LMFDB - Embedded newform 2842.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.369849.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 6x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.12550$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.655021 q^{3} +1.00000 q^{4} -2.17277 q^{5} +0.655021 q^{6} -1.00000 q^{8} -2.57095 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.655021 q^{3} +1.00000 q^{4} -2.17277 q^{5} +0.655021 q^{6} -1.00000 q^{8} -2.57095 q^{9} +2.17277 q^{10} +0.182674 q^{11} -0.655021 q^{12} +1.49551 q^{13} +1.42321 q^{15} +1.00000 q^{16} +4.61822 q^{17} +2.57095 q^{18} +0.344979 q^{19} -2.17277 q^{20} -0.182674 q^{22} -1.55176 q^{23} +0.655021 q^{24} -0.279081 q^{25} -1.49551 q^{26} +3.64909 q^{27} +1.00000 q^{29} -1.42321 q^{30} -8.74651 q^{31} -1.00000 q^{32} -0.119655 q^{33} -4.61822 q^{34} -2.57095 q^{36} -11.8207 q^{37} -0.344979 q^{38} -0.979589 q^{39} +2.17277 q^{40} -2.54465 q^{41} -3.71554 q^{43} +0.182674 q^{44} +5.58607 q^{45} +1.55176 q^{46} +3.97963 q^{47} -0.655021 q^{48} +0.279081 q^{50} -3.02503 q^{51} +1.49551 q^{52} -5.84697 q^{53} -3.64909 q^{54} -0.396908 q^{55} -0.225968 q^{57} -1.00000 q^{58} +1.53418 q^{59} +1.42321 q^{60} +14.3693 q^{61} +8.74651 q^{62} +1.00000 q^{64} -3.24939 q^{65} +0.119655 q^{66} -2.37057 q^{67} +4.61822 q^{68} +1.01644 q^{69} +2.17683 q^{71} +2.57095 q^{72} -8.73473 q^{73} +11.8207 q^{74} +0.182804 q^{75} +0.344979 q^{76} +0.979589 q^{78} +8.92334 q^{79} -2.17277 q^{80} +5.32261 q^{81} +2.54465 q^{82} +17.6287 q^{83} -10.0343 q^{85} +3.71554 q^{86} -0.655021 q^{87} -0.182674 q^{88} +7.04783 q^{89} -5.58607 q^{90} -1.55176 q^{92} +5.72915 q^{93} -3.97963 q^{94} -0.749558 q^{95} +0.655021 q^{96} +4.15180 q^{97} -0.469645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9	$ 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9} - 5 q^{10} + 4 q^{11} + 3 q^{12} + 2 q^{13} + 6 q^{15} + 5 q^{16} + 2 q^{17} - 4 q^{18} + 8 q^{19} + 5 q^{20} - 4 q^{22} - 9 q^{23} - 3 q^{24} + 8 q^{25} - 2 q^{26} + 15 q^{27} + 5 q^{29} - 6 q^{30} - 15 q^{31} - 5 q^{32} + 29 q^{33} - 2 q^{34} + 4 q^{36} - 22 q^{37} - 8 q^{38} + 32 q^{39} - 5 q^{40} + q^{41} + 7 q^{43} + 4 q^{44} - 8 q^{45} + 9 q^{46} + 20 q^{47} + 3 q^{48} - 8 q^{50} - 15 q^{51} + 2 q^{52} + 11 q^{53} - 15 q^{54} - 4 q^{55} + 22 q^{57} - 5 q^{58} + 13 q^{59} + 6 q^{60} - 15 q^{61} + 15 q^{62} + 5 q^{64} - 7 q^{65} - 29 q^{66} + 20 q^{67} + 2 q^{68} + 20 q^{69} - 4 q^{71} - 4 q^{72} + 22 q^{74} + 20 q^{75} + 8 q^{76} - 32 q^{78} + q^{79} + 5 q^{80} + 21 q^{81} - q^{82} + 48 q^{83} - 13 q^{85} - 7 q^{86} + 3 q^{87} - 4 q^{88} - 7 q^{89} + 8 q^{90} - 9 q^{92} - 23 q^{93} - 20 q^{94} + 11 q^{95} - 3 q^{96} + 6 q^{97} + 32 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9 - 5 * q^10 + 4 * q^11 + 3 * q^12 + 2 * q^13 + 6 * q^15 + 5 * q^16 + 2 * q^17 - 4 * q^18 + 8 * q^19 + 5 * q^20 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 8 * q^25 - 2 * q^26 + 15 * q^27 + 5 * q^29 - 6 * q^30 - 15 * q^31 - 5 * q^32 + 29 * q^33 - 2 * q^34 + 4 * q^36 - 22 * q^37 - 8 * q^38 + 32 * q^39 - 5 * q^40 + q^41 + 7 * q^43 + 4 * q^44 - 8 * q^45 + 9 * q^46 + 20 * q^47 + 3 * q^48 - 8 * q^50 - 15 * q^51 + 2 * q^52 + 11 * q^53 - 15 * q^54 - 4 * q^55 + 22 * q^57 - 5 * q^58 + 13 * q^59 + 6 * q^60 - 15 * q^61 + 15 * q^62 + 5 * q^64 - 7 * q^65 - 29 * q^66 + 20 * q^67 + 2 * q^68 + 20 * q^69 - 4 * q^71 - 4 * q^72 + 22 * q^74 + 20 * q^75 + 8 * q^76 - 32 * q^78 + q^79 + 5 * q^80 + 21 * q^81 - q^82 + 48 * q^83 - 13 * q^85 - 7 * q^86 + 3 * q^87 - 4 * q^88 - 7 * q^89 + 8 * q^90 - 9 * q^92 - 23 * q^93 - 20 * q^94 + 11 * q^95 - 3 * q^96 + 6 * q^97 + 32 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.655021	−0.378177	−0.189088	−	0.981960i	$-0.560553\pi$
$3$	−0.655021	−0.378177	−0.189088	+	0.981960i	$0.560553\pi$
$4$	1.00000	0.500000
$5$	−2.17277	−0.971691	−0.485846	−	0.874045i	$-0.661488\pi$
$5$	−2.17277	−0.971691	−0.485846	+	0.874045i	$0.661488\pi$
$6$	0.655021	0.267411
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.57095	−0.856982
$10$	2.17277	0.687089
$11$	0.182674	0.0550782	0.0275391	−	0.999621i	$-0.491233\pi$
$11$	0.182674	0.0550782	0.0275391	+	0.999621i	$0.491233\pi$
$12$	−0.655021	−0.189088
$13$	1.49551	0.414779	0.207390	−	0.978258i	$-0.433503\pi$
$13$	1.49551	0.414779	0.207390	+	0.978258i	$0.433503\pi$
$14$	0	0
$15$	1.42321	0.367471
$16$	1.00000	0.250000
$17$	4.61822	1.12008	0.560041	−	0.828465i	$-0.310785\pi$
$17$	4.61822	1.12008	0.560041	+	0.828465i	$0.310785\pi$
$18$	2.57095	0.605978
$19$	0.344979	0.0791435	0.0395718	−	0.999217i	$-0.487401\pi$
$19$	0.344979	0.0791435	0.0395718	+	0.999217i	$0.487401\pi$
$20$	−2.17277	−0.485846
$21$	0	0
$22$	−0.182674	−0.0389462
$23$	−1.55176	−0.323565	−0.161782	−	0.986826i	$-0.551724\pi$
$23$	−1.55176	−0.323565	−0.161782	+	0.986826i	$0.551724\pi$
$24$	0.655021	0.133706
$25$	−0.279081	−0.0558161
$26$	−1.49551	−0.293293
$27$	3.64909	0.702268
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.42321	−0.259841
$31$	−8.74651	−1.57092	−0.785459	−	0.618913i	$-0.787573\pi$
$31$	−8.74651	−1.57092	−0.785459	+	0.618913i	$0.787573\pi$
$32$	−1.00000	−0.176777
$33$	−0.119655	−0.0208293
$34$	−4.61822	−0.792017
$35$	0	0
$36$	−2.57095	−0.428491
$37$	−11.8207	−1.94331	−0.971653	−	0.236410i	$-0.924029\pi$
$37$	−11.8207	−1.94331	−0.971653	+	0.236410i	$0.924029\pi$
$38$	−0.344979	−0.0559629
$39$	−0.979589	−0.156860
$40$	2.17277	0.343545
$41$	−2.54465	−0.397407	−0.198703	−	0.980060i	$-0.563673\pi$
$41$	−2.54465	−0.397407	−0.198703	+	0.980060i	$0.563673\pi$
$42$	0	0
$43$	−3.71554	−0.566615	−0.283308	−	0.959029i	$-0.591432\pi$
$43$	−3.71554	−0.566615	−0.283308	+	0.959029i	$0.591432\pi$
$44$	0.182674	0.0275391
$45$	5.58607	0.832722
$46$	1.55176	0.228795
