LMFDB - Embedded newform 6027.2.a.bo.1.14

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			1.14
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)

$f(q)$	$=$	$q+1.11646 q^{2} +1.00000 q^{3} -0.753512 q^{4} -0.900581 q^{5} +1.11646 q^{6} -3.07419 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.11646 q^{2} +1.00000 q^{3} -0.753512 q^{4} -0.900581 q^{5} +1.11646 q^{6} -3.07419 q^{8} +1.00000 q^{9} -1.00546 q^{10} -4.69451 q^{11} -0.753512 q^{12} +1.15587 q^{13} -0.900581 q^{15} -1.92519 q^{16} +5.04891 q^{17} +1.11646 q^{18} +0.849395 q^{19} +0.678599 q^{20} -5.24124 q^{22} -1.63546 q^{23} -3.07419 q^{24} -4.18895 q^{25} +1.29048 q^{26} +1.00000 q^{27} +7.97364 q^{29} -1.00546 q^{30} +2.94278 q^{31} +3.99898 q^{32} -4.69451 q^{33} +5.63692 q^{34} -0.753512 q^{36} +3.09905 q^{37} +0.948318 q^{38} +1.15587 q^{39} +2.76856 q^{40} -1.00000 q^{41} -3.01389 q^{43} +3.53737 q^{44} -0.900581 q^{45} -1.82593 q^{46} -8.14340 q^{47} -1.92519 q^{48} -4.67681 q^{50} +5.04891 q^{51} -0.870962 q^{52} -8.01568 q^{53} +1.11646 q^{54} +4.22779 q^{55} +0.849395 q^{57} +8.90226 q^{58} -2.60113 q^{59} +0.678599 q^{60} -7.31482 q^{61} +3.28551 q^{62} +8.31510 q^{64} -1.04095 q^{65} -5.24124 q^{66} +0.796475 q^{67} -3.80442 q^{68} -1.63546 q^{69} +10.7265 q^{71} -3.07419 q^{72} +1.76040 q^{73} +3.45997 q^{74} -4.18895 q^{75} -0.640030 q^{76} +1.29048 q^{78} +13.8908 q^{79} +1.73379 q^{80} +1.00000 q^{81} -1.11646 q^{82} +10.3080 q^{83} -4.54695 q^{85} -3.36490 q^{86} +7.97364 q^{87} +14.4318 q^{88} +15.1741 q^{89} -1.00546 q^{90} +1.23234 q^{92} +2.94278 q^{93} -9.09180 q^{94} -0.764949 q^{95} +3.99898 q^{96} -0.878601 q^{97} -4.69451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.11646	0.789458	0.394729	−	0.918798i	$-0.370838\pi$
$2$	1.11646	0.789458	0.394729	+	0.918798i	$0.370838\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.753512	−0.376756
$5$	−0.900581	−0.402752	−0.201376	−	0.979514i	$-0.564541\pi$
$5$	−0.900581	−0.402752	−0.201376	+	0.979514i	$0.564541\pi$
$6$	1.11646	0.455794
$7$	0	0
$7$	0	0
$8$	−3.07419	−1.08689
$9$	1.00000	0.333333
$10$	−1.00546	−0.317956
$11$	−4.69451	−1.41545	−0.707724	−	0.706489i	$-0.750278\pi$
$11$	−4.69451	−1.41545	−0.707724	+	0.706489i	$0.750278\pi$
$12$	−0.753512	−0.217520
$13$	1.15587	0.320581	0.160290	−	0.987070i	$-0.448757\pi$
$13$	1.15587	0.320581	0.160290	+	0.987070i	$0.448757\pi$
$14$	0	0
$15$	−0.900581	−0.232529
$16$	−1.92519	−0.481299
$17$	5.04891	1.22454	0.612271	−	0.790648i	$-0.290256\pi$
$17$	5.04891	1.22454	0.612271	+	0.790648i	$0.290256\pi$
$18$	1.11646	0.263153
$19$	0.849395	0.194865	0.0974323	−	0.995242i	$-0.468937\pi$
$19$	0.849395	0.194865	0.0974323	+	0.995242i	$0.468937\pi$
$20$	0.678599	0.151739
$21$	0	0
$22$	−5.24124	−1.11744
$23$	−1.63546	−0.341016	−0.170508	−	0.985356i	$-0.554541\pi$
$23$	−1.63546	−0.341016	−0.170508	+	0.985356i	$0.554541\pi$
$24$	−3.07419	−0.627517
$25$	−4.18895	−0.837791
$26$	1.29048	0.253085
$27$	1.00000	0.192450
$28$	0	0
$29$	7.97364	1.48067	0.740334	−	0.672240i	$-0.234668\pi$
$29$	7.97364	1.48067	0.740334	+	0.672240i	$0.234668\pi$
$30$	−1.00546	−0.183572
$31$	2.94278	0.528539	0.264270	−	0.964449i	$-0.414869\pi$
$31$	2.94278	0.528539	0.264270	+	0.964449i	$0.414869\pi$
$32$	3.99898	0.706926
$33$	−4.69451	−0.817210
$34$	5.63692	0.966724
$35$	0	0
$36$	−0.753512	−0.125585
$37$	3.09905	0.509480	0.254740	−	0.967010i	$-0.418010\pi$
$37$	3.09905	0.509480	0.254740	+	0.967010i	$0.418010\pi$
$38$	0.948318	0.153837
$39$	1.15587	0.185087
$40$	2.76856	0.437748
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−3.01389	−0.459614	−0.229807	−	0.973236i	$-0.573810\pi$
$43$	−3.01389	−0.459614	−0.229807	+	0.973236i	$0.573810\pi$
$44$	3.53737	0.533279
$45$	−0.900581	−0.134251
$46$	−1.82593	−0.269218
$47$	−8.14340	−1.18784	−0.593918	−	0.804525i	$-0.702420\pi$
$47$	−8.14340	−1.18784	−0.593918	+	0.804525i	$0.702420\pi$
$48$	−1.92519	−0.277878
$49$	0	0
$50$	−4.67681	−0.661401
$51$	5.04891	0.706989
$52$	−0.870962	−0.120781
$53$	−8.01568	−1.10104	−0.550519	−	0.834822i	$-0.685570\pi$
$53$	−8.01568	−1.10104	−0.550519	+	0.834822i	$0.685570\pi$
$54$	1.11646	0.151931
$55$	4.22779	0.570075
$56$	0	0
$57$	0.849395	0.112505
$58$	8.90226	1.16892
$59$	−2.60113	−0.338638	−0.169319	−	0.985561i	$-0.554157\pi$
$59$	−2.60113	−0.338638	−0.169319	+	0.985561i	$0.554157\pi$
$60$	0.678599	0.0876067
$61$	−7.31482	−0.936567	−0.468283	−	0.883578i	$-0.655127\pi$
$61$	−7.31482	−0.936567	−0.468283	+	0.883578i	$0.655127\pi$
$62$	3.28551	0.417260
$63$	0	0
$64$	8.31510	1.03939
$65$	−1.04095	−0.129114
$66$	−5.24124	−0.645153
$67$	0.796475	0.0973049	0.0486524	−	0.998816i	$-0.484507\pi$
$67$	0.796475	0.0973049	0.0486524	+	0.998816i	$0.484507\pi$
$68$	−3.80442	−0.461353
$69$	−1.63546	−0.196886
$70$	0	0
$71$	10.7265	1.27300	0.636501	−	0.771276i	$-0.280381\pi$
$71$	10.7265	1.27300	0.636501	+	0.771276i	$0.280381\pi$
$72$	−3.07419	−0.362297
$73$	1.76040	0.206040	0.103020	−	0.994679i	$-0.467149\pi$
$73$	1.76040	0.206040	0.103020	+	0.994679i	$0.467149\pi$
$74$	3.45997	0.402213
$75$	−4.18895	−0.483699
$76$	−0.640030	−0.0734164
$77$	0	0
$78$	1.29048	0.146119
$79$	13.8908	1.56283	0.781417	−	0.624009i	$-0.214497\pi$
$79$	13.8908	1.56283	0.781417	+	0.624009i	$0.214497\pi$
