LMFDB - Embedded newform 6027.2.a.bo.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25316 q^{2} +1.00000 q^{3} -0.429590 q^{4} -1.76265 q^{5} -1.25316 q^{6} +3.04466 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.25316 q^{2} +1.00000 q^{3} -0.429590 q^{4} -1.76265 q^{5} -1.25316 q^{6} +3.04466 q^{8} +1.00000 q^{9} +2.20889 q^{10} -4.84306 q^{11} -0.429590 q^{12} -3.18902 q^{13} -1.76265 q^{15} -2.95627 q^{16} +6.61037 q^{17} -1.25316 q^{18} -8.31403 q^{19} +0.757219 q^{20} +6.06913 q^{22} -8.32423 q^{23} +3.04466 q^{24} -1.89305 q^{25} +3.99635 q^{26} +1.00000 q^{27} -7.79558 q^{29} +2.20889 q^{30} -1.04110 q^{31} -2.38465 q^{32} -4.84306 q^{33} -8.28385 q^{34} -0.429590 q^{36} +3.58658 q^{37} +10.4188 q^{38} -3.18902 q^{39} -5.36669 q^{40} -1.00000 q^{41} +4.05595 q^{43} +2.08053 q^{44} -1.76265 q^{45} +10.4316 q^{46} +0.963735 q^{47} -2.95627 q^{48} +2.37229 q^{50} +6.61037 q^{51} +1.36997 q^{52} +5.52023 q^{53} -1.25316 q^{54} +8.53664 q^{55} -8.31403 q^{57} +9.76911 q^{58} -9.28053 q^{59} +0.757219 q^{60} +11.2178 q^{61} +1.30466 q^{62} +8.90089 q^{64} +5.62114 q^{65} +6.06913 q^{66} +6.04854 q^{67} -2.83975 q^{68} -8.32423 q^{69} +9.94007 q^{71} +3.04466 q^{72} -3.75792 q^{73} -4.49456 q^{74} -1.89305 q^{75} +3.57162 q^{76} +3.99635 q^{78} -13.7937 q^{79} +5.21089 q^{80} +1.00000 q^{81} +1.25316 q^{82} +8.11111 q^{83} -11.6518 q^{85} -5.08276 q^{86} -7.79558 q^{87} -14.7455 q^{88} -10.4911 q^{89} +2.20889 q^{90} +3.57601 q^{92} -1.04110 q^{93} -1.20771 q^{94} +14.6548 q^{95} -2.38465 q^{96} -11.2995 q^{97} -4.84306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * 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 $

$2$	−1.25316	−0.886118	−0.443059	−	0.896492i	$-0.646107\pi$
$2$	−1.25316	−0.886118	−0.443059	+	0.896492i	$0.646107\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.429590	−0.214795
$5$	−1.76265	−0.788283	−0.394142	−	0.919050i	$-0.628958\pi$
$5$	−1.76265	−0.788283	−0.394142	+	0.919050i	$0.628958\pi$
$6$	−1.25316	−0.511600
$7$	0	0
$7$	0	0
$8$	3.04466	1.07645
$9$	1.00000	0.333333
$10$	2.20889	0.698512
$11$	−4.84306	−1.46024	−0.730119	−	0.683320i	$-0.760535\pi$
$11$	−4.84306	−1.46024	−0.730119	+	0.683320i	$0.760535\pi$
$12$	−0.429590	−0.124012
$13$	−3.18902	−0.884475	−0.442237	−	0.896898i	$-0.645815\pi$
$13$	−3.18902	−0.884475	−0.442237	+	0.896898i	$0.645815\pi$
$14$	0	0
$15$	−1.76265	−0.455115
$16$	−2.95627	−0.739068
$17$	6.61037	1.60325	0.801625	−	0.597827i	$-0.203969\pi$
$17$	6.61037	1.60325	0.801625	+	0.597827i	$0.203969\pi$
$18$	−1.25316	−0.295373
$19$	−8.31403	−1.90737	−0.953685	−	0.300808i	$-0.902744\pi$
$19$	−8.31403	−1.90737	−0.953685	+	0.300808i	$0.902744\pi$
$20$	0.757219	0.169319
$21$	0	0
$22$	6.06913	1.29394
$23$	−8.32423	−1.73572	−0.867861	−	0.496807i	$-0.834506\pi$
$23$	−8.32423	−1.73572	−0.867861	+	0.496807i	$0.834506\pi$
$24$	3.04466	0.621490
$25$	−1.89305	−0.378610
$26$	3.99635	0.783749
$27$	1.00000	0.192450
$28$	0	0
$29$	−7.79558	−1.44760	−0.723802	−	0.690008i	$-0.757607\pi$
$29$	−7.79558	−1.44760	−0.723802	+	0.690008i	$0.757607\pi$
$30$	2.20889	0.403286
$31$	−1.04110	−0.186986	−0.0934932	−	0.995620i	$-0.529803\pi$
$31$	−1.04110	−0.186986	−0.0934932	+	0.995620i	$0.529803\pi$
$32$	−2.38465	−0.421550
$33$	−4.84306	−0.843068
$34$	−8.28385	−1.42067
$35$	0	0
$36$	−0.429590	−0.0715983
$37$	3.58658	0.589630	0.294815	−	0.955554i	$-0.404742\pi$
$37$	3.58658	0.589630	0.294815	+	0.955554i	$0.404742\pi$
$38$	10.4188	1.69015
$39$	−3.18902	−0.510652
$40$	−5.36669	−0.848549
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	4.05595	0.618527	0.309263	−	0.950976i	$-0.399918\pi$
$43$	4.05595	0.618527	0.309263	+	0.950976i	$0.399918\pi$
$44$	2.08053	0.313652
$45$	−1.76265	−0.262761
$46$	10.4316	1.53805
$47$	0.963735	0.140575	0.0702876	−	0.997527i	$-0.477608\pi$
$47$	0.963735	0.140575	0.0702876	+	0.997527i	$0.477608\pi$
$48$	−2.95627	−0.426701
$49$	0	0
$50$	2.37229	0.335493
$51$	6.61037	0.925637
$52$	1.36997	0.189981
$53$	5.52023	0.758262	0.379131	−	0.925343i	$-0.376223\pi$
$53$	5.52023	0.758262	0.379131	+	0.925343i	$0.376223\pi$
$54$	−1.25316	−0.170533
$55$	8.53664	1.15108
$56$	0	0
$57$	−8.31403	−1.10122
$58$	9.76911	1.28275
$59$	−9.28053	−1.20822	−0.604111	−	0.796900i	$-0.706472\pi$
$59$	−9.28053	−1.20822	−0.604111	+	0.796900i	$0.706472\pi$
$60$	0.757219	0.0977565
$61$	11.2178	1.43629	0.718145	−	0.695893i	$-0.244991\pi$
$61$	11.2178	1.43629	0.718145	+	0.695893i	$0.244991\pi$
$62$	1.30466	0.165692
$63$	0	0
$64$	8.90089	1.11261
$65$	5.62114	0.697217
$66$	6.06913	0.747058
$67$	6.04854	0.738946	0.369473	−	0.929241i	$-0.379538\pi$
$67$	6.04854	0.738946	0.369473	+	0.929241i	$0.379538\pi$
$68$	−2.83975	−0.344370
$69$	−8.32423	−1.00212
$70$	0	0
$71$	9.94007	1.17967	0.589834	−	0.807524i	$-0.299193\pi$
$71$	9.94007	1.17967	0.589834	+	0.807524i	$0.299193\pi$
$72$	3.04466	0.358817
$73$	−3.75792	−0.439832	−0.219916	−	0.975519i	$-0.570578\pi$
$73$	−3.75792	−0.439832	−0.219916	+	0.975519i	$0.570578\pi$
$74$	−4.49456	−0.522482
$75$	−1.89305	−0.218590
$76$	3.57162	0.409693
$77$	0	0
$78$	3.99635	0.452498
$79$	−13.7937	−1.55192	−0.775958	−	0.630784i	$-0.782733\pi$
$79$	−13.7937	−1.55192	−0.775958	+	0.630784i	$0.782733\pi$
