LMFDB - Embedded newform 3825.2.a.bh.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3825,2,Mod(1,3825)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3825.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3825, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$3825 = 3^{2} \cdot 5^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3825.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,4,0,0,10,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$30.5427787731$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.6224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - 6x^{2} - 2x + 5$ x^4 - 6x^2 - 2x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.44579$ of defining polynomial
Character	$\chi$	$=$	3825.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-0.134632 q^{2} -1.98187 q^{4} +2.86537 q^{7} +0.536087 q^{8} +3.84724 q^{11} +6.22085 q^{13} -0.385770 q^{14} +3.89157 q^{16} +1.00000 q^{17} +6.62231 q^{19} -0.517961 q^{22} -4.51796 q^{23} -0.837525 q^{26} -5.67880 q^{28} +0.658562 q^{29} +3.49984 q^{31} -1.59610 q^{32} -0.134632 q^{34} +3.34144 q^{37} -0.891574 q^{38} -2.04189 q^{41} -1.29303 q^{43} -7.62475 q^{44} +0.608262 q^{46} -6.22085 q^{47} +1.21033 q^{49} -12.3290 q^{52} +9.92750 q^{53} +1.53609 q^{56} -0.0886634 q^{58} +2.00000 q^{59} -7.61634 q^{61} -0.471189 q^{62} -7.56826 q^{64} +0.257106 q^{67} -1.98187 q^{68} -1.18868 q^{71} +3.26330 q^{73} -0.449864 q^{74} -13.1246 q^{76} +11.0238 q^{77} -4.99756 q^{79} +0.274904 q^{82} -7.91534 q^{83} +0.174083 q^{86} +2.06246 q^{88} -12.8013 q^{89} +17.8250 q^{91} +8.95403 q^{92} +0.837525 q^{94} -4.08866 q^{97} -0.162950 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{2} + 4 q^{4} + 10 q^{7} + 2 q^{11} + 6 q^{13} + 6 q^{14} - 4 q^{16} + 4 q^{17} + 4 q^{19} + 12 q^{22} - 4 q^{23} + 8 q^{28} + 4 q^{29} - 12 q^{31} - 2 q^{32} - 2 q^{34} + 12 q^{37} + 16 q^{38}+ \cdots + 60 q^{98}+O(q^{100})$ 4 * q - 2 * q^2 + 4 * q^4 + 10 * q^7 + 2 * q^11 + 6 * q^13 + 6 * q^14 - 4 * q^16 + 4 * q^17 + 4 * q^19 + 12 * q^22 - 4 * q^23 + 8 * q^28 + 4 * q^29 - 12 * q^31 - 2 * q^32 - 2 * q^34 + 12 * q^37 + 16 * q^38 + 6 * q^41 + 18 * q^43 - 16 * q^44 - 4 * q^46 - 6 * q^47 + 8 * q^49 + 2 * q^52 - 8 * q^53 + 4 * q^56 + 12 * q^58 + 8 * q^59 + 6 * q^61 + 14 * q^62 - 24 * q^64 + 6 * q^67 + 4 * q^68 + 10 * q^71 + 2 * q^73 - 20 * q^74 - 12 * q^76 + 18 * q^77 - 12 * q^79 - 34 * q^82 + 14 * q^83 - 20 * q^86 + 14 * q^88 - 24 * q^89 + 18 * q^91 + 22 * q^92 - 4 * q^97 + 60 * q^98

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.134632	−0.0951991	−0.0475996	−	0.998866i	$-0.515157\pi$
$2$	−0.134632	−0.0951991	−0.0475996	+	0.998866i	$0.515157\pi$
$3$	0	0
$3$	0	0
$4$	−1.98187	−0.990937
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.86537	1.08301	0.541504	−	0.840698i	$-0.317855\pi$
$7$	2.86537	1.08301	0.541504	+	0.840698i	$0.317855\pi$
$8$	0.536087	0.189535
$9$	0	0
$10$	0	0
$11$	3.84724	1.15999	0.579994	−	0.814621i	$-0.303055\pi$
$11$	3.84724	1.15999	0.579994	+	0.814621i	$0.303055\pi$
$12$	0	0
$13$	6.22085	1.72535	0.862677	−	0.505755i	$-0.168786\pi$
$13$	6.22085	1.72535	0.862677	+	0.505755i	$0.168786\pi$
$14$	−0.385770	−0.103101
$15$	0	0
$16$	3.89157	0.972894
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0	0
$19$	6.62231	1.51926	0.759631	−	0.650354i	$-0.225380\pi$
$19$	6.62231	1.51926	0.759631	+	0.650354i	$0.225380\pi$
$20$	0	0
$21$	0	0
$22$	−0.517961	−0.110430
$23$	−4.51796	−0.942060	−0.471030	−	0.882117i	$-0.656118\pi$
$23$	−4.51796	−0.942060	−0.471030	+	0.882117i	$0.656118\pi$
$24$	0	0
$25$	0	0
$26$	−0.837525	−0.164252
$27$	0	0
$28$	−5.67880	−1.07319
$29$	0.658562	0.122292	0.0611459	−	0.998129i	$-0.480524\pi$
$29$	0.658562	0.122292	0.0611459	+	0.998129i	$0.480524\pi$
$30$	0	0
$31$	3.49984	0.628589	0.314295	−	0.949326i	$-0.398232\pi$
$31$	3.49984	0.628589	0.314295	+	0.949326i	$0.398232\pi$
$32$	−1.59610	−0.282154
$33$	0	0
$34$	−0.134632	−0.0230892
$35$	0	0
$36$	0	0
$37$	3.34144	0.549329	0.274665	−	0.961540i	$-0.411433\pi$
$37$	3.34144	0.549329	0.274665	+	0.961540i	$0.411433\pi$
$38$	−0.891574	−0.144632
$39$	0	0
$40$	0	0
$41$	−2.04189	−0.318890	−0.159445	−	0.987207i	$-0.550970\pi$
$41$	−2.04189	−0.318890	−0.159445	+	0.987207i	$0.550970\pi$
$42$	0	0
$43$	−1.29303	−0.197185	−0.0985926	−	0.995128i	$-0.531434\pi$
$43$	−1.29303	−0.197185	−0.0985926	+	0.995128i	$0.531434\pi$
$44$	−7.62475	−1.14947
$45$	0	0
$46$	0.608262	0.0896833
$47$	−6.22085	−0.907405	−0.453702	−	0.891153i	$-0.649897\pi$
$47$	−6.22085	−0.907405	−0.453702	+	0.891153i	$0.649897\pi$
$48$	0	0
$49$	1.21033	0.172905
$50$	0	0
$51$	0	0
$52$	−12.3290	−1.70972
$53$	9.92750	1.36365	0.681823	−	0.731517i	$-0.261187\pi$
