LMFDB - Embedded newform 6027.2.a.bn.1.12

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			1.12
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)

$f(q)$	$=$	$q+0.154130 q^{2} -1.00000 q^{3} -1.97624 q^{4} -1.29015 q^{5} -0.154130 q^{6} -0.612860 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.154130 q^{2} -1.00000 q^{3} -1.97624 q^{4} -1.29015 q^{5} -0.154130 q^{6} -0.612860 q^{8} +1.00000 q^{9} -0.198852 q^{10} -3.77802 q^{11} +1.97624 q^{12} +5.50821 q^{13} +1.29015 q^{15} +3.85803 q^{16} +0.121569 q^{17} +0.154130 q^{18} -6.50386 q^{19} +2.54966 q^{20} -0.582308 q^{22} +2.09276 q^{23} +0.612860 q^{24} -3.33550 q^{25} +0.848983 q^{26} -1.00000 q^{27} -1.13312 q^{29} +0.198852 q^{30} -0.113328 q^{31} +1.82036 q^{32} +3.77802 q^{33} +0.0187375 q^{34} -1.97624 q^{36} -4.51508 q^{37} -1.00244 q^{38} -5.50821 q^{39} +0.790684 q^{40} +1.00000 q^{41} +4.61175 q^{43} +7.46629 q^{44} -1.29015 q^{45} +0.322558 q^{46} -3.21303 q^{47} -3.85803 q^{48} -0.514103 q^{50} -0.121569 q^{51} -10.8856 q^{52} -3.27698 q^{53} -0.154130 q^{54} +4.87422 q^{55} +6.50386 q^{57} -0.174649 q^{58} -14.3034 q^{59} -2.54966 q^{60} -2.67949 q^{61} -0.0174672 q^{62} -7.43548 q^{64} -7.10643 q^{65} +0.582308 q^{66} +7.34269 q^{67} -0.240250 q^{68} -2.09276 q^{69} +3.10604 q^{71} -0.612860 q^{72} -0.731899 q^{73} -0.695912 q^{74} +3.33550 q^{75} +12.8532 q^{76} -0.848983 q^{78} -2.88303 q^{79} -4.97745 q^{80} +1.00000 q^{81} +0.154130 q^{82} -6.55587 q^{83} -0.156842 q^{85} +0.710811 q^{86} +1.13312 q^{87} +2.31540 q^{88} -3.36880 q^{89} -0.198852 q^{90} -4.13580 q^{92} +0.113328 q^{93} -0.495226 q^{94} +8.39098 q^{95} -1.82036 q^{96} -6.52076 q^{97} -3.77802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.154130	0.108987	0.0544933	−	0.998514i	$-0.482646\pi$
$2$	0.154130	0.108987	0.0544933	+	0.998514i	$0.482646\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97624	−0.988122
$5$	−1.29015	−0.576974	−0.288487	−	0.957484i	$-0.593152\pi$
$5$	−1.29015	−0.576974	−0.288487	+	0.957484i	$0.593152\pi$
$6$	−0.154130	−0.0629235
$7$	0	0
$7$	0	0
$8$	−0.612860	−0.216679
$9$	1.00000	0.333333
$10$	−0.198852	−0.0628825
$11$	−3.77802	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$11$	−3.77802	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$12$	1.97624	0.570492
$13$	5.50821	1.52770	0.763851	−	0.645393i	$-0.223306\pi$
$13$	5.50821	1.52770	0.763851	+	0.645393i	$0.223306\pi$
$14$	0	0
$15$	1.29015	0.333116
$16$	3.85803	0.964507
$17$	0.121569	0.0294848	0.0147424	−	0.999891i	$-0.495307\pi$
$17$	0.121569	0.0294848	0.0147424	+	0.999891i	$0.495307\pi$
$18$	0.154130	0.0363289
$19$	−6.50386	−1.49209	−0.746044	−	0.665897i	$-0.768049\pi$
$19$	−6.50386	−1.49209	−0.746044	+	0.665897i	$0.768049\pi$
$20$	2.54966	0.570121
$21$	0	0
$22$	−0.582308	−0.124148
$23$	2.09276	0.436370	0.218185	−	0.975907i	$-0.429986\pi$
$23$	2.09276	0.436370	0.218185	+	0.975907i	$0.429986\pi$
$24$	0.612860	0.125100
$25$	−3.33550	−0.667101
$26$	0.848983	0.166499
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.13312	−0.210416	−0.105208	−	0.994450i	$-0.533551\pi$
$29$	−1.13312	−0.210416	−0.105208	+	0.994450i	$0.533551\pi$
$30$	0.198852	0.0363052
$31$	−0.113328	−0.0203543	−0.0101771	−	0.999948i	$-0.503240\pi$
$31$	−0.113328	−0.0203543	−0.0101771	+	0.999948i	$0.503240\pi$
$32$	1.82036	0.321797
$33$	3.77802	0.657669
$34$	0.0187375	0.00321345
$35$	0	0
$36$	−1.97624	−0.329374
$37$	−4.51508	−0.742275	−0.371137	−	0.928578i	$-0.621032\pi$
$37$	−4.51508	−0.742275	−0.371137	+	0.928578i	$0.621032\pi$
$38$	−1.00244	−0.162618
$39$	−5.50821	−0.882019
$40$	0.790684	0.125018
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	4.61175	0.703285	0.351642	−	0.936134i	$-0.385623\pi$
$43$	4.61175	0.703285	0.351642	+	0.936134i	$0.385623\pi$
$44$	7.46629	1.12558
$45$	−1.29015	−0.192325
$46$	0.322558	0.0475586
$47$	−3.21303	−0.468669	−0.234334	−	0.972156i	$-0.575291\pi$
$47$	−3.21303	−0.468669	−0.234334	+	0.972156i	$0.575291\pi$
$48$	−3.85803	−0.556858
$49$	0	0
$50$	−0.514103	−0.0727051
$51$	−0.121569	−0.0170230
$52$	−10.8856	−1.50956
$53$	−3.27698	−0.450128	−0.225064	−	0.974344i	$-0.572259\pi$
$53$	−3.27698	−0.450128	−0.225064	+	0.974344i	$0.572259\pi$
$54$	−0.154130	−0.0209745
$55$	4.87422	0.657240
$56$	0	0
$57$	6.50386	0.861457
$58$	−0.174649	−0.0229325
$59$	−14.3034	−1.86214	−0.931071	−	0.364838i	$-0.881124\pi$
$59$	−14.3034	−1.86214	−0.931071	+	0.364838i	$0.881124\pi$
$60$	−2.54966	−0.329159
$61$	−2.67949	−0.343073	−0.171537	−	0.985178i	$-0.554873\pi$
$61$	−2.67949	−0.343073	−0.171537	+	0.985178i	$0.554873\pi$
$62$	−0.0174672	−0.00221834
$63$	0	0
$64$	−7.43548	−0.929435
$65$	−7.10643	−0.881445
$66$	0.582308	0.0716771
$67$	7.34269	0.897052	0.448526	−	0.893770i	$-0.351949\pi$
$67$	7.34269	0.897052	0.448526	+	0.893770i	$0.351949\pi$
$68$	−0.240250	−0.0291346
$69$	−2.09276	−0.251939
$70$	0	0
$71$	3.10604	0.368619	0.184310	−	0.982868i	$-0.440995\pi$
$71$	3.10604	0.368619	0.184310	+	0.982868i	$0.440995\pi$
$72$	−0.612860	−0.0722263
$73$	−0.731899	−0.0856622	−0.0428311	−	0.999082i	$-0.513638\pi$
$73$	−0.731899	−0.0856622	−0.0428311	+	0.999082i	$0.513638\pi$
$74$	−0.695912	−0.0808981
$75$	3.33550	0.385151
$76$	12.8532	1.47436
$77$	0	0
$78$	−0.848983	−0.0961284
$79$	−2.88303	−0.324367	−0.162183	−	0.986761i	$-0.551854\pi$
