LMFDB - Embedded newform 110.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(1,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, 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("110.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.37228 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.37228 q^{6} -2.37228 q^{7} -1.00000 q^{8} +2.62772 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.37228 q^{12} +2.00000 q^{13} +2.37228 q^{14} +2.37228 q^{15} +1.00000 q^{16} -4.37228 q^{17} -2.62772 q^{18} +6.37228 q^{19} +1.00000 q^{20} -5.62772 q^{21} +1.00000 q^{22} -8.74456 q^{23} -2.37228 q^{24} +1.00000 q^{25} -2.00000 q^{26} -0.883156 q^{27} -2.37228 q^{28} -4.37228 q^{29} -2.37228 q^{30} -2.37228 q^{31} -1.00000 q^{32} -2.37228 q^{33} +4.37228 q^{34} -2.37228 q^{35} +2.62772 q^{36} +3.62772 q^{37} -6.37228 q^{38} +4.74456 q^{39} -1.00000 q^{40} +11.4891 q^{41} +5.62772 q^{42} -4.00000 q^{43} -1.00000 q^{44} +2.62772 q^{45} +8.74456 q^{46} -8.74456 q^{47} +2.37228 q^{48} -1.37228 q^{49} -1.00000 q^{50} -10.3723 q^{51} +2.00000 q^{52} +13.1168 q^{53} +0.883156 q^{54} -1.00000 q^{55} +2.37228 q^{56} +15.1168 q^{57} +4.37228 q^{58} +8.74456 q^{59} +2.37228 q^{60} +0.372281 q^{61} +2.37228 q^{62} -6.23369 q^{63} +1.00000 q^{64} +2.00000 q^{65} +2.37228 q^{66} +8.00000 q^{67} -4.37228 q^{68} -20.7446 q^{69} +2.37228 q^{70} -7.11684 q^{71} -2.62772 q^{72} +7.48913 q^{73} -3.62772 q^{74} +2.37228 q^{75} +6.37228 q^{76} +2.37228 q^{77} -4.74456 q^{78} -12.7446 q^{79} +1.00000 q^{80} -9.97825 q^{81} -11.4891 q^{82} +8.74456 q^{83} -5.62772 q^{84} -4.37228 q^{85} +4.00000 q^{86} -10.3723 q^{87} +1.00000 q^{88} +4.37228 q^{89} -2.62772 q^{90} -4.74456 q^{91} -8.74456 q^{92} -5.62772 q^{93} +8.74456 q^{94} +6.37228 q^{95} -2.37228 q^{96} -1.25544 q^{97} +1.37228 q^{98} -2.62772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 11 q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 4 q^{13} - q^{14} - q^{15} + 2 q^{16} - 3 q^{17} - 11 q^{18} + 7 q^{19} + 2 q^{20} - 17 q^{21}+ \cdots - 11 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 + q^7 - 2 * q^8 + 11 * q^9 - 2 * q^10 - 2 * q^11 - q^12 + 4 * q^13 - q^14 - q^15 + 2 * q^16 - 3 * q^17 - 11 * q^18 + 7 * q^19 + 2 * q^20 - 17 * q^21 + 2 * q^22 - 6 * q^23 + q^24 + 2 * q^25 - 4 * q^26 - 19 * q^27 + q^28 - 3 * q^29 + q^30 + q^31 - 2 * q^32 + q^33 + 3 * q^34 + q^35 + 11 * q^36 + 13 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 17 * q^42 - 8 * q^43 - 2 * q^44 + 11 * q^45 + 6 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 2 * q^50 - 15 * q^51 + 4 * q^52 + 9 * q^53 + 19 * q^54 - 2 * q^55 - q^56 + 13 * q^57 + 3 * q^58 + 6 * q^59 - q^60 - 5 * q^61 - q^62 + 22 * q^63 + 2 * q^64 + 4 * q^65 - q^66 + 16 * q^67 - 3 * q^68 - 30 * q^69 - q^70 + 3 * q^71 - 11 * q^72 - 8 * q^73 - 13 * q^74 - q^75 + 7 * q^76 - q^77 + 2 * q^78 - 14 * q^79 + 2 * q^80 + 26 * q^81 + 6 * q^83 - 17 * q^84 - 3 * q^85 + 8 * q^86 - 15 * q^87 + 2 * q^88 + 3 * q^89 - 11 * q^90 + 2 * q^91 - 6 * q^92 - 17 * q^93 + 6 * q^94 + 7 * q^95 + q^96 - 14 * q^97 - 3 * q^98 - 11 * q^99

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
$3$	2.37228	1.36964	0.684819	−	0.728714i	$-0.259881\pi$
$3$	2.37228	1.36964	0.684819	+	0.728714i	$0.259881\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.37228	−0.968480
$7$	−2.37228	−0.896638	−0.448319	−	0.893874i	$-0.647977\pi$
$7$	−2.37228	−0.896638	−0.448319	+	0.893874i	$0.647977\pi$
$8$	−1.00000	−0.353553
$9$	2.62772	0.875906
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.37228	0.684819
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	2.37228	0.634019
$15$	2.37228	0.612520
$16$	1.00000	0.250000
$17$	−4.37228	−1.06043	−0.530217	−	0.847862i	$-0.677890\pi$
$17$	−4.37228	−1.06043	−0.530217	+	0.847862i	$0.677890\pi$
$18$	−2.62772	−0.619359
$19$	6.37228	1.46190	0.730951	−	0.682430i	$-0.239077\pi$
$19$	6.37228	1.46190	0.730951	+	0.682430i	$0.239077\pi$
$20$	1.00000	0.223607
$21$	−5.62772	−1.22807
$22$	1.00000	0.213201
$23$	−8.74456	−1.82337	−0.911684	−	0.410893i	$-0.865217\pi$
$23$	−8.74456	−1.82337	−0.911684	+	0.410893i	$0.865217\pi$
$24$	−2.37228	−0.484240
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−0.883156	−0.169963
$28$	−2.37228	−0.448319
$29$	−4.37228	−0.811912	−0.405956	−	0.913893i	$-0.633061\pi$
$29$	−4.37228	−0.811912	−0.405956	+	0.913893i	$0.633061\pi$
$30$	−2.37228	−0.433117
$31$	−2.37228	−0.426074	−0.213037	−	0.977044i	$-0.568336\pi$
$31$	−2.37228	−0.426074	−0.213037	+	0.977044i	$0.568336\pi$
$32$	−1.00000	−0.176777
$33$	−2.37228	−0.412961
$34$	4.37228	0.749840
$35$	−2.37228	−0.400989
$36$	2.62772	0.437953
$37$	3.62772	0.596393	0.298197	−	0.954504i	$-0.403615\pi$
$37$	3.62772	0.596393	0.298197	+	0.954504i	$0.403615\pi$
$38$	−6.37228	−1.03372
$39$	4.74456	0.759738
$40$	−1.00000	−0.158114
$41$	11.4891	1.79430	0.897150	−	0.441726i	$-0.145634\pi$
$41$	11.4891	1.79430	0.897150	+	0.441726i	$0.145634\pi$
$42$	5.62772	0.868376
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	2.62772	0.391717
$46$	8.74456	1.28932
$47$	−8.74456	−1.27553	−0.637763	−	0.770233i	$-0.720140\pi$
$47$	−8.74456	−1.27553	−0.637763	+	0.770233i	$0.720140\pi$
$48$	2.37228	0.342409
$49$	−1.37228	−0.196040
$50$	−1.00000	−0.141421
$51$	−10.3723	−1.45241
$52$	2.00000	0.277350
$53$	13.1168	1.80174	0.900869	−	0.434092i	$-0.142931\pi$
$53$	13.1168	1.80174	0.900869	+	0.434092i	$0.142931\pi$
$54$	0.883156	0.120182
$55$	−1.00000	−0.134840
$56$	2.37228	0.317009
$57$	15.1168	2.00227
$58$	4.37228	0.574109
$59$	8.74456	1.13845	0.569223	−	0.822183i	$-0.307244\pi$
$59$	8.74456	1.13845	0.569223	+	0.822183i	$0.307244\pi$
