LMFDB - Embedded newform 5566.2.a.bt.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5566,2,Mod(1,5566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5566, 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("5566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5566 = 2 \cdot 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5566.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:	$44.4447337650$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 14x^{8} + 50x^{7} + 85x^{6} - 188x^{5} - 248x^{4} + 186x^{3} + 260x^{2} + 52x - 4 $ x^10 - 4x^9 - 14x^8 + 50x^7 + 85x^6 - 188x^5 - 248x^4 + 186x^3 + 260x^2 + 52*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 506)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.40934$ of defining polynomial
Character	$\chi$	$=$	5566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.40934 q^{3} +1.00000 q^{4} +1.21899 q^{5} -2.40934 q^{6} -4.62522 q^{7} -1.00000 q^{8} +2.80492 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.40934 q^{3} +1.00000 q^{4} +1.21899 q^{5} -2.40934 q^{6} -4.62522 q^{7} -1.00000 q^{8} +2.80492 q^{9} -1.21899 q^{10} +2.40934 q^{12} +2.85854 q^{13} +4.62522 q^{14} +2.93696 q^{15} +1.00000 q^{16} +4.99877 q^{17} -2.80492 q^{18} -5.76317 q^{19} +1.21899 q^{20} -11.1437 q^{21} -1.00000 q^{23} -2.40934 q^{24} -3.51407 q^{25} -2.85854 q^{26} -0.470019 q^{27} -4.62522 q^{28} -2.00573 q^{29} -2.93696 q^{30} +0.543930 q^{31} -1.00000 q^{32} -4.99877 q^{34} -5.63809 q^{35} +2.80492 q^{36} +5.62928 q^{37} +5.76317 q^{38} +6.88720 q^{39} -1.21899 q^{40} -2.42203 q^{41} +11.1437 q^{42} +9.95488 q^{43} +3.41916 q^{45} +1.00000 q^{46} +5.96849 q^{47} +2.40934 q^{48} +14.3927 q^{49} +3.51407 q^{50} +12.0437 q^{51} +2.85854 q^{52} +1.60881 q^{53} +0.470019 q^{54} +4.62522 q^{56} -13.8854 q^{57} +2.00573 q^{58} +12.3412 q^{59} +2.93696 q^{60} +8.79389 q^{61} -0.543930 q^{62} -12.9734 q^{63} +1.00000 q^{64} +3.48453 q^{65} +13.8257 q^{67} +4.99877 q^{68} -2.40934 q^{69} +5.63809 q^{70} +2.05009 q^{71} -2.80492 q^{72} +3.16257 q^{73} -5.62928 q^{74} -8.46658 q^{75} -5.76317 q^{76} -6.88720 q^{78} +4.27504 q^{79} +1.21899 q^{80} -9.54719 q^{81} +2.42203 q^{82} +7.59289 q^{83} -11.1437 q^{84} +6.09345 q^{85} -9.95488 q^{86} -4.83248 q^{87} -3.87961 q^{89} -3.41916 q^{90} -13.2214 q^{91} -1.00000 q^{92} +1.31051 q^{93} -5.96849 q^{94} -7.02524 q^{95} -2.40934 q^{96} +12.9890 q^{97} -14.3927 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

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
$3$	2.40934	1.39103	0.695516	−	0.718510i	$-0.255176\pi$
$3$	2.40934	1.39103	0.695516	+	0.718510i	$0.255176\pi$
$4$	1.00000	0.500000
$5$	1.21899	0.545148	0.272574	−	0.962135i	$-0.412125\pi$
$5$	1.21899	0.545148	0.272574	+	0.962135i	$0.412125\pi$
$6$	−2.40934	−0.983609
$7$	−4.62522	−1.74817	−0.874085	−	0.485774i	$-0.838538\pi$
$7$	−4.62522	−1.74817	−0.874085	+	0.485774i	$0.838538\pi$
$8$	−1.00000	−0.353553
$9$	2.80492	0.934973
$10$	−1.21899	−0.385478
$11$	0	0
$11$	0	0
$12$	2.40934	0.695516
$13$	2.85854	0.792817	0.396409	−	0.918074i	$-0.370256\pi$
$13$	2.85854	0.792817	0.396409	+	0.918074i	$0.370256\pi$
$14$	4.62522	1.23614
$15$	2.93696	0.758319
$16$	1.00000	0.250000
$17$	4.99877	1.21238	0.606190	−	0.795320i	$-0.292697\pi$
$17$	4.99877	1.21238	0.606190	+	0.795320i	$0.292697\pi$
$18$	−2.80492	−0.661125
$19$	−5.76317	−1.32216	−0.661081	−	0.750315i	$-0.729902\pi$
$19$	−5.76317	−1.32216	−0.661081	+	0.750315i	$0.729902\pi$
$20$	1.21899	0.272574
$21$	−11.1437	−2.43176
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.40934	−0.491804
$25$	−3.51407	−0.702813
$26$	−2.85854	−0.560607
$27$	−0.470019	−0.0904553
$28$	−4.62522	−0.874085
$29$	−2.00573	−0.372454	−0.186227	−	0.982507i	$-0.559626\pi$
$29$	−2.00573	−0.372454	−0.186227	+	0.982507i	$0.559626\pi$
$30$	−2.93696	−0.536213
$31$	0.543930	0.0976927	0.0488463	−	0.998806i	$-0.484446\pi$
$31$	0.543930	0.0976927	0.0488463	+	0.998806i	$0.484446\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−4.99877	−0.857283
$35$	−5.63809	−0.953012
$36$	2.80492	0.467486
$37$	5.62928	0.925449	0.462724	−	0.886502i	$-0.346872\pi$
$37$	5.62928	0.925449	0.462724	+	0.886502i	$0.346872\pi$
$38$	5.76317	0.934909
$39$	6.88720	1.10284
$40$	−1.21899	−0.192739
$41$	−2.42203	−0.378257	−0.189128	−	0.981952i	$-0.560566\pi$
$41$	−2.42203	−0.378257	−0.189128	+	0.981952i	$0.560566\pi$
$42$	11.1437	1.71951
$43$	9.95488	1.51810	0.759052	−	0.651030i	$-0.225663\pi$
$43$	9.95488	1.51810	0.759052	+	0.651030i	$0.225663\pi$
$44$	0	0
$45$	3.41916	0.509699
$46$	1.00000	0.147442
$47$	5.96849	0.870594	0.435297	−	0.900287i	$-0.356643\pi$
$47$	5.96849	0.870594	0.435297	+	0.900287i	$0.356643\pi$
$48$	2.40934	0.347758
$49$	14.3927	2.05610
$50$	3.51407	0.496964
$51$	12.0437	1.68646
$52$	2.85854	0.396409
$53$	1.60881	0.220988	0.110494	−	0.993877i	$-0.464757\pi$
$53$	1.60881	0.220988	0.110494	+	0.993877i	$0.464757\pi$
$54$	0.470019	0.0639615
$55$	0	0
$56$	4.62522	0.618071
$57$	−13.8854	−1.83917
$58$	2.00573	0.263365
$59$	12.3412	1.60668	0.803342	−	0.595518i	$-0.203053\pi$
$59$	12.3412	1.60668	0.803342	+	0.595518i	$0.203053\pi$
$60$	2.93696	0.379160
$61$	8.79389	1.12594	0.562971	−	0.826476i	$-0.309658\pi$
$61$	8.79389	1.12594	0.562971	+	0.826476i	$0.309658\pi$
$62$	−0.543930	−0.0690792
$63$	−12.9734	−1.63449
$64$	1.00000	0.125000
$65$	3.48453	0.432203
$66$	0	0
$67$	13.8257	1.68908	0.844542	−	0.535490i	$-0.179873\pi$
