LMFDB - Embedded newform 6027.2.a.bo.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.95065 q^{2} +1.00000 q^{3} +1.80504 q^{4} +2.46699 q^{5} +1.95065 q^{6} -0.380308 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.95065 q^{2} +1.00000 q^{3} +1.80504 q^{4} +2.46699 q^{5} +1.95065 q^{6} -0.380308 q^{8} +1.00000 q^{9} +4.81223 q^{10} +3.40967 q^{11} +1.80504 q^{12} +3.78591 q^{13} +2.46699 q^{15} -4.35192 q^{16} -7.48620 q^{17} +1.95065 q^{18} +1.93227 q^{19} +4.45300 q^{20} +6.65108 q^{22} -1.38797 q^{23} -0.380308 q^{24} +1.08602 q^{25} +7.38498 q^{26} +1.00000 q^{27} +4.33428 q^{29} +4.81223 q^{30} +10.1756 q^{31} -7.72845 q^{32} +3.40967 q^{33} -14.6030 q^{34} +1.80504 q^{36} +8.77161 q^{37} +3.76918 q^{38} +3.78591 q^{39} -0.938215 q^{40} -1.00000 q^{41} -5.71076 q^{43} +6.15458 q^{44} +2.46699 q^{45} -2.70744 q^{46} +4.34350 q^{47} -4.35192 q^{48} +2.11845 q^{50} -7.48620 q^{51} +6.83369 q^{52} +4.49496 q^{53} +1.95065 q^{54} +8.41161 q^{55} +1.93227 q^{57} +8.45467 q^{58} +9.48620 q^{59} +4.45300 q^{60} -12.7058 q^{61} +19.8490 q^{62} -6.37167 q^{64} +9.33978 q^{65} +6.65108 q^{66} +8.88133 q^{67} -13.5129 q^{68} -1.38797 q^{69} +16.4496 q^{71} -0.380308 q^{72} -0.523059 q^{73} +17.1103 q^{74} +1.08602 q^{75} +3.48781 q^{76} +7.38498 q^{78} -11.0022 q^{79} -10.7361 q^{80} +1.00000 q^{81} -1.95065 q^{82} +14.1159 q^{83} -18.4684 q^{85} -11.1397 q^{86} +4.33428 q^{87} -1.29673 q^{88} -18.8161 q^{89} +4.81223 q^{90} -2.50533 q^{92} +10.1756 q^{93} +8.47265 q^{94} +4.76688 q^{95} -7.72845 q^{96} -8.05622 q^{97} +3.40967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.95065	1.37932	0.689659	−	0.724134i	$-0.257760\pi$
$2$	1.95065	1.37932	0.689659	+	0.724134i	$0.257760\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.80504	0.902518
$5$	2.46699	1.10327	0.551635	−	0.834086i	$-0.314004\pi$
$5$	2.46699	1.10327	0.551635	+	0.834086i	$0.314004\pi$
$6$	1.95065	0.796349
$7$	0	0
$7$	0	0
$8$	−0.380308	−0.134459
$9$	1.00000	0.333333
$10$	4.81223	1.52176
$11$	3.40967	1.02805	0.514027	−	0.857774i	$-0.328153\pi$
$11$	3.40967	1.02805	0.514027	+	0.857774i	$0.328153\pi$
$12$	1.80504	0.521069
$13$	3.78591	1.05002	0.525011	−	0.851096i	$-0.324061\pi$
$13$	3.78591	1.05002	0.525011	+	0.851096i	$0.324061\pi$
$14$	0	0
$15$	2.46699	0.636973
$16$	−4.35192	−1.08798
$17$	−7.48620	−1.81567	−0.907835	−	0.419327i	$-0.862266\pi$
$17$	−7.48620	−1.81567	−0.907835	+	0.419327i	$0.862266\pi$
$18$	1.95065	0.459773
$19$	1.93227	0.443293	0.221646	−	0.975127i	$-0.428857\pi$
$19$	1.93227	0.443293	0.221646	+	0.975127i	$0.428857\pi$
$20$	4.45300	0.995720
$21$	0	0
$22$	6.65108	1.41801
$23$	−1.38797	−0.289412	−0.144706	−	0.989475i	$-0.546224\pi$
$23$	−1.38797	−0.289412	−0.144706	+	0.989475i	$0.546224\pi$
$24$	−0.380308	−0.0776301
$25$	1.08602	0.217204
$26$	7.38498	1.44831
$27$	1.00000	0.192450
$28$	0	0
$29$	4.33428	0.804856	0.402428	−	0.915452i	$-0.368166\pi$
$29$	4.33428	0.804856	0.402428	+	0.915452i	$0.368166\pi$
$30$	4.81223	0.878588
$31$	10.1756	1.82759	0.913795	−	0.406175i	$-0.133138\pi$
$31$	10.1756	1.82759	0.913795	+	0.406175i	$0.133138\pi$
$32$	−7.72845	−1.36621
$33$	3.40967	0.593548
$34$	−14.6030	−2.50439
$35$	0	0
$36$	1.80504	0.300839
$37$	8.77161	1.44204	0.721022	−	0.692913i	$-0.243673\pi$
$37$	8.77161	1.44204	0.721022	+	0.692913i	$0.243673\pi$
$38$	3.76918	0.611441
$39$	3.78591	0.606230
$40$	−0.938215	−0.148345
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−5.71076	−0.870883	−0.435442	−	0.900217i	$-0.643408\pi$
$43$	−5.71076	−0.870883	−0.435442	+	0.900217i	$0.643408\pi$
$44$	6.15458	0.927838
$45$	2.46699	0.367757
$46$	−2.70744	−0.399191
$47$	4.34350	0.633565	0.316782	−	0.948498i	$-0.397398\pi$
$47$	4.34350	0.633565	0.316782	+	0.948498i	$0.397398\pi$
$48$	−4.35192	−0.628145
$49$	0	0
$50$	2.11845	0.299593
$51$	−7.48620	−1.04828
$52$	6.83369	0.947662
$53$	4.49496	0.617430	0.308715	−	0.951155i	$-0.400101\pi$
$53$	4.49496	0.617430	0.308715	+	0.951155i	$0.400101\pi$
$54$	1.95065	0.265450
$55$	8.41161	1.13422
$56$	0	0
$57$	1.93227	0.255935
$58$	8.45467	1.11015
$59$	9.48620	1.23500	0.617499	−	0.786571i	$-0.288146\pi$
$59$	9.48620	1.23500	0.617499	+	0.786571i	$0.288146\pi$
$60$	4.45300	0.574879
$61$	−12.7058	−1.62681	−0.813404	−	0.581699i	$-0.802388\pi$
$61$	−12.7058	−1.62681	−0.813404	+	0.581699i	$0.802388\pi$
$62$	19.8490	2.52083
$63$	0	0
$64$	−6.37167	−0.796459
$65$	9.33978	1.15846
$66$	6.65108	0.818691
$67$	8.88133	1.08503	0.542514	−	0.840047i	$-0.317473\pi$
$67$	8.88133	1.08503	0.542514	+	0.840047i	$0.317473\pi$
$68$	−13.5129	−1.63867
$69$	−1.38797	−0.167092
$70$	0	0
$71$	16.4496	1.95221	0.976106	−	0.217294i	$-0.0697230\pi$
$71$	16.4496	1.95221	0.976106	+	0.217294i	$0.0697230\pi$
$72$	−0.380308	−0.0448198
$73$	−0.523059	−0.0612195	−0.0306097	−	0.999531i	$-0.509745\pi$
$73$	−0.523059	−0.0612195	−0.0306097	+	0.999531i	$0.509745\pi$
$74$	17.1103	1.98904
$75$	1.08602	0.125403
$76$	3.48781	0.400079
$77$	0	0
$78$	7.38498	0.836184
$79$	−11.0022	−1.23784	−0.618922	−	0.785452i	$-0.712430\pi$
$79$	−11.0022	−1.23784	−0.618922	+	0.785452i	$0.712430\pi$
$80$	−10.7361	−1.20033
$81$	1.00000	0.111111
$82$	−1.95065	−0.215413
$83$	14.1159	1.54942	0.774709	−	0.632318i	$-0.217896\pi$
