LMFDB - Embedded newform 6027.2.a.bo.1.19

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			1.19
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)

$f(q)$	$=$	$q+2.26259 q^{2} +1.00000 q^{3} +3.11931 q^{4} +3.51535 q^{5} +2.26259 q^{6} +2.53253 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.26259 q^{2} +1.00000 q^{3} +3.11931 q^{4} +3.51535 q^{5} +2.26259 q^{6} +2.53253 q^{8} +1.00000 q^{9} +7.95379 q^{10} -3.79341 q^{11} +3.11931 q^{12} +1.46159 q^{13} +3.51535 q^{15} -0.508546 q^{16} +6.67693 q^{17} +2.26259 q^{18} -2.27770 q^{19} +10.9654 q^{20} -8.58292 q^{22} +8.49274 q^{23} +2.53253 q^{24} +7.35768 q^{25} +3.30698 q^{26} +1.00000 q^{27} -5.04769 q^{29} +7.95379 q^{30} -1.44795 q^{31} -6.21568 q^{32} -3.79341 q^{33} +15.1071 q^{34} +3.11931 q^{36} -0.996436 q^{37} -5.15350 q^{38} +1.46159 q^{39} +8.90272 q^{40} -1.00000 q^{41} +10.8446 q^{43} -11.8328 q^{44} +3.51535 q^{45} +19.2156 q^{46} -0.748913 q^{47} -0.508546 q^{48} +16.6474 q^{50} +6.67693 q^{51} +4.55916 q^{52} +9.47305 q^{53} +2.26259 q^{54} -13.3352 q^{55} -2.27770 q^{57} -11.4208 q^{58} -9.62699 q^{59} +10.9654 q^{60} -13.5721 q^{61} -3.27611 q^{62} -13.0464 q^{64} +5.13801 q^{65} -8.58292 q^{66} +8.40378 q^{67} +20.8274 q^{68} +8.49274 q^{69} -6.50992 q^{71} +2.53253 q^{72} -2.28092 q^{73} -2.25452 q^{74} +7.35768 q^{75} -7.10484 q^{76} +3.30698 q^{78} -1.03517 q^{79} -1.78772 q^{80} +1.00000 q^{81} -2.26259 q^{82} -1.84818 q^{83} +23.4718 q^{85} +24.5369 q^{86} -5.04769 q^{87} -9.60691 q^{88} -1.76420 q^{89} +7.95379 q^{90} +26.4914 q^{92} -1.44795 q^{93} -1.69448 q^{94} -8.00692 q^{95} -6.21568 q^{96} +17.4604 q^{97} -3.79341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.26259	1.59989	0.799946	−	0.600072i	$-0.204862\pi$
$2$	2.26259	1.59989	0.799946	+	0.600072i	$0.204862\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.11931	1.55965
$5$	3.51535	1.57211	0.786056	−	0.618155i	$-0.212120\pi$
$5$	3.51535	1.57211	0.786056	+	0.618155i	$0.212120\pi$
$6$	2.26259	0.923698
$7$	0	0
$7$	0	0
$8$	2.53253	0.895383
$9$	1.00000	0.333333
$10$	7.95379	2.51521
$11$	−3.79341	−1.14376	−0.571878	−	0.820339i	$-0.693785\pi$
$11$	−3.79341	−1.14376	−0.571878	+	0.820339i	$0.693785\pi$
$12$	3.11931	0.900466
$13$	1.46159	0.405373	0.202687	−	0.979244i	$-0.435033\pi$
$13$	1.46159	0.405373	0.202687	+	0.979244i	$0.435033\pi$
$14$	0	0
$15$	3.51535	0.907659
$16$	−0.508546	−0.127136
$17$	6.67693	1.61939	0.809697	−	0.586848i	$-0.199631\pi$
$17$	6.67693	1.61939	0.809697	+	0.586848i	$0.199631\pi$
$18$	2.26259	0.533297
$19$	−2.27770	−0.522540	−0.261270	−	0.965266i	$-0.584141\pi$
$19$	−2.27770	−0.522540	−0.261270	+	0.965266i	$0.584141\pi$
$20$	10.9654	2.45195
$21$	0	0
$22$	−8.58292	−1.82988
$23$	8.49274	1.77086	0.885429	−	0.464774i	$-0.153864\pi$
$23$	8.49274	1.77086	0.885429	+	0.464774i	$0.153864\pi$
$24$	2.53253	0.516950
$25$	7.35768	1.47154
$26$	3.30698	0.648553
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.04769	−0.937332	−0.468666	−	0.883376i	$-0.655265\pi$
$29$	−5.04769	−0.937332	−0.468666	+	0.883376i	$0.655265\pi$
$30$	7.95379	1.45216
$31$	−1.44795	−0.260059	−0.130029	−	0.991510i	$-0.541507\pi$
$31$	−1.44795	−0.260059	−0.130029	+	0.991510i	$0.541507\pi$
$32$	−6.21568	−1.09879
$33$	−3.79341	−0.660348
$34$	15.1071	2.59085
$35$	0	0
$36$	3.11931	0.519884
$37$	−0.996436	−0.163813	−0.0819066	−	0.996640i	$-0.526101\pi$
$37$	−0.996436	−0.163813	−0.0819066	+	0.996640i	$0.526101\pi$
$38$	−5.15350	−0.836008
$39$	1.46159	0.234042
$40$	8.90272	1.40764
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	10.8446	1.65379	0.826893	−	0.562359i	$-0.190106\pi$
$43$	10.8446	1.65379	0.826893	+	0.562359i	$0.190106\pi$
$44$	−11.8328	−1.78386
$45$	3.51535	0.524037
$46$	19.2156	2.83318
$47$	−0.748913	−0.109240	−0.0546201	−	0.998507i	$-0.517395\pi$
$47$	−0.748913	−0.109240	−0.0546201	+	0.998507i	$0.517395\pi$
$48$	−0.508546	−0.0734023
$49$	0	0
$50$	16.6474	2.35430
$51$	6.67693	0.934958
$52$	4.55916	0.632241
$53$	9.47305	1.30122	0.650611	−	0.759411i	$-0.274513\pi$
$53$	9.47305	1.30122	0.650611	+	0.759411i	$0.274513\pi$
$54$	2.26259	0.307899
$55$	−13.3352	−1.79811
$56$	0	0
$57$	−2.27770	−0.301689
$58$	−11.4208	−1.49963
$59$	−9.62699	−1.25333	−0.626664	−	0.779290i	$-0.715580\pi$
$59$	−9.62699	−1.25333	−0.626664	+	0.779290i	$0.715580\pi$
$60$	10.9654	1.41563
$61$	−13.5721	−1.73773	−0.868867	−	0.495046i	$-0.835151\pi$
$61$	−13.5721	−1.73773	−0.868867	+	0.495046i	$0.835151\pi$
$62$	−3.27611	−0.416066
$63$	0	0
$64$	−13.0464	−1.63080
$65$	5.13801	0.637292
$66$	−8.58292	−1.05648
$67$	8.40378	1.02668	0.513342	−	0.858184i	$-0.328407\pi$
$67$	8.40378	1.02668	0.513342	+	0.858184i	$0.328407\pi$
$68$	20.8274	2.52569
$69$	8.49274	1.02241
$70$	0	0
$71$	−6.50992	−0.772585	−0.386293	−	0.922376i	$-0.626245\pi$
$71$	−6.50992	−0.772585	−0.386293	+	0.922376i	$0.626245\pi$
$72$	2.53253	0.298461
$73$	−2.28092	−0.266962	−0.133481	−	0.991051i	$-0.542615\pi$
$73$	−2.28092	−0.266962	−0.133481	+	0.991051i	$0.542615\pi$
$74$	−2.25452	−0.262083
$75$	7.35768	0.849592
$76$	−7.10484	−0.814982
$77$	0	0
$78$	3.30698	0.374442
$79$	−1.03517	−0.116466	−0.0582331	−	0.998303i	$-0.518547\pi$
$79$	−1.03517	−0.116466	−0.0582331	+	0.998303i	$0.518547\pi$
