LMFDB - Embedded newform 637.2.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, 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("637.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.4507648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.146243$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83237 q^{2} +0.853757 q^{3} +1.35758 q^{4} +2.62555 q^{5} +1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} +O(q^{10})$	\(q+1.83237 q^{2} +0.853757 q^{3} +1.35758 q^{4} +2.62555 q^{5} +1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} +4.81098 q^{10} +3.26469 q^{11} +1.15904 q^{12} +1.00000 q^{13} +2.24158 q^{15} -4.87214 q^{16} +4.53021 q^{17} -4.16149 q^{18} +4.06615 q^{19} +3.56440 q^{20} +5.98212 q^{22} -4.53266 q^{23} -1.00500 q^{24} +1.89352 q^{25} +1.83237 q^{26} -4.50024 q^{27} -1.42268 q^{29} +4.10741 q^{30} -2.80328 q^{31} -6.57326 q^{32} +2.78725 q^{33} +8.30102 q^{34} -3.08320 q^{36} -10.0503 q^{37} +7.45070 q^{38} +0.853757 q^{39} -3.09067 q^{40} -2.84271 q^{41} +9.72632 q^{43} +4.43208 q^{44} -5.96289 q^{45} -8.30551 q^{46} -9.44956 q^{47} -4.15962 q^{48} +3.46963 q^{50} +3.86770 q^{51} +1.35758 q^{52} +5.26439 q^{53} -8.24610 q^{54} +8.57161 q^{55} +3.47151 q^{57} -2.60687 q^{58} -2.56791 q^{59} +3.04313 q^{60} -11.1830 q^{61} -5.13664 q^{62} -2.30037 q^{64} +2.62555 q^{65} +5.10728 q^{66} -1.98172 q^{67} +6.15013 q^{68} -3.86979 q^{69} -11.7544 q^{71} +2.67342 q^{72} +12.1391 q^{73} -18.4159 q^{74} +1.61661 q^{75} +5.52013 q^{76} +1.56440 q^{78} +11.9089 q^{79} -12.7920 q^{80} +2.97118 q^{81} -5.20889 q^{82} +13.2233 q^{83} +11.8943 q^{85} +17.8222 q^{86} -1.21462 q^{87} -3.84303 q^{88} +10.6666 q^{89} -10.9262 q^{90} -6.15345 q^{92} -2.39332 q^{93} -17.3151 q^{94} +10.6759 q^{95} -5.61197 q^{96} -13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) $ 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9	$ 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 + 6 * q^13 + 12 * q^15 + 16 * q^17 - 4 * q^18 + 2 * q^19 + 16 * q^20 - 12 * q^22 - 6 * q^23 + 12 * q^24 - 4 * q^25 + 20 * q^27 - 6 * q^29 + 6 * q^31 - 20 * q^32 + 4 * q^33 - 24 * q^36 + 8 * q^38 + 8 * q^39 + 4 * q^40 - 8 * q^41 + 2 * q^43 - 4 * q^44 + 14 * q^45 + 8 * q^46 + 30 * q^47 - 8 * q^48 + 8 * q^50 - 4 * q^51 + 4 * q^52 - 14 * q^53 - 48 * q^54 - 8 * q^55 + 4 * q^57 - 8 * q^58 + 24 * q^59 + 12 * q^60 + 28 * q^62 - 20 * q^64 + 6 * q^65 - 4 * q^66 + 16 * q^67 + 28 * q^68 - 20 * q^69 + 8 * q^71 + 28 * q^72 - 6 * q^73 - 12 * q^74 + 12 * q^75 - 16 * q^76 + 4 * q^78 - 22 * q^79 - 28 * q^80 + 46 * q^81 - 40 * q^82 + 50 * q^83 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 44 * q^88 + 26 * q^89 - 40 * q^90 + 20 * q^92 + 16 * q^93 - 32 * q^94 - 6 * q^95 - 20 * q^96 - 14 * q^97 + 12 * 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 $

$2$	1.83237	1.29568	0.647841	−	0.761776i	$-0.275672\pi$
$2$	1.83237	1.29568	0.647841	+	0.761776i	$0.275672\pi$
$3$	0.853757	0.492917	0.246458	−	0.969153i	$-0.420733\pi$
$3$	0.853757	0.492917	0.246458	+	0.969153i	$0.420733\pi$
$4$	1.35758	0.678791
$5$	2.62555	1.17418	0.587091	−	0.809521i	$-0.300273\pi$
$5$	2.62555	1.17418	0.587091	+	0.809521i	$0.300273\pi$
$6$	1.56440	0.638663
$7$	0	0
$7$	0	0
$8$	−1.17715	−0.416185
$9$	−2.27110	−0.757033
$10$	4.81098	1.52137
$11$	3.26469	0.984341	0.492170	−	0.870499i	$-0.336204\pi$
$11$	3.26469	0.984341	0.492170	+	0.870499i	$0.336204\pi$
$12$	1.15904	0.334587
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	2.24158	0.578775
$16$	−4.87214	−1.21803
$17$	4.53021	1.09874	0.549369	−	0.835580i	$-0.314868\pi$
$17$	4.53021	1.09874	0.549369	+	0.835580i	$0.314868\pi$
$18$	−4.16149	−0.980873
$19$	4.06615	0.932839	0.466420	−	0.884564i	$-0.345544\pi$
$19$	4.06615	0.932839	0.466420	+	0.884564i	$0.345544\pi$
$20$	3.56440	0.797024
$21$	0	0
$22$	5.98212	1.27539
$23$	−4.53266	−0.945125	−0.472562	−	0.881297i	$-0.656671\pi$
$23$	−4.53266	−0.945125	−0.472562	+	0.881297i	$0.656671\pi$
$24$	−1.00500	−0.205145
$25$	1.89352	0.378705
$26$	1.83237	0.359357
$27$	−4.50024	−0.866071
$28$	0	0
$29$	−1.42268	−0.264184	−0.132092	−	0.991237i	$-0.542169\pi$
$29$	−1.42268	−0.264184	−0.132092	+	0.991237i	$0.542169\pi$
$30$	4.10741	0.749907
$31$	−2.80328	−0.503484	−0.251742	−	0.967794i	$-0.581003\pi$
$31$	−2.80328	−0.503484	−0.251742	+	0.967794i	$0.581003\pi$
$32$	−6.57326	−1.16200
$33$	2.78725	0.485198
$34$	8.30102	1.42361
$35$	0	0
$36$	−3.08320	−0.513867
$37$	−10.0503	−1.65227	−0.826133	−	0.563475i	$-0.809464\pi$
$37$	−10.0503	−1.65227	−0.826133	+	0.563475i	$0.809464\pi$
$38$	7.45070	1.20866
$39$	0.853757	0.136711
$40$	−3.09067	−0.488677
$41$	−2.84271	−0.443956	−0.221978	−	0.975052i	$-0.571251\pi$
$41$	−2.84271	−0.443956	−0.221978	+	0.975052i	$0.571251\pi$
$42$	0	0
$43$	9.72632	1.48325	0.741625	−	0.670815i	$-0.234056\pi$
$43$	9.72632	1.48325	0.741625	+	0.670815i	$0.234056\pi$
$44$	4.43208	0.668161
$45$	−5.96289	−0.888895
$46$	−8.30551	−1.22458
$47$	−9.44956	−1.37836	−0.689180	−	0.724590i	$-0.742029\pi$
$47$	−9.44956	−1.37836	−0.689180	+	0.724590i	$0.742029\pi$
$48$	−4.15962	−0.600390
$49$	0	0
$50$	3.46963	0.490680
$51$	3.86770	0.541586
$52$	1.35758	0.188263
$53$	5.26439	0.723119	0.361559	−	0.932349i	$-0.382244\pi$
$53$	5.26439	0.723119	0.361559	+	0.932349i	$0.382244\pi$
$54$	−8.24610	−1.12215
$55$	8.57161	1.15580
$56$	0	0
$57$	3.47151	0.459812
$58$	−2.60687	−0.342299
$59$	−2.56791	−0.334313	−0.167156	−	0.985930i	$-0.553458\pi$
$59$	−2.56791	−0.334313	−0.167156	+	0.985930i	$0.553458\pi$
$60$	3.04313	0.392867
