LMFDB - Embedded newform 6027.2.a.bn.1.5

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			1.5
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80081 q^{2} -1.00000 q^{3} +1.24292 q^{4} +2.17778 q^{5} +1.80081 q^{6} +1.36336 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.80081 q^{2} -1.00000 q^{3} +1.24292 q^{4} +2.17778 q^{5} +1.80081 q^{6} +1.36336 q^{8} +1.00000 q^{9} -3.92176 q^{10} -0.798673 q^{11} -1.24292 q^{12} -1.19276 q^{13} -2.17778 q^{15} -4.94099 q^{16} +5.17880 q^{17} -1.80081 q^{18} +4.47213 q^{19} +2.70680 q^{20} +1.43826 q^{22} +6.71919 q^{23} -1.36336 q^{24} -0.257287 q^{25} +2.14794 q^{26} -1.00000 q^{27} +4.22854 q^{29} +3.92176 q^{30} -0.168434 q^{31} +6.17106 q^{32} +0.798673 q^{33} -9.32603 q^{34} +1.24292 q^{36} -5.83538 q^{37} -8.05346 q^{38} +1.19276 q^{39} +2.96910 q^{40} +1.00000 q^{41} +1.82010 q^{43} -0.992684 q^{44} +2.17778 q^{45} -12.1000 q^{46} +5.26975 q^{47} +4.94099 q^{48} +0.463325 q^{50} -5.17880 q^{51} -1.48251 q^{52} -1.21884 q^{53} +1.80081 q^{54} -1.73933 q^{55} -4.47213 q^{57} -7.61479 q^{58} -11.7353 q^{59} -2.70680 q^{60} +12.5796 q^{61} +0.303318 q^{62} -1.23093 q^{64} -2.59757 q^{65} -1.43826 q^{66} -2.41092 q^{67} +6.43681 q^{68} -6.71919 q^{69} +0.255861 q^{71} +1.36336 q^{72} +5.27880 q^{73} +10.5084 q^{74} +0.257287 q^{75} +5.55849 q^{76} -2.14794 q^{78} +13.1519 q^{79} -10.7604 q^{80} +1.00000 q^{81} -1.80081 q^{82} -10.9425 q^{83} +11.2783 q^{85} -3.27766 q^{86} -4.22854 q^{87} -1.08888 q^{88} +9.74201 q^{89} -3.92176 q^{90} +8.35140 q^{92} +0.168434 q^{93} -9.48982 q^{94} +9.73931 q^{95} -6.17106 q^{96} -4.79462 q^{97} -0.798673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.80081	−1.27337	−0.636683	−	0.771126i	$-0.719694\pi$
$2$	−1.80081	−1.27337	−0.636683	+	0.771126i	$0.719694\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.24292	0.621458
$5$	2.17778	0.973932	0.486966	−	0.873421i	$-0.338104\pi$
$5$	2.17778	0.973932	0.486966	+	0.873421i	$0.338104\pi$
$6$	1.80081	0.735178
$7$	0	0
$7$	0	0
$8$	1.36336	0.482022
$9$	1.00000	0.333333
$10$	−3.92176	−1.24017
$11$	−0.798673	−0.240809	−0.120404	−	0.992725i	$-0.538419\pi$
$11$	−0.798673	−0.240809	−0.120404	+	0.992725i	$0.538419\pi$
$12$	−1.24292	−0.358799
$13$	−1.19276	−0.330813	−0.165406	−	0.986225i	$-0.552894\pi$
$13$	−1.19276	−0.330813	−0.165406	+	0.986225i	$0.552894\pi$
$14$	0	0
$15$	−2.17778	−0.562300
$16$	−4.94099	−1.23525
$17$	5.17880	1.25604	0.628021	−	0.778196i	$-0.283865\pi$
$17$	5.17880	1.25604	0.628021	+	0.778196i	$0.283865\pi$
$18$	−1.80081	−0.424455
$19$	4.47213	1.02598	0.512989	−	0.858395i	$-0.328538\pi$
$19$	4.47213	1.02598	0.512989	+	0.858395i	$0.328538\pi$
$20$	2.70680	0.605258
$21$	0	0
$22$	1.43826	0.306638
$23$	6.71919	1.40105	0.700524	−	0.713629i	$-0.252950\pi$
$23$	6.71919	1.40105	0.700524	+	0.713629i	$0.252950\pi$
$24$	−1.36336	−0.278295
$25$	−0.257287	−0.0514574
$26$	2.14794	0.421246
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.22854	0.785220	0.392610	−	0.919705i	$-0.371572\pi$
$29$	4.22854	0.785220	0.392610	+	0.919705i	$0.371572\pi$
$30$	3.92176	0.716013
$31$	−0.168434	−0.0302517	−0.0151258	−	0.999886i	$-0.504815\pi$
$31$	−0.168434	−0.0302517	−0.0151258	+	0.999886i	$0.504815\pi$
$32$	6.17106	1.09090
$33$	0.798673	0.139031
$34$	−9.32603	−1.59940
$35$	0	0
$36$	1.24292	0.207153
$37$	−5.83538	−0.959330	−0.479665	−	0.877452i	$-0.659242\pi$
$37$	−5.83538	−0.959330	−0.479665	+	0.877452i	$0.659242\pi$
$38$	−8.05346	−1.30644
$39$	1.19276	0.190995
$40$	2.96910	0.469456
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	1.82010	0.277563	0.138782	−	0.990323i	$-0.455681\pi$
$43$	1.82010	0.277563	0.138782	+	0.990323i	$0.455681\pi$
$44$	−0.992684	−0.149653
$45$	2.17778	0.324644
$46$	−12.1000	−1.78405
$47$	5.26975	0.768672	0.384336	−	0.923193i	$-0.374430\pi$
$47$	5.26975	0.768672	0.384336	+	0.923193i	$0.374430\pi$
$48$	4.94099	0.713171
$49$	0	0
$50$	0.463325	0.0655241
$51$	−5.17880	−0.725177
$52$	−1.48251	−0.205587
$53$	−1.21884	−0.167421	−0.0837103	−	0.996490i	$-0.526677\pi$
$53$	−1.21884	−0.167421	−0.0837103	+	0.996490i	$0.526677\pi$
$54$	1.80081	0.245059
$55$	−1.73933	−0.234531
$56$	0	0
$57$	−4.47213	−0.592348
$58$	−7.61479	−0.999871
$59$	−11.7353	−1.52780	−0.763900	−	0.645334i	$-0.776718\pi$
$59$	−11.7353	−1.52780	−0.763900	+	0.645334i	$0.776718\pi$
$60$	−2.70680	−0.349446
$61$	12.5796	1.61065	0.805325	−	0.592833i	$-0.201991\pi$
$61$	12.5796	1.61065	0.805325	+	0.592833i	$0.201991\pi$
$62$	0.303318	0.0385214
$63$	0	0
$64$	−1.23093	−0.153866
$65$	−2.59757	−0.322189
$66$	−1.43826	−0.177037
$67$	−2.41092	−0.294541	−0.147271	−	0.989096i	$-0.547049\pi$
$67$	−2.41092	−0.294541	−0.147271	+	0.989096i	$0.547049\pi$
$68$	6.43681	0.780578
$69$	−6.71919	−0.808895
$70$	0	0
$71$	0.255861	0.0303651	0.0151826	−	0.999885i	$-0.495167\pi$
$71$	0.255861	0.0303651	0.0151826	+	0.999885i	$0.495167\pi$
$72$	1.36336	0.160674
$73$	5.27880	0.617837	0.308918	−	0.951089i	$-0.400033\pi$
$73$	5.27880	0.617837	0.308918	+	0.951089i	$0.400033\pi$
$74$	10.5084	1.22158
$75$	0.257287	0.0297089
$76$	5.55849	0.637602
$77$	0	0
$78$	−2.14794	−0.243206
$79$	13.1519	1.47970	0.739851	−	0.672771i	$-0.234896\pi$
$79$	13.1519	1.47970	0.739851	+	0.672771i	$0.234896\pi$
