LMFDB - Embedded newform 5733.2.a.bx.1.9

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			1.9
Root			$-1.83272$ 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)

$f(q)$	$=$	$q+1.83272 q^{2} +1.35888 q^{4} -3.20067 q^{5} -1.17500 q^{8} +O(q^{10})$	$q+1.83272 q^{2} +1.35888 q^{4} -3.20067 q^{5} -1.17500 q^{8} -5.86594 q^{10} -5.67943 q^{11} -1.00000 q^{13} -4.87121 q^{16} +2.74858 q^{17} +2.63704 q^{19} -4.34931 q^{20} -10.4088 q^{22} -5.82034 q^{23} +5.24426 q^{25} -1.83272 q^{26} +2.07847 q^{29} +7.93474 q^{31} -6.57757 q^{32} +5.03739 q^{34} +3.50097 q^{37} +4.83296 q^{38} +3.76080 q^{40} +6.73861 q^{41} -10.3670 q^{43} -7.71764 q^{44} -10.6671 q^{46} -9.73815 q^{47} +9.61129 q^{50} -1.35888 q^{52} +8.46587 q^{53} +18.1780 q^{55} +3.80927 q^{58} +11.8308 q^{59} +1.29664 q^{61} +14.5422 q^{62} -2.31245 q^{64} +3.20067 q^{65} +6.61732 q^{67} +3.73498 q^{68} -5.71717 q^{71} +0.843989 q^{73} +6.41631 q^{74} +3.58340 q^{76} +6.97595 q^{79} +15.5911 q^{80} +12.3500 q^{82} +16.1132 q^{83} -8.79730 q^{85} -18.9998 q^{86} +6.67336 q^{88} -6.84672 q^{89} -7.90912 q^{92} -17.8473 q^{94} -8.44028 q^{95} -10.0233 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.83272	1.29593	0.647966	−	0.761670i	$-0.275620\pi$
$2$	1.83272	1.29593	0.647966	+	0.761670i	$0.275620\pi$
$3$	0	0
$3$	0	0
$4$	1.35888	0.679438
$5$	−3.20067	−1.43138	−0.715691	−	0.698417i	$-0.753888\pi$
$5$	−3.20067	−1.43138	−0.715691	+	0.698417i	$0.753888\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.17500	−0.415427
$9$	0	0
$10$	−5.86594	−1.85497
$11$	−5.67943	−1.71241	−0.856207	−	0.516633i	$-0.827185\pi$
$11$	−5.67943	−1.71241	−0.856207	+	0.516633i	$0.827185\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−4.87121	−1.21780
$17$	2.74858	0.666630	0.333315	−	0.942816i	$-0.391833\pi$
$17$	2.74858	0.666630	0.333315	+	0.942816i	$0.391833\pi$
$18$	0	0
$19$	2.63704	0.604978	0.302489	−	0.953153i	$-0.402182\pi$
$19$	2.63704	0.604978	0.302489	+	0.953153i	$0.402182\pi$
$20$	−4.34931	−0.972534
$21$	0	0
$22$	−10.4088	−2.21917
$23$	−5.82034	−1.21363	−0.606813	−	0.794845i	$-0.707552\pi$
$23$	−5.82034	−1.21363	−0.606813	+	0.794845i	$0.707552\pi$
$24$	0	0
$25$	5.24426	1.04885
$26$	−1.83272	−0.359427
$27$	0	0
$28$	0	0
$29$	2.07847	0.385963	0.192982	−	0.981202i	$-0.438184\pi$
$29$	2.07847	0.385963	0.192982	+	0.981202i	$0.438184\pi$
$30$	0	0
$31$	7.93474	1.42512	0.712561	−	0.701610i	$-0.247535\pi$
$31$	7.93474	1.42512	0.712561	+	0.701610i	$0.247535\pi$
$32$	−6.57757	−1.16276
$33$	0	0
$34$	5.03739	0.863906
$35$	0	0
$36$	0	0
$37$	3.50097	0.575556	0.287778	−	0.957697i	$-0.407083\pi$
$37$	3.50097	0.575556	0.287778	+	0.957697i	$0.407083\pi$
$38$	4.83296	0.784010
$39$	0	0
$40$	3.76080	0.594634
$41$	6.73861	1.05239	0.526197	−	0.850363i	$-0.323617\pi$
$41$	6.73861	1.05239	0.526197	+	0.850363i	$0.323617\pi$
$42$	0	0
$43$	−10.3670	−1.58095	−0.790474	−	0.612496i	$-0.790166\pi$
$43$	−10.3670	−1.58095	−0.790474	+	0.612496i	$0.790166\pi$
$44$	−7.71764	−1.16348
$45$	0	0
$46$	−10.6671	−1.57278
$47$	−9.73815	−1.42045	−0.710227	−	0.703972i	$-0.751408\pi$
$47$	−9.73815	−1.42045	−0.710227	+	0.703972i	$0.751408\pi$
$48$	0	0
$49$	0	0
$50$	9.61129	1.35924
$51$	0	0
$52$	−1.35888	−0.188442
$53$	8.46587	1.16288	0.581438	−	0.813591i	$-0.302490\pi$
$53$	8.46587	1.16288	0.581438	+	0.813591i	$0.302490\pi$
$54$	0	0
$55$	18.1780	2.45112
$56$	0	0
$57$	0	0
$58$	3.80927	0.500182
$59$	11.8308	1.54024	0.770119	−	0.637900i	$-0.220197\pi$
$59$	11.8308	1.54024	0.770119	+	0.637900i	$0.220197\pi$
$60$	0	0
$61$	1.29664	0.166018	0.0830088	−	0.996549i	$-0.473547\pi$
$61$	1.29664	0.166018	0.0830088	+	0.996549i	$0.473547\pi$
$62$	14.5422	1.84686
$63$	0	0
$64$	−2.31245	−0.289056
$65$	3.20067	0.396994
$66$	0	0
$67$	6.61732	0.808435	0.404217	−	0.914663i	$-0.367544\pi$
$67$	6.61732	0.808435	0.404217	+	0.914663i	$0.367544\pi$
$68$	3.73498	0.452933
$69$	0	0
$70$	0	0
$71$	−5.71717	−0.678503	−0.339252	−	0.940696i	$-0.610174\pi$
$71$	−5.71717	−0.678503	−0.339252	+	0.940696i	$0.610174\pi$
$72$	0	0
$73$	0.843989	0.0987814	0.0493907	−	0.998780i	$-0.484272\pi$
$73$	0.843989	0.0987814	0.0493907	+	0.998780i	$0.484272\pi$
$74$	6.41631	0.745881
$75$	0	0
$76$	3.58340	0.411045
$77$	0	0
$78$	0	0
$79$	6.97595	0.784856	0.392428	−	0.919783i	$-0.371635\pi$
$79$	6.97595	0.784856	0.392428	+	0.919783i	$0.371635\pi$
$80$	15.5911	1.74314
$81$	0	0
$82$	12.3500	1.36383
$83$	16.1132	1.76866	0.884328	−	0.466866i	$-0.154617\pi$
$83$	16.1132	1.76866	0.884328	+	0.466866i	$0.154617\pi$
$84$	0	0
$85$	−8.79730	−0.954201
$86$	−18.9998	−2.04880
$87$	0	0
$88$	6.67336	0.711383