$61$	−11.1830	−1.43183	−0.715917	−	0.698185i	$-0.753991\pi$
$61$	−11.1830	−1.43183	−0.715917	+	0.698185i	$0.753991\pi$
$62$	−5.13664	−0.652354
$63$	0	0
$64$	−2.30037	−0.287546
$65$	2.62555	0.325660
$66$	5.10728	0.628662
$67$	−1.98172	−0.242106	−0.121053	−	0.992646i	$-0.538627\pi$
$67$	−1.98172	−0.242106	−0.121053	+	0.992646i	$0.538627\pi$
$68$	6.15013	0.745813
$69$	−3.86979	−0.465868
$70$	0	0
$71$	−11.7544	−1.39499	−0.697495	−	0.716590i	$-0.745702\pi$
$71$	−11.7544	−1.39499	−0.697495	+	0.716590i	$0.745702\pi$
$72$	2.67342	0.315066
$73$	12.1391	1.42078	0.710388	−	0.703810i	$-0.248519\pi$
$73$	12.1391	1.42078	0.710388	+	0.703810i	$0.248519\pi$
$74$	−18.4159	−2.14081
$75$	1.61661	0.186670
$76$	5.52013	0.633202
$77$	0	0
$78$	1.56440	0.177133
$79$	11.9089	1.33986	0.669928	−	0.742426i	$-0.266325\pi$
$79$	11.9089	1.33986	0.669928	+	0.742426i	$0.266325\pi$
$80$	−12.7920	−1.43019
$81$	2.97118	0.330132
$82$	−5.20889	−0.575226
$83$	13.2233	1.45145	0.725723	−	0.687987i	$-0.241505\pi$
$83$	13.2233	1.45145	0.725723	+	0.687987i	$0.241505\pi$
$84$	0	0
$85$	11.8943	1.29012
$86$	17.8222	1.92182
$87$	−1.21462	−0.130221
$88$	−3.84303	−0.409668
$89$	10.6666	1.13065	0.565326	−	0.824867i	$-0.308750\pi$
$89$	10.6666	1.13065	0.565326	+	0.824867i	$0.308750\pi$
$90$	−10.9262	−1.15172
$91$	0	0
$92$	−6.15345	−0.641542
$93$	−2.39332	−0.248176
$94$	−17.3151	−1.78592
$95$	10.6759	1.09532
$96$	−5.61197	−0.572769
$97$	−13.7422	−1.39531	−0.697655	−	0.716433i	$-0.745773\pi$
$97$	−13.7422	−1.39531	−0.697655	+	0.716433i	$0.745773\pi$
$98$	0	0
$99$	−7.41443	−0.745178
$100$	2.57061	0.257061
$101$	5.89458	0.586533	0.293266	−	0.956031i	$-0.405258\pi$
$101$	5.89458	0.586533	0.293266	+	0.956031i	$0.405258\pi$
$102$	7.08706	0.701723
$103$	2.78737	0.274647	0.137324	−	0.990526i	$-0.456150\pi$
$103$	2.78737	0.274647	0.137324	+	0.990526i	$0.456150\pi$
$104$	−1.17715	−0.115429
$105$	0	0
$106$	9.64630	0.936932
$107$	−17.6647	−1.70771	−0.853856	−	0.520509i	$-0.825742\pi$
$107$	−17.6647	−1.70771	−0.853856	+	0.520509i	$0.825742\pi$
$108$	−6.10944	−0.587881
$109$	−9.56450	−0.916113	−0.458057	−	0.888923i	$-0.651454\pi$
$109$	−9.56450	−0.916113	−0.458057	+	0.888923i	$0.651454\pi$
$110$	15.7064	1.49754
$111$	−8.58055	−0.814430
$112$	0	0
$113$	−17.6017	−1.65583	−0.827916	−	0.560852i	$-0.810474\pi$
$113$	−17.6017	−1.65583	−0.827916	+	0.560852i	$0.810474\pi$
$114$	6.36109	0.595770
$115$	−11.9007	−1.10975
$116$	−1.93140	−0.179326
$117$	−2.27110	−0.209963
$118$	−4.70535	−0.433163
$119$	0	0
$120$	−2.63868	−0.240877
$121$	−0.341808	−0.0310735
$122$	−20.4914	−1.85520
$123$	−2.42698	−0.218833
$124$	−3.80568	−0.341760
$125$	−8.15622	−0.729514
$126$	0	0
$127$	−1.59482	−0.141517	−0.0707586	−	0.997493i	$-0.522542\pi$
$127$	−1.59482	−0.141517	−0.0707586	+	0.997493i	$0.522542\pi$
$128$	8.93138	0.789430
$129$	8.30391	0.731119
$130$	4.81098	0.421951
$131$	4.30279	0.375937	0.187968	−	0.982175i	$-0.439810\pi$
$131$	4.30279	0.375937	0.187968	+	0.982175i	$0.439810\pi$
$132$	3.78392	0.329348
$133$	0	0
$134$	−3.63125	−0.313692
$135$	−11.8156	−1.01693
$136$	−5.33273	−0.457278
$137$	9.82234	0.839179	0.419590	−	0.907714i	$-0.362174\pi$
$137$	9.82234	0.839179	0.419590	+	0.907714i	$0.362174\pi$
$138$	−7.09089	−0.603617
$139$	10.0811	0.855070	0.427535	−	0.903999i	$-0.359382\pi$
$139$	10.0811	0.855070	0.427535	+	0.903999i	$0.359382\pi$
$140$	0	0
$141$	−8.06763	−0.679417
$142$	−21.5384	−1.80746
$143$	3.26469	0.273007
$144$	11.0651	0.922092
$145$	−3.73531	−0.310201
$146$	22.2434	1.84087
$147$	0	0
$148$	−13.6442	−1.12154
$149$	−13.8124	−1.13155	−0.565777	−	0.824558i	$-0.691424\pi$
$149$	−13.8124	−1.13155	−0.565777	+	0.824558i	$0.691424\pi$
$150$	2.96223	0.241865
$151$	21.2123	1.72623	0.863117	−	0.505004i	$-0.168509\pi$
$151$	21.2123	1.72623	0.863117	+	0.505004i	$0.168509\pi$
$152$	−4.78647	−0.388234
$153$	−10.2886	−0.831780
$154$	0	0
$155$	−7.36015	−0.591182
$156$	1.15904	0.0927978
$157$	23.5155	1.87674	0.938372	−	0.345627i	$-0.112334\pi$
$157$	23.5155	1.87674	0.938372	+	0.345627i	$0.112334\pi$
$158$	21.8215	1.73603
$159$	4.49451	0.356438
$160$	−17.2584	−1.36440
$161$	0	0
$162$	5.44431	0.427745
$163$	7.83062	0.613341	0.306671	−	0.951816i	$-0.400785\pi$
$163$	7.83062	0.613341	0.306671	+	0.951816i	$0.400785\pi$
$164$	−3.85920	−0.301353
$165$	7.31807	0.569711
$166$	24.2300	1.88061
$167$	12.7116	0.983654	0.491827	−	0.870693i	$-0.336329\pi$
$167$	12.7116	0.983654	0.491827	+	0.870693i	$0.336329\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	21.7948	1.67158
$171$	−9.23463	−0.706190
$172$	13.2043	1.00682
$173$	5.24907	0.399079	0.199540	−	0.979890i	$-0.436055\pi$
$173$	5.24907	0.399079	0.199540	+	0.979890i	$0.436055\pi$
$174$	−2.22563	−0.168725
$175$	0	0
$176$	−15.9060	−1.19896
$177$	−2.19237	−0.164788
$178$	19.5451	1.46497
$179$	−10.5255	−0.786714	−0.393357	−	0.919386i	$-0.628686\pi$
$179$	−10.5255	−0.786714	−0.393357	+	0.919386i	$0.628686\pi$
$180$	−8.09510	−0.603373
$181$	−18.8177	−1.39871	−0.699356	−	0.714774i	$-0.746530\pi$
$181$	−18.8177	−1.39871	−0.699356	+	0.714774i	$0.746530\pi$
$182$	0	0
$183$	−9.54755	−0.705775
$184$	5.33562	0.393347
$185$	−26.3877	−1.94006
$186$	−4.38545	−0.321557
$187$	14.7897	1.08153
$188$	−12.8285	−0.935618
$189$	0	0
$190$	19.5622	1.41919
$191$	14.9144	1.07917	0.539585	−	0.841931i	$-0.318581\pi$
$191$	14.9144	1.07917	0.539585	+	0.841931i	$0.318581\pi$
$192$	−1.96396	−0.141737
$193$	−0.0531356	−0.00382479	−0.00191239	−	0.999998i	$-0.500609\pi$
$193$	−0.0531356	−0.00382479	−0.00191239	+	0.999998i	$0.500609\pi$