$83$	14.1159	1.54942	0.774709	+	0.632318i	$0.217896\pi$
$84$	0	0
$85$	−18.4684	−2.00317
$86$	−11.1397	−1.20122
$87$	4.33428	0.464684
$88$	−1.29673	−0.138232
$89$	−18.8161	−1.99450	−0.997251	−	0.0740962i	$-0.976393\pi$
$89$	−18.8161	−1.99450	−0.997251	+	0.0740962i	$0.976393\pi$
$90$	4.81223	0.507253
$91$	0	0
$92$	−2.50533	−0.261199
$93$	10.1756	1.05516
$94$	8.47265	0.873887
$95$	4.76688	0.489071
$96$	−7.72845	−0.788782
$97$	−8.05622	−0.817985	−0.408993	−	0.912538i	$-0.634120\pi$
$97$	−8.05622	−0.817985	−0.408993	+	0.912538i	$0.634120\pi$
$98$	0	0
$99$	3.40967	0.342685
$100$	1.96030	0.196030
$101$	−19.1657	−1.90706	−0.953529	−	0.301302i	$-0.902579\pi$
$101$	−19.1657	−1.90706	−0.953529	+	0.301302i	$0.902579\pi$
$102$	−14.6030	−1.44591
$103$	−15.3244	−1.50996	−0.754979	−	0.655749i	$-0.772353\pi$
$103$	−15.3244	−1.50996	−0.754979	+	0.655749i	$0.772353\pi$
$104$	−1.43981	−0.141185
$105$	0	0
$106$	8.76810	0.851633
$107$	8.53803	0.825403	0.412701	−	0.910866i	$-0.364585\pi$
$107$	8.53803	0.825403	0.412701	+	0.910866i	$0.364585\pi$
$108$	1.80504	0.173690
$109$	14.3317	1.37273	0.686366	−	0.727256i	$-0.259205\pi$
$109$	14.3317	1.37273	0.686366	+	0.727256i	$0.259205\pi$
$110$	16.4081	1.56445
$111$	8.77161	0.832564
$112$	0	0
$113$	0.0125194	0.00117773	0.000588865	−	1.00000i	$-0.499813\pi$
$113$	0.0125194	0.00117773	0.000588865		1.00000i	$0.499813\pi$
$114$	3.76918	0.353016
$115$	−3.42410	−0.319299
$116$	7.82353	0.726397
$117$	3.78591	0.350007
$118$	18.5043	1.70346
$119$	0	0
$120$	−0.938215	−0.0856469
$121$	0.625868	0.0568971
$122$	−24.7845	−2.24389
$123$	−1.00000	−0.0901670
$124$	18.3673	1.64943
$125$	−9.65573	−0.863635
$126$	0	0
$127$	−2.83107	−0.251217	−0.125608	−	0.992080i	$-0.540088\pi$
$127$	−2.83107	−0.251217	−0.125608	+	0.992080i	$0.540088\pi$
$128$	3.02801	0.267641
$129$	−5.71076	−0.502805
$130$	18.2186	1.59788
$131$	−8.54530	−0.746607	−0.373303	−	0.927709i	$-0.621775\pi$
$131$	−8.54530	−0.746607	−0.373303	+	0.927709i	$0.621775\pi$
$132$	6.15458	0.535687
$133$	0	0
$134$	17.3244	1.49660
$135$	2.46699	0.212324
$136$	2.84706	0.244134
$137$	−3.47348	−0.296760	−0.148380	−	0.988930i	$-0.547406\pi$
$137$	−3.47348	−0.296760	−0.148380	+	0.988930i	$0.547406\pi$
$138$	−2.70744	−0.230473
$139$	2.23775	0.189804	0.0949018	−	0.995487i	$-0.469746\pi$
$139$	2.23775	0.189804	0.0949018	+	0.995487i	$0.469746\pi$
$140$	0	0
$141$	4.34350	0.365789
$142$	32.0875	2.69272
$143$	12.9087	1.07948
$144$	−4.35192	−0.362660
$145$	10.6926	0.887973
$146$	−1.02031	−0.0844411
$147$	0	0
$148$	15.8331	1.30147
$149$	8.91994	0.730750	0.365375	−	0.930860i	$-0.380941\pi$
$149$	8.91994	0.730750	0.365375	+	0.930860i	$0.380941\pi$
$150$	2.11845	0.172970
$151$	−11.9438	−0.971974	−0.485987	−	0.873966i	$-0.661540\pi$
$151$	−11.9438	−0.971974	−0.485987	+	0.873966i	$0.661540\pi$
$152$	−0.734858	−0.0596048
$153$	−7.48620	−0.605223
$154$	0	0
$155$	25.1031	2.01633
$156$	6.83369	0.547133
$157$	−17.3359	−1.38356	−0.691778	−	0.722110i	$-0.743172\pi$
$157$	−17.3359	−1.38356	−0.691778	+	0.722110i	$0.743172\pi$
$158$	−21.4614	−1.70738
$159$	4.49496	0.356474
$160$	−19.0660	−1.50730
$161$	0	0
$162$	1.95065	0.153258
$163$	−1.43399	−0.112319	−0.0561593	−	0.998422i	$-0.517885\pi$
$163$	−1.43399	−0.112319	−0.0561593	+	0.998422i	$0.517885\pi$
$164$	−1.80504	−0.140950
$165$	8.41161	0.654843
$166$	27.5351	2.13714
$167$	−16.8506	−1.30394	−0.651971	−	0.758244i	$-0.726058\pi$
$167$	−16.8506	−1.30394	−0.651971	+	0.758244i	$0.726058\pi$
$168$	0	0
$169$	1.33308	0.102544
$170$	−36.0253	−2.76301
$171$	1.93227	0.147764
$172$	−10.3081	−0.785987
$173$	−2.36949	−0.180149	−0.0900744	−	0.995935i	$-0.528710\pi$
$173$	−2.36949	−0.180149	−0.0900744	+	0.995935i	$0.528710\pi$
$174$	8.45467	0.640947
$175$	0	0
$176$	−14.8386	−1.11850
$177$	9.48620	0.713027
$178$	−36.7036	−2.75105
$179$	−12.3125	−0.920279	−0.460139	−	0.887847i	$-0.652201\pi$
$179$	−12.3125	−0.920279	−0.460139	+	0.887847i	$0.652201\pi$
$180$	4.45300	0.331907
$181$	24.0143	1.78497	0.892483	−	0.451080i	$-0.148961\pi$
$181$	24.0143	1.78497	0.892483	+	0.451080i	$0.148961\pi$
$182$	0	0
$183$	−12.7058	−0.939238
$184$	0.527856	0.0389141
$185$	21.6394	1.59096
$186$	19.8490	1.45540
$187$	−25.5255	−1.86661
$188$	7.84017	0.571803
$189$	0	0
$190$	9.29851	0.674585
$191$	10.0853	0.729747	0.364873	−	0.931057i	$-0.381112\pi$
$191$	10.0853	0.729747	0.364873	+	0.931057i	$0.381112\pi$
$192$	−6.37167	−0.459836
$193$	4.38437	0.315594	0.157797	−	0.987472i	$-0.449561\pi$
$193$	4.38437	0.315594	0.157797	+	0.987472i	$0.449561\pi$
$194$	−15.7149	−1.12826
$195$	9.33978	0.668835
$196$	0	0
$197$	−5.57135	−0.396942	−0.198471	−	0.980107i	$-0.563598\pi$
$197$	−5.57135	−0.396942	−0.198471	+	0.980107i	$0.563598\pi$
$198$	6.65108	0.472672
$199$	−19.2500	−1.36460	−0.682300	−	0.731072i	$-0.739020\pi$
$199$	−19.2500	−1.36460	−0.682300	+	0.731072i	$0.739020\pi$
$200$	−0.413023	−0.0292051
$201$	8.88133	0.626441
$202$	−37.3856	−2.63044
$203$	0	0
$204$	−13.5129	−0.946089
$205$	−2.46699	−0.172302
$206$	−29.8925	−2.08271
$207$	−1.38797	−0.0964705
$208$	−16.4760	−1.14240
$209$	6.58840	0.455729
$210$	0	0
$211$	−5.16241	−0.355395	−0.177698	−	0.984085i	$-0.556865\pi$
