LMFDB - Embedded newform 5733.2.a.v.1.2

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
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			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	$q+2.61803 q^{2} +4.85410 q^{4} -2.23607 q^{5} +7.47214 q^{8} +O(q^{10})$	$q+2.61803 q^{2} +4.85410 q^{4} -2.23607 q^{5} +7.47214 q^{8} -5.85410 q^{10} +3.00000 q^{11} -1.00000 q^{13} +9.85410 q^{16} -1.47214 q^{17} +3.00000 q^{19} -10.8541 q^{20} +7.85410 q^{22} +8.23607 q^{23} -2.61803 q^{26} -4.47214 q^{29} +5.00000 q^{31} +10.8541 q^{32} -3.85410 q^{34} +4.70820 q^{37} +7.85410 q^{38} -16.7082 q^{40} +4.47214 q^{41} -8.00000 q^{43} +14.5623 q^{44} +21.5623 q^{46} +7.47214 q^{47} -4.85410 q^{52} +7.47214 q^{53} -6.70820 q^{55} -11.7082 q^{58} +1.47214 q^{59} +3.00000 q^{61} +13.0902 q^{62} +8.70820 q^{64} +2.23607 q^{65} -3.00000 q^{67} -7.14590 q^{68} +8.94427 q^{71} -2.70820 q^{73} +12.3262 q^{74} +14.5623 q^{76} -2.70820 q^{79} -22.0344 q^{80} +11.7082 q^{82} +3.29180 q^{85} -20.9443 q^{86} +22.4164 q^{88} -2.23607 q^{89} +39.9787 q^{92} +19.5623 q^{94} -6.70820 q^{95} +9.41641 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{4} + 6 q^{8}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^4 + 6 * q^8	$ 2 q + 3 q^{2} + 3 q^{4} + 6 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 13 q^{16} + 6 q^{17} + 6 q^{19} - 15 q^{20} + 9 q^{22} + 12 q^{23} - 3 q^{26} + 10 q^{31} + 15 q^{32} - q^{34} - 4 q^{37} + 9 q^{38} - 20 q^{40} - 16 q^{43} + 9 q^{44} + 23 q^{46} + 6 q^{47} - 3 q^{52} + 6 q^{53} - 10 q^{58} - 6 q^{59} + 6 q^{61} + 15 q^{62} + 4 q^{64} - 6 q^{67} - 21 q^{68} + 8 q^{73} + 9 q^{74} + 9 q^{76} + 8 q^{79} - 15 q^{80} + 10 q^{82} + 20 q^{85} - 24 q^{86} + 18 q^{88} + 33 q^{92} + 19 q^{94} - 8 q^{97}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^4 + 6 * q^8 - 5 * q^10 + 6 * q^11 - 2 * q^13 + 13 * q^16 + 6 * q^17 + 6 * q^19 - 15 * q^20 + 9 * q^22 + 12 * q^23 - 3 * q^26 + 10 * q^31 + 15 * q^32 - q^34 - 4 * q^37 + 9 * q^38 - 20 * q^40 - 16 * q^43 + 9 * q^44 + 23 * q^46 + 6 * q^47 - 3 * q^52 + 6 * q^53 - 10 * q^58 - 6 * q^59 + 6 * q^61 + 15 * q^62 + 4 * q^64 - 6 * q^67 - 21 * q^68 + 8 * q^73 + 9 * q^74 + 9 * q^76 + 8 * q^79 - 15 * q^80 + 10 * q^82 + 20 * q^85 - 24 * q^86 + 18 * q^88 + 33 * q^92 + 19 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.61803	1.85123	0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803	1.85123	0.925615	+	0.378467i	$0.123549\pi$
$3$	0	0
$3$	0	0
$4$	4.85410	2.42705
$5$	−2.23607	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	7.47214	2.64180
$9$	0	0
$10$	−5.85410	−1.85123
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	9.85410	2.46353
$17$	−1.47214	−0.357045	−0.178523	−	0.983936i	$-0.557132\pi$
$17$	−1.47214	−0.357045	−0.178523	+	0.983936i	$0.557132\pi$
$18$	0	0
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−10.8541	−2.42705
$21$	0	0
$22$	7.85410	1.67450
$23$	8.23607	1.71734	0.858669	−	0.512530i	$-0.171292\pi$
$23$	8.23607	1.71734	0.858669	+	0.512530i	$0.171292\pi$
$24$	0	0
$25$	0	0
$26$	−2.61803	−0.513439
$27$	0	0
$28$	0	0
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	10.8541	1.91875
$33$	0	0
$34$	−3.85410	−0.660973
$35$	0	0
$36$	0	0
$37$	4.70820	0.774024	0.387012	−	0.922075i	$-0.373507\pi$
$37$	4.70820	0.774024	0.387012	+	0.922075i	$0.373507\pi$
$38$	7.85410	1.27410
$39$	0	0
$40$	−16.7082	−2.64180
$41$	4.47214	0.698430	0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214	0.698430	0.349215	+	0.937043i	$0.386448\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	14.5623	2.19535
$45$	0	0
$46$	21.5623	3.17919
$47$	7.47214	1.08992	0.544962	−	0.838461i	$-0.316544\pi$
$47$	7.47214	1.08992	0.544962	+	0.838461i	$0.316544\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	0	0
$52$	−4.85410	−0.673143
$53$	7.47214	1.02638	0.513188	−	0.858276i	$-0.328464\pi$
$53$	7.47214	1.02638	0.513188	+	0.858276i	$0.328464\pi$
$54$	0	0
$55$	−6.70820	−0.904534
$56$	0	0
$57$	0	0
$58$	−11.7082	−1.53736
$59$	1.47214	0.191656	0.0958279	−	0.995398i	$-0.469450\pi$
$59$	1.47214	0.191656	0.0958279	+	0.995398i	$0.469450\pi$
$60$	0	0
$61$	3.00000	0.384111	0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000	0.384111	0.192055	+	0.981384i	$0.438485\pi$
$62$	13.0902	1.66245
$63$	0	0
$64$	8.70820	1.08853
$65$	2.23607	0.277350
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	−7.14590	−0.866567
$69$	0	0
$70$	0	0
$71$	8.94427	1.06149	0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427	1.06149	0.530745	+	0.847532i	$0.321912\pi$
$72$	0	0
$73$	−2.70820	−0.316971	−0.158486	−	0.987361i	$-0.550661\pi$
$73$	−2.70820	−0.316971	−0.158486	+	0.987361i	$0.550661\pi$
$74$	12.3262	1.43290
$75$	0	0
$76$	14.5623	1.67041
$77$	0	0