$60$	2.37228	0.306260
$61$	0.372281	0.0476657	0.0238329	−	0.999716i	$-0.492413\pi$
$61$	0.372281	0.0476657	0.0238329	+	0.999716i	$0.492413\pi$
$62$	2.37228	0.301280
$63$	−6.23369	−0.785371
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	2.37228	0.292008
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−4.37228	−0.530217
$69$	−20.7446	−2.49735
$70$	2.37228	0.283542
$71$	−7.11684	−0.844614	−0.422307	−	0.906453i	$-0.638780\pi$
$71$	−7.11684	−0.844614	−0.422307	+	0.906453i	$0.638780\pi$
$72$	−2.62772	−0.309680
$73$	7.48913	0.876536	0.438268	−	0.898844i	$-0.355592\pi$
$73$	7.48913	0.876536	0.438268	+	0.898844i	$0.355592\pi$
$74$	−3.62772	−0.421714
$75$	2.37228	0.273927
$76$	6.37228	0.730951
$77$	2.37228	0.270347
$78$	−4.74456	−0.537216
$79$	−12.7446	−1.43388	−0.716938	−	0.697137i	$-0.754457\pi$
$79$	−12.7446	−1.43388	−0.716938	+	0.697137i	$0.754457\pi$
$80$	1.00000	0.111803
$81$	−9.97825	−1.10869
$82$	−11.4891	−1.26876
$83$	8.74456	0.959840	0.479920	−	0.877312i	$-0.340666\pi$
$83$	8.74456	0.959840	0.479920	+	0.877312i	$0.340666\pi$
$84$	−5.62772	−0.614034
$85$	−4.37228	−0.474240
$86$	4.00000	0.431331
$87$	−10.3723	−1.11203
$88$	1.00000	0.106600
$89$	4.37228	0.463461	0.231730	−	0.972780i	$-0.425561\pi$
$89$	4.37228	0.463461	0.231730	+	0.972780i	$0.425561\pi$
$90$	−2.62772	−0.276986
$91$	−4.74456	−0.497365
$92$	−8.74456	−0.911684
$93$	−5.62772	−0.583567
$94$	8.74456	0.901933
$95$	6.37228	0.653782
$96$	−2.37228	−0.242120
$97$	−1.25544	−0.127470	−0.0637352	−	0.997967i	$-0.520301\pi$
$97$	−1.25544	−0.127470	−0.0637352	+	0.997967i	$0.520301\pi$
$98$	1.37228	0.138621
$99$	−2.62772	−0.264096
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	10.3723	1.02701
$103$	13.4891	1.32912	0.664562	−	0.747234i	$-0.268618\pi$
$103$	13.4891	1.32912	0.664562	+	0.747234i	$0.268618\pi$
$104$	−2.00000	−0.196116
$105$	−5.62772	−0.549209
$106$	−13.1168	−1.27402
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−0.883156	−0.0849817
$109$	7.48913	0.717328	0.358664	−	0.933467i	$-0.383232\pi$
$109$	7.48913	0.717328	0.358664	+	0.933467i	$0.383232\pi$
$110$	1.00000	0.0953463
$111$	8.60597	0.816842
$112$	−2.37228	−0.224160
$113$	14.7446	1.38705	0.693526	−	0.720432i	$-0.256056\pi$
$113$	14.7446	1.38705	0.693526	+	0.720432i	$0.256056\pi$
$114$	−15.1168	−1.41582
$115$	−8.74456	−0.815435
$116$	−4.37228	−0.405956
$117$	5.25544	0.485865
$118$	−8.74456	−0.805002
$119$	10.3723	0.950825
$120$	−2.37228	−0.216559
$121$	1.00000	0.0909091
$122$	−0.372281	−0.0337048
$123$	27.2554	2.45754
$124$	−2.37228	−0.213037
$125$	1.00000	0.0894427
$126$	6.23369	0.555341
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−9.48913	−0.835471
$130$	−2.00000	−0.175412
$131$	4.88316	0.426643	0.213322	−	0.976982i	$-0.431572\pi$
$131$	4.88316	0.426643	0.213322	+	0.976982i	$0.431572\pi$
$132$	−2.37228	−0.206481
$133$	−15.1168	−1.31080
$134$	−8.00000	−0.691095
$135$	−0.883156	−0.0760100
$136$	4.37228	0.374920
$137$	−2.74456	−0.234484	−0.117242	−	0.993103i	$-0.537405\pi$
$137$	−2.74456	−0.234484	−0.117242	+	0.993103i	$0.537405\pi$
$138$	20.7446	1.76589
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.37228	−0.200494
$141$	−20.7446	−1.74701
$142$	7.11684	0.597232
$143$	−2.00000	−0.167248
$144$	2.62772	0.218977
$145$	−4.37228	−0.363098
$146$	−7.48913	−0.619804
$147$	−3.25544	−0.268504
$148$	3.62772	0.298197
$149$	−18.6060	−1.52426	−0.762130	−	0.647424i	$-0.775846\pi$
$149$	−18.6060	−1.52426	−0.762130	+	0.647424i	$0.775846\pi$
$150$	−2.37228	−0.193696
$151$	22.2337	1.80935	0.904676	−	0.426100i	$-0.140113\pi$
$151$	22.2337	1.80935	0.904676	+	0.426100i	$0.140113\pi$
$152$	−6.37228	−0.516860
$153$	−11.4891	−0.928841
$154$	−2.37228	−0.191164
$155$	−2.37228	−0.190546
$156$	4.74456	0.379869
$157$	3.62772	0.289523	0.144762	−	0.989467i	$-0.453758\pi$
$157$	3.62772	0.289523	0.144762	+	0.989467i	$0.453758\pi$
$158$	12.7446	1.01390
$159$	31.1168	2.46773
$160$	−1.00000	−0.0790569
$161$	20.7446	1.63490
$162$	9.97825	0.783965
$163$	−23.1168	−1.81065	−0.905325	−	0.424718i	$-0.860373\pi$
$163$	−23.1168	−1.81065	−0.905325	+	0.424718i	$0.860373\pi$
$164$	11.4891	0.897150
$165$	−2.37228	−0.184682
$166$	−8.74456	−0.678710
$167$	−10.3723	−0.802631	−0.401316	−	0.915940i	$-0.631447\pi$
$167$	−10.3723	−0.802631	−0.401316	+	0.915940i	$0.631447\pi$
$168$	5.62772	0.434188
$169$	−9.00000	−0.692308
$170$	4.37228	0.335339
$171$	16.7446	1.28049
$172$	−4.00000	−0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	10.3723	0.786321
$175$	−2.37228	−0.179328
$176$	−1.00000	−0.0753778
$177$	20.7446	1.55926
$178$	−4.37228	−0.327716
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	2.62772	0.195859
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	4.74456	0.351690
$183$	0.883156	0.0652848
$184$	8.74456	0.644658
$185$	3.62772	0.266715
$186$	5.62772	0.412644
$187$	4.37228	0.319733
$188$	−8.74456	−0.637763
$189$	2.09509	0.152396
$190$	−6.37228	−0.462294
$191$	17.4891	1.26547	0.632734	−	0.774369i	$-0.281933\pi$
$191$	17.4891	1.26547	0.632734	+	0.774369i	$0.281933\pi$
$192$	2.37228	0.171205
$193$	−13.8614	−0.997766	−0.498883	−	0.866669i	$-0.666256\pi$
$193$	−13.8614	−0.997766	−0.498883	+	0.866669i	$0.666256\pi$
$194$	1.25544	0.0901351
$195$	4.74456	0.339765
$196$	−1.37228	−0.0980201
$197$	−9.25544	−0.659423	−0.329711	−	0.944082i	$-0.606951\pi$
$197$	−9.25544	−0.659423	−0.329711	+	0.944082i	$0.606951\pi$
$198$	2.62772	0.186744
$199$	0.883156	0.0626053	0.0313026	−	0.999510i	$-0.490034\pi$
$199$	0.883156	0.0626053	0.0313026	+	0.999510i	$0.490034\pi$
$200$	−1.00000	−0.0707107
$201$	18.9783	1.33862
