LMFDB - Embedded newform 2883.2.a.r.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2883,2,Mod(1,2883)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2883, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2883.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2883 = 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2883.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,4,8,4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$23.0208709027$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.1413480448.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 2x^{6} + 16x^{5} - x^{4} - 16x^{3} + 2x^{2} + 4x - 1 $ x^8 - 4x^7 - 2x^6 + 16x^5 - x^4 - 16x^3 + 2x^2 + 4x - 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			1.8
Root			$1.13761$ of defining polynomial
Character	$\chi$	$=$	2883.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.55182 q^{2} +1.00000 q^{3} +4.51180 q^{4} -3.99832 q^{5} +2.55182 q^{6} -2.72957 q^{7} +6.40966 q^{8} +1.00000 q^{9} -10.2030 q^{10} -2.41812 q^{11} +4.51180 q^{12} -1.70470 q^{13} -6.96538 q^{14} -3.99832 q^{15} +7.33272 q^{16} -0.933445 q^{17} +2.55182 q^{18} -2.19748 q^{19} -18.0396 q^{20} -2.72957 q^{21} -6.17061 q^{22} -6.25483 q^{23} +6.40966 q^{24} +10.9866 q^{25} -4.35008 q^{26} +1.00000 q^{27} -12.3153 q^{28} +0.762139 q^{29} -10.2030 q^{30} +5.89248 q^{32} -2.41812 q^{33} -2.38199 q^{34} +10.9137 q^{35} +4.51180 q^{36} -11.6934 q^{37} -5.60759 q^{38} -1.70470 q^{39} -25.6279 q^{40} +11.6920 q^{41} -6.96538 q^{42} -2.08795 q^{43} -10.9101 q^{44} -3.99832 q^{45} -15.9612 q^{46} -3.12589 q^{47} +7.33272 q^{48} +0.450549 q^{49} +28.0358 q^{50} -0.933445 q^{51} -7.69125 q^{52} -5.23989 q^{53} +2.55182 q^{54} +9.66842 q^{55} -17.4956 q^{56} -2.19748 q^{57} +1.94484 q^{58} +6.93133 q^{59} -18.0396 q^{60} -6.64318 q^{61} -2.72957 q^{63} +0.371123 q^{64} +6.81593 q^{65} -6.17061 q^{66} -3.86409 q^{67} -4.21152 q^{68} -6.25483 q^{69} +27.8498 q^{70} -2.62805 q^{71} +6.40966 q^{72} +2.32021 q^{73} -29.8395 q^{74} +10.9866 q^{75} -9.91460 q^{76} +6.60042 q^{77} -4.35008 q^{78} -8.41452 q^{79} -29.3186 q^{80} +1.00000 q^{81} +29.8358 q^{82} +12.7355 q^{83} -12.3153 q^{84} +3.73222 q^{85} -5.32809 q^{86} +0.762139 q^{87} -15.4993 q^{88} +11.6131 q^{89} -10.2030 q^{90} +4.65309 q^{91} -28.2205 q^{92} -7.97671 q^{94} +8.78625 q^{95} +5.89248 q^{96} +4.40969 q^{97} +1.14972 q^{98} -2.41812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 8 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} + 8 q^{9} - 20 q^{10} - 8 q^{11} + 4 q^{12} - 16 q^{13} - 12 q^{14} + 4 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 16 q^{23} + 8 q^{25}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 8 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 + 8 * q^9 - 20 * q^10 - 8 * q^11 + 4 * q^12 - 16 * q^13 - 12 * q^14 + 4 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 16 * q^23 + 8 * q^25 - 8 * q^26 + 8 * q^27 - 4 * q^28 - 16 * q^29 - 20 * q^30 + 4 * q^32 - 8 * q^33 - 16 * q^34 - 24 * q^35 + 4 * q^36 - 16 * q^37 - 12 * q^38 - 16 * q^39 - 16 * q^40 - 12 * q^42 - 32 * q^43 - 24 * q^44 - 16 * q^46 - 8 * q^47 + 4 * q^48 + 40 * q^49 + 8 * q^50 - 32 * q^52 - 16 * q^53 + 4 * q^54 + 16 * q^55 - 24 * q^56 - 16 * q^57 + 16 * q^58 + 24 * q^59 - 12 * q^60 - 48 * q^61 - 8 * q^63 - 16 * q^64 - 24 * q^65 - 40 * q^67 + 24 * q^68 - 16 * q^69 + 4 * q^70 + 16 * q^71 - 48 * q^73 - 48 * q^74 + 8 * q^75 - 20 * q^76 - 48 * q^77 - 8 * q^78 - 36 * q^80 + 8 * q^81 + 52 * q^82 - 24 * q^83 - 4 * q^84 - 16 * q^87 - 16 * q^88 - 24 * q^89 - 20 * q^90 + 16 * q^91 - 80 * q^92 - 24 * q^94 + 40 * q^95 + 4 * q^96 + 64 * q^98 - 8 * q^99

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 $

$2$	2.55182	1.80441	0.902205	−	0.431307i	$-0.141947\pi$
$2$	2.55182	1.80441	0.902205	+	0.431307i	$0.141947\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.51180	2.25590
$5$	−3.99832	−1.78810	−0.894052	−	0.447963i	$-0.852150\pi$
$5$	−3.99832	−1.78810	−0.894052	+	0.447963i	$0.852150\pi$
$6$	2.55182	1.04178
$7$	−2.72957	−1.03168	−0.515840	−	0.856685i	$-0.672520\pi$
$7$	−2.72957	−1.03168	−0.515840	+	0.856685i	$0.672520\pi$
$8$	6.40966	2.26616
$9$	1.00000	0.333333
$10$	−10.2030	−3.22648
$11$	−2.41812	−0.729090	−0.364545	−	0.931186i	$-0.618776\pi$
$11$	−2.41812	−0.729090	−0.364545	+	0.931186i	$0.618776\pi$
$12$	4.51180	1.30244
$13$	−1.70470	−0.472798	−0.236399	−	0.971656i	$-0.575967\pi$
$13$	−1.70470	−0.472798	−0.236399	+	0.971656i	$0.575967\pi$
$14$	−6.96538	−1.86158
$15$	−3.99832	−1.03236
$16$	7.33272	1.83318
$17$	−0.933445	−0.226394	−0.113197	−	0.993573i	$-0.536109\pi$
$17$	−0.933445	−0.226394	−0.113197	+	0.993573i	$0.536109\pi$
$18$	2.55182	0.601470
$19$	−2.19748	−0.504137	−0.252069	−	0.967709i	$-0.581111\pi$
$19$	−2.19748	−0.504137	−0.252069	+	0.967709i	$0.581111\pi$
$20$	−18.0396	−4.03378
$21$	−2.72957	−0.595641
$22$	−6.17061	−1.31558
$23$	−6.25483	−1.30422	−0.652111	−	0.758124i	$-0.726116\pi$
$23$	−6.25483	−1.30422	−0.652111	+	0.758124i	$0.726116\pi$
$24$	6.40966	1.30837
$25$	10.9866	2.19732
$26$	−4.35008	−0.853122
$27$	1.00000	0.192450
$28$	−12.3153	−2.32737
$29$	0.762139	0.141526	0.0707629	−	0.997493i	$-0.477457\pi$
$29$	0.762139	0.141526	0.0707629	+	0.997493i	$0.477457\pi$
$30$	−10.2030	−1.86281
$31$	0	0
$31$	0	0
$32$	5.89248	1.04165
$33$	−2.41812	−0.420941
$34$	−2.38199	−0.408507
$35$	10.9137	1.84475
$36$	4.51180	0.751966
$37$	−11.6934	−1.92238	−0.961191	−	0.275884i	$-0.911029\pi$
$37$	−11.6934	−1.92238	−0.961191	+	0.275884i	$0.911029\pi$
$38$	−5.60759	−0.909671
$39$	−1.70470	−0.272970
$40$	−25.6279	−4.05213
$41$	11.6920	1.82598	0.912988	−	0.407986i	$-0.133769\pi$
$41$	11.6920	1.82598	0.912988	+	0.407986i	$0.133769\pi$
$42$	−6.96538	−1.07478
$43$	−2.08795	−0.318410	−0.159205	−	0.987246i	$-0.550893\pi$