$79$	−2.88303	−0.324367	−0.162183	+	0.986761i	$0.551854\pi$
$80$	−4.97745	−0.556495
$81$	1.00000	0.111111
$82$	0.154130	0.0170209
$83$	−6.55587	−0.719600	−0.359800	−	0.933029i	$-0.617155\pi$
$83$	−6.55587	−0.719600	−0.359800	+	0.933029i	$0.617155\pi$
$84$	0	0
$85$	−0.156842	−0.0170120
$86$	0.710811	0.0766487
$87$	1.13312	0.121483
$88$	2.31540	0.246822
$89$	−3.36880	−0.357092	−0.178546	−	0.983932i	$-0.557139\pi$
$89$	−3.36880	−0.357092	−0.178546	+	0.983932i	$0.557139\pi$
$90$	−0.198852	−0.0209608
$91$	0	0
$92$	−4.13580	−0.431187
$93$	0.113328	0.0117515
$94$	−0.495226	−0.0510787
$95$	8.39098	0.860896
$96$	−1.82036	−0.185790
$97$	−6.52076	−0.662083	−0.331042	−	0.943616i	$-0.607400\pi$
$97$	−6.52076	−0.662083	−0.331042	+	0.943616i	$0.607400\pi$
$98$	0	0
$99$	−3.77802	−0.379705
$100$	6.59177	0.659177
$101$	−3.97834	−0.395860	−0.197930	−	0.980216i	$-0.563422\pi$
$101$	−3.97834	−0.395860	−0.197930	+	0.980216i	$0.563422\pi$
$102$	−0.0187375	−0.00185529
$103$	−2.95010	−0.290682	−0.145341	−	0.989382i	$-0.546428\pi$
$103$	−2.95010	−0.290682	−0.145341	+	0.989382i	$0.546428\pi$
$104$	−3.37576	−0.331021
$105$	0	0
$106$	−0.505083	−0.0490580
$107$	−1.30384	−0.126047	−0.0630236	−	0.998012i	$-0.520074\pi$
$107$	−1.30384	−0.126047	−0.0630236	+	0.998012i	$0.520074\pi$
$108$	1.97624	0.190164
$109$	10.5669	1.01213	0.506064	−	0.862496i	$-0.331100\pi$
$109$	10.5669	1.01213	0.506064	+	0.862496i	$0.331100\pi$
$110$	0.751266	0.0716304
$111$	4.51508	0.428553
$112$	0	0
$113$	−4.50316	−0.423622	−0.211811	−	0.977311i	$-0.567936\pi$
$113$	−4.50316	−0.423622	−0.211811	+	0.977311i	$0.567936\pi$
$114$	1.00244	0.0938874
$115$	−2.69998	−0.251774
$116$	2.23933	0.207916
$117$	5.50821	0.509234
$118$	−2.20459	−0.202949
$119$	0	0
$120$	−0.790684	−0.0721792
$121$	3.27343	0.297584
$122$	−0.412991	−0.0373904
$123$	−1.00000	−0.0901670
$124$	0.223963	0.0201125
$125$	10.7541	0.961874
$126$	0	0
$127$	4.04765	0.359171	0.179586	−	0.983742i	$-0.442524\pi$
$127$	4.04765	0.359171	0.179586	+	0.983742i	$0.442524\pi$
$128$	−4.78675	−0.423093
$129$	−4.61175	−0.406042
$130$	−1.09532	−0.0960657
$131$	7.14901	0.624611	0.312306	−	0.949982i	$-0.398899\pi$
$131$	7.14901	0.624611	0.312306	+	0.949982i	$0.398899\pi$
$132$	−7.46629	−0.649857
$133$	0	0
$134$	1.13173	0.0977667
$135$	1.29015	0.111039
$136$	−0.0745047	−0.00638873
$137$	−17.5752	−1.50155	−0.750776	−	0.660557i	$-0.770320\pi$
$137$	−17.5752	−1.50155	−0.750776	+	0.660557i	$0.770320\pi$
$138$	−0.322558	−0.0274579
$139$	−3.95483	−0.335444	−0.167722	−	0.985834i	$-0.553641\pi$
$139$	−3.95483	−0.335444	−0.167722	+	0.985834i	$0.553641\pi$
$140$	0	0
$141$	3.21303	0.270586
$142$	0.478735	0.0401746
$143$	−20.8101	−1.74023
$144$	3.85803	0.321502
$145$	1.46190	0.121404
$146$	−0.112808	−0.00933604
$147$	0	0
$148$	8.92290	0.733458
$149$	16.2067	1.32770	0.663851	−	0.747865i	$-0.268921\pi$
$149$	16.2067	1.32770	0.663851	+	0.747865i	$0.268921\pi$
$150$	0.514103	0.0419763
$151$	14.5427	1.18347	0.591733	−	0.806134i	$-0.298444\pi$
$151$	14.5427	1.18347	0.591733	+	0.806134i	$0.298444\pi$
$152$	3.98596	0.323304
$153$	0.121569	0.00982826
$154$	0	0
$155$	0.146210	0.0117439
$156$	10.8856	0.871543
$157$	4.06842	0.324695	0.162348	−	0.986734i	$-0.448093\pi$
$157$	4.06842	0.324695	0.162348	+	0.986734i	$0.448093\pi$
$158$	−0.444363	−0.0353516
$159$	3.27698	0.259881
$160$	−2.34854	−0.185669
$161$	0	0
$162$	0.154130	0.0121096
$163$	7.98083	0.625107	0.312553	−	0.949900i	$-0.398816\pi$
$163$	7.98083	0.625107	0.312553	+	0.949900i	$0.398816\pi$
$164$	−1.97624	−0.154319
$165$	−4.87422	−0.379458
$166$	−1.01046	−0.0784268
$167$	−14.5338	−1.12466	−0.562328	−	0.826914i	$-0.690094\pi$
$167$	−14.5338	−1.12466	−0.562328	+	0.826914i	$0.690094\pi$
$168$	0	0
$169$	17.3404	1.33387
$170$	−0.0241742	−0.00185408
$171$	−6.50386	−0.497363
$172$	−9.11394	−0.694931
$173$	−14.8784	−1.13118	−0.565590	−	0.824686i	$-0.691352\pi$
$173$	−14.8784	−1.13118	−0.565590	+	0.824686i	$0.691352\pi$
$174$	0.174649	0.0132401
$175$	0	0
$176$	−14.5757	−1.09868
$177$	14.3034	1.07511
$178$	−0.519234	−0.0389182
$179$	4.68426	0.350118	0.175059	−	0.984558i	$-0.443988\pi$
$179$	4.68426	0.350118	0.175059	+	0.984558i	$0.443988\pi$
$180$	2.54966	0.190040
$181$	8.01866	0.596022	0.298011	−	0.954562i	$-0.403677\pi$
$181$	8.01866	0.596022	0.298011	+	0.954562i	$0.403677\pi$
$182$	0	0
$183$	2.67949	0.198074
$184$	−1.28257	−0.0945522
$185$	5.82515	0.428273
$186$	0.0174672	0.00128076
$187$	−0.459289	−0.0335866
$188$	6.34973	0.463102
$189$	0	0
$190$	1.29330	0.0938262
$191$	13.6428	0.987159	0.493580	−	0.869701i	$-0.335688\pi$
$191$	13.6428	0.987159	0.493580	+	0.869701i	$0.335688\pi$
$192$	7.43548	0.536610
$193$	18.4776	1.33005	0.665024	−	0.746822i	$-0.268422\pi$
$193$	18.4776	1.33005	0.665024	+	0.746822i	$0.268422\pi$
$194$	−1.00505	−0.0721583
$195$	7.10643	0.508902
$196$	0	0
$197$	17.1601	1.22261	0.611305	−	0.791395i	$-0.290645\pi$
$197$	17.1601	1.22261	0.611305	+	0.791395i	$0.290645\pi$
$198$	−0.582308	−0.0413828
$199$	−25.7822	−1.82765	−0.913827	−	0.406104i	$-0.866887\pi$
$199$	−25.7822	−1.82765	−0.913827	+	0.406104i	$0.866887\pi$
$200$	2.04420	0.144547
$201$	−7.34269	−0.517913
$202$	−0.613184	−0.0431435
$203$	0	0
$204$	0.240250	0.0168208
$205$	−1.29015	−0.0901082
$206$	−0.454700	−0.0316805
$207$	2.09276	0.145457
