q^{52} - 10 q^{53} + 12 q^{55} + 12 q^{58} + 12 q^{59} - 4 q^{61} - 4 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 40 q^{68} - 32 q^{71} - 18 q^{73} - 24 q^{74} + 32 q^{76} + 34 q^{79} + 32 q^{80} + 48 q^{82} + 30 q^{83} - 40 q^{86} + 32 q^{88} + 10 q^{89} + 40 q^{92} - 24 q^{94} + 30 q^{95} - 2 q^{97}+O(q^{100}) $ 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8 + 8 * q^10 - 12 * q^11 - 10 * q^13 + 24 * q^16 + 10 * q^19 + 16 * q^20 + 8 * q^22 - 14 * q^23 + 32 * q^25 + 4 * q^26 - 18 * q^29 + 14 * q^31 - 28 * q^32 + 4 * q^34 + 24 * q^37 + 4 * q^38 + 16 * q^40 + 24 * q^41 + 2 * q^43 - 48 * q^44 + 20 * q^46 + 18 * q^47 + 28 * q^50 - 16 * q^52 - 10 * q^53 + 12 * q^55 + 12 * q^58 + 12 * q^59 - 4 * q^61 - 4 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 40 * q^68 - 32 * q^71 - 18 * q^73 - 24 * q^74 + 32 * q^76 + 34 * q^79 + 32 * q^80 + 48 * q^82 + 30 * q^83 - 40 * q^86 + 32 * q^88 + 10 * q^89 + 40 * q^92 - 24 * q^94 + 30 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.56844	1.10906	0.554528	−	0.832165i	$-0.312899\pi$
$2$	1.56844	1.10906	0.554528	+	0.832165i	$0.312899\pi$
$3$	0	0
$3$	0	0
$4$	0.460010	0.230005
$5$	4.07203	1.82107	0.910534	−	0.413435i	$-0.135671\pi$
$5$	4.07203	1.82107	0.910534	+	0.413435i	$0.135671\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−2.41539	−0.853968
$9$	0	0
$10$	6.38674	2.01967
$11$	4.60112	1.38729	0.693645	−	0.720317i	$-0.256004\pi$
$11$	4.60112	1.38729	0.693645	+	0.720317i	$0.256004\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−4.70841	−1.17710
$17$	3.53841	0.858190	0.429095	−	0.903259i	$-0.358833\pi$
$17$	3.53841	0.858190	0.429095	+	0.903259i	$0.358833\pi$
$18$	0	0
$19$	−5.76389	−1.32233	−0.661164	−	0.750242i	$-0.729937\pi$
$19$	−5.76389	−1.32233	−0.661164	+	0.750242i	$0.729937\pi$
$20$	1.87317	0.418854
$21$	0	0
$22$	7.21659	1.53858
$23$	4.38609	0.914563	0.457282	−	0.889322i	$-0.348823\pi$
$23$	4.38609	0.914563	0.457282	+	0.889322i	$0.348823\pi$
$24$	0	0
$25$	11.5814	2.31629
$26$	−1.56844	−0.307597
$27$	0	0
$28$	0	0
$29$	−4.06860	−0.755521	−0.377760	−	0.925903i	$-0.623306\pi$
$29$	−4.06860	−0.755521	−0.377760	+	0.925903i	$0.623306\pi$
$30$	0	0
$31$	3.28375	0.589778	0.294889	−	0.955532i	$-0.404717\pi$
$31$	3.28375	0.589778	0.294889	+	0.955532i	$0.404717\pi$
$32$	−2.55410	−0.451505
$33$	0	0
$34$	5.54979	0.951781
$35$	0	0
$36$	0	0
$37$	8.96014	1.47304	0.736519	−	0.676416i	$-0.236468\pi$
$37$	8.96014	1.47304	0.736519	+	0.676416i	$0.236468\pi$
$38$	−9.04033	−1.46653
$39$	0	0
$40$	−9.83552	−1.55513
$41$	1.14388	0.178644	0.0893218	−	0.996003i	$-0.471530\pi$
$41$	1.14388	0.178644	0.0893218	+	0.996003i	$0.471530\pi$
$42$	0	0
$43$	−7.33023	−1.11785	−0.558925	−	0.829219i	$-0.688786\pi$
$43$	−7.33023	−1.11785	−0.558925	+	0.829219i	$0.688786\pi$
$44$	2.11656	0.319083
$45$	0	0
$46$	6.87933	1.01430
$47$	7.46654	1.08911	0.544553	−	0.838726i	$-0.316699\pi$
$47$	7.46654	1.08911	0.544553	+	0.838726i	$0.316699\pi$
$48$	0	0
$49$	0	0
$50$	18.1648	2.56889
$51$	0	0
$52$	−0.460010	−0.0637919
$53$	−4.15199	−0.570319	−0.285160	−	0.958480i	$-0.592047\pi$
$53$	−4.15199	−0.570319	−0.285160	+	0.958480i	$0.592047\pi$
$54$	0	0
$55$	18.7359	2.52635
$56$	0	0
$57$	0	0
$58$	−6.38137	−0.837915
$59$	5.96858	0.777043	0.388522	−	0.921440i	$-0.372986\pi$
$59$	5.96858	0.777043	0.388522	+	0.921440i	$0.372986\pi$
$60$	0	0
$61$	0.567843	0.0727049	0.0363524	−	0.999339i	$-0.488426\pi$
$61$	0.567843	0.0727049	0.0363524	+	0.999339i	$0.488426\pi$
$62$	5.15036	0.654097
$63$	0	0
$64$	5.41087	0.676359
$65$	−4.07203	−0.505073
$66$	0	0
$67$	−9.76134	−1.19254	−0.596269	−	0.802785i	$-0.703351\pi$
$67$	−9.76134	−1.19254	−0.596269	+	0.802785i	$0.703351\pi$
$68$	1.62770	0.197388
$69$	0	0
$70$	0	0
$71$	11.7872	1.39889	0.699444	−	0.714688i	$-0.253431\pi$
$71$	11.7872	1.39889	0.699444	+	0.714688i	$0.253431\pi$
$72$	0	0
$73$	1.93497	0.226471	0.113236	−	0.993568i	$-0.463879\pi$
$73$	1.93497	0.226471	0.113236	+	0.993568i	$0.463879\pi$
$74$	14.0535	1.63368
$75$	0	0
$76$	−2.65144	−0.304142
$77$	0	0
$78$	0	0
$79$	3.44078	0.387118	0.193559	−	0.981089i	$-0.437997\pi$
$79$	3.44078	0.387118	0.193559	+	0.981089i	$0.437997\pi$
$80$	−19.1728	−2.14358
$81$	0	0
$82$	1.79411	0.198126
$83$	8.69728	0.954651	0.477325	−	0.878727i	$-0.341606\pi$
$83$	8.69728	0.954651	0.477325	+	0.878727i	$0.341606\pi$
$84$	0	0
$85$	14.4085	1.56282
$86$	−11.4970	−1.23976
$87$	0	0
$88$	−11.1135	−1.18470
$89$	−14.5467	−1.54194	−0.770971	−	0.636870i	$-0.780229\pi$
$89$	−14.5467	−1.54194	−0.770971	+	0.636870i	$0.780229\pi$
$90$	0	0
$91$	0	0
$92$	2.01764	0.210354
$93$	0	0
$94$	11.7108	1.20788
$95$	−23.4707	−2.40805
$96$	0	0
$97$	13.4353	1.36415	0.682073	−	0.731284i	$-0.261079\pi$
$97$	13.4353	1.36415	0.682073	+	0.731284i	$0.261079\pi$