$67$	13.8257	1.68908	0.844542	+	0.535490i	$0.179873\pi$
$68$	4.99877	0.606190
$69$	−2.40934	−0.290050
$70$	5.63809	0.673881
$71$	2.05009	0.243300	0.121650	−	0.992573i	$-0.461181\pi$
$71$	2.05009	0.243300	0.121650	+	0.992573i	$0.461181\pi$
$72$	−2.80492	−0.330563
$73$	3.16257	0.370151	0.185075	−	0.982724i	$-0.440747\pi$
$73$	3.16257	0.370151	0.185075	+	0.982724i	$0.440747\pi$
$74$	−5.62928	−0.654391
$75$	−8.46658	−0.977636
$76$	−5.76317	−0.661081
$77$	0	0
$78$	−6.88720	−0.779822
$79$	4.27504	0.480980	0.240490	−	0.970652i	$-0.422692\pi$
$79$	4.27504	0.480980	0.240490	+	0.970652i	$0.422692\pi$
$80$	1.21899	0.136287
$81$	−9.54719	−1.06080
$82$	2.42203	0.267468
$83$	7.59289	0.833428	0.416714	−	0.909038i	$-0.363182\pi$
$83$	7.59289	0.833428	0.416714	+	0.909038i	$0.363182\pi$
$84$	−11.1437	−1.21588
$85$	6.09345	0.660928
$86$	−9.95488	−1.07346
$87$	−4.83248	−0.518096
$88$	0	0
$89$	−3.87961	−0.411238	−0.205619	−	0.978632i	$-0.565921\pi$
$89$	−3.87961	−0.411238	−0.205619	+	0.978632i	$0.565921\pi$
$90$	−3.41916	−0.360412
$91$	−13.2214	−1.38598
$92$	−1.00000	−0.104257
$93$	1.31051	0.135894
$94$	−5.96849	−0.615603
$95$	−7.02524	−0.720774
$96$	−2.40934	−0.245902
$97$	12.9890	1.31883	0.659416	−	0.751779i	$-0.270804\pi$
$97$	12.9890	1.31883	0.659416	+	0.751779i	$0.270804\pi$
$98$	−14.3927	−1.45388
$99$	0	0
$100$	−3.51407	−0.351407
$101$	−1.10910	−0.110360	−0.0551798	−	0.998476i	$-0.517573\pi$
$101$	−1.10910	−0.110360	−0.0551798	+	0.998476i	$0.517573\pi$
$102$	−12.0437	−1.19251
$103$	−4.74508	−0.467546	−0.233773	−	0.972291i	$-0.575107\pi$
$103$	−4.74508	−0.467546	−0.233773	+	0.972291i	$0.575107\pi$
$104$	−2.85854	−0.280303
$105$	−13.5841	−1.32567
$106$	−1.60881	−0.156262
$107$	−2.80448	−0.271119	−0.135559	−	0.990769i	$-0.543283\pi$
$107$	−2.80448	−0.271119	−0.135559	+	0.990769i	$0.543283\pi$
$108$	−0.470019	−0.0452276
$109$	16.1238	1.54438	0.772188	−	0.635394i	$-0.219162\pi$
$109$	16.1238	1.54438	0.772188	+	0.635394i	$0.219162\pi$
$110$	0	0
$111$	13.5629	1.28733
$112$	−4.62522	−0.437042
$113$	−10.4753	−0.985435	−0.492718	−	0.870189i	$-0.663996\pi$
$113$	−10.4753	−0.985435	−0.492718	+	0.870189i	$0.663996\pi$
$114$	13.8854	1.30049
$115$	−1.21899	−0.113671
$116$	−2.00573	−0.186227
$117$	8.01798	0.741263
$118$	−12.3412	−1.13610
$119$	−23.1204	−2.11945
$120$	−2.93696	−0.268106
$121$	0	0
$122$	−8.79389	−0.796162
$123$	−5.83548	−0.526168
$124$	0.543930	0.0488463
$125$	−10.3786	−0.928286
$126$	12.9734	1.15576
$127$	−5.26848	−0.467502	−0.233751	−	0.972296i	$-0.575100\pi$
$127$	−5.26848	−0.467502	−0.233751	+	0.972296i	$0.575100\pi$
$128$	−1.00000	−0.0883883
$129$	23.9847	2.11173
$130$	−3.48453	−0.305614
$131$	13.2189	1.15494	0.577472	−	0.816410i	$-0.304039\pi$
$131$	13.2189	1.15494	0.577472	+	0.816410i	$0.304039\pi$
$132$	0	0
$133$	26.6559	2.31136
$134$	−13.8257	−1.19436
$135$	−0.572948	−0.0493115
$136$	−4.99877	−0.428641
$137$	16.3199	1.39430	0.697152	−	0.716924i	$-0.254450\pi$
$137$	16.3199	1.39430	0.697152	+	0.716924i	$0.254450\pi$
$138$	2.40934	0.205097
$139$	−9.42181	−0.799147	−0.399574	−	0.916701i	$-0.630842\pi$
$139$	−9.42181	−0.799147	−0.399574	+	0.916701i	$0.630842\pi$
$140$	−5.63809	−0.476506
$141$	14.3801	1.21102
$142$	−2.05009	−0.172039
$143$	0	0
$144$	2.80492	0.233743
$145$	−2.44496	−0.203043
$146$	−3.16257	−0.261736
$147$	34.6768	2.86010
$148$	5.62928	0.462724
$149$	−11.9128	−0.975931	−0.487966	−	0.872863i	$-0.662261\pi$
$149$	−11.9128	−0.975931	−0.487966	+	0.872863i	$0.662261\pi$
$150$	8.46658	0.691293
$151$	12.5875	1.02435	0.512177	−	0.858880i	$-0.328839\pi$
$151$	12.5875	1.02435	0.512177	+	0.858880i	$0.328839\pi$
$152$	5.76317	0.467455
$153$	14.0212	1.13354
$154$	0	0
$155$	0.663045	0.0532570
$156$	6.88720	0.551418
$157$	−22.0766	−1.76191	−0.880953	−	0.473204i	$-0.843098\pi$
$157$	−22.0766	−1.76191	−0.880953	+	0.473204i	$0.843098\pi$
$158$	−4.27504	−0.340104
$159$	3.87618	0.307401
$160$	−1.21899	−0.0963695
$161$	4.62522	0.364518
$162$	9.54719	0.750098
$163$	−19.1925	−1.50327	−0.751637	−	0.659577i	$-0.770735\pi$
$163$	−19.1925	−1.50327	−0.751637	+	0.659577i	$0.770735\pi$
$164$	−2.42203	−0.189128
$165$	0	0
$166$	−7.59289	−0.589323
$167$	5.71181	0.441993	0.220997	−	0.975275i	$-0.429069\pi$
$167$	5.71181	0.441993	0.220997	+	0.975275i	$0.429069\pi$
$168$	11.1437	0.859757
$169$	−4.82873	−0.371441
$170$	−6.09345	−0.467346
$171$	−16.1652	−1.23618
$172$	9.95488	0.759052
$173$	−5.62765	−0.427863	−0.213931	−	0.976849i	$-0.568627\pi$
$173$	−5.62765	−0.427863	−0.213931	+	0.976849i	$0.568627\pi$
$174$	4.83248	0.366349
$175$	16.2533	1.22864
$176$	0	0
$177$	29.7341	2.23495
$178$	3.87961	0.290789
$179$	10.2686	0.767511	0.383756	−	0.923435i	$-0.374630\pi$
$179$	10.2686	0.767511	0.383756	+	0.923435i	$0.374630\pi$
$180$	3.41916	0.254849
$181$	19.3552	1.43866	0.719331	−	0.694668i	$-0.244449\pi$
$181$	19.3552	1.43866	0.719331	+	0.694668i	$0.244449\pi$
$182$	13.2214	0.980035
$183$	21.1875	1.56622
$184$	1.00000	0.0737210
$185$	6.86204	0.504507
$186$	−1.31051	−0.0960914
$187$	0	0
$188$	5.96849	0.435297
$189$	2.17394	0.158131
$190$	7.02524	0.509664
$191$	−18.0554	−1.30645	−0.653223	−	0.757166i	$-0.726584\pi$
$191$	−18.0554	−1.30645	−0.653223	+	0.757166i	$0.726584\pi$
$192$	2.40934	0.173879
$193$	24.9431	1.79545	0.897723	−	0.440560i	$-0.145220\pi$
$193$	24.9431	1.79545	0.897723	+	0.440560i	$0.145220\pi$
$194$	−12.9890	−0.932555
$195$	8.39542	0.601209
$196$	14.3927	1.02805
$197$	−1.09628	−0.0781065	−0.0390533	−	0.999237i	$-0.512434\pi$
