LMFDB - Embedded newform 6027.2.a.bk.1.9

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:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.712717$ of defining polynomial
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)

$f(q)$	$=$	$q+0.712717 q^{2} +1.00000 q^{3} -1.49203 q^{4} -0.415066 q^{5} +0.712717 q^{6} -2.48883 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.712717 q^{2} +1.00000 q^{3} -1.49203 q^{4} -0.415066 q^{5} +0.712717 q^{6} -2.48883 q^{8} +1.00000 q^{9} -0.295824 q^{10} +2.75935 q^{11} -1.49203 q^{12} -4.20250 q^{13} -0.415066 q^{15} +1.21024 q^{16} +4.39412 q^{17} +0.712717 q^{18} -1.26769 q^{19} +0.619292 q^{20} +1.96663 q^{22} +4.53011 q^{23} -2.48883 q^{24} -4.82772 q^{25} -2.99519 q^{26} +1.00000 q^{27} -5.42809 q^{29} -0.295824 q^{30} -8.86379 q^{31} +5.84022 q^{32} +2.75935 q^{33} +3.13176 q^{34} -1.49203 q^{36} -2.60043 q^{37} -0.903505 q^{38} -4.20250 q^{39} +1.03303 q^{40} -1.00000 q^{41} +4.38379 q^{43} -4.11704 q^{44} -0.415066 q^{45} +3.22869 q^{46} +10.9478 q^{47} +1.21024 q^{48} -3.44080 q^{50} +4.39412 q^{51} +6.27028 q^{52} -2.30090 q^{53} +0.712717 q^{54} -1.14531 q^{55} -1.26769 q^{57} -3.86869 q^{58} -1.43254 q^{59} +0.619292 q^{60} -12.2775 q^{61} -6.31737 q^{62} +1.74195 q^{64} +1.74431 q^{65} +1.96663 q^{66} -1.10634 q^{67} -6.55618 q^{68} +4.53011 q^{69} +2.83634 q^{71} -2.48883 q^{72} -3.91272 q^{73} -1.85337 q^{74} -4.82772 q^{75} +1.89144 q^{76} -2.99519 q^{78} -15.3997 q^{79} -0.502327 q^{80} +1.00000 q^{81} -0.712717 q^{82} +4.04351 q^{83} -1.82385 q^{85} +3.12440 q^{86} -5.42809 q^{87} -6.86756 q^{88} +1.02847 q^{89} -0.295824 q^{90} -6.75908 q^{92} -8.86379 q^{93} +7.80271 q^{94} +0.526175 q^{95} +5.84022 q^{96} +7.88278 q^{97} +2.75935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * 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 $

$2$	0.712717	0.503967	0.251983	−	0.967732i	$-0.418917\pi$
$2$	0.712717	0.503967	0.251983	+	0.967732i	$0.418917\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.49203	−0.746017
$5$	−0.415066	−0.185623	−0.0928115	−	0.995684i	$-0.529585\pi$
$5$	−0.415066	−0.185623	−0.0928115	+	0.995684i	$0.529585\pi$
$6$	0.712717	0.290965
$7$	0	0
$7$	0	0
$8$	−2.48883	−0.879935
$9$	1.00000	0.333333
$10$	−0.295824	−0.0935479
$11$	2.75935	0.831975	0.415988	−	0.909370i	$-0.363436\pi$
$11$	2.75935	0.831975	0.415988	+	0.909370i	$0.363436\pi$
$12$	−1.49203	−0.430713
$13$	−4.20250	−1.16556	−0.582782	−	0.812628i	$-0.698036\pi$
$13$	−4.20250	−1.16556	−0.582782	+	0.812628i	$0.698036\pi$
$14$	0	0
$15$	−0.415066	−0.107169
$16$	1.21024	0.302559
$17$	4.39412	1.06573	0.532865	−	0.846200i	$-0.321115\pi$
$17$	4.39412	1.06573	0.532865	+	0.846200i	$0.321115\pi$
$18$	0.712717	0.167989
$19$	−1.26769	−0.290828	−0.145414	−	0.989371i	$-0.546451\pi$
$19$	−1.26769	−0.290828	−0.145414	+	0.989371i	$0.546451\pi$
$20$	0.619292	0.138478
$21$	0	0
$22$	1.96663	0.419288
$23$	4.53011	0.944594	0.472297	−	0.881440i	$-0.343425\pi$
$23$	4.53011	0.944594	0.472297	+	0.881440i	$0.343425\pi$
$24$	−2.48883	−0.508031
$25$	−4.82772	−0.965544
$26$	−2.99519	−0.587406
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.42809	−1.00797	−0.503985	−	0.863712i	$-0.668133\pi$
$29$	−5.42809	−1.00797	−0.503985	+	0.863712i	$0.668133\pi$
$30$	−0.295824	−0.0540099
$31$	−8.86379	−1.59198	−0.795992	−	0.605307i	$-0.793050\pi$
$31$	−8.86379	−1.59198	−0.795992	+	0.605307i	$0.793050\pi$
$32$	5.84022	1.03241
$33$	2.75935	0.480341
$34$	3.13176	0.537093
$35$	0	0
$36$	−1.49203	−0.248672
$37$	−2.60043	−0.427508	−0.213754	−	0.976887i	$-0.568569\pi$
$37$	−2.60043	−0.427508	−0.213754	+	0.976887i	$0.568569\pi$
$38$	−0.903505	−0.146568
$39$	−4.20250	−0.672939
$40$	1.03303	0.163336
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	4.38379	0.668522	0.334261	−	0.942480i	$-0.391513\pi$
$43$	4.38379	0.668522	0.334261	+	0.942480i	$0.391513\pi$
$44$	−4.11704	−0.620668
$45$	−0.415066	−0.0618743
$46$	3.22869	0.476044
$47$	10.9478	1.59691	0.798453	−	0.602057i	$-0.205652\pi$
$47$	10.9478	1.59691	0.798453	+	0.602057i	$0.205652\pi$
$48$	1.21024	0.174683
$49$	0	0
$50$	−3.44080	−0.486602
$51$	4.39412	0.615300
$52$	6.27028	0.869531
$53$	−2.30090	−0.316053	−0.158027	−	0.987435i	$-0.550513\pi$
$53$	−2.30090	−0.316053	−0.158027	+	0.987435i	$0.550513\pi$
$54$	0.712717	0.0969885
$55$	−1.14531	−0.154434
$56$	0	0
$57$	−1.26769	−0.167910
$58$	−3.86869	−0.507984
$59$	−1.43254	−0.186501	−0.0932506	−	0.995643i	$-0.529726\pi$
$59$	−1.43254	−0.186501	−0.0932506	+	0.995643i	$0.529726\pi$
$60$	0.619292	0.0799503
$61$	−12.2775	−1.57197	−0.785986	−	0.618245i	$-0.787844\pi$
$61$	−12.2775	−1.57197	−0.785986	+	0.618245i	$0.787844\pi$
$62$	−6.31737	−0.802307
$63$	0	0
$64$	1.74195	0.217744
$65$	1.74431	0.216356
$66$	1.96663	0.242076
$67$	−1.10634	−0.135161	−0.0675806	−	0.997714i	$-0.521528\pi$
$67$	−1.10634	−0.135161	−0.0675806	+	0.997714i	$0.521528\pi$
$68$	−6.55618	−0.795054
$69$	4.53011	0.545361
$70$	0	0
$71$	2.83634	0.336611	0.168306	−	0.985735i	$-0.446170\pi$
$71$	2.83634	0.336611	0.168306	+	0.985735i	$0.446170\pi$
$72$	−2.48883	−0.293312
$73$	−3.91272	−0.457949	−0.228975	−	0.973432i	$-0.573537\pi$
$73$	−3.91272	−0.457949	−0.228975	+	0.973432i	$0.573537\pi$
$74$	−1.85337	−0.215450
$75$	−4.82772	−0.557457
$76$	1.89144	0.216963
$77$	0	0