$53$	9.92750	1.36365	0.681823	+	0.731517i	$0.261187\pi$
$54$	0	0
$55$	0	0
$56$	1.53609	0.205268
$57$	0	0
$58$	−0.0886634	−0.0116421
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	−7.61634	−0.975173	−0.487586	−	0.873075i	$-0.662123\pi$
$61$	−7.61634	−0.975173	−0.487586	+	0.873075i	$0.662123\pi$
$62$	−0.471189	−0.0598411
$63$	0	0
$64$	−7.56826	−0.946033
$65$	0	0
$66$	0	0
$67$	0.257106	0.0314106	0.0157053	−	0.999877i	$-0.495001\pi$
$67$	0.257106	0.0314106	0.0157053	+	0.999877i	$0.495001\pi$
$68$	−1.98187	−0.240338
$69$	0	0
$70$	0	0
$71$	−1.18868	−0.141070	−0.0705352	−	0.997509i	$-0.522471\pi$
$71$	−1.18868	−0.141070	−0.0705352	+	0.997509i	$0.522471\pi$
$72$	0	0
$73$	3.26330	0.381940	0.190970	−	0.981596i	$-0.438837\pi$
$73$	3.26330	0.381940	0.190970	+	0.981596i	$0.438837\pi$
$74$	−0.449864	−0.0522956
$75$	0	0
$76$	−13.1246	−1.50549
$77$	11.0238	1.25627
$78$	0	0
$79$	−4.99756	−0.562269	−0.281135	−	0.959668i	$-0.590711\pi$
$79$	−4.99756	−0.562269	−0.281135	+	0.959668i	$0.590711\pi$
$80$	0	0
$81$	0	0
$82$	0.274904	0.0303580
$83$	−7.91534	−0.868821	−0.434411	−	0.900715i	$-0.643043\pi$
$83$	−7.91534	−0.868821	−0.434411	+	0.900715i	$0.643043\pi$
$84$	0	0
$85$	0	0
$86$	0.174083	0.0187719
$87$	0	0
$88$	2.06246	0.219859
$89$	−12.8013	−1.35693	−0.678466	−	0.734632i	$-0.737355\pi$
$89$	−12.8013	−1.35693	−0.678466	+	0.734632i	$0.737355\pi$
$90$	0	0
$91$	17.8250	1.86857
$92$	8.95403	0.933522
$93$	0	0
$94$	0.837525	0.0863841
$95$	0	0
$96$	0	0
$97$	−4.08866	−0.415141	−0.207570	−	0.978220i	$-0.566556\pi$
$97$	−4.08866	−0.415141	−0.207570	+	0.978220i	$0.566556\pi$
$98$	−0.162950	−0.0164604
$99$	0	0
$100$	0	0
$101$	−12.2871	−1.22261	−0.611304	−	0.791396i	$-0.709355\pi$
$101$	−12.2871	−1.22261	−0.611304	+	0.791396i	$0.709355\pi$
$102$	0	0
$103$	13.5623	1.33633	0.668166	−	0.744012i	$-0.267079\pi$
$103$	13.5623	1.33633	0.668166	+	0.744012i	$0.267079\pi$
$104$	3.33492	0.327016
$105$	0	0
$106$	−1.33656	−0.129818
$107$	6.63800	0.641719	0.320860	−	0.947127i	$-0.396028\pi$
$107$	6.63800	0.641719	0.320860	+	0.947127i	$0.396028\pi$
$108$	0	0
$109$	−2.58042	−0.247159	−0.123580	−	0.992335i	$-0.539437\pi$
$109$	−2.58042	−0.247159	−0.123580	+	0.992335i	$0.539437\pi$
$110$	0	0
$111$	0	0
$112$	11.1508	1.05365
$113$	8.63283	0.812108	0.406054	−	0.913849i	$-0.366904\pi$
$113$	8.63283	0.812108	0.406054	+	0.913849i	$0.366904\pi$
$114$	0	0
$115$	0	0
$116$	−1.30519	−0.121184
$117$	0	0
$118$	−0.269264	−0.0247877
$119$	2.86537	0.262668
$120$	0	0
$121$	3.80127	0.345570
$122$	1.02540	0.0928356
$123$	0	0
$124$	−6.93623	−0.622892
$125$	0	0
$126$	0	0
$127$	3.24550	0.287991	0.143996	−	0.989578i	$-0.454005\pi$
$127$	3.24550	0.287991	0.143996	+	0.989578i	$0.454005\pi$
$128$	4.21114	0.372216
$129$	0	0
$130$	0	0
$131$	3.44742	0.301203	0.150601	−	0.988595i	$-0.451879\pi$
$131$	3.44742	0.301203	0.150601	+	0.988595i	$0.451879\pi$
$132$	0	0
$133$	18.9754	1.64537
$134$	−0.0346147	−0.00299026
$135$	0	0
$136$	0.536087	0.0459691
$137$	−14.6869	−1.25478	−0.627392	−	0.778703i	$-0.715878\pi$
$137$	−14.6869	−1.25478	−0.627392	+	0.778703i	$0.715878\pi$
$138$	0	0
$139$	13.9883	1.18647	0.593237	−	0.805028i	$-0.297850\pi$
$139$	13.9883	1.18647	0.593237	+	0.805028i	$0.297850\pi$
$140$	0	0
$141$	0	0
$142$	0.160034	0.0134298
$143$	23.9331	2.00139
$144$	0	0
$145$	0	0
$146$	−0.439344	−0.0363603
$147$	0	0
$148$	−6.62231	−0.544351
$149$	17.8388	1.46141	0.730707	−	0.682691i	$-0.239191\pi$
$149$	17.8388	1.46141	0.730707	+	0.682691i	$0.239191\pi$
$150$	0	0
$151$	−2.80291	−0.228098	−0.114049	−	0.993475i	$-0.536382\pi$
$151$	−2.80291	−0.228098	−0.114049	+	0.993475i	$0.536382\pi$
$152$	3.55014	0.287954
$153$	0	0
$154$	−1.48415	−0.119596
$155$	0	0
$156$	0	0
$157$	3.60582	0.287776	0.143888	−	0.989594i	$-0.454040\pi$
$157$	3.60582	0.287776	0.143888	+	0.989594i	$0.454040\pi$
$158$	0.672831	0.0535275
$159$	0	0
$160$	0	0
$161$	−12.9456	−1.02026
$162$	0	0
$163$	13.7256	1.07507	0.537535	−	0.843242i	$-0.319356\pi$
$163$	13.7256	1.07507	0.537535	+	0.843242i	$0.319356\pi$
$164$	4.04677	0.316000
$165$	0	0
$166$	1.06566	0.0827110
$167$	−6.32684	−0.489586	−0.244793	−	0.969575i	$-0.578720\pi$
$167$	−6.32684	−0.489586	−0.244793	+	0.969575i	$0.578720\pi$
$168$	0	0
$169$	25.6990	1.97685
$170$	0	0
$171$	0	0
$172$	2.56262	0.195398
$173$	1.76699	0.134342	0.0671708	−	0.997741i	$-0.478603\pi$
$173$	1.76699	0.134342	0.0671708	+	0.997741i	$0.478603\pi$
$174$	0	0
$175$	0	0
$176$	14.9718	1.12854
$177$	0	0
$178$	1.72346	0.129179
$179$	−1.10843	−0.0828476	−0.0414238	−	0.999142i	$-0.513189\pi$
$179$	−1.10843	−0.0828476	−0.0414238	+	0.999142i	$0.513189\pi$
$180$	0	0
$181$	−10.8310	−0.805062	−0.402531	−	0.915406i	$-0.631870\pi$
$181$	−10.8310	−0.805062	−0.402531	+	0.915406i	$0.631870\pi$