$197$	−1.09628	−0.0781065	−0.0390533	+	0.999237i	$0.512434\pi$
$198$	0	0
$199$	−27.3349	−1.93772	−0.968859	−	0.247611i	$-0.920354\pi$
$199$	−27.3349	−1.93772	−0.968859	+	0.247611i	$0.920354\pi$
$200$	3.51407	0.248482
$201$	33.3109	2.34957
$202$	1.10910	0.0780360
$203$	9.27693	0.651113
$204$	12.0437	0.843231
$205$	−2.95242	−0.206206
$206$	4.74508	0.330605
$207$	−2.80492	−0.194955
$208$	2.85854	0.198204
$209$	0	0
$210$	13.5841	0.937391
$211$	11.1607	0.768335	0.384168	−	0.923263i	$-0.374488\pi$
$211$	11.1607	0.768335	0.384168	+	0.923263i	$0.374488\pi$
$212$	1.60881	0.110494
$213$	4.93935	0.338439
$214$	2.80448	0.191710
$215$	12.1349	0.827592
$216$	0.470019	0.0319808
$217$	−2.51580	−0.170783
$218$	−16.1238	−1.09204
$219$	7.61971	0.514892
$220$	0	0
$221$	14.2892	0.961197
$222$	−13.5629	−0.910279
$223$	−16.0539	−1.07505	−0.537523	−	0.843249i	$-0.680640\pi$
$223$	−16.0539	−1.07505	−0.537523	+	0.843249i	$0.680640\pi$
$224$	4.62522	0.309036
$225$	−9.85667	−0.657111
$226$	10.4753	0.696808
$227$	22.7592	1.51058	0.755291	−	0.655389i	$-0.227495\pi$
$227$	22.7592	1.51058	0.755291	+	0.655389i	$0.227495\pi$
$228$	−13.8854	−0.919585
$229$	8.64321	0.571159	0.285580	−	0.958355i	$-0.407814\pi$
$229$	8.64321	0.571159	0.285580	+	0.958355i	$0.407814\pi$
$230$	1.21899	0.0803778
$231$	0	0
$232$	2.00573	0.131682
$233$	−21.2558	−1.39251	−0.696257	−	0.717792i	$-0.745153\pi$
$233$	−21.2558	−1.39251	−0.696257	+	0.717792i	$0.745153\pi$
$234$	−8.01798	−0.524152
$235$	7.27552	0.474603
$236$	12.3412	0.803342
$237$	10.3000	0.669059
$238$	23.1204	1.49868
$239$	−1.59030	−0.102868	−0.0514341	−	0.998676i	$-0.516379\pi$
$239$	−1.59030	−0.102868	−0.0514341	+	0.998676i	$0.516379\pi$
$240$	2.93696	0.189580
$241$	−0.519057	−0.0334354	−0.0167177	−	0.999860i	$-0.505322\pi$
$241$	−0.519057	−0.0334354	−0.0167177	+	0.999860i	$0.505322\pi$
$242$	0	0
$243$	−21.5924	−1.38515
$244$	8.79389	0.562971
$245$	17.5445	1.12088
$246$	5.83548	0.372057
$247$	−16.4743	−1.04823
$248$	−0.543930	−0.0345396
$249$	18.2939	1.15933
$250$	10.3786	0.656397
$251$	−18.5431	−1.17043	−0.585215	−	0.810878i	$-0.698990\pi$
$251$	−18.5431	−1.17043	−0.585215	+	0.810878i	$0.698990\pi$
$252$	−12.9734	−0.817245
$253$	0	0
$254$	5.26848	0.330574
$255$	14.6812	0.919372
$256$	1.00000	0.0625000
$257$	14.0052	0.873621	0.436810	−	0.899554i	$-0.356108\pi$
$257$	14.0052	0.873621	0.436810	+	0.899554i	$0.356108\pi$
$258$	−23.9847	−1.49322
$259$	−26.0367	−1.61784
$260$	3.48453	0.216102
$261$	−5.62590	−0.348234
$262$	−13.2189	−0.816669
$263$	−22.5302	−1.38927	−0.694636	−	0.719361i	$-0.744435\pi$
$263$	−22.5302	−1.38927	−0.694636	+	0.719361i	$0.744435\pi$
$264$	0	0
$265$	1.96113	0.120471
$266$	−26.6559	−1.63438
$267$	−9.34730	−0.572045
$268$	13.8257	0.844542
$269$	11.5876	0.706511	0.353255	−	0.935527i	$-0.385075\pi$
$269$	11.5876	0.706511	0.353255	+	0.935527i	$0.385075\pi$
$270$	0.572948	0.0348685
$271$	−0.973432	−0.0591318	−0.0295659	−	0.999563i	$-0.509412\pi$
$271$	−0.973432	−0.0591318	−0.0295659	+	0.999563i	$0.509412\pi$
$272$	4.99877	0.303095
$273$	−31.8548	−1.92794
$274$	−16.3199	−0.985922
$275$	0	0
$276$	−2.40934	−0.145025
$277$	31.2669	1.87865	0.939323	−	0.343034i	$-0.111455\pi$
$277$	31.2669	1.87865	0.939323	+	0.343034i	$0.111455\pi$
$278$	9.42181	0.565083
$279$	1.52568	0.0913400
$280$	5.63809	0.336941
$281$	−22.0469	−1.31521	−0.657604	−	0.753363i	$-0.728430\pi$
$281$	−22.0469	−1.31521	−0.657604	+	0.753363i	$0.728430\pi$
$282$	−14.3801	−0.856324
$283$	2.23300	0.132738	0.0663692	−	0.997795i	$-0.478859\pi$
$283$	2.23300	0.132738	0.0663692	+	0.997795i	$0.478859\pi$
$284$	2.05009	0.121650
$285$	−16.9262	−1.00262
$286$	0	0
$287$	11.2024	0.661257
$288$	−2.80492	−0.165281
$289$	7.98774	0.469867
$290$	2.44496	0.143573
$291$	31.2949	1.83454
$292$	3.16257	0.185075
$293$	33.4265	1.95280	0.976398	−	0.215981i	$-0.0692949\pi$
$293$	33.4265	1.95280	0.976398	+	0.215981i	$0.0692949\pi$
$294$	−34.6768	−2.02239
$295$	15.0438	0.875881
$296$	−5.62928	−0.327196
$297$	0	0
$298$	11.9128	0.690087
$299$	−2.85854	−0.165314
$300$	−8.46658	−0.488818
$301$	−46.0435	−2.65390
$302$	−12.5875	−0.724327
$303$	−2.67220	−0.153514
$304$	−5.76317	−0.330540
$305$	10.7197	0.613806
$306$	−14.0212	−0.801536
$307$	−21.6574	−1.23606	−0.618028	−	0.786156i	$-0.712068\pi$
$307$	−21.6574	−1.23606	−0.618028	+	0.786156i	$0.712068\pi$
$308$	0	0
$309$	−11.4325	−0.650372
$310$	−0.663045	−0.0376584
$311$	−18.8468	−1.06870	−0.534352	−	0.845262i	$-0.679444\pi$
$311$	−18.8468	−1.06870	−0.534352	+	0.845262i	$0.679444\pi$
$312$	−6.88720	−0.389911
$313$	8.88355	0.502128	0.251064	−	0.967971i	$-0.419220\pi$
$313$	8.88355	0.502128	0.251064	+	0.967971i	$0.419220\pi$
$314$	22.0766	1.24586
$315$	−15.8144	−0.891040
$316$	4.27504	0.240490
$317$	15.8195	0.888511	0.444256	−	0.895900i	$-0.353468\pi$
$317$	15.8195	0.888511	0.444256	+	0.895900i	$0.353468\pi$
$318$	−3.87618	−0.217365
$319$	0	0
$320$	1.21899	0.0681436
$321$	−6.75693	−0.377135
$322$	−4.62522	−0.257753
$323$	−28.8088	−1.60296
$324$	−9.54719	−0.530399
$325$	−10.0451	−0.557202
$326$	19.1925	1.06298
$327$	38.8476	2.14828
$328$	2.42203	0.133734
$329$	−27.6056	−1.52195
$330$	0	0
$331$	−30.8846	−1.69757	−0.848785	−	0.528739i	$-0.822665\pi$
$331$	−30.8846	−1.69757	−0.848785	+	0.528739i	$0.822665\pi$
$332$	7.59289	0.416714
$333$	15.7897	0.865269
$334$	−5.71181	−0.312537
$335$	16.8534	0.920801
$336$	−11.1437	−0.607940
