LMFDB - Embedded newform 6027.2.a.bn.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.22021 q^{2} -1.00000 q^{3} +2.92934 q^{4} -0.165927 q^{5} +2.22021 q^{6} -2.06334 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22021 q^{2} -1.00000 q^{3} +2.92934 q^{4} -0.165927 q^{5} +2.22021 q^{6} -2.06334 q^{8} +1.00000 q^{9} +0.368393 q^{10} +2.45014 q^{11} -2.92934 q^{12} -0.862086 q^{13} +0.165927 q^{15} -1.27763 q^{16} -4.02184 q^{17} -2.22021 q^{18} -2.72504 q^{19} -0.486057 q^{20} -5.43984 q^{22} -4.73844 q^{23} +2.06334 q^{24} -4.97247 q^{25} +1.91401 q^{26} -1.00000 q^{27} -6.41611 q^{29} -0.368393 q^{30} -4.79993 q^{31} +6.96329 q^{32} -2.45014 q^{33} +8.92935 q^{34} +2.92934 q^{36} -7.78311 q^{37} +6.05018 q^{38} +0.862086 q^{39} +0.342364 q^{40} +1.00000 q^{41} +7.56342 q^{43} +7.17732 q^{44} -0.165927 q^{45} +10.5203 q^{46} -10.2804 q^{47} +1.27763 q^{48} +11.0399 q^{50} +4.02184 q^{51} -2.52535 q^{52} +6.13697 q^{53} +2.22021 q^{54} -0.406545 q^{55} +2.72504 q^{57} +14.2451 q^{58} -8.52045 q^{59} +0.486057 q^{60} +0.773934 q^{61} +10.6569 q^{62} -12.9047 q^{64} +0.143043 q^{65} +5.43984 q^{66} +11.6535 q^{67} -11.7814 q^{68} +4.73844 q^{69} -4.99642 q^{71} -2.06334 q^{72} +15.8299 q^{73} +17.2801 q^{74} +4.97247 q^{75} -7.98259 q^{76} -1.91401 q^{78} +10.2409 q^{79} +0.211993 q^{80} +1.00000 q^{81} -2.22021 q^{82} -5.29386 q^{83} +0.667332 q^{85} -16.7924 q^{86} +6.41611 q^{87} -5.05549 q^{88} -9.60949 q^{89} +0.368393 q^{90} -13.8805 q^{92} +4.79993 q^{93} +22.8246 q^{94} +0.452158 q^{95} -6.96329 q^{96} +18.6836 q^{97} +2.45014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.22021	−1.56993	−0.784964	−	0.619542i	$-0.787318\pi$
$2$	−2.22021	−1.56993	−0.784964	+	0.619542i	$0.787318\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.92934	1.46467
$5$	−0.165927	−0.0742047	−0.0371024	−	0.999311i	$-0.511813\pi$
$5$	−0.165927	−0.0742047	−0.0371024	+	0.999311i	$0.511813\pi$
$6$	2.22021	0.906398
$7$	0	0
$7$	0	0
$8$	−2.06334	−0.729502
$9$	1.00000	0.333333
$10$	0.368393	0.116496
$11$	2.45014	0.738746	0.369373	−	0.929281i	$-0.379572\pi$
$11$	2.45014	0.738746	0.369373	+	0.929281i	$0.379572\pi$
$12$	−2.92934	−0.845629
$13$	−0.862086	−0.239100	−0.119550	−	0.992828i	$-0.538145\pi$
$13$	−0.862086	−0.239100	−0.119550	+	0.992828i	$0.538145\pi$
$14$	0	0
$15$	0.165927	0.0428421
$16$	−1.27763	−0.319407
$17$	−4.02184	−0.975440	−0.487720	−	0.873000i	$-0.662171\pi$
$17$	−4.02184	−0.975440	−0.487720	+	0.873000i	$0.662171\pi$
$18$	−2.22021	−0.523309
$19$	−2.72504	−0.625168	−0.312584	−	0.949890i	$-0.601195\pi$
$19$	−2.72504	−0.625168	−0.312584	+	0.949890i	$0.601195\pi$
$20$	−0.486057	−0.108686
$21$	0	0
$22$	−5.43984	−1.15978
$23$	−4.73844	−0.988033	−0.494016	−	0.869453i	$-0.664472\pi$
$23$	−4.73844	−0.988033	−0.494016	+	0.869453i	$0.664472\pi$
$24$	2.06334	0.421178
$25$	−4.97247	−0.994494
$26$	1.91401	0.375369
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.41611	−1.19144	−0.595720	−	0.803192i	$-0.703133\pi$
$29$	−6.41611	−1.19144	−0.595720	+	0.803192i	$0.703133\pi$
$30$	−0.368393	−0.0672590
$31$	−4.79993	−0.862094	−0.431047	−	0.902330i	$-0.641856\pi$
$31$	−4.79993	−0.862094	−0.431047	+	0.902330i	$0.641856\pi$
$32$	6.96329	1.23095
$33$	−2.45014	−0.426515
$34$	8.92935	1.53137
$35$	0	0
$36$	2.92934	0.488224
$37$	−7.78311	−1.27953	−0.639767	−	0.768569i	$-0.720969\pi$
$37$	−7.78311	−1.27953	−0.639767	+	0.768569i	$0.720969\pi$
$38$	6.05018	0.981468
$39$	0.862086	0.138044
$40$	0.342364	0.0541325
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	7.56342	1.15341	0.576705	−	0.816952i	$-0.304338\pi$
$43$	7.56342	1.15341	0.576705	+	0.816952i	$0.304338\pi$
$44$	7.17732	1.08202
$45$	−0.165927	−0.0247349
$46$	10.5203	1.55114
$47$	−10.2804	−1.49955	−0.749774	−	0.661694i	$-0.769838\pi$
$47$	−10.2804	−1.49955	−0.749774	+	0.661694i	$0.769838\pi$
$48$	1.27763	0.184410
$49$	0	0
$50$	11.0399	1.56128
$51$	4.02184	0.563171
$52$	−2.52535	−0.350203
$53$	6.13697	0.842977	0.421489	−	0.906834i	$-0.361508\pi$
$53$	6.13697	0.842977	0.421489	+	0.906834i	$0.361508\pi$
$54$	2.22021	0.302133
$55$	−0.406545	−0.0548185
$56$	0	0
$57$	2.72504	0.360941
$58$	14.2451	1.87048
$59$	−8.52045	−1.10927	−0.554634	−	0.832095i	$-0.687142\pi$
$59$	−8.52045	−1.10927	−0.554634	+	0.832095i	$0.687142\pi$
$60$	0.486057	0.0627497
$61$	0.773934	0.0990922	0.0495461	−	0.998772i	$-0.484223\pi$
$61$	0.773934	0.0990922	0.0495461	+	0.998772i	$0.484223\pi$
$62$	10.6569	1.35342
$63$	0	0
$64$	−12.9047	−1.61309
$65$	0.143043	0.0177423
$66$	5.43984	0.669598
$67$	11.6535	1.42370	0.711850	−	0.702332i	$-0.247858\pi$
$67$	11.6535	1.42370	0.711850	+	0.702332i	$0.247858\pi$
$68$	−11.7814	−1.42870
$69$	4.73844	0.570441
$70$	0	0
$71$	−4.99642	−0.592966	−0.296483	−	0.955038i	$-0.595814\pi$
$71$	−4.99642	−0.592966	−0.296483	+	0.955038i	$0.595814\pi$
$72$	−2.06334	−0.243167
$73$	15.8299	1.85275	0.926376	−	0.376599i	$-0.122907\pi$
$73$	15.8299	1.85275	0.926376	+	0.376599i	$0.122907\pi$
$74$	17.2801	2.00878
$75$	4.97247	0.574171
$76$	−7.98259	−0.915666
$77$	0	0
$78$	−1.91401	−0.216719
$79$	10.2409	1.15219	0.576097	−	0.817382i	$-0.304575\pi$
$79$	10.2409	1.15219	0.576097	+	0.817382i	$0.304575\pi$
$80$	0.211993	0.0237015
$81$	1.00000	0.111111