$80$	−1.78772	−0.199873
$81$	1.00000	0.111111
$82$	−2.26259	−0.249861
$83$	−1.84818	−0.202865	−0.101432	−	0.994842i	$-0.532343\pi$
$83$	−1.84818	−0.202865	−0.101432	+	0.994842i	$0.532343\pi$
$84$	0	0
$85$	23.4718	2.54587
$86$	24.5369	2.64588
$87$	−5.04769	−0.541169
$88$	−9.60691	−1.02410
$89$	−1.76420	−0.187005	−0.0935023	−	0.995619i	$-0.529806\pi$
$89$	−1.76420	−0.187005	−0.0935023	+	0.995619i	$0.529806\pi$
$90$	7.95379	0.838403
$91$	0	0
$92$	26.4914	2.76192
$93$	−1.44795	−0.150145
$94$	−1.69448	−0.174773
$95$	−8.00692	−0.821492
$96$	−6.21568	−0.634385
$97$	17.4604	1.77284	0.886419	−	0.462883i	$-0.153185\pi$
$97$	17.4604	1.77284	0.886419	+	0.462883i	$0.153185\pi$
$98$	0	0
$99$	−3.79341	−0.381252
$100$	22.9509	2.29509
$101$	19.4496	1.93531	0.967653	−	0.252287i	$-0.0811826\pi$
$101$	19.4496	1.93531	0.967653	+	0.252287i	$0.0811826\pi$
$102$	15.1071	1.49583
$103$	−4.41489	−0.435012	−0.217506	−	0.976059i	$-0.569792\pi$
$103$	−4.41489	−0.435012	−0.217506	+	0.976059i	$0.569792\pi$
$104$	3.70152	0.362964
$105$	0	0
$106$	21.4336	2.08182
$107$	−15.1587	−1.46544	−0.732721	−	0.680529i	$-0.761750\pi$
$107$	−15.1587	−1.46544	−0.732721	+	0.680529i	$0.761750\pi$
$108$	3.11931	0.300155
$109$	−9.37929	−0.898374	−0.449187	−	0.893438i	$-0.648286\pi$
$109$	−9.37929	−0.898374	−0.449187	+	0.893438i	$0.648286\pi$
$110$	−30.1720	−2.87678
$111$	−0.996436	−0.0945775
$112$	0	0
$113$	1.40865	0.132515	0.0662574	−	0.997803i	$-0.478894\pi$
$113$	1.40865	0.132515	0.0662574	+	0.997803i	$0.478894\pi$
$114$	−5.15350	−0.482669
$115$	29.8549	2.78399
$116$	−15.7453	−1.46191
$117$	1.46159	0.135124
$118$	−21.7819	−2.00519
$119$	0	0
$120$	8.90272	0.812703
$121$	3.38994	0.308177
$122$	−30.7081	−2.78018
$123$	−1.00000	−0.0901670
$124$	−4.51659	−0.405601
$125$	8.28808	0.741309
$126$	0	0
$127$	−2.83967	−0.251980	−0.125990	−	0.992032i	$-0.540211\pi$
$127$	−2.83967	−0.251980	−0.125990	+	0.992032i	$0.540211\pi$
$128$	−17.0874	−1.51032
$129$	10.8446	0.954814
$130$	11.6252	1.01960
$131$	−14.7028	−1.28459	−0.642295	−	0.766458i	$-0.722018\pi$
$131$	−14.7028	−1.28459	−0.642295	+	0.766458i	$0.722018\pi$
$132$	−11.8328	−1.02991
$133$	0	0
$134$	19.0143	1.64258
$135$	3.51535	0.302553
$136$	16.9095	1.44998
$137$	−9.39271	−0.802474	−0.401237	−	0.915974i	$-0.631420\pi$
$137$	−9.39271	−0.802474	−0.401237	+	0.915974i	$0.631420\pi$
$138$	19.2156	1.63574
$139$	−11.1571	−0.946333	−0.473166	−	0.880973i	$-0.656889\pi$
$139$	−11.1571	−0.946333	−0.473166	+	0.880973i	$0.656889\pi$
$140$	0	0
$141$	−0.748913	−0.0630699
$142$	−14.7293	−1.23605
$143$	−5.54442	−0.463648
$144$	−0.508546	−0.0423788
$145$	−17.7444	−1.47359
$146$	−5.16078	−0.427109
$147$	0	0
$148$	−3.10819	−0.255492
$149$	0.818797	0.0670785	0.0335392	−	0.999437i	$-0.489322\pi$
$149$	0.818797	0.0670785	0.0335392	+	0.999437i	$0.489322\pi$
$150$	16.6474	1.35926
$151$	20.6578	1.68111	0.840554	−	0.541728i	$-0.182230\pi$
$151$	20.6578	1.68111	0.840554	+	0.541728i	$0.182230\pi$
$152$	−5.76834	−0.467874
$153$	6.67693	0.539798
$154$	0	0
$155$	−5.09004	−0.408842
$156$	4.55916	0.365025
$157$	−3.57661	−0.285445	−0.142722	−	0.989763i	$-0.545586\pi$
$157$	−3.57661	−0.285445	−0.142722	+	0.989763i	$0.545586\pi$
$158$	−2.34217	−0.186333
$159$	9.47305	0.751261
$160$	−21.8503	−1.72742
$161$	0	0
$162$	2.26259	0.177766
$163$	12.6245	0.988830	0.494415	−	0.869226i	$-0.335382\pi$
$163$	12.6245	0.988830	0.494415	+	0.869226i	$0.335382\pi$
$164$	−3.11931	−0.243577
$165$	−13.3352	−1.03814
$166$	−4.18168	−0.324561
$167$	4.48125	0.346770	0.173385	−	0.984854i	$-0.444530\pi$
$167$	4.48125	0.346770	0.173385	+	0.984854i	$0.444530\pi$
$168$	0	0
$169$	−10.8637	−0.835673
$170$	53.1069	4.07311
$171$	−2.27770	−0.174180
$172$	33.8276	2.57933
$173$	−22.5618	−1.71534	−0.857670	−	0.514201i	$-0.828089\pi$
$173$	−22.5618	−1.71534	−0.857670	+	0.514201i	$0.828089\pi$
$174$	−11.4208	−0.865811
$175$	0	0
$176$	1.92912	0.145413
$177$	−9.62699	−0.723609
$178$	−3.99165	−0.299187
$179$	14.9892	1.12035	0.560173	−	0.828375i	$-0.310735\pi$
$179$	14.9892	1.12035	0.560173	+	0.828375i	$0.310735\pi$
$180$	10.9654	0.817316
$181$	1.00879	0.0749830	0.0374915	−	0.999297i	$-0.488063\pi$
$181$	1.00879	0.0749830	0.0374915	+	0.999297i	$0.488063\pi$
$182$	0	0
$183$	−13.5721	−1.00328
$184$	21.5081	1.58560
$185$	−3.50282	−0.257533
$186$	−3.27611	−0.240216
$187$	−25.3283	−1.85219
$188$	−2.33609	−0.170377
$189$	0	0
$190$	−18.1164	−1.31430
$191$	20.0147	1.44821	0.724106	−	0.689689i	$-0.242253\pi$
$191$	20.0147	1.44821	0.724106	+	0.689689i	$0.242253\pi$
$192$	−13.0464	−0.941546
$193$	3.47028	0.249796	0.124898	−	0.992170i	$-0.460140\pi$
$193$	3.47028	0.249796	0.124898	+	0.992170i	$0.460140\pi$
$194$	39.5058	2.83635
$195$	5.13801	0.367941
$196$	0	0
$197$	11.6030	0.826681	0.413340	−	0.910577i	$-0.364362\pi$
$197$	11.6030	0.826681	0.413340	+	0.910577i	$0.364362\pi$
$198$	−8.58292	−0.609962
$199$	−7.82824	−0.554929	−0.277464	−	0.960736i	$-0.589494\pi$
$199$	−7.82824	−0.554929	−0.277464	+	0.960736i	$0.589494\pi$
$200$	18.6335	1.31759
$201$	8.40378	0.592757
$202$	44.0064	3.09628
$203$	0	0
$204$	20.8274	1.45821
$205$	−3.51535	−0.245523
$206$	−9.98908	−0.695972
$207$	8.49274	0.590286
$208$	−0.743287	−0.0515377
$209$	8.64025	0.597659
$210$	0	0