$202$	−6.00000	−0.422159
$203$	10.3723	0.727991
$204$	−10.3723	−0.726205
$205$	11.4891	0.802435
$206$	−13.4891	−0.939832
$207$	−22.9783	−1.59710
$208$	2.00000	0.138675
$209$	−6.37228	−0.440780
$210$	5.62772	0.388349
$211$	−11.1168	−0.765315	−0.382658	−	0.923890i	$-0.624991\pi$
$211$	−11.1168	−0.765315	−0.382658	+	0.923890i	$0.624991\pi$
$212$	13.1168	0.900869
$213$	−16.8832	−1.15681
$214$	12.0000	0.820303
$215$	−4.00000	−0.272798
$216$	0.883156	0.0600912
$217$	5.62772	0.382034
$218$	−7.48913	−0.507228
$219$	17.7663	1.20054
$220$	−1.00000	−0.0674200
$221$	−8.74456	−0.588223
$222$	−8.60597	−0.577595
$223$	−7.25544	−0.485860	−0.242930	−	0.970044i	$-0.578109\pi$
$223$	−7.25544	−0.485860	−0.242930	+	0.970044i	$0.578109\pi$
$224$	2.37228	0.158505
$225$	2.62772	0.175181
$226$	−14.7446	−0.980794
$227$	8.74456	0.580397	0.290199	−	0.956966i	$-0.406279\pi$
$227$	8.74456	0.580397	0.290199	+	0.956966i	$0.406279\pi$
$228$	15.1168	1.00114
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	8.74456	0.576599
$231$	5.62772	0.370277
$232$	4.37228	0.287054
$233$	−4.37228	−0.286438	−0.143219	−	0.989691i	$-0.545745\pi$
$233$	−4.37228	−0.286438	−0.143219	+	0.989691i	$0.545745\pi$
$234$	−5.25544	−0.343559
$235$	−8.74456	−0.570432
$236$	8.74456	0.569223
$237$	−30.2337	−1.96389
$238$	−10.3723	−0.672335
$239$	−3.25544	−0.210577	−0.105288	−	0.994442i	$-0.533577\pi$
$239$	−3.25544	−0.210577	−0.105288	+	0.994442i	$0.533577\pi$
$240$	2.37228	0.153130
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−1.00000	−0.0642824
$243$	−21.0217	−1.34855
$244$	0.372281	0.0238329
$245$	−1.37228	−0.0876718
$246$	−27.2554	−1.73774
$247$	12.7446	0.810917
$248$	2.37228	0.150640
$249$	20.7446	1.31463
$250$	−1.00000	−0.0632456
$251$	−8.74456	−0.551952	−0.275976	−	0.961165i	$-0.589001\pi$
$251$	−8.74456	−0.551952	−0.275976	+	0.961165i	$0.589001\pi$
$252$	−6.23369	−0.392685
$253$	8.74456	0.549766
$254$	−8.00000	−0.501965
$255$	−10.3723	−0.649537
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	9.48913	0.590767
$259$	−8.60597	−0.534749
$260$	2.00000	0.124035
$261$	−11.4891	−0.711159
$262$	−4.88316	−0.301682
$263$	3.86141	0.238105	0.119052	−	0.992888i	$-0.462014\pi$
$263$	3.86141	0.238105	0.119052	+	0.992888i	$0.462014\pi$
$264$	2.37228	0.146004
$265$	13.1168	0.805761
$266$	15.1168	0.926873
$267$	10.3723	0.634773
$268$	8.00000	0.488678
$269$	2.74456	0.167339	0.0836695	−	0.996494i	$-0.473336\pi$
$269$	2.74456	0.167339	0.0836695	+	0.996494i	$0.473336\pi$
$270$	0.883156	0.0537472
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−4.37228	−0.265108
$273$	−11.2554	−0.681210
$274$	2.74456	0.165805
$275$	−1.00000	−0.0603023
$276$	−20.7446	−1.24868
$277$	−1.25544	−0.0754319	−0.0377160	−	0.999289i	$-0.512008\pi$
$277$	−1.25544	−0.0754319	−0.0377160	+	0.999289i	$0.512008\pi$
$278$	4.00000	0.239904
$279$	−6.23369	−0.373201
$280$	2.37228	0.141771
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	20.7446	1.23532
$283$	16.7446	0.995361	0.497680	−	0.867360i	$-0.334185\pi$
$283$	16.7446	0.995361	0.497680	+	0.867360i	$0.334185\pi$
$284$	−7.11684	−0.422307
$285$	15.1168	0.895445
$286$	2.00000	0.118262
$287$	−27.2554	−1.60884
$288$	−2.62772	−0.154840
$289$	2.11684	0.124520
$290$	4.37228	0.256749
$291$	−2.97825	−0.174588
$292$	7.48913	0.438268
$293$	0.510875	0.0298456	0.0149228	−	0.999889i	$-0.495250\pi$
$293$	0.510875	0.0298456	0.0149228	+	0.999889i	$0.495250\pi$
$294$	3.25544	0.189861
$295$	8.74456	0.509128
$296$	−3.62772	−0.210857
$297$	0.883156	0.0512459
$298$	18.6060	1.07781
$299$	−17.4891	−1.01142
$300$	2.37228	0.136964
$301$	9.48913	0.546944
$302$	−22.2337	−1.27940
$303$	14.2337	0.817704
$304$	6.37228	0.365475
$305$	0.372281	0.0213168
$306$	11.4891	0.656790
$307$	16.7446	0.955663	0.477831	−	0.878452i	$-0.341423\pi$
$307$	16.7446	0.955663	0.477831	+	0.878452i	$0.341423\pi$
$308$	2.37228	0.135173
$309$	32.0000	1.82042
$310$	2.37228	0.134737
$311$	13.6277	0.772757	0.386379	−	0.922340i	$-0.373726\pi$
$311$	13.6277	0.772757	0.386379	+	0.922340i	$0.373726\pi$
$312$	−4.74456	−0.268608
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−3.62772	−0.204724
$315$	−6.23369	−0.351229
$316$	−12.7446	−0.716938
$317$	27.3505	1.53616	0.768079	−	0.640355i	$-0.221213\pi$
$317$	27.3505	1.53616	0.768079	+	0.640355i	$0.221213\pi$
$318$	−31.1168	−1.74495
$319$	4.37228	0.244801
$320$	1.00000	0.0559017
$321$	−28.4674	−1.58889
$322$	−20.7446	−1.15605
$323$	−27.8614	−1.55025
$324$	−9.97825	−0.554347
$325$	2.00000	0.110940
$326$	23.1168	1.28032
$327$	17.7663	0.982479
$328$	−11.4891	−0.634381
$329$	20.7446	1.14368
$330$	2.37228	0.130590
$331$	−14.9783	−0.823279	−0.411640	−	0.911347i	$-0.635044\pi$
$331$	−14.9783	−0.823279	−0.411640	+	0.911347i	$0.635044\pi$
$332$	8.74456	0.479920
$333$	9.53262	0.522385
$334$	10.3723	0.567546
$335$	8.00000	0.437087
$336$	−5.62772	−0.307017
$337$	6.88316	0.374949	0.187475	−	0.982269i	$-0.439970\pi$
$337$	6.88316	0.374949	0.187475	+	0.982269i	$0.439970\pi$
$338$	9.00000	0.489535
$339$	34.9783	1.89976
$340$	−4.37228	−0.237120
$341$	2.37228	0.128466
$342$	−16.7446	−0.905442
$343$	19.8614	1.07242
$344$	4.00000	0.215666
$345$	−20.7446	−1.11685
$346$	6.00000	0.322562
$347$	2.23369	0.119911	0.0599553	−	0.998201i	$-0.480904\pi$
$347$	2.23369	0.119911	0.0599553	+	0.998201i	$0.480904\pi$
$348$	−10.3723	−0.556013
$349$	−3.48913	−0.186769	−0.0933843	−	0.995630i	$-0.529769\pi$
$349$	−3.48913	−0.186769	−0.0933843	+	0.995630i	$0.529769\pi$
$350$	2.37228	0.126804
$351$	−1.76631	−0.0942788
$352$	1.00000	0.0533002
$353$	−23.4891	−1.25020	−0.625100	−	0.780545i	$-0.714942\pi$
$353$	−23.4891	−1.25020	−0.625100	+	0.780545i	$0.714942\pi$
