LMFDB - Embedded newform 550.2.b.f.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(199,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,0,2,0,0,-22,0,-4,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{33})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 17x^{2} + 64 $ x^4 + 17*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-3.37228i$ of defining polynomial
Character	$\chi$	$=$	550.199
Dual form			550.2.b.f.199.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -2.37228i q^{3} -1.00000 q^{4} -2.37228 q^{6} -2.37228i q^{7} +1.00000i q^{8} -2.62772 q^{9} -1.00000 q^{11} +2.37228i q^{12} -2.00000i q^{13} -2.37228 q^{14} +1.00000 q^{16} -4.37228i q^{17} +2.62772i q^{18} -6.37228 q^{19} -5.62772 q^{21} +1.00000i q^{22} +8.74456i q^{23} +2.37228 q^{24} -2.00000 q^{26} -0.883156i q^{27} +2.37228i q^{28} +4.37228 q^{29} -2.37228 q^{31} -1.00000i q^{32} +2.37228i q^{33} -4.37228 q^{34} +2.62772 q^{36} +3.62772i q^{37} +6.37228i q^{38} -4.74456 q^{39} +11.4891 q^{41} +5.62772i q^{42} +4.00000i q^{43} +1.00000 q^{44} +8.74456 q^{46} -8.74456i q^{47} -2.37228i q^{48} +1.37228 q^{49} -10.3723 q^{51} +2.00000i q^{52} -13.1168i q^{53} -0.883156 q^{54} +2.37228 q^{56} +15.1168i q^{57} -4.37228i q^{58} -8.74456 q^{59} +0.372281 q^{61} +2.37228i q^{62} +6.23369i q^{63} -1.00000 q^{64} +2.37228 q^{66} +8.00000i q^{67} +4.37228i q^{68} +20.7446 q^{69} -7.11684 q^{71} -2.62772i q^{72} -7.48913i q^{73} +3.62772 q^{74} +6.37228 q^{76} +2.37228i q^{77} +4.74456i q^{78} +12.7446 q^{79} -9.97825 q^{81} -11.4891i q^{82} -8.74456i q^{83} +5.62772 q^{84} +4.00000 q^{86} -10.3723i q^{87} -1.00000i q^{88} -4.37228 q^{89} -4.74456 q^{91} -8.74456i q^{92} +5.62772i q^{93} -8.74456 q^{94} -2.37228 q^{96} -1.25544i q^{97} -1.37228i q^{98} +2.62772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{6} - 22 q^{9} - 4 q^{11} + 2 q^{14} + 4 q^{16} - 14 q^{19} - 34 q^{21} - 2 q^{24} - 8 q^{26} + 6 q^{29} + 2 q^{31} - 6 q^{34} + 22 q^{36} + 4 q^{39} + 4 q^{44} + 12 q^{46} - 6 q^{49}+ \cdots + 22 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^6 - 22 * q^9 - 4 * q^11 + 2 * q^14 + 4 * q^16 - 14 * q^19 - 34 * q^21 - 2 * q^24 - 8 * q^26 + 6 * q^29 + 2 * q^31 - 6 * q^34 + 22 * q^36 + 4 * q^39 + 4 * q^44 + 12 * q^46 - 6 * q^49 - 30 * q^51 - 38 * q^54 - 2 * q^56 - 12 * q^59 - 10 * q^61 - 4 * q^64 - 2 * q^66 + 60 * q^69 + 6 * q^71 + 26 * q^74 + 14 * q^76 + 28 * q^79 + 52 * q^81 + 34 * q^84 + 16 * q^86 - 6 * q^89 + 4 * q^91 - 12 * q^94 + 2 * q^96 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 2.37228i	− 1.36964i	−0.728714	−	0.684819i	$-0.759881\pi$
$3$	− 2.37228i	− 1.36964i	0.728714	−	0.684819i	$-0.240119\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−2.37228	−0.968480
$7$	− 2.37228i	− 0.896638i	−0.893874	−	0.448319i	$-0.852023\pi$
$7$	− 2.37228i	− 0.896638i	0.893874	−	0.448319i	$-0.147977\pi$
$8$	1.00000i	0.353553i
$9$	−2.62772	−0.875906
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.37228i	0.684819i
$13$	− 2.00000i	− 0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$	− 2.00000i	− 0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−2.37228	−0.634019
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.37228i	− 1.06043i	−0.847862	−	0.530217i	$-0.822110\pi$
$17$	− 4.37228i	− 1.06043i	0.847862	−	0.530217i	$-0.177890\pi$
$18$	2.62772i	0.619359i
$19$	−6.37228	−1.46190	−0.730951	−	0.682430i	$-0.760923\pi$
$19$	−6.37228	−1.46190	−0.730951	+	0.682430i	$0.760923\pi$
$20$	0	0
$21$	−5.62772	−1.22807
$22$	1.00000i	0.213201i
$23$	8.74456i	1.82337i	0.410893	+	0.911684i	$0.365217\pi$
$23$	8.74456i	1.82337i	−0.410893	+	0.911684i	$0.634783\pi$
$24$	2.37228	0.484240
$25$	0	0
$26$	−2.00000	−0.392232
$27$	− 0.883156i	− 0.169963i
$28$	2.37228i	0.448319i
$29$	4.37228	0.811912	0.405956	−	0.913893i	$-0.366939\pi$
$29$	4.37228	0.811912	0.405956	+	0.913893i	$0.366939\pi$
$30$	0	0
$31$	−2.37228	−0.426074	−0.213037	−	0.977044i	$-0.568336\pi$
$31$	−2.37228	−0.426074	−0.213037	+	0.977044i	$0.568336\pi$
$32$	− 1.00000i	− 0.176777i
$33$	2.37228i	0.412961i
$34$	−4.37228	−0.749840
$35$	0	0
$36$	2.62772	0.437953
$37$	3.62772i	0.596393i	0.954504	+	0.298197i	$0.0963851\pi$
$37$	3.62772i	0.596393i	−0.954504	+	0.298197i	$0.903615\pi$
$38$	6.37228i	1.03372i
$39$	−4.74456	−0.759738
$40$	0	0
$41$	11.4891	1.79430	0.897150	−	0.441726i	$-0.145634\pi$
$41$	11.4891	1.79430	0.897150	+	0.441726i	$0.145634\pi$
$42$	5.62772i	0.868376i
$43$	4.00000i	0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$	4.00000i	0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	8.74456	1.28932
$47$	− 8.74456i	− 1.27553i	−0.770233	−	0.637763i	$-0.779860\pi$
$47$	− 8.74456i	− 1.27553i	0.770233	−	0.637763i	$-0.220140\pi$
$48$	− 2.37228i	− 0.342409i
$49$	1.37228	0.196040
$50$	0	0
$51$	−10.3723	−1.45241
$52$	2.00000i	0.277350i
$53$	− 13.1168i	− 1.80174i	−0.434092	−	0.900869i	$-0.642931\pi$
$53$	− 13.1168i	− 1.80174i	0.434092	−	0.900869i	$-0.357069\pi$
$54$	−0.883156	−0.120182
$55$	0	0
$56$	2.37228	0.317009
$57$	15.1168i	2.00227i
$58$	− 4.37228i	− 0.574109i
$59$	−8.74456	−1.13845	−0.569223	−	0.822183i	$-0.692756\pi$
$59$	−8.74456	−1.13845	−0.569223	+	0.822183i	$0.692756\pi$
$60$	0	0
$61$	0.372281	0.0476657	0.0238329	−	0.999716i	$-0.492413\pi$
$61$	0.372281	0.0476657	0.0238329	+	0.999716i	$0.492413\pi$
$62$	2.37228i	0.301280i
$63$	6.23369i	0.785371i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.37228	0.292008