$80$	−10.7604	−1.20305
$81$	1.00000	0.111111
$82$	−1.80081	−0.198866
$83$	−10.9425	−1.20109	−0.600546	−	0.799590i	$-0.705050\pi$
$83$	−10.9425	−1.20109	−0.600546	+	0.799590i	$0.705050\pi$
$84$	0	0
$85$	11.2783	1.22330
$86$	−3.27766	−0.353439
$87$	−4.22854	−0.453347
$88$	−1.08888	−0.116075
$89$	9.74201	1.03265	0.516325	−	0.856392i	$-0.327300\pi$
$89$	9.74201	1.03265	0.516325	+	0.856392i	$0.327300\pi$
$90$	−3.92176	−0.413390
$91$	0	0
$92$	8.35140	0.870693
$93$	0.168434	0.0174658
$94$	−9.48982	−0.978800
$95$	9.73931	0.999232
$96$	−6.17106	−0.629831
$97$	−4.79462	−0.486820	−0.243410	−	0.969923i	$-0.578266\pi$
$97$	−4.79462	−0.486820	−0.243410	+	0.969923i	$0.578266\pi$
$98$	0	0
$99$	−0.798673	−0.0802696
$100$	−0.319786	−0.0319786
$101$	2.54061	0.252800	0.126400	−	0.991979i	$-0.459658\pi$
$101$	2.54061	0.252800	0.126400	+	0.991979i	$0.459658\pi$
$102$	9.32603	0.923415
$103$	5.43950	0.535970	0.267985	−	0.963423i	$-0.413642\pi$
$103$	5.43950	0.535970	0.267985	+	0.963423i	$0.413642\pi$
$104$	−1.62617	−0.159459
$105$	0	0
$106$	2.19490	0.213188
$107$	16.2891	1.57473	0.787364	−	0.616489i	$-0.211445\pi$
$107$	16.2891	1.57473	0.787364	+	0.616489i	$0.211445\pi$
$108$	−1.24292	−0.119600
$109$	10.3602	0.992326	0.496163	−	0.868229i	$-0.334742\pi$
$109$	10.3602	0.992326	0.496163	+	0.868229i	$0.334742\pi$
$110$	3.13221	0.298644
$111$	5.83538	0.553869
$112$	0	0
$113$	2.79770	0.263185	0.131593	−	0.991304i	$-0.457991\pi$
$113$	2.79770	0.263185	0.131593	+	0.991304i	$0.457991\pi$
$114$	8.05346	0.754276
$115$	14.6329	1.36452
$116$	5.25572	0.487981
$117$	−1.19276	−0.110271
$118$	21.1330	1.94545
$119$	0	0
$120$	−2.96910	−0.271041
$121$	−10.3621	−0.942011
$122$	−22.6534	−2.05095
$123$	−1.00000	−0.0901670
$124$	−0.209350	−0.0188001
$125$	−11.4492	−1.02405
$126$	0	0
$127$	−14.5164	−1.28812	−0.644062	−	0.764973i	$-0.722752\pi$
$127$	−14.5164	−1.28812	−0.644062	+	0.764973i	$0.722752\pi$
$128$	−10.1255	−0.894972
$129$	−1.82010	−0.160251
$130$	4.67773	0.410264
$131$	−0.770663	−0.0673331	−0.0336666	−	0.999433i	$-0.510718\pi$
$131$	−0.770663	−0.0673331	−0.0336666	+	0.999433i	$0.510718\pi$
$132$	0.992684	0.0864020
$133$	0	0
$134$	4.34161	0.375058
$135$	−2.17778	−0.187433
$136$	7.06058	0.605440
$137$	4.75720	0.406435	0.203218	−	0.979134i	$-0.434860\pi$
$137$	4.75720	0.406435	0.203218	+	0.979134i	$0.434860\pi$
$138$	12.1000	1.03002
$139$	−0.628119	−0.0532764	−0.0266382	−	0.999645i	$-0.508480\pi$
$139$	−0.628119	−0.0532764	−0.0266382	+	0.999645i	$0.508480\pi$
$140$	0	0
$141$	−5.26975	−0.443793
$142$	−0.460758	−0.0386659
$143$	0.952627	0.0796627
$144$	−4.94099	−0.411749
$145$	9.20881	0.764750
$146$	−9.50612	−0.786732
$147$	0	0
$148$	−7.25289	−0.596184
$149$	−0.960953	−0.0787243	−0.0393622	−	0.999225i	$-0.512533\pi$
$149$	−0.960953	−0.0787243	−0.0393622	+	0.999225i	$0.512533\pi$
$150$	−0.463325	−0.0378303
$151$	−5.66573	−0.461071	−0.230535	−	0.973064i	$-0.574048\pi$
$151$	−5.66573	−0.461071	−0.230535	+	0.973064i	$0.574048\pi$
$152$	6.09714	0.494543
$153$	5.17880	0.418681
$154$	0	0
$155$	−0.366812	−0.0294630
$156$	1.48251	0.118695
$157$	14.1792	1.13162	0.565812	−	0.824534i	$-0.308563\pi$
$157$	14.1792	1.13162	0.565812	+	0.824534i	$0.308563\pi$
$158$	−23.6840	−1.88420
$159$	1.21884	0.0966603
$160$	13.4392	1.06246
$161$	0	0
$162$	−1.80081	−0.141485
$163$	10.5373	0.825346	0.412673	−	0.910879i	$-0.364595\pi$
$163$	10.5373	0.825346	0.412673	+	0.910879i	$0.364595\pi$
$164$	1.24292	0.0970555
$165$	1.73933	0.135407
$166$	19.7053	1.52943
$167$	−13.9834	−1.08207	−0.541034	−	0.841001i	$-0.681967\pi$
$167$	−13.9834	−1.08207	−0.541034	+	0.841001i	$0.681967\pi$
$168$	0	0
$169$	−11.5773	−0.890563
$170$	−20.3100	−1.55771
$171$	4.47213	0.341992
$172$	2.26224	0.172494
$173$	−5.17342	−0.393328	−0.196664	−	0.980471i	$-0.563011\pi$
$173$	−5.17342	−0.393328	−0.196664	+	0.980471i	$0.563011\pi$
$174$	7.61479	0.577276
$175$	0	0
$176$	3.94624	0.297459
$177$	11.7353	0.882076
$178$	−17.5435	−1.31494
$179$	−0.884735	−0.0661282	−0.0330641	−	0.999453i	$-0.510527\pi$
$179$	−0.884735	−0.0661282	−0.0330641	+	0.999453i	$0.510527\pi$
$180$	2.70680	0.201753
$181$	10.6540	0.791905	0.395952	−	0.918271i	$-0.370414\pi$
$181$	10.6540	0.791905	0.395952	+	0.918271i	$0.370414\pi$
$182$	0	0
$183$	−12.5796	−0.929910
$184$	9.16069	0.675335
$185$	−12.7081	−0.934321
$186$	−0.303318	−0.0222403
$187$	−4.13616	−0.302466
$188$	6.54986	0.477698
$189$	0	0
$190$	−17.5386	−1.27239
$191$	−5.78471	−0.418567	−0.209283	−	0.977855i	$-0.567113\pi$
$191$	−5.78471	−0.418567	−0.209283	+	0.977855i	$0.567113\pi$
$192$	1.23093	0.0888345
$193$	16.6099	1.19561	0.597803	−	0.801643i	$-0.296040\pi$
$193$	16.6099	1.19561	0.597803	+	0.801643i	$0.296040\pi$
$194$	8.63420	0.619900
$195$	2.59757	0.186016
$196$	0	0
$197$	−16.2889	−1.16054	−0.580268	−	0.814426i	$-0.697052\pi$
$197$	−16.2889	−1.16054	−0.580268	+	0.814426i	$0.697052\pi$
$198$	1.43826	0.102213
$199$	−21.9239	−1.55414	−0.777070	−	0.629414i	$-0.783295\pi$
$199$	−21.9239	−1.55414	−0.777070	+	0.629414i	$0.783295\pi$
$200$	−0.350776	−0.0248036
$201$	2.41092	0.170053
$202$	−4.57515	−0.321907
$203$	0	0
$204$	−6.43681	−0.450667
$205$	2.17778	0.152103
$206$	−9.79550	−0.682485
$207$	6.71919	0.467016
$208$	5.89343	0.408636
$209$	−3.57177	−0.247064