$78$	0	0
$79$	−2.70820	−0.304697	−0.152348	−	0.988327i	$-0.548684\pi$
$79$	−2.70820	−0.304697	−0.152348	+	0.988327i	$0.548684\pi$
$80$	−22.0344	−2.46353
$81$	0	0
$82$	11.7082	1.29295
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	3.29180	0.357045
$86$	−20.9443	−2.25848
$87$	0	0
$88$	22.4164	2.38960
$89$	−2.23607	−0.237023	−0.118511	−	0.992953i	$-0.537812\pi$
$89$	−2.23607	−0.237023	−0.118511	+	0.992953i	$0.537812\pi$
$90$	0	0
$91$	0	0
$92$	39.9787	4.16807
$93$	0	0
$94$	19.5623	2.01770
$95$	−6.70820	−0.688247
$96$	0	0
$97$	9.41641	0.956091	0.478046	−	0.878335i	$-0.341345\pi$
$97$	9.41641	0.956091	0.478046	+	0.878335i	$0.341345\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	0	0
$103$	−2.70820	−0.266847	−0.133424	−	0.991059i	$-0.542597\pi$
$103$	−2.70820	−0.266847	−0.133424	+	0.991059i	$0.542597\pi$
$104$	−7.47214	−0.732703
$105$	0	0
$106$	19.5623	1.90006
$107$	9.76393	0.943915	0.471957	−	0.881621i	$-0.343548\pi$
$107$	9.76393	0.943915	0.471957	+	0.881621i	$0.343548\pi$
$108$	0	0
$109$	−2.70820	−0.259399	−0.129699	−	0.991553i	$-0.541401\pi$
$109$	−2.70820	−0.259399	−0.129699	+	0.991553i	$0.541401\pi$
$110$	−17.5623	−1.67450
$111$	0	0
$112$	0	0
$113$	−2.94427	−0.276974	−0.138487	−	0.990364i	$-0.544224\pi$
$113$	−2.94427	−0.276974	−0.138487	+	0.990364i	$0.544224\pi$
$114$	0	0
$115$	−18.4164	−1.71734
$116$	−21.7082	−2.01556
$117$	0	0
$118$	3.85410	0.354799
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	7.85410	0.711077
$123$	0	0
$124$	24.2705	2.17956
$125$	11.1803	1.00000
$126$	0	0
$127$	−11.4164	−1.01304	−0.506521	−	0.862228i	$-0.669069\pi$
$127$	−11.4164	−1.01304	−0.506521	+	0.862228i	$0.669069\pi$
$128$	1.09017	0.0963583
$129$	0	0
$130$	5.85410	0.513439
$131$	8.23607	0.719589	0.359794	−	0.933032i	$-0.382847\pi$
$131$	8.23607	0.719589	0.359794	+	0.933032i	$0.382847\pi$
$132$	0	0
$133$	0	0
$134$	−7.85410	−0.678491
$135$	0	0
$136$	−11.0000	−0.943242
$137$	8.23607	0.703655	0.351827	−	0.936065i	$-0.385560\pi$
$137$	8.23607	0.703655	0.351827	+	0.936065i	$0.385560\pi$
$138$	0	0
$139$	−23.4164	−1.98615	−0.993077	−	0.117466i	$-0.962523\pi$
$139$	−23.4164	−1.98615	−0.993077	+	0.117466i	$0.962523\pi$
$140$	0	0
$141$	0	0
$142$	23.4164	1.96506
$143$	−3.00000	−0.250873
$144$	0	0
$145$	10.0000	0.830455
$146$	−7.09017	−0.586787
$147$	0	0
$148$	22.8541	1.87860
$149$	−0.708204	−0.0580183	−0.0290092	−	0.999579i	$-0.509235\pi$
$149$	−0.708204	−0.0580183	−0.0290092	+	0.999579i	$0.509235\pi$
$150$	0	0
$151$	20.4164	1.66146	0.830732	−	0.556673i	$-0.187922\pi$
$151$	20.4164	1.66146	0.830732	+	0.556673i	$0.187922\pi$
$152$	22.4164	1.81821
$153$	0	0
$154$	0	0
$155$	−11.1803	−0.898027
$156$	0	0
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	−7.09017	−0.564064
$159$	0	0
$160$	−24.2705	−1.91875
$161$	0	0
$162$	0	0
$163$	−16.4164	−1.28583	−0.642916	−	0.765937i	$-0.722276\pi$
$163$	−16.4164	−1.28583	−0.642916	+	0.765937i	$0.722276\pi$
$164$	21.7082	1.69513
$165$	0	0
$166$	0	0
$167$	−22.4721	−1.73895	−0.869473	−	0.493980i	$-0.835541\pi$
$167$	−22.4721	−1.73895	−0.869473	+	0.493980i	$0.835541\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	8.61803	0.660973
$171$	0	0
$172$	−38.8328	−2.96097
$173$	16.4164	1.24812	0.624058	−	0.781378i	$-0.285483\pi$
$173$	16.4164	1.24812	0.624058	+	0.781378i	$0.285483\pi$
$174$	0	0
$175$	0	0
$176$	29.5623	2.22834
$177$	0	0
$178$	−5.85410	−0.438783
$179$	20.1246	1.50418	0.752092	−	0.659058i	$-0.229045\pi$
$179$	20.1246	1.50418	0.752092	+	0.659058i	$0.229045\pi$
$180$	0	0
$181$	−25.4164	−1.88919	−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164	−1.88919	−0.944593	+	0.328243i	$0.893544\pi$
$182$	0	0
$183$	0	0
$184$	61.5410	4.53686
$185$	−10.5279	−0.774024
$186$	0	0
$187$	−4.41641	−0.322960
$188$	36.2705	2.64530
$189$	0	0
$190$	−17.5623	−1.27410
$191$	−11.1803	−0.808981	−0.404491	−	0.914542i	$-0.632551\pi$
$191$	−11.1803	−0.808981	−0.404491	+	0.914542i	$0.632551\pi$
$192$	0	0
$193$	0.708204	0.0509776	0.0254888	−	0.999675i	$-0.491886\pi$
$193$	0.708204	0.0509776	0.0254888	+	0.999675i	$0.491886\pi$
$194$	24.6525	1.76994
$195$	0	0
$196$	0	0
$197$	9.05573	0.645194	0.322597	−	0.946536i	$-0.395444\pi$
$197$	9.05573	0.645194	0.322597	+	0.946536i	$0.395444\pi$
$198$	0	0
$199$	−20.7082	−1.46797	−0.733983	−	0.679168i	$-0.762341\pi$
$199$	−20.7082	−1.46797	−0.733983	+	0.679168i	$0.762341\pi$
$200$	0	0
$201$	0	0
$202$	23.5623	1.65784
$203$	0	0
$204$	0	0
$205$	−10.0000	−0.698430
$206$	−7.09017	−0.493996
$207$	0	0
$208$	−9.85410	−0.683259
$209$	9.00000	0.622543
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	36.2705	2.49107
$213$	0	0
$214$	25.5623	1.74740
$215$	17.8885	1.21999
$216$	0	0
$217$	0	0
$218$	−7.09017	−0.480207
$219$	0	0
$220$	−32.5623	−2.19535
