LMFDB - Embedded newform 1083.2.a.m.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1083,2,Mod(1,1083)] 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("1083.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1083, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1083 = 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1083.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$8.64779853890$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	1083.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.347296 q^{2} -1.00000 q^{3} -1.87939 q^{4} -1.34730 q^{5} +0.347296 q^{6} -0.652704 q^{7} +1.34730 q^{8} +1.00000 q^{9} +0.467911 q^{10} +3.94356 q^{11} +1.87939 q^{12} +1.69459 q^{13} +0.226682 q^{14} +1.34730 q^{15} +3.29086 q^{16} -3.83750 q^{17} -0.347296 q^{18} +2.53209 q^{20} +0.652704 q^{21} -1.36959 q^{22} -3.63816 q^{23} -1.34730 q^{24} -3.18479 q^{25} -0.588526 q^{26} -1.00000 q^{27} +1.22668 q^{28} +10.5175 q^{29} -0.467911 q^{30} +6.46791 q^{31} -3.83750 q^{32} -3.94356 q^{33} +1.33275 q^{34} +0.879385 q^{35} -1.87939 q^{36} -2.94356 q^{37} -1.69459 q^{39} -1.81521 q^{40} -1.50980 q^{41} -0.226682 q^{42} -9.36959 q^{43} -7.41147 q^{44} -1.34730 q^{45} +1.26352 q^{46} -12.7665 q^{47} -3.29086 q^{48} -6.57398 q^{49} +1.10607 q^{50} +3.83750 q^{51} -3.18479 q^{52} -10.8007 q^{53} +0.347296 q^{54} -5.31315 q^{55} -0.879385 q^{56} -3.65270 q^{58} -2.77332 q^{59} -2.53209 q^{60} +4.31315 q^{61} -2.24628 q^{62} -0.652704 q^{63} -5.24897 q^{64} -2.28312 q^{65} +1.36959 q^{66} +7.88713 q^{67} +7.21213 q^{68} +3.63816 q^{69} -0.305407 q^{70} -5.36959 q^{71} +1.34730 q^{72} +5.86484 q^{73} +1.02229 q^{74} +3.18479 q^{75} -2.57398 q^{77} +0.588526 q^{78} -3.12836 q^{79} -4.43376 q^{80} +1.00000 q^{81} +0.524348 q^{82} -4.50980 q^{83} -1.22668 q^{84} +5.17024 q^{85} +3.25402 q^{86} -10.5175 q^{87} +5.31315 q^{88} -11.1334 q^{89} +0.467911 q^{90} -1.10607 q^{91} +6.83750 q^{92} -6.46791 q^{93} +4.43376 q^{94} +3.83750 q^{96} +6.70233 q^{97} +2.28312 q^{98} +3.94356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} - 6 q^{25} - 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 - 6 * q^25 - 12 * q^26 - 3 * q^27 - 3 * q^28 + 9 * q^29 - 6 * q^30 + 24 * q^31 - 9 * q^32 + 3 * q^33 - 15 * q^34 - 3 * q^35 + 6 * q^37 - 3 * q^39 - 9 * q^40 - 6 * q^41 + 6 * q^42 - 21 * q^43 - 12 * q^44 - 3 * q^45 + 9 * q^46 - 3 * q^47 + 6 * q^48 - 12 * q^49 - 9 * q^50 + 9 * q^51 - 6 * q^52 - 18 * q^53 + 6 * q^55 + 3 * q^56 - 12 * q^58 - 15 * q^59 - 3 * q^60 - 9 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 - 15 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 - 6 * q^69 - 3 * q^70 - 9 * q^71 + 3 * q^72 - 6 * q^73 - 3 * q^74 + 6 * q^75 + 12 * q^78 + 9 * q^79 + 3 * q^80 + 3 * q^81 + 21 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^85 - 18 * q^86 - 9 * q^87 - 6 * q^88 + 6 * q^90 + 9 * q^91 + 18 * q^92 - 24 * q^93 - 3 * q^94 + 9 * q^96 - 6 * q^97 + 15 * q^98 - 3 * 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 $

$2$	−0.347296	−0.245576	−0.122788	−	0.992433i	$-0.539183\pi$
$2$	−0.347296	−0.245576	−0.122788	+	0.992433i	$0.539183\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.87939	−0.939693
$5$	−1.34730	−0.602529	−0.301265	−	0.953541i	$-0.597409\pi$
$5$	−1.34730	−0.602529	−0.301265	+	0.953541i	$0.597409\pi$
$6$	0.347296	0.141783
$7$	−0.652704	−0.246699	−0.123349	−	0.992363i	$-0.539364\pi$
$7$	−0.652704	−0.246699	−0.123349	+	0.992363i	$0.539364\pi$
$8$	1.34730	0.476341
$9$	1.00000	0.333333
$10$	0.467911	0.147966
$11$	3.94356	1.18903	0.594514	−	0.804085i	$-0.297344\pi$
$11$	3.94356	1.18903	0.594514	+	0.804085i	$0.297344\pi$
$12$	1.87939	0.542532
$13$	1.69459	0.469995	0.234998	−	0.971996i	$-0.424492\pi$
$13$	1.69459	0.469995	0.234998	+	0.971996i	$0.424492\pi$
$14$	0.226682	0.0605832
$15$	1.34730	0.347870
$16$	3.29086	0.822715
$17$	−3.83750	−0.930730	−0.465365	−	0.885119i	$-0.654077\pi$
$17$	−3.83750	−0.930730	−0.465365	+	0.885119i	$0.654077\pi$
$18$	−0.347296	−0.0818585
$19$	0	0
$19$	0	0
$20$	2.53209	0.566192
$21$	0.652704	0.142432
$22$	−1.36959	−0.291997
$23$	−3.63816	−0.758608	−0.379304	−	0.925272i	$-0.623837\pi$
$23$	−3.63816	−0.758608	−0.379304	+	0.925272i	$0.623837\pi$
$24$	−1.34730	−0.275016
$25$	−3.18479	−0.636959
$26$	−0.588526	−0.115419
$27$	−1.00000	−0.192450
$28$	1.22668	0.231821
$29$	10.5175	1.95306	0.976529	−	0.215385i	$-0.0691007\pi$
$29$	10.5175	1.95306	0.976529	+	0.215385i	$0.0691007\pi$
$30$	−0.467911	−0.0854285
$31$	6.46791	1.16167	0.580836	−	0.814021i	$-0.302726\pi$
$31$	6.46791	1.16167	0.580836	+	0.814021i	$0.302726\pi$
$32$	−3.83750	−0.678380
$33$	−3.94356	−0.686486
$34$	1.33275	0.228564
$35$	0.879385	0.148643
$36$	−1.87939	−0.313231
$37$	−2.94356	−0.483919	−0.241959	−	0.970286i	$-0.577790\pi$
$37$	−2.94356	−0.483919	−0.241959	+	0.970286i	$0.577790\pi$
$38$	0	0
$39$	−1.69459	−0.271352
$40$	−1.81521	−0.287010
$41$	−1.50980	−0.235791	−0.117896	−	0.993026i	$-0.537615\pi$
$41$	−1.50980	−0.235791	−0.117896	+	0.993026i	$0.537615\pi$
$42$	−0.226682	−0.0349777
$43$	−9.36959	−1.42885	−0.714424	−	0.699713i	$-0.753311\pi$
$43$	−9.36959	−1.42885	−0.714424	+	0.699713i	$0.753311\pi$
$44$	−7.41147	−1.11732
$45$	−1.34730	−0.200843
$46$	1.26352	0.186296
$47$	−12.7665	−1.86219	−0.931094	−	0.364781i	$-0.881144\pi$
$47$	−12.7665	−1.86219	−0.931094	+	0.364781i	$0.881144\pi$
$48$	−3.29086	−0.474995
$49$	−6.57398	−0.939140
$50$	1.10607	0.156421
$51$	3.83750	0.537357
$52$	−3.18479	−0.441651
$53$	−10.8007	−1.48358	−0.741792	−	0.670630i	$-0.766024\pi$
$53$	−10.8007	−1.48358	−0.741792	+	0.670630i	$0.766024\pi$
$54$	0.347296	0.0472610
$55$	−5.31315	−0.716425
$56$	−0.879385	−0.117513
$57$	0	0
$58$	−3.65270	−0.479623
$59$	−2.77332	−0.361055	−0.180528	−	0.983570i	$-0.557781\pi$