$208$	21.2508	1.47348
$209$	24.5717	1.69966
$210$	0	0
$211$	12.0460	0.829278	0.414639	−	0.909986i	$-0.363908\pi$
$211$	12.0460	0.829278	0.414639	+	0.909986i	$0.363908\pi$
$212$	6.47611	0.444781
$213$	−3.10604	−0.212822
$214$	−0.200962	−0.0137375
$215$	−5.94986	−0.405777
$216$	0.612860	0.0416999
$217$	0	0
$218$	1.62868	0.110308
$219$	0.731899	0.0494571
$220$	−9.63265	−0.649433
$221$	0.669627	0.0450440
$222$	0.695912	0.0467065
$223$	−8.09744	−0.542244	−0.271122	−	0.962545i	$-0.587395\pi$
$223$	−8.09744	−0.542244	−0.271122	+	0.962545i	$0.587395\pi$
$224$	0	0
$225$	−3.33550	−0.222367
$226$	−0.694074	−0.0461691
$227$	11.4711	0.761361	0.380680	−	0.924707i	$-0.375690\pi$
$227$	11.4711	0.761361	0.380680	+	0.924707i	$0.375690\pi$
$228$	−12.8532	−0.851225
$229$	24.3289	1.60770	0.803850	−	0.594831i	$-0.202781\pi$
$229$	24.3289	1.60770	0.803850	+	0.594831i	$0.202781\pi$
$230$	−0.416149	−0.0274401
$231$	0	0
$232$	0.694446	0.0455926
$233$	25.1806	1.64964	0.824818	−	0.565399i	$-0.191278\pi$
$233$	25.1806	1.64964	0.824818	+	0.565399i	$0.191278\pi$
$234$	0.848983	0.0554997
$235$	4.14530	0.270410
$236$	28.2670	1.84002
$237$	2.88303	0.187273
$238$	0	0
$239$	−9.08432	−0.587616	−0.293808	−	0.955864i	$-0.594923\pi$
$239$	−9.08432	−0.587616	−0.293808	+	0.955864i	$0.594923\pi$
$240$	4.97745	0.321293
$241$	14.4274	0.929354	0.464677	−	0.885480i	$-0.346171\pi$
$241$	14.4274	0.929354	0.464677	+	0.885480i	$0.346171\pi$
$242$	0.504535	0.0324327
$243$	−1.00000	−0.0641500
$244$	5.29532	0.338998
$245$	0	0
$246$	−0.154130	−0.00982700
$247$	−35.8246	−2.27947
$248$	0.0694540	0.00441034
$249$	6.55587	0.415461
$250$	1.65753	0.104831
$251$	26.3124	1.66082	0.830412	−	0.557151i	$-0.188105\pi$
$251$	26.3124	1.66082	0.830412	+	0.557151i	$0.188105\pi$
$252$	0	0
$253$	−7.90648	−0.497076
$254$	0.623866	0.0391449
$255$	0.156842	0.00982186
$256$	14.1332	0.883324
$257$	18.3673	1.14572	0.572862	−	0.819652i	$-0.305833\pi$
$257$	18.3673	1.14572	0.572862	+	0.819652i	$0.305833\pi$
$258$	−0.710811	−0.0442531
$259$	0	0
$260$	14.0440	0.870975
$261$	−1.13312	−0.0701385
$262$	1.10188	0.0680743
$263$	−13.5912	−0.838068	−0.419034	−	0.907971i	$-0.637631\pi$
$263$	−13.5912	−0.838068	−0.419034	+	0.907971i	$0.637631\pi$
$264$	−2.31540	−0.142503
$265$	4.22781	0.259712
$266$	0	0
$267$	3.36880	0.206167
$268$	−14.5109	−0.886397
$269$	−1.77787	−0.108398	−0.0541992	−	0.998530i	$-0.517261\pi$
$269$	−1.77787	−0.108398	−0.0541992	+	0.998530i	$0.517261\pi$
$270$	0.198852	0.0121017
$271$	8.39209	0.509783	0.254892	−	0.966970i	$-0.417960\pi$
$271$	8.39209	0.509783	0.254892	+	0.966970i	$0.417960\pi$
$272$	0.469016	0.0284383
$273$	0	0
$274$	−2.70888	−0.163649
$275$	12.6016	0.759905
$276$	4.13580	0.248946
$277$	29.7741	1.78895	0.894477	−	0.447113i	$-0.147548\pi$
$277$	29.7741	1.78895	0.894477	+	0.447113i	$0.147548\pi$
$278$	−0.609560	−0.0365590
$279$	−0.113328	−0.00678475
$280$	0	0
$281$	−4.65730	−0.277831	−0.138915	−	0.990304i	$-0.544362\pi$
$281$	−4.65730	−0.277831	−0.138915	+	0.990304i	$0.544362\pi$
$282$	0.495226	0.0294903
$283$	2.98479	0.177427	0.0887136	−	0.996057i	$-0.471724\pi$
$283$	2.98479	0.177427	0.0887136	+	0.996057i	$0.471724\pi$
$284$	−6.13829	−0.364241
$285$	−8.39098	−0.497038
$286$	−3.20747	−0.189662
$287$	0	0
$288$	1.82036	0.107266
$289$	−16.9852	−0.999131
$290$	0.225324	0.0132315
$291$	6.52076	0.382254
$292$	1.44641	0.0846447
$293$	0.465557	0.0271982	0.0135991	−	0.999908i	$-0.495671\pi$
$293$	0.465557	0.0271982	0.0135991	+	0.999908i	$0.495671\pi$
$294$	0	0
$295$	18.4536	1.07441
$296$	2.76711	0.160835
$297$	3.77802	0.219223
$298$	2.49794	0.144702
$299$	11.5274	0.666644
$300$	−6.59177	−0.380576
$301$	0	0
$302$	2.24147	0.128982
$303$	3.97834	0.228550
$304$	−25.0921	−1.43913
$305$	3.45695	0.197944
$306$	0.0187375	0.00107115
$307$	4.58705	0.261797	0.130898	−	0.991396i	$-0.458214\pi$
$307$	4.58705	0.261797	0.130898	+	0.991396i	$0.458214\pi$
$308$	0	0
$309$	2.95010	0.167825
$310$	0.0225354	0.00127993
$311$	−6.72674	−0.381439	−0.190719	−	0.981645i	$-0.561082\pi$
$311$	−6.72674	−0.381439	−0.190719	+	0.981645i	$0.561082\pi$
$312$	3.37576	0.191115
$313$	7.56580	0.427644	0.213822	−	0.976873i	$-0.431409\pi$
$313$	7.56580	0.427644	0.213822	+	0.976873i	$0.431409\pi$
$314$	0.627067	0.0353874
$315$	0	0
$316$	5.69758	0.320514
$317$	−6.60093	−0.370745	−0.185373	−	0.982668i	$-0.559349\pi$
$317$	−6.60093	−0.370745	−0.185373	+	0.982668i	$0.559349\pi$
$318$	0.505083	0.0283236
$319$	4.28096	0.239688
$320$	9.59291	0.536260
$321$	1.30384	0.0727734
$322$	0	0
$323$	−0.790667	−0.0439939
$324$	−1.97624	−0.109791
$325$	−18.3727	−1.01913
$326$	1.23009	0.0681283
$327$	−10.5669	−0.584352
$328$	−0.612860	−0.0338395
$329$	0	0
$330$	−0.751266	−0.0413558
$331$	−1.51697	−0.0833804	−0.0416902	−	0.999131i	$-0.513274\pi$
$331$	−1.51697	−0.0833804	−0.0416902	+	0.999131i	$0.513274\pi$
$332$	12.9560	0.711053
$333$	−4.51508	−0.247425
$334$	−2.24010	−0.122573
$335$	−9.47319	−0.517576
$336$	0	0
$337$	−9.49236	−0.517082	−0.258541	−	0.966000i	$-0.583242\pi$
$337$	−9.49236	−0.517082	−0.258541	+	0.966000i	$0.583242\pi$
$338$	2.67268	0.145374
$339$	4.50316	0.244578
$340$	0.309959	0.0168099
$341$	0.428154	0.0231858
$342$	−1.00244	−0.0542059
$343$	0	0
$344$	−2.82636	−0.152387
$345$	2.69998	0.145362
$346$	−2.29321	−0.123284
