LMFDB - Embedded newform 6027.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.626512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 4x^{2} + 6x - 2 $ x^5 - 2x^4 - 6x^3 + 4x^2 + 6x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.302390$ of defining polynomial
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)

$f(q)$	$=$	$q+0.697610 q^{2} -1.00000 q^{3} -1.51334 q^{4} -3.10064 q^{5} -0.697610 q^{6} -2.45094 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.697610 q^{2} -1.00000 q^{3} -1.51334 q^{4} -3.10064 q^{5} -0.697610 q^{6} -2.45094 q^{8} +1.00000 q^{9} -2.16304 q^{10} +1.68312 q^{11} +1.51334 q^{12} -1.74552 q^{13} +3.10064 q^{15} +1.31688 q^{16} +0.100642 q^{17} +0.697610 q^{18} -4.73585 q^{19} +4.69233 q^{20} +1.17416 q^{22} +6.23325 q^{23} +2.45094 q^{24} +4.61398 q^{25} -1.21769 q^{26} -1.00000 q^{27} -6.80746 q^{29} +2.16304 q^{30} +0.735855 q^{31} +5.82055 q^{32} -1.68312 q^{33} +0.0702090 q^{34} -1.51334 q^{36} +5.71462 q^{37} -3.30378 q^{38} +1.74552 q^{39} +7.59949 q^{40} +1.00000 q^{41} +2.92604 q^{43} -2.54714 q^{44} -3.10064 q^{45} +4.34838 q^{46} +9.74506 q^{47} -1.31688 q^{48} +3.21876 q^{50} -0.100642 q^{51} +2.64157 q^{52} +3.28116 q^{53} -0.697610 q^{54} -5.21876 q^{55} +4.73585 q^{57} -4.74895 q^{58} +0.705422 q^{59} -4.69233 q^{60} +12.3319 q^{61} +0.513340 q^{62} +1.42672 q^{64} +5.41223 q^{65} -1.17416 q^{66} -5.41898 q^{67} -0.152306 q^{68} -6.23325 q^{69} -8.17523 q^{71} -2.45094 q^{72} -0.0702090 q^{73} +3.98658 q^{74} -4.61398 q^{75} +7.16696 q^{76} +1.21769 q^{78} +9.33236 q^{79} -4.08317 q^{80} +1.00000 q^{81} +0.697610 q^{82} -7.84331 q^{83} -0.312055 q^{85} +2.04123 q^{86} +6.80746 q^{87} -4.12524 q^{88} -2.28790 q^{89} -2.16304 q^{90} -9.43302 q^{92} -0.735855 q^{93} +6.79825 q^{94} +14.6842 q^{95} -5.82055 q^{96} +14.4679 q^{97} +1.68312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} - 5 q^{3} + 7 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 - 5 * q^3 + 7 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 + 5 * q^9	$ 5 q + 3 q^{2} - 5 q^{3} + 7 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} + 5 q^{9} + q^{10} + 4 q^{11} - 7 q^{12} - 5 q^{13} + 3 q^{15} + 11 q^{16} - 12 q^{17} + 3 q^{18} - 10 q^{19} - 9 q^{20} - 6 q^{22} + 9 q^{23} - 3 q^{24} - 4 q^{25} - 13 q^{26} - 5 q^{27} + 7 q^{29} - q^{30} - 10 q^{31} + 9 q^{32} - 4 q^{33} - 10 q^{34} + 7 q^{36} - 11 q^{37} + 5 q^{39} + 7 q^{40} + 5 q^{41} - 2 q^{43} - 3 q^{45} - 9 q^{46} + 7 q^{47} - 11 q^{48} - 10 q^{50} + 12 q^{51} + 11 q^{52} - 9 q^{53} - 3 q^{54} + 10 q^{57} - 31 q^{58} - 8 q^{59} + 9 q^{60} + 6 q^{61} - 12 q^{62} - 29 q^{64} - 13 q^{65} + 6 q^{66} - 9 q^{67} - 12 q^{68} - 9 q^{69} + 4 q^{71} + 3 q^{72} + 10 q^{73} - 17 q^{74} + 4 q^{75} - 36 q^{76} + 13 q^{78} + 7 q^{79} - 9 q^{80} + 5 q^{81} + 3 q^{82} - 50 q^{83} - 12 q^{85} - 8 q^{86} - 7 q^{87} - 38 q^{88} - 8 q^{89} + q^{90} - 17 q^{92} + 10 q^{93} + 21 q^{94} + 36 q^{95} - 9 q^{96} + 11 q^{97} + 4 q^{99}+O(q^{100}) $ 5 * q + 3 * q^2 - 5 * q^3 + 7 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 + 5 * q^9 + q^10 + 4 * q^11 - 7 * q^12 - 5 * q^13 + 3 * q^15 + 11 * q^16 - 12 * q^17 + 3 * q^18 - 10 * q^19 - 9 * q^20 - 6 * q^22 + 9 * q^23 - 3 * q^24 - 4 * q^25 - 13 * q^26 - 5 * q^27 + 7 * q^29 - q^30 - 10 * q^31 + 9 * q^32 - 4 * q^33 - 10 * q^34 + 7 * q^36 - 11 * q^37 + 5 * q^39 + 7 * q^40 + 5 * q^41 - 2 * q^43 - 3 * q^45 - 9 * q^46 + 7 * q^47 - 11 * q^48 - 10 * q^50 + 12 * q^51 + 11 * q^52 - 9 * q^53 - 3 * q^54 + 10 * q^57 - 31 * q^58 - 8 * q^59 + 9 * q^60 + 6 * q^61 - 12 * q^62 - 29 * q^64 - 13 * q^65 + 6 * q^66 - 9 * q^67 - 12 * q^68 - 9 * q^69 + 4 * q^71 + 3 * q^72 + 10 * q^73 - 17 * q^74 + 4 * q^75 - 36 * q^76 + 13 * q^78 + 7 * q^79 - 9 * q^80 + 5 * q^81 + 3 * q^82 - 50 * q^83 - 12 * q^85 - 8 * q^86 - 7 * q^87 - 38 * q^88 - 8 * q^89 + q^90 - 17 * q^92 + 10 * q^93 + 21 * q^94 + 36 * q^95 - 9 * q^96 + 11 * q^97 + 4 * 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 $

$2$	0.697610	0.493285	0.246642	−	0.969107i	$-0.420673\pi$
$2$	0.697610	0.493285	0.246642	+	0.969107i	$0.420673\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.51334	−0.756670
$5$	−3.10064	−1.38665	−0.693325	−	0.720625i	$-0.743855\pi$
$5$	−3.10064	−1.38665	−0.693325	+	0.720625i	$0.743855\pi$
$6$	−0.697610	−0.284798
$7$	0	0
$7$	0	0
$8$	−2.45094	−0.866539
$9$	1.00000	0.333333
$10$	−2.16304	−0.684013
$11$	1.68312	0.507481	0.253740	−	0.967272i	$-0.418339\pi$
$11$	1.68312	0.507481	0.253740	+	0.967272i	$0.418339\pi$
$12$	1.51334	0.436864
$13$	−1.74552	−0.484120	−0.242060	−	0.970261i	$-0.577823\pi$
$13$	−1.74552	−0.484120	−0.242060	+	0.970261i	$0.577823\pi$
$14$	0	0
$15$	3.10064	0.800582
$16$	1.31688	0.329219
$17$	0.100642	0.0244093	0.0122047	−	0.999926i	$-0.496115\pi$
$17$	0.100642	0.0244093	0.0122047	+	0.999926i	$0.496115\pi$
$18$	0.697610	0.164428
$19$	−4.73585	−1.08648	−0.543240	−	0.839578i	$-0.682803\pi$
$19$	−4.73585	−1.08648	−0.543240	+	0.839578i	$0.682803\pi$
$20$	4.69233	1.04924
$21$	0	0
$22$	1.17416	0.250333
$23$	6.23325	1.29972	0.649861	−	0.760053i	$-0.274827\pi$
$23$	6.23325	1.29972	0.649861	+	0.760053i	$0.274827\pi$
$24$	2.45094	0.500296
$25$	4.61398	0.922796
$26$	−1.21769	−0.238809
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.80746	−1.26411	−0.632056	−	0.774922i	$-0.717789\pi$
$29$	−6.80746	−1.26411	−0.632056	+	0.774922i	$0.717789\pi$
$30$	2.16304	0.394915
$31$	0.735855	0.132163	0.0660817	−	0.997814i	$-0.478950\pi$
$31$	0.735855	0.132163	0.0660817	+	0.997814i	$0.478950\pi$
$32$	5.82055	1.02894
$33$	−1.68312	−0.292994
$34$	0.0702090	0.0120408
$35$	0	0
$36$	−1.51334	−0.252223
$37$	5.71462	0.939478	0.469739	−	0.882805i	$-0.344348\pi$
$37$	5.71462	0.939478	0.469739	+	0.882805i	$0.344348\pi$
$38$	−3.30378	−0.535944
