LMFDB - Embedded newform 7942.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.79129$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} -2.79129 q^{6} -0.208712 q^{7} -1.00000 q^{8} +4.79129 q^{9} +0.791288 q^{10} +1.00000 q^{11} +2.79129 q^{12} -5.79129 q^{13} +0.208712 q^{14} -2.20871 q^{15} +1.00000 q^{16} +1.58258 q^{17} -4.79129 q^{18} -0.791288 q^{20} -0.582576 q^{21} -1.00000 q^{22} +7.58258 q^{23} -2.79129 q^{24} -4.37386 q^{25} +5.79129 q^{26} +5.00000 q^{27} -0.208712 q^{28} -6.79129 q^{29} +2.20871 q^{30} +6.20871 q^{31} -1.00000 q^{32} +2.79129 q^{33} -1.58258 q^{34} +0.165151 q^{35} +4.79129 q^{36} -8.00000 q^{37} -16.1652 q^{39} +0.791288 q^{40} -3.79129 q^{41} +0.582576 q^{42} -6.37386 q^{43} +1.00000 q^{44} -3.79129 q^{45} -7.58258 q^{46} -9.16515 q^{47} +2.79129 q^{48} -6.95644 q^{49} +4.37386 q^{50} +4.41742 q^{51} -5.79129 q^{52} -7.58258 q^{53} -5.00000 q^{54} -0.791288 q^{55} +0.208712 q^{56} +6.79129 q^{58} -2.20871 q^{60} +2.00000 q^{61} -6.20871 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.58258 q^{65} -2.79129 q^{66} +0.208712 q^{67} +1.58258 q^{68} +21.1652 q^{69} -0.165151 q^{70} -2.37386 q^{71} -4.79129 q^{72} +0.417424 q^{73} +8.00000 q^{74} -12.2087 q^{75} -0.208712 q^{77} +16.1652 q^{78} -3.58258 q^{79} -0.791288 q^{80} -0.417424 q^{81} +3.79129 q^{82} +0.791288 q^{83} -0.582576 q^{84} -1.25227 q^{85} +6.37386 q^{86} -18.9564 q^{87} -1.00000 q^{88} +13.5826 q^{89} +3.79129 q^{90} +1.20871 q^{91} +7.58258 q^{92} +17.3303 q^{93} +9.16515 q^{94} -2.79129 q^{96} -8.00000 q^{97} +6.95644 q^{98} +4.79129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 5 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} + 2 q^{11} + q^{12} - 7 q^{13} + 5 q^{14} - 9 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 3 q^{20} + 8 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 5 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 + 2 * q^11 + q^12 - 7 * q^13 + 5 * q^14 - 9 * q^15 + 2 * q^16 - 6 * q^17 - 5 * q^18 + 3 * q^20 + 8 * q^21 - 2 * q^22 + 6 * q^23 - q^24 + 5 * q^25 + 7 * q^26 + 10 * q^27 - 5 * q^28 - 9 * q^29 + 9 * q^30 + 17 * q^31 - 2 * q^32 + q^33 + 6 * q^34 - 18 * q^35 + 5 * q^36 - 16 * q^37 - 14 * q^39 - 3 * q^40 - 3 * q^41 - 8 * q^42 + q^43 + 2 * q^44 - 3 * q^45 - 6 * q^46 + q^48 + 9 * q^49 - 5 * q^50 + 18 * q^51 - 7 * q^52 - 6 * q^53 - 10 * q^54 + 3 * q^55 + 5 * q^56 + 9 * q^58 - 9 * q^60 + 4 * q^61 - 17 * q^62 - 2 * q^63 + 2 * q^64 - q^66 + 5 * q^67 - 6 * q^68 + 24 * q^69 + 18 * q^70 + 9 * q^71 - 5 * q^72 + 10 * q^73 + 16 * q^74 - 29 * q^75 - 5 * q^77 + 14 * q^78 + 2 * q^79 + 3 * q^80 - 10 * q^81 + 3 * q^82 - 3 * q^83 + 8 * q^84 - 30 * q^85 - q^86 - 15 * q^87 - 2 * q^88 + 18 * q^89 + 3 * q^90 + 7 * q^91 + 6 * q^92 - 2 * q^93 - q^96 - 16 * q^97 - 9 * q^98 + 5 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.79129	1.61155	0.805775	−	0.592221i	$-0.201749\pi$
$3$	2.79129	1.61155	0.805775	+	0.592221i	$0.201749\pi$
$4$	1.00000	0.500000
$5$	−0.791288	−0.353875	−0.176937	−	0.984222i	$-0.556619\pi$
$5$	−0.791288	−0.353875	−0.176937	+	0.984222i	$0.556619\pi$
$6$	−2.79129	−1.13954
$7$	−0.208712	−0.0788858	−0.0394429	−	0.999222i	$-0.512558\pi$
$7$	−0.208712	−0.0788858	−0.0394429	+	0.999222i	$0.512558\pi$
$8$	−1.00000	−0.353553
$9$	4.79129	1.59710
$10$	0.791288	0.250227
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.79129	0.805775
$13$	−5.79129	−1.60621	−0.803107	−	0.595835i	$-0.796821\pi$
$13$	−5.79129	−1.60621	−0.803107	+	0.595835i	$0.796821\pi$
$14$	0.208712	0.0557807
$15$	−2.20871	−0.570287
$16$	1.00000	0.250000
$17$	1.58258	0.383831	0.191915	−	0.981411i	$-0.438530\pi$
$17$	1.58258	0.383831	0.191915	+	0.981411i	$0.438530\pi$
$18$	−4.79129	−1.12932
$19$	0	0
$19$	0	0
$20$	−0.791288	−0.176937
$21$	−0.582576	−0.127128
$22$	−1.00000	−0.213201
$23$	7.58258	1.58108	0.790538	−	0.612413i	$-0.209801\pi$
$23$	7.58258	1.58108	0.790538	+	0.612413i	$0.209801\pi$
$24$	−2.79129	−0.569769
$25$	−4.37386	−0.874773
$26$	5.79129	1.13576
$27$	5.00000	0.962250
$28$	−0.208712	−0.0394429
$29$	−6.79129	−1.26111	−0.630555	−	0.776144i	$-0.717173\pi$
$29$	−6.79129	−1.26111	−0.630555	+	0.776144i	$0.717173\pi$
$30$	2.20871	0.403254
$31$	6.20871	1.11512	0.557559	−	0.830137i	$-0.311738\pi$
$31$	6.20871	1.11512	0.557559	+	0.830137i	$0.311738\pi$
$32$	−1.00000	−0.176777
$33$	2.79129	0.485901
$34$	−1.58258	−0.271409
$35$	0.165151	0.0279157
$36$	4.79129	0.798548
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	−16.1652	−2.58850
$40$	0.791288	0.125114
$41$	−3.79129	−0.592100	−0.296050	−	0.955172i	$-0.595669\pi$
$41$	−3.79129	−0.592100	−0.296050	+	0.955172i	$0.595669\pi$
$42$	0.582576	0.0898934
$43$	−6.37386	−0.972005	−0.486003	−	0.873957i	$-0.661545\pi$
$43$	−6.37386	−0.972005	−0.486003	+	0.873957i	$0.661545\pi$
$44$	1.00000	0.150756
$45$	−3.79129	−0.565172
$46$	−7.58258	−1.11799
$47$	−9.16515	−1.33687	−0.668437	−	0.743768i	$-0.733037\pi$
$47$	−9.16515	−1.33687	−0.668437	+	0.743768i	$0.733037\pi$
$48$	2.79129	0.402888
$49$	−6.95644	−0.993777
$50$	4.37386	0.618558
$51$	4.41742	0.618563
$52$	−5.79129	−0.803107
$53$	−7.58258	−1.04155	−0.520773	−	0.853695i	$-0.674356\pi$
$53$	−7.58258	−1.04155	−0.520773	+	0.853695i	$0.674356\pi$
$54$	−5.00000	−0.680414
$55$	−0.791288	−0.106697
$56$	0.208712	0.0278903
$57$	0	0
$58$	6.79129	0.891740
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−2.20871	−0.285144
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−6.20871	−0.788507
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	4.58258	0.568399