$78$	−2.99519	−0.339139
$79$	−15.3997	−1.73260	−0.866298	−	0.499527i	$-0.833507\pi$
$79$	−15.3997	−1.73260	−0.866298	+	0.499527i	$0.833507\pi$
$80$	−0.502327	−0.0561619
$81$	1.00000	0.111111
$82$	−0.712717	−0.0787064
$83$	4.04351	0.443833	0.221916	−	0.975066i	$-0.428769\pi$
$83$	4.04351	0.443833	0.221916	+	0.975066i	$0.428769\pi$
$84$	0	0
$85$	−1.82385	−0.197824
$86$	3.12440	0.336913
$87$	−5.42809	−0.581952
$88$	−6.86756	−0.732084
$89$	1.02847	0.109018	0.0545090	−	0.998513i	$-0.482641\pi$
$89$	1.02847	0.109018	0.0545090	+	0.998513i	$0.482641\pi$
$90$	−0.295824	−0.0311826
$91$	0	0
$92$	−6.75908	−0.704683
$93$	−8.86379	−0.919132
$94$	7.80271	0.804788
$95$	0.526175	0.0539844
$96$	5.84022	0.596065
$97$	7.88278	0.800375	0.400187	−	0.916433i	$-0.368945\pi$
$97$	7.88278	0.800375	0.400187	+	0.916433i	$0.368945\pi$
$98$	0	0
$99$	2.75935	0.277325
$100$	7.20313	0.720313
$101$	8.38909	0.834746	0.417373	−	0.908735i	$-0.362951\pi$
$101$	8.38909	0.834746	0.417373	+	0.908735i	$0.362951\pi$
$102$	3.13176	0.310091
$103$	−17.2901	−1.70365	−0.851823	−	0.523830i	$-0.824503\pi$
$103$	−17.2901	−1.70365	−0.851823	+	0.523830i	$0.824503\pi$
$104$	10.4593	1.02562
$105$	0	0
$106$	−1.63989	−0.159281
$107$	−9.58485	−0.926602	−0.463301	−	0.886201i	$-0.653335\pi$
$107$	−9.58485	−0.926602	−0.463301	+	0.886201i	$0.653335\pi$
$108$	−1.49203	−0.143571
$109$	−0.616655	−0.0590648	−0.0295324	−	0.999564i	$-0.509402\pi$
$109$	−0.616655	−0.0590648	−0.0295324	+	0.999564i	$0.509402\pi$
$110$	−0.816283	−0.0778295
$111$	−2.60043	−0.246822
$112$	0	0
$113$	14.7844	1.39080	0.695401	−	0.718622i	$-0.255227\pi$
$113$	14.7844	1.39080	0.695401	+	0.718622i	$0.255227\pi$
$114$	−0.903505	−0.0846210
$115$	−1.88029	−0.175338
$116$	8.09889	0.751963
$117$	−4.20250	−0.388521
$118$	−1.02100	−0.0939904
$119$	0	0
$120$	1.03303	0.0943022
$121$	−3.38599	−0.307817
$122$	−8.75037	−0.792222
$123$	−1.00000	−0.0901670
$124$	13.2251	1.18765
$125$	4.07915	0.364850
$126$	0	0
$127$	17.0528	1.51319	0.756594	−	0.653885i	$-0.226862\pi$
$127$	17.0528	1.51319	0.756594	+	0.653885i	$0.226862\pi$
$128$	−10.4389	−0.922679
$129$	4.38379	0.385972
$130$	1.24320	0.109036
$131$	−22.2167	−1.94108	−0.970540	−	0.240939i	$-0.922544\pi$
$131$	−22.2167	−1.94108	−0.970540	+	0.240939i	$0.922544\pi$
$132$	−4.11704	−0.358343
$133$	0	0
$134$	−0.788509	−0.0681168
$135$	−0.415066	−0.0357232
$136$	−10.9362	−0.937774
$137$	8.05455	0.688147	0.344073	−	0.938943i	$-0.388193\pi$
$137$	8.05455	0.688147	0.344073	+	0.938943i	$0.388193\pi$
$138$	3.22869	0.274844
$139$	−22.4539	−1.90451	−0.952257	−	0.305299i	$-0.901244\pi$
$139$	−22.4539	−1.90451	−0.952257	+	0.305299i	$0.901244\pi$
$140$	0	0
$141$	10.9478	0.921974
$142$	2.02150	0.169641
$143$	−11.5962	−0.969721
$144$	1.21024	0.100853
$145$	2.25301	0.187103
$146$	−2.78866	−0.230791
$147$	0	0
$148$	3.87993	0.318929
$149$	−5.09508	−0.417405	−0.208702	−	0.977979i	$-0.566924\pi$
$149$	−5.09508	−0.417405	−0.208702	+	0.977979i	$0.566924\pi$
$150$	−3.44080	−0.280940
$151$	−17.6500	−1.43634	−0.718168	−	0.695870i	$-0.755019\pi$
$151$	−17.6500	−1.43634	−0.718168	+	0.695870i	$0.755019\pi$
$152$	3.15507	0.255910
$153$	4.39412	0.355244
$154$	0	0
$155$	3.67906	0.295509
$156$	6.27028	0.502024
$157$	5.78121	0.461391	0.230695	−	0.973026i	$-0.425900\pi$
$157$	5.78121	0.461391	0.230695	+	0.973026i	$0.425900\pi$
$158$	−10.9756	−0.873172
$159$	−2.30090	−0.182474
$160$	−2.42407	−0.191640
$161$	0	0
$162$	0.712717	0.0559963
$163$	−0.157705	−0.0123524	−0.00617621	−	0.999981i	$-0.501966\pi$
$163$	−0.157705	−0.0123524	−0.00617621	+	0.999981i	$0.501966\pi$
$164$	1.49203	0.116508
$165$	−1.14531	−0.0891623
$166$	2.88188	0.223677
$167$	−22.1528	−1.71424	−0.857118	−	0.515120i	$-0.827747\pi$
$167$	−22.1528	−1.71424	−0.857118	+	0.515120i	$0.827747\pi$
$168$	0	0
$169$	4.66102	0.358540
$170$	−1.29989	−0.0996969
$171$	−1.26769	−0.0969428
$172$	−6.54077	−0.498729
$173$	−18.2812	−1.38989	−0.694947	−	0.719061i	$-0.744572\pi$
$173$	−18.2812	−1.38989	−0.694947	+	0.719061i	$0.744572\pi$
$174$	−3.86869	−0.293285
$175$	0	0
$176$	3.33946	0.251722
$177$	−1.43254	−0.107677
$178$	0.733010	0.0549414
$179$	−19.7583	−1.47680	−0.738402	−	0.674361i	$-0.764419\pi$
$179$	−19.7583	−1.47680	−0.738402	+	0.674361i	$0.764419\pi$
$180$	0.619292	0.0461593
$181$	−13.0870	−0.972748	−0.486374	−	0.873751i	$-0.661681\pi$
$181$	−13.0870	−0.972748	−0.486374	+	0.873751i	$0.661681\pi$
$182$	0	0
$183$	−12.2775	−0.907578
$184$	−11.2747	−0.831181
$185$	1.07935	0.0793554
$186$	−6.31737	−0.463212
$187$	12.1249	0.886661
$188$	−16.3345	−1.19132
$189$	0	0
$190$	0.375014	0.0272064
$191$	−22.8221	−1.65135	−0.825675	−	0.564146i	$-0.809205\pi$
$191$	−22.8221	−1.65135	−0.825675	+	0.564146i	$0.809205\pi$
$192$	1.74195	0.125715
$193$	13.0794	0.941472	0.470736	−	0.882274i	$-0.343988\pi$
$193$	13.0794	0.941472	0.470736	+	0.882274i	$0.343988\pi$
$194$	5.61819	0.403362
$195$	1.74431	0.124913
$196$	0	0
$197$	−0.844299	−0.0601538	−0.0300769	−	0.999548i	$-0.509575\pi$
$197$	−0.844299	−0.0601538	−0.0300769	+	0.999548i	$0.509575\pi$
$198$	1.96663	0.139763
$199$	−8.12795	−0.576175	−0.288088	−	0.957604i	$-0.593019\pi$
$199$	−8.12795	−0.576175	−0.288088	+	0.957604i	$0.593019\pi$
$200$	12.0154	0.849616
$201$	−1.10634	−0.0780353
$202$	5.97905	0.420684
$203$	0	0
$204$	−6.55618	−0.459024
