LMFDB - Embedded newform 3267.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3267,2,Mod(1,3267)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3267, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3267.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3267 = 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3267.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:	$26.0871263404$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.321.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 1 $ x^3 - x^2 - 4*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.46050$ of defining polynomial
Character	$\chi$	$=$	3267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46050 q^{2} +4.05408 q^{4} -0.406421 q^{5} -3.05408 q^{7} +5.05408 q^{8} -1.00000 q^{10} -6.32743 q^{13} -7.51459 q^{14} +4.32743 q^{16} -4.64766 q^{17} +3.00000 q^{19} -1.64766 q^{20} -7.64766 q^{23} -4.83482 q^{25} -15.5687 q^{26} -12.3815 q^{28} +4.10817 q^{29} -8.43560 q^{31} +0.539495 q^{32} -11.4356 q^{34} +1.24124 q^{35} +2.32743 q^{37} +7.38151 q^{38} -2.05408 q^{40} +12.5687 q^{41} +5.32743 q^{43} -18.8171 q^{46} +2.73385 q^{47} +2.32743 q^{49} -11.8961 q^{50} -25.6519 q^{52} -8.32743 q^{53} -15.4356 q^{56} +10.1082 q^{58} +5.89610 q^{59} +8.05408 q^{61} -20.7558 q^{62} -7.32743 q^{64} +2.57160 q^{65} -4.43560 q^{67} -18.8420 q^{68} +3.05408 q^{70} -3.94592 q^{71} +6.78074 q^{73} +5.72665 q^{74} +12.1623 q^{76} +5.50739 q^{79} -1.75876 q^{80} +30.9253 q^{82} +10.5438 q^{83} +1.88891 q^{85} +13.1082 q^{86} -2.05408 q^{89} +19.3245 q^{91} -31.0043 q^{92} +6.72665 q^{94} -1.21926 q^{95} -15.7630 q^{97} +5.72665 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{4} - 4 q^{5} + 6 q^{8} - 3 q^{10} - 9 q^{13} - 7 q^{14} + 3 q^{16} - 2 q^{17} + 9 q^{19} + 7 q^{20} - 11 q^{23} + 3 q^{25} - 22 q^{26} - 18 q^{28} - 6 q^{29} + 3 q^{31} + 8 q^{32} - 6 q^{34}+ \cdots + 18 q^{98}+O(q^{100}) $ 3 * q + q^2 + 3 * q^4 - 4 * q^5 + 6 * q^8 - 3 * q^10 - 9 * q^13 - 7 * q^14 + 3 * q^16 - 2 * q^17 + 9 * q^19 + 7 * q^20 - 11 * q^23 + 3 * q^25 - 22 * q^26 - 18 * q^28 - 6 * q^29 + 3 * q^31 + 8 * q^32 - 6 * q^34 - 11 * q^35 - 3 * q^37 + 3 * q^38 + 3 * q^40 + 13 * q^41 + 6 * q^43 - 9 * q^46 + q^47 - 3 * q^49 - q^50 - 12 * q^52 - 15 * q^53 - 18 * q^56 + 12 * q^58 - 17 * q^59 + 15 * q^61 - 32 * q^62 - 12 * q^64 + 28 * q^65 + 15 * q^67 - 31 * q^68 - 21 * q^71 + 12 * q^73 + 18 * q^74 + 9 * q^76 + 9 * q^79 - 20 * q^80 + 27 * q^82 - 15 * q^83 - 21 * q^85 + 21 * q^86 + 3 * q^89 + 3 * q^91 - 40 * q^92 + 21 * q^94 - 12 * q^95 - 9 * q^97 + 18 * 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 $

$2$	2.46050	1.73984	0.869920	−	0.493193i	$-0.164170\pi$
$2$	2.46050	1.73984	0.869920	+	0.493193i	$0.164170\pi$
$3$	0	0
$3$	0	0
$4$	4.05408	2.02704
$5$	−0.406421	−0.181757	−0.0908784	−	0.995862i	$-0.528967\pi$
$5$	−0.406421	−0.181757	−0.0908784	+	0.995862i	$0.528967\pi$
$6$	0	0
$7$	−3.05408	−1.15434	−0.577168	−	0.816626i	$-0.695842\pi$
$7$	−3.05408	−1.15434	−0.577168	+	0.816626i	$0.695842\pi$
$8$	5.05408	1.78689
$9$	0	0
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−6.32743	−1.75491	−0.877457	−	0.479656i	$-0.840762\pi$
$13$	−6.32743	−1.75491	−0.877457	+	0.479656i	$0.840762\pi$
$14$	−7.51459	−2.00836
$15$	0	0
$16$	4.32743	1.08186
$17$	−4.64766	−1.12722	−0.563612	−	0.826040i	$-0.690589\pi$
$17$	−4.64766	−1.12722	−0.563612	+	0.826040i	$0.690589\pi$
$18$	0	0
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−1.64766	−0.368429
$21$	0	0
$22$	0	0
$23$	−7.64766	−1.59465	−0.797324	−	0.603551i	$-0.793752\pi$
$23$	−7.64766	−1.59465	−0.797324	+	0.603551i	$0.793752\pi$
$24$	0	0
$25$	−4.83482	−0.966964
$26$	−15.5687	−3.05327
$27$	0	0
$28$	−12.3815	−2.33989
$29$	4.10817	0.762868	0.381434	−	0.924396i	$-0.375430\pi$
$29$	4.10817	0.762868	0.381434	+	0.924396i	$0.375430\pi$
$30$	0	0
$31$	−8.43560	−1.51508	−0.757539	−	0.652790i	$-0.773599\pi$
$31$	−8.43560	−1.51508	−0.757539	+	0.652790i	$0.773599\pi$
$32$	0.539495	0.0953702
$33$	0	0
$34$	−11.4356	−1.96119
$35$	1.24124	0.209808
$36$	0	0
$37$	2.32743	0.382627	0.191314	−	0.981529i	$-0.438725\pi$
$37$	2.32743	0.382627	0.191314	+	0.981529i	$0.438725\pi$
$38$	7.38151	1.19744
$39$	0	0
$40$	−2.05408	−0.324779
$41$	12.5687	1.96290	0.981448	−	0.191726i	$-0.0614085\pi$
$41$	12.5687	1.96290	0.981448	+	0.191726i	$0.0614085\pi$
$42$	0	0
$43$	5.32743	0.812426	0.406213	−	0.913779i	$-0.366849\pi$
$43$	5.32743	0.812426	0.406213	+	0.913779i	$0.366849\pi$
$44$	0	0
$45$	0	0
$46$	−18.8171	−2.77443
$47$	2.73385	0.398773	0.199387	−	0.979921i	$-0.436105\pi$
$47$	2.73385	0.398773	0.199387	+	0.979921i	$0.436105\pi$
$48$	0	0
$49$	2.32743	0.332490
$50$	−11.8961	−1.68236
$51$	0	0
$52$	−25.6519	−3.55728
$53$	−8.32743	−1.14386	−0.571930	−	0.820302i	$-0.693805\pi$
$53$	−8.32743	−1.14386	−0.571930	+	0.820302i	$0.693805\pi$
$54$	0	0
$55$	0	0
$56$	−15.4356	−2.06267
$57$	0	0
$58$	10.1082	1.32727
$59$	5.89610	0.767607	0.383804	−	0.923415i	$-0.374614\pi$