$66$	−2.79129	−0.343584
$67$	0.208712	0.0254982	0.0127491	−	0.999919i	$-0.495942\pi$
$67$	0.208712	0.0254982	0.0127491	+	0.999919i	$0.495942\pi$
$68$	1.58258	0.191915
$69$	21.1652	2.54798
$70$	−0.165151	−0.0197394
$71$	−2.37386	−0.281726	−0.140863	−	0.990029i	$-0.544988\pi$
$71$	−2.37386	−0.281726	−0.140863	+	0.990029i	$0.544988\pi$
$72$	−4.79129	−0.564659
$73$	0.417424	0.0488558	0.0244279	−	0.999702i	$-0.492224\pi$
$73$	0.417424	0.0488558	0.0244279	+	0.999702i	$0.492224\pi$
$74$	8.00000	0.929981
$75$	−12.2087	−1.40974
$76$	0	0
$77$	−0.208712	−0.0237850
$78$	16.1652	1.83034
$79$	−3.58258	−0.403071	−0.201536	−	0.979481i	$-0.564593\pi$
$79$	−3.58258	−0.403071	−0.201536	+	0.979481i	$0.564593\pi$
$80$	−0.791288	−0.0884687
$81$	−0.417424	−0.0463805
$82$	3.79129	0.418678
$83$	0.791288	0.0868551	0.0434276	−	0.999057i	$-0.486172\pi$
$83$	0.791288	0.0868551	0.0434276	+	0.999057i	$0.486172\pi$
$84$	−0.582576	−0.0635642
$85$	−1.25227	−0.135828
$86$	6.37386	0.687311
$87$	−18.9564	−2.03234
$88$	−1.00000	−0.106600
$89$	13.5826	1.43975	0.719875	−	0.694104i	$-0.244199\pi$
$89$	13.5826	1.43975	0.719875	+	0.694104i	$0.244199\pi$
$90$	3.79129	0.399637
$91$	1.20871	0.126707
$92$	7.58258	0.790538
$93$	17.3303	1.79707
$94$	9.16515	0.945313
$95$	0	0
$96$	−2.79129	−0.284885
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	6.95644	0.702706
$99$	4.79129	0.481543
$100$	−4.37386	−0.437386
$101$	−4.41742	−0.439550	−0.219775	−	0.975551i	$-0.570532\pi$
$101$	−4.41742	−0.439550	−0.219775	+	0.975551i	$0.570532\pi$
$102$	−4.41742	−0.437390
$103$	19.9564	1.96637	0.983183	−	0.182622i	$-0.0584585\pi$
$103$	19.9564	1.96637	0.983183	+	0.182622i	$0.0584585\pi$
$104$	5.79129	0.567882
$105$	0.460985	0.0449875
$106$	7.58258	0.736485
$107$	−18.0000	−1.74013	−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000	−1.74013	−0.870063	+	0.492941i	$0.835922\pi$
$108$	5.00000	0.481125
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0.791288	0.0754463
$111$	−22.3303	−2.11950
$112$	−0.208712	−0.0197214
$113$	3.16515	0.297752	0.148876	−	0.988856i	$-0.452434\pi$
$113$	3.16515	0.297752	0.148876	+	0.988856i	$0.452434\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	−6.79129	−0.630555
$117$	−27.7477	−2.56528
$118$	0	0
$119$	−0.330303	−0.0302788
$120$	2.20871	0.201627
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−10.5826	−0.954199
$124$	6.20871	0.557559
$125$	7.41742	0.663435
$126$	1.00000	0.0890871
$127$	−18.7477	−1.66359	−0.831796	−	0.555082i	$-0.812687\pi$
$127$	−18.7477	−1.66359	−0.831796	+	0.555082i	$0.812687\pi$
$128$	−1.00000	−0.0883883
$129$	−17.7913	−1.56644
$130$	−4.58258	−0.401918
$131$	17.3739	1.51796	0.758981	−	0.651113i	$-0.225698\pi$
$131$	17.3739	1.51796	0.758981	+	0.651113i	$0.225698\pi$
$132$	2.79129	0.242950
$133$	0	0
$134$	−0.208712	−0.0180300
$135$	−3.95644	−0.340516
$136$	−1.58258	−0.135705
$137$	9.79129	0.836526	0.418263	−	0.908326i	$-0.362639\pi$
$137$	9.79129	0.836526	0.418263	+	0.908326i	$0.362639\pi$
$138$	−21.1652	−1.80170
$139$	−16.7913	−1.42422	−0.712109	−	0.702069i	$-0.752260\pi$
$139$	−16.7913	−1.42422	−0.712109	+	0.702069i	$0.752260\pi$
$140$	0.165151	0.0139578
$141$	−25.5826	−2.15444
$142$	2.37386	0.199210
$143$	−5.79129	−0.484292
$144$	4.79129	0.399274
$145$	5.37386	0.446275
$146$	−0.417424	−0.0345463
$147$	−19.4174	−1.60152
$148$	−8.00000	−0.657596
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	12.2087	0.996837
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	0	0
$153$	7.58258	0.613015
$154$	0.208712	0.0168185
$155$	−4.91288	−0.394612
$156$	−16.1652	−1.29425
$157$	11.9564	0.954228	0.477114	−	0.878841i	$-0.341683\pi$
$157$	11.9564	0.954228	0.477114	+	0.878841i	$0.341683\pi$
$158$	3.58258	0.285014
$159$	−21.1652	−1.67851
$160$	0.791288	0.0625568
$161$	−1.58258	−0.124724
$162$	0.417424	0.0327960
$163$	−2.41742	−0.189347	−0.0946736	−	0.995508i	$-0.530181\pi$
$163$	−2.41742	−0.189347	−0.0946736	+	0.995508i	$0.530181\pi$
$164$	−3.79129	−0.296050
$165$	−2.20871	−0.171948
$166$	−0.791288	−0.0614158
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	0.582576	0.0449467
$169$	20.5390	1.57992
$170$	1.25227	0.0960449
$171$	0	0
$172$	−6.37386	−0.486003
$173$	9.95644	0.756974	0.378487	−	0.925607i	$-0.376444\pi$
$173$	9.95644	0.756974	0.378487	+	0.925607i	$0.376444\pi$
$174$	18.9564	1.43708
$175$	0.912878	0.0690071
$176$	1.00000	0.0753778
$177$	0	0
$178$	−13.5826	−1.01806
$179$	18.9564	1.41687	0.708435	−	0.705776i	$-0.249401\pi$
$179$	18.9564	1.41687	0.708435	+	0.705776i	$0.249401\pi$
$180$	−3.79129	−0.282586
$181$	8.74773	0.650213	0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773	0.650213	0.325107	+	0.945677i	$0.394600\pi$
$182$	−1.20871	−0.0895957
$183$	5.58258	0.412676
$184$	−7.58258	−0.558995
$185$	6.33030	0.465413
$186$	−17.3303	−1.27072
$187$	1.58258	0.115729
$188$	−9.16515	−0.668437
$189$	−1.04356	−0.0759079
$190$	0	0
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	2.79129	0.201444
$193$	6.37386	0.458801	0.229400	−	0.973332i	$-0.426323\pi$
$193$	6.37386	0.458801	0.229400	+	0.973332i	$0.426323\pi$
$194$	8.00000	0.574367
$195$	12.7913	0.916003
$196$	−6.95644	−0.496889
$197$	−9.16515	−0.652990	−0.326495	−	0.945199i	$-0.605868\pi$
$197$	−9.16515	−0.652990	−0.326495	+	0.945199i	$0.605868\pi$
$198$	−4.79129	−0.340502
$199$	−20.7477	−1.47077	−0.735384	−	0.677651i	$-0.762998\pi$
$199$	−20.7477	−1.47077	−0.735384	+	0.677651i	$0.762998\pi$
$200$	4.37386	0.309279
$201$	0.582576	0.0410917
$202$	4.41742	0.310809
$203$	1.41742	0.0994837