$67$	8.00000i	0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$	8.00000i	0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$	4.37228i	0.530217i
$69$	20.7446	2.49735
$70$	0	0
$71$	−7.11684	−0.844614	−0.422307	−	0.906453i	$-0.638780\pi$
$71$	−7.11684	−0.844614	−0.422307	+	0.906453i	$0.638780\pi$
$72$	− 2.62772i	− 0.309680i
$73$	− 7.48913i	− 0.876536i	−0.898844	−	0.438268i	$-0.855592\pi$
$73$	− 7.48913i	− 0.876536i	0.898844	−	0.438268i	$-0.144408\pi$
$74$	3.62772	0.421714
$75$	0	0
$76$	6.37228	0.730951
$77$	2.37228i	0.270347i
$78$	4.74456i	0.537216i
$79$	12.7446	1.43388	0.716938	−	0.697137i	$-0.245543\pi$
$79$	12.7446	1.43388	0.716938	+	0.697137i	$0.245543\pi$
$80$	0	0
$81$	−9.97825	−1.10869
$82$	− 11.4891i	− 1.26876i
$83$	− 8.74456i	− 0.959840i	−0.877312	−	0.479920i	$-0.840666\pi$
$83$	− 8.74456i	− 0.959840i	0.877312	−	0.479920i	$-0.159334\pi$
$84$	5.62772	0.614034
$85$	0	0
$86$	4.00000	0.431331
$87$	− 10.3723i	− 1.11203i
$88$	− 1.00000i	− 0.106600i
$89$	−4.37228	−0.463461	−0.231730	−	0.972780i	$-0.574439\pi$
$89$	−4.37228	−0.463461	−0.231730	+	0.972780i	$0.574439\pi$
$90$	0	0
$91$	−4.74456	−0.497365
$92$	− 8.74456i	− 0.911684i
$93$	5.62772i	0.583567i
$94$	−8.74456	−0.901933
$95$	0	0
$96$	−2.37228	−0.242120
$97$	− 1.25544i	− 0.127470i	−0.997967	−	0.0637352i	$-0.979699\pi$
$97$	− 1.25544i	− 0.127470i	0.997967	−	0.0637352i	$-0.0203013\pi$
$98$	− 1.37228i	− 0.138621i
$99$	2.62772	0.264096
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	10.3723i	1.02701i
$103$	− 13.4891i	− 1.32912i	−0.747234	−	0.664562i	$-0.768618\pi$
$103$	− 13.4891i	− 1.32912i	0.747234	−	0.664562i	$-0.231382\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−13.1168	−1.27402
$107$	− 12.0000i	− 1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$	− 12.0000i	− 1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	0.883156i	0.0849817i
$109$	−7.48913	−0.717328	−0.358664	−	0.933467i	$-0.616768\pi$
$109$	−7.48913	−0.717328	−0.358664	+	0.933467i	$0.616768\pi$
$110$	0	0
$111$	8.60597	0.816842
$112$	− 2.37228i	− 0.224160i
$113$	− 14.7446i	− 1.38705i	−0.720432	−	0.693526i	$-0.756056\pi$
$113$	− 14.7446i	− 1.38705i	0.720432	−	0.693526i	$-0.243944\pi$
$114$	15.1168	1.41582
$115$	0	0
$116$	−4.37228	−0.405956
$117$	5.25544i	0.485865i
$118$	8.74456i	0.805002i
$119$	−10.3723	−0.950825
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 0.372281i	− 0.0337048i
$123$	− 27.2554i	− 2.45754i
$124$	2.37228	0.213037
$125$	0	0
$126$	6.23369	0.555341
$127$	8.00000i	0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$	8.00000i	0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	1.00000i	0.0883883i
$129$	9.48913	0.835471
$130$	0	0
$131$	4.88316	0.426643	0.213322	−	0.976982i	$-0.431572\pi$
$131$	4.88316	0.426643	0.213322	+	0.976982i	$0.431572\pi$
$132$	− 2.37228i	− 0.206481i
$133$	15.1168i	1.31080i
$134$	8.00000	0.691095
$135$	0	0
$136$	4.37228	0.374920
$137$	− 2.74456i	− 0.234484i	−0.993103	−	0.117242i	$-0.962595\pi$
$137$	− 2.74456i	− 0.234484i	0.993103	−	0.117242i	$-0.0374053\pi$
$138$	− 20.7446i	− 1.76589i
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−20.7446	−1.74701
$142$	7.11684i	0.597232i
$143$	2.00000i	0.167248i
$144$	−2.62772	−0.218977
$145$	0	0
$146$	−7.48913	−0.619804
$147$	− 3.25544i	− 0.268504i
$148$	− 3.62772i	− 0.298197i
$149$	18.6060	1.52426	0.762130	−	0.647424i	$-0.224154\pi$
$149$	18.6060	1.52426	0.762130	+	0.647424i	$0.224154\pi$
$150$	0	0
$151$	22.2337	1.80935	0.904676	−	0.426100i	$-0.140113\pi$
$151$	22.2337	1.80935	0.904676	+	0.426100i	$0.140113\pi$
$152$	− 6.37228i	− 0.516860i
$153$	11.4891i	0.928841i
$154$	2.37228	0.191164
$155$	0	0
$156$	4.74456	0.379869
$157$	3.62772i	0.289523i	0.989467	+	0.144762i	$0.0462416\pi$
$157$	3.62772i	0.289523i	−0.989467	+	0.144762i	$0.953758\pi$
$158$	− 12.7446i	− 1.01390i
$159$	−31.1168	−2.46773
$160$	0	0
$161$	20.7446	1.63490
$162$	9.97825i	0.783965i
$163$	23.1168i	1.81065i	0.424718	+	0.905325i	$0.360373\pi$
$163$	23.1168i	1.81065i	−0.424718	+	0.905325i	$0.639627\pi$
$164$	−11.4891	−0.897150
$165$	0	0
$166$	−8.74456	−0.678710
$167$	− 10.3723i	− 0.802631i	−0.915940	−	0.401316i	$-0.868553\pi$
$167$	− 10.3723i	− 0.802631i	0.915940	−	0.401316i	$-0.131447\pi$
$168$	− 5.62772i	− 0.434188i
$169$	9.00000	0.692308
$170$	0	0
$171$	16.7446	1.28049
$172$	− 4.00000i	− 0.304997i
$173$	6.00000i	0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$	6.00000i	0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	−10.3723	−0.786321
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	20.7446i	1.55926i
$178$	4.37228i	0.327716i
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	4.74456i	0.351690i
$183$	− 0.883156i	− 0.0652848i
$184$	−8.74456	−0.644658
$185$	0	0
$186$	5.62772	0.412644
$187$	4.37228i	0.319733i
$188$	8.74456i	0.637763i
$189$	−2.09509	−0.152396
$190$	0	0
$191$	17.4891	1.26547	0.632734	−	0.774369i	$-0.281933\pi$
$191$	17.4891	1.26547	0.632734	+	0.774369i	$0.281933\pi$
$192$	2.37228i	0.171205i
$193$	13.8614i	0.997766i	0.866669	+	0.498883i	$0.166256\pi$
$193$	13.8614i	0.997766i	−0.866669	+	0.498883i	$0.833744\pi$
$194$	−1.25544	−0.0901351
$195$	0	0
$196$	−1.37228	−0.0980201
$197$	− 9.25544i	− 0.659423i	−0.944082	−	0.329711i	$-0.893049\pi$
$197$	− 9.25544i	− 0.659423i	0.944082	−	0.329711i	$-0.106951\pi$
$198$	− 2.62772i	− 0.186744i
$199$	−0.883156	−0.0626053	−0.0313026	−	0.999510i	$-0.509966\pi$
$199$	−0.883156	−0.0626053	−0.0313026	+	0.999510i	$0.509966\pi$
$200$	0	0
$201$	18.9783	1.33862