$47$	3.97963	0.580489	0.290244	−	0.956953i	$-0.406263\pi$
$47$	3.97963	0.580489	0.290244	+	0.956953i	$0.406263\pi$
$48$	−0.655021	−0.0945442
$49$	0	0
$50$	0.279081	0.0394680
$51$	−3.02503	−0.423589
$52$	1.49551	0.207390
$53$	−5.84697	−0.803144	−0.401572	−	0.915828i	$-0.631536\pi$
$53$	−5.84697	−0.803144	−0.401572	+	0.915828i	$0.631536\pi$
$54$	−3.64909	−0.496578
$55$	−0.396908	−0.0535191
$56$	0	0
$57$	−0.225968	−0.0299302
$58$	−1.00000	−0.131306
$59$	1.53418	0.199734	0.0998668	−	0.995001i	$-0.468158\pi$
$59$	1.53418	0.199734	0.0998668	+	0.995001i	$0.468158\pi$
$60$	1.42321	0.183736
$61$	14.3693	1.83981	0.919903	−	0.392147i	$-0.128267\pi$
$61$	14.3693	1.83981	0.919903	+	0.392147i	$0.128267\pi$
$62$	8.74651	1.11081
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.24939	−0.403037
$66$	0.119655	0.0147285
$67$	−2.37057	−0.289611	−0.144805	−	0.989460i	$-0.546256\pi$
$67$	−2.37057	−0.289611	−0.144805	+	0.989460i	$0.546256\pi$
$68$	4.61822	0.560041
$69$	1.01644	0.122365
$70$	0	0
$71$	2.17683	0.258342	0.129171	−	0.991622i	$-0.458768\pi$
$71$	2.17683	0.258342	0.129171	+	0.991622i	$0.458768\pi$
$72$	2.57095	0.302989
$73$	−8.73473	−1.02232	−0.511161	−	0.859485i	$-0.670785\pi$
$73$	−8.73473	−1.02232	−0.511161	+	0.859485i	$0.670785\pi$
$74$	11.8207	1.37413
$75$	0.182804	0.0211084
$76$	0.344979	0.0395718
$77$	0	0
$78$	0.979589	0.110917
$79$	8.92334	1.00395	0.501977	−	0.864881i	$-0.332606\pi$
$79$	8.92334	1.00395	0.501977	+	0.864881i	$0.332606\pi$
$80$	−2.17277	−0.242923
$81$	5.32261	0.591401
$82$	2.54465	0.281009
$83$	17.6287	1.93500	0.967499	−	0.252873i	$-0.0813756\pi$
$83$	17.6287	1.93500	0.967499	+	0.252873i	$0.0813756\pi$
$84$	0	0
$85$	−10.0343	−1.08837
$86$	3.71554	0.400657
$87$	−0.655021	−0.0702257
$88$	−0.182674	−0.0194731
$89$	7.04783	0.747068	0.373534	−	0.927616i	$-0.378146\pi$
$89$	7.04783	0.747068	0.373534	+	0.927616i	$0.378146\pi$
$90$	−5.58607	−0.588824
$91$	0	0
$92$	−1.55176	−0.161782
$93$	5.72915	0.594085
$94$	−3.97963	−0.410468
$95$	−0.749558	−0.0769031
$96$	0.655021	0.0668528
$97$	4.15180	0.421551	0.210776	−	0.977534i	$-0.432401\pi$
$97$	4.15180	0.421551	0.210776	+	0.977534i	$0.432401\pi$
$98$	0	0
$99$	−0.469645	−0.0472011
$100$	−0.279081	−0.0279081
$101$	−4.53474	−0.451223	−0.225612	−	0.974217i	$-0.572438\pi$
$101$	−4.53474	−0.451223	−0.225612	+	0.974217i	$0.572438\pi$
$102$	3.02503	0.299523
$103$	4.71987	0.465062	0.232531	−	0.972589i	$-0.425299\pi$
$103$	4.71987	0.465062	0.232531	+	0.972589i	$0.425299\pi$
$104$	−1.49551	−0.146647
$105$	0	0
$106$	5.84697	0.567908
$107$	−15.0711	−1.45698	−0.728488	−	0.685059i	$-0.759777\pi$
$107$	−15.0711	−1.45698	−0.728488	+	0.685059i	$0.759777\pi$
$108$	3.64909	0.351134
$109$	7.22164	0.691708	0.345854	−	0.938288i	$-0.387589\pi$
$109$	7.22164	0.691708	0.345854	+	0.938288i	$0.387589\pi$
$110$	0.396908	0.0378437
$111$	7.74279	0.734913
$112$	0	0
$113$	15.8166	1.48790	0.743949	−	0.668237i	$-0.232951\pi$
$113$	15.8166	1.48790	0.743949	+	0.668237i	$0.232951\pi$
$114$	0.225968	0.0211639
$115$	3.37162	0.314405
$116$	1.00000	0.0928477
$117$	−3.84487	−0.355458
$118$	−1.53418	−0.141233
$119$	0	0
$120$	−1.42321	−0.129921
$121$	−10.9666	−0.996966
$122$	−14.3693	−1.30094
$123$	1.66680	0.150290
$124$	−8.74651	−0.785459
$125$	11.4702	1.02593
$126$	0	0
$127$	−5.83677	−0.517930	−0.258965	−	0.965887i	$-0.583381\pi$
$127$	−5.83677	−0.517930	−0.258965	+	0.965887i	$0.583381\pi$
$128$	−1.00000	−0.0883883
$129$	2.43376	0.214281
$130$	3.24939	0.284990
$131$	9.43833	0.824631	0.412315	−	0.911041i	$-0.364720\pi$
$131$	9.43833	0.824631	0.412315	+	0.911041i	$0.364720\pi$
$132$	−0.119655	−0.0104147
$133$	0	0
$134$	2.37057	0.204786
$135$	−7.92862	−0.682387
$136$	−4.61822	−0.396009
$137$	21.3961	1.82799	0.913997	−	0.405722i	$-0.132980\pi$
$137$	21.3961	1.82799	0.913997	+	0.405722i	$0.132980\pi$
$138$	−1.01644	−0.0865248
$139$	−12.5948	−1.06827	−0.534136	−	0.845398i	$-0.679363\pi$
$139$	−12.5948	−1.06827	−0.534136	+	0.845398i	$0.679363\pi$
$140$	0	0
$141$	−2.60674	−0.219527
$142$	−2.17683	−0.182676
$143$	0.273190	0.0228453
$144$	−2.57095	−0.214246
$145$	−2.17277	−0.180439
$146$	8.73473	0.722891
$147$	0	0
$148$	−11.8207	−0.971653
$149$	7.75884	0.635629	0.317814	−	0.948153i	$-0.397051\pi$
$149$	7.75884	0.635629	0.317814	+	0.948153i	$0.397051\pi$
$150$	−0.182804	−0.0149259
$151$	4.47756	0.364379	0.182190	−	0.983263i	$-0.441682\pi$
$151$	4.47756	0.364379	0.182190	+	0.983263i	$0.441682\pi$
$152$	−0.344979	−0.0279815
$153$	−11.8732	−0.959890
$154$	0	0
$155$	19.0041	1.52645
$156$	−0.979589	−0.0784299
$157$	3.56908	0.284843	0.142422	−	0.989806i	$-0.454511\pi$
$157$	3.56908	0.284843	0.142422	+	0.989806i	$0.454511\pi$
$158$	−8.92334	−0.709902
$159$	3.82989	0.303730
$160$	2.17277	0.171772
$161$	0	0
$162$	−5.32261	−0.418184
$163$	13.6128	1.06624	0.533120	−	0.846040i	$-0.321019\pi$
$163$	13.6128	1.06624	0.533120	+	0.846040i	$0.321019\pi$
$164$	−2.54465	−0.198703
$165$	0.259983	0.0202397
$166$	−17.6287	−1.36825
$167$	6.20678	0.480295	0.240148	−	0.970736i	$-0.422804\pi$
$167$	6.20678	0.480295	0.240148	+	0.970736i	$0.422804\pi$
$168$	0	0
$169$	−10.7635	−0.827958
$170$	10.0343	0.769596
$171$	−0.886922	−0.0678246
$172$	−3.71554	−0.283308
$173$	11.0433	0.839606	0.419803	−	0.907615i	$-0.362099\pi$
$173$	11.0433	0.839606	0.419803	+	0.907615i	$0.362099\pi$
$174$	0.655021	0.0496570
$175$	0	0
$176$	0.182674	0.0137696
$177$	−1.00492	−0.0755346
$178$	−7.04783	−0.528257
$179$	12.0210	0.898493	0.449246	−	0.893408i	$-0.351693\pi$
$179$	12.0210	0.898493	0.449246	+	0.893408i	$0.351693\pi$
$180$	5.58607	0.416361
$181$	−2.10545	−0.156497	−0.0782485	−	0.996934i	$-0.524933\pi$
$181$	−2.10545	−0.156497	−0.0782485	+	0.996934i	$0.524933\pi$
$182$	0	0
$183$	−9.41222	−0.695772
$184$	1.55176	0.114397
$185$	25.6836	1.88829