$80$	1.73379	0.193844
$81$	1.00000	0.111111
$82$	−1.11646	−0.123293
$83$	10.3080	1.13145	0.565725	−	0.824594i	$-0.308596\pi$
$83$	10.3080	1.13145	0.565725	+	0.824594i	$0.308596\pi$
$84$	0	0
$85$	−4.54695	−0.493186
$86$	−3.36490	−0.362846
$87$	7.97364	0.854864
$88$	14.4318	1.53844
$89$	15.1741	1.60846	0.804228	−	0.594321i	$-0.202579\pi$
$89$	15.1741	1.60846	0.804228	+	0.594321i	$0.202579\pi$
$90$	−1.00546	−0.105985
$91$	0	0
$92$	1.23234	0.128480
$93$	2.94278	0.305152
$94$	−9.09180	−0.937747
$95$	−0.764949	−0.0784821
$96$	3.99898	0.408144
$97$	−0.878601	−0.0892084	−0.0446042	−	0.999005i	$-0.514203\pi$
$97$	−0.878601	−0.0892084	−0.0446042	+	0.999005i	$0.514203\pi$
$98$	0	0
$99$	−4.69451	−0.471816
$100$	3.15643	0.315643
$101$	4.56591	0.454325	0.227162	−	0.973857i	$-0.427055\pi$
$101$	4.56591	0.454325	0.227162	+	0.973857i	$0.427055\pi$
$102$	5.63692	0.558138
$103$	−0.218199	−0.0214998	−0.0107499	−	0.999942i	$-0.503422\pi$
$103$	−0.218199	−0.0214998	−0.0107499	+	0.999942i	$0.503422\pi$
$104$	−3.55336	−0.348436
$105$	0	0
$106$	−8.94920	−0.869224
$107$	8.05109	0.778328	0.389164	−	0.921168i	$-0.372764\pi$
$107$	8.05109	0.778328	0.389164	+	0.921168i	$0.372764\pi$
$108$	−0.753512	−0.0725068
$109$	15.5123	1.48581	0.742905	−	0.669397i	$-0.233448\pi$
$109$	15.5123	1.48581	0.742905	+	0.669397i	$0.233448\pi$
$110$	4.72016	0.450050
$111$	3.09905	0.294149
$112$	0	0
$113$	16.0560	1.51042	0.755211	−	0.655482i	$-0.227534\pi$
$113$	16.0560	1.51042	0.755211	+	0.655482i	$0.227534\pi$
$114$	0.948318	0.0888181
$115$	1.47286	0.137345
$116$	−6.00823	−0.557850
$117$	1.15587	0.106860
$118$	−2.90406	−0.267340
$119$	0	0
$120$	2.76856	0.252734
$121$	11.0384	1.00349
$122$	−8.16672	−0.739380
$123$	−1.00000	−0.0901670
$124$	−2.21742	−0.199130
$125$	8.27540	0.740174
$126$	0	0
$127$	9.08915	0.806532	0.403266	−	0.915083i	$-0.367875\pi$
$127$	9.08915	0.806532	0.403266	+	0.915083i	$0.367875\pi$
$128$	1.28554	0.113626
$129$	−3.01389	−0.265358
$130$	−1.16219	−0.101930
$131$	20.4776	1.78914	0.894570	−	0.446928i	$-0.147482\pi$
$131$	20.4776	1.78914	0.894570	+	0.446928i	$0.147482\pi$
$132$	3.53737	0.307889
$133$	0	0
$134$	0.889234	0.0768181
$135$	−0.900581	−0.0775096
$136$	−15.5213	−1.33094
$137$	20.8453	1.78094	0.890468	−	0.455047i	$-0.150377\pi$
$137$	20.8453	1.78094	0.890468	+	0.455047i	$0.150377\pi$
$138$	−1.82593	−0.155433
$139$	−0.173141	−0.0146856	−0.00734280	−	0.999973i	$-0.502337\pi$
$139$	−0.173141	−0.0146856	−0.00734280	+	0.999973i	$0.502337\pi$
$140$	0	0
$141$	−8.14340	−0.685798
$142$	11.9757	1.00498
$143$	−5.42624	−0.453765
$144$	−1.92519	−0.160433
$145$	−7.18090	−0.596342
$146$	1.96542	0.162660
$147$	0	0
$148$	−2.33517	−0.191950
$149$	1.04440	0.0855607	0.0427803	−	0.999085i	$-0.486378\pi$
$149$	1.04440	0.0855607	0.0427803	+	0.999085i	$0.486378\pi$
$150$	−4.67681	−0.381860
$151$	−11.9553	−0.972907	−0.486453	−	0.873707i	$-0.661710\pi$
$151$	−11.9553	−0.972907	−0.486453	+	0.873707i	$0.661710\pi$
$152$	−2.61120	−0.211797
$153$	5.04891	0.408180
$154$	0	0
$155$	−2.65021	−0.212870
$156$	−0.870962	−0.0697328
$157$	−4.18839	−0.334270	−0.167135	−	0.985934i	$-0.553452\pi$
$157$	−4.18839	−0.334270	−0.167135	+	0.985934i	$0.553452\pi$
$158$	15.5085	1.23379
$159$	−8.01568	−0.635685
$160$	−3.60140	−0.284716
$161$	0	0
$162$	1.11646	0.0877176
$163$	10.8840	0.852499	0.426250	−	0.904606i	$-0.359834\pi$
$163$	10.8840	0.852499	0.426250	+	0.904606i	$0.359834\pi$
$164$	0.753512	0.0588394
$165$	4.22779	0.329133
$166$	11.5085	0.893232
$167$	12.7952	0.990120	0.495060	−	0.868859i	$-0.335146\pi$
$167$	12.7952	0.990120	0.495060	+	0.868859i	$0.335146\pi$
$168$	0	0
$169$	−11.6640	−0.897228
$170$	−5.07650	−0.389350
$171$	0.849395	0.0649549
$172$	2.27100	0.173162
$173$	5.07018	0.385479	0.192739	−	0.981250i	$-0.438263\pi$
$173$	5.07018	0.385479	0.192739	+	0.981250i	$0.438263\pi$
$174$	8.90226	0.674879
$175$	0	0
$176$	9.03785	0.681253
$177$	−2.60113	−0.195513
$178$	16.9414	1.26981
$179$	2.27988	0.170406	0.0852032	−	0.996364i	$-0.472846\pi$
$179$	2.27988	0.170406	0.0852032	+	0.996364i	$0.472846\pi$
$180$	0.678599	0.0505798
$181$	−8.62106	−0.640798	−0.320399	−	0.947283i	$-0.603817\pi$
$181$	−8.62106	−0.640798	−0.320399	+	0.947283i	$0.603817\pi$
$182$	0	0
$183$	−7.31482	−0.540727
$184$	5.02771	0.370648
$185$	−2.79094	−0.205194
$186$	3.28551	0.240905
$187$	−23.7022	−1.73328
$188$	6.13615	0.447525
$189$	0	0
$190$	−0.854037	−0.0619583
$191$	−21.2101	−1.53471	−0.767356	−	0.641222i	$-0.778428\pi$
$191$	−21.2101	−1.53471	−0.767356	+	0.641222i	$0.778428\pi$
$192$	8.31510	0.600090
$193$	−11.2364	−0.808814	−0.404407	−	0.914579i	$-0.632522\pi$
$193$	−11.2364	−0.808814	−0.404407	+	0.914579i	$0.632522\pi$
$194$	−0.980925	−0.0704263
$195$	−1.04095	−0.0745442
$196$	0	0
$197$	20.4011	1.45352	0.726758	−	0.686894i	$-0.241026\pi$
$197$	20.4011	1.45352	0.726758	+	0.686894i	$0.241026\pi$
$198$	−5.24124	−0.372479
$199$	1.26866	0.0899326	0.0449663	−	0.998989i	$-0.485682\pi$
$199$	1.26866	0.0899326	0.0449663	+	0.998989i	$0.485682\pi$
$200$	12.8777	0.910587
$201$	0.796475	0.0561790
$202$	5.09767	0.358670
$203$	0	0
$204$	−3.80442	−0.266363
$205$	0.900581	0.0628993
$206$	−0.243611	−0.0169732
$207$	−1.63546	−0.113672
$208$	−2.22527	−0.154295
$209$	−3.98750	−0.275821
$210$	0	0