$205$	0.415066	0.0289894
$206$	−12.3230	−0.858581
$207$	4.53011	0.314865
$208$	−5.08602	−0.352652
$209$	−3.49800	−0.241962
$210$	0	0
$211$	11.6549	0.802357	0.401178	−	0.916000i	$-0.368601\pi$
$211$	11.6549	0.802357	0.401178	+	0.916000i	$0.368601\pi$
$212$	3.43303	0.235781
$213$	2.83634	0.194342
$214$	−6.83128	−0.466977
$215$	−1.81956	−0.124093
$216$	−2.48883	−0.169344
$217$	0	0
$218$	−0.439500	−0.0297667
$219$	−3.91272	−0.264397
$220$	1.70884	0.115210
$221$	−18.4663	−1.24218
$222$	−1.85337	−0.124390
$223$	−11.7288	−0.785416	−0.392708	−	0.919663i	$-0.628462\pi$
$223$	−11.7288	−0.785416	−0.392708	+	0.919663i	$0.628462\pi$
$224$	0	0
$225$	−4.82772	−0.321848
$226$	10.5371	0.700919
$227$	1.94495	0.129091	0.0645455	−	0.997915i	$-0.479440\pi$
$227$	1.94495	0.129091	0.0645455	+	0.997915i	$0.479440\pi$
$228$	1.89144	0.125264
$229$	−11.2389	−0.742686	−0.371343	−	0.928496i	$-0.621103\pi$
$229$	−11.2389	−0.742686	−0.371343	+	0.928496i	$0.621103\pi$
$230$	−1.34012	−0.0883647
$231$	0	0
$232$	13.5096	0.886949
$233$	13.3117	0.872079	0.436039	−	0.899928i	$-0.356381\pi$
$233$	13.3117	0.872079	0.436039	+	0.899928i	$0.356381\pi$
$234$	−2.99519	−0.195802
$235$	−4.54407	−0.296423
$236$	2.13740	0.139133
$237$	−15.3997	−1.00032
$238$	0	0
$239$	15.1521	0.980106	0.490053	−	0.871693i	$-0.336977\pi$
$239$	15.1521	0.980106	0.490053	+	0.871693i	$0.336977\pi$
$240$	−0.502327	−0.0324251
$241$	−25.5139	−1.64350	−0.821749	−	0.569850i	$-0.807001\pi$
$241$	−25.5139	−1.64350	−0.821749	+	0.569850i	$0.807001\pi$
$242$	−2.41325	−0.155130
$243$	1.00000	0.0641500
$244$	18.3184	1.17272
$245$	0	0
$246$	−0.712717	−0.0454412
$247$	5.32748	0.338979
$248$	22.0605	1.40084
$249$	4.04351	0.256247
$250$	2.90728	0.183872
$251$	−9.41888	−0.594514	−0.297257	−	0.954797i	$-0.596072\pi$
$251$	−9.41888	−0.594514	−0.297257	+	0.954797i	$0.596072\pi$
$252$	0	0
$253$	12.5002	0.785878
$254$	12.1538	0.762597
$255$	−1.82385	−0.114214
$256$	−10.9239	−0.682744
$257$	−1.07261	−0.0669075	−0.0334537	−	0.999440i	$-0.510651\pi$
$257$	−1.07261	−0.0669075	−0.0334537	+	0.999440i	$0.510651\pi$
$258$	3.12440	0.194517
$259$	0	0
$260$	−2.60258	−0.161405
$261$	−5.42809	−0.335990
$262$	−15.8342	−0.978240
$263$	26.2752	1.62020	0.810100	−	0.586292i	$-0.199413\pi$
$263$	26.2752	1.62020	0.810100	+	0.586292i	$0.199413\pi$
$264$	−6.86756	−0.422669
$265$	0.955026	0.0586668
$266$	0	0
$267$	1.02847	0.0629415
$268$	1.65070	0.100833
$269$	−19.8799	−1.21210	−0.606049	−	0.795427i	$-0.707247\pi$
$269$	−19.8799	−1.21210	−0.606049	+	0.795427i	$0.707247\pi$
$270$	−0.295824	−0.0180033
$271$	15.1791	0.922062	0.461031	−	0.887384i	$-0.347480\pi$
$271$	15.1791	0.922062	0.461031	+	0.887384i	$0.347480\pi$
$272$	5.31792	0.322446
$273$	0	0
$274$	5.74062	0.346803
$275$	−13.3214	−0.803309
$276$	−6.75908	−0.406849
$277$	14.8072	0.889681	0.444840	−	0.895610i	$-0.353260\pi$
$277$	14.8072	0.889681	0.444840	+	0.895610i	$0.353260\pi$
$278$	−16.0033	−0.959812
$279$	−8.86379	−0.530661
$280$	0	0
$281$	12.5292	0.747429	0.373715	−	0.927544i	$-0.378084\pi$
$281$	12.5292	0.747429	0.373715	+	0.927544i	$0.378084\pi$
$282$	7.80271	0.464645
$283$	−0.286081	−0.0170058	−0.00850289	−	0.999964i	$-0.502707\pi$
$283$	−0.286081	−0.0170058	−0.00850289	+	0.999964i	$0.502707\pi$
$284$	−4.23191	−0.251118
$285$	0.526175	0.0311679
$286$	−8.26479	−0.488707
$287$	0	0
$288$	5.84022	0.344138
$289$	2.30830	0.135782
$290$	1.60576	0.0942935
$291$	7.88278	0.462096
$292$	5.83792	0.341638
$293$	−16.1124	−0.941299	−0.470650	−	0.882320i	$-0.655980\pi$
$293$	−16.1124	−0.941299	−0.470650	+	0.882320i	$0.655980\pi$
$294$	0	0
$295$	0.594599	0.0346189
$296$	6.47204	0.376180
$297$	2.75935	0.160114
$298$	−3.63135	−0.210358
$299$	−19.0378	−1.10098
$300$	7.20313	0.415873
$301$	0	0
$302$	−12.5794	−0.723866
$303$	8.38909	0.481941
$304$	−1.53421	−0.0879927
$305$	5.09596	0.291794
$306$	3.13176	0.179031
$307$	8.82967	0.503936	0.251968	−	0.967736i	$-0.418922\pi$
$307$	8.82967	0.503936	0.251968	+	0.967736i	$0.418922\pi$
$308$	0	0
$309$	−17.2901	−0.983600
$310$	2.62213	0.148927
$311$	−6.70085	−0.379971	−0.189985	−	0.981787i	$-0.560844\pi$
$311$	−6.70085	−0.379971	−0.189985	+	0.981787i	$0.560844\pi$
$312$	10.4593	0.592143
$313$	−2.34758	−0.132693	−0.0663465	−	0.997797i	$-0.521134\pi$
$313$	−2.34758	−0.132693	−0.0663465	+	0.997797i	$0.521134\pi$
$314$	4.12037	0.232526
$315$	0	0
$316$	22.9768	1.29255
$317$	22.8746	1.28477	0.642384	−	0.766383i	$-0.277945\pi$
$317$	22.8746	1.28477	0.642384	+	0.766383i	$0.277945\pi$
$318$	−1.63989	−0.0919606
$319$	−14.9780	−0.838606
$320$	−0.723024	−0.0404183
$321$	−9.58485	−0.534974
$322$	0	0
$323$	−5.57039	−0.309945
$324$	−1.49203	−0.0828908
$325$	20.2885	1.12540
$326$	−0.112399	−0.00622521
$327$	−0.616655	−0.0341011
$328$	2.48883	0.137423
$329$	0	0
$330$	−0.816283	−0.0449349
$331$	−10.6287	−0.584209	−0.292104	−	0.956386i	$-0.594355\pi$
$331$	−10.6287	−0.584209	−0.292104	+	0.956386i	$0.594355\pi$
$332$	−6.03306	−0.331107
$333$	−2.60043	−0.142503
$334$	−15.7887	−0.863918
$335$	0.459205	0.0250890
$336$	0	0
$337$	−16.0676	−0.875259	−0.437630	−	0.899155i	$-0.644182\pi$
$337$	−16.0676	−0.875259	−0.437630	+	0.899155i	$0.644182\pi$
$338$	3.32199	0.180692
$339$	14.7844	0.802980
$340$	2.72125	0.147580
$341$	−24.4583	−1.32449
$342$	−0.903505	−0.0488560
$343$	0	0
