LMFDB - Embedded newform 6027.2.a.bo.1.4

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			1.4
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)

$f(q)$	$=$	$q-1.96907 q^{2} +1.00000 q^{3} +1.87725 q^{4} -4.10878 q^{5} -1.96907 q^{6} +0.241710 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.96907 q^{2} +1.00000 q^{3} +1.87725 q^{4} -4.10878 q^{5} -1.96907 q^{6} +0.241710 q^{8} +1.00000 q^{9} +8.09048 q^{10} +4.87993 q^{11} +1.87725 q^{12} -2.68737 q^{13} -4.10878 q^{15} -4.23044 q^{16} -3.34460 q^{17} -1.96907 q^{18} -0.186064 q^{19} -7.71319 q^{20} -9.60894 q^{22} +5.74714 q^{23} +0.241710 q^{24} +11.8820 q^{25} +5.29162 q^{26} +1.00000 q^{27} +2.28935 q^{29} +8.09048 q^{30} +0.783246 q^{31} +7.84662 q^{32} +4.87993 q^{33} +6.58576 q^{34} +1.87725 q^{36} +1.26983 q^{37} +0.366374 q^{38} -2.68737 q^{39} -0.993134 q^{40} -1.00000 q^{41} -11.2503 q^{43} +9.16084 q^{44} -4.10878 q^{45} -11.3165 q^{46} +2.29201 q^{47} -4.23044 q^{48} -23.3966 q^{50} -3.34460 q^{51} -5.04485 q^{52} +11.2502 q^{53} -1.96907 q^{54} -20.0506 q^{55} -0.186064 q^{57} -4.50789 q^{58} -11.9843 q^{59} -7.71319 q^{60} -1.36157 q^{61} -1.54227 q^{62} -6.98969 q^{64} +11.0418 q^{65} -9.60894 q^{66} -2.74258 q^{67} -6.27864 q^{68} +5.74714 q^{69} +6.59530 q^{71} +0.241710 q^{72} +3.81962 q^{73} -2.50039 q^{74} +11.8820 q^{75} -0.349289 q^{76} +5.29162 q^{78} -10.7548 q^{79} +17.3819 q^{80} +1.00000 q^{81} +1.96907 q^{82} +3.54877 q^{83} +13.7422 q^{85} +22.1526 q^{86} +2.28935 q^{87} +1.17953 q^{88} +9.08983 q^{89} +8.09048 q^{90} +10.7888 q^{92} +0.783246 q^{93} -4.51313 q^{94} +0.764497 q^{95} +7.84662 q^{96} -10.0278 q^{97} +4.87993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.96907	−1.39234	−0.696172	−	0.717875i	$-0.745115\pi$
$2$	−1.96907	−1.39234	−0.696172	+	0.717875i	$0.745115\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.87725	0.938623
$5$	−4.10878	−1.83750	−0.918750	−	0.394839i	$-0.870800\pi$
$5$	−4.10878	−1.83750	−0.918750	+	0.394839i	$0.870800\pi$
$6$	−1.96907	−0.803870
$7$	0	0
$7$	0	0
$8$	0.241710	0.0854575
$9$	1.00000	0.333333
$10$	8.09048	2.55843
$11$	4.87993	1.47136	0.735678	−	0.677332i	$-0.236864\pi$
$11$	4.87993	1.47136	0.735678	+	0.677332i	$0.236864\pi$
$12$	1.87725	0.541914
$13$	−2.68737	−0.745341	−0.372671	−	0.927964i	$-0.621558\pi$
$13$	−2.68737	−0.745341	−0.372671	+	0.927964i	$0.621558\pi$
$14$	0	0
$15$	−4.10878	−1.06088
$16$	−4.23044	−1.05761
$17$	−3.34460	−0.811184	−0.405592	−	0.914054i	$-0.632935\pi$
$17$	−3.34460	−0.811184	−0.405592	+	0.914054i	$0.632935\pi$
$18$	−1.96907	−0.464115
$19$	−0.186064	−0.0426861	−0.0213431	−	0.999772i	$-0.506794\pi$
$19$	−0.186064	−0.0426861	−0.0213431	+	0.999772i	$0.506794\pi$
$20$	−7.71319	−1.72472
$21$	0	0
$22$	−9.60894	−2.04863
$23$	5.74714	1.19836	0.599181	−	0.800614i	$-0.295493\pi$
$23$	5.74714	1.19836	0.599181	+	0.800614i	$0.295493\pi$
$24$	0.241710	0.0493389
$25$	11.8820	2.37641
$26$	5.29162	1.03777
$27$	1.00000	0.192450
$28$	0	0
$29$	2.28935	0.425121	0.212561	−	0.977148i	$-0.431820\pi$
$29$	2.28935	0.425121	0.212561	+	0.977148i	$0.431820\pi$
$30$	8.09048	1.47711
$31$	0.783246	0.140675	0.0703376	−	0.997523i	$-0.477592\pi$
$31$	0.783246	0.140675	0.0703376	+	0.997523i	$0.477592\pi$
$32$	7.84662	1.38710
$33$	4.87993	0.849488
$34$	6.58576	1.12945
$35$	0	0
$36$	1.87725	0.312874
$37$	1.26983	0.208759	0.104380	−	0.994538i	$-0.466714\pi$
$37$	1.26983	0.208759	0.104380	+	0.994538i	$0.466714\pi$
$38$	0.366374	0.0594338
$39$	−2.68737	−0.430323
$40$	−0.993134	−0.157028
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−11.2503	−1.71565	−0.857824	−	0.513944i	$-0.828184\pi$
$43$	−11.2503	−1.71565	−0.857824	+	0.513944i	$0.828184\pi$
$44$	9.16084	1.38105
$45$	−4.10878	−0.612500
$46$	−11.3165	−1.66853
$47$	2.29201	0.334324	0.167162	−	0.985929i	$-0.446540\pi$
$47$	2.29201	0.334324	0.167162	+	0.985929i	$0.446540\pi$
$48$	−4.23044	−0.610611
$49$	0	0
$50$	−23.3966	−3.30878
$51$	−3.34460	−0.468338
$52$	−5.04485	−0.699595
$53$	11.2502	1.54533	0.772667	−	0.634812i	$-0.218922\pi$
$53$	11.2502	1.54533	0.772667	+	0.634812i	$0.218922\pi$
$54$	−1.96907	−0.267957
$55$	−20.0506	−2.70362
$56$	0	0
$57$	−0.186064	−0.0246448
$58$	−4.50789	−0.591915
$59$	−11.9843	−1.56023	−0.780113	−	0.625639i	$-0.784838\pi$
$59$	−11.9843	−1.56023	−0.780113	+	0.625639i	$0.784838\pi$
$60$	−7.71319	−0.995768
$61$	−1.36157	−0.174331	−0.0871654	−	0.996194i	$-0.527781\pi$
$61$	−1.36157	−0.174331	−0.0871654	+	0.996194i	$0.527781\pi$
$62$	−1.54227	−0.195868
$63$	0	0
$64$	−6.98969	−0.873711
$65$	11.0418	1.36957
$66$	−9.60894	−1.18278
$67$	−2.74258	−0.335059	−0.167529	−	0.985867i	$-0.553579\pi$
$67$	−2.74258	−0.335059	−0.167529	+	0.985867i	$0.553579\pi$
$68$	−6.27864	−0.761397
$69$	5.74714	0.691875
$70$	0	0
$71$	6.59530	0.782719	0.391359	−	0.920238i	$-0.372005\pi$
$71$	6.59530	0.782719	0.391359	+	0.920238i	$0.372005\pi$
$72$	0.241710	0.0284858
$73$	3.81962	0.447053	0.223527	−	0.974698i	$-0.428243\pi$
$73$	3.81962	0.447053	0.223527	+	0.974698i	$0.428243\pi$
$74$	−2.50039	−0.290665
$75$	11.8820	1.37202
$76$	−0.349289	−0.0400662
$77$	0	0
$78$	5.29162	0.599158
$79$	−10.7548	−1.21001	−0.605003	−	0.796223i	$-0.706828\pi$