$210$	0	0
$211$	−9.48428	−0.652925	−0.326462	−	0.945210i	$-0.605857\pi$
$211$	−9.48428	−0.652925	−0.326462	+	0.945210i	$0.605857\pi$
$212$	−1.51492	−0.104045
$213$	−0.255861	−0.0175313
$214$	−29.3336	−2.00520
$215$	3.96378	0.270327
$216$	−1.36336	−0.0927651
$217$	0	0
$218$	−18.6567	−1.26359
$219$	−5.27880	−0.356708
$220$	−2.16184	−0.145752
$221$	−6.17708	−0.415515
$222$	−10.5084	−0.705278
$223$	−5.77091	−0.386449	−0.193224	−	0.981155i	$-0.561895\pi$
$223$	−5.77091	−0.386449	−0.193224	+	0.981155i	$0.561895\pi$
$224$	0	0
$225$	−0.257287	−0.0171525
$226$	−5.03813	−0.335131
$227$	0.172461	0.0114466	0.00572332	−	0.999984i	$-0.498178\pi$
$227$	0.172461	0.0114466	0.00572332	+	0.999984i	$0.498178\pi$
$228$	−5.55849	−0.368120
$229$	−2.34851	−0.155194	−0.0775970	−	0.996985i	$-0.524725\pi$
$229$	−2.34851	−0.155194	−0.0775970	+	0.996985i	$0.524725\pi$
$230$	−26.3511	−1.73754
$231$	0	0
$232$	5.76503	0.378493
$233$	−2.17060	−0.142201	−0.0711004	−	0.997469i	$-0.522651\pi$
$233$	−2.17060	−0.142201	−0.0711004	+	0.997469i	$0.522651\pi$
$234$	2.14794	0.140415
$235$	11.4763	0.748634
$236$	−14.5860	−0.949465
$237$	−13.1519	−0.854306
$238$	0	0
$239$	16.2909	1.05377	0.526886	−	0.849936i	$-0.323359\pi$
$239$	16.2909	1.05377	0.526886	+	0.849936i	$0.323359\pi$
$240$	10.7604	0.694579
$241$	−22.5603	−1.45324	−0.726619	−	0.687041i	$-0.758909\pi$
$241$	−22.5603	−1.45324	−0.726619	+	0.687041i	$0.758909\pi$
$242$	18.6602	1.19952
$243$	−1.00000	−0.0641500
$244$	15.6354	1.00095
$245$	0	0
$246$	1.80081	0.114815
$247$	−5.33419	−0.339407
$248$	−0.229637	−0.0145819
$249$	10.9425	0.693451
$250$	20.6178	1.30399
$251$	−15.9372	−1.00594	−0.502972	−	0.864303i	$-0.667760\pi$
$251$	−15.9372	−1.00594	−0.502972	+	0.864303i	$0.667760\pi$
$252$	0	0
$253$	−5.36643	−0.337385
$254$	26.1413	1.64025
$255$	−11.2783	−0.706272
$256$	20.6959	1.29349
$257$	−4.67166	−0.291410	−0.145705	−	0.989328i	$-0.546545\pi$
$257$	−4.67166	−0.291410	−0.145705	+	0.989328i	$0.546545\pi$
$258$	3.27766	0.204058
$259$	0	0
$260$	−3.22857	−0.200227
$261$	4.22854	0.261740
$262$	1.38782	0.0857397
$263$	−27.7645	−1.71203	−0.856017	−	0.516948i	$-0.827068\pi$
$263$	−27.7645	−1.71203	−0.856017	+	0.516948i	$0.827068\pi$
$264$	1.08888	0.0670160
$265$	−2.65436	−0.163056
$266$	0	0
$267$	−9.74201	−0.596201
$268$	−2.99658	−0.183045
$269$	−0.216531	−0.0132021	−0.00660106	−	0.999978i	$-0.502101\pi$
$269$	−0.216531	−0.0132021	−0.00660106	+	0.999978i	$0.502101\pi$
$270$	3.92176	0.238671
$271$	−15.4909	−0.941007	−0.470504	−	0.882398i	$-0.655928\pi$
$271$	−15.4909	−0.941007	−0.470504	+	0.882398i	$0.655928\pi$
$272$	−25.5884	−1.55152
$273$	0	0
$274$	−8.56682	−0.517540
$275$	0.205488	0.0123914
$276$	−8.35140	−0.502695
$277$	2.35151	0.141289	0.0706443	−	0.997502i	$-0.477494\pi$
$277$	2.35151	0.141289	0.0706443	+	0.997502i	$0.477494\pi$
$278$	1.13112	0.0678403
$279$	−0.168434	−0.0100839
$280$	0	0
$281$	23.8868	1.42497	0.712483	−	0.701690i	$-0.247571\pi$
$281$	23.8868	1.42497	0.712483	+	0.701690i	$0.247571\pi$
$282$	9.48982	0.565111
$283$	7.09006	0.421461	0.210730	−	0.977544i	$-0.432416\pi$
$283$	7.09006	0.421461	0.210730	+	0.977544i	$0.432416\pi$
$284$	0.318014	0.0188707
$285$	−9.73931	−0.576907
$286$	−1.71550	−0.101440
$287$	0	0
$288$	6.17106	0.363633
$289$	9.81994	0.577644
$290$	−16.5833	−0.973806
$291$	4.79462	0.281066
$292$	6.56111	0.383960
$293$	29.3669	1.71563	0.857815	−	0.513958i	$-0.171821\pi$
$293$	29.3669	1.71563	0.857815	+	0.513958i	$0.171821\pi$
$294$	0	0
$295$	−25.5568	−1.48797
$296$	−7.95573	−0.462418
$297$	0.798673	0.0463437
$298$	1.73049	0.100245
$299$	−8.01440	−0.463485
$300$	0.319786	0.0184629
$301$	0	0
$302$	10.2029	0.587111
$303$	−2.54061	−0.145954
$304$	−22.0968	−1.26734
$305$	27.3955	1.56866
$306$	−9.32603	−0.533134
$307$	30.7496	1.75497	0.877485	−	0.479604i	$-0.159220\pi$
$307$	30.7496	1.75497	0.877485	+	0.479604i	$0.159220\pi$
$308$	0	0
$309$	−5.43950	−0.309442
$310$	0.660558	0.0375172
$311$	−17.9250	−1.01644	−0.508218	−	0.861228i	$-0.669696\pi$
$311$	−17.9250	−1.01644	−0.508218	+	0.861228i	$0.669696\pi$
$312$	1.62617	0.0920637
$313$	−15.7109	−0.888035	−0.444018	−	0.896018i	$-0.646447\pi$
$313$	−15.7109	−0.888035	−0.444018	+	0.896018i	$0.646447\pi$
$314$	−25.5340	−1.44097
$315$	0	0
$316$	16.3467	0.919573
$317$	−3.37598	−0.189614	−0.0948070	−	0.995496i	$-0.530223\pi$
$317$	−3.37598	−0.189614	−0.0948070	+	0.995496i	$0.530223\pi$
$318$	−2.19490	−0.123084
$319$	−3.37722	−0.189088
$320$	−2.68069	−0.149855
$321$	−16.2891	−0.909169
$322$	0	0
$323$	23.1603	1.28867
$324$	1.24292	0.0690509
$325$	0.306882	0.0170228
$326$	−18.9757	−1.05097
$327$	−10.3602	−0.572920
$328$	1.36336	0.0752791
$329$	0	0
$330$	−3.13221	−0.172422
$331$	22.9215	1.25988	0.629940	−	0.776644i	$-0.283079\pi$
$331$	22.9215	1.25988	0.629940	+	0.776644i	$0.283079\pi$
$332$	−13.6006	−0.746429
$333$	−5.83538	−0.319777
$334$	25.1815	1.37787
$335$	−5.25045	−0.286863
$336$	0	0
$337$	18.3916	1.00185	0.500927	−	0.865489i	$-0.332992\pi$
$337$	18.3916	1.00185	0.500927	+	0.865489i	$0.332992\pi$
$338$	20.8485	1.13401
$339$	−2.79770	−0.151950
$340$	14.0179	0.760230
$341$	0.134524	0.00728487
$342$	−8.05346	−0.435481
$343$	0	0
$344$	2.48146	0.133791
$345$	−14.6329	−0.787809
$346$	9.31635	0.500850