$202$	− 6.00000i	− 0.422159i
$203$	− 10.3723i	− 0.727991i
$204$	10.3723	0.726205
$205$	0	0
$206$	−13.4891	−0.939832
$207$	− 22.9783i	− 1.59710i
$208$	− 2.00000i	− 0.138675i
$209$	6.37228	0.440780
$210$	0	0
$211$	−11.1168	−0.765315	−0.382658	−	0.923890i	$-0.624991\pi$
$211$	−11.1168	−0.765315	−0.382658	+	0.923890i	$0.624991\pi$
$212$	13.1168i	0.900869i
$213$	16.8832i	1.15681i
$214$	−12.0000	−0.820303
$215$	0	0
$216$	0.883156	0.0600912
$217$	5.62772i	0.382034i
$218$	7.48913i	0.507228i
$219$	−17.7663	−1.20054
$220$	0	0
$221$	−8.74456	−0.588223
$222$	− 8.60597i	− 0.577595i
$223$	7.25544i	0.485860i	0.970044	+	0.242930i	$0.0781085\pi$
$223$	7.25544i	0.485860i	−0.970044	+	0.242930i	$0.921891\pi$
$224$	−2.37228	−0.158505
$225$	0	0
$226$	−14.7446	−0.980794
$227$	8.74456i	0.580397i	0.956966	+	0.290199i	$0.0937213\pi$
$227$	8.74456i	0.580397i	−0.956966	+	0.290199i	$0.906279\pi$
$228$	− 15.1168i	− 1.00114i
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	5.62772	0.370277
$232$	4.37228i	0.287054i
$233$	4.37228i	0.286438i	0.989691	+	0.143219i	$0.0457453\pi$
$233$	4.37228i	0.286438i	−0.989691	+	0.143219i	$0.954255\pi$
$234$	5.25544	0.343559
$235$	0	0
$236$	8.74456	0.569223
$237$	− 30.2337i	− 1.96389i
$238$	10.3723i	0.672335i
$239$	3.25544	0.210577	0.105288	−	0.994442i	$-0.466423\pi$
$239$	3.25544	0.210577	0.105288	+	0.994442i	$0.466423\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	− 1.00000i	− 0.0642824i
$243$	21.0217i	1.34855i
$244$	−0.372281	−0.0238329
$245$	0	0
$246$	−27.2554	−1.73774
$247$	12.7446i	0.810917i
$248$	− 2.37228i	− 0.150640i
$249$	−20.7446	−1.31463
$250$	0	0
$251$	−8.74456	−0.551952	−0.275976	−	0.961165i	$-0.589001\pi$
$251$	−8.74456	−0.551952	−0.275976	+	0.961165i	$0.589001\pi$
$252$	− 6.23369i	− 0.392685i
$253$	− 8.74456i	− 0.549766i
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000i	1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$	18.0000i	1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$	− 9.48913i	− 0.590767i
$259$	8.60597	0.534749
$260$	0	0
$261$	−11.4891	−0.711159
$262$	− 4.88316i	− 0.301682i
$263$	− 3.86141i	− 0.238105i	−0.992888	−	0.119052i	$-0.962014\pi$
$263$	− 3.86141i	− 0.238105i	0.992888	−	0.119052i	$-0.0379856\pi$
$264$	−2.37228	−0.146004
$265$	0	0
$266$	15.1168	0.926873
$267$	10.3723i	0.634773i
$268$	− 8.00000i	− 0.488678i
$269$	−2.74456	−0.167339	−0.0836695	−	0.996494i	$-0.526664\pi$
$269$	−2.74456	−0.167339	−0.0836695	+	0.996494i	$0.526664\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	− 4.37228i	− 0.265108i
$273$	11.2554i	0.681210i
$274$	−2.74456	−0.165805
$275$	0	0
$276$	−20.7446	−1.24868
$277$	− 1.25544i	− 0.0754319i	−0.999289	−	0.0377160i	$-0.987992\pi$
$277$	− 1.25544i	− 0.0754319i	0.999289	−	0.0377160i	$-0.0120082\pi$
$278$	− 4.00000i	− 0.239904i
$279$	6.23369	0.373201
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	20.7446i	1.23532i
$283$	− 16.7446i	− 0.995361i	−0.867360	−	0.497680i	$-0.834185\pi$
$283$	− 16.7446i	− 0.995361i	0.867360	−	0.497680i	$-0.165815\pi$
$284$	7.11684	0.422307
$285$	0	0
$286$	2.00000	0.118262
$287$	− 27.2554i	− 1.60884i
$288$	2.62772i	0.154840i
$289$	−2.11684	−0.124520
$290$	0	0
$291$	−2.97825	−0.174588
$292$	7.48913i	0.438268i
$293$	− 0.510875i	− 0.0298456i	−0.999889	−	0.0149228i	$-0.995250\pi$
$293$	− 0.510875i	− 0.0298456i	0.999889	−	0.0149228i	$-0.00475025\pi$
$294$	−3.25544	−0.189861
$295$	0	0
$296$	−3.62772	−0.210857
$297$	0.883156i	0.0512459i
$298$	− 18.6060i	− 1.07781i
$299$	17.4891	1.01142
$300$	0	0
$301$	9.48913	0.546944
$302$	− 22.2337i	− 1.27940i
$303$	− 14.2337i	− 0.817704i
$304$	−6.37228	−0.365475
$305$	0	0
$306$	11.4891	0.656790
$307$	16.7446i	0.955663i	0.878452	+	0.477831i	$0.158577\pi$
$307$	16.7446i	0.955663i	−0.878452	+	0.477831i	$0.841423\pi$
$308$	− 2.37228i	− 0.135173i
$309$	−32.0000	−1.82042
$310$	0	0
$311$	13.6277	0.772757	0.386379	−	0.922340i	$-0.373726\pi$
$311$	13.6277	0.772757	0.386379	+	0.922340i	$0.373726\pi$
$312$	− 4.74456i	− 0.268608i
$313$	22.0000i	1.24351i	0.783210	+	0.621757i	$0.213581\pi$
$313$	22.0000i	1.24351i	−0.783210	+	0.621757i	$0.786419\pi$
$314$	3.62772	0.204724
$315$	0	0
$316$	−12.7446	−0.716938
$317$	27.3505i	1.53616i	0.640355	+	0.768079i	$0.278787\pi$
$317$	27.3505i	1.53616i	−0.640355	+	0.768079i	$0.721213\pi$
$318$	31.1168i	1.74495i
$319$	−4.37228	−0.244801
$320$	0	0
$321$	−28.4674	−1.58889
$322$	− 20.7446i	− 1.15605i
$323$	27.8614i	1.55025i
$324$	9.97825	0.554347
$325$	0	0
$326$	23.1168	1.28032
$327$	17.7663i	0.982479i
$328$	11.4891i	0.634381i
$329$	−20.7446	−1.14368
$330$	0	0
$331$	−14.9783	−0.823279	−0.411640	−	0.911347i	$-0.635044\pi$
$331$	−14.9783	−0.823279	−0.411640	+	0.911347i	$0.635044\pi$
$332$	8.74456i	0.479920i
$333$	− 9.53262i	− 0.522385i
$334$	−10.3723	−0.567546
$335$	0	0
$336$	−5.62772	−0.307017
$337$	6.88316i	0.374949i	0.982269	+	0.187475i	$0.0600303\pi$
$337$	6.88316i	0.374949i	−0.982269	+	0.187475i	$0.939970\pi$
$338$	− 9.00000i	− 0.489535i
$339$	−34.9783	−1.89976
$340$	0	0
$341$	2.37228	0.128466
$342$	− 16.7446i	− 0.905442i
$343$	− 19.8614i	− 1.07242i
$344$	−4.00000	−0.215666
$345$	0	0
$346$	6.00000	0.322562
$347$	2.23369i	0.119911i	0.998201	+	0.0599553i	$0.0190958\pi$
$347$	2.23369i	0.119911i	−0.998201	+	0.0599553i	$0.980904\pi$
$348$	10.3723i	0.556013i
$349$	3.48913	0.186769	0.0933843	−	0.995630i	$-0.470231\pi$
$349$	3.48913	0.186769	0.0933843	+	0.995630i	$0.470231\pi$
$350$	0	0
$351$	−1.76631	−0.0942788
$352$	1.00000i	0.0533002i