$59$	5.89610	0.767607	0.383804	+	0.923415i	$0.374614\pi$
$60$	0	0
$61$	8.05408	1.03122	0.515610	−	0.856823i	$-0.327565\pi$
$61$	8.05408	1.03122	0.515610	+	0.856823i	$0.327565\pi$
$62$	−20.7558	−2.63599
$63$	0	0
$64$	−7.32743	−0.915929
$65$	2.57160	0.318968
$66$	0	0
$67$	−4.43560	−0.541895	−0.270947	−	0.962594i	$-0.587337\pi$
$67$	−4.43560	−0.541895	−0.270947	+	0.962594i	$0.587337\pi$
$68$	−18.8420	−2.28493
$69$	0	0
$70$	3.05408	0.365033
$71$	−3.94592	−0.468294	−0.234147	−	0.972201i	$-0.575230\pi$
$71$	−3.94592	−0.468294	−0.234147	+	0.972201i	$0.575230\pi$
$72$	0	0
$73$	6.78074	0.793625	0.396813	−	0.917900i	$-0.370116\pi$
$73$	6.78074	0.793625	0.396813	+	0.917900i	$0.370116\pi$
$74$	5.72665	0.665710
$75$	0	0
$76$	12.1623	1.39511
$77$	0	0
$78$	0	0
$79$	5.50739	0.619630	0.309815	−	0.950797i	$-0.399733\pi$
$79$	5.50739	0.619630	0.309815	+	0.950797i	$0.399733\pi$
$80$	−1.75876	−0.196635
$81$	0	0
$82$	30.9253	3.41513
$83$	10.5438	1.15733	0.578664	−	0.815566i	$-0.303574\pi$
$83$	10.5438	1.15733	0.578664	+	0.815566i	$0.303574\pi$
$84$	0	0
$85$	1.88891	0.204881
$86$	13.1082	1.41349
$87$	0	0
$88$	0	0
$89$	−2.05408	−0.217732	−0.108866	−	0.994056i	$-0.534722\pi$
$89$	−2.05408	−0.217732	−0.108866	+	0.994056i	$0.534722\pi$
$90$	0	0
$91$	19.3245	2.02576
$92$	−31.0043	−3.23242
$93$	0	0
$94$	6.72665	0.693801
$95$	−1.21926	−0.125094
$96$	0	0
$97$	−15.7630	−1.60049	−0.800247	−	0.599671i	$-0.795298\pi$
$97$	−15.7630	−1.60049	−0.800247	+	0.599671i	$0.795298\pi$
$98$	5.72665	0.578479
$99$	0	0
$100$	−19.6008	−1.96008
$101$	2.46770	0.245546	0.122773	−	0.992435i	$-0.460821\pi$
$101$	2.46770	0.245546	0.122773	+	0.992435i	$0.460821\pi$
$102$	0	0
$103$	9.65486	0.951322	0.475661	−	0.879629i	$-0.342209\pi$
$103$	9.65486	0.951322	0.475661	+	0.879629i	$0.342209\pi$
$104$	−31.9794	−3.13583
$105$	0	0
$106$	−20.4897	−1.99013
$107$	−16.2704	−1.57292	−0.786460	−	0.617641i	$-0.788089\pi$
$107$	−16.2704	−1.57292	−0.786460	+	0.617641i	$0.788089\pi$
$108$	0	0
$109$	−1.67257	−0.160203	−0.0801016	−	0.996787i	$-0.525524\pi$
$109$	−1.67257	−0.160203	−0.0801016	+	0.996787i	$0.525524\pi$
$110$	0	0
$111$	0	0
$112$	−13.2163	−1.24883
$113$	−13.9282	−1.31026	−0.655128	−	0.755518i	$-0.727385\pi$
$113$	−13.9282	−1.31026	−0.655128	+	0.755518i	$0.727385\pi$
$114$	0	0
$115$	3.10817	0.289838
$116$	16.6549	1.54637
$117$	0	0
$118$	14.5074	1.33551
$119$	14.1944	1.30119
$120$	0	0
$121$	0	0
$122$	19.8171	1.79416
$123$	0	0
$124$	−34.1986	−3.07113
$125$	3.99707	0.357509
$126$	0	0
$127$	−1.45331	−0.128960	−0.0644801	−	0.997919i	$-0.520539\pi$
$127$	−1.45331	−0.128960	−0.0644801	+	0.997919i	$0.520539\pi$
$128$	−19.1082	−1.68894
$129$	0	0
$130$	6.32743	0.554952
$131$	−0.708945	−0.0619408	−0.0309704	−	0.999520i	$-0.509860\pi$
$131$	−0.708945	−0.0619408	−0.0309704	+	0.999520i	$0.509860\pi$
$132$	0	0
$133$	−9.16225	−0.794468
$134$	−10.9138	−0.942810
$135$	0	0
$136$	−23.4897	−2.01422
$137$	−9.26615	−0.791661	−0.395830	−	0.918324i	$-0.629543\pi$
$137$	−9.26615	−0.791661	−0.395830	+	0.918324i	$0.629543\pi$
$138$	0	0
$139$	−12.6008	−1.06878	−0.534392	−	0.845237i	$-0.679459\pi$
$139$	−12.6008	−1.06878	−0.534392	+	0.845237i	$0.679459\pi$
$140$	5.03210	0.425290
$141$	0	0
$142$	−9.70895	−0.814757
$143$	0	0
$144$	0	0
$145$	−1.66964	−0.138656
$146$	16.6840	1.38078
$147$	0	0
$148$	9.43560	0.775601
$149$	−9.44280	−0.773584	−0.386792	−	0.922167i	$-0.626417\pi$
$149$	−9.44280	−0.773584	−0.386792	+	0.922167i	$0.626417\pi$
$150$	0	0
$151$	−0.618485	−0.0503316	−0.0251658	−	0.999683i	$-0.508011\pi$
$151$	−0.618485	−0.0503316	−0.0251658	+	0.999683i	$0.508011\pi$
$152$	15.1623	1.22982
$153$	0	0
$154$	0	0
$155$	3.42840	0.275376
$156$	0	0
$157$	13.4897	1.07659	0.538297	−	0.842755i	$-0.319068\pi$
$157$	13.4897	1.07659	0.538297	+	0.842755i	$0.319068\pi$
$158$	13.5510	1.07806
$159$	0	0
$160$	−0.219262	−0.0173342
$161$	23.3566	1.84076
$162$	0	0
$163$	2.78074	0.217804	0.108902	−	0.994052i	$-0.465266\pi$
$163$	2.78074	0.217804	0.108902	+	0.994052i	$0.465266\pi$
$164$	50.9545	3.97887
$165$	0	0
$166$	25.9430	2.01357
$167$	−10.6549	−0.824498	−0.412249	−	0.911071i	$-0.635257\pi$
$167$	−10.6549	−0.824498	−0.412249	+	0.911071i	$0.635257\pi$
$168$	0	0
$169$	27.0364	2.07972
$170$	4.64766	0.356460
$171$	0	0
$172$	21.5979	1.64682
$173$	−12.1623	−0.924679	−0.462339	−	0.886703i	$-0.652990\pi$
$173$	−12.1623	−0.924679	−0.462339	+	0.886703i	$0.652990\pi$
$174$	0	0
$175$	14.7660	1.11620
$176$	0	0
$177$	0	0
$178$	−5.05408	−0.378820
$179$	17.7630	1.32767	0.663836	−	0.747879i	$-0.268927\pi$
$179$	17.7630	1.32767	0.663836	+	0.747879i	$0.268927\pi$
$180$	0	0
$181$	−20.8712	−1.55134	−0.775672	−	0.631136i	$-0.782589\pi$
$181$	−20.8712	−1.55134	−0.775672	+	0.631136i	$0.782589\pi$
$182$	47.5480	3.52450
$183$	0	0
$184$	−38.6519	−2.84946
$185$	−0.945916	−0.0695451
$186$	0	0
$187$	0	0
$188$	11.0833	0.808330
$189$	0	0
$190$	−3.00000	−0.217643
$191$	−21.8492	−1.58095	−0.790477	−	0.612492i	$-0.790167\pi$