$80$	5.21089	0.582595
$81$	1.00000	0.111111
$82$	1.25316	0.138388
$83$	8.11111	0.890309	0.445155	−	0.895454i	$-0.353149\pi$
$83$	8.11111	0.890309	0.445155	+	0.895454i	$0.353149\pi$
$84$	0	0
$85$	−11.6518	−1.26382
$86$	−5.08276	−0.548088
$87$	−7.79558	−0.835774
$88$	−14.7455	−1.57187
$89$	−10.4911	−1.11206	−0.556029	−	0.831163i	$-0.687676\pi$
$89$	−10.4911	−1.11206	−0.556029	+	0.831163i	$0.687676\pi$
$90$	2.20889	0.232837
$91$	0	0
$92$	3.57601	0.372824
$93$	−1.04110	−0.107957
$94$	−1.20771	−0.124566
$95$	14.6548	1.50355
$96$	−2.38465	−0.243382
$97$	−11.2995	−1.14729	−0.573644	−	0.819104i	$-0.694471\pi$
$97$	−11.2995	−1.14729	−0.573644	+	0.819104i	$0.694471\pi$
$98$	0	0
$99$	−4.84306	−0.486746
$100$	0.813234	0.0813234
$101$	16.1294	1.60494	0.802469	−	0.596694i	$-0.203519\pi$
$101$	16.1294	1.60494	0.802469	+	0.596694i	$0.203519\pi$
$102$	−8.28385	−0.820224
$103$	−14.9966	−1.47766	−0.738828	−	0.673894i	$-0.764620\pi$
$103$	−14.9966	−1.47766	−0.738828	+	0.673894i	$0.764620\pi$
$104$	−9.70950	−0.952094
$105$	0	0
$106$	−6.91773	−0.671909
$107$	−14.7499	−1.42593	−0.712963	−	0.701202i	$-0.752647\pi$
$107$	−14.7499	−1.42593	−0.712963	+	0.701202i	$0.752647\pi$
$108$	−0.429590	−0.0413373
$109$	6.63410	0.635432	0.317716	−	0.948186i	$-0.397084\pi$
$109$	6.63410	0.635432	0.317716	+	0.948186i	$0.397084\pi$
$110$	−10.6978	−1.01999
$111$	3.58658	0.340423
$112$	0	0
$113$	−1.35078	−0.127071	−0.0635354	−	0.997980i	$-0.520238\pi$
$113$	−1.35078	−0.127071	−0.0635354	+	0.997980i	$0.520238\pi$
$114$	10.4188	0.975811
$115$	14.6727	1.36824
$116$	3.34890	0.310938
$117$	−3.18902	−0.294825
$118$	11.6300	1.07063
$119$	0	0
$120$	−5.36669	−0.489910
$121$	12.4552	1.13229
$122$	−14.0577	−1.27272
$123$	−1.00000	−0.0901670
$124$	0.447244	0.0401637
$125$	12.1501	1.08673
$126$	0	0
$127$	−9.16265	−0.813054	−0.406527	−	0.913639i	$-0.633260\pi$
$127$	−9.16265	−0.813054	−0.406527	+	0.913639i	$0.633260\pi$
$128$	−6.38495	−0.564355
$129$	4.05595	0.357107
$130$	−7.04419	−0.617816
$131$	5.34838	0.467291	0.233645	−	0.972322i	$-0.424935\pi$
$131$	5.34838	0.467291	0.233645	+	0.972322i	$0.424935\pi$
$132$	2.08053	0.181087
$133$	0	0
$134$	−7.57979	−0.654794
$135$	−1.76265	−0.151705
$136$	20.1264	1.72582
$137$	20.2802	1.73266	0.866329	−	0.499474i	$-0.166473\pi$
$137$	20.2802	1.73266	0.866329	+	0.499474i	$0.166473\pi$
$138$	10.4316	0.887996
$139$	2.75452	0.233635	0.116818	−	0.993153i	$-0.462731\pi$
$139$	2.75452	0.233635	0.116818	+	0.993153i	$0.462731\pi$
$140$	0	0
$141$	0.963735	0.0811611
$142$	−12.4565	−1.04533
$143$	15.4446	1.29154
$144$	−2.95627	−0.246356
$145$	13.7409	1.14112
$146$	4.70928	0.389743
$147$	0	0
$148$	−1.54076	−0.126650
$149$	9.53225	0.780912	0.390456	−	0.920622i	$-0.372317\pi$
$149$	9.53225	0.780912	0.390456	+	0.920622i	$0.372317\pi$
$150$	2.37229	0.193697
$151$	−5.68919	−0.462979	−0.231490	−	0.972837i	$-0.574360\pi$
$151$	−5.68919	−0.462979	−0.231490	+	0.972837i	$0.574360\pi$
$152$	−25.3134	−2.05319
$153$	6.61037	0.534417
$154$	0	0
$155$	1.83509	0.147398
$156$	1.36997	0.109685
$157$	−10.9120	−0.870869	−0.435434	−	0.900221i	$-0.643405\pi$
$157$	−10.9120	−0.870869	−0.435434	+	0.900221i	$0.643405\pi$
$158$	17.2858	1.37518
$159$	5.52023	0.437783
$160$	4.20331	0.332301
$161$	0	0
$162$	−1.25316	−0.0984576
$163$	−2.69969	−0.211456	−0.105728	−	0.994395i	$-0.533717\pi$
$163$	−2.69969	−0.211456	−0.105728	+	0.994395i	$0.533717\pi$
$164$	0.429590	0.0335453
$165$	8.53664	0.664577
$166$	−10.1645	−0.788919
$167$	−10.8810	−0.841998	−0.420999	−	0.907061i	$-0.638320\pi$
$167$	−10.8810	−0.841998	−0.420999	+	0.907061i	$0.638320\pi$
$168$	0	0
$169$	−2.83016	−0.217704
$170$	14.6016	1.11989
$171$	−8.31403	−0.635790
$172$	−1.74240	−0.132856
$173$	−14.5148	−1.10354	−0.551769	−	0.833997i	$-0.686047\pi$
$173$	−14.5148	−1.10354	−0.551769	+	0.833997i	$0.686047\pi$
$174$	9.76911	0.740594
$175$	0	0
$176$	14.3174	1.07921
$177$	−9.28053	−0.697567
$178$	13.1471	0.985415
$179$	14.3925	1.07575	0.537873	−	0.843026i	$-0.319228\pi$
$179$	14.3925	1.07575	0.537873	+	0.843026i	$0.319228\pi$
$180$	0.757219	0.0564397
$181$	−10.9137	−0.811208	−0.405604	−	0.914049i	$-0.632939\pi$
$181$	−10.9137	−0.811208	−0.405604	+	0.914049i	$0.632939\pi$
$182$	0	0
$183$	11.2178	0.829243
$184$	−25.3445	−1.86842
$185$	−6.32190	−0.464795
$186$	1.30466	0.0956623
$187$	−32.0144	−2.34113
$188$	−0.414011	−0.0301948
$189$	0	0
$190$	−18.3648	−1.33232
$191$	2.59146	0.187512	0.0937558	−	0.995595i	$-0.470113\pi$
$191$	2.59146	0.187512	0.0937558	+	0.995595i	$0.470113\pi$
$192$	8.90089	0.642366
$193$	−15.2810	−1.09995	−0.549977	−	0.835180i	$-0.685363\pi$
$193$	−15.2810	−1.09995	−0.549977	+	0.835180i	$0.685363\pi$
$194$	14.1601	1.01663
$195$	5.62114	0.402538
$196$	0	0
$197$	14.9063	1.06203	0.531013	−	0.847363i	$-0.321811\pi$
$197$	14.9063	1.06203	0.531013	+	0.847363i	$0.321811\pi$
$198$	6.06913	0.431314
$199$	−3.57408	−0.253360	−0.126680	−	0.991944i	$-0.540432\pi$
$199$	−3.57408	−0.253360	−0.126680	+	0.991944i	$0.540432\pi$
$200$	−5.76370	−0.407555
$201$	6.04854	0.426631
$202$	−20.2128	−1.42216
$203$	0	0
$204$	−2.83975	−0.198822
$205$	1.76265	0.123109
$206$	18.7931	1.30938
$207$	−8.32423	−0.578574
$208$	9.42761	0.653687
$209$	40.2653	2.78521