$211$	−0.767110	−0.0528100	−0.0264050	−	0.999651i	$-0.508406\pi$
$211$	−0.767110	−0.0528100	−0.0264050	+	0.999651i	$0.508406\pi$
$212$	29.5493	2.02946
$213$	−6.50992	−0.446052
$214$	−34.2978	−2.34455
$215$	38.1226	2.59994
$216$	2.53253	0.172317
$217$	0	0
$218$	−21.2215	−1.43730
$219$	−2.28092	−0.154130
$220$	−41.5964	−2.80443
$221$	9.75896	0.656459
$222$	−2.25452	−0.151314
$223$	−5.48934	−0.367594	−0.183797	−	0.982964i	$-0.558839\pi$
$223$	−5.48934	−0.367594	−0.183797	+	0.982964i	$0.558839\pi$
$224$	0	0
$225$	7.35768	0.490512
$226$	3.18720	0.212009
$227$	−24.0590	−1.59685	−0.798426	−	0.602093i	$-0.794334\pi$
$227$	−24.0590	−1.59685	−0.798426	+	0.602093i	$0.794334\pi$
$228$	−7.10484	−0.470530
$229$	−10.3429	−0.683476	−0.341738	−	0.939795i	$-0.611015\pi$
$229$	−10.3429	−0.683476	−0.341738	+	0.939795i	$0.611015\pi$
$230$	67.5495	4.45408
$231$	0	0
$232$	−12.7834	−0.839271
$233$	−17.3807	−1.13865	−0.569325	−	0.822112i	$-0.692795\pi$
$233$	−17.3807	−1.13865	−0.569325	+	0.822112i	$0.692795\pi$
$234$	3.30698	0.216184
$235$	−2.63269	−0.171738
$236$	−30.0295	−1.95476
$237$	−1.03517	−0.0672418
$238$	0	0
$239$	−7.43783	−0.481113	−0.240557	−	0.970635i	$-0.577330\pi$
$239$	−7.43783	−0.481113	−0.240557	+	0.970635i	$0.577330\pi$
$240$	−1.78772	−0.115397
$241$	−7.82930	−0.504329	−0.252165	−	0.967684i	$-0.581142\pi$
$241$	−7.82930	−0.504329	−0.252165	+	0.967684i	$0.581142\pi$
$242$	7.67005	0.493049
$243$	1.00000	0.0641500
$244$	−42.3356	−2.71026
$245$	0	0
$246$	−2.26259	−0.144257
$247$	−3.32907	−0.211824
$248$	−3.66696	−0.232852
$249$	−1.84818	−0.117124
$250$	18.7525	1.18601
$251$	−11.4230	−0.721012	−0.360506	−	0.932757i	$-0.617396\pi$
$251$	−11.4230	−0.721012	−0.360506	+	0.932757i	$0.617396\pi$
$252$	0	0
$253$	−32.2164	−2.02543
$254$	−6.42500	−0.403141
$255$	23.4718	1.46986
$256$	−12.5688	−0.785548
$257$	−14.8155	−0.924168	−0.462084	−	0.886836i	$-0.652898\pi$
$257$	−14.8155	−0.924168	−0.462084	+	0.886836i	$0.652898\pi$
$258$	24.5369	1.52760
$259$	0	0
$260$	16.0270	0.993954
$261$	−5.04769	−0.312444
$262$	−33.2664	−2.05520
$263$	−21.3829	−1.31853	−0.659264	−	0.751912i	$-0.729132\pi$
$263$	−21.3829	−1.31853	−0.659264	+	0.751912i	$0.729132\pi$
$264$	−9.60691	−0.591264
$265$	33.3011	2.04567
$266$	0	0
$267$	−1.76420	−0.107967
$268$	26.2139	1.60127
$269$	29.0758	1.77278	0.886391	−	0.462937i	$-0.153204\pi$
$269$	29.0758	1.77278	0.886391	+	0.462937i	$0.153204\pi$
$270$	7.95379	0.484052
$271$	−21.8299	−1.32607	−0.663035	−	0.748588i	$-0.730732\pi$
$271$	−21.8299	−1.32607	−0.663035	+	0.748588i	$0.730732\pi$
$272$	−3.39553	−0.205884
$273$	0	0
$274$	−21.2518	−1.28387
$275$	−27.9107	−1.68308
$276$	26.4914	1.59460
$277$	−26.3880	−1.58550	−0.792751	−	0.609546i	$-0.791352\pi$
$277$	−26.3880	−1.58550	−0.792751	+	0.609546i	$0.791352\pi$
$278$	−25.2439	−1.51403
$279$	−1.44795	−0.0866863
$280$	0	0
$281$	10.8668	0.648256	0.324128	−	0.946013i	$-0.394929\pi$
$281$	10.8668	0.648256	0.324128	+	0.946013i	$0.394929\pi$
$282$	−1.69448	−0.100905
$283$	−30.8486	−1.83376	−0.916879	−	0.399165i	$-0.869300\pi$
$283$	−30.8486	−1.83376	−0.916879	+	0.399165i	$0.869300\pi$
$284$	−20.3064	−1.20496
$285$	−8.00692	−0.474289
$286$	−12.5447	−0.741786
$287$	0	0
$288$	−6.21568	−0.366263
$289$	27.5814	1.62244
$290$	−40.1482	−2.35759
$291$	17.4604	1.02355
$292$	−7.11489	−0.416367
$293$	10.1999	0.595885	0.297942	−	0.954584i	$-0.403700\pi$
$293$	10.1999	0.595885	0.297942	+	0.954584i	$0.403700\pi$
$294$	0	0
$295$	−33.8422	−1.97037
$296$	−2.52350	−0.146676
$297$	−3.79341	−0.220116
$298$	1.85260	0.107318
$299$	12.4129	0.717858
$300$	22.9509	1.32507
$301$	0	0
$302$	46.7401	2.68959
$303$	19.4496	1.11735
$304$	1.15832	0.0664340
$305$	−47.7108	−2.73191
$306$	15.1071	0.863618
$307$	22.0097	1.25616	0.628081	−	0.778148i	$-0.283841\pi$
$307$	22.0097	1.25616	0.628081	+	0.778148i	$0.283841\pi$
$308$	0	0
$309$	−4.41489	−0.251154
$310$	−11.5167	−0.654102
$311$	−0.628039	−0.0356128	−0.0178064	−	0.999841i	$-0.505668\pi$
$311$	−0.628039	−0.0356128	−0.0178064	+	0.999841i	$0.505668\pi$
$312$	3.70152	0.209557
$313$	17.9356	1.01378	0.506891	−	0.862010i	$-0.330795\pi$
$313$	17.9356	1.01378	0.506891	+	0.862010i	$0.330795\pi$
$314$	−8.09240	−0.456681
$315$	0	0
$316$	−3.22902	−0.181647
$317$	15.2704	0.857668	0.428834	−	0.903383i	$-0.358924\pi$
$317$	15.2704	0.857668	0.428834	+	0.903383i	$0.358924\pi$
$318$	21.4336	1.20194
$319$	19.1479	1.07208
$320$	−45.8628	−2.56381
$321$	−15.1587	−0.846074
$322$	0	0
$323$	−15.2081	−0.846199
$324$	3.11931	0.173295
$325$	10.7539	0.596521
$326$	28.5641	1.58202
$327$	−9.37929	−0.518676
$328$	−2.53253	−0.139835
$329$	0	0
$330$	−30.1720	−1.66091
$331$	30.8713	1.69684	0.848421	−	0.529322i	$-0.177554\pi$
$331$	30.8713	1.69684	0.848421	+	0.529322i	$0.177554\pi$
$332$	−5.76505	−0.316398
$333$	−0.996436	−0.0546044
$334$	10.1392	0.554794
$335$	29.5422	1.61406
$336$	0	0
$337$	−13.7318	−0.748017	−0.374008	−	0.927425i	$-0.622017\pi$
$337$	−13.7318	−0.748017	−0.374008	+	0.927425i	$0.622017\pi$
$338$	−24.5802	−1.33699
$339$	1.40865	0.0765074
$340$	73.2156	3.97067
$341$	5.49265	0.297444
$342$	−5.15350	−0.278669
$343$	0	0
$344$	27.4642	1.48077
$345$	29.8549	1.60734
$346$	−51.0480	−2.74436
$347$	−16.9673	−0.910854	−0.455427	−	0.890273i	$-0.650513\pi$