$344$	−10.9105	−0.588256
$345$	−1.88029	−0.101232
$346$	−13.0293	−0.700460
$347$	31.3886	1.68503	0.842515	−	0.538674i	$-0.181074\pi$
$347$	31.3886	1.68503	0.842515	+	0.538674i	$0.181074\pi$
$348$	8.09889	0.434146
$349$	24.1638	1.29346	0.646728	−	0.762720i	$-0.276137\pi$
$349$	24.1638	1.29346	0.646728	+	0.762720i	$0.276137\pi$
$350$	0	0
$351$	−4.20250	−0.224313
$352$	16.1152	0.858943
$353$	26.2342	1.39631	0.698153	−	0.715949i	$-0.254006\pi$
$353$	26.2342	1.39631	0.698153	+	0.715949i	$0.254006\pi$
$354$	−1.02100	−0.0542654
$355$	−1.17727	−0.0624828
$356$	−1.53452	−0.0813293
$357$	0	0
$358$	−14.0821	−0.744260
$359$	20.7642	1.09589	0.547945	−	0.836514i	$-0.315410\pi$
$359$	20.7642	1.09589	0.547945	+	0.836514i	$0.315410\pi$
$360$	1.03303	0.0544454
$361$	−17.3930	−0.915419
$362$	−9.32732	−0.490233
$363$	−3.38599	−0.177718
$364$	0	0
$365$	1.62404	0.0850060
$366$	−8.75037	−0.457389
$367$	−25.4996	−1.33107	−0.665534	−	0.746368i	$-0.731796\pi$
$367$	−25.4996	−1.33107	−0.665534	+	0.746368i	$0.731796\pi$
$368$	5.48250	0.285795
$369$	−1.00000	−0.0520579
$370$	0.769271	0.0399925
$371$	0	0
$372$	13.2251	0.685689
$373$	−24.8633	−1.28737	−0.643685	−	0.765290i	$-0.722595\pi$
$373$	−24.8633	−1.28737	−0.643685	+	0.765290i	$0.722595\pi$
$374$	8.64163	0.446848
$375$	4.07915	0.210646
$376$	−27.2473	−1.40517
$377$	22.8115	1.17485
$378$	0	0
$379$	15.7940	0.811285	0.405642	−	0.914032i	$-0.367048\pi$
$379$	15.7940	0.811285	0.405642	+	0.914032i	$0.367048\pi$
$380$	−0.785072	−0.0402733
$381$	17.0528	0.873639
$382$	−16.2657	−0.832226
$383$	−13.6516	−0.697563	−0.348781	−	0.937204i	$-0.613404\pi$
$383$	−13.6516	−0.697563	−0.348781	+	0.937204i	$0.613404\pi$
$384$	−10.4389	−0.532709
$385$	0	0
$386$	9.32188	0.474471
$387$	4.38379	0.222841
$388$	−11.7614	−0.597093
$389$	−15.8822	−0.805260	−0.402630	−	0.915363i	$-0.631904\pi$
$389$	−15.8822	−0.805260	−0.402630	+	0.915363i	$0.631904\pi$
$390$	1.24320	0.0629520
$391$	19.9059	1.00668
$392$	0	0
$393$	−22.2167	−1.12068
$394$	−0.601746	−0.0303155
$395$	6.39187	0.321610
$396$	−4.11704	−0.206889
$397$	0.506673	0.0254292	0.0127146	−	0.999919i	$-0.495953\pi$
$397$	0.506673	0.0254292	0.0127146	+	0.999919i	$0.495953\pi$
$398$	−5.79293	−0.290373
$399$	0	0
$400$	−5.84268	−0.292134
$401$	−11.8880	−0.593660	−0.296830	−	0.954930i	$-0.595929\pi$
$401$	−11.8880	−0.593660	−0.296830	+	0.954930i	$0.595929\pi$
$402$	−0.788509	−0.0393272
$403$	37.2501	1.85556
$404$	−12.5168	−0.622735
$405$	−0.415066	−0.0206248
$406$	0	0
$407$	−7.17550	−0.355676
$408$	−10.9362	−0.541424
$409$	−27.4784	−1.35872	−0.679359	−	0.733806i	$-0.737742\pi$
$409$	−27.4784	−1.35872	−0.679359	+	0.733806i	$0.737742\pi$
$410$	0.295824	0.0146097
$411$	8.05455	0.397302
$412$	25.7974	1.27095
$413$	0	0
$414$	3.22869	0.158681
$415$	−1.67832	−0.0823856
$416$	−24.5435	−1.20335
$417$	−22.4539	−1.09957
$418$	−2.49309	−0.121941
$419$	3.97916	0.194394	0.0971972	−	0.995265i	$-0.469012\pi$
$419$	3.97916	0.194394	0.0971972	+	0.995265i	$0.469012\pi$
$420$	0	0
$421$	−10.5438	−0.513874	−0.256937	−	0.966428i	$-0.582713\pi$
$421$	−10.5438	−0.513874	−0.256937	+	0.966428i	$0.582713\pi$
$422$	8.30665	0.404361
$423$	10.9478	0.532302
$424$	5.72656	0.278107
$425$	−21.2136	−1.02901
$426$	2.02150	0.0979422
$427$	0	0
$428$	14.3009	0.691261
$429$	−11.5962	−0.559868
$430$	−1.29683	−0.0625389
$431$	−14.7089	−0.708503	−0.354252	−	0.935150i	$-0.615264\pi$
$431$	−14.7089	−0.708503	−0.354252	+	0.935150i	$0.615264\pi$
$432$	1.21024	0.0582275
$433$	−4.20424	−0.202043	−0.101021	−	0.994884i	$-0.532211\pi$
$433$	−4.20424	−0.202043	−0.101021	+	0.994884i	$0.532211\pi$
$434$	0	0
$435$	2.25301	0.108024
$436$	0.920070	0.0440634
$437$	−5.74278	−0.274715
$438$	−2.78866	−0.133247
$439$	9.46738	0.451854	0.225927	−	0.974144i	$-0.427459\pi$
$439$	9.46738	0.451854	0.225927	+	0.974144i	$0.427459\pi$
$440$	2.85049	0.135892
$441$	0	0
$442$	−13.1612	−0.626017
$443$	−14.5808	−0.692753	−0.346377	−	0.938096i	$-0.612588\pi$
$443$	−14.5808	−0.692753	−0.346377	+	0.938096i	$0.612588\pi$
$444$	3.87993	0.184134
$445$	−0.426884	−0.0202362
$446$	−8.35929	−0.395824
$447$	−5.09508	−0.240989
$448$	0	0
$449$	20.0362	0.945567	0.472783	−	0.881179i	$-0.343249\pi$
$449$	20.0362	0.945567	0.472783	+	0.881179i	$0.343249\pi$
$450$	−3.44080	−0.162201
$451$	−2.75935	−0.129933
$452$	−22.0589	−1.03756
$453$	−17.6500	−0.829269
$454$	1.38620	0.0650576
$455$	0	0
$456$	3.15507	0.147750
$457$	27.5760	1.28995	0.644975	−	0.764204i	$-0.276868\pi$
$457$	27.5760	1.28995	0.644975	+	0.764204i	$0.276868\pi$
$458$	−8.01014	−0.374289
$459$	4.39412	0.205100
$460$	2.80546	0.130805
$461$	27.9697	1.30268	0.651340	−	0.758786i	$-0.274207\pi$
$461$	27.9697	1.30268	0.651340	+	0.758786i	$0.274207\pi$
$462$	0	0
$463$	8.96307	0.416549	0.208275	−	0.978070i	$-0.433215\pi$
$463$	8.96307	0.416549	0.208275	+	0.978070i	$0.433215\pi$
$464$	−6.56927	−0.304971
$465$	3.67906	0.170612
$466$	9.48748	0.439499
$467$	20.6797	0.956944	0.478472	−	0.878103i	$-0.341191\pi$
$467$	20.6797	0.956944	0.478472	+	0.878103i	$0.341191\pi$
$468$	6.27028	0.289844
$469$	0	0
$470$	−3.23864	−0.149387
$471$	5.78121	0.266384
$472$	3.56536	0.164109
$473$	12.0964	0.556194
$474$	−10.9756	−0.504126
$475$	6.12006	0.280808
$476$	0	0
$477$	−2.30090	−0.105351
$478$	10.7991	0.493941
$479$	−0.0182962	−0.000835976 0	−0.000417988	−	1.00000i	$-0.500133\pi$