$210$	0	0
$211$	1.16912	0.0804857	0.0402428	−	0.999190i	$-0.487187\pi$
$211$	1.16912	0.0804857	0.0402428	+	0.999190i	$0.487187\pi$
$212$	−2.37143	−0.162871
$213$	9.94007	0.681082
$214$	18.4840	1.26354
$215$	−7.14924	−0.487574
$216$	3.04466	0.207163
$217$	0	0
$218$	−8.31359	−0.563067
$219$	−3.75792	−0.253937
$220$	−3.66725	−0.247246
$221$	−21.0806	−1.41803
$222$	−4.49456	−0.301655
$223$	−1.28838	−0.0862763	−0.0431382	−	0.999069i	$-0.513736\pi$
$223$	−1.28838	−0.0862763	−0.0431382	+	0.999069i	$0.513736\pi$
$224$	0	0
$225$	−1.89305	−0.126203
$226$	1.69274	0.112600
$227$	24.1040	1.59984	0.799919	−	0.600108i	$-0.204876\pi$
$227$	24.1040	1.59984	0.799919	+	0.600108i	$0.204876\pi$
$228$	3.57162	0.236537
$229$	0.361413	0.0238828	0.0119414	−	0.999929i	$-0.496199\pi$
$229$	0.361413	0.0238828	0.0119414	+	0.999929i	$0.496199\pi$
$230$	−18.3873	−1.21242
$231$	0	0
$232$	−23.7349	−1.55827
$233$	0.141975	0.00930108	0.00465054	−	0.999989i	$-0.498520\pi$
$233$	0.141975	0.00930108	0.00465054	+	0.999989i	$0.498520\pi$
$234$	3.99635	0.261250
$235$	−1.69873	−0.110813
$236$	3.98682	0.259520
$237$	−13.7937	−0.896000
$238$	0	0
$239$	11.9975	0.776055	0.388027	−	0.921648i	$-0.373157\pi$
$239$	11.9975	0.776055	0.388027	+	0.921648i	$0.373157\pi$
$240$	5.21089	0.336361
$241$	−1.49883	−0.0965478	−0.0482739	−	0.998834i	$-0.515372\pi$
$241$	−1.49883	−0.0965478	−0.0482739	+	0.998834i	$0.515372\pi$
$242$	−15.6084	−1.00335
$243$	1.00000	0.0641500
$244$	−4.81905	−0.308508
$245$	0	0
$246$	1.25316	0.0798986
$247$	26.5136	1.68702
$248$	−3.16979	−0.201282
$249$	8.11111	0.514020
$250$	−15.2260	−0.962975
$251$	6.61735	0.417683	0.208842	−	0.977949i	$-0.433031\pi$
$251$	6.61735	0.417683	0.208842	+	0.977949i	$0.433031\pi$
$252$	0	0
$253$	40.3147	2.53457
$254$	11.4823	0.720462
$255$	−11.6518	−0.729664
$256$	−9.80042	−0.612526
$257$	7.49560	0.467563	0.233781	−	0.972289i	$-0.424890\pi$
$257$	7.49560	0.467563	0.233781	+	0.972289i	$0.424890\pi$
$258$	−5.08276	−0.316439
$259$	0	0
$260$	−2.41479	−0.149759
$261$	−7.79558	−0.482534
$262$	−6.70238	−0.414075
$263$	−18.6115	−1.14764	−0.573818	−	0.818983i	$-0.694538\pi$
$263$	−18.6115	−1.14764	−0.573818	+	0.818983i	$0.694538\pi$
$264$	−14.7455	−0.907522
$265$	−9.73025	−0.597725
$266$	0	0
$267$	−10.4911	−0.642047
$268$	−2.59839	−0.158722
$269$	11.7570	0.716839	0.358419	−	0.933561i	$-0.383316\pi$
$269$	11.7570	0.716839	0.358419	+	0.933561i	$0.383316\pi$
$270$	2.20889	0.134429
$271$	23.0447	1.39987	0.699933	−	0.714208i	$-0.253213\pi$
$271$	23.0447	1.39987	0.699933	+	0.714208i	$0.253213\pi$
$272$	−19.5421	−1.18491
$273$	0	0
$274$	−25.4144	−1.53534
$275$	9.16814	0.552860
$276$	3.57601	0.215250
$277$	29.0686	1.74656	0.873282	−	0.487216i	$-0.161987\pi$
$277$	29.0686	1.74656	0.873282	+	0.487216i	$0.161987\pi$
$278$	−3.45185	−0.207028
$279$	−1.04110	−0.0623288
$280$	0	0
$281$	14.9373	0.891087	0.445543	−	0.895260i	$-0.353010\pi$
$281$	14.9373	0.891087	0.445543	+	0.895260i	$0.353010\pi$
$282$	−1.20771	−0.0719183
$283$	−10.5976	−0.629960	−0.314980	−	0.949098i	$-0.601998\pi$
$283$	−10.5976	−0.629960	−0.314980	+	0.949098i	$0.601998\pi$
$284$	−4.27015	−0.253387
$285$	14.6548	0.868073
$286$	−19.3546	−1.14446
$287$	0	0
$288$	−2.38465	−0.140517
$289$	26.6970	1.57041
$290$	−17.2196	−1.01117
$291$	−11.2995	−0.662388
$292$	1.61437	0.0944736
$293$	32.6469	1.90725	0.953625	−	0.300998i	$-0.0973198\pi$
$293$	32.6469	1.90725	0.953625	+	0.300998i	$0.0973198\pi$
$294$	0	0
$295$	16.3584	0.952421
$296$	10.9199	0.634708
$297$	−4.84306	−0.281023
$298$	−11.9454	−0.691980
$299$	26.5461	1.53520
$300$	0.813234	0.0469521
$301$	0	0
$302$	7.12946	0.410254
$303$	16.1294	0.926611
$304$	24.5785	1.40968
$305$	−19.7731	−1.13220
$306$	−8.28385	−0.473556
$307$	14.5205	0.828728	0.414364	−	0.910111i	$-0.364004\pi$
$307$	14.5205	0.828728	0.414364	+	0.910111i	$0.364004\pi$
$308$	0	0
$309$	−14.9966	−0.853125
$310$	−2.29967	−0.130612
$311$	−3.08406	−0.174881	−0.0874404	−	0.996170i	$-0.527869\pi$
$311$	−3.08406	−0.174881	−0.0874404	+	0.996170i	$0.527869\pi$
$312$	−9.70950	−0.549692
$313$	8.36990	0.473094	0.236547	−	0.971620i	$-0.423984\pi$
$313$	8.36990	0.473094	0.236547	+	0.971620i	$0.423984\pi$
$314$	13.6744	0.771692
$315$	0	0
$316$	5.92565	0.333344
$317$	24.4448	1.37295	0.686477	−	0.727151i	$-0.259156\pi$
$317$	24.4448	1.37295	0.686477	+	0.727151i	$0.259156\pi$
$318$	−6.91773	−0.387927
$319$	37.7545	2.11384
$320$	−15.6892	−0.877053
$321$	−14.7499	−0.823259
$322$	0	0
$323$	−54.9588	−3.05799
$324$	−0.429590	−0.0238661
$325$	6.03697	0.334871
$326$	3.38315	0.187375
$327$	6.63410	0.366867
$328$	−3.04466	−0.168114
$329$	0	0
$330$	−10.6978	−0.588893
$331$	−17.2362	−0.947390	−0.473695	−	0.880689i	$-0.657080\pi$
$331$	−17.2362	−0.947390	−0.473695	+	0.880689i	$0.657080\pi$
$332$	−3.48445	−0.191234
$333$	3.58658	0.196543
$334$	13.6357	0.746110
$335$	−10.6615	−0.582499
$336$	0	0
$337$	−12.2679	−0.668274	−0.334137	−	0.942525i	$-0.608445\pi$
$337$	−12.2679	−0.668274	−0.334137	+	0.942525i	$0.608445\pi$
$338$	3.54664	0.192912
$339$	−1.35078	−0.0733643
$340$	5.00550	0.271461
$341$	5.04209	0.273045
$342$	10.4188	0.563385
$343$	0	0
$344$	12.3490	0.665814
$345$	14.6727	0.789954
$346$	18.1893	0.977864