$347$	−16.9673	−0.910854	−0.455427	+	0.890273i	$0.650513\pi$
$348$	−15.7453	−0.844035
$349$	5.94969	0.318479	0.159240	−	0.987240i	$-0.449096\pi$
$349$	5.94969	0.318479	0.159240	+	0.987240i	$0.449096\pi$
$350$	0	0
$351$	1.46159	0.0780141
$352$	23.5786	1.25674
$353$	−5.44568	−0.289844	−0.144922	−	0.989443i	$-0.546293\pi$
$353$	−5.44568	−0.289844	−0.144922	+	0.989443i	$0.546293\pi$
$354$	−21.7819	−1.15770
$355$	−22.8846	−1.21459
$356$	−5.50307	−0.291662
$357$	0	0
$358$	33.9144	1.79243
$359$	−23.9295	−1.26295	−0.631476	−	0.775396i	$-0.717550\pi$
$359$	−23.9295	−1.26295	−0.631476	+	0.775396i	$0.717550\pi$
$360$	8.90272	0.469214
$361$	−13.8121	−0.726951
$362$	2.28248	0.119965
$363$	3.38994	0.177926
$364$	0	0
$365$	−8.01823	−0.419694
$366$	−30.7081	−1.60514
$367$	−3.62240	−0.189088	−0.0945438	−	0.995521i	$-0.530139\pi$
$367$	−3.62240	−0.189088	−0.0945438	+	0.995521i	$0.530139\pi$
$368$	−4.31895	−0.225141
$369$	−1.00000	−0.0520579
$370$	−7.92544	−0.412024
$371$	0	0
$372$	−4.51659	−0.234174
$373$	30.5324	1.58091	0.790455	−	0.612521i	$-0.209844\pi$
$373$	30.5324	1.58091	0.790455	+	0.612521i	$0.209844\pi$
$374$	−57.3076	−2.96330
$375$	8.28808	0.427995
$376$	−1.89664	−0.0978119
$377$	−7.37766	−0.379969
$378$	0	0
$379$	−14.5620	−0.748002	−0.374001	−	0.927428i	$-0.622014\pi$
$379$	−14.5620	−0.748002	−0.374001	+	0.927428i	$0.622014\pi$
$380$	−24.9760	−1.28124
$381$	−2.83967	−0.145481
$382$	45.2850	2.31698
$383$	−4.84686	−0.247663	−0.123831	−	0.992303i	$-0.539518\pi$
$383$	−4.84686	−0.247663	−0.123831	+	0.992303i	$0.539518\pi$
$384$	−17.0874	−0.871985
$385$	0	0
$386$	7.85181	0.399646
$387$	10.8446	0.551262
$388$	54.4644	2.76501
$389$	−0.685686	−0.0347657	−0.0173828	−	0.999849i	$-0.505533\pi$
$389$	−0.685686	−0.0347657	−0.0173828	+	0.999849i	$0.505533\pi$
$390$	11.6252	0.588665
$391$	56.7054	2.86772
$392$	0	0
$393$	−14.7028	−0.741658
$394$	26.2529	1.32260
$395$	−3.63900	−0.183098
$396$	−11.8328	−0.594620
$397$	0.404290	0.0202907	0.0101454	−	0.999949i	$-0.496771\pi$
$397$	0.404290	0.0202907	0.0101454	+	0.999949i	$0.496771\pi$
$398$	−17.7121	−0.887826
$399$	0	0
$400$	−3.74172	−0.187086
$401$	−28.1364	−1.40506	−0.702532	−	0.711652i	$-0.747947\pi$
$401$	−28.1364	−1.40506	−0.702532	+	0.711652i	$0.747947\pi$
$402$	19.0143	0.948347
$403$	−2.11631	−0.105421
$404$	60.6692	3.01840
$405$	3.51535	0.174679
$406$	0	0
$407$	3.77989	0.187362
$408$	16.9095	0.837145
$409$	−16.9935	−0.840273	−0.420137	−	0.907461i	$-0.638018\pi$
$409$	−16.9935	−0.840273	−0.420137	+	0.907461i	$0.638018\pi$
$410$	−7.95379	−0.392810
$411$	−9.39271	−0.463308
$412$	−13.7714	−0.678468
$413$	0	0
$414$	19.2156	0.944394
$415$	−6.49702	−0.318926
$416$	−9.08480	−0.445419
$417$	−11.1571	−0.546366
$418$	19.5493	0.956189
$419$	10.1348	0.495116	0.247558	−	0.968873i	$-0.420372\pi$
$419$	10.1348	0.495116	0.247558	+	0.968873i	$0.420372\pi$
$420$	0	0
$421$	7.95651	0.387777	0.193888	−	0.981024i	$-0.437890\pi$
$421$	7.95651	0.387777	0.193888	+	0.981024i	$0.437890\pi$
$422$	−1.73565	−0.0844903
$423$	−0.748913	−0.0364134
$424$	23.9907	1.16509
$425$	49.1268	2.38300
$426$	−14.7293	−0.713635
$427$	0	0
$428$	−47.2845	−2.28558
$429$	−5.54442	−0.267687
$430$	86.2557	4.15962
$431$	−27.1478	−1.30766	−0.653832	−	0.756640i	$-0.726840\pi$
$431$	−27.1478	−1.30766	−0.653832	+	0.756640i	$0.726840\pi$
$432$	−0.508546	−0.0244674
$433$	27.6879	1.33060	0.665298	−	0.746578i	$-0.268304\pi$
$433$	27.6879	1.33060	0.665298	+	0.746578i	$0.268304\pi$
$434$	0	0
$435$	−17.7444	−0.850778
$436$	−29.2569	−1.40115
$437$	−19.3439	−0.925345
$438$	−5.16078	−0.246592
$439$	−8.75911	−0.418049	−0.209025	−	0.977910i	$-0.567029\pi$
$439$	−8.75911	−0.418049	−0.209025	+	0.977910i	$0.567029\pi$
$440$	−33.7716	−1.61000
$441$	0	0
$442$	22.0805	1.05026
$443$	−35.5985	−1.69133	−0.845667	−	0.533711i	$-0.820797\pi$
$443$	−35.5985	−1.69133	−0.845667	+	0.533711i	$0.820797\pi$
$444$	−3.10819	−0.147508
$445$	−6.20177	−0.293992
$446$	−12.4201	−0.588110
$447$	0.818797	0.0387278
$448$	0	0
$449$	35.3648	1.66897	0.834484	−	0.551032i	$-0.185766\pi$
$449$	35.3648	1.66897	0.834484	+	0.551032i	$0.185766\pi$
$450$	16.6474	0.784766
$451$	3.79341	0.178625
$452$	4.39401	0.206677
$453$	20.6578	0.970588
$454$	−54.4356	−2.55479
$455$	0	0
$456$	−5.76834	−0.270127
$457$	19.7650	0.924570	0.462285	−	0.886731i	$-0.347030\pi$
$457$	19.7650	0.924570	0.462285	+	0.886731i	$0.347030\pi$
$458$	−23.4016	−1.09349
$459$	6.67693	0.311653
$460$	93.1267	4.34205
$461$	10.7489	0.500626	0.250313	−	0.968165i	$-0.419466\pi$
$461$	10.7489	0.500626	0.250313	+	0.968165i	$0.419466\pi$
$462$	0	0
$463$	2.89539	0.134560	0.0672801	−	0.997734i	$-0.478568\pi$
$463$	2.89539	0.134560	0.0672801	+	0.997734i	$0.478568\pi$
$464$	2.56698	0.119169
$465$	−5.09004	−0.236045
$466$	−39.3255	−1.82172
$467$	−5.98144	−0.276788	−0.138394	−	0.990377i	$-0.544194\pi$
$467$	−5.98144	−0.276788	−0.138394	+	0.990377i	$0.544194\pi$
$468$	4.55916	0.210747
$469$	0	0
$470$	−5.95670	−0.274762
$471$	−3.57661	−0.164802
$472$	−24.3806	−1.12221
$473$	−41.1380	−1.89153
$474$	−2.34217	−0.107580
$475$	−16.7586	−0.768937
$476$	0	0
$477$	9.47305	0.433741
$478$	−16.8287	−0.769729
$479$	−15.0728	−0.688693	−0.344346	−	0.938843i	$-0.611899\pi$