$82$	−2.22021	−0.245181
$83$	−5.29386	−0.581076	−0.290538	−	0.956863i	$-0.593834\pi$
$83$	−5.29386	−0.581076	−0.290538	+	0.956863i	$0.593834\pi$
$84$	0	0
$85$	0.667332	0.0723823
$86$	−16.7924	−1.81077
$87$	6.41611	0.687879
$88$	−5.05549	−0.538917
$89$	−9.60949	−1.01860	−0.509302	−	0.860588i	$-0.670096\pi$
$89$	−9.60949	−1.01860	−0.509302	+	0.860588i	$0.670096\pi$
$90$	0.368393	0.0388320
$91$	0	0
$92$	−13.8805	−1.44714
$93$	4.79993	0.497730
$94$	22.8246	2.35418
$95$	0.452158	0.0463904
$96$	−6.96329	−0.710688
$97$	18.6836	1.89703	0.948514	−	0.316736i	$-0.102587\pi$
$97$	18.6836	1.89703	0.948514	+	0.316736i	$0.102587\pi$
$98$	0	0
$99$	2.45014	0.246249
$100$	−14.5661	−1.45661
$101$	−9.94335	−0.989400	−0.494700	−	0.869064i	$-0.664722\pi$
$101$	−9.94335	−0.989400	−0.494700	+	0.869064i	$0.664722\pi$
$102$	−8.92935	−0.884137
$103$	−8.14668	−0.802716	−0.401358	−	0.915921i	$-0.631462\pi$
$103$	−8.14668	−0.802716	−0.401358	+	0.915921i	$0.631462\pi$
$104$	1.77878	0.174424
$105$	0	0
$106$	−13.6254	−1.32341
$107$	5.74895	0.555772	0.277886	−	0.960614i	$-0.410366\pi$
$107$	5.74895	0.555772	0.277886	+	0.960614i	$0.410366\pi$
$108$	−2.92934	−0.281876
$109$	−2.62119	−0.251065	−0.125532	−	0.992090i	$-0.540064\pi$
$109$	−2.62119	−0.251065	−0.125532	+	0.992090i	$0.540064\pi$
$110$	0.902616	0.0860610
$111$	7.78311	0.738740
$112$	0	0
$113$	−4.82467	−0.453866	−0.226933	−	0.973910i	$-0.572870\pi$
$113$	−4.82467	−0.453866	−0.226933	+	0.973910i	$0.572870\pi$
$114$	−6.05018	−0.566651
$115$	0.786234	0.0733167
$116$	−18.7950	−1.74507
$117$	−0.862086	−0.0796998
$118$	18.9172	1.74147
$119$	0	0
$120$	−0.342364	−0.0312534
$121$	−4.99679	−0.454254
$122$	−1.71830	−0.155568
$123$	−1.00000	−0.0901670
$124$	−14.0607	−1.26268
$125$	1.65470	0.148001
$126$	0	0
$127$	13.7531	1.22039	0.610193	−	0.792253i	$-0.291092\pi$
$127$	13.7531	1.22039	0.610193	+	0.792253i	$0.291092\pi$
$128$	14.7247	1.30149
$129$	−7.56342	−0.665922
$130$	−0.317586	−0.0278541
$131$	−0.254327	−0.0222207	−0.0111103	−	0.999938i	$-0.503537\pi$
$131$	−0.254327	−0.0222207	−0.0111103	+	0.999938i	$0.503537\pi$
$132$	−7.17732	−0.624705
$133$	0	0
$134$	−25.8732	−2.23511
$135$	0.165927	0.0142807
$136$	8.29844	0.711586
$137$	13.0440	1.11443	0.557214	−	0.830369i	$-0.311870\pi$
$137$	13.0440	1.11443	0.557214	+	0.830369i	$0.311870\pi$
$138$	−10.5203	−0.895551
$139$	2.08977	0.177252	0.0886262	−	0.996065i	$-0.471752\pi$
$139$	2.08977	0.177252	0.0886262	+	0.996065i	$0.471752\pi$
$140$	0	0
$141$	10.2804	0.865764
$142$	11.0931	0.930914
$143$	−2.11223	−0.176634
$144$	−1.27763	−0.106469
$145$	1.06460	0.0884105
$146$	−35.1458	−2.90869
$147$	0	0
$148$	−22.7994	−1.87410
$149$	1.42493	0.116735	0.0583674	−	0.998295i	$-0.481411\pi$
$149$	1.42493	0.116735	0.0583674	+	0.998295i	$0.481411\pi$
$150$	−11.0399	−0.901407
$151$	11.7421	0.955559	0.477779	−	0.878480i	$-0.341442\pi$
$151$	11.7421	0.955559	0.477779	+	0.878480i	$0.341442\pi$
$152$	5.62270	0.456061
$153$	−4.02184	−0.325147
$154$	0	0
$155$	0.796438	0.0639714
$156$	2.52535	0.202190
$157$	20.9461	1.67168	0.835841	−	0.548972i	$-0.184981\pi$
$157$	20.9461	1.67168	0.835841	+	0.548972i	$0.184981\pi$
$158$	−22.7370	−1.80886
$159$	−6.13697	−0.486693
$160$	−1.15540	−0.0913421
$161$	0	0
$162$	−2.22021	−0.174436
$163$	−14.4528	−1.13203	−0.566015	−	0.824395i	$-0.691515\pi$
$163$	−14.4528	−1.13203	−0.566015	+	0.824395i	$0.691515\pi$
$164$	2.92934	0.228743
$165$	0.406545	0.0316495
$166$	11.7535	0.912248
$167$	11.7930	0.912567	0.456284	−	0.889834i	$-0.349180\pi$
$167$	11.7930	0.912567	0.456284	+	0.889834i	$0.349180\pi$
$168$	0	0
$169$	−12.2568	−0.942831
$170$	−1.48162	−0.113635
$171$	−2.72504	−0.208389
$172$	22.1559	1.68937
$173$	−20.7992	−1.58133	−0.790667	−	0.612246i	$-0.790266\pi$
$173$	−20.7992	−1.58133	−0.790667	+	0.612246i	$0.790266\pi$
$174$	−14.2451	−1.07992
$175$	0	0
$176$	−3.13037	−0.235961
$177$	8.52045	0.640436
$178$	21.3351	1.59913
$179$	−5.07361	−0.379220	−0.189610	−	0.981860i	$-0.560722\pi$
$179$	−5.07361	−0.379220	−0.189610	+	0.981860i	$0.560722\pi$
$180$	−0.486057	−0.0362285
$181$	−4.61958	−0.343371	−0.171685	−	0.985152i	$-0.554921\pi$
$181$	−4.61958	−0.343371	−0.171685	+	0.985152i	$0.554921\pi$
$182$	0	0
$183$	−0.773934	−0.0572109
$184$	9.77702	0.720772
$185$	1.29143	0.0949475
$186$	−10.6569	−0.781400
$187$	−9.85410	−0.720603
$188$	−30.1148	−2.19635
$189$	0	0
$190$	−1.00389	−0.0728296
$191$	23.6825	1.71361	0.856803	−	0.515644i	$-0.172447\pi$
$191$	23.6825	1.71361	0.856803	+	0.515644i	$0.172447\pi$
$192$	12.9047	0.931319
$193$	−1.20281	−0.0865802	−0.0432901	−	0.999063i	$-0.513784\pi$
$193$	−1.20281	−0.0865802	−0.0432901	+	0.999063i	$0.513784\pi$
$194$	−41.4815	−2.97820
$195$	−0.143043	−0.0102435
$196$	0	0
$197$	8.05510	0.573902	0.286951	−	0.957945i	$-0.407358\pi$
$197$	8.05510	0.573902	0.286951	+	0.957945i	$0.407358\pi$
$198$	−5.43984	−0.386593
$199$	−7.58393	−0.537610	−0.268805	−	0.963195i	$-0.586629\pi$
$199$	−7.58393	−0.537610	−0.268805	+	0.963195i	$0.586629\pi$
$200$	10.2599	0.725485
$201$	−11.6535	−0.821974
$202$	22.0763	1.55329
$203$	0	0
$204$	11.7814	0.824861
$205$	−0.165927	−0.0115888
$206$	18.0874	1.26021
$207$	−4.73844	−0.329344
$208$	1.10143	0.0763701
$209$	−6.67675	−0.461841
$210$	0	0