$353$	23.4891i	1.25020i	0.780545	+	0.625100i	$0.214942\pi$
$353$	23.4891i	1.25020i	−0.780545	+	0.625100i	$0.785058\pi$
$354$	20.7446	1.10256
$355$	0	0
$356$	4.37228	0.231730
$357$	24.6060i	1.30229i
$358$	− 12.0000i	− 0.634220i
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	21.6060	1.13716
$362$	10.0000i	0.525588i
$363$	− 2.37228i	− 0.124512i
$364$	4.74456	0.248683
$365$	0	0
$366$	−0.883156	−0.0461633
$367$	− 4.00000i	− 0.208798i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	− 4.00000i	− 0.208798i	0.994535	−	0.104399i	$-0.0332919\pi$
$368$	8.74456i	0.455842i
$369$	−30.1902	−1.57164
$370$	0	0
$371$	−31.1168	−1.61551
$372$	− 5.62772i	− 0.291784i
$373$	− 8.51087i	− 0.440676i	−0.975424	−	0.220338i	$-0.929284\pi$
$373$	− 8.51087i	− 0.440676i	0.975424	−	0.220338i	$-0.0707161\pi$
$374$	4.37228	0.226085
$375$	0	0
$376$	8.74456	0.450966
$377$	− 8.74456i	− 0.450368i
$378$	2.09509i	0.107760i
$379$	−34.2337	−1.75847	−0.879233	−	0.476392i	$-0.841944\pi$
$379$	−34.2337	−1.75847	−0.879233	+	0.476392i	$0.841944\pi$
$380$	0	0
$381$	18.9783	0.972285
$382$	− 17.4891i	− 0.894821i
$383$	2.23369i	0.114136i	0.998370	+	0.0570681i	$0.0181752\pi$
$383$	2.23369i	0.114136i	−0.998370	+	0.0570681i	$0.981825\pi$
$384$	2.37228	0.121060
$385$	0	0
$386$	13.8614	0.705527
$387$	− 10.5109i	− 0.534298i
$388$	1.25544i	0.0637352i
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	38.2337	1.93356
$392$	1.37228i	0.0693107i
$393$	− 11.5842i	− 0.584347i
$394$	−9.25544	−0.466282
$395$	0	0
$396$	−2.62772	−0.132048
$397$	− 20.9783i	− 1.05287i	−0.850216	−	0.526434i	$-0.823529\pi$
$397$	− 20.9783i	− 1.05287i	0.850216	−	0.526434i	$-0.176471\pi$
$398$	0.883156i	0.0442686i
$399$	35.8614	1.79532
$400$	0	0
$401$	7.62772	0.380910	0.190455	−	0.981696i	$-0.439004\pi$
$401$	7.62772	0.380910	0.190455	+	0.981696i	$0.439004\pi$
$402$	− 18.9783i	− 0.946549i
$403$	4.74456i	0.236343i
$404$	−6.00000	−0.298511
$405$	0	0
$406$	−10.3723	−0.514768
$407$	− 3.62772i	− 0.179819i
$408$	− 10.3723i	− 0.513504i
$409$	36.2337	1.79164	0.895820	−	0.444417i	$-0.146589\pi$
$409$	36.2337	1.79164	0.895820	+	0.444417i	$0.146589\pi$
$410$	0	0
$411$	−6.51087	−0.321158
$412$	13.4891i	0.664562i
$413$	20.7446i	1.02077i
$414$	−22.9783	−1.12932
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	− 9.48913i	− 0.464684i
$418$	− 6.37228i	− 0.311678i
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−24.2337	−1.18108	−0.590539	−	0.807009i	$-0.701085\pi$
$421$	−24.2337	−1.18108	−0.590539	+	0.807009i	$0.701085\pi$
$422$	11.1168i	0.541159i
$423$	22.9783i	1.11724i
$424$	13.1168	0.637010
$425$	0	0
$426$	16.8832	0.817992
$427$	− 0.883156i	− 0.0427389i
$428$	12.0000i	0.580042i
$429$	4.74456	0.229070
$430$	0	0
$431$	10.9783	0.528804	0.264402	−	0.964413i	$-0.414825\pi$
$431$	10.9783	0.528804	0.264402	+	0.964413i	$0.414825\pi$
$432$	− 0.883156i	− 0.0424909i
$433$	29.7228i	1.42839i	0.699948	+	0.714194i	$0.253206\pi$
$433$	29.7228i	1.42839i	−0.699948	+	0.714194i	$0.746794\pi$
$434$	5.62772	0.270139
$435$	0	0
$436$	7.48913	0.358664
$437$	− 55.7228i	− 2.66558i
$438$	17.7663i	0.848907i
$439$	26.9783	1.28760	0.643801	−	0.765193i	$-0.277357\pi$
$439$	26.9783	1.28760	0.643801	+	0.765193i	$0.277357\pi$
$440$	0	0
$441$	−3.60597	−0.171713
$442$	8.74456i	0.415936i
$443$	− 6.51087i	− 0.309341i	−0.987966	−	0.154670i	$-0.950568\pi$
$443$	− 6.51087i	− 0.309341i	0.987966	−	0.154670i	$-0.0494316\pi$
$444$	−8.60597	−0.408421
$445$	0	0
$446$	7.25544	0.343555
$447$	− 44.1386i	− 2.08768i
$448$	2.37228i	0.112080i
$449$	16.9783	0.801253	0.400627	−	0.916241i	$-0.368792\pi$
$449$	16.9783	0.801253	0.400627	+	0.916241i	$0.368792\pi$
$450$	0	0
$451$	−11.4891	−0.541002
$452$	14.7446i	0.693526i
$453$	− 52.7446i	− 2.47816i
$454$	8.74456	0.410403
$455$	0	0
$456$	−15.1168	−0.707911
$457$	35.3505i	1.65363i	0.562475	+	0.826814i	$0.309849\pi$
$457$	35.3505i	1.65363i	−0.562475	+	0.826814i	$0.690151\pi$
$458$	− 10.0000i	− 0.467269i
$459$	−3.86141	−0.180235
$460$	0	0
$461$	−1.11684	−0.0520166	−0.0260083	−	0.999662i	$-0.508280\pi$
$461$	−1.11684	−0.0520166	−0.0260083	+	0.999662i	$0.508280\pi$
$462$	− 5.62772i	− 0.261825i
$463$	− 34.2337i	− 1.59097i	−0.605970	−	0.795487i	$-0.707215\pi$
$463$	− 34.2337i	− 1.59097i	0.605970	−	0.795487i	$-0.292785\pi$
$464$	4.37228	0.202978
$465$	0	0
$466$	4.37228	0.202542
$467$	− 13.6277i	− 0.630616i	−0.948989	−	0.315308i	$-0.897892\pi$
$467$	− 13.6277i	− 0.630616i	0.948989	−	0.315308i	$-0.102108\pi$
$468$	− 5.25544i	− 0.242933i
$469$	18.9783	0.876334
$470$	0	0
$471$	8.60597	0.396542
$472$	− 8.74456i	− 0.402501i
$473$	− 4.00000i	− 0.183920i
$474$	−30.2337	−1.38868
$475$	0	0
$476$	10.3723	0.475413
$477$	34.4674i	1.57815i
$478$	− 3.25544i	− 0.148900i
$479$	17.4891	0.799099	0.399549	−	0.916712i	$-0.369167\pi$
$479$	17.4891	0.799099	0.399549	+	0.916712i	$0.369167\pi$
$480$	0	0
$481$	7.25544	0.330819
$482$	22.0000i	1.00207i
$483$	− 49.2119i	− 2.23922i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	21.0217	0.953566
$487$	20.0000i	0.906287i	0.891438	+	0.453143i	$0.149697\pi$
$487$	20.0000i	0.906287i	−0.891438	+	0.453143i	$0.850303\pi$
$488$	0.372281i	0.0168524i
$489$	54.8397	2.47994
$490$	0	0
$491$	−1.62772	−0.0734579	−0.0367290	−	0.999325i	$-0.511694\pi$
$491$	−1.62772	−0.0734579	−0.0367290	+	0.999325i	$0.511694\pi$
$492$	27.2554i	1.22877i
$493$	− 19.1168i	− 0.860979i
$494$	12.7446	0.573405
$495$	0	0
$496$	−2.37228	−0.106519
$497$	16.8832i	0.757313i
$498$	20.7446i	0.929586i