$43$	−2.08795	−0.318410	−0.159205	+	0.987246i	$0.550893\pi$
$44$	−10.9101	−1.64475
$45$	−3.99832	−0.596035
$46$	−15.9612	−2.35335
$47$	−3.12589	−0.455958	−0.227979	−	0.973666i	$-0.573212\pi$
$47$	−3.12589	−0.455958	−0.227979	+	0.973666i	$0.573212\pi$
$48$	7.33272	1.05839
$49$	0.450549	0.0643642
$50$	28.0358	3.96487
$51$	−0.933445	−0.130709
$52$	−7.69125	−1.06658
$53$	−5.23989	−0.719754	−0.359877	−	0.933000i	$-0.617181\pi$
$53$	−5.23989	−0.719754	−0.359877	+	0.933000i	$0.617181\pi$
$54$	2.55182	0.347259
$55$	9.66842	1.30369
$56$	−17.4956	−2.33795
$57$	−2.19748	−0.291064
$58$	1.94484	0.255371
$59$	6.93133	0.902382	0.451191	−	0.892427i	$-0.350999\pi$
$59$	6.93133	0.902382	0.451191	+	0.892427i	$0.350999\pi$
$60$	−18.0396	−2.32891
$61$	−6.64318	−0.850572	−0.425286	−	0.905059i	$-0.639827\pi$
$61$	−6.64318	−0.850572	−0.425286	+	0.905059i	$0.639827\pi$
$62$	0	0
$63$	−2.72957	−0.343893
$64$	0.371123	0.0463903
$65$	6.81593	0.845412
$66$	−6.17061	−0.759550
$67$	−3.86409	−0.472073	−0.236037	−	0.971744i	$-0.575849\pi$
$67$	−3.86409	−0.472073	−0.236037	+	0.971744i	$0.575849\pi$
$68$	−4.21152	−0.510721
$69$	−6.25483	−0.752993
$70$	27.8498	3.32869
$71$	−2.62805	−0.311892	−0.155946	−	0.987766i	$-0.549843\pi$
$71$	−2.62805	−0.311892	−0.155946	+	0.987766i	$0.549843\pi$
$72$	6.40966	0.755386
$73$	2.32021	0.271560	0.135780	−	0.990739i	$-0.456646\pi$
$73$	2.32021	0.271560	0.135780	+	0.990739i	$0.456646\pi$
$74$	−29.8395	−3.46877
$75$	10.9866	1.26862
$76$	−9.91460	−1.13728
$77$	6.60042	0.752188
$78$	−4.35008	−0.492550
$79$	−8.41452	−0.946707	−0.473353	−	0.880873i	$-0.656957\pi$
$79$	−8.41452	−0.946707	−0.473353	+	0.880873i	$0.656957\pi$
$80$	−29.3186	−3.27792
$81$	1.00000	0.111111
$82$	29.8358	3.29481
$83$	12.7355	1.39790	0.698950	−	0.715171i	$-0.253651\pi$
$83$	12.7355	1.39790	0.698950	+	0.715171i	$0.253651\pi$
$84$	−12.3153	−1.34371
$85$	3.73222	0.404816
$86$	−5.32809	−0.574543
$87$	0.762139	0.0817099
$88$	−15.4993	−1.65223
$89$	11.6131	1.23099	0.615495	−	0.788141i	$-0.288956\pi$
$89$	11.6131	1.23099	0.615495	+	0.788141i	$0.288956\pi$
$90$	−10.2030	−1.07549
$91$	4.65309	0.487776
$92$	−28.2205	−2.94219
$93$	0	0
$94$	−7.97671	−0.822735
$95$	8.78625	0.901451
$96$	5.89248	0.601399
$97$	4.40969	0.447736	0.223868	−	0.974619i	$-0.428132\pi$
$97$	4.40969	0.447736	0.223868	+	0.974619i	$0.428132\pi$
$98$	1.14972	0.116139
$99$	−2.41812	−0.243030
$100$	49.5693	4.95693
$101$	−5.26496	−0.523883	−0.261942	−	0.965084i	$-0.584363\pi$
$101$	−5.26496	−0.523883	−0.261942	+	0.965084i	$0.584363\pi$
$102$	−2.38199	−0.235852
$103$	7.72596	0.761261	0.380631	−	0.924727i	$-0.375707\pi$
$103$	7.72596	0.761261	0.380631	+	0.924727i	$0.375707\pi$
$104$	−10.9265	−1.07143
$105$	10.9137	1.06507
$106$	−13.3713	−1.29873
$107$	9.12641	0.882283	0.441142	−	0.897437i	$-0.354574\pi$
$107$	9.12641	0.882283	0.441142	+	0.897437i	$0.354574\pi$
$108$	4.51180	0.434148
$109$	6.62864	0.634908	0.317454	−	0.948274i	$-0.397172\pi$
$109$	6.62864	0.634908	0.317454	+	0.948274i	$0.397172\pi$
$110$	24.6721	2.35239
$111$	−11.6934	−1.10989
$112$	−20.0152	−1.89126
$113$	−3.50827	−0.330030	−0.165015	−	0.986291i	$-0.552767\pi$
$113$	−3.50827	−0.330030	−0.165015	+	0.986291i	$0.552767\pi$
$114$	−5.60759	−0.525199
$115$	25.0088	2.33208
$116$	3.43862	0.319268
$117$	−1.70470	−0.157599
$118$	17.6875	1.62827
$119$	2.54790	0.233566
$120$	−25.6279	−2.33950
$121$	−5.15270	−0.468427
$122$	−16.9522	−1.53478
$123$	11.6920	1.05423
$124$	0	0
$125$	−23.9363	−2.14093
$126$	−6.96538	−0.620525
$127$	12.3067	1.09205	0.546023	−	0.837770i	$-0.316141\pi$
$127$	12.3067	1.09205	0.546023	+	0.837770i	$0.316141\pi$
$128$	−10.8379	−0.957946
$129$	−2.08795	−0.183834
$130$	17.3930	1.52547
$131$	11.0603	0.966343	0.483171	−	0.875526i	$-0.339485\pi$
$131$	11.0603	0.966343	0.483171	+	0.875526i	$0.339485\pi$
$132$	−10.9101	−0.949599
$133$	5.99819	0.520109
$134$	−9.86046	−0.851814
$135$	−3.99832	−0.344121
$136$	−5.98307	−0.513044
$137$	−20.5211	−1.75324	−0.876619	−	0.481185i	$-0.840207\pi$
$137$	−20.5211	−1.75324	−0.876619	+	0.481185i	$0.840207\pi$
$138$	−15.9612	−1.35871
$139$	−20.5914	−1.74654	−0.873272	−	0.487234i	$-0.838006\pi$
$139$	−20.5914	−1.74654	−0.873272	+	0.487234i	$0.838006\pi$
$140$	49.2404	4.16157
$141$	−3.12589	−0.263247
$142$	−6.70631	−0.562781
$143$	4.12216	0.344712
$144$	7.33272	0.611060
$145$	−3.04728	−0.253063
$146$	5.92077	0.490006
$147$	0.450549	0.0371607
$148$	−52.7582	−4.33670
$149$	13.1296	1.07562	0.537810	−	0.843066i	$-0.319252\pi$
$149$	13.1296	1.07562	0.537810	+	0.843066i	$0.319252\pi$
$150$	28.0358	2.28912
$151$	8.38954	0.682731	0.341365	−	0.939931i	$-0.389111\pi$
$151$	8.38954	0.682731	0.341365	+	0.939931i	$0.389111\pi$
$152$	−14.0851	−1.14245
$153$	−0.933445	−0.0754646
$154$	16.8431	1.35726
$155$	0	0
$156$	−7.69125	−0.615793
$157$	3.01163	0.240355	0.120177	−	0.992752i	$-0.461654\pi$
$157$	3.01163	0.240355	0.120177	+	0.992752i	$0.461654\pi$
$158$	−21.4723	−1.70825
$159$	−5.23989	−0.415550
$160$	−23.5600	−1.86259
$161$	17.0730	1.34554
$162$	2.55182	0.200490
$163$	−9.76076	−0.764522	−0.382261	−	0.924054i	$-0.624854\pi$
$163$	−9.76076	−0.764522	−0.382261	+	0.924054i	$0.624854\pi$
$164$	52.7517	4.11922
$165$	9.66842	0.752686
$166$	32.4987	2.52239
$167$	−6.05312	−0.468404	−0.234202	−	0.972188i	$-0.575248\pi$
$167$	−6.05312	−0.468404	−0.234202	+	0.972188i	$0.575248\pi$
$168$	−17.4956	−1.34982
$169$	−10.0940	−0.776462
$170$	9.52395	0.730454
$171$	−2.19748	−0.168046
$172$	−9.42043	−0.718301
$173$	−1.78486	−0.135700	−0.0678501	−	0.997696i	$-0.521614\pi$
$173$	−1.78486	−0.135700	−0.0678501	+	0.997696i	$0.521614\pi$
$174$	1.94484	0.147438
$175$	−29.9887	−2.26693
$176$	−17.7314	−1.33655
$177$	6.93133	0.520991
$178$	29.6347	2.22121
$179$	24.8227	1.85534	0.927668	−	0.373406i	$-0.121810\pi$
$179$	24.8227	1.85534	0.927668	+	0.373406i	$0.121810\pi$
$180$	−18.0396	−1.34459