$186$	−5.72915	−0.420081
$187$	0.843627	0.0616921
$188$	3.97963	0.290244
$189$	0	0
$190$	0.749558	0.0543787
$191$	−8.48898	−0.614241	−0.307120	−	0.951671i	$-0.599365\pi$
$191$	−8.48898	−0.614241	−0.307120	+	0.951671i	$0.599365\pi$
$192$	−0.655021	−0.0472721
$193$	18.5575	1.33580	0.667899	−	0.744252i	$-0.267194\pi$
$193$	18.5575	1.33580	0.667899	+	0.744252i	$0.267194\pi$
$194$	−4.15180	−0.298082
$195$	2.12842	0.152419
$196$	0	0
$197$	−0.581995	−0.0414654	−0.0207327	−	0.999785i	$-0.506600\pi$
$197$	−0.581995	−0.0414654	−0.0207327	+	0.999785i	$0.506600\pi$
$198$	0.469645	0.0333762
$199$	−4.39526	−0.311572	−0.155786	−	0.987791i	$-0.549791\pi$
$199$	−4.39526	−0.311572	−0.155786	+	0.987791i	$0.549791\pi$
$200$	0.279081	0.0197340
$201$	1.55277	0.109524
$202$	4.53474	0.319063
$203$	0	0
$204$	−3.02503	−0.211794
$205$	5.52892	0.386157
$206$	−4.71987	−0.328849
$207$	3.98950	0.277289
$208$	1.49551	0.103695
$209$	0.0630186	0.00435909
$210$	0	0
$211$	−2.05399	−0.141403	−0.0707013	−	0.997498i	$-0.522524\pi$
$211$	−2.05399	−0.141403	−0.0707013	+	0.997498i	$0.522524\pi$
$212$	−5.84697	−0.401572
$213$	−1.42587	−0.0976990
$214$	15.0711	1.03024
$215$	8.07301	0.550575
$216$	−3.64909	−0.248289
$217$	0	0
$218$	−7.22164	−0.489111
$219$	5.72143	0.386619
$220$	−0.396908	−0.0267595
$221$	6.90658	0.464587
$222$	−7.74279	−0.519662
$223$	−6.07321	−0.406692	−0.203346	−	0.979107i	$-0.565182\pi$
$223$	−6.07321	−0.406692	−0.203346	+	0.979107i	$0.565182\pi$
$224$	0	0
$225$	0.717502	0.0478335
$226$	−15.8166	−1.05210
$227$	6.31529	0.419160	0.209580	−	0.977791i	$-0.432790\pi$
$227$	6.31529	0.419160	0.209580	+	0.977791i	$0.432790\pi$
$228$	−0.225968	−0.0149651
$229$	−6.01863	−0.397722	−0.198861	−	0.980028i	$-0.563724\pi$
$229$	−6.01863	−0.397722	−0.198861	+	0.980028i	$0.563724\pi$
$230$	−3.37162	−0.222318
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−2.45844	−0.161058	−0.0805289	−	0.996752i	$-0.525661\pi$
$233$	−2.45844	−0.161058	−0.0805289	+	0.996752i	$0.525661\pi$
$234$	3.84487	0.251347
$235$	−8.64681	−0.564056
$236$	1.53418	0.0998668
$237$	−5.84498	−0.379672
$238$	0	0
$239$	2.30173	0.148887	0.0744433	−	0.997225i	$-0.476282\pi$
$239$	2.30173	0.148887	0.0744433	+	0.997225i	$0.476282\pi$
$240$	1.42321	0.0918678
$241$	17.1214	1.10289	0.551443	−	0.834213i	$-0.314077\pi$
$241$	17.1214	1.10289	0.551443	+	0.834213i	$0.314077\pi$
$242$	10.9666	0.704962
$243$	−14.4337	−0.925922
$244$	14.3693	0.919903
$245$	0	0
$246$	−1.66680	−0.106271
$247$	0.515918	0.0328271
$248$	8.74651	0.555404
$249$	−11.5472	−0.731772
$250$	−11.4702	−0.725440
$251$	19.2883	1.21747	0.608734	−	0.793374i	$-0.291678\pi$
$251$	19.2883	1.21747	0.608734	+	0.793374i	$0.291678\pi$
$252$	0	0
$253$	−0.283466	−0.0178214
$254$	5.83677	0.366232
$255$	6.57269	0.411598
$256$	1.00000	0.0625000
$257$	−2.93101	−0.182831	−0.0914156	−	0.995813i	$-0.529139\pi$
$257$	−2.93101	−0.182831	−0.0914156	+	0.995813i	$0.529139\pi$
$258$	−2.43376	−0.151519
$259$	0	0
$260$	−3.24939	−0.201519
$261$	−2.57095	−0.159138
$262$	−9.43833	−0.583102
$263$	−22.3668	−1.37920	−0.689599	−	0.724191i	$-0.742213\pi$
$263$	−22.3668	−1.37920	−0.689599	+	0.724191i	$0.742213\pi$
$264$	0.119655	0.00736427
$265$	12.7041	0.780408
$266$	0	0
$267$	−4.61648	−0.282524
$268$	−2.37057	−0.144805
$269$	8.37486	0.510624	0.255312	−	0.966859i	$-0.417822\pi$
$269$	8.37486	0.510624	0.255312	+	0.966859i	$0.417822\pi$
$270$	7.92862	0.482521
$271$	22.1777	1.34720	0.673599	−	0.739097i	$-0.264747\pi$
$271$	22.1777	1.34720	0.673599	+	0.739097i	$0.264747\pi$
$272$	4.61822	0.280020
$273$	0	0
$274$	−21.3961	−1.29259
$275$	−0.0509808	−0.00307426
$276$	1.01644	0.0611823
$277$	−19.1585	−1.15112	−0.575561	−	0.817759i	$-0.695216\pi$
$277$	−19.1585	−1.15112	−0.575561	+	0.817759i	$0.695216\pi$
$278$	12.5948	0.755383
$279$	22.4868	1.34625
$280$	0	0
$281$	24.6753	1.47201	0.736003	−	0.676978i	$-0.236711\pi$
$281$	24.6753	1.47201	0.736003	+	0.676978i	$0.236711\pi$
$282$	2.60674	0.155229
$283$	25.2237	1.49939	0.749696	−	0.661782i	$-0.230200\pi$
$283$	25.2237	1.49939	0.749696	+	0.661782i	$0.230200\pi$
$284$	2.17683	0.129171
$285$	0.490977	0.0290830
$286$	−0.273190	−0.0161541
$287$	0	0
$288$	2.57095	0.151495
$289$	4.32792	0.254583
$290$	2.17277	0.127589
$291$	−2.71952	−0.159421
$292$	−8.73473	−0.511161
$293$	−14.4654	−0.845079	−0.422540	−	0.906344i	$-0.638861\pi$
$293$	−14.4654	−0.845079	−0.422540	+	0.906344i	$0.638861\pi$
$294$	0	0
$295$	−3.33342	−0.194079
$296$	11.8207	0.687063
$297$	0.666593	0.0386797
$298$	−7.75884	−0.449457
$299$	−2.32067	−0.134208
$300$	0.182804	0.0105542
$301$	0	0
$302$	−4.47756	−0.257655
$303$	2.97035	0.170642
$304$	0.344979	0.0197859
$305$	−31.2212	−1.78772
$306$	11.8732	0.678745
$307$	21.7267	1.24001	0.620003	−	0.784600i	$-0.287131\pi$
$307$	21.7267	1.24001	0.620003	+	0.784600i	$0.287131\pi$
$308$	0	0
$309$	−3.09161	−0.175876
$310$	−19.0041	−1.07936
$311$	14.3673	0.814693	0.407346	−	0.913274i	$-0.366454\pi$
$311$	14.3673	0.814693	0.407346	+	0.913274i	$0.366454\pi$
$312$	0.979589	0.0554583
$313$	−11.5202	−0.651162	−0.325581	−	0.945514i	$-0.605560\pi$
$313$	−11.5202	−0.651162	−0.325581	+	0.945514i	$0.605560\pi$
$314$	−3.56908	−0.201415
$315$	0	0
$316$	8.92334	0.501977
$317$	16.0481	0.901352	0.450676	−	0.892688i	$-0.351183\pi$
$317$	16.0481	0.901352	0.450676	+	0.892688i	$0.351183\pi$
$318$	−3.82989	−0.214770
$319$	0.182674	0.0102278
$320$	−2.17277	−0.121461
$321$	9.87187	0.550994
$322$	0	0
$323$	1.59319	0.0886472
$324$	5.32261	0.295701
$325$	−0.417367	−0.0231514
$326$	−13.6128	−0.753945
$327$	−4.73033	−0.261588
$328$	2.54465	0.140505
$329$	0	0
$330$	−0.259983	−0.0143116
$331$	23.0296	1.26582	0.632910	−	0.774225i	$-0.281860\pi$
$331$	23.0296	1.26582	0.632910	+	0.774225i	$0.281860\pi$
$332$	17.6287	0.967499