$479$	−15.0728	−0.688693	−0.344346	+	0.938843i	$0.611899\pi$
$480$	−21.8503	−0.997325
$481$	−1.45638	−0.0664054
$482$	−17.7145	−0.806872
$483$	0	0
$484$	10.5743	0.480649
$485$	61.3795	2.78710
$486$	2.26259	0.102633
$487$	−26.7979	−1.21433	−0.607165	−	0.794576i	$-0.707693\pi$
$487$	−26.7979	−1.21433	−0.607165	+	0.794576i	$0.707693\pi$
$488$	−34.3718	−1.55594
$489$	12.6245	0.570901
$490$	0	0
$491$	14.6716	0.662120	0.331060	−	0.943610i	$-0.392594\pi$
$491$	14.6716	0.662120	0.331060	+	0.943610i	$0.392594\pi$
$492$	−3.11931	−0.140629
$493$	−33.7031	−1.51791
$494$	−7.53232	−0.338895
$495$	−13.3352	−0.599371
$496$	0.736347	0.0330630
$497$	0	0
$498$	−4.18168	−0.187386
$499$	33.3116	1.49123	0.745616	−	0.666376i	$-0.232155\pi$
$499$	33.3116	1.49123	0.745616	+	0.666376i	$0.232155\pi$
$500$	25.8531	1.15618
$501$	4.48125	0.200208
$502$	−25.8455	−1.15354
$503$	−36.2073	−1.61440	−0.807201	−	0.590277i	$-0.799019\pi$
$503$	−36.2073	−1.61440	−0.807201	+	0.590277i	$0.799019\pi$
$504$	0	0
$505$	68.3721	3.04252
$506$	−72.8925	−3.24047
$507$	−10.8637	−0.482476
$508$	−8.85780	−0.393001
$509$	17.9330	0.794867	0.397433	−	0.917631i	$-0.369901\pi$
$509$	17.9330	0.794867	0.397433	+	0.917631i	$0.369901\pi$
$510$	53.1069	2.35161
$511$	0	0
$512$	5.73677	0.253532
$513$	−2.27770	−0.100563
$514$	−33.5215	−1.47857
$515$	−15.5199	−0.683888
$516$	33.8276	1.48918
$517$	2.84093	0.124944
$518$	0	0
$519$	−22.5618	−0.990352
$520$	13.0121	0.570621
$521$	34.4137	1.50769	0.753846	−	0.657051i	$-0.228197\pi$
$521$	34.4137	1.50769	0.753846	+	0.657051i	$0.228197\pi$
$522$	−11.4208	−0.499876
$523$	1.82322	0.0797237	0.0398618	−	0.999205i	$-0.487308\pi$
$523$	1.82322	0.0797237	0.0398618	+	0.999205i	$0.487308\pi$
$524$	−45.8625	−2.00351
$525$	0	0
$526$	−48.3808	−2.10950
$527$	−9.66784	−0.421138
$528$	1.92912	0.0839543
$529$	49.1266	2.13594
$530$	75.3466	3.27285
$531$	−9.62699	−0.417776
$532$	0	0
$533$	−1.46159	−0.0633086
$534$	−3.99165	−0.172736
$535$	−53.2880	−2.30384
$536$	21.2828	0.919277
$537$	14.9892	0.646832
$538$	65.7865	2.83626
$539$	0	0
$540$	10.9654	0.471878
$541$	31.9421	1.37330	0.686650	−	0.726988i	$-0.259080\pi$
$541$	31.9421	1.37330	0.686650	+	0.726988i	$0.259080\pi$
$542$	−49.3920	−2.12157
$543$	1.00879	0.0432915
$544$	−41.5017	−1.77937
$545$	−32.9715	−1.41234
$546$	0	0
$547$	−0.486837	−0.0208156	−0.0104078	−	0.999946i	$-0.503313\pi$
$547$	−0.486837	−0.0208156	−0.0104078	+	0.999946i	$0.503313\pi$
$548$	−29.2987	−1.25158
$549$	−13.5721	−0.579244
$550$	−63.1504	−2.69274
$551$	11.4971	0.489794
$552$	21.5081	0.915445
$553$	0	0
$554$	−59.7052	−2.53663
$555$	−3.50282	−0.148687
$556$	−34.8024	−1.47595
$557$	22.0350	0.933653	0.466827	−	0.884349i	$-0.345397\pi$
$557$	22.0350	0.933653	0.466827	+	0.884349i	$0.345397\pi$
$558$	−3.27611	−0.138689
$559$	15.8504	0.670400
$560$	0	0
$561$	−25.3283	−1.06936
$562$	24.5870	1.03714
$563$	2.55811	0.107812	0.0539058	−	0.998546i	$-0.482833\pi$
$563$	2.55811	0.107812	0.0539058	+	0.998546i	$0.482833\pi$
$564$	−2.33609	−0.0983671
$565$	4.95190	0.208328
$566$	−69.7976	−2.93381
$567$	0	0
$568$	−16.4865	−0.691760
$569$	31.6305	1.32602	0.663010	−	0.748610i	$-0.269279\pi$
$569$	31.6305	1.32602	0.663010	+	0.748610i	$0.269279\pi$
$570$	−18.1164	−0.758810
$571$	−34.5220	−1.44470	−0.722349	−	0.691528i	$-0.756938\pi$
$571$	−34.5220	−1.44470	−0.722349	+	0.691528i	$0.756938\pi$
$572$	−17.2947	−0.723129
$573$	20.0147	0.836125
$574$	0	0
$575$	62.4869	2.60588
$576$	−13.0464	−0.543602
$577$	41.9733	1.74737	0.873686	−	0.486491i	$-0.161723\pi$
$577$	41.9733	1.74737	0.873686	+	0.486491i	$0.161723\pi$
$578$	62.4054	2.59572
$579$	3.47028	0.144220
$580$	−55.3501	−2.29829
$581$	0	0
$582$	39.5058	1.63757
$583$	−35.9351	−1.48828
$584$	−5.77649	−0.239033
$585$	5.13801	0.212431
$586$	23.0782	0.953351
$587$	27.5287	1.13623	0.568115	−	0.822949i	$-0.307673\pi$
$587$	27.5287	1.13623	0.568115	+	0.822949i	$0.307673\pi$
$588$	0	0
$589$	3.29799	0.135891
$590$	−76.5710	−3.15238
$591$	11.6030	0.477284
$592$	0.506734	0.0208266
$593$	−2.59633	−0.106618	−0.0533092	−	0.998578i	$-0.516977\pi$
$593$	−2.59633	−0.106618	−0.0533092	+	0.998578i	$0.516977\pi$
$594$	−8.58292	−0.352161
$595$	0	0
$596$	2.55408	0.104619
$597$	−7.82824	−0.320388
$598$	28.0853	1.14850
$599$	−7.58409	−0.309878	−0.154939	−	0.987924i	$-0.549518\pi$
$599$	−7.58409	−0.309878	−0.154939	+	0.987924i	$0.549518\pi$
$600$	18.6335	0.760711
$601$	−25.1438	−1.02564	−0.512818	−	0.858497i	$-0.671398\pi$
$601$	−25.1438	−1.02564	−0.512818	+	0.858497i	$0.671398\pi$
$602$	0	0
$603$	8.40378	0.342228
$604$	64.4380	2.62194
$605$	11.9168	0.484488
$606$	44.0064	1.78764
$607$	36.2667	1.47202	0.736011	−	0.676970i	$-0.236707\pi$
$607$	36.2667	1.47202	0.736011	+	0.676970i	$0.236707\pi$
$608$	14.1575	0.574161
$609$	0	0
$610$	−107.950	−4.37076
$611$	−1.09461	−0.0442830
$612$	20.8274	0.841897
$613$	42.1617	1.70290	0.851448	−	0.524439i	$-0.175725\pi$
$613$	42.1617	1.70290	0.851448	+	0.524439i	$0.175725\pi$
$614$	49.7990	2.00972
$615$	−3.51535	−0.141753
$616$	0	0
$617$	−5.94775	−0.239447	−0.119724	−	0.992807i	$-0.538201\pi$
$617$	−5.94775	−0.239447	−0.119724	+	0.992807i	$0.538201\pi$
$618$	−9.98908	−0.401820
$619$	−11.3756	−0.457224	−0.228612	−	0.973518i	$-0.573419\pi$