$337$	25.6030	1.39468	0.697341	−	0.716740i	$-0.254366\pi$
$337$	25.6030	1.39468	0.697341	+	0.716740i	$0.254366\pi$
$338$	4.82873	0.262648
$339$	−25.2386	−1.37077
$340$	6.09345	0.330464
$341$	0	0
$342$	16.1652	0.874114
$343$	−34.1927	−1.84623
$344$	−9.95488	−0.536731
$345$	−2.93696	−0.158121
$346$	5.62765	0.302544
$347$	5.98432	0.321255	0.160627	−	0.987015i	$-0.448648\pi$
$347$	5.98432	0.321255	0.160627	+	0.987015i	$0.448648\pi$
$348$	−4.83248	−0.259048
$349$	−5.18398	−0.277492	−0.138746	−	0.990328i	$-0.544307\pi$
$349$	−5.18398	−0.277492	−0.138746	+	0.990328i	$0.544307\pi$
$350$	−16.2533	−0.868777
$351$	−1.34357	−0.0717145
$352$	0	0
$353$	8.47517	0.451088	0.225544	−	0.974233i	$-0.427584\pi$
$353$	8.47517	0.451088	0.225544	+	0.974233i	$0.427584\pi$
$354$	−29.7341	−1.58035
$355$	2.49903	0.132635
$356$	−3.87961	−0.205619
$357$	−55.7050	−2.94822
$358$	−10.2686	−0.542712
$359$	19.6699	1.03814	0.519068	−	0.854733i	$-0.326279\pi$
$359$	19.6699	1.03814	0.519068	+	0.854733i	$0.326279\pi$
$360$	−3.41916	−0.180206
$361$	14.2141	0.748110
$362$	−19.3552	−1.01729
$363$	0	0
$364$	−13.2214	−0.692989
$365$	3.85514	0.201787
$366$	−21.1875	−1.10749
$367$	11.7178	0.611666	0.305833	−	0.952085i	$-0.401065\pi$
$367$	11.7178	0.611666	0.305833	+	0.952085i	$0.401065\pi$
$368$	−1.00000	−0.0521286
$369$	−6.79358	−0.353660
$370$	−6.86204	−0.356740
$371$	−7.44112	−0.386324
$372$	1.31051	0.0679469
$373$	−15.9595	−0.826350	−0.413175	−	0.910652i	$-0.635580\pi$
$373$	−15.9595	−0.826350	−0.413175	+	0.910652i	$0.635580\pi$
$374$	0	0
$375$	−25.0055	−1.29128
$376$	−5.96849	−0.307801
$377$	−5.73346	−0.295288
$378$	−2.17394	−0.111816
$379$	22.3945	1.15033	0.575164	−	0.818038i	$-0.304938\pi$
$379$	22.3945	1.15033	0.575164	+	0.818038i	$0.304938\pi$
$380$	−7.02524	−0.360387
$381$	−12.6936	−0.650311
$382$	18.0554	0.923797
$383$	18.9742	0.969535	0.484768	−	0.874643i	$-0.338904\pi$
$383$	18.9742	0.969535	0.484768	+	0.874643i	$0.338904\pi$
$384$	−2.40934	−0.122951
$385$	0	0
$386$	−24.9431	−1.26957
$387$	27.9226	1.41939
$388$	12.9890	0.659416
$389$	−2.99333	−0.151768	−0.0758840	−	0.997117i	$-0.524178\pi$
$389$	−2.99333	−0.151768	−0.0758840	+	0.997117i	$0.524178\pi$
$390$	−8.39542	−0.425119
$391$	−4.99877	−0.252799
$392$	−14.3927	−0.726940
$393$	31.8489	1.60657
$394$	1.09628	0.0552297
$395$	5.21123	0.262205
$396$	0	0
$397$	−13.7215	−0.688661	−0.344330	−	0.938849i	$-0.611894\pi$
$397$	−13.7215	−0.688661	−0.344330	+	0.938849i	$0.611894\pi$
$398$	27.3349	1.37017
$399$	64.2232	3.21518
$400$	−3.51407	−0.175703
$401$	31.1296	1.55454	0.777269	−	0.629168i	$-0.216604\pi$
$401$	31.1296	1.55454	0.777269	+	0.629168i	$0.216604\pi$
$402$	−33.3109	−1.66140
$403$	1.55485	0.0774525
$404$	−1.10910	−0.0551798
$405$	−11.6379	−0.578293
$406$	−9.27693	−0.460406
$407$	0	0
$408$	−12.0437	−0.596254
$409$	−5.88488	−0.290989	−0.145494	−	0.989359i	$-0.546477\pi$
$409$	−5.88488	−0.290989	−0.145494	+	0.989359i	$0.546477\pi$
$410$	2.95242	0.145810
$411$	39.3202	1.93952
$412$	−4.74508	−0.233773
$413$	−57.0807	−2.80876
$414$	2.80492	0.137854
$415$	9.25565	0.454342
$416$	−2.85854	−0.140152
$417$	−22.7003	−1.11164
$418$	0	0
$419$	20.7265	1.01256	0.506278	−	0.862370i	$-0.331021\pi$
$419$	20.7265	1.01256	0.506278	+	0.862370i	$0.331021\pi$
$420$	−13.5841	−0.662835
$421$	26.9832	1.31508	0.657541	−	0.753419i	$-0.271597\pi$
$421$	26.9832	1.31508	0.657541	+	0.753419i	$0.271597\pi$
$422$	−11.1607	−0.543295
$423$	16.7411	0.813981
$424$	−1.60881	−0.0781309
$425$	−17.5660	−0.852077
$426$	−4.93935	−0.239312
$427$	−40.6737	−1.96834
$428$	−2.80448	−0.135559
$429$	0	0
$430$	−12.1349	−0.585196
$431$	−38.0189	−1.83131	−0.915653	−	0.401969i	$-0.868326\pi$
$431$	−38.0189	−1.83131	−0.915653	+	0.401969i	$0.868326\pi$
$432$	−0.470019	−0.0226138
$433$	−0.936227	−0.0449922	−0.0224961	−	0.999747i	$-0.507161\pi$
$433$	−0.936227	−0.0449922	−0.0224961	+	0.999747i	$0.507161\pi$
$434$	2.51580	0.120762
$435$	−5.89074	−0.282439
$436$	16.1238	0.772188
$437$	5.76317	0.275690
$438$	−7.61971	−0.364084
$439$	−25.8960	−1.23595	−0.617974	−	0.786199i	$-0.712046\pi$
$439$	−25.8960	−1.23595	−0.617974	+	0.786199i	$0.712046\pi$
$440$	0	0
$441$	40.3703	1.92239
$442$	−14.2892	−0.679669
$443$	3.56148	0.169211	0.0846056	−	0.996415i	$-0.473037\pi$
$443$	3.56148	0.169211	0.0846056	+	0.996415i	$0.473037\pi$
$444$	13.5629	0.643665
$445$	−4.72920	−0.224186
$446$	16.0539	0.760172
$447$	−28.7019	−1.35755
$448$	−4.62522	−0.218521
$449$	12.1832	0.574962	0.287481	−	0.957786i	$-0.407182\pi$
$449$	12.1832	0.574962	0.287481	+	0.957786i	$0.407182\pi$
$450$	9.85667	0.464648
$451$	0	0
$452$	−10.4753	−0.492718
$453$	30.3275	1.42491
$454$	−22.7592	−1.06814
$455$	−16.1167	−0.755564
$456$	13.8854	0.650245
$457$	3.83608	0.179444	0.0897222	−	0.995967i	$-0.471402\pi$
$457$	3.83608	0.179444	0.0897222	+	0.995967i	$0.471402\pi$
$458$	−8.64321	−0.403871
$459$	−2.34952	−0.109666
$460$	−1.21899	−0.0568357
$461$	33.9954	1.58332	0.791661	−	0.610960i	$-0.209217\pi$
$461$	33.9954	1.58332	0.791661	+	0.610960i	$0.209217\pi$
$462$	0	0
$463$	−9.54565	−0.443624	−0.221812	−	0.975089i	$-0.571197\pi$
$463$	−9.54565	−0.443624	−0.221812	+	0.975089i	$0.571197\pi$
$464$	−2.00573	−0.0931136
$465$	1.59750	0.0740823
$466$	21.2558	0.984656
$467$	−10.4265	−0.482481	−0.241241	−	0.970465i	$-0.577554\pi$
$467$	−10.4265	−0.482481	−0.241241	+	0.970465i	$0.577554\pi$
$468$	8.01798	0.370631
$469$	−63.9471	−2.95280
$470$	−7.27552	−0.335595
$471$	−53.1901	−2.45087
$472$	−12.3412	−0.568049