$204$	4.41742	0.309282
$205$	3.00000	0.209529
$206$	−19.9564	−1.39043
$207$	36.3303	2.52513
$208$	−5.79129	−0.401554
$209$	0	0
$210$	−0.460985	−0.0318110
$211$	8.74773	0.602218	0.301109	−	0.953590i	$-0.402643\pi$
$211$	8.74773	0.602218	0.301109	+	0.953590i	$0.402643\pi$
$212$	−7.58258	−0.520773
$213$	−6.62614	−0.454015
$214$	18.0000	1.23045
$215$	5.04356	0.343968
$216$	−5.00000	−0.340207
$217$	−1.29583	−0.0879669
$218$	−10.0000	−0.677285
$219$	1.16515	0.0787336
$220$	−0.791288	−0.0533486
$221$	−9.16515	−0.616515
$222$	22.3303	1.49871
$223$	−11.1652	−0.747674	−0.373837	−	0.927494i	$-0.621958\pi$
$223$	−11.1652	−0.747674	−0.373837	+	0.927494i	$0.621958\pi$
$224$	0.208712	0.0139452
$225$	−20.9564	−1.39710
$226$	−3.16515	−0.210543
$227$	−1.58258	−0.105039	−0.0525196	−	0.998620i	$-0.516725\pi$
$227$	−1.58258	−0.105039	−0.0525196	+	0.998620i	$0.516725\pi$
$228$	0	0
$229$	−4.62614	−0.305704	−0.152852	−	0.988249i	$-0.548846\pi$
$229$	−4.62614	−0.305704	−0.152852	+	0.988249i	$0.548846\pi$
$230$	6.00000	0.395628
$231$	−0.582576	−0.0383307
$232$	6.79129	0.445870
$233$	−3.16515	−0.207356	−0.103678	−	0.994611i	$-0.533061\pi$
$233$	−3.16515	−0.207356	−0.103678	+	0.994611i	$0.533061\pi$
$234$	27.7477	1.81393
$235$	7.25227	0.473086
$236$	0	0
$237$	−10.0000	−0.649570
$238$	0.330303	0.0214103
$239$	−6.79129	−0.439292	−0.219646	−	0.975580i	$-0.570490\pi$
$239$	−6.79129	−0.439292	−0.219646	+	0.975580i	$0.570490\pi$
$240$	−2.20871	−0.142572
$241$	4.79129	0.308634	0.154317	−	0.988021i	$-0.450682\pi$
$241$	4.79129	0.308634	0.154317	+	0.988021i	$0.450682\pi$
$242$	−1.00000	−0.0642824
$243$	−16.1652	−1.03699
$244$	2.00000	0.128037
$245$	5.50455	0.351673
$246$	10.5826	0.674720
$247$	0	0
$248$	−6.20871	−0.394254
$249$	2.20871	0.139971
$250$	−7.41742	−0.469119
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−1.00000	−0.0629941
$253$	7.58258	0.476712
$254$	18.7477	1.17634
$255$	−3.49545	−0.218894
$256$	1.00000	0.0625000
$257$	−1.58258	−0.0987184	−0.0493592	−	0.998781i	$-0.515718\pi$
$257$	−1.58258	−0.0987184	−0.0493592	+	0.998781i	$0.515718\pi$
$258$	17.7913	1.10764
$259$	1.66970	0.103750
$260$	4.58258	0.284199
$261$	−32.5390	−2.01411
$262$	−17.3739	−1.07336
$263$	−9.95644	−0.613940	−0.306970	−	0.951719i	$-0.599315\pi$
$263$	−9.95644	−0.613940	−0.306970	+	0.951719i	$0.599315\pi$
$264$	−2.79129	−0.171792
$265$	6.00000	0.368577
$266$	0	0
$267$	37.9129	2.32023
$268$	0.208712	0.0127491
$269$	−10.7477	−0.655300	−0.327650	−	0.944799i	$-0.606257\pi$
$269$	−10.7477	−0.655300	−0.327650	+	0.944799i	$0.606257\pi$
$270$	3.95644	0.240781
$271$	7.37386	0.447930	0.223965	−	0.974597i	$-0.428100\pi$
$271$	7.37386	0.447930	0.223965	+	0.974597i	$0.428100\pi$
$272$	1.58258	0.0959577
$273$	3.37386	0.204196
$274$	−9.79129	−0.591513
$275$	−4.37386	−0.263754
$276$	21.1652	1.27399
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	16.7913	1.00707
$279$	29.7477	1.78095
$280$	−0.165151	−0.00986968
$281$	19.1216	1.14070	0.570349	−	0.821402i	$-0.306808\pi$
$281$	19.1216	1.14070	0.570349	+	0.821402i	$0.306808\pi$
$282$	25.5826	1.52342
$283$	−32.1216	−1.90943	−0.954715	−	0.297521i	$-0.903840\pi$
$283$	−32.1216	−1.90943	−0.954715	+	0.297521i	$0.903840\pi$
$284$	−2.37386	−0.140863
$285$	0	0
$286$	5.79129	0.342446
$287$	0.791288	0.0467082
$288$	−4.79129	−0.282329
$289$	−14.4955	−0.852674
$290$	−5.37386	−0.315564
$291$	−22.3303	−1.30903
$292$	0.417424	0.0244279
$293$	−2.20871	−0.129034	−0.0645172	−	0.997917i	$-0.520551\pi$
$293$	−2.20871	−0.129034	−0.0645172	+	0.997917i	$0.520551\pi$
$294$	19.4174	1.13245
$295$	0	0
$296$	8.00000	0.464991
$297$	5.00000	0.290129
$298$	0	0
$299$	−43.9129	−2.53955
$300$	−12.2087	−0.704870
$301$	1.33030	0.0766774
$302$	2.00000	0.115087
$303$	−12.3303	−0.708357
$304$	0	0
$305$	−1.58258	−0.0906180
$306$	−7.58258	−0.433467
$307$	32.7477	1.86901	0.934506	−	0.355948i	$-0.115842\pi$
$307$	32.7477	1.86901	0.934506	+	0.355948i	$0.115842\pi$
$308$	−0.208712	−0.0118925
$309$	55.7042	3.16890
$310$	4.91288	0.279033
$311$	19.9129	1.12916	0.564578	−	0.825380i	$-0.309039\pi$
$311$	19.9129	1.12916	0.564578	+	0.825380i	$0.309039\pi$
$312$	16.1652	0.915171
$313$	4.37386	0.247225	0.123613	−	0.992331i	$-0.460552\pi$
$313$	4.37386	0.247225	0.123613	+	0.992331i	$0.460552\pi$
$314$	−11.9564	−0.674741
$315$	0.791288	0.0445840
$316$	−3.58258	−0.201536
$317$	−28.7477	−1.61463	−0.807317	−	0.590119i	$-0.799081\pi$
$317$	−28.7477	−1.61463	−0.807317	+	0.590119i	$0.799081\pi$
$318$	21.1652	1.18688
$319$	−6.79129	−0.380239
$320$	−0.791288	−0.0442343
$321$	−50.2432	−2.80430
$322$	1.58258	0.0881935
$323$	0	0
$324$	−0.417424	−0.0231902
$325$	25.3303	1.40507
$326$	2.41742	0.133889
$327$	27.9129	1.54359
$328$	3.79129	0.209339
$329$	1.91288	0.105460
$330$	2.20871	0.121586
$331$	−25.2087	−1.38560	−0.692798	−	0.721132i	$-0.743622\pi$
$331$	−25.2087	−1.38560	−0.692798	+	0.721132i	$0.743622\pi$
$332$	0.791288	0.0434276
$333$	−38.3303	−2.10049
$334$	18.0000	0.984916
$335$	−0.165151	−0.00902318
$336$	−0.582576	−0.0317821
$337$	27.3739	1.49115	0.745575	−	0.666422i	$-0.232175\pi$
$337$	27.3739	1.49115	0.745575	+	0.666422i	$0.232175\pi$
$338$	−20.5390	−1.11718
$339$	8.83485	0.479843
$340$	−1.25227	−0.0679140
$341$	6.20871	0.336221
$342$	0	0
$343$	2.91288	0.157281
$344$	6.37386	0.343656
$345$	−16.7477	−0.901667
$346$	−9.95644	−0.535261
$347$	15.1652	0.814108	0.407054	−	0.913404i	$-0.366556\pi$
$347$	15.1652	0.814108	0.407054	+	0.913404i	$0.366556\pi$
$348$	−18.9564	−1.01617
$349$	−31.4955	−1.68591	−0.842957	−	0.537982i	$-0.819187\pi$