$347$	−28.5063	−1.53030	−0.765149	−	0.643853i	$-0.777335\pi$
$347$	−28.5063	−1.53030	−0.765149	+	0.643853i	$0.777335\pi$
$348$	3.34890	0.179520
$349$	−25.5334	−1.36677	−0.683385	−	0.730058i	$-0.739493\pi$
$349$	−25.5334	−1.36677	−0.683385	+	0.730058i	$0.739493\pi$
$350$	0	0
$351$	−3.18902	−0.170217
$352$	11.5490	0.615563
$353$	−13.8669	−0.738058	−0.369029	−	0.929418i	$-0.620310\pi$
$353$	−13.8669	−0.738058	−0.369029	+	0.929418i	$0.620310\pi$
$354$	11.6300	0.618127
$355$	−17.5209	−0.929913
$356$	4.50689	0.238865
$357$	0	0
$358$	−18.0361	−0.953237
$359$	31.5191	1.66352	0.831758	−	0.555139i	$-0.187335\pi$
$359$	31.5191	1.66352	0.831758	+	0.555139i	$0.187335\pi$
$360$	−5.36669	−0.282850
$361$	50.1231	2.63806
$362$	13.6766	0.718826
$363$	12.4552	0.653730
$364$	0	0
$365$	6.62392	0.346712
$366$	−14.0577	−0.734807
$367$	9.06523	0.473201	0.236601	−	0.971607i	$-0.423967\pi$
$367$	9.06523	0.473201	0.236601	+	0.971607i	$0.423967\pi$
$368$	24.6087	1.28282
$369$	−1.00000	−0.0520579
$370$	7.92235	0.411864
$371$	0	0
$372$	0.447244	0.0231885
$373$	8.28576	0.429021	0.214510	−	0.976722i	$-0.431184\pi$
$373$	8.28576	0.429021	0.214510	+	0.976722i	$0.431184\pi$
$374$	40.1192	2.07451
$375$	12.1501	0.627427
$376$	2.93425	0.151322
$377$	24.8603	1.28037
$378$	0	0
$379$	−20.9123	−1.07419	−0.537096	−	0.843521i	$-0.680479\pi$
$379$	−20.9123	−1.07419	−0.537096	+	0.843521i	$0.680479\pi$
$380$	−6.29554	−0.322954
$381$	−9.16265	−0.469417
$382$	−3.24752	−0.166157
$383$	−4.72176	−0.241270	−0.120635	−	0.992697i	$-0.538493\pi$
$383$	−4.72176	−0.241270	−0.120635	+	0.992697i	$0.538493\pi$
$384$	−6.38495	−0.325830
$385$	0	0
$386$	19.1496	0.974688
$387$	4.05595	0.206176
$388$	4.85414	0.246432
$389$	27.0332	1.37064	0.685319	−	0.728243i	$-0.259663\pi$
$389$	27.0332	1.37064	0.685319	+	0.728243i	$0.259663\pi$
$390$	−7.04419	−0.356696
$391$	−55.0263	−2.78280
$392$	0	0
$393$	5.34838	0.269790
$394$	−18.6799	−0.941081
$395$	24.3136	1.22335
$396$	2.08053	0.104551
$397$	−28.9049	−1.45070	−0.725348	−	0.688383i	$-0.758321\pi$
$397$	−28.9049	−1.45070	−0.725348	+	0.688383i	$0.758321\pi$
$398$	4.47890	0.224507
$399$	0	0
$400$	5.59637	0.279818
$401$	35.6608	1.78082	0.890408	−	0.455163i	$-0.150419\pi$
$401$	35.6608	1.78082	0.890408	+	0.455163i	$0.150419\pi$
$402$	−7.57979	−0.378045
$403$	3.32008	0.165385
$404$	−6.92904	−0.344733
$405$	−1.76265	−0.0875870
$406$	0	0
$407$	−17.3700	−0.861000
$408$	20.1264	0.996404
$409$	−1.70039	−0.0840788	−0.0420394	−	0.999116i	$-0.513386\pi$
$409$	−1.70039	−0.0840788	−0.0420394	+	0.999116i	$0.513386\pi$
$410$	−2.20889	−0.109089
$411$	20.2802	1.00035
$412$	6.44237	0.317393
$413$	0	0
$414$	10.4316	0.512685
$415$	−14.2971	−0.701816
$416$	7.60469	0.372850
$417$	2.75452	0.134889
$418$	−50.4589	−2.46803
$419$	−12.6493	−0.617957	−0.308978	−	0.951069i	$-0.599987\pi$
$419$	−12.6493	−0.617957	−0.308978	+	0.951069i	$0.599987\pi$
$420$	0	0
$421$	32.5413	1.58597	0.792983	−	0.609244i	$-0.208527\pi$
$421$	32.5413	1.58597	0.792983	+	0.609244i	$0.208527\pi$
$422$	−1.46510	−0.0713198
$423$	0.963735	0.0468584
$424$	16.8072	0.816232
$425$	−12.5138	−0.607006
$426$	−12.4565	−0.603519
$427$	0	0
$428$	6.33640	0.306282
$429$	15.4446	0.745673
$430$	8.95914	0.432048
$431$	−24.0660	−1.15922	−0.579609	−	0.814895i	$-0.696795\pi$
$431$	−24.0660	−1.15922	−0.579609	+	0.814895i	$0.696795\pi$
$432$	−2.95627	−0.142234
$433$	−2.53991	−0.122061	−0.0610303	−	0.998136i	$-0.519439\pi$
$433$	−2.53991	−0.122061	−0.0610303	+	0.998136i	$0.519439\pi$
$434$	0	0
$435$	13.7409	0.658827
$436$	−2.84994	−0.136488
$437$	69.2079	3.31066
$438$	4.70928	0.225018
$439$	−12.6793	−0.605149	−0.302575	−	0.953126i	$-0.597846\pi$
$439$	−12.6793	−0.605149	−0.302575	+	0.953126i	$0.597846\pi$
$440$	25.9912	1.23908
$441$	0	0
$442$	26.4174	1.25655
$443$	10.4222	0.495175	0.247587	−	0.968866i	$-0.420362\pi$
$443$	10.4222	0.495175	0.247587	+	0.968866i	$0.420362\pi$
$444$	−1.54076	−0.0731212
$445$	18.4923	0.876617
$446$	1.61455	0.0764510
$447$	9.53225	0.450860
$448$	0	0
$449$	36.1665	1.70680	0.853401	−	0.521255i	$-0.174536\pi$
$449$	36.1665	1.70680	0.853401	+	0.521255i	$0.174536\pi$
$450$	2.37229	0.111831
$451$	4.84306	0.228051
$452$	0.580282	0.0272942
$453$	−5.68919	−0.267301
$454$	−30.2061	−1.41764
$455$	0	0
$456$	−25.3134	−1.18541
$457$	−3.44773	−0.161278	−0.0806390	−	0.996743i	$-0.525696\pi$
$457$	−3.44773	−0.161278	−0.0806390	+	0.996743i	$0.525696\pi$
$458$	−0.452908	−0.0211630
$459$	6.61037	0.308546
$460$	−6.30326	−0.293891
$461$	−39.2660	−1.82880	−0.914400	−	0.404811i	$-0.867337\pi$
$461$	−39.2660	−1.82880	−0.914400	+	0.404811i	$0.867337\pi$
$462$	0	0
$463$	17.1115	0.795240	0.397620	−	0.917550i	$-0.369836\pi$
$463$	17.1115	0.795240	0.397620	+	0.917550i	$0.369836\pi$
$464$	23.0459	1.06988
$465$	1.83509	0.0851004
$466$	−0.177917	−0.00824185
$467$	−41.0229	−1.89831	−0.949157	−	0.314802i	$-0.898062\pi$
$467$	−41.0229	−1.89831	−0.949157	+	0.314802i	$0.898062\pi$
$468$	1.36997	0.0633269
$469$	0	0
$470$	2.12878	0.0981934
$471$	−10.9120	−0.502796
$472$	−28.2561	−1.30059
$473$	−19.6432	−0.903196
$474$	17.2858	0.793961
$475$	15.7389	0.722148
$476$	0	0
$477$	5.52023	0.252754
$478$	−15.0348	−0.687676
$479$	1.39675	0.0638191	0.0319096	−	0.999491i	$-0.489841\pi$