$79$	−10.7548	−1.21001	−0.605003	+	0.796223i	$0.706828\pi$
$80$	17.3819	1.94336
$81$	1.00000	0.111111
$82$	1.96907	0.217448
$83$	3.54877	0.389528	0.194764	−	0.980850i	$-0.437606\pi$
$83$	3.54877	0.389528	0.194764	+	0.980850i	$0.437606\pi$
$84$	0	0
$85$	13.7422	1.49055
$86$	22.1526	2.38877
$87$	2.28935	0.245444
$88$	1.17953	0.125738
$89$	9.08983	0.963520	0.481760	−	0.876303i	$-0.339998\pi$
$89$	9.08983	0.963520	0.481760	+	0.876303i	$0.339998\pi$
$90$	8.09048	0.852811
$91$	0	0
$92$	10.7888	1.12481
$93$	0.783246	0.0812189
$94$	−4.51313	−0.465494
$95$	0.764497	0.0784357
$96$	7.84662	0.800842
$97$	−10.0278	−1.01817	−0.509083	−	0.860717i	$-0.670015\pi$
$97$	−10.0278	−1.01817	−0.509083	+	0.860717i	$0.670015\pi$
$98$	0	0
$99$	4.87993	0.490452
$100$	22.3055	2.23055
$101$	−5.67306	−0.564490	−0.282245	−	0.959342i	$-0.591079\pi$
$101$	−5.67306	−0.564490	−0.282245	+	0.959342i	$0.591079\pi$
$102$	6.58576	0.652087
$103$	−8.59023	−0.846421	−0.423210	−	0.906031i	$-0.639097\pi$
$103$	−8.59023	−0.846421	−0.423210	+	0.906031i	$0.639097\pi$
$104$	−0.649564	−0.0636950
$105$	0	0
$106$	−22.1525	−2.15164
$107$	−3.10612	−0.300279	−0.150140	−	0.988665i	$-0.547972\pi$
$107$	−3.10612	−0.300279	−0.150140	+	0.988665i	$0.547972\pi$
$108$	1.87725	0.180638
$109$	10.4576	1.00166	0.500830	−	0.865546i	$-0.333028\pi$
$109$	10.4576	1.00166	0.500830	+	0.865546i	$0.333028\pi$
$110$	39.4810	3.76437
$111$	1.26983	0.120527
$112$	0	0
$113$	−8.24364	−0.775497	−0.387748	−	0.921765i	$-0.626747\pi$
$113$	−8.24364	−0.775497	−0.387748	+	0.921765i	$0.626747\pi$
$114$	0.366374	0.0343141
$115$	−23.6137	−2.20199
$116$	4.29767	0.399029
$117$	−2.68737	−0.248447
$118$	23.5980	2.17237
$119$	0	0
$120$	−0.993134	−0.0906603
$121$	12.8138	1.16489
$122$	2.68103	0.242729
$123$	−1.00000	−0.0901670
$124$	1.47035	0.132041
$125$	−28.2768	−2.52915
$126$	0	0
$127$	17.7620	1.57612	0.788060	−	0.615598i	$-0.211086\pi$
$127$	17.7620	1.57612	0.788060	+	0.615598i	$0.211086\pi$
$128$	−1.93004	−0.170593
$129$	−11.2503	−0.990530
$130$	−21.7421	−1.90691
$131$	12.1215	1.05906	0.529529	−	0.848292i	$-0.322369\pi$
$131$	12.1215	1.05906	0.529529	+	0.848292i	$0.322369\pi$
$132$	9.16084	0.797349
$133$	0	0
$134$	5.40033	0.466517
$135$	−4.10878	−0.353627
$136$	−0.808424	−0.0693218
$137$	13.6412	1.16545	0.582725	−	0.812669i	$-0.301986\pi$
$137$	13.6412	1.16545	0.582725	+	0.812669i	$0.301986\pi$
$138$	−11.3165	−0.963328
$139$	−7.04836	−0.597834	−0.298917	−	0.954279i	$-0.596625\pi$
$139$	−7.04836	−0.597834	−0.298917	+	0.954279i	$0.596625\pi$
$140$	0	0
$141$	2.29201	0.193022
$142$	−12.9866	−1.08981
$143$	−13.1142	−1.09666
$144$	−4.23044	−0.352537
$145$	−9.40642	−0.781161
$146$	−7.52112	−0.622452
$147$	0	0
$148$	2.38379	0.195946
$149$	−22.0836	−1.80916	−0.904579	−	0.426305i	$-0.859815\pi$
$149$	−22.0836	−1.80916	−0.904579	+	0.426305i	$0.859815\pi$
$150$	−23.3966	−1.91032
$151$	−13.9955	−1.13894	−0.569469	−	0.822013i	$-0.692851\pi$
$151$	−13.9955	−1.13894	−0.569469	+	0.822013i	$0.692851\pi$
$152$	−0.0449737	−0.00364785
$153$	−3.34460	−0.270395
$154$	0	0
$155$	−3.21818	−0.258491
$156$	−5.04485	−0.403911
$157$	22.2994	1.77968	0.889841	−	0.456270i	$-0.150815\pi$
$157$	22.2994	1.77968	0.889841	+	0.456270i	$0.150815\pi$
$158$	21.1769	1.68475
$159$	11.2502	0.892199
$160$	−32.2400	−2.54880
$161$	0	0
$162$	−1.96907	−0.154705
$163$	−12.0403	−0.943070	−0.471535	−	0.881847i	$-0.656300\pi$
$163$	−12.0403	−0.943070	−0.471535	+	0.881847i	$0.656300\pi$
$164$	−1.87725	−0.146588
$165$	−20.0506	−1.56093
$166$	−6.98778	−0.542357
$167$	8.09156	0.626144	0.313072	−	0.949729i	$-0.398642\pi$
$167$	8.09156	0.626144	0.313072	+	0.949729i	$0.398642\pi$
$168$	0	0
$169$	−5.77806	−0.444466
$170$	−27.0594	−2.07536
$171$	−0.186064	−0.0142287
$172$	−21.1195	−1.61035
$173$	−6.27533	−0.477104	−0.238552	−	0.971130i	$-0.576673\pi$
$173$	−6.27533	−0.477104	−0.238552	+	0.971130i	$0.576673\pi$
$174$	−4.50789	−0.341743
$175$	0	0
$176$	−20.6443	−1.55612
$177$	−11.9843	−0.900797
$178$	−17.8985	−1.34155
$179$	20.9156	1.56331	0.781654	−	0.623712i	$-0.214376\pi$
$179$	20.9156	1.56331	0.781654	+	0.623712i	$0.214376\pi$
$180$	−7.71319	−0.574907
$181$	1.55997	0.115952	0.0579758	−	0.998318i	$-0.481535\pi$
$181$	1.55997	0.115952	0.0579758	+	0.998318i	$0.481535\pi$
$182$	0	0
$183$	−1.36157	−0.100650
$184$	1.38914	0.102409
$185$	−5.21746	−0.383595
$186$	−1.54227	−0.113085
$187$	−16.3214	−1.19354
$188$	4.30267	0.313804
$189$	0	0
$190$	−1.50535	−0.109210
$191$	−17.2164	−1.24574	−0.622868	−	0.782327i	$-0.714033\pi$
$191$	−17.2164	−1.24574	−0.622868	+	0.782327i	$0.714033\pi$
$192$	−6.98969	−0.504437
$193$	−15.9807	−1.15031	−0.575157	−	0.818043i	$-0.695059\pi$
$193$	−15.9807	−1.15031	−0.575157	+	0.818043i	$0.695059\pi$
$194$	19.7454	1.41764
$195$	11.0418	0.790719
$196$	0	0
$197$	9.32916	0.664675	0.332337	−	0.943161i	$-0.392163\pi$
$197$	9.32916	0.664675	0.332337	+	0.943161i	$0.392163\pi$
$198$	−9.60894	−0.682878
$199$	−12.6095	−0.893866	−0.446933	−	0.894567i	$-0.647484\pi$
$199$	−12.6095	−0.893866	−0.446933	+	0.894567i	$0.647484\pi$
$200$	2.87201	0.203082
$201$	−2.74258	−0.193446
$202$	11.1707	0.785965
$203$	0	0
$204$	−6.27864	−0.439593
$205$	4.10878	0.286969
$206$	16.9148	1.17851
$207$	5.74714	0.399454