$479$	−0.0182962	−0.000835976 0	−0.000417988		1.00000i	$0.500133\pi$
$480$	−2.42407	−0.110643
$481$	10.9283	0.498289
$482$	−18.1842	−0.828268
$483$	0	0
$484$	5.05202	0.229637
$485$	−3.27187	−0.148568
$486$	0.712717	0.0323295
$487$	26.5955	1.20516	0.602579	−	0.798059i	$-0.294140\pi$
$487$	26.5955	1.20516	0.602579	+	0.798059i	$0.294140\pi$
$488$	30.5566	1.38323
$489$	−0.157705	−0.00713168
$490$	0	0
$491$	−26.4915	−1.19555	−0.597773	−	0.801665i	$-0.703948\pi$
$491$	−26.4915	−1.19555	−0.597773	+	0.801665i	$0.703948\pi$
$492$	1.49203	0.0672661
$493$	−23.8517	−1.07423
$494$	3.79698	0.170834
$495$	−1.14531	−0.0514779
$496$	−10.7273	−0.481669
$497$	0	0
$498$	2.88188	0.129140
$499$	−2.14122	−0.0958541	−0.0479270	−	0.998851i	$-0.515261\pi$
$499$	−2.14122	−0.0958541	−0.0479270	+	0.998851i	$0.515261\pi$
$500$	−6.08623	−0.272185
$501$	−22.1528	−0.989715
$502$	−6.71299	−0.299616
$503$	14.0491	0.626417	0.313209	−	0.949684i	$-0.398596\pi$
$503$	14.0491	0.626417	0.313209	+	0.949684i	$0.398596\pi$
$504$	0	0
$505$	−3.48203	−0.154948
$506$	8.90908	0.396057
$507$	4.66102	0.207003
$508$	−25.4433	−1.12886
$509$	−8.88531	−0.393834	−0.196917	−	0.980420i	$-0.563093\pi$
$509$	−8.88531	−0.393834	−0.196917	+	0.980420i	$0.563093\pi$
$510$	−1.29989	−0.0575600
$511$	0	0
$512$	13.0922	0.578599
$513$	−1.26769	−0.0559699
$514$	−0.764466	−0.0337192
$515$	7.17653	0.316236
$516$	−6.54077	−0.287941
$517$	30.2089	1.32859
$518$	0	0
$519$	−18.2812	−0.802455
$520$	−4.34131	−0.190379
$521$	12.9008	0.565194	0.282597	−	0.959239i	$-0.408804\pi$
$521$	12.9008	0.565194	0.282597	+	0.959239i	$0.408804\pi$
$522$	−3.86869	−0.169328
$523$	−8.93640	−0.390762	−0.195381	−	0.980727i	$-0.562594\pi$
$523$	−8.93640	−0.390762	−0.195381	+	0.980727i	$0.562594\pi$
$524$	33.1481	1.44808
$525$	0	0
$526$	18.7268	0.816527
$527$	−38.9486	−1.69663
$528$	3.33946	0.145332
$529$	−2.47809	−0.107743
$530$	0.680663	0.0295661
$531$	−1.43254	−0.0621671
$532$	0	0
$533$	4.20250	0.182031
$534$	0.733010	0.0317205
$535$	3.97834	0.171999
$536$	2.75350	0.118933
$537$	−19.7583	−0.852633
$538$	−14.1687	−0.610858
$539$	0	0
$540$	0.619292	0.0266501
$541$	30.4024	1.30710	0.653550	−	0.756884i	$-0.273279\pi$
$541$	30.4024	1.30710	0.653550	+	0.756884i	$0.273279\pi$
$542$	10.8184	0.464689
$543$	−13.0870	−0.561616
$544$	25.6626	1.10028
$545$	0.255952	0.0109638
$546$	0	0
$547$	−32.5850	−1.39323	−0.696617	−	0.717443i	$-0.745312\pi$
$547$	−32.5850	−1.39323	−0.696617	+	0.717443i	$0.745312\pi$
$548$	−12.0177	−0.513369
$549$	−12.2775	−0.523990
$550$	−9.49436	−0.404841
$551$	6.88114	0.293146
$552$	−11.2747	−0.479883
$553$	0	0
$554$	10.5534	0.448370
$555$	1.07935	0.0458159
$556$	33.5020	1.42080
$557$	−16.0876	−0.681654	−0.340827	−	0.940126i	$-0.610707\pi$
$557$	−16.0876	−0.681654	−0.340827	+	0.940126i	$0.610707\pi$
$558$	−6.31737	−0.267436
$559$	−18.4229	−0.779206
$560$	0	0
$561$	12.1249	0.511914
$562$	8.92977	0.376680
$563$	33.1478	1.39701	0.698507	−	0.715603i	$-0.253848\pi$
$563$	33.1478	1.39701	0.698507	+	0.715603i	$0.253848\pi$
$564$	−16.3345	−0.687809
$565$	−6.13651	−0.258165
$566$	−0.203895	−0.00857035
$567$	0	0
$568$	−7.05916	−0.296196
$569$	19.8175	0.830791	0.415396	−	0.909641i	$-0.363643\pi$
$569$	19.8175	0.830791	0.415396	+	0.909641i	$0.363643\pi$
$570$	0.375014	0.0157076
$571$	29.5390	1.23617	0.618085	−	0.786112i	$-0.287909\pi$
$571$	29.5390	1.23617	0.618085	+	0.786112i	$0.287909\pi$
$572$	17.3019	0.723428
$573$	−22.8221	−0.953407
$574$	0	0
$575$	−21.8701	−0.912047
$576$	1.74195	0.0725813
$577$	−32.6770	−1.36036	−0.680181	−	0.733044i	$-0.738099\pi$
$577$	−32.6770	−1.36036	−0.680181	+	0.733044i	$0.738099\pi$
$578$	1.64516	0.0684298
$579$	13.0794	0.543559
$580$	−3.36157	−0.139582
$581$	0	0
$582$	5.61819	0.232881
$583$	−6.34900	−0.262949
$584$	9.73811	0.402966
$585$	1.74431	0.0721185
$586$	−11.4836	−0.474384
$587$	40.6133	1.67629	0.838146	−	0.545447i	$-0.183640\pi$
$587$	40.6133	1.67629	0.838146	+	0.545447i	$0.183640\pi$
$588$	0	0
$589$	11.2366	0.462994
$590$	0.423781	0.0174468
$591$	−0.844299	−0.0347298
$592$	−3.14714	−0.129347
$593$	−11.9727	−0.491660	−0.245830	−	0.969313i	$-0.579060\pi$
$593$	−11.9727	−0.491660	−0.245830	+	0.969313i	$0.579060\pi$
$594$	1.96663	0.0806920
$595$	0	0
$596$	7.60203	0.311391
$597$	−8.12795	−0.332655
$598$	−13.5686	−0.554860
$599$	−6.16091	−0.251728	−0.125864	−	0.992048i	$-0.540170\pi$
$599$	−6.16091	−0.251728	−0.125864	+	0.992048i	$0.540170\pi$
$600$	12.0154	0.490526
$601$	33.4325	1.36374	0.681871	−	0.731473i	$-0.261167\pi$
$601$	33.4325	1.36374	0.681871	+	0.731473i	$0.261167\pi$
$602$	0	0
$603$	−1.10634	−0.0450537
$604$	26.3344	1.07153
$605$	1.40541	0.0571380
$606$	5.97905	0.242882
$607$	39.8822	1.61877	0.809385	−	0.587279i	$-0.199801\pi$
$607$	39.8822	1.61877	0.809385	+	0.587279i	$0.199801\pi$
$608$	−7.40360	−0.300256
$609$	0	0
$610$	3.63198	0.147055
$611$	−46.0083	−1.86130
$612$	−6.55618	−0.265018
$613$	9.30534	0.375839	0.187920	−	0.982184i	$-0.439826\pi$
$613$	9.30534	0.375839	0.187920	+	0.982184i	$0.439826\pi$
$614$	6.29306	0.253967
$615$	0.415066	0.0167371
$616$	0	0
$617$	35.3926	1.42485	0.712426	−	0.701747i	$-0.247596\pi$
$617$	35.3926	1.42485	0.712426	+	0.701747i	$0.247596\pi$
$618$	−12.3230	−0.495702
$619$	5.72703	0.230189	0.115094	−	0.993355i	$-0.463283\pi$