$211$	3.58783	0.246997	0.123498	−	0.992345i	$-0.460589\pi$
$211$	3.58783	0.246997	0.123498	+	0.992345i	$0.460589\pi$
$212$	17.9773	1.23469
$213$	4.99642	0.342349
$214$	−12.7639	−0.872521
$215$	−1.25497	−0.0855885
$216$	2.06334	0.140393
$217$	0	0
$218$	5.81961	0.394154
$219$	−15.8299	−1.06969
$220$	−1.19091	−0.0802911
$221$	3.46717	0.233227
$222$	−17.2801	−1.15977
$223$	−6.85227	−0.458862	−0.229431	−	0.973325i	$-0.573687\pi$
$223$	−6.85227	−0.458862	−0.229431	+	0.973325i	$0.573687\pi$
$224$	0	0
$225$	−4.97247	−0.331498
$226$	10.7118	0.712537
$227$	12.4504	0.826364	0.413182	−	0.910648i	$-0.364417\pi$
$227$	12.4504	0.826364	0.413182	+	0.910648i	$0.364417\pi$
$228$	7.98259	0.528660
$229$	19.0902	1.26152	0.630758	−	0.775979i	$-0.282744\pi$
$229$	19.0902	1.26152	0.630758	+	0.775979i	$0.282744\pi$
$230$	−1.74561	−0.115102
$231$	0	0
$232$	13.2386	0.869159
$233$	9.45836	0.619638	0.309819	−	0.950796i	$-0.399732\pi$
$233$	9.45836	0.619638	0.309819	+	0.950796i	$0.399732\pi$
$234$	1.91401	0.125123
$235$	1.70579	0.111273
$236$	−24.9593	−1.62471
$237$	−10.2409	−0.665219
$238$	0	0
$239$	13.9203	0.900429	0.450215	−	0.892920i	$-0.351347\pi$
$239$	13.9203	0.900429	0.450215	+	0.892920i	$0.351347\pi$
$240$	−0.211993	−0.0136841
$241$	−0.583754	−0.0376029	−0.0188014	−	0.999823i	$-0.505985\pi$
$241$	−0.583754	−0.0376029	−0.0188014	+	0.999823i	$0.505985\pi$
$242$	11.0939	0.713145
$243$	−1.00000	−0.0641500
$244$	2.26712	0.145138
$245$	0	0
$246$	2.22021	0.141556
$247$	2.34922	0.149477
$248$	9.90391	0.628899
$249$	5.29386	0.335485
$250$	−3.67378	−0.232351
$251$	0.426212	0.0269023	0.0134511	−	0.999910i	$-0.495718\pi$
$251$	0.426212	0.0269023	0.0134511	+	0.999910i	$0.495718\pi$
$252$	0	0
$253$	−11.6099	−0.729906
$254$	−30.5347	−1.91592
$255$	−0.667332	−0.0417899
$256$	−6.88244	−0.430152
$257$	−9.16194	−0.571506	−0.285753	−	0.958303i	$-0.592244\pi$
$257$	−9.16194	−0.571506	−0.285753	+	0.958303i	$0.592244\pi$
$258$	16.7924	1.04545
$259$	0	0
$260$	0.419023	0.0259867
$261$	−6.41611	−0.397147
$262$	0.564661	0.0348848
$263$	8.97300	0.553299	0.276649	−	0.960971i	$-0.410776\pi$
$263$	8.97300	0.553299	0.276649	+	0.960971i	$0.410776\pi$
$264$	5.05549	0.311144
$265$	−1.01829	−0.0625529
$266$	0	0
$267$	9.60949	0.588091
$268$	34.1371	2.08525
$269$	8.74443	0.533157	0.266579	−	0.963813i	$-0.414107\pi$
$269$	8.74443	0.533157	0.266579	+	0.963813i	$0.414107\pi$
$270$	−0.368393	−0.0224197
$271$	17.6472	1.07199	0.535996	−	0.844221i	$-0.319936\pi$
$271$	17.6472	1.07199	0.535996	+	0.844221i	$0.319936\pi$
$272$	5.13842	0.311563
$273$	0	0
$274$	−28.9606	−1.74957
$275$	−12.1833	−0.734679
$276$	13.8805	0.835509
$277$	10.8785	0.653625	0.326812	−	0.945089i	$-0.394025\pi$
$277$	10.8785	0.653625	0.326812	+	0.945089i	$0.394025\pi$
$278$	−4.63974	−0.278273
$279$	−4.79993	−0.287365
$280$	0	0
$281$	−20.2375	−1.20727	−0.603633	−	0.797263i	$-0.706281\pi$
$281$	−20.2375	−1.20727	−0.603633	+	0.797263i	$0.706281\pi$
$282$	−22.8246	−1.35919
$283$	−6.49723	−0.386220	−0.193110	−	0.981177i	$-0.561857\pi$
$283$	−6.49723	−0.386220	−0.193110	+	0.981177i	$0.561857\pi$
$284$	−14.6362	−0.868502
$285$	−0.452158	−0.0267835
$286$	4.68961	0.277302
$287$	0	0
$288$	6.96329	0.410316
$289$	−0.824772	−0.0485160
$290$	−2.36365	−0.138798
$291$	−18.6836	−1.09525
$292$	46.3713	2.71368
$293$	−5.51194	−0.322011	−0.161005	−	0.986954i	$-0.551474\pi$
$293$	−5.51194	−0.322011	−0.161005	+	0.986954i	$0.551474\pi$
$294$	0	0
$295$	1.41377	0.0823129
$296$	16.0592	0.933423
$297$	−2.45014	−0.142172
$298$	−3.16365	−0.183265
$299$	4.08494	0.236238
$300$	14.5661	0.840973
$301$	0	0
$302$	−26.0700	−1.50016
$303$	9.94335	0.571230
$304$	3.48159	0.199683
$305$	−0.128416	−0.00735310
$306$	8.92935	0.510457
$307$	2.22394	0.126927	0.0634634	−	0.997984i	$-0.479785\pi$
$307$	2.22394	0.126927	0.0634634	+	0.997984i	$0.479785\pi$
$308$	0	0
$309$	8.14668	0.463448
$310$	−1.76826	−0.100430
$311$	−22.5977	−1.28140	−0.640698	−	0.767793i	$-0.721355\pi$
$311$	−22.5977	−1.28140	−0.640698	+	0.767793i	$0.721355\pi$
$312$	−1.77878	−0.100704
$313$	−11.7856	−0.666161	−0.333080	−	0.942898i	$-0.608088\pi$
$313$	−11.7856	−0.666161	−0.333080	+	0.942898i	$0.608088\pi$
$314$	−46.5048	−2.62442
$315$	0	0
$316$	29.9992	1.68759
$317$	−5.48705	−0.308183	−0.154092	−	0.988057i	$-0.549245\pi$
$317$	−5.48705	−0.308183	−0.154092	+	0.988057i	$0.549245\pi$
$318$	13.6254	0.764073
$319$	−15.7204	−0.880173
$320$	2.14124	0.119699
$321$	−5.74895	−0.320875
$322$	0	0
$323$	10.9597	0.609814
$324$	2.92934	0.162741
$325$	4.28669	0.237783
$326$	32.0883	1.77720
$327$	2.62119	0.144952
$328$	−2.06334	−0.113929
$329$	0	0
$330$	−0.902616	−0.0496874
$331$	−27.8774	−1.53228	−0.766141	−	0.642673i	$-0.777825\pi$
$331$	−27.8774	−1.53228	−0.766141	+	0.642673i	$0.777825\pi$
$332$	−15.5075	−0.851086
$333$	−7.78311	−0.426512
$334$	−26.1829	−1.43266
$335$	−1.93363	−0.105645
$336$	0	0
$337$	33.3457	1.81645	0.908227	−	0.418478i	$-0.137436\pi$
$337$	33.3457	1.81645	0.908227	+	0.418478i	$0.137436\pi$
$338$	27.2127	1.48018
$339$	4.82467	0.262040
$340$	1.95484	0.106016
$341$	−11.7605	−0.636869
$342$	6.05018	0.327156
$343$	0	0
$344$	−15.6059	−0.841415
$345$	−0.786234	−0.0423294
$346$	46.1787	2.48258
$347$	−14.1721	−0.760800	−0.380400	−	0.924822i	$-0.624214\pi$