$499$	10.5109	0.470531	0.235266	−	0.971931i	$-0.424404\pi$
$499$	10.5109	0.470531	0.235266	+	0.971931i	$0.424404\pi$
$500$	0	0
$501$	−24.6060	−1.09931
$502$	8.74456i	0.390289i
$503$	− 10.9783i	− 0.489496i	−0.969587	−	0.244748i	$-0.921295\pi$
$503$	− 10.9783i	− 0.489496i	0.969587	−	0.244748i	$-0.0787052\pi$
$504$	−6.23369	−0.277671
$505$	0	0
$506$	−8.74456	−0.388743
$507$	− 21.3505i	− 0.948210i
$508$	− 8.00000i	− 0.354943i
$509$	−44.2337	−1.96062	−0.980312	−	0.197455i	$-0.936732\pi$
$509$	−44.2337	−1.96062	−0.980312	+	0.197455i	$0.936732\pi$
$510$	0	0
$511$	−17.7663	−0.785935
$512$	− 1.00000i	− 0.0441942i
$513$	5.62772i	0.248470i
$514$	18.0000	0.793946
$515$	0	0
$516$	−9.48913	−0.417735
$517$	8.74456i	0.384585i
$518$	− 8.60597i	− 0.378125i
$519$	14.2337	0.624790
$520$	0	0
$521$	35.4891	1.55481	0.777403	−	0.629002i	$-0.216536\pi$
$521$	35.4891	1.55481	0.777403	+	0.629002i	$0.216536\pi$
$522$	11.4891i	0.502865i
$523$	14.9783i	0.654953i	0.944859	+	0.327477i	$0.106198\pi$
$523$	14.9783i	0.654953i	−0.944859	+	0.327477i	$0.893802\pi$
$524$	−4.88316	−0.213322
$525$	0	0
$526$	−3.86141	−0.168365
$527$	10.3723i	0.451824i
$528$	2.37228i	0.103240i
$529$	−53.4674	−2.32467
$530$	0	0
$531$	22.9783	0.997171
$532$	− 15.1168i	− 0.655398i
$533$	− 22.9783i	− 0.995299i
$534$	10.3723	0.448853
$535$	0	0
$536$	−8.00000	−0.345547
$537$	− 28.4674i	− 1.22846i
$538$	2.74456i	0.118326i
$539$	−1.37228	−0.0591083
$540$	0	0
$541$	−2.88316	−0.123957	−0.0619783	−	0.998077i	$-0.519741\pi$
$541$	−2.88316	−0.123957	−0.0619783	+	0.998077i	$0.519741\pi$
$542$	16.0000i	0.687259i
$543$	23.7228i	1.01804i
$544$	−4.37228	−0.187460
$545$	0	0
$546$	11.2554	0.481688
$547$	20.0000i	0.855138i	0.903983	+	0.427569i	$0.140630\pi$
$547$	20.0000i	0.855138i	−0.903983	+	0.427569i	$0.859370\pi$
$548$	2.74456i	0.117242i
$549$	−0.978251	−0.0417507
$550$	0	0
$551$	−27.8614	−1.18694
$552$	20.7446i	0.882947i
$553$	− 30.2337i	− 1.28567i
$554$	−1.25544	−0.0533384
$555$	0	0
$556$	−4.00000	−0.169638
$557$	− 40.9783i	− 1.73630i	−0.496298	−	0.868152i	$-0.665308\pi$
$557$	− 40.9783i	− 1.73630i	0.496298	−	0.868152i	$-0.334692\pi$
$558$	− 6.23369i	− 0.263893i
$559$	8.00000	0.338364
$560$	0	0
$561$	10.3723	0.437918
$562$	− 18.0000i	− 0.759284i
$563$	− 26.2337i	− 1.10562i	−0.833308	−	0.552809i	$-0.813556\pi$
$563$	− 26.2337i	− 1.10562i	0.833308	−	0.552809i	$-0.186444\pi$
$564$	20.7446	0.873504
$565$	0	0
$566$	−16.7446	−0.703826
$567$	23.6712i	0.994098i
$568$	− 7.11684i	− 0.298616i
$569$	26.7446	1.12119	0.560595	−	0.828090i	$-0.310572\pi$
$569$	26.7446	1.12119	0.560595	+	0.828090i	$0.310572\pi$
$570$	0	0
$571$	9.62772	0.402907	0.201454	−	0.979498i	$-0.435433\pi$
$571$	9.62772	0.402907	0.201454	+	0.979498i	$0.435433\pi$
$572$	− 2.00000i	− 0.0836242i
$573$	− 41.4891i	− 1.73323i
$574$	−27.2554	−1.13762
$575$	0	0
$576$	2.62772	0.109488
$577$	− 8.97825i	− 0.373769i	−0.982382	−	0.186885i	$-0.940161\pi$
$577$	− 8.97825i	− 0.373769i	0.982382	−	0.186885i	$-0.0598391\pi$
$578$	2.11684i	0.0880491i
$579$	32.8832	1.36658
$580$	0	0
$581$	−20.7446	−0.860629
$582$	2.97825i	0.123452i
$583$	13.1168i	0.543244i
$584$	7.48913	0.309902
$585$	0	0
$586$	−0.510875	−0.0211040
$587$	− 3.86141i	− 0.159377i	−0.996820	−	0.0796887i	$-0.974607\pi$
$587$	− 3.86141i	− 0.159377i	0.996820	−	0.0796887i	$-0.0253926\pi$
$588$	3.25544i	0.134252i
$589$	15.1168	0.622879
$590$	0	0
$591$	−21.9565	−0.903170
$592$	3.62772i	0.149098i
$593$	35.4891i	1.45736i	0.684852	+	0.728682i	$0.259867\pi$
$593$	35.4891i	1.45736i	−0.684852	+	0.728682i	$0.740133\pi$
$594$	0.883156	0.0362363
$595$	0	0
$596$	−18.6060	−0.762130
$597$	2.09509i	0.0857465i
$598$	− 17.4891i	− 0.715184i
$599$	−0.605969	−0.0247592	−0.0123796	−	0.999923i	$-0.503941\pi$
$599$	−0.605969	−0.0247592	−0.0123796	+	0.999923i	$0.503941\pi$
$600$	0	0
$601$	−39.4891	−1.61080	−0.805398	−	0.592735i	$-0.798048\pi$
$601$	−39.4891	−1.61080	−0.805398	+	0.592735i	$0.798048\pi$
$602$	− 9.48913i	− 0.386748i
$603$	− 21.0217i	− 0.856072i
$604$	−22.2337	−0.904676
$605$	0	0
$606$	−14.2337	−0.578204
$607$	− 23.1168i	− 0.938284i	−0.883123	−	0.469142i	$-0.844563\pi$
$607$	− 23.1168i	− 0.938284i	0.883123	−	0.469142i	$-0.155437\pi$
$608$	6.37228i	0.258430i
$609$	−24.6060	−0.997084
$610$	0	0
$611$	−17.4891	−0.707534
$612$	− 11.4891i	− 0.464420i
$613$	− 43.4891i	− 1.75651i	−0.478193	−	0.878255i	$-0.658708\pi$
$613$	− 43.4891i	− 1.75651i	0.478193	−	0.878255i	$-0.341292\pi$
$614$	16.7446	0.675756
$615$	0	0
$616$	−2.37228	−0.0955819
$617$	32.2337i	1.29768i	0.760925	+	0.648840i	$0.224745\pi$
$617$	32.2337i	1.29768i	−0.760925	+	0.648840i	$0.775255\pi$
$618$	32.0000i	1.28723i
$619$	−24.4674	−0.983427	−0.491713	−	0.870757i	$-0.663629\pi$
$619$	−24.4674	−0.983427	−0.491713	+	0.870757i	$0.663629\pi$
$620$	0	0
$621$	7.72281	0.309906
$622$	− 13.6277i	− 0.546422i
$623$	10.3723i	0.415557i
$624$	−4.74456	−0.189935
$625$	0	0
$626$	22.0000	0.879297
$627$	− 15.1168i	− 0.603709i
$628$	− 3.62772i	− 0.144762i
$629$	15.8614	0.632436
$630$	0	0
$631$	24.8832	0.990583	0.495291	−	0.868727i	$-0.335061\pi$
$631$	24.8832	0.990583	0.495291	+	0.868727i	$0.335061\pi$
$632$	12.7446i	0.506951i
$633$	26.3723i	1.04820i
$634$	27.3505	1.08623
$635$	0	0
$636$	31.1168	1.23386
$637$	− 2.74456i	− 0.108744i
$638$	4.37228i	0.173100i
$639$	18.7011	0.739803
$640$	0	0
$641$	36.0951	1.42567	0.712835	−	0.701332i	$-0.247411\pi$
$641$	36.0951	1.42567	0.712835	+	0.701332i	$0.247411\pi$
$642$	28.4674i	1.12352i
$643$	23.1168i	0.911639i	0.890072	+	0.455820i	$0.150654\pi$