$479$	1.39675	0.0638191	0.0319096	+	0.999491i	$0.489841\pi$
$480$	4.20331	0.191854
$481$	−11.4377	−0.521513
$482$	1.87827	0.0855527
$483$	0	0
$484$	−5.35064	−0.243211
$485$	19.9171	0.904388
$486$	−1.25316	−0.0568445
$487$	30.7325	1.39262	0.696312	−	0.717739i	$-0.254823\pi$
$487$	30.7325	1.39262	0.696312	+	0.717739i	$0.254823\pi$
$488$	34.1544	1.54610
$489$	−2.69969	−0.122084
$490$	0	0
$491$	23.7792	1.07314	0.536570	−	0.843856i	$-0.319720\pi$
$491$	23.7792	1.07314	0.536570	+	0.843856i	$0.319720\pi$
$492$	0.429590	0.0193674
$493$	−51.5317	−2.32087
$494$	−33.2258	−1.49490
$495$	8.53664	0.383693
$496$	3.07776	0.138196
$497$	0	0
$498$	−10.1645	−0.455483
$499$	−8.09580	−0.362418	−0.181209	−	0.983445i	$-0.558001\pi$
$499$	−8.09580	−0.362418	−0.181209	+	0.983445i	$0.558001\pi$
$500$	−5.21954	−0.233425
$501$	−10.8810	−0.486128
$502$	−8.29260	−0.370117
$503$	−28.9531	−1.29095	−0.645476	−	0.763780i	$-0.723341\pi$
$503$	−28.9531	−1.29095	−0.645476	+	0.763780i	$0.723341\pi$
$504$	0	0
$505$	−28.4306	−1.26515
$506$	−50.5208	−2.24592
$507$	−2.83016	−0.125692
$508$	3.93618	0.174640
$509$	16.0637	0.712009	0.356005	−	0.934484i	$-0.384139\pi$
$509$	16.0637	0.712009	0.356005	+	0.934484i	$0.384139\pi$
$510$	14.6016	0.646569
$511$	0	0
$512$	25.0514	1.10713
$513$	−8.31403	−0.367073
$514$	−9.39319	−0.414316
$515$	26.4338	1.16481
$516$	−1.74240	−0.0767047
$517$	−4.66743	−0.205273
$518$	0	0
$519$	−14.5148	−0.637128
$520$	17.1145	0.750520
$521$	−39.7632	−1.74206	−0.871028	−	0.491234i	$-0.836546\pi$
$521$	−39.7632	−1.74206	−0.871028	+	0.491234i	$0.836546\pi$
$522$	9.76911	0.427582
$523$	22.5014	0.983918	0.491959	−	0.870618i	$-0.336281\pi$
$523$	22.5014	0.983918	0.491959	+	0.870618i	$0.336281\pi$
$524$	−2.29761	−0.100372
$525$	0	0
$526$	23.3232	1.01694
$527$	−6.88203	−0.299786
$528$	14.3174	0.623085
$529$	46.2928	2.01273
$530$	12.1936	0.529655
$531$	−9.28053	−0.402741
$532$	0	0
$533$	3.18902	0.138132
$534$	13.1471	0.568930
$535$	25.9990	1.12403
$536$	18.4158	0.795440
$537$	14.3925	0.621082
$538$	−14.7334	−0.635204
$539$	0	0
$540$	0.757219	0.0325855
$541$	−15.6936	−0.674720	−0.337360	−	0.941376i	$-0.609534\pi$
$541$	−15.6936	−0.674720	−0.337360	+	0.941376i	$0.609534\pi$
$542$	−28.8787	−1.24045
$543$	−10.9137	−0.468351
$544$	−15.7634	−0.675850
$545$	−11.6936	−0.500900
$546$	0	0
$547$	9.27073	0.396388	0.198194	−	0.980163i	$-0.436492\pi$
$547$	9.27073	0.396388	0.198194	+	0.980163i	$0.436492\pi$
$548$	−8.71219	−0.372166
$549$	11.2178	0.478764
$550$	−11.4892	−0.489899
$551$	64.8127	2.76111
$552$	−25.3445	−1.07873
$553$	0	0
$554$	−36.4276	−1.54766
$555$	−6.32190	−0.268350
$556$	−1.18331	−0.0501837
$557$	−5.25651	−0.222725	−0.111363	−	0.993780i	$-0.535522\pi$
$557$	−5.25651	−0.222725	−0.111363	+	0.993780i	$0.535522\pi$
$558$	1.30466	0.0552307
$559$	−12.9345	−0.547071
$560$	0	0
$561$	−32.0144	−1.35165
$562$	−18.7189	−0.789608
$563$	−32.3319	−1.36263	−0.681313	−	0.731992i	$-0.738591\pi$
$563$	−32.3319	−1.36263	−0.681313	+	0.731992i	$0.738591\pi$
$564$	−0.414011	−0.0174330
$565$	2.38096	0.100168
$566$	13.2804	0.558219
$567$	0	0
$568$	30.2642	1.26986
$569$	26.4828	1.11022	0.555109	−	0.831777i	$-0.312676\pi$
$569$	26.4828	1.11022	0.555109	+	0.831777i	$0.312676\pi$
$570$	−18.3648	−0.769215
$571$	−20.4141	−0.854304	−0.427152	−	0.904180i	$-0.640483\pi$
$571$	−20.4141	−0.854304	−0.427152	+	0.904180i	$0.640483\pi$
$572$	−6.63485	−0.277417
$573$	2.59146	0.108260
$574$	0	0
$575$	15.7582	0.657161
$576$	8.90089	0.370870
$577$	−19.1030	−0.795267	−0.397633	−	0.917544i	$-0.630168\pi$
$577$	−19.1030	−0.795267	−0.397633	+	0.917544i	$0.630168\pi$
$578$	−33.4556	−1.39157
$579$	−15.2810	−0.635058
$580$	−5.90296	−0.245107
$581$	0	0
$582$	14.1601	0.586953
$583$	−26.7348	−1.10724
$584$	−11.4416	−0.473457
$585$	5.62114	0.232406
$586$	−40.9117	−1.69005
$587$	40.4928	1.67132	0.835658	−	0.549251i	$-0.185087\pi$
$587$	40.4928	1.67132	0.835658	+	0.549251i	$0.185087\pi$
$588$	0	0
$589$	8.65571	0.356652
$590$	−20.4997	−0.843957
$591$	14.9063	0.613161
$592$	−10.6029	−0.435777
$593$	−25.7064	−1.05563	−0.527817	−	0.849358i	$-0.676989\pi$
$593$	−25.7064	−1.05563	−0.527817	+	0.849358i	$0.676989\pi$
$594$	6.06913	0.249019
$595$	0	0
$596$	−4.09496	−0.167736
$597$	−3.57408	−0.146277
$598$	−33.2666	−1.36037
$599$	−33.6227	−1.37378	−0.686892	−	0.726759i	$-0.741026\pi$
$599$	−33.6227	−1.37378	−0.686892	+	0.726759i	$0.741026\pi$
$600$	−5.76370	−0.235302
$601$	28.5731	1.16552	0.582760	−	0.812644i	$-0.301973\pi$
$601$	28.5731	1.16552	0.582760	+	0.812644i	$0.301973\pi$
$602$	0	0
$603$	6.04854	0.246315
$604$	2.44402	0.0994456
$605$	−21.9543	−0.892567
$606$	−20.2128	−0.821087
$607$	4.85008	0.196859	0.0984293	−	0.995144i	$-0.468618\pi$
$607$	4.85008	0.196859	0.0984293	+	0.995144i	$0.468618\pi$
$608$	19.8260	0.804052
$609$	0	0
$610$	24.7788	1.00327
$611$	−3.07337	−0.124335
$612$	−2.83975	−0.114790
$613$	38.6074	1.55934	0.779668	−	0.626193i	$-0.215388\pi$
$613$	38.6074	1.55934	0.779668	+	0.626193i	$0.215388\pi$
$614$	−18.1965	−0.734351
$615$	1.76265	0.0710771
$616$	0	0
$617$	3.33494	0.134260	0.0671298	−	0.997744i	$-0.478616\pi$
$617$	3.33494	0.134260	0.0671298	+	0.997744i	$0.478616\pi$
$618$	18.7931	0.755969
