LMFDB - Embedded newform 6034.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.46410 q^{11} +2.00000 q^{12} -1.26795 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.46410 q^{17} +1.00000 q^{18} +7.46410 q^{19} +2.00000 q^{21} -1.46410 q^{22} +6.00000 q^{23} +2.00000 q^{24} -5.00000 q^{25} -1.26795 q^{26} -4.00000 q^{27} +1.00000 q^{28} +0.535898 q^{29} +5.46410 q^{31} +1.00000 q^{32} -2.92820 q^{33} -3.46410 q^{34} +1.00000 q^{36} +8.73205 q^{37} +7.46410 q^{38} -2.53590 q^{39} +6.92820 q^{41} +2.00000 q^{42} -5.66025 q^{43} -1.46410 q^{44} +6.00000 q^{46} +12.3923 q^{47} +2.00000 q^{48} +1.00000 q^{49} -5.00000 q^{50} -6.92820 q^{51} -1.26795 q^{52} +2.00000 q^{53} -4.00000 q^{54} +1.00000 q^{56} +14.9282 q^{57} +0.535898 q^{58} +3.46410 q^{59} +5.46410 q^{61} +5.46410 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.92820 q^{66} -2.73205 q^{67} -3.46410 q^{68} +12.0000 q^{69} +10.9282 q^{71} +1.00000 q^{72} +2.00000 q^{73} +8.73205 q^{74} -10.0000 q^{75} +7.46410 q^{76} -1.46410 q^{77} -2.53590 q^{78} +12.0000 q^{79} -11.0000 q^{81} +6.92820 q^{82} -11.6603 q^{83} +2.00000 q^{84} -5.66025 q^{86} +1.07180 q^{87} -1.46410 q^{88} -2.00000 q^{89} -1.26795 q^{91} +6.00000 q^{92} +10.9282 q^{93} +12.3923 q^{94} +2.00000 q^{96} -8.00000 q^{97} +1.00000 q^{98} -1.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 4 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} + 2 q^{16} + 2 q^{18} + 8 q^{19} + 4 q^{21} + 4 q^{22} + 12 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 2 q^{28} + 8 q^{29} + 4 q^{31} + 2 q^{32} + 8 q^{33} + 2 q^{36} + 14 q^{37} + 8 q^{38} - 12 q^{39} + 4 q^{42} + 6 q^{43} + 4 q^{44} + 12 q^{46} + 4 q^{47} + 4 q^{48} + 2 q^{49} - 10 q^{50} - 6 q^{52} + 4 q^{53} - 8 q^{54} + 2 q^{56} + 16 q^{57} + 8 q^{58} + 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 8 q^{66} - 2 q^{67} + 24 q^{69} + 8 q^{71} + 2 q^{72} + 4 q^{73} + 14 q^{74} - 20 q^{75} + 8 q^{76} + 4 q^{77} - 12 q^{78} + 24 q^{79} - 22 q^{81} - 6 q^{83} + 4 q^{84} + 6 q^{86} + 16 q^{87} + 4 q^{88} - 4 q^{89} - 6 q^{91} + 12 q^{92} + 8 q^{93} + 4 q^{94} + 4 q^{96} - 16 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 4 * q^11 + 4 * q^12 - 6 * q^13 + 2 * q^14 + 2 * q^16 + 2 * q^18 + 8 * q^19 + 4 * q^21 + 4 * q^22 + 12 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 2 * q^28 + 8 * q^29 + 4 * q^31 + 2 * q^32 + 8 * q^33 + 2 * q^36 + 14 * q^37 + 8 * q^38 - 12 * q^39 + 4 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^46 + 4 * q^47 + 4 * q^48 + 2 * q^49 - 10 * q^50 - 6 * q^52 + 4 * q^53 - 8 * q^54 + 2 * q^56 + 16 * q^57 + 8 * q^58 + 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 8 * q^66 - 2 * q^67 + 24 * q^69 + 8 * q^71 + 2 * q^72 + 4 * q^73 + 14 * q^74 - 20 * q^75 + 8 * q^76 + 4 * q^77 - 12 * q^78 + 24 * q^79 - 22 * q^81 - 6 * q^83 + 4 * q^84 + 6 * q^86 + 16 * q^87 + 4 * q^88 - 4 * q^89 - 6 * q^91 + 12 * q^92 + 8 * q^93 + 4 * q^94 + 4 * q^96 - 16 * q^97 + 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	2.00000	0.816497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.46410	−0.441443	−0.220722	−	0.975337i	$-0.570841\pi$
$11$	−1.46410	−0.441443	−0.220722	+	0.975337i	$0.570841\pi$
$12$	2.00000	0.577350
$13$	−1.26795	−0.351666	−0.175833	−	0.984420i	$-0.556262\pi$
$13$	−1.26795	−0.351666	−0.175833	+	0.984420i	$0.556262\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.46410	−0.840168	−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410	−0.840168	−0.420084	+	0.907485i	$0.637999\pi$
$18$	1.00000	0.235702
$19$	7.46410	1.71238	0.856191	−	0.516659i	$-0.172825\pi$
$19$	7.46410	1.71238	0.856191	+	0.516659i	$0.172825\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	−1.46410	−0.312148
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	2.00000	0.408248
$25$	−5.00000	−1.00000
$26$	−1.26795	−0.248665
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	0.535898	0.0995138	0.0497569	−	0.998761i	$-0.484155\pi$
$29$	0.535898	0.0995138	0.0497569	+	0.998761i	$0.484155\pi$
$30$	0	0
$31$	5.46410	0.981382	0.490691	−	0.871334i	$-0.336744\pi$
$31$	5.46410	0.981382	0.490691	+	0.871334i	$0.336744\pi$
$32$	1.00000	0.176777
$33$	−2.92820	−0.509735
$34$	−3.46410	−0.594089
$35$	0	0
$36$	1.00000	0.166667
$37$	8.73205	1.43554	0.717770	−	0.696280i	$-0.245163\pi$
$37$	8.73205	1.43554	0.717770	+	0.696280i	$0.245163\pi$
$38$	7.46410	1.21084
$39$	−2.53590	−0.406069
$40$	0	0
$41$	6.92820	1.08200	0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820	1.08200	0.541002	+	0.841021i	$0.318045\pi$
$42$	2.00000	0.308607
$43$	−5.66025	−0.863181	−0.431590	−	0.902070i	$-0.642047\pi$
$43$	−5.66025	−0.863181	−0.431590	+	0.902070i	$0.642047\pi$
$44$	−1.46410	−0.220722
$45$	0	0
$46$	6.00000	0.884652
$47$	12.3923	1.80760	0.903802	−	0.427951i	$-0.140765\pi$
$47$	12.3923	1.80760	0.903802	+	0.427951i	$0.140765\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	−5.00000	−0.707107
$51$	−6.92820	−0.970143
$52$	−1.26795	−0.175833
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	14.9282	1.97729
$58$	0.535898	0.0703669
$59$	3.46410	0.450988	0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410	0.450988	0.225494	+	0.974245i	$0.427600\pi$
$60$	0	0
$61$	5.46410	0.699607	0.349803	−	0.936823i	$-0.386248\pi$
$61$	5.46410	0.699607	0.349803	+	0.936823i	$0.386248\pi$