$39$	1.74552	0.279507
$40$	7.59949	1.20159
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	2.92604	0.446217	0.223108	−	0.974794i	$-0.428380\pi$
$43$	2.92604	0.446217	0.223108	+	0.974794i	$0.428380\pi$
$44$	−2.54714	−0.383995
$45$	−3.10064	−0.462216
$46$	4.34838	0.641133
$47$	9.74506	1.42146	0.710731	−	0.703464i	$-0.248364\pi$
$47$	9.74506	1.42146	0.710731	+	0.703464i	$0.248364\pi$
$48$	−1.31688	−0.190075
$49$	0	0
$50$	3.21876	0.455202
$51$	−0.100642	−0.0140927
$52$	2.64157	0.366319
$53$	3.28116	0.450702	0.225351	−	0.974278i	$-0.427647\pi$
$53$	3.28116	0.450702	0.225351	+	0.974278i	$0.427647\pi$
$54$	−0.697610	−0.0949327
$55$	−5.21876	−0.703698
$56$	0	0
$57$	4.73585	0.627279
$58$	−4.74895	−0.623568
$59$	0.705422	0.0918381	0.0459190	−	0.998945i	$-0.485378\pi$
$59$	0.705422	0.0918381	0.0459190	+	0.998945i	$0.485378\pi$
$60$	−4.69233	−0.605777
$61$	12.3319	1.57894	0.789470	−	0.613789i	$-0.210355\pi$
$61$	12.3319	1.57894	0.789470	+	0.613789i	$0.210355\pi$
$62$	0.513340	0.0651942
$63$	0	0
$64$	1.42672	0.178340
$65$	5.41223	0.671305
$66$	−1.17416	−0.144530
$67$	−5.41898	−0.662033	−0.331017	−	0.943625i	$-0.607392\pi$
$67$	−5.41898	−0.662033	−0.331017	+	0.943625i	$0.607392\pi$
$68$	−0.152306	−0.0184698
$69$	−6.23325	−0.750395
$70$	0	0
$71$	−8.17523	−0.970222	−0.485111	−	0.874453i	$-0.661221\pi$
$71$	−8.17523	−0.970222	−0.485111	+	0.874453i	$0.661221\pi$
$72$	−2.45094	−0.288846
$73$	−0.0702090	−0.00821735	−0.00410867	−	0.999992i	$-0.501308\pi$
$73$	−0.0702090	−0.00821735	−0.00410867	+	0.999992i	$0.501308\pi$
$74$	3.98658	0.463431
$75$	−4.61398	−0.532777
$76$	7.16696	0.822106
$77$	0	0
$78$	1.21769	0.137877
$79$	9.33236	1.04997	0.524986	−	0.851111i	$-0.324070\pi$
$79$	9.33236	1.04997	0.524986	+	0.851111i	$0.324070\pi$
$80$	−4.08317	−0.456512
$81$	1.00000	0.111111
$82$	0.697610	0.0770382
$83$	−7.84331	−0.860915	−0.430458	−	0.902611i	$-0.641648\pi$
$83$	−7.84331	−0.860915	−0.430458	+	0.902611i	$0.641648\pi$
$84$	0	0
$85$	−0.312055	−0.0338472
$86$	2.04123	0.220112
$87$	6.80746	0.729836
$88$	−4.12524	−0.439752
$89$	−2.28790	−0.242517	−0.121259	−	0.992621i	$-0.538693\pi$
$89$	−2.28790	−0.242517	−0.121259	+	0.992621i	$0.538693\pi$
$90$	−2.16304	−0.228004
$91$	0	0
$92$	−9.43302	−0.983461
$93$	−0.735855	−0.0763046
$94$	6.79825	0.701186
$95$	14.6842	1.50657
$96$	−5.82055	−0.594058
$97$	14.4679	1.46899	0.734496	−	0.678613i	$-0.237419\pi$
$97$	14.4679	1.46899	0.734496	+	0.678613i	$0.237419\pi$
$98$	0	0
$99$	1.68312	0.169160
$100$	−6.98252	−0.698252
$101$	−6.67485	−0.664172	−0.332086	−	0.943249i	$-0.607752\pi$
$101$	−6.67485	−0.664172	−0.332086	+	0.943249i	$0.607752\pi$
$102$	−0.0702090	−0.00695173
$103$	0.188791	0.0186022	0.00930108	−	0.999957i	$-0.497039\pi$
$103$	0.188791	0.0186022	0.00930108	+	0.999957i	$0.497039\pi$
$104$	4.27817	0.419509
$105$	0	0
$106$	2.28897	0.222324
$107$	10.9691	1.06042	0.530212	−	0.847865i	$-0.322112\pi$
$107$	10.9691	1.06042	0.530212	+	0.847865i	$0.322112\pi$
$108$	1.51334	0.145621
$109$	−11.6745	−1.11821	−0.559105	−	0.829097i	$-0.688855\pi$
$109$	−11.6745	−1.11821	−0.559105	+	0.829097i	$0.688855\pi$
$110$	−3.64066	−0.347123
$111$	−5.71462	−0.542408
$112$	0	0
$113$	−10.4118	−0.979457	−0.489729	−	0.871875i	$-0.662904\pi$
$113$	−10.4118	−0.979457	−0.489729	+	0.871875i	$0.662904\pi$
$114$	3.30378	0.309427
$115$	−19.3271	−1.80226
$116$	10.3020	0.956516
$117$	−1.74552	−0.161373
$118$	0.492109	0.0453023
$119$	0	0
$120$	−7.59949	−0.693736
$121$	−8.16710	−0.742463
$122$	8.60287	0.778868
$123$	−1.00000	−0.0901670
$124$	−1.11360	−0.100004
$125$	1.19690	0.107054
$126$	0	0
$127$	−8.89546	−0.789345	−0.394672	−	0.918822i	$-0.629142\pi$
$127$	−8.89546	−0.789345	−0.394672	+	0.918822i	$0.629142\pi$
$128$	−10.6458	−0.940965
$129$	−2.92604	−0.257623
$130$	3.77563	0.331145
$131$	1.05419	0.0921050	0.0460525	−	0.998939i	$-0.485336\pi$
$131$	1.05419	0.0921050	0.0460525	+	0.998939i	$0.485336\pi$
$132$	2.54714	0.221700
$133$	0	0
$134$	−3.78033	−0.326571
$135$	3.10064	0.266861
$136$	−0.246668	−0.0211516
$137$	3.65554	0.312314	0.156157	−	0.987732i	$-0.450089\pi$
$137$	3.65554	0.312314	0.156157	+	0.987732i	$0.450089\pi$
$138$	−4.34838	−0.370159
$139$	−0.592587	−0.0502626	−0.0251313	−	0.999684i	$-0.508000\pi$
$139$	−0.592587	−0.0502626	−0.0251313	+	0.999684i	$0.508000\pi$
$140$	0	0
$141$	−9.74506	−0.820682
$142$	−5.70313	−0.478596
$143$	−2.93793	−0.245682
$144$	1.31688	0.109740
$145$	21.1075	1.75288
$146$	−0.0489785	−0.00405349
$147$	0	0
$148$	−8.64817	−0.710875
$149$	6.61690	0.542078	0.271039	−	0.962568i	$-0.412633\pi$
$149$	6.61690	0.542078	0.271039	+	0.962568i	$0.412633\pi$
$150$	−3.21876	−0.262811
$151$	−5.97425	−0.486177	−0.243089	−	0.970004i	$-0.578161\pi$
$151$	−5.97425	−0.486177	−0.243089	+	0.970004i	$0.578161\pi$
$152$	11.6073	0.941477
$153$	0.100642	0.00813644
$154$	0	0
$155$	−2.28162	−0.183264
$156$	−2.64157	−0.211495
$157$	21.3620	1.70487	0.852435	−	0.522833i	$-0.175125\pi$
$157$	21.3620	1.70487	0.852435	+	0.522833i	$0.175125\pi$
$158$	6.51035	0.517936
$159$	−3.28116	−0.260213
$160$	−18.0474	−1.42678
$161$	0	0
$162$	0.697610	0.0548094
$163$	−19.1811	−1.50238	−0.751191	−	0.660085i	$-0.770520\pi$
$163$	−19.1811	−1.50238	−0.751191	+	0.660085i	$0.770520\pi$
$164$	−1.51334	−0.118172
$165$	5.21876	0.406280
$166$	−5.47158	−0.424677
$167$	−21.7297	−1.68149	−0.840746	−	0.541430i	$-0.817883\pi$
$167$	−21.7297	−1.68149	−0.840746	+	0.541430i	$0.817883\pi$
$168$	0	0
$169$	−9.95316	−0.765628
$170$	−0.217693	−0.0166963
$171$	−4.73585	−0.362160
$172$	−4.42809	−0.337639
$173$	9.59465	0.729468	0.364734	−	0.931112i	$-0.381160\pi$
$173$	9.59465	0.729468	0.364734	+	0.931112i	$0.381160\pi$
$174$	4.74895	0.360017
$175$	0	0
$176$	2.21647	0.167072
$177$	−0.705422	−0.0530227
$178$	−1.59606	−0.119630
$179$	2.60814	0.194942	0.0974709	−	0.995238i	$-0.468925\pi$