$191$	−21.8492	−1.58095	−0.790477	+	0.612492i	$0.790167\pi$
$192$	0	0
$193$	−5.94299	−0.427786	−0.213893	−	0.976857i	$-0.568614\pi$
$193$	−5.94299	−0.427786	−0.213893	+	0.976857i	$0.568614\pi$
$194$	−38.7850	−2.78460
$195$	0	0
$196$	9.43560	0.673971
$197$	18.5687	1.32296	0.661482	−	0.749961i	$-0.269928\pi$
$197$	18.5687	1.32296	0.661482	+	0.749961i	$0.269928\pi$
$198$	0	0
$199$	4.54377	0.322099	0.161050	−	0.986946i	$-0.448512\pi$
$199$	4.54377	0.322099	0.161050	+	0.986946i	$0.448512\pi$
$200$	−24.4356	−1.72786
$201$	0	0
$202$	6.07179	0.427210
$203$	−12.5467	−0.880605
$204$	0	0
$205$	−5.10817	−0.356770
$206$	23.7558	1.65515
$207$	0	0
$208$	−27.3815	−1.89857
$209$	0	0
$210$	0	0
$211$	−0.510317	−0.0351317	−0.0175658	−	0.999846i	$-0.505592\pi$
$211$	−0.510317	−0.0351317	−0.0175658	+	0.999846i	$0.505592\pi$
$212$	−33.7601	−2.31865
$213$	0	0
$214$	−40.0335	−2.73663
$215$	−2.16518	−0.147664
$216$	0	0
$217$	25.7630	1.74891
$218$	−4.11537	−0.278728
$219$	0	0
$220$	0	0
$221$	29.4078	1.97818
$222$	0	0
$223$	−1.72665	−0.115625	−0.0578126	−	0.998327i	$-0.518413\pi$
$223$	−1.72665	−0.115625	−0.0578126	+	0.998327i	$0.518413\pi$
$224$	−1.64766	−0.110089
$225$	0	0
$226$	−34.2704	−2.27963
$227$	11.4897	0.762597	0.381299	−	0.924452i	$-0.375477\pi$
$227$	11.4897	0.762597	0.381299	+	0.924452i	$0.375477\pi$
$228$	0	0
$229$	4.78074	0.315920	0.157960	−	0.987446i	$-0.449508\pi$
$229$	4.78074	0.315920	0.157960	+	0.987446i	$0.449508\pi$
$230$	7.64766	0.504272
$231$	0	0
$232$	20.7630	1.36316
$233$	−19.9282	−1.30554	−0.652770	−	0.757556i	$-0.726393\pi$
$233$	−19.9282	−1.30554	−0.652770	+	0.757556i	$0.726393\pi$
$234$	0	0
$235$	−1.11109	−0.0724798
$236$	23.9033	1.55597
$237$	0	0
$238$	34.9253	2.26387
$239$	−25.3815	−1.64179	−0.820897	−	0.571076i	$-0.806526\pi$
$239$	−25.3815	−1.64179	−0.820897	+	0.571076i	$0.806526\pi$
$240$	0	0
$241$	17.3245	1.11597	0.557985	−	0.829851i	$-0.311575\pi$
$241$	17.3245	1.11597	0.557985	+	0.829851i	$0.311575\pi$
$242$	0	0
$243$	0	0
$244$	32.6519	2.09033
$245$	−0.945916	−0.0604323
$246$	0	0
$247$	−18.9823	−1.20781
$248$	−42.6342	−2.70728
$249$	0	0
$250$	9.83482	0.622009
$251$	1.48541	0.0937583	0.0468792	−	0.998901i	$-0.485072\pi$
$251$	1.48541	0.0937583	0.0468792	+	0.998901i	$0.485072\pi$
$252$	0	0
$253$	0	0
$254$	−3.57587	−0.224370
$255$	0	0
$256$	−32.3609	−2.02256
$257$	12.7381	0.794582	0.397291	−	0.917693i	$-0.369950\pi$
$257$	12.7381	0.794582	0.397291	+	0.917693i	$0.369950\pi$
$258$	0	0
$259$	−7.10817	−0.441680
$260$	10.4255	0.646561
$261$	0	0
$262$	−1.74436	−0.107767
$263$	1.10097	0.0678888	0.0339444	−	0.999424i	$-0.489193\pi$
$263$	1.10097	0.0678888	0.0339444	+	0.999424i	$0.489193\pi$
$264$	0	0
$265$	3.38444	0.207904
$266$	−22.5438	−1.38225
$267$	0	0
$268$	−17.9823	−1.09844
$269$	1.79513	0.109451	0.0547256	−	0.998501i	$-0.482572\pi$
$269$	1.79513	0.109451	0.0547256	+	0.998501i	$0.482572\pi$
$270$	0	0
$271$	−23.0512	−1.40026	−0.700129	−	0.714016i	$-0.746874\pi$
$271$	−23.0512	−1.40026	−0.700129	+	0.714016i	$0.746874\pi$
$272$	−20.1124	−1.21950
$273$	0	0
$274$	−22.7994	−1.37736
$275$	0	0
$276$	0	0
$277$	27.5801	1.65713	0.828565	−	0.559893i	$-0.189158\pi$
$277$	27.5801	1.65713	0.828565	+	0.559893i	$0.189158\pi$
$278$	−31.0043	−1.85951
$279$	0	0
$280$	6.27335	0.374904
$281$	−5.74144	−0.342505	−0.171253	−	0.985227i	$-0.554781\pi$
$281$	−5.74144	−0.342505	−0.171253	+	0.985227i	$0.554781\pi$
$282$	0	0
$283$	31.7994	1.89028	0.945139	−	0.326668i	$-0.105926\pi$
$283$	31.7994	1.89028	0.945139	+	0.326668i	$0.105926\pi$
$284$	−15.9971	−0.949252
$285$	0	0
$286$	0	0
$287$	−38.3858	−2.26584
$288$	0	0
$289$	4.60078	0.270634
$290$	−4.10817	−0.241240
$291$	0	0
$292$	27.4897	1.60871
$293$	−15.8712	−0.927205	−0.463603	−	0.886043i	$-0.653443\pi$
$293$	−15.8712	−0.927205	−0.463603	+	0.886043i	$0.653443\pi$
$294$	0	0
$295$	−2.39630	−0.139518
$296$	11.7630	0.683712
$297$	0	0
$298$	−23.2340	−1.34591
$299$	48.3901	2.79847
$300$	0	0
$301$	−16.2704	−0.937811
$302$	−1.52179	−0.0875690
$303$	0	0
$304$	12.9823	0.744585
$305$	−3.27335	−0.187431
$306$	0	0
$307$	−3.89183	−0.222119	−0.111059	−	0.993814i	$-0.535424\pi$
$307$	−3.89183	−0.222119	−0.111059	+	0.993814i	$0.535424\pi$
$308$	0	0
$309$	0	0
$310$	8.43560	0.479110
$311$	20.3422	1.15350	0.576751	−	0.816920i	$-0.304320\pi$
$311$	20.3422	1.15350	0.576751	+	0.816920i	$0.304320\pi$
$312$	0	0
$313$	2.51032	0.141892	0.0709458	−	0.997480i	$-0.477398\pi$
$313$	2.51032	0.141892	0.0709458	+	0.997480i	$0.477398\pi$
$314$	33.1914	1.87310
$315$	0	0
$316$	22.3274	1.25602
$317$	−19.3523	−1.08694	−0.543468	−	0.839430i	$-0.682889\pi$
$317$	−19.3523	−1.08694	−0.543468	+	0.839430i	$0.682889\pi$
$318$	0	0
$319$	0	0
$320$	2.97802	0.166476
$321$	0	0
$322$	57.4690	3.20262
$323$	−13.9430	−0.775809
$324$	0	0
$325$	30.5920	1.69694
$326$	6.84202	0.378944
$327$	0	0
$328$	63.5231	3.50748
$329$	−8.34941	−0.460318
$330$	0	0
$331$	23.5438	1.29408	0.647041	−	0.762455i	$-0.276006\pi$