$473$	0	0
$474$	−10.3000	−0.473096
$475$	20.2521	0.929232
$476$	−23.1204	−1.05972
$477$	4.51259	0.206617
$478$	1.59030	0.0727388
$479$	18.6860	0.853785	0.426893	−	0.904302i	$-0.359608\pi$
$479$	18.6860	0.853785	0.426893	+	0.904302i	$0.359608\pi$
$480$	−2.93696	−0.134053
$481$	16.0916	0.733712
$482$	0.519057	0.0236424
$483$	11.1437	0.507057
$484$	0	0
$485$	15.8334	0.718959
$486$	21.5924	0.979450
$487$	21.2749	0.964058	0.482029	−	0.876155i	$-0.339900\pi$
$487$	21.2749	0.964058	0.482029	+	0.876155i	$0.339900\pi$
$488$	−8.79389	−0.398081
$489$	−46.2413	−2.09110
$490$	−17.5445	−0.792580
$491$	−16.4971	−0.744506	−0.372253	−	0.928131i	$-0.621415\pi$
$491$	−16.4971	−0.744506	−0.372253	+	0.928131i	$0.621415\pi$
$492$	−5.83548	−0.263084
$493$	−10.0262	−0.451556
$494$	16.4743	0.741212
$495$	0	0
$496$	0.543930	0.0244232
$497$	−9.48210	−0.425330
$498$	−18.2939	−0.819767
$499$	−30.7364	−1.37595	−0.687976	−	0.725734i	$-0.741500\pi$
$499$	−30.7364	−1.37595	−0.687976	+	0.725734i	$0.741500\pi$
$500$	−10.3786	−0.464143
$501$	13.7617	0.614827
$502$	18.5431	0.827619
$503$	−32.4062	−1.44492	−0.722460	−	0.691413i	$-0.756989\pi$
$503$	−32.4062	−1.44492	−0.722460	+	0.691413i	$0.756989\pi$
$504$	12.9734	0.577880
$505$	−1.35198	−0.0601623
$506$	0	0
$507$	−11.6340	−0.516686
$508$	−5.26848	−0.233751
$509$	−9.82814	−0.435625	−0.217812	−	0.975991i	$-0.569892\pi$
$509$	−9.82814	−0.435625	−0.217812	+	0.975991i	$0.569892\pi$
$510$	−14.6812	−0.650094
$511$	−14.6276	−0.647086
$512$	−1.00000	−0.0441942
$513$	2.70880	0.119596
$514$	−14.0052	−0.617743
$515$	−5.78420	−0.254882
$516$	23.9847	1.05587
$517$	0	0
$518$	26.0367	1.14399
$519$	−13.5589	−0.595171
$520$	−3.48453	−0.152807
$521$	33.7774	1.47981	0.739907	−	0.672709i	$-0.234869\pi$
$521$	33.7774	1.47981	0.739907	+	0.672709i	$0.234869\pi$
$522$	5.62590	0.246239
$523$	33.6045	1.46942	0.734711	−	0.678380i	$-0.237318\pi$
$523$	33.6045	1.46942	0.734711	+	0.678380i	$0.237318\pi$
$524$	13.2189	0.577472
$525$	39.1598	1.70907
$526$	22.5302	0.982364
$527$	2.71898	0.118441
$528$	0	0
$529$	1.00000	0.0434783
$530$	−1.96113	−0.0851859
$531$	34.6160	1.50221
$532$	26.6559	1.15568
$533$	−6.92347	−0.299889
$534$	9.34730	0.404497
$535$	−3.41862	−0.147800
$536$	−13.8257	−0.597181
$537$	24.7406	1.06763
$538$	−11.5876	−0.499578
$539$	0	0
$540$	−0.572948	−0.0246558
$541$	−12.8125	−0.550851	−0.275426	−	0.961322i	$-0.588819\pi$
$541$	−12.8125	−0.550851	−0.275426	+	0.961322i	$0.588819\pi$
$542$	0.973432	0.0418125
$543$	46.6333	2.00123
$544$	−4.99877	−0.214321
$545$	19.6547	0.841915
$546$	31.8548	1.36326
$547$	9.47435	0.405094	0.202547	−	0.979273i	$-0.435078\pi$
$547$	9.47435	0.405094	0.202547	+	0.979273i	$0.435078\pi$
$548$	16.3199	0.697152
$549$	24.6661	1.05273
$550$	0	0
$551$	11.5593	0.492445
$552$	2.40934	0.102548
$553$	−19.7730	−0.840834
$554$	−31.2669	−1.32840
$555$	16.5330	0.701786
$556$	−9.42181	−0.399574
$557$	16.8200	0.712688	0.356344	−	0.934355i	$-0.384023\pi$
$557$	16.8200	0.712688	0.356344	+	0.934355i	$0.384023\pi$
$558$	−1.52568	−0.0645871
$559$	28.4564	1.20358
$560$	−5.63809	−0.238253
$561$	0	0
$562$	22.0469	0.929993
$563$	−12.8300	−0.540719	−0.270359	−	0.962759i	$-0.587143\pi$
$563$	−12.8300	−0.540719	−0.270359	+	0.962759i	$0.587143\pi$
$564$	14.3801	0.605512
$565$	−12.7693	−0.537209
$566$	−2.23300	−0.0938602
$567$	44.1579	1.85446
$568$	−2.05009	−0.0860197
$569$	35.9493	1.50707	0.753536	−	0.657406i	$-0.228346\pi$
$569$	35.9493	1.50707	0.753536	+	0.657406i	$0.228346\pi$
$570$	16.9262	0.708960
$571$	−39.7130	−1.66194	−0.830969	−	0.556319i	$-0.812213\pi$
$571$	−39.7130	−1.66194	−0.830969	+	0.556319i	$0.812213\pi$
$572$	0	0
$573$	−43.5017	−1.81731
$574$	−11.2024	−0.467579
$575$	3.51407	0.146547
$576$	2.80492	0.116872
$577$	−15.8680	−0.660595	−0.330298	−	0.943877i	$-0.607149\pi$
$577$	−15.8680	−0.660595	−0.330298	+	0.943877i	$0.607149\pi$
$578$	−7.98774	−0.332246
$579$	60.0965	2.49753
$580$	−2.44496	−0.101521
$581$	−35.1188	−1.45697
$582$	−31.2949	−1.29721
$583$	0	0
$584$	−3.16257	−0.130868
$585$	9.77383	0.404098
$586$	−33.4265	−1.38083
$587$	28.6429	1.18222	0.591109	−	0.806592i	$-0.298690\pi$
$587$	28.6429	1.18222	0.591109	+	0.806592i	$0.298690\pi$
$588$	34.6768	1.43005
$589$	−3.13476	−0.129165
$590$	−15.0438	−0.619342
$591$	−2.64131	−0.108649
$592$	5.62928	0.231362
$593$	21.4553	0.881064	0.440532	−	0.897737i	$-0.354790\pi$
$593$	21.4553	0.881064	0.440532	+	0.897737i	$0.354790\pi$
$594$	0	0
$595$	−28.1836	−1.15541
$596$	−11.9128	−0.487966
$597$	−65.8590	−2.69543
$598$	2.85854	0.116895
$599$	−8.21225	−0.335543	−0.167772	−	0.985826i	$-0.553657\pi$
$599$	−8.21225	−0.335543	−0.167772	+	0.985826i	$0.553657\pi$
$600$	8.46658	0.345647
$601$	−23.5219	−0.959480	−0.479740	−	0.877411i	$-0.659269\pi$
$601$	−23.5219	−0.959480	−0.479740	+	0.877411i	$0.659269\pi$
$602$	46.0435	1.87659
$603$	38.7801	1.57925
$604$	12.5875	0.512177
$605$	0	0
$606$	2.67220	0.108551
$607$	1.48704	0.0603569	0.0301785	−	0.999545i	$-0.490392\pi$
$607$	1.48704	0.0603569	0.0301785	+	0.999545i	$0.490392\pi$
$608$	5.76317	0.233727
$609$	22.3513	0.905720
$610$	−10.7197	−0.434026
$611$	17.0612	0.690222
$612$	14.0212	0.566771
$613$	−22.6932	−0.916570	−0.458285	−	0.888805i	$-0.651536\pi$
$613$	−22.6932	−0.916570	−0.458285	+	0.888805i	$0.651536\pi$
$614$	21.6574	0.874023
$615$	−7.11339	−0.286840
$616$	0	0
$617$	8.91380	0.358856	0.179428	−	0.983771i	$-0.442575\pi$
$617$	8.91380	0.358856	0.179428	+	0.983771i	$0.442575\pi$