$62$	5.46410	0.693942
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.92820	−0.360437
$67$	−2.73205	−0.333773	−0.166887	−	0.985976i	$-0.553371\pi$
$67$	−2.73205	−0.333773	−0.166887	+	0.985976i	$0.553371\pi$
$68$	−3.46410	−0.420084
$69$	12.0000	1.44463
$70$	0	0
$71$	10.9282	1.29694	0.648470	−	0.761241i	$-0.275409\pi$
$71$	10.9282	1.29694	0.648470	+	0.761241i	$0.275409\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	8.73205	1.01508
$75$	−10.0000	−1.15470
$76$	7.46410	0.856191
$77$	−1.46410	−0.166850
$78$	−2.53590	−0.287134
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	6.92820	0.765092
$83$	−11.6603	−1.27988	−0.639940	−	0.768425i	$-0.721041\pi$
$83$	−11.6603	−1.27988	−0.639940	+	0.768425i	$0.721041\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−5.66025	−0.610361
$87$	1.07180	0.114909
$88$	−1.46410	−0.156074
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	−1.26795	−0.132917
$92$	6.00000	0.625543
$93$	10.9282	1.13320
$94$	12.3923	1.27817
$95$	0	0
$96$	2.00000	0.204124
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	1.00000	0.101015
$99$	−1.46410	−0.147148
$100$	−5.00000	−0.500000
$101$	−1.26795	−0.126166	−0.0630828	−	0.998008i	$-0.520093\pi$
$101$	−1.26795	−0.126166	−0.0630828	+	0.998008i	$0.520093\pi$
$102$	−6.92820	−0.685994
$103$	9.46410	0.932526	0.466263	−	0.884646i	$-0.345600\pi$
$103$	9.46410	0.932526	0.466263	+	0.884646i	$0.345600\pi$
$104$	−1.26795	−0.124333
$105$	0	0
$106$	2.00000	0.194257
$107$	8.19615	0.792352	0.396176	−	0.918175i	$-0.370337\pi$
$107$	8.19615	0.792352	0.396176	+	0.918175i	$0.370337\pi$
$108$	−4.00000	−0.384900
$109$	−8.92820	−0.855167	−0.427583	−	0.903976i	$-0.640635\pi$
$109$	−8.92820	−0.855167	−0.427583	+	0.903976i	$0.640635\pi$
$110$	0	0
$111$	17.4641	1.65762
$112$	1.00000	0.0944911
$113$	−11.4641	−1.07845	−0.539226	−	0.842161i	$-0.681283\pi$
$113$	−11.4641	−1.07845	−0.539226	+	0.842161i	$0.681283\pi$
$114$	14.9282	1.39815
$115$	0	0
$116$	0.535898	0.0497569
$117$	−1.26795	−0.117222
$118$	3.46410	0.318896
$119$	−3.46410	−0.317554
$120$	0	0
$121$	−8.85641	−0.805128
$122$	5.46410	0.494697
$123$	13.8564	1.24939
$124$	5.46410	0.490691
$125$	0	0
$126$	1.00000	0.0890871
$127$	−6.92820	−0.614779	−0.307389	−	0.951584i	$-0.599455\pi$
$127$	−6.92820	−0.614779	−0.307389	+	0.951584i	$0.599455\pi$
$128$	1.00000	0.0883883
$129$	−11.3205	−0.996715
$130$	0	0
$131$	4.73205	0.413441	0.206721	−	0.978400i	$-0.433721\pi$
$131$	4.73205	0.413441	0.206721	+	0.978400i	$0.433721\pi$
$132$	−2.92820	−0.254867
$133$	7.46410	0.647220
$134$	−2.73205	−0.236013
$135$	0	0
$136$	−3.46410	−0.297044
$137$	−10.3923	−0.887875	−0.443937	−	0.896058i	$-0.646419\pi$
$137$	−10.3923	−0.887875	−0.443937	+	0.896058i	$0.646419\pi$
$138$	12.0000	1.02151
$139$	−2.39230	−0.202913	−0.101456	−	0.994840i	$-0.532350\pi$
$139$	−2.39230	−0.202913	−0.101456	+	0.994840i	$0.532350\pi$
$140$	0	0
$141$	24.7846	2.08724
$142$	10.9282	0.917074
$143$	1.85641	0.155241
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	2.00000	0.164957
$148$	8.73205	0.717770
$149$	7.85641	0.643622	0.321811	−	0.946804i	$-0.395708\pi$
$149$	7.85641	0.643622	0.321811	+	0.946804i	$0.395708\pi$
$150$	−10.0000	−0.816497
$151$	8.92820	0.726567	0.363283	−	0.931679i	$-0.381656\pi$
$151$	8.92820	0.726567	0.363283	+	0.931679i	$0.381656\pi$
$152$	7.46410	0.605419
$153$	−3.46410	−0.280056
$154$	−1.46410	−0.117981
$155$	0	0
$156$	−2.53590	−0.203034
$157$	−24.3923	−1.94672	−0.973359	−	0.229287i	$-0.926361\pi$
$157$	−24.3923	−1.94672	−0.973359	+	0.229287i	$0.926361\pi$
$158$	12.0000	0.954669
$159$	4.00000	0.317221
$160$	0	0
$161$	6.00000	0.472866
$162$	−11.0000	−0.864242
$163$	13.4641	1.05459	0.527295	−	0.849682i	$-0.323206\pi$
$163$	13.4641	1.05459	0.527295	+	0.849682i	$0.323206\pi$
$164$	6.92820	0.541002
$165$	0	0
$166$	−11.6603	−0.905011
$167$	−19.3205	−1.49507	−0.747533	−	0.664225i	$-0.768762\pi$
$167$	−19.3205	−1.49507	−0.747533	+	0.664225i	$0.768762\pi$
$168$	2.00000	0.154303
$169$	−11.3923	−0.876331
$170$	0	0
$171$	7.46410	0.570794
$172$	−5.66025	−0.431590
$173$	5.85641	0.445254	0.222627	−	0.974904i	$-0.428537\pi$
$173$	5.85641	0.445254	0.222627	+	0.974904i	$0.428537\pi$
$174$	1.07180	0.0812527
$175$	−5.00000	−0.377964
$176$	−1.46410	−0.110361
$177$	6.92820	0.520756
$178$	−2.00000	−0.149906
$179$	−2.53590	−0.189542	−0.0947710	−	0.995499i	$-0.530212\pi$
$179$	−2.53590	−0.189542	−0.0947710	+	0.995499i	$0.530212\pi$
$180$	0	0
$181$	3.12436	0.232232	0.116116	−	0.993236i	$-0.462956\pi$
$181$	3.12436	0.232232	0.116116	+	0.993236i	$0.462956\pi$
$182$	−1.26795	−0.0939866
$183$	10.9282	0.807836
$184$	6.00000	0.442326
$185$	0	0
$186$	10.9282	0.801295
$187$	5.07180	0.370887
$188$	12.3923	0.903802
$189$	−4.00000	−0.290957
$190$	0	0
$191$	1.46410	0.105939	0.0529693	−	0.998596i	$-0.483131\pi$
$191$	1.46410	0.105939	0.0529693	+	0.998596i	$0.483131\pi$
$192$	2.00000	0.144338
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−8.00000	−0.574367
$195$	0	0
$196$	1.00000	0.0714286
$197$	−17.3205	−1.23404	−0.617018	−	0.786949i	$-0.711659\pi$
$197$	−17.3205	−1.23404	−0.617018	+	0.786949i	$0.711659\pi$
$198$	−1.46410	−0.104049
$199$	2.53590	0.179765	0.0898825	−	0.995952i	$-0.471351\pi$
$199$	2.53590	0.179765	0.0898825	+	0.995952i	$0.471351\pi$
$200$	−5.00000	−0.353553
$201$	−5.46410	−0.385408
$202$	−1.26795	−0.0892126