$89$	−6.84672	−0.725751	−0.362876	−	0.931838i	$-0.618205\pi$
$89$	−6.84672	−0.725751	−0.362876	+	0.931838i	$0.618205\pi$
$90$	0	0
$91$	0	0
$92$	−7.90912	−0.824583
$93$	0	0
$94$	−17.8473	−1.84081
$95$	−8.44028	−0.865954
$96$	0	0
$97$	−10.0233	−1.01771	−0.508857	−	0.860851i	$-0.669932\pi$
$97$	−10.0233	−1.01771	−0.508857	+	0.860851i	$0.669932\pi$
$98$	0	0
$99$	0	0
$100$	7.12630	0.712630
$101$	−6.29770	−0.626644	−0.313322	−	0.949647i	$-0.601442\pi$
$101$	−6.29770	−0.626644	−0.313322	+	0.949647i	$0.601442\pi$
$102$	0	0
$103$	−2.93567	−0.289261	−0.144630	−	0.989486i	$-0.546199\pi$
$103$	−2.93567	−0.289261	−0.144630	+	0.989486i	$0.546199\pi$
$104$	1.17500	0.115219
$105$	0	0
$106$	15.5156	1.50701
$107$	17.8553	1.72614	0.863070	−	0.505084i	$-0.168538\pi$
$107$	17.8553	1.72614	0.863070	+	0.505084i	$0.168538\pi$
$108$	0	0
$109$	−16.2152	−1.55314	−0.776568	−	0.630034i	$-0.783041\pi$
$109$	−16.2152	−1.55314	−0.776568	+	0.630034i	$0.783041\pi$
$110$	33.3152	3.17648
$111$	0	0
$112$	0	0
$113$	−0.240076	−0.0225845	−0.0112922	−	0.999936i	$-0.503595\pi$
$113$	−0.240076	−0.0225845	−0.0112922	+	0.999936i	$0.503595\pi$
$114$	0	0
$115$	18.6290	1.73716
$116$	2.82439	0.262238
$117$	0	0
$118$	21.6826	1.99604
$119$	0	0
$120$	0	0
$121$	21.2560	1.93236
$122$	2.37638	0.215147
$123$	0	0
$124$	10.7823	0.968281
$125$	−0.781809	−0.0699271
$126$	0	0
$127$	1.24409	0.110395	0.0551976	−	0.998475i	$-0.482421\pi$
$127$	1.24409	0.110395	0.0551976	+	0.998475i	$0.482421\pi$
$128$	8.91706	0.788164
$129$	0	0
$130$	5.86594	0.514477
$131$	22.0119	1.92319	0.961596	−	0.274468i	$-0.0885017\pi$
$131$	22.0119	1.92319	0.961596	+	0.274468i	$0.0885017\pi$
$132$	0	0
$133$	0	0
$134$	12.1277	1.04768
$135$	0	0
$136$	−3.22960	−0.276936
$137$	4.46793	0.381721	0.190861	−	0.981617i	$-0.438872\pi$
$137$	4.46793	0.381721	0.190861	+	0.981617i	$0.438872\pi$
$138$	0	0
$139$	−1.82180	−0.154523	−0.0772613	−	0.997011i	$-0.524618\pi$
$139$	−1.82180	−0.154523	−0.0772613	+	0.997011i	$0.524618\pi$
$140$	0	0
$141$	0	0
$142$	−10.4780	−0.879294
$143$	5.67943	0.474938
$144$	0	0
$145$	−6.65250	−0.552460
$146$	1.54680	0.128014
$147$	0	0
$148$	4.75738	0.391055
$149$	−8.48048	−0.694748	−0.347374	−	0.937727i	$-0.612927\pi$
$149$	−8.48048	−0.694748	−0.347374	+	0.937727i	$0.612927\pi$
$150$	0	0
$151$	17.3277	1.41011	0.705054	−	0.709154i	$-0.250923\pi$
$151$	17.3277	1.41011	0.705054	+	0.709154i	$0.250923\pi$
$152$	−3.09853	−0.251324
$153$	0	0
$154$	0	0
$155$	−25.3965	−2.03989
$156$	0	0
$157$	8.11660	0.647776	0.323888	−	0.946096i	$-0.395010\pi$
$157$	8.11660	0.647776	0.323888	+	0.946096i	$0.395010\pi$
$158$	12.7850	1.01712
$159$	0	0
$160$	21.0526	1.66435
$161$	0	0
$162$	0	0
$163$	−8.01231	−0.627573	−0.313786	−	0.949494i	$-0.601598\pi$
$163$	−8.01231	−0.627573	−0.313786	+	0.949494i	$0.601598\pi$
$164$	9.15693	0.715036
$165$	0	0
$166$	29.5311	2.29206
$167$	−15.3653	−1.18900	−0.594500	−	0.804096i	$-0.702650\pi$
$167$	−15.3653	−1.18900	−0.594500	+	0.804096i	$0.702650\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−16.1230	−1.23658
$171$	0	0
$172$	−14.0874	−1.07416
$173$	−8.24434	−0.626805	−0.313403	−	0.949620i	$-0.601469\pi$
$173$	−8.24434	−0.626805	−0.313403	+	0.949620i	$0.601469\pi$
$174$	0	0
$175$	0	0
$176$	27.6657	2.08538
$177$	0	0
$178$	−12.5481	−0.940523
$179$	−9.01379	−0.673722	−0.336861	−	0.941554i	$-0.609365\pi$
$179$	−9.01379	−0.673722	−0.336861	+	0.941554i	$0.609365\pi$
$180$	0	0
$181$	6.55833	0.487477	0.243739	−	0.969841i	$-0.421626\pi$
$181$	6.55833	0.487477	0.243739	+	0.969841i	$0.421626\pi$
$182$	0	0
$183$	0	0
$184$	6.83893	0.504173
$185$	−11.2054	−0.823841
$186$	0	0
$187$	−15.6104	−1.14155
$188$	−13.2329	−0.965110
$189$	0	0
$190$	−15.4687	−1.12222
$191$	−17.3249	−1.25359	−0.626793	−	0.779186i	$-0.715633\pi$
$191$	−17.3249	−1.25359	−0.626793	+	0.779186i	$0.715633\pi$
$192$	0	0
$193$	23.5276	1.69355	0.846776	−	0.531950i	$-0.178541\pi$
$193$	23.5276	1.69355	0.846776	+	0.531950i	$0.178541\pi$
$194$	−18.3700	−1.31889
$195$	0	0
$196$	0	0
$197$	9.24392	0.658602	0.329301	−	0.944225i	$-0.393187\pi$
$197$	9.24392	0.658602	0.329301	+	0.944225i	$0.393187\pi$
$198$	0	0
$199$	1.19455	0.0846794	0.0423397	−	0.999103i	$-0.486519\pi$
$199$	1.19455	0.0846794	0.0423397	+	0.999103i	$0.486519\pi$
$200$	−6.16204	−0.435722
$201$	0	0
$202$	−11.5419	−0.812088
$203$	0	0
$204$	0	0
$205$	−21.5680	−1.50638
$206$	−5.38028	−0.374862
$207$	0	0
$208$	4.87121	0.337758
$209$	−14.9769	−1.03597
$210$	0	0
$211$	22.4835	1.54783	0.773914	−	0.633290i	$-0.218296\pi$
$211$	22.4835	1.54783	0.773914	+	0.633290i	$0.218296\pi$
$212$	11.5041	0.790102