$211$	−5.16241	−0.355395	−0.177698	+	0.984085i	$0.556865\pi$
$212$	8.11356	0.557242
$213$	16.4496	1.12711
$214$	16.6547	1.13849
$215$	−14.0884	−0.960819
$216$	−0.380308	−0.0258767
$217$	0	0
$218$	27.9562	1.89343
$219$	−0.523059	−0.0353451
$220$	15.1833	1.02366
$221$	−28.3420	−1.90649
$222$	17.1103	1.14837
$223$	5.91934	0.396388	0.198194	−	0.980163i	$-0.436492\pi$
$223$	5.91934	0.396388	0.198194	+	0.980163i	$0.436492\pi$
$224$	0	0
$225$	1.08602	0.0724014
$226$	0.0244210	0.00162446
$227$	−24.0214	−1.59435	−0.797177	−	0.603746i	$-0.793674\pi$
$227$	−24.0214	−1.59435	−0.797177	+	0.603746i	$0.793674\pi$
$228$	3.48781	0.230986
$229$	−5.99435	−0.396118	−0.198059	−	0.980190i	$-0.563464\pi$
$229$	−5.99435	−0.396118	−0.198059	+	0.980190i	$0.563464\pi$
$230$	−6.67922	−0.440415
$231$	0	0
$232$	−1.64836	−0.108220
$233$	16.8529	1.10407	0.552035	−	0.833821i	$-0.313851\pi$
$233$	16.8529	1.10407	0.552035	+	0.833821i	$0.313851\pi$
$234$	7.38498	0.482771
$235$	10.7154	0.698993
$236$	17.1229	1.11461
$237$	−11.0022	−0.714670
$238$	0	0
$239$	1.05568	0.0682864	0.0341432	−	0.999417i	$-0.489130\pi$
$239$	1.05568	0.0682864	0.0341432	+	0.999417i	$0.489130\pi$
$240$	−10.7361	−0.693014
$241$	29.7927	1.91911	0.959557	−	0.281515i	$-0.0908368\pi$
$241$	29.7927	1.91911	0.959557	+	0.281515i	$0.0908368\pi$
$242$	1.22085	0.0784791
$243$	1.00000	0.0641500
$244$	−22.9344	−1.46822
$245$	0	0
$246$	−1.95065	−0.124369
$247$	7.31538	0.465467
$248$	−3.86986	−0.245737
$249$	14.1159	0.894557
$250$	−18.8350	−1.19123
$251$	16.0282	1.01169	0.505845	−	0.862624i	$-0.331181\pi$
$251$	16.0282	1.01169	0.505845	+	0.862624i	$0.331181\pi$
$252$	0	0
$253$	−4.73252	−0.297531
$254$	−5.52243	−0.346508
$255$	−18.4684	−1.15653
$256$	18.6499	1.16562
$257$	−3.41486	−0.213013	−0.106507	−	0.994312i	$-0.533967\pi$
$257$	−3.41486	−0.213013	−0.106507	+	0.994312i	$0.533967\pi$
$258$	−11.1397	−0.693527
$259$	0	0
$260$	16.8586	1.04553
$261$	4.33428	0.268285
$262$	−16.6689	−1.02981
$263$	−6.96532	−0.429500	−0.214750	−	0.976669i	$-0.568894\pi$
$263$	−6.96532	−0.429500	−0.214750	+	0.976669i	$0.568894\pi$
$264$	−1.29673	−0.0798080
$265$	11.0890	0.681192
$266$	0	0
$267$	−18.8161	−1.15153
$268$	16.0311	0.979256
$269$	7.67353	0.467863	0.233932	−	0.972253i	$-0.424841\pi$
$269$	7.67353	0.467863	0.233932	+	0.972253i	$0.424841\pi$
$270$	4.81223	0.292863
$271$	−28.1522	−1.71013	−0.855063	−	0.518525i	$-0.826481\pi$
$271$	−28.1522	−1.71013	−0.855063	+	0.518525i	$0.826481\pi$
$272$	32.5793	1.97541
$273$	0	0
$274$	−6.77555	−0.409326
$275$	3.70297	0.223298
$276$	−2.50533	−0.150803
$277$	4.85108	0.291473	0.145737	−	0.989323i	$-0.453445\pi$
$277$	4.85108	0.291473	0.145737	+	0.989323i	$0.453445\pi$
$278$	4.36507	0.261800
$279$	10.1756	0.609197
$280$	0	0
$281$	−13.4939	−0.804977	−0.402489	−	0.915425i	$-0.631855\pi$
$281$	−13.4939	−0.804977	−0.402489	+	0.915425i	$0.631855\pi$
$282$	8.47265	0.504539
$283$	−3.39249	−0.201662	−0.100831	−	0.994904i	$-0.532150\pi$
$283$	−3.39249	−0.201662	−0.100831	+	0.994904i	$0.532150\pi$
$284$	29.6922	1.76191
$285$	4.76688	0.282365
$286$	25.1803	1.48895
$287$	0	0
$288$	−7.72845	−0.455403
$289$	39.0432	2.29666
$290$	20.8576	1.22480
$291$	−8.05622	−0.472264
$292$	−0.944140	−0.0552516
$293$	19.8814	1.16148	0.580742	−	0.814088i	$-0.302763\pi$
$293$	19.8814	1.16148	0.580742	+	0.814088i	$0.302763\pi$
$294$	0	0
$295$	23.4023	1.36254
$296$	−3.33592	−0.193896
$297$	3.40967	0.197849
$298$	17.3997	1.00794
$299$	−5.25472	−0.303888
$300$	1.96030	0.113178
$301$	0	0
$302$	−23.2982	−1.34066
$303$	−19.1657	−1.10104
$304$	−8.40907	−0.482293
$305$	−31.3450	−1.79481
$306$	−14.6030	−0.834795
$307$	20.5502	1.17286	0.586431	−	0.809999i	$-0.300533\pi$
$307$	20.5502	1.17286	0.586431	+	0.809999i	$0.300533\pi$
$308$	0	0
$309$	−15.3244	−0.871774
$310$	48.9673	2.78115
$311$	−7.09527	−0.402336	−0.201168	−	0.979557i	$-0.564474\pi$
$311$	−7.09527	−0.402336	−0.201168	+	0.979557i	$0.564474\pi$
$312$	−1.43981	−0.0815133
$313$	−10.8328	−0.612308	−0.306154	−	0.951982i	$-0.599042\pi$
$313$	−10.8328	−0.612308	−0.306154	+	0.951982i	$0.599042\pi$
$314$	−33.8163	−1.90836
$315$	0	0
$316$	−19.8594	−1.11718
$317$	15.8780	0.891799	0.445900	−	0.895083i	$-0.352884\pi$
$317$	15.8780	0.891799	0.445900	+	0.895083i	$0.352884\pi$
$318$	8.76810	0.491690
$319$	14.7785	0.827436
$320$	−15.7188	−0.878709
$321$	8.53803	0.476547
$322$	0	0
$323$	−14.4653	−0.804873
$324$	1.80504	0.100280
$325$	4.11157	0.228069
$326$	−2.79721	−0.154923
$327$	14.3317	0.792548
$328$	0.380308	0.0209990
$329$	0	0
$330$	16.4081	0.903237
$331$	8.57678	0.471423	0.235711	−	0.971823i	$-0.424258\pi$
$331$	8.57678	0.471423	0.235711	+	0.971823i	$0.424258\pi$
$332$	25.4796	1.39838
$333$	8.77161	0.480681
$334$	−32.8697	−1.79855
$335$	21.9101	1.19708
$336$	0	0
$337$	−11.6799	−0.636247	−0.318123	−	0.948049i	$-0.603053\pi$
$337$	−11.6799	−0.636247	−0.318123	+	0.948049i	$0.603053\pi$
$338$	2.60037	0.141441
$339$	0.0125194	0.000679963 0
$340$	−33.3360	−1.80790
$341$	34.6954	1.87886
$342$	3.76918	0.203814
$343$	0	0
$344$	2.17185	0.117098
$345$	−3.42410	−0.184347
$346$	−4.62204	−0.248483
$347$	−8.68399	−0.466181	−0.233091	−	0.972455i	$-0.574884\pi$
$347$	−8.68399	−0.466181	−0.233091	+	0.972455i	$0.574884\pi$