$203$	0.535898	0.0376127
$204$	−6.92820	−0.485071
$205$	0	0
$206$	9.46410	0.659395
$207$	6.00000	0.417029
$208$	−1.26795	−0.0879165
$209$	−10.9282	−0.755920
$210$	0	0
$211$	20.5885	1.41737	0.708684	−	0.705526i	$-0.249289\pi$
$211$	20.5885	1.41737	0.708684	+	0.705526i	$0.249289\pi$
$212$	2.00000	0.137361
$213$	21.8564	1.49758
$214$	8.19615	0.560277
$215$	0	0
$216$	−4.00000	−0.272166
$217$	5.46410	0.370927
$218$	−8.92820	−0.604694
$219$	4.00000	0.270295
$220$	0	0
$221$	4.39230	0.295458
$222$	17.4641	1.17211
$223$	−24.2487	−1.62381	−0.811907	−	0.583787i	$-0.801570\pi$
$223$	−24.2487	−1.62381	−0.811907	+	0.583787i	$0.801570\pi$
$224$	1.00000	0.0668153
$225$	−5.00000	−0.333333
$226$	−11.4641	−0.762581
$227$	15.4641	1.02639	0.513194	−	0.858272i	$-0.328462\pi$
$227$	15.4641	1.02639	0.513194	+	0.858272i	$0.328462\pi$
$228$	14.9282	0.988644
$229$	−7.60770	−0.502731	−0.251365	−	0.967892i	$-0.580880\pi$
$229$	−7.60770	−0.502731	−0.251365	+	0.967892i	$0.580880\pi$
$230$	0	0
$231$	−2.92820	−0.192662
$232$	0.535898	0.0351835
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	−1.26795	−0.0828884
$235$	0	0
$236$	3.46410	0.225494
$237$	24.0000	1.55897
$238$	−3.46410	−0.224544
$239$	10.5359	0.681511	0.340755	−	0.940152i	$-0.389317\pi$
$239$	10.5359	0.681511	0.340755	+	0.940152i	$0.389317\pi$
$240$	0	0
$241$	−20.9282	−1.34810	−0.674052	−	0.738684i	$-0.735448\pi$
$241$	−20.9282	−1.34810	−0.674052	+	0.738684i	$0.735448\pi$
$242$	−8.85641	−0.569311
$243$	−10.0000	−0.641500
$244$	5.46410	0.349803
$245$	0	0
$246$	13.8564	0.883452
$247$	−9.46410	−0.602186
$248$	5.46410	0.346971
$249$	−23.3205	−1.47788
$250$	0	0
$251$	3.66025	0.231033	0.115517	−	0.993306i	$-0.463148\pi$
$251$	3.66025	0.231033	0.115517	+	0.993306i	$0.463148\pi$
$252$	1.00000	0.0629941
$253$	−8.78461	−0.552284
$254$	−6.92820	−0.434714
$255$	0	0
$256$	1.00000	0.0625000
$257$	7.46410	0.465598	0.232799	−	0.972525i	$-0.425212\pi$
$257$	7.46410	0.465598	0.232799	+	0.972525i	$0.425212\pi$
$258$	−11.3205	−0.704784
$259$	8.73205	0.542583
$260$	0	0
$261$	0.535898	0.0331713
$262$	4.73205	0.292347
$263$	19.8564	1.22440	0.612199	−	0.790704i	$-0.290285\pi$
$263$	19.8564	1.22440	0.612199	+	0.790704i	$0.290285\pi$
$264$	−2.92820	−0.180218
$265$	0	0
$266$	7.46410	0.457653
$267$	−4.00000	−0.244796
$268$	−2.73205	−0.166887
$269$	12.5885	0.767532	0.383766	−	0.923430i	$-0.374627\pi$
$269$	12.5885	0.767532	0.383766	+	0.923430i	$0.374627\pi$
$270$	0	0
$271$	−32.7846	−1.99152	−0.995762	−	0.0919719i	$-0.970683\pi$
$271$	−32.7846	−1.99152	−0.995762	+	0.0919719i	$0.970683\pi$
$272$	−3.46410	−0.210042
$273$	−2.53590	−0.153480
$274$	−10.3923	−0.627822
$275$	7.32051	0.441443
$276$	12.0000	0.722315
$277$	−30.3923	−1.82610	−0.913048	−	0.407851i	$-0.866278\pi$
$277$	−30.3923	−1.82610	−0.913048	+	0.407851i	$0.866278\pi$
$278$	−2.39230	−0.143481
$279$	5.46410	0.327127
$280$	0	0
$281$	−15.8564	−0.945914	−0.472957	−	0.881086i	$-0.656813\pi$
$281$	−15.8564	−0.945914	−0.472957	+	0.881086i	$0.656813\pi$
$282$	24.7846	1.47590
$283$	7.07180	0.420375	0.210187	−	0.977661i	$-0.432593\pi$
$283$	7.07180	0.420375	0.210187	+	0.977661i	$0.432593\pi$
$284$	10.9282	0.648470
$285$	0	0
$286$	1.85641	0.109772
$287$	6.92820	0.408959
$288$	1.00000	0.0589256
$289$	−5.00000	−0.294118
$290$	0	0
$291$	−16.0000	−0.937937
$292$	2.00000	0.117041
$293$	5.66025	0.330676	0.165338	−	0.986237i	$-0.447129\pi$
$293$	5.66025	0.330676	0.165338	+	0.986237i	$0.447129\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	8.73205	0.507540
$297$	5.85641	0.339823
$298$	7.85641	0.455109
$299$	−7.60770	−0.439964
$300$	−10.0000	−0.577350
$301$	−5.66025	−0.326252
$302$	8.92820	0.513760
$303$	−2.53590	−0.145684
$304$	7.46410	0.428096
$305$	0	0
$306$	−3.46410	−0.198030
$307$	0.535898	0.0305853	0.0152927	−	0.999883i	$-0.495132\pi$
$307$	0.535898	0.0305853	0.0152927	+	0.999883i	$0.495132\pi$
$308$	−1.46410	−0.0834249
$309$	18.9282	1.07679
$310$	0	0
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−2.53590	−0.143567
$313$	−7.46410	−0.421896	−0.210948	−	0.977497i	$-0.567655\pi$
$313$	−7.46410	−0.421896	−0.210948	+	0.977497i	$0.567655\pi$
$314$	−24.3923	−1.37654
$315$	0	0
$316$	12.0000	0.675053
$317$	−19.2679	−1.08220	−0.541098	−	0.840960i	$-0.681991\pi$
$317$	−19.2679	−1.08220	−0.541098	+	0.840960i	$0.681991\pi$
$318$	4.00000	0.224309
$319$	−0.784610	−0.0439297
$320$	0	0
$321$	16.3923	0.914929
$322$	6.00000	0.334367
$323$	−25.8564	−1.43869
$324$	−11.0000	−0.611111
$325$	6.33975	0.351666
$326$	13.4641	0.745708
$327$	−17.8564	−0.987462
$328$	6.92820	0.382546
$329$	12.3923	0.683210
$330$	0	0
$331$	−32.9808	−1.81279	−0.906393	−	0.422435i	$-0.861176\pi$
$331$	−32.9808	−1.81279	−0.906393	+	0.422435i	$0.861176\pi$
$332$	−11.6603	−0.639940
$333$	8.73205	0.478513
$334$	−19.3205	−1.05717
$335$	0	0
$336$	2.00000	0.109109
$337$	−4.39230	−0.239264	−0.119632	−	0.992818i	$-0.538171\pi$
$337$	−4.39230	−0.239264	−0.119632	+	0.992818i	$0.538171\pi$
$338$	−11.3923	−0.619660
$339$	−22.9282	−1.24529
$340$	0	0
$341$	−8.00000	−0.433224
$342$	7.46410	0.403612
$343$	1.00000	0.0539949
$344$	−5.66025	−0.305180
$345$	0	0
$346$	5.85641	0.314842
$347$	18.9282	1.01612	0.508060	−	0.861322i	$-0.330363\pi$
$347$	18.9282	1.01612	0.508060	+	0.861322i	$0.330363\pi$
$348$	1.07180	0.0574543
$349$	−6.33975	−0.339359	−0.169679	−	0.985499i	$-0.554273\pi$