$213$	0	0
$214$	32.7239	2.23696
$215$	33.1812	2.26294
$216$	0	0
$217$	0	0
$218$	−29.7180	−2.01276
$219$	0	0
$220$	24.7016	1.66538
$221$	−2.74858	−0.184890
$222$	0	0
$223$	1.50230	0.100601	0.0503007	−	0.998734i	$-0.483982\pi$
$223$	1.50230	0.100601	0.0503007	+	0.998734i	$0.483982\pi$
$224$	0	0
$225$	0	0
$226$	−0.439994	−0.0292680
$227$	−3.77309	−0.250429	−0.125214	−	0.992130i	$-0.539962\pi$
$227$	−3.77309	−0.250429	−0.125214	+	0.992130i	$0.539962\pi$
$228$	0	0
$229$	−27.2129	−1.79828	−0.899139	−	0.437663i	$-0.855806\pi$
$229$	−27.2129	−1.79828	−0.899139	+	0.437663i	$0.855806\pi$
$230$	34.1418	2.25124
$231$	0	0
$232$	−2.44222	−0.160339
$233$	−23.6783	−1.55122	−0.775608	−	0.631215i	$-0.782556\pi$
$233$	−23.6783	−1.55122	−0.775608	+	0.631215i	$0.782556\pi$
$234$	0	0
$235$	31.1686	2.03321
$236$	16.0766	1.04650
$237$	0	0
$238$	0	0
$239$	−8.74263	−0.565514	−0.282757	−	0.959192i	$-0.591249\pi$
$239$	−8.74263	−0.565514	−0.282757	+	0.959192i	$0.591249\pi$
$240$	0	0
$241$	13.5672	0.873938	0.436969	−	0.899476i	$-0.356052\pi$
$241$	13.5672	0.873938	0.436969	+	0.899476i	$0.356052\pi$
$242$	38.9563	2.50421
$243$	0	0
$244$	1.76197	0.112799
$245$	0	0
$246$	0	0
$247$	−2.63704	−0.167791
$248$	−9.32336	−0.592034
$249$	0	0
$250$	−1.43284	−0.0906207
$251$	23.1529	1.46140	0.730699	−	0.682700i	$-0.239194\pi$
$251$	23.1529	1.46140	0.730699	+	0.682700i	$0.239194\pi$
$252$	0	0
$253$	33.0563	2.07823
$254$	2.28007	0.143065
$255$	0	0
$256$	20.9674	1.31046
$257$	−14.8259	−0.924814	−0.462407	−	0.886668i	$-0.653014\pi$
$257$	−14.8259	−0.924814	−0.462407	+	0.886668i	$0.653014\pi$
$258$	0	0
$259$	0	0
$260$	4.34931	0.269732
$261$	0	0
$262$	40.3418	2.49233
$263$	29.8842	1.84274	0.921370	−	0.388688i	$-0.127071\pi$
$263$	29.8842	1.84274	0.921370	+	0.388688i	$0.127071\pi$
$264$	0	0
$265$	−27.0964	−1.66452
$266$	0	0
$267$	0	0
$268$	8.99211	0.549281
$269$	0.880250	0.0536698	0.0268349	−	0.999640i	$-0.491457\pi$
$269$	0.880250	0.0536698	0.0268349	+	0.999640i	$0.491457\pi$
$270$	0	0
$271$	−7.49693	−0.455406	−0.227703	−	0.973731i	$-0.573122\pi$
$271$	−7.49693	−0.455406	−0.227703	+	0.973731i	$0.573122\pi$
$272$	−13.3889	−0.811823
$273$	0	0
$274$	8.18848	0.494684
$275$	−29.7844	−1.79607
$276$	0	0
$277$	−5.43935	−0.326819	−0.163409	−	0.986558i	$-0.552249\pi$
$277$	−5.43935	−0.326819	−0.163409	+	0.986558i	$0.552249\pi$
$278$	−3.33885	−0.200251
$279$	0	0
$280$	0	0
$281$	−32.0864	−1.91411	−0.957056	−	0.289903i	$-0.906377\pi$
$281$	−32.0864	−1.91411	−0.957056	+	0.289903i	$0.906377\pi$
$282$	0	0
$283$	18.0073	1.07042	0.535212	−	0.844718i	$-0.320232\pi$
$283$	18.0073	1.07042	0.535212	+	0.844718i	$0.320232\pi$
$284$	−7.76892	−0.461001
$285$	0	0
$286$	10.4088	0.615487
$287$	0	0
$288$	0	0
$289$	−9.44528	−0.555605
$290$	−12.1922	−0.715951
$291$	0	0
$292$	1.14687	0.0671158
$293$	33.5028	1.95726	0.978628	−	0.205638i	$-0.0659269\pi$
$293$	33.5028	1.95726	0.978628	+	0.205638i	$0.0659269\pi$
$294$	0	0
$295$	−37.8664	−2.20467
$296$	−4.11366	−0.239102
$297$	0	0
$298$	−15.5424	−0.900346
$299$	5.82034	0.336599
$300$	0	0
$301$	0	0
$302$	31.7569	1.82740
$303$	0	0
$304$	−12.8456	−0.736743
$305$	−4.15011	−0.237635
$306$	0	0
$307$	1.51263	0.0863306	0.0431653	−	0.999068i	$-0.486256\pi$
$307$	1.51263	0.0863306	0.0431653	+	0.999068i	$0.486256\pi$
$308$	0	0
$309$	0	0
$310$	−46.5447	−2.64356
$311$	11.5094	0.652639	0.326319	−	0.945260i	$-0.394192\pi$
$311$	11.5094	0.652639	0.326319	+	0.945260i	$0.394192\pi$
$312$	0	0
$313$	−2.45068	−0.138521	−0.0692604	−	0.997599i	$-0.522064\pi$
$313$	−2.45068	−0.138521	−0.0692604	+	0.997599i	$0.522064\pi$
$314$	14.8755	0.839472
$315$	0	0
$316$	9.47945	0.533261
$317$	−22.0516	−1.23854	−0.619272	−	0.785177i	$-0.712572\pi$
$317$	−22.0516	−1.23854	−0.619272	+	0.785177i	$0.712572\pi$
$318$	0	0
$319$	−11.8046	−0.660928
$320$	7.40137	0.413749
$321$	0	0
$322$	0	0
$323$	7.24812	0.403296
$324$	0	0
$325$	−5.24426	−0.290899
$326$	−14.6843	−0.813291
$327$	0	0
$328$	−7.91790	−0.437193
$329$	0	0
$330$	0	0
$331$	−11.3314	−0.622828	−0.311414	−	0.950274i	$-0.600803\pi$
$331$	−11.3314	−0.622828	−0.311414	+	0.950274i	$0.600803\pi$
$332$	21.8959	1.20169
$333$	0	0
$334$	−28.1603	−1.54086
$335$	−21.1798	−1.15718
$336$	0	0
$337$	19.0689	1.03875	0.519375	−	0.854546i	$-0.326165\pi$
$337$	19.0689	1.03875	0.519375	+	0.854546i	$0.326165\pi$
$338$	1.83272	0.0996870
$339$	0	0
$340$	−11.9544	−0.648320
$341$	−45.0648	−2.44040
$342$	0	0
$343$	0	0
$344$	12.1812	0.656768
$345$	0	0
$346$	−15.1096	−0.812296
$347$	27.9460	1.50022	0.750109	−	0.661314i	$-0.230001\pi$
$347$	27.9460	1.50022	0.750109	+	0.661314i	$0.230001\pi$