$211$	−2.25243	−0.155064	−0.0775320	−	0.996990i	$-0.524704\pi$
$211$	−2.25243	−0.155064	−0.0775320	+	0.996990i	$0.524704\pi$
$212$	6.03991	0.414823
$213$	10.7265	0.734969
$214$	8.98874	0.614458
$215$	2.71425	0.185110
$216$	−3.07419	−0.209172
$217$	0	0
$218$	17.3189	1.17298
$219$	1.76040	0.118957
$220$	−3.18569	−0.214779
$221$	5.83588	0.392564
$222$	3.45997	0.232218
$223$	4.43952	0.297292	0.148646	−	0.988890i	$-0.452509\pi$
$223$	4.43952	0.297292	0.148646	+	0.988890i	$0.452509\pi$
$224$	0	0
$225$	−4.18895	−0.279264
$226$	17.9259	1.19241
$227$	−20.3906	−1.35337	−0.676686	−	0.736271i	$-0.736585\pi$
$227$	−20.3906	−1.35337	−0.676686	+	0.736271i	$0.736585\pi$
$228$	−0.640030	−0.0423870
$229$	20.3158	1.34251	0.671254	−	0.741227i	$-0.265756\pi$
$229$	20.3158	1.34251	0.671254	+	0.741227i	$0.265756\pi$
$230$	1.64439	0.108428
$231$	0	0
$232$	−24.5125	−1.60932
$233$	19.5481	1.28064	0.640319	−	0.768109i	$-0.278802\pi$
$233$	19.5481	1.28064	0.640319	+	0.768109i	$0.278802\pi$
$234$	1.29048	0.0843616
$235$	7.33379	0.478404
$236$	1.95998	0.127584
$237$	13.8908	0.902303
$238$	0	0
$239$	−2.84235	−0.183856	−0.0919280	−	0.995766i	$-0.529303\pi$
$239$	−2.84235	−0.183856	−0.0919280	+	0.995766i	$0.529303\pi$
$240$	1.73379	0.111916
$241$	−27.2252	−1.75373	−0.876866	−	0.480735i	$-0.840370\pi$
$241$	−27.2252	−1.75373	−0.876866	+	0.480735i	$0.840370\pi$
$242$	12.3240	0.792217
$243$	1.00000	0.0641500
$244$	5.51181	0.352857
$245$	0	0
$246$	−1.11646	−0.0711830
$247$	0.981790	0.0624698
$248$	−9.04668	−0.574465
$249$	10.3080	0.653243
$250$	9.23917	0.584336
$251$	0.890691	0.0562199	0.0281100	−	0.999605i	$-0.491051\pi$
$251$	0.890691	0.0562199	0.0281100	+	0.999605i	$0.491051\pi$
$252$	0	0
$253$	7.67767	0.482691
$254$	10.1477	0.636723
$255$	−4.54695	−0.284741
$256$	−15.1949	−0.949684
$257$	−15.0505	−0.938822	−0.469411	−	0.882980i	$-0.655534\pi$
$257$	−15.0505	−0.938822	−0.469411	+	0.882980i	$0.655534\pi$
$258$	−3.36490	−0.209489
$259$	0	0
$260$	0.784371	0.0486447
$261$	7.97364	0.493556
$262$	22.8625	1.41245
$263$	−6.76685	−0.417262	−0.208631	−	0.977994i	$-0.566901\pi$
$263$	−6.76685	−0.417262	−0.208631	+	0.977994i	$0.566901\pi$
$264$	14.4318	0.888218
$265$	7.21877	0.443445
$266$	0	0
$267$	15.1741	0.928643
$268$	−0.600153	−0.0366602
$269$	−20.7195	−1.26329	−0.631646	−	0.775257i	$-0.717620\pi$
$269$	−20.7195	−1.26329	−0.631646	+	0.775257i	$0.717620\pi$
$270$	−1.00546	−0.0611906
$271$	−2.59986	−0.157930	−0.0789651	−	0.996877i	$-0.525162\pi$
$271$	−2.59986	−0.157930	−0.0789651	+	0.996877i	$0.525162\pi$
$272$	−9.72014	−0.589370
$273$	0	0
$274$	23.2730	1.40597
$275$	19.6651	1.18585
$276$	1.23234	0.0741780
$277$	17.8530	1.07268	0.536342	−	0.844000i	$-0.319806\pi$
$277$	17.8530	1.07268	0.536342	+	0.844000i	$0.319806\pi$
$278$	−0.193305	−0.0115937
$279$	2.94278	0.176180
$280$	0	0
$281$	0.0898344	0.00535907	0.00267954	−	0.999996i	$-0.499147\pi$
$281$	0.0898344	0.00535907	0.00267954	+	0.999996i	$0.499147\pi$
$282$	−9.09180	−0.541409
$283$	−14.7404	−0.876226	−0.438113	−	0.898920i	$-0.644353\pi$
$283$	−14.7404	−0.876226	−0.438113	+	0.898920i	$0.644353\pi$
$284$	−8.08256	−0.479612
$285$	−0.764949	−0.0453117
$286$	−6.05819	−0.358229
$287$	0	0
$288$	3.99898	0.235642
$289$	8.49152	0.499501
$290$	−8.01721	−0.470787
$291$	−0.878601	−0.0515045
$292$	−1.32649	−0.0776267
$293$	6.71475	0.392280	0.196140	−	0.980576i	$-0.437159\pi$
$293$	6.71475	0.392280	0.196140	+	0.980576i	$0.437159\pi$
$294$	0	0
$295$	2.34252	0.136387
$296$	−9.52707	−0.553750
$297$	−4.69451	−0.272403
$298$	1.16603	0.0675465
$299$	−1.89038	−0.109323
$300$	3.15643	0.182236
$301$	0	0
$302$	−13.3476	−0.768069
$303$	4.56591	0.262305
$304$	−1.63525	−0.0937881
$305$	6.58758	0.377204
$306$	5.63692	0.322241
$307$	2.35297	0.134291	0.0671455	−	0.997743i	$-0.478611\pi$
$307$	2.35297	0.134291	0.0671455	+	0.997743i	$0.478611\pi$
$308$	0	0
$309$	−0.218199	−0.0124129
$310$	−2.95886	−0.168052
$311$	−24.4048	−1.38387	−0.691934	−	0.721961i	$-0.743241\pi$
$311$	−24.4048	−1.38387	−0.691934	+	0.721961i	$0.743241\pi$
$312$	−3.55336	−0.201170
$313$	−8.88540	−0.502232	−0.251116	−	0.967957i	$-0.580798\pi$
$313$	−8.88540	−0.502232	−0.251116	+	0.967957i	$0.580798\pi$
$314$	−4.67618	−0.263892
$315$	0	0
$316$	−10.4669	−0.588808
$317$	−0.0289702	−0.00162713	−0.000813564	−	1.00000i	$-0.500259\pi$
$317$	−0.0289702	−0.00162713	−0.000813564		1.00000i	$0.500259\pi$
$318$	−8.94920	−0.501846
$319$	−37.4323	−2.09581
$320$	−7.48842	−0.418615
$321$	8.05109	0.449368
$322$	0	0
$323$	4.28852	0.238620
$324$	−0.753512	−0.0418618
$325$	−4.84188	−0.268579
$326$	12.1516	0.673012
$327$	15.5123	0.857832
$328$	3.07419	0.169744
$329$	0	0
$330$	4.72016	0.259836
$331$	7.32795	0.402780	0.201390	−	0.979511i	$-0.435454\pi$
$331$	7.32795	0.402780	0.201390	+	0.979511i	$0.435454\pi$
$332$	−7.76720	−0.426281
$333$	3.09905	0.169827
$334$	14.2853	0.781658
$335$	−0.717290	−0.0391897
$336$	0	0
$337$	35.0551	1.90957	0.954785	−	0.297296i	$-0.0960847\pi$
$337$	35.0551	1.90957	0.954785	+	0.297296i	$0.0960847\pi$
$338$	−13.0224	−0.708324
$339$	16.0560	0.872042
$340$	3.42619	0.185811
$341$	−13.8149	−0.748120
$342$	0.948318	0.0512791
$343$	0	0
$344$	9.26528	0.499550
$345$	1.47286	0.0792962
$346$	5.66067	0.304319
$347$	−22.7234	−1.21986	−0.609929	−	0.792456i	$-0.708802\pi$