$348$	7.82353	0.419385
$349$	−18.9911	−1.01657	−0.508284	−	0.861189i	$-0.669720\pi$
$349$	−18.9911	−1.01657	−0.508284	+	0.861189i	$0.669720\pi$
$350$	0	0
$351$	3.78591	0.202077
$352$	−26.3515	−1.40454
$353$	11.8748	0.632030	0.316015	−	0.948754i	$-0.397655\pi$
$353$	11.8748	0.632030	0.316015	+	0.948754i	$0.397655\pi$
$354$	18.5043	0.983490
$355$	40.5810	2.15382
$356$	−33.9637	−1.80007
$357$	0	0
$358$	−24.0174	−1.26936
$359$	−30.1157	−1.58944	−0.794722	−	0.606973i	$-0.792384\pi$
$359$	−30.1157	−1.58944	−0.794722	+	0.606973i	$0.792384\pi$
$360$	−0.938215	−0.0494483
$361$	−15.2663	−0.803492
$362$	46.8434	2.46204
$363$	0.625868	0.0328495
$364$	0	0
$365$	−1.29038	−0.0675416
$366$	−24.7845	−1.29551
$367$	4.88812	0.255158	0.127579	−	0.991828i	$-0.459279\pi$
$367$	4.88812	0.255158	0.127579	+	0.991828i	$0.459279\pi$
$368$	6.04033	0.314874
$369$	−1.00000	−0.0520579
$370$	42.2110	2.19444
$371$	0	0
$372$	18.3673	0.952300
$373$	−15.8244	−0.819358	−0.409679	−	0.912230i	$-0.634359\pi$
$373$	−15.8244	−0.819358	−0.409679	+	0.912230i	$0.634359\pi$
$374$	−49.7913	−2.57465
$375$	−9.65573	−0.498620
$376$	−1.65187	−0.0851886
$377$	16.4092	0.845116
$378$	0	0
$379$	13.5020	0.693549	0.346774	−	0.937949i	$-0.387277\pi$
$379$	13.5020	0.693549	0.346774	+	0.937949i	$0.387277\pi$
$380$	8.60438	0.441395
$381$	−2.83107	−0.145040
$382$	19.6729	1.00655
$383$	25.0776	1.28140	0.640702	−	0.767790i	$-0.278643\pi$
$383$	25.0776	1.28140	0.640702	+	0.767790i	$0.278643\pi$
$384$	3.02801	0.154523
$385$	0	0
$386$	8.55238	0.435305
$387$	−5.71076	−0.290294
$388$	−14.5418	−0.738246
$389$	−34.0257	−1.72517	−0.862585	−	0.505912i	$-0.831156\pi$
$389$	−34.0257	−1.72517	−0.862585	+	0.505912i	$0.831156\pi$
$390$	18.2186	0.922536
$391$	10.3906	0.525476
$392$	0	0
$393$	−8.54530	−0.431054
$394$	−10.8677	−0.547509
$395$	−27.1423	−1.36568
$396$	6.15458	0.309279
$397$	2.33249	0.117064	0.0585321	−	0.998286i	$-0.481358\pi$
$397$	2.33249	0.117064	0.0585321	+	0.998286i	$0.481358\pi$
$398$	−37.5501	−1.88222
$399$	0	0
$400$	−4.72627	−0.236314
$401$	−1.65085	−0.0824396	−0.0412198	−	0.999150i	$-0.513124\pi$
$401$	−1.65085	−0.0824396	−0.0412198	+	0.999150i	$0.513124\pi$
$402$	17.3244	0.864061
$403$	38.5238	1.91901
$404$	−34.5947	−1.72115
$405$	2.46699	0.122586
$406$	0	0
$407$	29.9083	1.48250
$408$	2.84706	0.140951
$409$	−9.18226	−0.454033	−0.227017	−	0.973891i	$-0.572897\pi$
$409$	−9.18226	−0.454033	−0.227017	+	0.973891i	$0.572897\pi$
$410$	−4.81223	−0.237659
$411$	−3.47348	−0.171334
$412$	−27.6611	−1.36276
$413$	0	0
$414$	−2.70744	−0.133064
$415$	34.8236	1.70943
$416$	−29.2592	−1.43455
$417$	2.23775	0.109583
$418$	12.8517	0.628595
$419$	3.34417	0.163374	0.0816868	−	0.996658i	$-0.473969\pi$
$419$	3.34417	0.163374	0.0816868	+	0.996658i	$0.473969\pi$
$420$	0	0
$421$	21.9541	1.06998	0.534988	−	0.844860i	$-0.320316\pi$
$421$	21.9541	1.06998	0.534988	+	0.844860i	$0.320316\pi$
$422$	−10.0701	−0.490203
$423$	4.34350	0.211188
$424$	−1.70947	−0.0830193
$425$	−8.13016	−0.394371
$426$	32.0875	1.55464
$427$	0	0
$428$	15.4115	0.744941
$429$	12.9087	0.623238
$430$	−27.4815	−1.32527
$431$	9.23239	0.444709	0.222354	−	0.974966i	$-0.428626\pi$
$431$	9.23239	0.444709	0.222354	+	0.974966i	$0.428626\pi$
$432$	−4.35192	−0.209382
$433$	−17.2047	−0.826807	−0.413403	−	0.910548i	$-0.635660\pi$
$433$	−17.2047	−0.826807	−0.413403	+	0.910548i	$0.635660\pi$
$434$	0	0
$435$	10.6926	0.512672
$436$	25.8693	1.23892
$437$	−2.68193	−0.128294
$438$	−1.02031	−0.0487521
$439$	−40.7622	−1.94548	−0.972738	−	0.231907i	$-0.925503\pi$
$439$	−40.7622	−1.94548	−0.972738	+	0.231907i	$0.925503\pi$
$440$	−3.19901	−0.152507
$441$	0	0
$442$	−55.2854	−2.62966
$443$	15.9825	0.759350	0.379675	−	0.925120i	$-0.376036\pi$
$443$	15.9825	0.759350	0.379675	+	0.925120i	$0.376036\pi$
$444$	15.8331	0.751404
$445$	−46.4190	−2.20047
$446$	11.5466	0.546745
$447$	8.91994	0.421899
$448$	0	0
$449$	27.3328	1.28991	0.644957	−	0.764218i	$-0.276875\pi$
$449$	27.3328	1.28991	0.644957	+	0.764218i	$0.276875\pi$
$450$	2.11845	0.0998645
$451$	−3.40967	−0.160555
$452$	0.0225980	0.00106292
$453$	−11.9438	−0.561169
$454$	−46.8572	−2.19912
$455$	0	0
$456$	−0.734858	−0.0344129
$457$	30.3192	1.41827	0.709136	−	0.705072i	$-0.249085\pi$
$457$	30.3192	1.41827	0.709136	+	0.705072i	$0.249085\pi$
$458$	−11.6929	−0.546373
$459$	−7.48620	−0.349426
$460$	−6.18062	−0.288173
$461$	−14.9967	−0.698465	−0.349232	−	0.937036i	$-0.613558\pi$
$461$	−14.9967	−0.698465	−0.349232	+	0.937036i	$0.613558\pi$
$462$	0	0
$463$	−18.4478	−0.857343	−0.428671	−	0.903461i	$-0.641018\pi$
$463$	−18.4478	−0.857343	−0.428671	+	0.903461i	$0.641018\pi$
$464$	−18.8624	−0.875667
$465$	25.1031	1.16413
$466$	32.8741	1.52286
$467$	14.8885	0.688957	0.344478	−	0.938794i	$-0.388056\pi$
$467$	14.8885	0.688957	0.344478	+	0.938794i	$0.388056\pi$
$468$	6.83369	0.315887
$469$	0	0
$470$	20.9019	0.964133
$471$	−17.3359	−0.798797
$472$	−3.60768	−0.166057
$473$	−19.4718	−0.895316
$474$	−21.4614	−0.985757
$475$	2.09848	0.0962850
$476$	0	0
$477$	4.49496	0.205810
$478$	2.05927	0.0941886
$479$	20.8298	0.951736	0.475868	−	0.879517i	$-0.342134\pi$
$479$	20.8298	0.951736	0.475868	+	0.879517i	$0.342134\pi$
$480$	−19.0660	−0.870239
$481$	33.2085	1.51418