$619$	−11.3756	−0.457224	−0.228612	+	0.973518i	$0.573419\pi$
$620$	−15.8774	−0.637651
$621$	8.49274	0.340802
$622$	−1.42099	−0.0569766
$623$	0	0
$624$	−0.743287	−0.0297553
$625$	−7.65291	−0.306116
$626$	40.5810	1.62194
$627$	8.64025	0.345058
$628$	−11.1565	−0.445195
$629$	−6.65314	−0.265278
$630$	0	0
$631$	34.5226	1.37432	0.687161	−	0.726505i	$-0.258857\pi$
$631$	34.5226	1.37432	0.687161	+	0.726505i	$0.258857\pi$
$632$	−2.62161	−0.104282
$633$	−0.767110	−0.0304899
$634$	34.5505	1.37218
$635$	−9.98243	−0.396141
$636$	29.5493	1.17171
$637$	0	0
$638$	43.3239	1.71521
$639$	−6.50992	−0.257528
$640$	−60.0680	−2.37440
$641$	−10.2549	−0.405044	−0.202522	−	0.979278i	$-0.564914\pi$
$641$	−10.2549	−0.405044	−0.202522	+	0.979278i	$0.564914\pi$
$642$	−34.2978	−1.35363
$643$	−14.0531	−0.554199	−0.277100	−	0.960841i	$-0.589373\pi$
$643$	−14.0531	−0.554199	−0.277100	+	0.960841i	$0.589373\pi$
$644$	0	0
$645$	38.1226	1.50107
$646$	−34.4096	−1.35383
$647$	−12.1956	−0.479458	−0.239729	−	0.970840i	$-0.577059\pi$
$647$	−12.1956	−0.479458	−0.239729	+	0.970840i	$0.577059\pi$
$648$	2.53253	0.0994870
$649$	36.5191	1.43350
$650$	24.3317	0.954369
$651$	0	0
$652$	39.3798	1.54223
$653$	3.31551	0.129746	0.0648729	−	0.997894i	$-0.479336\pi$
$653$	3.31551	0.129746	0.0648729	+	0.997894i	$0.479336\pi$
$654$	−21.2215	−0.829826
$655$	−51.6855	−2.01952
$656$	0.508546	0.0198554
$657$	−2.28092	−0.0889872
$658$	0	0
$659$	−8.07950	−0.314733	−0.157366	−	0.987540i	$-0.550300\pi$
$659$	−8.07950	−0.314733	−0.157366	+	0.987540i	$0.550300\pi$
$660$	−41.5964	−1.61914
$661$	33.3359	1.29661	0.648307	−	0.761379i	$-0.275477\pi$
$661$	33.3359	1.29661	0.648307	+	0.761379i	$0.275477\pi$
$662$	69.8491	2.71476
$663$	9.75896	0.379007
$664$	−4.68058	−0.181642
$665$	0	0
$666$	−2.25452	−0.0873611
$667$	−42.8687	−1.65988
$668$	13.9784	0.540841
$669$	−5.48934	−0.212230
$670$	66.8419	2.58233
$671$	51.4846	1.98754
$672$	0	0
$673$	16.8487	0.649469	0.324735	−	0.945805i	$-0.394725\pi$
$673$	16.8487	0.649469	0.324735	+	0.945805i	$0.394725\pi$
$674$	−31.0693	−1.19675
$675$	7.35768	0.283197
$676$	−33.8873	−1.30336
$677$	28.5473	1.09716	0.548580	−	0.836098i	$-0.315169\pi$
$677$	28.5473	1.09716	0.548580	+	0.836098i	$0.315169\pi$
$678$	3.18720	0.122404
$679$	0	0
$680$	59.4428	2.27953
$681$	−24.0590	−0.921943
$682$	12.4276	0.475878
$683$	18.4684	0.706674	0.353337	−	0.935496i	$-0.385047\pi$
$683$	18.4684	0.706674	0.353337	+	0.935496i	$0.385047\pi$
$684$	−7.10484	−0.271661
$685$	−33.0187	−1.26158
$686$	0	0
$687$	−10.3429	−0.394605
$688$	−5.51498	−0.210257
$689$	13.8457	0.527481
$690$	67.5495	2.57156
$691$	−33.1686	−1.26179	−0.630896	−	0.775868i	$-0.717312\pi$
$691$	−33.1686	−1.26179	−0.630896	+	0.775868i	$0.717312\pi$
$692$	−70.3770	−2.67533
$693$	0	0
$694$	−38.3901	−1.45727
$695$	−39.2211	−1.48774
$696$	−12.7834	−0.484553
$697$	−6.67693	−0.252907
$698$	13.4617	0.509533
$699$	−17.3807	−0.657400
$700$	0	0
$701$	44.1339	1.66692	0.833458	−	0.552583i	$-0.186358\pi$
$701$	44.1339	1.66692	0.833458	+	0.552583i	$0.186358\pi$
$702$	3.30698	0.124814
$703$	2.26958	0.0855990
$704$	49.4905	1.86524
$705$	−2.63269	−0.0991529
$706$	−12.3213	−0.463719
$707$	0	0
$708$	−30.0295	−1.12858
$709$	−22.1547	−0.832039	−0.416019	−	0.909356i	$-0.636575\pi$
$709$	−22.1547	−0.832039	−0.416019	+	0.909356i	$0.636575\pi$
$710$	−51.7785	−1.94321
$711$	−1.03517	−0.0388221
$712$	−4.46788	−0.167441
$713$	−12.2970	−0.460528
$714$	0	0
$715$	−19.4906	−0.728906
$716$	46.7559	1.74735
$717$	−7.43783	−0.277771
$718$	−54.1426	−2.02059
$719$	2.80563	0.104633	0.0523163	−	0.998631i	$-0.483340\pi$
$719$	2.80563	0.104633	0.0523163	+	0.998631i	$0.483340\pi$
$720$	−1.78772	−0.0666243
$721$	0	0
$722$	−31.2510	−1.16304
$723$	−7.82930	−0.291175
$724$	3.14674	0.116947
$725$	−37.1393	−1.37932
$726$	7.67005	0.284662
$727$	−25.3472	−0.940076	−0.470038	−	0.882646i	$-0.655760\pi$
$727$	−25.3472	−0.940076	−0.470038	+	0.882646i	$0.655760\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−18.1420	−0.671464
$731$	72.4087	2.67813
$732$	−42.3356	−1.56477
$733$	−10.8205	−0.399664	−0.199832	−	0.979830i	$-0.564040\pi$
$733$	−10.8205	−0.399664	−0.199832	+	0.979830i	$0.564040\pi$
$734$	−8.19600	−0.302520
$735$	0	0
$736$	−52.7882	−1.94580
$737$	−31.8790	−1.17428
$738$	−2.26259	−0.0832870
$739$	15.7485	0.579318	0.289659	−	0.957130i	$-0.406458\pi$
$739$	15.7485	0.579318	0.289659	+	0.957130i	$0.406458\pi$
$740$	−10.9264	−0.401661
$741$	−3.32907	−0.122297
$742$	0	0
$743$	−30.4834	−1.11833	−0.559164	−	0.829057i	$-0.688878\pi$
$743$	−30.4834	−1.11833	−0.559164	+	0.829057i	$0.688878\pi$
$744$	−3.66696	−0.134437
$745$	2.87836	0.105455
$746$	69.0823	2.52928
$747$	−1.84818	−0.0676215
$748$	−79.0068	−2.88877
$749$	0	0
$750$	18.7525	0.684745
$751$	−34.4554	−1.25729	−0.628647	−	0.777690i	$-0.716391\pi$
$751$	−34.4554	−1.25729	−0.628647	+	0.777690i	$0.716391\pi$
$752$	0.380857	0.0138884
$753$	−11.4230	−0.416276
$754$	−16.6926	−0.607909
$755$	72.6194	2.64289
$756$	0	0
$757$	−30.0474	−1.09209	−0.546045	−	0.837756i	$-0.683867\pi$
$757$	−30.0474	−1.09209	−0.546045	+	0.837756i	$0.683867\pi$
$758$	−32.9479	−1.19672
$759$	−32.2164	−1.16938
$760$	−20.2777	−0.735550
$761$	−38.0425	−1.37904	−0.689520	−	0.724266i	$-0.742179\pi$