$182$	−2.39982	−0.177886
$183$	0	0
$184$	−2.42202	−0.178554
$185$	0	0
$186$	0	0
$187$	3.84724	0.281338
$188$	12.3290	0.899181
$189$	0	0
$190$	0	0
$191$	−3.19221	−0.230980	−0.115490	−	0.993309i	$-0.536844\pi$
$191$	−3.19221	−0.230980	−0.115490	+	0.993309i	$0.536844\pi$
$192$	0	0
$193$	7.11407	0.512082	0.256041	−	0.966666i	$-0.417582\pi$
$193$	7.11407	0.512082	0.256041	+	0.966666i	$0.417582\pi$
$194$	0.550464	0.0395210
$195$	0	0
$196$	−2.39873	−0.171338
$197$	23.1721	1.65095	0.825473	−	0.564442i	$-0.190909\pi$
$197$	23.1721	1.65095	0.825473	+	0.564442i	$0.190909\pi$
$198$	0	0
$199$	−24.7131	−1.75186	−0.875932	−	0.482434i	$-0.839753\pi$
$199$	−24.7131	−1.75186	−0.875932	+	0.482434i	$0.839753\pi$
$200$	0	0
$201$	0	0
$202$	1.65423	0.116391
$203$	1.88702	0.132443
$204$	0	0
$205$	0	0
$206$	−1.82592	−0.127218
$207$	0	0
$208$	24.2089	1.67859
$209$	25.4776	1.76232
$210$	0	0
$211$	−4.27138	−0.294054	−0.147027	−	0.989133i	$-0.546970\pi$
$211$	−4.27138	−0.294054	−0.147027	+	0.989133i	$0.546970\pi$
$212$	−19.6751	−1.35129
$213$	0	0
$214$	−0.893686	−0.0610911
$215$	0	0
$216$	0	0
$217$	10.0283	0.680767
$218$	0.347407	0.0235293
$219$	0	0
$220$	0	0
$221$	6.22085	0.418460
$222$	0	0
$223$	3.65423	0.244705	0.122353	−	0.992487i	$-0.460956\pi$
$223$	3.65423	0.244705	0.122353	+	0.992487i	$0.460956\pi$
$224$	−4.57343	−0.305575
$225$	0	0
$226$	−1.16225	−0.0773120
$227$	−19.0016	−1.26118	−0.630589	−	0.776117i	$-0.717187\pi$
$227$	−19.0016	−1.26118	−0.630589	+	0.776117i	$0.717187\pi$
$228$	0	0
$229$	−20.8851	−1.38012	−0.690062	−	0.723751i	$-0.742417\pi$
$229$	−20.8851	−1.38012	−0.690062	+	0.723751i	$0.742417\pi$
$230$	0	0
$231$	0	0
$232$	0.353047	0.0231786
$233$	0.682876	0.0447367	0.0223684	−	0.999750i	$-0.492879\pi$
$233$	0.682876	0.0447367	0.0223684	+	0.999750i	$0.492879\pi$
$234$	0	0
$235$	0	0
$236$	−3.96375	−0.258018
$237$	0	0
$238$	−0.385770	−0.0250057
$239$	−28.9915	−1.87531	−0.937653	−	0.347574i	$-0.887006\pi$
$239$	−28.9915	−1.87531	−0.937653	+	0.347574i	$0.887006\pi$
$240$	0	0
$241$	−18.0943	−1.16556	−0.582778	−	0.812631i	$-0.698034\pi$
$241$	−18.0943	−1.16556	−0.582778	+	0.812631i	$0.698034\pi$
$242$	−0.511773	−0.0328980
$243$	0	0
$244$	15.0946	0.966335
$245$	0	0
$246$	0	0
$247$	41.1964	2.62127
$248$	1.87622	0.119140
$249$	0	0
$250$	0	0
$251$	7.21325	0.455296	0.227648	−	0.973743i	$-0.426896\pi$
$251$	7.21325	0.455296	0.227648	+	0.973743i	$0.426896\pi$
$252$	0	0
$253$	−17.3817	−1.09278
$254$	−0.436948	−0.0274165
$255$	0	0
$256$	14.5696	0.910598
$257$	4.87942	0.304370	0.152185	−	0.988352i	$-0.451369\pi$
$257$	4.87942	0.304370	0.152185	+	0.988352i	$0.451369\pi$
$258$	0	0
$259$	9.57445	0.594927
$260$	0	0
$261$	0	0
$262$	−0.464133	−0.0286742
$263$	−30.0234	−1.85132	−0.925662	−	0.378351i	$-0.876491\pi$
$263$	−30.0234	−1.85132	−0.925662	+	0.378351i	$0.876491\pi$
$264$	0	0
$265$	0	0
$266$	−2.55469	−0.156638
$267$	0	0
$268$	−0.509553	−0.0311259
$269$	29.6568	1.80821	0.904104	−	0.427312i	$-0.140540\pi$
$269$	29.6568	1.80821	0.904104	+	0.427312i	$0.140540\pi$
$270$	0	0
$271$	3.91622	0.237893	0.118947	−	0.992901i	$-0.462048\pi$
$271$	3.91622	0.237893	0.118947	+	0.992901i	$0.462048\pi$
$272$	3.89157	0.235961
$273$	0	0
$274$	1.97732	0.119454
$275$	0	0
$276$	0	0
$277$	−0.455504	−0.0273686	−0.0136843	−	0.999906i	$-0.504356\pi$
$277$	−0.455504	−0.0273686	−0.0136843	+	0.999906i	$0.504356\pi$
$278$	−1.88327	−0.112951
$279$	0	0
$280$	0	0
$281$	−16.4941	−0.983957	−0.491978	−	0.870607i	$-0.663726\pi$
$281$	−16.4941	−0.983957	−0.491978	+	0.870607i	$0.663726\pi$
$282$	0	0
$283$	8.79775	0.522972	0.261486	−	0.965207i	$-0.415788\pi$
$283$	8.79775	0.522972	0.261486	+	0.965207i	$0.415788\pi$
$284$	2.35582	0.139792
$285$	0	0
$286$	−3.22216	−0.190531
$287$	−5.85077	−0.345360
$288$	0	0
$289$	1.00000	0.0588235
$290$	0	0
$291$	0	0
$292$	−6.46744	−0.378478
$293$	22.5023	1.31460	0.657299	−	0.753630i	$-0.271699\pi$
$293$	22.5023	1.31460	0.657299	+	0.753630i	$0.271699\pi$
$294$	0	0
$295$	0	0
$296$	1.79130	0.104117
$297$	0	0
$298$	−2.40168	−0.139125
$299$	−28.1056	−1.62539
$300$	0	0
$301$	−3.70501	−0.213553
$302$	0.377361	0.0217147
$303$	0	0
$304$	25.7712	1.47808
$305$	0	0
$306$	0	0
$307$	11.7034	0.667947	0.333973	−	0.942583i	$-0.391610\pi$
$307$	11.7034	0.667947	0.333973	+	0.942583i	$0.391610\pi$
$308$	−21.8477	−1.24489
$309$	0	0
$310$	0	0
$311$	21.0605	1.19423	0.597115	−	0.802155i	$-0.296313\pi$
$311$	21.0605	1.19423	0.597115	+	0.802155i	$0.296313\pi$
$312$	0	0
$313$	22.2911	1.25997	0.629983	−	0.776609i	$-0.283062\pi$
$313$	22.2911	1.25997	0.629983	+	0.776609i	$0.283062\pi$
$314$	−0.485459	−0.0273960
$315$	0	0
$316$	9.90453	0.557174
$317$	27.8613	1.56485	0.782423	−	0.622747i	$-0.213984\pi$