$349$	−31.4955	−1.68591	−0.842957	+	0.537982i	$0.819187\pi$
$350$	−0.912878	−0.0487954
$351$	−28.9564	−1.54558
$352$	−1.00000	−0.0533002
$353$	−33.1652	−1.76520	−0.882601	−	0.470122i	$-0.844210\pi$
$353$	−33.1652	−1.76520	−0.882601	+	0.470122i	$0.844210\pi$
$354$	0	0
$355$	1.87841	0.0996956
$356$	13.5826	0.719875
$357$	−0.921970	−0.0487958
$358$	−18.9564	−1.00188
$359$	−29.7042	−1.56773	−0.783863	−	0.620934i	$-0.786754\pi$
$359$	−29.7042	−1.56773	−0.783863	+	0.620934i	$0.786754\pi$
$360$	3.79129	0.199818
$361$	0	0
$362$	−8.74773	−0.459770
$363$	2.79129	0.146505
$364$	1.20871	0.0633537
$365$	−0.330303	−0.0172888
$366$	−5.58258	−0.291806
$367$	−16.3303	−0.852435	−0.426217	−	0.904621i	$-0.640154\pi$
$367$	−16.3303	−0.852435	−0.426217	+	0.904621i	$0.640154\pi$
$368$	7.58258	0.395269
$369$	−18.1652	−0.945640
$370$	−6.33030	−0.329097
$371$	1.58258	0.0821632
$372$	17.3303	0.898534
$373$	−4.37386	−0.226470	−0.113235	−	0.993568i	$-0.536121\pi$
$373$	−4.37386	−0.226470	−0.113235	+	0.993568i	$0.536121\pi$
$374$	−1.58258	−0.0818330
$375$	20.7042	1.06916
$376$	9.16515	0.472657
$377$	39.3303	2.02561
$378$	1.04356	0.0536750
$379$	−28.2087	−1.44898	−0.724492	−	0.689283i	$-0.757926\pi$
$379$	−28.2087	−1.44898	−0.724492	+	0.689283i	$0.757926\pi$
$380$	0	0
$381$	−52.3303	−2.68096
$382$	18.0000	0.920960
$383$	−12.9564	−0.662043	−0.331022	−	0.943623i	$-0.607393\pi$
$383$	−12.9564	−0.662043	−0.331022	+	0.943623i	$0.607393\pi$
$384$	−2.79129	−0.142442
$385$	0.165151	0.00841689
$386$	−6.37386	−0.324421
$387$	−30.5390	−1.55239
$388$	−8.00000	−0.406138
$389$	−31.1216	−1.57793	−0.788964	−	0.614440i	$-0.789382\pi$
$389$	−31.1216	−1.57793	−0.788964	+	0.614440i	$0.789382\pi$
$390$	−12.7913	−0.647712
$391$	12.0000	0.606866
$392$	6.95644	0.351353
$393$	48.4955	2.44627
$394$	9.16515	0.461734
$395$	2.83485	0.142637
$396$	4.79129	0.240771
$397$	26.9564	1.35290	0.676452	−	0.736486i	$-0.263516\pi$
$397$	26.9564	1.35290	0.676452	+	0.736486i	$0.263516\pi$
$398$	20.7477	1.03999
$399$	0	0
$400$	−4.37386	−0.218693
$401$	4.41742	0.220596	0.110298	−	0.993899i	$-0.464820\pi$
$401$	4.41742	0.220596	0.110298	+	0.993899i	$0.464820\pi$
$402$	−0.582576	−0.0290562
$403$	−35.9564	−1.79112
$404$	−4.41742	−0.219775
$405$	0.330303	0.0164129
$406$	−1.41742	−0.0703456
$407$	−8.00000	−0.396545
$408$	−4.41742	−0.218695
$409$	−10.3739	−0.512955	−0.256477	−	0.966550i	$-0.582562\pi$
$409$	−10.3739	−0.512955	−0.256477	+	0.966550i	$0.582562\pi$
$410$	−3.00000	−0.148159
$411$	27.3303	1.34810
$412$	19.9564	0.983183
$413$	0	0
$414$	−36.3303	−1.78554
$415$	−0.626136	−0.0307358
$416$	5.79129	0.283941
$417$	−46.8693	−2.29520
$418$	0	0
$419$	−24.3303	−1.18861	−0.594307	−	0.804239i	$-0.702573\pi$
$419$	−24.3303	−1.18861	−0.594307	+	0.804239i	$0.702573\pi$
$420$	0.460985	0.0224938
$421$	38.7477	1.88845	0.944224	−	0.329303i	$-0.106814\pi$
$421$	38.7477	1.88845	0.944224	+	0.329303i	$0.106814\pi$
$422$	−8.74773	−0.425833
$423$	−43.9129	−2.13512
$424$	7.58258	0.368242
$425$	−6.92197	−0.335765
$426$	6.62614	0.321037
$427$	−0.417424	−0.0202006
$428$	−18.0000	−0.870063
$429$	−16.1652	−0.780461
$430$	−5.04356	−0.243222
$431$	−33.4955	−1.61342	−0.806710	−	0.590948i	$-0.798754\pi$
$431$	−33.4955	−1.61342	−0.806710	+	0.590948i	$0.798754\pi$
$432$	5.00000	0.240563
$433$	2.41742	0.116174	0.0580870	−	0.998312i	$-0.481500\pi$
$433$	2.41742	0.116174	0.0580870	+	0.998312i	$0.481500\pi$
$434$	1.29583	0.0622020
$435$	15.0000	0.719195
$436$	10.0000	0.478913
$437$	0	0
$438$	−1.16515	−0.0556731
$439$	12.8348	0.612574	0.306287	−	0.951939i	$-0.400913\pi$
$439$	12.8348	0.612574	0.306287	+	0.951939i	$0.400913\pi$
$440$	0.791288	0.0377232
$441$	−33.3303	−1.58716
$442$	9.16515	0.435942
$443$	18.3303	0.870899	0.435449	−	0.900213i	$-0.356589\pi$
$443$	18.3303	0.870899	0.435449	+	0.900213i	$0.356589\pi$
$444$	−22.3303	−1.05975
$445$	−10.7477	−0.509491
$446$	11.1652	0.528685
$447$	0	0
$448$	−0.208712	−0.00986072
$449$	10.7477	0.507217	0.253608	−	0.967307i	$-0.418383\pi$
$449$	10.7477	0.507217	0.253608	+	0.967307i	$0.418383\pi$
$450$	20.9564	0.987896
$451$	−3.79129	−0.178525
$452$	3.16515	0.148876
$453$	−5.58258	−0.262292
$454$	1.58258	0.0742740
$455$	−0.956439	−0.0448386
$456$	0	0
$457$	−32.7477	−1.53187	−0.765937	−	0.642916i	$-0.777725\pi$
$457$	−32.7477	−1.53187	−0.765937	+	0.642916i	$0.777725\pi$
$458$	4.62614	0.216165
$459$	7.91288	0.369342
$460$	−6.00000	−0.279751
$461$	6.33030	0.294832	0.147416	−	0.989075i	$-0.452904\pi$
$461$	6.33030	0.294832	0.147416	+	0.989075i	$0.452904\pi$
$462$	0.582576	0.0271039
$463$	32.6606	1.51787	0.758934	−	0.651168i	$-0.225721\pi$
$463$	32.6606	1.51787	0.758934	+	0.651168i	$0.225721\pi$
$464$	−6.79129	−0.315278
$465$	−13.7133	−0.635937
$466$	3.16515	0.146623
$467$	4.41742	0.204414	0.102207	−	0.994763i	$-0.467410\pi$
$467$	4.41742	0.204414	0.102207	+	0.994763i	$0.467410\pi$
$468$	−27.7477	−1.28264
$469$	−0.0435608	−0.00201145
$470$	−7.25227	−0.334522
$471$	33.3739	1.53779
$472$	0	0
$473$	−6.37386	−0.293071
$474$	10.0000	0.459315
$475$	0	0
$476$	−0.330303	−0.0151394
$477$	−36.3303	−1.66345
$478$	6.79129	0.310626
$479$	−8.20871	−0.375066	−0.187533	−	0.982258i	$-0.560049\pi$
$479$	−8.20871	−0.375066	−0.187533	+	0.982258i	$0.560049\pi$
$480$	2.20871	0.100813
$481$	46.3303	2.11248
$482$	−4.79129	−0.218237
$483$	−4.41742	−0.201000
$484$	1.00000	0.0454545
$485$	6.33030	0.287444
$486$	16.1652	0.733266
$487$	23.1216	1.04774	0.523870	−	0.851798i	$-0.324488\pi$
$487$	23.1216	1.04774	0.523870	+	0.851798i	$0.324488\pi$
$488$	−2.00000	−0.0905357