$179$	2.60814	0.194942	0.0974709	+	0.995238i	$0.468925\pi$
$180$	4.69233	0.349745
$181$	−13.2982	−0.988445	−0.494223	−	0.869335i	$-0.664547\pi$
$181$	−13.2982	−0.988445	−0.494223	+	0.869335i	$0.664547\pi$
$182$	0	0
$183$	−12.3319	−0.911602
$184$	−15.2773	−1.12626
$185$	−17.7190	−1.30273
$186$	−0.513340	−0.0376399
$187$	0.169393	0.0123873
$188$	−14.7476	−1.07558
$189$	0	0
$190$	10.2438	0.743166
$191$	−19.8449	−1.43592	−0.717962	−	0.696082i	$-0.754925\pi$
$191$	−19.8449	−1.43592	−0.717962	+	0.696082i	$0.754925\pi$
$192$	−1.42672	−0.102965
$193$	−10.1675	−0.731872	−0.365936	−	0.930640i	$-0.619251\pi$
$193$	−10.1675	−0.731872	−0.365936	+	0.930640i	$0.619251\pi$
$194$	10.0929	0.724631
$195$	−5.41223	−0.387578
$196$	0	0
$197$	−19.8646	−1.41530	−0.707648	−	0.706565i	$-0.750244\pi$
$197$	−19.8646	−1.41530	−0.707648	+	0.706565i	$0.750244\pi$
$198$	1.17416	0.0834442
$199$	−12.0058	−0.851071	−0.425536	−	0.904942i	$-0.639914\pi$
$199$	−12.0058	−0.851071	−0.425536	+	0.904942i	$0.639914\pi$
$200$	−11.3086	−0.799639
$201$	5.41898	0.382225
$202$	−4.65644	−0.327626
$203$	0	0
$204$	0.152306	0.0106635
$205$	−3.10064	−0.216558
$206$	0.131703	0.00917617
$207$	6.23325	0.433241
$208$	−2.29864	−0.159382
$209$	−7.97102	−0.551367
$210$	0	0
$211$	1.70994	0.117717	0.0588586	−	0.998266i	$-0.481254\pi$
$211$	1.70994	0.117717	0.0588586	+	0.998266i	$0.481254\pi$
$212$	−4.96551	−0.341033
$213$	8.17523	0.560158
$214$	7.65216	0.523091
$215$	−9.07260	−0.618746
$216$	2.45094	0.166765
$217$	0	0
$218$	−8.14422	−0.551596
$219$	0.0702090	0.00474429
$220$	7.89776	0.532467
$221$	−0.175673	−0.0118170
$222$	−3.98658	−0.267562
$223$	−7.29811	−0.488717	−0.244359	−	0.969685i	$-0.578577\pi$
$223$	−7.29811	−0.488717	−0.244359	+	0.969685i	$0.578577\pi$
$224$	0	0
$225$	4.61398	0.307599
$226$	−7.26336	−0.483151
$227$	8.04523	0.533980	0.266990	−	0.963699i	$-0.413971\pi$
$227$	8.04523	0.533980	0.266990	+	0.963699i	$0.413971\pi$
$228$	−7.16696	−0.474643
$229$	7.50942	0.496237	0.248118	−	0.968730i	$-0.420188\pi$
$229$	7.50942	0.496237	0.248118	+	0.968730i	$0.420188\pi$
$230$	−13.4828	−0.889027
$231$	0	0
$232$	16.6847	1.09540
$233$	20.0983	1.31668	0.658340	−	0.752720i	$-0.271259\pi$
$233$	20.0983	1.31668	0.658340	+	0.752720i	$0.271259\pi$
$234$	−1.21769	−0.0796031
$235$	−30.2159	−1.97107
$236$	−1.06754	−0.0694911
$237$	−9.33236	−0.606202
$238$	0	0
$239$	18.4726	1.19490	0.597448	−	0.801908i	$-0.296182\pi$
$239$	18.4726	1.19490	0.597448	+	0.801908i	$0.296182\pi$
$240$	4.08317	0.263567
$241$	−29.6333	−1.90885	−0.954425	−	0.298451i	$-0.903530\pi$
$241$	−29.6333	−1.90885	−0.954425	+	0.298451i	$0.903530\pi$
$242$	−5.69745	−0.366246
$243$	−1.00000	−0.0641500
$244$	−18.6624	−1.19474
$245$	0	0
$246$	−0.697610	−0.0444780
$247$	8.26653	0.525987
$248$	−1.80354	−0.114525
$249$	7.84331	0.497050
$250$	0.834972	0.0528083
$251$	11.7624	0.742436	0.371218	−	0.928546i	$-0.378940\pi$
$251$	11.7624	0.742436	0.371218	+	0.928546i	$0.378940\pi$
$252$	0	0
$253$	10.4913	0.659584
$254$	−6.20557	−0.389372
$255$	0.312055	0.0195417
$256$	−10.2801	−0.642504
$257$	22.0843	1.37758	0.688791	−	0.724960i	$-0.258142\pi$
$257$	22.0843	1.37758	0.688791	+	0.724960i	$0.258142\pi$
$258$	−2.04123	−0.127082
$259$	0	0
$260$	−8.19055	−0.507956
$261$	−6.80746	−0.421371
$262$	0.735414	0.0454340
$263$	23.6241	1.45673	0.728363	−	0.685192i	$-0.240282\pi$
$263$	23.6241	1.45673	0.728363	+	0.685192i	$0.240282\pi$
$264$	4.12524	0.253891
$265$	−10.1737	−0.624965
$266$	0	0
$267$	2.28790	0.140017
$268$	8.20075	0.500941
$269$	−12.2093	−0.744413	−0.372206	−	0.928150i	$-0.621399\pi$
$269$	−12.2093	−0.744413	−0.372206	+	0.928150i	$0.621399\pi$
$270$	2.16304	0.131638
$271$	−4.78972	−0.290955	−0.145477	−	0.989362i	$-0.546472\pi$
$271$	−4.78972	−0.290955	−0.145477	+	0.989362i	$0.546472\pi$
$272$	0.132533	0.00803602
$273$	0	0
$274$	2.55014	0.154060
$275$	7.76590	0.468301
$276$	9.43302	0.567801
$277$	−14.7181	−0.884324	−0.442162	−	0.896935i	$-0.645788\pi$
$277$	−14.7181	−0.884324	−0.442162	+	0.896935i	$0.645788\pi$
$278$	−0.413395	−0.0247938
$279$	0.735855	0.0440545
$280$	0	0
$281$	9.36471	0.558652	0.279326	−	0.960196i	$-0.409889\pi$
$281$	9.36471	0.558652	0.279326	+	0.960196i	$0.409889\pi$
$282$	−6.79825	−0.404830
$283$	−27.4382	−1.63103	−0.815514	−	0.578737i	$-0.803546\pi$
$283$	−27.4382	−1.63103	−0.815514	+	0.578737i	$0.803546\pi$
$284$	12.3719	0.734137
$285$	−14.6842	−0.869816
$286$	−2.04953	−0.121191
$287$	0	0
$288$	5.82055	0.342979
$289$	−16.9899	−0.999404
$290$	14.7248	0.864670
$291$	−14.4679	−0.848123
$292$	0.106250	0.00621782
$293$	6.42964	0.375623	0.187812	−	0.982205i	$-0.439861\pi$
$293$	6.42964	0.375623	0.187812	+	0.982205i	$0.439861\pi$
$294$	0	0
$295$	−2.18726	−0.127347
$296$	−14.0062	−0.814095
$297$	−1.68312	−0.0976647
$298$	4.61602	0.267399
$299$	−10.8803	−0.629222
$300$	6.98252	0.403136
$301$	0	0
$302$	−4.16770	−0.239824
$303$	6.67485	0.383460
$304$	−6.23654	−0.357690
$305$	−38.2369	−2.18944
$306$	0.0702090	0.00401358
$307$	−9.73057	−0.555353	−0.277676	−	0.960675i	$-0.589564\pi$
$307$	−9.73057	−0.555353	−0.277676	+	0.960675i	$0.589564\pi$
$308$	0	0
$309$	−0.188791	−0.0107400
$310$	−1.59168	−0.0904015
$311$	19.2706	1.09273	0.546367	−	0.837546i	$-0.316010\pi$
$311$	19.2706	1.09273	0.546367	+	0.837546i	$0.316010\pi$
$312$	−4.27817	−0.242204
$313$	15.1915	0.858673	0.429337	−	0.903145i	$-0.358747\pi$
$313$	15.1915	0.858673	0.429337	+	0.903145i	$0.358747\pi$
$314$	14.9023	0.840987
$315$	0	0
$316$	−14.1230	−0.794483
$317$	−31.5800	−1.77371	−0.886854	−	0.462050i	$-0.847114\pi$
$317$	−31.5800	−1.77371	−0.886854	+	0.462050i	$0.847114\pi$
$318$	−2.28897	−0.128359
$319$	−11.4578	−0.641513
$320$	−4.42375	−0.247295
$321$	−10.9691	−0.612236
$322$	0	0
$323$	−0.476627	−0.0265202
$324$	−1.51334	−0.0840744
$325$	−8.05380	−0.446744