$317$	27.8613	1.56485	0.782423	+	0.622747i	$0.213984\pi$
$318$	0	0
$319$	2.53365	0.141857
$320$	0	0
$321$	0	0
$322$	1.74289	0.0971277
$323$	6.62231	0.368475
$324$	0	0
$325$	0	0
$326$	−1.84790	−0.102346
$327$	0	0
$328$	−1.09463	−0.0604409
$329$	−17.8250	−0.982726
$330$	0	0
$331$	−13.0067	−0.714914	−0.357457	−	0.933930i	$-0.616356\pi$
$331$	−13.0067	−0.714914	−0.357457	+	0.933930i	$0.616356\pi$
$332$	15.6872	0.860947
$333$	0	0
$334$	0.851794	0.0466081
$335$	0	0
$336$	0	0
$337$	−15.1126	−0.823238	−0.411619	−	0.911356i	$-0.635037\pi$
$337$	−15.1126	−0.823238	−0.411619	+	0.911356i	$0.635037\pi$
$338$	−3.45991	−0.188194
$339$	0	0
$340$	0	0
$341$	13.4647	0.729155
$342$	0	0
$343$	−16.5895	−0.895750
$344$	−0.693177	−0.0373736
$345$	0	0
$346$	−0.237893	−0.0127892
$347$	3.58828	0.192629	0.0963144	−	0.995351i	$-0.469295\pi$
$347$	3.58828	0.192629	0.0963144	+	0.995351i	$0.469295\pi$
$348$	0	0
$349$	31.2851	1.67465	0.837326	−	0.546703i	$-0.184117\pi$
$349$	31.2851	1.67465	0.837326	+	0.546703i	$0.184117\pi$
$350$	0	0
$351$	0	0
$352$	−6.14060	−0.327295
$353$	24.4417	1.30090	0.650450	−	0.759549i	$-0.274580\pi$
$353$	24.4417	1.30090	0.650450	+	0.759549i	$0.274580\pi$
$354$	0	0
$355$	0	0
$356$	25.3705	1.34463
$357$	0	0
$358$	0.149229	0.00788702
$359$	0.136195	0.00718808	0.00359404	−	0.999994i	$-0.498856\pi$
$359$	0.136195	0.00718808	0.00359404	+	0.999994i	$0.498856\pi$
$360$	0	0
$361$	24.8550	1.30816
$362$	1.45820	0.0766412
$363$	0	0
$364$	−35.3270	−1.85164
$365$	0	0
$366$	0	0
$367$	−16.9896	−0.886851	−0.443426	−	0.896311i	$-0.646237\pi$
$367$	−16.9896	−0.886851	−0.443426	+	0.896311i	$0.646237\pi$
$368$	−17.5820	−0.916524
$369$	0	0
$370$	0	0
$371$	28.4459	1.47684
$372$	0	0
$373$	−18.3533	−0.950296	−0.475148	−	0.879906i	$-0.657606\pi$
$373$	−18.3533	−0.950296	−0.475148	+	0.879906i	$0.657606\pi$
$374$	−0.517961	−0.0267832
$375$	0	0
$376$	−3.33492	−0.171985
$377$	4.09682	0.210997
$378$	0	0
$379$	−35.1943	−1.80781	−0.903905	−	0.427732i	$-0.859313\pi$
$379$	−35.1943	−1.80781	−0.903905	+	0.427732i	$0.859313\pi$
$380$	0	0
$381$	0	0
$382$	0.429773	0.0219891
$383$	−10.8237	−0.553067	−0.276533	−	0.961004i	$-0.589186\pi$
$383$	−10.8237	−0.553067	−0.276533	+	0.961004i	$0.589186\pi$
$384$	0	0
$385$	0	0
$386$	−0.957780	−0.0487497
$387$	0	0
$388$	8.10322	0.411379
$389$	−0.174083	−0.00882636	−0.00441318	−	0.999990i	$-0.501405\pi$
$389$	−0.174083	−0.00882636	−0.00441318	+	0.999990i	$0.501405\pi$
$390$	0	0
$391$	−4.51796	−0.228483
$392$	0.648845	0.0327716
$393$	0	0
$394$	−3.11971	−0.157169
$395$	0	0
$396$	0	0
$397$	2.75287	0.138162	0.0690812	−	0.997611i	$-0.477993\pi$
$397$	2.75287	0.138162	0.0690812	+	0.997611i	$0.477993\pi$
$398$	3.32717	0.166776
$399$	0	0
$400$	0	0
$401$	−33.9912	−1.69744	−0.848719	−	0.528843i	$-0.822626\pi$
$401$	−33.9912	−1.69744	−0.848719	+	0.528843i	$0.822626\pi$
$402$	0	0
$403$	21.7720	1.08454
$404$	24.3514	1.21153
$405$	0	0
$406$	−0.254053	−0.0126085
$407$	12.8553	0.637215
$408$	0	0
$409$	−4.68288	−0.231553	−0.115777	−	0.993275i	$-0.536936\pi$
$409$	−4.68288	−0.231553	−0.115777	+	0.993275i	$0.536936\pi$
$410$	0	0
$411$	0	0
$412$	−26.8788	−1.32422
$413$	5.73074	0.281991
$414$	0	0
$415$	0	0
$416$	−9.92913	−0.486816
$417$	0	0
$418$	−3.43010	−0.167772
$419$	29.0991	1.42158	0.710792	−	0.703402i	$-0.248337\pi$
$419$	29.0991	1.42158	0.710792	+	0.703402i	$0.248337\pi$
$420$	0	0
$421$	7.19057	0.350447	0.175224	−	0.984529i	$-0.443935\pi$
$421$	7.19057	0.350447	0.175224	+	0.984529i	$0.443935\pi$
$422$	0.575063	0.0279936
$423$	0	0
$424$	5.32200	0.258459
$425$	0	0
$426$	0	0
$427$	−21.8236	−1.05612
$428$	−13.1557	−0.635903
$429$	0	0
$430$	0	0
$431$	−7.63181	−0.367611	−0.183806	−	0.982963i	$-0.558842\pi$
$431$	−7.63181	−0.367611	−0.183806	+	0.982963i	$0.558842\pi$
$432$	0	0
$433$	−32.2894	−1.55173	−0.775865	−	0.630898i	$-0.782686\pi$
$433$	−32.2894	−1.55173	−0.775865	+	0.630898i	$0.782686\pi$
$434$	−1.35013	−0.0648084
$435$	0	0
$436$	5.11407	0.244919
$437$	−29.9193	−1.43124
$438$	0	0
$439$	−13.3974	−0.639422	−0.319711	−	0.947515i	$-0.603586\pi$
$439$	−13.3974	−0.639422	−0.319711	+	0.947515i	$0.603586\pi$
$440$	0	0
$441$	0	0
$442$	−0.837525	−0.0398370
$443$	−6.89070	−0.327387	−0.163693	−	0.986511i	$-0.552341\pi$
$443$	−6.89070	−0.327387	−0.163693	+	0.986511i	$0.552341\pi$
$444$	0	0
$445$	0	0
$446$	−0.491976	−0.0232957
$447$	0	0
$448$	−21.6859	−1.02456
$449$	−21.1778	−0.999440	−0.499720	−	0.866187i	$-0.666564\pi$
$449$	−21.1778	−0.999440	−0.499720	+	0.866187i	$0.666564\pi$
$450$	0	0
$451$	−7.85565	−0.369908
$452$	−17.1092	−0.804748
$453$	0	0
$454$	2.55822	0.120063
$455$	0	0
$456$	0	0
$457$	−30.2321	−1.41420	−0.707100	−	0.707114i	$-0.749997\pi$
$457$	−30.2321	−1.41420	−0.707100	+	0.707114i	$0.749997\pi$