$194$	−25.1808	−1.80788
$195$	2.24158	0.160523
$196$	0	0
$197$	10.0478	0.715875	0.357938	−	0.933745i	$-0.383480\pi$
$197$	10.0478	0.715875	0.357938	+	0.933745i	$0.383480\pi$
$198$	−13.5860	−0.965514
$199$	23.2914	1.65109	0.825543	−	0.564340i	$-0.190869\pi$
$199$	23.2914	1.65109	0.825543	+	0.564340i	$0.190869\pi$
$200$	−2.22896	−0.157611
$201$	−1.69191	−0.119338
$202$	10.8011	0.759959
$203$	0	0
$204$	5.25072	0.367624
$205$	−7.46367	−0.521285
$206$	5.10749	0.355855
$207$	10.2941	0.715491
$208$	−4.87214	−0.337822
$209$	13.2747	0.918232
$210$	0	0
$211$	−2.47457	−0.170356	−0.0851780	−	0.996366i	$-0.527146\pi$
$211$	−2.47457	−0.170356	−0.0851780	+	0.996366i	$0.527146\pi$
$212$	7.14683	0.490846
$213$	−10.0354	−0.687614
$214$	−32.3683	−2.21265
$215$	25.5369	1.74161
$216$	5.29745	0.360446
$217$	0	0
$218$	−17.5257	−1.18699
$219$	10.3639	0.700325
$220$	11.6367	0.784543
$221$	4.53021	0.304735
$222$	−15.7227	−1.05524
$223$	6.17027	0.413192	0.206596	−	0.978426i	$-0.433761\pi$
$223$	6.17027	0.413192	0.206596	+	0.978426i	$0.433761\pi$
$224$	0	0
$225$	−4.30038	−0.286692
$226$	−32.2529	−2.14543
$227$	11.5939	0.769513	0.384757	−	0.923018i	$-0.374285\pi$
$227$	11.5939	0.769513	0.384757	+	0.923018i	$0.374285\pi$
$228$	4.71285	0.312116
$229$	−10.2382	−0.676558	−0.338279	−	0.941046i	$-0.609845\pi$
$229$	−10.2382	−0.676558	−0.338279	+	0.941046i	$0.609845\pi$
$230$	−21.8065	−1.43788
$231$	0	0
$232$	1.67470	0.109950
$233$	21.4822	1.40735	0.703673	−	0.710524i	$-0.251542\pi$
$233$	21.4822	1.40735	0.703673	+	0.710524i	$0.251542\pi$
$234$	−4.16149	−0.272045
$235$	−24.8103	−1.61845
$236$	−3.48614	−0.226928
$237$	10.1673	0.660437
$238$	0	0
$239$	1.08591	0.0702414	0.0351207	−	0.999383i	$-0.488818\pi$
$239$	1.08591	0.0702414	0.0351207	+	0.999383i	$0.488818\pi$
$240$	−10.9213	−0.704967
$241$	−19.9830	−1.28722	−0.643608	−	0.765355i	$-0.722563\pi$
$241$	−19.9830	−1.28722	−0.643608	+	0.765355i	$0.722563\pi$
$242$	−0.626319	−0.0402613
$243$	16.0374	1.02880
$244$	−15.1818	−0.971915
$245$	0	0
$246$	−4.44713	−0.283538
$247$	4.06615	0.258723
$248$	3.29988	0.209542
$249$	11.2895	0.715443
$250$	−14.9452	−0.945218
$251$	20.1497	1.27184	0.635920	−	0.771755i	$-0.280621\pi$
$251$	20.1497	1.27184	0.635920	+	0.771755i	$0.280621\pi$
$252$	0	0
$253$	−14.7977	−0.930325
$254$	−2.92230	−0.183361
$255$	10.1548	0.635921
$256$	20.9663	1.31040
$257$	−15.0174	−0.936759	−0.468379	−	0.883527i	$-0.655162\pi$
$257$	−15.0174	−0.936759	−0.468379	+	0.883527i	$0.655162\pi$
$258$	15.2158	0.947297
$259$	0	0
$260$	3.56440	0.221055
$261$	3.23104	0.199996
$262$	7.88431	0.487094
$263$	−21.1662	−1.30516	−0.652582	−	0.757718i	$-0.726314\pi$
$263$	−21.1662	−1.30516	−0.652582	+	0.757718i	$0.726314\pi$
$264$	−3.28101	−0.201932
$265$	13.8219	0.849074
$266$	0	0
$267$	9.10665	0.557318
$268$	−2.69035	−0.164339
$269$	−4.10480	−0.250274	−0.125137	−	0.992139i	$-0.539937\pi$
$269$	−4.10480	−0.250274	−0.125137	+	0.992139i	$0.539937\pi$
$270$	−21.6506	−1.31761
$271$	3.43244	0.208506	0.104253	−	0.994551i	$-0.466755\pi$
$271$	3.43244	0.208506	0.104253	+	0.994551i	$0.466755\pi$
$272$	−22.0718	−1.33830
$273$	0	0
$274$	17.9982	1.08731
$275$	6.18176	0.372774
$276$	−5.25355	−0.316227
$277$	−0.361012	−0.0216911	−0.0108455	−	0.999941i	$-0.503452\pi$
$277$	−0.361012	−0.0216911	−0.0108455	+	0.999941i	$0.503452\pi$
$278$	18.4724	1.10790
$279$	6.36652	0.381154
$280$	0	0
$281$	18.5213	1.10489	0.552445	−	0.833550i	$-0.313695\pi$
$281$	18.5213	1.10489	0.552445	+	0.833550i	$0.313695\pi$
$282$	−14.7829	−0.880308
$283$	−1.61158	−0.0957983	−0.0478991	−	0.998852i	$-0.515253\pi$
$283$	−1.61158	−0.0957983	−0.0478991	+	0.998852i	$0.515253\pi$
$284$	−15.9575	−0.946906
$285$	9.11462	0.539904
$286$	5.98212	0.353730
$287$	0	0
$288$	14.9285	0.879671
$289$	3.52281	0.207224
$290$	−6.84447	−0.401921
$291$	−11.7325	−0.687772
$292$	16.4798	0.964410
$293$	−4.41671	−0.258027	−0.129013	−	0.991643i	$-0.541181\pi$
$293$	−4.41671	−0.258027	−0.129013	+	0.991643i	$0.541181\pi$
$294$	0	0
$295$	−6.74217	−0.392544
$296$	11.8308	0.687649
$297$	−14.6919	−0.852509
$298$	−25.3094	−1.46613
$299$	−4.53266	−0.262130
$300$	2.19468	0.126710
$301$	0	0
$302$	38.8688	2.23665
$303$	5.03254	0.289112
$304$	−19.8108	−1.13623
$305$	−29.3615	−1.68123
$306$	−18.8524	−1.07772
$307$	−5.78353	−0.330083	−0.165042	−	0.986287i	$-0.552776\pi$
$307$	−5.78353	−0.330083	−0.165042	+	0.986287i	$0.552776\pi$
$308$	0	0
$309$	2.37973	0.135378
$310$	−13.4865	−0.765983
$311$	14.2895	0.810284	0.405142	−	0.914254i	$-0.367222\pi$
$311$	14.2895	0.810284	0.405142	+	0.914254i	$0.367222\pi$
$312$	−1.00500	−0.0568969
$313$	2.73725	0.154718	0.0773592	−	0.997003i	$-0.475351\pi$
$313$	2.73725	0.154718	0.0773592	+	0.997003i	$0.475351\pi$
$314$	43.0892	2.43166
$315$	0	0
$316$	16.1673	0.909481
$317$	10.6512	0.598231	0.299116	−	0.954217i	$-0.403308\pi$
$317$	10.6512	0.598231	0.299116	+	0.954217i	$0.403308\pi$
$318$	8.23560	0.461830
$319$	−4.64460	−0.260047
$320$	−6.03975	−0.337632
$321$	−15.0814	−0.841761
$322$	0	0
$323$	18.4205	1.02495
$324$	4.03362	0.224090
$325$	1.89352	0.105034
$326$	14.3486	0.794695
$327$	−8.16576	−0.451568
$328$	3.34629	0.184768
$329$	0	0
$330$	13.4094	0.738164
$331$	−3.41626	−0.187774	−0.0938872	−	0.995583i	$-0.529929\pi$
$331$	−3.41626	−0.187774	−0.0938872	+	0.995583i	$0.529929\pi$
$332$	17.9517	0.985228
$333$	22.8253	1.25082
$334$	23.2924	1.27450
$335$	−5.20312	−0.284277
$336$	0	0
$337$	24.9606	1.35969	0.679844	−	0.733357i	$-0.262047\pi$
$337$	24.9606	1.35969	0.679844	+	0.733357i	$0.262047\pi$