$354$	−20.7446	−1.10256
$355$	−7.11684	−0.377723
$356$	4.37228	0.231730
$357$	24.6060	1.30229
$358$	12.0000	0.634220
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−2.62772	−0.138493
$361$	21.6060	1.13716
$362$	10.0000	0.525588
$363$	2.37228	0.124512
$364$	−4.74456	−0.248683
$365$	7.48913	0.391999
$366$	−0.883156	−0.0461633
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−8.74456	−0.455842
$369$	30.1902	1.57164
$370$	−3.62772	−0.188596
$371$	−31.1168	−1.61551
$372$	−5.62772	−0.291784
$373$	8.51087	0.440676	0.220338	−	0.975424i	$-0.429284\pi$
$373$	8.51087	0.440676	0.220338	+	0.975424i	$0.429284\pi$
$374$	−4.37228	−0.226085
$375$	2.37228	0.122504
$376$	8.74456	0.450966
$377$	−8.74456	−0.450368
$378$	−2.09509	−0.107760
$379$	34.2337	1.75847	0.879233	−	0.476392i	$-0.158056\pi$
$379$	34.2337	1.75847	0.879233	+	0.476392i	$0.158056\pi$
$380$	6.37228	0.326891
$381$	18.9783	0.972285
$382$	−17.4891	−0.894821
$383$	−2.23369	−0.114136	−0.0570681	−	0.998370i	$-0.518175\pi$
$383$	−2.23369	−0.114136	−0.0570681	+	0.998370i	$0.518175\pi$
$384$	−2.37228	−0.121060
$385$	2.37228	0.120903
$386$	13.8614	0.705527
$387$	−10.5109	−0.534298
$388$	−1.25544	−0.0637352
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	−4.74456	−0.240250
$391$	38.2337	1.93356
$392$	1.37228	0.0693107
$393$	11.5842	0.584347
$394$	9.25544	0.466282
$395$	−12.7446	−0.641249
$396$	−2.62772	−0.132048
$397$	−20.9783	−1.05287	−0.526434	−	0.850216i	$-0.676471\pi$
$397$	−20.9783	−1.05287	−0.526434	+	0.850216i	$0.676471\pi$
$398$	−0.883156	−0.0442686
$399$	−35.8614	−1.79532
$400$	1.00000	0.0500000
$401$	7.62772	0.380910	0.190455	−	0.981696i	$-0.439004\pi$
$401$	7.62772	0.380910	0.190455	+	0.981696i	$0.439004\pi$
$402$	−18.9783	−0.946549
$403$	−4.74456	−0.236343
$404$	6.00000	0.298511
$405$	−9.97825	−0.495823
$406$	−10.3723	−0.514768
$407$	−3.62772	−0.179819
$408$	10.3723	0.513504
$409$	−36.2337	−1.79164	−0.895820	−	0.444417i	$-0.853411\pi$
$409$	−36.2337	−1.79164	−0.895820	+	0.444417i	$0.853411\pi$
$410$	−11.4891	−0.567407
$411$	−6.51087	−0.321158
$412$	13.4891	0.664562
$413$	−20.7446	−1.02077
$414$	22.9783	1.12932
$415$	8.74456	0.429254
$416$	−2.00000	−0.0980581
$417$	−9.48913	−0.464684
$418$	6.37228	0.311678
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	−5.62772	−0.274605
$421$	−24.2337	−1.18108	−0.590539	−	0.807009i	$-0.701085\pi$
$421$	−24.2337	−1.18108	−0.590539	+	0.807009i	$0.701085\pi$
$422$	11.1168	0.541159
$423$	−22.9783	−1.11724
$424$	−13.1168	−0.637010
$425$	−4.37228	−0.212087
$426$	16.8832	0.817992
$427$	−0.883156	−0.0427389
$428$	−12.0000	−0.580042
$429$	−4.74456	−0.229070
$430$	4.00000	0.192897
$431$	10.9783	0.528804	0.264402	−	0.964413i	$-0.414825\pi$
$431$	10.9783	0.528804	0.264402	+	0.964413i	$0.414825\pi$
$432$	−0.883156	−0.0424909
$433$	−29.7228	−1.42839	−0.714194	−	0.699948i	$-0.753206\pi$
$433$	−29.7228	−1.42839	−0.714194	+	0.699948i	$0.753206\pi$
$434$	−5.62772	−0.270139
$435$	−10.3723	−0.497313
$436$	7.48913	0.358664
$437$	−55.7228	−2.66558
$438$	−17.7663	−0.848907
$439$	−26.9783	−1.28760	−0.643801	−	0.765193i	$-0.722643\pi$
$439$	−26.9783	−1.28760	−0.643801	+	0.765193i	$0.722643\pi$
$440$	1.00000	0.0476731
$441$	−3.60597	−0.171713
$442$	8.74456	0.415936
$443$	6.51087	0.309341	0.154670	−	0.987966i	$-0.450568\pi$
$443$	6.51087	0.309341	0.154670	+	0.987966i	$0.450568\pi$
$444$	8.60597	0.408421
$445$	4.37228	0.207266
$446$	7.25544	0.343555
$447$	−44.1386	−2.08768
$448$	−2.37228	−0.112080
$449$	−16.9783	−0.801253	−0.400627	−	0.916241i	$-0.631208\pi$
$449$	−16.9783	−0.801253	−0.400627	+	0.916241i	$0.631208\pi$
$450$	−2.62772	−0.123872
$451$	−11.4891	−0.541002
$452$	14.7446	0.693526
$453$	52.7446	2.47816
$454$	−8.74456	−0.410403
$455$	−4.74456	−0.222429
$456$	−15.1168	−0.707911
$457$	35.3505	1.65363	0.826814	−	0.562475i	$-0.190151\pi$
$457$	35.3505	1.65363	0.826814	+	0.562475i	$0.190151\pi$
$458$	10.0000	0.467269
$459$	3.86141	0.180235
$460$	−8.74456	−0.407717
$461$	−1.11684	−0.0520166	−0.0260083	−	0.999662i	$-0.508280\pi$
$461$	−1.11684	−0.0520166	−0.0260083	+	0.999662i	$0.508280\pi$
$462$	−5.62772	−0.261825
$463$	34.2337	1.59097	0.795487	−	0.605970i	$-0.207215\pi$
$463$	34.2337	1.59097	0.795487	+	0.605970i	$0.207215\pi$
$464$	−4.37228	−0.202978
$465$	−5.62772	−0.260979
$466$	4.37228	0.202542
$467$	−13.6277	−0.630616	−0.315308	−	0.948989i	$-0.602108\pi$
$467$	−13.6277	−0.630616	−0.315308	+	0.948989i	$0.602108\pi$
$468$	5.25544	0.242933
$469$	−18.9783	−0.876334
$470$	8.74456	0.403357
$471$	8.60597	0.396542
$472$	−8.74456	−0.402501
$473$	4.00000	0.183920
$474$	30.2337	1.38868
$475$	6.37228	0.292380
$476$	10.3723	0.475413
$477$	34.4674	1.57815
$478$	3.25544	0.148900
$479$	−17.4891	−0.799099	−0.399549	−	0.916712i	$-0.630833\pi$
$479$	−17.4891	−0.799099	−0.399549	+	0.916712i	$0.630833\pi$
$480$	−2.37228	−0.108279
$481$	7.25544	0.330819
$482$	22.0000	1.00207
$483$	49.2119	2.23922
$484$	1.00000	0.0454545
$485$	−1.25544	−0.0570065
$486$	21.0217	0.953566
$487$	20.0000	0.906287	0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000	0.906287	0.453143	+	0.891438i	$0.350303\pi$
$488$	−0.372281	−0.0168524
$489$	−54.8397	−2.47994
$490$	1.37228	0.0619934
$491$	−1.62772	−0.0734579	−0.0367290	−	0.999325i	$-0.511694\pi$
$491$	−1.62772	−0.0734579	−0.0367290	+	0.999325i	$0.511694\pi$
$492$	27.2554	1.22877
$493$	19.1168	0.860979
$494$	−12.7446	−0.573405
$495$	−2.62772	−0.118107
$496$	−2.37228	−0.106519
$497$	16.8832	0.757313
$498$	−20.7446	−0.929586
$499$	−10.5109	−0.470531	−0.235266	−	0.971931i	$-0.575596\pi$
$499$	−10.5109	−0.470531	−0.235266	+	0.971931i	$0.575596\pi$