$98$	0	0
$99$	0	0
$100$	5.32757	0.532757
$101$	−0.583693	−0.0580796	−0.0290398	−	0.999578i	$-0.509245\pi$
$101$	−0.583693	−0.0580796	−0.0290398	+	0.999578i	$0.509245\pi$
$102$	0	0
$103$	14.0473	1.38412	0.692060	−	0.721840i	$-0.256703\pi$
$103$	14.0473	1.38412	0.692060	+	0.721840i	$0.256703\pi$
$104$	2.41539	0.236848
$105$	0	0
$106$	−6.51215	−0.632516
$107$	−17.5274	−1.69444	−0.847221	−	0.531240i	$-0.821726\pi$
$107$	−17.5274	−1.69444	−0.847221	+	0.531240i	$0.821726\pi$
$108$	0	0
$109$	−4.60883	−0.441446	−0.220723	−	0.975336i	$-0.570842\pi$
$109$	−4.60883	−0.441446	−0.220723	+	0.975336i	$0.570842\pi$
$110$	29.3862	2.80186
$111$	0	0
$112$	0	0
$113$	−21.1046	−1.98535	−0.992677	−	0.120797i	$-0.961455\pi$
$113$	−21.1046	−1.98535	−0.992677	+	0.120797i	$0.961455\pi$
$114$	0	0
$115$	17.8603	1.66548
$116$	−1.87160	−0.173773
$117$	0	0
$118$	9.36138	0.861785
$119$	0	0
$120$	0	0
$121$	10.1703	0.924574
$122$	0.890629	0.0806337
$123$	0	0
$124$	1.51055	0.135652
$125$	26.7998	2.39705
$126$	0	0
$127$	10.9327	0.970122	0.485061	−	0.874480i	$-0.338797\pi$
$127$	10.9327	0.970122	0.485061	+	0.874480i	$0.338797\pi$
$128$	13.5948	1.20162
$129$	0	0
$130$	−6.38674	−0.560154
$131$	8.69633	0.759801	0.379901	−	0.925027i	$-0.375958\pi$
$131$	8.69633	0.759801	0.379901	+	0.925027i	$0.375958\pi$
$132$	0	0
$133$	0	0
$134$	−15.3101	−1.32259
$135$	0	0
$136$	−8.54662	−0.732867
$137$	−19.7875	−1.69056	−0.845280	−	0.534323i	$-0.820567\pi$
$137$	−19.7875	−1.69056	−0.845280	+	0.534323i	$0.820567\pi$
$138$	0	0
$139$	−18.9914	−1.61083	−0.805416	−	0.592710i	$-0.798058\pi$
$139$	−18.9914	−1.61083	−0.805416	+	0.592710i	$0.798058\pi$
$140$	0	0
$141$	0	0
$142$	18.4876	1.55144
$143$	−4.60112	−0.384765
$144$	0	0
$145$	−16.5675	−1.37585
$146$	3.03489	0.251169
$147$	0	0
$148$	4.12175	0.338806
$149$	1.17361	0.0961458	0.0480729	−	0.998844i	$-0.484692\pi$
$149$	1.17361	0.0961458	0.0480729	+	0.998844i	$0.484692\pi$
$150$	0	0
$151$	13.3332	1.08504	0.542520	−	0.840043i	$-0.317470\pi$
$151$	13.3332	1.08504	0.542520	+	0.840043i	$0.317470\pi$
$152$	13.9220	1.12922
$153$	0	0
$154$	0	0
$155$	13.3715	1.07403
$156$	0	0
$157$	15.8299	1.26336	0.631681	−	0.775229i	$-0.282365\pi$
$157$	15.8299	1.26336	0.631681	+	0.775229i	$0.282365\pi$
$158$	5.39666	0.429335
$159$	0	0
$160$	−10.4004	−0.822221
$161$	0	0
$162$	0	0
$163$	11.4827	0.899394	0.449697	−	0.893181i	$-0.351532\pi$
$163$	11.4827	0.899394	0.449697	+	0.893181i	$0.351532\pi$
$164$	0.526195	0.0410889
$165$	0	0
$166$	13.6412	1.05876
$167$	19.8532	1.53629	0.768144	−	0.640278i	$-0.221181\pi$
$167$	19.8532	1.53629	0.768144	+	0.640278i	$0.221181\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	22.5989	1.73326
$171$	0	0
$172$	−3.37197	−0.257111
$173$	−8.78471	−0.667889	−0.333944	−	0.942593i	$-0.608380\pi$
$173$	−8.78471	−0.667889	−0.333944	+	0.942593i	$0.608380\pi$
$174$	0	0
$175$	0	0
$176$	−21.6640	−1.63298
$177$	0	0
$178$	−22.8156	−1.71010
$179$	−18.0234	−1.34713	−0.673565	−	0.739128i	$-0.735238\pi$
$179$	−18.0234	−1.34713	−0.673565	+	0.739128i	$0.735238\pi$
$180$	0	0
$181$	3.28601	0.244247	0.122124	−	0.992515i	$-0.461030\pi$
$181$	3.28601	0.244247	0.122124	+	0.992515i	$0.461030\pi$
$182$	0	0
$183$	0	0
$184$	−10.5941	−0.781007
$185$	36.4860	2.68250
$186$	0	0
$187$	16.2806	1.19056
$188$	3.43468	0.250500
$189$	0	0
$190$	−36.8125	−2.67066
$191$	3.15363	0.228189	0.114094	−	0.993470i	$-0.463603\pi$
$191$	3.15363	0.228189	0.114094	+	0.993470i	$0.463603\pi$
$192$	0	0
$193$	−22.5336	−1.62200	−0.811001	−	0.585045i	$-0.801077\pi$
$193$	−22.5336	−1.62200	−0.811001	+	0.585045i	$0.801077\pi$
$194$	21.0724	1.51291
$195$	0	0
$196$	0	0
$197$	−6.90510	−0.491968	−0.245984	−	0.969274i	$-0.579111\pi$
$197$	−6.90510	−0.491968	−0.245984	+	0.969274i	$0.579111\pi$
$198$	0	0
$199$	−12.5484	−0.889532	−0.444766	−	0.895647i	$-0.646713\pi$
$199$	−12.5484	−0.889532	−0.444766	+	0.895647i	$0.646713\pi$
$200$	−27.9736	−1.97803
$201$	0	0
$202$	−0.915488	−0.0644135
$203$	0	0
$204$	0	0
$205$	4.65790	0.325322
$206$	22.0324	1.53507
$207$	0	0
$208$	4.70841	0.326470
$209$	−26.5204	−1.83445
$210$	0	0
$211$	16.9769	1.16874	0.584368	−	0.811489i	$-0.301343\pi$
$211$	16.9769	1.16874	0.584368	+	0.811489i	$0.301343\pi$
$212$	−1.90995	−0.131176
$213$	0	0
$214$	−27.4908	−1.87923
$215$	−29.8489	−2.03568
$216$	0	0
$217$	0	0
$218$	−7.22869	−0.489589
$219$	0	0
$220$	8.61870	0.581072
$221$	−3.53841	−0.238019
$222$	0	0
$223$	−6.52248	−0.436778	−0.218389	−	0.975862i	$-0.570080\pi$
$223$	−6.52248	−0.436778	−0.218389	+	0.975862i	$0.570080\pi$
$224$	0	0
$225$	0	0
$226$	−33.1013	−2.20187
$227$	−10.7148	−0.711165	−0.355582	−	0.934645i	$-0.615717\pi$
$227$	−10.7148	−0.711165	−0.355582	+	0.934645i	$0.615717\pi$
$228$	0	0