$181$	13.0823	0.972401	0.486201	−	0.873847i	$-0.338382\pi$
$181$	13.0823	0.972401	0.486201	+	0.873847i	$0.338382\pi$
$182$	11.8739	0.880149
$183$	−6.64318	−0.491078
$184$	−40.0913	−2.95557
$185$	46.7540	3.43742
$186$	0	0
$187$	2.25718	0.165062
$188$	−14.1034	−1.02859
$189$	−2.72957	−0.198547
$190$	22.4210	1.62659
$191$	16.6264	1.20304	0.601521	−	0.798857i	$-0.294562\pi$
$191$	16.6264	1.20304	0.601521	+	0.798857i	$0.294562\pi$
$192$	0.371123	0.0267835
$193$	−13.8340	−0.995796	−0.497898	−	0.867236i	$-0.665895\pi$
$193$	−13.8340	−0.995796	−0.497898	+	0.867236i	$0.665895\pi$
$194$	11.2527	0.807900
$195$	6.81593	0.488099
$196$	2.03279	0.145199
$197$	−24.0564	−1.71395	−0.856973	−	0.515362i	$-0.827658\pi$
$197$	−24.0564	−1.71395	−0.856973	+	0.515362i	$0.827658\pi$
$198$	−6.17061	−0.438526
$199$	−0.477485	−0.0338480	−0.0169240	−	0.999857i	$-0.505387\pi$
$199$	−0.477485	−0.0338480	−0.0169240	+	0.999857i	$0.505387\pi$
$200$	70.4203	4.97947
$201$	−3.86409	−0.272552
$202$	−13.4352	−0.945300
$203$	−2.08031	−0.146009
$204$	−4.21152	−0.294865
$205$	−46.7482	−3.26504
$206$	19.7153	1.37363
$207$	−6.25483	−0.434741
$208$	−12.5001	−0.866724
$209$	5.31378	0.367562
$210$	27.8498	1.92182
$211$	−24.5285	−1.68861	−0.844307	−	0.535860i	$-0.819987\pi$
$211$	−24.5285	−1.68861	−0.844307	+	0.535860i	$0.819987\pi$
$212$	−23.6413	−1.62369
$213$	−2.62805	−0.180071
$214$	23.2890	1.59200
$215$	8.34832	0.569351
$216$	6.40966	0.436122
$217$	0	0
$218$	16.9151	1.14564
$219$	2.32021	0.156785
$220$	43.6220	2.94099
$221$	1.59124	0.107039
$222$	−29.8395	−2.00269
$223$	0.111301	0.00745330	0.00372665	−	0.999993i	$-0.498814\pi$
$223$	0.111301	0.00745330	0.00372665	+	0.999993i	$0.498814\pi$
$224$	−16.0839	−1.07465
$225$	10.9866	0.732439
$226$	−8.95248	−0.595510
$227$	14.6566	0.972795	0.486398	−	0.873738i	$-0.338311\pi$
$227$	14.6566	0.972795	0.486398	+	0.873738i	$0.338311\pi$
$228$	−9.91460	−0.656611
$229$	−17.4538	−1.15338	−0.576691	−	0.816962i	$-0.695656\pi$
$229$	−17.4538	−1.15338	−0.576691	+	0.816962i	$0.695656\pi$
$230$	63.8181	4.20804
$231$	6.60042	0.434276
$232$	4.88506	0.320720
$233$	7.95412	0.521092	0.260546	−	0.965461i	$-0.416098\pi$
$233$	7.95412	0.521092	0.260546	+	0.965461i	$0.416098\pi$
$234$	−4.35008	−0.284374
$235$	12.4983	0.815300
$236$	31.2728	2.03568
$237$	−8.41452	−0.546581
$238$	6.50180	0.421449
$239$	−2.55515	−0.165279	−0.0826394	−	0.996580i	$-0.526335\pi$
$239$	−2.55515	−0.165279	−0.0826394	+	0.996580i	$0.526335\pi$
$240$	−29.3186	−1.89251
$241$	10.6788	0.687882	0.343941	−	0.938991i	$-0.388238\pi$
$241$	10.6788	0.687882	0.343941	+	0.938991i	$0.388238\pi$
$242$	−13.1488	−0.845235
$243$	1.00000	0.0641500
$244$	−29.9727	−1.91880
$245$	−1.80144	−0.115090
$246$	29.8358	1.90226
$247$	3.74605	0.238355
$248$	0	0
$249$	12.7355	0.807078
$250$	−61.0813	−3.86312
$251$	−29.6514	−1.87158	−0.935791	−	0.352555i	$-0.885313\pi$
$251$	−29.6514	−1.87158	−0.935791	+	0.352555i	$0.885313\pi$
$252$	−12.3153	−0.775789
$253$	15.1249	0.950895
$254$	31.4046	1.97050
$255$	3.73222	0.233720
$256$	−28.3987	−1.77492
$257$	−10.4989	−0.654905	−0.327453	−	0.944868i	$-0.606190\pi$
$257$	−10.4989	−0.654905	−0.327453	+	0.944868i	$0.606190\pi$
$258$	−5.32809	−0.331712
$259$	31.9179	1.98328
$260$	30.7521	1.90716
$261$	0.762139	0.0471752
$262$	28.2239	1.74368
$263$	−9.75396	−0.601455	−0.300728	−	0.953710i	$-0.597230\pi$
$263$	−9.75396	−0.601455	−0.300728	+	0.953710i	$0.597230\pi$
$264$	−15.4993	−0.953917
$265$	20.9508	1.28700
$266$	15.3063	0.938490
$267$	11.6131	0.710712
$268$	−17.4340	−1.06495
$269$	−3.92734	−0.239454	−0.119727	−	0.992807i	$-0.538202\pi$
$269$	−3.92734	−0.239454	−0.119727	+	0.992807i	$0.538202\pi$
$270$	−10.2030	−0.620936
$271$	17.8088	1.08181	0.540905	−	0.841084i	$-0.318082\pi$
$271$	17.8088	1.08181	0.540905	+	0.841084i	$0.318082\pi$
$272$	−6.84470	−0.415021
$273$	4.65309	0.281618
$274$	−52.3663	−3.16356
$275$	−26.5669	−1.60204
$276$	−28.2205	−1.69868
$277$	−1.28699	−0.0773278	−0.0386639	−	0.999252i	$-0.512310\pi$
$277$	−1.28699	−0.0773278	−0.0386639	+	0.999252i	$0.512310\pi$
$278$	−52.5457	−3.15148
$279$	0	0
$280$	69.9531	4.18050
$281$	11.3771	0.678703	0.339352	−	0.940660i	$-0.389792\pi$
$281$	11.3771	0.678703	0.339352	+	0.940660i	$0.389792\pi$
$282$	−7.97671	−0.475006
$283$	−15.6331	−0.929289	−0.464645	−	0.885497i	$-0.653818\pi$
$283$	−15.6331	−0.929289	−0.464645	+	0.885497i	$0.653818\pi$
$284$	−11.8572	−0.703596
$285$	8.78625	0.520453
$286$	10.5190	0.622003
$287$	−31.9140	−1.88382
$288$	5.89248	0.347218
$289$	−16.1287	−0.948746
$290$	−7.77612	−0.456629
$291$	4.40969	0.258501
$292$	10.4683	0.612613
$293$	−20.8849	−1.22011	−0.610055	−	0.792359i	$-0.708853\pi$
$293$	−20.8849	−1.22011	−0.610055	+	0.792359i	$0.708853\pi$
$294$	1.14972	0.0670531
$295$	−27.7137	−1.61355
$296$	−74.9507	−4.35642
$297$	−2.41812	−0.140314
$298$	33.5045	1.94086
$299$	10.6626	0.616633
$300$	49.5693	2.86188
$301$	5.69922	0.328497
$302$	21.4086	1.23193
$303$	−5.26496	−0.302464
$304$	−16.1135	−0.924175
$305$	26.5616	1.52091
$306$	−2.38199	−0.136169
$307$	−6.92691	−0.395340	−0.197670	−	0.980269i	$-0.563337\pi$
$307$	−6.92691	−0.395340	−0.197670	+	0.980269i	$0.563337\pi$
$308$	29.7798	1.69686
$309$	7.72596	0.439515
$310$	0	0
$311$	21.8019	1.23627	0.618136	−	0.786072i	$-0.287888\pi$
$311$	21.8019	1.23627	0.618136	+	0.786072i	$0.287888\pi$
$312$	−10.9265	−0.618593
$313$	−19.4262	−1.09804	−0.549018	−	0.835811i	$-0.684998\pi$
$313$	−19.4262	−1.09804	−0.549018	+	0.835811i	$0.684998\pi$
$314$	7.68516	0.433698
$315$	10.9137	0.614917
$316$	−37.9646	−2.13567
$317$	−13.7195	−0.770561	−0.385281	−	0.922799i	$-0.625895\pi$
$317$	−13.7195	−0.770561	−0.385281	+	0.922799i	$0.625895\pi$
$318$	−13.3713	−0.749823
$319$	−1.84294	−0.103185
$320$	−1.48387	−0.0829508
$321$	9.12641	0.509386
$322$	43.5672	2.42791
$323$	2.05123	0.114134
$324$	4.51180	0.250655