$59$	−2.77332	−0.361055	−0.180528	+	0.983570i	$0.557781\pi$
$60$	−2.53209	−0.326891
$61$	4.31315	0.552242	0.276121	−	0.961123i	$-0.410951\pi$
$61$	4.31315	0.552242	0.276121	+	0.961123i	$0.410951\pi$
$62$	−2.24628	−0.285278
$63$	−0.652704	−0.0822329
$64$	−5.24897	−0.656121
$65$	−2.28312	−0.283186
$66$	1.36959	0.168584
$67$	7.88713	0.963566	0.481783	−	0.876291i	$-0.339989\pi$
$67$	7.88713	0.963566	0.481783	+	0.876291i	$0.339989\pi$
$68$	7.21213	0.874600
$69$	3.63816	0.437982
$70$	−0.305407	−0.0365032
$71$	−5.36959	−0.637253	−0.318626	−	0.947880i	$-0.603221\pi$
$71$	−5.36959	−0.637253	−0.318626	+	0.947880i	$0.603221\pi$
$72$	1.34730	0.158780
$73$	5.86484	0.686427	0.343214	−	0.939257i	$-0.388485\pi$
$73$	5.86484	0.686427	0.343214	+	0.939257i	$0.388485\pi$
$74$	1.02229	0.118839
$75$	3.18479	0.367748
$76$	0	0
$77$	−2.57398	−0.293332
$78$	0.588526	0.0666374
$79$	−3.12836	−0.351967	−0.175984	−	0.984393i	$-0.556311\pi$
$79$	−3.12836	−0.351967	−0.175984	+	0.984393i	$0.556311\pi$
$80$	−4.43376	−0.495710
$81$	1.00000	0.111111
$82$	0.524348	0.0579046
$83$	−4.50980	−0.495015	−0.247507	−	0.968886i	$-0.579611\pi$
$83$	−4.50980	−0.495015	−0.247507	+	0.968886i	$0.579611\pi$
$84$	−1.22668	−0.133842
$85$	5.17024	0.560792
$86$	3.25402	0.350890
$87$	−10.5175	−1.12760
$88$	5.31315	0.566383
$89$	−11.1334	−1.18014	−0.590069	−	0.807352i	$-0.700900\pi$
$89$	−11.1334	−1.18014	−0.590069	+	0.807352i	$0.700900\pi$
$90$	0.467911	0.0493222
$91$	−1.10607	−0.115947
$92$	6.83750	0.712858
$93$	−6.46791	−0.670691
$94$	4.43376	0.457308
$95$	0	0
$96$	3.83750	0.391663
$97$	6.70233	0.680519	0.340259	−	0.940332i	$-0.389485\pi$
$97$	6.70233	0.680519	0.340259	+	0.940332i	$0.389485\pi$
$98$	2.28312	0.230630
$99$	3.94356	0.396343
$100$	5.98545	0.598545
$101$	−1.93582	−0.192622	−0.0963108	−	0.995351i	$-0.530704\pi$
$101$	−1.93582	−0.192622	−0.0963108	+	0.995351i	$0.530704\pi$
$102$	−1.33275	−0.131962
$103$	1.03684	0.102163	0.0510813	−	0.998694i	$-0.483733\pi$
$103$	1.03684	0.102163	0.0510813	+	0.998694i	$0.483733\pi$
$104$	2.28312	0.223878
$105$	−0.879385	−0.0858192
$106$	3.75103	0.364332
$107$	−12.2121	−1.18059	−0.590296	−	0.807187i	$-0.700989\pi$
$107$	−12.2121	−1.18059	−0.590296	+	0.807187i	$0.700989\pi$
$108$	1.87939	0.180844
$109$	−4.02734	−0.385749	−0.192875	−	0.981223i	$-0.561781\pi$
$109$	−4.02734	−0.385749	−0.192875	+	0.981223i	$0.561781\pi$
$110$	1.84524	0.175936
$111$	2.94356	0.279391
$112$	−2.14796	−0.202963
$113$	−13.1925	−1.24105	−0.620525	−	0.784187i	$-0.713080\pi$
$113$	−13.1925	−1.24105	−0.620525	+	0.784187i	$0.713080\pi$
$114$	0	0
$115$	4.90167	0.457083
$116$	−19.7665	−1.83527
$117$	1.69459	0.156665
$118$	0.963163	0.0886664
$119$	2.50475	0.229610
$120$	1.81521	0.165705
$121$	4.55169	0.413790
$122$	−1.49794	−0.135617
$123$	1.50980	0.136134
$124$	−12.1557	−1.09161
$125$	11.0273	0.986315
$126$	0.226682	0.0201944
$127$	13.2490	1.17566	0.587828	−	0.808986i	$-0.299983\pi$
$127$	13.2490	1.17566	0.587828	+	0.808986i	$0.299983\pi$
$128$	9.49794	0.839507
$129$	9.36959	0.824946
$130$	0.792919	0.0695436
$131$	17.1780	1.50085	0.750424	−	0.660957i	$-0.229849\pi$
$131$	17.1780	1.50085	0.750424	+	0.660957i	$0.229849\pi$
$132$	7.41147	0.645086
$133$	0	0
$134$	−2.73917	−0.236628
$135$	1.34730	0.115957
$136$	−5.17024	−0.443345
$137$	−10.5466	−0.901060	−0.450530	−	0.892761i	$-0.648765\pi$
$137$	−10.5466	−0.901060	−0.450530	+	0.892761i	$0.648765\pi$
$138$	−1.26352	−0.107558
$139$	10.7811	0.914438	0.457219	−	0.889354i	$-0.348846\pi$
$139$	10.7811	0.914438	0.457219	+	0.889354i	$0.348846\pi$
$140$	−1.65270	−0.139679
$141$	12.7665	1.07513
$142$	1.86484	0.156494
$143$	6.68273	0.558838
$144$	3.29086	0.274238
$145$	−14.1702	−1.17677
$146$	−2.03684	−0.168570
$147$	6.57398	0.542213
$148$	5.53209	0.454735
$149$	−19.7520	−1.61814	−0.809072	−	0.587710i	$-0.800030\pi$
$149$	−19.7520	−1.61814	−0.809072	+	0.587710i	$0.800030\pi$
$150$	−1.10607	−0.0903100
$151$	3.10607	0.252768	0.126384	−	0.991981i	$-0.459663\pi$
$151$	3.10607	0.252768	0.126384	+	0.991981i	$0.459663\pi$
$152$	0	0
$153$	−3.83750	−0.310243
$154$	0.893933	0.0720352
$155$	−8.71419	−0.699941
$156$	3.18479	0.254987
$157$	0.736482	0.0587776	0.0293888	−	0.999568i	$-0.490644\pi$
$157$	0.736482	0.0587776	0.0293888	+	0.999568i	$0.490644\pi$
$158$	1.08647	0.0864346
$159$	10.8007	0.856548
$160$	5.17024	0.408744
$161$	2.37464	0.187148
$162$	−0.347296	−0.0272862
$163$	−12.6236	−0.988757	−0.494379	−	0.869247i	$-0.664604\pi$
$163$	−12.6236	−0.988757	−0.494379	+	0.869247i	$0.664604\pi$
$164$	2.83750	0.221571
$165$	5.31315	0.413628
$166$	1.56624	0.121564
$167$	−5.51754	−0.426960	−0.213480	−	0.976947i	$-0.568480\pi$
$167$	−5.51754	−0.426960	−0.213480	+	0.976947i	$0.568480\pi$
$168$	0.879385	0.0678460
$169$	−10.1284	−0.779104
$170$	−1.79561	−0.137717
$171$	0	0
$172$	17.6091	1.34268
$173$	12.9290	0.982975	0.491487	−	0.870885i	$-0.336453\pi$
$173$	12.9290	0.982975	0.491487	+	0.870885i	$0.336453\pi$
$174$	3.65270	0.276911
$175$	2.07873	0.157137
$176$	12.9777	0.978232
$177$	2.77332	0.208455
$178$	3.86659	0.289813
$179$	−15.0865	−1.12762	−0.563808	−	0.825906i	$-0.690664\pi$
$179$	−15.0865	−1.12762	−0.563808	+	0.825906i	$0.690664\pi$
$180$	2.53209	0.188731
$181$	−18.6827	−1.38868	−0.694338	−	0.719649i	$-0.744303\pi$
$181$	−18.6827	−1.38868	−0.694338	+	0.719649i	$0.744303\pi$
$182$	0.384133	0.0284738
$183$	−4.31315	−0.318837
$184$	−4.90167	−0.361356
$185$	3.96585	0.291575
$186$	2.24628	0.164705
$187$	−15.1334	−1.10666
$188$	23.9932	1.74988
$189$	0.652704	0.0474772
$190$	0	0
$191$	−8.55169	−0.618779	−0.309389	−	0.950935i	$-0.600125\pi$
$191$	−8.55169	−0.618779	−0.309389	+	0.950935i	$0.600125\pi$
$192$	5.24897	0.378812
$193$	16.9590	1.22074	0.610369	−	0.792117i	$-0.291021\pi$