$347$	−14.1721	−0.760800	−0.380400	+	0.924822i	$0.624214\pi$
$348$	18.7950	1.00752
$349$	−2.16435	−0.115855	−0.0579275	−	0.998321i	$-0.518449\pi$
$349$	−2.16435	−0.115855	−0.0579275	+	0.998321i	$0.518449\pi$
$350$	0	0
$351$	0.862086	0.0460147
$352$	17.0611	0.909359
$353$	−33.5484	−1.78560	−0.892800	−	0.450453i	$-0.851263\pi$
$353$	−33.5484	−1.78560	−0.892800	+	0.450453i	$0.851263\pi$
$354$	−18.9172	−1.00544
$355$	0.829041	0.0440009
$356$	−28.1495	−1.49192
$357$	0	0
$358$	11.2645	0.595347
$359$	17.8178	0.940386	0.470193	−	0.882563i	$-0.344184\pi$
$359$	17.8178	0.940386	0.470193	+	0.882563i	$0.344184\pi$
$360$	0.342364	0.0180442
$361$	−11.5741	−0.609165
$362$	10.2565	0.539067
$363$	4.99679	0.262263
$364$	0	0
$365$	−2.62661	−0.137483
$366$	1.71830	0.0898169
$367$	−2.57938	−0.134643	−0.0673213	−	0.997731i	$-0.521445\pi$
$367$	−2.57938	−0.134643	−0.0673213	+	0.997731i	$0.521445\pi$
$368$	6.05396	0.315585
$369$	1.00000	0.0520579
$370$	−2.86724	−0.149061
$371$	0	0
$372$	14.0607	0.729011
$373$	20.4331	1.05799	0.528993	−	0.848626i	$-0.322570\pi$
$373$	20.4331	1.05799	0.528993	+	0.848626i	$0.322570\pi$
$374$	21.8782	1.13129
$375$	−1.65470	−0.0854483
$376$	21.2120	1.09392
$377$	5.53123	0.284873
$378$	0	0
$379$	−13.6675	−0.702051	−0.351025	−	0.936366i	$-0.614167\pi$
$379$	−13.6675	−0.702051	−0.351025	+	0.936366i	$0.614167\pi$
$380$	1.32453	0.0679467
$381$	−13.7531	−0.704590
$382$	−52.5802	−2.69024
$383$	31.0004	1.58405	0.792024	−	0.610490i	$-0.209027\pi$
$383$	31.0004	1.58405	0.792024	+	0.610490i	$0.209027\pi$
$384$	−14.7247	−0.751415
$385$	0	0
$386$	2.67049	0.135925
$387$	7.56342	0.384470
$388$	54.7306	2.77852
$389$	25.5540	1.29564	0.647819	−	0.761794i	$-0.275681\pi$
$389$	25.5540	1.29564	0.647819	+	0.761794i	$0.275681\pi$
$390$	0.317586	0.0160816
$391$	19.0573	0.963767
$392$	0	0
$393$	0.254327	0.0128291
$394$	−17.8840	−0.900985
$395$	−1.69924	−0.0854982
$396$	7.17732	0.360674
$397$	−10.7669	−0.540375	−0.270187	−	0.962808i	$-0.587086\pi$
$397$	−10.7669	−0.540375	−0.270187	+	0.962808i	$0.587086\pi$
$398$	16.8379	0.844009
$399$	0	0
$400$	6.35297	0.317648
$401$	−21.3162	−1.06448	−0.532241	−	0.846593i	$-0.678650\pi$
$401$	−21.3162	−1.06448	−0.532241	+	0.846593i	$0.678650\pi$
$402$	25.8732	1.29044
$403$	4.13795	0.206126
$404$	−29.1275	−1.44915
$405$	−0.165927	−0.00824497
$406$	0	0
$407$	−19.0697	−0.945252
$408$	−8.29844	−0.410834
$409$	−21.2963	−1.05303	−0.526517	−	0.850165i	$-0.676502\pi$
$409$	−21.2963	−1.05303	−0.526517	+	0.850165i	$0.676502\pi$
$410$	0.368393	0.0181936
$411$	−13.0440	−0.643415
$412$	−23.8644	−1.17572
$413$	0	0
$414$	10.5203	0.517047
$415$	0.878393	0.0431186
$416$	−6.00296	−0.294319
$417$	−2.08977	−0.102337
$418$	14.8238	0.725056
$419$	−6.18534	−0.302174	−0.151087	−	0.988520i	$-0.548277\pi$
$419$	−6.18534	−0.302174	−0.151087	+	0.988520i	$0.548277\pi$
$420$	0	0
$421$	18.2006	0.887041	0.443521	−	0.896264i	$-0.353729\pi$
$421$	18.2006	0.887041	0.443521	+	0.896264i	$0.353729\pi$
$422$	−7.96575	−0.387767
$423$	−10.2804	−0.499849
$424$	−12.6627	−0.614954
$425$	19.9985	0.970069
$426$	−11.0931	−0.537464
$427$	0	0
$428$	16.8407	0.814024
$429$	2.11223	0.101980
$430$	2.78631	0.134368
$431$	−22.7537	−1.09601	−0.548004	−	0.836475i	$-0.684612\pi$
$431$	−22.7537	−1.09601	−0.548004	+	0.836475i	$0.684612\pi$
$432$	1.27763	0.0614699
$433$	29.0237	1.39479	0.697396	−	0.716686i	$-0.254342\pi$
$433$	29.0237	1.39479	0.697396	+	0.716686i	$0.254342\pi$
$434$	0	0
$435$	−1.06460	−0.0510438
$436$	−7.67838	−0.367728
$437$	12.9125	0.617686
$438$	35.1458	1.67933
$439$	22.6255	1.07986	0.539928	−	0.841711i	$-0.318451\pi$
$439$	22.6255	1.07986	0.539928	+	0.841711i	$0.318451\pi$
$440$	0.838841	0.0399902
$441$	0	0
$442$	−7.69786	−0.366150
$443$	13.3204	0.632870	0.316435	−	0.948614i	$-0.397514\pi$
$443$	13.3204	0.632870	0.316435	+	0.948614i	$0.397514\pi$
$444$	22.7994	1.08201
$445$	1.59447	0.0755852
$446$	15.2135	0.720380
$447$	−1.42493	−0.0673969
$448$	0	0
$449$	12.6589	0.597412	0.298706	−	0.954345i	$-0.403445\pi$
$449$	12.6589	0.597412	0.298706	+	0.954345i	$0.403445\pi$
$450$	11.0399	0.520428
$451$	2.45014	0.115373
$452$	−14.1331	−0.664766
$453$	−11.7421	−0.551692
$454$	−27.6426	−1.29733
$455$	0	0
$456$	−5.62270	−0.263307
$457$	−10.1104	−0.472943	−0.236471	−	0.971638i	$-0.575991\pi$
$457$	−10.1104	−0.472943	−0.236471	+	0.971638i	$0.575991\pi$
$458$	−42.3843	−1.98049
$459$	4.02184	0.187724
$460$	2.30315	0.107385
$461$	−10.9322	−0.509161	−0.254580	−	0.967052i	$-0.581937\pi$
$461$	−10.9322	−0.509161	−0.254580	+	0.967052i	$0.581937\pi$
$462$	0	0
$463$	25.7020	1.19447	0.597237	−	0.802064i	$-0.296265\pi$
$463$	25.7020	1.19447	0.597237	+	0.802064i	$0.296265\pi$
$464$	8.19740	0.380555
$465$	−0.796438	−0.0369339
$466$	−20.9996	−0.972787
$467$	21.4674	0.993395	0.496697	−	0.867924i	$-0.334546\pi$
$467$	21.4674	0.993395	0.496697	+	0.867924i	$0.334546\pi$
$468$	−2.52535	−0.116734
$469$	0	0
$470$	−3.78722	−0.174691
$471$	−20.9461	−0.965146
$472$	17.5806	0.809213
$473$	18.5315	0.852078
$474$	22.7370	1.04435
$475$	13.5502	0.621726
$476$	0	0
$477$	6.13697	0.280992
$478$	−30.9060	−1.41361
$479$	−3.81420	−0.174275	−0.0871376	−	0.996196i	$-0.527772\pi$
$479$	−3.81420	−0.174275	−0.0871376	+	0.996196i	$0.527772\pi$