$325$	−18.7288	−1.03889
$326$	−24.9077	−1.37951
$327$	6.62864	0.366564
$328$	74.9415	4.13795
$329$	8.53233	0.470403
$330$	24.6721	1.35815
$331$	18.3803	1.01027	0.505137	−	0.863039i	$-0.331442\pi$
$331$	18.3803	1.01027	0.505137	+	0.863039i	$0.331442\pi$
$332$	57.4599	3.15352
$333$	−11.6934	−0.640794
$334$	−15.4465	−0.845194
$335$	15.4499	0.844117
$336$	−20.0152	−1.09192
$337$	14.9250	0.813017	0.406508	−	0.913647i	$-0.366746\pi$
$337$	14.9250	0.813017	0.406508	+	0.913647i	$0.366746\pi$
$338$	−25.7581	−1.40106
$339$	−3.50827	−0.190543
$340$	16.8390	0.913223
$341$	0	0
$342$	−5.60759	−0.303224
$343$	17.8772	0.965277
$344$	−13.3831	−0.721567
$345$	25.0088	1.34643
$346$	−4.55464	−0.244859
$347$	−10.8392	−0.581876	−0.290938	−	0.956742i	$-0.593967\pi$
$347$	−10.8392	−0.581876	−0.290938	+	0.956742i	$0.593967\pi$
$348$	3.43862	0.184329
$349$	15.3503	0.821681	0.410840	−	0.911707i	$-0.365235\pi$
$349$	15.3503	0.821681	0.410840	+	0.911707i	$0.365235\pi$
$350$	−76.5257	−4.09047
$351$	−1.70470	−0.0909900
$352$	−14.2487	−0.759459
$353$	16.5951	0.883268	0.441634	−	0.897195i	$-0.354399\pi$
$353$	16.5951	0.883268	0.441634	+	0.897195i	$0.354399\pi$
$354$	17.6875	0.940081
$355$	10.5078	0.557695
$356$	52.3961	2.77699
$357$	2.54790	0.134849
$358$	63.3431	3.34779
$359$	−0.262969	−0.0138790	−0.00693948	−	0.999976i	$-0.502209\pi$
$359$	−0.262969	−0.0138790	−0.00693948	+	0.999976i	$0.502209\pi$
$360$	−25.6279	−1.35071
$361$	−14.1711	−0.745845
$362$	33.3838	1.75461
$363$	−5.15270	−0.270447
$364$	20.9938	1.10037
$365$	−9.27696	−0.485578
$366$	−16.9522	−0.886107
$367$	−22.5773	−1.17853	−0.589263	−	0.807941i	$-0.700582\pi$
$367$	−22.5773	−1.17853	−0.589263	+	0.807941i	$0.700582\pi$
$368$	−45.8649	−2.39087
$369$	11.6920	0.608659
$370$	119.308	6.20252
$371$	14.3026	0.742556
$372$	0	0
$373$	−32.4618	−1.68081	−0.840404	−	0.541960i	$-0.817682\pi$
$373$	−32.4618	−1.68081	−0.840404	+	0.541960i	$0.817682\pi$
$374$	5.75993	0.297839
$375$	−23.9363	−1.23607
$376$	−20.0359	−1.03327
$377$	−1.29922	−0.0669131
$378$	−6.96538	−0.358260
$379$	−27.8484	−1.43047	−0.715237	−	0.698882i	$-0.753681\pi$
$379$	−27.8484	−1.43047	−0.715237	+	0.698882i	$0.753681\pi$
$380$	39.6418	2.03358
$381$	12.3067	0.630494
$382$	42.4275	2.17078
$383$	17.8180	0.910460	0.455230	−	0.890374i	$-0.349557\pi$
$383$	17.8180	0.910460	0.455230	+	0.890374i	$0.349557\pi$
$384$	−10.8379	−0.553070
$385$	−26.3906	−1.34499
$386$	−35.3020	−1.79682
$387$	−2.08795	−0.106137
$388$	19.8956	1.01005
$389$	−12.8204	−0.650019	−0.325009	−	0.945711i	$-0.605367\pi$
$389$	−12.8204	−0.650019	−0.325009	+	0.945711i	$0.605367\pi$
$390$	17.3930	0.880731
$391$	5.83854	0.295268
$392$	2.88787	0.145859
$393$	11.0603	0.557918
$394$	−61.3876	−3.09266
$395$	33.6440	1.69281
$396$	−10.9101	−0.548251
$397$	26.1075	1.31030	0.655148	−	0.755500i	$-0.272606\pi$
$397$	26.1075	1.31030	0.655148	+	0.755500i	$0.272606\pi$
$398$	−1.21846	−0.0610757
$399$	5.99819	0.300285
$400$	80.5616	4.02808
$401$	−6.20676	−0.309951	−0.154975	−	0.987918i	$-0.549530\pi$
$401$	−6.20676	−0.309951	−0.154975	+	0.987918i	$0.549530\pi$
$402$	−9.86046	−0.491795
$403$	0	0
$404$	−23.7544	−1.18183
$405$	−3.99832	−0.198678
$406$	−5.30859	−0.263461
$407$	28.2760	1.40159
$408$	−5.98307	−0.296206
$409$	38.7733	1.91722	0.958609	−	0.284726i	$-0.0919025\pi$
$409$	38.7733	1.91722	0.958609	+	0.284726i	$0.0919025\pi$
$410$	−119.293	−5.89147
$411$	−20.5211	−1.01223
$412$	34.8580	1.71733
$413$	−18.9195	−0.930970
$414$	−15.9612	−0.784451
$415$	−50.9205	−2.49959
$416$	−10.0449	−0.492492
$417$	−20.5914	−1.00837
$418$	13.5598	0.663232
$419$	−20.2328	−0.988437	−0.494219	−	0.869338i	$-0.664546\pi$
$419$	−20.2328	−0.988437	−0.494219	+	0.869338i	$0.664546\pi$
$420$	49.2404	2.40269
$421$	36.8539	1.79615	0.898074	−	0.439845i	$-0.144967\pi$
$421$	36.8539	1.79615	0.898074	+	0.439845i	$0.144967\pi$
$422$	−62.5925	−3.04695
$423$	−3.12589	−0.151986
$424$	−33.5859	−1.63108
$425$	−10.2554	−0.497459
$426$	−6.70631	−0.324922
$427$	18.1330	0.877519
$428$	41.1765	1.99034
$429$	4.12216	0.199020
$430$	21.3034	1.02734
$431$	5.06706	0.244072	0.122036	−	0.992526i	$-0.461058\pi$
$431$	5.06706	0.244072	0.122036	+	0.992526i	$0.461058\pi$
$432$	7.33272	0.352796
$433$	−15.8658	−0.762460	−0.381230	−	0.924480i	$-0.624499\pi$
$433$	−15.8658	−0.762460	−0.381230	+	0.924480i	$0.624499\pi$
$434$	0	0
$435$	−3.04728	−0.146106
$436$	29.9071	1.43229
$437$	13.7449	0.657507
$438$	5.92077	0.282905
$439$	−23.8862	−1.14002	−0.570012	−	0.821636i	$-0.693062\pi$
$439$	−23.8862	−1.14002	−0.570012	+	0.821636i	$0.693062\pi$
$440$	61.9713	2.95437
$441$	0.450549	0.0214547
$442$	4.06057	0.193141
$443$	26.4674	1.25750	0.628752	−	0.777606i	$-0.283566\pi$
$443$	26.4674	1.25750	0.628752	+	0.777606i	$0.283566\pi$
$444$	−52.7582	−2.50379
$445$	−46.4331	−2.20114
$446$	0.284022	0.0134488
$447$	13.1296	0.621010
$448$	−1.01301	−0.0478600
$449$	−6.56169	−0.309665	−0.154833	−	0.987941i	$-0.549484\pi$
$449$	−6.56169	−0.309665	−0.154833	+	0.987941i	$0.549484\pi$
$450$	28.0358	1.32162
$451$	−28.2725	−1.33130
$452$	−15.8286	−0.744515
$453$	8.38954	0.394175
$454$	37.4011	1.75532
$455$	−18.6046	−0.872195
$456$	−14.0851	−0.659597
$457$	−3.19578	−0.149492	−0.0747461	−	0.997203i	$-0.523815\pi$
$457$	−3.19578	−0.149492	−0.0747461	+	0.997203i	$0.523815\pi$
$458$	−44.5391	−2.08117
$459$	−0.933445	−0.0435695
$460$	112.835	5.26095
$461$	−34.7154	−1.61686	−0.808429	−	0.588594i	$-0.799682\pi$
$461$	−34.7154	−1.61686	−0.808429	+	0.588594i	$0.799682\pi$
$462$	16.8431	0.783612
$463$	−13.8525	−0.643782	−0.321891	−	0.946777i	$-0.604318\pi$
$463$	−13.8525	−0.643782	−0.321891	+	0.946777i	$0.604318\pi$
$464$	5.58856	0.259442
$465$	0	0
$466$	20.2975	0.940263
$467$	−19.8229	−0.917293	−0.458647	−	0.888619i	$-0.651666\pi$
$467$	−19.8229	−0.917293	−0.458647	+	0.888619i	$0.651666\pi$
$468$	−7.69125	−0.355528