$193$	16.9590	1.22074	0.610369	+	0.792117i	$0.291021\pi$
$194$	−2.32770	−0.167119
$195$	2.28312	0.163498
$196$	12.3550	0.882503
$197$	4.51754	0.321861	0.160931	−	0.986966i	$-0.448550\pi$
$197$	4.51754	0.321861	0.160931	+	0.986966i	$0.448550\pi$
$198$	−1.36959	−0.0973322
$199$	−8.04694	−0.570433	−0.285216	−	0.958463i	$-0.592065\pi$
$199$	−8.04694	−0.570433	−0.285216	+	0.958463i	$0.592065\pi$
$200$	−4.29086	−0.303410
$201$	−7.88713	−0.556315
$202$	0.672304	0.0473031
$203$	−6.86484	−0.481817
$204$	−7.21213	−0.504950
$205$	2.03415	0.142071
$206$	−0.360090	−0.0250886
$207$	−3.63816	−0.252869
$208$	5.57667	0.386672
$209$	0	0
$210$	0.305407	0.0210751
$211$	20.0838	1.38262	0.691312	−	0.722556i	$-0.257033\pi$
$211$	20.0838	1.38262	0.691312	+	0.722556i	$0.257033\pi$
$212$	20.2986	1.39411
$213$	5.36959	0.367918
$214$	4.24123	0.289924
$215$	12.6236	0.860923
$216$	−1.34730	−0.0916719
$217$	−4.22163	−0.286583
$218$	1.39868	0.0947306
$219$	−5.86484	−0.396309
$220$	9.98545	0.673219
$221$	−6.50299	−0.437439
$222$	−1.02229	−0.0686115
$223$	19.5895	1.31181	0.655904	−	0.754845i	$-0.272288\pi$
$223$	19.5895	1.31181	0.655904	+	0.754845i	$0.272288\pi$
$224$	2.50475	0.167355
$225$	−3.18479	−0.212320
$226$	4.58172	0.304771
$227$	−18.4979	−1.22775	−0.613876	−	0.789403i	$-0.710390\pi$
$227$	−18.4979	−1.22775	−0.613876	+	0.789403i	$0.710390\pi$
$228$	0	0
$229$	−28.1634	−1.86109	−0.930546	−	0.366175i	$-0.880667\pi$
$229$	−28.1634	−1.86109	−0.930546	+	0.366175i	$0.880667\pi$
$230$	−1.70233	−0.112249
$231$	2.57398	0.169355
$232$	14.1702	0.930322
$233$	0.155697	0.0102000	0.00510001	−	0.999987i	$-0.498377\pi$
$233$	0.155697	0.0102000	0.00510001	+	0.999987i	$0.498377\pi$
$234$	−0.588526	−0.0384731
$235$	17.2003	1.12202
$236$	5.21213	0.339281
$237$	3.12836	0.203209
$238$	−0.869890	−0.0563866
$239$	6.63041	0.428886	0.214443	−	0.976737i	$-0.431206\pi$
$239$	6.63041	0.428886	0.214443	+	0.976737i	$0.431206\pi$
$240$	4.43376	0.286198
$241$	−5.26083	−0.338880	−0.169440	−	0.985541i	$-0.554196\pi$
$241$	−5.26083	−0.338880	−0.169440	+	0.985541i	$0.554196\pi$
$242$	−1.58079	−0.101617
$243$	−1.00000	−0.0641500
$244$	−8.10607	−0.518938
$245$	8.85710	0.565859
$246$	−0.524348	−0.0334312
$247$	0	0
$248$	8.71419	0.553352
$249$	4.50980	0.285797
$250$	−3.82976	−0.242215
$251$	14.8152	0.935128	0.467564	−	0.883959i	$-0.345132\pi$
$251$	14.8152	0.935128	0.467564	+	0.883959i	$0.345132\pi$
$252$	1.22668	0.0772737
$253$	−14.3473	−0.902007
$254$	−4.60132	−0.288712
$255$	−5.17024	−0.323773
$256$	7.19934	0.449959
$257$	−19.1634	−1.19538	−0.597691	−	0.801726i	$-0.703915\pi$
$257$	−19.1634	−1.19538	−0.597691	+	0.801726i	$0.703915\pi$
$258$	−3.25402	−0.202587
$259$	1.92127	0.119382
$260$	4.29086	0.266108
$261$	10.5175	0.651019
$262$	−5.96585	−0.368572
$263$	−16.4979	−1.01731	−0.508653	−	0.860971i	$-0.669856\pi$
$263$	−16.4979	−1.01731	−0.508653	+	0.860971i	$0.669856\pi$
$264$	−5.31315	−0.327002
$265$	14.5517	0.893903
$266$	0	0
$267$	11.1334	0.681354
$268$	−14.8229	−0.905456
$269$	4.21213	0.256818	0.128409	−	0.991721i	$-0.459013\pi$
$269$	4.21213	0.256818	0.128409	+	0.991721i	$0.459013\pi$
$270$	−0.467911	−0.0284762
$271$	9.16250	0.556582	0.278291	−	0.960497i	$-0.410232\pi$
$271$	9.16250	0.556582	0.278291	+	0.960497i	$0.410232\pi$
$272$	−12.6287	−0.765725
$273$	1.10607	0.0669422
$274$	3.66281	0.221278
$275$	−12.5594	−0.757362
$276$	−6.83750	−0.411569
$277$	−22.4953	−1.35161	−0.675804	−	0.737081i	$-0.736204\pi$
$277$	−22.4953	−1.35161	−0.675804	+	0.737081i	$0.736204\pi$
$278$	−3.74422	−0.224564
$279$	6.46791	0.387224
$280$	1.18479	0.0708049
$281$	−23.5280	−1.40356	−0.701781	−	0.712393i	$-0.747611\pi$
$281$	−23.5280	−1.40356	−0.701781	+	0.712393i	$0.747611\pi$
$282$	−4.43376	−0.264027
$283$	26.7469	1.58994	0.794969	−	0.606650i	$-0.207487\pi$
$283$	26.7469	1.58994	0.794969	+	0.606650i	$0.207487\pi$
$284$	10.0915	0.598821
$285$	0	0
$286$	−2.32089	−0.137237
$287$	0.985452	0.0581694
$288$	−3.83750	−0.226127
$289$	−2.27362	−0.133743
$290$	4.92127	0.288987
$291$	−6.70233	−0.392898
$292$	−11.0223	−0.645031
$293$	−0.207081	−0.0120978	−0.00604891	−	0.999982i	$-0.501925\pi$
$293$	−0.207081	−0.0120978	−0.00604891	+	0.999982i	$0.501925\pi$
$294$	−2.28312	−0.133154
$295$	3.73648	0.217546
$296$	−3.96585	−0.230510
$297$	−3.94356	−0.228829
$298$	6.85978	0.397377
$299$	−6.16519	−0.356542
$300$	−5.98545	−0.345570
$301$	6.11556	0.352495
$302$	−1.07873	−0.0620737
$303$	1.93582	0.111210
$304$	0	0
$305$	−5.81109	−0.332742
$306$	1.33275	0.0761882
$307$	15.3182	0.874256	0.437128	−	0.899399i	$-0.355996\pi$
$307$	15.3182	0.874256	0.437128	+	0.899399i	$0.355996\pi$
$308$	4.83750	0.275642
$309$	−1.03684	−0.0589836
$310$	3.02641	0.171888
$311$	15.6432	0.887045	0.443522	−	0.896263i	$-0.353729\pi$
$311$	15.6432	0.887045	0.443522	+	0.896263i	$0.353729\pi$
$312$	−2.28312	−0.129256
$313$	10.1625	0.574419	0.287209	−	0.957868i	$-0.407272\pi$
$313$	10.1625	0.574419	0.287209	+	0.957868i	$0.407272\pi$
$314$	−0.255777	−0.0144344
$315$	0.879385	0.0495477
$316$	5.87939	0.330741
$317$	−7.64765	−0.429535	−0.214767	−	0.976665i	$-0.568899\pi$
$317$	−7.64765	−0.429535	−0.214767	+	0.976665i	$0.568899\pi$
$318$	−3.75103	−0.210347
$319$	41.4766	2.32224
$320$	7.07192	0.395332
$321$	12.2121	0.681615
$322$	−0.824703	−0.0459589
$323$	0	0
$324$	−1.87939	−0.104410
$325$	−5.39693	−0.299368
$326$	4.38413	0.242815
$327$	4.02734	0.222712
$328$	−2.03415	−0.112317
$329$	8.33275	0.459399
$330$	−1.84524	−0.101577
$331$	−4.10607	−0.225690	−0.112845	−	0.993613i	$-0.535996\pi$
$331$	−4.10607	−0.225690	−0.112845	+	0.993613i	$0.535996\pi$
$332$	8.47565	0.465162
$333$	−2.94356	−0.161306
$334$	1.91622	0.104851
$335$	−10.6263	−0.580577
$336$	2.14796	0.117181
$337$	−12.0915	−0.658667	−0.329334	−	0.944214i	$-0.606824\pi$