$326$	−13.3809	−0.741102
$327$	11.6745	0.645599
$328$	−2.45094	−0.135331
$329$	0	0
$330$	3.64066	0.200412
$331$	−28.0520	−1.54188	−0.770940	−	0.636908i	$-0.780213\pi$
$331$	−28.0520	−1.54188	−0.770940	+	0.636908i	$0.780213\pi$
$332$	11.8696	0.651429
$333$	5.71462	0.313159
$334$	−15.1588	−0.829455
$335$	16.8023	0.918008
$336$	0	0
$337$	27.1687	1.47997	0.739987	−	0.672622i	$-0.234832\pi$
$337$	27.1687	1.47997	0.739987	+	0.672622i	$0.234832\pi$
$338$	−6.94343	−0.377673
$339$	10.4118	0.565490
$340$	0.472246	0.0256111
$341$	1.23853	0.0670704
$342$	−3.30378	−0.178648
$343$	0	0
$344$	−7.17155	−0.386664
$345$	19.3271	1.04053
$346$	6.69333	0.359835
$347$	9.46914	0.508330	0.254165	−	0.967161i	$-0.418199\pi$
$347$	9.46914	0.508330	0.254165	+	0.967161i	$0.418199\pi$
$348$	−10.3020	−0.552245
$349$	−9.93257	−0.531678	−0.265839	−	0.964017i	$-0.585649\pi$
$349$	−9.93257	−0.531678	−0.265839	+	0.964017i	$0.585649\pi$
$350$	0	0
$351$	1.74552	0.0931690
$352$	9.79670	0.522166
$353$	−18.5850	−0.989180	−0.494590	−	0.869126i	$-0.664682\pi$
$353$	−18.5850	−0.989180	−0.494590	+	0.869126i	$0.664682\pi$
$354$	−0.492109	−0.0261553
$355$	25.3485	1.34536
$356$	3.46237	0.183505
$357$	0	0
$358$	1.81947	0.0961618
$359$	−3.47471	−0.183388	−0.0916940	−	0.995787i	$-0.529228\pi$
$359$	−3.47471	−0.183388	−0.0916940	+	0.995787i	$0.529228\pi$
$360$	7.59949	0.400529
$361$	3.42832	0.180438
$362$	−9.27694	−0.487585
$363$	8.16710	0.428661
$364$	0	0
$365$	0.217693	0.0113946
$366$	−8.60287	−0.449679
$367$	1.97645	0.103170	0.0515850	−	0.998669i	$-0.483573\pi$
$367$	1.97645	0.103170	0.0515850	+	0.998669i	$0.483573\pi$
$368$	8.20842	0.427894
$369$	1.00000	0.0520579
$370$	−12.3610	−0.642616
$371$	0	0
$372$	1.11360	0.0577374
$373$	2.93339	0.151885	0.0759425	−	0.997112i	$-0.475803\pi$
$373$	2.93339	0.151885	0.0759425	+	0.997112i	$0.475803\pi$
$374$	0.118170	0.00611045
$375$	−1.19690	−0.0618078
$376$	−23.8846	−1.23175
$377$	11.8826	0.611983
$378$	0	0
$379$	−10.4877	−0.538718	−0.269359	−	0.963040i	$-0.586812\pi$
$379$	−10.4877	−0.538718	−0.269359	+	0.963040i	$0.586812\pi$
$380$	−22.2222	−1.13997
$381$	8.89546	0.455728
$382$	−13.8440	−0.708320
$383$	−22.6486	−1.15729	−0.578646	−	0.815579i	$-0.696419\pi$
$383$	−22.6486	−1.15729	−0.578646	+	0.815579i	$0.696419\pi$
$384$	10.6458	0.543267
$385$	0	0
$386$	−7.09294	−0.361021
$387$	2.92604	0.148739
$388$	−21.8948	−1.11154
$389$	18.6004	0.943075	0.471538	−	0.881846i	$-0.343699\pi$
$389$	18.6004	0.943075	0.471538	+	0.881846i	$0.343699\pi$
$390$	−3.77563	−0.191186
$391$	0.627328	0.0317253
$392$	0	0
$393$	−1.05419	−0.0531769
$394$	−13.8578	−0.698145
$395$	−28.9363	−1.45594
$396$	−2.54714	−0.127998
$397$	−4.63253	−0.232500	−0.116250	−	0.993220i	$-0.537087\pi$
$397$	−4.63253	−0.232500	−0.116250	+	0.993220i	$0.537087\pi$
$398$	−8.37540	−0.419821
$399$	0	0
$400$	6.07605	0.303802
$401$	19.1570	0.956653	0.478327	−	0.878182i	$-0.341243\pi$
$401$	19.1570	0.956653	0.478327	+	0.878182i	$0.341243\pi$
$402$	3.78033	0.188546
$403$	−1.28445	−0.0639830
$404$	10.1013	0.502559
$405$	−3.10064	−0.154072
$406$	0	0
$407$	9.61841	0.476767
$408$	0.246668	0.0122119
$409$	30.5735	1.51176	0.755881	−	0.654709i	$-0.227209\pi$
$409$	30.5735	1.51176	0.755881	+	0.654709i	$0.227209\pi$
$410$	−2.16304	−0.106825
$411$	−3.65554	−0.180314
$412$	−0.285706	−0.0140757
$413$	0	0
$414$	4.34838	0.213711
$415$	24.3193	1.19379
$416$	−10.1599	−0.498130
$417$	0.592587	0.0290191
$418$	−5.56067	−0.271981
$419$	−33.4612	−1.63469	−0.817344	−	0.576150i	$-0.804555\pi$
$419$	−33.4612	−1.63469	−0.817344	+	0.576150i	$0.804555\pi$
$420$	0	0
$421$	−3.57314	−0.174144	−0.0870722	−	0.996202i	$-0.527751\pi$
$421$	−3.57314	−0.174144	−0.0870722	+	0.996202i	$0.527751\pi$
$422$	1.19287	0.0580682
$423$	9.74506	0.473821
$424$	−8.04193	−0.390551
$425$	0.464361	0.0225248
$426$	5.70313	0.276317
$427$	0	0
$428$	−16.6000	−0.802390
$429$	2.93793	0.141844
$430$	−6.32914	−0.305218
$431$	20.3285	0.979190	0.489595	−	0.871950i	$-0.337145\pi$
$431$	20.3285	0.979190	0.489595	+	0.871950i	$0.337145\pi$
$432$	−1.31688	−0.0633583
$433$	−30.6030	−1.47068	−0.735342	−	0.677696i	$-0.762979\pi$
$433$	−30.6030	−1.47068	−0.735342	+	0.677696i	$0.762979\pi$
$434$	0	0
$435$	−21.1075	−1.01203
$436$	17.6674	0.846116
$437$	−29.5198	−1.41212
$438$	0.0489785	0.00234029
$439$	−5.66764	−0.270502	−0.135251	−	0.990811i	$-0.543184\pi$
$439$	−5.66764	−0.270502	−0.135251	+	0.990811i	$0.543184\pi$
$440$	12.7909	0.609781
$441$	0	0
$442$	−0.122551	−0.00582917
$443$	16.1527	0.767437	0.383718	−	0.923450i	$-0.374643\pi$
$443$	16.1527	0.767437	0.383718	+	0.923450i	$0.374643\pi$
$444$	8.64817	0.410424
$445$	7.09397	0.336286
$446$	−5.09123	−0.241077
$447$	−6.61690	−0.312969
$448$	0	0
$449$	31.3451	1.47927	0.739634	−	0.673010i	$-0.234999\pi$
$449$	31.3451	1.47927	0.739634	+	0.673010i	$0.234999\pi$
$450$	3.21876	0.151734
$451$	1.68312	0.0792552
$452$	15.7565	0.741126
$453$	5.97425	0.280695
$454$	5.61243	0.263404
$455$	0	0
$456$	−11.6073	−0.543562
$457$	24.1667	1.13047	0.565234	−	0.824930i	$-0.308786\pi$
$457$	24.1667	1.13047	0.565234	+	0.824930i	$0.308786\pi$
$458$	5.23865	0.244786
$459$	−0.100642	−0.00469758
$460$	29.2484	1.36372
$461$	−1.01562	−0.0473023	−0.0236511	−	0.999720i	$-0.507529\pi$
$461$	−1.01562	−0.0473023	−0.0236511	+	0.999720i	$0.507529\pi$
$462$	0	0
$463$	−19.0089	−0.883417	−0.441708	−	0.897159i	$-0.645627\pi$
$463$	−19.0089	−0.883417	−0.441708	+	0.897159i	$0.645627\pi$
$464$	−8.96458	−0.416170
$465$	2.28162	0.105808
$466$	14.0208	0.649499
$467$	−27.9841	−1.29495	−0.647475	−	0.762086i	$-0.724175\pi$
$467$	−27.9841	−1.29495	−0.647475	+	0.762086i	$0.724175\pi$
$468$	2.64157	0.122106
$469$	0	0
$470$	−21.0789	−0.972299
$471$	−21.3620	−0.984307
$472$	−1.72895	−0.0795813
$473$	4.92488	0.226446
$474$	−6.51035	−0.299030
$475$	−21.8511	−1.00260