$221$	1.47214	0.0990266
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	0	0
$225$	0	0
$226$	−7.70820	−0.512742
$227$	−5.94427	−0.394535	−0.197268	−	0.980350i	$-0.563207\pi$
$227$	−5.94427	−0.394535	−0.197268	+	0.980350i	$0.563207\pi$
$228$	0	0
$229$	24.1246	1.59420	0.797100	−	0.603848i	$-0.206367\pi$
$229$	24.1246	1.59420	0.797100	+	0.603848i	$0.206367\pi$
$230$	−48.2148	−3.17919
$231$	0	0
$232$	−33.4164	−2.19389
$233$	−11.9443	−0.782495	−0.391248	−	0.920285i	$-0.627956\pi$
$233$	−11.9443	−0.782495	−0.391248	+	0.920285i	$0.627956\pi$
$234$	0	0
$235$	−16.7082	−1.08992
$236$	7.14590	0.465158
$237$	0	0
$238$	0	0
$239$	−19.4164	−1.25594	−0.627972	−	0.778236i	$-0.716115\pi$
$239$	−19.4164	−1.25594	−0.627972	+	0.778236i	$0.716115\pi$
$240$	0	0
$241$	4.70820	0.303282	0.151641	−	0.988436i	$-0.451544\pi$
$241$	4.70820	0.303282	0.151641	+	0.988436i	$0.451544\pi$
$242$	−5.23607	−0.336587
$243$	0	0
$244$	14.5623	0.932256
$245$	0	0
$246$	0	0
$247$	−3.00000	−0.190885
$248$	37.3607	2.37241
$249$	0	0
$250$	29.2705	1.85123
$251$	−1.52786	−0.0964379	−0.0482190	−	0.998837i	$-0.515355\pi$
$251$	−1.52786	−0.0964379	−0.0482190	+	0.998837i	$0.515355\pi$
$252$	0	0
$253$	24.7082	1.55339
$254$	−29.8885	−1.87537
$255$	0	0
$256$	−14.5623	−0.910144
$257$	0.0557281	0.00347622	0.00173811	−	0.999998i	$-0.499447\pi$
$257$	0.0557281	0.00347622	0.00173811	+	0.999998i	$0.499447\pi$
$258$	0	0
$259$	0	0
$260$	10.8541	0.673143
$261$	0	0
$262$	21.5623	1.33212
$263$	−26.1246	−1.61091	−0.805456	−	0.592655i	$-0.798080\pi$
$263$	−26.1246	−1.61091	−0.805456	+	0.592655i	$0.798080\pi$
$264$	0	0
$265$	−16.7082	−1.02638
$266$	0	0
$267$	0	0
$268$	−14.5623	−0.889534
$269$	−13.4721	−0.821411	−0.410705	−	0.911768i	$-0.634717\pi$
$269$	−13.4721	−0.821411	−0.410705	+	0.911768i	$0.634717\pi$
$270$	0	0
$271$	−20.4164	−1.24021	−0.620104	−	0.784519i	$-0.712910\pi$
$271$	−20.4164	−1.24021	−0.620104	+	0.784519i	$0.712910\pi$
$272$	−14.5066	−0.879590
$273$	0	0
$274$	21.5623	1.30263
$275$	0	0
$276$	0	0
$277$	−0.416408	−0.0250195	−0.0125098	−	0.999922i	$-0.503982\pi$
$277$	−0.416408	−0.0250195	−0.0125098	+	0.999922i	$0.503982\pi$
$278$	−61.3050	−3.67683
$279$	0	0
$280$	0	0
$281$	−26.9443	−1.60736	−0.803680	−	0.595061i	$-0.797128\pi$
$281$	−26.9443	−1.60736	−0.803680	+	0.595061i	$0.797128\pi$
$282$	0	0
$283$	26.1246	1.55295	0.776473	−	0.630150i	$-0.217007\pi$
$283$	26.1246	1.55295	0.776473	+	0.630150i	$0.217007\pi$
$284$	43.4164	2.57629
$285$	0	0
$286$	−7.85410	−0.464423
$287$	0	0
$288$	0	0
$289$	−14.8328	−0.872519
$290$	26.1803	1.53736
$291$	0	0
$292$	−13.1459	−0.769305
$293$	14.9443	0.873054	0.436527	−	0.899691i	$-0.356208\pi$
$293$	14.9443	0.873054	0.436527	+	0.899691i	$0.356208\pi$
$294$	0	0
$295$	−3.29180	−0.191656
$296$	35.1803	2.04482
$297$	0	0
$298$	−1.85410	−0.107405
$299$	−8.23607	−0.476304
$300$	0	0
$301$	0	0
$302$	53.4508	3.07575
$303$	0	0
$304$	29.5623	1.69551
$305$	−6.70820	−0.384111
$306$	0	0
$307$	19.4164	1.10815	0.554076	−	0.832466i	$-0.313072\pi$
$307$	19.4164	1.10815	0.554076	+	0.832466i	$0.313072\pi$
$308$	0	0
$309$	0	0
$310$	−29.2705	−1.66245
$311$	27.7639	1.57435	0.787174	−	0.616731i	$-0.211543\pi$
$311$	27.7639	1.57435	0.787174	+	0.616731i	$0.211543\pi$
$312$	0	0
$313$	−5.58359	−0.315603	−0.157802	−	0.987471i	$-0.550441\pi$
$313$	−5.58359	−0.315603	−0.157802	+	0.987471i	$0.550441\pi$
$314$	18.3262	1.03421
$315$	0	0
$316$	−13.1459	−0.739515
$317$	8.23607	0.462584	0.231292	−	0.972884i	$-0.425705\pi$
$317$	8.23607	0.462584	0.231292	+	0.972884i	$0.425705\pi$
$318$	0	0
$319$	−13.4164	−0.751175
$320$	−19.4721	−1.08853
$321$	0	0
$322$	0	0
$323$	−4.41641	−0.245736
$324$	0	0
$325$	0	0
$326$	−42.9787	−2.38037
$327$	0	0
$328$	33.4164	1.84511
$329$	0	0
$330$	0	0
$331$	−1.58359	−0.0870421	−0.0435210	−	0.999053i	$-0.513858\pi$
$331$	−1.58359	−0.0870421	−0.0435210	+	0.999053i	$0.513858\pi$
$332$	0	0
$333$	0	0
$334$	−58.8328	−3.21919
$335$	6.70820	0.366508
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	2.61803	0.142402
$339$	0	0
$340$	15.9787	0.866567
$341$	15.0000	0.812296
$342$	0	0
$343$	0	0
$344$	−59.7771	−3.22296
$345$	0	0
$346$	42.9787	2.31055
$347$	−23.0689	−1.23840	−0.619201	−	0.785232i	$-0.712544\pi$
$347$	−23.0689	−1.23840	−0.619201	+	0.785232i	$0.712544\pi$
$348$	0	0
$349$	−29.4164	−1.57462	−0.787312	−	0.616555i	$-0.788528\pi$
$349$	−29.4164	−1.57462	−0.787312	+	0.616555i	$0.788528\pi$
$350$	0	0
$351$	0	0
$352$	32.5623	1.73558
$353$	−17.2918	−0.920349	−0.460175	−	0.887828i	$-0.652213\pi$
$353$	−17.2918	−0.920349	−0.460175	+	0.887828i	$0.652213\pi$
$354$	0	0
$355$	−20.0000	−1.06149
$356$	−10.8541	−0.575266
$357$	0	0
$358$	52.6869	2.78459
$359$	−11.9443	−0.630395	−0.315197	−	0.949026i	$-0.602071\pi$