$337$	−12.0915	−0.658667	−0.329334	+	0.944214i	$0.606824\pi$
$338$	3.51754	0.191329
$339$	13.1925	0.716520
$340$	−9.71688	−0.526972
$341$	25.5066	1.38126
$342$	0	0
$343$	8.85978	0.478383
$344$	−12.6236	−0.680619
$345$	−4.90167	−0.263897
$346$	−4.49020	−0.241395
$347$	−4.14290	−0.222403	−0.111201	−	0.993798i	$-0.535470\pi$
$347$	−4.14290	−0.222403	−0.111201	+	0.993798i	$0.535470\pi$
$348$	19.7665	1.05960
$349$	−0.0392007	−0.00209837	−0.00104918	−	0.999999i	$-0.500334\pi$
$349$	−0.0392007	−0.00209837	−0.00104918	+	0.999999i	$0.500334\pi$
$350$	−0.721934	−0.0385890
$351$	−1.69459	−0.0904507
$352$	−15.1334	−0.806613
$353$	7.16250	0.381222	0.190611	−	0.981666i	$-0.438953\pi$
$353$	7.16250	0.381222	0.190611	+	0.981666i	$0.438953\pi$
$354$	−0.963163	−0.0511916
$355$	7.23442	0.383963
$356$	20.9240	1.10897
$357$	−2.50475	−0.132565
$358$	5.23947	0.276915
$359$	−20.4415	−1.07886	−0.539431	−	0.842030i	$-0.681360\pi$
$359$	−20.4415	−1.07886	−0.539431	+	0.842030i	$0.681360\pi$
$360$	−1.81521	−0.0956698
$361$	0	0
$362$	6.48845	0.341025
$363$	−4.55169	−0.238902
$364$	2.07873	0.108955
$365$	−7.90167	−0.413593
$366$	1.49794	0.0782986
$367$	−1.59533	−0.0832757	−0.0416379	−	0.999133i	$-0.513258\pi$
$367$	−1.59533	−0.0832757	−0.0416379	+	0.999133i	$0.513258\pi$
$368$	−11.9727	−0.624118
$369$	−1.50980	−0.0785971
$370$	−1.37733	−0.0716038
$371$	7.04963	0.365999
$372$	12.1557	0.630244
$373$	−12.8520	−0.665454	−0.332727	−	0.943023i	$-0.607969\pi$
$373$	−12.8520	−0.665454	−0.332727	+	0.943023i	$0.607969\pi$
$374$	5.25578	0.271770
$375$	−11.0273	−0.569449
$376$	−17.2003	−0.887036
$377$	17.8229	0.917929
$378$	−0.226682	−0.0116592
$379$	−15.7023	−0.806575	−0.403287	−	0.915073i	$-0.632132\pi$
$379$	−15.7023	−0.806575	−0.403287	+	0.915073i	$0.632132\pi$
$380$	0	0
$381$	−13.2490	−0.678765
$382$	2.96997	0.151957
$383$	−16.4483	−0.840469	−0.420235	−	0.907415i	$-0.638052\pi$
$383$	−16.4483	−0.840469	−0.420235	+	0.907415i	$0.638052\pi$
$384$	−9.49794	−0.484690
$385$	3.46791	0.176741
$386$	−5.88981	−0.299784
$387$	−9.36959	−0.476283
$388$	−12.5963	−0.639479
$389$	7.53302	0.381939	0.190970	−	0.981596i	$-0.438837\pi$
$389$	7.53302	0.381939	0.190970	+	0.981596i	$0.438837\pi$
$390$	−0.792919	−0.0401510
$391$	13.9614	0.706059
$392$	−8.85710	−0.447351
$393$	−17.1780	−0.866515
$394$	−1.56893	−0.0790413
$395$	4.21482	0.212071
$396$	−7.41147	−0.372441
$397$	−11.2189	−0.563062	−0.281531	−	0.959552i	$-0.590842\pi$
$397$	−11.2189	−0.563062	−0.281531	+	0.959552i	$0.590842\pi$
$398$	2.79467	0.140084
$399$	0	0
$400$	−10.4807	−0.524035
$401$	24.2550	1.21123	0.605617	−	0.795756i	$-0.292926\pi$
$401$	24.2550	1.21123	0.605617	+	0.795756i	$0.292926\pi$
$402$	2.73917	0.136617
$403$	10.9605	0.545980
$404$	3.63816	0.181005
$405$	−1.34730	−0.0669477
$406$	2.38413	0.118323
$407$	−11.6081	−0.575393
$408$	5.17024	0.255965
$409$	26.2841	1.29966	0.649831	−	0.760078i	$-0.274840\pi$
$409$	26.2841	1.29966	0.649831	+	0.760078i	$0.274840\pi$
$410$	−0.706452	−0.0348892
$411$	10.5466	0.520227
$412$	−1.94862	−0.0960014
$413$	1.81016	0.0890719
$414$	1.26352	0.0620985
$415$	6.07604	0.298261
$416$	−6.50299	−0.318835
$417$	−10.7811	−0.527951
$418$	0	0
$419$	13.2226	0.645964	0.322982	−	0.946405i	$-0.395315\pi$
$419$	13.2226	0.645964	0.322982	+	0.946405i	$0.395315\pi$
$420$	1.65270	0.0806437
$421$	−37.0360	−1.80502	−0.902512	−	0.430664i	$-0.858280\pi$
$421$	−37.0360	−1.80502	−0.902512	+	0.430664i	$0.858280\pi$
$422$	−6.97502	−0.339539
$423$	−12.7665	−0.620729
$424$	−14.5517	−0.706693
$425$	12.2216	0.592836
$426$	−1.86484	−0.0903517
$427$	−2.81521	−0.136237
$428$	22.9513	1.10939
$429$	−6.68273	−0.322645
$430$	−4.38413	−0.211422
$431$	9.47296	0.456297	0.228148	−	0.973626i	$-0.426733\pi$
$431$	9.47296	0.456297	0.228148	+	0.973626i	$0.426733\pi$
$432$	−3.29086	−0.158332
$433$	−22.5226	−1.08237	−0.541183	−	0.840905i	$-0.682024\pi$
$433$	−22.5226	−1.08237	−0.541183	+	0.840905i	$0.682024\pi$
$434$	1.46616	0.0703778
$435$	14.1702	0.679411
$436$	7.56893	0.362486
$437$	0	0
$438$	2.03684	0.0973238
$439$	−33.2327	−1.58611	−0.793054	−	0.609151i	$-0.791510\pi$
$439$	−33.2327	−1.58611	−0.793054	+	0.609151i	$0.791510\pi$
$440$	−7.15839	−0.341263
$441$	−6.57398	−0.313047
$442$	2.25847	0.107424
$443$	30.6290	1.45523	0.727613	−	0.685987i	$-0.240629\pi$
$443$	30.6290	1.45523	0.727613	+	0.685987i	$0.240629\pi$
$444$	−5.53209	−0.262541
$445$	15.0000	0.711068
$446$	−6.80335	−0.322148
$447$	19.7520	0.934236
$448$	3.42602	0.161864
$449$	15.0925	0.712257	0.356128	−	0.934437i	$-0.384097\pi$
$449$	15.0925	0.712257	0.356128	+	0.934437i	$0.384097\pi$
$450$	1.10607	0.0521405
$451$	−5.95399	−0.280363
$452$	24.7939	1.16620
$453$	−3.10607	−0.145936
$454$	6.42427	0.301506
$455$	1.49020	0.0698616
$456$	0	0
$457$	19.8462	0.928365	0.464182	−	0.885740i	$-0.346348\pi$
$457$	19.8462	0.928365	0.464182	+	0.885740i	$0.346348\pi$
$458$	9.78106	0.457039
$459$	3.83750	0.179119
$460$	−9.21213	−0.429518
$461$	−34.7648	−1.61916	−0.809578	−	0.587012i	$-0.800304\pi$
$461$	−34.7648	−1.61916	−0.809578	+	0.587012i	$0.800304\pi$
$462$	−0.893933	−0.0415895
$463$	−3.42602	−0.159221	−0.0796104	−	0.996826i	$-0.525368\pi$
$463$	−3.42602	−0.159221	−0.0796104	+	0.996826i	$0.525368\pi$
$464$	34.6117	1.60681
$465$	8.71419	0.404111
$466$	−0.0540729	−0.00250488
$467$	−11.3250	−0.524059	−0.262029	−	0.965060i	$-0.584392\pi$
$467$	−11.3250	−0.524059	−0.262029	+	0.965060i	$0.584392\pi$
$468$	−3.18479	−0.147217
$469$	−5.14796	−0.237711
$470$	−5.97359	−0.275541
$471$	−0.736482	−0.0339353
$472$	−3.73648	−0.171986
$473$	−36.9495	−1.69894
$474$	−1.08647	−0.0499031
$475$	0	0
$476$	−4.70739	−0.215763
$477$	−10.8007	−0.494528
$478$	−2.30272	−0.105324
$479$	11.5672	0.528518	0.264259	−	0.964452i	$-0.414873\pi$
$479$	11.5672	0.528518	0.264259	+	0.964452i	$0.414873\pi$