$348$	0	0
$349$	−7.75995	−0.415381	−0.207690	−	0.978195i	$-0.566595\pi$
$349$	−7.75995	−0.415381	−0.207690	+	0.978195i	$0.566595\pi$
$350$	0	0
$351$	0	0
$352$	37.3569	1.99113
$353$	21.3890	1.13842	0.569211	−	0.822192i	$-0.307249\pi$
$353$	21.3890	1.13842	0.569211	+	0.822192i	$0.307249\pi$
$354$	0	0
$355$	18.2988	0.971197
$356$	−9.30384	−0.493102
$357$	0	0
$358$	−16.5198	−0.873097
$359$	13.3682	0.705549	0.352775	−	0.935708i	$-0.385238\pi$
$359$	13.3682	0.705549	0.352775	+	0.935708i	$0.385238\pi$
$360$	0	0
$361$	−12.0460	−0.634002
$362$	12.0196	0.631737
$363$	0	0
$364$	0	0
$365$	−2.70133	−0.141394
$366$	0	0
$367$	−3.19207	−0.166625	−0.0833123	−	0.996523i	$-0.526550\pi$
$367$	−3.19207	−0.166625	−0.0833123	+	0.996523i	$0.526550\pi$
$368$	28.3521	1.47796
$369$	0	0
$370$	−20.5365	−1.06764
$371$	0	0
$372$	0	0
$373$	2.01225	0.104191	0.0520953	−	0.998642i	$-0.483410\pi$
$373$	2.01225	0.104191	0.0520953	+	0.998642i	$0.483410\pi$
$374$	−28.6095	−1.47936
$375$	0	0
$376$	11.4424	0.590095
$377$	−2.07847	−0.107047
$378$	0	0
$379$	−26.7419	−1.37364	−0.686821	−	0.726827i	$-0.740994\pi$
$379$	−26.7419	−1.37364	−0.686821	+	0.726827i	$0.740994\pi$
$380$	−11.4693	−0.588362
$381$	0	0
$382$	−31.7517	−1.62456
$383$	29.5278	1.50880	0.754401	−	0.656414i	$-0.227927\pi$
$383$	29.5278	1.50880	0.754401	+	0.656414i	$0.227927\pi$
$384$	0	0
$385$	0	0
$386$	43.1195	2.19473
$387$	0	0
$388$	−13.6204	−0.691473
$389$	−4.83461	−0.245124	−0.122562	−	0.992461i	$-0.539111\pi$
$389$	−4.83461	−0.245124	−0.122562	+	0.992461i	$0.539111\pi$
$390$	0	0
$391$	−15.9977	−0.809039
$392$	0	0
$393$	0	0
$394$	16.9416	0.853503
$395$	−22.3277	−1.12343
$396$	0	0
$397$	−1.03593	−0.0519921	−0.0259960	−	0.999662i	$-0.508276\pi$
$397$	−1.03593	−0.0519921	−0.0259960	+	0.999662i	$0.508276\pi$
$398$	2.18928	0.109739
$399$	0	0
$400$	−25.5459	−1.27730
$401$	−22.6950	−1.13334	−0.566668	−	0.823946i	$-0.691768\pi$
$401$	−22.6950	−1.13334	−0.566668	+	0.823946i	$0.691768\pi$
$402$	0	0
$403$	−7.93474	−0.395258
$404$	−8.55778	−0.425766
$405$	0	0
$406$	0	0
$407$	−19.8835	−0.985590
$408$	0	0
$409$	2.65706	0.131383	0.0656915	−	0.997840i	$-0.479075\pi$
$409$	2.65706	0.131383	0.0656915	+	0.997840i	$0.479075\pi$
$410$	−39.5283	−1.95216
$411$	0	0
$412$	−3.98921	−0.196534
$413$	0	0
$414$	0	0
$415$	−51.5731	−2.53162
$416$	6.57757	0.322492
$417$	0	0
$418$	−27.4485	−1.34255
$419$	−18.2174	−0.889978	−0.444989	−	0.895536i	$-0.646792\pi$
$419$	−18.2174	−0.889978	−0.444989	+	0.895536i	$0.646792\pi$
$420$	0	0
$421$	9.67391	0.471478	0.235739	−	0.971816i	$-0.424249\pi$
$421$	9.67391	0.471478	0.235739	+	0.971816i	$0.424249\pi$
$422$	41.2060	2.00588
$423$	0	0
$424$	−9.94744	−0.483090
$425$	14.4143	0.699196
$426$	0	0
$427$	0	0
$428$	24.2632	1.17280
$429$	0	0
$430$	60.8120	2.93261
$431$	−15.1445	−0.729487	−0.364743	−	0.931108i	$-0.618843\pi$
$431$	−15.1445	−0.729487	−0.364743	+	0.931108i	$0.618843\pi$
$432$	0	0
$433$	7.68241	0.369193	0.184597	−	0.982814i	$-0.440902\pi$
$433$	7.68241	0.369193	0.184597	+	0.982814i	$0.440902\pi$
$434$	0	0
$435$	0	0
$436$	−22.0344	−1.05526
$437$	−15.3485	−0.734217
$438$	0	0
$439$	−3.83944	−0.183246	−0.0916232	−	0.995794i	$-0.529206\pi$
$439$	−3.83944	−0.183246	−0.0916232	+	0.995794i	$0.529206\pi$
$440$	−21.3592	−1.01826
$441$	0	0
$442$	−5.03739	−0.239604
$443$	18.3806	0.873290	0.436645	−	0.899634i	$-0.356167\pi$
$443$	18.3806	0.873290	0.436645	+	0.899634i	$0.356167\pi$
$444$	0	0
$445$	21.9141	1.03883
$446$	2.75330	0.130372
$447$	0	0
$448$	0	0
$449$	−15.7230	−0.742016	−0.371008	−	0.928630i	$-0.620988\pi$
$449$	−15.7230	−0.742016	−0.371008	+	0.928630i	$0.620988\pi$
$450$	0	0
$451$	−38.2715	−1.80213
$452$	−0.326234	−0.0153448
$453$	0	0
$454$	−6.91503	−0.324538
$455$	0	0
$456$	0	0
$457$	38.5101	1.80143	0.900714	−	0.434412i	$-0.143044\pi$
$457$	38.5101	1.80143	0.900714	+	0.434412i	$0.143044\pi$
$458$	−49.8737	−2.33044
$459$	0	0
$460$	25.3145	1.18029
$461$	17.8083	0.829414	0.414707	−	0.909955i	$-0.363884\pi$
$461$	17.8083	0.829414	0.414707	+	0.909955i	$0.363884\pi$
$462$	0	0
$463$	−24.7427	−1.14989	−0.574946	−	0.818191i	$-0.694977\pi$
$463$	−24.7427	−1.14989	−0.574946	+	0.818191i	$0.694977\pi$
$464$	−10.1247	−0.470027
$465$	0	0
$466$	−43.3957	−2.01027
$467$	−18.4019	−0.851541	−0.425770	−	0.904831i	$-0.639997\pi$
$467$	−18.4019	−0.851541	−0.425770	+	0.904831i	$0.639997\pi$
$468$	0	0
$469$	0	0
$470$	57.1233	2.63490
$471$	0	0
$472$	−13.9012	−0.639857
$473$	58.8785	2.70724
$474$	0	0
$475$	13.8293	0.634533
$476$	0	0
$477$	0	0
$478$	−16.0228	−0.732867
$479$	22.9647	1.04929	0.524643	−	0.851323i	$-0.324199\pi$