$208$	11.3687	0.788280
$209$	−0.907982	−0.0628064
$210$	0	0
$211$	−15.9027	−1.09479	−0.547394	−	0.836875i	$-0.684380\pi$
$211$	−15.9027	−1.09479	−0.547394	+	0.836875i	$0.684380\pi$
$212$	21.1194	1.45049
$213$	6.59530	0.451903
$214$	6.11617	0.418092
$215$	46.2248	3.15250
$216$	0.241710	0.0164463
$217$	0	0
$218$	−20.5918	−1.39465
$219$	3.81962	0.258106
$220$	−37.6398	−2.53768
$221$	8.98816	0.604609
$222$	−2.50039	−0.167815
$223$	29.0062	1.94240	0.971199	−	0.238268i	$-0.0765796\pi$
$223$	29.0062	1.94240	0.971199	+	0.238268i	$0.0765796\pi$
$224$	0	0
$225$	11.8820	0.792136
$226$	16.2323	1.07976
$227$	20.3453	1.35036	0.675182	−	0.737651i	$-0.264065\pi$
$227$	20.3453	1.35036	0.675182	+	0.737651i	$0.264065\pi$
$228$	−0.349289	−0.0231322
$229$	24.6741	1.63051	0.815257	−	0.579100i	$-0.196596\pi$
$229$	24.6741	1.63051	0.815257	+	0.579100i	$0.196596\pi$
$230$	46.4971	3.06593
$231$	0	0
$232$	0.553359	0.0363298
$233$	7.08960	0.464455	0.232227	−	0.972661i	$-0.425399\pi$
$233$	7.08960	0.464455	0.232227	+	0.972661i	$0.425399\pi$
$234$	5.29162	0.345924
$235$	−9.41736	−0.614321
$236$	−22.4975	−1.46446
$237$	−10.7548	−0.698598
$238$	0	0
$239$	−19.3453	−1.25134	−0.625672	−	0.780086i	$-0.715175\pi$
$239$	−19.3453	−1.25134	−0.625672	+	0.780086i	$0.715175\pi$
$240$	17.3819	1.12200
$241$	−26.5629	−1.71107	−0.855534	−	0.517747i	$-0.826771\pi$
$241$	−26.5629	−1.71107	−0.855534	+	0.517747i	$0.826771\pi$
$242$	−25.2312	−1.62192
$243$	1.00000	0.0641500
$244$	−2.55600	−0.163631
$245$	0	0
$246$	1.96907	0.125543
$247$	0.500023	0.0318157
$248$	0.189319	0.0120218
$249$	3.54877	0.224894
$250$	55.6790	3.52145
$251$	25.9956	1.64083	0.820414	−	0.571770i	$-0.193743\pi$
$251$	25.9956	1.64083	0.820414	+	0.571770i	$0.193743\pi$
$252$	0	0
$253$	28.0457	1.76322
$254$	−34.9746	−2.19450
$255$	13.7422	0.860570
$256$	17.7798	1.11124
$257$	21.1096	1.31678	0.658391	−	0.752676i	$-0.271237\pi$
$257$	21.1096	1.31678	0.658391	+	0.752676i	$0.271237\pi$
$258$	22.1526	1.37916
$259$	0	0
$260$	20.7282	1.28551
$261$	2.28935	0.141707
$262$	−23.8681	−1.47457
$263$	−10.5110	−0.648136	−0.324068	−	0.946034i	$-0.605051\pi$
$263$	−10.5110	−0.648136	−0.324068	+	0.946034i	$0.605051\pi$
$264$	1.17953	0.0725951
$265$	−46.2245	−2.83955
$266$	0	0
$267$	9.08983	0.556288
$268$	−5.14849	−0.314494
$269$	21.1796	1.29135	0.645673	−	0.763614i	$-0.276577\pi$
$269$	21.1796	1.29135	0.645673	+	0.763614i	$0.276577\pi$
$270$	8.09048	0.492371
$271$	−2.53803	−0.154175	−0.0770873	−	0.997024i	$-0.524562\pi$
$271$	−2.53803	−0.154175	−0.0770873	+	0.997024i	$0.524562\pi$
$272$	14.1491	0.857916
$273$	0	0
$274$	−26.8606	−1.62271
$275$	57.9836	3.49654
$276$	10.7888	0.649410
$277$	20.2870	1.21893	0.609465	−	0.792813i	$-0.291384\pi$
$277$	20.2870	1.21893	0.609465	+	0.792813i	$0.291384\pi$
$278$	13.8787	0.832390
$279$	0.783246	0.0468917
$280$	0	0
$281$	−18.2747	−1.09018	−0.545088	−	0.838379i	$-0.683504\pi$
$281$	−18.2747	−1.09018	−0.545088	+	0.838379i	$0.683504\pi$
$282$	−4.51313	−0.268753
$283$	−4.14431	−0.246354	−0.123177	−	0.992385i	$-0.539308\pi$
$283$	−4.14431	−0.246354	−0.123177	+	0.992385i	$0.539308\pi$
$284$	12.3810	0.734678
$285$	0.764497	0.0452849
$286$	25.8228	1.52693
$287$	0	0
$288$	7.84662	0.462366
$289$	−5.81366	−0.341980
$290$	18.5219	1.08765
$291$	−10.0278	−0.587839
$292$	7.17038	0.419615
$293$	2.08588	0.121859	0.0609293	−	0.998142i	$-0.480594\pi$
$293$	2.08588	0.121859	0.0609293	+	0.998142i	$0.480594\pi$
$294$	0	0
$295$	49.2409	2.86692
$296$	0.306932	0.0178401
$297$	4.87993	0.283163
$298$	43.4842	2.51897
$299$	−15.4447	−0.893189
$300$	22.3055	1.28781
$301$	0	0
$302$	27.5582	1.58579
$303$	−5.67306	−0.325909
$304$	0.787134	0.0451452
$305$	5.59438	0.320333
$306$	6.58576	0.376483
$307$	6.30305	0.359734	0.179867	−	0.983691i	$-0.442433\pi$
$307$	6.30305	0.359734	0.179867	+	0.983691i	$0.442433\pi$
$308$	0	0
$309$	−8.59023	−0.488681
$310$	6.33684	0.359908
$311$	16.3846	0.929083	0.464541	−	0.885551i	$-0.346219\pi$
$311$	16.3846	0.929083	0.464541	+	0.885551i	$0.346219\pi$
$312$	−0.649564	−0.0367743
$313$	−14.1093	−0.797504	−0.398752	−	0.917059i	$-0.630557\pi$
$313$	−14.1093	−0.797504	−0.398752	+	0.917059i	$0.630557\pi$
$314$	−43.9091	−2.47793
$315$	0	0
$316$	−20.1894	−1.13574
$317$	6.97987	0.392029	0.196014	−	0.980601i	$-0.437200\pi$
$317$	6.97987	0.392029	0.196014	+	0.980601i	$0.437200\pi$
$318$	−22.1525	−1.24225
$319$	11.1719	0.625505
$320$	28.7191	1.60544
$321$	−3.10612	−0.173366
$322$	0	0
$323$	0.622311	0.0346263
$324$	1.87725	0.104291
$325$	−31.9314	−1.77124
$326$	23.7082	1.31308
$327$	10.4576	0.578308
$328$	−0.241710	−0.0133462
$329$	0	0
$330$	39.4810	2.17336
$331$	10.6727	0.586626	0.293313	−	0.956016i	$-0.405242\pi$
$331$	10.6727	0.586626	0.293313	+	0.956016i	$0.405242\pi$
$332$	6.66192	0.365620
$333$	1.26983	0.0695864
$334$	−15.9329	−0.871808
$335$	11.2686	0.615671
$336$	0	0
$337$	−5.30369	−0.288910	−0.144455	−	0.989511i	$-0.546143\pi$
$337$	−5.30369	−0.288910	−0.144455	+	0.989511i	$0.546143\pi$
$338$	11.3774	0.618850
$339$	−8.24364	−0.447733
$340$	25.7975	1.39907
$341$	3.82219	0.206983
$342$	0.366374	0.0198113
$343$	0	0
$344$	−2.71930	−0.146615
$345$	−23.6137	−1.27132
$346$	12.3566	0.664293
$347$	5.01085	0.268996	0.134498	−	0.990914i	$-0.457058\pi$