$480$	−5.17024	−0.235988
$481$	−4.98814	−0.227440
$482$	1.82707	0.0832206
$483$	−2.37464	−0.108050
$484$	−8.55438	−0.388835
$485$	−9.03003	−0.410033
$486$	0.347296	0.0157537
$487$	11.7469	0.532303	0.266152	−	0.963931i	$-0.414248\pi$
$487$	11.7469	0.532303	0.266152	+	0.963931i	$0.414248\pi$
$488$	5.81109	0.263056
$489$	12.6236	0.570859
$490$	−3.07604	−0.138961
$491$	10.2540	0.462758	0.231379	−	0.972864i	$-0.425676\pi$
$491$	10.2540	0.462758	0.231379	+	0.972864i	$0.425676\pi$
$492$	−2.83750	−0.127924
$493$	−40.3610	−1.81777
$494$	0	0
$495$	−5.31315	−0.238808
$496$	21.2850	0.955724
$497$	3.50475	0.157209
$498$	−1.56624	−0.0701848
$499$	−6.45842	−0.289118	−0.144559	−	0.989496i	$-0.546176\pi$
$499$	−6.45842	−0.289118	−0.144559	+	0.989496i	$0.546176\pi$
$500$	−20.7246	−0.926833
$501$	5.51754	0.246506
$502$	−5.14527	−0.229645
$503$	−18.3081	−0.816318	−0.408159	−	0.912911i	$-0.633829\pi$
$503$	−18.3081	−0.816318	−0.408159	+	0.912911i	$0.633829\pi$
$504$	−0.879385	−0.0391709
$505$	2.60813	0.116060
$506$	4.98276	0.221511
$507$	10.1284	0.449816
$508$	−24.8999	−1.10476
$509$	12.0692	0.534959	0.267480	−	0.963564i	$-0.413809\pi$
$509$	12.0692	0.534959	0.267480	+	0.963564i	$0.413809\pi$
$510$	1.79561	0.0795108
$511$	−3.82800	−0.169341
$512$	−21.4962	−0.950006
$513$	0	0
$514$	6.65539	0.293557
$515$	−1.39693	−0.0615559
$516$	−17.6091	−0.775196
$517$	−50.3455	−2.21419
$518$	−0.667252	−0.0293174
$519$	−12.9290	−0.567521
$520$	−3.07604	−0.134893
$521$	28.5699	1.25167	0.625834	−	0.779956i	$-0.284759\pi$
$521$	28.5699	1.25167	0.625834	+	0.779956i	$0.284759\pi$
$522$	−3.65270	−0.159874
$523$	18.6459	0.815328	0.407664	−	0.913132i	$-0.366343\pi$
$523$	18.6459	0.815328	0.407664	+	0.913132i	$0.366343\pi$
$524$	−32.2841	−1.41034
$525$	−2.07873	−0.0907230
$526$	5.72967	0.249826
$527$	−24.8206	−1.08120
$528$	−12.9777	−0.564782
$529$	−9.76382	−0.424514
$530$	−5.05375	−0.219521
$531$	−2.77332	−0.120352
$532$	0	0
$533$	−2.55850	−0.110821
$534$	−3.86659	−0.167324
$535$	16.4534	0.711341
$536$	10.6263	0.458986
$537$	15.0865	0.651029
$538$	−1.46286	−0.0630683
$539$	−25.9249	−1.11666
$540$	−2.53209	−0.108964
$541$	−17.3628	−0.746484	−0.373242	−	0.927734i	$-0.621754\pi$
$541$	−17.3628	−0.746484	−0.373242	+	0.927734i	$0.621754\pi$
$542$	−3.18210	−0.136683
$543$	18.6827	0.801753
$544$	14.7264	0.631388
$545$	5.42602	0.232425
$546$	−0.384133	−0.0164394
$547$	5.05232	0.216022	0.108011	−	0.994150i	$-0.465552\pi$
$547$	5.05232	0.216022	0.108011	+	0.994150i	$0.465552\pi$
$548$	19.8212	0.846719
$549$	4.31315	0.184081
$550$	4.36184	0.185990
$551$	0	0
$552$	4.90167	0.208629
$553$	2.04189	0.0868300
$554$	7.81252	0.331922
$555$	−3.96585	−0.168341
$556$	−20.2618	−0.859290
$557$	−23.9763	−1.01591	−0.507954	−	0.861384i	$-0.669598\pi$
$557$	−23.9763	−1.01591	−0.507954	+	0.861384i	$0.669598\pi$
$558$	−2.24628	−0.0950927
$559$	−15.8776	−0.671552
$560$	2.89393	0.122291
$561$	15.1334	0.638933
$562$	8.17118	0.344680
$563$	42.6837	1.79890	0.899451	−	0.437022i	$-0.143967\pi$
$563$	42.6837	1.79890	0.899451	+	0.437022i	$0.143967\pi$
$564$	−23.9932	−1.01030
$565$	17.7743	0.747768
$566$	−9.28910	−0.390450
$567$	−0.652704	−0.0274110
$568$	−7.23442	−0.303550
$569$	21.9358	0.919598	0.459799	−	0.888023i	$-0.347922\pi$
$569$	21.9358	0.919598	0.459799	+	0.888023i	$0.347922\pi$
$570$	0	0
$571$	−32.3063	−1.35198	−0.675989	−	0.736912i	$-0.736283\pi$
$571$	−32.3063	−1.35198	−0.675989	+	0.736912i	$0.736283\pi$
$572$	−12.5594	−0.525136
$573$	8.55169	0.357252
$574$	−0.342244	−0.0142850
$575$	11.5868	0.483202
$576$	−5.24897	−0.218707
$577$	−46.8120	−1.94881	−0.974405	−	0.224800i	$-0.927827\pi$
$577$	−46.8120	−1.94881	−0.974405	+	0.224800i	$0.927827\pi$
$578$	0.789621	0.0328439
$579$	−16.9590	−0.704794
$580$	26.6313	1.10581
$581$	2.94356	0.122120
$582$	2.32770	0.0964861
$583$	−42.5931	−1.76403
$584$	7.90167	0.326974
$585$	−2.28312	−0.0943953
$586$	0.0719186	0.00297093
$587$	−24.7820	−1.02286	−0.511431	−	0.859324i	$-0.670884\pi$
$587$	−24.7820	−1.02286	−0.511431	+	0.859324i	$0.670884\pi$
$588$	−12.3550	−0.509513
$589$	0	0
$590$	−1.29767	−0.0534241
$591$	−4.51754	−0.185827
$592$	−9.68685	−0.398127
$593$	−3.65364	−0.150037	−0.0750185	−	0.997182i	$-0.523902\pi$
$593$	−3.65364	−0.150037	−0.0750185	+	0.997182i	$0.523902\pi$
$594$	1.36959	0.0561948
$595$	−3.37464	−0.138347
$596$	37.1215	1.52056
$597$	8.04694	0.329339
$598$	2.14115	0.0875581
$599$	1.49701	0.0611660	0.0305830	−	0.999532i	$-0.490264\pi$
$599$	1.49701	0.0611660	0.0305830	+	0.999532i	$0.490264\pi$
$600$	4.29086	0.175174
$601$	23.8239	0.971796	0.485898	−	0.874015i	$-0.338493\pi$
$601$	23.8239	0.971796	0.485898	+	0.874015i	$0.338493\pi$
$602$	−2.12391	−0.0865642
$603$	7.88713	0.321189
$604$	−5.83750	−0.237524
$605$	−6.13247	−0.249321
$606$	−0.672304	−0.0273105
$607$	16.4757	0.668726	0.334363	−	0.942444i	$-0.391479\pi$
$607$	16.4757	0.668726	0.334363	+	0.942444i	$0.391479\pi$
$608$	0	0
$609$	6.86484	0.278177
$610$	2.01817	0.0817133
$611$	−21.6340	−0.875219
$612$	7.21213	0.291533
$613$	1.33368	0.0538669	0.0269335	−	0.999637i	$-0.491426\pi$
$613$	1.33368	0.0538669	0.0269335	+	0.999637i	$0.491426\pi$
$614$	−5.31996	−0.214696
$615$	−2.03415	−0.0820248
$616$	−3.46791	−0.139726
$617$	36.1421	1.45503	0.727513	−	0.686094i	$-0.240676\pi$
$617$	36.1421	1.45503	0.727513	+	0.686094i	$0.240676\pi$
$618$	0.360090	0.0144849
$619$	19.3158	0.776369	0.388185	−	0.921582i	$-0.373102\pi$
$619$	19.3158	0.776369	0.388185	+	0.921582i	$0.373102\pi$
$620$	16.3773	0.657729
$621$	3.63816	0.145994
$622$	−5.43283	−0.217837
$623$	7.26682	0.291139
$624$	−5.57667	−0.223245
$625$	1.06687	0.0426746
$626$	−3.52940	−0.141063
$627$	0	0
$628$	−1.38413	−0.0552329
$629$	11.2959	0.450397
$630$	−0.305407	−0.0121677