$619$	5.72703	0.230189	0.115094	+	0.993355i	$0.463283\pi$
$620$	−5.48928	−0.220455
$621$	4.53011	0.181787
$622$	−4.77581	−0.191493
$623$	0	0
$624$	−5.08602	−0.203604
$625$	22.4455	0.897820
$626$	−1.67316	−0.0668729
$627$	−3.49800	−0.139697
$628$	−8.62576	−0.344205
$629$	−11.4266	−0.455609
$630$	0	0
$631$	2.10310	0.0837233	0.0418616	−	0.999123i	$-0.486671\pi$
$631$	2.10310	0.0837233	0.0418616	+	0.999123i	$0.486671\pi$
$632$	38.3272	1.52457
$633$	11.6549	0.463241
$634$	16.3031	0.647481
$635$	−7.07802	−0.280882
$636$	3.43303	0.136128
$637$	0	0
$638$	−10.6751	−0.422630
$639$	2.83634	0.112204
$640$	4.33284	0.171270
$641$	−7.39557	−0.292107	−0.146054	−	0.989277i	$-0.546657\pi$
$641$	−7.39557	−0.292107	−0.146054	+	0.989277i	$0.546657\pi$
$642$	−6.83128	−0.269609
$643$	−13.9177	−0.548861	−0.274431	−	0.961607i	$-0.588489\pi$
$643$	−13.9177	−0.548861	−0.274431	+	0.961607i	$0.588489\pi$
$644$	0	0
$645$	−1.81956	−0.0716452
$646$	−3.97011	−0.156202
$647$	−22.1622	−0.871287	−0.435643	−	0.900119i	$-0.643479\pi$
$647$	−22.1622	−0.871287	−0.435643	+	0.900119i	$0.643479\pi$
$648$	−2.48883	−0.0977706
$649$	−3.95289	−0.155164
$650$	14.4600	0.567166
$651$	0	0
$652$	0.235302	0.00921512
$653$	−9.10805	−0.356425	−0.178213	−	0.983992i	$-0.557032\pi$
$653$	−9.10805	−0.356425	−0.178213	+	0.983992i	$0.557032\pi$
$654$	−0.439500	−0.0171858
$655$	9.22138	0.360309
$656$	−1.21024	−0.0472518
$657$	−3.91272	−0.152650
$658$	0	0
$659$	−15.1797	−0.591318	−0.295659	−	0.955294i	$-0.595539\pi$
$659$	−15.1797	−0.591318	−0.295659	+	0.955294i	$0.595539\pi$
$660$	1.70884	0.0665167
$661$	19.9463	0.775823	0.387911	−	0.921697i	$-0.373197\pi$
$661$	19.9463	0.775823	0.387911	+	0.921697i	$0.373197\pi$
$662$	−7.57529	−0.294422
$663$	−18.4663	−0.717172
$664$	−10.0636	−0.390544
$665$	0	0
$666$	−1.85337	−0.0718167
$667$	−24.5898	−0.952123
$668$	33.0528	1.27885
$669$	−11.7288	−0.453460
$670$	0.327283	0.0126440
$671$	−33.8779	−1.30784
$672$	0	0
$673$	24.3373	0.938136	0.469068	−	0.883162i	$-0.344590\pi$
$673$	24.3373	0.938136	0.469068	+	0.883162i	$0.344590\pi$
$674$	−11.4517	−0.441102
$675$	−4.82772	−0.185819
$676$	−6.95441	−0.267477
$677$	16.7296	0.642971	0.321485	−	0.946915i	$-0.395818\pi$
$677$	16.7296	0.642971	0.321485	+	0.946915i	$0.395818\pi$
$678$	10.5371	0.404676
$679$	0	0
$680$	4.53925	0.174072
$681$	1.94495	0.0745307
$682$	−17.4318	−0.667500
$683$	−13.7682	−0.526827	−0.263413	−	0.964683i	$-0.584848\pi$
$683$	−13.7682	−0.526827	−0.263413	+	0.964683i	$0.584848\pi$
$684$	1.89144	0.0723210
$685$	−3.34317	−0.127736
$686$	0	0
$687$	−11.2389	−0.428790
$688$	5.30543	0.202268
$689$	9.66955	0.368381
$690$	−1.34012	−0.0510174
$691$	−14.5283	−0.552684	−0.276342	−	0.961059i	$-0.589122\pi$
$691$	−14.5283	−0.552684	−0.276342	+	0.961059i	$0.589122\pi$
$692$	27.2762	1.03688
$693$	0	0
$694$	22.3712	0.849199
$695$	9.31983	0.353521
$696$	13.5096	0.512080
$697$	−4.39412	−0.166439
$698$	17.2219	0.651860
$699$	13.3117	0.503495
$700$	0	0
$701$	41.6703	1.57386	0.786932	−	0.617040i	$-0.211668\pi$
$701$	41.6703	1.57386	0.786932	+	0.617040i	$0.211668\pi$
$702$	−2.99519	−0.113046
$703$	3.29655	0.124332
$704$	4.80665	0.181158
$705$	−4.54407	−0.171140
$706$	18.6976	0.703692
$707$	0	0
$708$	2.13740	0.0803285
$709$	9.18522	0.344958	0.172479	−	0.985013i	$-0.444822\pi$
$709$	9.18522	0.344958	0.172479	+	0.985013i	$0.444822\pi$
$710$	−0.839057	−0.0314892
$711$	−15.3997	−0.577532
$712$	−2.55970	−0.0959287
$713$	−40.1540	−1.50378
$714$	0	0
$715$	4.81317	0.180002
$716$	29.4800	1.10172
$717$	15.1521	0.565864
$718$	14.7990	0.552292
$719$	9.93068	0.370352	0.185176	−	0.982705i	$-0.440714\pi$
$719$	9.93068	0.370352	0.185176	+	0.982705i	$0.440714\pi$
$720$	−0.502327	−0.0187206
$721$	0	0
$722$	−12.3963	−0.461341
$723$	−25.5139	−0.948874
$724$	19.5262	0.725687
$725$	26.2053	0.973240
$726$	−2.41325	−0.0895643
$727$	34.7960	1.29051	0.645256	−	0.763966i	$-0.276751\pi$
$727$	34.7960	1.29051	0.645256	+	0.763966i	$0.276751\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.15748	0.0428402
$731$	19.2629	0.712465
$732$	18.3184	0.677069
$733$	−3.15245	−0.116438	−0.0582192	−	0.998304i	$-0.518542\pi$
$733$	−3.15245	−0.116438	−0.0582192	+	0.998304i	$0.518542\pi$
$734$	−18.1740	−0.670814
$735$	0	0
$736$	26.4569	0.975212
$737$	−3.05278	−0.112451
$738$	−0.712717	−0.0262355
$739$	46.0474	1.69388	0.846941	−	0.531686i	$-0.178441\pi$
$739$	46.0474	1.69388	0.846941	+	0.531686i	$0.178441\pi$
$740$	−1.61043	−0.0592005
$741$	5.32748	0.195710
$742$	0	0
$743$	35.9816	1.32004	0.660019	−	0.751249i	$-0.270548\pi$
$743$	35.9816	1.32004	0.660019	+	0.751249i	$0.270548\pi$
$744$	22.0605	0.808777
$745$	2.11479	0.0774799
$746$	−17.7205	−0.648792
$747$	4.04351	0.147944
$748$	−18.0908	−0.661465
$749$	0	0
$750$	2.90728	0.106159
$751$	−29.6433	−1.08170	−0.540850	−	0.841119i	$-0.681897\pi$
$751$	−29.6433	−1.08170	−0.540850	+	0.841119i	$0.681897\pi$
$752$	13.2495	0.483158
$753$	−9.41888	−0.343243
$754$	16.2582	0.592088
$755$	7.32590	0.266617
$756$	0	0
$757$	16.7775	0.609790	0.304895	−	0.952386i	$-0.401379\pi$
$757$	16.7775	0.609790	0.304895	+	0.952386i	$0.401379\pi$
$758$	11.2567	0.408861
$759$	12.5002	0.453727
$760$	−1.30956	−0.0475028
$761$	23.0227	0.834574	0.417287	−	0.908775i	$-0.362981\pi$
$761$	23.0227	0.834574	0.417287	+	0.908775i	$0.362981\pi$