$347$	−8.34881	−0.448187	−0.224094	−	0.974568i	$-0.571942\pi$
$347$	−8.34881	−0.448187	−0.224094	+	0.974568i	$0.571942\pi$
$348$	−2.23933	−0.120040
$349$	29.3068	1.56875	0.784377	−	0.620284i	$-0.212983\pi$
$349$	29.3068	1.56875	0.784377	+	0.620284i	$0.212983\pi$
$350$	0	0
$351$	−5.50821	−0.294006
$352$	−6.87735	−0.366564
$353$	10.7354	0.571387	0.285693	−	0.958321i	$-0.407776\pi$
$353$	10.7354	0.571387	0.285693	+	0.958321i	$0.407776\pi$
$354$	2.20459	0.117172
$355$	−4.00727	−0.212684
$356$	6.65756	0.352850
$357$	0	0
$358$	0.721987	0.0381582
$359$	6.31700	0.333398	0.166699	−	0.986008i	$-0.446689\pi$
$359$	6.31700	0.333398	0.166699	+	0.986008i	$0.446689\pi$
$360$	0.790684	0.0416727
$361$	23.3002	1.22633
$362$	1.23592	0.0649585
$363$	−3.27343	−0.171810
$364$	0	0
$365$	0.944261	0.0494249
$366$	0.412991	0.0215874
$367$	−29.4744	−1.53855	−0.769275	−	0.638918i	$-0.779382\pi$
$367$	−29.4744	−1.53855	−0.769275	+	0.638918i	$0.779382\pi$
$368$	8.07392	0.420882
$369$	1.00000	0.0520579
$370$	0.897833	0.0466761
$371$	0	0
$372$	−0.223963	−0.0116119
$373$	23.6804	1.22612	0.613062	−	0.790035i	$-0.289938\pi$
$373$	23.6804	1.22612	0.613062	+	0.790035i	$0.289938\pi$
$374$	−0.0707905	−0.00366049
$375$	−10.7541	−0.555338
$376$	1.96914	0.101551
$377$	−6.24147	−0.321452
$378$	0	0
$379$	−3.19736	−0.164238	−0.0821188	−	0.996623i	$-0.526169\pi$
$379$	−3.19736	−0.164238	−0.0821188	+	0.996623i	$0.526169\pi$
$380$	−16.5826	−0.850670
$381$	−4.04765	−0.207368
$382$	2.10277	0.107587
$383$	−24.0506	−1.22893	−0.614463	−	0.788945i	$-0.710627\pi$
$383$	−24.0506	−1.22893	−0.614463	+	0.788945i	$0.710627\pi$
$384$	4.78675	0.244273
$385$	0	0
$386$	2.84796	0.144957
$387$	4.61175	0.234428
$388$	12.8866	0.654219
$389$	21.5294	1.09158	0.545792	−	0.837921i	$-0.316229\pi$
$389$	21.5294	1.09158	0.545792	+	0.837921i	$0.316229\pi$
$390$	1.09532	0.0554636
$391$	0.254414	0.0128663
$392$	0	0
$393$	−7.14901	−0.360620
$394$	2.64490	0.133248
$395$	3.71956	0.187151
$396$	7.46629	0.375195
$397$	−7.77612	−0.390272	−0.195136	−	0.980776i	$-0.562515\pi$
$397$	−7.77612	−0.390272	−0.195136	+	0.980776i	$0.562515\pi$
$398$	−3.97383	−0.199190
$399$	0	0
$400$	−12.8685	−0.643423
$401$	33.4974	1.67278	0.836391	−	0.548134i	$-0.184661\pi$
$401$	33.4974	1.67278	0.836391	+	0.548134i	$0.184661\pi$
$402$	−1.13173	−0.0564456
$403$	−0.624233	−0.0310952
$404$	7.86217	0.391158
$405$	−1.29015	−0.0641082
$406$	0	0
$407$	17.0581	0.845537
$408$	0.0745047	0.00368853
$409$	24.0491	1.18915	0.594576	−	0.804040i	$-0.297320\pi$
$409$	24.0491	1.18915	0.594576	+	0.804040i	$0.297320\pi$
$410$	−0.198852	−0.00982060
$411$	17.5752	0.866921
$412$	5.83011	0.287229
$413$	0	0
$414$	0.322558	0.0158529
$415$	8.45808	0.415191
$416$	10.0269	0.491610
$417$	3.95483	0.193669
$418$	3.78725	0.185240
$419$	−16.1119	−0.787120	−0.393560	−	0.919299i	$-0.628757\pi$
$419$	−16.1119	−0.787120	−0.393560	+	0.919299i	$0.628757\pi$
$420$	0	0
$421$	−19.6558	−0.957965	−0.478983	−	0.877824i	$-0.658994\pi$
$421$	−19.6558	−0.957965	−0.478983	+	0.877824i	$0.658994\pi$
$422$	1.85665	0.0903802
$423$	−3.21303	−0.156223
$424$	2.00833	0.0975332
$425$	−0.405494	−0.0196693
$426$	−0.478735	−0.0231948
$427$	0	0
$428$	2.57671	0.124550
$429$	20.8101	1.00472
$430$	−0.917055	−0.0442243
$431$	18.4967	0.890954	0.445477	−	0.895293i	$-0.353034\pi$
$431$	18.4967	0.890954	0.445477	+	0.895293i	$0.353034\pi$
$432$	−3.85803	−0.185619
$433$	−23.4044	−1.12474	−0.562371	−	0.826885i	$-0.690111\pi$
$433$	−23.4044	−1.12474	−0.562371	+	0.826885i	$0.690111\pi$
$434$	0	0
$435$	−1.46190	−0.0700928
$436$	−20.8828	−1.00011
$437$	−13.6110	−0.651103
$438$	0.112808	0.00539017
$439$	0.517097	0.0246797	0.0123399	−	0.999924i	$-0.496072\pi$
$439$	0.517097	0.0246797	0.0123399	+	0.999924i	$0.496072\pi$
$440$	−2.98722	−0.142410
$441$	0	0
$442$	0.103210	0.00490919
$443$	17.2656	0.820315	0.410158	−	0.912015i	$-0.365474\pi$
$443$	17.2656	0.820315	0.410158	+	0.912015i	$0.365474\pi$
$444$	−8.92290	−0.423462
$445$	4.34626	0.206033
$446$	−1.24806	−0.0590974
$447$	−16.2067	−0.766549
$448$	0	0
$449$	10.2397	0.483243	0.241621	−	0.970371i	$-0.422321\pi$
$449$	10.2397	0.483243	0.241621	+	0.970371i	$0.422321\pi$
$450$	−0.514103	−0.0242350
$451$	−3.77802	−0.177900
$452$	8.89934	0.418590
$453$	−14.5427	−0.683274
$454$	1.76804	0.0829782
$455$	0	0
$456$	−3.98596	−0.186660
$457$	6.07076	0.283978	0.141989	−	0.989868i	$-0.454650\pi$
$457$	6.07076	0.283978	0.141989	+	0.989868i	$0.454650\pi$
$458$	3.74983	0.175218
$459$	−0.121569	−0.00567435
$460$	5.33582	0.248784
$461$	−4.64500	−0.216339	−0.108170	−	0.994132i	$-0.534499\pi$
$461$	−4.64500	−0.216339	−0.108170	+	0.994132i	$0.534499\pi$
$462$	0	0
$463$	−34.1752	−1.58826	−0.794128	−	0.607751i	$-0.792072\pi$
$463$	−34.1752	−1.58826	−0.794128	+	0.607751i	$0.792072\pi$
$464$	−4.37162	−0.202947
$465$	−0.146210	−0.00678033
$466$	3.88110	0.179788
$467$	−13.8420	−0.640530	−0.320265	−	0.947328i	$-0.603772\pi$
$467$	−13.8420	−0.640530	−0.320265	+	0.947328i	$0.603772\pi$
$468$	−10.8856	−0.503185
$469$	0	0
$470$	0.638917	0.0294711
$471$	−4.06842	−0.187463
$472$	8.76598	0.403487
$473$	−17.4233	−0.801123
$474$	0.444363	0.0204103
$475$	21.6936	0.995373
$476$	0	0
$477$	−3.27698	−0.150043
$478$	−1.40017	−0.0640423
$479$	23.3850	1.06849	0.534245	−	0.845330i	$-0.320596\pi$
$479$	23.3850	1.06849	0.534245	+	0.845330i	$0.320596\pi$