$347$	8.01891	0.430477	0.215239	−	0.976561i	$-0.430947\pi$
$347$	8.01891	0.430477	0.215239	+	0.976561i	$0.430947\pi$
$348$	−5.25572	−0.281736
$349$	14.8361	0.794159	0.397079	−	0.917784i	$-0.370024\pi$
$349$	14.8361	0.794159	0.397079	+	0.917784i	$0.370024\pi$
$350$	0	0
$351$	1.19276	0.0636650
$352$	−4.92866	−0.262698
$353$	−31.7462	−1.68968	−0.844840	−	0.535020i	$-0.820304\pi$
$353$	−31.7462	−1.68968	−0.844840	+	0.535020i	$0.820304\pi$
$354$	−21.1330	−1.12320
$355$	0.557209	0.0295736
$356$	12.1085	0.641750
$357$	0	0
$358$	1.59324	0.0842054
$359$	20.9734	1.10693	0.553466	−	0.832872i	$-0.313305\pi$
$359$	20.9734	1.10693	0.553466	+	0.832872i	$0.313305\pi$
$360$	2.96910	0.156485
$361$	0.999965	0.0526297
$362$	−19.1858	−1.00838
$363$	10.3621	0.543870
$364$	0	0
$365$	11.4961	0.601731
$366$	22.6534	1.18411
$367$	−9.23972	−0.482309	−0.241155	−	0.970487i	$-0.577526\pi$
$367$	−9.23972	−0.482309	−0.241155	+	0.970487i	$0.577526\pi$
$368$	−33.1995	−1.73064
$369$	1.00000	0.0520579
$370$	22.8850	1.18973
$371$	0	0
$372$	0.209350	0.0108543
$373$	35.1745	1.82127	0.910634	−	0.413214i	$-0.135594\pi$
$373$	35.1745	1.82127	0.910634	+	0.413214i	$0.135594\pi$
$374$	7.44845	0.385150
$375$	11.4492	0.591234
$376$	7.18458	0.370517
$377$	−5.04364	−0.259761
$378$	0	0
$379$	28.1280	1.44484	0.722419	−	0.691456i	$-0.243030\pi$
$379$	28.1280	1.44484	0.722419	+	0.691456i	$0.243030\pi$
$380$	12.1051	0.620981
$381$	14.5164	0.743699
$382$	10.4172	0.532988
$383$	−1.11304	−0.0568738	−0.0284369	−	0.999596i	$-0.509053\pi$
$383$	−1.11304	−0.0568738	−0.0284369	+	0.999596i	$0.509053\pi$
$384$	10.1255	0.516713
$385$	0	0
$386$	−29.9113	−1.52244
$387$	1.82010	0.0925210
$388$	−5.95932	−0.302538
$389$	−24.4665	−1.24050	−0.620251	−	0.784404i	$-0.712969\pi$
$389$	−24.4665	−1.24050	−0.620251	+	0.784404i	$0.712969\pi$
$390$	−4.67773	−0.236866
$391$	34.7973	1.75978
$392$	0	0
$393$	0.770663	0.0388748
$394$	29.3332	1.47779
$395$	28.6419	1.44113
$396$	−0.992684	−0.0498842
$397$	−4.87136	−0.244487	−0.122243	−	0.992500i	$-0.539009\pi$
$397$	−4.87136	−0.244487	−0.122243	+	0.992500i	$0.539009\pi$
$398$	39.4807	1.97899
$399$	0	0
$400$	1.27125	0.0635626
$401$	−8.56547	−0.427739	−0.213869	−	0.976862i	$-0.568607\pi$
$401$	−8.56547	−0.427739	−0.213869	+	0.976862i	$0.568607\pi$
$402$	−4.34161	−0.216540
$403$	0.200902	0.0100076
$404$	3.15777	0.157105
$405$	2.17778	0.108215
$406$	0	0
$407$	4.66056	0.231015
$408$	−7.06058	−0.349551
$409$	30.9507	1.53041	0.765207	−	0.643784i	$-0.222637\pi$
$409$	30.9507	1.53041	0.765207	+	0.643784i	$0.222637\pi$
$410$	−3.92176	−0.193682
$411$	−4.75720	−0.234655
$412$	6.76085	0.333083
$413$	0	0
$414$	−12.1000	−0.594682
$415$	−23.8303	−1.16978
$416$	−7.36061	−0.360884
$417$	0.628119	0.0307591
$418$	6.43208	0.314603
$419$	21.7112	1.06066	0.530331	−	0.847791i	$-0.322068\pi$
$419$	21.7112	1.06066	0.530331	+	0.847791i	$0.322068\pi$
$420$	0	0
$421$	27.4470	1.33768	0.668841	−	0.743405i	$-0.266791\pi$
$421$	27.4470	1.33768	0.668841	+	0.743405i	$0.266791\pi$
$422$	17.0794	0.831412
$423$	5.26975	0.256224
$424$	−1.66172	−0.0807003
$425$	−1.33244	−0.0646327
$426$	0.460758	0.0223238
$427$	0	0
$428$	20.2460	0.978628
$429$	−0.952627	−0.0459933
$430$	−7.13801	−0.344226
$431$	17.8045	0.857611	0.428806	−	0.903397i	$-0.358934\pi$
$431$	17.8045	0.857611	0.428806	+	0.903397i	$0.358934\pi$
$432$	4.94099	0.237724
$433$	13.7451	0.660549	0.330274	−	0.943885i	$-0.392859\pi$
$433$	13.7451	0.660549	0.330274	+	0.943885i	$0.392859\pi$
$434$	0	0
$435$	−9.20881	−0.441529
$436$	12.8769	0.616690
$437$	30.0491	1.43744
$438$	9.50612	0.454220
$439$	4.70167	0.224398	0.112199	−	0.993686i	$-0.464211\pi$
$439$	4.70167	0.224398	0.112199	+	0.993686i	$0.464211\pi$
$440$	−2.37134	−0.113049
$441$	0	0
$442$	11.1237	0.529103
$443$	31.8616	1.51379	0.756894	−	0.653537i	$-0.226716\pi$
$443$	31.8616	1.51379	0.756894	+	0.653537i	$0.226716\pi$
$444$	7.25289	0.344207
$445$	21.2159	1.00573
$446$	10.3923	0.492091
$447$	0.960953	0.0454515
$448$	0	0
$449$	30.7586	1.45159	0.725795	−	0.687911i	$-0.241472\pi$
$449$	30.7586	1.45159	0.725795	+	0.687911i	$0.241472\pi$
$450$	0.463325	0.0218414
$451$	−0.798673	−0.0376080
$452$	3.47731	0.163559
$453$	5.66573	0.266199
$454$	−0.310569	−0.0145757
$455$	0	0
$456$	−6.09714	−0.285525
$457$	4.85756	0.227227	0.113614	−	0.993525i	$-0.463757\pi$
$457$	4.85756	0.227227	0.113614	+	0.993525i	$0.463757\pi$
$458$	4.22922	0.197619
$459$	−5.17880	−0.241726
$460$	18.1875	0.847995
$461$	−34.9988	−1.63006	−0.815028	−	0.579422i	$-0.803278\pi$
$461$	−34.9988	−1.63006	−0.815028	+	0.579422i	$0.803278\pi$
$462$	0	0
$463$	−0.712122	−0.0330951	−0.0165476	−	0.999863i	$-0.505267\pi$
$463$	−0.712122	−0.0330951	−0.0165476	+	0.999863i	$0.505267\pi$
$464$	−20.8932	−0.969941
$465$	0.366812	0.0170105
$466$	3.90884	0.181073
$467$	−20.5280	−0.949922	−0.474961	−	0.880007i	$-0.657538\pi$
$467$	−20.5280	−0.949922	−0.474961	+	0.880007i	$0.657538\pi$
$468$	−1.48251	−0.0685288
$469$	0	0
$470$	−20.6667	−0.953284
$471$	−14.1792	−0.653343
$472$	−15.9994	−0.736433
$473$	−1.45367	−0.0668397
$474$	23.6840	1.08784
$475$	−1.15062	−0.0527941
$476$	0	0
$477$	−1.21884	−0.0558069
$478$	−29.3369	−1.34184
$479$	−41.3853	−1.89094	−0.945471	−	0.325705i	$-0.894398\pi$