$359$	−11.9443	−0.630395	−0.315197	+	0.949026i	$0.602071\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−66.5410	−3.49732
$363$	0	0
$364$	0	0
$365$	6.05573	0.316971
$366$	0	0
$367$	−12.7082	−0.663363	−0.331681	−	0.943391i	$-0.607616\pi$
$367$	−12.7082	−0.663363	−0.331681	+	0.943391i	$0.607616\pi$
$368$	81.1591	4.23071
$369$	0	0
$370$	−27.5623	−1.43290
$371$	0	0
$372$	0	0
$373$	−1.58359	−0.0819953	−0.0409976	−	0.999159i	$-0.513054\pi$
$373$	−1.58359	−0.0819953	−0.0409976	+	0.999159i	$0.513054\pi$
$374$	−11.5623	−0.597873
$375$	0	0
$376$	55.8328	2.87936
$377$	4.47214	0.230327
$378$	0	0
$379$	−15.4164	−0.791888	−0.395944	−	0.918275i	$-0.629583\pi$
$379$	−15.4164	−0.791888	−0.395944	+	0.918275i	$0.629583\pi$
$380$	−32.5623	−1.67041
$381$	0	0
$382$	−29.2705	−1.49761
$383$	−15.0000	−0.766464	−0.383232	−	0.923652i	$-0.625189\pi$
$383$	−15.0000	−0.766464	−0.383232	+	0.923652i	$0.625189\pi$
$384$	0	0
$385$	0	0
$386$	1.85410	0.0943713
$387$	0	0
$388$	45.7082	2.32048
$389$	−1.47214	−0.0746403	−0.0373201	−	0.999303i	$-0.511882\pi$
$389$	−1.47214	−0.0746403	−0.0373201	+	0.999303i	$0.511882\pi$
$390$	0	0
$391$	−12.1246	−0.613168
$392$	0	0
$393$	0	0
$394$	23.7082	1.19440
$395$	6.05573	0.304697
$396$	0	0
$397$	−26.1246	−1.31116	−0.655578	−	0.755127i	$-0.727575\pi$
$397$	−26.1246	−1.31116	−0.655578	+	0.755127i	$0.727575\pi$
$398$	−54.2148	−2.71754
$399$	0	0
$400$	0	0
$401$	−14.2361	−0.710915	−0.355458	−	0.934692i	$-0.615675\pi$
$401$	−14.2361	−0.710915	−0.355458	+	0.934692i	$0.615675\pi$
$402$	0	0
$403$	−5.00000	−0.249068
$404$	43.6869	2.17351
$405$	0	0
$406$	0	0
$407$	14.1246	0.700131
$408$	0	0
$409$	8.70820	0.430593	0.215296	−	0.976549i	$-0.430928\pi$
$409$	8.70820	0.430593	0.215296	+	0.976549i	$0.430928\pi$
$410$	−26.1803	−1.29295
$411$	0	0
$412$	−13.1459	−0.647652
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−10.8541	−0.532166
$417$	0	0
$418$	23.5623	1.15247
$419$	−32.9443	−1.60943	−0.804717	−	0.593659i	$-0.797683\pi$
$419$	−32.9443	−1.60943	−0.804717	+	0.593659i	$0.797683\pi$
$420$	0	0
$421$	13.4164	0.653876	0.326938	−	0.945046i	$-0.393983\pi$
$421$	13.4164	0.653876	0.326938	+	0.945046i	$0.393983\pi$
$422$	10.4721	0.509776
$423$	0	0
$424$	55.8328	2.71148
$425$	0	0
$426$	0	0
$427$	0	0
$428$	47.3951	2.29093
$429$	0	0
$430$	46.8328	2.25848
$431$	31.3607	1.51059	0.755295	−	0.655385i	$-0.227493\pi$
$431$	31.3607	1.51059	0.755295	+	0.655385i	$0.227493\pi$
$432$	0	0
$433$	29.4164	1.41366	0.706831	−	0.707382i	$-0.250124\pi$
$433$	29.4164	1.41366	0.706831	+	0.707382i	$0.250124\pi$
$434$	0	0
$435$	0	0
$436$	−13.1459	−0.629574
$437$	24.7082	1.18195
$438$	0	0
$439$	24.1246	1.15140	0.575702	−	0.817659i	$-0.304729\pi$
$439$	24.1246	1.15140	0.575702	+	0.817659i	$0.304729\pi$
$440$	−50.1246	−2.38960
$441$	0	0
$442$	3.85410	0.183321
$443$	−2.23607	−0.106239	−0.0531194	−	0.998588i	$-0.516916\pi$
$443$	−2.23607	−0.106239	−0.0531194	+	0.998588i	$0.516916\pi$
$444$	0	0
$445$	5.00000	0.237023
$446$	−10.4721	−0.495870
$447$	0	0
$448$	0	0
$449$	34.3607	1.62158	0.810790	−	0.585337i	$-0.199038\pi$
$449$	34.3607	1.62158	0.810790	+	0.585337i	$0.199038\pi$
$450$	0	0
$451$	13.4164	0.631754
$452$	−14.2918	−0.672230
$453$	0	0
$454$	−15.5623	−0.730375
$455$	0	0
$456$	0	0
$457$	−6.12461	−0.286497	−0.143249	−	0.989687i	$-0.545755\pi$
$457$	−6.12461	−0.286497	−0.143249	+	0.989687i	$0.545755\pi$
$458$	63.1591	2.95123
$459$	0	0
$460$	−89.3951	−4.16807
$461$	−34.3607	−1.60034	−0.800168	−	0.599776i	$-0.795256\pi$
$461$	−34.3607	−1.60034	−0.800168	+	0.599776i	$0.795256\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−44.0689	−2.04585
$465$	0	0
$466$	−31.2705	−1.44858
$467$	−9.65248	−0.446663	−0.223332	−	0.974743i	$-0.571693\pi$
$467$	−9.65248	−0.446663	−0.223332	+	0.974743i	$0.571693\pi$
$468$	0	0
$469$	0	0
$470$	−43.7426	−2.01770
$471$	0	0
$472$	11.0000	0.506316
$473$	−24.0000	−1.10352
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	−50.8328	−2.32504
$479$	−23.8328	−1.08895	−0.544475	−	0.838777i	$-0.683271\pi$
$479$	−23.8328	−1.08895	−0.544475	+	0.838777i	$0.683271\pi$
$480$	0	0
$481$	−4.70820	−0.214676
$482$	12.3262	0.561445
$483$	0	0
$484$	−9.70820	−0.441282
$485$	−21.0557	−0.956091
$486$	0	0
$487$	−21.8328	−0.989339	−0.494670	−	0.869081i	$-0.664711\pi$
$487$	−21.8328	−0.989339	−0.494670	+	0.869081i	$0.664711\pi$
$488$	22.4164	1.01474
$489$	0	0
$490$	0	0
$491$	25.5279	1.15206	0.576028	−	0.817430i	$-0.304602\pi$
$491$	25.5279	1.15206	0.576028	+	0.817430i	$0.304602\pi$
$492$	0	0
$493$	6.58359	0.296510
$494$	−7.85410	−0.353373
$495$	0	0
$496$	49.2705	2.21231
$497$	0	0
$498$	0	0
$499$	26.4164	1.18256	0.591280	−	0.806466i	$-0.298623\pi$
$499$	26.4164	1.18256	0.591280	+	0.806466i	$0.298623\pi$
$500$	54.2705	2.42705
$501$	0	0