$618$	11.4325	0.459883
$619$	0.795461	0.0319723	0.0159861	−	0.999872i	$-0.494911\pi$
$619$	0.795461	0.0319723	0.0159861	+	0.999872i	$0.494911\pi$
$620$	0.663045	0.0266285
$621$	0.470019	0.0188612
$622$	18.8468	0.755688
$623$	17.9440	0.718913
$624$	6.88720	0.275709
$625$	4.91899	0.196759
$626$	−8.88355	−0.355058
$627$	0	0
$628$	−22.0766	−0.880953
$629$	28.1395	1.12200
$630$	15.8144	0.630060
$631$	−3.81838	−0.152007	−0.0760036	−	0.997108i	$-0.524216\pi$
$631$	−3.81838	−0.152007	−0.0760036	+	0.997108i	$0.524216\pi$
$632$	−4.27504	−0.170052
$633$	26.8900	1.06878
$634$	−15.8195	−0.628272
$635$	−6.42222	−0.254858
$636$	3.87618	0.153701
$637$	41.1421	1.63011
$638$	0	0
$639$	5.75032	0.227479
$640$	−1.21899	−0.0481848
$641$	41.1704	1.62613	0.813066	−	0.582172i	$-0.197797\pi$
$641$	41.1704	1.62613	0.813066	+	0.582172i	$0.197797\pi$
$642$	6.75693	0.266675
$643$	−28.7859	−1.13521	−0.567603	−	0.823303i	$-0.692129\pi$
$643$	−28.7859	−1.13521	−0.567603	+	0.823303i	$0.692129\pi$
$644$	4.62522	0.182259
$645$	29.2371	1.15121
$646$	28.8088	1.13347
$647$	−13.4278	−0.527901	−0.263950	−	0.964536i	$-0.585026\pi$
$647$	−13.4278	−0.527901	−0.263950	+	0.964536i	$0.585026\pi$
$648$	9.54719	0.375049
$649$	0	0
$650$	10.0451	0.394002
$651$	−6.06141	−0.237565
$652$	−19.1925	−0.751637
$653$	−14.5828	−0.570670	−0.285335	−	0.958428i	$-0.592105\pi$
$653$	−14.5828	−0.570670	−0.285335	+	0.958428i	$0.592105\pi$
$654$	−38.8476	−1.51906
$655$	16.1137	0.629616
$656$	−2.42203	−0.0945642
$657$	8.87075	0.346081
$658$	27.6056	1.07618
$659$	−6.58678	−0.256584	−0.128292	−	0.991736i	$-0.540950\pi$
$659$	−6.58678	−0.256584	−0.128292	+	0.991736i	$0.540950\pi$
$660$	0	0
$661$	42.7084	1.66116	0.830582	−	0.556896i	$-0.188008\pi$
$661$	42.7084	1.66116	0.830582	+	0.556896i	$0.188008\pi$
$662$	30.8846	1.20036
$663$	34.4276	1.33706
$664$	−7.59289	−0.294661
$665$	32.4933	1.26004
$666$	−15.7897	−0.611838
$667$	2.00573	0.0776621
$668$	5.71181	0.220997
$669$	−38.6792	−1.49542
$670$	−16.8534	−0.651105
$671$	0	0
$672$	11.1437	0.429879
$673$	8.02456	0.309324	0.154662	−	0.987967i	$-0.450571\pi$
$673$	8.02456	0.309324	0.154662	+	0.987967i	$0.450571\pi$
$674$	−25.6030	−0.986189
$675$	1.65168	0.0635731
$676$	−4.82873	−0.185720
$677$	−25.2192	−0.969251	−0.484625	−	0.874722i	$-0.661044\pi$
$677$	−25.2192	−0.969251	−0.484625	+	0.874722i	$0.661044\pi$
$678$	25.2386	0.969283
$679$	−60.0769	−2.30554
$680$	−6.09345	−0.233673
$681$	54.8347	2.10127
$682$	0	0
$683$	−26.8087	−1.02581	−0.512903	−	0.858447i	$-0.671430\pi$
$683$	−26.8087	−1.02581	−0.512903	+	0.858447i	$0.671430\pi$
$684$	−16.1652	−0.618092
$685$	19.8938	0.760103
$686$	34.1927	1.30548
$687$	20.8244	0.794501
$688$	9.95488	0.379526
$689$	4.59887	0.175203
$690$	2.93696	0.111808
$691$	−6.53168	−0.248477	−0.124238	−	0.992252i	$-0.539649\pi$
$691$	−6.53168	−0.248477	−0.124238	+	0.992252i	$0.539649\pi$
$692$	−5.62765	−0.213931
$693$	0	0
$694$	−5.98432	−0.227162
$695$	−11.4851	−0.435654
$696$	4.83248	0.183175
$697$	−12.1072	−0.458591
$698$	5.18398	0.196217
$699$	−51.2125	−1.93703
$700$	16.2533	0.614318
$701$	1.84313	0.0696139	0.0348070	−	0.999394i	$-0.488918\pi$
$701$	1.84313	0.0696139	0.0348070	+	0.999394i	$0.488918\pi$
$702$	1.34357	0.0507098
$703$	−32.4425	−1.22359
$704$	0	0
$705$	17.5292	0.660188
$706$	−8.47517	−0.318967
$707$	5.12983	0.192927
$708$	29.7341	1.11748
$709$	−28.8260	−1.08258	−0.541292	−	0.840835i	$-0.682065\pi$
$709$	−28.8260	−1.08258	−0.541292	+	0.840835i	$0.682065\pi$
$710$	−2.49903	−0.0937870
$711$	11.9911	0.449703
$712$	3.87961	0.145394
$713$	−0.543930	−0.0203703
$714$	55.7050	2.08471
$715$	0	0
$716$	10.2686	0.383756
$717$	−3.83158	−0.143093
$718$	−19.6699	−0.734073
$719$	−9.66049	−0.360275	−0.180138	−	0.983641i	$-0.557654\pi$
$719$	−9.66049	−0.360275	−0.180138	+	0.983641i	$0.557654\pi$
$720$	3.41916	0.127425
$721$	21.9470	0.817350
$722$	−14.2141	−0.528994
$723$	−1.25058	−0.0465098
$724$	19.3552	0.719331
$725$	7.04826	0.261766
$726$	0	0
$727$	−4.10333	−0.152184	−0.0760920	−	0.997101i	$-0.524244\pi$
$727$	−4.10333	−0.152184	−0.0760920	+	0.997101i	$0.524244\pi$
$728$	13.2214	0.490018
$729$	−23.3818	−0.865992
$730$	−3.85514	−0.142685
$731$	49.7622	1.84052
$732$	21.1875	0.783112
$733$	−25.6806	−0.948536	−0.474268	−	0.880380i	$-0.657287\pi$
$733$	−25.6806	−0.948536	−0.474268	+	0.880380i	$0.657287\pi$
$734$	−11.7178	−0.432513
$735$	42.2707	1.55918
$736$	1.00000	0.0368605
$737$	0	0
$738$	6.79358	0.250075
$739$	6.65946	0.244972	0.122486	−	0.992470i	$-0.460913\pi$
$739$	6.65946	0.244972	0.122486	+	0.992470i	$0.460913\pi$
$740$	6.86204	0.252253
$741$	−39.6921	−1.45813
$742$	7.44112	0.273172
$743$	−14.2387	−0.522368	−0.261184	−	0.965289i	$-0.584113\pi$
$743$	−14.2387	−0.522368	−0.261184	+	0.965289i	$0.584113\pi$
$744$	−1.31051	−0.0480457
$745$	−14.5215	−0.532027
$746$	15.9595	0.584318
$747$	21.2974	0.779233
$748$	0	0
$749$	12.9713	0.473962
$750$	25.0055	0.913070
$751$	−48.1258	−1.75614	−0.878068	−	0.478536i	$-0.841167\pi$
$751$	−48.1258	−1.75614	−0.878068	+	0.478536i	$0.841167\pi$
$752$	5.96849	0.217648
$753$	−44.6766	−1.62811
$754$	5.73346	0.208800
$755$	15.3440	0.558424
$756$	2.17394	0.0790655
$757$	35.4326	1.28782	0.643911	−	0.765101i	$-0.277311\pi$
$757$	35.4326	1.28782	0.643911	+	0.765101i	$0.277311\pi$
$758$	−22.3945	−0.813405
$759$	0	0
$760$	7.02524	0.254832
$761$	27.8379	1.00912	0.504561	−	0.863376i	$-0.331654\pi$
$761$	27.8379	1.00912	0.504561	+	0.863376i	$0.331654\pi$