$458$	2.81179	0.131387
$459$	0	0
$460$	0	0
$461$	−3.74267	−0.174314	−0.0871568	−	0.996195i	$-0.527778\pi$
$461$	−3.74267	−0.174314	−0.0871568	+	0.996195i	$0.527778\pi$
$462$	0	0
$463$	2.53452	0.117789	0.0588947	−	0.998264i	$-0.481242\pi$
$463$	2.53452	0.117789	0.0588947	+	0.998264i	$0.481242\pi$
$464$	2.56284	0.118977
$465$	0	0
$466$	−0.0919369	−0.00425890
$467$	30.1170	1.39365	0.696824	−	0.717242i	$-0.254596\pi$
$467$	30.1170	1.39365	0.696824	+	0.717242i	$0.254596\pi$
$468$	0	0
$469$	0.736705	0.0340179
$470$	0	0
$471$	0	0
$472$	1.07217	0.0493508
$473$	−4.97460	−0.228732
$474$	0	0
$475$	0	0
$476$	−5.67880	−0.260287
$477$	0	0
$478$	3.90318	0.178527
$479$	−14.4995	−0.662499	−0.331250	−	0.943543i	$-0.607470\pi$
$479$	−14.4995	−0.662499	−0.331250	+	0.943543i	$0.607470\pi$
$480$	0	0
$481$	20.7866	0.947787
$482$	2.43607	0.110960
$483$	0	0
$484$	−7.53365	−0.342438
$485$	0	0
$486$	0	0
$487$	23.9424	1.08493	0.542467	−	0.840077i	$-0.317490\pi$
$487$	23.9424	1.08493	0.542467	+	0.840077i	$0.317490\pi$
$488$	−4.08302	−0.184830
$489$	0	0
$490$	0	0
$491$	21.1295	0.953559	0.476780	−	0.879023i	$-0.341804\pi$
$491$	21.1295	0.953559	0.476780	+	0.879023i	$0.341804\pi$
$492$	0	0
$493$	0.658562	0.0296601
$494$	−5.54635	−0.249542
$495$	0	0
$496$	13.6199	0.611550
$497$	−3.40601	−0.152780
$498$	0	0
$499$	4.01027	0.179524	0.0897621	−	0.995963i	$-0.471389\pi$
$499$	4.01027	0.179524	0.0897621	+	0.995963i	$0.471389\pi$
$500$	0	0
$501$	0	0
$502$	−0.971133	−0.0433438
$503$	−1.44015	−0.0642130	−0.0321065	−	0.999484i	$-0.510222\pi$
$503$	−1.44015	−0.0642130	−0.0321065	+	0.999484i	$0.510222\pi$
$504$	0	0
$505$	0	0
$506$	2.34013	0.104031
$507$	0	0
$508$	−6.43217	−0.285381
$509$	−31.1478	−1.38060	−0.690301	−	0.723522i	$-0.742522\pi$
$509$	−31.1478	−1.38060	−0.690301	+	0.723522i	$0.742522\pi$
$510$	0	0
$511$	9.35054	0.413644
$512$	−10.3838	−0.458904
$513$	0	0
$514$	−0.656925	−0.0289757
$515$	0	0
$516$	0	0
$517$	−23.9331	−1.05258
$518$	−1.28903	−0.0566366
$519$	0	0
$520$	0	0
$521$	39.1197	1.71387	0.856933	−	0.515428i	$-0.172367\pi$
$521$	39.1197	1.71387	0.856933	+	0.515428i	$0.172367\pi$
$522$	0	0
$523$	−40.4813	−1.77012	−0.885062	−	0.465473i	$-0.845884\pi$
$523$	−40.4813	−1.77012	−0.885062	+	0.465473i	$0.845884\pi$
$524$	−6.83236	−0.298473
$525$	0	0
$526$	4.04211	0.176244
$527$	3.49984	0.152455
$528$	0	0
$529$	−2.58802	−0.112523
$530$	0	0
$531$	0	0
$532$	−37.6068	−1.63046
$533$	−12.7023	−0.550198
$534$	0	0
$535$	0	0
$536$	0.137831	0.00595341
$537$	0	0
$538$	−3.99275	−0.172140
$539$	4.65645	0.200568
$540$	0	0
$541$	−18.5288	−0.796614	−0.398307	−	0.917252i	$-0.630402\pi$
$541$	−18.5288	−0.796614	−0.398307	+	0.917252i	$0.630402\pi$
$542$	−0.527248	−0.0226472
$543$	0	0
$544$	−1.59610	−0.0684324
$545$	0	0
$546$	0	0
$547$	43.2959	1.85120	0.925600	−	0.378504i	$-0.123561\pi$
$547$	43.2959	1.85120	0.925600	+	0.378504i	$0.123561\pi$
$548$	29.1075	1.24341
$549$	0	0
$550$	0	0
$551$	4.36120	0.185793
$552$	0	0
$553$	−14.3198	−0.608942
$554$	0.0613254	0.00260546
$555$	0	0
$556$	−27.7231	−1.17572
$557$	25.3698	1.07495	0.537476	−	0.843279i	$-0.319378\pi$
$557$	25.3698	1.07495	0.537476	+	0.843279i	$0.319378\pi$
$558$	0	0
$559$	−8.04375	−0.340214
$560$	0	0
$561$	0	0
$562$	2.22063	0.0936718
$563$	35.6622	1.50298	0.751492	−	0.659742i	$-0.229335\pi$
$563$	35.6622	1.50298	0.751492	+	0.659742i	$0.229335\pi$
$564$	0	0
$565$	0	0
$566$	−1.18446	−0.0497864
$567$	0	0
$568$	−0.637236	−0.0267378
$569$	−27.7944	−1.16520	−0.582602	−	0.812758i	$-0.697965\pi$
$569$	−27.7944	−1.16520	−0.582602	+	0.812758i	$0.697965\pi$
$570$	0	0
$571$	−15.8578	−0.663627	−0.331813	−	0.943345i	$-0.607660\pi$
$571$	−15.8578	−0.663627	−0.331813	+	0.943345i	$0.607660\pi$
$572$	−47.4325	−1.98325
$573$	0	0
$574$	0.787700	0.0328780
$575$	0	0
$576$	0	0
$577$	25.2762	1.05226	0.526131	−	0.850403i	$-0.323642\pi$
$577$	25.2762	1.05226	0.526131	+	0.850403i	$0.323642\pi$
$578$	−0.134632	−0.00559995
$579$	0	0
$580$	0	0
$581$	−22.6804	−0.940940
$582$	0	0
$583$	38.1935	1.58181
$584$	1.74941	0.0723911
$585$	0	0
$586$	−3.02952	−0.125148
$587$	−15.7829	−0.651431	−0.325716	−	0.945468i	$-0.605605\pi$
$587$	−15.7829	−0.651431	−0.325716	+	0.945468i	$0.605605\pi$
$588$	0	0
$589$	23.1770	0.954992
$590$	0	0
$591$	0	0
$592$	13.0035	0.534439
$593$	−19.3560	−0.794855	−0.397428	−	0.917634i	$-0.630097\pi$
$593$	−19.3560	−0.794855	−0.397428	+	0.917634i	$0.630097\pi$
$594$	0	0
$595$	0	0
$596$	−35.3543	−1.44817
$597$	0	0
$598$	3.78391	0.154735
$599$	15.8356	0.647023	0.323512	−	0.946224i	$-0.395136\pi$
$599$	15.8356	0.647023	0.323512	+	0.946224i	$0.395136\pi$
$600$	0	0
$601$	9.30443	0.379536	0.189768	−	0.981829i	$-0.439226\pi$
$601$	9.30443	0.379536	0.189768	+	0.981829i	$0.439226\pi$