$479$	22.9647	1.04929	0.524643	+	0.851323i	$0.324199\pi$
$480$	0	0
$481$	−3.50097	−0.159631
$482$	24.8649	1.13256
$483$	0	0
$484$	28.8842	1.31292
$485$	32.0813	1.45674
$486$	0	0
$487$	5.87198	0.266085	0.133042	−	0.991110i	$-0.457525\pi$
$487$	5.87198	0.266085	0.133042	+	0.991110i	$0.457525\pi$
$488$	−1.52356	−0.0689682
$489$	0	0
$490$	0	0
$491$	25.6157	1.15602	0.578010	−	0.816030i	$-0.303829\pi$
$491$	25.6157	1.15602	0.578010	+	0.816030i	$0.303829\pi$
$492$	0	0
$493$	5.71286	0.257294
$494$	−4.83296	−0.217445
$495$	0	0
$496$	−38.6518	−1.73552
$497$	0	0
$498$	0	0
$499$	−11.2143	−0.502023	−0.251011	−	0.967984i	$-0.580763\pi$
$499$	−11.2143	−0.502023	−0.251011	+	0.967984i	$0.580763\pi$
$500$	−1.06238	−0.0475111
$501$	0	0
$502$	42.4328	1.89387
$503$	23.3270	1.04010	0.520050	−	0.854136i	$-0.325913\pi$
$503$	23.3270	1.04010	0.520050	+	0.854136i	$0.325913\pi$
$504$	0	0
$505$	20.1568	0.896967
$506$	60.5830	2.69324
$507$	0	0
$508$	1.69056	0.0750066
$509$	43.1674	1.91336	0.956682	−	0.291136i	$-0.0940333\pi$
$509$	43.1674	1.91336	0.956682	+	0.291136i	$0.0940333\pi$
$510$	0	0
$511$	0	0
$512$	20.5933	0.910105
$513$	0	0
$514$	−27.1718	−1.19849
$515$	9.39611	0.414042
$516$	0	0
$517$	55.3072	2.43241
$518$	0	0
$519$	0	0
$520$	−3.76080	−0.164922
$521$	−11.7420	−0.514425	−0.257213	−	0.966355i	$-0.582804\pi$
$521$	−11.7420	−0.514425	−0.257213	+	0.966355i	$0.582804\pi$
$522$	0	0
$523$	16.7153	0.730911	0.365455	−	0.930829i	$-0.380913\pi$
$523$	16.7153	0.730911	0.365455	+	0.930829i	$0.380913\pi$
$524$	29.9115	1.30669
$525$	0	0
$526$	54.7695	2.38806
$527$	21.8093	0.950029
$528$	0	0
$529$	10.8764	0.472887
$530$	−49.6602	−2.15710
$531$	0	0
$532$	0	0
$533$	−6.73861	−0.291882
$534$	0	0
$535$	−57.1490	−2.47077
$536$	−7.77539	−0.335846
$537$	0	0
$538$	1.61325	0.0695523
$539$	0	0
$540$	0	0
$541$	−8.80225	−0.378438	−0.189219	−	0.981935i	$-0.560596\pi$
$541$	−8.80225	−0.378438	−0.189219	+	0.981935i	$0.560596\pi$
$542$	−13.7398	−0.590175
$543$	0	0
$544$	−18.0790	−0.775131
$545$	51.8995	2.22313
$546$	0	0
$547$	−8.44115	−0.360917	−0.180459	−	0.983583i	$-0.557758\pi$
$547$	−8.44115	−0.360917	−0.180459	+	0.983583i	$0.557758\pi$
$548$	6.07136	0.259356
$549$	0	0
$550$	−54.5867	−2.32758
$551$	5.48102	0.233499
$552$	0	0
$553$	0	0
$554$	−9.96882	−0.423534
$555$	0	0
$556$	−2.47559	−0.104988
$557$	−2.33151	−0.0987892	−0.0493946	−	0.998779i	$-0.515729\pi$
$557$	−2.33151	−0.0987892	−0.0493946	+	0.998779i	$0.515729\pi$
$558$	0	0
$559$	10.3670	0.438476
$560$	0	0
$561$	0	0
$562$	−58.8054	−2.48056
$563$	18.1053	0.763047	0.381523	−	0.924359i	$-0.375400\pi$
$563$	18.1053	0.763047	0.381523	+	0.924359i	$0.375400\pi$
$564$	0	0
$565$	0.768405	0.0323270
$566$	33.0024	1.38720
$567$	0	0
$568$	6.71770	0.281869
$569$	−19.0200	−0.797360	−0.398680	−	0.917090i	$-0.630532\pi$
$569$	−19.0200	−0.797360	−0.398680	+	0.917090i	$0.630532\pi$
$570$	0	0
$571$	38.4311	1.60829	0.804146	−	0.594431i	$-0.202623\pi$
$571$	38.4311	1.60829	0.804146	+	0.594431i	$0.202623\pi$
$572$	7.71764	0.322691
$573$	0	0
$574$	0	0
$575$	−30.5234	−1.27291
$576$	0	0
$577$	−29.3325	−1.22113	−0.610564	−	0.791967i	$-0.709057\pi$
$577$	−29.3325	−1.22113	−0.610564	+	0.791967i	$0.709057\pi$
$578$	−17.3106	−0.720026
$579$	0	0
$580$	−9.03992	−0.375362
$581$	0	0
$582$	0	0
$583$	−48.0813	−1.99133
$584$	−0.991691	−0.0410364
$585$	0	0
$586$	61.4014	2.53647
$587$	−37.1284	−1.53245	−0.766227	−	0.642570i	$-0.777868\pi$
$587$	−37.1284	−1.53245	−0.766227	+	0.642570i	$0.777868\pi$
$588$	0	0
$589$	20.9242	0.862167
$590$	−69.3987	−2.85710
$591$	0	0
$592$	−17.0540	−0.700914
$593$	24.9331	1.02388	0.511940	−	0.859021i	$-0.328927\pi$
$593$	24.9331	1.02388	0.511940	+	0.859021i	$0.328927\pi$
$594$	0	0
$595$	0	0
$596$	−11.5239	−0.472038
$597$	0	0
$598$	10.6671	0.436209
$599$	34.2290	1.39856	0.699279	−	0.714849i	$-0.253504\pi$
$599$	34.2290	1.39856	0.699279	+	0.714849i	$0.253504\pi$
$600$	0	0
$601$	14.5971	0.595429	0.297715	−	0.954655i	$-0.403776\pi$
$601$	14.5971	0.595429	0.297715	+	0.954655i	$0.403776\pi$
$602$	0	0
$603$	0	0
$604$	23.5462	0.958080
$605$	−68.0332	−2.76594
$606$	0	0
$607$	−20.6085	−0.836473	−0.418236	−	0.908338i	$-0.637352\pi$
$607$	−20.6085	−0.836473	−0.418236	+	0.908338i	$0.637352\pi$
$608$	−17.3453	−0.703445
$609$	0	0
$610$	−7.60600	−0.307958
$611$	9.73815	0.393963
$612$	0	0
$613$	−15.6338	−0.631441	−0.315721	−	0.948852i	$-0.602246\pi$
$613$	−15.6338	−0.631441	−0.315721	+	0.948852i	$0.602246\pi$
$614$	2.77224	0.111878
$615$	0	0
$616$	0	0
$617$	21.7130	0.874134	0.437067	−	0.899429i	$-0.356017\pi$
$617$	21.7130	0.874134	0.437067	+	0.899429i	$0.356017\pi$