$469$	10.5473	0.487029
$470$	31.8935	1.47114
$471$	3.01163	0.138769
$472$	44.4275	2.04494
$473$	5.04892	0.232150
$474$	−21.4723	−0.986258
$475$	−24.1429	−1.10775
$476$	11.4956	0.526901
$477$	−5.23989	−0.239918
$478$	−6.52029	−0.298231
$479$	−5.75785	−0.263083	−0.131542	−	0.991311i	$-0.541993\pi$
$479$	−5.75785	−0.263083	−0.131542	+	0.991311i	$0.541993\pi$
$480$	−23.5600	−1.07536
$481$	19.9337	0.908898
$482$	27.2504	1.24122
$483$	17.0730	0.776848
$484$	−23.2479	−1.05672
$485$	−17.6314	−0.800599
$486$	2.55182	0.115753
$487$	−6.31188	−0.286019	−0.143009	−	0.989721i	$-0.545678\pi$
$487$	−6.31188	−0.286019	−0.143009	+	0.989721i	$0.545678\pi$
$488$	−42.5805	−1.92753
$489$	−9.76076	−0.441397
$490$	−4.59696	−0.207669
$491$	−19.3808	−0.874643	−0.437322	−	0.899305i	$-0.644073\pi$
$491$	−19.3808	−0.874643	−0.437322	+	0.899305i	$0.644073\pi$
$492$	52.7517	2.37823
$493$	−0.711416	−0.0320405
$494$	9.55924	0.430091
$495$	9.66842	0.434563
$496$	0	0
$497$	7.17344	0.321773
$498$	32.4987	1.45630
$499$	1.60294	0.0717575	0.0358787	−	0.999356i	$-0.488577\pi$
$499$	1.60294	0.0717575	0.0358787	+	0.999356i	$0.488577\pi$
$500$	−107.996	−4.82972
$501$	−6.05312	−0.270433
$502$	−75.6652	−3.37710
$503$	11.5436	0.514702	0.257351	−	0.966318i	$-0.417150\pi$
$503$	11.5436	0.514702	0.257351	+	0.966318i	$0.417150\pi$
$504$	−17.4956	−0.779317
$505$	21.0510	0.936758
$506$	38.5961	1.71581
$507$	−10.0940	−0.448291
$508$	55.5255	2.46355
$509$	−3.67075	−0.162703	−0.0813516	−	0.996685i	$-0.525924\pi$
$509$	−3.67075	−0.162703	−0.0813516	+	0.996685i	$0.525924\pi$
$510$	9.52395	0.421728
$511$	−6.33318	−0.280163
$512$	−50.7926	−2.24474
$513$	−2.19748	−0.0970213
$514$	−26.7914	−1.18172
$515$	−30.8909	−1.36122
$516$	−9.42043	−0.414711
$517$	7.55877	0.332434
$518$	81.4489	3.57866
$519$	−1.78486	−0.0783465
$520$	43.6878	1.91584
$521$	22.7219	0.995463	0.497731	−	0.867331i	$-0.334166\pi$
$521$	22.7219	0.995463	0.497731	+	0.867331i	$0.334166\pi$
$522$	1.94484	0.0851235
$523$	−24.0422	−1.05129	−0.525645	−	0.850704i	$-0.676176\pi$
$523$	−24.0422	−1.05129	−0.525645	+	0.850704i	$0.676176\pi$
$524$	49.9018	2.17997
$525$	−29.9887	−1.30881
$526$	−24.8904	−1.08527
$527$	0	0
$528$	−17.7314	−0.771660
$529$	16.1229	0.700994
$530$	53.4626	2.32227
$531$	6.93133	0.300794
$532$	27.0626	1.17331
$533$	−19.9312	−0.863318
$534$	29.6347	1.28242
$535$	−36.4903	−1.57761
$536$	−24.7675	−1.06979
$537$	24.8227	1.07118
$538$	−10.0219	−0.432074
$539$	−1.08948	−0.0469273
$540$	−18.0396	−0.776302
$541$	29.9787	1.28888	0.644442	−	0.764653i	$-0.277090\pi$
$541$	29.9787	1.28888	0.644442	+	0.764653i	$0.277090\pi$
$542$	45.4450	1.95203
$543$	13.0823	0.561416
$544$	−5.50031	−0.235824
$545$	−26.5034	−1.13528
$546$	11.8739	0.508154
$547$	−19.0057	−0.812625	−0.406313	−	0.913734i	$-0.633186\pi$
$547$	−19.0057	−0.812625	−0.406313	+	0.913734i	$0.633186\pi$
$548$	−92.5872	−3.95513
$549$	−6.64318	−0.283524
$550$	−67.7940	−2.89074
$551$	−1.67479	−0.0713484
$552$	−40.0913	−1.70640
$553$	22.9680	0.976699
$554$	−3.28417	−0.139531
$555$	46.7540	1.98460
$556$	−92.9044	−3.94003
$557$	−9.48713	−0.401983	−0.200991	−	0.979593i	$-0.564416\pi$
$557$	−9.48713	−0.401983	−0.200991	+	0.979593i	$0.564416\pi$
$558$	0	0
$559$	3.55933	0.150544
$560$	80.0271	3.38176
$561$	2.25718	0.0952983
$562$	29.0324	1.22466
$563$	−10.2935	−0.433818	−0.216909	−	0.976192i	$-0.569598\pi$
$563$	−10.2935	−0.433818	−0.216909	+	0.976192i	$0.569598\pi$
$564$	−14.1034	−0.593859
$565$	14.0272	0.590129
$566$	−39.8928	−1.67682
$567$	−2.72957	−0.114631
$568$	−16.8449	−0.706796
$569$	−2.22077	−0.0930994	−0.0465497	−	0.998916i	$-0.514823\pi$
$569$	−2.22077	−0.0930994	−0.0465497	+	0.998916i	$0.514823\pi$
$570$	22.4210	0.939111
$571$	−2.05535	−0.0860135	−0.0430068	−	0.999075i	$-0.513694\pi$
$571$	−2.05535	−0.0860135	−0.0430068	+	0.999075i	$0.513694\pi$
$572$	18.5984	0.777636
$573$	16.6264	0.694576
$574$	−81.4389	−3.39919
$575$	−68.7192	−2.86579
$576$	0.371123	0.0154634
$577$	13.0913	0.544996	0.272498	−	0.962156i	$-0.412150\pi$
$577$	13.0913	0.544996	0.272498	+	0.962156i	$0.412150\pi$
$578$	−41.1575	−1.71193
$579$	−13.8340	−0.574923
$580$	−13.7487	−0.570884
$581$	−34.7624	−1.44219
$582$	11.2527	0.466441
$583$	12.6707	0.524766
$584$	14.8718	0.615399
$585$	6.81593	0.281804
$586$	−53.2946	−2.20158
$587$	−42.6528	−1.76047	−0.880235	−	0.474539i	$-0.842615\pi$
$587$	−42.6528	−1.76047	−0.880235	+	0.474539i	$0.842615\pi$
$588$	2.03279	0.0838307
$589$	0	0
$590$	−70.7204	−2.91151
$591$	−24.0564	−0.989547
$592$	−85.7444	−3.52407
$593$	−6.77953	−0.278402	−0.139201	−	0.990264i	$-0.544453\pi$
$593$	−6.77953	−0.278402	−0.139201	+	0.990264i	$0.544453\pi$
$594$	−6.17061	−0.253183
$595$	−10.1873	−0.417640
$596$	59.2382	2.42649
$597$	−0.477485	−0.0195422
$598$	27.2090	1.11266
$599$	−29.2175	−1.19380	−0.596898	−	0.802317i	$-0.703600\pi$
$599$	−29.2175	−1.19380	−0.596898	+	0.802317i	$0.703600\pi$
$600$	70.4203	2.87490
$601$	−23.8290	−0.972005	−0.486003	−	0.873957i	$-0.661545\pi$
$601$	−23.8290	−0.972005	−0.486003	+	0.873957i	$0.661545\pi$
$602$	14.5434	0.592744
$603$	−3.86409	−0.157358
$604$	37.8519	1.54017
$605$	20.6022	0.837597
$606$	−13.4352	−0.545769
$607$	−34.1847	−1.38752	−0.693758	−	0.720209i	$-0.744046\pi$
$607$	−34.1847	−1.38752	−0.693758	+	0.720209i	$0.744046\pi$
$608$	−12.9486	−0.525137
$609$	−2.08031	−0.0842985
$610$	67.7805	2.74435
$611$	5.32869	0.215576
$612$	−4.21152	−0.170240
$613$	−21.2778	−0.859401	−0.429701	−	0.902971i	$-0.641381\pi$
$613$	−21.2778	−0.859401	−0.429701	+	0.902971i	$0.641381\pi$
$614$	−17.6762	−0.713355
$615$	−46.7482	−1.88507
$616$	42.3065	1.70458
$617$	−13.2846	−0.534817	−0.267409	−	0.963583i	$-0.586167\pi$
$617$	−13.2846	−0.534817	−0.267409	+	0.963583i	$0.586167\pi$
$618$	19.7153	0.793065
$619$	25.3551	1.01911	0.509554	−	0.860439i	$-0.329810\pi$
$619$	25.3551	1.01911	0.509554	+	0.860439i	$0.329810\pi$