$502$	−4.00000	−0.178529
$503$	−20.9443	−0.933859	−0.466929	−	0.884295i	$-0.654640\pi$
$503$	−20.9443	−0.933859	−0.466929	+	0.884295i	$0.654640\pi$
$504$	0	0
$505$	−20.1246	−0.895533
$506$	64.6869	2.87568
$507$	0	0
$508$	−55.4164	−2.45871
$509$	20.2361	0.896948	0.448474	−	0.893796i	$-0.351968\pi$
$509$	20.2361	0.896948	0.448474	+	0.893796i	$0.351968\pi$
$510$	0	0
$511$	0	0
$512$	−40.3050	−1.78124
$513$	0	0
$514$	0.145898	0.00643529
$515$	6.05573	0.266847
$516$	0	0
$517$	22.4164	0.985872
$518$	0	0
$519$	0	0
$520$	16.7082	0.732703
$521$	17.9443	0.786153	0.393076	−	0.919506i	$-0.371411\pi$
$521$	17.9443	0.786153	0.393076	+	0.919506i	$0.371411\pi$
$522$	0	0
$523$	32.7082	1.43023	0.715115	−	0.699007i	$-0.246374\pi$
$523$	32.7082	1.43023	0.715115	+	0.699007i	$0.246374\pi$
$524$	39.9787	1.74648
$525$	0	0
$526$	−68.3951	−2.98217
$527$	−7.36068	−0.320636
$528$	0	0
$529$	44.8328	1.94925
$530$	−43.7426	−1.90006
$531$	0	0
$532$	0	0
$533$	−4.47214	−0.193710
$534$	0	0
$535$	−21.8328	−0.943915
$536$	−22.4164	−0.968241
$537$	0	0
$538$	−35.2705	−1.52062
$539$	0	0
$540$	0	0
$541$	1.29180	0.0555387	0.0277693	−	0.999614i	$-0.491160\pi$
$541$	1.29180	0.0555387	0.0277693	+	0.999614i	$0.491160\pi$
$542$	−53.4508	−2.29591
$543$	0	0
$544$	−15.9787	−0.685082
$545$	6.05573	0.259399
$546$	0	0
$547$	−4.58359	−0.195980	−0.0979901	−	0.995187i	$-0.531241\pi$
$547$	−4.58359	−0.195980	−0.0979901	+	0.995187i	$0.531241\pi$
$548$	39.9787	1.70781
$549$	0	0
$550$	0	0
$551$	−13.4164	−0.571558
$552$	0	0
$553$	0	0
$554$	−1.09017	−0.0463169
$555$	0	0
$556$	−113.666	−4.82050
$557$	18.7082	0.792692	0.396346	−	0.918101i	$-0.370278\pi$
$557$	18.7082	0.792692	0.396346	+	0.918101i	$0.370278\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	0	0
$561$	0	0
$562$	−70.5410	−2.97559
$563$	−12.5967	−0.530890	−0.265445	−	0.964126i	$-0.585519\pi$
$563$	−12.5967	−0.530890	−0.265445	+	0.964126i	$0.585519\pi$
$564$	0	0
$565$	6.58359	0.276974
$566$	68.3951	2.87486
$567$	0	0
$568$	66.8328	2.80424
$569$	−25.4721	−1.06785	−0.533924	−	0.845533i	$-0.679283\pi$
$569$	−25.4721	−1.06785	−0.533924	+	0.845533i	$0.679283\pi$
$570$	0	0
$571$	−36.1246	−1.51177	−0.755884	−	0.654706i	$-0.772793\pi$
$571$	−36.1246	−1.51177	−0.755884	+	0.654706i	$0.772793\pi$
$572$	−14.5623	−0.608881
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−19.2918	−0.803128	−0.401564	−	0.915831i	$-0.631533\pi$
$577$	−19.2918	−0.803128	−0.401564	+	0.915831i	$0.631533\pi$
$578$	−38.8328	−1.61523
$579$	0	0
$580$	48.5410	2.01556
$581$	0	0
$582$	0	0
$583$	22.4164	0.928393
$584$	−20.2361	−0.837374
$585$	0	0
$586$	39.1246	1.61622
$587$	6.11146	0.252247	0.126123	−	0.992015i	$-0.459746\pi$
$587$	6.11146	0.252247	0.126123	+	0.992015i	$0.459746\pi$
$588$	0	0
$589$	15.0000	0.618064
$590$	−8.61803	−0.354799
$591$	0	0
$592$	46.3951	1.90683
$593$	−27.7639	−1.14013	−0.570064	−	0.821600i	$-0.693082\pi$
$593$	−27.7639	−1.14013	−0.570064	+	0.821600i	$0.693082\pi$
$594$	0	0
$595$	0	0
$596$	−3.43769	−0.140813
$597$	0	0
$598$	−21.5623	−0.881748
$599$	17.0689	0.697416	0.348708	−	0.937231i	$-0.386621\pi$
$599$	17.0689	0.697416	0.348708	+	0.937231i	$0.386621\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	0	0
$604$	99.1033	4.03246
$605$	4.47214	0.181818
$606$	0	0
$607$	24.1246	0.979188	0.489594	−	0.871951i	$-0.337145\pi$
$607$	24.1246	0.979188	0.489594	+	0.871951i	$0.337145\pi$
$608$	32.5623	1.32058
$609$	0	0
$610$	−17.5623	−0.711077
$611$	−7.47214	−0.302290
$612$	0	0
$613$	−18.1246	−0.732046	−0.366023	−	0.930606i	$-0.619281\pi$
$613$	−18.1246	−0.732046	−0.366023	+	0.930606i	$0.619281\pi$
$614$	50.8328	2.05145
$615$	0	0
$616$	0	0
$617$	4.47214	0.180041	0.0900207	−	0.995940i	$-0.471307\pi$
$617$	4.47214	0.180041	0.0900207	+	0.995940i	$0.471307\pi$
$618$	0	0
$619$	17.0000	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$620$	−54.2705	−2.17956
$621$	0	0
$622$	72.6869	2.91448
$623$	0	0
$624$	0	0
$625$	−25.0000	−1.00000
$626$	−14.6180	−0.584254
$627$	0	0
$628$	33.9787	1.35590
$629$	−6.93112	−0.276362
$630$	0	0
$631$	22.8328	0.908960	0.454480	−	0.890757i	$-0.349825\pi$
$631$	22.8328	0.908960	0.454480	+	0.890757i	$0.349825\pi$
$632$	−20.2361	−0.804948
$633$	0	0
$634$	21.5623	0.856349
$635$	25.5279	1.01304
$636$	0	0
$637$	0	0
$638$	−35.1246	−1.39060
$639$	0	0
$640$	−2.43769	−0.0963583
$641$	−11.9443	−0.471770	−0.235885	−	0.971781i	$-0.575799\pi$
$641$	−11.9443	−0.471770	−0.235885	+	0.971781i	$0.575799\pi$
$642$	0	0
$643$	34.8328	1.37367	0.686836	−	0.726812i	$-0.258999\pi$
$643$	34.8328	1.37367	0.686836	+	0.726812i	$0.258999\pi$
$644$	0	0
$645$	0	0
$646$	−11.5623	−0.454913
$647$	−20.2361	−0.795562	−0.397781	−	0.917480i	$-0.630220\pi$
$647$	−20.2361	−0.795562	−0.397781	+	0.917480i	$0.630220\pi$