$331$	23.5438	1.29408	0.647041	+	0.762455i	$0.276006\pi$
$332$	42.7453	2.34595
$333$	0	0
$334$	−26.2163	−1.43449
$335$	1.80272	0.0984931
$336$	0	0
$337$	−10.3422	−0.563376	−0.281688	−	0.959506i	$-0.590894\pi$
$337$	−10.3422	−0.563376	−0.281688	+	0.959506i	$0.590894\pi$
$338$	66.5231	3.61838
$339$	0	0
$340$	7.65779	0.415302
$341$	0	0
$342$	0	0
$343$	14.2704	0.770530
$344$	26.9253	1.45171
$345$	0	0
$346$	−29.9253	−1.60879
$347$	−23.0833	−1.23917	−0.619587	−	0.784928i	$-0.712700\pi$
$347$	−23.0833	−1.23917	−0.619587	+	0.784928i	$0.712700\pi$
$348$	0	0
$349$	28.5801	1.52986	0.764930	−	0.644113i	$-0.222774\pi$
$349$	28.5801	1.52986	0.764930	+	0.644113i	$0.222774\pi$
$350$	36.3317	1.94201
$351$	0	0
$352$	0	0
$353$	−1.90662	−0.101479	−0.0507394	−	0.998712i	$-0.516158\pi$
$353$	−1.90662	−0.101479	−0.0507394	+	0.998712i	$0.516158\pi$
$354$	0	0
$355$	1.60370	0.0851156
$356$	−8.32743	−0.441353
$357$	0	0
$358$	43.7060	2.30993
$359$	−17.2455	−0.910183	−0.455092	−	0.890445i	$-0.650394\pi$
$359$	−17.2455	−0.910183	−0.455092	+	0.890445i	$0.650394\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−51.3537	−2.69909
$363$	0	0
$364$	78.3432	4.10630
$365$	−2.75583	−0.144247
$366$	0	0
$367$	−6.09338	−0.318072	−0.159036	−	0.987273i	$-0.550839\pi$
$367$	−6.09338	−0.318072	−0.159036	+	0.987273i	$0.550839\pi$
$368$	−33.0947	−1.72518
$369$	0	0
$370$	−2.32743	−0.120997
$371$	25.4327	1.32040
$372$	0	0
$373$	8.12588	0.420742	0.210371	−	0.977622i	$-0.432533\pi$
$373$	8.12588	0.420742	0.210371	+	0.977622i	$0.432533\pi$
$374$	0	0
$375$	0	0
$376$	13.8171	0.712563
$377$	−25.9941	−1.33877
$378$	0	0
$379$	0.690278	0.0354572	0.0177286	−	0.999843i	$-0.494357\pi$
$379$	0.690278	0.0354572	0.0177286	+	0.999843i	$0.494357\pi$
$380$	−4.94299	−0.253570
$381$	0	0
$382$	−53.7601	−2.75061
$383$	−11.7558	−0.600695	−0.300347	−	0.953830i	$-0.597103\pi$
$383$	−11.7558	−0.600695	−0.300347	+	0.953830i	$0.597103\pi$
$384$	0	0
$385$	0	0
$386$	−14.6228	−0.744279
$387$	0	0
$388$	−63.9046	−3.24427
$389$	−21.0364	−1.06659	−0.533293	−	0.845930i	$-0.679046\pi$
$389$	−21.0364	−1.06659	−0.533293	+	0.845930i	$0.679046\pi$
$390$	0	0
$391$	35.5438	1.79753
$392$	11.7630	0.594123
$393$	0	0
$394$	45.6883	2.30174
$395$	−2.23832	−0.112622
$396$	0	0
$397$	−12.6185	−0.633304	−0.316652	−	0.948542i	$-0.602559\pi$
$397$	−12.6185	−0.633304	−0.316652	+	0.948542i	$0.602559\pi$
$398$	11.1800	0.560401
$399$	0	0
$400$	−20.9224	−1.04612
$401$	−12.3025	−0.614359	−0.307179	−	0.951652i	$-0.599385\pi$
$401$	−12.3025	−0.614359	−0.307179	+	0.951652i	$0.599385\pi$
$402$	0	0
$403$	53.3757	2.65883
$404$	10.0043	0.497731
$405$	0	0
$406$	−30.8712	−1.53211
$407$	0	0
$408$	0	0
$409$	10.8171	0.534872	0.267436	−	0.963576i	$-0.413824\pi$
$409$	10.8171	0.534872	0.267436	+	0.963576i	$0.413824\pi$
$410$	−12.5687	−0.620723
$411$	0	0
$412$	39.1416	1.92837
$413$	−18.0072	−0.886076
$414$	0	0
$415$	−4.28520	−0.210352
$416$	−3.41362	−0.167366
$417$	0	0
$418$	0	0
$419$	−16.5366	−0.807864	−0.403932	−	0.914789i	$-0.632357\pi$
$419$	−16.5366	−0.807864	−0.403932	+	0.914789i	$0.632357\pi$
$420$	0	0
$421$	34.5979	1.68620	0.843098	−	0.537760i	$-0.180729\pi$
$421$	34.5979	1.68620	0.843098	+	0.537760i	$0.180729\pi$
$422$	−1.25564	−0.0611235
$423$	0	0
$424$	−42.0875	−2.04395
$425$	22.4706	1.08999
$426$	0	0
$427$	−24.5979	−1.19037
$428$	−65.9617	−3.18838
$429$	0	0
$430$	−5.32743	−0.256912
$431$	−18.7601	−0.903642	−0.451821	−	0.892109i	$-0.649226\pi$
$431$	−18.7601	−0.903642	−0.451821	+	0.892109i	$0.649226\pi$
$432$	0	0
$433$	27.9253	1.34200	0.671002	−	0.741456i	$-0.265864\pi$
$433$	27.9253	1.34200	0.671002	+	0.741456i	$0.265864\pi$
$434$	63.3901	3.04282
$435$	0	0
$436$	−6.78074	−0.324738
$437$	−22.9430	−1.09751
$438$	0	0
$439$	−18.3274	−0.874721	−0.437360	−	0.899286i	$-0.644087\pi$
$439$	−18.3274	−0.874721	−0.437360	+	0.899286i	$0.644087\pi$
$440$	0	0
$441$	0	0
$442$	72.3580	3.44172
$443$	15.8640	0.753721	0.376861	−	0.926270i	$-0.377004\pi$
$443$	15.8640	0.753721	0.376861	+	0.926270i	$0.377004\pi$
$444$	0	0
$445$	0.834822	0.0395744
$446$	−4.24844	−0.201169
$447$	0	0
$448$	22.3786	1.05729
$449$	−33.4796	−1.58000	−0.789999	−	0.613108i	$-0.789919\pi$
$449$	−33.4796	−1.58000	−0.789999	+	0.613108i	$0.789919\pi$
$450$	0	0
$451$	0	0
$452$	−56.4661	−2.65594
$453$	0	0
$454$	28.2704	1.32680
$455$	−7.85388	−0.368195
$456$	0	0
$457$	−6.68735	−0.312821	−0.156411	−	0.987692i	$-0.549992\pi$
$457$	−6.68735	−0.312821	−0.156411	+	0.987692i	$0.549992\pi$
$458$	11.7630	0.549650
$459$	0	0
$460$	12.6008	0.587514
$461$	−21.8348	−1.01695	−0.508475	−	0.861077i	$-0.669790\pi$
$461$	−21.8348	−1.01695	−0.508475	+	0.861077i	$0.669790\pi$
$462$	0	0
$463$	−18.5438	−0.861802	−0.430901	−	0.902399i	$-0.641804\pi$
$463$	−18.5438	−0.861802	−0.430901	+	0.902399i	$0.641804\pi$
$464$	17.7778	0.825314
$465$	0	0
$466$	−49.0335	−2.27143
$467$	18.3097	0.847273	0.423636	−	0.905832i	$-0.360753\pi$
$467$	18.3097	0.847273	0.423636	+	0.905832i	$0.360753\pi$