$347$	−22.7234	−1.21986	−0.609929	+	0.792456i	$0.708802\pi$
$348$	−6.00823	−0.322075
$349$	7.64444	0.409197	0.204599	−	0.978846i	$-0.434411\pi$
$349$	7.64444	0.409197	0.204599	+	0.978846i	$0.434411\pi$
$350$	0	0
$351$	1.15587	0.0616957
$352$	−18.7732	−1.00062
$353$	−0.643130	−0.0342303	−0.0171152	−	0.999854i	$-0.505448\pi$
$353$	−0.643130	−0.0342303	−0.0171152	+	0.999854i	$0.505448\pi$
$354$	−2.90406	−0.154349
$355$	−9.66009	−0.512704
$356$	−11.4339	−0.605996
$357$	0	0
$358$	2.54540	0.134529
$359$	−28.7366	−1.51666	−0.758330	−	0.651871i	$-0.773984\pi$
$359$	−28.7366	−1.51666	−0.758330	+	0.651871i	$0.773984\pi$
$360$	2.76856	0.145916
$361$	−18.2785	−0.962028
$362$	−9.62509	−0.505883
$363$	11.0384	0.579368
$364$	0	0
$365$	−1.58539	−0.0829829
$366$	−8.16672	−0.426881
$367$	5.33033	0.278241	0.139120	−	0.990275i	$-0.455573\pi$
$367$	5.33033	0.278241	0.139120	+	0.990275i	$0.455573\pi$
$368$	3.14857	0.164131
$369$	−1.00000	−0.0520579
$370$	−3.11598	−0.161992
$371$	0	0
$372$	−2.21742	−0.114968
$373$	9.39088	0.486241	0.243121	−	0.969996i	$-0.421829\pi$
$373$	9.39088	0.486241	0.243121	+	0.969996i	$0.421829\pi$
$374$	−26.4626	−1.36835
$375$	8.27540	0.427340
$376$	25.0344	1.29105
$377$	9.21648	0.474673
$378$	0	0
$379$	−5.32747	−0.273654	−0.136827	−	0.990595i	$-0.543690\pi$
$379$	−5.32747	−0.273654	−0.136827	+	0.990595i	$0.543690\pi$
$380$	0.576398	0.0295686
$381$	9.08915	0.465651
$382$	−23.6803	−1.21159
$383$	−10.5597	−0.539575	−0.269788	−	0.962920i	$-0.586953\pi$
$383$	−10.5597	−0.539575	−0.269788	+	0.962920i	$0.586953\pi$
$384$	1.28554	0.0656022
$385$	0	0
$386$	−12.5450	−0.638525
$387$	−3.01389	−0.153205
$388$	0.662037	0.0336098
$389$	30.7591	1.55955	0.779775	−	0.626060i	$-0.215333\pi$
$389$	30.7591	1.55955	0.779775	+	0.626060i	$0.215333\pi$
$390$	−1.16219	−0.0588495
$391$	−8.25728	−0.417589
$392$	0	0
$393$	20.4776	1.03296
$394$	22.7770	1.14749
$395$	−12.5098	−0.629435
$396$	3.53737	0.177760
$397$	−23.3508	−1.17194	−0.585972	−	0.810331i	$-0.699287\pi$
$397$	−23.3508	−1.17194	−0.585972	+	0.810331i	$0.699287\pi$
$398$	1.41641	0.0709980
$399$	0	0
$400$	8.06455	0.403228
$401$	12.0188	0.600190	0.300095	−	0.953909i	$-0.402982\pi$
$401$	12.0188	0.600190	0.300095	+	0.953909i	$0.402982\pi$
$402$	0.889234	0.0443509
$403$	3.40147	0.169439
$404$	−3.44047	−0.171170
$405$	−0.900581	−0.0447502
$406$	0	0
$407$	−14.5485	−0.721143
$408$	−15.5213	−0.768420
$409$	−2.07020	−0.102365	−0.0511825	−	0.998689i	$-0.516299\pi$
$409$	−2.07020	−0.102365	−0.0511825	+	0.998689i	$0.516299\pi$
$410$	1.00546	0.0496563
$411$	20.8453	1.02822
$412$	0.164416	0.00810018
$413$	0	0
$414$	−1.82593	−0.0897394
$415$	−9.28318	−0.455693
$416$	4.62230	0.226627
$417$	−0.173141	−0.00847873
$418$	−4.45189	−0.217749
$419$	−37.9166	−1.85235	−0.926173	−	0.377099i	$-0.876922\pi$
$419$	−37.9166	−1.85235	−0.926173	+	0.377099i	$0.876922\pi$
$420$	0	0
$421$	−9.80911	−0.478067	−0.239033	−	0.971011i	$-0.576831\pi$
$421$	−9.80911	−0.478067	−0.239033	+	0.971011i	$0.576831\pi$
$422$	−2.51476	−0.122416
$423$	−8.14340	−0.395946
$424$	24.6417	1.19671
$425$	−21.1497	−1.02591
$426$	11.9757	0.580227
$427$	0	0
$428$	−6.06660	−0.293240
$429$	−5.42624	−0.261981
$430$	3.03036	0.146137
$431$	−32.4424	−1.56270	−0.781348	−	0.624096i	$-0.785467\pi$
$431$	−32.4424	−1.56270	−0.781348	+	0.624096i	$0.785467\pi$
$432$	−1.92519	−0.0926260
$433$	−34.9870	−1.68137	−0.840683	−	0.541527i	$-0.817846\pi$
$433$	−34.9870	−1.68137	−0.840683	+	0.541527i	$0.817846\pi$
$434$	0	0
$435$	−7.18090	−0.344298
$436$	−11.6887	−0.559788
$437$	−1.38915	−0.0664521
$438$	1.96542	0.0939116
$439$	20.0625	0.957530	0.478765	−	0.877943i	$-0.341085\pi$
$439$	20.0625	0.957530	0.478765	+	0.877943i	$0.341085\pi$
$440$	−12.9970	−0.619609
$441$	0	0
$442$	6.51554	0.309913
$443$	−12.7373	−0.605165	−0.302583	−	0.953123i	$-0.597849\pi$
$443$	−12.7373	−0.605165	−0.302583	+	0.953123i	$0.597849\pi$
$444$	−2.33517	−0.110822
$445$	−13.6655	−0.647809
$446$	4.95655	0.234699
$447$	1.04440	0.0493985
$448$	0	0
$449$	20.5999	0.972170	0.486085	−	0.873912i	$-0.338425\pi$
$449$	20.5999	0.972170	0.486085	+	0.873912i	$0.338425\pi$
$450$	−4.67681	−0.220467
$451$	4.69451	0.221056
$452$	−12.0984	−0.569061
$453$	−11.9553	−0.561708
$454$	−22.7653	−1.06843
$455$	0	0
$456$	−2.61120	−0.122281
$457$	7.53127	0.352298	0.176149	−	0.984364i	$-0.443636\pi$
$457$	7.53127	0.352298	0.176149	+	0.984364i	$0.443636\pi$
$458$	22.6819	1.05985
$459$	5.04891	0.235663
$460$	−1.10982	−0.0517456
$461$	14.5150	0.676032	0.338016	−	0.941140i	$-0.390244\pi$
$461$	14.5150	0.676032	0.338016	+	0.941140i	$0.390244\pi$
$462$	0	0
$463$	−1.59229	−0.0739998	−0.0369999	−	0.999315i	$-0.511780\pi$
$463$	−1.59229	−0.0739998	−0.0369999	+	0.999315i	$0.511780\pi$
$464$	−15.3508	−0.712643
$465$	−2.65021	−0.122901
$466$	21.8247	1.01101
$467$	33.8659	1.56713	0.783565	−	0.621310i	$-0.213399\pi$
$467$	33.8659	1.56713	0.783565	+	0.621310i	$0.213399\pi$
$468$	−0.870962	−0.0402602
$469$	0	0
$470$	8.18790	0.377679
$471$	−4.18839	−0.192991
$472$	7.99636	0.368062
$473$	14.1487	0.650560
$474$	15.5085	0.712330
$475$	−3.55808	−0.163256
$476$	0	0
$477$	−8.01568	−0.367013
$478$	−3.17337	−0.145147
$479$	−9.40167	−0.429573	−0.214787	−	0.976661i	$-0.568906\pi$
$479$	−9.40167	−0.429573	−0.214787	+	0.976661i	$0.568906\pi$