$479$	−41.3853	−1.89094	−0.945471	+	0.325705i	$0.894398\pi$
$480$	−13.4392	−0.613413
$481$	6.96022	0.317359
$482$	40.6268	1.85050
$483$	0	0
$484$	−12.8793	−0.585421
$485$	−10.4416	−0.474129
$486$	1.80081	0.0816864
$487$	9.90202	0.448703	0.224352	−	0.974508i	$-0.427974\pi$
$487$	9.90202	0.448703	0.224352	+	0.974508i	$0.427974\pi$
$488$	17.1505	0.776368
$489$	−10.5373	−0.476513
$490$	0	0
$491$	−29.9292	−1.35069	−0.675343	−	0.737504i	$-0.736004\pi$
$491$	−29.9292	−1.35069	−0.675343	+	0.737504i	$0.736004\pi$
$492$	−1.24292	−0.0560350
$493$	21.8987	0.986269
$494$	9.60587	0.432189
$495$	−1.73933	−0.0781771
$496$	0.832231	0.0373683
$497$	0	0
$498$	−19.7053	−0.883017
$499$	−26.4456	−1.18387	−0.591934	−	0.805986i	$-0.701635\pi$
$499$	−26.4456	−1.18387	−0.591934	+	0.805986i	$0.701635\pi$
$500$	−14.2304	−0.636403
$501$	13.9834	0.624733
$502$	28.6998	1.28093
$503$	−0.150863	−0.00672665	−0.00336333	−	0.999994i	$-0.501071\pi$
$503$	−0.150863	−0.00672665	−0.00336333	+	0.999994i	$0.501071\pi$
$504$	0	0
$505$	5.53288	0.246210
$506$	9.66393	0.429614
$507$	11.5773	0.514167
$508$	−18.0427	−0.800516
$509$	−36.0422	−1.59754	−0.798771	−	0.601635i	$-0.794516\pi$
$509$	−36.0422	−1.59754	−0.798771	+	0.601635i	$0.794516\pi$
$510$	20.3100	0.899343
$511$	0	0
$512$	−17.0184	−0.752116
$513$	−4.47213	−0.197449
$514$	8.41276	0.371071
$515$	11.8460	0.521998
$516$	−2.26224	−0.0995894
$517$	−4.20881	−0.185103
$518$	0	0
$519$	5.17342	0.227088
$520$	−3.54143	−0.155302
$521$	−20.8532	−0.913594	−0.456797	−	0.889571i	$-0.651004\pi$
$521$	−20.8532	−0.913594	−0.456797	+	0.889571i	$0.651004\pi$
$522$	−7.61479	−0.333290
$523$	−14.0673	−0.615122	−0.307561	−	0.951528i	$-0.599513\pi$
$523$	−14.0673	−0.615122	−0.307561	+	0.951528i	$0.599513\pi$
$524$	−0.957870	−0.0418448
$525$	0	0
$526$	49.9986	2.18004
$527$	−0.872286	−0.0379974
$528$	−3.94624	−0.171738
$529$	22.1475	0.962935
$530$	4.78000	0.207630
$531$	−11.7353	−0.509267
$532$	0	0
$533$	−1.19276	−0.0516643
$534$	17.5435	0.759182
$535$	35.4741	1.53368
$536$	−3.28696	−0.141975
$537$	0.884735	0.0381791
$538$	0.389931	0.0168111
$539$	0	0
$540$	−2.70680	−0.116482
$541$	16.8592	0.724835	0.362417	−	0.932016i	$-0.381952\pi$
$541$	16.8592	0.724835	0.362417	+	0.932016i	$0.381952\pi$
$542$	27.8962	1.19825
$543$	−10.6540	−0.457207
$544$	31.9587	1.37022
$545$	22.5622	0.966458
$546$	0	0
$547$	−0.789938	−0.0337753	−0.0168877	−	0.999857i	$-0.505376\pi$
$547$	−0.789938	−0.0337753	−0.0168877	+	0.999857i	$0.505376\pi$
$548$	5.91281	0.252583
$549$	12.5796	0.536884
$550$	−0.370045	−0.0157788
$551$	18.9106	0.805618
$552$	−9.16069	−0.389905
$553$	0	0
$554$	−4.23463	−0.179912
$555$	12.7081	0.539431
$556$	−0.780700	−0.0331091
$557$	22.2700	0.943610	0.471805	−	0.881703i	$-0.343603\pi$
$557$	22.2700	0.943610	0.471805	+	0.881703i	$0.343603\pi$
$558$	0.303318	0.0128405
$559$	−2.17095	−0.0918215
$560$	0	0
$561$	4.13616	0.174629
$562$	−43.0155	−1.81450
$563$	−0.488170	−0.0205739	−0.0102870	−	0.999947i	$-0.503274\pi$
$563$	−0.488170	−0.0205739	−0.0102870	+	0.999947i	$0.503274\pi$
$564$	−6.54986	−0.275799
$565$	6.09277	0.256325
$566$	−12.7679	−0.536673
$567$	0	0
$568$	0.348832	0.0146367
$569$	20.2741	0.849936	0.424968	−	0.905208i	$-0.360285\pi$
$569$	20.2741	0.849936	0.424968	+	0.905208i	$0.360285\pi$
$570$	17.5386	0.734613
$571$	29.6973	1.24279	0.621397	−	0.783496i	$-0.286566\pi$
$571$	29.6973	1.24279	0.621397	+	0.783496i	$0.286566\pi$
$572$	1.18404	0.0495071
$573$	5.78471	0.241660
$574$	0	0
$575$	−1.72876	−0.0720943
$576$	−1.23093	−0.0512886
$577$	38.6879	1.61060	0.805300	−	0.592868i	$-0.202004\pi$
$577$	38.6879	1.61060	0.805300	+	0.592868i	$0.202004\pi$
$578$	−17.6838	−0.735551
$579$	−16.6099	−0.690284
$580$	11.4458	0.475260
$581$	0	0
$582$	−8.63420	−0.357899
$583$	0.973455	0.0403164
$584$	7.19692	0.297811
$585$	−2.59757	−0.107396
$586$	−52.8841	−2.18462
$587$	−9.27772	−0.382932	−0.191466	−	0.981499i	$-0.561324\pi$
$587$	−9.27772	−0.382932	−0.191466	+	0.981499i	$0.561324\pi$
$588$	0	0
$589$	−0.753259	−0.0310375
$590$	46.0229	1.89473
$591$	16.2889	0.670036
$592$	28.8325	1.18501
$593$	42.3599	1.73951	0.869756	−	0.493482i	$-0.164276\pi$
$593$	42.3599	1.73951	0.869756	+	0.493482i	$0.164276\pi$
$594$	−1.43826	−0.0590124
$595$	0	0
$596$	−1.19438	−0.0489239
$597$	21.9239	0.897284
$598$	14.4324	0.590185
$599$	12.3390	0.504159	0.252080	−	0.967706i	$-0.418886\pi$
$599$	12.3390	0.504159	0.252080	+	0.967706i	$0.418886\pi$
$600$	0.350776	0.0143204
$601$	16.6041	0.677297	0.338648	−	0.940913i	$-0.390030\pi$
$601$	16.6041	0.677297	0.338648	+	0.940913i	$0.390030\pi$
$602$	0	0
$603$	−2.41092	−0.0981803
$604$	−7.04203	−0.286536
$605$	−22.5664	−0.917454
$606$	4.57515	0.185853
$607$	−3.93533	−0.159730	−0.0798652	−	0.996806i	$-0.525449\pi$
$607$	−3.93533	−0.159730	−0.0798652	+	0.996806i	$0.525449\pi$
$608$	27.5978	1.11924
$609$	0	0
$610$	−49.3342	−1.99748
$611$	−6.28556	−0.254287
$612$	6.43681	0.260193
$613$	31.1638	1.25870	0.629348	−	0.777124i	$-0.283322\pi$
$613$	31.1638	1.25870	0.629348	+	0.777124i	$0.283322\pi$
$614$	−55.3741	−2.23472
$615$	−2.17778	−0.0878164
$616$	0	0
$617$	21.9486	0.883615	0.441808	−	0.897110i	$-0.354337\pi$
$617$	21.9486	0.883615	0.441808	+	0.897110i	$0.354337\pi$
$618$	9.79550	0.394033
$619$	17.1921	0.691010	0.345505	−	0.938417i	$-0.387708\pi$