$468$	0	0
$469$	13.5467	0.625528
$470$	−2.73385	−0.126103
$471$	0	0
$472$	29.7994	1.37163
$473$	0	0
$474$	0	0
$475$	−14.5045	−0.665511
$476$	57.5451	2.63758
$477$	0	0
$478$	−62.4513	−2.85646
$479$	−8.85973	−0.404811	−0.202406	−	0.979302i	$-0.564876\pi$
$479$	−8.85973	−0.404811	−0.202406	+	0.979302i	$0.564876\pi$
$480$	0	0
$481$	−14.7267	−0.671478
$482$	42.6270	1.94161
$483$	0	0
$484$	0	0
$485$	6.40642	0.290901
$486$	0	0
$487$	−19.9459	−0.903836	−0.451918	−	0.892060i	$-0.649260\pi$
$487$	−19.9459	−0.903836	−0.451918	+	0.892060i	$0.649260\pi$
$488$	40.7060	1.84267
$489$	0	0
$490$	−2.32743	−0.105143
$491$	34.9650	1.57795	0.788974	−	0.614427i	$-0.210613\pi$
$491$	34.9650	1.57795	0.788974	+	0.614427i	$0.210613\pi$
$492$	0	0
$493$	−19.0934	−0.859923
$494$	−46.7060	−2.10140
$495$	0	0
$496$	−36.5045	−1.63910
$497$	12.0512	0.540568
$498$	0	0
$499$	12.4327	0.556563	0.278281	−	0.960500i	$-0.410235\pi$
$499$	12.4327	0.556563	0.278281	+	0.960500i	$0.410235\pi$
$500$	16.2045	0.724686
$501$	0	0
$502$	3.65486	0.163124
$503$	5.46050	0.243472	0.121736	−	0.992563i	$-0.461154\pi$
$503$	5.46050	0.243472	0.121736	+	0.992563i	$0.461154\pi$
$504$	0	0
$505$	−1.00293	−0.0446296
$506$	0	0
$507$	0	0
$508$	−5.89183	−0.261408
$509$	−7.23405	−0.320643	−0.160322	−	0.987065i	$-0.551253\pi$
$509$	−7.23405	−0.320643	−0.160322	+	0.987065i	$0.551253\pi$
$510$	0	0
$511$	−20.7089	−0.916110
$512$	−41.4078	−1.82998
$513$	0	0
$514$	31.3422	1.38245
$515$	−3.92393	−0.172909
$516$	0	0
$517$	0	0
$518$	−17.4897	−0.768453
$519$	0	0
$520$	12.9971	0.569959
$521$	8.03930	0.352208	0.176104	−	0.984372i	$-0.443650\pi$
$521$	8.03930	0.352208	0.176104	+	0.984372i	$0.443650\pi$
$522$	0	0
$523$	−6.21926	−0.271949	−0.135975	−	0.990712i	$-0.543417\pi$
$523$	−6.21926	−0.271949	−0.135975	+	0.990712i	$0.543417\pi$
$524$	−2.87412	−0.125557
$525$	0	0
$526$	2.70895	0.118116
$527$	39.2058	1.70783
$528$	0	0
$529$	35.4868	1.54290
$530$	8.32743	0.361720
$531$	0	0
$532$	−37.1445	−1.61042
$533$	−79.5274	−3.44471
$534$	0	0
$535$	6.61264	0.285889
$536$	−22.4179	−0.968305
$537$	0	0
$538$	4.41693	0.190427
$539$	0	0
$540$	0	0
$541$	13.8377	0.594931	0.297466	−	0.954733i	$-0.403859\pi$
$541$	13.8377	0.594931	0.297466	+	0.954733i	$0.403859\pi$
$542$	−56.7175	−2.43622
$543$	0	0
$544$	−2.50739	−0.107504
$545$	0.679767	0.0291180
$546$	0	0
$547$	13.7237	0.586784	0.293392	−	0.955992i	$-0.405216\pi$
$547$	13.7237	0.586784	0.293392	+	0.955992i	$0.405216\pi$
$548$	−37.5657	−1.60473
$549$	0	0
$550$	0	0
$551$	12.3245	0.525042
$552$	0	0
$553$	−16.8200	−0.715261
$554$	67.8611	2.88314
$555$	0	0
$556$	−51.0846	−2.16647
$557$	−36.6634	−1.55348	−0.776739	−	0.629822i	$-0.783128\pi$
$557$	−36.6634	−1.55348	−0.776739	+	0.629822i	$0.783128\pi$
$558$	0	0
$559$	−33.7089	−1.42574
$560$	5.37139	0.226983
$561$	0	0
$562$	−14.1268	−0.595905
$563$	25.6257	1.07999	0.539997	−	0.841667i	$-0.318425\pi$
$563$	25.6257	1.07999	0.539997	+	0.841667i	$0.318425\pi$
$564$	0	0
$565$	5.66071	0.238148
$566$	78.2426	3.28878
$567$	0	0
$568$	−19.9430	−0.836789
$569$	17.4150	0.730073	0.365037	−	0.930993i	$-0.381056\pi$
$569$	17.4150	0.730073	0.365037	+	0.930993i	$0.381056\pi$
$570$	0	0
$571$	11.3304	0.474161	0.237080	−	0.971490i	$-0.423810\pi$
$571$	11.3304	0.474161	0.237080	+	0.971490i	$0.423810\pi$
$572$	0	0
$573$	0	0
$574$	−94.4484	−3.94220
$575$	36.9751	1.54197
$576$	0	0
$577$	−7.52218	−0.313152	−0.156576	−	0.987666i	$-0.550046\pi$
$577$	−7.52218	−0.313152	−0.156576	+	0.987666i	$0.550046\pi$
$578$	11.3202	0.470860
$579$	0	0
$580$	−6.76888	−0.281062
$581$	−32.2016	−1.33595
$582$	0	0
$583$	0	0
$584$	34.2704	1.41812
$585$	0	0
$586$	−39.0512	−1.61319
$587$	5.54242	0.228760	0.114380	−	0.993437i	$-0.463512\pi$
$587$	5.54242	0.228760	0.114380	+	0.993437i	$0.463512\pi$
$588$	0	0
$589$	−25.3068	−1.04275
$590$	−5.89610	−0.242739
$591$	0	0
$592$	10.0718	0.413948
$593$	−3.48114	−0.142953	−0.0714766	−	0.997442i	$-0.522771\pi$
$593$	−3.48114	−0.142953	−0.0714766	+	0.997442i	$0.522771\pi$
$594$	0	0
$595$	−5.76888	−0.236501
$596$	−38.2819	−1.56809
$597$	0	0
$598$	119.064	4.86889
$599$	−11.0249	−0.450465	−0.225233	−	0.974305i	$-0.572314\pi$
$599$	−11.0249	−0.450465	−0.225233	+	0.974305i	$0.572314\pi$
$600$	0	0
$601$	−21.8171	−0.889939	−0.444969	−	0.895546i	$-0.646785\pi$
$601$	−21.8171	−0.889939	−0.444969	+	0.895546i	$0.646785\pi$
$602$	−40.0335	−1.63164
$603$	0	0
$604$	−2.50739	−0.102024
$605$	0	0
$606$	0	0
$607$	−7.17996	−0.291426	−0.145713	−	0.989327i	$-0.546548\pi$
$607$	−7.17996	−0.291426	−0.145713	+	0.989327i	$0.546548\pi$
$608$	1.61849	0.0656383
$609$	0	0
$610$	−8.05408	−0.326100
$611$	−17.2983	−0.699812
$612$	0	0
$613$	−36.0335	−1.45538	−0.727689	−	0.685908i	$-0.759405\pi$
$613$	−36.0335	−1.45538	−0.727689	+	0.685908i	$0.759405\pi$
$614$	−9.57587	−0.386451
$615$	0	0
$616$	0	0
$617$	−44.4002	−1.78748	−0.893742	−	0.448581i	$-0.851929\pi$
$617$	−44.4002	−1.78748	−0.893742	+	0.448581i	$0.851929\pi$
$618$	0	0