$229$	−11.5517	−0.763359	−0.381680	−	0.924295i	$-0.624654\pi$
$229$	−11.5517	−0.763359	−0.381680	+	0.924295i	$0.624654\pi$
$230$	28.0128	1.84711
$231$	0	0
$232$	9.82725	0.645190
$233$	−8.20034	−0.537222	−0.268611	−	0.963249i	$-0.586565\pi$
$233$	−8.20034	−0.537222	−0.268611	+	0.963249i	$0.586565\pi$
$234$	0	0
$235$	30.4040	1.98334
$236$	2.74561	0.178724
$237$	0	0
$238$	0	0
$239$	−2.61709	−0.169286	−0.0846429	−	0.996411i	$-0.526975\pi$
$239$	−2.61709	−0.169286	−0.0846429	+	0.996411i	$0.526975\pi$
$240$	0	0
$241$	19.3871	1.24883	0.624416	−	0.781092i	$-0.285337\pi$
$241$	19.3871	1.24883	0.624416	+	0.781092i	$0.285337\pi$
$242$	15.9515	1.02540
$243$	0	0
$244$	0.261213	0.0167225
$245$	0	0
$246$	0	0
$247$	5.76389	0.366748
$248$	−7.93151	−0.503651
$249$	0	0
$250$	42.0339	2.65846
$251$	−15.4043	−0.972311	−0.486156	−	0.873872i	$-0.661601\pi$
$251$	−15.4043	−0.972311	−0.486156	+	0.873872i	$0.661601\pi$
$252$	0	0
$253$	20.1809	1.26876
$254$	17.1473	1.07592
$255$	0	0
$256$	10.5010	0.656310
$257$	−11.7467	−0.732741	−0.366371	−	0.930469i	$-0.619400\pi$
$257$	−11.7467	−0.732741	−0.366371	+	0.930469i	$0.619400\pi$
$258$	0	0
$259$	0	0
$260$	−1.87317	−0.116169
$261$	0	0
$262$	13.6397	0.842662
$263$	16.6278	1.02532	0.512658	−	0.858593i	$-0.328661\pi$
$263$	16.6278	1.02532	0.512658	+	0.858593i	$0.328661\pi$
$264$	0	0
$265$	−16.9070	−1.03859
$266$	0	0
$267$	0	0
$268$	−4.49031	−0.274289
$269$	23.2608	1.41823	0.709117	−	0.705091i	$-0.249094\pi$
$269$	23.2608	1.41823	0.709117	+	0.705091i	$0.249094\pi$
$270$	0	0
$271$	−6.92931	−0.420926	−0.210463	−	0.977602i	$-0.567497\pi$
$271$	−6.92931	−0.420926	−0.210463	+	0.977602i	$0.567497\pi$
$272$	−16.6603	−1.01018
$273$	0	0
$274$	−31.0356	−1.87493
$275$	53.2876	3.21336
$276$	0	0
$277$	−30.4994	−1.83253	−0.916265	−	0.400572i	$-0.868811\pi$
$277$	−30.4994	−1.83253	−0.916265	+	0.400572i	$0.868811\pi$
$278$	−29.7870	−1.78650
$279$	0	0
$280$	0	0
$281$	−17.6855	−1.05503	−0.527515	−	0.849546i	$-0.676876\pi$
$281$	−17.6855	−1.05503	−0.527515	+	0.849546i	$0.676876\pi$
$282$	0	0
$283$	−1.38350	−0.0822405	−0.0411203	−	0.999154i	$-0.513093\pi$
$283$	−1.38350	−0.0822405	−0.0411203	+	0.999154i	$0.513093\pi$
$284$	5.42224	0.321751
$285$	0	0
$286$	−7.21659	−0.426726
$287$	0	0
$288$	0	0
$289$	−4.47966	−0.263509
$290$	−25.9851	−1.52590
$291$	0	0
$292$	0.890105	0.0520895
$293$	16.2793	0.951049	0.475524	−	0.879702i	$-0.342258\pi$
$293$	16.2793	0.951049	0.475524	+	0.879702i	$0.342258\pi$
$294$	0	0
$295$	24.3043	1.41505
$296$	−21.6422	−1.25793
$297$	0	0
$298$	1.84074	0.106631
$299$	−4.38609	−0.253654
$300$	0	0
$301$	0	0
$302$	20.9123	1.20337
$303$	0	0
$304$	27.1388	1.55651
$305$	2.31227	0.132400
$306$	0	0
$307$	−4.45151	−0.254061	−0.127030	−	0.991899i	$-0.540545\pi$
$307$	−4.45151	−0.254061	−0.127030	+	0.991899i	$0.540545\pi$
$308$	0	0
$309$	0	0
$310$	20.9724	1.19115
$311$	26.9233	1.52668	0.763340	−	0.645997i	$-0.223558\pi$
$311$	26.9233	1.52668	0.763340	+	0.645997i	$0.223558\pi$
$312$	0	0
$313$	−10.9157	−0.616991	−0.308496	−	0.951226i	$-0.599826\pi$
$313$	−10.9157	−0.616991	−0.308496	+	0.951226i	$0.599826\pi$
$314$	24.8282	1.40114
$315$	0	0
$316$	1.58279	0.0890389
$317$	21.9087	1.23052	0.615258	−	0.788326i	$-0.289052\pi$
$317$	21.9087	1.23052	0.615258	+	0.788326i	$0.289052\pi$
$318$	0	0
$319$	−18.7201	−1.04813
$320$	22.0332	1.23169
$321$	0	0
$322$	0	0
$323$	−20.3950	−1.13481
$324$	0	0
$325$	−11.5814	−0.642423
$326$	18.0099	0.997478
$327$	0	0
$328$	−2.76290	−0.152556
$329$	0	0
$330$	0	0
$331$	3.28480	0.180549	0.0902745	−	0.995917i	$-0.471226\pi$
$331$	3.28480	0.180549	0.0902745	+	0.995917i	$0.471226\pi$
$332$	4.00083	0.219574
$333$	0	0
$334$	31.1386	1.70383
$335$	−39.7485	−2.17169
$336$	0	0
$337$	−18.6336	−1.01504	−0.507518	−	0.861641i	$-0.669437\pi$
$337$	−18.6336	−1.01504	−0.507518	+	0.861641i	$0.669437\pi$
$338$	1.56844	0.0853120
$339$	0	0
$340$	6.62805	0.359457
$341$	15.1089	0.818193
$342$	0	0
$343$	0	0
$344$	17.7053	0.954607
$345$	0	0
$346$	−13.7783	−0.740726
$347$	9.05462	0.486077	0.243039	−	0.970017i	$-0.421856\pi$
$347$	9.05462	0.486077	0.243039	+	0.970017i	$0.421856\pi$
$348$	0	0
$349$	31.4538	1.68368	0.841840	−	0.539727i	$-0.181472\pi$
$349$	31.4538	1.68368	0.841840	+	0.539727i	$0.181472\pi$
$350$	0	0
$351$	0	0
$352$	−11.7517	−0.626368
$353$	12.5525	0.668104	0.334052	−	0.942555i	$-0.391584\pi$
$353$	12.5525	0.668104	0.334052	+	0.942555i	$0.391584\pi$
$354$	0	0
$355$	47.9980	2.54747
$356$	−6.69160	−0.354654
$357$	0	0
$358$	−28.2686	−1.49404
$359$	12.4124	0.655099	0.327550	−	0.944834i	$-0.393777\pi$
$359$	12.4124	0.655099	0.327550	+	0.944834i	$0.393777\pi$
$360$	0	0
$361$	14.2224	0.748549
$362$	5.15391	0.270884
$363$	0	0
$364$	0	0
$365$	7.87926	0.412419
$366$	0	0