$489$	−6.74773	−0.305143
$490$	−5.50455	−0.248670
$491$	38.8693	1.75415	0.877074	−	0.480356i	$-0.159492\pi$
$491$	38.8693	1.75415	0.877074	+	0.480356i	$0.159492\pi$
$492$	−10.5826	−0.477099
$493$	−10.7477	−0.484053
$494$	0	0
$495$	−3.79129	−0.170406
$496$	6.20871	0.278779
$497$	0.495454	0.0222242
$498$	−2.20871	−0.0989748
$499$	17.1652	0.768418	0.384209	−	0.923246i	$-0.374474\pi$
$499$	17.1652	0.768418	0.384209	+	0.923246i	$0.374474\pi$
$500$	7.41742	0.331717
$501$	−50.2432	−2.24470
$502$	−12.0000	−0.535586
$503$	−9.95644	−0.443936	−0.221968	−	0.975054i	$-0.571248\pi$
$503$	−9.95644	−0.443936	−0.221968	+	0.975054i	$0.571248\pi$
$504$	1.00000	0.0445435
$505$	3.49545	0.155546
$506$	−7.58258	−0.337087
$507$	57.3303	2.54613
$508$	−18.7477	−0.831796
$509$	27.1652	1.20407	0.602037	−	0.798468i	$-0.294356\pi$
$509$	27.1652	1.20407	0.602037	+	0.798468i	$0.294356\pi$
$510$	3.49545	0.154781
$511$	−0.0871215	−0.00385403
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	1.58258	0.0698044
$515$	−15.7913	−0.695847
$516$	−17.7913	−0.783218
$517$	−9.16515	−0.403083
$518$	−1.66970	−0.0733623
$519$	27.7913	1.21990
$520$	−4.58258	−0.200959
$521$	−14.8348	−0.649927	−0.324963	−	0.945727i	$-0.605352\pi$
$521$	−14.8348	−0.649927	−0.324963	+	0.945727i	$0.605352\pi$
$522$	32.5390	1.42419
$523$	−24.7477	−1.08214	−0.541071	−	0.840977i	$-0.681981\pi$
$523$	−24.7477	−1.08214	−0.541071	+	0.840977i	$0.681981\pi$
$524$	17.3739	0.758981
$525$	2.54811	0.111208
$526$	9.95644	0.434121
$527$	9.82576	0.428017
$528$	2.79129	0.121475
$529$	34.4955	1.49980
$530$	−6.00000	−0.260623
$531$	0	0
$532$	0	0
$533$	21.9564	0.951039
$534$	−37.9129	−1.64065
$535$	14.2432	0.615786
$536$	−0.208712	−0.00901499
$537$	52.9129	2.28336
$538$	10.7477	0.463367
$539$	−6.95644	−0.299635
$540$	−3.95644	−0.170258
$541$	9.91288	0.426188	0.213094	−	0.977032i	$-0.431646\pi$
$541$	9.91288	0.426188	0.213094	+	0.977032i	$0.431646\pi$
$542$	−7.37386	−0.316735
$543$	24.4174	1.04785
$544$	−1.58258	−0.0678524
$545$	−7.91288	−0.338950
$546$	−3.37386	−0.144388
$547$	24.8348	1.06186	0.530931	−	0.847415i	$-0.321842\pi$
$547$	24.8348	1.06186	0.530931	+	0.847415i	$0.321842\pi$
$548$	9.79129	0.418263
$549$	9.58258	0.408974
$550$	4.37386	0.186502
$551$	0	0
$552$	−21.1652	−0.900849
$553$	0.747727	0.0317966
$554$	22.0000	0.934690
$555$	17.6697	0.750037
$556$	−16.7913	−0.712109
$557$	−39.1652	−1.65948	−0.829740	−	0.558150i	$-0.811512\pi$
$557$	−39.1652	−1.65948	−0.829740	+	0.558150i	$0.811512\pi$
$558$	−29.7477	−1.25932
$559$	36.9129	1.56125
$560$	0.165151	0.00697892
$561$	4.41742	0.186504
$562$	−19.1216	−0.806596
$563$	−42.6606	−1.79793	−0.898965	−	0.438020i	$-0.855680\pi$
$563$	−42.6606	−1.79793	−0.898965	+	0.438020i	$0.855680\pi$
$564$	−25.5826	−1.07722
$565$	−2.50455	−0.105367
$566$	32.1216	1.35017
$567$	0.0871215	0.00365876
$568$	2.37386	0.0996051
$569$	−18.9564	−0.794695	−0.397348	−	0.917668i	$-0.630069\pi$
$569$	−18.9564	−0.794695	−0.397348	+	0.917668i	$0.630069\pi$
$570$	0	0
$571$	10.2087	0.427221	0.213611	−	0.976919i	$-0.431478\pi$
$571$	10.2087	0.427221	0.213611	+	0.976919i	$0.431478\pi$
$572$	−5.79129	−0.242146
$573$	−50.2432	−2.09894
$574$	−0.791288	−0.0330277
$575$	−33.1652	−1.38308
$576$	4.79129	0.199637
$577$	34.8693	1.45163	0.725814	−	0.687891i	$-0.241463\pi$
$577$	34.8693	1.45163	0.725814	+	0.687891i	$0.241463\pi$
$578$	14.4955	0.602931
$579$	17.7913	0.739381
$580$	5.37386	0.223138
$581$	−0.165151	−0.00685163
$582$	22.3303	0.925621
$583$	−7.58258	−0.314038
$584$	−0.417424	−0.0172731
$585$	21.9564	0.907787
$586$	2.20871	0.0912411
$587$	15.1652	0.625933	0.312966	−	0.949764i	$-0.398677\pi$
$587$	15.1652	0.625933	0.312966	+	0.949764i	$0.398677\pi$
$588$	−19.4174	−0.800761
$589$	0	0
$590$	0	0
$591$	−25.5826	−1.05233
$592$	−8.00000	−0.328798
$593$	21.1652	0.869149	0.434574	−	0.900636i	$-0.356899\pi$
$593$	21.1652	0.869149	0.434574	+	0.900636i	$0.356899\pi$
$594$	−5.00000	−0.205152
$595$	0.261365	0.0107149
$596$	0	0
$597$	−57.9129	−2.37022
$598$	43.9129	1.79573
$599$	−3.95644	−0.161656	−0.0808279	−	0.996728i	$-0.525756\pi$
$599$	−3.95644	−0.161656	−0.0808279	+	0.996728i	$0.525756\pi$
$600$	12.2087	0.498419
$601$	19.7913	0.807303	0.403652	−	0.914913i	$-0.367741\pi$
$601$	19.7913	0.807303	0.403652	+	0.914913i	$0.367741\pi$
$602$	−1.33030	−0.0542191
$603$	1.00000	0.0407231
$604$	−2.00000	−0.0813788
$605$	−0.791288	−0.0321704
$606$	12.3303	0.500884
$607$	29.9129	1.21413	0.607063	−	0.794654i	$-0.292347\pi$
$607$	29.9129	1.21413	0.607063	+	0.794654i	$0.292347\pi$
$608$	0	0
$609$	3.95644	0.160323
$610$	1.58258	0.0640766
$611$	53.0780	2.14731
$612$	7.58258	0.306507
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	−32.7477	−1.32159
$615$	8.37386	0.337667
$616$	0.208712	0.00840925
$617$	9.79129	0.394182	0.197091	−	0.980385i	$-0.436850\pi$
$617$	9.79129	0.394182	0.197091	+	0.980385i	$0.436850\pi$
$618$	−55.7042	−2.24075
$619$	17.1652	0.689926	0.344963	−	0.938616i	$-0.387892\pi$
$619$	17.1652	0.689926	0.344963	+	0.938616i	$0.387892\pi$
$620$	−4.91288	−0.197306
$621$	37.9129	1.52139
$622$	−19.9129	−0.798434
$623$	−2.83485	−0.113576
$624$	−16.1652	−0.647124
$625$	16.0000	0.640000
$626$	−4.37386	−0.174815
$627$	0	0
$628$	11.9564	0.477114
$629$	−12.6606	−0.504811
$630$	−0.791288	−0.0315257
$631$	9.91288	0.394625	0.197313	−	0.980341i	$-0.436779\pi$
$631$	9.91288	0.394625	0.197313	+	0.980341i	$0.436779\pi$
$632$	3.58258	0.142507
$633$	24.4174	0.970505
$634$	28.7477	1.14172
$635$	14.8348	0.588703
$636$	−21.1652	−0.839253
$637$	40.2867	1.59622