$631$	28.5226	1.13547	0.567733	−	0.823213i	$-0.307821\pi$
$631$	28.5226	1.13547	0.567733	+	0.823213i	$0.307821\pi$
$632$	−4.21482	−0.167657
$633$	−20.0838	−0.798259
$634$	2.65600	0.105483
$635$	−17.8503	−0.708367
$636$	−20.2986	−0.804892
$637$	−11.1402	−0.441391
$638$	−14.4047	−0.570286
$639$	−5.36959	−0.212418
$640$	−12.7965	−0.505828
$641$	−31.0019	−1.22450	−0.612250	−	0.790664i	$-0.709735\pi$
$641$	−31.0019	−1.22450	−0.612250	+	0.790664i	$0.709735\pi$
$642$	−4.24123	−0.167388
$643$	23.6628	0.933170	0.466585	−	0.884476i	$-0.345484\pi$
$643$	23.6628	0.933170	0.466585	+	0.884476i	$0.345484\pi$
$644$	−4.46286	−0.175861
$645$	−12.6236	−0.497054
$646$	0	0
$647$	36.0865	1.41871	0.709353	−	0.704854i	$-0.248987\pi$
$647$	36.0865	1.41871	0.709353	+	0.704854i	$0.248987\pi$
$648$	1.34730	0.0529268
$649$	−10.9368	−0.429305
$650$	1.87433	0.0735174
$651$	4.22163	0.165459
$652$	23.7246	0.929128
$653$	−37.4489	−1.46549	−0.732745	−	0.680504i	$-0.761761\pi$
$653$	−37.4489	−1.46549	−0.732745	+	0.680504i	$0.761761\pi$
$654$	−1.39868	−0.0546928
$655$	−23.1438	−0.904305
$656$	−4.96854	−0.193989
$657$	5.86484	0.228809
$658$	−2.89393	−0.112817
$659$	19.3310	0.753029	0.376514	−	0.926411i	$-0.377123\pi$
$659$	19.3310	0.753029	0.376514	+	0.926411i	$0.377123\pi$
$660$	−9.98545	−0.388683
$661$	−24.6236	−0.957747	−0.478874	−	0.877884i	$-0.658955\pi$
$661$	−24.6236	−0.957747	−0.478874	+	0.877884i	$0.658955\pi$
$662$	1.42602	0.0554239
$663$	6.50299	0.252555
$664$	−6.07604	−0.235796
$665$	0	0
$666$	1.02229	0.0396129
$667$	−38.2645	−1.48161
$668$	10.3696	0.401211
$669$	−19.5895	−0.757372
$670$	3.69047	0.142575
$671$	17.0092	0.656632
$672$	−2.50475	−0.0966227
$673$	42.4347	1.63574	0.817869	−	0.575405i	$-0.195156\pi$
$673$	42.4347	1.63574	0.817869	+	0.575405i	$0.195156\pi$
$674$	4.19934	0.161753
$675$	3.18479	0.122583
$676$	19.0351	0.732119
$677$	14.5963	0.560980	0.280490	−	0.959857i	$-0.409503\pi$
$677$	14.5963	0.560980	0.280490	+	0.959857i	$0.409503\pi$
$678$	−4.58172	−0.175960
$679$	−4.37464	−0.167883
$680$	6.96585	0.267128
$681$	18.4979	0.708843
$682$	−8.85835	−0.339204
$683$	17.8043	0.681262	0.340631	−	0.940197i	$-0.389359\pi$
$683$	17.8043	0.681262	0.340631	+	0.940197i	$0.389359\pi$
$684$	0	0
$685$	14.2094	0.542915
$686$	−3.07697	−0.117479
$687$	28.1634	1.07450
$688$	−30.8340	−1.17553
$689$	−18.3027	−0.697278
$690$	1.70233	0.0648067
$691$	12.4730	0.474494	0.237247	−	0.971449i	$-0.423755\pi$
$691$	12.4730	0.474494	0.237247	+	0.971449i	$0.423755\pi$
$692$	−24.2986	−0.923694
$693$	−2.57398	−0.0977773
$694$	1.43882	0.0546167
$695$	−14.5253	−0.550975
$696$	−14.1702	−0.537122
$697$	5.79385	0.219458
$698$	0.0136143	0.000515308 0
$699$	−0.155697	−0.00588899
$700$	−3.90673	−0.147660
$701$	−3.23349	−0.122127	−0.0610636	−	0.998134i	$-0.519449\pi$
$701$	−3.23349	−0.122127	−0.0610636	+	0.998134i	$0.519449\pi$
$702$	0.588526	0.0222125
$703$	0	0
$704$	−20.6996	−0.780147
$705$	−17.2003	−0.647800
$706$	−2.48751	−0.0936187
$707$	1.26352	0.0475195
$708$	−5.21213	−0.195884
$709$	−21.0256	−0.789632	−0.394816	−	0.918760i	$-0.629192\pi$
$709$	−21.0256	−0.789632	−0.394816	+	0.918760i	$0.629192\pi$
$710$	−2.51249	−0.0942920
$711$	−3.12836	−0.117322
$712$	−15.0000	−0.562149
$713$	−23.5313	−0.881253
$714$	0.869890	0.0325548
$715$	−9.00362	−0.336716
$716$	28.3533	1.05961
$717$	−6.63041	−0.247617
$718$	7.09926	0.264942
$719$	−4.05232	−0.151126	−0.0755630	−	0.997141i	$-0.524075\pi$
$719$	−4.05232	−0.151126	−0.0755630	+	0.997141i	$0.524075\pi$
$720$	−4.43376	−0.165237
$721$	−0.676747	−0.0252034
$722$	0	0
$723$	5.26083	0.195652
$724$	35.1121	1.30493
$725$	−33.4962	−1.24402
$726$	1.58079	0.0586684
$727$	−40.9231	−1.51776	−0.758878	−	0.651233i	$-0.774252\pi$
$727$	−40.9231	−1.51776	−0.758878	+	0.651233i	$0.774252\pi$
$728$	−1.49020	−0.0552305
$729$	1.00000	0.0370370
$730$	2.74422	0.101568
$731$	35.9557	1.32987
$732$	8.10607	0.299609
$733$	7.26857	0.268471	0.134235	−	0.990949i	$-0.457142\pi$
$733$	7.26857	0.268471	0.134235	+	0.990949i	$0.457142\pi$
$734$	0.554053	0.0204505
$735$	−8.85710	−0.326699
$736$	13.9614	0.514624
$737$	31.1034	1.14571
$738$	0.524348	0.0193015
$739$	4.65002	0.171054	0.0855268	−	0.996336i	$-0.472743\pi$
$739$	4.65002	0.171054	0.0855268	+	0.996336i	$0.472743\pi$
$740$	−7.45336	−0.273991
$741$	0	0
$742$	−2.44831	−0.0898803
$743$	−2.68241	−0.0984080	−0.0492040	−	0.998789i	$-0.515668\pi$
$743$	−2.68241	−0.0984080	−0.0492040	+	0.998789i	$0.515668\pi$
$744$	−8.71419	−0.319478
$745$	26.6117	0.974979
$746$	4.46347	0.163419
$747$	−4.50980	−0.165005
$748$	28.4415	1.03992
$749$	7.97090	0.291250
$750$	3.82976	0.139843
$751$	32.4320	1.18346	0.591730	−	0.806136i	$-0.298445\pi$
$751$	32.4320	1.18346	0.591730	+	0.806136i	$0.298445\pi$
$752$	−42.0128	−1.53205
$753$	−14.8152	−0.539896
$754$	−6.18984	−0.225421
$755$	−4.18479	−0.152300
$756$	−1.22668	−0.0446140
$757$	4.75970	0.172994	0.0864972	−	0.996252i	$-0.472433\pi$
$757$	4.75970	0.172994	0.0864972	+	0.996252i	$0.472433\pi$
$758$	5.45336	0.198075
$759$	14.3473	0.520774
$760$	0	0
$761$	−30.2481	−1.09649	−0.548247	−	0.836316i	$-0.684705\pi$
$761$	−30.2481	−1.09649	−0.548247	+	0.836316i	$0.684705\pi$
$762$	4.60132	0.166688
$763$	2.62866	0.0951639
$764$	16.0719	0.581462
$765$	5.17024	0.186931
$766$	5.71244	0.206399
$767$	−4.69965	−0.169694
$768$	−7.19934	−0.259784
$769$	31.6049	1.13970	0.569852	−	0.821748i	$-0.307001\pi$
$769$	31.6049	1.13970	0.569852	+	0.821748i	$0.307001\pi$
$770$	−1.20439	−0.0434033
$771$	19.1634	0.690154
$772$	−31.8726	−1.14712
$773$	46.3996	1.66888	0.834439	−	0.551100i	$-0.185792\pi$
$773$	46.3996	1.66888	0.834439	+	0.551100i	$0.185792\pi$
$774$	3.25402	0.116963
$775$	−20.5990	−0.739936
$776$	9.03003	0.324159
$777$	−1.92127	−0.0689253
$778$	−2.61619	−0.0937950
$779$	0	0
$780$	−4.29086	−0.153637