$367$	8.17287	0.426621	0.213310	−	0.976985i	$-0.431575\pi$
$367$	8.17287	0.426621	0.213310	+	0.976985i	$0.431575\pi$
$368$	−20.6515	−1.07653
$369$	0	0
$370$	57.2261	2.97505
$371$	0	0
$372$	0	0
$373$	−17.7190	−0.917454	−0.458727	−	0.888577i	$-0.651694\pi$
$373$	−17.7190	−0.917454	−0.458727	+	0.888577i	$0.651694\pi$
$374$	25.5352	1.32040
$375$	0	0
$376$	−18.0346	−0.930062
$377$	4.06860	0.209544
$378$	0	0
$379$	11.8142	0.606855	0.303428	−	0.952855i	$-0.401869\pi$
$379$	11.8142	0.606855	0.303428	+	0.952855i	$0.401869\pi$
$380$	−10.7968	−0.553862
$381$	0	0
$382$	4.94629	0.253074
$383$	−20.0568	−1.02486	−0.512428	−	0.858730i	$-0.671254\pi$
$383$	−20.0568	−1.02486	−0.512428	+	0.858730i	$0.671254\pi$
$384$	0	0
$385$	0	0
$386$	−35.3426	−1.79889
$387$	0	0
$388$	6.18036	0.313760
$389$	21.6519	1.09780	0.548898	−	0.835889i	$-0.315048\pi$
$389$	21.6519	1.09780	0.548898	+	0.835889i	$0.315048\pi$
$390$	0	0
$391$	15.5198	0.784869
$392$	0	0
$393$	0	0
$394$	−10.8302	−0.545620
$395$	14.0109	0.704967
$396$	0	0
$397$	−15.2147	−0.763605	−0.381802	−	0.924244i	$-0.624697\pi$
$397$	−15.2147	−0.763605	−0.381802	+	0.924244i	$0.624697\pi$
$398$	−19.6814	−0.986541
$399$	0	0
$400$	−54.5302	−2.72651
$401$	−35.3974	−1.76766	−0.883831	−	0.467806i	$-0.845045\pi$
$401$	−35.3974	−1.76766	−0.883831	+	0.467806i	$0.845045\pi$
$402$	0	0
$403$	−3.28375	−0.163575
$404$	−0.268504	−0.0133586
$405$	0	0
$406$	0	0
$407$	41.2267	2.04353
$408$	0	0
$409$	−26.3040	−1.30065	−0.650324	−	0.759657i	$-0.725367\pi$
$409$	−26.3040	−1.30065	−0.650324	+	0.759657i	$0.725367\pi$
$410$	7.30565	0.360800
$411$	0	0
$412$	6.46189	0.318354
$413$	0	0
$414$	0	0
$415$	35.4156	1.73848
$416$	2.55410	0.125225
$417$	0	0
$418$	−41.5956	−2.03451
$419$	21.1113	1.03135	0.515676	−	0.856783i	$-0.327541\pi$
$419$	21.1113	1.03135	0.515676	+	0.856783i	$0.327541\pi$
$420$	0	0
$421$	32.4626	1.58213	0.791065	−	0.611732i	$-0.209527\pi$
$421$	32.4626	1.58213	0.791065	+	0.611732i	$0.209527\pi$
$422$	26.6272	1.29619
$423$	0	0
$424$	10.0286	0.487034
$425$	40.9799	1.98782
$426$	0	0
$427$	0	0
$428$	−8.06279	−0.389730
$429$	0	0
$430$	−46.8163	−2.25768
$431$	−36.4767	−1.75702	−0.878510	−	0.477725i	$-0.841462\pi$
$431$	−36.4767	−1.75702	−0.878510	+	0.477725i	$0.841462\pi$
$432$	0	0
$433$	−17.7417	−0.852611	−0.426306	−	0.904579i	$-0.640185\pi$
$433$	−17.7417	−0.852611	−0.426306	+	0.904579i	$0.640185\pi$
$434$	0	0
$435$	0	0
$436$	−2.12011	−0.101535
$437$	−25.2809	−1.20935
$438$	0	0
$439$	−6.43986	−0.307358	−0.153679	−	0.988121i	$-0.549112\pi$
$439$	−6.43986	−0.307358	−0.153679	+	0.988121i	$0.549112\pi$
$440$	−45.2544	−2.15742
$441$	0	0
$442$	−5.54979	−0.263977
$443$	−2.88090	−0.136875	−0.0684377	−	0.997655i	$-0.521801\pi$
$443$	−2.88090	−0.136875	−0.0684377	+	0.997655i	$0.521801\pi$
$444$	0	0
$445$	−59.2344	−2.80798
$446$	−10.2301	−0.484411
$447$	0	0
$448$	0	0
$449$	−4.32686	−0.204197	−0.102099	−	0.994774i	$-0.532556\pi$
$449$	−4.32686	−0.204197	−0.102099	+	0.994774i	$0.532556\pi$
$450$	0	0
$451$	5.26312	0.247831
$452$	−9.70832	−0.456641
$453$	0	0
$454$	−16.8055	−0.788722
$455$	0	0
$456$	0	0
$457$	−8.66919	−0.405527	−0.202764	−	0.979228i	$-0.564992\pi$
$457$	−8.66919	−0.405527	−0.202764	+	0.979228i	$0.564992\pi$
$458$	−18.1182	−0.846608
$459$	0	0
$460$	8.21591	0.383069
$461$	9.23553	0.430141	0.215071	−	0.976598i	$-0.431002\pi$
$461$	9.23553	0.430141	0.215071	+	0.976598i	$0.431002\pi$
$462$	0	0
$463$	−18.4173	−0.855925	−0.427962	−	0.903797i	$-0.640768\pi$
$463$	−18.4173	−0.855925	−0.427962	+	0.903797i	$0.640768\pi$
$464$	19.1567	0.889325
$465$	0	0
$466$	−12.8618	−0.595809
$467$	−5.58503	−0.258444	−0.129222	−	0.991616i	$-0.541248\pi$
$467$	−5.58503	−0.258444	−0.129222	+	0.991616i	$0.541248\pi$
$468$	0	0
$469$	0	0
$470$	47.6869	2.19963
$471$	0	0
$472$	−14.4164	−0.663570
$473$	−33.7273	−1.55078
$474$	0	0
$475$	−66.7541	−3.06289
$476$	0	0
$477$	0	0
$478$	−4.10476	−0.187747
$479$	−22.9022	−1.04643	−0.523215	−	0.852201i	$-0.675267\pi$
$479$	−22.9022	−1.04643	−0.523215	+	0.852201i	$0.675267\pi$
$480$	0	0
$481$	−8.96014	−0.408547
$482$	30.4075	1.38503
$483$	0	0
$484$	4.67844	0.212656
$485$	54.7089	2.48420
$486$	0	0
$487$	−10.2038	−0.462377	−0.231188	−	0.972909i	$-0.574261\pi$
$487$	−10.2038	−0.462377	−0.231188	+	0.972909i	$0.574261\pi$
$488$	−1.37156	−0.0620876
$489$	0	0
$490$	0	0
$491$	−12.7192	−0.574010	−0.287005	−	0.957929i	$-0.592660\pi$
$491$	−12.7192	−0.574010	−0.287005	+	0.957929i	$0.592660\pi$
$492$	0	0
$493$	−14.3964	−0.648381
$494$	9.04033	0.406743
$495$	0	0
$496$	−15.4612	−0.694229
$497$	0	0
$498$	0	0
$499$	11.2552	0.503850	0.251925	−	0.967747i	$-0.418936\pi$
$499$	11.2552	0.503850	0.251925	+	0.967747i	$0.418936\pi$
$500$	12.3282	0.551333
$501$	0	0
$502$	−24.1608	−1.07835