$480$	1.15540	0.0527364
$481$	6.70970	0.305936
$482$	1.29606	0.0590338
$483$	0	0
$484$	−14.6373	−0.665333
$485$	−3.10010	−0.140768
$486$	2.22021	0.100711
$487$	35.2293	1.59639	0.798197	−	0.602396i	$-0.205787\pi$
$487$	35.2293	1.59639	0.798197	+	0.602396i	$0.205787\pi$
$488$	−1.59689	−0.0722879
$489$	14.4528	0.653577
$490$	0	0
$491$	−28.8483	−1.30190	−0.650952	−	0.759119i	$-0.725630\pi$
$491$	−28.8483	−1.30190	−0.650952	+	0.759119i	$0.725630\pi$
$492$	−2.92934	−0.132065
$493$	25.8046	1.16218
$494$	−5.21577	−0.234669
$495$	−0.406545	−0.0182728
$496$	6.13253	0.275359
$497$	0	0
$498$	−11.7535	−0.526686
$499$	−6.51441	−0.291625	−0.145813	−	0.989312i	$-0.546580\pi$
$499$	−6.51441	−0.291625	−0.145813	+	0.989312i	$0.546580\pi$
$500$	4.84719	0.216773
$501$	−11.7930	−0.526871
$502$	−0.946282	−0.0422346
$503$	−15.2400	−0.679516	−0.339758	−	0.940513i	$-0.610345\pi$
$503$	−15.2400	−0.679516	−0.339758	+	0.940513i	$0.610345\pi$
$504$	0	0
$505$	1.64987	0.0734181
$506$	25.7764	1.14590
$507$	12.2568	0.544344
$508$	40.2874	1.78747
$509$	32.4515	1.43839	0.719193	−	0.694810i	$-0.244511\pi$
$509$	32.4515	1.43839	0.719193	+	0.694810i	$0.244511\pi$
$510$	1.48162	0.0656071
$511$	0	0
$512$	−14.1689	−0.626182
$513$	2.72504	0.120314
$514$	20.3415	0.897223
$515$	1.35175	0.0595653
$516$	−22.1559	−0.975357
$517$	−25.1884	−1.10779
$518$	0	0
$519$	20.7992	0.912984
$520$	−0.295147	−0.0129431
$521$	8.46956	0.371058	0.185529	−	0.982639i	$-0.440600\pi$
$521$	8.46956	0.371058	0.185529	+	0.982639i	$0.440600\pi$
$522$	14.2451	0.623492
$523$	40.6091	1.77571	0.887857	−	0.460120i	$-0.152194\pi$
$523$	40.6091	1.77571	0.887857	+	0.460120i	$0.152194\pi$
$524$	−0.745012	−0.0325460
$525$	0	0
$526$	−19.9220	−0.868639
$527$	19.3046	0.840921
$528$	3.13037	0.136232
$529$	−0.547203	−0.0237914
$530$	2.26081	0.0982035
$531$	−8.52045	−0.369756
$532$	0	0
$533$	−0.862086	−0.0373411
$534$	−21.3351	−0.923261
$535$	−0.953904	−0.0412409
$536$	−24.0451	−1.03859
$537$	5.07361	0.218943
$538$	−19.4145	−0.837019
$539$	0	0
$540$	0.486057	0.0209166
$541$	38.7394	1.66554	0.832768	−	0.553622i	$-0.186755\pi$
$541$	38.7394	1.66554	0.832768	+	0.553622i	$0.186755\pi$
$542$	−39.1806	−1.68295
$543$	4.61958	0.198245
$544$	−28.0053	−1.20072
$545$	0.434926	0.0186302
$546$	0	0
$547$	−11.6384	−0.497623	−0.248811	−	0.968552i	$-0.580040\pi$
$547$	−11.6384	−0.497623	−0.248811	+	0.968552i	$0.580040\pi$
$548$	38.2105	1.63227
$549$	0.773934	0.0330307
$550$	27.0494	1.15339
$551$	17.4842	0.744851
$552$	−9.77702	−0.416138
$553$	0	0
$554$	−24.1526	−1.02614
$555$	−1.29143	−0.0548180
$556$	6.12167	0.259617
$557$	0.391654	0.0165949	0.00829746	−	0.999966i	$-0.497359\pi$
$557$	0.391654	0.0165949	0.00829746	+	0.999966i	$0.497359\pi$
$558$	10.6569	0.451142
$559$	−6.52031	−0.275780
$560$	0	0
$561$	9.85410	0.416040
$562$	44.9315	1.89532
$563$	−22.6577	−0.954907	−0.477453	−	0.878657i	$-0.658440\pi$
$563$	−22.6577	−0.954907	−0.477453	+	0.878657i	$0.658440\pi$
$564$	30.1148	1.26806
$565$	0.800541	0.0336790
$566$	14.4252	0.606338
$567$	0	0
$568$	10.3093	0.432570
$569$	−5.50248	−0.230676	−0.115338	−	0.993326i	$-0.536795\pi$
$569$	−5.50248	−0.230676	−0.115338	+	0.993326i	$0.536795\pi$
$570$	1.00389	0.0420482
$571$	−28.9417	−1.21117	−0.605586	−	0.795780i	$-0.707061\pi$
$571$	−28.9417	−1.21117	−0.605586	+	0.795780i	$0.707061\pi$
$572$	−6.18746	−0.258711
$573$	−23.6825	−0.989351
$574$	0	0
$575$	23.5617	0.982592
$576$	−12.9047	−0.537697
$577$	−25.4503	−1.05951	−0.529754	−	0.848151i	$-0.677716\pi$
$577$	−25.4503	−1.05951	−0.529754	+	0.848151i	$0.677716\pi$
$578$	1.83117	0.0761666
$579$	1.20281	0.0499871
$580$	3.11859	0.129492
$581$	0	0
$582$	41.4815	1.71946
$583$	15.0365	0.622747
$584$	−32.6626	−1.35159
$585$	0.143043	0.00591410
$586$	12.2377	0.505534
$587$	−12.9184	−0.533199	−0.266600	−	0.963807i	$-0.585900\pi$
$587$	−12.9184	−0.533199	−0.266600	+	0.963807i	$0.585900\pi$
$588$	0	0
$589$	13.0800	0.538953
$590$	−3.13887	−0.129225
$591$	−8.05510	−0.331342
$592$	9.94392	0.408692
$593$	−20.5182	−0.842581	−0.421291	−	0.906926i	$-0.638423\pi$
$593$	−20.5182	−0.842581	−0.421291	+	0.906926i	$0.638423\pi$
$594$	5.43984	0.223199
$595$	0	0
$596$	4.17411	0.170978
$597$	7.58393	0.310390
$598$	−9.06944	−0.370877
$599$	46.2714	1.89060	0.945299	−	0.326206i	$-0.105770\pi$
$599$	46.2714	1.89060	0.945299	+	0.326206i	$0.105770\pi$
$600$	−10.2599	−0.418859
$601$	32.3347	1.31896	0.659480	−	0.751722i	$-0.270776\pi$
$601$	32.3347	1.31896	0.659480	+	0.751722i	$0.270776\pi$
$602$	0	0
$603$	11.6535	0.474567
$604$	34.3967	1.39958
$605$	0.829101	0.0337078
$606$	−22.0763	−0.896790
$607$	−26.6961	−1.08356	−0.541781	−	0.840520i	$-0.682250\pi$
$607$	−26.6961	−1.08356	−0.541781	+	0.840520i	$0.682250\pi$
$608$	−18.9753	−0.769549
$609$	0	0
$610$	0.285112	0.0115438
$611$	8.86257	0.358541
$612$	−11.7814	−0.476234
$613$	13.3137	0.537737	0.268868	−	0.963177i	$-0.413350\pi$
$613$	13.3137	0.537737	0.268868	+	0.963177i	$0.413350\pi$
$614$	−4.93761	−0.199266
$615$	0.165927	0.00669081
$616$	0	0
$617$	20.4322	0.822569	0.411284	−	0.911507i	$-0.365080\pi$
$617$	20.4322	0.822569	0.411284	+	0.911507i	$0.365080\pi$
$618$	−18.0874	−0.727580
$619$	−25.4517	−1.02299	−0.511495	−	0.859286i	$-0.670908\pi$
$619$	−25.4517	−1.02299	−0.511495	+	0.859286i	$0.670908\pi$