$333$	30.3903	1.66538
$334$	−6.20678	−0.339620
$335$	5.15069	0.281412
$336$	0	0
$337$	10.3475	0.563662	0.281831	−	0.959464i	$-0.409058\pi$
$337$	10.3475	0.563662	0.281831	+	0.959464i	$0.409058\pi$
$338$	10.7635	0.585455
$339$	−10.3602	−0.562688
$340$	−10.0343	−0.544187
$341$	−1.59776	−0.0865235
$342$	0.886922	0.0479592
$343$	0	0
$344$	3.71554	0.200329
$345$	−2.20848	−0.118901
$346$	−11.0433	−0.593691
$347$	11.6067	0.623079	0.311539	−	0.950233i	$-0.399155\pi$
$347$	11.6067	0.623079	0.311539	+	0.950233i	$0.399155\pi$
$348$	−0.655021	−0.0351128
$349$	−31.0495	−1.66204	−0.831020	−	0.556242i	$-0.812243\pi$
$349$	−31.0495	−1.66204	−0.831020	+	0.556242i	$0.812243\pi$
$350$	0	0
$351$	5.45724	0.291286
$352$	−0.182674	−0.00973655
$353$	14.6989	0.782343	0.391171	−	0.920318i	$-0.372070\pi$
$353$	14.6989	0.782343	0.391171	+	0.920318i	$0.372070\pi$
$354$	1.00492	0.0534110
$355$	−4.72975	−0.251029
$356$	7.04783	0.373534
$357$	0	0
$358$	−12.0210	−0.635330
$359$	−30.5300	−1.61131	−0.805656	−	0.592383i	$-0.798187\pi$
$359$	−30.5300	−1.61131	−0.805656	+	0.592383i	$0.798187\pi$
$360$	−5.58607	−0.294412
$361$	−18.8810	−0.993736
$362$	2.10545	0.110660
$363$	7.18338	0.377030
$364$	0	0
$365$	18.9785	0.993382
$366$	9.41222	0.491985
$367$	−5.12021	−0.267273	−0.133636	−	0.991030i	$-0.542665\pi$
$367$	−5.12021	−0.267273	−0.133636	+	0.991030i	$0.542665\pi$
$368$	−1.55176	−0.0808911
$369$	6.54215	0.340571
$370$	−25.6836	−1.33523
$371$	0	0
$372$	5.72915	0.297042
$373$	14.0322	0.726562	0.363281	−	0.931680i	$-0.381657\pi$
$373$	14.0322	0.726562	0.363281	+	0.931680i	$0.381657\pi$
$374$	−0.843627	−0.0436229
$375$	−7.51324	−0.387982
$376$	−3.97963	−0.205234
$377$	1.49551	0.0770226
$378$	0	0
$379$	−17.0722	−0.876941	−0.438471	−	0.898745i	$-0.644480\pi$
$379$	−17.0722	−0.876941	−0.438471	+	0.898745i	$0.644480\pi$
$380$	−0.749558	−0.0384515
$381$	3.82321	0.195869
$382$	8.48898	0.434334
$383$	24.9613	1.27546	0.637730	−	0.770260i	$-0.279873\pi$
$383$	24.9613	1.27546	0.637730	+	0.770260i	$0.279873\pi$
$384$	0.655021	0.0334264
$385$	0	0
$386$	−18.5575	−0.944552
$387$	9.55247	0.485579
$388$	4.15180	0.210776
$389$	−39.1586	−1.98542	−0.992710	−	0.120531i	$-0.961540\pi$
$389$	−39.1586	−1.98542	−0.992710	+	0.120531i	$0.961540\pi$
$390$	−2.12842	−0.107777
$391$	−7.16637	−0.362419
$392$	0	0
$393$	−6.18231	−0.311856
$394$	0.581995	0.0293205
$395$	−19.3883	−0.975533
$396$	−0.469645	−0.0236005
$397$	18.2632	0.916602	0.458301	−	0.888797i	$-0.348458\pi$
$397$	18.2632	0.916602	0.458301	+	0.888797i	$0.348458\pi$
$398$	4.39526	0.220314
$399$	0	0
$400$	−0.279081	−0.0139540
$401$	−7.60891	−0.379971	−0.189985	−	0.981787i	$-0.560844\pi$
$401$	−7.60891	−0.379971	−0.189985	+	0.981787i	$0.560844\pi$
$402$	−1.55277	−0.0774452
$403$	−13.0805	−0.651584
$404$	−4.53474	−0.225612
$405$	−11.5648	−0.574659
$406$	0	0
$407$	−2.15933	−0.107034
$408$	3.02503	0.149761
$409$	−35.6379	−1.76218	−0.881090	−	0.472949i	$-0.843189\pi$
$409$	−35.6379	−1.76218	−0.881090	+	0.472949i	$0.843189\pi$
$410$	−5.52892	−0.273054
$411$	−14.0149	−0.691304
$412$	4.71987	0.232531
$413$	0	0
$414$	−3.98950	−0.196073
$415$	−38.3030	−1.88022
$416$	−1.49551	−0.0733233
$417$	8.24983	0.403996
$418$	−0.0630186	−0.00308234
$419$	−14.2401	−0.695677	−0.347838	−	0.937555i	$-0.613084\pi$
$419$	−14.2401	−0.695677	−0.347838	+	0.937555i	$0.613084\pi$
$420$	0	0
$421$	14.5354	0.708411	0.354205	−	0.935168i	$-0.384751\pi$
$421$	14.5354	0.708411	0.354205	+	0.935168i	$0.384751\pi$
$422$	2.05399	0.0999868
$423$	−10.2314	−0.497469
$424$	5.84697	0.283954
$425$	−1.28886	−0.0625187
$426$	1.42587	0.0690836
$427$	0	0
$428$	−15.0711	−0.728488
$429$	−0.178945	−0.00863956
$430$	−8.07301	−0.389315
$431$	−27.8928	−1.34355	−0.671775	−	0.740755i	$-0.734468\pi$
$431$	−27.8928	−1.34355	−0.671775	+	0.740755i	$0.734468\pi$
$432$	3.64909	0.175567
$433$	0.743364	0.0357238	0.0178619	−	0.999840i	$-0.494314\pi$
$433$	0.743364	0.0357238	0.0178619	+	0.999840i	$0.494314\pi$
$434$	0	0
$435$	1.42321	0.0682377
$436$	7.22164	0.345854
$437$	−0.535324	−0.0256080
$438$	−5.72143	−0.273381
$439$	24.2553	1.15764	0.578821	−	0.815454i	$-0.303513\pi$
$439$	24.2553	1.15764	0.578821	+	0.815454i	$0.303513\pi$
$440$	0.396908	0.0189218
$441$	0	0
$442$	−6.90658	−0.328512
$443$	32.8126	1.55897	0.779486	−	0.626420i	$-0.215480\pi$
$443$	32.8126	1.55897	0.779486	+	0.626420i	$0.215480\pi$
$444$	7.74279	0.367457
$445$	−15.3133	−0.725919
$446$	6.07321	0.287575
$447$	−5.08220	−0.240380
$448$	0	0
$449$	6.24045	0.294505	0.147252	−	0.989099i	$-0.452957\pi$
$449$	6.24045	0.294505	0.147252	+	0.989099i	$0.452957\pi$
$450$	−0.717502	−0.0338234
$451$	−0.464840	−0.0218885
$452$	15.8166	0.743949
$453$	−2.93290	−0.137800
$454$	−6.31529	−0.296391
$455$	0	0
$456$	0.225968	0.0105819
$457$	13.6157	0.636914	0.318457	−	0.947937i	$-0.396835\pi$
$457$	13.6157	0.636914	0.318457	+	0.947937i	$0.396835\pi$
$458$	6.01863	0.281232
$459$	16.8523	0.786597
$460$	3.37162	0.157202
$461$	−8.97688	−0.418095	−0.209048	−	0.977905i	$-0.567036\pi$
$461$	−8.97688	−0.418095	−0.209048	+	0.977905i	$0.567036\pi$
$462$	0	0
$463$	39.7503	1.84735	0.923676	−	0.383176i	$-0.125170\pi$
$463$	39.7503	1.84735	0.923676	+	0.383176i	$0.125170\pi$
$464$	1.00000	0.0464238
$465$	−12.4481	−0.577267
$466$	2.45844	0.113885
$467$	17.5763	0.813334	0.406667	−	0.913576i	$-0.366691\pi$
$467$	17.5763	0.813334	0.406667	+	0.913576i	$0.366691\pi$
$468$	−3.84487	−0.177729
$469$	0	0
$470$	8.64681	0.398848
$471$	−2.33782	−0.107721
$472$	−1.53418	−0.0706165
$473$	−0.678733	−0.0312082
$474$	5.84498	0.268469
$475$	−0.0962769	−0.00441749
$476$	0	0
$477$	15.0323	0.688280
$478$	−2.30173	−0.105279
$479$	−5.68285	−0.259656	−0.129828	−	0.991537i	$-0.541443\pi$
$479$	−5.68285	−0.259656	−0.129828	+	0.991537i	$0.541443\pi$