$602$	0.498812	0.0203301
$603$	0	0
$604$	5.55502	0.226030
$605$	0	0
$606$	0	0
$607$	26.6661	1.08234	0.541172	−	0.840912i	$-0.317981\pi$
$607$	26.6661	1.08234	0.541172	+	0.840912i	$0.317981\pi$
$608$	−10.5699	−0.428666
$609$	0	0
$610$	0	0
$611$	−38.6990	−1.56560
$612$	0	0
$613$	26.0929	1.05388	0.526941	−	0.849902i	$-0.323339\pi$
$613$	26.0929	1.05388	0.526941	+	0.849902i	$0.323339\pi$
$614$	−1.57565	−0.0635879
$615$	0	0
$616$	5.90970	0.238109
$617$	−23.4622	−0.944554	−0.472277	−	0.881450i	$-0.656568\pi$
$617$	−23.4622	−0.944554	−0.472277	+	0.881450i	$0.656568\pi$
$618$	0	0
$619$	3.50613	0.140923	0.0704617	−	0.997514i	$-0.477553\pi$
$619$	3.50613	0.140923	0.0704617	+	0.997514i	$0.477553\pi$
$620$	0	0
$621$	0	0
$622$	−2.83541	−0.113690
$623$	−36.6804	−1.46957
$624$	0	0
$625$	0	0
$626$	−3.00109	−0.119948
$627$	0	0
$628$	−7.14628	−0.285168
$629$	3.34144	0.133232
$630$	0	0
$631$	−7.57823	−0.301685	−0.150842	−	0.988558i	$-0.548199\pi$
$631$	−7.57823	−0.301685	−0.150842	+	0.988558i	$0.548199\pi$
$632$	−2.67913	−0.106570
$633$	0	0
$634$	−3.75102	−0.148972
$635$	0	0
$636$	0	0
$637$	7.52932	0.298322
$638$	−0.341110	−0.0135047
$639$	0	0
$640$	0	0
$641$	−4.21055	−0.166307	−0.0831535	−	0.996537i	$-0.526499\pi$
$641$	−4.21055	−0.166307	−0.0831535	+	0.996537i	$0.526499\pi$
$642$	0	0
$643$	−39.0726	−1.54087	−0.770437	−	0.637516i	$-0.779962\pi$
$643$	−39.0726	−1.54087	−0.770437	+	0.637516i	$0.779962\pi$
$644$	25.6566	1.01101
$645$	0	0
$646$	−0.891574	−0.0350785
$647$	27.0481	1.06337	0.531685	−	0.846942i	$-0.321559\pi$
$647$	27.0481	1.06337	0.531685	+	0.846942i	$0.321559\pi$
$648$	0	0
$649$	7.69448	0.302035
$650$	0	0
$651$	0	0
$652$	−27.2024	−1.06533
$653$	−35.6550	−1.39529	−0.697643	−	0.716445i	$-0.745768\pi$
$653$	−35.6550	−1.39529	−0.697643	+	0.716445i	$0.745768\pi$
$654$	0	0
$655$	0	0
$656$	−7.94617	−0.310246
$657$	0	0
$658$	2.39982	0.0935547
$659$	−0.586716	−0.0228552	−0.0114276	−	0.999935i	$-0.503638\pi$
$659$	−0.586716	−0.0228552	−0.0114276	+	0.999935i	$0.503638\pi$
$660$	0	0
$661$	18.8785	0.734290	0.367145	−	0.930164i	$-0.380335\pi$
$661$	18.8785	0.734290	0.367145	+	0.930164i	$0.380335\pi$
$662$	1.75112	0.0680592
$663$	0	0
$664$	−4.24331	−0.164672
$665$	0	0
$666$	0	0
$667$	−2.97536	−0.115206
$668$	12.5390	0.485149
$669$	0	0
$670$	0	0
$671$	−29.3019	−1.13119
$672$	0	0
$673$	−44.9680	−1.73339	−0.866694	−	0.498841i	$-0.833759\pi$
$673$	−44.9680	−1.73339	−0.866694	+	0.498841i	$0.833759\pi$
$674$	2.03464	0.0783716
$675$	0	0
$676$	−50.9323	−1.95893
$677$	−33.3876	−1.28319	−0.641594	−	0.767044i	$-0.721727\pi$
$677$	−33.3876	−1.28319	−0.641594	+	0.767044i	$0.721727\pi$
$678$	0	0
$679$	−11.7155	−0.449601
$680$	0	0
$681$	0	0
$682$	−1.81278	−0.0694149
$683$	22.0237	0.842713	0.421357	−	0.906895i	$-0.361554\pi$
$683$	22.0237	0.842713	0.421357	+	0.906895i	$0.361554\pi$
$684$	0	0
$685$	0	0
$686$	2.23348	0.0852746
$687$	0	0
$688$	−5.03192	−0.191840
$689$	61.7575	2.35277
$690$	0	0
$691$	4.51396	0.171719	0.0858595	−	0.996307i	$-0.472636\pi$
$691$	4.51396	0.171719	0.0858595	+	0.996307i	$0.472636\pi$
$692$	−3.50195	−0.133124
$693$	0	0
$694$	−0.483097	−0.0183381
$695$	0	0
$696$	0	0
$697$	−2.04189	−0.0773422
$698$	−4.21197	−0.159425
$699$	0	0
$700$	0	0
$701$	29.3948	1.11023	0.555114	−	0.831774i	$-0.312675\pi$
$701$	29.3948	1.11023	0.555114	+	0.831774i	$0.312675\pi$
$702$	0	0
$703$	22.1280	0.834575
$704$	−29.1169	−1.09739
$705$	0	0
$706$	−3.29063	−0.123845
$707$	−35.2070	−1.32409
$708$	0	0
$709$	−1.86205	−0.0699308	−0.0349654	−	0.999389i	$-0.511132\pi$
$709$	−1.86205	−0.0699308	−0.0349654	+	0.999389i	$0.511132\pi$
$710$	0	0
$711$	0	0
$712$	−6.86260	−0.257187
$713$	−15.8121	−0.592169
$714$	0	0
$715$	0	0
$716$	2.19676	0.0820968
$717$	0	0
$718$	−0.0183362	−0.000684299 0
$719$	15.8028	0.589346	0.294673	−	0.955598i	$-0.404789\pi$
$719$	15.8028	0.589346	0.294673	+	0.955598i	$0.404789\pi$
$720$	0	0
$721$	38.8610	1.44726
$722$	−3.34627	−0.124535
$723$	0	0
$724$	21.4657	0.797766
$725$	0	0
$726$	0	0
$727$	21.0930	0.782296	0.391148	−	0.920328i	$-0.372078\pi$
$727$	21.0930	0.782296	0.391148	+	0.920328i	$0.372078\pi$
$728$	9.55578	0.354161
$729$	0	0
$730$	0	0
$731$	−1.29303	−0.0478244
$732$	0	0
$733$	40.8012	1.50703	0.753513	−	0.657434i	$-0.228358\pi$
$733$	40.8012	1.50703	0.753513	+	0.657434i	$0.228358\pi$
$734$	2.28735	0.0844275
$735$	0	0
$736$	7.21114	0.265806
$737$	0.989151	0.0364358
$738$	0	0
$739$	13.8161	0.508234	0.254117	−	0.967173i	$-0.418215\pi$
$739$	13.8161	0.508234	0.254117	+	0.967173i	$0.418215\pi$
$740$	0	0
$741$	0	0
$742$	−3.82973	−0.140594
$743$	−3.01696	−0.110682	−0.0553408	−	0.998468i	$-0.517625\pi$
$743$	−3.01696	−0.110682	−0.0553408	+	0.998468i	$0.517625\pi$
$744$	0	0
$745$	0	0
$746$	2.47093	0.0904674