$482$	58.1150	2.64707
$483$	0	0
$484$	1.12971	0.0513506
$485$	−19.8746	−0.902459
$486$	1.95065	0.0884833
$487$	−34.9111	−1.58197	−0.790986	−	0.611834i	$-0.790432\pi$
$487$	−34.9111	−1.58197	−0.790986	+	0.611834i	$0.790432\pi$
$488$	4.83211	0.218740
$489$	−1.43399	−0.0648472
$490$	0	0
$491$	−29.0789	−1.31231	−0.656156	−	0.754625i	$-0.727819\pi$
$491$	−29.0789	−1.31231	−0.656156	+	0.754625i	$0.727819\pi$
$492$	−1.80504	−0.0813773
$493$	−32.4473	−1.46135
$494$	14.2698	0.642026
$495$	8.41161	0.378074
$496$	−44.2834	−1.98838
$497$	0	0
$498$	27.5351	1.23388
$499$	6.60144	0.295521	0.147760	−	0.989023i	$-0.452794\pi$
$499$	6.60144	0.295521	0.147760	+	0.989023i	$0.452794\pi$
$500$	−17.4289	−0.779446
$501$	−16.8506	−0.752831
$502$	31.2654	1.39544
$503$	−32.6788	−1.45708	−0.728539	−	0.685005i	$-0.759800\pi$
$503$	−32.6788	−1.45708	−0.728539	+	0.685005i	$0.759800\pi$
$504$	0	0
$505$	−47.2815	−2.10400
$506$	−9.23149	−0.410390
$507$	1.33308	0.0592040
$508$	−5.11018	−0.226728
$509$	−30.5152	−1.35256	−0.676281	−	0.736644i	$-0.736409\pi$
$509$	−30.5152	−1.35256	−0.676281	+	0.736644i	$0.736409\pi$
$510$	−36.0253	−1.59523
$511$	0	0
$512$	30.3235	1.34012
$513$	1.93227	0.0853117
$514$	−6.66120	−0.293813
$515$	−37.8051	−1.66589
$516$	−10.3081	−0.453790
$517$	14.8099	0.651339
$518$	0	0
$519$	−2.36949	−0.104009
$520$	−3.55199	−0.155765
$521$	−18.8954	−0.827820	−0.413910	−	0.910318i	$-0.635837\pi$
$521$	−18.8954	−0.827820	−0.413910	+	0.910318i	$0.635837\pi$
$522$	8.45467	0.370051
$523$	−9.39131	−0.410653	−0.205327	−	0.978694i	$-0.565826\pi$
$523$	−9.39131	−0.410653	−0.205327	+	0.978694i	$0.565826\pi$
$524$	−15.4246	−0.673826
$525$	0	0
$526$	−13.5869	−0.592417
$527$	−76.1765	−3.31830
$528$	−14.8386	−0.645768
$529$	−21.0735	−0.916241
$530$	21.6308	0.939581
$531$	9.48620	0.411666
$532$	0	0
$533$	−3.78591	−0.163986
$534$	−36.7036	−1.58832
$535$	21.0632	0.910642
$536$	−3.37764	−0.145892
$537$	−12.3125	−0.531323
$538$	14.9684	0.645332
$539$	0	0
$540$	4.45300	0.191626
$541$	7.79461	0.335116	0.167558	−	0.985862i	$-0.446412\pi$
$541$	7.79461	0.335116	0.167558	+	0.985862i	$0.446412\pi$
$542$	−54.9151	−2.35881
$543$	24.0143	1.03055
$544$	57.8567	2.48059
$545$	35.3562	1.51449
$546$	0	0
$547$	32.8239	1.40345	0.701725	−	0.712448i	$-0.252414\pi$
$547$	32.8239	1.40345	0.701725	+	0.712448i	$0.252414\pi$
$548$	−6.26976	−0.267831
$549$	−12.7058	−0.542270
$550$	7.22321	0.307999
$551$	8.37500	0.356787
$552$	0.527856	0.0224671
$553$	0	0
$554$	9.46276	0.402034
$555$	21.6394	0.918543
$556$	4.03922	0.171301
$557$	−8.23895	−0.349096	−0.174548	−	0.984649i	$-0.555846\pi$
$557$	−8.23895	−0.349096	−0.174548	+	0.984649i	$0.555846\pi$
$558$	19.8490	0.840276
$559$	−21.6204	−0.914446
$560$	0	0
$561$	−25.5255	−1.07769
$562$	−26.3218	−1.11032
$563$	−2.24259	−0.0945137	−0.0472569	−	0.998883i	$-0.515048\pi$
$563$	−2.24259	−0.0945137	−0.0472569	+	0.998883i	$0.515048\pi$
$564$	7.84017	0.330131
$565$	0.0308853	0.00129935
$566$	−6.61756	−0.278157
$567$	0	0
$568$	−6.25593	−0.262493
$569$	−22.0558	−0.924625	−0.462313	−	0.886717i	$-0.652980\pi$
$569$	−22.0558	−0.924625	−0.462313	+	0.886717i	$0.652980\pi$
$570$	9.29851	0.389472
$571$	−22.8597	−0.956650	−0.478325	−	0.878183i	$-0.658756\pi$
$571$	−22.8597	−0.956650	−0.478325	+	0.878183i	$0.658756\pi$
$572$	23.3007	0.974249
$573$	10.0853	0.421319
$574$	0	0
$575$	−1.50736	−0.0628614
$576$	−6.37167	−0.265486
$577$	−6.08498	−0.253321	−0.126660	−	0.991946i	$-0.540426\pi$
$577$	−6.08498	−0.253321	−0.126660	+	0.991946i	$0.540426\pi$
$578$	76.1596	3.16782
$579$	4.38437	0.182208
$580$	19.3005	0.801412
$581$	0	0
$582$	−15.7149	−0.651402
$583$	15.3263	0.634752
$584$	0.198924	0.00823152
$585$	9.33978	0.386152
$586$	38.7816	1.60205
$587$	9.48311	0.391410	0.195705	−	0.980663i	$-0.437301\pi$
$587$	9.48311	0.391410	0.195705	+	0.980663i	$0.437301\pi$
$588$	0	0
$589$	19.6620	0.810158
$590$	45.6498	1.87937
$591$	−5.57135	−0.229175
$592$	−38.1733	−1.56891
$593$	26.7188	1.09721	0.548604	−	0.836082i	$-0.315160\pi$
$593$	26.7188	1.09721	0.548604	+	0.836082i	$0.315160\pi$
$594$	6.65108	0.272897
$595$	0	0
$596$	16.1008	0.659514
$597$	−19.2500	−0.787852
$598$	−10.2501	−0.419159
$599$	−10.9319	−0.446667	−0.223333	−	0.974742i	$-0.571694\pi$
$599$	−10.9319	−0.446667	−0.223333	+	0.974742i	$0.571694\pi$
$600$	−0.413023	−0.0168616
$601$	31.5604	1.28738	0.643688	−	0.765288i	$-0.277403\pi$
$601$	31.5604	1.28738	0.643688	+	0.765288i	$0.277403\pi$
$602$	0	0
$603$	8.88133	0.361676
$604$	−21.5590	−0.877224
$605$	1.54401	0.0627728
$606$	−37.3856	−1.51868
$607$	−24.8257	−1.00765	−0.503823	−	0.863807i	$-0.668074\pi$
$607$	−24.8257	−1.00765	−0.503823	+	0.863807i	$0.668074\pi$
$608$	−14.9334	−0.605631
$609$	0	0
$610$	−61.1431	−2.47561
$611$	16.4441	0.665256
$612$	−13.5129	−0.546225
$613$	−17.3856	−0.702198	−0.351099	−	0.936338i	$-0.614192\pi$
$613$	−17.3856	−0.702198	−0.351099	+	0.936338i	$0.614192\pi$
$614$	40.0862	1.61775
$615$	−2.46699	−0.0994785
$616$	0	0
$617$	37.7106	1.51817	0.759085	−	0.650992i	$-0.225647\pi$
$617$	37.7106	1.51817	0.759085	+	0.650992i	$0.225647\pi$
$618$	−29.8925	−1.20245
$619$	−30.7411	−1.23559	−0.617794	−	0.786340i	$-0.711974\pi$
$619$	−30.7411	−1.23559	−0.617794	+	0.786340i	$0.711974\pi$