$618$	0	0
$619$	31.4271	1.26316	0.631581	−	0.775310i	$-0.282406\pi$
$619$	31.4271	1.26316	0.631581	+	0.775310i	$0.282406\pi$
$620$	−34.5106	−1.38598
$621$	0	0
$622$	21.0936	0.845775
$623$	0	0
$624$	0	0
$625$	−23.7190	−0.948761
$626$	−4.49142	−0.179513
$627$	0	0
$628$	11.0295	0.440123
$629$	9.62272	0.383683
$630$	0	0
$631$	0.596170	0.0237331	0.0118666	−	0.999930i	$-0.496223\pi$
$631$	0.596170	0.0237331	0.0118666	+	0.999930i	$0.496223\pi$
$632$	−8.19678	−0.326050
$633$	0	0
$634$	−40.4146	−1.60507
$635$	−3.98192	−0.158018
$636$	0	0
$637$	0	0
$638$	−21.6345	−0.856518
$639$	0	0
$640$	−28.5405	−1.12816
$641$	−31.0945	−1.22816	−0.614079	−	0.789244i	$-0.710473\pi$
$641$	−31.0945	−1.22816	−0.614079	+	0.789244i	$0.710473\pi$
$642$	0	0
$643$	−30.7762	−1.21370	−0.606848	−	0.794818i	$-0.707566\pi$
$643$	−30.7762	−1.21370	−0.606848	+	0.794818i	$0.707566\pi$
$644$	0	0
$645$	0	0
$646$	13.2838	0.522644
$647$	41.0714	1.61468	0.807341	−	0.590085i	$-0.200906\pi$
$647$	41.0714	1.61468	0.807341	+	0.590085i	$0.200906\pi$
$648$	0	0
$649$	−67.1922	−2.63753
$650$	−9.61129	−0.376986
$651$	0	0
$652$	−10.8877	−0.426396
$653$	36.0708	1.41156	0.705779	−	0.708432i	$-0.250597\pi$
$653$	36.0708	1.41156	0.705779	+	0.708432i	$0.250597\pi$
$654$	0	0
$655$	−70.4529	−2.75282
$656$	−32.8252	−1.28161
$657$	0	0
$658$	0	0
$659$	6.87163	0.267681	0.133840	−	0.991003i	$-0.457269\pi$
$659$	6.87163	0.267681	0.133840	+	0.991003i	$0.457269\pi$
$660$	0	0
$661$	3.66008	0.142361	0.0711804	−	0.997463i	$-0.477323\pi$
$661$	3.66008	0.142361	0.0711804	+	0.997463i	$0.477323\pi$
$662$	−20.7673	−0.807143
$663$	0	0
$664$	−18.9331	−0.734747
$665$	0	0
$666$	0	0
$667$	−12.0974	−0.468415
$668$	−20.8795	−0.807851
$669$	0	0
$670$	−38.8168	−1.49962
$671$	−7.36418	−0.284291
$672$	0	0
$673$	−3.32417	−0.128137	−0.0640686	−	0.997945i	$-0.520408\pi$
$673$	−3.32417	−0.128137	−0.0640686	+	0.997945i	$0.520408\pi$
$674$	34.9481	1.34615
$675$	0	0
$676$	1.35888	0.0522644
$677$	11.8259	0.454505	0.227252	−	0.973836i	$-0.427026\pi$
$677$	11.8259	0.454505	0.227252	+	0.973836i	$0.427026\pi$
$678$	0	0
$679$	0	0
$680$	10.3369	0.396401
$681$	0	0
$682$	−82.5914	−3.16259
$683$	−40.1132	−1.53489	−0.767445	−	0.641114i	$-0.778472\pi$
$683$	−40.1132	−1.53489	−0.767445	+	0.641114i	$0.778472\pi$
$684$	0	0
$685$	−14.3004	−0.546389
$686$	0	0
$687$	0	0
$688$	50.4997	1.92528
$689$	−8.46587	−0.322524
$690$	0	0
$691$	−2.22119	−0.0844980	−0.0422490	−	0.999107i	$-0.513452\pi$
$691$	−2.22119	−0.0844980	−0.0422490	+	0.999107i	$0.513452\pi$
$692$	−11.2030	−0.425875
$693$	0	0
$694$	51.2172	1.94418
$695$	5.83096	0.221181
$696$	0	0
$697$	18.5216	0.701557
$698$	−14.2218	−0.538305
$699$	0	0
$700$	0	0
$701$	14.0357	0.530121	0.265060	−	0.964232i	$-0.414608\pi$
$701$	14.0357	0.530121	0.265060	+	0.964232i	$0.414608\pi$
$702$	0	0
$703$	9.23220	0.348199
$704$	13.1334	0.494983
$705$	0	0
$706$	39.2001	1.47532
$707$	0	0
$708$	0	0
$709$	19.8639	0.746005	0.373002	−	0.927830i	$-0.378328\pi$
$709$	19.8639	0.746005	0.373002	+	0.927830i	$0.378328\pi$
$710$	33.5366	1.25860
$711$	0	0
$712$	8.04493	0.301497
$713$	−46.1829	−1.72956
$714$	0	0
$715$	−18.1780	−0.679818
$716$	−12.2486	−0.457752
$717$	0	0
$718$	24.5003	0.914343
$719$	−0.249553	−0.00930675	−0.00465337	−	0.999989i	$-0.501481\pi$
$719$	−0.249553	−0.00930675	−0.00465337	+	0.999989i	$0.501481\pi$
$720$	0	0
$721$	0	0
$722$	−22.0770	−0.821622
$723$	0	0
$724$	8.91196	0.331210
$725$	10.9001	0.404818
$726$	0	0
$727$	43.0687	1.59733	0.798666	−	0.601775i	$-0.205540\pi$
$727$	43.0687	1.59733	0.798666	+	0.601775i	$0.205540\pi$
$728$	0	0
$729$	0	0
$730$	−4.95078	−0.183237
$731$	−28.4945	−1.05391
$732$	0	0
$733$	−4.99559	−0.184516	−0.0922582	−	0.995735i	$-0.529409\pi$
$733$	−4.99559	−0.184516	−0.0922582	+	0.995735i	$0.529409\pi$
$734$	−5.85018	−0.215934
$735$	0	0
$736$	38.2837	1.41116
$737$	−37.5826	−1.38437
$738$	0	0
$739$	13.9131	0.511803	0.255902	−	0.966703i	$-0.417628\pi$
$739$	13.9131	0.511803	0.255902	+	0.966703i	$0.417628\pi$
$740$	−15.2268	−0.559748
$741$	0	0
$742$	0	0
$743$	9.62472	0.353097	0.176548	−	0.984292i	$-0.443507\pi$
$743$	9.62472	0.353097	0.176548	+	0.984292i	$0.443507\pi$
$744$	0	0
$745$	27.1432	0.994450
$746$	3.68790	0.135024
$747$	0	0
$748$	−21.2126	−0.775609
$749$	0	0
$750$	0	0
$751$	41.4798	1.51362	0.756810	−	0.653635i	$-0.226757\pi$
$751$	41.4798	1.51362	0.756810	+	0.653635i	$0.226757\pi$
$752$	47.4365	1.72983
$753$	0	0
$754$	−3.80927	−0.138725
$755$	−55.4601	−2.01840
$756$	0	0
$757$	24.3721	0.885819	0.442910	−	0.896566i	$-0.353946\pi$
$757$	24.3721	0.885819	0.442910	+	0.896566i	$0.353946\pi$