$338$	1.83237	0.0996678
$339$	−15.0276	−0.816188
$340$	16.1475	0.875720
$341$	−9.15183	−0.495599
$342$	−16.9213	−0.914997
$343$	0	0
$344$	−11.4493	−0.617306
$345$	−10.1603	−0.547014
$346$	9.61824	0.517080
$347$	−19.1833	−1.02981	−0.514907	−	0.857246i	$-0.672173\pi$
$347$	−19.1833	−1.02981	−0.514907	+	0.857246i	$0.672173\pi$
$348$	−1.64895	−0.0883928
$349$	−3.94421	−0.211129	−0.105564	−	0.994412i	$-0.533665\pi$
$349$	−3.94421	−0.211129	−0.105564	+	0.994412i	$0.533665\pi$
$350$	0	0
$351$	−4.50024	−0.240205
$352$	−21.4596	−1.14380
$353$	28.0232	1.49152	0.745762	−	0.666212i	$-0.232086\pi$
$353$	28.0232	1.49152	0.745762	+	0.666212i	$0.232086\pi$
$354$	−4.01723	−0.213513
$355$	−30.8618	−1.63797
$356$	14.4807	0.767476
$357$	0	0
$358$	−19.2866	−1.01933
$359$	33.2232	1.75345	0.876726	−	0.480989i	$-0.159722\pi$
$359$	33.2232	1.75345	0.876726	+	0.480989i	$0.159722\pi$
$360$	7.01921	0.369945
$361$	−2.46641	−0.129811
$362$	−34.4811	−1.81228
$363$	−0.291821	−0.0153166
$364$	0	0
$365$	31.8719	1.66825
$366$	−17.4947	−0.914460
$367$	−28.3091	−1.47772	−0.738862	−	0.673857i	$-0.764637\pi$
$367$	−28.3091	−1.47772	−0.738862	+	0.673857i	$0.764637\pi$
$368$	22.0837	1.15119
$369$	6.45606	0.336089
$370$	−48.3520	−2.51370
$371$	0	0
$372$	−3.24912	−0.168459
$373$	−12.9515	−0.670602	−0.335301	−	0.942111i	$-0.608838\pi$
$373$	−12.9515	−0.670602	−0.335301	+	0.942111i	$0.608838\pi$
$374$	27.1003	1.40132
$375$	−6.96343	−0.359590
$376$	11.1235	0.573653
$377$	−1.42268	−0.0732716
$378$	0	0
$379$	0.168981	0.00867995	0.00433997	−	0.999991i	$-0.498619\pi$
$379$	0.168981	0.00867995	0.00433997	+	0.999991i	$0.498619\pi$
$380$	14.4934	0.743495
$381$	−1.36159	−0.0697562
$382$	27.3288	1.39826
$383$	10.1933	0.520854	0.260427	−	0.965494i	$-0.416137\pi$
$383$	10.1933	0.520854	0.260427	+	0.965494i	$0.416137\pi$
$384$	7.62523	0.389124
$385$	0	0
$386$	−0.0973641	−0.00495570
$387$	−22.0894	−1.12287
$388$	−18.6562	−0.947124
$389$	−28.6665	−1.45345	−0.726723	−	0.686930i	$-0.758958\pi$
$389$	−28.6665	−1.45345	−0.726723	+	0.686930i	$0.758958\pi$
$390$	4.10741	0.207987
$391$	−20.5339	−1.03844
$392$	0	0
$393$	3.67354	0.185306
$394$	18.4113	0.927547
$395$	31.2674	1.57323
$396$	−10.0657	−0.505820
$397$	−28.6411	−1.43746	−0.718728	−	0.695292i	$-0.755275\pi$
$397$	−28.6411	−1.43746	−0.718728	+	0.695292i	$0.755275\pi$
$398$	42.6785	2.13928
$399$	0	0
$400$	−9.22550	−0.461275
$401$	−14.2963	−0.713922	−0.356961	−	0.934119i	$-0.616187\pi$
$401$	−14.2963	−0.713922	−0.356961	+	0.934119i	$0.616187\pi$
$402$	−3.10021	−0.154624
$403$	−2.80328	−0.139641
$404$	8.00237	0.398133
$405$	7.80100	0.387635
$406$	0	0
$407$	−32.8112	−1.62639
$408$	−4.55286	−0.225400
$409$	25.6988	1.27072	0.635362	−	0.772215i	$-0.280851\pi$
$409$	25.6988	1.27072	0.635362	+	0.772215i	$0.280851\pi$
$410$	−13.6762	−0.675420
$411$	8.38590	0.413646
$412$	3.78408	0.186428
$413$	0	0
$414$	18.8626	0.927048
$415$	34.7185	1.70426
$416$	−6.57326	−0.322281
$417$	8.60684	0.421479
$418$	24.3242	1.18974
$419$	18.7999	0.918433	0.459216	−	0.888324i	$-0.348130\pi$
$419$	18.7999	0.918433	0.459216	+	0.888324i	$0.348130\pi$
$420$	0	0
$421$	−18.0283	−0.878645	−0.439322	−	0.898329i	$-0.644781\pi$
$421$	−18.0283	−0.878645	−0.439322	+	0.898329i	$0.644781\pi$
$422$	−4.53432	−0.220727
$423$	21.4609	1.04346
$424$	−6.19697	−0.300951
$425$	8.57806	0.416097
$426$	−18.3886	−0.890929
$427$	0	0
$428$	−23.9813	−1.15918
$429$	2.78725	0.134570
$430$	46.7931	2.25657
$431$	20.5583	0.990256	0.495128	−	0.868820i	$-0.335121\pi$
$431$	20.5583	0.990256	0.495128	+	0.868820i	$0.335121\pi$
$432$	21.9258	1.05490
$433$	18.9235	0.909404	0.454702	−	0.890644i	$-0.349746\pi$
$433$	18.9235	0.909404	0.454702	+	0.890644i	$0.349746\pi$
$434$	0	0
$435$	−3.18905	−0.152903
$436$	−12.9846	−0.621849
$437$	−18.4305	−0.881650
$438$	18.9904	0.907398
$439$	−14.6550	−0.699445	−0.349723	−	0.936853i	$-0.613724\pi$
$439$	−14.6550	−0.699445	−0.349723	+	0.936853i	$0.613724\pi$
$440$	−10.0901	−0.481025
$441$	0	0
$442$	8.30102	0.394839
$443$	−11.9592	−0.568201	−0.284100	−	0.958795i	$-0.591695\pi$
$443$	−11.9592	−0.568201	−0.284100	+	0.958795i	$0.591695\pi$
$444$	−11.6488	−0.552827
$445$	28.0056	1.32759
$446$	11.3062	0.535365
$447$	−11.7924	−0.557762
$448$	0	0
$449$	−2.32245	−0.109603	−0.0548015	−	0.998497i	$-0.517453\pi$
$449$	−2.32245	−0.109603	−0.0548015	+	0.998497i	$0.517453\pi$
$450$	−7.87988	−0.371461
$451$	−9.28055	−0.437004
$452$	−23.8958	−1.12396
$453$	18.1102	0.850890
$454$	21.2443	0.997044
$455$	0	0
$456$	−4.08648	−0.191367
$457$	−18.5805	−0.869157	−0.434579	−	0.900634i	$-0.643103\pi$
$457$	−18.5805	−0.869157	−0.434579	+	0.900634i	$0.643103\pi$
$458$	−18.7601	−0.876604
$459$	−20.3870	−0.951585
$460$	−16.1562	−0.753287
$461$	27.8926	1.29909	0.649543	−	0.760325i	$-0.274960\pi$
$461$	27.8926	1.29909	0.649543	+	0.760325i	$0.274960\pi$
$462$	0	0
$463$	−3.66462	−0.170309	−0.0851547	−	0.996368i	$-0.527138\pi$
$463$	−3.66462	−0.170309	−0.0851547	+	0.996368i	$0.527138\pi$
$464$	6.93147	0.321786
$465$	−6.28378	−0.291403
$466$	39.3634	1.82347
$467$	38.7532	1.79328	0.896641	−	0.442757i	$-0.146000\pi$
$467$	38.7532	1.79328	0.896641	+	0.442757i	$0.146000\pi$
$468$	−3.08320	−0.142521
$469$	0	0
$470$	−45.4617	−2.09699
$471$	20.0766	0.925079
$472$	3.02281	0.139136
$473$	31.7534	1.46002
$474$	18.6303	0.855716
$475$	7.69935	0.353270
$476$	0	0
$477$	−11.9559	−0.547425
$478$	1.98978	0.0910105
$479$	−6.03430	−0.275714	−0.137857	−	0.990452i	$-0.544021\pi$
$479$	−6.03430	−0.275714	−0.137857	+	0.990452i	$0.544021\pi$