$620$	0	0
$621$	−6.25483	−0.250998
$622$	55.6345	2.23074
$623$	−31.6989	−1.26999
$624$	−12.5001	−0.500403
$625$	40.7722	1.63089
$626$	−49.5723	−1.98131
$627$	5.31378	0.212212
$628$	13.5879	0.542216
$629$	10.9151	0.435215
$630$	27.8498	1.10956
$631$	0.709689	0.0282523	0.0141261	−	0.999900i	$-0.495503\pi$
$631$	0.709689	0.0282523	0.0141261	+	0.999900i	$0.495503\pi$
$632$	−53.9342	−2.14539
$633$	−24.5285	−0.974922
$634$	−35.0096	−1.39041
$635$	−49.2063	−1.95269
$636$	−23.6413	−0.937439
$637$	−0.768050	−0.0304312
$638$	−4.70287	−0.186188
$639$	−2.62805	−0.103964
$640$	43.3335	1.71291
$641$	−13.6470	−0.539026	−0.269513	−	0.962997i	$-0.586863\pi$
$641$	−13.6470	−0.539026	−0.269513	+	0.962997i	$0.586863\pi$
$642$	23.2890	0.919143
$643$	−36.2538	−1.42971	−0.714856	−	0.699272i	$-0.753508\pi$
$643$	−36.2538	−1.42971	−0.714856	+	0.699272i	$0.753508\pi$
$644$	77.0299	3.03540
$645$	8.34832	0.328715
$646$	5.23438	0.205944
$647$	43.9056	1.72611	0.863055	−	0.505111i	$-0.168548\pi$
$647$	43.9056	1.72611	0.863055	+	0.505111i	$0.168548\pi$
$648$	6.40966	0.251795
$649$	−16.7608	−0.657918
$650$	−47.7926	−1.87458
$651$	0	0
$652$	−44.0386	−1.72468
$653$	−23.2495	−0.909825	−0.454912	−	0.890536i	$-0.650329\pi$
$653$	−23.2495	−0.909825	−0.454912	+	0.890536i	$0.650329\pi$
$654$	16.9151	0.661433
$655$	−44.2226	−1.72792
$656$	85.7338	3.34734
$657$	2.32021	0.0905201
$658$	21.7730	0.848800
$659$	40.3057	1.57009	0.785043	−	0.619442i	$-0.212641\pi$
$659$	40.3057	1.57009	0.785043	+	0.619442i	$0.212641\pi$
$660$	43.6220	1.69798
$661$	−27.6976	−1.07731	−0.538655	−	0.842526i	$-0.681067\pi$
$661$	−27.6976	−1.07731	−0.538655	+	0.842526i	$0.681067\pi$
$662$	46.9033	1.82295
$663$	1.59124	0.0617987
$664$	81.6301	3.16786
$665$	−23.9827	−0.930009
$666$	−29.8395	−1.15626
$667$	−4.76705	−0.184581
$668$	−27.3104	−1.05667
$669$	0.111301	0.00430316
$670$	39.4253	1.52313
$671$	16.0640	0.620144
$672$	−16.0839	−0.620451
$673$	−11.9164	−0.459343	−0.229671	−	0.973268i	$-0.573765\pi$
$673$	−11.9164	−0.459343	−0.229671	+	0.973268i	$0.573765\pi$
$674$	38.0860	1.46702
$675$	10.9866	0.422874
$676$	−45.5421	−1.75162
$677$	35.6541	1.37030	0.685149	−	0.728403i	$-0.259737\pi$
$677$	35.6541	1.37030	0.685149	+	0.728403i	$0.259737\pi$
$678$	−8.95248	−0.343818
$679$	−12.0366	−0.461921
$680$	23.9222	0.917376
$681$	14.6566	0.561644
$682$	0	0
$683$	22.0333	0.843081	0.421541	−	0.906809i	$-0.361489\pi$
$683$	22.0333	0.843081	0.421541	+	0.906809i	$0.361489\pi$
$684$	−9.91460	−0.379094
$685$	82.0501	3.13497
$686$	45.6194	1.74176
$687$	−17.4538	−0.665905
$688$	−15.3104	−0.583703
$689$	8.93242	0.340298
$690$	63.8181	2.42951
$691$	−31.0331	−1.18055	−0.590277	−	0.807201i	$-0.700981\pi$
$691$	−31.0331	−1.18055	−0.590277	+	0.807201i	$0.700981\pi$
$692$	−8.05291	−0.306126
$693$	6.60042	0.250729
$694$	−27.6596	−1.04994
$695$	82.3312	3.12300
$696$	4.88506	0.185168
$697$	−10.9138	−0.413390
$698$	39.1711	1.48265
$699$	7.95412	0.300852
$700$	−135.303	−5.11396
$701$	31.5677	1.19230	0.596149	−	0.802874i	$-0.296697\pi$
$701$	31.5677	1.19230	0.596149	+	0.802874i	$0.296697\pi$
$702$	−4.35008	−0.164183
$703$	25.6960	0.969145
$704$	−0.897419	−0.0338228
$705$	12.4983	0.470714
$706$	42.3477	1.59378
$707$	14.3711	0.540480
$708$	31.2728	1.17530
$709$	51.9991	1.95287	0.976434	−	0.215817i	$-0.0692414\pi$
$709$	51.9991	1.95287	0.976434	+	0.215817i	$0.0692414\pi$
$710$	26.8140	1.00631
$711$	−8.41452	−0.315569
$712$	74.4363	2.78962
$713$	0	0
$714$	6.50180	0.243324
$715$	−16.4817	−0.616382
$716$	111.995	4.18545
$717$	−2.55515	−0.0954238
$718$	−0.671050	−0.0250434
$719$	0.258190	0.00962886	0.00481443	−	0.999988i	$-0.498468\pi$
$719$	0.258190	0.00962886	0.00481443	+	0.999988i	$0.498468\pi$
$720$	−29.3186	−1.09264
$721$	−21.0885	−0.785378
$722$	−36.1620	−1.34581
$723$	10.6788	0.397149
$724$	59.0248	2.19364
$725$	8.37331	0.310977
$726$	−13.1488	−0.487997
$727$	45.5600	1.68973	0.844864	−	0.534981i	$-0.179681\pi$
$727$	45.5600	1.68973	0.844864	+	0.534981i	$0.179681\pi$
$728$	29.8247	1.10538
$729$	1.00000	0.0370370
$730$	−23.6732	−0.876183
$731$	1.94899	0.0720861
$732$	−29.9727	−1.10782
$733$	18.6755	0.689796	0.344898	−	0.938640i	$-0.387913\pi$
$733$	18.6755	0.689796	0.344898	+	0.938640i	$0.387913\pi$
$734$	−57.6133	−2.12655
$735$	−1.80144	−0.0664472
$736$	−36.8565	−1.35855
$737$	9.34382	0.344184
$738$	29.8358	1.09827
$739$	37.5050	1.37965	0.689823	−	0.723979i	$-0.257689\pi$
$739$	37.5050	1.37965	0.689823	+	0.723979i	$0.257689\pi$
$740$	210.944	7.75447
$741$	3.74605	0.137614
$742$	36.4978	1.33988
$743$	16.9700	0.622569	0.311285	−	0.950317i	$-0.399241\pi$
$743$	16.9700	0.622569	0.311285	+	0.950317i	$0.399241\pi$
$744$	0	0
$745$	−52.4965	−1.92332
$746$	−82.8368	−3.03287
$747$	12.7355	0.465967
$748$	10.1839	0.372362
$749$	−24.9112	−0.910234
$750$	−61.0813	−2.23037
$751$	−39.1241	−1.42766	−0.713830	−	0.700319i	$-0.753041\pi$
$751$	−39.1241	−1.42766	−0.713830	+	0.700319i	$0.753041\pi$
$752$	−22.9213	−0.835853
$753$	−29.6514	−1.08056
$754$	−3.31537	−0.120739
$755$	−33.5441	−1.22079
$756$	−12.3153	−0.447902
$757$	−23.9289	−0.869709	−0.434855	−	0.900501i	$-0.643200\pi$
$757$	−23.9289	−0.869709	−0.434855	+	0.900501i	$0.643200\pi$
$758$	−71.0641	−2.58116
$759$	15.1249	0.549000
$760$	56.3169	2.04283
$761$	36.2067	1.31249	0.656245	−	0.754547i	$-0.272144\pi$
$761$	36.2067	1.31249	0.656245	+	0.754547i	$0.272144\pi$
$762$	31.4046	1.13767
$763$	−18.0933	−0.655022
$764$	75.0148	2.71394
$765$	3.73222	0.134939
$766$	45.4685	1.64284
$767$	−11.8158	−0.426644
$768$	−28.3987	−1.02475
$769$	−41.4245	−1.49380	−0.746902	−	0.664934i	$-0.768460\pi$
$769$	−41.4245	−1.49380	−0.746902	+	0.664934i	$0.768460\pi$
$770$	−67.3442	−2.42692
$771$	−10.4989	−0.378110
$772$	−62.4164	−2.24641
$773$	−4.93527	−0.177509	−0.0887546	−	0.996054i	$-0.528289\pi$