$619$	1.19475	0.0480209	0.0240104	−	0.999712i	$-0.492357\pi$
$619$	1.19475	0.0480209	0.0240104	+	0.999712i	$0.492357\pi$
$620$	13.8990	0.558198
$621$	0	0
$622$	50.0521	2.00691
$623$	6.27335	0.251336
$624$	0	0
$625$	22.5496	0.901985
$626$	6.17665	0.246868
$627$	0	0
$628$	54.6883	2.18230
$629$	−10.8171	−0.431307
$630$	0	0
$631$	16.3245	0.649868	0.324934	−	0.945737i	$-0.394658\pi$
$631$	16.3245	0.649868	0.324934	+	0.945737i	$0.394658\pi$
$632$	27.8348	1.10721
$633$	0	0
$634$	−47.6165	−1.89109
$635$	0.590654	0.0234394
$636$	0	0
$637$	−14.7267	−0.583491
$638$	0	0
$639$	0	0
$640$	7.76595	0.306976
$641$	22.1082	0.873220	0.436610	−	0.899651i	$-0.356179\pi$
$641$	22.1082	0.873220	0.436610	+	0.899651i	$0.356179\pi$
$642$	0	0
$643$	−34.1623	−1.34723	−0.673614	−	0.739083i	$-0.735259\pi$
$643$	−34.1623	−1.34723	−0.673614	+	0.739083i	$0.735259\pi$
$644$	94.6897	3.73130
$645$	0	0
$646$	−34.3068	−1.34978
$647$	−22.2848	−0.876107	−0.438053	−	0.898949i	$-0.644332\pi$
$647$	−22.2848	−0.876107	−0.438053	+	0.898949i	$0.644332\pi$
$648$	0	0
$649$	0	0
$650$	75.2718	2.95240
$651$	0	0
$652$	11.2733	0.441498
$653$	−14.8813	−0.582351	−0.291176	−	0.956670i	$-0.594046\pi$
$653$	−14.8813	−0.582351	−0.291176	+	0.956670i	$0.594046\pi$
$654$	0	0
$655$	0.288130	0.0112582
$656$	54.3901	2.12358
$657$	0	0
$658$	−20.5438	−0.800879
$659$	42.7457	1.66514	0.832568	−	0.553923i	$-0.186870\pi$
$659$	42.7457	1.66514	0.832568	+	0.553923i	$0.186870\pi$
$660$	0	0
$661$	19.7237	0.767164	0.383582	−	0.923507i	$-0.374690\pi$
$661$	19.7237	0.767164	0.383582	+	0.923507i	$0.374690\pi$
$662$	57.9296	2.25150
$663$	0	0
$664$	53.2891	2.06802
$665$	3.72373	0.144400
$666$	0	0
$667$	−31.4179	−1.21651
$668$	−43.1957	−1.67129
$669$	0	0
$670$	4.43560	0.171362
$671$	0	0
$672$	0	0
$673$	−30.3580	−1.17021	−0.585107	−	0.810956i	$-0.698947\pi$
$673$	−30.3580	−1.17021	−0.585107	+	0.810956i	$0.698947\pi$
$674$	−25.4471	−0.980184
$675$	0	0
$676$	109.608	4.21568
$677$	19.2340	0.739224	0.369612	−	0.929186i	$-0.379491\pi$
$677$	19.2340	0.739224	0.369612	+	0.929186i	$0.379491\pi$
$678$	0	0
$679$	48.1416	1.84751
$680$	9.54669	0.366099
$681$	0	0
$682$	0	0
$683$	28.8391	1.10350	0.551749	−	0.834010i	$-0.313961\pi$
$683$	28.8391	1.10350	0.551749	+	0.834010i	$0.313961\pi$
$684$	0	0
$685$	3.76595	0.143890
$686$	35.1124	1.34060
$687$	0	0
$688$	23.0541	0.878929
$689$	52.6912	2.00738
$690$	0	0
$691$	13.5045	0.513734	0.256867	−	0.966447i	$-0.417310\pi$
$691$	13.5045	0.513734	0.256867	+	0.966447i	$0.417310\pi$
$692$	−49.3068	−1.87436
$693$	0	0
$694$	−56.7965	−2.15596
$695$	5.12122	0.194259
$696$	0	0
$697$	−58.4150	−2.21262
$698$	70.3216	2.66171
$699$	0	0
$700$	59.8624	2.26259
$701$	−33.5687	−1.26787	−0.633936	−	0.773386i	$-0.718562\pi$
$701$	−33.5687	−1.26787	−0.633936	+	0.773386i	$0.718562\pi$
$702$	0	0
$703$	6.98229	0.263342
$704$	0	0
$705$	0	0
$706$	−4.69124	−0.176557
$707$	−7.53657	−0.283442
$708$	0	0
$709$	34.6667	1.30194	0.650968	−	0.759105i	$-0.274363\pi$
$709$	34.6667	1.30194	0.650968	+	0.759105i	$0.274363\pi$
$710$	3.94592	0.148088
$711$	0	0
$712$	−10.3815	−0.389064
$713$	64.5126	2.41602
$714$	0	0
$715$	0	0
$716$	72.0128	2.69125
$717$	0	0
$718$	−42.4327	−1.58357
$719$	44.2675	1.65090	0.825450	−	0.564476i	$-0.190922\pi$
$719$	44.2675	1.65090	0.825450	+	0.564476i	$0.190922\pi$
$720$	0	0
$721$	−29.4868	−1.09814
$722$	−24.6050	−0.915705
$723$	0	0
$724$	−84.6136	−3.14464
$725$	−19.8623	−0.737666
$726$	0	0
$727$	−41.0157	−1.52119	−0.760595	−	0.649227i	$-0.775093\pi$
$727$	−41.0157	−1.52119	−0.760595	+	0.649227i	$0.775093\pi$
$728$	97.6677	3.61980
$729$	0	0
$730$	−6.78074	−0.250966
$731$	−24.7601	−0.915786
$732$	0	0
$733$	−21.6126	−0.798281	−0.399140	−	0.916890i	$-0.630691\pi$
$733$	−21.6126	−0.798281	−0.399140	+	0.916890i	$0.630691\pi$
$734$	−14.9928	−0.553394
$735$	0	0
$736$	−4.12588	−0.152082
$737$	0	0
$738$	0	0
$739$	−27.2920	−1.00395	−0.501976	−	0.864881i	$-0.667394\pi$
$739$	−27.2920	−1.00395	−0.501976	+	0.864881i	$0.667394\pi$
$740$	−3.83482	−0.140971
$741$	0	0
$742$	62.5772	2.29728
$743$	−12.5031	−0.458695	−0.229347	−	0.973345i	$-0.573659\pi$
$743$	−12.5031	−0.458695	−0.229347	+	0.973345i	$0.573659\pi$
$744$	0	0
$745$	3.83775	0.140604
$746$	19.9938	0.732024
$747$	0	0
$748$	0	0
$749$	49.6912	1.81568
$750$	0	0
$751$	6.37859	0.232758	0.116379	−	0.993205i	$-0.462871\pi$
$751$	6.37859	0.232758	0.116379	+	0.993205i	$0.462871\pi$
$752$	11.8306	0.431416
$753$	0	0
$754$	−63.9587	−2.32924
$755$	0.251365	0.00914812
$756$	0	0
$757$	10.2311	0.371856	0.185928	−	0.982563i	$-0.440471\pi$
$757$	10.2311	0.371856	0.185928	+	0.982563i	$0.440471\pi$
$758$	1.69843	0.0616899
$759$	0	0
$760$	−6.16225	−0.223528
$761$	−47.9401	−1.73783	−0.868913	−	0.494965i	$-0.835181\pi$
$761$	−47.9401	−1.73783	−0.868913	+	0.494965i	$0.835181\pi$
$762$	0	0
$763$	5.10817	0.184928
$764$	−88.5786	−3.20466
$765$	0	0
$766$	−28.9253	−1.04511
$767$	−37.3072	−1.34708
$768$	0	0
$769$	−14.5831	−0.525879	−0.262939	−	0.964812i	$-0.584692\pi$