$480$	2.34854	0.107196
$481$	−24.8700	−1.13397
$482$	2.22371	0.101287
$483$	0	0
$484$	−6.46909	−0.294049
$485$	8.41279	0.382005
$486$	−0.154130	−0.00699150
$487$	6.83886	0.309898	0.154949	−	0.987922i	$-0.450479\pi$
$487$	6.83886	0.309898	0.154949	+	0.987922i	$0.450479\pi$
$488$	1.64215	0.0743367
$489$	−7.98083	−0.360905
$490$	0	0
$491$	−39.3373	−1.77527	−0.887634	−	0.460550i	$-0.847652\pi$
$491$	−39.3373	−1.77527	−0.887634	+	0.460550i	$0.847652\pi$
$492$	1.97624	0.0890960
$493$	−0.137752	−0.00620406
$494$	−5.52166	−0.248431
$495$	4.87422	0.219080
$496$	−0.437221	−0.0196318
$497$	0	0
$498$	1.01046	0.0452798
$499$	12.7479	0.570675	0.285338	−	0.958427i	$-0.407894\pi$
$499$	12.7479	0.570675	0.285338	+	0.958427i	$0.407894\pi$
$500$	−21.2527	−0.950449
$501$	14.5338	0.649321
$502$	4.05554	0.181008
$503$	−36.4861	−1.62684	−0.813418	−	0.581680i	$-0.802396\pi$
$503$	−36.4861	−1.62684	−0.813418	+	0.581680i	$0.802396\pi$
$504$	0	0
$505$	5.13267	0.228401
$506$	−1.21863	−0.0541747
$507$	−17.3404	−0.770112
$508$	−7.99915	−0.354905
$509$	1.47556	0.0654028	0.0327014	−	0.999465i	$-0.489589\pi$
$509$	1.47556	0.0654028	0.0327014	+	0.999465i	$0.489589\pi$
$510$	0.0241742	0.00107045
$511$	0	0
$512$	11.7519	0.519364
$513$	6.50386	0.287152
$514$	2.83097	0.124869
$515$	3.80608	0.167716
$516$	9.11394	0.401219
$517$	12.1389	0.533868
$518$	0	0
$519$	14.8784	0.653088
$520$	4.35525	0.190990
$521$	−37.2361	−1.63134	−0.815672	−	0.578515i	$-0.803633\pi$
$521$	−37.2361	−1.63134	−0.815672	+	0.578515i	$0.803633\pi$
$522$	−0.174649	−0.00764416
$523$	28.3629	1.24022	0.620111	−	0.784514i	$-0.287087\pi$
$523$	28.3629	1.24022	0.620111	+	0.784514i	$0.287087\pi$
$524$	−14.1282	−0.617192
$525$	0	0
$526$	−2.09481	−0.0913382
$527$	−0.0137771	−0.000600141 0
$528$	14.5757	0.634326
$529$	−18.6204	−0.809581
$530$	0.651634	0.0283052
$531$	−14.3034	−0.620714
$532$	0	0
$533$	5.50821	0.238587
$534$	0.519234	0.0224695
$535$	1.68216	0.0727260
$536$	−4.50004	−0.194372
$537$	−4.68426	−0.202141
$538$	−0.274023	−0.0118140
$539$	0	0
$540$	−2.54966	−0.109720
$541$	−25.2475	−1.08547	−0.542737	−	0.839903i	$-0.682612\pi$
$541$	−25.2475	−1.08547	−0.542737	+	0.839903i	$0.682612\pi$
$542$	1.29348	0.0555596
$543$	−8.01866	−0.344113
$544$	0.221299	0.00948812
$545$	−13.6330	−0.583971
$546$	0	0
$547$	40.2326	1.72022	0.860110	−	0.510108i	$-0.170395\pi$
$547$	40.2326	1.72022	0.860110	+	0.510108i	$0.170395\pi$
$548$	34.7329	1.48372
$549$	−2.67949	−0.114358
$550$	1.94229	0.0828195
$551$	7.36967	0.313958
$552$	1.28257	0.0545897
$553$	0	0
$554$	4.58910	0.194972
$555$	−5.82515	−0.247264
$556$	7.81571	0.331460
$557$	35.8092	1.51728	0.758641	−	0.651509i	$-0.225864\pi$
$557$	35.8092	1.51728	0.758641	+	0.651509i	$0.225864\pi$
$558$	−0.0174672	−0.000739448 0
$559$	25.4025	1.07441
$560$	0	0
$561$	0.459289	0.0193912
$562$	−0.717831	−0.0302799
$563$	46.0498	1.94077	0.970384	−	0.241567i	$-0.0776615\pi$
$563$	46.0498	1.94077	0.970384	+	0.241567i	$0.0776615\pi$
$564$	−6.34973	−0.267372
$565$	5.80977	0.244419
$566$	0.460047	0.0193372
$567$	0	0
$568$	−1.90357	−0.0798720
$569$	12.4998	0.524020	0.262010	−	0.965065i	$-0.415615\pi$
$569$	12.4998	0.524020	0.262010	+	0.965065i	$0.415615\pi$
$570$	−1.29330	−0.0541706
$571$	23.9412	1.00191	0.500955	−	0.865473i	$-0.332982\pi$
$571$	23.9412	1.00191	0.500955	+	0.865473i	$0.332982\pi$
$572$	41.1259	1.71956
$573$	−13.6428	−0.569937
$574$	0	0
$575$	−6.98041	−0.291103
$576$	−7.43548	−0.309812
$577$	1.55255	0.0646333	0.0323167	−	0.999478i	$-0.489711\pi$
$577$	1.55255	0.0646333	0.0323167	+	0.999478i	$0.489711\pi$
$578$	−2.61794	−0.108892
$579$	−18.4776	−0.767903
$580$	−2.88907	−0.119962
$581$	0	0
$582$	1.00505	0.0416606
$583$	12.3805	0.512748
$584$	0.448552	0.0185612
$585$	−7.10643	−0.293815
$586$	0.0717566	0.00296424
$587$	22.9983	0.949241	0.474620	−	0.880191i	$-0.342585\pi$
$587$	22.9983	0.949241	0.474620	+	0.880191i	$0.342585\pi$
$588$	0	0
$589$	0.737067	0.0303703
$590$	2.84426	0.117096
$591$	−17.1601	−0.705874
$592$	−17.4193	−0.715929
$593$	−42.4147	−1.74176	−0.870882	−	0.491493i	$-0.836451\pi$
$593$	−42.4147	−1.74176	−0.870882	+	0.491493i	$0.836451\pi$
$594$	0.582308	0.0238924
$595$	0	0
$596$	−32.0283	−1.31193
$597$	25.7822	1.05520
$598$	1.77672	0.0726553
$599$	−23.6434	−0.966044	−0.483022	−	0.875608i	$-0.660461\pi$
$599$	−23.6434	−0.966044	−0.483022	+	0.875608i	$0.660461\pi$
$600$	−2.04420	−0.0834540
$601$	16.8107	0.685723	0.342861	−	0.939386i	$-0.388604\pi$
$601$	16.8107	0.685723	0.342861	+	0.939386i	$0.388604\pi$
$602$	0	0
$603$	7.34269	0.299017
$604$	−28.7398	−1.16941
$605$	−4.22322	−0.171698
$606$	0.613184	0.0249089
$607$	−6.34679	−0.257608	−0.128804	−	0.991670i	$-0.541114\pi$
$607$	−6.34679	−0.257608	−0.128804	+	0.991670i	$0.541114\pi$
$608$	−11.8394	−0.480150
$609$	0	0
$610$	0.532821	0.0215733
$611$	−17.6980	−0.715986
$612$	−0.240250	−0.00971152
$613$	24.9933	1.00947	0.504735	−	0.863274i	$-0.331590\pi$
$613$	24.9933	1.00947	0.504735	+	0.863274i	$0.331590\pi$
$614$	0.707004	0.0285324
$615$	1.29015	0.0520240
$616$	0	0
$617$	7.73786	0.311514	0.155757	−	0.987795i	$-0.450218\pi$
$617$	7.73786	0.311514	0.155757	+	0.987795i	$0.450218\pi$
$618$	0.454700	0.0182907
$619$	−10.8909	−0.437740	−0.218870	−	0.975754i	$-0.570237\pi$
$619$	−10.8909	−0.437740	−0.218870	+	0.975754i	$0.570237\pi$