$480$	−3.60140	−0.164381
$481$	3.58209	0.163329
$482$	−30.3960	−1.38450
$483$	0	0
$484$	−8.31760	−0.378073
$485$	0.791251	0.0359289
$486$	1.11646	0.0506438
$487$	24.6937	1.11898	0.559488	−	0.828838i	$-0.310998\pi$
$487$	24.6937	1.11898	0.559488	+	0.828838i	$0.310998\pi$
$488$	22.4872	1.01795
$489$	10.8840	0.492191
$490$	0	0
$491$	34.9667	1.57802	0.789012	−	0.614378i	$-0.210593\pi$
$491$	34.9667	1.57802	0.789012	+	0.614378i	$0.210593\pi$
$492$	0.753512	0.0339710
$493$	40.2582	1.81314
$494$	1.09613	0.0493173
$495$	4.22779	0.190025
$496$	−5.66543	−0.254385
$497$	0	0
$498$	11.5085	0.515708
$499$	18.5443	0.830155	0.415077	−	0.909786i	$-0.363755\pi$
$499$	18.5443	0.830155	0.415077	+	0.909786i	$0.363755\pi$
$500$	−6.23561	−0.278865
$501$	12.7952	0.571646
$502$	0.994423	0.0443833
$503$	33.0348	1.47295	0.736473	−	0.676466i	$-0.236490\pi$
$503$	33.0348	1.47295	0.736473	+	0.676466i	$0.236490\pi$
$504$	0	0
$505$	−4.11197	−0.182980
$506$	8.57183	0.381064
$507$	−11.6640	−0.518015
$508$	−6.84879	−0.303866
$509$	21.5526	0.955302	0.477651	−	0.878550i	$-0.341488\pi$
$509$	21.5526	0.955302	0.477651	+	0.878550i	$0.341488\pi$
$510$	−5.07650	−0.224791
$511$	0	0
$512$	−19.5356	−0.863362
$513$	0.849395	0.0375017
$514$	−16.8033	−0.741161
$515$	0.196506	0.00865908
$516$	2.27100	0.0999754
$517$	38.2293	1.68132
$518$	0	0
$519$	5.07018	0.222556
$520$	3.20009	0.140333
$521$	36.0597	1.57981	0.789903	−	0.613232i	$-0.210131\pi$
$521$	36.0597	1.57981	0.789903	+	0.613232i	$0.210131\pi$
$522$	8.90226	0.389642
$523$	2.02031	0.0883421	0.0441710	−	0.999024i	$-0.485935\pi$
$523$	2.02031	0.0883421	0.0441710	+	0.999024i	$0.485935\pi$
$524$	−15.4302	−0.674069
$525$	0	0
$526$	−7.55494	−0.329411
$527$	14.8579	0.647218
$528$	9.03785	0.393322
$529$	−20.3253	−0.883708
$530$	8.05948	0.350081
$531$	−2.60113	−0.112879
$532$	0	0
$533$	−1.15587	−0.0500663
$534$	16.9414	0.733124
$535$	−7.25066	−0.313473
$536$	−2.44852	−0.105760
$537$	2.27988	0.0983842
$538$	−23.1326	−0.997316
$539$	0	0
$540$	0.678599	0.0292022
$541$	28.2526	1.21467	0.607337	−	0.794444i	$-0.292238\pi$
$541$	28.2526	1.21467	0.607337	+	0.794444i	$0.292238\pi$
$542$	−2.90264	−0.124679
$543$	−8.62106	−0.369965
$544$	20.1905	0.865660
$545$	−13.9701	−0.598413
$546$	0	0
$547$	−36.6219	−1.56584	−0.782919	−	0.622123i	$-0.786270\pi$
$547$	−36.6219	−1.56584	−0.782919	+	0.622123i	$0.786270\pi$
$548$	−15.7072	−0.670978
$549$	−7.31482	−0.312189
$550$	21.9553	0.936179
$551$	6.77277	0.288530
$552$	5.02771	0.213994
$553$	0	0
$554$	19.9322	0.846840
$555$	−2.79094	−0.118469
$556$	0.130464	0.00553289
$557$	−38.9992	−1.65245	−0.826224	−	0.563342i	$-0.809515\pi$
$557$	−38.9992	−1.65245	−0.826224	+	0.563342i	$0.809515\pi$
$558$	3.28551	0.139087
$559$	−3.48366	−0.147343
$560$	0	0
$561$	−23.7022	−1.00071
$562$	0.100297	0.00423076
$563$	27.9805	1.17924	0.589619	−	0.807682i	$-0.299278\pi$
$563$	27.9805	1.17924	0.589619	+	0.807682i	$0.299278\pi$
$564$	6.13615	0.258379
$565$	−14.4597	−0.608325
$566$	−16.4571	−0.691744
$567$	0	0
$568$	−32.9754	−1.38362
$569$	9.11873	0.382277	0.191139	−	0.981563i	$-0.438782\pi$
$569$	9.11873	0.382277	0.191139	+	0.981563i	$0.438782\pi$
$570$	−0.854037	−0.0357717
$571$	21.4215	0.896460	0.448230	−	0.893918i	$-0.352055\pi$
$571$	21.4215	0.896460	0.448230	+	0.893918i	$0.352055\pi$
$572$	4.08874	0.170959
$573$	−21.2101	−0.886066
$574$	0	0
$575$	6.85086	0.285700
$576$	8.31510	0.346462
$577$	−31.0255	−1.29161	−0.645805	−	0.763502i	$-0.723478\pi$
$577$	−31.0255	−1.29161	−0.645805	+	0.763502i	$0.723478\pi$
$578$	9.48047	0.394335
$579$	−11.2364	−0.466969
$580$	5.41090	0.224675
$581$	0	0
$582$	−0.980925	−0.0406606
$583$	37.6297	1.55846
$584$	−5.41182	−0.223943
$585$	−1.04095	−0.0430381
$586$	7.49677	0.309689
$587$	−2.11563	−0.0873215	−0.0436608	−	0.999046i	$-0.513902\pi$
$587$	−2.11563	−0.0873215	−0.0436608	+	0.999046i	$0.513902\pi$
$588$	0	0
$589$	2.49959	0.102994
$590$	2.61534	0.107672
$591$	20.4011	0.839187
$592$	−5.96627	−0.245212
$593$	3.84915	0.158066	0.0790328	−	0.996872i	$-0.474817\pi$
$593$	3.84915	0.158066	0.0790328	+	0.996872i	$0.474817\pi$
$594$	−5.24124	−0.215051
$595$	0	0
$596$	−0.786969	−0.0322355
$597$	1.26866	0.0519226
$598$	−2.11053	−0.0863061
$599$	13.0766	0.534297	0.267148	−	0.963655i	$-0.413919\pi$
$599$	13.0766	0.534297	0.267148	+	0.963655i	$0.413919\pi$
$600$	12.8777	0.525728
$601$	37.2633	1.52000	0.760001	−	0.649922i	$-0.225199\pi$
$601$	37.2633	1.52000	0.760001	+	0.649922i	$0.225199\pi$
$602$	0	0
$603$	0.796475	0.0324350
$604$	9.00845	0.366549
$605$	−9.94100	−0.404159
$606$	5.09767	0.207078
$607$	6.25992	0.254082	0.127041	−	0.991897i	$-0.459452\pi$
$607$	6.25992	0.254082	0.127041	+	0.991897i	$0.459452\pi$
$608$	3.39671	0.137755
$609$	0	0
$610$	7.35479	0.297787
$611$	−9.41270	−0.380797
$612$	−3.80442	−0.153784
$613$	9.94899	0.401836	0.200918	−	0.979608i	$-0.435608\pi$
$613$	9.94899	0.401836	0.200918	+	0.979608i	$0.435608\pi$
$614$	2.62700	0.106017
$615$	0.900581	0.0363149
$616$	0	0
$617$	13.0271	0.524452	0.262226	−	0.965007i	$-0.415543\pi$
$617$	13.0271	0.524452	0.262226	+	0.965007i	$0.415543\pi$
$618$	−0.243611	−0.00979947
$619$	−23.8933	−0.960354	−0.480177	−	0.877172i	$-0.659428\pi$
$619$	−23.8933	−0.960354	−0.480177	+	0.877172i	$0.659428\pi$
$620$	1.99697	0.0802002