$648$	0	0
$649$	4.41641	0.173359
$650$	0	0
$651$	0	0
$652$	−79.6869	−3.12078
$653$	−4.52786	−0.177189	−0.0885945	−	0.996068i	$-0.528238\pi$
$653$	−4.52786	−0.177189	−0.0885945	+	0.996068i	$0.528238\pi$
$654$	0	0
$655$	−18.4164	−0.719589
$656$	44.0689	1.72060
$657$	0	0
$658$	0	0
$659$	8.94427	0.348419	0.174210	−	0.984709i	$-0.444263\pi$
$659$	8.94427	0.348419	0.174210	+	0.984709i	$0.444263\pi$
$660$	0	0
$661$	−6.70820	−0.260919	−0.130459	−	0.991454i	$-0.541645\pi$
$661$	−6.70820	−0.260919	−0.130459	+	0.991454i	$0.541645\pi$
$662$	−4.14590	−0.161135
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−36.8328	−1.42617
$668$	−109.082	−4.22051
$669$	0	0
$670$	17.5623	0.678491
$671$	9.00000	0.347441
$672$	0	0
$673$	−9.41641	−0.362976	−0.181488	−	0.983393i	$-0.558091\pi$
$673$	−9.41641	−0.362976	−0.181488	+	0.983393i	$0.558091\pi$
$674$	47.1246	1.81517
$675$	0	0
$676$	4.85410	0.186696
$677$	2.88854	0.111016	0.0555079	−	0.998458i	$-0.482322\pi$
$677$	2.88854	0.111016	0.0555079	+	0.998458i	$0.482322\pi$
$678$	0	0
$679$	0	0
$680$	24.5967	0.943242
$681$	0	0
$682$	39.2705	1.50375
$683$	13.4721	0.515497	0.257748	−	0.966212i	$-0.417019\pi$
$683$	13.4721	0.515497	0.257748	+	0.966212i	$0.417019\pi$
$684$	0	0
$685$	−18.4164	−0.703655
$686$	0	0
$687$	0	0
$688$	−78.8328	−3.00547
$689$	−7.47214	−0.284666
$690$	0	0
$691$	−51.8328	−1.97181	−0.985907	−	0.167297i	$-0.946496\pi$
$691$	−51.8328	−1.97181	−0.985907	+	0.167297i	$0.946496\pi$
$692$	79.6869	3.02924
$693$	0	0
$694$	−60.3951	−2.29257
$695$	52.3607	1.98615
$696$	0	0
$697$	−6.58359	−0.249371
$698$	−77.0132	−2.91499
$699$	0	0
$700$	0	0
$701$	22.3607	0.844551	0.422276	−	0.906467i	$-0.361231\pi$
$701$	22.3607	0.844551	0.422276	+	0.906467i	$0.361231\pi$
$702$	0	0
$703$	14.1246	0.532720
$704$	26.1246	0.984608
$705$	0	0
$706$	−45.2705	−1.70378
$707$	0	0
$708$	0	0
$709$	−50.1246	−1.88247	−0.941235	−	0.337753i	$-0.890333\pi$
$709$	−50.1246	−1.88247	−0.941235	+	0.337753i	$0.890333\pi$
$710$	−52.3607	−1.96506
$711$	0	0
$712$	−16.7082	−0.626166
$713$	41.1803	1.54222
$714$	0	0
$715$	6.70820	0.250873
$716$	97.6869	3.65073
$717$	0	0
$718$	−31.2705	−1.16701
$719$	−24.7082	−0.921461	−0.460730	−	0.887540i	$-0.652412\pi$
$719$	−24.7082	−0.921461	−0.460730	+	0.887540i	$0.652412\pi$
$720$	0	0
$721$	0	0
$722$	−26.1803	−0.974331
$723$	0	0
$724$	−123.374	−4.58515
$725$	0	0
$726$	0	0
$727$	−38.8328	−1.44023	−0.720115	−	0.693855i	$-0.755911\pi$
$727$	−38.8328	−1.44023	−0.720115	+	0.693855i	$0.755911\pi$
$728$	0	0
$729$	0	0
$730$	15.8541	0.586787
$731$	11.7771	0.435591
$732$	0	0
$733$	28.7082	1.06036	0.530181	−	0.847885i	$-0.322124\pi$
$733$	28.7082	1.06036	0.530181	+	0.847885i	$0.322124\pi$
$734$	−33.2705	−1.22804
$735$	0	0
$736$	89.3951	3.29515
$737$	−9.00000	−0.331519
$738$	0	0
$739$	−17.8328	−0.655991	−0.327995	−	0.944679i	$-0.606373\pi$
$739$	−17.8328	−0.655991	−0.327995	+	0.944679i	$0.606373\pi$
$740$	−51.1033	−1.87860
$741$	0	0
$742$	0	0
$743$	−32.9443	−1.20861	−0.604304	−	0.796754i	$-0.706549\pi$
$743$	−32.9443	−1.20861	−0.604304	+	0.796754i	$0.706549\pi$
$744$	0	0
$745$	1.58359	0.0580183
$746$	−4.14590	−0.151792
$747$	0	0
$748$	−21.4377	−0.783840
$749$	0	0
$750$	0	0
$751$	−10.1246	−0.369452	−0.184726	−	0.982790i	$-0.559140\pi$
$751$	−10.1246	−0.369452	−0.184726	+	0.982790i	$0.559140\pi$
$752$	73.6312	2.68505
$753$	0	0
$754$	11.7082	0.426388
$755$	−45.6525	−1.66146
$756$	0	0
$757$	−52.8328	−1.92024	−0.960121	−	0.279586i	$-0.909803\pi$
$757$	−52.8328	−1.92024	−0.960121	+	0.279586i	$0.909803\pi$
$758$	−40.3607	−1.46597
$759$	0	0
$760$	−50.1246	−1.81821
$761$	33.5410	1.21586	0.607931	−	0.793990i	$-0.292000\pi$
$761$	33.5410	1.21586	0.607931	+	0.793990i	$0.292000\pi$
$762$	0	0
$763$	0	0
$764$	−54.2705	−1.96344
$765$	0	0
$766$	−39.2705	−1.41890
$767$	−1.47214	−0.0531557
$768$	0	0
$769$	46.0000	1.65880	0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000	1.65880	0.829401	+	0.558653i	$0.188682\pi$
$770$	0	0
$771$	0	0
$772$	3.43769	0.123725
$773$	47.0689	1.69295	0.846475	−	0.532428i	$-0.178720\pi$
$773$	47.0689	1.69295	0.846475	+	0.532428i	$0.178720\pi$
$774$	0	0
$775$	0	0
$776$	70.3607	2.52580
$777$	0	0
$778$	−3.85410	−0.138176
$779$	13.4164	0.480693
$780$	0	0
$781$	26.8328	0.960154
$782$	−31.7426	−1.13511
$783$	0	0
$784$	0	0
$785$	−15.6525	−0.558661
$786$	0	0
$787$	20.4164	0.727766	0.363883	−	0.931445i	$-0.381451\pi$
$787$	20.4164	0.727766	0.363883	+	0.931445i	$0.381451\pi$
$788$	43.9574	1.56592
$789$	0	0
$790$	15.8541	0.564064
$791$	0	0
$792$	0	0
$793$	−3.00000	−0.106533
$794$	−68.3951	−2.42725
$795$	0	0
$796$	−100.520	−3.56283
$797$	−9.05573	−0.320770	−0.160385	−	0.987055i	$-0.551274\pi$
$797$	−9.05573	−0.320770	−0.160385	+	0.987055i	$0.551274\pi$
$798$	0	0