$620$	45.3119	1.81977
$621$	−1.38797	−0.0556973
$622$	−13.8404	−0.554949
$623$	0	0
$624$	−16.4760	−0.659566
$625$	−29.2507	−1.17003
$626$	−21.1311	−0.844567
$627$	6.58840	0.263115
$628$	−31.2919	−1.24868
$629$	−65.6660	−2.61827
$630$	0	0
$631$	2.48516	0.0989325	0.0494663	−	0.998776i	$-0.484248\pi$
$631$	2.48516	0.0989325	0.0494663	+	0.998776i	$0.484248\pi$
$632$	4.18423	0.166440
$633$	−5.16241	−0.205188
$634$	30.9725	1.23007
$635$	−6.98421	−0.277160
$636$	8.11356	0.321724
$637$	0	0
$638$	28.8277	1.14130
$639$	16.4496	0.650737
$640$	7.47006	0.295280
$641$	−3.47852	−0.137393	−0.0686967	−	0.997638i	$-0.521884\pi$
$641$	−3.47852	−0.137393	−0.0686967	+	0.997638i	$0.521884\pi$
$642$	16.6547	0.657309
$643$	6.66666	0.262907	0.131454	−	0.991322i	$-0.458036\pi$
$643$	6.66666	0.262907	0.131454	+	0.991322i	$0.458036\pi$
$644$	0	0
$645$	−14.0884	−0.554729
$646$	−28.2168	−1.11018
$647$	−12.7615	−0.501707	−0.250853	−	0.968025i	$-0.580711\pi$
$647$	−12.7615	−0.501707	−0.250853	+	0.968025i	$0.580711\pi$
$648$	−0.380308	−0.0149399
$649$	32.3448	1.26965
$650$	8.02023	0.314579
$651$	0	0
$652$	−2.58840	−0.101369
$653$	−48.3605	−1.89249	−0.946247	−	0.323445i	$-0.895159\pi$
$653$	−48.3605	−1.89249	−0.946247	+	0.323445i	$0.895159\pi$
$654$	27.9562	1.09317
$655$	−21.0811	−0.823708
$656$	4.35192	0.169914
$657$	−0.523059	−0.0204065
$658$	0	0
$659$	−31.3864	−1.22264	−0.611320	−	0.791383i	$-0.709361\pi$
$659$	−31.3864	−1.22264	−0.611320	+	0.791383i	$0.709361\pi$
$660$	15.1833	0.591008
$661$	−27.8855	−1.08462	−0.542310	−	0.840178i	$-0.682450\pi$
$661$	−27.8855	−1.08462	−0.542310	+	0.840178i	$0.682450\pi$
$662$	16.7303	0.650242
$663$	−28.3420	−1.10071
$664$	−5.36838	−0.208334
$665$	0	0
$666$	17.1103	0.663012
$667$	−6.01585	−0.232935
$668$	−30.4160	−1.17683
$669$	5.91934	0.228855
$670$	42.7390	1.65115
$671$	−43.3226	−1.67245
$672$	0	0
$673$	−19.8350	−0.764583	−0.382291	−	0.924042i	$-0.624865\pi$
$673$	−19.8350	−0.764583	−0.382291	+	0.924042i	$0.624865\pi$
$674$	−22.7835	−0.877586
$675$	1.08602	0.0418009
$676$	2.40625	0.0925481
$677$	3.64538	0.140103	0.0700517	−	0.997543i	$-0.477684\pi$
$677$	3.64538	0.140103	0.0700517	+	0.997543i	$0.477684\pi$
$678$	0.0244210	0.000937885 0
$679$	0	0
$680$	7.02367	0.269345
$681$	−24.0214	−0.920500
$682$	67.6787	2.59155
$683$	39.2949	1.50358	0.751790	−	0.659403i	$-0.229191\pi$
$683$	39.2949	1.50358	0.751790	+	0.659403i	$0.229191\pi$
$684$	3.48781	0.133360
$685$	−8.56903	−0.327406
$686$	0	0
$687$	−5.99435	−0.228699
$688$	24.8528	0.947503
$689$	17.0175	0.648315
$690$	−6.67922	−0.254274
$691$	−0.957556	−0.0364272	−0.0182136	−	0.999834i	$-0.505798\pi$
$691$	−0.957556	−0.0364272	−0.0182136	+	0.999834i	$0.505798\pi$
$692$	−4.27701	−0.162588
$693$	0	0
$694$	−16.9394	−0.643012
$695$	5.52050	0.209405
$696$	−1.64836	−0.0624811
$697$	7.48620	0.283560
$698$	−37.0449	−1.40217
$699$	16.8529	0.637435
$700$	0	0
$701$	30.4024	1.14828	0.574141	−	0.818757i	$-0.305336\pi$
$701$	30.4024	1.14828	0.574141	+	0.818757i	$0.305336\pi$
$702$	7.38498	0.278728
$703$	16.9491	0.639247
$704$	−21.7253	−0.818803
$705$	10.7154	0.403564
$706$	23.1635	0.871770
$707$	0	0
$708$	17.1229	0.643519
$709$	48.6578	1.82738	0.913691	−	0.406410i	$-0.133220\pi$
$709$	48.6578	1.82738	0.913691	+	0.406410i	$0.133220\pi$
$710$	79.1594	2.97080
$711$	−11.0022	−0.412615
$712$	7.15592	0.268179
$713$	−14.1234	−0.528926
$714$	0	0
$715$	31.8456	1.19096
$716$	−22.2245	−0.830568
$717$	1.05568	0.0394252
$718$	−58.7451	−2.19235
$719$	1.65328	0.0616570	0.0308285	−	0.999525i	$-0.490185\pi$
$719$	1.65328	0.0616570	0.0308285	+	0.999525i	$0.490185\pi$
$720$	−10.7361	−0.400112
$721$	0	0
$722$	−29.7793	−1.10827
$723$	29.7927	1.10800
$724$	43.3466	1.61096
$725$	4.70712	0.174818
$726$	1.22085	0.0453099
$727$	32.4853	1.20481	0.602407	−	0.798189i	$-0.294208\pi$
$727$	32.4853	1.20481	0.602407	+	0.798189i	$0.294208\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.51708	−0.0931613
$731$	42.7519	1.58124
$732$	−22.9344	−0.847679
$733$	18.1869	0.671750	0.335875	−	0.941907i	$-0.390968\pi$
$733$	18.1869	0.671750	0.335875	+	0.941907i	$0.390968\pi$
$734$	9.53501	0.351944
$735$	0	0
$736$	10.7269	0.395397
$737$	30.2824	1.11547
$738$	−1.95065	−0.0718044
$739$	−12.5060	−0.460042	−0.230021	−	0.973186i	$-0.573880\pi$
$739$	−12.5060	−0.460042	−0.230021	+	0.973186i	$0.573880\pi$
$740$	39.0599	1.43587
$741$	7.31538	0.268737
$742$	0	0
$743$	13.6638	0.501277	0.250639	−	0.968081i	$-0.419359\pi$
$743$	13.6638	0.501277	0.250639	+	0.968081i	$0.419359\pi$
$744$	−3.86986	−0.141876
$745$	22.0054	0.806214
$746$	−30.8679	−1.13015
$747$	14.1159	0.516473
$748$	−46.0744	−1.68465
$749$	0	0
$750$	−18.8350	−0.687755
$751$	−25.4172	−0.927487	−0.463743	−	0.885970i	$-0.653494\pi$
$751$	−25.4172	−0.927487	−0.463743	+	0.885970i	$0.653494\pi$
$752$	−18.9026	−0.689305
$753$	16.0282	0.584100
$754$	32.0086	1.16568
$755$	−29.4652	−1.07235
$756$	0	0
$757$	38.3522	1.39393	0.696967	−	0.717103i	$-0.254532\pi$
$757$	38.3522	1.39393	0.696967	+	0.717103i	$0.254532\pi$
$758$	26.3376	0.956624
$759$	−4.73252	−0.171780
$760$	−1.81288	−0.0657602
$761$	3.94762	0.143101	0.0715506	−	0.997437i	$-0.477205\pi$
$761$	3.94762	0.143101	0.0715506	+	0.997437i	$0.477205\pi$