$476$	0	0
$477$	3.28116	0.150234
$478$	12.8867	0.589424
$479$	−11.9349	−0.545317	−0.272659	−	0.962111i	$-0.587903\pi$
$479$	−11.9349	−0.545317	−0.272659	+	0.962111i	$0.587903\pi$
$480$	18.0474	0.823749
$481$	−9.97499	−0.454821
$482$	−20.6725	−0.941607
$483$	0	0
$484$	12.3596	0.561800
$485$	−44.8597	−2.03698
$486$	−0.697610	−0.0316442
$487$	35.0793	1.58959	0.794797	−	0.606876i	$-0.207577\pi$
$487$	35.0793	1.58959	0.794797	+	0.606876i	$0.207577\pi$
$488$	−30.2248	−1.36821
$489$	19.1811	0.867400
$490$	0	0
$491$	−8.34463	−0.376588	−0.188294	−	0.982113i	$-0.560296\pi$
$491$	−8.34463	−0.376588	−0.188294	+	0.982113i	$0.560296\pi$
$492$	1.51334	0.0682266
$493$	−0.685117	−0.0308561
$494$	5.76682	0.259461
$495$	−5.21876	−0.234566
$496$	0.969030	0.0435107
$497$	0	0
$498$	5.47158	0.245187
$499$	6.42020	0.287408	0.143704	−	0.989621i	$-0.454099\pi$
$499$	6.42020	0.287408	0.143704	+	0.989621i	$0.454099\pi$
$500$	−1.81132	−0.0810048
$501$	21.7297	0.970810
$502$	8.20557	0.366232
$503$	15.2090	0.678137	0.339069	−	0.940762i	$-0.389888\pi$
$503$	15.2090	0.678137	0.339069	+	0.940762i	$0.389888\pi$
$504$	0	0
$505$	20.6963	0.920974
$506$	7.31886	0.325363
$507$	9.95316	0.442035
$508$	13.4619	0.597273
$509$	−25.0340	−1.10961	−0.554806	−	0.831980i	$-0.687207\pi$
$509$	−25.0340	−1.10961	−0.554806	+	0.831980i	$0.687207\pi$
$510$	0.217693	0.00963961
$511$	0	0
$512$	14.1201	0.624028
$513$	4.73585	0.209093
$514$	15.4063	0.679541
$515$	−0.585374	−0.0257947
$516$	4.42809	0.194936
$517$	16.4021	0.721365
$518$	0	0
$519$	−9.59465	−0.421158
$520$	−13.2651	−0.581712
$521$	20.0713	0.879341	0.439670	−	0.898159i	$-0.355095\pi$
$521$	20.0713	0.879341	0.439670	+	0.898159i	$0.355095\pi$
$522$	−4.74895	−0.207856
$523$	18.0633	0.789853	0.394927	−	0.918713i	$-0.370770\pi$
$523$	18.0633	0.789853	0.394927	+	0.918713i	$0.370770\pi$
$524$	−1.59535	−0.0696931
$525$	0	0
$526$	16.4804	0.718581
$527$	0.0740580	0.00322602
$528$	−2.21647	−0.0964593
$529$	15.8534	0.689278
$530$	−7.09728	−0.308286
$531$	0.705422	0.0306127
$532$	0	0
$533$	−1.74552	−0.0756069
$534$	1.59606	0.0690684
$535$	−34.0113	−1.47044
$536$	13.2816	0.573678
$537$	−2.60814	−0.112550
$538$	−8.51732	−0.367208
$539$	0	0
$540$	−4.69233	−0.201926
$541$	−24.5556	−1.05573	−0.527865	−	0.849328i	$-0.677007\pi$
$541$	−24.5556	−1.05573	−0.527865	+	0.849328i	$0.677007\pi$
$542$	−3.34136	−0.143524
$543$	13.2982	0.570679
$544$	0.585793	0.0251157
$545$	36.1983	1.55057
$546$	0	0
$547$	−45.0367	−1.92563	−0.962815	−	0.270161i	$-0.912923\pi$
$547$	−45.0367	−1.92563	−0.962815	+	0.270161i	$0.912923\pi$
$548$	−5.53207	−0.236318
$549$	12.3319	0.526313
$550$	5.41757	0.231006
$551$	32.2391	1.37343
$552$	15.2773	0.650246
$553$	0	0
$554$	−10.2675	−0.436224
$555$	17.7190	0.752130
$556$	0.896786	0.0380322
$557$	−31.2915	−1.32587	−0.662933	−	0.748679i	$-0.730688\pi$
$557$	−31.2915	−1.32587	−0.662933	+	0.748679i	$0.730688\pi$
$558$	0.513340	0.0217314
$559$	−5.10746	−0.216022
$560$	0	0
$561$	−0.169393	−0.00715179
$562$	6.53292	0.275575
$563$	−10.9665	−0.462183	−0.231092	−	0.972932i	$-0.574230\pi$
$563$	−10.9665	−0.462183	−0.231092	+	0.972932i	$0.574230\pi$
$564$	14.7476	0.620985
$565$	32.2832	1.35816
$566$	−19.1411	−0.804562
$567$	0	0
$568$	20.0370	0.840735
$569$	−22.4357	−0.940554	−0.470277	−	0.882519i	$-0.655846\pi$
$569$	−22.4357	−0.940554	−0.470277	+	0.882519i	$0.655846\pi$
$570$	−10.2438	−0.429067
$571$	33.5110	1.40239	0.701196	−	0.712969i	$-0.252650\pi$
$571$	33.5110	1.40239	0.701196	+	0.712969i	$0.252650\pi$
$572$	4.44608	0.185900
$573$	19.8449	0.829031
$574$	0	0
$575$	28.7601	1.19938
$576$	1.42672	0.0594468
$577$	36.8030	1.53213	0.766064	−	0.642764i	$-0.222212\pi$
$577$	36.8030	1.53213	0.766064	+	0.642764i	$0.222212\pi$
$578$	−11.8523	−0.492991
$579$	10.1675	0.422546
$580$	−31.9428	−1.32635
$581$	0	0
$582$	−10.0929	−0.418366
$583$	5.52259	0.228722
$584$	0.172078	0.00712065
$585$	5.41223	0.223768
$586$	4.48538	0.185289
$587$	37.7990	1.56013	0.780067	−	0.625696i	$-0.215185\pi$
$587$	37.7990	1.56013	0.780067	+	0.625696i	$0.215185\pi$
$588$	0	0
$589$	−3.48490	−0.143593
$590$	−1.52586	−0.0628185
$591$	19.8646	0.817122
$592$	7.52546	0.309294
$593$	−28.0649	−1.15249	−0.576243	−	0.817279i	$-0.695482\pi$
$593$	−28.0649	−1.15249	−0.576243	+	0.817279i	$0.695482\pi$
$594$	−1.17416	−0.0481765
$595$	0	0
$596$	−10.0136	−0.410174
$597$	12.0058	0.491366
$598$	−7.59018	−0.310386
$599$	10.4888	0.428562	0.214281	−	0.976772i	$-0.431259\pi$
$599$	10.4888	0.428562	0.214281	+	0.976772i	$0.431259\pi$
$600$	11.3086	0.461672
$601$	2.64863	0.108040	0.0540200	−	0.998540i	$-0.482797\pi$
$601$	2.64863	0.108040	0.0540200	+	0.998540i	$0.482797\pi$
$602$	0	0
$603$	−5.41898	−0.220678
$604$	9.04107	0.367876
$605$	25.3232	1.02954
$606$	4.65644	0.189155
$607$	−18.7292	−0.760196	−0.380098	−	0.924946i	$-0.624110\pi$
$607$	−18.7292	−0.760196	−0.380098	+	0.924946i	$0.624110\pi$
$608$	−27.5653	−1.11792
$609$	0	0
$610$	−26.6744	−1.08002
$611$	−17.0102	−0.688159
$612$	−0.152306	−0.00615660
$613$	6.82584	0.275693	0.137847	−	0.990454i	$-0.455982\pi$
$613$	6.82584	0.275693	0.137847	+	0.990454i	$0.455982\pi$
$614$	−6.78815	−0.273947
$615$	3.10064	0.125030
$616$	0	0
$617$	32.9959	1.32836	0.664181	−	0.747571i	$-0.268780\pi$
$617$	32.9959	1.32836	0.664181	+	0.747571i	$0.268780\pi$
$618$	−0.131703	−0.00529786
$619$	−30.6619	−1.23240	−0.616202	−	0.787588i	$-0.711330\pi$
$619$	−30.6619	−1.23240	−0.616202	+	0.787588i	$0.711330\pi$
$620$	3.45287	0.138671
$621$	−6.23325	−0.250132
$622$	13.4433	0.539029
$623$	0	0
$624$	2.29864	0.0920191
$625$	−26.7811	−1.07124
$626$	10.5977	0.423571
$627$	7.97102	0.318332
$628$	−32.3279	−1.29002
$629$	0.575132	0.0229320
$630$	0	0
$631$	2.82553	0.112483	0.0562413	−	0.998417i	$-0.482088\pi$
$631$	2.82553	0.112483	0.0562413	+	0.998417i	$0.482088\pi$