$799$	−11.0000	−0.389152
$800$	0	0
$801$	0	0
$802$	−37.2705	−1.31607
$803$	−8.12461	−0.286711
$804$	0	0
$805$	0	0
$806$	−13.0902	−0.461082
$807$	0	0
$808$	67.2492	2.36582
$809$	−22.4164	−0.788119	−0.394059	−	0.919085i	$-0.628930\pi$
$809$	−22.4164	−0.788119	−0.394059	+	0.919085i	$0.628930\pi$
$810$	0	0
$811$	−14.8328	−0.520851	−0.260425	−	0.965494i	$-0.583863\pi$
$811$	−14.8328	−0.520851	−0.260425	+	0.965494i	$0.583863\pi$
$812$	0	0
$813$	0	0
$814$	36.9787	1.29610
$815$	36.7082	1.28583
$816$	0	0
$817$	−24.0000	−0.839654
$818$	22.7984	0.797126
$819$	0	0
$820$	−48.5410	−1.69513
$821$	−38.2361	−1.33445	−0.667224	−	0.744857i	$-0.732518\pi$
$821$	−38.2361	−1.33445	−0.667224	+	0.744857i	$0.732518\pi$
$822$	0	0
$823$	34.1246	1.18951	0.594755	−	0.803907i	$-0.297249\pi$
$823$	34.1246	1.18951	0.594755	+	0.803907i	$0.297249\pi$
$824$	−20.2361	−0.704957
$825$	0	0
$826$	0	0
$827$	−26.8328	−0.933068	−0.466534	−	0.884503i	$-0.654498\pi$
$827$	−26.8328	−0.933068	−0.466534	+	0.884503i	$0.654498\pi$
$828$	0	0
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	0	0
$831$	0	0
$832$	−8.70820	−0.301903
$833$	0	0
$834$	0	0
$835$	50.2492	1.73895
$836$	43.6869	1.51094
$837$	0	0
$838$	−86.2492	−2.97943
$839$	5.88854	0.203295	0.101648	−	0.994820i	$-0.467589\pi$
$839$	5.88854	0.203295	0.101648	+	0.994820i	$0.467589\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	35.1246	1.21047
$843$	0	0
$844$	19.4164	0.668340
$845$	−2.23607	−0.0769231
$846$	0	0
$847$	0	0
$848$	73.6312	2.52851
$849$	0	0
$850$	0	0
$851$	38.7771	1.32926
$852$	0	0
$853$	−52.2492	−1.78898	−0.894490	−	0.447089i	$-0.852461\pi$
$853$	−52.2492	−1.78898	−0.894490	+	0.447089i	$0.852461\pi$
$854$	0	0
$855$	0	0
$856$	72.9574	2.49363
$857$	1.36068	0.0464799	0.0232400	−	0.999730i	$-0.492602\pi$
$857$	1.36068	0.0464799	0.0232400	+	0.999730i	$0.492602\pi$
$858$	0	0
$859$	20.7082	0.706555	0.353277	−	0.935519i	$-0.385067\pi$
$859$	20.7082	0.706555	0.353277	+	0.935519i	$0.385067\pi$
$860$	86.8328	2.96097
$861$	0	0
$862$	82.1033	2.79645
$863$	−23.9443	−0.815072	−0.407536	−	0.913189i	$-0.633612\pi$
$863$	−23.9443	−0.815072	−0.407536	+	0.913189i	$0.633612\pi$
$864$	0	0
$865$	−36.7082	−1.24812
$866$	77.0132	2.61701
$867$	0	0
$868$	0	0
$869$	−8.12461	−0.275609
$870$	0	0
$871$	3.00000	0.101651
$872$	−20.2361	−0.685280
$873$	0	0
$874$	64.6869	2.18807
$875$	0	0
$876$	0	0
$877$	32.1246	1.08477	0.542386	−	0.840130i	$-0.317521\pi$
$877$	32.1246	1.08477	0.542386	+	0.840130i	$0.317521\pi$
$878$	63.1591	2.13151
$879$	0	0
$880$	−66.1033	−2.22834
$881$	−43.3050	−1.45898	−0.729490	−	0.683991i	$-0.760243\pi$
$881$	−43.3050	−1.45898	−0.729490	+	0.683991i	$0.760243\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	7.14590	0.240343
$885$	0	0
$886$	−5.85410	−0.196672
$887$	20.2361	0.679461	0.339730	−	0.940523i	$-0.389664\pi$
$887$	20.2361	0.679461	0.339730	+	0.940523i	$0.389664\pi$
$888$	0	0
$889$	0	0
$890$	13.0902	0.438783
$891$	0	0
$892$	−19.4164	−0.650109
$893$	22.4164	0.750136
$894$	0	0
$895$	−45.0000	−1.50418
$896$	0	0
$897$	0	0
$898$	89.9574	3.00192
$899$	−22.3607	−0.745770
$900$	0	0
$901$	−11.0000	−0.366463
$902$	35.1246	1.16952
$903$	0	0
$904$	−22.0000	−0.731709
$905$	56.8328	1.88919
$906$	0	0
$907$	18.7082	0.621196	0.310598	−	0.950541i	$-0.399471\pi$
$907$	18.7082	0.621196	0.310598	+	0.950541i	$0.399471\pi$
$908$	−28.8541	−0.957557
$909$	0	0
$910$	0	0
$911$	34.2492	1.13473	0.567364	−	0.823467i	$-0.307963\pi$
$911$	34.2492	1.13473	0.567364	+	0.823467i	$0.307963\pi$
$912$	0	0
$913$	0	0
$914$	−16.0344	−0.530372
$915$	0	0
$916$	117.103	3.86920
$917$	0	0
$918$	0	0
$919$	20.1246	0.663850	0.331925	−	0.943306i	$-0.392302\pi$
$919$	20.1246	0.663850	0.331925	+	0.943306i	$0.392302\pi$
$920$	−137.610	−4.53686
$921$	0	0
$922$	−89.9574	−2.96259
$923$	−8.94427	−0.294404
$924$	0	0
$925$	0	0
$926$	−62.8328	−2.06481
$927$	0	0
$928$	−48.5410	−1.59344
$929$	24.8197	0.814307	0.407153	−	0.913360i	$-0.366521\pi$
$929$	24.8197	0.814307	0.407153	+	0.913360i	$0.366521\pi$
$930$	0	0
$931$	0	0
$932$	−57.9787	−1.89916
$933$	0	0
$934$	−25.2705	−0.826876
$935$	9.87539	0.322960
$936$	0	0
$937$	25.4164	0.830318	0.415159	−	0.909749i	$-0.363726\pi$
$937$	25.4164	0.830318	0.415159	+	0.909749i	$0.363726\pi$
$938$	0	0
$939$	0	0
$940$	−81.1033	−2.64530
$941$	−50.2361	−1.63765	−0.818825	−	0.574044i	$-0.805374\pi$
$941$	−50.2361	−1.63765	−0.818825	+	0.574044i	$0.805374\pi$
$942$	0	0
$943$	36.8328	1.19944
$944$	14.5066	0.472149
$945$	0	0
$946$	−62.8328	−2.04287
$947$	22.5279	0.732057	0.366029	−	0.930604i	$-0.380717\pi$
$947$	22.5279	0.732057	0.366029	+	0.930604i	$0.380717\pi$
$948$	0	0
$949$	2.70820	0.0879120
$950$	0	0
$951$	0	0
$952$	0	0
$953$	41.7771	1.35329	0.676646	−	0.736308i	$-0.263433\pi$