$347$	5.01085	0.268996	0.134498	+	0.990914i	$0.457058\pi$
$348$	4.29767	0.230379
$349$	30.8522	1.65148	0.825740	−	0.564051i	$-0.190758\pi$
$349$	30.8522	1.65148	0.825740	+	0.564051i	$0.190758\pi$
$350$	0	0
$351$	−2.68737	−0.143441
$352$	38.2910	2.04092
$353$	−6.06809	−0.322972	−0.161486	−	0.986875i	$-0.551629\pi$
$353$	−6.06809	−0.322972	−0.161486	+	0.986875i	$0.551629\pi$
$354$	23.5980	1.25422
$355$	−27.0986	−1.43825
$356$	17.0638	0.904382
$357$	0	0
$358$	−41.1844	−2.17666
$359$	14.9483	0.788940	0.394470	−	0.918909i	$-0.370928\pi$
$359$	14.9483	0.788940	0.394470	+	0.918909i	$0.370928\pi$
$360$	−0.993134	−0.0523427
$361$	−18.9654	−0.998178
$362$	−3.07169	−0.161445
$363$	12.8138	0.672548
$364$	0	0
$365$	−15.6940	−0.821461
$366$	2.68103	0.140139
$367$	24.3316	1.27010	0.635051	−	0.772470i	$-0.280979\pi$
$367$	24.3316	1.27010	0.635051	+	0.772470i	$0.280979\pi$
$368$	−24.3129	−1.26740
$369$	−1.00000	−0.0520579
$370$	10.2736	0.534097
$371$	0	0
$372$	1.47035	0.0762339
$373$	−24.1138	−1.24856	−0.624281	−	0.781200i	$-0.714608\pi$
$373$	−24.1138	−1.24856	−0.624281	+	0.781200i	$0.714608\pi$
$374$	32.1381	1.66182
$375$	−28.2768	−1.46021
$376$	0.554003	0.0285705
$377$	−6.15232	−0.316861
$378$	0	0
$379$	38.8760	1.99692	0.998462	−	0.0554442i	$-0.0176575\pi$
$379$	38.8760	1.99692	0.998462	+	0.0554442i	$0.0176575\pi$
$380$	1.43515	0.0736216
$381$	17.7620	0.909973
$382$	33.9004	1.73449
$383$	2.85283	0.145773	0.0728865	−	0.997340i	$-0.476779\pi$
$383$	2.85283	0.145773	0.0728865	+	0.997340i	$0.476779\pi$
$384$	−1.93004	−0.0984920
$385$	0	0
$386$	31.4671	1.60163
$387$	−11.2503	−0.571882
$388$	−18.8246	−0.955675
$389$	3.62480	0.183785	0.0918924	−	0.995769i	$-0.470708\pi$
$389$	3.62480	0.183785	0.0918924	+	0.995769i	$0.470708\pi$
$390$	−21.7421	−1.10095
$391$	−19.2219	−0.972093
$392$	0	0
$393$	12.1215	0.611448
$394$	−18.3698	−0.925456
$395$	44.1890	2.22339
$396$	9.16084	0.460350
$397$	−24.5418	−1.23172	−0.615859	−	0.787857i	$-0.711191\pi$
$397$	−24.5418	−1.23172	−0.615859	+	0.787857i	$0.711191\pi$
$398$	24.8291	1.24457
$399$	0	0
$400$	−50.2662	−2.51331
$401$	−16.6130	−0.829612	−0.414806	−	0.909910i	$-0.636151\pi$
$401$	−16.6130	−0.829612	−0.414806	+	0.909910i	$0.636151\pi$
$402$	5.40033	0.269344
$403$	−2.10487	−0.104851
$404$	−10.6497	−0.529844
$405$	−4.10878	−0.204167
$406$	0	0
$407$	6.19670	0.307159
$408$	−0.808424	−0.0400230
$409$	6.47251	0.320045	0.160023	−	0.987113i	$-0.448843\pi$
$409$	6.47251	0.320045	0.160023	+	0.987113i	$0.448843\pi$
$410$	−8.09048	−0.399560
$411$	13.6412	0.672873
$412$	−16.1260	−0.794470
$413$	0	0
$414$	−11.3165	−0.556178
$415$	−14.5811	−0.715758
$416$	−21.0867	−1.03386
$417$	−7.04836	−0.345159
$418$	1.78788	0.0874482
$419$	36.5645	1.78629	0.893145	−	0.449768i	$-0.148493\pi$
$419$	36.5645	1.78629	0.893145	+	0.449768i	$0.148493\pi$
$420$	0	0
$421$	19.5817	0.954352	0.477176	−	0.878808i	$-0.341660\pi$
$421$	19.5817	0.954352	0.477176	+	0.878808i	$0.341660\pi$
$422$	31.3136	1.52432
$423$	2.29201	0.111441
$424$	2.71929	0.132060
$425$	−39.7407	−1.92771
$426$	−12.9866	−0.629204
$427$	0	0
$428$	−5.83094	−0.281849
$429$	−13.1142	−0.633158
$430$	−91.0199	−4.38937
$431$	−14.7266	−0.709358	−0.354679	−	0.934988i	$-0.615410\pi$
$431$	−14.7266	−0.709358	−0.354679	+	0.934988i	$0.615410\pi$
$432$	−4.23044	−0.203537
$433$	36.9867	1.77747	0.888734	−	0.458423i	$-0.151586\pi$
$433$	36.9867	1.77747	0.888734	+	0.458423i	$0.151586\pi$
$434$	0	0
$435$	−9.40642	−0.451003
$436$	19.6316	0.940181
$437$	−1.06934	−0.0511534
$438$	−7.52112	−0.359373
$439$	37.3318	1.78175	0.890875	−	0.454248i	$-0.150092\pi$
$439$	37.3318	1.78175	0.890875	+	0.454248i	$0.150092\pi$
$440$	−4.84643	−0.231044
$441$	0	0
$442$	−17.6983	−0.841824
$443$	12.9322	0.614427	0.307214	−	0.951641i	$-0.400603\pi$
$443$	12.9322	0.614427	0.307214	+	0.951641i	$0.400603\pi$
$444$	2.38379	0.113130
$445$	−37.3481	−1.77047
$446$	−57.1153	−2.70449
$447$	−22.0836	−1.04452
$448$	0	0
$449$	16.2013	0.764585	0.382293	−	0.924041i	$-0.375135\pi$
$449$	16.2013	0.764585	0.382293	+	0.924041i	$0.375135\pi$
$450$	−23.3966	−1.10293
$451$	−4.87993	−0.229787
$452$	−15.4754	−0.727899
$453$	−13.9955	−0.657566
$454$	−40.0613	−1.88017
$455$	0	0
$456$	−0.0449737	−0.00210609
$457$	34.1158	1.59587	0.797934	−	0.602745i	$-0.205926\pi$
$457$	34.1158	1.59587	0.797934	+	0.602745i	$0.205926\pi$
$458$	−48.5852	−2.27024
$459$	−3.34460	−0.156113
$460$	−44.3288	−2.06684
$461$	−4.85915	−0.226313	−0.113157	−	0.993577i	$-0.536096\pi$
$461$	−4.85915	−0.226313	−0.113157	+	0.993577i	$0.536096\pi$
$462$	0	0
$463$	14.8794	0.691505	0.345752	−	0.938326i	$-0.387624\pi$
$463$	14.8794	0.691505	0.345752	+	0.938326i	$0.387624\pi$
$464$	−9.68495	−0.449612
$465$	−3.21818	−0.149240
$466$	−13.9599	−0.646681
$467$	−10.9481	−0.506616	−0.253308	−	0.967386i	$-0.581519\pi$
$467$	−10.9481	−0.506616	−0.253308	+	0.967386i	$0.581519\pi$
$468$	−5.04485	−0.233198
$469$	0	0
$470$	18.5435	0.855346
$471$	22.2994	1.02750
$472$	−2.89673	−0.133333
$473$	−54.9005	−2.52433
$474$	21.1769	0.972689
$475$	−2.21083	−0.101440
$476$	0	0
$477$	11.2502	0.515111
$478$	38.0923	1.74230
$479$	12.9076	0.589765	0.294882	−	0.955534i	$-0.404719\pi$