$480$	−1.42321	−0.0649603
$481$	−17.6779	−0.806043
$482$	−17.1214	−0.779858
$483$	0	0
$484$	−10.9666	−0.498483
$485$	−9.02090	−0.409618
$486$	14.4337	0.654725
$487$	33.6464	1.52467	0.762333	−	0.647185i	$-0.224054\pi$
$487$	33.6464	1.52467	0.762333	+	0.647185i	$0.224054\pi$
$488$	−14.3693	−0.650469
$489$	−8.91670	−0.403227
$490$	0	0
$491$	−7.39966	−0.333942	−0.166971	−	0.985962i	$-0.553399\pi$
$491$	−7.39966	−0.333942	−0.166971	+	0.985962i	$0.553399\pi$
$492$	1.66680	0.0751450
$493$	4.61822	0.207994
$494$	−0.515918	−0.0232123
$495$	1.02043	0.0458649
$496$	−8.74651	−0.392730
$497$	0	0
$498$	11.5472	0.517441
$499$	35.2672	1.57878	0.789388	−	0.613894i	$-0.210398\pi$
$499$	35.2672	1.57878	0.789388	+	0.613894i	$0.210398\pi$
$500$	11.4702	0.512964
$501$	−4.06557	−0.181636
$502$	−19.2883	−0.860880
$503$	−6.35232	−0.283236	−0.141618	−	0.989921i	$-0.545230\pi$
$503$	−6.35232	−0.283236	−0.141618	+	0.989921i	$0.545230\pi$
$504$	0	0
$505$	9.85294	0.438450
$506$	0.283466	0.0126016
$507$	7.05029	0.313115
$508$	−5.83677	−0.258965
$509$	31.2445	1.38489	0.692445	−	0.721471i	$-0.256534\pi$
$509$	31.2445	1.38489	0.692445	+	0.721471i	$0.256534\pi$
$510$	−6.57269	−0.291043
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	1.25886	0.0555799
$514$	2.93101	0.129281
$515$	−10.2552	−0.451897
$516$	2.43376	0.107140
$517$	0.726975	0.0319723
$518$	0	0
$519$	−7.23359	−0.317520
$520$	3.24939	0.142495
$521$	−30.4330	−1.33329	−0.666647	−	0.745373i	$-0.732271\pi$
$521$	−30.4330	−1.33329	−0.666647	+	0.745373i	$0.732271\pi$
$522$	2.57095	0.112527
$523$	−9.56130	−0.418087	−0.209043	−	0.977906i	$-0.567035\pi$
$523$	−9.56130	−0.418087	−0.209043	+	0.977906i	$0.567035\pi$
$524$	9.43833	0.412315
$525$	0	0
$526$	22.3668	0.975241
$527$	−40.3932	−1.75956
$528$	−0.119655	−0.00520733
$529$	−20.5920	−0.895306
$530$	−12.7041	−0.551832
$531$	−3.94430	−0.171168
$532$	0	0
$533$	−3.80554	−0.164836
$534$	4.61648	0.199774
$535$	32.7459	1.41573
$536$	2.37057	0.102393
$537$	−7.87402	−0.339789
$538$	−8.37486	−0.361066
$539$	0	0
$540$	−7.92862	−0.341194
$541$	19.2986	0.829711	0.414856	−	0.909887i	$-0.363832\pi$
$541$	19.2986	0.829711	0.414856	+	0.909887i	$0.363832\pi$
$542$	−22.1777	−0.952613
$543$	1.37912	0.0591836
$544$	−4.61822	−0.198004
$545$	−15.6910	−0.672127
$546$	0	0
$547$	−17.5286	−0.749467	−0.374733	−	0.927133i	$-0.622266\pi$
$547$	−17.5286	−0.749467	−0.374733	+	0.927133i	$0.622266\pi$
$548$	21.3961	0.913997
$549$	−36.9428	−1.57668
$550$	0.0509808	0.00217383
$551$	0.344979	0.0146966
$552$	−1.01644	−0.0432624
$553$	0	0
$554$	19.1585	0.813966
$555$	−16.8233	−0.714109
$556$	−12.5948	−0.534136
$557$	−12.3726	−0.524242	−0.262121	−	0.965035i	$-0.584422\pi$
$557$	−12.3726	−0.524242	−0.262121	+	0.965035i	$0.584422\pi$
$558$	−22.4868	−0.951942
$559$	−5.55662	−0.235020
$560$	0	0
$561$	−0.552594	−0.0233305
$562$	−24.6753	−1.04087
$563$	38.3780	1.61744	0.808721	−	0.588193i	$-0.200160\pi$
$563$	38.3780	1.61744	0.808721	+	0.588193i	$0.200160\pi$
$564$	−2.60674	−0.109764
$565$	−34.3657	−1.44578
$566$	−25.2237	−1.06023
$567$	0	0
$568$	−2.17683	−0.0913378
$569$	−40.3838	−1.69298	−0.846488	−	0.532407i	$-0.821288\pi$
$569$	−40.3838	−1.69298	−0.846488	+	0.532407i	$0.821288\pi$
$570$	−0.490977	−0.0205648
$571$	45.6116	1.90879	0.954393	−	0.298552i	$-0.0965035\pi$
$571$	45.6116	1.90879	0.954393	+	0.298552i	$0.0965035\pi$
$572$	0.273190	0.0114227
$573$	5.56046	0.232292
$574$	0	0
$575$	0.433067	0.0180601
$576$	−2.57095	−0.107123
$577$	−36.3253	−1.51224	−0.756121	−	0.654432i	$-0.772908\pi$
$577$	−36.3253	−1.51224	−0.756121	+	0.654432i	$0.772908\pi$
$578$	−4.32792	−0.180018
$579$	−12.1556	−0.505168
$580$	−2.17277	−0.0902193
$581$	0	0
$582$	2.71952	0.112728
$583$	−1.06809	−0.0442358
$584$	8.73473	0.361446
$585$	8.35401	0.345396
$586$	14.4654	0.597561
$587$	27.7476	1.14527	0.572633	−	0.819812i	$-0.305922\pi$
$587$	27.7476	1.14527	0.572633	+	0.819812i	$0.305922\pi$
$588$	0	0
$589$	−3.01736	−0.124328
$590$	3.33342	0.137235
$591$	0.381219	0.0156813
$592$	−11.8207	−0.485827
$593$	−13.9179	−0.571539	−0.285769	−	0.958298i	$-0.592249\pi$
$593$	−13.9179	−0.571539	−0.285769	+	0.958298i	$0.592249\pi$
$594$	−0.666593	−0.0273507
$595$	0	0
$596$	7.75884	0.317814
$597$	2.87899	0.117829
$598$	2.32067	0.0948993
$599$	42.6617	1.74311	0.871555	−	0.490298i	$-0.163112\pi$
$599$	42.6617	1.74311	0.871555	+	0.490298i	$0.163112\pi$
$600$	−0.182804	−0.00746294
$601$	−45.2196	−1.84455	−0.922274	−	0.386538i	$-0.873671\pi$
$601$	−45.2196	−1.84455	−0.922274	+	0.386538i	$0.873671\pi$
$602$	0	0
$603$	6.09460	0.248191
$604$	4.47756	0.182190
$605$	23.8279	0.968743
$606$	−2.97035	−0.120662
$607$	−31.2128	−1.26689	−0.633444	−	0.773788i	$-0.718359\pi$
$607$	−31.2128	−1.26689	−0.633444	+	0.773788i	$0.718359\pi$
$608$	−0.344979	−0.0139907
$609$	0	0
$610$	31.2212	1.26411
$611$	5.95157	0.240775
$612$	−11.8732	−0.479945
$613$	−5.22075	−0.210864	−0.105432	−	0.994427i	$-0.533623\pi$
$613$	−5.22075	−0.210864	−0.105432	+	0.994427i	$0.533623\pi$
$614$	−21.7267	−0.876816
$615$	−3.62156	−0.146036
$616$	0	0
$617$	21.9929	0.885400	0.442700	−	0.896670i	$-0.354021\pi$
$617$	21.9929	0.885400	0.442700	+	0.896670i	$0.354021\pi$
$618$	3.09161	0.124363
$619$	−27.7414	−1.11502	−0.557510	−	0.830170i	$-0.688243\pi$
$619$	−27.7414	−1.11502	−0.557510	+	0.830170i	$0.688243\pi$
$620$	19.0041	0.763224
$621$	−5.66251	−0.227229
$622$	−14.3673	−0.576075
$623$	0	0
$624$	−0.979589	−0.0392150
$625$	−23.5267	−0.941068
$626$	11.5202	0.460441
$627$	−0.0412785	−0.00164851
$628$	3.56908	0.142422
$629$	−54.5904	−2.17666
$630$	0	0
$631$	−10.5596	−0.420370	−0.210185	−	0.977662i	$-0.567407\pi$
$631$	−10.5596	−0.420370	−0.210185	+	0.977662i	$0.567407\pi$
$632$	−8.92334	−0.354951
$633$	1.34541	0.0534752
$634$	−16.0481	−0.637352
$635$	12.6820	0.503268