$500$	1.00000	0.0447214
$501$	−24.6060	−1.09931
$502$	8.74456	0.390289
$503$	10.9783	0.489496	0.244748	−	0.969587i	$-0.421295\pi$
$503$	10.9783	0.489496	0.244748	+	0.969587i	$0.421295\pi$
$504$	6.23369	0.277671
$505$	6.00000	0.266996
$506$	−8.74456	−0.388743
$507$	−21.3505	−0.948210
$508$	8.00000	0.354943
$509$	44.2337	1.96062	0.980312	−	0.197455i	$-0.0632678\pi$
$509$	44.2337	1.96062	0.980312	+	0.197455i	$0.0632678\pi$
$510$	10.3723	0.459292
$511$	−17.7663	−0.785935
$512$	−1.00000	−0.0441942
$513$	−5.62772	−0.248470
$514$	−18.0000	−0.793946
$515$	13.4891	0.594402
$516$	−9.48913	−0.417735
$517$	8.74456	0.384585
$518$	8.60597	0.378125
$519$	−14.2337	−0.624790
$520$	−2.00000	−0.0877058
$521$	35.4891	1.55481	0.777403	−	0.629002i	$-0.216536\pi$
$521$	35.4891	1.55481	0.777403	+	0.629002i	$0.216536\pi$
$522$	11.4891	0.502865
$523$	−14.9783	−0.654953	−0.327477	−	0.944859i	$-0.606198\pi$
$523$	−14.9783	−0.654953	−0.327477	+	0.944859i	$0.606198\pi$
$524$	4.88316	0.213322
$525$	−5.62772	−0.245614
$526$	−3.86141	−0.168365
$527$	10.3723	0.451824
$528$	−2.37228	−0.103240
$529$	53.4674	2.32467
$530$	−13.1168	−0.569759
$531$	22.9783	0.997171
$532$	−15.1168	−0.655398
$533$	22.9783	0.995299
$534$	−10.3723	−0.448853
$535$	−12.0000	−0.518805
$536$	−8.00000	−0.345547
$537$	−28.4674	−1.22846
$538$	−2.74456	−0.118326
$539$	1.37228	0.0591083
$540$	−0.883156	−0.0380050
$541$	−2.88316	−0.123957	−0.0619783	−	0.998077i	$-0.519741\pi$
$541$	−2.88316	−0.123957	−0.0619783	+	0.998077i	$0.519741\pi$
$542$	16.0000	0.687259
$543$	−23.7228	−1.01804
$544$	4.37228	0.187460
$545$	7.48913	0.320799
$546$	11.2554	0.481688
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	−2.74456	−0.117242
$549$	0.978251	0.0417507
$550$	1.00000	0.0426401
$551$	−27.8614	−1.18694
$552$	20.7446	0.882947
$553$	30.2337	1.28567
$554$	1.25544	0.0533384
$555$	8.60597	0.365303
$556$	−4.00000	−0.169638
$557$	−40.9783	−1.73630	−0.868152	−	0.496298i	$-0.834692\pi$
$557$	−40.9783	−1.73630	−0.868152	+	0.496298i	$0.834692\pi$
$558$	6.23369	0.263893
$559$	−8.00000	−0.338364
$560$	−2.37228	−0.100247
$561$	10.3723	0.437918
$562$	−18.0000	−0.759284
$563$	26.2337	1.10562	0.552809	−	0.833308i	$-0.313556\pi$
$563$	26.2337	1.10562	0.552809	+	0.833308i	$0.313556\pi$
$564$	−20.7446	−0.873504
$565$	14.7446	0.620308
$566$	−16.7446	−0.703826
$567$	23.6712	0.994098
$568$	7.11684	0.298616
$569$	−26.7446	−1.12119	−0.560595	−	0.828090i	$-0.689428\pi$
$569$	−26.7446	−1.12119	−0.560595	+	0.828090i	$0.689428\pi$
$570$	−15.1168	−0.633175
$571$	9.62772	0.402907	0.201454	−	0.979498i	$-0.435433\pi$
$571$	9.62772	0.402907	0.201454	+	0.979498i	$0.435433\pi$
$572$	−2.00000	−0.0836242
$573$	41.4891	1.73323
$574$	27.2554	1.13762
$575$	−8.74456	−0.364673
$576$	2.62772	0.109488
$577$	−8.97825	−0.373769	−0.186885	−	0.982382i	$-0.559839\pi$
$577$	−8.97825	−0.373769	−0.186885	+	0.982382i	$0.559839\pi$
$578$	−2.11684	−0.0880491
$579$	−32.8832	−1.36658
$580$	−4.37228	−0.181549
$581$	−20.7446	−0.860629
$582$	2.97825	0.123452
$583$	−13.1168	−0.543244
$584$	−7.48913	−0.309902
$585$	5.25544	0.217286
$586$	−0.510875	−0.0211040
$587$	−3.86141	−0.159377	−0.0796887	−	0.996820i	$-0.525393\pi$
$587$	−3.86141	−0.159377	−0.0796887	+	0.996820i	$0.525393\pi$
$588$	−3.25544	−0.134252
$589$	−15.1168	−0.622879
$590$	−8.74456	−0.360008
$591$	−21.9565	−0.903170
$592$	3.62772	0.149098
$593$	−35.4891	−1.45736	−0.728682	−	0.684852i	$-0.759867\pi$
$593$	−35.4891	−1.45736	−0.728682	+	0.684852i	$0.759867\pi$
$594$	−0.883156	−0.0362363
$595$	10.3723	0.425222
$596$	−18.6060	−0.762130
$597$	2.09509	0.0857465
$598$	17.4891	0.715184
$599$	0.605969	0.0247592	0.0123796	−	0.999923i	$-0.496059\pi$
$599$	0.605969	0.0247592	0.0123796	+	0.999923i	$0.496059\pi$
$600$	−2.37228	−0.0968480
$601$	−39.4891	−1.61080	−0.805398	−	0.592735i	$-0.798048\pi$
$601$	−39.4891	−1.61080	−0.805398	+	0.592735i	$0.798048\pi$
$602$	−9.48913	−0.386748
$603$	21.0217	0.856072
$604$	22.2337	0.904676
$605$	1.00000	0.0406558
$606$	−14.2337	−0.578204
$607$	−23.1168	−0.938284	−0.469142	−	0.883123i	$-0.655437\pi$
$607$	−23.1168	−0.938284	−0.469142	+	0.883123i	$0.655437\pi$
$608$	−6.37228	−0.258430
$609$	24.6060	0.997084
$610$	−0.372281	−0.0150732
$611$	−17.4891	−0.707534
$612$	−11.4891	−0.464420
$613$	43.4891	1.75651	0.878255	−	0.478193i	$-0.158708\pi$
$613$	43.4891	1.75651	0.878255	+	0.478193i	$0.158708\pi$
$614$	−16.7446	−0.675756
$615$	27.2554	1.09905
$616$	−2.37228	−0.0955819
$617$	32.2337	1.29768	0.648840	−	0.760925i	$-0.275255\pi$
$617$	32.2337	1.29768	0.648840	+	0.760925i	$0.275255\pi$
$618$	−32.0000	−1.28723
$619$	24.4674	0.983427	0.491713	−	0.870757i	$-0.336371\pi$
$619$	24.4674	0.983427	0.491713	+	0.870757i	$0.336371\pi$
$620$	−2.37228	−0.0952731
$621$	7.72281	0.309906
$622$	−13.6277	−0.546422
$623$	−10.3723	−0.415557
$624$	4.74456	0.189935
$625$	1.00000	0.0400000
$626$	22.0000	0.879297
$627$	−15.1168	−0.603709
$628$	3.62772	0.144762
$629$	−15.8614	−0.632436
$630$	6.23369	0.248356
$631$	24.8832	0.990583	0.495291	−	0.868727i	$-0.335061\pi$
$631$	24.8832	0.990583	0.495291	+	0.868727i	$0.335061\pi$
$632$	12.7446	0.506951
$633$	−26.3723	−1.04820
$634$	−27.3505	−1.08623
$635$	8.00000	0.317470
$636$	31.1168	1.23386
$637$	−2.74456	−0.108744
$638$	−4.37228	−0.173100
$639$	−18.7011	−0.739803
$640$	−1.00000	−0.0395285
$641$	36.0951	1.42567	0.712835	−	0.701332i	$-0.247411\pi$
$641$	36.0951	1.42567	0.712835	+	0.701332i	$0.247411\pi$
$642$	28.4674	1.12352
$643$	−23.1168	−0.911639	−0.455820	−	0.890072i	$-0.650654\pi$
$643$	−23.1168	−0.911639	−0.455820	+	0.890072i	$0.650654\pi$
$644$	20.7446	0.817450