$479$	12.9076	0.589765	0.294882	+	0.955534i	$0.404719\pi$
$480$	−32.2400	−1.47155
$481$	−3.41251	−0.155597
$482$	52.3043	2.38239
$483$	0	0
$484$	24.0546	1.09339
$485$	41.2019	1.87088
$486$	−1.96907	−0.0893189
$487$	36.1750	1.63925	0.819623	−	0.572903i	$-0.194183\pi$
$487$	36.1750	1.63925	0.819623	+	0.572903i	$0.194183\pi$
$488$	−0.329105	−0.0148979
$489$	−12.0403	−0.544482
$490$	0	0
$491$	−26.5961	−1.20027	−0.600134	−	0.799900i	$-0.704886\pi$
$491$	−26.5961	−1.20027	−0.600134	+	0.799900i	$0.704886\pi$
$492$	−1.87725	−0.0846328
$493$	−7.65695	−0.344852
$494$	−0.984582	−0.0442984
$495$	−20.0506	−0.901206
$496$	−3.31348	−0.148779
$497$	0	0
$498$	−6.98778	−0.313130
$499$	2.92760	0.131058	0.0655288	−	0.997851i	$-0.479127\pi$
$499$	2.92760	0.131058	0.0655288	+	0.997851i	$0.479127\pi$
$500$	−53.0825	−2.37392
$501$	8.09156	0.361504
$502$	−51.1872	−2.28460
$503$	24.7773	1.10477	0.552383	−	0.833590i	$-0.313719\pi$
$503$	24.7773	1.10477	0.552383	+	0.833590i	$0.313719\pi$
$504$	0	0
$505$	23.3093	1.03725
$506$	−55.2240	−2.45501
$507$	−5.77806	−0.256613
$508$	33.3436	1.47938
$509$	0.0377927	0.00167513	0.000837566	−	1.00000i	$-0.499733\pi$
$509$	0.0377927	0.00167513	0.000837566		1.00000i	$0.499733\pi$
$510$	−27.0594	−1.19821
$511$	0	0
$512$	−31.1496	−1.37663
$513$	−0.186064	−0.00821494
$514$	−41.5664	−1.83341
$515$	35.2953	1.55530
$516$	−21.1195	−0.929734
$517$	11.1849	0.491910
$518$	0	0
$519$	−6.27533	−0.275456
$520$	2.66891	0.117040
$521$	−31.0842	−1.36182	−0.680911	−	0.732366i	$-0.738416\pi$
$521$	−31.0842	−1.36182	−0.680911	+	0.732366i	$0.738416\pi$
$522$	−4.50789	−0.197305
$523$	−3.42589	−0.149804	−0.0749018	−	0.997191i	$-0.523864\pi$
$523$	−3.42589	−0.149804	−0.0749018	+	0.997191i	$0.523864\pi$
$524$	22.7550	0.994057
$525$	0	0
$526$	20.6969	0.902428
$527$	−2.61965	−0.114114
$528$	−20.6443	−0.898426
$529$	10.0297	0.436072
$530$	91.0195	3.95363
$531$	−11.9843	−0.520075
$532$	0	0
$533$	2.68737	0.116403
$534$	−17.8985	−0.774545
$535$	12.7623	0.551764
$536$	−0.662909	−0.0286333
$537$	20.9156	0.902576
$538$	−41.7042	−1.79800
$539$	0	0
$540$	−7.71319	−0.331923
$541$	−18.9563	−0.814996	−0.407498	−	0.913206i	$-0.633599\pi$
$541$	−18.9563	−0.814996	−0.407498	+	0.913206i	$0.633599\pi$
$542$	4.99757	0.214664
$543$	1.55997	0.0669447
$544$	−26.2438	−1.12519
$545$	−42.9681	−1.84055
$546$	0	0
$547$	29.9021	1.27852	0.639261	−	0.768989i	$-0.279240\pi$
$547$	29.9021	1.27852	0.639261	+	0.768989i	$0.279240\pi$
$548$	25.6080	1.09392
$549$	−1.36157	−0.0581103
$550$	−114.174	−4.86839
$551$	−0.425966	−0.0181468
$552$	1.38914	0.0591259
$553$	0	0
$554$	−39.9466	−1.69717
$555$	−5.21746	−0.221469
$556$	−13.2315	−0.561141
$557$	39.7964	1.68623	0.843114	−	0.537735i	$-0.180720\pi$
$557$	39.7964	1.68623	0.843114	+	0.537735i	$0.180720\pi$
$558$	−1.54227	−0.0652895
$559$	30.2335	1.27874
$560$	0	0
$561$	−16.3214	−0.689091
$562$	35.9842	1.51790
$563$	19.6406	0.827754	0.413877	−	0.910333i	$-0.364174\pi$
$563$	19.6406	0.827754	0.413877	+	0.910333i	$0.364174\pi$
$564$	4.30267	0.181175
$565$	33.8713	1.42498
$566$	8.16044	0.343009
$567$	0	0
$568$	1.59415	0.0668892
$569$	19.4591	0.815766	0.407883	−	0.913034i	$-0.366267\pi$
$569$	19.4591	0.815766	0.407883	+	0.913034i	$0.366267\pi$
$570$	−1.50535	−0.0630522
$571$	−12.9550	−0.542150	−0.271075	−	0.962558i	$-0.587379\pi$
$571$	−12.9550	−0.542150	−0.271075	+	0.962558i	$0.587379\pi$
$572$	−24.6185	−1.02935
$573$	−17.2164	−0.719226
$574$	0	0
$575$	68.2878	2.84780
$576$	−6.98969	−0.291237
$577$	16.9641	0.706225	0.353113	−	0.935581i	$-0.385123\pi$
$577$	16.9641	0.706225	0.353113	+	0.935581i	$0.385123\pi$
$578$	11.4475	0.476154
$579$	−15.9807	−0.664134
$580$	−17.6582	−0.733216
$581$	0	0
$582$	19.7454	0.818474
$583$	54.9002	2.27373
$584$	0.923243	0.0382041
$585$	11.0418	0.456522
$586$	−4.10725	−0.169669
$587$	−39.4502	−1.62828	−0.814142	−	0.580667i	$-0.802792\pi$
$587$	−39.4502	−1.62828	−0.814142	+	0.580667i	$0.802792\pi$
$588$	0	0
$589$	−0.145734	−0.00600488
$590$	−96.9589	−3.99173
$591$	9.32916	0.383750
$592$	−5.37195	−0.220786
$593$	−12.4924	−0.513003	−0.256501	−	0.966544i	$-0.582570\pi$
$593$	−12.4924	−0.513003	−0.256501	+	0.966544i	$0.582570\pi$
$594$	−9.60894	−0.394260
$595$	0	0
$596$	−41.4564	−1.69812
$597$	−12.6095	−0.516074
$598$	30.4117	1.24363
$599$	−42.6285	−1.74175	−0.870876	−	0.491502i	$-0.836448\pi$
$599$	−42.6285	−1.74175	−0.870876	+	0.491502i	$0.836448\pi$
$600$	2.87201	0.117249
$601$	−45.6087	−1.86042	−0.930210	−	0.367028i	$-0.880375\pi$
$601$	−45.6087	−1.86042	−0.930210	+	0.367028i	$0.880375\pi$
$602$	0	0
$603$	−2.74258	−0.111686
$604$	−26.2730	−1.06903
$605$	−52.6489	−2.14048
$606$	11.1707	0.453777
$607$	−14.2458	−0.578220	−0.289110	−	0.957296i	$-0.593359\pi$
$607$	−14.2458	−0.578220	−0.289110	+	0.957296i	$0.593359\pi$
$608$	−1.45998	−0.0592099
$609$	0	0
$610$	−11.0157	−0.446014
$611$	−6.15947	−0.249186
$612$	−6.27864	−0.253799
$613$	43.8828	1.77241	0.886206	−	0.463292i	$-0.153332\pi$
$613$	43.8828	1.77241	0.886206	+	0.463292i	$0.153332\pi$
$614$	−12.4112	−0.500874
$615$	4.10878	0.165682
$616$	0	0
$617$	41.1419	1.65631	0.828154	−	0.560500i	$-0.189391\pi$
$617$	41.1419	1.65631	0.828154	+	0.560500i	$0.189391\pi$
$618$	16.9148	0.680413