$620$	2.33304	0.0936971
$621$	4.73844	0.190147
$622$	50.1716	2.01170
$623$	0	0
$624$	−1.10143	−0.0440923
$625$	24.5878	0.983511
$626$	26.1665	1.04582
$627$	6.67675	0.266644
$628$	61.3584	2.44847
$629$	31.3024	1.24811
$630$	0	0
$631$	45.4277	1.80845	0.904225	−	0.427057i	$-0.140450\pi$
$631$	45.4277	1.80845	0.904225	+	0.427057i	$0.140450\pi$
$632$	−21.1305	−0.840527
$633$	−3.58783	−0.142604
$634$	12.1824	0.483825
$635$	−2.28200	−0.0905584
$636$	−17.9773	−0.712846
$637$	0	0
$638$	34.9026	1.38181
$639$	−4.99642	−0.197655
$640$	−2.44322	−0.0965767
$641$	24.3972	0.963633	0.481816	−	0.876272i	$-0.339977\pi$
$641$	24.3972	0.963633	0.481816	+	0.876272i	$0.339977\pi$
$642$	12.7639	0.503750
$643$	−24.3477	−0.960180	−0.480090	−	0.877219i	$-0.659396\pi$
$643$	−24.3477	−0.960180	−0.480090	+	0.877219i	$0.659396\pi$
$644$	0	0
$645$	1.25497	0.0494145
$646$	−24.3329	−0.957364
$647$	21.7620	0.855552	0.427776	−	0.903885i	$-0.359297\pi$
$647$	21.7620	0.855552	0.427776	+	0.903885i	$0.359297\pi$
$648$	−2.06334	−0.0810558
$649$	−20.8763	−0.819468
$650$	−9.51737	−0.373302
$651$	0	0
$652$	−42.3372	−1.65805
$653$	5.37080	0.210176	0.105088	−	0.994463i	$-0.466488\pi$
$653$	5.37080	0.210176	0.105088	+	0.994463i	$0.466488\pi$
$654$	−5.81961	−0.227565
$655$	0.0421997	0.00164888
$656$	−1.27763	−0.0498830
$657$	15.8299	0.617584
$658$	0	0
$659$	−26.7004	−1.04010	−0.520049	−	0.854136i	$-0.674086\pi$
$659$	−26.7004	−1.04010	−0.520049	+	0.854136i	$0.674086\pi$
$660$	1.19091	0.0463561
$661$	−35.6937	−1.38832	−0.694161	−	0.719820i	$-0.744225\pi$
$661$	−35.6937	−1.38832	−0.694161	+	0.719820i	$0.744225\pi$
$662$	61.8938	2.40557
$663$	−3.46717	−0.134654
$664$	10.9230	0.423896
$665$	0	0
$666$	17.2801	0.669592
$667$	30.4023	1.17718
$668$	34.5457	1.33661
$669$	6.85227	0.264924
$670$	4.29306	0.165855
$671$	1.89625	0.0732040
$672$	0	0
$673$	27.9802	1.07856	0.539280	−	0.842127i	$-0.318697\pi$
$673$	27.9802	1.07856	0.539280	+	0.842127i	$0.318697\pi$
$674$	−74.0345	−2.85170
$675$	4.97247	0.191390
$676$	−35.9044	−1.38094
$677$	8.16920	0.313968	0.156984	−	0.987601i	$-0.449823\pi$
$677$	8.16920	0.313968	0.156984	+	0.987601i	$0.449823\pi$
$678$	−10.7118	−0.411384
$679$	0	0
$680$	−1.37693	−0.0528030
$681$	−12.4504	−0.477101
$682$	26.1109	0.999838
$683$	−10.3176	−0.394791	−0.197396	−	0.980324i	$-0.563248\pi$
$683$	−10.3176	−0.394791	−0.197396	+	0.980324i	$0.563248\pi$
$684$	−7.98259	−0.305222
$685$	−2.16436	−0.0826958
$686$	0	0
$687$	−19.0902	−0.728337
$688$	−9.66324	−0.368407
$689$	−5.29059	−0.201556
$690$	1.74561	0.0664541
$691$	2.89735	0.110220	0.0551101	−	0.998480i	$-0.482449\pi$
$691$	2.89735	0.110220	0.0551101	+	0.998480i	$0.482449\pi$
$692$	−60.9280	−2.31614
$693$	0	0
$694$	31.4652	1.19440
$695$	−0.346750	−0.0131530
$696$	−13.2386	−0.501809
$697$	−4.02184	−0.152338
$698$	4.80532	0.181884
$699$	−9.45836	−0.357748
$700$	0	0
$701$	33.2272	1.25497	0.627487	−	0.778627i	$-0.284084\pi$
$701$	33.2272	1.25497	0.627487	+	0.778627i	$0.284084\pi$
$702$	−1.91401	−0.0722398
$703$	21.2093	0.799924
$704$	−31.6185	−1.19167
$705$	−1.70579	−0.0642438
$706$	74.4846	2.80326
$707$	0	0
$708$	24.9593	0.938029
$709$	44.1099	1.65658	0.828291	−	0.560298i	$-0.189313\pi$
$709$	44.1099	1.65658	0.828291	+	0.560298i	$0.189313\pi$
$710$	−1.84065	−0.0690782
$711$	10.2409	0.384064
$712$	19.8277	0.743074
$713$	22.7442	0.851777
$714$	0	0
$715$	0.350476	0.0131071
$716$	−14.8624	−0.555433
$717$	−13.9203	−0.519863
$718$	−39.5593	−1.47634
$719$	1.17550	0.0438388	0.0219194	−	0.999760i	$-0.493022\pi$
$719$	1.17550	0.0438388	0.0219194	+	0.999760i	$0.493022\pi$
$720$	0.211993	0.00790050
$721$	0	0
$722$	25.6970	0.956345
$723$	0.583754	0.0217100
$724$	−13.5323	−0.502926
$725$	31.9039	1.18488
$726$	−11.0939	−0.411735
$727$	−38.3481	−1.42225	−0.711126	−	0.703064i	$-0.751815\pi$
$727$	−38.3481	−1.42225	−0.711126	+	0.703064i	$0.751815\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	5.83163	0.215838
$731$	−30.4189	−1.12508
$732$	−2.26712	−0.0837952
$733$	8.22560	0.303820	0.151910	−	0.988394i	$-0.451458\pi$
$733$	8.22560	0.303820	0.151910	+	0.988394i	$0.451458\pi$
$734$	5.72677	0.211379
$735$	0	0
$736$	−32.9951	−1.21622
$737$	28.5527	1.05175
$738$	−2.22021	−0.0817272
$739$	−27.9329	−1.02753	−0.513765	−	0.857931i	$-0.671750\pi$
$739$	−27.9329	−1.02753	−0.513765	+	0.857931i	$0.671750\pi$
$740$	3.78303	0.139067
$741$	−2.34922	−0.0863008
$742$	0	0
$743$	−33.8794	−1.24291	−0.621457	−	0.783448i	$-0.713459\pi$
$743$	−33.8794	−1.24291	−0.621457	+	0.783448i	$0.713459\pi$
$744$	−9.90391	−0.363095
$745$	−0.236434	−0.00866227
$746$	−45.3658	−1.66096
$747$	−5.29386	−0.193692
$748$	−28.8661	−1.05545
$749$	0	0
$750$	3.67378	0.134148
$751$	29.1721	1.06450	0.532252	−	0.846586i	$-0.321346\pi$
$751$	29.1721	1.06450	0.532252	+	0.846586i	$0.321346\pi$
$752$	13.1345	0.478966
$753$	−0.426212	−0.0155320
$754$	−12.2805	−0.447230
$755$	−1.94833	−0.0709070
$756$	0	0
$757$	−2.85953	−0.103932	−0.0519658	−	0.998649i	$-0.516549\pi$
$757$	−2.85953	−0.103932	−0.0519658	+	0.998649i	$0.516549\pi$
$758$	30.3447	1.10217
$759$	11.6099	0.421411
$760$	−0.932957	−0.0338419
$761$	33.5286	1.21541	0.607706	−	0.794162i	$-0.292090\pi$
$761$	33.5286	1.21541	0.607706	+	0.794162i	$0.292090\pi$