$638$	6.79129	0.268870
$639$	−11.3739	−0.449943
$640$	0.791288	0.0312784
$641$	−25.5826	−1.01045	−0.505225	−	0.862987i	$-0.668591\pi$
$641$	−25.5826	−1.01045	−0.505225	+	0.862987i	$0.668591\pi$
$642$	50.2432	1.98294
$643$	−10.3303	−0.407387	−0.203694	−	0.979035i	$-0.565295\pi$
$643$	−10.3303	−0.407387	−0.203694	+	0.979035i	$0.565295\pi$
$644$	−1.58258	−0.0623622
$645$	14.0780	0.554322
$646$	0	0
$647$	−19.9129	−0.782856	−0.391428	−	0.920209i	$-0.628019\pi$
$647$	−19.9129	−0.782856	−0.391428	+	0.920209i	$0.628019\pi$
$648$	0.417424	0.0163980
$649$	0	0
$650$	−25.3303	−0.993536
$651$	−3.61704	−0.141763
$652$	−2.41742	−0.0946736
$653$	−49.2867	−1.92874	−0.964370	−	0.264559i	$-0.914774\pi$
$653$	−49.2867	−1.92874	−0.964370	+	0.264559i	$0.914774\pi$
$654$	−27.9129	−1.09148
$655$	−13.7477	−0.537168
$656$	−3.79129	−0.148025
$657$	2.00000	0.0780274
$658$	−1.91288	−0.0745718
$659$	37.9129	1.47688	0.738438	−	0.674321i	$-0.235564\pi$
$659$	37.9129	1.47688	0.738438	+	0.674321i	$0.235564\pi$
$660$	−2.20871	−0.0859740
$661$	−32.0000	−1.24466	−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000	−1.24466	−0.622328	+	0.782757i	$0.713813\pi$
$662$	25.2087	0.979764
$663$	−25.5826	−0.993545
$664$	−0.791288	−0.0307079
$665$	0	0
$666$	38.3303	1.48527
$667$	−51.4955	−1.99391
$668$	−18.0000	−0.696441
$669$	−31.1652	−1.20491
$670$	0.165151	0.00638035
$671$	2.00000	0.0772091
$672$	0.582576	0.0224733
$673$	34.9564	1.34747	0.673736	−	0.738972i	$-0.264689\pi$
$673$	34.9564	1.34747	0.673736	+	0.738972i	$0.264689\pi$
$674$	−27.3739	−1.05440
$675$	−21.8693	−0.841750
$676$	20.5390	0.789962
$677$	−0.460985	−0.0177171	−0.00885855	−	0.999961i	$-0.502820\pi$
$677$	−0.460985	−0.0177171	−0.00885855	+	0.999961i	$0.502820\pi$
$678$	−8.83485	−0.339300
$679$	1.66970	0.0640771
$680$	1.25227	0.0480225
$681$	−4.41742	−0.169276
$682$	−6.20871	−0.237744
$683$	24.6606	0.943612	0.471806	−	0.881702i	$-0.343602\pi$
$683$	24.6606	0.943612	0.471806	+	0.881702i	$0.343602\pi$
$684$	0	0
$685$	−7.74773	−0.296025
$686$	−2.91288	−0.111214
$687$	−12.9129	−0.492657
$688$	−6.37386	−0.243001
$689$	43.9129	1.67295
$690$	16.7477	0.637575
$691$	23.4955	0.893809	0.446905	−	0.894582i	$-0.352526\pi$
$691$	23.4955	0.893809	0.446905	+	0.894582i	$0.352526\pi$
$692$	9.95644	0.378487
$693$	−1.00000	−0.0379869
$694$	−15.1652	−0.575661
$695$	13.2867	0.503995
$696$	18.9564	0.718542
$697$	−6.00000	−0.227266
$698$	31.4955	1.19212
$699$	−8.83485	−0.334165
$700$	0.912878	0.0345036
$701$	−42.3303	−1.59879	−0.799397	−	0.600804i	$-0.794847\pi$
$701$	−42.3303	−1.59879	−0.799397	+	0.600804i	$0.794847\pi$
$702$	28.9564	1.09289
$703$	0	0
$704$	1.00000	0.0376889
$705$	20.2432	0.762402
$706$	33.1652	1.24819
$707$	0.921970	0.0346743
$708$	0	0
$709$	28.2087	1.05940	0.529700	−	0.848185i	$-0.322304\pi$
$709$	28.2087	1.05940	0.529700	+	0.848185i	$0.322304\pi$
$710$	−1.87841	−0.0704954
$711$	−17.1652	−0.643743
$712$	−13.5826	−0.509029
$713$	47.0780	1.76309
$714$	0.921970	0.0345039
$715$	4.58258	0.171379
$716$	18.9564	0.708435
$717$	−18.9564	−0.707941
$718$	29.7042	1.10855
$719$	35.0780	1.30819	0.654095	−	0.756413i	$-0.273050\pi$
$719$	35.0780	1.30819	0.654095	+	0.756413i	$0.273050\pi$
$720$	−3.79129	−0.141293
$721$	−4.16515	−0.155118
$722$	0	0
$723$	13.3739	0.497379
$724$	8.74773	0.325107
$725$	29.7042	1.10319
$726$	−2.79129	−0.103594
$727$	29.4955	1.09393	0.546963	−	0.837157i	$-0.315784\pi$
$727$	29.4955	1.09393	0.546963	+	0.837157i	$0.315784\pi$
$728$	−1.20871	−0.0447979
$729$	−43.8693	−1.62479
$730$	0.330303	0.0122251
$731$	−10.0871	−0.373086
$732$	5.58258	0.206338
$733$	35.4955	1.31105	0.655527	−	0.755172i	$-0.272446\pi$
$733$	35.4955	1.31105	0.655527	+	0.755172i	$0.272446\pi$
$734$	16.3303	0.602762
$735$	15.3648	0.566738
$736$	−7.58258	−0.279497
$737$	0.208712	0.00768801
$738$	18.1652	0.668668
$739$	16.0436	0.590172	0.295086	−	0.955471i	$-0.404652\pi$
$739$	16.0436	0.590172	0.295086	+	0.955471i	$0.404652\pi$
$740$	6.33030	0.232707
$741$	0	0
$742$	−1.58258	−0.0580982
$743$	−26.8348	−0.984475	−0.492238	−	0.870461i	$-0.663821\pi$
$743$	−26.8348	−0.984475	−0.492238	+	0.870461i	$0.663821\pi$
$744$	−17.3303	−0.635360
$745$	0	0
$746$	4.37386	0.160139
$747$	3.79129	0.138716
$748$	1.58258	0.0578647
$749$	3.75682	0.137271
$750$	−20.7042	−0.756009
$751$	−26.3303	−0.960806	−0.480403	−	0.877048i	$-0.659510\pi$
$751$	−26.3303	−0.960806	−0.480403	+	0.877048i	$0.659510\pi$
$752$	−9.16515	−0.334219
$753$	33.4955	1.22064
$754$	−39.3303	−1.43233
$755$	1.58258	0.0575958
$756$	−1.04356	−0.0379539
$757$	−28.7913	−1.04644	−0.523219	−	0.852199i	$-0.675269\pi$
$757$	−28.7913	−1.04644	−0.523219	+	0.852199i	$0.675269\pi$
$758$	28.2087	1.02459
$759$	21.1652	0.768246
$760$	0	0
$761$	4.08712	0.148158	0.0740790	−	0.997252i	$-0.476398\pi$
$761$	4.08712	0.148158	0.0740790	+	0.997252i	$0.476398\pi$
$762$	52.3303	1.89573
$763$	−2.08712	−0.0755589
$764$	−18.0000	−0.651217
$765$	−6.00000	−0.216930
$766$	12.9564	0.468135
$767$	0	0
$768$	2.79129	0.100722
$769$	44.3303	1.59859	0.799296	−	0.600938i	$-0.205206\pi$
$769$	44.3303	1.59859	0.799296	+	0.600938i	$0.205206\pi$
$770$	−0.165151	−0.00595164
$771$	−4.41742	−0.159090
$772$	6.37386	0.229400
$773$	−15.4955	−0.557333	−0.278666	−	0.960388i	$-0.589892\pi$
$773$	−15.4955	−0.557333	−0.278666	+	0.960388i	$0.589892\pi$
$774$	30.5390	1.09770
$775$	−27.1561	−0.975474
$776$	8.00000	0.287183
$777$	4.66061	0.167198
$778$	31.1216	1.11576
$779$	0	0
$780$	12.7913	0.458002
$781$	−2.37386	−0.0849435
$782$	−12.0000	−0.429119
$783$	−33.9564	−1.21350
$784$	−6.95644	−0.248444