$636$	3.82989	0.151865
$637$	0	0
$638$	−0.182674	−0.00723213
$639$	−5.59651	−0.221395
$640$	2.17277	0.0858862
$641$	−16.9817	−0.670738	−0.335369	−	0.942087i	$-0.608861\pi$
$641$	−16.9817	−0.670738	−0.335369	+	0.942087i	$0.608861\pi$
$642$	−9.87187	−0.389612
$643$	−0.682699	−0.0269230	−0.0134615	−	0.999909i	$-0.504285\pi$
$643$	−0.682699	−0.0269230	−0.0134615	+	0.999909i	$0.504285\pi$
$644$	0	0
$645$	−5.28800	−0.208215
$646$	−1.59319	−0.0626831
$647$	37.1130	1.45906	0.729531	−	0.683948i	$-0.239739\pi$
$647$	37.1130	1.45906	0.729531	+	0.683948i	$0.239739\pi$
$648$	−5.32261	−0.209092
$649$	0.280255	0.0110010
$650$	0.417367	0.0163705
$651$	0	0
$652$	13.6128	0.533120
$653$	3.09765	0.121220	0.0606102	−	0.998162i	$-0.480695\pi$
$653$	3.09765	0.121220	0.0606102	+	0.998162i	$0.480695\pi$
$654$	4.73033	0.184971
$655$	−20.5073	−0.801287
$656$	−2.54465	−0.0993517
$657$	22.4565	0.876113
$658$	0	0
$659$	−26.0668	−1.01542	−0.507710	−	0.861528i	$-0.669508\pi$
$659$	−26.0668	−1.01542	−0.507710	+	0.861528i	$0.669508\pi$
$660$	0.259983	0.0101198
$661$	23.3673	0.908883	0.454442	−	0.890777i	$-0.349839\pi$
$661$	23.3673	0.908883	0.454442	+	0.890777i	$0.349839\pi$
$662$	−23.0296	−0.895070
$663$	−4.52395	−0.175696
$664$	−17.6287	−0.684125
$665$	0	0
$666$	−30.3903	−1.17760
$667$	−1.55176	−0.0600844
$668$	6.20678	0.240148
$669$	3.97808	0.153801
$670$	−5.15069	−0.198988
$671$	2.62490	0.101333
$672$	0	0
$673$	−8.32895	−0.321057	−0.160529	−	0.987031i	$-0.551320\pi$
$673$	−8.32895	−0.321057	−0.160529	+	0.987031i	$0.551320\pi$
$674$	−10.3475	−0.398570
$675$	−1.01839	−0.0391979
$676$	−10.7635	−0.413979
$677$	22.4125	0.861382	0.430691	−	0.902499i	$-0.358270\pi$
$677$	22.4125	0.861382	0.430691	+	0.902499i	$0.358270\pi$
$678$	10.3602	0.397881
$679$	0	0
$680$	10.0343	0.384798
$681$	−4.13665	−0.158517
$682$	1.59776	0.0611813
$683$	47.3566	1.81205	0.906026	−	0.423223i	$-0.139101\pi$
$683$	47.3566	1.81205	0.906026	+	0.423223i	$0.139101\pi$
$684$	−0.886922	−0.0339123
$685$	−46.4888	−1.77624
$686$	0	0
$687$	3.94233	0.150409
$688$	−3.71554	−0.141654
$689$	−8.74419	−0.333127
$690$	2.20848	0.0840754
$691$	−6.26210	−0.238222	−0.119111	−	0.992881i	$-0.538004\pi$
$691$	−6.26210	−0.238222	−0.119111	+	0.992881i	$0.538004\pi$
$692$	11.0433	0.419803
$693$	0	0
$694$	−11.6067	−0.440583
$695$	27.3655	1.03803
$696$	0.655021	0.0248285
$697$	−11.7517	−0.445128
$698$	31.0495	1.17524
$699$	1.61033	0.0609083
$700$	0	0
$701$	−33.6230	−1.26992	−0.634961	−	0.772544i	$-0.718984\pi$
$701$	−33.6230	−1.26992	−0.634961	+	0.772544i	$0.718984\pi$
$702$	−5.45724	−0.205970
$703$	−4.07788	−0.153800
$704$	0.182674	0.00688478
$705$	5.66385	0.213313
$706$	−14.6989	−0.553200
$707$	0	0
$708$	−1.00492	−0.0377673
$709$	12.0256	0.451632	0.225816	−	0.974170i	$-0.427495\pi$
$709$	12.0256	0.451632	0.225816	+	0.974170i	$0.427495\pi$
$710$	4.72975	0.177504
$711$	−22.9414	−0.860371
$712$	−7.04783	−0.264128
$713$	13.5725	0.508294
$714$	0	0
$715$	−0.593579	−0.0221986
$716$	12.0210	0.449246
$717$	−1.50768	−0.0563054
$718$	30.5300	1.13937
$719$	−1.18966	−0.0443667	−0.0221834	−	0.999754i	$-0.507062\pi$
$719$	−1.18966	−0.0443667	−0.0221834	+	0.999754i	$0.507062\pi$
$720$	5.58607	0.208181
$721$	0	0
$722$	18.8810	0.702678
$723$	−11.2149	−0.417086
$724$	−2.10545	−0.0782485
$725$	−0.279081	−0.0103648
$726$	−7.18338	−0.266600
$727$	−32.6917	−1.21247	−0.606234	−	0.795286i	$-0.707320\pi$
$727$	−32.6917	−1.21247	−0.606234	+	0.795286i	$0.707320\pi$
$728$	0	0
$729$	−6.51345	−0.241239
$730$	−18.9785	−0.702427
$731$	−17.1592	−0.634655
$732$	−9.41222	−0.347886
$733$	−38.5068	−1.42228	−0.711140	−	0.703051i	$-0.751821\pi$
$733$	−38.5068	−1.42228	−0.711140	+	0.703051i	$0.751821\pi$
$734$	5.12021	0.188990
$735$	0	0
$736$	1.55176	0.0571987
$737$	−0.433040	−0.0159512
$738$	−6.54215	−0.240820
$739$	−39.5798	−1.45597	−0.727984	−	0.685594i	$-0.759542\pi$
$739$	−39.5798	−1.45597	−0.727984	+	0.685594i	$0.759542\pi$
$740$	25.6836	0.944147
$741$	−0.337937	−0.0124144
$742$	0	0
$743$	−3.57236	−0.131057	−0.0655285	−	0.997851i	$-0.520873\pi$
$743$	−3.57236	−0.131057	−0.0655285	+	0.997851i	$0.520873\pi$
$744$	−5.72915	−0.210041
$745$	−16.8582	−0.617635
$746$	−14.0322	−0.513757
$747$	−45.3224	−1.65826
$748$	0.843627	0.0308461
$749$	0	0
$750$	7.51324	0.274345
$751$	15.8617	0.578803	0.289401	−	0.957208i	$-0.406544\pi$
$751$	15.8617	0.578803	0.289401	+	0.957208i	$0.406544\pi$
$752$	3.97963	0.145122
$753$	−12.6343	−0.460418
$754$	−1.49551	−0.0544632
$755$	−9.72871	−0.354064
$756$	0	0
$757$	16.0996	0.585149	0.292574	−	0.956243i	$-0.405488\pi$
$757$	16.0996	0.585149	0.292574	+	0.956243i	$0.405488\pi$
$758$	17.0722	0.620091
$759$	0.185676	0.00673963
$760$	0.749558	0.0271893
$761$	−34.0662	−1.23490	−0.617449	−	0.786611i	$-0.711834\pi$
$761$	−34.0662	−1.23490	−0.617449	+	0.786611i	$0.711834\pi$
$762$	−3.82321	−0.138500
$763$	0	0
$764$	−8.48898	−0.307120
$765$	25.7977	0.932717
$766$	−24.9613	−0.901887
$767$	2.29438	0.0828453
$768$	−0.655021	−0.0236360
$769$	6.28420	0.226614	0.113307	−	0.993560i	$-0.463856\pi$
$769$	6.28420	0.226614	0.113307	+	0.993560i	$0.463856\pi$
$770$	0	0
$771$	1.91987	0.0691425
$772$	18.5575	0.667899
$773$	−10.9152	−0.392592	−0.196296	−	0.980545i	$-0.562891\pi$
$773$	−10.9152	−0.392592	−0.196296	+	0.980545i	$0.562891\pi$
$774$	−9.55247	−0.343356
$775$	2.44098	0.0876826
$776$	−4.15180	−0.149041
$777$	0	0
$778$	39.1586	1.40390
$779$	−0.877849	−0.0314522
$780$	2.12842	0.0762097
$781$	0.397650	0.0142290
$782$	7.16637	0.256269
$783$	3.64909	0.130408
$784$	0	0
$785$	−7.75478	−0.276780
$786$	6.18231	0.220516
$787$	11.3654	0.405133	0.202567	−	0.979268i	$-0.435072\pi$
$787$	11.3654	0.405133	0.202567	+	0.979268i	$0.435072\pi$
$788$	−0.581995	−0.0207327
$789$	14.6508	0.521581
$790$	19.3883	0.689806