$503$	12.3951	0.552670	0.276335	−	0.961061i	$-0.410880\pi$
$503$	12.3951	0.552670	0.276335	+	0.961061i	$0.410880\pi$
$504$	0	0
$505$	−2.37681	−0.105767
$506$	31.6526	1.40713
$507$	0	0
$508$	5.02915	0.223133
$509$	20.8830	0.925624	0.462812	−	0.886456i	$-0.346840\pi$
$509$	20.8830	0.925624	0.462812	+	0.886456i	$0.346840\pi$
$510$	0	0
$511$	0	0
$512$	−10.7195	−0.473740
$513$	0	0
$514$	−18.4241	−0.812651
$515$	57.2010	2.52058
$516$	0	0
$517$	34.3544	1.51091
$518$	0	0
$519$	0	0
$520$	9.83552	0.431316
$521$	−37.5800	−1.64641	−0.823205	−	0.567745i	$-0.807816\pi$
$521$	−37.5800	−1.64641	−0.823205	+	0.567745i	$0.807816\pi$
$522$	0	0
$523$	19.9218	0.871117	0.435559	−	0.900160i	$-0.356551\pi$
$523$	19.9218	0.871117	0.435559	+	0.900160i	$0.356551\pi$
$524$	4.00039	0.174758
$525$	0	0
$526$	26.0798	1.13713
$527$	11.6192	0.506142
$528$	0	0
$529$	−3.76221	−0.163574
$530$	−26.5177	−1.15185
$531$	0	0
$532$	0	0
$533$	−1.14388	−0.0495468
$534$	0	0
$535$	−71.3723	−3.08569
$536$	23.5774	1.01839
$537$	0	0
$538$	36.4832	1.57290
$539$	0	0
$540$	0	0
$541$	−20.5016	−0.881431	−0.440716	−	0.897647i	$-0.645275\pi$
$541$	−20.5016	−0.881431	−0.440716	+	0.897647i	$0.645275\pi$
$542$	−10.8682	−0.466830
$543$	0	0
$544$	−9.03744	−0.387477
$545$	−18.7673	−0.803904
$546$	0	0
$547$	−26.4004	−1.12880	−0.564399	−	0.825502i	$-0.690892\pi$
$547$	−26.4004	−1.12880	−0.564399	+	0.825502i	$0.690892\pi$
$548$	−9.10244	−0.388837
$549$	0	0
$550$	83.5785	3.56380
$551$	23.4510	0.999045
$552$	0	0
$553$	0	0
$554$	−47.8365	−2.03238
$555$	0	0
$556$	−8.73624	−0.370499
$557$	2.17426	0.0921262	0.0460631	−	0.998939i	$-0.485332\pi$
$557$	2.17426	0.0921262	0.0460631	+	0.998939i	$0.485332\pi$
$558$	0	0
$559$	7.33023	0.310036
$560$	0	0
$561$	0	0
$562$	−27.7387	−1.17009
$563$	−42.5447	−1.79305	−0.896523	−	0.442997i	$-0.853915\pi$
$563$	−42.5447	−1.79305	−0.896523	+	0.442997i	$0.853915\pi$
$564$	0	0
$565$	−85.9386	−3.61546
$566$	−2.16994	−0.0912093
$567$	0	0
$568$	−28.4707	−1.19460
$569$	−26.2861	−1.10197	−0.550986	−	0.834514i	$-0.685748\pi$
$569$	−26.2861	−1.10197	−0.550986	+	0.834514i	$0.685748\pi$
$570$	0	0
$571$	10.5325	0.440771	0.220386	−	0.975413i	$-0.429268\pi$
$571$	10.5325	0.440771	0.220386	+	0.975413i	$0.429268\pi$
$572$	−2.11656	−0.0884978
$573$	0	0
$574$	0	0
$575$	50.7972	2.11839
$576$	0	0
$577$	5.44898	0.226844	0.113422	−	0.993547i	$-0.463819\pi$
$577$	5.44898	0.226844	0.113422	+	0.993547i	$0.463819\pi$
$578$	−7.02609	−0.292247
$579$	0	0
$580$	−7.62120	−0.316453
$581$	0	0
$582$	0	0
$583$	−19.1038	−0.791198
$584$	−4.67370	−0.193399
$585$	0	0
$586$	25.5332	1.05477
$587$	5.10820	0.210838	0.105419	−	0.994428i	$-0.466382\pi$
$587$	5.10820	0.210838	0.105419	+	0.994428i	$0.466382\pi$
$588$	0	0
$589$	−18.9271	−0.779879
$590$	38.1198	1.56937
$591$	0	0
$592$	−42.1880	−1.73392
$593$	−30.2686	−1.24298	−0.621492	−	0.783421i	$-0.713473\pi$
$593$	−30.2686	−1.24298	−0.621492	+	0.783421i	$0.713473\pi$
$594$	0	0
$595$	0	0
$596$	0.539871	0.0221140
$597$	0	0
$598$	−6.87933	−0.281317
$599$	5.92652	0.242151	0.121075	−	0.992643i	$-0.461366\pi$
$599$	5.92652	0.242151	0.121075	+	0.992643i	$0.461366\pi$
$600$	0	0
$601$	37.4912	1.52930	0.764649	−	0.644447i	$-0.222912\pi$
$601$	37.4912	1.52930	0.764649	+	0.644447i	$0.222912\pi$
$602$	0	0
$603$	0	0
$604$	6.13339	0.249564
$605$	41.4138	1.68371
$606$	0	0
$607$	−18.0265	−0.731671	−0.365836	−	0.930679i	$-0.619217\pi$
$607$	−18.0265	−0.731671	−0.365836	+	0.930679i	$0.619217\pi$
$608$	14.7215	0.597037
$609$	0	0
$610$	3.62667	0.146840
$611$	−7.46654	−0.302064
$612$	0	0
$613$	46.2600	1.86842	0.934211	−	0.356720i	$-0.116105\pi$
$613$	46.2600	1.86842	0.934211	+	0.356720i	$0.116105\pi$
$614$	−6.98193	−0.281768
$615$	0	0
$616$	0	0
$617$	−2.10137	−0.0845981	−0.0422990	−	0.999105i	$-0.513468\pi$
$617$	−2.10137	−0.0845981	−0.0422990	+	0.999105i	$0.513468\pi$
$618$	0	0
$619$	−12.5459	−0.504262	−0.252131	−	0.967693i	$-0.581131\pi$
$619$	−12.5459	−0.504262	−0.252131	+	0.967693i	$0.581131\pi$
$620$	6.15102	0.247031
$621$	0	0
$622$	42.2276	1.69317
$623$	0	0
$624$	0	0
$625$	51.2225	2.04890
$626$	−17.1206	−0.684278
$627$	0	0
$628$	7.28189	0.290579
$629$	31.7047	1.26415
$630$	0	0
$631$	0.262923	0.0104668	0.00523339	−	0.999986i	$-0.498334\pi$
$631$	0.262923	0.0104668	0.00523339	+	0.999986i	$0.498334\pi$
$632$	−8.31080	−0.330586
$633$	0	0
$634$	34.3625	1.36471
$635$	44.5184	1.76666
$636$	0	0
$637$	0	0
$638$	−29.3614	−1.16243
$639$	0	0
$640$	55.3586	2.18824
$641$	−1.34976	−0.0533123	−0.0266561	−	0.999645i	$-0.508486\pi$
$641$	−1.34976	−0.0533123	−0.0266561	+	0.999645i	$0.508486\pi$
$642$	0	0
$643$	7.89870	0.311494	0.155747	−	0.987797i	$-0.450222\pi$
$643$	7.89870	0.311494	0.155747	+	0.987797i	$0.450222\pi$
$644$	0	0
$645$	0	0