$621$	−1.63546	−0.0656286
$622$	−27.2470	−1.09251
$623$	0	0
$624$	−2.22527	−0.0890822
$625$	13.4921	0.539684
$626$	−9.92021	−0.396491
$627$	−3.98750	−0.159245
$628$	3.15601	0.125938
$629$	15.6468	0.623880
$630$	0	0
$631$	−27.1911	−1.08246	−0.541230	−	0.840875i	$-0.682041\pi$
$631$	−27.1911	−1.08246	−0.541230	+	0.840875i	$0.682041\pi$
$632$	−42.7029	−1.69863
$633$	−2.25243	−0.0895262
$634$	−0.0323441	−0.00128455
$635$	−8.18552	−0.324832
$636$	6.03991	0.239498
$637$	0	0
$638$	−41.7918	−1.65455
$639$	10.7265	0.424334
$640$	−1.15773	−0.0457632
$641$	−9.85980	−0.389439	−0.194719	−	0.980859i	$-0.562380\pi$
$641$	−9.85980	−0.389439	−0.194719	+	0.980859i	$0.562380\pi$
$642$	8.98874	0.354757
$643$	−15.5002	−0.611270	−0.305635	−	0.952149i	$-0.598869\pi$
$643$	−15.5002	−0.611270	−0.305635	+	0.952149i	$0.598869\pi$
$644$	0	0
$645$	2.71425	0.106874
$646$	4.78797	0.188380
$647$	−39.1567	−1.53941	−0.769705	−	0.638400i	$-0.779596\pi$
$647$	−39.1567	−1.53941	−0.769705	+	0.638400i	$0.779596\pi$
$648$	−3.07419	−0.120766
$649$	12.2110	0.479324
$650$	−5.40578	−0.212032
$651$	0	0
$652$	−8.20122	−0.321184
$653$	−29.5384	−1.15593	−0.577964	−	0.816062i	$-0.696153\pi$
$653$	−29.5384	−1.15593	−0.577964	+	0.816062i	$0.696153\pi$
$654$	17.3189	0.677223
$655$	−18.4418	−0.720580
$656$	1.92519	0.0751662
$657$	1.76040	0.0686799
$658$	0	0
$659$	−9.39226	−0.365871	−0.182935	−	0.983125i	$-0.558560\pi$
$659$	−9.39226	−0.365871	−0.182935	+	0.983125i	$0.558560\pi$
$660$	−3.18569	−0.124003
$661$	−42.1189	−1.63824	−0.819118	−	0.573625i	$-0.805537\pi$
$661$	−42.1189	−1.63824	−0.819118	+	0.573625i	$0.805537\pi$
$662$	8.18137	0.317978
$663$	5.83588	0.226647
$664$	−31.6888	−1.22976
$665$	0	0
$666$	3.45997	0.134071
$667$	−13.0405	−0.504932
$668$	−9.64132	−0.373034
$669$	4.43952	0.171642
$670$	−0.800827	−0.0309386
$671$	34.3395	1.32566
$672$	0	0
$673$	−2.92211	−0.112639	−0.0563195	−	0.998413i	$-0.517937\pi$
$673$	−2.92211	−0.112639	−0.0563195	+	0.998413i	$0.517937\pi$
$674$	39.1377	1.50753
$675$	−4.18895	−0.161233
$676$	8.78894	0.338036
$677$	36.7706	1.41321	0.706604	−	0.707609i	$-0.250226\pi$
$677$	36.7706	1.41321	0.706604	+	0.707609i	$0.250226\pi$
$678$	17.9259	0.688441
$679$	0	0
$680$	13.9782	0.536040
$681$	−20.3906	−0.781370
$682$	−15.4238	−0.590609
$683$	−8.03451	−0.307432	−0.153716	−	0.988115i	$-0.549124\pi$
$683$	−8.03451	−0.307432	−0.153716	+	0.988115i	$0.549124\pi$
$684$	−0.640030	−0.0244721
$685$	−18.7729	−0.717275
$686$	0	0
$687$	20.3158	0.775098
$688$	5.80233	0.221212
$689$	−9.26508	−0.352971
$690$	1.64439	0.0626010
$691$	6.60782	0.251373	0.125687	−	0.992070i	$-0.459887\pi$
$691$	6.60782	0.251373	0.125687	+	0.992070i	$0.459887\pi$
$692$	−3.82045	−0.145232
$693$	0	0
$694$	−25.3699	−0.963027
$695$	0.155927	0.00591465
$696$	−24.5125	−0.929144
$697$	−5.04891	−0.191241
$698$	8.53473	0.323044
$699$	19.5481	0.739377
$700$	0	0
$701$	11.0961	0.419094	0.209547	−	0.977799i	$-0.432801\pi$
$701$	11.0961	0.419094	0.209547	+	0.977799i	$0.432801\pi$
$702$	1.29048	0.0487062
$703$	2.63232	0.0992797
$704$	−39.0353	−1.47120
$705$	7.33379	0.276206
$706$	−0.718030	−0.0270234
$707$	0	0
$708$	1.95998	0.0736606
$709$	8.02154	0.301255	0.150628	−	0.988591i	$-0.451871\pi$
$709$	8.02154	0.301255	0.150628	+	0.988591i	$0.451871\pi$
$710$	−10.7851	−0.404759
$711$	13.8908	0.520945
$712$	−46.6482	−1.74822
$713$	−4.81280	−0.180241
$714$	0	0
$715$	4.88677	0.182755
$716$	−1.71792	−0.0642017
$717$	−2.84235	−0.106149
$718$	−32.0833	−1.19734
$719$	−26.9116	−1.00363	−0.501816	−	0.864974i	$-0.667335\pi$
$719$	−26.9116	−1.00363	−0.501816	+	0.864974i	$0.667335\pi$
$720$	1.73379	0.0646147
$721$	0	0
$722$	−20.4073	−0.759480
$723$	−27.2252	−1.01252
$724$	6.49608	0.241425
$725$	−33.4012	−1.24049
$726$	12.3240	0.457386
$727$	3.40083	0.126130	0.0630648	−	0.998009i	$-0.479913\pi$
$727$	3.40083	0.126130	0.0630648	+	0.998009i	$0.479913\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.77002	−0.0655115
$731$	−15.2169	−0.562816
$732$	5.51181	0.203722
$733$	−31.6864	−1.17036	−0.585181	−	0.810903i	$-0.698977\pi$
$733$	−31.6864	−1.17036	−0.585181	+	0.810903i	$0.698977\pi$
$734$	5.95111	0.219659
$735$	0	0
$736$	−6.54016	−0.241073
$737$	−3.73906	−0.137730
$738$	−1.11646	−0.0410975
$739$	2.74615	0.101019	0.0505095	−	0.998724i	$-0.483915\pi$
$739$	2.74615	0.101019	0.0505095	+	0.998724i	$0.483915\pi$
$740$	2.10301	0.0773082
$741$	0.981790	0.0360670
$742$	0	0
$743$	7.91699	0.290446	0.145223	−	0.989399i	$-0.453610\pi$
$743$	7.91699	0.290446	0.145223	+	0.989399i	$0.453610\pi$
$744$	−9.04668	−0.331667
$745$	−0.940567	−0.0344597
$746$	10.4846	0.383867
$747$	10.3080	0.377150
$748$	17.8599	0.653022
$749$	0	0
$750$	9.23917	0.337367
$751$	−26.8980	−0.981524	−0.490762	−	0.871294i	$-0.663281\pi$
$751$	−26.8980	−0.981524	−0.490762	+	0.871294i	$0.663281\pi$
$752$	15.6776	0.571704
$753$	0.890691	0.0324586
$754$	10.2899	0.374734
$755$	10.7667	0.391840
$756$	0	0
$757$	−36.1992	−1.31568	−0.657842	−	0.753156i	$-0.728530\pi$
$757$	−36.1992	−1.31568	−0.657842	+	0.753156i	$0.728530\pi$
$758$	−5.94792	−0.216038
$759$	7.67767	0.278682
$760$	2.35160	0.0853015
$761$	9.07694	0.329039	0.164519	−	0.986374i	$-0.447393\pi$
$761$	9.07694	0.329039	0.164519	+	0.986374i	$0.447393\pi$
$762$	10.1477	0.367612
$763$	0	0