$349$	−6.33975	−0.339359	−0.169679	+	0.985499i	$0.554273\pi$
$350$	−5.00000	−0.267261
$351$	5.07180	0.270712
$352$	−1.46410	−0.0780369
$353$	−30.9282	−1.64614	−0.823071	−	0.567938i	$-0.807741\pi$
$353$	−30.9282	−1.64614	−0.823071	+	0.567938i	$0.807741\pi$
$354$	6.92820	0.368230
$355$	0	0
$356$	−2.00000	−0.106000
$357$	−6.92820	−0.366679
$358$	−2.53590	−0.134026
$359$	−5.07180	−0.267679	−0.133840	−	0.991003i	$-0.542731\pi$
$359$	−5.07180	−0.267679	−0.133840	+	0.991003i	$0.542731\pi$
$360$	0	0
$361$	36.7128	1.93225
$362$	3.12436	0.164212
$363$	−17.7128	−0.929682
$364$	−1.26795	−0.0664586
$365$	0	0
$366$	10.9282	0.571226
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	6.00000	0.312772
$369$	6.92820	0.360668
$370$	0	0
$371$	2.00000	0.103835
$372$	10.9282	0.566601
$373$	−8.33975	−0.431816	−0.215908	−	0.976414i	$-0.569271\pi$
$373$	−8.33975	−0.431816	−0.215908	+	0.976414i	$0.569271\pi$
$374$	5.07180	0.262256
$375$	0	0
$376$	12.3923	0.639084
$377$	−0.679492	−0.0349956
$378$	−4.00000	−0.205738
$379$	16.7846	0.862167	0.431084	−	0.902312i	$-0.358131\pi$
$379$	16.7846	0.862167	0.431084	+	0.902312i	$0.358131\pi$
$380$	0	0
$381$	−13.8564	−0.709885
$382$	1.46410	0.0749100
$383$	−1.46410	−0.0748121	−0.0374060	−	0.999300i	$-0.511909\pi$
$383$	−1.46410	−0.0748121	−0.0374060	+	0.999300i	$0.511909\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−10.0000	−0.508987
$387$	−5.66025	−0.287727
$388$	−8.00000	−0.406138
$389$	16.2487	0.823842	0.411921	−	0.911219i	$-0.364858\pi$
$389$	16.2487	0.823842	0.411921	+	0.911219i	$0.364858\pi$
$390$	0	0
$391$	−20.7846	−1.05112
$392$	1.00000	0.0505076
$393$	9.46410	0.477401
$394$	−17.3205	−0.872595
$395$	0	0
$396$	−1.46410	−0.0735739
$397$	5.07180	0.254546	0.127273	−	0.991868i	$-0.459378\pi$
$397$	5.07180	0.254546	0.127273	+	0.991868i	$0.459378\pi$
$398$	2.53590	0.127113
$399$	14.9282	0.747345
$400$	−5.00000	−0.250000
$401$	3.07180	0.153398	0.0766991	−	0.997054i	$-0.475562\pi$
$401$	3.07180	0.153398	0.0766991	+	0.997054i	$0.475562\pi$
$402$	−5.46410	−0.272525
$403$	−6.92820	−0.345118
$404$	−1.26795	−0.0630828
$405$	0	0
$406$	0.535898	0.0265962
$407$	−12.7846	−0.633710
$408$	−6.92820	−0.342997
$409$	15.4641	0.764651	0.382325	−	0.924028i	$-0.375123\pi$
$409$	15.4641	0.764651	0.382325	+	0.924028i	$0.375123\pi$
$410$	0	0
$411$	−20.7846	−1.02523
$412$	9.46410	0.466263
$413$	3.46410	0.170457
$414$	6.00000	0.294884
$415$	0	0
$416$	−1.26795	−0.0621663
$417$	−4.78461	−0.234303
$418$	−10.9282	−0.534516
$419$	−2.19615	−0.107289	−0.0536445	−	0.998560i	$-0.517084\pi$
$419$	−2.19615	−0.107289	−0.0536445	+	0.998560i	$0.517084\pi$
$420$	0	0
$421$	−11.2679	−0.549166	−0.274583	−	0.961563i	$-0.588540\pi$
$421$	−11.2679	−0.549166	−0.274583	+	0.961563i	$0.588540\pi$
$422$	20.5885	1.00223
$423$	12.3923	0.602534
$424$	2.00000	0.0971286
$425$	17.3205	0.840168
$426$	21.8564	1.05895
$427$	5.46410	0.264426
$428$	8.19615	0.396176
$429$	3.71281	0.179256
$430$	0	0
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−4.00000	−0.192450
$433$	18.0000	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$434$	5.46410	0.262285
$435$	0	0
$436$	−8.92820	−0.427583
$437$	44.7846	2.14234
$438$	4.00000	0.191127
$439$	−24.0000	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	4.39230	0.208921
$443$	8.39230	0.398730	0.199365	−	0.979925i	$-0.436112\pi$
$443$	8.39230	0.398730	0.199365	+	0.979925i	$0.436112\pi$
$444$	17.4641	0.828810
$445$	0	0
$446$	−24.2487	−1.14821
$447$	15.7128	0.743191
$448$	1.00000	0.0472456
$449$	27.8564	1.31463	0.657313	−	0.753618i	$-0.271693\pi$
$449$	27.8564	1.31463	0.657313	+	0.753618i	$0.271693\pi$
$450$	−5.00000	−0.235702
$451$	−10.1436	−0.477643
$452$	−11.4641	−0.539226
$453$	17.8564	0.838967
$454$	15.4641	0.725766
$455$	0	0
$456$	14.9282	0.699077
$457$	32.9282	1.54032	0.770158	−	0.637853i	$-0.220177\pi$
$457$	32.9282	1.54032	0.770158	+	0.637853i	$0.220177\pi$
$458$	−7.60770	−0.355484
$459$	13.8564	0.646762
$460$	0	0
$461$	−0.392305	−0.0182715	−0.00913573	−	0.999958i	$-0.502908\pi$
$461$	−0.392305	−0.0182715	−0.00913573	+	0.999958i	$0.502908\pi$
$462$	−2.92820	−0.136232
$463$	−13.0718	−0.607498	−0.303749	−	0.952752i	$-0.598238\pi$
$463$	−13.0718	−0.607498	−0.303749	+	0.952752i	$0.598238\pi$
$464$	0.535898	0.0248785
$465$	0	0
$466$	−14.0000	−0.648537
$467$	11.0718	0.512342	0.256171	−	0.966632i	$-0.417539\pi$
$467$	11.0718	0.512342	0.256171	+	0.966632i	$0.417539\pi$
$468$	−1.26795	−0.0586110
$469$	−2.73205	−0.126154
$470$	0	0
$471$	−48.7846	−2.24788
$472$	3.46410	0.159448
$473$	8.28719	0.381045
$474$	24.0000	1.10236
$475$	−37.3205	−1.71238
$476$	−3.46410	−0.158777
$477$	2.00000	0.0915737
$478$	10.5359	0.481901
$479$	35.4641	1.62040	0.810198	−	0.586156i	$-0.199360\pi$
$479$	35.4641	1.62040	0.810198	+	0.586156i	$0.199360\pi$
$480$	0	0
$481$	−11.0718	−0.504830
$482$	−20.9282	−0.953254
$483$	12.0000	0.546019
$484$	−8.85641	−0.402564
$485$	0	0
$486$	−10.0000	−0.453609
$487$	10.9282	0.495204	0.247602	−	0.968862i	$-0.420357\pi$
$487$	10.9282	0.495204	0.247602	+	0.968862i	$0.420357\pi$
$488$	5.46410	0.247348
$489$	26.9282	1.21774
$490$	0	0
$491$	13.4641	0.607626	0.303813	−	0.952732i	$-0.401740\pi$
$491$	13.4641	0.607626	0.303813	+	0.952732i	$0.401740\pi$
$492$	13.8564	0.624695
$493$	−1.85641	−0.0836083
$494$	−9.46410	−0.425810
$495$	0	0
$496$	5.46410	0.245345