$953$	41.7771	1.35329	0.676646	+	0.736308i	$0.263433\pi$
$954$	0	0
$955$	25.0000	0.808981
$956$	−94.2492	−3.04824
$957$	0	0
$958$	−62.3951	−2.01589
$959$	0	0
$960$	0	0
$961$	−6.00000	−0.193548
$962$	−12.3262	−0.397414
$963$	0	0
$964$	22.8541	0.736081
$965$	−1.58359	−0.0509776
$966$	0	0
$967$	16.5836	0.533292	0.266646	−	0.963794i	$-0.414084\pi$
$967$	16.5836	0.533292	0.266646	+	0.963794i	$0.414084\pi$
$968$	−14.9443	−0.480327
$969$	0	0
$970$	−55.1246	−1.76994
$971$	11.2918	0.362371	0.181185	−	0.983449i	$-0.442007\pi$
$971$	11.2918	0.362371	0.181185	+	0.983449i	$0.442007\pi$
$972$	0	0
$973$	0	0
$974$	−57.1591	−1.83149
$975$	0	0
$976$	29.5623	0.946266
$977$	2.34752	0.0751040	0.0375520	−	0.999295i	$-0.488044\pi$
$977$	2.34752	0.0751040	0.0375520	+	0.999295i	$0.488044\pi$
$978$	0	0
$979$	−6.70820	−0.214395
$980$	0	0
$981$	0	0
$982$	66.8328	2.13272
$983$	−7.47214	−0.238324	−0.119162	−	0.992875i	$-0.538021\pi$
$983$	−7.47214	−0.238324	−0.119162	+	0.992875i	$0.538021\pi$
$984$	0	0
$985$	−20.2492	−0.645194
$986$	17.2361	0.548908
$987$	0	0
$988$	−14.5623	−0.463289
$989$	−65.8885	−2.09513
$990$	0	0
$991$	30.7082	0.975478	0.487739	−	0.872989i	$-0.337822\pi$
$991$	30.7082	0.975478	0.487739	+	0.872989i	$0.337822\pi$
$992$	54.2705	1.72309
$993$	0	0
$994$	0	0
$995$	46.3050	1.46797
$996$	0	0
$997$	26.4164	0.836616	0.418308	−	0.908305i	$-0.362623\pi$
$997$	26.4164	0.836616	0.418308	+	0.908305i	$0.362623\pi$
$998$	69.1591	2.18919
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.v.1.2		2
3.2	odd	2		637.2.a.f.1.1		2
7.2	even	3		819.2.j.c.235.1		4
7.4	even	3		819.2.j.c.352.1		4
7.6	odd	2		5733.2.a.w.1.2		2
21.2	odd	6		91.2.e.b.53.2	✓	4
21.5	even	6		637.2.e.h.508.2		4
21.11	odd	6		91.2.e.b.79.2	yes	4
21.17	even	6		637.2.e.h.79.2		4
21.20	even	2		637.2.a.e.1.1		2
39.38	odd	2		8281.2.a.z.1.2		2
84.11	even	6		1456.2.r.j.625.1		4
84.23	even	6		1456.2.r.j.417.1		4
273.116	odd	6		1183.2.e.d.170.1		4
273.233	odd	6		1183.2.e.d.508.1		4
273.272	even	2		8281.2.a.ba.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.2	✓	4	21.2	odd	6
91.2.e.b.79.2	yes	4	21.11	odd	6
637.2.a.e.1.1		2	21.20	even	2
637.2.a.f.1.1		2	3.2	odd	2
637.2.e.h.79.2		4	21.17	even	6
637.2.e.h.508.2		4	21.5	even	6
819.2.j.c.235.1		4	7.2	even	3
819.2.j.c.352.1		4	7.4	even	3
1183.2.e.d.170.1		4	273.116	odd	6
1183.2.e.d.508.1		4	273.233	odd	6
1456.2.r.j.417.1		4	84.23	even	6
1456.2.r.j.625.1		4	84.11	even	6
5733.2.a.v.1.2		2	1.1	even	1	trivial
5733.2.a.w.1.2		2	7.6	odd	2
8281.2.a.z.1.2		2	39.38	odd	2
8281.2.a.ba.1.2		2	273.272	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} +4.85410 q^{4} -2.23607 q^{5} +7.47214 q^{8} +O(q^{10})\)	\(q+2.61803 q^{2} +4.85410 q^{4} -2.23607 q^{5} +7.47214 q^{8} -5.85410 q^{10} +3.00000 q^{11} -1.00000 q^{13} +9.85410 q^{16} -1.47214 q^{17} +3.00000 q^{19} -10.8541 q^{20} +7.85410 q^{22} +8.23607 q^{23} -2.61803 q^{26} -4.47214 q^{29} +5.00000 q^{31} +10.8541 q^{32} -3.85410 q^{34} +4.70820 q^{37} +7.85410 q^{38} -16.7082 q^{40} +4.47214 q^{41} -8.00000 q^{43} +14.5623 q^{44} +21.5623 q^{46} +7.47214 q^{47} -4.85410 q^{52} +7.47214 q^{53} -6.70820 q^{55} -11.7082 q^{58} +1.47214 q^{59} +3.00000 q^{61} +13.0902 q^{62} +8.70820 q^{64} +2.23607 q^{65} -3.00000 q^{67} -7.14590 q^{68} +8.94427 q^{71} -2.70820 q^{73} +12.3262 q^{74} +14.5623 q^{76} -2.70820 q^{79} -22.0344 q^{80} +11.7082 q^{82} +3.29180 q^{85} -20.9443 q^{86} +22.4164 q^{88} -2.23607 q^{89} +39.9787 q^{92} +19.5623 q^{94} -6.70820 q^{95} +9.41641 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{4} + 6 q^{8}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^4 + 6 * q^8	\( 2 q + 3 q^{2} + 3 q^{4} + 6 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 13 q^{16} + 6 q^{17} + 6 q^{19} - 15 q^{20} + 9 q^{22} + 12 q^{23} - 3 q^{26} + 10 q^{31} + 15 q^{32} - q^{34} - 4 q^{37} + 9 q^{38} - 20 q^{40} - 16 q^{43} + 9 q^{44} + 23 q^{46} + 6 q^{47} - 3 q^{52} + 6 q^{53} - 10 q^{58} - 6 q^{59} + 6 q^{61} + 15 q^{62} + 4 q^{64} - 6 q^{67} - 21 q^{68} + 8 q^{73} + 9 q^{74} + 9 q^{76} + 8 q^{79} - 15 q^{80} + 10 q^{82} + 20 q^{85} - 24 q^{86} + 18 q^{88} + 33 q^{92} + 19 q^{94} - 8 q^{97}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^4 + 6 * q^8 - 5 * q^10 + 6 * q^11 - 2 * q^13 + 13 * q^16 + 6 * q^17 + 6 * q^19 - 15 * q^20 + 9 * q^22 + 12 * q^23 - 3 * q^26 + 10 * q^31 + 15 * q^32 - q^34 - 4 * q^37 + 9 * q^38 - 20 * q^40 - 16 * q^43 + 9 * q^44 + 23 * q^46 + 6 * q^47 - 3 * q^52 + 6 * q^53 - 10 * q^58 - 6 * q^59 + 6 * q^61 + 15 * q^62 + 4 * q^64 - 6 * q^67 - 21 * q^68 + 8 * q^73 + 9 * q^74 + 9 * q^76 + 8 * q^79 - 15 * q^80 + 10 * q^82 + 20 * q^85 - 24 * q^86 + 18 * q^88 + 33 * q^92 + 19 * q^94 - 8 * q^97

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