$747$	0	0
$748$	−7.62475	−0.278788
$749$	19.0203	0.694987
$750$	0	0
$751$	−44.6641	−1.62982	−0.814909	−	0.579589i	$-0.803213\pi$
$751$	−44.6641	−1.62982	−0.814909	+	0.579589i	$0.803213\pi$
$752$	−24.2089	−0.882808
$753$	0	0
$754$	−0.551562	−0.0200867
$755$	0	0
$756$	0	0
$757$	−12.3652	−0.449421	−0.224710	−	0.974426i	$-0.572144\pi$
$757$	−12.3652	−0.449421	−0.224710	+	0.974426i	$0.572144\pi$
$758$	4.73828	0.172102
$759$	0	0
$760$	0	0
$761$	−16.7175	−0.606009	−0.303004	−	0.952989i	$-0.597990\pi$
$761$	−16.7175	−0.606009	−0.303004	+	0.952989i	$0.597990\pi$
$762$	0	0
$763$	−7.39385	−0.267675
$764$	6.32656	0.228887
$765$	0	0
$766$	1.45722	0.0526515
$767$	12.4417	0.449244
$768$	0	0
$769$	13.4025	0.483308	0.241654	−	0.970362i	$-0.422310\pi$
$769$	13.4025	0.483308	0.241654	+	0.970362i	$0.422310\pi$
$770$	0	0
$771$	0	0
$772$	−14.0992	−0.507441
$773$	25.8358	0.929248	0.464624	−	0.885508i	$-0.346189\pi$
$773$	25.8358	0.929248	0.464624	+	0.885508i	$0.346189\pi$
$774$	0	0
$775$	0	0
$776$	−2.19188	−0.0786839
$777$	0	0
$778$	0.0234371	0.000840261 0
$779$	−13.5220	−0.484477
$780$	0	0
$781$	−4.57314	−0.163640
$782$	0.608262	0.0217514
$783$	0	0
$784$	4.71011	0.168218
$785$	0	0
$786$	0	0
$787$	−45.2989	−1.61473	−0.807366	−	0.590051i	$-0.799108\pi$
$787$	−45.2989	−1.61473	−0.807366	+	0.590051i	$0.799108\pi$
$788$	−45.9242	−1.63598
$789$	0	0
$790$	0	0
$791$	24.7362	0.879519
$792$	0	0
$793$	−47.3802	−1.68252
$794$	−0.370623	−0.0131529
$795$	0	0
$796$	48.9782	1.73599
$797$	29.3607	1.04001	0.520005	−	0.854163i	$-0.325930\pi$
$797$	29.3607	1.04001	0.520005	+	0.854163i	$0.325930\pi$
$798$	0	0
$799$	−6.22085	−0.220078
$800$	0	0
$801$	0	0
$802$	4.57630	0.161595
$803$	12.5547	0.443045
$804$	0	0
$805$	0	0
$806$	−2.93120	−0.103247
$807$	0	0
$808$	−6.58694	−0.231728
$809$	−5.04830	−0.177489	−0.0887444	−	0.996054i	$-0.528285\pi$
$809$	−5.04830	−0.177489	−0.0887444	+	0.996054i	$0.528285\pi$
$810$	0	0
$811$	54.3374	1.90805	0.954023	−	0.299734i	$-0.0968981\pi$
$811$	54.3374	1.90805	0.954023	+	0.299734i	$0.0968981\pi$
$812$	−3.73984	−0.131243
$813$	0	0
$814$	−1.73074	−0.0606623
$815$	0	0
$816$	0	0
$817$	−8.56284	−0.299576
$818$	0.630464	0.0220437
$819$	0	0
$820$	0	0
$821$	−3.05948	−0.106777	−0.0533883	−	0.998574i	$-0.517002\pi$
$821$	−3.05948	−0.106777	−0.0533883	+	0.998574i	$0.517002\pi$
$822$	0	0
$823$	−6.87523	−0.239656	−0.119828	−	0.992795i	$-0.538234\pi$
$823$	−6.87523	−0.239656	−0.119828	+	0.992795i	$0.538234\pi$
$824$	7.27057	0.253282
$825$	0	0
$826$	−0.771540	−0.0268453
$827$	24.2438	0.843040	0.421520	−	0.906819i	$-0.361497\pi$
$827$	24.2438	0.843040	0.421520	+	0.906819i	$0.361497\pi$
$828$	0	0
$829$	15.7734	0.547832	0.273916	−	0.961754i	$-0.411681\pi$
$829$	15.7734	0.547832	0.273916	+	0.961754i	$0.411681\pi$
$830$	0	0
$831$	0	0
$832$	−47.0811	−1.63224
$833$	1.21033	0.0419356
$834$	0	0
$835$	0	0
$836$	−50.4935	−1.74635
$837$	0	0
$838$	−3.91767	−0.135334
$839$	−9.98832	−0.344835	−0.172418	−	0.985024i	$-0.555158\pi$
$839$	−9.98832	−0.344835	−0.172418	+	0.985024i	$0.555158\pi$
$840$	0	0
$841$	−28.5663	−0.985045
$842$	−0.968080	−0.0333622
$843$	0	0
$844$	8.46533	0.291389
$845$	0	0
$846$	0	0
$847$	10.8920	0.374255
$848$	38.6336	1.32668
$849$	0	0
$850$	0	0
$851$	−15.0965	−0.517501
$852$	0	0
$853$	−31.1852	−1.06776	−0.533880	−	0.845560i	$-0.679266\pi$
$853$	−31.1852	−1.06776	−0.533880	+	0.845560i	$0.679266\pi$
$854$	2.93816	0.100542
$855$	0	0
$856$	3.55854	0.121629
$857$	−26.4712	−0.904240	−0.452120	−	0.891957i	$-0.649332\pi$
$857$	−26.4712	−0.904240	−0.452120	+	0.891957i	$0.649332\pi$
$858$	0	0
$859$	22.7223	0.775273	0.387637	−	0.921812i	$-0.373292\pi$
$859$	22.7223	0.775273	0.387637	+	0.921812i	$0.373292\pi$
$860$	0	0
$861$	0	0
$862$	1.02748	0.0349963
$863$	−35.3962	−1.20490	−0.602451	−	0.798156i	$-0.705809\pi$
$863$	−35.3962	−1.20490	−0.602451	+	0.798156i	$0.705809\pi$
$864$	0	0
$865$	0	0
$866$	4.34719	0.147723
$867$	0	0
$868$	−19.8749	−0.674597
$869$	−19.2268	−0.652225
$870$	0	0
$871$	1.59942	0.0541944
$872$	−1.38333	−0.0468455
$873$	0	0
$874$	4.02810	0.136252
$875$	0	0
$876$	0	0
$877$	1.09791	0.0370736	0.0185368	−	0.999828i	$-0.494099\pi$
$877$	1.09791	0.0370736	0.0185368	+	0.999828i	$0.494099\pi$
$878$	1.80371	0.0608724
$879$	0	0
$880$	0	0
$881$	16.5399	0.557245	0.278622	−	0.960401i	$-0.410122\pi$
$881$	16.5399	0.557245	0.278622	+	0.960401i	$0.410122\pi$
$882$	0	0
$883$	22.1505	0.745425	0.372712	−	0.927947i	$-0.378428\pi$
$883$	22.1505	0.745425	0.372712	+	0.927947i	$0.378428\pi$
$884$	−12.3290	−0.414668
$885$	0	0
$886$	0.927707	0.0311669
$887$	19.5836	0.657553	0.328776	−	0.944408i	$-0.393364\pi$
$887$	19.5836	0.657553	0.328776	+	0.944408i	$0.393364\pi$
$888$	0	0
$889$	9.29955	0.311897