$480$	−14.7345	−0.672535
$481$	−10.0503	−0.458256
$482$	−36.6162	−1.66782
$483$	0	0
$484$	−0.464032	−0.0210924
$485$	−36.0809	−1.63835
$486$	29.3864	1.33300
$487$	−3.80249	−0.172307	−0.0861537	−	0.996282i	$-0.527458\pi$
$487$	−3.80249	−0.172307	−0.0861537	+	0.996282i	$0.527458\pi$
$488$	13.1640	0.595908
$489$	6.68545	0.302326
$490$	0	0
$491$	−0.381464	−0.0172152	−0.00860761	−	0.999963i	$-0.502740\pi$
$491$	−0.381464	−0.0172152	−0.00860761	+	0.999963i	$0.502740\pi$
$492$	−3.29482	−0.148542
$493$	−6.44502	−0.290269
$494$	7.45070	0.335223
$495$	−19.4670	−0.874975
$496$	13.6580	0.613260
$497$	0	0
$498$	20.6865	0.926986
$499$	34.5739	1.54774	0.773871	−	0.633343i	$-0.218318\pi$
$499$	34.5739	1.54774	0.773871	+	0.633343i	$0.218318\pi$
$500$	−11.0727	−0.495187
$501$	10.8526	0.484860
$502$	36.9218	1.64790
$503$	−2.41090	−0.107497	−0.0537485	−	0.998555i	$-0.517117\pi$
$503$	−2.41090	−0.107497	−0.0537485	+	0.998555i	$0.517117\pi$
$504$	0	0
$505$	15.4765	0.688696
$506$	−27.1149	−1.20540
$507$	0.853757	0.0379167
$508$	−2.16509	−0.0960605
$509$	−21.9153	−0.971380	−0.485690	−	0.874131i	$-0.661432\pi$
$509$	−21.9153	−0.971380	−0.485690	+	0.874131i	$0.661432\pi$
$510$	18.6074	0.823951
$511$	0	0
$512$	20.5553	0.908426
$513$	−18.2987	−0.807905
$514$	−27.5174	−1.21374
$515$	7.31837	0.322486
$516$	11.2732	0.496276
$517$	−30.8499	−1.35678
$518$	0	0
$519$	4.48143	0.196713
$520$	−3.09067	−0.135535
$521$	−30.1450	−1.32068	−0.660338	−	0.750968i	$-0.729587\pi$
$521$	−30.1450	−1.32068	−0.660338	+	0.750968i	$0.729587\pi$
$522$	5.92046	0.259131
$523$	−18.0993	−0.791428	−0.395714	−	0.918374i	$-0.629503\pi$
$523$	−18.0993	−0.791428	−0.395714	+	0.918374i	$0.629503\pi$
$524$	5.84139	0.255182
$525$	0	0
$526$	−38.7843	−1.69108
$527$	−12.6994	−0.553196
$528$	−13.5799	−0.590988
$529$	−2.45500	−0.106739
$530$	25.3269	1.10013
$531$	5.83197	0.253086
$532$	0	0
$533$	−2.84271	−0.123131
$534$	16.6868	0.722106
$535$	−46.3796	−2.00517
$536$	2.33278	0.100761
$537$	−8.98623	−0.387784
$538$	−7.52151	−0.324275
$539$	0	0
$540$	−16.0406	−0.690280
$541$	4.08890	0.175795	0.0878977	−	0.996130i	$-0.471985\pi$
$541$	4.08890	0.175795	0.0878977	+	0.996130i	$0.471985\pi$
$542$	6.28950	0.270157
$543$	−16.0658	−0.689449
$544$	−29.7782	−1.27673
$545$	−25.1121	−1.07568
$546$	0	0
$547$	−40.4264	−1.72851	−0.864255	−	0.503055i	$-0.832209\pi$
$547$	−40.4264	−1.72851	−0.864255	+	0.503055i	$0.832209\pi$
$548$	13.3346	0.569627
$549$	25.3977	1.08395
$550$	11.3273	0.482997
$551$	−5.78482	−0.246442
$552$	4.55532	0.193887
$553$	0	0
$554$	−0.661507	−0.0281047
$555$	−22.5287	−0.956289
$556$	13.6859	0.580413
$557$	19.7690	0.837640	0.418820	−	0.908069i	$-0.362444\pi$
$557$	19.7690	0.837640	0.418820	+	0.908069i	$0.362444\pi$
$558$	11.6658	0.493854
$559$	9.72632	0.411379
$560$	0	0
$561$	12.6268	0.533105
$562$	33.9379	1.43158
$563$	8.22392	0.346597	0.173298	−	0.984869i	$-0.444557\pi$
$563$	8.22392	0.346597	0.173298	+	0.984869i	$0.444557\pi$
$564$	−10.9525	−0.461182
$565$	−46.2143	−1.94425
$566$	−2.95300	−0.124124
$567$	0	0
$568$	13.8367	0.580574
$569$	14.5770	0.611099	0.305550	−	0.952176i	$-0.401160\pi$
$569$	14.5770	0.611099	0.305550	+	0.952176i	$0.401160\pi$
$570$	16.7014	0.699543
$571$	−2.58822	−0.108314	−0.0541568	−	0.998532i	$-0.517247\pi$
$571$	−2.58822	−0.108314	−0.0541568	+	0.998532i	$0.517247\pi$
$572$	4.43208	0.185315
$573$	12.7333	0.531942
$574$	0	0
$575$	−8.58269	−0.357923
$576$	5.22437	0.217682
$577$	−23.8937	−0.994707	−0.497353	−	0.867548i	$-0.665695\pi$
$577$	−23.8937	−0.994707	−0.497353	+	0.867548i	$0.665695\pi$
$578$	6.45509	0.268496
$579$	−0.0453649	−0.00188530
$580$	−5.07099	−0.210561
$581$	0	0
$582$	−21.4983	−0.891134
$583$	17.1866	0.711795
$584$	−14.2896	−0.591306
$585$	−5.96289	−0.246535
$586$	−8.09304	−0.334320
$587$	28.5759	1.17945	0.589726	−	0.807604i	$-0.299236\pi$
$587$	28.5759	1.17945	0.589726	+	0.807604i	$0.299236\pi$
$588$	0	0
$589$	−11.3986	−0.469669
$590$	−12.3541	−0.508612
$591$	8.57837	0.352867
$592$	48.9666	2.01252
$593$	−19.9575	−0.819556	−0.409778	−	0.912185i	$-0.634394\pi$
$593$	−19.9575	−0.819556	−0.409778	+	0.912185i	$0.634394\pi$
$594$	−26.9210	−1.10458
$595$	0	0
$596$	−18.7514	−0.768088
$597$	19.8852	0.813848
$598$	−8.30551	−0.339638
$599$	1.17716	0.0480973	0.0240486	−	0.999711i	$-0.492344\pi$
$599$	1.17716	0.0480973	0.0240486	+	0.999711i	$0.492344\pi$
$600$	−1.90299	−0.0776892
$601$	−30.9250	−1.26146	−0.630729	−	0.776003i	$-0.717244\pi$
$601$	−30.9250	−1.26146	−0.630729	+	0.776003i	$0.717244\pi$
$602$	0	0
$603$	4.50069	0.183282
$604$	28.7974	1.17175
$605$	−0.897435	−0.0364859
$606$	9.22148	0.374597
$607$	2.40708	0.0977005	0.0488503	−	0.998806i	$-0.484444\pi$
$607$	2.40708	0.0977005	0.0488503	+	0.998806i	$0.484444\pi$
$608$	−26.7279	−1.08396
$609$	0	0
$610$	−53.8011	−2.17834
$611$	−9.44956	−0.382288
$612$	−13.9675	−0.564605
$613$	−27.7742	−1.12179	−0.560895	−	0.827887i	$-0.689543\pi$
$613$	−27.7742	−1.12179	−0.560895	+	0.827887i	$0.689543\pi$
$614$	−10.5976	−0.427683
$615$	−6.37216	−0.256950
$616$	0	0
$617$	26.2125	1.05527	0.527637	−	0.849470i	$-0.323078\pi$
$617$	26.2125	1.05527	0.527637	+	0.849470i	$0.323078\pi$
$618$	4.36055	0.175407
$619$	−17.2357	−0.692763	−0.346381	−	0.938094i	$-0.612590\pi$
$619$	−17.2357	−0.692763	−0.346381	+	0.938094i	$0.612590\pi$
$620$	−9.99200	−0.401288
$621$	20.3980	0.818546
$622$	26.1837	1.04987
$623$	0	0
$624$	−4.15962	−0.166518
$625$	−30.8822	−1.23529
$626$	5.01565	0.200466
$627$	11.3334	0.452612
$628$	31.9242	1.27392
$629$	−45.5302	−1.81541
$630$	0	0