$497$	10.9282	0.490197
$498$	−23.3205	−1.04502
$499$	13.6603	0.611517	0.305758	−	0.952109i	$-0.401090\pi$
$499$	13.6603	0.611517	0.305758	+	0.952109i	$0.401090\pi$
$500$	0	0
$501$	−38.6410	−1.72635
$502$	3.66025	0.163365
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	−8.78461	−0.390524
$507$	−22.7846	−1.01190
$508$	−6.92820	−0.307389
$509$	13.2679	0.588092	0.294046	−	0.955791i	$-0.404998\pi$
$509$	13.2679	0.588092	0.294046	+	0.955791i	$0.404998\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	1.00000	0.0441942
$513$	−29.8564	−1.31819
$514$	7.46410	0.329227
$515$	0	0
$516$	−11.3205	−0.498358
$517$	−18.1436	−0.797954
$518$	8.73205	0.383664
$519$	11.7128	0.514135
$520$	0	0
$521$	34.9282	1.53023	0.765116	−	0.643892i	$-0.222682\pi$
$521$	34.9282	1.53023	0.765116	+	0.643892i	$0.222682\pi$
$522$	0.535898	0.0234556
$523$	−8.53590	−0.373249	−0.186624	−	0.982431i	$-0.559755\pi$
$523$	−8.53590	−0.373249	−0.186624	+	0.982431i	$0.559755\pi$
$524$	4.73205	0.206721
$525$	−10.0000	−0.436436
$526$	19.8564	0.865780
$527$	−18.9282	−0.824525
$528$	−2.92820	−0.127434
$529$	13.0000	0.565217
$530$	0	0
$531$	3.46410	0.150329
$532$	7.46410	0.323610
$533$	−8.78461	−0.380504
$534$	−4.00000	−0.173097
$535$	0	0
$536$	−2.73205	−0.118007
$537$	−5.07180	−0.218864
$538$	12.5885	0.542727
$539$	−1.46410	−0.0630633
$540$	0	0
$541$	−15.0718	−0.647987	−0.323994	−	0.946059i	$-0.605026\pi$
$541$	−15.0718	−0.647987	−0.323994	+	0.946059i	$0.605026\pi$
$542$	−32.7846	−1.40822
$543$	6.24871	0.268158
$544$	−3.46410	−0.148522
$545$	0	0
$546$	−2.53590	−0.108526
$547$	29.1769	1.24751	0.623757	−	0.781618i	$-0.285605\pi$
$547$	29.1769	1.24751	0.623757	+	0.781618i	$0.285605\pi$
$548$	−10.3923	−0.443937
$549$	5.46410	0.233202
$550$	7.32051	0.312148
$551$	4.00000	0.170406
$552$	12.0000	0.510754
$553$	12.0000	0.510292
$554$	−30.3923	−1.29125
$555$	0	0
$556$	−2.39230	−0.101456
$557$	−35.6603	−1.51097	−0.755487	−	0.655164i	$-0.772600\pi$
$557$	−35.6603	−1.51097	−0.755487	+	0.655164i	$0.772600\pi$
$558$	5.46410	0.231314
$559$	7.17691	0.303551
$560$	0	0
$561$	10.1436	0.428263
$562$	−15.8564	−0.668862
$563$	−19.8564	−0.836848	−0.418424	−	0.908252i	$-0.637417\pi$
$563$	−19.8564	−0.836848	−0.418424	+	0.908252i	$0.637417\pi$
$564$	24.7846	1.04362
$565$	0	0
$566$	7.07180	0.297250
$567$	−11.0000	−0.461957
$568$	10.9282	0.458537
$569$	−2.53590	−0.106310	−0.0531552	−	0.998586i	$-0.516928\pi$
$569$	−2.53590	−0.106310	−0.0531552	+	0.998586i	$0.516928\pi$
$570$	0	0
$571$	−12.9808	−0.543228	−0.271614	−	0.962406i	$-0.587557\pi$
$571$	−12.9808	−0.543228	−0.271614	+	0.962406i	$0.587557\pi$
$572$	1.85641	0.0776203
$573$	2.92820	0.122327
$574$	6.92820	0.289178
$575$	−30.0000	−1.25109
$576$	1.00000	0.0416667
$577$	20.2487	0.842965	0.421482	−	0.906837i	$-0.361510\pi$
$577$	20.2487	0.842965	0.421482	+	0.906837i	$0.361510\pi$
$578$	−5.00000	−0.207973
$579$	−20.0000	−0.831172
$580$	0	0
$581$	−11.6603	−0.483749
$582$	−16.0000	−0.663221
$583$	−2.92820	−0.121274
$584$	2.00000	0.0827606
$585$	0	0
$586$	5.66025	0.233823
$587$	24.7321	1.02080	0.510400	−	0.859937i	$-0.329497\pi$
$587$	24.7321	1.02080	0.510400	+	0.859937i	$0.329497\pi$
$588$	2.00000	0.0824786
$589$	40.7846	1.68050
$590$	0	0
$591$	−34.6410	−1.42494
$592$	8.73205	0.358885
$593$	−45.7128	−1.87720	−0.938600	−	0.345007i	$-0.887877\pi$
$593$	−45.7128	−1.87720	−0.938600	+	0.345007i	$0.887877\pi$
$594$	5.85641	0.240291
$595$	0	0
$596$	7.85641	0.321811
$597$	5.07180	0.207575
$598$	−7.60770	−0.311102
$599$	−18.5359	−0.757356	−0.378678	−	0.925528i	$-0.623621\pi$
$599$	−18.5359	−0.757356	−0.378678	+	0.925528i	$0.623621\pi$
$600$	−10.0000	−0.408248
$601$	15.4641	0.630794	0.315397	−	0.948960i	$-0.397862\pi$
$601$	15.4641	0.630794	0.315397	+	0.948960i	$0.397862\pi$
$602$	−5.66025	−0.230695
$603$	−2.73205	−0.111258
$604$	8.92820	0.363283
$605$	0	0
$606$	−2.53590	−0.103014
$607$	−9.60770	−0.389964	−0.194982	−	0.980807i	$-0.562465\pi$
$607$	−9.60770	−0.389964	−0.194982	+	0.980807i	$0.562465\pi$
$608$	7.46410	0.302709
$609$	1.07180	0.0434314
$610$	0	0
$611$	−15.7128	−0.635672
$612$	−3.46410	−0.140028
$613$	−36.5359	−1.47567	−0.737836	−	0.674981i	$-0.764152\pi$
$613$	−36.5359	−1.47567	−0.737836	+	0.674981i	$0.764152\pi$
$614$	0.535898	0.0216271
$615$	0	0
$616$	−1.46410	−0.0589903
$617$	−11.4641	−0.461527	−0.230764	−	0.973010i	$-0.574122\pi$
$617$	−11.4641	−0.461527	−0.230764	+	0.973010i	$0.574122\pi$
$618$	18.9282	0.761404
$619$	15.6603	0.629439	0.314719	−	0.949185i	$-0.398090\pi$
$619$	15.6603	0.629439	0.314719	+	0.949185i	$0.398090\pi$
$620$	0	0
$621$	−24.0000	−0.963087
$622$	4.00000	0.160385
$623$	−2.00000	−0.0801283
$624$	−2.53590	−0.101517
$625$	25.0000	1.00000
$626$	−7.46410	−0.298325
$627$	−21.8564	−0.872861
$628$	−24.3923	−0.973359
$629$	−30.2487	−1.20610
$630$	0	0
$631$	40.7846	1.62361	0.811805	−	0.583929i	$-0.198485\pi$
$631$	40.7846	1.62361	0.811805	+	0.583929i	$0.198485\pi$
$632$	12.0000	0.477334
$633$	41.1769	1.63664
$634$	−19.2679	−0.765228
$635$	0	0
$636$	4.00000	0.158610
$637$	−1.26795	−0.0502380
$638$	−0.784610	−0.0310630
$639$	10.9282	0.432313
$640$	0	0
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	16.3923	0.646953
$643$	−12.5359	−0.494368	−0.247184	−	0.968969i	$-0.579505\pi$
$643$	−12.5359	−0.494368	−0.247184	+	0.968969i	$0.579505\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	−25.8564	−1.01731