$620$	−0.288947	−0.0116044
$621$	−2.09276	−0.0839795
$622$	−1.03680	−0.0415717
$623$	0	0
$624$	−21.2508	−0.850714
$625$	2.80311	0.112124
$626$	1.16612	0.0466075
$627$	−24.5717	−0.981299
$628$	−8.04019	−0.320838
$629$	−0.548893	−0.0218858
$630$	0	0
$631$	40.7070	1.62052	0.810260	−	0.586070i	$-0.199326\pi$
$631$	40.7070	1.62052	0.810260	+	0.586070i	$0.199326\pi$
$632$	1.76690	0.0702834
$633$	−12.0460	−0.478784
$634$	−1.01740	−0.0404063
$635$	−5.22209	−0.207232
$636$	−6.47611	−0.256795
$637$	0	0
$638$	0.659826	0.0261228
$639$	3.10604	0.122873
$640$	6.17565	0.244114
$641$	26.8036	1.05868	0.529339	−	0.848410i	$-0.322440\pi$
$641$	26.8036	1.05868	0.529339	+	0.848410i	$0.322440\pi$
$642$	0.200962	0.00793134
$643$	35.7750	1.41083	0.705415	−	0.708795i	$-0.250761\pi$
$643$	35.7750	1.41083	0.705415	+	0.708795i	$0.250761\pi$
$644$	0	0
$645$	5.94986	0.234276
$646$	−0.121866	−0.00479475
$647$	−45.1241	−1.77401	−0.887006	−	0.461758i	$-0.847219\pi$
$647$	−45.1241	−1.77401	−0.887006	+	0.461758i	$0.847219\pi$
$648$	−0.612860	−0.0240754
$649$	54.0385	2.12119
$650$	−2.83179	−0.111072
$651$	0	0
$652$	−15.7721	−0.617681
$653$	−2.37175	−0.0928136	−0.0464068	−	0.998923i	$-0.514777\pi$
$653$	−2.37175	−0.0928136	−0.0464068	+	0.998923i	$0.514777\pi$
$654$	−1.62868	−0.0636866
$655$	−9.22331	−0.360385
$656$	3.85803	0.150631
$657$	−0.731899	−0.0285541
$658$	0	0
$659$	−50.6766	−1.97408	−0.987039	−	0.160478i	$-0.948696\pi$
$659$	−50.6766	−1.97408	−0.987039	+	0.160478i	$0.948696\pi$
$660$	9.63265	0.374951
$661$	46.2182	1.79768	0.898840	−	0.438277i	$-0.144411\pi$
$661$	46.2182	1.79768	0.898840	+	0.438277i	$0.144411\pi$
$662$	−0.233812	−0.00908735
$663$	−0.669627	−0.0260061
$664$	4.01783	0.155922
$665$	0	0
$666$	−0.695912	−0.0269660
$667$	−2.37135	−0.0918191
$668$	28.7223	1.11130
$669$	8.09744	0.313065
$670$	−1.46011	−0.0564089
$671$	10.1232	0.390800
$672$	0	0
$673$	15.7924	0.608752	0.304376	−	0.952552i	$-0.401552\pi$
$673$	15.7924	0.608752	0.304376	+	0.952552i	$0.401552\pi$
$674$	−1.46306	−0.0563550
$675$	3.33550	0.128384
$676$	−34.2688	−1.31803
$677$	−29.9752	−1.15204	−0.576019	−	0.817436i	$-0.695395\pi$
$677$	−29.9752	−1.15204	−0.576019	+	0.817436i	$0.695395\pi$
$678$	0.694074	0.0266557
$679$	0	0
$680$	0.0961225	0.00368613
$681$	−11.4711	−0.439572
$682$	0.0659916	0.00252695
$683$	−7.05810	−0.270071	−0.135035	−	0.990841i	$-0.543115\pi$
$683$	−7.05810	−0.270071	−0.135035	+	0.990841i	$0.543115\pi$
$684$	12.8532	0.491455
$685$	22.6747	0.866357
$686$	0	0
$687$	−24.3289	−0.928207
$688$	17.7922	0.678323
$689$	−18.0503	−0.687661
$690$	0.416149	0.0158425
$691$	−24.5716	−0.934749	−0.467375	−	0.884059i	$-0.654800\pi$
$691$	−24.5716	−0.934749	−0.467375	+	0.884059i	$0.654800\pi$
$692$	29.4033	1.11774
$693$	0	0
$694$	−1.28681	−0.0488465
$695$	5.10234	0.193543
$696$	−0.694446	−0.0263229
$697$	0.121569	0.00460475
$698$	4.51706	0.170973
$699$	−25.1806	−0.952417
$700$	0	0
$701$	28.8840	1.09093	0.545467	−	0.838132i	$-0.316352\pi$
$701$	28.8840	1.09093	0.545467	+	0.838132i	$0.316352\pi$
$702$	−0.848983	−0.0320428
$703$	29.3655	1.10754
$704$	28.0914	1.05873
$705$	−4.14530	−0.156121
$706$	1.65465	0.0622735
$707$	0	0
$708$	−28.2670	−1.06234
$709$	−17.6966	−0.664610	−0.332305	−	0.943172i	$-0.607826\pi$
$709$	−17.6966	−0.664610	−0.332305	+	0.943172i	$0.607826\pi$
$710$	−0.617642	−0.0231797
$711$	−2.88303	−0.108122
$712$	2.06460	0.0773742
$713$	−0.237167	−0.00888199
$714$	0	0
$715$	26.8482	1.00407
$716$	−9.25723	−0.345959
$717$	9.08432	0.339260
$718$	0.973642	0.0363360
$719$	12.1944	0.454773	0.227386	−	0.973805i	$-0.426982\pi$
$719$	12.1944	0.454773	0.227386	+	0.973805i	$0.426982\pi$
$720$	−4.97745	−0.185498
$721$	0	0
$722$	3.59127	0.133653
$723$	−14.4274	−0.536563
$724$	−15.8468	−0.588942
$725$	3.77953	0.140368
$726$	−0.504535	−0.0187250
$727$	17.4629	0.647662	0.323831	−	0.946115i	$-0.395029\pi$
$727$	17.4629	0.647662	0.323831	+	0.946115i	$0.395029\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.145539	0.00538666
$731$	0.560645	0.0207362
$732$	−5.29532	−0.195721
$733$	1.36251	0.0503254	0.0251627	−	0.999683i	$-0.491990\pi$
$733$	1.36251	0.0503254	0.0251627	+	0.999683i	$0.491990\pi$
$734$	−4.54290	−0.167681
$735$	0	0
$736$	3.80957	0.140423
$737$	−27.7408	−1.02185
$738$	0.154130	0.00567362
$739$	−50.2109	−1.84704	−0.923520	−	0.383551i	$-0.874701\pi$
$739$	−50.2109	−1.84704	−0.923520	+	0.383551i	$0.874701\pi$
$740$	−11.5119	−0.423186
$741$	35.8246	1.31605
$742$	0	0
$743$	−17.6408	−0.647177	−0.323588	−	0.946198i	$-0.604889\pi$
$743$	−17.6408	−0.647177	−0.323588	+	0.946198i	$0.604889\pi$
$744$	−0.0694540	−0.00254631
$745$	−20.9091	−0.766050
$746$	3.64987	0.133631
$747$	−6.55587	−0.239867
$748$	0.907668	0.0331876
$749$	0	0
$750$	−1.65753	−0.0605245
$751$	30.8991	1.12752	0.563762	−	0.825938i	$-0.309354\pi$
$751$	30.8991	1.12752	0.563762	+	0.825938i	$0.309354\pi$
$752$	−12.3960	−0.452034
$753$	−26.3124	−0.958877
$754$	−0.962001	−0.0350340
$755$	−18.7623	−0.682829
$756$	0	0
$757$	20.5550	0.747084	0.373542	−	0.927613i	$-0.378143\pi$
$757$	20.5550	0.747084	0.373542	+	0.927613i	$0.378143\pi$
$758$	−0.492811	−0.0178997
$759$	7.90648	0.286987
$760$	−5.14250	−0.186538
$761$	18.8363	0.682816	0.341408	−	0.939915i	$-0.389096\pi$
$761$	18.8363	0.682816	0.341408	+	0.939915i	$0.389096\pi$