$632$	−22.8731	−0.909842
$633$	−1.70994	−0.0679641
$634$	−22.0305	−0.874943
$635$	27.5817	1.09454
$636$	4.96551	0.196895
$637$	0	0
$638$	−7.99307	−0.316449
$639$	−8.17523	−0.323407
$640$	33.0088	1.30479
$641$	29.0623	1.14789	0.573945	−	0.818894i	$-0.305412\pi$
$641$	29.0623	1.14789	0.573945	+	0.818894i	$0.305412\pi$
$642$	−7.65216	−0.302007
$643$	8.93670	0.352429	0.176214	−	0.984352i	$-0.443615\pi$
$643$	8.93670	0.352429	0.176214	+	0.984352i	$0.443615\pi$
$644$	0	0
$645$	9.07260	0.357233
$646$	−0.332500	−0.0130820
$647$	37.5199	1.47506	0.737530	−	0.675314i	$-0.235992\pi$
$647$	37.5199	1.47506	0.737530	+	0.675314i	$0.235992\pi$
$648$	−2.45094	−0.0962821
$649$	1.18731	0.0466060
$650$	−5.61841	−0.220372
$651$	0	0
$652$	29.0276	1.13681
$653$	15.5985	0.610418	0.305209	−	0.952285i	$-0.401274\pi$
$653$	15.5985	0.610418	0.305209	+	0.952285i	$0.401274\pi$
$654$	8.14422	0.318464
$655$	−3.26867	−0.127717
$656$	1.31688	0.0514154
$657$	−0.0702090	−0.00273912
$658$	0	0
$659$	22.4445	0.874312	0.437156	−	0.899386i	$-0.355986\pi$
$659$	22.4445	0.874312	0.437156	+	0.899386i	$0.355986\pi$
$660$	−7.89776	−0.307420
$661$	−41.8944	−1.62950	−0.814751	−	0.579811i	$-0.803127\pi$
$661$	−41.8944	−1.62950	−0.814751	+	0.579811i	$0.803127\pi$
$662$	−19.5694	−0.760586
$663$	0.175673	0.00682258
$664$	19.2235	0.746017
$665$	0	0
$666$	3.98658	0.154477
$667$	−42.4326	−1.64300
$668$	32.8844	1.27233
$669$	7.29811	0.282161
$670$	11.7215	0.452840
$671$	20.7561	0.801282
$672$	0	0
$673$	−29.9830	−1.15576	−0.577881	−	0.816121i	$-0.696120\pi$
$673$	−29.9830	−1.15576	−0.577881	+	0.816121i	$0.696120\pi$
$674$	18.9532	0.730049
$675$	−4.61398	−0.177592
$676$	15.0625	0.579327
$677$	37.3900	1.43701	0.718507	−	0.695519i	$-0.244826\pi$
$677$	37.3900	1.43701	0.718507	+	0.695519i	$0.244826\pi$
$678$	7.26336	0.278948
$679$	0	0
$680$	0.764830	0.0293299
$681$	−8.04523	−0.308294
$682$	0.864014	0.0330848
$683$	−23.8925	−0.914222	−0.457111	−	0.889410i	$-0.651116\pi$
$683$	−23.8925	−0.914222	−0.457111	+	0.889410i	$0.651116\pi$
$684$	7.16696	0.274035
$685$	−11.3345	−0.433070
$686$	0	0
$687$	−7.50942	−0.286502
$688$	3.85323	0.146903
$689$	−5.72733	−0.218194
$690$	13.4828	0.513280
$691$	11.6822	0.444412	0.222206	−	0.975000i	$-0.428674\pi$
$691$	11.6822	0.444412	0.222206	+	0.975000i	$0.428674\pi$
$692$	−14.5200	−0.551966
$693$	0	0
$694$	6.60577	0.250752
$695$	1.83740	0.0696966
$696$	−16.6847	−0.632431
$697$	0.100642	0.00381210
$698$	−6.92907	−0.262269
$699$	−20.0983	−0.760186
$700$	0	0
$701$	−16.2297	−0.612986	−0.306493	−	0.951873i	$-0.599156\pi$
$701$	−16.2297	−0.612986	−0.306493	+	0.951873i	$0.599156\pi$
$702$	1.21769	0.0459589
$703$	−27.0636	−1.02072
$704$	2.40135	0.0905042
$705$	30.2159	1.13800
$706$	−12.9651	−0.487948
$707$	0	0
$708$	1.06754	0.0401207
$709$	−30.7014	−1.15301	−0.576507	−	0.817092i	$-0.695585\pi$
$709$	−30.7014	−1.15301	−0.576507	+	0.817092i	$0.695585\pi$
$710$	17.6834	0.663644
$711$	9.33236	0.349991
$712$	5.60752	0.210151
$713$	4.58677	0.171776
$714$	0	0
$715$	9.10946	0.340674
$716$	−3.94701	−0.147507
$717$	−18.4726	−0.689873
$718$	−2.42399	−0.0904625
$719$	12.9335	0.482337	0.241169	−	0.970483i	$-0.422469\pi$
$719$	12.9335	0.482337	0.241169	+	0.970483i	$0.422469\pi$
$720$	−4.08317	−0.152171
$721$	0	0
$722$	2.39163	0.0890073
$723$	29.6333	1.10207
$724$	20.1247	0.747927
$725$	−31.4095	−1.16652
$726$	5.69745	0.211452
$727$	29.8801	1.10819	0.554096	−	0.832453i	$-0.313064\pi$
$727$	29.8801	1.10819	0.554096	+	0.832453i	$0.313064\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.151865	0.00562077
$731$	0.294483	0.0108918
$732$	18.6624	0.689782
$733$	29.1951	1.07835	0.539174	−	0.842195i	$-0.318737\pi$
$733$	29.1951	1.07835	0.539174	+	0.842195i	$0.318737\pi$
$734$	1.37879	0.0508922
$735$	0	0
$736$	36.2809	1.33733
$737$	−9.12080	−0.335969
$738$	0.697610	0.0256794
$739$	−24.4480	−0.899336	−0.449668	−	0.893196i	$-0.648458\pi$
$739$	−24.4480	−0.899336	−0.449668	+	0.893196i	$0.648458\pi$
$740$	26.8149	0.985734
$741$	−8.26653	−0.303679
$742$	0	0
$743$	−27.1734	−0.996895	−0.498447	−	0.866920i	$-0.666096\pi$
$743$	−27.1734	−0.996895	−0.498447	+	0.866920i	$0.666096\pi$
$744$	1.80354	0.0661209
$745$	−20.5167	−0.751672
$746$	2.04636	0.0749226
$747$	−7.84331	−0.286972
$748$	−0.256349	−0.00937306
$749$	0	0
$750$	−0.834972	−0.0304889
$751$	45.9889	1.67816	0.839079	−	0.544010i	$-0.183095\pi$
$751$	45.9889	1.67816	0.839079	+	0.544010i	$0.183095\pi$
$752$	12.8330	0.467973
$753$	−11.7624	−0.428645
$754$	8.28939	0.301882
$755$	18.5240	0.674158
$756$	0	0
$757$	−15.7714	−0.573223	−0.286611	−	0.958047i	$-0.592529\pi$
$757$	−15.7714	−0.573223	−0.286611	+	0.958047i	$0.592529\pi$
$758$	−7.31634	−0.265742
$759$	−10.4913	−0.380811
$760$	−35.9901	−1.30550
$761$	−31.5386	−1.14327	−0.571637	−	0.820507i	$-0.693691\pi$
$761$	−31.5386	−1.14327	−0.571637	+	0.820507i	$0.693691\pi$
$762$	6.20557	0.224804
$763$	0	0
$764$	30.0320	1.08652
$765$	−0.312055	−0.0112824
$766$	−15.7999	−0.570874
$767$	−1.23133	−0.0444607
$768$	10.2801	0.370950
$769$	7.14179	0.257539	0.128770	−	0.991675i	$-0.458897\pi$
$769$	7.14179	0.257539	0.128770	+	0.991675i	$0.458897\pi$
$770$	0	0
$771$	−22.0843	−0.795348
$772$	15.3869	0.553785
$773$	−10.8464	−0.390117	−0.195059	−	0.980792i	$-0.562490\pi$
$773$	−10.8464	−0.390117	−0.195059	+	0.980792i	$0.562490\pi$
$774$	2.04123	0.0733706
$775$	3.39522	0.121960
$776$	−35.4600	−1.27294
$777$	0	0
$778$	12.9758	0.465205
$779$	−4.73585	−0.169680
$780$	8.19055	0.293269
$781$	−13.7599	−0.492369
$782$	0.437630	0.0156496
$783$	6.80746	0.243279
$784$	0	0
$785$	−66.2358	−2.36406
$786$	−0.735414	−0.0262313
$787$	−26.5585	−0.946710	−0.473355	−	0.880872i	$-0.656957\pi$
$787$	−26.5585	−0.946710	−0.473355	+	0.880872i	$0.656957\pi$
$788$	30.0619	1.07091
$789$	−23.6241	−0.841041
$790$	−20.1863	−0.718195