$785$	−9.46099	−0.337677
$786$	−48.4955	−1.72978
$787$	5.58258	0.198997	0.0994987	−	0.995038i	$-0.468276\pi$
$787$	5.58258	0.198997	0.0994987	+	0.995038i	$0.468276\pi$
$788$	−9.16515	−0.326495
$789$	−27.7913	−0.989396
$790$	−2.83485	−0.100859
$791$	−0.660606	−0.0234884
$792$	−4.79129	−0.170251
$793$	−11.5826	−0.411309
$794$	−26.9564	−0.956648
$795$	16.7477	0.593981
$796$	−20.7477	−0.735384
$797$	−50.2432	−1.77970	−0.889852	−	0.456249i	$-0.849193\pi$
$797$	−50.2432	−1.77970	−0.889852	+	0.456249i	$0.849193\pi$
$798$	0	0
$799$	−14.5045	−0.513134
$800$	4.37386	0.154639
$801$	65.0780	2.29942
$802$	−4.41742	−0.155985
$803$	0.417424	0.0147306
$804$	0.582576	0.0205459
$805$	1.25227	0.0441368
$806$	35.9564	1.26651
$807$	−30.0000	−1.05605
$808$	4.41742	0.155404
$809$	−5.66970	−0.199336	−0.0996680	−	0.995021i	$-0.531778\pi$
$809$	−5.66970	−0.199336	−0.0996680	+	0.995021i	$0.531778\pi$
$810$	−0.330303	−0.0116057
$811$	−23.4955	−0.825037	−0.412518	−	0.910949i	$-0.635351\pi$
$811$	−23.4955	−0.825037	−0.412518	+	0.910949i	$0.635351\pi$
$812$	1.41742	0.0497418
$813$	20.5826	0.721862
$814$	8.00000	0.280400
$815$	1.91288	0.0670052
$816$	4.41742	0.154641
$817$	0	0
$818$	10.3739	0.362714
$819$	5.79129	0.202364
$820$	3.00000	0.104765
$821$	17.0780	0.596027	0.298014	−	0.954562i	$-0.403676\pi$
$821$	17.0780	0.596027	0.298014	+	0.954562i	$0.403676\pi$
$822$	−27.3303	−0.953254
$823$	−37.4955	−1.30701	−0.653505	−	0.756922i	$-0.726702\pi$
$823$	−37.4955	−1.30701	−0.653505	+	0.756922i	$0.726702\pi$
$824$	−19.9564	−0.695216
$825$	−12.2087	−0.425053
$826$	0	0
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	36.3303	1.26257
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	0.626136	0.0217335
$831$	−61.4083	−2.13023
$832$	−5.79129	−0.200777
$833$	−11.0091	−0.381442
$834$	46.8693	1.62295
$835$	14.2432	0.492906
$836$	0	0
$837$	31.0436	1.07302
$838$	24.3303	0.840476
$839$	3.95644	0.136591	0.0682957	−	0.997665i	$-0.478244\pi$
$839$	3.95644	0.136591	0.0682957	+	0.997665i	$0.478244\pi$
$840$	−0.460985	−0.0159055
$841$	17.1216	0.590400
$842$	−38.7477	−1.33533
$843$	53.3739	1.83829
$844$	8.74773	0.301109
$845$	−16.2523	−0.559095
$846$	43.9129	1.50976
$847$	−0.208712	−0.00717143
$848$	−7.58258	−0.260387
$849$	−89.6606	−3.07714
$850$	6.92197	0.237422
$851$	−60.6606	−2.07942
$852$	−6.62614	−0.227008
$853$	11.1652	0.382288	0.191144	−	0.981562i	$-0.438780\pi$
$853$	11.1652	0.382288	0.191144	+	0.981562i	$0.438780\pi$
$854$	0.417424	0.0142840
$855$	0	0
$856$	18.0000	0.615227
$857$	25.2867	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$857$	25.2867	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$858$	16.1652	0.551869
$859$	41.4955	1.41581	0.707903	−	0.706309i	$-0.249641\pi$
$859$	41.4955	1.41581	0.707903	+	0.706309i	$0.249641\pi$
$860$	5.04356	0.171984
$861$	2.20871	0.0752727
$862$	33.4955	1.14086
$863$	8.53901	0.290671	0.145336	−	0.989382i	$-0.453574\pi$
$863$	8.53901	0.290671	0.145336	+	0.989382i	$0.453574\pi$
$864$	−5.00000	−0.170103
$865$	−7.87841	−0.267874
$866$	−2.41742	−0.0821474
$867$	−40.4610	−1.37413
$868$	−1.29583	−0.0439835
$869$	−3.58258	−0.121531
$870$	−15.0000	−0.508548
$871$	−1.20871	−0.0409556
$872$	−10.0000	−0.338643
$873$	−38.3303	−1.29728
$874$	0	0
$875$	−1.54811	−0.0523356
$876$	1.16515	0.0393668
$877$	53.1216	1.79379	0.896894	−	0.442245i	$-0.145818\pi$
$877$	53.1216	1.79379	0.896894	+	0.442245i	$0.145818\pi$
$878$	−12.8348	−0.433155
$879$	−6.16515	−0.207945
$880$	−0.791288	−0.0266743
$881$	28.1216	0.947440	0.473720	−	0.880675i	$-0.342911\pi$
$881$	28.1216	0.947440	0.473720	+	0.880675i	$0.342911\pi$
$882$	33.3303	1.12229
$883$	−23.9129	−0.804732	−0.402366	−	0.915479i	$-0.631812\pi$
$883$	−23.9129	−0.804732	−0.402366	+	0.915479i	$0.631812\pi$
$884$	−9.16515	−0.308257
$885$	0	0
$886$	−18.3303	−0.615819
$887$	33.4955	1.12467	0.562334	−	0.826910i	$-0.309904\pi$
$887$	33.4955	1.12467	0.562334	+	0.826910i	$0.309904\pi$
$888$	22.3303	0.749356
$889$	3.91288	0.131234
$890$	10.7477	0.360265
$891$	−0.417424	−0.0139842
$892$	−11.1652	−0.373837
$893$	0	0
$894$	0	0
$895$	−15.0000	−0.501395
$896$	0.208712	0.00697258
$897$	−122.573	−4.09261
$898$	−10.7477	−0.358656
$899$	−42.1652	−1.40629
$900$	−20.9564	−0.698548
$901$	−12.0000	−0.399778
$902$	3.79129	0.126236
$903$	3.71326	0.123569
$904$	−3.16515	−0.105271
$905$	−6.92197	−0.230094
$906$	5.58258	0.185469
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	−1.58258	−0.0525196
$909$	−21.1652	−0.702004
$910$	0.956439	0.0317057
$911$	20.8348	0.690289	0.345145	−	0.938549i	$-0.387830\pi$
$911$	20.8348	0.690289	0.345145	+	0.938549i	$0.387830\pi$
$912$	0	0
$913$	0.791288	0.0261878
$914$	32.7477	1.08320
$915$	−4.41742	−0.146036
$916$	−4.62614	−0.152852
$917$	−3.62614	−0.119746
$918$	−7.91288	−0.261164
$919$	−8.28674	−0.273354	−0.136677	−	0.990616i	$-0.543642\pi$
$919$	−8.28674	−0.273354	−0.136677	+	0.990616i	$0.543642\pi$
$920$	6.00000	0.197814
$921$	91.4083	3.01201
$922$	−6.33030	−0.208477
$923$	13.7477	0.452512
$924$	−0.582576	−0.0191653
$925$	34.9909	1.15049
$926$	−32.6606	−1.07329
$927$	95.6170	3.14048
$928$	6.79129	0.222935
$929$	−21.7913	−0.714949	−0.357474	−	0.933923i	$-0.616362\pi$
$929$	−21.7913	−0.714949	−0.357474	+	0.933923i	$0.616362\pi$
$930$	13.7133	0.449675
$931$	0	0
$932$	−3.16515	−0.103678
$933$	55.5826	1.81969
$934$	−4.41742	−0.144543
$935$	−1.25227	−0.0409537
$936$	27.7477	0.906963
$937$	53.8258	1.75841	0.879205	−	0.476443i	$-0.158074\pi$
$937$	53.8258	1.75841	0.879205	+	0.476443i	$0.158074\pi$
$938$	0.0435608	0.00142231