$773$	−4.93527	−0.177509	−0.0887546	+	0.996054i	$0.528289\pi$
$774$	−5.32809	−0.191514
$775$	0	0
$776$	28.2646	1.01464
$777$	31.9179	1.14505
$778$	−32.7153	−1.17290
$779$	−25.6929	−0.920543
$780$	30.7521	1.10110
$781$	6.35493	0.227397
$782$	14.8989	0.532784
$783$	0.762139	0.0272366
$784$	3.30375	0.117991
$785$	−12.0415	−0.429779
$786$	28.2239	1.00671
$787$	43.1715	1.53890	0.769448	−	0.638709i	$-0.220531\pi$
$787$	43.1715	1.53890	0.769448	+	0.638709i	$0.220531\pi$
$788$	−108.537	−3.86649
$789$	−9.75396	−0.347250
$790$	85.8534	3.05453
$791$	9.57607	0.340486
$792$	−15.4993	−0.550745
$793$	11.3246	0.402149
$794$	66.6216	2.36431
$795$	20.9508	0.743047
$796$	−2.15431	−0.0763577
$797$	−32.6896	−1.15792	−0.578962	−	0.815354i	$-0.696542\pi$
$797$	−32.6896	−1.15792	−0.578962	+	0.815354i	$0.696542\pi$
$798$	15.3063	0.541837
$799$	2.91785	0.103226
$800$	64.7383	2.28884
$801$	11.6131	0.410330
$802$	−15.8385	−0.559278
$803$	−5.61055	−0.197992
$804$	−17.4340	−0.614849
$805$	−68.2633	−2.40597
$806$	0	0
$807$	−3.92734	−0.138249
$808$	−33.7466	−1.18720
$809$	−22.1429	−0.778502	−0.389251	−	0.921132i	$-0.627266\pi$
$809$	−22.1429	−0.778502	−0.389251	+	0.921132i	$0.627266\pi$
$810$	−10.2030	−0.358497
$811$	−8.79261	−0.308750	−0.154375	−	0.988012i	$-0.549336\pi$
$811$	−8.79261	−0.308750	−0.154375	+	0.988012i	$0.549336\pi$
$812$	−9.38595	−0.329382
$813$	17.8088	0.624583
$814$	72.1554	2.52904
$815$	39.0267	1.36705
$816$	−6.84470	−0.239612
$817$	4.58825	0.160522
$818$	98.9427	3.45945
$819$	4.65309	0.162592
$820$	−210.918	−7.36559
$821$	15.7261	0.548844	0.274422	−	0.961609i	$-0.411514\pi$
$821$	15.7261	0.548844	0.274422	+	0.961609i	$0.411514\pi$
$822$	−52.3663	−1.82648
$823$	17.4226	0.607314	0.303657	−	0.952781i	$-0.401792\pi$
$823$	17.4226	0.607314	0.303657	+	0.952781i	$0.401792\pi$
$824$	49.5208	1.72514
$825$	−26.5669	−0.924940
$826$	−48.2793	−1.67985
$827$	−1.04692	−0.0364050	−0.0182025	−	0.999834i	$-0.505794\pi$
$827$	−1.04692	−0.0364050	−0.0182025	+	0.999834i	$0.505794\pi$
$828$	−28.2205	−0.980731
$829$	−38.8456	−1.34916	−0.674582	−	0.738200i	$-0.735676\pi$
$829$	−38.8456	−1.34916	−0.674582	+	0.738200i	$0.735676\pi$
$830$	−129.940	−4.51029
$831$	−1.28699	−0.0446452
$832$	−0.632652	−0.0219333
$833$	−0.420563	−0.0145716
$834$	−52.5457	−1.81951
$835$	24.2023	0.837556
$836$	23.9747	0.829182
$837$	0	0
$838$	−51.6305	−1.78355
$839$	3.95938	0.136693	0.0683465	−	0.997662i	$-0.478228\pi$
$839$	3.95938	0.136693	0.0683465	+	0.997662i	$0.478228\pi$
$840$	69.9531	2.41361
$841$	−28.4191	−0.979970
$842$	94.0445	3.24099
$843$	11.3771	0.391850
$844$	−110.668	−3.80934
$845$	40.3591	1.38840
$846$	−7.97671	−0.274245
$847$	14.0647	0.483267
$848$	−38.4226	−1.31944
$849$	−15.6331	−0.536525
$850$	−26.1699	−0.897621
$851$	73.1401	2.50721
$852$	−11.8572	−0.406222
$853$	24.1468	0.826770	0.413385	−	0.910556i	$-0.364346\pi$
$853$	24.1468	0.826770	0.413385	+	0.910556i	$0.364346\pi$
$854$	46.2723	1.58340
$855$	8.78625	0.300484
$856$	58.4972	1.99939
$857$	−9.46706	−0.323388	−0.161694	−	0.986841i	$-0.551696\pi$
$857$	−9.46706	−0.323388	−0.161694	+	0.986841i	$0.551696\pi$
$858$	10.5190	0.359114
$859$	13.8191	0.471500	0.235750	−	0.971814i	$-0.424245\pi$
$859$	13.8191	0.471500	0.235750	+	0.971814i	$0.424245\pi$
$860$	37.6659	1.28440
$861$	−31.9140	−1.08763
$862$	12.9302	0.440406
$863$	22.9998	0.782921	0.391460	−	0.920195i	$-0.371970\pi$
$863$	22.9998	0.782921	0.391460	+	0.920195i	$0.371970\pi$
$864$	5.89248	0.200466
$865$	7.13644	0.242646
$866$	−40.4866	−1.37579
$867$	−16.1287	−0.547759
$868$	0	0
$869$	20.3473	0.690235
$870$	−7.77612	−0.263635
$871$	6.58710	0.223195
$872$	42.4873	1.43880
$873$	4.40969	0.149245
$874$	35.0745	1.18641
$875$	65.3359	2.20876
$876$	10.4683	0.353692
$877$	17.0271	0.574964	0.287482	−	0.957786i	$-0.407182\pi$
$877$	17.0271	0.574964	0.287482	+	0.957786i	$0.407182\pi$
$878$	−60.9533	−2.05707
$879$	−20.8849	−0.704431
$880$	70.8959	2.38990
$881$	0.0975295	0.00328585	0.00164293	−	0.999999i	$-0.499477\pi$
$881$	0.0975295	0.00328585	0.00164293	+	0.999999i	$0.499477\pi$
$882$	1.14972	0.0387131
$883$	−19.2011	−0.646170	−0.323085	−	0.946370i	$-0.604720\pi$
$883$	−19.2011	−0.646170	−0.323085	+	0.946370i	$0.604720\pi$
$884$	7.17936	0.241468
$885$	−27.7137	−0.931586
$886$	67.5401	2.26905
$887$	−11.1920	−0.375792	−0.187896	−	0.982189i	$-0.560167\pi$
$887$	−11.1920	−0.375792	−0.187896	+	0.982189i	$0.560167\pi$
$888$	−74.9507	−2.51518
$889$	−33.5921	−1.12664
$890$	−118.489	−3.97176
$891$	−2.41812	−0.0810100
$892$	0.502170	0.0168139
$893$	6.86909	0.229865
$894$	33.5045	1.12056
$895$	−99.2492	−3.31753
$896$	29.5829	0.988294
$897$	10.6626	0.356013
$898$	−16.7443	−0.558764
$899$	0	0
$900$	49.5693	1.65231
$901$	4.89115	0.162948
$902$	−72.1465	−2.40222
$903$	5.69922	0.189658
$904$	−22.4868	−0.747901
$905$	−52.3073	−1.73876
$906$	21.4086	0.711253
$907$	37.7984	1.25507	0.627537	−	0.778587i	$-0.284063\pi$
$907$	37.7984	1.25507	0.627537	+	0.778587i	$0.284063\pi$
$908$	66.1278	2.19453
$909$	−5.26496	−0.174628
$910$	−47.4755	−1.57380
$911$	23.4570	0.777164	0.388582	−	0.921414i	$-0.372965\pi$
$911$	23.4570	0.777164	0.388582	+	0.921414i	$0.372965\pi$
$912$	−16.1135	−0.533573
$913$	−30.7959	−1.01920
$914$	−8.15505	−0.269745
$915$	26.5616	0.878099
$916$	−78.7482	−2.60191
$917$	−30.1898	−0.996957
$918$	−2.38199	−0.0786173
$919$	−5.59965	−0.184715	−0.0923577	−	0.995726i	$-0.529440\pi$
$919$	−5.59965	−0.184715	−0.0923577	+	0.995726i	$0.529440\pi$
$920$	160.298	5.28487
$921$	−6.92691	−0.228249
$922$	−88.5876	−2.91748
$923$	4.48002	0.147462
$924$	29.7798	0.979683
$925$	−128.471	−4.22408
$926$	−35.3492	−1.16165
$927$	7.72596	0.253754
$928$	4.49089	0.147421
$929$	5.98842	0.196474	0.0982369	−	0.995163i	$-0.468680\pi$
$929$	5.98842	0.196474	0.0982369	+	0.995163i	$0.468680\pi$
$930$	0	0
$931$	−0.990075	−0.0324484
$932$	35.8874	1.17553
$933$	21.8019	0.713761