$791$	0	0
$792$	−4.12524	−0.146584
$793$	−21.5256	−0.764397
$794$	−3.23170	−0.114689
$795$	10.1737	0.360824
$796$	18.1689	0.643980
$797$	−14.7607	−0.522850	−0.261425	−	0.965224i	$-0.584192\pi$
$797$	−14.7607	−0.522850	−0.261425	+	0.965224i	$0.584192\pi$
$798$	0	0
$799$	0.980764	0.0346969
$800$	26.8559	0.949500
$801$	−2.28790	−0.0808390
$802$	13.3641	0.471903
$803$	−0.118170	−0.00417014
$804$	−8.20075	−0.289218
$805$	0	0
$806$	−0.896045	−0.0315618
$807$	12.2093	0.429787
$808$	16.3597	0.575531
$809$	−16.5702	−0.582577	−0.291289	−	0.956635i	$-0.594084\pi$
$809$	−16.5702	−0.582577	−0.291289	+	0.956635i	$0.594084\pi$
$810$	−2.16304	−0.0760015
$811$	2.08085	0.0730686	0.0365343	−	0.999332i	$-0.488368\pi$
$811$	2.08085	0.0730686	0.0365343	+	0.999332i	$0.488368\pi$
$812$	0	0
$813$	4.78972	0.167983
$814$	6.70990	0.235182
$815$	59.4738	2.08328
$816$	−0.132533	−0.00463960
$817$	−13.8573	−0.484805
$818$	21.3284	0.745730
$819$	0	0
$820$	4.69233	0.163863
$821$	−18.2487	−0.636883	−0.318441	−	0.947943i	$-0.603159\pi$
$821$	−18.2487	−0.636883	−0.318441	+	0.947943i	$0.603159\pi$
$822$	−2.55014	−0.0889464
$823$	6.74278	0.235039	0.117519	−	0.993071i	$-0.462506\pi$
$823$	6.74278	0.235039	0.117519	+	0.993071i	$0.462506\pi$
$824$	−0.462717	−0.0161195
$825$	−7.76590	−0.270374
$826$	0	0
$827$	−40.8338	−1.41993	−0.709966	−	0.704236i	$-0.751290\pi$
$827$	−40.8338	−1.41993	−0.709966	+	0.704236i	$0.751290\pi$
$828$	−9.43302	−0.327820
$829$	52.8995	1.83727	0.918637	−	0.395102i	$-0.129291\pi$
$829$	52.8995	1.83727	0.918637	+	0.395102i	$0.129291\pi$
$830$	16.9654	0.588878
$831$	14.7181	0.510564
$832$	−2.49037	−0.0863381
$833$	0	0
$834$	0.413395	0.0143147
$835$	67.3759	2.33164
$836$	12.0629	0.417203
$837$	−0.735855	−0.0254349
$838$	−23.3429	−0.806367
$839$	31.0666	1.07254	0.536269	−	0.844047i	$-0.319833\pi$
$839$	31.0666	1.07254	0.536269	+	0.844047i	$0.319833\pi$
$840$	0	0
$841$	17.3414	0.597981
$842$	−2.49266	−0.0859028
$843$	−9.36471	−0.322538
$844$	−2.58772	−0.0890731
$845$	30.8612	1.06166
$846$	6.79825	0.233729
$847$	0	0
$848$	4.32088	0.148380
$849$	27.4382	0.941675
$850$	0.323943	0.0111112
$851$	35.6207	1.22106
$852$	−12.3719	−0.423854
$853$	−23.4152	−0.801720	−0.400860	−	0.916139i	$-0.631289\pi$
$853$	−23.4152	−0.801720	−0.400860	+	0.916139i	$0.631289\pi$
$854$	0	0
$855$	14.6842	0.502189
$856$	−26.8846	−0.918898
$857$	−12.9076	−0.440916	−0.220458	−	0.975396i	$-0.570755\pi$
$857$	−12.9076	−0.440916	−0.220458	+	0.975396i	$0.570755\pi$
$858$	2.04953	0.0699697
$859$	−33.7993	−1.15322	−0.576608	−	0.817021i	$-0.695624\pi$
$859$	−33.7993	−1.15322	−0.576608	+	0.817021i	$0.695624\pi$
$860$	13.7299	0.468186
$861$	0	0
$862$	14.1814	0.483020
$863$	3.56146	0.121233	0.0606167	−	0.998161i	$-0.480693\pi$
$863$	3.56146	0.121233	0.0606167	+	0.998161i	$0.480693\pi$
$864$	−5.82055	−0.198019
$865$	−29.7496	−1.01152
$866$	−21.3489	−0.725467
$867$	16.9899	0.577006
$868$	0	0
$869$	15.7075	0.532841
$870$	−14.7248	−0.499217
$871$	9.45894	0.320504
$872$	28.6134	0.968973
$873$	14.4679	0.489664
$874$	−20.5933	−0.696578
$875$	0	0
$876$	−0.106250	−0.00358986
$877$	−6.05502	−0.204464	−0.102232	−	0.994761i	$-0.532598\pi$
$877$	−6.05502	−0.204464	−0.102232	+	0.994761i	$0.532598\pi$
$878$	−3.95380	−0.133434
$879$	−6.42964	−0.216866
$880$	−6.87247	−0.231671
$881$	11.9562	0.402816	0.201408	−	0.979507i	$-0.435448\pi$
$881$	11.9562	0.402816	0.201408	+	0.979507i	$0.435448\pi$
$882$	0	0
$883$	−20.0257	−0.673917	−0.336959	−	0.941519i	$-0.609398\pi$
$883$	−20.0257	−0.673917	−0.336959	+	0.941519i	$0.609398\pi$
$884$	0.265853	0.00894160
$885$	2.18726	0.0735239
$886$	11.2683	0.378565
$887$	−57.8406	−1.94210	−0.971049	−	0.238880i	$-0.923220\pi$
$887$	−57.8406	−1.94210	−0.971049	+	0.238880i	$0.923220\pi$
$888$	14.0062	0.470018
$889$	0	0
$890$	4.94882	0.165885
$891$	1.68312	0.0563867
$892$	11.0445	0.369798
$893$	−46.1512	−1.54439
$894$	−4.61602	−0.154383
$895$	−8.08692	−0.270316
$896$	0	0
$897$	10.8803	0.363281
$898$	21.8667	0.729700
$899$	−5.00930	−0.167069
$900$	−6.98252	−0.232751
$901$	0.330223	0.0110013
$902$	1.17416	0.0390954
$903$	0	0
$904$	25.5186	0.848738
$905$	41.2329	1.37063
$906$	4.16770	0.138462
$907$	−44.4957	−1.47745	−0.738727	−	0.674005i	$-0.764573\pi$
$907$	−44.4957	−1.47745	−0.738727	+	0.674005i	$0.764573\pi$
$908$	−12.1752	−0.404047
$909$	−6.67485	−0.221391
$910$	0	0
$911$	−21.8943	−0.725389	−0.362695	−	0.931908i	$-0.618143\pi$
$911$	−21.8943	−0.725389	−0.362695	+	0.931908i	$0.618143\pi$
$912$	6.23654	0.206512
$913$	−13.2013	−0.436898
$914$	16.8589	0.557643
$915$	38.2369	1.26407
$916$	−11.3643	−0.375487
$917$	0	0
$918$	−0.0702090	−0.00231724
$919$	14.4124	0.475423	0.237711	−	0.971336i	$-0.423603\pi$
$919$	14.4124	0.475423	0.237711	+	0.971336i	$0.423603\pi$
$920$	47.3695	1.56173
$921$	9.73057	0.320633
$922$	−0.708509	−0.0233335
$923$	14.2700	0.469704
$924$	0	0
$925$	26.3672	0.866947
$926$	−13.2608	−0.435776
$927$	0.188791	0.00620072
$928$	−39.6231	−1.30069
$929$	−42.8267	−1.40510	−0.702549	−	0.711635i	$-0.747955\pi$
$929$	−42.8267	−1.40510	−0.702549	+	0.711635i	$0.747955\pi$
$930$	1.59168	0.0521933
$931$	0	0
$932$	−30.4155	−0.996293
$933$	−19.2706	−0.630890
$934$	−19.5220	−0.638780
$935$	−0.525228	−0.0171768
$936$	4.27817	0.139836
$937$	52.3973	1.71174	0.855872	−	0.517188i	$-0.173021\pi$
$937$	52.3973	1.71174	0.855872	+	0.517188i	$0.173021\pi$
$938$	0	0
$939$	−15.1915	−0.495755
$940$	45.7270	1.49145
$941$	42.9842	1.40125	0.700623	−	0.713532i	$-0.252906\pi$
$941$	42.9842	1.40125	0.700623	+	0.713532i	$0.252906\pi$
$942$	−14.9023	−0.485544
$943$	6.23325	0.202983
$944$	0.928954	0.0302349
$945$	0	0
$946$	3.43565	0.111703
$947$	40.7859	1.32536	0.662682	−	0.748901i	$-0.269418\pi$
$947$	40.7859	1.32536	0.662682	+	0.748901i	$0.269418\pi$
$948$	14.1230	0.458695
$949$	0.122551	0.00397818