$646$	−31.9884	−1.25857
$647$	−28.1325	−1.10600	−0.553001	−	0.833181i	$-0.686517\pi$
$647$	−28.1325	−1.10600	−0.553001	+	0.833181i	$0.686517\pi$
$648$	0	0
$649$	27.4622	1.07798
$650$	−18.1648	−0.712482
$651$	0	0
$652$	5.28215	0.206865
$653$	19.2013	0.751404	0.375702	−	0.926741i	$-0.377402\pi$
$653$	19.2013	0.751404	0.375702	+	0.926741i	$0.377402\pi$
$654$	0	0
$655$	35.4117	1.38365
$656$	−5.38584	−0.210282
$657$	0	0
$658$	0	0
$659$	−12.9388	−0.504026	−0.252013	−	0.967724i	$-0.581093\pi$
$659$	−12.9388	−0.504026	−0.252013	+	0.967724i	$0.581093\pi$
$660$	0	0
$661$	−32.2877	−1.25585	−0.627924	−	0.778275i	$-0.716095\pi$
$661$	−32.2877	−1.25585	−0.627924	+	0.778275i	$0.716095\pi$
$662$	5.15202	0.200239
$663$	0	0
$664$	−21.0073	−0.815241
$665$	0	0
$666$	0	0
$667$	−17.8453	−0.690971
$668$	9.13266	0.353353
$669$	0	0
$670$	−62.3432	−2.40853
$671$	2.61271	0.100863
$672$	0	0
$673$	2.69092	0.103727	0.0518637	−	0.998654i	$-0.483484\pi$
$673$	2.69092	0.103727	0.0518637	+	0.998654i	$0.483484\pi$
$674$	−29.2257	−1.12573
$675$	0	0
$676$	0.460010	0.0176927
$677$	−39.4057	−1.51448	−0.757242	−	0.653134i	$-0.773454\pi$
$677$	−39.4057	−1.51448	−0.757242	+	0.653134i	$0.773454\pi$
$678$	0	0
$679$	0	0
$680$	−34.8021	−1.33460
$681$	0	0
$682$	23.6974	0.907422
$683$	25.7397	0.984902	0.492451	−	0.870340i	$-0.336101\pi$
$683$	25.7397	0.984902	0.492451	+	0.870340i	$0.336101\pi$
$684$	0	0
$685$	−80.5753	−3.07863
$686$	0	0
$687$	0	0
$688$	34.5137	1.31582
$689$	4.15199	0.158178
$690$	0	0
$691$	47.3570	1.80155	0.900773	−	0.434291i	$-0.143001\pi$
$691$	47.3570	1.80155	0.900773	+	0.434291i	$0.143001\pi$
$692$	−4.04105	−0.153618
$693$	0	0
$694$	14.2016	0.539087
$695$	−77.3337	−2.93344
$696$	0	0
$697$	4.04751	0.153310
$698$	49.3334	1.86730
$699$	0	0
$700$	0	0
$701$	−2.39707	−0.0905361	−0.0452680	−	0.998975i	$-0.514414\pi$
$701$	−2.39707	−0.0905361	−0.0452680	+	0.998975i	$0.514414\pi$
$702$	0	0
$703$	−51.6453	−1.94784
$704$	24.8961	0.938306
$705$	0	0
$706$	19.6879	0.740965
$707$	0	0
$708$	0	0
$709$	9.19194	0.345211	0.172605	−	0.984991i	$-0.444781\pi$
$709$	9.19194	0.345211	0.172605	+	0.984991i	$0.444781\pi$
$710$	75.2821	2.82529
$711$	0	0
$712$	35.1358	1.31677
$713$	14.4028	0.539389
$714$	0	0
$715$	−18.7359	−0.700683
$716$	−8.29092	−0.309846
$717$	0	0
$718$	19.4681	0.726542
$719$	−30.2655	−1.12871	−0.564356	−	0.825532i	$-0.690875\pi$
$719$	−30.2655	−1.12871	−0.564356	+	0.825532i	$0.690875\pi$
$720$	0	0
$721$	0	0
$722$	22.3070	0.830182
$723$	0	0
$724$	1.51160	0.0561780
$725$	−47.1203	−1.75000
$726$	0	0
$727$	1.08475	0.0402311	0.0201156	−	0.999798i	$-0.493597\pi$
$727$	1.08475	0.0402311	0.0201156	+	0.999798i	$0.493597\pi$
$728$	0	0
$729$	0	0
$730$	12.3582	0.457396
$731$	−25.9373	−0.959327
$732$	0	0
$733$	1.00679	0.0371865	0.0185933	−	0.999827i	$-0.494081\pi$
$733$	1.00679	0.0371865	0.0185933	+	0.999827i	$0.494081\pi$
$734$	12.8187	0.473146
$735$	0	0
$736$	−11.2025	−0.412930
$737$	−44.9131	−1.65440
$738$	0	0
$739$	−13.9633	−0.513649	−0.256825	−	0.966458i	$-0.582676\pi$
$739$	−13.9633	−0.513649	−0.256825	+	0.966458i	$0.582676\pi$
$740$	16.7839	0.616989
$741$	0	0
$742$	0	0
$743$	−0.134889	−0.00494861	−0.00247431	−	0.999997i	$-0.500788\pi$
$743$	−0.134889	−0.00494861	−0.00247431	+	0.999997i	$0.500788\pi$
$744$	0	0
$745$	4.77897	0.175088
$746$	−27.7912	−1.01751
$747$	0	0
$748$	7.48925	0.273834
$749$	0	0
$750$	0	0
$751$	−13.3462	−0.487010	−0.243505	−	0.969900i	$-0.578297\pi$
$751$	−13.3462	−0.487010	−0.243505	+	0.969900i	$0.578297\pi$
$752$	−35.1555	−1.28199
$753$	0	0
$754$	6.38137	0.232396
$755$	54.2931	1.97593
$756$	0	0
$757$	−43.6217	−1.58546	−0.792729	−	0.609574i	$-0.791341\pi$
$757$	−43.6217	−1.58546	−0.792729	+	0.609574i	$0.791341\pi$
$758$	18.5299	0.673036
$759$	0	0
$760$	56.6909	2.05639
$761$	2.96599	0.107517	0.0537585	−	0.998554i	$-0.482880\pi$
$761$	2.96599	0.107517	0.0537585	+	0.998554i	$0.482880\pi$
$762$	0	0
$763$	0	0
$764$	1.45070	0.0524846
$765$	0	0
$766$	−31.4580	−1.13662
$767$	−5.96858	−0.215513
$768$	0	0
$769$	28.6571	1.03340	0.516700	−	0.856166i	$-0.327160\pi$
$769$	28.6571	1.03340	0.516700	+	0.856166i	$0.327160\pi$
$770$	0	0
$771$	0	0
$772$	−10.3657	−0.373068
$773$	44.6810	1.60707	0.803533	−	0.595261i	$-0.202951\pi$
$773$	44.6810	1.60707	0.803533	+	0.595261i	$0.202951\pi$
$774$	0	0
$775$	38.0305	1.36610
$776$	−32.4514	−1.16494
$777$	0	0
$778$	33.9598	1.21752
$779$	−6.59318	−0.236225
$780$	0	0
$781$	54.2345	1.94066
$782$	24.3419	0.870464
$783$	0	0
$784$	0	0
$785$	64.4597	2.30067
$786$	0	0
$787$	46.4162	1.65456	0.827280	−	0.561790i	$-0.189887\pi$
$787$	46.4162	1.65456	0.827280	+	0.561790i	$0.189887\pi$
$788$	−3.17641	−0.113155
$789$	0	0
$790$	21.9754	0.781848
$791$	0	0
$792$	0	0
$793$	−0.567843	−0.0201647