$762$	30.5347	1.10616
$763$	0	0
$764$	69.3742	2.50987
$765$	0.667332	0.0241274
$766$	−68.8276	−2.48684
$767$	7.34535	0.265225
$768$	6.88244	0.248349
$769$	47.9449	1.72894	0.864469	−	0.502686i	$-0.167655\pi$
$769$	47.9449	1.72894	0.864469	+	0.502686i	$0.167655\pi$
$770$	0	0
$771$	9.16194	0.329959
$772$	−3.52345	−0.126812
$773$	−21.1871	−0.762046	−0.381023	−	0.924566i	$-0.624428\pi$
$773$	−21.1871	−0.762046	−0.381023	+	0.924566i	$0.624428\pi$
$774$	−16.7924	−0.603590
$775$	23.8675	0.857347
$776$	−38.5506	−1.38389
$777$	0	0
$778$	−56.7353	−2.03406
$779$	−2.72504	−0.0976348
$780$	−0.419023	−0.0150034
$781$	−12.2420	−0.438052
$782$	−42.3112	−1.51304
$783$	6.41611	0.229293
$784$	0	0
$785$	−3.47552	−0.124047
$786$	−0.564661	−0.0201408
$787$	−14.7694	−0.526473	−0.263236	−	0.964731i	$-0.584790\pi$
$787$	−14.7694	−0.526473	−0.263236	+	0.964731i	$0.584790\pi$
$788$	23.5962	0.840578
$789$	−8.97300	−0.319447
$790$	3.77268	0.134226
$791$	0	0
$792$	−5.05549	−0.179639
$793$	−0.667198	−0.0236929
$794$	23.9048	0.848349
$795$	1.01829	0.0361149
$796$	−22.2159	−0.787423
$797$	30.0351	1.06390	0.531949	−	0.846776i	$-0.321460\pi$
$797$	30.0351	1.06390	0.531949	+	0.846776i	$0.321460\pi$
$798$	0	0
$799$	41.3461	1.46272
$800$	−34.6248	−1.22417
$801$	−9.60949	−0.339535
$802$	47.3266	1.67116
$803$	38.7856	1.36871
$804$	−34.1371	−1.20392
$805$	0	0
$806$	−9.18714	−0.323603
$807$	−8.74443	−0.307819
$808$	20.5165	0.721769
$809$	26.5142	0.932191	0.466095	−	0.884734i	$-0.345660\pi$
$809$	26.5142	0.932191	0.466095	+	0.884734i	$0.345660\pi$
$810$	0.368393	0.0129440
$811$	32.3215	1.13496	0.567481	−	0.823386i	$-0.307918\pi$
$811$	32.3215	1.13496	0.567481	+	0.823386i	$0.307918\pi$
$812$	0	0
$813$	−17.6472	−0.618915
$814$	42.3389	1.48398
$815$	2.39810	0.0840019
$816$	−5.13842	−0.179881
$817$	−20.6106	−0.721075
$818$	47.2823	1.65319
$819$	0	0
$820$	−0.486057	−0.0169738
$821$	41.1997	1.43788	0.718939	−	0.695073i	$-0.244628\pi$
$821$	41.1997	1.43788	0.718939	+	0.695073i	$0.244628\pi$
$822$	28.9606	1.01012
$823$	−9.13478	−0.318418	−0.159209	−	0.987245i	$-0.550894\pi$
$823$	−9.13478	−0.318418	−0.159209	+	0.987245i	$0.550894\pi$
$824$	16.8094	0.585583
$825$	12.1833	0.424167
$826$	0	0
$827$	45.1279	1.56925	0.784626	−	0.619970i	$-0.212855\pi$
$827$	45.1279	1.56925	0.784626	+	0.619970i	$0.212855\pi$
$828$	−13.8805	−0.482381
$829$	−0.645036	−0.0224030	−0.0112015	−	0.999937i	$-0.503566\pi$
$829$	−0.645036	−0.0224030	−0.0112015	+	0.999937i	$0.503566\pi$
$830$	−1.95022	−0.0676931
$831$	−10.8785	−0.377370
$832$	11.1250	0.385690
$833$	0	0
$834$	4.63974	0.160661
$835$	−1.95677	−0.0677168
$836$	−19.5585	−0.676445
$837$	4.79993	0.165910
$838$	13.7328	0.474391
$839$	−31.9401	−1.10269	−0.551347	−	0.834276i	$-0.685886\pi$
$839$	−31.9401	−1.10269	−0.551347	+	0.834276i	$0.685886\pi$
$840$	0	0
$841$	12.1664	0.419531
$842$	−40.4091	−1.39259
$843$	20.2375	0.697015
$844$	10.5100	0.361769
$845$	2.03373	0.0699625
$846$	22.8246	0.784727
$847$	0	0
$848$	−7.84077	−0.269253
$849$	6.49723	0.222984
$850$	−44.4009	−1.52294
$851$	36.8798	1.26422
$852$	14.6362	0.501430
$853$	−20.0907	−0.687893	−0.343947	−	0.938989i	$-0.611764\pi$
$853$	−20.0907	−0.687893	−0.343947	+	0.938989i	$0.611764\pi$
$854$	0	0
$855$	0.452158	0.0154635
$856$	−11.8621	−0.405437
$857$	−5.17839	−0.176890	−0.0884452	−	0.996081i	$-0.528190\pi$
$857$	−5.17839	−0.176890	−0.0884452	+	0.996081i	$0.528190\pi$
$858$	−4.68961	−0.160101
$859$	−41.7012	−1.42283	−0.711413	−	0.702775i	$-0.751944\pi$
$859$	−41.7012	−1.42283	−0.711413	+	0.702775i	$0.751944\pi$
$860$	−3.67625	−0.125359
$861$	0	0
$862$	50.5181	1.72065
$863$	−23.7810	−0.809514	−0.404757	−	0.914424i	$-0.632644\pi$
$863$	−23.7810	−0.809514	−0.404757	+	0.914424i	$0.632644\pi$
$864$	−6.96329	−0.236896
$865$	3.45114	0.117342
$866$	−64.4389	−2.18972
$867$	0.824772	0.0280107
$868$	0	0
$869$	25.0917	0.851179
$870$	2.36365	0.0801351
$871$	−10.0463	−0.340406
$872$	5.40842	0.183152
$873$	18.6836	0.632342
$874$	−28.6684	−0.969723
$875$	0	0
$876$	−46.3713	−1.56674
$877$	41.2107	1.39159	0.695793	−	0.718242i	$-0.255053\pi$
$877$	41.2107	1.39159	0.695793	+	0.718242i	$0.255053\pi$
$878$	−50.2335	−1.69530
$879$	5.51194	0.185913
$880$	0.519413	0.0175094
$881$	40.0194	1.34829	0.674143	−	0.738601i	$-0.264513\pi$
$881$	40.0194	1.34829	0.674143	+	0.738601i	$0.264513\pi$
$882$	0	0
$883$	37.5006	1.26200	0.630998	−	0.775785i	$-0.282646\pi$
$883$	37.5006	1.26200	0.630998	+	0.775785i	$0.282646\pi$
$884$	10.1565	0.341602
$885$	−1.41377	−0.0475234
$886$	−29.5740	−0.993560
$887$	−6.99132	−0.234745	−0.117373	−	0.993088i	$-0.537447\pi$
$887$	−6.99132	−0.234745	−0.117373	+	0.993088i	$0.537447\pi$
$888$	−16.0592	−0.538912
$889$	0	0
$890$	−3.54007	−0.118663
$891$	2.45014	0.0820829
$892$	−20.0727	−0.672082
$893$	28.0145	0.937469
$894$	3.16365	0.105808
$895$	0.841848	0.0281399
$896$	0	0
$897$	−4.08494	−0.136392
$898$	−28.1055	−0.937893
$899$	30.7969	1.02713
$900$	−14.5661	−0.485536
$901$	−24.6819	−0.822274
$902$	−5.43984	−0.181127
$903$	0	0
$904$	9.95494	0.331096
$905$	0.766512	0.0254797
$906$	26.0700	0.866117
$907$	17.5799	0.583730	0.291865	−	0.956460i	$-0.405724\pi$
$907$	17.5799	0.583730	0.291865	+	0.956460i	$0.405724\pi$
$908$	36.4716	1.21035
$909$	−9.94335	−0.329800