$762$	−5.52243	−0.200056
$763$	0	0
$764$	18.2043	0.658609
$765$	−18.4684	−0.667725
$766$	48.9176	1.76746
$767$	35.9139	1.29677
$768$	18.6499	0.672971
$769$	39.2114	1.41400	0.707000	−	0.707214i	$-0.250048\pi$
$769$	39.2114	1.41400	0.707000	+	0.707214i	$0.250048\pi$
$770$	0	0
$771$	−3.41486	−0.122983
$772$	7.91395	0.284829
$773$	12.5429	0.451137	0.225569	−	0.974227i	$-0.427576\pi$
$773$	12.5429	0.451137	0.225569	+	0.974227i	$0.427576\pi$
$774$	−11.1397	−0.400408
$775$	11.0509	0.396960
$776$	3.06385	0.109986
$777$	0	0
$778$	−66.3722	−2.37956
$779$	−1.93227	−0.0692307
$780$	16.8586	0.603635
$781$	56.0879	2.00698
$782$	20.2685	0.724798
$783$	4.33428	0.154895
$784$	0	0
$785$	−42.7675	−1.52644
$786$	−16.6689	−0.594560
$787$	−40.8000	−1.45436	−0.727182	−	0.686445i	$-0.759170\pi$
$787$	−40.8000	−1.45436	−0.727182	+	0.686445i	$0.759170\pi$
$788$	−10.0565	−0.358247
$789$	−6.96532	−0.247972
$790$	−52.9451	−1.88370
$791$	0	0
$792$	−1.29673	−0.0460772
$793$	−48.1029	−1.70818
$794$	4.54987	0.161469
$795$	11.0890	0.393287
$796$	−34.7470	−1.23158
$797$	22.4983	0.796930	0.398465	−	0.917184i	$-0.369543\pi$
$797$	22.4983	0.796930	0.398465	+	0.917184i	$0.369543\pi$
$798$	0	0
$799$	−32.5163	−1.15034
$800$	−8.39326	−0.296746
$801$	−18.8161	−0.664834
$802$	−3.22023	−0.113710
$803$	−1.78346	−0.0629370
$804$	16.0311	0.565374
$805$	0	0
$806$	75.1465	2.64692
$807$	7.67353	0.270121
$808$	7.28887	0.256422
$809$	32.3502	1.13737	0.568686	−	0.822555i	$-0.307452\pi$
$809$	32.3502	1.13737	0.568686	+	0.822555i	$0.307452\pi$
$810$	4.81223	0.169084
$811$	−41.8941	−1.47110	−0.735551	−	0.677469i	$-0.763077\pi$
$811$	−41.8941	−1.47110	−0.735551	+	0.677469i	$0.763077\pi$
$812$	0	0
$813$	−28.1522	−0.987341
$814$	58.3406	2.04484
$815$	−3.53763	−0.123918
$816$	32.5793	1.14050
$817$	−11.0347	−0.386056
$818$	−17.9114	−0.626256
$819$	0	0
$820$	−4.45300	−0.155505
$821$	−38.7515	−1.35244	−0.676219	−	0.736701i	$-0.736383\pi$
$821$	−38.7515	−1.35244	−0.676219	+	0.736701i	$0.736383\pi$
$822$	−6.77555	−0.236324
$823$	38.8323	1.35361	0.676804	−	0.736163i	$-0.263364\pi$
$823$	38.8323	1.35361	0.676804	+	0.736163i	$0.263364\pi$
$824$	5.82799	0.203028
$825$	3.70297	0.128921
$826$	0	0
$827$	12.4060	0.431397	0.215699	−	0.976460i	$-0.430797\pi$
$827$	12.4060	0.431397	0.215699	+	0.976460i	$0.430797\pi$
$828$	−2.50533	−0.0870664
$829$	−21.5753	−0.749341	−0.374670	−	0.927158i	$-0.622244\pi$
$829$	−21.5753	−0.749341	−0.374670	+	0.927158i	$0.622244\pi$
$830$	67.9287	2.35784
$831$	4.85108	0.168282
$832$	−24.1225	−0.836298
$833$	0	0
$834$	4.36507	0.151150
$835$	−41.5703	−1.43860
$836$	11.8923	0.411304
$837$	10.1756	0.351720
$838$	6.52331	0.225344
$839$	9.21299	0.318068	0.159034	−	0.987273i	$-0.449162\pi$
$839$	9.21299	0.318068	0.159034	+	0.987273i	$0.449162\pi$
$840$	0	0
$841$	−10.2140	−0.352207
$842$	42.8247	1.47584
$843$	−13.4939	−0.464754
$844$	−9.31834	−0.320750
$845$	3.28868	0.113134
$846$	8.47265	0.291296
$847$	0	0
$848$	−19.5617	−0.671752
$849$	−3.39249	−0.116430
$850$	−15.8591	−0.543963
$851$	−12.1747	−0.417344
$852$	29.6922	1.01724
$853$	12.8696	0.440646	0.220323	−	0.975427i	$-0.429289\pi$
$853$	12.8696	0.440646	0.220323	+	0.975427i	$0.429289\pi$
$854$	0	0
$855$	4.76688	0.163024
$856$	−3.24709	−0.110983
$857$	−0.400158	−0.0136691	−0.00683457	−	0.999977i	$-0.502176\pi$
$857$	−0.400158	−0.0136691	−0.00683457	+	0.999977i	$0.502176\pi$
$858$	25.1803	0.859643
$859$	−28.9248	−0.986902	−0.493451	−	0.869774i	$-0.664265\pi$
$859$	−28.9248	−0.986902	−0.493451	+	0.869774i	$0.664265\pi$
$860$	−25.4300	−0.867156
$861$	0	0
$862$	18.0092	0.613394
$863$	−10.5621	−0.359540	−0.179770	−	0.983709i	$-0.557535\pi$
$863$	−10.5621	−0.359540	−0.179770	+	0.983709i	$0.557535\pi$
$864$	−7.72845	−0.262927
$865$	−5.84550	−0.198753
$866$	−33.5604	−1.14043
$867$	39.0432	1.32598
$868$	0	0
$869$	−37.5139	−1.27257
$870$	20.8576	0.707137
$871$	33.6239	1.13930
$872$	−5.45048	−0.184577
$873$	−8.05622	−0.272662
$874$	−5.23150	−0.176958
$875$	0	0
$876$	−0.944140	−0.0318995
$877$	1.53055	0.0516830	0.0258415	−	0.999666i	$-0.491773\pi$
$877$	1.53055	0.0516830	0.0258415	+	0.999666i	$0.491773\pi$
$878$	−79.5129	−2.68343
$879$	19.8814	0.670583
$880$	−36.6067	−1.23401
$881$	8.25921	0.278260	0.139130	−	0.990274i	$-0.455569\pi$
$881$	8.25921	0.278260	0.139130	+	0.990274i	$0.455569\pi$
$882$	0	0
$883$	16.5389	0.556578	0.278289	−	0.960497i	$-0.410233\pi$
$883$	16.5389	0.556578	0.278289	+	0.960497i	$0.410233\pi$
$884$	−51.1584	−1.72064
$885$	23.4023	0.786661
$886$	31.1762	1.04738
$887$	28.9877	0.973310	0.486655	−	0.873594i	$-0.338217\pi$
$887$	28.9877	0.973310	0.486655	+	0.873594i	$0.338217\pi$
$888$	−3.33592	−0.111946
$889$	0	0
$890$	−90.5473	−3.03515
$891$	3.40967	0.114228
$892$	10.6846	0.357747
$893$	8.39281	0.280855
$894$	17.3997	0.581932
$895$	−30.3747	−1.01532
$896$	0	0
$897$	−5.25472	−0.175450
$898$	53.3167	1.77920
$899$	44.1039	1.47095
$900$	1.96030	0.0653435
$901$	−33.6502	−1.12105
$902$	−6.65108	−0.221457
$903$	0	0
$904$	−0.00476125	−0.000158357 0
$905$	59.2429	1.96930
$906$	−23.2982	−0.774031
$907$	−4.20847	−0.139740	−0.0698700	−	0.997556i	$-0.522258\pi$
$907$	−4.20847	−0.139740	−0.0698700	+	0.997556i	$0.522258\pi$