$619$	17.1921	0.691010	0.345505	+	0.938417i	$0.387708\pi$
$620$	−0.455917	−0.0183101
$621$	−6.71919	−0.269632
$622$	32.2796	1.29429
$623$	0	0
$624$	−5.89343	−0.235926
$625$	−23.6474	−0.945895
$626$	28.2924	1.13079
$627$	3.57177	0.142643
$628$	17.6236	0.703257
$629$	−30.2202	−1.20496
$630$	0	0
$631$	−12.5560	−0.499847	−0.249923	−	0.968266i	$-0.580405\pi$
$631$	−12.5560	−0.499847	−0.249923	+	0.968266i	$0.580405\pi$
$632$	17.9308	0.713248
$633$	9.48428	0.376966
$634$	6.07950	0.241448
$635$	−31.6135	−1.25454
$636$	1.51492	0.0600704
$637$	0	0
$638$	6.08173	0.240778
$639$	0.255861	0.0101217
$640$	−22.0510	−0.871642
$641$	−28.6102	−1.13003	−0.565017	−	0.825079i	$-0.691130\pi$
$641$	−28.6102	−1.13003	−0.565017	+	0.825079i	$0.691130\pi$
$642$	29.3336	1.15770
$643$	0.325302	0.0128287	0.00641434	−	0.999979i	$-0.497958\pi$
$643$	0.325302	0.0128287	0.00641434	+	0.999979i	$0.497958\pi$
$644$	0	0
$645$	−3.96378	−0.156074
$646$	−41.7072	−1.64095
$647$	2.72658	0.107193	0.0535965	−	0.998563i	$-0.482932\pi$
$647$	2.72658	0.107193	0.0535965	+	0.998563i	$0.482932\pi$
$648$	1.36336	0.0535579
$649$	9.37263	0.367908
$650$	−0.552637	−0.0216762
$651$	0	0
$652$	13.0970	0.512918
$653$	−3.40058	−0.133075	−0.0665375	−	0.997784i	$-0.521195\pi$
$653$	−3.40058	−0.133075	−0.0665375	+	0.997784i	$0.521195\pi$
$654$	18.6567	0.729536
$655$	−1.67833	−0.0655779
$656$	−4.94099	−0.192913
$657$	5.27880	0.205946
$658$	0	0
$659$	6.29196	0.245100	0.122550	−	0.992462i	$-0.460893\pi$
$659$	6.29196	0.245100	0.122550	+	0.992462i	$0.460893\pi$
$660$	2.16184	0.0841497
$661$	16.2199	0.630880	0.315440	−	0.948945i	$-0.397848\pi$
$661$	16.2199	0.630880	0.315440	+	0.948945i	$0.397848\pi$
$662$	−41.2773	−1.60429
$663$	6.17708	0.239898
$664$	−14.9186	−0.578953
$665$	0	0
$666$	10.5084	0.407192
$667$	28.4123	1.10013
$668$	−17.3802	−0.672461
$669$	5.77091	0.223116
$670$	9.45507	0.365281
$671$	−10.0470	−0.387859
$672$	0	0
$673$	16.2265	0.625486	0.312743	−	0.949838i	$-0.398752\pi$
$673$	16.2265	0.625486	0.312743	+	0.949838i	$0.398752\pi$
$674$	−33.1198	−1.27573
$675$	0.257287	0.00990298
$676$	−14.3896	−0.553448
$677$	34.2117	1.31486	0.657432	−	0.753514i	$-0.271643\pi$
$677$	34.2117	1.31486	0.657432	+	0.753514i	$0.271643\pi$
$678$	5.03813	0.193488
$679$	0	0
$680$	15.3764	0.589657
$681$	−0.172461	−0.00660872
$682$	−0.242252	−0.00927629
$683$	3.88638	0.148708	0.0743540	−	0.997232i	$-0.476311\pi$
$683$	3.88638	0.148708	0.0743540	+	0.997232i	$0.476311\pi$
$684$	5.55849	0.212534
$685$	10.3601	0.395840
$686$	0	0
$687$	2.34851	0.0896013
$688$	−8.99311	−0.342859
$689$	1.45379	0.0553849
$690$	26.3511	1.00317
$691$	−47.1900	−1.79519	−0.897595	−	0.440821i	$-0.854687\pi$
$691$	−47.1900	−1.79519	−0.897595	+	0.440821i	$0.854687\pi$
$692$	−6.43013	−0.244437
$693$	0	0
$694$	−14.4405	−0.548155
$695$	−1.36790	−0.0518876
$696$	−5.76503	−0.218523
$697$	5.17880	0.196161
$698$	−26.7170	−1.01125
$699$	2.17060	0.0820997
$700$	0	0
$701$	17.0103	0.642469	0.321234	−	0.947000i	$-0.395902\pi$
$701$	17.0103	0.642469	0.321234	+	0.947000i	$0.395902\pi$
$702$	−2.14794	−0.0810688
$703$	−26.0966	−0.984251
$704$	0.983108	0.0370523
$705$	−11.4763	−0.432224
$706$	57.1689	2.15158
$707$	0	0
$708$	14.5860	0.548174
$709$	24.8723	0.934100	0.467050	−	0.884231i	$-0.345317\pi$
$709$	24.8723	0.934100	0.467050	+	0.884231i	$0.345317\pi$
$710$	−1.00343	−0.0376580
$711$	13.1519	0.493234
$712$	13.2819	0.497760
$713$	−1.13174	−0.0423840
$714$	0	0
$715$	2.07461	0.0775860
$716$	−1.09965	−0.0410959
$717$	−16.2909	−0.608396
$718$	−37.7690	−1.40953
$719$	−24.7701	−0.923768	−0.461884	−	0.886940i	$-0.652826\pi$
$719$	−24.7701	−0.923768	−0.461884	+	0.886940i	$0.652826\pi$
$720$	−10.7604	−0.401016
$721$	0	0
$722$	−1.80075	−0.0670169
$723$	22.5603	0.839027
$724$	13.2420	0.492136
$725$	−1.08795	−0.0404054
$726$	−18.6602	−0.692545
$727$	−29.1958	−1.08281	−0.541406	−	0.840761i	$-0.682108\pi$
$727$	−29.1958	−1.08281	−0.541406	+	0.840761i	$0.682108\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−20.7022	−0.766223
$731$	9.42595	0.348631
$732$	−15.6354	−0.577900
$733$	−17.8678	−0.659961	−0.329981	−	0.943988i	$-0.607042\pi$
$733$	−17.8678	−0.659961	−0.329981	+	0.943988i	$0.607042\pi$
$734$	16.6390	0.614156
$735$	0	0
$736$	41.4645	1.52840
$737$	1.92554	0.0709281
$738$	−1.80081	−0.0662887
$739$	14.4976	0.533303	0.266651	−	0.963793i	$-0.414083\pi$
$739$	14.4976	0.533303	0.266651	+	0.963793i	$0.414083\pi$
$740$	−15.7952	−0.580642
$741$	5.33419	0.195956
$742$	0	0
$743$	28.9665	1.06268	0.531339	−	0.847160i	$-0.321689\pi$
$743$	28.9665	1.06268	0.531339	+	0.847160i	$0.321689\pi$
$744$	0.229637	0.00841889
$745$	−2.09274	−0.0766721
$746$	−63.3426	−2.31914
$747$	−10.9425	−0.400364
$748$	−5.14091	−0.187970
$749$	0	0
$750$	−20.6178	−0.752857
$751$	−22.0943	−0.806234	−0.403117	−	0.915148i	$-0.632073\pi$
$751$	−22.0943	−0.806234	−0.403117	+	0.915148i	$0.632073\pi$
$752$	−26.0378	−0.949501
$753$	15.9372	0.580782
$754$	9.08264	0.330770
$755$	−12.3387	−0.449051
$756$	0	0
$757$	41.0884	1.49338	0.746692	−	0.665170i	$-0.231641\pi$
$757$	41.0884	1.49338	0.746692	+	0.665170i	$0.231641\pi$
$758$	−50.6532	−1.83981
$759$	5.36643	0.194789
$760$	13.2782	0.481651
$761$	23.2864	0.844132	0.422066	−	0.906565i	$-0.361305\pi$