$647$	21.3205	0.838196	0.419098	−	0.907941i	$-0.362346\pi$
$647$	21.3205	0.838196	0.419098	+	0.907941i	$0.362346\pi$
$648$	−11.0000	−0.432121
$649$	−5.07180	−0.199085
$650$	6.33975	0.248665
$651$	10.9282	0.428310
$652$	13.4641	0.527295
$653$	−17.8038	−0.696718	−0.348359	−	0.937361i	$-0.613261\pi$
$653$	−17.8038	−0.696718	−0.348359	+	0.937361i	$0.613261\pi$
$654$	−17.8564	−0.698241
$655$	0	0
$656$	6.92820	0.270501
$657$	2.00000	0.0780274
$658$	12.3923	0.483102
$659$	17.4641	0.680305	0.340152	−	0.940370i	$-0.389521\pi$
$659$	17.4641	0.680305	0.340152	+	0.940370i	$0.389521\pi$
$660$	0	0
$661$	−24.3923	−0.948751	−0.474375	−	0.880323i	$-0.657326\pi$
$661$	−24.3923	−0.948751	−0.474375	+	0.880323i	$0.657326\pi$
$662$	−32.9808	−1.28183
$663$	8.78461	0.341166
$664$	−11.6603	−0.452506
$665$	0	0
$666$	8.73205	0.338360
$667$	3.21539	0.124500
$668$	−19.3205	−0.747533
$669$	−48.4974	−1.87502
$670$	0	0
$671$	−8.00000	−0.308837
$672$	2.00000	0.0771517
$673$	−20.1436	−0.776478	−0.388239	−	0.921559i	$-0.626917\pi$
$673$	−20.1436	−0.776478	−0.388239	+	0.921559i	$0.626917\pi$
$674$	−4.39230	−0.169185
$675$	20.0000	0.769800
$676$	−11.3923	−0.438166
$677$	−28.3923	−1.09120	−0.545602	−	0.838044i	$-0.683699\pi$
$677$	−28.3923	−1.09120	−0.545602	+	0.838044i	$0.683699\pi$
$678$	−22.9282	−0.880552
$679$	−8.00000	−0.307012
$680$	0	0
$681$	30.9282	1.18517
$682$	−8.00000	−0.306336
$683$	−23.5167	−0.899840	−0.449920	−	0.893069i	$-0.648548\pi$
$683$	−23.5167	−0.899840	−0.449920	+	0.893069i	$0.648548\pi$
$684$	7.46410	0.285397
$685$	0	0
$686$	1.00000	0.0381802
$687$	−15.2154	−0.580503
$688$	−5.66025	−0.215795
$689$	−2.53590	−0.0966100
$690$	0	0
$691$	−20.0526	−0.762835	−0.381418	−	0.924403i	$-0.624564\pi$
$691$	−20.0526	−0.762835	−0.381418	+	0.924403i	$0.624564\pi$
$692$	5.85641	0.222627
$693$	−1.46410	−0.0556166
$694$	18.9282	0.718505
$695$	0	0
$696$	1.07180	0.0406264
$697$	−24.0000	−0.909065
$698$	−6.33975	−0.239963
$699$	−28.0000	−1.05906
$700$	−5.00000	−0.188982
$701$	12.5359	0.473474	0.236737	−	0.971574i	$-0.423922\pi$
$701$	12.5359	0.473474	0.236737	+	0.971574i	$0.423922\pi$
$702$	5.07180	0.191423
$703$	65.1769	2.45819
$704$	−1.46410	−0.0551804
$705$	0	0
$706$	−30.9282	−1.16400
$707$	−1.26795	−0.0476861
$708$	6.92820	0.260378
$709$	15.1769	0.569981	0.284990	−	0.958530i	$-0.408010\pi$
$709$	15.1769	0.569981	0.284990	+	0.958530i	$0.408010\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	−2.00000	−0.0749532
$713$	32.7846	1.22779
$714$	−6.92820	−0.259281
$715$	0	0
$716$	−2.53590	−0.0947710
$717$	21.0718	0.786941
$718$	−5.07180	−0.189278
$719$	48.4974	1.80865	0.904324	−	0.426846i	$-0.140375\pi$
$719$	48.4974	1.80865	0.904324	+	0.426846i	$0.140375\pi$
$720$	0	0
$721$	9.46410	0.352462
$722$	36.7128	1.36631
$723$	−41.8564	−1.55666
$724$	3.12436	0.116116
$725$	−2.67949	−0.0995138
$726$	−17.7128	−0.657384
$727$	−41.4641	−1.53782	−0.768909	−	0.639358i	$-0.779200\pi$
$727$	−41.4641	−1.53782	−0.768909	+	0.639358i	$0.779200\pi$
$728$	−1.26795	−0.0469933
$729$	13.0000	0.481481
$730$	0	0
$731$	19.6077	0.725217
$732$	10.9282	0.403918
$733$	−16.7846	−0.619954	−0.309977	−	0.950744i	$-0.600321\pi$
$733$	−16.7846	−0.619954	−0.309977	+	0.950744i	$0.600321\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	6.00000	0.221163
$737$	4.00000	0.147342
$738$	6.92820	0.255031
$739$	−9.26795	−0.340927	−0.170464	−	0.985364i	$-0.554526\pi$
$739$	−9.26795	−0.340927	−0.170464	+	0.985364i	$0.554526\pi$
$740$	0	0
$741$	−18.9282	−0.695345
$742$	2.00000	0.0734223
$743$	23.7128	0.869939	0.434969	−	0.900445i	$-0.356759\pi$
$743$	23.7128	0.869939	0.434969	+	0.900445i	$0.356759\pi$
$744$	10.9282	0.400647
$745$	0	0
$746$	−8.33975	−0.305340
$747$	−11.6603	−0.426626
$748$	5.07180	0.185443
$749$	8.19615	0.299481
$750$	0	0
$751$	26.0000	0.948753	0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000	0.948753	0.474377	+	0.880322i	$0.342673\pi$
$752$	12.3923	0.451901
$753$	7.32051	0.266774
$754$	−0.679492	−0.0247456
$755$	0	0
$756$	−4.00000	−0.145479
$757$	52.6410	1.91327	0.956635	−	0.291289i	$-0.0940841\pi$
$757$	52.6410	1.91327	0.956635	+	0.291289i	$0.0940841\pi$
$758$	16.7846	0.609644
$759$	−17.5692	−0.637722
$760$	0	0
$761$	−28.7846	−1.04344	−0.521721	−	0.853116i	$-0.674710\pi$
$761$	−28.7846	−1.04344	−0.521721	+	0.853116i	$0.674710\pi$
$762$	−13.8564	−0.501965
$763$	−8.92820	−0.323223
$764$	1.46410	0.0529693
$765$	0	0
$766$	−1.46410	−0.0529001
$767$	−4.39230	−0.158597
$768$	2.00000	0.0721688
$769$	−22.7846	−0.821634	−0.410817	−	0.911718i	$-0.634756\pi$
$769$	−22.7846	−0.821634	−0.410817	+	0.911718i	$0.634756\pi$
$770$	0	0
$771$	14.9282	0.537626
$772$	−10.0000	−0.359908
$773$	−5.07180	−0.182420	−0.0912099	−	0.995832i	$-0.529073\pi$
$773$	−5.07180	−0.182420	−0.0912099	+	0.995832i	$0.529073\pi$
$774$	−5.66025	−0.203454
$775$	−27.3205	−0.981382
$776$	−8.00000	−0.287183
$777$	17.4641	0.626521
$778$	16.2487	0.582545
$779$	51.7128	1.85280
$780$	0	0
$781$	−16.0000	−0.572525
$782$	−20.7846	−0.743256
$783$	−2.14359	−0.0766058
$784$	1.00000	0.0357143
$785$	0	0
$786$	9.46410	0.337573
$787$	10.5885	0.377438	0.188719	−	0.982031i	$-0.439567\pi$
$787$	10.5885	0.377438	0.188719	+	0.982031i	$0.439567\pi$
$788$	−17.3205	−0.617018
$789$	39.7128	1.41381
$790$	0	0
$791$	−11.4641	−0.407617
$792$	−1.46410	−0.0520246