$762$	12.6936	0.459839
$763$	−74.5760	−2.69983
$764$	−18.0554	−0.653223
$765$	17.0916	0.617949
$766$	−18.9742	−0.685565
$767$	35.2778	1.27381
$768$	2.40934	0.0869396
$769$	−17.7384	−0.639664	−0.319832	−	0.947474i	$-0.603626\pi$
$769$	−17.7384	−0.639664	−0.319832	+	0.947474i	$0.603626\pi$
$770$	0	0
$771$	33.7433	1.21523
$772$	24.9431	0.897723
$773$	−18.3226	−0.659019	−0.329510	−	0.944152i	$-0.606883\pi$
$773$	−18.3226	−0.659019	−0.329510	+	0.944152i	$0.606883\pi$
$774$	−27.9226	−1.00366
$775$	−1.91141	−0.0686597
$776$	−12.9890	−0.466277
$777$	−62.7312	−2.25047
$778$	2.99333	0.107316
$779$	13.9585	0.500117
$780$	8.39542	0.300604
$781$	0	0
$782$	4.99877	0.178756
$783$	0.942731	0.0336904
$784$	14.3927	0.514024
$785$	−26.9112	−0.960500
$786$	−31.8489	−1.13601
$787$	−1.31841	−0.0469963	−0.0234981	−	0.999724i	$-0.507480\pi$
$787$	−1.31841	−0.0469963	−0.0234981	+	0.999724i	$0.507480\pi$
$788$	−1.09628	−0.0390533
$789$	−54.2829	−1.93252
$790$	−5.21123	−0.185407
$791$	48.4507	1.72271
$792$	0	0
$793$	25.1377	0.892667
$794$	13.7215	0.486957
$795$	4.72502	0.167579
$796$	−27.3349	−0.968859
$797$	−13.9991	−0.495874	−0.247937	−	0.968776i	$-0.579753\pi$
$797$	−13.9991	−0.495874	−0.247937	+	0.968776i	$0.579753\pi$
$798$	−64.2232	−2.27348
$799$	29.8351	1.05549
$800$	3.51407	0.124241
$801$	−10.8820	−0.384496
$802$	−31.1296	−1.09922
$803$	0	0
$804$	33.3109	1.17479
$805$	5.63809	0.198717
$806$	−1.55485	−0.0547672
$807$	27.9186	0.982780
$808$	1.10910	0.0390180
$809$	−43.8494	−1.54166	−0.770831	−	0.637040i	$-0.780159\pi$
$809$	−43.8494	−1.54166	−0.770831	+	0.637040i	$0.780159\pi$
$810$	11.6379	0.408915
$811$	17.7129	0.621983	0.310992	−	0.950413i	$-0.399339\pi$
$811$	17.7129	0.621983	0.310992	+	0.950413i	$0.399339\pi$
$812$	9.27693	0.325556
$813$	−2.34533	−0.0822543
$814$	0	0
$815$	−23.3955	−0.819508
$816$	12.0437	0.421615
$817$	−57.3716	−2.00718
$818$	5.88488	0.205760
$819$	−37.0849	−1.29585
$820$	−2.95242	−0.103103
$821$	−32.1884	−1.12338	−0.561692	−	0.827347i	$-0.689849\pi$
$821$	−32.1884	−1.12338	−0.561692	+	0.827347i	$0.689849\pi$
$822$	−39.3202	−1.37145
$823$	−50.6464	−1.76542	−0.882712	−	0.469914i	$-0.844285\pi$
$823$	−50.6464	−1.76542	−0.882712	+	0.469914i	$0.844285\pi$
$824$	4.74508	0.165303
$825$	0	0
$826$	57.0807	1.98609
$827$	19.1070	0.664416	0.332208	−	0.943206i	$-0.392206\pi$
$827$	19.1070	0.664416	0.332208	+	0.943206i	$0.392206\pi$
$828$	−2.80492	−0.0974776
$829$	39.0382	1.35585	0.677927	−	0.735129i	$-0.262879\pi$
$829$	39.0382	1.35585	0.677927	+	0.735129i	$0.262879\pi$
$830$	−9.25565	−0.321268
$831$	75.3326	2.61326
$832$	2.85854	0.0991022
$833$	71.9457	2.49277
$834$	22.7003	0.786048
$835$	6.96264	0.240952
$836$	0	0
$837$	−0.255658	−0.00883682
$838$	−20.7265	−0.715985
$839$	20.9704	0.723978	0.361989	−	0.932182i	$-0.382098\pi$
$839$	20.9704	0.723978	0.361989	+	0.932182i	$0.382098\pi$
$840$	13.5841	0.468695
$841$	−24.9771	−0.861278
$842$	−26.9832	−0.929903
$843$	−53.1185	−1.82950
$844$	11.1607	0.384168
$845$	−5.88617	−0.202490
$846$	−16.7411	−0.575572
$847$	0	0
$848$	1.60881	0.0552469
$849$	5.38006	0.184643
$850$	17.5660	0.602510
$851$	−5.62928	−0.192969
$852$	4.93935	0.169219
$853$	−38.1201	−1.30521	−0.652603	−	0.757700i	$-0.726323\pi$
$853$	−38.1201	−1.30521	−0.652603	+	0.757700i	$0.726323\pi$
$854$	40.6737	1.39183
$855$	−19.7052	−0.673904
$856$	2.80448	0.0958550
$857$	−33.0364	−1.12850	−0.564251	−	0.825604i	$-0.690835\pi$
$857$	−33.0364	−1.12850	−0.564251	+	0.825604i	$0.690835\pi$
$858$	0	0
$859$	15.2860	0.521553	0.260776	−	0.965399i	$-0.416022\pi$
$859$	15.2860	0.521553	0.260776	+	0.965399i	$0.416022\pi$
$860$	12.1349	0.413796
$861$	26.9904	0.919830
$862$	38.0189	1.29493
$863$	−19.7769	−0.673212	−0.336606	−	0.941646i	$-0.609279\pi$
$863$	−19.7769	−0.673212	−0.336606	+	0.941646i	$0.609279\pi$
$864$	0.470019	0.0159904
$865$	−6.86005	−0.233249
$866$	0.936227	0.0318143
$867$	19.2452	0.653601
$868$	−2.51580	−0.0853917
$869$	0	0
$870$	5.89074	0.199715
$871$	39.5215	1.33913
$872$	−16.1238	−0.546020
$873$	36.4330	1.23307
$874$	−5.76317	−0.194942
$875$	48.0031	1.62280
$876$	7.61971	0.257446
$877$	9.89956	0.334284	0.167142	−	0.985933i	$-0.446546\pi$
$877$	9.89956	0.334284	0.167142	+	0.985933i	$0.446546\pi$
$878$	25.8960	0.873947
$879$	80.5357	2.71640
$880$	0	0
$881$	−9.98001	−0.336235	−0.168117	−	0.985767i	$-0.553769\pi$
$881$	−9.98001	−0.336235	−0.168117	+	0.985767i	$0.553769\pi$
$882$	−40.3703	−1.35934
$883$	12.3375	0.415189	0.207594	−	0.978215i	$-0.433437\pi$
$883$	12.3375	0.415189	0.207594	+	0.978215i	$0.433437\pi$
$884$	14.2892	0.480598
$885$	36.2455	1.21838
$886$	−3.56148	−0.119650
$887$	−50.1372	−1.68344	−0.841721	−	0.539913i	$-0.818457\pi$
$887$	−50.1372	−1.68344	−0.841721	+	0.539913i	$0.818457\pi$
$888$	−13.5629	−0.455140
$889$	24.3679	0.817273
$890$	4.72920	0.158523
$891$	0	0
$892$	−16.0539	−0.537523
$893$	−34.3974	−1.15107
$894$	28.7019	0.959934
$895$	12.5173	0.418408
$896$	4.62522	0.154518
$897$	−6.88720	−0.229957
$898$	−12.1832	−0.406560
$899$	−1.09097	−0.0363861
$900$	−9.85667	−0.328556
$901$	8.04210	0.267921
$902$	0	0
$903$	−110.934	−3.69167
$904$	10.4753	0.348404
$905$	23.5938	0.784284
$906$	−30.3275	−1.00756
$907$	22.3422	0.741861	0.370930	−	0.928661i	$-0.379039\pi$
$907$	22.3422	0.741861	0.370930	+	0.928661i	$0.379039\pi$
$908$	22.7592	0.755291
$909$	−3.11093	−0.103183
$910$	16.1167	0.534265
$911$	39.6549	1.31383	0.656913	−	0.753967i	$-0.271862\pi$