$643$	23.1168i	0.911639i	−0.890072	+	0.455820i	$0.849346\pi$
$644$	−20.7446	−0.817450
$645$	0	0
$646$	27.8614	1.09619
$647$	19.7228i	0.775384i	0.921789	+	0.387692i	$0.126728\pi$
$647$	19.7228i	0.775384i	−0.921789	+	0.387692i	$0.873272\pi$
$648$	− 9.97825i	− 0.391983i
$649$	8.74456	0.343254
$650$	0	0
$651$	13.3505	0.523249
$652$	− 23.1168i	− 0.905325i
$653$	− 16.3723i	− 0.640697i	−0.947300	−	0.320348i	$-0.896200\pi$
$653$	− 16.3723i	− 0.640697i	0.947300	−	0.320348i	$-0.103800\pi$
$654$	17.7663	0.694718
$655$	0	0
$656$	11.4891	0.448575
$657$	19.6793i	0.767763i
$658$	20.7446i	0.808707i
$659$	15.8614	0.617873	0.308936	−	0.951083i	$-0.400027\pi$
$659$	15.8614	0.617873	0.308936	+	0.951083i	$0.400027\pi$
$660$	0	0
$661$	31.4891	1.22479	0.612393	−	0.790554i	$-0.290207\pi$
$661$	31.4891	1.22479	0.612393	+	0.790554i	$0.290207\pi$
$662$	14.9783i	0.582146i
$663$	20.7446i	0.805652i
$664$	8.74456	0.339355
$665$	0	0
$666$	−9.53262	−0.369382
$667$	38.2337i	1.48041i
$668$	10.3723i	0.401316i
$669$	17.2119	0.665452
$670$	0	0
$671$	−0.372281	−0.0143718
$672$	5.62772i	0.217094i
$673$	13.8614i	0.534318i	0.963652	+	0.267159i	$0.0860849\pi$
$673$	13.8614i	0.534318i	−0.963652	+	0.267159i	$0.913915\pi$
$674$	6.88316	0.265129
$675$	0	0
$676$	−9.00000	−0.346154
$677$	14.7446i	0.566680i	0.959020	+	0.283340i	$0.0914424\pi$
$677$	14.7446i	0.566680i	−0.959020	+	0.283340i	$0.908558\pi$
$678$	34.9783i	1.34333i
$679$	−2.97825	−0.114295
$680$	0	0
$681$	20.7446	0.794933
$682$	− 2.37228i	− 0.0908393i
$683$	34.3723i	1.31522i	0.753359	+	0.657609i	$0.228432\pi$
$683$	34.3723i	1.31522i	−0.753359	+	0.657609i	$0.771568\pi$
$684$	−16.7446	−0.640244
$685$	0	0
$686$	−19.8614	−0.758312
$687$	− 23.7228i	− 0.905082i
$688$	4.00000i	0.152499i
$689$	−26.2337	−0.999424
$690$	0	0
$691$	5.76631	0.219361	0.109680	−	0.993967i	$-0.465017\pi$
$691$	5.76631	0.219361	0.109680	+	0.993967i	$0.465017\pi$
$692$	− 6.00000i	− 0.228086i
$693$	− 6.23369i	− 0.236798i
$694$	2.23369	0.0847896
$695$	0	0
$696$	10.3723	0.393160
$697$	− 50.2337i	− 1.90274i
$698$	− 3.48913i	− 0.132065i
$699$	10.3723	0.392316
$700$	0	0
$701$	−31.6277	−1.19456	−0.597281	−	0.802032i	$-0.703752\pi$
$701$	−31.6277	−1.19456	−0.597281	+	0.802032i	$0.703752\pi$
$702$	1.76631i	0.0666652i
$703$	− 23.1168i	− 0.871868i
$704$	1.00000	0.0376889
$705$	0	0
$706$	23.4891	0.884025
$707$	− 14.2337i	− 0.535313i
$708$	− 20.7446i	− 0.779628i
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	0	0
$711$	−33.4891	−1.25594
$712$	− 4.37228i	− 0.163858i
$713$	− 20.7446i	− 0.776890i
$714$	24.6060	0.920855
$715$	0	0
$716$	−12.0000	−0.448461
$717$	− 7.72281i	− 0.288414i
$718$	0	0
$719$	−31.1168	−1.16046	−0.580231	−	0.814452i	$-0.697038\pi$
$719$	−31.1168	−1.16046	−0.580231	+	0.814452i	$0.697038\pi$
$720$	0	0
$721$	−32.0000	−1.19174
$722$	− 21.6060i	− 0.804091i
$723$	52.1902i	1.94097i
$724$	10.0000	0.371647
$725$	0	0
$726$	−2.37228	−0.0880436
$727$	10.2337i	0.379546i	0.981828	+	0.189773i	$0.0607753\pi$
$727$	10.2337i	0.379546i	−0.981828	+	0.189773i	$0.939225\pi$
$728$	− 4.74456i	− 0.175845i
$729$	19.9348	0.738324
$730$	0	0
$731$	17.4891	0.646859
$732$	0.883156i	0.0326424i
$733$	− 11.7663i	− 0.434599i	−0.976105	−	0.217299i	$-0.930275\pi$
$733$	− 11.7663i	− 0.434599i	0.976105	−	0.217299i	$-0.0697248\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	8.74456	0.322329
$737$	− 8.00000i	− 0.294684i
$738$	30.1902i	1.11132i
$739$	−48.4674	−1.78290	−0.891451	−	0.453118i	$-0.850312\pi$
$739$	−48.4674	−1.78290	−0.891451	+	0.453118i	$0.850312\pi$
$740$	0	0
$741$	30.2337	1.11066
$742$	31.1168i	1.14234i
$743$	10.3723i	0.380522i	0.981734	+	0.190261i	$0.0609334\pi$
$743$	10.3723i	0.380522i	−0.981734	+	0.190261i	$0.939067\pi$
$744$	−5.62772	−0.206322
$745$	0	0
$746$	−8.51087	−0.311605
$747$	22.9783i	0.840730i
$748$	− 4.37228i	− 0.159866i
$749$	−28.4674	−1.04018
$750$	0	0
$751$	−19.8614	−0.724753	−0.362377	−	0.932032i	$-0.618035\pi$
$751$	−19.8614	−0.724753	−0.362377	+	0.932032i	$0.618035\pi$
$752$	− 8.74456i	− 0.318881i
$753$	20.7446i	0.755974i
$754$	−8.74456	−0.318458
$755$	0	0
$756$	2.09509	0.0761979
$757$	24.9783i	0.907850i	0.891040	+	0.453925i	$0.149977\pi$
$757$	24.9783i	0.907850i	−0.891040	+	0.453925i	$0.850023\pi$
$758$	34.2337i	1.24342i
$759$	−20.7446	−0.752980
$760$	0	0
$761$	−40.9783	−1.48546	−0.742730	−	0.669591i	$-0.766469\pi$
$761$	−40.9783	−1.48546	−0.742730	+	0.669591i	$0.766469\pi$
$762$	− 18.9783i	− 0.687509i
$763$	17.7663i	0.643184i
$764$	−17.4891	−0.632734
$765$	0	0
$766$	2.23369	0.0807064
$767$	17.4891i	0.631496i
$768$	− 2.37228i	− 0.0856023i
$769$	22.0000	0.793340	0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000	0.793340	0.396670	+	0.917961i	$0.370166\pi$
$770$	0	0
$771$	42.7011	1.53784
$772$	− 13.8614i	− 0.498883i
$773$	− 6.60597i	− 0.237600i	−0.992918	−	0.118800i	$-0.962095\pi$
$773$	− 6.60597i	− 0.237600i	0.992918	−	0.118800i	$-0.0379048\pi$
$774$	−10.5109	−0.377806
$775$	0	0
$776$	1.25544	0.0450676
$777$	− 20.4158i	− 0.732412i
$778$	6.00000i	0.215110i
$779$	−73.2119	−2.62309
$780$	0	0
$781$	7.11684	0.254661
$782$	− 38.2337i	− 1.36723i
$783$	− 3.86141i	− 0.137995i
$784$	1.37228	0.0490100
$785$	0	0
$786$	−11.5842	−0.413195
$787$	24.4674i	0.872168i	0.899906	+	0.436084i	$0.143635\pi$
$787$	24.4674i	0.872168i	−0.899906	+	0.436084i	$0.856365\pi$
$788$	9.25544i	0.329711i
$789$	−9.16034	−0.326117
$790$	0	0
$791$	−34.9783	−1.24368
$792$	2.62772i	0.0933719i
$793$	− 0.744563i	− 0.0264402i