$619$	12.7195	0.511239	0.255620	−	0.966777i	$-0.417721\pi$
$619$	12.7195	0.511239	0.255620	+	0.966777i	$0.417721\pi$
$620$	−0.788338	−0.0316604
$621$	−8.32423	−0.334040
$622$	3.86482	0.154965
$623$	0	0
$624$	9.42761	0.377406
$625$	−11.9511	−0.478045
$626$	−10.4888	−0.419217
$627$	40.2653	1.60804
$628$	4.68766	0.187058
$629$	23.7086	0.945325
$630$	0	0
$631$	11.7041	0.465934	0.232967	−	0.972485i	$-0.425157\pi$
$631$	11.7041	0.465934	0.232967	+	0.972485i	$0.425157\pi$
$632$	−41.9973	−1.67056
$633$	1.16912	0.0464684
$634$	−30.6332	−1.21660
$635$	16.1506	0.640917
$636$	−2.37143	−0.0940335
$637$	0	0
$638$	−47.3124	−1.87312
$639$	9.94007	0.393223
$640$	11.2545	0.444871
$641$	−26.0873	−1.03039	−0.515193	−	0.857074i	$-0.672280\pi$
$641$	−26.0873	−1.03039	−0.515193	+	0.857074i	$0.672280\pi$
$642$	18.4840	0.729504
$643$	−29.1704	−1.15037	−0.575183	−	0.818025i	$-0.695069\pi$
$643$	−29.1704	−1.15037	−0.575183	+	0.818025i	$0.695069\pi$
$644$	0	0
$645$	−7.14924	−0.281501
$646$	68.8722	2.70974
$647$	−23.9403	−0.941190	−0.470595	−	0.882349i	$-0.655961\pi$
$647$	−23.9403	−0.941190	−0.470595	+	0.882349i	$0.655961\pi$
$648$	3.04466	0.119606
$649$	44.9461	1.76429
$650$	−7.56529	−0.296735
$651$	0	0
$652$	1.15976	0.0454198
$653$	−2.94297	−0.115167	−0.0575837	−	0.998341i	$-0.518340\pi$
$653$	−2.94297	−0.115167	−0.0575837	+	0.998341i	$0.518340\pi$
$654$	−8.31359	−0.325087
$655$	−9.42736	−0.368357
$656$	2.95627	0.115423
$657$	−3.75792	−0.146611
$658$	0	0
$659$	12.3049	0.479330	0.239665	−	0.970856i	$-0.422962\pi$
$659$	12.3049	0.479330	0.239665	+	0.970856i	$0.422962\pi$
$660$	−3.66725	−0.142748
$661$	−14.4635	−0.562565	−0.281283	−	0.959625i	$-0.590760\pi$
$661$	−14.4635	−0.562565	−0.281283	+	0.959625i	$0.590760\pi$
$662$	21.5998	0.839499
$663$	−21.0806	−0.818703
$664$	24.6956	0.958375
$665$	0	0
$666$	−4.49456	−0.174161
$667$	64.8922	2.51264
$668$	4.67437	0.180857
$669$	−1.28838	−0.0498117
$670$	13.3605	0.516163
$671$	−54.3284	−2.09733
$672$	0	0
$673$	15.1510	0.584028	0.292014	−	0.956414i	$-0.405675\pi$
$673$	15.1510	0.584028	0.292014	+	0.956414i	$0.405675\pi$
$674$	15.3736	0.592169
$675$	−1.89305	−0.0728635
$676$	1.21581	0.0467618
$677$	1.19895	0.0460794	0.0230397	−	0.999735i	$-0.492666\pi$
$677$	1.19895	0.0460794	0.0230397	+	0.999735i	$0.492666\pi$
$678$	1.69274	0.0650095
$679$	0	0
$680$	−35.4758	−1.36044
$681$	24.1040	0.923667
$682$	−6.31855	−0.241950
$683$	47.9227	1.83371	0.916855	−	0.399219i	$-0.130719\pi$
$683$	47.9227	1.83371	0.916855	+	0.399219i	$0.130719\pi$
$684$	3.57162	0.136564
$685$	−35.7471	−1.36583
$686$	0	0
$687$	0.361413	0.0137888
$688$	−11.9905	−0.457133
$689$	−17.6041	−0.670663
$690$	−18.3873	−0.699993
$691$	20.1592	0.766891	0.383446	−	0.923563i	$-0.374737\pi$
$691$	20.1592	0.766891	0.383446	+	0.923563i	$0.374737\pi$
$692$	6.23540	0.237034
$693$	0	0
$694$	35.7229	1.35602
$695$	−4.85527	−0.184171
$696$	−23.7349	−0.899670
$697$	−6.61037	−0.250386
$698$	31.9974	1.21112
$699$	0.141975	0.00536998
$700$	0	0
$701$	−23.4825	−0.886921	−0.443461	−	0.896294i	$-0.646249\pi$
$701$	−23.4825	−0.886921	−0.443461	+	0.896294i	$0.646249\pi$
$702$	3.99635	0.150833
$703$	−29.8189	−1.12464
$704$	−43.1075	−1.62468
$705$	−1.69873	−0.0639780
$706$	17.3774	0.654007
$707$	0	0
$708$	3.98682	0.149834
$709$	−37.8630	−1.42197	−0.710987	−	0.703205i	$-0.751752\pi$
$709$	−37.8630	−1.42197	−0.710987	+	0.703205i	$0.751752\pi$
$710$	21.9565	0.824013
$711$	−13.7937	−0.517306
$712$	−31.9420	−1.19708
$713$	8.66633	0.324556
$714$	0	0
$715$	−27.2235	−1.01810
$716$	−6.18287	−0.231065
$717$	11.9975	0.448056
$718$	−39.4985	−1.47407
$719$	11.3752	0.424222	0.212111	−	0.977246i	$-0.431966\pi$
$719$	11.3752	0.424222	0.212111	+	0.977246i	$0.431966\pi$
$720$	5.21089	0.194198
$721$	0	0
$722$	−62.8123	−2.33763
$723$	−1.49883	−0.0557419
$724$	4.68841	0.174243
$725$	14.7574	0.548077
$726$	−15.6084	−0.579282
$727$	16.0406	0.594913	0.297456	−	0.954735i	$-0.403862\pi$
$727$	16.0406	0.594913	0.297456	+	0.954735i	$0.403862\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.30083	−0.307228
$731$	26.8113	0.991654
$732$	−4.81905	−0.178117
$733$	51.7349	1.91087	0.955436	−	0.295197i	$-0.0953853\pi$
$733$	51.7349	1.91087	0.955436	+	0.295197i	$0.0953853\pi$
$734$	−11.3602	−0.419312
$735$	0	0
$736$	19.8504	0.731694
$737$	−29.2934	−1.07904
$738$	1.25316	0.0461295
$739$	−6.31420	−0.232272	−0.116136	−	0.993233i	$-0.537051\pi$
$739$	−6.31420	−0.232272	−0.116136	+	0.993233i	$0.537051\pi$
$740$	2.71582	0.0998357
$741$	26.5136	0.974002
$742$	0	0
$743$	21.6582	0.794562	0.397281	−	0.917697i	$-0.369954\pi$
$743$	21.6582	0.794562	0.397281	+	0.917697i	$0.369954\pi$
$744$	−3.16979	−0.116210
$745$	−16.8021	−0.615580
$746$	−10.3834	−0.380163
$747$	8.11111	0.296770
$748$	13.7531	0.502862
$749$	0	0
$750$	−15.2260	−0.555974
$751$	−44.2185	−1.61355	−0.806777	−	0.590856i	$-0.798790\pi$
$751$	−44.2185	−1.61355	−0.806777	+	0.590856i	$0.798790\pi$
$752$	−2.84906	−0.103895
$753$	6.61735	0.241150
$754$	−31.1539	−1.13456
$755$	10.0281	0.364959
$756$	0	0
$757$	7.39895	0.268919	0.134460	−	0.990919i	$-0.457070\pi$
$757$	7.39895	0.268919	0.134460	+	0.990919i	$0.457070\pi$
$758$	26.2064	0.951861
$759$	40.3147	1.46333