$910$	0	0
$911$	−3.56905	−0.118248	−0.0591240	−	0.998251i	$-0.518831\pi$
$911$	−3.56905	−0.118248	−0.0591240	+	0.998251i	$0.518831\pi$
$912$	−3.48159	−0.115287
$913$	−12.9707	−0.429268
$914$	22.4472	0.742486
$915$	0.128416	0.00424532
$916$	55.9218	1.84771
$917$	0	0
$918$	−8.92935	−0.294712
$919$	−56.3987	−1.86042	−0.930210	−	0.367026i	$-0.880376\pi$
$919$	−56.3987	−1.86042	−0.930210	+	0.367026i	$0.880376\pi$
$920$	−1.62227	−0.0534847
$921$	−2.22394	−0.0732812
$922$	24.2717	0.799346
$923$	4.30735	0.141778
$924$	0	0
$925$	38.7012	1.27249
$926$	−57.0640	−1.87524
$927$	−8.14668	−0.267572
$928$	−44.6772	−1.46660
$929$	35.5398	1.16602	0.583011	−	0.812464i	$-0.301874\pi$
$929$	35.5398	1.16602	0.583011	+	0.812464i	$0.301874\pi$
$930$	1.76826	0.0579836
$931$	0	0
$932$	27.7068	0.907567
$933$	22.5977	0.739814
$934$	−47.6623	−1.55956
$935$	1.63506	0.0534721
$936$	1.77878	0.0581412
$937$	8.98177	0.293422	0.146711	−	0.989179i	$-0.453131\pi$
$937$	8.98177	0.293422	0.146711	+	0.989179i	$0.453131\pi$
$938$	0	0
$939$	11.7856	0.384608
$940$	4.99685	0.162979
$941$	−39.4769	−1.28691	−0.643455	−	0.765484i	$-0.722500\pi$
$941$	−39.4769	−1.28691	−0.643455	+	0.765484i	$0.722500\pi$
$942$	46.5048	1.51521
$943$	−4.73844	−0.154305
$944$	10.8860	0.354308
$945$	0	0
$946$	−41.1438	−1.33770
$947$	−30.4765	−0.990353	−0.495176	−	0.868792i	$-0.664897\pi$
$947$	−30.4765	−0.990353	−0.495176	+	0.868792i	$0.664897\pi$
$948$	−29.9992	−0.974328
$949$	−13.6468	−0.442992
$950$	−30.0843	−0.976064
$951$	5.48705	0.177930
$952$	0	0
$953$	−38.1639	−1.23625	−0.618125	−	0.786080i	$-0.712107\pi$
$953$	−38.1639	−1.23625	−0.618125	+	0.786080i	$0.712107\pi$
$954$	−13.6254	−0.441138
$955$	−3.92956	−0.127158
$956$	40.7774	1.31883
$957$	15.7204	0.508168
$958$	8.46834	0.273600
$959$	0	0
$960$	−2.14124	−0.0691083
$961$	−7.96063	−0.256795
$962$	−14.8970	−0.480298
$963$	5.74895	0.185257
$964$	−1.71002	−0.0550759
$965$	0.199578	0.00642465
$966$	0	0
$967$	12.7300	0.409368	0.204684	−	0.978828i	$-0.434383\pi$
$967$	12.7300	0.409368	0.204684	+	0.978828i	$0.434383\pi$
$968$	10.3101	0.331379
$969$	−10.9597	−0.352076
$970$	6.88288	0.220996
$971$	−15.8759	−0.509482	−0.254741	−	0.967009i	$-0.581990\pi$
$971$	−15.8759	−0.509482	−0.254741	+	0.967009i	$0.581990\pi$
$972$	−2.92934	−0.0939588
$973$	0	0
$974$	−78.2166	−2.50622
$975$	−4.28669	−0.137284
$976$	−0.988801	−0.0316507
$977$	11.6369	0.372298	0.186149	−	0.982522i	$-0.440399\pi$
$977$	11.6369	0.372298	0.186149	+	0.982522i	$0.440399\pi$
$978$	−32.0883	−1.02607
$979$	−23.5446	−0.752490
$980$	0	0
$981$	−2.62119	−0.0836883
$982$	64.0493	2.04389
$983$	−43.2367	−1.37904	−0.689518	−	0.724268i	$-0.742178\pi$
$983$	−43.2367	−1.37904	−0.689518	+	0.724268i	$0.742178\pi$
$984$	2.06334	0.0657770
$985$	−1.33656	−0.0425862
$986$	−57.2916	−1.82454
$987$	0	0
$988$	6.88168	0.218935
$989$	−35.8388	−1.13961
$990$	0.902616	0.0286870
$991$	−34.6510	−1.10072	−0.550362	−	0.834926i	$-0.685510\pi$
$991$	−34.6510	−1.10072	−0.550362	+	0.834926i	$0.685510\pi$
$992$	−33.4234	−1.06119
$993$	27.8774	0.884663
$994$	0	0
$995$	1.25838	0.0398932
$996$	15.5075	0.491375
$997$	−16.9551	−0.536973	−0.268486	−	0.963284i	$-0.586523\pi$
$997$	−16.9551	−0.536973	−0.268486	+	0.963284i	$0.586523\pi$
$998$	14.4634	0.457830
$999$	7.78311	0.246247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.3	✓	24
7.6	odd	2		6027.2.a.bo.1.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.3	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.3	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)

\(f(q)\)	\(=\)	\(q-2.22021 q^{2} -1.00000 q^{3} +2.92934 q^{4} -0.165927 q^{5} +2.22021 q^{6} -2.06334 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22021 q^{2} -1.00000 q^{3} +2.92934 q^{4} -0.165927 q^{5} +2.22021 q^{6} -2.06334 q^{8} +1.00000 q^{9} +0.368393 q^{10} +2.45014 q^{11} -2.92934 q^{12} -0.862086 q^{13} +0.165927 q^{15} -1.27763 q^{16} -4.02184 q^{17} -2.22021 q^{18} -2.72504 q^{19} -0.486057 q^{20} -5.43984 q^{22} -4.73844 q^{23} +2.06334 q^{24} -4.97247 q^{25} +1.91401 q^{26} -1.00000 q^{27} -6.41611 q^{29} -0.368393 q^{30} -4.79993 q^{31} +6.96329 q^{32} -2.45014 q^{33} +8.92935 q^{34} +2.92934 q^{36} -7.78311 q^{37} +6.05018 q^{38} +0.862086 q^{39} +0.342364 q^{40} +1.00000 q^{41} +7.56342 q^{43} +7.17732 q^{44} -0.165927 q^{45} +10.5203 q^{46} -10.2804 q^{47} +1.27763 q^{48} +11.0399 q^{50} +4.02184 q^{51} -2.52535 q^{52} +6.13697 q^{53} +2.22021 q^{54} -0.406545 q^{55} +2.72504 q^{57} +14.2451 q^{58} -8.52045 q^{59} +0.486057 q^{60} +0.773934 q^{61} +10.6569 q^{62} -12.9047 q^{64} +0.143043 q^{65} +5.43984 q^{66} +11.6535 q^{67} -11.7814 q^{68} +4.73844 q^{69} -4.99642 q^{71} -2.06334 q^{72} +15.8299 q^{73} +17.2801 q^{74} +4.97247 q^{75} -7.98259 q^{76} -1.91401 q^{78} +10.2409 q^{79} +0.211993 q^{80} +1.00000 q^{81} -2.22021 q^{82} -5.29386 q^{83} +0.667332 q^{85} -16.7924 q^{86} +6.41611 q^{87} -5.05549 q^{88} -9.60949 q^{89} +0.368393 q^{90} -13.8805 q^{92} +4.79993 q^{93} +22.8246 q^{94} +0.452158 q^{95} -6.96329 q^{96} +18.6836 q^{97} +2.45014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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

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