$762$	−0.623866	−0.0226003
$763$	0	0
$764$	−26.9615	−0.975434
$765$	−0.156842	−0.00567065
$766$	−3.70693	−0.133937
$767$	−78.7860	−2.84480
$768$	−14.1332	−0.509987
$769$	48.7818	1.75912	0.879558	−	0.475791i	$-0.157838\pi$
$769$	48.7818	1.75912	0.879558	+	0.475791i	$0.157838\pi$
$770$	0	0
$771$	−18.3673	−0.661484
$772$	−36.5163	−1.31425
$773$	−32.9107	−1.18371	−0.591857	−	0.806043i	$-0.701605\pi$
$773$	−32.9107	−1.18371	−0.591857	+	0.806043i	$0.701605\pi$
$774$	0.710811	0.0255496
$775$	0.378005	0.0135783
$776$	3.99632	0.143459
$777$	0	0
$778$	3.31834	0.118968
$779$	−6.50386	−0.233025
$780$	−14.0440	−0.502857
$781$	−11.7347	−0.419900
$782$	0.0392130	0.00140225
$783$	1.13312	0.0404945
$784$	0	0
$785$	−5.24888	−0.187341
$786$	−1.10188	−0.0393027
$787$	−16.6540	−0.593651	−0.296825	−	0.954932i	$-0.595928\pi$
$787$	−16.6540	−0.593651	−0.296825	+	0.954932i	$0.595928\pi$
$788$	−33.9126	−1.20809
$789$	13.5912	0.483859
$790$	0.573297	0.0203970
$791$	0	0
$792$	2.31540	0.0822741
$793$	−14.7592	−0.524114
$794$	−1.19854	−0.0425345
$795$	−4.22781	−0.149945
$796$	50.9520	1.80594
$797$	−28.7105	−1.01698	−0.508490	−	0.861068i	$-0.669796\pi$
$797$	−28.7105	−1.01698	−0.508490	+	0.861068i	$0.669796\pi$
$798$	0	0
$799$	−0.390605	−0.0138186
$800$	−6.07182	−0.214671
$801$	−3.36880	−0.119031
$802$	5.16297	0.182311
$803$	2.76513	0.0975792
$804$	14.5109	0.511761
$805$	0	0
$806$	−0.0962132	−0.00338897
$807$	1.77787	0.0625838
$808$	2.43817	0.0857744
$809$	−4.33830	−0.152527	−0.0762633	−	0.997088i	$-0.524299\pi$
$809$	−4.33830	−0.152527	−0.0762633	+	0.997088i	$0.524299\pi$
$810$	−0.198852	−0.00698694
$811$	35.4046	1.24323	0.621613	−	0.783325i	$-0.286478\pi$
$811$	35.4046	1.24323	0.621613	+	0.783325i	$0.286478\pi$
$812$	0	0
$813$	−8.39209	−0.294324
$814$	2.62917	0.0921523
$815$	−10.2965	−0.360670
$816$	−0.469016	−0.0164188
$817$	−29.9942	−1.04936
$818$	3.70670	0.129602
$819$	0	0
$820$	2.54966	0.0890379
$821$	−32.8474	−1.14638	−0.573192	−	0.819421i	$-0.694295\pi$
$821$	−32.8474	−1.14638	−0.573192	+	0.819421i	$0.694295\pi$
$822$	2.70888	0.0944829
$823$	−22.3021	−0.777401	−0.388701	−	0.921364i	$-0.627076\pi$
$823$	−22.3021	−0.777401	−0.388701	+	0.921364i	$0.627076\pi$
$824$	1.80800	0.0629846
$825$	−12.6016	−0.438731
$826$	0	0
$827$	5.75475	0.200112	0.100056	−	0.994982i	$-0.468098\pi$
$827$	5.75475	0.200112	0.100056	+	0.994982i	$0.468098\pi$
$828$	−4.13580	−0.143729
$829$	15.2253	0.528797	0.264398	−	0.964414i	$-0.414827\pi$
$829$	15.2253	0.528797	0.264398	+	0.964414i	$0.414827\pi$
$830$	1.30365	0.0452503
$831$	−29.7741	−1.03285
$832$	−40.9562	−1.41990
$833$	0	0
$834$	0.609560	0.0211073
$835$	18.7508	0.648898
$836$	−48.5597	−1.67947
$837$	0.113328	0.00391718
$838$	−2.48334	−0.0857856
$839$	−8.99897	−0.310679	−0.155339	−	0.987861i	$-0.549647\pi$
$839$	−8.99897	−0.310679	−0.155339	+	0.987861i	$0.549647\pi$
$840$	0	0
$841$	−27.7160	−0.955725
$842$	−3.02956	−0.104405
$843$	4.65730	0.160406
$844$	−23.8057	−0.819427
$845$	−22.3717	−0.769611
$846$	−0.495226	−0.0170262
$847$	0	0
$848$	−12.6427	−0.434151
$849$	−2.98479	−0.102438
$850$	−0.0624989	−0.00214369
$851$	−9.44898	−0.323907
$852$	6.13829	0.210294
$853$	42.2817	1.44770	0.723848	−	0.689959i	$-0.242371\pi$
$853$	42.2817	1.44770	0.723848	+	0.689959i	$0.242371\pi$
$854$	0	0
$855$	8.39098	0.286965
$856$	0.799074	0.0273118
$857$	54.4644	1.86047	0.930235	−	0.366965i	$-0.119603\pi$
$857$	54.4644	1.86047	0.930235	+	0.366965i	$0.119603\pi$
$858$	3.20747	0.109501
$859$	33.0384	1.12725	0.563627	−	0.826029i	$-0.309405\pi$
$859$	33.0384	1.12725	0.563627	+	0.826029i	$0.309405\pi$
$860$	11.7584	0.400957
$861$	0	0
$862$	2.85090	0.0971021
$863$	0.592175	0.0201579	0.0100789	−	0.999949i	$-0.496792\pi$
$863$	0.592175	0.0201579	0.0100789	+	0.999949i	$0.496792\pi$
$864$	−1.82036	−0.0619299
$865$	19.1954	0.652662
$866$	−3.60732	−0.122582
$867$	16.9852	0.576848
$868$	0	0
$869$	10.8922	0.369491
$870$	−0.225324	−0.00763918
$871$	40.4450	1.37043
$872$	−6.47605	−0.219307
$873$	−6.52076	−0.220694
$874$	−2.09787	−0.0709615
$875$	0	0
$876$	−1.44641	−0.0488697
$877$	−53.9735	−1.82256	−0.911278	−	0.411791i	$-0.864903\pi$
$877$	−53.9735	−1.82256	−0.911278	+	0.411791i	$0.864903\pi$
$878$	0.0797005	0.00268976
$879$	−0.465557	−0.0157029
$880$	18.8049	0.633913
$881$	−38.5587	−1.29908	−0.649538	−	0.760329i	$-0.725038\pi$
$881$	−38.5587	−1.29908	−0.649538	+	0.760329i	$0.725038\pi$
$882$	0	0
$883$	36.6057	1.23188	0.615941	−	0.787793i	$-0.288776\pi$
$883$	36.6057	1.23188	0.615941	+	0.787793i	$0.288776\pi$
$884$	−1.32335	−0.0445089
$885$	−18.4536	−0.620310
$886$	2.66116	0.0894035
$887$	−25.7602	−0.864943	−0.432472	−	0.901648i	$-0.642358\pi$
$887$	−25.7602	−0.864943	−0.432472	+	0.901648i	$0.642358\pi$
$888$	−2.76711	−0.0928583
$889$	0	0
$890$	0.669892	0.0224548
$891$	−3.77802	−0.126568
$892$	16.0025	0.535804
$893$	20.8971	0.699295
$894$	−2.49794	−0.0835436
$895$	−6.04341	−0.202009
$896$	0	0
$897$	−11.5274	−0.384887
$898$	1.57825	0.0526670
$899$	0.128414	0.00428285
$900$	6.59177	0.219726
$901$	−0.398379	−0.0132719
$902$	−0.582308	−0.0193887
$903$	0	0
$904$	2.75981	0.0917898
$905$	−10.3453	−0.343889
$906$	−2.24147	−0.0744678
$907$	−21.8000	−0.723858	−0.361929	−	0.932206i	$-0.617882\pi$
$907$	−21.8000	−0.723858	−0.361929	+	0.932206i	$0.617882\pi$
$908$	−22.6696	−0.752317