$939$	12.2087	0.398416
$940$	7.25227	0.236543
$941$	45.1652	1.47234	0.736171	−	0.676796i	$-0.236632\pi$
$941$	45.1652	1.47234	0.736171	+	0.676796i	$0.236632\pi$
$942$	−33.3739	−1.08738
$943$	−28.7477	−0.936155
$944$	0	0
$945$	0.825757	0.0268619
$946$	6.37386	0.207232
$947$	−47.0780	−1.52983	−0.764915	−	0.644131i	$-0.777219\pi$
$947$	−47.0780	−1.52983	−0.764915	+	0.644131i	$0.777219\pi$
$948$	−10.0000	−0.324785
$949$	−2.41742	−0.0784729
$950$	0	0
$951$	−80.2432	−2.60206
$952$	0.330303	0.0107052
$953$	33.1652	1.07432	0.537162	−	0.843479i	$-0.319496\pi$
$953$	33.1652	1.07432	0.537162	+	0.843479i	$0.319496\pi$
$954$	36.3303	1.17624
$955$	14.2432	0.460899
$956$	−6.79129	−0.219646
$957$	−18.9564	−0.612775
$958$	8.20871	0.265211
$959$	−2.04356	−0.0659900
$960$	−2.20871	−0.0712859
$961$	7.54811	0.243487
$962$	−46.3303	−1.49375
$963$	−86.2432	−2.77915
$964$	4.79129	0.154317
$965$	−5.04356	−0.162358
$966$	4.41742	0.142128
$967$	−13.4955	−0.433985	−0.216992	−	0.976173i	$-0.569625\pi$
$967$	−13.4955	−0.433985	−0.216992	+	0.976173i	$0.569625\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−6.33030	−0.203254
$971$	−40.2867	−1.29286	−0.646432	−	0.762972i	$-0.723739\pi$
$971$	−40.2867	−1.29286	−0.646432	+	0.762972i	$0.723739\pi$
$972$	−16.1652	−0.518497
$973$	3.50455	0.112351
$974$	−23.1216	−0.740864
$975$	70.7042	2.26435
$976$	2.00000	0.0640184
$977$	39.1652	1.25300	0.626502	−	0.779420i	$-0.284486\pi$
$977$	39.1652	1.25300	0.626502	+	0.779420i	$0.284486\pi$
$978$	6.74773	0.215769
$979$	13.5826	0.434101
$980$	5.50455	0.175836
$981$	47.9129	1.52974
$982$	−38.8693	−1.24037
$983$	−2.20871	−0.0704470	−0.0352235	−	0.999379i	$-0.511214\pi$
$983$	−2.20871	−0.0704470	−0.0352235	+	0.999379i	$0.511214\pi$
$984$	10.5826	0.337360
$985$	7.25227	0.231077
$986$	10.7477	0.342277
$987$	5.33939	0.169955
$988$	0	0
$989$	−48.3303	−1.53681
$990$	3.79129	0.120495
$991$	16.9564	0.538639	0.269320	−	0.963051i	$-0.413201\pi$
$991$	16.9564	0.538639	0.269320	+	0.963051i	$0.413201\pi$
$992$	−6.20871	−0.197127
$993$	−70.3648	−2.23296
$994$	−0.495454	−0.0157149
$995$	16.4174	0.520467
$996$	2.20871	0.0699857
$997$	−14.0871	−0.446144	−0.223072	−	0.974802i	$-0.571608\pi$
$997$	−14.0871	−0.446144	−0.223072	+	0.974802i	$0.571608\pi$
$998$	−17.1652	−0.543353
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.w.1.2		2
19.18	odd	2		418.2.a.f.1.1	✓	2
57.56	even	2		3762.2.a.s.1.2		2
76.75	even	2		3344.2.a.l.1.2		2
209.208	even	2		4598.2.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.f.1.1	✓	2	19.18	odd	2
3344.2.a.l.1.2		2	76.75	even	2
3762.2.a.s.1.2		2	57.56	even	2
4598.2.a.y.1.1		2	209.208	even	2
7942.2.a.w.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} -2.79129 q^{6} -0.208712 q^{7} -1.00000 q^{8} +4.79129 q^{9} +0.791288 q^{10} +1.00000 q^{11} +2.79129 q^{12} -5.79129 q^{13} +0.208712 q^{14} -2.20871 q^{15} +1.00000 q^{16} +1.58258 q^{17} -4.79129 q^{18} -0.791288 q^{20} -0.582576 q^{21} -1.00000 q^{22} +7.58258 q^{23} -2.79129 q^{24} -4.37386 q^{25} +5.79129 q^{26} +5.00000 q^{27} -0.208712 q^{28} -6.79129 q^{29} +2.20871 q^{30} +6.20871 q^{31} -1.00000 q^{32} +2.79129 q^{33} -1.58258 q^{34} +0.165151 q^{35} +4.79129 q^{36} -8.00000 q^{37} -16.1652 q^{39} +0.791288 q^{40} -3.79129 q^{41} +0.582576 q^{42} -6.37386 q^{43} +1.00000 q^{44} -3.79129 q^{45} -7.58258 q^{46} -9.16515 q^{47} +2.79129 q^{48} -6.95644 q^{49} +4.37386 q^{50} +4.41742 q^{51} -5.79129 q^{52} -7.58258 q^{53} -5.00000 q^{54} -0.791288 q^{55} +0.208712 q^{56} +6.79129 q^{58} -2.20871 q^{60} +2.00000 q^{61} -6.20871 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.58258 q^{65} -2.79129 q^{66} +0.208712 q^{67} +1.58258 q^{68} +21.1652 q^{69} -0.165151 q^{70} -2.37386 q^{71} -4.79129 q^{72} +0.417424 q^{73} +8.00000 q^{74} -12.2087 q^{75} -0.208712 q^{77} +16.1652 q^{78} -3.58258 q^{79} -0.791288 q^{80} -0.417424 q^{81} +3.79129 q^{82} +0.791288 q^{83} -0.582576 q^{84} -1.25227 q^{85} +6.37386 q^{86} -18.9564 q^{87} -1.00000 q^{88} +13.5826 q^{89} +3.79129 q^{90} +1.20871 q^{91} +7.58258 q^{92} +17.3303 q^{93} +9.16515 q^{94} -2.79129 q^{96} -8.00000 q^{97} +6.95644 q^{98} +4.79129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 5 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} + 2 q^{11} + q^{12} - 7 q^{13} + 5 q^{14} - 9 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 3 q^{20} + 8 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 5 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 + 2 * q^11 + q^12 - 7 * q^13 + 5 * q^14 - 9 * q^15 + 2 * q^16 - 6 * q^17 - 5 * q^18 + 3 * q^20 + 8 * q^21 - 2 * q^22 + 6 * q^23 - q^24 + 5 * q^25 + 7 * q^26 + 10 * q^27 - 5 * q^28 - 9 * q^29 + 9 * q^30 + 17 * q^31 - 2 * q^32 + q^33 + 6 * q^34 - 18 * q^35 + 5 * q^36 - 16 * q^37 - 14 * q^39 - 3 * q^40 - 3 * q^41 - 8 * q^42 + q^43 + 2 * q^44 - 3 * q^45 - 6 * q^46 + q^48 + 9 * q^49 - 5 * q^50 + 18 * q^51 - 7 * q^52 - 6 * q^53 - 10 * q^54 + 3 * q^55 + 5 * q^56 + 9 * q^58 - 9 * q^60 + 4 * q^61 - 17 * q^62 - 2 * q^63 + 2 * q^64 - q^66 + 5 * q^67 - 6 * q^68 + 24 * q^69 + 18 * q^70 + 9 * q^71 - 5 * q^72 + 10 * q^73 + 16 * q^74 - 29 * q^75 - 5 * q^77 + 14 * q^78 + 2 * q^79 + 3 * q^80 - 10 * q^81 + 3 * q^82 - 3 * q^83 + 8 * q^84 - 30 * q^85 - q^86 - 15 * q^87 - 2 * q^88 + 18 * q^89 + 3 * q^90 + 7 * q^91 + 6 * q^92 - 2 * q^93 - q^96 - 16 * q^97 - 9 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

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Database

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