$769$	−14.5831	−0.525879	−0.262939	+	0.964812i	$0.584692\pi$
$770$	0	0
$771$	0	0
$772$	−24.0934	−0.867140
$773$	7.81711	0.281162	0.140581	−	0.990069i	$-0.455103\pi$
$773$	7.81711	0.281162	0.140581	+	0.990069i	$0.455103\pi$
$774$	0	0
$775$	40.7846	1.46503
$776$	−79.6677	−2.85990
$777$	0	0
$778$	−51.7601	−1.85569
$779$	37.7060	1.35096
$780$	0	0
$781$	0	0
$782$	87.4556	3.12741
$783$	0	0
$784$	10.0718	0.359707
$785$	−5.48249	−0.195678
$786$	0	0
$787$	31.2527	1.11404	0.557019	−	0.830499i	$-0.311945\pi$
$787$	31.2527	1.11404	0.557019	+	0.830499i	$0.311945\pi$
$788$	75.2790	2.68170
$789$	0	0
$790$	−5.50739	−0.195944
$791$	42.5379	1.51247
$792$	0	0
$793$	−50.9617	−1.80970
$794$	−31.0478	−1.10185
$795$	0	0
$796$	18.4208	0.652908
$797$	3.87839	0.137380	0.0686899	−	0.997638i	$-0.478118\pi$
$797$	3.87839	0.137380	0.0686899	+	0.997638i	$0.478118\pi$
$798$	0	0
$799$	−12.7060	−0.449507
$800$	−2.60836	−0.0922196
$801$	0	0
$802$	−30.2704	−1.06889
$803$	0	0
$804$	0	0
$805$	−9.49261	−0.334570
$806$	131.331	4.62594
$807$	0	0
$808$	12.4720	0.438763
$809$	23.8377	0.838091	0.419045	−	0.907965i	$-0.362365\pi$
$809$	23.8377	0.838091	0.419045	+	0.907965i	$0.362365\pi$
$810$	0	0
$811$	−15.5261	−0.545194	−0.272597	−	0.962128i	$-0.587883\pi$
$811$	−15.5261	−0.545194	−0.272597	+	0.962128i	$0.587883\pi$
$812$	−50.8653	−1.78502
$813$	0	0
$814$	0	0
$815$	−1.13015	−0.0395874
$816$	0	0
$817$	15.9823	0.559150
$818$	26.6156	0.930591
$819$	0	0
$820$	−20.7089	−0.723188
$821$	16.2560	0.567339	0.283670	−	0.958922i	$-0.408448\pi$
$821$	16.2560	0.567339	0.283670	+	0.958922i	$0.408448\pi$
$822$	0	0
$823$	42.6126	1.48538	0.742692	−	0.669634i	$-0.233549\pi$
$823$	42.6126	1.48538	0.742692	+	0.669634i	$0.233549\pi$
$824$	48.7965	1.69991
$825$	0	0
$826$	−44.3068	−1.54163
$827$	−2.75544	−0.0958161	−0.0479081	−	0.998852i	$-0.515255\pi$
$827$	−2.75544	−0.0958161	−0.0479081	+	0.998852i	$0.515255\pi$
$828$	0	0
$829$	2.14454	0.0744831	0.0372415	−	0.999306i	$-0.488143\pi$
$829$	2.14454	0.0744831	0.0372415	+	0.999306i	$0.488143\pi$
$830$	−10.5438	−0.365980
$831$	0	0
$832$	46.3638	1.60738
$833$	−10.8171	−0.374791
$834$	0	0
$835$	4.33036	0.149858
$836$	0	0
$837$	0	0
$838$	−40.6883	−1.40555
$839$	−45.2934	−1.56370	−0.781850	−	0.623466i	$-0.785724\pi$
$839$	−45.2934	−1.56370	−0.781850	+	0.623466i	$0.785724\pi$
$840$	0	0
$841$	−12.1230	−0.418033
$842$	85.1282	2.93371
$843$	0	0
$844$	−2.06887	−0.0712134
$845$	−10.9881	−0.378004
$846$	0	0
$847$	0	0
$848$	−36.0364	−1.23749
$849$	0	0
$850$	55.2891	1.89640
$851$	−17.7994	−0.610156
$852$	0	0
$853$	3.30584	0.113190	0.0565949	−	0.998397i	$-0.481976\pi$
$853$	3.30584	0.113190	0.0565949	+	0.998397i	$0.481976\pi$
$854$	−60.5231	−2.07106
$855$	0	0
$856$	−82.2321	−2.81063
$857$	−27.8784	−0.952308	−0.476154	−	0.879362i	$-0.657969\pi$
$857$	−27.8784	−0.952308	−0.476154	+	0.879362i	$0.657969\pi$
$858$	0	0
$859$	−20.3934	−0.695813	−0.347906	−	0.937529i	$-0.613107\pi$
$859$	−20.3934	−0.695813	−0.347906	+	0.937529i	$0.613107\pi$
$860$	−8.77781	−0.299321
$861$	0	0
$862$	−46.1593	−1.57219
$863$	40.2920	1.37156	0.685778	−	0.727811i	$-0.259462\pi$
$863$	40.2920	1.37156	0.685778	+	0.727811i	$0.259462\pi$
$864$	0	0
$865$	4.94299	0.168067
$866$	68.7103	2.33487
$867$	0	0
$868$	104.445	3.54511
$869$	0	0
$870$	0	0
$871$	28.0659	0.950978
$872$	−8.45331	−0.286265
$873$	0	0
$874$	−56.4513	−1.90950
$875$	−12.2074	−0.412686
$876$	0	0
$877$	−19.5654	−0.660675	−0.330338	−	0.943863i	$-0.607163\pi$
$877$	−19.5654	−0.660675	−0.330338	+	0.943863i	$0.607163\pi$
$878$	−45.0947	−1.52187
$879$	0	0
$880$	0	0
$881$	−37.8679	−1.27580	−0.637901	−	0.770119i	$-0.720197\pi$
$881$	−37.8679	−1.27580	−0.637901	+	0.770119i	$0.720197\pi$
$882$	0	0
$883$	17.1082	0.575736	0.287868	−	0.957670i	$-0.407054\pi$
$883$	17.1082	0.575736	0.287868	+	0.957670i	$0.407054\pi$
$884$	119.222	4.00986
$885$	0	0
$886$	39.0335	1.31135
$887$	−33.2354	−1.11594	−0.557968	−	0.829863i	$-0.688419\pi$
$887$	−33.2354	−1.11594	−0.557968	+	0.829863i	$0.688419\pi$
$888$	0	0
$889$	4.43852	0.148863
$890$	2.05408	0.0688531
$891$	0	0
$892$	−7.00000	−0.234377
$893$	8.20155	0.274455
$894$	0	0
$895$	−7.21926	−0.241313
$896$	58.3580	1.94960
$897$	0	0
$898$	−82.3766	−2.74894
$899$	−34.6549	−1.15580
$900$	0	0
$901$	38.7031	1.28939
$902$	0	0
$903$	0	0
$904$	−70.3943	−2.34128
$905$	8.48249	0.281967
$906$	0	0
$907$	47.5624	1.57928	0.789642	−	0.613567i	$-0.210266\pi$
$907$	47.5624	1.57928	0.789642	+	0.613567i	$0.210266\pi$
$908$	46.5801	1.54582
$909$	0	0
$910$	−19.3245	−0.640601
$911$	25.2556	0.836757	0.418378	−	0.908273i	$-0.362599\pi$
$911$	25.2556	0.836757	0.418378	+	0.908273i	$0.362599\pi$
$912$	0	0
$913$	0	0
$914$	−16.4543	−0.544259
$915$	0	0
$916$	19.3815	0.640383
$917$	2.16518	0.0715005
$918$	0	0
$919$	−7.69416	−0.253807	−0.126903	−	0.991915i	$-0.540504\pi$
$919$	−7.69416	−0.253807	−0.126903	+	0.991915i	$0.540504\pi$
$920$	15.7089	0.517909
$921$	0	0
$922$	−53.7247	−1.76933