$781$	−21.1753	−0.757712
$782$	−4.84875	−0.173391
$783$	−10.5175	−0.375866
$784$	−21.6340	−0.772644
$785$	−0.992259	−0.0354152
$786$	5.96585	0.212795
$787$	−36.8489	−1.31352	−0.656760	−	0.754100i	$-0.728074\pi$
$787$	−36.8489	−1.31352	−0.656760	+	0.754100i	$0.728074\pi$
$788$	−8.49020	−0.302451
$789$	16.4979	0.587342
$790$	−1.46379	−0.0520794
$791$	8.61081	0.306165
$792$	5.31315	0.188794
$793$	7.30903	0.259551
$794$	3.89630	0.138274
$795$	−14.5517	−0.516095
$796$	15.1233	0.536031
$797$	18.7939	0.665712	0.332856	−	0.942978i	$-0.391988\pi$
$797$	18.7939	0.665712	0.332856	+	0.942978i	$0.391988\pi$
$798$	0	0
$799$	48.9914	1.73319
$800$	12.2216	0.432100
$801$	−11.1334	−0.393380
$802$	−8.42366	−0.297450
$803$	23.1284	0.816182
$804$	14.8229	0.522765
$805$	−3.19934	−0.112762
$806$	−3.80653	−0.134079
$807$	−4.21213	−0.148274
$808$	−2.60813	−0.0917536
$809$	6.04551	0.212549	0.106274	−	0.994337i	$-0.466108\pi$
$809$	6.04551	0.212549	0.106274	+	0.994337i	$0.466108\pi$
$810$	0.467911	0.0164407
$811$	8.95367	0.314406	0.157203	−	0.987566i	$-0.449752\pi$
$811$	8.95367	0.314406	0.157203	+	0.987566i	$0.449752\pi$
$812$	12.9017	0.452760
$813$	−9.16250	−0.321343
$814$	4.03146	0.141303
$815$	17.0077	0.595755
$816$	12.6287	0.442092
$817$	0	0
$818$	−9.12836	−0.319165
$819$	−1.10607	−0.0386491
$820$	−3.82295	−0.133503
$821$	8.14384	0.284222	0.142111	−	0.989851i	$-0.454611\pi$
$821$	8.14384	0.284222	0.142111	+	0.989851i	$0.454611\pi$
$822$	−3.66281	−0.127755
$823$	−2.64321	−0.0921364	−0.0460682	−	0.998938i	$-0.514669\pi$
$823$	−2.64321	−0.0921364	−0.0460682	+	0.998938i	$0.514669\pi$
$824$	1.39693	0.0486642
$825$	12.5594	0.437263
$826$	−0.628660	−0.0218739
$827$	−36.7425	−1.27766	−0.638830	−	0.769348i	$-0.720581\pi$
$827$	−36.7425	−1.27766	−0.638830	+	0.769348i	$0.720581\pi$
$828$	6.83750	0.237619
$829$	−43.7434	−1.51927	−0.759636	−	0.650349i	$-0.774623\pi$
$829$	−43.7434	−1.51927	−0.759636	+	0.650349i	$0.774623\pi$
$830$	−2.11019	−0.0732456
$831$	22.4953	0.780352
$832$	−8.89487	−0.308374
$833$	25.2276	0.874085
$834$	3.74422	0.129652
$835$	7.43376	0.257256
$836$	0	0
$837$	−6.46791	−0.223564
$838$	−4.59215	−0.158633
$839$	13.7820	0.475807	0.237904	−	0.971289i	$-0.423540\pi$
$839$	13.7820	0.475807	0.237904	+	0.971289i	$0.423540\pi$
$840$	−1.18479	−0.0408792
$841$	81.6187	2.81444
$842$	12.8625	0.443270
$843$	23.5280	0.810346
$844$	−37.7452	−1.29924
$845$	13.6459	0.469433
$846$	4.43376	0.152436
$847$	−2.97090	−0.102081
$848$	−35.5435	−1.22057
$849$	−26.7469	−0.917952
$850$	−4.24453	−0.145586
$851$	10.7091	0.367105
$852$	−10.0915	−0.345730
$853$	10.5695	0.361894	0.180947	−	0.983493i	$-0.442084\pi$
$853$	10.5695	0.361894	0.180947	+	0.983493i	$0.442084\pi$
$854$	0.977711	0.0334566
$855$	0	0
$856$	−16.4534	−0.562364
$857$	36.8571	1.25901	0.629507	−	0.776995i	$-0.283257\pi$
$857$	36.8571	1.25901	0.629507	+	0.776995i	$0.283257\pi$
$858$	2.32089	0.0792338
$859$	−35.1138	−1.19807	−0.599034	−	0.800724i	$-0.704449\pi$
$859$	−35.1138	−1.19807	−0.599034	+	0.800724i	$0.704449\pi$
$860$	−23.7246	−0.809003
$861$	−0.985452	−0.0335841
$862$	−3.28993	−0.112055
$863$	3.01691	0.102697	0.0513484	−	0.998681i	$-0.483648\pi$
$863$	3.01691	0.102697	0.0513484	+	0.998681i	$0.483648\pi$
$864$	3.83750	0.130554
$865$	−17.4192	−0.592271
$866$	7.82201	0.265803
$867$	2.27362	0.0772163
$868$	7.93407	0.269300
$869$	−12.3369	−0.418500
$870$	−4.92127	−0.166847
$871$	13.3655	0.452872
$872$	−5.42602	−0.183748
$873$	6.70233	0.226840
$874$	0	0
$875$	−7.19759	−0.243323
$876$	11.0223	0.372409
$877$	58.1976	1.96519	0.982596	−	0.185753i	$-0.0594725\pi$
$877$	58.1976	1.96519	0.982596	+	0.185753i	$0.0594725\pi$
$878$	11.5416	0.389510
$879$	0.207081	0.00698468
$880$	−17.4848	−0.589413
$881$	25.6382	0.863771	0.431886	−	0.901928i	$-0.357848\pi$
$881$	25.6382	0.863771	0.431886	+	0.901928i	$0.357848\pi$
$882$	2.28312	0.0768766
$883$	20.2189	0.680422	0.340211	−	0.940349i	$-0.389502\pi$
$883$	20.2189	0.680422	0.340211	+	0.940349i	$0.389502\pi$
$884$	12.2216	0.411058
$885$	−3.73648	−0.125600
$886$	−10.6373	−0.357368
$887$	−21.1061	−0.708672	−0.354336	−	0.935118i	$-0.615293\pi$
$887$	−21.1061	−0.708672	−0.354336	+	0.935118i	$0.615293\pi$
$888$	3.96585	0.133085
$889$	−8.64765	−0.290033
$890$	−5.20945	−0.174621
$891$	3.94356	0.132114
$892$	−36.8161	−1.23270
$893$	0	0
$894$	−6.85978	−0.229426
$895$	20.3259	0.679421
$896$	−6.19934	−0.207105
$897$	6.16519	0.205850
$898$	−5.24155	−0.174913
$899$	68.0265	2.26881
$900$	5.98545	0.199515
$901$	41.4475	1.38082
$902$	2.06780	0.0688502
$903$	−6.11556	−0.203513
$904$	−17.7743	−0.591163
$905$	25.1712	0.836718
$906$	1.07873	0.0358383
$907$	25.8289	0.857636	0.428818	−	0.903391i	$-0.358930\pi$
$907$	25.8289	0.857636	0.428818	+	0.903391i	$0.358930\pi$
$908$	34.7648	1.15371
$909$	−1.93582	−0.0642072
$910$	−0.517541	−0.0171563
$911$	15.4415	0.511600	0.255800	−	0.966730i	$-0.417661\pi$
$911$	15.4415	0.511600	0.255800	+	0.966730i	$0.417661\pi$
$912$	0	0
$913$	−17.7847	−0.588587
$914$	−6.89250	−0.227984
$915$	5.81109	0.192109
$916$	52.9299	1.74885
$917$	−11.2121	−0.370257
$918$	−1.33275	−0.0439873
$919$	9.26445	0.305606	0.152803	−	0.988257i	$-0.451170\pi$
$919$	9.26445	0.305606	0.152803	+	0.988257i	$0.451170\pi$
$920$	6.60401	0.217728
$921$	−15.3182	−0.504752
$922$	12.0737	0.397625
$923$	−9.09926	−0.299506
$924$	−4.83750	−0.159142
$925$	9.37464	0.308236
$926$	1.18984	0.0391007
$927$	1.03684	0.0340542
$928$	−40.3610	−1.32492
$929$	−18.4029	−0.603780	−0.301890	−	0.953343i	$-0.597618\pi$
$929$	−18.4029	−0.603780	−0.301890	+	0.953343i	$0.597618\pi$
$930$	−3.02641	−0.0992398
$931$	0	0
$932$	−0.292614	−0.00958489
$933$	−15.6432	−0.512136
$934$	3.93313	0.128696
$935$	20.3892	0.666798
$936$	2.28312	0.0746261