$631$	39.2125	1.56103	0.780513	−	0.625140i	$-0.214958\pi$
$631$	39.2125	1.56103	0.780513	+	0.625140i	$0.214958\pi$
$632$	−14.0185	−0.557628
$633$	−2.11268	−0.0839714
$634$	19.5170	0.775117
$635$	−4.18728	−0.166167
$636$	6.10166	0.241946
$637$	0	0
$638$	−8.51062	−0.336939
$639$	26.6954	1.05605
$640$	23.4498	0.926935
$641$	−22.8735	−0.903451	−0.451725	−	0.892157i	$-0.649191\pi$
$641$	−22.8735	−0.903451	−0.451725	+	0.892157i	$0.649191\pi$
$642$	−27.6347	−1.09065
$643$	−46.7072	−1.84195	−0.920976	−	0.389620i	$-0.872606\pi$
$643$	−46.7072	−1.84195	−0.920976	+	0.389620i	$0.872606\pi$
$644$	0	0
$645$	21.8024	0.858467
$646$	33.7532	1.32800
$647$	5.93075	0.233162	0.116581	−	0.993181i	$-0.462807\pi$
$647$	5.93075	0.233162	0.116581	+	0.993181i	$0.462807\pi$
$648$	−3.49753	−0.137396
$649$	−8.38341	−0.329078
$650$	3.46963	0.136090
$651$	0	0
$652$	10.6307	0.416330
$653$	−18.8046	−0.735881	−0.367940	−	0.929849i	$-0.619937\pi$
$653$	−18.8046	−0.735881	−0.367940	+	0.929849i	$0.619937\pi$
$654$	−14.9627	−0.585088
$655$	11.2972	0.441419
$656$	13.8500	0.540754
$657$	−27.5691	−1.07557
$658$	0	0
$659$	23.1086	0.900184	0.450092	−	0.892982i	$-0.351391\pi$
$659$	23.1086	0.900184	0.450092	+	0.892982i	$0.351391\pi$
$660$	9.93488	0.386715
$661$	−33.9087	−1.31889	−0.659447	−	0.751751i	$-0.729210\pi$
$661$	−33.9087	−1.31889	−0.659447	+	0.751751i	$0.729210\pi$
$662$	−6.25985	−0.243296
$663$	3.86770	0.150209
$664$	−15.5658	−0.604071
$665$	0	0
$666$	41.8244	1.62066
$667$	6.44851	0.249687
$668$	17.2570	0.667695
$669$	5.26792	0.203669
$670$	−9.53404	−0.368332
$671$	−36.5090	−1.40941
$672$	0	0
$673$	6.00430	0.231449	0.115724	−	0.993281i	$-0.463081\pi$
$673$	6.00430	0.231449	0.115724	+	0.993281i	$0.463081\pi$
$674$	45.7370	1.76172
$675$	−8.52130	−0.327985
$676$	1.35758	0.0522147
$677$	20.2075	0.776637	0.388318	−	0.921525i	$-0.373056\pi$
$677$	20.2075	0.776637	0.388318	+	0.921525i	$0.373056\pi$
$678$	−27.5361	−1.05752
$679$	0	0
$680$	−14.0014	−0.536928
$681$	9.89837	0.379306
$682$	−16.7695	−0.642139
$683$	−31.6508	−1.21108	−0.605541	−	0.795814i	$-0.707043\pi$
$683$	−31.6508	−1.21108	−0.605541	+	0.795814i	$0.707043\pi$
$684$	−12.5368	−0.479355
$685$	25.7891	0.985350
$686$	0	0
$687$	−8.74092	−0.333487
$688$	−47.3879	−1.80665
$689$	5.26439	0.200557
$690$	−18.6175	−0.708756
$691$	9.69199	0.368701	0.184350	−	0.982861i	$-0.440982\pi$
$691$	9.69199	0.368701	0.184350	+	0.982861i	$0.440982\pi$
$692$	7.12604	0.270891
$693$	0	0
$694$	−35.1509	−1.33431
$695$	26.4685	1.00401
$696$	1.42979	0.0541960
$697$	−12.8781	−0.487791
$698$	−7.22725	−0.273556
$699$	18.3406	0.693705
$700$	0	0
$701$	−5.10365	−0.192762	−0.0963811	−	0.995345i	$-0.530727\pi$
$701$	−5.10365	−0.192762	−0.0963811	+	0.995345i	$0.530727\pi$
$702$	−8.24610	−0.311229
$703$	−40.8662	−1.54130
$704$	−7.51000	−0.283044
$705$	−21.1820	−0.797760
$706$	51.3489	1.93254
$707$	0	0
$708$	−2.97632	−0.111857
$709$	26.1445	0.981878	0.490939	−	0.871194i	$-0.336654\pi$
$709$	26.1445	0.981878	0.490939	+	0.871194i	$0.336654\pi$
$710$	−56.5502	−2.12229
$711$	−27.0463	−1.01431
$712$	−12.5561	−0.470561
$713$	12.7063	0.475855
$714$	0	0
$715$	8.57161	0.320560
$716$	−14.2892	−0.534014
$717$	0.927100	0.0346232
$718$	60.8772	2.27192
$719$	−8.72884	−0.325531	−0.162765	−	0.986665i	$-0.552041\pi$
$719$	−8.72884	−0.325531	−0.162765	+	0.986665i	$0.552041\pi$
$720$	29.0520	1.08270
$721$	0	0
$722$	−4.51937	−0.168193
$723$	−17.0606	−0.634491
$724$	−25.5466	−0.949432
$725$	−2.69387	−0.100048
$726$	−0.534725	−0.0198455
$727$	−21.8712	−0.811158	−0.405579	−	0.914060i	$-0.632930\pi$
$727$	−21.8712	−0.811158	−0.405579	+	0.914060i	$0.632930\pi$
$728$	0	0
$729$	4.77848	0.176981
$730$	58.4011	2.16152
$731$	44.0623	1.62970
$732$	−12.9616	−0.479074
$733$	−35.5640	−1.31359	−0.656793	−	0.754071i	$-0.728088\pi$
$733$	−35.5640	−1.31359	−0.656793	+	0.754071i	$0.728088\pi$
$734$	−51.8728	−1.91466
$735$	0	0
$736$	29.7943	1.09823
$737$	−6.46971	−0.238315
$738$	11.8299	0.435465
$739$	−36.4894	−1.34228	−0.671142	−	0.741329i	$-0.734196\pi$
$739$	−36.4894	−1.34228	−0.671142	+	0.741329i	$0.734196\pi$
$740$	−35.8234	−1.31690
$741$	3.47151	0.127529
$742$	0	0
$743$	12.4588	0.457071	0.228535	−	0.973536i	$-0.426606\pi$
$743$	12.4588	0.457071	0.228535	+	0.973536i	$0.426606\pi$
$744$	2.81729	0.103287
$745$	−36.2651	−1.32865
$746$	−23.7319	−0.868886
$747$	−30.0314	−1.09879
$748$	20.0783	0.734134
$749$	0	0
$750$	−12.7596	−0.465914
$751$	−18.9424	−0.691217	−0.345608	−	0.938379i	$-0.612327\pi$
$751$	−18.9424	−0.691217	−0.345608	+	0.938379i	$0.612327\pi$
$752$	46.0395	1.67889
$753$	17.2030	0.626912
$754$	−2.60687	−0.0949366
$755$	55.6940	2.02691
$756$	0	0
$757$	−25.0956	−0.912114	−0.456057	−	0.889951i	$-0.650739\pi$
$757$	−25.0956	−0.912114	−0.456057	+	0.889951i	$0.650739\pi$
$758$	0.309635	0.0112464
$759$	−12.6337	−0.458573
$760$	−12.5671	−0.455857
$761$	28.0617	1.01723	0.508617	−	0.860993i	$-0.330157\pi$
$761$	28.0617	1.01723	0.508617	+	0.860993i	$0.330157\pi$
$762$	−2.49493	−0.0903818
$763$	0	0
$764$	20.2476	0.732531
$765$	−27.0131	−0.976662
$766$	18.6779	0.674861
$767$	−2.56791	−0.0927217
$768$	17.9002	0.645917
$769$	−23.2636	−0.838907	−0.419454	−	0.907777i	$-0.637778\pi$
$769$	−23.2636	−0.838907	−0.419454	+	0.907777i	$0.637778\pi$
$770$	0	0
$771$	−12.8212	−0.461744
$772$	−0.0721359	−0.00259623
$773$	45.8118	1.64774	0.823869	−	0.566781i	$-0.191811\pi$
$773$	45.8118	1.64774	0.823869	+	0.566781i	$0.191811\pi$
$774$	−40.4760	−1.45488
$775$	−5.30807	−0.190672
$776$	16.1766	0.580708
$777$	0	0
$778$	−52.5276	−1.88320