$794$	−23.8634	−0.846880
$795$	0	0
$796$	−5.77238	−0.204597
$797$	−3.09573	−0.109656	−0.0548282	−	0.998496i	$-0.517461\pi$
$797$	−3.09573	−0.109656	−0.0548282	+	0.998496i	$0.517461\pi$
$798$	0	0
$799$	26.4197	0.934661
$800$	−29.5801	−1.04581
$801$	0	0
$802$	−55.5188	−1.96044
$803$	8.90304	0.314181
$804$	0	0
$805$	0	0
$806$	−5.15036	−0.181414
$807$	0	0
$808$	1.40984	0.0495981
$809$	−28.8937	−1.01585	−0.507924	−	0.861402i	$-0.669587\pi$
$809$	−28.8937	−1.01585	−0.507924	+	0.861402i	$0.669587\pi$
$810$	0	0
$811$	−1.22047	−0.0428564	−0.0214282	−	0.999770i	$-0.506821\pi$
$811$	−1.22047	−0.0428564	−0.0214282	+	0.999770i	$0.506821\pi$
$812$	0	0
$813$	0	0
$814$	64.6617	2.26639
$815$	46.7579	1.63786
$816$	0	0
$817$	42.2506	1.47816
$818$	−41.2563	−1.44249
$819$	0	0
$820$	2.14268	0.0748257
$821$	26.4548	0.923279	0.461639	−	0.887068i	$-0.347261\pi$
$821$	26.4548	0.923279	0.461639	+	0.887068i	$0.347261\pi$
$822$	0	0
$823$	−35.7622	−1.24659	−0.623296	−	0.781986i	$-0.714207\pi$
$823$	−35.7622	−1.24659	−0.623296	+	0.781986i	$0.714207\pi$
$824$	−33.9296	−1.18199
$825$	0	0
$826$	0	0
$827$	17.9518	0.624245	0.312122	−	0.950042i	$-0.398960\pi$
$827$	17.9518	0.624245	0.312122	+	0.950042i	$0.398960\pi$
$828$	0	0
$829$	25.4594	0.884240	0.442120	−	0.896956i	$-0.354227\pi$
$829$	25.4594	0.884240	0.442120	+	0.896956i	$0.354227\pi$
$830$	55.5473	1.92808
$831$	0	0
$832$	−5.41087	−0.187588
$833$	0	0
$834$	0	0
$835$	80.8429	2.79768
$836$	−12.1996	−0.421933
$837$	0	0
$838$	33.1118	1.14383
$839$	−20.0448	−0.692022	−0.346011	−	0.938230i	$-0.612464\pi$
$839$	−20.0448	−0.692022	−0.346011	+	0.938230i	$0.612464\pi$
$840$	0	0
$841$	−12.4465	−0.429188
$842$	50.9157	1.75467
$843$	0	0
$844$	7.80952	0.268815
$845$	4.07203	0.140082
$846$	0	0
$847$	0	0
$848$	19.5493	0.671324
$849$	0	0
$850$	64.2745	2.20460
$851$	39.3000	1.34719
$852$	0	0
$853$	7.78420	0.266526	0.133263	−	0.991081i	$-0.457455\pi$
$853$	7.78420	0.266526	0.133263	+	0.991081i	$0.457455\pi$
$854$	0	0
$855$	0	0
$856$	42.3355	1.44700
$857$	12.4762	0.426179	0.213090	−	0.977033i	$-0.431647\pi$
$857$	12.4762	0.426179	0.213090	+	0.977033i	$0.431647\pi$
$858$	0	0
$859$	−6.48868	−0.221391	−0.110696	−	0.993854i	$-0.535308\pi$
$859$	−6.48868	−0.221391	−0.110696	+	0.993854i	$0.535308\pi$
$860$	−13.7308	−0.468216
$861$	0	0
$862$	−57.2115	−1.94863
$863$	−30.7541	−1.04688	−0.523441	−	0.852062i	$-0.675352\pi$
$863$	−30.7541	−1.04688	−0.523441	+	0.852062i	$0.675352\pi$
$864$	0	0
$865$	−35.7716	−1.21627
$866$	−27.8268	−0.945593
$867$	0	0
$868$	0	0
$869$	15.8314	0.537044
$870$	0	0
$871$	9.76134	0.330750
$872$	11.1321	0.376981
$873$	0	0
$874$	−39.6517	−1.34124
$875$	0	0
$876$	0	0
$877$	−27.8274	−0.939666	−0.469833	−	0.882755i	$-0.655686\pi$
$877$	−27.8274	−0.939666	−0.469833	+	0.882755i	$0.655686\pi$
$878$	−10.1005	−0.340877
$879$	0	0
$880$	−88.2163	−2.97377
$881$	−9.94004	−0.334889	−0.167444	−	0.985882i	$-0.553551\pi$
$881$	−9.94004	−0.334889	−0.167444	+	0.985882i	$0.553551\pi$
$882$	0	0
$883$	−15.9098	−0.535409	−0.267704	−	0.963501i	$-0.586265\pi$
$883$	−15.9098	−0.535409	−0.267704	+	0.963501i	$0.586265\pi$
$884$	−1.62770	−0.0547455
$885$	0	0
$886$	−4.51852	−0.151803
$887$	−24.1568	−0.811106	−0.405553	−	0.914072i	$-0.632921\pi$
$887$	−24.1568	−0.811106	−0.405553	+	0.914072i	$0.632921\pi$
$888$	0	0
$889$	0	0
$890$	−92.9057	−3.11421
$891$	0	0
$892$	−3.00040	−0.100461
$893$	−43.0363	−1.44015
$894$	0	0
$895$	−73.3917	−2.45321
$896$	0	0
$897$	0	0
$898$	−6.78643	−0.226466
$899$	−13.3603	−0.445590
$900$	0	0
$901$	−14.6914	−0.489442
$902$	8.25490	0.274858
$903$	0	0
$904$	50.9758	1.69543
$905$	13.3807	0.444791
$906$	0	0
$907$	−40.0985	−1.33145	−0.665725	−	0.746197i	$-0.731878\pi$
$907$	−40.0985	−1.33145	−0.665725	+	0.746197i	$0.731878\pi$
$908$	−4.92890	−0.163571
$909$	0	0
$910$	0	0
$911$	−27.5863	−0.913974	−0.456987	−	0.889473i	$-0.651071\pi$
$911$	−27.5863	−0.913974	−0.456987	+	0.889473i	$0.651071\pi$
$912$	0	0
$913$	40.0173	1.32438
$914$	−13.5971	−0.449753
$915$	0	0
$916$	−5.31390	−0.175576
$917$	0	0
$918$	0	0
$919$	−2.47113	−0.0815149	−0.0407575	−	0.999169i	$-0.512977\pi$
$919$	−2.47113	−0.0815149	−0.0407575	+	0.999169i	$0.512977\pi$
$920$	−43.1395	−1.42227
$921$	0	0
$922$	14.4854	0.477051
$923$	−11.7872	−0.387982
$924$	0	0
$925$	103.771	3.41198
$926$	−28.8865	−0.949268
$927$	0	0
$928$	10.3916	0.341121
$929$	−52.6033	−1.72586	−0.862928	−	0.505326i	$-0.831372\pi$
$929$	−52.6033	−1.72586	−0.862928	+	0.505326i	$0.831372\pi$
$930$	0	0
$931$	0	0
$932$	−3.77223	−0.123564
$933$	0	0
$934$	−8.75980	−0.286629
$935$	66.2953	2.16809
$936$	0	0
$937$	15.0724	0.492393	0.246196	−	0.969220i	$-0.420819\pi$
$937$	15.0724	0.492393	0.246196	+	0.969220i	$0.420819\pi$
$938$	0	0
$939$	0	0