$645$	−9.48913	−0.373634
$646$	27.8614	1.09619
$647$	19.7228	0.775384	0.387692	−	0.921789i	$-0.373272\pi$
$647$	19.7228	0.775384	0.387692	+	0.921789i	$0.373272\pi$
$648$	9.97825	0.391983
$649$	−8.74456	−0.343254
$650$	−2.00000	−0.0784465
$651$	13.3505	0.523249
$652$	−23.1168	−0.905325
$653$	16.3723	0.640697	0.320348	−	0.947300i	$-0.396200\pi$
$653$	16.3723	0.640697	0.320348	+	0.947300i	$0.396200\pi$
$654$	−17.7663	−0.694718
$655$	4.88316	0.190801
$656$	11.4891	0.448575
$657$	19.6793	0.767763
$658$	−20.7446	−0.808707
$659$	−15.8614	−0.617873	−0.308936	−	0.951083i	$-0.599973\pi$
$659$	−15.8614	−0.617873	−0.308936	+	0.951083i	$0.599973\pi$
$660$	−2.37228	−0.0923409
$661$	31.4891	1.22479	0.612393	−	0.790554i	$-0.290207\pi$
$661$	31.4891	1.22479	0.612393	+	0.790554i	$0.290207\pi$
$662$	14.9783	0.582146
$663$	−20.7446	−0.805652
$664$	−8.74456	−0.339355
$665$	−15.1168	−0.586206
$666$	−9.53262	−0.369382
$667$	38.2337	1.48041
$668$	−10.3723	−0.401316
$669$	−17.2119	−0.665452
$670$	−8.00000	−0.309067
$671$	−0.372281	−0.0143718
$672$	5.62772	0.217094
$673$	−13.8614	−0.534318	−0.267159	−	0.963652i	$-0.586085\pi$
$673$	−13.8614	−0.534318	−0.267159	+	0.963652i	$0.586085\pi$
$674$	−6.88316	−0.265129
$675$	−0.883156	−0.0339927
$676$	−9.00000	−0.346154
$677$	14.7446	0.566680	0.283340	−	0.959020i	$-0.408558\pi$
$677$	14.7446	0.566680	0.283340	+	0.959020i	$0.408558\pi$
$678$	−34.9783	−1.34333
$679$	2.97825	0.114295
$680$	4.37228	0.167669
$681$	20.7446	0.794933
$682$	−2.37228	−0.0908393
$683$	−34.3723	−1.31522	−0.657609	−	0.753359i	$-0.728432\pi$
$683$	−34.3723	−1.31522	−0.657609	+	0.753359i	$0.728432\pi$
$684$	16.7446	0.640244
$685$	−2.74456	−0.104864
$686$	−19.8614	−0.758312
$687$	−23.7228	−0.905082
$688$	−4.00000	−0.152499
$689$	26.2337	0.999424
$690$	20.7446	0.789732
$691$	5.76631	0.219361	0.109680	−	0.993967i	$-0.465017\pi$
$691$	5.76631	0.219361	0.109680	+	0.993967i	$0.465017\pi$
$692$	−6.00000	−0.228086
$693$	6.23369	0.236798
$694$	−2.23369	−0.0847896
$695$	−4.00000	−0.151729
$696$	10.3723	0.393160
$697$	−50.2337	−1.90274
$698$	3.48913	0.132065
$699$	−10.3723	−0.392316
$700$	−2.37228	−0.0896638
$701$	−31.6277	−1.19456	−0.597281	−	0.802032i	$-0.703752\pi$
$701$	−31.6277	−1.19456	−0.597281	+	0.802032i	$0.703752\pi$
$702$	1.76631	0.0666652
$703$	23.1168	0.871868
$704$	−1.00000	−0.0376889
$705$	−20.7446	−0.781285
$706$	23.4891	0.884025
$707$	−14.2337	−0.535313
$708$	20.7446	0.779628
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	7.11684	0.267090
$711$	−33.4891	−1.25594
$712$	−4.37228	−0.163858
$713$	20.7446	0.776890
$714$	−24.6060	−0.920855
$715$	−2.00000	−0.0747958
$716$	−12.0000	−0.448461
$717$	−7.72281	−0.288414
$718$	0	0
$719$	31.1168	1.16046	0.580231	−	0.814452i	$-0.302962\pi$
$719$	31.1168	1.16046	0.580231	+	0.814452i	$0.302962\pi$
$720$	2.62772	0.0979293
$721$	−32.0000	−1.19174
$722$	−21.6060	−0.804091
$723$	−52.1902	−1.94097
$724$	−10.0000	−0.371647
$725$	−4.37228	−0.162382
$726$	−2.37228	−0.0880436
$727$	10.2337	0.379546	0.189773	−	0.981828i	$-0.439225\pi$
$727$	10.2337	0.379546	0.189773	+	0.981828i	$0.439225\pi$
$728$	4.74456	0.175845
$729$	−19.9348	−0.738324
$730$	−7.48913	−0.277185
$731$	17.4891	0.646859
$732$	0.883156	0.0326424
$733$	11.7663	0.434599	0.217299	−	0.976105i	$-0.430275\pi$
$733$	11.7663	0.434599	0.217299	+	0.976105i	$0.430275\pi$
$734$	4.00000	0.147643
$735$	−3.25544	−0.120079
$736$	8.74456	0.322329
$737$	−8.00000	−0.294684
$738$	−30.1902	−1.11132
$739$	48.4674	1.78290	0.891451	−	0.453118i	$-0.149688\pi$
$739$	48.4674	1.78290	0.891451	+	0.453118i	$0.149688\pi$
$740$	3.62772	0.133358
$741$	30.2337	1.11066
$742$	31.1168	1.14234
$743$	−10.3723	−0.380522	−0.190261	−	0.981734i	$-0.560933\pi$
$743$	−10.3723	−0.380522	−0.190261	+	0.981734i	$0.560933\pi$
$744$	5.62772	0.206322
$745$	−18.6060	−0.681670
$746$	−8.51087	−0.311605
$747$	22.9783	0.840730
$748$	4.37228	0.159866
$749$	28.4674	1.04018
$750$	−2.37228	−0.0866235
$751$	−19.8614	−0.724753	−0.362377	−	0.932032i	$-0.618035\pi$
$751$	−19.8614	−0.724753	−0.362377	+	0.932032i	$0.618035\pi$
$752$	−8.74456	−0.318881
$753$	−20.7446	−0.755974
$754$	8.74456	0.318458
$755$	22.2337	0.809167
$756$	2.09509	0.0761979
$757$	24.9783	0.907850	0.453925	−	0.891040i	$-0.350023\pi$
$757$	24.9783	0.907850	0.453925	+	0.891040i	$0.350023\pi$
$758$	−34.2337	−1.24342
$759$	20.7446	0.752980
$760$	−6.37228	−0.231147
$761$	−40.9783	−1.48546	−0.742730	−	0.669591i	$-0.766469\pi$
$761$	−40.9783	−1.48546	−0.742730	+	0.669591i	$0.766469\pi$
$762$	−18.9783	−0.687509
$763$	−17.7663	−0.643184
$764$	17.4891	0.632734
$765$	−11.4891	−0.415390
$766$	2.23369	0.0807064
$767$	17.4891	0.631496
$768$	2.37228	0.0856023
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	−2.37228	−0.0854911
$771$	42.7011	1.53784
$772$	−13.8614	−0.498883
$773$	6.60597	0.237600	0.118800	−	0.992918i	$-0.462095\pi$
$773$	6.60597	0.237600	0.118800	+	0.992918i	$0.462095\pi$
$774$	10.5109	0.377806
$775$	−2.37228	−0.0852149
$776$	1.25544	0.0450676
$777$	−20.4158	−0.732412
$778$	−6.00000	−0.215110
$779$	73.2119	2.62309
$780$	4.74456	0.169883
$781$	7.11684	0.254661
$782$	−38.2337	−1.36723
$783$	3.86141	0.137995
$784$	−1.37228	−0.0490100
$785$	3.62772	0.129479
$786$	−11.5842	−0.413195
$787$	24.4674	0.872168	0.436084	−	0.899906i	$-0.356365\pi$
$787$	24.4674	0.872168	0.436084	+	0.899906i	$0.356365\pi$
$788$	−9.25544	−0.329711
$789$	9.16034	0.326117
$790$	12.7446	0.453431
$791$	−34.9783	−1.24368
$792$	2.62772	0.0933719
$793$	0.744563	0.0264402
$794$	20.9783	0.744490
$795$	31.1168	1.10360
$796$	0.883156	0.0313026
$797$	−11.4891	−0.406966	−0.203483	−	0.979079i	$-0.565226\pi$