$937$	7.85204	0.256515	0.128258	−	0.991741i	$-0.459062\pi$
$937$	7.85204	0.256515	0.128258	+	0.991741i	$0.459062\pi$
$938$	1.78787	0.0583759
$939$	−10.1625	−0.331641
$940$	−32.3259	−1.05436
$941$	−58.4374	−1.90500	−0.952502	−	0.304532i	$-0.901500\pi$
$941$	−58.4374	−1.90500	−0.952502	+	0.304532i	$0.901500\pi$
$942$	0.255777	0.00833368
$943$	5.49289	0.178873
$944$	−9.12660	−0.297046
$945$	−0.879385	−0.0286064
$946$	12.8324	0.417219
$947$	−36.0286	−1.17077	−0.585386	−	0.810755i	$-0.699057\pi$
$947$	−36.0286	−1.17077	−0.585386	+	0.810755i	$0.699057\pi$
$948$	−5.87939	−0.190954
$949$	9.93851	0.322618
$950$	0	0
$951$	7.64765	0.247992
$952$	3.37464	0.109373
$953$	12.9976	0.421035	0.210517	−	0.977590i	$-0.432485\pi$
$953$	12.9976	0.421035	0.210517	+	0.977590i	$0.432485\pi$
$954$	3.75103	0.121444
$955$	11.5217	0.372832
$956$	−12.4611	−0.403021
$957$	−41.4766	−1.34075
$958$	−4.01724	−0.129791
$959$	6.88383	0.222290
$960$	−7.07192	−0.228245
$961$	10.8339	0.349480
$962$	1.73236	0.0558536
$963$	−12.2121	−0.393531
$964$	9.88713	0.318443
$965$	−22.8489	−0.735531
$966$	0.824703	0.0265344
$967$	50.3141	1.61799	0.808996	−	0.587814i	$-0.200011\pi$
$967$	50.3141	1.61799	0.808996	+	0.587814i	$0.200011\pi$
$968$	6.13247	0.197105
$969$	0	0
$970$	3.13610	0.100694
$971$	−30.6973	−0.985123	−0.492561	−	0.870278i	$-0.663939\pi$
$971$	−30.6973	−0.985123	−0.492561	+	0.870278i	$0.663939\pi$
$972$	1.87939	0.0602813
$973$	−7.03684	−0.225591
$974$	−4.07966	−0.130721
$975$	5.39693	0.172840
$976$	14.1940	0.454338
$977$	−35.0806	−1.12233	−0.561164	−	0.827705i	$-0.689646\pi$
$977$	−35.0806	−1.12233	−0.561164	+	0.827705i	$0.689646\pi$
$978$	−4.38413	−0.140189
$979$	−43.9053	−1.40322
$980$	−16.6459	−0.531734
$981$	−4.02734	−0.128583
$982$	−3.56118	−0.113642
$983$	18.7811	0.599023	0.299511	−	0.954093i	$-0.403176\pi$
$983$	18.7811	0.599023	0.299511	+	0.954093i	$0.403176\pi$
$984$	2.03415	0.0648463
$985$	−6.08647	−0.193931
$986$	14.0172	0.446400
$987$	−8.33275	−0.265234
$988$	0	0
$989$	34.0880	1.08394
$990$	1.84524	0.0586455
$991$	−13.5371	−0.430021	−0.215011	−	0.976612i	$-0.568979\pi$
$991$	−13.5371	−0.430021	−0.215011	+	0.976612i	$0.568979\pi$
$992$	−24.8206	−0.788054
$993$	4.10607	0.130302
$994$	−1.21719	−0.0386068
$995$	10.8416	0.343702
$996$	−8.47565	−0.268561
$997$	6.90673	0.218738	0.109369	−	0.994001i	$-0.465117\pi$
$997$	6.90673	0.218738	0.109369	+	0.994001i	$0.465117\pi$
$998$	2.24298	0.0710004
$999$	2.94356	0.0931302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1083.2.a.m.1.2		3
3.2	odd	2		3249.2.a.w.1.2		3
19.4	even	9		57.2.i.a.16.1	✓	6
19.5	even	9		57.2.i.a.25.1	yes	6
19.18	odd	2		1083.2.a.n.1.2		3
57.5	odd	18		171.2.u.a.82.1		6
57.23	odd	18		171.2.u.a.73.1		6
57.56	even	2		3249.2.a.x.1.2		3
76.23	odd	18		912.2.bo.b.529.1		6
76.43	odd	18		912.2.bo.b.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.16.1	✓	6	19.4	even	9
57.2.i.a.25.1	yes	6	19.5	even	9
171.2.u.a.73.1		6	57.23	odd	18
171.2.u.a.82.1		6	57.5	odd	18
912.2.bo.b.481.1		6	76.43	odd	18
912.2.bo.b.529.1		6	76.23	odd	18
1083.2.a.m.1.2		3	1.1	even	1	trivial
1083.2.a.n.1.2		3	19.18	odd	2
3249.2.a.w.1.2		3	3.2	odd	2
3249.2.a.x.1.2		3	57.56	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1083.a (trivial)

\(f(q)\)	\(=\)	\(q-0.347296 q^{2} -1.00000 q^{3} -1.87939 q^{4} -1.34730 q^{5} +0.347296 q^{6} -0.652704 q^{7} +1.34730 q^{8} +1.00000 q^{9} +0.467911 q^{10} +3.94356 q^{11} +1.87939 q^{12} +1.69459 q^{13} +0.226682 q^{14} +1.34730 q^{15} +3.29086 q^{16} -3.83750 q^{17} -0.347296 q^{18} +2.53209 q^{20} +0.652704 q^{21} -1.36959 q^{22} -3.63816 q^{23} -1.34730 q^{24} -3.18479 q^{25} -0.588526 q^{26} -1.00000 q^{27} +1.22668 q^{28} +10.5175 q^{29} -0.467911 q^{30} +6.46791 q^{31} -3.83750 q^{32} -3.94356 q^{33} +1.33275 q^{34} +0.879385 q^{35} -1.87939 q^{36} -2.94356 q^{37} -1.69459 q^{39} -1.81521 q^{40} -1.50980 q^{41} -0.226682 q^{42} -9.36959 q^{43} -7.41147 q^{44} -1.34730 q^{45} +1.26352 q^{46} -12.7665 q^{47} -3.29086 q^{48} -6.57398 q^{49} +1.10607 q^{50} +3.83750 q^{51} -3.18479 q^{52} -10.8007 q^{53} +0.347296 q^{54} -5.31315 q^{55} -0.879385 q^{56} -3.65270 q^{58} -2.77332 q^{59} -2.53209 q^{60} +4.31315 q^{61} -2.24628 q^{62} -0.652704 q^{63} -5.24897 q^{64} -2.28312 q^{65} +1.36959 q^{66} +7.88713 q^{67} +7.21213 q^{68} +3.63816 q^{69} -0.305407 q^{70} -5.36959 q^{71} +1.34730 q^{72} +5.86484 q^{73} +1.02229 q^{74} +3.18479 q^{75} -2.57398 q^{77} +0.588526 q^{78} -3.12836 q^{79} -4.43376 q^{80} +1.00000 q^{81} +0.524348 q^{82} -4.50980 q^{83} -1.22668 q^{84} +5.17024 q^{85} +3.25402 q^{86} -10.5175 q^{87} +5.31315 q^{88} -11.1334 q^{89} +0.467911 q^{90} -1.10607 q^{91} +6.83750 q^{92} -6.46791 q^{93} +4.43376 q^{94} +3.83750 q^{96} +6.70233 q^{97} +2.28312 q^{98} +3.94356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} - 6 q^{25} - 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 - 6 * q^25 - 12 * q^26 - 3 * q^27 - 3 * q^28 + 9 * q^29 - 6 * q^30 + 24 * q^31 - 9 * q^32 + 3 * q^33 - 15 * q^34 - 3 * q^35 + 6 * q^37 - 3 * q^39 - 9 * q^40 - 6 * q^41 + 6 * q^42 - 21 * q^43 - 12 * q^44 - 3 * q^45 + 9 * q^46 - 3 * q^47 + 6 * q^48 - 12 * q^49 - 9 * q^50 + 9 * q^51 - 6 * q^52 - 18 * q^53 + 6 * q^55 + 3 * q^56 - 12 * q^58 - 15 * q^59 - 3 * q^60 - 9 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 - 15 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 - 6 * q^69 - 3 * q^70 - 9 * q^71 + 3 * q^72 - 6 * q^73 - 3 * q^74 + 6 * q^75 + 12 * q^78 + 9 * q^79 + 3 * q^80 + 3 * q^81 + 21 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^85 - 18 * q^86 - 9 * q^87 - 6 * q^88 + 6 * q^90 + 9 * q^91 + 18 * q^92 - 24 * q^93 - 3 * q^94 + 9 * q^96 - 6 * q^97 + 15 * q^98 - 3 * q^99

Introduction

L-functions

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