$619$	17.9272	0.720556	0.360278	−	0.932845i	$-0.382682\pi$
$619$	17.9272	0.720556	0.360278	+	0.932845i	$0.382682\pi$
$620$	−6.04133	−0.242625
$621$	5.74714	0.230625
$622$	−32.2624	−1.29360
$623$	0	0
$624$	11.3687	0.455114
$625$	56.7727	2.27091
$626$	27.7822	1.11040
$627$	−0.907982	−0.0362613
$628$	41.8614	1.67045
$629$	−4.24708	−0.169342
$630$	0	0
$631$	10.2409	0.407685	0.203843	−	0.979004i	$-0.434657\pi$
$631$	10.2409	0.407685	0.203843	+	0.979004i	$0.434657\pi$
$632$	−2.59954	−0.103404
$633$	−15.9027	−0.632077
$634$	−13.7439	−0.545839
$635$	−72.9800	−2.89612
$636$	21.1194	0.837438
$637$	0	0
$638$	−21.9982	−0.870918
$639$	6.59530	0.260906
$640$	7.93010	0.313465
$641$	26.1190	1.03164	0.515819	−	0.856697i	$-0.327488\pi$
$641$	26.1190	1.03164	0.515819	+	0.856697i	$0.327488\pi$
$642$	6.11617	0.241386
$643$	21.4692	0.846662	0.423331	−	0.905975i	$-0.360861\pi$
$643$	21.4692	0.846662	0.423331	+	0.905975i	$0.360861\pi$
$644$	0	0
$645$	46.2248	1.82010
$646$	−1.22538	−0.0482117
$647$	0.229609	0.00902684	0.00451342	−	0.999990i	$-0.498563\pi$
$647$	0.229609	0.00902684	0.00451342	+	0.999990i	$0.498563\pi$
$648$	0.241710	0.00949528
$649$	−58.4827	−2.29565
$650$	62.8752	2.46617
$651$	0	0
$652$	−22.6026	−0.885187
$653$	15.5172	0.607234	0.303617	−	0.952794i	$-0.401806\pi$
$653$	15.5172	0.607234	0.303617	+	0.952794i	$0.401806\pi$
$654$	−20.5918	−0.805204
$655$	−49.8044	−1.94602
$656$	4.23044	0.165171
$657$	3.81962	0.149018
$658$	0	0
$659$	43.0279	1.67613	0.838064	−	0.545571i	$-0.183687\pi$
$659$	43.0279	1.67613	0.838064	+	0.545571i	$0.183687\pi$
$660$	−37.6398	−1.46513
$661$	43.4018	1.68814	0.844068	−	0.536236i	$-0.180154\pi$
$661$	43.4018	1.68814	0.844068	+	0.536236i	$0.180154\pi$
$662$	−21.0154	−0.816786
$663$	8.98816	0.349071
$664$	0.857774	0.0332881
$665$	0	0
$666$	−2.50039	−0.0968883
$667$	13.1572	0.509449
$668$	15.1899	0.587713
$669$	29.0062	1.12144
$670$	−22.1887	−0.857226
$671$	−6.64436	−0.256503
$672$	0	0
$673$	−6.47233	−0.249490	−0.124745	−	0.992189i	$-0.539811\pi$
$673$	−6.47233	−0.249490	−0.124745	+	0.992189i	$0.539811\pi$
$674$	10.4433	0.402263
$675$	11.8820	0.457340
$676$	−10.8468	−0.417187
$677$	27.7353	1.06595	0.532977	−	0.846130i	$-0.321073\pi$
$677$	27.7353	1.06595	0.532977	+	0.846130i	$0.321073\pi$
$678$	16.2323	0.623399
$679$	0	0
$680$	3.32163	0.127379
$681$	20.3453	0.779633
$682$	−7.52617	−0.288192
$683$	20.3012	0.776803	0.388401	−	0.921490i	$-0.373027\pi$
$683$	20.3012	0.776803	0.388401	+	0.921490i	$0.373027\pi$
$684$	−0.349289	−0.0133554
$685$	−56.0488	−2.14151
$686$	0	0
$687$	24.6741	0.941378
$688$	47.5935	1.81449
$689$	−30.2334	−1.15180
$690$	46.4971	1.77012
$691$	38.7781	1.47519	0.737593	−	0.675245i	$-0.235962\pi$
$691$	38.7781	1.47519	0.737593	+	0.675245i	$0.235962\pi$
$692$	−11.7803	−0.447821
$693$	0	0
$694$	−9.86672	−0.374535
$695$	28.9601	1.09852
$696$	0.553359	0.0209750
$697$	3.34460	0.126686
$698$	−60.7502	−2.29943
$699$	7.08960	0.268153
$700$	0	0
$701$	5.57108	0.210417	0.105208	−	0.994450i	$-0.466449\pi$
$701$	5.57108	0.210417	0.105208	+	0.994450i	$0.466449\pi$
$702$	5.29162	0.199719
$703$	−0.236271	−0.00891112
$704$	−34.1092	−1.28554
$705$	−9.41736	−0.354678
$706$	11.9485	0.449688
$707$	0	0
$708$	−22.4975	−0.845509
$709$	−17.4267	−0.654473	−0.327236	−	0.944942i	$-0.606117\pi$
$709$	−17.4267	−0.654473	−0.327236	+	0.944942i	$0.606117\pi$
$710$	53.3592	2.00253
$711$	−10.7548	−0.403336
$712$	2.19710	0.0823400
$713$	4.50143	0.168580
$714$	0	0
$715$	53.8832	2.01512
$716$	39.2638	1.46736
$717$	−19.3453	−0.722464
$718$	−29.4343	−1.09848
$719$	−43.7743	−1.63250	−0.816252	−	0.577696i	$-0.803952\pi$
$719$	−43.7743	−1.63250	−0.816252	+	0.577696i	$0.803952\pi$
$720$	17.3819	0.647786
$721$	0	0
$722$	37.3442	1.38981
$723$	−26.5629	−0.987885
$724$	2.92845	0.108835
$725$	27.2021	1.01026
$726$	−25.2312	−0.936418
$727$	−34.2841	−1.27153	−0.635763	−	0.771885i	$-0.719314\pi$
$727$	−34.2841	−1.27153	−0.635763	+	0.771885i	$0.719314\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	30.9026	1.14376
$731$	37.6276	1.39171
$732$	−2.55600	−0.0944724
$733$	20.6748	0.763640	0.381820	−	0.924237i	$-0.375297\pi$
$733$	20.6748	0.763640	0.381820	+	0.924237i	$0.375297\pi$
$734$	−47.9108	−1.76842
$735$	0	0
$736$	45.0956	1.66225
$737$	−13.3836	−0.492991
$738$	1.96907	0.0724826
$739$	−45.0202	−1.65610	−0.828048	−	0.560657i	$-0.810549\pi$
$739$	−45.0202	−1.65610	−0.828048	+	0.560657i	$0.810549\pi$
$740$	−9.79446	−0.360052
$741$	0.500023	0.0183688
$742$	0	0
$743$	−23.4216	−0.859256	−0.429628	−	0.903006i	$-0.641355\pi$
$743$	−23.4216	−0.859256	−0.429628	+	0.903006i	$0.641355\pi$
$744$	0.189319	0.00694076
$745$	90.7366	3.32433
$746$	47.4817	1.73843
$747$	3.54877	0.129843
$748$	−30.6393	−1.12029
$749$	0	0
$750$	55.6790	2.03311
$751$	24.0476	0.877509	0.438754	−	0.898607i	$-0.355420\pi$
$751$	24.0476	0.877509	0.438754	+	0.898607i	$0.355420\pi$
$752$	−9.69621	−0.353584
$753$	25.9956	0.947333
$754$	12.1144	0.441179
$755$	57.5044	2.09280
$756$	0	0
$757$	−52.0114	−1.89039	−0.945194	−	0.326510i	$-0.894127\pi$
$757$	−52.0114	−1.89039	−0.945194	+	0.326510i	$0.894127\pi$
$758$	−76.5496	−2.78041
$759$	28.0457	1.01799
$760$	0.184787	0.00670292
$761$	16.0058	0.580209	0.290104	−	0.956995i	$-0.406310\pi$