$909$	−3.97834	−0.131953
$910$	0	0
$911$	−0.945390	−0.0313222	−0.0156611	−	0.999877i	$-0.504985\pi$
$911$	−0.945390	−0.0313222	−0.0156611	+	0.999877i	$0.504985\pi$
$912$	25.0921	0.830881
$913$	24.7682	0.819708
$914$	0.935689	0.0309498
$915$	−3.45695	−0.114283
$916$	−48.0799	−1.58860
$917$	0	0
$918$	−0.0187375	−0.000618429 0
$919$	37.0061	1.22072	0.610359	−	0.792125i	$-0.291025\pi$
$919$	37.0061	1.22072	0.610359	+	0.792125i	$0.291025\pi$
$920$	1.65471	0.0545542
$921$	−4.58705	−0.151148
$922$	−0.715936	−0.0235781
$923$	17.1087	0.563140
$924$	0	0
$925$	15.0601	0.495172
$926$	−5.26744	−0.173099
$927$	−2.95010	−0.0968940
$928$	−2.06269	−0.0677111
$929$	−21.1484	−0.693856	−0.346928	−	0.937892i	$-0.612775\pi$
$929$	−21.1484	−0.693856	−0.346928	+	0.937892i	$0.612775\pi$
$930$	−0.0225354	−0.000738966 0
$931$	0	0
$932$	−49.7630	−1.63004
$933$	6.72674	0.220224
$934$	−2.13347	−0.0698093
$935$	0.592554	0.0193786
$936$	−3.37576	−0.110340
$937$	−41.7132	−1.36271	−0.681355	−	0.731953i	$-0.738609\pi$
$937$	−41.7132	−1.36271	−0.681355	+	0.731953i	$0.738609\pi$
$938$	0	0
$939$	−7.56580	−0.246901
$940$	−8.19213	−0.267198
$941$	27.3925	0.892969	0.446484	−	0.894791i	$-0.352676\pi$
$941$	27.3925	0.892969	0.446484	+	0.894791i	$0.352676\pi$
$942$	−0.627067	−0.0204309
$943$	2.09276	0.0681496
$944$	−55.1828	−1.79605
$945$	0	0
$946$	−2.68546	−0.0873117
$947$	−54.1364	−1.75920	−0.879598	−	0.475718i	$-0.842188\pi$
$947$	−54.1364	−1.75920	−0.879598	+	0.475718i	$0.842188\pi$
$948$	−5.69758	−0.185049
$949$	−4.03145	−0.130866
$950$	3.34365	0.108482
$951$	6.60093	0.214050
$952$	0	0
$953$	−1.05940	−0.0343173	−0.0171587	−	0.999853i	$-0.505462\pi$
$953$	−1.05940	−0.0343173	−0.0171587	+	0.999853i	$0.505462\pi$
$954$	−0.505083	−0.0163527
$955$	−17.6013	−0.569565
$956$	17.9528	0.580636
$957$	−4.28096	−0.138384
$958$	3.60435	0.116451
$959$	0	0
$960$	−9.59291	−0.309610
$961$	−30.9872	−0.999586
$962$	−3.83323	−0.123588
$963$	−1.30384	−0.0420158
$964$	−28.5122	−0.918315
$965$	−23.8389	−0.767403
$966$	0	0
$967$	−50.6626	−1.62920	−0.814600	−	0.580023i	$-0.803043\pi$
$967$	−50.6626	−1.62920	−0.814600	+	0.580023i	$0.803043\pi$
$968$	−2.00615	−0.0644802
$969$	0.790667	0.0253999
$970$	1.29667	0.0416334
$971$	−41.8803	−1.34400	−0.672001	−	0.740550i	$-0.734565\pi$
$971$	−41.8803	−1.34400	−0.672001	+	0.740550i	$0.734565\pi$
$972$	1.97624	0.0633880
$973$	0	0
$974$	1.05408	0.0337748
$975$	18.3727	0.588396
$976$	−10.3375	−0.330897
$977$	15.2242	0.487064	0.243532	−	0.969893i	$-0.421694\pi$
$977$	15.2242	0.487064	0.243532	+	0.969893i	$0.421694\pi$
$978$	−1.23009	−0.0393339
$979$	12.7274	0.406769
$980$	0	0
$981$	10.5669	0.337376
$982$	−6.06308	−0.193481
$983$	36.9964	1.18000	0.590001	−	0.807402i	$-0.299127\pi$
$983$	36.9964	1.18000	0.590001	+	0.807402i	$0.299127\pi$
$984$	0.612860	0.0195373
$985$	−22.1392	−0.705414
$986$	−0.0212318	−0.000676160 0
$987$	0	0
$988$	70.7982	2.25239
$989$	9.65128	0.306893
$990$	0.751266	0.0238768
$991$	−18.9571	−0.602194	−0.301097	−	0.953594i	$-0.597353\pi$
$991$	−18.9571	−0.602194	−0.301097	+	0.953594i	$0.597353\pi$
$992$	−0.206297	−0.00654994
$993$	1.51697	0.0481397
$994$	0	0
$995$	33.2630	1.05451
$996$	−12.9560	−0.410526
$997$	5.80926	0.183981	0.0919905	−	0.995760i	$-0.470677\pi$
$997$	5.80926	0.183981	0.0919905	+	0.995760i	$0.470677\pi$
$998$	1.96484	0.0621960
$999$	4.51508	0.142851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.12	✓	24
7.6	odd	2		6027.2.a.bo.1.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.12	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.12	yes	24	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.154130 q^{2} -1.00000 q^{3} -1.97624 q^{4} -1.29015 q^{5} -0.154130 q^{6} -0.612860 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.154130 q^{2} -1.00000 q^{3} -1.97624 q^{4} -1.29015 q^{5} -0.154130 q^{6} -0.612860 q^{8} +1.00000 q^{9} -0.198852 q^{10} -3.77802 q^{11} +1.97624 q^{12} +5.50821 q^{13} +1.29015 q^{15} +3.85803 q^{16} +0.121569 q^{17} +0.154130 q^{18} -6.50386 q^{19} +2.54966 q^{20} -0.582308 q^{22} +2.09276 q^{23} +0.612860 q^{24} -3.33550 q^{25} +0.848983 q^{26} -1.00000 q^{27} -1.13312 q^{29} +0.198852 q^{30} -0.113328 q^{31} +1.82036 q^{32} +3.77802 q^{33} +0.0187375 q^{34} -1.97624 q^{36} -4.51508 q^{37} -1.00244 q^{38} -5.50821 q^{39} +0.790684 q^{40} +1.00000 q^{41} +4.61175 q^{43} +7.46629 q^{44} -1.29015 q^{45} +0.322558 q^{46} -3.21303 q^{47} -3.85803 q^{48} -0.514103 q^{50} -0.121569 q^{51} -10.8856 q^{52} -3.27698 q^{53} -0.154130 q^{54} +4.87422 q^{55} +6.50386 q^{57} -0.174649 q^{58} -14.3034 q^{59} -2.54966 q^{60} -2.67949 q^{61} -0.0174672 q^{62} -7.43548 q^{64} -7.10643 q^{65} +0.582308 q^{66} +7.34269 q^{67} -0.240250 q^{68} -2.09276 q^{69} +3.10604 q^{71} -0.612860 q^{72} -0.731899 q^{73} -0.695912 q^{74} +3.33550 q^{75} +12.8532 q^{76} -0.848983 q^{78} -2.88303 q^{79} -4.97745 q^{80} +1.00000 q^{81} +0.154130 q^{82} -6.55587 q^{83} -0.156842 q^{85} +0.710811 q^{86} +1.13312 q^{87} +2.31540 q^{88} -3.36880 q^{89} -0.198852 q^{90} -4.13580 q^{92} +0.113328 q^{93} -0.495226 q^{94} +8.39098 q^{95} -1.82036 q^{96} -6.52076 q^{97} -3.77802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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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