$764$	15.9821	0.578212
$765$	−4.54695	−0.164395
$766$	−11.7895	−0.425972
$767$	−3.00656	−0.108561
$768$	−15.1949	−0.548300
$769$	−19.5528	−0.705093	−0.352547	−	0.935794i	$-0.614684\pi$
$769$	−19.5528	−0.705093	−0.352547	+	0.935794i	$0.614684\pi$
$770$	0	0
$771$	−15.0505	−0.542029
$772$	8.46677	0.304726
$773$	53.8122	1.93549	0.967746	−	0.251928i	$-0.0810646\pi$
$773$	53.8122	1.93549	0.967746	+	0.251928i	$0.0810646\pi$
$774$	−3.36490	−0.120949
$775$	−12.3272	−0.442805
$776$	2.70099	0.0969598
$777$	0	0
$778$	34.3414	1.23120
$779$	−0.849395	−0.0304327
$780$	0.784371	0.0280850
$781$	−50.3557	−1.80187
$782$	−9.21894	−0.329669
$783$	7.97364	0.284955
$784$	0	0
$785$	3.77199	0.134628
$786$	22.8625	0.815479
$787$	38.1745	1.36077	0.680387	−	0.732853i	$-0.261812\pi$
$787$	38.1745	1.36077	0.680387	+	0.732853i	$0.261812\pi$
$788$	−15.3724	−0.547621
$789$	−6.76685	−0.240906
$790$	−13.9667	−0.496912
$791$	0	0
$792$	14.4318	0.512813
$793$	−8.45498	−0.300245
$794$	−26.0703	−0.925200
$795$	7.21877	0.256023
$796$	−0.955947	−0.0338827
$797$	−0.638938	−0.0226323	−0.0113162	−	0.999936i	$-0.503602\pi$
$797$	−0.638938	−0.0226323	−0.0113162	+	0.999936i	$0.503602\pi$
$798$	0	0
$799$	−41.1153	−1.45455
$800$	−16.7515	−0.592256
$801$	15.1741	0.536152
$802$	13.4185	0.473825
$803$	−8.26424	−0.291639
$804$	−0.600153	−0.0211658
$805$	0	0
$806$	3.79762	0.133765
$807$	−20.7195	−0.729362
$808$	−14.0365	−0.493802
$809$	1.14199	0.0401501	0.0200750	−	0.999798i	$-0.493609\pi$
$809$	1.14199	0.0401501	0.0200750	+	0.999798i	$0.493609\pi$
$810$	−1.00546	−0.0353284
$811$	1.96493	0.0689979	0.0344990	−	0.999405i	$-0.489016\pi$
$811$	1.96493	0.0689979	0.0344990	+	0.999405i	$0.489016\pi$
$812$	0	0
$813$	−2.59986	−0.0911811
$814$	−16.2429	−0.569312
$815$	−9.80191	−0.343346
$816$	−9.72014	−0.340273
$817$	−2.55998	−0.0895625
$818$	−2.31131	−0.0808129
$819$	0	0
$820$	−0.678599	−0.0236977
$821$	7.23373	0.252459	0.126230	−	0.992001i	$-0.459712\pi$
$821$	7.23373	0.252459	0.126230	+	0.992001i	$0.459712\pi$
$822$	23.2730	0.811739
$823$	−16.6287	−0.579640	−0.289820	−	0.957081i	$-0.593595\pi$
$823$	−16.6287	−0.579640	−0.289820	+	0.957081i	$0.593595\pi$
$824$	0.670786	0.0233679
$825$	19.6651	0.684651
$826$	0	0
$827$	27.9766	0.972842	0.486421	−	0.873725i	$-0.338302\pi$
$827$	27.9766	0.972842	0.486421	+	0.873725i	$0.338302\pi$
$828$	1.23234	0.0428267
$829$	22.7571	0.790388	0.395194	−	0.918598i	$-0.370677\pi$
$829$	22.7571	0.790388	0.395194	+	0.918598i	$0.370677\pi$
$830$	−10.3643	−0.359751
$831$	17.8530	0.619315
$832$	9.61117	0.333207
$833$	0	0
$834$	−0.193305	−0.00669360
$835$	−11.5231	−0.398773
$836$	3.00463	0.103917
$837$	2.94278	0.101717
$838$	−42.3324	−1.46235
$839$	14.9814	0.517214	0.258607	−	0.965983i	$-0.416737\pi$
$839$	14.9814	0.517214	0.258607	+	0.965983i	$0.416737\pi$
$840$	0	0
$841$	34.5789	1.19238
$842$	−10.9515	−0.377414
$843$	0.0898344	0.00309406
$844$	1.69724	0.0584213
$845$	10.5043	0.361360
$846$	−9.09180	−0.312582
$847$	0	0
$848$	15.4317	0.529928
$849$	−14.7404	−0.505890
$850$	−23.6128	−0.809912
$851$	−5.06836	−0.173741
$852$	−8.08256	−0.276904
$853$	−38.1171	−1.30510	−0.652552	−	0.757744i	$-0.726301\pi$
$853$	−38.1171	−1.30510	−0.652552	+	0.757744i	$0.726301\pi$
$854$	0	0
$855$	−0.764949	−0.0261607
$856$	−24.7506	−0.845958
$857$	−29.6584	−1.01311	−0.506556	−	0.862207i	$-0.669082\pi$
$857$	−29.6584	−1.01311	−0.506556	+	0.862207i	$0.669082\pi$
$858$	−6.05819	−0.206823
$859$	14.7355	0.502770	0.251385	−	0.967887i	$-0.419114\pi$
$859$	14.7355	0.502770	0.251385	+	0.967887i	$0.419114\pi$
$860$	−2.04522	−0.0697415
$861$	0	0
$862$	−36.2207	−1.23368
$863$	13.1014	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$863$	13.1014	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$864$	3.99898	0.136048
$865$	−4.56611	−0.155252
$866$	−39.0616	−1.32737
$867$	8.49152	0.288387
$868$	0	0
$869$	−65.2104	−2.21211
$870$	−8.01721	−0.271809
$871$	0.920621	0.0311940
$872$	−47.6878	−1.61491
$873$	−0.878601	−0.0297361
$874$	−1.55093	−0.0524611
$875$	0	0
$876$	−1.32649	−0.0448178
$877$	3.85074	0.130030	0.0650152	−	0.997884i	$-0.479290\pi$
$877$	3.85074	0.130030	0.0650152	+	0.997884i	$0.479290\pi$
$878$	22.3990	0.755930
$879$	6.71475	0.226483
$880$	−8.13931	−0.274376
$881$	31.4622	1.05999	0.529995	−	0.848001i	$-0.322194\pi$
$881$	31.4622	1.05999	0.529995	+	0.848001i	$0.322194\pi$
$882$	0	0
$883$	−20.4706	−0.688889	−0.344445	−	0.938807i	$-0.611933\pi$
$883$	−20.4706	−0.688889	−0.344445	+	0.938807i	$0.611933\pi$
$884$	−4.39741	−0.147901
$885$	2.34252	0.0787431
$886$	−14.2207	−0.477753
$887$	−21.2614	−0.713887	−0.356944	−	0.934126i	$-0.616181\pi$
$887$	−21.2614	−0.713887	−0.356944	+	0.934126i	$0.616181\pi$
$888$	−9.52707	−0.319707
$889$	0	0
$890$	−15.2571	−0.511418
$891$	−4.69451	−0.157272
$892$	−3.34523	−0.112007
$893$	−6.91696	−0.231467
$894$	1.16603	0.0389980
$895$	−2.05322	−0.0686315
$896$	0	0
$897$	−1.89038	−0.0631178
$898$	22.9990	0.767487
$899$	23.4647	0.782591
$900$	3.15643	0.105214
$901$	−40.4705	−1.34827
$902$	5.24124	0.174514
$903$	0	0
$904$	−49.3592	−1.64166
$905$	7.76396	0.258083
$906$	−13.3476	−0.443445
$907$	24.4166	0.810739	0.405370	−	0.914153i	$-0.367143\pi$
$907$	24.4166	0.810739	0.405370	+	0.914153i	$0.367143\pi$
$908$	15.3646	0.509891
$909$	4.56591	0.151442