$758$	−49.0106	−1.78014
$759$	0	0
$760$	9.91737	0.359741
$761$	13.3525	0.484029	0.242014	−	0.970273i	$-0.422192\pi$
$761$	13.3525	0.484029	0.242014	+	0.970273i	$0.422192\pi$
$762$	0	0
$763$	0	0
$764$	−23.5424	−0.851733
$765$	0	0
$766$	54.1164	1.95530
$767$	−11.8308	−0.427185
$768$	0	0
$769$	−12.3428	−0.445093	−0.222546	−	0.974922i	$-0.571437\pi$
$769$	−12.3428	−0.445093	−0.222546	+	0.974922i	$0.571437\pi$
$770$	0	0
$771$	0	0
$772$	31.9710	1.15066
$773$	22.8922	0.823373	0.411687	−	0.911325i	$-0.364940\pi$
$773$	22.8922	0.823373	0.411687	+	0.911325i	$0.364940\pi$
$774$	0	0
$775$	41.6119	1.49474
$776$	11.7774	0.422786
$777$	0	0
$778$	−8.86050	−0.317664
$779$	17.7700	0.636675
$780$	0	0
$781$	32.4703	1.16188
$782$	−29.3194	−1.04846
$783$	0	0
$784$	0	0
$785$	−25.9785	−0.927214
$786$	0	0
$787$	−53.5916	−1.91034	−0.955168	−	0.296065i	$-0.904325\pi$
$787$	−53.5916	−1.91034	−0.955168	+	0.296065i	$0.904325\pi$
$788$	12.5613	0.447479
$789$	0	0
$790$	−40.9205	−1.45589
$791$	0	0
$792$	0	0
$793$	−1.29664	−0.0460450
$794$	−1.89858	−0.0673781
$795$	0	0
$796$	1.62324	0.0575344
$797$	21.9657	0.778066	0.389033	−	0.921224i	$-0.372809\pi$
$797$	21.9657	0.778066	0.389033	+	0.921224i	$0.372809\pi$
$798$	0	0
$799$	−26.7661	−0.946917
$800$	−34.4945	−1.21957
$801$	0	0
$802$	−41.5937	−1.46872
$803$	−4.79338	−0.169155
$804$	0	0
$805$	0	0
$806$	−14.5422	−0.512227
$807$	0	0
$808$	7.39982	0.260325
$809$	−31.5768	−1.11018	−0.555091	−	0.831790i	$-0.687317\pi$
$809$	−31.5768	−1.11018	−0.555091	+	0.831790i	$0.687317\pi$
$810$	0	0
$811$	−13.7957	−0.484432	−0.242216	−	0.970222i	$-0.577874\pi$
$811$	−13.7957	−0.484432	−0.242216	+	0.970222i	$0.577874\pi$
$812$	0	0
$813$	0	0
$814$	−36.4410	−1.27726
$815$	25.6447	0.898296
$816$	0	0
$817$	−27.3381	−0.956439
$818$	4.86965	0.170263
$819$	0	0
$820$	−29.3083	−1.02349
$821$	12.3071	0.429521	0.214760	−	0.976667i	$-0.431103\pi$
$821$	12.3071	0.429521	0.214760	+	0.976667i	$0.431103\pi$
$822$	0	0
$823$	1.03319	0.0360149	0.0180074	−	0.999838i	$-0.494268\pi$
$823$	1.03319	0.0360149	0.0180074	+	0.999838i	$0.494268\pi$
$824$	3.44943	0.120167
$825$	0	0
$826$	0	0
$827$	22.8766	0.795499	0.397749	−	0.917494i	$-0.369791\pi$
$827$	22.8766	0.795499	0.397749	+	0.917494i	$0.369791\pi$
$828$	0	0
$829$	7.79306	0.270664	0.135332	−	0.990800i	$-0.456790\pi$
$829$	7.79306	0.270664	0.135332	+	0.990800i	$0.456790\pi$
$830$	−94.5191	−3.28081
$831$	0	0
$832$	2.31245	0.0801697
$833$	0	0
$834$	0	0
$835$	49.1791	1.70191
$836$	−20.3517	−0.703879
$837$	0	0
$838$	−33.3874	−1.15335
$839$	−38.7724	−1.33857	−0.669287	−	0.743004i	$-0.733400\pi$
$839$	−38.7724	−1.33857	−0.669287	+	0.743004i	$0.733400\pi$
$840$	0	0
$841$	−24.6799	−0.851033
$842$	17.7296	0.611003
$843$	0	0
$844$	30.5523	1.05165
$845$	−3.20067	−0.110106
$846$	0	0
$847$	0	0
$848$	−41.2390	−1.41615
$849$	0	0
$850$	26.4174	0.906110
$851$	−20.3769	−0.698510
$852$	0	0
$853$	−50.2892	−1.72187	−0.860935	−	0.508715i	$-0.830121\pi$
$853$	−50.2892	−1.72187	−0.860935	+	0.508715i	$0.830121\pi$
$854$	0	0
$855$	0	0
$856$	−20.9801	−0.717085
$857$	16.6030	0.567148	0.283574	−	0.958950i	$-0.408480\pi$
$857$	16.6030	0.567148	0.283574	+	0.958950i	$0.408480\pi$
$858$	0	0
$859$	14.7042	0.501700	0.250850	−	0.968026i	$-0.419290\pi$
$859$	14.7042	0.501700	0.250850	+	0.968026i	$0.419290\pi$
$860$	45.0891	1.53753
$861$	0	0
$862$	−27.7558	−0.945365
$863$	−34.8159	−1.18515	−0.592573	−	0.805517i	$-0.701888\pi$
$863$	−34.8159	−1.18515	−0.592573	+	0.805517i	$0.701888\pi$
$864$	0	0
$865$	26.3874	0.897197
$866$	14.0797	0.478449
$867$	0	0
$868$	0	0
$869$	−39.6195	−1.34400
$870$	0	0
$871$	−6.61732	−0.224219
$872$	19.0530	0.645214
$873$	0	0
$874$	−28.1295	−0.951494
$875$	0	0
$876$	0	0
$877$	−41.4534	−1.39978	−0.699890	−	0.714250i	$-0.746768\pi$
$877$	−41.4534	−1.39978	−0.699890	+	0.714250i	$0.746768\pi$
$878$	−7.03663	−0.237475
$879$	0	0
$880$	−88.5487	−2.98498
$881$	21.1258	0.711746	0.355873	−	0.934534i	$-0.384184\pi$
$881$	21.1258	0.711746	0.355873	+	0.934534i	$0.384184\pi$
$882$	0	0
$883$	14.7237	0.495492	0.247746	−	0.968825i	$-0.420310\pi$
$883$	14.7237	0.495492	0.247746	+	0.968825i	$0.420310\pi$
$884$	−3.73498	−0.125621
$885$	0	0
$886$	33.6866	1.13172
$887$	17.5577	0.589529	0.294765	−	0.955570i	$-0.404759\pi$
$887$	17.5577	0.589529	0.294765	+	0.955570i	$0.404759\pi$
$888$	0	0
$889$	0	0
$890$	40.1624	1.34625
$891$	0	0
$892$	2.04144	0.0683523
$893$	−25.6799	−0.859344
$894$	0	0
$895$	28.8501	0.964353
$896$	0	0
$897$	0	0
$898$	−28.8160	−0.961601
$899$	16.4922	0.550044
$900$	0	0
$901$	23.2692	0.775208
$902$	−70.1411	−2.33544
$903$	0	0
$904$	0.282091	0.00938221