$760$	44.6189	1.61850
$761$	19.8652	0.720112	0.360056	−	0.932931i	$-0.382758\pi$
$761$	19.8652	0.720112	0.360056	+	0.932931i	$0.382758\pi$
$762$	11.4823	0.415959
$763$	0	0
$764$	−1.11327	−0.0402765
$765$	−11.6518	−0.421272
$766$	5.91712	0.213794
$767$	29.5958	1.06864
$768$	−9.80042	−0.353642
$769$	−39.2767	−1.41635	−0.708177	−	0.706034i	$-0.750482\pi$
$769$	−39.2767	−1.41635	−0.708177	+	0.706034i	$0.750482\pi$
$770$	0	0
$771$	7.49560	0.269947
$772$	6.56458	0.236264
$773$	47.1966	1.69754	0.848771	−	0.528760i	$-0.177343\pi$
$773$	47.1966	1.69754	0.848771	+	0.528760i	$0.177343\pi$
$774$	−5.08276	−0.182696
$775$	1.97085	0.0707949
$776$	−34.4031	−1.23500
$777$	0	0
$778$	−33.8769	−1.21455
$779$	8.31403	0.297881
$780$	−2.41479	−0.0864632
$781$	−48.1403	−1.72260
$782$	68.9567	2.46589
$783$	−7.79558	−0.278591
$784$	0	0
$785$	19.2340	0.686491
$786$	−6.70238	−0.239066
$787$	−13.5666	−0.483598	−0.241799	−	0.970326i	$-0.577738\pi$
$787$	−13.5666	−0.483598	−0.241799	+	0.970326i	$0.577738\pi$
$788$	−6.40358	−0.228118
$789$	−18.6115	−0.662588
$790$	−30.4688	−1.08403
$791$	0	0
$792$	−14.7455	−0.523958
$793$	−35.7738	−1.27036
$794$	36.2225	1.28549
$795$	−9.73025	−0.345097
$796$	1.53539	0.0544204
$797$	11.8546	0.419911	0.209955	−	0.977711i	$-0.432668\pi$
$797$	11.8546	0.419911	0.209955	+	0.977711i	$0.432668\pi$
$798$	0	0
$799$	6.37065	0.225377
$800$	4.51425	0.159603
$801$	−10.4911	−0.370686
$802$	−44.6887	−1.57801
$803$	18.1998	0.642258
$804$	−2.59839	−0.0916382
$805$	0	0
$806$	−4.16059	−0.146550
$807$	11.7570	0.413867
$808$	49.1087	1.72764
$809$	15.5888	0.548072	0.274036	−	0.961719i	$-0.411641\pi$
$809$	15.5888	0.548072	0.274036	+	0.961719i	$0.411641\pi$
$810$	2.20889	0.0776124
$811$	18.1848	0.638556	0.319278	−	0.947661i	$-0.396560\pi$
$811$	18.1848	0.638556	0.319278	+	0.947661i	$0.396560\pi$
$812$	0	0
$813$	23.0447	0.808213
$814$	21.7674	0.762947
$815$	4.75863	0.166687
$816$	−19.5421	−0.684109
$817$	−33.7213	−1.17976
$818$	2.13086	0.0745038
$819$	0	0
$820$	−0.757219	−0.0264432
$821$	2.30128	0.0803152	0.0401576	−	0.999193i	$-0.487214\pi$
$821$	2.30128	0.0803152	0.0401576	+	0.999193i	$0.487214\pi$
$822$	−25.4144	−0.886429
$823$	−12.7773	−0.445389	−0.222694	−	0.974888i	$-0.571485\pi$
$823$	−12.7773	−0.445389	−0.222694	+	0.974888i	$0.571485\pi$
$824$	−45.6595	−1.59062
$825$	9.16814	0.319194
$826$	0	0
$827$	−11.2044	−0.389615	−0.194808	−	0.980841i	$-0.562408\pi$
$827$	−11.2044	−0.389615	−0.194808	+	0.980841i	$0.562408\pi$
$828$	3.57601	0.124275
$829$	−39.4628	−1.37060	−0.685300	−	0.728261i	$-0.740329\pi$
$829$	−39.4628	−1.37060	−0.685300	+	0.728261i	$0.740329\pi$
$830$	17.9165	0.621892
$831$	29.0686	1.00838
$832$	−28.3851	−0.984077
$833$	0	0
$834$	−3.45185	−0.119528
$835$	19.1795	0.663733
$836$	−17.2976	−0.598249
$837$	−1.04110	−0.0359856
$838$	15.8515	0.547582
$839$	36.6572	1.26555	0.632773	−	0.774338i	$-0.281917\pi$
$839$	36.6572	1.26555	0.632773	+	0.774338i	$0.281917\pi$
$840$	0	0
$841$	31.7711	1.09555
$842$	−40.7794	−1.40535
$843$	14.9373	0.514469
$844$	−0.502243	−0.0172879
$845$	4.98859	0.171613
$846$	−1.20771	−0.0415221
$847$	0	0
$848$	−16.3193	−0.560407
$849$	−10.5976	−0.363707
$850$	15.6817	0.537879
$851$	−29.8555	−1.02343
$852$	−4.27015	−0.146293
$853$	−31.0819	−1.06422	−0.532112	−	0.846674i	$-0.678601\pi$
$853$	−31.0819	−1.06422	−0.532112	+	0.846674i	$0.678601\pi$
$854$	0	0
$855$	14.6548	0.501182
$856$	−44.9085	−1.53494
$857$	−53.1841	−1.81674	−0.908368	−	0.418173i	$-0.862671\pi$
$857$	−53.1841	−1.81674	−0.908368	+	0.418173i	$0.862671\pi$
$858$	−19.3546	−0.660754
$859$	12.7611	0.435404	0.217702	−	0.976015i	$-0.430144\pi$
$859$	12.7611	0.435404	0.217702	+	0.976015i	$0.430144\pi$
$860$	3.07124	0.104728
$861$	0	0
$862$	30.1585	1.02720
$863$	−9.99019	−0.340070	−0.170035	−	0.985438i	$-0.554388\pi$
$863$	−9.99019	−0.340070	−0.170035	+	0.985438i	$0.554388\pi$
$864$	−2.38465	−0.0811273
$865$	25.5845	0.869900
$866$	3.18292	0.108160
$867$	26.6970	0.906678
$868$	0	0
$869$	66.8039	2.26617
$870$	−17.2196	−0.583798
$871$	−19.2889	−0.653580
$872$	20.1986	0.684011
$873$	−11.2995	−0.382430
$874$	−86.7286	−2.93364
$875$	0	0
$876$	1.61437	0.0545444
$877$	33.4455	1.12938	0.564688	−	0.825305i	$-0.308997\pi$
$877$	33.4455	1.12938	0.564688	+	0.825305i	$0.308997\pi$
$878$	15.8892	0.536234
$879$	32.6469	1.10115
$880$	−25.2366	−0.850727
$881$	−42.8300	−1.44298	−0.721489	−	0.692425i	$-0.756542\pi$
$881$	−42.8300	−1.44298	−0.721489	+	0.692425i	$0.756542\pi$
$882$	0	0
$883$	−35.3926	−1.19106	−0.595529	−	0.803334i	$-0.703057\pi$
$883$	−35.3926	−1.19106	−0.595529	+	0.803334i	$0.703057\pi$
$884$	9.05602	0.304587
$885$	16.3584	0.549881
$886$	−13.0607	−0.438783
$887$	3.59794	0.120807	0.0604035	−	0.998174i	$-0.480761\pi$
$887$	3.59794	0.120807	0.0604035	+	0.998174i	$0.480761\pi$
$888$	10.9199	0.366449
$889$	0	0
$890$	−23.1738	−0.776786
$891$	−4.84306	−0.162249
$892$	0.553475	0.0185317
$893$	−8.01252	−0.268129
$894$	−11.9454	−0.399515
$895$	−25.3690	−0.847992
$896$	0	0
$897$	26.5461	0.886350
$898$	−45.3224	−1.51243
$899$	8.11595	0.270682
$900$	0.813234	0.0271078
$901$	36.4908	1.21568
$902$	−6.06913	−0.202080
$903$	0	0
$904$	−4.11268	−0.136786
$905$	19.2371	0.639462
$906$	7.12946	0.236860