$761$	23.2864	0.844132	0.422066	+	0.906565i	$0.361305\pi$
$762$	−26.1413	−0.947000
$763$	0	0
$764$	−7.18991	−0.260122
$765$	11.2783	0.407767
$766$	2.00438	0.0724212
$767$	13.9974	0.505416
$768$	−20.6959	−0.746798
$769$	15.2750	0.550832	0.275416	−	0.961325i	$-0.411184\pi$
$769$	15.2750	0.550832	0.275416	+	0.961325i	$0.411184\pi$
$770$	0	0
$771$	4.67166	0.168246
$772$	20.6447	0.743020
$773$	−9.69680	−0.348770	−0.174385	−	0.984678i	$-0.555794\pi$
$773$	−9.69680	−0.348770	−0.174385	+	0.984678i	$0.555794\pi$
$774$	−3.27766	−0.117813
$775$	0.0433359	0.00155667
$776$	−6.53681	−0.234658
$777$	0	0
$778$	44.0595	1.57961
$779$	4.47213	0.160231
$780$	3.22857	0.115601
$781$	−0.204349	−0.00731220
$782$	−62.6634	−2.24084
$783$	−4.22854	−0.151116
$784$	0	0
$785$	30.8791	1.10212
$786$	−1.38782	−0.0495018
$787$	18.3462	0.653972	0.326986	−	0.945029i	$-0.393967\pi$
$787$	18.3462	0.653972	0.326986	+	0.945029i	$0.393967\pi$
$788$	−20.2458	−0.721225
$789$	27.7645	0.988443
$790$	−51.5786	−1.83508
$791$	0	0
$792$	−1.08888	−0.0386917
$793$	−15.0045	−0.532824
$794$	8.77240	0.311321
$795$	2.65436	0.0941406
$796$	−27.2495	−0.965834
$797$	29.5627	1.04717	0.523583	−	0.851975i	$-0.324595\pi$
$797$	29.5627	1.04717	0.523583	+	0.851975i	$0.324595\pi$
$798$	0	0
$799$	27.2910	0.965485
$800$	−1.58773	−0.0561349
$801$	9.74201	0.344217
$802$	15.4248	0.544668
$803$	−4.21603	−0.148781
$804$	2.99658	0.105681
$805$	0	0
$806$	−0.361786	−0.0127434
$807$	0.216531	0.00762224
$808$	3.46377	0.121855
$809$	−18.4302	−0.647970	−0.323985	−	0.946062i	$-0.605023\pi$
$809$	−18.4302	−0.647970	−0.323985	+	0.946062i	$0.605023\pi$
$810$	−3.92176	−0.137797
$811$	−19.9706	−0.701264	−0.350632	−	0.936513i	$-0.614033\pi$
$811$	−19.9706	−0.701264	−0.350632	+	0.936513i	$0.614033\pi$
$812$	0	0
$813$	15.4909	0.543291
$814$	−8.39277	−0.294167
$815$	22.9479	0.803830
$816$	25.5884	0.895773
$817$	8.13974	0.284774
$818$	−55.7364	−1.94878
$819$	0	0
$820$	2.70680	0.0945254
$821$	37.2773	1.30099	0.650493	−	0.759512i	$-0.274562\pi$
$821$	37.2773	1.30099	0.650493	+	0.759512i	$0.274562\pi$
$822$	8.56682	0.298802
$823$	42.9513	1.49719	0.748593	−	0.663029i	$-0.230730\pi$
$823$	42.9513	1.49719	0.748593	+	0.663029i	$0.230730\pi$
$824$	7.41601	0.258349
$825$	−0.205488	−0.00715418
$826$	0	0
$827$	41.0895	1.42882	0.714411	−	0.699726i	$-0.246695\pi$
$827$	41.0895	1.42882	0.714411	+	0.699726i	$0.246695\pi$
$828$	8.35140	0.290231
$829$	−9.71580	−0.337444	−0.168722	−	0.985664i	$-0.553964\pi$
$829$	−9.71580	−0.337444	−0.168722	+	0.985664i	$0.553964\pi$
$830$	42.9138	1.48956
$831$	−2.35151	−0.0815730
$832$	1.46820	0.0509008
$833$	0	0
$834$	−1.13112	−0.0391676
$835$	−30.4527	−1.05386
$836$	−4.43941	−0.153540
$837$	0.168434	0.00582193
$838$	−39.0978	−1.35061
$839$	−18.1433	−0.626378	−0.313189	−	0.949691i	$-0.601397\pi$
$839$	−18.1433	−0.626378	−0.313189	+	0.949691i	$0.601397\pi$
$840$	0	0
$841$	−11.1195	−0.383430
$842$	−49.4268	−1.70336
$843$	−23.8868	−0.822704
$844$	−11.7882	−0.405766
$845$	−25.2128	−0.867347
$846$	−9.48982	−0.326267
$847$	0	0
$848$	6.02228	0.206806
$849$	−7.09006	−0.243330
$850$	2.39947	0.0823010
$851$	−39.2090	−1.34407
$852$	−0.318014	−0.0108950
$853$	3.18526	0.109061	0.0545306	−	0.998512i	$-0.482634\pi$
$853$	3.18526	0.109061	0.0545306	+	0.998512i	$0.482634\pi$
$854$	0	0
$855$	9.73931	0.333077
$856$	22.2080	0.759053
$857$	−23.0555	−0.787562	−0.393781	−	0.919204i	$-0.628833\pi$
$857$	−23.0555	−0.787562	−0.393781	+	0.919204i	$0.628833\pi$
$858$	1.71550	0.0585662
$859$	−7.33171	−0.250155	−0.125077	−	0.992147i	$-0.539918\pi$
$859$	−7.33171	−0.250155	−0.125077	+	0.992147i	$0.539918\pi$
$860$	4.92665	0.167997
$861$	0	0
$862$	−32.0625	−1.09205
$863$	27.6924	0.942660	0.471330	−	0.881957i	$-0.343774\pi$
$863$	27.6924	0.942660	0.471330	+	0.881957i	$0.343774\pi$
$864$	−6.17106	−0.209944
$865$	−11.2666	−0.383074
$866$	−24.7524	−0.841120
$867$	−9.81994	−0.333503
$868$	0	0
$869$	−10.5040	−0.356325
$870$	16.5833	0.562227
$871$	2.87566	0.0974380
$872$	14.1247	0.478323
$873$	−4.79462	−0.162273
$874$	−54.1127	−1.83039
$875$	0	0
$876$	−6.56111	−0.221679
$877$	3.66484	0.123753	0.0618764	−	0.998084i	$-0.480292\pi$
$877$	3.66484	0.123753	0.0618764	+	0.998084i	$0.480292\pi$
$878$	−8.46681	−0.285741
$879$	−29.3669	−0.990520
$880$	8.59402	0.289704
$881$	15.2030	0.512203	0.256101	−	0.966650i	$-0.417562\pi$
$881$	15.2030	0.512203	0.256101	+	0.966650i	$0.417562\pi$
$882$	0	0
$883$	−0.478768	−0.0161118	−0.00805591	−	0.999968i	$-0.502564\pi$
$883$	−0.478768	−0.0161118	−0.00805591	+	0.999968i	$0.502564\pi$
$884$	−7.67759	−0.258225
$885$	25.5568	0.859082
$886$	−57.3766	−1.92761
$887$	−2.63212	−0.0883781	−0.0441890	−	0.999023i	$-0.514070\pi$
$887$	−2.63212	−0.0883781	−0.0441890	+	0.999023i	$0.514070\pi$
$888$	7.95573	0.266977
$889$	0	0
$890$	−38.2058	−1.28066
$891$	−0.798673	−0.0267565
$892$	−7.17277	−0.240162
$893$	23.5670	0.788640
$894$	−1.73049	−0.0578764
$895$	−1.92676	−0.0644044
$896$	0	0
$897$	8.01440	0.267593
$898$	−55.3905	−1.84840
$899$	−0.712230	−0.0237542
$900$	−0.319786	−0.0106595
$901$	−6.31213	−0.210287
$902$	1.43826	0.0478888
$903$	0	0
$904$	3.81428	0.126861
$905$	23.2020	0.771261
$906$	−10.2029	−0.338969
$907$	11.6650	0.387329	0.193664	−	0.981068i	$-0.437963\pi$