$934$	−50.5845	−1.65517
$935$	−9.02495	−0.295147
$936$	−10.9265	−0.357145
$937$	16.4832	0.538481	0.269241	−	0.963073i	$-0.413227\pi$
$937$	16.4832	0.538481	0.269241	+	0.963073i	$0.413227\pi$
$938$	26.9148	0.878800
$939$	−19.4262	−0.633951
$940$	56.3899	1.83923
$941$	18.7850	0.612373	0.306186	−	0.951972i	$-0.400947\pi$
$941$	18.7850	0.612373	0.306186	+	0.951972i	$0.400947\pi$
$942$	7.68516	0.250396
$943$	−73.1312	−2.38148
$944$	50.8255	1.65423
$945$	10.9137	0.355023
$946$	12.8840	0.418893
$947$	18.6276	0.605316	0.302658	−	0.953099i	$-0.402126\pi$
$947$	18.6276	0.605316	0.302658	+	0.953099i	$0.402126\pi$
$948$	−37.9646	−1.23303
$949$	−3.95526	−0.128393
$950$	−61.6083	−1.99884
$951$	−13.7195	−0.444884
$952$	16.3312	0.529297
$953$	13.5379	0.438535	0.219268	−	0.975665i	$-0.429633\pi$
$953$	13.5379	0.438535	0.219268	+	0.975665i	$0.429633\pi$
$954$	−13.3713	−0.432911
$955$	−66.4776	−2.15116
$956$	−11.5283	−0.372852
$957$	−1.84294	−0.0595739
$958$	−14.6930	−0.474710
$959$	56.0138	1.80878
$960$	−1.48387	−0.0478917
$961$	0	0
$962$	50.8672	1.64003
$963$	9.12641	0.294094
$964$	48.1806	1.55179
$965$	55.3130	1.78059
$966$	43.5672	1.40175
$967$	52.7910	1.69764	0.848822	−	0.528679i	$-0.177312\pi$
$967$	52.7910	1.69764	0.848822	+	0.528679i	$0.177312\pi$
$968$	−33.0271	−1.06153
$969$	2.05123	0.0658951
$970$	−44.9921	−1.44461
$971$	−5.05817	−0.162324	−0.0811622	−	0.996701i	$-0.525863\pi$
$971$	−5.05817	−0.162324	−0.0811622	+	0.996701i	$0.525863\pi$
$972$	4.51180	0.144716
$973$	56.2058	1.80187
$974$	−16.1068	−0.516095
$975$	−18.7288	−0.599802
$976$	−48.7126	−1.55925
$977$	37.6772	1.20540	0.602701	−	0.797967i	$-0.294091\pi$
$977$	37.6772	1.20540	0.602701	+	0.797967i	$0.294091\pi$
$978$	−24.9077	−0.796461
$979$	−28.0819	−0.897503
$980$	−8.12774	−0.259631
$981$	6.62864	0.211636
$982$	−49.4564	−1.57822
$983$	19.9815	0.637309	0.318655	−	0.947871i	$-0.396769\pi$
$983$	19.9815	0.637309	0.318655	+	0.947871i	$0.396769\pi$
$984$	74.9415	2.38905
$985$	96.1852	3.06471
$986$	−1.81541	−0.0578143
$987$	8.53233	0.271587
$988$	16.9014	0.537705
$989$	13.0598	0.415277
$990$	24.6721	0.784131
$991$	−27.9100	−0.886591	−0.443295	−	0.896376i	$-0.646191\pi$
$991$	−27.9100	−0.886591	−0.443295	+	0.896376i	$0.646191\pi$
$992$	0	0
$993$	18.3803	0.583282
$994$	18.3053	0.580610
$995$	1.90914	0.0605238
$996$	57.4599	1.82069
$997$	−1.06805	−0.0338254	−0.0169127	−	0.999857i	$-0.505384\pi$
$997$	−1.06805	−0.0338254	−0.0169127	+	0.999857i	$0.505384\pi$
$998$	4.09042	0.129480
$999$	−11.6934	−0.369963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.2.a.r.1.8	yes	8
3.2	odd	2		8649.2.a.bd.1.1		8
31.30	odd	2		2883.2.a.q.1.8	✓	8
93.92	even	2		8649.2.a.bc.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2883.2.a.q.1.8	✓	8	31.30	odd	2
2883.2.a.r.1.8	yes	8	1.1	even	1	trivial
8649.2.a.bc.1.1		8	93.92	even	2
8649.2.a.bd.1.1		8	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2883 = 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2883.a (trivial)

\(f(q)\)	\(=\)	\(q+2.55182 q^{2} +1.00000 q^{3} +4.51180 q^{4} -3.99832 q^{5} +2.55182 q^{6} -2.72957 q^{7} +6.40966 q^{8} +1.00000 q^{9} -10.2030 q^{10} -2.41812 q^{11} +4.51180 q^{12} -1.70470 q^{13} -6.96538 q^{14} -3.99832 q^{15} +7.33272 q^{16} -0.933445 q^{17} +2.55182 q^{18} -2.19748 q^{19} -18.0396 q^{20} -2.72957 q^{21} -6.17061 q^{22} -6.25483 q^{23} +6.40966 q^{24} +10.9866 q^{25} -4.35008 q^{26} +1.00000 q^{27} -12.3153 q^{28} +0.762139 q^{29} -10.2030 q^{30} +5.89248 q^{32} -2.41812 q^{33} -2.38199 q^{34} +10.9137 q^{35} +4.51180 q^{36} -11.6934 q^{37} -5.60759 q^{38} -1.70470 q^{39} -25.6279 q^{40} +11.6920 q^{41} -6.96538 q^{42} -2.08795 q^{43} -10.9101 q^{44} -3.99832 q^{45} -15.9612 q^{46} -3.12589 q^{47} +7.33272 q^{48} +0.450549 q^{49} +28.0358 q^{50} -0.933445 q^{51} -7.69125 q^{52} -5.23989 q^{53} +2.55182 q^{54} +9.66842 q^{55} -17.4956 q^{56} -2.19748 q^{57} +1.94484 q^{58} +6.93133 q^{59} -18.0396 q^{60} -6.64318 q^{61} -2.72957 q^{63} +0.371123 q^{64} +6.81593 q^{65} -6.17061 q^{66} -3.86409 q^{67} -4.21152 q^{68} -6.25483 q^{69} +27.8498 q^{70} -2.62805 q^{71} +6.40966 q^{72} +2.32021 q^{73} -29.8395 q^{74} +10.9866 q^{75} -9.91460 q^{76} +6.60042 q^{77} -4.35008 q^{78} -8.41452 q^{79} -29.3186 q^{80} +1.00000 q^{81} +29.8358 q^{82} +12.7355 q^{83} -12.3153 q^{84} +3.73222 q^{85} -5.32809 q^{86} +0.762139 q^{87} -15.4993 q^{88} +11.6131 q^{89} -10.2030 q^{90} +4.65309 q^{91} -28.2205 q^{92} -7.97671 q^{94} +8.78625 q^{95} +5.89248 q^{96} +4.40969 q^{97} +1.14972 q^{98} -2.41812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 8 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} + 8 q^{9} - 20 q^{10} - 8 q^{11} + 4 q^{12} - 16 q^{13} - 12 q^{14} + 4 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 16 q^{23} + 8 q^{25}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 + 8 * q^9 - 20 * q^10 - 8 * q^11 + 4 * q^12 - 16 * q^13 - 12 * q^14 + 4 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 16 * q^23 + 8 * q^25 - 8 * q^26 + 8 * q^27 - 4 * q^28 - 16 * q^29 - 20 * q^30 + 4 * q^32 - 8 * q^33 - 16 * q^34 - 24 * q^35 + 4 * q^36 - 16 * q^37 - 12 * q^38 - 16 * q^39 - 16 * q^40 - 12 * q^42 - 32 * q^43 - 24 * q^44 - 16 * q^46 - 8 * q^47 + 4 * q^48 + 40 * q^49 + 8 * q^50 - 32 * q^52 - 16 * q^53 + 4 * q^54 + 16 * q^55 - 24 * q^56 - 16 * q^57 + 16 * q^58 + 24 * q^59 - 12 * q^60 - 48 * q^61 - 8 * q^63 - 16 * q^64 - 24 * q^65 - 40 * q^67 + 24 * q^68 - 16 * q^69 + 4 * q^70 + 16 * q^71 - 48 * q^73 - 48 * q^74 + 8 * q^75 - 20 * q^76 - 48 * q^77 - 8 * q^78 - 36 * q^80 + 8 * q^81 + 52 * q^82 - 24 * q^83 - 4 * q^84 - 16 * q^87 - 16 * q^88 - 24 * q^89 - 20 * q^90 + 16 * q^91 - 80 * q^92 - 24 * q^94 + 40 * q^95 + 4 * q^96 + 64 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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