$761$	−38.0425	−1.37904	−0.689520	+	0.724266i	$0.742179\pi$
$762$	−6.42500	−0.232753
$763$	0	0
$764$	62.4319	2.25871
$765$	23.4718	0.848623
$766$	−10.9664	−0.396234
$767$	−14.0707	−0.508065
$768$	−12.5688	−0.453536
$769$	44.6290	1.60936	0.804681	−	0.593708i	$-0.202337\pi$
$769$	44.6290	1.60936	0.804681	+	0.593708i	$0.202337\pi$
$770$	0	0
$771$	−14.8155	−0.533569
$772$	10.8249	0.389595
$773$	9.92149	0.356851	0.178426	−	0.983953i	$-0.442900\pi$
$773$	9.92149	0.356851	0.178426	+	0.983953i	$0.442900\pi$
$774$	24.5369	0.881960
$775$	−10.6535	−0.382686
$776$	44.2190	1.58737
$777$	0	0
$778$	−1.55142	−0.0556213
$779$	2.27770	0.0816071
$780$	16.0270	0.573860
$781$	24.6948	0.883649
$782$	128.301	4.58804
$783$	−5.04769	−0.180390
$784$	0	0
$785$	−12.5730	−0.448751
$786$	−33.2664	−1.18657
$787$	−9.83436	−0.350557	−0.175279	−	0.984519i	$-0.556083\pi$
$787$	−9.83436	−0.350557	−0.175279	+	0.984519i	$0.556083\pi$
$788$	36.1934	1.28934
$789$	−21.3829	−0.761253
$790$	−8.23356	−0.292937
$791$	0	0
$792$	−9.60691	−0.341367
$793$	−19.8369	−0.704430
$794$	0.914742	0.0324630
$795$	33.3011	1.18107
$796$	−24.4187	−0.865496
$797$	−37.5618	−1.33051	−0.665253	−	0.746618i	$-0.731677\pi$
$797$	−37.5618	−1.33051	−0.665253	+	0.746618i	$0.731677\pi$
$798$	0	0
$799$	−5.00044	−0.176903
$800$	−45.7330	−1.61691
$801$	−1.76420	−0.0623348
$802$	−63.6611	−2.24795
$803$	8.65246	0.305339
$804$	26.2139	0.924495
$805$	0	0
$806$	−4.78834	−0.168662
$807$	29.0758	1.02352
$808$	49.2566	1.73284
$809$	21.9434	0.771489	0.385744	−	0.922606i	$-0.373945\pi$
$809$	21.9434	0.771489	0.385744	+	0.922606i	$0.373945\pi$
$810$	7.95379	0.279468
$811$	1.08414	0.0380692	0.0190346	−	0.999819i	$-0.493941\pi$
$811$	1.08414	0.0380692	0.0190346	+	0.999819i	$0.493941\pi$
$812$	0	0
$813$	−21.8299	−0.765607
$814$	8.55233	0.299759
$815$	44.3796	1.55455
$816$	−3.39553	−0.118867
$817$	−24.7008	−0.864170
$818$	−38.4492	−1.34435
$819$	0	0
$820$	−10.9654	−0.382930
$821$	30.1425	1.05198	0.525990	−	0.850491i	$-0.323695\pi$
$821$	30.1425	1.05198	0.525990	+	0.850491i	$0.323695\pi$
$822$	−21.2518	−0.741243
$823$	8.54130	0.297731	0.148866	−	0.988857i	$-0.452438\pi$
$823$	8.54130	0.297731	0.148866	+	0.988857i	$0.452438\pi$
$824$	−11.1808	−0.389503
$825$	−27.9107	−0.971726
$826$	0	0
$827$	45.6006	1.58569	0.792843	−	0.609426i	$-0.208600\pi$
$827$	45.6006	1.58569	0.792843	+	0.609426i	$0.208600\pi$
$828$	26.4914	0.920641
$829$	34.3490	1.19299	0.596495	−	0.802617i	$-0.296560\pi$
$829$	34.3490	1.19299	0.596495	+	0.802617i	$0.296560\pi$
$830$	−14.7001	−0.510247
$831$	−26.3880	−0.915390
$832$	−19.0686	−0.661084
$833$	0	0
$834$	−25.2439	−0.874126
$835$	15.7532	0.545161
$836$	26.9516	0.932140
$837$	−1.44795	−0.0500484
$838$	22.9308	0.792131
$839$	−40.4048	−1.39493	−0.697464	−	0.716619i	$-0.745688\pi$
$839$	−40.4048	−1.39493	−0.697464	+	0.716619i	$0.745688\pi$
$840$	0	0
$841$	−3.52086	−0.121409
$842$	18.0023	0.620401
$843$	10.8668	0.374271
$844$	−2.39285	−0.0823653
$845$	−38.1899	−1.31377
$846$	−1.69448	−0.0582575
$847$	0	0
$848$	−4.81748	−0.165433
$849$	−30.8486	−1.05872
$850$	111.154	3.81254
$851$	−8.46247	−0.290090
$852$	−20.3064	−0.695687
$853$	3.69729	0.126593	0.0632965	−	0.997995i	$-0.479839\pi$
$853$	3.69729	0.126593	0.0632965	+	0.997995i	$0.479839\pi$
$854$	0	0
$855$	−8.00692	−0.273831
$856$	−38.3897	−1.31213
$857$	5.08270	0.173622	0.0868108	−	0.996225i	$-0.472332\pi$
$857$	5.08270	0.173622	0.0868108	+	0.996225i	$0.472332\pi$
$858$	−12.5447	−0.428270
$859$	47.7419	1.62893	0.814467	−	0.580210i	$-0.197030\pi$
$859$	47.7419	1.62893	0.814467	+	0.580210i	$0.197030\pi$
$860$	118.916	4.05500
$861$	0	0
$862$	−61.4243	−2.09212
$863$	16.7136	0.568938	0.284469	−	0.958685i	$-0.408183\pi$
$863$	16.7136	0.568938	0.284469	+	0.958685i	$0.408183\pi$
$864$	−6.21568	−0.211462
$865$	−79.3125	−2.69671
$866$	62.6464	2.12881
$867$	27.5814	0.936714
$868$	0	0
$869$	3.92684	0.133209
$870$	−40.1482	−1.36115
$871$	12.2829	0.416190
$872$	−23.7533	−0.804389
$873$	17.4604	0.590946
$874$	−43.7673	−1.48045
$875$	0	0
$876$	−7.11489	−0.240390
$877$	−8.44843	−0.285283	−0.142642	−	0.989774i	$-0.545560\pi$
$877$	−8.44843	−0.285283	−0.142642	+	0.989774i	$0.545560\pi$
$878$	−19.8183	−0.668834
$879$	10.1999	0.344034
$880$	6.78154	0.228606
$881$	25.5874	0.862062	0.431031	−	0.902337i	$-0.358150\pi$
$881$	25.5874	0.862062	0.431031	+	0.902337i	$0.358150\pi$
$882$	0	0
$883$	54.4322	1.83179	0.915895	−	0.401418i	$-0.131483\pi$
$883$	54.4322	1.83179	0.915895	+	0.401418i	$0.131483\pi$
$884$	30.4412	1.02385
$885$	−33.8422	−1.13759
$886$	−80.5446	−2.70595
$887$	−54.1148	−1.81700	−0.908498	−	0.417889i	$-0.862770\pi$
$887$	−54.1148	−1.81700	−0.908498	+	0.417889i	$0.862770\pi$
$888$	−2.52350	−0.0846832
$889$	0	0
$890$	−14.0321	−0.470355
$891$	−3.79341	−0.127084
$892$	−17.1229	−0.573318
$893$	1.70580	0.0570824
$894$	1.85260	0.0619602
$895$	52.6923	1.76131
$896$	0	0
$897$	12.4129	0.414456
$898$	80.0160	2.67017
$899$	7.30878	0.243761
$900$	22.9509	0.765029
$901$	63.2509	2.10719
$902$	8.58292	0.285780
$903$	0	0
$904$	3.56745	0.118651
$905$	3.54626	0.117882
$906$	46.7401	1.55284
$907$	−5.56564	−0.184804	−0.0924021	−	0.995722i	$-0.529455\pi$
$907$	−5.56564	−0.184804	−0.0924021	+	0.995722i	$0.529455\pi$
$908$	−75.0474	−2.49053