$794$	−20.9783	−0.744490
$795$	0	0
$796$	0.883156	0.0313026
$797$	− 11.4891i	− 0.406966i	−0.979079	−	0.203483i	$-0.934774\pi$
$797$	− 11.4891i	− 0.406966i	0.979079	−	0.203483i	$-0.0652261\pi$
$798$	− 35.8614i	− 1.26948i
$799$	−38.2337	−1.35261
$800$	0	0
$801$	11.4891	0.405948
$802$	− 7.62772i	− 0.269344i
$803$	7.48913i	0.264285i
$804$	−18.9783	−0.669311
$805$	0	0
$806$	4.74456	0.167120
$807$	6.51087i	0.229194i
$808$	6.00000i	0.211079i
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	16.1386	0.566703	0.283351	−	0.959016i	$-0.408554\pi$
$811$	16.1386	0.566703	0.283351	+	0.959016i	$0.408554\pi$
$812$	10.3723i	0.363996i
$813$	37.9565i	1.33119i
$814$	−3.62772	−0.127151
$815$	0	0
$816$	−10.3723	−0.363102
$817$	− 25.4891i	− 0.891752i
$818$	− 36.2337i	− 1.26688i
$819$	12.4674	0.435645
$820$	0	0
$821$	−11.4891	−0.400973	−0.200487	−	0.979696i	$-0.564252\pi$
$821$	−11.4891	−0.400973	−0.200487	+	0.979696i	$0.564252\pi$
$822$	6.51087i	0.227093i
$823$	28.0000i	0.976019i	0.872838	+	0.488009i	$0.162277\pi$
$823$	28.0000i	0.976019i	−0.872838	+	0.488009i	$0.837723\pi$
$824$	13.4891	0.469916
$825$	0	0
$826$	20.7446	0.721796
$827$	1.02175i	0.0355297i	0.999842	+	0.0177649i	$0.00565503\pi$
$827$	1.02175i	0.0355297i	−0.999842	+	0.0177649i	$0.994345\pi$
$828$	22.9783i	0.798549i
$829$	13.2554	0.460380	0.230190	−	0.973146i	$-0.426065\pi$
$829$	13.2554	0.460380	0.230190	+	0.973146i	$0.426065\pi$
$830$	0	0
$831$	−2.97825	−0.103314
$832$	2.00000i	0.0693375i
$833$	− 6.00000i	− 0.207888i
$834$	−9.48913	−0.328582
$835$	0	0
$836$	−6.37228	−0.220390
$837$	2.09509i	0.0724171i
$838$	− 12.0000i	− 0.414533i
$839$	−34.9783	−1.20758	−0.603792	−	0.797142i	$-0.706344\pi$
$839$	−34.9783	−1.20758	−0.603792	+	0.797142i	$0.706344\pi$
$840$	0	0
$841$	−9.88316	−0.340798
$842$	24.2337i	0.835148i
$843$	− 42.7011i	− 1.47070i
$844$	11.1168	0.382658
$845$	0	0
$846$	22.9783	0.790009
$847$	− 2.37228i	− 0.0815126i
$848$	− 13.1168i	− 0.450434i
$849$	−39.7228	−1.36328
$850$	0	0
$851$	−31.7228	−1.08744
$852$	− 16.8832i	− 0.578407i
$853$	− 30.4674i	− 1.04318i	−0.853195	−	0.521592i	$-0.825339\pi$
$853$	− 30.4674i	− 1.04318i	0.853195	−	0.521592i	$-0.174661\pi$
$854$	−0.883156	−0.0302210
$855$	0	0
$856$	12.0000	0.410152
$857$	− 15.3505i	− 0.524364i	−0.965018	−	0.262182i	$-0.915558\pi$
$857$	− 15.3505i	− 0.524364i	0.965018	−	0.262182i	$-0.0844421\pi$
$858$	− 4.74456i	− 0.161977i
$859$	31.2554	1.06642	0.533211	−	0.845982i	$-0.320985\pi$
$859$	31.2554	1.06642	0.533211	+	0.845982i	$0.320985\pi$
$860$	0	0
$861$	−64.6576	−2.20352
$862$	− 10.9783i	− 0.373921i
$863$	− 32.7446i	− 1.11464i	−0.830299	−	0.557319i	$-0.811830\pi$
$863$	− 32.7446i	− 1.11464i	0.830299	−	0.557319i	$-0.188170\pi$
$864$	−0.883156	−0.0300456
$865$	0	0
$866$	29.7228	1.01002
$867$	5.02175i	0.170548i
$868$	− 5.62772i	− 0.191017i
$869$	−12.7446	−0.432330
$870$	0	0
$871$	16.0000	0.542139
$872$	− 7.48913i	− 0.253614i
$873$	3.29894i	0.111652i
$874$	−55.7228	−1.88485
$875$	0	0
$876$	17.7663	0.600268
$877$	− 8.97825i	− 0.303174i	−0.988444	−	0.151587i	$-0.951562\pi$
$877$	− 8.97825i	− 0.303174i	0.988444	−	0.151587i	$-0.0484384\pi$
$878$	− 26.9783i	− 0.910472i
$879$	−1.21194	−0.0408777
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	3.60597i	0.121419i
$883$	2.37228i	0.0798336i	0.999203	+	0.0399168i	$0.0127093\pi$
$883$	2.37228i	0.0798336i	−0.999203	+	0.0399168i	$0.987291\pi$
$884$	8.74456	0.294111
$885$	0	0
$886$	−6.51087	−0.218737
$887$	34.9783i	1.17445i	0.809422	+	0.587227i	$0.199781\pi$
$887$	34.9783i	1.17445i	−0.809422	+	0.587227i	$0.800219\pi$
$888$	8.60597i	0.288797i
$889$	18.9783	0.636510
$890$	0	0
$891$	9.97825	0.334284
$892$	− 7.25544i	− 0.242930i
$893$	55.7228i	1.86469i
$894$	−44.1386	−1.47622
$895$	0	0
$896$	2.37228	0.0792524
$897$	− 41.4891i	− 1.38528i
$898$	− 16.9783i	− 0.566572i
$899$	−10.3723	−0.345935
$900$	0	0
$901$	−57.3505	−1.91062
$902$	11.4891i	0.382546i
$903$	− 22.5109i	− 0.749115i
$904$	14.7446	0.490397
$905$	0	0
$906$	−52.7446	−1.75232
$907$	− 40.6060i	− 1.34830i	−0.738595	−	0.674150i	$-0.764510\pi$
$907$	− 40.6060i	− 1.34830i	0.738595	−	0.674150i	$-0.235490\pi$
$908$	− 8.74456i	− 0.290199i
$909$	−15.7663	−0.522936
$910$	0	0
$911$	−48.6060	−1.61039	−0.805194	−	0.593012i	$-0.797939\pi$
$911$	−48.6060	−1.61039	−0.805194	+	0.593012i	$0.797939\pi$
$912$	15.1168i	0.500569i
$913$	8.74456i	0.289403i
$914$	35.3505	1.16929
$915$	0	0
$916$	−10.0000	−0.330409
$917$	− 11.5842i	− 0.382545i
$918$	3.86141i	0.127445i
$919$	26.9783	0.889930	0.444965	−	0.895548i	$-0.353216\pi$
$919$	26.9783	0.889930	0.444965	+	0.895548i	$0.353216\pi$
$920$	0	0
$921$	39.7228	1.30891
$922$	1.11684i	0.0367813i
$923$	14.2337i	0.468508i
$924$	−5.62772	−0.185138
$925$	0	0
$926$	−34.2337	−1.12499
$927$	35.4456i	1.16419i
$928$	− 4.37228i	− 0.143527i
$929$	27.3505	0.897342	0.448671	−	0.893697i	$-0.351898\pi$
$929$	27.3505	0.897342	0.448671	+	0.893697i	$0.351898\pi$
$930$	0	0
$931$	−8.74456	−0.286591
$932$	− 4.37228i	− 0.143219i
$933$	− 32.3288i	− 1.05840i
$934$	−13.6277	−0.445913
$935$	0	0
$936$	−5.25544	−0.171779
$937$	− 51.4891i	− 1.68208i	−0.540976	−	0.841038i	$-0.681945\pi$
$937$	− 51.4891i	− 1.68208i	0.540976	−	0.841038i	$-0.318055\pi$
$938$	− 18.9783i	− 0.619662i
$939$	52.1902	1.70316
$940$	0	0
$941$	48.0951	1.56786	0.783928	−	0.620852i	$-0.213213\pi$
$941$	48.0951	1.56786	0.783928	+	0.620852i	$0.213213\pi$
$942$	− 8.60597i	− 0.280398i
$943$	100.467i	3.27167i
$944$	−8.74456	−0.284611