$762$	12.1538	0.440285
$763$	0	0
$764$	34.0514	1.23194
$765$	−1.82385	−0.0659414
$766$	−9.72971	−0.351549
$767$	6.02026	0.217379
$768$	−10.9239	−0.394182
$769$	−6.17449	−0.222658	−0.111329	−	0.993784i	$-0.535511\pi$
$769$	−6.17449	−0.222658	−0.111329	+	0.993784i	$0.535511\pi$
$770$	0	0
$771$	−1.07261	−0.0386291
$772$	−19.5148	−0.702355
$773$	−37.5482	−1.35051	−0.675257	−	0.737583i	$-0.735967\pi$
$773$	−37.5482	−1.35051	−0.675257	+	0.737583i	$0.735967\pi$
$774$	3.12440	0.112304
$775$	42.7919	1.53713
$776$	−19.6189	−0.704278
$777$	0	0
$778$	−11.3195	−0.405825
$779$	1.26769	0.0454198
$780$	−2.60258	−0.0931872
$781$	7.82644	0.280052
$782$	14.1872	0.507335
$783$	−5.42809	−0.193984
$784$	0	0
$785$	−2.39958	−0.0856447
$786$	−15.8342	−0.564787
$787$	−37.2802	−1.32890	−0.664448	−	0.747335i	$-0.731333\pi$
$787$	−37.2802	−1.32890	−0.664448	+	0.747335i	$0.731333\pi$
$788$	1.25972	0.0448758
$789$	26.2752	0.935422
$790$	4.55559	0.162081
$791$	0	0
$792$	−6.86756	−0.244028
$793$	51.5962	1.83223
$794$	0.361114	0.0128155
$795$	0.955026	0.0338713
$796$	12.1272	0.429837
$797$	−22.0377	−0.780617	−0.390308	−	0.920684i	$-0.627632\pi$
$797$	−22.0377	−0.780617	−0.390308	+	0.920684i	$0.627632\pi$
$798$	0	0
$799$	48.1061	1.70187
$800$	−28.1950	−0.996842
$801$	1.02847	0.0363393
$802$	−8.47280	−0.299185
$803$	−10.7966	−0.381003
$804$	1.65070	0.0582157
$805$	0	0
$806$	26.5488	0.935141
$807$	−19.8799	−0.699806
$808$	−20.8790	−0.734522
$809$	34.8178	1.22413	0.612065	−	0.790807i	$-0.290339\pi$
$809$	34.8178	1.22413	0.612065	+	0.790807i	$0.290339\pi$
$810$	−0.295824	−0.0103942
$811$	9.01482	0.316553	0.158277	−	0.987395i	$-0.449406\pi$
$811$	9.01482	0.316553	0.158277	+	0.987395i	$0.449406\pi$
$812$	0	0
$813$	15.1791	0.532353
$814$	−5.11410	−0.179249
$815$	0.0654580	0.00229289
$816$	5.31792	0.186165
$817$	−5.55730	−0.194425
$818$	−19.5843	−0.684749
$819$	0	0
$820$	−0.619292	−0.0216266
$821$	−15.2878	−0.533547	−0.266774	−	0.963759i	$-0.585958\pi$
$821$	−15.2878	−0.533547	−0.266774	+	0.963759i	$0.585958\pi$
$822$	5.74062	0.200227
$823$	−32.2809	−1.12524	−0.562621	−	0.826715i	$-0.690207\pi$
$823$	−32.2809	−1.12524	−0.562621	+	0.826715i	$0.690207\pi$
$824$	43.0322	1.49910
$825$	−13.3214	−0.463790
$826$	0	0
$827$	−41.5227	−1.44389	−0.721943	−	0.691952i	$-0.756751\pi$
$827$	−41.5227	−1.44389	−0.721943	+	0.691952i	$0.756751\pi$
$828$	−6.75908	−0.234894
$829$	−5.55425	−0.192907	−0.0964535	−	0.995337i	$-0.530750\pi$
$829$	−5.55425	−0.192907	−0.0964535	+	0.995337i	$0.530750\pi$
$830$	−1.19617	−0.0415196
$831$	14.8072	0.513657
$832$	−7.32056	−0.253795
$833$	0	0
$834$	−16.0033	−0.554148
$835$	9.19487	0.318202
$836$	5.21914	0.180508
$837$	−8.86379	−0.306377
$838$	2.83601	0.0979684
$839$	40.4477	1.39641	0.698204	−	0.715899i	$-0.253983\pi$
$839$	40.4477	1.39641	0.698204	+	0.715899i	$0.253983\pi$
$840$	0	0
$841$	0.464135	0.0160046
$842$	−7.51476	−0.258976
$843$	12.5292	0.431528
$844$	−17.3895	−0.598572
$845$	−1.93463	−0.0665533
$846$	7.80271	0.268263
$847$	0	0
$848$	−2.78464	−0.0956248
$849$	−0.286081	−0.00981829
$850$	−15.1193	−0.518587
$851$	−11.7802	−0.403822
$852$	−4.23191	−0.144983
$853$	−16.5141	−0.565431	−0.282715	−	0.959204i	$-0.591235\pi$
$853$	−16.5141	−0.565431	−0.282715	+	0.959204i	$0.591235\pi$
$854$	0	0
$855$	0.526175	0.0179948
$856$	23.8551	0.815350
$857$	−14.7078	−0.502410	−0.251205	−	0.967934i	$-0.580827\pi$
$857$	−14.7078	−0.502410	−0.251205	+	0.967934i	$0.580827\pi$
$858$	−8.26479	−0.282155
$859$	−42.3688	−1.44561	−0.722803	−	0.691055i	$-0.757146\pi$
$859$	−42.3688	−1.44561	−0.722803	+	0.691055i	$0.757146\pi$
$860$	2.71485	0.0925756
$861$	0	0
$862$	−10.4833	−0.357062
$863$	−57.6490	−1.96239	−0.981197	−	0.193009i	$-0.938175\pi$
$863$	−57.6490	−1.96239	−0.981197	+	0.193009i	$0.938175\pi$
$864$	5.84022	0.198688
$865$	7.58790	0.257996
$866$	−2.99643	−0.101823
$867$	2.30830	0.0783939
$868$	0	0
$869$	−42.4930	−1.44148
$870$	1.60576	0.0544404
$871$	4.64940	0.157539
$872$	1.53475	0.0519732
$873$	7.88278	0.266792
$874$	−4.09298	−0.138447
$875$	0	0
$876$	5.83792	0.197245
$877$	−40.9161	−1.38164	−0.690819	−	0.723028i	$-0.742750\pi$
$877$	−40.9161	−1.38164	−0.690819	+	0.723028i	$0.742750\pi$
$878$	6.74757	0.227719
$879$	−16.1124	−0.543459
$880$	−1.38610	−0.0467253
$881$	−4.58413	−0.154443	−0.0772216	−	0.997014i	$-0.524605\pi$
$881$	−4.58413	−0.154443	−0.0772216	+	0.997014i	$0.524605\pi$
$882$	0	0
$883$	−38.8738	−1.30821	−0.654104	−	0.756404i	$-0.726954\pi$
$883$	−38.8738	−1.30821	−0.654104	+	0.756404i	$0.726954\pi$
$884$	27.5524	0.926686
$885$	0.594599	0.0199872
$886$	−10.3920	−0.349125
$887$	8.32382	0.279487	0.139743	−	0.990188i	$-0.455372\pi$
$887$	8.32382	0.279487	0.139743	+	0.990188i	$0.455372\pi$
$888$	6.47204	0.217187
$889$	0	0
$890$	−0.304247	−0.0101984
$891$	2.75935	0.0924417
$892$	17.4997	0.585934
$893$	−13.8785	−0.464426
$894$	−3.63135	−0.121450
$895$	8.20098	0.274129
$896$	0	0
$897$	−19.0378	−0.635654
$898$	14.2801	0.476534
$899$	48.1134	1.60467
$900$	7.20313	0.240104
$901$	−10.1104	−0.336828
$902$	−1.96663	−0.0654818
$903$	0	0
$904$	−36.7960	−1.22382
$905$	5.43196	0.180564
$906$	−12.5794	−0.417924
$907$	28.0918	0.932772	0.466386	−	0.884581i	$-0.345556\pi$
$907$	28.0918	0.932772	0.466386	+	0.884581i	$0.345556\pi$
$908$	−2.90194	−0.0963041
$909$	8.38909	0.278249