$911$	39.6549	1.31383	0.656913	+	0.753967i	$0.271862\pi$
$912$	−13.8854	−0.459792
$913$	0	0
$914$	−3.83608	−0.126886
$915$	25.8273	0.853824
$916$	8.64321	0.285580
$917$	−61.1405	−2.01904
$918$	2.34952	0.0775457
$919$	−13.7296	−0.452898	−0.226449	−	0.974023i	$-0.572712\pi$
$919$	−13.7296	−0.452898	−0.226449	+	0.974023i	$0.572712\pi$
$920$	1.21899	0.0401889
$921$	−52.1801	−1.71939
$922$	−33.9954	−1.11958
$923$	5.86026	0.192893
$924$	0	0
$925$	−19.7817	−0.650417
$926$	9.54565	0.313689
$927$	−13.3095	−0.437143
$928$	2.00573	0.0658412
$929$	−18.2800	−0.599746	−0.299873	−	0.953979i	$-0.596944\pi$
$929$	−18.2800	−0.599746	−0.299873	+	0.953979i	$0.596944\pi$
$930$	−1.59750	−0.0523841
$931$	−82.9474	−2.71849
$932$	−21.2558	−0.696257
$933$	−45.4084	−1.48660
$934$	10.4265	0.341166
$935$	0	0
$936$	−8.01798	−0.262076
$937$	1.00647	0.0328800	0.0164400	−	0.999865i	$-0.494767\pi$
$937$	1.00647	0.0328800	0.0164400	+	0.999865i	$0.494767\pi$
$938$	63.9471	2.08795
$939$	21.4035	0.698476
$940$	7.27552	0.237301
$941$	47.5994	1.55170	0.775848	−	0.630919i	$-0.217322\pi$
$941$	47.5994	1.55170	0.775848	+	0.630919i	$0.217322\pi$
$942$	53.1901	1.73303
$943$	2.42203	0.0788720
$944$	12.3412	0.401671
$945$	2.65001	0.0862049
$946$	0	0
$947$	−44.3548	−1.44134	−0.720669	−	0.693279i	$-0.756165\pi$
$947$	−44.3548	−1.44134	−0.720669	+	0.693279i	$0.756165\pi$
$948$	10.3000	0.334529
$949$	9.04035	0.293462
$950$	−20.2521	−0.657066
$951$	38.1145	1.23595
$952$	23.1204	0.749338
$953$	47.4720	1.53777	0.768884	−	0.639388i	$-0.220812\pi$
$953$	47.4720	1.53777	0.768884	+	0.639388i	$0.220812\pi$
$954$	−4.51259	−0.146101
$955$	−22.0094	−0.712207
$956$	−1.59030	−0.0514341
$957$	0	0
$958$	−18.6860	−0.603717
$959$	−75.4832	−2.43748
$960$	2.93696	0.0947899
$961$	−30.7041	−0.990456
$962$	−16.0916	−0.518813
$963$	−7.86632	−0.253489
$964$	−0.519057	−0.0167177
$965$	30.4054	0.978785
$966$	−11.1437	−0.358544
$967$	−21.8015	−0.701088	−0.350544	−	0.936546i	$-0.614003\pi$
$967$	−21.8015	−0.701088	−0.350544	+	0.936546i	$0.614003\pi$
$968$	0	0
$969$	−69.4101	−2.22977
$970$	−15.8334	−0.508381
$971$	35.7008	1.14569	0.572846	−	0.819663i	$-0.305839\pi$
$971$	35.7008	1.14569	0.572846	+	0.819663i	$0.305839\pi$
$972$	−21.5924	−0.692575
$973$	43.5779	1.39704
$974$	−21.2749	−0.681692
$975$	−24.2021	−0.775087
$976$	8.79389	0.281486
$977$	24.5960	0.786897	0.393448	−	0.919347i	$-0.371282\pi$
$977$	24.5960	0.786897	0.393448	+	0.919347i	$0.371282\pi$
$978$	46.2413	1.47863
$979$	0	0
$980$	17.5445	0.560439
$981$	45.2258	1.44395
$982$	16.4971	0.526445
$983$	−2.34057	−0.0746527	−0.0373264	−	0.999303i	$-0.511884\pi$
$983$	−2.34057	−0.0746527	−0.0373264	+	0.999303i	$0.511884\pi$
$984$	5.83548	0.186028
$985$	−1.33635	−0.0425797
$986$	10.0262	0.319299
$987$	−66.5112	−2.11708
$988$	−16.4743	−0.524116
$989$	−9.95488	−0.316547
$990$	0	0
$991$	−3.10734	−0.0987080	−0.0493540	−	0.998781i	$-0.515716\pi$
$991$	−3.10734	−0.0987080	−0.0493540	+	0.998781i	$0.515716\pi$
$992$	−0.543930	−0.0172698
$993$	−74.4114	−2.36137
$994$	9.48210	0.300754
$995$	−33.3209	−1.05634
$996$	18.2939	0.579663
$997$	−32.1275	−1.01749	−0.508744	−	0.860918i	$-0.669890\pi$
$997$	−32.1275	−1.01749	−0.508744	+	0.860918i	$0.669890\pi$
$998$	30.7364	0.972945
$999$	−2.64587	−0.0837117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5566.2.a.bt.1.8		10
11.2	odd	10		506.2.e.h.323.4	yes	20
11.6	odd	10		506.2.e.h.47.4	✓	20
11.10	odd	2		5566.2.a.bu.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.47.4	✓	20	11.6	odd	10
506.2.e.h.323.4	yes	20	11.2	odd	10
5566.2.a.bt.1.8		10	1.1	even	1	trivial
5566.2.a.bu.1.8		10	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5566 = 2 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5566.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.40934 q^{3} +1.00000 q^{4} +1.21899 q^{5} -2.40934 q^{6} -4.62522 q^{7} -1.00000 q^{8} +2.80492 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.40934 q^{3} +1.00000 q^{4} +1.21899 q^{5} -2.40934 q^{6} -4.62522 q^{7} -1.00000 q^{8} +2.80492 q^{9} -1.21899 q^{10} +2.40934 q^{12} +2.85854 q^{13} +4.62522 q^{14} +2.93696 q^{15} +1.00000 q^{16} +4.99877 q^{17} -2.80492 q^{18} -5.76317 q^{19} +1.21899 q^{20} -11.1437 q^{21} -1.00000 q^{23} -2.40934 q^{24} -3.51407 q^{25} -2.85854 q^{26} -0.470019 q^{27} -4.62522 q^{28} -2.00573 q^{29} -2.93696 q^{30} +0.543930 q^{31} -1.00000 q^{32} -4.99877 q^{34} -5.63809 q^{35} +2.80492 q^{36} +5.62928 q^{37} +5.76317 q^{38} +6.88720 q^{39} -1.21899 q^{40} -2.42203 q^{41} +11.1437 q^{42} +9.95488 q^{43} +3.41916 q^{45} +1.00000 q^{46} +5.96849 q^{47} +2.40934 q^{48} +14.3927 q^{49} +3.51407 q^{50} +12.0437 q^{51} +2.85854 q^{52} +1.60881 q^{53} +0.470019 q^{54} +4.62522 q^{56} -13.8854 q^{57} +2.00573 q^{58} +12.3412 q^{59} +2.93696 q^{60} +8.79389 q^{61} -0.543930 q^{62} -12.9734 q^{63} +1.00000 q^{64} +3.48453 q^{65} +13.8257 q^{67} +4.99877 q^{68} -2.40934 q^{69} +5.63809 q^{70} +2.05009 q^{71} -2.80492 q^{72} +3.16257 q^{73} -5.62928 q^{74} -8.46658 q^{75} -5.76317 q^{76} -6.88720 q^{78} +4.27504 q^{79} +1.21899 q^{80} -9.54719 q^{81} +2.42203 q^{82} +7.59289 q^{83} -11.1437 q^{84} +6.09345 q^{85} -9.95488 q^{86} -4.83248 q^{87} -3.87961 q^{89} -3.41916 q^{90} -13.2214 q^{91} -1.00000 q^{92} +1.31051 q^{93} -5.96849 q^{94} -7.02524 q^{95} -2.40934 q^{96} +12.9890 q^{97} -14.3927 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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