$909$	19.4496	0.645102
$910$	0	0
$911$	8.67651	0.287466	0.143733	−	0.989617i	$-0.454089\pi$
$911$	8.67651	0.287466	0.143733	+	0.989617i	$0.454089\pi$
$912$	1.15832	0.0383557
$913$	7.01092	0.232028
$914$	44.7202	1.47921
$915$	−47.7108	−1.57727
$916$	−32.2626	−1.06598
$917$	0	0
$918$	15.1071	0.498610
$919$	31.0314	1.02363	0.511816	−	0.859095i	$-0.328973\pi$
$919$	31.0314	1.02363	0.511816	+	0.859095i	$0.328973\pi$
$920$	75.6084	2.49274
$921$	22.0097	0.725246
$922$	24.3203	0.800947
$923$	−9.51486	−0.313185
$924$	0	0
$925$	−7.33146	−0.241057
$926$	6.55107	0.215282
$927$	−4.41489	−0.145004
$928$	31.3748	1.02993
$929$	0.0908696	0.00298133	0.00149067	−	0.999999i	$-0.499526\pi$
$929$	0.0908696	0.00298133	0.00149067	+	0.999999i	$0.499526\pi$
$930$	−11.5167	−0.377646
$931$	0	0
$932$	−54.2158	−1.77590
$933$	−0.628039	−0.0205611
$934$	−13.5335	−0.442831
$935$	−89.0379	−2.91185
$936$	3.70152	0.120988
$937$	−39.5068	−1.29063	−0.645316	−	0.763916i	$-0.723274\pi$
$937$	−39.5068	−1.29063	−0.645316	+	0.763916i	$0.723274\pi$
$938$	0	0
$939$	17.9356	0.585308
$940$	−8.21217	−0.267851
$941$	1.91194	0.0623275	0.0311638	−	0.999514i	$-0.490079\pi$
$941$	1.91194	0.0623275	0.0311638	+	0.999514i	$0.490079\pi$
$942$	−8.09240	−0.263665
$943$	−8.49274	−0.276562
$944$	4.89577	0.159344
$945$	0	0
$946$	−93.0784	−3.02624
$947$	10.0939	0.328007	0.164004	−	0.986460i	$-0.447559\pi$
$947$	10.0939	0.328007	0.164004	+	0.986460i	$0.447559\pi$
$948$	−3.22902	−0.104874
$949$	−3.33378	−0.108219
$950$	−37.9178	−1.23022
$951$	15.2704	0.495175
$952$	0	0
$953$	54.1757	1.75492	0.877461	−	0.479647i	$-0.159235\pi$
$953$	54.1757	1.75492	0.877461	+	0.479647i	$0.159235\pi$
$954$	21.4336	0.693938
$955$	70.3586	2.27675
$956$	−23.2009	−0.750370
$957$	19.1479	0.618965
$958$	−34.1035	−1.10183
$959$	0	0
$960$	−45.8628	−1.48022
$961$	−28.9035	−0.932369
$962$	−3.29520	−0.106241
$963$	−15.1587	−0.488481
$964$	−24.4220	−0.786579
$965$	12.1992	0.392707
$966$	0	0
$967$	−1.86574	−0.0599983	−0.0299991	−	0.999550i	$-0.509550\pi$
$967$	−1.86574	−0.0599983	−0.0299991	+	0.999550i	$0.509550\pi$
$968$	8.58512	0.275936
$969$	−15.2081	−0.488553
$970$	138.877	4.45906
$971$	−35.0800	−1.12577	−0.562886	−	0.826535i	$-0.690309\pi$
$971$	−35.0800	−1.12577	−0.562886	+	0.826535i	$0.690309\pi$
$972$	3.11931	0.100052
$973$	0	0
$974$	−60.6327	−1.94280
$975$	10.7539	0.344402
$976$	6.90205	0.220929
$977$	−3.77558	−0.120792	−0.0603958	−	0.998175i	$-0.519236\pi$
$977$	−3.77558	−0.120792	−0.0603958	+	0.998175i	$0.519236\pi$
$978$	28.5641	0.913380
$979$	6.69232	0.213887
$980$	0	0
$981$	−9.37929	−0.299458
$982$	33.1958	1.05932
$983$	−30.5146	−0.973265	−0.486632	−	0.873607i	$-0.661775\pi$
$983$	−30.5146	−0.973265	−0.486632	+	0.873607i	$0.661775\pi$
$984$	−2.53253	−0.0807340
$985$	40.7887	1.29964
$986$	−76.2561	−2.42849
$987$	0	0
$988$	−10.3844	−0.330372
$989$	92.1004	2.92862
$990$	−30.1720	−0.958928
$991$	−3.83662	−0.121874	−0.0609371	−	0.998142i	$-0.519409\pi$
$991$	−3.83662	−0.121874	−0.0609371	+	0.998142i	$0.519409\pi$
$992$	8.99998	0.285750
$993$	30.8713	0.979672
$994$	0	0
$995$	−27.5190	−0.872411
$996$	−5.76505	−0.182673
$997$	0.932058	0.0295186	0.0147593	−	0.999891i	$-0.495302\pi$
$997$	0.932058	0.0295186	0.0147593	+	0.999891i	$0.495302\pi$
$998$	75.3705	2.38581
$999$	−0.996436	−0.0315258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.19	yes	24
7.6	odd	2		6027.2.a.bn.1.19	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.19	✓	24	7.6	odd	2
6027.2.a.bo.1.19	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)

\(f(q)\)	\(=\)	\(q+2.26259 q^{2} +1.00000 q^{3} +3.11931 q^{4} +3.51535 q^{5} +2.26259 q^{6} +2.53253 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.26259 q^{2} +1.00000 q^{3} +3.11931 q^{4} +3.51535 q^{5} +2.26259 q^{6} +2.53253 q^{8} +1.00000 q^{9} +7.95379 q^{10} -3.79341 q^{11} +3.11931 q^{12} +1.46159 q^{13} +3.51535 q^{15} -0.508546 q^{16} +6.67693 q^{17} +2.26259 q^{18} -2.27770 q^{19} +10.9654 q^{20} -8.58292 q^{22} +8.49274 q^{23} +2.53253 q^{24} +7.35768 q^{25} +3.30698 q^{26} +1.00000 q^{27} -5.04769 q^{29} +7.95379 q^{30} -1.44795 q^{31} -6.21568 q^{32} -3.79341 q^{33} +15.1071 q^{34} +3.11931 q^{36} -0.996436 q^{37} -5.15350 q^{38} +1.46159 q^{39} +8.90272 q^{40} -1.00000 q^{41} +10.8446 q^{43} -11.8328 q^{44} +3.51535 q^{45} +19.2156 q^{46} -0.748913 q^{47} -0.508546 q^{48} +16.6474 q^{50} +6.67693 q^{51} +4.55916 q^{52} +9.47305 q^{53} +2.26259 q^{54} -13.3352 q^{55} -2.27770 q^{57} -11.4208 q^{58} -9.62699 q^{59} +10.9654 q^{60} -13.5721 q^{61} -3.27611 q^{62} -13.0464 q^{64} +5.13801 q^{65} -8.58292 q^{66} +8.40378 q^{67} +20.8274 q^{68} +8.49274 q^{69} -6.50992 q^{71} +2.53253 q^{72} -2.28092 q^{73} -2.25452 q^{74} +7.35768 q^{75} -7.10484 q^{76} +3.30698 q^{78} -1.03517 q^{79} -1.78772 q^{80} +1.00000 q^{81} -2.26259 q^{82} -1.84818 q^{83} +23.4718 q^{85} +24.5369 q^{86} -5.04769 q^{87} -9.60691 q^{88} -1.76420 q^{89} +7.95379 q^{90} +26.4914 q^{92} -1.44795 q^{93} -1.69448 q^{94} -8.00692 q^{95} -6.21568 q^{96} +17.4604 q^{97} -3.79341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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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