$779$	−11.5589	−0.414140
$780$	3.04313	0.108962
$781$	−38.3744	−1.37315
$782$	−37.6257	−1.34549
$783$	6.40238	0.228803
$784$	0	0
$785$	61.7413	2.20364
$786$	6.73129	0.240097
$787$	31.2715	1.11471	0.557355	−	0.830274i	$-0.311816\pi$
$787$	31.2715	1.11471	0.557355	+	0.830274i	$0.311816\pi$
$788$	13.6407	0.485929
$789$	−18.0708	−0.643338
$790$	57.2935	2.03841
$791$	0	0
$792$	8.72789	0.310132
$793$	−11.1830	−0.397119
$794$	−52.4811	−1.86248
$795$	11.8006	0.418523
$796$	31.6200	1.12074
$797$	−11.6121	−0.411323	−0.205661	−	0.978623i	$-0.565935\pi$
$797$	−11.6121	−0.411323	−0.205661	+	0.978623i	$0.565935\pi$
$798$	0	0
$799$	−42.8085	−1.51446
$800$	−12.4466	−0.440054
$801$	−24.2248	−0.855941
$802$	−26.1961	−0.925016
$803$	39.6304	1.39853
$804$	−2.29691	−0.0810056
$805$	0	0
$806$	−5.13664	−0.180931
$807$	−3.50450	−0.123364
$808$	−6.93880	−0.244106
$809$	7.30665	0.256888	0.128444	−	0.991717i	$-0.459002\pi$
$809$	7.30665	0.256888	0.128444	+	0.991717i	$0.459002\pi$
$810$	14.2943	0.502251
$811$	−15.9662	−0.560651	−0.280325	−	0.959905i	$-0.590442\pi$
$811$	−15.9662	−0.560651	−0.280325	+	0.959905i	$0.590442\pi$
$812$	0	0
$813$	2.93047	0.102776
$814$	−60.1223	−2.10729
$815$	20.5597	0.720175
$816$	−18.8440	−0.659671
$817$	39.5487	1.38363
$818$	47.0897	1.64645
$819$	0	0
$820$	−10.1325	−0.353844
$821$	1.12788	0.0393634	0.0196817	−	0.999806i	$-0.493735\pi$
$821$	1.12788	0.0393634	0.0196817	+	0.999806i	$0.493735\pi$
$822$	15.3661	0.535953
$823$	22.4044	0.780968	0.390484	−	0.920610i	$-0.372308\pi$
$823$	22.4044	0.780968	0.390484	+	0.920610i	$0.372308\pi$
$824$	−3.28115	−0.114304
$825$	5.27772	0.183747
$826$	0	0
$827$	−6.32296	−0.219871	−0.109935	−	0.993939i	$-0.535064\pi$
$827$	−6.32296	−0.219871	−0.109935	+	0.993939i	$0.535064\pi$
$828$	13.9751	0.485668
$829$	−44.3704	−1.54105	−0.770523	−	0.637412i	$-0.780005\pi$
$829$	−44.3704	−1.54105	−0.770523	+	0.637412i	$0.780005\pi$
$830$	63.6171	2.20818
$831$	−0.308216	−0.0106919
$832$	−2.30037	−0.0797510
$833$	0	0
$834$	15.7709	0.546102
$835$	33.3750	1.15499
$836$	18.0215	0.623287
$837$	12.6154	0.436053
$838$	34.4483	1.19000
$839$	−9.89476	−0.341605	−0.170803	−	0.985305i	$-0.554636\pi$
$839$	−9.89476	−0.341605	−0.170803	+	0.985305i	$0.554636\pi$
$840$	0	0
$841$	−26.9760	−0.930207
$842$	−33.0345	−1.13844
$843$	15.8127	0.544619
$844$	−3.35942	−0.115636
$845$	2.62555	0.0903217
$846$	39.3243	1.35200
$847$	0	0
$848$	−25.6488	−0.880783
$849$	−1.37589	−0.0472206
$850$	15.7182	0.539129
$851$	45.5548	1.56160
$852$	−13.6239	−0.466746
$853$	25.9407	0.888193	0.444097	−	0.895979i	$-0.353525\pi$
$853$	25.9407	0.888193	0.444097	+	0.895979i	$0.353525\pi$
$854$	0	0
$855$	−24.2460	−0.829196
$856$	20.7940	0.710725
$857$	10.0244	0.342426	0.171213	−	0.985234i	$-0.445231\pi$
$857$	10.0244	0.342426	0.171213	+	0.985234i	$0.445231\pi$
$858$	5.10728	0.174360
$859$	37.4378	1.27736	0.638680	−	0.769472i	$-0.279481\pi$
$859$	37.4378	1.27736	0.638680	+	0.769472i	$0.279481\pi$
$860$	34.6685	1.18219
$861$	0	0
$862$	37.6703	1.28306
$863$	21.0026	0.714938	0.357469	−	0.933925i	$-0.383640\pi$
$863$	21.0026	0.714938	0.357469	+	0.933925i	$0.383640\pi$
$864$	29.5812	1.00637
$865$	13.7817	0.468592
$866$	34.6748	1.17830
$867$	3.00762	0.102144
$868$	0	0
$869$	38.8788	1.31887
$870$	−5.84352	−0.198114
$871$	−1.98172	−0.0671481
$872$	11.2588	0.381273
$873$	31.2099	1.05630
$874$	−33.7715	−1.14234
$875$	0	0
$876$	14.0698	0.475374
$877$	7.56302	0.255385	0.127692	−	0.991814i	$-0.459243\pi$
$877$	7.56302	0.255385	0.127692	+	0.991814i	$0.459243\pi$
$878$	−26.8534	−0.906258
$879$	−3.77080	−0.127186
$880$	−41.7620	−1.40780
$881$	−34.3550	−1.15745	−0.578725	−	0.815522i	$-0.696450\pi$
$881$	−34.3550	−1.15745	−0.578725	+	0.815522i	$0.696450\pi$
$882$	0	0
$883$	49.6697	1.67152	0.835759	−	0.549096i	$-0.185028\pi$
$883$	49.6697	1.67152	0.835759	+	0.549096i	$0.185028\pi$
$884$	6.15013	0.206851
$885$	−5.75617	−0.193492
$886$	−21.9138	−0.736207
$887$	−48.0325	−1.61277	−0.806386	−	0.591389i	$-0.798580\pi$
$887$	−48.0325	−1.61277	−0.806386	+	0.591389i	$0.798580\pi$
$888$	10.1006	0.338954
$889$	0	0
$890$	51.3166	1.72014
$891$	9.69999	0.324962
$892$	8.37665	0.280471
$893$	−38.4234	−1.28579
$894$	−21.6081	−0.722682
$895$	−27.6353	−0.923745
$896$	0	0
$897$	−3.86979	−0.129209
$898$	−4.25558	−0.142011
$899$	3.98816	0.133013
$900$	−5.83811	−0.194604
$901$	23.8488	0.794518
$902$	−17.0054	−0.566218
$903$	0	0
$904$	20.7199	0.689133
$905$	−49.4069	−1.64234
$906$	33.1845	1.10248
$907$	2.40195	0.0797556	0.0398778	−	0.999205i	$-0.487303\pi$
$907$	2.40195	0.0797556	0.0398778	+	0.999205i	$0.487303\pi$
$908$	15.7396	0.522338
$909$	−13.3872	−0.444024
$910$	0	0
$911$	−33.9555	−1.12500	−0.562499	−	0.826798i	$-0.690160\pi$
$911$	−33.9555	−1.12500	−0.562499	+	0.826798i	$0.690160\pi$
$912$	−16.9137	−0.560067
$913$	43.1700	1.42872
$914$	−34.0463	−1.12615
$915$	−25.0676	−0.828709
$916$	−13.8992	−0.459241
$917$	0	0
$918$	−37.3566	−1.23295
$919$	−9.37134	−0.309132	−0.154566	−	0.987982i	$-0.549398\pi$
$919$	−9.37134	−0.309132	−0.154566	+	0.987982i	$0.549398\pi$
$920$	14.0089	0.461861
$921$	−4.93773	−0.162704
$922$	51.1095	1.68320
$923$	−11.7544	−0.386901
$924$	0	0
$925$	−19.0306	−0.625721
$926$	−6.71494	−0.220667
$927$	−6.33038	−0.207917
$928$	9.35162	0.306982
$929$	−43.4273	−1.42480	−0.712402	−	0.701771i	$-0.752393\pi$
$929$	−43.4273	−1.42480	−0.712402	+	0.701771i	$0.752393\pi$
$930$	−11.5142	−0.377566
$931$	0	0
$932$	29.1639	0.955294
$933$	12.1998	0.399403
$934$	71.0102	2.32352
$935$	38.8312	1.26992