$791$	0	0
$792$	0.469645	0.0166881
$793$	21.4895	0.763113
$794$	−18.2632	−0.648136
$795$	−8.32147	−0.295132
$796$	−4.39526	−0.155786
$797$	−19.3906	−0.686849	−0.343424	−	0.939180i	$-0.611587\pi$
$797$	−19.3906	−0.686849	−0.343424	+	0.939180i	$0.611587\pi$
$798$	0	0
$799$	18.3788	0.650195
$800$	0.279081	0.00986699
$801$	−18.1196	−0.640224
$802$	7.60891	0.268680
$803$	−1.59561	−0.0563077
$804$	1.55277	0.0547620
$805$	0	0
$806$	13.0805	0.460740
$807$	−5.48571	−0.193106
$808$	4.53474	0.159532
$809$	−13.6474	−0.479817	−0.239908	−	0.970796i	$-0.577117\pi$
$809$	−13.6474	−0.479817	−0.239908	+	0.970796i	$0.577117\pi$
$810$	11.5648	0.406345
$811$	36.5351	1.28292	0.641461	−	0.767156i	$-0.278329\pi$
$811$	36.5351	1.28292	0.641461	+	0.767156i	$0.278329\pi$
$812$	0	0
$813$	−14.5269	−0.509479
$814$	2.15933	0.0756844
$815$	−29.5775	−1.03606
$816$	−3.02503	−0.105897
$817$	−1.28178	−0.0448439
$818$	35.6379	1.24605
$819$	0	0
$820$	5.52892	0.193078
$821$	31.7549	1.10825	0.554127	−	0.832432i	$-0.313052\pi$
$821$	31.7549	1.10825	0.554127	+	0.832432i	$0.313052\pi$
$822$	14.0149	0.488826
$823$	31.8926	1.11171	0.555853	−	0.831280i	$-0.312392\pi$
$823$	31.8926	1.11171	0.555853	+	0.831280i	$0.312392\pi$
$824$	−4.71987	−0.164424
$825$	0.0333935	0.00116261
$826$	0	0
$827$	19.0931	0.663932	0.331966	−	0.943291i	$-0.392288\pi$
$827$	19.0931	0.663932	0.331966	+	0.943291i	$0.392288\pi$
$828$	3.98950	0.138645
$829$	−51.4884	−1.78827	−0.894133	−	0.447802i	$-0.852207\pi$
$829$	−51.4884	−1.78827	−0.894133	+	0.447802i	$0.852207\pi$
$830$	38.3030	1.32952
$831$	12.5492	0.435328
$832$	1.49551	0.0518474
$833$	0	0
$834$	−8.24983	−0.285668
$835$	−13.4859	−0.466699
$836$	0.0630186	0.00217954
$837$	−31.9168	−1.10321
$838$	14.2401	0.491918
$839$	10.9093	0.376632	0.188316	−	0.982109i	$-0.439697\pi$
$839$	10.9093	0.376632	0.188316	+	0.982109i	$0.439697\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−14.5354	−0.500922
$843$	−16.1629	−0.556679
$844$	−2.05399	−0.0707013
$845$	23.3865	0.804520
$846$	10.2314	0.351763
$847$	0	0
$848$	−5.84697	−0.200786
$849$	−16.5221	−0.567036
$850$	1.28886	0.0442074
$851$	18.3429	0.628785
$852$	−1.42587	−0.0488495
$853$	1.10114	0.0377025	0.0188512	−	0.999822i	$-0.493999\pi$
$853$	1.10114	0.0377025	0.0188512	+	0.999822i	$0.493999\pi$
$854$	0	0
$855$	1.92708	0.0659046
$856$	15.0711	0.515119
$857$	42.7839	1.46147	0.730736	−	0.682661i	$-0.239177\pi$
$857$	42.7839	1.46147	0.730736	+	0.682661i	$0.239177\pi$
$858$	0.178945	0.00610909
$859$	−17.1574	−0.585402	−0.292701	−	0.956204i	$-0.594554\pi$
$859$	−17.1574	−0.585402	−0.292701	+	0.956204i	$0.594554\pi$
$860$	8.07301	0.275287
$861$	0	0
$862$	27.8928	0.950033
$863$	7.25848	0.247081	0.123541	−	0.992340i	$-0.460575\pi$
$863$	7.25848	0.247081	0.123541	+	0.992340i	$0.460575\pi$
$864$	−3.64909	−0.124145
$865$	−23.9945	−0.815838
$866$	−0.743364	−0.0252606
$867$	−2.83488	−0.0962775
$868$	0	0
$869$	1.63006	0.0552960
$870$	−1.42321	−0.0482513
$871$	−3.54520	−0.120124
$872$	−7.22164	−0.244556
$873$	−10.6741	−0.361262
$874$	0.535324	0.0181076
$875$	0	0
$876$	5.72143	0.193309
$877$	26.1902	0.884381	0.442190	−	0.896921i	$-0.354202\pi$
$877$	26.1902	0.884381	0.442190	+	0.896921i	$0.354202\pi$
$878$	−24.2553	−0.818577
$879$	9.47516	0.319589
$880$	−0.396908	−0.0133798
$881$	−11.8928	−0.400679	−0.200339	−	0.979727i	$-0.564204\pi$
$881$	−11.8928	−0.400679	−0.200339	+	0.979727i	$0.564204\pi$
$882$	0	0
$883$	−46.0076	−1.54828	−0.774139	−	0.633016i	$-0.781817\pi$
$883$	−46.0076	−1.54828	−0.774139	+	0.633016i	$0.781817\pi$
$884$	6.90658	0.232293
$885$	2.18346	0.0733963
$886$	−32.8126	−1.10236
$887$	−8.50061	−0.285423	−0.142711	−	0.989764i	$-0.545582\pi$
$887$	−8.50061	−0.285423	−0.142711	+	0.989764i	$0.545582\pi$
$888$	−7.74279	−0.259831
$889$	0	0
$890$	15.3133	0.513303
$891$	0.972302	0.0325733
$892$	−6.07321	−0.203346
$893$	1.37289	0.0459419
$894$	5.08220	0.169974
$895$	−26.1189	−0.873058
$896$	0	0
$897$	1.52009	0.0507543
$898$	−6.24045	−0.208246
$899$	−8.74651	−0.291712
$900$	0.717502	0.0239167
$901$	−27.0026	−0.899587
$902$	0.464840	0.0154775
$903$	0	0
$904$	−15.8166	−0.526051
$905$	4.57466	0.152067
$906$	2.93290	0.0974391
$907$	−15.7459	−0.522832	−0.261416	−	0.965226i	$-0.584190\pi$
$907$	−15.7459	−0.522832	−0.261416	+	0.965226i	$0.584190\pi$
$908$	6.31529	0.209580
$909$	11.6586	0.386691
$910$	0	0
$911$	−5.08255	−0.168392	−0.0841961	−	0.996449i	$-0.526832\pi$
$911$	−5.08255	−0.168392	−0.0841961	+	0.996449i	$0.526832\pi$
$912$	−0.225968	−0.00748256
$913$	3.22030	0.106576
$914$	−13.6157	−0.450366
$915$	20.4506	0.676075
$916$	−6.01863	−0.198861
$917$	0	0
$918$	−16.8523	−0.556208
$919$	22.6567	0.747376	0.373688	−	0.927554i	$-0.378093\pi$
$919$	22.6567	0.747376	0.373688	+	0.927554i	$0.378093\pi$
$920$	−3.37162	−0.111159
$921$	−14.2314	−0.468941
$922$	8.97688	0.295638
$923$	3.25547	0.107155
$924$	0	0
$925$	3.29892	0.108468
$926$	−39.7503	−1.30627
$927$	−12.1345	−0.398550
$928$	−1.00000	−0.0328266
$929$	−54.6708	−1.79369	−0.896846	−	0.442343i	$-0.854147\pi$
$929$	−54.6708	−1.79369	−0.896846	+	0.442343i	$0.854147\pi$
$930$	12.4481	0.408190
$931$	0	0
$932$	−2.45844	−0.0805289
$933$	−9.41086	−0.308098
$934$	−17.5763	−0.575114
$935$	−1.83301	−0.0599457
$936$	3.84487	0.125674
$937$	51.0073	1.66633	0.833167	−	0.553021i	$-0.186525\pi$
$937$	51.0073	1.66633	0.833167	+	0.553021i	$0.186525\pi$
$938$	0	0
$939$	7.54600	0.246254
$940$	−8.64681	−0.282028
$941$	−16.2572	−0.529970	−0.264985	−	0.964252i	$-0.585367\pi$
$941$	−16.2572	−0.529970	−0.264985	+	0.964252i	$0.585367\pi$
$942$	2.33782	0.0761704
$943$	3.94868	0.128587
$944$	1.53418	0.0499334
$945$	0	0
$946$	0.678733	0.0220675
$947$	−43.4893	−1.41321	−0.706606	−	0.707607i	$-0.749775\pi$
$947$	−43.4893	−1.41321	−0.706606	+	0.707607i	$0.749775\pi$