$950$	−15.2436	−0.494567
$951$	31.5800	1.02405
$952$	0	0
$953$	40.7815	1.32104	0.660521	−	0.750807i	$-0.270335\pi$
$953$	40.7815	1.32104	0.660521	+	0.750807i	$0.270335\pi$
$954$	2.28897	0.0741082
$955$	61.5318	1.99112
$956$	−27.9554	−0.904142
$957$	11.4578	0.370378
$958$	−8.32587	−0.268997
$959$	0	0
$960$	4.42375	0.142776
$961$	−30.4585	−0.982533
$962$	−6.95866	−0.224356
$963$	10.9691	0.353474
$964$	44.8453	1.44437
$965$	31.5257	1.01485
$966$	0	0
$967$	−47.7320	−1.53496	−0.767479	−	0.641074i	$-0.778489\pi$
$967$	−47.7320	−1.53496	−0.767479	+	0.641074i	$0.778489\pi$
$968$	20.0171	0.643373
$969$	0.476627	0.0153115
$970$	−31.2946	−1.00481
$971$	35.4277	1.13693	0.568465	−	0.822707i	$-0.307537\pi$
$971$	35.4277	1.13693	0.568465	+	0.822707i	$0.307537\pi$
$972$	1.51334	0.0485404
$973$	0	0
$974$	24.4717	0.784123
$975$	8.05380	0.257928
$976$	16.2396	0.519818
$977$	16.6916	0.534011	0.267006	−	0.963695i	$-0.413966\pi$
$977$	16.6916	0.534011	0.267006	+	0.963695i	$0.413966\pi$
$978$	13.3809	0.427876
$979$	−3.85082	−0.123073
$980$	0	0
$981$	−11.6745	−0.372737
$982$	−5.82130	−0.185765
$983$	−34.3442	−1.09541	−0.547705	−	0.836671i	$-0.684499\pi$
$983$	−34.3442	−1.09541	−0.547705	+	0.836671i	$0.684499\pi$
$984$	2.45094	0.0781332
$985$	61.5931	1.96252
$986$	−0.477945	−0.0152209
$987$	0	0
$988$	−12.5101	−0.397998
$989$	18.2387	0.579958
$990$	−3.64066	−0.115708
$991$	−28.5554	−0.907091	−0.453545	−	0.891233i	$-0.649841\pi$
$991$	−28.5554	−0.907091	−0.453545	+	0.891233i	$0.649841\pi$
$992$	4.28308	0.135988
$993$	28.0520	0.890204
$994$	0	0
$995$	37.2258	1.18014
$996$	−11.8696	−0.376103
$997$	−44.8737	−1.42116	−0.710582	−	0.703615i	$-0.751568\pi$
$997$	−44.8737	−1.42116	−0.710582	+	0.703615i	$0.751568\pi$
$998$	4.47880	0.141774
$999$	−5.71462	−0.180803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.w.1.3		5
7.6	odd	2		861.2.a.l.1.3	✓	5
21.20	even	2		2583.2.a.p.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.l.1.3	✓	5	7.6	odd	2
2583.2.a.p.1.3		5	21.20	even	2
6027.2.a.w.1.3		5	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)

\(f(q)\)	\(=\)	\(q+0.697610 q^{2} -1.00000 q^{3} -1.51334 q^{4} -3.10064 q^{5} -0.697610 q^{6} -2.45094 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.697610 q^{2} -1.00000 q^{3} -1.51334 q^{4} -3.10064 q^{5} -0.697610 q^{6} -2.45094 q^{8} +1.00000 q^{9} -2.16304 q^{10} +1.68312 q^{11} +1.51334 q^{12} -1.74552 q^{13} +3.10064 q^{15} +1.31688 q^{16} +0.100642 q^{17} +0.697610 q^{18} -4.73585 q^{19} +4.69233 q^{20} +1.17416 q^{22} +6.23325 q^{23} +2.45094 q^{24} +4.61398 q^{25} -1.21769 q^{26} -1.00000 q^{27} -6.80746 q^{29} +2.16304 q^{30} +0.735855 q^{31} +5.82055 q^{32} -1.68312 q^{33} +0.0702090 q^{34} -1.51334 q^{36} +5.71462 q^{37} -3.30378 q^{38} +1.74552 q^{39} +7.59949 q^{40} +1.00000 q^{41} +2.92604 q^{43} -2.54714 q^{44} -3.10064 q^{45} +4.34838 q^{46} +9.74506 q^{47} -1.31688 q^{48} +3.21876 q^{50} -0.100642 q^{51} +2.64157 q^{52} +3.28116 q^{53} -0.697610 q^{54} -5.21876 q^{55} +4.73585 q^{57} -4.74895 q^{58} +0.705422 q^{59} -4.69233 q^{60} +12.3319 q^{61} +0.513340 q^{62} +1.42672 q^{64} +5.41223 q^{65} -1.17416 q^{66} -5.41898 q^{67} -0.152306 q^{68} -6.23325 q^{69} -8.17523 q^{71} -2.45094 q^{72} -0.0702090 q^{73} +3.98658 q^{74} -4.61398 q^{75} +7.16696 q^{76} +1.21769 q^{78} +9.33236 q^{79} -4.08317 q^{80} +1.00000 q^{81} +0.697610 q^{82} -7.84331 q^{83} -0.312055 q^{85} +2.04123 q^{86} +6.80746 q^{87} -4.12524 q^{88} -2.28790 q^{89} -2.16304 q^{90} -9.43302 q^{92} -0.735855 q^{93} +6.79825 q^{94} +14.6842 q^{95} -5.82055 q^{96} +14.4679 q^{97} +1.68312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} - 5 q^{3} + 7 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 - 5 * q^3 + 7 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 + 5 * q^9	\( 5 q + 3 q^{2} - 5 q^{3} + 7 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} + 5 q^{9} + q^{10} + 4 q^{11} - 7 q^{12} - 5 q^{13} + 3 q^{15} + 11 q^{16} - 12 q^{17} + 3 q^{18} - 10 q^{19} - 9 q^{20} - 6 q^{22} + 9 q^{23} - 3 q^{24} - 4 q^{25} - 13 q^{26} - 5 q^{27} + 7 q^{29} - q^{30} - 10 q^{31} + 9 q^{32} - 4 q^{33} - 10 q^{34} + 7 q^{36} - 11 q^{37} + 5 q^{39} + 7 q^{40} + 5 q^{41} - 2 q^{43} - 3 q^{45} - 9 q^{46} + 7 q^{47} - 11 q^{48} - 10 q^{50} + 12 q^{51} + 11 q^{52} - 9 q^{53} - 3 q^{54} + 10 q^{57} - 31 q^{58} - 8 q^{59} + 9 q^{60} + 6 q^{61} - 12 q^{62} - 29 q^{64} - 13 q^{65} + 6 q^{66} - 9 q^{67} - 12 q^{68} - 9 q^{69} + 4 q^{71} + 3 q^{72} + 10 q^{73} - 17 q^{74} + 4 q^{75} - 36 q^{76} + 13 q^{78} + 7 q^{79} - 9 q^{80} + 5 q^{81} + 3 q^{82} - 50 q^{83} - 12 q^{85} - 8 q^{86} - 7 q^{87} - 38 q^{88} - 8 q^{89} + q^{90} - 17 q^{92} + 10 q^{93} + 21 q^{94} + 36 q^{95} - 9 q^{96} + 11 q^{97} + 4 q^{99}+O(q^{100}) \) 5 * q + 3 * q^2 - 5 * q^3 + 7 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 + 5 * q^9 + q^10 + 4 * q^11 - 7 * q^12 - 5 * q^13 + 3 * q^15 + 11 * q^16 - 12 * q^17 + 3 * q^18 - 10 * q^19 - 9 * q^20 - 6 * q^22 + 9 * q^23 - 3 * q^24 - 4 * q^25 - 13 * q^26 - 5 * q^27 + 7 * q^29 - q^30 - 10 * q^31 + 9 * q^32 - 4 * q^33 - 10 * q^34 + 7 * q^36 - 11 * q^37 + 5 * q^39 + 7 * q^40 + 5 * q^41 - 2 * q^43 - 3 * q^45 - 9 * q^46 + 7 * q^47 - 11 * q^48 - 10 * q^50 + 12 * q^51 + 11 * q^52 - 9 * q^53 - 3 * q^54 + 10 * q^57 - 31 * q^58 - 8 * q^59 + 9 * q^60 + 6 * q^61 - 12 * q^62 - 29 * q^64 - 13 * q^65 + 6 * q^66 - 9 * q^67 - 12 * q^68 - 9 * q^69 + 4 * q^71 + 3 * q^72 + 10 * q^73 - 17 * q^74 + 4 * q^75 - 36 * q^76 + 13 * q^78 + 7 * q^79 - 9 * q^80 + 5 * q^81 + 3 * q^82 - 50 * q^83 - 12 * q^85 - 8 * q^86 - 7 * q^87 - 38 * q^88 - 8 * q^89 + q^90 - 17 * q^92 + 10 * q^93 + 21 * q^94 + 36 * q^95 - 9 * q^96 + 11 * q^97 + 4 * q^99

Introduction

L-functions

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