$793$	−6.92820	−0.246028
$794$	5.07180	0.179991
$795$	0	0
$796$	2.53590	0.0898825
$797$	−47.0333	−1.66601	−0.833003	−	0.553269i	$-0.813380\pi$
$797$	−47.0333	−1.66601	−0.833003	+	0.553269i	$0.813380\pi$
$798$	14.9282	0.528453
$799$	−42.9282	−1.51869
$800$	−5.00000	−0.176777
$801$	−2.00000	−0.0706665
$802$	3.07180	0.108469
$803$	−2.92820	−0.103334
$804$	−5.46410	−0.192704
$805$	0	0
$806$	−6.92820	−0.244036
$807$	25.1769	0.886269
$808$	−1.26795	−0.0446063
$809$	22.0000	0.773479	0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000	0.773479	0.386739	+	0.922189i	$0.373601\pi$
$810$	0	0
$811$	13.2154	0.464055	0.232028	−	0.972709i	$-0.425464\pi$
$811$	13.2154	0.464055	0.232028	+	0.972709i	$0.425464\pi$
$812$	0.535898	0.0188063
$813$	−65.5692	−2.29961
$814$	−12.7846	−0.448100
$815$	0	0
$816$	−6.92820	−0.242536
$817$	−42.2487	−1.47810
$818$	15.4641	0.540690
$819$	−1.26795	−0.0443057
$820$	0	0
$821$	43.7654	1.52742	0.763711	−	0.645558i	$-0.223375\pi$
$821$	43.7654	1.52742	0.763711	+	0.645558i	$0.223375\pi$
$822$	−20.7846	−0.724947
$823$	11.7128	0.408283	0.204141	−	0.978941i	$-0.434560\pi$
$823$	11.7128	0.408283	0.204141	+	0.978941i	$0.434560\pi$
$824$	9.46410	0.329698
$825$	14.6410	0.509735
$826$	3.46410	0.120532
$827$	22.6410	0.787305	0.393653	−	0.919259i	$-0.371211\pi$
$827$	22.6410	0.787305	0.393653	+	0.919259i	$0.371211\pi$
$828$	6.00000	0.208514
$829$	5.94744	0.206563	0.103282	−	0.994652i	$-0.467066\pi$
$829$	5.94744	0.206563	0.103282	+	0.994652i	$0.467066\pi$
$830$	0	0
$831$	−60.7846	−2.10859
$832$	−1.26795	−0.0439582
$833$	−3.46410	−0.120024
$834$	−4.78461	−0.165677
$835$	0	0
$836$	−10.9282	−0.377960
$837$	−21.8564	−0.755468
$838$	−2.19615	−0.0758648
$839$	−36.3923	−1.25640	−0.628201	−	0.778051i	$-0.716208\pi$
$839$	−36.3923	−1.25640	−0.628201	+	0.778051i	$0.716208\pi$
$840$	0	0
$841$	−28.7128	−0.990097
$842$	−11.2679	−0.388319
$843$	−31.7128	−1.09225
$844$	20.5885	0.708684
$845$	0	0
$846$	12.3923	0.426056
$847$	−8.85641	−0.304310
$848$	2.00000	0.0686803
$849$	14.1436	0.485407
$850$	17.3205	0.594089
$851$	52.3923	1.79599
$852$	21.8564	0.748788
$853$	40.5885	1.38972	0.694861	−	0.719144i	$-0.255466\pi$
$853$	40.5885	1.38972	0.694861	+	0.719144i	$0.255466\pi$
$854$	5.46410	0.186978
$855$	0	0
$856$	8.19615	0.280139
$857$	−26.1051	−0.891734	−0.445867	−	0.895099i	$-0.647105\pi$
$857$	−26.1051	−0.891734	−0.445867	+	0.895099i	$0.647105\pi$
$858$	3.71281	0.126753
$859$	−12.3397	−0.421027	−0.210513	−	0.977591i	$-0.567514\pi$
$859$	−12.3397	−0.421027	−0.210513	+	0.977591i	$0.567514\pi$
$860$	0	0
$861$	13.8564	0.472225
$862$	1.00000	0.0340601
$863$	−22.6410	−0.770709	−0.385355	−	0.922769i	$-0.625921\pi$
$863$	−22.6410	−0.770709	−0.385355	+	0.922769i	$0.625921\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	18.0000	0.611665
$867$	−10.0000	−0.339618
$868$	5.46410	0.185464
$869$	−17.5692	−0.595995
$870$	0	0
$871$	3.46410	0.117377
$872$	−8.92820	−0.302347
$873$	−8.00000	−0.270759
$874$	44.7846	1.51486
$875$	0	0
$876$	4.00000	0.135147
$877$	−21.3205	−0.719942	−0.359971	−	0.932963i	$-0.617213\pi$
$877$	−21.3205	−0.719942	−0.359971	+	0.932963i	$0.617213\pi$
$878$	−24.0000	−0.809961
$879$	11.3205	0.381831
$880$	0	0
$881$	−12.9282	−0.435562	−0.217781	−	0.975998i	$-0.569882\pi$
$881$	−12.9282	−0.435562	−0.217781	+	0.975998i	$0.569882\pi$
$882$	1.00000	0.0336718
$883$	12.8756	0.433300	0.216650	−	0.976249i	$-0.430487\pi$
$883$	12.8756	0.433300	0.216650	+	0.976249i	$0.430487\pi$
$884$	4.39230	0.147729
$885$	0	0
$886$	8.39230	0.281945
$887$	−31.7128	−1.06481	−0.532406	−	0.846489i	$-0.678712\pi$
$887$	−31.7128	−1.06481	−0.532406	+	0.846489i	$0.678712\pi$
$888$	17.4641	0.586057
$889$	−6.92820	−0.232364
$890$	0	0
$891$	16.1051	0.539542
$892$	−24.2487	−0.811907
$893$	92.4974	3.09531
$894$	15.7128	0.525515
$895$	0	0
$896$	1.00000	0.0334077
$897$	−15.2154	−0.508027
$898$	27.8564	0.929580
$899$	2.92820	0.0976610
$900$	−5.00000	−0.166667
$901$	−6.92820	−0.230812
$902$	−10.1436	−0.337745
$903$	−11.3205	−0.376723
$904$	−11.4641	−0.381290
$905$	0	0
$906$	17.8564	0.593239
$907$	−18.6410	−0.618965	−0.309482	−	0.950905i	$-0.600156\pi$
$907$	−18.6410	−0.618965	−0.309482	+	0.950905i	$0.600156\pi$
$908$	15.4641	0.513194
$909$	−1.26795	−0.0420552
$910$	0	0
$911$	58.9282	1.95238	0.976189	−	0.216921i	$-0.0696013\pi$
$911$	58.9282	1.95238	0.976189	+	0.216921i	$0.0696013\pi$
$912$	14.9282	0.494322
$913$	17.0718	0.564994
$914$	32.9282	1.08917
$915$	0	0
$916$	−7.60770	−0.251365
$917$	4.73205	0.156266
$918$	13.8564	0.457330
$919$	10.0000	0.329870	0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000	0.329870	0.164935	+	0.986304i	$0.447259\pi$
$920$	0	0
$921$	1.07180	0.0353169
$922$	−0.392305	−0.0129199
$923$	−13.8564	−0.456089
$924$	−2.92820	−0.0963308
$925$	−43.6603	−1.43554
$926$	−13.0718	−0.429566
$927$	9.46410	0.310842
$928$	0.535898	0.0175917
$929$	−19.8564	−0.651468	−0.325734	−	0.945462i	$-0.605611\pi$
$929$	−19.8564	−0.651468	−0.325734	+	0.945462i	$0.605611\pi$
$930$	0	0
$931$	7.46410	0.244626
$932$	−14.0000	−0.458585
$933$	8.00000	0.261908
$934$	11.0718	0.362280
$935$	0	0
$936$	−1.26795	−0.0414442
$937$	−1.07180	−0.0350141	−0.0175070	−	0.999847i	$-0.505573\pi$
$937$	−1.07180	−0.0350141	−0.0175070	+	0.999847i	$0.505573\pi$
$938$	−2.73205	−0.0892046
$939$	−14.9282	−0.487164
$940$	0	0