$905$	−20.9910	−0.697766
$906$	0	0
$907$	−18.0268	−0.598569	−0.299284	−	0.954164i	$-0.596748\pi$
$907$	−18.0268	−0.598569	−0.299284	+	0.954164i	$0.596748\pi$
$908$	−5.12716	−0.170151
$909$	0	0
$910$	0	0
$911$	21.5618	0.714376	0.357188	−	0.934033i	$-0.383736\pi$
$911$	21.5618	0.714376	0.357188	+	0.934033i	$0.383736\pi$
$912$	0	0
$913$	−91.5140	−3.02867
$914$	70.5784	2.33453
$915$	0	0
$916$	−36.9789	−1.22182
$917$	0	0
$918$	0	0
$919$	35.7292	1.17860	0.589298	−	0.807916i	$-0.299404\pi$
$919$	35.7292	1.17860	0.589298	+	0.807916i	$0.299404\pi$
$920$	−21.8891	−0.721664
$921$	0	0
$922$	32.6376	1.07486
$923$	5.71717	0.188183
$924$	0	0
$925$	18.3600	0.603674
$926$	−45.3466	−1.49018
$927$	0	0
$928$	−13.6713	−0.448783
$929$	−45.3708	−1.48857	−0.744284	−	0.667863i	$-0.767209\pi$
$929$	−45.3708	−1.48857	−0.744284	+	0.667863i	$0.767209\pi$
$930$	0	0
$931$	0	0
$932$	−32.1758	−1.05395
$933$	0	0
$934$	−33.7257	−1.10354
$935$	49.9637	1.63399
$936$	0	0
$937$	−36.4136	−1.18958	−0.594790	−	0.803881i	$-0.702765\pi$
$937$	−36.4136	−1.18958	−0.594790	+	0.803881i	$0.702765\pi$
$938$	0	0
$939$	0	0
$940$	42.3542	1.38144
$941$	16.9117	0.551307	0.275653	−	0.961257i	$-0.411106\pi$
$941$	16.9117	0.551307	0.275653	+	0.961257i	$0.411106\pi$
$942$	0	0
$943$	−39.2210	−1.27721
$944$	−57.6303	−1.87571
$945$	0	0
$946$	107.908	3.50839
$947$	6.67410	0.216879	0.108440	−	0.994103i	$-0.465415\pi$
$947$	6.67410	0.216879	0.108440	+	0.994103i	$0.465415\pi$
$948$	0	0
$949$	−0.843989	−0.0273970
$950$	25.3453	0.822311
$951$	0	0
$952$	0	0
$953$	−18.2345	−0.590674	−0.295337	−	0.955393i	$-0.595432\pi$
$953$	−18.2345	−0.590674	−0.295337	+	0.955393i	$0.595432\pi$
$954$	0	0
$955$	55.4512	1.79436
$956$	−11.8801	−0.384231
$957$	0	0
$958$	42.0880	1.35980
$959$	0	0
$960$	0	0
$961$	31.9602	1.03097
$962$	−6.41631	−0.206870
$963$	0	0
$964$	18.4361	0.593786
$965$	−75.3039	−2.42412
$966$	0	0
$967$	−25.7044	−0.826599	−0.413300	−	0.910595i	$-0.635624\pi$
$967$	−25.7044	−0.826599	−0.413300	+	0.910595i	$0.635624\pi$
$968$	−24.9759	−0.802754
$969$	0	0
$970$	58.7961	1.88783
$971$	52.8590	1.69633	0.848163	−	0.529736i	$-0.177709\pi$
$971$	52.8590	1.69633	0.848163	+	0.529736i	$0.177709\pi$
$972$	0	0
$973$	0	0
$974$	10.7617	0.344827
$975$	0	0
$976$	−6.31620	−0.202177
$977$	40.2006	1.28613	0.643065	−	0.765812i	$-0.277662\pi$
$977$	40.2006	1.28613	0.643065	+	0.765812i	$0.277662\pi$
$978$	0	0
$979$	38.8855	1.24279
$980$	0	0
$981$	0	0
$982$	46.9465	1.49812
$983$	−30.2326	−0.964270	−0.482135	−	0.876097i	$-0.660138\pi$
$983$	−30.2326	−0.964270	−0.482135	+	0.876097i	$0.660138\pi$
$984$	0	0
$985$	−29.5867	−0.942711
$986$	10.4701	0.333436
$987$	0	0
$988$	−3.58340	−0.114003
$989$	60.3393	1.91868
$990$	0	0
$991$	−60.6184	−1.92561	−0.962804	−	0.270201i	$-0.912910\pi$
$991$	−60.6184	−1.92561	−0.962804	+	0.270201i	$0.912910\pi$
$992$	−52.1913	−1.65708
$993$	0	0
$994$	0	0
$995$	−3.82336	−0.121209
$996$	0	0
$997$	−4.50192	−0.142577	−0.0712886	−	0.997456i	$-0.522711\pi$
$997$	−4.50192	−0.142577	−0.0712886	+	0.997456i	$0.522711\pi$
$998$	−20.5528	−0.650587
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bx.1.9		10
3.2	odd	2		1911.2.a.y.1.2	yes	10
7.6	odd	2		5733.2.a.bw.1.9		10
21.20	even	2		1911.2.a.x.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.x.1.2	✓	10	21.20	even	2
1911.2.a.y.1.2	yes	10	3.2	odd	2
5733.2.a.bw.1.9		10	7.6	odd	2
5733.2.a.bx.1.9		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)

\(f(q)\)	\(=\)	\(q+1.83272 q^{2} +1.35888 q^{4} -3.20067 q^{5} -1.17500 q^{8} +O(q^{10})\)	\(q+1.83272 q^{2} +1.35888 q^{4} -3.20067 q^{5} -1.17500 q^{8} -5.86594 q^{10} -5.67943 q^{11} -1.00000 q^{13} -4.87121 q^{16} +2.74858 q^{17} +2.63704 q^{19} -4.34931 q^{20} -10.4088 q^{22} -5.82034 q^{23} +5.24426 q^{25} -1.83272 q^{26} +2.07847 q^{29} +7.93474 q^{31} -6.57757 q^{32} +5.03739 q^{34} +3.50097 q^{37} +4.83296 q^{38} +3.76080 q^{40} +6.73861 q^{41} -10.3670 q^{43} -7.71764 q^{44} -10.6671 q^{46} -9.73815 q^{47} +9.61129 q^{50} -1.35888 q^{52} +8.46587 q^{53} +18.1780 q^{55} +3.80927 q^{58} +11.8308 q^{59} +1.29664 q^{61} +14.5422 q^{62} -2.31245 q^{64} +3.20067 q^{65} +6.61732 q^{67} +3.73498 q^{68} -5.71717 q^{71} +0.843989 q^{73} +6.41631 q^{74} +3.58340 q^{76} +6.97595 q^{79} +15.5911 q^{80} +12.3500 q^{82} +16.1132 q^{83} -8.79730 q^{85} -18.9998 q^{86} +6.67336 q^{88} -6.84672 q^{89} -7.90912 q^{92} -17.8473 q^{94} -8.44028 q^{95} -10.0233 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 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

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