$910$	0	0
$911$	31.2660	1.03589	0.517944	−	0.855415i	$-0.326698\pi$
$911$	31.2660	1.03589	0.517944	+	0.855415i	$0.326698\pi$
$912$	−1.63525	−0.0541486
$913$	−48.3910	−1.60151
$914$	8.40838	0.278125
$915$	6.58758	0.217779
$916$	−15.3082	−0.505798
$917$	0	0
$918$	5.63692	0.186046
$919$	53.3081	1.75847	0.879237	−	0.476385i	$-0.158053\pi$
$919$	53.3081	1.75847	0.879237	+	0.476385i	$0.158053\pi$
$920$	−4.52786	−0.149279
$921$	2.35297	0.0775330
$922$	16.2055	0.533699
$923$	12.3984	0.408100
$924$	0	0
$925$	−12.9818	−0.426838
$926$	−1.77773	−0.0584197
$927$	−0.218199	−0.00716660
$928$	31.8864	1.04672
$929$	43.0707	1.41310	0.706552	−	0.707662i	$-0.250250\pi$
$929$	43.0707	1.41310	0.706552	+	0.707662i	$0.250250\pi$
$930$	−2.95886	−0.0970249
$931$	0	0
$932$	−14.7297	−0.482489
$933$	−24.4048	−0.798977
$934$	37.8100	1.23718
$935$	21.3457	0.698080
$936$	−3.55336	−0.116145
$937$	−35.0260	−1.14425	−0.572125	−	0.820166i	$-0.693881\pi$
$937$	−35.0260	−1.14425	−0.572125	+	0.820166i	$0.693881\pi$
$938$	0	0
$939$	−8.88540	−0.289964
$940$	−5.52610	−0.180241
$941$	44.2501	1.44251	0.721257	−	0.692668i	$-0.243565\pi$
$941$	44.2501	1.44251	0.721257	+	0.692668i	$0.243565\pi$
$942$	−4.67618	−0.152358
$943$	1.63546	0.0532578
$944$	5.00768	0.162986
$945$	0	0
$946$	15.7965	0.513590
$947$	−3.06304	−0.0995353	−0.0497677	−	0.998761i	$-0.515848\pi$
$947$	−3.06304	−0.0995353	−0.0497677	+	0.998761i	$0.515848\pi$
$948$	−10.4669	−0.339948
$949$	2.03480	0.0660523
$950$	−3.97246	−0.128884
$951$	−0.0289702	−0.000939423 0
$952$	0	0
$953$	−3.51397	−0.113829	−0.0569143	−	0.998379i	$-0.518126\pi$
$953$	−3.51397	−0.113829	−0.0569143	+	0.998379i	$0.518126\pi$
$954$	−8.94920	−0.289741
$955$	19.1014	0.618108
$956$	2.14174	0.0692689
$957$	−37.4323	−1.21002
$958$	−10.4966	−0.339130
$959$	0	0
$960$	−7.48842	−0.241688
$961$	−22.3400	−0.720646
$962$	3.99927	0.128942
$963$	8.05109	0.259443
$964$	20.5146	0.660729
$965$	10.1193	0.325751
$966$	0	0
$967$	−10.9509	−0.352158	−0.176079	−	0.984376i	$-0.556341\pi$
$967$	−10.9509	−0.352158	−0.176079	+	0.984376i	$0.556341\pi$
$968$	−33.9343	−1.09069
$969$	4.28852	0.137767
$970$	0.883402	0.0283643
$971$	15.9606	0.512199	0.256100	−	0.966650i	$-0.417563\pi$
$971$	15.9606	0.512199	0.256100	+	0.966650i	$0.417563\pi$
$972$	−0.753512	−0.0241689
$973$	0	0
$974$	27.5695	0.883385
$975$	−4.84188	−0.155064
$976$	14.0825	0.450768
$977$	43.3664	1.38741	0.693707	−	0.720257i	$-0.255976\pi$
$977$	43.3664	1.38741	0.693707	+	0.720257i	$0.255976\pi$
$978$	12.1516	0.388564
$979$	−71.2352	−2.27669
$980$	0	0
$981$	15.5123	0.495270
$982$	39.0390	1.24578
$983$	4.84144	0.154418	0.0772089	−	0.997015i	$-0.475399\pi$
$983$	4.84144	0.154418	0.0772089	+	0.997015i	$0.475399\pi$
$984$	3.07419	0.0980017
$985$	−18.3728	−0.585406
$986$	44.9468	1.43140
$987$	0	0
$988$	−0.739791	−0.0235359
$989$	4.92909	0.156736
$990$	4.72016	0.150017
$991$	−3.88753	−0.123492	−0.0617458	−	0.998092i	$-0.519667\pi$
$991$	−3.88753	−0.123492	−0.0617458	+	0.998092i	$0.519667\pi$
$992$	11.7681	0.373638
$993$	7.32795	0.232545
$994$	0	0
$995$	−1.14253	−0.0362205
$996$	−7.76720	−0.246113
$997$	37.9574	1.20212	0.601062	−	0.799203i	$-0.294745\pi$
$997$	37.9574	1.20212	0.601062	+	0.799203i	$0.294745\pi$
$998$	20.7040	0.655372
$999$	3.09905	0.0980495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.14	yes	24
7.6	odd	2		6027.2.a.bn.1.14	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.14	✓	24	7.6	odd	2
6027.2.a.bo.1.14	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)

\(f(q)\)	\(=\)	\(q+1.11646 q^{2} +1.00000 q^{3} -0.753512 q^{4} -0.900581 q^{5} +1.11646 q^{6} -3.07419 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.11646 q^{2} +1.00000 q^{3} -0.753512 q^{4} -0.900581 q^{5} +1.11646 q^{6} -3.07419 q^{8} +1.00000 q^{9} -1.00546 q^{10} -4.69451 q^{11} -0.753512 q^{12} +1.15587 q^{13} -0.900581 q^{15} -1.92519 q^{16} +5.04891 q^{17} +1.11646 q^{18} +0.849395 q^{19} +0.678599 q^{20} -5.24124 q^{22} -1.63546 q^{23} -3.07419 q^{24} -4.18895 q^{25} +1.29048 q^{26} +1.00000 q^{27} +7.97364 q^{29} -1.00546 q^{30} +2.94278 q^{31} +3.99898 q^{32} -4.69451 q^{33} +5.63692 q^{34} -0.753512 q^{36} +3.09905 q^{37} +0.948318 q^{38} +1.15587 q^{39} +2.76856 q^{40} -1.00000 q^{41} -3.01389 q^{43} +3.53737 q^{44} -0.900581 q^{45} -1.82593 q^{46} -8.14340 q^{47} -1.92519 q^{48} -4.67681 q^{50} +5.04891 q^{51} -0.870962 q^{52} -8.01568 q^{53} +1.11646 q^{54} +4.22779 q^{55} +0.849395 q^{57} +8.90226 q^{58} -2.60113 q^{59} +0.678599 q^{60} -7.31482 q^{61} +3.28551 q^{62} +8.31510 q^{64} -1.04095 q^{65} -5.24124 q^{66} +0.796475 q^{67} -3.80442 q^{68} -1.63546 q^{69} +10.7265 q^{71} -3.07419 q^{72} +1.76040 q^{73} +3.45997 q^{74} -4.18895 q^{75} -0.640030 q^{76} +1.29048 q^{78} +13.8908 q^{79} +1.73379 q^{80} +1.00000 q^{81} -1.11646 q^{82} +10.3080 q^{83} -4.54695 q^{85} -3.36490 q^{86} +7.97364 q^{87} +14.4318 q^{88} +15.1741 q^{89} -1.00546 q^{90} +1.23234 q^{92} +2.94278 q^{93} -9.09180 q^{94} -0.764949 q^{95} +3.99898 q^{96} -0.878601 q^{97} -4.69451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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

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Database

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