$910$	0	0
$911$	−55.7190	−1.84605	−0.923027	−	0.384736i	$-0.874292\pi$
$911$	−55.7190	−1.84605	−0.923027	+	0.384736i	$0.874292\pi$
$912$	−1.53421	−0.0508026
$913$	11.1575	0.369258
$914$	19.6539	0.650092
$915$	5.09596	0.168467
$916$	16.7688	0.554057
$917$	0	0
$918$	3.13176	0.103364
$919$	−12.6642	−0.417752	−0.208876	−	0.977942i	$-0.566981\pi$
$919$	−12.6642	−0.417752	−0.208876	+	0.977942i	$0.566981\pi$
$920$	4.67974	0.154286
$921$	8.82967	0.290948
$922$	19.9345	0.656508
$923$	−11.9197	−0.392342
$924$	0	0
$925$	12.5542	0.412778
$926$	6.38813	0.209927
$927$	−17.2901	−0.567882
$928$	−31.7012	−1.04064
$929$	−38.2432	−1.25472	−0.627359	−	0.778730i	$-0.715864\pi$
$929$	−38.2432	−1.25472	−0.627359	+	0.778730i	$0.715864\pi$
$930$	2.62213	0.0859829
$931$	0	0
$932$	−19.8615	−0.650586
$933$	−6.70085	−0.219376
$934$	14.7388	0.482268
$935$	−5.03264	−0.164585
$936$	10.4593	0.341874
$937$	−49.0781	−1.60331	−0.801656	−	0.597785i	$-0.796048\pi$
$937$	−49.0781	−1.60331	−0.801656	+	0.597785i	$0.796048\pi$
$938$	0	0
$939$	−2.34758	−0.0766103
$940$	6.77991	0.221136
$941$	−31.8341	−1.03776	−0.518882	−	0.854846i	$-0.673651\pi$
$941$	−31.8341	−1.03776	−0.518882	+	0.854846i	$0.673651\pi$
$942$	4.12037	0.134249
$943$	−4.53011	−0.147521
$944$	−1.73372	−0.0564276
$945$	0	0
$946$	8.62132	0.280303
$947$	33.8537	1.10010	0.550049	−	0.835132i	$-0.314609\pi$
$947$	33.8537	1.10010	0.550049	+	0.835132i	$0.314609\pi$
$948$	22.9768	0.746252
$949$	16.4432	0.533770
$950$	4.36187	0.141518
$951$	22.8746	0.741761
$952$	0	0
$953$	−41.1049	−1.33152	−0.665759	−	0.746167i	$-0.731892\pi$
$953$	−41.1049	−1.33152	−0.665759	+	0.746167i	$0.731892\pi$
$954$	−1.63989	−0.0530935
$955$	9.47267	0.306528
$956$	−22.6074	−0.731176
$957$	−14.9780	−0.484170
$958$	−0.0130400	−0.000421304 0
$959$	0	0
$960$	−0.723024	−0.0233355
$961$	47.5668	1.53441
$962$	7.78880	0.251121
$963$	−9.58485	−0.308867
$964$	38.0677	1.22608
$965$	−5.42879	−0.174759
$966$	0	0
$967$	44.3207	1.42526	0.712628	−	0.701542i	$-0.247505\pi$
$967$	44.3207	1.42526	0.712628	+	0.701542i	$0.247505\pi$
$968$	8.42717	0.270859
$969$	−5.57039	−0.178947
$970$	−2.33192	−0.0748733
$971$	−24.4418	−0.784374	−0.392187	−	0.919885i	$-0.628281\pi$
$971$	−24.4418	−0.784374	−0.392187	+	0.919885i	$0.628281\pi$
$972$	−1.49203	−0.0478570
$973$	0	0
$974$	18.9551	0.607360
$975$	20.2885	0.649752
$976$	−14.8587	−0.475614
$977$	15.7803	0.504857	0.252429	−	0.967615i	$-0.418771\pi$
$977$	15.7803	0.504857	0.252429	+	0.967615i	$0.418771\pi$
$978$	−0.112399	−0.00359413
$979$	2.83792	0.0907002
$980$	0	0
$981$	−0.616655	−0.0196883
$982$	−18.8810	−0.602516
$983$	25.3592	0.808832	0.404416	−	0.914575i	$-0.367475\pi$
$983$	25.3592	0.808832	0.404416	+	0.914575i	$0.367475\pi$
$984$	2.48883	0.0793411
$985$	0.350439	0.0111659
$986$	−16.9995	−0.541374
$987$	0	0
$988$	−7.94878	−0.252884
$989$	19.8591	0.631482
$990$	−0.816283	−0.0259432
$991$	−9.51391	−0.302219	−0.151110	−	0.988517i	$-0.548285\pi$
$991$	−9.51391	−0.302219	−0.151110	+	0.988517i	$0.548285\pi$
$992$	−51.7665	−1.64359
$993$	−10.6287	−0.337293
$994$	0	0
$995$	3.37363	0.106951
$996$	−6.03306	−0.191165
$997$	−44.0831	−1.39612	−0.698062	−	0.716037i	$-0.745954\pi$
$997$	−44.0831	−1.39612	−0.698062	+	0.716037i	$0.745954\pi$
$998$	−1.52608	−0.0483073
$999$	−2.60043	−0.0822740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.9		14
7.3	odd	6		861.2.i.g.247.6	✓	28
7.5	odd	6		861.2.i.g.739.6	yes	28
7.6	odd	2		6027.2.a.bj.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.6	✓	28	7.3	odd	6
861.2.i.g.739.6	yes	28	7.5	odd	6
6027.2.a.bj.1.9		14	7.6	odd	2
6027.2.a.bk.1.9		14	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)

\(f(q)\)	\(=\)	\(q+0.712717 q^{2} +1.00000 q^{3} -1.49203 q^{4} -0.415066 q^{5} +0.712717 q^{6} -2.48883 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.712717 q^{2} +1.00000 q^{3} -1.49203 q^{4} -0.415066 q^{5} +0.712717 q^{6} -2.48883 q^{8} +1.00000 q^{9} -0.295824 q^{10} +2.75935 q^{11} -1.49203 q^{12} -4.20250 q^{13} -0.415066 q^{15} +1.21024 q^{16} +4.39412 q^{17} +0.712717 q^{18} -1.26769 q^{19} +0.619292 q^{20} +1.96663 q^{22} +4.53011 q^{23} -2.48883 q^{24} -4.82772 q^{25} -2.99519 q^{26} +1.00000 q^{27} -5.42809 q^{29} -0.295824 q^{30} -8.86379 q^{31} +5.84022 q^{32} +2.75935 q^{33} +3.13176 q^{34} -1.49203 q^{36} -2.60043 q^{37} -0.903505 q^{38} -4.20250 q^{39} +1.03303 q^{40} -1.00000 q^{41} +4.38379 q^{43} -4.11704 q^{44} -0.415066 q^{45} +3.22869 q^{46} +10.9478 q^{47} +1.21024 q^{48} -3.44080 q^{50} +4.39412 q^{51} +6.27028 q^{52} -2.30090 q^{53} +0.712717 q^{54} -1.14531 q^{55} -1.26769 q^{57} -3.86869 q^{58} -1.43254 q^{59} +0.619292 q^{60} -12.2775 q^{61} -6.31737 q^{62} +1.74195 q^{64} +1.74431 q^{65} +1.96663 q^{66} -1.10634 q^{67} -6.55618 q^{68} +4.53011 q^{69} +2.83634 q^{71} -2.48883 q^{72} -3.91272 q^{73} -1.85337 q^{74} -4.82772 q^{75} +1.89144 q^{76} -2.99519 q^{78} -15.3997 q^{79} -0.502327 q^{80} +1.00000 q^{81} -0.712717 q^{82} +4.04351 q^{83} -1.82385 q^{85} +3.12440 q^{86} -5.42809 q^{87} -6.86756 q^{88} +1.02847 q^{89} -0.295824 q^{90} -6.75908 q^{92} -8.86379 q^{93} +7.80271 q^{94} +0.526175 q^{95} +5.84022 q^{96} +7.88278 q^{97} +2.75935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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