$907$	11.6650	0.387329	0.193664	+	0.981068i	$0.437963\pi$
$908$	0.214355	0.00711361
$909$	2.54061	0.0842667
$910$	0	0
$911$	20.4241	0.676680	0.338340	−	0.941024i	$-0.390135\pi$
$911$	20.4241	0.676680	0.338340	+	0.941024i	$0.390135\pi$
$912$	22.0968	0.731697
$913$	8.73946	0.289234
$914$	−8.74755	−0.289343
$915$	−27.3955	−0.905668
$916$	−2.91900	−0.0964466
$917$	0	0
$918$	9.32603	0.307805
$919$	−46.0665	−1.51959	−0.759797	−	0.650161i	$-0.774702\pi$
$919$	−46.0665	−1.51959	−0.759797	+	0.650161i	$0.774702\pi$
$920$	19.9499	0.657730
$921$	−30.7496	−1.01323
$922$	63.0261	2.07566
$923$	−0.305182	−0.0100452
$924$	0	0
$925$	1.50137	0.0493646
$926$	1.28240	0.0421422
$927$	5.43950	0.178657
$928$	26.0946	0.856596
$929$	9.23449	0.302974	0.151487	−	0.988459i	$-0.451594\pi$
$929$	9.23449	0.302974	0.151487	+	0.988459i	$0.451594\pi$
$930$	−0.660558	−0.0216606
$931$	0	0
$932$	−2.69788	−0.0883719
$933$	17.9250	0.586840
$934$	36.9670	1.20960
$935$	−9.00764	−0.294581
$936$	−1.62617	−0.0531530
$937$	−5.01754	−0.163916	−0.0819580	−	0.996636i	$-0.526117\pi$
$937$	−5.01754	−0.163916	−0.0819580	+	0.996636i	$0.526117\pi$
$938$	0	0
$939$	15.7109	0.512707
$940$	14.2641	0.465245
$941$	34.8594	1.13638	0.568191	−	0.822897i	$-0.307643\pi$
$941$	34.8594	1.13638	0.568191	+	0.822897i	$0.307643\pi$
$942$	25.5340	0.831944
$943$	6.71919	0.218807
$944$	57.9838	1.88721
$945$	0	0
$946$	2.61778	0.0851113
$947$	0.0282576	0.000918248 0	0.000459124	−	1.00000i	$-0.499854\pi$
$947$	0.0282576	0.000918248 0	0.000459124		1.00000i	$0.499854\pi$
$948$	−16.3467	−0.530916
$949$	−6.29636	−0.204388
$950$	2.07205	0.0672262
$951$	3.37598	0.109474
$952$	0	0
$953$	46.0320	1.49112	0.745562	−	0.666436i	$-0.232181\pi$
$953$	46.0320	1.49112	0.745562	+	0.666436i	$0.232181\pi$
$954$	2.19490	0.0710625
$955$	−12.5978	−0.407655
$956$	20.2483	0.654876
$957$	3.37722	0.109170
$958$	74.5271	2.40786
$959$	0	0
$960$	2.68069	0.0865187
$961$	−30.9716	−0.999085
$962$	−12.5340	−0.404113
$963$	16.2891	0.524909
$964$	−28.0406	−0.903127
$965$	36.1726	1.16444
$966$	0	0
$967$	−19.8768	−0.639196	−0.319598	−	0.947553i	$-0.603548\pi$
$967$	−19.8768	−0.639196	−0.319598	+	0.947553i	$0.603548\pi$
$968$	−14.1273	−0.454070
$969$	−23.1603	−0.744015
$970$	18.8034	0.603740
$971$	−11.5108	−0.369400	−0.184700	−	0.982795i	$-0.559131\pi$
$971$	−11.5108	−0.369400	−0.184700	+	0.982795i	$0.559131\pi$
$972$	−1.24292	−0.0398666
$973$	0	0
$974$	−17.8317	−0.571363
$975$	−0.306882	−0.00982810
$976$	−62.1556	−1.98955
$977$	8.68854	0.277971	0.138985	−	0.990294i	$-0.455616\pi$
$977$	8.68854	0.277971	0.138985	+	0.990294i	$0.455616\pi$
$978$	18.9757	0.606776
$979$	−7.78068	−0.248671
$980$	0	0
$981$	10.3602	0.330775
$982$	53.8968	1.71992
$983$	−7.47496	−0.238414	−0.119207	−	0.992869i	$-0.538035\pi$
$983$	−7.47496	−0.238414	−0.119207	+	0.992869i	$0.538035\pi$
$984$	−1.36336	−0.0434624
$985$	−35.4736	−1.13028
$986$	−39.4355	−1.25588
$987$	0	0
$988$	−6.62996	−0.210927
$989$	12.2296	0.388879
$990$	3.13221	0.0995480
$991$	−27.3575	−0.869040	−0.434520	−	0.900662i	$-0.643082\pi$
$991$	−27.3575	−0.869040	−0.434520	+	0.900662i	$0.643082\pi$
$992$	−1.03942	−0.0330015
$993$	−22.9215	−0.727392
$994$	0	0
$995$	−47.7453	−1.51363
$996$	13.6006	0.430951
$997$	28.2187	0.893695	0.446848	−	0.894610i	$-0.352547\pi$
$997$	28.2187	0.893695	0.446848	+	0.894610i	$0.352547\pi$
$998$	47.6235	1.50750
$999$	5.83538	0.184623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.5	✓	24
7.6	odd	2		6027.2.a.bo.1.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.5	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.5	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)

\(f(q)\)	\(=\)	\(q-1.80081 q^{2} -1.00000 q^{3} +1.24292 q^{4} +2.17778 q^{5} +1.80081 q^{6} +1.36336 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.80081 q^{2} -1.00000 q^{3} +1.24292 q^{4} +2.17778 q^{5} +1.80081 q^{6} +1.36336 q^{8} +1.00000 q^{9} -3.92176 q^{10} -0.798673 q^{11} -1.24292 q^{12} -1.19276 q^{13} -2.17778 q^{15} -4.94099 q^{16} +5.17880 q^{17} -1.80081 q^{18} +4.47213 q^{19} +2.70680 q^{20} +1.43826 q^{22} +6.71919 q^{23} -1.36336 q^{24} -0.257287 q^{25} +2.14794 q^{26} -1.00000 q^{27} +4.22854 q^{29} +3.92176 q^{30} -0.168434 q^{31} +6.17106 q^{32} +0.798673 q^{33} -9.32603 q^{34} +1.24292 q^{36} -5.83538 q^{37} -8.05346 q^{38} +1.19276 q^{39} +2.96910 q^{40} +1.00000 q^{41} +1.82010 q^{43} -0.992684 q^{44} +2.17778 q^{45} -12.1000 q^{46} +5.26975 q^{47} +4.94099 q^{48} +0.463325 q^{50} -5.17880 q^{51} -1.48251 q^{52} -1.21884 q^{53} +1.80081 q^{54} -1.73933 q^{55} -4.47213 q^{57} -7.61479 q^{58} -11.7353 q^{59} -2.70680 q^{60} +12.5796 q^{61} +0.303318 q^{62} -1.23093 q^{64} -2.59757 q^{65} -1.43826 q^{66} -2.41092 q^{67} +6.43681 q^{68} -6.71919 q^{69} +0.255861 q^{71} +1.36336 q^{72} +5.27880 q^{73} +10.5084 q^{74} +0.257287 q^{75} +5.55849 q^{76} -2.14794 q^{78} +13.1519 q^{79} -10.7604 q^{80} +1.00000 q^{81} -1.80081 q^{82} -10.9425 q^{83} +11.2783 q^{85} -3.27766 q^{86} -4.22854 q^{87} -1.08888 q^{88} +9.74201 q^{89} -3.92176 q^{90} +8.35140 q^{92} +0.168434 q^{93} -9.48982 q^{94} +9.73931 q^{95} -6.17106 q^{96} -4.79462 q^{97} -0.798673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more