$948$	−5.84498	−0.189836
$949$	−13.0629	−0.424038
$950$	0.0962769	0.00312364
$951$	−10.5119	−0.340870
$952$	0	0
$953$	−58.4091	−1.89206	−0.946028	−	0.324086i	$-0.894943\pi$
$953$	−58.4091	−1.89206	−0.946028	+	0.324086i	$0.894943\pi$
$954$	−15.0323	−0.486687
$955$	18.4446	0.596852
$956$	2.30173	0.0744433
$957$	−0.119655	−0.00386791
$958$	5.68285	0.183604
$959$	0	0
$960$	1.42321	0.0459339
$961$	45.5014	1.46779
$962$	17.6779	0.569959
$963$	38.7469	1.24860
$964$	17.1214	0.551443
$965$	−40.3211	−1.29798
$966$	0	0
$967$	38.4330	1.23592	0.617962	−	0.786208i	$-0.287959\pi$
$967$	38.4330	1.23592	0.617962	+	0.786208i	$0.287959\pi$
$968$	10.9666	0.352481
$969$	−1.04357	−0.0335243
$970$	9.02090	0.289644
$971$	53.3265	1.71133	0.855665	−	0.517530i	$-0.173148\pi$
$971$	53.3265	1.71133	0.855665	+	0.517530i	$0.173148\pi$
$972$	−14.4337	−0.462961
$973$	0	0
$974$	−33.6464	−1.07810
$975$	0.273385	0.00875531
$976$	14.3693	0.459951
$977$	−6.61351	−0.211585	−0.105792	−	0.994388i	$-0.533738\pi$
$977$	−6.61351	−0.211585	−0.105792	+	0.994388i	$0.533738\pi$
$978$	8.91670	0.285125
$979$	1.28745	0.0411472
$980$	0	0
$981$	−18.5665	−0.592782
$982$	7.39966	0.236133
$983$	−6.76041	−0.215624	−0.107812	−	0.994171i	$-0.534384\pi$
$983$	−6.76041	−0.215624	−0.107812	+	0.994171i	$0.534384\pi$
$984$	−1.66680	−0.0531356
$985$	1.26454	0.0402916
$986$	−4.61822	−0.147074
$987$	0	0
$988$	0.515918	0.0164135
$989$	5.76564	0.183337
$990$	−1.02043	−0.0324314
$991$	44.9290	1.42722	0.713608	−	0.700545i	$-0.247060\pi$
$991$	44.9290	1.42722	0.713608	+	0.700545i	$0.247060\pi$
$992$	8.74651	0.277702
$993$	−15.0849	−0.478704
$994$	0	0
$995$	9.54988	0.302751
$996$	−11.5472	−0.365886
$997$	35.1613	1.11357	0.556786	−	0.830656i	$-0.312035\pi$
$997$	35.1613	1.11357	0.556786	+	0.830656i	$0.312035\pi$
$998$	−35.2672	−1.11636
$999$	−43.1347	−1.36472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.v.1.2		5
7.2	even	3		406.2.e.c.291.4	yes	10
7.4	even	3		406.2.e.c.233.4	✓	10
7.6	odd	2		2842.2.a.s.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.c.233.4	✓	10	7.4	even	3
406.2.e.c.291.4	yes	10	7.2	even	3
2842.2.a.s.1.4		5	7.6	odd	2
2842.2.a.v.1.2		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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.655021 q^{3} +1.00000 q^{4} -2.17277 q^{5} +0.655021 q^{6} -1.00000 q^{8} -2.57095 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.655021 q^{3} +1.00000 q^{4} -2.17277 q^{5} +0.655021 q^{6} -1.00000 q^{8} -2.57095 q^{9} +2.17277 q^{10} +0.182674 q^{11} -0.655021 q^{12} +1.49551 q^{13} +1.42321 q^{15} +1.00000 q^{16} +4.61822 q^{17} +2.57095 q^{18} +0.344979 q^{19} -2.17277 q^{20} -0.182674 q^{22} -1.55176 q^{23} +0.655021 q^{24} -0.279081 q^{25} -1.49551 q^{26} +3.64909 q^{27} +1.00000 q^{29} -1.42321 q^{30} -8.74651 q^{31} -1.00000 q^{32} -0.119655 q^{33} -4.61822 q^{34} -2.57095 q^{36} -11.8207 q^{37} -0.344979 q^{38} -0.979589 q^{39} +2.17277 q^{40} -2.54465 q^{41} -3.71554 q^{43} +0.182674 q^{44} +5.58607 q^{45} +1.55176 q^{46} +3.97963 q^{47} -0.655021 q^{48} +0.279081 q^{50} -3.02503 q^{51} +1.49551 q^{52} -5.84697 q^{53} -3.64909 q^{54} -0.396908 q^{55} -0.225968 q^{57} -1.00000 q^{58} +1.53418 q^{59} +1.42321 q^{60} +14.3693 q^{61} +8.74651 q^{62} +1.00000 q^{64} -3.24939 q^{65} +0.119655 q^{66} -2.37057 q^{67} +4.61822 q^{68} +1.01644 q^{69} +2.17683 q^{71} +2.57095 q^{72} -8.73473 q^{73} +11.8207 q^{74} +0.182804 q^{75} +0.344979 q^{76} +0.979589 q^{78} +8.92334 q^{79} -2.17277 q^{80} +5.32261 q^{81} +2.54465 q^{82} +17.6287 q^{83} -10.0343 q^{85} +3.71554 q^{86} -0.655021 q^{87} -0.182674 q^{88} +7.04783 q^{89} -5.58607 q^{90} -1.55176 q^{92} +5.72915 q^{93} -3.97963 q^{94} -0.749558 q^{95} +0.655021 q^{96} +4.15180 q^{97} -0.469645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9	\( 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9} - 5 q^{10} + 4 q^{11} + 3 q^{12} + 2 q^{13} + 6 q^{15} + 5 q^{16} + 2 q^{17} - 4 q^{18} + 8 q^{19} + 5 q^{20} - 4 q^{22} - 9 q^{23} - 3 q^{24} + 8 q^{25} - 2 q^{26} + 15 q^{27} + 5 q^{29} - 6 q^{30} - 15 q^{31} - 5 q^{32} + 29 q^{33} - 2 q^{34} + 4 q^{36} - 22 q^{37} - 8 q^{38} + 32 q^{39} - 5 q^{40} + q^{41} + 7 q^{43} + 4 q^{44} - 8 q^{45} + 9 q^{46} + 20 q^{47} + 3 q^{48} - 8 q^{50} - 15 q^{51} + 2 q^{52} + 11 q^{53} - 15 q^{54} - 4 q^{55} + 22 q^{57} - 5 q^{58} + 13 q^{59} + 6 q^{60} - 15 q^{61} + 15 q^{62} + 5 q^{64} - 7 q^{65} - 29 q^{66} + 20 q^{67} + 2 q^{68} + 20 q^{69} - 4 q^{71} - 4 q^{72} + 22 q^{74} + 20 q^{75} + 8 q^{76} - 32 q^{78} + q^{79} + 5 q^{80} + 21 q^{81} - q^{82} + 48 q^{83} - 13 q^{85} - 7 q^{86} + 3 q^{87} - 4 q^{88} - 7 q^{89} + 8 q^{90} - 9 q^{92} - 23 q^{93} - 20 q^{94} + 11 q^{95} - 3 q^{96} + 6 q^{97} + 32 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9 - 5 * q^10 + 4 * q^11 + 3 * q^12 + 2 * q^13 + 6 * q^15 + 5 * q^16 + 2 * q^17 - 4 * q^18 + 8 * q^19 + 5 * q^20 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 8 * q^25 - 2 * q^26 + 15 * q^27 + 5 * q^29 - 6 * q^30 - 15 * q^31 - 5 * q^32 + 29 * q^33 - 2 * q^34 + 4 * q^36 - 22 * q^37 - 8 * q^38 + 32 * q^39 - 5 * q^40 + q^41 + 7 * q^43 + 4 * q^44 - 8 * q^45 + 9 * q^46 + 20 * q^47 + 3 * q^48 - 8 * q^50 - 15 * q^51 + 2 * q^52 + 11 * q^53 - 15 * q^54 - 4 * q^55 + 22 * q^57 - 5 * q^58 + 13 * q^59 + 6 * q^60 - 15 * q^61 + 15 * q^62 + 5 * q^64 - 7 * q^65 - 29 * q^66 + 20 * q^67 + 2 * q^68 + 20 * q^69 - 4 * q^71 - 4 * q^72 + 22 * q^74 + 20 * q^75 + 8 * q^76 - 32 * q^78 + q^79 + 5 * q^80 + 21 * q^81 - q^82 + 48 * q^83 - 13 * q^85 - 7 * q^86 + 3 * q^87 - 4 * q^88 - 7 * q^89 + 8 * q^90 - 9 * q^92 - 23 * q^93 - 20 * q^94 + 11 * q^95 - 3 * q^96 + 6 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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