$908$	−43.3594	−1.43893
$909$	−19.1657	−0.635686
$910$	0	0
$911$	−45.2126	−1.49796	−0.748980	−	0.662593i	$-0.769456\pi$
$911$	−45.2126	−1.49796	−0.748980	+	0.662593i	$0.769456\pi$
$912$	−8.40907	−0.278452
$913$	48.1305	1.59289
$914$	59.1421	1.95625
$915$	−31.3450	−1.03623
$916$	−10.8200	−0.357504
$917$	0	0
$918$	−14.6030	−0.481969
$919$	−39.1541	−1.29158	−0.645788	−	0.763517i	$-0.723471\pi$
$919$	−39.1541	−1.29158	−0.645788	+	0.763517i	$0.723471\pi$
$920$	1.30221	0.0429327
$921$	20.5502	0.677152
$922$	−29.2533	−0.963405
$923$	62.2768	2.04986
$924$	0	0
$925$	9.52614	0.313218
$926$	−35.9852	−1.18255
$927$	−15.3244	−0.503319
$928$	−33.4973	−1.09960
$929$	13.0337	0.427621	0.213811	−	0.976875i	$-0.431412\pi$
$929$	13.0337	0.427621	0.213811	+	0.976875i	$0.431412\pi$
$930$	48.9673	1.60570
$931$	0	0
$932$	30.4201	0.996442
$933$	−7.09527	−0.232289
$934$	29.0422	0.950290
$935$	−62.9710	−2.05937
$936$	−1.43981	−0.0470617
$937$	−27.4537	−0.896874	−0.448437	−	0.893815i	$-0.648019\pi$
$937$	−27.4537	−0.896874	−0.448437	+	0.893815i	$0.648019\pi$
$938$	0	0
$939$	−10.8328	−0.353516
$940$	19.3416	0.630853
$941$	52.6685	1.71694	0.858472	−	0.512861i	$-0.171414\pi$
$941$	52.6685	1.71694	0.858472	+	0.512861i	$0.171414\pi$
$942$	−33.8163	−1.10179
$943$	1.38797	0.0451985
$944$	−41.2832	−1.34365
$945$	0	0
$946$	−37.9827	−1.23492
$947$	−35.1078	−1.14085	−0.570425	−	0.821350i	$-0.693221\pi$
$947$	−35.1078	−1.14085	−0.570425	+	0.821350i	$0.693221\pi$
$948$	−19.8594	−0.645002
$949$	−1.98025	−0.0642817
$950$	4.09340	0.132808
$951$	15.8780	0.514880
$952$	0	0
$953$	19.7506	0.639784	0.319892	−	0.947454i	$-0.396353\pi$
$953$	19.7506	0.639784	0.319892	+	0.947454i	$0.396353\pi$
$954$	8.76810	0.283878
$955$	24.8803	0.805107
$956$	1.90554	0.0616297
$957$	14.7785	0.477721
$958$	40.6316	1.31275
$959$	0	0
$960$	−15.7188	−0.507323
$961$	72.5427	2.34009
$962$	64.7781	2.08853
$963$	8.53803	0.275134
$964$	53.7768	1.73203
$965$	10.8162	0.348186
$966$	0	0
$967$	15.7402	0.506171	0.253085	−	0.967444i	$-0.418555\pi$
$967$	15.7402	0.506171	0.253085	+	0.967444i	$0.418555\pi$
$968$	−0.238023	−0.00765034
$969$	−14.4653	−0.464694
$970$	−38.7684	−1.24478
$971$	−16.8101	−0.539462	−0.269731	−	0.962936i	$-0.586935\pi$
$971$	−16.8101	−0.539462	−0.269731	+	0.962936i	$0.586935\pi$
$972$	1.80504	0.0578965
$973$	0	0
$974$	−68.0993	−2.18204
$975$	4.11157	0.131676
$976$	55.2945	1.76993
$977$	4.71491	0.150843	0.0754217	−	0.997152i	$-0.475970\pi$
$977$	4.71491	0.150843	0.0754217	+	0.997152i	$0.475970\pi$
$978$	−2.79721	−0.0894448
$979$	−64.1567	−2.05046
$980$	0	0
$981$	14.3317	0.457578
$982$	−56.7228	−1.81010
$983$	24.6443	0.786032	0.393016	−	0.919532i	$-0.371432\pi$
$983$	24.6443	0.786032	0.393016	+	0.919532i	$0.371432\pi$
$984$	0.380308	0.0121238
$985$	−13.7444	−0.437934
$986$	−63.2933	−2.01567
$987$	0	0
$988$	13.2045	0.420092
$989$	7.92636	0.252044
$990$	16.4081	0.521484
$991$	0.939287	0.0298374	0.0149187	−	0.999889i	$-0.495251\pi$
$991$	0.939287	0.0298374	0.0149187	+	0.999889i	$0.495251\pi$
$992$	−78.6416	−2.49687
$993$	8.57678	0.272176
$994$	0	0
$995$	−47.4896	−1.50552
$996$	25.4796	0.807353
$997$	−20.4352	−0.647188	−0.323594	−	0.946196i	$-0.604891\pi$
$997$	−20.4352	−0.647188	−0.323594	+	0.946196i	$0.604891\pi$
$998$	12.8771	0.407617
$999$	8.77161	0.277521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.18	yes	24
7.6	odd	2		6027.2.a.bn.1.18	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.18	✓	24	7.6	odd	2
6027.2.a.bo.1.18	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.95065 q^{2} +1.00000 q^{3} +1.80504 q^{4} +2.46699 q^{5} +1.95065 q^{6} -0.380308 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.95065 q^{2} +1.00000 q^{3} +1.80504 q^{4} +2.46699 q^{5} +1.95065 q^{6} -0.380308 q^{8} +1.00000 q^{9} +4.81223 q^{10} +3.40967 q^{11} +1.80504 q^{12} +3.78591 q^{13} +2.46699 q^{15} -4.35192 q^{16} -7.48620 q^{17} +1.95065 q^{18} +1.93227 q^{19} +4.45300 q^{20} +6.65108 q^{22} -1.38797 q^{23} -0.380308 q^{24} +1.08602 q^{25} +7.38498 q^{26} +1.00000 q^{27} +4.33428 q^{29} +4.81223 q^{30} +10.1756 q^{31} -7.72845 q^{32} +3.40967 q^{33} -14.6030 q^{34} +1.80504 q^{36} +8.77161 q^{37} +3.76918 q^{38} +3.78591 q^{39} -0.938215 q^{40} -1.00000 q^{41} -5.71076 q^{43} +6.15458 q^{44} +2.46699 q^{45} -2.70744 q^{46} +4.34350 q^{47} -4.35192 q^{48} +2.11845 q^{50} -7.48620 q^{51} +6.83369 q^{52} +4.49496 q^{53} +1.95065 q^{54} +8.41161 q^{55} +1.93227 q^{57} +8.45467 q^{58} +9.48620 q^{59} +4.45300 q^{60} -12.7058 q^{61} +19.8490 q^{62} -6.37167 q^{64} +9.33978 q^{65} +6.65108 q^{66} +8.88133 q^{67} -13.5129 q^{68} -1.38797 q^{69} +16.4496 q^{71} -0.380308 q^{72} -0.523059 q^{73} +17.1103 q^{74} +1.08602 q^{75} +3.48781 q^{76} +7.38498 q^{78} -11.0022 q^{79} -10.7361 q^{80} +1.00000 q^{81} -1.95065 q^{82} +14.1159 q^{83} -18.4684 q^{85} -11.1397 q^{86} +4.33428 q^{87} -1.29673 q^{88} -18.8161 q^{89} +4.81223 q^{90} -2.50533 q^{92} +10.1756 q^{93} +8.47265 q^{94} +4.76688 q^{95} -7.72845 q^{96} -8.05622 q^{97} +3.40967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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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