$797$	−11.4891	−0.406966	−0.203483	+	0.979079i	$0.565226\pi$
$798$	35.8614	1.26948
$799$	38.2337	1.35261
$800$	−1.00000	−0.0353553
$801$	11.4891	0.405948
$802$	−7.62772	−0.269344
$803$	−7.48913	−0.264285
$804$	18.9783	0.669311
$805$	20.7446	0.731150
$806$	4.74456	0.167120
$807$	6.51087	0.229194
$808$	−6.00000	−0.211079
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	9.97825	0.350600
$811$	16.1386	0.566703	0.283351	−	0.959016i	$-0.408554\pi$
$811$	16.1386	0.566703	0.283351	+	0.959016i	$0.408554\pi$
$812$	10.3723	0.363996
$813$	−37.9565	−1.33119
$814$	3.62772	0.127151
$815$	−23.1168	−0.809748
$816$	−10.3723	−0.363102
$817$	−25.4891	−0.891752
$818$	36.2337	1.26688
$819$	−12.4674	−0.435645
$820$	11.4891	0.401218
$821$	−11.4891	−0.400973	−0.200487	−	0.979696i	$-0.564252\pi$
$821$	−11.4891	−0.400973	−0.200487	+	0.979696i	$0.564252\pi$
$822$	6.51087	0.227093
$823$	−28.0000	−0.976019	−0.488009	−	0.872838i	$-0.662277\pi$
$823$	−28.0000	−0.976019	−0.488009	+	0.872838i	$0.662277\pi$
$824$	−13.4891	−0.469916
$825$	−2.37228	−0.0825922
$826$	20.7446	0.721796
$827$	1.02175	0.0355297	0.0177649	−	0.999842i	$-0.494345\pi$
$827$	1.02175	0.0355297	0.0177649	+	0.999842i	$0.494345\pi$
$828$	−22.9783	−0.798549
$829$	−13.2554	−0.460380	−0.230190	−	0.973146i	$-0.573935\pi$
$829$	−13.2554	−0.460380	−0.230190	+	0.973146i	$0.573935\pi$
$830$	−8.74456	−0.303528
$831$	−2.97825	−0.103314
$832$	2.00000	0.0693375
$833$	6.00000	0.207888
$834$	9.48913	0.328582
$835$	−10.3723	−0.358948
$836$	−6.37228	−0.220390
$837$	2.09509	0.0724171
$838$	12.0000	0.414533
$839$	34.9783	1.20758	0.603792	−	0.797142i	$-0.293656\pi$
$839$	34.9783	1.20758	0.603792	+	0.797142i	$0.293656\pi$
$840$	5.62772	0.194175
$841$	−9.88316	−0.340798
$842$	24.2337	0.835148
$843$	42.7011	1.47070
$844$	−11.1168	−0.382658
$845$	−9.00000	−0.309609
$846$	22.9783	0.790009
$847$	−2.37228	−0.0815126
$848$	13.1168	0.450434
$849$	39.7228	1.36328
$850$	4.37228	0.149968
$851$	−31.7228	−1.08744
$852$	−16.8832	−0.578407
$853$	30.4674	1.04318	0.521592	−	0.853195i	$-0.325339\pi$
$853$	30.4674	1.04318	0.521592	+	0.853195i	$0.325339\pi$
$854$	0.883156	0.0302210
$855$	16.7446	0.572652
$856$	12.0000	0.410152
$857$	−15.3505	−0.524364	−0.262182	−	0.965018i	$-0.584442\pi$
$857$	−15.3505	−0.524364	−0.262182	+	0.965018i	$0.584442\pi$
$858$	4.74456	0.161977
$859$	−31.2554	−1.06642	−0.533211	−	0.845982i	$-0.679015\pi$
$859$	−31.2554	−1.06642	−0.533211	+	0.845982i	$0.679015\pi$
$860$	−4.00000	−0.136399
$861$	−64.6576	−2.20352
$862$	−10.9783	−0.373921
$863$	32.7446	1.11464	0.557319	−	0.830299i	$-0.311830\pi$
$863$	32.7446	1.11464	0.557319	+	0.830299i	$0.311830\pi$
$864$	0.883156	0.0300456
$865$	−6.00000	−0.204006
$866$	29.7228	1.01002
$867$	5.02175	0.170548
$868$	5.62772	0.191017
$869$	12.7446	0.432330
$870$	10.3723	0.351653
$871$	16.0000	0.542139
$872$	−7.48913	−0.253614
$873$	−3.29894	−0.111652
$874$	55.7228	1.88485
$875$	−2.37228	−0.0801977
$876$	17.7663	0.600268
$877$	−8.97825	−0.303174	−0.151587	−	0.988444i	$-0.548438\pi$
$877$	−8.97825	−0.303174	−0.151587	+	0.988444i	$0.548438\pi$
$878$	26.9783	0.910472
$879$	1.21194	0.0408777
$880$	−1.00000	−0.0337100
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	3.60597	0.121419
$883$	−2.37228	−0.0798336	−0.0399168	−	0.999203i	$-0.512709\pi$
$883$	−2.37228	−0.0798336	−0.0399168	+	0.999203i	$0.512709\pi$
$884$	−8.74456	−0.294111
$885$	20.7446	0.697321
$886$	−6.51087	−0.218737
$887$	34.9783	1.17445	0.587227	−	0.809422i	$-0.300219\pi$
$887$	34.9783	1.17445	0.587227	+	0.809422i	$0.300219\pi$
$888$	−8.60597	−0.288797
$889$	−18.9783	−0.636510
$890$	−4.37228	−0.146559
$891$	9.97825	0.334284
$892$	−7.25544	−0.242930
$893$	−55.7228	−1.86469
$894$	44.1386	1.47622
$895$	−12.0000	−0.401116
$896$	2.37228	0.0792524
$897$	−41.4891	−1.38528
$898$	16.9783	0.566572
$899$	10.3723	0.345935
$900$	2.62772	0.0875906
$901$	−57.3505	−1.91062
$902$	11.4891	0.382546
$903$	22.5109	0.749115
$904$	−14.7446	−0.490397
$905$	−10.0000	−0.332411
$906$	−52.7446	−1.75232
$907$	−40.6060	−1.34830	−0.674150	−	0.738595i	$-0.735490\pi$
$907$	−40.6060	−1.34830	−0.674150	+	0.738595i	$0.735490\pi$
$908$	8.74456	0.290199
$909$	15.7663	0.522936
$910$	4.74456	0.157281
$911$	−48.6060	−1.61039	−0.805194	−	0.593012i	$-0.797939\pi$
$911$	−48.6060	−1.61039	−0.805194	+	0.593012i	$0.797939\pi$
$912$	15.1168	0.500569
$913$	−8.74456	−0.289403
$914$	−35.3505	−1.16929
$915$	0.883156	0.0291962
$916$	−10.0000	−0.330409
$917$	−11.5842	−0.382545
$918$	−3.86141	−0.127445
$919$	−26.9783	−0.889930	−0.444965	−	0.895548i	$-0.646784\pi$
$919$	−26.9783	−0.889930	−0.444965	+	0.895548i	$0.646784\pi$
$920$	8.74456	0.288300
$921$	39.7228	1.30891
$922$	1.11684	0.0367813
$923$	−14.2337	−0.468508
$924$	5.62772	0.185138
$925$	3.62772	0.119279
$926$	−34.2337	−1.12499
$927$	35.4456	1.16419
$928$	4.37228	0.143527
$929$	−27.3505	−0.897342	−0.448671	−	0.893697i	$-0.648102\pi$
$929$	−27.3505	−0.897342	−0.448671	+	0.893697i	$0.648102\pi$
$930$	5.62772	0.184540
$931$	−8.74456	−0.286591
$932$	−4.37228	−0.143219
$933$	32.3288	1.05840
$934$	13.6277	0.445913
$935$	4.37228	0.142989
$936$	−5.25544	−0.171779
$937$	−51.4891	−1.68208	−0.841038	−	0.540976i	$-0.818055\pi$
$937$	−51.4891	−1.68208	−0.841038	+	0.540976i	$0.818055\pi$
$938$	18.9783	0.619662
$939$	−52.1902	−1.70316
$940$	−8.74456	−0.285216
$941$	48.0951	1.56786	0.783928	−	0.620852i	$-0.213213\pi$
$941$	48.0951	1.56786	0.783928	+	0.620852i	$0.213213\pi$
$942$	−8.60597	−0.280398
$943$	−100.467	−3.27167
$944$	8.74456	0.284611
$945$	2.09509	0.0681534
$946$	−4.00000	−0.130051
$947$	20.1386	0.654416	0.327208	−	0.944952i	$-0.393892\pi$