$890$	0	0
$891$	0	0
$892$	−7.24222	−0.242488
$893$	−41.1964	−1.37859
$894$	0	0
$895$	0	0
$896$	12.0665	0.403112
$897$	0	0
$898$	2.85120	0.0951458
$899$	2.30486	0.0768713
$900$	0	0
$901$	9.92750	0.330733
$902$	1.05762	0.0352149
$903$	0	0
$904$	4.62795	0.153923
$905$	0	0
$906$	0	0
$907$	38.3180	1.27233	0.636165	−	0.771553i	$-0.280520\pi$
$907$	38.3180	1.27233	0.636165	+	0.771553i	$0.280520\pi$
$908$	37.6587	1.24975
$909$	0	0
$910$	0	0
$911$	37.8395	1.25368	0.626840	−	0.779148i	$-0.284348\pi$
$911$	37.8395	1.25368	0.626840	+	0.779148i	$0.284348\pi$
$912$	0	0
$913$	−30.4522	−1.00782
$914$	4.07021	0.134631
$915$	0	0
$916$	41.3916	1.36762
$917$	9.87814	0.326205
$918$	0	0
$919$	−28.8996	−0.953309	−0.476655	−	0.879091i	$-0.658151\pi$
$919$	−28.8996	−0.953309	−0.476655	+	0.879091i	$0.658151\pi$
$920$	0	0
$921$	0	0
$922$	0.503883	0.0165945
$923$	−7.39461	−0.243397
$924$	0	0
$925$	0	0
$926$	−0.341228	−0.0112134
$927$	0	0
$928$	−1.05113	−0.0345051
$929$	47.2978	1.55179	0.775895	−	0.630862i	$-0.217299\pi$
$929$	47.2978	1.55179	0.775895	+	0.630862i	$0.217299\pi$
$930$	0	0
$931$	8.01521	0.262688
$932$	−1.35338	−0.0443313
$933$	0	0
$934$	−4.05471	−0.132674
$935$	0	0
$936$	0	0
$937$	−1.24572	−0.0406958	−0.0203479	−	0.999793i	$-0.506477\pi$
$937$	−1.24572	−0.0406958	−0.0203479	+	0.999793i	$0.506477\pi$
$938$	−0.0991839	−0.00323847
$939$	0	0
$940$	0	0
$941$	−37.9458	−1.23700	−0.618499	−	0.785785i	$-0.712259\pi$
$941$	−37.9458	−1.23700	−0.618499	+	0.785785i	$0.712259\pi$
$942$	0	0
$943$	9.22519	0.300413
$944$	7.78315	0.253320
$945$	0	0
$946$	0.669739	0.0217751
$947$	52.2986	1.69948	0.849738	−	0.527205i	$-0.176760\pi$
$947$	52.2986	1.69948	0.849738	+	0.527205i	$0.176760\pi$
$948$	0	0
$949$	20.3005	0.658982
$950$	0	0
$951$	0	0
$952$	1.53609	0.0497849
$953$	−0.806914	−0.0261385	−0.0130693	−	0.999915i	$-0.504160\pi$
$953$	−0.806914	−0.0261385	−0.0130693	+	0.999915i	$0.504160\pi$
$954$	0	0
$955$	0	0
$956$	57.4575	1.85831
$957$	0	0
$958$	1.95210	0.0630694
$959$	−42.0833	−1.35894
$960$	0	0
$961$	−18.7511	−0.604876
$962$	−2.79854	−0.0902285
$963$	0	0
$964$	35.8606	1.15499
$965$	0	0
$966$	0	0
$967$	27.3892	0.880777	0.440388	−	0.897807i	$-0.354841\pi$
$967$	27.3892	0.880777	0.440388	+	0.897807i	$0.354841\pi$
$968$	2.03781	0.0654978
$969$	0	0
$970$	0	0
$971$	−26.7596	−0.858757	−0.429378	−	0.903125i	$-0.641267\pi$
$971$	−26.7596	−0.858757	−0.429378	+	0.903125i	$0.641267\pi$
$972$	0	0
$973$	40.0817	1.28496
$974$	−3.22341	−0.103285
$975$	0	0
$976$	−29.6396	−0.948739
$977$	−2.64662	−0.0846730	−0.0423365	−	0.999103i	$-0.513480\pi$
$977$	−2.64662	−0.0846730	−0.0423365	+	0.999103i	$0.513480\pi$
$978$	0	0
$979$	−49.2496	−1.57402
$980$	0	0
$981$	0	0
$982$	−2.84470	−0.0907780
$983$	−33.0275	−1.05341	−0.526707	−	0.850047i	$-0.676573\pi$
$983$	−33.0275	−1.05341	−0.526707	+	0.850047i	$0.676573\pi$
$984$	0	0
$985$	0	0
$986$	−0.0886634	−0.00282362
$987$	0	0
$988$	−81.6461	−2.59751
$989$	5.84186	0.185760
$990$	0	0
$991$	−32.2132	−1.02329	−0.511643	−	0.859198i	$-0.670963\pi$
$991$	−32.2132	−1.02329	−0.511643	+	0.859198i	$0.670963\pi$
$992$	−5.58610	−0.177359
$993$	0	0
$994$	0.458557	0.0145446
$995$	0	0
$996$	0	0
$997$	52.7919	1.67194	0.835969	−	0.548777i	$-0.184907\pi$
$997$	52.7919	1.67194	0.835969	+	0.548777i	$0.184907\pi$
$998$	−0.539910	−0.0170905
$999$	0	0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3825.2.a.bh.1.3		4
3.2	odd	2		425.2.a.h.1.2		4
5.2	odd	4		765.2.b.c.154.4		8
5.3	odd	4		765.2.b.c.154.5		8
5.4	even	2		3825.2.a.bj.1.2		4
12.11	even	2		6800.2.a.bt.1.4		4
15.2	even	4		85.2.b.a.69.5	yes	8
15.8	even	4		85.2.b.a.69.4	✓	8
15.14	odd	2		425.2.a.g.1.3		4
51.50	odd	2		7225.2.a.w.1.2		4
60.23	odd	4		1360.2.e.d.1089.6		8
60.47	odd	4		1360.2.e.d.1089.3		8
60.59	even	2		6800.2.a.bw.1.1		4
255.152	even	4		1445.2.b.e.579.5		8
255.203	even	4		1445.2.b.e.579.4		8
255.254	odd	2		7225.2.a.v.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.b.a.69.4	✓	8	15.8	even	4
85.2.b.a.69.5	yes	8	15.2	even	4
425.2.a.g.1.3		4	15.14	odd	2
425.2.a.h.1.2		4	3.2	odd	2
765.2.b.c.154.4		8	5.2	odd	4
765.2.b.c.154.5		8	5.3	odd	4
1360.2.e.d.1089.3		8	60.47	odd	4
1360.2.e.d.1089.6		8	60.23	odd	4
1445.2.b.e.579.4		8	255.203	even	4
1445.2.b.e.579.5		8	255.152	even	4
3825.2.a.bh.1.3		4	1.1	even	1	trivial
3825.2.a.bj.1.2		4	5.4	even	2
6800.2.a.bt.1.4		4	12.11	even	2
6800.2.a.bw.1.1		4	60.59	even	2
7225.2.a.v.1.3		4	255.254	odd	2
7225.2.a.w.1.2		4	51.50	odd	2

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

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

Label	3825.2.a.bh.1.3

Level	$3825$
Weight	$2$
Character	3825.1
Self dual	yes
Analytic conductor	$30.543$
Analytic rank	$0$
Dimension	$4$
CM	no
Inner twists	$1$