$761$	16.0058	0.580209	0.290104	+	0.956995i	$0.406310\pi$
$762$	−34.9746	−1.26700
$763$	0	0
$764$	−32.3195	−1.16928
$765$	13.7422	0.496851
$766$	−5.61743	−0.202966
$767$	32.2063	1.16290
$768$	17.7798	0.641572
$769$	42.7047	1.53997	0.769985	−	0.638062i	$-0.220263\pi$
$769$	42.7047	1.53997	0.769985	+	0.638062i	$0.220263\pi$
$770$	0	0
$771$	21.1096	0.760244
$772$	−29.9997	−1.07971
$773$	−13.8164	−0.496943	−0.248471	−	0.968639i	$-0.579928\pi$
$773$	−13.8164	−0.496943	−0.248471	+	0.968639i	$0.579928\pi$
$774$	22.1526	0.796257
$775$	9.30657	0.334302
$776$	−2.42382	−0.0870100
$777$	0	0
$778$	−7.13750	−0.255892
$779$	0.186064	0.00666645
$780$	20.7282	0.742187
$781$	32.1847	1.15166
$782$	37.8493	1.35349
$783$	2.28935	0.0818147
$784$	0	0
$785$	−91.6231	−3.27017
$786$	−23.8681	−0.851346
$787$	−5.73213	−0.204328	−0.102164	−	0.994768i	$-0.532577\pi$
$787$	−5.73213	−0.204328	−0.102164	+	0.994768i	$0.532577\pi$
$788$	17.5131	0.623879
$789$	−10.5110	−0.374201
$790$	−87.0113	−3.09572
$791$	0	0
$792$	1.17953	0.0419128
$793$	3.65903	0.129936
$794$	48.3246	1.71498
$795$	−46.2245	−1.63942
$796$	−23.6712	−0.839004
$797$	−4.96900	−0.176011	−0.0880055	−	0.996120i	$-0.528049\pi$
$797$	−4.96900	−0.176011	−0.0880055	+	0.996120i	$0.528049\pi$
$798$	0	0
$799$	−7.66586	−0.271198
$800$	93.2339	3.29631
$801$	9.08983	0.321173
$802$	32.7121	1.15511
$803$	18.6395	0.657774
$804$	−5.14849	−0.181573
$805$	0	0
$806$	4.14464	0.145989
$807$	21.1796	0.745559
$808$	−1.37124	−0.0482399
$809$	48.0152	1.68813	0.844063	−	0.536244i	$-0.180157\pi$
$809$	48.0152	1.68813	0.844063	+	0.536244i	$0.180157\pi$
$810$	8.09048	0.284270
$811$	−15.3782	−0.540003	−0.270001	−	0.962860i	$-0.587024\pi$
$811$	−15.3782	−0.540003	−0.270001	+	0.962860i	$0.587024\pi$
$812$	0	0
$813$	−2.53803	−0.0890127
$814$	−12.2018	−0.427671
$815$	49.4709	1.73289
$816$	14.1491	0.495318
$817$	2.09327	0.0732343
$818$	−12.7449	−0.445613
$819$	0	0
$820$	7.71319	0.269356
$821$	−8.08265	−0.282086	−0.141043	−	0.990003i	$-0.545046\pi$
$821$	−8.08265	−0.282086	−0.141043	+	0.990003i	$0.545046\pi$
$822$	−26.8606	−0.936871
$823$	37.3193	1.30087	0.650435	−	0.759562i	$-0.274587\pi$
$823$	37.3193	1.30087	0.650435	+	0.759562i	$0.274587\pi$
$824$	−2.07635	−0.0723330
$825$	57.9836	2.01873
$826$	0	0
$827$	−20.4901	−0.712510	−0.356255	−	0.934389i	$-0.615947\pi$
$827$	−20.4901	−0.712510	−0.356255	+	0.934389i	$0.615947\pi$
$828$	10.7888	0.374937
$829$	32.8011	1.13923	0.569614	−	0.821912i	$-0.307093\pi$
$829$	32.8011	1.13923	0.569614	+	0.821912i	$0.307093\pi$
$830$	28.7112	0.996582
$831$	20.2870	0.703749
$832$	18.7838	0.651213
$833$	0	0
$834$	13.8787	0.480581
$835$	−33.2464	−1.15054
$836$	−1.70451	−0.0589516
$837$	0.783246	0.0270730
$838$	−71.9981	−2.48713
$839$	10.1261	0.349591	0.174796	−	0.984605i	$-0.444074\pi$
$839$	10.1261	0.349591	0.174796	+	0.984605i	$0.444074\pi$
$840$	0	0
$841$	−23.7589	−0.819272
$842$	−38.5577	−1.32879
$843$	−18.2747	−0.629413
$844$	−29.8533	−1.02759
$845$	23.7408	0.816707
$846$	−4.51313	−0.155165
$847$	0	0
$848$	−47.5933	−1.63436
$849$	−4.14431	−0.142232
$850$	78.2523	2.68403
$851$	7.29791	0.250169
$852$	12.3810	0.424167
$853$	−5.07879	−0.173894	−0.0869472	−	0.996213i	$-0.527711\pi$
$853$	−5.07879	−0.173894	−0.0869472	+	0.996213i	$0.527711\pi$
$854$	0	0
$855$	0.764497	0.0261452
$856$	−0.750780	−0.0256611
$857$	−8.24571	−0.281668	−0.140834	−	0.990033i	$-0.544978\pi$
$857$	−8.24571	−0.281668	−0.140834	+	0.990033i	$0.544978\pi$
$858$	25.8228	0.881574
$859$	−55.2489	−1.88507	−0.942533	−	0.334112i	$-0.891564\pi$
$859$	−55.2489	−1.88507	−0.942533	+	0.334112i	$0.891564\pi$
$860$	86.7753	2.95901
$861$	0	0
$862$	28.9978	0.987670
$863$	17.2958	0.588757	0.294378	−	0.955689i	$-0.404887\pi$
$863$	17.2958	0.588757	0.294378	+	0.955689i	$0.404887\pi$
$864$	7.84662	0.266947
$865$	25.7839	0.876679
$866$	−72.8295	−2.47485
$867$	−5.81366	−0.197442
$868$	0	0
$869$	−52.4826	−1.78035
$870$	18.5219	0.627952
$871$	7.37030	0.249733
$872$	2.52772	0.0855993
$873$	−10.0278	−0.339389
$874$	2.10561	0.0712232
$875$	0	0
$876$	7.17038	0.242265
$877$	45.7039	1.54331	0.771656	−	0.636040i	$-0.219429\pi$
$877$	45.7039	1.54331	0.771656	+	0.636040i	$0.219429\pi$
$878$	−73.5091	−2.48081
$879$	2.08588	0.0703550
$880$	84.8227	2.85937
$881$	−42.8769	−1.44456	−0.722279	−	0.691602i	$-0.756905\pi$
$881$	−42.8769	−1.44456	−0.722279	+	0.691602i	$0.756905\pi$
$882$	0	0
$883$	20.6767	0.695826	0.347913	−	0.937527i	$-0.386890\pi$
$883$	20.6767	0.695826	0.347913	+	0.937527i	$0.386890\pi$
$884$	16.8730	0.567500
$885$	49.2409	1.65521
$886$	−25.4644	−0.855495
$887$	−17.4997	−0.587583	−0.293791	−	0.955870i	$-0.594917\pi$
$887$	−17.4997	−0.587583	−0.293791	+	0.955870i	$0.594917\pi$
$888$	0.306932	0.0103000
$889$	0	0
$890$	73.5410	2.46510
$891$	4.87993	0.163484
$892$	54.4518	1.82318
$893$	−0.426462	−0.0142710
$894$	43.4842	1.45433
$895$	−85.9377	−2.87258
$896$	0	0
$897$	−15.4447	−0.515683
$898$	−31.9015	−1.06457
$899$	1.79312	0.0598040
$900$	22.3055	0.743517
$901$	−37.6274	−1.25355
$902$	9.60894	0.319943
$903$	0	0
$904$	−1.99257	−0.0662720
$905$	−6.40956	−0.213061
$906$	27.5582	0.915559
$907$	−23.9979	−0.796837	−0.398418	−	0.917204i	$-0.630441\pi$