$947$	20.1386	0.654416	0.327208	+	0.944952i	$0.393892\pi$
$948$	−30.2337	−0.981945
$949$	14.9783	0.486215
$950$	−6.37228	−0.206744
$951$	64.8832	2.10398
$952$	−10.3723	−0.336168
$953$	22.8832	0.741258	0.370629	−	0.928781i	$-0.379142\pi$
$953$	22.8832	0.741258	0.370629	+	0.928781i	$0.379142\pi$
$954$	−34.4674	−1.11592
$955$	17.4891	0.565935
$956$	−3.25544	−0.105288
$957$	10.3723	0.335288
$958$	17.4891	0.565048
$959$	6.51087	0.210247
$960$	2.37228	0.0765651
$961$	−25.3723	−0.818461
$962$	−7.25544	−0.233925
$963$	−31.5326	−1.01612
$964$	−22.0000	−0.708572
$965$	−13.8614	−0.446214
$966$	−49.2119	−1.58337
$967$	7.39403	0.237776	0.118888	−	0.992908i	$-0.462067\pi$
$967$	7.39403	0.237776	0.118888	+	0.992908i	$0.462067\pi$
$968$	−1.00000	−0.0321412
$969$	−66.0951	−2.12328
$970$	1.25544	0.0403097
$971$	−46.9783	−1.50760	−0.753802	−	0.657102i	$-0.771782\pi$
$971$	−46.9783	−1.50760	−0.753802	+	0.657102i	$0.771782\pi$
$972$	−21.0217	−0.674273
$973$	9.48913	0.304207
$974$	−20.0000	−0.640841
$975$	4.74456	0.151948
$976$	0.372281	0.0119164
$977$	−20.2337	−0.647333	−0.323667	−	0.946171i	$-0.604916\pi$
$977$	−20.2337	−0.647333	−0.323667	+	0.946171i	$0.604916\pi$
$978$	54.8397	1.75358
$979$	−4.37228	−0.139739
$980$	−1.37228	−0.0438359
$981$	19.6793	0.628312
$982$	1.62772	0.0519426
$983$	43.7228	1.39454	0.697271	−	0.716808i	$-0.254398\pi$
$983$	43.7228	1.39454	0.697271	+	0.716808i	$0.254398\pi$
$984$	−27.2554	−0.868872
$985$	−9.25544	−0.294903
$986$	−19.1168	−0.608804
$987$	49.2119	1.56643
$988$	12.7446	0.405459
$989$	34.9783	1.11224
$990$	2.62772	0.0835144
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	2.37228	0.0753200
$993$	−35.5326	−1.12759
$994$	−16.8832	−0.535501
$995$	0.883156	0.0279979
$996$	20.7446	0.657317
$997$	−12.2337	−0.387445	−0.193722	−	0.981056i	$-0.562056\pi$
$997$	−12.2337	−0.387445	−0.193722	+	0.981056i	$0.562056\pi$
$998$	10.5109	0.332716
$999$	−3.20384	−0.101365

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.a.d.1.2	✓	2	1.1	even	1	trivial
550.2.a.n.1.1		2	5.4	even	2
550.2.b.f.199.1		4	5.2	odd	4
550.2.b.f.199.4		4	5.3	odd	4
880.2.a.n.1.1		2	4.3	odd	2
990.2.a.m.1.1		2	3.2	odd	2
1210.2.a.r.1.2		2	11.10	odd	2
3520.2.a.bj.1.2		2	8.3	odd	2
3520.2.a.bq.1.1		2	8.5	even	2
4400.2.a.bl.1.2		2	20.19	odd	2
4400.2.b.p.4049.2		4	20.3	even	4
4400.2.b.p.4049.3		4	20.7	even	4
4950.2.a.bw.1.2		2	15.14	odd	2
4950.2.c.bc.199.2		4	15.8	even	4
4950.2.c.bc.199.3		4	15.2	even	4
5390.2.a.bp.1.1		2	7.6	odd	2
6050.2.a.cb.1.1		2	55.54	odd	2
7920.2.a.bq.1.2		2	12.11	even	2
9680.2.a.bt.1.1		2	44.43	even	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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.37228 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.37228 q^{6} -2.37228 q^{7} -1.00000 q^{8} +2.62772 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.37228 q^{12} +2.00000 q^{13} +2.37228 q^{14} +2.37228 q^{15} +1.00000 q^{16} -4.37228 q^{17} -2.62772 q^{18} +6.37228 q^{19} +1.00000 q^{20} -5.62772 q^{21} +1.00000 q^{22} -8.74456 q^{23} -2.37228 q^{24} +1.00000 q^{25} -2.00000 q^{26} -0.883156 q^{27} -2.37228 q^{28} -4.37228 q^{29} -2.37228 q^{30} -2.37228 q^{31} -1.00000 q^{32} -2.37228 q^{33} +4.37228 q^{34} -2.37228 q^{35} +2.62772 q^{36} +3.62772 q^{37} -6.37228 q^{38} +4.74456 q^{39} -1.00000 q^{40} +11.4891 q^{41} +5.62772 q^{42} -4.00000 q^{43} -1.00000 q^{44} +2.62772 q^{45} +8.74456 q^{46} -8.74456 q^{47} +2.37228 q^{48} -1.37228 q^{49} -1.00000 q^{50} -10.3723 q^{51} +2.00000 q^{52} +13.1168 q^{53} +0.883156 q^{54} -1.00000 q^{55} +2.37228 q^{56} +15.1168 q^{57} +4.37228 q^{58} +8.74456 q^{59} +2.37228 q^{60} +0.372281 q^{61} +2.37228 q^{62} -6.23369 q^{63} +1.00000 q^{64} +2.00000 q^{65} +2.37228 q^{66} +8.00000 q^{67} -4.37228 q^{68} -20.7446 q^{69} +2.37228 q^{70} -7.11684 q^{71} -2.62772 q^{72} +7.48913 q^{73} -3.62772 q^{74} +2.37228 q^{75} +6.37228 q^{76} +2.37228 q^{77} -4.74456 q^{78} -12.7446 q^{79} +1.00000 q^{80} -9.97825 q^{81} -11.4891 q^{82} +8.74456 q^{83} -5.62772 q^{84} -4.37228 q^{85} +4.00000 q^{86} -10.3723 q^{87} +1.00000 q^{88} +4.37228 q^{89} -2.62772 q^{90} -4.74456 q^{91} -8.74456 q^{92} -5.62772 q^{93} +8.74456 q^{94} +6.37228 q^{95} -2.37228 q^{96} -1.25544 q^{97} +1.37228 q^{98} -2.62772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 11 q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 4 q^{13} - q^{14} - q^{15} + 2 q^{16} - 3 q^{17} - 11 q^{18} + 7 q^{19} + 2 q^{20} - 17 q^{21}+ \cdots - 11 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 + q^7 - 2 * q^8 + 11 * q^9 - 2 * q^10 - 2 * q^11 - q^12 + 4 * q^13 - q^14 - q^15 + 2 * q^16 - 3 * q^17 - 11 * q^18 + 7 * q^19 + 2 * q^20 - 17 * q^21 + 2 * q^22 - 6 * q^23 + q^24 + 2 * q^25 - 4 * q^26 - 19 * q^27 + q^28 - 3 * q^29 + q^30 + q^31 - 2 * q^32 + q^33 + 3 * q^34 + q^35 + 11 * q^36 + 13 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 17 * q^42 - 8 * q^43 - 2 * q^44 + 11 * q^45 + 6 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 2 * q^50 - 15 * q^51 + 4 * q^52 + 9 * q^53 + 19 * q^54 - 2 * q^55 - q^56 + 13 * q^57 + 3 * q^58 + 6 * q^59 - q^60 - 5 * q^61 - q^62 + 22 * q^63 + 2 * q^64 + 4 * q^65 - q^66 + 16 * q^67 - 3 * q^68 - 30 * q^69 - q^70 + 3 * q^71 - 11 * q^72 - 8 * q^73 - 13 * q^74 - q^75 + 7 * q^76 - q^77 + 2 * q^78 - 14 * q^79 + 2 * q^80 + 26 * q^81 + 6 * q^83 - 17 * q^84 - 3 * q^85 + 8 * q^86 - 15 * q^87 + 2 * q^88 + 3 * q^89 - 11 * q^90 + 2 * q^91 - 6 * q^92 - 17 * q^93 + 6 * q^94 + 7 * q^95 + q^96 - 14 * q^97 - 3 * q^98 - 11 * q^99

Introduction

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