$907$	−17.9810	−0.597050	−0.298525	−	0.954402i	$-0.596495\pi$
$907$	−17.9810	−0.597050	−0.298525	+	0.954402i	$0.596495\pi$
$908$	−10.3548	−0.343637
$909$	16.1294	0.534979
$910$	0	0
$911$	45.4282	1.50510	0.752552	−	0.658533i	$-0.228823\pi$
$911$	45.4282	1.50510	0.752552	+	0.658533i	$0.228823\pi$
$912$	24.5785	0.813877
$913$	−39.2826	−1.30006
$914$	4.32056	0.142911
$915$	−19.7731	−0.653678
$916$	−0.155259	−0.00512991
$917$	0	0
$918$	−8.28385	−0.273408
$919$	17.0040	0.560910	0.280455	−	0.959867i	$-0.409515\pi$
$919$	17.0040	0.560910	0.280455	+	0.959867i	$0.409515\pi$
$920$	44.6736	1.47284
$921$	14.5205	0.478467
$922$	49.2066	1.62053
$923$	−31.6991	−1.04339
$924$	0	0
$925$	−6.78957	−0.223240
$926$	−21.4435	−0.704676
$927$	−14.9966	−0.492552
$928$	18.5897	0.610237
$929$	6.37929	0.209298	0.104649	−	0.994509i	$-0.466628\pi$
$929$	6.37929	0.209298	0.104649	+	0.994509i	$0.466628\pi$
$930$	−2.29967	−0.0754090
$931$	0	0
$932$	−0.0609909	−0.00199782
$933$	−3.08406	−0.100967
$934$	51.4083	1.68213
$935$	56.4304	1.84547
$936$	−9.70950	−0.317365
$937$	−25.1791	−0.822565	−0.411282	−	0.911508i	$-0.634919\pi$
$937$	−25.1791	−0.822565	−0.411282	+	0.911508i	$0.634919\pi$
$938$	0	0
$939$	8.36990	0.273141
$940$	0.729758	0.0238021
$941$	23.3195	0.760195	0.380097	−	0.924946i	$-0.375890\pi$
$941$	23.3195	0.760195	0.380097	+	0.924946i	$0.375890\pi$
$942$	13.6744	0.445537
$943$	8.32423	0.271074
$944$	27.4358	0.892958
$945$	0	0
$946$	24.6161	0.800338
$947$	31.0089	1.00765	0.503827	−	0.863805i	$-0.331925\pi$
$947$	31.0089	1.00765	0.503827	+	0.863805i	$0.331925\pi$
$948$	5.92565	0.192456
$949$	11.9841	0.389020
$950$	−19.7233	−0.639909
$951$	24.4448	0.792676
$952$	0	0
$953$	32.2352	1.04420	0.522101	−	0.852884i	$-0.325149\pi$
$953$	32.2352	1.04420	0.522101	+	0.852884i	$0.325149\pi$
$954$	−6.91773	−0.223970
$955$	−4.56785	−0.147812
$956$	−5.15401	−0.166693
$957$	37.7545	1.22043
$958$	−1.75035	−0.0565513
$959$	0	0
$960$	−15.6892	−0.506367
$961$	−29.9161	−0.965036
$962$	14.3332	0.462122
$963$	−14.7499	−0.475309
$964$	0.643880	0.0207380
$965$	26.9352	0.867075
$966$	0	0
$967$	40.3185	1.29656	0.648279	−	0.761403i	$-0.275489\pi$
$967$	40.3185	1.29656	0.648279	+	0.761403i	$0.275489\pi$
$968$	37.9220	1.21886
$969$	−54.9588	−1.76553
$970$	−24.9593	−0.801395
$971$	32.0847	1.02965	0.514824	−	0.857296i	$-0.327857\pi$
$971$	32.0847	1.02965	0.514824	+	0.857296i	$0.327857\pi$
$972$	−0.429590	−0.0137791
$973$	0	0
$974$	−38.5128	−1.23403
$975$	6.03697	0.193338
$976$	−33.1628	−1.06152
$977$	−57.6281	−1.84369	−0.921844	−	0.387562i	$-0.873317\pi$
$977$	−57.6281	−1.84369	−0.921844	+	0.387562i	$0.873317\pi$
$978$	3.38315	0.108181
$979$	50.8092	1.62387
$980$	0	0
$981$	6.63410	0.211811
$982$	−29.7991	−0.950929
$983$	−3.19824	−0.102008	−0.0510040	−	0.998698i	$-0.516242\pi$
$983$	−3.19824	−0.102008	−0.0510040	+	0.998698i	$0.516242\pi$
$984$	−3.04466	−0.0970604
$985$	−26.2746	−0.837178
$986$	64.5775	2.05657
$987$	0	0
$988$	−11.3900	−0.362363
$989$	−33.7627	−1.07359
$990$	−10.6978	−0.339998
$991$	59.2649	1.88261	0.941306	−	0.337553i	$-0.109599\pi$
$991$	59.2649	1.88261	0.941306	+	0.337553i	$0.109599\pi$
$992$	2.48265	0.0788241
$993$	−17.2362	−0.546976
$994$	0	0
$995$	6.29987	0.199719
$996$	−3.48445	−0.110409
$997$	−37.9055	−1.20048	−0.600239	−	0.799820i	$-0.704928\pi$
$997$	−37.9055	−1.20048	−0.600239	+	0.799820i	$0.704928\pi$
$998$	10.1453	0.321145
$999$	3.58658	0.113474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.7	yes	24
7.6	odd	2		6027.2.a.bn.1.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.7	✓	24	7.6	odd	2
6027.2.a.bo.1.7	yes	24	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.25316 q^{2} +1.00000 q^{3} -0.429590 q^{4} -1.76265 q^{5} -1.25316 q^{6} +3.04466 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.25316 q^{2} +1.00000 q^{3} -0.429590 q^{4} -1.76265 q^{5} -1.25316 q^{6} +3.04466 q^{8} +1.00000 q^{9} +2.20889 q^{10} -4.84306 q^{11} -0.429590 q^{12} -3.18902 q^{13} -1.76265 q^{15} -2.95627 q^{16} +6.61037 q^{17} -1.25316 q^{18} -8.31403 q^{19} +0.757219 q^{20} +6.06913 q^{22} -8.32423 q^{23} +3.04466 q^{24} -1.89305 q^{25} +3.99635 q^{26} +1.00000 q^{27} -7.79558 q^{29} +2.20889 q^{30} -1.04110 q^{31} -2.38465 q^{32} -4.84306 q^{33} -8.28385 q^{34} -0.429590 q^{36} +3.58658 q^{37} +10.4188 q^{38} -3.18902 q^{39} -5.36669 q^{40} -1.00000 q^{41} +4.05595 q^{43} +2.08053 q^{44} -1.76265 q^{45} +10.4316 q^{46} +0.963735 q^{47} -2.95627 q^{48} +2.37229 q^{50} +6.61037 q^{51} +1.36997 q^{52} +5.52023 q^{53} -1.25316 q^{54} +8.53664 q^{55} -8.31403 q^{57} +9.76911 q^{58} -9.28053 q^{59} +0.757219 q^{60} +11.2178 q^{61} +1.30466 q^{62} +8.90089 q^{64} +5.62114 q^{65} +6.06913 q^{66} +6.04854 q^{67} -2.83975 q^{68} -8.32423 q^{69} +9.94007 q^{71} +3.04466 q^{72} -3.75792 q^{73} -4.49456 q^{74} -1.89305 q^{75} +3.57162 q^{76} +3.99635 q^{78} -13.7937 q^{79} +5.21089 q^{80} +1.00000 q^{81} +1.25316 q^{82} +8.11111 q^{83} -11.6518 q^{85} -5.08276 q^{86} -7.79558 q^{87} -14.7455 q^{88} -10.4911 q^{89} +2.20889 q^{90} +3.57601 q^{92} -1.04110 q^{93} -1.20771 q^{94} +14.6548 q^{95} -2.38465 q^{96} -11.2995 q^{97} -4.84306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more