$945$	0	0
$946$	−4.00000	−0.130051
$947$	20.1386i	0.654416i	0.944952	+	0.327208i	$0.106108\pi$
$947$	20.1386i	0.654416i	−0.944952	+	0.327208i	$0.893892\pi$
$948$	30.2337i	0.981945i
$949$	−14.9783	−0.486215
$950$	0	0
$951$	64.8832	2.10398
$952$	− 10.3723i	− 0.336168i
$953$	− 22.8832i	− 0.741258i	−0.928781	−	0.370629i	$-0.879142\pi$
$953$	− 22.8832i	− 0.741258i	0.928781	−	0.370629i	$-0.120858\pi$
$954$	34.4674	1.11592
$955$	0	0
$956$	−3.25544	−0.105288
$957$	10.3723i	0.335288i
$958$	− 17.4891i	− 0.565048i
$959$	−6.51087	−0.210247
$960$	0	0
$961$	−25.3723	−0.818461
$962$	− 7.25544i	− 0.233925i
$963$	31.5326i	1.01612i
$964$	22.0000	0.708572
$965$	0	0
$966$	−49.2119	−1.58337
$967$	7.39403i	0.237776i	0.992908	+	0.118888i	$0.0379329\pi$
$967$	7.39403i	0.237776i	−0.992908	+	0.118888i	$0.962067\pi$
$968$	1.00000i	0.0321412i
$969$	66.0951	2.12328
$970$	0	0
$971$	−46.9783	−1.50760	−0.753802	−	0.657102i	$-0.771782\pi$
$971$	−46.9783	−1.50760	−0.753802	+	0.657102i	$0.771782\pi$
$972$	− 21.0217i	− 0.674273i
$973$	− 9.48913i	− 0.304207i
$974$	20.0000	0.640841
$975$	0	0
$976$	0.372281	0.0119164
$977$	− 20.2337i	− 0.647333i	−0.946171	−	0.323667i	$-0.895084\pi$
$977$	− 20.2337i	− 0.647333i	0.946171	−	0.323667i	$-0.104916\pi$
$978$	− 54.8397i	− 1.75358i
$979$	4.37228	0.139739
$980$	0	0
$981$	19.6793	0.628312
$982$	1.62772i	0.0519426i
$983$	− 43.7228i	− 1.39454i	−0.716808	−	0.697271i	$-0.754398\pi$
$983$	− 43.7228i	− 1.39454i	0.716808	−	0.697271i	$-0.245602\pi$
$984$	27.2554	0.868872
$985$	0	0
$986$	−19.1168	−0.608804
$987$	49.2119i	1.56643i
$988$	− 12.7446i	− 0.405459i
$989$	−34.9783	−1.11224
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	2.37228i	0.0753200i
$993$	35.5326i	1.12759i
$994$	16.8832	0.535501
$995$	0	0
$996$	20.7446	0.657317
$997$	− 12.2337i	− 0.387445i	−0.981056	−	0.193722i	$-0.937944\pi$
$997$	− 12.2337i	− 0.387445i	0.981056	−	0.193722i	$-0.0620561\pi$
$998$	− 10.5109i	− 0.332716i
$999$	3.20384	0.101365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.b.f.199.1		4
3.2	odd	2		4950.2.c.bc.199.3		4
4.3	odd	2		4400.2.b.p.4049.3		4
5.2	odd	4		550.2.a.n.1.1		2
5.3	odd	4		110.2.a.d.1.2	✓	2
5.4	even	2	inner	550.2.b.f.199.4		4
15.2	even	4		4950.2.a.bw.1.2		2
15.8	even	4		990.2.a.m.1.1		2
15.14	odd	2		4950.2.c.bc.199.2		4
20.3	even	4		880.2.a.n.1.1		2
20.7	even	4		4400.2.a.bl.1.2		2
20.19	odd	2		4400.2.b.p.4049.2		4
35.13	even	4		5390.2.a.bp.1.1		2
40.3	even	4		3520.2.a.bj.1.2		2
40.13	odd	4		3520.2.a.bq.1.1		2
55.32	even	4		6050.2.a.cb.1.1		2
55.43	even	4		1210.2.a.r.1.2		2
60.23	odd	4		7920.2.a.bq.1.2		2
220.43	odd	4		9680.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.a.d.1.2	✓	2	5.3	odd	4
550.2.a.n.1.1		2	5.2	odd	4
550.2.b.f.199.1		4	1.1	even	1	trivial
550.2.b.f.199.4		4	5.4	even	2	inner
880.2.a.n.1.1		2	20.3	even	4
990.2.a.m.1.1		2	15.8	even	4
1210.2.a.r.1.2		2	55.43	even	4
3520.2.a.bj.1.2		2	40.3	even	4
3520.2.a.bq.1.1		2	40.13	odd	4
4400.2.a.bl.1.2		2	20.7	even	4
4400.2.b.p.4049.2		4	20.19	odd	2
4400.2.b.p.4049.3		4	4.3	odd	2
4950.2.a.bw.1.2		2	15.2	even	4
4950.2.c.bc.199.2		4	15.14	odd	2
4950.2.c.bc.199.3		4	3.2	odd	2
5390.2.a.bp.1.1		2	35.13	even	4
6050.2.a.cb.1.1		2	55.32	even	4
7920.2.a.bq.1.2		2	60.23	odd	4
9680.2.a.bt.1.1		2	220.43	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.37228i q^{3} -1.00000 q^{4} -2.37228 q^{6} -2.37228i q^{7} +1.00000i q^{8} -2.62772 q^{9} -1.00000 q^{11} +2.37228i q^{12} -2.00000i q^{13} -2.37228 q^{14} +1.00000 q^{16} -4.37228i q^{17} +2.62772i q^{18} -6.37228 q^{19} -5.62772 q^{21} +1.00000i q^{22} +8.74456i q^{23} +2.37228 q^{24} -2.00000 q^{26} -0.883156i q^{27} +2.37228i q^{28} +4.37228 q^{29} -2.37228 q^{31} -1.00000i q^{32} +2.37228i q^{33} -4.37228 q^{34} +2.62772 q^{36} +3.62772i q^{37} +6.37228i q^{38} -4.74456 q^{39} +11.4891 q^{41} +5.62772i q^{42} +4.00000i q^{43} +1.00000 q^{44} +8.74456 q^{46} -8.74456i q^{47} -2.37228i q^{48} +1.37228 q^{49} -10.3723 q^{51} +2.00000i q^{52} -13.1168i q^{53} -0.883156 q^{54} +2.37228 q^{56} +15.1168i q^{57} -4.37228i q^{58} -8.74456 q^{59} +0.372281 q^{61} +2.37228i q^{62} +6.23369i q^{63} -1.00000 q^{64} +2.37228 q^{66} +8.00000i q^{67} +4.37228i q^{68} +20.7446 q^{69} -7.11684 q^{71} -2.62772i q^{72} -7.48913i q^{73} +3.62772 q^{74} +6.37228 q^{76} +2.37228i q^{77} +4.74456i q^{78} +12.7446 q^{79} -9.97825 q^{81} -11.4891i q^{82} -8.74456i q^{83} +5.62772 q^{84} +4.00000 q^{86} -10.3723i q^{87} -1.00000i q^{88} -4.37228 q^{89} -4.74456 q^{91} -8.74456i q^{92} +5.62772i q^{93} -8.74456 q^{94} -2.37228 q^{96} -1.25544i q^{97} -1.37228i q^{98} +2.62772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{6} - 22 q^{9} - 4 q^{11} + 2 q^{14} + 4 q^{16} - 14 q^{19} - 34 q^{21} - 2 q^{24} - 8 q^{26} + 6 q^{29} + 2 q^{31} - 6 q^{34} + 22 q^{36} + 4 q^{39} + 4 q^{44} + 12 q^{46} - 6 q^{49}+ \cdots + 22 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^6 - 22 * q^9 - 4 * q^11 + 2 * q^14 + 4 * q^16 - 14 * q^19 - 34 * q^21 - 2 * q^24 - 8 * q^26 + 6 * q^29 + 2 * q^31 - 6 * q^34 + 22 * q^36 + 4 * q^39 + 4 * q^44 + 12 * q^46 - 6 * q^49 - 30 * q^51 - 38 * q^54 - 2 * q^56 - 12 * q^59 - 10 * q^61 - 4 * q^64 - 2 * q^66 + 60 * q^69 + 6 * q^71 + 26 * q^74 + 14 * q^76 + 28 * q^79 + 52 * q^81 + 34 * q^84 + 16 * q^86 - 6 * q^89 + 4 * q^91 - 12 * q^94 + 2 * q^96 + 22 * q^99

Introduction

L-functions

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Database

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