$941$	11.4115	0.372006	0.186003	−	0.982549i	$-0.440447\pi$
$941$	11.4115	0.372006	0.186003	+	0.982549i	$0.440447\pi$
$942$	−48.7846	−1.58949
$943$	41.5692	1.35368
$944$	3.46410	0.112747
$945$	0	0
$946$	8.28719	0.269440
$947$	18.4449	0.599378	0.299689	−	0.954037i	$-0.403117\pi$
$947$	18.4449	0.599378	0.299689	+	0.954037i	$0.403117\pi$
$948$	24.0000	0.779484
$949$	−2.53590	−0.0823187
$950$	−37.3205	−1.21084
$951$	−38.5359	−1.24961
$952$	−3.46410	−0.112272
$953$	52.1051	1.68785	0.843925	−	0.536461i	$-0.180239\pi$
$953$	52.1051	1.68785	0.843925	+	0.536461i	$0.180239\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	10.5359	0.340755
$957$	−1.56922	−0.0507257
$958$	35.4641	1.14579
$959$	−10.3923	−0.335585
$960$	0	0
$961$	−1.14359	−0.0368901
$962$	−11.0718	−0.356969
$963$	8.19615	0.264117
$964$	−20.9282	−0.674052
$965$	0	0
$966$	12.0000	0.386094
$967$	−33.1769	−1.06690	−0.533449	−	0.845832i	$-0.679104\pi$
$967$	−33.1769	−1.06690	−0.533449	+	0.845832i	$0.679104\pi$
$968$	−8.85641	−0.284656
$969$	−51.7128	−1.66125
$970$	0	0
$971$	−34.1051	−1.09449	−0.547243	−	0.836974i	$-0.684323\pi$
$971$	−34.1051	−1.09449	−0.547243	+	0.836974i	$0.684323\pi$
$972$	−10.0000	−0.320750
$973$	−2.39230	−0.0766938
$974$	10.9282	0.350162
$975$	12.6795	0.406069
$976$	5.46410	0.174902
$977$	−16.3923	−0.524436	−0.262218	−	0.965009i	$-0.584454\pi$
$977$	−16.3923	−0.524436	−0.262218	+	0.965009i	$0.584454\pi$
$978$	26.9282	0.861069
$979$	2.92820	0.0935858
$980$	0	0
$981$	−8.92820	−0.285056
$982$	13.4641	0.429657
$983$	38.9282	1.24162	0.620808	−	0.783962i	$-0.286804\pi$
$983$	38.9282	1.24162	0.620808	+	0.783962i	$0.286804\pi$
$984$	13.8564	0.441726
$985$	0	0
$986$	−1.85641	−0.0591200
$987$	24.7846	0.788903
$988$	−9.46410	−0.301093
$989$	−33.9615	−1.07991
$990$	0	0
$991$	44.7846	1.42263	0.711315	−	0.702873i	$-0.248100\pi$
$991$	44.7846	1.42263	0.711315	+	0.702873i	$0.248100\pi$
$992$	5.46410	0.173485
$993$	−65.9615	−2.09323
$994$	10.9282	0.346622
$995$	0	0
$996$	−23.3205	−0.738939
$997$	15.7128	0.497630	0.248815	−	0.968551i	$-0.419959\pi$
$997$	15.7128	0.497630	0.248815	+	0.968551i	$0.419959\pi$
$998$	13.6603	0.432408
$999$	−34.9282	−1.10508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.i.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.i.1.1	✓	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.46410 q^{11} +2.00000 q^{12} -1.26795 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.46410 q^{17} +1.00000 q^{18} +7.46410 q^{19} +2.00000 q^{21} -1.46410 q^{22} +6.00000 q^{23} +2.00000 q^{24} -5.00000 q^{25} -1.26795 q^{26} -4.00000 q^{27} +1.00000 q^{28} +0.535898 q^{29} +5.46410 q^{31} +1.00000 q^{32} -2.92820 q^{33} -3.46410 q^{34} +1.00000 q^{36} +8.73205 q^{37} +7.46410 q^{38} -2.53590 q^{39} +6.92820 q^{41} +2.00000 q^{42} -5.66025 q^{43} -1.46410 q^{44} +6.00000 q^{46} +12.3923 q^{47} +2.00000 q^{48} +1.00000 q^{49} -5.00000 q^{50} -6.92820 q^{51} -1.26795 q^{52} +2.00000 q^{53} -4.00000 q^{54} +1.00000 q^{56} +14.9282 q^{57} +0.535898 q^{58} +3.46410 q^{59} +5.46410 q^{61} +5.46410 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.92820 q^{66} -2.73205 q^{67} -3.46410 q^{68} +12.0000 q^{69} +10.9282 q^{71} +1.00000 q^{72} +2.00000 q^{73} +8.73205 q^{74} -10.0000 q^{75} +7.46410 q^{76} -1.46410 q^{77} -2.53590 q^{78} +12.0000 q^{79} -11.0000 q^{81} +6.92820 q^{82} -11.6603 q^{83} +2.00000 q^{84} -5.66025 q^{86} +1.07180 q^{87} -1.46410 q^{88} -2.00000 q^{89} -1.26795 q^{91} +6.00000 q^{92} +10.9282 q^{93} +12.3923 q^{94} +2.00000 q^{96} -8.00000 q^{97} +1.00000 q^{98} -1.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 4 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} + 2 q^{16} + 2 q^{18} + 8 q^{19} + 4 q^{21} + 4 q^{22} + 12 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 2 q^{28} + 8 q^{29} + 4 q^{31} + 2 q^{32} + 8 q^{33} + 2 q^{36} + 14 q^{37} + 8 q^{38} - 12 q^{39} + 4 q^{42} + 6 q^{43} + 4 q^{44} + 12 q^{46} + 4 q^{47} + 4 q^{48} + 2 q^{49} - 10 q^{50} - 6 q^{52} + 4 q^{53} - 8 q^{54} + 2 q^{56} + 16 q^{57} + 8 q^{58} + 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 8 q^{66} - 2 q^{67} + 24 q^{69} + 8 q^{71} + 2 q^{72} + 4 q^{73} + 14 q^{74} - 20 q^{75} + 8 q^{76} + 4 q^{77} - 12 q^{78} + 24 q^{79} - 22 q^{81} - 6 q^{83} + 4 q^{84} + 6 q^{86} + 16 q^{87} + 4 q^{88} - 4 q^{89} - 6 q^{91} + 12 q^{92} + 8 q^{93} + 4 q^{94} + 4 q^{96} - 16 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 4 * q^11 + 4 * q^12 - 6 * q^13 + 2 * q^14 + 2 * q^16 + 2 * q^18 + 8 * q^19 + 4 * q^21 + 4 * q^22 + 12 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 2 * q^28 + 8 * q^29 + 4 * q^31 + 2 * q^32 + 8 * q^33 + 2 * q^36 + 14 * q^37 + 8 * q^38 - 12 * q^39 + 4 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^46 + 4 * q^47 + 4 * q^48 + 2 * q^49 - 10 * q^50 - 6 * q^52 + 4 * q^53 - 8 * q^54 + 2 * q^56 + 16 * q^57 + 8 * q^58 + 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 8 * q^66 - 2 * q^67 + 24 * q^69 + 8 * q^71 + 2 * q^72 + 4 * q^73 + 14 * q^74 - 20 * q^75 + 8 * q^76 + 4 * q^77 - 12 * q^78 + 24 * q^79 - 22 * q^81 - 6 * q^83 + 4 * q^84 + 6 * q^86 + 16 * q^87 + 4 * q^88 - 4 * q^89 - 6 * q^91 + 12 * q^92 + 8 * q^93 + 4 * q^94 + 4 * q^96 - 16 * q^97 + 2 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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