$936$	2.67342	0.0873835
$937$	2.59416	0.0847476	0.0423738	−	0.999102i	$-0.486508\pi$
$937$	2.59416	0.0847476	0.0423738	+	0.999102i	$0.486508\pi$
$938$	0	0
$939$	2.33695	0.0762633
$940$	−33.6820	−1.09859
$941$	43.4060	1.41499	0.707497	−	0.706716i	$-0.249824\pi$
$941$	43.4060	1.41499	0.707497	+	0.706716i	$0.249824\pi$
$942$	36.7877	1.19861
$943$	12.8850	0.419594
$944$	12.5112	0.407204
$945$	0	0
$946$	58.1840	1.89172
$947$	−7.50058	−0.243736	−0.121868	−	0.992546i	$-0.538888\pi$
$947$	−7.50058	−0.243736	−0.121868	+	0.992546i	$0.538888\pi$
$948$	13.8029	0.448299
$949$	12.1391	0.394052
$950$	14.1081	0.457726
$951$	9.09355	0.294878
$952$	0	0
$953$	−0.708439	−0.0229486	−0.0114743	−	0.999934i	$-0.503652\pi$
$953$	−0.708439	−0.0229486	−0.0114743	+	0.999934i	$0.503652\pi$
$954$	−21.9077	−0.709288
$955$	39.1586	1.26714
$956$	1.47421	0.0476792
$957$	−3.96536	−0.128182
$958$	−11.0571	−0.357238
$959$	0	0
$960$	−5.15648	−0.166425
$961$	−23.1416	−0.746504
$962$	−18.4159	−0.593754
$963$	40.1183	1.29279
$964$	−27.1285	−0.873750
$965$	−0.139510	−0.00449100
$966$	0	0
$967$	−16.9761	−0.545915	−0.272957	−	0.962026i	$-0.588002\pi$
$967$	−16.9761	−0.545915	−0.272957	+	0.962026i	$0.588002\pi$
$968$	0.402359	0.0129323
$969$	15.7267	0.505213
$970$	−66.1136	−2.12278
$971$	−6.86359	−0.220263	−0.110132	−	0.993917i	$-0.535127\pi$
$971$	−6.86359	−0.220263	−0.110132	+	0.993917i	$0.535127\pi$
$972$	21.7721	0.698339
$973$	0	0
$974$	−6.96757	−0.223255
$975$	1.61661	0.0517729
$976$	54.4850	1.74402
$977$	0.581913	0.0186171	0.00930853	−	0.999957i	$-0.497037\pi$
$977$	0.581913	0.0186171	0.00930853	+	0.999957i	$0.497037\pi$
$978$	12.2502	0.391719
$979$	34.8230	1.11295
$980$	0	0
$981$	21.7219	0.693528
$982$	−0.698983	−0.0223054
$983$	34.7195	1.10738	0.553689	−	0.832723i	$-0.313220\pi$
$983$	34.7195	1.10738	0.553689	+	0.832723i	$0.313220\pi$
$984$	2.85692	0.0910752
$985$	26.3810	0.840568
$986$	−11.8097	−0.376097
$987$	0	0
$988$	5.52013	0.175619
$989$	−44.0861	−1.40186
$990$	−35.6707	−1.13369
$991$	24.1688	0.767748	0.383874	−	0.923385i	$-0.374590\pi$
$991$	24.1688	0.767748	0.383874	+	0.923385i	$0.374590\pi$
$992$	18.4267	0.585047
$993$	−2.91665	−0.0925572
$994$	0	0
$995$	61.1528	1.93868
$996$	15.3264	0.485636
$997$	−35.1852	−1.11433	−0.557163	−	0.830403i	$-0.688110\pi$
$997$	−35.1852	−1.11433	−0.557163	+	0.830403i	$0.688110\pi$
$998$	63.3523	2.00538
$999$	45.2289	1.43098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.a.n.1.5	yes	6
3.2	odd	2		5733.2.a.br.1.2		6
7.2	even	3		637.2.e.n.508.2		12
7.3	odd	6		637.2.e.o.79.2		12
7.4	even	3		637.2.e.n.79.2		12
7.5	odd	6		637.2.e.o.508.2		12
7.6	odd	2		637.2.a.m.1.5	✓	6
13.12	even	2		8281.2.a.cd.1.2		6
21.20	even	2		5733.2.a.bu.1.2		6
91.90	odd	2		8281.2.a.cc.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.5	✓	6	7.6	odd	2
637.2.a.n.1.5	yes	6	1.1	even	1	trivial
637.2.e.n.79.2		12	7.4	even	3
637.2.e.n.508.2		12	7.2	even	3
637.2.e.o.79.2		12	7.3	odd	6
637.2.e.o.508.2		12	7.5	odd	6
5733.2.a.br.1.2		6	3.2	odd	2
5733.2.a.bu.1.2		6	21.20	even	2
8281.2.a.cc.1.2		6	91.90	odd	2
8281.2.a.cd.1.2		6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83237 q^{2} +0.853757 q^{3} +1.35758 q^{4} +2.62555 q^{5} +1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} +O(q^{10})\)	\(q+1.83237 q^{2} +0.853757 q^{3} +1.35758 q^{4} +2.62555 q^{5} +1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} +4.81098 q^{10} +3.26469 q^{11} +1.15904 q^{12} +1.00000 q^{13} +2.24158 q^{15} -4.87214 q^{16} +4.53021 q^{17} -4.16149 q^{18} +4.06615 q^{19} +3.56440 q^{20} +5.98212 q^{22} -4.53266 q^{23} -1.00500 q^{24} +1.89352 q^{25} +1.83237 q^{26} -4.50024 q^{27} -1.42268 q^{29} +4.10741 q^{30} -2.80328 q^{31} -6.57326 q^{32} +2.78725 q^{33} +8.30102 q^{34} -3.08320 q^{36} -10.0503 q^{37} +7.45070 q^{38} +0.853757 q^{39} -3.09067 q^{40} -2.84271 q^{41} +9.72632 q^{43} +4.43208 q^{44} -5.96289 q^{45} -8.30551 q^{46} -9.44956 q^{47} -4.15962 q^{48} +3.46963 q^{50} +3.86770 q^{51} +1.35758 q^{52} +5.26439 q^{53} -8.24610 q^{54} +8.57161 q^{55} +3.47151 q^{57} -2.60687 q^{58} -2.56791 q^{59} +3.04313 q^{60} -11.1830 q^{61} -5.13664 q^{62} -2.30037 q^{64} +2.62555 q^{65} +5.10728 q^{66} -1.98172 q^{67} +6.15013 q^{68} -3.86979 q^{69} -11.7544 q^{71} +2.67342 q^{72} +12.1391 q^{73} -18.4159 q^{74} +1.61661 q^{75} +5.52013 q^{76} +1.56440 q^{78} +11.9089 q^{79} -12.7920 q^{80} +2.97118 q^{81} -5.20889 q^{82} +13.2233 q^{83} +11.8943 q^{85} +17.8222 q^{86} -1.21462 q^{87} -3.84303 q^{88} +10.6666 q^{89} -10.9262 q^{90} -6.15345 q^{92} -2.39332 q^{93} -17.3151 q^{94} +10.6759 q^{95} -5.61197 q^{96} -13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 + 6 * q^13 + 12 * q^15 + 16 * q^17 - 4 * q^18 + 2 * q^19 + 16 * q^20 - 12 * q^22 - 6 * q^23 + 12 * q^24 - 4 * q^25 + 20 * q^27 - 6 * q^29 + 6 * q^31 - 20 * q^32 + 4 * q^33 - 24 * q^36 + 8 * q^38 + 8 * q^39 + 4 * q^40 - 8 * q^41 + 2 * q^43 - 4 * q^44 + 14 * q^45 + 8 * q^46 + 30 * q^47 - 8 * q^48 + 8 * q^50 - 4 * q^51 + 4 * q^52 - 14 * q^53 - 48 * q^54 - 8 * q^55 + 4 * q^57 - 8 * q^58 + 24 * q^59 + 12 * q^60 + 28 * q^62 - 20 * q^64 + 6 * q^65 - 4 * q^66 + 16 * q^67 + 28 * q^68 - 20 * q^69 + 8 * q^71 + 28 * q^72 - 6 * q^73 - 12 * q^74 + 12 * q^75 - 16 * q^76 + 4 * q^78 - 22 * q^79 - 28 * q^80 + 46 * q^81 - 40 * q^82 + 50 * q^83 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 44 * q^88 + 26 * q^89 - 40 * q^90 + 20 * q^92 + 16 * q^93 - 32 * q^94 - 6 * q^95 - 20 * q^96 - 14 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more