$907$	−23.9979	−0.796837	−0.398418	+	0.917204i	$0.630441\pi$
$908$	38.1931	1.26748
$909$	−5.67306	−0.188163
$910$	0	0
$911$	−13.1362	−0.435222	−0.217611	−	0.976036i	$-0.569826\pi$
$911$	−13.1362	−0.435222	−0.217611	+	0.976036i	$0.569826\pi$
$912$	0.787134	0.0260646
$913$	17.3178	0.573134
$914$	−67.1764	−2.22200
$915$	5.59438	0.184944
$916$	46.3195	1.53044
$917$	0	0
$918$	6.58576	0.217362
$919$	30.7304	1.01370	0.506852	−	0.862033i	$-0.330809\pi$
$919$	30.7304	1.01370	0.506852	+	0.862033i	$0.330809\pi$
$920$	−5.70768	−0.188177
$921$	6.30305	0.207693
$922$	9.56803	0.315106
$923$	−17.7240	−0.583392
$924$	0	0
$925$	15.0882	0.496097
$926$	−29.2986	−0.962813
$927$	−8.59023	−0.282140
$928$	17.9636	0.589686
$929$	30.6801	1.00658	0.503292	−	0.864117i	$-0.332122\pi$
$929$	30.6801	1.00658	0.503292	+	0.864117i	$0.332122\pi$
$930$	6.33684	0.207793
$931$	0	0
$932$	13.3089	0.435948
$933$	16.3846	0.536406
$934$	21.5575	0.705384
$935$	67.0611	2.19313
$936$	−0.649564	−0.0212317
$937$	26.1785	0.855214	0.427607	−	0.903965i	$-0.359357\pi$
$937$	26.1785	0.855214	0.427607	+	0.903965i	$0.359357\pi$
$938$	0	0
$939$	−14.1093	−0.460439
$940$	−17.6787	−0.576616
$941$	−19.3605	−0.631135	−0.315567	−	0.948903i	$-0.602195\pi$
$941$	−19.3605	−0.631135	−0.315567	+	0.948903i	$0.602195\pi$
$942$	−43.9091	−1.43063
$943$	−5.74714	−0.187153
$944$	50.6989	1.65011
$945$	0	0
$946$	108.103	3.51473
$947$	28.8451	0.937339	0.468670	−	0.883374i	$-0.344733\pi$
$947$	28.8451	0.937339	0.468670	+	0.883374i	$0.344733\pi$
$948$	−20.1894	−0.655720
$949$	−10.2647	−0.333207
$950$	4.35328	0.141239
$951$	6.97987	0.226338
$952$	0	0
$953$	−38.3762	−1.24313	−0.621563	−	0.783364i	$-0.713502\pi$
$953$	−38.3762	−1.24313	−0.621563	+	0.783364i	$0.713502\pi$
$954$	−22.1525	−0.717212
$955$	70.7384	2.28904
$956$	−36.3159	−1.17454
$957$	11.1719	0.361135
$958$	−25.4161	−0.821156
$959$	0	0
$960$	28.7191	0.926904
$961$	−30.3865	−0.980210
$962$	6.71947	0.216645
$963$	−3.10612	−0.100093
$964$	−49.8651	−1.60605
$965$	65.6610	2.11370
$966$	0	0
$967$	−49.5741	−1.59419	−0.797097	−	0.603851i	$-0.793632\pi$
$967$	−49.5741	−1.59419	−0.797097	+	0.603851i	$0.793632\pi$
$968$	3.09722	0.0995484
$969$	0.622311	0.0199915
$970$	−81.1295	−2.60491
$971$	13.3866	0.429596	0.214798	−	0.976658i	$-0.431091\pi$
$971$	13.3866	0.429596	0.214798	+	0.976658i	$0.431091\pi$
$972$	1.87725	0.0602127
$973$	0	0
$974$	−71.2312	−2.28240
$975$	−31.9314	−1.02262
$976$	5.76003	0.184374
$977$	−9.38029	−0.300102	−0.150051	−	0.988678i	$-0.547944\pi$
$977$	−9.38029	−0.300102	−0.150051	+	0.988678i	$0.547944\pi$
$978$	23.7082	0.758106
$979$	44.3578	1.41768
$980$	0	0
$981$	10.4576	0.333886
$982$	52.3697	1.67119
$983$	−0.842818	−0.0268817	−0.0134409	−	0.999910i	$-0.504278\pi$
$983$	−0.842818	−0.0268817	−0.0134409	+	0.999910i	$0.504278\pi$
$984$	−0.241710	−0.00770544
$985$	−38.3314	−1.22134
$986$	15.0771	0.480153
$987$	0	0
$988$	0.938667	0.0298630
$989$	−64.6568	−2.05597
$990$	39.4810	1.25479
$991$	−59.1465	−1.87885	−0.939425	−	0.342755i	$-0.888640\pi$
$991$	−59.1465	−1.87885	−0.939425	+	0.342755i	$0.888640\pi$
$992$	6.14584	0.195131
$993$	10.6727	0.338689
$994$	0	0
$995$	51.8097	1.64248
$996$	6.66192	0.211091
$997$	−1.87911	−0.0595121	−0.0297560	−	0.999557i	$-0.509473\pi$
$997$	−1.87911	−0.0595121	−0.0297560	+	0.999557i	$0.509473\pi$
$998$	−5.76467	−0.182477
$999$	1.26983	0.0401758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.4	yes	24
7.6	odd	2		6027.2.a.bn.1.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.4	✓	24	7.6	odd	2
6027.2.a.bo.1.4	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)

\(f(q)\)	\(=\)	\(q-1.96907 q^{2} +1.00000 q^{3} +1.87725 q^{4} -4.10878 q^{5} -1.96907 q^{6} +0.241710 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.96907 q^{2} +1.00000 q^{3} +1.87725 q^{4} -4.10878 q^{5} -1.96907 q^{6} +0.241710 q^{8} +1.00000 q^{9} +8.09048 q^{10} +4.87993 q^{11} +1.87725 q^{12} -2.68737 q^{13} -4.10878 q^{15} -4.23044 q^{16} -3.34460 q^{17} -1.96907 q^{18} -0.186064 q^{19} -7.71319 q^{20} -9.60894 q^{22} +5.74714 q^{23} +0.241710 q^{24} +11.8820 q^{25} +5.29162 q^{26} +1.00000 q^{27} +2.28935 q^{29} +8.09048 q^{30} +0.783246 q^{31} +7.84662 q^{32} +4.87993 q^{33} +6.58576 q^{34} +1.87725 q^{36} +1.26983 q^{37} +0.366374 q^{38} -2.68737 q^{39} -0.993134 q^{40} -1.00000 q^{41} -11.2503 q^{43} +9.16084 q^{44} -4.10878 q^{45} -11.3165 q^{46} +2.29201 q^{47} -4.23044 q^{48} -23.3966 q^{50} -3.34460 q^{51} -5.04485 q^{52} +11.2502 q^{53} -1.96907 q^{54} -20.0506 q^{55} -0.186064 q^{57} -4.50789 q^{58} -11.9843 q^{59} -7.71319 q^{60} -1.36157 q^{61} -1.54227 q^{62} -6.98969 q^{64} +11.0418 q^{65} -9.60894 q^{66} -2.74258 q^{67} -6.27864 q^{68} +5.74714 q^{69} +6.59530 q^{71} +0.241710 q^{72} +3.81962 q^{73} -2.50039 q^{74} +11.8820 q^{75} -0.349289 q^{76} +5.29162 q^{78} -10.7548 q^{79} +17.3819 q^{80} +1.00000 q^{81} +1.96907 q^{82} +3.54877 q^{83} +13.7422 q^{85} +22.1526 q^{86} +2.28935 q^{87} +1.17953 q^{88} +9.08983 q^{89} +8.09048 q^{90} +10.7888 q^{92} +0.783246 q^{93} -4.51313 q^{94} +0.764497 q^{95} +7.84662 q^{96} -10.0278 q^{97} +4.87993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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