$940$	13.9861	0.456177
$941$	−10.4483	−0.340606	−0.170303	−	0.985392i	$-0.554475\pi$
$941$	−10.4483	−0.340606	−0.170303	+	0.985392i	$0.554475\pi$
$942$	0	0
$943$	5.01715	0.163381
$944$	−28.1025	−0.914660
$945$	0	0
$946$	−52.8992	−1.71990
$947$	−45.1536	−1.46729	−0.733647	−	0.679531i	$-0.762183\pi$
$947$	−45.1536	−1.46729	−0.733647	+	0.679531i	$0.762183\pi$
$948$	0	0
$949$	−1.93497	−0.0628118
$950$	−104.700	−3.39692
$951$	0	0
$952$	0	0
$953$	43.1993	1.39936	0.699681	−	0.714455i	$-0.253325\pi$
$953$	43.1993	1.39936	0.699681	+	0.714455i	$0.253325\pi$
$954$	0	0
$955$	12.8417	0.415548
$956$	−1.20389	−0.0389365
$957$	0	0
$958$	−35.9208	−1.16055
$959$	0	0
$960$	0	0
$961$	−20.2170	−0.652162
$962$	−14.0535	−0.453102
$963$	0	0
$964$	8.91825	0.287237
$965$	−91.7574	−2.95377
$966$	0	0
$967$	21.4260	0.689014	0.344507	−	0.938784i	$-0.388046\pi$
$967$	21.4260	0.689014	0.344507	+	0.938784i	$0.388046\pi$
$968$	−24.5652	−0.789556
$969$	0	0
$970$	85.8077	2.75512
$971$	18.1710	0.583134	0.291567	−	0.956550i	$-0.405823\pi$
$971$	18.1710	0.583134	0.291567	+	0.956550i	$0.405823\pi$
$972$	0	0
$973$	0	0
$974$	−16.0040	−0.512802
$975$	0	0
$976$	−2.67364	−0.0855811
$977$	21.7732	0.696586	0.348293	−	0.937386i	$-0.386761\pi$
$977$	21.7732	0.696586	0.348293	+	0.937386i	$0.386761\pi$
$978$	0	0
$979$	−66.9309	−2.13912
$980$	0	0
$981$	0	0
$982$	−19.9493	−0.636609
$983$	−22.5164	−0.718163	−0.359082	−	0.933306i	$-0.616910\pi$
$983$	−22.5164	−0.718163	−0.359082	+	0.933306i	$0.616910\pi$
$984$	0	0
$985$	−28.1178	−0.895907
$986$	−22.5799	−0.719090
$987$	0	0
$988$	2.65144	0.0843537
$989$	−32.1510	−1.02234
$990$	0	0
$991$	−4.75019	−0.150895	−0.0754474	−	0.997150i	$-0.524038\pi$
$991$	−4.75019	−0.150895	−0.0754474	+	0.997150i	$0.524038\pi$
$992$	−8.38700	−0.266288
$993$	0	0
$994$	0	0
$995$	−51.0974	−1.61990
$996$	0	0
$997$	−19.0546	−0.603465	−0.301733	−	0.953393i	$-0.597565\pi$
$997$	−19.0546	−0.603465	−0.301733	+	0.953393i	$0.597565\pi$
$998$	17.6531	0.558798
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bx.1.8		10
3.2	odd	2		1911.2.a.y.1.3	yes	10
7.6	odd	2		5733.2.a.bw.1.8		10
21.20	even	2		1911.2.a.x.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.x.1.3	✓	10	21.20	even	2
1911.2.a.y.1.3	yes	10	3.2	odd	2
5733.2.a.bw.1.8		10	7.6	odd	2
5733.2.a.bx.1.8		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.56844 q^{2} +0.460010 q^{4} +4.07203 q^{5} -2.41539 q^{8} +O(q^{10})\)	\(q+1.56844 q^{2} +0.460010 q^{4} +4.07203 q^{5} -2.41539 q^{8} +6.38674 q^{10} +4.60112 q^{11} -1.00000 q^{13} -4.70841 q^{16} +3.53841 q^{17} -5.76389 q^{19} +1.87317 q^{20} +7.21659 q^{22} +4.38609 q^{23} +11.5814 q^{25} -1.56844 q^{26} -4.06860 q^{29} +3.28375 q^{31} -2.55410 q^{32} +5.54979 q^{34} +8.96014 q^{37} -9.04033 q^{38} -9.83552 q^{40} +1.14388 q^{41} -7.33023 q^{43} +2.11656 q^{44} +6.87933 q^{46} +7.46654 q^{47} +18.1648 q^{50} -0.460010 q^{52} -4.15199 q^{53} +18.7359 q^{55} -6.38137 q^{58} +5.96858 q^{59} +0.567843 q^{61} +5.15036 q^{62} +5.41087 q^{64} -4.07203 q^{65} -9.76134 q^{67} +1.62770 q^{68} +11.7872 q^{71} +1.93497 q^{73} +14.0535 q^{74} -2.65144 q^{76} +3.44078 q^{79} -19.1728 q^{80} +1.79411 q^{82} +8.69728 q^{83} +14.4085 q^{85} -11.4970 q^{86} -11.1135 q^{88} -14.5467 q^{89} +2.01764 q^{92} +11.7108 q^{94} -23.4707 q^{95} +13.4353 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8	\( 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8} + 8 q^{10} - 12 q^{11} - 10 q^{13} + 24 q^{16} + 10 q^{19} + 16 q^{20} + 8 q^{22} - 14 q^{23} + 32 q^{25} + 4 q^{26} - 18 q^{29} + 14 q^{31} - 28 q^{32} + 4 q^{34} + 24 q^{37} + 4 q^{38} + 16 q^{40} + 24 q^{41} + 2 q^{43} - 48 q^{44} + 20 q^{46} + 18 q^{47} + 28 q^{50} - 16 q^{52} - 10 q^{53} + 12 q^{55} + 12 q^{58} + 12 q^{59} - 4 q^{61} - 4 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 40 q^{68} - 32 q^{71} - 18 q^{73} - 24 q^{74} + 32 q^{76} + 34 q^{79} + 32 q^{80} + 48 q^{82} + 30 q^{83} - 40 q^{86} + 32 q^{88} + 10 q^{89} + 40 q^{92} - 24 q^{94} + 30 q^{95} - 2 q^{97}+O(q^{100}) \) 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8 + 8 * q^10 - 12 * q^11 - 10 * q^13 + 24 * q^16 + 10 * q^19 + 16 * q^20 + 8 * q^22 - 14 * q^23 + 32 * q^25 + 4 * q^26 - 18 * q^29 + 14 * q^31 - 28 * q^32 + 4 * q^34 + 24 * q^37 + 4 * q^38 + 16 * q^40 + 24 * q^41 + 2 * q^43 - 48 * q^44 + 20 * q^46 + 18 * q^47 + 28 * q^50 - 16 * q^52 - 10 * q^53 + 12 * q^55 + 12 * q^58 + 12 * q^59 - 4 * q^61 - 4 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 40 * q^68 - 32 * q^71 - 18 * q^73 - 24 * q^74 + 32 * q^76 + 34 * q^79 + 32 * q^80 + 48 * q^82 + 30 * q^83 - 40 * q^86 + 32 * q^88 + 10 * q^89 + 40 * q^92 - 24 * q^94 + 30 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more