$923$	24.9675	0.821816
$924$	0	0
$925$	−11.2527	−0.369987
$926$	−45.6270	−1.49940
$927$	0	0
$928$	2.21634	0.0727548
$929$	−39.7817	−1.30520	−0.652598	−	0.757705i	$-0.726321\pi$
$929$	−39.7817	−1.30520	−0.652598	+	0.757705i	$0.726321\pi$
$930$	0	0
$931$	6.98229	0.228835
$932$	−80.7906	−2.64639
$933$	0	0
$934$	45.0512	1.47412
$935$	0	0
$936$	0	0
$937$	−4.43852	−0.145000	−0.0725001	−	0.997368i	$-0.523098\pi$
$937$	−4.43852	−0.145000	−0.0725001	+	0.997368i	$0.523098\pi$
$938$	33.3317	1.08832
$939$	0	0
$940$	−4.50447	−0.146920
$941$	2.09046	0.0681470	0.0340735	−	0.999419i	$-0.489152\pi$
$941$	2.09046	0.0681470	0.0340735	+	0.999419i	$0.489152\pi$
$942$	0	0
$943$	−96.1210	−3.13013
$944$	25.5150	0.830442
$945$	0	0
$946$	0	0
$947$	22.3432	0.726056	0.363028	−	0.931778i	$-0.381743\pi$
$947$	22.3432	0.726056	0.363028	+	0.931778i	$0.381743\pi$
$948$	0	0
$949$	−42.9046	−1.39274
$950$	−35.6883	−1.15788
$951$	0	0
$952$	71.7395	2.32509
$953$	42.9679	1.39187	0.695933	−	0.718106i	$-0.254991\pi$
$953$	42.9679	1.39187	0.695933	+	0.718106i	$0.254991\pi$
$954$	0	0
$955$	8.87997	0.287349
$956$	−102.899	−3.32798
$957$	0	0
$958$	−21.7994	−0.704307
$959$	28.2996	0.913842
$960$	0	0
$961$	40.1593	1.29546
$962$	−36.2350	−1.16826
$963$	0	0
$964$	70.2350	2.26212
$965$	2.41535	0.0777530
$966$	0	0
$967$	51.8683	1.66797	0.833986	−	0.551786i	$-0.186054\pi$
$967$	51.8683	1.66797	0.833986	+	0.551786i	$0.186054\pi$
$968$	0	0
$969$	0	0
$970$	15.7630	0.506120
$971$	−41.8138	−1.34187	−0.670934	−	0.741517i	$-0.734107\pi$
$971$	−41.8138	−1.34187	−0.670934	+	0.741517i	$0.734107\pi$
$972$	0	0
$973$	38.4838	1.23374
$974$	−49.0770	−1.57253
$975$	0	0
$976$	34.8535	1.11563
$977$	−27.9459	−0.894069	−0.447035	−	0.894517i	$-0.647520\pi$
$977$	−27.9459	−0.894069	−0.447035	+	0.894517i	$0.647520\pi$
$978$	0	0
$979$	0	0
$980$	−3.83482	−0.122499
$981$	0	0
$982$	86.0315	2.74537
$983$	26.1416	0.833788	0.416894	−	0.908955i	$-0.363119\pi$
$983$	26.1416	0.833788	0.416894	+	0.908955i	$0.363119\pi$
$984$	0	0
$985$	−7.54669	−0.240458
$986$	−46.9794	−1.49613
$987$	0	0
$988$	−76.9558	−2.44829
$989$	−40.7424	−1.29553
$990$	0	0
$991$	52.4720	1.66683	0.833414	−	0.552650i	$-0.186383\pi$
$991$	52.4720	1.66683	0.833414	+	0.552650i	$0.186383\pi$
$992$	−4.55096	−0.144493
$993$	0	0
$994$	29.6519	0.940502
$995$	−1.84668	−0.0585437
$996$	0	0
$997$	21.4749	0.680117	0.340058	−	0.940404i	$-0.389553\pi$
$997$	21.4749	0.680117	0.340058	+	0.940404i	$0.389553\pi$
$998$	30.5907	0.968330
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3267.2.a.u.1.3	yes	3
3.2	odd	2		3267.2.a.s.1.1	yes	3
11.10	odd	2		3267.2.a.r.1.1	✓	3
33.32	even	2		3267.2.a.v.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3267.2.a.r.1.1	✓	3	11.10	odd	2
3267.2.a.s.1.1	yes	3	3.2	odd	2
3267.2.a.u.1.3	yes	3	1.1	even	1	trivial
3267.2.a.v.1.3	yes	3	33.32	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:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3267.a (trivial)

\(f(q)\)	\(=\)	\(q+2.46050 q^{2} +4.05408 q^{4} -0.406421 q^{5} -3.05408 q^{7} +5.05408 q^{8} -1.00000 q^{10} -6.32743 q^{13} -7.51459 q^{14} +4.32743 q^{16} -4.64766 q^{17} +3.00000 q^{19} -1.64766 q^{20} -7.64766 q^{23} -4.83482 q^{25} -15.5687 q^{26} -12.3815 q^{28} +4.10817 q^{29} -8.43560 q^{31} +0.539495 q^{32} -11.4356 q^{34} +1.24124 q^{35} +2.32743 q^{37} +7.38151 q^{38} -2.05408 q^{40} +12.5687 q^{41} +5.32743 q^{43} -18.8171 q^{46} +2.73385 q^{47} +2.32743 q^{49} -11.8961 q^{50} -25.6519 q^{52} -8.32743 q^{53} -15.4356 q^{56} +10.1082 q^{58} +5.89610 q^{59} +8.05408 q^{61} -20.7558 q^{62} -7.32743 q^{64} +2.57160 q^{65} -4.43560 q^{67} -18.8420 q^{68} +3.05408 q^{70} -3.94592 q^{71} +6.78074 q^{73} +5.72665 q^{74} +12.1623 q^{76} +5.50739 q^{79} -1.75876 q^{80} +30.9253 q^{82} +10.5438 q^{83} +1.88891 q^{85} +13.1082 q^{86} -2.05408 q^{89} +19.3245 q^{91} -31.0043 q^{92} +6.72665 q^{94} -1.21926 q^{95} -15.7630 q^{97} +5.72665 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{4} - 4 q^{5} + 6 q^{8} - 3 q^{10} - 9 q^{13} - 7 q^{14} + 3 q^{16} - 2 q^{17} + 9 q^{19} + 7 q^{20} - 11 q^{23} + 3 q^{25} - 22 q^{26} - 18 q^{28} - 6 q^{29} + 3 q^{31} + 8 q^{32} - 6 q^{34}+ \cdots + 18 q^{98}+O(q^{100}) \) 3 * q + q^2 + 3 * q^4 - 4 * q^5 + 6 * q^8 - 3 * q^10 - 9 * q^13 - 7 * q^14 + 3 * q^16 - 2 * q^17 + 9 * q^19 + 7 * q^20 - 11 * q^23 + 3 * q^25 - 22 * q^26 - 18 * q^28 - 6 * q^29 + 3 * q^31 + 8 * q^32 - 6 * q^34 - 11 * q^35 - 3 * q^37 + 3 * q^38 + 3 * q^40 + 13 * q^41 + 6 * q^43 - 9 * q^46 + q^47 - 3 * q^49 - q^50 - 12 * q^52 - 15 * q^53 - 18 * q^56 + 12 * q^58 - 17 * q^59 + 15 * q^61 - 32 * q^62 - 12 * q^64 + 28 * q^65 + 15 * q^67 - 31 * q^68 - 21 * q^71 + 12 * q^73 + 18 * q^74 + 9 * q^76 + 9 * q^79 - 20 * q^80 + 27 * q^82 - 15 * q^83 - 21 * q^85 + 21 * q^86 + 3 * q^89 + 3 * q^91 - 40 * q^92 + 21 * q^94 - 12 * q^95 - 9 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

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